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Jones %Copyright: Copyright (c) 1997, 2009 American Mathematical Society %Copyright: (), with Reserved Font Name CMSLTT10. % This Font Software is licensed under the SIL Open Font License, Version 1.1. % This license is in the accompanying file OFL.txt, and is also % available with a FAQ at: http://scripts.sil.org/OFL. %%EndComments FontDirectory/CMSLTT10 known{/CMSLTT10 findfont dup/UniqueID known{dup /UniqueID get 5000800 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /CMSLTT10 def /FontBBox {-20 -233 617 696 }readonly def /UniqueID 5000800 def /PaintType 0 def /FontInfo 9 dict dup begin /version (003.002) readonly def /Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMSLTT10.) readonly def /FullName (CMSLTT10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def 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Jones %Copyright: Copyright (c) 1997, 2009 American Mathematical Society %Copyright: (), with Reserved Font Name CMR8. % This Font Software is licensed under the SIL Open Font License, Version 1.1. % This license is in the accompanying file OFL.txt, and is also % available with a FAQ at: http://scripts.sil.org/OFL. %%EndComments FontDirectory/CMR8 known{/CMR8 findfont dup/UniqueID known{dup /UniqueID get 5000791 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /CMR8 def /FontBBox {-36 -250 1070 750 }readonly def /UniqueID 5000791 def /PaintType 0 def /FontInfo 9 dict dup begin /version (003.002) readonly def /Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMR8.) readonly def /FullName (CMR8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark {restore}if %%EndFont %%BeginFont: CMB10 %!PS-AdobeFont-1.0: CMB10 003.002 %%Title: CMB10 %Version: 003.002 %%CreationDate: Mon Jul 13 16:17:00 2009 %%Creator: David M. Jones %Copyright: Copyright (c) 1997, 2009 American Mathematical Society %Copyright: (), with Reserved Font Name CMB10. % This Font Software is licensed under the SIL Open Font License, Version 1.1. % This license is in the accompanying file OFL.txt, and is also % available with a FAQ at: http://scripts.sil.org/OFL. %%EndComments FontDirectory/CMB10 known{/CMB10 findfont dup/UniqueID known{dup /UniqueID get 5000761 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /CMB10 def /FontBBox {-62 -250 1011 750 }readonly def /UniqueID 5000761 def /PaintType 0 def /FontInfo 9 dict dup begin /version (003.002) readonly def /Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMB10.) readonly def /FullName (CMB10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 46 /period put dup 49 /one put dup 50 /two put dup 51 /three put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 93 /bracketright put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 103 /g put dup 104 /h put dup 105 /i put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 127 /dieresis put readonly def currentdict 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Jones %Copyright: Copyright (c) 1997, 2009 American Mathematical Society %Copyright: (), with Reserved Font Name CMR5. % This Font Software is licensed under the SIL Open Font License, Version 1.1. % This license is in the accompanying file OFL.txt, and is also % available with a FAQ at: http://scripts.sil.org/OFL. %%EndComments FontDirectory/CMR5 known{/CMR5 findfont dup/UniqueID known{dup /UniqueID get 5000788 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /CMR5 def /FontBBox {-10 -250 1304 750 }readonly def /UniqueID 5000788 def /PaintType 0 def /FontInfo 9 dict dup begin /version (003.002) readonly def /Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMR5.) readonly def /FullName (CMR5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch 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Jones %Copyright: Copyright (c) 1997, 2009 American Mathematical Society %Copyright: (), with Reserved Font Name CMTT9. % This Font Software is licensed under the SIL Open Font License, Version 1.1. % This license is in the accompanying file OFL.txt, and is also % available with a FAQ at: http://scripts.sil.org/OFL. %%EndComments FontDirectory/CMTT9 known{/CMTT9 findfont dup/UniqueID known{dup /UniqueID get 5000831 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /CMTT9 def /FontBBox {-6 -233 542 698 }readonly def /UniqueID 5000831 def /PaintType 0 def /FontInfo 9 dict dup begin /version (003.002) readonly def /Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMTT9.) readonly def /FullName (CMTT9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def 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Jones %Copyright: Copyright (c) 1997, 2009 American Mathematical Society %Copyright: (), with Reserved Font Name CMR7. % This Font Software is licensed under the SIL Open Font License, Version 1.1. % This license is in the accompanying file OFL.txt, and is also % available with a FAQ at: http://scripts.sil.org/OFL. %%EndComments FontDirectory/CMR7 known{/CMR7 findfont dup/UniqueID known{dup /UniqueID get 5000790 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /CMR7 def /FontBBox {-27 -250 1122 750 }readonly def /UniqueID 5000790 def /PaintType 0 def /FontInfo 9 dict dup begin /version (003.002) readonly def /Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMR7.) readonly def /FullName (CMR7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch 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Jones %Copyright: Copyright (c) 1997, 2009 American Mathematical Society %Copyright: (), with Reserved Font Name CMMI10. % This Font Software is licensed under the SIL Open Font License, Version 1.1. % This license is in the accompanying file OFL.txt, and is also % available with a FAQ at: http://scripts.sil.org/OFL. %%EndComments FontDirectory/CMMI10 known{/CMMI10 findfont dup/UniqueID known{dup /UniqueID get 5087385 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /CMMI10 def /FontBBox {-32 -250 1048 750 }readonly def /UniqueID 5087385 def /PaintType 0 def /FontInfo 10 dict dup begin /version (003.002) readonly def /Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMMI10.) readonly def /FullName (CMMI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 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Jones %Copyright: Copyright (c) 1997, 2009 American Mathematical Society %Copyright: (), with Reserved Font Name CMSY10. % This Font Software is licensed under the SIL Open Font License, Version 1.1. % This license is in the accompanying file OFL.txt, and is also % available with a FAQ at: http://scripts.sil.org/OFL. %%EndComments FontDirectory/CMSY10 known{/CMSY10 findfont dup/UniqueID known{dup /UniqueID get 5096651 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /CMSY10 def /FontBBox {-29 -960 1116 775 }readonly def /UniqueID 5096651 def /PaintType 0 def /FontInfo 9 dict dup begin /version (003.002) readonly def /Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMSY10.) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 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Jones %Copyright: Copyright (c) 1997, 2009 American Mathematical Society %Copyright: (), with Reserved Font Name CMR10. % This Font Software is licensed under the SIL Open Font License, Version 1.1. % This license is in the accompanying file OFL.txt, and is also % available with a FAQ at: http://scripts.sil.org/OFL. %%EndComments FontDirectory/CMR10 known{/CMR10 findfont dup/UniqueID known{dup /UniqueID get 5000793 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /CMR10 def /FontBBox {-40 -250 1009 750 }readonly def /UniqueID 5000793 def /PaintType 0 def /FontInfo 9 dict dup begin /version (003.002) readonly def /Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMR10.) readonly def /FullName (CMR10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def 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45[{}21 66.4176 /CMTT8 rf /Fe 240[35 1[71 13[{}2 66.4176 /CMSY8 rf /Ff 131[71 35 31 37 37 51 37 39 27 28 28 37 39 35 39 59 20 37 22 20 39 35 22 31 39 31 39 35 20 3[35 1[43 53 53 72 53 53 51 39 52 55 48 55 53 65 44 55 36 25 53 55 46 48 54 51 50 53 5[20 20 35 35 35 35 35 35 35 35 35 35 35 20 24 20 2[27 27 20 4[35 19[59 39 39 41 11[{}80 66.4176 /CMR8 rf /Fg 134[44 42 60 1[49 30 37 38 1[46 46 51 74 23 2[28 46 42 28 42 46 42 42 46 11[68 65 51 66 5[57 2[35 3[62 2[64 68 18[28 33 28 31[51 56 11[{}35 90.9091 /CMTI10 rf /Fh 149[21 102[38 2[60{}3 74.7198 /CMSY9 rf /Fi 135[44 4[36 1[34 2[46 4[26 3[36 1[33 20[61 17[60 21 21 58[{}11 74.7198 /CMMI9 rf /Fj 140[34 6[38 8[44 43 46 97[{}5 74.7198 /CMCSC10 rf /Fk 128[45 4[40 48 48 66 48 51 35 36 39 2[45 51 76 25 48 1[25 51 45 1[42 51 40 51 44 6[56 69 69 94 69 70 63 51 69 1[62 68 71 86 55 71 47 36 71 71 57 60 70 66 65 69 13[45 45 45 2[25 46[{}52 90.9091 /CMB10 rf /Fl 135[33 2[35 4[31 1[37 51 20 31 1[22 7[32 21[47 32 61[33 38 11[{}13 41.511 /CMMI5 rf /Fm 207[18 47[45{}2 41.511 /CMSY5 rf /Fn 204[28 28 28 5[43 43[{}4 41.511 /CMR5 rf /Fo 162[28 1[28 91[{}2 99.6264 /CMB10 rf /Fp 134[30 8[55 5[20 55[45 66 19 14[66 12[52 16[34 1[20 52{}11 58.1154 /CMSY7 rf /Fq 133[32 34 38 48 33 39 25 31 31 30 34 33 41 59 21 35 27 23 39 32 32 31 35 30 29 36 8[54 62 2[39 1[50 3[53 63 46 56 37 29 54 52 42 49 54 48 50 50 35 1[52 34 52 20 20 27[40 1[31 38 1[39 1[33 40 39 2[32 2[28 30 1[38 43 11[{}62 58.1154 /CMMI7 rf /Fr 135[41 120[{}1 74.7198 /CMSL9 rf /Fs 140[83 83 83 83 21[46 106 120 5[39 78 88 12[73 73 73 73 2[74 74 74 74 74 74 6[73 73 6[67 67 6[66 66 4[62 62 4[44 44 61 61 50 50 6[48 48 6[38 38{}38 83.022 /CMEX10 rf /Ft 133[52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 1[52 4[52 1[52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 14[52 52 52 48[{}55 99.6264 /CMSLTT10 rf /Fu 214[35 35 40[{}2 90.9091 /CMSS10 rf /Fv 133[52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 1[52 4[52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 7[52 52 52 52 52 52 52 52 52 52 5[52 1[52 40[{}65 99.6264 /CMTT10 rf /Fw 212[62 43[{}1 119.552 /CMTT12 rf /Fx 131[77 38 34 41 41 55 41 43 30 30 30 41 43 38 43 64 21 41 23 21 43 38 23 34 43 34 43 38 6[47 58 58 79 58 58 55 43 57 60 52 60 58 70 48 60 39 28 58 60 50 52 59 55 54 58 3[60 3[38 38 38 38 38 38 38 38 38 38 38 21 26 21 2[30 30 21 24[64 43 43 45 11[{}76 74.7198 /CMR9 rf /Fy 131[123 1[55 65 65 89 65 68 48 48 50 65 68 61 68 102 34 65 37 34 68 61 37 56 68 55 68 60 6[75 2[127 93 1[85 68 92 92 84 92 96 116 74 2[46 96 96 77 81 94 89 87 93 7[61 61 61 61 61 61 61 61 61 61 1[34 41 3[48 48 27[68 12[{}63 109.091 /CMBX12 rf /Fz 130[39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 1[39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 33[{}92 74.7198 /CMTT9 rf /FA 135[48 1[48 48 1[48 48 1[48 48 48 48 3[48 1[48 48 48 48 48 1[48 1[48 10[48 9[48 25[48 48[{}20 90.9091 /CMSLTT10 rf /FB 161[33 32[51 3[33 33 33 33 33 33 33 33 33 33 4[51 1[26 26 38[55 1[{}16 58.1154 /CMR7 rf /FC 133[46 56 56 76 56 56 54 42 55 58 51 58 56 68 47 58 39 27 56 58 49 51 57 54 53 56 46[50 3[29 46[{}28 90.9091 /CMCSC10 rf /FD 133[40 48 48 66 48 51 35 36 36 48 51 45 51 76 25 48 28 25 51 45 28 40 51 40 51 45 4[45 1[56 1[68 93 68 68 66 51 67 71 62 71 68 83 57 71 47 33 68 71 59 62 69 66 64 68 3[71 1[25 25 45 45 45 45 45 45 45 45 45 45 45 25 30 25 1[45 35 35 25 71 1[45 1[45 19[76 51 51 53 11[{}80 90.9091 /CMSL10 rf /FE 129[45 3[42 45 52 65 44 52 33 43 41 41 46 44 55 80 27 47 37 31 52 43 45 42 47 39 39 48 6[62 53 75 86 53 62 53 56 69 72 58 69 73 88 62 77 50 40 76 71 58 67 75 65 69 68 48 1[71 45 71 25 25 24[57 59 57 54 1[40 52 47 52 1[45 55 53 2[43 45 40 37 40 47 51 58 11[{}78 90.9091 /CMMI10 rf /FF 197[33 58[{}1 119.552 /CMMI12 rf /FG 133[72 85 85 1[85 90 63 64 66 85 90 81 90 134 45 85 1[45 90 81 49 74 90 72 90 78 9[167 122 124 112 90 120 121 110 121 126 153 97 2[60 126 127 101 106 124 117 115 122 7[81 81 81 81 81 81 81 81 81 81 2[54 3[63 63 26[90 1[94 11[{}60 143.462 /CMBX12 rf /FH 129[48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 1[48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 33[{}93 90.9091 /CMTT10 rf /FI 141[76 1[76 5[25 35 35 45 45 2[40 40 21[63 69 20[0 3[61 91 25 14[91 91 2[91 91 2[71 71 2[71 71 4[45 1[91 4[71 1[71 2[45 71 25 71{}31 90.9091 /CMSY10 rf /FJ 133[60 71 71 97 71 75 52 53 55 71 75 67 75 112 37 71 41 37 75 67 41 61 75 60 75 65 6[82 102 1[139 102 103 94 75 100 101 92 101 105 128 81 105 69 50 105 106 85 88 103 97 96 102 6[37 67 67 67 67 67 67 67 67 67 67 1[37 45 37 2[52 52 3[67 20[112 112 75 75 78 11[{}73 119.552 /CMBX12 rf /FK 128[45 45 1[91 45 40 48 48 66 48 51 35 36 36 48 51 45 51 76 25 48 28 25 51 45 28 40 51 40 51 45 25 1[45 25 45 25 56 68 68 93 68 68 66 51 67 71 62 71 68 83 57 71 47 33 68 71 59 62 69 66 64 68 3[71 1[25 25 45 45 45 45 45 45 45 45 45 45 45 25 30 25 71 45 35 35 25 71 76 2[45 25 10[45 1[45 45 3[76 76 51 51 53 2[66 1[66 68 3[76 57{}100 90.9091 /CMR10 rf /FL 134[102 4[75 1[79 3[108 4[54 3[88 1[86 108 94 11[149 1[108 4[151 1[116 4[152 58[108 12[{}15 172.154 /CMBX12 rf end %%EndProlog %%BeginSetup %%Feature: *Resolution 600dpi TeXDict begin %%BeginPaperSize: a4 /setpagedevice where { pop << /PageSize [595 842] >> setpagedevice } { /a4 where { pop a4 } if } ifelse %%EndPaperSize end %%EndSetup %%Page: 1 1 TeXDict begin 1 0 bop 150 1318 a FL(GNU)65 b(Scien)-5 b(ti\014c)63 b(Library)p 150 1418 3600 34 v 3039 1515 a FK(Reference)31 b(Man)m(ual)2466 1623 y(Edition)f(2.3,)i(for)e(GSL)g (V)-8 b(ersion)31 b(2.3)3069 1731 y(9)g(Decem)m(b)s(er)g(2016)150 1943 y FJ(Mark)45 b(Galassi)150 2077 y FK(Los)30 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TeXDict begin 2 1 bop 150 4042 a FK(Cop)m(yrigh)m(t)602 4039 y(c)577 4042 y FI(\015)30 b FK(1996,)i(1997,)g(1998,)g(1999,)g (2000,)g(2001,)g(2002,)g(2003,)g(2004,)h(2005,)f(2006,)g(2007,)g(2008,) 150 4152 y(2009,)g(2010,)h(2011,)f(2012,)g(2013,)h(2014,)f(2015,)h (2016)f(The)e(GSL)g(T)-8 b(eam.)150 4286 y(P)m(ermission)32 b(is)f(gran)m(ted)i(to)f(cop)m(y)-8 b(,)33 b(distribute)e(and/or)h(mo)s (dify)f(this)g(do)s(cumen)m(t)g(under)g(the)g(terms)h(of)150 4396 y(the)22 b(GNU)h(F)-8 b(ree)23 b(Do)s(cumen)m(tation)h(License,)h (V)-8 b(ersion)23 b(1.3)g(or)f(an)m(y)g(later)i(v)m(ersion)e(published) e(b)m(y)i(the)h(F)-8 b(ree)150 4505 y(Soft)m(w)m(are)27 b(F)-8 b(oundation;)28 b(with)e(the)g(In)m(v)-5 b(arian)m(t)26 b(Sections)h(b)s(eing)e(\\GNU)i(General)g(Public)f(License")h(and)150 4615 y(\\F)-8 b(ree)28 b(Soft)m(w)m(are)g(Needs)f(F)-8 b(ree)28 b(Do)s(cumen)m(tation",)i(the)d(F)-8 b(ron)m(t-Co)m(v)m(er)29 b(text)f(b)s(eing)f(\\A)g(GNU)g(Man)m(ual",)150 4725 y(and)34 b(with)g(the)g(Bac)m(k-Co)m(v)m(er)j(T)-8 b(ext)35 b(b)s(eing)f(\(a\))h(\(see)g(b)s(elo)m(w\).)53 b(A)35 b(cop)m(y)f(of)h(the)f(license)i(is)e(included)f(in)150 4834 y(the)e(section)g(en)m(titled)h(\\GNU)f(F)-8 b(ree)32 b(Do)s(cumen)m(tation)g(License".)150 4969 y(\(a\))25 b(The)f(Bac)m(k-Co)m(v)m(er)i(T)-8 b(ext)25 b(is:)38 b(\\Y)-8 b(ou)25 b(ha)m(v)m(e)g(the)f(freedom)g(to)h(cop)m(y)f(and)g (mo)s(dify)f(this)h(GNU)g(Man)m(ual.")150 5078 y(Prin)m(ted)29 b(copies)h(of)f(this)g(man)m(ual)g(can)g(b)s(e)f(purc)m(hased)g(from)h (Net)m(w)m(ork)h(Theory)f(Ltd)f(at)i FH(http://www.)150 5188 y(network-theory.co.uk/gsl)o(/man)o(ual/)o FK(.)150 5322 y(The)g(money)g(raised)h(from)f(sales)h(of)f(the)h(man)m(ual)f (helps)g(supp)s(ort)f(the)i(dev)m(elopmen)m(t)g(of)g(GSL.)p eop end %%Page: -1 3 TeXDict begin -1 2 bop 3725 -116 a FK(i)150 299 y FG(T)-13 b(able)53 b(of)h(Con)l(ten)l(ts)150 606 y FJ(1)135 b(In)l(tro)t (duction)13 b FF(:)19 b(:)h(:)f(:)h(:)f(:)g(:)h(:)f(:)h(:)f(:)h(:)f(:)g 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g(also)150 3732 y(need)23 b(to)h(pro)m(vide)g(its)g(lo)s(cation)h(to)f (the)f(prepro)s(cessor)g(as)g(a)h(command)f(line)h(\015ag.)39 b(The)23 b(default)g(lo)s(cation)150 3842 y(of)37 b(the)g FH(gsl)f FK(directory)h(is)g FH(/usr/local/include/gsl)p FK(.)53 b(A)37 b(t)m(ypical)h(compilation)h(command)d(for)h(a)150 3951 y(source)31 b(\014le)f FH(example.c)e FK(with)i(the)g(GNU)h(C)f (compiler)h FH(gcc)f FK(is,)390 4092 y FH($)47 b(gcc)g(-Wall)g (-I/usr/local/include)42 b(-c)47 b(example.c)150 4232 y FK(This)j(results)g(in)g(an)h(ob)5 b(ject)51 b(\014le)f FH(example.o)p FK(.)99 b(The)50 b(default)h(include)f(path)g(for)g FH(gcc)g FK(searc)m(hes)150 4342 y FH(/usr/local/include)32 b FK(automatically)39 b(so)e(the)g FH(-I)f FK(option)h(can)g(actually)i (b)s(e)d(omitted)i(when)d(GSL)150 4452 y(is)30 b(installed)i(in)e(its)g (default)h(lo)s(cation.)150 4657 y Fy(2.2.1)63 b(Linking)41 b(programs)h(with)f(the)g(library)150 4804 y FK(The)24 b(library)h(is)f(installed)i(as)f(a)g(single)g(\014le,)i FH(libgsl.a)p FK(.)36 b(A)25 b(shared)f(v)m(ersion)h(of)g(the)g (library)f FH(libgsl.so)150 4914 y FK(is)k(also)g(installed)h(on)f (systems)f(that)i(supp)s(ort)d(shared)h(libraries.)39 b(The)28 b(default)g(lo)s(cation)h(of)f(these)g(\014les)150 5023 y(is)j FH(/usr/local/lib)p FK(.)39 b(If)30 b(this)h(directory)h (is)f(not)g(on)g(the)g(standard)g(searc)m(h)g(path)g(of)g(y)m(our)g (link)m(er)h(y)m(ou)150 5133 y(will)f(also)g(need)f(to)h(pro)m(vide)g (its)g(lo)s(cation)g(as)g(a)g(command)f(line)h(\015ag.)p 150 5241 1200 4 v 199 5308 a FB(1)275 5340 y Fx(The)25 b(last)i(few)g(digits)f(ma)n(y)f(v)l(ary)g(sligh)n(tly)h(dep)r(ending)g (on)f(the)h(compiler)g(and)g(platform)g(used|this)g(is)g(normal.)p eop end %%Page: 5 23 TeXDict begin 5 22 bop 150 -116 a FK(Chapter)30 b(2:)41 b(Using)30 b(the)h(library)2412 b(5)275 299 y(T)-8 b(o)32 b(link)g(against)h(the)g(library)e(y)m(ou)i(need)f(to)g(sp)s(ecify)g(b) s(oth)g(the)g(main)g(library)g(and)f(a)h(supp)s(orting)150 408 y FC(cblas)d FK(library)-8 b(,)30 b(whic)m(h)g(pro)m(vides)g (standard)g(basic)g(linear)h(algebra)g(subroutines.)39 b(A)31 b(suitable)f FC(cblas)150 518 y FK(implemen)m(tation)k(is)e(pro) m(vided)g(in)h(the)f(library)g FH(libgslcblas.a)d FK(if)j(y)m(our)h (system)f(do)s(es)g(not)h(pro)m(vide)150 628 y(one.)41 b(The)30 b(follo)m(wing)i(example)f(sho)m(ws)f(ho)m(w)g(to)h(link)g(an) f(application)i(with)e(the)g(library)-8 b(,)390 766 y FH($)47 b(gcc)g(-L/usr/local/lib)d(example.o)h(-lgsl)h(-lgslcblas)f (-lm)150 905 y FK(The)31 b(default)h(library)f(path)h(for)f FH(gcc)g FK(searc)m(hes)i FH(/usr/local/lib)28 b FK(automatically)34 b(so)e(the)g FH(-L)f FK(option)150 1014 y(can)g(b)s(e)e(omitted)j(when) d(GSL)h(is)h(installed)g(in)f(its)h(default)f(lo)s(cation.)275 1153 y(The)f(option)i FH(-lm)e FK(links)g(with)h(the)g(system)h(math)f (library)-8 b(.)40 b(On)29 b(some)i(systems)f(it)g(is)h(not)f(needed.) 3713 1120 y FB(2)275 1291 y FK(F)-8 b(or)28 b(a)g(tutorial)h(in)m(tro)s (duction)f(to)g(the)g(GNU)g(C)g(Compiler)f(and)g(related)i(programs,)f (see)g FD(An)f(In)m(tro-)150 1401 y(duction)j(to)h(GCC)38 b FK(\(ISBN)31 b(0954161793\).)1622 1368 y FB(3)150 1604 y Fy(2.2.2)63 b(Linking)41 b(with)f(an)h(alternativ)m(e)f(BLAS)h (library)150 1751 y FK(The)28 b(follo)m(wing)i(command)f(line)g(sho)m (ws)f(ho)m(w)h(y)m(ou)g(w)m(ould)g(link)f(the)h(same)h(application)g (with)e(an)h(alter-)150 1860 y(nativ)m(e)j FC(cblas)d FK(library)g FH(libcblas.a)p FK(,)390 1999 y FH($)47 b(gcc)g(example.o)f(-lgsl)g(-lcblas)g(-lm)150 2137 y FK(F)-8 b(or)33 b(the)g(b)s(est)f(p)s(erformance)g(an)h(optimized)g (platform-sp)s(eci\014c)g FC(cblas)e FK(library)h(should)f(b)s(e)h (used)g(for)150 2247 y FH(-lcblas)p FK(.)47 b(The)33 b(library)g(m)m(ust)g(conform)g(to)h(the)f FC(cblas)f FK(standard.)48 b(The)33 b FC(a)-6 b(tlas)32 b FK(pac)m(k)-5 b(age)35 b(pro)m(vides)150 2356 y(a)h(p)s(ortable)g(high-p)s (erformance)f FC(blas)g FK(library)g(with)h(a)g FC(cblas)e FK(in)m(terface.)59 b(It)36 b(is)f(free)h(soft)m(w)m(are)i(and)150 2466 y(should)27 b(b)s(e)f(installed)j(for)e(an)m(y)h(w)m(ork)g (requiring)f(fast)g(v)m(ector)j(and)c(matrix)i(op)s(erations.)40 b(The)27 b(follo)m(wing)150 2575 y(command)j(line)h(will)g(link)f(with) g(the)h FC(a)-6 b(tlas)28 b FK(library)i(and)g(its)h FC(cblas)e FK(in)m(terface,)390 2714 y FH($)47 b(gcc)g(example.o)f (-lgsl)g(-lcblas)g(-latlas)g(-lm)150 2852 y FK(If)31 b(the)g FC(a)-6 b(tlas)30 b FK(library)h(is)g(installed)i(in)e(a)g (non-standard)g(directory)g(use)g(the)h FH(-L)f FK(option)h(to)g(add)e (it)i(to)150 2962 y(the)f(searc)m(h)g(path,)f(as)h(describ)s(ed)e(ab)s (o)m(v)m(e.)275 3100 y(F)-8 b(or)31 b(more)f(information)h(ab)s(out)f FC(blas)f FK(functions)h(see)h(Chapter)f(13)h([BLAS)f(Supp)s(ort],)f (page)i(125.)150 3339 y FJ(2.3)68 b(Shared)45 b(Libraries)150 3498 y FK(T)-8 b(o)32 b(run)e(a)h(program)h(link)m(ed)f(with)g(the)h (shared)e(v)m(ersion)i(of)g(the)f(library)g(the)h(op)s(erating)g (system)f(m)m(ust)150 3608 y(b)s(e)e(able)h(to)g(lo)s(cate)i(the)d (corresp)s(onding)g FH(.so)g FK(\014le)g(at)i(run)m(time.)40 b(If)29 b(the)h(library)f(cannot)h(b)s(e)f(found,)g(the)150 3717 y(follo)m(wing)j(error)e(will)h(o)s(ccur:)390 3856 y FH($)47 b(./a.out)390 3965 y(./a.out:)f(error)g(while)g(loading)g (shared)g(libraries:)390 4075 y(libgsl.so.0:)e(cannot)j(open)f(shared)g (object)g(file:)h(No)g(such)390 4184 y(file)g(or)g(directory)150 4323 y FK(T)-8 b(o)36 b(a)m(v)m(oid)i(this)d(error,)i(either)g(mo)s (dify)e(the)h(system)g(dynamic)f(link)m(er)h(con\014guration)3165 4290 y FB(4)3239 4323 y FK(or)g(de\014ne)f(the)150 4433 y(shell)c(v)-5 b(ariable)31 b FH(LD_LIBRARY_PATH)26 b FK(to)31 b(include)f(the)h(directory)g(where)e(the)i(library)f(is)g (installed.)275 4571 y(F)-8 b(or)33 b(example,)i(in)d(the)i(Bourne)e (shell)i(\()p FH(/bin/sh)d FK(or)i FH(/bin/bash)p FK(\),)f(the)h (library)f(searc)m(h)i(path)f(can)150 4681 y(b)s(e)d(set)h(with)f(the)g (follo)m(wing)i(commands:)390 4819 y FH($)47 b (LD_LIBRARY_PATH=/usr/local)o(/lib)390 4929 y($)g(export)g (LD_LIBRARY_PATH)p 150 5035 1200 4 v 199 5102 a FB(2)275 5134 y Fx(It)25 b(is)h(not)f(needed)h(on)f(MacOS)h(X.)199 5205 y FB(3)275 5237 y Fz(http://www.network-theory.co.uk)q(/gcc/)q (intr)q(o/)199 5308 y FB(4)275 5340 y Fz(/etc/ld.so.conf)j Fx(on)c(GNU/Lin)n(ux)g(systems.)p eop end %%Page: 6 24 TeXDict begin 6 23 bop 150 -116 a FK(Chapter)30 b(2:)41 b(Using)30 b(the)h(library)2412 b(6)390 299 y FH($)47 b(./example)150 431 y FK(In)30 b(the)g(C-shell)h(\()p FH(/bin/csh)d FK(or)j FH(/bin/tcsh)p FK(\))d(the)i(equiv)-5 b(alen)m(t)32 b(command)e(is,)390 564 y FH(\045)47 b(setenv)g (LD_LIBRARY_PATH)c(/usr/local/lib)150 696 y FK(The)28 b(standard)f(prompt)g(for)h(the)g(C-shell)g(in)g(the)g(example)h(ab)s (o)m(v)m(e)g(is)f(the)h(p)s(ercen)m(t)f(c)m(haracter)i(`)p FH(\045)p FK(',)f(and)150 806 y(should)g(not)i(b)s(e)f(t)m(yp)s(ed)g (as)g(part)h(of)f(the)h(command.)275 938 y(T)-8 b(o)36 b(sa)m(v)m(e)i(ret)m(yping)f(these)g(commands)f(eac)m(h)h(session)g (they)f(can)h(b)s(e)e(placed)i(in)f(an)g(individual)g(or)150 1048 y(system-wide)31 b(login)g(\014le.)275 1180 y(T)-8 b(o)30 b(compile)i(a)e(statically)j(link)m(ed)e(v)m(ersion)g(of)f(the)h (program,)f(use)g(the)h FH(-static)d FK(\015ag)j(in)f FH(gcc)p FK(,)390 1313 y FH($)47 b(gcc)g(-static)f(example.o)f(-lgsl)i (-lgslcblas)e(-lm)150 1541 y FJ(2.4)68 b(ANSI)44 b(C)h(Compliance)150 1701 y FK(The)24 b(library)h(is)g(written)g(in)g(ANSI)f(C)h(and)f(is)h (in)m(tended)g(to)h(conform)e(to)i(the)f(ANSI)g(C)f(standard)g (\(C89\).)150 1810 y(It)30 b(should)g(b)s(e)g(p)s(ortable)g(to)h(an)m (y)g(system)f(with)g(a)h(w)m(orking)g(ANSI)f(C)g(compiler.)275 1943 y(The)f(library)h(do)s(es)g(not)h(rely)g(on)f(an)m(y)h(non-ANSI)e (extensions)i(in)f(the)h(in)m(terface)h(it)f(exp)s(orts)f(to)h(the)150 2052 y(user.)38 b(Programs)24 b(y)m(ou)h(write)g(using)f(GSL)g(can)h(b) s(e)e(ANSI)i(complian)m(t.)40 b(Extensions)24 b(whic)m(h)g(can)h(b)s(e) f(used)150 2162 y(in)g(a)g(w)m(a)m(y)i(compatible)f(with)f(pure)f(ANSI) h(C)f(are)i(supp)s(orted,)f(ho)m(w)m(ev)m(er,)j(via)e(conditional)g (compilation.)150 2271 y(This)31 b(allo)m(ws)i(the)g(library)e(to)i (tak)m(e)g(adv)-5 b(an)m(tage)34 b(of)e(compiler)h(extensions)f(on)g (those)g(platforms)g(whic)m(h)150 2381 y(supp)s(ort)d(them.)275 2514 y(When)h(an)g(ANSI)g(C)h(feature)g(is)f(kno)m(wn)g(to)h(b)s(e)f (brok)m(en)h(on)f(a)h(particular)g(system)g(the)f(library)h(will)150 2623 y(exclude)39 b(an)m(y)f(related)h(functions)f(at)h(compile-time.) 66 b(This)38 b(should)f(mak)m(e)i(it)g(imp)s(ossible)e(to)i(link)g(a) 150 2733 y(program)30 b(that)h(w)m(ould)f(use)g(these)h(functions)f (and)g(giv)m(e)i(incorrect)f(results.)275 2865 y(T)-8 b(o)31 b(a)m(v)m(oid)i(namespace)e(con\015icts)h(all)g(exp)s(orted)f (function)f(names)h(and)g(v)-5 b(ariables)31 b(ha)m(v)m(e)i(the)e (pre\014x)150 2975 y FH(gsl_)p FK(,)e(while)i(exp)s(orted)f(macros)h 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y(functions)f(this)f(w)m(a)m(y)i(while)f (retaining)h(p)s(ortabilit)m(y)-8 b(.)42 b(The)28 b(follo)m(wing)j (lines)e(demonstrate)g(the)h(use)e(of)i(a)150 1225 y(platform-dep)s (enden)m(t)g(c)m(hoice)i(of)f(metho)s(ds)e(for)h(sampling)h(from)f(the) g(Gaussian)h(distribution,)390 1374 y FH(#ifdef)46 b(SPARC)390 1484 y(#define)g(gsl_ran_gaussian)d(gsl_ran_gaussian_ratio_me)o(thod) 390 1593 y(#endif)390 1703 y(#ifdef)j(INTEL)390 1812 y(#define)g(gsl_ran_gaussian)d(my_gaussian)390 1922 y(#endif)150 2070 y FK(These)35 b(lines)h(w)m(ould)f(b)s(e)g(placed)h(in)g(the)f (con\014guration)h(header)g(\014le)g FH(config.h)d FK(of)j(the)f (application,)150 2180 y(whic)m(h)c(should)f(then)g(b)s(e)h(included)f (b)m(y)h(all)h(the)f(source)g(\014les.)42 b(Note)33 b(that)e(the)g (alternativ)m(e)j(implemen-)150 2290 y(tations)42 b(will)g(not)g(pro)s (duce)e(bit-for-bit)i(iden)m(tical)h(results,)h(and)c(in)h(the)h(case)g (of)g(random)e(n)m(um)m(b)s(er)150 2399 y(distributions)30 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b(double)390 3618 y(gsl_foo_float_fn)425 b(float)390 3728 y(gsl_foo_long_fn)473 b(long)390 3837 y(gsl_foo_ulong_fn)425 b(unsigned)46 b(long)390 3947 y(gsl_foo_int_fn)521 b(int)390 4057 y(gsl_foo_uint_fn)473 b(unsigned)46 b(int)390 4166 y(gsl_foo_short_fn)425 b(short)390 4276 y(gsl_foo_ushort_fn)377 b(unsigned)46 b(short)390 4385 y(gsl_foo_char_fn)473 b(char)390 4495 y(gsl_foo_uchar_fn)425 b(unsigned)46 b(char)150 4643 y FK(The)d(normal)g(n)m(umeric)g(precision)h FH(double)e FK(is)h(considered)g(the)h(default)f(and)g(do)s(es)g(not)h (require)f(a)150 4753 y(su\016x.)h(F)-8 b(or)33 b(example,)g(the)f (function)f FH(gsl_stats_mean)d FK(computes)k(the)g(mean)g(of)g(double) g(precision)150 4863 y(n)m(um)m(b)s(ers,)d(while)i(the)f(function)g FH(gsl_stats_int_mean)c FK(computes)k(the)h(mean)f(of)h(in)m(tegers.) 275 5011 y(A)d(corresp)s(onding)g(sc)m(heme)h(is)g(used)e(for)i (library)f(de\014ned)f(t)m(yp)s(es,)i(suc)m(h)g(as)f FH(gsl_vector)e FK(and)i FH(gsl_)150 5121 y(matrix)p FK(.)40 b(In)30 b(this)g(case)i(the)f(mo)s(di\014er)e(is)i(app)s(ended) e(to)i(the)g(t)m(yp)s(e)g(name.)41 b(F)-8 b(or)31 b(example,)h(if)f(a)g (mo)s(dule)150 5230 y(de\014nes)36 b(a)h(new)f(t)m(yp)s(e-dep)s(enden)m (t)g(struct)g(or)h(t)m(yp)s(edef)f FH(gsl_foo)f FK(it)i(is)f(mo)s (di\014ed)g(for)g(other)h(t)m(yp)s(es)f(in)150 5340 y(the)31 b(follo)m(wing)g(w)m(a)m(y)-8 b(,)p eop end %%Page: 9 27 TeXDict begin 9 26 bop 150 -116 a FK(Chapter)30 b(2:)41 b(Using)30 b(the)h(library)2412 b(9)390 299 y FH(gsl_foo)857 b(double)390 408 y(gsl_foo_long_double)281 b(long)47 b(double)390 518 y(gsl_foo_float)569 b(float)390 628 y(gsl_foo_long)617 b(long)390 737 y(gsl_foo_ulong)569 b(unsigned)46 b(long)390 847 y(gsl_foo_int)665 b(int)390 956 y(gsl_foo_uint)617 b(unsigned)46 b(int)390 1066 y(gsl_foo_short)569 b(short)390 1176 y(gsl_foo_ushort)521 b(unsigned)46 b(short)390 1285 y(gsl_foo_char)617 b(char)390 1395 y(gsl_foo_uchar)569 b(unsigned)46 b(char)150 1569 y FK(When)30 b(a)g(mo)s(dule)g(con)m 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b(is)h(the)g(t)m(yp)s(e)g(of)g(GSL)g(error)f(handler)g(functions.)40 b(An)27 b(error)h(handler)f(will)h(b)s(e)f(passed)h(four)390 4902 y(argumen)m(ts)d(whic)m(h)f(sp)s(ecify)g(the)h(reason)g(for)f(the) h(error)f(\(a)h(string\),)h(the)f(name)g(of)f(the)h(source)g(\014le)390 5011 y(in)31 b(whic)m(h)f(it)i(o)s(ccurred)e(\(also)i(a)g(string\),)f (the)g(line)h(n)m(um)m(b)s(er)d(in)i(that)h(\014le)f(\(an)g(in)m (teger\))h(and)f(the)390 5121 y(error)j(n)m(um)m(b)s(er)f(\(an)i(in)m (teger\).)55 b(The)34 b(source)h(\014le)f(and)g(line)h(n)m(um)m(b)s(er) e(are)i(set)g(at)h(compile)f(time)390 5230 y(using)g(the)h FH(__FILE__)d FK(and)i FH(__LINE__)e FK(directiv)m(es)k(in)e(the)h (prepro)s(cessor.)55 b(An)36 b(error)f(handler)390 5340 y(function)30 b(returns)f(t)m(yp)s(e)i FH(void)p FK(.)39 b(Error)30 b(handler)f(functions)h(should)g(b)s(e)f(de\014ned)g(lik)m (e)j(this,)p eop end %%Page: 13 31 TeXDict begin 13 30 bop 150 -116 a FK(Chapter)30 b(3:)41 b(Error)29 b(Handling)2439 b(13)630 299 y FH(void)47 b(handler)e(\(const)i(char)f(*)i(reason,)1298 408 y(const)f(char)f(*)i (file,)1298 518 y(int)f(line,)1298 628 y(int)g(gsl_errno\))150 798 y FK(T)-8 b(o)27 b(request)g(the)f(use)g(of)h(y)m(our)g(o)m(wn)f (error)g(handler)g(y)m(ou)h(need)f(to)h(call)h(the)f(function)f FH(gsl_set_error_)150 908 y(handler)i FK(whic)m(h)i(is)h(also)g (declared)g(in)f FH(gsl_errno.h)p FK(,)3350 1078 y([F)-8 b(unction])-3599 b Fv(gsl_error_handler_t)58 b(*)53 b (gsl_set_error_handler)565 1187 y Fu(\()p FD(gsl)p 712 1187 28 4 v 41 w(error)p 946 1187 V 40 w(handler)p 1285 1187 V 39 w(t)31 b(*)f Ft(new_handler)p Fu(\))390 1297 y FK(This)36 b(function)h(sets)h(a)f(new)g(error)f(handler,)j FD(new)p 2183 1297 V 39 w(handler)p FK(,)f(for)f(the)g(GSL)g(library)g (routines.)390 1407 y(The)h(previous)f(handler)g(is)i(returned)e(\(so)h (that)h(y)m(ou)f(can)h(restore)g(it)f(later\).)66 b(Note)39 b(that)g(the)390 1516 y(p)s(oin)m(ter)28 b(to)i(a)e(user)g(de\014ned)f (error)h(handler)g(function)g(is)h(stored)f(in)g(a)h(static)h(v)-5 b(ariable,)30 b(so)f(there)390 1626 y(can)34 b(b)s(e)e(only)h(one)h (error)f(handler)f(p)s(er)g(program.)50 b(This)32 b(function)h(should)f (b)s(e)h(not)g(b)s(e)g(used)f(in)390 1735 y(m)m(ulti-threaded)23 b(programs)g(except)g(to)h(set)f(up)f(a)h(program-wide)g(error)f (handler)g(from)g(a)i(master)390 1845 y(thread.)40 b(The)30 b(follo)m(wing)i(example)f(sho)m(ws)f(ho)m(w)h(to)g(set)g(and)f (restore)h(a)f(new)g(error)g(handler,)630 1975 y FH(/*)47 b(save)g(original)e(handler,)h(install)g(new)h(handler)e(*/)630 2084 y(old_handler)g(=)i(gsl_set_error_handler)42 b(\(&my_handler\);) 630 2304 y(/*)47 b(code)g(uses)f(new)h(handler)f(*/)630 2413 y(.....)630 2632 y(/*)h(restore)f(original)g(handler)f(*/)630 2742 y(gsl_set_error_handler)d(\(old_handler\);)390 2872 y FK(T)-8 b(o)31 b(use)f(the)g(default)h(b)s(eha)m(vior)f(\()p FH(abort)g FK(on)g(error\))g(set)h(the)g(error)f(handler)f(to)i FH(NULL)p FK(,)630 3002 y FH(old_handler)45 b(=)i (gsl_set_error_handler)42 b(\(NULL\);)3350 3172 y FK([F)-8 b(unction])-3599 b Fv(gsl_error_handler_t)58 b(*)53 b (gsl_set_error_handler_o)q(ff)f Fu(\(\))390 3282 y FK(This)40 b(function)h(turns)f(o\013)h(the)h(error)e(handler)h(b)m(y)f (de\014ning)h(an)g(error)f(handler)g(whic)m(h)h(do)s(es)390 3391 y(nothing.)e(This)26 b(will)h(cause)h(the)f(program)f(to)i(con)m (tin)m(ue)g(after)f(an)m(y)g(error,)g(so)g(the)g(return)f(v)-5 b(alues)390 3501 y(from)37 b(an)m(y)h(library)f(routines)g(m)m(ust)g(b) s(e)g(c)m(hec)m(k)m(ed.)64 b(This)37 b(is)g(the)h(recommended)f(b)s (eha)m(vior)g(for)390 3610 y(pro)s(duction)e(programs.)58 b(The)36 b(previous)g(handler)f(is)i(returned)e(\(so)h(that)h(y)m(ou)g (can)g(restore)f(it)390 3720 y(later\).)275 3890 y(The)e(error)g(b)s (eha)m(vior)h(can)g(b)s(e)f(c)m(hanged)i(for)e(sp)s(eci\014c)h (applications)h(b)m(y)f(recompiling)g(the)g(library)150 4000 y(with)30 b(a)h(customized)g(de\014nition)f(of)h(the)f FH(GSL_ERROR)e FK(macro)j(in)f(the)h(\014le)f FH(gsl_errno.h)p FK(.)150 4223 y FJ(3.4)68 b(Using)46 b(GSL)e(error)h(rep)t(orting)g(in) g(y)l(our)g(o)l(wn)g(functions)150 4382 y FK(If)26 b(y)m(ou)i(are)f (writing)g(n)m(umerical)g(functions)f(in)h(a)g(program)g(whic)m(h)f (also)i(uses)e(GSL)h(co)s(de)g(y)m(ou)g(ma)m(y)g(\014nd)150 4492 y(it)k(con)m(v)m(enien)m(t)h(to)g(adopt)e(the)h(same)f(error)g (rep)s(orting)g(con)m(v)m(en)m(tions)j(as)d(in)g(the)h(library)-8 b(.)275 4622 y(T)g(o)29 b(rep)s(ort)g(an)g(error)g(y)m(ou)h(need)f(to)h (call)h(the)f(function)f FH(gsl_error)e FK(with)i(a)g(string)h (describing)f(the)150 4731 y(error)d(and)h(then)f(return)g(an)h (appropriate)g(error)f(co)s(de)h(from)g FH(gsl_errno.h)p FK(,)d(or)j(a)h(sp)s(ecial)f(v)-5 b(alue,)28 b(suc)m(h)150 4841 y(as)39 b FH(NaN)p FK(.)64 b(F)-8 b(or)39 b(con)m(v)m(enience)i (the)e(\014le)f FH(gsl_errno.h)e FK(de\014nes)h(t)m(w)m(o)j(macros)f (whic)m(h)f(carry)h(out)f(these)150 4950 y(steps:)3449 5121 y([Macro])-3598 b Fv(GSL_ERROR)48 b Fu(\()p Ft(reason)p FD(,)33 b Ft(gsl_errno)p Fu(\))390 5230 y FK(This)28 b(macro)i(rep)s(orts)e(an)h(error)g(using)f(the)i(GSL)e(con)m(v)m(en)m (tions)j(and)e(returns)e(a)j(status)f(v)-5 b(alue)30 b(of)390 5340 y FH(gsl_errno)p FK(.)38 b(It)31 b(expands)e(to)i(the)g (follo)m(wing)h(co)s(de)e(fragmen)m(t,)p eop end %%Page: 14 32 TeXDict begin 14 31 bop 150 -116 a FK(Chapter)30 b(3:)41 b(Error)29 b(Handling)2439 b(14)630 299 y FH(gsl_error)45 b(\(reason,)h(__FILE__,)f(__LINE__,)g(gsl_errno\);)630 408 y(return)h(gsl_errno;)390 547 y FK(The)28 b(macro)i(de\014nition)e (in)h FH(gsl_errno.h)d FK(actually)k(wraps)e(the)h(co)s(de)g(in)g(a)g FH(do)h({)g(...)f(})h(while)390 657 y(\(0\))f FK(blo)s(c)m(k)i(to)g (prev)m(en)m(t)h(p)s(ossible)d(parsing)h(problems.)275 850 y(Here)38 b(is)g(an)g(example)h(of)f(ho)m(w)g(the)g(macro)h(could)f (b)s(e)f(used)g(to)i(rep)s(ort)e(that)i(a)f(routine)g(did)g(not)150 960 y(ac)m(hiev)m(e)j(a)e(requested)f(tolerance.)67 b(T)-8 b(o)39 b(rep)s(ort)f(the)h(error)f(the)h(routine)g(needs)f(to)h(return) f(the)g(error)150 1069 y(co)s(de)31 b FH(GSL_ETOL)p FK(.)390 1208 y FH(if)47 b(\(residual)e(>)j(tolerance\))485 1318 y({)581 1428 y(GSL_ERROR\("residual)42 b(exceeds)k(tolerance",)f (GSL_ETOL\);)485 1537 y(})3449 1730 y FK([Macro])-3598 b Fv(GSL_ERROR_VAL)49 b Fu(\()p Ft(reason)p FD(,)33 b Ft(gsl_errno)p FD(,)g Ft(value)p Fu(\))390 1840 y FK(This)23 b(macro)h(is)g(the)g(same)h(as)f FH(GSL_ERROR)d FK(but)i(returns)g(a)h (user-de\014ned)e(v)-5 b(alue)24 b(of)g FD(v)-5 b(alue)30 b FK(instead)390 1950 y(of)38 b(an)f(error)g(co)s(de.)63 b(It)38 b(can)f(b)s(e)g(used)g(for)g(mathematical)j(functions)d(that)i (return)d(a)i(\015oating)390 2059 y(p)s(oin)m(t)30 b(v)-5 b(alue.)275 2252 y(The)33 b(follo)m(wing)i(example)f(sho)m(ws)g(ho)m(w) g(to)g(return)f(a)h FH(NaN)f FK(at)i(a)f(mathematical)i(singularit)m(y) e(using)150 2362 y(the)d FH(GSL_ERROR_VAL)26 b FK(macro,)390 2501 y FH(if)47 b(\(x)g(==)h(0\))485 2611 y({)581 2720 y(GSL_ERROR_VAL\("argument)41 b(lies)47 b(on)g(singularity",)1249 2830 y(GSL_ERANGE,)e(GSL_NAN\);)485 2939 y(})150 3179 y FJ(3.5)68 b(Examples)150 3338 y FK(Here)28 b(is)f(an)f(example)i(of)f (some)h(co)s(de)f(whic)m(h)g(c)m(hec)m(ks)h(the)f(return)f(v)-5 b(alue)28 b(of)f(a)g(function)g(where)f(an)h(error)150 3448 y(migh)m(t)k(b)s(e)f(rep)s(orted,)390 3587 y FH(#include)46 b()390 3696 y(#include)g()390 3806 y(#include)g()390 4025 y(...)485 4134 y(int)h(status;)485 4244 y(size_t)g(n)g(=)g(37;)485 4463 y(gsl_set_error_handler_off\()o(\);)485 4682 y(status)g(=)g (gsl_fft_complex_radix2_f)o(orwa)o(rd)42 b(\(data,)k(stride,)f(n\);)485 4902 y(if)j(\(status\))d({)581 5011 y(if)i(\(status)f(==)h (GSL_EINVAL\))e({)724 5121 y(fprintf)h(\(stderr,)f("invalid)h (argument,)f(n=\045d\\n",)h(n\);)581 5230 y(})h(else)g({)724 5340 y(fprintf)f(\(stderr,)f("failed,)h(gsl_errno=\045d\\n",)p eop end %%Page: 15 33 TeXDict begin 15 32 bop 150 -116 a FK(Chapter)30 b(3:)41 b(Error)29 b(Handling)2439 b(15)1535 299 y FH(status\);)581 408 y(})581 518 y(exit)47 b(\(-1\);)485 628 y(})390 737 y(...)150 872 y FK(The)31 b(function)h FH(gsl_fft_complex_radix2)26 b FK(only)32 b(accepts)i(in)m(teger)f(lengths)f(whic)m(h)g(are)g(a)h(p) s(o)m(w)m(er)f(of)150 981 y(t)m(w)m(o.)42 b(If)29 b(the)h(v)-5 b(ariable)30 b FH(n)g FK(is)f(not)h(a)g(p)s(o)m(w)m(er)g(of)g(t)m(w)m (o)h(then)e(the)h(call)h(to)g(the)e(library)h(function)f(will)h(return) 150 1091 y FH(GSL_EINVAL)p FK(,)d(indicating)i(that)h(the)f(length)g (argumen)m(t)g(is)g(in)m(v)-5 b(alid.)41 b(The)28 b(function)h(call)h (to)f FH(gsl_set_)150 1200 y(error_handler_off)c FK(stops)30 b(the)g(default)h(error)e(handler)g(from)h(ab)s(orting)g(the)g (program.)41 b(The)29 b FH(else)150 1310 y FK(clause)i(catc)m(hes)h(an) m(y)f(other)g(p)s(ossible)f(errors.)p eop end %%Page: 16 34 TeXDict begin 16 33 bop 150 -116 a FK(Chapter)30 b(4:)41 b(Mathematical)33 b(F)-8 b(unctions)2081 b(16)150 299 y FG(4)80 b(Mathematical)54 b(F)-13 b(unctions)150 518 y FK(This)33 b(c)m(hapter)h(describ)s(es)f(basic)i(mathematical)h (functions.)50 b(Some)34 b(of)g(these)g(functions)g(are)g(presen)m(t) 150 627 y(in)26 b(system)h(libraries,)g(but)f(the)h(alternativ)m(e)i(v) m(ersions)e(giv)m(en)g(here)g(can)f(b)s(e)g(used)g(as)h(a)g(substitute) f(when)150 737 y(the)31 b(system)f(functions)g(are)h(not)f(a)m(v)-5 b(ailable.)275 868 y(The)32 b(functions)h(and)g(macros)h(describ)s(ed)e (in)h(this)g(c)m(hapter)h(are)g(de\014ned)e(in)h(the)h(header)f(\014le) g FH(gsl_)150 978 y(math.h)p FK(.)150 1204 y FJ(4.1)68 b(Mathematical)47 b(Constan)l(ts)150 1363 y FK(The)32 b(library)h(ensures)f(that)i(the)f(standard)f FC(bsd)g FK(mathematical)j(constan)m(ts)f(are)g(de\014ned.)47 b(F)-8 b(or)34 b(refer-)150 1473 y(ence,)d(here)f(is)h(a)g(list)g(of)f (the)h(constan)m(ts:)150 1626 y FH(M_E)336 b FK(The)30 b(base)g(of)h(exp)s(onen)m(tials,)g FE(e)150 1780 y FH(M_LOG2E)144 b FK(The)30 b(base-2)h(logarithm)h(of)e FE(e)p FK(,)h(log)1828 1801 y FB(2)1866 1780 y FK(\()p FE(e)p FK(\))150 1933 y FH(M_LOG10E)96 b FK(The)30 b(base-10)i(logarithm)f(of)g FE(e)p FK(,)f(log)1874 1955 y FB(10)1944 1933 y FK(\()p FE(e)p FK(\))150 2086 y FH(M_SQRT2)144 b FK(The)30 b(square)g(ro)s(ot)h (of)f(t)m(w)m(o,)1598 2011 y FI(p)p 1674 2011 46 4 v 75 x FK(2)150 2239 y FH(M_SQRT1_2)630 2349 y FK(The)g(square)g(ro)s(ot) h(of)f(one-half,)1772 2276 y Fs(p)p 1855 2276 137 4 v 73 x FK(1)p FE(=)p FK(2)150 2502 y FH(M_SQRT3)144 b FK(The)30 b(square)g(ro)s(ot)h(of)f(three,)1659 2427 y FI(p)p 1735 2427 46 4 v 75 x FK(3)150 2655 y FH(M_PI)288 b FK(The)30 b(constan)m(t)i(pi,)e FE(\031)150 2809 y FH(M_PI_2)192 b FK(Pi)30 b(divided)g(b)m(y)g(t)m(w)m(o,)i FE(\031)s(=)p FK(2)150 2962 y FH(M_PI_4)192 b FK(Pi)30 b(divided)g(b)m(y)g(four,)g FE(\031)s(=)p FK(4)150 3115 y FH(M_SQRTPI)96 b FK(The)30 b(square)g(ro)s(ot)h(of)f(pi,)1533 3050 y FI(p)p 1608 3050 56 4 v 1608 3115 a FE(\031)150 3268 y FH(M_2_SQRTPI)630 3378 y FK(Tw)m(o)h(divided)e(b)m(y)i(the)f(square)g(ro)s(ot)h(of)f(pi,) h(2)p FE(=)2244 3313 y FI(p)p 2320 3313 V 65 x FE(\031)150 3531 y FH(M_1_PI)192 b FK(The)30 b(recipro)s(cal)h(of)g(pi,)f(1)p FE(=\031)150 3684 y FH(M_2_PI)192 b FK(Twice)31 b(the)f(recipro)s(cal)h (of)g(pi,)f(2)p FE(=\031)150 3838 y FH(M_LN10)192 b FK(The)30 b(natural)g(logarithm)i(of)e(ten,)h(ln\(10\))150 3991 y FH(M_LN2)240 b FK(The)30 b(natural)g(logarithm)i(of)e(t)m(w)m(o,)i (ln\(2\))150 4144 y FH(M_LNPI)192 b FK(The)30 b(natural)g(logarithm)i (of)e(pi,)h(ln)o(\()p FE(\031)s FK(\))150 4297 y FH(M_EULER)144 b FK(Euler's)30 b(constan)m(t,)i FE(\015)150 4524 y FJ(4.2)68 b(In\014nities)46 b(and)e(Not-a-n)l(um)l(b)t(er)3449 4727 y FK([Macro])-3598 b Fv(GSL_POSINF)390 4836 y FK(This)25 b(macro)h(con)m(tains)h(the)e(IEEE)g(represen)m(tation)i(of)f(p)s (ositiv)m(e)g(in\014nit)m(y)-8 b(,)27 b(+)p FI(1)p FK(.)39 b(It)26 b(is)f(computed)390 4946 y(from)30 b(the)g(expression)h FH(+1.0/0.0)p FK(.)3449 5121 y([Macro])-3598 b Fv(GSL_NEGINF)390 5230 y FK(This)23 b(macro)h(con)m(tains)h(the)e(IEEE)g(represen)m (tation)i(of)f(negativ)m(e)h(in\014nit)m(y)-8 b(,)26 b FI(\0001)p FK(.)38 b(It)24 b(is)f(computed)390 5340 y(from)30 b(the)g(expression)h FH(-1.0/0.0)p FK(.)p eop end %%Page: 17 35 TeXDict begin 17 34 bop 150 -116 a FK(Chapter)30 b(4:)41 b(Mathematical)33 b(F)-8 b(unctions)2081 b(17)3449 299 y([Macro])-3598 b Fv(GSL_NAN)390 408 y FK(This)33 b(macro)h(con)m (tains)h(the)f(IEEE)f(represen)m(tation)h(of)g(the)g(Not-a-Num)m(b)s (er)h(sym)m(b)s(ol,)f FH(NaN)p FK(.)50 b(It)390 518 y(is)30 b(computed)h(from)f(the)g(ratio)h FH(0.0/0.0)p FK(.)3350 698 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_isnan)48 b Fu(\()p FD(const)32 b(double)e Ft(x)p Fu(\))390 808 y FK(This)g(function)g(returns)f(1)i(if)f FD(x)36 b FK(is)31 b(not-a-n)m(um)m(b)s(er.)3350 988 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_isinf)48 b Fu(\()p FD(const)32 b(double)e Ft(x)p Fu(\))390 1097 y FK(This)36 b(function)h(returns)f(+1)h(if)g FD(x)44 b FK(is)37 b(p)s(ositiv)m(e)h(in\014nit)m(y)-8 b(,)39 b FI(\000)p FK(1)e(if)g FD(x)44 b FK(is)37 b(negativ)m(e)i (in\014nit)m(y)e(and)g(0)390 1207 y(otherwise.)789 1174 y FB(1)3350 1387 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_finite)c Fu(\()p FD(const)31 b(double)f Ft(x)p Fu(\))390 1497 y FK(This)g(function)g(returns)f(1)i(if)f FD(x)36 b FK(is)31 b(a)g(real)g(n)m(um)m(b)s(er,)e(and)h(0)g(if)h(it)g (is)f(in\014nite)g(or)h(not-a-n)m(um)m(b)s(er.)150 1726 y FJ(4.3)68 b(Elemen)l(tary)47 b(F)-11 b(unctions)150 1886 y FK(The)40 b(follo)m(wing)i(routines)f(pro)m(vide)f(p)s(ortable)h (implemen)m(tations)h(of)f(functions)f(found)g(in)g(the)h(BSD)150 1995 y(math)34 b(library)-8 b(.)53 b(When)35 b(nativ)m(e)g(v)m(ersions) g(are)g(not)g(a)m(v)-5 b(ailable)37 b(the)d(functions)g(describ)s(ed)g (here)g(can)h(b)s(e)150 2105 y(used)30 b(instead.)42 b(The)30 b(substitution)h(can)g(b)s(e)f(made)h(automatically)j(if)c(y)m (ou)h(use)g FH(autoconf)d FK(to)k(compile)150 2214 y(y)m(our)e (application)i(\(see)f(Section)h(2.7)f([P)m(ortabilit)m(y)i (functions],)d(page)h(7\).)3350 2394 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_log1p)48 b Fu(\()p FD(const)32 b(double)d Ft(x)p Fu(\))390 2504 y FK(This)h(function)g(computes)g(the)h(v)-5 b(alue)31 b(of)g(log)r(\(1)21 b(+)f FE(x)p FK(\))31 b(in)f(a)h(w)m(a)m (y)g(that)g(is)g(accurate)h(for)e(small)h FD(x)p FK(.)390 2614 y(It)f(pro)m(vides)h(an)f(alternativ)m(e)j(to)e(the)g(BSD)f(math)h (function)f FH(log1p\(x\))p FK(.)3350 2794 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_expm1)48 b Fu(\()p FD(const)32 b(double)d Ft(x)p Fu(\))390 2903 y FK(This)g(function)g(computes)g(the)g(v)-5 b(alue)30 b(of)g(exp\()p FE(x)p FK(\))18 b FI(\000)g FK(1)30 b(in)f(a)h(w)m(a)m(y)g(that)g(is)f(accurate)i(for)e(small)h FD(x)p FK(.)390 3013 y(It)g(pro)m(vides)h(an)f(alternativ)m(e)j(to)e (the)g(BSD)f(math)h(function)f FH(expm1\(x\))p FK(.)3350 3193 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_hypot)48 b Fu(\()p FD(const)32 b(double)d Ft(x)p FD(,)i(const)g(double)f Ft(y)p Fu(\))390 3302 y FK(This)44 b(function)g(computes)g(the)h(v)-5 b(alue)44 b(of)1937 3234 y FI(p)p 2013 3234 286 4 v 68 x FE(x)2065 3276 y FB(2)2122 3302 y FK(+)20 b FE(y)2261 3276 y FB(2)2342 3302 y FK(in)44 b(a)h(w)m(a)m(y)g(that)g(a)m(v)m(oids) h(o)m(v)m(er\015o)m(w.)84 b(It)390 3412 y(pro)m(vides)30 b(an)h(alternativ)m(e)h(to)g(the)e(BSD)h(math)f(function)g FH(hypot\(x,y\))p FK(.)3350 3592 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_hypot3)49 b Fu(\()p FD(const)31 b(double)f Ft(x)p FD(,)h(const)g(double)e Ft(y)p FD(,)i(const)g(double) f Ft(z)p Fu(\))390 3702 y FK(This)g(function)g(computes)g(the)h(v)-5 b(alue)31 b(of)1853 3633 y FI(p)p 1929 3633 481 4 v 69 x FE(x)1981 3675 y FB(2)2038 3702 y FK(+)20 b FE(y)2177 3675 y FB(2)2234 3702 y FK(+)g FE(z)2371 3675 y FB(2)2439 3702 y FK(in)30 b(a)h(w)m(a)m(y)g(that)g(a)m(v)m(oids)h(o)m(v)m (er\015o)m(w.)3350 3882 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_acosh)48 b Fu(\()p FD(const)32 b(double)d Ft(x)p Fu(\))390 3991 y FK(This)39 b(function)h(computes)h(the)f(v)-5 b(alue)41 b(of)g(arccosh\()p FE(x)p FK(\).)71 b(It)41 b(pro)m(vides)f(an)g(alternativ)m(e)j(to)e(the)390 4101 y(standard)30 b(math)g(function)g FH(acosh\(x\))p FK(.)3350 4281 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_asinh)48 b Fu(\()p FD(const)32 b(double)d Ft(x)p Fu(\))390 4391 y FK(This)40 b(function)h(computes)g(the)g(v)-5 b(alue)42 b(of)f(arcsinh)o(\()p FE(x)p FK(\).)74 b(It)41 b(pro)m(vides)g(an)g (alternativ)m(e)i(to)f(the)390 4500 y(standard)30 b(math)g(function)g FH(asinh\(x\))p FK(.)3350 4680 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_atanh)48 b Fu(\()p FD(const)32 b(double)d Ft(x)p Fu(\))390 4790 y FK(This)39 b(function)g(computes)h(the)g(v)-5 b(alue)40 b(of)f(arctanh)q(\()p FE(x)p FK(\).)69 b(It)39 b(pro)m(vides)h(an)f(alternativ)m(e)j(to)f(the)390 4899 y(standard)30 b(math)g(function)g FH(atanh\(x\))p FK(.)p 150 4979 1200 4 v 199 5047 a FB(1)275 5078 y Fx(Note)23 b(that)g(the)f(C99)j(standard)e(only)g(requires)g(the)g(system)h Fz(isinf)g Fx(function)f(to)h(return)e(a)i(non-zero)f(v)l(alue,)h (without)275 5166 y(the)33 b(sign)h(of)g(the)f(in\014nit)n(y)-6 b(.)56 b(The)34 b(implemen)n(tation)g(in)g(some)g(earlier)h(v)n (ersions)f(of)g(GSL)f(used)g(the)g(system)h Fz(isinf)275 5253 y Fx(function)26 b(and)h(ma)n(y)f(ha)n(v)n(e)g(this)h(b)r(eha)n (vior)f(on)h(some)g(platforms.)39 b(Therefore,)29 b(it)d(is)i (advisable)f(to)g(test)f(the)h(sign)g(of)g Fr(x)275 5340 y Fx(separately)-6 b(,)26 b(if)g(needed,)g(rather)f(than)h(relying)g (the)f(sign)h(of)h(the)e(return)g(v)l(alue)g(from)i Fz(gsl_isinf\(\))p Fx(.)p eop end %%Page: 18 36 TeXDict begin 18 35 bop 150 -116 a FK(Chapter)30 b(4:)41 b(Mathematical)33 b(F)-8 b(unctions)2081 b(18)3350 299 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_ldexp)48 b Fu(\()p FD(double)31 b Ft(x)p FD(,)f(in)m(t)h Ft(e)p Fu(\))390 408 y FK(This)c(function)g(computes)h(the)g(v)-5 b(alue)28 b(of)g FE(x)15 b FI(\003)g FK(2)2009 375 y Fq(e)2045 408 y FK(.)40 b(It)28 b(pro)m(vides)g(an)f(alternativ)m(e)j (to)f(the)f(standard)390 518 y(math)i(function)g FH(ldexp\(x,e\))p FK(.)3350 700 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_frexp)48 b Fu(\()p FD(double)31 b Ft(x)p FD(,)f(in)m(t)h(*)g Ft(e)p Fu(\))390 810 y FK(This)26 b(function)g(splits)h(the)g(n)m(um)m (b)s(er)f FE(x)g FK(in)m(to)i(its)f(normalized)h(fraction)f FE(f)36 b FK(and)26 b(exp)s(onen)m(t)h FE(e)p FK(,)h(suc)m(h)390 919 y(that)k FE(x)c FK(=)f FE(f)k FI(\003)21 b FK(2)953 886 y Fq(e)1021 919 y FK(and)32 b(0)p FE(:)p FK(5)c FI(\024)g FE(f)37 b(<)27 b FK(1.)45 b(The)32 b(function)f(returns)g FE(f)41 b FK(and)31 b(stores)h(the)g(exp)s(onen)m(t)g(in)390 1029 y FE(e)p FK(.)42 b(If)30 b FE(x)g FK(is)h(zero,)g(b)s(oth)f FE(f)40 b FK(and)30 b FE(e)h FK(are)g(set)g(to)g(zero.)42 b(This)30 b(function)g(pro)m(vides)h(an)f(alternativ)m(e)j(to)390 1139 y(the)e(standard)e(math)h(function)h FH(frexp\(x,)d(e\))p FK(.)150 1370 y FJ(4.4)68 b(Small)46 b(in)l(teger)g(p)t(o)l(w)l(ers)150 1529 y FK(A)32 b(common)g(complain)m(t)h(ab)s(out)e(the)h(standard)f(C) g(library)g(is)h(its)g(lac)m(k)h(of)f(a)g(function)f(for)h(calculating) 150 1639 y(\(small\))g(in)m(teger)f(p)s(o)m(w)m(ers.)41 b(GSL)30 b(pro)m(vides)g(some)h(simple)f(functions)g(to)h(\014ll)g (this)f(gap.)41 b(F)-8 b(or)31 b(reasons)g(of)150 1748 y(e\016ciency)-8 b(,)32 b(these)f(functions)f(do)g(not)h(c)m(hec)m(k)h (for)e(o)m(v)m(er\015o)m(w)i(or)e(under\015o)m(w)f(conditions.)3350 1930 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_pow_int)49 b Fu(\()p FD(double)30 b Ft(x)p FD(,)h(in)m(t)g Ft(n)p Fu(\))3350 2040 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_pow_uint)49 b Fu(\()p FD(double)31 b Ft(x)p FD(,)f(unsigned)g(in) m(t)h Ft(n)p Fu(\))390 2150 y FK(These)52 b(routines)g(computes)g(the)h (p)s(o)m(w)m(er)f FE(x)1990 2117 y Fq(n)2087 2150 y FK(for)g(in)m (teger)i FD(n)p FK(.)105 b(The)52 b(p)s(o)m(w)m(er)g(is)g(computed)390 2259 y(e\016cien)m(tly|for)31 b(example,)f FE(x)1430 2226 y FB(8)1497 2259 y FK(is)g(computed)f(as)h(\(\()p FE(x)2239 2226 y FB(2)2276 2259 y FK(\))2311 2226 y FB(2)2349 2259 y FK(\))2384 2226 y FB(2)2422 2259 y FK(,)f(requiring)g(only)h(3)g (m)m(ultiplications.)390 2369 y(A)37 b(v)m(ersion)h(of)f(this)g (function)g(whic)m(h)g(also)h(computes)g(the)f(n)m(umerical)h(error)f (in)f(the)i(result)f(is)390 2478 y(a)m(v)-5 b(ailable)33 b(as)d FH(gsl_sf_pow_int_e)p FK(.)3350 2660 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_pow_2)48 b Fu(\()p FD(const)32 b(double)d Ft(x)p Fu(\))3350 2770 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_pow_3)48 b Fu(\()p FD(const)32 b(double)d Ft(x)p Fu(\))3350 2880 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_pow_4)48 b Fu(\()p FD(const)32 b(double)d Ft(x)p Fu(\))3350 2989 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_pow_5)48 b Fu(\()p FD(const)32 b(double)d Ft(x)p Fu(\))3350 3099 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_pow_6)48 b Fu(\()p FD(const)32 b(double)d Ft(x)p Fu(\))3350 3208 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_pow_7)48 b Fu(\()p FD(const)32 b(double)d Ft(x)p Fu(\))3350 3318 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_pow_8)48 b Fu(\()p FD(const)32 b(double)d Ft(x)p Fu(\))3350 3428 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_pow_9)48 b Fu(\()p FD(const)32 b(double)d Ft(x)p Fu(\))390 3537 y FK(These)i(functions)h(can)f(b)s(e)g(used)g(to) i(compute)f(small)g(in)m(teger)h(p)s(o)m(w)m(ers)e FE(x)2927 3504 y FB(2)2964 3537 y FK(,)i FE(x)3074 3504 y FB(3)3111 3537 y FK(,)f(etc.)46 b(e\016cien)m(tly)-8 b(.)390 3647 y(The)27 b(functions)h(will)g(b)s(e)f(inlined)g(when)g FH(HAVE_INLINE)e FK(is)i(de\014ned,)h(so)g(that)g(use)f(of)h(these)h (func-)390 3756 y(tions)d(should)e(b)s(e)g(as)i(e\016cien)m(t)h(as)e (explicitly)i(writing)e(the)h(corresp)s(onding)e(pro)s(duct)g (expression.)390 3914 y FH(#include)46 b()390 4024 y(double)g(y)i(=)f(gsl_pow_4)e(\(3.141\))94 b(/*)47 b(compute)f(3.141**4)f(*/)150 4255 y FJ(4.5)68 b(T)-11 b(esting)45 b(the)h(Sign)e(of)i(Num)l(b)t(ers)3449 4463 y FK([Macro])-3598 b Fv(GSL_SIGN)48 b Fu(\()p FD(x)p Fu(\))390 4572 y FK(This)38 b(macro)g(returns)g(the)g(sign)g(of)h FD(x)p FK(.)64 b(It)39 b(is)f(de\014ned)f(as)i FH(\(\(x\))29 b(>=)h(0)g(?)g(1)g(:)g(-1\))p FK(.)64 b(Note)39 b(that)390 4682 y(with)30 b(this)g(de\014nition)g(the)h(sign)f(of)h(zero)g(is)f(p) s(ositiv)m(e)i(\(regardless)f(of)f(its)h FC(ieee)f FK(sign)g(bit\).)150 4913 y FJ(4.6)68 b(T)-11 b(esting)45 b(for)g(Odd)g(and)f(Ev)l(en)i(Num) l(b)t(ers)3449 5121 y FK([Macro])-3598 b Fv(GSL_IS_ODD)48 b Fu(\()p FD(n)p Fu(\))390 5230 y FK(This)30 b(macro)i(ev)-5 b(aluates)33 b(to)f(1)g(if)f FD(n)f FK(is)i(o)s(dd)e(and)g(0)i(if)f FD(n)g FK(is)g(ev)m(en.)44 b(The)31 b(argumen)m(t)g FD(n)g FK(m)m(ust)g(b)s(e)g(of)390 5340 y(in)m(teger)h(t)m(yp)s(e.)p eop end %%Page: 19 37 TeXDict begin 19 36 bop 150 -116 a FK(Chapter)30 b(4:)41 b(Mathematical)33 b(F)-8 b(unctions)2081 b(19)3449 299 y([Macro])-3598 b Fv(GSL_IS_EVEN)49 b Fu(\()p FD(n)p Fu(\))390 408 y FK(This)31 b(macro)i(is)f(the)h(opp)s(osite)f(of)h FH(GSL_IS_ODD\(n\))p FK(.)42 b(It)33 b(ev)-5 b(aluates)33 b(to)g(1)g(if)f FD(n)g FK(is)g(ev)m(en)h(and)e(0)i(if)390 518 y FD(n)d FK(is)g(o)s(dd.)40 b(The)30 b(argumen)m(t)h FD(n)e FK(m)m(ust)i(b)s(e)e(of)i(in)m(teger)h(t)m(yp)s(e.)150 770 y FJ(4.7)68 b(Maxim)l(um)45 b(and)g(Minim)l(um)g(functions)150 929 y FK(Note)39 b(that)f(the)f(follo)m(wing)i(macros)f(p)s(erform)e(m) m(ultiple)i(ev)-5 b(aluations)39 b(of)f(their)f(argumen)m(ts,)j(so)e (they)150 1039 y(should)23 b(not)h(b)s(e)f(used)g(with)h(argumen)m(ts)g (that)g(ha)m(v)m(e)h(side)f(e\013ects)h(\(suc)m(h)f(as)g(a)g(call)h(to) g(a)f(random)f(n)m(um)m(b)s(er)150 1148 y(generator\).)3449 1358 y([Macro])-3598 b Fv(GSL_MAX)48 b Fu(\()p FD(a,)31 b(b)p Fu(\))390 1468 y FK(This)25 b(macro)h(returns)e(the)i(maxim)m(um) f(of)h FD(a)g FK(and)f FD(b)p FK(.)38 b(It)26 b(is)f(de\014ned)f(as)i FH(\(\(a\))j(>)h(\(b\))g(?)g(\(a\):\(b\)\))p FK(.)3449 1678 y([Macro])-3598 b Fv(GSL_MIN)48 b Fu(\()p FD(a,)31 b(b)p Fu(\))390 1788 y FK(This)26 b(macro)i(returns)d(the)i(minim)m(um) g(of)g FD(a)g FK(and)f FD(b)p FK(.)39 b(It)27 b(is)g(de\014ned)f(as)h FH(\(\(a\))i(<)h(\(b\))g(?)g(\(a\):\(b\)\))p FK(.)3350 1998 y([F)-8 b(unction])-3599 b Fv(extern)54 b(inline)g(double)g (GSL_MAX_DBL)49 b Fu(\()p FD(double)30 b Ft(a)p FD(,)h(double)f Ft(b)p Fu(\))390 2107 y FK(This)k(function)h(returns)e(the)i(maxim)m (um)g(of)g(the)g(double)g(precision)g(n)m(um)m(b)s(ers)e FD(a)j FK(and)e FD(b)i FK(using)390 2217 y(an)e(inline)h(function.)52 b(The)33 b(use)h(of)h(a)g(function)f(allo)m(ws)h(for)f(t)m(yp)s(e)h(c)m (hec)m(king)h(of)e(the)h(argumen)m(ts)390 2326 y(as)c(an)g(extra)h (safet)m(y)g(feature.)44 b(On)30 b(platforms)h(where)g(inline)g (functions)f(are)i(not)f(a)m(v)-5 b(ailable)34 b(the)390 2436 y(macro)d FH(GSL_MAX)d FK(will)j(b)s(e)f(automatically)j (substituted.)3350 2646 y([F)-8 b(unction])-3599 b Fv(extern)54 b(inline)g(double)g(GSL_MIN_DBL)49 b Fu(\()p FD(double)30 b Ft(a)p FD(,)h(double)f Ft(b)p Fu(\))390 2755 y FK(This)35 b(function)h(returns)f(the)i(minim)m(um)e(of)i(the)f(double)g (precision)h(n)m(um)m(b)s(ers)d FD(a)j FK(and)f FD(b)h FK(using)390 2865 y(an)d(inline)h(function.)52 b(The)33 b(use)h(of)h(a)g(function)f(allo)m(ws)h(for)f(t)m(yp)s(e)h(c)m(hec)m (king)h(of)e(the)h(argumen)m(ts)390 2975 y(as)c(an)g(extra)h(safet)m(y) g(feature.)44 b(On)30 b(platforms)h(where)g(inline)g(functions)f(are)i (not)f(a)m(v)-5 b(ailable)34 b(the)390 3084 y(macro)d FH(GSL_MIN)d FK(will)j(b)s(e)f(automatically)j(substituted.)3350 3294 y([F)-8 b(unction])-3599 b Fv(extern)54 b(inline)g(int)f (GSL_MAX_INT)c Fu(\()p FD(in)m(t)31 b Ft(a)p FD(,)g(in)m(t)g Ft(b)p Fu(\))3350 3404 y FK([F)-8 b(unction])-3599 b Fv(extern)54 b(inline)g(int)f(GSL_MIN_INT)c Fu(\()p FD(in)m(t)31 b Ft(a)p FD(,)g(in)m(t)g Ft(b)p Fu(\))390 3513 y FK(These)k(functions)f (return)g(the)h(maxim)m(um)f(or)h(minim)m(um)f(of)h(the)g(in)m(tegers)h FD(a)f FK(and)f FD(b)j FK(using)d(an)390 3623 y(inline)41 b(function.)72 b(On)40 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y([Macro])-3598 b Fv(GSL_SET_REAL)49 b Fu(\()p Ft(zp)p FD(,)p Ft(x)p Fu(\))3449 408 y FK([Macro])-3598 b Fv(GSL_SET_IMAG)49 b Fu(\()p Ft(zp)p FD(,)p Ft(y)p Fu(\))390 518 y FK(These)32 b(macros)h(allo)m(w)h(the)f(real)g(and)e(imaginary)i(parts)g(of)f(the)h (complex)g(n)m(um)m(b)s(er)e(p)s(oin)m(ted)h(to)390 628 y(b)m(y)e FD(zp)j FK(to)e(b)s(e)f(set)h(indep)s(enden)m(tly)-8 b(.)150 873 y FJ(5.2)68 b(Prop)t(erties)46 b(of)f(complex)g(n)l(um)l(b) t(ers)3350 1091 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_complex_arg)c Fu(\()p FD(gsl)p 1493 1091 28 4 v 41 w(complex)31 b Ft(z)p Fu(\))390 1200 y FK(This)36 b(function)h(returns)e(the)i(argumen)m(t)h(of)f(the)g(complex)g(n)m(um) m(b)s(er)f FD(z)p FK(,)j(arg\()p FE(z)t FK(\),)h(where)c FI(\000)p FE(\031)j(<)390 1310 y FK(arg)q(\()p FE(z)t FK(\))26 b FI(\024)f FE(\031)s FK(.)3350 1511 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_complex_abs)c Fu(\()p FD(gsl)p 1493 1511 V 41 w(complex)31 b Ft(z)p Fu(\))390 1621 y FK(This)f(function)g(returns)f(the)h(magnitude)h(of)f(the)h (complex)g(n)m(um)m(b)s(er)e FD(z)p FK(,)i FI(j)p FE(z)t FI(j)p FK(.)3350 1823 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_complex_abs2)c Fu(\()p FD(gsl)p 1545 1823 V 41 w(complex)31 b Ft(z)p Fu(\))390 1932 y FK(This)f(function)g(returns)f (the)h(squared)g(magnitude)g(of)h(the)g(complex)g(n)m(um)m(b)s(er)e FD(z)p FK(,)i FI(j)p FE(z)t FI(j)3350 1899 y FB(2)3388 1932 y FK(.)3350 2134 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_complex_logabs)d Fu(\()p FD(gsl)p 1650 2134 V 41 w(complex)31 b Ft(z)p Fu(\))390 2243 y FK(This)c(function)g(returns)f (the)i(natural)g(logarithm)g(of)g(the)g(magnitude)g(of)f(the)h(complex) g(n)m(um)m(b)s(er)390 2353 y FD(z)p FK(,)42 b(log)17 b FI(j)p FE(z)t FI(j)p FK(.)68 b(It)39 b(allo)m(ws)h(an)f(accurate)i (ev)-5 b(aluation)40 b(of)f(log)18 b FI(j)p FE(z)t FI(j)40 b FK(when)e FI(j)p FE(z)t FI(j)h FK(is)g(close)i(to)e(one.)67 b(The)390 2462 y(direct)36 b(ev)-5 b(aluation)37 b(of)f 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y([F)-8 b(unction])-3599 b Fv(gsl_complex)56 b(gsl_complex_sub_real)51 b Fu(\()p FD(gsl)p 2016 4700 V 41 w(complex)31 b Ft(a)p FD(,)g(double)f Ft(x)p Fu(\))390 4810 y FK(This)e(function)h(returns)f(the)h(di\013erence)g(of)h(the)f (complex)h(n)m(um)m(b)s(er)d FD(a)j FK(and)e(the)h(real)h(n)m(um)m(b)s (er)e FD(x)p FK(,)390 4919 y FE(z)i FK(=)24 b FE(a)d FI(\000)f FE(x)p FK(.)3350 5121 y([F)-8 b(unction])-3599 b Fv(gsl_complex)56 b(gsl_complex_mul_real)51 b Fu(\()p FD(gsl)p 2016 5121 V 41 w(complex)31 b Ft(a)p FD(,)g(double)f Ft(x)p Fu(\))390 5230 y FK(This)j(function)g(returns)g(the)h(pro)s (duct)e(of)i(the)g(complex)g(n)m(um)m(b)s(er)f FD(a)h FK(and)f(the)h(real)g(n)m(um)m(b)s(er)f FD(x)p FK(,)390 5340 y FE(z)d FK(=)24 b FE(ax)p FK(.)p eop end %%Page: 23 41 TeXDict begin 23 40 bop 150 -116 a FK(Chapter)30 b(5:)41 b(Complex)30 b(Num)m(b)s(ers)2305 b(23)3350 299 y([F)-8 b(unction])-3599 b Fv(gsl_complex)56 b(gsl_complex_div_real)51 b Fu(\()p FD(gsl)p 2016 299 28 4 v 41 w(complex)31 b Ft(a)p FD(,)g(double)f Ft(x)p Fu(\))390 408 y FK(This)i(function)g (returns)f(the)i(quotien)m(t)g(of)g(the)g(complex)g(n)m(um)m(b)s(er)e FD(a)i FK(and)f(the)g(real)i(n)m(um)m(b)s(er)d FD(x)p FK(,)390 518 y FE(z)f FK(=)24 b FE(a=x)p FK(.)3350 716 y([F)-8 b(unction])-3599 b Fv(gsl_complex)56 b(gsl_complex_add_imag)51 b Fu(\()p FD(gsl)p 2016 716 V 41 w(complex)31 b Ft(a)p FD(,)g(double)f Ft(y)p Fu(\))390 825 y FK(This)j(function)h(returns)f (the)h(sum)g(of)g(the)g(complex)h(n)m(um)m(b)s(er)e FD(a)i FK(and)e(the)h(imaginary)h(n)m(um)m(b)s(er)390 935 y FE(i)p FD(y)p FK(,)c FE(z)e FK(=)c FE(a)c FK(+)f FE(iy)s FK(.)3350 1132 y([F)-8 b(unction])-3599 b Fv(gsl_complex)56 b(gsl_complex_sub_imag)51 b Fu(\()p FD(gsl)p 2016 1132 V 41 w(complex)31 b Ft(a)p FD(,)g(double)f Ft(y)p Fu(\))390 1242 y FK(This)43 b(function)h(returns)f(the)i(di\013erence)f(of)h(the) f(complex)h(n)m(um)m(b)s(er)e FD(a)h FK(and)g(the)g(imaginary)390 1351 y(n)m(um)m(b)s(er)29 b FE(i)p FD(y)p FK(,)i FE(z)e FK(=)c FE(a)c FI(\000)f FE(iy)s FK(.)3350 1549 y([F)-8 b(unction])-3599 b Fv(gsl_complex)56 b(gsl_complex_mul_imag)51 b Fu(\()p FD(gsl)p 2016 1549 V 41 w(complex)31 b Ft(a)p FD(,)g(double)f Ft(y)p Fu(\))390 1658 y FK(This)22 b(function)g (returns)g(the)h(pro)s(duct)e(of)i(the)g(complex)g(n)m(um)m(b)s(er)f FD(a)h FK(and)f(the)h(imaginary)g(n)m(um)m(b)s(er)390 1768 y FE(i)p FD(y)p FK(,)31 b FE(z)e FK(=)c FE(a)c FI(\003)f FK(\()p FE(iy)s FK(\).)3350 1965 y([F)-8 b(unction])-3599 b Fv(gsl_complex)56 b(gsl_complex_div_imag)51 b Fu(\()p FD(gsl)p 2016 1965 V 41 w(complex)31 b Ft(a)p FD(,)g(double)f Ft(y)p Fu(\))390 2075 y FK(This)21 b(function)g(returns)f(the)h (quotien)m(t)i(of)e(the)h(complex)g(n)m(um)m(b)s(er)e FD(a)i FK(and)f(the)g(imaginary)h(n)m(um)m(b)s(er)390 2185 y FE(i)p FD(y)p FK(,)31 b FE(z)e FK(=)c FE(a=)p FK(\()p FE(iy)s FK(\).)3350 2382 y([F)-8 b(unction])-3599 b Fv(gsl_complex)56 b(gsl_complex_conjugate)51 b Fu(\()p FD(gsl)p 2068 2382 V 41 w(complex)31 b Ft(z)p Fu(\))390 2492 y FK(This)f(function)g(returns)f(the)h(complex)h(conjugate)h(of)f (the)f(complex)h(n)m(um)m(b)s(er)e FD(z)p FK(,)i FE(z)3281 2459 y Fp(\003)3345 2492 y FK(=)25 b FE(x)20 b FI(\000)g FE(iy)s FK(.)3350 2689 y([F)-8 b(unction])-3599 b Fv(gsl_complex)56 b(gsl_complex_inverse)51 b Fu(\()p FD(gsl)p 1964 2689 V 41 w(complex)31 b Ft(z)p Fu(\))390 2799 y FK(This)41 b(function)h(returns)f(the)h(in)m(v)m(erse,)k(or)c(recipro)s(cal,)47 b(of)42 b(the)g(complex)h(n)m(um)m(b)s(er)e FD(z)p FK(,)k(1)p FE(=z)50 b FK(=)390 2908 y(\()p FE(x)21 b FI(\000)e FE(iy)s FK(\))p FE(=)p FK(\()p FE(x)834 2875 y FB(2)893 2908 y FK(+)h FE(y)1032 2875 y FB(2)1069 2908 y FK(\).)3350 3106 y([F)-8 b(unction])-3599 b Fv(gsl_complex)56 b (gsl_complex_negative)51 b Fu(\()p FD(gsl)p 2016 3106 V 41 w(complex)31 b Ft(z)p Fu(\))390 3215 y FK(This)f(function)g (returns)f(the)h(negativ)m(e)j(of)d(the)h(complex)g(n)m(um)m(b)s(er)e FD(z)p FK(,)i FI(\000)p FE(z)e FK(=)c(\()p FI(\000)p FE(x)p FK(\))c(+)f FE(i)p FK(\()p FI(\000)p FE(y)s FK(\).)150 3458 y FJ(5.4)68 b(Elemen)l(tary)47 b(Complex)f(F)-11 b(unctions)3350 3673 y FK([F)j(unction])-3599 b Fv(gsl_complex)56 b(gsl_complex_sqrt)50 b Fu(\()p FD(gsl)p 1807 3673 V 41 w(complex)31 b Ft(z)p Fu(\))390 3783 y FK(This)f(function)g(returns) f(the)h(square)g(ro)s(ot)h(of)g(the)f(complex)h(n)m(um)m(b)s(er)e FD(z)p FK(,)2948 3718 y FI(p)p 3024 3718 47 4 v 65 x FE(z)t FK(.)41 b(The)30 b(branc)m(h)g(cut)390 3893 y(is)d(the)h (negativ)m(e)h(real)f(axis.)40 b(The)27 b(result)g(alw)m(a)m(ys)i(lies) f(in)f(the)h(righ)m(t)g(half)f(of)g(the)h(complex)g(plane.)3350 4090 y([F)-8 b(unction])-3599 b Fv(gsl_complex)56 b (gsl_complex_sqrt_real)51 b Fu(\()p FD(double)31 b Ft(x)p Fu(\))390 4200 y FK(This)d(function)h(returns)f(the)h(complex)g(square) g(ro)s(ot)g(of)h(the)f(real)g(n)m(um)m(b)s(er)f FD(x)p FK(,)h(where)g FD(x)35 b FK(ma)m(y)30 b(b)s(e)390 4309 y(negativ)m(e.)3350 4507 y([F)-8 b(unction])-3599 b Fv(gsl_complex)56 b(gsl_complex_pow)50 b Fu(\()p FD(gsl)p 1755 4507 28 4 v 41 w(complex)31 b Ft(z)p FD(,)f(gsl)p 2365 4507 V 41 w(complex)h Ft(a)p Fu(\))390 4616 y FK(The)f(function)g(returns)f (the)i(complex)g(n)m(um)m(b)s(er)e FD(z)36 b FK(raised)30 b(to)h(the)g(complex)g(p)s(o)m(w)m(er)f FD(a)p FK(,)i FE(z)3467 4583 y Fq(a)3507 4616 y FK(.)41 b(This)390 4726 y(is)30 b(computed)h(as)f(exp\(log)s(\()p FE(z)t FK(\))21 b FI(\003)g FE(a)p FK(\))30 b(using)g(complex)h(logarithms)h (and)d(complex)i(exp)s(onen)m(tials.)3350 4923 y([F)-8 b(unction])-3599 b Fv(gsl_complex)56 b(gsl_complex_pow_real)51 b Fu(\()p FD(gsl)p 2016 4923 V 41 w(complex)31 b Ft(z)p FD(,)g(double)f Ft(x)p Fu(\))390 5033 y FK(This)g(function)g(returns)f (the)h(complex)h(n)m(um)m(b)s(er)e FD(z)36 b FK(raised)31 b(to)g(the)f(real)h(p)s(o)m(w)m(er)g FD(x)p FK(,)f FE(z)3310 5000 y Fq(x)3352 5033 y FK(.)3350 5230 y([F)-8 b(unction])-3599 b Fv(gsl_complex)56 b(gsl_complex_exp)50 b Fu(\()p FD(gsl)p 1755 5230 V 41 w(complex)31 b Ft(z)p Fu(\))390 5340 y FK(This)f(function)g(returns)f(the)h(complex)h(exp)s(onen)m(tial)h(of)e (the)h(complex)g(n)m(um)m(b)s(er)e FD(z)p FK(,)i(exp\()p FE(z)t FK(\).)p eop end %%Page: 24 42 TeXDict begin 24 41 bop 150 -116 a FK(Chapter)30 b(5:)41 b(Complex)30 b(Num)m(b)s(ers)2305 b(24)3350 299 y([F)-8 b(unction])-3599 b Fv(gsl_complex)56 b(gsl_complex_log)50 b Fu(\()p FD(gsl)p 1755 299 28 4 v 41 w(complex)31 b Ft(z)p Fu(\))390 408 y FK(This)c(function)h(returns)f(the)i(complex)g (natural)f(logarithm)h(\(base)g FE(e)p FK(\))g(of)f(the)g(complex)h(n)m (um)m(b)s(er)390 518 y FD(z)p FK(,)i(log)r(\()p FE(z)t FK(\).)42 b(The)30 b(branc)m(h)g(cut)g(is)h(the)f(negativ)m(e)j(real)e (axis.)3350 718 y([F)-8 b(unction])-3599 b Fv(gsl_complex)56 b(gsl_complex_log10)50 b Fu(\()p FD(gsl)p 1859 718 V 41 w(complex)31 b Ft(z)p Fu(\))390 827 y FK(This)49 b(function)h (returns)f(the)i(complex)g(base-10)g(logarithm)h(of)e(the)g(complex)h (n)m(um)m(b)s(er)e FD(z)p FK(,)390 937 y(log)507 959 y FB(10)578 937 y FK(\()p FE(z)t FK(\).)3350 1137 y([F)-8 b(unction])-3599 b Fv(gsl_complex)56 b(gsl_complex_log_b)50 b Fu(\()p FD(gsl)p 1859 1137 V 41 w(complex)31 b Ft(z)p FD(,)g(gsl)p 2470 1137 V 41 w(complex)g Ft(b)p Fu(\))390 1246 y FK(This)24 b(function)g(returns)g(the)h(complex)g(base-)p FD(b)i FK(logarithm)f(of)f(the)g(complex)g(n)m(um)m(b)s(er)f FD(z)p FK(,)i(log)3574 1268 y Fq(b)3608 1246 y FK(\()p FE(z)t FK(\).)390 1356 y(This)k(quan)m(tit)m(y)h(is)g(computed)f(as)g (the)h(ratio)g(log)s(\()p FE(z)t FK(\))p FE(=)15 b FK(log)t(\()p FE(b)p FK(\).)150 1600 y FJ(5.5)68 b(Complex)46 b(T)-11 b(rigonometric)46 b(F)-11 b(unctions)3350 1817 y FK([F)j(unction])-3599 b Fv(gsl_complex)56 b(gsl_complex_sin)50 b Fu(\()p FD(gsl)p 1755 1817 V 41 w(complex)31 b Ft(z)p Fu(\))390 1927 y FK(This)d(function)h(returns)e(the)i(complex)h(sine)f(of)g(the)g (complex)g(n)m(um)m(b)s(er)f FD(z)p FK(,)i(sin)o(\()p FE(z)t FK(\))d(=)e(\(exp\()p FE(iz)t FK(\))18 b FI(\000)390 2036 y FK(exp\()p FI(\000)p FE(iz)t FK(\)\))p FE(=)p FK(\(2)p FE(i)p FK(\).)3350 2236 y([F)-8 b(unction])-3599 b Fv(gsl_complex)56 b(gsl_complex_cos)50 b Fu(\()p FD(gsl)p 1755 2236 V 41 w(complex)31 b Ft(z)p Fu(\))390 2346 y FK(This)21 b(function)g(returns)f(the)h(complex)h(cosine)h(of)e(the)h (complex)g(n)m(um)m(b)s(er)e FD(z)p FK(,)k(cos\()p FE(z)t FK(\))j(=)e(\(exp\()p FE(iz)t FK(\))r(+)390 2455 y(exp\()p FI(\000)p FE(iz)t FK(\)\))p FE(=)p FK(2.)3350 2655 y([F)-8 b(unction])-3599 b Fv(gsl_complex)56 b(gsl_complex_tan)50 b Fu(\()p FD(gsl)p 1755 2655 V 41 w(complex)31 b Ft(z)p Fu(\))390 2765 y FK(This)92 b(function)h(returns)f(the)h(complex)g (tangen)m(t)i(of)e(the)g(complex)h(n)m(um)m(b)s(er)d FD(z)p FK(,)390 2874 y(tan\()p FE(z)t FK(\))27 b(=)e(sin)o(\()p FE(z)t FK(\))p FE(=)15 b FK(cos)r(\()p FE(z)t FK(\).)3350 3074 y([F)-8 b(unction])-3599 b Fv(gsl_complex)56 b(gsl_complex_sec)50 b Fu(\()p FD(gsl)p 1755 3074 V 41 w(complex)31 b Ft(z)p Fu(\))390 3184 y FK(This)23 b(function)g(returns)f(the)i(complex)g (secan)m(t)h(of)f(the)f(complex)h(n)m(um)m(b)s(er)f FD(z)p FK(,)i(sec)q(\()p FE(z)t FK(\))h(=)f(1)p FE(=)15 b FK(cos)r(\()p FE(z)t FK(\).)3350 3383 y([F)-8 b(unction])-3599 b Fv(gsl_complex)56 b(gsl_complex_csc)50 b Fu(\()p FD(gsl)p 1755 3383 V 41 w(complex)31 b Ft(z)p Fu(\))390 3493 y FK(This)48 b(function)g(returns) f(the)i(complex)g(cosecan)m(t)i(of)e(the)g(complex)g(n)m(um)m(b)s(er)e FD(z)p FK(,)54 b(csc)q(\()p FE(z)t FK(\))i(=)390 3603 y(1)p FE(=)15 b FK(sin)q(\()p FE(z)t FK(\).)3350 3802 y([F)-8 b(unction])-3599 b Fv(gsl_complex)56 b(gsl_complex_cot)50 b Fu(\()p FD(gsl)p 1755 3802 V 41 w(complex)31 b Ft(z)p Fu(\))390 3912 y FK(This)43 b(function)h(returns)f(the)h(complex)g (cotangen)m(t)j(of)d(the)g(complex)h(n)m(um)m(b)s(er)d FD(z)p FK(,)48 b(cot)q(\()p FE(z)t FK(\))h(=)390 4022 y(1)p FE(=)15 b FK(tan)q(\()p FE(z)t FK(\).)150 4266 y FJ(5.6)68 b(In)l(v)l(erse)46 b(Complex)g(T)-11 b(rigonometric)45 b(F)-11 b(unctions)3350 4483 y FK([F)j(unction])-3599 b Fv(gsl_complex)56 b(gsl_complex_arcsin)51 b Fu(\()p FD(gsl)p 1912 4483 V 40 w(complex)32 b Ft(z)p Fu(\))390 4592 y FK(This)h(function)h(returns)e(the)i(complex)h(arcsine)f(of)g (the)h(complex)f(n)m(um)m(b)s(er)f FD(z)p FK(,)i(arcsin\()p FE(z)t FK(\).)52 b(The)390 4702 y(branc)m(h)30 b(cuts)g(are)h(on)f(the) h(real)g(axis,)g(less)g(than)f FI(\000)p FK(1)g(and)g(greater)i(than)e (1.)3350 4902 y([F)-8 b(unction])-3599 b Fv(gsl_complex)56 b(gsl_complex_arcsin_real)c Fu(\()p FD(double)30 b Ft(z)p Fu(\))390 5011 y FK(This)41 b(function)h(returns)f(the)h(complex)g (arcsine)h(of)f(the)g(real)g(n)m(um)m(b)s(er)f FD(z)p FK(,)46 b(arcsin\()p FE(z)t FK(\).)76 b(F)-8 b(or)43 b FE(z)390 5121 y FK(b)s(et)m(w)m(een)33 b FI(\000)p FK(1)f(and)g(1,)h(the)f(function)g(returns)f(a)i(real)g(v)-5 b(alue)32 b(in)g(the)h(range)f([)p FI(\000)p FE(\031)s(=)p FK(2)p FE(;)15 b(\031)s(=)p FK(2].)49 b(F)-8 b(or)33 b FE(z)390 5230 y FK(less)e(than)f FI(\000)p FK(1)h(the)g(result)f(has) g(a)h(real)g(part)g(of)g FI(\000)p FE(\031)s(=)p FK(2)g(and)f(a)h(p)s (ositiv)m(e)g(imaginary)g(part.)41 b(F)-8 b(or)32 b FE(z)390 5340 y FK(greater)g(than)e(1)g(the)h(result)f(has)g(a)h(real)g(part)f (of)h FE(\031)s(=)p FK(2)g(and)f(a)h(negativ)m(e)h(imaginary)f(part.)p eop end %%Page: 25 43 TeXDict begin 25 42 bop 150 -116 a FK(Chapter)30 b(5:)41 b(Complex)30 b(Num)m(b)s(ers)2305 b(25)3350 299 y([F)-8 b(unction])-3599 b Fv(gsl_complex)56 b(gsl_complex_arccos)51 b Fu(\()p FD(gsl)p 1912 299 28 4 v 40 w(complex)32 b Ft(z)p Fu(\))390 408 y FK(This)25 b(function)h(returns)f(the)i(complex) g(arccosine)g(of)g(the)f(complex)h(n)m(um)m(b)s(er)e FD(z)p FK(,)j(arccos)q(\()p FE(z)t FK(\).)40 b(The)390 518 y(branc)m(h)30 b(cuts)g(are)h(on)f(the)h(real)g(axis,)g(less)g (than)f FI(\000)p FK(1)g(and)g(greater)i(than)e(1.)3350 694 y([F)-8 b(unction])-3599 b Fv(gsl_complex)56 b (gsl_complex_arccos_real)c Fu(\()p FD(double)30 b Ft(z)p Fu(\))390 804 y FK(This)35 b(function)g(returns)g(the)g(complex)i (arccosine)g(of)f(the)f(real)i(n)m(um)m(b)s(er)d 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b(storing)f(the)f(results)h(in)f(the)390 3196 y(arra)m(y)h FD(res)j FK(of)d(size)g FD(lenres)p FK(.)71 b(The)40 b(output)g(arra)m(y)h(con)m(tains)g(the)g(v)-5 b(alues)41 b(of)f FE(d)3141 3163 y Fq(k)3183 3196 y FE(P)8 b(=dx)3393 3163 y Fq(k)3475 3196 y FK(for)40 b(the)390 3306 y(sp)s(eci\014ed)30 b(v)-5 b(alue)31 b(of)f FD(x)37 b FK(starting)31 b(with)f FE(k)e FK(=)d(0.)150 3527 y FJ(6.2)68 b(Divided)46 b(Di\013erence)g(Represen)l(tation)h(of)e(P)l (olynomials)150 3686 y FK(The)26 b(functions)h(describ)s(ed)e(here)i (manipulate)g(p)s(olynomials)g(stored)g(in)f(Newton's)i (divided-di\013erence)150 3796 y(represen)m(tation.)40 b(The)23 b(use)g(of)h(divided-di\013erences)g(is)f(describ)s(ed)g(in)g (Abramo)m(witz)i(&)f(Stegun)f(sections)150 3906 y(25.1.4)33 b(and)c(25.2.26,)34 b(and)29 b(Burden)h(and)f(F)-8 b(aires,)32 b(c)m(hapter)f(3,)g(and)f(discussed)g(brie\015y)f(b)s(elo)m(w.)150 4034 y(Giv)m(en)37 b(a)g(function)f FE(f)10 b FK(\()p FE(x)p FK(\),)39 b(an)d FE(n)p 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FI(\001)g(\001)g(\001)h FK(\()p FE(x)21 b FI(\000)f FE(x)3042 4486 y Fq(k)q Fp(\000)p FB(1)3168 4472 y FK(\))150 4708 y(where)27 b(the)h(divided)f(di\013erences)g([)p FE(x)1398 4722 y FB(0)1436 4708 y FE(;)15 b(x)1528 4722 y FB(1)1565 4708 y FE(;)g(:::;)g(x)1772 4722 y Fq(k)1815 4708 y FK(])28 b(are)f(de\014ned)g(in)g(section)i(25.1.4)g(of)f(Abramo) m(witz)h(and)150 4817 y(Stegun.)38 b(Additionally)-8 b(,)27 b(it)e(is)f(p)s(ossible)f(to)i(construct)f(an)g(in)m(terp)s (olating)i(p)s(olynomial)e(of)g(degree)h(2)p FE(n)7 b FK(+)g(1)150 4927 y(whic)m(h)34 b(also)g(matc)m(hes)h(the)f(\014rst)f (deriv)-5 b(ativ)m(es)36 b(of)e FE(f)43 b FK(at)34 b(the)g(p)s(oin)m (ts)g FE(x)2560 4941 y FB(0)2597 4927 y FE(;)15 b(x)2689 4941 y FB(1)2727 4927 y FE(;)g(:::;)g(x)2934 4941 y Fq(n)2981 4927 y FK(.)51 b(This)33 b(is)h(called)h(the)150 5036 y(Hermite)c(in)m(terp)s(olating)h(p)s(olynomial)f(and)e(is)i(de\014ned) e(as)645 5267 y FE(H)721 5281 y FB(2)p Fq(n)p FB(+1)883 5267 y FK(\()p FE(x)p FK(\))d(=)f FE(f)10 b FK(\()p FE(z)1259 5281 y FB(0)1296 5267 y FK(\))20 b(+)1442 5161 y FB(2)p Fq(n)p FB(+1)1462 5186 y Fs(X)1461 5365 y Fq(k)q FB(=1)1601 5267 y FK([)p FE(z)1668 5281 y FB(0)1705 5267 y FE(;)15 b(z)1787 5281 y FB(1)1825 5267 y FE(;)g(:::;)g(z)2022 5281 y Fq(k)2065 5267 y FK(]\()p FE(x)21 b FI(\000)f FE(z)2331 5281 y FB(0)2368 5267 y FK(\)\()p FE(x)h FI(\000)f FE(z)2644 5281 y FB(1)2681 5267 y FK(\))15 b FI(\001)g(\001)g(\001)i FK(\()p FE(x)k FI(\000)f FE(z)3094 5281 y Fq(k)q Fp(\000)p FB(1)3220 5267 y FK(\))p eop end %%Page: 29 47 TeXDict begin 29 46 bop 150 -116 a FK(Chapter)30 b(6:)41 b(P)m(olynomials)2564 b(29)150 299 y(where)34 b(the)g(elemen)m(ts)i(of) e FE(z)i FK(=)c FI(f)p FE(x)1338 313 y FB(0)1376 299 y FE(;)15 b(x)1468 313 y FB(0)1505 299 y FE(;)g(x)1597 313 y FB(1)1635 299 y FE(;)g(x)1727 313 y FB(1)1764 299 y FE(;)g(:::;)g(x)1971 313 y Fq(n)2018 299 y FE(;)g(x)2110 313 y Fq(n)2156 299 y FI(g)34 b FK(are)h(de\014ned)e(b)m(y)h FE(z)2880 313 y FB(2)p Fq(k)2986 299 y FK(=)e FE(z)3131 313 y FB(2)p Fq(k)q FB(+1)3321 299 y FK(=)f FE(x)3475 313 y Fq(k)3516 299 y FK(.)52 b(The)150 408 y(divided-di\013erences)30 b([)p FE(z)980 422 y FB(0)1018 408 y FE(;)15 b(z)1100 422 y FB(1)1138 408 y FE(;)g(:::;)g(z)1335 422 y Fq(k)1378 408 y FK(])30 b(are)h(discussed)f(in)g(Burden)f(and)h(F)-8 b(aires,)32 b(section)f(3.4.)3350 596 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_poly_dd_init)e Fu(\()p FD(double)30 b Ft(dd)p Fo([])p FD(,)h(const)g(double)f Ft(xa)p Fo([])p FD(,)h(const)f(double)565 706 y Ft(ya)p Fo([])p FD(,)h(size)p 928 706 28 4 v 41 w(t)g Ft(size)p Fu(\))390 815 y FK(This)e(function)g (computes)g(a)h(divided-di\013erence)g(represen)m(tation)g(of)g(the)f (in)m(terp)s(olating)i(p)s(oly-)390 925 y(nomial)g(for)e(the)h(p)s(oin) m(ts)g(\()p FD(x)p FK(,)h FD(y)8 b FK(\))30 b(stored)g(in)f(the)i(arra) m(ys)f FD(xa)g FK(and)g FD(y)m(a)g FK(of)g(length)h FD(size)p FK(.)41 b(On)29 b(output)390 1034 y(the)e(divided-di\013erences)f(of)g (\()p FD(xa)p FK(,)p FD(y)m(a)p 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Fv(int)53 b(gsl_poly_dd_taylor)e Fu(\()p FD(double)30 b Ft(c)p Fo([])p FD(,)h(double)f Ft(xp)p FD(,)h(const)g(double)f Ft(dd)p Fo([])p FD(,)565 2067 y(const)h(double)f Ft(xa)p Fo([])p FD(,)h(size)p 1459 2067 V 41 w(t)f Ft(size)p FD(,)i(double)e Ft(w)p Fo([])p Fu(\))390 2176 y FK(This)25 b(function)g(con)m(v)m(erts)i(the)e (divided-di\013erence)h(represen)m(tation)g(of)g(a)g(p)s(olynomial)g (to)g(a)g(T)-8 b(a)m(y-)390 2286 y(lor)30 b(expansion.)40 b(The)29 b(divided-di\013erence)g(represen)m(tation)h(is)g(supplied)e (in)h(the)g(arra)m(ys)h FD(dd)i FK(and)390 2396 y FD(xa)25 b FK(of)g(length)g FD(size)p FK(.)40 b(On)23 b(output)i(the)f(T)-8 b(a)m(ylor)26 b(co)s(e\016cien)m(ts)h(of)e(the)f(p)s(olynomial)h (expanded)f(ab)s(out)390 2505 y(the)31 b(p)s(oin)m(t)f FD(xp)i FK(are)f(stored)g(in)f(the)g(arra)m(y)h FD(c)36 b FK(also)31 b(of)g(length)g FD(size)p FK(.)41 b(A)31 b(w)m(orkspace)g(of)f(length)h FD(size)390 2615 y FK(m)m(ust)f(b)s(e)g (pro)m(vided)g(in)g(the)h(arra)m(y)f FD(w)p FK(.)3350 2802 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_poly_dd_hermite_i)q (nit)f Fu(\()p FD(double)30 b Ft(dd)p Fo([])p FD(,)h(double)f Ft(za)p Fo([])p FD(,)h(const)565 2912 y(double)f Ft(xa)p Fo([])p FD(,)h(const)g(double)f Ft(ya)p Fo([])p FD(,)h(const)g(double)f Ft(dya)p Fo([])p FD(,)h(const)g(size)p 3005 2912 V 41 w(t)f Ft(size)p Fu(\))390 3021 y FK(This)i(function)g(computes)g(a)h (divided-di\013erence)g(represen)m(tation)g(of)g(the)g(in)m(terp)s (olating)h(Her-)390 3131 y(mite)i(p)s(olynomial)f(for)g(the)g(p)s(oin)m (ts)f(\()p FD(x)p FK(,)j FD(y)8 b FK(\))35 b(stored)g(in)g(the)g(arra)m (ys)g FD(xa)g FK(and)g FD(y)m(a)g FK(of)h(length)f FD(size)p FK(.)390 3241 y(Hermite)23 b(in)m(terp)s(olation)h(constructs)f(p)s (olynomials)g(whic)m(h)f(also)h(matc)m(h)h(\014rst)d(deriv)-5 b(ativ)m(es)24 b FE(dy)s(=dx)390 3350 y FK(whic)m(h)33 b(are)g(pro)m(vided)g(in)f(the)h(arra)m(y)h FD(dy)m(a)f FK(also)h(of)f(length)g FD(size)p FK(.)49 b(The)33 b(\014rst)f(deriv)-5 b(ativ)m(es)34 b(can)g(b)s(e)390 3460 y(incorp)s(orted)44 b(in)m(to)h(the)f(usual)g(divided-di\013erence)g(algorithm)h(b)m(y)f (forming)g(a)h(new)f(dataset)390 3569 y FE(z)30 b FK(=)24 b FI(f)p FE(x)654 3583 y FB(0)692 3569 y FE(;)15 b(x)784 3583 y FB(0)822 3569 y FE(;)g(x)914 3583 y FB(1)951 3569 y FE(;)g(x)1043 3583 y FB(1)1081 3569 y FE(;)g(:::)p FI(g)p FK(,)31 b(whic)m(h)d(is)h(stored)g(in)f(the)h(arra)m(y)g FD(za)h FK(of)f(length)g(2*)p FD(size)35 b FK(on)29 b(output.)40 b(On)390 3679 y(output)34 b(the)g(divided-di\013erences)g(of)g(the)h (Hermite)g(represen)m(tation)g(are)f(stored)g(in)g(the)g(arra)m(y)390 3789 y FD(dd)p FK(,)27 b(also)h(of)g(length)f(2*)p FD(size)p FK(.)42 b(Using)27 b(the)g(notation)i(ab)s(o)m(v)m(e,)g FE(dd)p FK([)p FE(k)s FK(])e(=)e([)p FE(z)2826 3803 y FB(0)2864 3789 y FE(;)15 b(z)2946 3803 y FB(1)2983 3789 y FE(;)g(:::;)g(z)3180 3803 y Fq(k)3223 3789 y FK(].)40 b(The)27 b(result-)390 3898 y(ing)i(Hermite)g(p)s(olynomial)h(can)f(b)s (e)f(ev)-5 b(aluated)30 b(b)m(y)e(calling)i FH(gsl_poly_dd_eval)25 b FK(and)j(using)g FD(za)390 4008 y FK(for)i(the)h(input)e(argumen)m(t) i FD(xa)p FK(.)150 4243 y FJ(6.3)68 b(Quadratic)46 b(Equations)3350 4453 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_poly_solve_quadra)q (tic)f Fu(\()p FD(double)30 b Ft(a)p FD(,)h(double)f Ft(b)p FD(,)h(double)f Ft(c)p FD(,)h(double)565 4563 y(*)g Ft(x0)p FD(,)g(double)f(*)h Ft(x1)p Fu(\))390 4673 y FK(This)f(function)g(\014nds)e(the)j(real)g(ro)s(ots)f(of)h(the)g (quadratic)f(equation,)1622 4842 y FE(ax)1722 4804 y FB(2)1779 4842 y FK(+)20 b FE(bx)g FK(+)g FE(c)26 b FK(=)f(0)390 5011 y(The)i(n)m(um)m(b)s(er)e(of)j(real)f(ro)s(ots)h(\(either)f(zero,) i(one)f(or)f(t)m(w)m(o\))h(is)g(returned,)e(and)h(their)g(lo)s(cations) i(are)390 5121 y(stored)k(in)g FD(x0)40 b FK(and)32 b FD(x1)p FK(.)49 b(If)33 b(no)f(real)i(ro)s(ots)f(are)g(found)f(then)g FD(x0)41 b FK(and)32 b FD(x1)41 b FK(are)33 b(not)g(mo)s(di\014ed.)47 b(If)390 5230 y(one)32 b(real)g(ro)s(ot)f(is)h(found)e(\(i.e.)45 b(if)31 b FE(a)c FK(=)g(0\))32 b(then)f(it)h(is)f(stored)h(in)f FD(x0)p FK(.)44 b(When)31 b(t)m(w)m(o)i(real)f(ro)s(ots)g(are)390 5340 y(found)e(they)i(are)g(stored)g(in)f FD(x0)39 b FK(and)32 b FD(x1)39 b FK(in)31 b(ascending)h(order.)44 b(The)31 b(case)i(of)f(coinciden)m(t)h(ro)s(ots)p eop end %%Page: 30 48 TeXDict begin 30 47 bop 150 -116 a FK(Chapter)30 b(6:)41 b(P)m(olynomials)2564 b(30)390 299 y(is)26 b(not)h(considered)f(sp)s (ecial.)40 b(F)-8 b(or)27 b(example)g(\()p FE(x)12 b FI(\000)g FK(1\))2179 266 y FB(2)2243 299 y FK(=)24 b(0)j(will)g(ha)m (v)m(e)g(t)m(w)m(o)h(ro)s(ots,)g(whic)m(h)e(happ)s(en)390 408 y(to)31 b(ha)m(v)m(e)h(exactly)g(equal)f(v)-5 b(alues.)390 541 y(The)25 b(n)m(um)m(b)s(er)f(of)h(ro)s(ots)h(found)e(dep)s(ends)f (on)j(the)f(sign)g(of)h(the)g(discriminan)m(t)f FE(b)3081 508 y FB(2)3128 541 y FI(\000)10 b FK(4)p FE(ac)p FK(.)40 b(This)25 b(will)390 650 y(b)s(e)20 b(sub)5 b(ject)20 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FK(+)20 b FE(bz)25 b FK(+)20 b FE(c)25 b FK(=)g(0)390 1707 y(The)j(n)m(um)m(b)s(er)f(of)h(complex)h (ro)s(ots)f(is)h(returned)e(\(either)i(one)f(or)h(t)m(w)m(o\))h(and)d (the)i(lo)s(cations)g(of)g(the)390 1817 y(ro)s(ots)h(are)g(stored)g(in) g FD(z0)38 b FK(and)29 b FD(z1)p FK(.)42 b(The)29 b(ro)s(ots)h(are)g (returned)f(in)h(ascending)g(order,)g(sorted)g(\014rst)390 1926 y(b)m(y)j(their)h(real)g(comp)s(onen)m(ts)f(and)g(then)g(b)m(y)g (their)h(imaginary)g(comp)s(onen)m(ts.)49 b(If)33 b(only)h(one)f(real) 390 2036 y(ro)s(ot)e(is)f(found)f(\(i.e.)42 b(if)30 b FE(a)c FK(=)f(0\))31 b(then)f(it)h(is)f(stored)h(in)f FD(z0)p FK(.)150 2264 y FJ(6.4)68 b(Cubic)45 b(Equations)3350 2469 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_poly_solve_cubic)f Fu(\()p FD(double)30 b Ft(a)p FD(,)h(double)f Ft(b)p FD(,)h(double)f Ft(c)p FD(,)g(double)g(*)h Ft(x0)p FD(,)565 2578 y(double)f(*)h Ft(x1)p FD(,)g(double)f(*)h Ft(x2)p Fu(\))390 2688 y FK(This)f(function)g(\014nds)e(the)j(real)g(ro)s(ots)f 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b(6:)41 b(P)m(olynomials)2564 b(31)3350 299 y([F)-8 b(unction])-3599 b Fv(gsl_poly_complex_works)q(pac)q(e)58 b(*)565 408 y(gsl_poly_complex_works)q(pac)q(e_a)q(llo)q(c)51 b Fu(\()p FD(size)p 2466 408 28 4 v 42 w(t)30 b Ft(n)p Fu(\))390 518 y FK(This)53 b(function)g(allo)s(cates)j(space)f(for)e(a)h FH(gsl_poly_complex_workspac)o(e)48 b FK(struct)53 b(and)h(a)390 628 y(w)m(orkspace)47 b(suitable)f(for)f(solving)i(a)f(p)s(olynomial)g (with)g FD(n)f FK(co)s(e\016cien)m(ts)j(using)d(the)h(routine)390 737 y FH(gsl_poly_complex_solve)p FK(.)390 875 y(The)25 b(function)h(returns)e(a)i(p)s(oin)m(ter)g(to)h(the)f(newly)f(allo)s (cated)j FH(gsl_poly_complex_workspac)o(e)390 985 y FK(if)i(no)h (errors)e(w)m(ere)i(detected,)h(and)e(a)h(n)m(ull)f(p)s(oin)m(ter)g(in) g(the)h(case)g(of)g(error.)3350 1176 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_poly_complex_workspa)q(ce_)q(fre)q(e)565 1285 y Fu(\()p FD(gsl)p 712 1285 V 41 w(p)s(oly)p 925 1285 V 40 w(complex)p 1290 1285 V 41 w(w)m(orkspace)31 b(*)f 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FK(\),)g(and)f(is)g(1)h(for)f FE(x)25 b(<)g FK(0.)150 4913 y Fy(7.4.3)63 b(Zeros)41 b(of)h(Airy)f(F)-10 b(unctions)3350 5121 y FK([F)i(unction])-3599 b Fv(double)54 b(gsl_sf_airy_zero_Ai)d Fu(\()p FD(unsigned)30 b(in)m(t)h Ft(s)p Fu(\))3350 5230 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_airy_zero_Ai_e)f Fu(\()p FD(unsigned)30 b(in)m(t)h Ft(s)p FD(,)f(gsl)p 2276 5230 V 41 w(sf)p 2381 5230 V 40 w(result)g(*)h Ft(result)p Fu(\))390 5340 y FK(These)f(routines)g(compute)h(the)g(lo)s(cation)h(of)e(the)h FD(s)p FK(-th)f(zero)h(of)g(the)f(Airy)h(function)f FE(Ai)p FK(\()p FE(x)p FK(\).)p eop end %%Page: 36 54 TeXDict begin 36 53 bop 150 -116 a FK(Chapter)30 b(7:)41 b(Sp)s(ecial)31 b(F)-8 b(unctions)2348 b(36)3350 299 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_airy_zero_Bi)d Fu(\()p FD(unsigned)30 b(in)m(t)h Ft(s)p Fu(\))3350 408 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_airy_zero_Bi_e)f Fu(\()p FD(unsigned)30 b(in)m(t)h Ft(s)p FD(,)f(gsl)p 2276 408 28 4 v 41 w(sf)p 2381 408 V 40 w(result)g(*)h Ft(result)p Fu(\))390 518 y FK(These)f(routines)g(compute)h(the)g(lo)s (cation)h(of)e(the)h FD(s)p FK(-th)f(zero)h(of)g(the)f(Airy)h(function) f FE(B)5 b(i)p FK(\()p FE(x)p FK(\).)150 744 y Fy(7.4.4)63 b(Zeros)41 b(of)h(Deriv)-7 b(ativ)m(es)41 b(of)g(Airy)g(F)-10 b(unctions)3350 968 y FK([F)i(unction])-3599 b Fv(double)54 b(gsl_sf_airy_zero_Ai_de)q(riv)e Fu(\()p FD(unsigned)30 b(in)m(t)h Ft(s)p Fu(\))3350 1077 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_airy_zero_Ai_d)q(eriv)q(_e)f Fu(\()p FD(unsigned)30 b(in)m(t)g Ft(s)p FD(,)h(gsl)p 2590 1077 V 41 w(sf)p 2695 1077 V 39 w(result)g(*)565 1187 y Ft(result)p Fu(\))390 1297 y FK(These)i(routines)f(compute)h(the)g(lo)s(cation)i (of)e(the)g FD(s)p FK(-th)g(zero)g(of)g(the)g(Airy)g(function)f(deriv) -5 b(ativ)m(e)390 1406 y FE(Ai)489 1373 y Fp(0)513 1406 y FK(\()p FE(x)p FK(\).)3350 1644 y([F)d(unction])-3599 b Fv(double)54 b(gsl_sf_airy_zero_Bi_de)q(riv)e Fu(\()p FD(unsigned)30 b(in)m(t)h Ft(s)p Fu(\))3350 1754 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_airy_zero_Bi_d)q(eriv)q(_e)f Fu(\()p FD(unsigned)30 b(in)m(t)g Ft(s)p FD(,)h(gsl)p 2590 1754 V 41 w(sf)p 2695 1754 V 39 w(result)g(*)565 1863 y Ft(result)p Fu(\))390 1973 y FK(These)i(routines)f(compute)h (the)g(lo)s(cation)i(of)e(the)g FD(s)p FK(-th)g(zero)g(of)g(the)g(Airy) g(function)f(deriv)-5 b(ativ)m(e)390 2083 y FE(B)5 b(i)495 2050 y Fp(0)518 2083 y FK(\()p FE(x)p FK(\).)150 2355 y FJ(7.5)68 b(Bessel)46 b(F)-11 b(unctions)150 2515 y FK(The)21 b(routines)h(describ)s(ed)e(in)i(this)f(section)i(compute)f (the)g(Cylindrical)g(Bessel)h(functions)e FE(J)3287 2529 y Fq(n)3333 2515 y FK(\()p FE(x)p FK(\),)j FE(Y)3557 2529 y Fq(n)3602 2515 y FK(\()p FE(x)p FK(\),)150 2624 y(Mo)s(di\014ed)33 b(cylindrical)h(Bessel)h(functions)e FE(I)1688 2638 y Fq(n)1733 2624 y FK(\()p FE(x)p FK(\),)i FE(K)1992 2638 y Fq(n)2037 2624 y FK(\()p FE(x)p FK(\),)g(Spherical)f (Bessel)g(functions)f FE(j)3324 2638 y Fq(l)3350 2624 y FK(\()p FE(x)p FK(\),)i FE(y)3577 2638 y Fq(l)3602 2624 y FK(\()p FE(x)p FK(\),)150 2734 y(and)27 b(Mo)s(di\014ed)g (Spherical)h(Bessel)h(functions)e FE(i)1782 2748 y Fq(l)1808 2734 y FK(\()p FE(x)p FK(\),)i FE(k)2031 2748 y Fq(l)2057 2734 y FK(\()p FE(x)p FK(\).)41 b(F)-8 b(or)28 b(more)g(information)g (see)h(Abramo)m(witz)150 2843 y(&)i(Stegun,)h(Chapters)f(9)g(and)g(10.) 45 b(The)31 b(Bessel)i(functions)e(are)h(de\014ned)e(in)h(the)h(header) f(\014le)h FH(gsl_sf_)150 2953 y(bessel.h)p FK(.)150 3179 y Fy(7.5.1)63 b(Regular)40 b(Cylindrical)h(Bessel)h(F)-10 b(unctions)3350 3403 y FK([F)i(unction])-3599 b Fv(double)54 b(gsl_sf_bessel_J0)c Fu(\()p FD(double)31 b Ft(x)p Fu(\))3350 3512 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_J0_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1894 3512 V 41 w(sf)p 1999 3512 V 39 w(result)g(*)g Ft(result)p Fu(\))390 3622 y FK(These)c(routines)f(compute)i(the)f(regular)g (cylindrical)h(Bessel)g(function)e(of)h(zeroth)h(order,)f FE(J)3564 3636 y FB(0)3602 3622 y FK(\()p FE(x)p FK(\).)3350 3860 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_bessel_J1)c Fu(\()p FD(double)31 b Ft(x)p Fu(\))3350 3970 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_J1_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1894 3970 V 41 w(sf)p 1999 3970 V 39 w(result)g(*)g Ft(result)p Fu(\))390 4079 y FK(These)f(routines)g(compute)h(the)g(regular)f(cylindrical)h(Bessel) h(function)e(of)g(\014rst)g(order,)g FE(J)3511 4093 y FB(1)3549 4079 y FK(\()p FE(x)p FK(\).)3350 4317 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_bessel_Jn)c Fu(\()p FD(in)m(t)32 b Ft(n)p FD(,)f(double)e Ft(x)p Fu(\))3350 4427 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_Jn_e)e Fu(\()p FD(in)m(t)31 b Ft(n)p FD(,)g(double)f Ft(x)p FD(,)h(gsl)p 2141 4427 V 41 w(sf)p 2246 4427 V 39 w(result)g(*)f Ft(result)p Fu(\))390 4536 y FK(These)g(routines)g(compute)h(the)g(regular)f(cylindrical)h(Bessel) h(function)e(of)g(order)g FD(n)p FK(,)g FE(J)3404 4550 y Fq(n)3450 4536 y FK(\()p FE(x)p FK(\).)3350 4774 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_Jn_arra)q(y)e Fu(\()p FD(in)m(t)32 b Ft(nmin)p FD(,)f(in)m(t)g Ft(nmax)p FD(,)h(double)e Ft(x)p FD(,)h(double)565 4884 y Ft(result_array)p Fo([])p Fu(\))390 4994 y FK(This)c(routine)i(computes)f(the)h(v)-5 b(alues)28 b(of)h(the)f(regular)h(cylindrical)g(Bessel)g(functions)f FE(J)3445 5008 y Fq(n)3490 4994 y FK(\()p FE(x)p FK(\))h(for)390 5103 y FE(n)38 b FK(from)g FD(nmin)f FK(to)j FD(nmax)k FK(inclusiv)m(e,)d(storing)e(the)g(results)f(in)g(the)h(arra)m(y)g FD(result)p 3262 5103 V 40 w(arra)m(y)p FK(.)65 b(The)390 5213 y(v)-5 b(alues)27 b(are)g(computed)g(using)g(recurrence)f (relations)i(for)f(e\016ciency)-8 b(,)29 b(and)d(therefore)i(ma)m(y)f (di\013er)390 5322 y(sligh)m(tly)32 b(from)e(the)g(exact)i(v)-5 b(alues.)p eop end %%Page: 37 55 TeXDict begin 37 54 bop 150 -116 a FK(Chapter)30 b(7:)41 b(Sp)s(ecial)31 b(F)-8 b(unctions)2348 b(37)150 299 y Fy(7.5.2)63 b(Irregular)41 b(Cylindrical)f(Bessel)i(F)-10 b(unctions)3350 507 y FK([F)i(unction])-3599 b Fv(double)54 b(gsl_sf_bessel_Y0)c Fu(\()p FD(double)31 b Ft(x)p Fu(\))3350 616 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_Y0_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1894 616 28 4 v 41 w(sf)p 1999 616 V 39 w(result)g(*)g Ft(result)p Fu(\))390 726 y FK(These)21 b(routines)g(compute)g(the)g(irregular)h (cylindrical)f(Bessel)i(function)d(of)i(zeroth)f(order,)i FE(Y)3565 740 y FB(0)3602 726 y FK(\()p FE(x)p FK(\),)390 835 y(for)30 b FE(x)25 b(>)g FK(0.)3350 1042 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_bessel_Y1)c Fu(\()p FD(double)31 b Ft(x)p Fu(\))3350 1151 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_Y1_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1894 1151 V 41 w(sf)p 1999 1151 V 39 w(result)g(*)g Ft(result)p Fu(\))390 1261 y FK(These)e(routines)h(compute)f(the)h(irregular)f(cylindrical)i (Bessel)f(function)f(of)h(\014rst)f(order,)g FE(Y)3565 1275 y FB(1)3602 1261 y FK(\()p FE(x)p FK(\),)390 1370 y(for)h FE(x)25 b(>)g FK(0.)3350 1577 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_bessel_Yn)c Fu(\()p FD(in)m(t)32 b Ft(n)p FD(,)f(double)e Ft(x)p Fu(\))3350 1686 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_Yn_e)e Fu(\()p FD(in)m(t)31 b Ft(n)p FD(,)g(double)f Ft(x)p FD(,)h(gsl)p 2141 1686 V 41 w(sf)p 2246 1686 V 39 w(result)g(*)f Ft(result)p Fu(\))390 1796 y FK(These)c(routines)g(compute)g(the)g(irregular)g (cylindrical)h(Bessel)g(function)f(of)g(order)g FD(n)p FK(,)g FE(Y)3421 1810 y Fq(n)3466 1796 y FK(\()p FE(x)p FK(\),)i(for)390 1905 y FE(x)d(>)g FK(0.)3350 2112 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_Yn_arra)q(y)e Fu(\()p FD(in)m(t)32 b Ft(nmin)p FD(,)f(in)m(t)g Ft(nmax)p FD(,)h(double)e Ft(x)p FD(,)h(double)565 2221 y Ft(result_array)p Fo([])p Fu(\))390 2331 y FK(This)j(routine)h(computes)g(the)g(v)-5 b(alues)36 b(of)f(the)g(irregular)g(cylindrical)h(Bessel)g(functions)e FE(Y)3582 2345 y Fq(n)3627 2331 y FK(\()p FE(x)p FK(\))390 2440 y(for)29 b FE(n)g FK(from)f FD(nmin)g FK(to)i FD(nmax)35 b FK(inclusiv)m(e,)c(storing)e(the)h(results)f(in)g(the)g(arra)m(y)h FD(result)p 3287 2440 V 40 w(arra)m(y)p FK(.)40 b(The)390 2550 y(domain)30 b(of)h(the)f(function)g(is)g FE(x)c(>)f FK(0.)41 b(The)30 b(v)-5 b(alues)30 b(are)h(computed)f(using)g (recurrence)g(relations)390 2660 y(for)g(e\016ciency)-8 b(,)32 b(and)e(therefore)h(ma)m(y)g(di\013er)f(sligh)m(tly)i(from)d (the)i(exact)h(v)-5 b(alues.)150 2870 y Fy(7.5.3)63 b(Regular)40 b(Mo)s(di\014ed)j(Cylindrical)e(Bessel)h(F)-10 b(unctions)3350 3077 y FK([F)i(unction])-3599 b Fv(double)54 b(gsl_sf_bessel_I0)c Fu(\()p FD(double)31 b Ft(x)p Fu(\))3350 3187 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_I0_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1894 3187 V 41 w(sf)p 1999 3187 V 39 w(result)g(*)g Ft(result)p Fu(\))390 3297 y FK(These)42 b(routines)g(compute)h(the)g(regular)g(mo)s(di\014ed)e (cylindrical)i(Bessel)h(function)e(of)g(zeroth)390 3406 y(order,)30 b FE(I)693 3420 y FB(0)730 3406 y FK(\()p FE(x)p FK(\).)3350 3612 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_bessel_I1)c Fu(\()p FD(double)31 b Ft(x)p Fu(\))3350 3722 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_I1_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1894 3722 V 41 w(sf)p 1999 3722 V 39 w(result)g(*)g Ft(result)p Fu(\))390 3832 y FK(These)25 b(routines)h(compute)g(the)g(regular)g(mo) s(di\014ed)e(cylindrical)i(Bessel)h(function)e(of)h(\014rst)f(order,) 390 3941 y FE(I)430 3955 y FB(1)467 3941 y FK(\()p FE(x)p FK(\).)3350 4147 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_bessel_In)c Fu(\()p FD(in)m(t)32 b Ft(n)p FD(,)f(double)e Ft(x)p Fu(\))3350 4257 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_In_e)e Fu(\()p FD(in)m(t)31 b Ft(n)p FD(,)g(double)f Ft(x)p FD(,)h(gsl)p 2141 4257 V 41 w(sf)p 2246 4257 V 39 w(result)g(*)f Ft(result)p Fu(\))390 4367 y FK(These)35 b(routines)g(compute)h(the)g(regular)f(mo) s(di\014ed)f(cylindrical)i(Bessel)h(function)e(of)g(order)g FD(n)p FK(,)390 4476 y FE(I)430 4490 y Fq(n)475 4476 y FK(\()p FE(x)p FK(\).)3350 4682 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_In_arra)q(y)e Fu(\()p FD(in)m(t)32 b Ft(nmin)p FD(,)f(in)m(t)g Ft(nmax)p FD(,)h(double)e Ft(x)p FD(,)h(double)565 4792 y Ft(result_array)p Fo([])p Fu(\))390 4902 y FK(This)e(routine)g(computes)h(the)g(v)-5 b(alues)30 b(of)f(the)h(regular)g(mo)s(di\014ed)e(cylindrical)j(Bessel) f(functions)390 5011 y FE(I)430 5025 y Fq(n)475 5011 y FK(\()p FE(x)p FK(\))d(for)f FE(n)g FK(from)g FD(nmin)f FK(to)i FD(nmax)32 b FK(inclusiv)m(e,)c(storing)f(the)f(results)g(in)g (the)g(arra)m(y)h FD(result)p 3483 5011 V 40 w(arra)m(y)p FK(.)390 5121 y(The)g(start)g(of)h(the)f(range)h FD(nmin)e FK(m)m(ust)h(b)s(e)g(p)s(ositiv)m(e)h(or)f(zero.)41 b(The)26 b(v)-5 b(alues)28 b(are)f(computed)g(using)390 5230 y(recurrence)40 b(relations)h(for)g(e\016ciency)-8 b(,)44 b(and)c(therefore)h(ma)m(y)f (di\013er)g(sligh)m(tly)i(from)e(the)g(exact)390 5340 y(v)-5 b(alues.)p eop end %%Page: 38 56 TeXDict begin 38 55 bop 150 -116 a FK(Chapter)30 b(7:)41 b(Sp)s(ecial)31 b(F)-8 b(unctions)2348 b(38)3350 299 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_bessel_I0_scale)q(d)e Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 408 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_I0_scal)q(ed_e)f Fu(\()p FD(double)31 b Ft(x)p FD(,)f(gsl)p 2260 408 28 4 v 41 w(sf)p 2365 408 V 40 w(result)g(*)h Ft(result)p Fu(\))390 518 y FK(These)43 b(routines)g(compute)h(the)g(scaled)g (regular)g(mo)s(di\014ed)e(cylindrical)i(Bessel)h(function)e(of)390 628 y(zeroth)31 b(order)f(exp\()p FI(\000j)p FE(x)p FI(j)p FK(\))p FE(I)1328 642 y FB(0)1366 628 y FK(\()p FE(x)p FK(\).)3350 832 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_bessel_I1_scale)q(d)e Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 942 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_I1_scal)q(ed_e)f Fu(\()p FD(double)31 b Ft(x)p FD(,)f(gsl)p 2260 942 V 41 w(sf)p 2365 942 V 40 w(result)g(*)h Ft(result)p Fu(\))390 1051 y FK(These)25 b(routines)g(compute)g(the)h(scaled)g(regular)f(mo)s(di\014ed)f (cylindrical)i(Bessel)g(function)f(of)h(\014rst)390 1161 y(order)k(exp\()p FI(\000j)p FE(x)p FI(j)p FK(\))p FE(I)1050 1175 y FB(1)1088 1161 y FK(\()p FE(x)p FK(\).)3350 1366 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_bessel_In_scale)q(d)e Fu(\()p FD(in)m(t)31 b Ft(n)p FD(,)g(double)f Ft(x)p Fu(\))3350 1475 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_In_scal)q(ed_e)f Fu(\()p FD(in)m(t)31 b Ft(n)p FD(,)g(double)f Ft(x)p FD(,)h(gsl)p 2507 1475 V 41 w(sf)p 2612 1475 V 39 w(result)g(*)565 1585 y Ft(result)p Fu(\))390 1694 y FK(These)43 b(routines)g(compute)h(the)g(scaled)g (regular)g(mo)s(di\014ed)e(cylindrical)i(Bessel)h(function)e(of)390 1804 y(order)30 b FD(n)p FK(,)g(exp\()p FI(\000j)p FE(x)p FI(j)p FK(\))p FE(I)1156 1818 y Fq(n)1202 1804 y FK(\()p FE(x)p FK(\))3350 2009 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_In_scal)q(ed_a)q(rra)q(y)e Fu(\()p FD(in)m(t)32 b Ft(nmin)p FD(,)f(in)m(t)g Ft(nmax)p FD(,)h(double)e Ft(x)p FD(,)565 2118 y(double)g Ft(result_array)p Fo([])p Fu(\))390 2228 y FK(This)38 b(routine)h(computes)g(the)g(v)-5 b(alues)40 b(of)f(the)g(scaled)g(regular)h(cylindrical)f(Bessel)h (functions)390 2337 y(exp\()p FI(\000j)p FE(x)p FI(j)p FK(\))p FE(I)812 2351 y Fq(n)858 2337 y FK(\()p FE(x)p FK(\))d(for)g FE(n)f FK(from)h FD(nmin)f FK(to)h FD(nmax)43 b FK(inclusiv)m(e,)d(storing)d(the)g(results)g(in)f(the)h(arra)m(y)390 2447 y FD(result)p 619 2447 V 40 w(arra)m(y)p FK(.)54 b(The)34 b(start)h(of)g(the)f(range)h FD(nmin)f FK(m)m(ust)g(b)s(e)g(p) s(ositiv)m(e)i(or)e(zero.)55 b(The)34 b(v)-5 b(alues)35 b(are)390 2556 y(computed)i(using)f(recurrence)h(relations)g(for)g (e\016ciency)-8 b(,)40 b(and)c(therefore)i(ma)m(y)f(di\013er)g(sligh)m (tly)390 2666 y(from)30 b(the)g(exact)i(v)-5 b(alues.)150 2875 y Fy(7.5.4)63 b(Irregular)41 b(Mo)s(di\014ed)i(Cylindrical)d (Bessel)i(F)-10 b(unctions)3350 3082 y FK([F)i(unction])-3599 b Fv(double)54 b(gsl_sf_bessel_K0)c Fu(\()p FD(double)31 b Ft(x)p Fu(\))3350 3192 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_K0_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1894 3192 V 41 w(sf)p 1999 3192 V 39 w(result)g(*)g Ft(result)p Fu(\))390 3302 y FK(These)36 b(routines)g(compute)h(the)g(irregular)f(mo)s(di\014ed)f(cylindrical)i (Bessel)h(function)e(of)g(zeroth)390 3411 y(order,)30 b FE(K)730 3425 y FB(0)768 3411 y FK(\()p FE(x)p FK(\),)h(for)f FE(x)25 b(>)g FK(0.)3350 3616 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_bessel_K1)c Fu(\()p FD(double)31 b Ft(x)p Fu(\))3350 3725 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_K1_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1894 3725 V 41 w(sf)p 1999 3725 V 39 w(result)g(*)g Ft(result)p Fu(\))390 3835 y FK(These)45 b(routines)g(compute)h(the)g(irregular)f(mo)s(di\014ed)f(cylindrical)j (Bessel)f(function)f(of)h(\014rst)390 3944 y(order,)30 b FE(K)730 3958 y FB(1)768 3944 y FK(\()p FE(x)p FK(\),)h(for)f FE(x)25 b(>)g FK(0.)3350 4149 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_bessel_Kn)c Fu(\()p FD(in)m(t)32 b Ft(n)p FD(,)f(double)e Ft(x)p Fu(\))3350 4259 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_Kn_e)e Fu(\()p FD(in)m(t)31 b Ft(n)p FD(,)g(double)f Ft(x)p FD(,)h(gsl)p 2141 4259 V 41 w(sf)p 2246 4259 V 39 w(result)g(*)f Ft(result)p Fu(\))390 4368 y FK(These)g(routines)f(compute)h(the)g(irregular)g(mo)s (di\014ed)f(cylindrical)i(Bessel)f(function)g(of)g(order)f FD(n)p FK(,)390 4478 y FE(K)467 4492 y Fq(n)512 4478 y FK(\()p FE(x)p FK(\),)j(for)e FE(x)25 b(>)g FK(0.)3350 4682 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_Kn_arra)q(y)e Fu(\()p FD(in)m(t)32 b Ft(nmin)p FD(,)f(in)m(t)g Ft(nmax)p FD(,)h(double)e Ft(x)p FD(,)h(double)565 4792 y Ft(result_array)p Fo([])p Fu(\))390 4902 y FK(This)23 b(routine)h(computes)g(the)h(v)-5 b(alues)24 b(of)g(the)g(irregular)h(mo)s(di\014ed)d(cylindrical)j (Bessel)g(functions)390 5011 y FE(K)467 5025 y Fq(n)512 5011 y FK(\()p FE(x)p FK(\))g(for)e FE(n)g FK(from)g FD(nmin)f FK(to)j FD(nmax)k FK(inclusiv)m(e,)d(storing)e(the)g(results) f(in)g(the)h(arra)m(y)g FD(result)p 3483 5011 V 40 w(arra)m(y)p FK(.)390 5121 y(The)30 b(start)h(of)g(the)g(range)g FD(nmin)e FK(m)m(ust)i(b)s(e)e(p)s(ositiv)m(e)j(or)f(zero.)42 b(The)30 b(domain)g(of)h(the)g(function)f(is)390 5230 y FE(x)25 b(>)g FK(0.)39 b(The)22 b(v)-5 b(alues)23 b(are)g(computed)g(using)f (recurrence)h(relations)h(for)e(e\016ciency)-8 b(,)26 b(and)c(therefore)390 5340 y(ma)m(y)31 b(di\013er)f(sligh)m(tly)i(from) e(the)g(exact)i(v)-5 b(alues.)p eop end %%Page: 39 57 TeXDict begin 39 56 bop 150 -116 a FK(Chapter)30 b(7:)41 b(Sp)s(ecial)31 b(F)-8 b(unctions)2348 b(39)3350 299 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_bessel_K0_scale)q(d)e Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 408 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_K0_scal)q(ed_e)f Fu(\()p FD(double)31 b Ft(x)p FD(,)f(gsl)p 2260 408 28 4 v 41 w(sf)p 2365 408 V 40 w(result)g(*)h Ft(result)p Fu(\))390 518 y FK(These)37 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Fv(int)53 b(gsl_sf_bessel_Kn_scal)q(ed_e)f Fu(\()p FD(in)m(t)31 b Ft(n)p FD(,)g(double)f Ft(x)p FD(,)h(gsl)p 2507 1424 V 41 w(sf)p 2612 1424 V 39 w(result)g(*)565 1534 y Ft(result)p Fu(\))390 1644 y FK(These)37 b(routines)g(compute)h (the)f(scaled)i(irregular)e(mo)s(di\014ed)f(cylindrical)i(Bessel)h (function)e(of)390 1753 y(order)30 b FD(n)p FK(,)g(exp\()p FE(x)p FK(\))p FE(K)1072 1767 y Fq(n)1118 1753 y FK(\()p FE(x)p FK(\),)h(for)f FE(x)25 b(>)g FK(0.)3350 1932 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_Kn_scal)q(ed_a)q(rra)q(y)e Fu(\()p FD(in)m(t)32 b Ft(nmin)p FD(,)f(in)m(t)g Ft(nmax)p FD(,)h(double)e Ft(x)p FD(,)565 2042 y(double)g Ft(result_array)p Fo([])p Fu(\))390 2152 y FK(This)j(routine)g(computes)h(the)f(v)-5 b(alues)34 b(of)f(the)h(scaled)g(irregular)g(cylindrical)g(Bessel)g (functions)390 2261 y(exp\()p FE(x)p FK(\))p FE(K)728 2275 y Fq(n)774 2261 y FK(\()p FE(x)p FK(\))44 b(for)f FE(n)f FK(from)h FD(nmin)f FK(to)i FD(nmax)50 b FK(inclusiv)m(e,)d (storing)d(the)f(results)g(in)g(the)g(arra)m(y)390 2371 y FD(result)p 619 2371 V 40 w(arra)m(y)p FK(.)72 b(The)40 b(start)h(of)g(the)g(range)g FD(nmin)f FK(m)m(ust)g(b)s(e)g(p)s(ositiv) m(e)i(or)f(zero.)72 b(The)40 b(domain)390 2480 y(of)h(the)g(function)g (is)g FE(x)i(>)f FK(0.)73 b(The)41 b(v)-5 b(alues)41 b(are)g(computed)g(using)f(recurrence)h(relations)h(for)390 2590 y(e\016ciency)-8 b(,)32 b(and)e(therefore)h(ma)m(y)g(di\013er)f (sligh)m(tly)h(from)f(the)h(exact)h(v)-5 b(alues.)150 2786 y Fy(7.5.5)63 b(Regular)40 b(Spherical)h(Bessel)i(F)-10 b(unctions)3350 2979 y FK([F)i(unction])-3599 b Fv(double)54 b(gsl_sf_bessel_j0)c Fu(\()p FD(double)31 b Ft(x)p Fu(\))3350 3089 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_j0_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1894 3089 V 41 w(sf)p 1999 3089 V 39 w(result)g(*)g Ft(result)p Fu(\))390 3198 y FK(These)c(routines)g(compute)h(the)g(regular)f (spherical)h(Bessel)g(function)f(of)h(zeroth)g(order,)g FE(j)3494 3212 y FB(0)3531 3198 y FK(\()p FE(x)p FK(\))e(=)390 3308 y(sin\()p FE(x)p FK(\))p FE(=x)p FK(.)3350 3487 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_bessel_j1)c Fu(\()p FD(double)31 b Ft(x)p Fu(\))3350 3597 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_j1_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1894 3597 V 41 w(sf)p 1999 3597 V 39 w(result)g(*)g Ft(result)p Fu(\))390 3706 y FK(These)k(routines)f(compute)i(the)f(regular)g(spherical)g(Bessel)h (function)e(of)h(\014rst)f(order,)i FE(j)3486 3720 y FB(1)3524 3706 y FK(\()p FE(x)p FK(\))d(=)390 3816 y(\(sin\()p FE(x)p FK(\))p FE(=x)21 b FI(\000)f FK(cos)q(\()p FE(x)p FK(\)\))p FE(=x)p FK(.)3350 3995 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_bessel_j2)c Fu(\()p FD(double)31 b Ft(x)p Fu(\))3350 4105 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_j2_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1894 4105 V 41 w(sf)p 1999 4105 V 39 w(result)g(*)g Ft(result)p Fu(\))390 4214 y FK(These)26 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b(gsl_sf_bessel_jl_arra)q(y)e Fu(\()p FD(in)m(t)32 b Ft(lmax)p FD(,)f(double)f Ft(x)p FD(,)h(double)565 5121 y Ft(result_array)p Fo([])p Fu(\))390 5230 y FK(This)k(routine)i (computes)f(the)g(v)-5 b(alues)37 b(of)f(the)h(regular)f(spherical)g (Bessel)i(functions)d FE(j)3456 5244 y Fq(l)3482 5230 y FK(\()p FE(x)p FK(\))i(for)390 5340 y FE(l)f FK(from)e(0)g(to)h FD(lmax)41 b FK(inclusiv)m(e)35 b(for)f FE(l)r(max)d FI(\025)h FK(0)i(and)g FE(x)d FI(\025)h FK(0,)j(storing)g(the)f (results)g(in)g(the)g(arra)m(y)p eop end %%Page: 40 58 TeXDict begin 40 57 bop 150 -116 a FK(Chapter)30 b(7:)41 b(Sp)s(ecial)31 b(F)-8 b(unctions)2348 b(40)390 299 y FD(result)p 619 299 28 4 v 40 w(arra)m(y)p FK(.)54 b(The)34 b(v)-5 b(alues)35 b(are)h(computed)e(using)g(recurrence)h(relations)h (for)e(e\016ciency)-8 b(,)38 b(and)390 408 y(therefore)31 b(ma)m(y)g(di\013er)f(sligh)m(tly)i(from)d(the)i(exact)h(v)-5 b(alues.)3350 609 y([F)d(unction])-3599 b Fv(int)53 b (gsl_sf_bessel_jl_stee)q(d_ar)q(ray)f Fu(\()p FD(in)m(t)31 b Ft(lmax)p FD(,)h(double)e Ft(x)p FD(,)h(double)f(*)565 719 y Ft(result_array)p Fu(\))390 829 y FK(This)23 b(routine)g(uses)g (Steed's)h(metho)s(d)e(to)j(compute)e(the)h(v)-5 b(alues)24 b(of)f(the)h(regular)f(spherical)h(Bessel)390 938 y(functions)36 b FE(j)825 952 y Fq(l)851 938 y FK(\()p FE(x)p FK(\))h(for)f FE(l)i FK(from)e(0)h(to)g FD(lmax)43 b FK(inclusiv)m(e)37 b(for)g FE(l)r(max)e FI(\025)g FK(0)h(and)g FE(x)f FI(\025)g FK(0,)k(storing)e(the)390 1048 y(results)27 b(in)g(the)h(arra)m(y)g FD(result)p 1397 1048 V 40 w(arra)m(y)p FK(.)40 b(The)28 b(Steed/Barnett)h(algorithm)f(is)g(describ)s(ed)e(in)h FD(Comp.)390 1157 y(Ph)m(ys.)64 b(Comm.)f FK(21,)41 b(297)f(\(1981\).) 66 b(Steed's)38 b(metho)s(d)g(is)g(more)g(stable)h(than)f(the)g (recurrence)390 1267 y(used)30 b(in)g(the)g(other)h(functions)f(but)f (is)i(also)g(slo)m(w)m(er.)150 1474 y Fy(7.5.6)63 b(Irregular)41 b(Spherical)g(Bessel)h(F)-10 b(unctions)3350 1680 y FK([F)i(unction]) -3599 b Fv(double)54 b(gsl_sf_bessel_y0)c Fu(\()p FD(double)31 b Ft(x)p Fu(\))3350 1789 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_y0_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1894 1789 V 41 w(sf)p 1999 1789 V 39 w(result)g(*)g Ft(result)p Fu(\))390 1899 y FK(These)21 b(routines)g(compute)g(the)g(irregular)h(spherical)f(Bessel)h(function) f(of)g(zeroth)h(order,)h FE(y)3495 1913 y FB(0)3531 1899 y FK(\()p FE(x)p FK(\))j(=)390 2008 y FI(\000)15 b FK(cos)q(\()p FE(x)p FK(\))p FE(=x)p FK(.)3350 2209 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_bessel_y1)c Fu(\()p FD(double)31 b Ft(x)p Fu(\))3350 2319 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_y1_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1894 2319 V 41 w(sf)p 1999 2319 V 39 w(result)g(*)g Ft(result)p Fu(\))390 2428 y FK(These)e(routines)h (compute)f(the)h(irregular)f(spherical)h(Bessel)h(function)e(of)g (\014rst)g(order,)h FE(y)3495 2442 y FB(1)3531 2428 y FK(\()p FE(x)p FK(\))c(=)390 2538 y FI(\000)p FK(\(cos)q(\()p FE(x)p FK(\))p FE(=x)21 b FK(+)f(sin\()p FE(x)p FK(\)\))p FE(=x)p FK(.)3350 2739 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_bessel_y2)c Fu(\()p FD(double)31 b Ft(x)p Fu(\))3350 2848 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_y2_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1894 2848 V 41 w(sf)p 1999 2848 V 39 w(result)g(*)g Ft(result)p Fu(\))390 2958 y FK(These)52 b(routines)f(compute)i(the)f(irregular)g (spherical)g(Bessel)h(function)e(of)h(second)g(order,)390 3068 y FE(y)435 3082 y FB(2)472 3068 y FK(\()p FE(x)p FK(\))26 b(=)f(\()p FI(\000)p FK(3)p FE(=x)964 3035 y FB(3)1022 3068 y FK(+)20 b(1)p FE(=x)p FK(\))15 b(cos)r(\()p FE(x)p FK(\))21 b FI(\000)f FK(\(3)p FE(=x)1839 3035 y FB(2)1877 3068 y FK(\))15 b(sin\()p FE(x)p FK(\).)3350 3269 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_bessel_yl)c Fu(\()p FD(in)m(t)32 b Ft(l)p FD(,)f(double)e Ft(x)p Fu(\))3350 3378 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_yl_e)e Fu(\()p FD(in)m(t)31 b Ft(l)p FD(,)g(double)f Ft(x)p FD(,)h(gsl)p 2141 3378 V 41 w(sf)p 2246 3378 V 39 w(result)g(*)f Ft(result)p Fu(\))390 3488 y FK(These)35 b(routines)h(compute)g(the)g(irregular)f(spherical)h (Bessel)h(function)e(of)h(order)f FD(l)p FK(,)i FE(y)3431 3502 y Fq(l)3456 3488 y FK(\()p FE(x)p FK(\),)h(for)390 3597 y FE(l)27 b FI(\025)e FK(0.)3350 3798 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_yl_arra)q(y)e Fu(\()p FD(in)m(t)32 b Ft(lmax)p FD(,)f(double)f Ft(x)p FD(,)h(double)565 3908 y Ft(result_array)p Fo([])p Fu(\))390 4017 y FK(This)f(routine)g (computes)h(the)g(v)-5 b(alues)31 b(of)f(the)h(irregular)g(spherical)f (Bessel)i(functions)e FE(y)3463 4031 y Fq(l)3488 4017 y FK(\()p FE(x)p FK(\))h(for)390 4127 y FE(l)g FK(from)e(0)g(to)h FD(lmax)36 b FK(inclusiv)m(e)30 b(for)f FE(l)r(max)c FI(\025)g FK(0,)30 b(storing)f(the)h(results)e(in)h(the)h(arra)m(y)f FD(result)p 3483 4127 V 40 w(arra)m(y)p FK(.)390 4237 y(The)i(v)-5 b(alues)31 b(are)h(computed)f(using)g(recurrence)g (relations)i(for)e(e\016ciency)-8 b(,)33 b(and)e(therefore)g(ma)m(y)390 4346 y(di\013er)f(sligh)m(tly)i(from)e(the)g(exact)i(v)-5 b(alues.)150 4554 y Fy(7.5.7)63 b(Regular)40 b(Mo)s(di\014ed)j (Spherical)e(Bessel)h(F)-10 b(unctions)150 4701 y FK(The)42 b(regular)g(mo)s(di\014ed)g(spherical)g(Bessel)h(functions)f FE(i)2163 4715 y Fq(l)2189 4701 y FK(\()p FE(x)p FK(\))h(are)g(related) g(to)g(the)g(mo)s(di\014ed)e(Bessel)150 4810 y(functions)30 b(of)g(fractional)i(order,)e FE(i)1346 4824 y Fq(l)1372 4810 y FK(\()p FE(x)p FK(\))c(=)1616 4737 y Fs(p)p 1699 4737 269 4 v 73 x FE(\031)s(=)p FK(\(2)p FE(x)p FK(\))r FE(I)2008 4824 y Fq(l)p FB(+1)p Fq(=)p FB(2)2184 4810 y FK(\()p FE(x)p FK(\))3350 5011 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_bessel_i0_scale)q(d)e Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 5121 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_i0_scal)q(ed_e)f Fu(\()p FD(double)31 b Ft(x)p FD(,)f(gsl)p 2260 5121 28 4 v 41 w(sf)p 2365 5121 V 40 w(result)g(*)h Ft(result)p Fu(\))390 5230 y FK(These)22 b(routines)h(compute)g(the)g(scaled)g(regular)g(mo)s (di\014ed)f(spherical)g(Bessel)i(function)e(of)h(zeroth)390 5340 y(order,)30 b(exp\()p FI(\000j)p FE(x)p FI(j)p FK(\))p FE(i)1066 5354 y FB(0)1104 5340 y FK(\()p FE(x)p FK(\).)p eop end %%Page: 41 59 TeXDict begin 41 58 bop 150 -116 a FK(Chapter)30 b(7:)41 b(Sp)s(ecial)31 b(F)-8 b(unctions)2348 b(41)3350 299 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_bessel_i1_scale)q(d)e Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 408 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_i1_scal)q(ed_e)f Fu(\()p FD(double)31 b Ft(x)p FD(,)f(gsl)p 2260 408 28 4 v 41 w(sf)p 2365 408 V 40 w(result)g(*)h Ft(result)p Fu(\))390 518 y FK(These)g(routines)f(compute)i(the)f(scaled)g(regular) g(mo)s(di\014ed)f(spherical)h(Bessel)h(function)f(of)g(\014rst)390 628 y(order,)f(exp\()p FI(\000j)p FE(x)p FI(j)p FK(\))p FE(i)1066 642 y FB(1)1104 628 y FK(\()p FE(x)p FK(\).)3350 842 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_bessel_i2_scale)q (d)e Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 952 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_i2_scal)q(ed_e)f Fu(\()p FD(double)31 b Ft(x)p FD(,)f(gsl)p 2260 952 V 41 w(sf)p 2365 952 V 40 w(result)g(*)h Ft(result)p Fu(\))390 1061 y FK(These)21 b(routines)g(compute)h(the)f(scaled)h(regular)g(mo)s (di\014ed)e(spherical)h(Bessel)i(function)d(of)i(second)390 1171 y(order,)30 b(exp\()p FI(\000j)p FE(x)p FI(j)p FK(\))p FE(i)1066 1185 y FB(2)1104 1171 y FK(\()p FE(x)p FK(\))3350 1385 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_bessel_il_scale)q (d)e Fu(\()p FD(in)m(t)31 b Ft(l)p FD(,)g(double)f Ft(x)p Fu(\))3350 1495 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_il_scal)q(ed_e)f Fu(\()p FD(in)m(t)31 b Ft(l)p FD(,)g(double)f Ft(x)p FD(,)h(gsl)p 2507 1495 V 41 w(sf)p 2612 1495 V 39 w(result)g(*)565 1605 y Ft(result)p Fu(\))390 1714 y FK(These)26 b(routines)g(compute)h(the)f(scaled)h (regular)g(mo)s(di\014ed)e(spherical)i(Bessel)g(function)f(of)g(order) 390 1824 y FD(l)p FK(,)31 b(exp\()p FI(\000j)p FE(x)p FI(j)p FK(\))p FE(i)884 1838 y Fq(l)910 1824 y FK(\()p FE(x)p FK(\))3350 2038 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_il_scal)q(ed_a)q(rra)q(y)e Fu(\()p FD(in)m(t)32 b Ft(lmax)p FD(,)f(double)f Ft(x)p FD(,)h(double)565 2148 y Ft(result_array)p Fo([])p Fu(\))390 2258 y FK(This)25 b(routine)h(computes)g(the)h(v)-5 b(alues)26 b(of)g(the)g(scaled)h (regular)f(mo)s(di\014ed)f(spherical)h(Bessel)i(func-)390 2367 y(tions)34 b(exp\()p FI(\000j)p FE(x)p FI(j)p FK(\))p FE(i)1029 2381 y Fq(l)1056 2367 y FK(\()p FE(x)p FK(\))g(for)f FE(l)j FK(from)d(0)h(to)h FD(lmax)40 b FK(inclusiv)m(e)35 b(for)e FE(l)r(max)e FI(\025)f FK(0,)35 b(storing)f(the)g(results)390 2477 y(in)41 b(the)g(arra)m(y)g FD(result)p 1151 2477 V 40 w(arra)m(y)p FK(.)74 b(The)40 b(v)-5 b(alues)41 b(are)h(computed)f(using)f(recurrence)h(relations)h(for)390 2586 y(e\016ciency)-8 b(,)32 b(and)e(therefore)h(ma)m(y)g(di\013er)f (sligh)m(tly)h(from)f(the)h(exact)h(v)-5 b(alues.)150 2801 y Fy(7.5.8)63 b(Irregular)41 b(Mo)s(di\014ed)i(Spherical)e(Bessel) h(F)-10 b(unctions)150 2948 y FK(The)27 b(irregular)h(mo)s(di\014ed)f (spherical)h(Bessel)h(functions)e FE(k)2153 2962 y Fq(l)2179 2948 y FK(\()p FE(x)p FK(\))i(are)f(related)h(to)f(the)g(irregular)g (mo)s(di\014ed)150 3057 y(Bessel)j(functions)f(of)h(fractional)h (order,)e FE(k)1635 3071 y Fq(l)1661 3057 y FK(\()p FE(x)p FK(\))c(=)1905 2984 y Fs(p)p 1988 2984 269 4 v 73 x FE(\031)s(=)p FK(\(2)p FE(x)p FK(\))q FE(K)2333 3071 y Fq(l)p FB(+1)p Fq(=)p FB(2)2510 3057 y FK(\()p FE(x)p FK(\).)3350 3272 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_bessel_k0_scale)q(d)e Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 3381 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_k0_scal)q(ed_e)f Fu(\()p FD(double)31 b Ft(x)p FD(,)f(gsl)p 2260 3381 28 4 v 41 w(sf)p 2365 3381 V 40 w(result)g(*)h Ft(result)p Fu(\))390 3491 y FK(These)43 b(routines)h(compute)g(the)g(scaled)g (irregular)g(mo)s(di\014ed)e(spherical)i(Bessel)g(function)g(of)390 3600 y(zeroth)31 b(order,)f(exp\()p FE(x)p FK(\))p FE(k)1239 3614 y FB(0)1277 3600 y FK(\()p FE(x)p FK(\),)i(for)e FE(x)25 b(>)g FK(0.)3350 3815 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_bessel_k1_scale)q(d)e Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 3925 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_k1_scal)q(ed_e)f Fu(\()p FD(double)31 b Ft(x)p FD(,)f(gsl)p 2260 3925 V 41 w(sf)p 2365 3925 V 40 w(result)g(*)h Ft(result)p Fu(\))390 4034 y FK(These)25 b(routines)g(compute)h(the)f(scaled)i(irregular)e(mo)s (di\014ed)f(spherical)i(Bessel)g(function)f(of)h(\014rst)390 4144 y(order,)k(exp\()p FE(x)p FK(\))p FE(k)961 4158 y FB(1)999 4144 y FK(\()p FE(x)p FK(\),)h(for)g FE(x)25 b(>)g FK(0.)3350 4358 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_bessel_k2_scale)q(d)e Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 4468 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_k2_scal)q(ed_e)f Fu(\()p FD(double)31 b Ft(x)p FD(,)f(gsl)p 2260 4468 V 41 w(sf)p 2365 4468 V 40 w(result)g(*)h Ft(result)p Fu(\))390 4578 y FK(These)43 b(routines)h(compute)g(the)g(scaled)g(irregular)g(mo)s(di\014ed)e (spherical)i(Bessel)g(function)g(of)390 4687 y(second)30 b(order,)h(exp)o(\()p FE(x)p FK(\))p FE(k)1254 4701 y FB(2)1293 4687 y FK(\()p FE(x)p FK(\),)g(for)f FE(x)25 b(>)g FK(0.)3350 4902 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_bessel_kl_scale)q(d)e Fu(\()p FD(in)m(t)31 b Ft(l)p FD(,)g(double)f Ft(x)p Fu(\))3350 5011 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_kl_scal)q(ed_e)f Fu(\()p FD(in)m(t)31 b Ft(l)p FD(,)g(double)f Ft(x)p FD(,)h(gsl)p 2507 5011 V 41 w(sf)p 2612 5011 V 39 w(result)g(*)565 5121 y Ft(result)p Fu(\))390 5230 y FK(These)43 b(routines)h(compute)g (the)g(scaled)g(irregular)g(mo)s(di\014ed)e(spherical)i(Bessel)g (function)g(of)390 5340 y(order)30 b FD(l)p FK(,)h(exp\()p FE(x)p FK(\))p FE(k)1017 5354 y Fq(l)1043 5340 y FK(\()p FE(x)p FK(\),)g(for)f FE(x)c(>)f FK(0.)p eop end %%Page: 42 60 TeXDict begin 42 59 bop 150 -116 a FK(Chapter)30 b(7:)41 b(Sp)s(ecial)31 b(F)-8 b(unctions)2348 b(42)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_kl_scal)q(ed_a)q (rra)q(y)e Fu(\()p FD(in)m(t)32 b Ft(lmax)p FD(,)f(double)f Ft(x)p FD(,)h(double)565 408 y Ft(result_array)p Fo([])p Fu(\))390 518 y FK(This)40 b(routine)h(computes)g(the)g(v)-5 b(alues)42 b(of)f(the)g(scaled)h(irregular)f(mo)s(di\014ed)f(spherical) h(Bessel)390 628 y(functions)35 b(exp\()p FE(x)p FK(\))p FE(k)1095 642 y Fq(l)1121 628 y FK(\()p FE(x)p FK(\))h(for)g FE(l)h FK(from)e(0)h(to)g FD(lmax)42 b FK(inclusiv)m(e)37 b(for)e FE(l)r(max)e FI(\025)h FK(0)i(and)f FE(x)f(>)f FK(0,)k(stor-)390 737 y(ing)d(the)g(results)g(in)g(the)g(arra)m(y)g FD(result)p 1738 737 28 4 v 40 w(arra)m(y)p FK(.)52 b(The)33 b(v)-5 b(alues)35 b(are)f(computed)g(using)f(recurrence)390 847 y(relations)e(for)g(e\016ciency)-8 b(,)32 b(and)d(therefore)i(ma)m 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FK(This)i(function)h(computes)h(the)f(regular)h (cylindrical)g(Bessel)g(function)f(of)h(fractional)g(order)f FE(\027)6 b FK(,)390 2164 y FE(J)440 2178 y Fq(\027)482 2164 y FK(\()p FE(x)p FK(\),)40 b(ev)-5 b(aluated)38 b(at)g(a)g(series)f(of)h FE(x)f FK(v)-5 b(alues.)62 b(The)37 b(arra)m(y)h FD(v)45 b FK(of)37 b(length)h FD(size)43 b FK(con)m(tains)c(the)e FE(x)390 2274 y FK(v)-5 b(alues.)71 b(They)40 b(are)g(assumed)g(to)h(b)s(e)e(strictly)j(ordered)d(and)h(p)s (ositiv)m(e.)71 b(The)40 b(arra)m(y)h(is)f(o)m(v)m(er-)390 2384 y(written)30 b(with)h(the)f(v)-5 b(alues)31 b(of)f FE(J)1496 2398 y Fq(\027)1538 2384 y FK(\()p FE(x)1625 2398 y Fq(i)1653 2384 y FK(\).)150 2603 y Fy(7.5.10)63 b(Irregular)41 b(Bessel)h(F)-10 b(unctions|F)g(ractional)41 b(Order)3350 2819 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_bessel_Ynu)d Fu(\()p FD(double)30 b Ft(nu)p FD(,)h(double)f Ft(x)p Fu(\))3350 2929 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_Ynu_e)e Fu(\()p FD(double)28 b Ft(nu)p FD(,)h(double)e Ft(x)p FD(,)i(gsl)p 2390 2929 V 40 w(sf)p 2494 2929 V 40 w(result)e(*)h Ft(result)p Fu(\))390 3039 y FK(These)e(routines)h(compute)g(the)f(irregular)h (cylindrical)g(Bessel)h(function)e(of)h(fractional)h(order)e FE(\027)6 b FK(,)390 3148 y FE(Y)443 3162 y Fq(\027)484 3148 y FK(\()p FE(x)p FK(\).)150 3367 y Fy(7.5.11)63 b(Regular)41 b(Mo)s(di\014ed)i(Bessel)f(F)-10 b(unctions|F)g(ractional) 40 b(Order)3350 3584 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_bessel_Inu)d Fu(\()p FD(double)30 b Ft(nu)p FD(,)h(double)f Ft(x)p Fu(\))3350 3694 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_Inu_e)e Fu(\()p FD(double)28 b Ft(nu)p FD(,)h(double)e Ft(x)p FD(,)i(gsl)p 2390 3694 V 40 w(sf)p 2494 3694 V 40 w(result)e(*)h Ft(result)p Fu(\))390 3803 y FK(These)38 b(routines)h(compute)g(the)f(regular)h(mo) s(di\014ed)e(Bessel)j(function)e(of)h(fractional)h(order)e FE(\027)6 b FK(,)390 3913 y FE(I)430 3927 y Fq(\027)471 3913 y FK(\()p FE(x)p FK(\))31 b(for)f FE(x)c(>)f FK(0,)31 b FE(\027)g(>)24 b FK(0.)3350 4137 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_bessel_Inu_scal)q(ed)e Fu(\()p FD(double)30 b Ft(nu)p FD(,)h(double)f Ft(x)p Fu(\))3350 4247 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_Inu_sca)q (led_)q(e)f Fu(\()p FD(double)29 b Ft(nu)p FD(,)i(double)e Ft(x)p FD(,)i(gsl)p 2764 4247 V 40 w(sf)p 2868 4247 V 40 w(result)f(*)565 4356 y Ft(result)p Fu(\))390 4466 y FK(These)24 b(routines)f(compute)h(the)g(scaled)h(regular)f(mo)s (di\014ed)f(Bessel)i(function)e(of)h(fractional)h(order)390 4575 y FE(\027)6 b FK(,)30 b(exp\()p FI(\000j)p FE(x)p FI(j)p FK(\))p FE(I)918 4589 y Fq(\027)960 4575 y FK(\()p FE(x)p FK(\))h(for)f FE(x)c(>)f FK(0,)31 b FE(\027)g(>)24 b FK(0.)150 4795 y Fy(7.5.12)63 b(Irregular)41 b(Mo)s(di\014ed)i (Bessel)f(F)-10 b(unctions|F)g(ractional)41 b(Order)3350 5011 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_bessel_Knu)d Fu(\()p FD(double)30 b Ft(nu)p FD(,)h(double)f Ft(x)p Fu(\))3350 5121 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_Knu_e)e Fu(\()p FD(double)28 b Ft(nu)p FD(,)h(double)e Ft(x)p FD(,)i(gsl)p 2390 5121 V 40 w(sf)p 2494 5121 V 40 w(result)e(*)h Ft(result)p Fu(\))390 5230 y FK(These)33 b(routines)g(compute)g(the)g(irregular)g(mo)s(di\014ed)f (Bessel)i(function)f(of)g(fractional)i(order)d FE(\027)6 b FK(,)390 5340 y FE(K)467 5354 y Fq(\027)509 5340 y FK(\()p FE(x)p FK(\))30 b(for)h FE(x)25 b(>)g FK(0,)31 b FE(\027)g(>)25 b FK(0.)p eop end %%Page: 43 61 TeXDict begin 43 60 bop 150 -116 a FK(Chapter)30 b(7:)41 b(Sp)s(ecial)31 b(F)-8 b(unctions)2348 b(43)3350 299 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_bessel_lnKnu)d Fu(\()p FD(double)31 b Ft(nu)p FD(,)g(double)f Ft(x)p Fu(\))3350 408 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_lnKnu_e)f Fu(\()p FD(double)30 b Ft(nu)p FD(,)h(double)f Ft(x)p FD(,)h(gsl)p 2504 408 28 4 v 41 w(sf)p 2609 408 V 39 w(result)g(*)565 518 y Ft(result)p Fu(\))390 628 y FK(These)40 b(routines)g(compute)g(the)g(logarithm)h (of)f(the)g(irregular)g(mo)s(di\014ed)f(Bessel)i(function)f(of)390 737 y(fractional)32 b(order)e FE(\027)6 b FK(,)30 b(ln\()p FE(K)1329 751 y Fq(\027)1371 737 y FK(\()p FE(x)p FK(\)\))h(for)f FE(x)25 b(>)g FK(0,)31 b FE(\027)g(>)25 b FK(0.)3350 961 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_bessel_Knu_scal)q (ed)e Fu(\()p FD(double)30 b Ft(nu)p FD(,)h(double)f Ft(x)p Fu(\))3350 1070 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_Knu_sca)q(led_)q(e)f Fu(\()p FD(double)29 b Ft(nu)p FD(,)i(double)e Ft(x)p FD(,)i(gsl)p 2764 1070 V 40 w(sf)p 2868 1070 V 40 w(result)f(*)565 1180 y Ft(result)p Fu(\))390 1290 y FK(These)41 b(routines)f(compute)i (the)f(scaled)g(irregular)g(mo)s(di\014ed)f(Bessel)i(function)e(of)h (fractional)390 1399 y(order)30 b FE(\027)6 b FK(,)30 b(exp\(+)p FI(j)p FE(x)p FI(j)p FK(\))p FE(K)1193 1413 y Fq(\027)1235 1399 y FK(\()p FE(x)p FK(\))h(for)g FE(x)25 b(>)g FK(0,)31 b FE(\027)g(>)25 b FK(0.)150 1618 y Fy(7.5.13)63 b(Zeros)42 b(of)g(Regular)e(Bessel)i(F)-10 b(unctions)3350 1834 y FK([F)i(unction])-3599 b Fv(double)54 b(gsl_sf_bessel_zero_J0)e Fu(\()p FD(unsigned)30 b(in)m(t)g Ft(s)p Fu(\))3350 1944 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_zero_J0)q(_e)f Fu(\()p FD(unsigned)29 b(in)m(t)i Ft(s)p FD(,)g(gsl)p 2381 1944 V 41 w(sf)p 2486 1944 V 39 w(result)g(*)f Ft(result)p Fu(\))390 2054 y FK(These)k(routines)g(compute)g(the)g(lo)s(cation)i (of)e(the)g FD(s)p FK(-th)g(p)s(ositiv)m(e)h(zero)g(of)f(the)g(Bessel)h (function)390 2163 y FE(J)440 2177 y FB(0)478 2163 y FK(\()p FE(x)p FK(\).)3350 2387 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_bessel_zero_J1)e Fu(\()p FD(unsigned)30 b(in)m(t)g Ft(s)p Fu(\))3350 2496 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_zero_J1)q(_e)f Fu(\()p FD(unsigned)29 b(in)m(t)i Ft(s)p FD(,)g(gsl)p 2381 2496 V 41 w(sf)p 2486 2496 V 39 w(result)g(*)f Ft(result)p Fu(\))390 2606 y FK(These)k(routines)g(compute)g(the)g(lo)s(cation)i(of)e(the)g FD(s)p FK(-th)g(p)s(ositiv)m(e)h(zero)g(of)f(the)g(Bessel)h(function) 390 2716 y FE(J)440 2730 y FB(1)478 2716 y FK(\()p FE(x)p FK(\).)3350 2939 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_bessel_zero_Jnu)e Fu(\()p FD(double)31 b Ft(nu)p FD(,)g(unsigned)e(in)m(t)i Ft(s)p Fu(\))3350 3049 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_zero_Jn)q(u_e)f Fu(\()p FD(double)30 b Ft(nu)p FD(,)h(unsigned)f(in)m(t)h Ft(s)p FD(,)565 3158 y(gsl)p 677 3158 V 41 w(sf)p 782 3158 V 39 w(result)g(*)f Ft(result)p Fu(\))390 3268 y FK(These)k(routines)g(compute)g(the)g(lo)s(cation)i(of)e(the)g FD(s)p FK(-th)g(p)s(ositiv)m(e)h(zero)g(of)f(the)g(Bessel)h(function) 390 3377 y FE(J)440 3391 y Fq(\027)482 3377 y FK(\()p FE(x)p FK(\).)41 b(The)30 b(curren)m(t)g(implemen)m(tation)i(do)s(es)e (not)h(supp)s(ort)d(negativ)m(e)33 b(v)-5 b(alues)31 b(of)f FD(n)m(u)p FK(.)150 3639 y FJ(7.6)68 b(Clausen)46 b(F)-11 b(unctions)150 3799 y FK(The)30 b(Clausen)g(function)g(is)g (de\014ned)f(b)m(y)i(the)f(follo)m(wing)i(in)m(tegral,)1322 4023 y FE(C)7 b(l)1421 4037 y FB(2)1458 4023 y FK(\()p FE(x)p FK(\))26 b(=)f FI(\000)1788 3908 y Fs(Z)1871 3928 y Fq(x)1834 4097 y FB(0)1928 4023 y FE(dt)15 b FK(log)r(\(2)g(sin)q(\() p FE(t=)p FK(2\)\))150 4257 y(It)21 b(is)h(related)g(to)g(the)g (dilogarithm)g(b)m(y)f FE(C)7 b(l)1563 4271 y FB(2)1600 4257 y FK(\()p FE(\022)s FK(\))25 b(=)g(Im)o(\()p FE(Li)2073 4271 y FB(2)2111 4257 y FK(\()p FE(e)2188 4224 y Fq(i\022)2250 4257 y FK(\)\).)38 b(The)21 b(Clausen)g(functions)g(are)g(declared)150 4366 y(in)30 b(the)h(header)f(\014le)g FH(gsl_sf_clausen.h)p FK(.)3350 4590 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_clausen)c Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 4699 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_clausen_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1790 4699 V 40 w(sf)p 1894 4699 V 40 w(result)f(*)h Ft(result)p Fu(\))390 4809 y FK(These)f(routines)g(compute)h(the)g(Clausen)f(in)m (tegral)i FE(C)7 b(l)2302 4823 y FB(2)2338 4809 y FK(\()p FE(x)p FK(\).)150 5071 y FJ(7.7)68 b(Coulom)l(b)46 b(F)-11 b(unctions)150 5230 y FK(The)23 b(protot)m(yp)s(es)h(of)g(the)g(Coulom) m(b)g(functions)f(are)h(declared)g(in)g(the)g(header)f(\014le)h FH(gsl_sf_coulomb.h)p FK(.)150 5340 y(Both)31 b(b)s(ound)d(state)k(and) e(scattering)i(solutions)f(are)f(a)m(v)-5 b(ailable.)p eop end %%Page: 44 62 TeXDict begin 44 61 bop 150 -116 a FK(Chapter)30 b(7:)41 b(Sp)s(ecial)31 b(F)-8 b(unctions)2348 b(44)150 299 y Fy(7.7.1)63 b(Normalized)41 b(Hydrogenic)g(Bound)h(States)3350 484 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_hydrogenicR_1)e Fu(\()p FD(double)30 b Ft(Z)p FD(,)h(double)f Ft(r)p Fu(\))3350 594 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_hydrogenicR_1_)q(e)e Fu(\()p FD(double)31 b Ft(Z)p FD(,)f(double)g Ft(r)p FD(,)h(gsl)p 2504 594 28 4 v 41 w(sf)p 2609 594 V 39 w(result)g(*)565 703 y Ft(result)p Fu(\))390 813 y FK(These)36 b(routines)h(compute)g(the)f(lo)m(w)m (est-order)j(normalized)e(h)m(ydrogenic)g(b)s(ound)e(state)i(radial)390 923 y(w)m(a)m(v)m(efunction)32 b FE(R)1007 937 y FB(1)1069 923 y FK(:=)26 b(2)p FE(Z)1305 846 y FI(p)p 1380 846 69 4 v 1380 923 a FE(Z)c FK(exp\()p FI(\000)p FE(Z)7 b(r)s FK(\).)3350 1090 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_hydrogenicR)d Fu(\()p FD(in)m(t)31 b Ft(n)p FD(,)g(in)m(t)g Ft(l)p FD(,)g(double)f Ft(Z)p FD(,)h(double)f Ft(r)p Fu(\))3350 1199 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_hydrogenicR_e)f Fu(\()p FD(in)m(t)31 b Ft(n)p FD(,)g(in)m(t)g Ft(l)p FD(,)g(double)f Ft(Z)p FD(,)g(double)g Ft(r)p FD(,)565 1309 y(gsl)p 677 1309 28 4 v 41 w(sf)p 782 1309 V 39 w(result)h(*)f Ft(result)p Fu(\))390 1419 y FK(These)25 b(routines)g(compute)h(the)f FD(n)p FK(-th)g(normalized)h(h)m(ydrogenic)f(b)s(ound)e(state)k(radial) f(w)m(a)m(v)m(efunc-)390 1528 y(tion,)685 1766 y FE(R)754 1780 y Fq(n)824 1766 y FK(:=)955 1704 y(2)p FE(Z)1069 1671 y FB(3)p Fq(=)p FB(2)p 955 1745 219 4 v 1018 1828 a FE(n)1073 1802 y FB(2)1199 1647 y Fs(\022)1270 1704 y FK(2)p FE(Z)7 b(r)p 1270 1745 158 4 v 1321 1828 a(n)1437 1647 y Fs(\023)1498 1663 y Fq(l)1539 1614 y Fs(s)p 1622 1614 468 4 v 1632 1704 a FK(\()p FE(n)20 b FI(\000)g FE(l)i FI(\000)e FK(1\)!)p 1632 1745 448 4 v 1710 1828 a(\()p FE(n)g FK(+)g FE(l)r FK(\)!)2104 1766 y(exp\()p FI(\000)p FE(Z)7 b(r)s(=n)p FK(\))p FE(L)2659 1728 y FB(2)p Fq(l)p FB(+1)2659 1788 y Fq(n)p Fp(\000)p Fq(l)p Fp(\000)p FB(1)2862 1766 y FK(\(2)p FE(Z)g(r)s(=n)p FK(\))p FE(:)390 1990 y FK(where)26 b FE(L)711 1957 y Fq(a)711 2012 y(b)751 1990 y FK(\()p FE(x)p FK(\))g(is)g(the)g(generalized)i (Laguerre)e(p)s(olynomial)h(\(see)g(Section)f(7.22)i([Laguerre)f(F)-8 b(unc-)390 2099 y(tions],)34 b(page)g(62\).)50 b(The)32 b(normalization)j(is)e(c)m(hosen)h(suc)m(h)e(that)i(the)f(w)m(a)m(v)m (efunction)i FE( )h FK(is)d(giv)m(en)390 2209 y(b)m(y)d FE( )s FK(\()p FE(n;)15 b(l)r(;)g(r)s FK(\))27 b(=)d FE(R)1047 2223 y Fq(n)1093 2209 y FE(Y)1146 2223 y Fq(lm)1230 2209 y FK(.)150 2397 y Fy(7.7.2)63 b(Coulom)m(b)41 b(W)-10 b(a)m(v)m(e)39 b(F)-10 b(unctions)150 2544 y FK(The)39 b(Coulom)m(b)g(w)m(a)m(v)m(e)i(functions)e FE(F)1431 2558 y Fq(L)1481 2544 y FK(\()p FE(\021)s(;)15 b(x)p FK(\),)43 b FE(G)1830 2558 y Fq(L)1880 2544 y FK(\()p FE(\021)s(;)15 b(x)p FK(\))41 b(are)f(describ)s(ed)e(in)h(Abramo)m (witz)h(&)f(Stegun,)150 2653 y(Chapter)i(14.)74 b(Because)42 b(there)g(can)f(b)s(e)g(a)h(large)g(dynamic)f(range)g(of)h(v)-5 b(alues)41 b(for)g(these)h(functions,)150 2763 y(o)m(v)m(er\015o)m(ws) 37 b(are)g(handled)e(gracefully)-8 b(.)58 b(If)36 b(an)g(o)m(v)m (er\015o)m(w)h(o)s(ccurs,)g FH(GSL_EOVRFLW)c FK(is)j(signalled)h(and)e (ex-)150 2872 y(p)s(onen)m(t\(s\))29 b(are)h(returned)e(through)g(the)i (mo)s(di\014able)e(parameters)i FD(exp)p 2630 2872 28 4 v 40 w(F)p FK(,)f FD(exp)p 2922 2872 V 40 w(G)p FK(.)41 b(The)29 b(full)f(solution)150 2982 y(can)j(b)s(e)e(reconstructed)i (from)f(the)h(follo)m(wing)g(relations,)1347 3139 y FE(F)1405 3153 y Fq(L)1455 3139 y FK(\()p FE(\021)s(;)15 b(x)p FK(\))27 b(=)e FE(f)10 b(c)p FK([)p FE(k)1954 3153 y Fq(L)2004 3139 y FK(])21 b FI(\003)f FK(exp\()p FE(exp)2429 3153 y Fq(F)2485 3139 y FK(\))1334 3273 y FE(G)1405 3287 y Fq(L)1455 3273 y FK(\()p FE(\021)s(;)15 b(x)p FK(\))27 b(=)e FE(g)s(c)p FK([)p FE(k)1945 3287 y Fq(L)1996 3273 y FK(])c FI(\003)f FK(exp\()p FE(exp)2421 3287 y Fq(G)2478 3273 y FK(\))1347 3542 y FE(F)1418 3505 y Fp(0)1405 3565 y Fq(L)1455 3542 y FK(\()p FE(\021)s(;)15 b(x)p FK(\))27 b(=)e FE(f)10 b(cp)p FK([)p FE(k)2000 3556 y Fq(L)2050 3542 y FK(])20 b FI(\003)h FK(exp\()p FE(exp)2475 3556 y Fq(F)2530 3542 y FK(\))1334 3677 y FE(G)1405 3639 y Fp(0)1405 3699 y Fq(L)1455 3677 y FK(\()p FE(\021)s(;)15 b(x)p FK(\))27 b(=)e FE(g)s(cp)p FK([)p FE(k)1991 3691 y Fq(L)2042 3677 y FK(])c FI(\003)f FK(exp\()p FE(exp)2467 3691 y Fq(G)2523 3677 y FK(\))3350 3858 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_coulomb_wave_F)q(G_e)f Fu(\()p FD(double)30 b Ft(eta)p FD(,)i(double)e Ft(x)p FD(,)g(double)g Ft(L_F)p FD(,)565 3967 y(in)m(t)h Ft(k)p FD(,)g(gsl)p 924 3967 V 40 w(sf)p 1028 3967 V 40 w(result)f(*)h Ft(F)p FD(,)g(gsl)p 1611 3967 V 41 w(sf)p 1716 3967 V 39 w(result)f(*)h Ft(Fp)p FD(,)g(gsl)p 2350 3967 V 41 w(sf)p 2455 3967 V 40 w(result)f(*)h Ft(G)p FD(,)f(gsl)p 3037 3967 V 41 w(sf)p 3142 3967 V 40 w(result)g(*)h Ft(Gp)p FD(,)565 4077 y(double)f(*)h Ft(exp_F)p FD(,)h(double)e(*)h Ft(exp_G)p Fu(\))390 4186 y FK(This)j(function)g(computes)h(the)g(Coulom)m(b)g(w)m(a)m(v)m(e)h (functions)e FE(F)2603 4200 y Fq(L)2654 4186 y FK(\()p FE(\021)s(;)15 b(x)p FK(\),)37 b FE(G)2997 4200 y Fq(L)p Fp(\000)p Fq(k)3136 4186 y FK(\()p FE(\021)s(;)15 b(x)p FK(\))36 b(and)e(their)390 4296 y(deriv)-5 b(ativ)m(es)35 b FE(F)917 4263 y Fp(0)904 4319 y Fq(L)954 4296 y FK(\()p FE(\021)s(;)15 b(x)p FK(\),)35 b FE(G)1295 4263 y Fp(0)1295 4319 y Fq(L)p Fp(\000)p Fq(k)1434 4296 y FK(\()p FE(\021)s(;)15 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begin 47 64 bop 150 -116 a FK(Chapter)30 b(7:)41 b(Sp)s(ecial)31 b(F)-8 b(unctions)2348 b(47)150 299 y FJ(7.10)68 b(Deb)l(y)l(e)46 b(F)-11 b(unctions)150 458 y FK(The)30 b(Deb)m(y)m(e)i(functions)e FE(D)1078 472 y Fq(n)1123 458 y FK(\()p FE(x)p FK(\))h(are)g(de\014ned)e(b)m(y)h(the) h(follo)m(wing)h(in)m(tegral,)1468 660 y FE(D)1543 674 y Fq(n)1588 660 y FK(\()p FE(x)p FK(\))26 b(=)1863 598 y FE(n)p 1842 639 98 4 v 1842 722 a(x)1894 696 y Fq(n)1964 545 y Fs(Z)2047 565 y Fq(x)2010 734 y FB(0)2104 660 y FE(dt)2269 598 y(t)2302 565 y Fq(n)p 2194 639 229 4 v 2194 722 a FE(e)2236 696 y Fq(t)2286 722 y FI(\000)20 b FK(1)150 856 y(F)-8 b(or)33 b(further)e(information)i(see)f(Abramo)m (witz)i(&)e(Stegun,)g(Section)h(27.1.)48 b(The)32 b(Deb)m(y)m(e)i (functions)e(are)150 966 y(declared)f(in)f(the)g(header)h(\014le)f FH(gsl_sf_debye.h)p FK(.)3350 1126 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_debye_1)c Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 1236 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_debye_1_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1790 1236 28 4 v 40 w(sf)p 1894 1236 V 40 w(result)f(*)h Ft(result)p Fu(\))390 1345 y FK(These)23 b(routines)f(compute)h(the)g(\014rst-order)f(Deb)m(y)m(e)i (function)f FE(D)2605 1359 y FB(1)2642 1345 y FK(\()p FE(x)p FK(\))j(=)f(\(1)p FE(=x)p FK(\))3113 1277 y Fs(R)3170 1297 y Fq(x)3154 1373 y FB(0)3227 1345 y FE(dt)p FK(\()p FE(t=)p FK(\()p FE(e)3497 1312 y Fq(t)3533 1345 y FI(\000)5 b FK(1\)\).)3350 1506 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_debye_2)c Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 1616 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_debye_2_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1790 1616 V 40 w(sf)p 1894 1616 V 40 w(result)f(*)h Ft(result)p Fu(\))390 1725 y FK(These)114 b(routines)h(compute)g(the)f (second-order)h(Deb)m(y)m(e)h(function)f FE(D)3354 1739 y FB(2)3391 1725 y FK(\()p FE(x)p FK(\))166 b(=)390 1835 y(\(2)p FE(=x)567 1802 y FB(2)605 1835 y FK(\))655 1766 y Fs(R)711 1787 y Fq(x)695 1862 y FB(0)768 1835 y FE(dt)p FK(\()p FE(t)916 1802 y FB(2)954 1835 y FE(=)p FK(\()p FE(e)1076 1802 y Fq(t)1126 1835 y FI(\000)20 b FK(1\)\).)3350 1996 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_debye_3)c Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 2105 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_debye_3_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1790 2105 V 40 w(sf)p 1894 2105 V 40 w(result)f(*)h Ft(result)p Fu(\))390 2215 y FK(These)26 b(routines)g(compute)h(the)f(third-order)g(Deb)m(y)m(e)i (function)e FE(D)2670 2229 y FB(3)2707 2215 y FK(\()p FE(x)p FK(\))g(=)f(\(3)p FE(=x)3128 2182 y FB(3)3166 2215 y FK(\))3216 2146 y Fs(R)3272 2166 y Fq(x)3256 2242 y FB(0)3329 2215 y FE(dt)p FK(\()p FE(t)3477 2182 y FB(3)3515 2215 y FE(=)p FK(\()p FE(e)3637 2182 y Fq(t)3679 2215 y FI(\000)390 2324 y FK(1\)\).)3350 2485 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_debye_4)c Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 2595 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_debye_4_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1790 2595 V 40 w(sf)p 1894 2595 V 40 w(result)f(*)h Ft(result)p Fu(\))390 2704 y FK(These)21 b(routines)g(compute)g(the)g(fourth-order)f(Deb)m(y)m(e)j(function)d FE(D)2680 2718 y FB(4)2718 2704 y FK(\()p FE(x)p FK(\))26 b(=)f(\(4)p FE(=x)3139 2671 y FB(4)3177 2704 y FK(\))3227 2635 y Fs(R)3283 2656 y Fq(x)3267 2732 y FB(0)3340 2704 y FE(dt)p FK(\()p FE(t)3488 2671 y FB(4)3526 2704 y FE(=)p FK(\()p FE(e)3648 2671 y Fq(t)3679 2704 y FI(\000)390 2814 y FK(1\)\).)3350 2974 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_debye_5)c Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 3084 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_debye_5_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1790 3084 V 40 w(sf)p 1894 3084 V 40 w(result)f(*)h Ft(result)p Fu(\))390 3194 y FK(These)f(routines)g (compute)g(the)g(\014fth-order)f(Deb)m(y)m(e)j(function)d FE(D)2662 3208 y FB(5)2700 3194 y FK(\()p FE(x)p FK(\))d(=)f(\(5)p FE(=x)3121 3161 y FB(5)3159 3194 y FK(\))3209 3125 y Fs(R)3265 3145 y Fq(x)3249 3221 y FB(0)3322 3194 y FE(dt)p FK(\()p FE(t)3470 3161 y FB(5)3508 3194 y FE(=)p FK(\()p FE(e)3630 3161 y Fq(t)3679 3194 y FI(\000)390 3303 y FK(1\)\).)3350 3464 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_debye_6)c Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 3573 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_debye_6_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1790 3573 V 40 w(sf)p 1894 3573 V 40 w(result)f(*)h Ft(result)p Fu(\))390 3683 y FK(These)26 b(routines)h(compute)g(the)f(sixth-order)h (Deb)m(y)m(e)h(function)e FE(D)2669 3697 y FB(6)2707 3683 y FK(\()p FE(x)p FK(\))g(=)f(\(6)p FE(=x)3128 3650 y FB(6)3166 3683 y FK(\))3216 3614 y Fs(R)3272 3635 y Fq(x)3256 3711 y FB(0)3329 3683 y FE(dt)p FK(\()p FE(t)3477 3650 y FB(6)3514 3683 y FE(=)p FK(\()p FE(e)3636 3650 y Fq(t)3679 3683 y FI(\000)390 3793 y FK(1\)\).)150 4009 y FJ(7.11)68 b(Dilogarithm)150 4169 y FK(The)30 b(functions)g(describ)s 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FE(s)p FK(\))p FE(=s)p FK(.)42 b(Note)32 b(that)g(Im)o(\()p FE(Li)2969 4985 y FB(2)3007 4971 y FK(\()p FE(x)p FK(\)\))27 b(=)f(0)32 b(for)e FE(x)c FI(\024)g FK(1,)390 5081 y(and)k FI(\000)p FE(\031)18 b FK(log)r(\()p FE(x)p FK(\))31 b(for)f FE(x)25 b(>)g FK(1.)390 5208 y(Note)37 b(that)f(Abramo)m(witz)h(&)e(Stegun)h (refer)f(to)i(the)e(Sp)s(ence)g(in)m(tegral)j FE(S)5 b FK(\()p FE(x)p FK(\))34 b(=)g FE(Li)3309 5222 y FB(2)3347 5208 y FK(\(1)24 b FI(\000)g FE(x)p FK(\))36 b(as)390 5317 y(the)31 b(dilogarithm)g(rather)f(than)g FE(Li)1615 5331 y FB(2)1653 5317 y FK(\()p FE(x)p FK(\).)p eop end %%Page: 48 66 TeXDict begin 48 65 bop 150 -116 a FK(Chapter)30 b(7:)41 b(Sp)s(ecial)31 b(F)-8 b(unctions)2348 b(48)150 299 y Fy(7.11.2)63 b(Complex)41 b(Argumen)m(t)3350 557 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_complex_dilog_)q(e)e Fu(\()p FD(double)31 b Ft(r)p FD(,)f(double)g Ft(theta)p FD(,)i(gsl)p 2713 557 28 4 v 41 w(sf)p 2818 557 V 40 w(result)e(*)565 666 y Ft(result_re)p 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Fu(\))390 2004 y FK(This)24 b(function)g(m)m(ultiplies)h FD(x)31 b FK(and)23 b FD(y)32 b FK(storing)25 b(the)g(pro)s(duct)e(and) h(its)h(asso)s(ciated)h(error)e(in)g FD(result)p FK(.)3350 2310 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_multiply_err_e)f Fu(\()p FD(double)30 b Ft(x)p FD(,)h(double)f Ft(dx)p FD(,)h(double)f Ft(y)p FD(,)h(double)565 2420 y Ft(dy)p FD(,)g(gsl)p 837 2420 V 41 w(sf)p 942 2420 V 39 w(result)g(*)g Ft(result)p Fu(\))390 2529 y FK(This)39 b(function)g(m)m(ultiplies)i FD(x)46 b FK(and)39 b FD(y)48 b FK(with)39 b(asso)s(ciated)j(absolute)e (errors)f FD(dx)46 b FK(and)39 b FD(dy)p FK(.)68 b(The)390 2639 y(pro)s(duct)29 b FE(xy)23 b FI(\006)d FE(xy)1042 2566 y Fs(p)p 1125 2566 713 4 v 73 x FK(\()p FE(dx=x)p FK(\))1391 2613 y FB(2)1450 2639 y FK(+)g(\()p FE(dy)s(=y)s FK(\))1799 2613 y FB(2)1867 2639 y FK(is)31 b(stored)f(in)g FD(result)p FK(.)150 2963 y FJ(7.13)68 b(Elliptic)47 b(In)l(tegrals)150 3122 y FK(The)36 b(functions)h(describ)s(ed)f(in)g 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Fq(\036)1553 4418 y FB(0)1649 4345 y FE(dt)1729 4238 y Fs(q)p 1812 4238 V 107 x FK(\(1)21 b FI(\000)f FE(k)2054 4318 y FB(2)2107 4345 y FK(sin)2218 4305 y FB(2)2256 4345 y FK(\()p FE(t)p FK(\)\))1007 4587 y(\005\()p FE(\036;)15 b(k)s(;)g(n)p FK(\))27 b(=)1507 4472 y Fs(Z)1590 4493 y Fq(\036)1553 4661 y FB(0)1649 4587 y FE(dt)2288 4526 y FK(1)p 1739 4566 1144 4 v 1739 4685 a(\(1)21 b(+)f FE(n)15 b FK(sin)2112 4645 y FB(2)2150 4685 y FK(\()p FE(t)p FK(\)\))2288 4583 y Fs(q)p 2372 4583 512 4 v 2372 4685 a FK(1)20 b FI(\000)g FE(k)2578 4659 y FB(2)2631 4685 y FK(sin)2742 4645 y FB(2)2780 4685 y FK(\()p FE(t)p FK(\))150 4925 y(The)30 b(complete)i(Legendre)e (forms)g(are)h(denoted)f(b)m(y)g FE(K)7 b FK(\()p FE(k)s FK(\))26 b(=)f FE(F)13 b FK(\()p FE(\031)s(=)p FK(2)p FE(;)i(k)s FK(\))33 b(and)d FE(E)5 b FK(\()p FE(k)s FK(\))26 b(=)f FE(E)5 b FK(\()p FE(\031)s(=)p FK(2)p FE(;)15 b(k)s FK(\).)275 5121 y(The)33 b(notation)j(used)e(here)g(is)g(based)g(on)g (Carlson,)i FD(Numerisc)m(he)e(Mathematik)42 b FK(33)35 b(\(1979\))i(1)e(and)150 5230 y(di\013ers)e(sligh)m(tly)i(from)e(that)h (used)e(b)m(y)i(Abramo)m(witz)g(&)f(Stegun,)h(where)f(the)h(functions)f (are)h(giv)m(en)g(in)150 5340 y(terms)c(of)h(the)f(parameter)h FE(m)25 b FK(=)g FE(k)1349 5307 y FB(2)1417 5340 y FK(and)30 b FE(n)g FK(is)g(replaced)h(b)m(y)f FI(\000)p FE(n)p FK(.)p eop end %%Page: 49 67 TeXDict begin 49 66 bop 150 -116 a FK(Chapter)30 b(7:)41 b(Sp)s(ecial)31 b(F)-8 b(unctions)2348 b(49)150 299 y Fy(7.13.2)63 b(De\014nition)42 b(of)g(Carlson)f(F)-10 b(orms)150 446 y FK(The)32 b(Carlson)g(symmetric)h(forms)f(of)h (elliptical)i(in)m(tegrals)f FE(R)q(C)7 b FK(\()p FE(x;)15 b(y)s FK(\),)33 b FE(R)q(D)s FK(\()p FE(x;)15 b(y)s(;)g(z)t FK(\),)35 b FE(R)q(F)13 b FK(\()p FE(x;)i(y)s(;)g(z)t FK(\))34 b(and)150 555 y FE(R)q(J)9 b FK(\()p FE(x;)15 b(y)s(;)g(z)t(;)g(p)p FK(\))32 b(are)f(de\014ned)e(b)m(y)-8 b(,)789 821 y FE(R)q(C)7 b FK(\()p FE(x;)15 b(y)s FK(\))26 b(=)f(1)p FE(=)p FK(2)1413 706 y Fs(Z)1497 727 y Fp(1)1460 895 y FB(0)1583 821 y FE(dt)p FK(\()p FE(t)20 b FK(+)g FE(x)p FK(\))1929 784 y Fp(\000)p FB(1)p Fq(=)p FB(2)2086 821 y FK(\()p FE(t)g FK(+)g FE(y)s FK(\))2348 784 y Fp(\000)p FB(1)696 1048 y FE(R)q(D)s FK(\()p FE(x;)15 b(y)s(;)g(z)t FK(\))27 b(=)e(3)p FE(=)p FK(2)1413 933 y Fs(Z)1497 954 y Fp(1)1460 1122 y FB(0)1583 1048 y FE(dt)p FK(\()p FE(t)20 b FK(+)g FE(x)p FK(\))1929 1011 y Fp(\000)p FB(1)p Fq(=)p FB(2)2086 1048 y FK(\()p FE(t)g FK(+)g FE(y)s FK(\))2348 1011 y Fp(\000)p FB(1)p Fq(=)p FB(2)2504 1048 y FK(\()p FE(t)h FK(+)f FE(z)t FK(\))2765 1011 y Fp(\000)p FB(3)p Fq(=)p FB(2)703 1275 y FE(R)q(F)13 b FK(\()p FE(x;)i(y)s(;)g(z)t FK(\))27 b(=)e(1)p FE(=)p FK(2)1413 1160 y Fs(Z)1497 1181 y Fp(1)1460 1349 y FB(0)1583 1275 y FE(dt)p FK(\()p FE(t)20 b FK(+)g FE(x)p FK(\))1929 1238 y Fp(\000)p FB(1)p Fq(=)p FB(2)2086 1275 y FK(\()p FE(t)g FK(+)g FE(y)s FK(\))2348 1238 y Fp(\000)p FB(1)p Fq(=)p FB(2)2504 1275 y FK(\()p FE(t)h FK(+)f FE(z)t FK(\))2765 1238 y Fp(\000)p FB(1)p Fq(=)p FB(2)629 1503 y FE(R)q(J)9 b FK(\()p FE(x;)15 b(y)s(;)g(z)t(;)g(p)p FK(\))27 b(=)e(3)p FE(=)p FK(2)1413 1388 y Fs(Z)1497 1408 y Fp(1)1460 1576 y FB(0)1583 1503 y FE(dt)p FK(\()p FE(t)20 b FK(+)g FE(x)p FK(\))1929 1465 y Fp(\000)p FB(1)p Fq(=)p FB(2)2086 1503 y FK(\()p FE(t)g FK(+)g FE(y)s FK(\))2348 1465 y Fp(\000)p FB(1)p Fq(=)p FB(2)2504 1503 y FK(\()p FE(t)h FK(+)f FE(z)t FK(\))2765 1465 y Fp(\000)p FB(1)p Fq(=)p FB(2)2922 1503 y FK(\()p FE(t)g FK(+)g FE(p)p FK(\))3182 1465 y Fp(\000)p FB(1)150 1793 y Fy(7.13.3)63 b(Legendre)41 b(F)-10 b(orm)42 b(of)g(Complete)f(Elliptic)f(In)m(tegrals)3350 2046 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_ellint_Kcomp)d Fu(\()p FD(double)31 b Ft(k)p FD(,)f(gsl)p 2103 2046 28 4 v 41 w(mo)s(de)p 2359 2046 V 40 w(t)g Ft(mode)p Fu(\))3350 2156 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_ellint_Kcomp_e)f Fu(\()p FD(double)30 b Ft(k)p FD(,)h(gsl)p 2051 2156 V 41 w(mo)s(de)p 2307 2156 V 39 w(t)g Ft(mode)p FD(,)h(gsl)p 2783 2156 V 40 w(sf)p 2887 2156 V 40 w(result)565 2265 y(*)f Ft(result)p Fu(\))390 2375 y FK(These)f(routines)f(compute)h(the)g(complete)i(elliptic)f(in)m (tegral)h FE(K)7 b FK(\()p FE(k)s FK(\))30 b(to)h(the)f(accuracy)h(sp)s (eci\014ed)390 2485 y(b)m(y)f(the)h(mo)s(de)f(v)-5 b(ariable)32 b FD(mo)s(de)p FK(.)41 b(Note)31 b(that)h(Abramo)m(witz)f(&)f(Stegun)h (de\014ne)f(this)g(function)g(in)390 2594 y(terms)g(of)h(the)f (parameter)h FE(m)25 b FK(=)g FE(k)1589 2561 y FB(2)1627 2594 y FK(.)3350 2891 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_ellint_Ecomp)d Fu(\()p FD(double)31 b Ft(k)p FD(,)f(gsl)p 2103 2891 V 41 w(mo)s(de)p 2359 2891 V 40 w(t)g Ft(mode)p Fu(\))3350 3001 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_ellint_Ecomp_e)f Fu(\()p FD(double)30 b Ft(k)p FD(,)h(gsl)p 2051 3001 V 41 w(mo)s(de)p 2307 3001 V 39 w(t)g Ft(mode)p FD(,)h(gsl)p 2783 3001 V 40 w(sf)p 2887 3001 V 40 w(result)565 3110 y(*)f Ft(result)p Fu(\))390 3220 y FK(These)g(routines)f(compute)i(the)f(complete)h (elliptic)g(in)m(tegral)h FE(E)5 b FK(\()p FE(k)s FK(\))32 b(to)g(the)f(accuracy)h(sp)s(eci\014ed)390 3329 y(b)m(y)e(the)h(mo)s (de)f(v)-5 b(ariable)32 b FD(mo)s(de)p FK(.)41 b(Note)31 b(that)h(Abramo)m(witz)f(&)f(Stegun)h(de\014ne)f(this)g(function)g(in) 390 3439 y(terms)g(of)h(the)f(parameter)h FE(m)25 b FK(=)g FE(k)1589 3406 y FB(2)1627 3439 y FK(.)3350 3736 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_ellint_Pcomp)d Fu(\()p FD(double)31 b Ft(k)p FD(,)f(double)g Ft(n)p FD(,)h(gsl)p 2504 3736 V 41 w(mo)s(de)p 2760 3736 V 39 w(t)g Ft(mode)p Fu(\))3350 3845 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_ellint_Pcomp_e)f Fu(\()p FD(double)30 b Ft(k)p FD(,)h(double)f Ft(n)p FD(,)h(gsl)p 2452 3845 V 41 w(mo)s(de)p 2708 3845 V 39 w(t)g Ft(mode)p FD(,)565 3955 y(gsl)p 677 3955 V 41 w(sf)p 782 3955 V 39 w(result)g(*)f Ft(result)p Fu(\))390 4064 y FK(These)22 b(routines)h(compute)g(the)g (complete)h(elliptic)g(in)m(tegral)g(\005\()p FE(k)s(;)15 b(n)p FK(\))24 b(to)f(the)g(accuracy)h(sp)s(eci\014ed)390 4174 y(b)m(y)30 b(the)h(mo)s(de)f(v)-5 b(ariable)32 b FD(mo)s(de)p FK(.)41 b(Note)31 b(that)h(Abramo)m(witz)f(&)f(Stegun)h (de\014ne)f(this)g(function)g(in)390 4284 y(terms)g(of)h(the)f (parameters)h FE(m)25 b FK(=)g FE(k)1625 4251 y FB(2)1693 4284 y FK(and)30 b(sin)1981 4243 y FB(2)2018 4284 y FK(\()p FE(\013)p FK(\))d(=)e FE(k)2319 4251 y FB(2)2356 4284 y FK(,)31 b(with)f(the)h(c)m(hange)g(of)g(sign)f FE(n)25 b FI(!)g(\000)p FE(n)p FK(.)150 4539 y Fy(7.13.4)63 b(Legendre)41 b(F)-10 b(orm)42 b(of)g(Incomplete)f(Elliptic)f(In)m(tegrals)3350 4792 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_ellint_F)c Fu(\()p FD(double)30 b Ft(phi)p FD(,)i(double)e Ft(k)p FD(,)h(gsl)p 2400 4792 V 40 w(mo)s(de)p 2655 4792 V 40 w(t)g Ft(mode)p Fu(\))3350 4902 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_ellint_F_e)e Fu(\()p FD(double)30 b Ft(phi)p FD(,)i(double)e Ft(k)p FD(,)g(gsl)p 2347 4902 V 41 w(mo)s(de)p 2603 4902 V 40 w(t)g Ft(mode)p FD(,)565 5011 y(gsl)p 677 5011 V 41 w(sf)p 782 5011 V 39 w(result)h(*)f Ft(result)p Fu(\))390 5121 y FK(These)25 b(routines)h(compute)g(the)g (incomplete)g(elliptic)i(in)m(tegral)f FE(F)13 b FK(\()p FE(\036;)i(k)s FK(\))27 b(to)f(the)g(accuracy)h(sp)s(eci-)390 5230 y(\014ed)e(b)m(y)g(the)g(mo)s(de)g(v)-5 b(ariable)26 b FD(mo)s(de)p FK(.)39 b(Note)26 b(that)g(Abramo)m(witz)h(&)e(Stegun)g (de\014ne)f(this)h(function)390 5340 y(in)30 b(terms)g(of)h(the)f (parameter)h FE(m)25 b FK(=)g FE(k)1695 5307 y FB(2)1733 5340 y FK(.)p eop end %%Page: 50 68 TeXDict begin 50 67 bop 150 -116 a FK(Chapter)30 b(7:)41 b(Sp)s(ecial)31 b(F)-8 b(unctions)2348 b(50)3350 299 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_ellint_E)c Fu(\()p FD(double)30 b Ft(phi)p FD(,)i(double)e Ft(k)p FD(,)h(gsl)p 2400 299 28 4 v 40 w(mo)s(de)p 2655 299 V 40 w(t)g Ft(mode)p Fu(\))3350 408 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_ellint_E_e)e Fu(\()p FD(double)30 b Ft(phi)p FD(,)i(double)e Ft(k)p FD(,)g(gsl)p 2347 408 V 41 w(mo)s(de)p 2603 408 V 40 w(t)g Ft(mode)p FD(,)565 518 y(gsl)p 677 518 V 41 w(sf)p 782 518 V 39 w(result)h(*)f Ft(result)p Fu(\))390 628 y FK(These)25 b(routines)h(compute)f(the)h (incomplete)h(elliptic)g(in)m(tegral)g FE(E)5 b FK(\()p FE(\036;)15 b(k)s FK(\))27 b(to)f(the)g(accuracy)h(sp)s(eci-)390 737 y(\014ed)e(b)m(y)g(the)g(mo)s(de)g(v)-5 b(ariable)26 b FD(mo)s(de)p FK(.)39 b(Note)26 b(that)g(Abramo)m(witz)h(&)e(Stegun)g (de\014ne)f(this)h(function)390 847 y(in)30 b(terms)g(of)h(the)f (parameter)h FE(m)25 b FK(=)g FE(k)1695 814 y FB(2)1733 847 y FK(.)3350 1101 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_ellint_P)c Fu(\()p FD(double)30 b Ft(phi)p FD(,)i(double)e Ft(k)p FD(,)h(double)f Ft(n)p FD(,)g(gsl)p 2800 1101 V 41 w(mo)s(de)p 3056 1101 V 40 w(t)565 1211 y Ft(mode)p Fu(\))3350 1321 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_ellint_P_e)e Fu(\()p FD(double)30 b Ft(phi)p FD(,)i(double)e Ft(k)p FD(,)g(double)g Ft(n)p FD(,)h(gsl)p 2748 1321 V 41 w(mo)s(de)p 3004 1321 V 39 w(t)565 1430 y Ft(mode)p FD(,)h(gsl)p 942 1430 V 40 w(sf)p 1046 1430 V 40 w(result)e(*)h Ft(result)p Fu(\))390 1540 y FK(These)41 b(routines)h(compute)f(the)h(incomplete)h(elliptic)g(in)m(tegral)g (\005\()p FE(\036;)15 b(k)s(;)g(n)p FK(\))43 b(to)f(the)g(accuracy)390 1649 y(sp)s(eci\014ed)37 b(b)m(y)g(the)h(mo)s(de)f(v)-5 b(ariable)38 b FD(mo)s(de)p FK(.)61 b(Note)39 b(that)f(Abramo)m(witz)g (&)f(Stegun)g(de\014ne)g(this)390 1759 y(function)26 b(in)h(terms)f(of)h(the)f(parameters)h FE(m)e FK(=)g FE(k)2064 1726 y FB(2)2128 1759 y FK(and)h(sin)2413 1719 y FB(2)2450 1759 y FK(\()p FE(\013)p FK(\))h(=)e FE(k)2751 1726 y FB(2)2788 1759 y FK(,)i(with)g(the)g(c)m(hange)g(of)g(sign)390 1868 y FE(n)e FI(!)g(\000)p FE(n)p FK(.)3350 2123 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_ellint_D)c Fu(\()p FD(double)30 b Ft(phi)p FD(,)i(double)e Ft(k)p FD(,)h(gsl)p 2400 2123 V 40 w(mo)s(de)p 2655 2123 V 40 w(t)g Ft(mode)p Fu(\))3350 2233 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_ellint_D_e)e Fu(\()p FD(double)30 b Ft(phi)p FD(,)i(double)e Ft(k)p FD(,)g(gsl)p 2347 2233 V 41 w(mo)s(de)p 2603 2233 V 40 w(t)g Ft(mode)p FD(,)565 2342 y(gsl)p 677 2342 V 41 w(sf)p 782 2342 V 39 w(result)h(*)f Ft(result)p Fu(\))390 2452 y FK(These)43 b(functions)h(compute)g(the)g(incomplete)g (elliptic)i(in)m(tegral)f FE(D)s FK(\()p FE(\036;)15 b(k)s FK(\))45 b(whic)m(h)e(is)h(de\014ned)390 2561 y(through)30 b(the)g(Carlson)g(form)g FE(R)q(D)s FK(\()p FE(x;)15 b(y)s(;)g(z)t FK(\))32 b(b)m(y)e(the)g(follo)m(wing)i(relation,)899 2807 y FE(D)s FK(\()p FE(\036;)15 b(k)s FK(\))27 b(=)1324 2745 y(1)p 1324 2785 46 4 v 1324 2869 a(3)1379 2807 y(\(sin)15 b FE(\036)p FK(\))1630 2769 y FB(3)1668 2807 y FE(R)q(D)s FK(\(1)20 b FI(\000)g FK(sin)2119 2766 y FB(2)2156 2807 y FK(\()p FE(\036)p FK(\))p FE(;)15 b FK(1)22 b FI(\000)e FE(k)2528 2769 y FB(2)2581 2807 y FK(sin)2692 2766 y FB(2)2729 2807 y FK(\()p FE(\036)p FK(\))p FE(;)15 b FK(1\))p FE(:)150 3065 y Fy(7.13.5)63 b(Carlson)41 b(F)-10 b(orms)3350 3297 y FK([F)i(unction])-3599 b Fv(double)54 b(gsl_sf_ellint_RC)c Fu(\()p FD(double)31 b Ft(x)p FD(,)g(double)f Ft(y)p FD(,)g(gsl)p 2347 3297 28 4 v 41 w(mo)s(de)p 2603 3297 V 40 w(t)g Ft(mode)p Fu(\))3350 3406 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_ellint_RC_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(double)f Ft(y)p FD(,)h(gsl)p 2295 3406 V 41 w(mo)s(de)p 2551 3406 V 39 w(t)g Ft(mode)p FD(,)565 3516 y(gsl)p 677 3516 V 41 w(sf)p 782 3516 V 39 w(result)g(*)f Ft(result)p Fu(\))390 3625 y FK(These)44 b(routines)g(compute)g(the)h(incomplete)g(elliptic)h(in)m(tegral)f FE(R)q(C)7 b FK(\()p FE(x;)15 b(y)s FK(\))45 b(to)f(the)h(accuracy)390 3735 y(sp)s(eci\014ed)30 b(b)m(y)g(the)g(mo)s(de)g(v)-5 b(ariable)32 b FD(mo)s(de)p FK(.)3350 3990 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_ellint_RD)c Fu(\()p FD(double)31 b Ft(x)p FD(,)g(double)f Ft(y)p FD(,)g(double)g Ft(z)p FD(,)h(gsl)p 2748 3990 V 41 w(mo)s(de)p 3004 3990 V 39 w(t)565 4099 y Ft(mode)p Fu(\))3350 4209 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_ellint_RD_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(double)f Ft(y)p FD(,)h(double)f Ft(z)p FD(,)h(gsl)p 2696 4209 V 40 w(mo)s(de)p 2951 4209 V 40 w(t)565 4318 y Ft(mode)p FD(,)h(gsl)p 942 4318 V 40 w(sf)p 1046 4318 V 40 w(result)e(*)h Ft(result)p Fu(\))390 4428 y FK(These)k(routines)f(compute)h(the)g(incomplete)h(elliptic)h(in)m (tegral)f FE(R)q(D)s FK(\()p FE(x;)15 b(y)s(;)g(z)t FK(\))36 b(to)g(the)f(accuracy)390 4538 y(sp)s(eci\014ed)30 b(b)m(y)g(the)g(mo)s (de)g(v)-5 b(ariable)32 b FD(mo)s(de)p FK(.)3350 4792 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_ellint_RF)c Fu(\()p FD(double)31 b Ft(x)p FD(,)g(double)f Ft(y)p FD(,)g(double)g Ft(z)p FD(,)h(gsl)p 2748 4792 V 41 w(mo)s(de)p 3004 4792 V 39 w(t)565 4902 y Ft(mode)p Fu(\))3350 5011 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_ellint_RF_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(double)f Ft(y)p FD(,)h(double)f Ft(z)p FD(,)h(gsl)p 2696 5011 V 40 w(mo)s(de)p 2951 5011 V 40 w(t)565 5121 y Ft(mode)p FD(,)h(gsl)p 942 5121 V 40 w(sf)p 1046 5121 V 40 w(result)e(*)h Ft(result)p Fu(\))390 5230 y FK(These)k(routines)h(compute)f(the)h(incomplete)h (elliptic)g(in)m(tegral)g FE(R)q(F)13 b FK(\()p FE(x;)i(y)s(;)g(z)t FK(\))37 b(to)f(the)g(accuracy)390 5340 y(sp)s(eci\014ed)30 b(b)m(y)g(the)g(mo)s(de)g(v)-5 b(ariable)32 b FD(mo)s(de)p FK(.)p eop end %%Page: 51 69 TeXDict begin 51 68 bop 150 -116 a FK(Chapter)30 b(7:)41 b(Sp)s(ecial)31 b(F)-8 b(unctions)2348 b(51)3350 299 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_ellint_RJ)c Fu(\()p FD(double)31 b Ft(x)p FD(,)g(double)f Ft(y)p FD(,)g(double)g Ft(z)p FD(,)h(double)f Ft(p)p FD(,)565 408 y(gsl)p 677 408 28 4 v 41 w(mo)s(de)p 933 408 V 39 w(t)h Ft(mode)p Fu(\))3350 518 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_ellint_RJ_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(double)f Ft(y)p FD(,)h(double)f Ft(z)p FD(,)h(double)f Ft(p)p FD(,)565 628 y(gsl)p 677 628 V 41 w(mo)s(de)p 933 628 V 39 w(t)h Ft(mode)p FD(,)h(gsl)p 1409 628 V 40 w(sf)p 1513 628 V 40 w(result)e(*)h Ft(result)p Fu(\))390 737 y FK(These)d(routines)g(compute)g(the)g(incomplete)i (elliptic)f(in)m(tegral)h FE(R)q(J)9 b FK(\()p FE(x;)15 b(y)s(;)g(z)t(;)g(p)p FK(\))30 b(to)f(the)f(accuracy)390 847 y(sp)s(eci\014ed)i(b)m(y)g(the)g(mo)s(de)g(v)-5 b(ariable)32 b FD(mo)s(de)p FK(.)150 1065 y FJ(7.14)68 b(Elliptic)47 b(F)-11 b(unctions)44 b(\(Jacobi\))150 1225 y FK(The)c(Jacobian)g (Elliptic)i(functions)d(are)i(de\014ned)e(in)h(Abramo)m(witz)h(&)f (Stegun,)i(Chapter)e(16.)70 b(The)150 1334 y(functions)30 b(are)h(declared)g(in)f(the)g(header)g(\014le)h FH(gsl_sf_elljac.h)p FK(.)3350 1498 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_elljac_e)d Fu(\()p FD(double)31 b Ft(u)p FD(,)f(double)g Ft(m)p FD(,)h(double)f(*)h Ft(sn)p FD(,)g(double)f(*)h Ft(cn)p FD(,)565 1608 y(double)f(*)h Ft(dn)p Fu(\))390 1717 y FK(This)25 b(function)g(computes)g(the)h(Jacobian)g(elliptic)g (functions)f FE(sn)p FK(\()p FE(u)p FI(j)p FE(m)p FK(\),)i FE(cn)p 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b(routines)g(compute)h(the)f(Gaussian)h(probabilit)m(y)g (densit)m(y)f(function)390 5340 y FE(Z)7 b FK(\()p FE(x)p FK(\))25 b(=)g(\(1)p FE(=)827 5265 y FI(p)p 904 5265 101 4 v 904 5340 a FK(2)p FE(\031)t FK(\))15 b(exp\()p FI(\000)p FE(x)1352 5307 y FB(2)1390 5340 y FE(=)p FK(2\).)p eop end %%Page: 52 70 TeXDict begin 52 69 bop 150 -116 a FK(Chapter)30 b(7:)41 b(Sp)s(ecial)31 b(F)-8 b(unctions)2348 b(52)3350 299 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_erf_Q)49 b Fu(\()p FD(double)31 b Ft(x)p Fu(\))3350 408 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_erf_Q_e)d Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1685 408 28 4 v 41 w(sf)p 1790 408 V 39 w(result)g(*)f Ft(result)p Fu(\))390 518 y FK(These)j(routines)g(compute)h(the)g(upp)s(er)d(tail)k(of)e(the) h(Gaussian)f(probabilit)m(y)h(function)f FE(Q)p FK(\()p FE(x)p FK(\))e(=)390 628 y(\(1)p FE(=)515 553 y FI(p)p 592 553 101 4 v 592 628 a FK(2)p FE(\031)t FK(\))743 559 y Fs(R)798 579 y Fp(1)782 655 y Fq(x)884 628 y FE(dt)15 b 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FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_hazard_e)d Fu(\()p FD(double)31 b Ft(x)p FD(,)f(gsl)p 1737 1731 28 4 v 41 w(sf)p 1842 1731 V 40 w(result)g(*)h Ft(result)p Fu(\))390 1841 y FK(These)f(routines)g(compute)h(the)g(hazard)f (function)g(for)g(the)h(normal)f(distribution.)150 2089 y FJ(7.16)68 b(Exp)t(onen)l(tial)47 b(F)-11 b(unctions)150 2248 y FK(The)30 b(functions)g(describ)s(ed)f(in)h(this)g(section)i (are)f(declared)g(in)f(the)g(header)g(\014le)h FH(gsl_sf_exp.h)p FK(.)150 2458 y Fy(7.16.1)63 b(Exp)s(onen)m(tial)41 b(F)-10 b(unction)3350 2665 y FK([F)i(unction])-3599 b Fv(double)54 b(gsl_sf_exp)49 b Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 2774 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_exp_e)c Fu(\()p FD(double)31 b Ft(x)p FD(,)f(gsl)p 1580 2774 V 41 w(sf)p 1685 2774 V 40 w(result)g(*)h Ft(result)p Fu(\))390 2884 y FK(These)24 b(routines)g(pro)m(vide)h(an)f(exp)s(onen) m(tial)h(function)f(exp\()p FE(x)p FK(\))h(using)f(GSL)g(seman)m(tics)i (and)d(error)390 2994 y(c)m(hec)m(king.)3350 3199 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_exp_e10_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1790 3199 V 40 w(sf)p 1894 3199 V 40 w(result)p 2157 3199 V 40 w(e10)g(*)g Ft(result)p Fu(\))390 3308 y FK(This)k(function)g(computes)g(the)h(exp) s(onen)m(tial)g(exp\()p FE(x)p FK(\))g(using)f(the)h FH(gsl_sf_result_e10)31 b FK(t)m(yp)s(e)390 3418 y(to)k(return)f(a)h (result)f(with)h(extended)f(range.)54 b(This)34 b(function)g(ma)m(y)h (b)s(e)f(useful)g(if)h(the)g(v)-5 b(alue)35 b(of)390 3527 y(exp\()p FE(x)p FK(\))c(w)m(ould)f(o)m(v)m(er\015o)m(w)i(the)e(n) m(umeric)h(range)f(of)h FH(double)p FK(.)3350 3732 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_exp_mult)c Fu(\()p FD(double)30 b Ft(x)p FD(,)h(double)f Ft(y)p Fu(\))3350 3842 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_exp_mult_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(double)f Ft(y)p FD(,)h(gsl)p 2243 3842 V 40 w(sf)p 2347 3842 V 40 w(result)f(*)h Ft(result)p Fu(\))390 3951 y FK(These)38 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V 39 w(result)g(*)f Ft(result)p Fu(\))390 5230 y FK(These)h(routines)g(compute)g(the)h(quan)m(tit)m(y)g (exp\()p FE(x)p FK(\))22 b FI(\000)e FK(1)32 b(using)e(an)h(algorithm)h (that)g(is)f(accurate)390 5340 y(for)f(small)h FE(x)p FK(.)p eop end %%Page: 53 71 TeXDict begin 53 70 bop 150 -116 a FK(Chapter)30 b(7:)41 b(Sp)s(ecial)31 b(F)-8 b(unctions)2348 b(53)3350 299 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_exprel)c Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 408 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_exprel_e)d Fu(\()p FD(double)31 b Ft(x)p FD(,)f(gsl)p 1737 408 28 4 v 41 w(sf)p 1842 408 V 40 w(result)g(*)h Ft(result)p Fu(\))390 518 y FK(These)d(routines)g(compute)h(the)f(quan)m(tit)m(y)i(\(exp\()p FE(x)p FK(\))17 b FI(\000)e FK(1\))p FE(=x)30 b FK(using)d(an)i (algorithm)g(that)g(is)f(accu-)390 628 y(rate)d(for)f(small)h FE(x)p FK(.)38 b(F)-8 b(or)25 b(small)g FE(x)f FK(the)g(algorithm)h(is) f(based)g(on)g(the)h(expansion)f(\(exp\()p FE(x)p FK(\))8 b FI(\000)g FK(1\))p 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FE(N)10 b FK(!)p FE(=x)1569 2224 y Fq(N)1648 2118 y Fs( )1714 2262 y FK(exp\()p FE(x)p FK(\))21 b FI(\000)2086 2156 y Fq(N)6 b Fp(\000)p FB(1)2098 2181 y Fs(X)2098 2359 y Fq(k)q FB(=0)2245 2262 y FE(x)2297 2224 y Fq(k)2338 2262 y FE(=k)s FK(!)2458 2118 y Fs(!)1268 2479 y FK(=)25 b(1)c(+)f FE(x=)p FK(\()p FE(N)31 b FK(+)20 b(1\))h(+)f FE(x)2092 2442 y FB(2)2129 2479 y FE(=)p FK(\(\()p FE(N)31 b FK(+)20 b(1\)\()p FE(N)31 b FK(+)20 b(2\)\))i(+)e FE(:)15 b(:)g(:)1268 2614 y FK(=)1364 2628 y FB(1)1402 2614 y FE(F)1460 2628 y FB(1)1497 2614 y FK(\(1)p FE(;)g FK(1)22 b(+)e FE(N)5 b(;)15 b(x)p FK(\))150 2815 y Fy(7.16.3)63 b(Exp)s(onen)m(tiation)41 b(With)g(Error)g(Estimate)3350 3020 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_exp_err_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(double)f Ft(dx)p FD(,)h(gsl)p 2243 3020 V 40 w(sf)p 2347 3020 V 40 w(result)f(*)h Ft(result)p Fu(\))390 3129 y FK(This)f(function)g(exp)s(onen)m(tiates)h FD(x)37 b FK(with)30 b(an)g(asso)s(ciated)i(absolute)f(error)f 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y(absolute)c(errors)f FD(dx)p FK(,)g FD(dy)p FK(.)3350 4388 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_exp_mult_err_e)q (10_e)f Fu(\()p FD(double)31 b Ft(x)p FD(,)f(double)g Ft(dx)p FD(,)h(double)f Ft(y)p FD(,)565 4498 y(double)g Ft(dy)p FD(,)h(gsl)p 1130 4498 V 41 w(sf)p 1235 4498 V 39 w(result)p 1497 4498 V 40 w(e10)h(*)f Ft(result)p Fu(\))390 4607 y FK(This)k(routine)h(computes)g(the)g(pro)s(duct)f FE(y)18 b FK(exp\()p FE(x)p FK(\))36 b(for)g(the)g(quan)m(tities)h FD(x)p FK(,)g FD(y)44 b FK(with)35 b(asso)s(ciated)390 4717 y(absolute)41 b(errors)e FD(dx)p FK(,)j FD(dy)47 b FK(using)39 b(the)h FH(gsl_sf_result_e10)35 b FK(t)m(yp)s(e)40 b(to)h(return)d(a)j(result)e(with)390 4826 y(extended)30 b(range.)150 5071 y FJ(7.17)68 b(Exp)t(onen)l(tial)47 b(In)l(tegrals)150 5230 y FK(Information)34 b(on)g(the)g(exp)s(onen)m (tial)g(in)m(tegrals)i(can)e(b)s(e)f(found)g(in)g(Abramo)m(witz)i(&)f (Stegun,)h(Chapter)150 5340 y(5.)41 b(These)30 b(functions)g(are)h (declared)g(in)f(the)g(header)h(\014le)f FH(gsl_sf_expint.h)p FK(.)p eop end %%Page: 54 72 TeXDict begin 54 71 bop 150 -116 a FK(Chapter)30 b(7:)41 b(Sp)s(ecial)31 b(F)-8 b(unctions)2348 b(54)150 299 y Fy(7.17.1)63 b(Exp)s(onen)m(tial)41 b(In)m(tegral)3350 504 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_expint_E1)c Fu(\()p FD(double)31 b Ft(x)p Fu(\))3350 613 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_expint_E1_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1894 613 28 4 v 41 w(sf)p 1999 613 V 39 w(result)g(*)g Ft(result)p Fu(\))390 723 y FK(These)f(routines)g(compute)h(the)g(exp)s(onen)m(tial)g(in)m (tegral)h FE(E)2413 737 y FB(1)2450 723 y FK(\()p FE(x)p FK(\),)1336 940 y FE(E)1403 954 y FB(1)1440 940 y FK(\()p FE(x)p FK(\))26 b(:=)f(Re)1832 825 y Fs(Z)1915 846 y Fp(1)1878 1014 y FB(1)2000 940 y FE(dt)15 b FK(exp\()p FI(\000)p FE(xt)p FK(\))p FE(=t:)3350 1191 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_expint_E2)c Fu(\()p FD(double)31 b Ft(x)p Fu(\))3350 1300 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_expint_E2_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1894 1300 V 41 w(sf)p 1999 1300 V 39 w(result)g(*)g Ft(result)p Fu(\))390 1410 y FK(These)f(routines)g(compute)h(the)g(second-order)f(exp)s(onen)m (tial)h(in)m(tegral)h FE(E)2944 1424 y FB(2)2982 1410 y FK(\()p FE(x)p FK(\),)1317 1627 y FE(E)1384 1641 y FB(2)1422 1627 y FK(\()p FE(x)p FK(\))25 b(:=)h(Re)1813 1512 y Fs(Z)1896 1533 y Fp(1)1859 1701 y FB(1)1982 1627 y FE(dt)15 b FK(exp\()p FI(\000)p FE(xt)p FK(\))p FE(=t)2520 1590 y FB(2)2558 1627 y FE(:)3350 1877 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_expint_En)c Fu(\()p FD(in)m(t)32 b Ft(n)p FD(,)f(double)e Ft(x)p Fu(\))3350 1987 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_expint_En_e)e Fu(\()p FD(in)m(t)31 b Ft(n)p FD(,)g(double)f Ft(x)p FD(,)h(gsl)p 2141 1987 V 41 w(sf)p 2246 1987 V 39 w(result)g(*)f Ft(result)p Fu(\))390 2097 y FK(These)g(routines)g(compute)h(the)g(exp)s(onen)m (tial)g(in)m(tegral)h FE(E)2413 2111 y Fq(n)2458 2097 y FK(\()p FE(x)p FK(\))f(of)g(order)f FE(n)p FK(,)1309 2314 y FE(E)1376 2328 y Fq(n)1422 2314 y FK(\()p FE(x)p FK(\))25 b(:=)h(Re)1813 2199 y Fs(Z)1896 2220 y Fp(1)1859 2388 y FB(1)1982 2314 y FE(dt)15 b FK(exp\()p FI(\000)p FE(xt)p FK(\))p FE(=t)2520 2277 y Fq(n)2566 2314 y FE(:)150 2563 y Fy(7.17.2)63 b(Ei\(x\))3350 2768 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_expint_Ei)c Fu(\()p FD(double)31 b Ft(x)p Fu(\))3350 2877 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_expint_Ei_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1894 2877 V 41 w(sf)p 1999 2877 V 39 w(result)g(*)g Ft(result)p Fu(\))390 2987 y FK(These)f(routines)g (compute)h(the)g(exp)s(onen)m(tial)g(in)m(tegral)h(Ei\()p FE(x)p FK(\),)1268 3207 y(Ei\()p FE(x)p FK(\))26 b(:=)f FI(\000)p FE(P)13 b(V)1854 3088 y Fs(\022)1916 3092 y(Z)1999 3113 y Fp(1)1962 3281 y(\000)p Fq(x)2084 3207 y FE(dt)i FK(exp\()p FI(\000)p FE(t)p FK(\))p FE(=t)2570 3088 y Fs(\023)390 3426 y FK(where)30 b FE(P)13 b(V)50 b FK(denotes)31 b(the)g(principal)f(v)-5 b(alue)31 b(of)f(the)h(in)m(tegral.)150 3633 y Fy(7.17.3)63 b(Hyp)s(erb)s(olic)42 b(In)m(tegrals)3350 3838 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_Shi)49 b Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 3948 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_Shi_e)c Fu(\()p FD(double)31 b Ft(x)p FD(,)f(gsl)p 1580 3948 V 41 w(sf)p 1685 3948 V 40 w(result)g(*)h Ft(result)p Fu(\))390 4057 y FK(These)f(routines)g(compute)h(the)g(in)m(tegral)h(Shi)o(\()p FE(x)p FK(\))26 b(=)2229 3989 y Fs(R)2284 4009 y Fq(x)2268 4085 y FB(0)2341 4057 y FE(dt)15 b FK(sinh\()p FE(t)p FK(\))p FE(=t)p FK(.)3350 4258 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_Chi)49 b Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 4368 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_Chi_e)c Fu(\()p FD(double)31 b Ft(x)p FD(,)f(gsl)p 1580 4368 V 41 w(sf)p 1685 4368 V 40 w(result)g(*)h Ft(result)p Fu(\))390 4477 y FK(These)d(routines)f(compute)i(the)f(in)m (tegral)h(Chi\()p FE(x)p FK(\))d(:=)f(Re[)p FE(\015)2436 4491 y Fq(E)2508 4477 y FK(+)15 b(log)s(\()p FE(x)p FK(\))g(+)2936 4408 y Fs(R)2991 4429 y Fq(x)2975 4505 y FB(0)3048 4477 y FE(dt)p FK(\(cosh)q(\()p FE(t)p FK(\))g FI(\000)g FK(1\))p FE(=t)p FK(],)390 4587 y(where)30 b FE(\015)700 4601 y Fq(E)786 4587 y FK(is)h(the)f(Euler)g(constan)m(t)i(\(a)m(v)-5 b(ailable)33 b(as)e(the)f(macro)h FH(M_EULER)p FK(\).)150 4794 y Fy(7.17.4)63 b(Ei)p 649 4794 37 5 v 54 w(3\(x\))3350 4999 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_expint_3)c Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 5108 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_expint_3_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1842 5108 28 4 v 41 w(sf)p 1947 5108 V 39 w(result)f(*)h Ft(result)p Fu(\))390 5218 y FK(These)g(routines)h(compute)g(the)f(third-order)g(exp)s(onen)m (tial)i(in)m(tegral)g(Ei)2907 5232 y FB(3)2944 5218 y FK(\()p FE(x)p FK(\))28 b(=)3192 5149 y Fs(R)3247 5170 y Fq(x)3231 5246 y FB(0)3304 5218 y FE(dt)15 b FK(exp)q(\()p FI(\000)p FE(t)3678 5185 y FB(3)3715 5218 y FK(\))390 5328 y(for)30 b FE(x)25 b FI(\025)g FK(0.)p eop end %%Page: 55 73 TeXDict begin 55 72 bop 150 -116 a FK(Chapter)30 b(7:)41 b(Sp)s(ecial)31 b(F)-8 b(unctions)2348 b(55)150 299 y Fy(7.17.5)63 b(T)-10 b(rigonometric)42 b(In)m(tegrals)3350 498 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_Si)48 b Fu(\()p FD(const)32 b(double)d Ft(x)p Fu(\))3350 608 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_Si_e)c Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1528 608 28 4 v 41 w(sf)p 1633 608 V 39 w(result)g(*)f Ft(result)p Fu(\))390 717 y FK(These)g(routines)g(compute)h(the)g(Sine)f(in)m (tegral)i(Si)o(\()p FE(x)p FK(\))26 b(=)2375 649 y Fs(R)2431 669 y Fq(x)2414 745 y FB(0)2488 717 y FE(dt)15 b FK(sin)o(\()p FE(t)p FK(\))p FE(=t)p FK(.)3350 907 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_Ci)48 b Fu(\()p FD(const)32 b(double)d Ft(x)p Fu(\))3350 1017 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_Ci_e)c Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1528 1017 V 41 w(sf)p 1633 1017 V 39 w(result)g(*)f Ft(result)p Fu(\))390 1126 y FK(These)g(routines)g(compute)h(the)g (Cosine)f(in)m(tegral)i(Ci\()p FE(x)p FK(\))26 b(=)f FI(\000)2573 1057 y Fs(R)2628 1078 y Fp(1)2612 1154 y Fq(x)2714 1126 y FE(dt)15 b FK(cos)q(\()p FE(t)p FK(\))p FE(=t)31 b FK(for)f FE(x)25 b(>)g FK(0.)150 1328 y Fy(7.17.6)63 b(Arctangen)m(t)40 b(In)m(tegral)3350 1528 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_atanint)c Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 1637 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_atanint_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1790 1637 V 40 w(sf)p 1894 1637 V 40 w(result)f(*)h Ft(result)p Fu(\))390 1747 y FK(These)37 b(routines)g(compute)h(the)f(Arctangen)m(t)i(in)m(tegral,)i(whic)m(h)d (is)f(de\014ned)f(as)i(A)m(tanIn)m(t)q(\()p FE(x)p FK(\))f(=)390 1788 y Fs(R)445 1808 y Fq(x)429 1884 y FB(0)502 1856 y FE(dt)15 b FK(arctan)q(\()p FE(t)p FK(\))p FE(=t)p FK(.)150 2093 y FJ(7.18)68 b(F)-11 b(ermi-Dirac)46 b(F)-11 b(unction)150 2252 y FK(The)46 b(functions)h(describ)s(ed)f(in)g(this)h (section)h(are)g(declared)f(in)g(the)g(header)g(\014le)g FH(gsl_sf_fermi_)150 2362 y(dirac.h)p FK(.)150 2564 y Fy(7.18.1)63 b(Complete)41 b(F)-10 b(ermi-Dirac)41 b(In)m(tegrals)150 2711 y FK(The)30 b(complete)i(F)-8 b(ermi-Dirac)32 b(in)m(tegral)g FE(F)1615 2725 y Fq(j)1651 2711 y FK(\()p FE(x)p FK(\))f(is)f(giv)m(en) i(b)m(y)-8 b(,)1137 2939 y FE(F)1195 2953 y Fq(j)1231 2939 y FK(\()p FE(x)p FK(\))25 b(:=)1650 2877 y(1)p 1510 2918 327 4 v 1510 3001 a(\000\()p FE(j)h FK(+)20 b(1\))1862 2824 y Fs(Z)1945 2844 y Fp(1)1908 3012 y FB(0)2030 2939 y FE(dt)2403 2877 y(t)2436 2844 y Fq(j)p 2120 2918 633 4 v 2120 3001 a FK(\(exp\()p FE(t)h FI(\000)f FE(x)p FK(\))g(+)g(1\))150 3157 y(Note)36 b(that)g(the)f(F)-8 b(ermi-Dirac)37 b(in)m(tegral)f(is)f(sometimes)h(de\014ned)d(without)i (the)g(normalisation)h(factor)150 3266 y(in)30 b(other)h(texts.)3350 3456 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_fermi_dirac_m1)e Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 3566 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_fermi_dirac_m1)q(_e)f Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 2156 3566 28 4 v 40 w(sf)p 2260 3566 V 40 w(result)f(*)h Ft(result)p Fu(\))390 3675 y FK(These)c(routines)f(compute)i(the)f(complete)h(F)-8 b(ermi-Dirac)29 b(in)m(tegral)g(with)e(an)f(index)h(of)g FI(\000)p FK(1.)40 b(This)390 3785 y(in)m(tegral)32 b(is)e(giv)m(en)i (b)m(y)e FE(F)1234 3799 y Fp(\000)p FB(1)1324 3785 y FK(\()p FE(x)p FK(\))c(=)f FE(e)1610 3752 y Fq(x)1652 3785 y FE(=)p FK(\(1)c(+)f FE(e)1931 3752 y Fq(x)1973 3785 y FK(\).)3350 3974 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_fermi_dirac_0)e Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 4084 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_fermi_dirac_0_)q(e)e Fu(\()p FD(double)31 b Ft(x)p FD(,)f(gsl)p 2103 4084 V 41 w(sf)p 2208 4084 V 40 w(result)g(*)h Ft(result)p Fu(\))390 4194 y FK(These)h(routines)h (compute)g(the)g(complete)h(F)-8 b(ermi-Dirac)35 b(in)m(tegral)f(with)e (an)h(index)f(of)h(0.)48 b(This)390 4303 y(in)m(tegral)32 b(is)e(giv)m(en)i(b)m(y)e FE(F)1234 4317 y FB(0)1272 4303 y FK(\()p FE(x)p FK(\))c(=)f(ln)o(\(1)c(+)f FE(e)1825 4270 y Fq(x)1867 4303 y FK(\).)3350 4493 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_fermi_dirac_1)e Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 4602 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_fermi_dirac_1_)q(e)e Fu(\()p FD(double)31 b Ft(x)p FD(,)f(gsl)p 2103 4602 V 41 w(sf)p 2208 4602 V 40 w(result)g(*)h Ft(result)p Fu(\))390 4712 y FK(These)22 b(routines)g(compute)h(the)f(complete)i(F)-8 b(ermi-Dirac)25 b(in)m(tegral)f(with)e(an)g(index)g(of)g(1,)j FE(F)3494 4726 y FB(1)3531 4712 y FK(\()p FE(x)p FK(\))h(=)390 4753 y Fs(R)445 4773 y Fp(1)429 4849 y FB(0)531 4822 y FE(dt)p FK(\()p FE(t=)p FK(\(exp)q(\()p FE(t)20 b FI(\000)g FE(x)p FK(\))h(+)f(1\)\).)3350 5011 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_fermi_dirac_2)e Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 5121 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_fermi_dirac_2_)q(e)e Fu(\()p FD(double)31 b Ft(x)p FD(,)f(gsl)p 2103 5121 V 41 w(sf)p 2208 5121 V 40 w(result)g(*)h Ft(result)p Fu(\))390 5230 y FK(These)22 b(routines)g(compute)h(the)f(complete)i(F)-8 b(ermi-Dirac)25 b(in)m(tegral)f(with)e(an)g(index)g(of)g(2,)j FE(F)3494 5244 y FB(2)3531 5230 y FK(\()p FE(x)p FK(\))h(=)390 5340 y(\(1)p FE(=)p FK(2\))610 5271 y Fs(R)668 5292 y Fp(1)651 5368 y FB(0)753 5340 y FE(dt)p FK(\()p FE(t)901 5307 y FB(2)939 5340 y FE(=)p FK(\(exp\()p FE(t)21 b FI(\000)f FE(x)p FK(\))g(+)g(1\)\).)p eop end %%Page: 56 74 TeXDict begin 56 73 bop 150 -116 a FK(Chapter)30 b(7:)41 b(Sp)s(ecial)31 b(F)-8 b(unctions)2348 b(56)3350 299 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_fermi_dirac_int)e Fu(\()p FD(in)m(t)31 b Ft(j)p FD(,)g(double)f Ft(x)p Fu(\))3350 408 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_fermi_dirac_in)q(t_e)f Fu(\()p FD(in)m(t)31 b Ft(j)p FD(,)g(double)f Ft(x)p FD(,)h(gsl)p 2455 408 28 4 v 40 w(sf)p 2559 408 V 40 w(result)f(*)565 518 y Ft(result)p Fu(\))390 628 y FK(These)35 b(routines)f(compute)i(the)f (complete)h(F)-8 b(ermi-Dirac)37 b(in)m(tegral)g(with)d(an)h(in)m (teger)h(index)f(of)390 737 y FE(j)5 b FK(,)31 b FE(F)546 751 y Fq(j)582 737 y FK(\()p FE(x)p FK(\))26 b(=)f(\(1)p FE(=)p FK(\000\()p FE(j)i FK(+)20 b(1\)\))1328 668 y Fs(R)1384 689 y Fp(1)1368 765 y FB(0)1470 737 y FE(dt)p FK(\()p FE(t)1618 704 y Fq(j)1653 737 y FE(=)p FK(\(exp)q(\()p FE(t)g FI(\000)g FE(x)p FK(\))h(+)f(1\)\).)3350 912 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_fermi_dirac_mha)q(lf)e Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 1021 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_fermi_dirac_mh)q(alf_)q(e)f Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 2313 1021 V 40 w(sf)p 2417 1021 V 40 w(result)f(*)h Ft(result)p Fu(\))390 1131 y FK(These)f(routines)g(compute)h(the)g(complete)g(F)-8 b(ermi-Dirac)33 b(in)m(tegral)f FE(F)2806 1145 y Fp(\000)p FB(1)p Fq(=)p FB(2)2963 1131 y FK(\()p FE(x)p FK(\).)3350 1305 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_fermi_dirac_hal)q (f)e Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 1415 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_fermi_dirac_ha)q(lf_e)f Fu(\()p FD(double)31 b Ft(x)p FD(,)f(gsl)p 2260 1415 V 41 w(sf)p 2365 1415 V 40 w(result)g(*)h Ft(result)p Fu(\))390 1525 y FK(These)f(routines)g(compute)h(the)g(complete)g(F)-8 b(ermi-Dirac)33 b(in)m(tegral)f FE(F)2806 1539 y FB(1)p Fq(=)p FB(2)2911 1525 y FK(\()p FE(x)p FK(\).)3350 1699 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_fermi_dirac_3ha)q(lf)e Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 1809 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_fermi_dirac_3h)q(alf_)q(e)f Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 2313 1809 V 40 w(sf)p 2417 1809 V 40 w(result)f(*)h Ft(result)p Fu(\))390 1918 y FK(These)f(routines)g(compute)h(the)g(complete)g(F)-8 b(ermi-Dirac)33 b(in)m(tegral)f FE(F)2806 1932 y FB(3)p Fq(=)p FB(2)2911 1918 y FK(\()p FE(x)p FK(\).)150 2111 y Fy(7.18.2)63 b(Incomplete)41 b(F)-10 b(ermi-Dirac)41 b(In)m(tegrals)150 2258 y FK(The)30 b(incomplete)h(F)-8 b(ermi-Dirac)33 b(in)m(tegral)f FE(F)1691 2272 y Fq(j)1727 2258 y FK(\()p FE(x;)15 b(b)p FK(\))31 b(is)f(giv)m(en)i(b)m(y)-8 b(,)1097 2480 y FE(F)1155 2494 y Fq(j)1191 2480 y FK(\()p FE(x;)15 b(b)p FK(\))26 b(:=)1690 2418 y(1)p 1549 2459 327 4 v 1549 2542 a(\000\()p FE(j)g FK(+)20 b(1\))1901 2365 y Fs(Z)1984 2385 y Fp(1)1947 2553 y Fq(b)2070 2480 y FE(dt)2442 2418 y(t)2475 2385 y Fq(j)p 2160 2459 633 4 v 2160 2542 a FK(\(exp\()p FE(t)g FI(\000)g FE(x)p FK(\))h(+)f(1\))3350 2719 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_fermi_dirac_inc)q(_0)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(double)f Ft(b)p Fu(\))3350 2828 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_fermi_dirac_in)q (c_0_)q(e)f Fu(\()p FD(double)30 b Ft(x)p FD(,)h(double)f Ft(b)p FD(,)g(gsl)p 2713 2828 28 4 v 41 w(sf)p 2818 2828 V 40 w(result)g(*)565 2938 y Ft(result)p Fu(\))390 3047 y FK(These)35 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FB(0)1893 4302 y FE(dt)15 b(t)2021 4265 y Fq(x)p Fp(\000)p FB(1)2163 4302 y FK(exp\()p FI(\000)p FE(t)p FK(\))150 4508 y(It)39 b(is)g(related)g(to)h(the)e(factorial)j (function)d(b)m(y)h(\000\()p FE(n)p FK(\))g(=)g(\()p FE(n)26 b FI(\000)f FK(1\)!)40 b(for)e(p)s(ositiv)m(e)i(in)m(teger)g FE(n)p FK(.)65 b(F)-8 b(urther)150 4618 y(information)31 b(on)f(the)h(Gamma)g(function)f(can)g(b)s(e)g(found)f(in)h(Abramo)m (witz)i(&)e(Stegun,)g(Chapter)g(6.)3350 4792 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_gamma)49 b Fu(\()p FD(double)31 b Ft(x)p Fu(\))3350 4902 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_gamma_e)d Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1685 4902 V 41 w(sf)p 1790 4902 V 39 w(result)g(*)f Ft(result)p Fu(\))390 5011 y FK(These)e(routines)f (compute)h(the)g(Gamma)h(function)e(\000\()p FE(x)p FK(\),)i(sub)5 b(ject)28 b(to)g FE(x)g FK(not)g(b)s(eing)g(a)g(negativ)m(e)390 5121 y(in)m(teger)46 b(or)f(zero.)84 b(The)44 b(function)g(is)h (computed)f(using)g(the)h(real)g(Lanczos)h(metho)s(d.)82 b(The)390 5230 y(maxim)m(um)40 b(v)-5 b(alue)40 b(of)g FE(x)g FK(suc)m(h)g(that)g(\000\()p FE(x)p FK(\))h(is)f(not)g (considered)g(an)g(o)m(v)m(er\015o)m(w)h(is)f(giv)m(en)h(b)m(y)f(the) 390 5340 y(macro)31 b FH(GSL_SF_GAMMA_XMAX)26 b FK(and)j(is)i(171.0.)p eop end %%Page: 57 75 TeXDict begin 57 74 bop 150 -116 a FK(Chapter)30 b(7:)41 b(Sp)s(ecial)31 b(F)-8 b(unctions)2348 b(57)3350 299 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_lngamma)c Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 408 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_lngamma_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1790 408 28 4 v 40 w(sf)p 1894 408 V 40 w(result)f(*)h Ft(result)p Fu(\))390 518 y FK(These)f(routines)h(compute)g(the)f(logarithm)i(of)f(the)g (Gamma)g(function,)f(log)s(\(\000\()p FE(x)p FK(\)\),)i(sub)5 b(ject)30 b(to)390 628 y FE(x)24 b FK(not)f(b)s(eing)h(a)g(negativ)m(e) i(in)m(teger)f(or)e(zero.)40 b(F)-8 b(or)24 b FE(x)h(<)g 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h(\000\()p FE(x)p FK(\))28 b(=)g FE(sg)s(n)21 b FI(\003)g FK(exp\()p FE(r)s(esul)r(t)p 2775 1658 V 40 w(l)r(g)s FK(\),)33 b(taking)g(in)m(to)f(accoun)m(t)390 1767 y(the)f(t)m(w)m(o)g (comp)s(onen)m(ts)g(of)f FD(result)p 1551 1767 V 40 w(lg)p FK(.)3350 2030 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_gammastar)c Fu(\()p FD(double)31 b Ft(x)p Fu(\))3350 2139 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_gammastar_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1894 2139 V 41 w(sf)p 1999 2139 V 39 w(result)g(*)g Ft(result)p Fu(\))390 2249 y FK(These)h(routines)h(compute)g(the)g(regulated)h (Gamma)f(F)-8 b(unction)33 b(\000)2724 2216 y Fp(\003)2762 2249 y FK(\()p FE(x)p FK(\))h(for)e FE(x)d(>)g FK(0.)49 b(The)32 b(regu-)390 2359 y(lated)f(gamma)g(function)g(is)f(giv)m(en)h (b)m(y)-8 b(,)1202 2570 y(\000)1259 2532 y Fp(\003)1297 2570 y FK(\()p FE(x)p FK(\))26 b(=)e(\000\()p FE(x)p FK(\))p FE(=)p FK(\()1799 2490 y FI(p)p 1877 2490 101 4 v 1877 2570 a FK(2)p FE(\031)s(x)2029 2532 y FB(\()p Fq(x)p Fp(\000)p FB(1)p Fq(=)p FB(2\))2290 2570 y FK(exp\()p FI(\000)p FE(x)p FK(\)\))1445 2758 y(=)1540 2639 y Fs(\022)1602 2758 y FK(1)c(+)1817 2696 y(1)p 1768 2737 143 4 v 1768 2820 a(12)p FE(x)1941 2758 y FK(+)g FE(:::)2107 2639 y Fs(\023)2275 2758 y FK(for)30 b FE(x)25 b FI(!)g(1)390 3004 y FK(and)30 b(is)g(a)h(useful)f(suggestion)h(of)f(T)-8 b(emme.)3350 3267 y([F)g(unction])-3599 b Fv(double)54 b(gsl_sf_gammainv)c Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 3377 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_gammainv_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1842 3377 28 4 v 41 w(sf)p 1947 3377 V 39 w(result)f(*)h Ft(result)p Fu(\))390 3486 y FK(These)f(routines)h(compute)g(the)g(recipro)s(cal)g (of)g(the)g(gamma)h(function,)e(1)p FE(=)p FK(\000\()p FE(x)p FK(\))i(using)e(the)h(real)390 3596 y(Lanczos)g(metho)s(d.)3350 3859 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_lngamma_comple)q (x_e)f Fu(\()p FD(double)30 b Ft(zr)p FD(,)h(double)f Ft(zi)p FD(,)h(gsl)p 2713 3859 V 41 w(sf)p 2818 3859 V 40 w(result)f(*)565 3968 y Ft(lnr)p FD(,)i(gsl)p 890 3968 V 40 w(sf)p 994 3968 V 40 w(result)e(*)h Ft(arg)p Fu(\))390 4078 y FK(This)26 b(routine)g(computes)h(log)r(\(\000\()p FE(z)t FK(\)\))h(for)f(complex)g FE(z)i FK(=)c FE(z)2389 4092 y Fq(r)2439 4078 y FK(+)12 b FE(iz)2595 4092 y Fq(i)2650 4078 y FK(and)25 b FE(z)31 b FK(not)c(a)g(negativ)m(e)i(in)m(teger)390 4187 y(or)42 b(zero,)j(using)c(the)h(complex)g(Lanczos)h(metho)s(d.)74 b(The)41 b(returned)f(parameters)i(are)g FE(l)r(nr)k FK(=)390 4297 y(log)18 b FI(j)p FK(\000\()p FE(z)t FK(\))p FI(j)30 b FK(and)f FE(ar)s(g)f FK(=)d(arg)q(\(\000\()p FE(z)t FK(\)\))30 b(in)f(\()p FI(\000)p FE(\031)s(;)15 b(\031)s FK(].)41 b(Note)31 b(that)f(the)f(phase)g(part)g(\()p FD(arg)8 b FK(\))30 b(is)f(not)h(w)m(ell-)390 4407 y(determined)d(when) f FI(j)p FE(z)t FI(j)i FK(is)g(v)m(ery)f(large,)j(due)c(to)i (inevitable)h(roundo\013)d(in)h(restricting)i(to)f(\()p FI(\000)p FE(\031)s(;)15 b(\031)s FK(].)390 4516 y(This)31 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FK(\)\).)p eop end %%Page: 59 77 TeXDict begin 59 76 bop 150 -116 a FK(Chapter)30 b(7:)41 b(Sp)s(ecial)31 b(F)-8 b(unctions)2348 b(59)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_lnpoch_sgn_e)e Fu(\()p FD(double)31 b Ft(a)p FD(,)g(double)f Ft(x)p FD(,)g(gsl)p 2347 299 28 4 v 41 w(sf)p 2452 299 V 40 w(result)g(*)h Ft(result)p FD(,)565 408 y(double)f(*)h Ft(sgn)p Fu(\))390 518 y FK(These)d(routines)f(compute)h(the)g(sign)g (of)g(the)g(P)m(o)s(c)m(hhammer)g(sym)m(b)s(ol)g(and)f(the)h(logarithm) h(of)f(its)390 628 y(magnitude.)45 b(The)31 b(computed)g(parameters)h (are)g FE(r)s(esul)r(t)27 b FK(=)g(log)r(\()p FI(j)p FK(\()p FE(a)p FK(\))2775 642 y Fq(x)2818 628 y FI(j)p FK(\))33 b(with)e(a)h(corresp)s(onding)390 737 y(error)e(term,)h(and)e FE(sg)s(n)c FK(=)g(sgn\(\()p FE(a)p FK(\))1582 751 y Fq(x)1625 737 y FK(\))31 b(where)f(\()p FE(a)p FK(\))2072 751 y Fq(x)2140 737 y FK(=)24 b(\000\()p FE(a)d FK(+)f FE(x)p FK(\))p FE(=)p FK(\000\()p FE(a)p FK(\).)3350 925 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_pochrel)c Fu(\()p FD(double)30 b Ft(a)p FD(,)h(double)f Ft(x)p Fu(\))3350 1034 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_pochrel_e)e Fu(\()p FD(double)30 b Ft(a)p FD(,)h(double)f Ft(x)p FD(,)g(gsl)p 2190 1034 V 41 w(sf)p 2295 1034 V 40 w(result)g(*)h Ft(result)p Fu(\))390 1144 y FK(These)f(routines)h (compute)g(the)g(relativ)m(e)h(P)m(o)s(c)m(hhammer)f(sym)m(b)s(ol)g (\(\()p FE(a)p FK(\))2867 1158 y Fq(x)2930 1144 y FI(\000)20 b FK(1\))p FE(=x)32 b FK(where)e(\()p FE(a)p FK(\))3611 1158 y Fq(x)3679 1144 y FK(=)390 1253 y(\000\()p FE(a)20 b FK(+)g FE(x)p FK(\))p FE(=)p FK(\000\()p FE(a)p FK(\).)150 1454 y Fy(7.19.4)63 b(Incomplete)41 b(Gamma)g(F)-10 b(unctions)3350 1652 y FK([F)i(unction])-3599 b Fv(double)54 b(gsl_sf_gamma_inc)c Fu(\()p FD(double)31 b Ft(a)p FD(,)g(double)f Ft(x)p Fu(\))3350 1762 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_gamma_inc_e)e Fu(\()p FD(double)30 b Ft(a)p FD(,)h(double)f Ft(x)p FD(,)h(gsl)p 2295 1762 V 41 w(sf)p 2400 1762 V 39 w(result)g(*)f Ft(result)p Fu(\))390 1871 y FK(These)37 b(functions)g(compute)g(the)h(unnormalized)e(incomplete)j (Gamma)f(F)-8 b(unction)38 b(\000\()p FE(a;)15 b(x)p FK(\))37 b(=)390 1912 y Fs(R)445 1933 y Fp(1)429 2009 y Fq(x)531 1981 y FE(dt)15 b(t)659 1948 y FB(\()p Fq(a)p Fp(\000)p FB(1\))851 1981 y FK(exp\()p FI(\000)p FE(t)p FK(\))31 b(for)f FE(a)g FK(real)h(and)f FE(x)25 b FI(\025)g FK(0.)3350 2168 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_gamma_inc_Q)d Fu(\()p FD(double)30 b Ft(a)p FD(,)h(double)f Ft(x)p Fu(\))3350 2278 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_gamma_inc_Q_e)f Fu(\()p FD(double)27 b Ft(a)p FD(,)i(double)e Ft(x)p FD(,)i(gsl)p 2390 2278 V 40 w(sf)p 2494 2278 V 40 w(result)e(*)h Ft(result)p Fu(\))390 2388 y FK(These)116 b(routines)h(compute)g(the)g(normalized)g (incomplete)h(Gamma)f(F)-8 b(unction)390 2497 y FE(Q)p FK(\()p FE(a;)15 b(x)p FK(\))26 b(=)f(1)p FE(=)p FK(\000\()p FE(a)p FK(\))1074 2428 y Fs(R)1131 2449 y Fp(1)1115 2525 y Fq(x)1217 2497 y FE(dt)15 b(t)1345 2464 y FB(\()p Fq(a)p Fp(\000)p FB(1\))1537 2497 y FK(exp\()p FI(\000)p FE(t)p FK(\))30 b(for)h FE(a)25 b(>)g FK(0,)31 b FE(x)25 b FI(\025)g FK(0.)3350 2684 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_gamma_inc_P)d Fu(\()p FD(double)30 b Ft(a)p FD(,)h(double)f Ft(x)p Fu(\))3350 2794 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_gamma_inc_P_e)f Fu(\()p FD(double)27 b Ft(a)p FD(,)i(double)e Ft(x)p FD(,)i(gsl)p 2390 2794 V 40 w(sf)p 2494 2794 V 40 w(result)e(*)h Ft(result)p Fu(\))390 2904 y FK(These)e(routines)g(compute)h(the)f(complemen)m (tary)i(normalized)f(incomplete)g(Gamma)g(F)-8 b(unction)390 3013 y FE(P)13 b FK(\()p FE(a;)i(x)p FK(\))26 b(=)f(1)c FI(\000)f FE(Q)p FK(\()p FE(a;)15 b(x)p FK(\))26 b(=)f(1)p FE(=)p FK(\000\()p FE(a)p FK(\))1634 2944 y Fs(R)1691 2965 y Fq(x)1675 3041 y FB(0)1748 3013 y FE(dt)15 b(t)1876 2980 y FB(\()p Fq(a)p Fp(\000)p FB(1\))2068 3013 y FK(exp\()p FI(\000)p FE(t)p FK(\))31 b(for)f FE(a)25 b(>)g FK(0,)31 b FE(x)25 b FI(\025)g FK(0.)390 3149 y(Note)i(that)f(Abramo)m(witz)g(&) f(Stegun)g(call)i FE(P)13 b FK(\()p FE(a;)i(x)p FK(\))27 b(the)e(incomplete)i(gamma)f(function)f(\(section)390 3259 y(6.5\).)150 3460 y Fy(7.19.5)63 b(Beta)41 b(F)-10 b(unctions)3350 3658 y FK([F)i(unction])-3599 b Fv(double)54 b(gsl_sf_beta)49 b Fu(\()p FD(double)30 b Ft(a)p FD(,)h(double)f Ft(b)p Fu(\))3350 3767 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_beta_e)d Fu(\()p FD(double)30 b Ft(a)p FD(,)h(double)f Ft(b)p FD(,)h(gsl)p 2034 3767 V 40 w(sf)p 2138 3767 V 40 w(result)f(*)h Ft(result)p Fu(\))390 3877 y FK(These)e(routines)h(compute)g(the)f(Beta)i(F)-8 b(unction,)31 b FE(B)5 b FK(\()p FE(a;)15 b(b)p FK(\))26 b(=)f(\000\()p FE(a)p FK(\)\000\()p FE(b)p FK(\))p FE(=)p FK(\000\()p FE(a)20 b FK(+)e FE(b)p FK(\))30 b(sub)5 b(ject)30 b(to)g FE(a)390 3987 y FK(and)g FE(b)g FK(not)h(b)s(eing)f(negativ)m(e)i(in)m (tegers.)3350 4174 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_lnbeta)c Fu(\()p FD(double)30 b 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b(routines)g(compute)h(the)g(normalized)g (incomplete)g(Beta)h(function)390 5340 y FE(I)430 5354 y Fq(x)472 5340 y FK(\()p FE(a;)15 b(b)p FK(\))139 b(=)e FE(B)1085 5354 y Fq(x)1127 5340 y FK(\()p FE(a;)15 b(b)p FK(\))p FE(=B)5 b FK(\()p FE(a;)15 b(b)p FK(\))100 b(where)d FE(B)2139 5354 y Fq(x)2181 5340 y FK(\()p FE(a;)15 b(b)p FK(\))138 b(=)2725 5271 y Fs(R)2780 5292 y Fq(x)2764 5368 y FB(0)2837 5340 y FE(t)2870 5307 y Fq(a)p Fp(\000)p FB(1)2995 5340 y FK(\(1)66 b FI(\000)f FE(t)p FK(\))3345 5307 y Fq(b)p Fp(\000)p FB(1)3463 5340 y FE(dt)98 b FK(for)p eop end %%Page: 60 78 TeXDict begin 60 77 bop 150 -116 a FK(Chapter)30 b(7:)41 b(Sp)s(ecial)31 b(F)-8 b(unctions)2348 b(60)390 299 y(0)67 b FI(\024)g FE(x)g FI(\024)g FK(1.)116 b(F)-8 b(or)56 b FE(a)67 b(>)g FK(0,)62 b FE(b)67 b(>)g FK(0)55 b(the)h(v)-5 b(alue)56 b(is)f(computed)g(using)g(a)h(con)m(tin)m(ued)390 408 y(fraction)67 b(expansion.)149 b(F)-8 b(or)67 b(all)h(other)e(v)-5 b(alues)67 b(it)g(is)g(computed)f(using)g(the)h(relation)390 518 y FE(I)430 532 y Fq(x)472 518 y FK(\()p FE(a;)15 b(b;)g(x)p FK(\))27 b(=)e(\(1)p FE(=a)p FK(\))p FE(x)1144 485 y Fq(a)1185 532 y FB(2)1223 518 y FE(F)1281 532 y FB(1)1318 518 y FK(\()p FE(a;)15 b FK(1)22 b FI(\000)e FE(b;)15 b(a)20 b FK(+)g(1)p FE(;)15 b(x)p FK(\))p FE(=B)5 b FK(\()p FE(a;)15 b(b)p FK(\).)150 781 y FJ(7.20)68 b(Gegen)l(bauer)46 b(F)-11 b(unctions)150 941 y FK(The)44 b(Gegen)m(bauer)h(p)s(olynomials)g(are)f(de\014ned)g(in)g(Abramo)m (witz)h(&)f(Stegun,)k(Chapter)43 b(22,)49 b(where)150 1050 y(they)32 b(are)h(kno)m(wn)e(as)i(Ultraspherical)g(p)s (olynomials.)46 b(The)32 b(functions)f(describ)s(ed)g(in)h(this)g (section)i(are)150 1160 y(declared)d(in)f(the)g(header)h(\014le)f FH(gsl_sf_gegenbauer.h)p FK(.)3350 1385 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_gegenpoly_1)d Fu(\()p FD(double)30 b Ft(lambda)p FD(,)j(double)d Ft(x)p Fu(\))3350 1495 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_gegenpoly_2)d Fu(\()p FD(double)30 b Ft(lambda)p FD(,)j(double)d Ft(x)p Fu(\))3350 1605 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_gegenpoly_3)d Fu(\()p FD(double)30 b Ft(lambda)p FD(,)j(double)d Ft(x)p Fu(\))3350 1714 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_gegenpoly_1_e)f Fu(\()p FD(double)30 b Ft(lambda)p FD(,)i(double)e Ft(x)p FD(,)h(gsl)p 2661 1714 28 4 v 41 w(sf)p 2766 1714 V 39 w(result)g(*)565 1824 y Ft(result)p Fu(\))3350 1933 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_gegenpoly_2_e)f Fu(\()p FD(double)30 b Ft(lambda)p FD(,)i(double)e Ft(x)p FD(,)h(gsl)p 2661 1933 V 41 w(sf)p 2766 1933 V 39 w(result)g(*)565 2043 y Ft(result)p Fu(\))3350 2153 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_gegenpoly_3_e)f Fu(\()p FD(double)30 b Ft(lambda)p FD(,)i(double)e Ft(x)p FD(,)h(gsl)p 2661 2153 V 41 w(sf)p 2766 2153 V 39 w(result)g(*)565 2262 y Ft(result)p Fu(\))390 2372 y FK(These)25 b(functions)f(ev)-5 b(aluate)27 b(the)e(Gegen)m(bauer)g(p)s(olynomials)g FE(C)2600 2339 y 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5230 y FK(\()p FE(m;)15 b(n;)g(x)p FK(\))77 b(=)390 5340 y FE(M)10 b FK(\()p FE(m;)15 b(n;)g(x)p FK(\))31 b(for)f(in)m(teger)i (parameters)f FD(m)p FK(,)f FD(n)p FK(.)p eop end %%Page: 61 79 TeXDict begin 61 78 bop 150 -116 a FK(Chapter)30 b(7:)41 b(Sp)s(ecial)31 b(F)-8 b(unctions)2348 b(61)3350 299 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_hyperg_1F1)d Fu(\()p FD(double)30 b Ft(a)p FD(,)h(double)f Ft(b)p FD(,)h(double)f Ft(x)p Fu(\))3350 408 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_hyperg_1F1_e)e Fu(\()p FD(double)31 b Ft(a)p FD(,)g(double)f Ft(b)p FD(,)g(double)g Ft(x)p FD(,)h(gsl)p 2748 408 28 4 v 41 w(sf)p 2853 408 V 39 w(result)g(*)565 518 y Ft(result)p Fu(\))390 628 y FK(These)67 b(routines)f(compute)h(the)g(con\015uen)m(t)g(h)m(yp)s(ergeometric)h (function)3170 642 y FB(1)3207 628 y FE(F)3265 642 y FB(1)3303 628 y FK(\()p FE(a;)15 b(b;)g(x)p FK(\))87 b(=)390 737 y FE(M)10 b FK(\()p FE(a;)15 b(b;)g(x)p FK(\))32 b(for)e(general)h(parameters)g FD(a)p FK(,)g FD(b)p 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FK(\()p FE(m;)15 b(n;)g(x)p FK(\))36 b(for)f(in)m(teger)390 1843 y(parameters)27 b FD(m)p FK(,)g FD(n)f FK(using)g(the)h FH(gsl_sf_result_e10)22 b FK(t)m(yp)s(e)27 b(to)g(return)e(a)i(result)g (with)f(extended)390 1953 y(range.)3350 2122 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_hyperg_U)c Fu(\()p FD(double)30 b Ft(a)p FD(,)h(double)f Ft(b)p FD(,)h(double)f Ft(x)p Fu(\))3350 2232 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_hyperg_U_e)e Fu(\()p FD(double)30 b Ft(a)p FD(,)h(double)f Ft(b)p FD(,)h(double)f Ft(x)p FD(,)h(gsl)p 2644 2232 V 40 w(sf)p 2748 2232 V 40 w(result)f(*)565 2341 y Ft(result)p Fu(\))390 2451 y FK(These)g(routines)g(compute)h (the)g(con\015uen)m(t)f(h)m(yp)s(ergeometric)h(function)f FE(U)10 b FK(\()p FE(a;)15 b(b;)g(x)p FK(\).)3350 2620 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_hyperg_U_e10_e)f Fu(\()p FD(double)30 b Ft(a)p FD(,)h(double)f Ft(b)p FD(,)h(double)f Ft(x)p FD(,)565 2730 y(gsl)p 677 2730 V 41 w(sf)p 782 2730 V 39 w(result)p 1044 2730 V 40 w(e10)i(*)f Ft(result)p Fu(\))390 2839 y FK(This)44 b(routine)i(computes)f(the)h (con\015uen)m(t)f(h)m(yp)s(ergeometric)h(function)f FE(U)10 b FK(\()p FE(a;)15 b(b;)g(x)p FK(\))47 b(using)e(the)390 2949 y FH(gsl_sf_result_e10)26 b FK(t)m(yp)s(e)k(to)h(return)f(a)g (result)h(with)f(extended)g(range.)3350 3118 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_hyperg_2F1)d Fu(\()p FD(double)30 b Ft(a)p FD(,)h(double)f Ft(b)p FD(,)h(double)f Ft(c)p FD(,)g(double)g Ft(x)p Fu(\))3350 3228 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_hyperg_2F1_e)e Fu(\()p FD(double)31 b Ft(a)p FD(,)g(double)f Ft(b)p FD(,)g(double)g Ft(c)p FD(,)h(double)f Ft(x)p FD(,)565 3337 y(gsl)p 677 3337 V 41 w(sf)p 782 3337 V 39 w(result)h(*)f Ft(result)p Fu(\))390 3447 y FK(These)71 b(routines)h(compute)g(the)g (Gauss)g(h)m(yp)s(ergeometric)g(function)3082 3461 y FB(2)3119 3447 y FE(F)3177 3461 y FB(1)3215 3447 y FK(\()p FE(a;)15 b(b;)g(c;)g(x)p FK(\))96 b(=)390 3557 y FE(F)13 b FK(\()p FE(a;)i(b;)g(c;)g(x)p 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b(and)390 2088 y FE(M)10 b(s)531 2055 y FB(\()p Fq(j)s FB(\))531 2111 y Fq(n)618 2088 y FK(\()p FE(q)s(;)15 b(x)p FK(\))31 b(of)f(order)g FD(n)p FK(.)390 2215 y(The)j(allo)m(w)m (ed)i(v)-5 b(alues)34 b(of)f FD(j)k FK(are)d(1)f(and)g(2.)50 b(The)33 b(functions)g(for)g FE(j)j FK(=)30 b(3)p FE(;)15 b FK(4)35 b(can)f(b)s(e)e(computed)i(as)390 2325 y FE(M)488 2292 y FB(\(3\))478 2347 y Fq(n)602 2325 y FK(=)25 b FE(M)796 2292 y FB(\(1\))786 2347 y Fq(n)906 2325 y FK(+)20 b FE(iM)1126 2292 y FB(\(2\))1116 2347 y Fq(n)1246 2325 y FK(and)29 b FE(M)1520 2292 y FB(\(4\))1510 2347 y Fq(n)1635 2325 y FK(=)c FE(M)1829 2292 y FB(\(1\))1819 2347 y Fq(n)1938 2325 y FI(\000)20 b FE(iM)2158 2292 y FB(\(2\))2148 2347 y Fq(n)2248 2325 y FK(,)30 b(where)g FE(M)2664 2292 y FB(\()p Fq(j)s FB(\))2654 2347 y Fq(n)2776 2325 y FK(=)25 b FE(M)10 b(c)3009 2292 y FB(\()p Fq(j)s FB(\))3009 2347 y Fq(n)3127 2325 y FK(or)30 b FE(M)10 b(s)3379 2292 y FB(\()p Fq(j)s FB(\))3379 2347 y Fq(n)3466 2325 y FK(.)3350 2486 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_mathieu_Mc_arr)q(ay) f Fu(\()p FD(in)m(t)31 b Ft(j)p FD(,)g(in)m(t)g Ft(nmin)p FD(,)g(in)m(t)g Ft(nmax)p FD(,)h(double)e Ft(q)p FD(,)565 2595 y(double)g Ft(x)p FD(,)h(gsl)p 1078 2595 V 40 w(sf)p 1182 2595 V 40 w(mathieu)p 1545 2595 V 40 w(w)m(orkspace)g(*)g Ft(work)p FD(,)h(double)e Ft(result_array)p Fo([])p Fu(\))3350 2705 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_mathieu_Ms_arr)q (ay)f Fu(\()p FD(in)m(t)31 b Ft(j)p FD(,)g(in)m(t)g Ft(nmin)p FD(,)g(in)m(t)g Ft(nmax)p FD(,)h(double)e Ft(q)p FD(,)565 2815 y(double)g Ft(x)p FD(,)h(gsl)p 1078 2815 V 40 w(sf)p 1182 2815 V 40 w(mathieu)p 1545 2815 V 40 w(w)m(orkspace)g(*)g Ft(work)p FD(,)h(double)e Ft(result_array)p Fo([])p Fu(\))390 2924 y FK(These)f(routines)g(compute)g(a)h(series)f(of)g(the)h(radial)f (Mathieu)h(functions)f(of)g(kind)f FD(j)p FK(,)i(with)e(order)390 3034 y(from)i FD(nmin)f FK(to)i FD(nmax)37 b FK(inclusiv)m(e,)31 b(storing)g(the)f(results)h(in)f(the)g(arra)m(y)h 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FE( )s FK(\()p FE(x)p FK(\))g(=)2079 5177 y Fs(\022)2176 5235 y FE(d)p 2150 5275 V 2150 5359 a(dx)2259 5177 y Fs(\023)2320 5192 y Fq(n)p FB(+1)2465 5296 y FK(log)r(\(\000\()p FE(x)p FK(\)\))p eop end %%Page: 72 90 TeXDict begin 72 89 bop 150 -116 a FK(Chapter)30 b(7:)41 b(Sp)s(ecial)31 b(F)-8 b(unctions)2348 b(72)150 299 y(where)30 b FE( )s FK(\()p FE(x)p FK(\))d(=)e(\000)777 266 y Fp(0)801 299 y FK(\()p FE(x)p FK(\))p FE(=)p FK(\000\()p FE(x)p FK(\))32 b(is)e(kno)m(wn)h(as)f(the)h(digamma)h(function.)41 b(These)30 b(functions)g(are)h(declared)150 408 y(in)f(the)h(header)f (\014le)g FH(gsl_sf_psi.h)p FK(.)150 626 y Fy(7.28.1)63 b(Digamma)41 b(F)-10 b(unction)3350 841 y FK([F)i(unction])-3599 b Fv(double)54 b(gsl_sf_psi_int)c Fu(\()p FD(in)m(t)31 b Ft(n)p Fu(\))3350 951 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_psi_int_e)e Fu(\()p FD(in)m(t)31 b Ft(n)p FD(,)g(gsl)p 1636 951 28 4 v 40 w(sf)p 1740 951 V 40 w(result)f(*)h Ft(result)p Fu(\))390 1060 y FK(These)46 b(routines)g(compute)g(the)h(digamma)g(function)e FE( )s FK(\()p FE(n)p FK(\))i(for)f(p)s(ositiv)m(e)h(in)m(teger)h FD(n)p FK(.)87 b(The)390 1170 y(digamma)31 b(function)f(is)g(also)i (called)f(the)g(Psi)f(function.)3350 1391 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_psi)49 b Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 1500 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_psi_e)c Fu(\()p FD(double)31 b Ft(x)p FD(,)f(gsl)p 1580 1500 V 41 w(sf)p 1685 1500 V 40 w(result)g(*)h Ft(result)p Fu(\))390 1610 y FK(These)f(routines)g(compute)h(the)g (digamma)g(function)f FE( )s FK(\()p FE(x)p FK(\))h(for)f(general)i FE(x)p FK(,)e FE(x)25 b FI(6)p FK(=)g(0.)3350 1831 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_psi_1piy)c Fu(\()p FD(double)30 b Ft(y)p Fu(\))3350 1940 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_psi_1piy_e)e Fu(\()p FD(double)30 b Ft(y)p FD(,)h(gsl)p 1842 1940 V 41 w(sf)p 1947 1940 V 39 w(result)f(*)h Ft(result)p Fu(\))390 2050 y FK(These)39 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FK(\()p FE(x)p FK(\))h(for)f FE(x)25 b FI(\025)g FK(0.)p eop end %%Page: 73 91 TeXDict begin 73 90 bop 150 -116 a FK(Chapter)30 b(7:)41 b(Sp)s(ecial)31 b(F)-8 b(unctions)2348 b(73)150 299 y FJ(7.30)68 b(T)-11 b(ransp)t(ort)45 b(F)-11 b(unctions)150 458 y FK(The)47 b(transp)s(ort)g(functions)h FE(J)9 b FK(\()p FE(n;)15 b(x)p FK(\))49 b(are)f(de\014ned)e(b)m(y)i(the)g(in)m (tegral)i(represen)m(tations)f FE(J)9 b FK(\()p FE(n;)15 b(x)p FK(\))55 b(:=)150 499 y Fs(R)205 520 y Fq(x)189 595 y FB(0)262 568 y FE(dt)15 b(t)390 535 y Fq(n)436 568 y FE(e)478 535 y Fq(t)507 568 y FE(=)p FK(\()p FE(e)629 535 y Fq(t)680 568 y FI(\000)20 b FK(1\))851 535 y FB(2)889 568 y FK(.)40 b(They)30 b(are)h(declared)g(in)f(the)g(header)h(\014le)f FH(gsl_sf_transport.h)p FK(.)3350 741 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_transport_2)d Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 851 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_transport_2_e)f Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1999 851 28 4 v 40 w(sf)p 2103 851 V 40 w(result)f(*)h Ft(result)p Fu(\))390 960 y FK(These)f (routines)g(compute)h(the)g(transp)s(ort)e(function)h FE(J)9 b FK(\(2)p FE(;)15 b(x)p FK(\).)3350 1134 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_transport_3)d Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 1243 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_transport_3_e)f Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1999 1243 V 40 w(sf)p 2103 1243 V 40 w(result)f(*)h Ft(result)p Fu(\))390 1353 y FK(These)f(routines)g(compute)h(the)g(transp)s(ort)e (function)h FE(J)9 b FK(\(3)p FE(;)15 b(x)p FK(\).)3350 1526 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_transport_4)d Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 1636 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_transport_4_e)f Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1999 1636 V 40 w(sf)p 2103 1636 V 40 w(result)f(*)h Ft(result)p Fu(\))390 1746 y FK(These)f(routines)g(compute)h(the)g(transp)s(ort)e (function)h FE(J)9 b FK(\(4)p FE(;)15 b(x)p FK(\).)3350 1919 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_transport_5)d Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 2029 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_transport_5_e)f Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1999 2029 V 40 w(sf)p 2103 2029 V 40 w(result)f(*)h Ft(result)p Fu(\))390 2138 y FK(These)f(routines)g(compute)h(the)g(transp)s(ort)e (function)h FE(J)9 b FK(\(5)p FE(;)15 b(x)p FK(\).)150 2363 y FJ(7.31)68 b(T)-11 b(rigonometric)46 b(F)-11 b(unctions)150 2523 y FK(The)30 b(library)g(includes)f(its)i(o)m(wn)f(trigonometric)i (functions)e(in)g(order)g(to)h(pro)m(vide)f(consistency)h(across)150 2632 y(platforms)e(and)f(reliable)i(error)e(estimates.)42 b(These)28 b(functions)h(are)g(declared)g(in)g(the)g(header)f(\014le)h FH(gsl_)150 2742 y(sf_trig.h)p FK(.)150 2934 y Fy(7.31.1)63 b(Circular)40 b(T)-10 b(rigonometric)43 b(F)-10 b(unctions)3350 3123 y FK([F)i(unction])-3599 b Fv(double)54 b(gsl_sf_sin)49 b Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 3233 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_sin_e)c Fu(\()p FD(double)31 b Ft(x)p FD(,)f(gsl)p 1580 3233 V 41 w(sf)p 1685 3233 V 40 w(result)g(*)h Ft(result)p Fu(\))390 3342 y FK(These)f(routines)g(compute)h(the)g(sine)f(function)g(sin\()p FE(x)p FK(\).)3350 3516 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_cos)49 b Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 3625 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_cos_e)c Fu(\()p FD(double)31 b Ft(x)p FD(,)f(gsl)p 1580 3625 V 41 w(sf)p 1685 3625 V 40 w(result)g(*)h Ft(result)p Fu(\))390 3735 y FK(These)f(routines)g(compute)h(the)g(cosine)g (function)f(cos)q(\()p FE(x)p FK(\).)3350 3908 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_hypot)49 b Fu(\()p FD(double)31 b Ft(x)p FD(,)f(double)g Ft(y)p Fu(\))3350 4018 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_hypot_e)d Fu(\()p FD(double)30 b Ft(x)p FD(,)h(double)f Ft(y)p FD(,)h(gsl)p 2086 4018 V 40 w(sf)p 2190 4018 V 40 w(result)f(*)h Ft(result)p Fu(\))390 4128 y FK(These)d(routines)g(compute)g(the)g(h)m (yp)s(oten)m(use)g(function)2345 4059 y FI(p)p 2421 4059 286 4 v 69 x FE(x)2473 4101 y FB(2)2530 4128 y FK(+)20 b FE(y)2669 4101 y FB(2)2734 4128 y FK(a)m(v)m(oiding)30 b(o)m(v)m(er\015o)m(w)f(and)f(un-)390 4237 y(der\015o)m(w.)3350 4411 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_sinc)49 b Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 4520 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_sinc_e)d Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1633 4520 28 4 v 40 w(sf)p 1737 4520 V 40 w(result)f(*)h Ft(result)p Fu(\))390 4630 y FK(These)f(routines)g(compute)h(sinc\()p FE(x)p FK(\))26 b(=)f(sin\()p FE(\031)s(x)p FK(\))p FE(=)p FK(\()p FE(\031)s(x)p FK(\))32 b(for)e(an)m(y)h(v)-5 b(alue)31 b(of)f FD(x)p FK(.)150 4822 y Fy(7.31.2)63 b(T)-10 b(rigonometric)42 b(F)-10 b(unctions)42 b(for)g(Complex)f(Argumen)m(ts)3350 5011 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_complex_sin_e)f Fu(\()p FD(double)30 b Ft(zr)p FD(,)h(double)f Ft(zi)p FD(,)h(gsl)p 2504 5011 V 41 w(sf)p 2609 5011 V 39 w(result)g(*)g Ft(szr)p FD(,)565 5121 y(gsl)p 677 5121 V 41 w(sf)p 782 5121 V 39 w(result)g(*)f Ft(szi)p Fu(\))390 5230 y FK(This)d(function)g (computes)g(the)h(complex)g(sine,)g(sin\()p FE(z)2250 5244 y Fq(r)2302 5230 y FK(+)14 b FE(iz)2460 5244 y Fq(i)2488 5230 y FK(\))28 b(storing)g(the)f(real)h(and)f(imaginary)390 5340 y(parts)j(in)g FD(szr)p FK(,)h FD(szi)p FK(.)p eop end %%Page: 74 92 TeXDict begin 74 91 bop 150 -116 a FK(Chapter)30 b(7:)41 b(Sp)s(ecial)31 b(F)-8 b(unctions)2348 b(74)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_complex_cos_e)f Fu(\()p FD(double)30 b Ft(zr)p FD(,)h(double)f Ft(zi)p FD(,)h(gsl)p 2504 299 28 4 v 41 w(sf)p 2609 299 V 39 w(result)g(*)g Ft(czr)p FD(,)565 408 y(gsl)p 677 408 V 41 w(sf)p 782 408 V 39 w(result)g(*)f Ft(czi)p Fu(\))390 518 y FK(This)20 b(function)h(computes)g(the)g(complex)h(cosine,)i (cos\()p FE(z)2308 532 y Fq(r)2347 518 y FK(+)q FE(iz)2492 532 y Fq(i)2521 518 y FK(\))d(storing)g(the)g(real)h(and)e(imaginary) 390 628 y(parts)30 b(in)g FD(czr)p FK(,)h FD(czi)p FK(.)3350 864 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_complex_logsin)q(_e)f Fu(\()p FD(double)30 b Ft(zr)p FD(,)h(double)f Ft(zi)p FD(,)h(gsl)p 2661 864 V 41 w(sf)p 2766 864 V 39 w(result)g(*)565 974 y Ft(lszr)p FD(,)h(gsl)p 942 974 V 40 w(sf)p 1046 974 V 40 w(result)e(*)h Ft(lszi)p Fu(\))390 1083 y FK(This)h(function)h (computes)g(the)h(logarithm)g(of)f(the)g(complex)h(sine,)g(log)r (\(sin\()p FE(z)3119 1097 y Fq(r)3179 1083 y FK(+)22 b FE(iz)3345 1097 y Fq(i)3373 1083 y FK(\)\))34 b(storing)390 1193 y(the)d(real)g(and)e(imaginary)i(parts)f(in)h FD(lszr)p FK(,)f FD(lszi)p FK(.)150 1418 y Fy(7.31.3)63 b(Hyp)s(erb)s(olic)42 b(T)-10 b(rigonometric)42 b(F)-10 b(unctions)3350 1641 y FK([F)i(unction])-3599 b Fv(double)54 b(gsl_sf_lnsinh)c Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 1751 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_lnsinh_e)d Fu(\()p FD(double)31 b Ft(x)p FD(,)f(gsl)p 1737 1751 V 41 w(sf)p 1842 1751 V 40 w(result)g(*)h Ft(result)p Fu(\))390 1860 y FK(These)f(routines)g(compute)h(log)r(\(sinh\()p FE(x)p FK(\)\))g(for)f FE(x)c(>)f FK(0.)3350 2097 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_lncosh)c Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 2207 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_lncosh_e)d Fu(\()p FD(double)31 b Ft(x)p FD(,)f(gsl)p 1737 2207 V 41 w(sf)p 1842 2207 V 40 w(result)g(*)h Ft(result)p Fu(\))390 2316 y FK(These)f(routines)g (compute)h(log)r(\(cosh)q(\()p FE(x)p FK(\)\))g(for)g(an)m(y)f FD(x)p FK(.)150 2542 y Fy(7.31.4)63 b(Con)m(v)m(ersion)41 b(F)-10 b(unctions)3350 2765 y FK([F)i(unction])-3599 b Fv(int)53 b(gsl_sf_polar_to_rect)f Fu(\()p FD(double)30 b Ft(r)p FD(,)h(double)f Ft(theta)p FD(,)i(gsl)p 2609 2765 V 40 w(sf)p 2713 2765 V 40 w(result)e(*)h Ft(x)p FD(,)565 2874 y(gsl)p 677 2874 V 41 w(sf)p 782 2874 V 39 w(result)g(*)f Ft(y)p Fu(\))p FD(;)390 2984 y FK(This)24 b(function)h(con)m(v)m(erts)i(the)e(p)s(olar)g(co)s(ordinates)g(\()p FD(r)p FK(,)p FD(theta)p FK(\))i(to)f(rectilinear)g(co)s(ordinates)g (\()p FD(x)p FK(,)p FD(y)8 b FK(\),)390 3093 y FE(x)25 b FK(=)g FE(r)18 b FK(cos)q(\()p FE(\022)s FK(\),)30 b FE(y)e FK(=)d FE(r)18 b FK(sin)o(\()p FE(\022)s FK(\).)3350 3330 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_rect_to_polar)f Fu(\()p FD(double)30 b Ft(x)p FD(,)h(double)f Ft(y)p FD(,)h(gsl)p 2400 3330 V 40 w(sf)p 2504 3330 V 40 w(result)f(*)h Ft(r)p FD(,)565 3439 y(gsl)p 677 3439 V 41 w(sf)p 782 3439 V 39 w(result)g(*)f Ft(theta)p Fu(\))390 3549 y FK(This)24 b(function)h(con)m(v)m(erts)i(the)e(rectilinear)h(co)s (ordinates)g(\()p FD(x)p FK(,)p FD(y)8 b FK(\))26 b(to)g(p)s(olar)e(co) s(ordinates)i(\()p FD(r)p FK(,)p FD(theta)p FK(\),)390 3659 y(suc)m(h)k(that)h FE(x)25 b FK(=)g FE(r)18 b FK(cos)q(\()p FE(\022)s FK(\),)30 b FE(y)e FK(=)d FE(r)18 b FK(sin)o(\()p FE(\022)s FK(\).)41 b(The)30 b(argumen)m(t)h FD(theta)g FK(lies)g(in)f(the)h(range)f([)p FI(\000)p FE(\031)s(;)15 b(\031)s FK(].)150 3884 y Fy(7.31.5)63 b(Restriction)41 b(F)-10 b(unctions)3350 4107 y FK([F)i(unction])-3599 b Fv(double)54 b(gsl_sf_angle_restrict_)q(sym)q(m)d Fu(\()p FD(double)31 b Ft(theta)p Fu(\))3350 4217 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_angle_restrict)q(_sym)q(m_e)f Fu(\()p FD(double)30 b(*)h Ft(theta)p Fu(\))390 4326 y FK(These)f(routines)g(force)h(the)g(angle)g FD(theta)h FK(to)f(lie)g(in)f(the)h(range)f(\()p FI(\000)p FE(\031)s(;)15 b(\031)s FK(].)390 4487 y(Note)33 b(that)g(the)f(mathematical)i(v)-5 b(alue)32 b(of)g FE(\031)j FK(is)d(sligh)m(tly)h(greater)g(than)f FH(M_PI)p FK(,)f(so)h(the)g(mac)m(hine)390 4596 y(n)m(um)m(b)s(ers)d FH(M_PI)g FK(and)h FH(-M_PI)f FK(are)i(included)e(in)h(the)h(range.) 3350 4833 y([F)-8 b(unction])-3599 b Fv(double)54 b (gsl_sf_angle_restrict_)q(pos)e Fu(\()p FD(double)30 b Ft(theta)p Fu(\))3350 4942 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_angle_restrict)q(_pos)q(_e)f Fu(\()p FD(double)30 b(*)h Ft(theta)p Fu(\))390 5052 y FK(These)f(routines)g (force)h(the)g(angle)g FD(theta)h FK(to)f(lie)g(in)f(the)h(range)f([0)p FE(;)15 b FK(2)p FE(\031)s FK(\).)390 5213 y(Note)23 b(that)f(the)g(mathematical)i(v)-5 b(alue)22 b(of)g(2)p FE(\031)j FK(is)d(sligh)m(tly)h(greater)g(than)e FH(2*M_PI)p FK(,)h(so)g(the)g(mac)m(hine)390 5322 y(n)m(um)m(b)s(er)29 b FH(2*M_PI)g FK(is)h(included)g(in)g(the)g(range.)p eop end %%Page: 75 93 TeXDict begin 75 92 bop 150 -116 a FK(Chapter)30 b(7:)41 b(Sp)s(ecial)31 b(F)-8 b(unctions)2348 b(75)150 299 y Fy(7.31.6)63 b(T)-10 b(rigonometric)42 b(F)-10 b(unctions)42 b(With)e(Error)i(Estimates)3350 514 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_sin_err_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(double)f Ft(dx)p FD(,)h(gsl)p 2243 514 28 4 v 40 w(sf)p 2347 514 V 40 w(result)f(*)h Ft(result)p Fu(\))390 623 y FK(This)k(routine)g(computes)h(the)g(sine)f(of)h(an)f (angle)i FD(x)k FK(with)36 b(an)f(asso)s(ciated)i(absolute)f(error)f FD(dx)p FK(,)390 733 y(sin\()p FE(x)16 b FI(\006)g FE(dx)p FK(\).)40 b(Note)30 b(that)f(this)f(function)g(is)g(pro)m(vided)g(in)g (the)h(error-handling)e(form)h(only)h(since)390 842 y(its)i(purp)s(ose) d(is)j(to)g(compute)g(the)f(propagated)h(error.)3350 1062 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_cos_err_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(double)f Ft(dx)p FD(,)h(gsl)p 2243 1062 V 40 w(sf)p 2347 1062 V 40 w(result)f(*)h Ft(result)p Fu(\))390 1172 y FK(This)e(routine)g(computes)h(the)f (cosine)h(of)g(an)f(angle)h FD(x)36 b FK(with)29 b(an)g(asso)s(ciated)i (absolute)f(error)f FD(dx)p FK(,)390 1281 y(cos)q(\()p FE(x)15 b FI(\006)g FE(dx)p FK(\).)40 b(Note)29 b(that)f(this)f (function)h(is)f(pro)m(vided)h(in)f(the)h(error-handling)f(form)g(only) h(since)390 1391 y(its)j(purp)s(ose)d(is)j(to)g(compute)g(the)f (propagated)h(error.)150 1650 y FJ(7.32)68 b(Zeta)46 b(F)-11 b(unctions)150 1810 y FK(The)24 b(Riemann)h(zeta)h(function)e 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FK(=)g(1.)3350 2943 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_zeta)49 b Fu(\()p FD(double)30 b Ft(s)p Fu(\))3350 3052 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_zeta_e)d Fu(\()p FD(double)30 b Ft(s)p FD(,)h(gsl)p 1633 3052 V 40 w(sf)p 1737 3052 V 40 w(result)f(*)h Ft(result)p Fu(\))390 3162 y FK(These)f(routines)g (compute)h(the)g(Riemann)f(zeta)i(function)e FE(\020)7 b FK(\()p FE(s)p FK(\))30 b(for)g(arbitrary)g FD(s)p FK(,)g FE(s)25 b FI(6)p FK(=)g(1.)150 3379 y Fy(7.32.2)63 b(Riemann)41 b(Zeta)f(F)-10 b(unction)41 b(Min)m(us)h(One)150 3526 y FK(F)-8 b(or)31 b(large)g(p)s(ositiv)m(e)g(argumen)m(t,)g(the)f (Riemann)g(zeta)i(function)d(approac)m(hes)i(one.)41 b(In)29 b(this)h(region)h(the)150 3636 y(fractional)h(part)e(is)g(in)m (teresting,)i(and)e(therefore)h(w)m(e)g(need)f(a)h(function)f(to)h(ev) -5 b(aluate)32 b(it)f(explicitly)-8 b(.)3350 3856 y([F)g(unction])-3599 b Fv(double)54 b(gsl_sf_zetam1_int)d Fu(\()p FD(in)m(t)31 b Ft(n)p Fu(\))3350 3965 y FK([F)-8 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Fp(1)2220 4901 y FB(0)2290 4878 y FK(\()p FE(k)f FK(+)c FE(q)s FK(\))2566 4845 y Fp(\000)p Fq(s)2653 4878 y FK(.)3350 5098 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_hzeta)49 b Fu(\()p FD(double)31 b Ft(s)p FD(,)f(double)g Ft(q)p Fu(\))3350 5208 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_hzeta_e)d Fu(\()p FD(double)30 b Ft(s)p FD(,)h(double)f Ft(q)p FD(,)h(gsl)p 2086 5208 V 40 w(sf)p 2190 5208 V 40 w(result)f(*)h Ft(result)p Fu(\))390 5317 y FK(These)f(routines)g(compute)h(the)g (Hurwitz)f(zeta)i(function)e FE(\020)7 b FK(\()p FE(s;)15 b(q)s FK(\))30 b(for)g FE(s)25 b(>)g FK(1,)31 b FE(q)d(>)d FK(0.)p eop end %%Page: 76 94 TeXDict begin 76 93 bop 150 -116 a FK(Chapter)30 b(7:)41 b(Sp)s(ecial)31 b(F)-8 b(unctions)2348 b(76)150 299 y Fy(7.32.4)63 b(Eta)40 b(F)-10 b(unction)150 446 y FK(The)30 b(eta)h(function)f(is)h(de\014ned)e(b)m(y)h FE(\021)s FK(\()p FE(s)p FK(\))c(=)f(\(1)c FI(\000)f FK(2)1895 413 y FB(1)p Fp(\000)p Fq(s)2016 446 y FK(\))p FE(\020)7 b FK(\()p FE(s)p 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b(=)47 b(success)390 4620 y(J0\(5.0\))f(=)h(-0.177596771314338264)676 4730 y(+/-)95 b(0.000000000000000193)390 4840 y(exact)142 b(=)47 b(-0.177596771314338292)150 4980 y FK(The)32 b(next)g(program)g (computes)g(the)h(same)f(quan)m(tit)m(y)i(using)e(the)g(natural)g(form) g(of)g(the)h(function.)46 b(In)150 5090 y(this)30 b(case)i(the)e(error) g(term)h FD(result.err)36 b FK(and)30 b(return)f(status)i(are)g(not)f (accessible.)390 5230 y FH(#include)46 b()390 5340 y(#include)g()p eop end %%Page: 77 95 TeXDict begin 77 94 bop 150 -116 a FK(Chapter)30 b(7:)41 b(Sp)s(ecial)31 b(F)-8 b(unctions)2348 b(77)390 408 y FH(int)390 518 y(main)47 b(\(void\))390 628 y({)485 737 y(double)g(x)g(=)g(5.0;)485 847 y(double)g(expected)e(=)j (-0.17759677131433830434)o(739)o(701;)485 1066 y(double)f(y)g(=)g (gsl_sf_bessel_J0)d(\(x\);)485 1285 y(printf)j(\("J0\(5.0\))e(=)i (\045.18f\\n",)f(y\);)485 1395 y(printf)h(\("exact)141 b(=)47 b(\045.18f\\n",)f(expected\);)485 1504 y(return)h(0;)390 1614 y(})150 1748 y 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y(handler)30 b(to)h(ab)s(ort)f(y)m(our)g(program)g(then)g(it)h(isn't)g(necessary)g (to)g(c)m(hec)m(k)h(ev)m(ery)f FH(alloc)p FK(.)3350 1062 y([F)-8 b(unction])-3599 b Fv(gsl_block)55 b(*)e(gsl_block_alloc)d Fu(\()p FD(size)p 1790 1062 28 4 v 41 w(t)31 b Ft(n)p Fu(\))390 1171 y FK(This)e(function)h(allo)s(cates)i(memory)e(for)g(a)g (blo)s(c)m(k)h(of)f FD(n)f FK(double-precision)h(elemen)m(ts,)i (returning)390 1281 y(a)39 b(p)s(oin)m(ter)g(to)g(the)g(blo)s(c)m(k)g (struct.)66 b(The)38 b(blo)s(c)m(k)h(is)g(not)g(initialized)i(and)d(so) h(the)g(v)-5 b(alues)39 b(of)g(its)390 1390 y(elemen)m(ts)e(are)e (unde\014ned.)54 b(Use)35 b(the)h(function)f FH(gsl_block_calloc)c FK(if)k(y)m(ou)h(w)m(an)m(t)g(to)g(ensure)390 1500 y(that)31 b(all)g(the)g(elemen)m(ts)h(are)e(initialized)i(to)g(zero.)390 1632 y(A)e(n)m(ull)h(p)s(oin)m(ter)f(is)h(returned)e(if)h(insu\016cien) m(t)h(memory)f(is)g(a)m(v)-5 b(ailable)33 b(to)e(create)h(the)f(blo)s (c)m(k.)3350 1810 y([F)-8 b(unction])-3599 b Fv(gsl_block)55 b(*)e(gsl_block_calloc)d Fu(\()p FD(size)p 1842 1810 V 41 w(t)31 b Ft(n)p Fu(\))390 1919 y FK(This)23 b(function)h(allo)s (cates)j(memory)d(for)g(a)g(blo)s(c)m(k)h(and)e(initializes)k(all)e (the)f(elemen)m(ts)i(of)e(the)g(blo)s(c)m(k)390 2029 y(to)31 b(zero.)3350 2206 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_block_free)49 b Fu(\()p FD(gsl)p 1336 2206 V 41 w(blo)s(c)m(k)31 b(*)g Ft(b)p Fu(\))390 2316 y FK(This)39 b(function)h(frees)g(the)g(memory)g(used)g(b)m(y)g(a)g (blo)s(c)m(k)h FD(b)g FK(previously)f(allo)s(cated)i(with)e FH(gsl_)390 2425 y(block_alloc)27 b FK(or)k FH(gsl_block_calloc)p FK(.)150 2620 y Fy(8.2.2)63 b(Reading)41 b(and)f(writing)i(blo)s(c)m (ks)150 2767 y FK(The)c(library)g(pro)m(vides)g(functions)g(for)g (reading)g(and)g(writing)g(blo)s(c)m(ks)h(to)g(a)g(\014le)f(as)g (binary)g(data)h(or)150 2877 y(formatted)31 b(text.)3350 3054 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_block_fwrite)e Fu(\()p FD(FILE)30 b(*)h Ft(stream)p FD(,)h(const)f(gsl)p 2313 3054 V 41 w(blo)s(c)m(k)g(*)f Ft(b)p Fu(\))390 3164 y FK(This)21 b(function)g(writes)h(the)g(elemen)m(ts)h(of)f(the)f(blo)s (c)m(k)i FD(b)g FK(to)f(the)g(stream)g FD(stream)g FK(in)f(binary)g (format.)390 3273 y(The)30 b(return)f(v)-5 b(alue)31 b(is)f(0)g(for)g(success)h(and)e FH(GSL_EFAILED)f FK(if)i(there)g(w)m (as)h(a)f(problem)g(writing)g(to)390 3383 y(the)g(\014le.)40 b(Since)30 b(the)g(data)h(is)e(written)h(in)f(the)h(nativ)m(e)h(binary) e(format)h(it)h(ma)m(y)f(not)g(b)s(e)f(p)s(ortable)390 3493 y(b)s(et)m(w)m(een)i(di\013eren)m(t)g(arc)m(hitectures.)3350 3670 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_block_fread)d Fu(\()p FD(FILE)31 b(*)f Ft(stream)p FD(,)j(gsl)p 2023 3670 V 40 w(blo)s(c)m(k)e(*)g Ft(b)p Fu(\))390 3780 y FK(This)g(function)h(reads)g(in)m(to)h(the)f(blo)s(c)m(k)h FD(b)g FK(from)f(the)g(op)s(en)f(stream)i FD(stream)f FK(in)g(binary)f(format.)390 3889 y(The)e(blo)s(c)m(k)h FD(b)h FK(m)m(ust)f(b)s(e)f(preallo)s(cated)i(with)e(the)h(correct)h (length)f(since)g(the)f(function)h(uses)f(the)390 3999 y(size)h(of)f FD(b)i FK(to)f(determine)f(ho)m(w)g(man)m(y)g(b)m(ytes)h (to)g(read.)40 b(The)29 b(return)f(v)-5 b(alue)30 b(is)f(0)g(for)g (success)h(and)390 4108 y FH(GSL_EFAILED)i FK(if)j(there)h(w)m(as)f(a)h (problem)e(reading)i(from)e(the)i(\014le.)55 b(The)35 b(data)h(is)f(assumed)f(to)390 4218 y(ha)m(v)m(e)e(b)s(een)d(written)i (in)f(the)g(nativ)m(e)i(binary)e(format)g(on)h(the)f(same)h(arc)m (hitecture.)3350 4395 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_block_fprintf)e Fu(\()p FD(FILE)30 b(*)h Ft(stream)p FD(,)h(const)f(gsl)p 2365 4395 V 41 w(blo)s(c)m(k)g(*)g Ft(b)p FD(,)f(const)565 4505 y(c)m(har)h(*)g Ft(format)p Fu(\))390 4615 y FK(This)38 b(function)h(writes)g(the)g(elemen)m(ts)i (of)e(the)g(blo)s(c)m(k)g FD(b)i FK(line-b)m(y-line)f(to)g(the)f (stream)h FD(stream)390 4724 y FK(using)26 b(the)h(format)g(sp)s (eci\014er)g FD(format)p FK(,)h(whic)m(h)e(should)g(b)s(e)g(one)h(of)g (the)g FH(\045g)p FK(,)g FH(\045e)f FK(or)h FH(\045f)f FK(formats)h(for)390 4834 y(\015oating)37 b(p)s(oin)m(t)f(n)m(um)m(b)s (ers)f(and)g FH(\045d)h FK(for)g(in)m(tegers.)59 b(The)35 b(function)h(returns)f(0)h(for)g(success)h(and)390 4943 y FH(GSL_EFAILED)27 b FK(if)k(there)f(w)m(as)h(a)g(problem)e(writing)i (to)g(the)g(\014le.)3350 5121 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_block_fscanf)e Fu(\()p FD(FILE)30 b(*)h Ft(stream)p FD(,)h(gsl)p 2075 5121 V 41 w(blo)s(c)m(k)f(*)f Ft(b)p Fu(\))390 5230 y FK(This)37 b(function)g(reads)g(formatted)h (data)g(from)f(the)h(stream)g FD(stream)g FK(in)m(to)g(the)g(blo)s(c)m (k)g FD(b)p FK(.)61 b(The)390 5340 y(blo)s(c)m(k)31 b FD(b)h FK(m)m(ust)f(b)s(e)f(preallo)s(cated)i(with)e(the)h(correct)h (length)f(since)g(the)g(function)f(uses)g(the)h(size)p eop end %%Page: 80 98 TeXDict begin 80 97 bop 150 -116 a FK(Chapter)30 b(8:)41 b(V)-8 b(ectors)32 b(and)e(Matrices)2203 b(80)390 299 y(of)28 b FD(b)g FK(to)h(determine)e(ho)m(w)h(man)m(y)f(n)m(um)m(b)s (ers)f(to)i(read.)40 b(The)27 b(function)g(returns)f(0)i(for)f(success) h(and)390 408 y FH(GSL_EFAILED)f FK(if)k(there)f(w)m(as)h(a)g(problem)e (reading)i(from)f(the)g(\014le.)150 619 y Fy(8.2.3)63 b(Example)40 b(programs)i(for)g(blo)s(c)m(ks)150 766 y FK(The)30 b(follo)m(wing)i(program)e(sho)m(ws)g(ho)m(w)g(to)h(allo)s (cate)i(a)e(blo)s(c)m(k,)390 912 y FH(#include)46 b()390 1022 y(#include)g()390 1241 y(int)390 1351 y(main)h(\(void\))390 1460 y({)485 1570 y(gsl_block)f(*)h(b)h(=)f (gsl_block_alloc)d(\(100\);)485 1789 y(printf)j(\("length)e(of)i(block) g(=)g(\045zu\\n",)f(b->size\);)485 1899 y(printf)h(\("block)e(data)i (address)f(=)h(\045p\\n",)f(b->data\);)485 2118 y(gsl_block_free)e (\(b\);)485 2227 y(return)j(0;)390 2337 y(})150 2483 y FK(Here)31 b(is)f(the)h(output)f(from)g(the)g(program,)390 2629 y FH(length)46 b(of)h(block)g(=)g(100)390 2739 y(block)f(data)h (address)f(=)h(0x804b0d8)150 2989 y FJ(8.3)68 b(V)-11 b(ectors)150 3148 y FK(V)j(ectors)31 b(are)f(de\014ned)e(b)m(y)i(a)g FH(gsl_vector)c FK(structure)j(whic)m(h)h(describ)s(es)e(a)i(slice)h (of)f(a)g(blo)s(c)m(k.)41 b(Di\013eren)m(t)150 3258 y(v)m(ectors)23 b(can)f(b)s(e)f(created)h(whic)m(h)g(p)s(oin)m(t)f(to)i(the)e(same)h (blo)s(c)m(k.)39 b(A)21 b(v)m(ector)j(slice)e(is)g(a)g(set)g(of)g (equally-spaced)150 3367 y(elemen)m(ts)32 b(of)e(an)h(area)g(of)f (memory)-8 b(.)275 3513 y(The)23 b FH(gsl_vector)f FK(structure)i(con)m (tains)i(\014v)m(e)e(comp)s(onen)m(ts,)i(the)f FD(size)p FK(,)i(the)d FD(stride)p FK(,)i(a)f(p)s(oin)m(ter)g(to)g(the)150 3623 y(memory)33 b(where)g(the)h(elemen)m(ts)h(are)e(stored,)i FD(data)p FK(,)g(a)f(p)s(oin)m(ter)f(to)h(the)g(blo)s(c)m(k)g(o)m(wned) f(b)m(y)g(the)h(v)m(ector,)150 3733 y FD(blo)s(c)m(k)p FK(,)28 b(if)d(an)m(y)-8 b(,)28 b(and)e(an)f(o)m(wnership)g(\015ag,)j FD(o)m(wner)p FK(.)39 b(The)25 b(structure)h(is)g(v)m(ery)g(simple)g (and)f(lo)s(oks)i(lik)m(e)g(this,)390 3879 y FH(typedef)46 b(struct)390 3988 y({)485 4098 y(size_t)h(size;)485 4208 y(size_t)g(stride;)485 4317 y(double)g(*)g(data;)485 4427 y(gsl_block)f(*)h(block;)485 4536 y(int)g(owner;)390 4646 y(})g(gsl_vector;)150 4792 y FK(The)33 b FD(size)40 b FK(is)34 b(simply)f(the)i(n)m(um)m(b)s(er)d(of)i(v)m(ector)i(elemen)m (ts.)52 b(The)33 b(range)i(of)f(v)-5 b(alid)34 b(indices)g(runs)e(from) i(0)150 4902 y(to)j FH(size-1)p FK(.)56 b(The)35 b FD(stride)41 b FK(is)36 b(the)g(step-size)i(from)d(one)h(elemen)m(t)i(to)f(the)f (next)g(in)g(ph)m(ysical)g(memory)-8 b(,)150 5011 y(measured)32 b(in)g(units)g(of)g(the)h(appropriate)f(datat)m(yp)s(e.)48 b(The)32 b(p)s(oin)m(ter)g FD(data)h FK(giv)m(es)h(the)e(lo)s(cation)i (of)f(the)150 5121 y(\014rst)28 b(elemen)m(t)h(of)g(the)f(v)m(ector)i (in)e(memory)-8 b(.)41 b(The)27 b(p)s(oin)m(ter)i FD(blo)s(c)m(k)34 b FK(stores)29 b(the)f(lo)s(cation)i(of)f(the)f(memory)150 5230 y(blo)s(c)m(k)k(in)g(whic)m(h)f(the)h(v)m(ector)h(elemen)m(ts)g (are)g(lo)s(cated)g(\(if)f(an)m(y\).)45 b(If)31 b(the)h(v)m(ector)i(o)m (wns)d(this)h(blo)s(c)m(k)g(then)150 5340 y(the)g FD(o)m(wner)39 b FK(\014eld)32 b(is)h(set)f(to)h(one)g(and)f(the)g(blo)s(c)m(k)h(will) g(b)s(e)e(deallo)s(cated)j(when)e(the)g(v)m(ector)i(is)e(freed.)46 b(If)p eop end %%Page: 81 99 TeXDict begin 81 98 bop 150 -116 a FK(Chapter)30 b(8:)41 b(V)-8 b(ectors)32 b(and)e(Matrices)2203 b(81)150 299 y(the)32 b(v)m(ector)h(p)s(oin)m(ts)e(to)i(a)f(blo)s(c)m(k)g(o)m(wned)f (b)m(y)h(another)g(ob)5 b(ject)32 b(then)f(the)h FD(o)m(wner)38 b FK(\014eld)32 b(is)f(zero)i(and)e(an)m(y)150 408 y(underlying)e(blo)s (c)m(k)i(will)g(not)g(b)s(e)e(deallo)s(cated)k(with)d(the)g(v)m(ector.) 275 545 y(The)f(functions)h(for)g(allo)s(cating)j(and)d(accessing)i(v)m (ectors)g(are)e(de\014ned)g(in)g FH(gsl_vector.h)150 747 y Fy(8.3.1)63 b(V)-10 b(ector)40 b(allo)s(cation)150 894 y FK(The)35 b(functions)g(for)g(allo)s(cating)j(memory)d(to)h(a)g (v)m(ector)h(follo)m(w)g(the)e(st)m(yle)i(of)e FH(malloc)f FK(and)h FH(free)p FK(.)55 b(In)150 1004 y(addition)23 b(they)h(also)g(p)s(erform)e(their)h(o)m(wn)g(error)g(c)m(hec)m(king.) 40 b(If)23 b(there)h(is)f(insu\016cien)m(t)g(memory)h(a)m(v)-5 b(ailable)150 1113 y(to)36 b(allo)s(cate)i(a)d(v)m(ector)i(then)e(the)g (functions)g(call)i(the)e(GSL)g(error)g(handler)f(\(with)h(an)g(error)g (n)m(um)m(b)s(er)150 1223 y(of)h FH(GSL_ENOMEM)p FK(\))d(in)i(addition) h(to)g(returning)e(a)i(n)m(ull)g(p)s(oin)m(ter.)56 b(Th)m(us)34 b(if)i(y)m(ou)f(use)h(the)f(library)g(error)150 1332 y(handler)30 b(to)h(ab)s(ort)f(y)m(our)g(program)g(then)g(it)h(isn't)g (necessary)g(to)g(c)m(hec)m(k)h(ev)m(ery)f FH(alloc)p FK(.)3350 1522 y([F)-8 b(unction])-3599 b Fv(gsl_vector)55 b(*)e(gsl_vector_alloc)d Fu(\()p FD(size)p 1894 1522 28 4 v 42 w(t)30 b Ft(n)p Fu(\))390 1631 y FK(This)i(function)g (creates)i(a)f(v)m(ector)h(of)f(length)g FD(n)p FK(,)g(returning)f(a)h (p)s(oin)m(ter)f(to)i(a)f(newly)f(initialized)390 1741 y(v)m(ector)i(struct.)46 b(A)33 b(new)f(blo)s(c)m(k)h(is)f(allo)s (cated)i(for)e(the)h(elemen)m(ts)g(of)g(the)f(v)m(ector,)j(and)d (stored)g(in)390 1850 y(the)h FD(blo)s(c)m(k)39 b FK(comp)s(onen)m(t)34 b(of)f(the)g(v)m(ector)i(struct.)49 b(The)33 b(blo)s(c)m(k)g(is)h(\\o)m (wned")g(b)m(y)f(the)g(v)m(ector,)j(and)390 1960 y(will)31 b(b)s(e)e(deallo)s(cated)k(when)c(the)i(v)m(ector)h(is)e(deallo)s (cated.)3350 2149 y([F)-8 b(unction])-3599 b Fv(gsl_vector)55 b(*)e(gsl_vector_calloc)e Fu(\()p FD(size)p 1947 2149 V 41 w(t)30 b Ft(n)p Fu(\))390 2259 y FK(This)24 b(function)g(allo)s (cates)j(memory)d(for)g(a)h(v)m(ector)h(of)f(length)g FD(n)f FK(and)g(initializes)i(all)g(the)f(elemen)m(ts)390 2368 y(of)31 b(the)f(v)m(ector)i(to)f(zero.)3350 2557 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_vector_free)c Fu(\()p FD(gsl)p 1389 2557 V 40 w(v)m(ector)32 b(*)f Ft(v)p Fu(\))390 2667 y FK(This)k(function)g(frees)h(a)g(previously)g (allo)s(cated)i(v)m(ector)f FD(v)p FK(.)57 b(If)35 b(the)h(v)m(ector)h (w)m(as)g(created)f(using)390 2777 y FH(gsl_vector_alloc)28 b FK(then)33 b(the)f(blo)s(c)m(k)i(underlying)d(the)i(v)m(ector)h(will) f(also)h(b)s(e)e(deallo)s(cated.)49 b(If)390 2886 y(the)34 b(v)m(ector)i(has)e(b)s(een)f(created)i(from)f(another)g(ob)5 b(ject)35 b(then)f(the)g(memory)g(is)g(still)h(o)m(wned)f(b)m(y)390 2996 y(that)d(ob)5 b(ject)31 b(and)f(will)h(not)f(b)s(e)g(deallo)s (cated.)150 3198 y Fy(8.3.2)63 b(Accessing)41 b(v)m(ector)f(elemen)m (ts)150 3344 y FK(Unlik)m(e)31 b FC(f)n(or)-6 b(tran)29 b FK(compilers,)i(C)e(compilers)i(do)f(not)h(usually)f(pro)m(vide)g (supp)s(ort)f(for)h(range)g(c)m(hec)m(king)150 3454 y(of)24 b(v)m(ectors)i(and)d(matrices.)1078 3421 y FB(1)1155 3454 y FK(The)h(functions)f FH(gsl_vector_get)d FK(and)k FH(gsl_vector_set)c FK(can)k(p)s(erform)150 3564 y(p)s(ortable)e(range) g(c)m(hec)m(king)i(for)e(y)m(ou)g(and)f(rep)s(ort)h(an)g(error)f(if)h (y)m(ou)g(attempt)h(to)g(access)g(elemen)m(ts)h(outside)150 3673 y(the)31 b(allo)m(w)m(ed)h(range.)275 3810 y(The)45 b(functions)g(for)h(accessing)i(the)e(elemen)m(ts)h(of)f(a)h(v)m(ector) g(or)f(matrix)g(are)h(de\014ned)d(in)i FH(gsl_)150 3920 y(vector.h)25 b FK(and)i(declared)g FH(extern)i(inline)c FK(to)j(eliminate)h(function-call)f(o)m(v)m(erhead.)41 b(Y)-8 b(ou)28 b(m)m(ust)f(com-)150 4029 y(pile)f(y)m(our)f(program)g (with)g(the)h(prepro)s(cessor)e(macro)i FH(HAVE_INLINE)c FK(de\014ned)i(to)i(use)f(these)h(functions.)275 4166 y(If)34 b(necessary)i(y)m(ou)f(can)g(turn)f(o\013)i(range)f(c)m(hec)m (king)i(completely)g(without)e(mo)s(difying)f(an)m(y)i(source)150 4276 y(\014les)31 b(b)m(y)g(recompiling)h(y)m(our)f(program)f(with)h (the)g(prepro)s(cessor)f(de\014nition)h FH(GSL_RANGE_CHECK_OFF)p FK(.)150 4385 y(Pro)m(vided)38 b(y)m(our)g(compiler)g(supp)s(orts)e (inline)i(functions)g(the)g(e\013ect)h(of)f(turning)g(o\013)g(range)g (c)m(hec)m(king)150 4495 y(is)d(to)g(replace)g(calls)h(to)f FH(gsl_vector_get\(v,i\))30 b FK(b)m(y)k FH(v->data[i*v->stride])29 b FK(and)34 b(calls)i(to)f FH(gsl_)150 4605 y(vector_set\(v,i,x\))28 b FK(b)m(y)33 b FH(v->data[i*v->stride]=x)p FK(.)42 b(Th)m(us)32 b(there)h(should)f(b)s(e)g(no)h(p)s(erformance)150 4714 y(p)s(enalt)m(y)e(for)f(using)g(the)g(range)h(c)m(hec)m(king)h (functions)e(when)g(range)g(c)m(hec)m(king)i(is)f(turned)e(o\013.)275 4851 y(If)j(y)m(ou)h(use)g(a)g(C99)g(compiler)h(whic)m(h)f(requires)f (inline)h(functions)f(in)h(header)g(\014les)g(to)g(b)s(e)f(declared)150 4961 y FH(inline)21 b FK(instead)i(of)h FH(extern)k(inline)p FK(,)23 b(de\014ne)f(the)i(macro)f FH(GSL_C99_INLINE)c FK(\(see)24 b(Section)g(2.5)g([Inline)p 150 5066 1200 4 v 199 5134 a FB(1)275 5166 y Fx(Range)g(c)n(hec)n(king)f(is)i(a)n(v)l (ailable)g(in)f(the)f(GNU)g(C)i(Compiler)g(b)r(ounds-c)n(hec)n(king)e (extension,)h(but)f(it)h(is)h(not)f(part)g(of)g(the)275 5253 y(default)k(installation)h(of)f(GCC.)h(Memory)f(accesses)h(can)f (also)h(b)r(e)e(c)n(hec)n(k)n(ed)g(with)g(V)-6 b(algrind)28 b(or)g(the)f Fz(gcc)f(-fmudflap)275 5340 y Fx(memory)f(protection)h (option.)p eop end %%Page: 82 100 TeXDict begin 82 99 bop 150 -116 a FK(Chapter)30 b(8:)41 b(V)-8 b(ectors)32 b(and)e(Matrices)2203 b(82)150 299 y(functions],)30 b(page)g(6\).)41 b(With)31 b(GCC)e(this)g(is)h (selected)h(automatically)i(when)28 b(compiling)j(in)e(C99)h(mo)s(de) 150 408 y(\()p FH(-std=c99)p FK(\).)275 540 y(If)24 b(inline)h (functions)g(are)g(not)g(used,)h(calls)g(to)g(the)f(functions)g FH(gsl_vector_get)c FK(and)j FH(gsl_vector_)150 650 y(set)37 b FK(will)i(link)f(to)h(the)f(compiled)h(v)m(ersions)f(of)h(these)f (functions)g(in)g(the)g(library)g(itself.)65 b(The)38 b(range)150 759 y(c)m(hec)m(king)f(in)e(these)h(functions)f(is)h(con)m (trolled)h(b)m(y)e(the)h(global)h(in)m(teger)g(v)-5 b(ariable)36 b FH(gsl_check_range)p FK(.)150 869 y(It)d(is)f(enabled)h(b)m(y)f (default|to)h(disable)g(it,)h(set)f FH(gsl_check_range)28 b FK(to)34 b(zero.)48 b(Due)32 b(to)i(function-call)150 978 y(o)m(v)m(erhead,)e(there)e(is)h(less)f(b)s(ene\014t)g(in)g 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b(of)g(the)g FD(i)p FK(-th)g(elemen)m(t)h(of)e(a)h(v)m(ector) i FD(v)43 b FK(to)36 b FD(x)p FK(.)57 b(If)35 b FD(i)40 b FK(lies)d(outside)390 1877 y(the)28 b(allo)m(w)m(ed)i(range)e(of)g(0) h(to)f FD(n)15 b FI(\000)g FK(1)29 b(then)e(the)i(error)e(handler)g(is) h(in)m(v)m(ok)m(ed.)42 b(An)27 b(inline)h(v)m(ersion)h(of)390 1986 y(this)h(function)g(is)h(used)e(when)h FH(HAVE_INLINE)d FK(is)j(de\014ned.)3350 2162 y([F)-8 b(unction])-3599 b Fv(double)54 b(*)f(gsl_vector_ptr)c Fu(\()p FD(gsl)p 1545 2162 V 41 w(v)m(ector)32 b(*)f Ft(v)p FD(,)g(size)p 2184 2162 V 41 w(t)g Ft(i)p Fu(\))3350 2271 y FK([F)-8 b(unction])-3599 b Fv(const)54 b(double)g(*)f(gsl_vector_const_ptr)e Fu(\()p FD(const)31 b(gsl)p 2411 2271 V 41 w(v)m(ector)h(*)f Ft(v)p FD(,)f(size)p 3049 2271 V 41 w(t)565 2381 y Ft(i)p Fu(\))390 2490 y FK(These)36 b(functions)g(return)f(a)h(p)s(oin)m(ter)h (to)f(the)h FD(i)p FK(-th)f(elemen)m(t)i(of)e(a)h(v)m(ector)h FD(v)p FK(.)58 b(If)36 b FD(i)41 b FK(lies)c(outside)390 2600 y(the)29 b(allo)m(w)m(ed)h(range)f(of)g(0)g(to)g FD(n)16 b FI(\000)g FK(1)29 b(then)f(the)h(error)f(handler)g(is)g(in)m (v)m(ok)m(ed)i(and)e(a)h(n)m(ull)f(p)s(oin)m(ter)h(is)390 2709 y(returned.)40 b(Inline)30 b(v)m(ersions)g(of)h(these)g(functions) f(are)g(used)g(when)f FH(HAVE_INLINE)f FK(is)i(de\014ned.)150 2903 y Fy(8.3.3)63 b(Initializing)40 b(v)m(ector)g(elemen)m(ts)3350 3093 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_vector_set_all)c Fu(\()p FD(gsl)p 1545 3093 V 41 w(v)m(ector)32 b(*)f Ft(v)p FD(,)g(double)f Ft(x)p Fu(\))390 3203 y FK(This)g(function)g (sets)g(all)i(the)e(elemen)m(ts)i(of)e(the)h(v)m(ector)h FD(v)38 b FK(to)31 b(the)g(v)-5 b(alue)31 b FD(x)p FK(.)3350 3378 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_vector_set_zero)d Fu(\()p FD(gsl)p 1598 3378 V 41 w(v)m(ector)32 b(*)e Ft(v)p Fu(\))390 3488 y FK(This)g(function)g(sets)g(all)i(the)e(elemen) m(ts)i(of)e(the)h(v)m(ector)h FD(v)38 b FK(to)31 b(zero.)3350 3663 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_vector_set_basis)f Fu(\()p FD(gsl)p 1598 3663 V 41 w(v)m(ector)32 b(*)e Ft(v)p FD(,)h(size)p 2236 3663 V 41 w(t)g Ft(i)p Fu(\))390 3773 y FK(This)d(function)h(mak)m(es)h(a)g(basis)f(v)m(ector)h(b)m(y)f (setting)h(all)g(the)g(elemen)m(ts)g(of)f(the)h(v)m(ector)g FD(v)37 b FK(to)30 b(zero)390 3882 y(except)h(for)f(the)h FD(i)p FK(-th)g(elemen)m(t)h(whic)m(h)e(is)g(set)h(to)g(one.)150 4075 y Fy(8.3.4)63 b(Reading)41 b(and)f(writing)i(v)m(ectors)150 4222 y FK(The)36 b(library)f(pro)m(vides)h(functions)g(for)g(reading)g (and)f(writing)i(v)m(ectors)g(to)g(a)f(\014le)h(as)f(binary)f(data)i (or)150 4332 y(formatted)31 b(text.)3350 4507 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_vector_fwrite)e Fu(\()p FD(FILE)30 b(*)h Ft(stream)p FD(,)h(const)f(gsl)p 2365 4507 V 41 w(v)m(ector)h(*)f Ft(v)p Fu(\))390 4617 y FK(This)41 b(function)g(writes)g(the)h(elemen)m(ts)g(of)g(the)f(v)m(ector)i FD(v)49 b FK(to)43 b(the)e(stream)h FD(stream)g FK(in)f(binary)390 4726 y(format.)58 b(The)36 b(return)f(v)-5 b(alue)36 b(is)g(0)h(for)f(success)g(and)f FH(GSL_EFAILED)e FK(if)j(there)h(w)m (as)f(a)h(problem)390 4836 y(writing)c(to)h(the)f(\014le.)50 b(Since)33 b(the)g(data)h(is)f(written)h(in)e(the)i(nativ)m(e)g(binary) f(format)g(it)h(ma)m(y)g(not)390 4946 y(b)s(e)c(p)s(ortable)g(b)s(et)m (w)m(een)h(di\013eren)m(t)g(arc)m(hitectures.)3350 5121 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_vector_fread)e Fu(\()p FD(FILE)30 b(*)h Ft(stream)p FD(,)h(gsl)p 2075 5121 V 41 w(v)m(ector)g(*)e Ft(v)p Fu(\))390 5230 y FK(This)f(function) g(reads)g(in)m(to)h(the)g(v)m(ector)h FD(v)37 b FK(from)29 b(the)h(op)s(en)f(stream)h FD(stream)f FK(in)h(binary)e(format.)390 5340 y(The)e(v)m(ector)j FD(v)35 b FK(m)m(ust)27 b(b)s(e)f(preallo)s (cated)j(with)d(the)h(correct)i(length)e(since)g(the)h(function)e(uses) h(the)p eop end %%Page: 83 101 TeXDict begin 83 100 bop 150 -116 a FK(Chapter)30 b(8:)41 b(V)-8 b(ectors)32 b(and)e(Matrices)2203 b(83)390 299 y(size)30 b(of)f FD(v)37 b FK(to)29 b(determine)g(ho)m(w)g(man)m(y)g(b) m(ytes)h(to)f(read.)41 b(The)28 b(return)g(v)-5 b(alue)29 b(is)g(0)h(for)e(success)i(and)390 408 y FH(GSL_EFAILED)i FK(if)j(there)h(w)m(as)f(a)h(problem)e(reading)i(from)e(the)i(\014le.) 55 b(The)35 b(data)h(is)f(assumed)f(to)390 518 y(ha)m(v)m(e)e(b)s(een)d (written)i(in)f(the)g(nativ)m(e)i(binary)e(format)g(on)h(the)f(same)h (arc)m(hitecture.)3350 691 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_vector_fprintf)e Fu(\()p FD(FILE)31 b(*)f Ft(stream)p FD(,)j(const)e(gsl)p 2418 691 28 4 v 40 w(v)m(ector)h(*)f Ft(v)p FD(,)g(const)565 801 y(c)m(har)g(*)g Ft(format)p Fu(\))390 911 y FK(This)k(function)h(writes)h(the)f(elemen)m(ts)i(of)e (the)g(v)m(ector)i FD(v)44 b FK(line-b)m(y-line)38 b(to)f(the)f(stream) h FD(stream)390 1020 y FK(using)26 b(the)h(format)g(sp)s(eci\014er)g FD(format)p FK(,)h(whic)m(h)e(should)g(b)s(e)g(one)h(of)g(the)g FH(\045g)p FK(,)g FH(\045e)f FK(or)h FH(\045f)f FK(formats)h(for)390 1130 y(\015oating)37 b(p)s(oin)m(t)f(n)m(um)m(b)s(ers)f(and)g FH(\045d)h 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b(addition)i(to)g(creating)g(v)m (ectors)h(from)e(slices)h(of)f(blo)s(c)m(ks)h(it)g(is)f(also)h(p)s (ossible)f(to)h(slice)g(v)m(ectors)h(and)150 2299 y(create)i(v)m(ector) g(views.)58 b(F)-8 b(or)37 b(example,)i(a)d(sub)m(v)m(ector)i(of)e (another)g(v)m(ector)i(can)f(b)s(e)e(describ)s(ed)h(with)g(a)150 2409 y(view,)i(or)e(t)m(w)m(o)i(views)e(can)g(b)s(e)g(made)g(whic)m(h)g (pro)m(vide)g(access)i(to)f(the)f(ev)m(en)h(and)f(o)s(dd)f(elemen)m(ts) i(of)g(a)150 2519 y(v)m(ector.)275 2649 y(A)30 b(v)m(ector)i(view)f(is) g(a)g(temp)s(orary)f(ob)5 b(ject,)31 b(stored)g(on)f(the)h(stac)m(k,)h (whic)m(h)f(can)f(b)s(e)g(used)g(to)h(op)s(erate)150 2759 y(on)38 b(a)g(subset)f(of)h(v)m(ector)h(elemen)m(ts.)64 b(V)-8 b(ector)39 b(views)f(can)g(b)s(e)f(de\014ned)g(for)g(b)s(oth)g (constan)m(t)i(and)e(non-)150 2869 y(constan)m(t)32 b(v)m(ectors,)g (using)e(separate)h(t)m(yp)s(es)f(that)h(preserv)m(e)g(constness.)41 b(A)30 b(v)m(ector)i(view)f(has)f(the)h(t)m(yp)s(e)150 2978 y FH(gsl_vector_view)i FK(and)j(a)h(constan)m(t)h(v)m(ector)h (view)e(has)f(the)h(t)m(yp)s(e)g FH(gsl_vector_const_view)p FK(.)55 b(In)150 3088 y(b)s(oth)39 b(cases)h(the)f(elemen)m(ts)i(of)e (the)h(view)f(can)h(b)s(e)e(accessed)j(as)e(a)h FH(gsl_vector)c FK(using)j(the)h FH(vector)150 3197 y FK(comp)s(onen)m(t)32 b(of)f(the)h(view)g(ob)5 b(ject.)45 b(A)32 b(p)s(oin)m(ter)f(to)h(a)g (v)m(ector)i(of)d(t)m(yp)s(e)h FH(gsl_vector)27 b(*)32 b FK(or)f FH(const)e(gsl_)150 3307 y(vector)g(*)h FK(can)g(b)s(e)g (obtained)h(b)m(y)f(taking)h(the)g(address)e(of)i(this)f(comp)s(onen)m (t)h(with)f(the)h FH(&)f FK(op)s(erator.)275 3438 y(When)c(using)g (this)g(p)s(oin)m(ter)g(it)h(is)g(imp)s(ortan)m(t)f(to)i(ensure)d(that) i(the)g(view)f(itself)i(remains)e(in)g(scop)s(e|)150 3547 y(the)40 b(simplest)f(w)m(a)m(y)i(to)f(do)f(so)h(is)f(b)m(y)h(alw) m(a)m(ys)h(writing)e(the)h(p)s(oin)m(ter)f(as)h FH(&)p FD(view)8 b FH(.vector)p FK(,)40 b(and)f(nev)m(er)150 3657 y(storing)31 b(this)f(v)-5 b(alue)31 b(in)f(another)h(v)-5 b(ariable.)3350 3830 y([F)d(unction])-3599 b Fv(gsl_vector_view)57 b(gsl_vector_subvector)51 b Fu(\()p FD(gsl)p 2225 3830 V 41 w(v)m(ector)32 b(*)f Ft(v)p FD(,)g(size)p 2864 3830 V 41 w(t)565 3940 y Ft(offset)p FD(,)h(size)p 1081 3940 V 41 w(t)f Ft(n)p Fu(\))3350 4050 y FK([F)-8 b(unction])-3599 b Fv(gsl_vector_const_view)59 b(gsl_vector_const_subvec)q(tor)52 b Fu(\()p FD(const)565 4159 y(gsl)p 677 4159 V 41 w(v)m(ector)32 b(*)e Ft(v)p FD(,)h(size)p 1315 4159 V 41 w(t)g Ft(offset)p FD(,)h(size)p 1932 4159 V 41 w(t)f Ft(n)p Fu(\))390 4269 y FK(These)e(functions)f(return)g(a)h(v)m(ector)i(view)e(of)g(a)h(sub)m (v)m(ector)g(of)f(another)g(v)m(ector)i FD(v)p FK(.)40 b(The)28 b(start)i(of)390 4378 y(the)i(new)g(v)m(ector)h(is)g(o\013set) g(b)m(y)f FD(o\013set)j FK(elemen)m(ts)e(from)f(the)g(start)g(of)h(the) f(original)h(v)m(ector.)47 b(The)390 4488 y(new)32 b(v)m(ector)h(has)f FD(n)f FK(elemen)m(ts.)47 b(Mathematically)-8 b(,)37 b(the)32 b FD(i)p FK(-th)g(elemen)m(t)i(of)e(the)g(new)g(v)m(ector)h FD(v')38 b FK(is)390 4597 y(giv)m(en)31 b(b)m(y)-8 b(,)630 4728 y FH(v'\(i\))46 b(=)i(v->data[\(offset)43 b(+)48 b(i\)*v->stride])390 4859 y FK(where)30 b(the)g(index)g FD(i)36 b FK(runs)29 b(from)g(0)i(to)g FH(n-1)p FK(.)390 4990 y(The)21 b FH(data)f FK(p)s(oin)m(ter)h(of)g(the)h(returned)e(v)m (ector)i(struct)g(is)f(set)h(to)g(n)m(ull)f(if)g(the)g(com)m(bined)h (parameters)390 5100 y(\()p FD(o\013set)p FK(,)p FD(n)p FK(\))32 b(o)m(v)m(errun)e(the)h(end)e(of)i(the)g(original)g(v)m (ector.)390 5230 y(The)23 b(new)f(v)m(ector)j(is)e(only)h(a)f(view)h (of)f(the)g(blo)s(c)m(k)h(underlying)e(the)i(original)g(v)m(ector,)i FD(v)p FK(.)39 b(The)22 b(blo)s(c)m(k)390 5340 y(con)m(taining)37 b(the)f(elemen)m(ts)h(of)e FD(v)44 b FK(is)35 b(not)h(o)m(wned)f(b)m(y) h(the)g(new)f(v)m(ector.)57 b(When)36 b(the)g(view)f(go)s(es)p eop end %%Page: 84 102 TeXDict begin 84 101 bop 150 -116 a FK(Chapter)30 b(8:)41 b(V)-8 b(ectors)32 b(and)e(Matrices)2203 b(84)390 299 y(out)35 b(of)h(scop)s(e)f(the)g(original)h(v)m(ector)h FD(v)43 b FK(and)34 b(its)i(blo)s(c)m(k)f(will)h(con)m(tin)m(ue)g(to)g (exist.)55 b(The)35 b(original)390 408 y(memory)25 b(can)h(only)f(b)s (e)g(deallo)s(cated)i(b)m(y)e(freeing)h(the)g(original)g(v)m(ector.)41 b(Of)24 b(course,)j(the)f(original)390 518 y(v)m(ector)32 b(should)d(not)i(b)s(e)f(deallo)s(cated)i(while)e(the)h(view)g(is)f (still)h(in)f(use.)390 646 y(The)23 b(function)g FH (gsl_vector_const_subvec)o(tor)17 b FK(is)23 b(equiv)-5 b(alen)m(t)25 b(to)e FH(gsl_vector_subvector)390 756 y FK(but)30 b(can)g(b)s(e)g(used)g(for)g(v)m(ectors)i(whic)m(h)e(are)g (declared)h FH(const)p FK(.)3350 920 y([F)-8 b(unction])-3599 b Fv(gsl_vector_view)57 b(gsl_vector_subvector_w)q(ith_)q(str)q(ide)52 b Fu(\()p FD(gsl)p 2853 920 28 4 v 41 w(v)m(ector)565 1029 y(*)31 b Ft(v)p FD(,)g(size)p 896 1029 V 41 w(t)f Ft(offset)p FD(,)j(size)p 1513 1029 V 41 w(t)d Ft(stride)p FD(,)j(size)p 2130 1029 V 41 w(t)d Ft(n)p Fu(\))3350 1139 y FK([F)-8 b(unction])-3599 b Fv(gsl_vector_const_view)565 1249 y(gsl_vector_const_subve)q(cto)q(r_w)q(ith)q(_str)q(ide)52 b Fu(\()p FD(const)31 b(gsl)p 2983 1249 V 41 w(v)m(ector)h(*)f Ft(v)p FD(,)f(size)p 3621 1249 V 41 w(t)565 1358 y Ft(offset)p FD(,)i(size)p 1081 1358 V 41 w(t)f Ft(stride)p FD(,)h(size)p 1698 1358 V 41 w(t)f Ft(n)p Fu(\))390 1468 y FK(These)43 b(functions)g(return)f(a)i(v)m(ector)h(view)f(of)f(a)h(sub)m(v)m(ector) h(of)e(another)h(v)m(ector)h FD(v)51 b FK(with)43 b(an)390 1577 y(additional)d(stride)f(argumen)m(t.)66 b(The)39 b(sub)m(v)m(ector)g(is)g(formed)g(in)f(the)h(same)h(w)m(a)m(y)f(as)g (for)g FH(gsl_)390 1687 y(vector_subvector)24 b FK(but)k(the)g(new)g(v) m(ector)i(has)e FD(n)g FK(elemen)m(ts)i(with)e(a)h(step-size)g(of)g FD(stride)k FK(from)390 1797 y(one)j(elemen)m(t)h(to)f(the)g(next)g(in) f(the)h(original)g(v)m(ector.)58 b(Mathematically)-8 b(,)41 b(the)36 b FD(i)p FK(-th)g(elemen)m(t)h(of)390 1906 y(the)31 b(new)e(v)m(ector)j FD(v')k FK(is)31 b(giv)m(en)g(b)m(y) -8 b(,)630 2034 y FH(v'\(i\))46 b(=)i(v->data[\(offset)43 b(+)48 b(i*stride\)*v->stride])390 2162 y FK(where)30 b(the)g(index)g FD(i)36 b FK(runs)29 b(from)g(0)i(to)g FH(n-1)p FK(.)390 2290 y(Note)26 b(that)f(sub)m(v)m(ector)h(views)f (giv)m(e)h(direct)g(access)g(to)f(the)g(underlying)f(elemen)m(ts)i(of)f (the)g(original)390 2399 y(v)m(ector.)42 b(F)-8 b(or)29 b(example,)h(the)e(follo)m(wing)i(co)s(de)f(will)g(zero)g(the)g(ev)m (en)g(elemen)m(ts)h(of)f(the)f(v)m(ector)j FH(v)d FK(of)390 2509 y(length)j FH(n)p FK(,)f(while)g(lea)m(ving)j(the)d(o)s(dd)f (elemen)m(ts)j(un)m(touc)m(hed,)630 2637 y FH(gsl_vector_view)44 b(v_even)725 2746 y(=)k(gsl_vector_subvector_wit)o(h_st)o(rid)o(e)42 b(\(v,)47 b(0,)g(2,)g(n/2\);)630 2856 y(gsl_vector_set_zero)c (\(&v_even.vector\);)390 2984 y FK(A)28 b(v)m(ector)h(view)e(can)h(b)s (e)f(passed)g(to)h(an)m(y)g(subroutine)f(whic)m(h)g(tak)m(es)i(a)f(v)m (ector)h(argumen)m(t)f(just)f(as)390 3093 y(a)f(directly)g(allo)s (cated)i(v)m(ector)f(w)m(ould)f(b)s(e,)g(using)f FH(&)p FD(view)8 b FH(.vector)p FK(.)37 b(F)-8 b(or)26 b(example,)i(the)d (follo)m(wing)390 3203 y(co)s(de)31 b(computes)f(the)h(norm)e(of)i(the) f(o)s(dd)g(elemen)m(ts)h(of)g FH(v)f FK(using)g(the)g FC(blas)g FK(routine)g FC(dnrm2)p FK(,)630 3331 y FH(gsl_vector_view)44 b(v_odd)725 3440 y(=)k(gsl_vector_subvector_wit)o(h_st)o(rid)o(e)42 b(\(v,)47 b(1,)g(2,)g(n/2\);)630 3550 y(double)f(r)i(=)f (gsl_blas_dnrm2)d(\(&v_odd.vector\);)390 3678 y FK(The)104 b(function)g FH(gsl_vector_const_subvec)o(tor)o(_wit)o(h_st)o(rid)o(e) 98 b FK(is)105 b(equiv)-5 b(alen)m(t)105 b(to)390 3787 y FH(gsl_vector_subvector_wit)o(h_st)o(ride)62 b FK(but)68 b(can)h(b)s(e)g(used)f(for)h(v)m(ectors)h(whic)m(h)f(are)390 3897 y(declared)31 b FH(const)p FK(.)3350 4061 y([F)-8 b(unction])-3599 b Fv(gsl_vector_view)57 b(gsl_vector_complex_rea)q(l) 51 b Fu(\()p FD(gsl)p 2382 4061 V 41 w(v)m(ector)p 2664 4061 V 42 w(complex)31 b(*)565 4171 y Ft(v)p Fu(\))3350 4281 y FK([F)-8 b(unction])-3599 b Fv(gsl_vector_const_view)59 b(gsl_vector_complex_cons)q(t_r)q(eal)52 b Fu(\()p FD(const)565 4390 y(gsl)p 677 4390 V 41 w(v)m(ector)p 959 4390 V 41 w(complex)31 b(*)g Ft(v)p Fu(\))390 4500 y FK(These)f(functions)g (return)f(a)i(v)m(ector)h(view)f(of)f(the)h(real)g(parts)f(of)g(the)h (complex)g(v)m(ector)h FD(v)p FK(.)390 4628 y(The)70 b(function)h FH(gsl_vector_complex_const)o(_rea)o(l)65 b FK(is)71 b(equiv)-5 b(alen)m(t)72 b(to)g FH(gsl_vector_)390 4737 y(complex_real)27 b FK(but)j(can)g(b)s(e)g(used)g(for)g(v)m (ectors)i(whic)m(h)e(are)h(declared)f FH(const)p FK(.)3350 4902 y([F)-8 b(unction])-3599 b Fv(gsl_vector_view)57 b(gsl_vector_complex_ima)q(g)51 b Fu(\()p FD(gsl)p 2382 4902 V 41 w(v)m(ector)p 2664 4902 V 42 w(complex)31 b(*)565 5011 y Ft(v)p Fu(\))3350 5121 y FK([F)-8 b(unction])-3599 b Fv(gsl_vector_const_view)59 b(gsl_vector_complex_cons)q(t_i)q(mag)52 b Fu(\()p FD(const)565 5230 y(gsl)p 677 5230 V 41 w(v)m(ector)p 959 5230 V 41 w(complex)31 b(*)g Ft(v)p Fu(\))390 5340 y FK(These)e(functions)g(return)f(a)i(v)m(ector)h(view)f(of)f(the)h (imaginary)g(parts)f(of)g(the)h(complex)g(v)m(ector)h FD(v)p FK(.)p eop end %%Page: 85 103 TeXDict begin 85 102 bop 150 -116 a FK(Chapter)30 b(8:)41 b(V)-8 b(ectors)32 b(and)e(Matrices)2203 b(85)390 299 y(The)70 b(function)h FH(gsl_vector_complex_const)o(_ima)o(g)65 b FK(is)71 b(equiv)-5 b(alen)m(t)72 b(to)g FH(gsl_vector_)390 408 y(complex_imag)27 b FK(but)j(can)g(b)s(e)g(used)g(for)g(v)m(ectors) i(whic)m(h)e(are)h(declared)f FH(const)p FK(.)3350 592 y([F)-8 b(unction])-3599 b Fv(gsl_vector_view)57 b (gsl_vector_view_array)52 b Fu(\()p FD(double)30 b(*)h Ft(base)p FD(,)g(size)p 2946 592 28 4 v 41 w(t)g Ft(n)p Fu(\))3350 702 y FK([F)-8 b(unction])-3599 b Fv(gsl_vector_const_view) 59 b(gsl_vector_const_view_a)q(rra)q(y)51 b Fu(\()p FD(const)565 812 y(double)30 b(*)h Ft(base)p FD(,)h(size)p 1346 812 V 40 w(t)f Ft(n)p Fu(\))390 921 y FK(These)c(functions)f(return)g(a)i (v)m(ector)h(view)e(of)g(an)g(arra)m(y)-8 b(.)41 b(The)26 b(start)i(of)f(the)h(new)e(v)m(ector)j(is)e(giv)m(en)390 1031 y(b)m(y)i FD(base)34 b FK(and)28 b(has)g FD(n)g FK(elemen)m(ts.)42 b(Mathematically)-8 b(,)33 b(the)28 b FD(i)p FK(-th)h(elemen)m(t)i(of)d(the)h(new)g(v)m(ector)h FD(v')k FK(is)390 1140 y(giv)m(en)d(b)m(y)-8 b(,)630 1275 y FH(v'\(i\))46 b(=)i(base[i])390 1409 y FK(where)30 b(the)g(index)g FD(i)36 b FK(runs)29 b(from)g(0)i(to)g FH(n-1)p FK(.)390 1543 y(The)g(arra)m(y)h(con)m(taining)h(the)f(elemen) m(ts)h(of)e FD(v)40 b FK(is)31 b(not)h(o)m(wned)f(b)m(y)h(the)g(new)f (v)m(ector)i(view.)44 b(When)390 1653 y(the)e(view)f(go)s(es)i(out)e (of)h(scop)s(e)g(the)f(original)i(arra)m(y)f(will)g(con)m(tin)m(ue)h (to)f(exist.)75 b(The)41 b(original)390 1763 y(memory)32 b(can)g(only)g(b)s(e)g(deallo)s(cated)h(b)m(y)f(freeing)h(the)f (original)h(p)s(oin)m(ter)f FD(base)p FK(.)46 b(Of)31 b(course,)i(the)390 1872 y(original)f(arra)m(y)e(should)g(not)g(b)s(e)g (deallo)s(cated)i(while)f(the)f(view)h(is)f(still)i(in)e(use.)390 2007 y(The)47 b(function)f FH(gsl_vector_const_view_arr)o(ay)41 b FK(is)47 b(equiv)-5 b(alen)m(t)49 b(to)e FH(gsl_vector_view_)390 2116 y(array)29 b FK(but)h(can)g(b)s(e)g(used)g(for)g(arra)m(ys)g(whic) m(h)h(are)f(declared)h FH(const)p FK(.)3350 2300 y([F)-8 b(unction])-3599 b Fv(gsl_vector_view)57 b(gsl_vector_view_array_)q (with)q(_st)q(rid)q(e)51 b Fu(\()p FD(double)31 b(*)565 2410 y Ft(base)p FD(,)h(size)p 977 2410 V 41 w(t)e Ft(stride)p FD(,)j(size)p 1594 2410 V 41 w(t)d Ft(n)p Fu(\))3350 2519 y FK([F)-8 b(unction])-3599 b Fv(gsl_vector_const_view)565 2629 y(gsl_vector_const_view_)q(arr)q(ay_)q(wit)q(h_st)q(rid)q(e)51 b Fu(\()p FD(const)32 b(double)e(*)g Ft(base)p FD(,)565 2738 y(size)p 712 2738 V 41 w(t)h Ft(stride)p FD(,)h(size)p 1329 2738 V 41 w(t)f Ft(n)p Fu(\))390 2848 y FK(These)d(functions)g (return)f(a)h(v)m(ector)i(view)f(of)f(an)g(arra)m(y)h FD(base)k FK(with)28 b(an)g(additional)i(stride)e(argu-)390 2958 y(men)m(t.)43 b(The)31 b(sub)m(v)m(ector)h(is)f(formed)f(in)h(the) g(same)g(w)m(a)m(y)h(as)g(for)e FH(gsl_vector_view_array)c FK(but)390 3067 y(the)i(new)f(v)m(ector)j(has)e FD(n)f FK(elemen)m(ts)i(with)f(a)g(step-size)h(of)f FD(stride)33 b FK(from)28 b(one)g(elemen)m(t)h(to)g(the)f(next)390 3177 y(in)33 b(the)g(original)h(arra)m(y)-8 b(.)50 b(Mathematically)-8 b(,)37 b(the)c FD(i)p FK(-th)h(elemen)m(t)g(of)f(the)g(new)g(v)m(ector) i FD(v')j FK(is)33 b(giv)m(en)390 3286 y(b)m(y)-8 b(,)630 3421 y FH(v'\(i\))46 b(=)i(base[i*stride])390 3555 y FK(where)30 b(the)g(index)g FD(i)36 b FK(runs)29 b(from)g(0)i(to)g FH(n-1)p FK(.)390 3689 y(Note)26 b(that)g(the)f(view)g(giv)m(es)h (direct)f(access)h(to)g(the)f(underlying)f(elemen)m(ts)i(of)f(the)g (original)h(arra)m(y)-8 b(.)390 3799 y(A)28 b(v)m(ector)h(view)e(can)h (b)s(e)f(passed)g(to)h(an)m(y)g(subroutine)f(whic)m(h)g(tak)m(es)i(a)f (v)m(ector)h(argumen)m(t)f(just)f(as)390 3909 y(a)k(directly)g(allo)s (cated)h(v)m(ector)g(w)m(ould)e(b)s(e,)g(using)g FH(&)p FD(view)8 b FH(.vector)p FK(.)390 4043 y(The)47 b(function)f FH(gsl_vector_const_view_arr)o(ay_w)o(ith_)o(str)o(ide)41 b FK(is)47 b(equiv)-5 b(alen)m(t)48 b(to)g FH(gsl_)390 4153 y(vector_view_array_with_s)o(trid)o(e)39 b FK(but)k(can)i(b)s(e)f (used)g(for)g(arra)m(ys)h(whic)m(h)g(are)f(declared)390 4262 y FH(const)p FK(.)150 4461 y Fy(8.3.6)63 b(Cop)m(ying)41 b(v)m(ectors)150 4608 y FK(Common)23 b(op)s(erations)h(on)g(v)m(ectors) h(suc)m(h)e(as)h(addition)g(and)f(m)m(ultiplication)j(are)e(a)m(v)-5 b(ailable)26 b(in)d(the)h FC(blas)150 4718 y FK(part)h(of)g(the)g (library)f(\(see)i(Chapter)e(13)i([BLAS)f(Supp)s(ort],)f(page)i(125\).) 40 b(Ho)m(w)m(ev)m(er,)29 b(it)c(is)g(useful)f(to)i(ha)m(v)m(e)150 4827 y(a)31 b(small)g(n)m(um)m(b)s(er)f(of)g(utilit)m(y)i(functions)f (whic)m(h)f(do)h(not)g(require)f(the)h(full)f FC(blas)f FK(co)s(de.)42 b(The)30 b(follo)m(wing)150 4937 y(functions)g(fall)h (in)m(to)g(this)g(category)-8 b(.)3350 5121 y([F)g(unction])-3599 b Fv(int)53 b(gsl_vector_memcpy)e Fu(\()p FD(gsl)p 1441 5121 V 41 w(v)m(ector)32 b(*)e Ft(dest)p FD(,)i(const)f(gsl)p 2439 5121 V 41 w(v)m(ector)h(*)e Ft(src)p Fu(\))390 5230 y FK(This)39 b(function)g(copies)i(the)f(elemen)m(ts)h(of)f(the)f(v)m (ector)j FD(src)j FK(in)m(to)40 b(the)g(v)m(ector)i FD(dest)p FK(.)68 b(The)40 b(t)m(w)m(o)390 5340 y(v)m(ectors)32 b(m)m(ust)e(ha)m(v)m(e)i(the)e(same)h(length.)p eop end %%Page: 86 104 TeXDict begin 86 103 bop 150 -116 a FK(Chapter)30 b(8:)41 b(V)-8 b(ectors)32 b(and)e(Matrices)2203 b(86)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_vector_swap)d Fu(\()p FD(gsl)p 1336 299 28 4 v 41 w(v)m(ector)32 b(*)f Ft(v)p FD(,)g(gsl)p 1940 299 V 40 w(v)m(ector)h(*)f Ft(w)p Fu(\))390 408 y FK(This)k(function)g(exc)m(hanges)i(the)f(elemen)m(ts)h (of)f(the)g(v)m(ectors)h FD(v)43 b FK(and)35 b FD(w)43 b FK(b)m(y)36 b(cop)m(ying.)57 b(The)36 b(t)m(w)m(o)390 518 y(v)m(ectors)c(m)m(ust)e(ha)m(v)m(e)i(the)e(same)h(length.)150 711 y Fy(8.3.7)63 b(Exc)m(hanging)40 b(elemen)m(ts)150 858 y FK(The)30 b(follo)m(wing)i(function)e(can)g(b)s(e)g(used)g(to)h (exc)m(hange,)h(or)e(p)s(erm)m(ute,)g(the)h(elemen)m(ts)h(of)e(a)h(v)m (ector.)3350 1032 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_vector_swap_eleme)q(nts)f Fu(\()p FD(gsl)p 1807 1032 V 41 w(v)m(ector)32 b(*)f Ft(v)p FD(,)f(size)p 2445 1032 V 41 w(t)h Ft(i)p FD(,)g(size)p 2801 1032 V 41 w(t)f Ft(j)p Fu(\))390 1141 y FK(This)g(function)g(exc)m(hanges)h(the)g FD(i)p FK(-th)g(and)e FD(j)p FK(-th)i(elemen)m(ts)g(of)g(the)f(v)m (ector)i FD(v)39 b FK(in-place.)3350 1316 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_vector_reverse)e Fu(\()p FD(gsl)p 1493 1316 V 41 w(v)m(ector)32 b(*)f Ft(v)p Fu(\))390 1425 y FK(This)f(function)g(rev)m(erses)h(the)f(order)g(of)h(the)f(elemen)m (ts)i(of)e(the)h(v)m(ector)h FD(v)p FK(.)150 1618 y Fy(8.3.8)63 b(V)-10 b(ector)40 b(op)s(erations)3350 1808 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_vector_add)d Fu(\()p FD(gsl)p 1284 1808 V 41 w(v)m(ector)32 b(*)f Ft(a)p FD(,)f(const)h(gsl) p 2125 1808 V 41 w(v)m(ector)h(*)f Ft(b)p Fu(\))390 1918 y FK(This)i(function)h(adds)f(the)h(elemen)m(ts)h(of)f(v)m(ector)h FD(b)h FK(to)e(the)g(elemen)m(ts)i(of)e(v)m(ector)h FD(a)p FK(.)52 b(The)33 b(result)390 2027 y FE(a)438 2041 y Fq(i)491 2027 y FI( )25 b FE(a)655 2041 y Fq(i)703 2027 y FK(+)19 b FE(b)832 2041 y Fq(i)890 2027 y FK(is)31 b(stored)f(in)g FD(a)g FK(and)g FD(b)i FK(remains)e(unc)m(hanged.)40 b(The)30 b(t)m(w)m(o)h(v)m(ectors)h(m)m(ust)e(ha)m(v)m(e)i(the)390 2137 y(same)f(length.)3350 2311 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_vector_sub)d Fu(\()p FD(gsl)p 1284 2311 V 41 w(v)m(ector)32 b(*)f Ft(a)p FD(,)f(const)h(gsl)p 2125 2311 V 41 w(v)m(ector)h(*)f Ft(b)p Fu(\))390 2421 y FK(This)g(function)h(subtracts)g(the)g(elemen)m(ts)h(of)f(v)m(ector)i FD(b)g FK(from)d(the)h(elemen)m(ts)i(of)e(v)m(ector)h FD(a)p FK(.)46 b(The)390 2530 y(result)36 b FE(a)697 2544 y Fq(i)759 2530 y FI( )f FE(a)933 2544 y Fq(i)984 2530 y FI(\000)24 b FE(b)1118 2544 y Fq(i)1182 2530 y FK(is)36 b(stored)g(in)g FD(a)g FK(and)f FD(b)j FK(remains)d(unc)m (hanged.)58 b(The)35 b(t)m(w)m(o)j(v)m(ectors)f(m)m(ust)390 2640 y(ha)m(v)m(e)32 b(the)e(same)h(length.)3350 2814 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_vector_mul)d Fu(\()p FD(gsl)p 1284 2814 V 41 w(v)m(ector)32 b(*)f Ft(a)p FD(,)f(const)h(gsl)p 2125 2814 V 41 w(v)m(ector)h(*)f Ft(b)p Fu(\))390 2924 y FK(This)36 b(function)f(m)m(ultiplies)j(the)e (elemen)m(ts)i(of)e(v)m(ector)i FD(a)f FK(b)m(y)f(the)g(elemen)m(ts)i (of)f(v)m(ector)g FD(b)p FK(.)58 b(The)390 3033 y(result)26 b FE(a)687 3047 y Fq(i)740 3033 y FI( )f FE(a)904 3047 y Fq(i)944 3033 y FI(\003)12 b FE(b)1040 3047 y Fq(i)1093 3033 y FK(is)27 b(stored)f(in)g FD(a)g FK(and)g FD(b)h FK(remains)f(unc)m(hanged.)39 b(The)26 b(t)m(w)m(o)h(v)m(ectors)h(m)m (ust)e(ha)m(v)m(e)390 3143 y(the)31 b(same)f(length.)3350 3317 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_vector_div)d Fu(\()p FD(gsl)p 1284 3317 V 41 w(v)m(ector)32 b(*)f Ft(a)p FD(,)f(const)h(gsl)p 2125 3317 V 41 w(v)m(ector)h(*)f Ft(b)p Fu(\))390 3427 y FK(This)26 b(function)h(divides)g(the)g(elemen) m(ts)h(of)g(v)m(ector)g FD(a)g FK(b)m(y)f(the)g(elemen)m(ts)h(of)g(v)m (ector)g FD(b)p FK(.)39 b(The)27 b(result)390 3536 y FE(a)438 3550 y Fq(i)496 3536 y FI( )k FE(a)666 3550 y Fq(i)694 3536 y FE(=b)778 3550 y Fq(i)839 3536 y FK(is)j(stored)g(in) f FD(a)h FK(and)f FD(b)i FK(remains)f(unc)m(hanged.)50 b(The)33 b(t)m(w)m(o)i(v)m(ectors)g(m)m(ust)f(ha)m(v)m(e)h(the)390 3646 y(same)c(length.)3350 3820 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_vector_scale)e Fu(\()p FD(gsl)p 1389 3820 V 40 w(v)m(ector)32 b(*)f Ft(a)p FD(,)g(const)g(double)f Ft(x)p Fu(\))390 3930 y FK(This)d(function)g(m)m(ultiplies)i(the)f (elemen)m(ts)h(of)f(v)m(ector)h FD(a)g FK(b)m(y)e(the)h(constan)m(t)h (factor)g FD(x)p FK(.)40 b(The)27 b(result)390 4039 y FE(a)438 4053 y Fq(i)491 4039 y FI( )e FE(xa)707 4053 y Fq(i)765 4039 y FK(is)30 b(stored)h(in)f FD(a)p FK(.)3350 4214 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_vector_add_consta)q(nt) f Fu(\()p FD(gsl)p 1755 4214 V 41 w(v)m(ector)32 b(*)e Ft(a)p FD(,)h(const)g(double)f Ft(x)p Fu(\))390 4323 y FK(This)i(function)h(adds)g(the)g(constan)m(t)i(v)-5 b(alue)33 b FD(x)40 b FK(to)33 b(the)h(elemen)m(ts)g(of)g(the)f(v)m (ector)i FD(a)p FK(.)49 b(The)33 b(result)390 4433 y FE(a)438 4447 y Fq(i)491 4433 y FI( )25 b FE(a)655 4447 y Fq(i)703 4433 y FK(+)20 b FE(x)30 b FK(is)h(stored)f(in)g FD(a)p FK(.)150 4625 y Fy(8.3.9)63 b(Finding)42 b(maxim)m(um)f(and)g (minim)m(um)h(elemen)m(ts)f(of)h(v)m(ectors)150 4772 y FK(The)30 b(follo)m(wing)i(op)s(erations)e(are)h(only)g(de\014ned)e (for)h(real)h(v)m(ectors.)3350 4947 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_vector_max)c Fu(\()p FD(const)31 b(gsl)p 1679 4947 V 41 w(v)m(ector)h(*)e Ft(v)p Fu(\))390 5056 y FK(This)g(function)g(returns)f(the)h(maxim)m(um)h(v)-5 b(alue)30 b(in)g(the)h(v)m(ector)h FD(v)p FK(.)3350 5230 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_vector_min)c Fu(\()p FD(const)31 b(gsl)p 1679 5230 V 41 w(v)m(ector)h(*)e Ft(v)p Fu(\))390 5340 y FK(This)g(function)g(returns)f(the)h(minim)m (um)g(v)-5 b(alue)31 b(in)f(the)g(v)m(ector)i FD(v)p FK(.)p eop end %%Page: 87 105 TeXDict begin 87 104 bop 150 -116 a FK(Chapter)30 b(8:)41 b(V)-8 b(ectors)32 b(and)e(Matrices)2203 b(87)3350 299 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_vector_minmax)c Fu(\()p FD(const)31 b(gsl)p 1731 299 28 4 v 41 w(v)m(ector)h(*)f Ft(v)p FD(,)g(double)e(*)i Ft(min_out)p FD(,)565 408 y(double)f(*)h Ft(max_out)p Fu(\))390 518 y FK(This)41 b(function)g(returns)f(the)h(minim)m(um)g(and)g(maxim)m(um)g(v)-5 b(alues)42 b(in)f(the)g(v)m(ector)i FD(v)p FK(,)i(storing)390 628 y(them)30 b(in)g FD(min)p 886 628 V 40 w(out)i FK(and)e FD(max)p 1435 628 V 40 w(out)p FK(.)3350 813 y([F)-8 b(unction])-3599 b Fv(size_t)54 b(gsl_vector_max_index)e Fu(\()p FD(const)31 b(gsl)p 1993 813 V 40 w(v)m(ector)h(*)f Ft(v)p Fu(\))390 922 y FK(This)h(function)h(returns)f(the)i(index)e(of) i(the)f(maxim)m(um)g(v)-5 b(alue)34 b(in)f(the)g(v)m(ector)i FD(v)p FK(.)49 b(When)33 b(there)390 1032 y(are)e(sev)m(eral)h(equal)e (maxim)m(um)h(elemen)m(ts)g(then)f(the)h(lo)m(w)m(est)h(index)e(is)h (returned.)3350 1217 y([F)-8 b(unction])-3599 b Fv(size_t)54 b(gsl_vector_min_index)e Fu(\()p FD(const)31 b(gsl)p 1993 1217 V 40 w(v)m(ector)h(*)f Ft(v)p Fu(\))390 1327 y FK(This)i(function)h(returns)f(the)i(index)f(of)g(the)h(minim)m(um)e (v)-5 b(alue)35 b(in)f(the)g(v)m(ector)i FD(v)p FK(.)53 b(When)34 b(there)390 1436 y(are)d(sev)m(eral)h(equal)e(minim)m(um)g (elemen)m(ts)i(then)e(the)g(lo)m(w)m(est)j(index)d(is)g(returned.)3350 1621 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_vector_minmax_index)e Fu(\()p FD(const)31 b(gsl)p 2045 1621 V 41 w(v)m(ector)h(*)e Ft(v)p FD(,)h(size)p 2683 1621 V 41 w(t)g(*)g Ft(imin)p FD(,)565 1731 y(size)p 712 1731 V 41 w(t)g(*)f Ft(imax)p Fu(\))390 1840 y FK(This)21 b(function)g(returns)g(the)h(indices)g(of)g (the)g(minim)m(um)f(and)g(maxim)m(um)h(v)-5 b(alues)22 b(in)f(the)h(v)m(ector)i FD(v)p FK(,)390 1950 y(storing)29 b(them)f(in)g FD(imin)g FK(and)f FD(imax)p FK(.)41 b(When)28 b(there)g(are)h(sev)m(eral)h(equal)e(minim)m(um)g(or)g(maxim)m(um)390 2060 y(elemen)m(ts)k(then)e(the)g(lo)m(w)m(est)j(indices)d(are)h (returned.)150 2259 y Fy(8.3.10)63 b(V)-10 b(ector)40 b(prop)s(erties)150 2406 y FK(The)27 b(follo)m(wing)i(functions)f(are)g (de\014ned)e(for)i(real)g(and)f(complex)h(v)m(ectors.)42 b(F)-8 b(or)28 b(complex)g(v)m(ectors)i(b)s(oth)150 2516 y(the)h(real)g(and)e(imaginary)i(parts)f(m)m(ust)h(satisfy)g(the)f (conditions.)3350 2701 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_vector_isnull)e Fu(\()p FD(const)31 b(gsl)p 1679 2701 V 41 w(v)m(ector)h(*)e Ft(v)p Fu(\))3350 2810 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_vector_ispos)e Fu(\()p FD(const)31 b(gsl)p 1627 2810 V 40 w(v)m(ector)h(*)f Ft(v)p Fu(\))3350 2920 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_vector_isneg)e Fu(\()p FD(const)31 b(gsl)p 1627 2920 V 40 w(v)m(ector)h(*)f Ft(v)p Fu(\))3350 3030 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_vector_isnonneg)e Fu(\()p FD(const)32 b(gsl)p 1784 3030 V 40 w(v)m(ector)g(*)f Ft(v)p Fu(\))390 3139 y FK(These)e(functions)g(return)f(1)h(if)g(all)h (the)g(elemen)m(ts)g(of)g(the)f(v)m(ector)i FD(v)37 b FK(are)29 b(zero,)i(strictly)f(p)s(ositiv)m(e,)390 3249 y(strictly)h(negativ)m(e,)i(or)e(non-negativ)m(e)h(resp)s(ectiv)m(ely) -8 b(,)32 b(and)e(0)h(otherwise.)3350 3434 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_vector_equal)e Fu(\()p FD(const)31 b(gsl)p 1627 3434 V 40 w(v)m(ector)h(*)f Ft(u)p FD(,)g(const)g(gsl)p 2468 3434 V 40 w(v)m(ector)h(*)f Ft(v)p Fu(\))390 3543 y FK(This)j(function)h(returns)f(1)i(if)f(the)g(v)m(ectors)h FD(u)f FK(and)g FD(v)42 b FK(are)36 b(equal)g(\(b)m(y)f(comparison)g (of)g(elemen)m(t)390 3653 y(v)-5 b(alues\))31 b(and)f(0)h(otherwise.) 150 3853 y Fy(8.3.11)63 b(Example)40 b(programs)j(for)f(v)m(ectors)150 4000 y FK(This)32 b(program)h(sho)m(ws)g(ho)m(w)g(to)h(allo)s(cate,)i (initialize)g(and)c(read)h(from)f(a)i(v)m(ector)h(using)d(the)h (functions)150 4109 y FH(gsl_vector_alloc)p FK(,)26 b FH(gsl_vector_set)h FK(and)i FH(gsl_vector_get)p FK(.)390 4244 y FH(#include)46 b()390 4354 y(#include)g ()390 4573 y(int)390 4682 y(main)h(\(void\))390 4792 y({)485 4902 y(int)g(i;)485 5011 y(gsl_vector)e(*)j(v)f(=)h (gsl_vector_alloc)43 b(\(3\);)485 5230 y(for)k(\(i)h(=)f(0;)g(i)h(<)f (3;)g(i++\))581 5340 y({)p eop end %%Page: 88 106 TeXDict begin 88 105 bop 150 -116 a FK(Chapter)30 b(8:)41 b(V)-8 b(ectors)32 b(and)e(Matrices)2203 b(88)676 299 y FH(gsl_vector_set)44 b(\(v,)j(i,)g(1.23)g(+)g(i\);)581 408 y(})485 628 y(for)g(\(i)h(=)f(0;)g(i)h(<)f(100;)g(i++\))f(/*)i(OUT) e(OF)i(RANGE)e(ERROR)g(*/)581 737 y({)676 847 y(printf)g(\("v_\045d)h (=)g(\045g\\n",)f(i,)h(gsl_vector_get)d(\(v,)j(i\)\);)581 956 y(})485 1176 y(gsl_vector_free)d(\(v\);)485 1285 y(return)j(0;)390 1395 y(})150 1587 y FK(Here)30 b(is)g(the)g(output)f (from)h(the)g(program.)40 b(The)29 b(\014nal)h(lo)s(op)g(attempts)g(to) h(read)f(outside)g(the)g(range)g(of)150 1696 y(the)h(v)m(ector)h FH(v)p FK(,)e(and)g(the)g(error)g(is)h(trapp)s(ed)e(b)m(y)h(the)h (range-c)m(hec)m(king)h(co)s(de)f(in)f FH(gsl_vector_get)p FK(.)390 1888 y FH($)47 b(./a.out)390 1998 y(v_0)g(=)g(1.23)390 2107 y(v_1)g(=)g(2.23)390 2217 y(v_2)g(=)g(3.23)390 2326 y(gsl:)g(vector_source.c:12:)42 b(ERROR:)k(index)h(out)g(of)g(range)390 2436 y(Default)f(GSL)h(error)f(handler)g(invoked.)390 2545 y(Aborted)g(\(core)g(dumped\))150 2737 y FK(The)30 b(next)g(program)h(sho)m(ws)f(ho)m(w)g(to)h(write)g(a)g(v)m(ector)g(to) h(a)e(\014le.)390 2929 y FH(#include)46 b()390 3039 y(#include)g()390 3258 y(int)390 3367 y(main)h(\(void\))390 3477 y({)485 3587 y(int)g(i;)485 3696 y(gsl_vector)e(*)j(v)f(=)h(gsl_vector_alloc)43 b(\(100\);)485 3915 y(for)k(\(i)h(=)f(0;)g(i)h(<)f(100;)g(i++\))581 4025 y({)676 4134 y(gsl_vector_set)d(\(v,)j(i,)g(1.23)g(+)g(i\);)581 4244 y(})485 4463 y({)629 4573 y(FILE)f(*)i(f)f(=)h(fopen)e (\("test.dat",)e("w"\);)629 4682 y(gsl_vector_fprintf)e(\(f,)47 b(v,)h("\045.5g"\);)629 4792 y(fclose)e(\(f\);)485 4902 y(})485 5121 y(gsl_vector_free)e(\(v\);)485 5230 y(return)j(0;)390 5340 y(})p eop end %%Page: 89 107 TeXDict begin 89 106 bop 150 -116 a FK(Chapter)30 b(8:)41 b(V)-8 b(ectors)32 b(and)e(Matrices)2203 b(89)150 299 y(After)41 b(running)e(this)h(program)g(the)h(\014le)g FH(test.dat)d FK(should)i(con)m(tain)i(the)e(elemen)m(ts)i(of)f FH(v)p FK(,)i(written)150 408 y(using)32 b(the)g(format)g(sp)s (eci\014er)f FH(\045.5g)p FK(.)45 b(The)31 b(v)m(ector)j(could)e(then)g (b)s(e)f(read)h(bac)m(k)h(in)f(using)f(the)h(function)150 518 y FH(gsl_vector_fscanf)26 b(\(f,)j(v\))h FK(as)h(follo)m(ws:)390 647 y FH(#include)46 b()390 756 y(#include)g ()390 976 y(int)390 1085 y(main)h(\(void\))390 1195 y({)485 1304 y(int)g(i;)485 1414 y(gsl_vector)e(*)j(v)f(=)h (gsl_vector_alloc)43 b(\(10\);)485 1633 y({)629 1743 y(FILE)j(*)i(f)f(=)h(fopen)e(\("test.dat",)e("r"\);)629 1852 y(gsl_vector_fscanf)f(\(f,)k(v\);)629 1962 y(fclose)f(\(f\);)485 2072 y(})485 2291 y(for)h(\(i)h(=)f(0;)g(i)h(<)f(10;)g(i++\))581 2400 y({)676 2510 y(printf)f(\("\045g\\n",)g(gsl_vector_get\(v,)d (i\)\);)581 2620 y(})485 2839 y(gsl_vector_free)h(\(v\);)485 2948 y(return)j(0;)390 3058 y(})150 3279 y FJ(8.4)68 b(Matrices)150 3438 y FK(Matrices)41 b(are)g(de\014ned)d(b)m(y)i(a)g FH(gsl_matrix)e FK(structure)h(whic)m(h)h(describ)s(es)f(a)h (generalized)h(slice)g(of)g(a)150 3548 y(blo)s(c)m(k.)67 b(Lik)m(e)39 b(a)g(v)m(ector)i(it)e(represen)m(ts)g(a)g(set)h(of)f (elemen)m(ts)h(in)e(an)h(area)h(of)f(memory)-8 b(,)41 b(but)d(uses)h(t)m(w)m(o)150 3658 y(indices)30 b(instead)h(of)g(one.) 275 3786 y(The)h FH(gsl_matrix)d FK(structure)j(con)m(tains)i(six)f (comp)s(onen)m(ts,)g(the)g(t)m(w)m(o)h(dimensions)e(of)h(the)f(matrix,) 150 3896 y(a)27 b(ph)m(ysical)g(dimension,)g(a)g(p)s(oin)m(ter)g(to)g (the)g(memory)g(where)f(the)h(elemen)m(ts)h(of)f(the)g(matrix)g(are)g (stored,)150 4006 y FD(data)p FK(,)45 b(a)c(p)s(oin)m(ter)g(to)g(the)h (blo)s(c)m(k)f(o)m(wned)g(b)m(y)g(the)g(matrix)g FD(blo)s(c)m(k)p FK(,)k(if)40 b(an)m(y)-8 b(,)45 b(and)40 b(an)h(o)m(wnership)f(\015ag,) 150 4115 y FD(o)m(wner)p FK(.)77 b(The)42 b(ph)m(ysical)h(dimension)f (determines)h(the)g(memory)f(la)m(y)m(out)j(and)d(can)g(di\013er)h (from)f(the)150 4225 y(matrix)26 b(dimension)g(to)h(allo)m(w)g(the)f (use)g(of)g(submatrices.)39 b(The)26 b FH(gsl_matrix)d FK(structure)j(is)g(v)m(ery)g(simple)150 4334 y(and)k(lo)s(oks)h(lik)m (e)g(this,)390 4463 y FH(typedef)46 b(struct)390 4573 y({)485 4682 y(size_t)h(size1;)485 4792 y(size_t)g(size2;)485 4902 y(size_t)g(tda;)485 5011 y(double)g(*)g(data;)485 5121 y(gsl_block)f(*)h(block;)485 5230 y(int)g(owner;)390 5340 y(})g(gsl_matrix;)p eop end %%Page: 90 108 TeXDict begin 90 107 bop 150 -116 a FK(Chapter)30 b(8:)41 b(V)-8 b(ectors)32 b(and)e(Matrices)2203 b(90)150 299 y(Matrices)38 b(are)f(stored)f(in)g(ro)m(w-ma)5 b(jor)37 b(order,)h(meaning)f(that)f(eac)m(h)i(ro)m(w)f(of)f(elemen)m(ts)i (forms)e(a)g(con-)150 408 y(tiguous)f(blo)s(c)m(k)f(in)g(memory)-8 b(.)53 b(This)34 b(is)g(the)h(standard)e(\\C-language)j(ordering")f(of) f(t)m(w)m(o-dimensional)150 518 y(arra)m(ys.)56 b(Note)36 b(that)g FC(f)n(or)-6 b(tran)33 b FK(stores)j(arra)m(ys)g(in)e (column-ma)5 b(jor)36 b(order.)55 b(The)34 b(n)m(um)m(b)s(er)g(of)i(ro) m(ws)f(is)150 628 y FD(size1)p FK(.)41 b(The)26 b(range)i(of)f(v)-5 b(alid)28 b(ro)m(w)f(indices)g(runs)e(from)i(0)g(to)h FH(size1-1)p FK(.)38 b(Similarly)27 b FD(size2)36 b FK(is)27 b(the)g(n)m(um)m(b)s(er)150 737 y(of)33 b(columns.)48 b(The)32 b(range)i(of)f(v)-5 b(alid)33 b(column)g(indices)g(runs)e (from)i(0)g(to)h FH(size2-1)p FK(.)46 b(The)32 b(ph)m(ysical)i(ro)m(w) 150 847 y(dimension)29 b FD(tda)p FK(,)h(or)f FD(trailing)h(dimension)p FK(,)g(sp)s(eci\014es)f(the)g(size)h(of)g(a)f(ro)m(w)h(of)f(the)h (matrix)f(as)h(laid)g(out)f(in)150 956 y(memory)-8 b(.)275 1083 y(F)g(or)36 b(example,)i(in)e(the)g(follo)m(wing)h(matrix)f FD(size1)45 b FK(is)35 b(3,)j FD(size2)45 b FK(is)36 b(4,)h(and)f FD(tda)g FK(is)g(8.)57 b(The)35 b(ph)m(ysical)150 1192 y(memory)e(la)m(y)m(out)i(of)f(the)f(matrix)h(b)s(egins)f(in)g (the)g(top)h(left)g(hand-corner)f(and)f(pro)s(ceeds)h(from)g(left)h(to) 150 1302 y(righ)m(t)d(along)g(eac)m(h)h(ro)m(w)e(in)g(turn.)390 1428 y FH(00)47 b(01)g(02)h(03)f(XX)g(XX)g(XX)g(XX)390 1538 y(10)g(11)g(12)h(13)f(XX)g(XX)g(XX)g(XX)390 1647 y(20)g(21)g(22)h(23)f(XX)g(XX)g(XX)g(XX)150 1774 y FK(Eac)m(h)32 b(un)m(used)e(memory)h(lo)s(cation)i(is)f(represen)m(ted)f(b)m(y)g(\\)p FH(XX)p FK(".)45 b(The)30 b(p)s(oin)m(ter)i FD(data)g FK(giv)m(es)h(the)e(lo)s(cation)150 1883 y(of)i(the)f(\014rst)g(elemen) m(t)i(of)f(the)g(matrix)f(in)h(memory)-8 b(.)47 b(The)32 b(p)s(oin)m(ter)h FD(blo)s(c)m(k)38 b FK(stores)33 b(the)g(lo)s(cation) h(of)f(the)150 1993 y(memory)d(blo)s(c)m(k)g(in)g(whic)m(h)f(the)h (elemen)m(ts)h(of)f(the)g(matrix)h(are)f(lo)s(cated)h(\(if)f(an)m(y\).) 41 b(If)30 b(the)g(matrix)g(o)m(wns)150 2102 y(this)38 b(blo)s(c)m(k)g(then)g(the)g FD(o)m(wner)45 b FK(\014eld)37 b(is)h(set)h(to)g(one)f(and)f(the)i(blo)s(c)m(k)f(will)g(b)s(e)g (deallo)s(cated)i(when)d(the)150 2212 y(matrix)e(is)f(freed.)52 b(If)34 b(the)g(matrix)h(is)f(only)g(a)h(slice)g(of)g(a)f(blo)s(c)m(k)h (o)m(wned)f(b)m(y)g(another)h(ob)5 b(ject)35 b(then)f(the)150 2322 y FD(o)m(wner)j FK(\014eld)30 b(is)g(zero)h(and)f(an)m(y)h (underlying)e(blo)s(c)m(k)i(will)g(not)f(b)s(e)g(freed.)275 2448 y(The)f(functions)h(for)g(allo)s(cating)j(and)d(accessing)i (matrices)f(are)g(de\014ned)e(in)h FH(gsl_matrix.h)150 2631 y Fy(8.4.1)63 b(Matrix)40 b(allo)s(cation)150 2778 y FK(The)26 b(functions)g(for)g(allo)s(cating)i(memory)f(to)g(a)f (matrix)h(follo)m(w)g(the)g(st)m(yle)g(of)g FH(malloc)e FK(and)g FH(free)p FK(.)38 b(They)150 2887 y(also)28 b(p)s(erform)d(their)i(o)m(wn)g(error)f(c)m(hec)m(king.)42 b(If)26 b(there)h(is)g(insu\016cien)m(t)g(memory)g(a)m(v)-5 b(ailable)29 b(to)e(allo)s(cate)j(a)150 2997 y(matrix)25 b(then)g(the)h(functions)e(call)j(the)e(GSL)g(error)f(handler)g(\(with) i(an)f(error)f(n)m(um)m(b)s(er)g(of)h FH(GSL_ENOMEM)p FK(\))150 3106 y(in)33 b(addition)g(to)h(returning)e(a)h(n)m(ull)g(p)s (oin)m(ter.)49 b(Th)m(us)32 b(if)h(y)m(ou)h(use)e(the)i(library)e (error)h(handler)f(to)i(ab)s(ort)150 3216 y(y)m(our)c(program)g(then)h (it)f(isn't)h(necessary)g(to)g(c)m(hec)m(k)h(ev)m(ery)f FH(alloc)p FK(.)3350 3376 y([F)-8 b(unction])-3599 b Fv(gsl_matrix)55 b(*)e(gsl_matrix_alloc)d Fu(\()p FD(size)p 1894 3376 28 4 v 42 w(t)30 b Ft(n1)p FD(,)h(size)p 2302 3376 V 41 w(t)g Ft(n2)p Fu(\))390 3485 y FK(This)37 b(function)g (creates)i(a)f(matrix)g(of)g(size)h FD(n1)45 b FK(ro)m(ws)37 b(b)m(y)h FD(n2)45 b FK(columns,)39 b(returning)e(a)h(p)s(oin)m(ter)390 3595 y(to)j(a)f(newly)g(initialized)i(matrix)f(struct.)69 b(A)41 b(new)e(blo)s(c)m(k)i(is)f(allo)s(cated)i(for)e(the)g(elemen)m (ts)i(of)390 3704 y(the)c(matrix,)i(and)d(stored)g(in)h(the)f FD(blo)s(c)m(k)44 b FK(comp)s(onen)m(t)38 b(of)g(the)f(matrix)h (struct.)63 b(The)37 b(blo)s(c)m(k)h(is)390 3814 y(\\o)m(wned")31 b(b)m(y)f(the)h(matrix,)g(and)f(will)g(b)s(e)g(deallo)s(cated)i(when)e (the)g(matrix)h(is)g(deallo)s(cated.)3350 3974 y([F)-8 b(unction])-3599 b Fv(gsl_matrix)55 b(*)e(gsl_matrix_calloc)e Fu(\()p FD(size)p 1947 3974 V 41 w(t)30 b Ft(n1)p FD(,)i(size)p 2355 3974 V 41 w(t)e Ft(n2)p Fu(\))390 4083 y FK(This)43 b(function)g(allo)s(cates)j(memory)d(for)g(a)h(matrix)g(of)f(size)i FD(n1)50 b FK(ro)m(ws)44 b(b)m(y)f FD(n2)50 b FK(columns)44 b(and)390 4193 y(initializes)33 b(all)e(the)f(elemen)m(ts)i(of)f(the)f (matrix)h(to)g(zero.)3350 4353 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_matrix_free)c Fu(\()p FD(gsl)p 1389 4353 V 40 w(matrix)31 b(*)g Ft(m)p Fu(\))390 4462 y FK(This)f(function) h(frees)g(a)g(previously)f(allo)s(cated)j(matrix)f FD(m)p FK(.)41 b(If)31 b(the)g(matrix)g(w)m(as)g(created)h(using)390 4572 y FH(gsl_matrix_alloc)26 b FK(then)31 b(the)g(blo)s(c)m(k)h (underlying)d(the)j(matrix)f(will)g(also)h(b)s(e)e(deallo)s(cated.)44 b(If)390 4681 y(the)33 b(matrix)f(has)h(b)s(een)e(created)j(from)e (another)g(ob)5 b(ject)34 b(then)e(the)h(memory)f(is)g(still)i(o)m (wned)e(b)m(y)390 4791 y(that)f(ob)5 b(ject)31 b(and)f(will)h(not)f(b)s (e)g(deallo)s(cated.)150 4974 y Fy(8.4.2)63 b(Accessing)41 b(matrix)f(elemen)m(ts)150 5121 y FK(The)27 b(functions)f(for)h (accessing)i(the)e(elemen)m(ts)h(of)g(a)f(matrix)h(use)e(the)i(same)f (range)h(c)m(hec)m(king)g(system)g(as)150 5230 y(v)m(ectors.)40 b(Y)-8 b(ou)24 b(can)f(turn)f(o\013)i(range)f(c)m(hec)m(king)i(b)m(y)e (recompiling)h(y)m(our)g(program)f(with)f(the)i(prepro)s(cessor)150 5340 y(de\014nition)30 b FH(GSL_RANGE_CHECK_OFF)p FK(.)p eop end %%Page: 91 109 TeXDict begin 91 108 bop 150 -116 a FK(Chapter)30 b(8:)41 b(V)-8 b(ectors)32 b(and)e(Matrices)2203 b(91)275 299 y(The)43 b(elemen)m(ts)j(of)e(the)g(matrix)g(are)h(stored)f(in)g (\\C-order",)k(where)c(the)g(second)g(index)g(mo)m(v)m(es)150 408 y(con)m(tin)m(uously)34 b(through)f(memory)-8 b(.)51 b(More)34 b(precisely)-8 b(,)36 b(the)e(elemen)m(t)h(accessed)g(b)m(y)e (the)h(function)f FH(gsl_)150 518 y(matrix_get\(m,i,j\))26 b FK(and)j FH(gsl_matrix_set\(m,i,j,x\))24 b FK(is)390 657 y FH(m->data[i)45 b(*)j(m->tda)e(+)h(j])150 796 y FK(where)30 b FD(tda)g FK(is)h(the)f(ph)m(ysical)h(ro)m(w-length)h(of)e (the)h(matrix.)3350 989 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_matrix_get)c Fu(\()p FD(const)31 b(gsl)p 1679 989 28 4 v 41 w(matrix)f(*)h Ft(m)p FD(,)g(const)g(size)p 2578 989 V 41 w(t)f Ft(i)p FD(,)h(const)565 1099 y(size)p 712 1099 V 41 w(t)g Ft(j)p Fu(\))390 1208 y FK(This)38 b(function)h(returns)f(the)h(\()p FE(i;)15 b(j)5 b FK(\)-th)41 b(elemen)m(t)g(of)e(a)h(matrix)f FD(m)p FK(.)67 b(If)38 b FD(i)44 b FK(or)39 b FD(j)j FK(lie)e(outside)g(the)390 1318 y(allo)m(w)m(ed)32 b(range)f(of)f(0)g(to)h FD(n1)c FI(\000)20 b FK(1)31 b(and)e(0)i(to)g FD(n2)c FI(\000)19 b FK(1)31 b(then)f(the)g(error)g(handler)f(is)h(in)m(v)m(ok)m(ed)i(and) e(0)390 1427 y(is)g(returned.)40 b(An)30 b(inline)g(v)m(ersion)h(of)g (this)f(function)g(is)h(used)e(when)g FH(HAVE_INLINE)f FK(is)i(de\014ned.)3350 1620 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_matrix_set)49 b Fu(\()p FD(gsl)p 1336 1620 V 41 w(matrix)31 b(*)g Ft(m)p FD(,)f(const)h(size)p 2235 1620 V 41 w(t)g Ft(i)p FD(,)g(const)g(size)p 2829 1620 V 41 w(t)f Ft(j)p FD(,)565 1730 y(double)g Ft(x)p Fu(\))390 1840 y FK(This)i(function)g(sets)h(the)f(v)-5 b(alue)33 b(of)g(the)f(\()p FE(i;)15 b(j)5 b FK(\)-th)35 b(elemen)m(t)f(of)e(a)h(matrix)g FD(m)f FK(to)h FD(x)p FK(.)47 b(If)32 b FD(i)37 b FK(or)c FD(j)i FK(lies)390 1949 y(outside)h(the)h(allo)m(w)m(ed)h(range)e(of)h(0)f(to)h FD(n1)31 b FI(\000)24 b FK(1)37 b(and)e(0)i(to)g FD(n2)31 b FI(\000)24 b FK(1)37 b(then)e(the)i(error)f(handler)f(is)390 2059 y(in)m(v)m(ok)m(ed.)42 b(An)30 b(inline)h(v)m(ersion)f(of)h(this)f (function)g(is)h(used)e(when)h FH(HAVE_INLINE)d FK(is)j(de\014ned.)3350 2252 y([F)-8 b(unction])-3599 b Fv(double)54 b(*)f(gsl_matrix_ptr)c Fu(\()p FD(gsl)p 1545 2252 V 41 w(matrix)31 b(*)g Ft(m)p FD(,)g(size)p 2207 2252 V 41 w(t)f Ft(i)p FD(,)h(size)p 2562 2252 V 41 w(t)g Ft(j)p Fu(\))3350 2361 y FK([F)-8 b(unction])-3599 b Fv(const)54 b(double)g(*)f(gsl_matrix_const_ptr)e Fu(\()p FD(const)31 b(gsl)p 2411 2361 V 41 w(matrix)g(*)f Ft(m)p FD(,)h(size)p 3072 2361 V 41 w(t)565 2471 y Ft(i)p FD(,)g(size)p 820 2471 V 41 w(t)g Ft(j)p Fu(\))390 2581 y FK(These)j(functions)g(return)f(a)h(p)s(oin)m(ter)g(to)h(the)f(\()p FE(i;)15 b(j)5 b FK(\)-th)37 b(elemen)m(t)e(of)g(a)f(matrix)h FD(m)p FK(.)51 b(If)34 b FD(i)39 b FK(or)34 b FD(j)j FK(lie)390 2690 y(outside)f(the)h(allo)m(w)m(ed)h(range)e(of)h(0)f(to)h FD(n1)31 b FI(\000)24 b FK(1)37 b(and)e(0)i(to)g FD(n2)31 b FI(\000)24 b FK(1)37 b(then)e(the)i(error)f(handler)f(is)390 2800 y(in)m(v)m(ok)m(ed)41 b(and)d(a)i(n)m(ull)f(p)s(oin)m(ter)g(is)g (returned.)66 b(Inline)38 b(v)m(ersions)i(of)f(these)h(functions)e(are) i(used)390 2909 y(when)29 b FH(HAVE_INLINE)f FK(is)i(de\014ned.)150 3113 y Fy(8.4.3)63 b(Initializing)40 b(matrix)h(elemen)m(ts)3350 3314 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_matrix_set_all)c Fu(\()p FD(gsl)p 1545 3314 V 41 w(matrix)31 b(*)g Ft(m)p FD(,)g(double)f Ft(x)p Fu(\))390 3424 y FK(This)g(function)g(sets)g (all)i(the)e(elemen)m(ts)i(of)e(the)h(matrix)g FD(m)f FK(to)h(the)g(v)-5 b(alue)30 b FD(x)p FK(.)3350 3617 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_matrix_set_zero)d Fu(\()p FD(gsl)p 1598 3617 V 41 w(matrix)30 b(*)h Ft(m)p Fu(\))390 3726 y FK(This)f(function)g(sets)g(all)i(the)e(elemen)m(ts)i (of)e(the)h(matrix)g FD(m)f FK(to)h(zero.)3350 3920 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_matrix_set_identity)e Fu(\()p FD(gsl)p 1807 3920 V 41 w(matrix)31 b(*)f Ft(m)p Fu(\))390 4029 y FK(This)e(function)g(sets)h(the)g(elemen)m(ts)h(of)e (the)h(matrix)g FD(m)f FK(to)i(the)f(corresp)s(onding)e(elemen)m(ts)j (of)f(the)390 4139 y(iden)m(tit)m(y)37 b(matrix,)g FE(m)p FK(\()p FE(i;)15 b(j)5 b FK(\))35 b(=)e FE(\016)s FK(\()p FE(i;)15 b(j)5 b FK(\),)40 b(i.e.)56 b(a)36 b(unit)f(diagonal)h(with)f (all)h(o\013-diagonal)i(elemen)m(ts)390 4248 y(zero.)k(This)29 b(applies)i(to)g(b)s(oth)e(square)i(and)e(rectangular)j(matrices.)150 4452 y Fy(8.4.4)63 b(Reading)41 b(and)f(writing)i(matrices)150 4599 y FK(The)32 b(library)g(pro)m(vides)g(functions)g(for)g(reading)h (and)f(writing)g(matrices)h(to)g(a)g(\014le)g(as)f(binary)g(data)h(or) 150 4709 y(formatted)e(text.)3350 4902 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_matrix_fwrite)e Fu(\()p FD(FILE)30 b(*)h Ft(stream)p FD(,)h(const)f(gsl)p 2365 4902 V 41 w(matrix)g(*)f Ft(m)p Fu(\))390 5011 y FK(This)38 b(function)g(writes)g (the)g(elemen)m(ts)i(of)f(the)f(matrix)h FD(m)f FK(to)h(the)f(stream)h FD(stream)g FK(in)f(binary)390 5121 y(format.)58 b(The)36 b(return)f(v)-5 b(alue)36 b(is)g(0)h(for)f(success)g(and)f FH(GSL_EFAILED)e FK(if)j(there)h(w)m(as)f(a)h(problem)390 5230 y(writing)c(to)h(the)f(\014le.)50 b(Since)33 b(the)g(data)h(is)f (written)h(in)e(the)i(nativ)m(e)g(binary)f(format)g(it)h(ma)m(y)g(not) 390 5340 y(b)s(e)c(p)s(ortable)g(b)s(et)m(w)m(een)h(di\013eren)m(t)g (arc)m(hitectures.)p eop end %%Page: 92 110 TeXDict begin 92 109 bop 150 -116 a FK(Chapter)30 b(8:)41 b(V)-8 b(ectors)32 b(and)e(Matrices)2203 b(92)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_matrix_fread)e Fu(\()p FD(FILE)30 b(*)h Ft(stream)p FD(,)h(gsl)p 2075 299 28 4 v 41 w(matrix)e(*)h Ft(m)p Fu(\))390 408 y FK(This)26 b(function)g(reads)g(in)m(to)h(the)g(matrix)g FD(m)f FK(from)g(the)g(op)s(en)g(stream)h FD(stream)g FK(in)f(binary)f (format.)390 518 y(The)36 b(matrix)h FD(m)f FK(m)m(ust)g(b)s(e)f (preallo)s(cated)j(with)e(the)h(correct)g(dimensions)f(since)h(the)f (function)390 628 y(uses)f(the)g(size)h(of)g FD(m)f FK(to)h(determine)f (ho)m(w)h(man)m(y)f(b)m(ytes)h(to)g(read.)55 b(The)35 b(return)f(v)-5 b(alue)36 b(is)f(0)h(for)390 737 y(success)f(and)f FH(GSL_EFAILED)d FK(if)k(there)f(w)m(as)h(a)g(problem)f(reading)h(from) f(the)g(\014le.)54 b(The)34 b(data)h(is)390 847 y(assumed)30 b(to)h(ha)m(v)m(e)g(b)s(een)f(written)g(in)g(the)h(nativ)m(e)h(binary)d (format)i(on)f(the)h(same)g(arc)m(hitecture.)3350 1049 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_matrix_fprintf)e Fu(\()p FD(FILE)31 b(*)f Ft(stream)p FD(,)j(const)e(gsl)p 2418 1049 V 40 w(matrix)g(*)g Ft(m)p FD(,)g(const)565 1158 y(c)m(har)g(*)g Ft(format)p Fu(\))390 1268 y FK(This)h(function)h (writes)g(the)g(elemen)m(ts)h(of)f(the)g(matrix)h FD(m)e FK(line-b)m(y-line)i(to)g(the)f(stream)h FD(stream)390 1378 y FK(using)26 b(the)h(format)g(sp)s(eci\014er)g FD(format)p FK(,)h(whic)m(h)e(should)g(b)s(e)g(one)h(of)g(the)g FH(\045g)p FK(,)g FH(\045e)f FK(or)h FH(\045f)f FK(formats)h(for)390 1487 y(\015oating)37 b(p)s(oin)m(t)f(n)m(um)m(b)s(ers)f(and)g FH(\045d)h FK(for)g(in)m(tegers.)59 b(The)35 b(function)h(returns)f(0)h (for)g(success)h(and)390 1597 y FH(GSL_EFAILED)27 b FK(if)k(there)f(w)m (as)h(a)g(problem)e(writing)i(to)g(the)g(\014le.)3350 1799 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_matrix_fscanf)e Fu(\()p FD(FILE)30 b(*)h Ft(stream)p FD(,)h(gsl)p 2127 1799 V 41 w(matrix)f(*)g Ft(m)p Fu(\))390 1908 y FK(This)g(function)h (reads)g(formatted)h(data)f(from)g(the)g(stream)h FD(stream)f FK(in)m(to)h(the)f(matrix)h FD(m)p FK(.)45 b(The)390 2018 y(matrix)36 b FD(m)g FK(m)m(ust)f(b)s(e)h(preallo)s(cated)h(with)e (the)i(correct)g(dimensions)e(since)h(the)g(function)f(uses)390 2127 y(the)h(size)h(of)f FD(m)f FK(to)h(determine)g(ho)m(w)g(man)m(y)g (n)m(um)m(b)s(ers)e(to)j(read.)57 b(The)35 b(function)g(returns)g(0)h (for)390 2237 y(success)31 b(and)e FH(GSL_EFAILED)f FK(if)i(there)h(w)m (as)f(a)h(problem)f(reading)g(from)g(the)h(\014le.)150 2445 y Fy(8.4.5)63 b(Matrix)40 b(views)150 2592 y FK(A)d(matrix)g(view) g(is)f(a)i(temp)s(orary)e(ob)5 b(ject,)39 b(stored)e(on)g(the)g(stac)m (k,)i(whic)m(h)e(can)g(b)s(e)f(used)g(to)h(op)s(erate)150 2702 y(on)e(a)h(subset)f(of)h(matrix)g(elemen)m(ts.)57 b(Matrix)36 b(views)g(can)g(b)s(e)e(de\014ned)h(for)g(b)s(oth)g (constan)m(t)h(and)f(non-)150 2811 y(constan)m(t)27 b(matrices)h(using) d(separate)i(t)m(yp)s(es)f(that)h(preserv)m(e)f(constness.)40 b(A)26 b(matrix)g(view)h(has)e(the)i(t)m(yp)s(e)150 2921 y FH(gsl_matrix_view)k FK(and)j(a)h(constan)m(t)i(matrix)e(view)g(has)g (the)g(t)m(yp)s(e)g FH(gsl_matrix_const_view)p FK(.)49 b(In)150 3030 y(b)s(oth)36 b(cases)i(the)g(elemen)m(ts)g(of)f(the)h (view)f(can)g(b)m(y)g(accessed)i(using)d(the)i FH(matrix)d FK(comp)s(onen)m(t)i(of)h(the)150 3140 y(view)e(ob)5 b(ject.)60 b(A)36 b(p)s(oin)m(ter)g FH(gsl_matrix)28 b(*)36 b FK(or)g FH(const)29 b(gsl_matrix)e(*)36 b FK(can)h(b)s(e)e (obtained)i(b)m(y)f(taking)150 3250 y(the)d(address)g(of)g(the)h FH(matrix)d FK(comp)s(onen)m(t)j(with)f(the)g FH(&)g FK(op)s(erator.)50 b(In)32 b(addition)i(to)f(matrix)h(views)f(it)150 3359 y(is)d(also)i(p)s(ossible)e(to)h(create)h(v)m(ector)g(views)e(of)h (a)f(matrix,)h(suc)m(h)f(as)h(ro)m(w)g(or)f(column)g(views.)3350 3561 y([F)-8 b(unction])-3599 b Fv(gsl_matrix_view)57 b(gsl_matrix_submatrix)51 b Fu(\()p FD(gsl)p 2225 3561 V 41 w(matrix)31 b(*)g Ft(m)p FD(,)g(size)p 2887 3561 V 41 w(t)f Ft(k1)p FD(,)565 3671 y(size)p 712 3671 V 41 w(t)h Ft(k2)p FD(,)g(size)p 1120 3671 V 41 w(t)f Ft(n1)p FD(,)i(size)p 1528 3671 V 41 w(t)e Ft(n2)p Fu(\))3350 3780 y FK([F)-8 b(unction])-3599 b Fv(gsl_matrix_const_view)59 b(gsl_matrix_const_submat)q(rix)52 b Fu(\()p FD(const)565 3890 y(gsl)p 677 3890 V 41 w(matrix)30 b(*)h Ft(m)p FD(,)g(size)p 1338 3890 V 41 w(t)g Ft(k1)p FD(,)g(size)p 1746 3890 V 41 w(t)f Ft(k2)p FD(,)h(size)p 2153 3890 V 41 w(t)g Ft(n1)p FD(,)g(size)p 2561 3890 V 41 w(t)g Ft(n2)p Fu(\))390 4000 y FK(These)c(functions)g(return)f(a)i(matrix)g(view)g(of)f(a)h (submatrix)f(of)g(the)h(matrix)g FD(m)p FK(.)39 b(The)27 b(upp)s(er-left)390 4109 y(elemen)m(t)e(of)f(the)g(submatrix)f(is)h (the)g(elemen)m(t)h(\()p FD(k1)p FK(,)p FD(k2)7 b FK(\))26 b(of)e(the)g(original)h(matrix.)38 b(The)24 b(submatrix)390 4219 y(has)33 b FD(n1)40 b FK(ro)m(ws)32 b(and)h FD(n2)39 b FK(columns.)48 b(The)33 b(ph)m(ysical)g(n)m(um)m(b)s(er)f(of)g (columns)h(in)g(memory)f(giv)m(en)i(b)m(y)390 4328 y FD(tda)j FK(is)f(unc)m(hanged.)58 b(Mathematically)-8 b(,)42 b(the)37 b(\()p FE(i;)15 b(j)5 b FK(\)-th)38 b(elemen)m(t)g(of)e (the)h(new)f(matrix)h(is)f(giv)m(en)390 4438 y(b)m(y)-8 b(,)630 4581 y FH(m'\(i,j\))46 b(=)h(m->data[\(k1*m->tda)c(+)48 b(k2\))e(+)i(i*m->tda)d(+)j(j])390 4725 y FK(where)30 b(the)g(index)g FD(i)36 b FK(runs)29 b(from)g(0)i(to)g FH(n1-1)f FK(and)f(the)i(index)f FD(j)j FK(runs)c(from)h(0)g(to)i FH(n2-1)p FK(.)390 4868 y(The)e FH(data)f FK(p)s(oin)m(ter)h(of)g(the)h (returned)e(matrix)h(struct)g(is)g(set)h(to)g(n)m(ull)f(if)g(the)h(com) m(bined)f(param-)390 4977 y(eters)h(\()p FD(i)p FK(,)p FD(j)p FK(,)p FD(n1)p FK(,)p FD(n2)p FK(,)p FD(tda)p FK(\))h(o)m(v)m(errun)f(the)f(ends)g(of)g(the)h(original)g(matrix.)390 5121 y(The)42 b(new)g(matrix)h(view)f(is)h(only)f(a)h(view)g(of)f(the)h (blo)s(c)m(k)g(underlying)e(the)i(existing)g(matrix,)390 5230 y FD(m)p FK(.)60 b(The)36 b(blo)s(c)m(k)h(con)m(taining)h(the)f (elemen)m(ts)i(of)d FD(m)h FK(is)g(not)g(o)m(wned)f(b)m(y)h(the)g(new)f (matrix)h(view.)390 5340 y(When)28 b(the)h(view)g(go)s(es)g(out)g(of)g (scop)s(e)f(the)h(original)h(matrix)f FD(m)f FK(and)g(its)h(blo)s(c)m (k)g(will)g(con)m(tin)m(ue)h(to)p eop end %%Page: 93 111 TeXDict begin 93 110 bop 150 -116 a FK(Chapter)30 b(8:)41 b(V)-8 b(ectors)32 b(and)e(Matrices)2203 b(93)390 299 y(exist.)58 b(The)36 b(original)h(memory)f(can)g(only)g(b)s(e)f(deallo) s(cated)j(b)m(y)e(freeing)g(the)g(original)h(matrix.)390 408 y(Of)27 b(course,)i(the)g(original)g(matrix)f(should)f(not)h(b)s(e) g(deallo)s(cated)i(while)e(the)g(view)g(is)g(still)h(in)f(use.)390 536 y(The)23 b(function)g FH(gsl_matrix_const_submat)o(rix)17 b FK(is)23 b(equiv)-5 b(alen)m(t)25 b(to)e FH(gsl_matrix_submatrix)390 646 y FK(but)30 b(can)g(b)s(e)g(used)g(for)g(matrices)h(whic)m(h)f(are) h(declared)g FH(const)p FK(.)3350 810 y([F)-8 b(unction])-3599 b Fv(gsl_matrix_view)57 b(gsl_matrix_view_array)52 b Fu(\()p FD(double)30 b(*)h Ft(base)p FD(,)g(size)p 2946 810 28 4 v 41 w(t)g Ft(n1)p FD(,)565 920 y(size)p 712 920 V 41 w(t)g Ft(n2)p Fu(\))3350 1029 y FK([F)-8 b(unction])-3599 b Fv(gsl_matrix_const_view)59 b(gsl_matrix_const_view_a)q(rra)q(y)51 b Fu(\()p FD(const)565 1139 y(double)30 b(*)h Ft(base)p FD(,)h(size)p 1346 1139 V 40 w(t)f Ft(n1)p FD(,)g(size)p 1753 1139 V 41 w(t)g Ft(n2)p Fu(\))390 1249 y FK(These)40 b(functions)f(return)g(a)h(matrix)g(view)g(of)g(the)g(arra)m(y)h FD(base)p FK(.)69 b(The)39 b(matrix)h(has)g FD(n1)47 b FK(ro)m(ws)390 1358 y(and)37 b FD(n2)45 b FK(columns.)63 b(The)38 b(ph)m(ysical)g(n)m(um)m(b)s(er)f(of)h(columns)f(in)h(memory)f (is)h(also)h(giv)m(en)g(b)m(y)f FD(n2)p FK(.)390 1468 y(Mathematically)-8 b(,)34 b(the)d(\()p FE(i;)15 b(j)5 b FK(\)-th)32 b(elemen)m(t)g(of)f(the)f(new)g(matrix)h(is)f(giv)m(en)i (b)m(y)-8 b(,)630 1596 y FH(m'\(i,j\))46 b(=)h(base[i*n2)f(+)h(j])390 1724 y FK(where)30 b(the)g(index)g FD(i)36 b FK(runs)29 b(from)g(0)i(to)g FH(n1-1)f FK(and)f(the)i(index)f FD(j)j FK(runs)c(from)h(0)g(to)i FH(n2-1)p FK(.)390 1851 y(The)h(new)h(matrix) g(is)g(only)g(a)g(view)g(of)g(the)g(arra)m(y)h FD(base)p FK(.)51 b(When)34 b(the)g(view)g(go)s(es)h(out)f(of)g(scop)s(e)390 1961 y(the)44 b(original)i(arra)m(y)e FD(base)50 b FK(will)44 b(con)m(tin)m(ue)h(to)g(exist.)83 b(The)44 b(original)h(memory)f(can)g (only)h(b)s(e)390 2071 y(deallo)s(cated)33 b(b)m(y)e(freeing)g(the)h (original)g(arra)m(y)-8 b(.)44 b(Of)30 b(course,)i(the)f(original)i (arra)m(y)e(should)f(not)i(b)s(e)390 2180 y(deallo)s(cated)g(while)f (the)f(view)h(is)f(still)h(in)g(use.)390 2308 y(The)47 b(function)f FH(gsl_matrix_const_view_arr)o(ay)41 b FK(is)47 b(equiv)-5 b(alen)m(t)49 b(to)e FH(gsl_matrix_view_)390 2418 y(array)29 b FK(but)h(can)g(b)s(e)g(used)g(for)g(matrices)h(whic)m (h)f(are)h(declared)g FH(const)p FK(.)3350 2582 y([F)-8 b(unction])-3599 b Fv(gsl_matrix_view)57 b(gsl_matrix_view_array_)q (with)q(_td)q(a)51 b Fu(\()p FD(double)31 b(*)565 2692 y Ft(base)p FD(,)h(size)p 977 2692 V 41 w(t)e Ft(n1)p FD(,)i(size)p 1385 2692 V 41 w(t)e Ft(n2)p FD(,)h(size)p 1792 2692 V 41 w(t)g Ft(tda)p Fu(\))3350 2801 y FK([F)-8 b(unction])-3599 b Fv(gsl_matrix_const_view)59 b (gsl_matrix_const_view_a)q(rra)q(y_wi)q(th_)q(tda)565 2911 y Fu(\()p FD(const)31 b(double)f(*)h Ft(base)p FD(,)h(size)p 1619 2911 V 41 w(t)e Ft(n1)p FD(,)i(size)p 2027 2911 V 40 w(t)f Ft(n2)p FD(,)g(size)p 2434 2911 V 41 w(t)g Ft(tda)p Fu(\))390 3020 y FK(These)38 b(functions)f(return)g(a)h (matrix)g(view)g(of)g(the)g(arra)m(y)g FD(base)43 b FK(with)38 b(a)g(ph)m(ysical)g(n)m(um)m(b)s(er)f(of)390 3130 y(columns)31 b FD(tda)h FK(whic)m(h)g(ma)m(y)g(di\013er)g(from)f(the)h(corresp)s (onding)e(dimension)i(of)f(the)h(matrix.)45 b(The)390 3240 y(matrix)29 b(has)f FD(n1)35 b FK(ro)m(ws)28 b(and)g FD(n2)35 b FK(columns,)29 b(and)e(the)i(ph)m(ysical)g(n)m(um)m(b)s(er)e (of)h(columns)g(in)g(memory)390 3349 y(is)i(giv)m(en)i(b)m(y)e FD(tda)p FK(.)41 b(Mathematically)-8 b(,)34 b(the)d(\()p FE(i;)15 b(j)5 b FK(\)-th)32 b(elemen)m(t)g(of)f(the)f(new)g(matrix)h (is)f(giv)m(en)i(b)m(y)-8 b(,)630 3477 y FH(m'\(i,j\))46 b(=)h(base[i*tda)e(+)j(j])390 3605 y FK(where)30 b(the)g(index)g FD(i)36 b FK(runs)29 b(from)g(0)i(to)g FH(n1-1)f FK(and)f(the)i(index)f FD(j)j FK(runs)c(from)h(0)g(to)i FH(n2-1)p FK(.)390 3733 y(The)h(new)h(matrix)g(is)g(only)g(a)g(view)g(of)g(the)g(arra)m(y)h FD(base)p FK(.)51 b(When)34 b(the)g(view)g(go)s(es)h(out)f(of)g(scop)s (e)390 3842 y(the)44 b(original)i(arra)m(y)e FD(base)50 b FK(will)44 b(con)m(tin)m(ue)h(to)g(exist.)83 b(The)44 b(original)h(memory)f(can)g(only)h(b)s(e)390 3952 y(deallo)s(cated)33 b(b)m(y)e(freeing)g(the)h(original)g(arra)m(y)-8 b(.)44 b(Of)30 b(course,)i(the)f(original)i(arra)m(y)e(should)f(not)i(b)s(e) 390 4061 y(deallo)s(cated)g(while)f(the)f(view)h(is)f(still)h(in)g (use.)390 4189 y(The)70 b(function)h FH(gsl_matrix_const_view_ar)o (ray_)o(with)o(_td)o(a)65 b FK(is)71 b(equiv)-5 b(alen)m(t)72 b(to)g FH(gsl_)390 4299 y(matrix_view_array_with_t)o(da)44 b FK(but)50 b(can)h(b)s(e)e(used)h(for)g(matrices)i(whic)m(h)e(are)g (declared)390 4408 y FH(const)p FK(.)3350 4573 y([F)-8 b(unction])-3599 b Fv(gsl_matrix_view)57 b(gsl_matrix_view_vector)52 b Fu(\()p FD(gsl)p 2330 4573 V 41 w(v)m(ector)32 b(*)f Ft(v)p FD(,)g(size)p 2969 4573 V 40 w(t)g Ft(n1)p FD(,)565 4682 y(size)p 712 4682 V 41 w(t)g Ft(n2)p Fu(\))3350 4792 y FK([F)-8 b(unction])-3599 b Fv(gsl_matrix_const_view)59 b(gsl_matrix_const_view_v)q(ect)q(or)52 b Fu(\()p FD(const)565 4902 y(gsl)p 677 4902 V 41 w(v)m(ector)32 b(*)e Ft(v)p FD(,)h(size)p 1315 4902 V 41 w(t)g Ft(n1)p FD(,)g(size)p 1723 4902 V 41 w(t)g Ft(n2)p Fu(\))390 5011 y FK(These)j(functions)g (return)f(a)h(matrix)h(view)f(of)g(the)h(v)m(ector)g FD(v)p FK(.)52 b(The)34 b(matrix)g(has)g FD(n1)41 b FK(ro)m(ws)35 b(and)390 5121 y FD(n2)41 b FK(columns.)51 b(The)34 b(v)m(ector)h(m)m (ust)f(ha)m(v)m(e)i(unit)d(stride.)52 b(The)33 b(ph)m(ysical)i(n)m(um)m (b)s(er)d(of)j(columns)e(in)390 5230 y(memory)e(is)f(also)i(giv)m(en)f (b)m(y)g FD(n2)p FK(.)41 b(Mathematically)-8 b(,)35 b(the)c(\()p FE(i;)15 b(j)5 b FK(\)-th)33 b(elemen)m(t)f(of)f(the)f(new)h(matrix)390 5340 y(is)f(giv)m(en)i(b)m(y)-8 b(,)p eop end %%Page: 94 112 TeXDict begin 94 111 bop 150 -116 a FK(Chapter)30 b(8:)41 b(V)-8 b(ectors)32 b(and)e(Matrices)2203 b(94)630 299 y FH(m'\(i,j\))46 b(=)h(v->data[i*n2)e(+)i(j])390 464 y FK(where)30 b(the)g(index)g FD(i)36 b FK(runs)29 b(from)g(0)i(to)g FH(n1-1)f FK(and)f(the)i(index)f FD(j)j FK(runs)c(from)h(0)g(to)i FH(n2-1)p FK(.)390 630 y(The)e(new)g(matrix)g(is)h(only)f(a)h(view)f (of)h(the)f(v)m(ector)i FD(v)p 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1698 y FK([F)-8 b(unction])-3599 b Fv(gsl_matrix_const_view)565 1808 y(gsl_matrix_const_view_)q(vec)q (tor)q(_wi)q(th_t)q(da)52 b Fu(\()p FD(const)31 b(gsl)p 2931 1808 V 41 w(v)m(ector)h(*)e Ft(v)p FD(,)h(size)p 3569 1808 V 41 w(t)565 1918 y Ft(n1)p FD(,)g(size)p 872 1918 V 41 w(t)g Ft(n2)p FD(,)g(size)p 1280 1918 V 41 w(t)g Ft(tda)p Fu(\))390 2027 y FK(These)44 b(functions)f(return)g(a)h (matrix)h(view)f(of)g(the)g(v)m(ector)i FD(v)52 b FK(with)43 b(a)i(ph)m(ysical)f(n)m(um)m(b)s(er)f(of)390 2137 y(columns)30 b FD(tda)i FK(whic)m(h)e(ma)m(y)i(di\013er)e(from)g(the)h(corresp)s (onding)f(matrix)h(dimension.)42 b(The)30 b(v)m(ector)390 2246 y(m)m(ust)37 b(ha)m(v)m(e)i(unit)e(stride.)62 b(The)37 b(matrix)g(has)g FD(n1)45 b FK(ro)m(ws)37 b(and)g FD(n2)45 b FK(columns,)39 b(and)e(the)g(ph)m(ysical)390 2356 y(n)m(um)m(b)s(er) 29 b(of)h(columns)g(in)g(memory)h(is)f(giv)m(en)h(b)m(y)f FD(tda)p FK(.)41 b(Mathematically)-8 b(,)34 b(the)d(\()p FE(i;)15 b(j)5 b FK(\)-th)32 b(elemen)m(t)390 2466 y(of)f(the)f(new)g (matrix)h(is)f(giv)m(en)h(b)m(y)-8 b(,)630 2631 y FH(m'\(i,j\))46 b(=)h(v->data[i*tda)d(+)k(j])390 2796 y FK(where)30 b(the)g(index)g FD(i)36 b FK(runs)29 b(from)g(0)i(to)g FH(n1-1)f FK(and)f(the)i(index)f FD(j)j FK(runs)c(from)h(0)g(to)i FH(n2-1)p FK(.)390 2962 y(The)e(new)g(matrix)g(is)h(only)f(a)h(view)f(of)h(the)f(v)m(ector)i FD(v)p FK(.)41 b(When)30 b(the)h(view)f(go)s(es)h(out)g(of)f(scop)s(e)h (the)390 3071 y(original)e(v)m(ector)h FD(v)36 b FK(will)28 b(con)m(tin)m(ue)i(to)e(exist.)41 b(The)28 b(original)h(memory)f(can)g (only)h(b)s(e)e(deallo)s(cated)390 3181 y(b)m(y)e(freeing)g(the)g (original)h(v)m(ector.)41 b(Of)24 b(course,)i(the)f(original)h(v)m (ector)h(should)d(not)h(b)s(e)f(deallo)s(cated)390 3290 y(while)30 b(the)h(view)g(is)f(still)h(in)f(use.)390 3456 y(The)113 b(function)h FH(gsl_matrix_const_view_v)o(ecto)o(r_w)o (ith_)o(tda)107 b FK(is)114 b(equiv)-5 b(alen)m(t)115 b(to)390 3565 y FH(gsl_matrix_view_vector_w)o(ith_)o(tda)61 b FK(but)68 b(can)g(b)s(e)f(used)g(for)h(matrices)h(whic)m(h)f(are)390 3675 y(declared)31 b FH(const)p FK(.)150 3905 y Fy(8.4.6)63 b(Creating)40 b(ro)m(w)h(and)g(column)g(views)150 4052 y FK(In)25 b(general)h(there)g(are)g(t)m(w)m(o)h(w)m(a)m(ys)f(to)h (access)g(an)e(ob)5 b(ject,)28 b(b)m(y)d(reference)h(or)g(b)m(y)f(cop)m (ying.)40 b(The)25 b(functions)150 4162 y(describ)s(ed)37 b(in)g(this)h(section)h(create)h(v)m(ector)f(views)f(whic)m(h)g(allo)m (w)h(access)h(to)e(a)h(ro)m(w)f(or)g(column)f(of)i(a)150 4271 y(matrix)29 b(b)m(y)f(reference.)41 b(Mo)s(difying)28 b(elemen)m(ts)i(of)f(the)f(view)h(is)g(equiv)-5 b(alen)m(t)30 b(to)f(mo)s(difying)f(the)g(matrix,)150 4381 y(since)j(b)s(oth)e(the)i (v)m(ector)h(view)f(and)e(the)i(matrix)g(p)s(oin)m(t)f(to)h(the)g(same) f(memory)h(blo)s(c)m(k.)3350 4627 y([F)-8 b(unction])-3599 b Fv(gsl_vector_view)57 b(gsl_matrix_row)50 b Fu(\()p FD(gsl)p 1912 4627 V 40 w(matrix)31 b(*)g Ft(m)p FD(,)g(size)p 2573 4627 V 41 w(t)f Ft(i)p Fu(\))3350 4736 y FK([F)-8 b(unction])-3599 b Fv(gsl_vector_const_view)59 b(gsl_matrix_const_row) 51 b Fu(\()p FD(const)31 b(gsl)p 2777 4736 V 41 w(matrix)g(*)565 4846 y Ft(m)p FD(,)g(size)p 820 4846 V 41 w(t)g Ft(i)p Fu(\))390 4955 y FK(These)41 b(functions)g(return)f(a)i(v)m(ector)h (view)f(of)f(the)h FD(i)p FK(-th)f(ro)m(w)h(of)g(the)f(matrix)h FD(m)p FK(.)73 b(The)41 b FH(data)390 5065 y FK(p)s(oin)m(ter)30 b(of)h(the)f(new)g(v)m(ector)i(is)f(set)g(to)g(n)m(ull)f(if)g FD(i)36 b FK(is)30 b(out)h(of)f(range.)390 5230 y(The)38 b(function)g FH(gsl_vector_const_row)33 b FK(is)38 b(equiv)-5 b(alen)m(t)40 b(to)g FH(gsl_matrix_row)34 b FK(but)k(can)h(b)s(e)390 5340 y(used)30 b(for)g(matrices)h(whic)m(h)f(are)h(declared)g FH(const)p FK(.)p eop end %%Page: 95 113 TeXDict begin 95 112 bop 150 -116 a FK(Chapter)30 b(8:)41 b(V)-8 b(ectors)32 b(and)e(Matrices)2203 b(95)3350 299 y([F)-8 b(unction])-3599 b Fv(gsl_vector_view)57 b(gsl_matrix_column)50 b Fu(\()p FD(gsl)p 2068 299 28 4 v 41 w(matrix)31 b(*)g Ft(m)p FD(,)g(size)p 2730 299 V 41 w(t)f Ft(j)p Fu(\))3350 408 y FK([F)-8 b(unction])-3599 b Fv(gsl_vector_const_view)59 b(gsl_matrix_const_column)52 b Fu(\()p FD(const)565 518 y(gsl)p 677 518 V 41 w(matrix)30 b(*)h Ft(m)p FD(,)g(size)p 1338 518 V 41 w(t)g Ft(j)p Fu(\))390 628 y FK(These)i(functions)f (return)g(a)h(v)m(ector)h(view)f(of)g(the)g FD(j)p FK(-th)g(column)f (of)h(the)g(matrix)g FD(m)p FK(.)48 b(The)32 b FH(data)390 737 y FK(p)s(oin)m(ter)e(of)h(the)f(new)g(v)m(ector)i(is)f(set)g(to)g (n)m(ull)f(if)g FD(j)k FK(is)c(out)h(of)f(range.)390 890 y(The)41 b(function)g FH(gsl_vector_const_column)35 b FK(is)41 b(equiv)-5 b(alen)m(t)43 b(to)f FH(gsl_matrix_column)37 b FK(but)390 999 y(can)31 b(b)s(e)e(used)h(for)g(matrices)i(whic)m(h)e (are)g(declared)h FH(const)p FK(.)3350 1220 y([F)-8 b(unction])-3599 b Fv(gsl_vector_view)57 b(gsl_matrix_subrow)50 b Fu(\()p FD(gsl)p 2068 1220 V 41 w(matrix)31 b(*)g Ft(m)p FD(,)g(size)p 2730 1220 V 41 w(t)f Ft(i)p FD(,)h(size)p 3085 1220 V 41 w(t)565 1329 y Ft(offset)p FD(,)h(size)p 1081 1329 V 41 w(t)f Ft(n)p Fu(\))3350 1439 y FK([F)-8 b(unction])-3599 b Fv(gsl_vector_const_view)59 b(gsl_matrix_const_subrow)52 b Fu(\()p FD(const)565 1548 y(gsl)p 677 1548 V 41 w(matrix)30 b(*)h Ft(m)p FD(,)g(size)p 1338 1548 V 41 w(t)g Ft(i)p FD(,)f(size)p 1693 1548 V 41 w(t)h Ft(offset)p FD(,)h(size)p 2310 1548 V 41 w(t)f Ft(n)p Fu(\))390 1658 y FK(These)37 b(functions)g(return)f(a)h(v)m(ector)i(view)f(of)f(the)h FD(i)p FK(-th)f(ro)m(w)g(of)h(the)f(matrix)h FD(m)f FK(b)s(eginning)f (at)390 1768 y FD(o\013set)c FK(elemen)m(ts)f(past)e(the)g(\014rst)g (column)g(and)f(con)m(taining)j FD(n)d FK(elemen)m(ts.)42 b(The)29 b FH(data)f FK(p)s(oin)m(ter)h(of)390 1877 y(the)i(new)e(v)m (ector)j(is)f(set)g(to)g(n)m(ull)f(if)g FD(i)p FK(,)h FD(o\013set)p FK(,)h(or)e FD(n)g FK(are)h(out)g(of)f(range.)390 2030 y(The)41 b(function)g FH(gsl_vector_const_subrow)35 b FK(is)41 b(equiv)-5 b(alen)m(t)43 b(to)f FH(gsl_matrix_subrow)37 b FK(but)390 2139 y(can)31 b(b)s(e)e(used)h(for)g(matrices)i(whic)m(h)e (are)g(declared)h FH(const)p FK(.)3350 2360 y([F)-8 b(unction])-3599 b Fv(gsl_vector_view)57 b(gsl_matrix_subcolumn)51 b Fu(\()p FD(gsl)p 2225 2360 V 41 w(matrix)31 b(*)g Ft(m)p FD(,)g(size)p 2887 2360 V 41 w(t)f Ft(j)p FD(,)565 2469 y(size)p 712 2469 V 41 w(t)h Ft(offset)p FD(,)h(size)p 1329 2469 V 41 w(t)f Ft(n)p Fu(\))3350 2579 y FK([F)-8 b(unction])-3599 b Fv(gsl_vector_const_view)59 b(gsl_matrix_const_subcol)q(umn)52 b Fu(\()p FD(const)565 2688 y(gsl)p 677 2688 V 41 w(matrix)30 b(*)h Ft(m)p FD(,)g(size)p 1338 2688 V 41 w(t)g Ft(j)p FD(,)f(size)p 1693 2688 V 41 w(t)h Ft(offset)p FD(,)h(size)p 2310 2688 V 41 w(t)f Ft(n)p Fu(\))390 2798 y FK(These)c(functions)g (return)g(a)g(v)m(ector)j(view)d(of)h(the)g FD(j)p FK(-th)f(column)g (of)h(the)f(matrix)h FD(m)f FK(b)s(eginning)g(at)390 2908 y FD(o\013set)k FK(elemen)m(ts)f(past)e(the)h(\014rst)e(ro)m(w)i (and)e(con)m(taining)j FD(n)e FK(elemen)m(ts.)41 b(The)28 b FH(data)f FK(p)s(oin)m(ter)h(of)h(the)390 3017 y(new)h(v)m(ector)i (is)e(set)h(to)g(n)m(ull)g(if)f FD(j)p FK(,)g FD(o\013set)p FK(,)i(or)e FD(n)g FK(are)h(out)f(of)h(range.)390 3170 y(The)23 b(function)g FH(gsl_vector_const_subcol)o(umn)17 b FK(is)23 b(equiv)-5 b(alen)m(t)25 b(to)e FH(gsl_matrix_subcolumn)390 3279 y FK(but)30 b(can)g(b)s(e)g(used)g(for)g(matrices)h(whic)m(h)f (are)h(declared)g FH(const)p FK(.)3350 3500 y([F)-8 b(unction])-3599 b Fv(gsl_vector_view)57 b(gsl_matrix_diagonal)51 b Fu(\()p FD(gsl)p 2173 3500 V 41 w(matrix)31 b(*)f Ft(m)p Fu(\))3350 3609 y FK([F)-8 b(unction])-3599 b Fv(gsl_vector_const_view)59 b(gsl_matrix_const_diagon)q(al)52 b Fu(\()p FD(const)565 3719 y(gsl)p 677 3719 V 41 w(matrix)30 b(*)h Ft(m)p Fu(\))390 3828 y FK(These)e(functions)h(return)e(a)i(v)m(ector)h(view)f(of)g(the) g(diagonal)h(of)e(the)h(matrix)g FD(m)p FK(.)40 b(The)29 b(matrix)h FD(m)390 3938 y FK(is)k(not)g(required)f(to)i(b)s(e)e (square.)51 b(F)-8 b(or)35 b(a)f(rectangular)h(matrix)f(the)g(length)h (of)f(the)g(diagonal)h(is)390 4048 y(the)c(same)f(as)h(the)g(smaller)f (dimension)g(of)h(the)f(matrix.)390 4200 y(The)39 b(function)f FH(gsl_matrix_const_diagonal)33 b FK(is)39 b(equiv)-5 b(alen)m(t)40 b(to)g FH(gsl_matrix_diagonal)390 4310 y FK(but)30 b(can)g(b)s(e)g(used)g(for)g(matrices)h(whic)m(h)f(are)h (declared)g FH(const)p FK(.)3350 4530 y([F)-8 b(unction])-3599 b Fv(gsl_vector_view)57 b(gsl_matrix_subdiagonal)52 b Fu(\()p FD(gsl)p 2330 4530 V 41 w(matrix)31 b(*)f Ft(m)p FD(,)h(size)p 2991 4530 V 41 w(t)g Ft(k)p Fu(\))3350 4640 y FK([F)-8 b(unction])-3599 b Fv(gsl_vector_const_view)59 b(gsl_matrix_const_subdia)q(gon)q(al)52 b Fu(\()p FD(const)565 4749 y(gsl)p 677 4749 V 41 w(matrix)30 b(*)h Ft(m)p FD(,)g(size)p 1338 4749 V 41 w(t)g Ft(k)p Fu(\))390 4859 y FK(These)j(functions)f (return)g(a)h(v)m(ector)i(view)e(of)g(the)g FD(k)p FK(-th)g(sub)s (diagonal)g(of)g(the)g(matrix)g FD(m)p FK(.)51 b(The)390 4968 y(matrix)37 b FD(m)g FK(is)g(not)g(required)g(to)g(b)s(e)g (square.)60 b(The)37 b(diagonal)h(of)f(the)g(matrix)h(corresp)s(onds)d (to)390 5078 y FE(k)28 b FK(=)d(0.)390 5230 y(The)78 b(function)h FH(gsl_matrix_const_subdiag)o(onal)72 b FK(is)79 b(equiv)-5 b(alen)m(t)80 b(to)g FH(gsl_matrix_)390 5340 y(subdiagonal)27 b FK(but)j(can)h(b)s(e)e(used)h(for)g(matrices)h (whic)m(h)g(are)f(declared)h FH(const)p FK(.)p eop end %%Page: 96 114 TeXDict begin 96 113 bop 150 -116 a FK(Chapter)30 b(8:)41 b(V)-8 b(ectors)32 b(and)e(Matrices)2203 b(96)3350 299 y([F)-8 b(unction])-3599 b Fv(gsl_vector_view)57 b (gsl_matrix_superdiagon)q(al)52 b Fu(\()p FD(gsl)p 2435 299 28 4 v 41 w(matrix)30 b(*)h Ft(m)p FD(,)g(size)p 3096 299 V 41 w(t)565 408 y Ft(k)p Fu(\))3350 518 y FK([F)-8 b(unction])-3599 b Fv(gsl_vector_const_view)59 b (gsl_matrix_const_superd)q(iag)q(onal)52 b Fu(\()p FD(const)565 628 y(gsl)p 677 628 V 41 w(matrix)30 b(*)h Ft(m)p FD(,)g(size)p 1338 628 V 41 w(t)g Ft(k)p Fu(\))390 737 y FK(These)e(functions)f (return)g(a)h(v)m(ector)i(view)e(of)g(the)g FD(k)p FK(-th)g(sup)s (erdiagonal)g(of)g(the)g(matrix)g FD(m)p FK(.)40 b(The)390 847 y(matrix)d FD(m)g FK(is)g(not)g(required)g(to)g(b)s(e)g(square.)60 b(The)37 b(diagonal)h(of)f(the)g(matrix)h(corresp)s(onds)d(to)390 956 y FE(k)28 b FK(=)d(0.)390 1096 y(The)62 b(function)h FH(gsl_matrix_const_superdia)o(gon)o(al)57 b FK(is)63 b(equiv)-5 b(alen)m(t)64 b(to)g FH(gsl_matrix_)390 1205 y(superdiagonal)27 b FK(but)i(can)i(b)s(e)f(used)f(for)i(matrices)g (whic)m(h)f(are)h(declared)g FH(const)p FK(.)150 1409 y Fy(8.4.7)63 b(Cop)m(ying)41 b(matrices)3350 1611 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_matrix_memcpy)e Fu(\()p FD(gsl)p 1441 1611 V 41 w(matrix)30 b(*)h Ft(dest)p FD(,)h(const)f(gsl)p 2462 1611 V 40 w(matrix)g(*)g Ft(src)p Fu(\))390 1721 y FK(This)36 b(function)h(copies)g(the)g(elemen)m(ts)i (of)e(the)g(matrix)g FD(src)42 b FK(in)m(to)c(the)f(matrix)g FD(dest)p FK(.)60 b(The)37 b(t)m(w)m(o)390 1830 y(matrices)31 b(m)m(ust)g(ha)m(v)m(e)g(the)g(same)g(size.)3350 2024 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_matrix_swap)d Fu(\()p FD(gsl)p 1336 2024 V 41 w(matrix)31 b(*)g Ft(m1)p FD(,)g(gsl)p 2015 2024 V 40 w(matrix)g(*)g Ft(m2)p Fu(\))390 2134 y FK(This)j(function)h(exc)m(hanges)i(the)e(elemen)m(ts)i(of)e (the)h(matrices)g FD(m1)43 b FK(and)34 b FD(m2)43 b FK(b)m(y)35 b(cop)m(ying.)56 b(The)390 2243 y(t)m(w)m(o)32 b(matrices)f(m)m(ust)f (ha)m(v)m(e)i(the)f(same)f(size.)150 2447 y Fy(8.4.8)63 b(Cop)m(ying)41 b(ro)m(ws)g(and)g(columns)150 2594 y FK(The)25 b(functions)g(describ)s(ed)f(in)h(this)h(section)g(cop)m(y)h (a)e(ro)m(w)h(or)f(column)h(of)f(a)h(matrix)g(in)m(to)g(a)g(v)m(ector.) 41 b(This)150 2704 y(allo)m(ws)34 b(the)e(elemen)m(ts)i(of)e(the)h(v)m (ector)g(and)f(the)h(matrix)f(to)h(b)s(e)f(mo)s(di\014ed)f(indep)s (enden)m(tly)-8 b(.)46 b(Note)33 b(that)150 2814 y(if)c(the)g(matrix)g (and)f(the)i(v)m(ector)g(p)s(oin)m(t)f(to)h(o)m(v)m(erlapping)g (regions)f(of)g(memory)g(then)f(the)i(result)e(will)i(b)s(e)150 2923 y(unde\014ned.)36 b(The)24 b(same)h(e\013ect)g(can)g(b)s(e)e(ac)m (hiev)m(ed)j(with)e(more)h(generalit)m(y)h(using)e FH (gsl_vector_memcpy)150 3033 y FK(with)30 b(v)m(ector)i(views)f(of)f(ro) m(ws)g(and)g(columns.)3350 3227 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_matrix_get_row)e Fu(\()p FD(gsl)p 1493 3227 V 41 w(v)m(ector)32 b(*)f Ft(v)p FD(,)g(const)g(gsl)p 2335 3227 V 40 w(matrix)g(*)g Ft(m)p FD(,)f(size)p 2995 3227 V 41 w(t)h Ft(i)p Fu(\))390 3336 y FK(This)h(function)h(copies)h (the)g(elemen)m(ts)g(of)f(the)h FD(i)p FK(-th)f(ro)m(w)g(of)h(the)f (matrix)h FD(m)f FK(in)m(to)h(the)f(v)m(ector)i FD(v)p FK(.)390 3446 y(The)30 b(length)h(of)f(the)h(v)m(ector)h(m)m(ust)e(b)s (e)g(the)g(same)h(as)g(the)f(length)h(of)g(the)f(ro)m(w.)3350 3640 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_matrix_get_col)e Fu(\()p FD(gsl)p 1493 3640 V 41 w(v)m(ector)32 b(*)f Ft(v)p FD(,)g(const)g(gsl)p 2335 3640 V 40 w(matrix)g(*)g Ft(m)p FD(,)f(size)p 2995 3640 V 41 w(t)h Ft(j)p Fu(\))390 3749 y FK(This)f(function)g(copies)h(the)g(elemen)m(ts)h(of)e(the)h FD(j)p FK(-th)f(column)h(of)f(the)h(matrix)g FD(m)f FK(in)m(to)i(the)e (v)m(ector)390 3859 y FD(v)p FK(.)41 b(The)30 b(length)g(of)h(the)f(v)m (ector)i(m)m(ust)f(b)s(e)e(the)i(same)g(as)f(the)h(length)g(of)f(the)h (column.)3350 4053 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_matrix_set_row)e Fu(\()p FD(gsl)p 1493 4053 V 41 w(matrix)31 b(*)g Ft(m)p FD(,)f(size)p 2154 4053 V 41 w(t)h Ft(i)p FD(,)g(const)g(gsl)p 2713 4053 V 40 w(v)m(ector)h(*)f Ft(v)p Fu(\))390 4163 y FK(This)h(function)g(copies)i(the)f(elemen)m (ts)h(of)e(the)h(v)m(ector)i FD(v)40 b FK(in)m(to)34 b(the)e FD(i)p FK(-th)h(ro)m(w)g(of)g(the)g(matrix)g FD(m)p FK(.)390 4272 y(The)d(length)h(of)f(the)h(v)m(ector)h(m)m(ust)e (b)s(e)g(the)g(same)h(as)g(the)f(length)h(of)g(the)f(ro)m(w.)3350 4466 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_matrix_set_col)e Fu(\()p FD(gsl)p 1493 4466 V 41 w(matrix)31 b(*)g Ft(m)p FD(,)f(size)p 2154 4466 V 41 w(t)h Ft(j)p FD(,)g(const)g(gsl)p 2713 4466 V 40 w(v)m(ector)h(*)f Ft(v)p Fu(\))390 4576 y FK(This)g(function)h(copies)g(the)g(elemen)m(ts)h(of)f(the)g(v)m (ector)i FD(v)39 b FK(in)m(to)33 b(the)f FD(j)p FK(-th)g(column)g(of)g (the)g(matrix)390 4685 y FD(m)p FK(.)40 b(The)30 b(length)h(of)g(the)f (v)m(ector)i(m)m(ust)e(b)s(e)g(the)h(same)f(as)h(the)g(length)f(of)h (the)g(column.)150 4889 y Fy(8.4.9)63 b(Exc)m(hanging)40 b(ro)m(ws)h(and)g(columns)150 5036 y FK(The)30 b(follo)m(wing)i (functions)e(can)g(b)s(e)g(used)g(to)h(exc)m(hange)h(the)e(ro)m(ws)h (and)e(columns)h(of)h(a)g(matrix.)3350 5230 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_matrix_swap_rows)f Fu(\()p FD(gsl)p 1598 5230 V 41 w(matrix)30 b(*)h Ft(m)p FD(,)g(size)p 2259 5230 V 41 w(t)g Ft(i)p FD(,)f(size)p 2614 5230 V 41 w(t)h Ft(j)p Fu(\))390 5340 y FK(This)f(function)g(exc)m(hanges)h (the)g FD(i)p FK(-th)g(and)e FD(j)p FK(-th)i(ro)m(ws)f(of)h(the)f (matrix)h FD(m)f FK(in-place.)p eop end %%Page: 97 115 TeXDict begin 97 114 bop 150 -116 a FK(Chapter)30 b(8:)41 b(V)-8 b(ectors)32 b(and)e(Matrices)2203 b(97)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_matrix_swap_colum)q(ns)f Fu(\()p FD(gsl)p 1755 299 28 4 v 41 w(matrix)30 b(*)h Ft(m)p FD(,)g(size)p 2416 299 V 41 w(t)f Ft(i)p FD(,)h(size)p 2771 299 V 41 w(t)g Ft(j)p Fu(\))390 408 y FK(This)f(function)g(exc)m (hanges)h(the)g FD(i)p FK(-th)g(and)e FD(j)p FK(-th)i(columns)f(of)g (the)h(matrix)g FD(m)f FK(in-place.)3350 622 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_matrix_swap_rowco)q(l)e Fu(\()p FD(gsl)p 1702 622 V 41 w(matrix)31 b(*)g Ft(m)p FD(,)g(size)p 2364 622 V 41 w(t)f Ft(i)p FD(,)h(size)p 2719 622 V 41 w(t)g Ft(j)p Fu(\))390 731 y FK(This)f(function)h(exc)m (hanges)h(the)f FD(i)p FK(-th)g(ro)m(w)g(and)f FD(j)p FK(-th)h(column)g(of)g(the)g(matrix)g FD(m)f FK(in-place.)43 b(The)390 841 y(matrix)31 b(m)m(ust)f(b)s(e)g(square)g(for)g(this)g(op) s(eration)h(to)g(b)s(e)f(p)s(ossible.)3350 1054 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_matrix_transpose_)q(memc)q(py)f Fu(\()p FD(gsl)p 1964 1054 V 41 w(matrix)30 b(*)h Ft(dest)p FD(,)h(const)565 1163 y(gsl)p 677 1163 V 41 w(matrix)e(*)h Ft(src)p Fu(\))390 1273 y FK(This)g(function)h(mak)m(es)h(the)f(matrix) g FD(dest)i FK(the)e(transp)s(ose)g(of)g(the)g(matrix)h FD(src)k FK(b)m(y)32 b(cop)m(ying)h(the)390 1383 y(elemen)m(ts)43 b(of)g FD(src)k FK(in)m(to)c FD(dest)p FK(.)76 b(This)41 b(function)h(w)m(orks)g(for)g(all)h(matrices)g(pro)m(vided)f(that)h (the)390 1492 y(dimensions)30 b(of)g(the)h(matrix)f FD(dest)j FK(matc)m(h)e(the)g(transp)s(osed)e(dimensions)h(of)g(the)h(matrix)f FD(src)p FK(.)3350 1705 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_matrix_transpose)f Fu(\()p FD(gsl)p 1598 1705 V 41 w(matrix)30 b(*)h Ft(m)p Fu(\))390 1815 y FK(This)g(function)g (replaces)h(the)g(matrix)g FD(m)f FK(b)m(y)g(its)h(transp)s(ose)f(b)m (y)g(cop)m(ying)i(the)e(elemen)m(ts)i(of)f(the)390 1925 y(matrix)f(in-place.)41 b(The)30 b(matrix)h(m)m(ust)f(b)s(e)g(square)g (for)g(this)h(op)s(eration)f(to)h(b)s(e)f(p)s(ossible.)150 2138 y Fy(8.4.10)63 b(Matrix)41 b(op)s(erations)150 2285 y FK(The)30 b(follo)m(wing)i(op)s(erations)e(are)h(de\014ned)e(for)h (real)h(and)f(complex)h(matrices.)3350 2498 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_matrix_add)d Fu(\()p FD(gsl)p 1284 2498 V 41 w(matrix)31 b(*)f Ft(a)p FD(,)h(const)g(gsl)p 2148 2498 V 41 w(matrix)f(*)h Ft(b)p Fu(\))390 2608 y FK(This)f(function)h(adds)g(the)g(elemen)m(ts)i(of)e(matrix)g FD(b)i FK(to)f(the)f(elemen)m(ts)i(of)e(matrix)h FD(a)p FK(.)43 b(The)31 b(result)390 2717 y FE(a)p FK(\()p FE(i;)15 b(j)5 b FK(\))33 b FI( )e FE(a)p FK(\()p FE(i;)15 b(j)5 b FK(\))25 b(+)d FE(b)p FK(\()p FE(i;)15 b(j)5 b FK(\))36 b(is)e(stored)g(in)f FD(a)h FK(and)g FD(b)h FK(remains)f(unc)m(hanged.) 50 b(The)34 b(t)m(w)m(o)h(matrices)390 2827 y(m)m(ust)30 b(ha)m(v)m(e)i(the)e(same)h(dimensions.)3350 3040 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_matrix_sub)d Fu(\()p FD(gsl)p 1284 3040 V 41 w(matrix)31 b(*)f Ft(a)p FD(,)h(const)g(gsl)p 2148 3040 V 41 w(matrix)f(*)h Ft(b)p Fu(\))390 3150 y FK(This)d(function)h(subtracts)f(the)i(elemen)m(ts)g(of)f(matrix)g FD(b)i FK(from)d(the)h(elemen)m(ts)h(of)g(matrix)f FD(a)p FK(.)40 b(The)390 3259 y(result)g FE(a)p FK(\()p FE(i;)15 b(j)5 b FK(\))44 b FI( )d FE(a)p FK(\()p FE(i;)15 b(j)5 b FK(\))29 b FI(\000)d FE(b)p FK(\()p FE(i;)15 b(j)5 b FK(\))43 b(is)d(stored)g(in)g FD(a)g FK(and)g FD(b)h FK(remains)f(unc)m(hanged.)70 b(The)40 b(t)m(w)m(o)390 3369 y(matrices)31 b(m)m(ust)g(ha)m(v)m(e)g(the)g(same)g(dimensions.) 3350 3582 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_matrix_mul_elemen) q(ts)f Fu(\()p FD(gsl)p 1755 3582 V 41 w(matrix)30 b(*)h Ft(a)p FD(,)g(const)g(gsl)p 2619 3582 V 40 w(matrix)g(*)g Ft(b)p Fu(\))390 3692 y FK(This)i(function)g(m)m(ultiplies)h(the)g (elemen)m(ts)h(of)e(matrix)h FD(a)g FK(b)m(y)f(the)h(elemen)m(ts)h(of)e (matrix)h FD(b)p FK(.)49 b(The)390 3801 y(result)41 b FE(a)p FK(\()p FE(i;)15 b(j)5 b FK(\))47 b FI( )c FE(a)p FK(\()p FE(i;)15 b(j)5 b FK(\))30 b FI(\003)e FE(b)p FK(\()p FE(i;)15 b(j)5 b FK(\))44 b(is)d(stored)h(in)f FD(a)h FK(and)f FD(b)i FK(remains)f(unc)m(hanged.)74 b(The)41 b(t)m(w)m(o)390 3911 y(matrices)31 b(m)m(ust)g(ha)m(v)m(e)g (the)g(same)g(dimensions.)3350 4124 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_matrix_div_elemen)q(ts)f Fu(\()p FD(gsl)p 1755 4124 V 41 w(matrix)30 b(*)h Ft(a)p FD(,)g(const)g(gsl)p 2619 4124 V 40 w(matrix)g(*)g Ft(b)p Fu(\))390 4233 y FK(This)23 b(function)h(divides)f(the)h(elemen)m(ts)i(of)e(matrix)g FD(a)g FK(b)m(y)g(the)g(elemen)m(ts)h(of)f(matrix)h FD(b)p FK(.)38 b(The)23 b(result)390 4343 y FE(a)p FK(\()p FE(i;)15 b(j)5 b FK(\))27 b FI( )f FE(a)p FK(\()p FE(i;)15 b(j)5 b FK(\))p FE(=b)p FK(\()p FE(i;)15 b(j)5 b FK(\))26 b(is)c(stored)f(in) h FD(a)g FK(and)f FD(b)i FK(remains)f(unc)m(hanged.)37 b(The)21 b(t)m(w)m(o)i(matrices)g(m)m(ust)390 4453 y(ha)m(v)m(e)32 b(the)e(same)h(dimensions.)3350 4666 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_matrix_scale)e Fu(\()p 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b(and)e(Matrices)2203 b(98)150 299 y Fy(8.4.11)63 b(Finding)42 b(maxim)m(um)f(and)g(minim)m(um)h(elemen)m (ts)f(of)h(matrices)150 446 y FK(The)30 b(follo)m(wing)i(op)s(erations) e(are)h(only)g(de\014ned)e(for)h(real)h(matrices.)3350 628 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_matrix_max)c Fu(\()p FD(const)31 b(gsl)p 1679 628 28 4 v 41 w(matrix)f(*)h Ft(m)p Fu(\))390 738 y FK(This)f(function)g(returns)f(the)h(maxim)m(um) h(v)-5 b(alue)30 b(in)g(the)h(matrix)g FD(m)p FK(.)3350 920 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_matrix_min)c Fu(\()p FD(const)31 b(gsl)p 1679 920 V 41 w(matrix)f(*)h Ft(m)p Fu(\))390 1030 y FK(This)f(function)g(returns)f(the)h(minim)m (um)g(v)-5 b(alue)31 b(in)f(the)g(matrix)h FD(m)p FK(.)3350 1212 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_matrix_minmax)c Fu(\()p FD(const)31 b(gsl)p 1731 1212 V 41 w(matrix)g(*)f Ft(m)p FD(,)h(double)f(*)h Ft(min_out)p FD(,)565 1321 y(double)f(*)h Ft(max_out)p Fu(\))390 1431 y FK(This)36 b(function)h(returns)f(the)i(minim)m(um)e(and)h(maxim)m(um)g(v)-5 b(alues)38 b(in)f(the)g(matrix)h FD(m)p FK(,)h(storing)390 1541 y(them)30 b(in)g FD(min)p 886 1541 V 40 w(out)i FK(and)e FD(max)p 1435 1541 V 40 w(out)p FK(.)3350 1723 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_matrix_max_index)d Fu(\()p FD(const)30 b(gsl)p 1887 1723 V 41 w(matrix)f(*)h Ft(m)p FD(,)g(size)p 2545 1723 V 41 w(t)f(*)h Ft(imax)p FD(,)h(size)p 3130 1723 V 41 w(t)565 1832 y(*)g Ft(jmax)p Fu(\))390 1942 y FK(This)23 b(function)h(returns)f(the)h(indices)g(of)g (the)h(maxim)m(um)e(v)-5 b(alue)25 b(in)f(the)g(matrix)g FD(m)p FK(,)i(storing)e(them)390 2052 y(in)35 b FD(imax)43 b FK(and)35 b FD(jmax)p FK(.)56 b(When)35 b(there)h(are)g(sev)m(eral)h (equal)f(maxim)m(um)g(elemen)m(ts)h(then)e(the)h(\014rst)390 2161 y(elemen)m(t)c(found)d(is)h(returned,)g(searc)m(hing)h(in)f(ro)m (w-ma)5 b(jor)31 b(order.)3350 2343 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_matrix_min_index)d Fu(\()p FD(const)30 b(gsl)p 1887 2343 V 41 w(matrix)f(*)h Ft(m)p FD(,)g(size)p 2545 2343 V 41 w(t)f(*)h Ft(imin)p FD(,)h(size)p 3130 2343 V 41 w(t)565 2453 y(*)g Ft(jmin)p Fu(\))390 2563 y FK(This)25 b(function)g(returns)f(the)h(indices)h(of)f(the)h(minim)m (um)e(v)-5 b(alue)26 b(in)f(the)g(matrix)h FD(m)p FK(,)g(storing)g (them)390 2672 y(in)39 b FD(imin)g FK(and)g FD(jmin)p FK(.)68 b(When)39 b(there)h(are)g(sev)m(eral)h(equal)f(minim)m(um)f (elemen)m(ts)i(then)e(the)h(\014rst)390 2782 y(elemen)m(t)32 b(found)d(is)h(returned,)g(searc)m(hing)h(in)f(ro)m(w-ma)5 b(jor)31 b(order.)3350 2964 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_matrix_minmax_index)e Fu(\()p FD(const)31 b(gsl)p 2045 2964 V 41 w(matrix)f(*)h Ft(m)p FD(,)g(size)p 2706 2964 V 41 w(t)g(*)f Ft(imin)p FD(,)565 3074 y(size)p 712 3074 V 41 w(t)h(*)f Ft(jmin)p FD(,)i(size)p 1300 3074 V 41 w(t)f(*)g Ft(imax)p FD(,)g(size)p 1888 3074 V 41 w(t)g(*)g Ft(jmax)p Fu(\))390 3183 y FK(This)c(function)g(returns) f(the)h(indices)h(of)f(the)h(minim)m(um)e(and)h(maxim)m(um)g(v)-5 b(alues)28 b(in)f(the)h(matrix)390 3293 y FD(m)p FK(,)i(storing)h(them) f(in)g(\()p FD(imin)p FK(,)p FD(jmin)p FK(\))g(and)g(\()p FD(imax)p FK(,)p FD(jmax)6 b FK(\).)42 b(When)30 b(there)g(are)h(sev)m (eral)g(equal)g(min-)390 3402 y(im)m(um)f(or)g(maxim)m(um)h(elemen)m (ts)h(then)e(the)g(\014rst)g(elemen)m(ts)i(found)d(are)i(returned,)e (searc)m(hing)i(in)390 3512 y(ro)m(w-ma)5 b(jor)31 b(order.)150 3710 y Fy(8.4.12)63 b(Matrix)41 b(prop)s(erties)150 3857 y FK(The)35 b(follo)m(wing)i(functions)e(are)h(de\014ned)e(for)h(real)h (and)f(complex)h(matrices.)57 b(F)-8 b(or)36 b(complex)g(matrices)150 3966 y(b)s(oth)30 b(the)g(real)h(and)f(imaginary)h(parts)f(m)m(ust)g (satisfy)h(the)g(conditions.)3350 4149 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_matrix_isnull)e Fu(\()p FD(const)31 b(gsl)p 1679 4149 V 41 w(matrix)f(*)h Ft(m)p Fu(\))3350 4258 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_matrix_ispos)e Fu(\()p FD(const)31 b(gsl)p 1627 4258 V 40 w(matrix)g(*)g Ft(m)p Fu(\))3350 4368 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_matrix_isneg)e Fu(\()p FD(const)31 b(gsl)p 1627 4368 V 40 w(matrix)g(*)g Ft(m)p Fu(\))3350 4477 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_matrix_isnonneg)e Fu(\()p FD(const)32 b(gsl)p 1784 4477 V 40 w(matrix)f(*)g Ft(m)p Fu(\))390 4587 y FK(These)26 b(functions)g(return)f(1)i(if)f (all)h(the)g(elemen)m(ts)g(of)g(the)f(matrix)h FD(m)f FK(are)g(zero,)i(strictly)g(p)s(ositiv)m(e,)390 4697 y(strictly)39 b(negativ)m(e,)k(or)38 b(non-negativ)m(e)j(resp)s(ectiv)m (ely)-8 b(,)42 b(and)37 b(0)i(otherwise.)65 b(T)-8 b(o)39 b(test)g(whether)f(a)390 4806 y(matrix)21 b(is)h(p)s(ositiv)m (e-de\014nite,)i(use)d(the)g(Cholesky)g(decomp)s(osition)h(\(see)g (Section)g(14.6)h([Cholesky)390 4916 y(Decomp)s(osition],)32 b(page)g(145\).)3350 5098 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_matrix_equal)e Fu(\()p FD(const)31 b(gsl)p 1627 5098 V 40 w(matrix)g(*)g Ft(a)p FD(,)g(const)g(gsl)p 2491 5098 V 40 w(matrix)g(*)g Ft(b)p Fu(\))390 5208 y FK(This)g(function)h(returns)f(1)h(if)g(the)g(matrices)h FD(a)f FK(and)g FD(b)h FK(are)f(equal)h(\(b)m(y)f(comparison)g(of)g (elemen)m(t)390 5317 y(v)-5 b(alues\))31 b(and)f(0)h(otherwise.)p eop end %%Page: 99 117 TeXDict begin 99 116 bop 150 -116 a FK(Chapter)30 b(8:)41 b(V)-8 b(ectors)32 b(and)e(Matrices)2203 b(99)150 299 y Fy(8.4.13)63 b(Example)40 b(programs)j(for)f(matrices)150 446 y FK(The)g(program)g(b)s(elo)m(w)g(sho)m(ws)h(ho)m(w)f(to)h(allo)s (cate,)48 b(initialize)d(and)c(read)i(from)f(a)g(matrix)h(using)f(the) 150 555 y(functions)30 b FH(gsl_matrix_alloc)p FK(,)c FH(gsl_matrix_set)h FK(and)i FH(gsl_matrix_get)p FK(.)390 701 y FH(#include)46 b()390 811 y(#include)g ()390 1030 y(int)390 1140 y(main)h(\(void\))390 1249 y({)485 1359 y(int)g(i,)h(j;)485 1468 y(gsl_matrix)d(*)j(m)f(=)h (gsl_matrix_alloc)43 b(\(10,)k(3\);)485 1688 y(for)g(\(i)h(=)f(0;)g(i)h (<)f(10;)g(i++\))581 1797 y(for)g(\(j)g(=)g(0;)h(j)f(<)h(3;)f(j++\))676 1907 y(gsl_matrix_set)d(\(m,)j(i,)g(j,)h(0.23)e(+)i(100*i)e(+)h(j\);) 485 2126 y(for)g(\(i)h(=)f(0;)g(i)h(<)f(100;)g(i++\))94 b(/*)47 b(OUT)g(OF)g(RANGE)g(ERROR)f(*/)581 2236 y(for)h(\(j)g(=)g(0;)h (j)f(<)h(3;)f(j++\))676 2345 y(printf)f(\("m\(\045d,\045d\))f(=)j (\045g\\n",)e(i,)h(j,)1058 2455 y(gsl_matrix_get)d(\(m,)j(i,)g(j\)\);) 485 2674 y(gsl_matrix_free)d(\(m\);)485 2893 y(return)j(0;)390 3003 y(})150 3149 y FK(Here)30 b(is)g(the)g(output)f(from)h(the)g (program.)40 b(The)29 b(\014nal)h(lo)s(op)g(attempts)g(to)h(read)f (outside)g(the)g(range)g(of)150 3258 y(the)h(matrix)f FH(m)p FK(,)h(and)e(the)i(error)f(is)g(trapp)s(ed)f(b)m(y)i(the)f (range-c)m(hec)m(king)j(co)s(de)e(in)f FH(gsl_matrix_get)p FK(.)390 3404 y FH($)47 b(./a.out)390 3514 y(m\(0,0\))f(=)i(0.23)390 3623 y(m\(0,1\))e(=)i(1.23)390 3733 y(m\(0,2\))e(=)i(2.23)390 3843 y(m\(1,0\))e(=)i(100.23)390 3952 y(m\(1,1\))e(=)i(101.23)390 4062 y(m\(1,2\))e(=)i(102.23)390 4171 y(...)390 4281 y(m\(9,2\))e(=)i(902.23)390 4391 y(gsl:)f(matrix_source.c:13:)42 b(ERROR:)k(first)h(index)f(out)h(of)g(range)390 4500 y(Default)f(GSL)h(error)f(handler)g(invoked.)390 4610 y(Aborted)g(\(core)g(dumped\))150 4756 y FK(The)30 b(next)g(program)h (sho)m(ws)f(ho)m(w)g(to)h(write)g(a)g(matrix)f(to)h(a)g(\014le.)390 4902 y FH(#include)46 b()390 5011 y(#include)g ()390 5230 y(int)390 5340 y(main)h(\(void\))p eop end %%Page: 100 118 TeXDict begin 100 117 bop 150 -116 a FK(Chapter)30 b(8:)41 b(V)-8 b(ectors)32 b(and)e(Matrices)2158 b(100)390 299 y FH({)485 408 y(int)47 b(i,)h(j,)f(k)g(=)h(0;)485 518 y(gsl_matrix)d(*)j(m)f(=)h(gsl_matrix_alloc)43 b(\(100,)k(100\);)485 628 y(gsl_matrix)e(*)j(a)f(=)h(gsl_matrix_alloc)43 b(\(100,)k(100\);) 485 847 y(for)g(\(i)h(=)f(0;)g(i)h(<)f(100;)g(i++\))581 956 y(for)g(\(j)g(=)g(0;)h(j)f(<)h(100;)e(j++\))676 1066 y(gsl_matrix_set)e(\(m,)j(i,)g(j,)h(0.23)e(+)i(i)f(+)h(j\);)485 1285 y({)629 1395 y(FILE)e(*)i(f)f(=)h(fopen)e(\("test.dat",)e("wb"\);) 629 1504 y(gsl_matrix_fwrite)f(\(f,)k(m\);)629 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FH(gsl_matrix_fread)150 4390 y FK(should)29 b(b)s(e)h(exactly)i(equal)f(to)g(the)g(original)g (matrix.)275 4536 y(The)36 b(follo)m(wing)j(program)e(demonstrates)g (the)g(use)g(of)h(v)m(ector)g(views.)61 b(The)37 b(program)g(computes) 150 4646 y(the)31 b(column)f(norms)f(of)i(a)g(matrix.)390 4792 y FH(#include)46 b()390 4902 y(#include)g()390 5011 y(#include)g()390 5121 y(#include)g ()390 5340 y(int)p eop end %%Page: 101 119 TeXDict begin 101 118 bop 150 -116 a FK(Chapter)30 b(8:)41 b(V)-8 b(ectors)32 b(and)e(Matrices)2158 b(101)390 299 y FH(main)47 b(\(void\))390 408 y({)485 518 y(size_t)g(i,j;)485 737 y(gsl_matrix)e(*m)j(=)f(gsl_matrix_alloc)c(\(10,)k(10\);)485 956 y(for)g(\(i)h(=)f(0;)g(i)h(<)f(10;)g(i++\))581 1066 y(for)g(\(j)g(=)g(0;)h(j)f(<)h(10;)e(j++\))676 1176 y(gsl_matrix_set)e (\(m,)j(i,)g(j,)h(sin)e(\(i\))h(+)h(cos)f(\(j\)\);)485 1395 y(for)g(\(j)h(=)f(0;)g(j)h(<)f(10;)g(j++\))581 1504 y({)676 1614 y(gsl_vector_view)d(column)i(=)i(gsl_matrix_column)43 b(\(m,)k(j\);)676 1724 y(double)f(d;)676 1943 y(d)i(=)f(gsl_blas_dnrm2) d(\(&column.vector\);)676 2162 y(printf)i(\("matrix)g(column)g(\045zu,) h(norm)f(=)i(\045g\\n",)e(j,)h(d\);)581 2271 y(})485 2491 y(gsl_matrix_free)d(\(m\);)485 2710 y(return)j(0;)390 2819 y(})150 2984 y FK(Here)31 b(is)f(the)h(output)f(of)g(the)h (program,)390 3148 y FH($)47 b(./a.out)390 3258 y(matrix)f(column)g(0,) h(norm)g(=)g(4.31461)390 3367 y(matrix)f(column)g(1,)h(norm)g(=)g (3.1205)390 3477 y(matrix)f(column)g(2,)h(norm)g(=)g(2.19316)390 3587 y(matrix)f(column)g(3,)h(norm)g(=)g(3.26114)390 3696 y(matrix)f(column)g(4,)h(norm)g(=)g(2.53416)390 3806 y(matrix)f(column)g(5,)h(norm)g(=)g(2.57281)390 3915 y(matrix)f(column)g(6,)h(norm)g(=)g(4.20469)390 4025 y(matrix)f(column)g(7,)h(norm)g(=)g(3.65202)390 4134 y(matrix)f(column)g(8,)h(norm)g(=)g(2.08524)390 4244 y(matrix)f(column)g(9,)h(norm)g(=)g(3.07313)150 4408 y FK(The)30 b(results)g(can)h(b)s(e)e(con\014rmed)h(using)g FC(gnu)k(oct)-6 b(a)e(ve)p FK(,)390 4573 y FH($)47 b(octave)390 4682 y(GNU)g(Octave,)f(version)g(2.0.16.92)390 4792 y(octave>)g(m)h(=)h (sin\(0:9\)')d(*)i(ones\(1,10\))1106 4902 y(+)g(ones\(10,1\))e(*)j (cos\(0:9\);)390 5011 y(octave>)e(sqrt\(sum\(m.^2\)\))390 5121 y(ans)h(=)485 5230 y(4.3146)94 b(3.1205)g(2.1932)g(3.2611)g (2.5342)g(2.5728)485 5340 y(4.2047)g(3.6520)g(2.0852)g(3.0731)p eop end %%Page: 102 120 TeXDict begin 102 119 bop 150 -116 a FK(Chapter)30 b(8:)41 b(V)-8 b(ectors)32 b(and)e(Matrices)2158 b(102)150 299 y FJ(8.5)68 b(References)46 b(and)f(F)-11 b(urther)44 b(Reading)150 458 y FK(The)25 b(blo)s(c)m(k,)j(v)m(ector)g(and)d (matrix)h(ob)5 b(jects)27 b(in)e(GSL)h(follo)m(w)h(the)f FH(valarray)e FK(mo)s(del)i(of)g(C)p FH(++)p FK(.)38 b(A)26 b(descrip-)150 568 y(tion)31 b(of)f(this)h(mo)s(del)f(can)h(b)s (e)e(found)g(in)h(the)h(follo)m(wing)h(reference,)330 702 y(B.)g(Stroustrup,)e FD(The)g(C)p FH(++)g FD(Programming)i (Language)37 b FK(\(3rd)31 b(Ed\),)g(Section)h(22.4)h(V)-8 b(ector)33 b(Arith-)330 812 y(metic.)42 b(Addison-W)-8 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FK(3)p FE(;)g FK(2\))39 b(represen)m(ts)34 b(a)h(p)s(erm)m(utation)150 984 y(whic)m(h)26 b(exc)m(hanges)i(the)f(last)g(t)m(w)m(o)h(elemen)m(ts)g(of)f(a)g(four)f (elemen)m(t)i(v)m(ector.)41 b(The)26 b(corresp)s(onding)f(iden)m(tit)m (y)150 1093 y(p)s(erm)m(utation)30 b(is)h(\(0)p FE(;)15 b FK(1)p FE(;)g FK(2)p FE(;)g FK(3\).)275 1232 y(Note)35 b(that)g(the)f(p)s(erm)m(utations)g(pro)s(duced)f(b)m(y)h(the)g(linear) h(algebra)g(routines)f(corresp)s(ond)f(to)i(the)150 1342 y(exc)m(hange)30 b(of)f(matrix)g(columns,)g(and)f(so)h(should)f(b)s(e)g (considered)h(as)g(applying)f(to)i(ro)m(w-v)m(ectors)g(in)f(the)150 1451 y(form)h FE(v)412 1418 y Fp(0)461 1451 y FK(=)25 b FE(v)s(P)43 b FK(rather)31 b(than)f(column-v)m(ectors,)i(when)d(p)s (erm)m(uting)h(the)h(elemen)m(ts)g(of)g(a)g(v)m(ector.)275 1590 y(The)20 b(functions)g(describ)s(ed)f(in)h(this)g(c)m(hapter)i (are)e(de\014ned)g(in)g(the)h(header)f(\014le)g FH(gsl_permutation.h)p FK(.)150 1829 y FJ(9.1)68 b(The)45 b(P)l(erm)l(utation)h(struct)150 1988 y FK(A)29 b(p)s(erm)m(utation)f(is)h(de\014ned)e(b)m(y)h(a)h (structure)f(con)m(taining)i(t)m(w)m(o)g(comp)s(onen)m(ts,)f(the)f (size)i(of)e(the)h(p)s(erm)m(u-)150 2098 y(tation)k(and)d(a)i(p)s(oin)m (ter)f(to)h(the)g(p)s(erm)m(utation)f(arra)m(y)-8 b(.)44 b(The)31 b(elemen)m(ts)i(of)e(the)g(p)s(erm)m(utation)h(arra)m(y)g(are) 150 2207 y(all)f(of)g(t)m(yp)s(e)f FH(size_t)p FK(.)39 b(The)30 b FH(gsl_permutation)c FK(structure)k(lo)s(oks)h(lik)m(e)h (this,)390 2346 y FH(typedef)46 b(struct)390 2456 y({)485 2565 y(size_t)h(size;)485 2675 y(size_t)g(*)g(data;)390 2784 y(})g(gsl_permutation;)150 3023 y FJ(9.2)68 b(P)l(erm)l(utation)47 b(allo)t(cation)3350 3237 y FK([F)-8 b(unction])-3599 b Fv(gsl_permutation)57 b(*)52 b(gsl_permutation_allo)q(c)f Fu(\()p FD(size)p 2417 3237 28 4 v 42 w(t)30 b Ft(n)p Fu(\))390 3346 y FK(This)f(function)g(allo)s(cates)j(memory)e(for)f(a)h (new)f(p)s(erm)m(utation)h(of)g(size)g FD(n)p FK(.)40 b(The)29 b(p)s(erm)m(utation)h(is)390 3456 y(not)35 b(initialized)h (and)e(its)i(elemen)m(ts)g(are)f(unde\014ned.)51 b(Use)35 b(the)g(function)f FH(gsl_permutation_)390 3565 y(calloc)25 b FK(if)h(y)m(ou)g(w)m(an)m(t)i(to)f(create)g(a)g(p)s(erm)m(utation)f (whic)m(h)g(is)h(initialized)h(to)f(the)f(iden)m(tit)m(y)-8 b(.)42 b(A)26 b(n)m(ull)390 3675 y(p)s(oin)m(ter)k(is)h(returned)e(if)h (insu\016cien)m(t)h(memory)f(is)h(a)m(v)-5 b(ailable)32 b(to)f(create)h(the)f(p)s(erm)m(utation.)3350 3868 y([F)-8 b(unction])-3599 b Fv(gsl_permutation)57 b(*)52 b(gsl_permutation_call) q(oc)g Fu(\()p FD(size)p 2470 3868 V 41 w(t)31 b Ft(n)p Fu(\))390 3977 y FK(This)i(function)g(allo)s(cates)i(memory)e(for)h(a)f (new)g(p)s(erm)m(utation)h(of)f(size)h FD(n)f FK(and)g(initializes)i (it)f(to)390 4087 y(the)i(iden)m(tit)m(y)-8 b(.)59 b(A)36 b(n)m(ull)g(p)s(oin)m(ter)g(is)f(returned)g(if)h(insu\016cien)m(t)g (memory)g(is)g(a)m(v)-5 b(ailable)38 b(to)e(create)390 4196 y(the)31 b(p)s(erm)m(utation.)3350 4389 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_permutation_init)d Fu(\()p FD(gsl)p 1650 4389 V 41 w(p)s(erm)m(utation)30 b(*)h Ft(p)p Fu(\))390 4499 y FK(This)f(function)g(initializes)i(the)f (p)s(erm)m(utation)f FD(p)j FK(to)e(the)f(iden)m(tit)m(y)-8 b(,)33 b(i.e.)42 b(\(0)p FE(;)15 b FK(1)p FE(;)g FK(2)p FE(;)g(:)g(:)g(:)k(;)c(n)20 b FI(\000)g FK(1\).)3350 4691 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_permutation_free)d Fu(\()p FD(gsl)p 1650 4691 V 41 w(p)s(erm)m(utation)30 b(*)h Ft(p)p Fu(\))390 4801 y FK(This)f(function)g(frees)g(all)h(the)g (memory)f(used)g(b)m(y)g(the)g(p)s(erm)m(utation)h FD(p)p FK(.)3350 4994 y([F)-8 b(unction])-3599 b Fv(int)53 b (gsl_permutation_memcp)q(y)e Fu(\()p FD(gsl)p 1702 4994 V 41 w(p)s(erm)m(utation)31 b(*)f Ft(dest)p FD(,)i(const)565 5103 y(gsl)p 677 5103 V 41 w(p)s(erm)m(utation)e(*)h Ft(src)p Fu(\))390 5213 y FK(This)g(function)h(copies)i(the)e(elemen)m (ts)i(of)e(the)h(p)s(erm)m(utation)f FD(src)38 b FK(in)m(to)33 b(the)f(p)s(erm)m(utation)h FD(dest)p FK(.)390 5322 y(The)d(t)m(w)m(o)i (p)s(erm)m(utations)e(m)m(ust)g(ha)m(v)m(e)i(the)e(same)h(size.)p eop end %%Page: 104 122 TeXDict begin 104 121 bop 150 -116 a FK(Chapter)30 b(9:)41 b(P)m(erm)m(utations)2468 b(104)150 299 y FJ(9.3)68 b(Accessing)45 b(p)t(erm)l(utation)h(elemen)l(ts)150 458 y FK(The)30 b(follo)m(wing)i(functions)e(can)g(b)s(e)g(used)g(to)h(access)g(and)f (manipulate)h(p)s(erm)m(utations.)3350 684 y([F)-8 b(unction])-3599 b Fv(size_t)54 b(gsl_permutation_get)d Fu(\()p FD(const)32 b(gsl)p 1941 684 28 4 v 40 w(p)s(erm)m(utation)f(*)f Ft(p)p FD(,)h(const)g(size)p 3064 684 V 41 w(t)565 793 y Ft(i)p Fu(\))390 903 y FK(This)38 b(function)h(returns)f(the)h(v)-5 b(alue)40 b(of)f(the)g FD(i)p FK(-th)h(elemen)m(t)g(of)g(the)f(p)s(erm) m(utation)g FD(p)p FK(.)66 b(If)39 b FD(i)44 b FK(lies)390 1012 y(outside)39 b(the)f(allo)m(w)m(ed)j(range)d(of)h(0)g(to)g FD(n)25 b FI(\000)h FK(1)38 b(then)g(the)h(error)f(handler)g(is)g(in)m (v)m(ok)m(ed)i(and)e(0)h(is)390 1122 y(returned.)h(An)30 b(inline)g(v)m(ersion)h(of)f(this)h(function)f(is)g(used)g(when)f FH(HAVE_INLINE)e FK(is)k(de\014ned.)3350 1347 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_permutation_swap)f Fu(\()p FD(gsl)p 1598 1347 V 41 w(p)s(erm)m(utation)30 b(*)h Ft(p)p FD(,)g(const)g(size)p 2722 1347 V 41 w(t)f Ft(i)p FD(,)h(const)565 1457 y(size)p 712 1457 V 41 w(t)g Ft(j)p Fu(\))390 1566 y FK(This)f(function)g(exc)m(hanges)h(the)g FD(i)p FK(-th)g(and)e FD(j)p FK(-th)i(elemen)m(ts)g(of)g(the)f(p)s(erm) m(utation)h FD(p)p FK(.)150 1830 y FJ(9.4)68 b(P)l(erm)l(utation)47 b(prop)t(erties)3350 2059 y FK([F)-8 b(unction])-3599 b Fv(size_t)54 b(gsl_permutation_size)e Fu(\()p FD(const)31 b(gsl)p 1993 2059 V 40 w(p)s(erm)m(utation)g(*)g Ft(p)p Fu(\))390 2169 y FK(This)f(function)g(returns)f(the)h(size)i(of)e(the)h (p)s(erm)m(utation)f FD(p)p FK(.)3350 2394 y([F)-8 b(unction])-3599 b Fv(size_t)54 b(*)f(gsl_permutation_data)e Fu(\()p FD(const)31 b(gsl)p 2097 2394 V 41 w(p)s(erm)m(utation)g(*)f Ft(p)p 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FK(to)g(the)e(elemen)m(ts)i(of)f(the)g(v)m(ector)h FD(v)p FK(,)f(considered)390 1698 y(as)d(a)f(ro)m(w-v)m(ector)j(acted)e (on)g(b)m(y)f(a)h(p)s(erm)m(utation)f(matrix)h(from)f(the)g(righ)m(t,)h FE(v)3075 1665 y Fp(0)3124 1698 y FK(=)25 b FE(v)s(P)13 b FK(.)41 b(The)30 b FE(j)5 b FK(-th)390 1807 y(column)40 b(of)g(the)g(p)s(erm)m(utation)g(matrix)g FE(P)53 b FK(is)40 b(giv)m(en)h(b)m(y)f(the)g FD(p)2647 1821 y Fq(j)2681 1807 y FK(-th)g(column)g(of)g(the)g(iden)m(tit)m(y)390 1917 y(matrix.)h(The)30 b(p)s(erm)m(utation)g FD(p)j FK(and)d(the)g(v)m(ector)i FD(v)38 b FK(m)m(ust)31 b(ha)m(v)m(e)g(the)g (same)g(length.)3350 2123 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_permute_vector_in)q(vers)q(e)f Fu(\()p FD(const)31 b(gsl)p 2150 2123 V 40 w(p)s(erm)m(utation)g(*)g Ft(p)p FD(,)565 2232 y(gsl)p 677 2232 V 41 w(v)m(ector)h(*)e Ft(v)p Fu(\))390 2342 y FK(This)i(function)g(applies)g(the)h(in)m(v)m (erse)g(of)g(the)f(p)s(erm)m(utation)h FD(p)i FK(to)e(the)f(elemen)m (ts)i(of)f(the)f(v)m(ector)390 2451 y FD(v)p FK(,)40 b(considered)d(as)h(a)g(ro)m(w-v)m(ector)i(acted)f(on)e(b)m(y)h(an)f (in)m(v)m(erse)i(p)s(erm)m(utation)f(matrix)g(from)f(the)390 2561 y(righ)m(t,)48 b FE(v)699 2528 y Fp(0)769 2561 y FK(=)f FE(v)s(P)1005 2528 y Fq(T)1058 2561 y FK(.)80 b(Note)45 b(that)f(for)f(p)s(erm)m(utation)h(matrices)g(the)g(in)m(v)m (erse)g(is)g(the)g(same)g(as)390 2671 y(the)35 b(transp)s(ose.)54 b(The)34 b FE(j)5 b FK(-th)36 b(column)f(of)g(the)g(p)s(erm)m(utation)g (matrix)g FE(P)48 b FK(is)35 b(giv)m(en)h(b)m(y)e(the)i FD(p)3600 2685 y Fq(j)3634 2671 y FK(-th)390 2780 y(column)f(of)g(the)f (iden)m(tit)m(y)j(matrix.)54 b(The)34 b(p)s(erm)m(utation)h FD(p)i FK(and)d(the)h(v)m(ector)i FD(v)42 b FK(m)m(ust)35 b(ha)m(v)m(e)h(the)390 2890 y(same)31 b(length.)3350 3096 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_permute_matrix)e Fu(\()p FD(const)31 b(gsl)p 1731 3096 V 41 w(p)s(erm)m(utation)f(*)h Ft(p)p FD(,)g(gsl)p 2582 3096 V 41 w(matrix)f(*)h Ft(A)p Fu(\))390 3205 y FK(This)20 b(function)h(applies)h(the)f(p)s(erm)m (utation)g FD(p)j FK(to)e(the)f(matrix)h FD(A)f FK(from)g(the)g(righ)m (t,)j FE(A)3247 3172 y Fp(0)3296 3205 y FK(=)h FE(AP)13 b FK(.)37 b(The)390 3315 y FE(j)5 b FK(-th)27 b(column)g(of)g(the)g(p)s (erm)m(utation)g(matrix)g FE(P)39 b FK(is)27 b(giv)m(en)h(b)m(y)e(the)h FD(p)2700 3329 y Fq(j)2734 3315 y FK(-th)g(column)g(of)g(the)f(iden)m (tit)m(y)390 3424 y(matrix.)45 b(This)30 b(e\013ectiv)m(ely)35 b(p)s(erm)m(utes)c(the)g(columns)h(of)f FD(A)h FK(according)h(to)f(the) g(p)s(erm)m(utation)f FD(p)p FK(,)390 3534 y(and)f(so)g(the)h(n)m(um)m (b)s(er)e(of)i(columns)f(of)g FD(A)h FK(m)m(ust)f(equal)h(the)f(size)i (of)e(the)h(p)s(erm)m(utation)f FD(p)p FK(.)3350 3740 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_permutation_mul)e Fu(\()p FD(gsl)p 1545 3740 V 41 w(p)s(erm)m(utation)31 b(*)g Ft(p)p FD(,)f(const)h(gsl)p 2634 3740 V 41 w(p)s(erm)m(utation) 565 3849 y(*)g Ft(pa)p FD(,)g(const)g(gsl)p 1151 3849 V 40 w(p)s(erm)m(utation)g(*)g Ft(pb)p Fu(\))390 3959 y FK(This)d(function)g(com)m(bines)h(the)f(t)m(w)m(o)i(p)s(erm)m (utations)e FD(pa)g FK(and)g FD(pb)i FK(in)m(to)f(a)g(single)g(p)s(erm) m(utation)f FD(p)p FK(,)390 4069 y(where)f FD(p)g FK(=)e FD(pa)14 b FI(\003)g FD(pb)r FK(.)39 b(The)27 b(p)s(erm)m(utation)h FD(p)h FK(is)e(equiv)-5 b(alen)m(t)29 b(to)f(applying)f FD(pb)i FK(\014rst)d(and)h(then)g FD(pa)p FK(.)150 4317 y FJ(9.7)68 b(Reading)46 b(and)f(writing)h(p)t(erm)l(utations)150 4477 y FK(The)26 b(library)h(pro)m(vides)f(functions)h(for)f(reading)h (and)f(writing)h(p)s(erm)m(utations)g(to)g(a)g(\014le)g(as)g(binary)f (data)150 4586 y(or)k(formatted)h(text.)3350 4792 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_permutation_fwrit)q(e)e Fu(\()p FD(FILE)31 b(*)g Ft(stream)p FD(,)h(const)f(gsl)p 2627 4792 V 40 w(p)s(erm)m(utation)565 4902 y(*)g Ft(p)p Fu(\))390 5011 y FK(This)23 b(function)h(writes)g(the)g(elemen)m(ts)h (of)f(the)g(p)s(erm)m(utation)g FD(p)i FK(to)f(the)f(stream)g FD(stream)g FK(in)g(binary)390 5121 y(format.)40 b(The)28 b(function)g(returns)f FH(GSL_EFAILED)e FK(if)j(there)h(w)m(as)g(a)f (problem)g(writing)g(to)h(the)g(\014le.)390 5230 y(Since)g(the)g(data)g (is)g(written)g(in)g(the)g(nativ)m(e)h(binary)e(format)h(it)h(ma)m(y)f (not)g(b)s(e)f(p)s(ortable)h(b)s(et)m(w)m(een)390 5340 y(di\013eren)m(t)i(arc)m(hitectures.)p eop end %%Page: 106 124 TeXDict begin 106 123 bop 150 -116 a FK(Chapter)30 b(9:)41 b(P)m(erm)m(utations)2468 b(106)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_permutation_fread)f Fu(\()p FD(FILE)31 b(*)f Ft(stream)p FD(,)j(gsl)p 2337 299 28 4 v 40 w(p)s(erm)m(utation)e (*)f Ft(p)p Fu(\))390 408 y FK(This)k(function)h(reads)g(in)m(to)i(the) e(p)s(erm)m(utation)g FD(p)j FK(from)d(the)g(op)s(en)g(stream)g FD(stream)h FK(in)f(binary)390 518 y(format.)59 b(The)35 b(p)s(erm)m(utation)i FD(p)h FK(m)m(ust)e(b)s(e)g(preallo)s(cated)i (with)e(the)g(correct)h(length)g(since)g(the)390 628 y(function)24 b(uses)f(the)i(size)f(of)h FD(p)h FK(to)f(determine)f(ho) m(w)g(man)m(y)g(b)m(ytes)h(to)f(read.)39 b(The)23 b(function)h(returns) 390 737 y FH(GSL_EFAILED)32 b FK(if)j(there)h(w)m(as)f(a)h(problem)e (reading)i(from)e(the)i(\014le.)55 b(The)35 b(data)h(is)f(assumed)f(to) 390 847 y(ha)m(v)m(e)e(b)s(een)d(written)i(in)f(the)g(nativ)m(e)i (binary)e(format)g(on)h(the)f(same)h(arc)m(hitecture.)3350 1035 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_permutation_fprin)q(tf) f Fu(\()p FD(FILE)29 b(*)h Ft(stream)p FD(,)i(const)e(gsl)p 2676 1035 V 40 w(p)s(erm)m(utation)565 1144 y(*)h Ft(p)p FD(,)g(const)g(c)m(har)f(*)h Ft(format)p Fu(\))390 1254 y FK(This)40 b(function)h(writes)g(the)h(elemen)m(ts)g(of)g(the)f(p)s (erm)m(utation)g FD(p)j FK(line-b)m(y-line)e(to)g(the)g(stream)390 1363 y FD(stream)j FK(using)g(the)g(format)h(sp)s(eci\014er)e FD(format)p FK(,)49 b(whic)m(h)c(should)f(b)s(e)h(suitable)g(for)g(a)h (t)m(yp)s(e)f(of)390 1473 y FD(size)p 537 1473 V 41 w(t)p FK(.)55 b(In)34 b(ISO)g(C99)h(the)h(t)m(yp)s(e)f(mo)s(di\014er)f FH(z)g FK(represen)m(ts)h FH(size_t)p FK(,)g(so)g FH("\045zu\\n")e FK(is)i(a)g(suitable)390 1583 y(format.)680 1550 y FB(1)757 1583 y FK(The)24 b(function)h(returns)f FH(GSL_EFAILED)e FK(if)k(there)f(w)m(as)h(a)f(problem)g(writing)g(to)h(the)g(\014le.) 3350 1770 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_permutation_fscan) q(f)e Fu(\()p FD(FILE)31 b(*)g Ft(stream)p FD(,)h(gsl)p 2389 1770 V 41 w(p)s(erm)m(utation)e(*)h Ft(p)p Fu(\))390 1880 y FK(This)g(function)h(reads)h(formatted)f(data)h(from)f(the)h (stream)f FD(stream)h FK(in)m(to)g(the)g(p)s(erm)m(utation)f FD(p)p FK(.)390 1989 y(The)j(p)s(erm)m(utation)g FD(p)i FK(m)m(ust)e(b)s(e)g(preallo)s(cated)h(with)f(the)h(correct)g(length)f (since)h(the)f(function)390 2099 y(uses)j(the)i(size)f(of)g FD(p)i FK(to)f(determine)f(ho)m(w)g(man)m(y)g(n)m(um)m(b)s(ers)e(to)j (read.)66 b(The)39 b(function)f(returns)390 2209 y FH(GSL_EFAILED)27 b FK(if)k(there)f(w)m(as)h(a)g(problem)e(reading)i(from)f(the)g (\014le.)150 2444 y FJ(9.8)68 b(P)l(erm)l(utations)47 b(in)e(cyclic)g(form)150 2603 y FK(A)34 b(p)s(erm)m(utation)h(can)g(b)s (e)e(represen)m(ted)i(in)f(b)s(oth)f FD(linear)42 b FK(and)34 b FD(cyclic)41 b FK(notations.)54 b(The)34 b(functions)g(de-)150 2713 y(scrib)s(ed)41 b(in)g(this)g(section)i(con)m(v)m(ert)g(b)s(et)m (w)m(een)g(the)e(t)m(w)m(o)i(forms.)74 b(The)41 b(linear)h(notation)h (is)f(an)f(index)150 2822 y(mapping,)30 b(and)f(has)h(already)h(b)s (een)f(describ)s(ed)f(ab)s(o)m(v)m(e.)42 b(The)29 b(cyclic)j(notation)g (expresses)e(a)g(p)s(erm)m(uta-)150 2932 y(tion)h(as)f(a)h(series)g(of) f(circular)h(rearrangemen)m(ts)g(of)g(groups)f(of)g(elemen)m(ts,)i(or)e FD(cycles)p FK(.)275 3068 y(F)-8 b(or)39 b(example,)j(under)37 b(the)i(cycle)h(\(1)g(2)f(3\),)j(1)d(is)f(replaced)i(b)m(y)e(2,)k(2)d (is)g(replaced)g(b)m(y)f(3)i(and)e(3)h(is)150 3178 y(replaced)f(b)m(y)f (1)g(in)g(a)g(circular)h(fashion.)60 b(Cycles)38 b(of)f(di\013eren)m(t) h(sets)f(of)g(elemen)m(ts)i(can)e(b)s(e)g(com)m(bined)150 3287 y(indep)s(enden)m(tly)-8 b(,)37 b(for)f(example)g(\(1)h(2)f(3\))h (\(4)g(5\))f(com)m(bines)h(the)f(cycle)h(\(1)g(2)f(3\))h(with)f(the)g (cycle)h(\(4)g(5\),)150 3397 y(whic)m(h)24 b(is)h(an)f(exc)m(hange)i (of)f(elemen)m(ts)g(4)g(and)f(5.)39 b(A)25 b(cycle)g(of)g(length)g(one) g(represen)m(ts)f(an)g(elemen)m(t)i(whic)m(h)150 3506 y(is)k(unc)m(hanged)g(b)m(y)h(the)f(p)s(erm)m(utation)h(and)e(is)i (referred)f(to)h(as)f(a)h FD(singleton)p FK(.)275 3643 y(It)c(can)g(b)s(e)g(sho)m(wn)f(that)i(ev)m(ery)g(p)s(erm)m(utation)f (can)g(b)s(e)g(decomp)s(osed)g(in)m(to)h(com)m(binations)g(of)f (cycles.)150 3752 y(The)32 b(decomp)s(osition)h(is)g(not)g(unique,)f (but)g(can)h(alw)m(a)m(ys)h(b)s(e)e(rearranged)g(in)m(to)i(a)f (standard)e FD(canonical)150 3862 y(form)i FK(b)m(y)h(a)g(reordering)g (of)g(elemen)m(ts.)53 b(The)33 b(library)g(uses)h(the)g(canonical)h (form)f(de\014ned)e(in)i(Kn)m(uth's)150 3971 y FD(Art)c(of)h(Computer)f (Programming)38 b FK(\(V)-8 b(ol)32 b(1,)f(3rd)f(Ed,)g(1997\))i 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(without)e(the)g(brac)m(k)m(ets.)41 b(In)25 b(addition,)i(b)m(y)f(remo) m(ving)h(the)f(brac)m(k)m(ets)i(it)e(can)h(b)s(e)p 150 5241 1200 4 v 199 5308 a FB(1)275 5340 y Fx(In)e(v)n(ersions)h(of)g (the)f(GNU)g(C)i(library)e(prior)i(to)e(the)h(ISO)e(C99)j(standard,)f (the)f(t)n(yp)r(e)g(mo)r(di\014er)h Fz(Z)g Fx(w)n(as)h(used)e(instead.) p eop end %%Page: 107 125 TeXDict begin 107 124 bop 150 -116 a FK(Chapter)30 b(9:)41 b(P)m(erm)m(utations)2468 b(107)150 299 y(considered)25 b(as)g(a)h(linear)f(represen)m(tation)i(of)e(a)g(di\013eren)m(t)h(p)s (erm)m(utation.)39 b(In)24 b(the)i(example)g(giv)m(en)g(ab)s(o)m(v)m(e) 150 408 y(the)h(p)s(erm)m(utation)f(\(2)h(4)g(3)g(0)g(1\))g(w)m(ould)f (b)s(ecome)h(\(1)g(4)g(0)g(2)f(3\).)41 b(This)25 b(mapping)h(has)g(man) m(y)h(applications)150 518 y(in)j(the)h(theory)f(of)h(p)s(erm)m (utations.)3350 698 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_permutation_linea)q(r_to)q(_ca)q(non)q(ica)q(l)e Fu(\()p FD(gsl)p 2382 698 28 4 v 41 w(p)s(erm)m(utation)31 b(*)f Ft(q)p FD(,)565 808 y(const)h(gsl)p 915 808 V 41 w(p)s(erm)m(utation)f(*)h Ft(p)p Fu(\))390 918 y FK(This)e(function)h (computes)h(the)f(canonical)i(form)e(of)g(the)h(p)s(erm)m(utation)f FD(p)j FK(and)c(stores)i(it)g(in)f(the)390 1027 y(output)g(argumen)m(t) h FD(q)p FK(.)3350 1208 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_permutation_canon)q(ical)q(_to)q(_li)q(nea)q(r)e Fu(\()p FD(gsl)p 2382 1208 V 41 w(p)s(erm)m(utation)31 b(*)f Ft(p)p FD(,)565 1317 y(const)h(gsl)p 915 1317 V 41 w(p)s(erm)m(utation)f(*)h Ft(q)p Fu(\))390 1427 y FK(This)22 b(function)h(con)m(v)m(erts)i(a)e(p)s(erm)m(utation)g FD(q)i FK(in)e(canonical)i(form)d(bac)m(k)i(in)m(to)g(linear)g(form)f (storing)390 1536 y(it)31 b(in)f(the)h(output)f(argumen)m(t)g FD(p)p FK(.)3350 1717 y([F)-8 b(unction])-3599 b Fv(size_t)54 b(gsl_permutation_invers)q(ion)q(s)d Fu(\()p FD(const)32 b(gsl)p 2307 1717 V 40 w(p)s(erm)m(utation)f(*)f Ft(p)p Fu(\))390 1826 y FK(This)37 b(function)g(coun)m(ts)h(the)g(n)m(um)m(b)s (er)e(of)i(in)m(v)m(ersions)g(in)g(the)f(p)s(erm)m(utation)h FD(p)p FK(.)62 b(An)37 b(in)m(v)m(ersion)390 1936 y(is)i(an)m(y)h(pair) e(of)i(elemen)m(ts)g(that)g(are)f(not)h(in)e(order.)67 b(F)-8 b(or)40 b(example,)i(the)d(p)s(erm)m(utation)g(2031)390 2046 y(has)e(three)f(in)m(v)m(ersions,)k(corresp)s(onding)35 b(to)j(the)f(pairs)f(\(2,0\))j(\(2,1\))f(and)e(\(3,1\).)62 b(The)36 b(iden)m(tit)m(y)390 2155 y(p)s(erm)m(utation)30 b(has)h(no)f(in)m(v)m(ersions.)3350 2336 y([F)-8 b(unction])-3599 b Fv(size_t)54 b(gsl_permutation_linear)q(_cy)q(cle)q(s)d Fu(\()p FD(const)32 b(gsl)p 2464 2336 V 40 w(p)s(erm)m(utation)f(*)f Ft(p)p Fu(\))390 2445 y FK(This)d(function)g(coun)m(ts)i(the)e(n)m(um)m (b)s(er)g(of)h(cycles)h(in)e(the)h(p)s(erm)m(utation)g FD(p)p FK(,)g(giv)m(en)h(in)e(linear)h(form.)3350 2626 y([F)-8 b(unction])-3599 b Fv(size_t)54 b(gsl_permutation_canoni)q(cal) q(_cy)q(cle)q(s)d Fu(\()p FD(const)32 b(gsl)p 2621 2626 V 40 w(p)s(erm)m(utation)565 2735 y(*)f Ft(q)p Fu(\))390 2845 y 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b(P)m(erm)m(utations)2468 b(108)485 299 y FH(r)48 b(=)f(gsl_rng_alloc)e (\(T\);)485 518 y(printf)i(\("initial)e(permutation:"\);)485 628 y(gsl_permutation_init)e(\(p\);)485 737 y(gsl_permutation_fprintf)f (\(stdout,)j(p,)j(")f(\045u"\);)485 847 y(printf)g(\("\\n"\);)485 1066 y(printf)g(\(")g(random)f(permutation:"\);)485 1176 y(gsl_ran_shuffle)e(\(r,)j(p->data,)f(N,)h(sizeof\(size_t\)\);)485 1285 y(gsl_permutation_fprintf)42 b(\(stdout,)j(p,)j(")f(\045u"\);)485 1395 y(printf)g(\("\\n"\);)485 1614 y(printf)g(\("inverse)e (permutation:"\);)485 1724 y(gsl_permutation_inverse)d(\(q,)47 b(p\);)485 1833 y(gsl_permutation_fprintf)42 b(\(stdout,)j(q,)j(")f (\045u"\);)485 1943 y(printf)g(\("\\n"\);)485 2162 y (gsl_permutation_free)c(\(p\);)485 2271 y(gsl_permutation_free)g (\(q\);)485 2381 y(gsl_rng_free)i(\(r\);)485 2600 y(return)i(0;)390 2710 y(})150 2841 y FK(Here)31 b(is)f(the)h(output)f(from)g(the)g (program,)390 2973 y FH($)47 b(./a.out)390 3082 y(initial)f 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y(printf)f(\("\\n"\);)p eop end %%Page: 109 127 TeXDict begin 109 126 bop 150 -116 a FK(Chapter)30 b(9:)41 b(P)m(erm)m(utations)2468 b(109)533 299 y FH(})485 408 y(while)47 b(\(gsl_permutation_next\(p\))41 b(==)47 b(GSL_SUCCESS\);) 485 628 y(gsl_permutation_free)c(\(p\);)485 847 y(return)k(0;)390 956 y(})150 1091 y FK(Here)31 b(is)f(the)h(output)f(from)g(the)g (program,)390 1225 y FH($)47 b(./a.out)438 1335 y(0)g(1)h(2)438 1445 y(0)f(2)h(1)438 1554 y(1)f(0)h(2)438 1664 y(1)f(2)h(0)438 1773 y(2)f(0)h(1)438 1883 y(2)f(1)h(0)150 2017 y FK(The)25 b(p)s(erm)m(utations)g(are)h(generated)h(in)e(lexicographic)i(order.)39 b(T)-8 b(o)25 b(rev)m(erse)i(the)e(sequence,)i(b)s(egin)e(with)150 2127 y(the)30 b(\014nal)f(p)s(erm)m(utation)h(\(whic)m(h)g(is)g(the)g (rev)m(erse)h(of)f(the)g(iden)m(tit)m(y\))h(and)f(replace)g FH(gsl_permutation_)150 2237 y(next)f FK(with)h FH (gsl_permutation_prev)p FK(.)150 2469 y FJ(9.10)68 b(References)47 b(and)d(F)-11 b(urther)44 b(Reading)150 2628 y FK(The)30 b(sub)5 b(ject)30 b(of)h(p)s(erm)m(utations)f(is)g(co)m(v)m(ered)i (extensiv)m(ely)g(in)f(Kn)m(uth's)e FD(Sorting)h(and)g(Searc)m(hing)p FK(,)330 2763 y(Donald)h(E.)f(Kn)m(uth,)f FD(The)g(Art)h(of)g(Computer) g(Programming:)40 b(Sorting)30 b(and)g(Searc)m(hing)38 b FK(\(V)-8 b(ol)31 b(3,)330 2873 y(3rd)f(Ed,)g(1997\),)j(Addison-W)-8 b(esley)g(,)32 b(ISBN)e(0201896850.)150 3032 y(F)-8 b(or)31 b(the)g(de\014nition)f(of)g(the)h FD(canonical)h(form)e FK(see,)330 3166 y(Donald)f(E.)g(Kn)m(uth,)f FD(The)h(Art)g(of)g (Computer)f(Programming:)40 b(F)-8 b(undamen)m(tal)29 b(Algorithms)k FK(\(V)-8 b(ol)330 3276 y(1,)34 b(3rd)d(Ed,)i(1997\),)i (Addison-W)-8 b(esley)g(,)35 b(ISBN)d(0201896850.)52 b(Section)33 b(1.3.3,)i FD(An)d(Un)m(usual)g(Cor-)330 3386 y(resp)s(ondence)p FK(,)e(p.178{179.)p eop end %%Page: 110 128 TeXDict begin 110 127 bop 150 -116 a FK(Chapter)30 b(10:)41 b(Com)m(binations)2406 b(110)150 299 y FG(10)80 b(Com)l(binations)150 573 y FK(This)31 b(c)m(hapter)i(describ)s(es)e(functions)g(for)h (creating)h(and)e(manipulating)h(com)m(binations.)47 b(A)32 b(com)m(bina-)150 683 y(tion)g FE(c)g FK(is)g(represen)m(ted)f (b)m(y)g(an)h(arra)m(y)g(of)g FE(k)i FK(in)m(tegers)f(in)e(the)h(range) g(0)g(to)g FE(n)21 b FI(\000)g FK(1,)32 b(where)f(eac)m(h)i(v)-5 b(alue)32 b FE(c)3722 697 y Fq(i)150 792 y FK(o)s(ccurs)g(at)h(most)f (once.)47 b(The)32 b(com)m(bination)h FE(c)g FK(corresp)s(onds)d(to)j (indices)g(of)f FE(k)j FK(elemen)m(ts)f(c)m(hosen)e(from)150 902 y(an)h FE(n)g FK(elemen)m(t)h(v)m(ector.)51 b(Com)m(binations)34 b(are)f(useful)g(for)f(iterating)j(o)m(v)m(er)g(all)f FE(k)s FK(-elemen)m(t)h(subsets)d(of)i(a)150 1012 y(set.)275 1159 y(The)20 b(functions)g(describ)s(ed)f(in)h(this)g(c)m(hapter)i (are)e(de\014ned)g(in)g(the)h(header)f(\014le)g FH(gsl_combination.h)p FK(.)150 1412 y FJ(10.1)68 b(The)45 b(Com)l(bination)h(struct)150 1571 y FK(A)32 b(com)m(bination)i(is)e(de\014ned)f(b)m(y)h(a)g 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FK(.)61 b(The)390 3290 y(com)m(bination)33 b(is)e(not)h(initialized)h (and)e(its)h(elemen)m(ts)h(are)f(unde\014ned.)41 b(Use)32 b(the)g(function)f FH(gsl_)390 3400 y(combination_calloc)26 b FK(if)32 b(y)m(ou)g(w)m(an)m(t)g(to)g(create)h(a)f(com)m(bination)h (whic)m(h)e(is)g(initialized)j(to)e(the)390 3509 y(lexicographically)i (\014rst)d(com)m(bination.)45 b(A)32 b(n)m(ull)f(p)s(oin)m(ter)h(is)g (returned)e(if)h(insu\016cien)m(t)h(memory)390 3619 y(is)e(a)m(v)-5 b(ailable)33 b(to)e(create)h(the)f(com)m(bination.)3350 3830 y([F)-8 b(unction])-3599 b Fv(gsl_combination)57 b(*)52 b(gsl_combination_call)q(oc)g Fu(\()p FD(size)p 2470 3830 V 41 w(t)31 b Ft(n)p FD(,)f(size)p 2825 3830 V 41 w(t)h Ft(k)p Fu(\))390 3940 y FK(This)41 b(function)g(allo)s (cates)k(memory)c(for)h(a)g(new)f(com)m(bination)i(with)f(parameters)g FD(n)p FK(,)i FD(k)k FK(and)390 4049 y(initializes)37 b(it)e(to)g(the)g(lexicographically)i(\014rst)d(com)m(bination.)55 b(A)35 b(n)m(ull)f(p)s(oin)m(ter)h(is)g(returned)e(if)390 4159 y(insu\016cien)m(t)e(memory)f(is)g(a)m(v)-5 b(ailable)33 b(to)e(create)h(the)f(com)m(bination.)3350 4370 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_combination_init_fir)q(st)e Fu(\()p FD(gsl)p 1964 4370 V 41 w(com)m(bination)31 b(*)g Ft(c)p Fu(\))390 4479 y FK(This)d(function)g(initializes)j(the)d(com)m (bination)i FD(c)k FK(to)c(the)e(lexicographically)k(\014rst)27 b(com)m(bination,)390 4589 y(i.e.)42 b(\(0)p FE(;)15 b FK(1)p FE(;)g FK(2)p FE(;)g(:)g(:)g(:)k(;)c(k)23 b FI(\000)d FK(1\).)3350 4800 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_combination_init_las)q(t)e Fu(\()p FD(gsl)p 1912 4800 V 40 w(com)m(bination)32 b(*)f Ft(c)p Fu(\))390 4910 y FK(This)e(function)h(initializes)i(the)e(com)m (bination)i FD(c)k FK(to)30 b(the)h(lexicographically)h(last)f(com)m (bination,)390 5019 y(i.e.)42 b(\()p FE(n)20 b FI(\000)g FE(k)s(;)15 b(n)20 b FI(\000)g FE(k)j FK(+)d(1)p FE(;)15 b(:)g(:)g(:)i(;)e(n)20 b FI(\000)g FK(1\).)3350 5230 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_combination_free)d Fu(\()p FD(gsl)p 1650 5230 V 41 w(com)m(bination)32 b(*)e Ft(c)p Fu(\))390 5340 y FK(This)g(function)g(frees)g(all)h(the)g (memory)f(used)g(b)m(y)g(the)g(com)m(bination)i FD(c)p FK(.)p eop end %%Page: 111 129 TeXDict begin 111 128 bop 150 -116 a FK(Chapter)30 b(10:)41 b(Com)m(binations)2406 b(111)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_combination_memcp)q(y)e Fu(\()p FD(gsl)p 1702 299 28 4 v 41 w(com)m(bination)32 b(*)f Ft(dest)p FD(,)g(const)565 408 y(gsl)p 677 408 V 41 w(com)m(bination)g(*)g Ft(src)p Fu(\))390 518 y FK(This)h(function)g(copies)i(the)f(elemen)m (ts)h(of)f(the)g(com)m(bination)h FD(src)k FK(in)m(to)c(the)f(com)m (bination)h FD(dest)p FK(.)390 628 y(The)c(t)m(w)m(o)i(com)m(binations) f(m)m(ust)f(ha)m(v)m(e)i(the)f(same)f(size.)150 873 y FJ(10.3)68 b(Accessing)45 b(com)l(bination)h(elemen)l(ts)150 1032 y FK(The)30 b(follo)m(wing)i(function)e(can)g(b)s(e)g(used)g(to)h (access)h(the)e(elemen)m(ts)i(of)e(a)h(com)m(bination.)3350 1233 y([F)-8 b(unction])-3599 b Fv(size_t)54 b(gsl_combination_get)d Fu(\()p FD(const)32 b(gsl)p 1941 1233 V 40 w(com)m(bination)g(*)f Ft(c)p FD(,)f(const)h(size)p 3061 1233 V 41 w(t)565 1343 y Ft(i)p Fu(\))390 1452 y FK(This)39 b(function)h(returns)e(the)i(v)-5 b(alue)41 b(of)f(the)g FD(i)p FK(-th)g(elemen)m(t)h(of)f(the)g(com)m (bination)h FD(c)p FK(.)70 b(If)39 b FD(i)45 b FK(lies)390 1562 y(outside)39 b(the)f(allo)m(w)m(ed)i(range)f(of)f(0)h(to)g FD(k)31 b FI(\000)25 b FK(1)39 b(then)f(the)g(error)g(handler)g(is)g (in)m(v)m(ok)m(ed)i(and)d(0)i(is)390 1672 y(returned.)h(An)30 b(inline)g(v)m(ersion)h(of)f(this)h(function)f(is)g(used)g(when)f FH(HAVE_INLINE)e FK(is)k(de\014ned.)150 1917 y FJ(10.4)68 b(Com)l(bination)47 b(prop)t(erties)3350 2134 y FK([F)-8 b(unction])-3599 b Fv(size_t)54 b(gsl_combination_n)d Fu(\()p FD(const)31 b(gsl)p 1836 2134 V 41 w(com)m(bination)g(*)g Ft(c)p Fu(\))390 2244 y FK(This)f(function)g(returns)f(the)h(range)h (\()p FE(n)p FK(\))g(of)f(the)h(com)m(bination)g FD(c)p FK(.)3350 2445 y([F)-8 b(unction])-3599 b Fv(size_t)54 b(gsl_combination_k)d Fu(\()p FD(const)31 b(gsl)p 1836 2445 V 41 w(com)m(bination)g(*)g Ft(c)p Fu(\))390 2554 y FK(This)f(function)g(returns)f(the)h(n)m(um)m(b)s(er)f(of)i(elemen)m (ts)h(\()p FE(k)s FK(\))f(in)f(the)g(com)m(bination)i FD(c)p FK(.)3350 2756 y([F)-8 b(unction])-3599 b Fv(size_t)54 b(*)f(gsl_combination_data)e Fu(\()p FD(const)31 b(gsl)p 2097 2756 V 41 w(com)m(bination)h(*)e Ft(c)p Fu(\))390 2865 y FK(This)g(function)g(returns)f(a)i(p)s(oin)m(ter)f(to)h(the)g (arra)m(y)f(of)h(elemen)m(ts)h(in)e(the)g(com)m(bination)i FD(c)p FK(.)3350 3066 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_combination_valid)f Fu(\()p FD(gsl)p 1650 3066 V 41 w(com)m(bination)32 b(*)e Ft(c)p Fu(\))390 3176 y FK(This)35 b(function)h(c)m(hec)m(ks)i(that)f(the)f(com)m(bination)i FD(c)k FK(is)36 b(v)-5 b(alid.)59 b(The)36 b FD(k)41 b FK(elemen)m(ts)d(should)d(lie)i(in)390 3285 y(the)29 b(range)h(0)f(to)h FD(n)17 b FI(\000)h FK(1,)30 b(with)e(eac)m(h)j(v)-5 b(alue)29 b(o)s(ccurring)g(once)h(at)g(most)f(and)g(in)f(increasing)i (order.)150 3531 y FJ(10.5)68 b(Com)l(bination)47 b(functions)3350 3748 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_combination_next)f Fu(\()p FD(gsl)p 1598 3748 V 41 w(com)m(bination)31 b(*)g Ft(c)p Fu(\))390 3858 y FK(This)j(function)h(adv)-5 b(ances)35 b(the)g(com)m(bination)i FD(c)j FK(to)c(the)f(next)g(com)m(bination)h (in)f(lexicographic)390 3967 y(order)g(and)f(returns)g FH(GSL_SUCCESS)p FK(.)53 b(If)35 b(no)g(further)f(com)m(binations)i (are)g(a)m(v)-5 b(ailable)37 b(it)f(returns)390 4077 y FH(GSL_FAILURE)d FK(and)j(lea)m(v)m(es)j FD(c)j FK(unmo)s(di\014ed.) 56 b(Starting)37 b(with)f(the)h(\014rst)e(com)m(bination)j(and)e(re-) 390 4186 y(p)s(eatedly)41 b(applying)f(this)h(function)f(will)h (iterate)h(through)e(all)i(p)s(ossible)e(com)m(binations)i(of)f(a)390 4296 y(giv)m(en)31 b(order.)3350 4497 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_combination_prev)f Fu(\()p FD(gsl)p 1598 4497 V 41 w(com)m(bination)31 b(*)g Ft(c)p Fu(\))390 4607 y FK(This)24 b(function)h(steps)g(bac)m(kw)m(ards)h(from)e(the)i (com)m(bination)g FD(c)31 b FK(to)26 b(the)f(previous)g(com)m(bination) h(in)390 4716 y(lexicographic)35 b(order,)e(returning)f FH(GSL_SUCCESS)p FK(.)44 b(If)33 b(no)f(previous)h(com)m(bination)h(is) f(a)m(v)-5 b(ailable)390 4826 y(it)31 b(returns)e FH(GSL_FAILURE)e FK(and)j(lea)m(v)m(es)j FD(c)j FK(unmo)s(di\014ed.)150 5071 y FJ(10.6)68 b(Reading)46 b(and)f(writing)h(com)l(binations)150 5230 y FK(The)26 b(library)h(pro)m(vides)g(functions)f(for)h(reading)g (and)g(writing)g(com)m(binations)h(to)f(a)h(\014le)f(as)g(binary)f (data)150 5340 y(or)k(formatted)h(text.)p eop end %%Page: 112 130 TeXDict begin 112 129 bop 150 -116 a FK(Chapter)30 b(10:)41 b(Com)m(binations)2406 b(112)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_combination_fwrit)q(e)e Fu(\()p FD(FILE)31 b(*)g Ft(stream)p FD(,)h(const)f(gsl)p 2627 299 28 4 v 40 w(com)m(bination)565 408 y(*)g Ft(c)p Fu(\))390 518 y FK(This)24 b(function)g(writes)h(the)g(elemen)m(ts)g(of)g(the)g (com)m(bination)h FD(c)k FK(to)c(the)e(stream)h FD(stream)g FK(in)g(binary)390 628 y(format.)40 b(The)28 b(function)g(returns)f FH(GSL_EFAILED)e FK(if)j(there)h(w)m(as)g(a)f(problem)g(writing)g(to)h (the)g(\014le.)390 737 y(Since)g(the)g(data)g(is)g(written)g(in)g(the)g (nativ)m(e)h(binary)e(format)h(it)h(ma)m(y)f(not)g(b)s(e)f(p)s(ortable) h(b)s(et)m(w)m(een)390 847 y(di\013eren)m(t)i(arc)m(hitectures.)3350 1041 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_combination_fread)f Fu(\()p FD(FILE)31 b(*)f Ft(stream)p FD(,)j(gsl)p 2337 1041 V 40 w(com)m(bination)f(*)f Ft(c)p Fu(\))390 1150 y FK(This)e(function)g(reads)g(elemen)m(ts)i(from)e(the)g(op)s(en)g (stream)h FD(stream)f FK(in)m(to)i(the)e(com)m(bination)i FD(c)k FK(in)390 1260 y(binary)28 b(format.)41 b(The)29 b(com)m(bination)h FD(c)35 b FK(m)m(ust)29 b(b)s(e)f(preallo)s(cated)j (with)e(correct)h(v)-5 b(alues)30 b(of)f FE(n)g FK(and)390 1370 y FE(k)41 b FK(since)c(the)h(function)f(uses)g(the)h(size)g(of)g FD(c)43 b FK(to)38 b(determine)g(ho)m(w)f(man)m(y)h(b)m(ytes)f(to)i (read.)61 b(The)390 1479 y(function)28 b(returns)f FH(GSL_EFAILED)e FK(if)j(there)h(w)m(as)f(a)h(problem)f(reading)g(from)g(the)g(\014le.) 40 b(The)28 b(data)390 1589 y(is)d(assumed)f(to)i(ha)m(v)m(e)g(b)s(een) f(written)g(in)f(the)i(nativ)m(e)g(binary)e(format)i(on)e(the)i(same)f (arc)m(hitecture.)3350 1783 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_combination_fprin)q(tf)f Fu(\()p FD(FILE)30 b(*)g Ft(stream)p FD(,)j(const)d(gsl)p 2678 1783 V 41 w(com)m(bination)565 1892 y(*)h Ft(c)p FD(,)g(const)g(c)m(har)f(*)h Ft(format)p Fu(\))390 2002 y FK(This)41 b(function)h(writes)g(the)g (elemen)m(ts)i(of)e(the)g(com)m(bination)h FD(c)48 b FK(line-b)m(y-line)c(to)e(the)h(stream)390 2112 y FD(stream)i FK(using)g(the)g(format)h(sp)s(eci\014er)e FD(format)p FK(,)49 b(whic)m(h)c(should)f(b)s(e)h(suitable)g(for)g(a)h(t)m(yp)s(e)f (of)390 2221 y FD(size)p 537 2221 V 41 w(t)p FK(.)55 b(In)34 b(ISO)g(C99)h(the)h(t)m(yp)s(e)f(mo)s(di\014er)f FH(z)g FK(represen)m(ts)h FH(size_t)p FK(,)g(so)g FH("\045zu\\n")e FK(is)i(a)g(suitable)390 2331 y(format.)680 2298 y FB(1)757 2331 y FK(The)24 b(function)h(returns)f FH(GSL_EFAILED)e FK(if)k(there)f(w)m(as)h(a)f(problem)g(writing)g(to)h(the)g(\014le.) 3350 2525 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_combination_fscan) q(f)e Fu(\()p FD(FILE)31 b(*)g Ft(stream)p FD(,)h(gsl)p 2389 2525 V 41 w(com)m(bination)f(*)g Ft(c)p Fu(\))390 2634 y FK(This)i(function)g(reads)g(formatted)h(data)g(from)f(the)g (stream)h FD(stream)g FK(in)m(to)g(the)g(com)m(bination)g FD(c)p FK(.)390 2744 y(The)40 b(com)m(bination)i FD(c)k FK(m)m(ust)40 b(b)s(e)g(preallo)s(cated)i(with)e(correct)i(v)-5 b(alues)41 b(of)f FE(n)g FK(and)g FE(k)k FK(since)d(the)390 2854 y(function)36 b(uses)h(the)g(size)g(of)g FD(c)43 b FK(to)37 b(determine)g(ho)m(w)g(man)m(y)g(n)m(um)m(b)s(ers)e(to)i (read.)60 b(The)36 b(function)390 2963 y(returns)29 b FH(GSL_EFAILED)e FK(if)k(there)f(w)m(as)h(a)g(problem)f(reading)g(from) g(the)h(\014le.)150 3203 y FJ(10.7)68 b(Examples)150 3362 y FK(The)26 b(example)h(program)f(b)s(elo)m(w)g(prin)m(ts)g(all)h (subsets)f(of)g(the)h(set)g FI(f)p FK(0)p FE(;)15 b FK(1)p FE(;)g FK(2)p FE(;)g FK(3)p FI(g)30 b FK(ordered)c(b)m(y)g(size.)40 b(Subsets)150 3472 y(of)31 b(the)f(same)h(size)g(are)g(ordered)f (lexicographically)-8 b(.)390 3611 y FH(#include)46 b()390 3721 y(#include)g()390 3940 y(int)390 4050 y(main)h(\(void\))390 4159 y({)485 4269 y(gsl_combination)d(*)k (c;)485 4378 y(size_t)f(i;)485 4597 y(printf)g(\("All)f(subsets)g(of)h ({0,1,2,3})e(by)i(size:\\n"\))f(;)485 4707 y(for)h(\(i)h(=)f(0;)g(i)h (<=)f(4;)g(i++\))581 4817 y({)676 4926 y(c)h(=)f (gsl_combination_calloc)42 b(\(4,)47 b(i\);)676 5036 y(do)772 5145 y({)p 150 5241 1200 4 v 199 5308 a FB(1)275 5340 y Fx(In)25 b(v)n(ersions)h(of)g(the)f(GNU)g(C)i(library)e(prior)i (to)e(the)h(ISO)e(C99)j(standard,)f(the)f(t)n(yp)r(e)g(mo)r(di\014er)h Fz(Z)g Fx(w)n(as)h(used)e(instead.)p eop end %%Page: 113 131 TeXDict begin 113 130 bop 150 -116 a FK(Chapter)30 b(10:)41 b(Com)m(binations)2406 b(113)867 299 y FH(printf)46 b(\("{"\);)867 408 y(gsl_combination_fprintf)c(\(stdout,)j(c,)i(")h(\045u"\);)867 518 y(printf)e(\(")i(}\\n"\);)772 628 y(})676 737 y(while)f (\(gsl_combination_next)42 b(\(c\))47 b(==)g(GSL_SUCCESS\);)676 847 y(gsl_combination_free)c(\(c\);)581 956 y(})485 1176 y(return)k(0;)390 1285 y(})150 1420 y FK(Here)31 b(is)f(the)h(output)f (from)g(the)g(program,)390 1554 y FH($)47 b(./a.out)390 1664 y(All)g(subsets)f(of)h({0,1,2,3})e(by)i(size:)390 1773 y({)g(})390 1883 y({)g(0)h(})390 1993 y({)f(1)h(})390 2102 y({)f(2)h(})390 2212 y({)f(3)h(})390 2321 y({)f(0)h(1)f(})390 2431 y({)g(0)h(2)f(})390 2540 y({)g(0)h(3)f(})390 2650 y({)g(1)h(2)f(})390 2760 y({)g(1)h(3)f(})390 2869 y({)g(2)h(3)f(})390 2979 y({)g(0)h(1)f(2)h(})390 3088 y({)f(0)h(1)f(3)h(})390 3198 y({)f(0)h(2)f(3)h(})390 3308 y({)f(1)h(2)f(3)h(})390 3417 y({)f(0)h(1)f(2)h(3)f(})150 3552 y FK(All)31 b(16)g(subsets)f(are) h(generated,)g(and)f(the)h(subsets)e(of)i(eac)m(h)g(size)h(are)e (sorted)h(lexicographically)-8 b(.)150 3784 y FJ(10.8)68 b(References)47 b(and)d(F)-11 b(urther)44 b(Reading)150 3944 y FK(F)-8 b(urther)30 b(information)h(on)f(com)m(binations)i(can)e (b)s(e)g(found)f(in,)330 4078 y(Donald)35 b(L.)g(Kreher,)h(Douglas)g (R.)f(Stinson,)h FD(Com)m(binatorial)g(Algorithms:)51 b(Generation,)37 b(En)m(u-)330 4188 y(meration)31 b(and)f(Searc)m(h)p FK(,)h(1998,)h(CR)m(C)e(Press)g(LLC,)g(ISBN)g(084933988X)p eop end %%Page: 114 132 TeXDict begin 114 131 bop 150 -116 a FK(Chapter)30 b(11:)41 b(Multisets)2588 b(114)150 299 y FG(11)80 b(Multisets)150 573 y FK(This)34 b(c)m(hapter)i(describ)s(es)e(functions)g(for)h (creating)h(and)e(manipulating)h(m)m(ultisets.)56 b(A)35 b(m)m(ultiset)h FE(c)f FK(is)150 683 y(represen)m(ted)40 b(b)m(y)f(an)h(arra)m(y)h(of)e FE(k)k FK(in)m(tegers)e(in)f(the)g (range)g(0)g(to)h FE(n)26 b FI(\000)g FK(1,)43 b(where)c(eac)m(h)i(v)-5 b(alue)41 b FE(c)3516 697 y Fq(i)3583 683 y FK(ma)m(y)150 792 y(o)s(ccur)d(more)g(than)g(once.)65 b(The)38 b(m)m(ultiset)h FE(c)g FK(corresp)s(onds)d(to)j(indices)g(of)f FE(k)j FK(elemen)m(ts)f(c)m(hosen)e(from)150 902 y(an)33 b FE(n)g FK(elemen)m(t)i(v)m(ector)g(with)e(replacemen)m(t.)52 b(In)32 b(mathematical)k(terms,)e FE(n)f FK(is)h(the)f(cardinalit)m(y)i (of)f(the)150 1012 y(m)m(ultiset)24 b(while)f FE(k)j FK(is)c(the)h(maxim)m(um)g(m)m(ultiplicit)m(y)i(of)e(an)m(y)g(v)-5 b(alue.)39 b(Multisets)23 b(are)h(useful,)f(for)g(example,)150 1121 y(when)29 b(iterating)j(o)m(v)m(er)g(the)f(indices)f(of)h(a)f FE(k)s FK(-th)h(order)f(symmetric)h(tensor)f(in)g FE(n)p FK(-space.)275 1269 y(The)f(functions)h(describ)s(ed)g(in)g(this)g(c)m (hapter)h(are)g(de\014ned)e(in)h(the)g(header)h(\014le)f FH(gsl_multiset.h)p FK(.)150 1522 y FJ(11.1)68 b(The)45 b(Multiset)h(struct)150 1681 y FK(A)25 b(m)m(ultiset)g(is)g(de\014ned)e (b)m(y)i(a)f(structure)g(con)m(taining)j(three)d(comp)s(onen)m(ts,)i (the)f(v)-5 b(alues)25 b(of)g FE(n)f FK(and)f FE(k)s FK(,)k(and)150 1790 y(a)32 b(p)s(oin)m(ter)f(to)i(the)e(m)m(ultiset)i (arra)m(y)-8 b(.)45 b(The)31 b(elemen)m(ts)i(of)e(the)h(m)m(ultiset)h (arra)m(y)f(are)g(all)g(of)g(t)m(yp)s(e)f FH(size_t)p FK(,)150 1900 y(and)f(are)h(stored)f(in)g(increasing)h(order.)40 b(The)30 b FH(gsl_multiset)d FK(structure)j(lo)s(oks)h(lik)m(e)h(this,) 390 2048 y FH(typedef)46 b(struct)390 2158 y({)485 2267 y(size_t)h(n;)485 2377 y(size_t)g(k;)485 2486 y(size_t)g(*data;)390 2596 y(})g(gsl_multiset;)150 2848 y FJ(11.2)68 b(Multiset)46 b(allo)t(cation)3350 3071 y FK([F)-8 b(unction])-3599 b Fv(gsl_multiset)56 b(*)d(gsl_multiset_alloc)d Fu(\()p FD(size)p 2103 3071 28 4 v 42 w(t)30 b Ft(n)p FD(,)h(size)p 2459 3071 V 41 w(t)g Ft(k)p Fu(\))390 3181 y FK(This)23 b(function)g(allo)s(cates)i(memory)e(for)h(a)f(new)g(m)m(ultiset)i (with)e(parameters)g FD(n)p FK(,)i FD(k)p FK(.)38 b(The)23 b(m)m(ultiset)390 3290 y(is)38 b(not)h(initialized)h(and)e(its)h (elemen)m(ts)g(are)g(unde\014ned.)62 b(Use)39 b(the)g(function)f FH(gsl_multiset_)390 3400 y(calloc)33 b FK(if)i(y)m(ou)g(w)m(an)m(t)h (to)g(create)g(a)g(m)m(ultiset)g(whic)m(h)f(is)g(initialized)h(to)g (the)f(lexicographically)390 3509 y(\014rst)26 b(m)m(ultiset)j(elemen)m (t.)41 b(A)27 b(n)m(ull)g(p)s(oin)m(ter)g(is)g(returned)f(if)h (insu\016cien)m(t)h(memory)f(is)g(a)m(v)-5 b(ailable)29 b(to)390 3619 y(create)j(the)e(m)m(ultiset.)3350 3830 y([F)-8 b(unction])-3599 b Fv(gsl_multiset)56 b(*)d (gsl_multiset_calloc)e Fu(\()p FD(size)p 2156 3830 V 41 w(t)31 b Ft(n)p FD(,)g(size)p 2512 3830 V 40 w(t)g Ft(k)p Fu(\))390 3940 y FK(This)g(function)g(allo)s(cates)i(memory)f (for)f(a)g(new)g(m)m(ultiset)i(with)e(parameters)h FD(n)p FK(,)f FD(k)37 b FK(and)30 b(initial-)390 4049 y(izes)39 b(it)g(to)h(the)e(lexicographically)k(\014rst)37 b(m)m(ultiset)j (elemen)m(t.)67 b(A)38 b(n)m(ull)h(p)s(oin)m(ter)f(is)h(returned)e(if) 390 4159 y(insu\016cien)m(t)31 b(memory)f(is)g(a)m(v)-5 b(ailable)33 b(to)e(create)h(the)f(m)m(ultiset.)3350 4370 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_multiset_init_first)e Fu(\()p FD(gsl)p 1807 4370 V 41 w(m)m(ultiset)31 b(*)g Ft(c)p Fu(\))390 4479 y FK(This)d(function)g(initializes)i(the)f(m)m (ultiset)g FD(c)34 b FK(to)29 b(the)g(lexicographically)i(\014rst)d(m)m (ultiset)h(elemen)m(t,)390 4589 y(i.e.)42 b(0)30 b(rep)s(eated)h FE(k)i FK(times.)3350 4800 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_multiset_init_last)e Fu(\()p FD(gsl)p 1755 4800 V 41 w(m)m(ultiset)31 b(*)g Ft(c)p Fu(\))390 4910 y FK(This)e(function)g(initializes)j(the)e(m)m(ultiset)h FD(c)36 b FK(to)30 b(the)g(lexicographically)j(last)d(m)m(ultiset)h (elemen)m(t,)390 5019 y(i.e.)42 b FE(n)19 b FI(\000)h FK(1)31 b(rep)s(eated)f FE(k)k FK(times.)3350 5230 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_multiset_free)c Fu(\()p FD(gsl)p 1493 5230 V 41 w(m)m(ultiset)32 b(*)e Ft(c)p Fu(\))390 5340 y FK(This)g(function)g(frees)g(all)h(the)g(memory)f (used)g(b)m(y)g(the)g(m)m(ultiset)i FD(c)p FK(.)p eop end %%Page: 115 133 TeXDict begin 115 132 bop 150 -116 a FK(Chapter)30 b(11:)41 b(Multisets)2588 b(115)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multiset_memcpy)e Fu(\()p FD(gsl)p 1545 299 28 4 v 41 w(m)m(ultiset)32 b(*)f Ft(dest)p FD(,)g(const)g(gsl) p 2622 299 V 41 w(m)m(ultiset)g(*)565 408 y Ft(src)p Fu(\))390 518 y FK(This)e(function)g(copies)i(the)f(elemen)m(ts)h(of)f (the)g(m)m(ultiset)h FD(src)k FK(in)m(to)c(the)f(m)m(ultiset)h FD(dest)p FK(.)40 b(The)30 b(t)m(w)m(o)390 628 y(m)m(ultisets)h(m)m (ust)g(ha)m(v)m(e)g(the)g(same)g(size.)150 882 y FJ(11.3)68 b(Accessing)45 b(m)l(ultiset)i(elemen)l(ts)150 1041 y FK(The)30 b(follo)m(wing)i(function)e(can)g(b)s(e)g(used)g(to)h(access) h(the)e(elemen)m(ts)i(of)e(a)h(m)m(ultiset.)3350 1255 y([F)-8 b(unction])-3599 b Fv(size_t)54 b(gsl_multiset_get)c Fu(\()p FD(const)32 b(gsl)p 1784 1255 V 40 w(m)m(ultiset)g(*)f Ft(c)p FD(,)f(const)h(size)p 2738 1255 V 41 w(t)g Ft(i)p Fu(\))390 1364 y FK(This)f(function)h(returns)f(the)h(v)-5 b(alue)32 b(of)f(the)h FD(i)p FK(-th)f(elemen)m(t)i(of)e(the)g(m)m (ultiset)i FD(c)p FK(.)43 b(If)31 b FD(i)36 b FK(lies)c(outside)390 1474 y(the)i(allo)m(w)m(ed)h(range)f(of)g(0)g(to)g FD(k)28 b FI(\000)22 b FK(1)34 b(then)g(the)f(error)h(handler)e(is)i(in)m(v)m (ok)m(ed)h(and)e(0)h(is)g(returned.)390 1583 y(An)c(inline)g(v)m (ersion)h(of)g(this)f(function)g(is)h(used)e(when)h FH(HAVE_INLINE)d FK(is)j(de\014ned.)150 1837 y FJ(11.4)68 b(Multiset)46 b(prop)t(erties)3350 2061 y FK([F)-8 b(unction])-3599 b Fv(size_t)54 b(gsl_multiset_n)c Fu(\()p FD(const)31 b(gsl)p 1679 2061 V 41 w(m)m(ultiset)g(*)g Ft(c)p Fu(\))390 2171 y FK(This)f(function)g(returns)f(the)h(range)h(\()p FE(n)p FK(\))g(of)f(the)h(m)m(ultiset)g FD(c)p FK(.)3350 2384 y([F)-8 b(unction])-3599 b Fv(size_t)54 b(gsl_multiset_k)c Fu(\()p FD(const)31 b(gsl)p 1679 2384 V 41 w(m)m(ultiset)g(*)g Ft(c)p Fu(\))390 2494 y FK(This)f(function)g(returns)f(the)h(n)m(um)m (b)s(er)f(of)i(elemen)m(ts)h(\()p FE(k)s FK(\))f(in)f(the)g(m)m (ultiset)i FD(c)p FK(.)3350 2707 y([F)-8 b(unction])-3599 b Fv(size_t)54 b(*)f(gsl_multiset_data)d Fu(\()p FD(const)32 b(gsl)p 1941 2707 V 40 w(m)m(ultiset)g(*)e Ft(c)p Fu(\))390 2816 y FK(This)g(function)g(returns)f(a)i(p)s(oin)m(ter)f(to)h(the)g (arra)m(y)f(of)h(elemen)m(ts)h(in)e(the)g(m)m(ultiset)i FD(c)p FK(.)3350 3030 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multiset_valid)e Fu(\()p FD(gsl)p 1493 3030 V 41 w(m)m(ultiset)32 b(*)e Ft(c)p Fu(\))390 3139 y FK(This)36 b(function)g(c)m(hec)m(ks)i(that)f(the)f(m)m(ultiset)i FD(c)k FK(is)37 b(v)-5 b(alid.)59 b(The)36 b FD(k)42 b FK(elemen)m(ts)c(should)d(lie)j(in)e(the)390 3249 y(range)31 b(0)f(to)i FD(n)19 b FI(\000)h FK(1,)31 b(with)f(eac)m(h)i(v)-5 b(alue)31 b(o)s(ccurring)f(in)g(nondecreasing)g(order.)150 3503 y FJ(11.5)68 b(Multiset)46 b(functions)3350 3727 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multiset_next)e Fu(\()p FD(gsl)p 1441 3727 V 41 w(m)m(ultiset)31 b(*)g Ft(c)p Fu(\))390 3836 y FK(This)i(function)h(adv)-5 b(ances)35 b(the)g(m)m(ultiset)g FD(c)40 b FK(to)35 b(the)g(next)f(m)m(ultiset)h (elemen)m(t)h(in)e(lexicographic)390 3946 y(order)43 b(and)g(returns)g FH(GSL_SUCCESS)p FK(.)77 b(If)43 b(no)h(further)e(m)m (ultisets)i(elemen)m(ts)h(are)f(a)m(v)-5 b(ailable)46 b(it)390 4056 y(returns)34 b FH(GSL_FAILURE)f FK(and)i(lea)m(v)m(es)i FD(c)42 b FK(unmo)s(di\014ed.)53 b(Starting)36 b(with)g(the)f(\014rst)g (m)m(ultiset)i(and)390 4165 y(rep)s(eatedly)28 b(applying)f(this)h (function)f(will)h(iterate)h(through)e(all)h(p)s(ossible)f(m)m (ultisets)h(of)g(a)g(giv)m(en)390 4275 y(order.)3350 4488 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multiset_prev)e Fu(\()p FD(gsl)p 1441 4488 V 41 w(m)m(ultiset)31 b(*)g Ft(c)p Fu(\))390 4598 y FK(This)i(function)g(steps)h(bac)m(kw)m(ards)g (from)f(the)h(m)m(ultiset)h FD(c)k FK(to)c(the)e(previous)h(m)m (ultiset)g(elemen)m(t)390 4707 y(in)c(lexicographic)i(order,)d (returning)g FH(GSL_SUCCESS)p FK(.)38 b(If)30 b(no)f(previous)h(m)m (ultiset)h(is)f(a)m(v)-5 b(ailable)32 b(it)390 4817 y(returns)d FH(GSL_FAILURE)e FK(and)j(lea)m(v)m(es)j FD(c)j FK(unmo)s(di\014ed.)150 5071 y FJ(11.6)68 b(Reading)46 b(and)f(writing)h(m)l(ultisets)150 5230 y FK(The)30 b(library)h(pro)m(vides)g(functions)f(for)h(reading)g (and)f(writing)h(m)m(ultisets)g(to)h(a)f(\014le)g(as)g(binary)f(data)i (or)150 5340 y(formatted)f(text.)p eop end %%Page: 116 134 TeXDict begin 116 133 bop 150 -116 a FK(Chapter)30 b(11:)41 b(Multisets)2588 b(116)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multiset_fwrite)e Fu(\()p FD(FILE)31 b(*)g Ft(stream)p FD(,)h(const)f(gsl)p 2470 299 28 4 v 41 w(m)m(ultiset)g(*)g Ft(c)p Fu(\))390 408 y FK(This)36 b(function)g(writes)g(the)h(elemen)m(ts)h(of)e(the)h(m)m(ultiset)h FD(c)k FK(to)37 b(the)g(stream)g FD(stream)g FK(in)f(binary)390 518 y(format.)k(The)28 b(function)g(returns)f FH(GSL_EFAILED)e FK(if)j(there)h(w)m(as)g(a)f(problem)g(writing)g(to)h(the)g(\014le.)390 628 y(Since)g(the)g(data)g(is)g(written)g(in)g(the)g(nativ)m(e)h (binary)e(format)h(it)h(ma)m(y)f(not)g(b)s(e)f(p)s(ortable)h(b)s(et)m (w)m(een)390 737 y(di\013eren)m(t)i(arc)m(hitectures.)3350 929 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multiset_fread)e Fu(\()p FD(FILE)31 b(*)f Ft(stream)p FD(,)j(gsl)p 2180 929 V 40 w(m)m(ultiset)f(*)f Ft(c)p Fu(\))390 1038 y FK(This)41 b(function)h(reads)g(elemen)m(ts)i(from)d(the)i(op)s(en)e (stream)i FD(stream)f FK(in)m(to)i(the)e(m)m(ultiset)h FD(c)48 b FK(in)390 1148 y(binary)40 b(format.)71 b(The)40 b(m)m(ultiset)h FD(c)47 b FK(m)m(ust)40 b(b)s(e)g(preallo)s(cated)i (with)e(correct)h(v)-5 b(alues)41 b(of)g FE(n)f FK(and)390 1258 y FE(k)h FK(since)c(the)h(function)f(uses)g(the)h(size)g(of)g FD(c)43 b FK(to)38 b(determine)g(ho)m(w)f(man)m(y)h(b)m(ytes)f(to)i (read.)61 b(The)390 1367 y(function)28 b(returns)f FH(GSL_EFAILED)e FK(if)j(there)h(w)m(as)f(a)h(problem)f(reading)g(from)g(the)g(\014le.) 40 b(The)28 b(data)390 1477 y(is)d(assumed)f(to)i(ha)m(v)m(e)g(b)s(een) f(written)g(in)f(the)i(nativ)m(e)g(binary)e(format)i(on)e(the)i(same)f (arc)m(hitecture.)3350 1668 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multiset_fprintf)f Fu(\()p FD(FILE)30 b(*)h Ft(stream)p FD(,)h(const)f(gsl)p 2522 1668 V 41 w(m)m(ultiset)g(*)g Ft(c)p FD(,)565 1778 y(const)g(c)m(har)g(*)f Ft(format)p Fu(\))390 1888 y FK(This)g(function)h(writes)g(the)g (elemen)m(ts)h(of)f(the)g(m)m(ultiset)h FD(c)37 b FK(line-b)m(y-line)32 b(to)g(the)f(stream)h FD(stream)390 1997 y FK(using)k(the)g(format)h (sp)s(eci\014er)f FD(format)p FK(,)i(whic)m(h)e(should)g(b)s(e)f (suitable)i(for)f(a)h(t)m(yp)s(e)f(of)h FD(size)p 3513 1997 V 41 w(t)p FK(.)59 b(In)390 2107 y(ISO)38 b(C99)h(the)g(t)m(yp)s (e)g(mo)s(di\014er)f FH(z)h FK(represen)m(ts)g FH(size_t)p FK(,)g(so)g FH("\045zu\\n")e 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y({)f(0)h(1)f(2)h(})390 4025 y({)f(0)h(1)f(3)h(})390 4134 y({)f(0)h(2)f(2)h(})390 4244 y({)f(0)h(2)f(3)h(})390 4354 y({)f(0)h(3)f(3)h(})390 4463 y({)f(1)h(1)f(1)h(})390 4573 y({)f(1)h(1)f(2)h(})390 4682 y({)f(1)h(1)f(3)h(})390 4792 y({)f(1)h(2)f(2)h(})390 4902 y({)f(1)h(2)f(3)h(})390 5011 y({)f(1)h(3)f(3)h(})390 5121 y({)f(2)h(2)f(2)h(})390 5230 y({)f(2)h(2)f(3)h(})390 5340 y({)f(2)h(3)f(3)h(})p eop end %%Page: 118 136 TeXDict begin 118 135 bop 150 -116 a FK(Chapter)30 b(11:)41 b(Multisets)2588 b(118)390 299 y FH({)47 b(3)h(3)f(3)h(})390 408 y({)f(0)h(0)f(0)h(0)f(})390 518 y({)g(0)h(0)f(0)h(1)f(})390 628 y({)g(0)h(0)f(0)h(2)f(})390 737 y({)g(0)h(0)f(0)h(3)f(})390 847 y({)g(0)h(0)f(1)h(1)f(})390 956 y({)g(0)h(0)f(1)h(2)f(})390 1066 y({)g(0)h(0)f(1)h(3)f(})390 1176 y({)g(0)h(0)f(2)h(2)f(})390 1285 y({)g(0)h(0)f(2)h(3)f(})390 1395 y({)g(0)h(0)f(3)h(3)f(})390 1504 y({)g(0)h(1)f(1)h(1)f(})390 1614 y({)g(0)h(1)f(1)h(2)f(})390 1724 y({)g(0)h(1)f(1)h(3)f(})390 1833 y({)g(0)h(1)f(2)h(2)f(})390 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b(*)g Ft(array)p FD(,)h(size)p 1857 2401 28 4 v 41 w(t)e Ft(count)p FD(,)i(size)p 2421 2401 V 41 w(t)f Ft(size)p FD(,)565 2511 y(gsl)p 677 2511 V 41 w(comparison)p 1168 2511 V 40 w(fn)p 1287 2511 V 39 w(t)g Ft(compare)p Fu(\))390 2621 y FK(This)44 b(function)g(sorts)g(the)h FD(coun)m(t)i FK(elemen)m(ts)f(of)f(the)f(arra)m(y)h FD(arra)m(y)p FK(,)k(eac)m(h)d(of)e(size)i FD(size)p FK(,)j(in)m(to)390 2730 y(ascending)28 b(order)g(using)f(the)h(comparison)h(function)e FD(compare)p FK(.)41 b(The)27 b(t)m(yp)s(e)h(of)h(the)f(comparison)390 2840 y(function)i(is)g(de\014ned)g(b)m(y)-8 b(,)630 2982 y FH(int)47 b(\(*gsl_comparison_fn_t\))42 b(\(const)k(void)g(*)i(a,) 1966 3092 y(const)f(void)f(*)i(b\))390 3235 y FK(A)35 b(comparison)g(function)g(should)f(return)g(a)h(negativ)m(e)i(in)m (teger)g(if)e(the)g(\014rst)f(argumen)m(t)i(is)f(less)390 3344 y(than)30 b(the)h(second)f(argumen)m(t,)h FH(0)f FK(if)g(the)h(t)m(w)m(o)g(argumen)m(ts)g(are)g(equal)g(and)e(a)i(p)s (ositiv)m(e)g(in)m(teger)h(if)390 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(ts)h(of)f(an)g(arra)m(y)h(or)e(v)m(ector,)51 b(either)45 b(directly)h(or)150 2167 y(indirectly)-8 b(.)70 b(They)39 b(are)h(de\014ned)e(for)i(all)g(real)h(and)e(in)m(teger)i(t)m(yp)s(es)f (using)f(the)h(normal)f(su\016x)g(rules.)150 2276 y(F)-8 b(or)46 b(example,)j(the)c FH(float)f FK(v)m(ersions)h(of)g(the)g(arra) m(y)g(functions)g(are)g FH(gsl_sort_float)c FK(and)j FH(gsl_)150 2386 y(sort_float_index)p FK(.)38 b(The)30 b(corresp)s(onding)g(v)m(ector)i(functions)e(are)i FH (gsl_sort_vector_float)25 b FK(and)150 2496 y FH (gsl_sort_vector_float_in)o(dex)p FK(.)76 b(The)43 b(protot)m(yp)s(es)i (are)f(a)m(v)-5 b(ailable)47 b(in)d(the)g(header)g(\014les)g FH(gsl_)150 2605 y(sort_float.h)20 b(gsl_sort_vector_float.h)p FK(.)32 b(The)23 b(complete)h(set)g(of)g(protot)m(yp)s(es)f(can)h(b)s (e)f(included)150 2715 y(using)30 b(the)g(header)h(\014les)f FH(gsl_sort.h)e FK(and)h FH(gsl_sort_vector.h)p FK(.)275 2845 y(There)g(are)h(no)f(functions)h(for)f(sorting)h(complex)h(arra)m (ys)f(or)f(v)m(ectors,)j(since)e(the)g(ordering)f(of)h(com-)150 2954 y(plex)22 b(n)m(um)m(b)s(ers)f(is)h(not)g(uniquely)f(de\014ned.)37 b(T)-8 b(o)23 b(sort)f(a)g(complex)h(v)m(ector)g(b)m(y)f(magnitude)h (compute)f(a)g(real)150 3064 y(v)m(ector)34 b(con)m(taining)g(the)f (magnitudes)f(of)h(the)g(complex)g(elemen)m(ts,)i(and)d(sort)g(this)h (v)m(ector)h(indirectly)-8 b(.)150 3173 y(The)30 b(resulting)g(index)g (giv)m(es)i(the)f(appropriate)f(ordering)g(of)h(the)f(original)i (complex)f(v)m(ector.)3350 3344 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_sort)47 b Fu(\()p FD(double)31 b(*)f Ft(data)p FD(,)i(const)f(size)p 1929 3344 V 41 w(t)g Ft(stride)p FD(,)h(size)p 2546 3344 V 41 w(t)f Ft(n)p Fu(\))390 3453 y FK(This)d(function)g(sorts)h(the)g FD(n)f FK(elemen)m(ts)i(of)f(the)g(arra)m(y)g FD(data)g FK(with)g(stride)f FD(stride)34 b FK(in)m(to)c(ascending)390 3563 y(n)m(umerical)h(order.) 3350 3733 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_sort2)48 b Fu(\()p FD(double)29 b(*)g Ft(data1)p FD(,)i(const)e(size)p 2028 3733 V 41 w(t)g Ft(stride1)p FD(,)j(double)c(*)i Ft(data2)p FD(,)565 3843 y(const)h(size)p 950 3843 V 41 w(t)g Ft(stride2)p FD(,)h(size)p 1619 3843 V 41 w(t)f Ft(n)p Fu(\))390 3952 y FK(This)21 b(function)g(sorts)h(the)f FD(n)g FK(elemen)m(ts)i(of)f(the)f(arra)m(y)h FD(data1)30 b FK(with)22 b(stride)f FD(stride1)29 b FK(in)m(to)23 b(ascending)390 4062 y(n)m(umerical)j(order,)h(while)e(making)i(the)e (same)i(rearrangemen)m(t)f(of)g(the)g(arra)m(y)g FD(data2)35 b FK(with)25 b(stride)390 4171 y FD(stride2)p FK(,)31 b(also)g(of)g(size)g FD(n)p FK(.)3350 4342 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_sort_vector)c Fu(\()p FD(gsl)p 1389 4342 V 40 w(v)m(ector)32 b(*)f Ft(v)p Fu(\))390 4451 y FK(This)f(function)g(sorts)g(the)h(elemen)m(ts)g(of)g(the)f(v)m (ector)i FD(v)39 b FK(in)m(to)31 b(ascending)f(n)m(umerical)h(order.) 3350 4622 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_sort_vector2)c Fu(\()p FD(gsl)p 1441 4622 V 41 w(v)m(ector)32 b(*)e Ft(v1)p FD(,)i(gsl)p 2097 4622 V 40 w(v)m(ector)g(*)f Ft(v2)p Fu(\))390 4731 y FK(This)41 b(function)g(sorts)h(the)g(elemen)m (ts)h(of)f(the)g(v)m(ector)i FD(v1)49 b FK(in)m(to)43 b(ascending)f(n)m(umerical)g(order,)390 4841 y(while)30 b(making)h(the)g(same)f(rearrangemen)m(t)i(of)e(the)h(v)m(ector)h FD(v2)p FK(.)3350 5011 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_sort_index)49 b Fu(\()p FD(size)p 1371 5011 V 41 w(t)31 b(*)g Ft(p)p FD(,)g(const)g(double)f(*)g Ft(data)p FD(,)i(size)p 2674 5011 V 41 w(t)f Ft(stride)p FD(,)565 5121 y(size)p 712 5121 V 41 w(t)g Ft(n)p Fu(\))390 5230 y FK(This)43 b(function)g(indirectly)g(sorts)h(the)f FD(n)g FK(elemen)m(ts)i(of)e(the)h(arra)m(y)g FD(data)g FK(with)f(stride)g FD(stride)390 5340 y FK(in)m(to)37 b(ascending)g(order,)h(storing)f(the)g(resulting)f(p)s(erm)m(utation)h (in)f FD(p)p FK(.)59 b(The)36 b(arra)m(y)h FD(p)h FK(m)m(ust)f(b)s(e)p eop end %%Page: 121 139 TeXDict begin 121 138 bop 150 -116 a FK(Chapter)30 b(12:)41 b(Sorting)2666 b(121)390 299 y(allo)s(cated)40 b(with)e(a)g(su\016cien) m(t)h(length)f(to)h(store)g(the)f FD(n)g FK(elemen)m(ts)h(of)f(the)h(p) s(erm)m(utation.)63 b(The)390 408 y(elemen)m(ts)37 b(of)f FD(p)i FK(giv)m(e)f(the)f(index)f(of)h(the)g(arra)m(y)g(elemen)m(t)i (whic)m(h)d(w)m(ould)g(ha)m(v)m(e)i(b)s(een)e(stored)h(in)390 518 y(that)31 b(p)s(osition)f(if)h(the)f(arra)m(y)h(had)f(b)s(een)g (sorted)g(in)g(place.)42 b(The)30 b(arra)m(y)h FD(data)g FK(is)f(not)h(c)m(hanged.)3350 724 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sort_vector_index)f Fu(\()p FD(gsl)p 1650 724 28 4 v 41 w(p)s(erm)m(utation)29 b(*)g Ft(p)p FD(,)g(const)h(gsl)p 2733 724 V 40 w(v)m(ector)h(*)e Ft(v)p Fu(\))390 834 y FK(This)21 b(function)g(indirectly)h(sorts)g (the)g(elemen)m(ts)h(of)e(the)h(v)m(ector)i FD(v)29 b FK(in)m(to)22 b(ascending)g(order,)i(storing)390 943 y(the)h(resulting)f(p)s(erm)m(utation)g(in)g FD(p)p FK(.)39 b(The)23 b(elemen)m(ts)j(of)f FD(p)h FK(giv)m(e)g(the)f(index)e(of)i (the)f(v)m(ector)i(elemen)m(t)390 1053 y(whic)m(h)j(w)m(ould)f(ha)m(v)m (e)i(b)s(een)e(stored)h(in)g(that)g(p)s(osition)g(if)g(the)g(v)m(ector) h(had)e(b)s(een)g(sorted)h(in)g(place.)390 1162 y(The)h(\014rst)h (elemen)m(t)h(of)f FD(p)i FK(giv)m(es)f(the)f(index)g(of)g(the)g(least) h(elemen)m(t)h(in)d FD(v)p FK(,)h(and)g(the)g(last)g(elemen)m(t)390 1272 y(of)g FD(p)h FK(giv)m(es)g(the)e(index)g(of)h(the)f(greatest)j (elemen)m(t)e(in)g FD(v)p FK(.)40 b(The)30 b(v)m(ector)i FD(v)38 b FK(is)31 b(not)f(c)m(hanged.)150 1521 y FJ(12.3)68 b(Selecting)46 b(the)g(k)e(smallest)j(or)e(largest)i(elemen)l(ts)150 1680 y FK(The)25 b(functions)g(describ)s(ed)g(in)g(this)g(section)i (select)g(the)f FE(k)j FK(smallest)d(or)g(largest)h(elemen)m(ts)f(of)g (a)g(data)g(set)150 1790 y(of)k(size)g FE(N)10 b FK(.)40 b(The)30 b(routines)f(use)g(an)h FE(O)s FK(\()p FE(k)s(N)10 b FK(\))30 b(direct)g(insertion)g(algorithm)g(whic)m(h)f(is)h(suited)f (to)i(subsets)150 1899 y(that)j(are)h(small)f(compared)g(with)g(the)g 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b(The)27 b(data)h FD(src)390 5340 y FK(is)i(not)h(mo)s(di\014ed)e(b)m(y)i(this)f(op)s(eration.)p eop end %%Page: 122 140 TeXDict begin 122 139 bop 150 -116 a FK(Chapter)30 b(12:)41 b(Sorting)2666 b(122)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sort_largest_inde)q(x)e Fu(\()p FD(size)p 1737 299 28 4 v 42 w(t)30 b(*)h Ft(p)p FD(,)g(size)p 2169 299 V 41 w(t)f Ft(k)p FD(,)h(const)g(double)f(*)h Ft(src)p FD(,)565 408 y(size)p 712 408 V 41 w(t)g Ft(stride)p FD(,)h(size)p 1329 408 V 41 w(t)f Ft(n)p Fu(\))390 518 y FK(This)k(function)g(stores)h(the)f(indices)h(of)f(the)h FD(k)41 b FK(largest)36 b(elemen)m(ts)h(of)f(the)f(arra)m(y)h FD(src)p FK(,)h(of)e(size)h FD(n)390 628 y FK(and)f(stride)h FD(stride)p FK(,)h(in)f(the)f(arra)m(y)i FD(p)p FK(.)56 b(The)35 b(indices)h(are)g(c)m(hosen)h(so)f(that)g(the)g(corresp)s (onding)390 737 y(data)e(is)f(in)f(descending)h(n)m(umerical)g(order.) 48 b FD(k)38 b FK(m)m(ust)33 b(b)s(e)f(less)i(than)e(or)h(equal)g(to)h FD(n)p FK(.)48 b(The)32 b(data)390 847 y FD(src)k FK(is)30 b(not)h(mo)s(di\014ed)e(b)m(y)h(this)g(op)s(eration.)3350 1055 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sort_vector_small)q (est_)q(ind)q(ex)f Fu(\()p FD(size)p 2156 1055 V 41 w(t)31 b(*)f Ft(p)p FD(,)h(size)p 2587 1055 V 41 w(t)g Ft(k)p FD(,)g(const)565 1165 y(gsl)p 677 1165 V 41 w(v)m(ector)h(*)e Ft(v)p Fu(\))3350 1275 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sort_vector_large)q(st_i)q(nde)q(x)e Fu(\()p FD(size)p 2103 1275 V 42 w(t)30 b(*)h Ft(p)p FD(,)g(size)p 2535 1275 V 41 w(t)g Ft(k)p FD(,)f(const)565 1384 y(gsl)p 677 1384 V 41 w(v)m(ector)i(*)e Ft(v)p Fu(\))390 1494 y FK(These)e(functions)g(store)h(the)f(indices)g(of)h(the)f FD(k)34 b FK(smallest)29 b(or)f(largest)i(elemen)m(ts)g(of)e(the)g(v)m (ector)i FD(v)390 1603 y FK(in)g(the)h(arra)m(y)g FD(p)p FK(.)40 b FD(k)35 b FK(m)m(ust)c(b)s(e)e(less)i(than)f(or)h(equal)g(to) g(the)f(length)h(of)g(the)f(v)m(ector)i FD(v)p FK(.)150 1854 y FJ(12.4)68 b(Computing)46 b(the)f(rank)150 2014 y FK(The)29 b FD(rank)34 b FK(of)29 b(an)g(elemen)m(t)i(is)e(its)g (order)g(in)g(the)g(sorted)g(data.)41 b(The)29 b(rank)f(is)h(the)h(in)m (v)m(erse)g(of)f(the)g(index)150 2123 y(p)s(erm)m(utation,)i FD(p)p FK(.)40 b(It)30 b(can)h(b)s(e)f(computed)g(using)g(the)g(follo)m (wing)i(algorithm,)390 2270 y FH(for)47 b(\(i)g(=)h(0;)f(i)g(<)h (p->size;)d(i++\))390 2379 y({)581 2489 y(size_t)h(pi)h(=)h (p->data[i];)581 2599 y(rank->data[pi])c(=)j(i;)390 2708 y(})150 2855 y FK(This)30 b(can)g(b)s(e)g(computed)g(directly)h(from)f (the)h(function)f FH(gsl_permutation_inverse)o(\(ran)o(k,p\))o FK(.)275 3002 y(The)f(follo)m(wing)j(function)e(will)h(prin)m(t)f(the)h (rank)e(of)i(eac)m(h)h(elemen)m(t)f(of)g(the)f(v)m(ector)i FD(v)p FK(,)390 3148 y FH(void)390 3258 y(print_rank)45 b(\(gsl_vector)g(*)i(v\))390 3367 y({)485 3477 y(size_t)g(i;)485 3587 y(size_t)g(n)g(=)g(v->size;)485 3696 y(gsl_permutation)d(*)k(perm) e(=)i(gsl_permutation_alloc\(n)o(\);)485 3806 y(gsl_permutation)c(*)k (rank)e(=)i(gsl_permutation_alloc\(n)o(\);)485 4025 y (gsl_sort_vector_index)42 b(\(perm,)47 b(v\);)485 4134 y(gsl_permutation_inverse)42 b(\(rank,)k(perm\);)485 4354 y(for)h(\(i)h(=)f(0;)g(i)h(<)f(n;)g(i++\))533 4463 y({)581 4573 y(double)f(vi)h(=)h(gsl_vector_get\(v,)43 b(i\);)581 4682 y(printf)j(\("element)f(=)j(\045d,)f(value)f(=)h (\045g,)g(rank)g(=)g(\045d\\n",)1010 4792 y(i,)h(vi,)f (rank->data[i]\);)533 4902 y(})485 5121 y(gsl_permutation_free)c (\(perm\);)485 5230 y(gsl_permutation_free)g(\(rank\);)390 5340 y(})p eop end %%Page: 123 141 TeXDict begin 123 140 bop 150 -116 a FK(Chapter)30 b(12:)41 b(Sorting)2666 b(123)150 299 y FJ(12.5)68 b(Examples)150 458 y FK(The)37 b(follo)m(wing)h(example)g(sho)m(ws)e(ho)m(w)i(to)f (use)g(the)g(p)s(erm)m(utation)g FD(p)j FK(to)d(prin)m(t)g(the)g (elemen)m(ts)i(of)e(the)150 568 y(v)m(ector)32 b FD(v)38 b FK(in)30 b(ascending)h(order,)390 697 y FH(gsl_sort_vector_index)42 b(\(p,)47 b(v\);)390 917 y(for)g(\(i)g(=)h(0;)f(i)g(<)h(v->size;)d (i++\))390 1026 y({)581 1136 y(double)h(vpi)h(=)g(gsl_vector_get)d (\(v,)j(p->data[i]\);)581 1245 y(printf)f(\("order)g(=)h(\045d,)g (value)g(=)g(\045g\\n",)f(i,)h(vpi\);)390 1355 y(})150 1484 y FK(The)32 b(next)h(example)g(uses)g(the)g(function)f FH(gsl_sort_smallest)c FK(to)33 b(select)i(the)e(5)g(smallest)g(n)m(um) m(b)s(ers)150 1594 y(from)d(100000)j(uniform)c(random)h(v)-5 b(ariates)31 b(stored)g(in)f(an)g(arra)m(y)-8 b(,)390 1724 y FH(#include)46 b()390 1833 y(#include)g ()390 2052 y(int)390 2162 y(main)h(\(void\))390 2271 y({)485 2381 y(const)g(gsl_rng_type)d(*)k(T;)485 2491 y(gsl_rng)e(*)i(r;)485 2710 y(size_t)f(i,)g(k)g(=)h(5,)f(N)g(=)h (100000;)485 2929 y(double)f(*)g(x)g(=)h(malloc)e(\(N)h(*)h (sizeof\(double\)\);)485 3039 y(double)f(*)g(small)f(=)i(malloc)e(\(k)h (*)h(sizeof\(double\)\);)485 3258 y(gsl_rng_env_setup\(\);)485 3477 y(T)g(=)f(gsl_rng_default;)485 3587 y(r)h(=)f(gsl_rng_alloc)e (\(T\);)485 3806 y(for)i(\(i)h(=)f(0;)g(i)h(<)f(N;)g(i++\))581 3915 y({)676 4025 y(x[i])g(=)g(gsl_rng_uniform\(r\);)581 4134 y(})485 4354 y(gsl_sort_smallest)d(\(small,)h(k,)j(x,)f(1,)g(N\);) 485 4573 y(printf)g(\("\045zu)f(smallest)f(values)i(from)f(\045zu\\n",) g(k,)h(N\);)485 4792 y(for)g(\(i)h(=)f(0;)g(i)h(<)f(k;)g(i++\))581 4902 y({)676 5011 y(printf)f(\("\045zu:)94 b(\045.18f\\n",)46 b(i,)h(small[i]\);)581 5121 y(})485 5340 y(free)g(\(x\);)p eop end %%Page: 124 142 TeXDict begin 124 141 bop 150 -116 a FK(Chapter)30 b(12:)41 b(Sorting)2666 b(124)485 299 y FH(free)47 b(\(small\);)485 408 y(gsl_rng_free)e(\(r\);)485 518 y(return)i(0;)390 628 y(})275 762 y FK(The)29 b(output)h(lists)h(the)g(5)g(smallest)g(v) -5 b(alues,)31 b(in)f(ascending)h(order,)390 897 y FH($)47 b(./a.out)390 1006 y(5)g(smallest)f(values)g(from)h(100000)390 1116 y(0:)95 b(0.000003489200025797)390 1225 y(1:)g (0.000008199829608202)390 1335 y(2:)g(0.000008953968062997)390 1445 y(3:)g(0.000010712770745158)390 1554 y(4:)g(0.000033531803637743) 150 1787 y FJ(12.6)68 b(References)47 b(and)d(F)-11 b(urther)44 b(Reading)150 1946 y FK(The)30 b(sub)5 b(ject)30 b(of)h(sorting)f(is)h (co)m(v)m(ered)h(extensiv)m(ely)g(in)e(Kn)m(uth's)f FD(Sorting)i(and)f (Searc)m(hing)p FK(,)330 2081 y(Donald)h(E.)f(Kn)m(uth,)f FD(The)g(Art)h(of)g(Computer)g(Programming:)40 b(Sorting)30 b(and)g(Searc)m(hing)38 b FK(\(V)-8 b(ol)31 b(3,)330 2190 y(3rd)f(Ed,)g(1997\),)j(Addison-W)-8 b(esley)g(,)32 b(ISBN)e(0201896850.)150 2350 y(The)g(Heapsort)h(algorithm)g(is)g (describ)s(ed)e(in)h(the)h(follo)m(wing)h(b)s(o)s(ok,)330 2484 y(Rob)s(ert)e(Sedgewic)m(k,)i FD(Algorithms)f(in)f(C)p FK(,)g(Addison-W)-8 b(esley)g(,)32 b(ISBN)e(0201514257.)p eop end %%Page: 125 143 TeXDict begin 125 142 bop 150 -116 a FK(Chapter)30 b(13:)41 b(BLAS)31 b(Supp)s(ort)2360 b(125)150 299 y FG(13)80 b(BLAS)53 b(Supp)t(ort)150 526 y FK(The)34 b(Basic)i(Linear)e(Algebra)h (Subprograms)e(\()p FC(blas)p FK(\))h(de\014ne)g(a)g(set)h(of)g (fundamen)m(tal)f(op)s(erations)h(on)150 635 y(v)m(ectors)46 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Fk(Lev)m(el)i(1)195 b FK(V)-8 b(ector)32 b(op)s(erations,)f(e.g.)42 b FE(y)28 b FK(=)d FE(\013x)c FK(+)e FE(y)150 3233 y Fk(Lev)m(el)31 b(2)195 b FK(Matrix-v)m(ector)33 b(op)s(erations,)e(e.g.)42 b FE(y)28 b FK(=)d FE(\013Ax)c FK(+)f FE(\014)5 b(y)150 3390 y Fk(Lev)m(el)31 b(3)195 b FK(Matrix-matrix)32 b(op)s(erations,)f (e.g.)42 b FE(C)31 b FK(=)25 b FE(\013AB)h FK(+)20 b FE(C)150 3546 y FK(Eac)m(h)34 b(routine)g(has)g(a)g(name)g(whic)m(h)f (sp)s(eci\014es)g(the)h(op)s(eration,)i(the)e(t)m(yp)s(e)f(of)h (matrices)h(in)m(v)m(olv)m(ed)h(and)150 3656 y(their)30 b(precisions.)41 b(Some)31 b(of)f(the)h(most)f(common)h(op)s(erations)g (and)f(their)g(names)g(are)h(giv)m(en)g(b)s(elo)m(w,)150 3812 y Fk(DOT)279 b FK(scalar)31 b(pro)s(duct,)f FE(x)1307 3779 y Fq(T)1359 3812 y FE(y)150 3969 y Fk(AXPY)211 b FK(v)m(ector)32 b(sum,)e FE(\013x)20 b FK(+)g FE(y)150 4125 y Fk(MV)325 b FK(matrix-v)m(ector)33 b(pro)s(duct,)c FE(Ax)150 4282 y Fk(SV)360 b FK(matrix-v)m(ector)33 b(solv)m(e,)f FE(inv)s FK(\()p FE(A)p FK(\))p FE(x)150 4438 y Fk(MM)308 b FK(matrix-matrix)31 b(pro)s(duct,)f FE(AB)150 4595 y Fk(SM)343 b FK(matrix-matrix)31 b(solv)m(e,)h FE(inv)s FK(\()p FE(A)p FK(\))p FE(B)150 4751 y FK(The)e(t)m(yp)s(es)g(of)h (matrices)g(are,)150 4907 y Fk(GE)349 b FK(general)150 5064 y Fk(GB)344 b FK(general)31 b(band)p 150 5154 1200 4 v 199 5221 a FB(1)275 5253 y Fx(In)25 b(the)h(lo)n(w-lev)n(el)h Fj(cblas)h Fx(in)n(terface,)f(a)g(negativ)n(e)g(stride)f(accesses)i (the)e(v)n(ector)h(elemen)n(ts)f(in)h(rev)n(erse)f(order,)h(i.e.)37 b(the)275 5340 y Fi(i)p Fx(-th)25 b(elemen)n(t)g(is)i(giv)n(en)e(b)n(y) g(\()p Fi(N)g Fh(\000)17 b Fi(i)p Fx(\))g Fh(\003)h(j)p Fi(incx)p Fh(j)26 b Fx(for)h Fi(incx)21 b(<)h Fx(0.)p eop end %%Page: 126 144 TeXDict begin 126 143 bop 150 -116 a FK(Chapter)30 b(13:)41 b(BLAS)31 b(Supp)s(ort)2360 b(126)150 299 y Fk(SY)360 b FK(symmetric)150 461 y Fk(SB)k FK(symmetric)31 b(band)150 623 y Fk(SP)367 b FK(symmetric)31 b(pac)m(k)m(ed)150 785 y Fk(HE)349 b 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(arra)m(ys)i(o)m(v)m(erlap)g(\(see)h(Section)f(2.11)g([Aliasing)h(of) 150 3038 y(arra)m(ys],)e(page)g(9\).)150 3274 y FJ(13.1)68 b(GSL)44 b(BLAS)g(In)l(terface)150 3434 y FK(GSL)34 b(pro)m(vides)h (dense)f(v)m(ector)j(and)d(matrix)h(ob)5 b(jects,)37 b(based)d(on)h(the)g(relev)-5 b(an)m(t)36 b(built-in)f(t)m(yp)s(es.)53 b(The)150 3543 y(library)40 b(pro)m(vides)h(an)g(in)m(terface)h(to)f (the)g FC(blas)f FK(op)s(erations)h(whic)m(h)f(apply)g(to)i(these)f(ob) 5 b(jects.)72 b(The)150 3653 y(in)m(terface)32 b(to)f(this)f (functionalit)m(y)i(is)f(giv)m(en)g(in)f(the)h(\014le)f FH(gsl_blas.h)p FK(.)150 3855 y Fy(13.1.1)63 b(Lev)m(el)40 b(1)3350 4054 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_sdsdot)d Fu(\()p FD(\015oat)32 b Ft(alpha)p FD(,)g(const)f(gsl)p 2099 4054 28 4 v 40 w(v)m(ector)p 2380 4054 V 42 w(\015oat)g(*)g Ft(x)p FD(,)g(const)565 4164 y(gsl)p 677 4164 V 41 w(v)m(ector)p 959 4164 V 41 w(\015oat)g(*)g Ft(y)p FD(,)g(\015oat)g(*)g Ft(result)p Fu(\))390 4274 y FK(This)26 b(function)h(computes)g(the)h(sum)e FE(\013)14 b FK(+)g FE(x)1900 4241 y Fq(T)1952 4274 y FE(y)30 b FK(for)d(the)g(v)m(ectors)i FD(x)k FK(and)26 b FD(y)p FK(,)i(returning)f(the)g(result)390 4383 y(in)j FD(result)p FK(.)3350 4573 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_sdot)d Fu(\()p FD(const)30 b(gsl)p 1469 4573 V 41 w(v)m(ector)p 1751 4573 V 41 w(\015oat)h(*)f Ft(x)p FD(,)g(const)g(gsl)p 2524 4573 V 41 w(v)m(ector)p 2806 4573 V 41 w(\015oat)h(*)f Ft(y)p FD(,)565 4682 y(\015oat)h(*)g Ft(result)p Fu(\))3350 4792 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_dsdot)d Fu(\()p FD(const)31 b(gsl)p 1522 4792 V 41 w(v)m(ector)p 1804 4792 V 41 w(\015oat)g(*)g Ft(x)p FD(,)g(const)g(gsl)p 2580 4792 V 41 w(v)m(ector)p 2862 4792 V 41 w(\015oat)g(*)565 4902 y Ft(y)p FD(,)g(double)f(*)h Ft(result)p Fu(\))3350 5011 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_ddot)d Fu(\()p FD(const)31 b(gsl)p 1470 5011 V 40 w(v)m(ector)h(*)f Ft(x)p FD(,)g(const)g(gsl)p 2311 5011 V 40 w(v)m(ector)h(*)f Ft(y)p FD(,)g(double)f(*)565 5121 y Ft(result)p Fu(\))390 5230 y FK(These)35 b(functions)f(compute)h (the)g(scalar)h(pro)s(duct)e FE(x)2249 5197 y Fq(T)2301 5230 y FE(y)j FK(for)e(the)g(v)m(ectors)h FD(x)41 b FK(and)35 b FD(y)p FK(,)h(returning)390 5340 y(the)31 b(result)f(in)g FD(result)p FK(.)p eop end %%Page: 127 145 TeXDict begin 127 144 bop 150 -116 a FK(Chapter)30 b(13:)41 b(BLAS)31 b(Supp)s(ort)2360 b(127)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_cdotu)d Fu(\()p FD(const)31 b(gsl)p 1522 299 28 4 v 41 w(v)m(ector)p 1804 299 V 41 w(complex)p 2170 299 V 41 w(\015oat)g(*)g Ft(x)p FD(,)g(const)565 408 y(gsl)p 677 408 V 41 w(v)m(ector)p 959 408 V 41 w(complex)p 1325 408 V 41 w(\015oat)g(*)g Ft(y)p FD(,)g(gsl)p 1863 408 V 40 w(complex)p 2228 408 V 41 w(\015oat)g(*)g Ft(dotu)p Fu(\))3350 518 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_zdotu)d Fu(\()p FD(const)31 b(gsl)p 1522 518 V 41 w(v)m(ector)p 1804 518 V 41 w(complex)g(*)g Ft(x)p FD(,)g(const)565 628 y(gsl)p 677 628 V 41 w(v)m(ector)p 959 628 V 41 w(complex)g(*)g Ft(y)p FD(,)g(gsl)p 1646 628 V 41 w(complex)g(*)f Ft(dotu)p Fu(\))390 737 y FK(These)38 b(functions)g(compute)g(the)h(complex)g(scalar)g(pro)s(duct)e FE(x)2633 704 y Fq(T)2685 737 y FE(y)k FK(for)d(the)h(v)m(ectors)h FD(x)k FK(and)38 b FD(y)p FK(,)390 847 y(returning)29 b(the)i(result)f(in)g FD(dotu)3350 1035 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_cdotc)d Fu(\()p FD(const)31 b(gsl)p 1522 1035 V 41 w(v)m(ector)p 1804 1035 V 41 w(complex)p 2170 1035 V 41 w(\015oat)g(*)g Ft(x)p FD(,)g(const)565 1145 y(gsl)p 677 1145 V 41 w(v)m(ector)p 959 1145 V 41 w(complex)p 1325 1145 V 41 w(\015oat)g(*)g Ft(y)p FD(,)g(gsl)p 1863 1145 V 40 w(complex)p 2228 1145 V 41 w(\015oat)g(*)g Ft(dotc)p Fu(\))3350 1254 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_zdotc)d Fu(\()p FD(const)31 b(gsl)p 1522 1254 V 41 w(v)m(ector)p 1804 1254 V 41 w(complex)g(*)g Ft(x)p FD(,)g(const)565 1364 y(gsl)p 677 1364 V 41 w(v)m(ector)p 959 1364 V 41 w(complex)g(*)g Ft(y)p FD(,)g(gsl)p 1646 1364 V 41 w(complex)g(*)f Ft(dotc)p Fu(\))390 1474 y FK(These)k(functions)g(compute)h(the)g(complex)g(conjugate)h(scalar)f (pro)s(duct)e FE(x)3022 1441 y Fq(H)3085 1474 y FE(y)38 b FK(for)c(the)g(v)m(ectors)390 1583 y FD(x)j FK(and)29 b FD(y)p FK(,)i(returning)e(the)i(result)f(in)g FD(dotc)3350 1771 y FK([F)-8 b(unction])-3599 b Fv(float)54 b(gsl_blas_snrm2)c Fu(\()p FD(const)31 b(gsl)p 1627 1771 V 40 w(v)m(ector)p 1908 1771 V 42 w(\015oat)g(*)g Ft(x)p Fu(\))3350 1881 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_blas_dnrm2)c Fu(\()p FD(const)31 b(gsl)p 1679 1881 V 41 w(v)m(ector)h(*)e Ft(x)p Fu(\))390 1991 y FK(These)g(functions)g(compute)h(the)f (Euclidean)h(norm)e FI(jj)p FE(x)p FI(jj)2380 2005 y FB(2)2444 1991 y FK(=)2540 1916 y Fs(p)p 2623 1916 192 4 v 10 x(P)2726 1991 y FE(x)2778 1959 y FB(2)2778 2011 y Fq(i)2845 1991 y FK(of)i(the)f(v)m(ector)i FD(x)p FK(.)3350 2179 y([F)-8 b(unction])-3599 b Fv(float)54 b(gsl_blas_scnrm2)c Fu(\()p FD(const)31 b(gsl)p 1679 2179 28 4 v 41 w(v)m(ector)p 1961 2179 V 41 w(complex)p 2327 2179 V 41 w(\015oat)g(*)g Ft(x)p Fu(\))3350 2289 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_blas_dznrm2)c Fu(\()p FD(const)31 b(gsl)p 1731 2289 V 41 w(v)m(ector)p 2013 2289 V 42 w(complex)g(*)f Ft(x)p Fu(\))390 2398 y FK(These)g(functions)g(compute)h(the)f (Euclidean)h(norm)e(of)i(the)f(complex)i(v)m(ector)g FD(x)p FK(,)1294 2594 y FI(jj)p FE(x)p FI(jj)1446 2608 y FB(2)1509 2594 y FK(=)1605 2492 y Fs(q)p 1688 2492 893 4 v 21 x(X)1808 2594 y FK(\(Re)q(\()p FE(x)2038 2608 y Fq(i)2066 2594 y FK(\))2101 2568 y FB(2)2159 2594 y FK(+)19 b(Im\()p FE(x)2445 2608 y Fq(i)2473 2594 y FK(\))2508 2568 y FB(2)2546 2594 y FK(\))p FE(:)3350 2802 y FK([F)-8 b(unction])-3599 b Fv(float)54 b(gsl_blas_sasum)c Fu(\()p FD(const)31 b(gsl)p 1627 2802 28 4 v 40 w(v)m(ector)p 1908 2802 V 42 w(\015oat)g(*)g Ft(x)p Fu(\))3350 2912 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_blas_dasum)c Fu(\()p FD(const)31 b(gsl)p 1679 2912 V 41 w(v)m(ector)h(*)e Ft(x)p Fu(\))390 3021 y FK(These)g(functions)g(compute)h(the)f (absolute)h(sum)2122 2957 y Fs(P)2225 3021 y FI(j)p FE(x)2302 3035 y Fq(i)2329 3021 y FI(j)g FK(of)g(the)f(elemen)m(ts)i(of)e(the)h (v)m(ector)h FD(x)p FK(.)3350 3210 y([F)-8 b(unction])-3599 b Fv(float)54 b(gsl_blas_scasum)c Fu(\()p FD(const)31 b(gsl)p 1679 3210 V 41 w(v)m(ector)p 1961 3210 V 41 w(complex)p 2327 3210 V 41 w(\015oat)g(*)g Ft(x)p Fu(\))3350 3319 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_blas_dzasum)c Fu(\()p FD(const)31 b(gsl)p 1731 3319 V 41 w(v)m(ector)p 2013 3319 V 42 w(complex)g(*)f Ft(x)p Fu(\))390 3429 y FK(These)g(functions)g(compute)g(the)h(sum)e(of)h(the)h(magnitudes)f (of)g(the)h(real)g(and)e(imaginary)i(parts)390 3539 y(of)g(the)f (complex)h(v)m(ector)h FD(x)p FK(,)1383 3474 y Fs(P)1485 3539 y FK(\()q FI(j)p FK(Re\()p FE(x)1740 3553 y Fq(i)1768 3539 y FK(\))p FI(j)21 b FK(+)f FI(j)p FK(Im\()p FE(x)2161 3553 y Fq(i)2189 3539 y FK(\))p FI(j)p FK(\))q(.)3350 3727 y([F)-8 b(unction])-3599 b Fv(CBLAS_INDEX_t)56 b(gsl_blas_isamax) 50 b Fu(\()p FD(const)31 b(gsl)p 2097 3727 V 41 w(v)m(ector)p 2379 3727 V 42 w(\015oat)g(*)g Ft(x)p Fu(\))3350 3837 y FK([F)-8 b(unction])-3599 b Fv(CBLAS_INDEX_t)56 b(gsl_blas_idamax)50 b Fu(\()p FD(const)31 b(gsl)p 2097 3837 V 41 w(v)m(ector)h(*)f Ft(x)p Fu(\))3350 3946 y FK([F)-8 b(unction])-3599 b Fv(CBLAS_INDEX_t)56 b(gsl_blas_icamax)50 b Fu(\()p FD(const)31 b(gsl)p 2097 3946 V 41 w(v)m(ector)p 2379 3946 V 42 w(complex)p 2746 3946 V 40 w(\015oat)h(*)e Ft(x)p Fu(\))3350 4056 y FK([F)-8 b(unction])-3599 b Fv(CBLAS_INDEX_t)56 b(gsl_blas_izamax)50 b Fu(\()p FD(const)31 b(gsl)p 2097 4056 V 41 w(v)m(ector)p 2379 4056 V 42 w(complex)g(*)g Ft(x)p Fu(\))390 4165 y FK(These)i(functions)f(return)g(the)h(index)f(of)h(the)g(largest)h (elemen)m(t)g(of)f(the)g(v)m(ector)h FD(x)p FK(.)48 b(The)33 b(largest)390 4275 y(elemen)m(t)43 b(is)f(determined)g(b)m(y)f(its)i (absolute)f(magnitude)g(for)g(real)g(v)m(ectors)i(and)d(b)m(y)h(the)g (sum)390 4384 y(of)e(the)g(magnitudes)g(of)g(the)g(real)g(and)g (imaginary)g(parts)g FI(j)p FK(Re\()p FE(x)2714 4398 y Fq(i)2742 4384 y FK(\))p FI(j)27 b FK(+)f FI(j)p FK(Im\()p FE(x)3147 4398 y Fq(i)3175 4384 y FK(\))p FI(j)41 b FK(for)e(complex) 390 4494 y(v)m(ectors.)i(If)25 b(the)h(largest)h(v)-5 b(alue)26 b(o)s(ccurs)g(sev)m(eral)h(times)f(then)g(the)g(index)f(of)h (the)g(\014rst)f(o)s(ccurrence)390 4604 y(is)30 b(returned.)3350 4792 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_sswap)d Fu(\()p FD(gsl)p 1284 4792 V 41 w(v)m(ector)p 1566 4792 V 42 w(\015oat)31 b(*)f Ft(x)p FD(,)h(gsl)p 2104 4792 V 41 w(v)m(ector)p 2386 4792 V 41 w(\015oat)h(*)e Ft(y)p Fu(\))3350 4902 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_dswap)d Fu(\()p FD(gsl)p 1284 4902 V 41 w(v)m(ector)32 b(*)f Ft(x)p FD(,)f(gsl)p 1887 4902 V 41 w(v)m(ector)i(*)f Ft(y)p Fu(\))3350 5011 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_cswap)d Fu(\()p FD(gsl)p 1284 5011 V 41 w(v)m(ector)p 1566 5011 V 42 w(complex)p 1933 5011 V 40 w(\015oat)31 b(*)g Ft(x)p FD(,)565 5121 y(gsl)p 677 5121 V 41 w(v)m(ector)p 959 5121 V 41 w(complex)p 1325 5121 V 41 w(\015oat)g(*)g Ft(y)p Fu(\))3350 5230 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_zswap)d Fu(\()p FD(gsl)p 1284 5230 V 41 w(v)m(ector)p 1566 5230 V 42 w(complex)31 b(*)f Ft(x)p FD(,)h(gsl)p 2253 5230 V 41 w(v)m(ector)p 2535 5230 V 41 w(complex)g(*)g Ft(y)p Fu(\))390 5340 y FK(These)f(functions)g(exc)m(hange)i(the)f(elemen)m (ts)g(of)g(the)f(v)m(ectors)i FD(x)37 b FK(and)29 b FD(y)p FK(.)p eop end %%Page: 128 146 TeXDict begin 128 145 bop 150 -116 a FK(Chapter)30 b(13:)41 b(BLAS)31 b(Supp)s(ort)2360 b(128)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_scopy)d Fu(\()p FD(const)31 b(gsl)p 1522 299 28 4 v 41 w(v)m(ector)p 1804 299 V 41 w(\015oat)g(*)g Ft(x)p FD(,)g(gsl)p 2342 299 V 41 w(v)m(ector)p 2624 299 V 41 w(\015oat)g(*)g Ft(y)p Fu(\))3350 408 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_dcopy)d Fu(\()p FD(const)31 b(gsl)p 1522 408 V 41 w(v)m(ector)h(*)e Ft(x)p FD(,)h(gsl)p 2125 408 V 41 w(v)m(ector)h(*)f Ft(y)p Fu(\))3350 518 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_ccopy)d Fu(\()p FD(const)31 b(gsl)p 1522 518 V 41 w(v)m(ector)p 1804 518 V 41 w(complex)p 2170 518 V 41 w(\015oat)g(*)g Ft(x)p FD(,)565 628 y(gsl)p 677 628 V 41 w(v)m(ector)p 959 628 V 41 w(complex)p 1325 628 V 41 w(\015oat)g(*)g Ft(y)p Fu(\))3350 737 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_zcopy)d Fu(\()p FD(const)31 b(gsl)p 1522 737 V 41 w(v)m(ector)p 1804 737 V 41 w(complex)g(*)g Ft(x)p FD(,)g(gsl)p 2491 737 V 41 w(v)m(ector)p 2773 737 V 41 w(complex)565 847 y(*)g Ft(y)p Fu(\))390 956 y FK(These)f(functions)g (cop)m(y)h(the)g(elemen)m(ts)g(of)g(the)g(v)m(ector)h FD(x)k FK(in)m(to)31 b(the)g(v)m(ector)h FD(y)p FK(.)3350 1154 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_saxpy)d Fu(\()p FD(\015oat)31 b Ft(alpha)p FD(,)h(const)f(gsl)p 2046 1154 V 41 w(v)m(ector)p 2328 1154 V 42 w(\015oat)g(*)f Ft(x)p FD(,)565 1264 y(gsl)p 677 1264 V 41 w(v)m(ector)p 959 1264 V 41 w(\015oat)h(*)g Ft(y)p Fu(\))3350 1374 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_daxpy)d Fu(\()p FD(double)29 b Ft(alpha)p FD(,)j(const)e(gsl)p 2130 1374 V 41 w(v)m(ector)h(*)f Ft(x)p FD(,)g(gsl)p 2731 1374 V 40 w(v)m(ector)i(*)e Ft(y)p Fu(\))3350 1483 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_caxpy)d Fu(\()p FD(const)31 b(gsl)p 1522 1483 V 41 w(complex)p 1888 1483 V 40 w(\015oat)h Ft(alpha)p FD(,)g(const)565 1593 y(gsl)p 677 1593 V 41 w(v)m(ector)p 959 1593 V 41 w(complex)p 1325 1593 V 41 w(\015oat)f(*)g Ft(x)p FD(,)g(gsl)p 1863 1593 V 40 w(v)m(ector)p 2144 1593 V 42 w(complex)p 2511 1593 V 41 w(\015oat)g(*)g Ft(y)p Fu(\))3350 1702 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_zaxpy)d Fu(\()p FD(const)31 b(gsl)p 1522 1702 V 41 w(complex)g Ft(alpha)p FD(,)h(const)565 1812 y(gsl)p 677 1812 V 41 w(v)m(ector)p 959 1812 V 41 w(complex)f(*)g Ft(x)p FD(,)g(gsl)p 1646 1812 V 41 w(v)m(ector)p 1928 1812 V 41 w(complex)g(*)g Ft(y)p Fu(\))390 1922 y FK(These)f(functions)g(compute)h(the)f(sum)g FE(y)e FK(=)d FE(\013x)20 b FK(+)g FE(y)33 b FK(for)e(the)f(v)m(ectors) i FD(x)37 b FK(and)29 b FD(y)p FK(.)3350 2120 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_blas_sscal)49 b Fu(\()p FD(\015oat)32 b Ft(alpha)p FD(,)g(gsl)p 1861 2120 V 40 w(v)m(ector)p 2142 2120 V 42 w(\015oat)f(*)g Ft(x)p Fu(\))3350 2229 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_blas_dscal)49 b Fu(\()p FD(double)31 b Ft(alpha)p FD(,)h(gsl)p 1947 2229 V 40 w(v)m(ector)g(*)f Ft(x)p Fu(\))3350 2339 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_blas_cscal)49 b Fu(\()p FD(const)31 b(gsl)p 1574 2339 V 41 w(complex)p 1940 2339 V 41 w(\015oat)g Ft(alpha)p FD(,)565 2448 y(gsl)p 677 2448 V 41 w(v)m(ector)p 959 2448 V 41 w(complex)p 1325 2448 V 41 w(\015oat)g(*)g Ft(x)p Fu(\))3350 2558 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_blas_zscal)49 b Fu(\()p FD(const)31 b(gsl)p 1574 2558 V 41 w(complex)g Ft(alpha)p FD(,)h(gsl)p 2394 2558 V 41 w(v)m(ector)p 2676 2558 V 41 w(complex)f(*)565 2668 y Ft(x)p Fu(\))3350 2777 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_blas_csscal)c Fu(\()p FD(\015oat)31 b Ft(alpha)p FD(,)h(gsl)p 1913 2777 V 41 w(v)m(ector)p 2195 2777 V 41 w(complex)p 2561 2777 V 41 w(\015oat)f(*)g Ft(x)p Fu(\))3350 2887 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_blas_zdscal)c Fu(\()p FD(double)30 b Ft(alpha)p FD(,)i(gsl)p 1999 2887 V 40 w(v)m(ector)p 2280 2887 V 42 w(complex)f(*)g Ft(x)p Fu(\))390 2996 y FK(These)f(functions)g(rescale)i(the)e(v)m(ector)i FD(x)37 b FK(b)m(y)30 b(the)h(m)m(ultiplicativ)m(e)i(factor)e FD(alpha)p FK(.)3350 3194 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_srotg)d Fu(\()p FD(\015oat)31 b Ft(a)p Fo([])p FD(,)g(\015oat)g Ft(b)p Fo([])p FD(,)g(\015oat)g Ft(c)p Fo([])p FD(,)f(\015oat)i Ft(s)p Fo([])p Fu(\))3350 3304 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_drotg)d Fu(\()p FD(double)30 b Ft(a)p Fo([])p FD(,)h(double)f Ft(b)p Fo([])p FD(,)g(double)g Ft(c)p Fo([])p FD(,)h(double)f Ft(s)p Fo([])p Fu(\))390 3413 y FK(These)g(functions)g(compute)h(a)f (Giv)m(ens)i(rotation)f(\()p FE(c;)15 b(s)p FK(\))32 b(whic)m(h)e(zero)s(es)h(the)f(v)m(ector)i(\()p FE(a;)15 b(b)p FK(\),)1472 3514 y Fs(\022)1585 3578 y FE(c)129 b(s)1548 3688 y FI(\000)p FE(s)92 b(c)1810 3514 y Fs(\023)16 b(\022)1963 3578 y FE(a)1967 3688 y(b)2026 3514 y Fs(\023)2113 3633 y FK(=)2208 3514 y Fs(\022)2285 3578 y FE(r)2329 3546 y Fp(0)2295 3688 y FK(0)2367 3514 y Fs(\023)390 3848 y FK(The)30 b(v)-5 b(ariables)31 b FD(a)g FK(and)e FD(b)j FK(are)f(o)m(v)m(erwritten)h(b)m(y)e(the)h(routine.)3350 4046 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_srot)d Fu(\()p FD(gsl)p 1232 4046 V 41 w(v)m(ector)p 1514 4046 V 41 w(\015oat)31 b(*)g Ft(x)p FD(,)g(gsl)p 2052 4046 V 40 w(v)m(ector)p 2333 4046 V 42 w(\015oat)g(*)g Ft(y)p FD(,)g(\015oat)g Ft(c)p FD(,)565 4156 y(\015oat)g Ft(s)p Fu(\))3350 4265 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_drot)d Fu(\()p FD(gsl)p 1232 4265 V 41 w(v)m(ector)32 b(*)e Ft(x)p FD(,)h(gsl)p 1835 4265 V 41 w(v)m(ector)h(*)e Ft(y)p FD(,)h(const)g(double)f Ft(c)p FD(,)h(const)565 4375 y(double)f Ft(s)p Fu(\))390 4484 y FK(These)h(functions)f(apply)h (a)g(Giv)m(ens)h(rotation)g(\()p FE(x)2109 4451 y Fp(0)2133 4484 y FE(;)15 b(y)2221 4451 y Fp(0)2244 4484 y FK(\))27 b(=)f(\()p FE(cx)21 b FK(+)f FE(sy)s(;)15 b FI(\000)p FE(sx)20 b FK(+)g FE(cy)s FK(\))32 b(to)f(the)g(v)m(ectors)390 4594 y FD(x)p FK(,)g FD(y)p FK(.)3350 4792 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_srotmg)d Fu(\()p FD(\015oat)30 b Ft(d1)p Fo([])p FD(,)g(\015oat)g Ft(d2)p Fo([])p FD(,)g(\015oat)f Ft(b1)p Fo([])p FD(,)h(\015oat)g Ft(b2)p FD(,)g(\015oat)g Ft(P)p Fo([])p Fu(\))3350 4902 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_drotmg)d Fu(\()p FD(double)31 b Ft(d1)p Fo([])p FD(,)f(double)g Ft(d2)p Fo([])p FD(,)h(double)f Ft(b1)p Fo([])p FD(,)h(double)f Ft(b2)p FD(,)565 5011 y(double)g Ft(P)p Fo([])p Fu(\))390 5121 y FK(These)40 b(functions)g(compute)g(a)h(mo)s(di\014ed)e(Giv)m(ens)i (transformation.)70 b(The)40 b(mo)s(di\014ed)f(Giv)m(ens)390 5230 y(transformation)33 b(is)f(de\014ned)g(in)g(the)g(original)i(Lev)m (el-1)g FC(blas)e FK(sp)s(eci\014cation,)i(giv)m(en)f(in)f(the)h(ref-) 390 5340 y(erences.)p eop end %%Page: 129 147 TeXDict begin 129 146 bop 150 -116 a FK(Chapter)30 b(13:)41 b(BLAS)31 b(Supp)s(ort)2360 b(129)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_srotm)d Fu(\()p FD(gsl)p 1284 299 28 4 v 41 w(v)m(ector)p 1566 299 V 42 w(\015oat)31 b(*)f Ft(x)p FD(,)h(gsl)p 2104 299 V 41 w(v)m(ector)p 2386 299 V 41 w(\015oat)h(*)e Ft(y)p FD(,)h(const)565 408 y(\015oat)g Ft(P)p Fo([])p Fu(\))3350 518 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_drotm)d Fu(\()p FD(gsl)p 1284 518 V 41 w(v)m(ector)32 b(*)f Ft(x)p FD(,)f(gsl)p 1887 518 V 41 w(v)m(ector)i(*)f Ft(y)p FD(,)g(const)f(double)g Ft(P)p Fo([])p Fu(\))390 628 y FK(These)g(functions)g(apply)g(a)h(mo)s (di\014ed)e(Giv)m(ens)i(transformation.)150 872 y Fy(13.1.2)63 b(Lev)m(el)40 b(2)3350 1113 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_sgemv)d Fu(\()p FD(CBLAS)p 1484 1113 V 40 w(TRANSPOSE)p 2090 1113 V 38 w(t)31 b Ft(TransA)p FD(,)h(\015oat)f Ft(alpha)p FD(,)565 1223 y(const)g(gsl)p 915 1223 V 41 w(matrix)p 1221 1223 V 40 w(\015oat)g(*)g Ft(A)p FD(,)g(const)g(gsl)p 1996 1223 V 40 w(v)m(ector)p 2277 1223 V 42 w(\015oat)g(*)g Ft(x)p FD(,)f(\015oat)i Ft(beta)p FD(,)565 1332 y(gsl)p 677 1332 V 41 w(v)m(ector)p 959 1332 V 41 w(\015oat)f(*)g Ft(y)p Fu(\))3350 1442 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_dgemv)d Fu(\()p FD(CBLAS)p 1484 1442 V 40 w(TRANSPOSE)p 2090 1442 V 38 w(t)31 b Ft(TransA)p FD(,)h(double)e Ft(alpha)p FD(,)565 1552 y(const)h(gsl)p 915 1552 V 41 w(matrix)f(*)h Ft(A)p FD(,)g(const)g(gsl)p 1779 1552 V 40 w(v)m(ector)h(*)f Ft(x)p FD(,)g(double)f Ft(beta)p FD(,)i(gsl)p 2940 1552 V 40 w(v)m(ector)g(*)f Ft(y)p Fu(\))3350 1661 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_cgemv)d Fu(\()p FD(CBLAS)p 1484 1661 V 40 w(TRANSPOSE)p 2090 1661 V 38 w(t)31 b Ft(TransA)p FD(,)h(const)565 1771 y(gsl)p 677 1771 V 41 w(complex)p 1043 1771 V 40 w(\015oat)g Ft(alpha)p FD(,)g(const)e(gsl)p 1951 1771 V 41 w(matrix)p 2257 1771 V 40 w(complex)p 2622 1771 V 41 w(\015oat)h(*)g Ft(A)p FD(,)g(const)565 1880 y(gsl)p 677 1880 V 41 w(v)m(ector)p 959 1880 V 41 w(complex)p 1325 1880 V 41 w(\015oat)g(*)g Ft(x)p FD(,)g(const)g(gsl)p 2101 1880 V 40 w(complex)p 2466 1880 V 41 w(\015oat)g Ft(beta)p FD(,)565 1990 y(gsl)p 677 1990 V 41 w(v)m(ector)p 959 1990 V 41 w(complex)p 1325 1990 V 41 w(\015oat)g(*)g Ft(y)p Fu(\))3350 2100 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_zgemv)d Fu(\()p FD(CBLAS)p 1484 2100 V 40 w(TRANSPOSE)p 2090 2100 V 38 w(t)31 b Ft(TransA)p FD(,)h(const)565 2209 y(gsl)p 677 2209 V 41 w(complex)f Ft(alpha)p FD(,)h(const)f(gsl)p 1735 2209 V 40 w(matrix)p 2040 2209 V 41 w(complex)g(*)f Ft(A)p FD(,)h(const)g(gsl)p 2964 2209 V 41 w(v)m(ector)p 3246 2209 V 41 w(complex)h(*)565 2319 y Ft(x)p FD(,)f(const)g(gsl)p 1023 2319 V 40 w(complex)g Ft(beta)p FD(,)h(gsl)p 1790 2319 V 41 w(v)m(ector)p 2072 2319 V 41 w(complex)g(*)e Ft(y)p Fu(\))390 2428 y FK(These)21 b(functions)h(compute)g(the)g (matrix-v)m(ector)i(pro)s(duct)c(and)h(sum)g FE(y)28 b FK(=)d FE(\013op)p FK(\()p FE(A)p FK(\))p FE(x)s FK(+)s FE(\014)5 b(y)s FK(,)24 b(where)390 2538 y FE(op)p FK(\()p FE(A)p FK(\))i(=)f FE(A)p FK(,)31 b FE(A)932 2505 y Fq(T)984 2538 y FK(,)g FE(A)1108 2505 y Fq(H)1201 2538 y FK(for)f FD(T)-8 b(ransA)30 b FK(=)g FH(CblasNoTrans)p FK(,)e FH(CblasTrans)p FK(,)f FH(CblasConjTrans)p FK(.)3350 2812 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_strmv)d Fu(\()p FD(CBLAS)p 1484 2812 V 40 w(UPLO)p 1782 2812 V 39 w(t)31 b Ft(Uplo)p FD(,)h(CBLAS)p 2458 2812 V 39 w(TRANSPOSE)p 3063 2812 V 39 w(t)565 2921 y Ft(TransA)p FD(,)e(CBLAS)p 1244 2921 V 40 w(DIA)m(G)p 1522 2921 V 41 w(t)e Ft(Diag)p FD(,)i(const)f(gsl)p 2231 2921 V 41 w(matrix)p 2537 2921 V 40 w(\015oat)g(*)f Ft(A)p FD(,)h(gsl)p 3067 2921 V 40 w(v)m(ector)p 3348 2921 V 42 w(\015oat)g(*)f Ft(x)p Fu(\))3350 3031 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_dtrmv)d Fu(\()p FD(CBLAS)p 1484 3031 V 40 w(UPLO)p 1782 3031 V 39 w(t)31 b Ft(Uplo)p FD(,)h(CBLAS)p 2458 3031 V 39 w(TRANSPOSE)p 3063 3031 V 39 w(t)565 3140 y Ft(TransA)p FD(,)g(CBLAS)p 1246 3140 V 40 w(DIA)m(G)p 1524 3140 V 41 w(t)f Ft(Diag)p FD(,)h(const)f(gsl)p 2240 3140 V 40 w(matrix)g(*)g Ft(A)p FD(,)g(gsl)p 2866 3140 V 40 w(v)m(ector)h(*)f Ft(x)p Fu(\))3350 3250 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_ctrmv)d Fu(\()p FD(CBLAS)p 1484 3250 V 40 w(UPLO)p 1782 3250 V 39 w(t)31 b Ft(Uplo)p FD(,)h(CBLAS)p 2458 3250 V 39 w(TRANSPOSE)p 3063 3250 V 39 w(t)565 3360 y Ft(TransA)p FD(,)g(CBLAS)p 1246 3360 V 40 w(DIA)m(G)p 1524 3360 V 41 w(t)f Ft(Diag)p FD(,)h(const)f(gsl)p 2240 3360 V 40 w(matrix)p 2545 3360 V 41 w(complex)p 2911 3360 V 40 w(\015oat)g(*)g Ft(A)p FD(,)565 3469 y(gsl)p 677 3469 V 41 w(v)m(ector)p 959 3469 V 41 w(complex)p 1325 3469 V 41 w(\015oat)g(*)g Ft(x)p Fu(\))3350 3579 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_ztrmv)d Fu(\()p FD(CBLAS)p 1484 3579 V 40 w(UPLO)p 1782 3579 V 39 w(t)31 b Ft(Uplo)p FD(,)h(CBLAS)p 2458 3579 V 39 w(TRANSPOSE)p 3063 3579 V 39 w(t)565 3688 y Ft(TransA)p FD(,)g(CBLAS)p 1246 3688 V 40 w(DIA)m(G)p 1524 3688 V 41 w(t)f Ft(Diag)p FD(,)h(const)f(gsl)p 2240 3688 V 40 w(matrix)p 2545 3688 V 41 w(complex)g(*)f Ft(A)p FD(,)565 3798 y(gsl)p 677 3798 V 41 w(v)m(ector)p 959 3798 V 41 w(complex)h(*)g Ft(x)p Fu(\))390 3908 y FK(These)38 b(functions)g(compute)g(the)g (matrix-v)m(ector)j(pro)s(duct)c FE(x)h FK(=)g FE(op)p FK(\()p FE(A)p FK(\))p FE(x)g FK(for)g(the)h(triangular)390 4017 y(matrix)k FD(A)p FK(,)i(where)d FE(op)p FK(\()p FE(A)p FK(\))k(=)f FE(A)p FK(,)h FE(A)1708 3984 y Fq(T)1760 4017 y FK(,)g FE(A)1899 3984 y Fq(H)2004 4017 y FK(for)c FD(T)-8 b(ransA)42 b FK(=)g FH(CblasNoTrans)p FK(,)g FH(CblasTrans)p FK(,)390 4127 y FH(CblasConjTrans)p FK(.)55 b(When)36 b FD(Uplo)41 b FK(is)c FH(CblasUpper)c FK(then)j(the)h(upp)s (er)d(triangle)k(of)f FD(A)f FK(is)g(used,)390 4236 y(and)46 b(when)g FD(Uplo)51 b FK(is)c FH(CblasLower)c FK(then)k(the)g(lo)m(w)m (er)g(triangle)h(of)f FD(A)g FK(is)f(used.)89 b(If)46 b FD(Diag)56 b FK(is)390 4346 y FH(CblasNonUnit)39 b FK(then)i(the)i(diagonal)g(of)f(the)h(matrix)f(is)g(used,)j(but)c(if)h FD(Diag)51 b FK(is)42 b FH(CblasUnit)390 4456 y FK(then)26 b(the)h(diagonal)g(elemen)m(ts)h(of)f(the)g(matrix)f FD(A)h FK(are)g(tak)m(en)g(as)g(unit)m(y)f(and)g(are)h(not)g (referenced.)3350 4729 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_strsv)d Fu(\()p FD(CBLAS)p 1484 4729 V 40 w(UPLO)p 1782 4729 V 39 w(t)31 b Ft(Uplo)p FD(,)h(CBLAS)p 2458 4729 V 39 w(TRANSPOSE)p 3063 4729 V 39 w(t)565 4839 y Ft(TransA)p FD(,)e(CBLAS)p 1244 4839 V 40 w(DIA)m(G)p 1522 4839 V 41 w(t)e Ft(Diag)p FD(,)i(const)f(gsl)p 2231 4839 V 41 w(matrix)p 2537 4839 V 40 w(\015oat)g(*)f Ft(A)p FD(,)h(gsl)p 3067 4839 V 40 w(v)m(ector)p 3348 4839 V 42 w(\015oat)g(*)f Ft(x)p Fu(\))3350 4949 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_dtrsv)d Fu(\()p FD(CBLAS)p 1484 4949 V 40 w(UPLO)p 1782 4949 V 39 w(t)31 b Ft(Uplo)p FD(,)h(CBLAS)p 2458 4949 V 39 w(TRANSPOSE)p 3063 4949 V 39 w(t)565 5058 y Ft(TransA)p FD(,)g(CBLAS)p 1246 5058 V 40 w(DIA)m(G)p 1524 5058 V 41 w(t)f Ft(Diag)p FD(,)h(const)f(gsl)p 2240 5058 V 40 w(matrix)g(*)g Ft(A)p FD(,)g(gsl)p 2866 5058 V 40 w(v)m(ector)h(*)f Ft(x)p Fu(\))3350 5168 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_ctrsv)d Fu(\()p FD(CBLAS)p 1484 5168 V 40 w(UPLO)p 1782 5168 V 39 w(t)31 b Ft(Uplo)p FD(,)h(CBLAS)p 2458 5168 V 39 w(TRANSPOSE)p 3063 5168 V 39 w(t)565 5277 y Ft(TransA)p FD(,)g(CBLAS)p 1246 5277 V 40 w(DIA)m(G)p 1524 5277 V 41 w(t)f Ft(Diag)p FD(,)h(const)f(gsl)p 2240 5277 V 40 w(matrix)p 2545 5277 V 41 w(complex)p 2911 5277 V 40 w(\015oat)g(*)g Ft(A)p FD(,)565 5387 y(gsl)p 677 5387 V 41 w(v)m(ector)p 959 5387 V 41 w(complex)p 1325 5387 V 41 w(\015oat)g(*)g Ft(x)p Fu(\))p eop end %%Page: 130 148 TeXDict begin 130 147 bop 150 -116 a FK(Chapter)30 b(13:)41 b(BLAS)31 b(Supp)s(ort)2360 b(130)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_ztrsv)d Fu(\()p FD(CBLAS)p 1484 299 28 4 v 40 w(UPLO)p 1782 299 V 39 w(t)31 b Ft(Uplo)p FD(,)h(CBLAS)p 2458 299 V 39 w(TRANSPOSE)p 3063 299 V 39 w(t)565 408 y Ft(TransA)p FD(,)g(CBLAS)p 1246 408 V 40 w(DIA)m(G)p 1524 408 V 41 w(t)f Ft(Diag)p FD(,)h(const)f(gsl)p 2240 408 V 40 w(matrix)p 2545 408 V 41 w(complex)g(*)f Ft(A)p FD(,)565 518 y(gsl)p 677 518 V 41 w(v)m(ector)p 959 518 V 41 w(complex)h(*)g Ft(x)p Fu(\))390 628 y FK(These)d (functions)f(compute)h FE(inv)s FK(\()p FE(op)p FK(\()p FE(A)p FK(\)\))p FE(x)h FK(for)f FD(x)p FK(,)g(where)g FE(op)p FK(\()p FE(A)p FK(\))e(=)f FE(A)p FK(,)j FE(A)2956 595 y Fq(T)3009 628 y FK(,)g FE(A)3130 595 y Fq(H)3221 628 y FK(for)g FD(T)-8 b(ransA)27 b FK(=)390 737 y FH(CblasNoTrans)p FK(,)32 b FH(CblasTrans)p FK(,)h FH(CblasConjTrans)p FK(.)50 b(When)34 b FD(Uplo)39 b FK(is)c FH(CblasUpper)d FK(then)i(the)390 847 y(upp)s(er)28 b(triangle)j(of)f FD(A)g FK(is)g(used,)g(and)f(when)g FD(Uplo)35 b FK(is)30 b FH(CblasLower)d FK(then)j(the)g(lo)m(w)m(er)i(triangle)f(of)390 956 y FD(A)k FK(is)h(used.)55 b(If)35 b FD(Diag)44 b FK(is)36 b FH(CblasNonUnit)c FK(then)j(the)g(diagonal)i(of)f(the)f (matrix)h(is)f(used,)h(but)f(if)390 1066 y FD(Diag)g FK(is)27 b FH(CblasUnit)c FK(then)j(the)h(diagonal)g(elemen)m(ts)h(of)e (the)g(matrix)h FD(A)f FK(are)h(tak)m(en)g(as)f(unit)m(y)h(and)390 1176 y(are)k(not)f(referenced.)3350 1541 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_ssymv)d Fu(\()p FD(CBLAS)p 1484 1541 V 40 w(UPLO)p 1782 1541 V 39 w(t)31 b Ft(Uplo)p FD(,)h(\015oat)f Ft(alpha)p FD(,)h(const)565 1650 y(gsl)p 677 1650 V 41 w(matrix)p 983 1650 V 40 w(\015oat)f(*)g Ft(A)p FD(,)g(const)g(gsl)p 1758 1650 V 40 w(v)m(ector)p 2039 1650 V 42 w(\015oat)g(*)g Ft(x)p FD(,)g(\015oat)g Ft(beta)p FD(,)g(gsl)p 3049 1650 V 41 w(v)m(ector)p 3331 1650 V 42 w(\015oat)g(*)f Ft(y)p Fu(\))3350 1760 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_dsymv)d Fu(\()p FD(CBLAS)p 1484 1760 V 40 w(UPLO)p 1782 1760 V 39 w(t)31 b Ft(Uplo)p FD(,)h(double)e Ft(alpha)p FD(,)i(const)565 1870 y(gsl)p 677 1870 V 41 w(matrix)e(*)h Ft(A)p FD(,)g(const)g(gsl)p 1541 1870 V 40 w(v)m(ector)h(*)f Ft(x)p FD(,)g(double)f Ft(beta)p FD(,)i(gsl)p 2702 1870 V 40 w(v)m(ector)g(*)f Ft(y)p Fu(\))390 1979 y FK(These)i(functions)g(compute)g(the)h (matrix-v)m(ector)h(pro)s(duct)d(and)h(sum)f FE(y)h FK(=)d FE(\013Ax)23 b FK(+)e FE(\014)5 b(y)37 b FK(for)c(the)390 2089 y(symmetric)24 b(matrix)g FD(A)p FK(.)38 b(Since)24 b(the)f(matrix)h FD(A)g FK(is)f(symmetric)h(only)g(its)g(upp)s(er)d (half)j(or)f(lo)m(w)m(er)i(half)390 2198 y(need)33 b(to)i(b)s(e)e (stored.)50 b(When)33 b FD(Uplo)39 b FK(is)34 b FH(CblasUpper)c FK(then)k(the)f(upp)s(er)f(triangle)j(and)e(diagonal)390 2308 y(of)d FD(A)f FK(are)h(used,)f(and)g(when)g FD(Uplo)34 b FK(is)c FH(CblasLower)d FK(then)i(the)h(lo)m(w)m(er)g(triangle)h(and) e(diagonal)i(of)390 2418 y FD(A)f FK(are)h(used.)3350 2783 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_chemv)d Fu(\()p FD(CBLAS)p 1484 2783 V 40 w(UPLO)p 1782 2783 V 39 w(t)31 b Ft(Uplo)p FD(,)h(const)f(gsl)p 2496 2783 V 40 w(complex)p 2861 2783 V 41 w(\015oat)565 2892 y Ft(alpha)p FD(,)h(const)f(gsl)p 1232 2892 V 41 w(matrix)p 1538 2892 V 40 w(complex)p 1903 2892 V 41 w(\015oat)g(*)g Ft(A)p FD(,)f(const)h(gsl)p 2678 2892 V 41 w(v)m(ector)p 2960 2892 V 42 w(complex)p 3327 2892 V 40 w(\015oat)g(*)g Ft(x)p FD(,)565 3002 y(const)g(gsl)p 915 3002 V 41 w(complex)p 1281 3002 V 40 w(\015oat)g Ft(beta)p FD(,)h(gsl)p 1899 3002 V 41 w(v)m(ector)p 2181 3002 V 41 w(complex)p 2547 3002 V 41 w(\015oat)f(*)g Ft(y)p Fu(\))3350 3112 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_zhemv)d Fu(\()p FD(CBLAS)p 1484 3112 V 40 w(UPLO)p 1782 3112 V 39 w(t)31 b Ft(Uplo)p FD(,)h(const)f(gsl)p 2496 3112 V 40 w(complex)g Ft(alpha)p FD(,)565 3221 y(const)g(gsl)p 915 3221 V 41 w(matrix)p 1221 3221 V 40 w(complex)g(*)g Ft(A)p FD(,)g(const)g(gsl)p 2145 3221 V 40 w(v)m(ector)p 2426 3221 V 42 w(complex)g(*)g Ft(x)p FD(,)f(const)h(gsl)p 3351 3221 V 41 w(complex)565 3331 y Ft(beta)p FD(,)h(gsl)p 942 3331 V 40 w(v)m(ector)p 1223 3331 V 42 w(complex)f(*)g Ft(y)p Fu(\))390 3440 y FK(These)i(functions)g(compute)g(the)h(matrix-v)m(ector)h(pro)s(duct) d(and)h(sum)f FE(y)h FK(=)d FE(\013Ax)23 b FK(+)e FE(\014)5 b(y)37 b FK(for)c(the)390 3550 y(hermitian)27 b(matrix)h FD(A)p FK(.)40 b(Since)28 b(the)f(matrix)h FD(A)g FK(is)f(hermitian)h (only)f(its)h(upp)s(er)d(half)j(or)f(lo)m(w)m(er)i(half)390 3660 y(need)k(to)i(b)s(e)e(stored.)50 b(When)33 b FD(Uplo)39 b FK(is)34 b FH(CblasUpper)c FK(then)k(the)f(upp)s(er)f(triangle)j(and) e(diagonal)390 3769 y(of)d FD(A)f FK(are)h(used,)f(and)g(when)g FD(Uplo)34 b FK(is)c FH(CblasLower)d FK(then)i(the)h(lo)m(w)m(er)g (triangle)h(and)e(diagonal)i(of)390 3879 y FD(A)d FK(are)f(used.)39 b(The)27 b(imaginary)h(elemen)m(ts)h(of)e(the)h(diagonal)h(are)f (automatically)i(assumed)c(to)j(b)s(e)390 3988 y(zero)i(and)f(are)h (not)f(referenced.)3350 4354 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_sger)d Fu(\()p FD(\015oat)31 b Ft(alpha)p FD(,)h(const)f(gsl)p 1994 4354 V 41 w(v)m(ector)p 2276 4354 V 41 w(\015oat)g(*)g Ft(x)p FD(,)g(const)565 4463 y(gsl)p 677 4463 V 41 w(v)m(ector)p 959 4463 V 41 w(\015oat)g(*)g Ft(y)p FD(,)g(gsl)p 1497 4463 V 41 w(matrix)p 1803 4463 V 40 w(\015oat)g(*)g Ft(A)p Fu(\))3350 4573 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_dger)d Fu(\()p FD(double)30 b Ft(alpha)p FD(,)i(const)f(gsl)p 2080 4573 V 40 w(v)m(ector)h(*)f Ft(x)p FD(,)g(const)g(gsl)p 2921 4573 V 40 w(v)m(ector)565 4682 y(*)g Ft(y)p FD(,)g(gsl)p 861 4682 V 40 w(matrix)g(*)g Ft(A)p Fu(\))3350 4792 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_cgeru)d Fu(\()p FD(const)31 b(gsl)p 1522 4792 V 41 w(complex)p 1888 4792 V 40 w(\015oat)h Ft(alpha)p FD(,)g(const)565 4902 y(gsl)p 677 4902 V 41 w(v)m(ector)p 959 4902 V 41 w(complex)p 1325 4902 V 41 w(\015oat)f(*)g Ft(x)p FD(,)g(const)g(gsl)p 2101 4902 V 40 w(v)m(ector)p 2382 4902 V 42 w(complex)p 2749 4902 V 41 w(\015oat)g(*)g Ft(y)p FD(,)565 5011 y(gsl)p 677 5011 V 41 w(matrix)p 983 5011 V 40 w(complex)p 1348 5011 V 41 w(\015oat)g(*)g Ft(A)p Fu(\))3350 5121 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_zgeru)d Fu(\()p FD(const)31 b(gsl)p 1522 5121 V 41 w(complex)g Ft(alpha)p FD(,)h(const)565 5230 y(gsl)p 677 5230 V 41 w(v)m(ector)p 959 5230 V 41 w(complex)f(*)g Ft(x)p FD(,)g(const)g(gsl)p 1884 5230 V 40 w(v)m(ector)p 2165 5230 V 42 w(complex)g(*)g Ft(y)p FD(,)g(gsl)p 2853 5230 V 40 w(matrix)p 3158 5230 V 41 w(complex)g(*)g Ft(A)p Fu(\))390 5340 y FK(These)f(functions)g (compute)h(the)f(rank-1)h(up)s(date)e FE(A)d FK(=)f FE(\013xy)2509 5307 y Fq(T)2582 5340 y FK(+)20 b FE(A)30 b FK(of)h(the)f(matrix)h FD(A)p FK(.)p eop end %%Page: 131 149 TeXDict begin 131 148 bop 150 -116 a FK(Chapter)30 b(13:)41 b(BLAS)31 b(Supp)s(ort)2360 b(131)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_cgerc)d Fu(\()p FD(const)31 b(gsl)p 1522 299 28 4 v 41 w(complex)p 1888 299 V 40 w(\015oat)h Ft(alpha)p FD(,)g(const)565 408 y(gsl)p 677 408 V 41 w(v)m(ector)p 959 408 V 41 w(complex)p 1325 408 V 41 w(\015oat)f(*)g Ft(x)p FD(,)g(const)g(gsl)p 2101 408 V 40 w(v)m(ector)p 2382 408 V 42 w(complex)p 2749 408 V 41 w(\015oat)g(*)g Ft(y)p FD(,)565 518 y(gsl)p 677 518 V 41 w(matrix)p 983 518 V 40 w(complex)p 1348 518 V 41 w(\015oat)g(*)g Ft(A)p Fu(\))3350 628 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_zgerc)d Fu(\()p FD(const)31 b(gsl)p 1522 628 V 41 w(complex)g Ft(alpha)p FD(,)h(const)565 737 y(gsl)p 677 737 V 41 w(v)m(ector)p 959 737 V 41 w(complex)f(*)g Ft(x)p FD(,)g(const)g(gsl)p 1884 737 V 40 w(v)m(ector)p 2165 737 V 42 w(complex)g(*)g Ft(y)p FD(,)g(gsl)p 2853 737 V 40 w(matrix)p 3158 737 V 41 w(complex)g(*)g Ft(A)p Fu(\))390 847 y FK(These)h(functions)g (compute)h(the)g(conjugate)h(rank-1)e(up)s(date)g FE(A)d FK(=)f FE(\013xy)2942 814 y Fq(H)3027 847 y FK(+)22 b FE(A)32 b FK(of)h(the)g(matrix)390 956 y FD(A)p FK(.)3350 1116 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_ssyr)d Fu(\()p FD(CBLAS)p 1432 1116 V 40 w(UPLO)p 1730 1116 V 39 w(t)31 b Ft(Uplo)p FD(,)h(\015oat)f Ft(alpha)p FD(,)h(const)565 1226 y(gsl)p 677 1226 V 41 w(v)m(ector)p 959 1226 V 41 w(\015oat)f(*)g Ft(x)p FD(,)g(gsl)p 1497 1226 V 41 w(matrix)p 1803 1226 V 40 w(\015oat)g(*)g Ft(A)p Fu(\))3350 1336 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_dsyr)d Fu(\()p FD(CBLAS)p 1432 1336 V 40 w(UPLO)p 1730 1336 V 39 w(t)31 b Ft(Uplo)p FD(,)h(double)d Ft(alpha)p FD(,)k(const)565 1445 y(gsl)p 677 1445 V 41 w(v)m(ector)f(*)e Ft(x)p FD(,)h(gsl)p 1280 1445 V 41 w(matrix)g(*)f Ft(A)p Fu(\))390 1555 y FK(These)20 b(functions)g(compute)h(the)f(symmetric)h(rank-1)f(up)s (date)g FE(A)25 b FK(=)g FE(\013xx)2885 1522 y Fq(T)2938 1555 y FK(+)p FE(A)c FK(of)f(the)h(symmetric)390 1664 y(matrix)32 b FD(A)p FK(.)44 b(Since)32 b(the)g(matrix)f FD(A)h FK(is)g(symmetric)f(only)h(its)g(upp)s(er)e(half)h(or)h(lo)m(w)m (er)g(half)g(need)f(to)390 1774 y(b)s(e)g(stored.)44 b(When)31 b FD(Uplo)37 b FK(is)31 b FH(CblasUpper)e FK(then)i(the)h (upp)s(er)d(triangle)k(and)e(diagonal)h(of)g FD(A)g FK(are)390 1884 y(used,)38 b(and)e(when)g FD(Uplo)41 b FK(is)c FH(CblasLower)d FK(then)j(the)g(lo)m(w)m(er)h(triangle)g(and)e(diagonal)i(of)f FD(A)g FK(are)390 1993 y(used.)3350 2153 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_cher)d Fu(\()p FD(CBLAS)p 1432 2153 V 40 w(UPLO)p 1730 2153 V 39 w(t)31 b Ft(Uplo)p FD(,)h(\015oat)f Ft(alpha)p FD(,)h(const)565 2263 y(gsl)p 677 2263 V 41 w(v)m(ector)p 959 2263 V 41 w(complex)p 1325 2263 V 41 w(\015oat)f(*)g Ft(x)p FD(,)g(gsl)p 1863 2263 V 40 w(matrix)p 2168 2263 V 41 w(complex)p 2534 2263 V 41 w(\015oat)g(*)f Ft(A)p Fu(\))3350 2372 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_zher)d Fu(\()p FD(CBLAS)p 1432 2372 V 40 w(UPLO)p 1730 2372 V 39 w(t)31 b Ft(Uplo)p FD(,)h(double)d Ft(alpha)p FD(,)k(const)565 2482 y(gsl)p 677 2482 V 41 w(v)m(ector)p 959 2482 V 41 w(complex)e(*)g Ft(x)p FD(,)g(gsl)p 1646 2482 V 41 w(matrix)p 1952 2482 V 40 w(complex)g(*)g Ft(A)p Fu(\))390 2591 y FK(These)23 b(functions)h(compute)g(the)f(hermitian)h(rank-1)g(up)s (date)f FE(A)i FK(=)g FE(\013xx)2880 2558 y Fq(H)2950 2591 y FK(+)7 b FE(A)23 b FK(of)h(the)g(hermitian)390 2701 y(matrix)33 b FD(A)p FK(.)50 b(Since)33 b(the)g(matrix)g FD(A)h FK(is)f(hermitian)g(only)g(its)h(upp)s(er)d(half)i(or)g(lo)m(w)m (er)h(half)f(need)g(to)390 2811 y(b)s(e)e(stored.)44 b(When)31 b FD(Uplo)37 b FK(is)31 b FH(CblasUpper)e FK(then)i(the)h (upp)s(er)d(triangle)k(and)e(diagonal)h(of)g FD(A)g FK(are)390 2920 y(used,)38 b(and)e(when)g FD(Uplo)41 b FK(is)c FH(CblasLower)d FK(then)j(the)g(lo)m(w)m(er)h(triangle)g(and)e(diagonal)i(of)f FD(A)g FK(are)390 3030 y(used.)j(The)30 b(imaginary)h(elemen)m(ts)h(of) e(the)h(diagonal)g(are)g(automatically)i(set)e(to)g(zero.)3350 3190 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_ssyr2)d Fu(\()p FD(CBLAS)p 1484 3190 V 40 w(UPLO)p 1782 3190 V 39 w(t)31 b Ft(Uplo)p FD(,)h(\015oat)f Ft(alpha)p FD(,)h(const)565 3299 y(gsl)p 677 3299 V 41 w(v)m(ector)p 959 3299 V 41 w(\015oat)f(*)g Ft(x)p FD(,)g(const)g(gsl)p 1735 3299 V 40 w(v)m(ector)p 2016 3299 V 42 w(\015oat)g(*)g Ft(y)p FD(,)g(gsl)p 2555 3299 V 40 w(matrix)p 2860 3299 V 41 w(\015oat)g(*)g Ft(A)p Fu(\))3350 3409 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_dsyr2)d Fu(\()p FD(CBLAS)p 1484 3409 V 40 w(UPLO)p 1782 3409 V 39 w(t)31 b Ft(Uplo)p FD(,)h(double)e Ft(alpha)p FD(,)i(const)565 3518 y(gsl)p 677 3518 V 41 w(v)m(ector)g(*)e Ft(x)p FD(,)h(const)g(gsl)p 1518 3518 V 41 w(v)m(ector)h(*)e Ft(y)p FD(,)h(gsl)p 2121 3518 V 41 w(matrix)g(*)f Ft(A)p Fu(\))390 3628 y FK(These)f(functions)g(compute)h(the)g(symmetric)g(rank-2)f(up)s(date)g FE(A)c FK(=)g FE(\013xy)2945 3595 y Fq(T)3016 3628 y FK(+)18 b FE(\013y)s(x)3263 3595 y Fq(T)3334 3628 y FK(+)h FE(A)29 b FK(of)h(the)390 3738 y(symmetric)24 b(matrix)g FD(A)p FK(.)38 b(Since)24 b(the)f(matrix)h FD(A)g FK(is)f(symmetric)h (only)g(its)g(upp)s(er)d(half)j(or)f(lo)m(w)m(er)i(half)390 3847 y(need)33 b(to)i(b)s(e)e(stored.)50 b(When)33 b FD(Uplo)39 b FK(is)34 b FH(CblasUpper)c FK(then)k(the)f(upp)s(er)f (triangle)j(and)e(diagonal)390 3957 y(of)d FD(A)f FK(are)h(used,)f(and) g(when)g FD(Uplo)34 b FK(is)c FH(CblasLower)d FK(then)i(the)h(lo)m(w)m (er)g(triangle)h(and)e(diagonal)i(of)390 4066 y FD(A)f FK(are)h(used.)3350 4226 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_cher2)d Fu(\()p FD(CBLAS)p 1484 4226 V 40 w(UPLO)p 1782 4226 V 39 w(t)31 b Ft(Uplo)p FD(,)h(const)f(gsl)p 2496 4226 V 40 w(complex)p 2861 4226 V 41 w(\015oat)565 4336 y Ft(alpha)p FD(,)h(const)f(gsl)p 1232 4336 V 41 w(v)m(ector)p 1514 4336 V 41 w(complex)p 1880 4336 V 41 w(\015oat)g(*)g Ft(x)p FD(,)g(const)g(gsl)p 2656 4336 V 40 w(v)m(ector)p 2937 4336 V 42 w(complex)p 3304 4336 V 41 w(\015oat)g(*)f Ft(y)p FD(,)565 4446 y(gsl)p 677 4446 V 41 w(matrix)p 983 4446 V 40 w(complex)p 1348 4446 V 41 w(\015oat)h(*)g Ft(A)p Fu(\))3350 4555 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_zher2)d Fu(\()p FD(CBLAS)p 1484 4555 V 40 w(UPLO)p 1782 4555 V 39 w(t)31 b Ft(Uplo)p FD(,)h(const)f(gsl)p 2496 4555 V 40 w(complex)g Ft(alpha)p FD(,)565 4665 y(const)f(gsl)p 914 4665 V 41 w(v)m(ector)p 1196 4665 V 41 w(complex)h(*)f Ft(x)p FD(,)g(const)g(gsl) p 2118 4665 V 40 w(v)m(ector)p 2399 4665 V 42 w(complex)g(*)g Ft(y)p FD(,)g(gsl)p 3084 4665 V 41 w(matrix)p 3390 4665 V 40 w(complex)565 4774 y(*)h Ft(A)p Fu(\))390 4884 y FK(These)c(functions)h(compute)g(the)f(hermitian)h(rank-2)g(up)s(date)f FE(A)e FK(=)g FE(\013xy)2904 4851 y Fq(H)2982 4884 y FK(+)15 b FE(\013)3126 4851 y Fp(\003)3164 4884 y FE(y)s(x)3264 4851 y Fq(H)3342 4884 y FK(+)g FE(A)27 b FK(of)h(the)390 4994 y(hermitian)f(matrix)h FD(A)p FK(.)40 b(Since)28 b(the)f(matrix)h FD(A)g FK(is)f(hermitian)h(only)f(its)h(upp)s(er)d (half)j(or)f(lo)m(w)m(er)i(half)390 5103 y(need)k(to)i(b)s(e)e(stored.) 50 b(When)33 b FD(Uplo)39 b FK(is)34 b FH(CblasUpper)c FK(then)k(the)f(upp)s(er)f(triangle)j(and)e(diagonal)390 5213 y(of)d FD(A)f FK(are)h(used,)f(and)g(when)g FD(Uplo)34 b FK(is)c FH(CblasLower)d FK(then)i(the)h(lo)m(w)m(er)g(triangle)h(and) e(diagonal)i(of)390 5322 y FD(A)f FK(are)h(used.)40 b(The)30 b(imaginary)h(elemen)m(ts)h(of)e(the)h(diagonal)h(are)e(automatically)k (set)c(to)i(zero.)p eop end %%Page: 132 150 TeXDict begin 132 149 bop 150 -116 a FK(Chapter)30 b(13:)41 b(BLAS)31 b(Supp)s(ort)2360 b(132)150 299 y Fy(13.1.3)63 b(Lev)m(el)40 b(3)3350 491 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_sgemm)d Fu(\()p FD(CBLAS)p 1484 491 28 4 v 40 w(TRANSPOSE)p 2090 491 V 38 w(t)31 b Ft(TransA)p FD(,)565 601 y(CBLAS)p 877 601 V 40 w(TRANSPOSE)p 1483 601 V 38 w(t)e Ft(TransB)p FD(,)i(\015oat)e Ft(alpha)p FD(,)i(const)f(gsl)p 2817 601 V 40 w(matrix)p 3122 601 V 40 w(\015oat)g(*)f Ft(A)p FD(,)g(const)565 710 y(gsl)p 677 710 V 41 w(matrix)p 983 710 V 40 w(\015oat)i(*)g Ft(B)p FD(,)g(\015oat)g Ft(beta)p FD(,)h(gsl)p 1992 710 V 40 w(matrix)p 2297 710 V 41 w(\015oat)f(*)f Ft(C)p Fu(\))3350 820 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_dgemm)d Fu(\()p FD(CBLAS)p 1484 820 V 40 w(TRANSPOSE)p 2090 820 V 38 w(t)31 b Ft(TransA)p FD(,)565 930 y(CBLAS)p 877 930 V 40 w(TRANSPOSE)p 1483 930 V 38 w(t)g Ft(TransB)p FD(,)h(double)e Ft(alpha)p FD(,)i(const)f(gsl)p 2910 930 V 41 w(matrix)f(*)h Ft(A)p FD(,)g(const)565 1039 y(gsl)p 677 1039 V 41 w(matrix)f(*)h Ft(B)p FD(,)g(double)f Ft(beta)p FD(,)i(gsl)p 1861 1039 V 40 w(matrix)f(*)g Ft(C)p Fu(\))3350 1149 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_cgemm)d Fu(\()p FD(CBLAS)p 1484 1149 V 40 w(TRANSPOSE)p 2090 1149 V 38 w(t)31 b Ft(TransA)p FD(,)565 1258 y(CBLAS)p 877 1258 V 40 w(TRANSPOSE)p 1483 1258 V 38 w(t)g Ft(TransB)p FD(,)h(const)f(gsl)p 2300 1258 V 41 w(complex)p 2666 1258 V 40 w(\015oat)g Ft(alpha)p FD(,)h(const)565 1368 y(gsl)p 677 1368 V 41 w(matrix)p 983 1368 V 40 w(complex)p 1348 1368 V 41 w(\015oat)f(*)g Ft(A)p FD(,)g(const)f(gsl)p 2123 1368 V 41 w(matrix)p 2429 1368 V 40 w(complex)p 2794 1368 V 41 w(\015oat)h(*)g Ft(B)p FD(,)g(const)565 1478 y(gsl)p 677 1478 V 41 w(complex)p 1043 1478 V 40 w(\015oat)h Ft(beta)p FD(,)f(gsl)p 1661 1478 V 41 w(matrix)p 1967 1478 V 40 w(complex)p 2332 1478 V 41 w(\015oat)g(*)g Ft(C)p Fu(\))3350 1587 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_zgemm)d Fu(\()p FD(CBLAS)p 1484 1587 V 40 w(TRANSPOSE)p 2090 1587 V 38 w(t)31 b Ft(TransA)p FD(,)565 1697 y(CBLAS)p 877 1697 V 40 w(TRANSPOSE)p 1483 1697 V 38 w(t)g Ft(TransB)p FD(,)h(const)f(gsl) p 2300 1697 V 41 w(complex)g Ft(alpha)p FD(,)h(const)565 1806 y(gsl)p 677 1806 V 41 w(matrix)p 983 1806 V 40 w(complex)e(*)f Ft(A)p FD(,)h(const)g(gsl)p 1902 1806 V 40 w(matrix)p 2207 1806 V 41 w(complex)f(*)h Ft(B)p FD(,)g(const)f(gsl)p 3126 1806 V 41 w(complex)h Ft(beta)p FD(,)565 1916 y(gsl)p 677 1916 V 41 w(matrix)p 983 1916 V 40 w(complex)h(*)g Ft(C)p Fu(\))390 2026 y FK(These)24 b(functions)g(compute)g(the)g (matrix-matrix)i(pro)s(duct)c(and)i(sum)f FE(C)32 b FK(=)25 b FE(\013op)p FK(\()p FE(A)p FK(\))p FE(op)p FK(\()p FE(B)5 b FK(\))j(+)g FE(\014)d(C)390 2135 y FK(where)79 b FE(op)p FK(\()p FE(A)p FK(\))107 b(=)g FE(A)p FK(,)92 b FE(A)1468 2102 y Fq(T)1520 2135 y FK(,)g FE(A)1705 2102 y Fq(H)1847 2135 y FK(for)79 b FD(T)-8 b(ransA)79 b FK(=)g FH(CblasNoTrans)p FK(,)88 b FH(CblasTrans)p FK(,)390 2245 y FH(CblasConjTrans)26 b FK(and)k(similarly)h(for)f(the)h (parameter)g FD(T)-8 b(ransB)p FK(.)3350 2422 y([F)g(unction])-3599 b Fv(int)53 b(gsl_blas_ssymm)d Fu(\()p FD(CBLAS)p 1484 2422 V 40 w(SIDE)p 1739 2422 V 39 w(t)31 b Ft(Side)p FD(,)h(CBLAS)p 2415 2422 V 39 w(UPLO)p 2712 2422 V 40 w(t)f Ft(Uplo)p FD(,)565 2532 y(\015oat)g Ft(alpha)p FD(,)h(const)f(gsl)p 1439 2532 V 41 w(matrix)p 1745 2532 V 40 w(\015oat)g(*)g Ft(A)p FD(,)g(const)g(gsl)p 2520 2532 V 40 w(matrix)p 2825 2532 V 41 w(\015oat)g(*)f Ft(B)p FD(,)h(\015oat)g Ft(beta)p FD(,)565 2642 y(gsl)p 677 2642 V 41 w(matrix)p 983 2642 V 40 w(\015oat)g(*)g Ft(C)p Fu(\))3350 2751 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_dsymm)d Fu(\()p FD(CBLAS)p 1484 2751 V 40 w(SIDE)p 1739 2751 V 39 w(t)31 b Ft(Side)p FD(,)h(CBLAS)p 2415 2751 V 39 w(UPLO)p 2712 2751 V 40 w(t)f Ft(Uplo)p FD(,)565 2861 y(double)f Ft(alpha)p FD(,)i(const)f(gsl)p 1525 2861 V 41 w(matrix)f(*)h Ft(A)p FD(,)g(const)g(gsl)p 2389 2861 V 40 w(matrix)g(*)g Ft(B)p FD(,)g(double)f Ft(beta)p FD(,)565 2970 y(gsl)p 677 2970 V 41 w(matrix)g(*)h Ft(C)p Fu(\))3350 3080 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_csymm)d Fu(\()p FD(CBLAS)p 1484 3080 V 40 w(SIDE)p 1739 3080 V 39 w(t)31 b Ft(Side)p FD(,)h(CBLAS)p 2415 3080 V 39 w(UPLO)p 2712 3080 V 40 w(t)f Ft(Uplo)p FD(,)565 3190 y(const)g(gsl)p 915 3190 V 41 w(complex)p 1281 3190 V 40 w(\015oat)g Ft(alpha)p FD(,)h(const)f(gsl)p 2189 3190 V 41 w(matrix)p 2495 3190 V 40 w(complex)p 2860 3190 V 41 w(\015oat)g(*)g Ft(A)p FD(,)g(const)565 3299 y(gsl)p 677 3299 V 41 w(matrix)p 983 3299 V 40 w(complex)p 1348 3299 V 41 w(\015oat)g(*)g Ft(B)p FD(,)g(const)f(gsl)p 2123 3299 V 41 w(complex)p 2489 3299 V 41 w(\015oat)h Ft(beta)p FD(,)565 3409 y(gsl)p 677 3409 V 41 w(matrix)p 983 3409 V 40 w(complex)p 1348 3409 V 41 w(\015oat)g(*)g Ft(C)p Fu(\))3350 3518 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_zsymm)d Fu(\()p FD(CBLAS)p 1484 3518 V 40 w(SIDE)p 1739 3518 V 39 w(t)31 b Ft(Side)p FD(,)h(CBLAS)p 2415 3518 V 39 w(UPLO)p 2712 3518 V 40 w(t)f Ft(Uplo)p FD(,)565 3628 y(const)g(gsl)p 915 3628 V 41 w(complex)g Ft(alpha)p FD(,)h(const)f(gsl)p 1973 3628 V 40 w(matrix)p 2278 3628 V 41 w(complex)g(*)f Ft(A)p FD(,)h(const)565 3738 y(gsl)p 677 3738 V 41 w(matrix)p 983 3738 V 40 w(complex)g(*)g Ft(B)p FD(,)g(const)g(gsl)p 1907 3738 V 40 w(complex)g Ft(beta)p FD(,)h(gsl)p 2674 3738 V 41 w(matrix)p 2980 3738 V 40 w(complex)f(*)g Ft(C)p Fu(\))390 3847 y FK(These)38 b(functions)g(compute)g(the)h (matrix-matrix)g(pro)s(duct)e(and)h(sum)f FE(C)45 b FK(=)38 b FE(\013AB)30 b FK(+)25 b FE(\014)5 b(C)45 b FK(for)390 3957 y FD(Side)36 b FK(is)c FH(CblasLeft)d FK(and)i FE(C)i FK(=)27 b FE(\013B)5 b(A)21 b FK(+)g FE(\014)5 b(C)38 b FK(for)31 b FD(Side)36 b FK(is)c FH(CblasRight)p FK(,)d(where)i(the)h (matrix)g FD(A)390 4066 y FK(is)h(symmetric.)47 b(When)32 b FD(Uplo)38 b FK(is)32 b FH(CblasUpper)e FK(then)i(the)h(upp)s(er)e (triangle)i(and)f(diagonal)i(of)f FD(A)390 4176 y FK(are)27 b(used,)f(and)g(when)f FD(Uplo)31 b FK(is)c FH(CblasLower)c FK(then)j(the)h(lo)m(w)m(er)g(triangle)h(and)d(diagonal)j(of)e FD(A)h FK(are)390 4285 y(used.)3350 4463 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_chemm)d Fu(\()p FD(CBLAS)p 1484 4463 V 40 w(SIDE)p 1739 4463 V 39 w(t)31 b Ft(Side)p FD(,)h(CBLAS)p 2415 4463 V 39 w(UPLO)p 2712 4463 V 40 w(t)f Ft(Uplo)p FD(,)565 4573 y(const)g(gsl)p 915 4573 V 41 w(complex)p 1281 4573 V 40 w(\015oat)g Ft(alpha)p FD(,)h(const)f(gsl)p 2189 4573 V 41 w(matrix)p 2495 4573 V 40 w(complex)p 2860 4573 V 41 w(\015oat)g(*)g Ft(A)p FD(,)g(const)565 4682 y(gsl)p 677 4682 V 41 w(matrix)p 983 4682 V 40 w(complex)p 1348 4682 V 41 w(\015oat)g(*)g Ft(B)p FD(,)g(const)f(gsl)p 2123 4682 V 41 w(complex)p 2489 4682 V 41 w(\015oat)h Ft(beta)p FD(,)565 4792 y(gsl)p 677 4792 V 41 w(matrix)p 983 4792 V 40 w(complex)p 1348 4792 V 41 w(\015oat)g(*)g Ft(C)p Fu(\))3350 4902 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_zhemm)d Fu(\()p FD(CBLAS)p 1484 4902 V 40 w(SIDE)p 1739 4902 V 39 w(t)31 b Ft(Side)p FD(,)h(CBLAS)p 2415 4902 V 39 w(UPLO)p 2712 4902 V 40 w(t)f Ft(Uplo)p FD(,)565 5011 y(const)g(gsl)p 915 5011 V 41 w(complex)g Ft(alpha)p FD(,)h(const)f(gsl)p 1973 5011 V 40 w(matrix)p 2278 5011 V 41 w(complex)g(*)f Ft(A)p FD(,)h(const)565 5121 y(gsl)p 677 5121 V 41 w(matrix)p 983 5121 V 40 w(complex)g(*)g Ft(B)p FD(,)g(const)g(gsl)p 1907 5121 V 40 w(complex)g Ft(beta)p FD(,)h(gsl)p 2674 5121 V 41 w(matrix)p 2980 5121 V 40 w(complex)f(*)g Ft(C)p Fu(\))390 5230 y FK(These)38 b(functions)g(compute)g(the)h (matrix-matrix)g(pro)s(duct)e(and)h(sum)f FE(C)45 b FK(=)38 b FE(\013AB)30 b FK(+)25 b FE(\014)5 b(C)45 b FK(for)390 5340 y FD(Side)36 b FK(is)c FH(CblasLeft)d FK(and)i FE(C)i FK(=)27 b FE(\013B)5 b(A)21 b FK(+)g FE(\014)5 b(C)38 b FK(for)31 b FD(Side)36 b FK(is)c FH(CblasRight)p FK(,)d(where)i(the)h (matrix)g FD(A)p eop end %%Page: 133 151 TeXDict begin 133 150 bop 150 -116 a FK(Chapter)30 b(13:)41 b(BLAS)31 b(Supp)s(ort)2360 b(133)390 299 y(is)34 b(hermitian.)53 b(When)35 b FD(Uplo)k FK(is)34 b FH(CblasUpper)e FK(then)i(the)h(upp)s (er)d(triangle)k(and)e(diagonal)h(of)g FD(A)390 408 y FK(are)27 b(used,)f(and)g(when)f FD(Uplo)31 b FK(is)c FH(CblasLower)c FK(then)j(the)h(lo)m(w)m(er)g(triangle)h(and)d (diagonal)j(of)e FD(A)h FK(are)390 518 y(used.)40 b(The)30 b(imaginary)h(elemen)m(ts)h(of)e(the)h(diagonal)g(are)g(automatically)i (set)e(to)g(zero.)3350 847 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_strmm)d Fu(\()p FD(CBLAS)p 1484 847 28 4 v 40 w(SIDE)p 1739 847 V 39 w(t)31 b Ft(Side)p FD(,)h(CBLAS)p 2415 847 V 39 w(UPLO)p 2712 847 V 40 w(t)f Ft(Uplo)p FD(,)565 956 y(CBLAS)p 877 956 V 40 w(TRANSPOSE)p 1483 956 V 38 w(t)g Ft(TransA)p FD(,)h(CBLAS)p 2262 956 V 40 w(DIA)m(G)p 2540 956 V 41 w(t)f Ft(Diag)p FD(,)g(\015oat)g Ft(alpha)p FD(,)h(const)565 1066 y(gsl)p 677 1066 V 41 w(matrix)p 983 1066 V 40 w(\015oat)f(*)g Ft(A)p FD(,)g(gsl)p 1520 1066 V 40 w(matrix)p 1825 1066 V 41 w(\015oat)g(*)g Ft(B)p Fu(\))3350 1176 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_dtrmm)d Fu(\()p FD(CBLAS)p 1484 1176 V 40 w(SIDE)p 1739 1176 V 39 w(t)31 b Ft(Side)p FD(,)h(CBLAS)p 2415 1176 V 39 w(UPLO)p 2712 1176 V 40 w(t)f Ft(Uplo)p FD(,)565 1285 y(CBLAS)p 877 1285 V 40 w(TRANSPOSE)p 1483 1285 V 38 w(t)g Ft(TransA)p FD(,)h(CBLAS)p 2262 1285 V 40 w(DIA)m(G)p 2540 1285 V 41 w(t)f Ft(Diag)p FD(,)g(double)f Ft(alpha)p FD(,)i(const)565 1395 y(gsl)p 677 1395 V 41 w(matrix)e(*)h Ft(A)p FD(,)g(gsl)p 1303 1395 V 41 w(matrix)f(*)h Ft(B)p Fu(\))3350 1504 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_ctrmm)d Fu(\()p FD(CBLAS)p 1484 1504 V 40 w(SIDE)p 1739 1504 V 39 w(t)31 b Ft(Side)p FD(,)h(CBLAS)p 2415 1504 V 39 w(UPLO)p 2712 1504 V 40 w(t)f Ft(Uplo)p FD(,)565 1614 y(CBLAS)p 877 1614 V 40 w(TRANSPOSE)p 1483 1614 V 38 w(t)g Ft(TransA)p FD(,)h(CBLAS)p 2262 1614 V 40 w(DIA)m(G)p 2540 1614 V 41 w(t)f Ft(Diag)p FD(,)g(const)565 1724 y(gsl)p 677 1724 V 41 w(complex)p 1043 1724 V 40 w(\015oat)h Ft(alpha)p FD(,)g(const)e(gsl)p 1951 1724 V 41 w(matrix)p 2257 1724 V 40 w(complex)p 2622 1724 V 41 w(\015oat)h(*)g Ft(A)p FD(,)565 1833 y(gsl)p 677 1833 V 41 w(matrix)p 983 1833 V 40 w(complex)p 1348 1833 V 41 w(\015oat)g(*)g Ft(B)p Fu(\))3350 1943 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_ztrmm)d Fu(\()p FD(CBLAS)p 1484 1943 V 40 w(SIDE)p 1739 1943 V 39 w(t)31 b Ft(Side)p FD(,)h(CBLAS)p 2415 1943 V 39 w(UPLO)p 2712 1943 V 40 w(t)f Ft(Uplo)p FD(,)565 2052 y(CBLAS)p 877 2052 V 40 w(TRANSPOSE)p 1483 2052 V 38 w(t)g Ft(TransA)p FD(,)h(CBLAS)p 2262 2052 V 40 w(DIA)m(G)p 2540 2052 V 41 w(t)f Ft(Diag)p 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3367 y({)485 3477 y(double)g(a[])f(=)i({)f (0.11,)g(0.12,)f(0.13,)1201 3587 y(0.21,)h(0.22,)f(0.23)h(};)485 3806 y(double)g(b[])f(=)i({)f(1011,)g(1012,)1201 3915 y(1021,)g(1022,)1201 4025 y(1031,)g(1032)f(};)485 4244 y(double)h(c[])f(=)i({)f(0.00,)g(0.00,)1201 4354 y(0.00,)g(0.00)f(};) 485 4573 y(gsl_matrix_view)e(A)k(=)f(gsl_matrix_view_array\(a,)41 b(2,)47 b(3\);)485 4682 y(gsl_matrix_view)d(B)k(=)f (gsl_matrix_view_array\(b,)41 b(3,)47 b(2\);)485 4792 y(gsl_matrix_view)d(C)k(=)f(gsl_matrix_view_array\(c,)41 b(2,)47 b(2\);)485 5011 y(/*)h(Compute)d(C)j(=)f(A)h(B)f(*/)485 5230 y(gsl_blas_dgemm)d(\(CblasNoTrans,)g(CblasNoTrans,)1249 5340 y(1.0,)j(&A.matrix,)e(&B.matrix,)p eop end %%Page: 136 154 TeXDict begin 136 153 bop 150 -116 a FK(Chapter)30 b(13:)41 b(BLAS)31 b(Supp)s(ort)2360 b(136)1249 299 y FH(0.0,)47 b(&C.matrix\);)485 518 y(printf)g(\("[)f(\045g,)h(\045g\\n",)f(c[0],)h (c[1]\);)485 628 y(printf)g(\(")94 b(\045g,)47 b(\045g)h(]\\n",)e (c[2],)g(c[3]\);)485 847 y(return)h(0;)390 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b(bac)m(k-substitution.)41 b(Note)32 b(that)f(the)g FE(LU)40 b FK(decomp)s(osition)31 b(is)f(v)-5 b(alid)31 b(for)f(singular)g (matrices.)3350 2669 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_LU_decomp)f Fu(\()p FD(gsl)p 1598 2669 28 4 v 41 w(matrix)30 b(*)h Ft(A)p FD(,)g(gsl)p 2224 2669 V 41 w(p)s(erm)m(utation)f(*)h Ft(p)p FD(,)g(in)m(t)g(*)565 2778 y Ft(signum)p Fu(\))3350 2888 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_complex_LU)q(_dec)q(omp)f Fu(\()p FD(gsl)p 2016 2888 V 41 w(matrix)p 2322 2888 V 40 w(complex)32 b(*)e Ft(A)p FD(,)565 2997 y(gsl)p 677 2997 V 41 w(p)s(erm)m(utation)g (*)h Ft(p)p FD(,)g(in)m(t)g(*)f Ft(signum)p Fu(\))390 3107 y FK(These)e(functions)g(factorize)i(the)f(square)f(matrix)h FD(A)f FK(in)m(to)i(the)e FE(LU)39 b FK(decomp)s(osition)29 b FE(P)13 b(A)25 b FK(=)g FE(LU)10 b FK(.)390 3217 y(On)29 b(output)g(the)g(diagonal)i(and)e(upp)s(er)e(triangular)j(part)g(of)f (the)h(input)f(matrix)g FD(A)h FK(con)m(tain)h(the)390 3326 y(matrix)39 b 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(gsl_linalg_QR_unpack)f Fu(\()p FD(const)31 b(gsl)p 1836 3114 V 41 w(matrix)f(*)h Ft(QR)p FD(,)g(const)g(gsl)p 2752 3114 V 41 w(v)m(ector)h(*)565 3224 y Ft(tau)p FD(,)g(gsl)p 890 3224 V 40 w(matrix)f(*)g Ft(Q)p FD(,)f(gsl)p 1515 3224 V 41 w(matrix)h(*)f Ft(R)p Fu(\))390 3333 y FK(This)f(function)g (unpac)m(ks)h(the)g(enco)s(ded)f FE(QR)h FK(decomp)s(osition)h(\()p FD(QR)p FK(,)p FD(tau)p FK(\))f(in)m(to)h(the)f(matrices)h FD(Q)390 3443 y FK(and)f FD(R)p FK(,)g(where)g FD(Q)35 b FK(is)30 b FE(M)10 b FK(-b)m(y-)p FE(M)41 b FK(and)30 b FD(R)g FK(is)h FE(M)10 b FK(-b)m(y-)p FE(N)g FK(.)3350 3611 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_QR_QRsolve)f Fu(\()p FD(gsl)p 1650 3611 V 41 w(matrix)31 b(*)f Ft(Q)p FD(,)h(gsl)p 2276 3611 V 41 w(matrix)g(*)f Ft(R)p FD(,)h(const)565 3721 y(gsl)p 677 3721 V 41 w(v)m(ector)h(*)e Ft(b)p FD(,)h(gsl)p 1280 3721 V 41 w(v)m(ector)h(*)f Ft(x)p Fu(\))390 3830 y FK(This)43 b(function)g(solv)m(es)i(the)f(system)g FE(R)q(x)j FK(=)h FE(Q)2097 3797 y Fq(T)2149 3830 y FE(b)43 b FK(for)h FD(x)p FK(.)81 b(It)44 b(can)g(b)s(e)f(used)g(when)f(the)i FE(QR)390 3940 y FK(decomp)s(osition)31 b(of)g(a)f(matrix)h(is)f(a)m(v) -5 b(ailable)33 b(in)d(unpac)m(k)m(ed)h(form)f(as)g(\()p FD(Q)p FK(,)h FD(R)p FK(\).)3350 4109 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_QR_update)f Fu(\()p FD(gsl)p 1598 4109 V 41 w(matrix)30 b(*)g Ft(Q)p FD(,)h(gsl)p 2223 4109 V 40 w(matrix)g(*)f Ft(R)p FD(,)h(gsl)p 2848 4109 V 40 w(v)m(ector)h(*)565 4218 y Ft(w)p FD(,)f(const)g(gsl)p 1023 4218 V 40 w(v)m(ector)h(*)f Ft(v)p Fu(\))390 4328 y FK(This)h(function)g(p)s(erforms)f(a)i(rank-1)g(up)s(date)f FE(w)r(v)2128 4295 y Fq(T)2214 4328 y FK(of)h(the)g FE(QR)g FK(decomp)s(osition)g(\()p FD(Q)p FK(,)h FD(R)p FK(\).)47 b(The)390 4437 y(up)s(date)27 b(is)h(giv)m(en)h(b)m(y)f FE(Q)1213 4404 y Fp(0)1236 4437 y FE(R)1306 4404 y Fp(0)1354 4437 y FK(=)d FE(Q)p FK(\()p FE(R)16 b FK(+)f FE(w)r(v)1842 4404 y Fq(T)1895 4437 y FK(\))29 b(where)e(the)h(output)g(matrices)h 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FD(gsl)p 1702 3057 28 4 v 41 w(matrix)31 b(*)g Ft(A)p FD(,)g(gsl)p 2329 3057 V 40 w(v)m(ector)h(*)f Ft(tau)p FD(,)565 3167 y(gsl)p 677 3167 V 41 w(p)s(erm)m(utation)f(*)h Ft(p)p FD(,)g(in)m(t)g(*)f Ft(signum)p FD(,)j(gsl)p 2112 3167 V 40 w(v)m(ector)f(*)f Ft(norm)p Fu(\))390 3276 y FK(This)36 b(function)g(factorizes)i(the)f FE(M)10 b FK(-b)m(y-)p FE(N)46 b FK(matrix)37 b FD(A)g FK(in)m(to)g(the)g FE(QR)q(P)2883 3243 y Fq(T)2971 3276 y FK(decomp)s(osition)g FE(A)e FK(=)390 3386 y FE(QR)q(P)603 3353 y Fq(T)655 3386 y FK(.)j(On)23 b(output)f(the)i(diagonal)g(and)f(upp)s(er)e(triangular)j (part)f(of)g(the)h(input)e(matrix)i(con)m(tain)390 3496 y(the)j(matrix)h FE(R)q FK(.)39 b(The)27 b(p)s(erm)m(utation)g(matrix)h FE(P)40 b FK(is)27 b(stored)g(in)g(the)h(p)s(erm)m(utation)f FD(p)p FK(.)39 b(The)27 b(sign)g(of)390 3605 y(the)33 b(p)s(erm)m(utation)g(is)g(giv)m(en)h(b)m(y)f FD(sign)m(um)p FK(.)49 b(It)33 b(has)f(the)i(v)-5 b(alue)33 b(\()p FI(\000)p FK(1\))2738 3572 y Fq(n)2784 3605 y FK(,)h(where)f FE(n)f FK(is)h(the)g(n)m(um)m(b)s(er)390 3715 y(of)40 b(in)m(terc)m(hanges)h (in)f(the)g(p)s(erm)m(utation.)69 b(The)39 b(v)m(ector)i FD(tau)f FK(and)f(the)h(columns)g(of)g(the)g(lo)m(w)m(er)390 3824 y(triangular)23 b(part)g(of)h(the)f(matrix)g FD(A)h FK(con)m(tain)g(the)f(Householder)g(co)s(e\016cien)m(ts)i(and)e(v)m (ectors)h(whic)m(h)390 3934 y(enco)s(de)32 b(the)g(orthogonal)i(matrix) e FD(Q)p FK(.)46 b(The)31 b(v)m(ector)j FD(tau)e FK(m)m(ust)g(b)s(e)f (of)i(length)f FE(k)f FK(=)d(min\()p FE(M)5 b(;)15 b(N)10 b FK(\).)390 4043 y(The)22 b(matrix)h FE(Q)f FK(is)g(related)h(to)h (these)e(comp)s(onen)m(ts)h(b)m(y)-8 b(,)24 b FE(Q)i FK(=)e FE(Q)2552 4057 y Fq(k)2593 4043 y FE(:::Q)2740 4057 y FB(2)2778 4043 y FE(Q)2850 4057 y FB(1)2909 4043 y FK(where)e FE(Q)3236 4057 y Fq(i)3289 4043 y FK(=)j FE(I)11 b FI(\000)t FE(\034)3551 4057 y Fq(i)3579 4043 y FE(v)3623 4057 y Fq(i)3650 4043 y FE(v)3697 4010 y Fq(T)3694 4066 y(i)390 4153 y FK(and)27 b FE(v)608 4167 y Fq(i)664 4153 y FK(is)g(the)h(Householder)g(v)m(ector)i FE(v)1737 4167 y Fq(i)1790 4153 y FK(=)25 b(\(0)p FE(;)15 b(:::;)g FK(1)p FE(;)g(A)p FK(\()p FE(i)g FK(+)g(1)p FE(;)g(i)p FK(\))p FE(;)g(A)p FK(\()p FE(i)g FK(+)g(2)q FE(;)g(i)p FK(\))q FE(;)g(:::)q(;)g(A)p FK(\()q FE(m;)g(i)p FK(\))q(\).)46 b(This)390 4263 y(is)34 b(the)g(same)h(storage)g(sc)m (heme)g(as)g(used)e(b)m(y)h FC(lap)-6 b(a)n(ck)p FK(.)50 b(The)33 b(v)m(ector)j FD(norm)d FK(is)i(a)f(w)m(orkspace)h(of)390 4372 y(length)c FD(N)40 b FK(used)30 b(for)g(column)g(piv)m(oting.)390 4540 y(The)36 b(algorithm)i(used)d(to)j(p)s(erform)d(the)h(decomp)s (osition)i(is)e(Householder)h(QR)f(with)g(column)390 4650 y(piv)m(oting)c(\(Golub)e(&)g(V)-8 b(an)31 b(Loan,)g FD(Matrix)g(Computations)p FK(,)g(Algorithm)g(5.4.1\).)3350 4902 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_QRPT_decom)q(p2) f Fu(\()p FD(const)31 b(gsl)p 1993 4902 V 40 w(matrix)g(*)g Ft(A)p FD(,)g(gsl)p 2619 4902 V 40 w(matrix)g(*)g Ft(q)p FD(,)565 5011 y(gsl)p 677 5011 V 41 w(matrix)f(*)h Ft(r)p FD(,)g(gsl)p 1303 5011 V 41 w(v)m(ector)h(*)e Ft(tau)p FD(,)i(gsl)p 2011 5011 V 40 w(p)s(erm)m(utation)f(*)g Ft(p)p FD(,)f(in)m(t)h(*)g Ft(signum)p FD(,)h(gsl)p 3445 5011 V 41 w(v)m(ector)565 5121 y(*)f Ft(norm)p Fu(\))390 5230 y FK(This)38 b(function)g(factorizes)j(the)e(matrix)g FD(A)g FK(in)m(to)g(the)g(decomp)s(osition)g FE(A)h FK(=)e FE(QR)q(P)3351 5197 y Fq(T)3442 5230 y FK(without)390 5340 y(mo)s(difying)30 b FD(A)g FK(itself)h(and)f(storing)h(the)g (output)f(in)g(the)g(separate)i(matrices)f FD(q)h FK(and)e FD(r)p FK(.)p eop end %%Page: 142 160 TeXDict begin 142 159 bop 150 -116 a FK(Chapter)30 b(14:)41 b(Linear)31 b(Algebra)2359 b(142)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_QRPT_solve)f Fu(\()p FD(const)31 b(gsl)p 1888 299 28 4 v 41 w(matrix)g(*)f Ft(QR)p FD(,)h(const)g(gsl)p 2804 299 V 41 w(v)m(ector)h(*)565 408 y Ft(tau)p FD(,)g(const)e(gsl)p 1127 408 V 41 w(p)s(erm)m(utation)g(*)h Ft(p)p FD(,)g(const)g(gsl)p 2216 408 V 41 w(v)m(ector)h(*)e Ft(b)p FD(,)h(gsl)p 2819 408 V 41 w(v)m(ector)h(*)e Ft(x)p Fu(\))390 518 y FK(This)38 b(function)h(solv)m(es)h(the)f(square)f(system)h FE(Ax)h FK(=)f FE(b)f FK(using)h(the)g FE(QR)q(P)2979 485 y Fq(T)3069 518 y FK(decomp)s(osition)h(of)390 628 y FE(A)31 b FK(held)g(in)g(\()p FD(QR)p FK(,)g FD(tau)p FK(,)h FD(p)s FK(\))e(whic)m(h)h(m)m(ust)g(ha)m (v)m(e)h(b)s(een)e(computed)h(previously)g(b)m(y)g FH(gsl_linalg_)390 737 y(QRPT_decomp)p FK(.)3350 978 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_QRPT_svx)e Fu(\()p FD(const)32 b(gsl)p 1784 978 V 40 w(matrix)f(*)g Ft(QR)p FD(,)g(const)g(gsl)p 2700 978 V 40 w(v)m(ector)h(*)565 1088 y Ft(tau)p FD(,)g(const)e(gsl)p 1127 1088 V 41 w(p)s(erm)m(utation)g(*)h Ft(p)p FD(,)g(gsl)p 1978 1088 V 41 w(v)m(ector)h(*)e Ft(x)p Fu(\))390 1198 y FK(This)g(function)h(solv)m(es)i(the)e(square)g(system)h FE(Ax)26 b FK(=)h FE(b)k FK(in-place)h(using)f(the)h FE(QR)q(P)3225 1165 y Fq(T)3308 1198 y FK(decomp)s(osi-)390 1307 y(tion)c(of)g FE(A)g FK(held)f(in)g(\()p FD(QR)p FK(,)p FD(tau)p FK(,)p FD(p)s FK(\).)40 b(On)27 b(input)g FD(x)33 b FK(should)27 b(con)m(tain)i(the)f(righ)m(t-hand)f(side)h FE(b)p FK(,)g(whic)m(h)390 1417 y(is)i(replaced)h(b)m(y)g(the)f (solution)h(on)f(output.)3350 1658 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_QRPT_lssol)q(ve)f Fu(\()p FD(const)31 b(gsl)p 1993 1658 V 40 w(matrix)g(*)g Ft(QR)p FD(,)g(const)g(gsl)p 2909 1658 V 41 w(v)m(ector)565 1767 y(*)g Ft(tau)p FD(,)g(const)g(gsl)p 1203 1767 V 41 w(p)s(erm)m(utation)f(*)h Ft(p)p FD(,)g(const)g(gsl)p 2292 1767 V 40 w(v)m(ector)h(*)f Ft(b)p FD(,)g(gsl)p 2895 1767 V 40 w(v)m(ector)h(*)f Ft(x)p FD(,)565 1877 y(gsl)p 677 1877 V 41 w(v)m(ector)h(*)e Ft(residual)p Fu(\))390 1987 y FK(This)j(function)h(\014nds)f(the)h(least)i(squares)d (solution)i(to)g(the)f(o)m(v)m(erdetermined)i(system)e FE(Ax)e FK(=)f FE(b)390 2096 y FK(where)j(the)h(matrix)g FD(A)f FK(has)h(more)f(ro)m(ws)h(than)f(columns)g(and)g(is)h(assumed)f (to)h(ha)m(v)m(e)h(full)e(rank.)390 2206 y(The)f(least)h(squares)f (solution)g(minimizes)h(the)f(Euclidean)g(norm)g(of)g(the)g(residual,)h FI(jj)p FE(b)22 b FI(\000)g FE(Ax)p FI(jj)p FK(.)390 2315 y(The)29 b(routine)g(requires)g(as)g(input)f(the)i FE(QR)f FK(decomp)s(osition)h(of)f FE(A)h FK(in)m(to)g(\()p FD(QR)p FK(,)f FD(tau)p FK(,)h FD(p)s FK(\))f(giv)m(en)h(b)m(y)390 2425 y FH(gsl_linalg_QRPT_decomp)p FK(.)40 b(The)32 b(solution)h(is)f (returned)g(in)g FD(x)p FK(.)46 b(The)32 b(residual)g(is)g(computed)390 2534 y(as)40 b(a)g(b)m(y-pro)s(duct)f(and)g(stored)h(in)g FD(residual)p FK(.)69 b(F)-8 b(or)41 b(rank)e(de\014cien)m(t)i (matrices,)i FH(gsl_linalg_)390 2644 y(QRPT_lssolve2)27 b FK(should)i(b)s(e)h(used)f(instead.)3350 2885 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_QRPT_lssol)q(ve2)f Fu(\()p FD(const)31 b(gsl)p 2045 2885 V 41 w(matrix)f(*)h Ft(QR)p FD(,)g(const)565 2995 y(gsl)p 677 2995 V 41 w(v)m(ector)h(*)e Ft(tau)p FD(,)i(const)f(gsl)p 1623 2995 V 40 w(p)s(erm)m(utation)g(*)g Ft(p)p FD(,)f(const)h(gsl)p 2711 2995 V 41 w(v)m(ector)h(*)f Ft(b)p FD(,)f(const)h(size)p 3587 2995 V 41 w(t)565 3104 y Ft(rank)p FD(,)h(gsl)p 942 3104 V 40 w(v)m(ector)g(*)f Ft(x)p FD(,)g(gsl)p 1545 3104 V 41 w(v)m(ector)h(*)e Ft(residual)p Fu(\))390 3214 y FK(This)j(function)h(\014nds)f(the)h (least)i(squares)d(solution)i(to)g(the)f(o)m(v)m(erdetermined)i(system) e FE(Ax)e FK(=)f FE(b)390 3324 y FK(where)36 b(the)i(matrix)f FD(A)g FK(has)g(more)g(ro)m(ws)g(than)g(columns)f(and)h(has)f(rank)h (giv)m(en)h(b)m(y)f(the)g(input)390 3433 y FD(rank)p FK(.)51 b(If)33 b(the)h(user)f(do)s(es)g(not)i(kno)m(w)e(the)h(rank)g (of)g FE(A)p FK(,)h(the)f(routine)f FH(gsl_linalg_QRPT_rank)390 3543 y FK(can)23 b(b)s(e)f(called)h(to)h(estimate)g(it.)39 b(The)22 b(least)i(squares)e(solution)h(is)f(the)h(so-called)i (\\basic")e(solution)390 3652 y(discussed)33 b(ab)s(o)m(v)m(e)j(and)e (ma)m(y)h(not)f(b)s(e)g(the)h(minim)m(um)e(norm)h(solution.)53 b(The)34 b(routine)g(requires)390 3762 y(as)f(input)f(the)g FE(QR)i FK(decomp)s(osition)f(of)g FE(A)f FK(in)m(to)i(\()p FD(QR)p FK(,)f FD(tau)p FK(,)h FD(p)s FK(\))e(giv)m(en)i(b)m(y)e FH(gsl_linalg_QRPT_)390 3871 y(decomp)p FK(.)38 b(The)27 b(solution)g(is)g(returned)f(in)h FD(x)p FK(.)40 b(The)26 b(residual)h(is)g(computed)g(as)h(a)f(b)m(y-pro)s(duct)g(and)390 3981 y(stored)j(in)h FD(residual)p FK(.)3350 4222 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_QRPT_QRsol)q(ve)f Fu(\()p FD(const)31 b(gsl)p 1993 4222 V 40 w(matrix)g(*)g Ft(Q)p FD(,)g(const)g(gsl)p 2857 4222 V 40 w(matrix)565 4332 y(*)g Ft(R)p FD(,)g(const)g(gsl)p 1099 4332 V 40 w(p)s(erm)m(utation)g(*)f Ft(p)p FD(,)h(const)g(gsl)p 2187 4332 V 41 w(v)m(ector)h(*)e Ft(b)p FD(,)h(gsl)p 2790 4332 V 41 w(v)m(ector)h(*)f Ft(x)p Fu(\))390 4441 y FK(This)g(function)g(solv)m(es)h(the)g(square)f(system)h FE(R)q(P)2104 4408 y Fq(T)2156 4441 y FE(x)27 b FK(=)g FE(Q)2405 4408 y Fq(T)2457 4441 y FE(b)k FK(for)h FD(x)p FK(.)43 b(It)32 b(can)g(b)s(e)f(used)f(when)h(the)390 4551 y FE(QR)g FK(decomp)s(osition)g(of)f(a)h(matrix)g(is)f(a)m(v)-5 b(ailable)33 b(in)d(unpac)m(k)m(ed)h(form)f(as)g(\()p FD(Q)p FK(,)h FD(R)p FK(\).)3350 4792 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_QRPT_updat)q(e)e Fu(\()p FD(gsl)p 1702 4792 V 41 w(matrix)31 b(*)g Ft(Q)p FD(,)g(gsl)p 2329 4792 V 40 w(matrix)g(*)g Ft(R)p FD(,)f(const)565 4902 y(gsl)p 677 4902 V 41 w(p)s(erm)m(utation)g(*)h Ft(p)p FD(,)g(gsl)p 1528 4902 V 40 w(v)m(ector)h(*)f Ft(w)p FD(,)g(const)g(gsl)p 2369 4902 V 40 w(v)m(ector)h(*)f Ft(v)p Fu(\))390 5011 y FK(This)f(function)g(p)s(erforms)e(a)j(rank-1)g (up)s(date)e FE(w)r(v)2114 4978 y Fq(T)2198 5011 y FK(of)h(the)h FE(QR)q(P)2671 4978 y Fq(T)2753 5011 y FK(decomp)s(osition)g(\()p FD(Q)p FK(,)g FD(R)p FK(,)f FD(p)s FK(\).)390 5121 y(The)i(up)s(date)g (is)g(giv)m(en)h(b)m(y)g FE(Q)1420 5088 y Fp(0)1443 5121 y FE(R)1513 5088 y Fp(0)1565 5121 y FK(=)28 b FE(Q)p FK(\()p FE(R)22 b FK(+)g FE(w)r(v)2069 5088 y Fq(T)2122 5121 y FE(P)13 b FK(\))33 b(where)f(the)g(output)g(matrices)i FE(Q)3423 5088 y Fp(0)3478 5121 y FK(and)e FE(R)3727 5088 y Fp(0)390 5230 y FK(are)38 b(also)h(orthogonal)g(and)e(righ)m(t)i (triangular.)63 b(Note)39 b(that)g FD(w)45 b FK(is)38 b(destro)m(y)m(ed)h(b)m(y)e(the)h(up)s(date.)390 5340 y(The)30 b(p)s(erm)m(utation)g FD(p)j FK(is)d(not)h(c)m(hanged.)p eop end %%Page: 143 161 TeXDict begin 143 160 bop 150 -116 a FK(Chapter)30 b(14:)41 b(Linear)31 b(Algebra)2359 b(143)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_QRPT_Rsolv)q(e)e Fu(\()p FD(const)32 b(gsl)p 1941 299 28 4 v 40 w(matrix)f(*)g Ft(QR)p FD(,)g(const)565 408 y(gsl)p 677 408 V 41 w(p)s(erm)m(utation)f(*)h Ft(p)p FD(,)g(const)g(gsl)p 1766 408 V 40 w(v)m(ector)h(*)f Ft(b)p FD(,)g(gsl)p 2369 408 V 40 w(v)m(ector)h(*)f Ft(x)p Fu(\))390 518 y FK(This)44 b(function)g(solv)m(es)i(the)f(triangular)g (system)g FE(R)q(P)2322 485 y Fq(T)2374 518 y FE(x)k FK(=)g FE(b)c FK(for)f(the)h FE(N)10 b FK(-b)m(y-)p FE(N)55 b FK(matrix)45 b FE(R)390 628 y FK(con)m(tained)32 b(in)e FD(QR)p FK(.)3350 794 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_QRPT_Rsvx)f Fu(\()p FD(const)31 b(gsl)p 1836 794 V 41 w(matrix)f(*)h Ft(QR)p FD(,)g(const)565 904 y(gsl)p 677 904 V 41 w(p)s(erm)m(utation)f(*)h Ft(p)p FD(,)g(gsl)p 1528 904 V 40 w(v)m(ector)h(*)f Ft(x)p Fu(\))390 1013 y FK(This)c(function)g(solv)m(es)h(the)g(triangular)g(system)f FE(R)q(P)2218 980 y Fq(T)2270 1013 y FE(x)e FK(=)g FE(b)j FK(in-place)g(for)f(the)h FE(N)10 b FK(-b)m(y-)p FE(N)38 b FK(matrix)390 1123 y FE(R)23 b FK(con)m(tained)h(in)f FD(QR)p FK(.)37 b(On)22 b(input)g FD(x)29 b FK(should)21 b(con)m(tain)j(the)f(righ)m(t-hand)f(side)h FE(b)p FK(,)h(whic)m(h)f (is)f(replaced)390 1232 y(b)m(y)30 b(the)h(solution)g(on)f(output.)3350 1399 y([F)-8 b(unction])-3599 b Fv(size_t)54 b(gsl_linalg_QRPT_rank)e Fu(\()p FD(const)31 b(gsl)p 1993 1399 V 40 w(matrix)g(*)g Ft(QR)p FD(,)g(const)g(double)565 1508 y Ft(tol)p Fu(\))390 1618 y FK(This)j(function)h(estimates)i(the)e(rank)g(of)g(the)h (triangular)f(matrix)h FE(R)g FK(con)m(tained)g(in)f FD(QR)p FK(.)54 b(The)390 1728 y(algorithm)32 b(simply)e(coun)m(ts)i (the)f(n)m(um)m(b)s(er)f(of)h(diagonal)h(elemen)m(ts)g(of)f FE(R)h FK(whose)f(absolute)g(v)-5 b(alue)390 1837 y(is)28 b(greater)i(than)e(the)h(sp)s(eci\014ed)f(tolerance)i FD(tol)p FK(.)41 b(If)28 b(the)h(input)e FD(tol)33 b FK(is)c(negativ)m(e,)i(a)e(default)f(v)-5 b(alue)390 1947 y(of)31 b(20\()p FE(M)g FK(+)20 b FE(N)10 b FK(\))p FE(eps)p FK(\()p FE(max)p FK(\()p FI(j)p FE(diag)s FK(\()p FE(R)q FK(\))p FI(j)p FK(\)\))34 b(is)c(used.)3350 2113 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_QRPT_rcond)f Fu(\()p FD(const)31 b(gsl)p 1888 2113 V 41 w(matrix)g(*)f Ft(QR)p FD(,)h(double)f(*)h Ft(rcond)p FD(,)565 2223 y(gsl)p 677 2223 V 41 w(v)m(ector)h(*)e Ft(work)p Fu(\))390 2332 y FK(This)e(function)h(estimates)i(the)e(recipro)s(cal)h (condition)f(n)m(um)m(b)s(er)f(\(using)h(the)g(1-norm\))h(of)f(the)g FE(R)390 2442 y FK(factor,)f(stored)d(in)g(the)h(upp)s(er)d(triangle)k (of)e FD(QR)p FK(.)39 b(The)25 b(recipro)s(cal)h(condition)g(n)m(um)m (b)s(er)e(estimate,)390 2552 y(de\014ned)29 b(as)i(1)p FE(=)p FK(\()p FI(jj)p FE(R)q FI(jj)1110 2566 y FB(1)1170 2552 y FI(\001)21 b(jj)p FE(R)1336 2519 y Fp(\000)p FB(1)1425 2552 y FI(jj)1475 2566 y FB(1)1513 2552 y FK(\),)31 b(is)g(stored)g(in) f FD(rcond)p FK(.)42 b(Additional)31 b(w)m(orkspace)g(of)g(size)h(3)p FE(N)41 b FK(is)390 2661 y(required)30 b(in)g FD(w)m(ork)p FK(.)150 2882 y FJ(14.4)68 b(Complete)47 b(Orthogonal)f(Decomp)t (osition)150 3041 y FK(The)34 b(complete)i(orthogonal)g(decomp)s (osition)g(of)f(a)g FE(M)10 b FK(-b)m(y-)p FE(N)45 b FK(matrix)35 b FE(A)g FK(is)f(a)i(generalization)h(of)e(the)150 3151 y(QR)30 b(decomp)s(osition)h(with)f(column)g(piv)m(oting,)i(giv)m (en)f(b)m(y)1520 3353 y FE(AP)39 b FK(=)25 b FE(Q)1868 3234 y Fs(\022)1944 3298 y FE(R)2013 3312 y FB(11)2174 3298 y FK(0)1991 3407 y(0)138 b(0)2235 3234 y Fs(\023)2311 3353 y FE(Z)150 3555 y FK(where)34 b FE(P)46 b FK(is)34 b(a)h FE(N)10 b FK(-b)m(y-)p FE(N)44 b FK(p)s(erm)m(utation)34 b(matrix,)i FE(Q)e FK(is)g FE(M)10 b FK(-b)m(y-)p FE(M)44 b FK(orthogonal,)37 b FE(R)3043 3569 y FB(11)3147 3555 y FK(is)d FE(r)s FK(-b)m(y-)p FE(r)j FK(upp)s(er)150 3664 y(triangular,)24 b(with)d FE(r)28 b FK(=)d(rank)o(\()p FE(A)p FK(\),)g(and)20 b FE(Z)28 b FK(is)22 b FE(N)10 b FK(-b)m(y-)p FE(N)31 b FK(orthogonal.)40 b(If)21 b FE(A)g FK(has)g(full)g(rank,)i(then)e FE(R)3463 3678 y FB(11)3559 3664 y FK(=)k FE(R)q FK(,)150 3774 y FE(Z)33 b FK(=)27 b FE(I)38 b FK(and)31 b(this)g(reduces)g(to)h(the)f(QR)g (decomp)s(osition)h(with)f(column)g(piv)m(oting.)45 b(The)31 b(adv)-5 b(an)m(tage)33 b(of)150 3883 y(using)k(the)g(complete)i (orthogonal)f(decomp)s(osition)g(for)f(rank)g(de\014cien)m(t)h (matrices)g(is)f(the)h(abilit)m(y)g(to)150 3993 y(compute)32 b(the)g(minim)m(um)f(norm)f(solution)j(to)f(the)g(linear)g(least)h (squares)e(problem)g FE(Ax)c FK(=)g FE(b)p FK(,)33 b(whic)m(h)e(is)150 4103 y(giv)m(en)g(b)m(y)1566 4304 y FE(x)25 b FK(=)g FE(P)13 b(Z)1879 4267 y Fq(T)1946 4185 y Fs(\022)2022 4250 y FE(R)2092 4211 y Fp(\000)p FB(1)2091 4269 y(11)2181 4250 y FE(c)2220 4264 y FB(1)2117 4359 y FK(0)2273 4185 y Fs(\023)150 4516 y FK(and)30 b(the)g(v)m(ector)i FE(c)795 4530 y FB(1)863 4516 y FK(is)f(the)f(\014rst)g FE(r)j FK(elemen)m(ts)e(of)g FE(Q)1920 4483 y Fq(T)1972 4516 y FE(b)p FK(.)3350 4682 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_COD_decomp)f Fu(\()p FD(gsl)p 1650 4682 V 41 w(matrix)31 b(*)f Ft(A)p FD(,)h(gsl)p 2276 4682 V 41 w(v)m(ector)h(*)f Ft(tau_Q)p FD(,)565 4792 y(gsl)p 677 4792 V 41 w(v)m(ector)h(*)e Ft(tau_Z)p FD(,)i(gsl)p 1489 4792 V 41 w(p)s(erm)m(utation)f(*)f Ft(p)p FD(,)h(size)p 2375 4792 V 41 w(t)g(*)f Ft(rank)p FD(,)i(gsl)p 2928 4792 V 41 w(v)m(ector)g(*)f Ft(work)p Fu(\))3350 4902 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_COD_decomp)q(_e)f Fu(\()p FD(gsl)p 1755 4902 V 41 w(matrix)30 b(*)h Ft(A)p FD(,)g(gsl)p 2381 4902 V 40 w(v)m(ector)h(*)f Ft(tau_Q)p FD(,)565 5011 y(gsl)p 677 5011 V 41 w(v)m(ector)h(*)e Ft(tau_Z)p FD(,)i(gsl)p 1489 5011 V 41 w(p)s(erm)m(utation)f(*)f Ft(p)p FD(,)h(double)f Ft(tol)p FD(,)i(size)p 2881 5011 V 40 w(t)f(*)g Ft(rank)p FD(,)h(gsl)p 3434 5011 V 40 w(v)m(ector)565 5121 y(*)f Ft(work)p Fu(\))390 5230 y FK(These)i(functions)g(factor)h(the)f FE(M)10 b FK(-b)m(y-)p FE(N)44 b FK(matrix)34 b FD(A)f FK(in)m(to)h(the)g(decomp)s(osition)f FE(A)e FK(=)e FE(QR)q(Z)7 b(P)3673 5197 y Fq(T)3725 5230 y FK(.)390 5340 y(The)27 b(rank)h(of)g FD(A)g FK(is)g(computed)g(as)g (the)h(n)m(um)m(b)s(er)d(of)i(diagonal)i(elemen)m(ts)f(of)f FE(R)h FK(greater)g(than)f(the)p eop end %%Page: 144 162 TeXDict begin 144 161 bop 150 -116 a FK(Chapter)30 b(14:)41 b(Linear)31 b(Algebra)2359 b(144)390 299 y(tolerance)36 b FD(tol)i FK(and)33 b(output)g(in)h FD(rank)p FK(.)50 b(If)34 b FD(tol)k FK(is)c(not)g(sp)s(eci\014ed,)g(a)g(default)g(v)-5 b(alue)34 b(is)g(used)f(\(see)390 408 y FH(gsl_linalg_QRPT_rank)p FK(\).)38 b(On)30 b(output,)h(the)h(p)s(erm)m(utation)f(matrix)h FE(P)44 b FK(is)31 b(stored)g(in)g FD(p)p FK(.)42 b(The)390 518 y(matrix)26 b FE(R)750 532 y FB(11)846 518 y FK(is)g(stored)f(in)h (the)g(upp)s(er)d FD(rank)p FK(-b)m(y-)p FD(rank)31 b FK(blo)s(c)m(k)26 b(of)g FD(A)p FK(.)39 b(The)25 b(matrices)i FE(Q)e FK(and)g FE(Z)33 b FK(are)390 628 y(enco)s(ded)27 b(in)h(pac)m(k)m(ed)g(storage)h(in)f FD(A)f FK(on)h(output.)39 b(The)27 b(v)m(ectors)i FD(tau)p 2732 628 28 4 v 41 w(Q)j FK(and)27 b FD(tau)p 3181 628 V 40 w(Z)35 b FK(con)m(tain)29 b(the)390 737 y(Householder)e(scalars)h(corresp)s(onding)e(to)i(the)g (matrices)g FE(Q)f FK(and)g FE(Z)33 b FK(resp)s(ectiv)m(ely)c(and)d(m)m (ust)i(b)s(e)390 847 y(of)j(length)f FE(k)f FK(=)c(min)o(\()p FE(M)5 b(;)15 b(N)10 b FK(\).)42 b(The)30 b(v)m(ector)i FD(w)m(ork)k FK(is)30 b(additional)i(w)m(orkspace)f(of)f(length)h FE(N)10 b FK(.)3350 1028 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_COD_lssolv)q(e)e 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FK(decomp)s(osition)37 b(of)g FE(A)g FK(in)m(to)g(\()p FD(QRZ)p FK(,)h FD(tau)p 1829 1686 V 40 w(Q)p FK(,)g FD(tau)p 2134 1686 V 41 w(Z)p FK(,)f FD(p)p FK(,)h FD(rank)6 b FK(\))36 b(giv)m(en)i(b)m(y)e FH(gsl_linalg_COD_)390 1795 y(decomp)p FK(.)i(The)27 b(solution)g(is)g(returned)f(in)h FD(x)p FK(.)40 b(The)26 b(residual)h(is)g(computed)g(as)h(a)f(b)m (y-pro)s(duct)g(and)390 1905 y(stored)j(in)h FD(residual)p FK(.)3350 2086 y([F)-8 b(unction])-3599 b Fv(int)53 b (gsl_linalg_COD_unpack)f Fu(\()p FD(const)30 b(gsl)p 1887 2086 V 40 w(matrix)f(*)h Ft(QRZ)p FD(,)g(const)f(gsl)p 2849 2086 V 40 w(v)m(ector)i(*)565 2196 y Ft(tau_Q)p FD(,)h(const)f(gsl)p 1232 2196 V 41 w(v)m(ector)h(*)e Ft(tau_Z)p FD(,)i(const)f(size)p 2317 2196 V 41 w(t)g Ft(rank)p FD(,)h(gsl)p 2795 2196 V 40 w(matrix)f(*)g Ft(Q)p FD(,)g(gsl)p 3421 2196 V 40 w(matrix)565 2305 y(*)g Ft(R)p FD(,)g(gsl)p 861 2305 V 40 w(matrix)g(*)g Ft(Z)p Fu(\))390 2415 y FK(This)g(function)h(unpac)m(ks)f(the)h(enco)s (ded)g FE(QR)q(Z)38 b FK(decomp)s(osition)32 b(\()p FD(QRZ)p FK(,)g FD(tau)p 3083 2415 V 40 w(Q)p FK(,)g FD(tau)p 3382 2415 V 41 w(Z)p FK(,)g FD(rank)6 b FK(\))390 2525 y(in)m(to)29 b(the)f(matrices)g FD(Q)p FK(,)h FD(R)p FK(,)f(and)f FD(Z)p FK(,)h(where)g FD(Q)k FK(is)27 b FE(M)10 b FK(-b)m(y-)p FE(M)g FK(,)30 b FD(R)d FK(is)h FE(M)10 b FK(-b)m(y-)p FE(N)g FK(,)29 b(and)e FD(Z)35 b FK(is)28 b FE(N)10 b FK(-b)m(y-)p FE(N)g FK(.)3350 2706 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_COD_matZ)e Fu(\()p FD(const)32 b(gsl)p 1784 2706 V 40 w(matrix)f(*)g Ft(QRZ)p FD(,)g(const)g(gsl)p 2752 2706 V 41 w(v)m(ector)h(*)565 2815 y Ft(tau_Z)p FD(,)g(const)f(size)p 1267 2815 V 41 w(t)g Ft(rank)p FD(,)g(gsl)p 1744 2815 V 41 w(matrix)g(*)f Ft(A)p FD(,)h(gsl)p 2370 2815 V 41 w(v)m(ector)h(*)f Ft(work)p Fu(\))390 2925 y FK(This)k(function)h(m)m(ultiplies)h(the)g (input)e(matrix)h FD(A)h FK(on)f(the)g(righ)m(t)h(b)m(y)f FD(Z)p FK(,)h FE(A)3043 2892 y Fp(0)3102 2925 y FK(=)d FE(AZ)43 b FK(using)36 b(the)390 3035 y(enco)s(ded)28 b FE(QR)q(Z)35 b FK(decomp)s(osition)30 b(\()p FD(QRZ)p FK(,)f FD(tau)p 1996 3035 V 40 w(Z)p FK(,)g FD(rank)6 b FK(\).)39 b FD(A)29 b FK(m)m(ust)g(ha)m(v)m(e)h FE(N)39 b FK(columns)28 b(but)g(ma)m(y)390 3144 y(ha)m(v)m(e)k(an)m(y)e(n)m(um) m(b)s(er)f(of)i(ro)m(ws.)41 b(Additional)31 b(w)m(orkspace)g(of)f (length)h FE(M)40 b FK(is)31 b(pro)m(vided)f(in)g FD(w)m(ork)p FK(.)150 3375 y FJ(14.5)68 b(Singular)46 b(V)-11 b(alue)45 b(Decomp)t(osition)150 3534 y FK(A)28 b(general)g(rectangular)h FE(M)10 b FK(-b)m(y-)p FE(N)38 b FK(matrix)28 b FE(A)g FK(has)f(a)h(singular)f(v)-5 b(alue)29 b(decomp)s(osition)f(\()p FC(svd)p FK(\))f(in)m(to)i(the)150 3644 y(pro)s(duct)d(of)h(an)g FE(M)10 b FK(-b)m(y-)p FE(N)37 b FK(orthogonal)29 b(matrix)e FE(U)10 b FK(,)28 b(an)f FE(N)10 b FK(-b)m(y-)p FE(N)37 b FK(diagonal)28 b(matrix)g(of)f(singular)g(v)-5 b(alues)150 3753 y FE(S)35 b FK(and)30 b(the)h(transp)s(ose)e(of)i(an)f FE(N)10 b FK(-b)m(y-)p FE(N)41 b FK(orthogonal)32 b(square)e(matrix)h FE(V)20 b FK(,)1726 3920 y FE(A)25 b FK(=)g FE(U)10 b(S)5 b(V)2122 3882 y Fq(T)150 4087 y FK(The)33 b(singular)h(v)-5 b(alues)35 b FE(\033)1015 4101 y Fq(i)1073 4087 y FK(=)c FE(S)1231 4101 y Fq(ii)1316 4087 y FK(are)j(all)h(non-negativ)m(e)h (and)e(are)g(generally)h(c)m(hosen)g(to)f(form)g(a)g(non-)150 4196 y(increasing)d(sequence)g FE(\033)1004 4210 y FB(1)1066 4196 y FI(\025)25 b FE(\033)1214 4210 y FB(2)1277 4196 y FI(\025)g FE(:::)h FI(\025)f FE(\033)1622 4210 y Fq(N)1710 4196 y FI(\025)g FK(0.)275 4330 y(The)34 b(singular)h(v)-5 b(alue)36 b(decomp)s(osition)g(of)f(a)h(matrix)g(has)e(man)m(y)i (practical)h(uses.)55 b(The)34 b(condition)150 4439 y(n)m(um)m(b)s(er) 39 b(of)i(the)g(matrix)g(is)g(giv)m(en)g(b)m(y)g(the)g(ratio)g(of)g (the)g(largest)h(singular)e(v)-5 b(alue)42 b(to)f(the)g(smallest)150 4549 y(singular)32 b(v)-5 b(alue.)46 b(The)31 b(presence)h(of)g(a)g (zero)h(singular)f(v)-5 b(alue)32 b(indicates)h(that)g(the)f(matrix)g (is)g(singular.)150 4659 y(The)21 b(n)m(um)m(b)s(er)g(of)h(non-zero)g (singular)g(v)-5 b(alues)22 b(indicates)h(the)f(rank)f(of)i(the)f (matrix.)38 b(In)21 b(practice)i(singular)150 4768 y(v)-5 b(alue)37 b(decomp)s(osition)h(of)f(a)g(rank-de\014cien)m(t)g(matrix)g (will)g(not)g(pro)s(duce)f(exact)i(zero)s(es)g(for)e(singular)150 4878 y(v)-5 b(alues,)27 b(due)e(to)h(\014nite)f(n)m(umerical)h (precision.)39 b(Small)26 b(singular)f(v)-5 b(alues)26 b(should)e(b)s(e)h(edited)h(b)m(y)f(c)m(ho)s(osing)150 4987 y(a)31 b(suitable)g(tolerance.)275 5121 y(F)-8 b(or)41 b(a)g(rank-de\014cien)m(t)g(matrix,)i(the)e(n)m(ull)f(space)h(of)g FE(A)f FK(is)h(giv)m(en)g(b)m(y)f(the)h(columns)f(of)h FE(V)60 b FK(corre-)150 5230 y(sp)s(onding)35 b(to)i(the)f(zero)h (singular)f(v)-5 b(alues.)59 b(Similarly)-8 b(,)39 b(the)d(range)h(of)f FE(A)h FK(is)f(giv)m(en)h(b)m(y)g(columns)f(of)g FE(U)150 5340 y FK(corresp)s(onding)29 b(to)i(the)g(non-zero)g(singular)f(v)-5 b(alues.)p eop end %%Page: 145 163 TeXDict begin 145 162 bop 150 -116 a 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b(from)g(the)g(diagonal)h(and)f(lo)m(w)m (er-triangular)h(part)f(of)g(the)h(matrix)f FD(A)g FK(are)g(used)f (\(the)i(upp)s(er)390 2127 y(triangular)32 b(part)f(is)h(ignored\).)44 b(On)31 b(output)g(the)h(diagonal)g(and)f(lo)m(w)m(er)i(triangular)f (part)f(of)h(the)390 2236 y(input)d(matrix)i FD(A)f FK(con)m(tain)i (the)e(matrix)h FE(L)p FK(,)f(while)g(the)h(upp)s(er)d(triangular)i (part)h(is)f(unmo)s(di\014ed.)390 2346 y(If)35 b(the)h(matrix)g(is)g (not)g(p)s(ositiv)m(e-de\014nite)h(then)e(the)h(decomp)s(osition)g (will)g(fail,)i(returning)d(the)390 2455 y(error)30 b(co)s(de)h FH(GSL_EDOM)p FK(.)390 2585 y(When)h(testing)h(whether)e(a)i(matrix)f (is)g(p)s(ositiv)m(e-de\014nite,)i(disable)e(the)g(error)g(handler)f (\014rst)g(to)390 2694 y(a)m(v)m(oid)h(triggering)g(an)e(error.)3350 2862 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_cholesky_d)q (ecom)q(p)f Fu(\()p FD(gsl)p 1912 2862 V 40 w(matrix)31 b(*)g Ft(A)p Fu(\))390 2972 y FK(This)f(function)g(is)g(no)m(w)g 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b(Linear)31 b(Algebra)2359 b(147)390 299 y FH(decomp)25 b FK(or)i FH(gsl_linalg_complex_cholesk)o(y_d)o(ecom)o(p)p FK(.)34 b(On)26 b(output,)h(the)h(in)m(v)m(erse)g(is)f(stored)390 408 y(in-place)k(in)f FD(c)m(holesky)p FK(.)3350 618 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_cholesky_d)q(ecom)q (p2)f Fu(\()p FD(gsl)p 1964 618 28 4 v 41 w(matrix)30 b(*)h Ft(A)p FD(,)g(gsl)p 2590 618 V 41 w(v)m(ector)h(*)e Ft(S)p Fu(\))390 728 y FK(This)50 b(function)g(calculates)i(a)f (diagonal)g(scaling)h(transformation)f FE(S)k FK(for)50 b(the)g(symmetric,)390 838 y(p)s(ositiv)m(e-de\014nite)42 b(square)e(matrix)g FD(A)p FK(,)j(and)d(then)g(computes)g(the)h (Cholesky)f(decomp)s(osition)390 947 y FE(S)5 b(AS)54 b FK(=)48 b FE(LL)872 914 y Fq(T)924 947 y FK(.)83 b(On)44 b(input,)j(the)e(v)-5 b(alues)44 b(from)g(the)h(diagonal)h(and)e(lo)m (w)m(er-triangular)i(part)390 1057 y(of)e(the)f(matrix)h FD(A)g FK(are)g(used)f(\(the)h(upp)s(er)d(triangular)j(part)g(is)f (ignored\).)81 b(On)43 b(output)g(the)390 1166 y(diagonal)29 b(and)e(lo)m(w)m(er)j(triangular)e(part)g(of)g(the)g(input)f(matrix)h FD(A)g FK(con)m(tain)h(the)f(matrix)g FE(L)p FK(,)h(while)390 1276 y(the)36 b(upp)s(er)e(triangular)i(part)g(of)g(the)g(input)f (matrix)h(is)g(o)m(v)m(erwritten)i(with)d FE(L)3131 1243 y Fq(T)3219 1276 y FK(\(the)i(diagonal)390 1386 y(terms)32 b(b)s(eing)f(iden)m(tical)j(for)e(b)s(oth)f FE(L)h FK(and)f FE(L)1950 1353 y Fq(T)2002 1386 y FK(\).)46 b(If)31 b(the)i(matrix)f (is)g(not)g(p)s(ositiv)m(e-de\014nite)h(then)390 1495 y(the)k(decomp)s(osition)g(will)f(fail,)j(returning)d(the)g(error)g(co) s(de)h FH(GSL_EDOM)p FK(.)56 b(The)36 b(diagonal)i(scale)390 1605 y(factors)31 b(are)g(stored)f(in)h FD(S)k FK(on)30 b(output.)390 1752 y(When)i(testing)h(whether)e(a)i(matrix)f(is)g(p)s (ositiv)m(e-de\014nite,)i(disable)e(the)g(error)g(handler)f(\014rst)g (to)390 1862 y(a)m(v)m(oid)h(triggering)g(an)e(error.)3350 2072 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_cholesky_s)q (olve)q(2)f Fu(\()p FD(const)31 b(gsl)p 2150 2072 V 40 w(matrix)g(*)g Ft(cholesky)p FD(,)565 2181 y(const)g(gsl)p 915 2181 V 41 w(v)m(ector)h(*)e Ft(S)p FD(,)h(const)g(gsl)p 1756 2181 V 41 w(v)m(ector)h(*)e Ft(b)p FD(,)h(gsl)p 2359 2181 V 41 w(v)m(ector)h(*)f Ft(x)p Fu(\))390 2291 y FK(This)23 b(function)h(solv)m(es)h(the)f(system)g(\()p FE(S)5 b(AS)g FK(\)\()p FE(S)1994 2258 y Fp(\000)p FB(1)2084 2291 y FE(x)p FK(\))26 b(=)f FE(S)5 b(b)24 b FK(using)f(the)h(Cholesky) g(decomp)s(osition)390 2400 y(of)34 b FE(S)5 b(AS)40 b FK(held)34 b(in)g(the)g(matrix)h FD(c)m(holesky)43 b FK(whic)m(h)34 b(m)m(ust)h(ha)m(v)m(e)g(b)s(een)f(previously)g (computed)g(b)m(y)390 2510 y FH(gsl_linalg_cholesky_deco)o(mp2)p FK(.)3350 2720 y([F)-8 b(unction])-3599 b Fv(int)53 b (gsl_linalg_cholesky_s)q(vx2)f Fu(\()p FD(const)31 b(gsl)p 2045 2720 V 41 w(matrix)f(*)h Ft(cholesky)p FD(,)i(const)565 2829 y(gsl)p 677 2829 V 41 w(v)m(ector)f(*)e Ft(S)p FD(,)h(gsl)p 1280 2829 V 41 w(v)m(ector)h(*)f Ft(x)p Fu(\))390 2939 y FK(This)i(function)h(solv)m(es)i(the)e(system)g(\()p FE(S)5 b(AS)g FK(\)\()p FE(S)2045 2906 y Fp(\000)p FB(1)2136 2939 y FE(x)p FK(\))32 b(=)f FE(S)5 b(b)34 b FK(in-place)h(using)f(the) h(Cholesky)f(de-)390 3049 y(comp)s(osition)k(of)g FE(S)5 b(AS)43 b FK(held)38 b(in)f(the)h(matrix)g FD(c)m(holesky)47 b FK(whic)m(h)37 b(m)m(ust)h(ha)m(v)m(e)h(b)s(een)e(previously)390 3158 y(computed)30 b(b)m(y)g FH(gsl_linalg_cholesky_dec)o(omp)o(2)p FK(.)35 b(On)29 b(input)g FD(x)36 b FK(should)29 b(con)m(tain)i(the)f (righ)m(t-)390 3268 y(hand)f(side)i FE(b)p FK(,)f(whic)m(h)g(is)h (replaced)g(b)m(y)f(the)g(solution)h(on)g(output.)3350 3478 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_cholesky_s)q (cale)f Fu(\()p FD(const)31 b(gsl)p 2097 3478 V 41 w(matrix)g(*)g Ft(A)p FD(,)f(gsl)p 2723 3478 V 41 w(v)m(ector)i(*)f Ft(S)p Fu(\))390 3587 y FK(This)e(function)g(calculates)i(a)f(diagonal) h(scaling)f(transformation)g(of)f(the)h(symmetric,)g(p)s(ositiv)m(e)390 3697 y(de\014nite)38 b(matrix)g FD(A)p FK(,)j(suc)m(h)d(that)g FE(S)5 b(AS)43 b FK(has)38 b(a)h(condition)g(n)m(um)m(b)s(er)d(within)i (a)g(factor)i(of)e FE(N)48 b FK(of)390 3807 y(the)33 b(matrix)g(of)g(smallest)h(p)s(ossible)e(condition)i(n)m(um)m(b)s(er)d (o)m(v)m(er)k(all)e(p)s(ossible)g(diagonal)h(scalings.)390 3916 y(On)d(output,)g FD(S)36 b FK(con)m(tains)d(the)f(scale)g (factors,)h(giv)m(en)g(b)m(y)e FE(S)2433 3930 y Fq(i)2488 3916 y FK(=)26 b(1)p FE(=)2675 3846 y FI(p)p 2752 3846 120 4 v 2752 3916 a FE(A)2820 3930 y Fq(ii)2871 3916 y FK(.)44 b(F)-8 b(or)32 b(an)m(y)g FE(A)3345 3930 y Fq(ii)3424 3916 y FI(\024)26 b FK(0,)33 b(the)390 4026 y(corresp)s(onding)c(scale)j(factor)f FE(S)1508 4040 y Fq(i)1566 4026 y FK(is)f(set)h(to)h(1.)3350 4236 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_cholesky_s)q(cale)q(_ap)q (ply)f Fu(\()p FD(gsl)p 2173 4236 28 4 v 41 w(matrix)31 b(*)f Ft(A)p FD(,)h(const)565 4345 y(gsl)p 677 4345 V 41 w(v)m(ector)h(*)e Ft(S)p Fu(\))390 4455 y FK(This)g(function)g 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b(is)390 5322 y(stored)h(in)h FD(rcond)p FK(.)40 b(Additional)31 b(w)m(orkspace)g(of)f(size)i(3)p FE(N)40 b FK(is)31 b(required)e(in)h FD(w)m(ork)p FK(.)p eop end %%Page: 148 166 TeXDict begin 148 165 bop 150 -116 a FK(Chapter)30 b(14:)41 b(Linear)31 b(Algebra)2359 b(148)150 299 y FJ(14.7)68 b(Piv)l(oted)46 b(Cholesky)g(Decomp)t(osition)150 458 y FK(A)36 b(symmetric,)i(p)s(ositiv)m(e)f(de\014nite)f(square)g(matrix) g FE(A)g FK(has)g(an)g(alternate)h(Cholesky)f(decomp)s(osition)150 568 y(in)m(to)d(a)f(pro)s(duct)f(of)h(a)h(lo)m(w)m(er)g(unit)f (triangular)g(matrix)g FE(L)p FK(,)h(a)f(diagonal)i(matrix)e FE(D)j FK(and)c FE(L)3305 535 y Fq(T)3357 568 y FK(,)i(giv)m(en)g(b)m (y)150 677 y FE(LD)s(L)352 644 y Fq(T)404 677 y FK(.)43 b(This)30 b(is)h(equiv)-5 b(alen)m(t)33 b(to)f(the)f(Cholesky)h(form)m (ulation)f(discussed)g(ab)s(o)m(v)m(e,)i(with)d(the)i(standard)150 787 y(Cholesky)37 b(lo)m(w)m(er)h(triangular)f(factor)h(giv)m(en)g(b)m (y)f FE(LD)2014 732 y Fn(1)p 2015 741 29 4 v 2015 774 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Ft(p)p Fu(\))390 1845 y FK(This)i(function)h(factors)h(the)f (symmetric,)h(p)s(ositiv)m(e-de\014nite)g(square)f(matrix)g FD(A)g FK(in)m(to)h(the)g(Piv-)390 1955 y(oted)22 b(Cholesky)f(decomp)s (osition)h FE(P)13 b(AP)1763 1922 y Fq(T)1840 1955 y FK(=)25 b FE(LD)s(L)2138 1922 y Fq(T)2190 1955 y FK(.)38 b(On)20 b(input,)i(the)f(v)-5 b(alues)22 b(from)e(the)i(diagonal)390 2064 y(and)k(lo)m(w)m(er-triangular)j(part)e(of)g(the)g(matrix)h FD(A)f FK(are)g(used)f(to)i(construct)f(the)h(factorization.)42 b(On)390 2174 y(output)c(the)g(diagonal)i(of)e(the)g(input)f(matrix)i FD(A)f FK(stores)h(the)f(diagonal)i(elemen)m(ts)f(of)f FE(D)s FK(,)j(and)390 2284 y(the)f(lo)m(w)m(er)i(triangular)e(p)s (ortion)g(of)g FD(A)g FK(con)m(tains)h(the)g(matrix)f FE(L)p FK(.)70 b(Since)40 b FE(L)g FK(has)f(ones)i(on)f(its)390 2393 y(diagonal)33 b(these)f(do)g(not)f(need)h(to)g(b)s(e)f (explicitely)j(stored.)45 b(The)31 b(upp)s(er)e(triangular)k(p)s (ortion)e(of)390 2503 y FD(A)f FK(is)h(unmo)s(di\014ed.)38 b(The)30 b(p)s(erm)m(utation)h(matrix)g FE(P)43 b FK(is)30 b(stored)h(in)f FD(p)i FK(on)f(output.)3350 2681 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_pcholesky_)q(solv)q(e)f Fu(\()p FD(const)31 b(gsl)p 2150 2681 V 40 w(matrix)g(*)g Ft(LDLT)p FD(,)h(const)565 2791 y(gsl)p 677 2791 V 41 w(p)s(erm)m(utation)e(*)h Ft(p)p FD(,)g(const)g(gsl)p 1766 2791 V 40 w(v)m(ector)h(*)f Ft(b)p FD(,)g(gsl)p 2369 2791 V 40 w(v)m(ector)h(*)f Ft(x)p Fu(\))390 2901 y FK(This)36 b(function)g(solv)m(es)i(the)e(system)h FE(Ax)f FK(=)f FE(b)h FK(using)g(the)h(Piv)m(oted)h(Cholesky)e(decomp)s (osition)390 3010 y(of)d FE(A)f FK(held)g(in)g(the)h(matrix)g FD(LDL)-8 b(T)39 b FK(and)32 b(p)s(erm)m(utation)h FD(p)h FK(whic)m(h)e(m)m(ust)h(ha)m(v)m(e)g(b)s(een)f(previously)390 3120 y(computed)e(b)m(y)g FH(gsl_linalg_pcholesky_decom)o(p)p FK(.)3350 3298 y([F)-8 b(unction])-3599 b Fv(int)53 b (gsl_linalg_pcholesky_)q(svx)f Fu(\()p FD(const)31 b(gsl)p 2045 3298 V 41 w(matrix)f(*)h Ft(LDLT)p FD(,)h(const)565 3408 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b(output)g(the)h(diagonal)h(of)f(the)g(input)f(matrix)h FD(A)g FK(stores)g(the)390 5011 y(diagonal)f(elemen)m(ts)h(of)e FE(D)s FK(,)i(and)e(the)g(lo)m(w)m(er)i(triangular)e(p)s(ortion)g(of)g FD(A)h FK(con)m(tains)g(the)g(matrix)390 5121 y FE(L)p FK(.)49 b(Since)33 b FE(L)g FK(has)f(ones)i(on)f(its)g(diagonal)h (these)g(do)f(not)g(need)g(to)h(b)s(e)e(explicitely)j(stored.)49 b(The)390 5230 y(upp)s(er)29 b(triangular)i(p)s(ortion)g(of)g FD(A)g FK(is)g(unmo)s(di\014ed.)40 b(The)30 b(p)s(erm)m(utation)h (matrix)g FE(P)44 b FK(is)31 b(stored)g(in)390 5340 y FD(p)i FK(on)d(output.)40 b(The)30 b(diagonal)i(scaling)f (transformation)g(is)f(stored)h(in)f FD(S)35 b FK(on)30 b(output.)p eop end %%Page: 149 167 TeXDict begin 149 166 bop 150 -116 a FK(Chapter)30 b(14:)41 b(Linear)31 b(Algebra)2359 b(149)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_pcholesky_)q(solv)q(e2)f Fu(\()p FD(const)31 b(gsl)p 2202 299 28 4 v 41 w(matrix)f(*)h Ft(LDLT)p FD(,)h(const)565 408 y(gsl)p 677 408 V 41 w(p)s(erm)m (utation)e(*)h Ft(p)p FD(,)g(const)g(gsl)p 1766 408 V 40 w(v)m(ector)h(*)f Ft(S)p FD(,)g(const)g(gsl)p 2607 408 V 40 w(v)m(ector)h(*)f Ft(b)p FD(,)g(gsl)p 3210 408 V 40 w(v)m(ector)h(*)f Ft(x)p Fu(\))390 518 y FK(This)j(function)g (solv)m(es)i(the)e(system)h(\()p FE(S)5 b(AS)g FK(\)\()p FE(S)2047 485 y Fp(\000)p FB(1)2137 518 y FE(x)p FK(\))33 b(=)e FE(S)5 b(b)35 b FK(using)f(the)h(Piv)m(oted)g(Cholesky)g(de-)390 628 y(comp)s(osition)h(of)f FE(S)5 b(AS)40 b FK(held)35 b(in)f(the)h(matrix)h FD(LDL)-8 b(T)p FK(,)36 b(p)s(erm)m(utation)f FD(p)p FK(,)h(and)f(v)m(ector)h FD(S)p FK(,)g(whic)m(h)390 737 y(m)m(ust)30 b(ha)m(v)m(e)i(b)s(een)d(previously)i(computed)f(b)m (y)g FH(gsl_linalg_pcholesky_dec)o(omp2)o FK(.)3350 914 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_pcholesky_)q(svx2)f Fu(\()p FD(const)31 b(gsl)p 2097 914 V 41 w(matrix)g(*)g Ft(LDLT)p FD(,)g(const)565 1024 y(gsl)p 677 1024 V 41 w(p)s(erm)m(utation)f(*)h Ft(p)p FD(,)g(const)g(gsl)p 1766 1024 V 40 w(v)m(ector)h(*)f Ft(S)p FD(,)g(gsl)p 2369 1024 V 40 w(v)m(ector)h(*)f Ft(x)p Fu(\))390 1133 y FK(This)50 b(function)h(solv)m(es)i(the)e(system)h(\()p FE(S)5 b(AS)g FK(\)\()p FE(S)2131 1100 y Fp(\000)p FB(1)2221 1133 y FE(x)p FK(\))60 b(=)g FE(S)5 b(b)51 b FK(in-place)i(using)d(the) i(Piv)m(oted)390 1243 y(Cholesky)28 b(decomp)s(osition)h(of)f FE(S)5 b(AS)33 b FK(held)28 b(in)f(the)h(matrix)h FD(LDL)-8 b(T)p FK(,)29 b(p)s(erm)m(utation)f FD(p)i FK(and)d(v)m(ector)390 1352 y FD(S)p FK(,)j(whic)m(h)h(m)m(ust)f(ha)m(v)m(e)i(b)s(een)e (previously)g(computed)h(b)m(y)f FH(gsl_linalg_pcholesky_decom)o(p2)p FK(.)390 1462 y(On)k(input,)h FD(x)40 b FK(con)m(tains)c(the)f(righ)m (t)g(hand)f(side)g(v)m(ector)j FE(b)d FK(whic)m(h)g(is)h(replaced)g(b)m (y)g(the)f(solution)390 1572 y(v)m(ector)e(on)e(output.)3350 1748 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_pcholesky_)q (inve)q(rt)f Fu(\()p FD(const)31 b(gsl)p 2202 1748 V 41 w(matrix)f(*)h Ft(LDLT)p FD(,)h(const)565 1858 y(gsl)p 677 1858 V 41 w(p)s(erm)m(utation)e(*)h Ft(p)p FD(,)g(gsl)p 1528 1858 V 40 w(matrix)g(*)g Ft(Ainv)p Fu(\))390 1968 y FK(This)43 b(function)h(computes)g(the)g(in)m(v)m(erse)h(of)f(the)g (matrix)g FE(A)p FK(,)k(using)c(the)g(Piv)m(oted)h(Cholesky)390 2077 y(decomp)s(osition)31 b(stored)f(in)h FD(LDL)-8 b(T)37 b FK(and)29 b FD(p)p FK(.)40 b(On)30 b(output,)g(the)h(matrix)g FD(Ain)m(v)38 b FK(con)m(tains)32 b FE(A)3519 2044 y Fp(\000)p FB(1)3608 2077 y FK(.)3350 2254 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_pcholesky_)q(rcon)q(d)f Fu(\()p FD(const)31 b(gsl)p 2150 2254 V 40 w(matrix)g(*)g Ft(LDLT)p FD(,)h(const)565 2364 y(gsl)p 677 2364 V 41 w(p)s(erm)m(utation)e(*)h Ft(p)p FD(,)g(double)f(*)g Ft(rcond)p FD(,)j(gsl)p 2214 2364 V 40 w(v)m(ector)f(*)f Ft(work)p Fu(\))390 2473 y FK(This)37 b(function)h(estimates)i(the)e(recipro)s(cal)h(condition)f (n)m(um)m(b)s(er)f(\(using)h(the)g(1-norm\))h(of)f(the)390 2583 y(symmetric)31 b(p)s(ositiv)m(e)g(de\014nite)f(matrix)h FE(A)p FK(,)g(using)f(its)g(piv)m(oted)i(Cholesky)e(decomp)s(osition)h (pro-)390 2692 y(vided)44 b(in)f FD(LDL)-8 b(T)p FK(.)82 b(The)43 b(recipro)s(cal)i(condition)g(n)m(um)m(b)s(er)d(estimate,)50 b(de\014ned)43 b(as)h(1)p FE(=)p FK(\()p FI(jj)p FE(A)p FI(jj)3656 2706 y FB(1)3725 2692 y FI(\001)390 2802 y(jj)p FE(A)508 2769 y Fp(\000)p FB(1)598 2802 y FI(jj)648 2816 y FB(1)686 2802 y FK(\),)30 b(is)h(stored)f(in)g FD(rcond)p FK(.)41 b(Additional)31 b(w)m(orkspace)g(of)f(size)h(3)p FE(N)41 b FK(is)31 b(required)e(in)h FD(w)m(ork)p FK(.)150 3029 y FJ(14.8)68 b(Mo)t(di\014ed)45 b(Cholesky)g(Decomp)t(osition)150 3189 y FK(The)32 b(mo)s(di\014ed)f(Cholesky)h(decomp)s(osition)h(is)g (suitable)f(for)h(solving)g(systems)f FE(Ax)c FK(=)h FE(b)j FK(where)g FE(A)g FK(is)h(a)150 3298 y(symmetric)25 b(inde\014nite)g(matrix.)39 b(Suc)m(h)24 b(matrices)i(arise)f(in)g (nonlinear)g(optimization)i(algorithms.)39 b(The)150 3408 y(standard)30 b(Cholesky)i(decomp)s(osition)f(requires)g(a)h(p)s (ositiv)m(e)g(de\014nite)f(matrix)h(and)e(w)m(ould)h(fail)h(in)f(this) 150 3518 y(case.)41 b(Instead)28 b(of)h(resorting)g(to)g(a)g(metho)s(d) f(lik)m(e)i(QR)e(or)g(SVD,)h(whic)m(h)f(do)h(not)f(tak)m(e)i(in)m(to)g (accoun)m(t)g(the)150 3627 y(symmetry)f(of)h(the)f(matrix,)h(w)m(e)g (can)g(instead)g(in)m(tro)s(duce)f(a)h(small)g(p)s(erturbation)e(to)i (the)g(matrix)g FE(A)f FK(to)150 3737 y(mak)m(e)h(it)g(p)s(ositiv)m(e)g (de\014nite,)f(and)g(then)g(use)f(a)i(Cholesky)f(decomp)s(osition)h(on) f(the)g(p)s(erturb)s(ed)d(matrix.)150 3846 y(The)k(resulting)g(decomp)s (osition)h(satis\014es)1504 4012 y FE(P)13 b FK(\()p FE(A)21 b FK(+)f FE(E)5 b FK(\))p FE(P)1968 3974 y Fq(T)2046 4012 y FK(=)25 b FE(LD)s(L)2344 3974 y Fq(T)150 4177 y FK(where)40 b FE(P)53 b FK(is)41 b(a)g(p)s(erm)m(utation)f(matrix,)k FE(E)i FK(is)40 b(a)h(diagonal)h(p)s(erturbation)d(matrix,)44 b FE(L)c FK(is)h(unit)f(lo)m(w)m(er)150 4286 y(triangular,)e(and)d FE(D)k FK(is)d(diagonal.)59 b(If)36 b FE(A)g 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FE(P)1820 5088 y Fq(T)1897 5121 y FK(=)25 b FE(LD)s(L)2195 5088 y Fq(T)2247 5121 y FK(.)40 b(On)25 b(input,)i(the)g(v)-5 b(alues)27 b(from)f(the)h(diago-)390 5230 y(nal)h(and)f(lo)m(w)m (er-triangular)j(part)e(of)g(the)g(matrix)g FD(A)h FK(are)f(used)f(to)i (construct)f(the)g(factorization.)390 5340 y(On)39 b(output)h(the)g (diagonal)i(of)e(the)g(input)f(matrix)i FD(A)f FK(stores)h(the)f (diagonal)h(elemen)m(ts)h(of)e FE(D)s FK(,)p eop end %%Page: 150 168 TeXDict begin 150 167 bop 150 -116 a FK(Chapter)30 b(14:)41 b(Linear)31 b(Algebra)2359 b(150)390 299 y(and)29 b(the)h(lo)m(w)m(er)h (triangular)f(p)s(ortion)f(of)h FD(A)f FK(con)m(tains)i(the)f(matrix)g FE(L)p FK(.)40 b(Since)30 b FE(L)f FK(has)g(ones)h(on)g(its)390 408 y(diagonal)j(these)f(do)g(not)f(need)h(to)g(b)s(e)f(explicitely)j (stored.)45 b(The)31 b(upp)s(er)e(triangular)k(p)s(ortion)e(of)390 518 y FD(A)h FK(is)g(unmo)s(di\014ed.)42 b(The)31 b(p)s(erm)m(utation)h (matrix)g FE(P)45 b FK(is)31 b(stored)h(in)g FD(p)i 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y(previously)i(computed)g(b)m(y)h FH(gsl_linalg_mcholesky_de)o(com)o(p) p FK(.)3350 1640 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_mcholesky_)q(svx)f Fu(\()p FD(const)31 b(gsl)p 2045 1640 V 41 w(matrix)f(*)h Ft(LDLT)p FD(,)h(const)565 1750 y(gsl)p 677 1750 V 41 w(p)s(erm)m(utation)e(*)h Ft(p)p FD(,)g(gsl)p 1528 1750 V 40 w(v)m(ector)h(*)f Ft(x)p Fu(\))390 1859 y FK(This)e(function)h(solv)m(es)i(the)e(p)s (erturb)s(ed)e(system)i(\()p FE(A)21 b FK(+)e FE(E)5 b FK(\))p FE(x)26 b FK(=)f FE(b)30 b FK(in-place)i(using)d(the)i (Cholesky)390 1969 y(decomp)s(osition)25 b(of)f FE(A)8 b FK(+)g FE(E)30 b FK(held)24 b(in)g(the)g(matrix)h FD(LDL)-8 b(T)31 b FK(and)24 b(p)s(erm)m(utation)g FD(p)i FK(whic)m(h)f(m)m(ust)f (ha)m(v)m(e)390 2079 y(b)s(een)j(previously)g(computed)h(b)m(y)f FH(gsl_linalg_mcholesky_deco)o(mp)p FK(.)34 b(On)26 b(input,)i FD(x)34 b FK(con)m(tains)390 2188 y(the)d(righ)m(t)g(hand)e(side)h(v)m (ector)i FE(b)e FK(whic)m(h)h(is)f(replaced)h(b)m(y)f(the)h(solution)g (v)m(ector)h(on)e(output.)3350 2420 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_mcholesky_)q(rcon)q(d)f Fu(\()p FD(const)31 b(gsl)p 2150 2420 V 40 w(matrix)g(*)g Ft(LDLT)p FD(,)h(const)565 2530 y(gsl)p 677 2530 V 41 w(p)s(erm)m(utation)e(*)h Ft(p)p FD(,)g(double)f(*)g Ft(rcond)p FD(,)j(gsl)p 2214 2530 V 40 w(v)m(ector)f(*)f Ft(work)p Fu(\))390 2640 y FK(This)37 b(function)h(estimates)i(the)e(recipro)s(cal)h(condition)f (n)m(um)m(b)s(er)f(\(using)h(the)g(1-norm\))h(of)f(the)390 2749 y(p)s(erturb)s(ed)21 b(matrix)j FE(A)7 b FK(+)g FE(E)e FK(,)26 b(using)d(its)i(piv)m(oted)f(Cholesky)g(decomp)s (osition)h(pro)m(vided)e(in)h FD(LDL)-8 b(T)p FK(.)390 2859 y(The)32 b(recipro)s(cal)h(condition)f(n)m(um)m(b)s(er)f (estimate,)k(de\014ned)c(as)h(1)p FE(=)p FK(\()p FI(jj)p FE(A)23 b FK(+)e FE(E)5 b FI(jj)3031 2873 y FB(1)3091 2859 y FI(\001)21 b(jj)p FK(\()p FE(A)i FK(+)e FE(E)5 b FK(\))3512 2826 y Fp(\000)p FB(1)3602 2859 y FI(jj)3652 2873 y FB(1)3689 2859 y FK(\),)390 2968 y(is)30 b(stored)h(in)f FD(rcond)p FK(.)40 b(Additional)31 b(w)m(orkspace)g(of)g(size)g(3)p FE(N)41 b FK(is)30 b(required)g(in)g FD(w)m(ork)p FK(.)150 3237 y FJ(14.9)68 b(T)-11 b(ridiagonal)46 b(Decomp)t(osition)g(of)g (Real)g(Symmetric)f(Matrices)150 3396 y FK(A)30 b(symmetric)h(matrix)g FE(A)f FK(can)h(b)s(e)f(factorized)i(b)m(y)e(similarit)m(y)i (transformations)e(in)m(to)i(the)e(form,)1724 3588 y FE(A)c FK(=)f FE(QT)13 b(Q)2124 3550 y Fq(T)150 3780 y FK(where)30 b FE(Q)g FK(is)g(an)h(orthogonal)h(matrix)e(and)g FE(T)43 b FK(is)30 b(a)h(symmetric)g(tridiagonal)h(matrix.)3350 4012 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_symmtd_dec)q (omp)f Fu(\()p FD(gsl)p 1807 4012 V 41 w(matrix)31 b(*)f Ft(A)p FD(,)h(gsl)p 2433 4012 V 41 w(v)m(ector)h(*)e Ft(tau)p Fu(\))390 4121 y FK(This)21 b(function)g(factorizes)i(the)f (symmetric)f(square)g(matrix)h FD(A)g FK(in)m(to)g(the)g(symmetric)f (tridiagonal)390 4231 y(decomp)s(osition)40 b FE(QT)13 b(Q)1208 4198 y Fq(T)1260 4231 y FK(.)67 b(On)38 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5011 V 41 w(v)m(ector)h(*)f Ft(subdiag)p Fu(\))390 5121 y FK(This)42 b(function)g(unpac)m(ks)g(the) h(enco)s(ded)f(symmetric)h(tridiagonal)h(decomp)s(osition)f(\()p FD(A)p FK(,)j FD(tau)p FK(\))390 5230 y(obtained)28 b(from)g FH(gsl_linalg_symmtd_decomp)21 b FK(in)m(to)29 b(the)f(orthogonal)i (matrix)e FD(Q)p FK(,)g(the)g(v)m(ector)390 5340 y(of)j(diagonal)g (elemen)m(ts)h FD(diag)39 b FK(and)29 b(the)i(v)m(ector)h(of)e(sub)s (diagonal)h(elemen)m(ts)g FD(sub)s(diag)p FK(.)p eop end %%Page: 151 169 TeXDict begin 151 168 bop 150 -116 a FK(Chapter)30 b(14:)41 b(Linear)31 b(Algebra)2359 b(151)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_symmtd_unp)q(ack_)q(T)f Fu(\()p FD(const)31 b(gsl)p 2150 299 28 4 v 40 w(matrix)g(*)g Ft(A)p FD(,)g(gsl)p 2776 299 V 40 w(v)m(ector)h(*)565 408 y Ft(diag)p FD(,)g(gsl)p 942 408 V 40 w(v)m(ector)g(*)f Ft(subdiag)p Fu(\))390 518 y FK(This)e(function)g(unpac)m(ks)g(the)h (diagonal)h(and)e(sub)s(diagonal)g(of)h(the)g(enco)s(ded)f(symmetric)h 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FD(,)565 3552 y(gsl)p 677 3552 V 41 w(v)m(ector)h(*)e Ft(diag)p FD(,)i(gsl)p 1437 3552 V 41 w(v)m(ector)g(*)e Ft(subdiag)p Fu(\))390 3661 y FK(This)35 b(function)g(unpac)m(ks)g(the) g(diagonal)i(and)e(sub)s(diagonal)g(of)g(the)h(enco)s(ded)f (tridiagonal)i(de-)390 3771 y(comp)s(osition)k(\()p FD(A)p FK(,)h FD(tau)p FK(\))f(obtained)f(from)f(the)h FH (gsl_linalg_hermtd_decomp)34 b FK(in)m(to)40 b(the)g(real)390 3880 y(v)m(ectors)32 b FD(diag)39 b FK(and)29 b FD(sub)s(diag)p FK(.)150 4113 y FJ(14.11)69 b(Hessen)l(b)t(erg)45 b(Decomp)t(osition)i (of)e(Real)h(Matrices)150 4272 y FK(A)32 b(general)i(real)f(matrix)f FE(A)h FK(can)f(b)s(e)g(decomp)s(osed)g(b)m(y)g(orthogonal)i(similarit) m(y)f(transformations)g(in)m(to)150 4382 y(the)e(form)1716 4550 y FE(A)25 b FK(=)g FE(U)10 b(H)d(U)2132 4512 y Fq(T)150 4717 y FK(where)21 b FE(U)31 b FK(is)21 b(orthogonal)i(and)e FE(H)28 b FK(is)22 b(an)f(upp)s(er)e(Hessen)m(b)s(erg)j(matrix,)h (meaning)f(that)g(it)g(has)f(zeros)h(b)s(elo)m(w)150 4827 y(the)k(\014rst)f(sub)s(diagonal.)38 b(The)25 b(Hessen)m(b)s(erg)h (reduction)g(is)f(the)h(\014rst)f(step)g(in)h(the)f(Sc)m(h)m(ur)g (decomp)s(osition)150 4936 y(for)30 b(the)h(nonsymmetric)f(eigen)m(v)-5 b(alue)32 b(problem,)e(but)g(has)g(applications)i(in)e(other)g(areas)h (as)g(w)m(ell.)3350 5121 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_hessenberg)q(_dec)q(omp)f Fu(\()p FD(gsl)p 2016 5121 V 41 w(matrix)27 b(*)g Ft(A)p FD(,)h(gsl)p 2632 5121 V 40 w(v)m(ector)h(*)e Ft(tau)p Fu(\))390 5230 y FK(This)33 b(function)h(computes)g(the)h(Hessen)m(b)s(erg)f(decomp)s (osition)h(of)f(the)g(matrix)h FD(A)f FK(b)m(y)g(applying)390 5340 y(the)43 b(similarit)m(y)g(transformation)g FE(H)52 b FK(=)45 b FE(U)1923 5307 y Fq(T)1976 5340 y FE(AU)10 b FK(.)76 b(On)42 b(output,)j FE(H)k FK(is)43 b(stored)f(in)g(the)h (upp)s(er)p eop end %%Page: 152 170 TeXDict begin 152 169 bop 150 -116 a FK(Chapter)30 b(14:)41 b(Linear)31 b(Algebra)2359 b(152)390 299 y(p)s(ortion)36 b(of)h FD(A)p FK(.)60 b(The)37 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1147 y(the)c(Hessen)m(b)s(erg)g(matrix)g FD(H)48 b FK(along)40 b(with)e(the)h(v)m(ector)i FD(tau)p FK(.)66 b FD(H)48 b FK(and)38 b FD(tau)h FK(are)g(outputs)f(from)390 1256 y FH(gsl_linalg_hessenberg_de)o(comp)o FK(.)3350 1446 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_hessenberg)q(_unp)q (ack)q(_ac)q(cum)f Fu(\()p FD(gsl)p 2330 1446 V 41 w(matrix)31 b(*)f Ft(H)p FD(,)565 1556 y(gsl)p 677 1556 V 41 w(v)m(ector)i(*)e Ft(tau)p FD(,)i(gsl)p 1385 1556 V 40 w(matrix)f(*)g Ft(V)p Fu(\))390 1665 y FK(This)k(function)g(is)h(similar)g(to)h FH(gsl_linalg_hessenberg_u)o(npac)o(k)p FK(,)31 b(except)37 b(it)f(accum)m(ulates)390 1775 y(the)f(matrix)g FD(U)45 b FK(in)m(to)35 b FD(V)p FK(,)i(so)e(that)g FE(V)1672 1742 y Fp(0)1728 1775 y FK(=)d FE(V)20 b(U)10 b FK(.)54 b(The)34 b(matrix)h FD(V)47 b FK(m)m(ust)34 b(b)s(e)h(initialized)h (prior)e(to)390 1885 y(calling)39 b(this)e(function.)61 b(Setting)38 b FD(V)49 b FK(to)38 b(the)f(iden)m(tit)m(y)i(matrix)e 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w(v)m(ector)h(*)f Ft(work)p Fu(\))390 4444 y FK(This)f(function)g (computes)h(the)g(Hessen)m(b)s(erg-T)-8 b(riangular)31 b(decomp)s(osition)g(of)g(the)g(matrix)g(pair)390 4554 y(\()p FD(A)p FK(,)g FD(B)5 b FK(\).)41 b(On)29 b(output,)h FE(H)36 b FK(is)30 b(stored)g(in)f FD(A)p FK(,)h(and)f FE(R)i FK(is)f(stored)f(in)h FD(B)p FK(.)41 b(If)29 b FD(U)40 b FK(and)29 b FD(V)41 b FK(are)30 b(pro)m(vided)390 4664 y(\(they)40 b(ma)m(y)g(b)s(e)f(n)m(ull\),)k(the)c(similarit)m(y)i (transformations)f(are)g(stored)g(in)f(them.)68 b(Additional)390 4773 y(w)m(orkspace)31 b(of)g(length)f FE(N)41 b FK(is)30 b(needed)g(in)g FD(w)m(ork)p FK(.)150 5010 y FJ(14.13)69 b(Bidiagonalization)150 5169 y FK(A)30 b(general)i(matrix)f FE(A)f FK(can)h(b)s(e)e(factorized)j(b)m(y)f(similarit)m(y)g (transformations)g(in)m(to)g(the)g(form,)1720 5340 y FE(A)25 b FK(=)g FE(U)10 b(B)5 b(V)2128 5302 y Fq(T)p eop end %%Page: 153 171 TeXDict begin 153 170 bop 150 -116 a FK(Chapter)30 b(14:)41 b(Linear)31 b(Algebra)2359 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1070 1769 V 41 w(matrix)e(*)h Ft(U)p FD(,)g(const)g(gsl)p 1934 1769 V 40 w(v)m(ector)h(*)f Ft(tau_V)p FD(,)h(gsl)p 2746 1769 V 41 w(matrix)e(*)h Ft(V)p FD(,)g(gsl)p 3372 1769 V 41 w(v)m(ector)h(*)565 1878 y Ft(diag)p FD(,)g(gsl)p 942 1878 V 40 w(v)m(ector)g(*)f Ft(superdiag)p Fu(\))390 1988 y FK(This)f(function)g(unpac)m(ks)g(the)h (bidiagonal)h(decomp)s(osition)f(of)g FD(A)g FK(pro)s(duced)d(b)m(y)j FH(gsl_linalg_)390 2097 y(bidiag_decomp)p FK(,)d(\()p FD(A)p FK(,)33 b FD(tau)p 1365 2097 V 40 w(U)p FK(,)f FD(tau)p 1661 2097 V 41 w(V)12 b FK(\))31 b(in)m(to)i(the)e(separate)i (orthogonal)g(matrices)f FD(U)p FK(,)g FD(V)44 b FK(and)390 2207 y(the)38 b(diagonal)h(v)m(ector)g FD(diag)47 b FK(and)37 b(sup)s(erdiagonal)g FD(sup)s(erdiag)p FK(.)62 b(Note)40 b(that)e FD(U)48 b FK(is)38 b(stored)f(as)i(a)390 2317 y(compact)32 b FE(M)10 b FK(-b)m(y-)p FE(N)41 b FK(orthogonal)31 b(matrix)g(satisfying)g FE(U)2349 2284 y Fq(T)2401 2317 y FE(U)36 b FK(=)25 b FE(I)37 b FK(for)30 b(e\016ciency)-8 b(.)3350 2504 y([F)g(unction])-3599 b Fv(int)53 b (gsl_linalg_bidiag_unp)q(ack2)f Fu(\()p FD(gsl)p 1859 2504 V 41 w(matrix)31 b(*)g Ft(A)p FD(,)f(gsl)p 2485 2504 V 41 w(v)m(ector)i(*)f Ft(tau_U)p FD(,)565 2613 y(gsl)p 677 2613 V 41 w(v)m(ector)h(*)e Ft(tau_V)p FD(,)i(gsl)p 1489 2613 V 41 w(matrix)f(*)g Ft(V)p Fu(\))390 2723 y FK(This)f(function)g(unpac)m(ks)g(the)h(bidiagonal)h(decomp)s(osition)f (of)g FD(A)g FK(pro)s(duced)d(b)m(y)j FH(gsl_linalg_)390 2832 y(bidiag_decomp)p FK(,)d(\()p FD(A)p FK(,)33 b FD(tau)p 1365 2832 V 40 w(U)p FK(,)f FD(tau)p 1661 2832 V 41 w(V)12 b FK(\))31 b(in)m(to)i(the)e(separate)i(orthogonal)g(matrices)f FD(U)p FK(,)g FD(V)44 b FK(and)390 2942 y(the)21 b(diagonal)i(v)m (ector)f FD(diag)30 b FK(and)20 b(sup)s(erdiagonal)h FD(sup)s(erdiag)p FK(.)37 b(The)20 b(matrix)i FD(U)31 b FK(is)21 b(stored)g(in-place)390 3052 y(in)30 b FD(A)p FK(.)3350 3239 y([F)-8 b(unction])-3599 b Fv(int)53 b (gsl_linalg_bidiag_unp)q(ack_)q(B)f Fu(\()p FD(const)31 b(gsl)p 2150 3239 V 40 w(matrix)g(*)g Ft(A)p FD(,)g(gsl)p 2776 3239 V 40 w(v)m(ector)h(*)565 3348 y Ft(diag)p FD(,)g(gsl)p 942 3348 V 40 w(v)m(ector)g(*)f Ft(superdiag)p Fu(\))390 3458 y FK(This)20 b(function)g(unpac)m(ks)h(the)f(diagonal)i(and)f(sup) s(erdiagonal)f(of)h(the)g(bidiagonal)g(decomp)s(osition)390 3567 y(of)28 b FD(A)f FK(from)g FH(gsl_linalg_bidiag_decomp)o FK(,)c(in)m(to)28 b(the)f(diagonal)i(v)m(ector)g FD(diag)36 b FK(and)27 b(sup)s(erdiag-)390 3677 y(onal)k(v)m(ector)h FD(sup)s(erdiag)p FK(.)150 3911 y FJ(14.14)69 b(Giv)l(ens)45 b(Rotations)150 4071 y FK(A)36 b(Giv)m(ens)g(rotation)h(is)e(a)h (rotation)h(in)e(the)h(plane)f(acting)i(on)e(t)m(w)m(o)i(elemen)m(ts)g (of)f(a)g(giv)m(en)g(v)m(ector.)58 b(It)150 4180 y(can)31 b(b)s(e)e(represen)m(ted)i(in)f(matrix)h(form)e(as)936 4705 y FE(G)p FK(\()p FE(i;)15 b(j;)g(\022)s FK(\))27 b(=)1394 4287 y Fs(0)1394 4434 y(B)1394 4483 y(B)1394 4533 y(B)1394 4583 y(B)1394 4633 y(B)1394 4683 y(B)1394 4732 y(B)1394 4782 y(B)1394 4832 y(B)1394 4882 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4933 y(.)2841 4966 y(.)1482 5076 y(0)f FE(:)15 b(:)g(:)161 b FK(0)e FE(:)15 b(:)g(:)198 b FK(0)g FE(:)15 b(:)g(:)92 b FK(1)2892 4287 y Fs(1)2892 4434 y(C)2892 4483 y(C)2892 4533 y(C)2892 4583 y(C)2892 4633 y(C)2892 4683 y(C)2892 4732 y(C)2892 4782 y(C)2892 4832 y(C)2892 4882 y(C)2892 4935 y(A)150 5230 y FK(where)33 b(the)h(cos)16 b FE(\022)36 b FK(and)d(sin)15 b FE(\022)36 b FK(app)s(ear)d(at)h(the)g(in)m(tersection)h(of)f(the)g FE(i)p FK(th)g(and)f FE(j)5 b FK(th)34 b(ro)m(ws)g(and)f(columns.)150 5340 y(When)45 b(acting)i(on)e(a)h(v)m(ector)h FE(x)p FK(,)i FE(G)p FK(\()p FE(i;)15 b(j;)g(\022)s FK(\))p FE(x)47 b FK(p)s(erforms)d(a)i(rotation)g(of)g(the)f(\()p FE(i;)15 b(j)5 b FK(\))48 b(elemen)m(ts)e(of)g FE(x)p FK(.)p eop end %%Page: 154 172 TeXDict begin 154 171 bop 150 -116 a FK(Chapter)30 b(14:)41 b(Linear)31 b(Algebra)2359 b(154)150 299 y(Giv)m(ens)38 b(rotations)h(are)f(t)m(ypically)i(used)c(to)j(in)m(tro)s(duce)e(zeros) i(in)e(v)m(ectors,)k(suc)m(h)c(as)h(during)f(the)g(QR)150 408 y(decomp)s(osition)31 b(of)g(a)f(matrix.)41 b(In)30 b(this)g(case,)i(it)f(is)f(t)m(ypically)i(desired)e(to)h(\014nd)e FE(c)i FK(and)f FE(s)g FK(suc)m(h)g(that)1483 535 y Fs(\022)1561 600 y FE(c)93 b FI(\000)p FE(s)1559 709 y(s)128 b(c)1821 535 y Fs(\023)15 b(\022)1974 600 y FE(a)1978 709 y(b)2037 535 y Fs(\023)2123 654 y FK(=)2219 535 y Fs(\022)2296 600 y FE(r)2295 709 y FK(0)2356 535 y Fs(\023)150 918 y FK(with)30 b FE(r)e FK(=)522 844 y FI(p)p 598 844 273 4 v 74 x FE(a)646 892 y FB(2)703 918 y FK(+)20 b FE(b)833 892 y FB(2)870 918 y FK(.)3350 1178 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_linalg_givens)c Fu(\()p FD(const)31 b(double)f Ft(a)p FD(,)h(const)g(double)f Ft(b)p FD(,)h(double)f(*)h Ft(c)p FD(,)565 1288 y(double)f(*)h Ft(s)p Fu(\))390 1398 y FK(This)26 b(function)g(computes)h FE(c)f FK(=)f(cos)16 b FE(\022)28 b FK(and)f FE(s)d FK(=)h(sin)15 b FE(\022)29 b FK(so)e(that)g(the)g(Giv)m(ens)h(matrix)f FE(G)p FK(\()p FE(\022)s FK(\))g(acting)390 1507 y(on)j(the)h(v)m(ector)h(\()p FE(a;)15 b(b)p FK(\))31 b(pro)s(duces)e(\()p FE(r)m(;)15 b FK(0\),)33 b(with)d FE(r)e FK(=)2179 1433 y FI(p)p 2255 1433 V 74 x FE(a)2303 1481 y FB(2)2360 1507 y FK(+)20 b FE(b)2490 1481 y FB(2)2527 1507 y FK(.)3350 1767 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_linalg_givens_gv)d Fu(\()p FD(gsl)p 1650 1767 28 4 v 41 w(v)m(ector)32 b(*)f Ft(v)p FD(,)g(const)f(size)p 2526 1767 V 41 w(t)h Ft(i)p FD(,)g(const)g(size)p 3120 1767 V 41 w(t)565 1877 y Ft(j)p FD(,)g(const)g(double)f Ft(c)p FD(,)h(const)g(double)e Ft(s)p Fu(\))390 1987 y FK(This)i(function)h(applies)h(the)f(Giv)m(ens) h(rotation)g(de\014ned)e(b)m(y)h FE(c)d FK(=)f(cos)16 b FE(\022)34 b FK(and)e FE(s)c FK(=)g(sin)14 b FE(\022)35 b FK(to)e(the)f FD(i)390 2096 y FK(and)e FD(j)j FK(elemen)m(ts)f(of)e FD(v)p FK(.)41 b(On)29 b(output,)i(\()p FE(v)s FK(\()p FE(i)p FK(\))p FE(;)15 b(v)s FK(\()p FE(j)5 b FK(\)\))29 b FI( )c FE(G)p FK(\()p FE(\022)s FK(\)\()p FE(v)s FK(\()p FE(i)p FK(\))p FE(;)15 b(v)s 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(gsl_linalg_householder)q(_tr)q(ans)q(for)q(m)d Fu(\()p FD(gsl)p 2382 3545 V 41 w(v)m(ector)32 b(*)f Ft(w)p Fu(\))3350 3655 y FK([F)-8 b(unction])-3599 b Fv(gsl_complex)56 b(gsl_linalg_complex_hous)q(eho)q(lder)q(_tr)q(ans)q(form)565 3765 y Fu(\()p FD(gsl)p 712 3765 V 41 w(v)m(ector)p 994 3765 V 42 w(complex)31 b(*)g Ft(w)p Fu(\))390 3874 y FK(This)38 b(function)h(prepares)g(a)g(Householder)g(transformation)h FE(P)53 b FK(=)39 b FE(I)33 b FI(\000)26 b FE(\034)10 b(v)s(v)3120 3841 y Fq(T)3212 3874 y FK(whic)m(h)39 b(can)h(b)s(e)390 3984 y(used)34 b(to)h(zero)g(all)h(the)e(elemen)m(ts)i(of)f(the)g (input)e(v)m(ector)j FD(w)42 b FK(except)36 b(the)f(\014rst.)52 b(On)34 b(output)g(the)390 4093 y(Householder)i(v)m(ector)h FD(v)43 b FK(is)36 b(stored)f(in)g FD(w)43 b FK(and)35 b(the)h(scalar)g FE(\034)46 b FK(is)35 b(returned.)56 b(The)35 b(householder)390 4203 y(v)m(ector)i FD(v)44 b FK(is)36 b(normalized)g(so)g(that)g FD(v)8 b FK([0])37 b(=)e(1,)j(ho)m(w)m(ev)m(er)f(this)f(1)g(is)g(not)g(stored)g(in)f(the)h (output)390 4313 y(v)m(ector.)51 b(Instead,)35 b FD(w)8 b FK([0])33 b(is)h(set)g(to)g(the)f(\014rst)g(elemen)m(t)i(of)e(the)h (transformed)e(v)m(ector,)k(so)e(that)g(if)390 4422 y FE(u)25 b FK(=)g FE(P)13 b(w)r FK(,)31 b FD(w)8 b FK([0])31 b(=)f FE(u)p FK([0])h(on)g(output)f(and)f(the)i(remainder)f(of)g FE(u)h FK(is)f(zero.)3350 4682 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_householde)q(r_hm)f Fu(\()p FD(double)31 b Ft(tau)p FD(,)g(const)g(gsl)p 2603 4682 V 40 w(v)m(ector)h(*)f Ft(v)p FD(,)565 4792 y(gsl)p 677 4792 V 41 w(matrix)f(*)h Ft(A)p Fu(\))3350 4902 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_complex_ho)q(useh)q(old)q (er_)q(hm)f Fu(\()p FD(gsl)p 2278 4902 V 41 w(complex)31 b Ft(tau)p FD(,)g(const)565 5011 y(gsl)p 677 5011 V 41 w(v)m(ector)p 959 5011 V 41 w(complex)g(*)g Ft(v)p FD(,)g(gsl)p 1646 5011 V 41 w(matrix)p 1952 5011 V 40 w(complex)g(*)g Ft(A)p Fu(\))390 5121 y FK(This)37 b(function)h(applies)h(the)f (Householder)g(matrix)h FE(P)51 b FK(de\014ned)37 b(b)m(y)h(the)h (scalar)g FD(tau)f FK(and)g(the)390 5230 y(v)m(ector)32 b FD(v)39 b FK(to)31 b(the)g(left-hand)g(side)f(of)h(the)g(matrix)g FD(A)p FK(.)42 b(On)29 b(output)i(the)f(result)h FE(P)13 b(A)31 b FK(is)f(stored)h(in)390 5340 y FD(A)p FK(.)p eop end %%Page: 155 173 TeXDict begin 155 172 bop 150 -116 a FK(Chapter)30 b(14:)41 b(Linear)31 b(Algebra)2359 b(155)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_householde)q(r_mh)f Fu(\()p FD(double)31 b Ft(tau)p FD(,)g(const)g(gsl)p 2603 299 28 4 v 40 w(v)m(ector)h(*)f Ft(v)p FD(,)565 408 y(gsl)p 677 408 V 41 w(matrix)f(*)h Ft(A)p Fu(\))3350 518 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_complex_ho)q(useh)q(old)q (er_)q(mh)f Fu(\()p FD(gsl)p 2278 518 V 41 w(complex)31 b Ft(tau)p FD(,)g(const)565 628 y(gsl)p 677 628 V 41 w(v)m(ector)p 959 628 V 41 w(complex)g(*)g Ft(v)p FD(,)g(gsl)p 1646 628 V 41 w(matrix)p 1952 628 V 40 w(complex)g(*)g Ft(A)p Fu(\))390 737 y FK(This)37 b(function)h(applies)h(the)f (Householder)g(matrix)h FE(P)51 b FK(de\014ned)37 b(b)m(y)h(the)h (scalar)g FD(tau)f FK(and)g(the)390 847 y(v)m(ector)d FD(v)41 b FK(to)34 b(the)f(righ)m(t-hand)g(side)g(of)h(the)f(matrix)g FD(A)p FK(.)50 b(On)32 b(output)h(the)g(result)g FE(AP)47 b FK(is)33 b(stored)390 956 y(in)d FD(A)p FK(.)3350 1128 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_householde)q(r_hv)f Fu(\()p FD(double)31 b Ft(tau)p FD(,)g(const)g(gsl)p 2603 1128 V 40 w(v)m(ector)h(*)f Ft(v)p FD(,)565 1237 y(gsl)p 677 1237 V 41 w(v)m(ector)h(*)e Ft(w)p Fu(\))3350 1347 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_complex_ho)q (useh)q(old)q(er_)q(hv)f Fu(\()p FD(gsl)p 2278 1347 V 41 w(complex)31 b Ft(tau)p FD(,)g(const)565 1456 y(gsl)p 677 1456 V 41 w(v)m(ector)p 959 1456 V 41 w(complex)g(*)g Ft(v)p FD(,)g(gsl)p 1646 1456 V 41 w(v)m(ector)p 1928 1456 V 41 w(complex)g(*)g Ft(w)p Fu(\))390 1566 y FK(This)24 b(function)h(applies)g(the)g(Householder)g(transformation)g FE(P)38 b FK(de\014ned)24 b(b)m(y)g(the)i(scalar)f FD(tau)h FK(and)390 1676 y(the)31 b(v)m(ector)h FD(v)38 b FK(to)31 b(the)f(v)m(ector)i FD(w)p FK(.)41 b(On)29 b(output)h(the)h(result)f FE(P)13 b(w)33 b FK(is)d(stored)h(in)f FD(w)p FK(.)150 1899 y FJ(14.16)69 b(Householder)45 b(solv)l(er)h(for)f(linear)h (systems)3350 2100 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_HH_solve)e Fu(\()p FD(gsl)p 1545 2100 V 41 w(matrix)31 b(*)g Ft(A)p FD(,)g(const)g(gsl)p 2410 2100 V 40 w(v)m(ector)h(*)f Ft(b)p FD(,)565 2209 y(gsl)p 677 2209 V 41 w(v)m(ector)h(*)e Ft(x)p Fu(\))390 2319 y FK(This)i(function)h(solv)m(es)h(the)f(system)g FE(Ax)d FK(=)f FE(b)k FK(directly)g(using)g(Householder)f(transformations.)390 2428 y(On)23 b(output)g(the)g(solution)h(is)f(stored)h(in)f FD(x)30 b FK(and)22 b FD(b)j FK(is)f(not)f(mo)s(di\014ed.)37 b(The)23 b(matrix)h FD(A)g FK(is)f(destro)m(y)m(ed)390 2538 y(b)m(y)30 b(the)h(Householder)f(transformations.)3350 2709 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_HH_svx)e Fu(\()p FD(gsl)p 1441 2709 V 41 w(matrix)30 b(*)h Ft(A)p FD(,)g(gsl)p 2067 2709 V 41 w(v)m(ector)h(*)e Ft(x)p Fu(\))390 2819 y FK(This)i(function)f(solv)m(es)j(the)f(system)f FE(Ax)d FK(=)f FE(b)k FK(in-place)h(using)f(Householder)g (transformations.)390 2928 y(On)27 b(input)f FD(x)34 b FK(should)27 b(con)m(tain)i(the)e(righ)m(t-hand)h(side)f FE(b)p FK(,)i(whic)m(h)e(is)h(replaced)g(b)m(y)f(the)h(solution)g(on) 390 3038 y(output.)40 b(The)30 b(matrix)h FD(A)f FK(is)h(destro)m(y)m (ed)g(b)m(y)f(the)h(Householder)f(transformations.)150 3262 y FJ(14.17)69 b(T)-11 b(ridiagonal)45 b(Systems)150 3421 y FK(The)22 b(functions)g(describ)s(ed)g(in)g(this)h(section)g (e\016cien)m(tly)i(solv)m(e)f(symmetric,)h(non-symmetric)d(and)g (cyclic)150 3531 y(tridiagonal)33 b(systems)e(with)g(minimal)h (storage.)45 b(Note)33 b(that)e(the)h(curren)m(t)f(implemen)m(tations)i (of)e(these)150 3640 y(functions)20 b(use)g(a)h(v)-5 b(arian)m(t)21 b(of)f(Cholesky)h(decomp)s(osition,)i(so)d(the)h (tridiagonal)g(matrix)g(m)m(ust)f(b)s(e)g(p)s(ositiv)m(e)150 3750 y(de\014nite.)40 b(F)-8 b(or)29 b(non-p)s(ositiv)m(e)h(de\014nite) e(matrices,)i(the)f(functions)f(return)g(the)g(error)g(co)s(de)h FH(GSL_ESING)p FK(.)3350 3921 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_solve_trid)q(iag)f Fu(\()p FD(const)31 b(gsl)p 2045 3921 V 41 w(v)m(ector)h(*)e Ft(diag)p FD(,)i(const)565 4031 y(gsl)p 677 4031 V 41 w(v)m(ector)g(*)e Ft(e)p FD(,)h(const)g(gsl) p 1518 4031 V 41 w(v)m(ector)h(*)e Ft(f)p FD(,)h(const)g(gsl)p 2359 4031 V 41 w(v)m(ector)h(*)f Ft(b)p FD(,)f(gsl)p 2962 4031 V 41 w(v)m(ector)i(*)f Ft(x)p Fu(\))390 4140 y FK(This)d(function)g(solv)m(es)h(the)g(general)g FE(N)10 b FK(-b)m(y-)p FE(N)39 b FK(system)28 b FE(Ax)e FK(=)f FE(b)j FK(where)g FD(A)g FK(is)h(tridiagonal)h(\()p FE(N)35 b FI(\025)390 4250 y FK(2\).)40 b(The)25 b(sup)s(er-diagonal)h(and)f (sub-diagonal)h(v)m(ectors)h 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w(v)m(ector)g(*)e Ft(e)p FD(,)h(const)g(gsl)p 1518 5121 V 41 w(v)m(ector)h(*)e Ft(b)p FD(,)h(gsl)p 2121 5121 V 41 w(v)m(ector)h(*)f Ft(x)p Fu(\))390 5230 y FK(This)f(function)g (solv)m(es)i(the)f(general)h FE(N)10 b FK(-b)m(y-)p FE(N)41 b FK(system)31 b FE(Ax)26 b FK(=)f FE(b)31 b FK(where)f FD(A)h FK(is)g(symmetric)g(tridi-)390 5340 y(agonal)41 b(\()p FE(N)51 b FI(\025)40 b FK(2\).)69 b(The)39 b(o\013-diagonal)j(v) m(ector)f FD(e)k FK(m)m(ust)39 b(b)s(e)g(one)h(elemen)m(t)h(shorter)e (than)h(the)p eop end %%Page: 156 174 TeXDict begin 156 173 bop 150 -116 a FK(Chapter)30 b(14:)41 b(Linear)31 b(Algebra)2359 b(156)390 299 y(diagonal)32 b(v)m(ector)g FD(diag)p FK(.)41 b(The)30 b(form)g(of)g FD(A)h FK(for)f(the)g(4-b)m(y-4)i(case)g(is)e(sho)m(wn)g(b)s(elo)m(w,) 1462 625 y FE(A)25 b FK(=)1651 406 y Fs(0)1651 552 y(B)1651 602 y(B)1651 655 y(@)1739 461 y FE(d)1786 475 y FB(0)1917 461 y FE(e)1959 475 y FB(0)2110 461 y FK(0)130 b(0)1742 570 y FE(e)1784 584 y FB(0)1915 570 y FE(d)1962 584 y FB(1)2093 570 y FE(e)2135 584 y FB(1)2285 570 y FK(0)1759 680 y(0)113 b FE(e)1959 694 y FB(1)2090 680 y FE(d)2137 694 y FB(2)2268 680 y FE(e)2310 694 y FB(2)1759 789 y FK(0)130 b(0)114 b FE(e)2135 803 y FB(2)2266 789 y FE(d)2313 803 y FB(3)2365 406 y Fs(1)2365 552 y(C)2365 602 y(C)2365 655 y(A)3350 990 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_solve_cyc_)q(trid)q(iag)f Fu(\()p FD(const)31 b(gsl)p 2254 990 28 4 v 41 w(v)m(ector)h(*)f Ft(diag)p FD(,)g(const)565 1099 y(gsl)p 677 1099 V 41 w(v)m(ector)h(*)e Ft(e)p FD(,)h(const)g(gsl)p 1518 1099 V 41 w(v)m(ector)h(*)e Ft(f)p FD(,)h(const)g(gsl)p 2359 1099 V 41 w(v)m(ector)h(*)f Ft(b)p FD(,)f(gsl)p 2962 1099 V 41 w(v)m(ector)i(*)f Ft(x)p Fu(\))390 1209 y FK(This)c(function)h(solv)m(es)h(the)f(general) h FE(N)10 b FK(-b)m(y-)p FE(N)38 b FK(system)28 b FE(Ax)e FK(=)f FE(b)i FK(where)h FD(A)g FK(is)g(cyclic)h(tridiagonal)390 1318 y(\()p FE(N)38 b FI(\025)27 b FK(3\).)45 b(The)31 b(cyclic)i(sup)s(er-diagonal)f(and)f(sub-diagonal)h(v)m(ectors)h FD(e)k FK(and)31 b FD(f)49 b FK(m)m(ust)32 b(ha)m(v)m(e)h(the)390 1428 y(same)g(n)m(um)m(b)s(er)f(of)h(elemen)m(ts)h(as)f(the)g(diagonal) h(v)m(ector)h FD(diag)p FK(.)48 b(The)33 b(form)f(of)h FD(A)g FK(for)f(the)i(4-b)m(y-4)390 1538 y(case)d(is)g(sho)m(wn)f(b)s (elo)m(w,)1462 1864 y FE(A)25 b FK(=)1651 1645 y Fs(0)1651 1791 y(B)1651 1841 y(B)1651 1894 y(@)1739 1699 y FE(d)1786 1713 y FB(0)1917 1699 y FE(e)1959 1713 y FB(0)2110 1699 y FK(0)112 b FE(f)2312 1713 y FB(3)1741 1809 y FE(f)1786 1823 y FB(0)1915 1809 y FE(d)1962 1823 y FB(1)2093 1809 y FE(e)2135 1823 y FB(1)2285 1809 y FK(0)1759 1918 y(0)g FE(f)1961 1932 y FB(1)2090 1918 y FE(d)2137 1932 y FB(2)2268 1918 y FE(e)2310 1932 y FB(2)1742 2028 y FE(e)1784 2042 y FB(3)1934 2028 y FK(0)h FE(f)2137 2042 y FB(2)2266 2028 y FE(d)2313 2042 y FB(3)2365 1645 y Fs(1)2365 1791 y(C)2365 1841 y(C)2365 1894 y(A)3350 2228 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_solve_symm)q(_cyc)q(_tr)q (idi)q(ag)f Fu(\()p FD(const)31 b(gsl)p 2516 2228 V 40 w(v)m(ector)h(*)f Ft(diag)p FD(,)565 2338 y(const)g(gsl)p 915 2338 V 41 w(v)m(ector)h(*)e Ft(e)p FD(,)h(const)g(gsl)p 1756 2338 V 41 w(v)m(ector)h(*)e Ft(b)p FD(,)h(gsl)p 2359 2338 V 41 w(v)m(ector)h(*)f Ft(x)p Fu(\))390 2447 y FK(This)e(function)g(solv)m(es)h(the)g(general)g FE(N)10 b FK(-b)m(y-)p FE(N)40 b FK(system)29 b FE(Ax)d FK(=)f FE(b)k FK(where)g FD(A)g FK(is)h(symmetric)f(cyclic)390 2557 y(tridiagonal)39 b(\()p FE(N)47 b FI(\025)37 b FK(3\).)63 b(The)37 b(cyclic)i(o\013-diagonal)h(v)m(ector)f FD(e)k FK(m)m(ust)37 b(ha)m(v)m(e)i(the)e(same)h(n)m(um)m(b)s(er)390 2667 y(of)33 b(elemen)m(ts)h(as)f(the)g(diagonal)g(v)m(ector)i FD(diag)p FK(.)48 b(The)32 b(form)g(of)h FD(A)g FK(for)f(the)h(4-b)m (y-4)h(case)g(is)f(sho)m(wn)390 2776 y(b)s(elo)m(w,)1462 3102 y FE(A)25 b FK(=)1651 2884 y Fs(0)1651 3030 y(B)1651 3080 y(B)1651 3133 y(@)1739 2938 y FE(d)1786 2952 y FB(0)1917 2938 y FE(e)1959 2952 y FB(0)2110 2938 y FK(0)113 b FE(e)2310 2952 y FB(3)1742 3047 y FE(e)1784 3061 y FB(0)1915 3047 y FE(d)1962 3061 y FB(1)2093 3047 y FE(e)2135 3061 y FB(1)2285 3047 y FK(0)1759 3157 y(0)g FE(e)1959 3171 y FB(1)2090 3157 y FE(d)2137 3171 y FB(2)2268 3157 y FE(e)2310 3171 y FB(2)1742 3267 y FE(e)1784 3281 y FB(3)1934 3267 y FK(0)h FE(e)2135 3281 y FB(2)2266 3267 y FE(d)2313 3281 y FB(3)2365 2884 y Fs(1)2365 3030 y(C)2365 3080 y(C)2365 3133 y(A)150 3496 y FJ(14.18)69 b(T)-11 b(riangular)45 b(Systems)3350 3714 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_tri_upper_)q(inve)q(rt)f Fu(\()p FD(gsl)p 1964 3714 V 41 w(matrix)30 b(*)h Ft(T)p Fu(\))3350 3823 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_tri_lower_)q(inve) q(rt)f Fu(\()p FD(gsl)p 1964 3823 V 41 w(matrix)30 b(*)h Ft(T)p Fu(\))3350 3933 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_tri_upper_)q(unit)q(_in)q(ver)q(t)e Fu(\()p FD(gsl)p 2225 3933 V 41 w(matrix)31 b(*)g Ft(T)p Fu(\))3350 4043 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_tri_lower_)q(unit)q(_in)q(ver)q(t)e Fu(\()p FD(gsl)p 2225 4043 V 41 w(matrix)31 b(*)g Ft(T)p Fu(\))390 4152 y FK(These)h(functions)g(calculate)j(the)d(in-place)h(in)m(v)m (erse)g(of)g(the)f(triangular)h(matrix)g FD(T)p FK(.)46 b(When)32 b(the)390 4262 y FH(upper)g FK(pre\014x)h(is)h(sp)s (eci\014ed,)h(then)e(the)h(upp)s(er)e(triangle)k(of)e FD(T)40 b FK(is)34 b(used,)g(and)f(when)g(the)h FH(lower)390 4371 y FK(pre\014x)40 b(is)h(sp)s(eci\014ed,)i(the)e(lo)m(w)m(er)i (triangle)f(is)f(used.)72 b(If)40 b(the)h FH(unit)f FK(pre\014x)g(is)h (sp)s(eci\014ed,)i(then)390 4481 y(the)e(diagonal)h(elemen)m(ts)g(of)f (the)f(matrix)h FD(T)47 b FK(are)41 b(tak)m(en)h(as)f(unit)m(y)g(and)f (are)h(not)g(referenced.)390 4591 y(Otherwise)30 b(the)h(diagonal)g (elemen)m(ts)h(are)f(used)e(in)h(the)h(in)m(v)m(ersion.)3350 4792 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_tri_upper_)q (rcon)q(d)f Fu(\()p FD(const)31 b(gsl)p 2150 4792 V 40 w(matrix)g(*)g Ft(T)p FD(,)g(double)f(*)565 4902 y Ft(rcond)p FD(,)i(gsl)p 994 4902 V 41 w(v)m(ector)g(*)e Ft(work)p Fu(\))3350 5011 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_tri_lower_)q(rcon)q(d)f Fu(\()p FD(const)31 b(gsl)p 2150 5011 V 40 w(matrix)g(*)g Ft(T)p FD(,)g(double)f(*)565 5121 y Ft(rcond)p FD(,)i(gsl)p 994 5121 V 41 w(v)m(ector)g(*)e Ft(work)p Fu(\))390 5230 y FK(These)23 b(functions)g(estimate)j(the)d (recipro)s(cal)i(condition)f(n)m(um)m(b)s(er,)g(in)f(the)g(1-norm,)j (of)d(the)h(upp)s(er)390 5340 y(or)33 b(lo)m(w)m(er)h FE(N)10 b FK(-b)m(y-)p FE(N)43 b FK(triangular)33 b(matrix)g FD(T)p FK(.)47 b(The)32 b(recipro)s(cal)h(condition)g(n)m(um)m(b)s(er)f (is)g(stored)h(in)p eop end %%Page: 157 175 TeXDict begin 157 174 bop 150 -116 a FK(Chapter)30 b(14:)41 b(Linear)31 b(Algebra)2359 b(157)390 299 y FD(rcond)35 b FK(on)d(output,)g(and)g(is)g(de\014ned)e(b)m(y)i(1)p FE(=)p FK(\()p FI(jj)p FE(T)13 b FI(jj)2106 313 y FB(1)2167 299 y FI(\001)21 b(jj)p FE(T)2329 266 y Fp(\000)p FB(1)2419 299 y FI(jj)2469 313 y FB(1)2507 299 y FK(\).)46 b(Additional)32 b(w)m(orkspace)h(of)f(size)390 408 y(3)p FE(N)41 b FK(is)30 b(required)g(in)g FD(w)m(ork)p FK(.)150 642 y FJ(14.19)69 b(Balancing)150 802 y FK(The)29 b(pro)s(cess)g(of)g(balancing)h(a)g (matrix)g(applies)f(similarit)m(y)i(transformations)e(to)h(mak)m(e)h (the)e(ro)m(ws)h(and)150 911 y(columns)j(ha)m(v)m(e)h(comparable)g (norms.)48 b(This)32 b(is)h(useful,)g(for)g(example,)i(to)f(reduce)f (roundo\013)f(errors)g(in)150 1021 y(the)j(solution)g(of)f(eigen)m(v)-5 b(alue)37 b(problems.)52 b(Balancing)36 b(a)f(matrix)g FE(A)f FK(consists)h(of)g(replacing)g FE(A)f FK(with)h(a)150 1130 y(similar)c(matrix)1687 1299 y FE(A)1755 1262 y Fp(0)1804 1299 y FK(=)25 b FE(D)1978 1262 y Fp(\000)p FB(1)2067 1299 y FE(AD)150 1468 y FK(where)30 b FE(D)j FK(is)d(a)h(diagonal)h(matrix)e(whose)h(en)m(tries)g(are)g(p)s(o)m(w)m (ers)f(of)g(the)h(\015oating)g(p)s(oin)m(t)g(radix.)3350 1654 y([F)-8 b(unction])-3599 b Fv(int)53 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Ft(eval)p FD(,)565 3696 y(gsl)p 677 3696 V 41 w(matrix)p 983 3696 V 40 w(complex)g(*)g Ft(evec)p FD(,)h(gsl)p 1826 3696 V 40 w(eigen)p 2067 3696 V 41 w(herm)m(v)p 2356 3696 V 40 w(w)m(orkspace)f(*)g Ft(w)p Fu(\))390 3805 y FK(This)38 b(function)g(computes)g(the)h(eigen) m(v)-5 b(alues)40 b(and)e(eigen)m(v)m(ectors)j(of)d(the)h(complex)g (hermitian)390 3915 y(matrix)31 b FD(A)p FK(.)41 b(Additional)32 b(w)m(orkspace)f(of)g(the)g(appropriate)f(size)i(m)m(ust)e(b)s(e)g(pro) m(vided)g(in)g FD(w)p FK(.)41 b(The)390 4024 y(diagonal)24 b(and)f(lo)m(w)m(er)h(triangular)f(part)g(of)g FD(A)g FK(are)h(destro)m(y)m(ed)g(during)e(the)h(computation,)i(but)e(the)390 4134 y(strict)37 b(upp)s(er)d(triangular)i(part)g(is)g(not)g (referenced.)58 b(The)35 b(imaginary)i(parts)e(of)h(the)h(diagonal)390 4244 y(are)j(assumed)e(to)j(b)s(e)d(zero)i(and)f(are)h(not)g (referenced.)67 b(The)39 b(eigen)m(v)-5 b(alues)41 b(are)f(stored)g(in) f(the)390 4353 y(v)m(ector)f FD(ev)-5 b(al)41 b FK(and)36 b(are)h(unordered.)58 b(The)36 b(corresp)s(onding)g(complex)h(eigen)m (v)m(ectors)j(are)d(stored)390 4463 y(in)c(the)g(columns)g(of)g(the)g (matrix)h FD(ev)m(ec)p FK(.)50 b(F)-8 b(or)34 b(example,)g(the)g(eigen) m(v)m(ector)i(in)d(the)g(\014rst)f(column)390 4572 y(corresp)s(onds)g (to)h(the)g(\014rst)g(eigen)m(v)-5 b(alue.)50 b(The)32 b(eigen)m(v)m(ectors)k(are)e(guaran)m(teed)g(to)f(b)s(e)f(m)m(utually) 390 4682 y(orthogonal)g(and)e(normalised)g(to)h(unit)f(magnitude.)150 4907 y FJ(15.3)68 b(Real)47 b(Nonsymmetric)e(Matrices)150 5066 y FK(The)33 b(solution)h(of)g(the)g(real)h(nonsymmetric)e (eigensystem)i(problem)e(for)g(a)i(matrix)f FE(A)f FK(in)m(v)m(olv)m (es)j(com-)150 5176 y(puting)30 b(the)g(Sc)m(h)m(ur)g(decomp)s(osition) 1728 5340 y FE(A)25 b FK(=)g FE(Z)7 b(T)13 b(Z)2121 5302 y Fq(T)p eop end %%Page: 162 180 TeXDict begin 162 179 bop 150 -116 a FK(Chapter)30 b(15:)41 b(Eigensystems)2424 b(162)150 299 y(where)36 b FE(Z)43 b FK(is)36 b(an)h(orthogonal)h(matrix)e(of)h(Sc)m(h)m(ur)f(v)m(ectors)i (and)e FE(T)13 b FK(,)38 b(the)e(Sc)m(h)m(ur)g(form,)i(is)f(quasi)f (upp)s(er)150 408 y(triangular)29 b(with)f(diagonal)i(1-b)m(y-1)g(blo)s (c)m(ks)f(whic)m(h)f(are)h(real)g(eigen)m(v)-5 b(alues)31 b(of)d FE(A)p FK(,)i(and)e(diagonal)i(2-b)m(y-2)150 518 y(blo)s(c)m(ks)37 b(whose)g(eigen)m(v)-5 b(alues)38 b(are)f(complex)h (conjugate)g(eigen)m(v)-5 b(alues)38 b(of)f FE(A)p FK(.)60 b(The)36 b(algorithm)i(used)e(is)150 628 y(the)31 b(double-shift)f(F)-8 b(rancis)31 b(metho)s(d.)3350 823 y([F)-8 b(unction])-3599 b Fv(gsl_eigen_nonsymm_work)q(spa)q(ce)58 b(*)53 b (gsl_eigen_nonsymm_allo)q(c)565 932 y Fu(\()p FD(const)31 b(size)p 985 932 28 4 v 41 w(t)g Ft(n)p Fu(\))390 1042 y FK(This)25 b(function)h(allo)s(cates)i(a)e(w)m(orkspace)h(for)e (computing)h(eigen)m(v)-5 b(alues)28 b(of)e FD(n)p FK(-b)m(y-)p FD(n)f FK(real)i(nonsym-)390 1152 y(metric)k(matrices.)42 b(The)30 b(size)h(of)f(the)h(w)m(orkspace)g(is)g FE(O)s FK(\(2)p FE(n)p 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2230 y(nonsymm)p FK(.)82 b(If)45 b(it)g(is)g(set)h (to)f(0,)50 b FE(T)57 b FK(will)46 b(not)f(b)s(e)f(computed)h(\(this)g (is)g(the)g(default)g(setting\).)390 2340 y(Computing)32 b(the)g(full)g(Sc)m(h)m(ur)g(form)g FE(T)45 b FK(requires)32 b(appro)m(ximately)i(1.5{2)g(times)f(the)g(n)m(um)m(b)s(er)e(of)390 2449 y(\015ops.)390 2589 y(If)37 b FD(balance)44 b FK(is)37 b(set)h(to)h(1,)g(a)f(balancing)h(transformation)f(is)f(applied)g(to)i (the)e(matrix)h(prior)f(to)390 2699 y(computing)21 b(eigen)m(v)-5 b(alues.)39 b(This)20 b(transformation)h(is)g(designed)g(to)g(mak)m(e)h (the)f(ro)m(ws)g(and)f(columns)390 2808 y(of)37 b(the)g(matrix)g(ha)m (v)m(e)g(comparable)h(norms,)f(and)f(can)h(result)g(in)f(more)h (accurate)h(eigen)m(v)-5 b(alues)390 2918 y(for)33 b(matrices)h(whose)e (en)m(tries)i(v)-5 b(ary)33 b(widely)g(in)f(magnitude.)49 b(See)33 b(Section)h(14.19)h([Balancing],)390 3027 y(page)43 b(157)g(for)e(more)h(information.)75 b(Note)43 b(that)g(the)f (balancing)g(transformation)g(do)s(es)g(not)390 3137 y(preserv)m(e)31 b(the)g(orthogonalit)m(y)j(of)d(the)g(Sc)m(h)m(ur)f(v) m(ectors,)j(so)e(if)g(y)m(ou)g(wish)f(to)i(compute)f(the)h(Sc)m(h)m(ur) 390 3247 y(v)m(ectors)c(with)e FH(gsl_eigen_nonsymm_Z)20 b FK(y)m(ou)27 b(will)g(obtain)f(the)h(Sc)m(h)m(ur)e(v)m(ectors)j(of)e (the)h(balanced)390 3356 y(matrix)k(instead)f(of)h(the)f(original)i (matrix.)41 b(The)30 b(relationship)h(will)f(b)s(e)1614 3529 y FE(T)38 b FK(=)25 b FE(Q)1873 3492 y Fq(t)1902 3529 y FE(D)1980 3492 y Fp(\000)p FB(1)2069 3529 y FE(AD)s(Q)390 3703 y FK(where)d FD(Q)27 b FK(is)c(the)g(matrix)g(of)g(Sc)m(h)m(ur)f (v)m(ectors)i(for)f(the)g(balanced)g(matrix,)i(and)d FD(D)28 b FK(is)22 b(the)h(balancing)390 3812 y(transformation.)39 b(Then)25 b FH(gsl_eigen_nonsymm_Z)20 b FK(will)26 b(compute)g(a)g (matrix)g FD(Z)33 b FK(whic)m(h)25 b(satis\014es)1709 3985 y FE(T)38 b FK(=)25 b FE(Z)1965 3948 y Fp(\000)p FB(1)2054 3985 y FE(AZ)390 4158 y FK(with)30 b FE(Z)j FK(=)26 b FE(D)s(Q)p FK(.)41 b(Note)32 b(that)g FD(Z)38 b FK(will)31 b(not)g(b)s(e)f(orthogonal.)44 b(F)-8 b(or)31 b(this)g(reason,)g(balancing)h(is)f(not)390 4268 y(p)s(erformed)e(b)m (y)h(default.)3350 4463 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_eigen_nonsymm)e Fu(\()p FD(gsl)p 1441 4463 V 41 w(matrix)30 b(*)h Ft(A)p FD(,)g(gsl)p 2067 4463 V 41 w(v)m(ector)p 2349 4463 V 41 w(complex)g(*)g Ft(eval)p FD(,)565 4573 y(gsl)p 677 4573 V 41 w(eigen)p 919 4573 V 41 w(nonsymm)p 1343 4573 V 39 w(w)m(orkspace)g(*)f Ft(w)p Fu(\))390 4682 y FK(This)25 b(function)g(computes)g(the)h(eigen) m(v)-5 b(alues)27 b(of)e(the)h(real)g(nonsymmetric)f(matrix)g FD(A)h FK(and)e(stores)390 4792 y(them)d(in)h(the)f(v)m(ector)i FD(ev)-5 b(al)p FK(.)39 b(If)21 b FE(T)34 b FK(is)22 b(desired,)h(it)f(is)f(stored)h(in)f(the)h(upp)s(er)d(p)s(ortion)i(of)h FD(A)g FK(on)f(output.)390 4902 y(Otherwise,)31 b(on)h(output,)f(the)h (diagonal)g(of)g FD(A)f FK(will)h(con)m(tain)g(the)g(1-b)m(y-1)g(real)g (eigen)m(v)-5 b(alues)34 b(and)390 5011 y(2-b)m(y-2)e(complex)f (conjugate)g(eigen)m(v)-5 b(alue)33 b(systems,)d(and)g(the)h(rest)f(of) h FD(A)f FK(is)h(destro)m(y)m(ed.)41 b(In)30 b(rare)390 5121 y(cases,)41 b(this)c(function)g(ma)m(y)h(fail)h(to)f(\014nd)e(all) i(eigen)m(v)-5 b(alues.)65 b(If)37 b(this)g(happ)s(ens,)h(an)g(error)f (co)s(de)390 5230 y(is)e(returned)f(and)h(the)h(n)m(um)m(b)s(er)e(of)h (con)m(v)m(erged)i(eigen)m(v)-5 b(alues)37 b(is)e(stored)h(in)f FH(w->n_evals)p FK(.)52 b(The)390 5340 y(con)m(v)m(erged)32 b(eigen)m(v)-5 b(alues)32 b(are)f(stored)f(in)g(the)h(b)s(eginning)f (of)g FD(ev)-5 b(al)p FK(.)p eop end %%Page: 163 181 TeXDict begin 163 180 bop 150 -116 a FK(Chapter)30 b(15:)41 b(Eigensystems)2424 b(163)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_eigen_nonsymm_Z)e Fu(\()p FD(gsl)p 1545 299 28 4 v 41 w(matrix)31 b(*)g Ft(A)p FD(,)g(gsl)p 2172 299 V 40 w(v)m(ector)p 2453 299 V 42 w(complex)g(*)g Ft(eval)p FD(,)565 408 y(gsl)p 677 408 V 41 w(matrix)f(*)h Ft(Z)p FD(,)g(gsl)p 1303 408 V 41 w(eigen)p 1545 408 V 41 w(nonsymm)p 1969 408 V 38 w(w)m(orkspace)h(*)e Ft(w)p Fu(\))390 518 y FK(This)39 b(function)g(is)g(iden)m(tical)i(to)g FH(gsl_eigen_nonsymm)34 b FK(except)41 b(that)f(it)g(also)g(computes)g (the)390 628 y(Sc)m(h)m(ur)30 b(v)m(ectors)i(and)d(stores)i(them)g(in)m (to)g FD(Z)p FK(.)3350 860 y([F)-8 b(unction])-3599 b Fv(gsl_eigen_nonsymmv_wor)q(ksp)q(ace)59 b(*)52 b (gsl_eigen_nonsymmv_al)q(loc)565 970 y Fu(\()p FD(const)31 b(size)p 985 970 V 41 w(t)g Ft(n)p Fu(\))390 1079 y FK(This)39 b(function)h(allo)s(cates)i(a)f(w)m(orkspace)g(for)e(computing)h(eigen) m(v)-5 b(alues)42 b(and)e(eigen)m(v)m(ectors)j(of)390 1189 y FD(n)p FK(-b)m(y-)p FD(n)30 b FK(real)h(nonsymmetric)f (matrices.)42 b(The)30 b(size)h(of)f(the)h(w)m(orkspace)g(is)f FE(O)s FK(\(5)p FE(n)p FK(\).)3350 1421 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_eigen_nonsymmv_free)e Fu(\()p FD(gsl)p 1807 1421 V 41 w(eigen)p 2049 1421 V 41 w(nonsymm)m(v)p 2518 1421 V 39 w(w)m(orkspace)31 b(*)g Ft(w)p Fu(\))390 1531 y FK(This)f(function)g(frees)g(the)h(memory)f(asso)s(ciated)i (with)e(the)g(w)m(orkspace)h FD(w)p FK(.)3350 1763 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_eigen_nonsymmv_param)q(s)e Fu(\()p FD(const)31 b(in)m(t)g Ft(balance)p FD(,)565 1872 y(gsl)p 677 1872 V 41 w(eigen)p 919 1872 V 41 w(nonsymm)p 1343 1872 V 39 w(w)m(orkspace)g(*)f Ft(w)p Fu(\))390 1982 y FK(This)f(function)h(sets)g(parameters)g(whic)m(h)g(determine)g (ho)m(w)g(the)g(eigen)m(v)-5 b(alue)32 b(problem)d(is)h(solv)m(ed)390 2092 y(in)d(subsequen)m(t)f(calls)j(to)f FH(gsl_eigen_nonsymmv)p FK(.)35 b(If)26 b FD(balance)34 b FK(is)27 b(set)h(to)g(1,)g(a)g (balancing)g(trans-)390 2201 y(formation)k(is)g(applied)f(to)i(the)f (matrix.)45 b(See)32 b FH(gsl_eigen_nonsymm_param)o(s)26 b FK(for)31 b(more)h(infor-)390 2311 y(mation.)39 b(Balancing)26 b(is)f(turned)e(o\013)i(b)m(y)f(default)h(since)g(it)g(do)s(es)f(not)g (preserv)m(e)h(the)f(orthogonalit)m(y)390 2420 y(of)31 b(the)f(Sc)m(h)m(ur)g(v)m(ectors.)3350 2653 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_eigen_nonsymmv)e Fu(\()p FD(gsl)p 1493 2653 V 41 w(matrix)31 b(*)g Ft(A)p FD(,)f(gsl)p 2119 2653 V 41 w(v)m(ector)p 2401 2653 V 42 w(complex)h(*)f Ft(eval)p FD(,)565 2762 y(gsl)p 677 2762 V 41 w(matrix)p 983 2762 V 40 w(complex)h(*)g Ft(evec)p FD(,)h(gsl)p 1826 2762 V 40 w(eigen)p 2067 2762 V 41 w(nonsymm)m(v)p 2536 2762 V 40 w(w)m(orkspace)f(*)f Ft(w)p Fu(\))390 2872 y FK(This)25 b(function)h(computes)h(eigen)m(v)-5 b(alues)28 b(and)e(righ)m(t)h(eigen)m(v)m(ectors)i(of)d(the)h FD(n)p FK(-b)m(y-)p FD(n)f FK(real)h(nonsym-)390 2981 y(metric)g(matrix)g FD(A)p FK(.)40 b(It)27 b(\014rst)f(calls)i FH(gsl_eigen_nonsymm)22 b FK(to)27 b(compute)g(the)g(eigen)m(v)-5 b(alues,)30 b(Sc)m(h)m(ur)390 3091 y(form)e FE(T)13 b FK(,)30 b(and)e(Sc)m(h)m(ur)g(v)m(ectors.)42 b(Then)28 b(it)h(\014nds)e(eigen)m(v)m(ectors)32 b(of)d FE(T)42 b FK(and)28 b(bac)m(ktransforms)h(them)390 3201 y(using)j(the)g(Sc)m(h) m(ur)g(v)m(ectors.)47 b(The)32 b(Sc)m(h)m(ur)g(v)m(ectors)h(are)g (destro)m(y)m(ed)g(in)f(the)g(pro)s(cess,)h(but)e(can)i(b)s(e)390 3310 y(sa)m(v)m(ed)h(b)m(y)g(using)e FH(gsl_eigen_nonsymmv_Z)p FK(.)44 b(The)33 b(computed)g(eigen)m(v)m(ectors)k(are)c(normalized)390 3420 y(to)e(ha)m(v)m(e)g(unit)f(magnitude.)41 b(On)29 b(output,)h(the)h(upp)s(er)d(p)s(ortion)h(of)i FD(A)f FK(con)m(tains)h(the)g(Sc)m(h)m(ur)e(form)390 3529 y FE(T)13 b FK(.)51 b(If)34 b FH(gsl_eigen_nonsymm)29 b FK(fails,)36 b(no)e(eigen)m(v)m(ectors)j(are)e(computed,)g(and)e(an)h (error)g(co)s(de)g(is)390 3639 y(returned.)3350 3871 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_eigen_nonsymmv_Z)f Fu(\()p FD(gsl)p 1598 3871 V 41 w(matrix)29 b(*)g Ft(A)p FD(,)h(gsl)p 2220 3871 V 40 w(v)m(ector)p 2501 3871 V 42 w(complex)g(*)f Ft(eval)p FD(,)565 3981 y(gsl)p 677 3981 V 41 w(matrix)p 983 3981 V 40 w(complex)i(*)g Ft(evec)p FD(,)h(gsl)p 1826 3981 V 40 w(matrix)f(*)g Ft(Z)p FD(,)g(gsl)p 2452 3981 V 40 w(eigen)p 2693 3981 V 41 w(nonsymm)m(v)p 3162 3981 V 39 w(w)m(orkspace)h(*)565 4090 y Ft(w)p Fu(\))390 4200 y FK(This)27 b(function)h(is)g(iden)m(tical)i(to)f FH(gsl_eigen_nonsymmv)23 b FK(except)29 b(that)g(it)g(also)g(sa)m(v)m (es)g(the)g(Sc)m(h)m(ur)390 4310 y(v)m(ectors)j(in)m(to)f FD(Z)p FK(.)150 4578 y FJ(15.4)68 b(Real)47 b(Generalized)e (Symmetric-De\014nite)i(Eigensystems)150 4737 y FK(The)41 b(real)i(generalized)h(symmetric-de\014nite)e(eigen)m(v)-5 b(alue)44 b(problem)e(is)g(to)g(\014nd)f(eigen)m(v)-5 b(alues)44 b FE(\025)e FK(and)150 4847 y(eigen)m(v)m(ectors)33 b FE(x)e FK(suc)m(h)f(that)1740 5039 y FE(Ax)25 b FK(=)g FE(\025B)5 b(x)150 5230 y FK(where)33 b FE(A)h FK(and)f FE(B)39 b FK(are)34 b(symmetric)g(matrices,)i(and)d FE(B)38 b FK(is)c(p)s(ositiv)m(e-de\014nite.)52 b(This)33 b(problem)g(reduces) 150 5340 y(to)e(the)f(standard)g(symmetric)g(eigen)m(v)-5 b(alue)33 b(problem)c(b)m(y)h(applying)h(the)f(Cholesky)g(decomp)s (osition)h(to)p eop end %%Page: 164 182 TeXDict begin 164 181 bop 150 -116 a FK(Chapter)30 b(15:)41 b(Eigensystems)2424 b(164)150 299 y FE(B)5 b FK(:)1939 444 y FE(Ax)25 b FK(=)g FE(\025B)5 b(x)1939 578 y(Ax)25 b FK(=)g FE(\025LL)2357 540 y Fq(t)2386 578 y FE(x)1462 643 y Fs(\000)1500 713 y FE(L)1562 675 y Fp(\000)p FB(1)1651 713 y FE(AL)1781 675 y Fp(\000)p Fq(t)1862 643 y Fs(\001)1916 713 y FE(L)1978 675 y Fq(t)2007 713 y FE(x)g FK(=)g FE(\025L)2295 675 y Fq(t)2324 713 y FE(x)150 882 y FK(Therefore,)43 b(the)e(problem)f(b)s(ecomes)g FE(C)7 b(y)45 b FK(=)d FE(\025y)h FK(where)d FE(C)49 b FK(=)42 b FE(L)2480 849 y Fp(\000)p FB(1)2569 882 y FE(AL)2699 849 y Fp(\000)p Fq(t)2820 882 y FK(is)f(symmetric,)i(and)d FE(y)45 b FK(=)150 992 y FE(L)212 959 y Fq(t)241 992 y FE(x)p FK(.)55 b(The)35 b(standard)f(symmetric)i(eigensolv)m(er)h(can)e(b)s(e)g (applied)g(to)h(the)f(matrix)h FE(C)7 b FK(.)54 b(The)35 b(resulting)150 1101 y(eigen)m(v)m(ectors)23 b(are)e(bac)m (ktransformed)f(to)i(\014nd)c(the)j(v)m(ectors)h(of)e(the)h(original)g (problem.)37 b(The)20 b(eigen)m(v)-5 b(alues)150 1211 y(and)30 b(eigen)m(v)m(ectors)j(of)e(the)f(generalized)i (symmetric-de\014nite)f(eigenproblem)g(are)g(alw)m(a)m(ys)h(real.)3350 1394 y([F)-8 b(unction])-3599 b Fv(gsl_eigen_gensymm_work)q(spa)q(ce)58 b(*)53 b(gsl_eigen_gensymm_allo)q(c)565 1504 y Fu(\()p FD(const)31 b(size)p 985 1504 28 4 v 41 w(t)g Ft(n)p Fu(\))390 1613 y FK(This)c(function)h(allo)s(cates)i(a)e(w)m(orkspace)h (for)f(computing)g(eigen)m(v)-5 b(alues)30 b(of)e FD(n)p FK(-b)m(y-)p FD(n)f FK(real)i(general-)390 1723 y(ized)i (symmetric-de\014nite)g(eigensystems.)42 b(The)29 b(size)j(of)e(the)h (w)m(orkspace)g(is)f FE(O)s FK(\(2)p FE(n)p FK(\).)3350 1907 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_eigen_gensymm_free)e Fu(\()p FD(gsl)p 1755 1907 V 41 w(eigen)p 1997 1907 V 41 w(gensymm)p 2410 1907 V 39 w(w)m(orkspace)31 b(*)g Ft(w)p Fu(\))390 2016 y FK(This)f(function)g(frees)g(the)h(memory)f (asso)s(ciated)i(with)e(the)g(w)m(orkspace)h FD(w)p FK(.)3350 2200 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_eigen_gensymm)e Fu(\()p FD(gsl)p 1441 2200 V 41 w(matrix)30 b(*)h Ft(A)p FD(,)g(gsl)p 2067 2200 V 41 w(matrix)f(*)h Ft(B)p FD(,)g(gsl)p 2693 2200 V 41 w(v)m(ector)h(*)565 2309 y Ft(eval)p FD(,)g(gsl)p 942 2309 V 40 w(eigen)p 1183 2309 V 41 w(gensymm)p 1596 2309 V 40 w(w)m(orkspace)f(*)g Ft(w)p Fu(\))390 2419 y FK(This)43 b(function)h(computes)g(the)g(eigen)m(v)-5 b(alues)46 b(of)e(the)g(real)h(generalized)g(symmetric-de\014nite)390 2529 y(matrix)36 b(pair)e(\()p FD(A)p FK(,)k FD(B)5 b FK(\),)37 b(and)e(stores)h(them)f(in)g FD(ev)-5 b(al)p FK(,)37 b(using)e(the)g(metho)s(d)g(outlined)g(ab)s(o)m(v)m(e.)57 b(On)390 2638 y(output,)30 b FD(B)36 b FK(con)m(tains)c(its)e(Cholesky) h(decomp)s(osition)g(and)f FD(A)g FK(is)h(destro)m(y)m(ed.)3350 2822 y([F)-8 b(unction])-3599 b Fv(gsl_eigen_gensymmv_wor)q(ksp)q(ace) 59 b(*)52 b(gsl_eigen_gensymmv_al)q(loc)565 2931 y Fu(\()p FD(const)31 b(size)p 985 2931 V 41 w(t)g Ft(n)p Fu(\))390 3041 y FK(This)39 b(function)h(allo)s(cates)i(a)f(w)m(orkspace)g(for)e (computing)h(eigen)m(v)-5 b(alues)42 b(and)e(eigen)m(v)m(ectors)j(of) 390 3151 y FD(n)p FK(-b)m(y-)p FD(n)27 b FK(real)g(generalized)i (symmetric-de\014nite)f(eigensystems.)40 b(The)27 b(size)h(of)f(the)g (w)m(orkspace)h(is)390 3260 y FE(O)s FK(\(4)p FE(n)p FK(\).)3350 3444 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_eigen_gensymmv_free)e Fu(\()p FD(gsl)p 1807 3444 V 41 w(eigen)p 2049 3444 V 41 w(gensymm)m(v)p 2507 3444 V 40 w(w)m(orkspace)31 b(*)g Ft(w)p Fu(\))390 3553 y FK(This)f(function)g(frees)g(the)h(memory)f(asso)s(ciated)i(with)e(the) g(w)m(orkspace)h FD(w)p FK(.)3350 3737 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_eigen_gensymmv)e Fu(\()p FD(gsl)p 1493 3737 V 41 w(matrix)31 b(*)g Ft(A)p FD(,)f(gsl)p 2119 3737 V 41 w(matrix)h(*)f Ft(B)p FD(,)h(gsl)p 2745 3737 V 41 w(v)m(ector)h(*)565 3847 y Ft(eval)p FD(,)g(gsl)p 942 3847 V 40 w(matrix)f(*)g Ft(evec)p FD(,)h(gsl)p 1725 3847 V 40 w(eigen)p 1966 3847 V 41 w(gensymm)m(v)p 2424 3847 V 40 w(w)m(orkspace)g(*)e Ft(w)p Fu(\))390 3956 y FK(This)50 b(function)g(computes)h(the)g(eigen)m(v)-5 b(alues)53 b(and)d(eigen)m(v)m(ectors)j(of)e(the)g(real)g(generalized) 390 4066 y(symmetric-de\014nite)28 b(matrix)g(pair)f(\()p FD(A)p FK(,)i FD(B)5 b FK(\),)29 b(and)e(stores)h(them)g(in)f FD(ev)-5 b(al)32 b FK(and)27 b FD(ev)m(ec)35 b FK(resp)s(ectiv)m(ely)-8 b(.)390 4175 y(The)36 b(computed)h(eigen)m(v)m(ectors)j(are)d (normalized)h(to)g(ha)m(v)m(e)g(unit)e(magnitude.)61 b(On)36 b(output,)i FD(B)390 4285 y FK(con)m(tains)32 b(its)e(Cholesky)h(decomp)s(osition)g(and)e FD(A)i FK(is)f(destro)m(y)m (ed.)150 4517 y FJ(15.5)68 b(Complex)46 b(Generalized)g (Hermitian-De\014nite)h(Eigensystems)150 4676 y FK(The)28 b(complex)h(generalized)h(hermitian-de\014nite)e(eigen)m(v)-5 b(alue)30 b(problem)e(is)g(to)h(\014nd)e(eigen)m(v)-5 b(alues)30 b FE(\025)f FK(and)150 4786 y(eigen)m(v)m(ectors)k FE(x)e FK(suc)m(h)f(that)1740 4953 y FE(Ax)25 b FK(=)g FE(\025B)5 b(x)150 5121 y FK(where)38 b FE(A)h FK(and)f FE(B)43 b FK(are)c(hermitian)g(matrices,)j(and)c FE(B)43 b FK(is)38 b(p)s(ositiv)m(e-de\014nite.)67 b(Similarly)39 b(to)g(the)g(real)150 5230 y(case,)31 b(this)f(can)g(b)s(e)f(reduced)g (to)h FE(C)7 b(y)28 b FK(=)d FE(\025y)32 b FK(where)e FE(C)h FK(=)25 b FE(L)2169 5197 y Fp(\000)p FB(1)2258 5230 y FE(AL)2388 5197 y Fp(\000y)2505 5230 y FK(is)k(hermitian,)h(and) g FE(y)e FK(=)d FE(L)3442 5197 y Fp(y)3476 5230 y FE(x)p FK(.)40 b(The)150 5340 y(standard)29 b(hermitian)h(eigensolv)m(er)j (can)d(b)s(e)f(applied)h(to)h(the)g(matrix)f FE(C)7 b FK(.)40 b(The)30 b(resulting)g(eigen)m(v)m(ectors)p eop end %%Page: 165 183 TeXDict begin 165 182 bop 150 -116 a FK(Chapter)30 b(15:)41 b(Eigensystems)2424 b(165)150 299 y(are)40 b(bac)m(ktransformed)f(to)h (\014nd)e(the)i(v)m(ectors)g(of)g(the)g(original)g(problem.)67 b(The)39 b(eigen)m(v)-5 b(alues)41 b(of)f(the)150 408 y(generalized)32 b(hermitian-de\014nite)f(eigenproblem)f(are)h(alw)m(a) m(ys)h(real.)3350 601 y([F)-8 b(unction])-3599 b Fv (gsl_eigen_genherm_work)q(spa)q(ce)58 b(*)53 b(gsl_eigen_genherm_allo)q (c)565 710 y Fu(\()p FD(const)31 b(size)p 985 710 28 4 v 41 w(t)g Ft(n)p Fu(\))390 820 y FK(This)43 b(function)h(allo)s (cates)j(a)d(w)m(orkspace)h(for)f(computing)g(eigen)m(v)-5 b(alues)46 b(of)f FD(n)p FK(-b)m(y-)p FD(n)e FK(complex)390 930 y(generalized)32 b(hermitian-de\014nite)f(eigensystems.)41 b(The)30 b(size)h(of)g(the)g(w)m(orkspace)g(is)f FE(O)s FK(\(3)p FE(n)p FK(\).)3350 1122 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_eigen_genherm_free)e Fu(\()p FD(gsl)p 1755 1122 V 41 w(eigen)p 1997 1122 V 41 w(genherm)p 2377 1122 V 39 w(w)m(orkspace)31 b(*)g Ft(w)p Fu(\))390 1232 y FK(This)f(function)g(frees)g(the)h(memory)f(asso)s(ciated)i(with)e (the)g(w)m(orkspace)h FD(w)p FK(.)3350 1424 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_eigen_genherm)e Fu(\()p FD(gsl)p 1441 1424 V 41 w(matrix)p 1747 1424 V 40 w(complex)31 b(*)g Ft(A)p FD(,)g(gsl)p 2433 1424 V 40 w(matrix)p 2738 1424 V 41 w(complex)g(*)565 1534 y Ft(B)p FD(,)g(gsl)p 785 1534 V 41 w(v)m(ector)h(*)e Ft(eval)p FD(,)i(gsl)p 1545 1534 V 41 w(eigen)p 1787 1534 V 41 w(genherm)p 2167 1534 V 39 w(w)m(orkspace)f(*)g Ft(w)p Fu(\))390 1643 y FK(This)26 b(function)h(computes)h(the)f(eigen)m(v)-5 b(alues)29 b(of)f(the)f(complex)h(generalized)h(hermitian-de\014nite)390 1753 y(matrix)36 b(pair)e(\()p FD(A)p FK(,)k FD(B)5 b FK(\),)37 b(and)e(stores)h(them)f(in)g FD(ev)-5 b(al)p FK(,)37 b(using)e(the)g(metho)s(d)g(outlined)g(ab)s(o)m(v)m(e.)57 b(On)390 1862 y(output,)30 b FD(B)36 b FK(con)m(tains)c(its)e(Cholesky) h(decomp)s(osition)g(and)f FD(A)g FK(is)h(destro)m(y)m(ed.)3350 2055 y([F)-8 b(unction])-3599 b Fv(gsl_eigen_genhermv_wor)q(ksp)q(ace) 59 b(*)52 b(gsl_eigen_genhermv_al)q(loc)565 2164 y Fu(\()p FD(const)31 b(size)p 985 2164 V 41 w(t)g Ft(n)p Fu(\))390 2274 y FK(This)d(function)h(allo)s(cates)i(a)f(w)m(orkspace)g(for)e (computing)i(eigen)m(v)-5 b(alues)31 b(and)d(eigen)m(v)m(ectors)k(of)d FD(n)p FK(-)390 2383 y(b)m(y-)p FD(n)g FK(complex)h(generalized)h (hermitian-de\014nite)e(eigensystems.)42 b(The)28 b(size)i(of)g(the)f (w)m(orkspace)390 2493 y(is)h FE(O)s FK(\(5)p FE(n)p FK(\).)3350 2685 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_eigen_genhermv_free)e Fu(\()p FD(gsl)p 1807 2685 V 41 w(eigen)p 2049 2685 V 41 w(genherm)m(v)p 2474 2685 V 40 w(w)m(orkspace)31 b(*)g Ft(w)p Fu(\))390 2795 y FK(This)f(function)g(frees)g(the)h(memory)f(asso)s(ciated)i(with)e(the) g(w)m(orkspace)h FD(w)p FK(.)3350 2987 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_eigen_genhermv)e Fu(\()p FD(gsl)p 1493 2987 V 41 w(matrix)p 1799 2987 V 40 w(complex)32 b(*)e Ft(A)p FD(,)h(gsl)p 2485 2987 V 41 w(matrix)p 2791 2987 V 40 w(complex)565 3097 y(*)g Ft(B)p FD(,)g(gsl)p 861 3097 V 40 w(v)m(ector)h(*)f Ft(eval)p FD(,)h(gsl)p 1621 3097 V 40 w(matrix)p 1926 3097 V 41 w(complex)f(*)g Ft(evec)p FD(,)565 3207 y(gsl)p 677 3207 V 41 w(eigen)p 919 3207 V 41 w(genherm)m(v)p 1344 3207 V 40 w(w)m(orkspace)g(*)g Ft(w)p Fu(\))390 3316 y 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b(ma)m(y)f(also)g (de\014ne)e(the)i(problem)f(as)g(\014nding)f(eigen)m(v)-5 b(alues)33 b FE(\026)d FK(and)g(eigen)m(v)m(ectors)j FE(y)g FK(suc)m(h)d(that)1743 4668 y FE(\026Ay)e FK(=)d FE(B)5 b(y)150 4839 y FK(Note)26 b(that)f(these)f(t)m(w)m(o)i(problems) e(are)g(equiv)-5 b(alen)m(t)26 b(\(with)f FE(\025)g FK(=)g(1)p FE(=\026)p FK(\))g(if)f(neither)h FE(\025)f FK(nor)g FE(\026)g FK(is)g(zero.)40 b(If)24 b(sa)m(y)-8 b(,)150 4949 y FE(\025)31 b FK(is)g(zero,)i(then)d(it)i(is)f(still)h(a)g(w)m (ell)g(de\014ned)d(eigenproblem,)j(but)f(its)g(alternate)i(problem)e (in)m(v)m(olving)h FE(\026)150 5059 y FK(is)c(not.)40 b(Therefore,)29 b(to)f(allo)m(w)i(for)d(zero)i(\(and)f(in\014nite\))g (eigen)m(v)-5 b(alues,)30 b(the)e(problem)g(whic)m(h)f(is)h(actually) 150 5168 y(solv)m(ed)j(is)1709 5340 y FE(\014)5 b(Ax)26 b FK(=)f FE(\013B)5 b(x)p eop end %%Page: 166 184 TeXDict begin 166 183 bop 150 -116 a FK(Chapter)30 b(15:)41 b(Eigensystems)2424 b(166)150 299 y(The)34 b(eigensolv)m(er)i(routines) 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b(gsl_eigen_gen_alloc)e Fu(\()p FD(const)31 b(size)p 2969 2242 28 4 v 41 w(t)g Ft(n)p Fu(\))390 2352 y FK(This)c(function)h (allo)s(cates)i(a)e(w)m(orkspace)h(for)f(computing)g(eigen)m(v)-5 b(alues)30 b(of)e FD(n)p FK(-b)m(y-)p FD(n)f FK(real)i(general-)390 2462 y(ized)i(nonsymmetric)f(eigensystems.)42 b(The)30 b(size)h(of)f(the)h(w)m(orkspace)g(is)f FE(O)s FK(\()p FE(n)p FK(\).)3350 2659 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_eigen_gen_free)c Fu(\()p FD(gsl)p 1545 2659 V 41 w(eigen)p 1787 2659 V 41 w(gen)p 1964 2659 V 41 w(w)m(orkspace)31 b(*)g Ft(w)p Fu(\))390 2769 y FK(This)f(function)g(frees)g(the)h (memory)f(asso)s(ciated)i(with)e(the)g(w)m(orkspace)h FD(w)p FK(.)3350 2966 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_eigen_gen_params)d Fu(\()p FD(const)31 b(in)m(t)g Ft(compute_s)p FD(,)i(const)e(in)m(t)565 3076 y Ft(compute_t)p FD(,)i(const)e(in)m(t)g Ft(balance)p FD(,)i(gsl)p 2002 3076 V 40 w(eigen)p 2243 3076 V 41 w(gen)p 2420 3076 V 41 w(w)m(orkspace)e(*)g Ft(w)p Fu(\))390 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b(b)s(e)e(computed)h(b)m(y)g FH(gsl_eigen_gen)p FK(.)390 4015 y(If)j(it)g(is)h(set)f(to)h(0,)h FE(T)47 b FK(will)35 b(not)f(b)s(e)g(computed)g(\(this)g(is)g(the)h (default)f(setting\).)54 b FE(T)47 b FK(is)34 b(an)g(upp)s(er)390 4125 y(triangular)h(matrix)f(with)g(non-negativ)m(e)i(elemen)m(ts)g(on) e(its)g(diagonal.)54 b(An)m(y)34 b(2-b)m(y-2)i(blo)s(c)m(ks)e(in)390 4234 y FE(S)h FK(will)c(corresp)s(ond)e(to)i(a)g(2-b)m(y-2)h(diagonal)f (blo)s(c)m(k)g(in)f FE(T)13 b FK(.)390 4375 y(The)39 b FD(balance)45 b FK(parameter)40 b(is)f(curren)m(tly)g(ignored,)j (since)d(generalized)i(balancing)f(is)f(not)h(y)m(et)390 4485 y(implemen)m(ted.)3350 4682 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_eigen_gen)d Fu(\()p FD(gsl)p 1232 4682 V 41 w(matrix)30 b(*)g Ft(A)p FD(,)h(gsl)p 1857 4682 V 40 w(matrix)g(*)f Ft(B)p FD(,)h(gsl)p 2482 4682 V 40 w(v)m(ector)p 2763 4682 V 42 w(complex)g(*)565 4792 y Ft(alpha)p FD(,)h(gsl)p 994 4792 V 41 w(v)m(ector)g(*)e Ft(beta)p FD(,)i(gsl)p 1754 4792 V 41 w(eigen)p 1996 4792 V 41 w(gen)p 2173 4792 V 40 w(w)m(orkspace)f(*)g Ft(w)p Fu(\))390 4902 y FK(This)f(function)g(computes)h(the)g(eigen)m (v)-5 b(alues)33 b(of)e(the)f(real)i(generalized)g(nonsymmetric)f (matrix)390 5011 y(pair)j(\()p FD(A)p FK(,)j FD(B)5 b FK(\),)36 b(and)e(stores)h(them)g(as)g(pairs)f(in)g(\()p FD(alpha)p FK(,)j FD(b)s(eta)p FK(\),)f(where)e FD(alpha)h FK(is)f(complex)i(and)390 5121 y FD(b)s(eta)k FK(is)f(real.)68 b(If)39 b FE(\014)1094 5135 y Fq(i)1162 5121 y FK(is)g(non-zero,)j (then)d FE(\025)i FK(=)f FE(\013)2146 5135 y Fq(i)2173 5121 y FE(=\014)2269 5135 y Fq(i)2337 5121 y FK(is)g(an)f(eigen)m(v)-5 b(alue.)70 b(Lik)m(ewise,)42 b(if)e FE(\013)3622 5135 y Fq(i)3689 5121 y FK(is)390 5230 y(non-zero,)35 b(then)e FE(\026)c FK(=)h FE(\014)1234 5244 y Fq(i)1262 5230 y FE(=\013)1365 5244 y Fq(i)1427 5230 y FK(is)j(an)g(eigen)m(v)-5 b(alue)35 b(of)e(the)h(alternate)h(problem)d FE(\026Ay)h FK(=)d FE(B)5 b(y)s FK(.)48 b(The)390 5340 y(elemen)m(ts)32 b(of)e FD(b)s(eta)h 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677 923 V 41 w(v)m(ector)p 959 923 V 41 w(complex)g(*)g Ft(alpha)p FD(,)h(gsl)p 1855 923 V 41 w(v)m(ector)g(*)f Ft(beta)p FD(,)g(gsl)p 2615 923 V 41 w(matrix)g(*)f Ft(Q)p FD(,)h(gsl)p 3241 923 V 41 w(matrix)f(*)h Ft(Z)p FD(,)565 1033 y(gsl)p 677 1033 V 41 w(eigen)p 919 1033 V 41 w(gen)p 1096 1033 V 40 w(w)m(orkspace)g(*)g Ft(w)p Fu(\))390 1142 y FK(This)26 b(function)h(is)g(iden)m(tical)h(to)g FH(gsl_eigen_gen)23 b FK(except)28 b(that)g(it)f(also)h(computes)f(the)g(left)h(and)390 1252 y(righ)m(t)j(Sc)m(h)m(ur)f(v)m(ectors)i(and)d(stores)i(them)f(in)m (to)i FD(Q)j FK(and)29 b FD(Z)38 b FK(resp)s(ectiv)m(ely)-8 b(.)3350 1438 y([F)g(unction])-3599 b Fv(gsl_eigen_genv_workspa)q(ce)59 b(*)52 b(gsl_eigen_genv_alloc)g Fu(\()p FD(const)31 b(size)p 3074 1438 V 41 w(t)565 1548 y Ft(n)p Fu(\))390 1657 y FK(This)39 b(function)h(allo)s(cates)i(a)f(w)m(orkspace)g(for)e (computing)h(eigen)m(v)-5 b(alues)42 b(and)e(eigen)m(v)m(ectors)j(of) 390 1767 y FD(n)p FK(-b)m(y-)p FD(n)f FK(real)h(generalized)h (nonsymmetric)f(eigensystems.)78 b(The)42 b(size)h(of)g(the)g(w)m (orkspace)g(is)390 1876 y FE(O)s FK(\(7)p FE(n)p FK(\).)3350 2062 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_eigen_genv_free)d Fu(\()p FD(gsl)p 1598 2062 V 41 w(eigen)p 1840 2062 V 41 w(gen)m(v)p 2062 2062 V 40 w(w)m(orkspace)32 b(*)e Ft(w)p Fu(\))390 2172 y FK(This)g(function)g(frees)g(the)h(memory)f (asso)s(ciated)i(with)e(the)g(w)m(orkspace)h FD(w)p FK(.)3350 2358 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_eigen_genv)d Fu(\()p FD(gsl)p 1284 2358 V 41 w(matrix)31 b(*)f Ft(A)p FD(,)h(gsl)p 1910 2358 V 41 w(matrix)f(*)h Ft(B)p FD(,)g(gsl)p 2536 2358 V 41 w(v)m(ector)p 2818 2358 V 41 w(complex)565 2467 y(*)g Ft(alpha)p FD(,)h(gsl)p 1070 2467 V 41 w(v)m(ector)f(*)g Ft(beta)p FD(,)h(gsl)p 1830 2467 V 41 w(matrix)p 2136 2467 V 40 w(complex)f(*)g Ft(evec)p FD(,)565 2577 y(gsl)p 677 2577 V 41 w(eigen)p 919 2577 V 41 w(gen)m(v)p 1141 2577 V 41 w(w)m(orkspace)g(*)f Ft(w)p Fu(\))390 2687 y 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b(eigen)m(v)m(ectors)j(are)e(normalized)g(to)g(ha)m(v)m(e)g(unit)f (magnitude.)59 b(On)35 b(output,)j(\()p FD(A)p FK(,)g FD(B)5 b FK(\))390 3454 y(con)m(tains)34 b(the)e(generalized)j(Sc)m(h)m (ur)d(form)g(\()p FE(S)5 b FK(,)33 b FE(T)13 b FK(\).)48 b(If)32 b FH(gsl_eigen_gen)d FK(fails,)34 b(no)e(eigen)m(v)m(ectors)390 3563 y(are)f(computed,)f(and)g(an)g(error)g(co)s(de)h(is)f(returned.) 3350 3749 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_eigen_genv_QZ)e Fu(\()p FD(gsl)p 1441 3749 V 41 w(matrix)30 b(*)h Ft(A)p FD(,)g(gsl)p 2067 3749 V 41 w(matrix)f(*)h Ft(B)p FD(,)565 3859 y(gsl)p 677 3859 V 41 w(v)m(ector)p 959 3859 V 41 w(complex)g(*)g Ft(alpha)p FD(,)h(gsl)p 1855 3859 V 41 w(v)m(ector)g(*)f Ft(beta)p FD(,)g(gsl)p 2615 3859 V 41 w(matrix)p 2921 3859 V 40 w(complex)g(*)g Ft(evec)p FD(,)565 3968 y(gsl)p 677 3968 V 41 w(matrix)f(*)h Ft(Q)p FD(,)g(gsl)p 1303 3968 V 41 w(matrix)f(*)h Ft(Z)p FD(,)g(gsl)p 1929 3968 V 40 w(eigen)p 2170 3968 V 41 w(gen)m(v)p 2392 3968 V 41 w(w)m(orkspace)g(*)g Ft(w)p Fu(\))390 4078 y FK(This)37 b(function)g(is)g(iden)m(tical)i(to)f FH(gsl_eigen_genv)c FK(except)k(that)g(it)g(also)g(computes)g(the)f(left)390 4188 y(and)30 b(righ)m(t)h(Sc)m(h)m(ur)e(v)m(ectors)j(and)e(stores)h (them)f(in)m(to)i FD(Q)i FK(and)c FD(Z)38 b FK(resp)s(ectiv)m(ely)-8 b(.)150 4421 y FJ(15.7)68 b(Sorting)46 b(Eigen)l(v)-7 b(alues)46 b(and)f(Eigen)l(v)l(ectors)3350 4631 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_eigen_symmv_sort)f Fu(\()p FD(gsl)p 1598 4631 V 41 w(v)m(ector)32 b(*)e Ft(eval)p FD(,)i(gsl)p 2358 4631 V 41 w(matrix)e(*)h Ft(evec)p FD(,)565 4741 y(gsl)p 677 4741 V 41 w(eigen)p 919 4741 V 41 w(sort)p 1112 4741 V 40 w(t)g Ft(sort_type)p Fu(\))390 4851 y FK(This)h(function)h(sim)m(ultaneously)h(sorts)g(the)f (eigen)m(v)-5 b(alues)35 b(stored)e(in)g(the)h(v)m(ector)g FD(ev)-5 b(al)38 b FK(and)33 b(the)390 4960 y(corresp)s(onding)26 b(real)i(eigen)m(v)m(ectors)j(stored)c(in)g(the)h(columns)f(of)g(the)h (matrix)g FD(ev)m(ec)34 b FK(in)m(to)29 b(ascend-)390 5070 y(ing)i(or)f(descending)g(order)g(according)h(to)g(the)g(v)-5 b(alue)31 b(of)f(the)h(parameter)g FD(sort)p 3116 5070 V 40 w(t)m(yp)s(e)p FK(,)390 5230 y FH(GSL_EIGEN_SORT_VAL_ASC)870 5340 y FK(ascending)g(order)f(in)g(n)m(umerical)h(v)-5 b(alue)p eop end %%Page: 168 186 TeXDict begin 168 185 bop 150 -116 a FK(Chapter)30 b(15:)41 b(Eigensystems)2424 b(168)390 299 y FH(GSL_EIGEN_SORT_VAL_DESC)870 408 y FK(descending)30 b(order)g(in)g(n)m(umerical)h(v)-5 b(alue)390 569 y FH(GSL_EIGEN_SORT_ABS_ASC)870 678 y FK(ascending)31 b(order)f(in)g(magnitude)390 839 y FH (GSL_EIGEN_SORT_ABS_DESC)870 948 y FK(descending)g(order)g(in)g (magnitude)3350 1134 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_eigen_hermv_sort)f Fu(\()p FD(gsl)p 1598 1134 28 4 v 41 w(v)m(ector)32 b(*)e Ft(eval)p FD(,)i(gsl)p 2358 1134 V 41 w(matrix)p 2664 1134 V 40 w(complex)f(*)565 1244 y Ft(evec)p FD(,)h(gsl)p 942 1244 V 40 w(eigen)p 1183 1244 V 41 w(sort)p 1376 1244 V 41 w(t)e Ft(sort_type)p Fu(\))390 1353 y FK(This)i(function)h(sim)m(ultaneously)h(sorts)g(the)f (eigen)m(v)-5 b(alues)35 b(stored)e(in)g(the)h(v)m(ector)g FD(ev)-5 b(al)38 b FK(and)33 b(the)390 1463 y(corresp)s(onding)39 b(complex)i(eigen)m(v)m(ectors)i(stored)e(in)f(the)g(columns)g(of)h (the)f(matrix)h FD(ev)m(ec)47 b FK(in)m(to)390 1573 y(ascending)34 b(or)h(descending)f(order)f(according)i(to)g(the)g(v)-5 b(alue)35 b(of)f(the)g(parameter)h FD(sort)p 3421 1573 V 40 w(t)m(yp)s(e)40 b FK(as)390 1682 y(sho)m(wn)30 b(ab)s(o)m(v)m(e.) 3350 1868 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_eigen_nonsymmv_so) q(rt)f Fu(\()p FD(gsl)p 1755 1868 V 41 w(v)m(ector)p 2037 1868 V 41 w(complex)31 b(*)g Ft(eval)p FD(,)565 1978 y(gsl)p 677 1978 V 41 w(matrix)p 983 1978 V 40 w(complex)g(*)g Ft(evec)p FD(,)h(gsl)p 1826 1978 V 40 w(eigen)p 2067 1978 V 41 w(sort)p 2260 1978 V 41 w(t)e Ft(sort_type)p Fu(\))390 2087 y FK(This)i(function)h(sim)m(ultaneously)h(sorts)g(the)f (eigen)m(v)-5 b(alues)35 b(stored)e(in)g(the)h(v)m(ector)g FD(ev)-5 b(al)38 b FK(and)33 b(the)390 2197 y(corresp)s(onding)39 b(complex)i(eigen)m(v)m(ectors)i(stored)e(in)f(the)g(columns)g(of)h (the)f(matrix)h FD(ev)m(ec)47 b FK(in)m(to)390 2307 y(ascending)34 b(or)h(descending)f(order)f(according)i(to)g(the)g(v)-5 b(alue)35 b(of)f(the)g(parameter)h FD(sort)p 3421 2307 V 40 w(t)m(yp)s(e)40 b FK(as)390 2416 y(sho)m(wn)d(ab)s(o)m(v)m(e.)65 b(Only)37 b FH(GSL_EIGEN_SORT_ABS_ASC)32 b FK(and)37 b FH(GSL_EIGEN_SORT_ABS_DESC)32 b FK(are)390 2526 y(supp)s(orted)d(due) g(to)i(the)g(eigen)m(v)-5 b(alues)32 b(b)s(eing)e(complex.)3350 2712 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_eigen_gensymmv_so)q(rt) f Fu(\()p FD(gsl)p 1755 2712 V 41 w(v)m(ector)32 b(*)e Ft(eval)p FD(,)i(gsl)p 2515 2712 V 41 w(matrix)e(*)h Ft(evec)p FD(,)565 2821 y(gsl)p 677 2821 V 41 w(eigen)p 919 2821 V 41 w(sort)p 1112 2821 V 40 w(t)g Ft(sort_type)p Fu(\))390 2931 y FK(This)h(function)h(sim)m(ultaneously)h(sorts)g(the)f (eigen)m(v)-5 b(alues)35 b(stored)e(in)g(the)h(v)m(ector)g FD(ev)-5 b(al)38 b FK(and)33 b(the)390 3041 y(corresp)s(onding)26 b(real)i(eigen)m(v)m(ectors)j(stored)c(in)g(the)h(columns)f(of)g(the)h (matrix)g FD(ev)m(ec)34 b FK(in)m(to)29 b(ascend-)390 3150 y(ing)k(or)g(descending)g(order)f(according)i(to)g(the)f(v)-5 b(alue)33 b(of)g(the)g(parameter)h FD(sort)p 3144 3150 V 40 w(t)m(yp)s(e)k FK(as)c(sho)m(wn)390 3260 y(ab)s(o)m(v)m(e.)3350 3446 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_eigen_genhermv_so)q(rt) f Fu(\()p FD(gsl)p 1755 3446 V 41 w(v)m(ector)32 b(*)e Ft(eval)p FD(,)i(gsl)p 2515 3446 V 41 w(matrix)p 2821 3446 V 40 w(complex)565 3555 y(*)f Ft(evec)p FD(,)h(gsl)p 1018 3555 V 40 w(eigen)p 1259 3555 V 41 w(sort)p 1452 3555 V 41 w(t)e Ft(sort_type)p Fu(\))390 3665 y FK(This)i(function)h (sim)m(ultaneously)h(sorts)g(the)f(eigen)m(v)-5 b(alues)35 b(stored)e(in)g(the)h(v)m(ector)g FD(ev)-5 b(al)38 b FK(and)33 b(the)390 3774 y(corresp)s(onding)39 b(complex)i(eigen)m(v)m (ectors)i(stored)e(in)f(the)g(columns)g(of)h(the)f(matrix)h FD(ev)m(ec)47 b FK(in)m(to)390 3884 y(ascending)34 b(or)h(descending)f (order)f(according)i(to)g(the)g(v)-5 b(alue)35 b(of)f(the)g(parameter)h FD(sort)p 3421 3884 V 40 w(t)m(yp)s(e)40 b FK(as)390 3994 y(sho)m(wn)30 b(ab)s(o)m(v)m(e.)3350 4180 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_eigen_genv_sort)e Fu(\()p FD(gsl)p 1545 4180 V 41 w(v)m(ector)p 1827 4180 V 42 w(complex)31 b(*)g Ft(alpha)p FD(,)h(gsl)p 2724 4180 V 40 w(v)m(ector)g(*)565 4289 y Ft(beta)p FD(,)g(gsl)p 942 4289 V 40 w(matrix)p 1247 4289 V 41 w(complex)f(*)g Ft(evec)p FD(,)g(gsl)p 2090 4289 V 41 w(eigen)p 2332 4289 V 41 w(sort)p 2525 4289 V 40 w(t)g Ft(sort_type)p Fu(\))390 4399 y FK(This)c(function)g(sim)m(ultaneously)i(sorts)f(the)g (eigen)m(v)-5 b(alues)29 b(stored)f(in)f(the)h(v)m(ectors)h(\()p FD(alpha)p FK(,)g FD(b)s(eta)p FK(\))390 4508 y(and)d(the)i(corresp)s (onding)e(complex)h(eigen)m(v)m(ectors)j(stored)d(in)g(the)g(columns)g (of)g(the)g(matrix)h FD(ev)m(ec)390 4618 y FK(in)m(to)h(ascending)g(or) f(descending)g(order)f(according)i(to)g(the)g(v)-5 b(alue)28 b(of)g(the)h(parameter)f FD(sort)p 3536 4618 V 41 w(t)m(yp)s(e)390 4728 y FK(as)22 b(sho)m(wn)g(ab)s(o)m(v)m(e.)39 b(Only)22 b FH(GSL_EIGEN_SORT_ABS_ASC)16 b FK(and)22 b FH (GSL_EIGEN_SORT_ABS_DESC)16 b FK(are)390 4837 y(supp)s(orted)29 b(due)g(to)i(the)g(eigen)m(v)-5 b(alues)32 b(b)s(eing)e(complex.)150 5071 y FJ(15.8)68 b(Examples)150 5230 y FK(The)28 b(follo)m(wing)i (program)e(computes)g(the)h(eigen)m(v)-5 b(alues)30 b(and)e(eigen)m(v)m (ectors)j(of)e(the)f(4-th)h(order)f(Hilb)s(ert)150 5340 y(matrix,)j FE(H)7 b FK(\()p FE(i;)15 b(j)5 b FK(\))27 b(=)e(1)p FE(=)p FK(\()p FE(i)d FK(+)e FE(j)26 b FK(+)20 b(1\).)p eop end %%Page: 169 187 TeXDict begin 169 186 bop 150 -116 a FK(Chapter)30 b(15:)41 b(Eigensystems)2424 b(169)390 299 y FH(#include)46 b()390 408 y(#include)g()390 518 y(#include)g ()390 737 y(int)390 847 y(main)h(\(void\))390 956 y({)485 1066 y(double)g(data[])f(=)h({)h(1.0)94 b(,)48 b(1/2.0,)e(1/3.0,)g(1/4.0,)1345 1176 y(1/2.0,)g(1/3.0,)g(1/4.0,)g (1/5.0,)1345 1285 y(1/3.0,)g(1/4.0,)g(1/5.0,)g(1/6.0,)1345 1395 y(1/4.0,)g(1/5.0,)g(1/6.0,)g(1/7.0)g(};)485 1614 y(gsl_matrix_view)e(m)581 1724 y(=)j(gsl_matrix_view_array)42 b(\(data,)k(4,)i(4\);)485 1943 y(gsl_vector)d(*eval)i(=)g (gsl_vector_alloc)d(\(4\);)485 2052 y(gsl_matrix)h(*evec)i(=)g (gsl_matrix_alloc)d(\(4,)j(4\);)485 2271 y(gsl_eigen_symmv_workspace)41 b(*)48 b(w)f(=)581 2381 y(gsl_eigen_symmv_alloc)42 b(\(4\);)485 2600 y(gsl_eigen_symmv)i(\(&m.matrix,)h(eval,)h(evec,)h(w\);)485 2819 y(gsl_eigen_symmv_free)c(\(w\);)485 3039 y(gsl_eigen_symmv_sort)g (\(eval,)j(evec,)1535 3148 y(GSL_EIGEN_SORT_ABS_ASC\);)485 3367 y({)581 3477 y(int)h(i;)581 3696 y(for)g(\(i)g(=)g(0;)h(i)f(<)h (4;)f(i++\))676 3806 y({)772 3915 y(double)f(eval_i)915 4025 y(=)h(gsl_vector_get)d(\(eval,)i(i\);)772 4134 y(gsl_vector_view)d (evec_i)915 4244 y(=)k(gsl_matrix_column)d(\(evec,)i(i\);)772 4463 y(printf)g(\("eigenvalue)e(=)k(\045g\\n",)e(eval_i\);)772 4573 y(printf)g(\("eigenvector)e(=)k(\\n"\);)772 4682 y(gsl_vector_fprintf)43 b(\(stdout,)1726 4792 y(&evec_i.vector,)h ("\045g"\);)676 4902 y(})485 5011 y(})485 5230 y(gsl_vector_free)g (\(eval\);)485 5340 y(gsl_matrix_free)g(\(evec\);)p eop end %%Page: 170 188 TeXDict begin 170 187 bop 150 -116 a FK(Chapter)30 b(15:)41 b(Eigensystems)2424 b(170)485 408 y FH(return)47 b(0;)390 518 y(})150 659 y FK(Here)31 b(is)f(the)h(b)s(eginning)f(of)g(the)h (output)f(from)g(the)g(program,)390 800 y FH($)47 b(./a.out)390 909 y(eigenvalue)e(=)i(9.67023e-05)390 1019 y(eigenvector)e(=)390 1129 y(-0.0291933)390 1238 y(0.328712)390 1348 y(-0.791411)390 1457 y(0.514553)390 1567 y(...)150 1708 y FK(This)30 b(can)g(b)s(e)g(compared)g(with)g(the)h(corresp)s(onding)e(output)h (from)g FC(gnu)k(oct)-6 b(a)e(ve)p FK(,)390 1849 y FH(octave>)46 b([v,d])g(=)i(eig\(hilb\(4\)\);)390 1958 y(octave>)e(diag\(d\))390 2068 y(ans)h(=)533 2287 y(9.6702e-05)533 2397 y(6.7383e-03)533 2506 y(1.6914e-01)533 2616 y(1.5002e+00)390 2835 y(octave>)f(v)390 2945 y(v)h(=)533 3164 y(0.029193)141 b(0.179186)93 b(-0.582076)141 b(0.792608)485 3273 y(-0.328712)93 b(-0.741918)141 b(0.370502)g (0.451923)533 3383 y(0.791411)g(0.100228)g(0.509579)g(0.322416)485 3493 y(-0.514553)g(0.638283)g(0.514048)g(0.252161)150 3634 y FK(Note)30 b(that)f(the)g(eigen)m(v)m(ectors)i(can)e(di\013er)f (b)m(y)g(a)h(c)m(hange)h(of)e(sign,)h(since)g(the)g(sign)f(of)h(an)f (eigen)m(v)m(ector)k(is)150 3743 y(arbitrary)-8 b(.)275 3884 y(The)23 b(follo)m(wing)i(program)e(illustrates)i(the)e(use)g(of)h (the)g(nonsymmetric)f(eigensolv)m(er,)k(b)m(y)d(computing)150 3994 y(the)39 b(eigen)m(v)-5 b(alues)40 b(and)d(eigen)m(v)m(ectors)42 b(of)c(the)h(V)-8 b(andermonde)38 b(matrix)g FE(V)21 b FK(\()p FE(x)p FK(;)15 b FE(i;)g(j)5 b FK(\))40 b(=)f FE(x)3208 3951 y Fq(n)p Fp(\000)p Fq(j)3208 4014 y(i)3374 3994 y FK(with)f FE(x)g FK(=)150 4103 y(\()p FI(\000)p FK(1)p FE(;)15 b FI(\000)p FK(2)p FE(;)g FK(3)p FE(;)g FK(4\).)390 4244 y FH(#include)46 b()390 4354 y(#include)g()390 4463 y(#include)g() 390 4682 y(int)390 4792 y(main)h(\(void\))390 4902 y({)485 5011 y(double)g(data[])f(=)h({)h(-1.0,)e(1.0,)h(-1.0,)f(1.0,)1345 5121 y(-8.0,)g(4.0,)h(-2.0,)f(1.0,)1345 5230 y(27.0,)g(9.0,)h(3.0,)f (1.0,)1345 5340 y(64.0,)g(16.0,)g(4.0,)h(1.0)g(};)p eop end %%Page: 171 189 TeXDict begin 171 188 bop 150 -116 a FK(Chapter)30 b(15:)41 b(Eigensystems)2424 b(171)485 408 y FH(gsl_matrix_view)44 b(m)581 518 y(=)j(gsl_matrix_view_array)42 b(\(data,)k(4,)i(4\);)485 737 y(gsl_vector_complex)43 b(*eval)k(=)g(gsl_vector_complex_alloc)41 b(\(4\);)485 847 y(gsl_matrix_complex)i(*evec)k(=)g (gsl_matrix_complex_alloc)41 b(\(4,)47 b(4\);)485 1066 y(gsl_eigen_nonsymmv_workspa)o(ce)42 b(*)47 b(w)g(=)581 1176 y(gsl_eigen_nonsymmv_alloc)41 b(\(4\);)485 1395 y(gsl_eigen_nonsymmv)i(\(&m.matrix,)i(eval,)h(evec,)h(w\);)485 1614 y(gsl_eigen_nonsymmv_free)42 b(\(w\);)485 1833 y (gsl_eigen_nonsymmv_sort)g(\(eval,)k(evec,)1679 1943 y(GSL_EIGEN_SORT_ABS_DESC)o(\);)485 2162 y({)581 2271 y(int)h(i,)g(j;)581 2491 y(for)g(\(i)g(=)g(0;)h(i)f(<)h(4;)f(i++\))676 2600 y({)772 2710 y(gsl_complex)e(eval_i)915 2819 y(=)i (gsl_vector_complex_get)42 b(\(eval,)k(i\);)772 2929 y(gsl_vector_complex_view)41 b(evec_i)915 3039 y(=)47 b(gsl_matrix_complex_column)41 b(\(evec,)46 b(i\);)772 3258 y(printf)g(\("eigenvalue)e(=)k(\045g)f(+)g(\045gi\\n",)1154 3367 y(GSL_REAL\(eval_i\),)c(GSL_IMAG\(eval_i\)\);)772 3477 y(printf)j(\("eigenvector)e(=)k(\\n"\);)772 3587 y(for)f(\(j)g(=)g(0;)h(j)f(<)g(4;)h(++j\))867 3696 y({)963 3806 y(gsl_complex)c(z)k(=)1058 3915 y(gsl_vector_complex_get\(&e)o (vec_)o(i.v)o(ecto)o(r,)42 b(j\);)963 4025 y(printf\("\045g)j(+)i (\045gi\\n",)f(GSL_REAL\(z\),)e(GSL_IMAG\(z\)\);)867 4134 y(})676 4244 y(})485 4354 y(})485 4573 y (gsl_vector_complex_free\(ev)o(al\);)485 4682 y (gsl_matrix_complex_free\(ev)o(ec\);)485 4902 y(return)j(0;)390 5011 y(})150 5176 y FK(Here)31 b(is)f(the)h(b)s(eginning)f(of)g(the)h (output)f(from)g(the)g(program,)390 5340 y FH($)47 b(./a.out)p eop end %%Page: 172 190 TeXDict begin 172 189 bop 150 -116 a FK(Chapter)30 b(15:)41 b(Eigensystems)2424 b(172)390 299 y FH(eigenvalue)45 b(=)i(-6.41391)f(+)h(0i)390 408 y(eigenvector)e(=)390 518 y(-0.0998822)g(+)i(0i)390 628 y(-0.111251)e(+)j(0i)390 737 y(0.292501)e(+)h(0i)390 847 y(0.944505)f(+)h(0i)390 956 y(eigenvalue)e(=)i(5.54555)f(+)i(3.08545i)390 1066 y(eigenvector)d(=)390 1176 y(-0.043487)g(+)j(-0.0076308i)390 1285 y(0.0642377)d(+)j(-0.142127i)390 1395 y(-0.515253)d(+)j (0.0405118i)390 1504 y(-0.840592)d(+)j(-0.00148565i)390 1614 y(...)150 1870 y FK(This)30 b(can)g(b)s(e)g(compared)g(with)g(the) h(corresp)s(onding)e(output)h(from)g FC(gnu)k(oct)-6 b(a)e(ve)p FK(,)390 2125 y FH(octave>)46 b([v,d])g(=)i (eig\(vander\([-1)c(-2)j(3)g(4]\)\);)390 2235 y(octave>)f(diag\(d\))390 2345 y(ans)h(=)485 2564 y(-6.4139)f(+)i(0.0000i)533 2673 y(5.5456)e(+)i(3.0854i)533 2783 y(5.5456)e(-)i(3.0854i)533 2892 y(2.3228)e(+)i(0.0000i)390 3112 y(octave>)e(v)390 3221 y(v)h(=)438 3440 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b(transform)f(is)h(a)g(matrix-v)m (ector)i(m)m(ultiplication)g FE(W)6 b(~)-38 b(z)t FK(.)54 b(A)35 b(general)h(matrix-v)m(ector)150 2769 y(m)m(ultiplication)31 b(tak)m(es)f FE(O)s FK(\()p FE(n)1125 2736 y FB(2)1162 2769 y FK(\))f(op)s(erations)g(for)g FE(n)f FK(data-p)s(oin)m(ts.)41 b(F)-8 b(ast)31 b(F)-8 b(ourier)29 b(transform)f(algorithms)150 2878 y(use)43 b(a)h(divide-and-conquer)f(strategy)i(to)f(factorize)i (the)d(matrix)h FE(W)56 b FK(in)m(to)45 b(smaller)e(sub-matrices,)150 2988 y(corresp)s(onding)25 b(to)j(the)e(in)m(teger)i(factors)f(of)g (the)f(length)h FE(n)p FK(.)39 b(If)26 b FE(n)g FK(can)h(b)s(e)e (factorized)j(in)m(to)g(a)f(pro)s(duct)e(of)150 3098 y(in)m(tegers)32 b FE(f)532 3112 y FB(1)569 3098 y FE(f)614 3112 y FB(2)666 3098 y FE(:)15 b(:)g(:)h(f)832 3112 y Fq(m)925 3098 y FK(then)31 b(the)g(DFT)g(can)g(b)s(e)f(computed)h(in)f FE(O)s FK(\()p FE(n)2509 3033 y Fs(P)2612 3098 y FE(f)2657 3112 y Fq(i)2684 3098 y FK(\))h(op)s(erations.)43 b(F)-8 b(or)31 b(a)g(radix-2)150 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b(\(FFTs\))1674 b(176)390 299 y FH(1)382 b(z\(t)46 b(=)i(1\))381 b(x\(f)47 b(=)h(1/\(n)e(Delta\)\))390 408 y(2)382 b(z\(t)46 b(=)i(2\))381 b(x\(f)47 b(=)h(2/\(n)e(Delta\)\))390 518 y(.)382 b(........)d(..................)390 628 y(n/2)286 b(z\(t)46 b(=)i(n/2\))285 b(x\(f)47 b(=)h(+1/\(2)e(Delta\),)1870 737 y(-1/\(2)g(Delta\)\))390 847 y(.)382 b(........)d (..................)390 956 y(n-3)286 b(z\(t)46 b(=)i(n-3\))285 b(x\(f)47 b(=)h(-3/\(n)e(Delta\)\))390 1066 y(n-2)286 b(z\(t)46 b(=)i(n-2\))285 b(x\(f)47 b(=)h(-2/\(n)e(Delta\)\))390 1176 y(n-1)286 b(z\(t)46 b(=)i(n-1\))285 b(x\(f)47 b(=)h(-1/\(n)e (Delta\)\))150 1331 y FK(When)i FE(n)f FK(is)i(ev)m(en)f(the)h(lo)s (cation)g FE(n=)p FK(2)g(con)m(tains)g(the)g(most)f(p)s(ositiv)m(e)h (and)f(negativ)m(e)i(frequencies)150 1440 y(\(+1)p FE(=)p FK(\(2\001\),)42 b FI(\000)p FK(1)p FE(=)p FK(\(2\001\)\))f(whic)m(h)d (are)g(equiv)-5 b(alen)m(t.)66 b(If)38 b FE(n)g FK(is)g(o)s(dd)g(then)g (general)h(structure)f(of)g(the)h(ta-)150 1550 y(ble)30 b(ab)s(o)m(v)m(e)i(still)f(applies,)g(but)f FE(n=)p FK(2)h(do)s(es)f (not)g(app)s(ear.)150 1813 y FJ(16.3)68 b(Radix-2)46 b(FFT)d(routines)j(for)f(complex)g(data)150 1972 y FK(The)d(radix-2)i (algorithms)f(describ)s(ed)f(in)g(this)h(section)h(are)f(simple)g(and)f (compact,)47 b(although)d(not)150 2082 y(necessarily)37 b(the)f(most)g(e\016cien)m(t.)58 b(They)35 b(use)h(the)g(Co)s(oley-T)-8 b(uk)m(ey)37 b(algorithm)f(to)h(compute)f(in-place)150 2191 y(complex)d(FFTs)g(for)g(lengths)g(whic)m(h)f(are)i(a)f(p)s(o)m(w) m(er)g(of)f(2|no)i(additional)f(storage)i(is)d(required.)47 b(The)150 2301 y(corresp)s(onding)32 b(self-sorting)h(mixed-radix)g (routines)f(o\013er)h(b)s(etter)g(p)s(erformance)f(at)h(the)g(exp)s (ense)f(of)150 2411 y(requiring)e(additional)h(w)m(orking)g(space.)275 2566 y(All)45 b(the)h(functions)f(describ)s(ed)f(in)h(this)g(section)i (are)e(declared)h(in)f(the)h(header)f(\014le)g FH(gsl_fft_)150 2675 y(complex.h)p FK(.)3350 2900 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_fft_complex_radix)q(2_fo)q(rwa)q(rd)f Fu(\()p FD(gsl)p 2121 2900 28 4 v 41 w(complex)p 2487 2900 V 40 w(pac)m(k)m(ed)p 2796 2900 V 42 w(arra)m(y)565 3010 y Ft(data)p FD(,)32 b(size)p 977 3010 V 41 w(t)e Ft(stride)p FD(,)j(size)p 1594 3010 V 41 w(t)d Ft(n)p Fu(\))3350 3119 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_fft_complex_radix)q(2_tr)q(ans)q(for)q(m)e Fu(\()p FD(gsl)p 2225 3119 V 41 w(complex)p 2591 3119 V 41 w(pac)m(k)m(ed)p 2901 3119 V 41 w(arra)m(y)565 3229 y Ft(data)p FD(,)32 b(size)p 977 3229 V 41 w(t)e Ft(stride)p FD(,)j(size)p 1594 3229 V 41 w(t)d Ft(n)p FD(,)h(gsl)p 1914 3229 V 41 w(\013t)p 2043 3229 V 40 w(direction)g Ft(sign)p Fu(\))3350 3339 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_fft_complex_radix)q (2_ba)q(ckw)q(ard)f Fu(\()p FD(gsl)p 2173 3339 V 41 w(complex)p 2539 3339 V 41 w(pac)m(k)m(ed)p 2849 3339 V 41 w(arra)m(y)565 3448 y Ft(data)p FD(,)32 b(size)p 977 3448 V 41 w(t)e Ft(stride)p FD(,)j(size)p 1594 3448 V 41 w(t)d Ft(n)p Fu(\))3350 3558 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_fft_complex_radix)q(2_in)q(ver)q(se)f Fu(\()p FD(gsl)p 2121 3558 V 41 w(complex)p 2487 3558 V 40 w(pac)m(k)m(ed)p 2796 3558 V 42 w(arra)m(y)565 3667 y Ft(data)p FD(,)32 b(size)p 977 3667 V 41 w(t)e Ft(stride)p FD(,)j(size)p 1594 3667 V 41 w(t)d Ft(n)p Fu(\))390 3777 y FK(These)c(functions)g (compute)g(forw)m(ard,)h(bac)m(kw)m(ard)f(and)g(in)m(v)m(erse)h(FFTs)f (of)g(length)h FD(n)e FK(with)h(stride)390 3887 y FD(stride)p FK(,)43 b(on)d(the)h(pac)m(k)m(ed)h(complex)f(arra)m(y)g FD(data)g FK(using)f(an)g(in-place)h(radix-2)g(decimation-in-)390 3996 y(time)29 b(algorithm.)41 b(The)28 b(length)g(of)h(the)f (transform)g FD(n)g FK(is)g(restricted)h(to)g(p)s(o)m(w)m(ers)f(of)g(t) m(w)m(o.)42 b(F)-8 b(or)29 b(the)390 4106 y FH(transform)g FK(v)m(ersion)j(of)f(the)h(function)f(the)h FD(sign)f FK(argumen)m(t)h(can)g(b)s(e)e(either)i FH(forward)e FK(\()p FI(\000)p FK(1\))i(or)390 4215 y FH(backward)c FK(\(+1\).)390 4370 y(The)g(functions)g(return)f(a)h(v)-5 b(alue)29 b(of)g FH(GSL_SUCCESS)c FK(if)j(no)g(errors)g(w)m(ere)h (detected,)h(or)e FH(GSL_EDOM)390 4480 y FK(if)i(the)h(length)g(of)f (the)h(data)g FD(n)f FK(is)g(not)h(a)f(p)s(o)m(w)m(er)h(of)f(t)m(w)m (o.)3350 4705 y([F)-8 b(unction])-3599 b Fv(int)53 b (gsl_fft_complex_radix)q(2_di)q(f_f)q(orw)q(ard)565 4815 y Fu(\()p FD(gsl)p 712 4815 V 41 w(complex)p 1078 4815 V 41 w(pac)m(k)m(ed)p 1388 4815 V 41 w(arra)m(y)31 b Ft(data)p FD(,)h(size)p 2073 4815 V 41 w(t)e Ft(stride)p FD(,)j(size)p 2690 4815 V 41 w(t)d Ft(n)p Fu(\))3350 4924 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_fft_complex_radix)q (2_di)q(f_t)q(ran)q(sfo)q(rm)565 5034 y Fu(\()p FD(gsl)p 712 5034 V 41 w(complex)p 1078 5034 V 41 w(pac)m(k)m(ed)p 1388 5034 V 41 w(arra)m(y)31 b Ft(data)p FD(,)h(size)p 2073 5034 V 41 w(t)e Ft(stride)p FD(,)j(size)p 2690 5034 V 41 w(t)d Ft(n)p FD(,)h(gsl)p 3010 5034 V 41 w(\013t)p 3139 5034 V 40 w(direction)565 5143 y Ft(sign)p Fu(\))3350 5253 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_fft_complex_radix)q (2_di)q(f_b)q(ack)q(war)q(d)565 5363 y Fu(\()p FD(gsl)p 712 5363 V 41 w(complex)p 1078 5363 V 41 w(pac)m(k)m(ed)p 1388 5363 V 41 w(arra)m(y)31 b Ft(data)p FD(,)h(size)p 2073 5363 V 41 w(t)e Ft(stride)p FD(,)j(size)p 2690 5363 V 41 w(t)d Ft(n)p Fu(\))p eop end %%Page: 177 195 TeXDict begin 177 194 bop 150 -116 a FK(Chapter)30 b(16:)41 b(F)-8 b(ast)32 b(F)-8 b(ourier)31 b(T)-8 b(ransforms)29 b(\(FFTs\))1674 b(177)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_fft_complex_radix)q(2_di)q(f_i)q(nve)q(rse)565 408 y Fu(\()p FD(gsl)p 712 408 28 4 v 41 w(complex)p 1078 408 V 41 w(pac)m(k)m(ed)p 1388 408 V 41 w(arra)m(y)31 b Ft(data)p FD(,)h(size)p 2073 408 V 41 w(t)e Ft(stride)p FD(,)j(size)p 2690 408 V 41 w(t)d Ft(n)p Fu(\))390 518 y FK(These)g(are)h(decimation-in-frequency)g(v)m(ersions)g(of)g(the)f (radix-2)h(FFT)g(functions.)275 709 y(Here)36 b(is)f(an)h(example)g 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2667 3250 V 41 w(w)m(orkspace)31 b(*)565 3360 y Ft(workspace)p Fu(\))390 3469 y FK(This)48 b(function)g(frees)h(the)g(memory)f(asso)s (ciated)i(with)f(the)g(w)m(orkspace)g FD(w)m(orkspace)p FK(.)96 b(The)390 3579 y(w)m(orkspace)31 b(can)g(b)s(e)f(freed)g(if)g (no)g(further)f(FFTs)i(of)f(the)h(same)g(length)f(will)h(b)s(e)f (needed.)150 3747 y(The)g(follo)m(wing)i(functions)e(compute)g(the)h (transform,)3350 3915 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_fft_complex_forwa)q(rd)f Fu(\()p FD(gsl)p 1755 3915 V 41 w(complex)p 2121 3915 V 40 w(pac)m(k)m(ed)p 2430 3915 V 42 w(arra)m(y)30 b Ft(data)p FD(,)i(size)p 3115 3915 V 41 w(t)565 4025 y Ft(stride)p FD(,)g(size)p 1081 4025 V 41 w(t)f Ft(n)p FD(,)g(const)g(gsl)p 1640 4025 V 40 w(\013t)p 1768 4025 V 41 w(complex)p 2134 4025 V 41 w(w)m(a)m(v)m(etable)i(*)d Ft(wavetable)p FD(,)565 4134 y(gsl)p 677 4134 V 41 w(\013t)p 806 4134 V 40 w(complex)p 1171 4134 V 41 w(w)m(orkspace)h(*)g Ft(work)p Fu(\))3350 4244 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_fft_complex_trans)q (form)f Fu(\()p FD(gsl)p 1859 4244 V 41 w(complex)p 2225 4244 V 41 w(pac)m(k)m(ed)p 2535 4244 V 41 w(arra)m(y)31 b Ft(data)p FD(,)565 4354 y(size)p 712 4354 V 41 w(t)g Ft(stride)p FD(,)h(size)p 1329 4354 V 41 w(t)f Ft(n)p FD(,)f(const)h(gsl)p 1887 4354 V 41 w(\013t)p 2016 4354 V 40 w(complex)p 2381 4354 V 41 w(w)m(a)m(v)m(etable)i(*)e Ft(wavetable)p FD(,)565 4463 y(gsl)p 677 4463 V 41 w(\013t)p 806 4463 V 40 w(complex)p 1171 4463 V 41 w(w)m(orkspace)g(*)g Ft(work)p FD(,)g(gsl)p 2093 4463 V 41 w(\013t)p 2222 4463 V 40 w(direction)g Ft(sign)p Fu(\))3350 4573 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_fft_complex_backw)q(ard)f Fu(\()p FD(gsl)p 1807 4573 V 41 w(complex)p 2173 4573 V 41 w(pac)m(k)m(ed)p 2483 4573 V 41 w(arra)m(y)31 b Ft(data)p FD(,)565 4682 y(size)p 712 4682 V 41 w(t)g Ft(stride)p FD(,)h(size)p 1329 4682 V 41 w(t)f Ft(n)p FD(,)f(const)h(gsl)p 1887 4682 V 41 w(\013t)p 2016 4682 V 40 w(complex)p 2381 4682 V 41 w(w)m(a)m(v)m(etable)i(*)e Ft(wavetable)p FD(,)565 4792 y(gsl)p 677 4792 V 41 w(\013t)p 806 4792 V 40 w(complex)p 1171 4792 V 41 w(w)m(orkspace)g(*)g Ft(work)p Fu(\))3350 4902 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_fft_complex_inver)q(se)f Fu(\()p FD(gsl)p 1755 4902 V 41 w(complex)p 2121 4902 V 40 w(pac)m(k)m(ed)p 2430 4902 V 42 w(arra)m(y)30 b Ft(data)p FD(,)i(size)p 3115 4902 V 41 w(t)565 5011 y Ft(stride)p FD(,)g(size)p 1081 5011 V 41 w(t)f Ft(n)p FD(,)g(const)g(gsl)p 1640 5011 V 40 w(\013t)p 1768 5011 V 41 w(complex)p 2134 5011 V 41 w(w)m(a)m(v)m(etable)i(*)d Ft(wavetable)p FD(,)565 5121 y(gsl)p 677 5121 V 41 w(\013t)p 806 5121 V 40 w(complex)p 1171 5121 V 41 w(w)m(orkspace)h(*)g Ft(work)p Fu(\))390 5230 y FK(These)26 b(functions)g(compute)g(forw)m(ard,)h(bac)m(kw)m (ard)f(and)g(in)m(v)m(erse)h(FFTs)f(of)g(length)h FD(n)e FK(with)h(stride)390 5340 y FD(stride)p FK(,)d(on)e(the)g(pac)m(k)m(ed) h(complex)g(arra)m(y)f FD(data)p FK(,)j(using)d(a)g(mixed)g(radix)g (decimation-in-frequency)p eop end %%Page: 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y(#define)h(IMAG\(z,i\))f(\(\(z\)[2*\(i\)+1]\))390 2819 y(int)390 2929 y(main)i(\(void\))390 3039 y({)485 3148 y(int)g(i;)485 3258 y(const)g(int)g(n)g(=)h(630;)485 3367 y(double)f(data[2*n];)485 3587 y(gsl_fft_complex_wavetable)41 b(*)48 b(wavetable;)485 3696 y(gsl_fft_complex_workspace)41 b(*)48 b(workspace;)485 3915 y(for)f(\(i)h(=)f(0;)g(i)h(<)f(n;)g(i++\)) 581 4025 y({)676 4134 y(REAL\(data,i\))e(=)i(0.0;)676 4244 y(IMAG\(data,i\))e(=)i(0.0;)581 4354 y(})485 4573 y(data[0])f(=)i(1.0;)485 4792 y(for)f(\(i)h(=)f(1;)g(i)h(<=)f(10;)g (i++\))581 4902 y({)676 5011 y(REAL\(data,i\))e(=)i(REAL\(data,n-i\))d (=)k(1.0;)581 5121 y(})485 5340 y(for)f(\(i)h(=)f(0;)g(i)h(<)f(n;)g (i++\))p eop end %%Page: 182 200 TeXDict begin 182 199 bop 150 -116 a FK(Chapter)30 b(16:)41 b(F)-8 b(ast)32 b(F)-8 b(ourier)31 b(T)-8 b(ransforms)29 b(\(FFTs\))1674 b(182)581 299 y FH({)676 408 y(printf)46 b(\("\045d:)95 b(\045e)47 b(\045e\\n",)f(i,)h(REAL\(data,i\),)1917 518 y(IMAG\(data,i\)\);)581 628 y(})485 737 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FK(.)41 b(This)27 b(di\013eren)m(t)150 5011 y(structure)40 b(requires)g(di\013eren)m(t)h(storage)g(la)m(y)m (outs)h(for)f(the)f(forw)m(ard)g(transform)f(\(from)i(real)g(to)g (half-)150 5121 y(complex\))e(and)e(in)m(v)m(erse)i(transform)f(\(from) g(half-complex)h(bac)m(k)f(to)h(real\).)65 b(As)38 b(a)g(consequence)h (the)150 5230 y(routines)f(are)h(divided)f(in)m(to)h(t)m(w)m(o)h(sets:) 57 b(functions)38 b(in)g FH(gsl_fft_real)d FK(whic)m(h)j(op)s(erate)h (on)f(real)h(se-)150 5340 y(quences)30 b(and)f(functions)h(in)g FH(gsl_fft_halfcomplex)24 b FK(whic)m(h)30 b(op)s(erate)h(on)e (half-complex)i(sequences.)p eop end %%Page: 183 201 TeXDict begin 183 200 bop 150 -116 a FK(Chapter)30 b(16:)41 b(F)-8 b(ast)32 b(F)-8 b(ourier)31 b(T)-8 b(ransforms)29 b(\(FFTs\))1674 b(183)275 299 y(F)-8 b(unctions)33 b(in)f FH(gsl_fft_real)d FK(compute)k(the)g(frequency)f(co)s(e\016cien)m(ts)i (of)f(a)g(real)g(sequence.)47 b(The)150 408 y(half-complex)31 b(co)s(e\016cien)m(ts)h FE(c)f 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(the)f(half-complex)i(sequence)f(implies)g(that)h(only)e(half)h(of)g (the)g(complex)g(n)m(um)m(b)s(ers)150 1697 y(in)34 b(the)g(output)g (need)f(to)i(b)s(e)f(stored.)51 b(The)34 b(remaining)g(half)g(can)g(b)s (e)g(reconstructed)g(using)f(the)i(half-)150 1807 y(complex)g(symmetry) e(condition.)52 b(This)33 b(w)m(orks)h(for)f(all)i(lengths,)g(ev)m(en)g (and)e(o)s(dd|when)f(the)i(length)150 1916 y(is)29 b(ev)m(en)h(the)g (middle)f(v)-5 b(alue)29 b(where)g FE(k)g FK(=)c FE(n=)p FK(2)k(is)h(also)g(real.)41 b(Th)m(us)28 b(only)i FD(n)e FK(real)i(n)m(um)m(b)s(ers)e(are)i(required)150 2026 y(to)k(store)g(the)g(half-complex)h(sequence,)g(and)e(the)g(transform)g (of)h(a)g(real)g(sequence)g(can)g(b)s(e)f(stored)g(in)150 2135 y(the)e(same)f(size)i(arra)m(y)e(as)h(the)g(original)g(data.)275 2271 y(The)c(precise)g(storage)j(arrangemen)m(ts)e(dep)s(end)e(on)h (the)h(algorithm,)h(and)e(are)h(di\013eren)m(t)g(for)f(radix-2)150 2381 y(and)41 b(mixed-radix)g(routines.)75 b(The)41 b(radix-2)h (function)f(op)s(erates)h(in-place,)k(whic)m(h)41 b(constrains)h(the) 150 2490 y(lo)s(cations)j(where)e(eac)m(h)i(elemen)m(t)h(can)e(b)s(e)f (stored.)81 b(The)43 b(restriction)i(forces)f(real)g(and)f(imaginary) 150 2600 y(parts)28 b(to)h(b)s(e)f(stored)h(far)f(apart.)40 b(The)28 b(mixed-radix)g(algorithm)i(do)s(es)e(not)h(ha)m(v)m(e)g(this) f(restriction,)j(and)150 2709 y(it)38 b(stores)g(the)g(real)g(and)e (imaginary)j(parts)e(of)g(a)h(giv)m(en)h(term)e(in)g(neigh)m(b)s(oring) g(lo)s(cations)i(\(whic)m(h)f(is)150 2819 y(desirable)31 b(for)f(b)s(etter)g(lo)s(calit)m(y)j(of)d(memory)h(accesses\).)150 3053 y FJ(16.6)68 b(Radix-2)46 b(FFT)d(routines)j(for)f(real)h(data)150 3212 y FK(This)35 b(section)i(describ)s(es)d(radix-2)i(FFT)g (algorithms)h(for)e(real)h(data.)57 b(They)35 b(use)h(the)g(Co)s (oley-T)-8 b(uk)m(ey)150 3322 y(algorithm)31 b(to)h(compute)e(in-place) i(FFTs)e(for)g(lengths)h(whic)m(h)f(are)h(a)f(p)s(o)m(w)m(er)h(of)f(2.) 275 3458 y(The)24 b(radix-2)i(FFT)f(functions)g(for)f(real)i(data)g (are)f(declared)h(in)f(the)g(header)g(\014les)g FH(gsl_fft_real.h)3350 3644 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_fft_real_radix2_t)q (rans)q(for)q(m)e Fu(\()p FD(double)31 b Ft(data)p Fo([])p FD(,)g(size)p 2717 3644 28 4 v 41 w(t)g Ft(stride)p FD(,)565 3754 y(size)p 712 3754 V 41 w(t)g Ft(n)p Fu(\))390 3863 y FK(This)e(function)h(computes)h(an)f(in-place)h(radix-2)g(FFT)g(of)f (length)h FD(n)e FK(and)h(stride)g FD(stride)36 b FK(on)30 b(the)390 3973 y(real)d(arra)m(y)h FD(data)p FK(.)40 b(The)26 b(output)g(is)h(a)g(half-complex)h(sequence,)g(whic)m(h)e(is)h (stored)g(in-place.)40 b(The)390 4082 y(arrangemen)m(t)d(of)g(the)f (half-complex)h(terms)g(uses)e(the)i(follo)m(wing)h(sc)m(heme:)53 b(for)36 b FE(k)i(<)d(n=)p FK(2)i(the)390 4192 y(real)f(part)g(of)f (the)h FE(k)s FK(-th)g(term)g(is)f(stored)h(in)f(lo)s(cation)j FE(k)s FK(,)f(and)e(the)h(corresp)s(onding)e(imaginary)390 4302 y(part)d(is)g(stored)g(in)g(lo)s(cation)h FE(n)21 b FI(\000)f FE(k)s FK(.)43 b(T)-8 b(erms)30 b(with)h FE(k)f(>)c(n=)p FK(2)31 b(can)g(b)s(e)g(reconstructed)g(using)g(the)390 4411 y(symmetry)36 b FE(z)863 4425 y Fq(k)939 4411 y FK(=)f FE(z)1091 4378 y Fp(\003)1087 4434 y Fq(n)p Fp(\000)p Fq(k)1221 4411 y FK(.)58 b(The)36 b(terms)g(for)g FE(k)i FK(=)d(0)i(and)f FE(k)i FK(=)d FE(n=)p FK(2)h(are)h(b)s(oth)e(purely)h (real,)j(and)390 4521 y(coun)m(t)25 b(as)g(a)g(sp)s(ecial)g(case.)40 b(Their)24 b(real)h(parts)f(are)h(stored)g(in)f(lo)s(cations)i(0)f(and) f FE(n=)p FK(2)h(resp)s(ectiv)m(ely)-8 b(,)390 4630 y(while)30 b(their)h(imaginary)g(parts)f(whic)m(h)g(are)h(zero)g(are)g(not)f (stored.)390 4766 y(The)23 b(follo)m(wing)j(table)e(sho)m(ws)g(the)g (corresp)s(ondence)f(b)s(et)m(w)m(een)h(the)g(output)g FD(data)g FK(and)g(the)g(equiv-)390 4876 y(alen)m(t)30 b(results)e(obtained)h(b)m(y)f(considering)h(the)g(input)e(data)i(as)g (a)g(complex)g(sequence)g(with)f(zero)390 4985 y(imaginary)j(part)f (\(assuming)h FD(stride=1)7 b FK(\),)630 5121 y FH(complex[0].real)187 b(=)j(data[0])630 5230 y(complex[0].imag)d(=)j(0)630 5340 y(complex[1].real)d(=)j(data[1])p eop end %%Page: 184 202 TeXDict begin 184 201 bop 150 -116 a FK(Chapter)30 b(16:)41 b(F)-8 b(ast)32 b(F)-8 b(ourier)31 b(T)-8 b(ransforms)29 b(\(FFTs\))1674 b(184)630 299 y FH(complex[1].imag)187 b(=)j(data[n-1])630 408 y(...............)425 b(................)630 518 y(complex[k].real)187 b(=)j(data[k])630 628 y(complex[k].imag)d(=)j (data[n-k])630 737 y(...............)425 b(................)630 847 y(complex[n/2].real)91 b(=)190 b(data[n/2])630 956 y(complex[n/2].imag)91 b(=)190 b(0)630 1066 y(...............)425 b(................)630 1176 y(complex[k'].real)139 b(=)190 b(data[k])380 b(k')48 b(=)f(n)g(-)h(k)630 1285 y(complex[k'].imag)139 b(=)k(-data[n-k])630 1395 y(...............)425 b(................)630 1504 y(complex[n-1].real)91 b(=)190 b(data[1])630 1614 y(complex[n-1].imag)91 b(=)143 b(-data[n-1])390 1755 y FK(Note)30 b(that)g(the)f(output)g(data)h(can)f(b)s(e)g(con)m(v)m (erted)i(in)m(to)f(the)f(full)g(complex)h(sequence)f(using)g(the)390 1865 y(function)h FH(gsl_fft_halfcomplex_radi)o(x2_u)o(npac)o(k)24 b FK(describ)s(ed)30 b(b)s(elo)m(w.)275 2063 y(The)24 b(radix-2)h(FFT)g(functions)f(for)g(halfcomplex)i(data)f(are)g (declared)g(in)f(the)h(header)f(\014le)h FH(gsl_fft_)150 2172 y(halfcomplex.h)p FK(.)3350 2370 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_fft_halfcomplex_r)q(adix)q(2_i)q(nve)q(rse)f Fu(\()p FD(double)30 b Ft(data)p Fo([])p FD(,)i(size)p 2979 2370 28 4 v 41 w(t)565 2480 y Ft(stride)p FD(,)g(size)p 1081 2480 V 41 w(t)f Ft(n)p Fu(\))3350 2590 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_fft_halfcomplex_r)q(adix)q(2_b)q (ack)q(war)q(d)e Fu(\()p FD(double)31 b Ft(data)p Fo([])p FD(,)g(size)p 3031 2590 V 41 w(t)565 2699 y Ft(stride)p FD(,)h(size)p 1081 2699 V 41 w(t)f Ft(n)p Fu(\))390 2809 y FK(These)40 b(functions)g(compute)h(the)f(in)m(v)m(erse)h(or)g(bac)m (kw)m(ards)f(in-place)i(radix-2)e(FFT)h(of)g(length)390 2918 y FD(n)c FK(and)f(stride)h FD(stride)42 b FK(on)c(the)f (half-complex)h(sequence)g FD(data)g FK(stored)f(according)h(the)f (output)390 3028 y(sc)m(heme)e(used)e(b)m(y)h FH(gsl_fft_real_radix2)p FK(.)47 b(The)34 b(result)g(is)g(a)g(real)h(arra)m(y)g(stored)f(in)g (natural)390 3138 y(order.)3350 3336 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_fft_halfcomplex_r)q(adix)q(2_u)q(npa)q(ck)f Fu(\()p FD(const)31 b(double)565 3445 y Ft(halfcomplex_coefficien)q(t)p Fo([])p FD(,)36 b(gsl)p 1991 3445 V 41 w(complex)p 2357 3445 V 41 w(pac)m(k)m(ed)p 2667 3445 V 41 w(arra)m(y)565 3555 y Ft(complex_coefficient)p FD(,)g(size)p 1761 3555 V 41 w(t)31 b Ft(stride)p FD(,)h(size)p 2378 3555 V 41 w(t)f Ft(n)p Fu(\))390 3664 y FK(This)k(function)g(con)m(v)m(erts)i FD(halfcomplex)p 1806 3664 V 41 w(co)s(e\016cien)m(t)p FK(,)i(an)c(arra)m(y)h(of)g(half-complex)g(co)s(e\016cien)m(ts)390 3774 y(as)h(returned)f(b)m(y)h FH(gsl_fft_real_radix2_tran)o(sfor)o(m)p FK(,)c(in)m(to)38 b(an)f(ordinary)f(complex)i(arra)m(y)-8 b(,)390 3884 y FD(complex)p 721 3884 V 41 w(co)s(e\016cien)m(t)p FK(.)61 b(It)37 b(\014lls)f(in)g(the)h(complex)g(arra)m(y)g(using)g (the)f(symmetry)h FE(z)3274 3898 y Fq(k)3350 3884 y FK(=)f FE(z)3503 3851 y Fp(\003)3499 3906 y Fq(n)p Fp(\000)p Fq(k)3669 3884 y FK(to)390 3993 y(reconstruct)31 b(the)f(redundan)m(t)f (elemen)m(ts.)43 b(The)29 b(algorithm)j(for)e(the)g(con)m(v)m(ersion)i (is,)630 4134 y FH(complex_coefficient[0].r)o(eal)725 4244 y(=)48 b(halfcomplex_coefficient[)o(0];)630 4354 y(complex_coefficient[0].i)o(mag)725 4463 y(=)g(0.0;)630 4682 y(for)f(\(i)g(=)h(1;)f(i)g(<)h(n)f(-)h(i;)f(i++\))725 4792 y({)821 4902 y(double)f(hc_real)916 5011 y(=)i (halfcomplex_coefficient[)o(i*s)o(trid)o(e];)821 5121 y(double)e(hc_imag)916 5230 y(=)i(halfcomplex_coefficient[)o(\(n-)o (i\)*s)o(trid)o(e];)821 5340 y(complex_coefficient[i*st)o(ride)o(].r)o (eal)41 b(=)48 b(hc_real;)p eop end %%Page: 185 203 TeXDict begin 185 202 bop 150 -116 a FK(Chapter)30 b(16:)41 b(F)-8 b(ast)32 b(F)-8 b(ourier)31 b(T)-8 b(ransforms)29 b(\(FFTs\))1674 b(185)821 299 y FH(complex_coefficient[i*st)o(ride)o (].i)o(mag)41 b(=)48 b(hc_imag;)821 408 y(complex_coefficient[\(n)42 b(-)47 b(i\)*stride].real)d(=)j(hc_real;)821 518 y (complex_coefficient[\(n)42 b(-)47 b(i\)*stride].imag)d(=)j(-hc_imag;) 725 628 y(})630 847 y(if)g(\(i)g(==)h(n)f(-)g(i\))725 956 y({)821 1066 y(complex_coefficient[i*st)o(ride)o(].r)o(eal)916 1176 y(=)h(halfcomplex_coefficient[)o(\(n)41 b(-)48 b(1\)*stride];)821 1285 y(complex_coefficient[i*st)o(ride)o(].i)o(mag)916 1395 y(=)g(0.0;)725 1504 y(})150 1752 y FJ(16.7)68 b(Mixed-radix)45 b(FFT)f(routines)h(for)g(real)h(data)150 1912 y FK(This)22 b(section)h(describ)s(es)f(mixed-radix)h(FFT)f(algorithms)i(for)e(real) h(data.)39 b(The)22 b(mixed-radix)g(functions)150 2021 y(w)m(ork)39 b(for)g(FFTs)g(of)f(an)m(y)i(length.)66 b(They)38 b(are)i(a)f(reimplemen)m(tation)h(of)f(the)g(real-FFT)i (routines)d(in)150 2131 y(the)f(F)-8 b(ortran)37 b FC(fftp)-6 b(a)n(ck)35 b FK(library)h(b)m(y)g(P)m(aul)h(Sw)m(arztraub)s(er.)59 b(The)36 b(theory)h(b)s(ehind)d(the)j(algorithm)h(is)150 2240 y(explained)h(in)f(the)g(article)i FD(F)-8 b(ast)40 b(Mixed-Radix)f(Real)h(F)-8 b(ourier)39 b(T)-8 b(ransforms)41 b FK(b)m(y)d(Cliv)m(e)h(T)-8 b(emp)s(erton.)150 2350 y(The)30 b(routines)g(here)g(use)g(the)h(same)g(indexing)f(sc)m(heme)h (and)f(basic)h(algorithms)g(as)f FC(fftp)-6 b(a)n(ck)p FK(.)275 2495 y(The)32 b(functions)i(use)f(the)g FC(fftp)-6 b(a)n(ck)32 b FK(storage)j(con)m(v)m(en)m(tion)g(for)f(half-complex)g (sequences.)50 b(In)33 b(this)150 2604 y(con)m(v)m(en)m(tion)k(the)d (half-complex)i(transform)e(of)g(a)h(real)g(sequence)g(is)g(stored)f (with)g(frequencies)h(in)f(in-)150 2714 y(creasing)41 b(order,)i(starting)e(at)h(zero,)i(with)c(the)h(real)g(and)f(imaginary) h(parts)f(of)h(eac)m(h)g(frequency)f(in)150 2824 y(neigh)m(b)s(oring)31 b(lo)s(cations.)46 b(When)31 b(a)h(v)-5 b(alue)32 b(is)f(kno)m(wn)g(to) h(b)s(e)f(real)h(the)g(imaginary)g(part)f(is)h(not)g(stored.)150 2933 y(The)26 b(imaginary)h(part)f(of)h(the)f(zero-frequency)h(comp)s (onen)m(t)g(is)f(nev)m(er)h(stored.)40 b(It)26 b(is)g(kno)m(wn)g(to)h (b)s(e)f(zero)150 3043 y(\(since)32 b(the)g(zero)h(frequency)e(comp)s (onen)m(t)h(is)f(simply)g(the)h(sum)f(of)h(the)f(input)g(data)h(\(all)h (real\)\).)46 b(F)-8 b(or)33 b(a)150 3152 y(sequence)e(of)g(ev)m(en)g (length)g(the)g(imaginary)g(part)g(of)g(the)g(frequency)f FE(n=)p FK(2)h(is)f(not)h(stored)g(either,)h(since)150 3262 y(the)f(symmetry)f FE(z)774 3276 y Fq(k)840 3262 y FK(=)25 b FE(z)982 3229 y Fp(\003)978 3284 y Fq(n)p Fp(\000)p Fq(k)1142 3262 y FK(implies)31 b(that)g(this)f(is)h(purely)e (real)i(to)s(o.)275 3407 y(The)c(storage)i(sc)m(heme)f(is)g(b)s(est)f (sho)m(wn)g(b)m(y)g(some)h(examples.)41 b(The)27 b(table)h(b)s(elo)m(w) g(sho)m(ws)g(the)f(output)150 3516 y(for)f(an)f(o)s(dd-length)h (sequence,)h FE(n)e FK(=)g(5.)40 b(The)25 b(t)m(w)m(o)i(columns)e(giv)m (e)j(the)e(corresp)s(ondence)f(b)s(et)m(w)m(een)i(the)f(5)150 3626 y(v)-5 b(alues)33 b(in)g(the)g(half-complex)h(sequence)g(returned) e(b)m(y)h FH(gsl_fft_real_transform)p FK(,)27 b FD(halfcomplex)6 b FK([])150 3735 y(and)23 b(the)g(v)-5 b(alues)24 b FD(complex)6 b FK([])25 b(that)f(w)m(ould)f(b)s(e)g(returned)f(if)i(the)f(same)h (real)g(input)f(sequence)h(w)m(ere)f(passed)150 3845 y(to)31 b FH(gsl_fft_complex_backward)24 b FK(as)30 b(a)h(complex)g (sequence)g(\(with)f(imaginary)i(parts)e(set)h(to)g FH(0)p FK(\),)390 3990 y FH(complex[0].real)91 b(=)96 b(halfcomplex[0])390 4099 y(complex[0].imag)91 b(=)96 b(0)390 4209 y(complex[1].real)91 b(=)96 b(halfcomplex[1])390 4319 y(complex[1].imag)91 b(=)96 b(halfcomplex[2])390 4428 y(complex[2].real)91 b(=)96 b(halfcomplex[3])390 4538 y(complex[2].imag)91 b(=)96 b(halfcomplex[4])390 4647 y(complex[3].real)91 b(=)96 b(halfcomplex[3])390 4757 y(complex[3].imag)91 b(=)48 b(-halfcomplex[4])390 4866 y(complex[4].real)91 b(=)96 b(halfcomplex[1])390 4976 y(complex[4].imag)91 b(=)48 b(-halfcomplex[2])150 5121 y FK(The)32 b(upp)s(er)e(elemen)m(ts) j(of)g(the)f FD(complex)39 b FK(arra)m(y)-8 b(,)34 b FH(complex[3])29 b FK(and)j FH(complex[4])d FK(are)k(\014lled)f(in)f (using)150 5230 y(the)d(symmetry)f(condition.)41 b(The)27 b(imaginary)h(part)g(of)g(the)g(zero-frequency)g(term)g FH(complex[0].imag)150 5340 y FK(is)i(kno)m(wn)g(to)h(b)s(e)f(zero)h(b) m(y)g(the)f(symmetry)-8 b(.)p eop end %%Page: 186 204 TeXDict begin 186 203 bop 150 -116 a FK(Chapter)30 b(16:)41 b(F)-8 b(ast)32 b(F)-8 b(ourier)31 b(T)-8 b(ransforms)29 b(\(FFTs\))1674 b(186)275 299 y(The)33 b(next)g(table)i(sho)m(ws)e(the) h(output)f(for)g(an)h(ev)m(en-length)h(sequence,)g FE(n)30 b FK(=)g(6.)51 b(In)33 b(the)h(ev)m(en)g(case)150 408 y(there)d(are)f(t)m(w)m(o)i(v)-5 b(alues)31 b(whic)m(h)f(are)h(purely)e (real,)390 554 y FH(complex[0].real)91 b(=)96 b(halfcomplex[0])390 664 y(complex[0].imag)91 b(=)96 b(0)390 774 y(complex[1].real)91 b(=)96 b(halfcomplex[1])390 883 y(complex[1].imag)91 b(=)96 b(halfcomplex[2])390 993 y(complex[2].real)91 b(=)96 b(halfcomplex[3])390 1102 y(complex[2].imag)91 b(=)96 b(halfcomplex[4])390 1212 y(complex[3].real)91 b(=)96 b(halfcomplex[5])390 1322 y(complex[3].imag)91 b(=)96 b(0)390 1431 y(complex[4].real)91 b(=)96 b(halfcomplex[3])390 1541 y(complex[4].imag)91 b(=)48 b(-halfcomplex[4])390 1650 y(complex[5].real)91 b(=)96 b(halfcomplex[1])390 1760 y(complex[5].imag)91 b(=)48 b(-halfcomplex[2])150 1906 y FK(The)32 b(upp)s(er)e(elemen)m(ts)j(of)g(the)f FD(complex)39 b FK(arra)m(y)-8 b(,)34 b FH(complex[4])29 b FK(and)j FH(complex[5])d FK(are)k(\014lled)f(in)f(using)150 2015 y(the)j(symmetry)g(condition.)53 b(Both)34 b FH(complex[0].imag)c FK(and)k FH(complex[3].imag)c FK(are)k(kno)m(wn)g(to)h(b)s(e)150 2125 y(zero.)275 2271 y(All)48 b(these)h(functions)f(are)g(declared)h (in)f(the)g(header)g(\014les)g FH(gsl_fft_real.h)d FK(and)i FH(gsl_fft_)150 2381 y(halfcomplex.h)p FK(.)3350 2588 y([F)-8 b(unction])-3599 b Fv(gsl_fft_real_wavetable)59 b(*)53 b(gsl_fft_real_wavetable_)q(allo)q(c)565 2697 y Fu(\()p FD(size)p 747 2697 28 4 v 41 w(t)31 b Ft(n)p Fu(\))3350 2807 y FK([F)-8 b(unction])-3599 b Fv (gsl_fft_halfcomplex_wa)q(vet)q(able)59 b(*)565 2917 y(gsl_fft_halfcomplex_wa)q(vet)q(abl)q(e_a)q(lloc)52 b Fu(\()p FD(size)p 2623 2917 V 41 w(t)31 b Ft(n)p Fu(\))390 3026 y FK(These)37 b(functions)h(prepare)f(trigonometric)i(lo)s(okup)e (tables)i(for)e(an)h(FFT)g(of)g(size)g FE(n)f FK(real)i(ele-)390 3136 y(men)m(ts.)i(The)29 b(functions)g(return)f(a)i(p)s(oin)m(ter)f (to)h(the)g(newly)f(allo)s(cated)i(struct)f(if)f(no)h(errors)e(w)m(ere) 390 3245 y(detected,)46 b(and)c(a)g(n)m(ull)g(p)s(oin)m(ter)g(in)g(the) g(case)h(of)g(error.)75 b(The)41 b(length)i FD(n)e FK(is)h(factorized)i (in)m(to)390 3355 y(a)35 b(pro)s(duct)f(of)h(subtransforms,)g(and)f (the)i(factors)f(and)g(their)g(trigonometric)i(co)s(e\016cien)m(ts)g (are)390 3465 y(stored)j(in)h(the)f(w)m(a)m(v)m(etable.)74 b(The)39 b(trigonometric)k(co)s(e\016cien)m(ts)f(are)e(computed)h (using)e(direct)390 3574 y(calls)30 b(to)g FH(sin)e FK(and)h FH(cos)p FK(,)g(for)f(accuracy)-8 b(.)42 b(Recursion)29 b(relations)h(could)g(b)s(e)e(used)g(to)i(compute)g(the)390 3684 y(lo)s(okup)37 b(table)i(faster,)i(but)c(if)h(an)g(application)h (p)s(erforms)d(man)m(y)i(FFTs)g(of)g(the)g(same)h(length)390 3793 y(then)d(computing)h(the)g(w)m(a)m(v)m(etable)j(is)d(a)g (one-o\013)h(o)m(v)m(erhead)g(whic)m(h)e(do)s(es)h(not)g(a\013ect)h (the)f(\014nal)390 3903 y(throughput.)390 4049 y(The)25 b(w)m(a)m(v)m(etable)j(structure)c(can)i(b)s(e)e(used)h(rep)s(eatedly)g (for)g(an)m(y)h(transform)e(of)h(the)h(same)f(length.)390 4158 y(The)g(table)g(is)h(not)f(mo)s(di\014ed)f(b)m(y)h(calls)h(to)g (an)m(y)f(of)g(the)g(other)h(FFT)f(functions.)38 b(The)25 b(appropriate)390 4268 y(t)m(yp)s(e)31 b(of)f(w)m(a)m(v)m(etable)j(m)m (ust)e(b)s(e)e(used)h(for)g(forw)m(ard)g(real)h(or)f(in)m(v)m(erse)h (half-complex)h(transforms.)3350 4475 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_fft_real_wavetable_f)q(ree)e Fu(\()p FD(gsl)p 2016 4475 V 41 w(\013t)p 2145 4475 V 40 w(real)p 2331 4475 V 41 w(w)m(a)m(v)m(etable)33 b(*)565 4585 y Ft(wavetable)p Fu(\))3350 4694 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_fft_halfcomplex_wave)q(tab)q(le_)q(fre)q(e)565 4804 y Fu(\()p FD(gsl)p 712 4804 V 41 w(\013t)p 841 4804 V 40 w(halfcomplex)p 1355 4804 V 41 w(w)m(a)m(v)m(etable)33 b(*)e Ft(wavetable)p Fu(\))390 4914 y FK(These)46 b(functions)h(free)g (the)f(memory)h(asso)s(ciated)h(with)f(the)f(w)m(a)m(v)m(etable)k FD(w)m(a)m(v)m(etable)p FK(.)92 b(The)390 5023 y(w)m(a)m(v)m(etable)33 b(can)e(b)s(e)f(freed)g(if)g(no)g(further)f(FFTs)i(of)f(the)h(same)g (length)f(will)h(b)s(e)f(needed.)150 5230 y(The)25 b(mixed)g(radix)g (algorithms)h(require)f(additional)i(w)m(orking)e(space)h(to)g(hold)f (the)h(in)m(termediate)h(steps)150 5340 y(of)k(the)f(transform,)p eop end %%Page: 187 205 TeXDict begin 187 204 bop 150 -116 a FK(Chapter)30 b(16:)41 b(F)-8 b(ast)32 b(F)-8 b(ourier)31 b(T)-8 b(ransforms)29 b(\(FFTs\))1674 b(187)3350 299 y([F)-8 b(unction])-3599 b Fv(gsl_fft_real_workspace)59 b(*)53 b(gsl_fft_real_workspace_)q(allo) q(c)565 408 y Fu(\()p FD(size)p 747 408 28 4 v 41 w(t)31 b Ft(n)p Fu(\))390 518 y FK(This)44 b(function)h(allo)s(cates)j(a)d(w)m (orkspace)h(for)f(a)h(real)g(transform)e(of)i(length)f FD(n)p FK(.)85 b(The)45 b(same)390 628 y(w)m(orkspace)31 b(can)g(b)s(e)f(used)f(for)h(b)s(oth)g(forw)m(ard)g(real)h(and)e(in)m (v)m(erse)j(halfcomplex)f(transforms.)3350 814 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_fft_real_workspace_f)q(ree)e Fu(\()p FD(gsl)p 2016 814 V 41 w(\013t)p 2145 814 V 40 w(real)p 2331 814 V 41 w(w)m(orkspace)31 b(*)565 924 y Ft(workspace)p Fu(\))390 1034 y FK(This)48 b(function)g(frees)h(the)g (memory)f(asso)s(ciated)i(with)f(the)g(w)m(orkspace)g FD(w)m(orkspace)p FK(.)96 b(The)390 1143 y(w)m(orkspace)31 b(can)g(b)s(e)f(freed)g(if)g(no)g(further)f(FFTs)i(of)f(the)h(same)g (length)f(will)h(b)s(e)f(needed.)150 1330 y(The)g(follo)m(wing)i (functions)e(compute)g(the)h(transforms)e(of)i(real)g(and)f (half-complex)h(data,)3350 1517 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_fft_real_transfor)q(m)e Fu(\()p FD(double)31 b Ft(data)p Fo([])p FD(,)g(size)p 2351 1517 V 41 w(t)g Ft(stride)p FD(,)h(size)p 2968 1517 V 41 w(t)f Ft(n)p FD(,)565 1626 y(const)g(gsl)p 915 1626 V 41 w(\013t)p 1044 1626 V 40 w(real)p 1230 1626 V 41 w(w)m(a)m(v)m(etable)i(*)e Ft(wavetable)p FD(,)i(gsl)p 2398 1626 V 40 w(\013t)p 2526 1626 V 41 w(real)p 2713 1626 V 41 w(w)m(orkspace)e(*)f Ft(work)p Fu(\))3350 1736 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_fft_halfcomplex_t)q(rans)q(for)q(m)e Fu(\()p FD(double)31 b Ft(data)p Fo([])p FD(,)g(size)p 2717 1736 V 41 w(t)g Ft(stride)p FD(,)565 1846 y(size)p 712 1846 V 41 w(t)g Ft(n)p FD(,)g(const)f(gsl)p 1270 1846 V 41 w(\013t)p 1399 1846 V 40 w(halfcomplex)p 1913 1846 V 41 w(w)m(a)m(v)m(etable)j(*)e Ft(wavetable)p FD(,)565 1955 y(gsl)p 677 1955 V 41 w(\013t)p 806 1955 V 40 w(real)p 992 1955 V 41 w(w)m(orkspace)g(*)g Ft(work)p Fu(\))390 2065 y FK(These)22 b(functions)h(compute)g(the)g(FFT)g(of)f FD(data)p FK(,)k(a)d(real)g(or)g(half-complex)g(arra)m(y)g(of)g(length) g FD(n)p FK(,)h(us-)390 2174 y(ing)k(a)g(mixed)f(radix)g (decimation-in-frequency)i(algorithm.)41 b(F)-8 b(or)28 b FH(gsl_fft_real_transform)390 2284 y FD(data)39 b FK(is)g(an)g(arra)m (y)g(of)g(time-ordered)g(real)g(data.)66 b(F)-8 b(or)40 b FH(gsl_fft_halfcomplex_tran)o(sfor)o(m)390 2394 y FD(data)24 b FK(con)m(tains)h(F)-8 b(ourier)24 b(co)s(e\016cien)m(ts)h(in)f(the)f (half-complex)i(ordering)e(describ)s(ed)g(ab)s(o)m(v)m(e.)39 b(There)390 2503 y(is)29 b(no)h(restriction)g(on)f(the)h(length)g FD(n)p FK(.)40 b(E\016cien)m(t)30 b(mo)s(dules)e(are)i(pro)m(vided)f (for)g(subtransforms)f(of)390 2613 y(length)d(2,)h(3,)g(4)f(and)f(5.)39 b(An)m(y)24 b(remaining)h(factors)g(are)g(computed)f(with)g(a)h(slo)m (w,)h FE(O)s FK(\()p FE(n)3313 2580 y FB(2)3350 2613 y FK(\),)h(general-)390 2722 y(n)d(mo)s(dule.)38 b(The)24 b(caller)i(m)m(ust)e(supply)f(a)i FD(w)m(a)m(v)m(etable)32 b FK(con)m(taining)26 b(trigonometric)g(lo)s(okup)e(tables)390 2832 y(and)30 b(a)h(w)m(orkspace)g FD(w)m(ork)p FK(.)3350 3019 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_fft_real_unpack)e Fu(\()p FD(const)32 b(double)e Ft(real_coefficient)p Fo([])p FD(,)565 3128 y(gsl)p 677 3128 V 41 w(complex)p 1043 3128 V 40 w(pac)m(k)m(ed)p 1352 3128 V 42 w(arra)m(y)h Ft(complex_coefficient)p FD(,)36 b(size)p 2822 3128 V 41 w(t)30 b Ft(stride)p FD(,)j(size)p 3439 3128 V 41 w(t)d Ft(n)p Fu(\))390 3238 y FK(This)f(function)h(con)m(v)m(erts)i(a)e (single)h(real)g(arra)m(y)-8 b(,)31 b FD(real)p 2222 3238 V 41 w(co)s(e\016cien)m(t)j FK(in)m(to)d(an)f(equiv)-5 b(alen)m(t)31 b(complex)390 3347 y(arra)m(y)-8 b(,)38 b FD(complex)p 983 3347 V 41 w(co)s(e\016cien)m(t)p FK(,)h(\(with)d (imaginary)g(part)g(set)g(to)g(zero\),)j(suitable)d(for)f FH(gsl_fft_)390 3457 y(complex)28 b FK(routines.)41 b(The)30 b(algorithm)h(for)f(the)h(con)m(v)m(ersion)h(is)e(simply)-8 b(,)630 3593 y FH(for)47 b(\(i)g(=)h(0;)f(i)g(<)h(n;)f(i++\))725 3702 y({)821 3812 y(complex_coefficient[i*st)o(ride)o(].r)o(eal)916 3922 y(=)h(real_coefficient[i*strid)o(e];)821 4031 y (complex_coefficient[i*st)o(ride)o(].i)o(mag)916 4141 y(=)g(0.0;)725 4250 y(})3350 4437 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_fft_halfcomplex_u)q(npac)q(k)f Fu(\()p FD(const)31 b(double)565 4547 y Ft(halfcomplex_coefficien)q(t)p Fo([])p FD(,)36 b(gsl)p 1991 4547 V 41 w(complex)p 2357 4547 V 41 w(pac)m(k)m(ed)p 2667 4547 V 41 w(arra)m(y)565 4656 y Ft(complex_coefficient)p FD(,)g(size)p 1761 4656 V 41 w(t)31 b Ft(stride)p FD(,)h(size)p 2378 4656 V 41 w(t)f Ft(n)p Fu(\))390 4766 y FK(This)k(function)g(con)m(v)m(erts)i FD(halfcomplex)p 1806 4766 V 41 w(co)s(e\016cien)m(t)p FK(,)i(an)c(arra)m(y)h(of)g(half-complex)g(co)s(e\016cien)m(ts)390 4875 y(as)48 b(returned)f(b)m(y)h FH(gsl_fft_real_transform)p FK(,)e(in)m(to)j(an)f(ordinary)f(complex)i(arra)m(y)-8 b(,)53 b FD(com-)390 4985 y(plex)p 560 4985 V 40 w(co)s(e\016cien)m(t)p FK(.)91 b(It)47 b(\014lls)f(in)g(the)h(complex)g(arra)m(y)g(using)f (the)h(symmetry)f FE(z)3231 4999 y Fq(k)3324 4985 y FK(=)52 b FE(z)3493 4952 y Fp(\003)3489 5008 y Fq(n)p Fp(\000)p Fq(k)3669 4985 y FK(to)390 5095 y(reconstruct)31 b(the)f(redundan)m(t)f (elemen)m(ts.)43 b(The)29 b(algorithm)j(for)e(the)g(con)m(v)m(ersion)i (is,)630 5230 y FH(complex_coefficient[0].r)o(eal)725 5340 y(=)48 b(halfcomplex_coefficient[)o(0];)p eop end %%Page: 188 206 TeXDict begin 188 205 bop 150 -116 a FK(Chapter)30 b(16:)41 b(F)-8 b(ast)32 b(F)-8 b(ourier)31 b(T)-8 b(ransforms)29 b(\(FFTs\))1674 b(188)630 299 y FH(complex_coefficient[0].i)o(mag)725 408 y(=)48 b(0.0;)630 628 y(for)f(\(i)g(=)h(1;)f(i)g(<)h(n)f(-)h(i;)f (i++\))725 737 y({)821 847 y(double)f(hc_real)916 956 y(=)i(halfcomplex_coefficient[)o(\(2)41 b(*)48 b(i)f(-)h(1\)*stride];) 821 1066 y(double)e(hc_imag)916 1176 y(=)i(halfcomplex_coefficient[)o (\(2)41 b(*)48 b(i\)*stride];)821 1285 y(complex_coefficient[i*st)o (ride)o(].r)o(eal)41 b(=)48 b(hc_real;)821 1395 y (complex_coefficient[i*st)o(ride)o(].i)o(mag)41 b(=)48 b(hc_imag;)821 1504 y(complex_coefficient[\(n)42 b(-)47 b(i\)*stride].real)d(=)j(hc_real;)821 1614 y(complex_coefficient[\(n)42 b(-)47 b(i\)*stride].imag)d(=)j(-hc_imag;)725 1724 y(})630 1943 y(if)g(\(i)g(==)h(n)f(-)g(i\))725 2052 y({)821 2162 y(complex_coefficient[i*st)o(ride)o(].r)o(eal)916 2271 y(=)h(halfcomplex_coefficient[)o(\(n)41 b(-)48 b(1\)*stride];)821 2381 y(complex_coefficient[i*st)o(ride)o(].i)o(mag)916 2491 y(=)g(0.0;)725 2600 y(})275 2776 y FK(Here)86 b(is)g(an)g(example) h(program)f(using)g FH(gsl_fft_real_transform)80 b FK(and)85 b FH(gsl_fft_)150 2885 y(halfcomplex_inverse)p FK(.)35 b(It)29 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(tegrals,)h(including)f(logarithmic)h(singularities,)150 979 y(computation)d(of)g(Cauc)m(h)m(y)g(principal)f(v)-5 b(alues)26 b(and)g(oscillatory)j(in)m(tegrals.)41 b(The)26 b(library)f(reimplemen)m(ts)150 1089 y(the)39 b(algorithms)h(used)f(in) g FC(quadp)-6 b(a)n(ck)p FK(,)39 b(a)h(n)m(umerical)f(in)m(tegration)i (pac)m(k)-5 b(age)42 b(written)d(b)m(y)g(Piessens,)150 1198 y(de)c(Donc)m(k)m(er-Kap)s(enga,)k(Ueb)s(erh)m(ub)s(er)33 b(and)i(Kahaner.)55 b(F)-8 b(ortran)36 b(co)s(de)g(for)f FC(quadp)-6 b(a)n(ck)33 b FK(is)j(a)m(v)-5 b(ailable)150 1308 y(on)27 b(Netlib.)41 b(Also)27 b(included)g(are)g(non-adaptiv)m (e,)i(\014xed-order)e(Gauss-Legendre)g(in)m(tegration)i(routines)150 1418 y(with)h(high)g(precision)h(co)s(e\016cien)m(ts)h(b)m(y)e(P)m(a)m (v)m(el)j(Holob)s(oro)s(dk)m(o.)275 1555 y(The)70 b(functions)g (describ)s(ed)f(in)h(this)g(c)m(hapter)i(are)e(declared)h(in)g(the)f (header)h(\014le)f FH(gsl_)150 1664 y(integration.h)p FK(.)150 1901 y FJ(17.1)e(In)l(tro)t(duction)150 2060 y FK(Eac)m(h)31 b(algorithm)g(computes)g(an)f(appro)m(ximation)i(to)f (a)f(de\014nite)h(in)m(tegral)h(of)e(the)h(form,)1559 2282 y FE(I)i FK(=)1728 2167 y Fs(Z)1811 2188 y Fq(b)1774 2356 y(a)1859 2282 y FE(f)10 b FK(\()p FE(x)p FK(\))p FE(w)r FK(\()p FE(x)p FK(\))15 b FE(dx)150 2494 y FK(where)42 b FE(w)r FK(\()p FE(x)p FK(\))h(is)g(a)g(w)m(eigh)m(t)h(function)e (\(for)g(general)i(in)m(tegrands)e FE(w)r FK(\()p FE(x)p FK(\))47 b(=)e(1\).)77 b(The)42 b(user)g(pro)m(vides)150 2604 y(absolute)h(and)f(relativ)m(e)j(error)d(b)s(ounds)f(\()p Fg(epsabs)q FE(;)15 b Fg(epsr)-5 b(el)17 b FK(\))42 b(whic)m(h)h(sp)s (ecify)f(the)h(follo)m(wing)h(accuracy)150 2713 y(requiremen)m(t,)1170 2884 y FI(j)p Fg(RESUL)-7 b(T)20 b FI(\000)g FE(I)7 b FI(j)26 b(\024)f FK(max\()p Fg(epsabs)q FE(;)15 b Fg(epsr)-5 b(el)17 b FI(j)p FE(I)7 b FI(j)p FK(\))150 3054 y(where)26 b Fg(RESUL)-7 b(T)26 b FK(is)h(the)g(n)m(umerical)g(appro)m(ximation)g (obtained)g(b)m(y)g(the)g(algorithm.)40 b(The)26 b(algorithms)150 3163 y(attempt)34 b(to)g(estimate)h(the)e(absolute)h(error)e Fg(ABSERR)e FK(=)f FI(j)p Fg(RESUL)-7 b(T)22 b FI(\000)g FE(I)7 b FI(j)33 b FK(in)g(suc)m(h)g(a)g(w)m(a)m(y)h(that)g(the)150 3273 y(follo)m(wing)e(inequalit)m(y)g(holds,)921 3443 y FI(j)p Fg(RESUL)-7 b(T)20 b FI(\000)g FE(I)7 b FI(j)26 b(\024)f Fg(ABSERR)g FI(\024)g FK(max\()p Fg(epsabs)q FE(;)15 b Fg(epsr)-5 b(el)17 b FI(j)p FE(I)7 b FI(j)p FK(\))150 3614 y(In)36 b(short,)h(the)g(routines)f(return)f(the)i (\014rst)f(appro)m(ximation)h(whic)m(h)f(has)g(an)g(absolute)h(error)f (smaller)150 3723 y(than)30 b Fg(epsabs)h FK(or)g(a)f(relativ)m(e)j (error)d(smaller)h(than)f Fg(epsr)-5 b(el)q FK(.)275 3860 y(Note)35 b(that)g(this)f(is)h(an)f Fg(either-or)45 b FK(constrain)m(t,)37 b(not)d(sim)m(ultaneous.)53 b(T)-8 b(o)35 b(compute)g(to)g(a)g(sp)s(eci\014ed)150 3970 y(absolute)j (error,)i(set)e Fg(epsr)-5 b(el)38 b FK(to)h(zero.)63 b(T)-8 b(o)38 b(compute)g(to)g(a)g(sp)s(eci\014ed)f(relativ)m(e)i (error,)h(set)e Fg(epsabs)g FK(to)150 4079 y(zero.)60 b(The)35 b(routines)i(will)f(fail)h(to)h(con)m(v)m(erge)g(if)e(the)h (error)f(b)s(ounds)e(are)j(to)s(o)g(stringen)m(t,)i(but)c(alw)m(a)m(ys) 150 4189 y(return)29 b(the)i(b)s(est)f(appro)m(ximation)h(obtained)g (up)e(to)i(that)g(stage.)275 4326 y(The)e(algorithms)j(in)e FC(quadp)-6 b(a)n(ck)28 b FK(use)i(a)h(naming)f(con)m(v)m(en)m(tion)j (based)d(on)g(the)g(follo)m(wing)i(letters,)390 4463 y FH(Q)e FK(-)h(quadrature)e(routine)390 4682 y FH(N)h FK(-)h(non-adaptiv)m(e)g(in)m(tegrator)390 4792 y FH(A)f FK(-)h(adaptiv)m(e)g(in)m(tegrator)390 5011 y FH(G)f FK(-)h(general)g(in)m(tegrand)g(\(user-de\014ned\))390 5121 y FH(W)f FK(-)h(w)m(eigh)m(t)h(function)e(with)g(in)m(tegrand)390 5340 y FH(S)g FK(-)h(singularities)g(can)g(b)s(e)e(more)i(readily)g(in) m(tegrated)p eop end %%Page: 193 211 TeXDict begin 193 210 bop 150 -116 a FK(Chapter)30 b(17:)41 b(Numerical)31 b(In)m(tegration)2079 b(193)390 299 y FH(P)30 b FK(-)h(p)s(oin)m(ts)f(of)g(sp)s(ecial)h(di\016cult)m(y)g(can) g(b)s(e)f(supplied)390 408 y FH(I)g FK(-)h(in\014nite)f(range)g(of)h (in)m(tegration)390 518 y FH(O)f FK(-)h(oscillatory)h(w)m(eigh)m(t)g (function,)e(cos)h(or)g(sin)390 628 y FH(F)f FK(-)h(F)-8 b(ourier)31 b(in)m(tegral)390 737 y FH(C)f FK(-)h(Cauc)m(h)m(y)f (principal)g(v)-5 b(alue)150 916 y(The)27 b(algorithms)i(are)f(built)g (on)f(pairs)h(of)g(quadrature)f(rules,)h(a)g(higher)f(order)h(rule)f (and)g(a)h(lo)m(w)m(er)h(order)150 1025 y(rule.)39 b(The)27 b(higher)g(order)g(rule)g(is)g(used)g(to)h(compute)f(the)h(b)s(est)f (appro)m(ximation)h(to)g(an)f(in)m(tegral)i(o)m(v)m(er)g(a)150 1135 y(small)f(range.)39 b(The)27 b(di\013erence)g(b)s(et)m(w)m(een)h (the)f(results)g(of)g(the)h(higher)e(order)h(rule)g(and)f(the)h(lo)m(w) m(er)h(order)150 1244 y(rule)i(giv)m(es)i(an)e(estimate)i(of)f(the)f (error)g(in)g(the)h(appro)m(ximation.)150 1488 y Fy(17.1.1)63 b(In)m(tegrands)41 b(without)g(w)m(eigh)m(t)f(functions)150 1635 y FK(The)46 b(algorithms)h(for)f(general)h(functions)e(\(without)i (a)f(w)m(eigh)m(t)i(function\))e(are)h(based)f(on)g(Gauss-)150 1744 y(Kronro)s(d)29 b(rules.)275 1923 y(A)c(Gauss-Kronro)s(d)f(rule)i (b)s(egins)f(with)g(a)h(classical)i(Gaussian)e(quadrature)f(rule)g(of)h (order)f FE(m)p FK(.)39 b(This)150 2032 y(is)i(extended)h(with)e (additional)j(p)s(oin)m(ts)e(b)s(et)m(w)m(een)h(eac)m(h)g(of)f(the)h (abscissae)g(to)g(giv)m(e)h(a)f(higher)e(order)150 2142 y(Kronro)s(d)h(rule)h(of)g(order)g(2)p FE(m)29 b FK(+)f(1.)77 b(The)42 b(Kronro)s(d)f(rule)h(is)h(e\016cien)m(t)h(b)s(ecause)e(it)h (reuses)f(existing)150 2251 y(function)30 b(ev)-5 b(aluations)32 b(from)e(the)g(Gaussian)h(rule.)275 2430 y(The)25 b(higher)g(order)g (Kronro)s(d)f(rule)h(is)g(used)g(as)h(the)g(b)s(est)f(appro)m(ximation) h(to)h(the)e(in)m(tegral,)k(and)c(the)150 2539 y(di\013erence)31 b(b)s(et)m(w)m(een)g(the)f(t)m(w)m(o)i(rules)e(is)g(used)g(as)h(an)f (estimate)i(of)f(the)f(error)g(in)g(the)h(appro)m(ximation.)150 2783 y Fy(17.1.2)63 b(In)m(tegrands)41 b(with)g(w)m(eigh)m(t)f (functions)150 2930 y FK(F)-8 b(or)29 b(in)m(tegrands)f(with)g(w)m (eigh)m(t)i(functions)d(the)i(algorithms)g(use)e(Clensha)m(w-Curtis)h (quadrature)f(rules.)275 3108 y(A)e(Clensha)m(w-Curtis)g(rule)h(b)s (egins)f(with)g(an)h FE(n)p FK(-th)f(order)g(Cheb)m(yshev)g(p)s (olynomial)h(appro)m(ximation)150 3218 y(to)36 b(the)e(in)m(tegrand.)55 b(This)34 b(p)s(olynomial)h(can)g(b)s(e)f(in)m(tegrated)j(exactly)f(to) g(giv)m(e)g(an)e(appro)m(ximation)i(to)150 3327 y(the)d(in)m(tegral)h (of)e(the)h(original)g(function.)47 b(The)32 b(Cheb)m(yshev)f (expansion)h(can)h(b)s(e)f(extended)g(to)h(higher)150 3437 y(orders)d(to)h(impro)m(v)m(e)g(the)g(appro)m(ximation)g(and)f (pro)m(vide)g(an)g(estimate)j(of)d(the)h(error.)150 3680 y Fy(17.1.3)63 b(In)m(tegrands)41 b(with)g(singular)h(w)m(eigh)m(t)e (functions)150 3827 y FK(The)22 b(presence)g(of)h(singularities)g(\(or) g(other)g(b)s(eha)m(vior\))f(in)g(the)h(in)m(tegrand)g(can)g(cause)g (slo)m(w)g(con)m(v)m(ergence)150 3937 y(in)32 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b(non-adaptiv)l(e)h(Gauss-Kronro)t(d)e(in)l (tegration)150 5121 y FK(The)23 b(QNG)h(algorithm)g(is)g(a)g (non-adaptiv)m(e)g(pro)s(cedure)f(whic)m(h)g(uses)g(\014xed)g (Gauss-Kronro)s(d-P)m(atterson)150 5230 y(abscissae)46 b(to)f(sample)g(the)g(in)m(tegrand)g(at)h(a)f(maxim)m(um)g(of)g(87)g(p) s(oin)m(ts.)84 b(It)45 b(is)g(pro)m(vided)f(for)h(fast)150 5340 y(in)m(tegration)32 b(of)f(smo)s(oth)f(functions.)p eop end %%Page: 194 212 TeXDict begin 194 211 bop 150 -116 a FK(Chapter)30 b(17:)41 b(Numerical)31 b(In)m(tegration)2079 b(194)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_integration_qng)e Fu(\()p FD(const)32 b(gsl)p 1784 299 28 4 v 40 w(function)e(*)h Ft(f)p FD(,)g(double)f Ft(a)p FD(,)h(double)f Ft(b)p FD(,)565 408 y(double)g Ft(epsabs)p FD(,)i(double)e Ft(epsrel)p FD(,)j(double)d(*)g Ft(result)p FD(,)j(double)d(*)g Ft(abserr)p FD(,)j(size)p 3513 408 V 41 w(t)d(*)565 518 y Ft(neval)p Fu(\))390 628 y FK(This)37 b(function)g(applies)h(the)g(Gauss-Kronro)s (d)e(10-p)s(oin)m(t,)41 b(21-p)s(oin)m(t,)g(43-p)s(oin)m(t)e(and)e (87-p)s(oin)m(t)390 737 y(in)m(tegration)45 b(rules)d(in)h(succession)g (un)m(til)g(an)g(estimate)h(of)f(the)g(in)m(tegral)i(of)e FE(f)52 b FK(o)m(v)m(er)44 b(\()p FE(a;)15 b(b)p FK(\))44 b(is)390 847 y(ac)m(hiev)m(ed)29 b(within)e(the)g(desired)g(absolute)h (and)f(relativ)m(e)i(error)e(limits,)i FD(epsabs)h FK(and)d FD(epsrel)p FK(.)39 b(The)390 956 y(function)f(returns)f(the)i(\014nal) f(appro)m(ximation,)k FD(result)p FK(,)f(an)d(estimate)i(of)f(the)g (absolute)g(error,)390 1066 y FD(abserr)33 b FK(and)27 b(the)h(n)m(um)m(b)s(er)e(of)h(function)g(ev)-5 b(aluations)29 b(used,)e FD(nev)-5 b(al)p FK(.)41 b(The)26 b(Gauss-Kronro)s(d)g(rules) 390 1176 y(are)35 b(designed)g(in)f(suc)m(h)h(a)g(w)m(a)m(y)g(that)h (eac)m(h)g(rule)e(uses)g(all)i(the)f(results)f(of)h(its)g (predecessors,)h(in)390 1285 y(order)30 b(to)h(minimize)g(the)f(total)j (n)m(um)m(b)s(er)c(of)h(function)g(ev)-5 b(aluations.)150 1516 y FJ(17.3)68 b(QA)l(G)45 b(adaptiv)l(e)h(in)l(tegration)150 1676 y FK(The)33 b(QA)m(G)g(algorithm)h(is)g(a)f(simple)g(adaptiv)m(e)i (in)m(tegration)g(pro)s(cedure.)47 b(The)33 b(in)m(tegration)i(region)f (is)150 1785 y(divided)e(in)m(to)i(subin)m(terv)-5 b(als,)33 b(and)f(on)h(eac)m(h)h(iteration)g(the)f(subin)m(terv)-5 b(al)32 b(with)h(the)g(largest)h(estimated)150 1895 y(error)j(is)h (bisected.)63 b(This)36 b(reduces)h(the)h(o)m(v)m(erall)i(error)d (rapidly)-8 b(,)40 b(as)d(the)h(subin)m(terv)-5 b(als)37 b(b)s(ecome)h(con-)150 2005 y(cen)m(trated)e(around)e(lo)s(cal)i (di\016culties)g(in)e(the)i(in)m(tegrand.)54 b(These)35 b(subin)m(terv)-5 b(als)35 b(are)g(managed)h(b)m(y)f(a)150 2114 y FH(gsl_integration_workspac)o(e)19 b FK(struct,)26 b(whic)m(h)f(handles)f(the)h(memory)g(for)g(the)g(subin)m(terv)-5 b(al)24 b(ranges,)150 2224 y(results)30 b(and)g(error)g(estimates.)3350 2406 y([F)-8 b(unction])-3599 b Fv(gsl_integration_worksp)q(ace)59 b(*)565 2516 y(gsl_integration_worksp)q(ace)q(_al)q(loc)52 b Fu(\()p FD(size)p 2414 2516 V 41 w(t)31 b Ft(n)p Fu(\))390 2625 y FK(This)39 b(function)h(allo)s(cates)i(a)f(w)m(orkspace)f (su\016cien)m(t)h(to)g(hold)e FD(n)h FK(double)f(precision)i(in)m(terv) -5 b(als,)390 2735 y(their)36 b(in)m(tegration)i(results)e(and)g(error) f(estimates.)60 b(One)36 b(w)m(orkspace)h(ma)m(y)f(b)s(e)g(used)f(m)m (ultiple)390 2844 y(times)h(as)h(all)g(necessary)f(reinitialization)j (is)d(p)s(erformed)e(automatically)39 b(b)m(y)d(the)g(in)m(tegration) 390 2954 y(routines.)3350 3136 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_integration_workspac)q(e_f)q(ree)e Fu(\()p FD(gsl)p 2173 3136 V 41 w(in)m(tegration)p 2644 3136 V 42 w(w)m(orkspace)31 b(*)565 3246 y Ft(w)p Fu(\))390 3356 y FK(This)f(function)g(frees)g(the)h(memory)f(asso)s(ciated)i (with)e(the)g(w)m(orkspace)h FD(w)p FK(.)3350 3538 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_integration_qag)e Fu(\()p FD(const)32 b(gsl)p 1784 3538 V 40 w(function)e(*)h Ft(f)p FD(,)g(double)f Ft(a)p FD(,)h(double)f Ft(b)p FD(,)565 3648 y(double)g Ft(epsabs)p FD(,)i(double)e Ft(epsrel)p FD(,)j(size)p 2037 3648 V 41 w(t)d Ft(limit)p FD(,)i(in)m(t)f Ft(key)p FD(,)565 3757 y(gsl)p 677 3757 V 41 w(in)m(tegration)p 1148 3757 V 42 w(w)m(orkspace)g(*)g Ft(workspace)p FD(,)i(double)d(*)h Ft(result)p FD(,)h(double)e(*)h Ft(abserr)p Fu(\))390 3867 y FK(This)g(function)g(applies)h(an)f(in)m (tegration)j(rule)d(adaptiv)m(ely)i(un)m(til)f(an)f(estimate)j(of)d (the)h(in)m(tegral)390 3976 y(of)25 b FE(f)34 b FK(o)m(v)m(er)25 b(\()p FE(a;)15 b(b)p FK(\))26 b(is)f(ac)m(hiev)m(ed)h(within)e(the)h (desired)f(absolute)h(and)f(relativ)m(e)j(error)d(limits,)j FD(epsabs)390 4086 y FK(and)k FD(epsrel)p FK(.)46 b(The)31 b(function)h(returns)f(the)h(\014nal)g(appro)m(ximation,)h FD(result)p FK(,)g(and)e(an)h(estimate)i(of)390 4196 y(the)k(absolute)g(error,)h FD(abserr)p FK(.)62 b(The)37 b(in)m(tegration)i(rule)e(is)h(determined)f(b)m(y)h(the)f(v)-5 b(alue)38 b(of)g FD(k)m(ey)p FK(,)390 4305 y(whic)m(h)30 b(should)f(b)s(e)h(c)m(hosen)h(from)f(the)h(follo)m(wing)g(sym)m(b)s (olic)g(names,)630 4439 y FH(GSL_INTEG_GAUSS15)91 b(\(key)46 b(=)i(1\))630 4549 y(GSL_INTEG_GAUSS21)91 b(\(key)46 b(=)i(2\))630 4658 y(GSL_INTEG_GAUSS31)91 b(\(key)46 b(=)i(3\))630 4768 y(GSL_INTEG_GAUSS41)91 b(\(key)46 b(=)i(4\))630 4877 y(GSL_INTEG_GAUSS51)91 b(\(key)46 b(=)i(5\))630 4987 y(GSL_INTEG_GAUSS61)91 b(\(key)46 b(=)i(6\))390 5121 y FK(corresp)s(onding)43 b(to)i(the)f(15,)49 b(21,)f(31,)h(41,)g(51)c(and)e(61)i(p)s(oin)m(t)f(Gauss-Kronro)s(d)f (rules.)81 b(The)390 5230 y(higher-order)31 b(rules)h(giv)m(e)h(b)s (etter)f(accuracy)h(for)e(smo)s(oth)h(functions,)g(while)f(lo)m(w)m (er-order)i(rules)390 5340 y(sa)m(v)m(e)f(time)f(when)e(the)i(function) f(con)m(tains)i(lo)s(cal)f(di\016culties,)g(suc)m(h)f(as)h(discon)m (tin)m(uities.)p eop end %%Page: 195 213 TeXDict begin 195 212 bop 150 -116 a FK(Chapter)30 b(17:)41 b(Numerical)31 b(In)m(tegration)2079 b(195)390 299 y(On)20 b(eac)m(h)j(iteration)f(the)g(adaptiv)m(e)g(in)m(tegration)h(strategy)g (bisects)f(the)f(in)m(terv)-5 b(al)22 b(with)f(the)h(largest)390 408 y(error)28 b(estimate.)42 b(The)29 b(subin)m(terv)-5 b(als)29 b(and)f(their)h(results)g(are)g(stored)g(in)f(the)i(memory)e (pro)m(vided)390 518 y(b)m(y)37 b FD(w)m(orkspace)p FK(.)61 b(The)36 b(maxim)m(um)h(n)m(um)m(b)s(er)e(of)i(subin)m(terv)-5 b(als)37 b(is)g(giv)m(en)h(b)m(y)e FD(limit)p FK(,)k(whic)m(h)c(ma)m(y) 390 628 y(not)31 b(exceed)g(the)g(allo)s(cated)h(size)f(of)g(the)f(w)m (orkspace.)150 895 y FJ(17.4)68 b(QA)l(GS)44 b(adaptiv)l(e)j(in)l (tegration)g(with)e(singularities)150 1054 y FK(The)22 b(presence)g(of)g(an)g(in)m(tegrable)h(singularit)m(y)g(in)f(the)g(in)m (tegration)i(region)f(causes)g(an)f(adaptiv)m(e)h(routine)150 1164 y(to)29 b(concen)m(trate)h(new)d(subin)m(terv)-5 b(als)28 b(around)e(the)i(singularit)m(y)-8 b(.)41 b(As)28 b(the)g(subin)m(terv)-5 b(als)28 b(decrease)h(in)e(size)150 1274 y(the)h(successiv)m(e)i(appro)m(ximations)f(to)g(the)f(in)m (tegral)i(con)m(v)m(erge)g(in)e(a)g(limiting)i(fashion.)39 b(This)28 b(approac)m(h)150 1383 y(to)39 b(the)g(limit)g(can)g(b)s(e)f (accelerated)j(using)c(an)i(extrap)s(olation)h(pro)s(cedure.)63 b(The)38 b(QA)m(GS)h(algorithm)150 1493 y(com)m(bines)33 b(adaptiv)m(e)h(bisection)g(with)e(the)h(Wynn)e(epsilon-algorithm)k(to) e(sp)s(eed)f(up)f(the)i(in)m(tegration)150 1602 y(of)e(man)m(y)f(t)m (yp)s(es)g(of)h(in)m(tegrable)h(singularities.)3350 1833 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_integration_qags)f Fu(\()p FD(const)31 b(gsl)p 1836 1833 28 4 v 41 w(function)f(*)g Ft(f)p FD(,)h(double)f Ft(a)p FD(,)h(double)f Ft(b)p FD(,)565 1943 y(double)g Ft(epsabs)p FD(,)i(double)e Ft(epsrel)p FD(,)j(size)p 2037 1943 V 41 w(t)d Ft(limit)p FD(,)i(gsl)p 2566 1943 V 41 w(in)m(tegration)p 3037 1943 V 42 w(w)m(orkspace)f(*)565 2053 y Ft(workspace)p FD(,)i(double)d(*)h Ft(result)p FD(,)h(double)e(*)h Ft(abserr)p Fu(\))390 2162 y FK(This)37 b(function)h(applies)h(the)f(Gauss-Kronro)s(d)f(21-p) s(oin)m(t)j(in)m(tegration)g(rule)e(adaptiv)m(ely)i(un)m(til)390 2272 y(an)g(estimate)h(of)f(the)g(in)m(tegral)i(of)e FE(f)49 b FK(o)m(v)m(er)41 b(\()p FE(a;)15 b(b)p FK(\))41 b(is)f(ac)m(hiev)m(ed)i(within)d(the)h(desired)f(absolute)390 2381 y(and)c(relativ)m(e)i(error)f(limits,)h FD(epsabs)i FK(and)c FD(epsrel)p FK(.)56 b(The)35 b(results)g(are)h(extrap)s (olated)h(using)e(the)390 2491 y(epsilon-algorithm,)k(whic)m(h)c (accelerates)k(the)d(con)m(v)m(ergence)i(of)e(the)f(in)m(tegral)j(in)d (the)h(presence)390 2601 y(of)31 b(discon)m(tin)m(uities)h(and)d(in)m (tegrable)j(singularities.)42 b(The)30 b(function)g(returns)f(the)i (\014nal)f(appro)m(x-)390 2710 y(imation)g(from)f(the)g(extrap)s (olation,)j FD(result)p FK(,)d(and)g(an)g(estimate)i(of)f(the)f (absolute)h(error,)f FD(abserr)p FK(.)390 2820 y(The)i(subin)m(terv)-5 b(als)32 b(and)g(their)g(results)f(are)i(stored)f(in)g(the)g(memory)g (pro)m(vided)f(b)m(y)h FD(w)m(orkspace)p FK(.)390 2929 y(The)k(maxim)m(um)g(n)m(um)m(b)s(er)f(of)i(subin)m(terv)-5 b(als)36 b(is)h(giv)m(en)g(b)m(y)f FD(limit)p FK(,)j(whic)m(h)e(ma)m(y) g(not)f(exceed)i(the)390 3039 y(allo)s(cated)32 b(size)g(of)e(the)h(w)m (orkspace.)150 3306 y FJ(17.5)68 b(QA)l(GP)45 b(adaptiv)l(e)h(in)l (tegration)h(with)e(kno)l(wn)g(singular)h(p)t(oin)l(ts)3350 3539 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_integration_qagp)f Fu(\()p FD(const)30 b(gsl)p 1835 3539 V 40 w(function)f(*)h Ft(f)p FD(,)f(double)g(*)h Ft(pts)p FD(,)g(size)p 3130 3539 V 41 w(t)565 3648 y Ft(npts)p FD(,)i(double)e Ft(epsabs)p FD(,)i(double)e Ft(epsrel)p FD(,)i(size)p 2301 3648 V 41 w(t)f Ft(limit)p FD(,)h(gsl)p 2831 3648 V 41 w(in)m(tegration)p 3302 3648 V 42 w(w)m(orkspace)565 3758 y(*)f Ft(workspace)p FD(,)i(double)d(*)h Ft(result)p FD(,)h(double)e(*)h Ft(abserr)p Fu(\))390 3868 y FK(This)26 b(function)g(applies)g(the)h(adaptiv)m(e)h (in)m(tegration)g(algorithm)f(QA)m(GS)g(taking)g(accoun)m(t)h(of)f(the) 390 3977 y(user-supplied)22 b(lo)s(cations)j(of)f(singular)f(p)s(oin)m (ts.)39 b(The)23 b(arra)m(y)h FD(pts)j FK(of)c(length)h FD(npts)j FK(should)c(con)m(tain)390 4087 y(the)h(endp)s(oin)m(ts)f(of) i(the)f(in)m(tegration)i(ranges)e(de\014ned)f(b)m(y)g(the)i(in)m (tegration)h(region)e(and)f(lo)s(cations)390 4196 y(of)28 b(the)f(singularities.)41 b(F)-8 b(or)28 b(example,)h(to)g(in)m (tegrate)g(o)m(v)m(er)g(the)f(region)g(\()p FE(a;)15 b(b)p FK(\))29 b(with)e(break-p)s(oin)m(ts)390 4306 y(at)k FE(x)553 4320 y FB(1)590 4306 y FE(;)15 b(x)682 4320 y FB(2)720 4306 y FE(;)g(x)812 4320 y FB(3)880 4306 y FK(\(where)30 b FE(a)25 b(<)g(x)1399 4320 y FB(1)1462 4306 y FE(<)g(x)1610 4320 y FB(2)1672 4306 y FE(<)g(x)1820 4320 y FB(3)1883 4306 y FE(<)g(b)p FK(\))30 b(the)h(follo)m(wing)h FD(pts)h FK(arra)m(y)e(should)f(b)s(e)f(used)630 4464 y FH(pts[0])46 b(=)i(a)630 4573 y(pts[1])e(=)i(x_1)630 4683 y(pts[2])e(=)i(x_2)630 4793 y(pts[3])e(=)i(x_3)630 4902 y(pts[4])e(=)i(b)390 5060 y FK(with)30 b FD(npts)j FK(=)d(5.)390 5218 y(If)36 b(y)m(ou)i(kno)m(w)f(the)g(lo)s(cations)h (of)f(the)h(singular)e(p)s(oin)m(ts)h(in)g(the)g(in)m(tegration)i (region)e(then)g(this)390 5327 y(routine)30 b(will)h(b)s(e)f(faster)h (than)f FH(QAGS)p FK(.)p eop end %%Page: 196 214 TeXDict begin 196 213 bop 150 -116 a FK(Chapter)30 b(17:)41 b(Numerical)31 b(In)m(tegration)2079 b(196)150 299 y FJ(17.6)68 b(QA)l(GI)45 b(adaptiv)l(e)h(in)l(tegration)h(on)e (in\014nite)g(in)l(terv)-7 b(als)3350 509 y FK([F)f(unction])-3599 b Fv(int)53 b(gsl_integration_qagi)f Fu(\()p FD(gsl)p 1598 509 28 4 v 41 w(function)30 b(*)g Ft(f)p FD(,)h(double)f Ft(epsabs)p FD(,)j(double)565 619 y Ft(epsrel)p FD(,)f(size)p 1081 619 V 41 w(t)f Ft(limit)p FD(,)h(gsl)p 1611 619 V 41 w(in)m(tegration)p 2082 619 V 42 w(w)m(orkspace)f(*)g Ft(workspace)p FD(,)i(double)d(*)565 728 y Ft(result)p FD(,)i(double)e(*)h Ft(abserr)p Fu(\))390 838 y FK(This)51 b(function)g(computes)h(the)g(in)m(tegral)h(of)f(the)g(function)f FD(f)69 b FK(o)m(v)m(er)53 b(the)e(in\014nite)h(in)m(terv)-5 b(al)390 947 y(\()p FI(\0001)p FE(;)15 b FK(+)p FI(1)p FK(\).)87 b(The)46 b(in)m(tegral)h(is)f(mapp)s(ed)f(on)m(to)i(the)f (semi-op)s(en)g(in)m(terv)-5 b(al)47 b(\(0)p FE(;)15 b FK(1])47 b(using)f(the)390 1057 y(transformation)31 b FE(x)25 b FK(=)g(\(1)c FI(\000)f FE(t)p FK(\))p FE(=t)p FK(,)859 1165 y Fs(Z)942 1185 y FB(+)p Fp(1)905 1353 y(\0001)1078 1280 y FE(dx)15 b(f)10 b FK(\()p FE(x)p FK(\))26 b(=)1491 1165 y Fs(Z)1574 1185 y FB(1)1537 1353 y(0)1626 1280 y FE(dt)15 b FK(\()p FE(f)10 b FK(\(\(1)21 b FI(\000)f FE(t)p FK(\))p FE(=t)p FK(\))h(+)f FE(f)10 b FK(\()p FI(\000)p FK(\(1)21 b FI(\000)e FE(t)p FK(\))p FE(=t)p FK(\)\))p FE(=t)2977 1242 y FB(2)3016 1280 y FE(:)390 1492 y FK(It)25 b(is)f(then)g(in)m(tegrated)i(using)e(the)h (QA)m(GS)g(algorithm.)39 b(The)24 b(normal)h(21-p)s(oin)m(t)g (Gauss-Kronro)s(d)390 1601 y(rule)i(of)g(QA)m(GS)g(is)f(replaced)i(b)m (y)e(a)i(15-p)s(oin)m(t)g(rule,)f(b)s(ecause)g(the)g(transformation)g (can)g(generate)390 1711 y(an)e(in)m(tegrable)i(singularit)m(y)g(at)f (the)g(origin.)39 b(In)25 b(this)g(case)i(a)e(lo)m(w)m(er-order)i(rule) e(is)h(more)f(e\016cien)m(t.)3350 1897 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_integration_qagiu)f Fu(\()p FD(gsl)p 1650 1897 V 41 w(function)30 b(*)h Ft(f)p FD(,)g(double)f Ft(a)p FD(,)g(double)565 2006 y Ft(epsabs)p FD(,)i(double)e Ft(epsrel)p FD(,)j(size)p 1744 2006 V 41 w(t)d Ft(limit)p FD(,)i(gsl)p 2273 2006 V 41 w(in)m(tegration)p 2744 2006 V 42 w(w)m(orkspace)f(*)565 2116 y Ft(workspace)p FD(,)i(double)d(*)h Ft(result)p FD(,)h(double)e(*)h Ft(abserr)p Fu(\))390 2226 y FK(This)j(function)g(computes)g(the)g(in)m(tegral)i(of)f(the)f (function)g FD(f)52 b FK(o)m(v)m(er)36 b(the)e(semi-in\014nite)h(in)m (terv)-5 b(al)390 2335 y(\()p FE(a;)15 b FK(+)p FI(1)p FK(\).)52 b(The)34 b(in)m(tegral)i(is)e(mapp)s(ed)f(on)m(to)i(the)f (semi-op)s(en)g(in)m(terv)-5 b(al)35 b(\(0)p FE(;)15 b FK(1])36 b(using)e(the)g(trans-)390 2445 y(formation)d FE(x)25 b FK(=)g FE(a)20 b FK(+)g(\(1)h FI(\000)f FE(t)p FK(\))p FE(=t)p FK(,)1150 2553 y Fs(Z)1233 2573 y FB(+)p Fp(1)1196 2741 y Fq(a)1369 2668 y FE(dx)15 b(f)10 b FK(\()p FE(x)p FK(\))26 b(=)1782 2553 y Fs(Z)1865 2573 y FB(1)1828 2741 y(0)1917 2668 y FE(dt)15 b(f)10 b FK(\()p FE(a)20 b FK(+)g(\(1)h FI(\000)f FE(t)p FK(\))p FE(=t)p FK(\))p FE(=t)2712 2630 y FB(2)390 2873 y FK(and)30 b(then)g(in)m(tegrated)i (using)e(the)g(QA)m(GS)h(algorithm.)3350 3059 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_integration_qagil)f Fu(\()p FD(gsl)p 1650 3059 V 41 w(function)30 b(*)h Ft(f)p FD(,)g(double)f Ft(b)p FD(,)g(double)565 3168 y Ft(epsabs)p FD(,)i(double)e Ft(epsrel)p FD(,)j(size)p 1744 3168 V 41 w(t)d Ft(limit)p FD(,)i(gsl)p 2273 3168 V 41 w(in)m(tegration)p 2744 3168 V 42 w(w)m(orkspace)f(*)565 3278 y Ft(workspace)p FD(,)i(double)d(*)h Ft(result)p FD(,)h(double)e(*)h Ft(abserr)p Fu(\))390 3387 y FK(This)j(function)g(computes)g(the)g(in)m(tegral)i (of)f(the)f(function)g FD(f)52 b FK(o)m(v)m(er)36 b(the)e (semi-in\014nite)h(in)m(terv)-5 b(al)390 3497 y(\()p FI(\0001)p FE(;)15 b(b)p FK(\).)54 b(The)35 b(in)m(tegral)h(is)f(mapp)s (ed)e(on)m(to)j(the)f(semi-op)s(en)f(in)m(terv)-5 b(al)36 b(\(0)p FE(;)15 b FK(1])37 b(using)d(the)h(trans-)390 3607 y(formation)c FE(x)25 b FK(=)g FE(b)20 b FI(\000)g FK(\(1)h FI(\000)f FE(t)p FK(\))p FE(=t)p FK(,)1172 3717 y Fs(Z)1255 3738 y Fq(b)1218 3906 y Fp(\0001)1356 3832 y FE(dx)15 b(f)10 b FK(\()p FE(x)p FK(\))25 b(=)1768 3717 y Fs(Z)1851 3738 y FB(1)1814 3906 y(0)1904 3832 y FE(dt)15 b(f)10 b FK(\()p FE(b)20 b FI(\000)g FK(\(1)h FI(\000)f FE(t)p FK(\))p FE(=t)p FK(\))p FE(=t)2690 3795 y FB(2)390 4044 y FK(and)30 b(then)g(in)m(tegrated)i(using)e(the)g(QA)m (GS)h(algorithm.)150 4257 y FJ(17.7)68 b(QA)-15 b(W)l(C)45 b(adaptiv)l(e)h(in)l(tegration)h(for)f(Cauc)l(h)l(y)f(principal)456 4390 y(v)-7 b(alues)3350 4600 y FK([F)f(unction])-3599 b Fv(int)53 b(gsl_integration_qawc)f Fu(\()p FD(gsl)p 1598 4600 V 41 w(function)30 b(*)g Ft(f)p FD(,)h(double)f Ft(a)p FD(,)h(double)f Ft(b)p FD(,)565 4710 y(double)g Ft(c)p FD(,)h(double)f Ft(epsabs)p FD(,)i(double)e Ft(epsrel)p FD(,)j(size)p 2438 4710 V 40 w(t)e Ft(limit)p FD(,)565 4819 y(gsl)p 677 4819 V 41 w(in)m(tegration)p 1148 4819 V 42 w(w)m(orkspace)g(*)g Ft(workspace)p FD(,)i(double)d(*)h Ft(result)p FD(,)h(double)e(*)h Ft(abserr)p Fu(\))390 4929 y FK(This)37 b(function)h(computes)g(the)g(Cauc)m(h)m(y)g (principal)g(v)-5 b(alue)38 b(of)g(the)g(in)m(tegral)i(of)e FE(f)47 b FK(o)m(v)m(er)40 b(\()p FE(a;)15 b(b)p FK(\),)390 5038 y(with)30 b(a)h(singularit)m(y)g(at)g FD(c)p FK(,)848 5271 y FE(I)i FK(=)1017 5156 y Fs(Z)1100 5177 y Fq(b)1063 5345 y(a)1148 5271 y FE(dx)1285 5210 y(f)10 b FK(\()p FE(x)p FK(\))p 1272 5250 203 4 v 1272 5334 a FE(x)21 b FI(\000)e FE(c)1510 5271 y FK(=)25 b(lim)1606 5323 y Fq(\017)p Fp(!)p FB(0)1748 5127 y Fs(\()1815 5156 y(Z)1898 5177 y Fq(c)p Fp(\000)p Fq(\017)1861 5345 y(a)2027 5271 y FE(dx)2164 5210 y(f)10 b FK(\()p FE(x)p FK(\))p 2151 5250 V 2151 5334 a FE(x)20 b FI(\000)g FE(c)2384 5271 y FK(+)2474 5156 y Fs(Z)2557 5177 y Fq(b)2521 5345 y(c)p FB(+)p Fq(\017)2648 5271 y FE(dx)2785 5210 y(f)10 b FK(\()p FE(x)p FK(\))p 2773 5250 V 2773 5334 a FE(x)20 b FI(\000)g FE(c)2985 5127 y Fs(\))p eop end %%Page: 197 215 TeXDict begin 197 214 bop 150 -116 a FK(Chapter)30 b(17:)41 b(Numerical)31 b(In)m(tegration)2079 b(197)390 299 y(The)31 b(adaptiv)m(e)i(bisection)g(algorithm)g(of)f(QA)m(G)h(is)e(used,)h (with)g(mo)s(di\014cations)g(to)g(ensure)f(that)390 408 y(sub)s(divisions)h(do)h(not)h(o)s(ccur)f(at)i(the)f(singular)f(p)s (oin)m(t)g FE(x)e FK(=)f FE(c)p FK(.)51 b(When)33 b(a)h(subin)m(terv)-5 b(al)34 b(con)m(tains)390 518 y(the)27 b(p)s(oin)m(t)g FE(x)f FK(=)f FE(c)i FK(or)g(is)g(close)i(to)f(it)f(then)g(a)h(sp)s (ecial)g(25-p)s(oin)m(t)g(mo)s(di\014ed)e(Clensha)m(w-Curtis)g(rule)390 628 y(is)37 b(used)f(to)h(con)m(trol)i(the)e(singularit)m(y)-8 b(.)61 b(F)-8 b(urther)36 b(a)m(w)m(a)m(y)j(from)d(the)h(singularit)m (y)h(the)f(algorithm)390 737 y(uses)30 b(an)g(ordinary)g(15-p)s(oin)m (t)h(Gauss-Kronro)s(d)e(in)m(tegration)k(rule.)150 987 y FJ(17.8)68 b(QA)-15 b(WS)44 b(adaptiv)l(e)j(in)l(tegration)g(for)e (singular)g(functions)150 1147 y FK(The)29 b(QA)-10 b(WS)30 b(algorithm)h(is)f(designed)f(for)h(in)m(tegrands)g(with)g (algebraic-logarithmic)j(singularities)e(at)150 1256 y(the)h(end-p)s(oin)m(ts)f(of)h(an)g(in)m(tegration)i(region.)45 b(In)31 b(order)h(to)g(w)m(ork)g(e\016cien)m(tly)i(the)e(algorithm)g (requires)150 1366 y(a)f(precomputed)e(table)j(of)e(Cheb)m(yshev)g (momen)m(ts.)3350 1574 y([F)-8 b(unction])-3599 b Fv (gsl_integration_qaws_t)q(abl)q(e)58 b(*)565 1684 y (gsl_integration_qaws_t)q(abl)q(e_a)q(llo)q(c)51 b Fu(\()p FD(double)29 b Ft(alpha)p FD(,)i(double)e Ft(beta)p FD(,)i(in)m(t)e Ft(mu)p FD(,)565 1793 y(in)m(t)i Ft(nu)p Fu(\))390 1903 y FK(This)j(function)g(allo)s(cates)j(space)e(for)f(a)h FH(gsl_integration_qaws_ta)o(ble)28 b FK(struct)34 b(describing)390 2012 y(a)d(singular)f(w)m(eigh)m(t)i(function)e FE(W)13 b FK(\()p FE(x)p FK(\))30 b(with)g(the)h(parameters)g(\()p FE(\013;)15 b(\014)5 b(;)15 b(\026;)g(\027)6 b FK(\),)1003 2192 y FE(W)13 b FK(\()p FE(x)p FK(\))25 b(=)g(\()p FE(x)c FI(\000)e FE(a)p FK(\))1626 2154 y Fq(\013)1674 2192 y FK(\()p FE(b)i FI(\000)f FE(x)p FK(\))1947 2154 y Fq(\014)2007 2192 y FK(log)2124 2149 y Fq(\026)2169 2192 y FK(\()p FE(x)g FI(\000)g FE(a)p FK(\))15 b(log)2583 2149 y Fq(\027)2625 2192 y FK(\()p FE(b)20 b FI(\000)g FE(x)p FK(\))390 2372 y(where)35 b FE(\013)f(>)f FI(\000)p FK(1,)k FE(\014)i(>)33 b FI(\000)p FK(1,)k(and)e FE(\026)e FK(=)g(0)p FE(;)15 b FK(1,)38 b FE(\027)h FK(=)34 b(0)p FE(;)15 b FK(1.)56 b(The)35 b(w)m(eigh)m(t)i(function)e(can)h(tak)m(e)h(four)390 2481 y(di\013eren)m(t)31 b(forms)f(dep)s(ending)e(on)j(the)f(v)-5 b(alues)31 b(of)g FE(\026)f FK(and)f FE(\027)6 b FK(,)755 2646 y FE(W)13 b FK(\()p FE(x)p FK(\))26 b(=)f(\()p FE(x)20 b FI(\000)g FE(a)p FK(\))1379 2613 y Fq(\013)1427 2646 y FK(\()p FE(b)h FI(\000)e FE(x)p FK(\))1699 2613 y Fq(\014)2595 2646 y FK(\()p FE(\026)25 b FK(=)g(0)p FE(;)15 b(\027)32 b FK(=)25 b(0\))755 2756 y FE(W)13 b FK(\()p FE(x)p FK(\))26 b(=)f(\()p FE(x)20 b FI(\000)g FE(a)p FK(\))1379 2723 y Fq(\013)1427 2756 y FK(\()p FE(b)h FI(\000)e FE(x)p FK(\))1699 2723 y Fq(\014)1760 2756 y FK(log)r(\()p FE(x)i FI(\000)f FE(a)p FK(\))436 b(\()p FE(\026)25 b FK(=)g(1)p FE(;)15 b(\027)32 b FK(=)25 b(0\))755 2865 y FE(W)13 b FK(\()p FE(x)p FK(\))26 b(=)f(\()p FE(x)20 b FI(\000)g FE(a)p FK(\))1379 2832 y Fq(\013)1427 2865 y FK(\()p FE(b)h FI(\000)e FE(x)p FK(\))1699 2832 y Fq(\014)1760 2865 y FK(log)r(\()p FE(b)i FI(\000)f FE(x)p FK(\))445 b(\()p FE(\026)25 b FK(=)g(0)p FE(;)15 b(\027)32 b FK(=)25 b(1\))755 2975 y FE(W)13 b FK(\()p FE(x)p FK(\))26 b(=)f(\()p FE(x)20 b FI(\000)g FE(a)p FK(\))1379 2942 y Fq(\013)1427 2975 y FK(\()p FE(b)h FI(\000)e FE(x)p FK(\))1699 2942 y Fq(\014)1760 2975 y FK(log)r(\()p FE(x)i FI(\000)f FE(a)p FK(\))15 b(log)s(\()p FE(b)20 b FI(\000)g FE(x)p FK(\))31 b(\()p FE(\026)25 b FK(=)g(1)p FE(;)15 b(\027)32 b FK(=)25 b(1\))390 3145 y(The)31 b(singular)h(p)s(oin)m(ts)g(\()p FE(a;)15 b(b)p FK(\))33 b(do)e(not)h(ha)m(v)m(e)h(to)g(b)s(e)e(sp)s (eci\014ed)g(un)m(til)h(the)g(in)m(tegral)i(is)e(computed,)390 3254 y(where)e(they)g(are)h(the)g(endp)s(oin)m(ts)e(of)i(the)g(in)m (tegration)h(range.)390 3401 y(The)27 b(function)g(returns)f(a)i(p)s (oin)m(ter)f(to)h(the)g(newly)f(allo)s(cated)i(table)g FH(gsl_integration_qaws_)390 3510 y(table)g FK(if)h(no)h(errors)e(w)m (ere)i(detected,)h(and)e(0)h(in)f(the)g(case)i(of)e(error.)3350 3718 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_integration_qaws_)q (tabl)q(e_s)q(et)f Fu(\()p FD(gsl)p 2121 3718 28 4 v 41 w(in)m(tegration)p 2592 3718 V 42 w(qa)m(ws)p 2826 3718 V 40 w(table)31 b(*)565 3828 y Ft(t)p FD(,)g(double)f Ft(alpha)p FD(,)i(double)e Ft(beta)p FD(,)i(in)m(t)f Ft(mu)p FD(,)g(in)m(t)g Ft(nu)p Fu(\))390 3938 y FK(This)j(function)h (mo)s(di\014es)f(the)h(parameters)g(\()p FE(\013;)15 b(\014)5 b(;)15 b(\026;)g(\027)6 b FK(\))37 b(of)e(an)g(existing)g FH(gsl_integration_)390 4047 y(qaws_table)28 b FK(struct)i FD(t)p FK(.)3350 4255 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_integration_qaws_tab)q(le_)q(fre)q(e)d Fu(\()p FD(gsl)p 2225 4255 V 41 w(in)m(tegration)p 2696 4255 V 42 w(qa)m(ws)p 2930 4255 V 41 w(table)565 4365 y(*)31 b Ft(t)p Fu(\))390 4474 y FK(This)20 b(function)h(frees)g(all)g(the)g (memory)g(asso)s(ciated)h(with)f(the)g FH(gsl_integration_qaws_tabl)o (e)390 4584 y FK(struct)30 b FD(t)p FK(.)3350 4792 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_integration_qaws)f Fu(\()p FD(gsl)p 1598 4792 V 41 w(function)30 b(*)g Ft(f)p FD(,)h(const)g(double)f Ft(a)p FD(,)h(const)565 4902 y(double)f Ft(b)p FD(,)h(gsl)p 1078 4902 V 40 w(in)m(tegration)p 1548 4902 V 43 w(qa)m(ws)p 1783 4902 V 40 w(table)g(*)g Ft(t)p FD(,)g(const)g(double)f Ft(epsabs)p FD(,)i(const)f(double)565 5011 y Ft(epsrel)p FD(,)h(const)f(size)p 1319 5011 V 41 w(t)g Ft(limit)p FD(,)h(gsl)p 1849 5011 V 41 w(in)m(tegration)p 2320 5011 V 42 w(w)m(orkspace)f(*)g Ft(workspace)p FD(,)i(double)d(*) 565 5121 y Ft(result)p FD(,)i(double)e(*)h Ft(abserr)p Fu(\))390 5230 y FK(This)e(function)h(computes)g(the)g(in)m(tegral)i (of)e(the)h(function)e FE(f)10 b FK(\()p FE(x)p FK(\))30 b(o)m(v)m(er)i(the)e(in)m(terv)-5 b(al)31 b(\()p FE(a;)15 b(b)p FK(\))31 b(with)390 5340 y(the)e(singular)g(w)m(eigh)m(t)h (function)f(\()p FE(x)18 b FI(\000)f FE(a)p FK(\))1805 5307 y Fq(\013)1853 5340 y FK(\()p FE(b)g FI(\000)g FE(x)p FK(\))2119 5307 y Fq(\014)2180 5340 y FK(log)2297 5297 y Fq(\026)2342 5340 y FK(\()p FE(x)g FI(\000)g FE(a)p FK(\))e(log)2750 5297 y Fq(\027)2792 5340 y FK(\()p FE(b)j FI(\000)f FE(x)p FK(\).)40 b(The)29 b(parameters)p eop end %%Page: 198 216 TeXDict begin 198 215 bop 150 -116 a FK(Chapter)30 b(17:)41 b(Numerical)31 b(In)m(tegration)2079 b(198)390 299 y(of)31 b(the)f(w)m(eigh)m(t)i(function)e(\()p FE(\013;)15 b(\014)5 b(;)15 b(\026;)g(\027)6 b FK(\))32 b(are)f(tak)m(en)h(from)e(the)g (table)h FD(t)p FK(.)41 b(The)30 b(in)m(tegral)i(is,)866 534 y FE(I)g FK(=)1034 419 y Fs(Z)1117 440 y Fq(b)1080 608 y(a)1165 534 y FE(dx)15 b(f)10 b FK(\()p FE(x)p FK(\)\()p FE(x)21 b FI(\000)f FE(a)p FK(\))1738 497 y Fq(\013)1786 534 y FK(\()p FE(b)h FI(\000)e FE(x)p FK(\))2058 497 y Fq(\014)2119 534 y FK(log)2236 492 y Fq(\026)2281 534 y FK(\()p FE(x)h FI(\000)g FE(a)p FK(\))15 b(log)2695 492 y Fq(\027)2736 534 y FK(\()p FE(b)21 b FI(\000)f FE(x)p FK(\))p FE(:)390 749 y FK(The)32 b(adaptiv)m(e)j(bisection)e (algorithm)h(of)g(QA)m(G)f(is)g(used.)48 b(When)32 b(a)i(subin)m(terv) -5 b(al)33 b(con)m(tains)h(one)390 858 y(of)41 b(the)h(endp)s(oin)m(ts) e(then)h(a)g(sp)s(ecial)h(25-p)s(oin)m(t)g(mo)s(di\014ed)e(Clensha)m (w-Curtis)h(rule)g(is)g(used)f(to)390 968 y(con)m(trol)k(the)f (singularities.)80 b(F)-8 b(or)44 b(subin)m(terv)-5 b(als)42 b(whic)m(h)h(do)g(not)g(include)g(the)g(endp)s(oin)m(ts)f(an)390 1078 y(ordinary)30 b(15-p)s(oin)m(t)h(Gauss-Kronro)s(d)e(in)m (tegration)k(rule)d(is)g(used.)150 1326 y FJ(17.9)68 b(QA)-15 b(W)l(O)45 b(adaptiv)l(e)h(in)l(tegration)h(for)e(oscillatory) i(functions)150 1485 y FK(The)d(QA)-10 b(W)m(O)45 b(algorithm)g(is)g (designed)f(for)h(in)m(tegrands)g(with)f(an)g(oscillatory)j(factor,)i (sin\()p FE(!)s(x)p FK(\))c(or)150 1595 y(cos)q(\()p FE(!)s(x)p FK(\).)c(In)30 b(order)g(to)h(w)m(ork)g(e\016cien)m(tly)h (the)f(algorithm)h(requires)e(a)h(table)g(of)g(Cheb)m(yshev)e(momen)m (ts)150 1704 y(whic)m(h)h(m)m(ust)g(b)s(e)g(pre-computed)g(with)g (calls)i(to)f(the)f(functions)g(b)s(elo)m(w.)3350 1910 y([F)-8 b(unction])-3599 b Fv(gsl_integration_qawo_t)q(abl)q(e)58 b(*)565 2019 y(gsl_integration_qawo_t)q(abl)q(e_a)q(llo)q(c)51 b Fu(\()p FD(double)31 b Ft(omega)p FD(,)h(double)e Ft(L)p FD(,)g(en)m(um)565 2129 y(gsl)p 677 2129 28 4 v 41 w(in)m(tegration)p 1148 2129 V 42 w(qa)m(w)m(o)p 1388 2129 V 41 w(en)m(um)g Ft(sine)p FD(,)i(size)p 2080 2129 V 41 w(t)f Ft(n)p Fu(\))390 2239 y FK(This)23 b(function)h(allo)s(cates)i(space)f(for)e(a)i FH(gsl_integration_qawo_ta)o(ble)17 b FK(struct)24 b(and)g(its)g(asso-) 390 2348 y(ciated)f(w)m(orkspace)e(describing)g(a)h(sine)f(or)g(cosine) h(w)m(eigh)m(t)h(function)e FE(W)13 b FK(\()p FE(x)p FK(\))21 b(with)g(the)h(parameters)390 2458 y(\()p FE(!)s(;)15 b(L)p FK(\),)1549 2681 y FE(W)e FK(\()p FE(x)p FK(\))26 b(=)1892 2562 y Fs(\032)1974 2626 y FK(sin\()p FE(!)s(x)p FK(\))1969 2736 y(cos)q(\()p FE(!)s(x)p FK(\))2288 2562 y Fs(\033)390 2900 y FK(The)33 b(parameter)h FD(L)f FK(m)m(ust)h(b)s(e) e(the)i(length)g(of)g(the)f(in)m(terv)-5 b(al)35 b(o)m(v)m(er)g(whic)m (h)e(the)h(function)f(will)h(b)s(e)390 3009 y(in)m(tegrated)i FE(L)31 b FK(=)f FE(b)23 b FI(\000)f FE(a)p FK(.)51 b(The)34 b(c)m(hoice)i(of)e(sine)f(or)h(cosine)h(is)f(made)g(with)f(the)i (parameter)f FD(sine)390 3119 y FK(whic)m(h)c(should)f(b)s(e)h(c)m (hosen)h(from)f(one)h(of)f(the)h(t)m(w)m(o)h(follo)m(wing)f(sym)m(b)s (olic)g(v)-5 b(alues:)630 3264 y FH(GSL_INTEG_COSINE)630 3373 y(GSL_INTEG_SINE)390 3518 y FK(The)43 b FH (gsl_integration_qawo_ta)o(ble)37 b FK(is)43 b(a)g(table)h(of)g(the)f (trigonometric)i(co)s(e\016cien)m(ts)g(re-)390 3628 y(quired)32 b(in)h(the)g(in)m(tegration)i(pro)s(cess.)48 b(The)32 b(parameter)h FD(n)g FK(determines)g(the)g(n)m(um)m(b)s(er)e(of)i(lev)m (els)390 3738 y(of)43 b(co)s(e\016cien)m(ts)i(that)e(are)g(computed.)78 b(Eac)m(h)43 b(lev)m(el)i(corresp)s(onds)c(to)j(one)f(bisection)h(of)f (the)390 3847 y(in)m(terv)-5 b(al)38 b FE(L)p FK(,)i(so)d(that)h FD(n)f FK(lev)m(els)i(are)e(su\016cien)m(t)h(for)f(subin)m(terv)-5 b(als)38 b(do)m(wn)e(to)j(the)e(length)h FE(L=)p FK(2)3679 3814 y Fq(n)3725 3847 y FK(.)390 3957 y(The)30 b(in)m(tegration)j (routine)d FH(gsl_integration_qawo)25 b FK(returns)30 b(the)g(error)g FH(GSL_ETABLE)e FK(if)j(the)390 4066 y(n)m(um)m(b)s(er)e(of)i(lev)m(els)h(is)e(insu\016cien)m(t)h(for)f(the) g(requested)h(accuracy)-8 b(.)3350 4272 y([F)g(unction])-3599 b Fv(int)53 b(gsl_integration_qawo_)q(tabl)q(e_s)q(et)f Fu(\()p FD(gsl)p 2121 4272 V 41 w(in)m(tegration)p 2592 4272 V 42 w(qa)m(w)m(o)p 2832 4272 V 41 w(table)32 b(*)565 4381 y Ft(t)p FD(,)f(double)f Ft(omega)p FD(,)i(double)e Ft(L)p FD(,)h(en)m(um)f(gsl)p 2041 4381 V 40 w(in)m(tegration)p 2511 4381 V 42 w(qa)m(w)m(o)p 2751 4381 V 42 w(en)m(um)g Ft(sine)p Fu(\))390 4491 y FK(This)e(function)h(c)m(hanges)h(the)f (parameters)g FD(omega)p FK(,)i FD(L)d FK(and)h FD(sine)34 b FK(of)29 b(the)g(existing)h(w)m(orkspace)f FD(t)p FK(.)3350 4696 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_integration_qawo_)q (tabl)q(e_s)q(et_)q(len)q(gth)565 4806 y Fu(\()p FD(gsl)p 712 4806 V 41 w(in)m(tegration)p 1183 4806 V 42 w(qa)m(w)m(o)p 1423 4806 V 42 w(table)31 b(*)g Ft(t)p FD(,)f(double)g Ft(L)p Fu(\))390 4915 y FK(This)g(function)g(allo)m(ws)h(the)g(length)g (parameter)g FD(L)f FK(of)g(the)h(w)m(orkspace)g FD(t)h FK(to)g(b)s(e)d(c)m(hanged.)3350 5121 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_integration_qawo_tab)q(le_)q(fre)q(e)d Fu(\()p FD(gsl)p 2225 5121 V 41 w(in)m(tegration)p 2696 5121 V 42 w(qa)m(w)m(o)p 2936 5121 V 42 w(table)565 5230 y(*)31 b Ft(t)p Fu(\))390 5340 y FK(This)f(function)g(frees)g(all)h (the)g(memory)f(asso)s(ciated)i(with)e(the)h(w)m(orkspace)g FD(t)p FK(.)p eop end %%Page: 199 217 TeXDict begin 199 216 bop 150 -116 a FK(Chapter)30 b(17:)41 b(Numerical)31 b(In)m(tegration)2079 b(199)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_integration_qawo)f Fu(\()p FD(gsl)p 1598 299 28 4 v 41 w(function)30 b(*)g Ft(f)p FD(,)h(const)g(double)f Ft(a)p FD(,)h(const)565 408 y(double)f Ft(epsabs)p FD(,)i(const)f(double)f Ft(epsrel)p FD(,)j(const)d(size)p 2512 408 V 41 w(t)h Ft(limit)p FD(,)565 518 y(gsl)p 677 518 V 41 w(in)m(tegration)p 1148 518 V 42 w(w)m(orkspace)g(*)g Ft(workspace)p FD(,)i(gsl)p 2333 518 V 40 w(in)m(tegration)p 2803 518 V 43 w(qa)m(w)m(o)p 3044 518 V 41 w(table)e(*)g Ft(wf)p FD(,)565 628 y(double)f(*)h Ft(result)p FD(,)h(double)e(*)h Ft(abserr)p Fu(\))390 737 y FK(This)25 b(function)h(uses)f(an)h(adaptiv)m(e)i(algorithm)f(to) f(compute)h(the)f(in)m(tegral)h(of)g FE(f)35 b FK(o)m(v)m(er)27 b(\()p FE(a;)15 b(b)p FK(\))27 b(with)390 847 y(the)k(w)m(eigh)m(t)g (function)g(sin)o(\()p FE(!)s(x)p FK(\))g(or)f(cos)q(\()p FE(!)s(x)p FK(\))h(de\014ned)e(b)m(y)h(the)h(table)g FD(wf)p FK(,)1417 1092 y FE(I)i FK(=)1586 977 y Fs(Z)1669 997 y Fq(b)1632 1165 y(a)1717 1092 y FE(dx)15 b(f)10 b FK(\()p FE(x)p FK(\))2023 973 y Fs(\032)2106 1037 y FK(sin\()p FE(!)s(x)p FK(\))2101 1146 y(cos)q(\()p FE(!)s(x)p FK(\))2420 973 y Fs(\033)390 1320 y FK(The)23 b(results)g(are)h(extrap) s(olated)g(using)f(the)h(epsilon-algorithm)g(to)h(accelerate)h(the)e (con)m(v)m(ergence)390 1429 y(of)29 b(the)g(in)m(tegral.)42 b(The)28 b(function)h(returns)e(the)i(\014nal)g(appro)m(ximation)h (from)e(the)h(extrap)s(olation,)390 1539 y FD(result)p FK(,)47 b(and)42 b(an)h(estimate)i(of)e(the)h(absolute)g(error,)i FD(abserr)p FK(.)79 b(The)42 b(subin)m(terv)-5 b(als)43 b(and)g(their)390 1648 y(results)f(are)g(stored)g(in)f(the)h(memory)g (pro)m(vided)g(b)m(y)f FD(w)m(orkspace)p FK(.)76 b(The)42 b(maxim)m(um)f(n)m(um)m(b)s(er)390 1758 y(of)k(subin)m(terv)-5 b(als)44 b(is)h(giv)m(en)h(b)m(y)e FD(limit)p FK(,)50 b(whic)m(h)44 b(ma)m(y)h(not)g(exceed)h(the)f(allo)s(cated)h(size)g(of) f(the)390 1868 y(w)m(orkspace.)390 2022 y(Those)23 b(subin)m(terv)-5 b(als)24 b(with)f(\\large")j(widths)d FE(d)h FK(where)f FE(d!)28 b(>)d FK(4)f(are)g(computed)g(using)f(a)h(25-p)s(oin)m(t)390 2132 y(Clensha)m(w-Curtis)c(in)m(tegration)i(rule,)h(whic)m(h)d (handles)g(the)g(oscillatory)j(b)s(eha)m(vior.)37 b(Subin)m(terv)-5 b(als)390 2241 y(with)33 b(a)g(\\small")i(widths)d(where)h FE(d!)g(<)c FK(4)34 b(are)f(computed)g(using)g(a)g(15-p)s(oin)m(t)h (Gauss-Kronro)s(d)390 2351 y(in)m(tegration.)150 2613 y FJ(17.10)69 b(QA)-15 b(WF)44 b(adaptiv)l(e)i(in)l(tegration)h(for)e (F)-11 b(ourier)45 b(in)l(tegrals)3350 2843 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_integration_qawf)f Fu(\()p FD(gsl)p 1598 2843 V 41 w(function)30 b(*)g Ft(f)p FD(,)h(const)g(double)f Ft(a)p FD(,)h(const)565 2952 y(double)f Ft(epsabs)p FD(,)i(const)f(size)p 1612 2952 V 41 w(t)g Ft(limit)p FD(,)h(gsl)p 2142 2952 V 41 w(in)m(tegration)p 2613 2952 V 42 w(w)m(orkspace)f(*)f Ft(workspace)p FD(,)565 3062 y(gsl)p 677 3062 V 41 w(in)m(tegration)p 1148 3062 V 42 w(w)m(orkspace)h(*)g Ft(cycle_workspace)p FD(,)k(gsl)p 2647 3062 V 40 w(in)m(tegration)p 3117 3062 V 42 w(qa)m(w)m(o)p 3357 3062 V 42 w(table)c(*)565 3171 y Ft(wf)p FD(,)g(double)f(*)h Ft(result)p FD(,)h(double)e(*)h Ft(abserr)p Fu(\))390 3281 y FK(This)c(function)g(attempts)h(to)h(compute)e(a)h(F)-8 b(ourier)28 b(in)m(tegral)i(of)d(the)h(function)f FD(f)45 b FK(o)m(v)m(er)29 b(the)e(semi-)390 3391 y(in\014nite)j(in)m(terv)-5 b(al)32 b([)p FE(a;)15 b FK(+)p FI(1)p FK(\).)1373 3631 y FE(I)33 b FK(=)1542 3516 y Fs(Z)1625 3537 y FB(+)p Fp(1)1588 3705 y Fq(a)1761 3631 y FE(dx)15 b(f)10 b FK(\()p FE(x)p FK(\))2067 3512 y Fs(\032)2150 3576 y FK(sin\()p FE(!)s(x)p FK(\))2145 3686 y(cos)q(\()p FE(!)s(x)p FK(\))2464 3512 y Fs(\033)390 3909 y FK(The)35 b(parameter)h FE(!)i FK(and)d(c)m(hoice)i(of)f(sin)f(or)h(cos)g(is)f(tak)m(en)i(from)e(the)g (table)i FD(wf)52 b FK(\(the)36 b(length)g FD(L)390 4019 y FK(can)d(tak)m(e)h(an)m(y)f(v)-5 b(alue,)33 b(since)g(it)g(is)f(o)m (v)m(erridden)h(b)m(y)f(this)h(function)f(to)h(a)g(v)-5 b(alue)33 b(appropriate)f(for)390 4128 y(the)h(F)-8 b(ourier)34 b(in)m(tegration\).)50 b(The)33 b(in)m(tegral)h(is)f(computed)g(using)f (the)h(QA)-10 b(W)m(O)34 b(algorithm)g(o)m(v)m(er)390 4238 y(eac)m(h)e(of)e(the)h(subin)m(terv)-5 b(als,)1432 4420 y FE(C)1497 4434 y FB(1)1560 4420 y FK(=)25 b([)p FE(a;)15 b(a)21 b FK(+)f FE(c)p FK(])1432 4555 y FE(C)1497 4569 y FB(2)1560 4555 y FK(=)25 b([)p FE(a)20 b FK(+)g FE(c;)15 b(a)21 b FK(+)f(2)p FE(c)p FK(])1429 4689 y FE(:)15 b(:)g(:)26 b FK(=)f FE(:)15 b(:)g(:)1429 4824 y(C)1494 4838 y Fq(k)1560 4824 y FK(=)25 b([)p FE(a)20 b FK(+)g(\()p FE(k)k FI(\000)c FK(1\))p FE(c;)15 b(a)22 b FK(+)e FE(k)s(c)p FK(])390 5011 y(where)33 b FE(c)e FK(=)f(\(2)15 b(\015o)s(or)q(\()p FI(j)p FE(!)s FI(j)p FK(\))23 b(+)f(1\))p FE(\031)s(=)p FI(j)p FE(!)s FI(j)p FK(.)52 b(The)33 b(width)g FE(c)g FK(is)h(c)m(hosen)g(to)g(co)m(v)m(er) i(an)d(o)s(dd)g(n)m(um)m(b)s(er)f(of)390 5121 y(p)s(erio)s(ds)f(so)j (that)f(the)g(con)m(tributions)g(from)g(the)g(in)m(terv)-5 b(als)34 b(alternate)g(in)f(sign)g(and)f(are)i(mono-)390 5230 y(tonically)27 b(decreasing)e(when)f FD(f)42 b FK(is)25 b(p)s(ositiv)m(e)h(and)e(monotonically)j(decreasing.)40 b(The)24 b(sum)g(of)h(this)390 5340 y(sequence)31 b(of)f(con)m (tributions)h(is)g(accelerated)h(using)e(the)h(epsilon-algorithm.)p eop end %%Page: 200 218 TeXDict begin 200 217 bop 150 -116 a FK(Chapter)30 b(17:)41 b(Numerical)31 b(In)m(tegration)2079 b(200)390 299 y(This)26 b(function)g(w)m(orks)h(to)g(an)f(o)m(v)m(erall)j(absolute)f(tolerance) g(of)f FD(abserr)p FK(.)38 b(The)26 b(follo)m(wing)j(strategy)390 408 y(is)h(used:)40 b(on)31 b(eac)m(h)g(in)m(terv)-5 b(al)32 b FE(C)1449 422 y Fq(k)1520 408 y FK(the)e(algorithm)i(tries)f (to)g(ac)m(hiev)m(e)h(the)f(tolerance)1601 586 y FE(T)13 b(O)s(L)1801 600 y Fq(k)1866 586 y FK(=)25 b FE(u)2014 600 y Fq(k)2055 586 y Fg(abserr)390 764 y FK(where)d FE(u)697 778 y Fq(k)764 764 y FK(=)i(\(1)5 b FI(\000)g FE(p)p FK(\))p FE(p)1147 731 y Fq(k)q Fp(\000)p FB(1)1297 764 y FK(and)22 b FE(p)j FK(=)g(9)p FE(=)p FK(10.)40 b(The)22 b(sum)g(of)h(the)g(geometric)i(series)e(of)h(con)m(tributions) 390 873 y(from)30 b(eac)m(h)h(in)m(terv)-5 b(al)32 b(giv)m(es)g(an)e(o) m(v)m(erall)j(tolerance)f(of)e FD(abserr)p FK(.)390 1018 y(If)h(the)h(in)m(tegration)i(of)e(a)g(subin)m(terv)-5 b(al)32 b(leads)g(to)g(di\016culties)h(then)e(the)h(accuracy)h (requiremen)m(t)390 1127 y(for)d(subsequen)m(t)g(in)m(terv)-5 b(als)31 b(is)g(relaxed,)1276 1305 y FE(T)13 b(O)s(L)1476 1319 y Fq(k)1541 1305 y FK(=)25 b FE(u)1689 1319 y Fq(k)1745 1305 y FK(max\()p Fg(abserr)r FE(;)15 b FK(max)2263 1359 y Fq(i)g(n)23 b FI(\000)h FK(1],)38 b(this)e(function)f(obtains)h(the)g FD(i)p FK(-th)g(Gauss-Legendre)g(p)s(oin)m(t)g FD(xi)390 4079 y FK(and)26 b(w)m(eigh)m(t)j FD(wi)j FK(on)27 b(the)g(in)m(terv)-5 b(al)28 b([)p FD(a)p FK(,)p FD(b)r FK(].)41 b(The)26 b(p)s(oin)m(ts)h(and)g(w)m(eigh)m(ts)h(are)g(ordered)e(b)m(y)h (increasing)390 4189 y(p)s(oin)m(t)j(v)-5 b(alue.)42 b(A)30 b(function)g FE(f)40 b FK(ma)m(y)31 b(b)s(e)e(in)m(tegrated)j (on)f([)p FD(a)p FK(,)p FD(b)r FK(])g(b)m(y)f(summing)f FE(w)r(i)21 b FI(\003)g FE(f)10 b FK(\()p FE(xi)p FK(\))31 b(o)m(v)m(er)g FD(i)p FK(.)3350 4363 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_integration_glfixed_)q(tab)q(le_)q(fre)q(e)565 4473 y Fu(\()p FD(gsl)p 712 4473 V 41 w(in)m(tegration)p 1183 4473 V 42 w(gl\014xed)p 1485 4473 V 40 w(table)31 b(*)g Ft(t)p Fu(\))390 4582 y FK(This)f(function)g(frees)g(the)h (memory)f(asso)s(ciated)i(with)e(the)g(table)i FD(t)p FK(.)150 4808 y FJ(17.13)69 b(Error)45 b(co)t(des)150 4968 y FK(In)31 b(addition)h(to)g(the)g(standard)f(error)g(co)s(des)h (for)f(in)m(v)-5 b(alid)32 b(argumen)m(ts)g(the)g(functions)f(can)h (return)f(the)150 5077 y(follo)m(wing)h(v)-5 b(alues,)150 5230 y FH(GSL_EMAXITER)630 5340 y FK(the)31 b(maxim)m(um)f(n)m(um)m(b)s (er)f(of)h(sub)s(divisions)f(w)m(as)i(exceeded.)p eop end %%Page: 202 220 TeXDict begin 202 219 bop 150 -116 a FK(Chapter)30 b(17:)41 b(Numerical)31 b(In)m(tegration)2079 b(202)150 299 y FH(GSL_EROUND)630 408 y FK(cannot)25 b(reac)m(h)h(tolerance)g(b)s (ecause)f(of)g(roundo\013)f(error,)i(or)e(roundo\013)g(error)h(w)m(as)g (detected)630 518 y(in)30 b(the)h(extrap)s(olation)g(table.)150 685 y FH(GSL_ESING)630 795 y FK(a)i(non-in)m(tegrable)i(singularit)m(y) f(or)f(other)g(bad)f(in)m(tegrand)i(b)s(eha)m(vior)f(w)m(as)g(found)f (in)h(the)630 904 y(in)m(tegration)f(in)m(terv)-5 b(al.)150 1071 y FH(GSL_EDIVERGE)630 1181 y FK(the)28 b(in)m(tegral)i(is)e(div)m (ergen)m(t,)j(or)d(to)s(o)h(slo)m(wly)g(con)m(v)m(ergen)m(t)h(to)f(b)s (e)f(in)m(tegrated)h(n)m(umerically)-8 b(.)150 1424 y FJ(17.14)69 b(Examples)150 1584 y FK(The)36 b(in)m(tegrator)j FH(QAGS)c FK(will)i(handle)f(a)i(large)f(class)h(of)f(de\014nite)f(in)m (tegrals.)61 b(F)-8 b(or)38 b(example,)h(consider)150 1693 y(the)31 b(follo)m(wing)g(in)m(tegral,)i(whic)m(h)d(has)g(an)g (algebraic-logarithmic)k(singularit)m(y)e(at)f(the)f(origin,)1475 1803 y Fs(Z)1558 1823 y FB(1)1521 1992 y(0)1610 1918 y FE(x)1662 1880 y Fp(\000)p FB(1)p Fq(=)p FB(2)1833 1918 y FK(log)s(\()p FE(x)p FK(\))15 b FE(dx)26 b FK(=)f FI(\000)p FK(4)150 2129 y(The)30 b(program)g(b)s(elo)m(w)h(computes)f (this)g(in)m(tegral)i(to)g(a)e(relativ)m(e)j(accuracy)e(b)s(ound)e(of)h FH(1e-7)p FK(.)390 2271 y FH(#include)46 b()390 2381 y(#include)g()390 2491 y(#include)g ()390 2710 y(double)g(f)i(\(double)d(x,)j(void)e (*)i(params\))d({)485 2819 y(double)i(alpha)f(=)h(*\(double)f(*\))h (params;)485 2929 y(double)g(f)g(=)g(log\(alpha*x\))e(/)i(sqrt\(x\);) 485 3039 y(return)g(f;)390 3148 y(})390 3367 y(int)390 3477 y(main)g(\(void\))390 3587 y({)485 3696 y (gsl_integration_workspace)41 b(*)48 b(w)581 3806 y(=)f (gsl_integration_workspace_)o(all)o(oc)42 b(\(1000\);)485 4025 y(double)47 b(result,)e(error;)485 4134 y(double)i(expected)e(=)j (-4.0;)485 4244 y(double)f(alpha)f(=)h(1.0;)485 4463 y(gsl_function)e(F;)485 4573 y(F.function)g(=)j(&f;)485 4682 y(F.params)e(=)h(α)485 4902 y(gsl_integration_qags)c(\(&F,)j (0,)i(1,)f(0,)g(1e-7,)f(1000,)1535 5011 y(w,)i(&result,)d(&error\);)485 5230 y(printf)i(\("result)475 b(=)47 b(\045)h(.18f\\n",)d(result\);)485 5340 y(printf)i(\("exact)e(result)190 b(=)47 b(\045)h(.18f\\n",)d (expected\);)p eop end %%Page: 203 221 TeXDict begin 203 220 bop 150 -116 a FK(Chapter)30 b(17:)41 b(Numerical)31 b(In)m(tegration)2079 b(203)485 299 y FH(printf)47 b(\("estimated)d(error)j(=)g(\045)h(.18f\\n",)d(error\);) 485 408 y(printf)i(\("actual)e(error)190 b(=)47 b(\045)h(.18f\\n",)d (result)h(-)i(expected\);)485 518 y(printf)f(\("intervals)331 b(=)47 b(\045zu\\n",)f(w->size\);)485 737 y(gsl_integration_workspace_) o(free)41 b(\(w\);)485 956 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b(Handb)s(o)s(ok)38 b(on)g(Sim)m(ulation,)k(Jerry)c(Banks,)j(ed.)65 b(\(Wiley)-8 b(,)43 b(1997\).)67 b(The)150 2810 y(c)m(hapter)31 b(is)g(a)m(v)-5 b(ailable)33 b(in)e(p)s(ostscript)f(from)h(L'Ecuy)m(er's)g(ftp)f(site)i (\(see)g(references\).)42 b(Kn)m(uth's)30 b(v)m(olume)150 2919 y(on)k(Semin)m(umerical)g(Algorithms)h(\(originally)g(published)d (in)i(1968\))i(dev)m(otes)f(170)h(pages)e(to)h(random)150 3029 y(n)m(um)m(b)s(er)24 b(generators,)j(and)e(has)g(recen)m(tly)h(b)s (een)f(up)s(dated)f(in)g(its)i(3rd)f(edition)g(\(1997\).)42 b(It)25 b(is)g(brillian)m(t,)j(a)150 3138 y(classic.)40 b(If)23 b(y)m(ou)i(don't)f(o)m(wn)g(it,)i(y)m(ou)e(should)f(stop)h (reading)g(righ)m(t)g(no)m(w,)i(run)c(to)j(the)f(nearest)h(b)s(o)s (okstore,)150 3248 y(and)30 b(buy)f(it.)275 3395 y(A)d(go)s(o)s(d)f (random)g(n)m(um)m(b)s(er)g(generator)i(will)f(satisfy)h(b)s(oth)e (theoretical)j(and)e(statistical)i(prop)s(erties.)150 3505 y(Theoretical)36 b(prop)s(erties)f(are)g(often)g(hard)f(to)h 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(most)g(generators)g(only)g(accept)h(32-bit)g(seeds,)i(with)c(higher)g (v)-5 b(alues)43 b(b)s(eing)390 4153 y(reduced)25 b(mo)s(dulo)h(2)1091 4120 y FB(32)1162 4153 y FK(.)39 b(F)-8 b(or)27 b(generators)g(with)f (smaller)g(ranges)h(the)f(maxim)m(um)g(seed)g(v)-5 b(alue)27 b(will)390 4263 y(t)m(ypically)32 b(b)s(e)e(lo)m(w)m(er.)3350 4483 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_rng_free)49 b Fu(\()p FD(gsl)p 1232 4483 V 41 w(rng)29 b(*)i Ft(r)p Fu(\))390 4593 y FK(This)f(function)g(frees)g(all)h(the)g(memory)f (asso)s(ciated)i(with)e(the)h(generator)g FD(r)p FK(.)150 4852 y FJ(18.4)68 b(Sampling)46 b(from)f(a)g(random)g(n)l(um)l(b)t(er)g (generator)150 5011 y FK(The)27 b(follo)m(wing)h(functions)f(return)f (uniformly)h(distributed)f(random)h(n)m(um)m(b)s(ers,)f(either)i(as)f (in)m(tegers)i(or)150 5121 y(double)35 b(precision)g(\015oating)h(p)s (oin)m(t)f(n)m(um)m(b)s(ers.)53 b(Inline)35 b(v)m(ersions)g(of)g(these) h(functions)e(are)i(used)e(when)150 5230 y FH(HAVE_INLINE)40 b FK(is)k(de\014ned.)79 b(T)-8 b(o)43 b(obtain)h(non-uniform)e (distributions)h(see)h(Chapter)f(20)h([Random)150 5340 y(Num)m(b)s(er)29 b(Distributions],)i(page)g(224.)p eop end %%Page: 206 224 TeXDict begin 206 223 bop 150 -116 a FK(Chapter)30 b(18:)41 b(Random)30 b(Num)m(b)s(er)g(Generation)1798 b(206)3350 299 y([F)-8 b(unction])-3599 b Fv(unsigned)55 b(long)e(int)g (gsl_rng_get)c Fu(\()p FD(const)31 b(gsl)p 2097 299 28 4 v 41 w(rng)f(*)h Ft(r)p Fu(\))390 408 y FK(This)41 b(function)g(returns)f(a)i(random)e(in)m(teger)j(from)e(the)h (generator)g FD(r)p FK(.)74 b(The)41 b(minim)m(um)g(and)390 518 y(maxim)m(um)21 b(v)-5 b(alues)21 b(dep)s(end)e(on)h(the)h (algorithm)h(used,)g(but)e(all)i(in)m(tegers)g(in)e(the)h(range)g([)p FD(min)p FK(,)p FD(max)6 b FK(])390 628 y(are)30 b(equally)h(lik)m(ely) -8 b(.)42 b(The)30 b(v)-5 b(alues)30 b(of)g FD(min)f FK(and)h FD(max)36 b FK(can)30 b(b)s(e)f(determined)h(using)f(the)h (auxiliary)390 737 y(functions)g FH(gsl_rng_max)d(\(r\))j FK(and)f FH(gsl_rng_min)f(\(r\))p FK(.)3350 908 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_rng_uniform)c Fu(\()p FD(const)31 b(gsl)p 1731 908 V 41 w(rng)f(*)h Ft(r)p Fu(\))390 1017 y FK(This)d(function)h(returns)f(a)i(double)e(precision) i(\015oating)g(p)s(oin)m(t)f(n)m(um)m(b)s(er)f(uniformly)g(distributed) 390 1127 y(in)36 b(the)h(range)g([0,1\).)61 b(The)37 b(range)g(includes)f(0.0)i(but)e(excludes)g(1.0.)61 b(The)36 b(v)-5 b(alue)37 b(is)g(t)m(ypically)390 1236 y(obtained)25 b(b)m(y)f(dividing)f(the)i(result)f(of)g FH(gsl_rng_get\(r\))d FK(b)m(y)j FH(gsl_rng_max\(r\))i(+)k(1.0)23 b FK(in)h(dou-)390 1346 y(ble)k(precision.)40 b(Some)28 b(generators)g(compute)g(this)g (ratio)h(in)m(ternally)g(so)f(that)g(they)g(can)g(pro)m(vide)390 1455 y(\015oating)g(p)s(oin)m(t)g(n)m(um)m(b)s(ers)e(with)h(more)h (than)f(32)h(bits)g(of)f(randomness)g(\(the)h(maxim)m(um)f(n)m(um)m(b)s (er)390 1565 y(of)k(bits)f(that)h(can)f(b)s(e)g(p)s(ortably)g(represen) m(ted)g(in)h(a)f(single)h FH(unsigned)d(long)i(int)p FK(\).)3350 1735 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_rng_uniform_pos)d Fu(\()p FD(const)32 b(gsl)p 1941 1735 V 40 w(rng)e(*)h Ft(r)p Fu(\))390 1845 y FK(This)41 b(function)h(returns)f(a)h(p)s(ositiv)m(e)h(double)f(precision)g (\015oating)h(p)s(oin)m(t)f(n)m(um)m(b)s(er)f(uniformly)390 1955 y(distributed)34 b(in)g(the)g(range)h(\(0,1\),)j(excluding)c(b)s (oth)g(0.0)i(and)e(1.0.)54 b(The)34 b(n)m(um)m(b)s(er)f(is)i(obtained) 390 2064 y(b)m(y)e(sampling)g(the)h(generator)g(with)f(the)h(algorithm) g(of)f FH(gsl_rng_uniform)c FK(un)m(til)34 b(a)f(non-zero)390 2174 y(v)-5 b(alue)30 b(is)f(obtained.)41 b(Y)-8 b(ou)30 b(can)f(use)g(this)h(function)f(if)g(y)m(ou)h(need)f(to)h(a)m(v)m(oid)h (a)e(singularit)m(y)i(at)f(0.0.)3350 2344 y([F)-8 b(unction])-3599 b Fv(unsigned)55 b(long)e(int)g(gsl_rng_uniform_int)f Fu(\()p FD(const)31 b(gsl)p 2516 2344 V 40 w(rng)f(*)h Ft(r)p FD(,)565 2454 y(unsigned)e(long)i(in)m(t)g Ft(n)p Fu(\))390 2563 y FK(This)38 b(function)h(returns)f(a)i(random)e(in)m (teger)i(from)f(0)h(to)f FE(n)26 b FI(\000)g FK(1)39 b(inclusiv)m(e)h(b)m(y)f(scaling)h(do)m(wn)390 2673 y(and/or)34 b(discarding)g(samples)h(from)f(the)g(generator)i FD(r)p FK(.)52 b(All)35 b(in)m(tegers)h(in)e(the)g(range)h([0)p FE(;)15 b(n)24 b FI(\000)e FK(1])390 2782 y(are)31 b(pro)s(duced)e (with)i(equal)g(probabilit)m(y)-8 b(.)43 b(F)-8 b(or)32 b(generators)f(with)g(a)g(non-zero)g(minim)m(um)f(v)-5 b(alue)390 2892 y(an)30 b(o\013set)i(is)e(applied)g(so)h(that)g(zero)g (is)f(returned)g(with)g(the)g(correct)i(probabilit)m(y)-8 b(.)390 3022 y(Note)34 b(that)f(this)f(function)g(is)h(designed)f(for)h (sampling)f(from)g(ranges)h(smaller)g(than)f(the)h(range)390 3131 y(of)26 b(the)h(underlying)e(generator.)40 b(The)26 b(parameter)h FD(n)e FK(m)m(ust)h(b)s(e)g(less)g(than)g(or)h(equal)f (to)h(the)g(range)390 3241 y(of)36 b(the)g(generator)i FD(r)p FK(.)57 b(If)36 b FD(n)f FK(is)h(larger)h(than)f(the)g(range)h (of)f(the)g(generator)h(then)f(the)g(function)390 3351 y(calls)c(the)e(error)g(handler)g(with)g(an)g(error)g(co)s(de)h(of)f FH(GSL_EINVAL)e FK(and)h(returns)h(zero.)390 3480 y(In)j(particular,)i (this)f(function)f(is)h(not)g(in)m(tended)f(for)h(generating)h(the)f (full)f(range)h(of)g(unsigned)390 3590 y(in)m(teger)c(v)-5 b(alues)28 b([0)p FE(;)15 b FK(2)1112 3557 y FB(32)1201 3590 y FI(\000)g FK(1].)41 b(Instead)28 b(c)m(ho)s(ose)i(a)e(generator) i(with)e(the)h(maximal)g(in)m(teger)h(range)390 3700 y(and)f(zero)i(minim)m(um)e(v)-5 b(alue,)31 b(suc)m(h)f(as)g FH(gsl_rng_ranlxd1)p FK(,)c FH(gsl_rng_mt19937)g FK(or)k FH(gsl_rng_)390 3809 y(taus)p FK(,)e(and)g(sample)g(it)h(directly)g (using)f FH(gsl_rng_get)p FK(.)37 b(The)28 b(range)g(of)h(eac)m(h)g (generator)h(can)f(b)s(e)390 3919 y(found)g(using)h(the)g(auxiliary)i (functions)d(describ)s(ed)h(in)g(the)g(next)h(section.)150 4142 y FJ(18.5)68 b(Auxiliary)46 b(random)f(n)l(um)l(b)t(er)f (generator)j(functions)150 4301 y FK(The)34 b(follo)m(wing)i(functions) f(pro)m(vide)g(information)g(ab)s(out)f(an)h(existing)g(generator.)55 b(Y)-8 b(ou)35 b(should)f(use)150 4411 y(them)c(in)g(preference)h(to)g (hard-co)s(ding)f(the)g(generator)i(parameters)e(in)m(to)i(y)m(our)e(o) m(wn)g(co)s(de.)3350 4581 y([F)-8 b(unction])-3599 b Fv(const)54 b(char)f(*)g(gsl_rng_name)c Fu(\()p FD(const)31 b(gsl)p 1888 4581 V 41 w(rng)f(*)g Ft(r)p Fu(\))390 4691 y FK(This)g(function)g(returns)f(a)i(p)s(oin)m(ter)f(to)h(the)g(name)f (of)h(the)f(generator.)42 b(F)-8 b(or)31 b(example,)630 4821 y FH(printf)46 b(\("r)h(is)g(a)h('\045s')e(generator\\n",)1012 4930 y(gsl_rng_name)e(\(r\)\);)390 5060 y FK(w)m(ould)30 b(prin)m(t)g(something)h(lik)m(e)h FH(r)e(is)f(a)h('taus')f(generator)p FK(.)3350 5230 y([F)-8 b(unction])-3599 b Fv(unsigned)55 b(long)e(int)g(gsl_rng_max)c Fu(\()p FD(const)31 b(gsl)p 2097 5230 V 41 w(rng)f(*)h Ft(r)p Fu(\))390 5340 y FH(gsl_rng_max)c FK(returns)i(the)i(largest)h(v)-5 b(alue)31 b(that)g FH(gsl_rng_get)c FK(can)j(return.)p eop end %%Page: 207 225 TeXDict begin 207 224 bop 150 -116 a FK(Chapter)30 b(18:)41 b(Random)30 b(Num)m(b)s(er)g(Generation)1798 b(207)3350 299 y([F)-8 b(unction])-3599 b Fv(unsigned)55 b(long)e(int)g (gsl_rng_min)c Fu(\()p FD(const)31 b(gsl)p 2097 299 28 4 v 41 w(rng)f(*)h Ft(r)p Fu(\))390 408 y FH(gsl_rng_min)g FK(returns)h(the)i(smallest)h(v)-5 b(alue)35 b(that)f FH(gsl_rng_get)d FK(can)j(return.)50 b(Usually)34 b(this)390 518 y(v)-5 b(alue)38 b(is)g(zero.)65 b(There)37 b(are)h(some)h (generators)g(with)e(algorithms)i(that)g(cannot)f(return)f(zero,)390 628 y(and)30 b(for)g(these)h(generators)g(the)g(minim)m(um)e(v)-5 b(alue)31 b(is)g(1.)3350 796 y([F)-8 b(unction])-3599 b Fv(void)54 b(*)e(gsl_rng_state)e Fu(\()p FD(const)31 b(gsl)p 1627 796 V 40 w(rng)f(*)h Ft(r)p Fu(\))3350 906 y FK([F)-8 b(unction])-3599 b Fv(size_t)54 b(gsl_rng_size)49 b Fu(\()p FD(const)31 b(gsl)p 1574 906 V 41 w(rng)f(*)h Ft(r)p Fu(\))390 1016 y FK(These)38 b(functions)g(return)f(a)h(p)s(oin) m(ter)g(to)h(the)g(state)g(of)f(generator)i FD(r)k FK(and)38 b(its)g(size.)65 b(Y)-8 b(ou)39 b(can)390 1125 y(use)28 b(this)h(information)g(to)g(access)h(the)f(state)h(directly)-8 b(.)41 b(F)-8 b(or)30 b(example,)g(the)f(follo)m(wing)h(co)s(de)f(will) 390 1235 y(write)i(the)f(state)i(of)e(a)h(generator)h(to)f(a)g(stream,) 630 1364 y FH(void)47 b(*)g(state)f(=)i(gsl_rng_state)c(\(r\);)630 1474 y(size_t)i(n)i(=)f(gsl_rng_size)d(\(r\);)630 1583 y(fwrite)i(\(state,)g(n,)h(1,)g(stream\);)3350 1752 y FK([F)-8 b(unction])-3599 b Fv(const)54 b(gsl_rng_type)i(**)d (gsl_rng_types_setup)e Fu(\()p FD(v)m(oid)p Fu(\))390 1862 y FK(This)33 b(function)g(returns)f(a)i(p)s(oin)m(ter)g(to)g(an)g (arra)m(y)g(of)g(all)g(the)g(a)m(v)-5 b(ailable)36 b(generator)f(t)m (yp)s(es,)f(ter-)390 1971 y(minated)39 b(b)m(y)f(a)h(n)m(ull)g(p)s(oin) m(ter.)66 b(The)38 b(function)g(should)g(b)s(e)g(called)i(once)f(at)h (the)f(start)g(of)g(the)390 2081 y(program,)29 b(if)f(needed.)40 b(The)28 b(follo)m(wing)i(co)s(de)e(fragmen)m(t)h(sho)m(ws)f(ho)m(w)h (to)g(iterate)h(o)m(v)m(er)g(the)e(arra)m(y)390 2190 y(of)j(generator)g(t)m(yp)s(es)f(to)i(prin)m(t)e(the)g(names)g(of)h (the)g(a)m(v)-5 b(ailable)32 b(algorithms,)630 2320 y FH(const)46 b(gsl_rng_type)f(**t,)h(**t0;)630 2539 y(t0)h(=)h (gsl_rng_types_setup)42 b(\(\);)630 2758 y(printf)k(\("Available)f (generators:\\n"\);)630 2977 y(for)i(\(t)g(=)h(t0;)e(*t)i(!=)f(0;)g (t++\))725 3087 y({)821 3196 y(printf)f(\("\045s\\n",)g (\(*t\)->name\);)725 3306 y(})150 3528 y FJ(18.6)68 b(Random)46 b(n)l(um)l(b)t(er)e(en)l(vironmen)l(t)i(v)-7 b(ariables)150 3687 y FK(The)21 b(library)g(allo)m(ws)i(y)m(ou)e(to)h(c)m(ho)s(ose)h (a)e(default)h(generator)h(and)d(seed)i(from)f(the)g(en)m(vironmen)m(t) h(v)-5 b(ariables)150 3797 y FH(GSL_RNG_TYPE)17 b FK(and)j FH(GSL_RNG_SEED)e FK(and)i(the)h(function)f FH(gsl_rng_env_setup)p FK(.)33 b(This)20 b(mak)m(es)h(it)g(easy)150 3907 y(try)30 b(out)h(di\013eren)m(t)g(generators)g(and)f(seeds)g(without)h(ha)m (ving)g(to)g(recompile)g(y)m(our)f(program.)3350 4075 y([F)-8 b(unction])-3599 b Fv(const)54 b(gsl_rng_type)i(*)c (gsl_rng_env_setup)f Fu(\()p FD(v)m(oid)p Fu(\))390 4185 y FK(This)27 b(function)f(reads)i(the)f(en)m(vironmen)m(t)h(v)-5 b(ariables)28 b FH(GSL_RNG_TYPE)c FK(and)j FH(GSL_RNG_SEED)d FK(and)390 4295 y(uses)42 b(their)g(v)-5 b(alues)43 b(to)g(set)g(the)f (corresp)s(onding)g(library)f(v)-5 b(ariables)43 b FH(gsl_rng_default)c FK(and)390 4404 y FH(gsl_rng_default_seed)p FK(.)c(These)30 b(global)i(v)-5 b(ariables)31 b(are)g(de\014ned)e(as)i(follo)m(ws,)630 4533 y FH(extern)46 b(const)g(gsl_rng_type)f(*gsl_rng_default)630 4643 y(extern)h(unsigned)g(long)g(int)h(gsl_rng_default_seed)390 4772 y FK(The)40 b(en)m(vironmen)m(t)h(v)-5 b(ariable)41 b FH(GSL_RNG_TYPE)c FK(should)i(b)s(e)g(the)i(name)f(of)g(a)h (generator,)j(suc)m(h)390 4882 y(as)d FH(taus)f FK(or)h FH(mt19937)p FK(.)70 b(The)41 b(en)m(vironmen)m(t)g(v)-5 b(ariable)42 b FH(GSL_RNG_SEED)c FK(should)h(con)m(tain)k(the)390 4991 y(desired)g(seed)g(v)-5 b(alue.)80 b(It)44 b(is)f(con)m(v)m(erted) i(to)f(an)f FH(unsigned)28 b(long)i(int)42 b FK(using)h(the)g(C)g (library)390 5101 y(function)30 b FH(strtoul)p FK(.)390 5230 y(If)g(y)m(ou)h(don't)g(sp)s(ecify)f(a)h(generator)h(for)e FH(GSL_RNG_TYPE)d FK(then)k FH(gsl_rng_mt19937)26 b FK(is)31 b(used)f(as)390 5340 y(the)h(default.)40 b(The)30 b(initial)i(v)-5 b(alue)31 b(of)f FH(gsl_rng_default_seed)25 b FK(is)31 b(zero.)p eop end %%Page: 208 226 TeXDict begin 208 225 bop 150 -116 a FK(Chapter)30 b(18:)41 b(Random)30 b(Num)m(b)s(er)g(Generation)1798 b(208)275 349 y(Here)35 b(is)g(a)h(short)f(program)g(whic)m(h)g(sho)m(ws)g(ho)m (w)g(to)h(create)h(a)e(global)i(generator)f(using)f(the)g(en)m(vi-)150 459 y(ronmen)m(t)30 b(v)-5 b(ariables)31 b FH(GSL_RNG_TYPE)c FK(and)j FH(GSL_RNG_SEED)p FK(,)390 624 y FH(#include)46 b()390 734 y(#include)g()390 953 y(gsl_rng)g(*)h(r;)95 b(/*)47 b(global)f(generator)g(*/)390 1172 y(int)390 1282 y(main)h(\(void\))390 1391 y({)485 1501 y(const)g(gsl_rng_type)d(*)k(T;)485 1720 y(gsl_rng_env_setup\(\);) 485 1939 y(T)g(=)f(gsl_rng_default;)485 2049 y(r)h(=)f(gsl_rng_alloc)e (\(T\);)485 2268 y(printf)i(\("generator)d(type:)94 b(\045s\\n",)46 b(gsl_rng_name)f(\(r\)\);)485 2378 y(printf)i(\("seed)f(=)h (\045lu\\n",)f(gsl_rng_default_seed\);)485 2487 y(printf)h(\("first)e (value)i(=)g(\045lu\\n",)f(gsl_rng_get)f(\(r\)\);)485 2706 y(gsl_rng_free)g(\(r\);)485 2816 y(return)i(0;)390 2926 y(})150 3091 y FK(Running)i(the)h(program)h(without)f(an)m(y)h(en) m(vironmen)m(t)f(v)-5 b(ariables)51 b(uses)f(the)h(initial)g(defaults,) 56 b(an)150 3200 y FH(mt19937)28 b FK(generator)k(with)e(a)h(seed)f(of) h(0,)390 3366 y FH($)47 b(./a.out)390 3475 y(generator)e(type:)94 b(mt19937)390 3585 y(seed)47 b(=)g(0)390 3695 y(first)f(value)h(=)g (4293858116)150 3860 y FK(By)29 b(setting)g(the)g(t)m(w)m(o)h(v)-5 b(ariables)29 b(on)f(the)h(command)f(line)h(w)m(e)f(can)h(c)m(hange)h (the)e(default)h(generator)h(and)150 3969 y(the)h(seed,)390 4135 y FH($)47 b(GSL_RNG_TYPE="taus")c(GSL_RNG_SEED=123)g(./a.out)390 4244 y(GSL_RNG_TYPE=taus)390 4354 y(GSL_RNG_SEED=123)390 4464 y(generator)i(type:)i(taus)390 4573 y(seed)g(=)g(123)390 4683 y(first)f(value)h(=)g(2720986350)150 4961 y FJ(18.7)68 b(Cop)l(ying)46 b(random)f(n)l(um)l(b)t(er)f(generator)j(state)150 5121 y FK(The)34 b(ab)s(o)m(v)m(e)h(metho)s(ds)f(do)g(not)g(exp)s(ose)h (the)f(random)g(n)m(um)m(b)s(er)f(`state')j(whic)m(h)e(c)m(hanges)h (from)f(call)h(to)150 5230 y(call.)42 b(It)29 b(is)g(often)h(useful)f (to)h(b)s(e)e(able)i(to)g(sa)m(v)m(e)h(and)e(restore)g(the)h(state.)42 b(T)-8 b(o)29 b(p)s(ermit)g(these)h(practices,)h(a)150 5340 y(few)f(somewhat)h(more)f(adv)-5 b(anced)31 b(functions)f(are)h (supplied.)39 b(These)30 b(include:)p eop end %%Page: 209 227 TeXDict begin 209 226 bop 150 -116 a FK(Chapter)30 b(18:)41 b(Random)30 b(Num)m(b)s(er)g(Generation)1798 b(209)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_rng_memcpy)d Fu(\()p FD(gsl)p 1284 299 28 4 v 41 w(rng)30 b(*)g Ft(dest)p FD(,)i(const)f(gsl)p 2171 299 V 41 w(rng)f(*)g Ft(src)p Fu(\))390 408 y FK(This)25 b(function)g(copies)h(the)g(random)f(n)m(um) m(b)s(er)f(generator)i FD(src)31 b FK(in)m(to)c(the)e(pre-existing)i (generator)390 518 y FD(dest)p FK(,)j(making)f FD(dest)i FK(in)m(to)f(an)e(exact)j(cop)m(y)f(of)f FD(src)p FK(.)40 b(The)28 b(t)m(w)m(o)i(generators)g(m)m(ust)f(b)s(e)f(of)h(the)h(same) 390 628 y(t)m(yp)s(e.)3350 810 y([F)-8 b(unction])-3599 b Fv(gsl_rng)54 b(*)f(gsl_rng_clone)c Fu(\()p FD(const)32 b(gsl)p 1784 810 V 40 w(rng)e(*)h Ft(r)p Fu(\))390 919 y FK(This)g(function)h(returns)f(a)h(p)s(oin)m(ter)g(to)h(a)g(newly)e (created)j(generator)f(whic)m(h)f(is)g(an)g(exact)h(cop)m(y)390 1029 y(of)e(the)f(generator)i FD(r)p FK(.)150 1260 y FJ(18.8)68 b(Reading)46 b(and)f(writing)h(random)f(n)l(um)l(b)t(er)f (generator)j(state)150 1420 y FK(The)27 b(library)g(pro)m(vides)g (functions)g(for)g(reading)h(and)e(writing)i(the)f(random)g(n)m(um)m(b) s(er)f(state)i(to)h(a)e(\014le)h(as)150 1529 y(binary)i(data.)3350 1711 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_rng_fwrite)d Fu(\()p FD(FILE)30 b(*)h Ft(stream)p FD(,)i(const)d(gsl)p 2208 1711 V 41 w(rng)g(*)h Ft(r)p Fu(\))390 1821 y FK(This)39 b(function)g(writes)h(the)g(random)f(n)m(um)m(b)s(er)g(state)i(of)f (the)g(random)f(n)m(um)m(b)s(er)f(generator)j FD(r)390 1931 y FK(to)36 b(the)g(stream)g FD(stream)g FK(in)f(binary)g(format.) 57 b(The)35 b(return)f(v)-5 b(alue)36 b(is)g(0)g(for)f(success)h(and)f FH(GSL_)390 2040 y(EFAILED)d FK(if)i(there)h(w)m(as)f(a)h(problem)f (writing)g(to)h(the)f(\014le.)53 b(Since)34 b(the)g(data)h(is)g (written)f(in)g(the)390 2150 y(nativ)m(e)e(binary)d(format)i(it)g(ma)m (y)g(not)g(b)s(e)e(p)s(ortable)i(b)s(et)m(w)m(een)g(di\013eren)m(t)f (arc)m(hitectures.)3350 2332 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_rng_fread)d Fu(\()p FD(FILE)30 b(*)h Ft(stream)p FD(,)h(gsl)p 1918 2332 V 41 w(rng)e(*)g Ft(r)p Fu(\))390 2442 y FK(This)35 b(function)g(reads)g(the)h(random)f(n)m(um) m(b)s(er)f(state)j(in)m(to)f(the)g(random)f(n)m(um)m(b)s(er)f (generator)j FD(r)390 2551 y FK(from)k(the)g(op)s(en)f(stream)i FD(stream)f FK(in)g(binary)g(format.)73 b(The)40 b(random)h(n)m(um)m(b) s(er)f(generator)i FD(r)390 2661 y FK(m)m(ust)g(b)s(e)f(preinitialized) i(with)f(the)g(correct)h(random)f(n)m(um)m(b)s(er)e(generator)j(t)m(yp) s(e)f(since)h(t)m(yp)s(e)390 2770 y(information)31 b(is)f(not)h(sa)m(v) m(ed.)41 b(The)30 b(return)g(v)-5 b(alue)30 b(is)h(0)g(for)f(success)g (and)g FH(GSL_EFAILED)d FK(if)k(there)390 2880 y(w)m(as)c(a)g(problem)f (reading)h(from)f(the)h(\014le.)39 b(The)27 b(data)g(is)g(assumed)f(to) h(ha)m(v)m(e)h(b)s(een)e(written)g(in)h(the)390 2990 y(nativ)m(e)32 b(binary)d(format)i(on)f(the)h(same)g(arc)m(hitecture.) 150 3221 y FJ(18.9)68 b(Random)46 b(n)l(um)l(b)t(er)e(generator)j (algorithms)150 3380 y FK(The)30 b(functions)f(describ)s(ed)h(ab)s(o)m (v)m(e)h(mak)m(e)g(no)f(reference)h(to)g(the)f(actual)i(algorithm)f (used.)40 b(This)30 b(is)g(de-)150 3490 y(lib)s(erate)c(so)f(that)h(y)m (ou)f(can)h(switc)m(h)f(algorithms)h(without)f(ha)m(ving)h(to)g(c)m (hange)g(an)m(y)f(of)h(y)m(our)f(application)150 3599 y(source)j(co)s(de.)40 b(The)27 b(library)h(pro)m(vides)g(a)g(large)h (n)m(um)m(b)s(er)d(of)i(generators)h(of)f(di\013eren)m(t)h(t)m(yp)s (es,)f(including)150 3709 y(sim)m(ulation)d(qualit)m(y)g(generators,)i (generators)d(pro)m(vided)g(for)g(compatibilit)m(y)i(with)d(other)i (libraries)f(and)150 3818 y(historical)32 b(generators)f(from)f(the)h (past.)275 3952 y(The)g(follo)m(wing)j(generators)f(are)f(recommended)g (for)g(use)g(in)g(sim)m(ulation.)47 b(They)31 b(ha)m(v)m(e)j(extremely) 150 4062 y(long)28 b(p)s(erio)s(ds,)f(lo)m(w)i(correlation)g(and)f (pass)f(most)h(statistical)j(tests.)40 b(F)-8 b(or)29 b(the)f(most)g(reliable)h(source)f(of)150 4171 y(uncorrelated)34 b(n)m(um)m(b)s(ers,)f(the)h(second-generation)h FC(ranlux)d FK(generators)i(ha)m(v)m(e)h(the)e(strongest)i(pro)s(of)150 4281 y(of)c(randomness.)3299 4463 y([Generator])-3598 b Fv(gsl_rng_mt19937)390 4573 y FK(The)39 b(MT19937)i(generator)g(of)e (Mak)m(oto)j(Matsumoto)e(and)f(T)-8 b(akuji)39 b(Nishim)m(ura)g(is)g(a) h(v)-5 b(arian)m(t)390 4682 y(of)47 b(the)f(t)m(wisted)h(generalized)h (feedbac)m(k)f(shift-register)h(algorithm,)j(and)46 b(is)g(kno)m(wn)g (as)h(the)390 4792 y(\\Mersenne)33 b(Twister")g(generator.)49 b(It)32 b(has)h(a)g(Mersenne)f(prime)g(p)s(erio)s(d)g(of)h(2)3123 4759 y FB(19937)3314 4792 y FI(\000)22 b FK(1)33 b(\(ab)s(out)390 4902 y(10)480 4869 y FB(6000)617 4902 y FK(\))28 b(and)f(is)g (equi-distributed)g(in)h(623)g(dimensions.)39 b(It)28 b(has)f(passed)g(the)h FC(diehard)e FK(statisti-)390 5011 y(cal)32 b(tests.)44 b(It)31 b(uses)g(624)h(w)m(ords)f(of)g(state) i(p)s(er)d(generator)i(and)f(is)g(comparable)h(in)f(sp)s(eed)f(to)i (the)390 5121 y(other)h(generators.)50 b(The)32 b(original)i(generator) h(used)d(a)h(default)g(seed)g(of)g(4357)i(and)e(c)m(ho)s(osing)g FD(s)390 5230 y FK(equal)28 b(to)g(zero)g(in)f FH(gsl_rng_set)e FK(repro)s(duces)h(this.)39 b(Later)28 b(v)m(ersions)g(switc)m(hed)g (to)g(5489)h(as)f(the)390 5340 y(default)g(seed,)h(y)m(ou)f(can)g(c)m (ho)s(ose)h(this)f(explicitly)i(via)e FH(gsl_rng_set)d FK(instead)j(if)g(y)m(ou)h(require)e(it.)p eop end %%Page: 210 228 TeXDict begin 210 227 bop 150 -116 a FK(Chapter)30 b(18:)41 b(Random)30 b(Num)m(b)s(er)g(Generation)1798 b(210)390 299 y(F)-8 b(or)31 b(more)g(information)f(see,)570 430 y(Mak)m(oto)71 b(Matsumoto)f(and)d(T)-8 b(akuji)69 b(Nishim)m(ura,)78 b(\\Mersenne)68 b(Twister:)117 b(A)68 b(623-)570 540 y(dimensionally)30 b(equidistributed)f(uniform)g(pseudorandom)g(n)m(um) m(b)s(er)f(generator".)42 b FD(A)m(CM)570 650 y(T)-8 b(ransactions)32 b(on)f(Mo)s(deling)h(and)f(Computer)g(Sim)m(ulation)p FK(,)h(V)-8 b(ol.)33 b(8,)f(No.)g(1)g(\(Jan.)44 b(1998\),)570 759 y(P)m(ages)32 b(3{30)390 913 y(The)37 b(generator)i FH(gsl_rng_mt19937)33 b FK(uses)k(the)h(second)g(revision)g(of)f(the)h (seeding)g(pro)s(cedure)390 1022 y(published)32 b(b)m(y)i(the)g(t)m(w)m (o)i(authors)e(ab)s(o)m(v)m(e)h(in)f(2002.)53 b(The)34 b(original)h(seeding)f(pro)s(cedures)f(could)390 1132 y(cause)40 b(spurious)d(artifacts)k(for)e(some)g(seed)g(v)-5 b(alues.)68 b(They)38 b(are)i(still)g(a)m(v)-5 b(ailable)41 b(through)e(the)390 1241 y(alternativ)m(e)33 b(generators)e FH(gsl_rng_mt19937_1999)25 b FK(and)30 b FH(gsl_rng_mt19937_1998)p FK(.)3299 1417 y([Generator])-3598 b Fv(gsl_rng_ranlxs0)3299 1526 y FK([Generator])g Fv(gsl_rng_ranlxs1)3299 1636 y FK([Generator])g Fv(gsl_rng_ranlxs2)390 1745 y FK(The)38 b(generator)h FH(ranlxs0)e FK(is)h(a)h(second-generation)h(v)m(ersion)f (of)f(the)h FC(ranlux)d FK(algorithm)k(of)390 1855 y(L)s(\177)-48 b(usc)m(her,)35 b(whic)m(h)f(pro)s(duces)f(\\luxury)h(random)g(n)m(um)m (b)s(ers".)52 b(This)33 b(generator)j(pro)m(vides)e(single)390 1965 y(precision)g(output)f(\(24)i(bits\))f(at)h(three)f(luxury)e(lev)m (els)k FH(ranlxs0)p FK(,)c FH(ranlxs1)g FK(and)h FH(ranlxs2)p FK(,)g(in)390 2074 y(increasing)f(order)f(of)h(strength.)45 b(It)31 b(uses)g(double-precision)h(\015oating)h(p)s(oin)m(t)e (arithmetic)i(in)m(ter-)390 2184 y(nally)g(and)f(can)g(b)s(e)g (signi\014can)m(tly)i(faster)f(than)f(the)h(in)m(teger)g(v)m(ersion)g (of)g FH(ranlux)p FK(,)e(particularly)390 2293 y(on)23 b(64-bit)i(arc)m(hitectures.)40 b(The)22 b(p)s(erio)s(d)h(of)g(the)g (generator)i(is)e(ab)s(out)g(10)2863 2260 y FB(171)2968 2293 y FK(.)38 b(The)23 b(algorithm)h(has)390 2403 y(mathematically)39 b(pro)m(v)m(en)e(prop)s(erties)f(and)g(can)h(pro)m(vide)f(truly)g (decorrelated)i(n)m(um)m(b)s(ers)d(at)j(a)390 2513 y(kno)m(wn)30 b(lev)m(el)i(of)f(randomness.)39 b(The)30 b(higher)g(luxury)f(lev)m (els)j(pro)m(vide)f(increased)f(decorrelation)390 2622 y(b)s(et)m(w)m(een)h(samples)f(as)h(an)f(additional)i(safet)m(y)f (margin.)390 2754 y(Note)40 b(that)e(the)h(range)g(of)f(allo)m(w)m(ed)i (seeds)e(for)h(this)f(generator)h(is)g([0)p FE(;)15 b FK(2)2926 2721 y FB(31)3023 2754 y FI(\000)25 b FK(1].)65 b(Higher)39 b(seed)390 2863 y(v)-5 b(alues)31 b(are)f(wrapp)s(ed)f(mo)s (dulo)h(2)1555 2830 y FB(31)1625 2863 y FK(.)3299 3039 y([Generator])-3598 b Fv(gsl_rng_ranlxd1)3299 3148 y FK([Generator])g Fv(gsl_rng_ranlxd2)390 3258 y FK(These)27 b(generators)i(pro)s(duce)e(double)g(precision)h(output)f(\(48)i (bits\))f(from)f(the)h FC(ranlxs)e FK(genera-)390 3367 y(tor.)40 b(The)27 b(library)f(pro)m(vides)h(t)m(w)m(o)i(luxury)d(lev)m (els)i FH(ranlxd1)d FK(and)i FH(ranlxd2)p FK(,)f(in)h(increasing)g (order)390 3477 y(of)k(strength.)3299 3652 y([Generator])-3598 b Fv(gsl_rng_ranlux)3299 3762 y FK([Generator])g Fv(gsl_rng_ranlux389) 390 3871 y FK(The)36 b FH(ranlux)e FK(generator)k(is)e(an)g(implemen)m (tation)i(of)e(the)h(original)g(algorithm)g(dev)m(elop)s(ed)g(b)m(y)390 3981 y(L)s(\177)-48 b(usc)m(her.)46 b(It)32 b(uses)g(a)g(lagged-\014b)s (onacci-with-skipping)i(algorithm)f(to)g(pro)s(duce)e(\\luxury)g(ran-) 390 4091 y(dom)e(n)m(um)m(b)s(ers".)40 b(It)29 b(is)h(a)g(24-bit)g (generator,)h(originally)g(designed)f(for)f(single-precision)i(IEEE)390 4200 y(\015oating)39 b(p)s(oin)m(t)f(n)m(um)m(b)s(ers.)62 b(This)37 b(implemen)m(tation)i(is)f(based)g(on)f(in)m(teger)j (arithmetic,)h(while)390 4310 y(the)23 b(second-generation)i(v)m (ersions)f FC(ranlxs)d FK(and)i FC(ranlxd)f FK(describ)s(ed)g(ab)s(o)m (v)m(e)i(pro)m(vide)g(\015oating-)390 4419 y(p)s(oin)m(t)39 b(implemen)m(tations)h(whic)m(h)e(will)h(b)s(e)f(faster)h(on)f(man)m(y) h(platforms.)66 b(The)38 b(p)s(erio)s(d)f(of)i(the)390 4529 y(generator)29 b(is)f(ab)s(out)g(10)1229 4496 y FB(171)1333 4529 y FK(.)40 b(The)28 b(algorithm)h(has)f(mathematically) i(pro)m(v)m(en)f(prop)s(erties)e(and)g(it)390 4639 y(can)i(pro)m(vide)g (truly)g(decorrelated)h(n)m(um)m(b)s(ers)d(at)j(a)f(kno)m(wn)g(lev)m (el)h(of)f(randomness.)39 b(The)29 b(default)390 4748 y(lev)m(el)d(of)f(decorrelation)g(recommended)f(b)m(y)h(L)s(\177)-48 b(usc)m(her)23 b(is)i(pro)m(vided)f(b)m(y)g FH(gsl_rng_ranlux)p FK(,)e(while)390 4858 y FH(gsl_rng_ranlux389)29 b FK(giv)m(es)36 b(the)e(highest)h(lev)m(el)h(of)e(randomness,)g(with)g(all)h(24)g(bits) f(decorre-)390 4967 y(lated.)42 b(Both)31 b(t)m(yp)s(es)f(of)h (generator)g(use)f(24)h(w)m(ords)f(of)h(state)h(p)s(er)d(generator.)390 5099 y(F)-8 b(or)31 b(more)g(information)f(see,)570 5230 y(M.)i(L)s(\177)-48 b(usc)m(her,)32 b(\\A)g(p)s(ortable)f(high-qualit)m (y)i(random)e(n)m(um)m(b)s(er)f(generator)j(for)e(lattice)j(\014eld)570 5340 y(theory)d(calculations",)i FD(Computer)c(Ph)m(ysics)i(Comm)m (unications)p FK(,)g(79)g(\(1994\))i(100{110.)p eop end %%Page: 211 229 TeXDict begin 211 228 bop 150 -116 a FK(Chapter)30 b(18:)41 b(Random)30 b(Num)m(b)s(er)g(Generation)1798 b(211)570 299 y(F.)44 b(James,)j(\\RANLUX:)d(A)f(F)-8 b(ortran)44 b(implemen)m(tation)h(of)f(the)f(high-qualit)m(y)h(pseudo-)570 408 y(random)33 b(n)m(um)m(b)s(er)g(generator)j(of)e(L)s(\177)-48 b(usc)m(her",)35 b FD(Computer)f(Ph)m(ysics)g(Comm)m(unications)p FK(,)i(79)570 518 y(\(1994\))d(111{114)3299 688 y([Generator])-3598 b Fv(gsl_rng_cmrg)390 798 y FK(This)30 b(is)g(a)h(com)m(bined)f(m)m (ultiple)h(recursiv)m(e)g(generator)h(b)m(y)e(L'Ecuy)m(er.)41 b(Its)30 b(sequence)h(is,)1500 961 y FE(z)1542 975 y Fq(n)1613 961 y FK(=)25 b(\()p FE(x)1796 975 y Fq(n)1862 961 y FI(\000)20 b FE(y)1998 975 y Fq(n)2043 961 y FK(\))15 b(mo)s(d)f FE(m)2362 975 y FB(1)390 1124 y FK(where)30 b(the)g(t)m(w)m(o)i(underlying)d(generators)j FE(x)1926 1138 y Fq(n)2001 1124 y FK(and)e FE(y)2223 1138 y Fq(n)2298 1124 y FK(are,)1132 1281 y FE(x)1184 1295 y Fq(n)1255 1281 y FK(=)25 b(\()p FE(a)1434 1295 y FB(1)1471 1281 y FE(x)1523 1295 y Fq(n)p Fp(\000)p FB(1)1674 1281 y FK(+)20 b FE(a)1813 1295 y FB(2)1850 1281 y FE(x)1902 1295 y Fq(n)p Fp(\000)p FB(2)2052 1281 y FK(+)g FE(a)2191 1295 y FB(3)2228 1281 y FE(x)2280 1295 y Fq(n)p Fp(\000)p FB(3)2411 1281 y FK(\))15 b(mo)s(d)g FE(m)2731 1295 y FB(1)1140 1416 y FE(y)1185 1430 y Fq(n)1255 1416 y FK(=)25 b(\()p FE(b)1425 1430 y FB(1)1462 1416 y FE(y)1507 1430 y Fq(n)p Fp(\000)p FB(1)1657 1416 y FK(+)20 b FE(b)1787 1430 y FB(2)1824 1416 y FE(y)1869 1430 y Fq(n)p Fp(\000)p FB(2)2019 1416 y FK(+)g FE(b)2149 1430 y FB(3)2187 1416 y FE(y)2232 1430 y Fq(n)p Fp(\000)p FB(3)2361 1416 y FK(\))15 b(mo)s(d)g FE(m)2681 1430 y FB(2)390 1573 y FK(with)21 b(co)s(e\016cien)m(ts)i FE(a)1087 1587 y FB(1)1150 1573 y FK(=)i(0,)e FE(a)1387 1587 y FB(2)1450 1573 y FK(=)i(63308,)g FE(a)1869 1587 y FB(3)1932 1573 y FK(=)g FI(\000)p FK(183326,)h FE(b)2459 1587 y FB(1)2521 1573 y FK(=)f(86098,)h FE(b)2932 1587 y FB(2)2994 1573 y FK(=)f(0,)f FE(b)3223 1587 y FB(3)3285 1573 y FK(=)h FI(\000)p FK(539608,)390 1683 y(and)30 b(mo)s(duli)f FE(m)952 1697 y FB(1)1015 1683 y FK(=)c(2)1156 1650 y FB(31)1247 1683 y FI(\000)19 b FK(1)26 b(=)f(2147483647)35 b(and)30 b FE(m)2246 1697 y FB(2)2308 1683 y FK(=)25 b(2145483479.)390 1813 y(The)e(p)s(erio)s(d) e(of)j(this)f(generator)h(is)f(lcm)q(\()p FE(m)1850 1780 y FB(3)1850 1835 y(1)1893 1813 y FI(\000)6 b FK(1)p FE(;)15 b(m)2135 1780 y FB(3)2135 1835 y(2)2178 1813 y FI(\000)6 b FK(1\),)24 b(whic)m(h)f(is)g(appro)m(ximately)i(2)3358 1780 y FB(185)3485 1813 y FK(\(ab)s(out)390 1922 y(10)480 1889 y FB(56)551 1922 y FK(\).)41 b(It)31 b(uses)f(6)g(w)m(ords)g(of)h (state)h(p)s(er)d(generator.)42 b(F)-8 b(or)31 b(more)f(information)h (see,)570 2052 y(P)-8 b(.)31 b(L'Ecuy)m(er,)f(\\Com)m(bined)h(Multiple) g(Recursiv)m(e)g(Random)e(Num)m(b)s(er)h(Generators",)h FD(Op-)570 2162 y(erations)g(Researc)m(h)p FK(,)h(44,)f(5)g(\(1996\),)i (816{822.)3299 2332 y([Generator])-3598 b Fv(gsl_rng_mrg)390 2441 y FK(This)26 b(is)h(a)h(\014fth-order)e(m)m(ultiple)i(recursiv)m (e)f(generator)h(b)m(y)f(L'Ecuy)m(er,)i(Blouin)e(and)f(Coutre.)40 b(Its)390 2551 y(sequence)31 b(is,)1340 2714 y FE(x)1392 2728 y Fq(n)1463 2714 y FK(=)25 b(\()p FE(a)1642 2728 y FB(1)1679 2714 y FE(x)1731 2728 y Fq(n)p Fp(\000)p FB(1)1882 2714 y FK(+)20 b FE(a)2021 2728 y FB(5)2058 2714 y FE(x)2110 2728 y Fq(n)p Fp(\000)p FB(5)2240 2714 y FK(\))15 b(mo)s(d)g FE(m)390 2877 y FK(with)30 b FE(a)645 2891 y FB(1)708 2877 y FK(=)25 b(107374182,)34 b FE(a)1316 2891 y FB(2)1379 2877 y FK(=)25 b FE(a)1523 2891 y FB(3)1585 2877 y FK(=)g FE(a)1729 2891 y FB(4)1792 2877 y FK(=)g(0,)31 b FE(a)2037 2891 y FB(5)2099 2877 y FK(=)25 b(104480)33 b(and)d FE(m)25 b FK(=)g(2)2921 2844 y FB(31)3012 2877 y FI(\000)20 b FK(1.)390 3007 y(The)37 b(p)s(erio)s(d)e(of)i(this)g (generator)i(is)e(ab)s(out)f(10)2033 2974 y FB(46)2105 3007 y FK(.)60 b(It)37 b(uses)g(5)g(w)m(ords)g(of)g(state)i(p)s(er)d (generator.)390 3116 y(More)31 b(information)g(can)f(b)s(e)g(found)f (in)h(the)h(follo)m(wing)h(pap)s(er,)570 3246 y(P)-8 b(.)40 b(L'Ecuy)m(er,)h(F.)f(Blouin,)i(and)d(R.)g(Coutre,)i(\\A)f (searc)m(h)g(for)f(go)s(o)s(d)g(m)m(ultiple)h(recursiv)m(e)570 3355 y(random)45 b(n)m(um)m(b)s(er)f(generators",)51 b FD(A)m(CM)46 b(T)-8 b(ransactions)46 b(on)f(Mo)s(deling)h(and)f (Computer)570 3465 y(Sim)m(ulation)31 b FK(3,)g(87{98)i(\(1993\).)3299 3635 y([Generator])-3598 b Fv(gsl_rng_taus)3299 3745 y FK([Generator])g Fv(gsl_rng_taus2)390 3854 y FK(This)41 b(is)h(a)g(maximally)g(equidistributed)f(com)m(bined)h(T)-8 b(ausw)m(orthe)42 b(generator)h(b)m(y)e(L'Ecuy)m(er.)390 3964 y(The)30 b(sequence)h(is,)1563 4127 y FE(x)1615 4141 y Fq(n)1685 4127 y FK(=)25 b(\()p FE(s)1859 4089 y FB(1)1859 4149 y Fq(n)1924 4127 y FI(\010)20 b FE(s)2058 4089 y FB(2)2058 4149 y Fq(n)2123 4127 y FI(\010)g FE(s)2257 4089 y FB(3)2257 4149 y Fq(n)2302 4127 y FK(\))390 4290 y(where,)737 4448 y FE(s)780 4410 y FB(1)780 4470 y Fq(n)p FB(+1)935 4448 y FK(=)k(\(\(\()p FE(s)1178 4410 y FB(1)1178 4470 y Fq(n)1224 4448 y FK(&4294967294\))30 b FI(\034)25 b FK(12\))d FI(\010)e FK(\(\(\()p FE(s)2312 4410 y FB(1)2312 4470 y Fq(n)2383 4448 y FI(\034)25 b FK(13\))c FI(\010)f FE(s)2779 4410 y FB(1)2779 4470 y Fq(n)2824 4448 y FK(\))26 b FI(\035)f FK(19\)\))737 4582 y FE(s)780 4545 y FB(2)780 4605 y Fq(n)p FB(+1)935 4582 y FK(=)f(\(\(\()p FE(s)1178 4545 y FB(2)1178 4605 y Fq(n)1224 4582 y FK(&4294967288\))30 b FI(\034)25 b FK(4\))c FI(\010)f FK(\(\(\()p FE(s)2266 4545 y FB(2)2266 4605 y Fq(n)2337 4582 y FI(\034)26 b FK(2\))21 b FI(\010)e FE(s)2688 4545 y FB(2)2688 4605 y Fq(n)2733 4582 y FK(\))26 b FI(\035)f FK(25\)\))737 4717 y FE(s)780 4679 y FB(3)780 4739 y Fq(n)p FB(+1)935 4717 y FK(=)f(\(\(\()p FE(s)1178 4679 y FB(3)1178 4739 y Fq(n)1224 4717 y FK(&4294967280\))30 b FI(\034)25 b FK(17\))d FI(\010)e FK(\(\(\()p FE(s)2312 4679 y FB(3)2312 4739 y Fq(n)2383 4717 y FI(\034)25 b FK(3\))c FI(\010)f FE(s)2734 4679 y FB(3)2734 4739 y Fq(n)2779 4717 y FK(\))25 b FI(\035)h FK(11\)\))390 4881 y(computed)37 b(mo)s(dulo)f(2)1193 4848 y FB(32)1264 4881 y FK(.)61 b(In)36 b(the)i(form)m(ulas)f(ab)s(o)m (v)m(e)h FI(\010)f FK(denotes)g(\\exclusiv)m(e-or".)64 b(Note)38 b(that)390 4991 y(the)28 b(algorithm)g(relies)g(on)g(the)f (prop)s(erties)g(of)h(32-bit)h(unsigned)d(in)m(tegers)j(and)e(has)g(b)s (een)g(imple-)390 5101 y(men)m(ted)k(using)f(a)g(bitmask)h(of)f FH(0xFFFFFFFF)e FK(to)j(mak)m(e)g(it)g(w)m(ork)g(on)f(64)h(bit)g(mac)m (hines.)390 5230 y(The)23 b(p)s(erio)s(d)f(of)i(this)g(generator)g(is)g (2)1641 5197 y FB(88)1735 5230 y FK(\(ab)s(out)g(10)2114 5197 y FB(26)2185 5230 y FK(\).)39 b(It)24 b(uses)f(3)h(w)m(ords)f(of)h (state)h(p)s(er)e(generator.)390 5340 y(F)-8 b(or)31 b(more)g(information)f(see,)p eop end %%Page: 212 230 TeXDict begin 212 229 bop 150 -116 a FK(Chapter)30 b(18:)41 b(Random)30 b(Num)m(b)s(er)g(Generation)1798 b(212)570 299 y(P)-8 b(.)44 b(L'Ecuy)m(er,)j(\\Maximally)e(Equidistributed)d(Com) m(bined)h(T)-8 b(ausw)m(orthe)43 b(Generators",)570 408 y FD(Mathematics)32 b(of)f(Computation)p FK(,)g(65,)g(213)h(\(1996\),)h (203{213.)390 558 y(The)k(generator)h FH(gsl_rng_taus2)c FK(uses)i(the)i(same)f(algorithm)h(as)g FH(gsl_rng_taus)c FK(but)i(with)390 667 y(an)30 b(impro)m(v)m(ed)h(seeding)g(pro)s (cedure)e(describ)s(ed)g(in)h(the)h(pap)s(er,)570 797 y(P)-8 b(.)44 b(L'Ecuy)m(er,)k(\\T)-8 b(ables)45 b(of)f(Maximally)h (Equidistributed)d(Com)m(bined)i(LFSR)f(Genera-)570 907 y(tors",)31 b FD(Mathematics)i(of)d(Computation)p FK(,)h(68,)h(225)f (\(1999\),)i(261{269)390 1056 y(The)d(generator)h FH(gsl_rng_taus2)c FK(should)j(no)m(w)g(b)s(e)g(used)f(in)h(preference)h(to)g FH(gsl_rng_taus)p FK(.)3299 1225 y([Generator])-3598 b Fv(gsl_rng_gfsr4)390 1335 y FK(The)31 b FH(gfsr4)e FK(generator)j(is)g(lik)m(e)g(a)f(lagged-\014b)s(onacci)i(generator,)g (and)d(pro)s(duces)g(eac)m(h)i(n)m(um)m(b)s(er)390 1445 y(as)f(an)f FH(xor)p FK('d)f(sum)h(of)g(four)g(previous)g(v)-5 b(alues.)1298 1607 y FE(r)1339 1621 y Fq(n)1410 1607 y FK(=)25 b FE(r)1547 1621 y Fq(n)p Fp(\000)p Fq(A)1714 1607 y FI(\010)20 b FE(r)1846 1621 y Fq(n)p Fp(\000)p Fq(B)2016 1607 y FI(\010)g FE(r)2148 1621 y Fq(n)p Fp(\000)p Fq(C)2317 1607 y FI(\010)g FE(r)2449 1621 y Fq(n)p Fp(\000)p Fq(D)390 1790 y FK(Zi\013)43 b(\(ref)g(b)s(elo)m(w\))g(notes)g(that)h (\\it)g(is)f(no)m(w)f(widely)h(kno)m(wn")g(that)g(t)m(w)m(o-tap)i (registers)f(\(suc)m(h)390 1900 y(as)38 b(R250,)i(whic)m(h)d(is)h (describ)s(ed)e(b)s(elo)m(w\))i(ha)m(v)m(e)g(serious)g(\015a)m(ws,)h (the)e(most)h(ob)m(vious)g(one)f(b)s(eing)390 2009 y(the)43 b(three-p)s(oin)m(t)h(correlation)g(that)g(comes)g(from)e(the)h (de\014nition)g(of)g(the)g(generator.)80 b(Nice)390 2119 y(mathematical)47 b(prop)s(erties)d(can)h(b)s(e)f(deriv)m(ed)h(for)g (GFSR's,)j(and)c(n)m(umerics)h(b)s(ears)f(out)h(the)390 2228 y(claim)34 b(that)g(4-tap)g(GFSR's)g(with)f(appropriately)g(c)m (hosen)h(o\013sets)g(are)g(as)f(random)g(as)g(can)h(b)s(e)390 2338 y(measured,)c(using)g(the)g(author's)h(test.)390 2467 y(This)f(implemen)m(tation)j(uses)e(the)g(v)-5 b(alues)31 b(suggested)h(the)f(example)h(on)f(p392)h(of)f(Zi\013)7 b('s)31 b(article:)390 2577 y FE(A)25 b FK(=)g(471,)32 b FE(B)e FK(=)25 b(1586,)32 b FE(C)g FK(=)25 b(6988,)32 b FE(D)d FK(=)24 b(9689.)390 2707 y(If)29 b(the)h(o\013sets)g(are)g (appropriately)g(c)m(hosen)g(\(suc)m(h)g(as)g(the)f(one)h(ones)g(in)f (this)h(implemen)m(tation\),)390 2816 y(then)e(the)g(sequence)g(is)g (said)g(to)h(b)s(e)e(maximal;)j(that)f(means)f(that)g(the)g(p)s(erio)s (d)f(is)h(2)3256 2783 y Fq(D)3332 2816 y FI(\000)15 b FK(1,)29 b(where)390 2926 y FE(D)37 b FK(is)e(the)g(longest)h(lag.)55 b(\(It)35 b(is)g(one)g(less)g(than)f(2)2105 2893 y Fq(D)2201 2926 y FK(b)s(ecause)g(it)i(is)e(not)h(p)s(ermitted)g(to)g(ha)m(v)m(e)h (all)390 3035 y(zeros)d(in)g(the)f FH(ra[])g FK(arra)m(y)-8 b(.\))49 b(F)-8 b(or)33 b(this)g(implemen)m(tation)h(with)e FE(D)g FK(=)d(9689)34 b(that)g(w)m(orks)e(out)h(to)390 3145 y(ab)s(out)d(10)740 3112 y FB(2917)878 3145 y FK(.)390 3274 y(Note)i(that)g(the)f(implemen)m(tation)h(of)f(this)g(generator)h (using)f(a)g(32-bit)h(in)m(teger)g(amoun)m(ts)f(to)h(32)390 3384 y(parallel)k(implemen)m(tations)h(of)f(one-bit)g(generators.)56 b(One)35 b(consequence)h(of)f(this)h(is)f(that)h(the)390 3494 y(p)s(erio)s(d)g(of)h(this)h(32-bit)g(generator)h(is)e(the)g(same) h(as)f(for)h(the)f(one-bit)h(generator.)63 b(Moreo)m(v)m(er,)390 3603 y(this)30 b(indep)s(endence)g(means)g(that)h(all)g(32-bit)h (patterns)f(are)g(equally)g(lik)m(ely)-8 b(,)33 b(and)c(in)i (particular)390 3713 y(that)e(0)g(is)f(an)h(allo)m(w)m(ed)h(random)e(v) -5 b(alue.)40 b(\(W)-8 b(e)30 b(are)f(grateful)h(to)f(Heik)m(o)h(Bauk)m (e)g(for)e(clarifying)h(for)390 3822 y(us)h(these)g(prop)s(erties)g(of) h(GFSR)f(random)g(n)m(um)m(b)s(er)f(generators.\))390 3952 y(F)-8 b(or)31 b(more)g(information)f(see,)570 4081 y(Rob)s(ert)42 b(M.)g(Zi\013,)j(\\F)-8 b(our-tap)43 b (shift-register-sequence)h(random-n)m(um)m(b)s(er)c(generators",)570 4191 y FD(Computers)29 b(in)h(Ph)m(ysics)p FK(,)h(12\(4\),)i(Jul/Aug)d (1998,)j(pp)c(385{392.)150 4413 y FJ(18.10)69 b(Unix)45 b(random)g(n)l(um)l(b)t(er)f(generators)150 4573 y FK(The)33 b(standard)g(Unix)h(random)f(n)m(um)m(b)s(er)g(generators)i FH(rand)p FK(,)e FH(random)g FK(and)g FH(rand48)f FK(are)i(pro)m(vided) g(as)150 4682 y(part)d(of)h(GSL.)f(Although)h(these)g(generators)g(are) g(widely)f(a)m(v)-5 b(ailable)34 b(individually)d(often)h(they)f (aren't)150 4792 y(all)26 b(a)m(v)-5 b(ailable)27 b(on)e(the)g(same)h (platform.)39 b(This)24 b(mak)m(es)i(it)f(di\016cult)g(to)h(write)f(p)s (ortable)g(co)s(de)g(using)g(them)150 4902 y(and)j(so)i(w)m(e)f(ha)m(v) m(e)h(included)e(the)i(complete)g(set)f(of)h(Unix)e(generators)i(in)f (GSL)g(for)f(con)m(v)m(enience.)43 b(Note)150 5011 y(that)34 b(these)g(generators)g(don't)f(pro)s(duce)g(high-qualit)m(y)h (randomness)e(and)h(aren't)h(suitable)g(for)f(w)m(ork)150 5121 y(requiring)d(accurate)h(statistics.)43 b(Ho)m(w)m(ev)m(er,)32 b(if)e(y)m(ou)g(w)m(on't)h(b)s(e)f(measuring)f(statistical)k(quan)m (tities)f(and)150 5230 y(just)k(w)m(an)m(t)i(to)g(in)m(tro)s(duce)f (some)g(v)-5 b(ariation)38 b(in)m(to)g(y)m(our)f(program)g(then)g (these)g(generators)h(are)g(quite)150 5340 y(acceptable.)p eop end %%Page: 213 231 TeXDict begin 213 230 bop 150 -116 a FK(Chapter)30 b(18:)41 b(Random)30 b(Num)m(b)s(er)g(Generation)1798 b(213)3299 299 y([Generator])-3598 b Fv(gsl_rng_rand)390 408 y FK(This)30 b(is)g(the)h(BSD)f FH(rand)f FK(generator.)42 b(Its)31 b(sequence)f(is)1473 602 y FE(x)1525 616 y Fq(n)p FB(+1)1680 602 y FK(=)25 b(\()p FE(ax)1911 616 y Fq(n)1977 602 y FK(+)20 b FE(c)p FK(\))15 b(mo)s(d)g FE(m)390 796 y FK(with)35 b FE(a)f FK(=)f(1103515245,)41 b FE(c)34 b FK(=)f(12345)38 b(and)d FE(m)e FK(=)g(2)2188 763 y FB(31)2259 796 y FK(.)56 b(The)35 b(seed)g(sp)s(eci\014es)g(the)h(initial)g(v)-5 b(alue,)390 906 y FE(x)442 920 y FB(1)479 906 y FK(.)41 b(The)30 b(p)s(erio)s(d)f(of)h(this)h(generator)g(is)g(2)1837 873 y FB(31)1907 906 y FK(,)g(and)f(it)h(uses)f(1)g(w)m(ord)g(of)h (storage)h(p)s(er)d(generator.)3299 1142 y([Generator])-3598 b Fv(gsl_rng_random_bsd)3299 1252 y FK([Generator])g Fv(gsl_rng_random_libc5)3299 1362 y FK([Generator])g Fv(gsl_rng_random_glibc2)390 1471 y FK(These)32 b(generators)h (implemen)m(t)g(the)g FH(random)d FK(family)j(of)f(functions,)h(a)f (set)h(of)f(linear)h(feedbac)m(k)390 1581 y(shift)i(register)h (generators)h(originally)g(used)e(in)g(BSD)g(Unix.)56 b(There)35 b(are)h(sev)m(eral)h(v)m(ersions)f(of)390 1690 y FH(random)i FK(in)i(use)g(to)s(da)m(y:)61 b(the)41 b(original)g(BSD)g(v)m(ersion)f(\(e.g.)72 b(on)40 b(SunOS4\),)h(a)g (lib)s(c5)f(v)m(ersion)390 1800 y(\(found)j(on)i(older)f(GNU/Lin)m(ux)h (systems\))g(and)f(a)g(glib)s(c2)i(v)m(ersion.)83 b(Eac)m(h)45 b(v)m(ersion)g(uses)f(a)390 1910 y(di\013eren)m(t)31 b(seeding)g(pro)s(cedure,)e(and)h(th)m(us)g(pro)s(duces)f(di\013eren)m (t)i(sequences.)390 2070 y(The)i(original)h(BSD)g(routines)f(accepted)h (a)g(v)-5 b(ariable)34 b(length)f(bu\013er)g(for)g(the)g(generator)h (state,)390 2180 y(with)25 b(longer)h(bu\013ers)e(pro)m(viding)h (higher-qualit)m(y)h(randomness.)38 b(The)25 b FH(random)f FK(function)h(imple-)390 2289 y(men)m(ted)e(algorithms)g(for)f (bu\013er)g(lengths)h(of)f(8,)j(32,)g(64,)g(128)f(and)e(256)i(b)m (ytes,)g(and)e(the)h(algorithm)390 2399 y(with)28 b(the)h(largest)h (length)f(that)g(w)m(ould)f(\014t)g(in)m(to)i(the)e(user-supplied)f (bu\013er)h(w)m(as)h(used.)39 b(T)-8 b(o)29 b(sup-)390 2509 y(p)s(ort)h(these)h(algorithms)g(additional)g(generators)h(are)e (a)m(v)-5 b(ailable)33 b(with)d(the)h(follo)m(wing)h(names,)630 2669 y FH(gsl_rng_random8_bsd)630 2779 y(gsl_rng_random32_bsd)630 2888 y(gsl_rng_random64_bsd)630 2998 y(gsl_rng_random128_bsd)630 3108 y(gsl_rng_random256_bsd)390 3268 y FK(where)e(the)g(n)m(umeric)g (su\016x)f(indicates)j(the)e(bu\013er)f(length.)41 b(The)30 b(original)h(BSD)g FH(random)e FK(func-)390 3378 y(tion)24 b(used)e(a)i(128-b)m(yte)i(default)d(bu\013er)g(and)f(so)i FH(gsl_rng_random_bsd)18 b FK(has)24 b(b)s(een)e(made)i(equiv-)390 3487 y(alen)m(t)33 b(to)f FH(gsl_rng_random128_bsd)p FK(.)37 b(Corresp)s(onding)30 b(v)m(ersions)h(of)h(the)f FH(libc5)f FK(and)h FH(glibc2)390 3597 y FK(generators)44 b(are)f(also)h(a)m(v)-5 b(ailable,)48 b(with)42 b(the)h(names)g FH(gsl_rng_random8_libc5)p FK(,)d FH(gsl_rng_)390 3707 y(random8_glibc2)p FK(,)27 b(etc.)3299 3943 y([Generator])-3598 b Fv(gsl_rng_rand48)390 4053 y FK(This)30 b(is)g(the)h(Unix)f FH(rand48)e FK(generator.)42 b(Its)31 b(sequence)f(is)1473 4247 y FE(x)1525 4261 y Fq(n)p FB(+1)1680 4247 y FK(=)25 b(\()p FE(ax)1911 4261 y Fq(n)1977 4247 y FK(+)20 b FE(c)p FK(\))15 b(mo)s(d)g FE(m)390 4441 y FK(de\014ned)30 b(on)h(48-bit)h (unsigned)e(in)m(tegers)i(with)e FE(a)d FK(=)f(25214903917,)36 b FE(c)26 b FK(=)g(11)32 b(and)e FE(m)c FK(=)g(2)3455 4408 y FB(48)3526 4441 y FK(.)42 b(The)390 4550 y(seed)33 b(sp)s(eci\014es)g(the)g(upp)s(er)e(32)i(bits)g(of)g(the)h(initial)g(v) -5 b(alue,)34 b FE(x)2516 4564 y FB(1)2553 4550 y FK(,)g(with)f(the)g (lo)m(w)m(er)h(16)g(bits)f(set)g(to)390 4660 y FH(0x330E)p FK(.)42 b(The)30 b(function)h FH(gsl_rng_get)e FK(returns)h(the)h(upp)s (er)e(32)k(bits)e(from)g(eac)m(h)h(term)f(of)h(the)390 4769 y(sequence.)50 b(This)33 b(do)s(es)g(not)g(ha)m(v)m(e)i(a)f (direct)f(parallel)i(in)e(the)h(original)g FH(rand48)e FK(functions,)i(but)390 4879 y(forcing)e(the)f(result)g(to)h(t)m(yp)s (e)f FH(long)e(int)h FK(repro)s(duces)g(the)i(output)e(of)i FH(mrand48)p FK(.)41 b(The)30 b(function)390 4988 y FH(gsl_rng_uniform) 23 b FK(uses)j(the)i(full)e(48)i(bits)f(of)g(in)m(ternal)h(state)g(to)g (return)e(the)h(double)g(precision)390 5098 y(n)m(um)m(b)s(er)h FE(x)772 5112 y Fq(n)817 5098 y FE(=m)p FK(,)i(whic)m(h)e(is)i(equiv)-5 b(alen)m(t)30 b(to)g(the)f(function)g FH(drand48)p FK(.)38 b(Note)30 b(that)g(some)g(v)m(ersions)390 5208 y(of)22 b(the)h(GNU)f(C)g(Library)f(con)m(tained)j(a)e(bug)g(in)g FH(mrand48)e FK(function)i(whic)m(h)f(caused)i(it)f(to)h(pro)s(duce)390 5317 y(di\013eren)m(t)31 b(results)f(\(only)h(the)f(lo)m(w)m(er)i (16-bits)g(of)e(the)h(return)e(v)-5 b(alue)31 b(w)m(ere)g(set\).)p eop end %%Page: 214 232 TeXDict begin 214 231 bop 150 -116 a FK(Chapter)30 b(18:)41 b(Random)30 b(Num)m(b)s(er)g(Generation)1798 b(214)150 299 y FJ(18.11)69 b(Other)45 b(random)g(n)l(um)l(b)t(er)f(generators) 150 458 y FK(The)30 b(generators)i(in)e(this)h(section)h(are)f(pro)m (vided)f(for)h(compatibilit)m(y)h(with)f(existing)h(libraries.)41 b(If)31 b(y)m(ou)150 568 y(are)42 b(con)m(v)m(erting)h(an)e(existing)i (program)e(to)h(use)f(GSL)g(then)g(y)m(ou)h(can)g(select)h(these)f (generators)g(to)150 677 y(c)m(hec)m(k)37 b(y)m(our)f(new)f(implemen)m (tation)i(against)g(the)f(original)h(one,)g(using)e(the)h(same)g (random)f(n)m(um)m(b)s(er)150 787 y(generator.)53 b(After)35 b(v)m(erifying)f(that)h(y)m(our)f(new)g(program)g(repro)s(duces)f(the)h (original)h(results)f(y)m(ou)h(can)150 897 y(then)30 b(switc)m(h)h(to)g(a)g(higher-qualit)m(y)g(generator.)275 1035 y(Note)36 b(that)h(most)e(of)h(the)g(generators)g(in)g(this)f (section)i(are)f(based)f(on)g(single)h(linear)g(congruence)150 1145 y(relations,)d(whic)m(h)f(are)g(the)g(least)h(sophisticated)g(t)m (yp)s(e)f(of)g(generator.)46 b(In)31 b(particular,)i(linear)f(congru-) 150 1254 y(ences)23 b(ha)m(v)m(e)h(p)s(o)s(or)d(prop)s(erties)h(when)g (used)g(with)g(a)h(non-prime)f(mo)s(dulus,)h(as)f(sev)m(eral)i(of)f (these)g(routines)150 1364 y(do)36 b(\(e.g.)60 b(with)36 b(a)h(p)s(o)m(w)m(er)f(of)g(t)m(w)m(o)i(mo)s(dulus,)e(2)1809 1331 y FB(31)1916 1364 y FK(or)h(2)2079 1331 y FB(32)2150 1364 y FK(\).)58 b(This)36 b(leads)g(to)i(p)s(erio)s(dicit)m(y)e(in)g (the)h(least)150 1473 y(signi\014can)m(t)c(bits)f(of)g(eac)m(h)i(n)m (um)m(b)s(er,)d(with)h(only)g(the)g(higher)g(bits)g(ha)m(ving)h(an)m(y) f(randomness.)45 b(Th)m(us)31 b(if)150 1583 y(y)m(ou)f(w)m(an)m(t)h(to) f(pro)s(duce)f(a)h(random)f(bitstream)h(it)g(is)g(b)s(est)f(to)i(a)m(v) m(oid)g(using)e(the)h(least)h(signi\014can)m(t)g(bits.)3299 1775 y([Generator])-3598 b Fv(gsl_rng_ranf)390 1885 y FK(This)30 b(is)g(the)h(CRA)-8 b(Y)30 b(random)g(n)m(um)m(b)s(er)f (generator)i FH(RANF)p FK(.)40 b(Its)30 b(sequence)h(is)1549 2057 y FE(x)1601 2071 y Fq(n)p FB(+1)1755 2057 y FK(=)25 b(\()p FE(ax)1986 2071 y Fq(n)2032 2057 y FK(\))15 b(mo)s(d)g FE(m)390 2228 y FK(de\014ned)28 b(on)g(48-bit)i(unsigned)e(in)m(tegers) i(with)f FE(a)c FK(=)g(44485709377909)35 b(and)29 b FE(m)c FK(=)g(2)3262 2195 y FB(48)3332 2228 y FK(.)40 b(The)29 b(seed)390 2338 y(sp)s(eci\014es)34 b(the)g(lo)m(w)m(er)h(32)g(bits)f (of)g(the)h(initial)g(v)-5 b(alue,)36 b FE(x)2304 2352 y FB(1)2341 2338 y FK(,)f(with)f(the)g(lo)m(w)m(est)i(bit)e(set)h(to)f (prev)m(en)m(t)390 2447 y(the)f(seed)g(taking)h(an)f(ev)m(en)h(v)-5 b(alue.)49 b(The)33 b(upp)s(er)e(16)j(bits)f(of)g FE(x)2564 2461 y FB(1)2634 2447 y FK(are)h(set)f(to)h(0.)49 b(A)33 b(consequence)390 2557 y(of)h(this)h(pro)s(cedure)e(is)h(that)h(the)g (pairs)f(of)g(seeds)g(2)h(and)f(3,)i(4)e(and)g(5,)i(etc.)g(pro)s(duce)d (the)i(same)390 2667 y(sequences.)390 2805 y(The)40 b(generator)i (compatible)g(with)f(the)g(CRA)-8 b(Y)41 b(MA)-8 b(THLIB)42 b(routine)f(RANF.)g(It)g(pro)s(duces)390 2915 y(double)32 b(precision)h(\015oating)g(p)s(oin)m(t)g(n)m(um)m(b)s(ers)e(whic)m(h)h (should)g(b)s(e)g(iden)m(tical)i(to)g(those)f(from)f(the)390 3024 y(original)g(RANF.)390 3163 y(There)27 b(is)h(a)h(subtlet)m(y)f (in)g(the)g(implemen)m(tation)h(of)g(the)f(seeding.)40 b(The)27 b(initial)j(state)f(is)f(rev)m(ersed)390 3272 y(through)33 b(one)h(step,)h(b)m(y)e(m)m(ultiplying)i(b)m(y)e(the)h(mo) s(dular)f(in)m(v)m(erse)h(of)g FE(a)g FK(mo)s(d)f FE(m)p FK(.)50 b(This)33 b(is)h(done)390 3382 y(for)c(compatibilit)m(y)j(with) d(the)g(original)i(CRA)-8 b(Y)31 b(implemen)m(tation.)390 3520 y(Note)h(that)e(y)m(ou)h(can)f(only)h(seed)f(the)g(generator)i (with)e(in)m(tegers)h(up)e(to)i(2)2932 3487 y FB(32)3003 3520 y FK(,)f(while)g(the)h(original)390 3630 y(CRA)-8 b(Y)29 b(implemen)m(tation)g(uses)f(non-p)s(ortable)g(wide)g(in)m (tegers)i(whic)m(h)e(can)h(co)m(v)m(er)h(all)f(2)3423 3597 y FB(48)3522 3630 y FK(states)390 3740 y(of)i(the)f(generator.)390 3878 y(The)d(function)g FH(gsl_rng_get)e FK(returns)h(the)i(upp)s(er)d (32)k(bits)e(from)g(eac)m(h)i(term)f(of)g(the)f(sequence.)390 3988 y(The)36 b(function)h FH(gsl_rng_uniform)32 b FK(uses)k(the)h (full)g(48)g(bits)g(to)g(return)f(the)h(double)f(precision)390 4097 y(n)m(um)m(b)s(er)29 b FE(x)773 4111 y Fq(n)818 4097 y FE(=m)p FK(.)390 4236 y(The)h(p)s(erio)s(d)f(of)h(this)h (generator)g(is)g(2)1682 4203 y FB(46)1753 4236 y FK(.)3299 4428 y([Generator])-3598 b Fv(gsl_rng_ranmar)390 4538 y FK(This)38 b(is)h(the)h(RANMAR)g(lagged-\014b)s(onacci)g(generator)h (of)e(Marsaglia,)44 b(Zaman)38 b(and)h(Tsang.)390 4647 y(It)e(is)g(a)h(24-bit)g(generator,)i(originally)f(designed)d(for)h (single-precision)i(IEEE)d(\015oating)i(p)s(oin)m(t)390 4757 y(n)m(um)m(b)s(ers.)h(It)31 b(w)m(as)g(included)e(in)h(the)h (CERNLIB)f(high-energy)g(ph)m(ysics)h(library)-8 b(.)3299 4949 y([Generator])-3598 b Fv(gsl_rng_r250)390 5059 y FK(This)35 b(is)h(the)g(shift-register)h(generator)g(of)f(Kirkpatric)m (k)g(and)g(Stoll.)58 b(The)35 b(sequence)h(is)g(based)390 5168 y(on)30 b(the)h(recurrence)1537 5340 y FE(x)1589 5354 y Fq(n)1659 5340 y FK(=)25 b FE(x)1807 5354 y Fq(n)p Fp(\000)p FB(103)2024 5340 y FI(\010)20 b FE(x)2167 5354 y Fq(n)p Fp(\000)p FB(250)p eop end %%Page: 215 233 TeXDict begin 215 232 bop 150 -116 a FK(Chapter)30 b(18:)41 b(Random)30 b(Num)m(b)s(er)g(Generation)1798 b(215)390 299 y(where)24 b FI(\010)g FK(denotes)h(\\exclusiv)m(e-or",)k (de\014ned)23 b(on)h(32-bit)i(w)m(ords.)38 b(The)24 b(p)s(erio)s(d)g (of)g(this)h(generator)390 408 y(is)30 b(ab)s(out)h(2)787 375 y FB(250)921 408 y FK(and)e(it)i(uses)f(250)i(w)m(ords)e(of)g (state)i(p)s(er)d(generator.)390 540 y(F)-8 b(or)31 b(more)g (information)f(see,)570 671 y(S.)g(Kirkpatric)m(k)g(and)f(E.)i(Stoll,)g (\\A)f(v)m(ery)g(fast)h(shift-register)g(sequence)f(random)f(n)m(um)m (b)s(er)570 781 y(generator",)j FD(Journal)e(of)h(Computational)g(Ph)m (ysics)p FK(,)g(40,)g(517{526)j(\(1981\))3299 956 y([Generator])-3598 b Fv(gsl_rng_tt800)390 1066 y FK(This)30 b(is)g(an)h(earlier)g(v)m (ersion)g(of)g(the)f(t)m(wisted)i(generalized)g(feedbac)m(k)f (shift-register)h(generator,)390 1175 y(and)39 b(has)g(b)s(een)g(sup)s (erseded)f(b)m(y)h(the)h(dev)m(elopmen)m(t)h(of)e(MT19937.)71 b(Ho)m(w)m(ev)m(er,)44 b(it)c(is)g(still)g(an)390 1285 y(acceptable)e(generator)g(in)e(its)g(o)m(wn)h(righ)m(t.)59 b(It)36 b(has)g(a)h(p)s(erio)s(d)e(of)h(2)2761 1252 y FB(800)2901 1285 y FK(and)g(uses)g(33)h(w)m(ords)f(of)390 1394 y(storage)c(p)s(er)d(generator.)390 1526 y(F)-8 b(or)31 b(more)g(information)f(see,)570 1657 y(Mak)m(oto)24 b(Matsumoto)e(and)e(Y)-8 b(oshiharu)21 b(Kurita,)i(\\Twisted)e(GFSR)g (Generators)h(I)s(I",)f FD(A)m(CM)570 1767 y(T)-8 b(ransactions)30 b(on)g(Mo)s(delling)h(and)e(Computer)g(Sim)m(ulation)p FK(,)i(V)-8 b(ol.)31 b(4,)f(No.)h(3,)f(1994,)i(pages)570 1876 y(254{266.)3299 2051 y([Generator])-3598 b Fv(gsl_rng_vax)390 2161 y FK(This)30 b(is)g(the)h(V)-10 b(AX)30 b(generator)i FH(MTH$RANDOM)p FK(.)38 b(Its)30 b(sequence)h(is,)1473 2326 y FE(x)1525 2340 y Fq(n)p FB(+1)1680 2326 y FK(=)25 b(\()p FE(ax)1911 2340 y Fq(n)1977 2326 y FK(+)20 b FE(c)p FK(\))15 b(mo)s(d)g FE(m)390 2490 y FK(with)37 b FE(a)f FK(=)g(69069,)42 b FE(c)37 b FK(=)f(1)h(and)g FE(m)f FK(=)g(2)1804 2457 y FB(32)1875 2490 y FK(.)61 b(The)36 b(seed)i(sp)s(eci\014es)e(the)i(initial)g(v)-5 b(alue,)39 b FE(x)3470 2504 y FB(1)3508 2490 y FK(.)60 b(The)390 2600 y(p)s(erio)s(d)29 b(of)i(this)f(generator)h(is)g(2)1495 2567 y FB(32)1596 2600 y FK(and)f(it)h(uses)f(1)g(w)m(ord)g(of)h (storage)h(p)s(er)d(generator.)3299 2775 y([Generator])-3598 b Fv(gsl_rng_transputer)390 2884 y FK(This)44 b(is)h(the)g(random)e(n)m (um)m(b)s(er)h(generator)i(from)e(the)h(INMOS)f(T)-8 b(ransputer)44 b(Dev)m(elopmen)m(t)390 2994 y(system.)d(Its)30 b(sequence)h(is,)1549 3159 y FE(x)1601 3173 y Fq(n)p FB(+1)1755 3159 y FK(=)25 b(\()p FE(ax)1986 3173 y Fq(n)2032 3159 y FK(\))15 b(mo)s(d)g FE(m)390 3323 y FK(with)30 b FE(a)25 b FK(=)g(1664525)34 b(and)c FE(m)25 b FK(=)g(2)1538 3290 y FB(32)1608 3323 y FK(.)41 b(The)30 b(seed)g(sp)s(eci\014es)g (the)h(initial)h(v)-5 b(alue,)31 b FE(x)3142 3337 y FB(1)3179 3323 y FK(.)3299 3498 y([Generator])-3598 b Fv(gsl_rng_randu)390 3608 y FK(This)30 b(is)g(the)h(IBM)f FH(RANDU)f FK(generator.)42 b(Its)31 b(sequence)f(is)1549 3773 y FE(x)1601 3787 y Fq(n)p FB(+1)1755 3773 y FK(=)25 b(\()p FE(ax)1986 3787 y Fq(n)2032 3773 y FK(\))15 b(mo)s(d)g FE(m)390 3937 y FK(with)32 b FE(a)d FK(=)g(65539)35 b(and)d FE(m)d FK(=)f(2)1468 3904 y FB(31)1539 3937 y FK(.)47 b(The)32 b(seed)h(sp)s(eci\014es)f(the)h(initial)h(v)-5 b(alue,)34 b FE(x)3093 3951 y FB(1)3130 3937 y FK(.)47 b(The)32 b(p)s(erio)s(d)g(of)390 4047 y(this)e(generator)i(w)m(as)f(only)f(2) 1391 4014 y FB(29)1462 4047 y FK(.)41 b(It)30 b(has)g(b)s(ecome)h(a)g (textb)s(o)s(ok)f(example)i(of)e(a)h(p)s(o)s(or)e(generator.)3299 4222 y([Generator])-3598 b Fv(gsl_rng_minstd)390 4331 y FK(This)27 b(is)h(P)m(ark)h(and)e(Miller's)j(\\minimal)e(standard")g FC(minstd)f FK(generator,)j(a)f(simple)f(linear)g(con-)390 4441 y(gruence)i(whic)m(h)f(tak)m(es)j(care)e(to)h(a)m(v)m(oid)g(the)f (ma)5 b(jor)30 b(pitfalls)g(of)g(suc)m(h)f(algorithms.)42 b(Its)30 b(sequence)390 4551 y(is,)1549 4715 y FE(x)1601 4729 y Fq(n)p FB(+1)1755 4715 y FK(=)25 b(\()p FE(ax)1986 4729 y Fq(n)2032 4715 y FK(\))15 b(mo)s(d)g FE(m)390 4880 y FK(with)32 b FE(a)d FK(=)g(16807)35 b(and)d FE(m)c FK(=)h(2)1468 4847 y FB(31)1560 4880 y FI(\000)22 b FK(1)29 b(=)g(2147483647.)52 b(The)32 b(seed)g(sp)s(eci\014es)h(the)f(initial)i (v)-5 b(alue,)390 4989 y FE(x)442 5003 y FB(1)479 4989 y FK(.)41 b(The)30 b(p)s(erio)s(d)f(of)h(this)h(generator)g(is)g(ab)s (out)f(2)2097 4956 y FB(31)2167 4989 y FK(.)390 5121 y(This)h(generator)i(w)m(as)f(used)f(in)h(the)g(IMSL)f(Library)g (\(subroutine)g(RNUN\))h(and)g(in)f(MA)-8 b(TLAB)390 5230 y(\(the)26 b(RAND)g(function\))g(in)f(the)h(past.)39 b(It)26 b(is)f(also)i(sometimes)f(kno)m(wn)f(b)m(y)h(the)f(acron)m(ym)i (\\GGL")390 5340 y(\(I'm)j(not)h(sure)f(what)g(that)h(stands)f(for\).)p eop end %%Page: 216 234 TeXDict begin 216 233 bop 150 -116 a FK(Chapter)30 b(18:)41 b(Random)30 b(Num)m(b)s(er)g(Generation)1798 b(216)390 299 y(F)-8 b(or)31 b(more)g(information)f(see,)570 433 y(P)m(ark)37 b(and)g(Miller,)j(\\Random)d(Num)m(b)s(er)f(Generators:)55 b(Go)s(o)s(d)37 b(ones)g(are)h(hard)e(to)i(\014nd",)570 543 y FD(Comm)m(unications)23 b(of)g(the)g(A)m(CM)p FK(,)g(Octob)s(er)f (1988,)27 b(V)-8 b(olume)23 b(31,)i(No)e(10,)i(pages)f(1192{1201.)3299 726 y([Generator])-3598 b Fv(gsl_rng_uni)3299 835 y FK([Generator])g Fv(gsl_rng_uni32)390 945 y FK(This)26 b(is)g(a)h(reimplemen)m(tation)i (of)e(the)f(16-bit)i(SLA)-8 b(TEC)26 b(random)g(n)m(um)m(b)s(er)f (generator)j(R)m(UNIF.)390 1055 y(A)43 b(generalization)i(of)e(the)g (generator)h(to)f(32)g(bits)g(is)g(pro)m(vided)f(b)m(y)g FH(gsl_rng_uni32)p FK(.)74 b(The)390 1164 y(original)32 b(source)e(co)s(de)h(is)f(a)m(v)-5 b(ailable)33 b(from)d(NETLIB.)3299 1347 y([Generator])-3598 b Fv(gsl_rng_slatec)390 1457 y FK(This)36 b(is)h(the)g(SLA)-8 b(TEC)36 b(random)g(n)m(um)m(b)s(er)f (generator)j(RAND.)g(It)e(is)h(ancien)m(t.)62 b(The)36 b(original)390 1567 y(source)31 b(co)s(de)f(is)h(a)m(v)-5 b(ailable)32 b(from)e(NETLIB.)3299 1750 y([Generator])-3598 b Fv(gsl_rng_zuf)390 1860 y FK(This)30 b(is)g(the)h(ZUF)-10 b(ALL)30 b(lagged)h(Fib)s(onacci)h(series)f(generator)g(of)g(P)m (eterson.)41 b(Its)31 b(sequence)f(is,)1601 2022 y FE(t)25 b FK(=)g FE(u)1807 2036 y Fq(n)p Fp(\000)p FB(273)2024 2022 y FK(+)20 b FE(u)2167 2036 y Fq(n)p Fp(\000)p FB(607)1537 2156 y FE(u)1589 2170 y Fq(n)1659 2156 y FK(=)25 b FE(t)20 b FI(\000)g FK(\015o)s(or\()p FE(t)p FK(\))390 2343 y(The)30 b(original)h(source)g(co)s(de)g(is)f(a)m(v)-5 b(ailable)33 b(from)d(NETLIB.)g(F)-8 b(or)31 b(more)g(information)f(see,)570 2477 y(W.)i(P)m(etersen,)g(\\Lagged)h(Fib)s(onacci)f(Random)f(Num)m(b)s (er)f(Generators)j(for)e(the)g(NEC)g(SX-)570 2587 y(3",)g FD(In)m(ternational)h(Journal)e(of)h(High)f(Sp)s(eed)f(Computing)38 b FK(\(1994\).)3299 2770 y([Generator])-3598 b Fv(gsl_rng_knuthran2)390 2879 y FK(This)36 b(is)h(a)h(second-order)f(m)m(ultiple)g(recursiv)m(e) h(generator)g(describ)s(ed)e(b)m(y)h(Kn)m(uth)f(in)g FD(Semin)m(u-)390 2989 y(merical)31 b(Algorithms)p FK(,)h(3rd)e(Ed.,)g (page)h(108.)42 b(Its)30 b(sequence)h(is,)1340 3156 y FE(x)1392 3170 y Fq(n)1463 3156 y FK(=)25 b(\()p FE(a)1642 3170 y FB(1)1679 3156 y FE(x)1731 3170 y Fq(n)p Fp(\000)p FB(1)1882 3156 y FK(+)20 b FE(a)2021 3170 y FB(2)2058 3156 y FE(x)2110 3170 y Fq(n)p Fp(\000)p FB(2)2240 3156 y FK(\))15 b(mo)s(d)g FE(m)390 3324 y FK(with)30 b FE(a)645 3338 y FB(1)708 3324 y FK(=)25 b(271828183,)34 b FE(a)1316 3338 y FB(2)1379 3324 y FK(=)25 b(314159269,)34 b(and)c FE(m)25 b FK(=)g(2)2362 3291 y FB(31)2453 3324 y FI(\000)20 b FK(1.)3299 3507 y([Generator])-3598 b Fv(gsl_rng_knuthran2002)3299 3617 y FK([Generator])g Fv(gsl_rng_knuthran)390 3726 y FK(This)36 b(is)h(a)h(second-order)f(m)m(ultiple)g(recursiv)m(e)h (generator)g(describ)s(ed)e(b)m(y)h(Kn)m(uth)f(in)g FD(Semin)m(u-)390 3836 y(merical)f(Algorithms)p FK(,)h(3rd)e(Ed.,)h(Section)g(3.6.)53 b(Kn)m(uth)34 b(pro)m(vides)g(its)g(C)g(co)s(de.)53 b(The)33 b(up)s(dated)390 3945 y(routine)k FH(gsl_rng_knuthran2002)32 b FK(is)38 b(from)f(the)h(revised)f(9th)h(prin)m(ting)f(and)g(corrects) i(some)390 4055 y(w)m(eaknesses)31 b(in)f(the)h(earlier)g(v)m(ersion,)g (whic)m(h)f(is)h(implemen)m(ted)g(as)f FH(gsl_rng_knuthran)p FK(.)3299 4238 y([Generator])-3598 b Fv(gsl_rng_borosh13)3299 4348 y FK([Generator])g Fv(gsl_rng_fishman18)3299 4457 y FK([Generator])g Fv(gsl_rng_fishman20)3299 4567 y FK([Generator])g Fv(gsl_rng_lecuyer21)3299 4676 y FK([Generator])g Fv (gsl_rng_waterman14)390 4786 y FK(These)36 b(m)m(ultiplicativ)m(e)j (generators)e(are)f(tak)m(en)i(from)d(Kn)m(uth's)g FD(Semin)m(umerical) i(Algorithms)p FK(,)390 4896 y(3rd)30 b(Ed.,)g(pages)h(106{108.)44 b(Their)30 b(sequence)g(is,)1549 5063 y FE(x)1601 5077 y Fq(n)p FB(+1)1755 5063 y FK(=)25 b(\()p FE(ax)1986 5077 y Fq(n)2032 5063 y FK(\))15 b(mo)s(d)g FE(m)390 5230 y FK(where)28 b(the)h(seed)g(sp)s(eci\014es)g(the)f(initial)i(v)-5 b(alue,)30 b FE(x)2079 5244 y FB(1)2116 5230 y FK(.)41 b(The)28 b(parameters)h FE(a)g FK(and)f FE(m)g FK(are)i(as)f(follo)m (ws,)390 5340 y(Borosh-Niederreiter:)63 b FE(a)42 b FK(=)g(1812433253,) 48 b FE(m)42 b FK(=)g(2)2263 5307 y FB(32)2334 5340 y FK(,)h(Fishman18:)62 b FE(a)42 b FK(=)g(62089911,)47 b FE(m)42 b FK(=)p eop end %%Page: 217 235 TeXDict begin 217 234 bop 150 -116 a FK(Chapter)30 b(18:)41 b(Random)30 b(Num)m(b)s(er)g(Generation)1798 b(217)390 299 y(2)435 266 y FB(31)528 299 y FI(\000)22 b FK(1,)36 b(Fishman20:)48 b FE(a)30 b FK(=)h(48271,)37 b FE(m)31 b FK(=)f(2)1957 266 y FB(31)2050 299 y FI(\000)23 b FK(1,)35 b(L'Ecuy)m(er:)47 b FE(a)31 b FK(=)g(40692,)37 b FE(m)30 b FK(=)h(2)3402 266 y FB(31)3495 299 y FI(\000)22 b FK(249,)390 408 y(W)-8 b(aterman:)42 b FE(a)25 b FK(=)g(1566083941,)35 b FE(m)25 b FK(=)g(2)1795 375 y FB(32)1866 408 y FK(.)3299 591 y([Generator])-3598 b Fv(gsl_rng_fishman2x)390 700 y FK(This)34 b(is)h(the)g(L'Ecuy)m(er{Fishman)g(random)f(n)m(um)m(b)s (er)f(generator.)55 b(It)35 b(is)g(tak)m(en)h(from)e(Kn)m(uth's)390 810 y FD(Semin)m(umerical)d(Algorithms)p FK(,)g(3rd)f(Ed.,)g(page)h (108.)42 b(Its)31 b(sequence)f(is,)1477 977 y FE(z)1519 991 y Fq(n)p FB(+1)1674 977 y FK(=)25 b(\()p FE(x)1857 991 y Fq(n)1923 977 y FI(\000)19 b FE(y)2058 991 y Fq(n)2103 977 y FK(\))c(mo)s(d)g FE(m)390 1144 y FK(with)29 b FE(m)c FK(=)g(2)842 1111 y FB(31)929 1144 y FI(\000)17 b FK(1.)41 b FE(x)1180 1158 y Fq(n)1254 1144 y FK(and)28 b FE(y)1474 1158 y Fq(n)1547 1144 y FK(are)i(giv)m(en)f(b)m(y)g(the)g FH(fishman20)d FK(and)j FH(lecuyer21)d FK(algorithms.)390 1254 y(The)k(seed)g(sp)s(eci\014es)g(the)h(initial)h(v)-5 b(alue,)31 b FE(x)1858 1268 y FB(1)1895 1254 y FK(.)3299 1436 y([Generator])-3598 b Fv(gsl_rng_coveyou)390 1546 y FK(This)26 b(is)h(the)h(Co)m(v)m(ey)m(ou)g(random)f(n)m(um)m(b)s(er)f (generator.)40 b(It)27 b(is)h(tak)m(en)g(from)e(Kn)m(uth's)h FD(Semin)m(umer-)390 1655 y(ical)32 b(Algorithms)p FK(,)f(3rd)f(Ed.,)g (Section)h(3.2.2.)43 b(Its)30 b(sequence)h(is,)1410 1823 y FE(x)1462 1837 y Fq(n)p FB(+1)1617 1823 y FK(=)25 b(\()p FE(x)1800 1837 y Fq(n)1845 1823 y FK(\()p FE(x)1932 1837 y Fq(n)1998 1823 y FK(+)20 b(1\)\))15 b(mo)s(d)h FE(m)390 1990 y FK(with)30 b FE(m)25 b FK(=)g(2)843 1957 y FB(32)914 1990 y FK(.)41 b(The)29 b(seed)i(sp)s(eci\014es)f(the)g(initial)i(v)-5 b(alue,)31 b FE(x)2447 2004 y FB(1)2484 1990 y FK(.)150 2221 y FJ(18.12)69 b(P)l(erformance)150 2380 y FK(The)43 b(follo)m(wing)i(table)f(sho)m(ws)g(the)g(relativ)m(e)h(p)s(erformance) e(of)h(a)g(selection)h(the)f(a)m(v)-5 b(ailable)46 b(random)150 2490 y(n)m(um)m(b)s(er)22 b(generators.)39 b(The)23 b(fastest)h(sim)m (ulation)h(qualit)m(y)f(generators)h(are)e FH(taus)p FK(,)h FH(gfsr4)e FK(and)h FH(mt19937)p FK(.)150 2599 y(The)31 b(generators)i(whic)m(h)e(o\013er)h(the)g(b)s(est)g (mathematically-pro)m(v)m(en)j(qualit)m(y)d(are)h(those)f(based)f(on)h (the)150 2709 y FC(ranlux)d FK(algorithm.)390 2843 y FH(1754)47 b(k)g(ints/sec,)189 b(870)46 b(k)i(doubles/sec,)c(taus)390 2952 y(1613)j(k)g(ints/sec,)189 b(855)46 b(k)i(doubles/sec,)c(gfsr4)390 3062 y(1370)j(k)g(ints/sec,)189 b(769)46 b(k)i(doubles/sec,)c(mt19937) 438 3172 y(565)j(k)g(ints/sec,)189 b(571)46 b(k)i(doubles/sec,)c (ranlxs0)438 3281 y(400)j(k)g(ints/sec,)189 b(405)46 b(k)i(doubles/sec,)c(ranlxs1)438 3391 y(490)j(k)g(ints/sec,)189 b(389)46 b(k)i(doubles/sec,)c(mrg)438 3500 y(407)j(k)g(ints/sec,)189 b(297)46 b(k)i(doubles/sec,)c(ranlux)438 3610 y(243)j(k)g(ints/sec,)189 b(254)46 b(k)i(doubles/sec,)c(ranlxd1)438 3720 y(251)j(k)g(ints/sec,) 189 b(253)46 b(k)i(doubles/sec,)c(ranlxs2)438 3829 y(238)j(k)g (ints/sec,)189 b(215)46 b(k)i(doubles/sec,)c(cmrg)438 3939 y(247)j(k)g(ints/sec,)189 b(198)46 b(k)i(doubles/sec,)c(ranlux389) 438 4048 y(141)j(k)g(ints/sec,)189 b(140)46 b(k)i(doubles/sec,)c (ranlxd2)150 4280 y FJ(18.13)69 b(Examples)150 4439 y FK(The)40 b(follo)m(wing)i(program)e(demonstrates)g(the)h(use)f(of)g(a) h(random)f(n)m(um)m(b)s(er)f(generator)i(to)g(pro)s(duce)150 4549 y(uniform)29 b(random)h(n)m(um)m(b)s(ers)f(in)h(the)g(range)h ([0.0,)h(1.0\),)390 4682 y FH(#include)46 b()390 4792 y(#include)g()390 5011 y(int)390 5121 y(main)h(\(void\))390 5230 y({)485 5340 y(const)g(gsl_rng_type)d (*)k(T;)p eop end %%Page: 218 236 TeXDict begin 218 235 bop 150 -116 a FK(Chapter)30 b(18:)41 b(Random)30 b(Num)m(b)s(er)g(Generation)1798 b(218)485 299 y FH(gsl_rng)46 b(*)i(r;)485 518 y(int)f(i,)h(n)f(=)g(10;)485 737 y(gsl_rng_env_setup\(\);)485 956 y(T)h(=)f(gsl_rng_default;)485 1066 y(r)h(=)f(gsl_rng_alloc)e(\(T\);)485 1285 y(for)i(\(i)h(=)f(0;)g (i)h(<)f(n;)g(i++\))581 1395 y({)676 1504 y(double)f(u)i(=)f (gsl_rng_uniform)d(\(r\);)676 1614 y(printf)i(\("\045.5f\\n",)f(u\);) 581 1724 y(})485 1943 y(gsl_rng_free)g(\(r\);)485 2162 y(return)i(0;)390 2271 y(})150 2408 y FK(Here)31 b(is)f(the)h(output)f (of)g(the)h(program,)390 2545 y FH($)47 b(./a.out)390 2655 y(0.99974)390 2765 y(0.16291)390 2874 y(0.28262)390 2984 y(0.94720)390 3093 y(0.23166)390 3203 y(0.48497)390 3313 y(0.95748)390 3422 y(0.74431)390 3532 y(0.54004)390 3641 y(0.73995)150 3778 y FK(The)31 b(n)m(um)m(b)s(ers)f(dep)s(end)g (on)h(the)h(seed)f(used)g(b)m(y)g(the)h(generator.)45 b(The)31 b(default)h(seed)g(can)f(b)s(e)g(c)m(hanged)150 3888 y(with)40 b(the)h FH(GSL_RNG_SEED)d FK(en)m(vironmen)m(t)j(v)-5 b(ariable)41 b(to)h(pro)s(duce)d(a)i(di\013eren)m(t)g(stream)g(of)g(n)m (um)m(b)s(ers.)150 3998 y(The)28 b(generator)h(itself)g(can)f(b)s(e)g (c)m(hanged)g(using)g(the)g(en)m(vironmen)m(t)h(v)-5 b(ariable)29 b FH(GSL_RNG_TYPE)p FK(.)36 b(Here)29 b(is)150 4107 y(the)35 b(output)f(of)h(the)g(program)g(using)f(a)h(seed)g(v)-5 b(alue)35 b(of)g(123)h(and)f(the)f(m)m(ultiple-recursiv)m(e)j (generator)150 4217 y FH(mrg)p FK(,)390 4354 y FH($)47 b(GSL_RNG_SEED=123)d(GSL_RNG_TYPE=mrg)f(./a.out)390 4463 y(0.33050)390 4573 y(0.86631)390 4682 y(0.32982)390 4792 y(0.67620)390 4902 y(0.53391)390 5011 y(0.06457)390 5121 y(0.16847)390 5230 y(0.70229)390 5340 y(0.04371)p eop end %%Page: 219 237 TeXDict begin 219 236 bop 150 -116 a FK(Chapter)30 b(18:)41 b(Random)30 b(Num)m(b)s(er)g(Generation)1798 b(219)390 299 y FH(0.86374)150 531 y FJ(18.14)69 b(References)46 b(and)e(F)-11 b(urther)45 b(Reading)150 691 y FK(The)35 b(sub)5 b(ject)34 b(of)i(random)e(n)m(um)m(b)s(er)g(generation)i(and)e (testing)j(is)e(review)m(ed)g(extensiv)m(ely)i(in)e(Kn)m(uth's)150 800 y FD(Semin)m(umerical)c(Algorithms)p FK(.)330 935 y(Donald)23 b(E.)f(Kn)m(uth,)i FD(The)d(Art)i(of)f(Computer)g (Programming:)37 b(Semin)m(umerical)23 b(Algorithms)j FK(\(V)-8 b(ol)330 1044 y(2,)31 b(3rd)f(Ed,)g(1997\),)j(Addison-W)-8 b(esley)g(,)32 b(ISBN)e(0201896842.)150 1204 y(F)-8 b(urther)30 b(information)h(is)f(a)m(v)-5 b(ailable)33 b(in)d(the)h(review)f(pap)s (er)f(written)i(b)m(y)f(Pierre)h(L'Ecuy)m(er,)330 1338 y(P)-8 b(.)34 b(L'Ecuy)m(er,)h(\\Random)f(Num)m(b)s(er)f(Generation",)k (Chapter)c(4)h(of)g(the)g(Handb)s(o)s(ok)f(on)g(Sim)m(ula-)330 1448 y(tion,)e(Jerry)f(Banks)g(Ed.,)g(Wiley)-8 b(,)33 b(1998,)f(93{137.)330 1582 y FH(http://www.iro.umontreal)o(.ca/)o(~lec) o(uye)o(r/pa)o(pers)o(.ht)o(ml)24 b FK(in)30 b(the)h(\014le)f FH(handsim.ps)p FK(.)150 1742 y(The)g(source)g(co)s(de)h(for)f(the)h FC(diehard)e FK(random)h(n)m(um)m(b)s(er)f(generator)i(tests)g(is)g (also)g(a)m(v)-5 b(ailable)33 b(online,)330 1876 y FD(DIEHARD)e(source) g(co)s(de)k FK(G.)c(Marsaglia,)330 2011 y FH(http://stat.fsu.edu/pub/)o (dieh)o(ard/)150 2170 y FK(A)f(comprehensiv)m(e)h(set)g(of)g(random)e (n)m(um)m(b)s(er)g(generator)j(tests)f(is)f(a)m(v)-5 b(ailable)33 b(from)d FC(nist)p FK(,)330 2305 y(NIST)h(Sp)s(ecial)i (Publication)g(800-22,)j(\\A)d(Statistical)i(T)-8 b(est)33 b(Suite)f(for)g(the)h(V)-8 b(alidation)34 b(of)f(Ran-)330 2414 y(dom)f(Num)m(b)s(er)e(Generators)j(and)e(Pseudo)h(Random)f(Num)m (b)s(er)g(Generators)i(for)e(Cryptographic)330 2524 y(Applications".) 330 2658 y FH(http://csrc.nist.gov/rng)o(/)150 2891 y FJ(18.15)69 b(Ac)l(kno)l(wledgemen)l(ts)150 3050 y FK(Thanks)39 b(to)i(Mak)m(oto)i(Matsumoto,)i(T)-8 b(akuji)40 b(Nishim)m(ura)g(and)g (Y)-8 b(oshiharu)40 b(Kurita)g(for)g(making)h(the)150 3160 y(source)d(co)s(de)h(to)g(their)f(generators)h(\(MT19937,)k (MM&TN;)c(TT800,)i(MM&YK\))e(a)m(v)-5 b(ailable)40 b(under)150 3269 y(the)26 b(GNU)g(General)g(Public)f(License.)40 b(Thanks)24 b(to)i(Martin)g(L)s(\177)-48 b(usc)m(her)25 b(for)h(pro)m(viding)f(notes)h(and)f(source)150 3379 y(co)s(de)31 b(for)f(the)g FC(ranlxs)f FK(and)h FC(ranlxd)e FK(generators.)p eop end %%Page: 220 238 TeXDict begin 220 237 bop 150 -116 a FK(Chapter)30 b(19:)41 b(Quasi-Random)30 b(Sequences)1934 b(220)150 299 y FG(19)80 b(Quasi-Random)54 b(Sequences)150 554 y FK(This)42 b(c)m(hapter)h (describ)s(es)f(functions)g(for)g(generating)i(quasi-random)e (sequences)h(in)g(arbitrary)f(di-)150 663 y(mensions.)47 b(A)33 b(quasi-random)f(sequence)h(progressiv)m(ely)g(co)m(v)m(ers)i(a) e FE(d)p FK(-dimensional)g(space)g(with)f(a)h(set)150 773 y(of)i(p)s(oin)m(ts)f(that)h(are)g(uniformly)e(distributed.)52 b(Quasi-random)34 b(sequences)h(are)g(also)g(kno)m(wn)f(as)h(lo)m(w-) 150 882 y(discrepancy)26 b(sequences.)39 b(The)25 b(quasi-random)h (sequence)g(generators)h(use)e(an)h(in)m(terface)h(that)g(is)f(simi-) 150 992 y(lar)e(to)g(the)g(in)m(terface)h(for)e(random)g(n)m(um)m(b)s (er)f(generators,)k(except)e(that)h(seeding)e(is)h(not)g(required|eac)m (h)150 1102 y(generator)32 b(pro)s(duces)d(a)h(single)h(sequence.)275 1243 y(The)e(functions)h(describ)s(ed)g(in)g(this)g(section)h(are)g (declared)g(in)f(the)h(header)f(\014le)g FH(gsl_qrng.h)p FK(.)150 1486 y FJ(19.1)68 b(Quasi-random)46 b(n)l(um)l(b)t(er)e (generator)j(initialization)3350 1702 y FK([F)-8 b(unction])-3599 b Fv(gsl_qrng)55 b(*)d(gsl_qrng_alloc)e Fu(\()p FD(const)31 b(gsl)p 1888 1702 28 4 v 41 w(qrng)p 2109 1702 V 39 w(t)m(yp)s(e)g(*)g Ft(T)p FD(,)g(unsigned)e(in)m(t)i Ft(d)p Fu(\))390 1811 y FK(This)19 b(function)h(returns)g(a)g(p)s(oin)m(ter)g(to)h(a)g (newly-created)h(instance)f(of)f(a)h(quasi-random)f(sequence)390 1921 y(generator)37 b(of)g(t)m(yp)s(e)f FD(T)42 b FK(and)36 b(dimension)g FD(d)p FK(.)57 b(If)36 b(there)g(is)h(insu\016cien)m(t)f (memory)g(to)h(create)h(the)390 2030 y(generator)f(then)f(the)h (function)f(returns)f(a)h(n)m(ull)h(p)s(oin)m(ter)f(and)f(the)i(error)f (handler)f(is)h(in)m(v)m(ok)m(ed)390 2140 y(with)30 b(an)g(error)g(co)s (de)h(of)f FH(GSL_ENOMEM)p FK(.)3350 2338 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_qrng_free)49 b Fu(\()p FD(gsl)p 1284 2338 V 41 w(qrng)30 b(*)g Ft(q)p Fu(\))390 2448 y FK(This)g(function)g (frees)g(all)h(the)g(memory)f(asso)s(ciated)i(with)e(the)h(generator)g FD(q)p FK(.)3350 2646 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_qrng_init)49 b Fu(\()p FD(gsl)p 1284 2646 V 41 w(qrng)30 b(*)g Ft(q)p Fu(\))390 2755 y FK(This)42 b(function)g (reinitializes)j(the)e(generator)h FD(q)h FK(to)e(its)g(starting)h(p)s (oin)m(t.)77 b(Note)44 b(that)g(quasi-)390 2865 y(random)30 b(sequences)g(do)g(not)h(use)f(a)h(seed)f(and)g(alw)m(a)m(ys)i(pro)s (duce)d(the)i(same)g(set)g(of)f(v)-5 b(alues.)150 3108 y FJ(19.2)68 b(Sampling)46 b(from)f(a)g(quasi-random)g(n)l(um)l(b)t(er) g(generator)3350 3324 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_qrng_get)c Fu(\()p FD(const)32 b(gsl)p 1418 3324 V 40 w(qrng)e(*)h Ft(q)p FD(,)g(double)f Ft(x)p Fo([])p Fu(\))390 3433 y FK(This)25 b(function)h(stores)g(the)g(next)g(p)s(oin) m(t)g(from)f(the)h(sequence)g(generator)i FD(q)f FK(in)f(the)g(arra)m (y)g FD(x)p FK(.)39 b(The)390 3543 y(space)28 b(a)m(v)-5 b(ailable)30 b(for)e FD(x)34 b FK(m)m(ust)27 b(matc)m(h)i(the)f (dimension)f(of)g(the)h(generator.)41 b(The)28 b(p)s(oin)m(t)f FD(x)34 b FK(will)28 b(lie)390 3652 y(in)33 b(the)g(range)h(0)d FE(<)f(x)1138 3666 y Fq(i)1195 3652 y FE(<)g FK(1)k(for)f(eac)m(h)h FE(x)1776 3666 y Fq(i)1804 3652 y FK(.)49 b(An)33 b(inline)h(v)m (ersion)f(of)h(this)f(function)g(is)g(used)g(when)390 3762 y FH(HAVE_INLINE)27 b FK(is)k(de\014ned.)150 4005 y FJ(19.3)68 b(Auxiliary)46 b(quasi-random)f(n)l(um)l(b)t(er)g (generator)h(functions)3350 4221 y FK([F)-8 b(unction])-3599 b Fv(const)54 b(char)f(*)g(gsl_qrng_name)c Fu(\()p FD(const)32 b(gsl)p 1941 4221 V 40 w(qrng)e(*)h Ft(q)p Fu(\))390 4330 y FK(This)f(function)g(returns)f(a)i(p)s(oin)m(ter)f(to)h(the)g (name)f(of)h(the)f(generator.)3350 4528 y([F)-8 b(unction])-3599 b Fv(size_t)54 b(gsl_qrng_size)c Fu(\()p FD(const)31 b(gsl)p 1627 4528 V 40 w(qrng)f(*)h Ft(q)p Fu(\))3350 4638 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(*)e(gsl_qrng_state)e Fu(\()p FD(const)31 b(gsl)p 1679 4638 V 41 w(qrng)e(*)i Ft(q)p Fu(\))390 4748 y FK(These)38 b(functions)g(return)f(a)h(p)s(oin) m(ter)g(to)h(the)g(state)g(of)f(generator)i FD(r)k FK(and)38 b(its)g(size.)65 b(Y)-8 b(ou)39 b(can)390 4857 y(use)28 b(this)h(information)g(to)g(access)h(the)f(state)h(directly)-8 b(.)41 b(F)-8 b(or)30 b(example,)g(the)f(follo)m(wing)h(co)s(de)f(will) 390 4967 y(write)i(the)f(state)i(of)e(a)h(generator)h(to)f(a)g(stream,) 630 5108 y FH(void)47 b(*)g(state)f(=)i(gsl_qrng_state)c(\(q\);)630 5218 y(size_t)i(n)i(=)f(gsl_qrng_size)d(\(q\);)630 5327 y(fwrite)i(\(state,)g(n,)h(1,)g(stream\);)p eop end %%Page: 221 239 TeXDict begin 221 238 bop 150 -116 a FK(Chapter)30 b(19:)41 b(Quasi-Random)30 b(Sequences)1934 b(221)150 166 y FJ(19.4)68 b(Sa)l(ving)46 b(and)e(restoring)i(quasi-random)g(n)l(um)l(b)t(er)e (generator)456 299 y(state)3350 508 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_qrng_memcpy)d Fu(\()p FD(gsl)p 1336 508 28 4 v 41 w(qrng)30 b(*)h Ft(dest)p FD(,)h(const)e(gsl)p 2271 508 V 41 w(qrng)g(*)h Ft(src)p Fu(\))390 618 y FK(This)37 b(function)g(copies)h(the)f(quasi-random)g(sequence)h(generator)h FD(src)j FK(in)m(to)d(the)e(pre-existing)390 727 y(generator)e FD(dest)p FK(,)h(making)e FD(dest)i FK(in)m(to)f(an)g(exact)g(cop)m(y)g (of)f FD(src)p FK(.)52 b(The)34 b(t)m(w)m(o)h(generators)h(m)m(ust)e(b) s(e)390 837 y(of)d(the)f(same)h(t)m(yp)s(e.)3350 1021 y([F)-8 b(unction])-3599 b Fv(gsl_qrng)55 b(*)d(gsl_qrng_clone)e Fu(\()p FD(const)31 b(gsl)p 1888 1021 V 41 w(qrng)f(*)g Ft(q)p Fu(\))390 1130 y FK(This)h(function)h(returns)f(a)h(p)s(oin)m (ter)g(to)h(a)g(newly)e(created)j(generator)f(whic)m(h)f(is)g(an)g (exact)h(cop)m(y)390 1240 y(of)e(the)f(generator)i FD(q)p FK(.)150 1472 y FJ(19.5)68 b(Quasi-random)46 b(n)l(um)l(b)t(er)e (generator)j(algorithms)150 1632 y FK(The)30 b(follo)m(wing)i (quasi-random)e(sequence)g(algorithms)i(are)e(a)m(v)-5 b(ailable,)3299 1816 y([Generator])-3598 b Fv(gsl_qrng_niederreiter_)q (2)390 1925 y FK(This)21 b(generator)i(uses)e(the)h(algorithm)h (describ)s(ed)e(in)g(Bratley)-8 b(,)26 b(F)-8 b(o)m(x,)25 b(Niederreiter,)g FD(A)m(CM)d(T)-8 b(rans.)390 2035 y(Mo)s(del.)41 b(Comp.)f(Sim.)g FK(2,)31 b(195)h(\(1992\).)43 b(It)31 b(is)f(v)-5 b(alid)31 b(up)e(to)i(12)g(dimensions.)3299 2219 y([Generator])-3598 b Fv(gsl_qrng_sobol)390 2328 y FK(This)25 b(generator)h(uses)g(the)f(Sob)s(ol)h(sequence)f(describ)s (ed)g(in)g(An)m(tono)m(v,)j(Saleev,)g FD(USSR)d(Comput.)390 2438 y(Maths.)41 b(Math.)g(Ph)m(ys.)g FK(19,)31 b(252)h(\(1980\).)43 b(It)31 b(is)f(v)-5 b(alid)31 b(up)e(to)i(40)g(dimensions.)3299 2622 y([Generator])-3598 b Fv(gsl_qrng_halton)3299 2732 y FK([Generator])g Fv(gsl_qrng_reversehalton)390 2841 y FK(These)28 b(generators)h(use)f(the)h(Halton)g(and)f(rev)m(erse)h (Halton)g(sequences)g(describ)s(ed)e(in)h(J.H.)h(Hal-)390 2951 y(ton,)40 b FD(Numerisc)m(he)e(Mathematik)45 b FK(2,)39 b(84-90)h(\(1960\))g(and)d(B.)h(V)-8 b(andew)m(o)s(est)m(yne)39 b(and)e(R.)h(Co)s(ols)390 3060 y FD(Computational)c(and)e(Applied)h (Mathematics)38 b FK(189,)e(1&2,)e(341-361)i(\(2006\).)51 b(They)32 b(are)i(v)-5 b(alid)390 3170 y(up)29 b(to)i(1229)i (dimensions.)150 3402 y FJ(19.6)68 b(Examples)150 3562 y FK(The)30 b(follo)m(wing)i(program)e(prin)m(ts)g(the)g(\014rst)g (1024)i(p)s(oin)m(ts)e(of)h(the)f(2-dimensional)i(Sob)s(ol)e(sequence.) 390 3696 y FH(#include)46 b()390 3806 y(#include)g ()390 4025 y(int)390 4134 y(main)h(\(void\))390 4244 y({)485 4354 y(int)g(i;)485 4463 y(gsl_qrng)f(*)h(q)h(=)f (gsl_qrng_alloc)d(\(gsl_qrng_sobol,)g(2\);)485 4682 y(for)j(\(i)h(=)f (0;)g(i)h(<)f(1024;)f(i++\))581 4792 y({)676 4902 y(double)g(v[2];)676 5011 y(gsl_qrng_get)f(\(q,)i(v\);)676 5121 y(printf)f(\("\045.5f)h (\045.5f\\n",)e(v[0],)h(v[1]\);)581 5230 y(})p eop end %%Page: 222 240 TeXDict begin 222 239 bop 150 -116 a FK(Chapter)30 b(19:)41 b(Quasi-Random)30 b(Sequences)1934 b(222)485 299 y FH(gsl_qrng_free)45 b(\(q\);)485 408 y(return)i(0;)390 518 y(})150 679 y FK(Here)31 b(is)f(the)h(output)f(from)g(the)g(program,)390 840 y FH($)47 b(./a.out)390 950 y(0.50000)f(0.50000)390 1060 y(0.75000)g(0.25000)390 1169 y(0.25000)g(0.75000)390 1279 y(0.37500)g(0.37500)390 1388 y(0.87500)g(0.87500)390 1498 y(0.62500)g(0.12500)390 1608 y(0.12500)g(0.62500)390 1717 y(....)150 1878 y FK(It)25 b(can)g(b)s(e)g(seen)g(that)g (successiv)m(e)i(p)s(oin)m(ts)d(progressiv)m(ely)i(\014ll-in)f(the)g (spaces)h(b)s(et)m(w)m(een)f(previous)g(p)s(oin)m(ts.)275 2034 y(The)31 b(follo)m(wing)j(plot)e(sho)m(ws)g(the)g(distribution)g (in)f(the)i(x-y)f(plane)g(of)g(the)g(\014rst)g(1024)h(p)s(oin)m(ts)f (from)150 2144 y(the)f(Sob)s(ol)f(sequence,)275 4420 y @beginspecial 50 @llx 50 @lly 302 @urx 302 @ury 2448 @rwi @setspecial %%BeginDocument: qrng.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: tmp.ps %%Creator: gnuplot 3.5 (pre 3.6) patchlevel beta 347 %%CreationDate: Tue Apr 17 17:18:33 2001 %%DocumentFonts: (atend) %%BoundingBox: 50 50 302 302 %%Orientation: Portrait %%EndComments /gnudict 120 dict def gnudict begin /Color false def /Solid false def 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def /LT1 { PL [4 dl 2 dl] 0 1 0 DL } def /LT2 { PL [2 dl 3 dl] 0 0 1 DL } def /LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def /LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def /LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def /LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def /LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def /LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def /Pnt { stroke [] 0 setdash gsave 1 setlinecap M 0 0 V stroke grestore } def /Dia { stroke [] 0 setdash 2 copy vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke Pnt } def /Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V currentpoint stroke M hpt neg vpt neg R hpt2 0 V stroke } def /Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke Pnt } def /Crs { stroke [] 0 setdash exch hpt sub exch vpt add M hpt2 vpt2 neg V currentpoint stroke M hpt2 neg 0 R hpt2 vpt2 V stroke } def /TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke Pnt } def /Star { 2 copy Pls Crs } def /BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath fill } def /TriUF { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath fill } def /TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke Pnt } def /TriDF { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath fill} def /DiaF { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath fill } def /Pent { stroke [] 0 setdash 2 copy gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore Pnt } def /PentF { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath fill grestore } def /Circle { stroke [] 0 setdash 2 copy hpt 0 360 arc stroke Pnt } def /CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def /C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def /C1 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill vpt 0 360 arc closepath } bind def /C2 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath } bind def /C3 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill vpt 0 360 arc closepath } bind def /C4 { BL [] 0 setdash 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc closepath } bind def /C5 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc } bind def /C6 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 270 arc closepath fill vpt 0 360 arc closepath } bind def /C7 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 270 arc closepath fill vpt 0 360 arc closepath } bind def /C8 { BL [] 0 setdash 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath } bind def /C9 { BL [] 0 setdash 2 copy moveto 2 copy vpt 270 450 arc closepath fill vpt 0 360 arc closepath } bind def /C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath } bind def /C11 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath } bind def /C12 { BL [] 0 setdash 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath } bind def /C13 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath } bind def /C14 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 360 arc closepath fill vpt 0 360 arc } bind def /C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill vpt 0 360 arc closepath } bind def /Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath } bind def /Square { dup Rec } bind def /Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def /S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def /S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def /S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def /S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def /S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def /S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def /S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill 2 copy vpt Square fill Bsquare } bind def /S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def /S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def /S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def /S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def /S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy vpt Square fill Bsquare } bind def /S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def /D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def /D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def /D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def /D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def /D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def /D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def /D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def /D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def /D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def /D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def /D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def /D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def /D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def /D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def /D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def /D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def /DiaE { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke } def /BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke } def /TriUE { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke } def /TriDE { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke } def /PentE { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore } def /CircE { stroke [] 0 setdash hpt 0 360 arc stroke } def /Opaque { gsave closepath 1 setgray fill grestore 0 setgray closepath } def /DiaW { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V Opaque stroke } def /BoxW { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V Opaque stroke } def /TriUW { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V Opaque stroke } def /TriDW { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V Opaque stroke } def /PentW { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat Opaque stroke grestore } def /CircW { stroke [] 0 setdash hpt 0 360 arc Opaque stroke } def /BoxFill { gsave Rec 1 setgray fill grestore } def end %%EndProlog gnudict begin gsave 50 50 translate 0.050 0.050 scale 0 setgray newpath (Helvetica) findfont 140 scalefont setfont 1.000 UL LTb 420 280 M 63 0 V 4529 0 R -63 0 V 336 280 M (0) Rshow 420 739 M 63 0 V 4529 0 R -63 0 V 336 739 M (0.1) Rshow 420 1198 M 63 0 V 4529 0 R -63 0 V -4613 0 R (0.2) Rshow 420 1658 M 63 0 V 4529 0 R -63 0 V -4613 0 R (0.3) Rshow 420 2117 M 63 0 V 4529 0 R -63 0 V -4613 0 R (0.4) Rshow 420 2576 M 63 0 V 4529 0 R -63 0 V -4613 0 R (0.5) Rshow 420 3035 M 63 0 V 4529 0 R -63 0 V -4613 0 R (0.6) Rshow 420 3494 M 63 0 V 4529 0 R -63 0 V -4613 0 R (0.7) Rshow 420 3954 M 63 0 V 4529 0 R -63 0 V -4613 0 R (0.8) Rshow 420 4413 M 63 0 V 4529 0 R -63 0 V -4613 0 R (0.9) Rshow 420 4872 M 63 0 V 4529 0 R -63 0 V -4613 0 R (1) Rshow 420 280 M 0 63 V 0 4529 R 0 -63 V 420 140 M (0) Cshow 879 280 M 0 63 V 0 4529 R 0 -63 V 879 140 M (0.1) Cshow 1338 280 M 0 63 V 0 4529 R 0 -63 V 0 -4669 R (0.2) Cshow 1798 280 M 0 63 V 0 4529 R 0 -63 V 0 -4669 R (0.3) Cshow 2257 280 M 0 63 V 0 4529 R 0 -63 V 0 -4669 R (0.4) Cshow 2716 280 M 0 63 V 0 4529 R 0 -63 V 0 -4669 R (0.5) Cshow 3175 280 M 0 63 V 0 4529 R 0 -63 V 0 -4669 R (0.6) Cshow 3634 280 M 0 63 V 0 4529 R 0 -63 V 0 -4669 R (0.7) Cshow 4094 280 M 0 63 V 0 4529 R 0 -63 V 0 -4669 R (0.8) Cshow 4553 280 M 0 63 V 0 4529 R 0 -63 V 0 -4669 R (0.9) Cshow 5012 280 M 0 63 V 0 4529 R 0 -63 V 0 -4669 R (1) Cshow 1.000 UL LTb 420 280 M 4592 0 V 0 4592 V -4592 0 V 420 280 L 1.000 UP 1.000 UL LT0 2716 2576 Pls 3864 1428 Pls 1568 3724 Pls 2142 2002 Pls 4438 4298 Pls 3290 854 Pls 994 3150 Pls 1281 1715 Pls 3577 4011 Pls 4725 567 Pls 2429 2863 Pls 1855 1141 Pls 4151 3437 Pls 3003 2289 Pls 707 4585 Pls 851 2433 Pls 3147 4729 Pls 4295 1285 Pls 1999 3581 Pls 2573 711 Pls 4869 3007 Pls 3721 1859 Pls 1425 4155 Pls 1138 998 Pls 3434 3294 Pls 4582 2146 Pls 2286 4442 Pls 1712 1572 Pls 4008 3868 Pls 2860 424 Pls 564 2720 Pls 635 1500 Pls 2931 3796 Pls 4079 352 Pls 1783 2648 Pls 2357 926 Pls 4653 3222 Pls 3505 2074 Pls 1209 4370 Pls 1496 639 Pls 3792 2935 Pls 4940 1787 Pls 2644 4083 Pls 2070 2361 Pls 4366 4657 Pls 3218 1213 Pls 922 3509 Pls 779 1356 Pls 3075 3652 Pls 4223 2504 Pls 1927 4800 Pls 2501 1930 Pls 4797 4226 Pls 3649 782 Pls 1353 3078 Pls 1066 2217 Pls 3362 4513 Pls 4510 1069 Pls 2214 3365 Pls 1640 495 Pls 3936 2791 Pls 2788 1643 Pls 492 3939 Pls 528 2110 Pls 2824 4406 Pls 3972 962 Pls 1676 3258 Pls 2250 388 Pls 4546 2684 Pls 3398 1536 Pls 1102 3832 Pls 1389 1249 Pls 3685 3545 Pls 4833 2397 Pls 2537 4693 Pls 1963 1823 Pls 4259 4119 Pls 3111 675 Pls 815 2971 Pls 958 818 Pls 3254 3114 Pls 4402 1966 Pls 2106 4262 Pls 2680 2540 Pls 4976 4836 Pls 3828 1392 Pls 1532 3688 Pls 1245 1679 Pls 3541 3975 Pls 4689 531 Pls 2393 2827 Pls 1819 1105 Pls 4115 3401 Pls 2967 2253 Pls 671 4549 Pls 599 890 Pls 2895 3186 Pls 4043 2038 Pls 1747 4334 Pls 2321 1464 Pls 4617 3760 Pls 3469 316 Pls 1173 2612 Pls 1460 2325 Pls 3756 4621 Pls 4904 1177 Pls 2608 3473 Pls 2034 603 Pls 4330 2899 Pls 3182 1751 Pls 886 4047 Pls 743 1894 Pls 3039 4190 Pls 4187 746 Pls 1891 3042 Pls 2465 1320 Pls 4761 3616 Pls 3613 2468 Pls 1317 4764 Pls 1030 459 Pls 3326 2755 Pls 4474 1607 Pls 2178 3903 Pls 1604 2181 Pls 3900 4477 Pls 2752 1033 Pls 456 3329 Pls 474 1805 Pls 2770 4101 Pls 3918 657 Pls 1622 2953 Pls 2196 1231 Pls 4492 3527 Pls 3344 2379 Pls 1048 4675 Pls 1335 370 Pls 3631 2666 Pls 4779 1518 Pls 2483 3814 Pls 1909 2092 Pls 4205 4388 Pls 3057 944 Pls 761 3240 Pls 904 1087 Pls 3200 3383 Pls 4348 2235 Pls 2052 4531 Pls 2626 1661 Pls 4922 3957 Pls 3774 513 Pls 1478 2809 Pls 1191 2522 Pls 3487 4818 Pls 4635 1374 Pls 2339 3670 Pls 1765 800 Pls 4061 3096 Pls 2913 1948 Pls 617 4244 Pls 689 585 Pls 2985 2881 Pls 4133 1733 Pls 1837 4029 Pls 2411 2307 Pls 4707 4603 Pls 3559 1159 Pls 1263 3455 Pls 1550 1446 Pls 3846 3742 Pls 4994 298 Pls 2698 2594 Pls 2124 872 Pls 4420 3168 Pls 3272 2020 Pls 976 4316 Pls 833 2163 Pls 3129 4459 Pls 4277 1015 Pls 1981 3311 Pls 2555 441 Pls 4851 2737 Pls 3703 1589 Pls 1407 3885 Pls 1120 1302 Pls 3416 3598 Pls 4564 2450 Pls 2268 4746 Pls 1694 1876 Pls 3990 4172 Pls 2842 728 Pls 546 3024 Pls 510 1195 Pls 2806 3491 Pls 3954 2343 Pls 1658 4639 Pls 2232 1769 Pls 4528 4065 Pls 3380 621 Pls 1084 2917 Pls 1371 2056 Pls 3667 4352 Pls 4815 908 Pls 2519 3204 Pls 1945 334 Pls 4241 2630 Pls 3093 1482 Pls 797 3778 Pls 940 1625 Pls 3236 3921 Pls 4384 477 Pls 2088 2773 Pls 2662 1051 Pls 4958 3347 Pls 3810 2199 Pls 1514 4495 Pls 1227 764 Pls 3523 3060 Pls 4671 1912 Pls 2375 4208 Pls 1801 2486 Pls 4097 4782 Pls 2949 1338 Pls 653 3634 Pls 581 2415 Pls 2877 4711 Pls 4025 1267 Pls 1729 3563 Pls 2303 693 Pls 4599 2989 Pls 3451 1841 Pls 1155 4137 Pls 1442 980 Pls 3738 3276 Pls 4886 2128 Pls 2590 4424 Pls 2016 1554 Pls 4312 3850 Pls 3164 406 Pls 868 2702 Pls 725 549 Pls 3021 2845 Pls 4169 1697 Pls 1873 3993 Pls 2447 2271 Pls 4743 4567 Pls 3595 1123 Pls 1299 3419 Pls 1012 1984 Pls 3308 4280 Pls 4456 836 Pls 2160 3132 Pls 1586 1410 Pls 3882 3706 Pls 2734 2558 Pls 438 4854 Pls 447 2567 Pls 2743 4863 Pls 3891 1419 Pls 1595 3715 Pls 2169 845 Pls 4465 3141 Pls 3317 1993 Pls 1021 4289 Pls 1308 1132 Pls 3604 3428 Pls 4752 2280 Pls 2456 4576 Pls 1882 1706 Pls 4178 4002 Pls 3030 558 Pls 734 2854 Pls 877 415 Pls 3173 2711 Pls 4321 1563 Pls 2025 3859 Pls 2599 2137 Pls 4895 4433 Pls 3747 989 Pls 1451 3285 Pls 1164 1850 Pls 3460 4146 Pls 4608 702 Pls 2312 2998 Pls 1738 1276 Pls 4034 3572 Pls 2886 2424 Pls 590 4720 Pls 662 1347 Pls 2958 3643 Pls 4106 2495 Pls 1810 4791 Pls 2384 1921 Pls 4680 4217 Pls 3532 773 Pls 1236 3069 Pls 1523 2208 Pls 3819 4504 Pls 4967 1060 Pls 2671 3356 Pls 2097 486 Pls 4393 2782 Pls 3245 1634 Pls 949 3930 Pls 806 1491 Pls 3102 3787 Pls 4250 343 Pls 1954 2639 Pls 2528 917 Pls 4824 3213 Pls 3676 2065 Pls 1380 4361 Pls 1093 630 Pls 3389 2926 Pls 4537 1778 Pls 2241 4074 Pls 1667 2352 Pls 3963 4648 Pls 2815 1204 Pls 519 3500 Pls 555 737 Pls 2851 3033 Pls 3999 1885 Pls 1703 4181 Pls 2277 2459 Pls 4573 4755 Pls 3425 1311 Pls 1129 3607 Pls 1416 1598 Pls 3712 3894 Pls 4860 450 Pls 2564 2746 Pls 1990 1024 Pls 4286 3320 Pls 3138 2172 Pls 842 4468 Pls 985 2029 Pls 3281 4325 Pls 4429 881 Pls 2133 3177 Pls 2707 307 Pls 5003 2603 Pls 3855 1455 Pls 1559 3751 Pls 1272 1168 Pls 3568 3464 Pls 4716 2316 Pls 2420 4612 Pls 1846 1742 Pls 4142 4038 Pls 2994 594 Pls 698 2890 Pls 626 1957 Pls 2922 4253 Pls 4070 809 Pls 1774 3105 Pls 2348 1383 Pls 4644 3679 Pls 3496 2531 Pls 1200 4827 Pls 1487 522 Pls 3783 2818 Pls 4931 1670 Pls 2635 3966 Pls 2061 2244 Pls 4357 4540 Pls 3209 1096 Pls 913 3392 Pls 770 953 Pls 3066 3249 Pls 4214 2101 Pls 1918 4397 Pls 2492 1527 Pls 4788 3823 Pls 3640 379 Pls 1344 2675 Pls 1057 2388 Pls 3353 4684 Pls 4501 1240 Pls 2205 3536 Pls 1631 666 Pls 3927 2962 Pls 2779 1814 Pls 483 4110 Pls 465 1042 Pls 2761 3338 Pls 3909 2190 Pls 1613 4486 Pls 2187 1616 Pls 4483 3912 Pls 3335 468 Pls 1039 2764 Pls 1326 2477 Pls 3622 4773 Pls 4770 1329 Pls 2474 3625 Pls 1900 755 Pls 4196 3051 Pls 3048 1903 Pls 752 4199 Pls 895 1760 Pls 3191 4056 Pls 4339 612 Pls 2043 2908 Pls 2617 1186 Pls 4913 3482 Pls 3765 2334 Pls 1469 4630 Pls 1182 325 Pls 3478 2621 Pls 4626 1473 Pls 2330 3769 Pls 1756 2047 Pls 4052 4343 Pls 2904 899 Pls 608 3195 Pls 680 2262 Pls 2976 4558 Pls 4124 1114 Pls 1828 3410 Pls 2402 540 Pls 4698 2836 Pls 3550 1688 Pls 1254 3984 Pls 1541 1401 Pls 3837 3697 Pls 4985 2549 Pls 2689 4845 Pls 2115 1975 Pls 4411 4271 Pls 3263 827 Pls 967 3123 Pls 824 684 Pls 3120 2980 Pls 4268 1832 Pls 1972 4128 Pls 2546 2406 Pls 4842 4702 Pls 3694 1258 Pls 1398 3554 Pls 1111 1545 Pls 3407 3841 Pls 4555 397 Pls 2259 2693 Pls 1685 971 Pls 3981 3267 Pls 2833 2119 Pls 537 4415 Pls 501 1652 Pls 2797 3948 Pls 3945 504 Pls 1649 2800 Pls 2223 1078 Pls 4519 3374 Pls 3371 2226 Pls 1075 4522 Pls 1362 791 Pls 3658 3087 Pls 4806 1939 Pls 2510 4235 Pls 1936 2513 Pls 4232 4809 Pls 3084 1365 Pls 788 3661 Pls 931 1222 Pls 3227 3518 Pls 4375 2370 Pls 2079 4666 Pls 2653 1796 Pls 4949 4092 Pls 3801 648 Pls 1505 2944 Pls 1218 2083 Pls 3514 4379 Pls 4662 935 Pls 2366 3231 Pls 1792 361 Pls 4088 2657 Pls 2940 1509 Pls 644 3805 Pls 572 432 Pls 2868 2728 Pls 4016 1580 Pls 1720 3876 Pls 2294 2154 Pls 4590 4450 Pls 3442 1006 Pls 1146 3302 Pls 1433 1867 Pls 3729 4163 Pls 4877 719 Pls 2581 3015 Pls 2007 1293 Pls 4303 3589 Pls 3155 2441 Pls 859 4737 Pls 716 2298 Pls 3012 4594 Pls 4160 1150 Pls 1864 3446 Pls 2438 576 Pls 4734 2872 Pls 3586 1724 Pls 1290 4020 Pls 1003 863 Pls 3299 3159 Pls 4447 2011 Pls 2151 4307 Pls 1577 1437 Pls 3873 3733 Pls 2725 289 Pls 429 2585 Pls 433 1433 Pls 2729 3729 Pls 3877 285 Pls 1581 2581 Pls 2155 859 Pls 4451 3155 Pls 3303 2007 Pls 1007 4303 Pls 1294 572 Pls 3590 2868 Pls 4738 1720 Pls 2442 4016 Pls 1868 2294 Pls 4164 4590 Pls 3016 1146 Pls 720 3442 Pls 864 1289 Pls 3160 3585 Pls 4308 2437 Pls 2012 4733 Pls 2586 1863 Pls 4882 4159 Pls 3734 715 Pls 1438 3011 Pls 1151 2150 Pls 3447 4446 Pls 4595 1002 Pls 2299 3298 Pls 1725 428 Pls 4021 2724 Pls 2873 1576 Pls 577 3872 Pls 649 356 Pls 2945 2652 Pls 4093 1504 Pls 1797 3800 Pls 2371 2078 Pls 4667 4374 Pls 3519 930 Pls 1223 3226 Pls 1510 1791 Pls 3806 4087 Pls 4954 643 Pls 2658 2939 Pls 2084 1217 Pls 4380 3513 Pls 3232 2365 Pls 936 4661 Pls 792 2509 Pls 3088 4805 Pls 4236 1361 Pls 1940 3657 Pls 2514 787 Pls 4810 3083 Pls 3662 1935 Pls 1366 4231 Pls 1079 1074 Pls 3375 3370 Pls 4523 2222 Pls 2227 4518 Pls 1653 1648 Pls 3949 3944 Pls 2801 500 Pls 505 2796 Pls 541 966 Pls 2837 3262 Pls 3985 2114 Pls 1689 4410 Pls 2263 1540 Pls 4559 3836 Pls 3411 392 Pls 1115 2688 Pls 1402 2401 Pls 3698 4697 Pls 4846 1253 Pls 2550 3549 Pls 1976 679 Pls 4272 2975 Pls 3124 1827 Pls 828 4123 Pls 972 1971 Pls 3268 4267 Pls 4416 823 Pls 2120 3119 Pls 2694 1397 Pls 4990 3693 Pls 3842 2545 Pls 1546 4841 Pls 1259 536 Pls 3555 2832 Pls 4703 1684 Pls 2407 3980 Pls 1833 2258 Pls 4129 4554 Pls 2981 1110 Pls 685 3406 Pls 613 2042 Pls 2909 4338 Pls 4057 894 Pls 1761 3190 Pls 2335 320 Pls 4631 2616 Pls 3483 1468 Pls 1187 3764 Pls 1474 1181 Pls 3770 3477 Pls 4918 2329 Pls 2622 4625 Pls 2048 1755 Pls 4344 4051 Pls 3196 607 Pls 900 2903 Pls 756 751 Pls 3052 3047 Pls 4200 1899 Pls 1904 4195 Pls 2478 2473 Pls 4774 4769 Pls 3626 1325 Pls 1330 3621 Pls 1043 1612 Pls 3339 3908 Pls 4487 464 Pls 2191 2760 Pls 1617 1038 Pls 3913 3334 Pls 2765 2186 Pls 469 4482 Pls 487 661 Pls 2783 2957 Pls 3931 1809 Pls 1635 4105 Pls 2209 2383 Pls 4505 4679 Pls 3357 1235 Pls 1061 3531 Pls 1348 1522 Pls 3644 3818 Pls 4792 374 Pls 2496 2670 Pls 1922 948 Pls 4218 3244 Pls 3070 2096 Pls 774 4392 Pls 918 2240 Pls 3214 4536 Pls 4362 1092 Pls 2066 3388 Pls 2640 518 Pls 4936 2814 Pls 3788 1666 Pls 1492 3962 Pls 1205 1379 Pls 3501 3675 Pls 4649 2527 Pls 2353 4823 Pls 1779 1953 Pls 4075 4249 Pls 2927 805 Pls 631 3101 Pls 702 1737 Pls 2998 4033 Pls 4146 589 Pls 1850 2885 Pls 2424 1163 Pls 4720 3459 Pls 3572 2311 Pls 1276 4607 Pls 1563 302 Pls 3859 2598 Pls 5007 1450 Pls 2711 3746 Pls 2137 2024 Pls 4433 4320 Pls 3285 876 Pls 989 3172 Pls 846 1020 Pls 3142 3316 Pls 4290 2168 Pls 1994 4464 Pls 2568 1594 Pls 4864 3890 Pls 3716 446 Pls 1420 2742 Pls 1133 2455 Pls 3429 4751 Pls 4577 1307 Pls 2281 3603 Pls 1707 733 Pls 4003 3029 Pls 2855 1881 Pls 559 4177 Pls 523 2347 Pls 2819 4643 Pls 3967 1199 Pls 1671 3495 Pls 2245 625 Pls 4541 2921 Pls 3393 1773 Pls 1097 4069 Pls 1384 912 Pls 3680 3208 Pls 4828 2060 Pls 2532 4356 Pls 1958 1486 Pls 4254 3782 Pls 3106 338 Pls 810 2634 Pls 954 482 Pls 3250 2778 Pls 4398 1630 Pls 2102 3926 Pls 2676 2204 Pls 4972 4500 Pls 3824 1056 Pls 1528 3352 Pls 1241 1917 Pls 3537 4213 Pls 4685 769 Pls 2389 3065 Pls 1815 1343 Pls 4111 3639 Pls 2963 2491 Pls 667 4787 Pls 595 1271 Pls 2891 3567 Pls 4039 2419 Pls 1743 4715 Pls 2317 1845 Pls 4613 4141 Pls 3465 697 Pls 1169 2993 Pls 1456 2132 Pls 3752 4428 Pls 4900 984 Pls 2604 3280 Pls 2030 410 Pls 4326 2706 Pls 3178 1558 Pls 882 3854 Pls 738 1702 Pls 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3092 Pls 1931 1370 Pls 4227 3666 Pls 3079 2518 Pls 783 4814 Pls 927 2374 Pls 3223 4670 Pls 4371 1226 Pls 2075 3522 Pls 2649 652 Pls 4945 2948 Pls 3797 1800 Pls 1501 4096 Pls 1214 939 Pls 3510 3235 Pls 4658 2087 Pls 2362 4383 Pls 1788 1513 Pls 4084 3809 Pls 2936 365 Pls 640 2661 Pls 568 1585 Pls 2864 3881 Pls 4012 437 Pls 1716 2733 Pls 2290 1011 Pls 4586 3307 Pls 3438 2159 Pls 1142 4455 Pls 1429 724 Pls 3725 3020 Pls 4873 1872 Pls 2577 4168 Pls 2003 2446 Pls 4299 4742 Pls 3151 1298 Pls 855 3594 Pls 712 1154 Pls 3008 3450 Pls 4156 2302 Pls 1860 4598 Pls 2434 1728 Pls 4730 4024 Pls 3582 580 Pls 1286 2876 Pls 999 2015 Pls 3295 4311 Pls 4443 867 Pls 2147 3163 Pls 1573 293 Pls 3869 2589 Pls 2721 1441 Pls 425 3737 Pls 427 2009 Pls stroke grestore end showpage %%Trailer %%DocumentFonts: Helvetica %%EndDocument @endspecial 1241 4689 a(Distribution)h(of)f(the)h(\014rst)f(1024)i(p)s (oin)m(ts)1182 4798 y(from)d(the)i(quasi-random)f(Sob)s(ol)g(sequence) 150 5071 y FJ(19.7)68 b(References)150 5230 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FK(These)f(functions)g(compute) h(the)g(cum)m(ulativ)m(e)h(distribution)e(functions)g FE(P)13 b FK(\()p FE(x)p FK(\),)31 b FE(Q)p FK(\()p FE(x)p FK(\))f(and)f(their)390 4757 y(in)m(v)m(erses)i(for)f(the)h(Laplace)g (distribution)f(with)g(width)g FD(a)p FK(.)p eop end %%Page: 234 252 TeXDict begin 234 251 bop 150 -116 a FK(Chapter)30 b(20:)41 b(Random)30 b(Num)m(b)s(er)g(Distributions)1717 b(234)150 299 y FJ(20.8)68 b(The)45 b(Exp)t(onen)l(tial)h(P)l(o)l(w)l(er)g (Distribution)3350 508 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_ran_exppow)c Fu(\()p FD(const)31 b(gsl)p 1679 508 28 4 v 41 w(rng)e(*)i Ft(r)p FD(,)g(double)f Ft(a)p FD(,)h(double)f Ft(b)p Fu(\))390 618 y FK(This)d(function)h (returns)f(a)i(random)e(v)-5 b(ariate)29 b(from)f(the)g(exp)s(onen)m (tial)i(p)s(o)m(w)m(er)e(distribution)f(with)390 727 y(scale)32 b(parameter)f FD(a)f FK(and)g(exp)s(onen)m(t)g FD(b)p FK(.)41 b(The)29 b(distribution)h(is,)1180 932 y FE(p)p FK(\()p FE(x)p FK(\))p FE(dx)c FK(=)1810 871 y(1)p 1579 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20 -11 V 20 -10 V 20 -11 V 21 -10 V 20 -11 V 20 -11 V 20 -11 V 21 -12 V 20 -11 V 20 -12 V 20 -11 V 21 -12 V 20 -12 V 20 -12 V 20 -13 V 20 -12 V 21 -13 V 20 -12 V 20 -13 V 20 -13 V 21 -13 V 20 -14 V 20 -13 V 20 -14 V 21 -14 V 20 -14 V 20 -14 V 20 -14 V 20 -14 V 21 -15 V 20 -14 V 20 -15 V 20 -15 V 21 -15 V 20 -15 V 20 -15 V 20 -16 V 21 -16 V 20 -15 V 20 -16 V 20 -16 V 20 -16 V 21 -17 V 20 -16 V 20 -17 V 20 -17 V 21 -17 V 20 -17 V 20 -17 V 20 -17 V 21 -18 V 20 -18 V 20 -17 V 20 -18 V 20 -18 V 21 -19 V 20 -18 V 20 -19 V 20 -18 V 21 -19 V 20 -19 V 20 -19 V 20 -19 V 21 -20 V 20 -19 V 20 -20 V 20 -20 V 20 -20 V 21 -20 V 20 -20 V 20 -21 V 20 -20 V 21 -21 V 20 -21 V 20 -21 V 20 -21 V 21 -21 V 20 -21 V 20 -22 V stroke LT1 LTb LT1 6077 4581 M 543 0 V 811 631 M 20 0 V 20 0 V 21 0 V 20 0 V 20 0 V 20 0 V 21 0 V 20 0 V 20 0 V 20 0 V 21 0 V 20 0 V 20 0 V 20 0 V 20 1 V 21 0 V 20 0 V 20 0 V 20 0 V 21 0 V 20 0 V 20 1 V 20 0 V 21 0 V 20 1 V 20 0 V 20 0 V 20 1 V 21 0 V 20 0 V 20 1 V 20 0 V 21 1 V 20 0 V 20 1 V 20 1 V 21 0 V 20 1 V 20 1 V 20 0 V 20 1 V 21 1 V 20 1 V 20 1 V 20 1 V 21 1 V 20 1 V 20 1 V 20 1 V 21 1 V 20 1 V 20 2 V 20 1 V 20 1 V 21 2 V 20 1 V 20 2 V 20 1 V 21 2 V 20 2 V 20 2 V 20 1 V 21 2 V 20 2 V 20 2 V 20 2 V 20 3 V 21 2 V 20 2 V 20 2 V 20 3 V 21 2 V 20 3 V 20 2 V 20 3 V 21 3 V 20 3 V 20 3 V 20 3 V 20 3 V 21 3 V 20 3 V 20 3 V 20 4 V 21 3 V 20 4 V 20 3 V 20 4 V 21 4 V 20 4 V 20 4 V 20 4 V 20 4 V 21 4 V 20 4 V 20 5 V 20 4 V 21 5 V 20 5 V 20 4 V 20 5 V 21 5 V 2895 807 L 20 5 V 20 6 V 20 5 V 21 6 V 20 5 V 20 6 V 20 6 V 21 6 V 20 6 V 20 6 V 20 6 V 21 6 V 20 7 V 20 6 V 20 7 V 20 7 V 21 7 V 20 7 V 20 7 V 20 7 V 21 8 V 20 7 V 20 8 V 20 8 V 21 7 V 20 8 V 20 8 V 20 9 V 20 8 V 21 9 V 20 8 V 20 9 V 20 9 V 21 9 V 20 9 V 20 9 V 20 10 V 21 9 V 20 10 V 20 10 V 20 10 V 20 10 V 21 10 V 20 11 V 20 10 V 20 11 V 21 11 V 20 11 V 20 11 V 20 11 V 21 11 V 20 12 V 20 12 V 20 11 V 20 12 V 21 13 V 20 12 V 20 12 V 20 13 V 21 13 V 20 13 V 20 13 V 20 13 V 21 13 V 20 14 V 20 14 V 20 14 V 20 14 V 21 14 V 20 14 V 20 15 V 20 15 V 21 15 V 20 15 V 20 15 V 20 15 V 21 16 V 20 16 V 20 16 V 20 16 V 20 16 V 21 17 V 20 16 V 20 17 V 20 17 V 21 17 V 20 18 V 20 17 V 20 18 V 21 18 V 20 18 V 20 18 V 20 19 V 20 19 V 21 18 V 20 20 V 20 19 V 20 19 V 21 20 V 20 20 V 20 20 V 20 20 V 21 20 V 20 21 V 5019 2083 L 20 21 V 20 21 V 21 22 V 20 21 V 20 22 V 20 22 V 21 23 V 20 22 V 20 23 V 20 23 V 21 23 V 20 23 V 20 24 V 20 23 V 20 24 V 21 24 V 20 25 V 20 24 V 20 25 V 21 25 V 20 26 V 20 25 V 20 26 V 21 26 V 20 26 V 20 26 V 20 27 V 20 27 V 21 27 V 20 27 V 20 28 V 20 27 V 21 28 V 20 29 V 20 28 V 20 29 V 21 29 V 20 29 V 20 29 V 20 30 V 20 30 V 21 30 V 20 30 V 20 31 V 20 31 V 21 31 V 20 31 V 20 32 V 20 32 V 21 32 V 20 32 V 20 33 V 20 33 V 20 33 V 21 33 V 20 34 V 20 34 V 20 34 V 21 34 V 20 35 V 20 35 V 20 35 V 21 35 V 20 36 V 20 36 V 20 36 V 20 37 V 21 36 V 20 37 V 20 38 V 20 37 V 21 38 V 20 38 V 20 38 V 20 39 V 21 39 V 20 39 V 20 40 V 20 39 V 20 40 V 21 41 V 20 40 V 20 41 V 20 41 V 21 42 V 20 41 V 20 42 V 20 42 V 21 43 V 20 43 V 20 43 V stroke LT2 LTb LT2 6077 4381 M 543 0 V 811 4944 M 20 -43 V 20 -43 V 21 -43 V 20 -42 V 20 -42 V 20 -41 V 21 -42 V 20 -41 V 20 -41 V 20 -40 V 21 -41 V 20 -40 V 20 -39 V 20 -40 V 20 -39 V 21 -39 V 20 -39 V 20 -38 V 20 -38 V 21 -38 V 20 -37 V 20 -38 V 20 -37 V 21 -36 V 20 -37 V 20 -36 V 20 -36 V 20 -36 V 21 -35 V 20 -35 V 20 -35 V 20 -35 V 21 -34 V 20 -34 V 20 -34 V 20 -34 V 21 -33 V 20 -33 V 20 -33 V 20 -33 V 20 -32 V 21 -32 V 20 -32 V 20 -32 V 20 -31 V 21 -31 V 20 -31 V 20 -31 V 20 -30 V 21 -30 V 20 -30 V 20 -30 V 20 -29 V 20 -29 V 21 -29 V 20 -29 V 20 -28 V 20 -29 V 21 -28 V 20 -27 V 20 -28 V 20 -27 V 21 -27 V 20 -27 V 20 -27 V 20 -26 V 20 -26 V 21 -26 V 20 -26 V 20 -25 V 20 -26 V 21 -25 V 20 -25 V 20 -24 V 20 -25 V 21 -24 V 20 -24 V 20 -23 V 20 -24 V 20 -23 V 21 -23 V 20 -23 V 20 -23 V 20 -22 V 21 -23 V 20 -22 V 20 -22 V 20 -21 V 21 -22 V 20 -21 V 20 -21 V 20 -21 V 20 -21 V 21 -20 V 20 -20 V 20 -20 V 20 -20 V 21 -20 V 20 -19 V 20 -19 V 20 -20 V 21 -18 V 2895 1846 L 20 -19 V 20 -18 V 20 -18 V 21 -18 V 20 -18 V 20 -17 V 20 -18 V 21 -17 V 20 -17 V 20 -17 V 20 -16 V 21 -17 V 20 -16 V 20 -16 V 20 -16 V 20 -16 V 21 -16 V 20 -15 V 20 -15 V 20 -15 V 21 -15 V 20 -15 V 20 -15 V 20 -14 V 21 -14 V 20 -14 V 20 -14 V 20 -14 V 20 -14 V 21 -13 V 20 -13 V 20 -13 V 20 -13 V 21 -13 V 20 -13 V 20 -12 V 20 -12 V 21 -13 V 20 -12 V 20 -11 V 20 -12 V 20 -12 V 21 -11 V 20 -11 V 20 -11 V 20 -11 V 21 -11 V 20 -11 V 20 -10 V 20 -11 V 21 -10 V 20 -10 V 20 -10 V 20 -10 V 20 -10 V 21 -9 V 20 -10 V 20 -9 V 20 -9 V 21 -9 V 20 -9 V 20 -9 V 20 -8 V 21 -9 V 20 -8 V 20 -9 V 20 -8 V 20 -8 V 21 -7 V 20 -8 V 20 -8 V 20 -7 V 21 -8 V 20 -7 V 20 -7 V 20 -7 V 21 -7 V 20 -7 V 20 -7 V 20 -6 V 20 -7 V 21 -6 V 20 -6 V 20 -6 V 20 -6 V 21 -6 V 20 -6 V 20 -6 V 20 -5 V 21 -6 V 20 -5 V 20 -6 V 20 -5 V 20 -5 V 21 -5 V 20 -5 V 20 -4 V 20 -5 V 21 -5 V 20 -4 V 20 -5 V 20 -4 V 21 -4 V 20 -4 V 5019 753 L 20 -4 V 20 -4 V 21 -4 V 20 -4 V 20 -3 V 20 -4 V 21 -3 V 20 -4 V 20 -3 V 20 -3 V 21 -3 V 20 -3 V 20 -3 V 20 -3 V 20 -3 V 21 -3 V 20 -3 V 20 -2 V 20 -3 V 21 -2 V 20 -3 V 20 -2 V 20 -2 V 21 -2 V 20 -3 V 20 -2 V 20 -2 V 20 -2 V 21 -2 V 20 -1 V 20 -2 V 20 -2 V 21 -2 V 20 -1 V 20 -2 V 20 -1 V 21 -2 V 20 -1 V 20 -1 V 20 -2 V 20 -1 V 21 -1 V 20 -1 V 20 -1 V 20 -1 V 21 -1 V 20 -1 V 20 -1 V 20 -1 V 21 -1 V 20 -1 V 20 0 V 20 -1 V 20 -1 V 21 0 V 20 -1 V 20 -1 V 20 0 V 21 -1 V 20 0 V 20 -1 V 20 0 V 21 0 V 20 -1 V 20 0 V 20 0 V 20 -1 V 21 0 V 20 0 V 20 -1 V 20 0 V 21 0 V 20 0 V 20 0 V 20 0 V 21 0 V 20 -1 V 20 0 V 20 0 V 20 0 V 21 0 V 20 0 V 20 0 V 20 0 V 21 0 V 20 0 V 20 0 V 20 0 V 21 0 V 20 0 V 20 0 V stroke 0.500 UL LTb 811 4944 M 811 631 L 6049 0 V 0 4313 V -6049 0 V 1.000 UP stroke grestore end showpage @endspecial 2471 2254 a FE(a)26 b FK(=)f(1)p FE(;)15 b(b)26 b FK(=)f(4)2471 2171 y FE(a)h FK(=)f(4)p FE(;)15 b(b)26 b FK(=)f(1)2471 2088 y FE(a)h FK(=)f(2)p FE(;)15 b(b)26 b FK(=)f(2)1698 1895 y(Beta)32 b(Distribution)2022 4038 y FE(x)533 2896 y gsave currentpoint currentpoint translate 270 rotate neg exch neg exch translate 533 2896 a 449 2919 a FE(p)p FK(\()p FE(x)p FK(\))533 2896 y currentpoint grestore moveto 533 2896 a 3286 3913 a FK(1)-733 b(0.75)-768 b(0.5)g(0.25)-732 b(0)680 2020 y(4)680 2469 y(3)680 2918 y(2)680 3368 y(1)680 3817 y(0)3350 4241 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_cdf_beta_P)c Fu(\()p FD(double)30 b Ft(x)p FD(,)h(double)f Ft(a)p FD(,)h(double)f Ft(b)p Fu(\))3350 4351 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_cdf_beta_Q)c Fu(\()p FD(double)30 b Ft(x)p FD(,)h(double)f Ft(a)p FD(,)h(double)f Ft(b)p Fu(\))3350 4460 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_cdf_beta_Pinv)d Fu(\()p FD(double)30 b Ft(P)p FD(,)h(double)f Ft(a)p FD(,)h(double)f Ft(b)p Fu(\))3350 4570 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_cdf_beta_Qinv)d Fu(\()p FD(double)30 b Ft(Q)p FD(,)h(double)f Ft(a)p FD(,)h(double)f Ft(b)p Fu(\))390 4680 y FK(These)f(functions)g(compute) h(the)g(cum)m(ulativ)m(e)h(distribution)e(functions)g FE(P)13 b FK(\()p FE(x)p FK(\),)31 b FE(Q)p FK(\()p FE(x)p FK(\))f(and)f(their)390 4789 y(in)m(v)m(erses)i(for)f(the)h(b)s(eta)f (distribution)g(with)g(parameters)h FD(a)g FK(and)e FD(b)p FK(.)p eop end %%Page: 251 269 TeXDict begin 251 268 bop 150 -116 a FK(Chapter)30 b(20:)41 b(Random)30 b(Num)m(b)s(er)g(Distributions)1717 b(251)150 299 y FJ(20.22)69 b(The)44 b(Logistic)i(Distribution)3350 508 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_ran_logistic)c Fu(\()p FD(const)32 b(gsl)p 1784 508 28 4 v 40 w(rng)e(*)h Ft(r)p FD(,)g(double)f Ft(a)p Fu(\))390 618 y FK(This)21 b(function)g(returns)f(a)i(random)f(v)-5 b(ariate)23 b(from)e(the)h(logistic)h(distribution.)38 b(The)21 b(distribution)390 727 y(function)30 b(is,)1327 942 y FE(p)p FK(\()p FE(x)p FK(\))p FE(dx)c FK(=)1882 880 y(exp\()p FI(\000)p FE(x=a)p FK(\))p 1726 921 739 4 v 1726 1004 a FE(a)p FK(\(1)21 b(+)f(exp)o(\()p FI(\000)p FE(x=a)p FK(\)\))2425 978 y FB(2)2474 942 y FE(dx)390 1157 y FK(for)30 b FI(\0001)25 b FE(<)g(x)g(<)g FK(+)p FI(1)p FK(.)3350 1342 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_ran_logistic_pdf)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(double)f Ft(a)p Fu(\))390 1451 y FK(This)36 b(function)g(computes)h(the)f(probabilit)m (y)h(densit)m(y)g FE(p)p FK(\()p FE(x)p FK(\))g(at)g FD(x)43 b FK(for)36 b(a)h(logistic)i(distribution)390 1561 y(with)30 b(scale)i(parameter)f FD(a)p FK(,)g(using)e(the)i(form)m (ula)g(giv)m(en)g(ab)s(o)m(v)m(e.)450 4057 y @beginspecial @setspecial /gnudict 256 dict def gnudict begin /Color false def /Blacktext true def /Solid false def /Dashlength 1 def /Landscape false def /Level1 false def /Rounded false def /TransparentPatterns false def /gnulinewidth 5.000 def /userlinewidth gnulinewidth def /vshift -66 def /dl1 { 10.0 Dashlength mul mul Rounded { currentlinewidth 0.75 mul sub dup 0 le { pop 0.01 } if } if } def /dl2 { 10.0 Dashlength mul mul Rounded { currentlinewidth 0.75 mul add } if } def /hpt_ 31.5 def /vpt_ 31.5 def /hpt hpt_ def /vpt vpt_ def Level1 {} { /SDict 10 dict def systemdict /pdfmark known not { userdict /pdfmark systemdict /cleartomark get put } if SDict begin [ /Title (rand-logistic.tex) /Subject (gnuplot plot) /Creator (gnuplot 4.2 patchlevel 2 ) /Author (Brian Gough) /CreationDate (Thu Feb 5 16:32:53 2009) /DOCINFO pdfmark end } ifelse /M {moveto} bind def /L {lineto} bind def /R {rmoveto} bind def /V {rlineto} bind def /N {newpath moveto} bind def /Z {closepath} bind def /C {setrgbcolor} bind def /f {rlineto fill} bind def /vpt2 vpt 2 mul def /hpt2 hpt 2 mul def /Lshow {currentpoint stroke M 0 vshift R Blacktext {gsave 0 setgray show grestore} {show} ifelse} def /Rshow {currentpoint stroke M dup stringwidth pop neg vshift R Blacktext {gsave 0 setgray show grestore} {show} ifelse} def /Cshow {currentpoint stroke M dup stringwidth pop -2 div vshift R Blacktext {gsave 0 setgray show grestore} {show} ifelse} def /UP {dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def} def /DL {Color {setrgbcolor Solid {pop []} if 0 setdash} {pop pop pop 0 setgray Solid {pop []} if 0 setdash} ifelse} def /BL {stroke userlinewidth 2 mul setlinewidth Rounded {1 setlinejoin 1 setlinecap} if} def /AL {stroke userlinewidth 2 div setlinewidth Rounded {1 setlinejoin 1 setlinecap} if} def /UL {dup gnulinewidth mul /userlinewidth exch def dup 1 lt {pop 1} if 10 mul /udl exch def} def /PL {stroke userlinewidth setlinewidth Rounded {1 setlinejoin 1 setlinecap} if} def /LCw {1 1 1} def /LCb {0 0 0} def /LCa {0 0 0} def /LC0 {1 0 0} def /LC1 {0 1 0} def /LC2 {0 0 1} def /LC3 {1 0 1} def /LC4 {0 1 1} def /LC5 {1 1 0} def /LC6 {0 0 0} def /LC7 {1 0.3 0} def /LC8 {0.5 0.5 0.5} def /LTw {PL [] 1 setgray} def /LTb {BL [] LCb DL} def /LTa {AL [1 udl mul 2 udl mul] 0 setdash LCa setrgbcolor} def /LT0 {PL [] LC0 DL} def /LT1 {PL [4 dl1 2 dl2] LC1 DL} def /LT2 {PL [2 dl1 3 dl2] LC2 DL} def /LT3 {PL [1 dl1 1.5 dl2] LC3 DL} def /LT4 {PL [6 dl1 2 dl2 1 dl1 2 dl2] LC4 DL} def /LT5 {PL [3 dl1 3 dl2 1 dl1 3 dl2] LC5 DL} def /LT6 {PL [2 dl1 2 dl2 2 dl1 6 dl2] LC6 DL} def /LT7 {PL [1 dl1 2 dl2 6 dl1 2 dl2 1 dl1 2 dl2] LC7 DL} def /LT8 {PL [2 dl1 2 dl2 2 dl1 2 dl2 2 dl1 2 dl2 2 dl1 4 dl2] LC8 DL} def /Pnt {stroke [] 0 setdash gsave 1 setlinecap M 0 0 V stroke grestore} def /Dia {stroke [] 0 setdash 2 copy vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke Pnt} def /Pls {stroke [] 0 setdash vpt sub M 0 vpt2 V currentpoint stroke M hpt neg vpt neg R hpt2 0 V stroke } def /Box {stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke Pnt} def /Crs {stroke [] 0 setdash exch hpt sub exch vpt add M hpt2 vpt2 neg V currentpoint stroke M hpt2 neg 0 R hpt2 vpt2 V stroke} def /TriU {stroke [] 0 setdash 2 copy vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke Pnt} def /Star {2 copy Pls Crs} def /BoxF {stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath fill} def /TriUF {stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath fill} def /TriD {stroke [] 0 setdash 2 copy vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke Pnt} def /TriDF {stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath fill} def /DiaF {stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath fill} def /Pent {stroke [] 0 setdash 2 copy gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore Pnt} def /PentF {stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath fill grestore} def /Circle {stroke [] 0 setdash 2 copy hpt 0 360 arc stroke Pnt} def /CircleF {stroke [] 0 setdash hpt 0 360 arc fill} def /C0 {BL [] 0 setdash 2 copy moveto vpt 90 450 arc} bind def /C1 {BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill vpt 0 360 arc closepath} bind def /C2 {BL [] 0 setdash 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath} bind def /C3 {BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill vpt 0 360 arc closepath} bind def /C4 {BL [] 0 setdash 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc closepath} bind def /C5 {BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc} bind def /C6 {BL [] 0 setdash 2 copy moveto 2 copy vpt 90 270 arc closepath fill vpt 0 360 arc closepath} bind def /C7 {BL [] 0 setdash 2 copy moveto 2 copy vpt 0 270 arc closepath fill vpt 0 360 arc closepath} bind def /C8 {BL [] 0 setdash 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath} bind def /C9 {BL [] 0 setdash 2 copy moveto 2 copy vpt 270 450 arc closepath fill vpt 0 360 arc closepath} bind def /C10 {BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath} bind def /C11 {BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath} bind def /C12 {BL [] 0 setdash 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath} bind def /C13 {BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath} bind def /C14 {BL [] 0 setdash 2 copy moveto 2 copy vpt 90 360 arc closepath fill vpt 0 360 arc} bind def /C15 {BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill vpt 0 360 arc closepath} bind def /Rec {newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath} bind def /Square {dup Rec} bind def /Bsquare {vpt sub exch vpt sub exch vpt2 Square} bind def /S0 {BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare} bind def /S1 {BL [] 0 setdash 2 copy vpt Square fill Bsquare} bind def /S2 {BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare} bind def /S3 {BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare} bind def /S4 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare} bind def /S5 {BL [] 0 setdash 2 copy 2 copy vpt Square fill exch vpt sub exch vpt sub vpt Square fill Bsquare} bind def /S6 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare} bind def /S7 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill 2 copy vpt Square fill Bsquare} bind def /S8 {BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare} bind def /S9 {BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare} bind def /S10 {BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill Bsquare} bind def /S11 {BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare} bind def /S12 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare} bind def /S13 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy vpt Square fill Bsquare} bind def /S14 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy exch vpt sub exch vpt Square fill Bsquare} bind def /S15 {BL [] 0 setdash 2 copy Bsquare fill Bsquare} bind def /D0 {gsave translate 45 rotate 0 0 S0 stroke grestore} bind def /D1 {gsave translate 45 rotate 0 0 S1 stroke grestore} bind def /D2 {gsave translate 45 rotate 0 0 S2 stroke grestore} bind def /D3 {gsave translate 45 rotate 0 0 S3 stroke grestore} bind def /D4 {gsave translate 45 rotate 0 0 S4 stroke grestore} bind def /D5 {gsave translate 45 rotate 0 0 S5 stroke grestore} bind def /D6 {gsave translate 45 rotate 0 0 S6 stroke grestore} bind def /D7 {gsave translate 45 rotate 0 0 S7 stroke grestore} bind def /D8 {gsave translate 45 rotate 0 0 S8 stroke grestore} bind def /D9 {gsave translate 45 rotate 0 0 S9 stroke grestore} bind def /D10 {gsave translate 45 rotate 0 0 S10 stroke grestore} bind def /D11 {gsave translate 45 rotate 0 0 S11 stroke grestore} bind def /D12 {gsave translate 45 rotate 0 0 S12 stroke grestore} bind def /D13 {gsave translate 45 rotate 0 0 S13 stroke grestore} bind def /D14 {gsave translate 45 rotate 0 0 S14 stroke grestore} bind def /D15 {gsave translate 45 rotate 0 0 S15 stroke grestore} bind def /DiaE {stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke} def /BoxE {stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke} def /TriUE {stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke} def /TriDE {stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke} def /PentE {stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore} def /CircE {stroke [] 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FK(\()p FE(x)p FK(\))f(and)f(their)390 4789 y(in)m(v)m(erses)i(for)f(the)h(logistic)h(distribution)e(with)g (scale)i(parameter)f FD(a)p FK(.)p eop end %%Page: 252 270 TeXDict begin 252 269 bop 150 -116 a FK(Chapter)30 b(20:)41 b(Random)30 b(Num)m(b)s(er)g(Distributions)1717 b(252)150 299 y FJ(20.23)69 b(The)44 b(P)l(areto)i(Distribution)3350 508 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_ran_pareto)c Fu(\()p FD(const)31 b(gsl)p 1679 508 28 4 v 41 w(rng)e(*)i Ft(r)p FD(,)g(double)f Ft(a)p FD(,)h(double)f Ft(b)p Fu(\))390 618 y FK(This)g(function)g(returns)g(a)h(random)e(v)-5 b(ariate)32 b(from)f(the)f(P)m(areto)j(distribution)d(of)g(order)h FD(a)p FK(.)41 b(The)390 727 y(distribution)30 b(function)g(is,)1416 895 y FE(p)p FK(\()p FE(x)p FK(\))p FE(dx)c FK(=)f(\()p FE(a=b)p FK(\))p FE(=)p FK(\()p FE(x=b)p FK(\))2258 857 y Fq(a)p FB(+1)2385 895 y FE(dx)390 1063 y FK(for)30 b FE(x)25 b FI(\025)g FE(b)p FK(.)3350 1247 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_ran_pareto_pdf)d 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w(t)e Ft(stride)p FD(,)565 3270 y(size)p 712 3270 V 41 w(t)h Ft(n)p Fu(\))390 3379 y FK(This)f(function)h(returns)f(the)h (estimated,)h(or)f FD(sample)p FK(,)h(v)-5 b(ariance)32 b(of)f FD(data)p FK(,)h(a)f(dataset)h(of)g(length)390 3489 y FD(n)e FK(with)g(stride)g FD(stride)p FK(.)41 b(The)30 b(estimated)h(v)-5 b(ariance)32 b(is)e(denoted)g(b)m(y)36 b(^)-50 b FE(\033)2794 3456 y FB(2)2861 3489 y FK(and)30 b(is)h(de\014ned)e(b)m(y)-8 b(,)1439 3708 y(^)-50 b FE(\033)1489 3671 y FB(2)1552 3708 y FK(=)1790 3647 y(1)p 1657 3687 311 4 v 1657 3771 a(\()p FE(N)31 b FI(\000)20 b FK(1\))1993 3628 y Fs(X)2113 3708 y FK(\()p FE(x)2200 3722 y Fq(i)2248 3708 y FI(\000)k FK(^)-49 b FE(\026)p FK(\))2429 3671 y FB(2)390 3939 y FK(where)30 b FE(x)705 3953 y Fq(i)763 3939 y FK(are)h(the)g(elemen)m(ts)h(of)f(the)f(dataset)i FD(data)p FK(.)42 b(Note)32 b(that)f(the)g(normalization)h(factor)g(of) 390 4048 y(1)p FE(=)p FK(\()p FE(N)21 b FI(\000)9 b FK(1\))25 b(results)g(from)g(the)g(deriv)-5 b(ation)26 b(of)k(^)-50 b FE(\033)2014 4015 y FB(2)2076 4048 y FK(as)25 b(an)g(un)m(biased)g (estimator)h(of)f(the)g(p)s(opulation)390 4158 y(v)-5 b(ariance)28 b FE(\033)798 4125 y FB(2)836 4158 y FK(.)39 b(F)-8 b(or)28 b(samples)g(dra)m(wn)e(from)h(a)g(Gaussian)h (distribution)e(the)i(v)-5 b(ariance)28 b(of)k(^)-50 b FE(\033)3495 4125 y FB(2)3560 4158 y FK(itself)390 4267 y(is)30 b(2)p FE(\033)581 4234 y FB(4)619 4267 y FE(=)-5 b(N)10 b FK(.)390 4416 y(This)29 b(function)h(computes)g(the)g (mean)g(via)g(a)g(call)h(to)g FH(gsl_stats_mean)p FK(.)37 b(If)29 b(y)m(ou)h(ha)m(v)m(e)h(already)390 4526 y(computed)f(the)h (mean)f(then)g(y)m(ou)h(can)g(pass)f(it)h(directly)g(to)g FH(gsl_stats_variance_m)p FK(.)3350 4740 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_stats_variance_m)e Fu(\()p FD(const)31 b(double)f Ft(data)p Fo([])p FD(,)h(size)p 2641 4740 28 4 v 41 w(t)g Ft(stride)p FD(,)565 4849 y(size)p 712 4849 V 41 w(t)g Ft(n)p FD(,)g(double)e Ft(mean)p Fu(\))390 4959 y FK(This)d(function)h(returns)e(the)i(sample)g(v)-5 b(ariance)28 b(of)f FD(data)h FK(relativ)m(e)h(to)e(the)g(giv)m(en)h(v) -5 b(alue)28 b(of)f FD(mean)p FK(.)390 5068 y(The)j(function)g(is)g (computed)h(with)j(^)-49 b FE(\026)30 b FK(replaced)h(b)m(y)f(the)g(v) -5 b(alue)31 b(of)g FD(mean)f FK(that)h(y)m(ou)g(supply)-8 b(,)1354 5288 y(^)-50 b FE(\033)1404 5251 y FB(2)1467 5288 y FK(=)1705 5227 y(1)p 1572 5267 311 4 v 1572 5350 a(\()p FE(N)31 b FI(\000)20 b FK(1\))1908 5207 y Fs(X)2028 5288 y FK(\()p FE(x)2115 5302 y Fq(i)2163 5288 y FI(\000)g FE(mean)p FK(\))2514 5251 y FB(2)p eop end %%Page: 275 293 TeXDict begin 275 292 bop 150 -116 a FK(Chapter)30 b(21:)41 b(Statistics)2591 b(275)3350 299 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_stats_sd)49 b Fu(\()p FD(const)31 b(double)f Ft(data)p Fo([])p FD(,)i(size)p 2223 299 28 4 v 41 w(t)f Ft(stride)p FD(,)h(size)p 2840 299 V 41 w(t)e Ft(n)p Fu(\))3350 408 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_stats_sd_m)c Fu(\()p FD(const)31 b(double)f Ft(data)p Fo([])p FD(,)i(size)p 2328 408 V 40 w(t)f Ft(stride)p FD(,)i(size)p 2945 408 V 40 w(t)e Ft(n)p FD(,)565 518 y(double)f Ft(mean)p Fu(\))390 628 y FK(The)d(standard)g(deviation)i(is)f(de\014ned)e(as)i(the)g(square)f (ro)s(ot)h(of)g(the)g(v)-5 b(ariance.)41 b(These)27 b(functions)390 737 y(return)i(the)i(square)f(ro)s(ot)h(of)f(the)h(corresp)s(onding)e (v)-5 b(ariance)31 b(functions)f(ab)s(o)m(v)m(e.)3350 928 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_stats_tss)c Fu(\()p FD(const)31 b(double)f Ft(data)p Fo([])p FD(,)h(size)p 2275 928 V 41 w(t)g Ft(stride)p FD(,)h(size)p 2892 928 V 41 w(t)f Ft(n)p Fu(\))3350 1037 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_stats_tss_m)c Fu(\()p FD(const)31 b(double)f Ft(data)p Fo([])p FD(,)i(size)p 2380 1037 V 41 w(t)e Ft(stride)p FD(,)j(size)p 2997 1037 V 41 w(t)d Ft(n)p FD(,)565 1147 y(double)g Ft(mean)p Fu(\))390 1256 y FK(These)i(functions)g(return)f(the)h(total)i(sum)e(of)g(squares)g (\(TSS\))f(of)i FD(data)g FK(ab)s(out)e(the)i(mean.)46 b(F)-8 b(or)390 1366 y FH(gsl_stats_tss_m)24 b FK(the)k(user-supplied)e (v)-5 b(alue)28 b(of)g FD(mean)g FK(is)g(used,)g(and)f(for)h FH(gsl_stats_tss)c FK(it)390 1476 y(is)30 b(computed)h(using)e FH(gsl_stats_mean)p FK(.)1484 1646 y(TSS)24 b(=)1772 1565 y Fs(X)1892 1646 y FK(\()p FE(x)1979 1660 y Fq(i)2027 1646 y FI(\000)c FE(mean)p FK(\))2378 1609 y FB(2)3350 1863 y FK([F)-8 b(unction])-3599 b Fv(double)54 b (gsl_stats_variance_wit)q(h_f)q(ixe)q(d_m)q(ean)e Fu(\()p FD(const)31 b(double)f Ft(data)p Fo([])p FD(,)565 1972 y(size)p 712 1972 V 41 w(t)h Ft(stride)p FD(,)h(size)p 1329 1972 V 41 w(t)f Ft(n)p FD(,)f(double)g Ft(mean)p Fu(\))390 2082 y FK(This)h(function)h(computes)h(an)f(un)m(biased)g (estimate)i(of)e(the)g(v)-5 b(ariance)34 b(of)e FD(data)h FK(when)e(the)i(p)s(op-)390 2192 y(ulation)e(mean)g FD(mean)f FK(of)g(the)h(underlying)e(distribution)h(is)g(kno)m(wn)g Fg(a)j(priori)p FK(.)42 b(In)30 b(this)g(case)i(the)390 2301 y(estimator)f(for)e(the)g(v)-5 b(ariance)30 b(uses)f(the)h(factor) g(1)p FE(=)-5 b(N)40 b FK(and)29 b(the)g(sample)h(mean)k(^)-50 b FE(\026)29 b FK(is)g(replaced)h(b)m(y)390 2411 y(the)h(kno)m(wn)e(p)s (opulation)i(mean)f FE(\026)p FK(,)1552 2619 y(^)-50 b FE(\033)1602 2581 y FB(2)1665 2619 y FK(=)1790 2557 y(1)p 1771 2598 83 4 v 1771 2681 a FE(N)1879 2538 y Fs(X)1999 2619 y FK(\()p FE(x)2086 2633 y Fq(i)2134 2619 y FI(\000)20 b FE(\026)p FK(\))2315 2581 y FB(2)3350 2854 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_stats_sd_with_fixe)q(d_m)q(ean)e Fu(\()p FD(const)31 b(double)f Ft(data)p Fo([])p FD(,)i(size)p 3060 2854 28 4 v 41 w(t)565 2964 y Ft(stride)p FD(,)g(size)p 1081 2964 V 41 w(t)f Ft(n)p FD(,)g(double)f Ft(mean)p Fu(\))390 3073 y FK(This)i(function)h(calculates)j(the)d(standard)g (deviation)h(of)g FD(data)g FK(for)f(a)g(\014xed)g(p)s(opulation)g (mean)390 3183 y FD(mean)p FK(.)41 b(The)30 b(result)g(is)g(the)h (square)f(ro)s(ot)h(of)f(the)h(corresp)s(onding)e(v)-5 b(ariance)31 b(function.)150 3420 y FJ(21.2)68 b(Absolute)46 b(deviation)3350 3632 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_stats_absdev)c Fu(\()p FD(const)32 b(double)e Ft(data)p Fo([])p FD(,)h(size)p 2432 3632 V 41 w(t)g Ft(stride)p FD(,)h(size)p 3049 3632 V 41 w(t)565 3742 y Ft(n)p Fu(\))390 3851 y FK(This)i(function)h(computes)g(the)h(absolute)f(deviation)i (from)d(the)h(mean)g(of)h FD(data)p FK(,)h(a)e(dataset)i(of)390 3961 y(length)31 b FD(n)f FK(with)g(stride)g FD(stride)p FK(.)41 b(The)29 b(absolute)j(deviation)f(from)f(the)g(mean)h(is)f (de\014ned)f(as,)1482 4169 y FE(absdev)f FK(=)1898 4107 y(1)p 1879 4148 83 4 v 1879 4231 a FE(N)1987 4088 y Fs(X)2122 4169 y FI(j)p FE(x)2199 4183 y Fq(i)2248 4169 y FI(\000)c FK(^)-50 b FE(\026)p FI(j)390 4365 y FK(where)27 b FE(x)702 4379 y Fq(i)757 4365 y FK(are)h(the)f(elemen)m(ts)i(of)e(the)h(dataset) h FD(data)p FK(.)40 b(The)27 b(absolute)h(deviation)g(from)f(the)h (mean)390 4474 y(pro)m(vides)d(a)g(more)h(robust)e(measure)h(of)g(the)g (width)g(of)g(a)g(distribution)g(than)g(the)g(v)-5 b(ariance.)40 b(This)390 4584 y(function)30 b(computes)h(the)f(mean)h(of)f FD(data)h FK(via)g(a)g(call)h(to)f FH(gsl_stats_mean)p FK(.)3350 4774 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_stats_absdev_m)d Fu(\()p FD(const)31 b(double)f Ft(data)p Fo([])p FD(,)i(size)p 2537 4774 28 4 v 41 w(t)e Ft(stride)p FD(,)565 4884 y(size)p 712 4884 V 41 w(t)h Ft(n)p FD(,)g(double)e Ft(mean)p Fu(\))390 4993 y FK(This)41 b(function)g(computes)g(the)h(absolute)g(deviation)h(of)e(the)h (dataset)h FD(data)f FK(relativ)m(e)i(to)e(the)390 5103 y(giv)m(en)31 b(v)-5 b(alue)31 b(of)g FD(mean)p FK(,)1397 5311 y FE(absdev)d FK(=)1813 5249 y(1)p 1794 5290 83 4 v 1794 5373 a FE(N)1902 5230 y Fs(X)2037 5311 y FI(j)p FE(x)2114 5325 y Fq(i)2163 5311 y FI(\000)19 b FE(mean)p FI(j)p eop end %%Page: 276 294 TeXDict begin 276 293 bop 150 -116 a FK(Chapter)30 b(21:)41 b(Statistics)2591 b(276)390 299 y(This)31 b(function)g(is)g(useful)g (if)g(y)m(ou)h(ha)m(v)m(e)g(already)g(computed)f(the)h(mean)f(of)h FD(data)g FK(\(and)f(w)m(an)m(t)h(to)390 408 y(a)m(v)m(oid)f (recomputing)e(it\),)h(or)f(wish)f(to)i(calculate)i(the)d(absolute)h (deviation)g(relativ)m(e)h(to)f(another)390 518 y(v)-5 b(alue)31 b(\(suc)m(h)f(as)h(zero,)g(or)g(the)f(median\).)150 761 y FJ(21.3)68 b(Higher)46 b(momen)l(ts)g(\(sk)l(ewness)g(and)f (kurtosis\))3350 978 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_stats_skew)c Fu(\()p FD(const)31 b(double)f Ft(data)p Fo([])p FD(,)i(size)p 2328 978 28 4 v 40 w(t)f Ft(stride)p FD(,)i(size)p 2945 978 V 40 w(t)e Ft(n)p Fu(\))390 1088 y FK(This)26 b(function)h(computes)g(the)g(sk)m(ewness)g(of)h FD(data)p FK(,)g(a)g(dataset)g(of)f(length)h FD(n)e FK(with)h(stride)g FD(stride)p FK(.)390 1197 y(The)j(sk)m(ewness)g(is)h(de\014ned)e(as,) 1449 1431 y FE(sk)s(ew)f FK(=)1802 1369 y(1)p 1783 1410 83 4 v 1783 1493 a FE(N)1891 1350 y Fs(X)2026 1312 y(\022)2097 1369 y FE(x)2149 1383 y Fq(i)2197 1369 y FI(\000)c FK(^)-49 b FE(\026)p 2097 1410 246 4 v 2197 1493 a FK(^)f FE(\033)2353 1312 y Fs(\023)2414 1327 y FB(3)390 1646 y FK(where)24 b FE(x)699 1660 y Fq(i)752 1646 y FK(are)h(the)g(elemen)m(ts)h(of)f (the)g(dataset)h FD(data)p FK(.)40 b(The)24 b(sk)m(ewness)h(measures)g (the)g(asymmetry)390 1755 y(of)31 b(the)f(tails)i(of)e(a)h (distribution.)390 1897 y(The)g(function)g(computes)h(the)g(mean)f(and) g(estimated)i(standard)e(deviation)i(of)e FD(data)i FK(via)f(calls)390 2006 y(to)f FH(gsl_stats_mean)c FK(and)i FH(gsl_stats_sd)p FK(.)3350 2205 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_stats_skew_m_sd)d Fu(\()p FD(const)32 b(double)e Ft(data)p Fo([])p FD(,)h(size)p 2589 2205 28 4 v 41 w(t)g Ft(stride)p FD(,)565 2315 y(size)p 712 2315 V 41 w(t)g Ft(n)p FD(,)g(double)e Ft(mean)p FD(,)j(double)e Ft(sd)p Fu(\))390 2425 y FK(This)25 b(function)h(computes)g(the)g(sk)m(ewness)f (of)h(the)h(dataset)g FD(data)f FK(using)g(the)g(giv)m(en)h(v)-5 b(alues)26 b(of)g(the)390 2534 y(mean)k FD(mean)h FK(and)f(standard)f (deviation)j FD(sd)p FK(,)1364 2766 y FE(sk)s(ew)c FK(=)1717 2704 y(1)p 1698 2745 83 4 v 1698 2828 a FE(N)1806 2685 y Fs(X)1941 2647 y(\022)2012 2704 y FE(x)2064 2718 y Fq(i)2112 2704 y FI(\000)20 b FE(mean)p 2012 2745 416 4 v 2175 2828 a(sd)2438 2647 y Fs(\023)2499 2664 y FB(3)390 2980 y FK(These)44 b(functions)f(are)i(useful)e(if)h(y)m(ou)g(ha)m(v)m (e)h(already)g(computed)e(the)h(mean)g(and)g(standard)390 3090 y(deviation)31 b(of)g FD(data)g FK(and)f(w)m(an)m(t)h(to)g(a)m(v)m (oid)h(recomputing)f(them.)3350 3289 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_stats_kurtosis)d Fu(\()p FD(const)31 b(double)f Ft(data)p Fo([])p FD(,)i(size)p 2537 3289 28 4 v 41 w(t)e Ft(stride)p FD(,)565 3398 y(size)p 712 3398 V 41 w(t)h Ft(n)p Fu(\))390 3508 y FK(This)e(function)g(computes)h (the)g(kurtosis)g(of)g FD(data)p FK(,)h(a)f(dataset)h(of)f(length)g FD(n)g FK(with)f(stride)h FD(stride)p FK(.)390 3618 y(The)g(kurtosis)g (is)g(de\014ned)g(as,)1237 3857 y FE(k)s(ur)s(tosis)24 b FK(=)1697 3713 y Fs( )1792 3795 y FK(1)p 1773 3836 83 4 v 1773 3919 a FE(N)1881 3776 y Fs(X)2016 3738 y(\022)2087 3795 y FE(x)2139 3809 y Fq(i)2187 3795 y FI(\000)g FK(^)-49 b FE(\026)p 2087 3836 246 4 v 2187 3919 a FK(^)f FE(\033)2343 3738 y Fs(\023)2404 3753 y FB(4)2441 3713 y Fs(!)2527 3857 y FI(\000)20 b FK(3)390 4096 y(The)k(kurtosis)g(measures)g(ho)m(w) g(sharply)f(p)s(eak)m(ed)i(a)f(distribution)g(is,)i(relativ)m(e)g(to)f (its)g(width.)37 b(The)390 4206 y(kurtosis)30 b(is)h(normalized)f(to)i (zero)f(for)f(a)h(Gaussian)f(distribution.)3350 4405 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_stats_kurtosis_m_s)q(d)e Fu(\()p FD(const)31 b(double)f Ft(data)p Fo([])p FD(,)h(size)p 2798 4405 28 4 v 41 w(t)565 4515 y Ft(stride)p FD(,)h(size)p 1081 4515 V 41 w(t)f Ft(n)p FD(,)g(double)f Ft(mean)p FD(,)i(double)e Ft(sd)p Fu(\))390 4624 y FK(This)e(function)g(computes) h(the)g(kurtosis)f(of)h(the)f(dataset)i FD(data)g FK(using)e(the)g(giv) m(en)i(v)-5 b(alues)29 b(of)g(the)390 4734 y(mean)h FD(mean)h FK(and)f(standard)f(deviation)j FD(sd)p FK(,)1152 4973 y FE(k)s(ur)s(tosis)24 b FK(=)1641 4912 y(1)p 1622 4952 83 4 v 1622 5036 a FE(N)1730 4829 y Fs( )1796 4892 y(X)1931 4854 y(\022)2002 4912 y FE(x)2054 4926 y Fq(i)2102 4912 y FI(\000)c FE(mean)p 2002 4952 416 4 v 2165 5036 a(sd)2428 4854 y Fs(\023)2489 4871 y FB(4)2526 4829 y Fs(!)2612 4973 y FI(\000)g FK(3)390 5213 y(This)j(function)h(is)g(useful)f(if)h (y)m(ou)h(ha)m(v)m(e)g(already)g(computed)f(the)g(mean)g(and)g (standard)f(deviation)390 5322 y(of)31 b FD(data)g FK(and)e(w)m(an)m(t) j(to)f(a)m(v)m(oid)h(recomputing)e(them.)p eop end %%Page: 277 295 TeXDict begin 277 294 bop 150 -116 a FK(Chapter)30 b(21:)41 b(Statistics)2591 b(277)150 299 y FJ(21.4)68 b(Auto)t(correlation)3350 510 y FK([F)-8 b(unction])-3599 b Fv(double)54 b (gsl_stats_lag1_autocor)q(rel)q(ati)q(on)e Fu(\()p FD(const)31 b(double)f Ft(data)p Fo([])p FD(,)565 620 y(const)h(size)p 950 620 28 4 v 41 w(t)g Ft(stride)p FD(,)h(const)f(size)p 1805 620 V 41 w(t)f Ft(n)p Fu(\))390 730 y FK(This)g(function)g (computes)g(the)h(lag-1)h(auto)s(correlation)g(of)f(the)f(dataset)i FD(data)p FK(.)1378 947 y FE(a)1426 961 y FB(1)1489 947 y FK(=)1595 821 y Fs(P)1683 842 y Fq(n)1683 909 y(i)p FB(=2)1794 886 y FK(\()p FE(x)1881 900 y Fq(i)1929 886 y FI(\000)25 b FK(^)-50 b FE(\026)p FK(\)\()p FE(x)2197 900 y Fq(i)p Fp(\000)p FB(1)2331 886 y FI(\000)24 b FK(^)-50 b FE(\026)p FK(\))p 1595 926 917 4 v 1637 945 a Fs(P)1725 966 y Fq(n)1725 1032 y(i)p FB(=1)1837 1010 y FK(\()p FE(x)1924 1024 y Fq(i)1972 1010 y FI(\000)24 b FK(^)-49 b FE(\026)p FK(\)\()p FE(x)2240 1024 y Fq(i)2288 1010 y FI(\000)25 b FK(^)-50 b FE(\026)p FK(\))3350 1204 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_stats_lag1_autocor)q(rel)q(ati)q (on_)q(m)d Fu(\()p FD(const)32 b(double)d Ft(data)p Fo([])p FD(,)565 1314 y(const)i(size)p 950 1314 28 4 v 41 w(t)g Ft(stride)p FD(,)h(const)f(size)p 1805 1314 V 41 w(t)f Ft(n)p FD(,)h(const)g(double)f Ft(mean)p Fu(\))390 1423 y FK(This)f(function)g(computes)h(the)g(lag-1)h(auto)s(correlation)h (of)e(the)g(dataset)h FD(data)f FK(using)f(the)h(giv)m(en)390 1533 y(v)-5 b(alue)31 b(of)f(the)h(mean)f FD(mean)p FK(.)150 1769 y FJ(21.5)68 b(Co)l(v)-7 b(ariance)3350 1981 y FK([F)f(unction]) -3599 b Fv(double)54 b(gsl_stats_covariance)e Fu(\()p FD(const)31 b(double)f Ft(data1)p Fo([])p FD(,)i(const)f(size)p 2932 1981 V 40 w(t)565 2090 y Ft(stride1)p FD(,)i(const)e(double)f Ft(data2)p Fo([])p FD(,)h(const)g(size)p 2275 2090 V 41 w(t)g Ft(stride2)p FD(,)i(const)d(size)p 3182 2090 V 41 w(t)h Ft(n)p Fu(\))390 2200 y FK(This)h(function)h(computes)g(the) g(co)m(v)-5 b(ariance)35 b(of)e(the)g(datasets)h FD(data1)41 b FK(and)32 b FD(data2)41 b FK(whic)m(h)33 b(m)m(ust)390 2309 y(b)s(oth)d(b)s(e)f(of)i(the)f(same)h(length)g FD(n)p FK(.)1252 2536 y FE(cov)s(ar)e FK(=)1724 2474 y(1)p 1606 2515 282 4 v 1606 2598 a(\()p FE(n)20 b FI(\000)g FK(1\))1952 2430 y Fq(n)1913 2455 y Fs(X)1919 2632 y Fq(i)p FB(=1)2033 2536 y FK(\()p FE(x)2120 2550 y Fq(i)2168 2536 y FI(\000)j FK(^)-48 b FE(x)p FK(\)\()p FE(y)2426 2550 y Fq(i)2474 2536 y FI(\000)21 b FK(^)-46 b FE(y)r FK(\))3350 2812 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_stats_covariance_m)e Fu(\()p FD(const)31 b(double)f Ft(data1)p Fo([])p FD(,)i(const)f(size)p 3036 2812 28 4 v 41 w(t)565 2921 y Ft(stride1)p FD(,)i(const)e(double)f Ft(data2)p Fo([])p FD(,)h(const)g(size)p 2275 2921 V 41 w(t)g Ft(stride2)p FD(,)i(const)d(size)p 3182 2921 V 41 w(t)h Ft(n)p FD(,)g(const)565 3031 y(double)f Ft(mean1)p FD(,)i(const)f(double)f Ft(mean2)p Fu(\))390 3140 y FK(This)40 b(function)g(computes)g(the)h(co)m(v)-5 b(ariance)43 b(of)d(the)h(datasets)g FD(data1)49 b FK(and)40 b FD(data2)49 b FK(using)40 b(the)390 3250 y(giv)m(en)i(v)-5 b(alues)42 b(of)g(the)f(means,)j FD(mean1)49 b FK(and)41 b FD(mean2)p FK(.)74 b(This)41 b(is)g(useful)g(if)g(y)m(ou)h(ha)m(v)m(e)g(already) 390 3360 y(computed)30 b(the)h(means)f(of)h FD(data1)38 b FK(and)30 b FD(data2)39 b FK(and)30 b(w)m(an)m(t)h(to)g(a)m(v)m(oid)h (recomputing)e(them.)150 3596 y FJ(21.6)68 b(Correlation)3350 3807 y FK([F)-8 b(unction])-3599 b Fv(double)54 b (gsl_stats_correlation)e Fu(\()p FD(const)31 b(double)f Ft(data1)p Fo([])p FD(,)i(const)f(size)p 2984 3807 V 41 w(t)565 3917 y Ft(stride1)p FD(,)i(const)e(double)f Ft(data2)p Fo([])p FD(,)h(const)g(size)p 2275 3917 V 41 w(t)g Ft(stride2)p FD(,)i(const)d(size)p 3182 3917 V 41 w(t)h Ft(n)p Fu(\))390 4026 y FK(This)44 b(function)g(e\016cien)m (tly)i(computes)f(the)f(P)m(earson)h(correlation)h(co)s(e\016cien)m(t)h (b)s(et)m(w)m(een)e(the)390 4136 y(datasets)32 b FD(data1)38 b FK(and)30 b FD(data2)39 b FK(whic)m(h)30 b(m)m(ust)g(b)s(oth)g(b)s(e) g(of)g(the)h(same)f(length)h FD(n)p FK(.)940 4369 y FE(r)c FK(=)1114 4308 y FE(cov)s FK(\()p FE(x;)15 b(y)s FK(\))p 1114 4348 342 4 v 1197 4432 a(^)-50 b FE(\033)1244 4446 y Fq(x)1291 4432 y FK(^)g FE(\033)1338 4446 y Fq(y)1491 4369 y FK(=)1898 4261 y FB(1)p 1852 4276 127 4 v 1852 4328 a Fq(n)p Fp(\000)p FB(1)2003 4232 y Fs(P)2091 4297 y FK(\()p FE(x)2178 4311 y Fq(i)2226 4297 y FI(\000)23 b FK(^)-48 b FE(x)p FK(\)\()p FE(y)2484 4311 y Fq(i)2532 4297 y FI(\000)21 b FK(^)-46 b FE(y)r FK(\))p 1597 4348 1354 4 v 1597 4365 a Fs(q)p 1680 4365 600 4 v 1737 4422 a FB(1)p 1690 4437 127 4 v 1690 4489 a Fq(n)p Fp(\000)p FB(1)1841 4393 y Fs(P)1929 4457 y FK(\()p FE(x)2016 4471 y Fq(i)2064 4457 y FI(\000)23 b FK(^)-48 b FE(x)p FK(\))2242 4431 y FB(2)2280 4365 y Fs(q)p 2363 4365 588 4 v 2419 4422 a FB(1)p 2373 4437 127 4 v 2373 4489 a Fq(n)p Fp(\000)p FB(1)2524 4393 y Fs(P)2611 4457 y FK(\()p FE(y)2691 4471 y Fq(i)2739 4457 y FI(\000)21 b FK(^)-46 b FE(y)s FK(\))2913 4431 y FB(2)3350 4682 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_stats_spearman)d Fu(\()p FD(const)31 b(double)f Ft(data1)p Fo([])p FD(,)i(const)f(size)p 2827 4682 28 4 v 41 w(t)565 4792 y Ft(stride1)p FD(,)i(const)e(double)f Ft(data2)p Fo([])p FD(,)h(const)g(size)p 2275 4792 V 41 w(t)g Ft(stride2)p FD(,)i(const)d(size)p 3182 4792 V 41 w(t)h Ft(n)p FD(,)g(double)565 4902 y Ft(work)p Fo([])p Fu(\))390 5011 y FK(This)56 b(function)h(computes)h(the)f(Sp)s (earman)f(rank)h(correlation)i(co)s(e\016cien)m(t)g(b)s(et)m(w)m(een)f (the)390 5121 y(datasets)44 b FD(data1)51 b FK(and)41 b FD(data2)51 b FK(whic)m(h)43 b(m)m(ust)f(b)s(oth)g(b)s(e)g(of)g(the)h (same)g(length)g FD(n)p FK(.)76 b(Additional)390 5230 y(w)m(orkspace)36 b(of)f(size)h(2*)p FD(n)f FK(is)h(required)e(in)h FD(w)m(ork)p FK(.)55 b(The)34 b(Sp)s(earman)g(rank)h(correlation)h(b)s (et)m(w)m(een)390 5340 y(v)m(ectors)f FE(x)e FK(and)g FE(y)k FK(is)c(equiv)-5 b(alen)m(t)35 b(to)f(the)g(P)m(earson)g (correlation)h(b)s(et)m(w)m(een)f(the)g(rank)m(ed)f(v)m(ectors)p eop end %%Page: 278 296 TeXDict begin 278 295 bop 150 -116 a FK(Chapter)30 b(21:)41 b(Statistics)2591 b(278)390 299 y FE(x)442 313 y Fq(R)528 299 y FK(and)31 b FE(y)751 313 y Fq(R)805 299 y FK(,)i(where)e(ranks)g (are)h(de\014ned)f(to)h(b)s(e)g(the)g(a)m(v)m(erage)i(of)e(the)g(p)s (ositions)g(of)g(an)f(elemen)m(t)390 408 y(in)f(the)h(ascending)f (order)g(of)h(the)f(v)-5 b(alues.)150 681 y FJ(21.7)68 b(W)-11 b(eigh)l(ted)46 b(Samples)150 841 y FK(The)41 b(functions)h(describ)s(ed)f(in)g(this)h(section)h(allo)m(w)h(the)e (computation)h(of)f(statistics)i(for)e(w)m(eigh)m(ted)150 950 y(samples.)50 b(The)33 b(functions)g(accept)h(an)g(arra)m(y)f(of)h (samples,)g FE(x)2301 964 y Fq(i)2329 950 y FK(,)g(with)f(asso)s (ciated)i(w)m(eigh)m(ts,)h FE(w)3452 964 y Fq(i)3480 950 y FK(.)49 b(Eac)m(h)150 1060 y(sample)34 b FE(x)509 1074 y Fq(i)570 1060 y FK(is)g(considered)g(as)g(ha)m(ving)g(b)s(een)g (dra)m(wn)f(from)g(a)h(Gaussian)g(distribution)f(with)h(v)-5 b(ariance)150 1170 y FE(\033)205 1137 y FB(2)202 1192 y Fq(i)242 1170 y FK(.)47 b(The)32 b(sample)g(w)m(eigh)m(t)i FE(w)1163 1184 y Fq(i)1223 1170 y FK(is)f(de\014ned)e(as)h(the)h (recipro)s(cal)g(of)f(this)h(v)-5 b(ariance,)34 b FE(w)3057 1184 y Fq(i)3113 1170 y FK(=)28 b(1)p FE(=\033)3357 1137 y FB(2)3354 1192 y Fq(i)3396 1170 y FK(.)46 b(Setting)150 1279 y(a)31 b(w)m(eigh)m(t)h(to)f(zero)g(corresp)s(onds)e(to)i(remo)m (ving)g(a)g(sample)g(from)e(a)i(dataset.)3350 1518 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_stats_wmean)c Fu(\()p FD(const)31 b(double)f Ft(w)p Fo([])p FD(,)h(size)p 2223 1518 28 4 v 41 w(t)g Ft(wstride)p FD(,)h(const)565 1627 y(double)e Ft(data)p Fo([])p FD(,)i(size)p 1326 1627 V 41 w(t)e Ft(stride)p FD(,)j(size)p 1943 1627 V 40 w(t)e Ft(n)p Fu(\))390 1737 y FK(This)j(function)g(returns)f(the)i(w)m(eigh)m (ted)h(mean)e(of)h(the)g(dataset)g FD(data)g FK(with)g(stride)f FD(stride)40 b FK(and)390 1846 y(length)32 b FD(n)p FK(,)f(using)g(the) h(set)g(of)f(w)m(eigh)m(ts)i FD(w)39 b FK(with)31 b(stride)g FD(wstride)37 b FK(and)30 b(length)i FD(n)p FK(.)44 b(The)31 b(w)m(eigh)m(ted)390 1956 y(mean)f(is)h(de\014ned)e(as,)1719 2194 y(^)-50 b FE(\026)26 b FK(=)1900 2068 y Fs(P)2003 2132 y FE(w)2068 2146 y Fq(i)2096 2132 y FE(x)2148 2146 y Fq(i)p 1900 2173 276 4 v 1940 2192 a Fs(P)2043 2256 y FE(w)2108 2270 y Fq(i)3350 2496 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_stats_wvariance)d Fu(\()p FD(const)32 b(double)e Ft(w)p Fo([])p FD(,)g(size)p 2432 2496 28 4 v 41 w(t)h Ft(wstride)p FD(,)h(const)565 2605 y(double)e Ft(data)p Fo([])p FD(,)i(size)p 1326 2605 V 41 w(t)e Ft(stride)p FD(,)j(size)p 1943 2605 V 40 w(t)e Ft(n)p Fu(\))390 2715 y FK(This)22 b(function)h(returns)f(the)h(estimated)h(v) -5 b(ariance)24 b(of)f(the)g(dataset)h FD(data)g FK(with)f(stride)g FD(stride)28 b FK(and)390 2825 y(length)i FD(n)p FK(,)f(using)f(the)i (set)f(of)h(w)m(eigh)m(ts)g FD(w)37 b FK(with)28 b(stride)h FD(wstride)34 b FK(and)29 b(length)g FD(n)p FK(.)40 b(The)29 b(estimated)390 2934 y(v)-5 b(ariance)31 b(of)g(a)g(w)m(eigh)m(ted)g (dataset)h(is)e(calculated)j(as,)1201 3172 y(^)-50 b FE(\033)1251 3134 y FB(2)1314 3172 y FK(=)1661 3046 y Fs(P)1764 3110 y FE(w)1829 3124 y Fq(i)p 1420 3151 678 4 v 1420 3234 a FK(\()1455 3170 y Fs(P)1558 3234 y FE(w)1623 3248 y Fq(i)1651 3234 y FK(\))1686 3208 y FB(2)1743 3234 y FI(\000)1834 3170 y Fs(P)1922 3234 y FK(\()p FE(w)2024 3203 y FB(2)2022 3255 y Fq(i)2062 3234 y FK(\))2123 3091 y Fs(X)2258 3172 y FE(w)2323 3186 y Fq(i)2350 3172 y FK(\()p FE(x)2437 3186 y Fq(i)2486 3172 y FI(\000)24 b FK(^)-50 b FE(\026)p FK(\))2666 3134 y FB(2)390 3419 y FK(Note)27 b(that)f(this)g(expression)f(reduces)g(to)i(an)e(un)m(w)m (eigh)m(ted)h(v)-5 b(ariance)27 b(with)e(the)h(familiar)g(1)p FE(=)p FK(\()p FE(N)c FI(\000)390 3529 y FK(1\))31 b(factor)g(when)f (there)g(are)h FE(N)40 b FK(equal)31 b(non-zero)g(w)m(eigh)m(ts.)3350 3767 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_stats_wvariance_m)e Fu(\()p FD(const)31 b(double)f Ft(w)p Fo([])p FD(,)h(size)p 2537 3767 28 4 v 41 w(t)f Ft(wstride)p FD(,)565 3877 y(const)h(double)f Ft(data)p Fo([])p FD(,)h(size)p 1563 3877 V 41 w(t)g Ft(stride)p FD(,)h(size)p 2180 3877 V 41 w(t)f Ft(n)p FD(,)g(double)f Ft(wmean)p Fu(\))390 3987 y FK(This)i(function)g(returns)f(the)i(estimated)h(v)-5 b(ariance)33 b(of)g(the)g(w)m(eigh)m(ted)h(dataset)f FD(data)h FK(using)e(the)390 4096 y(giv)m(en)f(w)m(eigh)m(ted)h(mean)f FD(wmean)p FK(.)3350 4334 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_stats_wsd)c Fu(\()p FD(const)31 b(double)f Ft(w)p Fo([])p FD(,)g(size)p 2118 4334 V 41 w(t)h Ft(wstride)p FD(,)i(const)d(double)565 4444 y Ft(data)p Fo([])p FD(,)i(size)p 1033 4444 V 41 w(t)e Ft(stride)p FD(,)j(size)p 1650 4444 V 41 w(t)d Ft(n)p Fu(\))390 4554 y FK(The)k(standard)f(deviation)j(is)e (de\014ned)f(as)h(the)h(square)f(ro)s(ot)h(of)f(the)g(v)-5 b(ariance.)54 b(This)33 b(function)390 4663 y(returns)23 b(the)h(square)g(ro)s(ot)h(of)f(the)h(corresp)s(onding)e(v)-5 b(ariance)25 b(function)f FH(gsl_stats_wvariance)390 4773 y FK(ab)s(o)m(v)m(e.)3350 5011 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_stats_wsd_m)c Fu(\()p FD(const)31 b(double)f Ft(w)p Fo([])p FD(,)h(size)p 2223 5011 V 41 w(t)g Ft(wstride)p FD(,)h(const)565 5121 y(double)e Ft(data)p Fo([])p FD(,)i(size)p 1326 5121 V 41 w(t)e Ft(stride)p FD(,)j(size)p 1943 5121 V 40 w(t)e Ft(n)p FD(,)g(double)f Ft(wmean)p Fu(\))390 5230 y FK(This)38 b(function)h(returns)f(the)i (square)f(ro)s(ot)g(of)g(the)h(corresp)s(onding)e(v)-5 b(ariance)40 b(function)f FH(gsl_)390 5340 y(stats_wvariance_m)26 b FK(ab)s(o)m(v)m(e.)p eop end %%Page: 279 297 TeXDict begin 279 296 bop 150 -116 a FK(Chapter)30 b(21:)41 b(Statistics)2591 b(279)3350 299 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_stats_wvariance_wi)q(th_)q(fix)q(ed_)q(mean)e Fu(\()p FD(const)31 b(double)f Ft(w)p Fo([])p FD(,)565 408 y(size)p 712 408 28 4 v 41 w(t)h Ft(wstride)p FD(,)h(const)f (double)f Ft(data)p Fo([])p FD(,)i(size)p 2233 408 V 41 w(t)e Ft(stride)p FD(,)j(size)p 2850 408 V 41 w(t)d Ft(n)p FD(,)h(const)g(double)565 518 y Ft(mean)p Fu(\))390 628 y FK(This)d(function)g(computes)h(an)g(un)m(biased)f(estimate)j(of) e(the)g(v)-5 b(ariance)29 b(of)g(the)g(w)m(eigh)m(ted)i(dataset)390 737 y FD(data)23 b FK(when)f(the)h(p)s(opulation)f(mean)h FD(mean)g FK(of)f(the)h(underlying)f(distribution)g(is)g(kno)m(wn)h Fg(a)i(priori)p FK(.)390 847 y(In)k(this)h(case)h(the)f(estimator)h (for)e(the)h(v)-5 b(ariance)31 b(replaces)g(the)f(sample)f(mean)35 b(^)-50 b FE(\026)30 b FK(b)m(y)f(the)h(kno)m(wn)390 956 y(p)s(opulation)g(mean)g FE(\026)p FK(,)1564 1177 y(^)-50 b FE(\033)1614 1139 y FB(2)1676 1177 y FK(=)1782 1051 y Fs(P)1885 1115 y FE(w)1950 1129 y Fq(i)1978 1115 y FK(\()p FE(x)2065 1129 y Fq(i)2113 1115 y FI(\000)20 b FE(\026)p FK(\))2294 1082 y FB(2)p 1782 1155 549 4 v 1959 1175 a Fs(P)2062 1239 y FE(w)2127 1253 y Fq(i)3350 1431 y FK([F)-8 b(unction])-3599 b Fv(double)54 b (gsl_stats_wsd_with_fix)q(ed_)q(mea)q(n)d Fu(\()p FD(const)32 b(double)e Ft(w)p Fo([])p FD(,)g(size)p 2955 1431 28 4 v 41 w(t)565 1541 y Ft(wstride)p FD(,)j(const)e(double)f Ft(data)p Fo([])p FD(,)h(size)p 1985 1541 V 41 w(t)g Ft(stride)p FD(,)h(size)p 2602 1541 V 41 w(t)f Ft(n)p FD(,)g(const)f(double)g Ft(mean)p Fu(\))390 1650 y FK(The)k(standard)f (deviation)j(is)e(de\014ned)f(as)h(the)h(square)f(ro)s(ot)h(of)f(the)g (v)-5 b(ariance.)54 b(This)33 b(function)390 1760 y(returns)c(the)i (square)f(ro)s(ot)h(of)f(the)h(corresp)s(onding)e(v)-5 b(ariance)31 b(function)f(ab)s(o)m(v)m(e.)3350 1951 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_stats_wtss)c Fu(\()p FD(const)31 b(double)f Ft(w)p Fo([])p FD(,)h(const)g(size)p 2409 1951 V 40 w(t)g Ft(wstride)p FD(,)i(const)565 2060 y(double)d Ft(data)p Fo([])p FD(,)i(size)p 1326 2060 V 41 w(t)e Ft(stride)p FD(,)j(size)p 1943 2060 V 40 w(t)e Ft(n)p Fu(\))3350 2170 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_stats_wtss_m)c Fu(\()p FD(const)32 b(double)e Ft(w)p Fo([])p FD(,)g(const)h(size)p 2513 2170 V 41 w(t)g Ft(wstride)p FD(,)565 2280 y(const)g(double)f Ft(data)p Fo([])p FD(,)h(size)p 1563 2280 V 41 w(t)g Ft(stride)p FD(,)h(size)p 2180 2280 V 41 w(t)f Ft(n)p FD(,)g(double)f Ft(wmean)p Fu(\))390 2389 y FK(These)37 b(functions)g(return)f(the)i(w)m(eigh)m(ted)h(total)g(sum)e(of)g (squares)g(\(TSS\))g(of)g FD(data)i FK(ab)s(out)e(the)390 2499 y(w)m(eigh)m(ted)j(mean.)65 b(F)-8 b(or)39 b FH(gsl_stats_wtss_m) 34 b FK(the)39 b(user-supplied)e(v)-5 b(alue)39 b(of)g FD(wmean)f FK(is)g(used,)390 2608 y(and)30 b(for)g FH(gsl_stats_wtss)c FK(it)31 b(is)g(computed)f(using)g FH(gsl_stats_wmean)p FK(.)1397 2779 y(TSS)24 b(=)1685 2698 y Fs(X)1820 2779 y FE(w)1885 2793 y Fq(i)1912 2779 y FK(\()p FE(x)1999 2793 y Fq(i)2048 2779 y FI(\000)19 b FE(w)r(mean)p FK(\))2465 2742 y FB(2)3350 2996 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_stats_wabsdev)d Fu(\()p FD(const)31 b(double)f Ft(w)p Fo([])p FD(,)h(size)p 2328 2996 V 40 w(t)g Ft(wstride)p FD(,)i(const)565 3106 y(double)d Ft(data)p Fo([])p FD(,)i(size)p 1326 3106 V 41 w(t)e Ft(stride)p FD(,)j(size)p 1943 3106 V 40 w(t)e Ft(n)p Fu(\))390 3216 y FK(This)i(function)g(computes)h(the) f(w)m(eigh)m(ted)i(absolute)g(deviation)f(from)f(the)h(w)m(eigh)m(ted)h (mean)f(of)390 3325 y FD(data)p FK(.)41 b(The)30 b(absolute)h (deviation)h(from)e(the)g(mean)h(is)f(de\014ned)f(as,)1500 3543 y FE(absdev)g FK(=)1898 3417 y Fs(P)2001 3482 y FE(w)2066 3496 y Fq(i)2094 3482 y FI(j)p FE(x)2171 3496 y Fq(i)2219 3482 y FI(\000)24 b FK(^)-49 b FE(\026)o FI(j)p 1898 3522 492 4 v 2046 3541 a Fs(P)2149 3605 y FE(w)2214 3619 y Fq(i)3350 3798 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_stats_wabsdev_m)d Fu(\()p FD(const)32 b(double)e Ft(w)p Fo([])p FD(,)g(size)p 2432 3798 28 4 v 41 w(t)h Ft(wstride)p FD(,)h(const)565 3907 y(double)e Ft(data)p Fo([])p FD(,)i(size)p 1326 3907 V 41 w(t)e Ft(stride)p FD(,)j(size)p 1943 3907 V 40 w(t)e Ft(n)p FD(,)g(double)f Ft(wmean)p Fu(\))390 4017 y FK(This)37 b(function)h(computes)g(the)h(absolute)g(deviation)g(of)f(the)g(w)m (eigh)m(ted)i(dataset)f FD(data)g FK(ab)s(out)390 4126 y(the)31 b(giv)m(en)g(w)m(eigh)m(ted)h(mean)e FD(wmean)p FK(.)3350 4317 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_stats_wskew)c Fu(\()p FD(const)31 b(double)f Ft(w)p Fo([])p FD(,)h(size)p 2223 4317 V 41 w(t)g Ft(wstride)p FD(,)h(const)565 4427 y(double)e Ft(data)p Fo([])p FD(,)i(size)p 1326 4427 V 41 w(t)e Ft(stride)p FD(,)j(size)p 1943 4427 V 40 w(t)e Ft(n)p Fu(\))390 4536 y FK(This)f(function)g(computes)g(the) h(w)m(eigh)m(ted)h(sk)m(ewness)e(of)g(the)h(dataset)h FD(data)p FK(.)1419 4757 y FE(sk)s(ew)c FK(=)1753 4631 y Fs(P)1856 4695 y FE(w)1921 4709 y Fq(i)1949 4695 y FK(\(\()p FE(x)2071 4709 y Fq(i)2119 4695 y FI(\000)23 b FK(^)-48 b FE(x)p FK(\))p FE(=)5 b FK(^)-50 b FE(\033)t FK(\))2433 4662 y FB(3)p 1753 4736 718 4 v 2014 4755 a Fs(P)2117 4819 y FE(w)2182 4833 y Fq(i)3350 5011 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_stats_wskew_m_sd)e Fu(\()p FD(const)31 b(double)f Ft(w)p Fo([])p FD(,)g(size)p 2484 5011 28 4 v 41 w(t)h Ft(wstride)p FD(,)565 5121 y(const)g(double)f Ft(data)p Fo([])p FD(,)h(size)p 1563 5121 V 41 w(t)g Ft(stride)p FD(,)h(size)p 2180 5121 V 41 w(t)f Ft(n)p FD(,)g(double)f Ft(wmean)p FD(,)i(double)e Ft(wsd)p Fu(\))390 5230 y FK(This)37 b(function)g(computes)h(the)g(w)m (eigh)m(ted)i(sk)m(ewness)d(of)h(the)g(dataset)h FD(data)g FK(using)e(the)h(giv)m(en)390 5340 y(v)-5 b(alues)31 b(of)f(the)h(w)m(eigh)m(ted)h(mean)e(and)g(w)m(eigh)m(ted)i(standard)d (deviation,)j FD(wmean)e FK(and)g FD(wsd)p FK(.)p eop end %%Page: 280 298 TeXDict begin 280 297 bop 150 -116 a FK(Chapter)30 b(21:)41 b(Statistics)2591 b(280)3350 299 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_stats_wkurtosis)d Fu(\()p FD(const)32 b(double)e Ft(w)p Fo([])p FD(,)g(size)p 2432 299 28 4 v 41 w(t)h Ft(wstride)p FD(,)h(const)565 408 y(double)e Ft(data)p Fo([])p FD(,)i(size)p 1326 408 V 41 w(t)e Ft(stride)p FD(,)j(size)p 1943 408 V 40 w(t)e Ft(n)p Fu(\))390 518 y FK(This)f(function)g(computes)g(the)h(w)m(eigh)m(ted)h(kurtosis)e(of) g(the)h(dataset)g FD(data)p FK(.)1273 737 y FE(k)s(ur)s(tosis)24 b FK(=)1743 611 y Fs(P)1846 676 y FE(w)1911 690 y Fq(i)1939 676 y FK(\(\()p FE(x)2061 690 y Fq(i)2109 676 y FI(\000)f FK(^)-48 b FE(x)p FK(\))p FE(=)5 b FK(^)-50 b FE(\033)t FK(\))2423 643 y FB(4)p 1743 716 718 4 v 2004 735 a Fs(P)2107 799 y FE(w)2172 813 y Fq(i)2491 737 y FI(\000)20 b FK(3)3350 989 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_stats_wkurtosis_m_)q (sd)e Fu(\()p FD(const)31 b(double)f Ft(w)p Fo([])p FD(,)h(size)p 2694 989 28 4 v 41 w(t)f Ft(wstride)p FD(,)565 1099 y(const)h(double)f Ft(data)p Fo([])p FD(,)h(size)p 1563 1099 V 41 w(t)g Ft(stride)p FD(,)h(size)p 2180 1099 V 41 w(t)f Ft(n)p FD(,)g(double)f Ft(wmean)p FD(,)i(double)e Ft(wsd)p Fu(\))390 1208 y FK(This)40 b(function)h(computes)g(the)g(w)m(eigh)m(ted)h (kurtosis)f(of)g(the)g(dataset)i FD(data)e FK(using)g(the)g(giv)m(en) 390 1318 y(v)-5 b(alues)31 b(of)f(the)h(w)m(eigh)m(ted)h(mean)e(and)g (w)m(eigh)m(ted)i(standard)d(deviation,)j FD(wmean)e FK(and)g FD(wsd)p FK(.)150 1554 y FJ(21.8)68 b(Maxim)l(um)46 b(and)e(Minim)l(um)h(v)-7 b(alues)150 1713 y FK(The)44 b(follo)m(wing)j(functions)d(\014nd)g(the)h(maxim)m(um)f(and)h(minim)m (um)f(v)-5 b(alues)45 b(of)g(a)g(dataset)i(\(or)e(their)150 1823 y(indices\).)72 b(If)41 b(the)g(data)g(con)m(tains)h FH(NaN)p FK(s)e(then)g(a)i FH(NaN)d FK(will)j(b)s(e)e(returned,)i (since)f(the)g(maxim)m(um)g(or)150 1932 y(minim)m(um)30 b(v)-5 b(alue)31 b(is)g(unde\014ned.)40 b(F)-8 b(or)32 b(functions)e(whic)m(h)h(return)f(an)g(index,)h(the)g(lo)s(cation)i(of) e(the)g(\014rst)150 2042 y FH(NaN)e FK(in)i(the)f(arra)m(y)h(is)f (returned.)3350 2230 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_stats_max)c Fu(\()p FD(const)31 b(double)f Ft(data)p Fo([])p FD(,)h(size)p 2275 2230 V 41 w(t)g Ft(stride)p FD(,)h(size)p 2892 2230 V 41 w(t)f Ft(n)p Fu(\))390 2340 y FK(This)h(function)h(returns)g(the)g(maxim)m(um)g(v)-5 b(alue)34 b(in)f FD(data)p FK(,)i(a)f(dataset)g(of)g(length)f FD(n)g FK(with)g(stride)390 2450 y FD(stride)p FK(.)50 b(The)32 b(maxim)m(um)i(v)-5 b(alue)33 b(is)h(de\014ned)e(as)h(the)h(v) -5 b(alue)34 b(of)f(the)h(elemen)m(t)h FE(x)3122 2464 y Fq(i)3182 2450 y FK(whic)m(h)e(satis\014es)390 2559 y FE(x)442 2573 y Fq(i)495 2559 y FI(\025)25 b FE(x)643 2573 y Fq(j)708 2559 y FK(for)30 b(all)h FE(j)5 b FK(.)390 2696 y(If)30 b(y)m(ou)g(w)m(an)m(t)h(instead)g(to)g(\014nd)d(the)j (elemen)m(t)g(with)f(the)g(largest)i(absolute)f(magnitude)f(y)m(ou)h (will)390 2805 y(need)f(to)h(apply)f FH(fabs)f FK(or)i FH(abs)e FK(to)i(y)m(our)g(data)g(b)s(efore)f(calling)i(this)e (function.)3350 2994 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_stats_min)c Fu(\()p FD(const)31 b(double)f Ft(data)p Fo([])p FD(,)h(size)p 2275 2994 V 41 w(t)g Ft(stride)p FD(,)h(size)p 2892 2994 V 41 w(t)f Ft(n)p Fu(\))390 3103 y FK(This)j(function)g(returns)f(the)i(minim)m(um)f(v)-5 b(alue)35 b(in)f FD(data)p FK(,)i(a)f(dataset)h(of)f(length)g FD(n)f FK(with)g(stride)390 3213 y FD(stride)p FK(.)53 b(The)34 b(minim)m(um)f(v)-5 b(alue)35 b(is)g(de\014ned)e(as)i(the)f(v) -5 b(alue)35 b(of)g(the)f(elemen)m(t)i FE(x)3119 3227 y Fq(i)3181 3213 y FK(whic)m(h)e(satis\014es)390 3323 y FE(x)442 3337 y Fq(i)495 3323 y FI(\024)25 b FE(x)643 3337 y Fq(j)708 3323 y FK(for)30 b(all)h FE(j)5 b FK(.)390 3459 y(If)26 b(y)m(ou)g(w)m(an)m(t)h(instead)g(to)g(\014nd)d(the)j (elemen)m(t)g(with)f(the)h(smallest)g(absolute)g(magnitude)f(y)m(ou)h (will)390 3569 y(need)j(to)h(apply)f FH(fabs)f FK(or)i FH(abs)e FK(to)i(y)m(our)g(data)g(b)s(efore)f(calling)i(this)e (function.)3350 3757 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_stats_minmax)c Fu(\()p FD(double)30 b(*)h Ft(min)p FD(,)g(double)f(*)h Ft(max)p FD(,)g(const)g(double)565 3867 y Ft(data)p Fo([])p FD(,)h(size)p 1033 3867 V 41 w(t)e Ft(stride)p FD(,)j(size)p 1650 3867 V 41 w(t)d Ft(n)p Fu(\))390 3977 y FK(This)j(function)h(\014nds)e(b)s(oth)h(the)i (minim)m(um)e(and)g(maxim)m(um)h(v)-5 b(alues)34 b FD(min)p FK(,)h FD(max)40 b FK(in)34 b FD(data)h FK(in)f(a)390 4086 y(single)d(pass.)3350 4275 y([F)-8 b(unction])-3599 b Fv(size_t)54 b(gsl_stats_max_index)d Fu(\()p FD(const)32 b(double)e Ft(data)p Fo([])p FD(,)h(size)p 2589 4275 V 41 w(t)g Ft(stride)p FD(,)565 4384 y(size)p 712 4384 V 41 w(t)g Ft(n)p Fu(\))390 4494 y FK(This)k(function)h(returns)e(the)i (index)g(of)g(the)g(maxim)m(um)f(v)-5 b(alue)37 b(in)e FD(data)p FK(,)j(a)e(dataset)i(of)e(length)390 4603 y FD(n)g FK(with)g(stride)g FD(stride)p FK(.)58 b(The)36 b(maxim)m(um)g(v)-5 b(alue)37 b(is)g(de\014ned)e(as)h(the)h(v)-5 b(alue)37 b(of)f(the)h(elemen)m(t)g FE(x)3722 4617 y Fq(i)390 4713 y FK(whic)m(h)g(satis\014es)h FE(x)1051 4727 y Fq(i)1115 4713 y FI(\025)f FE(x)1275 4727 y Fq(j)1347 4713 y FK(for)g(all)h FE(j)5 b FK(.)62 b(When)37 b(there)g(are)h(sev)m (eral)h(equal)e(maxim)m(um)h(elemen)m(ts)390 4823 y(then)30 b(the)h(\014rst)e(one)i(is)f(c)m(hosen.)3350 5011 y([F)-8 b(unction])-3599 b Fv(size_t)54 b(gsl_stats_min_index)d Fu(\()p FD(const)32 b(double)e Ft(data)p Fo([])p FD(,)h(size)p 2589 5011 V 41 w(t)g Ft(stride)p FD(,)565 5121 y(size)p 712 5121 V 41 w(t)g Ft(n)p Fu(\))390 5230 y FK(This)g(function)g (returns)f(the)h(index)g(of)h(the)f(minim)m(um)g(v)-5 b(alue)31 b(in)g FD(data)p FK(,)i(a)f(dataset)g(of)g(length)f FD(n)390 5340 y FK(with)26 b(stride)g FD(stride)p FK(.)39 b(The)26 b(minim)m(um)f(v)-5 b(alue)27 b(is)f(de\014ned)f(as)h(the)h(v) -5 b(alue)26 b(of)h(the)f(elemen)m(t)i FE(x)3467 5354 y Fq(i)3520 5340 y FK(whic)m(h)p eop end %%Page: 281 299 TeXDict begin 281 298 bop 150 -116 a FK(Chapter)30 b(21:)41 b(Statistics)2591 b(281)390 299 y(satis\014es)33 b FE(x)779 313 y Fq(i)835 299 y FI(\025)28 b FE(x)986 313 y Fq(j)1053 299 y FK(for)k(all)h FE(j)5 b FK(.)47 b(When)32 b(there)g(are)h(sev)m (eral)g(equal)g(minim)m(um)e(elemen)m(ts)j(then)e(the)390 408 y(\014rst)e(one)g(is)h(c)m(hosen.)3350 662 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_stats_minmax_index)e Fu(\()p FD(size)p 1790 662 28 4 v 41 w(t)31 b(*)f Ft(min_index)p FD(,)k(size)p 2640 662 V 41 w(t)c(*)565 771 y Ft(max_index)p FD(,)j(const)e(double)f Ft(data)p Fo([])p FD(,)i(size)p 2090 771 V 41 w(t)e Ft(stride)p FD(,)j(size)p 2707 771 V 41 w(t)d Ft(n)p Fu(\))390 881 y FK(This)h(function)g(returns)g(the)g (indexes)h FD(min)p 1910 881 V 39 w(index)p FK(,)g FD(max)p 2390 881 V 40 w(index)38 b FK(of)32 b(the)f(minim)m(um)g(and)g(maxi-) 390 991 y(m)m(um)f(v)-5 b(alues)31 b(in)f FD(data)h FK(in)f(a)g(single) h(pass.)150 1275 y FJ(21.9)68 b(Median)45 b(and)g(P)l(ercen)l(tiles)150 1434 y FK(The)31 b(median)h(and)f(p)s(ercen)m(tile)i(functions)e (describ)s(ed)g(in)h(this)f(section)i(op)s(erate)g(on)e(sorted)h(data.) 46 b(F)-8 b(or)150 1544 y(con)m(v)m(enience)36 b(w)m(e)e(use)g FD(quan)m(tiles)p FK(,)i(measured)d(on)h(a)g(scale)h(of)f(0)g(to)h(1,)g (instead)f(of)g(p)s(ercen)m(tiles)h(\(whic)m(h)150 1653 y(use)30 b(a)h(scale)h(of)e(0)h(to)g(100\).)3350 1907 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_stats_median_from_)q(sor) q(ted)q(_da)q(ta)e Fu(\()p FD(const)31 b(double)565 2016 y Ft(sorted_data)p Fo([])p FD(,)j(size)p 1399 2016 V 41 w(t)c Ft(stride)p FD(,)j(size)p 2016 2016 V 41 w(t)d Ft(n)p Fu(\))390 2126 y FK(This)39 b(function)g(returns)f(the)i(median) f(v)-5 b(alue)40 b(of)f FD(sorted)p 2393 2126 V 41 w(data)p FK(,)j(a)e(dataset)h(of)e(length)h FD(n)f FK(with)390 2235 y(stride)28 b FD(stride)p FK(.)39 b(The)28 b(elemen)m(ts)h(of)f (the)f(arra)m(y)i(m)m(ust)e(b)s(e)g(in)h(ascending)g(n)m(umerical)g (order.)39 b(There)390 2345 y(are)e(no)f(c)m(hec)m(ks)i(to)f(see)g (whether)f(the)g(data)h(are)g(sorted,)h(so)f(the)g(function)f FH(gsl_sort)e FK(should)390 2454 y(alw)m(a)m(ys)e(b)s(e)e(used)f (\014rst.)390 2623 y(When)g(the)g(dataset)h(has)f(an)g(o)s(dd)f(n)m(um) m(b)s(er)f(of)i(elemen)m(ts)i(the)e(median)g(is)g(the)g(v)-5 b(alue)29 b(of)g(elemen)m(t)390 2733 y(\()p FE(n)14 b FI(\000)g FK(1\))p FE(=)p FK(2.)41 b(When)26 b(the)i(dataset)g(has)f (an)g(ev)m(en)h(n)m(um)m(b)s(er)e(of)h(elemen)m(ts)i(the)e(median)g(is) h(the)f(mean)390 2843 y(of)g(the)g(t)m(w)m(o)h(nearest)f(middle)f(v)-5 b(alues,)28 b(elemen)m(ts)g(\()p FE(n)13 b FI(\000)g FK(1\))p FE(=)p FK(2)28 b(and)e FE(n=)p FK(2.)40 b(Since)27 b(the)f(algorithm)i(for)390 2952 y(computing)k(the)f(median)h(in)m(v)m (olv)m(es)h(in)m(terp)s(olation)g(this)e(function)h(alw)m(a)m(ys)h (returns)d(a)i(\015oating-)390 3062 y(p)s(oin)m(t)e(n)m(um)m(b)s(er,)g (ev)m(en)h(for)f(in)m(teger)i(data)f(t)m(yp)s(es.)3350 3315 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_stats_quantile_fro)q (m_s)q(ort)q(ed_)q(data)e Fu(\()p FD(const)31 b(double)565 3425 y Ft(sorted_data)p Fo([])p FD(,)j(size)p 1399 3425 V 41 w(t)c Ft(stride)p FD(,)j(size)p 2016 3425 V 41 w(t)d Ft(n)p FD(,)h(double)f Ft(f)p Fu(\))390 3534 y FK(This)42 b(function)h(returns)f(a)i(quan)m(tile)g(v)-5 b(alue)44 b(of)f FD(sorted)p 2369 3534 V 41 w(data)p FK(,)k(a)d(double-precision) f(arra)m(y)h(of)390 3644 y(length)26 b FD(n)g FK(with)f(stride)h FD(stride)p FK(.)39 b(The)25 b(elemen)m(ts)i(of)f(the)g(arra)m(y)h(m)m (ust)f(b)s(e)f(in)g(ascending)h(n)m(umerical)390 3753 y(order.)40 b(The)28 b(quan)m(tile)i(is)f(determined)f(b)m(y)h(the)g FD(f)p FK(,)g(a)g(fraction)g(b)s(et)m(w)m(een)h(0)f(and)f(1.)40 b(F)-8 b(or)30 b(example,)390 3863 y(to)h(compute)g(the)f(v)-5 b(alue)31 b(of)g(the)f(75th)h(p)s(ercen)m(tile)h FD(f)47 b FK(should)30 b(ha)m(v)m(e)h(the)g(v)-5 b(alue)31 b(0.75.)390 4032 y(There)38 b(are)g(no)g(c)m(hec)m(ks)i(to)f(see)g(whether)e(the)i (data)f(are)h(sorted,)i(so)d(the)g(function)g FH(gsl_sort)390 4142 y FK(should)29 b(alw)m(a)m(ys)j(b)s(e)e(used)g(\014rst.)390 4311 y(The)g(quan)m(tile)h(is)g(found)e(b)m(y)h(in)m(terp)s(olation,)i (using)e(the)g(form)m(ula)1396 4513 y(quan)m(tile)c(=)f(\(1)c FI(\000)f FE(\016)s FK(\))p FE(x)2157 4527 y Fq(i)2206 4513 y FK(+)g FE(\016)s(x)2392 4527 y Fq(i)p FB(+1)390 4715 y FK(where)30 b FE(i)g FK(is)h FH(floor)p FK(\(\()p FE(n)19 b FI(\000)h FK(1\))p FE(f)10 b FK(\))31 b(and)e FE(\016)35 b FK(is)30 b(\()p FE(n)20 b FI(\000)g FK(1\))p FE(f)30 b FI(\000)20 b FE(i)p FK(.)390 4884 y(Th)m(us)29 b(the)h(minim)m(um)g(v)-5 b(alue)30 b(of)g(the)h(arra)m(y)f(\()p FH(data[0*stride])p FK(\))d(is)j(giv)m(en)h(b)m(y)f FD(f)47 b FK(equal)31 b(to)g(zero,)390 4994 y(the)24 b(maxim)m(um)g(v)-5 b(alue)24 b(\()p FH(data[\(n-1\)*stride])p FK(\))19 b(is)24 b(giv)m(en)h(b)m(y)f FD(f)41 b FK(equal)24 b(to)h(one)f(and)f(the)h (median)390 5103 y(v)-5 b(alue)29 b(is)f(giv)m(en)h(b)m(y)f FD(f)45 b FK(equal)29 b(to)f(0.5.)41 b(Since)29 b(the)f(algorithm)h (for)f(computing)g(quan)m(tiles)h(in)m(v)m(olv)m(es)390 5213 y(in)m(terp)s(olation)38 b(this)f(function)f(alw)m(a)m(ys)j (returns)d(a)h(\015oating-p)s(oin)m(t)h(n)m(um)m(b)s(er,)f(ev)m(en)h (for)f(in)m(teger)390 5322 y(data)31 b(t)m(yp)s(es.)p eop end %%Page: 282 300 TeXDict begin 282 299 bop 150 -116 a FK(Chapter)30 b(21:)41 b(Statistics)2591 b(282)150 299 y FJ(21.10)69 b(Examples)150 458 y FK(Here)31 b(is)f(a)h(basic)g(example)g(of)f(ho)m(w)h(to)g(use)f (the)h(statistical)i(functions:)390 602 y FH(#include)46 b()390 711 y(#include)g()390 931 y(int)390 1040 y(main\(void\))390 1150 y({)485 1259 y(double)h(data[5])e(=)j({17.2,)e(18.1,)g(16.5,)h(18.3,)f(12.6};)485 1369 y(double)h(mean,)f(variance,)f(largest,)h(smallest;)485 1588 y(mean)238 b(=)47 b(gsl_stats_mean\(data,)c(1,)k(5\);)485 1698 y(variance)f(=)h(gsl_stats_variance\(data,)42 b(1,)47 b(5\);)485 1807 y(largest)94 b(=)47 b(gsl_stats_max\(data,)c(1,)k(5\);) 485 1917 y(smallest)f(=)h(gsl_stats_min\(data,)c(1,)k(5\);)485 2136 y(printf)g(\("The)f(dataset)g(is)h(\045g,)g(\045g,)g(\045g,)g (\045g,)g(\045g\\n",)820 2246 y(data[0],)e(data[1],)h(data[2],)f (data[3],)h(data[4]\);)485 2465 y(printf)h(\("The)f(sample)g(mean)h(is) g(\045g\\n",)f(mean\);)485 2574 y(printf)h(\("The)f(estimated)f (variance)h(is)h(\045g\\n",)f(variance\);)485 2684 y(printf)h(\("The)f (largest)g(value)g(is)h(\045g\\n",)f(largest\);)485 2794 y(printf)h(\("The)f(smallest)f(value)i(is)g(\045g\\n",)f(smallest\);) 485 2903 y(return)h(0;)390 3013 y(})275 3156 y FK(The)29 b(program)i(should)e(pro)s(duce)g(the)i(follo)m(wing)h(output,)390 3300 y FH(The)47 b(dataset)f(is)h(17.2,)f(18.1,)h(16.5,)f(18.3,)g(12.6) 390 3409 y(The)h(sample)f(mean)h(is)g(16.54)390 3519 y(The)g(estimated)e(variance)h(is)h(5.373)390 3628 y(The)g(largest)f (value)g(is)h(18.3)390 3738 y(The)g(smallest)e(value)i(is)g(12.6)275 3881 y FK(Here)30 b(is)h(an)f(example)h(using)f(sorted)h(data,)390 4025 y FH(#include)46 b()390 4134 y(#include)g ()390 4244 y(#include)g()390 4463 y(int)390 4573 y(main\(void\))390 4682 y({)485 4792 y(double)h(data[5])e(=)j({17.2,)e(18.1,)g(16.5,)h(18.3,)f(12.6};)485 4902 y(double)h(median,)e(upperq,)h(lowerq;)485 5121 y(printf)h(\("Original)e(dataset:)188 b(\045g,)47 b(\045g,)g(\045g,)g (\045g,)g(\045g\\n",)820 5230 y(data[0],)e(data[1],)h(data[2],)f (data[3],)h(data[4]\);)p eop end %%Page: 283 301 TeXDict begin 283 300 bop 150 -116 a FK(Chapter)30 b(21:)41 b(Statistics)2591 b(283)485 299 y FH(gsl_sort)46 b(\(data,)g(1,)h(5\);) 485 518 y(printf)g(\("Sorted)e(dataset:)93 b(\045g,)47 b(\045g,)g(\045g,)g(\045g,)g(\045g\\n",)820 628 y(data[0],)e(data[1],)h (data[2],)f(data[3],)h(data[4]\);)485 847 y(median)581 956 y(=)h(gsl_stats_median_from_sort)o(ed_)o(data)41 b(\(data,)2347 1066 y(1,)47 b(5\);)485 1285 y(upperq)581 1395 y(=)g(gsl_stats_quantile_from_so)o(rte)o(d_da)o(ta)42 b(\(data,)2442 1504 y(1,)47 b(5,)2442 1614 y(0.75\);)485 1724 y(lowerq)581 1833 y(=)g(gsl_stats_quantile_from_so)o(rte)o(d_da)o (ta)42 b(\(data,)2442 1943 y(1,)47 b(5,)2442 2052 y(0.25\);)485 2271 y(printf)g(\("The)f(median)g(is)h(\045g\\n",)f(median\);)485 2381 y(printf)h(\("The)f(upper)g(quartile)g(is)h(\045g\\n",)f (upperq\);)485 2491 y(printf)h(\("The)f(lower)g(quartile)g(is)h (\045g\\n",)f(lowerq\);)485 2600 y(return)h(0;)390 2710 y(})275 2849 y FK(This)29 b(program)h(should)g(pro)s(duce)f(the)h (follo)m(wing)i(output,)390 2988 y FH(Original)46 b(dataset:)188 b(17.2,)47 b(18.1,)f(16.5,)g(18.3,)h(12.6)390 3097 y(Sorted)f(dataset:) 93 b(12.6,)47 b(16.5,)f(17.2,)g(18.1,)h(18.3)390 3207 y(The)g(median)f(is)h(17.2)390 3316 y(The)g(upper)f(quartile)g(is)h (18.1)390 3426 y(The)g(lower)f(quartile)g(is)h(16.5)150 3665 y FJ(21.11)69 b(References)46 b(and)e(F)-11 b(urther)45 b(Reading)150 3824 y FK(The)d(standard)f(reference)i(for)f(almost)i(an) m(y)e(topic)i(in)e(statistics)i(is)f(the)f(m)m(ulti-v)m(olume)i FD(Adv)-5 b(anced)150 3934 y(Theory)30 b(of)g(Statistics)36 b FK(b)m(y)30 b(Kendall)h(and)f(Stuart.)330 4073 y(Maurice)k(Kendall,)f (Alan)g(Stuart,)g(and)f(J.)h(Keith)g(Ord.)46 b FD(The)32 b(Adv)-5 b(anced)32 b(Theory)h(of)f(Statistics)330 4182 y FK(\(m)m(ultiple)d(v)m(olumes\))g(reprin)m(ted)e(as)h FD(Kendall's)g(Adv)-5 b(anced)27 b(Theory)h(of)f(Statistics)p FK(.)42 b(Wiley)-8 b(,)30 b(ISBN)330 4292 y(047023380X.)150 4458 y(Man)m(y)42 b(statistical)i(concepts)e(can)f(b)s(e)g(more)g (easily)h(understo)s(o)s(d)d(b)m(y)i(a)h(Ba)m(y)m(esian)h(approac)m(h.) 73 b(The)150 4568 y(follo)m(wing)32 b(b)s(o)s(ok)e(b)m(y)g(Gelman,)i (Carlin,)e(Stern)g(and)g(Rubin)g(giv)m(es)h(a)g(comprehensiv)m(e)g(co)m (v)m(erage)j(of)d(the)150 4677 y(sub)5 b(ject.)330 4816 y(Andrew)43 b(Gelman,)48 b(John)43 b(B.)i(Carlin,)j(Hal)c(S.)g(Stern,)j (Donald)e(B.)g(Rubin.)80 b FD(Ba)m(y)m(esian)46 b(Data)330 4926 y(Analysis)p FK(.)41 b(Chapman)29 b(&)h(Hall,)i(ISBN)e (0412039915.)150 5092 y(F)-8 b(or)28 b(ph)m(ysicists)f(the)g(P)m (article)i(Data)g(Group)d(pro)m(vides)h(useful)g(reviews)g(of)g (Probabilit)m(y)h(and)e(Statistics)150 5201 y(in)k(the)h (\\Mathematical)i(T)-8 b(o)s(ols")32 b(section)f(of)g(its)g(Ann)m(ual)f (Review)h(of)f(P)m(article)j(Ph)m(ysics.)330 5340 y FD(Review)e(of)f(P) m(article)j(Prop)s(erties)h FK(R.M.)d(Barnett)g(et)g(al.,)h(Ph)m (ysical)f(Review)g(D54,)h(1)f(\(1996\))p eop end %%Page: 284 302 TeXDict begin 284 301 bop 150 -116 a FK(Chapter)30 b(21:)41 b(Statistics)2591 b(284)150 299 y(The)30 b(Review)h(of)f(P)m(article)j (Ph)m(ysics)d(is)h(a)m(v)-5 b(ailable)32 b(online)f(at)g(the)g(w)m (ebsite)g FH(http://pdg.lbl.gov/)p FK(.)p eop end %%Page: 285 303 TeXDict begin 285 302 bop 150 -116 a FK(Chapter)30 b(22:)41 b(Running)29 b(Statistics)2221 b(285)150 299 y FG(22)80 b(Running)52 b(Statistics)150 548 y FK(This)21 b(c)m(hapter)i(describ)s (es)f(routines)g(for)g(computing)g(running)f(statistics,)26 b(also)d(kno)m(wn)f(as)g(online)h(statis-)150 657 y(tics,)38 b(of)d(data.)57 b(These)35 b(routines)h(are)g(suitable)g(for)f (handling)g(large)h(datasets)h(for)e(whic)m(h)g(it)h(ma)m(y)h(b)s(e)150 767 y(incon)m(v)m(enien)m(t)e(or)e(impractical)i(to)f(store)g(in)f (memory)g(all)h(at)g(once.)51 b(The)32 b(data)i(can)g(b)s(e)f(pro)s (cessed)f(in)150 876 y(a)37 b(single)g(pass,)i(one)e(p)s(oin)m(t)f(at)i (a)f(time.)60 b(Eac)m(h)37 b(time)h(a)f(data)g(p)s(oin)m(t)g(is)g (added)f(to)h(the)g(accum)m(ulator,)150 986 y(in)m(ternal)30 b(parameters)g(are)g(up)s(dated)e(in)i(order)f(to)h(compute)g(the)g (curren)m(t)f(mean,)h(v)-5 b(ariance,)31 b(standard)150 1096 y(deviation,)g(sk)m(ewness,)e(and)g(kurtosis.)40 b(These)29 b(statistics)i(are)e(exact,)i(and)d(are)i(up)s(dated)e(with) g(n)m(umer-)150 1205 y(ically)k(stable)g(single-pass)f(algorithms.)43 b(The)30 b(median)g(and)g(arbitrary)h(quan)m(tiles)h(are)f(also)g(a)m (v)-5 b(ailable,)150 1315 y(ho)m(w)m(ev)m(er)39 b(these)e(calculations) j(use)d(algorithms)h(whic)m(h)f(pro)m(vide)g(appro)m(ximations,)j(and)d (gro)m(w)h(more)150 1424 y(accurate)32 b(as)f(more)f(data)h(is)g(added) e(to)i(the)g(accum)m(ulator.)275 1564 y(The)e(functions)h(describ)s(ed) g(in)g(this)g(c)m(hapter)h(are)g(declared)g(in)f(the)g(header)g(\014le) h FH(gsl_rstat.h)p FK(.)150 1803 y FJ(22.1)68 b(Initializing)47 b(the)e(Accum)l(ulator)3350 2018 y FK([F)-8 b(unction])-3599 b Fv(gsl_rstat_workspace)58 b(*)53 b(gsl_rstat_alloc)d Fu(\()p FD(v)m(oid)p Fu(\))390 2127 y FK(This)28 b(function)g(allo)s (cates)k(a)d(w)m(orkspace)g(for)g(computing)g(running)e(statistics.)42 b(The)28 b(size)i(of)f(the)390 2237 y(w)m(orkspace)i(is)g FE(O)s FK(\(1\).)3350 2431 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_rstat_free)49 b Fu(\()p FD(gsl)p 1336 2431 28 4 v 41 w(rstat)p 1564 2431 V 41 w(w)m(orkspace)31 b(*)g Ft(w)p Fu(\))390 2540 y FK(This)f(function)g(frees)g(the)h (memory)f(asso)s(ciated)i(with)e(the)g(w)m(orkspace)h FD(w)p FK(.)3350 2734 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_rstat_reset)d Fu(\()p FD(gsl)p 1336 2734 V 41 w(rstat)p 1564 2734 V 41 w(w)m(orkspace)31 b(*)g Ft(w)p Fu(\))390 2844 y FK(This)d(function)g(resets)h(the)f(w)m(orkspace)h FD(w)36 b FK(to)29 b(its)g(initial)h(state,)g(so)f(it)g(can)g(b)s(egin) f(w)m(orking)g(on)h(a)390 2954 y(new)h(set)h(of)f(data.)150 3193 y FJ(22.2)68 b(Adding)45 b(Data)g(to)h(the)f(Accum)l(ulator)3350 3407 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_rstat_add)d Fu(\()p FD(const)31 b(double)f Ft(x)p FD(,)h(gsl)p 1871 3407 V 40 w(rstat)p 2098 3407 V 41 w(w)m(orkspace)g(*)g Ft(w)p Fu(\))390 3517 y FK(This)d(function)h(adds)f(the)h(data)h(p)s (oin)m(t)f FD(x)35 b FK(to)29 b(the)g(statistical)j(accum)m(ulator,)f (up)s(dating)d(calcula-)390 3627 y(tions)j(of)f(the)h(mean,)g(v)-5 b(ariance,)31 b(standard)f(deviation,)h(sk)m(ewness,)g(kurtosis,)f(and) g(median.)3350 3821 y([F)-8 b(unction])-3599 b Fv(size_t)54 b(gsl_rstat_n)49 b Fu(\()p FD(gsl)p 1284 3821 V 41 w(rstat)p 1512 3821 V 40 w(w)m(orkspace)32 b(*)e Ft(w)p Fu(\))390 3930 y FK(This)g(function)g(returns)f(the)h(n)m(um)m(b)s(er)f(of)i (data)g(so)g(far)f(added)f(to)j(the)e(accum)m(ulator.)150 4170 y FJ(22.3)68 b(Curren)l(t)46 b(Statistics)3350 4384 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_rstat_min)c Fu(\()p FD(gsl)p 1389 4384 V 40 w(rstat)p 1616 4384 V 41 w(w)m(orkspace)31 b(*)g Ft(w)p Fu(\))390 4494 y FK(This)f(function)g (returns)f(the)h(minim)m(um)g(v)-5 b(alue)31 b(added)e(to)j(the)e (accum)m(ulator.)3350 4688 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_rstat_max)c Fu(\()p FD(gsl)p 1389 4688 V 40 w(rstat)p 1616 4688 V 41 w(w)m(orkspace)31 b(*)g Ft(w)p Fu(\))390 4797 y FK(This)f(function)g(returns)f(the)h (maxim)m(um)h(v)-5 b(alue)30 b(added)g(to)h(the)g(accum)m(ulator.)3350 4991 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_rstat_mean)c Fu(\()p FD(gsl)p 1441 4991 V 41 w(rstat)p 1669 4991 V 40 w(w)m(orkspace)31 b(*)g Ft(w)p Fu(\))390 5101 y FK(This)f(function)g (returns)f(the)h(mean)h(of)f(all)i(data)f(added)e(to)i(the)g(accum)m (ulator,)h(de\014ned)d(as)1700 5311 y(^)-49 b FE(\026)25 b FK(=)1900 5249 y(1)p 1882 5290 83 4 v 1882 5373 a FE(N)1990 5230 y Fs(X)2125 5311 y FE(x)2177 5325 y Fq(i)p eop end %%Page: 286 304 TeXDict begin 286 303 bop 150 -116 a FK(Chapter)30 b(22:)41 b(Running)29 b(Statistics)2221 b(286)3350 299 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_rstat_variance)d Fu(\()p FD(gsl)p 1650 299 28 4 v 41 w(rstat)p 1878 299 V 41 w(w)m(orkspace)31 b(*)f Ft(w)p Fu(\))390 408 y FK(This)g(function) g(returns)f(the)h(v)-5 b(ariance)32 b(of)e(all)h(data)h(added)d(to)i (the)g(accum)m(ulator,)h(de\014ned)d(as)1439 620 y(^)-50 b FE(\033)1489 582 y FB(2)1552 620 y FK(=)1790 558 y(1)p 1657 599 311 4 v 1657 682 a(\()p FE(N)31 b FI(\000)20 b FK(1\))1993 539 y Fs(X)2113 620 y FK(\()p FE(x)2200 634 y Fq(i)2248 620 y FI(\000)k FK(^)-49 b FE(\026)p FK(\))2429 582 y FB(2)3350 877 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_rstat_sd)49 b Fu(\()p FD(gsl)p 1336 877 28 4 v 41 w(rstat)p 1564 877 V 41 w(w)m(orkspace)31 b(*)g Ft(w)p Fu(\))390 987 y FK(This)k(function)g(returns)g(the)h (standard)f(deviation)i(of)f(all)g(data)h(added)e(to)h(the)g(accum)m (ulator,)390 1096 y(de\014ned)29 b(as)i(the)f(square)g(ro)s(ot)h(of)g (the)f(v)-5 b(ariance)32 b(giv)m(en)f(ab)s(o)m(v)m(e.)3350 1293 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_rstat_sd_mean)d Fu(\()p FD(gsl)p 1598 1293 V 41 w(rstat)p 1826 1293 V 40 w(w)m(orkspace)31 b(*)g Ft(w)p Fu(\))390 1403 y FK(This)f(function)g (returns)f(the)h(standard)g(deviation)h(of)g(the)f(mean,)h(de\014ned)e (as)1757 1618 y(^)-50 b FE(\033)1809 1632 y FB(^)-38 b Fq(\026)1874 1618 y FK(=)2036 1557 y(^)-50 b FE(\033)p 1979 1597 159 4 v 1979 1614 a FI(p)p 2055 1614 83 4 v 77 x FE(N)3350 1874 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_rstat_rms)c Fu(\()p FD(gsl)p 1389 1874 28 4 v 40 w(rstat)p 1616 1874 V 41 w(w)m(orkspace)31 b(*)g Ft(w)p Fu(\))390 1984 y FK(This)39 b(function)g(returns)f(the)h(ro)s(ot)h (mean)g(square)f(of)g(all)i(data)f(added)e(to)j(the)e(accum)m(ulator,) 390 2094 y(de\014ned)29 b(as)1594 2307 y FE(r)s(ms)24 b FK(=)1881 2174 y Fs(r)p 1964 2174 343 4 v 1993 2245 a FK(1)p 1974 2286 83 4 v 1974 2369 a FE(N)2082 2226 y Fs(X)2217 2307 y FE(x)2269 2276 y FB(2)2269 2327 y Fq(i)3350 2542 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_rstat_skew)c Fu(\()p FD(gsl)p 1441 2542 28 4 v 41 w(rstat)p 1669 2542 V 40 w(w)m(orkspace)31 b(*)g Ft(w)p Fu(\))390 2652 y FK(This)f(function)g(returns)f(the)h(sk)m(ewness)h(of) f(all)h(data)h(added)d(to)i(the)g(accum)m(ulator,)h(de\014ned)d(as)1449 2884 y FE(sk)s(ew)f FK(=)1802 2823 y(1)p 1783 2863 83 4 v 1783 2947 a FE(N)1891 2803 y Fs(X)2026 2765 y(\022)2097 2823 y FE(x)2149 2837 y Fq(i)2197 2823 y FI(\000)c FK(^)-49 b FE(\026)p 2097 2863 246 4 v 2197 2947 a FK(^)f FE(\033)2353 2765 y Fs(\023)2414 2780 y FB(3)3350 3134 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_rstat_kurtosis)d Fu(\()p FD(gsl)p 1650 3134 28 4 v 41 w(rstat)p 1878 3134 V 41 w(w)m(orkspace)31 b(*)f Ft(w)p Fu(\))390 3243 y FK(This)g(function)g(returns)f(the)h(kurtosis)h(of)f(all)h(data)g (added)f(to)h(the)g(accum)m(ulator,)h(de\014ned)d(as)1237 3482 y FE(k)s(ur)s(tosis)24 b FK(=)1697 3338 y Fs( )1792 3420 y FK(1)p 1773 3461 83 4 v 1773 3544 a FE(N)1881 3401 y Fs(X)2016 3363 y(\022)2087 3420 y FE(x)2139 3434 y Fq(i)2187 3420 y FI(\000)g FK(^)-49 b FE(\026)p 2087 3461 246 4 v 2187 3544 a FK(^)f FE(\033)2343 3363 y Fs(\023)2404 3378 y FB(4)2441 3338 y Fs(!)2527 3482 y FI(\000)20 b FK(3)3350 3756 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_rstat_median)c Fu(\()p FD(gsl)p 1545 3756 28 4 v 41 w(rstat)p 1773 3756 V 41 w(w)m(orkspace)31 b(*)g Ft(w)p Fu(\))390 3866 y FK(This)22 b(function)h(returns)f(an)h (estimate)i(of)e(the)g(median)g(of)h(the)f(data)h(added)e(to)i(the)f (accum)m(ulator.)150 4107 y FJ(22.4)68 b(Quan)l(tiles)150 4267 y FK(The)44 b(functions)f(in)h(this)g(section)i(estimate)g(quan)m (tiles)f(dynamically)g(without)f(storing)h(the)f(en)m(tire)150 4376 y(dataset,)39 b(using)d(the)g(algorithm)h(of)f(Jain)g(and)g(Chlam) m(tec,)i(1985.)60 b(Only)35 b(\014v)m(e)i(p)s(oin)m(ts)f(\(mark)m (ers\))h(are)150 4486 y(stored)25 b(whic)m(h)g(represen)m(t)f(the)i (minim)m(um)e(and)g(maxim)m(um)h(of)g(the)g(data,)i(as)e(w)m(ell)h(as)f (curren)m(t)f(estimates)150 4595 y(of)32 b(the)h FE(p=)p FK(2-,)h FE(p)p FK(-,)f(and)e(\(1)23 b(+)e FE(p)p FK(\))p FE(=)p FK(2-quan)m(tiles.)48 b(Eac)m(h)33 b(time)g(a)g(new)f(data)g(p)s (oin)m(t)h(is)f(added,)g(the)h(mark)m(er)150 4705 y(p)s(ositions)d(and) g(heigh)m(ts)h(are)g(up)s(dated.)3350 4902 y([F)-8 b(unction])-3599 b Fv(gsl_rstat_quantile_wor)q(ksp)q(ace)59 b(*)52 b (gsl_rstat_quantile_al)q(loc)565 5011 y Fu(\()p FD(const)31 b(double)f Ft(p)p Fu(\))390 5121 y FK(This)e(function)g(allo)s(cates)j (a)e(w)m(orkspace)g(for)f(the)h(dynamic)g(estimation)h(of)e FD(p)p FK(-quan)m(tiles,)i(where)390 5230 y FD(p)h FK(is)e(b)s(et)m(w)m (een)h(0)g(and)e(1.)41 b(The)28 b(median)h(corresp)s(onds)f(to)i FE(p)25 b FK(=)g(0)p FE(:)p FK(5.)41 b(The)29 b(size)h(of)f(the)g(w)m (orkspace)390 5340 y(is)h FE(O)s FK(\(1\).)p eop end %%Page: 287 305 TeXDict begin 287 304 bop 150 -116 a FK(Chapter)30 b(22:)41 b(Running)29 b(Statistics)2221 b(287)3350 299 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_rstat_quantile_free)e Fu(\()p FD(gsl)p 1807 299 28 4 v 41 w(rstat)p 2035 299 V 40 w(quan)m(tile)p 2392 299 V 42 w(w)m(orkspace)31 b(*)g Ft(w)p Fu(\))390 408 y FK(This)f(function)g(frees)g(the)h(memory) f(asso)s(ciated)i(with)e(the)g(w)m(orkspace)h FD(w)p FK(.)3350 597 y([F)-8 b(unction])-3599 b Fv(int)53 b (gsl_rstat_quantile_re)q(set)f Fu(\()p FD(gsl)p 1807 597 V 41 w(rstat)p 2035 597 V 40 w(quan)m(tile)p 2392 597 V 42 w(w)m(orkspace)31 b(*)g Ft(w)p Fu(\))390 706 y FK(This)d(function)g(resets)h(the)f(w)m(orkspace)h FD(w)36 b FK(to)29 b(its)g(initial)h(state,)g(so)f(it)g(can)g(b)s(egin) f(w)m(orking)g(on)h(a)390 816 y(new)h(set)h(of)f(data.)3350 1004 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_rstat_quantile_ad)q(d)e Fu(\()p FD(const)32 b(double)e Ft(x)p FD(,)565 1114 y(gsl)p 677 1114 V 41 w(rstat)p 905 1114 V 40 w(quan)m(tile)p 1262 1114 V 41 w(w)m(orkspace)i(*)e Ft(w)p Fu(\))390 1223 y FK(This)g(function)g(up)s(dates)f(the)i(estimate)h(of)e(the)h FE(p)p FK(-quan)m(tile)g(with)f(the)h(new)f(data)h(p)s(oin)m(t)f FD(x)p FK(.)3350 1411 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_rstat_quantile_get)e Fu(\()p FD(gsl)p 1859 1411 V 41 w(rstat)p 2087 1411 V 41 w(quan)m(tile)p 2445 1411 V 41 w(w)m(orkspace)31 b(*)g Ft(w)p Fu(\))390 1521 y FK(This)f(function)g(returns)f(the)h(curren)m(t)h(estimate)h(of)e(the)h FE(p)p FK(-quan)m(tile.)150 1756 y FJ(22.5)68 b(Examples)150 1916 y FK(Here)31 b(is)f(a)h(basic)g(example)g(of)f(ho)m(w)h(to)g(use)f (the)h(statistical)i(functions:)390 2052 y FH(#include)46 b()390 2162 y(#include)g()390 2381 y(int)390 2491 y(main\(void\))390 2600 y({)485 2710 y(double)h(data[5])e(=)j({17.2,)e(18.1,)g(16.5,)h(18.3,)f(12.6};)485 2819 y(double)h(mean,)f(variance,)f(largest,)h(smallest,)f(sd,)820 2929 y(rms,)h(sd_mean,)g(median,)g(skew,)g(kurtosis;)485 3039 y(gsl_rstat_workspace)d(*rstat_p)j(=)h(gsl_rstat_alloc\(\);)485 3148 y(size_t)g(i,)g(n;)485 3367 y(/*)h(add)f(data)f(to)h(rstat)g (accumulator)d(*/)485 3477 y(for)j(\(i)h(=)f(0;)g(i)h(<)f(5;)g(++i\)) 581 3587 y(gsl_rstat_add\(data[i],)42 b(rstat_p\);)485 3806 y(mean)238 b(=)47 b(gsl_rstat_mean\(rstat_p\);)485 3915 y(variance)f(=)h(gsl_rstat_variance\(rstat_p)o(\);)485 4025 y(largest)94 b(=)47 b(gsl_rstat_max\(rstat_p\);)485 4134 y(smallest)f(=)h(gsl_rstat_min\(rstat_p\);)485 4244 y(median)142 b(=)47 b(gsl_rstat_median\(rstat_p\);)485 4354 y(sd)334 b(=)47 b(gsl_rstat_sd\(rstat_p\);)485 4463 y(sd_mean)94 b(=)47 b(gsl_rstat_sd_mean\(rstat_p\))o(;)485 4573 y(skew)238 b(=)47 b(gsl_rstat_skew\(rstat_p\);)485 4682 y(rms)286 b(=)47 b(gsl_rstat_rms\(rstat_p\);)485 4792 y(kurtosis)f(=)h(gsl_rstat_kurtosis\(rstat_p)o(\);)485 4902 y(n)382 b(=)47 b(gsl_rstat_n\(rstat_p\);)485 5121 y(printf)g(\("The)f(dataset)g(is)h(\045g,)g(\045g,)g(\045g,)g(\045g,)g (\045g\\n",)820 5230 y(data[0],)e(data[1],)h(data[2],)f(data[3],)h (data[4]\);)p eop end %%Page: 288 306 TeXDict begin 288 305 bop 150 -116 a FK(Chapter)30 b(22:)41 b(Running)29 b(Statistics)2221 b(288)485 299 y FH(printf)47 b(\("The)f(sample)g(mean)h(is)g(\045g\\n",)f(mean\);)485 408 y(printf)h(\("The)f(estimated)f(variance)h(is)h(\045g\\n",)f (variance\);)485 518 y(printf)h(\("The)f(largest)g(value)g(is)h (\045g\\n",)f(largest\);)485 628 y(printf)h(\("The)f(smallest)f(value)i (is)g(\045g\\n",)f(smallest\);)485 737 y(printf\()g("The)h(median)f(is) h(\045g\\n",)f(median\);)485 847 y(printf\()g("The)h(standard)e (deviation)h(is)h(\045g\\n",)f(sd\);)485 956 y(printf\()g("The)h(root)g (mean)f(square)g(is)h(\045g\\n",)g(rms\);)485 1066 y(printf\()f("The)h (standard)e(devation)h(of)h(the)g(mean)g(is)g(\045g\\n",)f(sd_mean\);) 485 1176 y(printf\()g("The)h(skew)g(is)g(\045g\\n",)f(skew\);)485 1285 y(printf\()g("The)h(kurtosis)e(\045g\\n",)i(kurtosis\);)485 1395 y(printf\()f("There)g(are)h(\045zu)g(items)g(in)g(the)g (accumulator\\n",)c(n\);)485 1614 y(gsl_rstat_reset\(rstat_p\);)485 1724 y(n)48 b(=)f(gsl_rstat_n\(rstat_p\);)485 1833 y(printf\()f("There) g(are)h(\045zu)g(items)g(in)g(the)g(accumulator\\n",)c(n\);)485 2052 y(gsl_rstat_free\(rstat_p\);)485 2271 y(return)k(0;)390 2381 y(})275 2518 y FK(The)29 b(program)i(should)e(pro)s(duce)g(the)i (follo)m(wing)h(output,)390 2655 y FH(The)47 b(dataset)f(is)h(17.2,)f (18.1,)h(16.5,)f(18.3,)g(12.6)390 2765 y(The)h(sample)f(mean)h(is)g (16.54)390 2874 y(The)g(estimated)e(variance)h(is)h(5.373)390 2984 y(The)g(largest)f(value)g(is)h(18.3)390 3093 y(The)g(smallest)e (value)i(is)g(12.6)390 3203 y(The)g(median)f(is)h(16.5)390 3313 y(The)g(standard)e(deviation)h(is)h(2.31797)390 3422 y(The)g(root)g(mean)f(square)g(is)h(16.6694)390 3532 y(The)g(standard)e(devation)h(of)h(the)g(mean)g(is)g(1.03663)390 3641 y(The)g(skew)g(is)g(-0.829058)390 3751 y(The)g(kurtosis)e(-1.2217) 390 3861 y(There)h(are)h(5)h(items)e(in)h(the)g(accumulator)390 3970 y(There)f(are)h(0)h(items)e(in)h(the)g(accumulator)150 4107 y FK(This)39 b(next)g(program)g(estimates)i(the)e(lo)m(w)m(er)i (quartile,)i(median)c(and)f(upp)s(er)g(quartile)i(from)e(10,000)150 4217 y(samples)32 b(of)h(a)f(random)g(Ra)m(yleigh)h(distribution,)g (using)e(the)i FE(P)2379 4184 y FB(2)2448 4217 y FK(algorithm)g(of)g (Jain)f(and)f(Chlam)m(tec.)150 4326 y(F)-8 b(or)31 b(comparison,)g(the) g(exact)g(v)-5 b(alues)31 b(are)g(also)g(computed)f(from)g(the)h (sorted)f(dataset.)390 4463 y FH(#include)46 b()390 4573 y(#include)g()390 4682 y(#include)g() 390 4792 y(#include)g()390 4902 y(#include)g()390 5011 y(#include)g() 390 5121 y(#include)g()390 5340 y(int)p eop end %%Page: 289 307 TeXDict begin 289 306 bop 150 -116 a FK(Chapter)30 b(22:)41 b(Running)29 b(Statistics)2221 b(289)390 299 y FH(main\(void\))390 408 y({)485 518 y(const)47 b(size_t)f(N)h(=)h(10000;)485 628 y(double)f(*data)f(=)h(malloc\(N)f(*)h(sizeof\(double\)\);)485 737 y(gsl_rstat_quantile_workspa)o(ce)42 b(*work_25)j(=)j (gsl_rstat_quantile_allo)o(c\(0)o(.25\))o(;)485 847 y (gsl_rstat_quantile_workspa)o(ce)42 b(*work_50)j(=)j (gsl_rstat_quantile_allo)o(c\(0)o(.5\);)485 956 y (gsl_rstat_quantile_workspa)o(ce)42 b(*work_75)j(=)j (gsl_rstat_quantile_allo)o(c\(0)o(.75\))o(;)485 1066 y(gsl_rng)e(*r)h(=)h(gsl_rng_alloc\(gsl_rng_de)o(faul)o(t\);)485 1176 y(double)f(exact_p25,)e(exact_p50,)g(exact_p75;)485 1285 y(double)i(val_p25,)e(val_p50,)h(val_p75;)485 1395 y(size_t)h(i;)485 1614 y(/*)h(add)f(data)f(to)h(quantile)f (accumulators;)e(also)j(store)f(data)h(for)g(exact)533 1724 y(*)h(comparisons)c(*/)485 1833 y(for)j(\(i)h(=)f(0;)g(i)h(<)f(N;) g(++i\))581 1943 y({)676 2052 y(data[i])f(=)i(gsl_ran_rayleigh\(r,)42 b(1.0\);)676 2162 y(gsl_rstat_quantile_add\(dat)o(a[i)o(],)g (work_25\);)676 2271 y(gsl_rstat_quantile_add\(dat)o(a[i)o(],)g (work_50\);)676 2381 y(gsl_rstat_quantile_add\(dat)o(a[i)o(],)g (work_75\);)581 2491 y(})485 2710 y(/*)48 b(exact)e(values)g(*/)485 2819 y(gsl_sort\(data,)e(1,)k(N\);)485 2929 y(exact_p25)e(=)h (gsl_stats_quantile_from_s)o(orte)o(d_d)o(ata\()o(data)o(,)42 b(1,)47 b(N,)g(0.25\);)485 3039 y(exact_p50)f(=)h (gsl_stats_quantile_from_s)o(orte)o(d_d)o(ata\()o(data)o(,)42 b(1,)47 b(N,)g(0.5\);)485 3148 y(exact_p75)f(=)h (gsl_stats_quantile_from_s)o(orte)o(d_d)o(ata\()o(data)o(,)42 b(1,)47 b(N,)g(0.75\);)485 3367 y(/*)h(estimated)d(values)h(*/)485 3477 y(val_p25)g(=)i(gsl_rstat_quantile_get\()o(work)o(_25\))o(;)485 3587 y(val_p50)e(=)i(gsl_rstat_quantile_get\()o(work)o(_50\))o(;)485 3696 y(val_p75)e(=)i(gsl_rstat_quantile_get\()o(work)o(_75\))o(;)485 3915 y(printf)f(\("The)f(dataset)g(is)h(\045g,)g(\045g,)g(\045g,)g (\045g,)g(\045g,)f(...\\n",)820 4025 y(data[0],)f(data[1],)h(data[2],)f (data[3],)h(data[4]\);)485 4244 y(printf)h(\("0.25)f(quartile:)93 b(exact)46 b(=)h(\045.5f,)g(estimated)e(=)j(\045.5f,)e(error)g(=)i (\045.6e\\n",)867 4354 y(exact_p25,)d(val_p25,)h(\(val_p25)f(-)j (exact_p25\))d(/)i(exact_p25\);)485 4463 y(printf)g(\("0.50)f (quartile:)93 b(exact)46 b(=)h(\045.5f,)g(estimated)e(=)j(\045.5f,)e (error)g(=)i(\045.6e\\n",)867 4573 y(exact_p50,)d(val_p50,)h(\(val_p50) f(-)j(exact_p50\))d(/)i(exact_p50\);)485 4682 y(printf)g(\("0.75)f (quartile:)93 b(exact)46 b(=)h(\045.5f,)g(estimated)e(=)j(\045.5f,)e (error)g(=)i(\045.6e\\n",)867 4792 y(exact_p75,)d(val_p75,)h(\(val_p75) f(-)j(exact_p75\))d(/)i(exact_p75\);)485 5011 y (gsl_rstat_quantile_free\(wo)o(rk_2)o(5\);)485 5121 y (gsl_rstat_quantile_free\(wo)o(rk_5)o(0\);)485 5230 y (gsl_rstat_quantile_free\(wo)o(rk_7)o(5\);)485 5340 y (gsl_rng_free\(r\);)p eop end %%Page: 290 308 TeXDict begin 290 307 bop 150 -116 a FK(Chapter)30 b(22:)41 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y(of)f(the)f(histogram)h FD(src)p FK(.)150 1759 y FJ(23.4)68 b(Up)t(dating)46 b(and)e(accessing)i(histogram)g(elemen)l (ts)150 1919 y FK(There)21 b(are)h(t)m(w)m(o)h(w)m(a)m(ys)g(to)g (access)g(histogram)f(bins,)h(either)f(b)m(y)g(sp)s(ecifying)f(an)h FE(x)f FK(co)s(ordinate)i(or)f(b)m(y)f(using)150 2028 y(the)27 b(bin-index)f(directly)-8 b(.)40 b(The)26 b(functions)h(for)f (accessing)i(the)f(histogram)g(through)f FE(x)h FK(co)s(ordinates)g (use)150 2138 y(a)k(binary)e(searc)m(h)i(to)g(iden)m(tify)g(the)g(bin)e (whic)m(h)i(co)m(v)m(ers)g(the)g(appropriate)f(range.)3350 2303 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_histogram_increme)q(nt) f Fu(\()p FD(gsl)p 1755 2303 V 41 w(histogram)31 b(*)f Ft(h)p FD(,)h(double)f Ft(x)p Fu(\))390 2413 y FK(This)35 b(function)g(up)s(dates)g(the)h(histogram)g FD(h)f FK(b)m(y)h(adding)f (one)h(\(1.0\))i(to)e(the)g(bin)f(whose)h(range)390 2523 y(con)m(tains)c(the)e(co)s(ordinate)h FD(x)p FK(.)390 2651 y(If)d FD(x)34 b FK(lies)28 b(in)g(the)g(v)-5 b(alid)29 b(range)f(of)g(the)g(histogram)h(then)f(the)g(function)g(returns)e (zero)j(to)g(indicate)390 2761 y(success.)53 b(If)34 b FD(x)41 b FK(is)34 b(less)h(than)f(the)g(lo)m(w)m(er)i(limit)f(of)g (the)f(histogram)h(then)f(the)h(function)f(returns)390 2870 y FH(GSL_EDOM)p FK(,)c(and)h(none)h(of)g(bins)f(are)h(mo)s (di\014ed.)44 b(Similarly)-8 b(,)33 b(if)f(the)g(v)-5 b(alue)32 b(of)g FD(x)38 b FK(is)32 b(greater)h(than)390 2980 y(or)28 b(equal)g(to)g(the)g(upp)s(er)d(limit)j(of)g(the)g (histogram)g(then)f(the)h(function)f(returns)f FH(GSL_EDOM)p FK(,)h(and)390 3089 y(none)36 b(of)h(the)g(bins)f(are)h(mo)s(di\014ed.) 58 b(The)36 b(error)g(handler)g(is)h(not)f(called,)k(ho)m(w)m(ev)m(er,) g(since)d(it)g(is)390 3199 y(often)29 b(necessary)h(to)f(compute)h (histograms)f(for)g(a)g(small)g(range)h(of)f(a)g(larger)h(dataset,)h (ignoring)390 3309 y(the)g(v)-5 b(alues)30 b(outside)h(the)f(range)h (of)g(in)m(terest.)3350 3474 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_histogram_accumul)q(ate)f Fu(\()p FD(gsl)p 1807 3474 V 41 w(histogram)31 b(*)g Ft(h)p FD(,)f(double)g Ft(x)p FD(,)h(double)565 3584 y Ft(weight)p Fu(\))390 3693 y FK(This)e(function)h(is)h(similar)f(to)i FH (gsl_histogram_increment)23 b FK(but)30 b(increases)h(the)g(v)-5 b(alue)30 b(of)h(the)390 3803 y(appropriate)f(bin)g(in)g(the)h (histogram)g FD(h)e FK(b)m(y)i(the)f(\015oating-p)s(oin)m(t)i(n)m(um)m (b)s(er)d FD(w)m(eigh)m(t)p FK(.)3350 3969 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_histogram_get)d Fu(\()p FD(const)31 b(gsl)p 1836 3969 V 41 w(histogram)g(*)f Ft(h)p FD(,)h(size)p 2626 3969 V 41 w(t)g Ft(i)p Fu(\))390 4078 y FK(This)e(function)g (returns)f(the)h(con)m(ten)m(ts)j(of)d(the)h FD(i)p FK(-th)g(bin)e(of)i (the)f(histogram)h FD(h)p FK(.)40 b(If)29 b FD(i)35 b FK(lies)30 b(outside)390 4188 y(the)k(v)-5 b(alid)33 b(range)h(of)g(indices)f(for)h(the)f(histogram)h(then)f(the)h(error)f (handler)g(is)g(called)i(with)e(an)390 4298 y(error)d(co)s(de)h(of)f FH(GSL_EDOM)e FK(and)i(the)h(function)f(returns)f(0.)3350 4463 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_histogram_get_ran)q(ge) f Fu(\()p FD(const)31 b(gsl)p 1993 4463 V 40 w(histogram)g(*)g Ft(h)p FD(,)g(size)p 2783 4463 V 41 w(t)g Ft(i)p FD(,)565 4573 y(double)f(*)h Ft(lower)p FD(,)h(double)e(*)h Ft(upper)p Fu(\))390 4682 y FK(This)f(function)g(\014nds)f(the)i(upp)s(er)d(and)i (lo)m(w)m(er)i(range)f(limits)g(of)g(the)g FD(i)p FK(-th)g(bin)f(of)h (the)f(histogram)390 4792 y FD(h)p FK(.)42 b(If)30 b(the)h(index)g FD(i)36 b FK(is)30 b(v)-5 b(alid)32 b(then)e(the)h(corresp)s(onding)f (range)h(limits)h(are)f(stored)g(in)g FD(lo)m(w)m(er)39 b FK(and)390 4902 y FD(upp)s(er)p FK(.)d(The)24 b(lo)m(w)m(er)h(limit)f (is)g(inclusiv)m(e)g(\(i.e.)40 b(ev)m(en)m(ts)25 b(with)e(this)h(co)s (ordinate)g(are)g(included)f(in)h(the)390 5011 y(bin\))f(and)f(the)i (upp)s(er)d(limit)j(is)g(exclusiv)m(e)g(\(i.e.)40 b(ev)m(en)m(ts)24 b(with)f(the)h(co)s(ordinate)g(of)f(the)h(upp)s(er)d(limit)390 5121 y(are)28 b(excluded)f(and)g(fall)h(in)f(the)h(neigh)m(b)s(oring)f (higher)g(bin,)g(if)h(it)f(exists\).)41 b(The)27 b(function)g(returns) 390 5230 y(0)g(to)g(indicate)g(success.)40 b(If)26 b FD(i)31 b FK(lies)d(outside)e(the)h(v)-5 b(alid)27 b(range)f(of)h (indices)f(for)h(the)f(histogram)h(then)390 5340 y(the)k(error)f (handler)f(is)h(called)i(and)e(the)g(function)g(returns)g(an)g(error)g (co)s(de)g(of)h FH(GSL_EDOM)p FK(.)p eop end %%Page: 294 312 TeXDict begin 294 311 bop 150 -116 a FK(Chapter)30 b(23:)41 b(Histograms)2507 b(294)3350 299 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_histogram_max)d Fu(\()p FD(const)31 b(gsl)p 1836 299 28 4 v 41 w(histogram)g(*)f Ft(h)p Fu(\))3350 408 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_histogram_min)d Fu(\()p FD(const)31 b(gsl)p 1836 408 V 41 w(histogram)g(*)f Ft(h)p Fu(\))3350 518 y FK([F)-8 b(unction])-3599 b Fv(size_t)54 b(gsl_histogram_bins)d Fu(\()p FD(const)31 b(gsl)p 1888 518 V 41 w(histogram)g(*)g Ft(h)p Fu(\))390 628 y FK(These)c(functions) g(return)f(the)h(maxim)m(um)g(upp)s(er)e(and)h(minim)m(um)h(lo)m(w)m (er)h(range)f(limits)h(and)f(the)390 737 y(n)m(um)m(b)s(er)k(of)h(bins) g(of)g(the)h(histogram)g FD(h)p FK(.)46 b(They)32 b(pro)m(vide)g(a)h(w) m(a)m(y)g(of)g(determining)f(these)h(v)-5 b(alues)390 847 y(without)30 b(accessing)i(the)f FH(gsl_histogram)c FK(struct)j(directly)-8 b(.)3350 1039 y([F)g(unction])-3599 b Fv(void)54 b(gsl_histogram_reset)d Fu(\()p FD(gsl)p 1598 1039 V 41 w(histogram)31 b(*)f Ft(h)p Fu(\))390 1148 y FK(This)g(function)g(resets)g(all)i(the)e(bins)g(in)g(the)g (histogram)h FD(h)f FK(to)h(zero.)150 1386 y FJ(23.5)68 b(Searc)l(hing)46 b(histogram)g(ranges)150 1546 y FK(The)28 b(follo)m(wing)i(functions)f(are)g(used)f(b)m(y)h(the)f(access)j(and)d (up)s(date)g(routines)g(to)i(lo)s(cate)g(the)f(bin)f(whic)m(h)150 1655 y(corresp)s(onds)h(to)i(a)g(giv)m(en)g FE(x)f FK(co)s(ordinate.) 3350 1847 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_histogram_find)e Fu(\()p FD(const)31 b(gsl)p 1731 1847 V 41 w(histogram)g(*)g Ft(h)p FD(,)g(double)e Ft(x)p FD(,)i(size)p 2922 1847 V 41 w(t)g(*)g Ft(i)p Fu(\))390 1957 y FK(This)23 b(function)h(\014nds) e(and)h(sets)h(the)g(index)g FD(i)29 b FK(to)24 b(the)g(bin)f(n)m(um)m (b)s(er)g(whic)m(h)h(co)m(v)m(ers)h(the)f(co)s(ordinate)390 2066 y FD(x)38 b FK(in)32 b(the)g(histogram)g FD(h)p FK(.)45 b(The)31 b(bin)h(is)f(lo)s(cated)j(using)d(a)h(binary)f(searc)m (h.)46 b(The)32 b(searc)m(h)g(includes)390 2176 y(an)k(optimization)i (for)e(histograms)g(with)g(uniform)f(range,)j(and)d(will)h(return)f (the)i(correct)g(bin)390 2286 y(immediately)27 b(in)e(this)g(case.)40 b(If)25 b FD(x)32 b FK(is)25 b(found)g(in)g(the)g(range)h(of)g(the)f (histogram)h(then)g(the)f(function)390 2395 y(sets)39 b(the)g(index)f FD(i)43 b FK(and)38 b(returns)g FH(GSL_SUCCESS)p FK(.)62 b(If)38 b FD(x)45 b FK(lies)39 b(outside)g(the)f(v)-5 b(alid)39 b(range)g(of)g(the)390 2505 y(histogram)31 b(then)f(the)h(function)f(returns)f FH(GSL_EDOM)f FK(and)i(the)g(error) g(handler)g(is)g(in)m(v)m(ok)m(ed.)150 2743 y FJ(23.6)68 b(Histogram)47 b(Statistics)3350 2956 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_histogram_max_val)e Fu(\()p FD(const)31 b(gsl)p 2045 2956 V 41 w(histogram)g(*)g Ft(h)p Fu(\))390 3066 y FK(This)f(function)g(returns)f(the)h(maxim)m(um)h(v)-5 b(alue)30 b(con)m(tained)i(in)e(the)h(histogram)g(bins.)3350 3257 y([F)-8 b(unction])-3599 b Fv(size_t)54 b(gsl_histogram_max_bin)e Fu(\()p FD(const)31 b(gsl)p 2045 3257 V 41 w(histogram)g(*)g Ft(h)p Fu(\))390 3367 y FK(This)25 b(function)g(returns)g(the)h(index)f (of)h(the)g(bin)f(con)m(taining)j(the)e(maxim)m(um)f(v)-5 b(alue.)40 b(In)25 b(the)h(case)390 3477 y(where)k(sev)m(eral)i(bins)d (con)m(tain)j(the)e(same)h(maxim)m(um)f(v)-5 b(alue)31 b(the)g(smallest)g(index)f(is)h(returned.)3350 3668 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_histogram_min_val)e Fu(\()p FD(const)31 b(gsl)p 2045 3668 V 41 w(histogram)g(*)g Ft(h)p Fu(\))390 3778 y FK(This)f(function)g(returns)f(the)h(minim)m (um)g(v)-5 b(alue)31 b(con)m(tained)g(in)f(the)h(histogram)g(bins.)3350 3970 y([F)-8 b(unction])-3599 b Fv(size_t)54 b(gsl_histogram_min_bin)e Fu(\()p FD(const)31 b(gsl)p 2045 3970 V 41 w(histogram)g(*)g Ft(h)p Fu(\))390 4080 y FK(This)26 b(function)h(returns)f(the)h(index)g (of)g(the)h(bin)e(con)m(taining)i(the)g(minim)m(um)e(v)-5 b(alue.)40 b(In)27 b(the)g(case)390 4189 y(where)j(sev)m(eral)i(bins)d (con)m(tain)j(the)e(same)h(maxim)m(um)f(v)-5 b(alue)31 b(the)g(smallest)g(index)f(is)h(returned.)3350 4381 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_histogram_mean)d Fu(\()p FD(const)31 b(gsl)p 1888 4381 V 41 w(histogram)g(*)g Ft(h)p Fu(\))390 4491 y FK(This)j(function)h(returns)e(the)i(mean)g(of) g(the)h(histogrammed)f(v)-5 b(ariable,)37 b(where)d(the)h(histogram)390 4600 y(is)42 b(regarded)g(as)h(a)g(probabilit)m(y)g(distribution.)75 b(Negativ)m(e)45 b(bin)d(v)-5 b(alues)43 b(are)f(ignored)h(for)f(the) 390 4710 y(purp)s(oses)29 b(of)h(this)g(calculation.)43 b(The)30 b(accuracy)i(of)e(the)h(result)f(is)g(limited)i(b)m(y)e(the)g (bin)g(width.)3350 4902 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_histogram_sigma)d Fu(\()p FD(const)32 b(gsl)p 1941 4902 V 40 w(histogram)f(*)g Ft(h)p Fu(\))390 5011 y FK(This)24 b(function)h(returns)f(the)h(standard)f(deviation)i(of)g(the)f (histogrammed)g(v)-5 b(ariable,)27 b(where)e(the)390 5121 y(histogram)34 b(is)f(regarded)g(as)h(a)f(probabilit)m(y)h (distribution.)49 b(Negativ)m(e)36 b(bin)d(v)-5 b(alues)33 b(are)h(ignored)390 5230 y(for)e(the)g(purp)s(oses)e(of)i(this)g (calculation.)47 b(The)31 b(accuracy)i(of)g(the)f(result)f(is)h (limited)h(b)m(y)f(the)g(bin)390 5340 y(width.)p eop end %%Page: 295 313 TeXDict begin 295 312 bop 150 -116 a FK(Chapter)30 b(23:)41 b(Histograms)2507 b(295)3350 299 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_histogram_sum)d Fu(\()p FD(const)31 b(gsl)p 1836 299 28 4 v 41 w(histogram)g(*)f Ft(h)p Fu(\))390 408 y FK(This)i(function)h(returns)f(the)i(sum)e(of)i(all)g(bin)e(v)-5 b(alues.)50 b(Negativ)m(e)36 b(bin)c(v)-5 b(alues)34 b(are)g(included)e(in)390 518 y(the)f(sum.)150 756 y FJ(23.7)68 b(Histogram)47 b(Op)t(erations)3350 969 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_histogram_equal_b)q(ins_)q (p)f Fu(\()p FD(const)31 b(gsl)p 2150 969 V 40 w(histogram)g(*)g Ft(h1)p FD(,)g(const)565 1079 y(gsl)p 677 1079 V 41 w(histogram)g(*)f Ft(h2)p Fu(\))390 1188 y FK(This)j(function)g(returns)g(1)h(if)g(the)g (all)g(of)g(the)g(individual)g(bin)e(ranges)i(of)g(the)g(t)m(w)m(o)h (histograms)390 1298 y(are)c(iden)m(tical,)h(and)e(0)h(otherwise.)3350 1490 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_histogram_add)e Fu(\()p FD(gsl)p 1441 1490 V 41 w(histogram)31 b(*)g Ft(h1)p FD(,)g(const)g(gsl)p 2487 1490 V 40 w(histogram)g(*)g Ft(h2)p Fu(\))390 1599 y FK(This)25 b(function)h(adds)f(the)h(con)m (ten)m(ts)h(of)f(the)g(bins)f(in)h(histogram)g FD(h2)33 b FK(to)27 b(the)f(corresp)s(onding)f(bins)390 1709 y(of)34 b(histogram)g FD(h1)p FK(,)g(i.e.)52 b FE(h)1299 1676 y Fp(0)1299 1731 y FB(1)1336 1709 y FK(\()p FE(i)p FK(\))32 b(=)e FE(h)1622 1723 y FB(1)1660 1709 y FK(\()p FE(i)p FK(\))23 b(+)f FE(h)1929 1723 y FB(2)1967 1709 y FK(\()p FE(i)p FK(\).)51 b(The)33 b(t)m(w)m(o)i(histograms)f(m)m(ust)f(ha)m(v)m (e)i(iden)m(tical)390 1819 y(bin)30 b(ranges.)3350 2010 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_histogram_sub)e Fu(\()p FD(gsl)p 1441 2010 V 41 w(histogram)31 b(*)g Ft(h1)p FD(,)g(const)g(gsl)p 2487 2010 V 40 w(histogram)g(*)g Ft(h2)p Fu(\))390 2120 y FK(This)24 b(function)h(subtracts)h(the)f(con) m(ten)m(ts)i(of)e(the)h(bins)e(in)h(histogram)h FD(h2)33 b FK(from)24 b(the)i(corresp)s(ond-)390 2230 y(ing)35 b(bins)e(of)i(histogram)g FD(h1)p FK(,)h(i.e.)54 b FE(h)1657 2197 y Fp(0)1657 2252 y FB(1)1694 2230 y FK(\()p FE(i)p FK(\))34 b(=)d FE(h)1983 2244 y FB(1)2021 2230 y FK(\()p FE(i)p FK(\))24 b FI(\000)f FE(h)2292 2244 y FB(2)2329 2230 y FK(\()p FE(i)p FK(\).)54 b(The)34 b(t)m(w)m(o)i(histograms)f(m)m (ust)g(ha)m(v)m(e)390 2339 y(iden)m(tical)d(bin)e(ranges.)3350 2531 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_histogram_mul)e Fu(\()p FD(gsl)p 1441 2531 V 41 w(histogram)31 b(*)g Ft(h1)p FD(,)g(const)g(gsl)p 2487 2531 V 40 w(histogram)g(*)g Ft(h2)p Fu(\))390 2641 y FK(This)h(function)g(m)m(ultiplies)i(the)f (con)m(ten)m(ts)i(of)d(the)h(bins)f(of)h(histogram)h FD(h1)40 b FK(b)m(y)32 b(the)h(con)m(ten)m(ts)i(of)390 2750 y(the)27 b(corresp)s(onding)e(bins)g(in)i(histogram)g FD(h2)p FK(,)g(i.e.)40 b FE(h)2190 2717 y Fp(0)2190 2773 y FB(1)2228 2750 y FK(\()p FE(i)p FK(\))26 b(=)f FE(h)2503 2764 y FB(1)2541 2750 y FK(\()p FE(i)p FK(\))12 b FI(\003)g FE(h)2763 2764 y FB(2)2802 2750 y FK(\()p FE(i)p FK(\).)41 b(The)26 b(t)m(w)m(o)h(histograms)390 2860 y(m)m(ust)j(ha)m(v)m(e)i (iden)m(tical)g(bin)e(ranges.)3350 3052 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_histogram_div)e Fu(\()p FD(gsl)p 1441 3052 V 41 w(histogram)31 b(*)g Ft(h1)p FD(,)g(const)g(gsl)p 2487 3052 V 40 w(histogram)g(*)g Ft(h2)p Fu(\))390 3161 y FK(This)e(function)g(divides)g(the)h(con)m(ten)m(ts)h(of)f(the)g (bins)f(of)g(histogram)i FD(h1)36 b FK(b)m(y)30 b(the)g(con)m(ten)m(ts) h(of)f(the)390 3271 y(corresp)s(onding)38 b(bins)h(in)g(histogram)g FD(h2)p FK(,)j(i.e.)68 b FE(h)2131 3238 y Fp(0)2131 3293 y FB(1)2169 3271 y FK(\()p FE(i)p FK(\))41 b(=)f FE(h)2474 3285 y FB(1)2512 3271 y FK(\()p FE(i)p FK(\))p FE(=h)2710 3285 y FB(2)2749 3271 y FK(\()p FE(i)p FK(\).)68 b(The)39 b(t)m(w)m(o)h(histograms)390 3381 y(m)m(ust)30 b(ha)m(v)m(e)i(iden)m (tical)g(bin)e(ranges.)3350 3572 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_histogram_scale)e Fu(\()p FD(gsl)p 1545 3572 V 41 w(histogram)31 b(*)g Ft(h)p FD(,)g(double)f Ft(scale)p Fu(\))390 3682 y FK(This)25 b(function)h(m)m(ultiplies)h (the)f(con)m(ten)m(ts)i(of)e(the)g(bins)f(of)i(histogram)f FD(h)g FK(b)m(y)g(the)g(constan)m(t)h FD(scale)p FK(,)390 3792 y(i.e.)42 b FE(h)599 3759 y Fp(0)599 3814 y FB(1)636 3792 y FK(\()p FE(i)p FK(\))26 b(=)f FE(h)911 3806 y FB(1)949 3792 y FK(\()p FE(i)p FK(\))c FI(\003)g Fg(sc)-5 b(ale)q FK(.)3350 3983 y([F)d(unction])-3599 b Fv(int)53 b(gsl_histogram_shift)e Fu(\()p FD(gsl)p 1545 3983 V 41 w(histogram)31 b(*)g Ft(h)p FD(,)g(double)f Ft(offset)p Fu(\))390 4093 y FK(This)c(function)g(shifts)h(the)g(con)m(ten)m(ts)h (of)f(the)g(bins)f(of)h(histogram)g FD(h)f FK(b)m(y)h(the)g(constan)m (t)h FD(o\013set)p FK(,)h(i.e.)390 4203 y FE(h)442 4170 y Fp(0)442 4225 y FB(1)480 4203 y FK(\()p FE(i)p FK(\))d(=)f FE(h)755 4217 y FB(1)792 4203 y FK(\()p FE(i)p FK(\))d(+)e Fg(o\013set)p FK(.)150 4441 y FJ(23.8)68 b(Reading)46 b(and)f(writing)h(histograms)150 4600 y FK(The)33 b(library)g(pro)m (vides)h(functions)f(for)g(reading)h(and)f(writing)h(histograms)g(to)g (a)g(\014le)g(as)f(binary)g(data)150 4710 y(or)d(formatted)h(text.)3350 4902 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_histogram_fwrite)f Fu(\()p FD(FILE)30 b(*)h Ft(stream)p FD(,)h(const)f(gsl)p 2522 4902 V 41 w(histogram)g(*)g Ft(h)p Fu(\))390 5011 y FK(This)38 b(function)g(writes)h(the)g(ranges)g(and)f(bins)g(of)h (the)g(histogram)h FD(h)e FK(to)h(the)g(stream)h FD(stream)390 5121 y FK(in)33 b(binary)g(format.)50 b(The)33 b(return)g(v)-5 b(alue)34 b(is)f(0)h(for)f(success)h(and)f FH(GSL_EFAILED)e FK(if)i(there)h(w)m(as)g(a)390 5230 y(problem)f(writing)h(to)g(the)g (\014le.)50 b(Since)34 b(the)g(data)g(is)g(written)f(in)h(the)g(nativ)m (e)h(binary)d(format)i(it)390 5340 y(ma)m(y)d(not)g(b)s(e)e(p)s (ortable)i(b)s(et)m(w)m(een)g(di\013eren)m(t)g(arc)m(hitectures.)p eop end %%Page: 296 314 TeXDict begin 296 313 bop 150 -116 a FK(Chapter)30 b(23:)41 b(Histograms)2507 b(296)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_histogram_fread)e Fu(\()p FD(FILE)31 b(*)g Ft(stream)p FD(,)h(gsl)p 2232 299 28 4 v 41 w(histogram)f(*)f Ft(h)p Fu(\))390 408 y FK(This)42 b(function)g(reads)h(in)m(to)h(the)f (histogram)g FD(h)f FK(from)h(the)g(op)s(en)f(stream)h FD(stream)g FK(in)g(binary)390 518 y(format.)c(The)24 b(histogram)i FD(h)e 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y(are)h(formatted)g(using)f FD(bin)p 1338 2575 V 40 w(format)p FK(.)44 b(Eac)m(h)33 b(line)f(con)m(tains)g(the)g(lo)m(w)m(er)h(and)e (upp)s(er)f(limit)i(of)g(the)390 2684 y(range)i(of)f(the)h(bins)e(and)h (the)h(v)-5 b(alue)33 b(of)h(the)g(bin)e(itself.)51 b(Since)33 b(the)h(upp)s(er)d(limit)j(of)g(one)f(bin)g(is)390 2794 y(the)e(lo)m(w)m(er)h(limit)g(of)e(the)h(next)g(there)g(is)g (duplication)g(of)g(these)g(v)-5 b(alues)32 b(b)s(et)m(w)m(een)f(lines) g(but)f(this)390 2904 y(allo)m(ws)i(the)e(histogram)h(to)g(b)s(e)f (manipulated)g(with)g(line-orien)m(ted)i(to)s(ols.)3350 3064 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_histogram_fscanf)f Fu(\()p FD(FILE)30 b(*)h Ft(stream)p FD(,)h(gsl)p 2284 3064 V 41 w(histogram)f(*)g Ft(h)p Fu(\))390 3173 y FK(This)23 b(function)h(reads)g(formatted)g(data)h(from)f(the)g(stream)g FD(stream)h FK(in)m(to)g(the)f(histogram)g FD(h)p FK(.)38 b(The)390 3283 y(data)30 b(is)g(assumed)f(to)h(b)s(e)f(in)g(the)h (three-column)g(format)g(used)f(b)m(y)g FH(gsl_histogram_fprintf)p FK(.)390 3393 y(The)e(histogram)h FD(h)f FK(m)m(ust)g(b)s(e)g(preallo)s (cated)i(with)e(the)h(correct)h(length)f(since)g(the)f(function)g(uses) 390 3502 y(the)37 b(size)i(of)e FD(h)g FK(to)h(determine)f(ho)m(w)g (man)m(y)h(n)m(um)m(b)s(ers)e(to)h(read.)62 b(The)37 b(function)f(returns)h(0)g(for)390 3612 y(success)31 b(and)e FH(GSL_EFAILED)f FK(if)i(there)h(w)m(as)f(a)h(problem)f (reading)g(from)g(the)h(\014le.)150 3828 y FJ(23.9)68 b(Resampling)47 b(from)e(histograms)150 3987 y FK(A)33 b(histogram)h(made)g(b)m(y)f(coun)m(ting)h(ev)m(en)m(ts)h(can)e(b)s(e)g (regarded)g(as)h(a)g(measuremen)m(t)f(of)h(a)f(probabilit)m(y)150 4097 y(distribution.)39 b(Allo)m(wing)29 b(for)f(statistical)j(error,)d (the)g(heigh)m(t)h(of)f(eac)m(h)h(bin)e(represen)m(ts)g(the)h (probabilit)m(y)150 4207 y(of)h(an)g(ev)m(en)m(t)i(where)e(the)g(v)-5 b(alue)30 b(of)f FE(x)g FK(falls)h(in)f(the)g(range)h(of)f(that)h(bin.) 39 b(The)29 b(probabilit)m(y)h(distribution)150 4316 y(function)g(has)g(the)h(one-dimensional)g(form)f FE(p)p FK(\()p FE(x)p FK(\))p FE(dx)h FK(where,)1618 4476 y FE(p)p FK(\()p FE(x)p FK(\))26 b(=)f FE(n)1963 4490 y Fq(i)1990 4476 y FE(=)p FK(\()p FE(N)10 b(w)2218 4490 y Fq(i)2246 4476 y FK(\))150 4635 y(In)31 b(this)g(equation)i FE(n)871 4649 y Fq(i)929 4635 y FK(is)f(the)f(n)m(um)m(b)s(er)g(of)g (ev)m(en)m(ts)i(in)e(the)h(bin)f(whic)m(h)g(con)m(tains)i FE(x)p FK(,)f FE(w)3109 4649 y Fq(i)3168 4635 y FK(is)f(the)h(width)f (of)150 4745 y(the)h(bin)e(and)h FE(N)41 b FK(is)32 b(the)f(total)i(n)m (um)m(b)s(er)d(of)i(ev)m(en)m(ts.)45 b(The)31 b(distribution)g(of)g(ev) m(en)m(ts)i(within)e(eac)m(h)h(bin)f(is)150 4855 y(assumed)f(to)h(b)s (e)e(uniform.)150 5071 y FJ(23.10)69 b(The)44 b(histogram)i(probabilit) l(y)g(distribution)g(struct)150 5230 y FK(The)24 b(probabilit)m(y)h (distribution)f(function)g(for)g(a)h(histogram)g(consists)g(of)f(a)h (set)g(of)g FD(bins)i FK(whic)m(h)d(measure)150 5340 y(the)e(probabilit)m(y)f(of)h(an)f(ev)m(en)m(t)i(falling)f(in)m(to)h(a) f(giv)m(en)g(range)g(of)f(a)h(con)m(tin)m(uous)g(v)-5 b(ariable)22 b FE(x)p FK(.)38 b(A)21 b(probabilit)m(y)p eop end %%Page: 297 315 TeXDict begin 297 314 bop 150 -116 a FK(Chapter)30 b(23:)41 b(Histograms)2507 b(297)150 299 y(distribution)24 b(function)h(is)g (de\014ned)e(b)m(y)i(the)g(follo)m(wing)h(struct,)h(whic)m(h)d (actually)j(stores)e(the)g(cum)m(ulativ)m(e)150 408 y(probabilit)m(y)e (distribution)f(function.)38 b(This)22 b(is)g(the)h(natural)g(quan)m (tit)m(y)h(for)e(generating)i(samples)f(via)g(the)150 518 y(in)m(v)m(erse)34 b(transform)f(metho)s(d,)g(b)s(ecause)g(there)h (is)f(a)g(one-to-one)j(mapping)c(b)s(et)m(w)m(een)i(the)f(cum)m(ulativ) m(e)150 628 y(probabilit)m(y)42 b(distribution)e(and)g(the)i(range)f ([0,1].)75 b(It)41 b(can)g(b)s(e)g(sho)m(wn)f(that)i(b)m(y)f(taking)h (a)f(uniform)150 737 y(random)36 b(n)m(um)m(b)s(er)f(in)h(this)g(range) h(and)e(\014nding)g(its)i(corresp)s(onding)e(co)s(ordinate)j(in)e(the)g (cum)m(ulativ)m(e)150 847 y(probabilit)m(y)31 b(distribution)f(w)m(e)g (obtain)h(samples)g(with)f(the)g(desired)g(probabilit)m(y)h (distribution.)3269 1051 y([Data)h(T)m(yp)s(e])-3600 b Fv(gsl_histogram_pdf)390 1191 y FH(size_t)29 b(n)115 b FK(This)29 b(is)h(the)g(n)m(um)m(b)s(er)e(of)i(bins)f(used)f(to)j (appro)m(ximate)g(the)f(probabilit)m(y)g(distribu-)870 1300 y(tion)h(function.)390 1470 y FH(double)e(*)h(range)870 1579 y FK(The)j(ranges)i(of)f(the)g(bins)f(are)h(stored)g(in)g(an)g (arra)m(y)g(of)g FD(n)22 b FK(+)g(1)35 b(elemen)m(ts)g(p)s(oin)m(ted) 870 1689 y(to)c(b)m(y)f FD(range)p FK(.)390 1858 y FH(double)f(*)h(sum) 870 1968 y FK(The)23 b(cum)m(ulativ)m(e)j(probabilit)m(y)f(for)f(the)g (bins)f(is)h(stored)g(in)g(an)f(arra)m(y)i(of)f FD(n)g FK(elemen)m(ts)870 2077 y(p)s(oin)m(ted)30 b(to)h(b)m(y)g FD(sum)p FK(.)150 2282 y(The)g(follo)m(wing)i(functions)e(allo)m(w)i(y) m(ou)f(to)g(create)h(a)f FH(gsl_histogram_pdf)27 b FK(struct)32 b(whic)m(h)f(represen)m(ts)150 2391 y(this)f(probabilit)m(y)h (distribution)f(and)g(generate)i(random)d(samples)i(from)e(it.)3350 2596 y([F)-8 b(unction])-3599 b Fv(gsl_histogram_pdf)57 b(*)c(gsl_histogram_pdf_allo)q(c)e Fu(\()p FD(size)p 2626 2596 28 4 v 42 w(t)30 b Ft(n)p Fu(\))390 2705 y FK(This)c(function)g(allo)s(cates)k(memory)c(for)h(a)g(probabilit)m(y)g (distribution)f(with)h FD(n)f FK(bins)g(and)g(returns)390 2815 y(a)39 b(p)s(oin)m(ter)f(to)h(a)g(newly)f(initialized)i FH(gsl_histogram_pdf)33 b FK(struct.)65 b(If)38 b(insu\016cien)m(t)g (memory)390 2924 y(is)33 b(a)m(v)-5 b(ailable)35 b(a)d(n)m(ull)h(p)s (oin)m(ter)f(is)h(returned)e(and)h(the)h(error)f(handler)g(is)h(in)m(v) m(ok)m(ed)h(with)e(an)g(error)390 3034 y(co)s(de)f(of)f FH(GSL_ENOMEM)p FK(.)3350 3238 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_histogram_pdf_ini)q(t)e Fu(\()p FD(gsl)p 1702 3238 V 41 w(histogram)p 2137 3238 V 41 w(p)s(df)29 b(*)h Ft(p)p FD(,)h(const)565 3348 y(gsl)p 677 3348 V 41 w(histogram)g(*)f Ft(h)p Fu(\))390 3457 y FK(This)35 b(function)h(initializes)i(the)e(probabilit)m(y)g(distribution)g FD(p)i FK(with)d(the)h(con)m(ten)m(ts)i(of)e(the)g(his-)390 3567 y(togram)c FD(h)p FK(.)41 b(If)30 b(an)m(y)h(of)g(the)g(bins)f(of) h FD(h)f FK(are)h(negativ)m(e)i(then)d(the)h(error)f(handler)g(is)h(in) m(v)m(ok)m(ed)h(with)390 3677 y(an)27 b(error)g(co)s(de)h(of)f FH(GSL_EDOM)e FK(b)s(ecause)i(a)h(probabilit)m(y)g(distribution)e (cannot)i(con)m(tain)h(negativ)m(e)390 3786 y(v)-5 b(alues.)3350 3990 y([F)d(unction])-3599 b Fv(void)54 b(gsl_histogram_pdf_free)e Fu(\()p FD(gsl)p 1755 3990 V 41 w(histogram)p 2190 3990 V 40 w(p)s(df)29 b(*)i Ft(p)p Fu(\))390 4100 y FK(This)42 b(function)g(frees)g(the)h(probabilit)m(y)g(distribution)f(function)g FD(p)j FK(and)c(all)j(of)e(the)h(memory)390 4210 y(asso)s(ciated)32 b(with)e(it.)3350 4414 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_histogram_pdf_samp)q(le)e Fu(\()p FD(const)31 b(gsl)p 2202 4414 V 41 w(histogram)p 2637 4414 V 40 w(p)s(df)e(*)i Ft(p)p FD(,)565 4523 y(double)f Ft(r)p Fu(\))390 4633 y FK(This)35 b(function)g(uses)g FD(r)p FK(,)i(a)e(uniform)g(random)f (n)m(um)m(b)s(er)h(b)s(et)m(w)m(een)h(zero)g(and)f(one,)i(to)g(compute) 390 4743 y(a)e(single)g(random)e(sample)i(from)f(the)g(probabilit)m(y)h (distribution)f FD(p)p FK(.)52 b(The)34 b(algorithm)i(used)d(to)390 4852 y(compute)e(the)f(sample)h FE(s)f FK(is)g(giv)m(en)h(b)m(y)g(the)f (follo)m(wing)i(form)m(ula,)1130 5030 y FE(s)24 b FK(=)h(range)q([)p FE(i)p FK(])c(+)f FE(\016)k FI(\003)d FK(\(range[)p FE(i)g FK(+)f(1])h FI(\000)f FK(range[)p FE(i)p FK(]\))390 5208 y(where)45 b FE(i)g FK(is)h(the)f(index)g(whic)m(h)g(satis\014es)h FE(sum)p FK([)p FE(i)p FK(])51 b FI(\024)f FE(r)i(<)e(sum)p FK([)p FE(i)30 b FK(+)g(1])46 b(and)f FE(del)r(ta)h FK(is)f(\()p FE(r)33 b FI(\000)390 5317 y FE(sum)p FK([)p FE(i)p FK(]\))p FE(=)p FK(\()p FE(sum)p FK([)p FE(i)22 b FK(+)e(1])h FI(\000)e FE(sum)p FK([)p FE(i)p FK(]\).)p eop end %%Page: 298 316 TeXDict begin 298 315 bop 150 -116 a FK(Chapter)30 b(23:)41 b(Histograms)2507 b(298)150 299 y FJ(23.11)69 b(Example)46 b(programs)f(for)g(histograms)150 458 y FK(The)37 b(follo)m(wing)h (program)f(sho)m(ws)g(ho)m(w)g(to)h(mak)m(e)g(a)g(simple)f(histogram)g (of)h(a)f(column)g(of)g(n)m(umerical)150 568 y(data)j(supplied)f(on)g FH(stdin)p FK(.)68 b(The)39 b(program)h(tak)m(es)h(three)f(argumen)m (ts,)i(sp)s(ecifying)e(the)g(upp)s(er)e(and)150 677 y(lo)m(w)m(er)30 b(b)s(ounds)c(of)j(the)g(histogram)h(and)e(the)h(n)m(um)m(b)s(er)e(of)i (bins.)39 b(It)29 b(then)f(reads)h(n)m(um)m(b)s(ers)e(from)h FH(stdin)p FK(,)150 787 y(one)h(line)g(at)g(a)g(time,)h(and)e(adds)g (them)h(to)g(the)g(histogram.)41 b(When)28 b(there)h(is)g(no)f(more)h (data)g(to)h(read)e(it)150 897 y(prin)m(ts)i(out)g(the)h(accum)m (ulated)h(histogram)f(using)f FH(gsl_histogram_fprintf)p FK(.)390 1036 y FH(#include)46 b()390 1146 y(#include)g ()390 1255 y(#include)g()390 1474 y(int)390 1584 y(main)h(\(int)f(argc,)h(char)f(**argv\))390 1694 y({)485 1803 y(double)h(a,)g(b;)485 1913 y(size_t)g(n;)485 2132 y(if)h(\(argc)e(!=)h(4\))581 2242 y({)676 2351 y(printf)f (\("Usage:)94 b(gsl-histogram)44 b(xmin)j(xmax)f(n\\n")1058 2461 y("Computes)f(a)j(histogram)d(of)i(the)g(data)g(")1058 2570 y("on)g(stdin)f(using)h(n)g(bins)g(from)g(xmin)f(")1058 2680 y("to)h(xmax\\n"\);)676 2790 y(exit)g(\(0\);)581 2899 y(})485 3118 y(a)h(=)f(atof)g(\(argv[1]\);)485 3228 y(b)h(=)f(atof)g(\(argv[2]\);)485 3337 y(n)h(=)f(atoi)g(\(argv[3]\);) 485 3557 y({)581 3666 y(double)f(x;)581 3776 y(gsl_histogram)e(*)k(h)f (=)g(gsl_histogram_alloc)c(\(n\);)581 3885 y(gsl_histogram_set_ranges)o (_uni)o(for)o(m)f(\(h,)47 b(a,)g(b\);)581 4105 y(while)f(\(fscanf)g (\(stdin,)g("\045lg",)g(&x\))h(==)g(1\))676 4214 y({)772 4324 y(gsl_histogram_increment)41 b(\(h,)47 b(x\);)676 4433 y(})581 4543 y(gsl_histogram_fprintf)42 b(\(stdout,)j(h,)j ("\045g",)e("\045g"\);)581 4653 y(gsl_histogram_free)d(\(h\);)485 4762 y(})485 4872 y(exit)k(\(0\);)390 4981 y(})150 5121 y FK(Here)41 b(is)g(an)g(example)g(of)g(the)g(program)g(in)f(use.)72 b(W)-8 b(e)42 b(generate)g(10000)h(random)d(samples)h(from)g(a)150 5230 y(Cauc)m(h)m(y)d(distribution)f(with)h(a)g(width)f(of)h(30)g(and)f (histogram)i(them)e(o)m(v)m(er)j(the)d(range)i(-100)g(to)f(100,)150 5340 y(using)30 b(200)i(bins.)p eop end %%Page: 299 317 TeXDict begin 299 316 bop 150 -116 a FK(Chapter)30 b(23:)41 b(Histograms)2507 b(299)390 299 y FH($)47 b(gsl-randist)e(0)j(10000)e (cauchy)g(30)533 408 y(|)i(gsl-histogram)c(-100)i(100)h(200)g(>)h (histogram.dat)150 540 y FK(A)32 b(plot)g(of)g(the)g(resulting)f (histogram)i(sho)m(ws)e(the)h(familiar)g(shap)s(e)f(of)h(the)g(Cauc)m (h)m(y)g(distribution)f(and)150 650 y(the)g(\015uctuations)f(caused)g (b)m(y)h(the)f(\014nite)h(sample)f(size.)390 781 y FH($)47 b(awk)g('{print)f($1,)h($3)g(;)h(print)e($2,)h($3}')g(histogram.dat)533 891 y(|)h(graph)e(-T)h(X)275 2809 y @beginspecial 97 @llx 195 @lly 494 @urx 580 @ury 2160 @rwi 2016 @rhi @setspecial %%BeginDocument: histogram.eps %!PS-Adobe-3.0 EPSF-3.0 %%Creator: GNU libplot drawing library 1.6 %%Title: PostScript plot %%CreationDate: Sat Aug 18 20:49:32 2001 %%DocumentData: Clean7Bit %%LanguageLevel: 1 %%Pages: 1 %%PageOrder: Ascend %%Orientation: Portrait %%BoundingBox: 97 195 494 580 %%DocumentNeededResources: font Helvetica %%DocumentSuppliedResources: procset GNU_libplot 1.0 0 %%EndComments %%BeginDefaults %%PageResources: font Helvetica %%EndDefaults %%BeginProlog %%EndProlog %%BeginSetup %%IncludeResource: font Helvetica /DrawDict 50 dict def DrawDict begin /ISOLatin1Encoding [ /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /space/exclam/quotedbl/numbersign/dollar/percent/ampersand/quoteright 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SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4032 9216 4032 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4032 2304 4032 2442 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 300.956 213.1332 ] concat %I [ (0) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5760 9216 5760 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5760 2304 5760 2442 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 382.3119 213.1332 ] concat %I [ (50) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7488 9216 7488 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7488 2304 7488 2442 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 463.6679 213.1332 ] concat %I [ (100) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 9216 9216 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2304 9216 2442 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 9216 2304 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2304 2304 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2650 9216 2650 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2650 2304 2650 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2995 9216 2995 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2995 2304 2995 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3341 9216 3341 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3341 2304 3341 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3686 9216 3686 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3686 2304 3686 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4032 9216 4032 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4032 2304 4032 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4378 9216 4378 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4378 2304 4378 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4723 9216 4723 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4723 2304 4723 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5069 9216 5069 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5069 2304 5069 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5414 9216 5414 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5414 2304 5414 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5760 9216 5760 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5760 2304 5760 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6106 9216 6106 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6106 2304 6106 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6451 9216 6451 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6451 2304 6451 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6797 9216 6797 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6797 2304 6797 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7142 9216 7142 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7142 2304 7142 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7488 9216 7488 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7488 2304 7488 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7834 9216 7834 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7834 2304 7834 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8179 9216 8179 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8179 2304 8179 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8525 9216 8525 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8525 2304 8525 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8870 9216 8870 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8870 2304 8870 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 9216 9216 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2304 9216 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 34952 1 0 0 [ 1 3 1 3 ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5760 2304 5760 9216 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 117.9279 229.3306 ] concat %I [ (0) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2304 9078 2304 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2304 2442 2304 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 107.8399 278.702 ] concat %I [ (20) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 3291 9078 3291 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3291 2442 3291 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 107.8399 328.0734 ] concat %I [ (40) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 4279 9078 4279 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4279 2442 4279 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 107.8399 377.4449 ] concat %I [ (60) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5266 9078 5266 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5266 2442 5266 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 107.8399 426.8163 ] concat %I [ (80) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 6254 9078 6254 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 6254 2442 6254 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 97.75181 476.1877 ] concat %I [ (100) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 7241 9078 7241 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 7241 2442 7241 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 97.75181 525.5592 ] concat %I [ (120) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 8229 9078 8229 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 8229 2442 8229 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 97.75181 574.9306 ] concat %I [ (140) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 9216 9078 9216 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 9216 2442 9216 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2304 9161 2304 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2304 2359 2304 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2798 9161 2798 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2798 2359 2798 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 3291 9161 3291 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3291 2359 3291 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 3785 9161 3785 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3785 2359 3785 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 4279 9161 4279 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4279 2359 4279 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 4773 9161 4773 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4773 2359 4773 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5266 9161 5266 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5266 2359 5266 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5760 9161 5760 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5760 2359 5760 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 6254 9161 6254 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 6254 2359 6254 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 6747 9161 6747 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 6747 2359 6747 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 7241 9161 7241 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 7241 2359 7241 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 7735 9161 7735 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 7735 2359 7735 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 8229 9161 8229 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 8229 2359 8229 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 8722 9161 8722 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 8722 2359 8722 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 9216 9161 9216 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 9216 2359 9216 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 400 2304 2748 2339 2748 2339 2501 2373 2501 2373 2896 2408 2896 2408 2896 2442 2896 2442 2896 2477 2896 2477 2650 2511 2650 2511 2650 2546 2650 2546 2896 2580 2896 2580 2896 2615 2896 2615 2650 2650 2650 2650 2551 2684 2551 2684 2847 2719 2847 2719 2650 2753 2650 2753 2847 2788 2847 2788 2995 2822 2995 2822 2896 2857 2896 2857 3291 2892 3291 2892 2650 2926 2650 2926 3291 2961 3291 2961 3094 2995 3094 2995 2798 3030 2798 3030 3045 3064 3045 3064 2896 3099 2896 3099 2847 3133 2847 3133 3143 3168 3143 3168 3193 3203 3193 3203 2748 3237 2748 3237 3193 3272 3193 3272 2896 3306 2896 3306 3390 3341 3390 3341 2995 3375 2995 3375 3143 3410 3143 3410 3242 3444 3242 3444 3440 3479 3440 3479 3291 3514 3291 3514 2995 3548 2995 3548 2748 3583 2748 3583 3193 3617 3193 3617 3094 3652 3094 3652 3291 3686 3291 3686 3143 3721 3143 3721 3785 3756 3785 3756 3341 3790 3341 3790 3637 3825 3637 3825 3983 3859 3983 3859 3440 3894 3440 3894 3538 3928 3538 3928 3538 3963 3538 3963 3736 3997 3736 3997 3588 4032 3588 4032 3538 4067 3538 4067 3390 4101 3390 4101 4279 4136 4279 4136 3686 4170 3686 4170 4476 4205 4476 4205 4032 4239 4032 4239 4328 4274 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3785 7730 3440 7764 3440 7764 2946 7799 2946 7799 3094 7834 3094 7834 3045 7868 3045 7868 3094 7903 3094 7903 3686 7937 3686 7937 3242 7972 3242 7972 3686 8006 3686 8006 3242 8041 3242 8041 3637 8076 3637 8076 3242 8110 3242 8110 3143 8145 3143 8145 3143 8179 3143 8179 3291 8214 3291 8214 3094 8248 3094 8248 3045 8283 3045 8283 2896 8317 2896 8317 2748 8352 2748 8352 3440 8387 3440 8387 3045 8421 3045 8421 2798 8456 2798 8456 3143 8490 3143 8490 2798 8525 2798 8525 3045 8559 3045 8559 2551 8594 2551 8594 2798 8628 2798 8628 2995 8663 2995 8663 2946 8698 2946 8698 2699 8732 2699 8732 3045 8767 3045 8767 3094 8801 3094 8801 2650 8836 2650 8836 2798 8870 2798 8870 3045 8905 3045 8905 3045 8940 3045 8940 2798 8974 2798 8974 2748 9009 2748 9009 2798 9043 2798 9043 2650 9078 2650 9078 2650 9112 2650 9112 2995 9147 2995 9147 2847 9181 2847 9181 2748 9216 2748 400 MLine End %%PageTrailer End %I eop showpage %%Trailer end %%EOF %%EndDocument @endspecial 150 3085 a FJ(23.12)69 b(Tw)l(o)45 b(dimensional)h (histograms)150 3245 y FK(A)37 b(t)m(w)m(o)i(dimensional)e(histogram)h (consists)f(of)h(a)f(set)h(of)f FD(bins)j FK(whic)m(h)d(coun)m(t)h(the) f(n)m(um)m(b)s(er)f(of)i(ev)m(en)m(ts)150 3354 y(falling)43 b(in)f(a)h(giv)m(en)h(area)f(of)g(the)f(\()p FE(x;)15 b(y)s FK(\))44 b(plane.)77 b(The)42 b(simplest)g(w)m(a)m(y)i(to)f(use)f (a)h(t)m(w)m(o)h(dimensional)150 3464 y(histogram)28 b(is)g(to)h(record)e(t)m(w)m(o-dimensional)j(p)s(osition)e (information,)h FE(n)p FK(\()p FE(x;)15 b(y)s FK(\).)40 b(Another)28 b(p)s(ossibilit)m(y)g(is)150 3574 y(to)36 b(form)e(a)i FD(join)m(t)g(distribution)e FK(b)m(y)h(recording)g (related)h(v)-5 b(ariables.)56 b(F)-8 b(or)36 b(example)f(a)h(detector) g(migh)m(t)150 3683 y(record)d(b)s(oth)g(the)h(p)s(osition)f(of)h(an)f (ev)m(en)m(t)i(\()p FE(x)p FK(\))f(and)f(the)g(amoun)m(t)h(of)f(energy) h(it)g(dep)s(osited)f FE(E)5 b FK(.)50 b(These)150 3793 y(could)30 b(b)s(e)g(histogrammed)h(as)f(the)h(join)m(t)g(distribution) f FE(n)p FK(\()p FE(x;)15 b(E)5 b FK(\).)150 4019 y FJ(23.13)69 b(The)44 b(2D)h(histogram)h(struct)150 4179 y FK(Tw)m(o)31 b(dimensional)f(histograms)h(are)g(de\014ned)e(b)m(y)h(the)h(follo)m (wing)g(struct,)3269 4354 y([Data)h(T)m(yp)s(e])-3600 b Fv(gsl_histogram2d)390 4485 y FH(size_t)29 b(nx,)g(ny)870 4595 y FK(This)h(is)g(the)h(n)m(um)m(b)s(er)e(of)h(histogram)h(bins)f (in)g(the)g(x)g(and)g(y)h(directions.)390 4748 y FH(double)e(*)h (xrange)870 4858 y FK(The)f(ranges)g(of)g(the)g(bins)g(in)f(the)i (x-direction)g(are)f(stored)g(in)g(an)g(arra)m(y)h(of)f FD(nx)23 b FK(+)18 b(1)870 4967 y(elemen)m(ts)32 b(p)s(oin)m(ted)e(to)h (b)m(y)f FD(xrange)p FK(.)390 5121 y FH(double)f(*)h(yrange)870 5230 y FK(The)f(ranges)g(of)g(the)h(bins)e(in)h(the)g(y-direction)h (are)g(stored)f(in)g(an)g(arra)m(y)g(of)h FD(n)m(y)25 b FK(+)18 b(1)870 5340 y(elemen)m(ts)32 b(p)s(oin)m(ted)e(to)h(b)m(y)f FD(yrange)p FK(.)p eop end %%Page: 300 318 TeXDict begin 300 317 bop 150 -116 a FK(Chapter)30 b(23:)41 b(Histograms)2507 b(300)390 299 y FH(double)29 b(*)h(bin)870 408 y FK(The)23 b(coun)m(ts)h(for)g(eac)m(h)h(bin)e(are)h(stored)g(in)f (an)h(arra)m(y)g(p)s(oin)m(ted)g(to)g(b)m(y)g FD(bin)p FK(.)38 b(The)23 b(bins)870 518 y(are)41 b(\015oating-p)s(oin)m(t)g(n)m (um)m(b)s(ers,)h(so)f(y)m(ou)f(can)h(incremen)m(t)g(them)g(b)m(y)f (non-in)m(teger)870 628 y(v)-5 b(alues)40 b(if)f(necessary)-8 b(.)68 b(The)39 b(arra)m(y)g FD(bin)g FK(stores)h(the)f(t)m(w)m(o)i (dimensional)e(arra)m(y)h(of)870 737 y(bins)31 b(in)i(a)f(single)h(blo) s(c)m(k)g(of)g(memory)f(according)i(to)f(the)f(mapping)g FH(bin\(i,j\))e FK(=)870 847 y FH(bin[i)f(*)h(ny)g(+)g(j])p FK(.)150 1043 y(The)43 b(range)g(for)g FH(bin\(i,j\))e FK(is)i(giv)m(en)h(b)m(y)g FH(xrange[i])c FK(to)k FH(xrange[i+1])c FK(in)j(the)g(x-direction)i(and)150 1153 y FH(yrange[j])31 b FK(to)j FH(yrange[j+1])d FK(in)i(the)h(y-direction.)51 b(Eac)m(h)35 b(bin)d(is)i(inclusiv)m(e)h(at)f(the)g(lo)m(w)m(er)h(end)e (and)150 1262 y(exclusiv)m(e)39 b(at)f(the)g(upp)s(er)d(end.)61 b(Mathematically)41 b(this)c(means)g(that)h(the)g(bins)e(are)i (de\014ned)e(b)m(y)i(the)150 1372 y(follo)m(wing)32 b(inequalit)m(y)-8 b(,)886 1531 y(bin\(i,j\))31 b(corresp)s(onds)e(to)103 b Fg(xr)-5 b(ange)q FK([)p FE(i)p FK(])26 b FI(\024)f FE(x)g(<)g Fg(xr)-5 b(ange)q FK([)p FE(i)21 b FK(+)f(1])1256 1640 y(and)460 b Fg(yr)-5 b(ange)q FK([)p FE(j)5 b FK(])26 b FI(\024)f FE(y)j(<)d Fg(yr)-5 b(ange)q FK([)p FE(j)26 b FK(+)20 b(1])150 1799 y(Note)33 b(that)e(an)m(y)h(samples)f(whic)m(h) g(fall)h(on)f(the)h(upp)s(er)d(sides)i(of)h(the)f(histogram)h(are)g (excluded.)43 b(If)31 b(y)m(ou)150 1909 y(w)m(an)m(t)g(to)g(include)g (these)g(v)-5 b(alues)30 b(for)g(the)h(side)f(bins)g(y)m(ou)h(will)g (need)f(to)h(add)f(an)g(extra)h(ro)m(w)g(or)f(column)150 2019 y(to)h(y)m(our)f(histogram.)275 2159 y(The)h FH(gsl_histogram2d)c FK(struct)k(and)g(its)h(asso)s(ciated)h(functions)e(are)h(de\014ned)f (in)g(the)h(header)f(\014le)150 2269 y FH(gsl_histogram2d.h)p FK(.)150 2510 y FJ(23.14)69 b(2D)45 b(Histogram)h(allo)t(cation)150 2669 y FK(The)24 b(functions)g(for)g(allo)s(cating)j(memory)e(to)g(a)g (2D)g(histogram)g(follo)m(w)h(the)f(st)m(yle)g(of)g FH(malloc)e FK(and)h FH(free)p FK(.)150 2779 y(In)41 b(addition)h(they)g(also)h(p)s (erform)d(their)i(o)m(wn)g(error)g(c)m(hec)m(king.)77 b(If)41 b(there)h(is)g(insu\016cien)m(t)g(memory)150 2889 y(a)m(v)-5 b(ailable)39 b(to)e(allo)s(cate)i(a)e(histogram)g(then) g(the)g(functions)f(call)i(the)e(error)g(handler)g(\(with)h(an)f(error) 150 2998 y(n)m(um)m(b)s(er)28 b(of)h FH(GSL_ENOMEM)p FK(\))d(in)j(addition)g(to)g(returning)f(a)i(n)m(ull)f(p)s(oin)m(ter.) 40 b(Th)m(us)28 b(if)g(y)m(ou)i(use)e(the)h(library)150 3108 y(error)36 b(handler)f(to)i(ab)s(ort)f(y)m(our)g(program)g(then)g (it)h(isn't)f(necessary)h(to)g(c)m(hec)m(k)g(ev)m(ery)g(2D)g(histogram) 150 3217 y FH(alloc)p FK(.)3350 3413 y([F)-8 b(unction])-3599 b Fv(gsl_histogram2d)57 b(*)52 b(gsl_histogram2d_allo)q(c)f Fu(\()p FD(size)p 2417 3413 28 4 v 42 w(t)30 b Ft(nx)p FD(,)h(size)p 2825 3413 V 41 w(t)g Ft(ny)p Fu(\))390 3523 y FK(This)e(function)h(allo)s(cates)i(memory)e(for)f(a)i(t)m(w)m (o-dimensional)g(histogram)g(with)f FD(nx)35 b FK(bins)29 b(in)h(the)390 3633 y(x)f(direction)h(and)e FD(n)m(y)37 b FK(bins)28 b(in)h(the)h(y)f(direction.)41 b(The)28 b(function)h(returns)f(a)i(p)s(oin)m(ter)f(to)h(a)f(newly)390 3742 y(created)j FH(gsl_histogram2d)26 b FK(struct.)41 b(If)30 b(insu\016cien)m(t)h(memory)f(is)h(a)m(v)-5 b(ailable)33 b(a)e(n)m(ull)f(p)s(oin)m(ter)h(is)390 3852 y(returned)23 b(and)h(the)h(error)f(handler)g(is)h(in)m(v)m(ok)m(ed)h(with)e(an)g (error)g(co)s(de)h(of)g FH(GSL_ENOMEM)p FK(.)36 b(The)24 b(bins)390 3961 y(and)32 b(ranges)g(m)m(ust)g(b)s(e)g(initialized)i (with)e(one)g(of)h(the)f(functions)g(b)s(elo)m(w)g(b)s(efore)g(the)g (histogram)390 4071 y(is)e(ready)h(for)f(use.)3350 4267 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_histogram2d_set_r)q(ange)q (s)f Fu(\()p FD(gsl)p 1912 4267 V 40 w(histogram2d)31 b(*)g Ft(h)p FD(,)g(const)g(double)565 4377 y Ft(xrange)p Fo([])p FD(,)h(size)p 1137 4377 V 41 w(t)f Ft(xsize)p FD(,)h(const)f(double)f Ft(yrange)p Fo([])p FD(,)i(size)p 2658 4377 V 41 w(t)e Ft(ysize)p Fu(\))390 4486 y FK(This)d(function)g (sets)h(the)g(ranges)g(of)f(the)h(existing)h(histogram)f FD(h)f FK(using)g(the)h(arra)m(ys)g FD(xrange)33 b FK(and)390 4596 y FD(yrange)g FK(of)27 b(size)h FD(xsize)33 b FK(and)27 b FD(ysize)33 b FK(resp)s(ectiv)m(ely)-8 b(.)41 b(The)27 b(v)-5 b(alues)28 b(of)f(the)h(histogram)f(bins)g(are)g(reset)390 4705 y(to)k(zero.)3350 4902 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_histogram2d_set_r)q(ange)q(s_u)q(nif)q(orm)f Fu(\()p FD(gsl)p 2330 4902 V 41 w(histogram2d)31 b(*)g Ft(h)p FD(,)565 5011 y(double)f Ft(xmin)p FD(,)i(double)e Ft(xmax)p FD(,)i(double)d Ft(ymin)p FD(,)j(double)e Ft(ymax)p Fu(\))390 5121 y FK(This)36 b(function)h(sets)g(the)g(ranges)g(of)g (the)g(existing)h(histogram)f FD(h)f FK(to)i(co)m(v)m(er)g(the)f (ranges)h FD(xmin)390 5230 y FK(to)31 b FD(xmax)36 b FK(and)30 b FD(ymin)f FK(to)i FD(ymax)37 b FK(uniformly)-8 b(.)40 b(The)29 b(v)-5 b(alues)31 b(of)f(the)g(histogram)h(bins)e(are)i (reset)f(to)390 5340 y(zero.)p eop end %%Page: 301 319 TeXDict begin 301 318 bop 150 -116 a FK(Chapter)30 b(23:)41 b(Histograms)2507 b(301)3350 299 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_histogram2d_free)d Fu(\()p FD(gsl)p 1650 299 28 4 v 41 w(histogram2d)31 b(*)g Ft(h)p Fu(\))390 408 y FK(This)f(function)g(frees)g(the)h(2D)g(histogram)g FD(h)f FK(and)f(all)j(of)e(the)h(memory)f(asso)s(ciated)i(with)e(it.) 150 639 y FJ(23.15)69 b(Cop)l(ying)45 b(2D)g(Histograms)3350 845 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_histogram2d_memcp)q (y)e Fu(\()p FD(gsl)p 1702 845 V 41 w(histogram2d)31 b(*)g Ft(dest)p FD(,)h(const)565 955 y(gsl)p 677 955 V 41 w(histogram2d)f(*)f Ft(src)p Fu(\))390 1064 y FK(This)i(function)h (copies)h(the)g(histogram)f FD(src)39 b FK(in)m(to)34 b(the)g(pre-existing)g(histogram)f FD(dest)p FK(,)i(making)390 1174 y FD(dest)d FK(in)m(to)g(an)e(exact)i(cop)m(y)f(of)g FD(src)p FK(.)40 b(The)30 b(t)m(w)m(o)i(histograms)f(m)m(ust)f(b)s(e)g (of)g(the)h(same)f(size.)3350 1355 y([F)-8 b(unction])-3599 b Fv(gsl_histogram2d)57 b(*)52 b(gsl_histogram2d_clon)q(e)f Fu(\()p FD(const)32 b(gsl)p 2621 1355 V 40 w(histogram2d)565 1464 y(*)f Ft(src)p Fu(\))390 1574 y FK(This)f(function)g(returns)f(a)i (p)s(oin)m(ter)g(to)g(a)g(newly)g(created)g(histogram)h(whic)m(h)e(is)h (an)f(exact)i(cop)m(y)390 1684 y(of)f(the)f(histogram)h FD(src)p FK(.)150 1914 y FJ(23.16)69 b(Up)t(dating)45 b(and)g(accessing)g(2D)g(histogram)h(elemen)l(ts)150 2073 y FK(Y)-8 b(ou)46 b(can)g(access)g(the)g(bins)e(of)i(a)f(t)m(w)m (o-dimensional)j(histogram)e(either)f(b)m(y)h(sp)s(ecifying)f(a)h(pair) f(of)150 2183 y(\()p FE(x;)15 b(y)s FK(\))40 b(co)s(ordinates)h(or)e(b) m(y)g(using)g(the)h(bin)f(indices)g(\()p FE(i;)15 b(j)5 b FK(\))42 b(directly)-8 b(.)69 b(The)39 b(functions)g(for)g(accessing) 150 2292 y(the)c(histogram)h(through)e(\()p FE(x;)15 b(y)s FK(\))36 b(co)s(ordinates)f(use)g(binary)f(searc)m(hes)i(in)f (the)g(x)g(and)f(y)h(directions)g(to)150 2402 y(iden)m(tify)c(the)f (bin)g(whic)m(h)g(co)m(v)m(ers)i(the)f(appropriate)f(range.)3350 2582 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_histogram2d_incre)q (ment)f Fu(\()p FD(gsl)p 1859 2582 V 41 w(histogram2d)31 b(*)g Ft(h)p FD(,)g(double)f Ft(x)p FD(,)565 2692 y(double)g Ft(y)p Fu(\))390 2802 y FK(This)f(function)g(up)s(dates)g(the)h (histogram)g FD(h)f FK(b)m(y)h(adding)f(one)h(\(1.0\))i(to)e(the)g(bin) f(whose)g(x)h(and)f(y)390 2911 y(ranges)i(con)m(tain)g(the)g(co)s (ordinates)g(\()p FD(x)p FK(,)p FD(y)8 b FK(\).)390 3044 y(If)43 b(the)h(p)s(oin)m(t)f(\()p FE(x;)15 b(y)s FK(\))45 b(lies)f(inside)f(the)h(v)-5 b(alid)44 b(ranges)g(of)f(the)h(histogram) g(then)g(the)f(function)390 3154 y(returns)28 b(zero)h(to)h(indicate)g (success.)40 b(If)29 b(\()p FE(x;)15 b(y)s FK(\))29 b(lies)h(outside)f (the)g(limits)h(of)f(the)g(histogram)g(then)390 3264 y(the)g(function)g(returns)f FH(GSL_EDOM)p FK(,)f(and)h(none)h(of)g (the)g(bins)f(are)i(mo)s(di\014ed.)39 b(The)28 b(error)h(handler)390 3373 y(is)h(not)h(called,)g(since)g(it)f(is)h(often)f(necessary)h(to)g (compute)f(histograms)h(for)f(a)g(small)h(range)f(of)h(a)390 3483 y(larger)g(dataset,)h(ignoring)f(an)m(y)g(co)s(ordinates)g (outside)f(the)h(range)g(of)f(in)m(terest.)3350 3664 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_histogram2d_accum)q(ulat)q (e)f Fu(\()p FD(gsl)p 1912 3664 V 40 w(histogram2d)31 b(*)g Ft(h)p FD(,)g(double)f Ft(x)p FD(,)565 3773 y(double)g Ft(y)p FD(,)h(double)f Ft(weight)p Fu(\))390 3883 y FK(This)36 b(function)g(is)g(similar)h(to)g FH(gsl_histogram2d_incremen)o(t)31 b FK(but)k(increases)i(the)g(v)-5 b(alue)37 b(of)390 3992 y(the)31 b(appropriate)f(bin)g(in)g(the)g(histogram)h FD(h)f FK(b)m(y)g(the)h(\015oating-p)s(oin)m(t)g(n)m(um)m(b)s(er)f FD(w)m(eigh)m(t)p FK(.)3350 4173 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_histogram2d_get)d Fu(\()p FD(const)32 b(gsl)p 1941 4173 V 40 w(histogram2d)f(*)g Ft(h)p FD(,)g(size)p 2827 4173 V 41 w(t)f Ft(i)p FD(,)565 4283 y(size)p 712 4283 V 41 w(t)h Ft(j)p Fu(\))390 4392 y FK(This)i(function)f(returns)h (the)g(con)m(ten)m(ts)i(of)f(the)f(\()p FD(i)p FK(,)p FD(j)s FK(\)-th)i(bin)d(of)i(the)f(histogram)h FD(h)p FK(.)49 b(If)33 b(\()p FD(i)p FK(,)p FD(j)s FK(\))h(lies)390 4502 y(outside)h(the)h(v)-5 b(alid)35 b(range)g(of)h(indices)f(for)g (the)g(histogram)h(then)e(the)i(error)e(handler)h(is)g(called)390 4611 y(with)30 b(an)g(error)g(co)s(de)h(of)f FH(GSL_EDOM)f FK(and)g(the)i(function)f(returns)f(0.)3350 4792 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_histogram2d_get_x)q(rang)q(e)f Fu(\()p FD(const)31 b(gsl)p 2150 4792 V 40 w(histogram2d)g(*)g Ft(h)p FD(,)g(size)p 3036 4792 V 41 w(t)565 4902 y Ft(i)p FD(,)g(double)f(*)h Ft(xlower)p FD(,)h(double)e(*)h Ft(xupper)p Fu(\))3350 5011 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_histogram2d_get_y)q(rang)q(e)f Fu(\()p FD(const)31 b(gsl)p 2150 5011 V 40 w(histogram2d)g(*)g Ft(h)p FD(,)g(size)p 3036 5011 V 41 w(t)565 5121 y Ft(j)p FD(,)g(double)f(*)h Ft(ylower)p FD(,)h(double)e(*)h Ft(yupper)p Fu(\))390 5230 y FK(These)e(functions)g(\014nd)f(the)h(upp)s(er)f(and)g(lo)m(w)m (er)j(range)f(limits)g(of)f(the)h FD(i)p FK(-th)f(and)g FD(j)p FK(-th)g(bins)g(in)g(the)390 5340 y(x)39 b(and)g(y)g(directions) h(of)g(the)f(histogram)h FD(h)p FK(.)67 b(The)39 b(range)h(limits)g (are)g(stored)f(in)g FD(xlo)m(w)m(er)48 b FK(and)p eop end %%Page: 302 320 TeXDict begin 302 319 bop 150 -116 a FK(Chapter)30 b(23:)41 b(Histograms)2507 b(302)390 299 y FD(xupp)s(er)38 b FK(or)33 b FD(ylo)m(w)m(er)40 b FK(and)33 b FD(yupp)s(er)p FK(.)47 b(The)32 b(lo)m(w)m(er)i(limits)g(are)f(inclusiv)m(e)h(\(i.e.)50 b(ev)m(en)m(ts)35 b(with)d(these)390 408 y(co)s(ordinates)37 b(are)g(included)e(in)h(the)h(bin\))f(and)f(the)i(upp)s(er)d(limits)j (are)g(exclusiv)m(e)h(\(i.e.)60 b(ev)m(en)m(ts)390 518 y(with)31 b(the)g(v)-5 b(alue)32 b(of)f(the)g(upp)s(er)e(limit)j(are)f 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40 w(histogram2d)g(*)g Ft(h)p Fu(\))3350 1501 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_histogram2d_ymin) e Fu(\()p FD(const)31 b(gsl)p 1993 1501 V 40 w(histogram2d)g(*)g Ft(h)p Fu(\))3350 1610 y FK([F)-8 b(unction])-3599 b Fv(size_t)54 b(gsl_histogram2d_ny)d Fu(\()p FD(const)31 b(gsl)p 1888 1610 V 41 w(histogram2d)g(*)g Ft(h)p Fu(\))390 1720 y FK(These)c(functions)g(return)f(the)h(maxim)m(um)g(upp)s(er)e (and)h(minim)m(um)h(lo)m(w)m(er)h(range)f(limits)h(and)f(the)390 1829 y(n)m(um)m(b)s(er)i(of)h(bins)f(for)h(the)h(x)f(and)f(y)h (directions)h(of)f(the)g(histogram)h FD(h)p FK(.)40 b(They)30 b(pro)m(vide)g(a)h(w)m(a)m(y)g(of)390 1939 y(determining)f(these)h(v)-5 b(alues)31 b(without)f(accessing)i(the)f FH(gsl_histogram2d)26 b FK(struct)k(directly)-8 b(.)3350 2154 y([F)g(unction])-3599 b Fv(void)54 b(gsl_histogram2d_reset)d Fu(\()p FD(gsl)p 1702 2154 V 41 w(histogram2d)31 b(*)g Ft(h)p Fu(\))390 2264 y FK(This)f(function)g(resets)g(all)i(the)e(bins)g(of)g(the)h (histogram)g FD(h)f 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b(histograms)g(with)f(uniform)g(ranges,)i(and)f(will)g (return)e(the)i(correct)h(bin)e(immediately)i(in)390 3552 y(this)d(case.)52 b(If)33 b(\()p FE(x;)15 b(y)s FK(\))35 b(is)f(found)f(then)g(the)h(function)g(sets)g(the)g(indices)g (\()p FD(i)p FK(,)p FD(j)s FK(\))h(and)e(returns)g FH(GSL_)390 3662 y(SUCCESS)p FK(.)71 b(If)40 b(\()p FE(x;)15 b(y)s FK(\))42 b(lies)g(outside)f(the)g(v)-5 b(alid)41 b(range)h(of)f(the)g (histogram)g(then)g(the)g(function)390 3771 y(returns)29 b FH(GSL_EDOM)f FK(and)i(the)h(error)f(handler)f(is)i(in)m(v)m(ok)m (ed.)150 4027 y FJ(23.18)69 b(2D)45 b(Histogram)h(Statistics)3350 4252 y FK([F)-8 b(unction])-3599 b Fv(double)54 b (gsl_histogram2d_max_va)q(l)e Fu(\()p FD(const)31 b(gsl)p 2150 4252 V 40 w(histogram2d)g(*)g Ft(h)p Fu(\))390 4361 y FK(This)f(function)g(returns)f(the)h(maxim)m(um)h(v)-5 b(alue)30 b(con)m(tained)i(in)e(the)h(histogram)g(bins.)3350 4577 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_histogram2d_max_bin)e Fu(\()p FD(const)31 b(gsl)p 2045 4577 V 41 w(histogram2d)g(*)f Ft(h)p FD(,)h(size)p 2931 4577 V 41 w(t)g(*)g Ft(i)p FD(,)565 4686 y(size)p 712 4686 V 41 w(t)g(*)f Ft(j)p Fu(\))390 4796 y FK(This)j(function)g(\014nds)f(the)i(indices)f(of)h (the)g(bin)f(con)m(taining)i(the)f(maxim)m(um)f(v)-5 b(alue)34 b(in)f(the)h(his-)390 4905 y(togram)39 b FD(h)f FK(and)f(stores)i(the)f(result)h(in)e(\()p FD(i)p FK(,)p FD(j)s FK(\).)66 b(In)37 b(the)h(case)i(where)d(sev)m(eral)j(bins)d (con)m(tain)j(the)390 5015 y(same)31 b(maxim)m(um)f(v)-5 b(alue)31 b(the)f(\014rst)g(bin)g(found)f(is)h(returned.)3350 5230 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_histogram2d_min_va)q (l)e Fu(\()p FD(const)31 b(gsl)p 2150 5230 V 40 w(histogram2d)g(*)g Ft(h)p Fu(\))390 5340 y FK(This)f(function)g(returns)f(the)h(minim)m (um)g(v)-5 b(alue)31 b(con)m(tained)g(in)f(the)h(histogram)g(bins.)p eop end %%Page: 303 321 TeXDict begin 303 320 bop 150 -116 a FK(Chapter)30 b(23:)41 b(Histograms)2507 b(303)3350 299 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_histogram2d_min_bin)e Fu(\()p FD(const)31 b(gsl)p 2045 299 28 4 v 41 w(histogram2d)g(*)f Ft(h)p FD(,)h(size)p 2931 299 V 41 w(t)g(*)g Ft(i)p FD(,)565 408 y(size)p 712 408 V 41 w(t)g(*)f Ft(j)p Fu(\))390 518 y FK(This)k(function)h(\014nds)e(the)i(indices)g(of)g(the)g(bin)f (con)m(taining)i(the)f(minim)m(um)f(v)-5 b(alue)36 b(in)e(the)h(his-) 390 628 y(togram)k FD(h)f FK(and)f(stores)i(the)f(result)h(in)e(\()p FD(i)p FK(,)p FD(j)s FK(\).)66 b(In)37 b(the)h(case)i(where)d(sev)m (eral)j(bins)d(con)m(tain)j(the)390 737 y(same)31 b(maxim)m(um)f(v)-5 b(alue)31 b(the)f(\014rst)g(bin)g(found)f(is)h(returned.)3350 951 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_histogram2d_xmean)e Fu(\()p FD(const)31 b(gsl)p 2045 951 V 41 w(histogram2d)g(*)f Ft(h)p Fu(\))390 1060 y FK(This)d(function)h(returns)f(the)h(mean)g(of) g(the)h(histogrammed)f(x)g(v)-5 b(ariable,)29 b(where)f(the)g (histogram)390 1170 y(is)42 b(regarded)g(as)h(a)g(probabilit)m(y)g (distribution.)75 b(Negativ)m(e)45 b(bin)d(v)-5 b(alues)43 b(are)f(ignored)h(for)f(the)390 1279 y(purp)s(oses)29 b(of)h(this)g(calculation.)3350 1493 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_histogram2d_ymean)e Fu(\()p FD(const)31 b(gsl)p 2045 1493 V 41 w(histogram2d)g(*)f Ft(h)p Fu(\))390 1603 y FK(This)d(function)h(returns)f(the)h(mean)g(of)g(the)h (histogrammed)f(y)g(v)-5 b(ariable,)29 b(where)f(the)g(histogram)390 1712 y(is)42 b(regarded)g(as)h(a)g(probabilit)m(y)g(distribution.)75 b(Negativ)m(e)45 b(bin)d(v)-5 b(alues)43 b(are)f(ignored)h(for)f(the) 390 1822 y(purp)s(oses)29 b(of)h(this)g(calculation.)3350 2035 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_histogram2d_xsigma)e Fu(\()p FD(const)31 b(gsl)p 2097 2035 V 41 w(histogram2d)g(*)g Ft(h)p Fu(\))390 2145 y FK(This)g(function)h(returns)f(the)i(standard)e (deviation)i(of)g(the)f(histogrammed)h(x)f(v)-5 b(ariable,)33 b(where)390 2254 y(the)j(histogram)g(is)g(regarded)f(as)h(a)g (probabilit)m(y)g(distribution.)56 b(Negativ)m(e)38 b(bin)d(v)-5 b(alues)36 b(are)g(ig-)390 2364 y(nored)30 b(for)g(the)g(purp)s(oses)f (of)i(this)f(calculation.)3350 2578 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_histogram2d_ysigma)e Fu(\()p FD(const)31 b(gsl)p 2097 2578 V 41 w(histogram2d)g(*)g Ft(h)p Fu(\))390 2687 y FK(This)g(function)h(returns)f(the)i(standard)e(deviation)i(of)g (the)f(histogrammed)h(y)f(v)-5 b(ariable,)33 b(where)390 2797 y(the)j(histogram)g(is)g(regarded)f(as)h(a)g(probabilit)m(y)g (distribution.)56 b(Negativ)m(e)38 b(bin)d(v)-5 b(alues)36 b(are)g(ig-)390 2906 y(nored)30 b(for)g(the)g(purp)s(oses)f(of)i(this)f (calculation.)3350 3120 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_histogram2d_cov)d Fu(\()p FD(const)32 b(gsl)p 1941 3120 V 40 w(histogram2d)f(*)g Ft(h)p Fu(\))390 3229 y FK(This)23 b(function)f(returns)h(the)g(co)m(v)-5 b(ariance)26 b(of)d(the)h(histogrammed)f(x)g(and)g(y)g(v)-5 b(ariables,)26 b(where)d(the)390 3339 y(histogram)34 b(is)f(regarded)g(as)h(a)f (probabilit)m(y)h(distribution.)49 b(Negativ)m(e)36 b(bin)d(v)-5 b(alues)33 b(are)h(ignored)390 3449 y(for)c(the)h(purp)s(oses)d(of)j (this)f(calculation.)3350 3662 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_histogram2d_sum)d Fu(\()p FD(const)32 b(gsl)p 1941 3662 V 40 w(histogram2d)f(*)g Ft(h)p Fu(\))390 3772 y FK(This)h(function)h(returns)f(the)i(sum)e(of)i(all)g(bin)e(v)-5 b(alues.)50 b(Negativ)m(e)36 b(bin)c(v)-5 b(alues)34 b(are)g(included)e(in)390 3881 y(the)f(sum.)150 4136 y FJ(23.19)69 b(2D)45 b(Histogram)h(Op)t(erations)3350 4359 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_histogram2d_equal)q (_bin)q(s_p)f Fu(\()p FD(const)31 b(gsl)p 2254 4359 V 41 w(histogram2d)g(*)g Ft(h1)p FD(,)565 4469 y(const)g(gsl)p 915 4469 V 41 w(histogram2d)g(*)f Ft(h2)p Fu(\))390 4579 y FK(This)41 b(function)g(returns)g(1)h(if)g(all)g(the)g(individual)f (bin)g(ranges)h(of)g(the)g(t)m(w)m(o)h(histograms)g(are)390 4688 y(iden)m(tical,)32 b(and)e(0)h(otherwise.)3350 4902 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_histogram2d_add)e Fu(\()p FD(gsl)p 1545 4902 V 41 w(histogram2d)31 b(*)g Ft(h1)p FD(,)g(const)565 5011 y(gsl)p 677 5011 V 41 w(histogram2d)g(*)f Ft(h2)p Fu(\))390 5121 y FK(This)40 b(function)g(adds)f(the)i(con)m (ten)m(ts)h(of)e(the)h(bins)e(in)h(histogram)h FD(h2)47 b FK(to)41 b(the)g(corresp)s(onding)390 5230 y(bins)28 b(of)i(histogram)f FD(h1)p FK(,)h(i.e.)41 b FE(h)1466 5197 y Fp(0)1466 5253 y FB(1)1504 5230 y FK(\()p FE(i;)15 b(j)5 b FK(\))27 b(=)e FE(h)1862 5244 y FB(1)1900 5230 y FK(\()p FE(i;)15 b(j)5 b FK(\))19 b(+)f FE(h)2243 5244 y FB(2)2281 5230 y FK(\()p FE(i;)d(j)5 b FK(\).)42 b(The)29 b(t)m(w)m(o)h(histograms)g(m)m(ust)f(ha)m(v)m(e)390 5340 y(iden)m(tical)j(bin)e(ranges.)p eop end %%Page: 304 322 TeXDict begin 304 321 bop 150 -116 a FK(Chapter)30 b(23:)41 b(Histograms)2507 b(304)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_histogram2d_sub)e Fu(\()p FD(gsl)p 1545 299 28 4 v 41 w(histogram2d)31 b(*)g Ft(h1)p FD(,)g(const)565 408 y(gsl)p 677 408 V 41 w(histogram2d)g(*)f Ft(h2)p Fu(\))390 518 y FK(This)24 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/m21 {mb f} def /m25 {mb s} def /m22 {mt f} def /m26 {mt s} def /m23 {mp x y w2 sub m w2 w d w neg 0 d cl f} def /m27 {mp x y w2 add m w3 neg w2 neg d w3 w2 neg d w3 w2 d cl s} def /m28 {mp x w2 sub y w2 sub w3 add m w3 0 d 0 w3 neg d w3 0 d 0 w3 d w3 0 d 0 w3 d w3 neg 0 d 0 w3 d w3 neg 0 d 0 w3 neg d w3 neg 0 d cl s } def /m29 {mp gsave x w2 sub y w2 add w3 sub m currentpoint t 4 {side} repeat cl fill gr} def /m30 {mp gsave x w2 sub y w2 add w3 sub m currentpoint t 5 {side} repeat s gr} def /m31 {mp x y w2 sub m 0 w d x w2 sub y m w 0 d x w2 sub y w2 add m w w neg d x w2 sub y w2 sub m w w d s} def /m2 {mp x y w2 sub m 0 w d x w2 sub y m w 0 d s} def /m5 {mp x w2 sub y w2 sub m w w d x w2 sub y w2 add m w w neg d s} def /DP {/PT exch def gsave 47.2 47.2 scale PT 1 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 > } image } if PT 2 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE > } image } if PT 3 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FF FF BB BB FF FF EE EE FF FF BB BB FF FF EE EE FF FF BB BB FF FF EE EE FF FF BB BB FF FF EE EE > } image } if PT 4 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < DF DF BF BF 7F 7F FE FE FD FD FB FB F7 F7 EF EF DF DF BF BF 7F 7F FE FE FD FD FB FB F7 F7 EF EF > } image } if PT 5 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 7F 7F BF B F DF DF EF EF F7 F7 FB FB FD FD FE FE 7F 7F BF BF DF DF EF EF F7 F7 FB FB FD FD FE FE > } image } if PT 6 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB > } image } if PT 7 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FF FF FF FF FF FF 00 00 FF FF FF FF FF FF 00 00 FF FF FF FF FF FF 00 00 FF FF FF FF FF FF 00 00 > } image } if PT 8 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < EE EE 47 47 83 83 C5 C5 EE EE 5C 5C 38 38 74 74 EE EE 47 47 83 83 C5 C5 EE EE 5C 5C 38 38 74 74 > } image } if PT 9 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < EF EF EF EF D7 D7 38 38 FE FE FE FE 7D 7D 83 83 EF EF EF EF D7 D7 38 38 FE FE FE FE 7D 7D 83 83 > } image } if PT 10 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < EF EF EF EF EF EF 00 00 FE FE FE FE FE FE 00 00 EF EF EF EF EF EF 00 00 FE FE FE FE FE FE 00 00 > } image } if PT 11 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < F7 F7 B6 B6 D5 D5 E3 E3 D5 D5 B6 B6 F7 F7 FF FF 7F 7F 6B 6B 5D 5D 3E 3E 5D 5D 6B 6B 7F 7F FF FF > } image } if PT 12 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < E3 E3 DD DD BE BE BE BE BE BE DD DD E3 E3 FF FF 3E 3E DD DD EB EB EB EB EB EB DD DD 3E 3E FF FF > } image } if PT 13 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FE FE 7D 7D BB BB D7 D7 EF EF D7 D7 BB BB 7D 7D FE FE 7D 7D BB BB D7 D7 EF EF D7 D7 BB BB 7D 7D > } image } if PT 14 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 00 00 EE EF EE EF EE EF 0E E0 EE EE EE EE EE EE 00 EE FE EE FE EE FE EE 00 00 FE EF FE EF FE EF > } image } if PT 15 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < DD DD AA AA DD DD FF FF 77 77 AA AA 77 77 FF FF DD DD AA AA DD DD FF FF 77 77 AA AA 77 77 FF FF > } image } if PT 16 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < F1 F1 EE EE 1F 1F FF FF F1 F1 EE EE 1F 1F FF FF F1 F1 EE EE 1F 1F FF FF F1 F1 EE EE 1F 1F FF FF > } image } if PT 17 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < EE EE DD DD BB BB FF FF EE EE DD DD BB BB FF FF EE EE DD DD BB BB FF FF EE EE DD DD BB BB FF FF > } image } if PT 18 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < BB BB DD DD EE EE FF FF BB BB DD DD EE EE FF FF BB BB DD DD EE EE FF FF BB BB DD DD EE EE FF FF > } image } if PT 19 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 1F FC 67 F3 7B EF BD DE BD DE DE BD E6 B3 F8 0F E6 B3 DE BD BD DE BD DE 7B EF 67 F3 1F FC 7F FF > } image } if PT 20 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < DD DD EE EE EE EE EE EE DD DD BB BB BB BB BB BB DD DD EE EE EE EE EE EE DD DD BB BB BB BB BB BB > } image } if PT 21 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 0E 0E EF EF EF EF EF EF E0 E0 FE FE FE FE FE FE 0E 0E EF EF EF EF EF EF E0 E0 FE FE FE FE FE FE > } image } if PT 22 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 70 70 F7 F7 F7 F7 F7 F7 07 07 7F 7F 7F 7F 7F 7F 70 70 F7 F7 F7 F7 F7 F7 07 07 7F 7F 7F 7F 7F 7F > } image } if PT 23 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < AA AA 55 55 A9 A9 D1 D1 E1 E1 D1 D1 A9 A9 55 55 AA AA 55 55 A9 A9 D1 D1 E1 E1 D1 D1 A9 A9 55 55 > } image } if PT 24 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FF FE FF FC EA A8 D5 54 EA A8 D5 54 E8 28 D4 54 E8 E8 D4 D4 E8 EA 54 D5 A8 EA 54 D5 00 C0 00 80 > } image } if PT 25 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FF FE FF FC FF F8 FF F0 F0 00 F0 00 F0 20 F0 60 F0 E0 F1 E0 F3 E0 F0 00 E0 00 C0 00 80 00 00 00 > } image } if gr } def /FA { /PT exch def gsave clip 0 0 translate 1 1 54 { 1 sub 47.2 mul /Xcurr exch def 1 1 74 { 1 sub 47.2 mul /Ycurr exch def gsave Xcurr Ycurr translate PT DP gr } for } for gr newpath } def /reencdict 24 dict def /ReEncode {reencdict begin /nco&na exch def /nfnam exch def /basefontname exch def /basefontdict basefontname findfont def /newfont basefontdict maxlength dict def basefontdict {exch dup /FID ne {dup /Encoding eq {exch dup length array copy newfont 3 1 roll put} {exch newfont 3 1 roll put} ifelse} {pop pop} ifelse } forall newfont /FontName nfnam put nco&na aload pop nco&na length 2 idiv {newfont /Encoding get 3 1 roll put} repeat nfnam newfont definefont pop end } def /accvec [ 176 /agrave 181 /Agrave 190 /acircumflex 192 /Acircumflex 201 /adieresis 204 /Adieresis 209 /ccedilla 210 /Ccedilla 211 /eacute 212 /Eacute 213 /egrave 214 /Egrave 215 /ecircumflex 216 /Ecircumflex 217 /edieresis 218 /Edieresis 219 /icircumflex 220 /Icircumflex 221 /idieresis 222 /Idieresis 223 /ntilde 224 /Ntilde 226 /ocircumflex 228 /Ocircumflex 229 /odieresis 230 /Odieresis 231 /ucircumflex 236 /Ucircumflex 237 /udieresis 238 /Udieresis 239 /aring 242 /Aring 243 /ydieresis 244 /Ydieresis 246 /aacute 247 /Aacute 252 /ugrave 253 /Ugrave] def /Times-Roman /Times-Roman accvec ReEncode /Times-Italic /Times-Italic accvec ReEncode /Times-Bold /Times-Bold accvec ReEncode /Times-BoldItalic /Times-BoldItalic accvec ReEncode /Helvetica /Helvetica accvec ReEncode /Helvetica-Oblique /Helvetica-Oblique accvec ReEncode /Helvetica-Bold /Helvetica-Bold accvec ReEncode /Helvetica-BoldOblique /Helvetica-BoldOblique accvec ReEncode /Courier /Courier accvec ReEncode /Courier-Oblique /Courier-Oblique accvec ReEncode /Courier-Bold /Courier-Bold accvec ReEncode /Courier-BoldOblique /Courier-BoldOblique accvec ReEncode /oshow {gsave [] 0 sd true charpath stroke gr} def /stwn { /fs exch def /fn exch def /text exch def fn findfont fs sf text sw pop xs add /xs exch def} def /stwb { /fs exch def /fn exch def /nbas exch def /textf exch def textf length /tlen exch def nbas tlen gt {/nbas tlen def} if fn findfont fs sf textf dup length nbas sub nbas getinterval sw pop neg xs add /xs exch def} def /accspe [ 65 /plusminus 66 /bar 67 /existential 68 /universal 69 /exclam 70 /numbersign 71 /greater 72 /question 73 /integral 74 /colon 75 /semicolon 76 /less 77 /bracketleft 78 /bracketright 79 /greaterequal 80 /braceleft 81 /braceright 82 /radical 83 /spade 84 /heart 85 /diamond 86 /club 87 /lessequal 88 /multiply 89 /percent 90 /infinity 48 /circlemultiply 49 /circleplus 50 /emptyset 51 /lozenge 52 /bullet 53 /arrowright 54 /arrowup 55 /arrowleft 56 /arrowdown 57 /arrowboth 48 /degree 44 /comma 43 /plus 45 /angle 42 /angleleft 47 /divide 61 /notequal 40 /equivalence 41 /second 97 /approxequal 98 /congruent 99 /perpendicular 100 /partialdiff 101 /florin 102 /intersection 103 /union 104 /propersuperset 105 /reflexsuperset 106 /notsubset 107 /propersubset 108 /reflexsubset 109 /element 110 /notelement 111 /gradient 112 /logicaland 113 /logicalor 114 /arrowdblboth 115 /arrowdblleft 116 /arrowdblup 117 /arrowdblright 118 /arrowdbldown 119 /ampersand 120 /omega1 121 /similar 122 /aleph ] def /Symbol /Special accspe ReEncode %%EndProlog gsave .25 .25 scale gsave 0 0 t black [] 0 sd 1 lw 2268 2268 0 0 bl 2268 2268 0 0 C 1814 1814 227 227 C NC 891 227 m 38 10 d s 907 253 m 22 -16 d s 869 244 m 38 9 d s 869 244 m 22 -17 d s 929 237 m 39 9 d s 945 263 m 23 -17 d s 907 253 m 38 10 d s 968 246 m 38 10 d s 984 273 m 22 -17 d s 945 263 m 39 10 d s 1006 256 m 38 10 d s 1022 283 m 22 -17 d s 984 273 m 38 10 d s 1044 266 m 39 10 d s 1060 293 m 23 -17 d s 1022 283 m 38 10 d s 1083 276 m 38 9 d s 1099 302 m 22 -17 d s 1060 293 m 39 9 d s 1121 285 m 38 10 d s 1137 312 m 22 -17 d s 1099 302 m 38 10 d s 1159 295 m 39 10 d s 1176 322 m 22 -17 d s 1137 312 m 39 10 d s 1198 305 m 38 10 d s 1214 332 m 22 -17 d s 1176 322 m 38 10 d s 1236 315 m 38 9 d s 1252 341 m 22 -17 d s 1214 332 m 38 9 d s 1274 324 m 39 10 d s 1291 351 m 22 -17 d s 1252 341 m 39 10 d s 1313 334 m 38 10 d s 1329 361 m 22 -17 d s 1291 351 m 38 10 d s 1351 344 m 38 10 d s 1367 371 m 22 -17 d s 1329 361 m 38 10 d s 1329 361 m 12 -10 d s 1389 354 m 39 9 d s 1406 380 m 22 -17 d s 1367 371 m 39 9 d s 1428 363 m 38 10 d s 1444 390 m 22 -17 d s 1406 380 m 38 10 d s 1466 373 m 38 10 d s 1482 400 m 22 -17 d s 1444 390 m 38 10 d s 1504 383 m 39 10 d s 1521 410 m 22 -17 d s 1482 400 m 39 10 d s 1543 393 m 38 9 d s 1559 419 m 22 -17 d s 1521 410 m 38 9 d s 1581 402 m 38 10 d s 1597 429 m 22 -17 d s 1559 419 m 38 10 d s 1619 412 m 39 10 d s 1636 439 m 22 -17 d s 1597 429 m 39 10 d s 1658 422 m 38 10 d s 1674 449 m 22 -17 d s 1636 439 m 38 10 d s 1696 432 m 38 10 d s 1712 458 m 22 -16 d s 1674 449 m 38 9 d s 1734 442 m 39 9 d s 1751 468 m 22 -17 d s 1712 458 m 39 10 d s 1773 451 m 38 10 d s 1789 478 m 22 -17 d s 1751 468 m 38 10 d s 1811 461 m 38 10 d s 1827 488 m 22 -17 d s 1789 478 m 38 10 d s 1849 471 m 39 10 d s 1866 497 m 22 -16 d s 1827 488 m 39 9 d s 1888 481 m 38 9 d s 1904 507 m 22 -17 d s 1866 497 m 38 10 d s 1926 490 m 39 10 d s 1942 517 m 23 -17 d s 1904 507 m 38 10 d s 1965 500 m 38 10 d s 1981 527 m 22 -17 d s 1942 517 m 39 10 d s 2003 510 m 38 10 d s 2019 537 m 22 -17 d s 1981 527 m 38 10 d s 885 270 m 22 -17 d s 847 261 m 38 9 d s 847 261 m 22 -17 d s 923 280 m 22 -17 d s 885 270 m 38 10 d s 962 290 m 22 -17 d s 923 280 m 39 10 d s 1000 300 m 22 -17 d s 962 290 m 38 10 d s 1038 309 m 22 -16 d s 1000 300 m 38 9 d s 1077 319 m 22 -17 d s 1038 309 m 39 10 d s 1115 329 m 22 -17 d s 1077 319 m 38 10 d s 1153 339 m 23 -17 d s 1115 329 m 38 10 d s 1192 348 m 22 -16 d s 1153 339 m 39 9 d s 1230 358 m 22 -17 d s 1192 348 m 38 10 d s 1268 368 m 23 -17 d s 1230 358 m 38 10 d s 1307 378 m 22 -17 d s 1268 368 m 39 10 d s 1345 388 m 22 -17 d s 1307 378 m 38 10 d s 1319 368 m 10 -7 d s 1383 397 m 23 -17 d s 1345 388 m 38 9 d s 1422 407 m 22 -17 d s 1383 397 m 39 10 d s 1460 417 m 22 -17 d s 1422 407 m 38 10 d s 1498 427 m 23 -17 d s 1460 417 m 38 10 d s 1537 436 m 22 -17 d s 1498 427 m 39 9 d s 1575 446 m 22 -17 d s 1537 436 m 38 10 d s 1613 456 m 23 -17 d s 1575 446 m 38 10 d s 1652 466 m 22 -17 d s 1613 456 m 39 10 d s 1690 475 m 22 -17 d s 1652 466 m 38 9 d s 1729 485 m 22 -17 d s 1690 475 m 39 10 d s 1767 495 m 22 -17 d s 1729 485 m 38 10 d s 1805 505 m 22 -17 d s 1767 495 m 38 10 d s 1844 514 m 22 -17 d s 1805 505 m 39 9 d s 1882 524 m 22 -17 d s 1844 514 m 38 10 d s 1920 534 m 22 -17 d s 1882 524 m 38 10 d s 1959 544 m 22 -17 d s 1920 534 m 39 10 d s 1997 553 m 22 -16 d s 1959 544 m 38 9 d s 863 287 m 22 -17 d s 825 278 m 38 9 d s 825 278 m 22 -17 d s 901 297 m 22 -17 d s 863 287 m 38 10 d s 940 307 m 22 -17 d s 901 297 m 39 10 d s 978 317 m 22 -17 d s 940 307 m 38 10 d s 1016 326 m 22 -17 d s 978 317 m 38 9 d s 1055 336 m 22 -17 d s 1016 326 m 39 10 d s 1093 346 m 22 -17 d s 1055 336 m 38 10 d s 1131 356 m 22 -17 d s 1093 346 m 38 10 d s 1170 365 m 22 -17 d s 1131 356 m 39 9 d s 1208 375 m 22 -17 d s 1170 365 m 38 10 d s 1246 385 m 22 -17 d s 1208 375 m 38 10 d s 1285 395 m 22 -17 d s 1246 385 m 39 10 d s 1323 404 m 22 -16 d s 1285 395 m 38 9 d s 1361 414 m 22 -17 d s 1323 404 m 38 10 d s 1400 424 m 22 -17 d s 1361 414 m 39 10 d s 1438 434 m 22 -17 d s 1400 424 m 38 10 d s 1476 443 m 22 -16 d s 1438 434 m 38 9 d s 1515 453 m 22 -17 d s 1476 443 m 39 10 d s 1553 463 m 22 -17 d s 1515 453 m 38 10 d s 1591 473 m 22 -17 d s 1553 463 m 38 10 d s 1630 482 m 22 -16 d s 1591 473 m 39 9 d s 1594 471 m 3 -2 d s 1602 464 m 3 -2 d s 1605 462 m 3 -2 d s 1668 492 m 22 -17 d s 1630 482 m 38 10 d s 1706 502 m 23 -17 d s 1668 492 m 38 10 d s 1745 512 m 22 -17 d s 1706 502 m 39 10 d s 1783 522 m 22 -17 d s 1745 512 m 38 10 d s 1821 531 m 23 -17 d s 1783 522 m 38 9 d s 1860 541 m 22 -17 d s 1821 531 m 39 10 d s 1898 551 m 22 -17 d s 1860 541 m 38 10 d s 1936 561 m 23 -17 d s 1898 551 m 38 10 d s 1975 570 m 22 -17 d s 1936 561 m 39 9 d s 841 304 m 22 -17 d s 802 294 m 39 10 d s 802 294 m 23 -16 d s 879 314 m 22 -17 d s 841 304 m 38 10 d s 917 324 m 23 -17 d s 879 314 m 38 10 d s 956 333 m 22 -16 d s 917 324 m 39 9 d s 994 343 m 22 -17 d s 956 333 m 38 10 d s 1032 353 m 23 -17 d s 994 343 m 38 10 d s 1071 363 m 22 -17 d s 1032 353 m 39 10 d s 1109 373 m 22 -17 d s 1071 363 m 38 10 d s 1147 382 m 23 -17 d s 1109 373 m 38 9 d s 1186 392 m 22 -17 d s 1147 382 m 39 10 d s 1224 402 m 22 -17 d s 1186 392 m 38 10 d s 1262 412 m 23 -17 d s 1224 402 m 38 10 d s 1301 421 m 22 -17 d s 1262 412 m 39 9 d s 1339 431 m 22 -17 d s 1301 421 m 38 10 d s 1378 441 m 22 -17 d s 1339 431 m 39 10 d s 1416 451 m 22 -17 d s 1378 441 m 38 10 d s 1454 460 m 22 -17 d s 1416 451 m 38 9 d s 1493 470 m 22 -17 d s 1454 460 m 39 10 d s 1531 480 m 22 -17 d s 1493 470 m 38 10 d s 1501 464 m 3 -2 d s 1509 457 m 3 -2 d s 1512 455 m 3 -2 d s 1569 490 m 22 -17 d s 1531 480 m 38 10 d s 1608 499 m 22 -17 d s 1569 490 m 39 9 d s 1646 509 m 22 -17 d s 1608 499 m 38 10 d s 1684 519 m 22 -17 d s 1646 509 m 38 10 d s 1723 529 m 22 -17 d s 1684 519 m 39 10 d s 1761 538 m 22 -16 d s 1723 529 m 38 9 d s 1799 548 m 22 -17 d s 1761 538 m 38 10 d s 1838 558 m 22 -17 d s 1799 548 m 39 10 d s 1876 568 m 22 -17 d s 1838 558 m 38 10 d s 1914 577 m 22 -16 d s 1876 568 m 38 9 d s 1953 587 m 22 -17 d s 1914 577 m 39 10 d s 819 321 m 22 -17 d s 780 311 m 39 10 d s 780 311 m 22 -17 d s 857 331 m 22 -17 d s 819 321 m 38 10 d s 895 341 m 22 -17 d s 857 331 m 38 10 d s 934 350 m 22 -17 d s 895 341 m 39 9 d s 972 360 m 22 -17 d s 934 350 m 38 10 d s 1010 370 m 22 -17 d s 972 360 m 38 10 d s 1049 380 m 22 -17 d s 1010 370 m 39 10 d s 1087 389 m 22 -16 d s 1049 380 m 38 9 d s 1125 399 m 22 -17 d s 1087 389 m 38 10 d s 1164 409 m 22 -17 d s 1125 399 m 39 10 d s 1202 419 m 22 -17 d s 1164 409 m 38 10 d s 1240 428 m 22 -16 d s 1202 419 m 38 9 d s 1279 438 m 22 -17 d s 1240 428 m 39 10 d s 1317 448 m 22 -17 d s 1279 438 m 38 10 d s 1355 458 m 23 -17 d s 1317 448 m 38 10 d s 1394 468 m 22 -17 d s 1355 458 m 39 10 d s 1432 477 m 22 -17 d s 1394 468 m 38 9 d s 1470 487 m 23 -17 d s 1432 477 m 38 10 d s 1509 497 m 22 -17 d s 1470 487 m 39 10 d s 1547 507 m 22 -17 d s 1509 497 m 38 10 d s 1585 516 m 23 -17 d s 1547 507 m 38 9 d s 1624 526 m 22 -17 d s 1585 516 m 39 10 d s 1662 536 m 22 -17 d s 1624 526 m 38 10 d s 1700 546 m 23 -17 d s 1662 536 m 38 10 d s 1739 555 m 22 -17 d s 1700 546 m 39 9 d s 1777 565 m 22 -17 d s 1739 555 m 38 10 d s 1815 575 m 23 -17 d s 1777 565 m 38 10 d s 1854 585 m 22 -17 d s 1815 575 m 39 10 d s 1892 594 m 22 -17 d s 1854 585 m 38 9 d s 1931 604 m 22 -17 d s 1892 594 m 39 10 d s 796 338 m 23 -17 d s 758 328 m 38 10 d s 758 328 m 22 -17 d s 835 348 m 22 -17 d s 796 338 m 39 10 d s 873 358 m 22 -17 d s 835 348 m 38 10 d s 911 367 m 23 -17 d s 873 358 m 38 9 d s 950 377 m 22 -17 d s 911 367 m 39 10 d s 988 387 m 22 -17 d s 950 377 m 38 10 d s 1026 397 m 23 -17 d s 988 387 m 38 10 d s 1065 406 m 22 -17 d s 1026 397 m 39 9 d s 1103 416 m 22 -17 d s 1065 406 m 38 10 d s 1142 426 m 22 -17 d s 1103 416 m 39 10 d s 1180 436 m 22 -17 d s 1142 426 m 38 10 d s 1218 445 m 22 -17 d s 1180 436 m 38 9 d s 1257 455 m 22 -17 d s 1218 445 m 39 10 d s 1295 465 m 22 -17 d s 1257 455 m 38 10 d s 1333 475 m 22 -17 d s 1295 465 m 38 10 d s 1372 484 m 22 -16 d s 1333 475 m 39 9 d s 1410 494 m 22 -17 d s 1372 484 m 38 10 d s 1448 504 m 22 -17 d s 1410 494 m 38 10 d s 1487 514 m 22 -17 d s 1448 504 m 39 10 d s 1525 523 m 22 -16 d s 1487 514 m 38 9 d s 1563 533 m 22 -17 d s 1525 523 m 38 10 d s 1602 543 m 22 -17 d s 1563 533 m 39 10 d s 1640 553 m 22 -17 d s 1602 543 m 38 10 d s 1678 562 m 22 -16 d s 1640 553 m 38 9 d s 1717 572 m 22 -17 d s 1678 562 m 39 10 d s 1755 582 m 22 -17 d s 1717 572 m 38 10 d s 1793 592 m 22 -17 d s 1755 582 m 38 10 d s 1832 602 m 22 -17 d s 1793 592 m 39 10 d s 1870 611 m 22 -17 d s 1832 602 m 38 9 d s 1908 621 m 23 -17 d s 1870 611 m 38 10 d s 774 355 m 22 -17 d s 736 345 m 38 10 d s 736 345 m 22 -17 d s 813 365 m 22 -17 d s 774 355 m 39 10 d s 851 374 m 22 -16 d s 813 365 m 38 9 d s 889 384 m 22 -17 d s 851 374 m 38 10 d s 927 371 m 2 1 d s 932 372 m 2 1 d s 937 374 m 13 3 d s 928 394 m 22 -17 d s 889 384 m 39 10 d s 950 377 m 10 3 d s 963 380 m 5 2 d s 970 382 m 3 1 d s 978 384 m 2 1 d s 966 404 m 22 -17 d s 928 394 m 38 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10 d s 1199 733 m 22 -16 d s 1160 724 m 39 9 d s 1237 743 m 22 -17 d s 1199 733 m 38 10 d s 1276 753 m 22 -17 d s 1237 743 m 39 10 d s 1314 763 m 22 -17 d s 1276 753 m 38 10 d s 1352 773 m 22 -17 d s 1314 763 m 38 10 d s 1391 782 m 22 -17 d s 1352 773 m 39 9 d s 1429 792 m 22 -17 d s 1391 782 m 38 10 d s 1467 802 m 22 -17 d s 1429 792 m 38 10 d s 1506 812 m 22 -17 d s 1467 802 m 39 10 d s 1544 821 m 22 -17 d s 1506 812 m 38 9 d s 1582 831 m 22 -17 d s 1544 821 m 38 10 d s 1621 841 m 22 -17 d s 1582 831 m 39 10 d s 487 575 m 22 -17 d s 448 565 m 39 10 d s 448 565 m 22 -17 d s 525 584 m 22 -16 d s 487 575 m 38 9 d s 563 594 m 22 -17 d s 525 584 m 38 10 d s 602 604 m 22 -17 d s 563 594 m 39 10 d s 640 614 m 22 -17 d s 602 604 m 38 10 d s 678 623 m 22 -16 d s 640 614 m 38 9 d s 717 633 m 22 -17 d s 678 623 m 39 10 d s 755 643 m 22 -17 d s 717 633 m 38 10 d s 793 653 m 22 -17 d s 755 643 m 38 10 d s 832 663 m 22 -17 d s 793 653 m 39 10 d s 870 672 m 22 -17 d s 832 663 m 38 9 d s 908 682 m 22 -17 d s 870 672 m 38 10 d s 947 692 m 22 -17 d s 908 682 m 39 10 d s 916 676 m 5 -3 d s 926 669 m 4 -4 d s 947 692 m 23 6 d s 1062 721 m 22 -17 d s 1055 719 m 7 2 d s 1100 731 m 22 -17 d s 1062 721 m 38 10 d s 1138 741 m 22 -17 d s 1100 731 m 38 10 d s 1177 750 m 22 -17 d s 1138 741 m 39 9 d s 1215 760 m 22 -17 d s 1177 750 m 38 10 d s 1253 770 m 23 -17 d s 1215 760 m 38 10 d s 1292 780 m 22 -17 d s 1253 770 m 39 10 d s 1330 789 m 22 -16 d s 1292 780 m 38 9 d s 1368 799 m 23 -17 d s 1330 789 m 38 10 d s 1407 809 m 22 -17 d s 1368 799 m 39 10 d s 1445 819 m 22 -17 d s 1407 809 m 38 10 d s 1483 828 m 23 -16 d s 1445 819 m 38 9 d s 1522 838 m 22 -17 d s 1483 828 m 39 10 d s 1560 848 m 22 -17 d s 1522 838 m 38 10 d s 1598 858 m 23 -17 d s 1560 848 m 38 10 d s 464 592 m 23 -17 d s 426 582 m 38 10 d s 426 582 m 22 -17 d s 503 601 m 22 -17 d s 464 592 m 39 9 d s 541 611 m 22 -17 d s 503 601 m 38 10 d s 579 621 m 23 -17 d s 541 611 m 38 10 d s 618 631 m 22 -17 d s 579 621 m 39 10 d s 656 640 m 22 -17 d s 618 631 m 38 9 d s 694 650 m 23 -17 d s 656 640 m 38 10 d s 733 660 m 22 -17 d s 694 650 m 39 10 d s 771 670 m 22 -17 d s 733 660 m 38 10 d s 809 679 m 23 -16 d s 771 670 m 38 9 d s 848 689 m 22 -17 d s 809 679 m 39 10 d s 886 699 m 22 -17 d s 848 689 m 38 10 d s 924 709 m 23 -17 d s 886 699 m 38 10 d s 963 718 m 7 -5 d s 924 709 m 39 9 d s 963 718 m 7 2 d s 1040 738 m 22 -17 d s 1011 731 m 29 7 d s 1078 748 m 22 -17 d s 1040 738 m 38 10 d s 1116 758 m 22 -17 d s 1078 748 m 38 10 d s 1155 767 m 22 -17 d s 1116 758 m 39 9 d s 1193 777 m 22 -17 d s 1155 767 m 38 10 d s 1231 787 m 22 -17 d s 1193 777 m 38 10 d s 1270 797 m 22 -17 d s 1231 787 m 39 10 d s 1308 806 m 22 -17 d s 1270 797 m 38 9 d s 1346 816 m 22 -17 d s 1308 806 m 38 10 d s 1385 826 m 22 -17 d s 1346 816 m 39 10 d s 1423 836 m 22 -17 d s 1385 826 m 38 10 d s 1461 845 m 22 -17 d s 1423 836 m 38 9 d s 1500 855 m 22 -17 d s 1461 845 m 39 10 d s 1538 865 m 22 -17 d s 1500 855 m 38 10 d s 1576 875 m 22 -17 d s 1538 865 m 38 10 d s 442 609 m 22 -17 d s 404 599 m 38 10 d s 404 599 m 22 -17 d s 481 618 m 22 -17 d s 442 609 m 39 9 d s 519 628 m 22 -17 d s 481 618 m 38 10 d s 557 638 m 22 -17 d s 519 628 m 38 10 d s 596 648 m 22 -17 d s 557 638 m 39 10 d s 634 657 m 22 -17 d s 596 648 m 38 9 d s 672 667 m 22 -17 d s 634 657 m 38 10 d s 711 677 m 22 -17 d s 672 667 m 39 10 d s 749 687 m 22 -17 d s 711 677 m 38 10 d s 787 696 m 22 -17 d s 749 687 m 38 9 d s 826 706 m 22 -17 d s 787 696 m 39 10 d s 864 716 m 22 -17 d s 826 706 m 38 10 d s 902 726 m 22 -17 d s 864 716 m 38 10 d s 941 735 m 22 -17 d s 902 726 m 39 9 d s 979 745 m 18 -13 d s 941 735 m 38 10 d s 1017 755 m 23 -17 d s 979 745 m 38 10 d s 1056 765 m 22 -17 d s 1017 755 m 39 10 d s 1094 774 m 22 -16 d s 1056 765 m 38 9 d s 1132 784 m 23 -17 d s 1094 774 m 38 10 d s 1171 794 m 22 -17 d s 1132 784 m 39 10 d s 1209 804 m 22 -17 d s 1171 794 m 38 10 d s 1247 813 m 23 -16 d s 1209 804 m 38 9 d s 1286 823 m 22 -17 d s 1247 813 m 39 10 d s 1324 833 m 22 -17 d s 1286 823 m 38 10 d s 1362 843 m 23 -17 d s 1324 833 m 38 10 d s 1401 853 m 22 -17 d s 1362 843 m 39 10 d s 1439 862 m 22 -17 d s 1401 853 m 38 9 d s 1500 855 m 158 Y s 1461 1003 m 39 10 d s 1461 845 m 158 Y s 1439 1020 m 22 -17 d s 1439 862 m 158 Y s 1477 1030 m 23 -17 d s 1439 1020 m 38 10 d s 1538 865 m 79 Y s 1500 934 m 38 10 d s 1516 961 m 22 -17 d s 1498 956 m 18 5 d s 1576 875 m 108 Y s 1538 973 m 38 10 d s 1538 944 m 29 Y s 1516 990 m 22 -17 d s 1516 961 m 29 Y s 1554 1000 m 22 -17 d s 1516 990 m 38 10 d s 420 625 m 22 -16 d s 382 616 m 38 9 d s 382 616 m 22 -17 d s 458 635 m 23 -17 d s 420 625 m 38 10 d s 497 645 m 22 -17 d s 458 635 m 39 10 d s 535 655 m 22 -17 d s 497 645 m 38 10 d s 573 664 m 23 -16 d s 535 655 m 38 9 d s 612 674 m 22 -17 d s 573 664 m 39 10 d s 650 684 m 22 -17 d s 612 674 m 38 10 d s 689 694 m 22 -17 d s 650 684 m 39 10 d s 727 703 m 22 -16 d s 689 694 m 38 9 d s 765 713 m 22 -17 d s 727 703 m 38 10 d s 804 723 m 22 -17 d s 765 713 m 39 10 d s 842 733 m 22 -17 d s 804 723 m 38 10 d s 880 743 m 22 -17 d s 842 733 m 38 10 d s 919 752 m 22 -17 d s 880 743 m 39 9 d s 957 762 m 22 -17 d s 919 752 m 38 10 d s 995 772 m 22 -17 d s 957 762 m 38 10 d s 1034 782 m 22 -17 d s 995 772 m 39 10 d s 1072 791 m 22 -17 d s 1034 782 m 38 9 d s 1110 801 m 22 -17 d s 1072 791 m 38 10 d s 1149 811 m 22 -17 d s 1110 801 m 39 10 d s 1187 821 m 22 -17 d s 1149 811 m 38 10 d s 1225 830 m 22 -17 d s 1187 821 m 38 9 d s 1264 840 m 22 -17 d s 1225 830 m 39 10 d s 1302 850 m 22 -17 d s 1264 840 m 38 10 d s 1340 860 m 22 -17 d s 1302 850 m 38 10 d s 1379 869 m 22 -16 d s 1340 860 m 39 9 d s 1417 879 m 22 -17 d s 1379 869 m 38 10 d s 1417 958 m 22 -17 d s 1417 879 m 79 Y s 1417 958 m 23 6 d s 1498 966 m 18 4 d s 1499 984 m 17 -14 d s 1554 1000 m 20 Y s 1516 1010 m 38 10 d s 1516 990 m 20 Y s 1494 1027 m 22 -17 d s 1494 1017 m 10 Y s 1532 1037 m 22 -17 d s 1494 1027 m 38 10 d s 398 642 m 22 -17 d s 360 633 m 38 9 d s 360 633 m 22 -17 d s 436 652 m 22 -17 d s 398 642 m 38 10 d s 475 662 m 22 -17 d s 436 652 m 39 10 d s 513 672 m 22 -17 d s 475 662 m 38 10 d s 551 681 m 22 -17 d s 513 672 m 38 9 d s 590 691 m 22 -17 d s 551 681 m 39 10 d s 628 701 m 22 -17 d s 590 691 m 38 10 d s 666 711 m 23 -17 d s 628 701 m 38 10 d s 705 720 m 22 -17 d s 666 711 m 39 9 d s 743 730 m 22 -17 d s 705 720 m 38 10 d s 781 740 m 23 -17 d s 743 730 m 38 10 d s 820 750 m 22 -17 d s 781 740 m 39 10 d s 858 759 m 22 -16 d s 820 750 m 38 9 d s 896 769 m 23 -17 d s 858 759 m 38 10 d s 935 779 m 22 -17 d s 896 769 m 39 10 d s 973 789 m 22 -17 d s 935 779 m 38 10 d s 1011 798 m 23 -16 d s 973 789 m 38 9 d s 1050 808 m 22 -17 d s 1011 798 m 39 10 d s 1088 818 m 22 -17 d s 1050 808 m 38 10 d s 1126 828 m 23 -17 d s 1088 818 m 38 10 d s 1165 838 m 22 -17 d s 1126 828 m 39 10 d s 1203 847 m 22 -17 d s 1165 838 m 38 9 d s 1242 857 m 22 -17 d s 1203 847 m 39 10 d s 1280 867 m 22 -17 d s 1242 857 m 38 10 d s 1318 877 m 22 -17 d s 1280 867 m 38 10 d s 1357 886 m 22 -17 d s 1318 877 m 39 9 d s 1395 896 m 22 -17 d s 1357 886 m 38 10 d s 1395 955 m 22 -17 d s 1395 896 m 59 Y s 1433 965 m 3 -2 d s 1395 955 m 38 10 d s 376 659 m 22 -17 d s 337 649 m 39 10 d s 337 649 m 23 -16 d s 414 669 m 22 -17 d s 376 659 m 38 10 d s 453 679 m 22 -17 d s 414 669 m 39 10 d s 513 672 m 787 Y s 475 1450 m 38 9 d s 475 662 m 788 Y s 453 1467 m 22 -17 d s 453 679 m 788 Y s 491 1476 m 22 -17 d s 453 1467 m 38 9 d s 551 681 m 867 Y s 513 1538 m 38 10 d s 513 1459 m 79 Y s 491 1555 m 22 -17 d s 491 1476 m 79 Y s 529 1565 m 22 -17 d s 491 1555 m 38 10 d s 590 691 m 788 Y s 551 1469 m 39 10 d s 568 1496 m 22 -17 d s 552 1492 m 16 4 d s 606 718 m 22 -17 d s 591 714 m 15 4 d s 644 728 m 22 -17 d s 606 718 m 38 10 d s 683 737 m 22 -17 d s 644 728 m 39 9 d s 721 747 m 22 -17 d s 683 737 m 38 10 d s 759 757 m 22 -17 d s 721 747 m 38 10 d s 798 767 m 22 -17 d s 759 757 m 39 10 d s 836 776 m 22 -17 d s 798 767 m 38 9 d s 874 786 m 22 -17 d s 836 776 m 38 10 d s 913 796 m 22 -17 d s 874 786 m 39 10 d s 951 806 m 22 -17 d s 913 796 m 38 10 d s 989 815 m 22 -17 d s 951 806 m 38 9 d s 1028 825 m 22 -17 d s 989 815 m 39 10 d s 1066 835 m 22 -17 d s 1028 825 m 38 10 d s 1104 845 m 22 -17 d s 1066 835 m 38 10 d s 1143 854 m 22 -16 d s 1104 845 m 39 9 d s 1181 864 m 22 -17 d s 1143 854 m 38 10 d s 1219 874 m 23 -17 d s 1181 864 m 38 10 d s 1258 884 m 22 -17 d s 1219 874 m 39 10 d s 1296 893 m 22 -16 d s 1258 884 m 38 9 d s 1334 903 m 23 -17 d s 1296 893 m 38 10 d s 1373 913 m 22 -17 d s 1334 903 m 39 10 d s 1373 913 m 23 6 d s 337 649 m cl s 354 676 m 22 -17 d s 315 666 m 39 10 d s 315 666 m 22 -17 d s 392 686 m 22 -17 d s 354 676 m 38 10 d s 430 696 m 23 -17 d s 392 686 m 38 10 d s 453 1536 m 38 9 d s 453 1467 m 69 Y s 430 1552 m 23 -16 d s 430 696 m 856 Y s 469 1562 m 22 -17 d s 430 1552 m 39 10 d s 568 1496 m 226 Y s 529 1713 m 39 9 d s 529 1565 m 148 Y s 507 1730 m 22 -17 d s 507 1559 m 171 Y s 545 1739 m 23 -17 d s 507 1730 m 38 9 d s 589 730 m 17 -12 d s 622 744 m 22 -16 d s 589 736 m 33 8 d s 660 754 m 23 -17 d s 622 744 m 38 10 d s 699 764 m 22 -17 d s 660 754 m 39 10 d s 737 774 m 22 -17 d s 699 764 m 38 10 d s 775 783 m 23 -16 d s 737 774 m 38 9 d s 814 793 m 22 -17 d s 775 783 m 39 10 d s 852 803 m 22 -17 d s 814 793 m 38 10 d s 890 813 m 23 -17 d s 852 803 m 38 10 d s 929 823 m 22 -17 d s 890 813 m 39 10 d s 967 832 m 22 -17 d s 929 823 m 38 9 d s 1006 842 m 22 -17 d s 967 832 m 39 10 d s 1044 852 m 22 -17 d s 1006 842 m 38 10 d s 1082 862 m 22 -17 d s 1044 852 m 38 10 d s 1121 871 m 22 -17 d s 1082 862 m 39 9 d s 1159 881 m 22 -17 d s 1121 871 m 38 10 d s 1197 891 m 22 -17 d s 1159 881 m 38 10 d s 1236 901 m 22 -17 d s 1197 891 m 39 10 d s 1274 910 m 22 -17 d s 1236 901 m 38 9 d s 1312 920 m 22 -17 d s 1274 910 m 38 10 d s 1351 930 m 22 -17 d s 1312 920 m 39 10 d s 1389 940 m 5 -5 d s 1351 930 m 38 10 d s 1389 940 m 5 1 d s 332 693 m 22 -17 d s 293 683 m 39 10 d s 293 683 m 22 -17 d s 370 703 m 22 -17 d s 332 693 m 38 10 d s 408 713 m 22 -17 d s 370 703 m 38 10 d s 408 1530 m 22 -17 d s 408 713 m 817 Y s 408 1530 m 23 6 d s 485 1658 m 22 -17 d s 485 1549 m 109 Y s 485 1658 m 20 5 d s 600 761 m 22 -17 d s 590 759 m 10 2 d s 638 771 m 22 -17 d s 600 761 m 38 10 d s 677 781 m 22 -17 d s 638 771 m 39 10 d s 715 791 m 22 -17 d s 677 781 m 38 10 d s 753 800 m 22 -17 d s 715 791 m 38 9 d s 792 810 m 22 -17 d s 753 800 m 39 10 d s 830 820 m 22 -17 d s 792 810 m 38 10 d s 868 830 m 22 -17 d s 830 820 m 38 10 d s 907 839 m 22 -16 d s 868 830 m 39 9 d s 945 849 m 22 -17 d s 907 839 m 38 10 d s 983 859 m 23 -17 d s 945 849 m 38 10 d s 1022 869 m 22 -17 d s 983 859 m 39 10 d s 1060 878 m 22 -16 d s 1022 869 m 38 9 d s 1098 888 m 23 -17 d s 1060 878 m 38 10 d s 1137 898 m 22 -17 d s 1098 888 m 39 10 d s 1175 908 m 22 -17 d s 1137 898 m 38 10 d s 1213 918 m 23 -17 d s 1175 908 m 38 10 d s 1252 927 m 22 -17 d s 1213 918 m 39 9 d s 1290 937 m 22 -17 d s 1252 927 m 38 10 d s 1328 947 m 23 -17 d s 1290 937 m 38 10 d s 1367 957 m 22 -17 d s 1328 947 m 39 10 d s 1405 966 m 8 -6 d s 1367 957 m 38 9 d s 1405 966 m 36 9 d s 293 683 m cl s 309 710 m 23 -17 d s 271 700 m 38 10 d s 271 700 m 22 -17 d s 348 720 m 22 -17 d s 309 710 m 39 10 d s 386 729 m 22 -16 d s 348 720 m 38 9 d s 386 729 m 22 6 d s 590 769 m 10 -8 d s 616 788 m 22 -17 d s 591 782 m 25 6 d s 655 798 m 22 -17 d s 616 788 m 39 10 d s 693 808 m 22 -17 d s 655 798 m 38 10 d s 731 817 m 22 -17 d s 693 808 m 38 9 d s 770 827 m 22 -17 d s 731 817 m 39 10 d s 808 837 m 22 -17 d s 770 827 m 38 10 d s 846 847 m 22 -17 d s 808 837 m 38 10 d s 885 856 m 22 -17 d s 846 847 m 39 9 d s 923 866 m 22 -17 d s 885 856 m 38 10 d s 961 876 m 22 -17 d s 923 866 m 38 10 d s 1000 886 m 22 -17 d s 961 876 m 39 10 d s 1038 895 m 22 -17 d s 1000 886 m 38 9 d s 1076 905 m 22 -17 d s 1038 895 m 38 10 d s 1115 915 m 22 -17 d s 1076 905 m 39 10 d s 1153 925 m 22 -17 d s 1115 915 m 38 10 d s 1191 934 m 22 -16 d s 1153 925 m 38 9 d s 1230 944 m 22 -17 d s 1191 934 m 39 10 d s 1268 954 m 22 -17 d s 1230 944 m 38 10 d s 1323 946 m 3 X s 1306 964 m 22 -17 d s 1268 954 m 38 10 d s 1345 973 m 22 -16 d s 1306 964 m 39 9 d s 1383 983 m 22 -17 d s 1345 973 m 38 10 d s 1438 975 m 3 X s 1421 993 m 20 -15 d s 1383 983 m 38 10 d s 287 727 m 22 -17 d s 249 717 m 38 10 d s 249 717 m 22 -17 d s 326 737 m 22 -17 d s 287 727 m 39 10 d s 364 746 m 22 -17 d s 326 737 m 38 9 d s 402 756 m 5 -4 d s 364 746 m 38 10 d s 402 756 m 5 1 d s 594 805 m 22 -17 d s 589 804 m 5 1 d s 632 815 m 23 -17 d s 594 805 m 38 10 d s 671 824 m 22 -16 d s 632 815 m 39 9 d s 709 834 m 22 -17 d s 671 824 m 38 10 d s 747 844 m 23 -17 d s 709 834 m 38 10 d s 709 834 m 17 -13 d s 786 854 m 22 -17 d s 747 844 m 39 10 d s 824 863 m 22 -16 d s 786 854 m 38 9 d s 862 873 m 23 -17 d s 824 863 m 38 10 d s 901 883 m 22 -17 d s 862 873 m 39 10 d s 939 893 m 22 -17 d s 901 883 m 38 10 d s 977 903 m 23 -17 d s 939 893 m 38 10 d s 1016 912 m 22 -17 d s 977 903 m 39 9 d s 1054 922 m 22 -17 d s 1016 912 m 38 10 d s 1092 932 m 23 -17 d s 1054 922 m 38 10 d s 1131 942 m 22 -17 d s 1092 932 m 39 10 d s 1169 951 m 22 -17 d s 1131 942 m 38 9 d s 1208 961 m 22 -17 d s 1169 951 m 39 10 d s 1246 971 m 22 -17 d s 1208 961 m 38 10 d s 1284 981 m 22 -17 d s 1246 971 m 38 10 d s 1323 990 m 22 -17 d s 1284 981 m 39 9 d s 1361 1000 m 22 -17 d s 1323 990 m 38 10 d s 1399 1010 m 22 -17 d s 1361 1000 m 38 10 d s 249 717 m cl s 265 744 m 22 -17 d s 227 734 m 38 10 d s 227 734 m 22 -17 d s 303 754 m 23 -17 d s 265 744 m 38 10 d s 342 763 m 22 -17 d s 303 754 m 39 9 d s 380 773 m 22 -17 d s 342 763 m 38 10 d s 380 773 m 28 7 d s 589 809 m 5 -4 d s 610 832 m 22 -17 d s 590 826 m 20 6 d s 649 841 m 22 -17 d s 610 832 m 39 9 d s 687 851 m 22 -17 d s 649 841 m 38 10 d s 725 861 m 22 -17 d s 687 851 m 38 10 d s 764 871 m 22 -17 d s 725 861 m 39 10 d s 802 880 m 22 -17 d s 764 871 m 38 9 d s 840 890 m 22 -17 d s 802 880 m 38 10 d s 879 900 m 22 -17 d s 840 890 m 39 10 d s 917 910 m 22 -17 d s 879 900 m 38 10 d s 955 919 m 22 -16 d s 917 910 m 38 9 d s 994 929 m 22 -17 d s 955 919 m 39 10 d s 1032 939 m 22 -17 d s 994 929 m 38 10 d s 1070 949 m 22 -17 d s 1032 939 m 38 10 d s 1109 958 m 22 -16 d s 1070 949 m 39 9 d s 1147 968 m 22 -17 d s 1109 958 m 38 10 d s 1185 978 m 23 -17 d s 1147 968 m 38 10 d s 1224 988 m 22 -17 d s 1185 978 m 39 10 d s 1279 979 m 3 1 d s 1262 998 m 22 -17 d s 1224 988 m 38 10 d s 1300 1007 m 23 -17 d s 1262 998 m 38 9 d s 1339 1017 m 22 -17 d s 1300 1007 m 39 10 d s 1377 1027 m 22 -17 d s 1339 1017 m 38 10 d s [4 8] 0 sd 227 931 m 180 46 d s 589 1023 m 788 201 d s 227 1128 m 180 46 d s 589 1220 m 788 201 d s 227 1325 m 180 46 d s 589 1417 m 788 201 d s 227 1522 m 258 66 d s 566 1608 m 811 207 d s 227 1719 m 1150 293 d s [] 0 sd 227 734 m s 758 869 m 44 11 d s 979 925 m 111 29 d s 1244 993 m 133 34 d s 1377 1027 m 1014 Y s 227 1748 m 1150 293 d s 227 734 m 1014 Y s [4 8] 0 sd 1377 1224 m 664 -507 d s 1377 1421 m 664 -507 d s 1377 1618 m 664 -507 d s 1377 1815 m 664 -508 d s 1377 2012 m 664 -508 d s [] 0 sd 1377 1027 m s 1437 981 m 3 -3 d s 1619 842 m 7 -5 d s 1709 773 m s 1951 589 m 7 -6 d s 2041 520 m 1014 Y s 1377 2041 m 664 -507 d s 227 734 m 664 -507 d s 891 227 m 1014 Y s 227 1748 m 664 -507 d s 227 734 m 1014 Y s 891 227 m 1150 293 d s 2041 520 m 1014 Y s 891 1241 m 1150 293 d s 891 1241 m cl s 891 227 m 1150 293 d s 891 193 m 34 Y s 914 216 m 17 Y s 937 222 m 17 Y s 960 227 m 17 Y s 983 233 m 17 Y s 1006 222 m 34 Y s 1029 245 m 17 Y s 1052 251 m 17 Y s 1075 257 m 17 Y s 1098 262 m 18 Y s 1121 251 m 34 Y s 1144 274 m 17 Y s 1167 280 m 17 Y s 1190 286 m 17 Y s 1213 292 m 17 Y s 1236 281 m 34 Y s 1259 303 m 18 Y s 1282 309 m 17 Y s 1305 315 m 17 Y s 1328 321 m 17 Y s 1351 310 m 34 Y s 1374 333 m 17 Y s 1397 339 m 17 Y s 1420 344 m 18 Y s 1443 350 m 17 Y s 1466 339 m 34 Y s 1489 362 m 17 Y s 1512 368 m 17 Y s 1535 374 m 17 Y s 1558 380 m 17 Y s 1581 368 m 34 Y s 1604 391 m 17 Y s 1627 397 m 17 Y s 1650 403 m 17 Y s 1673 409 m 17 Y s 1696 398 m 34 Y s 1719 421 m 17 Y s 1742 426 m 17 Y s 1765 432 m 17 Y s 1788 438 m 17 Y s 1811 427 m 34 Y s 1834 450 m 17 Y s 1857 456 m 17 Y s 1880 462 m 17 Y s 1903 467 m 17 Y s 1926 456 m 34 Y s 1949 479 m 17 Y s 1972 485 m 17 Y s 1995 491 m 17 Y s 2018 497 m 17 Y s 2041 486 m 34 Y s 893 174 m -4 -2 d -3 -5 d -2 -7 d -5 Y 2 -7 d 3 -5 d 4 -1 d 3 X 5 1 d 3 5 d 1 7 d 5 Y -1 7 d -3 5 d -5 2 d -3 X cl s 994 203 m -5 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -4 d 5 -2 d 3 X 4 2 d 3 4 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -3 X cl s 1018 174 m -2 -1 d 2 -2 d 1 2 d -1 1 d cl s 1034 197 m 3 1 d 5 5 d -32 Y s 1109 232 m -5 -1 d -3 -5 d -2 -8 d -4 Y 2 -8 d 3 -4 d 5 -2 d 3 X 4 2 d 3 4 d 2 8 d 4 Y -2 8 d -3 5 d -4 1 d -3 X cl s 1133 203 m -2 -1 d 2 -2 d 1 2 d -1 1 d cl s 1146 225 m 1 Y 2 3 d 1 2 d 3 1 d 6 X 3 -1 d 2 -2 d 1 -3 d -3 Y -1 -3 d -3 -5 d -15 -15 d 21 X s 1224 261 m -5 -1 d -3 -5 d -2 -7 d -5 Y 2 -7 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 7 d 5 Y -2 7 d -3 5 d -4 1 d -3 X cl s 1248 233 m -2 -2 d 2 -1 d 1 1 d -1 2 d cl s 1263 261 m 17 X -10 -12 d 5 X 3 -1 d 2 -2 d 1 -4 d -3 Y -1 -5 d -4 -3 d -4 -1 d -5 X -4 1 d -2 2 d -1 3 d s 1339 291 m -5 -2 d -3 -4 d -1 -8 d -5 Y 1 -7 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 7 d 5 Y -2 8 d -3 4 d -4 2 d -3 X cl s 1363 262 m -2 -2 d 2 -1 d 1 1 d -1 2 d cl s 1390 291 m -15 -22 d 23 X s 1390 291 m -32 Y s 1454 320 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -4 d 5 -2 d 3 X 4 2 d 3 4 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -3 X cl s 1478 291 m -2 -1 d 2 -2 d 1 2 d -1 1 d cl s 1508 320 m -15 X -2 -14 d 2 2 d 4 1 d 5 X 5 -1 d 3 -3 d 1 -5 d -3 Y -1 -4 d -3 -3 d -5 -2 d -5 X -4 2 d -2 1 d -1 3 d s 1569 349 m -5 -1 d -3 -5 d -1 -7 d -5 Y 1 -8 d 3 -4 d 5 -2 d 3 X 4 2 d 3 4 d 2 8 d 5 Y -2 7 d -3 5 d -4 1 d -3 X cl s 1593 320 m -2 -1 d 2 -2 d 1 2 d -1 1 d cl s 1625 345 m -2 3 d -4 1 d -3 X -5 -1 d -3 -5 d -2 -7 d -8 Y 2 -6 d 3 -3 d 5 -2 d 1 X 5 2 d 3 3 d 1 5 d 1 Y -1 5 d -3 3 d -5 1 d -1 X -5 -1 d -3 -3 d -2 -5 d s 1684 378 m -5 -1 d -3 -5 d -1 -7 d -5 Y 1 -7 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 7 d 5 Y -2 7 d -3 5 d -4 1 d -3 X cl s 1708 350 m -2 -2 d 2 -1 d 1 1 d -1 2 d cl s 1741 378 m -15 -31 d s 1720 378 m 21 X s 1799 408 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -4 d 5 -2 d 3 X 4 2 d 3 4 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -3 X cl s 1823 379 m -2 -1 d 2 -2 d 1 2 d -1 1 d cl s 1843 408 m -5 -2 d -1 -3 d -3 Y 1 -3 d 3 -1 d 6 -2 d 5 -1 d 3 -3 d 1 -3 d -5 Y -1 -3 d -2 -1 d -4 -2 d -6 X -5 2 d -1 1 d -2 3 d 5 Y 2 3 d 3 3 d 4 1 d 6 2 d 3 1 d 2 3 d 3 Y -2 3 d -4 2 d -6 X cl s 1914 437 m -5 -1 d -3 -5 d -1 -8 d -4 Y 1 -8 d 3 -4 d 5 -2 d 3 X 4 2 d 3 4 d 2 8 d 4 Y -2 8 d -3 5 d -4 1 d -3 X cl s 1938 408 m -2 -1 d 2 -2 d 1 2 d -1 1 d cl s 1970 426 m -2 -4 d -3 -3 d -4 -2 d -2 X -4 2 d -3 3 d -2 4 d 2 Y 2 5 d 3 3 d 4 1 d 2 X 4 -1 d 3 -3 d 2 -7 d -7 Y -2 -8 d -3 -4 d -4 -2 d -3 X -5 2 d -1 3 d s 2039 460 m 3 2 d 5 4 d -31 Y s 891 227 m -664 507 d s 891 193 m 34 Y s 878 220 m 17 Y s 864 230 m 17 Y s 851 240 m 17 Y s 838 250 m 17 Y s 825 243 m 35 Y s 811 271 m 17 Y s 798 281 m 17 Y s 785 291 m 17 Y s 771 301 m 17 Y s 758 294 m 34 Y s 745 321 m 17 Y s 732 332 m 17 Y s 718 342 m 17 Y s 705 352 m 17 Y s 692 345 m 34 Y s 678 372 m 17 Y s 665 382 m 17 Y s 652 392 m 17 Y s 639 403 m 17 Y s 625 396 m 34 Y s 612 423 m 17 Y s 599 433 m 17 Y s 585 443 m 17 Y s 572 453 m 17 Y s 559 446 m 34 Y s 546 474 m 17 Y s 532 484 m 17 Y s 519 494 m 17 Y s 506 504 m 17 Y s 492 497 m 34 Y s 479 524 m 17 Y s 466 534 m 17 Y s 453 545 m 17 Y s 439 555 m 17 Y s 426 548 m 34 Y s 413 575 m 17 Y s 399 585 m 17 Y s 386 595 m 17 Y s 373 605 m 17 Y s 360 599 m 34 Y s 346 626 m 17 Y s 333 636 m 17 Y s 320 646 m 17 Y s 306 656 m 17 Y s 293 649 m 34 Y s 280 676 m 17 Y s 267 687 m 17 Y s 253 697 m 17 Y s 240 707 m 17 Y s 227 700 m 34 Y s 891 193 m 34 Y s 880 133 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -3 X cl s 771 183 m -4 -1 d -3 -5 d -2 -7 d -5 Y 2 -7 d 3 -5 d 4 -1 d 3 X 5 1 d 3 5 d 2 7 d 5 Y -2 7 d -3 5 d -5 1 d -3 X cl s 796 155 m -2 -2 d 2 -1 d 1 1 d -1 2 d cl s 812 177 m 3 2 d 5 4 d -31 Y s 705 234 m -5 -1 d -3 -5 d -1 -7 d -5 Y 1 -8 d 3 -4 d 5 -2 d 3 X 5 2 d 3 4 d 1 8 d 5 Y -1 7 d -3 5 d -5 1 d -3 X cl s 729 205 m -1 -1 d 1 -2 d 2 2 d -2 1 d cl s 743 227 m 1 Y 1 3 d 2 2 d 3 1 d 6 X 3 -1 d 1 -2 d 2 -3 d -3 Y -2 -3 d -3 -5 d -15 -15 d 21 X s 639 285 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -4 d 5 -2 d 3 X 4 2 d 3 4 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -3 X cl s 663 256 m -2 -1 d 2 -2 d 1 2 d -1 1 d cl s 678 285 m 17 X -10 -12 d 5 X 3 -2 d 2 -1 d 1 -5 d -3 Y -1 -4 d -3 -3 d -5 -2 d -5 X -4 2 d -2 1 d -1 3 d s 572 336 m -4 -2 d -3 -4 d -2 -8 d -5 Y 2 -7 d 3 -5 d 4 -1 d 3 X 5 1 d 3 5 d 1 7 d 5 Y -1 8 d -3 4 d -5 2 d -3 X cl s 596 307 m -1 -2 d 1 -1 d 2 1 d -2 2 d cl s 624 336 m -16 -22 d 23 X s 624 336 m -32 Y s 506 386 m -5 -1 d -3 -5 d -1 -7 d -5 Y 1 -7 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 7 d 5 Y -2 7 d -3 5 d -4 1 d -3 X cl s 530 358 m -2 -2 d 2 -1 d 1 1 d -1 2 d cl s 560 386 m -15 X -1 -13 d 1 1 d 5 2 d 4 X 5 -2 d 3 -3 d 1 -4 d -3 Y -1 -5 d -3 -3 d -5 -1 d -4 X -5 1 d -1 2 d -2 3 d s 439 437 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -4 d 4 -2 d 3 X 5 2 d 3 4 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 464 408 m -2 -1 d 2 -2 d 1 2 d -1 1 d cl s 495 432 m -1 3 d -5 2 d -3 X -4 -2 d -3 -4 d -2 -8 d -7 Y 2 -6 d 3 -3 d 4 -2 d 2 X 4 2 d 3 3 d 2 4 d 2 Y -2 4 d -3 3 d -4 2 d -2 X -4 -2 d -3 -3 d -2 -4 d s 373 488 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -5 d 5 -1 d 3 X 4 1 d 4 5 d 1 8 d 4 Y -1 8 d -4 4 d -4 2 d -3 X cl s 397 459 m -1 -2 d 1 -1 d 2 1 d -2 2 d cl s 430 488 m -15 -32 d s 409 488 m 21 X s 307 538 m -5 -1 d -3 -5 d -2 -7 d -5 Y 2 -7 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 7 d 5 Y -2 7 d -3 5 d -4 1 d -3 X cl s 331 510 m -2 -2 d 2 -1 d 1 1 d -1 2 d cl s 350 538 m -4 -1 d -2 -3 d -3 Y 2 -3 d 3 -2 d 6 -1 d 4 -2 d 3 -3 d 2 -3 d -4 Y -2 -3 d -1 -2 d -5 -1 d -6 X -4 1 d -2 2 d -1 3 d 4 Y 1 3 d 3 3 d 5 2 d 6 1 d 3 2 d 1 3 d 3 Y -1 3 d -5 1 d -6 X cl s 240 589 m -4 -1 d -3 -5 d -2 -7 d -5 Y 2 -8 d 3 -4 d 4 -2 d 3 X 5 2 d 3 4 d 1 8 d 5 Y -1 7 d -3 5 d -5 1 d -3 X cl s 264 560 m -1 -1 d 1 -2 d 2 2 d -2 1 d cl s 296 579 m -1 -5 d -3 -3 d -5 -2 d -2 X -4 2 d -3 3 d -2 5 d 1 Y 2 5 d 3 3 d 4 1 d 2 X 5 -1 d 3 -3 d 1 -6 d -8 Y -1 -8 d -3 -4 d -5 -2 d -3 X -5 2 d -1 3 d s 211 634 m 3 1 d 5 5 d -32 Y s 227 734 m 1014 Y s 193 734 m 34 X s 210 783 m 17 X s 210 832 m 17 X s 210 882 m 17 X s 193 931 m 34 X s 210 980 m 17 X s 210 1029 m 17 X s 210 1079 m 17 X s 193 1128 m 34 X s 210 1177 m 17 X s 210 1226 m 17 X s 210 1276 m 17 X s 193 1325 m 34 X s 210 1374 m 17 X s 210 1423 m 17 X s 210 1473 m 17 X s 193 1522 m 34 X s 210 1571 m 17 X s 210 1620 m 17 X s 210 1670 m 17 X s 193 1719 m 34 X s 193 1719 m 34 X s 153 750 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -4 d 4 -2 d 3 X 5 2 d 3 4 d 2 8 d 4 Y -2 8 d -3 4 d -5 2 d -3 X cl s 116 939 m 2 Y 1 3 d 2 1 d 3 2 d 6 X 3 -2 d 1 -1 d 2 -3 d -3 Y -2 -3 d -3 -5 d -15 -15 d 21 X s 153 947 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -4 d 4 -2 d 3 X 5 2 d 3 4 d 2 8 d 4 Y -2 8 d -3 4 d -5 2 d -3 X cl s 129 1144 m -15 -21 d 23 X s 129 1144 m -32 Y s 153 1144 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -4 d 4 -2 d 3 X 5 2 d 3 4 d 2 8 d 4 Y -2 8 d -3 4 d -5 2 d -3 X cl s 134 1336 m -2 3 d -4 2 d -3 X -5 -2 d -3 -4 d -1 -8 d -7 Y 1 -6 d 3 -3 d 5 -2 d 1 X 5 2 d 3 3 d 1 4 d 2 Y -1 4 d -3 3 d -5 2 d -1 X -5 -2 d -3 -3 d -1 -4 d s 153 1341 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -4 d 4 -2 d 3 X 5 2 d 3 4 d 2 8 d 4 Y -2 8 d -3 4 d -5 2 d -3 X cl s 122 1538 m -5 -2 d -1 -3 d -3 Y 1 -3 d 3 -1 d 6 -2 d 5 -1 d 3 -3 d 1 -3 d -5 Y -1 -3 d -2 -2 d -4 -1 d -6 X -5 1 d -1 2 d -2 3 d 5 Y 2 3 d 3 3 d 4 1 d 6 2 d 3 1 d 2 3 d 3 Y -2 3 d -4 2 d -6 X cl s 153 1538 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -5 d 4 -1 d 3 X 5 1 d 3 5 d 2 8 d 4 Y -2 8 d -3 4 d -5 2 d -3 X cl s 88 1729 m 3 1 d 5 5 d -32 Y s 123 1735 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -5 d 4 -1 d 3 X 5 1 d 3 5 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 153 1735 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -5 d 4 -1 d 3 X 5 1 d 3 5 d 2 8 d 4 Y -2 8 d -3 4 d -5 2 d -3 X cl s 1041 71 m 18 X 3 Y -1 3 d -2 2 d -3 1 d -4 X -3 -1 d -3 -3 d -2 -5 d -3 Y 2 -4 d 3 -4 d 3 -1 d 4 X 3 1 d 3 4 d s 1068 80 m 17 -21 d s 1085 80 m -17 -21 d s 1112 80 m -21 Y s 1112 76 m -3 3 d -3 1 d -5 X -3 -1 d -3 -3 d -1 -5 d -3 Y 1 -4 d 3 -4 d 3 -1 d 5 X 3 1 d 3 4 d s 1124 80 m -21 Y s 1124 74 m 5 5 d 3 1 d 4 X 3 -1 d 2 -5 d -15 Y s 1141 74 m 4 5 d 3 1 d 5 X 3 -1 d 1 -5 d -15 Y s 1170 80 m -32 Y s 1170 76 m 3 3 d 3 1 d 4 X 3 -1 d 3 -3 d 2 -5 d -3 Y -2 -4 d -3 -4 d -3 -1 d -4 X -3 1 d -3 4 d s 1198 91 m -32 Y s 1209 71 m 18 X 3 Y -2 3 d -1 2 d -3 1 d -5 X -3 -1 d -3 -3 d -1 -5 d -3 Y 1 -4 d 3 -4 d 3 -1 d 5 X 3 1 d 3 4 d s gr gr showpage end %%EOF %%EndDocument @endspecial eop end %%Page: 309 327 TeXDict begin 309 326 bop 150 -116 a FK(Chapter)30 b(24:)41 b(N-tuples)2618 b(309)150 299 y FG(24)80 b(N-tuples)150 610 y FK(This)35 b(c)m(hapter)h(describ)s(es)e(functions)h(for)g (creating)i(and)e(manipulating)h FD(n)m(tuples)p FK(,)g(sets)g(of)g(v) -5 b(alues)35 b(as-)150 719 y(so)s(ciated)e(with)e(ev)m(en)m(ts.)45 b(The)31 b(n)m(tuples)g(are)h(stored)g(in)f(\014les.)44 b(Their)30 b(v)-5 b(alues)32 b(can)g(b)s(e)f(extracted)h(in)g(an)m(y) 150 829 y(com)m(bination)g(and)d FD(b)s(o)s(ok)m(ed)34 b FK(in)c(a)h(histogram)g(using)f(a)h(selection)h(function.)275 989 y(The)22 b(v)-5 b(alues)24 b(to)g(b)s(e)f(stored)g(are)h(held)f(in) g(a)g(user-de\014ned)f(data)i(structure,)g(and)f(an)g(n)m(tuple)h(is)f (created)150 1099 y(asso)s(ciating)30 b(this)d(data)i(structure)e(with) g(a)h(\014le.)40 b(The)28 b(v)-5 b(alues)28 b(are)g(then)f(written)h (to)h(the)f(\014le)f(\(normally)150 1208 y(inside)j(a)h(lo)s(op\))g (using)f(the)g(n)m(tuple)g(functions)g(describ)s(ed)g(b)s(elo)m(w.)275 1368 y(A)36 b(histogram)h(can)g(b)s(e)f(created)i(from)e(n)m(tuple)h (data)g(b)m(y)f(pro)m(viding)h(a)g(selection)h(function)f(and)f(a)150 1478 y(v)-5 b(alue)30 b(function.)40 b(The)29 b(selection)i(function)e (sp)s(eci\014es)g(whether)f(an)h(ev)m(en)m(t)i(should)e(b)s(e)f 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b(*)e(gsl_ntuple_open)d Fu(\()p FD(c)m(har)31 b(*)g Ft(filename)p FD(,)i(v)m(oid)e(*)565 4884 y Ft(ntuple_data)p FD(,)j(size)p 1343 4884 V 41 w(t)d Ft(size)p Fu(\))390 4994 y FK(This)d(function)g(op)s(ens)g(an)g(existing)h(n)m(tuple)g (\014le)f FD(\014lename)34 b FK(for)28 b(reading)h(and)f(returns)f(a)i (p)s(oin)m(ter)390 5103 y(to)24 b(a)f(corresp)s(onding)g(n)m(tuple)g (struct.)38 b(The)23 b(n)m(tuples)g(in)f(the)i(\014le)f(m)m(ust)g(ha)m (v)m(e)h(size)g FD(size)p FK(.)40 b(A)23 b(p)s(oin)m(ter)390 5213 y(to)32 b(memory)f(for)f(the)i(curren)m(t)e(n)m(tuple)h(ro)m(w)g FD(n)m(tuple)p 2179 5213 V 40 w(data)h FK(m)m(ust)f(b)s(e)f (supplied|this)g(is)h(used)f(to)390 5322 y(cop)m(y)h(n)m(tuples)f(in)g (and)g(out)h(of)f(the)h(\014le.)p eop end %%Page: 310 328 TeXDict begin 310 327 bop 150 -116 a FK(Chapter)30 b(24:)41 b(N-tuples)2618 b(310)150 299 y FJ(24.4)68 b(W)-11 b(riting)46 b(n)l(tuples)3350 493 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_ntuple_write)e Fu(\()p FD(gsl)p 1389 493 28 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FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_ntuple_close)e Fu(\()p FD(gsl)p 1389 2027 V 40 w(n)m(tuple)31 b(*)g Ft(ntuple)p Fu(\))390 2136 y FK(This)f(function)g(closes)h(the)g(n)m(tuple)f(\014le)h FD(n)m(tuple)k FK(and)30 b(frees)g(its)h(asso)s(ciated)h(allo)s(cated)g (memory)-8 b(.)150 2354 y FJ(24.7)68 b(Histogramming)47 b(n)l(tuple)f(v)-7 b(alues)150 2513 y FK(Once)23 b(an)h(n)m(tuple)f (has)g(b)s(een)g(created)i(its)e(con)m(ten)m(ts)j(can)d(b)s(e)g (histogrammed)h(in)f(v)-5 b(arious)23 b(w)m(a)m(ys)i(using)e(the)150 2623 y(function)i FH(gsl_ntuple_project)p FK(.)34 b(Tw)m(o)26 b(user-de\014ned)e(functions)h(m)m(ust)h(b)s(e)f(pro)m(vided,)h(a)g (function)f(to)150 2732 y(select)30 b(ev)m(en)m(ts)g(and)e(a)g (function)g(to)i(compute)e(scalar)i(v)-5 b(alues.)40 b(The)28 b(selection)i(function)e(and)g(the)g(v)-5 b(alue)150 2842 y(function)31 b(b)s(oth)g(accept)i(the)f(n)m(tuple)f(ro)m(w)h(as)g (a)g(\014rst)f(argumen)m(t)h(and)e(other)i(parameters)g(as)g(a)g (second)150 2951 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y(})g(gsl_ntuple_value_fn;)150 4521 y FK(In)j(this)g(case)h(the)f (struct)h(comp)s(onen)m(t)f FD(function)g FK(should)f(return)g(the)i(v) -5 b(alue)43 b(to)g(b)s(e)e(added)h(to)h(the)150 4630 y(histogram)31 b(for)f(the)h(n)m(tuple)f(ro)m(w.)3350 4792 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_ntuple_project)e Fu(\()p FD(gsl)p 1493 4792 V 41 w(histogram)31 b(*)g Ft(h)p FD(,)g(gsl)p 2249 4792 V 40 w(n)m(tuple)g(*)f Ft(ntuple)p FD(,)565 4902 y(gsl)p 677 4902 V 41 w(n)m(tuple)p 968 4902 V 40 w(v)-5 b(alue)p 1212 4902 V 40 w(fn)30 b(*)h Ft(value_func)p FD(,)i(gsl)p 2121 4902 V 41 w(n)m(tuple)p 2412 4902 V 40 w(select)p 2668 4902 V 41 w(fn)d(*)h Ft(select_func)p Fu(\))390 5011 y FK(This)38 b(function)g(up)s(dates)g(the)h(histogram)g FD(h)f FK(from)g(the)h(n)m(tuple)g FD(n)m(tuple)k FK(using)c(the)f (functions)390 5121 y FD(v)-5 b(alue)p 600 5121 V 41 w(func)47 b FK(and)c FD(select)p 1264 5121 V 42 w(func)p FK(.)78 b(F)-8 b(or)44 b(eac)m(h)h(n)m(tuple)e(ro)m(w)g(where)g(the)g (selection)i(function)e FD(se-)390 5230 y(lect)p 536 5230 V 41 w(func)32 b FK(is)27 b(non-zero)h(the)f(corresp)s(onding)f(v) -5 b(alue)28 b(of)f(that)h(ro)m(w)f(is)h(computed)f(using)f(the)i (func-)390 5340 y(tion)38 b FD(v)-5 b(alue)p 794 5340 V 41 w(func)42 b FK(and)c(added)f(to)h(the)g(histogram.)64 b(Those)38 b(n)m(tuple)f(ro)m(ws)h(where)g FD(select)p 3540 5340 V 41 w(func)p eop end %%Page: 311 329 TeXDict begin 311 328 bop 150 -116 a FK(Chapter)30 b(24:)41 b(N-tuples)2618 b(311)390 299 y(returns)26 b(zero)i(are)f(ignored.)40 b(New)27 b(en)m(tries)h(are)g(added)e(to)i(the)f(histogram,)i(so)e (subsequen)m(t)g(calls)390 408 y(can)k(b)s(e)e(used)h(to)h(accum)m (ulate)h(further)d(data)i(in)g(the)f(same)h(histogram.)150 654 y FJ(24.8)68 b(Examples)150 813 y FK(The)21 b(follo)m(wing)i (example)g(programs)e(demonstrate)h(the)g(use)f(of)h(n)m(tuples)g(in)f (managing)i(a)f(large)g(dataset.)150 923 y(The)29 b(\014rst)g(program)g (creates)i(a)f(set)g(of)g(10,000)i(sim)m(ulated)e(\\ev)m(en)m(ts",)j (eac)m(h)d(with)g(3)g(asso)s(ciated)h(v)-5 b(alues)150 1032 y(\()p FE(x;)15 b(y)s(;)g(z)t FK(\).)46 b(These)31 b(are)h(generated)h(from)e(a)h(Gaussian)g(distribution)f(with)g(unit)h (v)-5 b(ariance,)33 b(for)e(demon-)150 1142 y(stration)g(purp)s(oses,)e (and)h(written)g(to)h(the)g(n)m(tuple)f(\014le)h FH(test.dat)p FK(.)390 1285 y FH(#include)46 b()390 1395 y(#include)g()390 1504 y(#include)g ()390 1724 y(struct)g(data)390 1833 y({)485 1943 y(double)h(x;)485 2052 y(double)g(y;)485 2162 y(double)g(z;)390 2271 y(};)390 2491 y(int)390 2600 y(main)g(\(void\))390 2710 y({)485 2819 y(const)g(gsl_rng_type)d(*)k (T;)485 2929 y(gsl_rng)e(*)i(r;)485 3148 y(struct)f(data)f(ntuple_row;) 485 3258 y(int)h(i;)485 3477 y(gsl_ntuple)e(*ntuple)581 3587 y(=)i(gsl_ntuple_create)c(\("test.dat",)i(&ntuple_row,)1583 3696 y(sizeof)h(\(ntuple_row\)\);)485 3915 y(gsl_rng_env_setup)e(\(\);) 485 4134 y(T)k(=)f(gsl_rng_default;)485 4244 y(r)h(=)f(gsl_rng_alloc)e (\(T\);)485 4463 y(for)i(\(i)h(=)f(0;)g(i)h(<)f(10000;)f(i++\))581 4573 y({)676 4682 y(ntuple_row.x)f(=)i(gsl_ran_ugaussian)c(\(r\);)676 4792 y(ntuple_row.y)i(=)i(gsl_ran_ugaussian)c(\(r\);)676 4902 y(ntuple_row.z)i(=)i(gsl_ran_ugaussian)c(\(r\);)676 5121 y(gsl_ntuple_write)h(\(ntuple\);)581 5230 y(})p eop end %%Page: 312 330 TeXDict begin 312 329 bop 150 -116 a FK(Chapter)30 b(24:)41 b(N-tuples)2618 b(312)485 299 y FH(gsl_ntuple_close)44 b(\(ntuple\);)485 408 y(gsl_rng_free)h(\(r\);)485 628 y(return)i(0;)390 737 y(})150 902 y FK(The)28 b(next)h(program)f (analyses)h(the)g(n)m(tuple)f(data)h(in)f(the)h(\014le)g FH(test.dat)p FK(.)38 b(The)28 b(analysis)h(pro)s(cedure)e(is)150 1011 y(to)k(compute)g(the)g(squared-magnitude)g(of)g(eac)m(h)h(ev)m(en) m(t,)g FE(E)2220 978 y FB(2)2284 1011 y FK(=)25 b FE(x)2432 978 y FB(2)2490 1011 y FK(+)20 b FE(y)2629 978 y FB(2)2686 1011 y FK(+)h FE(z)2824 978 y FB(2)2861 1011 y FK(,)31 b(and)f(select)j(only)d(those)150 1121 y(whic)m(h)k(exceed)h(a)f(lo)m (w)m(er)h(limit)g(of)f(1.5.)52 b(The)34 b(selected)h(ev)m(en)m(ts)g (are)g(then)e(histogrammed)h(using)g(their)150 1230 y FE(E)222 1197 y FB(2)290 1230 y FK(v)-5 b(alues.)390 1395 y FH(#include)46 b()390 1504 y(#include)g ()390 1614 y(#include)g()390 1833 y(struct)g(data)390 1943 y({)485 2052 y(double)h(x;)485 2162 y(double)g(y;)485 2271 y(double)g(z;)390 2381 y(};)390 2600 y(int)g(sel_func)e(\(void)i(*ntuple_data,)d(void)j(*params\);)390 2710 y(double)f(val_func)g(\(void)g(*ntuple_data,)e(void)j(*params\);) 390 2929 y(int)390 3039 y(main)g(\(void\))390 3148 y({)485 3258 y(struct)g(data)f(ntuple_row;)485 3477 y(gsl_ntuple)f(*ntuple)581 3587 y(=)i(gsl_ntuple_open)d(\("test.dat",)g(&ntuple_row,)1488 3696 y(sizeof)i(\(ntuple_row\)\);)485 3806 y(double)h(lower)f(=)h(1.5;) 485 4025 y(gsl_ntuple_select_fn)c(S;)485 4134 y(gsl_ntuple_value_fn)g (V;)485 4354 y(gsl_histogram)i(*h)i(=)g(gsl_histogram_alloc)c(\(100\);) 485 4463 y(gsl_histogram_set_ranges_u)o(nifo)o(rm\()o(h,)f(0.0,)k (10.0\);)485 4682 y(S.function)f(=)j(&sel_func;)485 4792 y(S.params)e(=)h(&lower;)485 5011 y(V.function)e(=)j(&val_func;)485 5121 y(V.params)e(=)h(0;)485 5340 y(gsl_ntuple_project)c(\(h,)k (ntuple,)f(&V,)h(&S\);)p eop end %%Page: 313 331 TeXDict begin 313 330 bop 150 -116 a FK(Chapter)30 b(24:)41 b(N-tuples)2618 b(313)485 299 y FH(gsl_histogram_fprintf)42 b(\(stdout,)k(h,)h("\045f",)g("\045f"\);)485 408 y(gsl_histogram_free)c (\(h\);)485 518 y(gsl_ntuple_close)h(\(ntuple\);)485 737 y(return)j(0;)390 847 y(})390 1066 y(int)390 1176 y(sel_func)f(\(void)g(*ntuple_data,)e(void)j(*params\))390 1285 y({)485 1395 y(struct)g(data)f(*)i(data)e(=)i(\(struct)e(data)g (*\))h(ntuple_data;)485 1504 y(double)g(x,)g(y,)g(z,)g(E2,)g(scale;)485 1614 y(scale)g(=)g(*\(double)f(*\))h(params;)485 1833 y(x)h(=)f(data->x;)485 1943 y(y)h(=)f(data->y;)485 2052 y(z)h(=)f(data->z;)485 2271 y(E2)h(=)f(x)h(*)f(x)g(+)h(y)f(*)h(y)f(+)h (z)f(*)h(z;)485 2491 y(return)f(E2)g(>)g(scale;)390 2600 y(})390 2819 y(double)390 2929 y(val_func)f(\(void)g(*ntuple_data,)e (void)j(*params\))390 3039 y({)485 3148 y(\(void\)\(params\);)d(/*)j (avoid)g(unused)f(parameter)f(warning)h(*/)485 3258 y(struct)h(data)f (*)i(data)e(=)i(\(struct)e(data)g(*\))h(ntuple_data;)485 3367 y(double)g(x,)g(y,)g(z;)485 3587 y(x)h(=)f(data->x;)485 3696 y(y)h(=)f(data->y;)485 3806 y(z)h(=)f(data->z;)485 4025 y(return)g(x)g(*)g(x)h(+)f(y)h(*)f(y)h(+)f(z)h(*)f(z;)390 4134 y(})p eop end %%Page: 314 332 TeXDict begin 314 331 bop 150 -116 a FK(Chapter)30 b(24:)41 b(N-tuples)2618 b(314)275 318 y(The)29 b(follo)m(wing)j(plot)e(sho)m (ws)g(the)g(distribution)f(of)i(the)f(selected)h(ev)m(en)m(ts.)42 b(Note)32 b(the)e(cut-o\013)h(at)g(the)150 428 y(lo)m(w)m(er)h(b)s (ound.)275 2074 y @beginspecial 50 @llx 50 @lly 410 @urx 302 @ury 2448 @rwi @setspecial %%BeginDocument: ntuple.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: tmp2.eps %%Creator: gnuplot 3.5 (pre 3.6) patchlevel beta 347 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hpt vpt V hpt neg vpt V closepath stroke } def /BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke } def /TriUE { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke } def /TriDE { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke } def /PentE { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore } def /CircE { stroke [] 0 setdash hpt 0 360 arc stroke } def /Opaque { gsave closepath 1 setgray fill grestore 0 setgray closepath } def /DiaW { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V Opaque stroke } def /BoxW { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V Opaque stroke } def /TriUW { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V 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65 0 V 0 72 V 65 0 V 0 -54 V 64 0 V 0 54 V stroke grestore end showpage %%Trailer %%DocumentFonts: Helvetica %%EndDocument @endspecial 150 2357 a FJ(24.9)68 b(References)47 b(and)d(F)-11 b(urther)44 b(Reading)150 2516 y FK(F)-8 b(urther)29 b(information)g(on)g(the)g(use)f(of)h(n)m(tuples)g(can)g(b)s(e)f(found) g(in)h(the)g(do)s(cumen)m(tation)g(for)g(the)g FC(cern)150 2626 y FK(pac)m(k)-5 b(ages)32 b FC(p)-6 b(a)e(w)30 b FK(and)g FC(hbook)f FK(\(a)m(v)-5 b(ailable)33 b(online\).)p eop end %%Page: 315 333 TeXDict begin 315 332 bop 150 -116 a FK(Chapter)30 b(25:)41 b(Mon)m(te)32 b(Carlo)f(In)m(tegration)1985 b(315)150 299 y FG(25)80 b(Mon)l(te)52 b(Carlo)i(In)l(tegration)150 537 y FK(This)36 b(c)m(hapter)i(describ)s(es)f(routines)g(for)g(m)m (ultidimensional)h(Mon)m(te)h(Carlo)e(in)m(tegration.)64 b(These)37 b(in-)150 647 y(clude)42 b(the)h(traditional)h(Mon)m(te)f (Carlo)g(metho)s(d)f(and)g(adaptiv)m(e)h(algorithms)h(suc)m(h)e(as)g FC(vegas)g FK(and)150 756 y FC(miser)31 b 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1513 y(should)h(b)s(e)h(tak)m(en)h(as) g(a)f(guide)h(rather)f(than)g(as)g(a)h(strict)g(error)f(b)s (ound|random)d(sampling)j(of)h(the)150 1622 y(region)31 b(ma)m(y)f(not)h(unco)m(v)m(er)g(all)f(the)h(imp)s(ortan)m(t)f (features)g(of)h(the)f(function,)g(resulting)g(in)g(an)g(underes-)150 1732 y(timate)i(of)e(the)h(error.)275 1868 y(The)c(functions)g(are)h (de\014ned)f(in)g(separate)i(header)f(\014les)f(for)h(eac)m(h)h (routine,)f FH(gsl_monte_plain.h)p FK(,)150 1977 y FH (gsl_monte_miser.h)e FK(and)j FH(gsl_monte_vegas.h)p FK(.)150 2212 y FJ(25.1)68 b(In)l(terface)150 2371 y FK(All)27 b(of)g(the)g(Mon)m(te)h(Carlo)f(in)m(tegration)i(routines)d (use)h(the)g(same)g(general)h(form)e(of)h(in)m(terface.)41 b(There)26 b(is)150 2481 y(an)k(allo)s(cator)j(to)e(allo)s(cate)i (memory)d(for)h(con)m(trol)h(v)-5 b(ariables)31 b(and)f(w)m(orkspace,)h (a)g(routine)f(to)i(initialize)150 2591 y(those)f(con)m(trol)h(v)-5 b(ariables,)31 b(the)g(in)m(tegrator)h(itself,)f(and)f(a)h(function)f (to)h(free)f(the)h(space)g(when)e(done.)275 2727 y(Eac)m(h)34 b(in)m(tegration)i(function)d(requires)h(a)g(random)f(n)m(um)m(b)s(er)f (generator)j(to)g(b)s(e)e(supplied,)h(and)f(re-)150 2836 y(turns)e(an)h(estimate)h(of)g(the)f(in)m(tegral)h(and)f(its)g (standard)f(deviation.)47 b(The)32 b(accuracy)h(of)f(the)g(result)g(is) 150 2946 y(determined)e(b)m(y)g(the)h(n)m(um)m(b)s(er)e(of)h(function)g (calls)i(sp)s(eci\014ed)d(b)m(y)h(the)h(user.)40 b(If)30 b(a)h(kno)m(wn)e(lev)m(el)j(of)f(accu-)150 3055 y(racy)i(is)g(required) e(this)i(can)g(b)s(e)e(ac)m(hiev)m(ed)k(b)m(y)d(calling)i(the)f(in)m (tegrator)i(sev)m(eral)e(times)h(and)d(a)m(v)m(eraging)150 3165 y(the)g(individual)e(results)h(un)m(til)h(the)g(desired)f (accuracy)h(is)f(obtained.)275 3301 y(Random)f(sample)h(p)s(oin)m(ts)f (used)g(within)g(the)h(Mon)m(te)i(Carlo)e(routines)f(are)h(alw)m(a)m (ys)i(c)m(hosen)e(strictly)150 3410 y(within)g(the)g(in)m(tegration)j (region,)e(so)g(that)g(endp)s(oin)m(t)e(singularities)j(are)e 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m(ts)g(randomly)g(from)g(the)g(in)m(tegration)i(region)f(to)150 3835 y(estimate)25 b(the)f(in)m(tegral)h(and)e(its)g(error.)38 b(Using)24 b(this)f(algorithm)h(the)g(estimate)h(of)f(the)f(in)m (tegral)i FE(E)5 b FK(\()p FE(f)10 b FK(;)15 b FE(N)10 b FK(\))150 3944 y(for)30 b FE(N)40 b FK(randomly)30 b(distributed)g(p)s(oin)m(ts)g FE(x)1600 3958 y Fq(i)1658 3944 y FK(is)g(giv)m(en)i(b)m(y)-8 b(,)1340 4183 y FE(E)5 b FK(\()p FE(f)10 b FK(;)15 b FE(N)10 b FK(\))26 b(=)f FE(V)c FI(h)p FE(f)10 b FI(i)25 b FK(=)2117 4122 y FE(V)p 2112 4162 83 4 v 2112 4245 a(N)2250 4077 y Fq(N)2220 4102 y Fs(X)2268 4279 y Fq(i)2355 4183 y FE(f)10 b FK(\()p FE(x)2497 4197 y Fq(i)2524 4183 y FK(\))150 4423 y(where)39 b FE(V)59 b FK(is)39 b(the)h(v)m(olume)g(of)f(the)h(in)m(tegration)h (region.)68 b(The)39 b(error)g(on)g(this)g(estimate)i FE(\033)s FK(\()p FE(E)5 b FK(;)15 b FE(N)10 b FK(\))41 b(is)150 4533 y(calculated)32 b(from)e(the)h(estimated)g(v)-5 b(ariance)32 b(of)e(the)h(mean,)1285 4771 y FE(\033)1340 4734 y FB(2)1378 4771 y FK(\()p FE(E)5 b FK(;)15 b FE(N)10 b FK(\))27 b(=)1780 4710 y FE(V)1854 4677 y FB(2)p 1775 4750 121 4 v 1775 4834 a FE(N)1858 4807 y FB(2)1951 4666 y Fq(N)1921 4691 y Fs(X)1969 4867 y Fq(i)2041 4771 y FK(\()p FE(f)10 b FK(\()p FE(x)2218 4785 y Fq(i)2245 4771 y FK(\))21 b FI(\000)f(h)p FE(f)10 b FI(i)p FK(\))2552 4734 y FB(2)2589 4771 y FE(:)150 5011 y FK(F)-8 b(or)34 b(large)g FE(N)43 b FK(this)32 b(v)-5 b(ariance)34 b(decreases)g (asymptotically)h(as)e(V)-8 b(ar)q(\()p FE(f)10 b FK(\))p FE(=)-5 b(N)10 b FK(,)34 b(where)f(V)-8 b(ar\()p FE(f)10 b FK(\))33 b(is)g(the)g(true)150 5121 y(v)-5 b(ariance)23 b(of)f(the)g(function)f(o)m(v)m(er)i(the)f(in)m(tegration)i(region.)38 b(The)22 b(error)f(estimate)j(itself)e(should)f(decrease)150 5230 y(as)34 b FE(\033)s FK(\()p FE(f)10 b FK(\))p FE(=)490 5154 y FI(p)p 566 5154 83 4 v 76 x FE(N)g FK(.)50 b(The)32 b(familiar)i(la)m(w)h(of)e(errors)g(decreasing)h(as)g(1)p FE(=)2436 5154 y FI(p)p 2512 5154 V 76 x FE(N)43 b FK(applies|to)35 b(reduce)e(the)g(error)150 5340 y(b)m(y)d(a)h(factor)g(of)g(10)g (requires)f(a)h(100-fold)h(increase)f(in)f(the)h(n)m(um)m(b)s(er)e(of)h (sample)h(p)s(oin)m(ts.)p eop end %%Page: 317 335 TeXDict begin 317 334 bop 150 -116 a FK(Chapter)30 b(25:)41 b(Mon)m(te)32 b(Carlo)f(In)m(tegration)1985 b(317)275 299 y(The)48 b(functions)g(describ)s(ed)f(in)h(this)h(section)g(are)g (declared)g(in)f(the)h(header)f(\014le)h FH(gsl_monte_)150 408 y(plain.h)p FK(.)3350 586 y([F)-8 b(unction])-3599 b Fv(gsl_monte_plain_state)59 b(*)52 b(gsl_monte_plain_alloc)g Fu(\()p FD(size)p 2731 586 28 4 v 41 w(t)31 b Ft(dim)p Fu(\))390 696 y FK(This)25 b(function)g(allo)s(cates)j(and)d (initializes)j(a)e(w)m(orkspace)g(for)g(Mon)m(te)h(Carlo)f(in)m (tegration)h(in)e FD(dim)390 805 y FK(dimensions.)3350 983 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_monte_plain_init)f Fu(\()p FD(gsl)p 1598 983 V 41 w(mon)m(te)p 1883 983 V 41 w(plain)p 2121 983 V 40 w(state*)32 b Ft(s)p Fu(\))390 1093 y FK(This)h(function)h(initializes)j(a)e(previously)f(allo)s (cated)i(in)m(tegration)g(state.)54 b(This)34 b(allo)m(ws)h(an)f(ex-) 390 1202 y(isting)d(w)m(orkspace)g(to)g(b)s(e)f(reused)g(for)g (di\013eren)m(t)g(in)m(tegrations.)3350 1380 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_monte_plain_integ)q(rate)f Fu(\()p FD(gsl)p 1859 1380 V 41 w(mon)m(te)p 2144 1380 V 41 w(function)30 b(*)h Ft(f)p FD(,)g(const)565 1489 y(double)f Ft(xl)p Fo([])p FD(,)h(const)g(double)f Ft(xu)p Fo([])p FD(,)h(size)p 1968 1489 V 41 w(t)f Ft(dim)p FD(,)i(size)p 2428 1489 V 41 w(t)e Ft(calls)p FD(,)i(gsl)p 2957 1489 V 41 w(rng)e(*)h Ft(r)p FD(,)565 1599 y(gsl)p 677 1599 V 41 w(mon)m(te)p 962 1599 V 41 w(plain)p 1200 1599 V 40 w(state)g(*)g Ft(s)p FD(,)g(double)f(*)h Ft(result)p FD(,)h(double)e(*)h Ft(abserr)p Fu(\))390 1709 y FK(This)h(routines)h (uses)g(the)g(plain)g(Mon)m(te)i(Carlo)f(algorithm)g(to)g(in)m(tegrate) h(the)e(function)g FD(f)51 b FK(o)m(v)m(er)390 1818 y(the)33 b FD(dim)p 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y(and)28 b FE(\033)380 3469 y FB(2)377 3524 y Fq(b)417 3502 y FK(\()p FE(f)10 b FK(\),)29 b(the)g(v)-5 b(ariance)29 b(V)-8 b(ar)q(\()p FE(f)10 b FK(\))28 b(of)g(the)h(com)m(bined)f (estimate)i FE(E)5 b FK(\()p FE(f)10 b FK(\))26 b(=)2751 3466 y FB(1)p 2751 3481 34 4 v 2751 3533 a(2)2794 3502 y FK(\()p FE(E)2896 3516 y Fq(a)2937 3502 y FK(\()p FE(f)10 b FK(\))16 b(+)g FE(E)3232 3516 y Fq(b)3265 3502 y FK(\()p FE(f)10 b FK(\)\))29 b(is)f(giv)m(en)150 3611 y(b)m(y)-8 b(,)1451 3826 y(V)g(ar\()p FE(f)10 b FK(\))25 b(=)1848 3764 y FE(\033)1903 3731 y FB(2)1900 3787 y Fq(a)1941 3764 y FK(\()p FE(f)10 b FK(\))p 1848 3805 218 4 v 1878 3888 a(4)p FE(N)1996 3902 y Fq(a)2096 3826 y FK(+)2197 3764 y FE(\033)2252 3731 y FB(2)2249 3787 y Fq(b)2289 3764 y FK(\()p FE(f)g FK(\))p 2197 3805 V 2230 3888 a(4)p FE(N)2348 3902 y Fq(b)2424 3826 y FE(:)150 4030 y FK(It)30 b(can)h(b)s(e)f(sho)m(wn)g(that)h(this)f(v)-5 b(ariance)31 b(is)g(minimized)f(b)m(y)g(distributing)g(the)h(p)s(oin)m(ts)f(suc)m(h) g(that,)1666 4175 y FE(N)1739 4189 y Fq(a)p 1557 4215 331 4 v 1557 4299 a FE(N)1630 4313 y Fq(a)1691 4299 y FK(+)20 b FE(N)1855 4313 y Fq(b)1923 4236 y FK(=)2127 4175 y FE(\033)2179 4189 y Fq(a)p 2029 4215 289 4 v 2029 4299 a FE(\033)2081 4313 y Fq(a)2141 4299 y FK(+)g FE(\033)2284 4313 y Fq(b)2328 4236 y FE(:)150 4441 y FK(Hence)32 b(the)g(smallest)g (error)f(estimate)i(is)f(obtained)f(b)m(y)g(allo)s(cating)j(sample)e(p) s(oin)m(ts)f(in)g(prop)s(ortion)f(to)150 4550 y(the)h(standard)e (deviation)j(of)e(the)h(function)f(in)g(eac)m(h)h(sub-region.)275 4682 y(The)f FC(miser)g FK(algorithm)i(pro)s(ceeds)f(b)m(y)f(bisecting) i(the)f(in)m(tegration)i(region)f(along)g(one)f(co)s(ordinate)150 4792 y(axis)24 b(to)h(giv)m(e)g(t)m(w)m(o)g(sub-regions)f(at)g(eac)m(h) h(step.)39 b(The)23 b(direction)i(is)e(c)m(hosen)i(b)m(y)e(examining)i (all)f FE(d)g FK(p)s(ossible)150 4902 y(bisections)29 b(and)g(selecting)h(the)f(one)g(whic)m(h)f(will)h(minimize)h(the)f(com) m(bined)f(v)-5 b(ariance)30 b(of)f(the)g(t)m(w)m(o)h(sub-)150 5011 y(regions.)62 b(The)36 b(v)-5 b(ariance)38 b(in)f(the)h (sub-regions)e(is)i(estimated)g(b)m(y)f(sampling)g(with)g(a)h(fraction) f(of)h(the)150 5121 y(total)33 b(n)m(um)m(b)s(er)d(of)h(p)s(oin)m(ts)g (a)m(v)-5 b(ailable)34 b(to)e(the)f(curren)m(t)g(step.)43 b(The)31 b(same)h(pro)s(cedure)e(is)h(then)g(rep)s(eated)150 5230 y(recursiv)m(ely)j(for)g(eac)m(h)g(of)g(the)g(t)m(w)m(o)h (half-spaces)f(from)f(the)h(b)s(est)f(bisection.)51 b(The)33 b(remaining)h(sample)150 5340 y(p)s(oin)m(ts)k(are)h(allo)s(cated)h(to) g(the)e(sub-regions)g(using)g(the)h(form)m(ula)f(for)g FE(N)2725 5354 y Fq(a)2804 5340 y FK(and)g FE(N)3062 5354 y Fq(b)3095 5340 y FK(.)65 b(This)38 b(recursiv)m(e)p eop end %%Page: 318 336 TeXDict begin 318 335 bop 150 -116 a FK(Chapter)30 b(25:)41 b(Mon)m(te)32 b(Carlo)f(In)m(tegration)1985 b(318)150 299 y(allo)s(cation)38 b(of)e(in)m(tegration)i(p)s(oin)m(ts)e(con)m (tin)m(ues)h(do)m(wn)e(to)i(a)f(user-sp)s(eci\014ed)f(depth)g(where)h (eac)m(h)h(sub-)150 408 y(region)32 b(is)e(in)m(tegrated)j(using)d(a)i (plain)f(Mon)m(te)h(Carlo)f(estimate.)44 b(These)31 b(individual)f(v)-5 b(alues)32 b(and)e(their)150 518 y(error)h(estimates)i(are)f(then)f (com)m(bined)h(up)m(w)m(ards)e(to)j(giv)m(e)g(an)e(o)m(v)m(erall)j (result)d(and)g(an)h(estimate)h(of)f(its)150 628 y(error.)275 772 y(The)48 b(functions)g(describ)s(ed)f(in)h(this)h(section)g(are)g (declared)g(in)f(the)h(header)f(\014le)h FH(gsl_monte_)150 882 y(miser.h)p FK(.)3350 1086 y([F)-8 b(unction])-3599 b Fv(gsl_monte_miser_state)59 b(*)52 b(gsl_monte_miser_alloc)g Fu(\()p FD(size)p 2731 1086 28 4 v 41 w(t)31 b Ft(dim)p Fu(\))390 1195 y FK(This)25 b(function)g(allo)s(cates)j(and)d (initializes)j(a)e(w)m(orkspace)g(for)g(Mon)m(te)h(Carlo)f(in)m (tegration)h(in)e FD(dim)390 1305 y FK(dimensions.)40 b(The)30 b(w)m(orkspace)h(is)f(used)g(to)h(main)m(tain)g(the)g(state)h (of)e(the)h(in)m(tegration.)3350 1509 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_monte_miser_init)f 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FK(Mon)m(te)j(Carlo)e(algorithm)g(to)h(in)m(tegrate)g(the)f (function)g FD(f)47 b FK(o)m(v)m(er)390 2371 y(the)33 b FD(dim)p FK(-dimensional)g(h)m(yp)s(ercubic)f(region)h(de\014ned)f(b) m(y)g(the)i(lo)m(w)m(er)g(and)e(upp)s(er)f(limits)i(in)g(the)390 2480 y(arra)m(ys)h FD(xl)j FK(and)c FD(xu)p FK(,)h(eac)m(h)g(of)g(size) g FD(dim)p FK(.)50 b(The)32 b(in)m(tegration)k(uses)d(a)h(\014xed)f(n)m (um)m(b)s(er)f(of)h(function)390 2590 y(calls)f FD(calls)p FK(,)h(and)e(obtains)g(random)g(sampling)g(p)s(oin)m(ts)g(using)g(the)g (random)g(n)m(um)m(b)s(er)f(generator)390 2700 y FD(r)p FK(.)39 b(A)27 b(previously)f(allo)s(cated)j(w)m(orkspace)f FD(s)i FK(m)m(ust)d(b)s(e)f(supplied.)38 b(The)26 b(result)h(of)g(the)g (in)m(tegration)390 2809 y(is)j(returned)g(in)g FD(result)p FK(,)g(with)g(an)h(estimated)g(absolute)g(error)f FD(abserr)p FK(.)3350 3013 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_monte_miser_free)d Fu(\()p FD(gsl)p 1650 3013 V 41 w(mon)m(te)p 1935 3013 V 41 w(miser)p 2189 3013 V 40 w(state)32 b(*)e Ft(s)p Fu(\))390 3123 y FK(This)g(function)g(frees) g(the)h(memory)f(asso)s(ciated)i(with)e(the)g(in)m(tegrator)j(state)e FD(s)p FK(.)275 3327 y(The)j FC(miser)g FK(algorithm)i(has)f(sev)m (eral)h(con\014gurable)f(parameters)h(whic)m(h)e(can)i(b)s(e)e(c)m (hanged)h(using)150 3437 y(the)c(follo)m(wing)g(t)m(w)m(o)h(functions.) 1249 3404 y FB(1)3350 3641 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_monte_miser_params_g)q(et)e Fu(\()p FD(const)31 b(gsl)p 2202 3641 V 41 w(mon)m(te)p 2487 3641 V 41 w(miser)p 2741 3641 V 39 w(state)h(*)f Ft(s)p FD(,)565 3750 y(gsl)p 677 3750 V 41 w(mon)m(te)p 962 3750 V 41 w(miser)p 1216 3750 V 40 w(params)e(*)i Ft(params)p Fu(\))390 3860 y FK(This)42 b(function)g(copies)h(the)g(parameters)g (of)f(the)h(in)m(tegrator)h(state)g(in)m(to)g(the)f(user-supplied)390 3970 y FD(params)34 b FK(structure.)3350 4174 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_monte_miser_params_s)q(et)e Fu(\()p FD(gsl)p 1964 4174 V 41 w(mon)m(te)p 2249 4174 V 41 w(miser)p 2503 4174 V 40 w(state)31 b(*)g Ft(s)p FD(,)g(const)565 4283 y(gsl)p 677 4283 V 41 w(mon)m(te)p 962 4283 V 41 w(miser)p 1216 4283 V 40 w(params)e(*)i Ft(params)p Fu(\))390 4393 y FK(This)e(function)g(sets)h(the)g(in)m (tegrator)h(parameters)f(based)f(on)h(v)-5 b(alues)29 b(pro)m(vided)h(in)f(the)h FD(params)390 4503 y FK(structure.)275 4707 y(T)m(ypically)35 b(the)f(v)-5 b(alues)35 b(of)f(the)h(parameters) f(are)h(\014rst)e(read)i(using)e FH(gsl_monte_miser_params_)150 4816 y(get)p FK(,)24 b(the)f(necessary)h(c)m(hanges)g(are)g(made)f(to)h (the)f(\014elds)g(of)g(the)g FD(params)k FK(structure,)d(and)f(the)g(v) -5 b(alues)24 b(are)150 4926 y(copied)33 b(bac)m(k)h(in)m(to)f(the)g (in)m(tegrator)i(state)f(using)e FH(gsl_monte_miser_params_set)o FK(.)42 b(The)32 b(functions)150 5035 y(use)e(the)h FH (gsl_monte_miser_params)24 b FK(structure)30 b(whic)m(h)g(con)m(tains)h (the)g(follo)m(wing)h(\014elds:)p 150 5154 1200 4 v 199 5221 a FB(1)275 5253 y Fx(The)21 b(previous)f(metho)r(d)h(of)g (accessing)i(these)e(\014elds)g(directly)f(through)h(the)f Fz(gsl_monte_miser_state)26 b Fx(struct)20 b(is)i(no)n(w)275 5340 y(deprecated.)p eop end %%Page: 319 337 TeXDict begin 319 336 bop 150 -116 a FK(Chapter)30 b(25:)41 b(Mon)m(te)32 b(Carlo)f(In)m(tegration)1985 b(319)3371 299 y([V)-8 b(ariable])-3598 b Fv(double)54 b(estimate_frac)390 408 y FK(This)38 b(parameter)h(sp)s(eci\014es)f(the)g(fraction)i(of)e (the)h(curren)m(tly)g(a)m(v)-5 b(ailable)40 b(n)m(um)m(b)s(er)e(of)g (function)390 518 y(calls)47 b(whic)m(h)e(are)g(allo)s(cated)j(to)e (estimating)h(the)f(v)-5 b(ariance)46 b(at)g(eac)m(h)h(recursiv)m(e)f (step.)85 b(The)390 628 y(default)31 b(v)-5 b(alue)30 b(is)h(0.1.)3371 833 y([V)-8 b(ariable])-3598 b Fv(size_t)54 b(min_calls)390 942 y FK(This)42 b(parameter)i(sp)s(eci\014es)e(the)i (minim)m(um)e(n)m(um)m(b)s(er)g(of)h(function)g(calls)h(required)e(for) h(eac)m(h)390 1052 y(estimate)23 b(of)e(the)h(v)-5 b(ariance.)38 b(If)21 b(the)g(n)m(um)m(b)s(er)f(of)i(function)f(calls)h(allo)s(cated) h(to)f(the)f(estimate)i(using)390 1162 y FD(estimate)p 728 1162 28 4 v 42 w(frac)31 b FK(falls)26 b(b)s(elo)m(w)g FD(min)p 1540 1162 V 39 w(calls)k FK(then)c FD(min)p 2135 1162 V 39 w(calls)k FK(are)c(used)f(instead.)39 b(This)25 b(ensures)f(that)390 1271 y(eac)m(h)i(estimate)h(main)m (tains)f(a)f(reasonable)h(lev)m(el)h(of)e(accuracy)-8 b(.)41 b(The)24 b(default)i(v)-5 b(alue)25 b(of)h FD(min)p 3541 1271 V 39 w(calls)390 1381 y FK(is)k FH(16)g(*)g(dim)p FK(.)3371 1586 y([V)-8 b(ariable])-3598 b Fv(size_t)54 b(min_calls_per_bisectio)q(n)390 1695 y FK(This)46 b(parameter)h(sp)s (eci\014es)f(the)h(minim)m(um)f(n)m(um)m(b)s(er)g(of)h(function)f (calls)i(required)e(to)h(pro-)390 1805 y(ceed)d(with)f(a)h(bisection)h (step.)80 b(When)43 b(a)h(recursiv)m(e)g(step)g(has)f(few)m(er)h(calls) g(a)m(v)-5 b(ailable)46 b(than)390 1915 y FD(min)p 548 1915 V 40 w(calls)p 759 1915 V 41 w(p)s(er)p 930 1915 V 39 w(bisection)31 b FK(it)f(p)s(erforms)f(a)h(plain)g(Mon)m(te)h (Carlo)g(estimate)h(of)e(the)g(curren)m(t)g(sub-)390 2024 y(region)c(and)e(terminates)i(its)g(branc)m(h)e(of)h(the)g (recursion.)39 b(The)24 b(default)i(v)-5 b(alue)25 b(of)g(this)g (parameter)390 2134 y(is)30 b FH(32)g(*)g(min_calls)p FK(.)3371 2339 y([V)-8 b(ariable])-3598 b Fv(double)54 b(alpha)390 2449 y FK(This)40 b(parameter)i(con)m(trols)h(ho)m(w)e(the) h(estimated)g(v)-5 b(ariances)42 b(for)f(the)h(t)m(w)m(o)g(sub-regions) f(of)h(a)390 2558 y(bisection)e(are)g(com)m(bined)g(when)e(allo)s (cating)k(p)s(oin)m(ts.)68 b(With)40 b(recursiv)m(e)g(sampling)g(the)f (o)m(v)m(er-)390 2668 y(all)33 b(v)-5 b(ariance)33 b(should)f(scale)h (b)s(etter)g(than)f(1)p FE(=)-5 b(N)10 b FK(,)34 b(since)e(the)h(v)-5 b(alues)32 b(from)g(the)h(sub-regions)f(will)390 2777 y(b)s(e)g(obtained)h(using)f(a)g(pro)s(cedure)g(whic)m(h)g(explicitly)i (minimizes)f(their)f(v)-5 b(ariance.)48 b(T)-8 b(o)33 b(accom-)390 2887 y(mo)s(date)h(this)g(b)s(eha)m(vior)f(the)h FC(miser)f FK(algorithm)i(allo)m(ws)g(the)f(total)h(v)-5 b(ariance)35 b(to)f(dep)s(end)e(on)i(a)390 2996 y(scaling)d(parameter)g FE(\013)p FK(,)1538 3192 y(V)-8 b(ar\()p FE(f)10 b FK(\))26 b(=)1955 3131 y FE(\033)2007 3145 y Fq(a)p 1936 3171 131 4 v 1936 3255 a FE(N)2019 3229 y Fq(\013)2009 3277 y(a)2096 3192 y FK(+)2219 3131 y FE(\033)2271 3145 y Fq(b)p 2197 3171 V 2197 3255 a FE(N)2280 3223 y Fq(\013)2270 3277 y(b)2337 3192 y FE(:)390 3418 y FK(The)35 b(authors)h(of)g(the)g (original)h(pap)s(er)e(describing)g FC(miser)g FK(recommend)h(the)g(v) -5 b(alue)36 b FE(\013)f FK(=)f(2)j(as)390 3528 y(a)c(go)s(o)s(d)g(c)m (hoice,)i(obtained)e(from)f(n)m(umerical)h(exp)s(erimen)m(ts,)h(and)e (this)g(is)h(used)f(as)h(the)g(default)390 3637 y(v)-5 b(alue)31 b(in)f(this)g(implemen)m(tation.)3371 3842 y([V)-8 b(ariable])-3598 b Fv(double)54 b(dither)390 3952 y FK(This)23 b(parameter)h(in)m(tro)s(duces)f(a)h(random)f (fractional)i(v)-5 b(ariation)24 b(of)g(size)g FD(dither)30 b FK(in)m(to)25 b(eac)m(h)f(bisec-)390 4062 y(tion,)30 b(whic)m(h)f(can)g(b)s(e)f(used)g(to)i(break)e(the)i(symmetry)e(of)h (in)m(tegrands)g(whic)m(h)g(are)g(concen)m(trated)390 4171 y(near)c(the)f(exact)j(cen)m(ter)e(of)g(the)g(h)m(yp)s(ercubic)e (in)m(tegration)k(region.)40 b(The)24 b(default)g(v)-5 b(alue)26 b(of)e(dither)390 4281 y(is)30 b(zero,)i(so)e(no)h(v)-5 b(ariation)31 b(is)g(in)m(tro)s(duced.)40 b(If)30 b(needed,)g(a)h(t)m (ypical)h(v)-5 b(alue)31 b(of)f FD(dither)37 b FK(is)30 b(0.1.)150 4529 y FJ(25.4)68 b(VEGAS)150 4688 y FK(The)32 b FC(vegas)f FK(algorithm)j(of)e(Lepage)h(is)g(based)f(on)g(imp)s (ortance)h(sampling.)46 b(It)33 b(samples)f(p)s(oin)m(ts)g(from)150 4798 y(the)21 b(probabilit)m(y)h(distribution)f(describ)s(ed)f(b)m(y)h (the)h(function)f FI(j)p FE(f)10 b FI(j)p FK(,)23 b(so)e(that)h(the)f (p)s(oin)m(ts)h(are)f(concen)m(trated)150 4907 y(in)30 b(the)h(regions)f(that)h(mak)m(e)h(the)e(largest)i(con)m(tribution)f (to)g(the)g(in)m(tegral.)275 5052 y(In)c(general,)i(if)f(the)g(Mon)m (te)h(Carlo)f(in)m(tegral)h(of)f FE(f)37 b FK(is)28 b(sampled)f(with)h (p)s(oin)m(ts)f(distributed)g(according)150 5162 y(to)k(a)g(probabilit) m(y)g(distribution)e(describ)s(ed)h(b)m(y)g(the)h(function)f FE(g)s FK(,)h(w)m(e)g(obtain)f(an)h(estimate)h FE(E)3415 5176 y Fq(g)3454 5162 y FK(\()p FE(f)10 b FK(;)15 b FE(N)10 b FK(\),)1506 5340 y FE(E)1573 5354 y Fq(g)1612 5340 y FK(\()p FE(f)g FK(;)15 b FE(N)10 b FK(\))25 b(=)g FE(E)5 b FK(\()p FE(f)10 b(=g)s FK(;)15 b FE(N)10 b FK(\))p eop end %%Page: 320 338 TeXDict begin 320 337 bop 150 -116 a FK(Chapter)30 b(25:)41 b(Mon)m(te)32 b(Carlo)f(In)m(tegration)1985 b(320)150 299 y(with)30 b(a)h(corresp)s(onding)e(v)-5 b(ariance,)1421 465 y(V)d(ar)1563 479 y Fq(g)1602 465 y FK(\()p FE(f)10 b FK(;)15 b FE(N)10 b FK(\))25 b(=)g(V)-8 b(ar)q(\()p FE(f)10 b(=g)s FK(;)15 b FE(N)10 b FK(\))p FE(:)150 631 y FK(If)38 b(the)h(probabilit)m(y)g(distribution)e(is)i(c)m(hosen)g(as) f FE(g)43 b FK(=)38 b FI(j)p FE(f)10 b FI(j)p FE(=I)d FK(\()p FI(j)p FE(f)j FI(j)p FK(\))39 b(then)f(it)h(can)g(b)s(e)f(sho)m (wn)g(that)h(the)150 741 y(v)-5 b(ariance)32 b FE(V)560 755 y Fq(g)599 741 y FK(\()p FE(f)10 b FK(;)15 b FE(N)10 b FK(\))31 b(v)-5 b(anishes,)31 b(and)g(the)g(error)g(in)g(the)g (estimate)i(will)f(b)s(e)e(zero.)44 b(In)30 b(practice)j(it)f(is)f(not) 150 850 y(p)s(ossible)k(to)h(sample)g(from)f(the)g(exact)i (distribution)e FE(g)k FK(for)c(an)g(arbitrary)h(function,)g(so)g(imp)s (ortance)150 960 y(sampling)30 b(algorithms)i(aim)e(to)h(pro)s(duce)f (e\016cien)m(t)i(appro)m(ximations)f(to)g(the)f(desired)g (distribution.)275 1093 y(The)23 b FC(vegas)h FK(algorithm)h(appro)m (ximates)g(the)g(exact)h(distribution)d(b)m(y)h(making)h(a)g(n)m(um)m (b)s(er)e(of)h(passes)150 1202 y(o)m(v)m(er)31 b(the)f(in)m(tegration)h (region)g(while)e(histogramming)h(the)g(function)g FE(f)10 b FK(.)39 b(Eac)m(h)30 b(histogram)h(is)e(used)g(to)150 1312 y(de\014ne)j(a)i(sampling)f(distribution)g(for)g(the)g(next)h (pass.)49 b(Asymptotically)35 b(this)e(pro)s(cedure)f(con)m(v)m(erges) 150 1421 y(to)38 b(the)f(desired)f(distribution.)59 b(In)37 b(order)f(to)i(a)m(v)m(oid)g(the)f(n)m(um)m(b)s(er)f(of)h(histogram)g (bins)f(gro)m(wing)i(lik)m(e)150 1531 y FE(K)234 1498 y Fq(d)310 1531 y FK(the)g(probabilit)m(y)g(distribution)f(is)g(appro)m (ximated)h(b)m(y)g(a)g(separable)g(function:)54 b FE(g)s FK(\()p FE(x)3292 1545 y FB(1)3331 1531 y FE(;)15 b(x)3423 1545 y FB(2)3460 1531 y FE(;)g(:)g(:)g(:)r FK(\))37 b(=)150 1641 y FE(g)193 1655 y FB(1)231 1641 y FK(\()p FE(x)318 1655 y FB(1)355 1641 y FK(\))p FE(g)433 1655 y FB(2)471 1641 y FK(\()p FE(x)558 1655 y FB(2)596 1641 y FK(\))15 b FE(:)g(:)g(:)23 b FK(so)f(that)g(the)f(n)m(um)m(b)s(er)g(of)g(bins)g (required)g(is)g(only)h FE(K)7 b(d)p FK(.)38 b(This)20 b(is)i(equiv)-5 b(alen)m(t)23 b(to)f(lo)s(cating)150 1750 y(the)35 b(p)s(eaks)g(of)g(the)g(function)g(from)f(the)i(pro)5 b(jections)35 b(of)g(the)g(in)m(tegrand)h(on)m(to)g(the)f(co)s (ordinate)h(axes.)150 1860 y(The)j(e\016ciency)i(of)f FC(vegas)f FK(dep)s(ends)f(on)h(the)h(v)-5 b(alidit)m(y)42 b(of)e(this)f(assumption.)69 b(It)39 b(is)h(most)g(e\016cien)m(t)150 1969 y(when)34 b(the)i(p)s(eaks)f(of)g(the)h(in)m(tegrand)f(are)h(w)m (ell-lo)s(calized.)58 b(If)35 b(an)g(in)m(tegrand)h(can)g(b)s(e)e (rewritten)i(in)f(a)150 2079 y(form)f(whic)m(h)h(is)f(appro)m(ximately) i(separable)f(this)g(will)g(increase)g(the)g(e\016ciency)h(of)f(in)m (tegration)h(with)150 2188 y FC(vegas)p FK(.)275 2321 y FC(vegas)29 b FK(incorp)s(orates)i(a)g(n)m(um)m(b)s(er)e(of)i (additional)h(features,)f(and)f(com)m(bines)h(b)s(oth)f(strati\014ed)h (sam-)150 2431 y(pling)25 b(and)f(imp)s(ortance)h(sampling.)39 b(The)25 b(in)m(tegration)i(region)e(is)g(divided)g(in)m(to)g(a)h(n)m (um)m(b)s(er)e(of)h(\\b)s(o)m(xes",)150 2540 y(with)33 b(eac)m(h)h(b)s(o)m(x)f(getting)h(a)g(\014xed)e(n)m(um)m(b)s(er)g(of)h (p)s(oin)m(ts)g(\(the)g(goal)i(is)e(2\).)49 b(Eac)m(h)34 b(b)s(o)m(x)e(can)i(then)e(ha)m(v)m(e)j(a)150 2650 y(fractional)f(n)m (um)m(b)s(er)d(of)i(bins,)g(but)e(if)i(the)g(ratio)g(of)g(bins-p)s (er-b)s(o)m(x)e(is)i(less)g(than)f(t)m(w)m(o,)j(V)-8 b(egas)34 b(switc)m(hes)150 2760 y(to)d(a)g(kind)e(v)-5 b(ariance)32 b(reduction)e(\(rather)h(than)f(imp)s(ortance)g (sampling\).)3350 2939 y([F)-8 b(unction])-3599 b Fv (gsl_monte_vegas_state)59 b(*)52 b(gsl_monte_vegas_alloc)g Fu(\()p FD(size)p 2731 2939 28 4 v 41 w(t)31 b Ft(dim)p Fu(\))390 3049 y FK(This)25 b(function)g(allo)s(cates)j(and)d (initializes)j(a)e(w)m(orkspace)g(for)g(Mon)m(te)h(Carlo)f(in)m (tegration)h(in)e FD(dim)390 3158 y FK(dimensions.)40 b(The)30 b(w)m(orkspace)h(is)f(used)g(to)h(main)m(tain)g(the)g(state)h (of)e(the)h(in)m(tegration.)3350 3337 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_monte_vegas_init)f Fu(\()p FD(gsl)p 1598 3337 V 41 w(mon)m(te)p 1883 3337 V 41 w(v)m(egas)p 2135 3337 V 41 w(state*)32 b Ft(s)p Fu(\))390 3447 y FK(This)h(function)h(initializes)j(a)e(previously)f(allo)s(cated)i(in)m (tegration)g(state.)54 b(This)34 b(allo)m(ws)h(an)f(ex-)390 3557 y(isting)d(w)m(orkspace)g(to)g(b)s(e)f(reused)g(for)g(di\013eren)m (t)g(in)m(tegrations.)3350 3736 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_monte_vegas_integ)q(rate)f Fu(\()p FD(gsl)p 1859 3736 V 41 w(mon)m(te)p 2144 3736 V 41 w(function)30 b(*)h Ft(f)p FD(,)g(double)f Ft(xl)p Fo([])p FD(,)565 3846 y(double)g Ft(xu)p Fo([])p FD(,)h(size)p 1221 3846 V 41 w(t)g Ft(dim)p FD(,)g(size)p 1681 3846 V 41 w(t)g Ft(calls)p FD(,)h(gsl)p 2211 3846 V 40 w(rng)e(*)h Ft(r)p FD(,)g(gsl)p 2703 3846 V 40 w(mon)m(te)p 2987 3846 V 41 w(v)m(egas)p 3239 3846 V 42 w(state)h(*)e Ft(s)p FD(,)565 3955 y(double)g(*)h Ft(result)p FD(,)h(double)e(*)h Ft(abserr)p Fu(\))390 4065 y FK(This)43 b(routines)h(uses)g(the)h FC(vegas)e FK(Mon)m(te)i(Carlo)g(algorithm)g(to)g(in)m(tegrate)h(the)f (function)f FD(f)390 4174 y FK(o)m(v)m(er)d(the)e FD(dim)p FK(-dimensional)g(h)m(yp)s(ercubic)f(region)i(de\014ned)e(b)m(y)h(the)h (lo)m(w)m(er)g(and)f(upp)s(er)e(limits)390 4284 y(in)h(the)h(arra)m(ys) f FD(xl)43 b FK(and)37 b FD(xu)p FK(,)j(eac)m(h)g(of)f(size)g FD(dim)p FK(.)64 b(The)38 b(in)m(tegration)i(uses)e(a)h(\014xed)f(n)m (um)m(b)s(er)f(of)390 4394 y(function)e(calls)i FD(calls)p FK(,)h(and)d(obtains)h(random)f(sampling)g(p)s(oin)m(ts)h(using)f(the)g (random)g(n)m(um)m(b)s(er)390 4503 y(generator)d FD(r)p FK(.)44 b(A)31 b(previously)g(allo)s(cated)i(w)m(orkspace)f FD(s)j FK(m)m(ust)c(b)s(e)g(supplied.)42 b(The)31 b(result)g(of)h(the) 390 4613 y(in)m(tegration)h(is)d(returned)g(in)g FD(result)p FK(,)h(with)f(an)h(estimated)h(absolute)f(error)f FD(abserr)p FK(.)41 b(The)30 b(result)390 4722 y(and)g(its)i(error)e(estimate)j (are)e(based)g(on)f(a)i(w)m(eigh)m(ted)g(a)m(v)m(erage)h(of)e(indep)s (enden)m(t)f(samples.)42 b(The)390 4832 y(c)m(hi-squared)33 b(p)s(er)e(degree)i(of)g(freedom)g(for)f(the)h(w)m(eigh)m(ted)h(a)m(v)m (erage)h(is)d(returned)g(via)h(the)g(state)390 4941 y(struct)g(comp)s (onen)m(t,)i FD(s-)p FH(>)p FD(c)m(hisq)p FK(,)g(and)e(m)m(ust)g(b)s(e) g(consisten)m(t)i(with)e(1)h(for)f(the)g(w)m(eigh)m(ted)i(a)m(v)m (erage)390 5051 y(to)c(b)s(e)f(reliable.)3350 5230 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_monte_vegas_free)d Fu(\()p FD(gsl)p 1650 5230 V 41 w(mon)m(te)p 1935 5230 V 41 w(v)m(egas)p 2187 5230 V 42 w(state)31 b(*)g Ft(s)p Fu(\))390 5340 y FK(This)f(function)g(frees)g(the)h(memory)f(asso)s (ciated)i(with)e(the)g(in)m(tegrator)j(state)e FD(s)p FK(.)p eop end %%Page: 321 339 TeXDict begin 321 338 bop 150 -116 a FK(Chapter)30 b(25:)41 b(Mon)m(te)32 b(Carlo)f(In)m(tegration)1985 b(321)275 299 y(The)25 b FC(vegas)g FK(algorithm)i(computes)f(a)g(n)m(um)m(b)s (er)e(of)i(indep)s(enden)m(t)f(estimates)j(of)e(the)g(in)m(tegral)h(in) m(ter-)150 408 y(nally)-8 b(,)31 b(according)g(to)g(the)f FH(iterations)d FK(parameter)k(describ)s(ed)e(b)s(elo)m(w,)h(and)g (returns)e(their)j(w)m(eigh)m(ted)150 518 y(a)m(v)m(erage.)62 b(Random)36 b(sampling)h(of)g(the)f(in)m(tegrand)h(can)g(o)s 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y(curren)m(t)30 b(estimate)i(has)e (zero)i(error,)e(w)m(eigh)m(ted)i(a)m(v)m(erage)h(has)d(\014nite)g (error)630 1574 y(The)37 b(curren)m(t)f(estimate)j(is)e(assigned)g(a)h (w)m(eigh)m(t)g(whic)m(h)f(is)g(the)g(a)m(v)m(erage)j(w)m(eigh)m(t)f (of)e(the)630 1683 y(preceding)30 b(estimates.)150 1856 y(curren)m(t)g(estimate)i(has)e(\014nite)h(error,)f(previous)g (estimates)i(had)e(zero)h(error)630 1965 y(The)41 b(previous)h (estimates)h(are)g(discarded)e(and)g(the)h(w)m(eigh)m(ted)i(a)m(v)m (eraging)g(pro)s(cedure)630 2075 y(b)s(egins)30 b(with)g(the)g(curren)m (t)h(estimate.)150 2247 y(curren)m(t)f(estimate)i(has)e(zero)i(error,)e (previous)g(estimates)i(had)d(zero)j(error)630 2357 y(The)20 b(estimates)i(are)f(a)m(v)m(eraged)h(using)e(the)g(arithmetic)i(mean,)h (but)c(no)i(error)e(is)i(computed.)275 2535 y(The)35 b(con)m(v)m(ergence)k(of)e(the)g(algorithm)g(can)g(b)s(e)f(tested)h (using)f(the)g(o)m(v)m(erall)j(c)m(hi-squared)e(v)-5 b(alue)37 b(of)150 2645 y(the)31 b(results,)f(whic)m(h)g(is)g(a)m(v)-5 b(ailable)33 b(from)d(the)h(follo)m(wing)h(function:)3350 2855 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_monte_vegas_chisq)e Fu(\()p FD(const)31 b(gsl)p 2045 2855 28 4 v 41 w(mon)m(te)p 2330 2855 V 41 w(v)m(egas)p 2582 2855 V 41 w(state)h(*)f Ft(s)p Fu(\))390 2965 y FK(This)25 b(function)g(returns)g(the)h(c)m (hi-squared)g(p)s(er)f(degree)h(of)g(freedom)g(for)f(the)h(w)m(eigh)m (ted)h(estimate)390 3074 y(of)45 b(the)g(in)m(tegral.)85 b(The)44 b(returned)f(v)-5 b(alue)45 b(should)f(b)s(e)g(close)i(to)f (1.)84 b(A)45 b(v)-5 b(alue)45 b(whic)m(h)f(di\013ers)390 3184 y(signi\014can)m(tly)26 b(from)e(1)h(indicates)g(that)h(the)e(v)-5 b(alues)25 b(from)f(di\013eren)m(t)i(iterations)g(are)f(inconsisten)m (t.)390 3294 y(In)30 b(this)h(case)h(the)f(w)m(eigh)m(ted)i(error)d (will)h(b)s(e)g(under-estimated,)g(and)g(further)e(iterations)k(of)e (the)390 3403 y(algorithm)g(are)g(needed)f(to)h(obtain)g(reliable)h (results.)3350 3613 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_monte_vegas_runval)e Fu(\()p FD(const)31 b(gsl)p 1993 3613 V 40 w(mon)m(te)p 2277 3613 V 41 w(v)m(egas)p 2529 3613 V 42 w(state)h(*)f Ft(s)p FD(,)565 3723 y(double)f(*)h Ft(result)p FD(,)h(double)e(*)h Ft(sigma)p Fu(\))390 3833 y FK(This)e(function)g(returns)f(the)i(ra)m(w)g(\(una)m(v)m (eraged\))h(v)-5 b(alues)30 b(of)g(the)g(in)m(tegral)h FD(result)g FK(and)e(its)h(error)390 3942 y FD(sigma)h FK(from)f(the)h(most)f(recen)m(t)i(iteration)g(of)e(the)h(algorithm.) 275 4152 y(The)h FC(vegas)g FK(algorithm)j(is)e(highly)g (con\014gurable.)49 b(Sev)m(eral)34 b(parameters)g(can)f(b)s(e)g(c)m (hanged)g(using)150 4262 y(the)e(follo)m(wing)g(t)m(w)m(o)h(functions.) 3350 4472 y([F)-8 b(unction])-3599 b Fv(void)54 b (gsl_monte_vegas_params_g)q(et)e Fu(\()p FD(const)31 b(gsl)p 2202 4472 V 41 w(mon)m(te)p 2487 4472 V 41 w(v)m(egas)p 2739 4472 V 41 w(state)h(*)f Ft(s)p FD(,)565 4582 y(gsl)p 677 4582 V 41 w(mon)m(te)p 962 4582 V 41 w(v)m(egas)p 1214 4582 V 41 w(params)f(*)h Ft(params)p Fu(\))390 4691 y FK(This)42 b(function)g(copies)h(the)g(parameters)g(of)f(the)h(in)m (tegrator)h(state)g(in)m(to)g(the)f(user-supplied)390 4801 y FD(params)34 b FK(structure.)3350 5011 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_monte_vegas_params_s)q(et)e Fu(\()p FD(gsl)p 1964 5011 V 41 w(mon)m(te)p 2249 5011 V 41 w(v)m(egas)p 2501 5011 V 41 w(state)32 b(*)f Ft(s)p FD(,)g(const)565 5121 y(gsl)p 677 5121 V 41 w(mon)m(te)p 962 5121 V 41 w(v)m(egas)p 1214 5121 V 41 w(params)f(*)h Ft(params)p Fu(\))390 5230 y FK(This)e(function)g(sets)h(the)g(in)m (tegrator)h(parameters)f(based)f(on)h(v)-5 b(alues)29 b(pro)m(vided)h(in)f(the)h FD(params)390 5340 y FK(structure.)p eop end %%Page: 322 340 TeXDict begin 322 339 bop 150 -116 a FK(Chapter)30 b(25:)41 b(Mon)m(te)32 b(Carlo)f(In)m(tegration)1985 b(322)275 299 y(T)m(ypically)35 b(the)f(v)-5 b(alues)35 b(of)f(the)h(parameters)f (are)h(\014rst)e(read)i(using)e FH(gsl_monte_vegas_params_)150 408 y(get)p FK(,)24 b(the)f(necessary)h(c)m(hanges)g(are)g(made)f(to)h (the)f(\014elds)g(of)g(the)g FD(params)k FK(structure,)d(and)f(the)g(v) -5 b(alues)24 b(are)150 518 y(copied)33 b(bac)m(k)h(in)m(to)f(the)g(in) m(tegrator)i(state)f(using)e FH(gsl_monte_vegas_params_set)o FK(.)42 b(The)32 b(functions)150 628 y(use)e(the)h FH (gsl_monte_vegas_params)24 b FK(structure)30 b(whic)m(h)g(con)m(tains)h (the)g(follo)m(wing)h(\014elds:)3371 810 y([V)-8 b(ariable])-3598 b Fv(double)54 b(alpha)390 920 y FK(The)28 b(parameter)i FH(alpha)d FK(con)m(trols)k(the)e(sti\013ness)g(of)g(the)g(rebinning)f (algorithm.)41 b(It)29 b(is)g(t)m(ypically)390 1029 y(set)g(b)s(et)m(w) m(een)h(one)e(and)h(t)m(w)m(o.)41 b(A)29 b(v)-5 b(alue)29 b(of)g(zero)g(prev)m(en)m(ts)g(rebinning)f(of)h(the)g(grid.)40 b(The)28 b(default)390 1139 y(v)-5 b(alue)31 b(is)f(1.5.)3371 1321 y([V)-8 b(ariable])-3598 b Fv(size_t)54 b(iterations)390 1431 y FK(The)33 b(n)m(um)m(b)s(er)g(of)h(iterations)h(to)g(p)s(erform) d(for)h(eac)m(h)i(call)h(to)e(the)g(routine.)51 b(The)33 b(default)h(v)-5 b(alue)390 1540 y(is)30 b(5)h(iterations.)3371 1723 y([V)-8 b(ariable])-3598 b Fv(int)53 b(stage)390 1832 y FK(Setting)22 b(this)f(determines)g(the)h FD(stage)27 b FK(of)22 b(the)f(calculation.)40 b(Normally)-8 b(,)25 b FH(stage)k(=)h(0)21 b FK(whic)m(h)f(b)s(egins)390 1942 y(with)33 b(a)g(new)g(uniform)f(grid)h(and)f(empt)m(y)i(w)m(eigh)m(ted) g(a)m(v)m(erage.)52 b(Calling)33 b FC(vegas)g FK(with)f FH(stage)d(=)390 2051 y(1)34 b FK(retains)h(the)g(grid)f(from)g(the)g (previous)g(run)f(but)h(discards)g(the)g(w)m(eigh)m(ted)i(a)m(v)m (erage,)j(so)34 b(that)390 2161 y(one)28 b(can)f(\\tune")h(the)g(grid)f (using)f(a)i(relativ)m(ely)i(small)e(n)m(um)m(b)s(er)e(of)h(p)s(oin)m (ts)g(and)g(then)g(do)g(a)h(large)390 2271 y(run)h(with)i FH(stage)e(=)h(1)h FK(on)g(the)g(optimized)h(grid.)42 b(Setting)31 b FH(stage)e(=)h(2)h FK(k)m(eeps)h(the)f(grid)f(and)h(the) 390 2380 y(w)m(eigh)m(ted)j(a)m(v)m(erage)h(from)c(the)i(previous)f (run,)f(but)h(ma)m(y)h(increase)g(\(or)f(decrease\))i(the)e(n)m(um)m(b) s(er)390 2490 y(of)i(histogram)h(bins)e(in)h(the)g(grid)g(dep)s(ending) f(on)h(the)g(n)m(um)m(b)s(er)f(of)i(calls)g(a)m(v)-5 b(ailable.)54 b(Cho)s(osing)390 2599 y FH(stage)29 b(=)h(3)k FK(en)m(ters)h(at)g(the)g(main)f(lo)s(op,)i(so)f(that)g(nothing)f(is)h (c)m(hanged,)h(and)e(is)g(equiv)-5 b(alen)m(t)36 b(to)390 2709 y(p)s(erforming)29 b(additional)i(iterations)h(in)e(a)h(previous)f (call.)3371 2891 y([V)-8 b(ariable])-3598 b Fv(int)53 b(mode)390 3001 y FK(The)108 b(p)s(ossible)g(c)m(hoices)h(are)g FH(GSL_VEGAS_MODE_IMPORTANC)o(E)p FK(,)122 b FH(GSL_VEGAS_MODE_)390 3110 y(STRATIFIED)p FK(,)37 b FH(GSL_VEGAS_MODE_IMPORTAN)o(CE_)o(ONLY)o FK(.)56 b(This)37 b(determines)g(whether)g FC(vegas)390 3220 y FK(will)52 b(use)f(imp)s(ortance)h(sampling)f(or)g(strati\014ed) h(sampling,)57 b(or)51 b(whether)g(it)h(can)g(pic)m(k)g(on)390 3330 y(its)42 b(o)m(wn.)76 b(In)41 b(lo)m(w)i(dimensions)e FC(vegas)g FK(uses)g(strict)i(strati\014ed)f(sampling)g(\(more)h (precisely)-8 b(,)390 3439 y(strati\014ed)31 b(sampling)f(is)g(c)m (hosen)h(if)g(there)f(are)h(few)m(er)g(than)f(2)g(bins)g(p)s(er)f(b)s (o)m(x\).)3371 3622 y([V)-8 b(ariable])-3598 b Fv(int)53 b(verbose)3371 3731 y FK([V)-8 b(ariable])-3598 b Fv(FILE)54 b(*)e(ostream)390 3841 y FK(These)34 b(parameters)g(set)h(the)f(lev)m (el)i(of)e(information)g(prin)m(ted)g(b)m(y)g FC(vegas)p FK(.)51 b(All)35 b(information)f(is)390 3950 y(written)e(to)h(the)g (stream)f FD(ostream)p FK(.)47 b(The)32 b(default)h(setting)g(of)f FD(v)m(erb)s(ose)38 b FK(is)32 b FH(-1)p FK(,)h(whic)m(h)f(turns)f (o\013)390 4060 y(all)41 b(output.)70 b(A)40 b FD(v)m(erb)s(ose)46 b FK(v)-5 b(alue)41 b(of)f FH(0)g FK(prin)m(ts)g(summary)f(information) h(ab)s(out)g(the)h(w)m(eigh)m(ted)390 4170 y(a)m(v)m(erage)30 b(and)c(\014nal)h(result,)h(while)f(a)h(v)-5 b(alue)28 b(of)f FH(1)g FK(also)h(displa)m(ys)f(the)h(grid)f(co)s(ordinates.)40 b(A)27 b(v)-5 b(alue)390 4279 y(of)31 b FH(2)f FK(prin)m(ts)f (information)i(from)f(the)h(rebinning)e(pro)s(cedure)g(for)h(eac)m(h)i (iteration.)275 4461 y(The)k(ab)s(o)m(v)m(e)j(\014elds)e(and)f(the)i FD(c)m(hisq)i FK(v)-5 b(alue)37 b(can)h(also)g(b)s(e)f(accessed)h (directly)g(in)f(the)h FH(gsl_monte_)150 4571 y(vegas_state)27 b FK(but)j(suc)m(h)g(use)g(is)g(deprecated.)150 4802 y FJ(25.5)68 b(Examples)150 4962 y FK(The)38 b(example)h(program)f(b)s (elo)m(w)g(uses)g(the)g(Mon)m(te)i(Carlo)e(routines)g(to)h(estimate)h (the)f(v)-5 b(alue)38 b(of)h(the)150 5071 y(follo)m(wing)32 b(3-dimensional)f(in)m(tegral)h(from)e(the)h(theory)f(of)h(random)e(w)m (alks,)757 5286 y FE(I)j FK(=)925 5171 y Fs(Z)1008 5191 y FB(+)p Fq(\031)971 5360 y Fp(\000)p Fq(\031)1129 5224 y FE(dk)1223 5238 y Fq(x)p 1129 5265 137 4 v 1147 5348 a FK(2)p FE(\031)1291 5171 y Fs(Z)1374 5191 y FB(+)p Fq(\031)1337 5360 y Fp(\000)p Fq(\031)1495 5224 y FE(dk)1589 5238 y Fq(y)p 1495 5265 135 4 v 1512 5348 a FK(2)p FE(\031)1654 5171 y Fs(Z)1737 5191 y FB(+)p Fq(\031)1701 5360 y Fp(\000)p Fq(\031)1859 5224 y FE(dk)1953 5238 y Fq(z)p 1859 5265 133 4 v 1875 5348 a FK(2)p FE(\031)2537 5224 y FK(1)p 2011 5265 1097 4 v 2011 5348 a(\(1)21 b FI(\000)f FK(cos)q(\()p FE(k)2407 5362 y Fq(x)2450 5348 y FK(\))15 b(cos)q(\()p FE(k)2704 5362 y Fq(y)2744 5348 y FK(\))g(cos)r(\()p FE(k)2999 5362 y Fq(z)3038 5348 y FK(\)\))3118 5286 y FE(:)p eop end %%Page: 323 341 TeXDict begin 323 340 bop 150 -116 a FK(Chapter)30 b(25:)41 b(Mon)m(te)32 b(Carlo)f(In)m(tegration)1985 b(323)150 299 y(The)67 b(analytic)j(v)-5 b(alue)68 b(of)g(this)g(in)m(tegral)i (can)e(b)s(e)f(sho)m(wn)g(to)i(b)s(e)e FE(I)95 b FK(=)87 b(\000\(1)p FE(=)p FK(4\))3298 266 y FB(4)3338 299 y FE(=)p FK(\(4)p FE(\031)3518 266 y FB(3)3556 299 y FK(\))h(=)150 408 y(1)p FE(:)p FK(3932039296856)q(76)q(859)q FE(:::)q FK(.)107 b(The)50 b(in)m(tegral)i(giv)m(es)g(the)f(mean)g(time)g(sp)s 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w(siman)p 2959 4220 V 40 w(destro)m(y)p 3287 4220 V 41 w(t)565 4330 y Ft(destructor)p FD(,)e(size)p 1291 4330 V 41 w(t)c Ft(element_size)p FD(,)k(gsl)p 2186 4330 V 41 w(siman)p 2460 4330 V 40 w(params)p 2789 4330 V 40 w(t)c Ft(params)p Fu(\))390 4439 y FK(This)22 b(function)g(p)s(erforms)e(a)j(sim)m(ulated)g (annealing)g(searc)m(h)g(through)f(a)h(giv)m(en)g(space.)39 b(The)21 b(space)390 4549 y(is)i(sp)s(eci\014ed)f(b)m(y)g(pro)m(viding) h(the)g(functions)f FD(Ef)40 b FK(and)22 b FD(distance)p FK(.)39 b(The)22 b(sim)m(ulated)i(annealing)f(steps)390 4658 y(are)31 b(generated)g(using)f(the)h(random)e(n)m(um)m(b)s(er)g (generator)j FD(r)k FK(and)30 b(the)h(function)f FD(tak)m(e)p 3353 4658 V 41 w(step)p FK(.)390 4792 y(The)f(starting)h (con\014guration)f(of)h(the)f(system)g(should)g(b)s(e)f(giv)m(en)i(b)m (y)g FD(x0)p 2892 4792 V 40 w(p)p FK(.)40 b(The)28 b(routine)i (o\013ers)390 4902 y(t)m(w)m(o)36 b(mo)s(des)f(for)f(up)s(dating)g 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299 28 4 v 41 w(constructor)30 b FK(and)22 b FD(destructor)30 b FK(are)390 408 y(used)f(to)i(create,)h(cop)m(y)e(and)g(destro)m(y)g (con\014gurations)g(in)m(ternally)-8 b(.)42 b(The)30 b(v)-5 b(ariable)30 b FD(elemen)m(t)p 3567 408 V 42 w(size)390 518 y FK(should)f(b)s(e)h(zero)h(in)f(the)h(v)-5 b(ariable-size)32 b(mo)s(de.)390 656 y(The)20 b FD(params)k FK(structure)19 b(\(describ)s(ed)h(b)s(elo)m(w\))h(con)m(trols)h(the)e(run)f(b)m(y)h (pro)m(viding)h(the)f(temp)s(erature)390 765 y(sc)m(hedule)31 b(and)e(other)i(tunable)f(parameters)h(to)g(the)g(algorithm.)390 903 y(On)24 b(exit)j(the)e(b)s(est)g(result)g(ac)m(hiev)m(ed)i(during)d (the)i(searc)m(h)f(is)h(placed)f(in)g FH(*)p FA(x0_p)p FK(.)38 b(If)25 b(the)g(annealing)390 1013 y(pro)s(cess)h(has)h(b)s (een)e(successful)i(this)f(should)g(b)s(e)g(a)h(go)s(o)s(d)g(appro)m (ximation)g(to)h(the)e(optimal)i(p)s(oin)m(t)390 1122 y(in)i(the)h(space.)390 1260 y(If)j(the)g(function)g(p)s(oin)m(ter)h FD(prin)m(t)p 1524 1260 V 39 w(p)s(osition)g FK(is)f(not)g(n)m(ull,)i (a)f(debugging)f(log)h(will)g(b)s(e)e(prin)m(ted)h(to)390 1370 y FH(stdout)29 b FK(with)h(the)g(follo)m(wing)i(columns:)630 1507 y FH(#-iter)94 b(#-evals)f(temperature)g(position)g(energy)h (best_energy)390 1645 y FK(and)32 b(the)g(output)g(of)h(the)f(function) g FD(prin)m(t)p 1850 1645 V 40 w(p)s(osition)h FK(itself.)47 b(If)32 b FD(prin)m(t)p 2788 1645 V 40 w(p)s(osition)g FK(is)h(n)m(ull)f(then)g(no)390 1754 y(information)f(is)f(prin)m(ted.) 150 1945 y(The)f(sim)m(ulated)h(annealing)g(routines)g(require)f(sev)m (eral)h(user-sp)s(eci\014ed)f(functions)g(to)h(de\014ne)f(the)g(con-) 150 2055 y(\014guration)h(space)h(and)f(energy)h(function.)40 b(The)30 b(protot)m(yp)s(es)h(for)f(these)h(functions)f(are)g(giv)m(en) i(b)s(elo)m(w.)3269 2246 y([Data)g(T)m(yp)s(e])-3600 b Fv(gsl_siman_Efunc_t)390 2355 y FK(This)30 b(function)g(t)m(yp)s(e)g (should)g(return)f(the)h(energy)h(of)g(a)f(con\014guration)h FD(xp)p FK(.)630 2493 y FH(double)46 b(\(*gsl_siman_Efunc_t\))c(\(void) 47 b(*xp\))3269 2684 y FK([Data)32 b(T)m(yp)s(e])-3600 b Fv(gsl_siman_step_t)390 2793 y FK(This)38 b(function)h(t)m(yp)s(e)g (should)f(mo)s(dify)g(the)h(con\014guration)g FD(xp)i FK(using)e(a)g(random)f(step)h(tak)m(en)390 2903 y(from)30 b(the)g(generator)i FD(r)p FK(,)e(up)f(to)j(a)e(maxim)m(um)h(distance)g (of)f FD(step)p 2625 2903 V 40 w(size)p FK(.)630 3040 y FH(void)47 b(\(*gsl_siman_step_t\))42 b(\(const)k(gsl_rng)g(*r,)h (void)g(*xp,)1871 3150 y(double)f(step_size\))3269 3341 y FK([Data)32 b(T)m(yp)s(e])-3600 b Fv(gsl_siman_metric_t)390 3450 y FK(This)27 b(function)h(t)m(yp)s(e)g(should)g(return)f(the)h (distance)h(b)s(et)m(w)m(een)g(t)m(w)m(o)g(con\014gurations)f FD(xp)j FK(and)c FD(yp)p FK(.)630 3588 y FH(double)46 b(\(*gsl_siman_metric_t\))c(\(void)k(*xp,)h(void)g(*yp\))3269 3779 y FK([Data)32 b(T)m(yp)s(e])-3600 b Fv(gsl_siman_print_t)390 3888 y FK(This)30 b(function)g(t)m(yp)s(e)g(should)g(prin)m(t)g(the)g (con)m(ten)m(ts)i(of)f(the)f(con\014guration)h FD(xp)p FK(.)630 4026 y FH(void)47 b(\(*gsl_siman_print_t\))42 b(\(void)k(*xp\))3269 4217 y FK([Data)32 b(T)m(yp)s(e])-3600 b Fv(gsl_siman_copy_t)390 4326 y FK(This)30 b(function)g(t)m(yp)s(e)g (should)g(cop)m(y)h(the)f(con\014guration)h FD(source)36 b FK(in)m(to)31 b FD(dest)p FK(.)630 4464 y FH(void)47 b(\(*gsl_siman_copy_t\))42 b(\(void)47 b(*source,)e(void)i(*dest\))3269 4655 y FK([Data)32 b(T)m(yp)s(e])-3600 b Fv(gsl_siman_copy_constru)q (ct_)q(t)390 4764 y FK(This)30 b(function)g(t)m(yp)s(e)g(should)g (create)h(a)g(new)f(cop)m(y)h(of)g(the)f(con\014guration)h FD(xp)p FK(.)630 4902 y FH(void)47 b(*)g(\(*gsl_siman_copy_construc)o (t_t)o(\))42 b(\(void)k(*xp\))3269 5093 y FK([Data)32 b(T)m(yp)s(e])-3600 b Fv(gsl_siman_destroy_t)390 5202 y FK(This)30 b(function)g(t)m(yp)s(e)g(should)g(destro)m(y)h(the)f (con\014guration)h FD(xp)p FK(,)f(freeing)h(its)f(memory)-8 b(.)630 5340 y FH(void)47 b(\(*gsl_siman_destroy_t\))41 b(\(void)47 b(*xp\))p eop end %%Page: 329 347 TeXDict begin 329 346 bop 150 -116 a FK(Chapter)30 b(26:)41 b(Sim)m(ulated)31 b(Annealing)2126 b(329)3269 299 y([Data)32 b(T)m(yp)s(e])-3600 b Fv(gsl_siman_params_t)390 408 y FK(These)39 b(are)h(the)g(parameters)g(that)g(con)m(trol)h(a)f(run)f (of)g FH(gsl_siman_solve)p FK(.)65 b(This)38 b(structure)390 518 y(con)m(tains)26 b(all)g(the)f(information)g(needed)g(to)h(con)m (trol)g(the)f(searc)m(h,)i(b)s(ey)m(ond)e(the)g(energy)g(function,)390 628 y(the)31 b(step)f(function)g(and)g(the)g(initial)i(guess.)390 783 y FH(int)d(n_tries)870 892 y FK(The)h(n)m(um)m(b)s(er)f(of)h(p)s (oin)m(ts)h(to)g(try)f(for)g(eac)m(h)i(step.)390 1047 y FH(int)d(iters_fixed_T)870 1157 y FK(The)h(n)m(um)m(b)s(er)f(of)h (iterations)i(at)f(eac)m(h)h(temp)s(erature.)390 1312 y FH(double)d(step_size)870 1422 y FK(The)h(maxim)m(um)g(step)h(size)g (in)f(the)g(random)g(w)m(alk.)390 1577 y FH(double)f(k,)g(t_initial,)f (mu_t,)h(t_min)870 1686 y FK(The)h(parameters)h(of)f(the)h(Boltzmann)g (distribution)f(and)g(co)s(oling)h(sc)m(hedule.)150 1914 y FJ(26.3)68 b(Examples)150 2074 y FK(The)25 b(sim)m(ulated)g (annealing)h(pac)m(k)-5 b(age)27 b(is)e(clumsy)-8 b(,)27 b(and)d(it)h(has)g(to)h(b)s(e)e(b)s(ecause)h(it)h(is)f(written)g(in)g (C,)g(for)f(C)150 2183 y(callers,)31 b(and)f(tries)g(to)h(b)s(e)e(p)s (olymorphic)g(at)i(the)f(same)g(time.)42 b(But)30 b(here)g(w)m(e)g(pro) m(vide)g(some)g(examples)150 2293 y(whic)m(h)d(can)g(b)s(e)f(pasted)h (in)m(to)h(y)m(our)f(application)h(with)e(little)j(c)m(hange)f(and)e (should)g(mak)m(e)i(things)f(easier.)150 2488 y Fy(26.3.1)63 b(T)-10 b(rivial)41 b(example)150 2635 y FK(The)29 b(\014rst)g (example,)i(in)e(one)h(dimensional)g(Cartesian)g(space,)g(sets)g(up)f (an)g(energy)h(function)g(whic)m(h)f(is)150 2744 y(a)d(damp)s(ed)d (sine)i(w)m(a)m(v)m(e;)k(this)d(has)e(man)m(y)i(lo)s(cal)g(minima,)h (but)d(only)h(one)h(global)g(minim)m(um,)g(somewhere)150 2854 y(b)s(et)m(w)m(een)38 b(1.0)g(and)f(1.5.)63 b(The)37 b(initial)h(guess)g(giv)m(en)g(is)f(15.5,)k(whic)m(h)c(is)h(sev)m(eral) g(lo)s(cal)h(minima)e(a)m(w)m(a)m(y)150 2964 y(from)30 b(the)g(global)i(minim)m(um.)390 3073 y Fz(#include)41 b()390 3161 y(#include)g()390 3248 y(#include)g()390 3335 y(#include)g()390 3509 y(/*)f(set)g(up)f(parameters)j(for)e(this)g(simulated)h(annealing) g(run)f(*/)390 3684 y(/*)g(how)g(many)g(points)g(do)g(we)g(try)g (before)g(stepping)h(*/)390 3771 y(#define)g(N_TRIES)g(200)390 3945 y(/*)f(how)g(many)g(iterations)h(for)f(each)g(T?)g(*/)390 4032 y(#define)h(ITERS_FIXED_T)h(1000)390 4207 y(/*)e(max)g(step)g (size)g(in)g(random)g(walk)g(*/)390 4294 y(#define)h(STEP_SIZE)g(1.0) 390 4468 y(/*)f(Boltzmann)h(constant)g(*/)390 4555 y(#define)g(K)e(1.0) 390 4730 y(/*)h(initial)g(temperature)i(*/)390 4817 y(#define)f (T_INITIAL)g(0.008)390 4991 y(/*)f(damping)g(factor)h(for)f (temperature)i(*/)390 5078 y(#define)f(MU_T)f(1.003)390 5166 y(#define)h(T_MIN)f(2.0e-6)390 5340 y(gsl_siman_params_t)j(params) p eop end %%Page: 330 348 TeXDict begin 330 347 bop 150 -116 a FK(Chapter)30 b(26:)41 b(Sim)m(ulated)31 b(Annealing)2126 b(330)468 299 y Fz(=)40 b({N_TRIES,)h(ITERS_FIXED_T,)i(STEP_SIZE,)586 386 y(K,)d(T_INITIAL,)h (MU_T,)g(T_MIN};)390 560 y(/*)f(now)g(some)g(functions)h(to)f(test)g (in)g(one)f(dimension)j(*/)390 648 y(double)f(E1\(void)f(*xp\))390 735 y({)468 822 y(double)h(x)e(=)h(*)f(\(\(double)i(*\))f(xp\);)468 996 y(return)h(exp\(-pow\(\(x-1.0\),2.0\)\)*sin\(8*)q(x\);)390 1083 y(})390 1258 y(double)g(M1\(void)f(*xp,)h(void)f(*yp\))390 1345 y({)468 1432 y(double)h(x)e(=)h(*\(\(double)h(*\))f(xp\);)468 1519 y(double)h(y)e(=)h(*\(\(double)h(*\))f(yp\);)468 1694 y(return)h(fabs\(x)g(-)e(y\);)390 1781 y(})390 1955 y(void)h(S1\(const)h(gsl_rng)g(*)e(r,)h(void)g(*xp,)g(double)h (step_size\))390 2042 y({)468 2130 y(double)g(old_x)f(=)g(*\(\(double)h (*\))f(xp\);)468 2217 y(double)h(new_x;)468 2391 y(double)g(u)e(=)h (gsl_rng_uniform\(r\);)468 2478 y(new_x)h(=)e(u)h(*)f(2)h(*)f (step_size)i(-)f(step_size)h(+)f(old_x;)468 2653 y(memcpy\(xp,)i (&new_x,)f(sizeof\(new_x\)\);)390 2740 y(})390 2914 y(void)f(P1\(void)h (*xp\))390 3001 y({)468 3088 y(printf)g(\("\04512g",)g(*\(\(double)g (*\))f(xp\)\);)390 3176 y(})390 3350 y(int)390 3437 y(main\(void\))390 3524 y({)468 3611 y(const)h(gsl_rng_type)h(*)d(T;)468 3699 y(gsl_rng)i(*)f(r;)468 3873 y(double)h(x_initial)g(=)f(15.5;)468 4047 y(gsl_rng_env_setup\(\);)468 4222 y(T)g(=)f(gsl_rng_default;)468 4309 y(r)h(=)f(gsl_rng_alloc\(T\);)468 4483 y(gsl_siman_solve\(r,)44 b(&x_initial,)e(E1,)d(S1,)h(M1,)g(P1,)1096 4570 y(NULL,)g(NULL,)h (NULL,)1096 4658 y(sizeof\(double\),)i(params\);)468 4832 y(gsl_rng_free)f(\(r\);)468 4919 y(return)f(0;)390 5006 y(})p eop end %%Page: 331 349 TeXDict begin 331 348 bop 150 -116 a FK(Chapter)30 b(26:)41 b(Sim)m(ulated)31 b(Annealing)2126 b(331)275 456 y(Here)36 b(are)g(a)f(couple)h(of)g(plots)g(that)g(are)g(generated)h(b)m(y)e (running)f FH(siman_test)f 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/descender fontDict begin 0 /FontBBox load 1 get FontMatrix end transform exch pop def /vertoffset 1 printSize sub descender sub def { 0 vertoffset moveto show /vertoffset vertoffset printSize sub def } forall grestore end } dup 0 3 dict put def /patternproc { 0 begin /patternByteLength patternString length def /patternHeight patternByteLength 8 mul sqrt cvi def /patternWidth patternHeight def /patternByteWidth patternWidth 8 idiv def /imageByteMaxLength imageByteWidth imageHeight mul stringLimit patternByteWidth sub min def /imageMaxHeight imageByteMaxLength imageByteWidth idiv patternHeight idiv patternHeight mul patternHeight max def /imageHeight imageHeight imageMaxHeight sub store /imageString imageByteWidth imageMaxHeight mul patternByteWidth add string def 0 1 imageMaxHeight 1 sub { /y exch def /patternRow y patternByteWidth mul patternByteLength mod def /patternRowString patternString patternRow patternByteWidth getinterval def /imageRow y imageByteWidth mul def 0 patternByteWidth imageByteWidth 1 sub { /x exch def imageString imageRow x add patternRowString putinterval } for } for imageString end } dup 0 12 dict put def /min { dup 3 2 roll dup 4 3 roll lt { exch } if pop } def /max { dup 3 2 roll dup 4 3 roll gt { exch } if pop } def /midpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 x1 add 2 div y0 y1 add 2 div end } dup 0 4 dict put def /thirdpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 2 mul x1 add 3 div y0 2 mul y1 add 3 div end } dup 0 4 dict put def /subspline { 0 begin /movetoNeeded exch def y exch get /y3 exch def x exch get /x3 exch def y exch get /y2 exch def x exch get /x2 exch def y exch get /y1 exch def x exch get /x1 exch def y exch get /y0 exch def x exch get /x0 exch def x1 y1 x2 y2 thirdpoint /p1y exch def /p1x exch def x2 y2 x1 y1 thirdpoint /p2y exch def /p2x exch def x1 y1 x0 y0 thirdpoint p1x p1y midpoint /p0y exch def /p0x exch def x2 y2 x3 y3 thirdpoint p2x p2y midpoint /p3y exch def /p3x exch def movetoNeeded { p0x p0y moveto } if p1x p1y p2x p2y p3x p3y curveto end } dup 0 17 dict put def /storexyn { /n exch def /y n array def /x n array def n 1 sub -1 0 { /i exch def y i 3 2 roll put x i 3 2 roll put } for } def /arrowhead { 0 begin transform originalCTM itransform /taily exch def /tailx exch def transform originalCTM itransform /tipy exch def /tipx exch def /dy tipy taily sub def /dx tipx tailx sub def /angle dx 0 ne dy 0 ne or { dy dx atan } { 90 } ifelse def gsave originalCTM setmatrix tipx tipy translate angle rotate newpath arrowHeight neg arrowWidth 2 div moveto 0 0 lineto arrowHeight neg arrowWidth 2 div neg lineto patternNone not { originalCTM setmatrix /padtip arrowHeight 2 exp 0.25 arrowWidth 2 exp mul add sqrt brushWidth mul arrowWidth div def /padtail brushWidth 2 div def tipx tipy translate angle rotate padtip 0 translate arrowHeight padtip add padtail add arrowHeight div dup scale arrowheadpath ifill } if brushNone not { originalCTM setmatrix tipx tipy translate angle rotate arrowheadpath istroke } if grestore end } dup 0 9 dict put def /arrowheadpath { newpath arrowHeight neg arrowWidth 2 div moveto 0 0 lineto arrowHeight neg arrowWidth 2 div neg lineto } def /leftarrow { 0 begin y exch get /taily exch def x exch get /tailx exch def y exch get /tipy exch def x exch get /tipx exch def brushLeftArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /rightarrow { 0 begin y exch get /tipy exch def x exch get /tipx exch def y exch get /taily exch def x exch get /tailx exch def brushRightArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def %%EndResource %%EndSetup %%Page: 1 1 %%PageResources: %%PageBoundingBox: 62 177 500 576 %%BeginPageSetup %I Idraw 8 Begin %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 1 0 0 1 0 0 ] concat /originalCTM matrix currentmatrix def /trueoriginalCTM matrix currentmatrix def %%EndPageSetup Begin %I Rect [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2304 2304 9216 9216 Rect End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 2315 2151 2348 2140 2370 2107 2381 2052 2381 2019 2370 1964 2348 1931 2315 1920 2293 1920 2260 1931 2238 1964 2227 2019 2227 2052 2238 2107 2260 2140 2293 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 2293 2151 2271 2140 2260 2129 2249 2107 2238 2052 2238 2019 2249 1964 2260 1942 2271 1931 2293 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 2315 1920 2337 1931 2348 1942 2359 1964 2370 2019 2370 2052 2359 2107 2348 2129 2337 2140 2315 2151 10 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 9216 2304 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2304 2304 2442 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3181 2151 3159 2041 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 19 3159 2041 3181 2063 3214 2074 3247 2074 3280 2063 3302 2041 3313 2008 3313 1986 3302 1953 3280 1931 3247 1920 3214 1920 3181 1931 3170 1942 3159 1964 3159 1975 3170 1986 3181 1975 3170 1964 19 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 3247 2074 3269 2063 3291 2041 3302 2008 3302 1986 3291 1953 3269 1931 3247 1920 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3181 2151 3291 2151 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 3181 2140 3236 2140 3291 2151 3 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 3467 2151 3500 2140 3522 2107 3533 2052 3533 2019 3522 1964 3500 1931 3467 1920 3445 1920 3412 1931 3390 1964 3379 2019 3379 2052 3390 2107 3412 2140 3445 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 3445 2151 3423 2140 3412 2129 3401 2107 3390 2052 3390 2019 3401 1964 3412 1942 3423 1931 3445 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 3467 1920 3489 1931 3500 1942 3511 1964 3522 2019 3522 2052 3511 2107 3500 2129 3489 2140 3467 2151 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 3687 2151 3720 2140 3742 2107 3753 2052 3753 2019 3742 1964 3720 1931 3687 1920 3665 1920 3632 1931 3610 1964 3599 2019 3599 2052 3610 2107 3632 2140 3665 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 3665 2151 3643 2140 3632 2129 3621 2107 3610 2052 3610 2019 3621 1964 3632 1942 3643 1931 3665 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 3687 1920 3709 1931 3720 1942 3731 1964 3742 2019 3742 2052 3731 2107 3720 2129 3709 2140 3687 2151 10 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3456 9216 3456 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3456 2304 3456 2442 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 4234 2107 4256 2118 4289 2151 4289 1920 4 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4278 2140 4278 1920 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4234 1920 4333 1920 2 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 4509 2151 4542 2140 4564 2107 4575 2052 4575 2019 4564 1964 4542 1931 4509 1920 4487 1920 4454 1931 4432 1964 4421 2019 4421 2052 4432 2107 4454 2140 4487 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 4487 2151 4465 2140 4454 2129 4443 2107 4432 2052 4432 2019 4443 1964 4454 1942 4465 1931 4487 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 4509 1920 4531 1931 4542 1942 4553 1964 4564 2019 4564 2052 4553 2107 4542 2129 4531 2140 4509 2151 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 4729 2151 4762 2140 4784 2107 4795 2052 4795 2019 4784 1964 4762 1931 4729 1920 4707 1920 4674 1931 4652 1964 4641 2019 4641 2052 4652 2107 4674 2140 4707 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 4707 2151 4685 2140 4674 2129 4663 2107 4652 2052 4652 2019 4663 1964 4674 1942 4685 1931 4707 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 4729 1920 4751 1931 4762 1942 4773 1964 4784 2019 4784 2052 4773 2107 4762 2129 4751 2140 4729 2151 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 4949 2151 4982 2140 5004 2107 5015 2052 5015 2019 5004 1964 4982 1931 4949 1920 4927 1920 4894 1931 4872 1964 4861 2019 4861 2052 4872 2107 4894 2140 4927 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 4927 2151 4905 2140 4894 2129 4883 2107 4872 2052 4872 2019 4883 1964 4894 1942 4905 1931 4927 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 4949 1920 4971 1931 4982 1942 4993 1964 5004 2019 5004 2052 4993 2107 4982 2129 4971 2140 4949 2151 10 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4608 9216 4608 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4608 2304 4608 2442 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 5386 2107 5408 2118 5441 2151 5441 1920 4 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5430 2140 5430 1920 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5386 1920 5485 1920 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5595 2151 5573 2041 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 19 5573 2041 5595 2063 5628 2074 5661 2074 5694 2063 5716 2041 5727 2008 5727 1986 5716 1953 5694 1931 5661 1920 5628 1920 5595 1931 5584 1942 5573 1964 5573 1975 5584 1986 5595 1975 5584 1964 19 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 5661 2074 5683 2063 5705 2041 5716 2008 5716 1986 5705 1953 5683 1931 5661 1920 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5595 2151 5705 2151 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 5595 2140 5650 2140 5705 2151 3 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 5881 2151 5914 2140 5936 2107 5947 2052 5947 2019 5936 1964 5914 1931 5881 1920 5859 1920 5826 1931 5804 1964 5793 2019 5793 2052 5804 2107 5826 2140 5859 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 5859 2151 5837 2140 5826 2129 5815 2107 5804 2052 5804 2019 5815 1964 5826 1942 5837 1931 5859 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 5881 1920 5903 1931 5914 1942 5925 1964 5936 2019 5936 2052 5925 2107 5914 2129 5903 2140 5881 2151 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 6101 2151 6134 2140 6156 2107 6167 2052 6167 2019 6156 1964 6134 1931 6101 1920 6079 1920 6046 1931 6024 1964 6013 2019 6013 2052 6024 2107 6046 2140 6079 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 6079 2151 6057 2140 6046 2129 6035 2107 6024 2052 6024 2019 6035 1964 6046 1942 6057 1931 6079 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 6101 1920 6123 1931 6134 1942 6145 1964 6156 2019 6156 2052 6145 2107 6134 2129 6123 2140 6101 2151 10 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5760 9216 5760 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5760 2304 5760 2442 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 20 6516 2107 6527 2096 6516 2085 6505 2096 6505 2107 6516 2129 6527 2140 6560 2151 6604 2151 6637 2140 6648 2129 6659 2107 6659 2085 6648 2063 6615 2041 6560 2019 6538 2008 6516 1986 6505 1953 6505 1920 20 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 6604 2151 6626 2140 6637 2129 6648 2107 6648 2085 6637 2063 6604 2041 6560 2019 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 6505 1942 6516 1953 6538 1953 6593 1931 6626 1931 6648 1942 6659 1953 7 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 6538 1953 6593 1920 6637 1920 6648 1931 6659 1953 6659 1975 6 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 6813 2151 6846 2140 6868 2107 6879 2052 6879 2019 6868 1964 6846 1931 6813 1920 6791 1920 6758 1931 6736 1964 6725 2019 6725 2052 6736 2107 6758 2140 6791 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 6791 2151 6769 2140 6758 2129 6747 2107 6736 2052 6736 2019 6747 1964 6758 1942 6769 1931 6791 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 6813 1920 6835 1931 6846 1942 6857 1964 6868 2019 6868 2052 6857 2107 6846 2129 6835 2140 6813 2151 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 7033 2151 7066 2140 7088 2107 7099 2052 7099 2019 7088 1964 7066 1931 7033 1920 7011 1920 6978 1931 6956 1964 6945 2019 6945 2052 6956 2107 6978 2140 7011 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 7011 2151 6989 2140 6978 2129 6967 2107 6956 2052 6956 2019 6967 1964 6978 1942 6989 1931 7011 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 7033 1920 7055 1931 7066 1942 7077 1964 7088 2019 7088 2052 7077 2107 7066 2129 7055 2140 7033 2151 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 7253 2151 7286 2140 7308 2107 7319 2052 7319 2019 7308 1964 7286 1931 7253 1920 7231 1920 7198 1931 7176 1964 7165 2019 7165 2052 7176 2107 7198 2140 7231 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 7231 2151 7209 2140 7198 2129 7187 2107 7176 2052 7176 2019 7187 1964 7198 1942 7209 1931 7231 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 7253 1920 7275 1931 7286 1942 7297 1964 7308 2019 7308 2052 7297 2107 7286 2129 7275 2140 7253 2151 10 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6912 9216 6912 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6912 2304 6912 2442 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 20 7668 2107 7679 2096 7668 2085 7657 2096 7657 2107 7668 2129 7679 2140 7712 2151 7756 2151 7789 2140 7800 2129 7811 2107 7811 2085 7800 2063 7767 2041 7712 2019 7690 2008 7668 1986 7657 1953 7657 1920 20 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 7756 2151 7778 2140 7789 2129 7800 2107 7800 2085 7789 2063 7756 2041 7712 2019 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 7657 1942 7668 1953 7690 1953 7745 1931 7778 1931 7800 1942 7811 1953 7 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 7690 1953 7745 1920 7789 1920 7800 1931 7811 1953 7811 1975 6 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7899 2151 7877 2041 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 19 7877 2041 7899 2063 7932 2074 7965 2074 7998 2063 8020 2041 8031 2008 8031 1986 8020 1953 7998 1931 7965 1920 7932 1920 7899 1931 7888 1942 7877 1964 7877 1975 7888 1986 7899 1975 7888 1964 19 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 7965 2074 7987 2063 8009 2041 8020 2008 8020 1986 8009 1953 7987 1931 7965 1920 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7899 2151 8009 2151 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 7899 2140 7954 2140 8009 2151 3 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 8185 2151 8218 2140 8240 2107 8251 2052 8251 2019 8240 1964 8218 1931 8185 1920 8163 1920 8130 1931 8108 1964 8097 2019 8097 2052 8108 2107 8130 2140 8163 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 8163 2151 8141 2140 8130 2129 8119 2107 8108 2052 8108 2019 8119 1964 8130 1942 8141 1931 8163 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 8185 1920 8207 1931 8218 1942 8229 1964 8240 2019 8240 2052 8229 2107 8218 2129 8207 2140 8185 2151 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 8405 2151 8438 2140 8460 2107 8471 2052 8471 2019 8460 1964 8438 1931 8405 1920 8383 1920 8350 1931 8328 1964 8317 2019 8317 2052 8328 2107 8350 2140 8383 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 8383 2151 8361 2140 8350 2129 8339 2107 8328 2052 8328 2019 8339 1964 8350 1942 8361 1931 8383 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 8405 1920 8427 1931 8438 1942 8449 1964 8460 2019 8460 2052 8449 2107 8438 2129 8427 2140 8405 2151 10 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8064 9216 8064 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8064 2304 8064 2442 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 8820 2107 8831 2096 8820 2085 8809 2096 8809 2107 8820 2129 8831 2140 8864 2151 8908 2151 8941 2140 8952 2118 8952 2085 8941 2063 8908 2052 8875 2052 15 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 8908 2151 8930 2140 8941 2118 8941 2085 8930 2063 8908 2052 6 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 8908 2052 8930 2041 8952 2019 8963 1997 8963 1964 8952 1942 8941 1931 8908 1920 8864 1920 8831 1931 8820 1942 8809 1964 8809 1975 8820 1986 8831 1975 8820 1964 16 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 8941 2030 8952 1997 8952 1964 8941 1942 8930 1931 8908 1920 6 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 9117 2151 9150 2140 9172 2107 9183 2052 9183 2019 9172 1964 9150 1931 9117 1920 9095 1920 9062 1931 9040 1964 9029 2019 9029 2052 9040 2107 9062 2140 9095 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 9095 2151 9073 2140 9062 2129 9051 2107 9040 2052 9040 2019 9051 1964 9062 1942 9073 1931 9095 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 9117 1920 9139 1931 9150 1942 9161 1964 9172 2019 9172 2052 9161 2107 9150 2129 9139 2140 9117 2151 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 9337 2151 9370 2140 9392 2107 9403 2052 9403 2019 9392 1964 9370 1931 9337 1920 9315 1920 9282 1931 9260 1964 9249 2019 9249 2052 9260 2107 9282 2140 9315 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 9315 2151 9293 2140 9282 2129 9271 2107 9260 2052 9260 2019 9271 1964 9282 1942 9293 1931 9315 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 9337 1920 9359 1931 9370 1942 9381 1964 9392 2019 9392 2052 9381 2107 9370 2129 9359 2140 9337 2151 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 9557 2151 9590 2140 9612 2107 9623 2052 9623 2019 9612 1964 9590 1931 9557 1920 9535 1920 9502 1931 9480 1964 9469 2019 9469 2052 9480 2107 9502 2140 9535 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 9535 2151 9513 2140 9502 2129 9491 2107 9480 2052 9480 2019 9491 1964 9502 1942 9513 1931 9535 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 9557 1920 9579 1931 9590 1942 9601 1964 9612 2019 9612 2052 9601 2107 9590 2129 9579 2140 9557 2151 10 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 9216 9216 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2304 9216 2442 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 1497 2392 1519 2403 1552 2436 1552 2205 4 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1541 2425 1541 2205 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1497 2205 1596 2205 2 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 1716 2216 1705 2205 1694 2216 1705 2227 4 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 1804 2392 1815 2381 1804 2370 1793 2381 1793 2392 1804 2414 1815 2425 1848 2436 1892 2436 1925 2425 1936 2403 1936 2370 1925 2348 1892 2337 1859 2337 15 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 1892 2436 1914 2425 1925 2403 1925 2370 1914 2348 1892 2337 6 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 1892 2337 1914 2326 1936 2304 1947 2282 1947 2249 1936 2227 1925 2216 1892 2205 1848 2205 1815 2216 1804 2227 1793 2249 1793 2260 1804 2271 1815 2260 1804 2249 16 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 1925 2315 1936 2282 1936 2249 1925 2227 1914 2216 1892 2205 6 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2112 2414 2112 2205 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2123 2436 2123 2205 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 2123 2436 2002 2271 2178 2271 3 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2079 2205 2156 2205 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2304 9078 2304 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2304 2442 2304 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 1497 3544 1519 3555 1552 3588 1552 3357 4 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1541 3577 1541 3357 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1497 3357 1596 3357 2 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 1716 3368 1705 3357 1694 3368 1705 3379 4 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 1804 3544 1815 3533 1804 3522 1793 3533 1793 3544 1804 3566 1815 3577 1848 3588 1892 3588 1925 3577 1936 3555 1936 3522 1925 3500 1892 3489 1859 3489 15 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 1892 3588 1914 3577 1925 3555 1925 3522 1914 3500 1892 3489 6 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 1892 3489 1914 3478 1936 3456 1947 3434 1947 3401 1936 3379 1925 3368 1892 3357 1848 3357 1815 3368 1804 3379 1793 3401 1793 3412 1804 3423 1815 3412 1804 3401 16 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 1925 3467 1936 3434 1936 3401 1925 3379 1914 3368 1892 3357 6 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2035 3588 2013 3478 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 19 2013 3478 2035 3500 2068 3511 2101 3511 2134 3500 2156 3478 2167 3445 2167 3423 2156 3390 2134 3368 2101 3357 2068 3357 2035 3368 2024 3379 2013 3401 2013 3412 2024 3423 2035 3412 2024 3401 19 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 2101 3511 2123 3500 2145 3478 2156 3445 2156 3423 2145 3390 2123 3368 2101 3357 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2035 3588 2145 3588 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 2035 3577 2090 3577 2145 3588 3 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 3456 9078 3456 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3456 2442 3456 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 1497 4696 1519 4707 1552 4740 1552 4509 4 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1541 4729 1541 4509 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1497 4509 1596 4509 2 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 1716 4520 1705 4509 1694 4520 1705 4531 4 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 1804 4696 1815 4685 1804 4674 1793 4685 1793 4696 1804 4718 1815 4729 1848 4740 1892 4740 1925 4729 1936 4707 1936 4674 1925 4652 1892 4641 1859 4641 15 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 1892 4740 1914 4729 1925 4707 1925 4674 1914 4652 1892 4641 6 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 1892 4641 1914 4630 1936 4608 1947 4586 1947 4553 1936 4531 1925 4520 1892 4509 1848 4509 1815 4520 1804 4531 1793 4553 1793 4564 1804 4575 1815 4564 1804 4553 16 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 1925 4619 1936 4586 1936 4553 1925 4531 1914 4520 1892 4509 6 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 28 2145 4707 2134 4696 2145 4685 2156 4696 2156 4707 2145 4729 2123 4740 2090 4740 2057 4729 2035 4707 2024 4685 2013 4641 2013 4575 2024 4542 2046 4520 2079 4509 2101 4509 2134 4520 2156 4542 2167 4575 2167 4586 2156 4619 2134 4641 2101 4652 2090 4652 2057 4641 2035 4619 2024 4586 28 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 9 2090 4740 2068 4729 2046 4707 2035 4685 2024 4641 2024 4575 2035 4542 2057 4520 2079 4509 9 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 2101 4509 2123 4520 2145 4542 2156 4575 2156 4586 2145 4619 2123 4641 2101 4652 8 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 4608 9078 4608 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4608 2442 4608 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 1497 5848 1519 5859 1552 5892 1552 5661 4 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1541 5881 1541 5661 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1497 5661 1596 5661 2 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 1716 5672 1705 5661 1694 5672 1705 5683 4 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 1804 5848 1815 5837 1804 5826 1793 5837 1793 5848 1804 5870 1815 5881 1848 5892 1892 5892 1925 5881 1936 5859 1936 5826 1925 5804 1892 5793 1859 5793 15 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 1892 5892 1914 5881 1925 5859 1925 5826 1914 5804 1892 5793 6 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 1892 5793 1914 5782 1936 5760 1947 5738 1947 5705 1936 5683 1925 5672 1892 5661 1848 5661 1815 5672 1804 5683 1793 5705 1793 5716 1804 5727 1815 5716 1804 5705 16 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 1925 5771 1936 5738 1936 5705 1925 5683 1914 5672 1892 5661 6 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2013 5892 2013 5826 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 2013 5848 2024 5870 2046 5892 2068 5892 2123 5859 2145 5859 2156 5870 2167 5892 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 2024 5870 2046 5881 2068 5881 2123 5859 4 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 2167 5892 2167 5859 2156 5826 2112 5771 2101 5749 2090 5716 2090 5661 7 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5 2156 5826 2101 5771 2090 5749 2079 5716 2079 5661 5 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5760 9078 5760 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5760 2442 5760 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 1497 7000 1519 7011 1552 7044 1552 6813 4 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1541 7033 1541 6813 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1497 6813 1596 6813 2 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 1716 6824 1705 6813 1694 6824 1705 6835 4 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 1804 7000 1815 6989 1804 6978 1793 6989 1793 7000 1804 7022 1815 7033 1848 7044 1892 7044 1925 7033 1936 7011 1936 6978 1925 6956 1892 6945 1859 6945 15 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 1892 7044 1914 7033 1925 7011 1925 6978 1914 6956 1892 6945 6 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 1892 6945 1914 6934 1936 6912 1947 6890 1947 6857 1936 6835 1925 6824 1892 6813 1848 6813 1815 6824 1804 6835 1793 6857 1793 6868 1804 6879 1815 6868 1804 6857 16 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 1925 6923 1936 6890 1936 6857 1925 6835 1914 6824 1892 6813 6 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 12 2112 7044 2145 7033 2156 7011 2156 6978 2145 6956 2112 6945 2068 6945 2035 6956 2024 6978 2024 7011 2035 7033 2068 7044 12 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2068 7044 2046 7033 2035 7011 2035 6978 2046 6956 2068 6945 6 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2112 6945 2134 6956 2145 6978 2145 7011 2134 7033 2112 7044 6 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 2068 6945 2035 6934 2024 6923 2013 6901 2013 6857 2024 6835 2035 6824 2068 6813 2112 6813 2145 6824 2156 6835 2167 6857 2167 6901 2156 6923 2145 6934 2112 6945 16 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 2068 6945 2046 6934 2035 6923 2024 6901 2024 6857 2035 6835 2046 6824 2068 6813 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 2112 6813 2134 6824 2145 6835 2156 6857 2156 6901 2145 6923 2134 6934 2112 6945 8 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 6912 9078 6912 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 6912 2442 6912 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 1497 8152 1519 8163 1552 8196 1552 7965 4 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1541 8185 1541 7965 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1497 7965 1596 7965 2 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 1716 7976 1705 7965 1694 7976 1705 7987 4 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 1804 8152 1815 8141 1804 8130 1793 8141 1793 8152 1804 8174 1815 8185 1848 8196 1892 8196 1925 8185 1936 8163 1936 8130 1925 8108 1892 8097 1859 8097 15 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 1892 8196 1914 8185 1925 8163 1925 8130 1914 8108 1892 8097 6 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 1892 8097 1914 8086 1936 8064 1947 8042 1947 8009 1936 7987 1925 7976 1892 7965 1848 7965 1815 7976 1804 7987 1793 8009 1793 8020 1804 8031 1815 8020 1804 8009 16 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 1925 8075 1936 8042 1936 8009 1925 7987 1914 7976 1892 7965 6 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 28 2156 8119 2145 8086 2123 8064 2090 8053 2079 8053 2046 8064 2024 8086 2013 8119 2013 8130 2024 8163 2046 8185 2079 8196 2101 8196 2134 8185 2156 8163 2167 8130 2167 8064 2156 8020 2145 7998 2123 7976 2090 7965 2057 7965 2035 7976 2024 7998 2024 8009 2035 8020 2046 8009 2035 7998 28 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 2079 8053 2057 8064 2035 8086 2024 8119 2024 8130 2035 8163 2057 8185 2079 8196 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 9 2101 8196 2123 8185 2145 8163 2156 8130 2156 8064 2145 8020 2134 7998 2112 7976 2090 7965 9 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 8064 9078 8064 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 8064 2442 8064 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 1497 9304 1519 9315 1552 9348 1552 9117 4 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1541 9337 1541 9117 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1497 9117 1596 9117 2 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 1716 9128 1705 9117 1694 9128 1705 9139 4 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1892 9326 1892 9117 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1903 9348 1903 9117 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 1903 9348 1782 9183 1958 9183 3 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1859 9117 1936 9117 2 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 2101 9348 2134 9337 2156 9304 2167 9249 2167 9216 2156 9161 2134 9128 2101 9117 2079 9117 2046 9128 2024 9161 2013 9216 2013 9249 2024 9304 2046 9337 2079 9348 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 2079 9348 2057 9337 2046 9326 2035 9304 2024 9249 2024 9216 2035 9161 2046 9139 2057 9128 2079 9117 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 2101 9117 2123 9128 2134 9139 2145 9161 2156 9216 2156 9249 2145 9304 2134 9326 2123 9337 2101 9348 10 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 9216 9078 9216 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 9216 2442 9216 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2304 9161 2304 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2304 2359 2304 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2880 9161 2880 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2880 2359 2880 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 3456 9161 3456 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3456 2359 3456 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 4032 9161 4032 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4032 2359 4032 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 4608 9161 4608 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4608 2359 4608 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5184 9161 5184 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5184 2359 5184 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5760 9161 5760 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5760 2359 5760 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 6336 9161 6336 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 6336 2359 6336 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 6912 9161 6912 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 6912 2359 6912 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 7488 9161 7488 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 7488 2359 7488 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 8064 9161 8064 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 8064 2359 8064 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 8640 9161 8640 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 8640 2359 8640 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 9216 9161 9216 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 9216 2359 9216 2 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 4858 1621 4880 1610 4891 1599 4902 1577 4902 1555 4891 1533 4880 1522 4858 1511 4836 1511 4814 1522 4803 1533 4792 1555 4792 1577 4803 1599 4814 1610 4836 1621 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 4814 1610 4803 1588 4803 1544 4814 1522 4 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 4880 1522 4891 1544 4891 1588 4880 1610 4 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5 4891 1599 4902 1610 4924 1621 4924 1610 4902 1610 5 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 9 4803 1533 4792 1522 4781 1500 4781 1489 4792 1467 4825 1456 4880 1456 4913 1445 4924 1434 9 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 4781 1489 4792 1478 4825 1467 4880 1467 4913 1456 4924 1434 4924 1423 4913 1401 4880 1390 4814 1390 4781 1401 4770 1423 4770 1434 4781 1456 4814 1467 15 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 17 5001 1555 5133 1555 5133 1577 5122 1599 5111 1610 5089 1621 5056 1621 5023 1610 5001 1588 4990 1555 4990 1533 5001 1500 5023 1478 5056 1467 5078 1467 5111 1478 5133 1500 17 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 5122 1555 5122 1588 5111 1610 3 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 5056 1621 5034 1610 5012 1588 5001 1555 5001 1533 5012 1500 5034 1478 5056 1467 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5221 1621 5221 1467 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5232 1621 5232 1467 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 5232 1588 5254 1610 5287 1621 5309 1621 5342 1610 5353 1588 5353 1467 7 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 5309 1621 5331 1610 5342 1588 5342 1467 4 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5188 1621 5232 1621 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5188 1467 5265 1467 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5309 1467 5386 1467 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 17 5452 1555 5584 1555 5584 1577 5573 1599 5562 1610 5540 1621 5507 1621 5474 1610 5452 1588 5441 1555 5441 1533 5452 1500 5474 1478 5507 1467 5529 1467 5562 1478 5584 1500 17 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 5573 1555 5573 1588 5562 1610 3 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 5507 1621 5485 1610 5463 1588 5452 1555 5452 1533 5463 1500 5485 1478 5507 1467 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5672 1621 5672 1467 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5683 1621 5683 1467 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 5683 1555 5694 1588 5716 1610 5738 1621 5771 1621 5782 1610 5782 1599 5771 1588 5760 1599 5771 1610 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5639 1621 5683 1621 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5639 1467 5716 1467 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 13 5859 1599 5859 1588 5848 1588 5848 1599 5859 1610 5881 1621 5925 1621 5947 1610 5958 1599 5969 1577 5969 1500 5980 1478 5991 1467 13 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5 5958 1599 5958 1500 5969 1478 5991 1467 6002 1467 5 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 11 5958 1577 5947 1566 5881 1555 5848 1544 5837 1522 5837 1500 5848 1478 5881 1467 5914 1467 5936 1478 5958 1500 11 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 5881 1555 5859 1544 5848 1522 5848 1500 5859 1478 5881 1467 6 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 6079 1698 6079 1511 6090 1478 6112 1467 6134 1467 6156 1478 6167 1500 7 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 6090 1698 6090 1511 6101 1478 6112 1467 4 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6046 1621 6134 1621 2 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 6255 1687 6244 1676 6233 1687 6244 1698 4 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6244 1621 6244 1467 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6255 1621 6255 1467 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6211 1621 6255 1621 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6211 1467 6288 1467 2 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 6431 1621 6464 1610 6486 1588 6497 1555 6497 1533 6486 1500 6464 1478 6431 1467 6409 1467 6376 1478 6354 1500 6343 1533 6343 1555 6354 1588 6376 1610 6409 1621 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 6409 1621 6387 1610 6365 1588 6354 1555 6354 1533 6365 1500 6387 1478 6409 1467 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 6431 1467 6453 1478 6475 1500 6486 1533 6486 1555 6475 1588 6453 1610 6431 1621 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6585 1621 6585 1467 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6596 1621 6596 1467 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 6596 1588 6618 1610 6651 1621 6673 1621 6706 1610 6717 1588 6717 1467 7 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 6673 1621 6695 1610 6706 1588 6706 1467 4 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6552 1621 6596 1621 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6552 1467 6629 1467 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6673 1467 6750 1467 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 974 5062 1205 5062 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 974 5073 1205 5073 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 14 1007 5073 985 5095 974 5117 974 5139 985 5172 1007 5194 1040 5205 1062 5205 1095 5194 1117 5172 1128 5139 1128 5117 1117 5095 1095 5073 14 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 974 5139 985 5161 1007 5183 1040 5194 1062 5194 1095 5183 1117 5161 1128 5139 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 974 5029 974 5073 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1205 5029 1205 5106 2 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 974 5359 985 5392 1007 5414 1040 5425 1062 5425 1095 5414 1117 5392 1128 5359 1128 5337 1117 5304 1095 5282 1062 5271 1040 5271 1007 5282 985 5304 974 5337 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 974 5337 985 5315 1007 5293 1040 5282 1062 5282 1095 5293 1117 5315 1128 5337 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 1128 5359 1117 5381 1095 5403 1062 5414 1040 5414 1007 5403 985 5381 974 5359 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 996 5601 974 5612 1018 5612 996 5601 985 5590 974 5568 974 5524 985 5502 996 5491 1018 5491 1029 5502 1040 5524 1062 5579 1073 5601 1084 5612 15 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 1007 5491 1018 5502 1029 5524 1051 5579 1062 5601 1073 5612 1106 5612 1117 5601 1128 5579 1128 5535 1117 5513 1106 5502 1084 5491 1128 5491 1106 5502 15 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 908 5711 919 5700 908 5689 897 5700 4 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 974 5700 1128 5700 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 974 5711 1128 5711 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 974 5667 974 5711 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1128 5667 1128 5744 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 897 5820 1084 5820 1117 5831 1128 5853 1128 5875 1117 5897 1095 5908 7 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 897 5831 1084 5831 1117 5842 1128 5853 4 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 974 5787 974 5875 2 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 908 5996 919 5985 908 5974 897 5985 4 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 974 5985 1128 5985 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 974 5996 1128 5996 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 974 5952 974 5996 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1128 5952 1128 6029 2 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 974 6172 985 6205 1007 6227 1040 6238 1062 6238 1095 6227 1117 6205 1128 6172 1128 6150 1117 6117 1095 6095 1062 6084 1040 6084 1007 6095 985 6117 974 6150 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 974 6150 985 6128 1007 6106 1040 6095 1062 6095 1095 6106 1117 6128 1128 6150 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 1128 6172 1117 6194 1095 6216 1062 6227 1040 6227 1007 6216 985 6194 974 6172 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 974 6326 1128 6326 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 974 6337 1128 6337 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 1007 6337 985 6359 974 6392 974 6414 985 6447 1007 6458 1128 6458 7 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 974 6414 985 6436 1007 6447 1128 6447 4 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 974 6293 974 6337 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1128 6293 1128 6370 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1128 6414 1128 6491 2 MLine End Begin %I MLine [1 0 0 1 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 0 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5 2304 3537 2306 5851 2309 6957 2311 5040 2311 2304 5 MLine End Begin %I MLine [1 0 0 1 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 0 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 2316 9216 2318 3782 2320 5046 2322 5694 2325 7425 2327 2809 2327 2304 7 MLine End Begin %I MLine [1 0 0 1 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 0 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 2332 2304 2332 6545 2334 3779 2336 2701 2339 2863 2341 4038 2343 4677 2343 2304 8 MLine End Begin %I MLine [1 0 0 1 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 0 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 2348 2304 2348 6745 2350 5723 2352 4676 2355 3001 2357 5031 2359 4958 2359 2304 8 MLine End Begin %I MLine [1 0 0 1 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 0 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 17 2364 2304 2364 5593 2366 6131 2369 5183 2371 4312 2373 4047 2375 6887 2378 3572 2380 2957 2382 6623 2385 5578 2387 5196 2389 3144 2392 5409 2394 5349 2396 3938 2396 2304 17 MLine End Begin %I MLine [1 0 0 1 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 0 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 23 2401 2304 2401 3893 2403 5522 2405 4905 2408 5492 2410 8222 2412 7351 2415 5980 2417 5113 2419 5349 2422 2946 2424 3768 2426 3987 2428 3116 2431 2943 2433 3963 2435 6127 2438 6093 2440 5254 2442 5632 2445 5956 2447 7000 2449 2304 23 MLine End Begin %I MLine [1 0 0 1 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 0 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 14 2449 2304 2451 5820 2454 7758 2456 5967 2458 3336 2461 4018 2463 5883 2465 5444 2468 5422 2470 3213 2472 5818 2474 6579 2477 3669 2477 2304 14 MLine End Begin %I MLine [1 0 0 1 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 0 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 52 2481 2304 2481 3929 2484 5008 2486 5156 2488 9181 2491 7231 2493 6319 2495 3796 2498 4272 2500 5322 2502 6001 2504 4344 2507 3939 2509 4495 2511 6707 2514 6862 2516 4186 2518 6898 2521 5929 2523 2683 2525 6786 2527 5745 2530 7087 2532 6073 2534 7508 2537 5712 2539 3585 2541 4588 2544 3257 2546 5062 2548 4287 2551 6107 2553 4268 2555 5516 2557 3495 2560 7006 2562 5126 2564 4795 2567 6427 2569 6482 2571 6155 2574 5672 2576 5571 2578 5941 2580 4184 2583 4580 2585 6938 2587 7021 2590 5638 2592 6728 2594 6274 2597 2304 52 MLine End Begin %I MLine [1 0 0 1 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 0 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 30 2597 2304 2599 5625 2601 4085 2604 3972 2606 7103 2608 4874 2610 3563 2613 5008 2615 5237 2617 4205 2620 5002 2622 6644 2624 4303 2627 3993 2629 5486 2631 3143 2633 5398 2636 2961 2638 5134 2640 4828 2643 3800 2645 5856 2647 4655 2650 5632 2652 4448 2654 6759 2657 4162 2659 5417 2661 5031 2663 2304 30 MLine End Begin %I MLine [1 0 0 1 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 0 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 12 2664 2304 2666 5439 2668 6260 2670 5887 2673 6677 2675 3635 2677 5685 2680 6228 2682 5760 2684 5455 2686 6136 2689 2304 12 MLine End Begin %I MLine [1 0 0 1 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 0 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 50 2689 2304 2691 5024 2693 6701 2696 5156 2698 2972 2700 5454 2703 3338 2705 4169 2707 7335 2710 5755 2712 3025 2714 3250 2716 7785 2719 3138 2721 3858 2723 5572 2726 6626 2728 3509 2730 5704 2733 4358 2735 6663 2737 2585 2739 4067 2742 5996 2744 4279 2746 4831 2749 5393 2751 3457 2753 4996 2756 5329 2758 4711 2760 5613 2762 4766 2765 6331 2767 6019 2769 3948 2772 5539 2774 3994 2776 6042 2779 5830 2781 4390 2783 3784 2786 4605 2788 4911 2790 6647 2792 4684 2795 5122 2797 4924 2799 4768 2799 2304 50 MLine End Begin %I MLine [1 0 0 1 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 0 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2804 2304 2804 5242 2806 4333 2809 3694 2811 6115 2811 2304 6 MLine End Begin %I MLine [1 0 0 1 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 0 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 500 2815 2304 2815 4467 2818 4577 2820 2438 2822 5659 2825 4704 2827 4326 2829 5129 2832 3356 2834 5948 2836 5731 2839 5003 2841 6929 2843 5010 2845 6503 2848 5508 2850 4844 2852 4207 2855 4908 2857 5596 2859 5035 2862 4658 2864 3556 2866 3631 2868 5071 2871 5299 2873 5722 2875 4846 2878 5313 2880 5105 2882 4724 2885 4666 2887 5480 2889 4429 2892 5102 2894 3208 2896 5477 2898 4912 2901 5978 2903 6812 2905 4435 2908 4117 2910 3539 2912 5100 2915 5103 2917 4579 2919 4502 2921 5469 2924 4849 2926 5587 2928 5009 2931 4724 2933 5662 2935 5433 2938 5155 2940 5584 2942 4712 2945 4849 2947 5169 2949 4890 2951 2614 2954 5378 2956 3964 2958 2365 2961 4798 2963 6236 2965 5300 2968 4452 2970 4730 2972 6526 2974 4494 2977 3588 2979 5140 2981 4810 2984 4655 2986 5072 2988 3927 2991 5600 2993 4667 2995 5611 2998 4792 3000 5403 3002 5353 3004 5246 3007 4527 3009 7247 3011 5939 3014 4158 3016 4188 3018 5535 3021 6841 3023 3405 3025 5342 3027 4717 3030 4895 3032 5026 3034 4201 3037 2962 3039 3987 3041 5061 3044 4744 3046 3880 3048 5879 3050 6122 3053 5621 3055 2487 3057 5431 3060 5492 3062 4565 3064 5669 3067 4395 3069 4125 3071 4975 3074 4476 3076 6096 3078 5557 3080 5672 3083 4699 3085 3673 3087 4429 3090 3668 3092 5839 3094 5223 3097 4999 3099 3406 3101 5109 3103 5254 3106 3251 3108 4486 3110 5880 3113 4431 3115 5721 3117 4393 3120 4941 3122 4302 3124 4320 3127 4424 3129 4504 3131 5623 3133 3928 3136 6113 3138 5371 3140 5003 3143 6304 3145 4655 3147 5484 3150 4500 3152 3724 3154 4679 3156 4937 3159 4296 3161 4444 3163 5901 3166 4381 3168 5522 3170 5929 3173 4851 3175 4986 3177 3870 3180 5414 3182 3886 3184 4957 3186 4988 3189 5250 3191 5554 3193 4910 3196 4632 3198 5334 3200 4401 3203 5663 3205 5207 3207 4188 3209 5253 3212 5965 3214 5414 3216 5223 3219 5346 3221 5186 3223 5702 3226 4887 3228 4813 3230 4958 3233 5399 3235 4439 3237 4607 3239 5723 3242 4556 3244 5758 3246 5238 3249 3989 3251 5187 3253 5354 3256 5395 3258 5384 3260 4405 3262 5695 3265 5284 3267 4783 3269 6017 3272 4313 3274 5041 3276 4289 3279 4922 3281 2568 3283 5001 3286 4472 3288 6198 3290 4679 3292 4732 3295 4601 3297 5628 3299 4872 3302 4235 3304 4272 3306 5159 3309 5456 3311 4979 3313 3544 3315 5845 3318 4297 3320 4715 3322 4241 3325 4155 3327 6127 3329 4949 3332 5663 3334 7135 3336 6070 3338 4776 3341 3711 3343 4841 3345 4666 3348 4580 3350 5700 3352 4175 3355 4755 3357 5891 3359 4288 3362 4761 3364 4206 3366 6330 3368 5722 3371 5133 3373 5191 3375 4366 3378 4523 3380 5576 3382 4902 3385 4596 3387 6145 3389 4578 3391 4242 3394 5414 3396 4061 3398 5454 3401 3813 3403 4829 3405 4015 3408 3936 3410 4625 3412 4686 3415 5942 3417 5630 3419 4603 3421 5883 3424 5757 3426 5687 3428 5088 3431 5724 3433 5345 3435 4432 3438 4290 3440 5754 3442 5237 3444 4678 3447 5493 3449 5110 3451 5526 3454 4421 3456 3996 3458 4873 3461 6145 3463 4156 3465 4670 3468 4872 3470 4465 3472 4470 3474 4697 3477 4071 3479 5492 3481 5191 3484 6397 3486 4783 3488 5121 3491 5867 3493 4828 3495 4516 3497 5792 3500 5033 3502 4759 3504 5772 3507 4804 3509 5069 3511 4818 3514 4310 3516 5510 3518 6439 3521 4828 3523 5190 3525 4826 3527 6038 3530 4626 3532 4145 3534 4726 3537 4729 3539 5912 3541 4813 3544 4724 3546 3617 3548 3524 3550 4776 3553 5115 3555 5425 3557 5289 3560 4423 3562 5103 3564 4669 3567 5011 3569 4038 3571 5312 3574 4374 3576 4433 3578 5816 3580 5225 3583 4792 3585 4320 3587 5230 3590 5429 3592 5146 3594 6043 3597 4608 3599 4724 3601 4995 3603 5955 3606 4970 3608 5198 3610 5223 3613 5098 3615 5289 3617 5018 3620 4799 3622 5859 3624 5077 3626 4886 3629 5030 3631 4722 3633 4902 3636 5249 3638 5146 3640 4894 3643 5205 3645 5113 3647 4019 3650 6192 3652 4959 3654 4908 3656 4151 3659 5368 3661 5460 3663 5533 3666 4432 3668 5306 3670 4747 3673 5517 3675 4903 3677 5888 3679 5045 3682 3707 3684 4496 3686 5224 3689 3817 3691 5335 3693 4246 3696 3908 3698 3978 3700 4389 3703 5548 3705 4863 3707 4990 3709 5449 3712 4750 3714 4948 3716 4503 3719 5024 3721 5842 3723 4975 3726 4969 3728 5672 3730 4207 3732 5094 3735 5487 3737 5905 3739 4975 3742 5292 3744 4716 3746 4578 3749 4806 3751 5140 3753 4651 3756 4398 3758 4084 3760 3932 3762 4535 3765 4530 3767 5463 3769 4177 3772 5480 3774 5624 3776 4472 3779 4549 3781 5584 3783 5168 3785 5452 3788 3898 3790 5100 3792 5481 3795 4696 3797 5129 3799 4514 3802 5556 3804 5008 3806 5725 3809 4827 3811 5357 3813 4856 3815 5141 3818 4934 3820 4390 3822 5634 3825 4602 3827 4882 3829 4937 3832 5407 3834 4768 3836 4654 3838 4381 3841 5030 3843 5045 3845 4798 3848 4707 3850 5390 3852 4503 3855 5255 3857 6042 3859 4896 3862 4401 3864 5028 3866 4492 3868 4866 3871 4663 3873 5255 3875 5130 3878 4599 3880 5406 3882 4901 3885 5557 3887 4326 3889 5076 3891 5056 3894 5139 3896 4070 3898 5221 3901 4788 3903 5081 3905 4399 3908 4964 3910 5117 3912 4909 3914 4777 3917 4040 3919 4724 3921 5427 3924 5186 3926 4993 3928 5212 3931 4986 3933 3864 3935 4739 3938 5034 3940 4072 3942 5754 3944 5316 3947 5252 3949 5204 3951 5875 3954 4977 3956 4313 3958 4613 3961 5136 3963 5681 500 MLine End Begin %I MLine [1 0 0 1 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 0 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 500 3963 5681 3965 4624 3967 4461 3970 5042 3972 4438 3974 5657 3977 5399 3979 3812 3981 5833 3984 5350 3986 5458 3988 4868 3991 4783 3993 5525 3995 5588 3997 5269 4000 4408 4002 4393 4004 4922 4007 5568 4009 4510 4011 4548 4014 4411 4016 4941 4018 4841 4020 4787 4023 5808 4025 4826 4027 5128 4030 4730 4032 5017 4034 5048 4037 4799 4039 4785 4041 4375 4044 5213 4046 5568 4048 4951 4050 4989 4053 4776 4055 3940 4057 4609 4060 4454 4062 4359 4064 4590 4067 4768 4069 5576 4071 5372 4073 5167 4076 5030 4078 5282 4080 5159 4083 5125 4085 4896 4087 4279 4090 4118 4092 5246 4094 4829 4097 4675 4099 4790 4101 4279 4103 4508 4106 5837 4108 5020 4110 6001 4113 5002 4115 5008 4117 4610 4120 4644 4122 4988 4124 4288 4126 5505 4129 4759 4131 4503 4133 5020 4136 5694 4138 4314 4140 5493 4143 4564 4145 5661 4147 5420 4150 5234 4152 5288 4154 4500 4156 5004 4159 5302 4161 5500 4163 4977 4166 5156 4168 5086 4170 4999 4173 4981 4175 4772 4177 4580 4179 5139 4182 5207 4184 4276 4186 4922 4189 4906 4191 5479 4193 4975 4196 5382 4198 5500 4200 5328 4202 4469 4205 4588 4207 5326 4209 4851 4212 4663 4214 5724 4216 5431 4219 4599 4221 4955 4223 5454 4226 5015 4228 4924 4230 5393 4232 5306 4235 4856 4237 4893 4239 4664 4242 5474 4244 4599 4246 5019 4249 4673 4251 4318 4253 5647 4255 5041 4258 5775 4260 5480 4262 4783 4265 4759 4267 4643 4269 4279 4272 5278 4274 5538 4276 4722 4279 5910 4281 4905 4283 4317 4285 4774 4288 4561 4290 4561 4292 4850 4295 5098 4297 4554 4299 4532 4302 5041 4304 4924 4306 4701 4308 5099 4311 5253 4313 5298 4315 5776 4318 5030 4320 4716 4322 5266 4325 4609 4327 4966 4329 4568 4332 5418 4334 4973 4336 5141 4338 4958 4341 5121 4343 5460 4345 5672 4348 4749 4350 5100 4352 4724 4355 4232 4357 5027 4359 5046 4361 5168 4364 5320 4366 5105 4368 4777 4371 5116 4373 5775 4375 4421 4378 5031 4380 4978 4382 4845 4385 5488 4387 4590 4389 4833 4391 4965 4394 4366 4396 5320 4398 4346 4401 5449 4403 4965 4405 4866 4408 5194 4410 5116 4412 5283 4414 5371 4417 5008 4419 4760 4421 4975 4424 4994 4426 5518 4428 5115 4431 4922 4433 5072 4435 5072 4438 5072 4440 5504 4442 4922 4444 4890 4447 4962 4449 4517 4451 4768 4454 5186 4456 4646 4458 5284 4461 4966 4463 5038 4465 4969 4467 4645 4470 5660 4472 4947 4474 5178 4477 5404 4479 5398 4481 5401 4484 4963 4486 5163 4488 4833 4490 5232 4493 5383 4495 5109 4497 5093 4500 4753 4502 4643 4504 4767 4507 5108 4509 4911 4511 5149 4514 4571 4516 4375 4518 4975 4520 5094 4523 4842 4525 4658 4527 5448 4530 5934 4532 5224 4534 5224 4537 4954 4539 5292 4541 4966 4543 5091 4546 4905 4548 4974 4550 4297 4553 4940 4555 4925 4557 4921 4560 4742 4562 4752 4564 5144 4567 4895 4569 5405 4571 4855 4573 4757 4576 5108 4578 5306 4580 4644 4583 5336 4585 4894 4587 4848 4590 4655 4592 5337 4594 5515 4596 4901 4599 5022 4601 5022 4603 5548 4606 4988 4608 4623 4610 4469 4613 4490 4615 4659 4617 4980 4620 5075 4622 5099 4624 4922 4626 5054 4629 5236 4631 5052 4633 5531 4636 5225 4638 5275 4640 4977 4643 4743 4645 4717 4647 5345 4649 5088 4652 4813 4654 5338 4656 5287 4659 5098 4661 4788 4663 5424 4666 4585 4668 4910 4670 5043 4673 5206 4675 5201 4677 4620 4679 5045 4682 4696 4684 4673 4686 5296 4689 4573 4691 5206 4693 5055 4696 4435 4698 4443 4700 4889 4702 5561 4705 4966 4707 4320 4709 4736 4712 4464 4714 5158 4716 4813 4719 5148 4721 5102 4723 5191 4726 5054 4728 5194 4730 4852 4732 5080 4735 5019 4737 4851 4739 4744 4742 4957 4744 4917 4746 4926 4749 5063 4751 4728 4753 4751 4755 4911 4758 4911 4760 5027 4762 5015 4765 5015 4767 5004 4769 5004 4772 4696 4774 4820 4776 4875 4778 4522 4781 5230 4783 4775 4785 5186 4788 5368 4790 5194 4792 5205 4795 4593 4797 4913 4799 5297 4802 4835 4804 4865 4806 5045 4808 4749 4811 4941 4813 4895 4815 5172 4818 4664 4820 5231 4822 4223 4825 5269 4827 4988 4829 4988 4831 5265 4834 5192 4836 4702 4838 4962 4841 5098 4843 5098 4845 5093 4848 4871 4850 4969 4852 4969 4855 4978 4857 4868 4859 5379 4861 5102 4864 5102 4866 4823 4868 5200 4871 5394 4873 5161 4875 4883 4878 5314 4880 4925 4882 4571 4884 4774 4887 5374 4889 4838 4891 4704 4894 4783 4896 5002 4898 5002 4901 4956 4903 5232 4905 4857 4908 4670 4910 4833 4912 4762 4914 5050 4917 5168 4919 4682 4921 5204 4924 4893 4926 5064 4928 4985 4931 5071 4933 4713 4935 4922 4937 5297 4940 5261 4942 4830 4944 4959 4947 4852 4949 5581 4951 4954 4954 5296 4956 4887 4958 5213 4961 4970 4963 4837 4965 5252 4967 4464 4970 5034 4972 4849 4974 5002 4977 4985 4979 4985 4981 5084 4984 5084 4986 4684 4988 4783 4990 5093 4993 4739 4995 4795 4997 5103 5000 5384 5002 5222 5004 4611 5007 5069 5009 4831 5011 4709 5014 4707 5016 4958 5018 4943 5020 4629 5023 4886 5025 5015 5027 5035 5030 4843 5032 4694 5034 5041 5037 5073 5039 5269 5041 5017 5043 4911 5046 4843 5048 4751 5050 5015 5053 4939 5055 4967 5057 4967 5060 4985 5062 4398 5064 4722 5066 4740 5069 4921 5071 5025 5073 4880 5076 4880 5078 4927 5080 5003 5083 4812 5085 5053 5087 4348 5090 4729 5092 4669 5094 5221 5096 4690 5099 4910 5101 4959 5103 4653 5106 5057 5108 4969 5110 5184 5113 4616 500 MLine End Begin %I MLine [1 0 0 1 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 0 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 500 5113 4616 5115 4936 5117 4540 5119 4891 5122 5043 5124 4992 5126 4778 5129 5068 5131 5131 5133 5131 5136 5045 5138 5231 5140 4833 5143 5131 5145 4709 5147 5427 5149 4974 5152 4730 5154 4888 5156 5125 5159 5035 5161 5109 5163 4732 5166 5046 5168 5046 5170 4913 5172 4913 5175 4757 5177 4984 5179 4897 5182 4825 5184 5268 5186 5224 5189 5204 5191 4592 5193 5284 5196 5072 5198 5063 5200 5062 5202 5110 5205 4821 5207 5222 5209 4620 5212 4789 5214 5325 5216 4757 5219 5111 5221 5252 5223 4927 5225 5057 5228 5170 5230 5213 5232 5114 5235 4661 5237 5304 5239 4687 5242 5291 5244 4886 5246 5107 5249 4927 5251 4770 5253 4770 5255 4834 5258 5052 5260 5234 5262 4922 5265 5106 5267 4969 5269 4969 5272 5047 5274 5101 5276 4732 5278 4789 5281 4984 5283 4820 5285 4762 5288 4758 5290 5325 5292 5300 5295 5152 5297 5128 5299 4924 5302 4948 5304 4948 5306 4948 5308 4993 5311 4662 5313 5063 5315 5118 5318 4630 5320 5277 5322 4788 5325 5040 5327 4895 5329 4819 5331 4819 5334 4972 5336 5243 5338 4697 5341 4708 5343 4735 5345 4944 5348 5163 5350 5094 5352 4961 5354 4702 5357 4737 5359 5242 5361 4990 5364 4830 5366 5019 5368 4972 5371 4972 5373 5282 5375 5063 5378 5126 5380 5103 5382 5103 5384 4722 5387 5052 5389 5354 5391 4988 5394 4971 5396 4941 5398 4941 5401 4961 5403 4670 5405 4846 5407 4982 5410 4975 5412 5088 5414 4652 5417 5151 5419 5213 5421 4920 5424 5019 5426 5019 5428 4846 5431 5164 5433 4990 5435 4942 5437 4957 5440 5141 5442 5118 5444 4895 5447 5205 5449 5178 5451 5178 5454 4697 5456 4697 5458 4591 5460 5278 5463 5107 5465 4720 5467 4883 5470 5075 5472 5075 5474 5060 5477 5473 5479 4735 5481 4941 5484 5004 5486 5054 5488 4836 5490 5050 5493 5047 5495 4856 5497 5001 5500 4828 5502 4963 5504 5065 5507 4942 5509 4840 5511 5395 5513 4773 5516 4962 5518 4972 5520 5125 5523 5100 5525 5015 5527 5017 5530 4844 5532 5343 5534 5009 5537 5065 5539 5384 5541 5182 5543 5004 5546 5109 5548 4874 5550 4995 5553 4971 5555 5002 5557 5002 5560 4792 5562 4593 5564 4773 5566 4773 5569 5186 5571 5155 5573 4967 5576 4978 5578 4731 5580 5171 5583 4789 5585 4789 5587 4789 5590 4996 5592 4996 5594 5008 5596 4823 5599 4823 5601 4875 5603 5014 5606 5230 5608 4985 5610 4865 5613 4880 5615 5204 5617 5122 5619 4957 5622 4826 5624 4835 5626 4881 5629 5042 5631 5197 5633 5026 5636 4863 5638 5049 5640 4837 5642 4870 5645 5100 5647 5098 5649 5138 5652 4545 5654 4803 5656 4999 5659 4950 5661 4913 5663 4995 5666 5133 5668 4899 5670 4799 5672 4887 5675 4798 5677 5091 5679 4990 5682 4853 5684 5096 5686 5096 5689 5032 5691 5032 5693 5032 5695 4999 5698 4791 5700 4800 5702 4800 5705 4874 5707 4856 5709 4943 5712 4808 5714 5105 5716 5032 5719 4985 5721 4745 5723 4780 5725 5016 5728 5016 5730 5063 5732 4903 5735 5186 5737 4701 5739 5222 5742 5039 5744 5016 5746 5016 5748 4882 5751 5087 5753 5087 5755 5115 5758 5402 5760 4911 5762 5054 5765 5054 5767 4908 5769 4908 5772 4973 5774 4989 5776 4989 5778 5011 5781 4889 5783 5015 5785 5077 5788 5139 5790 5245 5792 4767 5795 5118 5797 4922 5799 5041 5801 5007 5804 5073 5806 5039 5808 4969 5811 5111 5813 5111 5815 4875 5818 5111 5820 4901 5822 4912 5825 5042 5827 4773 5829 4886 5831 5244 5834 4826 5836 4982 5838 4996 5841 4996 5843 4996 5845 5085 5848 5017 5850 5017 5852 5037 5854 4850 5857 5118 5859 4948 5861 4755 5864 5069 5866 5172 5868 4966 5871 4717 5873 5193 5875 5160 5878 4758 5880 4785 5882 5106 5884 4889 5887 4898 5889 4921 5891 4921 5894 4709 5896 5255 5898 4906 5901 4906 5903 4799 5905 4860 5907 4912 5910 5085 5912 4821 5914 5015 5917 4876 5919 4908 5921 4996 5924 4996 5926 4870 5928 5102 5930 4948 5933 4804 5935 4804 5937 4899 5940 4973 5942 4973 5944 4973 5947 5193 5949 5193 5951 5197 5954 5084 5956 4980 5958 4844 5960 5138 5963 5081 5965 4743 5967 5055 5970 5055 5972 4734 5974 4863 5977 5062 5979 5103 5981 4989 5983 4952 5986 5019 5988 4744 5990 4856 5993 5131 5995 5131 5997 4985 6000 4926 6002 5111 6004 5012 6007 5207 6009 5159 6011 5159 6013 5026 6016 5159 6018 4791 6020 5094 6023 5122 6025 4870 6027 5126 6030 5008 6032 4911 6034 4772 6036 5192 6039 4828 6041 4813 6043 4813 6046 4811 6048 4961 6050 5075 6053 5075 6055 4982 6057 4882 6060 5048 6062 4684 6064 5190 6066 4956 6069 4956 6071 5168 6073 4899 6076 4891 6078 4754 6080 4754 6083 4910 6085 5053 6087 5057 6089 4921 6092 4921 6094 4899 6096 4899 6099 5004 6101 5009 6103 5009 6106 4985 6108 4934 6110 4934 6113 5063 6115 5063 6117 5040 6119 5040 6122 4826 6124 4802 6126 4729 6129 4729 6131 4903 6133 4951 6136 5091 6138 5091 6140 5009 6142 4810 6145 5070 6147 4822 6149 5028 6152 5028 6154 4874 6156 4985 6159 4952 6161 4918 6163 4790 6166 4972 6168 4944 6170 4873 6172 4924 6175 4723 6177 4942 6179 4994 6182 4958 6184 4958 6186 4958 6189 4975 6191 5000 6193 5267 6195 5080 6198 4910 6200 4838 6202 4838 6205 5128 6207 5136 6209 4845 6212 4840 6214 4840 6216 4840 6218 4840 6221 4897 6223 5000 6225 4893 6228 5148 6230 4831 6232 4994 6235 4908 6237 5023 6239 5014 6242 5032 6244 5032 6246 5060 6248 4918 6251 4918 6253 4999 6255 4919 6258 4925 6260 4957 6262 5204 500 MLine End Begin %I MLine [1 0 0 1 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 0 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 500 6262 5204 6265 4829 6267 4977 6269 4803 6271 5030 6274 5015 6276 4984 6278 4984 6281 4919 6283 4890 6285 4928 6288 4928 6290 4928 6292 4928 6295 4966 6297 5039 6299 5039 6301 5163 6304 4981 6306 4823 6308 4979 6311 4943 6313 4856 6315 4856 6318 4856 6320 4849 6322 4961 6324 4948 6327 4948 6329 4973 6331 4926 6334 4926 6336 4967 6338 4952 6341 5017 6343 5017 6345 4924 6348 4851 6350 4971 6352 4965 6354 4965 6357 5061 6359 4912 6361 4949 6364 4949 6366 4949 6368 5015 6371 4796 6373 4853 6375 4857 6377 4863 6380 4835 6382 4835 6384 4929 6387 4929 6389 5048 6391 4861 6394 4954 6396 4954 6398 4721 6401 4981 6403 4883 6405 4883 6407 4883 6410 5004 6412 5062 6414 5053 6417 5053 6419 5053 6421 4855 6424 4965 6426 4965 6428 4867 6430 4867 6433 5011 6435 4928 6437 5022 6440 5022 6442 5022 6444 4956 6447 4811 6449 4995 6451 4969 6454 4850 6456 5041 6458 5007 6460 5079 6463 4849 6465 4990 6467 4990 6470 5034 6472 4899 6474 4899 6477 4840 6479 4936 6481 5032 6483 5005 6486 4909 6488 5033 6490 5033 6493 5121 6495 5043 6497 5062 6500 5062 6502 5008 6504 4966 6506 4891 6509 4914 6511 4884 6513 4884 6516 4990 6518 4990 6520 4990 6523 4990 6525 5066 6527 5022 6530 4993 6532 4889 6534 5020 6536 5020 6539 5076 6541 4916 6543 5141 6546 5098 6548 5081 6550 4851 6553 5033 6555 4977 6557 4977 6559 5003 6562 4821 6564 5113 6566 4972 6569 5022 6571 4912 6573 5009 6576 5009 6578 5034 6580 4985 6583 5099 6585 4979 6587 4942 6589 4942 6592 4978 6594 4898 6596 4999 6599 4999 6601 4999 6603 4999 6606 4773 6608 5153 6610 5153 6612 4942 6615 4932 6617 4969 6619 5016 6622 5016 6624 5057 6626 4999 6629 4802 6631 4967 6633 5076 6636 4861 6638 4861 6640 4861 6642 4911 6645 5018 6647 5018 6649 5050 6652 5050 6654 5007 6656 5007 6659 4989 6661 4989 6663 4989 6665 4919 6668 5017 6670 5017 6672 4934 6675 4808 6677 4878 6679 4878 6682 4873 6684 4952 6686 4911 6689 4901 6691 4901 6693 4831 6695 4831 6698 5011 6700 4972 6702 4972 6705 4972 6707 4972 6709 4954 6712 5140 6714 5034 6716 4957 6718 4952 6721 4952 6723 4952 6725 4989 6728 4992 6730 5035 6732 5042 6735 5042 6737 5042 6739 4941 6742 4941 6744 4941 6746 5009 6748 5009 6751 4980 6753 5004 6755 4971 6758 5020 6760 5020 6762 4901 6765 4952 6767 4994 6769 4924 6771 4924 6774 4924 6776 4924 6778 4924 6781 4939 6783 5005 6785 4866 6788 4866 6790 5088 6792 4807 6794 4807 6797 5005 6799 4937 6801 4937 6804 4937 6806 4937 6808 5052 6811 4903 6813 4903 6815 4903 6818 4903 6820 5019 6822 4933 6824 4933 6827 5038 6829 5048 6831 4959 6834 5007 6836 4936 6838 4973 6841 4943 6843 4963 6845 4835 6847 4980 6850 4980 6852 4981 6854 4980 6857 4980 6859 5043 6861 4970 6864 4985 6866 4965 6868 4965 6871 4993 6873 4993 6875 4993 6877 4905 6880 4905 6882 4905 6884 4905 6887 5031 6889 4873 6891 4963 6894 4878 6896 4921 6898 4921 6900 4921 6903 4921 6905 4921 6907 4868 6910 4971 6912 4971 6914 4971 6917 5008 6919 4925 6921 4925 6924 4902 6926 4926 6928 4926 6930 4990 6933 4990 6935 4990 6937 5024 6940 5024 6942 5024 6944 4917 6947 4917 6949 5052 6951 5052 6953 5008 6956 4971 6958 4971 6960 4971 6963 4925 6965 4936 6967 4829 6970 4920 6972 4884 6974 4901 6977 4861 6979 4890 6981 5026 6983 5008 6986 4901 6988 4881 6990 4881 6993 4894 6995 4904 6997 5007 7000 5007 7002 5007 7004 5007 7006 5007 7009 5007 7011 4993 7013 4993 7016 5034 7018 5034 7020 5034 7023 5034 7025 4883 7027 5040 7030 4933 7032 4933 7034 4933 7036 4933 7039 4933 7041 4933 7043 4933 7046 4933 7048 4933 7050 4933 7053 4933 7055 4964 7057 4893 7059 4876 7062 4919 7064 4919 7066 4919 7069 4919 7071 4896 7073 5002 7076 4855 7078 4955 7080 5032 7082 4996 7085 4996 7087 4996 7089 4973 7092 5095 7094 4850 7096 4901 7099 4904 7101 4904 7103 4904 7106 4904 7108 4904 7110 4996 7112 4886 7115 4886 7117 4919 7119 4919 7122 4919 7124 5023 7126 4913 7129 4913 7131 4913 7133 4913 7135 4913 7138 5032 7140 4971 7142 4971 7145 4971 7147 4971 7149 4971 7152 4971 7154 4971 7156 4971 7159 4971 7161 4926 7163 5022 7165 5005 7168 5005 7170 4882 7172 4922 7175 4924 7177 4924 7179 4924 7182 4924 7184 5028 7186 4879 7188 4879 7191 4879 7193 4879 7195 4965 7198 4965 7200 4939 7202 4875 7205 4909 7207 4973 7209 4973 7212 4987 7214 4903 7216 4903 7218 4903 7221 4903 7223 4903 7225 4965 7228 4965 7230 4944 7232 4989 7235 4883 7237 4883 7239 4973 7241 4952 7244 4952 7246 4994 7248 4994 7251 4993 7253 4957 7255 4996 7258 4924 7260 4985 7262 4985 7265 4943 7267 4943 7269 4943 7271 4943 7274 4943 7276 4880 7278 4875 7281 4899 7283 4822 7285 4883 7288 4883 7290 4883 7292 4883 7294 4922 7297 4922 7299 5007 7301 5007 7304 5001 7306 5001 7308 5001 7311 4969 7313 4882 7315 4956 7318 4956 7320 4920 7322 4920 7324 4920 7327 4911 7329 4911 7331 4944 7334 4924 7336 4924 7338 5050 7341 5050 7343 5063 7345 4922 7347 4922 7350 4922 7352 4922 7354 4979 7357 4979 7359 4932 7361 4970 7364 5004 7366 4972 7368 4972 7370 4972 7373 4972 7375 4972 7377 4939 7380 4939 7382 4939 7384 4939 7387 4939 7389 4859 7391 4842 7394 4999 7396 4999 7398 4999 7400 4929 7403 4929 7405 4929 7407 4958 7410 4996 7412 4996 500 MLine End Begin %I MLine [1 0 0 1 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 0 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 500 7412 4996 7414 5039 7417 5039 7419 5035 7421 4922 7423 4952 7426 5009 7428 4898 7430 4898 7433 4898 7435 4868 7437 5033 7440 5033 7442 5033 7444 5033 7447 5033 7449 4988 7451 4988 7453 4941 7456 5012 7458 4980 7460 4980 7463 4980 7465 5018 7467 4935 7470 4935 7472 4962 7474 4962 7476 4962 7479 4996 7481 4996 7483 4959 7486 4959 7488 4973 7490 4973 7493 4973 7495 4999 7497 5052 7500 5102 7502 5066 7504 5066 7506 5066 7509 4905 7511 4905 7513 4905 7516 4965 7518 4961 7520 4961 7523 4961 7525 4961 7527 4994 7529 4994 7532 5001 7534 4928 7536 5045 7539 5045 7541 5045 7543 5023 7546 4995 7548 4974 7550 4974 7553 5037 7555 4990 7557 4990 7559 4990 7562 4990 7564 4990 7566 4990 7569 4990 7571 4990 7573 4905 7576 4905 7578 4905 7580 4905 7582 5017 7585 5017 7587 4984 7589 5049 7592 4999 7594 4999 7596 4999 7599 4931 7601 4981 7603 4981 7606 4981 7608 5007 7610 5007 7612 5007 7615 5007 7617 4948 7619 4950 7622 4950 7624 4979 7626 4935 7629 4935 7631 4935 7633 4936 7635 4956 7638 4956 7640 5011 7642 5011 7645 5011 7647 5011 7649 5011 7652 5011 7654 4984 7656 5012 7658 5012 7661 4975 7663 4975 7665 4975 7668 4975 7670 4916 7672 4916 7675 4903 7677 4903 7679 4903 7682 4979 7684 4979 7686 4949 7688 4871 7691 4852 7693 4852 7695 5010 7698 5010 7700 5010 7702 5010 7705 4982 7707 4911 7709 5007 7711 4901 7714 4924 7716 4954 7718 4954 7721 4954 7723 4956 7725 4967 7728 4967 7730 4967 7732 4947 7735 4947 7737 4948 7739 4948 7741 4948 7744 4948 7746 4948 7748 4948 7751 4919 7753 5012 7755 4956 7758 4956 7760 4956 7762 4956 7764 4956 7767 4961 7769 4961 7771 4980 7774 4980 7776 4980 7778 4980 7781 4980 7783 4980 7785 4980 7788 4959 7790 4959 7792 4959 7794 4959 7797 4959 7799 4959 7801 4959 7804 5049 7806 5049 7808 4919 7811 5015 7813 5015 7815 5015 7817 5015 7820 5015 7822 5010 7824 4959 7827 4959 7829 4959 7831 4980 7834 4980 7836 4980 7838 4966 7841 4966 7843 4966 7845 4966 7847 4974 7850 4974 7852 5012 7854 4913 7857 4913 7859 4952 7861 4952 7864 4952 7866 4952 7868 4952 7870 4986 7873 4942 7875 4942 7877 4919 7880 5031 7882 5031 7884 5031 7887 4927 7889 4927 7891 4966 7894 4966 7896 5030 7898 4948 7900 4948 7903 4948 7905 4975 7907 4975 7910 4967 7912 4888 7914 4917 7917 4987 7919 4944 7921 4909 7923 4909 7926 4909 7928 4975 7930 4975 7933 4975 7935 4916 7937 4921 7940 4950 7942 4950 7944 4979 7946 4979 7949 4979 7951 4979 7953 4979 7956 4972 7958 4947 7960 4980 7963 4946 7965 4946 7967 4940 7970 4940 7972 4940 7974 4940 7976 4975 7979 4989 7981 4989 7983 4989 7986 4936 7988 5001 7990 5001 7993 5001 7995 4965 7997 4933 7999 4933 8002 4948 8004 4971 8006 4971 8009 4971 8011 4971 8013 4971 8016 4979 8018 4979 8020 4979 8023 4969 8025 5017 8027 5017 8029 5017 8032 4928 8034 4966 8036 4940 8039 4940 8041 4940 8043 4940 8046 4940 8048 4940 8050 5024 8052 5024 8055 5024 8057 4995 8059 4996 8062 4996 8064 4996 8066 4996 8069 4996 8071 4996 8073 4996 8076 4996 8078 4996 8080 4996 8082 4940 8085 4940 8087 4940 8089 4940 8092 4980 8094 4980 8096 4980 8099 4996 8101 4996 8103 4979 8105 4990 8108 4990 8110 5019 8112 5019 8115 5019 8117 5019 8119 4944 8122 4966 8124 5002 8126 5002 8129 5002 8131 5002 8133 5002 8135 5002 8138 5009 8140 4946 8142 4946 8145 4946 8147 4946 8149 5002 8152 5002 8154 5002 8156 5002 8158 5002 8161 5002 8163 5002 8165 5012 8168 5012 8170 5012 8172 5012 8175 5012 8177 4919 8179 4919 8182 4980 8184 4985 8186 4985 8188 4985 8191 4985 8193 4985 8195 4985 8198 4979 8200 4979 8202 4937 8205 4937 8207 4937 8209 4937 8211 4937 8214 4937 8216 4937 8218 4937 8221 4937 8223 4937 8225 4937 8228 4937 8230 4937 8232 4937 8234 4961 8237 4966 8239 4966 8241 4966 8244 4966 8246 4966 8248 4966 8251 4966 8253 4966 8255 4966 8258 5002 8260 5002 8262 5002 8264 4995 8267 4965 8269 4965 8271 4965 8274 4965 8276 4965 8278 4933 8281 4933 8283 4933 8285 4933 8287 4933 8290 4933 8292 4933 8294 4996 8297 4996 8299 4996 8301 4996 8304 4996 8306 4996 8308 4996 8311 4996 8313 4996 8315 4996 8317 4929 8320 4988 8322 4988 8324 4988 8327 4939 8329 4979 8331 4964 8334 4964 8336 4964 8338 4964 8340 4964 8343 4964 8345 4964 8347 4964 8350 4964 8352 4964 8354 4964 8357 4964 8359 4964 8361 4964 8364 4964 8366 4964 8368 4964 8370 4964 8373 4964 8375 4964 8377 4964 8380 4964 8382 4964 8384 4966 8387 4966 8389 4966 8391 4952 8393 4952 8396 4952 8398 4952 8400 4952 8403 4986 8405 4986 8407 4986 8410 5018 8412 5018 8414 5018 8417 5018 8419 5005 8421 5005 8423 5005 8426 5005 8428 5005 8430 4949 8433 4949 8435 4941 8437 4941 8440 4941 8442 4941 8444 4941 8446 4961 8449 4954 8451 4957 8453 4957 8456 4971 8458 4971 8460 4970 8463 4970 8465 4946 8467 5009 8470 5009 8472 4959 8474 4959 8476 4959 8479 4959 8481 4984 8483 5020 8486 5020 8488 4914 8490 4914 8493 4914 8495 4973 8497 4973 8499 4973 8502 4973 8504 4973 8506 4973 8509 4973 8511 4973 8513 4973 8516 4973 8518 4947 8520 4979 8522 4979 8525 4979 8527 4979 8529 4979 8532 4979 8534 4979 8536 4955 8539 4955 8541 4955 8543 4955 8546 4986 8548 4951 8550 4951 8552 4951 8555 4951 8557 4951 8559 4951 8562 4951 500 MLine End Begin %I MLine [1 0 0 1 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 0 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 53 8562 4951 8564 4943 8566 4963 8569 4985 8571 4985 8573 4985 8575 4995 8578 4996 8580 4964 8582 4964 8585 4981 8587 4981 8589 4917 8592 4959 8594 4959 8596 4959 8599 4959 8601 4959 8603 4959 8605 4959 8608 4980 8610 4980 8612 4980 8615 4947 8617 4947 8619 4947 8622 4947 8624 4942 8626 4929 8628 4929 8631 4932 8633 4932 8635 4932 8638 4932 8640 4932 8642 4932 8645 4937 8647 4937 8649 4937 8652 4964 8654 4964 8656 4997 8658 5004 8661 4973 8663 4973 8665 4984 8668 4984 8670 4973 8672 4973 8675 4973 8677 4986 8679 4980 8681 4980 53 MLine End %%PageTrailer End %I eop showpage %%Trailer end %%EOF %%EndDocument @endspecial 1645 x @beginspecial 49 @llx 177 @lly 500 @urx 576 @ury 2016 @rwi @setspecial %%BeginDocument: siman-energy.eps %!PS-Adobe-3.0 EPSF-3.0 %%Creator: GNU libplot drawing library 4.1 %%Title: PostScript plot %%CreationDate: Wed Dec 20 22:05:31 2006 %%DocumentData: Clean7Bit %%LanguageLevel: 1 %%Pages: 1 %%PageOrder: Ascend %%Orientation: Portrait %%BoundingBox: 49 177 500 576 %%DocumentNeededResources: %%DocumentSuppliedResources: procset GNU_libplot 1.0 0 %%EndComments %%BeginDefaults %%PageResources: %%EndDefaults %%BeginProlog %%EndProlog %%BeginSetup /DrawDict 50 dict def DrawDict begin %%BeginResource procset GNU_libplot 1.0 0 /none null def /numGraphicParameters 17 def /stringLimit 65535 def /arrowHeight 8 def /eoFillRule true def /Begin { save numGraphicParameters dict begin } def /End { end restore } def /SetB { dup type /nulltype eq { pop false /brushRightArrow idef false /brushLeftArrow idef true /brushNone idef } { /brushDashOffset idef /brushDashArray idef 0 ne /brushRightArrow idef 0 ne /brushLeftArrow idef /brushWidth idef false /brushNone idef } ifelse } def /SetCFg { /fgblue idef /fggreen idef /fgred idef } def /SetCBg { /bgblue idef /bggreen idef /bgred idef } def /SetF { /printSize idef /printFont idef } def /SetP { dup type /nulltype eq { pop true /patternNone idef } { /patternGrayLevel idef patternGrayLevel -1 eq { /patternString idef } if false /patternNone idef } ifelse } def /BSpl { 0 begin storexyn newpath n 1 gt { 0 0 0 0 0 0 1 1 true subspline n 2 gt { 0 0 0 0 1 1 2 2 false subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 2 copy false subspline } if n 2 sub dup n 1 sub dup 2 copy 2 copy false subspline patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup 1 sub dup rightarrow } if end } dup 0 4 dict put def /Circ { newpath 0 360 arc closepath patternNone not { ifill } if brushNone not { istroke } if } def /CBSpl { 0 begin dup 2 gt { storexyn newpath n 1 sub dup 0 0 1 1 2 2 true subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 0 0 false subspline n 2 sub dup n 1 sub dup 0 0 1 1 false subspline patternNone not { ifill } if brushNone not { istroke } if } { Poly } ifelse end } dup 0 4 dict put def /Elli { 0 begin newpath 4 2 roll translate scale 0 0 1 0 360 arc closepath patternNone not { ifill } if brushNone not { istroke } if end } dup 0 1 dict put def /Line { 0 begin 2 storexyn newpath x 0 get y 0 get moveto x 1 get y 1 get lineto brushNone not { istroke } if 0 0 1 1 leftarrow 0 0 1 1 rightarrow end } dup 0 4 dict put def /MLine { 0 begin storexyn newpath n 1 gt { x 0 get y 0 get moveto 1 1 n 1 sub { /i exch def x i get y i get lineto } for patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Poly { 3 1 roll newpath moveto -1 add { lineto } repeat closepath patternNone not { ifill } if brushNone not { istroke } if } def /Rect { 0 begin /t exch def /r exch def /b exch def /l exch def newpath l b moveto l t lineto r t lineto r b lineto closepath patternNone not { ifill } if brushNone not { istroke } if end } dup 0 4 dict put def /Text { ishow } def /idef { dup where { pop pop pop } { exch def } ifelse } def /ifill { 0 begin gsave patternGrayLevel -1 ne { fgred bgred fgred sub patternGrayLevel mul add fggreen bggreen fggreen sub patternGrayLevel mul add fgblue bgblue fgblue sub patternGrayLevel mul add setrgbcolor eoFillRule { eofill } { fill } ifelse } { eoFillRule { eoclip } { clip } ifelse originalCTM setmatrix pathbbox /t exch def /r exch def /b exch def /l exch def /w r l sub ceiling cvi def /h t b sub ceiling cvi def /imageByteWidth w 8 div ceiling cvi def /imageHeight h def bgred bggreen bgblue setrgbcolor eoFillRule { eofill } { fill } ifelse fgred fggreen fgblue setrgbcolor w 0 gt h 0 gt and { l b translate w h scale w h true [w 0 0 h neg 0 h] { patternproc } imagemask } if } ifelse grestore end } dup 0 8 dict put def /istroke { gsave brushDashOffset -1 eq { [] 0 setdash 1 setgray } { brushDashArray brushDashOffset setdash fgred fggreen fgblue setrgbcolor } ifelse brushWidth setlinewidth originalCTM setmatrix stroke grestore } def /ishow { 0 begin gsave fgred fggreen fgblue setrgbcolor /fontDict printFont findfont printSize scalefont dup setfont def /descender fontDict begin 0 /FontBBox load 1 get FontMatrix end transform exch pop def /vertoffset 1 printSize sub descender sub def { 0 vertoffset moveto show /vertoffset vertoffset printSize sub def } forall grestore end } dup 0 3 dict put def /patternproc { 0 begin /patternByteLength patternString length def /patternHeight patternByteLength 8 mul sqrt cvi def /patternWidth patternHeight def /patternByteWidth patternWidth 8 idiv def /imageByteMaxLength imageByteWidth imageHeight mul stringLimit patternByteWidth sub min def /imageMaxHeight imageByteMaxLength imageByteWidth idiv patternHeight idiv patternHeight mul patternHeight max def /imageHeight imageHeight imageMaxHeight sub store /imageString imageByteWidth imageMaxHeight mul patternByteWidth add string def 0 1 imageMaxHeight 1 sub { /y exch def /patternRow y patternByteWidth mul patternByteLength mod def /patternRowString patternString patternRow patternByteWidth getinterval def /imageRow y imageByteWidth mul def 0 patternByteWidth imageByteWidth 1 sub { /x exch def imageString imageRow x add patternRowString putinterval } for } for imageString end } dup 0 12 dict put def /min { dup 3 2 roll dup 4 3 roll lt { exch } if pop } def /max { dup 3 2 roll dup 4 3 roll gt { exch } if pop } def /midpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 x1 add 2 div y0 y1 add 2 div end } dup 0 4 dict put def /thirdpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 2 mul x1 add 3 div y0 2 mul y1 add 3 div end } dup 0 4 dict put def /subspline { 0 begin /movetoNeeded exch def y exch get /y3 exch def x exch get /x3 exch def y exch get /y2 exch def x exch get /x2 exch def y exch get /y1 exch def x exch get /x1 exch def y exch get /y0 exch def x exch get /x0 exch def x1 y1 x2 y2 thirdpoint /p1y exch def /p1x exch def x2 y2 x1 y1 thirdpoint /p2y exch def /p2x exch def x1 y1 x0 y0 thirdpoint p1x p1y midpoint /p0y exch def /p0x exch def x2 y2 x3 y3 thirdpoint p2x p2y midpoint /p3y exch def /p3x exch def movetoNeeded { p0x p0y moveto } if p1x p1y p2x p2y p3x p3y curveto end } dup 0 17 dict put def /storexyn { /n exch def /y n array def /x n array def n 1 sub -1 0 { /i exch def y i 3 2 roll put x i 3 2 roll put } for } def /arrowhead { 0 begin transform originalCTM itransform /taily exch def /tailx exch def transform originalCTM itransform /tipy exch def /tipx exch def /dy tipy taily sub def /dx tipx tailx sub def /angle dx 0 ne dy 0 ne or { dy dx atan } { 90 } ifelse def gsave originalCTM setmatrix tipx tipy translate angle rotate newpath arrowHeight neg arrowWidth 2 div moveto 0 0 lineto arrowHeight neg arrowWidth 2 div neg lineto patternNone not { originalCTM setmatrix /padtip arrowHeight 2 exp 0.25 arrowWidth 2 exp mul add sqrt brushWidth mul arrowWidth div def /padtail brushWidth 2 div def tipx tipy translate angle rotate padtip 0 translate arrowHeight padtip add padtail add arrowHeight div dup scale arrowheadpath ifill } if brushNone not { originalCTM setmatrix tipx tipy translate angle rotate arrowheadpath istroke } if grestore end } dup 0 9 dict put def /arrowheadpath { newpath arrowHeight neg arrowWidth 2 div moveto 0 0 lineto arrowHeight neg arrowWidth 2 div neg lineto } def /leftarrow { 0 begin y exch get /taily exch def x exch get /tailx exch def y exch get /tipy exch def x exch get /tipx exch def brushLeftArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /rightarrow { 0 begin y exch get /tipy exch def x exch get /tipx exch def y exch get /taily exch def x exch get /tailx exch def brushRightArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def %%EndResource %%EndSetup %%Page: 1 1 %%PageResources: %%PageBoundingBox: 49 177 500 576 %%BeginPageSetup %I Idraw 8 Begin %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 1 0 0 1 0 0 ] concat /originalCTM matrix currentmatrix def /trueoriginalCTM matrix currentmatrix def %%EndPageSetup Begin %I Rect [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2304 2304 9216 9216 Rect End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 2315 2151 2348 2140 2370 2107 2381 2052 2381 2019 2370 1964 2348 1931 2315 1920 2293 1920 2260 1931 2238 1964 2227 2019 2227 2052 2238 2107 2260 2140 2293 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 2293 2151 2271 2140 2260 2129 2249 2107 2238 2052 2238 2019 2249 1964 2260 1942 2271 1931 2293 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 2315 1920 2337 1931 2348 1942 2359 1964 2370 2019 2370 2052 2359 2107 2348 2129 2337 2140 2315 2151 10 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 9216 2304 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2304 2304 2442 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3181 2151 3159 2041 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 19 3159 2041 3181 2063 3214 2074 3247 2074 3280 2063 3302 2041 3313 2008 3313 1986 3302 1953 3280 1931 3247 1920 3214 1920 3181 1931 3170 1942 3159 1964 3159 1975 3170 1986 3181 1975 3170 1964 19 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 3247 2074 3269 2063 3291 2041 3302 2008 3302 1986 3291 1953 3269 1931 3247 1920 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3181 2151 3291 2151 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 3181 2140 3236 2140 3291 2151 3 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 3467 2151 3500 2140 3522 2107 3533 2052 3533 2019 3522 1964 3500 1931 3467 1920 3445 1920 3412 1931 3390 1964 3379 2019 3379 2052 3390 2107 3412 2140 3445 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 3445 2151 3423 2140 3412 2129 3401 2107 3390 2052 3390 2019 3401 1964 3412 1942 3423 1931 3445 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 3467 1920 3489 1931 3500 1942 3511 1964 3522 2019 3522 2052 3511 2107 3500 2129 3489 2140 3467 2151 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 3687 2151 3720 2140 3742 2107 3753 2052 3753 2019 3742 1964 3720 1931 3687 1920 3665 1920 3632 1931 3610 1964 3599 2019 3599 2052 3610 2107 3632 2140 3665 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 3665 2151 3643 2140 3632 2129 3621 2107 3610 2052 3610 2019 3621 1964 3632 1942 3643 1931 3665 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 3687 1920 3709 1931 3720 1942 3731 1964 3742 2019 3742 2052 3731 2107 3720 2129 3709 2140 3687 2151 10 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3456 9216 3456 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3456 2304 3456 2442 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 4234 2107 4256 2118 4289 2151 4289 1920 4 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4278 2140 4278 1920 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4234 1920 4333 1920 2 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 4509 2151 4542 2140 4564 2107 4575 2052 4575 2019 4564 1964 4542 1931 4509 1920 4487 1920 4454 1931 4432 1964 4421 2019 4421 2052 4432 2107 4454 2140 4487 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 4487 2151 4465 2140 4454 2129 4443 2107 4432 2052 4432 2019 4443 1964 4454 1942 4465 1931 4487 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 4509 1920 4531 1931 4542 1942 4553 1964 4564 2019 4564 2052 4553 2107 4542 2129 4531 2140 4509 2151 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 4729 2151 4762 2140 4784 2107 4795 2052 4795 2019 4784 1964 4762 1931 4729 1920 4707 1920 4674 1931 4652 1964 4641 2019 4641 2052 4652 2107 4674 2140 4707 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 4707 2151 4685 2140 4674 2129 4663 2107 4652 2052 4652 2019 4663 1964 4674 1942 4685 1931 4707 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 4729 1920 4751 1931 4762 1942 4773 1964 4784 2019 4784 2052 4773 2107 4762 2129 4751 2140 4729 2151 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 4949 2151 4982 2140 5004 2107 5015 2052 5015 2019 5004 1964 4982 1931 4949 1920 4927 1920 4894 1931 4872 1964 4861 2019 4861 2052 4872 2107 4894 2140 4927 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 4927 2151 4905 2140 4894 2129 4883 2107 4872 2052 4872 2019 4883 1964 4894 1942 4905 1931 4927 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 4949 1920 4971 1931 4982 1942 4993 1964 5004 2019 5004 2052 4993 2107 4982 2129 4971 2140 4949 2151 10 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4608 9216 4608 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4608 2304 4608 2442 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 5386 2107 5408 2118 5441 2151 5441 1920 4 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5430 2140 5430 1920 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5386 1920 5485 1920 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5595 2151 5573 2041 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 19 5573 2041 5595 2063 5628 2074 5661 2074 5694 2063 5716 2041 5727 2008 5727 1986 5716 1953 5694 1931 5661 1920 5628 1920 5595 1931 5584 1942 5573 1964 5573 1975 5584 1986 5595 1975 5584 1964 19 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 5661 2074 5683 2063 5705 2041 5716 2008 5716 1986 5705 1953 5683 1931 5661 1920 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5595 2151 5705 2151 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 5595 2140 5650 2140 5705 2151 3 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 5881 2151 5914 2140 5936 2107 5947 2052 5947 2019 5936 1964 5914 1931 5881 1920 5859 1920 5826 1931 5804 1964 5793 2019 5793 2052 5804 2107 5826 2140 5859 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 5859 2151 5837 2140 5826 2129 5815 2107 5804 2052 5804 2019 5815 1964 5826 1942 5837 1931 5859 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 5881 1920 5903 1931 5914 1942 5925 1964 5936 2019 5936 2052 5925 2107 5914 2129 5903 2140 5881 2151 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 6101 2151 6134 2140 6156 2107 6167 2052 6167 2019 6156 1964 6134 1931 6101 1920 6079 1920 6046 1931 6024 1964 6013 2019 6013 2052 6024 2107 6046 2140 6079 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 6079 2151 6057 2140 6046 2129 6035 2107 6024 2052 6024 2019 6035 1964 6046 1942 6057 1931 6079 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 6101 1920 6123 1931 6134 1942 6145 1964 6156 2019 6156 2052 6145 2107 6134 2129 6123 2140 6101 2151 10 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5760 9216 5760 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5760 2304 5760 2442 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 20 6516 2107 6527 2096 6516 2085 6505 2096 6505 2107 6516 2129 6527 2140 6560 2151 6604 2151 6637 2140 6648 2129 6659 2107 6659 2085 6648 2063 6615 2041 6560 2019 6538 2008 6516 1986 6505 1953 6505 1920 20 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 6604 2151 6626 2140 6637 2129 6648 2107 6648 2085 6637 2063 6604 2041 6560 2019 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 6505 1942 6516 1953 6538 1953 6593 1931 6626 1931 6648 1942 6659 1953 7 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 6538 1953 6593 1920 6637 1920 6648 1931 6659 1953 6659 1975 6 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 6813 2151 6846 2140 6868 2107 6879 2052 6879 2019 6868 1964 6846 1931 6813 1920 6791 1920 6758 1931 6736 1964 6725 2019 6725 2052 6736 2107 6758 2140 6791 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 6791 2151 6769 2140 6758 2129 6747 2107 6736 2052 6736 2019 6747 1964 6758 1942 6769 1931 6791 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 6813 1920 6835 1931 6846 1942 6857 1964 6868 2019 6868 2052 6857 2107 6846 2129 6835 2140 6813 2151 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 7033 2151 7066 2140 7088 2107 7099 2052 7099 2019 7088 1964 7066 1931 7033 1920 7011 1920 6978 1931 6956 1964 6945 2019 6945 2052 6956 2107 6978 2140 7011 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 7011 2151 6989 2140 6978 2129 6967 2107 6956 2052 6956 2019 6967 1964 6978 1942 6989 1931 7011 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 7033 1920 7055 1931 7066 1942 7077 1964 7088 2019 7088 2052 7077 2107 7066 2129 7055 2140 7033 2151 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 7253 2151 7286 2140 7308 2107 7319 2052 7319 2019 7308 1964 7286 1931 7253 1920 7231 1920 7198 1931 7176 1964 7165 2019 7165 2052 7176 2107 7198 2140 7231 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 7231 2151 7209 2140 7198 2129 7187 2107 7176 2052 7176 2019 7187 1964 7198 1942 7209 1931 7231 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 7253 1920 7275 1931 7286 1942 7297 1964 7308 2019 7308 2052 7297 2107 7286 2129 7275 2140 7253 2151 10 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6912 9216 6912 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6912 2304 6912 2442 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 20 7668 2107 7679 2096 7668 2085 7657 2096 7657 2107 7668 2129 7679 2140 7712 2151 7756 2151 7789 2140 7800 2129 7811 2107 7811 2085 7800 2063 7767 2041 7712 2019 7690 2008 7668 1986 7657 1953 7657 1920 20 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 7756 2151 7778 2140 7789 2129 7800 2107 7800 2085 7789 2063 7756 2041 7712 2019 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 7657 1942 7668 1953 7690 1953 7745 1931 7778 1931 7800 1942 7811 1953 7 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 7690 1953 7745 1920 7789 1920 7800 1931 7811 1953 7811 1975 6 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7899 2151 7877 2041 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 19 7877 2041 7899 2063 7932 2074 7965 2074 7998 2063 8020 2041 8031 2008 8031 1986 8020 1953 7998 1931 7965 1920 7932 1920 7899 1931 7888 1942 7877 1964 7877 1975 7888 1986 7899 1975 7888 1964 19 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 7965 2074 7987 2063 8009 2041 8020 2008 8020 1986 8009 1953 7987 1931 7965 1920 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7899 2151 8009 2151 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 7899 2140 7954 2140 8009 2151 3 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 8185 2151 8218 2140 8240 2107 8251 2052 8251 2019 8240 1964 8218 1931 8185 1920 8163 1920 8130 1931 8108 1964 8097 2019 8097 2052 8108 2107 8130 2140 8163 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 8163 2151 8141 2140 8130 2129 8119 2107 8108 2052 8108 2019 8119 1964 8130 1942 8141 1931 8163 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 8185 1920 8207 1931 8218 1942 8229 1964 8240 2019 8240 2052 8229 2107 8218 2129 8207 2140 8185 2151 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 8405 2151 8438 2140 8460 2107 8471 2052 8471 2019 8460 1964 8438 1931 8405 1920 8383 1920 8350 1931 8328 1964 8317 2019 8317 2052 8328 2107 8350 2140 8383 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 8383 2151 8361 2140 8350 2129 8339 2107 8328 2052 8328 2019 8339 1964 8350 1942 8361 1931 8383 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 8405 1920 8427 1931 8438 1942 8449 1964 8460 2019 8460 2052 8449 2107 8438 2129 8427 2140 8405 2151 10 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8064 9216 8064 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8064 2304 8064 2442 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 8820 2107 8831 2096 8820 2085 8809 2096 8809 2107 8820 2129 8831 2140 8864 2151 8908 2151 8941 2140 8952 2118 8952 2085 8941 2063 8908 2052 8875 2052 15 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 8908 2151 8930 2140 8941 2118 8941 2085 8930 2063 8908 2052 6 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 8908 2052 8930 2041 8952 2019 8963 1997 8963 1964 8952 1942 8941 1931 8908 1920 8864 1920 8831 1931 8820 1942 8809 1964 8809 1975 8820 1986 8831 1975 8820 1964 16 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 8941 2030 8952 1997 8952 1964 8941 1942 8930 1931 8908 1920 6 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 9117 2151 9150 2140 9172 2107 9183 2052 9183 2019 9172 1964 9150 1931 9117 1920 9095 1920 9062 1931 9040 1964 9029 2019 9029 2052 9040 2107 9062 2140 9095 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 9095 2151 9073 2140 9062 2129 9051 2107 9040 2052 9040 2019 9051 1964 9062 1942 9073 1931 9095 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 9117 1920 9139 1931 9150 1942 9161 1964 9172 2019 9172 2052 9161 2107 9150 2129 9139 2140 9117 2151 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 9337 2151 9370 2140 9392 2107 9403 2052 9403 2019 9392 1964 9370 1931 9337 1920 9315 1920 9282 1931 9260 1964 9249 2019 9249 2052 9260 2107 9282 2140 9315 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 9315 2151 9293 2140 9282 2129 9271 2107 9260 2052 9260 2019 9271 1964 9282 1942 9293 1931 9315 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 9337 1920 9359 1931 9370 1942 9381 1964 9392 2019 9392 2052 9381 2107 9370 2129 9359 2140 9337 2151 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 9557 2151 9590 2140 9612 2107 9623 2052 9623 2019 9612 1964 9590 1931 9557 1920 9535 1920 9502 1931 9480 1964 9469 2019 9469 2052 9480 2107 9502 2140 9535 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 9535 2151 9513 2140 9502 2129 9491 2107 9480 2052 9480 2019 9491 1964 9502 1942 9513 1931 9535 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 9557 1920 9579 1931 9590 1942 9601 1964 9612 2019 9612 2052 9601 2107 9590 2129 9579 2140 9557 2151 10 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 9216 9216 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2304 9216 2442 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1189 2304 1387 2304 2 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 1552 2436 1585 2425 1607 2392 1618 2337 1618 2304 1607 2249 1585 2216 1552 2205 1530 2205 1497 2216 1475 2249 1464 2304 1464 2337 1475 2392 1497 2425 1530 2436 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 1530 2436 1508 2425 1497 2414 1486 2392 1475 2337 1475 2304 1486 2249 1497 2227 1508 2216 1530 2205 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 1552 2205 1574 2216 1585 2227 1596 2249 1607 2304 1607 2337 1596 2392 1585 2414 1574 2425 1552 2436 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 1716 2216 1705 2205 1694 2216 1705 2227 4 Poly End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 12 1892 2436 1925 2425 1936 2403 1936 2370 1925 2348 1892 2337 1848 2337 1815 2348 1804 2370 1804 2403 1815 2425 1848 2436 12 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 1848 2436 1826 2425 1815 2403 1815 2370 1826 2348 1848 2337 6 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 1892 2337 1914 2348 1925 2370 1925 2403 1914 2425 1892 2436 6 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 1848 2337 1815 2326 1804 2315 1793 2293 1793 2249 1804 2227 1815 2216 1848 2205 1892 2205 1925 2216 1936 2227 1947 2249 1947 2293 1936 2315 1925 2326 1892 2337 16 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 1848 2337 1826 2326 1815 2315 1804 2293 1804 2249 1815 2227 1826 2216 1848 2205 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 1892 2205 1914 2216 1925 2227 1936 2249 1936 2293 1925 2315 1914 2326 1892 2337 8 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 12 2112 2436 2145 2425 2156 2403 2156 2370 2145 2348 2112 2337 2068 2337 2035 2348 2024 2370 2024 2403 2035 2425 2068 2436 12 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2068 2436 2046 2425 2035 2403 2035 2370 2046 2348 2068 2337 6 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2112 2337 2134 2348 2145 2370 2145 2403 2134 2425 2112 2436 6 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 2068 2337 2035 2326 2024 2315 2013 2293 2013 2249 2024 2227 2035 2216 2068 2205 2112 2205 2145 2216 2156 2227 2167 2249 2167 2293 2156 2315 2145 2326 2112 2337 16 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 2068 2337 2046 2326 2035 2315 2024 2293 2024 2249 2035 2227 2046 2216 2068 2205 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 2112 2205 2134 2216 2145 2227 2156 2249 2156 2293 2145 2315 2134 2326 2112 2337 8 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2304 9078 2304 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2304 2442 2304 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1189 3686 1387 3686 2 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 1552 3818 1585 3807 1607 3774 1618 3719 1618 3686 1607 3631 1585 3598 1552 3587 1530 3587 1497 3598 1475 3631 1464 3686 1464 3719 1475 3774 1497 3807 1530 3818 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 1530 3818 1508 3807 1497 3796 1486 3774 1475 3719 1475 3686 1486 3631 1497 3609 1508 3598 1530 3587 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 1552 3587 1574 3598 1585 3609 1596 3631 1607 3686 1607 3719 1596 3774 1585 3796 1574 3807 1552 3818 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 1716 3598 1705 3587 1694 3598 1705 3609 4 Poly End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 12 1892 3818 1925 3807 1936 3785 1936 3752 1925 3730 1892 3719 1848 3719 1815 3730 1804 3752 1804 3785 1815 3807 1848 3818 12 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 1848 3818 1826 3807 1815 3785 1815 3752 1826 3730 1848 3719 6 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 1892 3719 1914 3730 1925 3752 1925 3785 1914 3807 1892 3818 6 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 1848 3719 1815 3708 1804 3697 1793 3675 1793 3631 1804 3609 1815 3598 1848 3587 1892 3587 1925 3598 1936 3609 1947 3631 1947 3675 1936 3697 1925 3708 1892 3719 16 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 1848 3719 1826 3708 1815 3697 1804 3675 1804 3631 1815 3609 1826 3598 1848 3587 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 1892 3587 1914 3598 1925 3609 1936 3631 1936 3675 1925 3697 1914 3708 1892 3719 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2013 3818 2013 3752 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 2013 3774 2024 3796 2046 3818 2068 3818 2123 3785 2145 3785 2156 3796 2167 3818 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 2024 3796 2046 3807 2068 3807 2123 3785 4 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 2167 3818 2167 3785 2156 3752 2112 3697 2101 3675 2090 3642 2090 3587 7 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5 2156 3752 2101 3697 2090 3675 2079 3642 2079 3587 5 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 3686 9078 3686 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3686 2442 3686 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1189 5069 1387 5069 2 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 1552 5201 1585 5190 1607 5157 1618 5102 1618 5069 1607 5014 1585 4981 1552 4970 1530 4970 1497 4981 1475 5014 1464 5069 1464 5102 1475 5157 1497 5190 1530 5201 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 1530 5201 1508 5190 1497 5179 1486 5157 1475 5102 1475 5069 1486 5014 1497 4992 1508 4981 1530 4970 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 1552 4970 1574 4981 1585 4992 1596 5014 1607 5069 1607 5102 1596 5157 1585 5179 1574 5190 1552 5201 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 1716 4981 1705 4970 1694 4981 1705 4992 4 Poly End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 12 1892 5201 1925 5190 1936 5168 1936 5135 1925 5113 1892 5102 1848 5102 1815 5113 1804 5135 1804 5168 1815 5190 1848 5201 12 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 1848 5201 1826 5190 1815 5168 1815 5135 1826 5113 1848 5102 6 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 1892 5102 1914 5113 1925 5135 1925 5168 1914 5190 1892 5201 6 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 1848 5102 1815 5091 1804 5080 1793 5058 1793 5014 1804 4992 1815 4981 1848 4970 1892 4970 1925 4981 1936 4992 1947 5014 1947 5058 1936 5080 1925 5091 1892 5102 16 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 1848 5102 1826 5091 1815 5080 1804 5058 1804 5014 1815 4992 1826 4981 1848 4970 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 1892 4970 1914 4981 1925 4992 1936 5014 1936 5058 1925 5080 1914 5091 1892 5102 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 28 2145 5168 2134 5157 2145 5146 2156 5157 2156 5168 2145 5190 2123 5201 2090 5201 2057 5190 2035 5168 2024 5146 2013 5102 2013 5036 2024 5003 2046 4981 2079 4970 2101 4970 2134 4981 2156 5003 2167 5036 2167 5047 2156 5080 2134 5102 2101 5113 2090 5113 2057 5102 2035 5080 2024 5047 28 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 9 2090 5201 2068 5190 2046 5168 2035 5146 2024 5102 2024 5036 2035 5003 2057 4981 2079 4970 9 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 2101 4970 2123 4981 2145 5003 2156 5036 2156 5047 2145 5080 2123 5102 2101 5113 8 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5069 9078 5069 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5069 2442 5069 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1189 6451 1387 6451 2 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 1552 6583 1585 6572 1607 6539 1618 6484 1618 6451 1607 6396 1585 6363 1552 6352 1530 6352 1497 6363 1475 6396 1464 6451 1464 6484 1475 6539 1497 6572 1530 6583 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 1530 6583 1508 6572 1497 6561 1486 6539 1475 6484 1475 6451 1486 6396 1497 6374 1508 6363 1530 6352 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 1552 6352 1574 6363 1585 6374 1596 6396 1607 6451 1607 6484 1596 6539 1585 6561 1574 6572 1552 6583 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 1716 6363 1705 6352 1694 6363 1705 6374 4 Poly End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 12 1892 6583 1925 6572 1936 6550 1936 6517 1925 6495 1892 6484 1848 6484 1815 6495 1804 6517 1804 6550 1815 6572 1848 6583 12 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 1848 6583 1826 6572 1815 6550 1815 6517 1826 6495 1848 6484 6 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 1892 6484 1914 6495 1925 6517 1925 6550 1914 6572 1892 6583 6 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 1848 6484 1815 6473 1804 6462 1793 6440 1793 6396 1804 6374 1815 6363 1848 6352 1892 6352 1925 6363 1936 6374 1947 6396 1947 6440 1936 6462 1925 6473 1892 6484 16 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 1848 6484 1826 6473 1815 6462 1804 6440 1804 6396 1815 6374 1826 6363 1848 6352 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 1892 6352 1914 6363 1925 6374 1936 6396 1936 6440 1925 6462 1914 6473 1892 6484 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2035 6583 2013 6473 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 19 2013 6473 2035 6495 2068 6506 2101 6506 2134 6495 2156 6473 2167 6440 2167 6418 2156 6385 2134 6363 2101 6352 2068 6352 2035 6363 2024 6374 2013 6396 2013 6407 2024 6418 2035 6407 2024 6396 19 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 2101 6506 2123 6495 2145 6473 2156 6440 2156 6418 2145 6385 2123 6363 2101 6352 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2035 6583 2145 6583 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 2035 6572 2090 6572 2145 6583 3 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 6451 9078 6451 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 6451 2442 6451 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1189 7834 1387 7834 2 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 1552 7966 1585 7955 1607 7922 1618 7867 1618 7834 1607 7779 1585 7746 1552 7735 1530 7735 1497 7746 1475 7779 1464 7834 1464 7867 1475 7922 1497 7955 1530 7966 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 1530 7966 1508 7955 1497 7944 1486 7922 1475 7867 1475 7834 1486 7779 1497 7757 1508 7746 1530 7735 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 1552 7735 1574 7746 1585 7757 1596 7779 1607 7834 1607 7867 1596 7922 1585 7944 1574 7955 1552 7966 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 1716 7746 1705 7735 1694 7746 1705 7757 4 Poly End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 12 1892 7966 1925 7955 1936 7933 1936 7900 1925 7878 1892 7867 1848 7867 1815 7878 1804 7900 1804 7933 1815 7955 1848 7966 12 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 1848 7966 1826 7955 1815 7933 1815 7900 1826 7878 1848 7867 6 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 1892 7867 1914 7878 1925 7900 1925 7933 1914 7955 1892 7966 6 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 1848 7867 1815 7856 1804 7845 1793 7823 1793 7779 1804 7757 1815 7746 1848 7735 1892 7735 1925 7746 1936 7757 1947 7779 1947 7823 1936 7845 1925 7856 1892 7867 16 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 1848 7867 1826 7856 1815 7845 1804 7823 1804 7779 1815 7757 1826 7746 1848 7735 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 1892 7735 1914 7746 1925 7757 1936 7779 1936 7823 1925 7845 1914 7856 1892 7867 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2112 7944 2112 7735 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2123 7966 2123 7735 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 2123 7966 2002 7801 2178 7801 3 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2079 7735 2156 7735 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 7834 9078 7834 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 7834 2442 7834 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1189 9216 1387 9216 2 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 1552 9348 1585 9337 1607 9304 1618 9249 1618 9216 1607 9161 1585 9128 1552 9117 1530 9117 1497 9128 1475 9161 1464 9216 1464 9249 1475 9304 1497 9337 1530 9348 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 1530 9348 1508 9337 1497 9326 1486 9304 1475 9249 1475 9216 1486 9161 1497 9139 1508 9128 1530 9117 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 1552 9117 1574 9128 1585 9139 1596 9161 1607 9216 1607 9249 1596 9304 1585 9326 1574 9337 1552 9348 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 1716 9128 1705 9117 1694 9128 1705 9139 4 Poly End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 12 1892 9348 1925 9337 1936 9315 1936 9282 1925 9260 1892 9249 1848 9249 1815 9260 1804 9282 1804 9315 1815 9337 1848 9348 12 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 1848 9348 1826 9337 1815 9315 1815 9282 1826 9260 1848 9249 6 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 1892 9249 1914 9260 1925 9282 1925 9315 1914 9337 1892 9348 6 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 1848 9249 1815 9238 1804 9227 1793 9205 1793 9161 1804 9139 1815 9128 1848 9117 1892 9117 1925 9128 1936 9139 1947 9161 1947 9205 1936 9227 1925 9238 1892 9249 16 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 1848 9249 1826 9238 1815 9227 1804 9205 1804 9161 1815 9139 1826 9128 1848 9117 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 1892 9117 1914 9128 1925 9139 1936 9161 1936 9205 1925 9227 1914 9238 1892 9249 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 2024 9304 2035 9293 2024 9282 2013 9293 2013 9304 2024 9326 2035 9337 2068 9348 2112 9348 2145 9337 2156 9315 2156 9282 2145 9260 2112 9249 2079 9249 15 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2112 9348 2134 9337 2145 9315 2145 9282 2134 9260 2112 9249 6 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 2112 9249 2134 9238 2156 9216 2167 9194 2167 9161 2156 9139 2145 9128 2112 9117 2068 9117 2035 9128 2024 9139 2013 9161 2013 9172 2024 9183 2035 9172 2024 9161 16 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2145 9227 2156 9194 2156 9161 2145 9139 2134 9128 2112 9117 6 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 9216 9078 9216 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 9216 2442 9216 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2304 9161 2304 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2304 2359 2304 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2580 9161 2580 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2580 2359 2580 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2857 9161 2857 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2857 2359 2857 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 3133 9161 3133 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3133 2359 3133 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 3410 9161 3410 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3410 2359 3410 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 3686 9161 3686 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3686 2359 3686 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 3963 9161 3963 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3963 2359 3963 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 4239 9161 4239 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4239 2359 4239 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 4516 9161 4516 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4516 2359 4516 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 4792 9161 4792 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4792 2359 4792 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5069 9161 5069 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5069 2359 5069 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5345 9161 5345 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5345 2359 5345 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5622 9161 5622 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5622 2359 5622 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5898 9161 5898 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5898 2359 5898 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 6175 9161 6175 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 6175 2359 6175 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 6451 9161 6451 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 6451 2359 6451 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 6728 9161 6728 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 6728 2359 6728 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 7004 9161 7004 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 7004 2359 7004 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 7281 9161 7281 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 7281 2359 7281 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 7557 9161 7557 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 7557 2359 7557 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 7834 9161 7834 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 7834 2359 7834 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 8110 9161 8110 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 8110 2359 8110 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 8387 9161 8387 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 8387 2359 8387 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 8663 9161 8663 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 8663 2359 8663 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 8940 9161 8940 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 8940 2359 8940 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 9216 9161 9216 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 9216 2359 9216 2 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 4858 1621 4880 1610 4891 1599 4902 1577 4902 1555 4891 1533 4880 1522 4858 1511 4836 1511 4814 1522 4803 1533 4792 1555 4792 1577 4803 1599 4814 1610 4836 1621 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 4814 1610 4803 1588 4803 1544 4814 1522 4 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 4880 1522 4891 1544 4891 1588 4880 1610 4 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5 4891 1599 4902 1610 4924 1621 4924 1610 4902 1610 5 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 9 4803 1533 4792 1522 4781 1500 4781 1489 4792 1467 4825 1456 4880 1456 4913 1445 4924 1434 9 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 4781 1489 4792 1478 4825 1467 4880 1467 4913 1456 4924 1434 4924 1423 4913 1401 4880 1390 4814 1390 4781 1401 4770 1423 4770 1434 4781 1456 4814 1467 15 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 17 5001 1555 5133 1555 5133 1577 5122 1599 5111 1610 5089 1621 5056 1621 5023 1610 5001 1588 4990 1555 4990 1533 5001 1500 5023 1478 5056 1467 5078 1467 5111 1478 5133 1500 17 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 5122 1555 5122 1588 5111 1610 3 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 5056 1621 5034 1610 5012 1588 5001 1555 5001 1533 5012 1500 5034 1478 5056 1467 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5221 1621 5221 1467 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5232 1621 5232 1467 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 5232 1588 5254 1610 5287 1621 5309 1621 5342 1610 5353 1588 5353 1467 7 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 5309 1621 5331 1610 5342 1588 5342 1467 4 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5188 1621 5232 1621 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5188 1467 5265 1467 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5309 1467 5386 1467 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 17 5452 1555 5584 1555 5584 1577 5573 1599 5562 1610 5540 1621 5507 1621 5474 1610 5452 1588 5441 1555 5441 1533 5452 1500 5474 1478 5507 1467 5529 1467 5562 1478 5584 1500 17 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 5573 1555 5573 1588 5562 1610 3 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 5507 1621 5485 1610 5463 1588 5452 1555 5452 1533 5463 1500 5485 1478 5507 1467 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5672 1621 5672 1467 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5683 1621 5683 1467 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 5683 1555 5694 1588 5716 1610 5738 1621 5771 1621 5782 1610 5782 1599 5771 1588 5760 1599 5771 1610 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5639 1621 5683 1621 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5639 1467 5716 1467 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 13 5859 1599 5859 1588 5848 1588 5848 1599 5859 1610 5881 1621 5925 1621 5947 1610 5958 1599 5969 1577 5969 1500 5980 1478 5991 1467 13 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5 5958 1599 5958 1500 5969 1478 5991 1467 6002 1467 5 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 11 5958 1577 5947 1566 5881 1555 5848 1544 5837 1522 5837 1500 5848 1478 5881 1467 5914 1467 5936 1478 5958 1500 11 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 5881 1555 5859 1544 5848 1522 5848 1500 5859 1478 5881 1467 6 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 6079 1698 6079 1511 6090 1478 6112 1467 6134 1467 6156 1478 6167 1500 7 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 6090 1698 6090 1511 6101 1478 6112 1467 4 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6046 1621 6134 1621 2 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 6255 1687 6244 1676 6233 1687 6244 1698 4 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6244 1621 6244 1467 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6255 1621 6255 1467 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6211 1621 6255 1621 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6211 1467 6288 1467 2 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 6431 1621 6464 1610 6486 1588 6497 1555 6497 1533 6486 1500 6464 1478 6431 1467 6409 1467 6376 1478 6354 1500 6343 1533 6343 1555 6354 1588 6376 1610 6409 1621 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 6409 1621 6387 1610 6365 1588 6354 1555 6354 1533 6365 1500 6387 1478 6409 1467 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 6431 1467 6453 1478 6475 1500 6486 1533 6486 1555 6475 1588 6453 1610 6431 1621 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6585 1621 6585 1467 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6596 1621 6596 1467 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 6596 1588 6618 1610 6651 1621 6673 1621 6706 1610 6717 1588 6717 1467 7 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 6673 1621 6695 1610 6706 1588 6706 1467 4 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6552 1621 6596 1621 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6552 1467 6629 1467 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6673 1467 6750 1467 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 17 711 5172 711 5304 689 5304 667 5293 656 5282 645 5260 645 5227 656 5194 678 5172 711 5161 733 5161 766 5172 788 5194 799 5227 799 5249 788 5282 766 5304 17 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 711 5293 678 5293 656 5282 3 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 645 5227 656 5205 678 5183 711 5172 733 5172 766 5183 788 5205 799 5227 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 645 5392 799 5392 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 645 5403 799 5403 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 678 5403 656 5425 645 5458 645 5480 656 5513 678 5524 799 5524 7 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 645 5480 656 5502 678 5513 799 5513 4 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 645 5359 645 5403 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 799 5359 799 5436 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 799 5480 799 5557 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 17 711 5623 711 5755 689 5755 667 5744 656 5733 645 5711 645 5678 656 5645 678 5623 711 5612 733 5612 766 5623 788 5645 799 5678 799 5700 788 5733 766 5755 17 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 711 5744 678 5744 656 5733 3 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 645 5678 656 5656 678 5634 711 5623 733 5623 766 5634 788 5656 799 5678 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 645 5842 799 5842 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 645 5853 799 5853 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 711 5853 678 5864 656 5886 645 5908 645 5941 656 5952 667 5952 678 5941 667 5930 656 5941 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 645 5809 645 5853 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 799 5809 799 5886 2 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 645 6084 656 6106 667 6117 689 6128 711 6128 733 6117 744 6106 755 6084 755 6062 744 6040 733 6029 711 6018 689 6018 667 6029 656 6040 645 6062 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 656 6040 678 6029 722 6029 744 6040 4 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 744 6106 722 6117 678 6117 656 6106 4 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5 667 6117 656 6128 645 6150 656 6150 656 6128 5 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 9 733 6029 744 6018 766 6007 777 6007 799 6018 810 6051 810 6106 821 6139 832 6150 9 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 777 6007 788 6018 799 6051 799 6106 810 6139 832 6150 843 6150 865 6139 876 6106 876 6040 865 6007 843 5996 832 5996 810 6007 799 6040 15 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 645 6227 799 6293 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 645 6238 777 6293 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 9 645 6359 799 6293 843 6271 865 6249 876 6227 876 6216 865 6205 854 6216 865 6227 9 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 645 6205 645 6271 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 645 6315 645 6381 2 MLine End Begin %I MLine [1 0 0 1 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 0 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 500 2304 3913 2306 3524 2309 4474 2311 3291 2313 7013 2316 9033 2318 3717 2320 3291 2322 3448 2325 5091 2327 4710 2329 6599 2332 4035 2334 3719 2336 4855 2339 4639 2341 3552 2343 3315 2345 6618 2348 4236 2350 3461 2352 3315 2355 4468 2357 3291 2359 3290 2362 7133 2364 3407 2366 3696 2369 3303 2371 3420 2373 3547 2375 4392 2378 3882 2380 4522 2382 4110 2385 3401 2387 3305 2389 4302 2392 3348 2394 3333 2396 3612 2398 6772 2401 3641 2403 3382 2405 3291 2408 3372 2410 6432 2412 4985 2415 3597 2417 3296 2419 3333 2422 4535 2424 3727 2426 3582 2428 4334 2431 4537 2433 3596 2435 3694 2438 3670 2440 3314 2442 3422 2445 3583 2447 4524 2449 6042 2451 3508 2454 5608 2456 3589 2458 4100 2461 3564 2463 3542 2465 3358 2468 3352 2470 4227 2472 3507 2474 4068 2477 3803 2479 7461 2481 3617 2484 3290 2486 3300 2488 8524 2491 4820 2493 3837 2495 3707 2498 3437 2500 3327 2502 3611 2504 3408 2507 3612 2509 3358 2511 4195 2514 4363 2516 3475 2518 4405 2521 3567 2523 4881 2525 4280 2527 3471 2530 4632 2532 3657 2534 5213 2537 3456 2539 3871 2541 3333 2544 4181 2546 3292 2548 3431 2551 3679 2553 3438 2555 3380 2557 3949 2560 4532 2562 3297 2564 3299 2567 3928 2569 3977 2571 3713 2574 3439 2576 3399 2578 3574 2580 3476 2583 3335 2585 4452 2587 4551 2590 3425 2592 4218 2594 3802 2597 5543 2599 3419 2601 3527 2604 3591 2606 4652 2608 3292 2610 3889 2613 3290 2615 3311 2617 3466 2620 3290 2622 4131 2624 3424 2627 3579 2629 3370 2631 4303 2633 3345 2636 4516 2638 3298 2640 3295 2643 3704 2645 3527 2647 3319 2650 3422 2652 3371 2654 4250 2657 3487 2659 3350 2661 3291 2663 5719 2666 3356 2668 3791 2670 3543 2673 4164 2675 3830 2677 3444 2680 3766 2682 3478 2684 3361 2686 3699 2689 6142 2691 3290 2693 4189 2696 3300 2698 4503 2700 3360 2703 4097 2705 3483 2707 4962 2710 3476 2712 4439 2714 4188 2716 5653 2719 4309 2721 3664 2723 3400 2726 4114 2728 3937 2730 3452 2733 3402 2735 4150 2737 5020 2739 3536 2742 3608 2744 3434 2746 3295 2749 3344 2751 3983 2753 3290 2756 3329 2758 3310 2760 3415 2762 3302 2765 3848 2767 3622 2769 3606 2772 3388 2774 3577 2776 3636 2779 3513 2781 3391 2783 3715 2786 3329 2788 3290 2790 4134 2792 3314 2795 3297 2797 3290 2799 3302 2802 6602 2804 3312 2806 3412 2809 3783 2811 3685 2813 6632 2815 3365 2818 3336 2820 5241 2822 3433 2825 3311 2827 3415 2829 3297 2832 4080 2834 3578 2836 3465 2839 3290 2841 4441 2843 3290 2845 3996 2848 3377 2850 3294 2852 3465 2855 3291 2857 3408 2859 3291 2862 3319 2864 3895 2866 3833 2868 3293 2871 3323 2873 3461 2875 3294 2878 3325 2880 3295 2882 3307 2885 3317 2887 3368 2889 3378 2892 3295 2894 4232 2896 3367 2898 3290 2901 3596 2903 4308 2905 3376 2908 3510 2910 3910 2912 3295 2915 3295 2917 3335 2919 3355 2921 3365 2924 3294 2926 3405 2928 3290 2931 3308 2933 3435 2935 3355 2938 3300 2940 3404 2942 3310 2945 3294 2947 3302 2949 3291 2951 4978 2954 3340 2956 3596 2958 5354 2961 3298 2963 3772 2965 3323 2968 3370 2970 3307 2972 4018 2974 3358 2977 3868 2979 3298 2981 3297 2984 3319 2986 3293 2988 3619 2991 3410 2993 3317 2995 3414 2998 3299 3000 3347 3002 3334 3004 3313 3007 3348 3009 4841 3011 3572 3014 3489 3016 3474 3018 3386 3021 4339 3023 4032 3025 3332 3027 3309 3030 3291 3032 3290 3034 3468 3037 4515 3039 3582 3041 3292 3044 3305 3046 3649 3048 3539 3050 3689 3053 3418 3055 5165 3057 3354 3060 3372 3062 3339 3064 3438 3067 3389 3069 3505 3071 3290 3074 3363 3076 3672 3078 3394 3080 3439 3083 3311 3085 3800 3087 3378 3090 3803 3092 3518 3094 3309 3097 3290 3099 4032 3101 3295 3103 3314 3106 4187 3108 3360 3110 3539 3113 3377 3115 3460 3117 3390 3120 3290 3122 3424 3124 3417 3127 3379 3129 3355 3131 3419 3133 3618 3136 3683 3138 3338 3140 3290 3143 3825 3145 3319 3147 3369 3150 3356 3152 3760 3154 3315 3156 3290 3159 3427 3161 3373 3163 3551 3166 3394 3168 3382 3170 3567 3173 3294 3175 3290 3177 3656 3180 3349 3182 3645 3184 3290 3186 3290 3189 3313 3191 3393 3193 3290 3196 3324 3198 3330 3200 3387 3203 3435 3205 3307 3207 3475 3209 3314 3212 3589 3214 3350 3216 3309 3219 3333 3221 3304 3223 3452 3226 3291 3228 3297 3230 3290 3233 3345 3235 3375 3237 3329 3239 3461 3242 3341 3244 3477 3246 3311 3249 3580 3251 3304 3253 3334 3256 3344 3258 3342 3260 3386 3262 3449 3265 3320 3267 3300 3269 3620 3272 3420 3274 3291 3276 3430 3279 3290 3281 5045 3283 3290 3286 3364 3288 3744 3290 3315 3292 3306 3295 3330 3297 3420 3299 3292 3302 3453 3304 3437 3306 3300 3309 3361 3311 3290 3313 3906 3315 3521 3318 3426 3320 3309 3322 3450 3325 3490 3327 3693 3329 3290 3332 3435 3334 4694 3336 3654 3338 3301 3341 3770 3343 3294 3345 3317 3348 3335 3350 3451 3352 3481 3355 3303 3357 3546 3359 3430 3362 3303 3364 3466 3366 3846 3368 3461 3371 3298 3373 3304 3375 3399 3378 3350 3380 3401 3382 3291 3385 3331 3387 3706 3389 3336 3391 3450 3394 3350 3396 3539 3398 3361 3401 3695 3403 3295 3405 3565 3408 3613 3410 3325 3412 3314 3415 3575 3417 3421 3419 3330 3421 3541 3424 3477 3426 3445 3428 3294 3431 3461 3433 3332 3435 3377 3438 3429 3440 3476 3442 3311 3444 3315 3447 3372 3449 3296 3451 3383 3454 3380 500 MLine End Begin %I MLine [1 0 0 1 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 0 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 500 3454 3380 3456 3576 3458 3292 3461 3706 3463 3489 3465 3316 3468 3292 3470 3366 3472 3365 3474 3312 3477 3534 3479 3372 3481 3304 3484 3903 3486 3300 3488 3296 3491 3533 3493 3295 3495 3352 3497 3494 3500 3291 3502 3303 3504 3484 3507 3298 3509 3293 3511 3296 3514 3421 3516 3378 3518 3939 3521 3295 3523 3304 3525 3296 3527 3633 3530 3325 3532 3495 3534 3307 3537 3307 3539 3558 3541 3297 3544 3307 3546 3844 3548 3924 3550 3301 3553 3296 3555 3352 3557 3320 3560 3380 3562 3295 3564 3317 3567 3290 3569 3553 3571 3325 3574 3397 3576 3377 3578 3506 3580 3309 3583 3299 3585 3417 3587 3310 3590 3354 3592 3299 3594 3637 3597 3329 3599 3308 3601 3290 3603 3582 3606 3290 3608 3305 3610 3309 3613 3294 3615 3320 3617 3290 3620 3298 3622 3529 3624 3293 3626 3292 3629 3291 3631 3308 3633 3291 3636 3313 3638 3299 3640 3291 3643 3306 3645 3296 3647 3563 3650 3740 3652 3290 3654 3291 3656 3493 3659 3338 3661 3362 3663 3386 3666 3377 3668 3324 3670 3304 3673 3380 3675 3291 3677 3544 3679 3291 3682 3773 3684 3357 3686 3309 3689 3693 3691 3330 3693 3448 3696 3631 3698 3587 3700 3391 3703 3391 3705 3293 3707 3290 3709 3359 3712 3304 3714 3290 3716 3355 3719 3290 3721 3519 3723 3290 3726 3290 3728 3439 3730 3465 3732 3294 3735 3371 3737 3553 3739 3290 3742 3321 3744 3309 3746 3336 3749 3298 3751 3298 3753 3320 3756 3388 3758 3527 3760 3616 3762 3346 3765 3348 3767 3363 3769 3479 3772 3369 3774 3419 3776 3364 3779 3343 3781 3404 3783 3302 3785 3360 3788 3637 3790 3295 3792 3369 3795 3312 3797 3297 3799 3352 3802 3393 3804 3290 3806 3462 3809 3296 3811 3335 3813 3293 3815 3298 3818 3290 3820 3391 3822 3423 3825 3330 3827 3292 3829 3290 3832 3348 3834 3302 3836 3319 3838 3394 3841 3291 3843 3291 3845 3298 3848 3310 3850 3343 3852 3355 3855 3314 3857 3637 3859 3291 3862 3387 3864 3290 3866 3358 3868 3293 3871 3318 3873 3314 3875 3297 3878 3331 3880 3347 3882 3291 3885 3394 3887 3415 3889 3293 3891 3292 3894 3298 3896 3534 3898 3309 3901 3299 3903 3293 3905 3388 3908 3290 3910 3296 3912 3291 3914 3301 3917 3551 3919 3307 3921 3353 3924 3304 3926 3290 3928 3307 3931 3290 3933 3660 3935 3305 3938 3291 3940 3533 3942 3476 3944 3326 3947 3314 3949 3306 3951 3537 3954 3290 3956 3420 3958 3328 3961 3298 3963 3442 3965 3325 3967 3368 3970 3291 3972 3375 3974 3432 3977 3345 3979 3696 3981 3515 3984 3333 3986 3362 3988 3293 3991 3300 3993 3383 3995 3405 3997 3317 4000 3385 4002 3390 4004 3290 4007 3398 4009 3353 4011 3343 4014 3384 4016 3290 4018 3294 4020 3300 4023 3502 4025 3296 4027 3297 4030 3307 4032 3290 4034 3291 4037 3298 4039 3300 4041 3396 4044 3307 4046 3398 4048 3290 4050 3290 4053 3301 4055 3611 4057 3329 4060 3370 4062 3402 4064 3333 4067 3302 4069 3401 4071 3339 4073 3301 4076 3291 4078 3319 4080 3300 4083 3297 4085 3291 4087 3434 4090 3508 4092 3313 4094 3295 4097 3316 4099 3299 4101 3434 4103 3354 4106 3517 4108 3290 4110 3610 4113 3290 4115 3290 4117 3328 4120 3321 4122 3290 4124 3430 4126 3376 4129 3303 4131 3355 4133 3290 4136 3448 4138 3419 4140 3372 4143 3339 4145 3434 4147 3351 4150 3311 4152 3320 4154 3356 4156 3290 4159 3323 4161 3375 4163 3290 4166 3300 4168 3294 4170 3290 4173 3290 4175 3301 4177 3335 4179 3298 4182 3307 4184 3435 4186 3290 4189 3291 4191 3368 4193 3290 4196 3341 4198 3374 4200 3329 4202 3365 4205 3333 4207 3328 4209 3294 4212 3318 4214 3461 4216 3354 4219 3331 4221 3290 4223 3360 4226 3290 4228 3290 4230 3344 4232 3324 4235 3293 4237 3291 4239 3318 4242 3367 4244 3331 4246 3290 4249 3316 4251 3418 4253 3428 4255 3291 4258 3485 4260 3368 4262 3300 4265 3303 4267 3322 4269 3434 4272 3319 4274 3387 4276 3308 4279 3556 4281 3291 4283 3418 4285 3301 4288 3340 4290 3340 4292 3294 4295 3294 4297 3342 4299 3347 4302 3291 4304 3290 4306 3311 4308 3295 4311 3314 4313 3322 4315 3486 4318 3291 4320 3309 4322 3316 4325 3329 4327 3290 4329 3338 4332 3350 4334 3290 4336 3298 4338 3290 4341 3297 4343 3363 4345 3439 4348 3304 4350 3295 4352 3307 4355 3454 4357 3290 4359 3291 4361 3301 4364 3327 4366 3295 4368 3301 4371 3296 4373 3485 4375 3380 4378 3291 4380 3290 4382 3294 4385 3371 4387 3333 4389 3295 4391 3290 4394 3399 4396 3327 4398 3407 4401 3359 4403 3290 4405 3293 4408 3305 4410 3296 4412 3319 4414 3338 4417 3290 4419 3303 4421 3290 4424 3290 4426 3381 4428 3296 4431 3290 4433 3293 4435 3293 4438 3293 4440 3376 4442 3290 4444 3291 4447 3290 4449 3351 4451 3302 4454 3304 4456 3321 4458 3320 4461 3290 4463 3291 4465 3290 4467 3321 4470 3433 4472 3290 4474 3303 4477 3347 4479 3345 4481 3346 4484 3290 4486 3301 4488 3295 4490 3311 4493 3341 4495 3295 4497 3294 4500 3303 4502 3322 4504 3302 4507 3295 4509 3290 4511 3299 4514 3337 4516 3396 4518 3290 4520 3294 4523 3294 4525 3319 4527 3359 4530 3570 4532 3309 4534 3309 4537 3290 4539 3321 4541 3290 4543 3294 4546 3291 4548 3290 4550 3426 4553 3290 4555 3290 4557 3290 4560 3305 4562 3304 4564 3299 4567 3291 4569 3347 4571 3293 4573 3303 4576 3295 4578 3324 4580 3321 4583 3330 4585 3291 4587 3294 4590 3319 4592 3331 4594 3380 4596 3291 4599 3290 4601 3290 4603 3391 500 MLine End Begin %I MLine [1 0 0 1 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 0 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 500 4603 3391 4606 3290 4608 3326 4610 3365 4613 3359 4615 3319 4617 3290 4620 3293 4622 3295 4624 3290 4626 3292 4629 3311 4631 3292 4633 3385 4636 3309 4638 3318 4640 3290 4643 3305 4645 3309 4647 3332 4649 3294 4652 3297 4654 3331 4656 3320 4659 3294 4661 3299 4663 3352 4666 3334 4668 3290 4670 3291 4673 3307 4675 3306 4677 3326 4679 3291 4682 3312 4684 3316 4686 3322 4689 3337 4691 3307 4693 3292 4696 3376 4698 3373 4700 3291 4702 3395 4705 3290 4707 3417 4709 3306 4712 3367 4714 3300 4716 3297 4719 3299 4721 3295 4723 3304 4726 3292 4728 3305 4730 3294 4732 3293 4735 3290 4737 3294 4739 3305 4742 3290 4744 3290 4746 3290 4749 3292 4751 3307 4753 3304 4755 3290 4758 3290 4760 3290 4762 3290 4765 3290 4767 3290 4769 3290 4772 3312 4774 3296 4776 3292 4778 3350 4781 3310 4783 3301 4785 3304 4788 3338 4790 3305 4792 3306 4795 3332 4797 3290 4799 3322 4802 3295 4804 3293 4806 3291 4808 3304 4811 3290 4813 3291 4815 3302 4818 3318 4820 3310 4822 3458 4825 3317 4827 3290 4829 3290 4831 3316 4834 3305 4836 3311 4838 3290 4841 3294 4843 3294 4845 3294 4848 3292 4850 3290 4852 3290 4855 3290 4857 3293 4859 3340 4861 3295 4864 3295 4866 3296 4868 3306 4871 3344 4873 3301 4875 3292 4878 3326 4880 3290 4882 3337 4884 3301 4887 3339 4889 3295 4891 3311 4894 3300 4896 3290 4898 3290 4901 3290 4903 3311 4905 3293 4908 3316 4910 3295 4912 3302 4914 3291 4917 3301 4919 3314 4921 3306 4924 3291 4926 3292 4928 3290 4931 3293 4933 3309 4935 3290 4937 3322 4940 3316 4942 3295 4944 3290 4947 3294 4949 3403 4951 3290 4954 3322 4956 3291 4958 3307 4961 3290 4963 3295 4965 3314 4967 3367 4970 3291 4972 3294 4974 3290 4977 3290 4979 3290 4981 3294 4984 3294 4986 3314 4988 3300 4990 3294 4993 3305 4995 3299 4997 3295 5000 3342 5002 3309 5004 3328 5007 3293 5009 3295 5011 3310 5014 3310 5016 3290 5018 3290 5020 3325 5023 3292 5025 3290 5027 3291 5030 3294 5032 3312 5034 3291 5037 3293 5039 3317 5041 3290 5043 3290 5046 3294 5048 3304 5050 3290 5053 3290 5055 3290 5057 3290 5060 3290 5062 3388 5064 3308 5066 3305 5069 3290 5071 3290 5073 3292 5076 3292 5078 3290 5080 3290 5083 3297 5085 3292 5087 3406 5090 3307 5092 3317 5094 3309 5096 3313 5099 3290 5101 3290 5103 3320 5106 3292 5108 3290 5110 3304 5113 3327 5115 3290 5117 3345 5119 3291 5122 3291 5124 3290 5126 3300 5129 3292 5131 3298 5133 3298 5136 3291 5138 3310 5140 3295 5143 3297 5145 3310 5147 3353 5149 3290 5152 3307 5154 3291 5156 3297 5159 3291 5161 3295 5163 3306 5166 3291 5168 3291 5170 3290 5172 3290 5175 3303 5177 3290 5179 3291 5182 3296 5184 3317 5186 3309 5189 3306 5191 3332 5193 3320 5196 3293 5198 3292 5200 3292 5202 3296 5205 3296 5207 3309 5209 3326 5212 3299 5214 3328 5216 3303 5219 3296 5221 3314 5223 3290 5225 3292 5228 3302 5230 3307 5232 3296 5235 3318 5237 3323 5239 3313 5242 3321 5244 3292 5246 3295 5249 3290 5251 3301 5253 3301 5255 3295 5258 3292 5260 3311 5262 3290 5265 3295 5267 3290 5269 3290 5272 3291 5274 3295 5276 3306 5278 3299 5281 3290 5283 3296 5285 3302 5288 3303 5290 3328 5292 3323 5295 3300 5297 3297 5299 3290 5302 3290 5304 3290 5306 3290 5308 3290 5311 3318 5313 3292 5315 3296 5318 3324 5320 3318 5322 3299 5325 3291 5327 3291 5329 3296 5331 3296 5334 3290 5336 3312 5338 3312 5341 3310 5343 3306 5345 3290 5348 3301 5350 3294 5352 3290 5354 3311 5357 3306 5359 3312 5361 3290 5364 3295 5366 3290 5368 3290 5371 3290 5373 3319 5375 3292 5378 3297 5380 3295 5382 3295 5384 3308 5387 3292 5389 3335 5391 3290 5394 3290 5396 3290 5398 3290 5401 3290 5403 3316 5405 3294 5407 3290 5410 3290 5412 3294 5414 3320 5417 3299 5419 3307 5421 3290 5424 3290 5426 3290 5428 3294 5431 3301 5433 3290 5435 3290 5437 3290 5440 3298 5442 3296 5444 3291 5447 3306 5449 3303 5451 3303 5454 3312 5456 3312 5458 3333 5460 3318 5463 3295 5465 3308 5467 3292 5470 3293 5472 3293 5474 3292 5477 3367 5479 3306 5481 3290 5484 3290 5486 3292 5488 3295 5490 3291 5493 3291 5495 3293 5497 3290 5500 3295 5502 3290 5504 3292 5507 3290 5509 3294 5511 3344 5513 3301 5516 3290 5518 3290 5520 3297 5523 3295 5525 3290 5527 3290 5530 3294 5532 3332 5534 3290 5537 3292 5539 3342 5541 3303 5543 3290 5546 3295 5548 3292 5550 3290 5553 3290 5555 3290 5557 3290 5560 3299 5562 3332 5564 3301 5566 3301 5569 3304 5571 3300 5573 3290 5576 3290 5578 3307 5580 3302 5583 3299 5585 3299 5587 3299 5590 3290 5592 3290 5594 3290 5596 3296 5599 3296 5601 3292 5603 3290 5606 3310 5608 3290 5610 3293 5613 3292 5615 3306 5617 3297 5619 3290 5622 3296 5624 3295 5626 3292 5629 3291 5631 3305 5633 3290 5636 3293 5638 3291 5640 3295 5642 3292 5645 3295 5647 3294 5649 3298 5652 3344 5654 3298 5656 3290 5659 3290 5661 3290 5663 3290 5666 3298 5668 3291 5670 3298 5672 3292 5675 3298 5677 3294 5679 3290 5682 3294 5684 3294 5686 3294 5689 3291 5691 3291 5693 3291 5695 3290 5698 3299 5700 3298 5702 3298 5705 3292 5707 3293 5709 3290 5712 3297 5714 3295 5716 3291 5719 3290 5721 3305 5723 3300 5725 3290 5728 3290 5730 3292 5732 3291 5735 3304 5737 3311 5739 3309 5742 3291 5744 3290 5746 3290 5748 3292 5751 3294 5753 3294 500 MLine End Begin %I MLine [1 0 0 1 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 0 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 500 5753 3294 5755 3296 5758 3346 5760 3290 5762 3292 5765 3292 5767 3291 5769 3291 5772 3290 5774 3290 5776 3290 5778 3290 5781 3291 5783 3290 5785 3293 5788 3298 5790 3312 5792 3302 5795 3296 5797 3290 5799 3291 5801 3290 5804 3293 5806 3291 5808 3290 5811 3296 5813 3296 5815 3292 5818 3296 5820 3291 5822 3290 5825 3291 5827 3301 5829 3292 5831 3312 5834 3296 5836 3290 5838 3290 5841 3290 5843 3290 5845 3294 5848 3290 5850 3290 5852 3291 5854 3294 5857 3296 5859 3290 5861 3303 5864 3293 5866 3302 5868 3290 5871 3309 5873 3305 5875 3300 5878 3303 5880 3300 5882 3295 5884 3291 5887 3291 5889 3290 5891 3290 5894 3310 5896 3314 5898 3291 5901 3291 5903 3298 5905 3293 5907 3290 5910 3294 5912 3296 5914 3290 5917 3292 5919 3291 5921 3290 5924 3290 5926 3292 5928 3295 5930 3290 5933 3298 5935 3298 5937 3291 5940 3290 5942 3290 5944 3290 5947 3305 5949 3305 5951 3305 5954 3294 5956 3290 5958 3294 5960 3298 5963 3293 5965 3305 5967 3292 5970 3292 5972 3306 5974 3293 5977 3292 5979 3295 5981 3290 5983 3290 5986 3290 5988 3305 5990 3293 5993 3298 5995 3298 5997 3290 6000 3290 6002 3296 6004 3290 6007 3307 6009 3300 6011 3300 6013 3290 6016 3300 6018 3299 6020 3294 6023 3297 6025 3292 6027 3297 6030 3290 6032 3290 6034 3301 6036 3305 6039 3295 6041 3297 6043 3297 6046 3297 6048 3290 6050 3293 6053 3293 6055 3290 6057 3292 6060 3291 6062 3314 6064 3304 6066 3290 6069 3290 6071 3302 6073 3291 6076 3291 6078 3303 6080 3303 6083 3290 6085 3292 6087 3292 6089 3290 6092 3290 6094 3291 6096 3291 6099 3290 6101 3290 6103 3290 6106 3290 6108 3290 6110 3290 6113 3292 6115 3292 6117 3291 6119 3291 6122 3296 6124 3298 6126 3307 6129 3307 6131 3291 6133 3290 6136 3294 6138 3294 6140 3290 6142 3297 6145 3293 6147 3296 6149 3290 6152 3290 6154 3292 6156 3290 6159 3290 6161 3290 6163 3299 6166 3290 6168 3290 6170 3292 6172 3290 6175 3308 6177 3290 6179 3290 6182 3290 6184 3290 6186 3290 6189 3290 6191 3290 6193 3316 6195 3293 6198 3290 6200 3295 6202 3295 6205 3297 6207 3298 6209 3294 6212 3294 6214 3294 6216 3294 6218 3294 6221 3291 6223 3290 6225 3291 6228 3299 6230 3295 6232 3290 6235 3291 6237 3290 6239 3290 6242 3291 6244 3291 6246 3292 6248 3290 6251 3290 6253 3290 6255 3290 6258 3290 6260 3290 6262 3306 6265 3295 6267 3290 6269 3298 6271 3291 6274 3290 6276 3290 6278 3290 6281 3290 6283 3291 6285 3290 6288 3290 6290 3290 6292 3290 6295 3290 6297 3291 6299 3291 6301 3301 6304 3290 6306 3296 6308 3290 6311 3290 6313 3293 6315 3293 6318 3293 6320 3294 6322 3290 6324 3290 6327 3290 6329 3290 6331 3290 6334 3290 6336 3290 6338 3290 6341 3290 6343 3290 6345 3290 6348 3294 6350 3290 6352 3290 6354 3290 6357 3292 6359 3290 6361 3290 6364 3290 6366 3290 6368 3290 6371 3298 6373 3294 6375 3293 6377 3293 6380 3295 6382 3295 6384 3290 6387 3290 6389 3291 6391 3293 6394 3290 6396 3290 6398 3308 6401 3290 6403 3292 6405 3292 6407 3292 6410 3290 6412 3292 6414 3292 6417 3292 6419 3292 6421 3293 6424 3290 6426 3290 6428 3293 6430 3293 6433 3290 6435 3290 6437 3290 6440 3290 6442 3290 6444 3290 6447 3297 6449 3290 6451 3290 6454 3294 6456 3291 6458 3290 6460 3293 6463 3294 6465 3290 6467 3290 6470 3291 6472 3291 6474 3291 6477 3294 6479 3290 6481 3291 6483 3290 6486 3291 6488 3291 6490 3291 6493 3297 6495 3291 6497 3292 6500 3292 6502 3290 6504 3290 6506 3291 6509 3290 6511 3292 6513 3292 6516 3290 6518 3290 6520 3290 6523 3290 6525 3292 6527 3290 6530 3290 6532 3291 6534 3290 6536 3290 6539 3293 6541 3290 6543 3298 6546 3294 6548 3293 6550 3294 6553 3291 6555 3290 6557 3290 6559 3290 6562 3296 6564 3296 6566 3290 6569 3290 6571 3290 6573 3290 6576 3290 6578 3291 6580 3290 6583 3295 6585 3290 6587 3290 6589 3290 6592 3290 6594 3291 6596 3290 6599 3290 6601 3290 6603 3290 6606 3301 6608 3300 6610 3300 6612 3290 6615 3290 6617 3290 6619 3290 6622 3290 6624 3292 6626 3290 6629 3298 6631 3290 6633 3293 6636 3293 6638 3293 6640 3293 6642 3290 6645 3290 6647 3290 6649 3291 6652 3291 6654 3290 6656 3290 6659 3290 6661 3290 6663 3290 6665 3290 6668 3290 6670 3290 6672 3290 6675 3297 6677 3292 6679 3292 6682 3292 6684 3290 6686 3290 6689 3291 6691 3291 6693 3295 6695 3295 6698 3290 6700 3290 6702 3290 6705 3290 6707 3290 6709 3290 6712 3298 6714 3291 6716 3290 6718 3290 6721 3290 6723 3290 6725 3290 6728 3290 6730 3291 6732 3291 6735 3291 6737 3291 6739 3290 6742 3290 6744 3290 6746 3290 6748 3290 6751 3290 6753 3290 6755 3290 6758 3290 6760 3290 6762 3291 6765 3290 6767 3290 6769 3290 6771 3290 6774 3290 6776 3290 6778 3290 6781 3290 6783 3290 6785 3293 6788 3293 6790 3294 6792 3297 6794 3297 6797 3290 6799 3290 6801 3290 6804 3290 6806 3290 6808 3292 6811 3291 6813 3291 6815 3291 6818 3291 6820 3290 6822 3290 6824 3290 6827 3291 6829 3291 6831 3290 6834 3290 6836 3290 6838 3290 6841 3290 6843 3290 6845 3295 6847 3290 6850 3290 6852 3290 6854 3290 6857 3290 6859 3291 6861 3290 6864 3290 6866 3290 6868 3290 6871 3290 6873 3290 6875 3290 6877 3291 6880 3291 6882 3291 6884 3291 6887 3291 6889 3292 6891 3290 6894 3292 6896 3290 6898 3290 6900 3290 6903 3290 500 MLine End Begin %I MLine [1 0 0 1 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 0 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 500 6903 3290 6905 3290 6907 3293 6910 3290 6912 3290 6914 3290 6917 3290 6919 3290 6921 3290 6924 3291 6926 3290 6928 3290 6930 3290 6933 3290 6935 3290 6937 3290 6940 3290 6942 3290 6944 3290 6947 3290 6949 3292 6951 3292 6953 3290 6956 3290 6958 3290 6960 3290 6963 3290 6965 3290 6967 3295 6970 3290 6972 3292 6974 3291 6977 3293 6979 3291 6981 3290 6983 3290 6986 3291 6988 3292 6990 3292 6993 3291 6995 3291 6997 3290 7000 3290 7002 3290 7004 3290 7006 3290 7009 3290 7011 3290 7013 3290 7016 3291 7018 3291 7020 3291 7023 3291 7025 3292 7027 3291 7030 3290 7032 3290 7034 3290 7036 3290 7039 3290 7041 3290 7043 3290 7046 3290 7048 3290 7050 3290 7053 3290 7055 3290 7057 3291 7059 3292 7062 3290 7064 3290 7066 3290 7069 3290 7071 3291 7073 3290 7076 3293 7078 3290 7080 3291 7082 3290 7085 3290 7087 3290 7089 3290 7092 3294 7094 3294 7096 3291 7099 3291 7101 3291 7103 3291 7106 3291 7108 3291 7110 3290 7112 3292 7115 3292 7117 3290 7119 3290 7122 3290 7124 3290 7126 3290 7129 3290 7131 3290 7133 3290 7135 3290 7138 3291 7140 3290 7142 3290 7145 3290 7147 3290 7149 3290 7152 3290 7154 3290 7156 3290 7159 3290 7161 3290 7163 3290 7165 3290 7168 3290 7170 3292 7172 3290 7175 3290 7177 3290 7179 3290 7182 3290 7184 3291 7186 3292 7188 3292 7191 3292 7193 3292 7195 3290 7198 3290 7200 3290 7202 3292 7205 3291 7207 3290 7209 3290 7212 3290 7214 3291 7216 3291 7218 3291 7221 3291 7223 3291 7225 3290 7228 3290 7230 3290 7232 3290 7235 3292 7237 3292 7239 3290 7241 3290 7244 3290 7246 3290 7248 3290 7251 3290 7253 3290 7255 3290 7258 3290 7260 3290 7262 3290 7265 3290 7267 3290 7269 3290 7271 3290 7274 3290 7276 3292 7278 3292 7281 3291 7283 3296 7285 3292 7288 3292 7290 3292 7292 3292 7294 3290 7297 3290 7299 3290 7301 3290 7304 3290 7306 3290 7308 3290 7311 3290 7313 3292 7315 3290 7318 3290 7320 3290 7322 3290 7324 3290 7327 3290 7329 3290 7331 3290 7334 3290 7336 3290 7338 3291 7341 3291 7343 3292 7345 3290 7347 3290 7350 3290 7352 3290 7354 3290 7357 3290 7359 3290 7361 3290 7364 3290 7366 3290 7368 3290 7370 3290 7373 3290 7375 3290 7377 3290 7380 3290 7382 3290 7384 3290 7387 3290 7389 3293 7391 3294 7394 3290 7396 3290 7398 3290 7400 3290 7403 3290 7405 3290 7407 3290 7410 3290 7412 3290 7414 3291 7417 3291 7419 3291 7421 3290 7423 3290 7426 3290 7428 3291 7430 3291 7433 3291 7435 3293 7437 3291 7440 3291 7442 3291 7444 3291 7447 3291 7449 3290 7451 3290 7453 3290 7456 3290 7458 3290 7460 3290 7463 3290 7465 3290 7467 3290 7470 3290 7472 3290 7474 3290 7476 3290 7479 3290 7481 3290 7483 3290 7486 3290 7488 3290 7490 3290 7493 3290 7495 3290 7497 3292 7500 3295 7502 3292 7504 3292 7506 3292 7509 3291 7511 3291 7513 3291 7516 3290 7518 3290 7520 3290 7523 3290 7525 3290 7527 3290 7529 3290 7532 3290 7534 3290 7536 3291 7539 3291 7541 3291 7543 3290 7546 3290 7548 3290 7550 3290 7553 3291 7555 3290 7557 3290 7559 3290 7562 3290 7564 3290 7566 3290 7569 3290 7571 3290 7573 3291 7576 3291 7578 3291 7580 3291 7582 3290 7585 3290 7587 3290 7589 3291 7592 3290 7594 3290 7596 3290 7599 3290 7601 3290 7603 3290 7606 3290 7608 3290 7610 3290 7612 3290 7615 3290 7617 3290 7619 3290 7622 3290 7624 3290 7626 3290 7629 3290 7631 3290 7633 3290 7635 3290 7638 3290 7640 3290 7642 3290 7645 3290 7647 3290 7649 3290 7652 3290 7654 3290 7656 3290 7658 3290 7661 3290 7663 3290 7665 3290 7668 3290 7670 3290 7672 3290 7675 3291 7677 3291 7679 3291 7682 3290 7684 3290 7686 3290 7688 3292 7691 3294 7693 3294 7695 3290 7698 3290 7700 3290 7702 3290 7705 3290 7707 3290 7709 3290 7711 3291 7714 3290 7716 3290 7718 3290 7721 3290 7723 3290 7725 3290 7728 3290 7730 3290 7732 3290 7735 3290 7737 3290 7739 3290 7741 3290 7744 3290 7746 3290 7748 3290 7751 3290 7753 3290 7755 3290 7758 3290 7760 3290 7762 3290 7764 3290 7767 3290 7769 3290 7771 3290 7774 3290 7776 3290 7778 3290 7781 3290 7783 3290 7785 3290 7788 3290 7790 3290 7792 3290 7794 3290 7797 3290 7799 3290 7801 3290 7804 3291 7806 3291 7808 3290 7811 3290 7813 3290 7815 3290 7817 3290 7820 3290 7822 3290 7824 3290 7827 3290 7829 3290 7831 3290 7834 3290 7836 3290 7838 3290 7841 3290 7843 3290 7845 3290 7847 3290 7850 3290 7852 3290 7854 3290 7857 3290 7859 3290 7861 3290 7864 3290 7866 3290 7868 3290 7870 3290 7873 3290 7875 3290 7877 3290 7880 3291 7882 3291 7884 3291 7887 3290 7889 3290 7891 3290 7894 3290 7896 3291 7898 3290 7900 3290 7903 3290 7905 3290 7907 3290 7910 3290 7912 3291 7914 3290 7917 3290 7919 3290 7921 3291 7923 3291 7926 3291 7928 3290 7930 3290 7933 3290 7935 3290 7937 3290 7940 3290 7942 3290 7944 3290 7946 3290 7949 3290 7951 3290 7953 3290 7956 3290 7958 3290 7960 3290 7963 3290 7965 3290 7967 3290 7970 3290 7972 3290 7974 3290 7976 3290 7979 3290 7981 3290 7983 3290 7986 3290 7988 3290 7990 3290 7993 3290 7995 3290 7997 3290 7999 3290 8002 3290 8004 3290 8006 3290 8009 3290 8011 3290 8013 3290 8016 3290 8018 3290 8020 3290 8023 3290 8025 3290 8027 3290 8029 3290 8032 3290 8034 3290 8036 3290 8039 3290 8041 3290 8043 3290 8046 3290 8048 3290 8050 3290 8052 3290 500 MLine End Begin %I MLine [1 0 0 1 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 0 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 274 8052 3290 8055 3290 8057 3290 8059 3290 8062 3290 8064 3290 8066 3290 8069 3290 8071 3290 8073 3290 8076 3290 8078 3290 8080 3290 8082 3290 8085 3290 8087 3290 8089 3290 8092 3290 8094 3290 8096 3290 8099 3290 8101 3290 8103 3290 8105 3290 8108 3290 8110 3290 8112 3290 8115 3290 8117 3290 8119 3290 8122 3290 8124 3290 8126 3290 8129 3290 8131 3290 8133 3290 8135 3290 8138 3290 8140 3290 8142 3290 8145 3290 8147 3290 8149 3290 8152 3290 8154 3290 8156 3290 8158 3290 8161 3290 8163 3290 8165 3290 8168 3290 8170 3290 8172 3290 8175 3290 8177 3290 8179 3290 8182 3290 8184 3290 8186 3290 8188 3290 8191 3290 8193 3290 8195 3290 8198 3290 8200 3290 8202 3290 8205 3290 8207 3290 8209 3290 8211 3290 8214 3290 8216 3290 8218 3290 8221 3290 8223 3290 8225 3290 8228 3290 8230 3290 8232 3290 8234 3290 8237 3290 8239 3290 8241 3290 8244 3290 8246 3290 8248 3290 8251 3290 8253 3290 8255 3290 8258 3290 8260 3290 8262 3290 8264 3290 8267 3290 8269 3290 8271 3290 8274 3290 8276 3290 8278 3290 8281 3290 8283 3290 8285 3290 8287 3290 8290 3290 8292 3290 8294 3290 8297 3290 8299 3290 8301 3290 8304 3290 8306 3290 8308 3290 8311 3290 8313 3290 8315 3290 8317 3290 8320 3290 8322 3290 8324 3290 8327 3290 8329 3290 8331 3290 8334 3290 8336 3290 8338 3290 8340 3290 8343 3290 8345 3290 8347 3290 8350 3290 8352 3290 8354 3290 8357 3290 8359 3290 8361 3290 8364 3290 8366 3290 8368 3290 8370 3290 8373 3290 8375 3290 8377 3290 8380 3290 8382 3290 8384 3290 8387 3290 8389 3290 8391 3290 8393 3290 8396 3290 8398 3290 8400 3290 8403 3290 8405 3290 8407 3290 8410 3290 8412 3290 8414 3290 8417 3290 8419 3290 8421 3290 8423 3290 8426 3290 8428 3290 8430 3290 8433 3290 8435 3290 8437 3290 8440 3290 8442 3290 8444 3290 8446 3290 8449 3290 8451 3290 8453 3290 8456 3290 8458 3290 8460 3290 8463 3290 8465 3290 8467 3290 8470 3290 8472 3290 8474 3290 8476 3290 8479 3290 8481 3290 8483 3290 8486 3290 8488 3290 8490 3290 8493 3290 8495 3290 8497 3290 8499 3290 8502 3290 8504 3290 8506 3290 8509 3290 8511 3290 8513 3290 8516 3290 8518 3290 8520 3290 8522 3290 8525 3290 8527 3290 8529 3290 8532 3290 8534 3290 8536 3290 8539 3290 8541 3290 8543 3290 8546 3290 8548 3290 8550 3290 8552 3290 8555 3290 8557 3290 8559 3290 8562 3290 8564 3290 8566 3290 8569 3290 8571 3290 8573 3290 8575 3290 8578 3290 8580 3290 8582 3290 8585 3290 8587 3290 8589 3290 8592 3290 8594 3290 8596 3290 8599 3290 8601 3290 8603 3290 8605 3290 8608 3290 8610 3290 8612 3290 8615 3290 8617 3290 8619 3290 8622 3290 8624 3290 8626 3290 8628 3290 8631 3290 8633 3290 8635 3290 8638 3290 8640 3290 8642 3290 8645 3290 8647 3290 8649 3290 8652 3290 8654 3290 8656 3290 8658 3290 8661 3290 8663 3290 8665 3290 8668 3290 8670 3290 8672 3290 8675 3290 8677 3290 8679 3290 8681 3290 274 MLine End %%PageTrailer End %I eop showpage %%Trailer end %%EOF %%EndDocument @endspecial 390 5121 a FK(Example)39 b(of)g(a)h(sim)m(ulated)g (annealing)f(run:)57 b(at)40 b(higher)e(temp)s(eratures)h(\(early)h(in) f(the)390 5230 y(plot\))46 b(y)m(ou)f(see)h(that)g(the)f(solution)h (can)f(\015uctuate,)50 b(but)44 b(at)i(lo)m(w)m(er)h(temp)s(eratures)d (it)390 5340 y(con)m(v)m(erges.)p eop end %%Page: 332 350 TeXDict begin 332 349 bop 150 -116 a FK(Chapter)30 b(26:)41 b(Sim)m(ulated)31 b(Annealing)2126 b(332)150 299 y Fy(26.3.2)63 b(T)-10 b(ra)m(v)m(eling)40 b(Salesman)i(Problem)150 446 y FK(The)29 b(TSP)f(\()p FD(T)-8 b(ra)m(v)m(eling)32 b(Salesman)e(Problem)p FK(\))f(is)h(the)f(classic)i(com)m(binatorial)h (optimization)f(problem.)150 555 y(I)f(ha)m(v)m(e)i(pro)m(vided)e(a)h (v)m(ery)f(simple)h(v)m(ersion)g(of)f(it,)h(based)f(on)h(the)f(co)s (ordinates)h(of)g(t)m(w)m(elv)m(e)i(cities)f(in)e(the)150 665 y(south)m(w)m(estern)37 b(United)f(States.)59 b(This)36 b(should)f(ma)m(yb)s(e)h(b)s(e)g(called)h(the)g FD(Flying)g(Salesman)f (Problem)p FK(,)150 775 y(since)d(I)g(am)g(using)f(the)h(great-circle)j (distance)e(b)s(et)m(w)m(een)f(cities,)i(rather)e(than)g(the)g(driving) f(distance.)150 884 y(Also:)41 b(I)31 b(assume)f(the)g(earth)h(is)f(a)h (sphere,)f(so)g(I)h(don't)f(use)g(geoid)h(distances.)275 1023 y(The)37 b FH(gsl_siman_solve)d FK(routine)k(\014nds)f(a)h(route)h (whic)m(h)f(is)g(3490.62)j(Kilometers)e(long;)k(this)38 b(is)150 1132 y(con\014rmed)29 b(b)m(y)i(an)f(exhaustiv)m(e)h(searc)m (h)g(of)g(all)g(p)s(ossible)f(routes)h(with)f(the)g(same)h(initial)h (cit)m(y)-8 b(.)275 1271 y(The)27 b(full)h(co)s(de)g(can)h(b)s(e)e (found)g(in)g FH(siman/siman_tsp.c)p FK(,)e(but)i(I)h(include)g(here)f (some)i(plots)f(gener-)150 1380 y(ated)j(in)f(the)h(follo)m(wing)g(w)m (a)m(y:)390 1496 y Fz($)39 b(./siman_tsp)j(>)e(tsp.output)390 1583 y($)f(grep)i(-v)e("^#")h(tsp.output)429 1671 y(|)g(awk)g('{print)g ($1,)g($NF}')429 1758 y(|)g(graph)g(-y)g(3300)g(6500)g(-W0)g(-X)g (generation)h(-Y)f(distance)547 1845 y(-L)g("TSP)g(-)f(12)h(southwest)h (cities")429 1932 y(|)f(plot)g(-Tps)g(>)f(12-cities.eps)390 2019 y($)g(grep)i(initial_city_coord)i(tsp.output)468 2106 y(|)d(awk)g('{print)h($2,)f($3}')468 2194 y(|)g(graph)g(-X)g ("longitude)h(\(-)f(means)h(west\)")f(-Y)g("latitude")586 2281 y(-L)g("TSP)g(-)f(initial-order")k(-f)d(0.03)g(-S)f(1)h(0.1)468 2368 y(|)g(plot)g(-Tps)g(>)g(initial-route.eps)390 2455 y($)f(grep)i(final_city_coord)h(tsp.output)468 2542 y(|)e(awk)g ('{print)h($2,)f($3}')468 2629 y(|)g(graph)g(-X)g("longitude)h(\(-)f (means)h(west\)")f(-Y)g("latitude")586 2717 y(-L)g("TSP)g(-)f (final-order")j(-f)e(0.03)g(-S)g(1)f(0.1)468 2804 y(|)h(plot)g(-Tps)g (>)g(final-route.eps)150 2942 y FK(This)34 b(is)h(the)g(output)g(sho)m (wing)g(the)g(initial)h(order)e(of)h(the)g(cities;)k(longitude)d(is)f (negativ)m(e,)j(since)d(it)h(is)150 3052 y(w)m(est)31 b(and)f(I)g(w)m(an)m(t)h(the)g(plot)g(to)g(lo)s(ok)g(lik)m(e)g(a)g (map.)390 3168 y Fz(#)39 b(initial)i(coordinates)h(of)e(cities)g (\(longitude)i(and)e(latitude\))390 3255 y(###initial_city_coord:)k (-105.95)d(35.68)f(Santa)h(Fe)390 3342 y(###initial_city_coord:)j (-112.07)d(33.54)f(Phoenix)390 3429 y(###initial_city_coord:)k(-106.62) d(35.12)f(Albuquerque)390 3516 y(###initial_city_coord:)k(-103.2)d (34.41)f(Clovis)390 3604 y(###initial_city_coord:)k(-107.87)d(37.29)f (Durango)390 3691 y(###initial_city_coord:)k(-96.77)d(32.79)f(Dallas) 390 3778 y(###initial_city_coord:)k(-105.92)d(35.77)f(Tesuque)390 3865 y(###initial_city_coord:)k(-107.84)d(35.15)f(Grants)390 3952 y(###initial_city_coord:)k(-106.28)d(35.89)f(Los)g(Alamos)390 4039 y(###initial_city_coord:)k(-106.76)d(32.34)f(Las)g(Cruces)390 4127 y(###initial_city_coord:)k(-108.58)d(37.35)f(Cortez)390 4214 y(###initial_city_coord:)k(-108.74)d(35.52)f(Gallup)390 4301 y(###initial_city_coord:)k(-105.95)d(35.68)f(Santa)h(Fe)275 4439 y FK(The)29 b(optimal)j(route)e(turns)f(out)i(to)g(b)s(e:)390 4555 y Fz(#)39 b(final)i(coordinates)h(of)d(cities)i(\(longitude)g(and) f(latitude\))390 4643 y(###final_city_coord:)k(-105.95)d(35.68)f(Santa) g(Fe)390 4730 y(###final_city_coord:)k(-103.2)c(34.41)h(Clovis)390 4817 y(###final_city_coord:)j(-96.77)c(32.79)h(Dallas)390 4904 y(###final_city_coord:)j(-106.76)d(32.34)f(Las)g(Cruces)390 4991 y(###final_city_coord:)k(-112.07)d(33.54)f(Phoenix)390 5078 y(###final_city_coord:)k(-108.74)d(35.52)f(Gallup)390 5166 y(###final_city_coord:)k(-108.58)d(37.35)f(Cortez)390 5253 y(###final_city_coord:)k(-107.87)d(37.29)f(Durango)390 5340 y(###final_city_coord:)k(-107.84)d(35.15)f(Grants)p eop end %%Page: 333 351 TeXDict begin 333 350 bop 150 -116 a FK(Chapter)30 b(26:)41 b(Sim)m(ulated)31 b(Annealing)2126 b(333)390 299 y Fz (###final_city_coord:)44 b(-106.62)d(35.12)f(Albuquerque)390 386 y(###final_city_coord:)k(-106.28)d(35.89)f(Los)g(Alamos)390 473 y(###final_city_coord:)k(-105.92)d(35.77)f(Tesuque)390 560 y(###final_city_coord:)k(-105.95)d(35.68)f(Santa)g(Fe)275 2211 y @beginspecial 101 @llx 194 @lly 489 @urx 610 @ury 1584 @rwi @setspecial %%BeginDocument: initial-route.eps %!PS-Adobe-3.0 EPSF-3.0 %%Creator: GNU libplot drawing library 4.1 %%Title: PostScript plot %%CreationDate: Thu Jan 4 10:56:26 2007 %%DocumentData: Clean7Bit %%LanguageLevel: 1 %%Pages: 1 %%PageOrder: Ascend %%Orientation: Portrait %%BoundingBox: 101 194 489 610 %%DocumentNeededResources: %%DocumentSuppliedResources: procset GNU_libplot 1.0 0 %%EndComments %%BeginDefaults %%PageResources: %%EndDefaults %%BeginProlog %%EndProlog %%BeginSetup /DrawDict 50 dict def DrawDict begin %%BeginResource procset GNU_libplot 1.0 0 /none null def /numGraphicParameters 17 def /stringLimit 65535 def /arrowHeight 8 def /eoFillRule true def /Begin { save numGraphicParameters dict begin } def /End { end restore } def /SetB { dup type /nulltype eq { pop false /brushRightArrow idef false /brushLeftArrow idef true /brushNone idef } { /brushDashOffset idef /brushDashArray idef 0 ne /brushRightArrow idef 0 ne /brushLeftArrow idef /brushWidth idef false /brushNone idef } ifelse } def /SetCFg { /fgblue idef /fggreen idef /fgred idef } def /SetCBg { /bgblue idef /bggreen idef /bgred idef } def /SetF { /printSize idef /printFont idef } def /SetP { dup type /nulltype eq { pop true /patternNone idef } { /patternGrayLevel idef patternGrayLevel -1 eq { /patternString idef } if false /patternNone idef } ifelse } def /BSpl { 0 begin storexyn newpath n 1 gt { 0 0 0 0 0 0 1 1 true subspline n 2 gt { 0 0 0 0 1 1 2 2 false subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 2 copy false subspline } if n 2 sub dup n 1 sub dup 2 copy 2 copy false subspline patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup 1 sub dup rightarrow } if end } dup 0 4 dict put def /Circ { newpath 0 360 arc closepath patternNone not { ifill } if brushNone not { istroke } if } def /CBSpl { 0 begin dup 2 gt { storexyn newpath n 1 sub dup 0 0 1 1 2 2 true subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 0 0 false subspline n 2 sub dup n 1 sub dup 0 0 1 1 false subspline patternNone not { ifill } if brushNone not { istroke } if } { Poly } ifelse end } dup 0 4 dict put def /Elli { 0 begin newpath 4 2 roll translate scale 0 0 1 0 360 arc closepath patternNone not { ifill } if brushNone not { istroke } if end } dup 0 1 dict put def /Line { 0 begin 2 storexyn newpath x 0 get y 0 get moveto x 1 get y 1 get lineto brushNone not { istroke } if 0 0 1 1 leftarrow 0 0 1 1 rightarrow end } dup 0 4 dict put def /MLine { 0 begin storexyn newpath n 1 gt { x 0 get y 0 get moveto 1 1 n 1 sub { /i exch def x i get y i get lineto } for patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Poly { 3 1 roll newpath moveto -1 add { lineto } repeat closepath patternNone not { ifill } if brushNone not { istroke } if } def /Rect { 0 begin /t exch def /r exch def /b exch def /l exch def newpath l b moveto l t lineto r t lineto r b lineto closepath patternNone not { ifill } if brushNone not { istroke } if end } dup 0 4 dict put def /Text { ishow } def /idef { dup where { pop pop pop } { exch def } ifelse } def /ifill { 0 begin gsave patternGrayLevel -1 ne { fgred bgred fgred sub patternGrayLevel mul add fggreen bggreen fggreen sub patternGrayLevel mul add fgblue bgblue fgblue sub patternGrayLevel mul add setrgbcolor eoFillRule { eofill } { fill } ifelse } { eoFillRule { eoclip } { clip } ifelse originalCTM setmatrix pathbbox /t exch def /r exch def /b exch def /l exch def /w r l sub ceiling cvi def /h t b sub ceiling cvi def /imageByteWidth w 8 div ceiling cvi def /imageHeight h def bgred bggreen bgblue setrgbcolor eoFillRule { eofill } { fill } ifelse fgred fggreen fgblue setrgbcolor w 0 gt h 0 gt and { l b translate w h scale w h true [w 0 0 h neg 0 h] { patternproc } imagemask } if } ifelse grestore end } dup 0 8 dict put def /istroke { gsave brushDashOffset -1 eq { [] 0 setdash 1 setgray } { brushDashArray brushDashOffset setdash fgred fggreen fgblue setrgbcolor } ifelse brushWidth setlinewidth originalCTM setmatrix stroke grestore } def /ishow { 0 begin gsave fgred fggreen fgblue setrgbcolor /fontDict printFont findfont printSize scalefont dup setfont def /descender fontDict begin 0 /FontBBox load 1 get FontMatrix end transform exch pop def /vertoffset 1 printSize sub descender sub def { 0 vertoffset moveto show /vertoffset vertoffset printSize sub def } forall grestore end } dup 0 3 dict put def /patternproc { 0 begin /patternByteLength patternString length def /patternHeight patternByteLength 8 mul sqrt cvi def /patternWidth patternHeight def /patternByteWidth patternWidth 8 idiv def /imageByteMaxLength imageByteWidth imageHeight mul stringLimit patternByteWidth sub min def /imageMaxHeight imageByteMaxLength imageByteWidth idiv patternHeight idiv patternHeight mul patternHeight max def /imageHeight imageHeight imageMaxHeight sub store /imageString imageByteWidth imageMaxHeight mul patternByteWidth add string def 0 1 imageMaxHeight 1 sub { /y exch def /patternRow y patternByteWidth mul patternByteLength mod def /patternRowString patternString patternRow patternByteWidth getinterval def /imageRow y imageByteWidth mul def 0 patternByteWidth imageByteWidth 1 sub { /x exch def imageString imageRow x add patternRowString putinterval } for } for imageString end } dup 0 12 dict put def /min { dup 3 2 roll dup 4 3 roll lt { exch } if pop } def /max { dup 3 2 roll dup 4 3 roll gt { exch } if pop } def /midpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 x1 add 2 div y0 y1 add 2 div end } dup 0 4 dict put def /thirdpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 2 mul x1 add 3 div y0 2 mul y1 add 3 div end } dup 0 4 dict put def /subspline { 0 begin /movetoNeeded exch def y exch get /y3 exch def x exch get /x3 exch def y exch get /y2 exch def x exch get /x2 exch def y exch get /y1 exch def x exch get /x1 exch def y exch get /y0 exch def x exch get /x0 exch def x1 y1 x2 y2 thirdpoint /p1y exch def /p1x exch def x2 y2 x1 y1 thirdpoint /p2y exch def /p2x exch def x1 y1 x0 y0 thirdpoint p1x p1y midpoint /p0y exch def /p0x exch def x2 y2 x3 y3 thirdpoint p2x p2y midpoint /p3y exch def /p3x exch def movetoNeeded { p0x p0y moveto } if p1x p1y p2x p2y p3x p3y curveto end } dup 0 17 dict put def /storexyn { /n exch def /y n array def /x n array def n 1 sub -1 0 { /i exch def y i 3 2 roll put x i 3 2 roll put } for } def /arrowhead { 0 begin transform originalCTM itransform /taily exch def /tailx exch def transform originalCTM itransform /tipy exch def /tipx exch def /dy tipy taily sub def /dx tipx tailx sub def /angle dx 0 ne dy 0 ne or { dy dx atan } { 90 } ifelse def gsave originalCTM setmatrix tipx tipy translate angle rotate newpath arrowHeight neg arrowWidth 2 div moveto 0 0 lineto arrowHeight neg arrowWidth 2 div neg lineto patternNone not { originalCTM setmatrix /padtip arrowHeight 2 exp 0.25 arrowWidth 2 exp mul add sqrt brushWidth mul arrowWidth div def /padtail brushWidth 2 div def tipx tipy translate angle rotate padtip 0 translate arrowHeight padtip add padtail add arrowHeight div dup scale arrowheadpath ifill } if brushNone not { originalCTM setmatrix tipx tipy translate angle rotate arrowheadpath istroke } if grestore end } dup 0 9 dict put def /arrowheadpath { newpath arrowHeight neg arrowWidth 2 div moveto 0 0 lineto arrowHeight neg arrowWidth 2 div neg lineto } def /leftarrow { 0 begin y exch get /taily exch def x exch get /tailx exch def y exch get /tipy exch def x exch get /tipx exch def brushLeftArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /rightarrow { 0 begin y exch get /tipy exch def x exch get /tipx exch def y exch get /taily exch def x exch get /tailx exch def brushRightArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def %%EndResource %%EndSetup %%Page: 1 1 %%PageResources: %%PageBoundingBox: 101 194 489 610 %%BeginPageSetup %I Idraw 8 Begin %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 1 0 0 1 0 0 ] concat /originalCTM matrix currentmatrix def /trueoriginalCTM matrix currentmatrix def %%EndPageSetup Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3399 10017 3399 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3414 10017 3414 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 3311 10017 3297 9930 3297 10017 3517 10017 3517 9930 3502 10017 6 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3355 9710 3458 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 3781 9973 3795 10017 3795 9930 3781 9973 3751 10003 3707 10017 3663 10017 3619 10003 3590 9973 3590 9944 3605 9915 3619 9900 3649 9886 3737 9856 3766 9842 3795 9812 16 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 3590 9944 3619 9915 3649 9900 3737 9871 3766 9856 3781 9842 3795 9812 3795 9754 3766 9724 3722 9710 3678 9710 3634 9724 3605 9754 3590 9798 3590 9710 3605 9754 16 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3913 10017 3913 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3927 10017 3927 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 3869 10017 4045 10017 4089 10003 4103 9988 4118 9959 4118 9915 4103 9886 4089 9871 4045 9856 3927 9856 10 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 4045 10017 4074 10003 4089 9988 4103 9959 4103 9915 4089 9886 4074 9871 4045 9856 8 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3869 9710 3971 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4455 9842 4719 9842 2 MLine End Begin %I Poly [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 5100 10003 5086 9988 5071 10003 5086 10017 4 Poly End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5086 9915 5086 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5100 9915 5100 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5042 9915 5100 9915 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5042 9710 5144 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5247 9915 5247 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5261 9915 5261 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 5261 9871 5291 9900 5335 9915 5364 9915 5408 9900 5423 9871 5423 9710 7 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 5364 9915 5393 9900 5408 9871 5408 9710 4 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5203 9915 5261 9915 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5203 9710 5305 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5364 9710 5467 9710 2 MLine End Begin %I Poly [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 5584 10003 5569 9988 5555 10003 5569 10017 4 Poly End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5569 9915 5569 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5584 9915 5584 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5525 9915 5584 9915 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5525 9710 5628 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 5731 10017 5731 9768 5745 9724 5775 9710 5804 9710 5833 9724 5848 9754 7 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 5745 10017 5745 9768 5760 9724 5775 9710 4 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5687 9915 5804 9915 2 MLine End Begin %I Poly [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 5965 10003 5951 9988 5936 10003 5951 10017 4 Poly End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5951 9915 5951 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5965 9915 5965 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5907 9915 5965 9915 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5907 9710 6009 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 13 6112 9886 6112 9871 6097 9871 6097 9886 6112 9900 6141 9915 6200 9915 6229 9900 6244 9886 6259 9856 6259 9754 6273 9724 6288 9710 13 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5 6244 9886 6244 9754 6259 9724 6288 9710 6302 9710 5 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 11 6244 9856 6229 9842 6141 9827 6097 9812 6083 9783 6083 9754 6097 9724 6141 9710 6185 9710 6215 9724 6244 9754 11 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 6141 9827 6112 9812 6097 9783 6097 9754 6112 9724 6141 9710 6 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6405 10017 6405 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6420 10017 6420 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6361 10017 6420 10017 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6361 9710 6464 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6552 9842 6816 9842 2 MLine End Begin %I Poly [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 7036 9915 7080 9900 7109 9871 7124 9827 7124 9798 7109 9754 7080 9724 7036 9710 7006 9710 6962 9724 6933 9754 6918 9798 6918 9827 6933 9871 6962 9900 7006 9915 16 Poly End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 7006 9915 6977 9900 6948 9871 6933 9827 6933 9798 6948 9754 6977 9724 7006 9710 8 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 7036 9710 7065 9724 7094 9754 7109 9798 7109 9827 7094 9871 7065 9900 7036 9915 8 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7241 9915 7241 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7256 9915 7256 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 7256 9827 7270 9871 7299 9900 7329 9915 7373 9915 7387 9900 7387 9886 7373 9871 7358 9886 7373 9900 10 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7197 9915 7256 9915 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7197 9710 7299 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7637 10017 7637 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7651 10017 7651 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 14 7637 9871 7607 9900 7578 9915 7549 9915 7505 9900 7475 9871 7461 9827 7461 9798 7475 9754 7505 9724 7549 9710 7578 9710 7607 9724 7637 9754 14 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 7549 9915 7519 9900 7490 9871 7475 9827 7475 9798 7490 9754 7519 9724 7549 9710 8 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7593 10017 7651 10017 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7637 9710 7695 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 17 7783 9827 7959 9827 7959 9856 7945 9886 7930 9900 7901 9915 7857 9915 7813 9900 7783 9871 7769 9827 7769 9798 7783 9754 7813 9724 7857 9710 7886 9710 7930 9724 7959 9754 17 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 7945 9827 7945 9871 7930 9900 3 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 7857 9915 7827 9900 7798 9871 7783 9827 7783 9798 7798 9754 7827 9724 7857 9710 8 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8077 9915 8077 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8091 9915 8091 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 8091 9827 8106 9871 8135 9900 8165 9915 8209 9915 8223 9900 8223 9886 8209 9871 8194 9886 8209 9900 10 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8033 9915 8091 9915 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8033 9710 8135 9710 2 MLine End Begin %I Rect [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2304 2304 9216 9216 Rect End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2059 2097 2172 2097 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 2235 2147 2247 2153 2266 2172 2266 2040 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2260 2166 2260 2040 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2235 2040 2291 2040 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 2361 2147 2373 2153 2392 2172 2392 2040 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2386 2166 2386 2040 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2361 2040 2417 2040 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2524 2159 2524 2040 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2530 2172 2530 2040 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 2530 2172 2461 2078 2562 2078 3 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2505 2040 2549 2040 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 9216 2304 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2304 2304 2442 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2827 2097 2940 2097 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 3003 2147 3015 2153 3034 2172 3034 2040 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3028 2166 3028 2040 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3003 2040 3059 2040 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 3129 2147 3141 2153 3160 2172 3160 2040 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3154 2166 3154 2040 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3129 2040 3185 2040 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 20 3242 2147 3248 2141 3242 2134 3235 2141 3235 2147 3242 2159 3248 2166 3267 2172 3292 2172 3311 2166 3317 2159 3323 2147 3323 2134 3317 2122 3298 2109 3267 2097 3254 2090 3242 2078 3235 2059 3235 2040 20 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 3292 2172 3304 2166 3311 2159 3317 2147 3317 2134 3311 2122 3292 2109 3267 2097 8 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 3235 2053 3242 2059 3254 2059 3286 2046 3304 2046 3317 2053 3323 2059 7 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 3254 2059 3286 2040 3311 2040 3317 2046 3323 2059 3323 2072 6 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3072 9216 3072 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3072 2304 3072 2442 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3595 2097 3708 2097 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 3771 2147 3783 2153 3802 2172 3802 2040 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3796 2166 3796 2040 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3771 2040 3827 2040 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 3897 2147 3909 2153 3928 2172 3928 2040 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3922 2166 3922 2040 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3897 2040 3953 2040 2 MLine End Begin %I Poly [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 4054 2172 4072 2166 4085 2147 4091 2115 4091 2097 4085 2065 4072 2046 4054 2040 4041 2040 4022 2046 4010 2065 4003 2097 4003 2115 4010 2147 4022 2166 4041 2172 16 Poly End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 4041 2172 4029 2166 4022 2159 4016 2147 4010 2115 4010 2097 4016 2065 4022 2053 4029 2046 4041 2040 10 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 4054 2040 4066 2046 4072 2053 4079 2065 4085 2097 4085 2115 4079 2147 4072 2159 4066 2166 4054 2172 10 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3840 9216 3840 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3840 2304 3840 2442 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4363 2097 4476 2097 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 4539 2147 4551 2153 4570 2172 4570 2040 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4564 2166 4564 2040 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4539 2040 4595 2040 2 MLine End Begin %I Poly [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 4696 2172 4715 2166 4727 2147 4734 2115 4734 2097 4727 2065 4715 2046 4696 2040 4683 2040 4665 2046 4652 2065 4646 2097 4646 2115 4652 2147 4665 2166 4683 2172 16 Poly End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 4683 2172 4671 2166 4665 2159 4658 2147 4652 2115 4652 2097 4658 2065 4665 2053 4671 2046 4683 2040 10 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 4696 2040 4709 2046 4715 2053 4721 2065 4727 2097 4727 2115 4721 2147 4715 2159 4709 2166 4696 2172 10 MLine End Begin %I Poly [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 12 4828 2172 4847 2166 4853 2153 4853 2134 4847 2122 4828 2115 4803 2115 4784 2122 4778 2134 4778 2153 4784 2166 4803 2172 12 Poly End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 4803 2172 4790 2166 4784 2153 4784 2134 4790 2122 4803 2115 6 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 4828 2115 4840 2122 4847 2134 4847 2153 4840 2166 4828 2172 6 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 4803 2115 4784 2109 4778 2103 4771 2090 4771 2065 4778 2053 4784 2046 4803 2040 4828 2040 4847 2046 4853 2053 4859 2065 4859 2090 4853 2103 4847 2109 4828 2115 16 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 4803 2115 4790 2109 4784 2103 4778 2090 4778 2065 4784 2053 4790 2046 4803 2040 8 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 4828 2040 4840 2046 4847 2053 4853 2065 4853 2090 4847 2103 4840 2109 4828 2115 8 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4608 9216 4608 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4608 2304 4608 2442 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5131 2097 5244 2097 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 5307 2147 5319 2153 5338 2172 5338 2040 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5332 2166 5332 2040 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5307 2040 5363 2040 2 MLine End Begin %I Poly [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 5464 2172 5483 2166 5495 2147 5502 2115 5502 2097 5495 2065 5483 2046 5464 2040 5451 2040 5433 2046 5420 2065 5414 2097 5414 2115 5420 2147 5433 2166 5451 2172 16 Poly End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 5451 2172 5439 2166 5433 2159 5426 2147 5420 2115 5420 2097 5426 2065 5433 2053 5439 2046 5451 2040 10 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 5464 2040 5477 2046 5483 2053 5489 2065 5495 2097 5495 2115 5489 2147 5483 2159 5477 2166 5464 2172 10 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 28 5615 2153 5608 2147 5615 2141 5621 2147 5621 2153 5615 2166 5602 2172 5583 2172 5565 2166 5552 2153 5546 2141 5539 2115 5539 2078 5546 2059 5558 2046 5577 2040 5590 2040 5608 2046 5621 2059 5627 2078 5627 2084 5621 2103 5608 2115 5590 2122 5583 2122 5565 2115 5552 2103 5546 2084 28 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 9 5583 2172 5571 2166 5558 2153 5552 2141 5546 2115 5546 2078 5552 2059 5565 2046 5577 2040 9 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 5590 2040 5602 2046 5615 2059 5621 2078 5621 2084 5615 2103 5602 2115 5590 2122 8 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5376 9216 5376 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5376 2304 5376 2442 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5899 2097 6012 2097 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 6075 2147 6087 2153 6106 2172 6106 2040 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6100 2166 6100 2040 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6075 2040 6131 2040 2 MLine End Begin %I Poly [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 6232 2172 6251 2166 6263 2147 6270 2115 6270 2097 6263 2065 6251 2046 6232 2040 6219 2040 6201 2046 6188 2065 6182 2097 6182 2115 6188 2147 6201 2166 6219 2172 16 Poly End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 6219 2172 6207 2166 6201 2159 6194 2147 6188 2115 6188 2097 6194 2065 6201 2053 6207 2046 6219 2040 10 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 6232 2040 6245 2046 6251 2053 6257 2065 6263 2097 6263 2115 6257 2147 6251 2159 6245 2166 6232 2172 10 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6364 2159 6364 2040 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6370 2172 6370 2040 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 6370 2172 6301 2078 6402 2078 3 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6345 2040 6389 2040 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6144 9216 6144 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6144 2304 6144 2442 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6667 2097 6780 2097 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 6843 2147 6855 2153 6874 2172 6874 2040 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6868 2166 6868 2040 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6843 2040 6899 2040 2 MLine End Begin %I Poly [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 7000 2172 7019 2166 7031 2147 7038 2115 7038 2097 7031 2065 7019 2046 7000 2040 6987 2040 6969 2046 6956 2065 6950 2097 6950 2115 6956 2147 6969 2166 6987 2172 16 Poly End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 6987 2172 6975 2166 6969 2159 6962 2147 6956 2115 6956 2097 6962 2065 6969 2053 6975 2046 6987 2040 10 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 7000 2040 7013 2046 7019 2053 7025 2065 7031 2097 7031 2115 7025 2147 7019 2159 7013 2166 7000 2172 10 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 20 7082 2147 7088 2141 7082 2134 7075 2141 7075 2147 7082 2159 7088 2166 7107 2172 7132 2172 7151 2166 7157 2159 7163 2147 7163 2134 7157 2122 7138 2109 7107 2097 7094 2090 7082 2078 7075 2059 7075 2040 20 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 7132 2172 7144 2166 7151 2159 7157 2147 7157 2134 7151 2122 7132 2109 7107 2097 8 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 7075 2053 7082 2059 7094 2059 7126 2046 7144 2046 7157 2053 7163 2059 7 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 7094 2059 7126 2040 7151 2040 7157 2046 7163 2059 7163 2072 6 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6912 9216 6912 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6912 2304 6912 2442 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7435 2097 7548 2097 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 7611 2147 7623 2153 7642 2172 7642 2040 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7636 2166 7636 2040 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7611 2040 7667 2040 2 MLine End Begin %I Poly [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 7768 2172 7787 2166 7799 2147 7806 2115 7806 2097 7799 2065 7787 2046 7768 2040 7755 2040 7737 2046 7724 2065 7718 2097 7718 2115 7724 2147 7737 2166 7755 2172 16 Poly End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 7755 2172 7743 2166 7737 2159 7730 2147 7724 2115 7724 2097 7730 2065 7737 2053 7743 2046 7755 2040 10 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 7768 2040 7781 2046 7787 2053 7793 2065 7799 2097 7799 2115 7793 2147 7787 2159 7781 2166 7768 2172 10 MLine End Begin %I Poly [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 7894 2172 7912 2166 7925 2147 7931 2115 7931 2097 7925 2065 7912 2046 7894 2040 7881 2040 7862 2046 7850 2065 7843 2097 7843 2115 7850 2147 7862 2166 7881 2172 16 Poly End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 7881 2172 7869 2166 7862 2159 7856 2147 7850 2115 7850 2097 7856 2065 7862 2053 7869 2046 7881 2040 10 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 7894 2040 7906 2046 7912 2053 7919 2065 7925 2097 7925 2115 7919 2147 7912 2159 7906 2166 7894 2172 10 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7680 9216 7680 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7680 2304 7680 2442 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8266 2097 8379 2097 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 28 8505 2128 8498 2109 8486 2097 8467 2090 8461 2090 8442 2097 8429 2109 8423 2128 8423 2134 8429 2153 8442 2166 8461 2172 8473 2172 8492 2166 8505 2153 8511 2134 8511 2097 8505 2072 8498 2059 8486 2046 8467 2040 8448 2040 8435 2046 8429 2059 8429 2065 8435 2072 8442 2065 8435 2059 28 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 8461 2090 8448 2097 8435 2109 8429 2128 8429 2134 8435 2153 8448 2166 8461 2172 8 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 9 8473 2172 8486 2166 8498 2153 8505 2134 8505 2097 8498 2072 8492 2059 8479 2046 8467 2040 9 MLine End Begin %I Poly [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 12 8605 2172 8624 2166 8630 2153 8630 2134 8624 2122 8605 2115 8580 2115 8561 2122 8555 2134 8555 2153 8561 2166 8580 2172 12 Poly End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 8580 2172 8567 2166 8561 2153 8561 2134 8567 2122 8580 2115 6 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 8605 2115 8618 2122 8624 2134 8624 2153 8618 2166 8605 2172 6 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 8580 2115 8561 2109 8555 2103 8549 2090 8549 2065 8555 2053 8561 2046 8580 2040 8605 2040 8624 2046 8630 2053 8637 2065 8637 2090 8630 2103 8624 2109 8605 2115 16 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 8580 2115 8567 2109 8561 2103 8555 2090 8555 2065 8561 2053 8567 2046 8580 2040 8 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 8605 2040 8618 2046 8624 2053 8630 2065 8630 2090 8624 2103 8618 2109 8605 2115 8 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8448 9216 8448 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8448 2304 8448 2442 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9034 2097 9147 2097 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 28 9273 2128 9266 2109 9254 2097 9235 2090 9229 2090 9210 2097 9197 2109 9191 2128 9191 2134 9197 2153 9210 2166 9229 2172 9241 2172 9260 2166 9273 2153 9279 2134 9279 2097 9273 2072 9266 2059 9254 2046 9235 2040 9216 2040 9203 2046 9197 2059 9197 2065 9203 2072 9210 2065 9203 2059 28 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 9229 2090 9216 2097 9203 2109 9197 2128 9197 2134 9203 2153 9216 2166 9229 2172 8 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 9 9241 2172 9254 2166 9266 2153 9273 2134 9273 2097 9266 2072 9260 2059 9247 2046 9235 2040 9 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 28 9392 2153 9386 2147 9392 2141 9398 2147 9398 2153 9392 2166 9379 2172 9361 2172 9342 2166 9329 2153 9323 2141 9317 2115 9317 2078 9323 2059 9335 2046 9354 2040 9367 2040 9386 2046 9398 2059 9405 2078 9405 2084 9398 2103 9386 2115 9367 2122 9361 2122 9342 2115 9329 2103 9323 2084 28 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 9 9361 2172 9348 2166 9335 2153 9329 2141 9323 2115 9323 2078 9329 2059 9342 2046 9354 2040 9 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 9367 2040 9379 2046 9392 2059 9398 2078 9398 2084 9392 2103 9379 2115 9367 2122 8 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 9216 9216 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2304 9216 2442 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 9216 2304 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2304 2304 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2688 9216 2688 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2688 2304 2688 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3072 9216 3072 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3072 2304 3072 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3456 9216 3456 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3456 2304 3456 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3840 9216 3840 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3840 2304 3840 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4224 9216 4224 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4224 2304 4224 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4608 9216 4608 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4608 2304 4608 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4992 9216 4992 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4992 2304 4992 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5376 9216 5376 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5376 2304 5376 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5760 9216 5760 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5760 2304 5760 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6144 9216 6144 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6144 2304 6144 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6528 9216 6528 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6528 2304 6528 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6912 9216 6912 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6912 2304 6912 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7296 9216 7296 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7296 2304 7296 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7680 9216 7680 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7680 2304 7680 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8064 9216 8064 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8064 2304 8064 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8448 9216 8448 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8448 2304 8448 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8832 9216 8832 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8832 2304 8832 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 9216 9216 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2304 9216 2359 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 1974 2354 1980 2348 1974 2342 1968 2348 1968 2354 1974 2367 1980 2373 1999 2379 2024 2379 2043 2373 2050 2361 2050 2342 2043 2329 2024 2323 2006 2323 15 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2024 2379 2037 2373 2043 2361 2043 2342 2037 2329 2024 2323 6 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 2024 2323 2037 2317 2050 2304 2056 2291 2056 2273 2050 2260 2043 2254 2024 2247 1999 2247 1980 2254 1974 2260 1968 2273 1968 2279 1974 2285 1980 2279 1974 2273 16 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2043 2310 2050 2291 2050 2273 2043 2260 2037 2254 2024 2247 6 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 20 2100 2354 2106 2348 2100 2342 2093 2348 2093 2354 2100 2367 2106 2373 2125 2379 2150 2379 2169 2373 2175 2367 2181 2354 2181 2342 2175 2329 2156 2317 2125 2304 2112 2298 2100 2285 2093 2266 2093 2247 20 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 2150 2379 2163 2373 2169 2367 2175 2354 2175 2342 2169 2329 2150 2317 2125 2304 8 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 2093 2260 2100 2266 2112 2266 2144 2254 2163 2254 2175 2260 2181 2266 7 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2112 2266 2144 2247 2169 2247 2175 2254 2181 2266 2181 2279 6 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2304 9078 2304 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2304 2442 2304 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 1974 3506 1980 3500 1974 3494 1968 3500 1968 3506 1974 3519 1980 3525 1999 3531 2024 3531 2043 3525 2050 3513 2050 3494 2043 3481 2024 3475 2006 3475 15 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2024 3531 2037 3525 2043 3513 2043 3494 2037 3481 2024 3475 6 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 2024 3475 2037 3469 2050 3456 2056 3443 2056 3425 2050 3412 2043 3406 2024 3399 1999 3399 1980 3406 1974 3412 1968 3425 1968 3431 1974 3437 1980 3431 1974 3425 16 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2043 3462 2050 3443 2050 3425 2043 3412 2037 3406 2024 3399 6 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 2100 3506 2106 3500 2100 3494 2093 3500 2093 3506 2100 3519 2106 3525 2125 3531 2150 3531 2169 3525 2175 3513 2175 3494 2169 3481 2150 3475 2131 3475 15 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2150 3531 2163 3525 2169 3513 2169 3494 2163 3481 2150 3475 6 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 2150 3475 2163 3469 2175 3456 2181 3443 2181 3425 2175 3412 2169 3406 2150 3399 2125 3399 2106 3406 2100 3412 2093 3425 2093 3431 2100 3437 2106 3431 2100 3425 16 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2169 3462 2175 3443 2175 3425 2169 3412 2163 3406 2150 3399 6 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 3456 9078 3456 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3456 2442 3456 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 1974 4658 1980 4652 1974 4646 1968 4652 1968 4658 1974 4671 1980 4677 1999 4683 2024 4683 2043 4677 2050 4665 2050 4646 2043 4633 2024 4627 2006 4627 15 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2024 4683 2037 4677 2043 4665 2043 4646 2037 4633 2024 4627 6 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 2024 4627 2037 4621 2050 4608 2056 4595 2056 4577 2050 4564 2043 4558 2024 4551 1999 4551 1980 4558 1974 4564 1968 4577 1968 4583 1974 4589 1980 4583 1974 4577 16 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2043 4614 2050 4595 2050 4577 2043 4564 2037 4558 2024 4551 6 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2150 4671 2150 4551 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2156 4683 2156 4551 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 2156 4683 2087 4589 2188 4589 3 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2131 4551 2175 4551 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 4608 9078 4608 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4608 2442 4608 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 1974 5810 1980 5804 1974 5798 1968 5804 1968 5810 1974 5823 1980 5829 1999 5835 2024 5835 2043 5829 2050 5817 2050 5798 2043 5785 2024 5779 2006 5779 15 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2024 5835 2037 5829 2043 5817 2043 5798 2037 5785 2024 5779 6 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 2024 5779 2037 5773 2050 5760 2056 5747 2056 5729 2050 5716 2043 5710 2024 5703 1999 5703 1980 5710 1974 5716 1968 5729 1968 5735 1974 5741 1980 5735 1974 5729 16 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2043 5766 2050 5747 2050 5729 2043 5716 2037 5710 2024 5703 6 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2106 5835 2093 5773 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 19 2093 5773 2106 5785 2125 5791 2144 5791 2163 5785 2175 5773 2181 5754 2181 5741 2175 5722 2163 5710 2144 5703 2125 5703 2106 5710 2100 5716 2093 5729 2093 5735 2100 5741 2106 5735 2100 5729 19 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 2144 5791 2156 5785 2169 5773 2175 5754 2175 5741 2169 5722 2156 5710 2144 5703 8 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2106 5835 2169 5835 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 2106 5829 2137 5829 2169 5835 3 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5760 9078 5760 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5760 2442 5760 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 1974 6962 1980 6956 1974 6950 1968 6956 1968 6962 1974 6975 1980 6981 1999 6987 2024 6987 2043 6981 2050 6969 2050 6950 2043 6937 2024 6931 2006 6931 15 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2024 6987 2037 6981 2043 6969 2043 6950 2037 6937 2024 6931 6 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 2024 6931 2037 6925 2050 6912 2056 6899 2056 6881 2050 6868 2043 6862 2024 6855 1999 6855 1980 6862 1974 6868 1968 6881 1968 6887 1974 6893 1980 6887 1974 6881 16 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2043 6918 2050 6899 2050 6881 2043 6868 2037 6862 2024 6855 6 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 28 2169 6969 2163 6962 2169 6956 2175 6962 2175 6969 2169 6981 2156 6987 2137 6987 2119 6981 2106 6969 2100 6956 2093 6931 2093 6893 2100 6874 2112 6862 2131 6855 2144 6855 2163 6862 2175 6874 2181 6893 2181 6899 2175 6918 2163 6931 2144 6937 2137 6937 2119 6931 2106 6918 2100 6899 28 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 9 2137 6987 2125 6981 2112 6969 2106 6956 2100 6931 2100 6893 2106 6874 2119 6862 2131 6855 9 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 2144 6855 2156 6862 2169 6874 2175 6893 2175 6899 2169 6918 2156 6931 2144 6937 8 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 6912 9078 6912 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 6912 2442 6912 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 1974 8114 1980 8108 1974 8102 1968 8108 1968 8114 1974 8127 1980 8133 1999 8139 2024 8139 2043 8133 2050 8121 2050 8102 2043 8089 2024 8083 2006 8083 15 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2024 8139 2037 8133 2043 8121 2043 8102 2037 8089 2024 8083 6 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 2024 8083 2037 8077 2050 8064 2056 8051 2056 8033 2050 8020 2043 8014 2024 8007 1999 8007 1980 8014 1974 8020 1968 8033 1968 8039 1974 8045 1980 8039 1974 8033 16 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2043 8070 2050 8051 2050 8033 2043 8020 2037 8014 2024 8007 6 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2093 8139 2093 8102 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 2093 8114 2100 8127 2112 8139 2125 8139 2156 8121 2169 8121 2175 8127 2181 8139 8 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 2100 8127 2112 8133 2125 8133 2156 8121 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 2181 8139 2181 8121 2175 8102 2150 8070 2144 8058 2137 8039 2137 8007 7 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5 2175 8102 2144 8070 2137 8058 2131 8039 2131 8007 5 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 8064 9078 8064 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 8064 2442 8064 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 1974 9266 1980 9260 1974 9254 1968 9260 1968 9266 1974 9279 1980 9285 1999 9291 2024 9291 2043 9285 2050 9273 2050 9254 2043 9241 2024 9235 2006 9235 15 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2024 9291 2037 9285 2043 9273 2043 9254 2037 9241 2024 9235 6 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 2024 9235 2037 9229 2050 9216 2056 9203 2056 9185 2050 9172 2043 9166 2024 9159 1999 9159 1980 9166 1974 9172 1968 9185 1968 9191 1974 9197 1980 9191 1974 9185 16 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2043 9222 2050 9203 2050 9185 2043 9172 2037 9166 2024 9159 6 MLine End Begin %I Poly [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 12 2150 9291 2169 9285 2175 9273 2175 9254 2169 9241 2150 9235 2125 9235 2106 9241 2100 9254 2100 9273 2106 9285 2125 9291 12 Poly End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2125 9291 2112 9285 2106 9273 2106 9254 2112 9241 2125 9235 6 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2150 9235 2163 9241 2169 9254 2169 9273 2163 9285 2150 9291 6 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 2125 9235 2106 9229 2100 9222 2093 9210 2093 9185 2100 9172 2106 9166 2125 9159 2150 9159 2169 9166 2175 9172 2181 9185 2181 9210 2175 9222 2169 9229 2150 9235 16 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 2125 9235 2112 9229 2106 9222 2100 9210 2100 9185 2106 9172 2112 9166 2125 9159 8 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 2150 9159 2163 9166 2169 9172 2175 9185 2175 9210 2169 9222 2163 9229 2150 9235 8 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 9216 9078 9216 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 9216 2442 9216 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2304 9161 2304 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2304 2359 2304 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2880 9161 2880 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2880 2359 2880 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 3456 9161 3456 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3456 2359 3456 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 4032 9161 4032 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4032 2359 4032 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 4608 9161 4608 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4608 2359 4608 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5184 9161 5184 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5184 2359 5184 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5760 9161 5760 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5760 2359 5760 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 6336 9161 6336 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 6336 2359 6336 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 6912 9161 6912 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 6912 2359 6912 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 7488 9161 7488 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 7488 2359 7488 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 8064 9161 8064 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 8064 2359 8064 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 8640 9161 8640 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 8640 2359 8640 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 9216 9161 9216 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 9216 2359 9216 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4384 1906 4384 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4390 1906 4390 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4365 1906 4390 1906 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4365 1774 4409 1774 2 MLine End Begin %I Poly [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 4491 1862 4510 1856 4522 1843 4528 1824 4528 1812 4522 1793 4510 1780 4491 1774 4478 1774 4459 1780 4447 1793 4440 1812 4440 1824 4447 1843 4459 1856 4478 1862 16 Poly End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 4478 1862 4466 1856 4453 1843 4447 1824 4447 1812 4453 1793 4466 1780 4478 1774 8 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 4491 1774 4503 1780 4516 1793 4522 1812 4522 1824 4516 1843 4503 1856 4491 1862 8 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4579 1862 4579 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4585 1862 4585 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 4585 1843 4598 1856 4616 1862 4629 1862 4648 1856 4654 1843 4654 1774 7 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 4629 1862 4642 1856 4648 1843 4648 1774 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4560 1862 4585 1862 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4560 1774 4604 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4629 1774 4673 1774 2 MLine End Begin %I Poly [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 4748 1862 4761 1856 4767 1849 4773 1837 4773 1824 4767 1812 4761 1805 4748 1799 4736 1799 4723 1805 4717 1812 4711 1824 4711 1837 4717 1849 4723 1856 4736 1862 16 Poly End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 4723 1856 4717 1843 4717 1818 4723 1805 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 4761 1805 4767 1818 4767 1843 4761 1856 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5 4767 1849 4773 1856 4786 1862 4786 1856 4773 1856 5 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 9 4717 1812 4711 1805 4704 1793 4704 1787 4711 1774 4729 1768 4761 1768 4780 1761 4786 1755 9 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 4704 1787 4711 1780 4729 1774 4761 1774 4780 1768 4786 1755 4786 1749 4780 1736 4761 1730 4723 1730 4704 1736 4698 1749 4698 1755 4704 1768 4723 1774 15 MLine End Begin %I Poly [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 4843 1900 4836 1893 4830 1900 4836 1906 4 Poly End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4836 1862 4836 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4843 1862 4843 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4817 1862 4843 1862 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4817 1774 4861 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 4905 1906 4905 1799 4912 1780 4924 1774 4937 1774 4949 1780 4956 1793 7 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 4912 1906 4912 1799 4918 1780 4924 1774 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4887 1862 4937 1862 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 5000 1862 5000 1793 5006 1780 5025 1774 5037 1774 5056 1780 5069 1793 7 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 5006 1862 5006 1793 5012 1780 5025 1774 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5069 1862 5069 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5075 1862 5075 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4981 1862 5006 1862 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5050 1862 5075 1862 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5069 1774 5094 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5201 1906 5201 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5207 1906 5207 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 14 5201 1843 5188 1856 5176 1862 5163 1862 5144 1856 5132 1843 5125 1824 5125 1812 5132 1793 5144 1780 5163 1774 5176 1774 5188 1780 5201 1793 14 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 5163 1862 5150 1856 5138 1843 5132 1824 5132 1812 5138 1793 5150 1780 5163 1774 8 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5182 1906 5207 1906 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5201 1774 5226 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 17 5264 1824 5339 1824 5339 1837 5333 1849 5326 1856 5314 1862 5295 1862 5276 1856 5264 1843 5257 1824 5257 1812 5264 1793 5276 1780 5295 1774 5308 1774 5326 1780 5339 1793 17 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 5333 1824 5333 1843 5326 1856 3 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 5295 1862 5282 1856 5270 1843 5264 1824 5264 1812 5270 1793 5282 1780 5295 1774 8 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 5528 1931 5515 1918 5502 1900 5490 1875 5484 1843 5484 1818 5490 1787 5502 1761 5515 1743 5528 1730 10 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 5515 1918 5502 1893 5496 1875 5490 1843 5490 1818 5496 1787 5502 1768 5515 1743 8 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5571 1831 5685 1831 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5842 1862 5842 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5848 1862 5848 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 5848 1843 5861 1856 5879 1862 5892 1862 5911 1856 5917 1843 5917 1774 7 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 5892 1862 5905 1856 5911 1843 5911 1774 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 5917 1843 5930 1856 5949 1862 5961 1862 5980 1856 5986 1843 5986 1774 7 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 5961 1862 5974 1856 5980 1843 5980 1774 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5823 1862 5848 1862 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5823 1774 5867 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5892 1774 5936 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5961 1774 6005 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 17 6043 1824 6118 1824 6118 1837 6112 1849 6106 1856 6093 1862 6074 1862 6055 1856 6043 1843 6036 1824 6036 1812 6043 1793 6055 1780 6074 1774 6087 1774 6106 1780 6118 1793 17 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 6112 1824 6112 1843 6106 1856 3 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 6074 1862 6062 1856 6049 1843 6043 1824 6043 1812 6049 1793 6062 1780 6074 1774 8 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 13 6168 1849 6168 1843 6162 1843 6162 1849 6168 1856 6181 1862 6206 1862 6219 1856 6225 1849 6231 1837 6231 1793 6238 1780 6244 1774 13 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5 6225 1849 6225 1793 6231 1780 6244 1774 6250 1774 5 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 11 6225 1837 6219 1831 6181 1824 6162 1818 6156 1805 6156 1793 6162 1780 6181 1774 6200 1774 6212 1780 6225 1793 11 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 6181 1824 6168 1818 6162 1805 6162 1793 6168 1780 6181 1774 6 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6294 1862 6294 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6300 1862 6300 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 6300 1843 6313 1856 6332 1862 6344 1862 6363 1856 6370 1843 6370 1774 7 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 6344 1862 6357 1856 6363 1843 6363 1774 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6275 1862 6300 1862 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6275 1774 6319 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6344 1774 6388 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 6483 1849 6489 1862 6489 1837 6483 1849 6476 1856 6464 1862 6439 1862 6426 1856 6420 1849 6420 1837 6426 1831 6439 1824 6470 1812 6483 1805 6489 1799 15 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 6420 1843 6426 1837 6439 1831 6470 1818 6483 1812 6489 1805 6489 1787 6483 1780 6470 1774 6445 1774 6432 1780 6426 1787 6420 1799 6420 1774 6426 1787 15 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6633 1862 6659 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6640 1862 6659 1793 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6684 1862 6659 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6684 1862 6709 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6690 1862 6709 1793 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6734 1862 6709 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6615 1862 6659 1862 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6715 1862 6753 1862 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 17 6784 1824 6860 1824 6860 1837 6853 1849 6847 1856 6835 1862 6816 1862 6797 1856 6784 1843 6778 1824 6778 1812 6784 1793 6797 1780 6816 1774 6828 1774 6847 1780 6860 1793 17 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 6853 1824 6853 1843 6847 1856 3 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 6816 1862 6803 1856 6791 1843 6784 1824 6784 1812 6791 1793 6803 1780 6816 1774 8 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 6960 1849 6966 1862 6966 1837 6960 1849 6954 1856 6941 1862 6916 1862 6904 1856 6897 1849 6897 1837 6904 1831 6916 1824 6948 1812 6960 1805 6966 1799 15 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 6897 1843 6904 1837 6916 1831 6948 1818 6960 1812 6966 1805 6966 1787 6960 1780 6948 1774 6922 1774 6910 1780 6904 1787 6897 1799 6897 1774 6904 1787 15 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 7017 1906 7017 1799 7023 1780 7036 1774 7048 1774 7061 1780 7067 1793 7 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 7023 1906 7023 1799 7029 1780 7036 1774 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6998 1862 7048 1862 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 7098 1931 7111 1918 7124 1900 7136 1875 7142 1843 7142 1818 7136 1787 7124 1761 7111 1743 7098 1730 10 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 7111 1918 7124 1893 7130 1875 7136 1843 7136 1818 7130 1787 7124 1768 7111 1743 8 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1672 5370 1804 5370 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1672 5377 1804 5377 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1672 5352 1672 5377 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1804 5352 1804 5396 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 13 1729 5440 1735 5440 1735 5433 1729 5433 1723 5440 1716 5452 1716 5477 1723 5490 1729 5496 1742 5502 1786 5502 1798 5509 1804 5515 13 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5 1729 5496 1786 5496 1798 5502 1804 5515 1804 5521 5 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 11 1742 5496 1748 5490 1754 5452 1760 5433 1773 5427 1786 5427 1798 5433 1804 5452 1804 5471 1798 5484 1786 5496 11 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 1754 5452 1760 5440 1773 5433 1786 5433 1798 5440 1804 5452 6 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 1672 5565 1779 5565 1798 5571 1804 5584 1804 5597 1798 5609 1786 5615 7 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 1672 5571 1779 5571 1798 5578 1804 5584 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1716 5546 1716 5597 2 MLine End Begin %I Poly [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 1679 5666 1685 5659 1679 5653 1672 5659 4 Poly End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1716 5659 1804 5659 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1716 5666 1804 5666 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1716 5641 1716 5666 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1804 5641 1804 5685 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 1672 5729 1779 5729 1798 5735 1804 5747 1804 5760 1798 5773 1786 5779 7 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 1672 5735 1779 5735 1798 5741 1804 5747 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1716 5710 1716 5760 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 1716 5823 1786 5823 1798 5829 1804 5848 1804 5861 1798 5879 1786 5892 7 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 1716 5829 1786 5829 1798 5835 1804 5848 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1716 5892 1804 5892 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1716 5898 1804 5898 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1716 5804 1716 5829 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1716 5873 1716 5898 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1804 5892 1804 5917 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1672 6024 1804 6024 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1672 6030 1804 6030 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 14 1735 6024 1723 6011 1716 5999 1716 5986 1723 5967 1735 5955 1754 5949 1767 5949 1786 5955 1798 5967 1804 5986 1804 5999 1798 6011 1786 6024 14 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 1716 5986 1723 5974 1735 5961 1754 5955 1767 5955 1786 5961 1798 5974 1804 5986 8 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1672 6005 1672 6030 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1804 6024 1804 6049 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 17 1754 6087 1754 6162 1742 6162 1729 6156 1723 6150 1716 6137 1716 6118 1723 6099 1735 6087 1754 6080 1767 6080 1786 6087 1798 6099 1804 6118 1804 6131 1798 6150 1786 6162 17 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 1754 6156 1735 6156 1723 6150 3 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 1716 6118 1723 6106 1735 6093 1754 6087 1767 6087 1786 6093 1798 6106 1804 6118 8 MLine End Begin %I Circ [1.08 0 0 1.08 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5395 6543 32 Circ End Begin %I Circ [1.08 0 0 1.08 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3045 4078 32 Circ End Begin %I Circ [1.08 0 0 1.08 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5138 5898 32 Circ End Begin %I Circ [1.08 0 0 1.08 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6451 5080 32 Circ End Begin %I Circ [1.08 0 0 1.08 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4658 8398 32 Circ End Begin %I Circ [1.08 0 0 1.08 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8920 3214 32 Circ End Begin %I Circ [1.08 0 0 1.08 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5407 6647 32 Circ End Begin %I Circ [1.08 0 0 1.08 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4669 5933 32 Circ End Begin %I Circ [1.08 0 0 1.08 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5268 6785 32 Circ End Begin %I Circ [1.08 0 0 1.08 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5084 2696 32 Circ End Begin %I Circ [1.08 0 0 1.08 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4385 8467 32 Circ End Begin %I Circ [1.08 0 0 1.08 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4324 6359 32 Circ End Begin %I Circ [1.08 0 0 1.08 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5395 6543 32 Circ End Begin %I Poly [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 12 4324 6359 4385 8467 5084 2696 5268 6785 4669 5933 5407 6647 8920 3214 4658 8398 6451 5080 5138 5898 3045 4078 5395 6543 12 Poly End %%PageTrailer End %I eop showpage %%Trailer end %%EOF %%EndDocument @endspecial 1573 x @beginspecial 101 @llx 194 @lly 489 @urx 610 @ury 1584 @rwi @setspecial %%BeginDocument: final-route.eps %!PS-Adobe-3.0 EPSF-3.0 %%Creator: GNU libplot drawing library 4.1 %%Title: PostScript plot %%CreationDate: Thu Jan 4 10:56:46 2007 %%DocumentData: Clean7Bit %%LanguageLevel: 1 %%Pages: 1 %%PageOrder: Ascend %%Orientation: Portrait %%BoundingBox: 101 194 489 610 %%DocumentNeededResources: %%DocumentSuppliedResources: procset GNU_libplot 1.0 0 %%EndComments %%BeginDefaults %%PageResources: %%EndDefaults %%BeginProlog %%EndProlog %%BeginSetup /DrawDict 50 dict def DrawDict begin %%BeginResource procset GNU_libplot 1.0 0 /none null def /numGraphicParameters 17 def /stringLimit 65535 def /arrowHeight 8 def /eoFillRule true def /Begin { save numGraphicParameters dict begin } def /End { end restore } def /SetB { dup type /nulltype eq { pop false /brushRightArrow idef false /brushLeftArrow idef true /brushNone idef } { /brushDashOffset idef /brushDashArray idef 0 ne /brushRightArrow idef 0 ne /brushLeftArrow idef /brushWidth idef false /brushNone idef } ifelse } def /SetCFg { /fgblue idef /fggreen idef /fgred idef } def /SetCBg { /bgblue idef /bggreen idef /bgred idef } def /SetF { /printSize idef /printFont idef } def /SetP { dup type /nulltype eq { pop true /patternNone idef } { /patternGrayLevel idef patternGrayLevel -1 eq { /patternString idef } if false /patternNone idef } ifelse } def /BSpl { 0 begin storexyn newpath n 1 gt { 0 0 0 0 0 0 1 1 true subspline n 2 gt { 0 0 0 0 1 1 2 2 false subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 2 copy false subspline } if n 2 sub dup n 1 sub dup 2 copy 2 copy false subspline patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup 1 sub dup rightarrow } if end } dup 0 4 dict put def /Circ { newpath 0 360 arc closepath patternNone not { ifill } if brushNone not { istroke } if } def /CBSpl { 0 begin dup 2 gt { storexyn newpath n 1 sub dup 0 0 1 1 2 2 true subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 0 0 false subspline n 2 sub dup n 1 sub dup 0 0 1 1 false subspline patternNone not { ifill } if brushNone not { istroke } if } { Poly } ifelse end } dup 0 4 dict put def /Elli { 0 begin newpath 4 2 roll translate scale 0 0 1 0 360 arc closepath patternNone not { ifill } if brushNone not { istroke } if end } dup 0 1 dict put def /Line { 0 begin 2 storexyn newpath x 0 get y 0 get moveto x 1 get y 1 get lineto brushNone not { istroke } if 0 0 1 1 leftarrow 0 0 1 1 rightarrow end } dup 0 4 dict put def /MLine { 0 begin storexyn newpath n 1 gt { x 0 get y 0 get moveto 1 1 n 1 sub { /i exch def x i get y i get lineto } for patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Poly { 3 1 roll newpath moveto -1 add { lineto } repeat closepath patternNone not { ifill } if brushNone not { istroke } if } def /Rect { 0 begin /t exch def /r exch def /b exch def /l exch def newpath l b moveto l t lineto r t lineto r b lineto closepath patternNone not { ifill } if brushNone not { istroke } if end } dup 0 4 dict put def /Text { ishow } def /idef { dup where { pop pop pop } { exch def } ifelse } def /ifill { 0 begin gsave patternGrayLevel -1 ne { fgred bgred fgred sub patternGrayLevel mul add fggreen bggreen fggreen sub patternGrayLevel mul add fgblue bgblue fgblue sub patternGrayLevel mul add setrgbcolor eoFillRule { eofill } { fill } ifelse } { eoFillRule { eoclip } { clip } ifelse originalCTM setmatrix pathbbox /t exch def /r exch def /b exch def /l exch def /w r l sub ceiling cvi def /h t b sub ceiling cvi def /imageByteWidth w 8 div ceiling cvi def /imageHeight h def bgred bggreen bgblue setrgbcolor eoFillRule { eofill } { fill } ifelse fgred fggreen fgblue setrgbcolor w 0 gt h 0 gt and { l b translate w h scale w h true [w 0 0 h neg 0 h] { patternproc } imagemask } if } ifelse grestore end } dup 0 8 dict put def /istroke { gsave brushDashOffset -1 eq { [] 0 setdash 1 setgray } { brushDashArray brushDashOffset setdash fgred fggreen fgblue setrgbcolor } ifelse brushWidth setlinewidth originalCTM setmatrix stroke grestore } def /ishow { 0 begin gsave fgred fggreen fgblue setrgbcolor /fontDict printFont findfont printSize scalefont dup setfont def /descender fontDict begin 0 /FontBBox load 1 get FontMatrix end transform exch pop def /vertoffset 1 printSize sub descender sub def { 0 vertoffset moveto show /vertoffset vertoffset printSize sub def } forall grestore end } dup 0 3 dict put def /patternproc { 0 begin /patternByteLength patternString length def /patternHeight patternByteLength 8 mul sqrt cvi def /patternWidth patternHeight def /patternByteWidth patternWidth 8 idiv def /imageByteMaxLength imageByteWidth imageHeight mul stringLimit patternByteWidth sub min def /imageMaxHeight imageByteMaxLength imageByteWidth idiv patternHeight idiv patternHeight mul patternHeight max def /imageHeight imageHeight imageMaxHeight sub store /imageString imageByteWidth imageMaxHeight mul patternByteWidth add string def 0 1 imageMaxHeight 1 sub { /y exch def /patternRow y patternByteWidth mul patternByteLength mod def /patternRowString patternString patternRow patternByteWidth getinterval def /imageRow y imageByteWidth mul def 0 patternByteWidth imageByteWidth 1 sub { /x exch def imageString imageRow x add patternRowString putinterval } for } for imageString end } dup 0 12 dict put def /min { dup 3 2 roll dup 4 3 roll lt { exch } if pop } def /max { dup 3 2 roll dup 4 3 roll gt { exch } if pop } def /midpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 x1 add 2 div y0 y1 add 2 div end } dup 0 4 dict put def /thirdpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 2 mul x1 add 3 div y0 2 mul y1 add 3 div end } dup 0 4 dict put def /subspline { 0 begin /movetoNeeded exch def y exch get /y3 exch def x exch get /x3 exch def y exch get /y2 exch def x exch get /x2 exch def y exch get /y1 exch def x exch get /x1 exch def y exch get /y0 exch def x exch get /x0 exch def x1 y1 x2 y2 thirdpoint /p1y exch def /p1x exch def x2 y2 x1 y1 thirdpoint /p2y exch def /p2x exch def x1 y1 x0 y0 thirdpoint p1x p1y midpoint /p0y exch def /p0x exch def x2 y2 x3 y3 thirdpoint p2x p2y midpoint /p3y exch def /p3x exch def movetoNeeded { p0x p0y moveto } if p1x p1y p2x p2y p3x p3y curveto end } dup 0 17 dict put def /storexyn { /n exch def /y n array def /x n array def n 1 sub -1 0 { /i exch def y i 3 2 roll put x i 3 2 roll put } for } def /arrowhead { 0 begin transform originalCTM itransform /taily exch def /tailx exch def transform originalCTM itransform /tipy exch def /tipx exch def /dy tipy taily sub def /dx tipx tailx sub def /angle dx 0 ne dy 0 ne or { dy dx atan } { 90 } ifelse def gsave originalCTM setmatrix tipx tipy translate angle rotate newpath arrowHeight neg arrowWidth 2 div moveto 0 0 lineto arrowHeight neg arrowWidth 2 div neg lineto patternNone not { originalCTM setmatrix /padtip arrowHeight 2 exp 0.25 arrowWidth 2 exp mul add sqrt brushWidth mul arrowWidth div def /padtail brushWidth 2 div def tipx tipy translate angle rotate padtip 0 translate arrowHeight padtip add padtail add arrowHeight div dup scale arrowheadpath ifill } if brushNone not { originalCTM setmatrix tipx tipy translate angle rotate arrowheadpath istroke } if grestore end } dup 0 9 dict put def /arrowheadpath { newpath arrowHeight neg arrowWidth 2 div moveto 0 0 lineto arrowHeight neg arrowWidth 2 div neg lineto } def /leftarrow { 0 begin y exch get /taily exch def x exch get /tailx exch def y exch get /tipy exch def x exch get /tipx exch def brushLeftArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /rightarrow { 0 begin y exch get /tipy exch def x exch get /tipx exch def y exch get /taily exch def x exch get /tailx exch def brushRightArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def %%EndResource %%EndSetup %%Page: 1 1 %%PageResources: %%PageBoundingBox: 101 194 489 610 %%BeginPageSetup %I Idraw 8 Begin %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 1 0 0 1 0 0 ] concat /originalCTM matrix currentmatrix def /trueoriginalCTM matrix currentmatrix def %%EndPageSetup Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3590 10017 3590 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3605 10017 3605 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 3502 10017 3487 9930 3487 10017 3707 10017 3707 9930 3693 10017 6 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3546 9710 3649 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 3971 9973 3986 10017 3986 9930 3971 9973 3942 10003 3898 10017 3854 10017 3810 10003 3781 9973 3781 9944 3795 9915 3810 9900 3839 9886 3927 9856 3957 9842 3986 9812 16 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 3781 9944 3810 9915 3839 9900 3927 9871 3957 9856 3971 9842 3986 9812 3986 9754 3957 9724 3913 9710 3869 9710 3825 9724 3795 9754 3781 9798 3781 9710 3795 9754 16 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4103 10017 4103 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4118 10017 4118 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 4059 10017 4235 10017 4279 10003 4294 9988 4308 9959 4308 9915 4294 9886 4279 9871 4235 9856 4118 9856 10 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 4235 10017 4264 10003 4279 9988 4294 9959 4294 9915 4279 9886 4264 9871 4235 9856 8 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4059 9710 4162 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4646 9842 4910 9842 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 11 5437 10003 5423 9988 5437 9973 5452 9988 5437 10003 5408 10017 5364 10017 5320 10003 5291 9973 5276 9930 5276 9710 11 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5 5364 10017 5335 10003 5305 9973 5291 9930 5291 9710 5 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5437 9915 5437 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5452 9915 5452 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5232 9915 5452 9915 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5232 9710 5335 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5393 9710 5496 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5599 9915 5599 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5613 9915 5613 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 5613 9871 5643 9900 5687 9915 5716 9915 5760 9900 5775 9871 5775 9710 7 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 5716 9915 5745 9900 5760 9871 5760 9710 4 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5555 9915 5613 9915 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5555 9710 5657 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5716 9710 5819 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 13 5921 9886 5921 9871 5907 9871 5907 9886 5921 9900 5951 9915 6009 9915 6039 9900 6053 9886 6068 9856 6068 9754 6083 9724 6097 9710 13 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5 6053 9886 6053 9754 6068 9724 6097 9710 6112 9710 5 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 11 6053 9856 6039 9842 5951 9827 5907 9812 5892 9783 5892 9754 5907 9724 5951 9710 5995 9710 6024 9724 6053 9754 11 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 5951 9827 5921 9812 5907 9783 5907 9754 5921 9724 5951 9710 6 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6215 10017 6215 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6229 10017 6229 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6171 10017 6229 10017 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6171 9710 6273 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6361 9842 6625 9842 2 MLine End Begin %I Poly [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 6845 9915 6889 9900 6918 9871 6933 9827 6933 9798 6918 9754 6889 9724 6845 9710 6816 9710 6772 9724 6742 9754 6728 9798 6728 9827 6742 9871 6772 9900 6816 9915 16 Poly End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 6816 9915 6786 9900 6757 9871 6742 9827 6742 9798 6757 9754 6786 9724 6816 9710 8 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 6845 9710 6874 9724 6904 9754 6918 9798 6918 9827 6904 9871 6874 9900 6845 9915 8 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7050 9915 7050 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7065 9915 7065 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 7065 9827 7080 9871 7109 9900 7138 9915 7182 9915 7197 9900 7197 9886 7182 9871 7168 9886 7182 9900 10 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7006 9915 7065 9915 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7006 9710 7109 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7446 10017 7446 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7461 10017 7461 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 14 7446 9871 7417 9900 7387 9915 7358 9915 7314 9900 7285 9871 7270 9827 7270 9798 7285 9754 7314 9724 7358 9710 7387 9710 7417 9724 7446 9754 14 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 7358 9915 7329 9900 7299 9871 7285 9827 7285 9798 7299 9754 7329 9724 7358 9710 8 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7402 10017 7461 10017 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7446 9710 7505 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 17 7593 9827 7769 9827 7769 9856 7754 9886 7739 9900 7710 9915 7666 9915 7622 9900 7593 9871 7578 9827 7578 9798 7593 9754 7622 9724 7666 9710 7695 9710 7739 9724 7769 9754 17 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 7754 9827 7754 9871 7739 9900 3 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 7666 9915 7637 9900 7607 9871 7593 9827 7593 9798 7607 9754 7637 9724 7666 9710 8 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7886 9915 7886 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7901 9915 7901 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 7901 9827 7915 9871 7945 9900 7974 9915 8018 9915 8033 9900 8033 9886 8018 9871 8003 9886 8018 9900 10 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7842 9915 7901 9915 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7842 9710 7945 9710 2 MLine End Begin %I Rect [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2304 2304 9216 9216 Rect End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2059 2097 2172 2097 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 2235 2147 2247 2153 2266 2172 2266 2040 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2260 2166 2260 2040 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2235 2040 2291 2040 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 2361 2147 2373 2153 2392 2172 2392 2040 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2386 2166 2386 2040 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2361 2040 2417 2040 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2524 2159 2524 2040 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2530 2172 2530 2040 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 2530 2172 2461 2078 2562 2078 3 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2505 2040 2549 2040 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 9216 2304 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2304 2304 2442 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2827 2097 2940 2097 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 3003 2147 3015 2153 3034 2172 3034 2040 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3028 2166 3028 2040 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3003 2040 3059 2040 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 3129 2147 3141 2153 3160 2172 3160 2040 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3154 2166 3154 2040 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3129 2040 3185 2040 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 20 3242 2147 3248 2141 3242 2134 3235 2141 3235 2147 3242 2159 3248 2166 3267 2172 3292 2172 3311 2166 3317 2159 3323 2147 3323 2134 3317 2122 3298 2109 3267 2097 3254 2090 3242 2078 3235 2059 3235 2040 20 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 3292 2172 3304 2166 3311 2159 3317 2147 3317 2134 3311 2122 3292 2109 3267 2097 8 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 3235 2053 3242 2059 3254 2059 3286 2046 3304 2046 3317 2053 3323 2059 7 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 3254 2059 3286 2040 3311 2040 3317 2046 3323 2059 3323 2072 6 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3072 9216 3072 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3072 2304 3072 2442 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3595 2097 3708 2097 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 3771 2147 3783 2153 3802 2172 3802 2040 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3796 2166 3796 2040 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3771 2040 3827 2040 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 3897 2147 3909 2153 3928 2172 3928 2040 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3922 2166 3922 2040 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3897 2040 3953 2040 2 MLine End Begin %I Poly [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 4054 2172 4072 2166 4085 2147 4091 2115 4091 2097 4085 2065 4072 2046 4054 2040 4041 2040 4022 2046 4010 2065 4003 2097 4003 2115 4010 2147 4022 2166 4041 2172 16 Poly End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 4041 2172 4029 2166 4022 2159 4016 2147 4010 2115 4010 2097 4016 2065 4022 2053 4029 2046 4041 2040 10 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 4054 2040 4066 2046 4072 2053 4079 2065 4085 2097 4085 2115 4079 2147 4072 2159 4066 2166 4054 2172 10 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3840 9216 3840 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3840 2304 3840 2442 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4363 2097 4476 2097 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 4539 2147 4551 2153 4570 2172 4570 2040 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4564 2166 4564 2040 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4539 2040 4595 2040 2 MLine End Begin %I Poly [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 4696 2172 4715 2166 4727 2147 4734 2115 4734 2097 4727 2065 4715 2046 4696 2040 4683 2040 4665 2046 4652 2065 4646 2097 4646 2115 4652 2147 4665 2166 4683 2172 16 Poly End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 4683 2172 4671 2166 4665 2159 4658 2147 4652 2115 4652 2097 4658 2065 4665 2053 4671 2046 4683 2040 10 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 4696 2040 4709 2046 4715 2053 4721 2065 4727 2097 4727 2115 4721 2147 4715 2159 4709 2166 4696 2172 10 MLine End Begin %I Poly [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 12 4828 2172 4847 2166 4853 2153 4853 2134 4847 2122 4828 2115 4803 2115 4784 2122 4778 2134 4778 2153 4784 2166 4803 2172 12 Poly End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 4803 2172 4790 2166 4784 2153 4784 2134 4790 2122 4803 2115 6 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 4828 2115 4840 2122 4847 2134 4847 2153 4840 2166 4828 2172 6 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 4803 2115 4784 2109 4778 2103 4771 2090 4771 2065 4778 2053 4784 2046 4803 2040 4828 2040 4847 2046 4853 2053 4859 2065 4859 2090 4853 2103 4847 2109 4828 2115 16 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 4803 2115 4790 2109 4784 2103 4778 2090 4778 2065 4784 2053 4790 2046 4803 2040 8 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 4828 2040 4840 2046 4847 2053 4853 2065 4853 2090 4847 2103 4840 2109 4828 2115 8 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4608 9216 4608 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4608 2304 4608 2442 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5131 2097 5244 2097 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 5307 2147 5319 2153 5338 2172 5338 2040 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5332 2166 5332 2040 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5307 2040 5363 2040 2 MLine End Begin %I Poly [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 5464 2172 5483 2166 5495 2147 5502 2115 5502 2097 5495 2065 5483 2046 5464 2040 5451 2040 5433 2046 5420 2065 5414 2097 5414 2115 5420 2147 5433 2166 5451 2172 16 Poly End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 5451 2172 5439 2166 5433 2159 5426 2147 5420 2115 5420 2097 5426 2065 5433 2053 5439 2046 5451 2040 10 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 5464 2040 5477 2046 5483 2053 5489 2065 5495 2097 5495 2115 5489 2147 5483 2159 5477 2166 5464 2172 10 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 28 5615 2153 5608 2147 5615 2141 5621 2147 5621 2153 5615 2166 5602 2172 5583 2172 5565 2166 5552 2153 5546 2141 5539 2115 5539 2078 5546 2059 5558 2046 5577 2040 5590 2040 5608 2046 5621 2059 5627 2078 5627 2084 5621 2103 5608 2115 5590 2122 5583 2122 5565 2115 5552 2103 5546 2084 28 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 9 5583 2172 5571 2166 5558 2153 5552 2141 5546 2115 5546 2078 5552 2059 5565 2046 5577 2040 9 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 5590 2040 5602 2046 5615 2059 5621 2078 5621 2084 5615 2103 5602 2115 5590 2122 8 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5376 9216 5376 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5376 2304 5376 2442 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5899 2097 6012 2097 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 6075 2147 6087 2153 6106 2172 6106 2040 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6100 2166 6100 2040 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6075 2040 6131 2040 2 MLine End Begin %I Poly [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 6232 2172 6251 2166 6263 2147 6270 2115 6270 2097 6263 2065 6251 2046 6232 2040 6219 2040 6201 2046 6188 2065 6182 2097 6182 2115 6188 2147 6201 2166 6219 2172 16 Poly End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 6219 2172 6207 2166 6201 2159 6194 2147 6188 2115 6188 2097 6194 2065 6201 2053 6207 2046 6219 2040 10 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 6232 2040 6245 2046 6251 2053 6257 2065 6263 2097 6263 2115 6257 2147 6251 2159 6245 2166 6232 2172 10 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6364 2159 6364 2040 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6370 2172 6370 2040 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 6370 2172 6301 2078 6402 2078 3 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6345 2040 6389 2040 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6144 9216 6144 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6144 2304 6144 2442 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6667 2097 6780 2097 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 6843 2147 6855 2153 6874 2172 6874 2040 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6868 2166 6868 2040 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6843 2040 6899 2040 2 MLine End Begin %I Poly [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 7000 2172 7019 2166 7031 2147 7038 2115 7038 2097 7031 2065 7019 2046 7000 2040 6987 2040 6969 2046 6956 2065 6950 2097 6950 2115 6956 2147 6969 2166 6987 2172 16 Poly End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 6987 2172 6975 2166 6969 2159 6962 2147 6956 2115 6956 2097 6962 2065 6969 2053 6975 2046 6987 2040 10 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 7000 2040 7013 2046 7019 2053 7025 2065 7031 2097 7031 2115 7025 2147 7019 2159 7013 2166 7000 2172 10 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 20 7082 2147 7088 2141 7082 2134 7075 2141 7075 2147 7082 2159 7088 2166 7107 2172 7132 2172 7151 2166 7157 2159 7163 2147 7163 2134 7157 2122 7138 2109 7107 2097 7094 2090 7082 2078 7075 2059 7075 2040 20 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 7132 2172 7144 2166 7151 2159 7157 2147 7157 2134 7151 2122 7132 2109 7107 2097 8 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 7075 2053 7082 2059 7094 2059 7126 2046 7144 2046 7157 2053 7163 2059 7 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 7094 2059 7126 2040 7151 2040 7157 2046 7163 2059 7163 2072 6 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6912 9216 6912 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6912 2304 6912 2442 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7435 2097 7548 2097 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 7611 2147 7623 2153 7642 2172 7642 2040 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7636 2166 7636 2040 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7611 2040 7667 2040 2 MLine End Begin %I Poly [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 7768 2172 7787 2166 7799 2147 7806 2115 7806 2097 7799 2065 7787 2046 7768 2040 7755 2040 7737 2046 7724 2065 7718 2097 7718 2115 7724 2147 7737 2166 7755 2172 16 Poly End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 7755 2172 7743 2166 7737 2159 7730 2147 7724 2115 7724 2097 7730 2065 7737 2053 7743 2046 7755 2040 10 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 7768 2040 7781 2046 7787 2053 7793 2065 7799 2097 7799 2115 7793 2147 7787 2159 7781 2166 7768 2172 10 MLine End Begin %I Poly [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 7894 2172 7912 2166 7925 2147 7931 2115 7931 2097 7925 2065 7912 2046 7894 2040 7881 2040 7862 2046 7850 2065 7843 2097 7843 2115 7850 2147 7862 2166 7881 2172 16 Poly End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 7881 2172 7869 2166 7862 2159 7856 2147 7850 2115 7850 2097 7856 2065 7862 2053 7869 2046 7881 2040 10 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 7894 2040 7906 2046 7912 2053 7919 2065 7925 2097 7925 2115 7919 2147 7912 2159 7906 2166 7894 2172 10 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7680 9216 7680 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7680 2304 7680 2442 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8266 2097 8379 2097 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 28 8505 2128 8498 2109 8486 2097 8467 2090 8461 2090 8442 2097 8429 2109 8423 2128 8423 2134 8429 2153 8442 2166 8461 2172 8473 2172 8492 2166 8505 2153 8511 2134 8511 2097 8505 2072 8498 2059 8486 2046 8467 2040 8448 2040 8435 2046 8429 2059 8429 2065 8435 2072 8442 2065 8435 2059 28 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 8461 2090 8448 2097 8435 2109 8429 2128 8429 2134 8435 2153 8448 2166 8461 2172 8 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 9 8473 2172 8486 2166 8498 2153 8505 2134 8505 2097 8498 2072 8492 2059 8479 2046 8467 2040 9 MLine End Begin %I Poly [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 12 8605 2172 8624 2166 8630 2153 8630 2134 8624 2122 8605 2115 8580 2115 8561 2122 8555 2134 8555 2153 8561 2166 8580 2172 12 Poly End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 8580 2172 8567 2166 8561 2153 8561 2134 8567 2122 8580 2115 6 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 8605 2115 8618 2122 8624 2134 8624 2153 8618 2166 8605 2172 6 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 8580 2115 8561 2109 8555 2103 8549 2090 8549 2065 8555 2053 8561 2046 8580 2040 8605 2040 8624 2046 8630 2053 8637 2065 8637 2090 8630 2103 8624 2109 8605 2115 16 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 8580 2115 8567 2109 8561 2103 8555 2090 8555 2065 8561 2053 8567 2046 8580 2040 8 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 8605 2040 8618 2046 8624 2053 8630 2065 8630 2090 8624 2103 8618 2109 8605 2115 8 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8448 9216 8448 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8448 2304 8448 2442 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9034 2097 9147 2097 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 28 9273 2128 9266 2109 9254 2097 9235 2090 9229 2090 9210 2097 9197 2109 9191 2128 9191 2134 9197 2153 9210 2166 9229 2172 9241 2172 9260 2166 9273 2153 9279 2134 9279 2097 9273 2072 9266 2059 9254 2046 9235 2040 9216 2040 9203 2046 9197 2059 9197 2065 9203 2072 9210 2065 9203 2059 28 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 9229 2090 9216 2097 9203 2109 9197 2128 9197 2134 9203 2153 9216 2166 9229 2172 8 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 9 9241 2172 9254 2166 9266 2153 9273 2134 9273 2097 9266 2072 9260 2059 9247 2046 9235 2040 9 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 28 9392 2153 9386 2147 9392 2141 9398 2147 9398 2153 9392 2166 9379 2172 9361 2172 9342 2166 9329 2153 9323 2141 9317 2115 9317 2078 9323 2059 9335 2046 9354 2040 9367 2040 9386 2046 9398 2059 9405 2078 9405 2084 9398 2103 9386 2115 9367 2122 9361 2122 9342 2115 9329 2103 9323 2084 28 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 9 9361 2172 9348 2166 9335 2153 9329 2141 9323 2115 9323 2078 9329 2059 9342 2046 9354 2040 9 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 9367 2040 9379 2046 9392 2059 9398 2078 9398 2084 9392 2103 9379 2115 9367 2122 8 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 9216 9216 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2304 9216 2442 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 9216 2304 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2304 2304 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2688 9216 2688 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2688 2304 2688 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3072 9216 3072 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3072 2304 3072 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3456 9216 3456 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3456 2304 3456 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3840 9216 3840 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3840 2304 3840 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4224 9216 4224 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4224 2304 4224 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4608 9216 4608 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4608 2304 4608 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4992 9216 4992 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4992 2304 4992 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5376 9216 5376 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5376 2304 5376 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5760 9216 5760 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5760 2304 5760 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6144 9216 6144 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6144 2304 6144 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6528 9216 6528 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6528 2304 6528 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6912 9216 6912 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6912 2304 6912 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7296 9216 7296 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7296 2304 7296 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7680 9216 7680 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7680 2304 7680 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8064 9216 8064 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8064 2304 8064 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8448 9216 8448 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8448 2304 8448 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8832 9216 8832 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8832 2304 8832 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 9216 9216 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2304 9216 2359 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 1974 2354 1980 2348 1974 2342 1968 2348 1968 2354 1974 2367 1980 2373 1999 2379 2024 2379 2043 2373 2050 2361 2050 2342 2043 2329 2024 2323 2006 2323 15 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2024 2379 2037 2373 2043 2361 2043 2342 2037 2329 2024 2323 6 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 2024 2323 2037 2317 2050 2304 2056 2291 2056 2273 2050 2260 2043 2254 2024 2247 1999 2247 1980 2254 1974 2260 1968 2273 1968 2279 1974 2285 1980 2279 1974 2273 16 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2043 2310 2050 2291 2050 2273 2043 2260 2037 2254 2024 2247 6 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 20 2100 2354 2106 2348 2100 2342 2093 2348 2093 2354 2100 2367 2106 2373 2125 2379 2150 2379 2169 2373 2175 2367 2181 2354 2181 2342 2175 2329 2156 2317 2125 2304 2112 2298 2100 2285 2093 2266 2093 2247 20 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 2150 2379 2163 2373 2169 2367 2175 2354 2175 2342 2169 2329 2150 2317 2125 2304 8 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 2093 2260 2100 2266 2112 2266 2144 2254 2163 2254 2175 2260 2181 2266 7 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2112 2266 2144 2247 2169 2247 2175 2254 2181 2266 2181 2279 6 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2304 9078 2304 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2304 2442 2304 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 1974 3506 1980 3500 1974 3494 1968 3500 1968 3506 1974 3519 1980 3525 1999 3531 2024 3531 2043 3525 2050 3513 2050 3494 2043 3481 2024 3475 2006 3475 15 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2024 3531 2037 3525 2043 3513 2043 3494 2037 3481 2024 3475 6 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 2024 3475 2037 3469 2050 3456 2056 3443 2056 3425 2050 3412 2043 3406 2024 3399 1999 3399 1980 3406 1974 3412 1968 3425 1968 3431 1974 3437 1980 3431 1974 3425 16 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2043 3462 2050 3443 2050 3425 2043 3412 2037 3406 2024 3399 6 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 2100 3506 2106 3500 2100 3494 2093 3500 2093 3506 2100 3519 2106 3525 2125 3531 2150 3531 2169 3525 2175 3513 2175 3494 2169 3481 2150 3475 2131 3475 15 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2150 3531 2163 3525 2169 3513 2169 3494 2163 3481 2150 3475 6 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 2150 3475 2163 3469 2175 3456 2181 3443 2181 3425 2175 3412 2169 3406 2150 3399 2125 3399 2106 3406 2100 3412 2093 3425 2093 3431 2100 3437 2106 3431 2100 3425 16 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2169 3462 2175 3443 2175 3425 2169 3412 2163 3406 2150 3399 6 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 3456 9078 3456 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3456 2442 3456 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 1974 4658 1980 4652 1974 4646 1968 4652 1968 4658 1974 4671 1980 4677 1999 4683 2024 4683 2043 4677 2050 4665 2050 4646 2043 4633 2024 4627 2006 4627 15 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2024 4683 2037 4677 2043 4665 2043 4646 2037 4633 2024 4627 6 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 2024 4627 2037 4621 2050 4608 2056 4595 2056 4577 2050 4564 2043 4558 2024 4551 1999 4551 1980 4558 1974 4564 1968 4577 1968 4583 1974 4589 1980 4583 1974 4577 16 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2043 4614 2050 4595 2050 4577 2043 4564 2037 4558 2024 4551 6 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2150 4671 2150 4551 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2156 4683 2156 4551 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 2156 4683 2087 4589 2188 4589 3 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2131 4551 2175 4551 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 4608 9078 4608 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4608 2442 4608 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 1974 5810 1980 5804 1974 5798 1968 5804 1968 5810 1974 5823 1980 5829 1999 5835 2024 5835 2043 5829 2050 5817 2050 5798 2043 5785 2024 5779 2006 5779 15 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2024 5835 2037 5829 2043 5817 2043 5798 2037 5785 2024 5779 6 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 2024 5779 2037 5773 2050 5760 2056 5747 2056 5729 2050 5716 2043 5710 2024 5703 1999 5703 1980 5710 1974 5716 1968 5729 1968 5735 1974 5741 1980 5735 1974 5729 16 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2043 5766 2050 5747 2050 5729 2043 5716 2037 5710 2024 5703 6 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2106 5835 2093 5773 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 19 2093 5773 2106 5785 2125 5791 2144 5791 2163 5785 2175 5773 2181 5754 2181 5741 2175 5722 2163 5710 2144 5703 2125 5703 2106 5710 2100 5716 2093 5729 2093 5735 2100 5741 2106 5735 2100 5729 19 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 2144 5791 2156 5785 2169 5773 2175 5754 2175 5741 2169 5722 2156 5710 2144 5703 8 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2106 5835 2169 5835 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 2106 5829 2137 5829 2169 5835 3 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5760 9078 5760 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5760 2442 5760 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 1974 6962 1980 6956 1974 6950 1968 6956 1968 6962 1974 6975 1980 6981 1999 6987 2024 6987 2043 6981 2050 6969 2050 6950 2043 6937 2024 6931 2006 6931 15 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2024 6987 2037 6981 2043 6969 2043 6950 2037 6937 2024 6931 6 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 2024 6931 2037 6925 2050 6912 2056 6899 2056 6881 2050 6868 2043 6862 2024 6855 1999 6855 1980 6862 1974 6868 1968 6881 1968 6887 1974 6893 1980 6887 1974 6881 16 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2043 6918 2050 6899 2050 6881 2043 6868 2037 6862 2024 6855 6 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 28 2169 6969 2163 6962 2169 6956 2175 6962 2175 6969 2169 6981 2156 6987 2137 6987 2119 6981 2106 6969 2100 6956 2093 6931 2093 6893 2100 6874 2112 6862 2131 6855 2144 6855 2163 6862 2175 6874 2181 6893 2181 6899 2175 6918 2163 6931 2144 6937 2137 6937 2119 6931 2106 6918 2100 6899 28 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 9 2137 6987 2125 6981 2112 6969 2106 6956 2100 6931 2100 6893 2106 6874 2119 6862 2131 6855 9 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 2144 6855 2156 6862 2169 6874 2175 6893 2175 6899 2169 6918 2156 6931 2144 6937 8 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 6912 9078 6912 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 6912 2442 6912 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 1974 8114 1980 8108 1974 8102 1968 8108 1968 8114 1974 8127 1980 8133 1999 8139 2024 8139 2043 8133 2050 8121 2050 8102 2043 8089 2024 8083 2006 8083 15 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2024 8139 2037 8133 2043 8121 2043 8102 2037 8089 2024 8083 6 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 2024 8083 2037 8077 2050 8064 2056 8051 2056 8033 2050 8020 2043 8014 2024 8007 1999 8007 1980 8014 1974 8020 1968 8033 1968 8039 1974 8045 1980 8039 1974 8033 16 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2043 8070 2050 8051 2050 8033 2043 8020 2037 8014 2024 8007 6 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2093 8139 2093 8102 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 2093 8114 2100 8127 2112 8139 2125 8139 2156 8121 2169 8121 2175 8127 2181 8139 8 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 2100 8127 2112 8133 2125 8133 2156 8121 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 2181 8139 2181 8121 2175 8102 2150 8070 2144 8058 2137 8039 2137 8007 7 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5 2175 8102 2144 8070 2137 8058 2131 8039 2131 8007 5 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 8064 9078 8064 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 8064 2442 8064 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 1974 9266 1980 9260 1974 9254 1968 9260 1968 9266 1974 9279 1980 9285 1999 9291 2024 9291 2043 9285 2050 9273 2050 9254 2043 9241 2024 9235 2006 9235 15 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2024 9291 2037 9285 2043 9273 2043 9254 2037 9241 2024 9235 6 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 2024 9235 2037 9229 2050 9216 2056 9203 2056 9185 2050 9172 2043 9166 2024 9159 1999 9159 1980 9166 1974 9172 1968 9185 1968 9191 1974 9197 1980 9191 1974 9185 16 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2043 9222 2050 9203 2050 9185 2043 9172 2037 9166 2024 9159 6 MLine End Begin %I Poly [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 12 2150 9291 2169 9285 2175 9273 2175 9254 2169 9241 2150 9235 2125 9235 2106 9241 2100 9254 2100 9273 2106 9285 2125 9291 12 Poly End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2125 9291 2112 9285 2106 9273 2106 9254 2112 9241 2125 9235 6 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2150 9235 2163 9241 2169 9254 2169 9273 2163 9285 2150 9291 6 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 2125 9235 2106 9229 2100 9222 2093 9210 2093 9185 2100 9172 2106 9166 2125 9159 2150 9159 2169 9166 2175 9172 2181 9185 2181 9210 2175 9222 2169 9229 2150 9235 16 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 2125 9235 2112 9229 2106 9222 2100 9210 2100 9185 2106 9172 2112 9166 2125 9159 8 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 2150 9159 2163 9166 2169 9172 2175 9185 2175 9210 2169 9222 2163 9229 2150 9235 8 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 9216 9078 9216 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 9216 2442 9216 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2304 9161 2304 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2304 2359 2304 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2880 9161 2880 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2880 2359 2880 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 3456 9161 3456 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3456 2359 3456 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 4032 9161 4032 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4032 2359 4032 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 4608 9161 4608 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4608 2359 4608 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5184 9161 5184 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5184 2359 5184 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5760 9161 5760 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5760 2359 5760 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 6336 9161 6336 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 6336 2359 6336 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 6912 9161 6912 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 6912 2359 6912 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 7488 9161 7488 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 7488 2359 7488 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 8064 9161 8064 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 8064 2359 8064 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 8640 9161 8640 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 8640 2359 8640 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 9216 9161 9216 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 9216 2359 9216 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4384 1906 4384 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4390 1906 4390 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4365 1906 4390 1906 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4365 1774 4409 1774 2 MLine End Begin %I Poly [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 4491 1862 4510 1856 4522 1843 4528 1824 4528 1812 4522 1793 4510 1780 4491 1774 4478 1774 4459 1780 4447 1793 4440 1812 4440 1824 4447 1843 4459 1856 4478 1862 16 Poly End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 4478 1862 4466 1856 4453 1843 4447 1824 4447 1812 4453 1793 4466 1780 4478 1774 8 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 4491 1774 4503 1780 4516 1793 4522 1812 4522 1824 4516 1843 4503 1856 4491 1862 8 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4579 1862 4579 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4585 1862 4585 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 4585 1843 4598 1856 4616 1862 4629 1862 4648 1856 4654 1843 4654 1774 7 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 4629 1862 4642 1856 4648 1843 4648 1774 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4560 1862 4585 1862 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4560 1774 4604 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4629 1774 4673 1774 2 MLine End Begin %I Poly [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 4748 1862 4761 1856 4767 1849 4773 1837 4773 1824 4767 1812 4761 1805 4748 1799 4736 1799 4723 1805 4717 1812 4711 1824 4711 1837 4717 1849 4723 1856 4736 1862 16 Poly End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 4723 1856 4717 1843 4717 1818 4723 1805 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 4761 1805 4767 1818 4767 1843 4761 1856 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5 4767 1849 4773 1856 4786 1862 4786 1856 4773 1856 5 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 9 4717 1812 4711 1805 4704 1793 4704 1787 4711 1774 4729 1768 4761 1768 4780 1761 4786 1755 9 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 4704 1787 4711 1780 4729 1774 4761 1774 4780 1768 4786 1755 4786 1749 4780 1736 4761 1730 4723 1730 4704 1736 4698 1749 4698 1755 4704 1768 4723 1774 15 MLine End Begin %I Poly [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 4843 1900 4836 1893 4830 1900 4836 1906 4 Poly End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4836 1862 4836 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4843 1862 4843 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4817 1862 4843 1862 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4817 1774 4861 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 4905 1906 4905 1799 4912 1780 4924 1774 4937 1774 4949 1780 4956 1793 7 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 4912 1906 4912 1799 4918 1780 4924 1774 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4887 1862 4937 1862 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 5000 1862 5000 1793 5006 1780 5025 1774 5037 1774 5056 1780 5069 1793 7 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 5006 1862 5006 1793 5012 1780 5025 1774 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5069 1862 5069 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5075 1862 5075 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4981 1862 5006 1862 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5050 1862 5075 1862 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5069 1774 5094 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5201 1906 5201 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5207 1906 5207 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 14 5201 1843 5188 1856 5176 1862 5163 1862 5144 1856 5132 1843 5125 1824 5125 1812 5132 1793 5144 1780 5163 1774 5176 1774 5188 1780 5201 1793 14 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 5163 1862 5150 1856 5138 1843 5132 1824 5132 1812 5138 1793 5150 1780 5163 1774 8 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5182 1906 5207 1906 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5201 1774 5226 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 17 5264 1824 5339 1824 5339 1837 5333 1849 5326 1856 5314 1862 5295 1862 5276 1856 5264 1843 5257 1824 5257 1812 5264 1793 5276 1780 5295 1774 5308 1774 5326 1780 5339 1793 17 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 5333 1824 5333 1843 5326 1856 3 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 5295 1862 5282 1856 5270 1843 5264 1824 5264 1812 5270 1793 5282 1780 5295 1774 8 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 5528 1931 5515 1918 5502 1900 5490 1875 5484 1843 5484 1818 5490 1787 5502 1761 5515 1743 5528 1730 10 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 5515 1918 5502 1893 5496 1875 5490 1843 5490 1818 5496 1787 5502 1768 5515 1743 8 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5571 1831 5685 1831 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5842 1862 5842 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5848 1862 5848 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 5848 1843 5861 1856 5879 1862 5892 1862 5911 1856 5917 1843 5917 1774 7 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 5892 1862 5905 1856 5911 1843 5911 1774 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 5917 1843 5930 1856 5949 1862 5961 1862 5980 1856 5986 1843 5986 1774 7 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 5961 1862 5974 1856 5980 1843 5980 1774 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5823 1862 5848 1862 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5823 1774 5867 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5892 1774 5936 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5961 1774 6005 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 17 6043 1824 6118 1824 6118 1837 6112 1849 6106 1856 6093 1862 6074 1862 6055 1856 6043 1843 6036 1824 6036 1812 6043 1793 6055 1780 6074 1774 6087 1774 6106 1780 6118 1793 17 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 6112 1824 6112 1843 6106 1856 3 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 6074 1862 6062 1856 6049 1843 6043 1824 6043 1812 6049 1793 6062 1780 6074 1774 8 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 13 6168 1849 6168 1843 6162 1843 6162 1849 6168 1856 6181 1862 6206 1862 6219 1856 6225 1849 6231 1837 6231 1793 6238 1780 6244 1774 13 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5 6225 1849 6225 1793 6231 1780 6244 1774 6250 1774 5 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 11 6225 1837 6219 1831 6181 1824 6162 1818 6156 1805 6156 1793 6162 1780 6181 1774 6200 1774 6212 1780 6225 1793 11 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 6181 1824 6168 1818 6162 1805 6162 1793 6168 1780 6181 1774 6 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6294 1862 6294 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6300 1862 6300 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 6300 1843 6313 1856 6332 1862 6344 1862 6363 1856 6370 1843 6370 1774 7 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 6344 1862 6357 1856 6363 1843 6363 1774 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6275 1862 6300 1862 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6275 1774 6319 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6344 1774 6388 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 6483 1849 6489 1862 6489 1837 6483 1849 6476 1856 6464 1862 6439 1862 6426 1856 6420 1849 6420 1837 6426 1831 6439 1824 6470 1812 6483 1805 6489 1799 15 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 6420 1843 6426 1837 6439 1831 6470 1818 6483 1812 6489 1805 6489 1787 6483 1780 6470 1774 6445 1774 6432 1780 6426 1787 6420 1799 6420 1774 6426 1787 15 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6633 1862 6659 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6640 1862 6659 1793 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6684 1862 6659 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6684 1862 6709 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6690 1862 6709 1793 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6734 1862 6709 1774 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6615 1862 6659 1862 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6715 1862 6753 1862 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 17 6784 1824 6860 1824 6860 1837 6853 1849 6847 1856 6835 1862 6816 1862 6797 1856 6784 1843 6778 1824 6778 1812 6784 1793 6797 1780 6816 1774 6828 1774 6847 1780 6860 1793 17 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 6853 1824 6853 1843 6847 1856 3 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 6816 1862 6803 1856 6791 1843 6784 1824 6784 1812 6791 1793 6803 1780 6816 1774 8 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 6960 1849 6966 1862 6966 1837 6960 1849 6954 1856 6941 1862 6916 1862 6904 1856 6897 1849 6897 1837 6904 1831 6916 1824 6948 1812 6960 1805 6966 1799 15 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 6897 1843 6904 1837 6916 1831 6948 1818 6960 1812 6966 1805 6966 1787 6960 1780 6948 1774 6922 1774 6910 1780 6904 1787 6897 1799 6897 1774 6904 1787 15 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 7017 1906 7017 1799 7023 1780 7036 1774 7048 1774 7061 1780 7067 1793 7 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 7023 1906 7023 1799 7029 1780 7036 1774 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6998 1862 7048 1862 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 7098 1931 7111 1918 7124 1900 7136 1875 7142 1843 7142 1818 7136 1787 7124 1761 7111 1743 7098 1730 10 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 7111 1918 7124 1893 7130 1875 7136 1843 7136 1818 7130 1787 7124 1768 7111 1743 8 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1672 5370 1804 5370 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1672 5377 1804 5377 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1672 5352 1672 5377 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1804 5352 1804 5396 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 13 1729 5440 1735 5440 1735 5433 1729 5433 1723 5440 1716 5452 1716 5477 1723 5490 1729 5496 1742 5502 1786 5502 1798 5509 1804 5515 13 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5 1729 5496 1786 5496 1798 5502 1804 5515 1804 5521 5 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 11 1742 5496 1748 5490 1754 5452 1760 5433 1773 5427 1786 5427 1798 5433 1804 5452 1804 5471 1798 5484 1786 5496 11 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 1754 5452 1760 5440 1773 5433 1786 5433 1798 5440 1804 5452 6 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 1672 5565 1779 5565 1798 5571 1804 5584 1804 5597 1798 5609 1786 5615 7 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 1672 5571 1779 5571 1798 5578 1804 5584 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1716 5546 1716 5597 2 MLine End Begin %I Poly [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 1679 5666 1685 5659 1679 5653 1672 5659 4 Poly End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1716 5659 1804 5659 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1716 5666 1804 5666 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1716 5641 1716 5666 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1804 5641 1804 5685 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 1672 5729 1779 5729 1798 5735 1804 5747 1804 5760 1798 5773 1786 5779 7 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 1672 5735 1779 5735 1798 5741 1804 5747 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1716 5710 1716 5760 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 1716 5823 1786 5823 1798 5829 1804 5848 1804 5861 1798 5879 1786 5892 7 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 1716 5829 1786 5829 1798 5835 1804 5848 4 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1716 5892 1804 5892 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1716 5898 1804 5898 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1716 5804 1716 5829 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1716 5873 1716 5898 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1804 5892 1804 5917 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1672 6024 1804 6024 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1672 6030 1804 6030 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 14 1735 6024 1723 6011 1716 5999 1716 5986 1723 5967 1735 5955 1754 5949 1767 5949 1786 5955 1798 5967 1804 5986 1804 5999 1798 6011 1786 6024 14 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 1716 5986 1723 5974 1735 5961 1754 5955 1767 5955 1786 5961 1798 5974 1804 5986 8 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1672 6005 1672 6030 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1804 6024 1804 6049 2 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 17 1754 6087 1754 6162 1742 6162 1729 6156 1723 6150 1716 6137 1716 6118 1723 6099 1735 6087 1754 6080 1767 6080 1786 6087 1798 6099 1804 6118 1804 6131 1798 6150 1786 6162 17 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 1754 6156 1735 6156 1723 6150 3 MLine End Begin %I MLine [0.4461382 0 0 0.4461382 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 1716 6118 1723 6106 1735 6093 1754 6087 1767 6087 1786 6093 1798 6106 1804 6118 8 MLine End Begin %I Circ [1.08 0 0 1.08 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5395 6543 32 Circ End Begin %I Circ [1.08 0 0 1.08 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6451 5080 32 Circ End Begin %I Circ [1.08 0 0 1.08 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8920 3214 32 Circ End Begin %I Circ [1.08 0 0 1.08 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5084 2696 32 Circ End Begin %I Circ [1.08 0 0 1.08 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3045 4078 32 Circ End Begin %I Circ [1.08 0 0 1.08 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4324 6359 32 Circ End Begin %I Circ [1.08 0 0 1.08 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4385 8467 32 Circ End Begin %I Circ [1.08 0 0 1.08 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4658 8398 32 Circ End Begin %I Circ [1.08 0 0 1.08 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4669 5933 32 Circ End Begin %I Circ [1.08 0 0 1.08 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5138 5898 32 Circ End Begin %I Circ [1.08 0 0 1.08 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5268 6785 32 Circ End Begin %I Circ [1.08 0 0 1.08 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5407 6647 32 Circ End Begin %I Circ [1.08 0 0 1.08 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5395 6543 32 Circ End Begin %I Poly [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 12 5407 6647 5268 6785 5138 5898 4669 5933 4658 8398 4385 8467 4324 6359 3045 4078 5084 2696 8920 3214 6451 5080 5395 6543 12 Poly End %%PageTrailer End %I eop showpage %%Trailer end %%EOF %%EndDocument @endspecial 390 4478 a FK(Initial)29 b(and)f(\014nal)g(\(optimal\))j (route)d(for)h(the)f(12)i(south)m(w)m(estern)f(cities)h(Flying)f (Salesman)390 4587 y(Problem.)150 5230 y(Here's)38 b(a)g(plot)g(of)g (the)g(cost)h(function)e(\(energy\))i(v)m(ersus)e(generation)i(\(p)s (oin)m(t)f(in)f(the)h(calculation)i(at)150 5340 y(whic)m(h)30 b(a)h(new)f(temp)s(erature)g(is)g(set\))i(for)e(this)g(problem:)p eop end %%Page: 334 352 TeXDict begin 334 351 bop 150 -116 a FK(Chapter)30 b(26:)41 b(Sim)m(ulated)31 b(Annealing)2126 b(334)275 1738 y @beginspecial 56 @llx 177 @lly 500 @urx 610 @ury 2016 @rwi @setspecial %%BeginDocument: 12-cities.eps %!PS-Adobe-3.0 EPSF-3.0 %%Creator: GNU libplot drawing library 4.1 %%Title: PostScript plot %%CreationDate: Thu Jan 4 06:48:42 2007 %%DocumentData: Clean7Bit %%LanguageLevel: 1 %%Pages: 1 %%PageOrder: Ascend %%Orientation: Portrait %%BoundingBox: 56 177 500 610 %%DocumentNeededResources: %%DocumentSuppliedResources: procset GNU_libplot 1.0 0 %%EndComments %%BeginDefaults %%PageResources: %%EndDefaults %%BeginProlog %%EndProlog %%BeginSetup /DrawDict 50 dict def DrawDict begin %%BeginResource procset GNU_libplot 1.0 0 /none null def /numGraphicParameters 17 def /stringLimit 65535 def /arrowHeight 8 def /eoFillRule true def /Begin { save numGraphicParameters dict begin } def /End { end restore } def /SetB { dup type /nulltype eq { pop false /brushRightArrow idef false /brushLeftArrow idef true /brushNone idef } { /brushDashOffset idef /brushDashArray idef 0 ne /brushRightArrow idef 0 ne /brushLeftArrow idef /brushWidth idef false /brushNone idef } ifelse } def /SetCFg { /fgblue idef /fggreen idef /fgred idef } def /SetCBg { /bgblue idef /bggreen idef /bgred idef } def /SetF { /printSize idef /printFont idef } def /SetP { dup type /nulltype eq { pop true /patternNone idef } { /patternGrayLevel idef patternGrayLevel -1 eq { /patternString idef } if false /patternNone idef } ifelse } def /BSpl { 0 begin storexyn newpath n 1 gt { 0 0 0 0 0 0 1 1 true subspline n 2 gt { 0 0 0 0 1 1 2 2 false subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 2 copy false subspline } if n 2 sub dup n 1 sub dup 2 copy 2 copy false subspline patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup 1 sub dup rightarrow } if end } dup 0 4 dict put def /Circ { newpath 0 360 arc closepath patternNone not { ifill } if brushNone not { istroke } if } def /CBSpl { 0 begin dup 2 gt { storexyn newpath n 1 sub dup 0 0 1 1 2 2 true subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 0 0 false subspline n 2 sub dup n 1 sub dup 0 0 1 1 false subspline patternNone not { ifill } if brushNone not { istroke } if } { Poly } ifelse end } dup 0 4 dict put def /Elli { 0 begin newpath 4 2 roll translate scale 0 0 1 0 360 arc closepath patternNone not { ifill } if brushNone not { istroke } if end } dup 0 1 dict put def /Line { 0 begin 2 storexyn newpath x 0 get y 0 get moveto x 1 get y 1 get lineto brushNone not { istroke } if 0 0 1 1 leftarrow 0 0 1 1 rightarrow end } dup 0 4 dict put def /MLine { 0 begin storexyn newpath n 1 gt { x 0 get y 0 get moveto 1 1 n 1 sub { /i exch def x i get y i get lineto } for patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Poly { 3 1 roll newpath moveto -1 add { lineto } repeat closepath patternNone not { ifill } if brushNone not { istroke } if } def /Rect { 0 begin /t exch def /r exch def /b exch def /l exch def newpath l b moveto l t lineto r t lineto r b lineto closepath patternNone not { ifill } if brushNone not { istroke } if end } dup 0 4 dict put def /Text { ishow } def /idef { dup where { pop pop pop } { exch def } ifelse } def /ifill { 0 begin gsave patternGrayLevel -1 ne { fgred bgred fgred sub patternGrayLevel mul add fggreen bggreen fggreen sub patternGrayLevel mul add fgblue bgblue fgblue sub patternGrayLevel mul add setrgbcolor eoFillRule { eofill } { fill } ifelse } { eoFillRule { eoclip } { clip } ifelse originalCTM setmatrix pathbbox /t exch def /r exch def /b exch def /l exch def /w r l sub ceiling cvi def /h t b sub ceiling cvi def /imageByteWidth w 8 div ceiling cvi def /imageHeight h def bgred bggreen bgblue setrgbcolor eoFillRule { eofill } { fill } ifelse fgred fggreen fgblue setrgbcolor w 0 gt h 0 gt and { l b translate w h scale w h true [w 0 0 h neg 0 h] { patternproc } imagemask } if } ifelse grestore end } dup 0 8 dict put def /istroke { gsave brushDashOffset -1 eq { [] 0 setdash 1 setgray } { brushDashArray brushDashOffset setdash fgred fggreen fgblue setrgbcolor } ifelse brushWidth setlinewidth originalCTM setmatrix stroke grestore } def /ishow { 0 begin gsave fgred fggreen fgblue setrgbcolor /fontDict printFont findfont printSize scalefont dup setfont def /descender fontDict begin 0 /FontBBox load 1 get FontMatrix end transform exch pop def /vertoffset 1 printSize sub descender sub def { 0 vertoffset moveto show /vertoffset vertoffset printSize sub def } forall grestore end } dup 0 3 dict put def /patternproc { 0 begin /patternByteLength patternString length def /patternHeight patternByteLength 8 mul sqrt cvi def /patternWidth patternHeight def /patternByteWidth patternWidth 8 idiv def /imageByteMaxLength imageByteWidth imageHeight mul stringLimit patternByteWidth sub min def /imageMaxHeight imageByteMaxLength imageByteWidth idiv patternHeight idiv patternHeight mul patternHeight max def /imageHeight imageHeight imageMaxHeight sub store /imageString imageByteWidth imageMaxHeight mul patternByteWidth add string def 0 1 imageMaxHeight 1 sub { /y exch def /patternRow y patternByteWidth mul patternByteLength mod def /patternRowString patternString patternRow patternByteWidth getinterval def /imageRow y imageByteWidth mul def 0 patternByteWidth imageByteWidth 1 sub { /x exch def imageString imageRow x add patternRowString putinterval } for } for imageString end } dup 0 12 dict put def /min { dup 3 2 roll dup 4 3 roll lt { exch } if pop } def /max { dup 3 2 roll dup 4 3 roll gt { exch } if pop } def /midpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 x1 add 2 div y0 y1 add 2 div end } dup 0 4 dict put def /thirdpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 2 mul x1 add 3 div y0 2 mul y1 add 3 div end } dup 0 4 dict put def /subspline { 0 begin /movetoNeeded exch def y exch get /y3 exch def x exch get /x3 exch def y exch get /y2 exch def x exch get /x2 exch def y exch get /y1 exch def x exch get /x1 exch def y exch get /y0 exch def x exch get /x0 exch def x1 y1 x2 y2 thirdpoint /p1y exch def /p1x exch def x2 y2 x1 y1 thirdpoint /p2y exch def /p2x exch def x1 y1 x0 y0 thirdpoint p1x p1y midpoint /p0y exch def /p0x exch def x2 y2 x3 y3 thirdpoint p2x p2y midpoint /p3y exch def /p3x exch def movetoNeeded { p0x p0y moveto } if p1x p1y p2x p2y p3x p3y curveto end } dup 0 17 dict put def /storexyn { /n exch def /y n array def /x n array def n 1 sub -1 0 { /i exch def y i 3 2 roll put x i 3 2 roll put } for } def /arrowhead { 0 begin transform originalCTM itransform /taily exch def /tailx exch def transform originalCTM itransform /tipy exch def /tipx exch def /dy tipy taily sub def /dx tipx tailx sub def /angle dx 0 ne dy 0 ne or { dy dx atan } { 90 } ifelse def gsave originalCTM setmatrix tipx tipy translate angle rotate newpath arrowHeight neg arrowWidth 2 div moveto 0 0 lineto arrowHeight neg arrowWidth 2 div neg lineto patternNone not { originalCTM setmatrix /padtip arrowHeight 2 exp 0.25 arrowWidth 2 exp mul add sqrt brushWidth mul arrowWidth div def /padtail brushWidth 2 div def tipx tipy translate angle rotate padtip 0 translate arrowHeight padtip add padtail add arrowHeight div dup scale arrowheadpath ifill } if brushNone not { originalCTM setmatrix tipx tipy translate angle rotate arrowheadpath istroke } if grestore end } dup 0 9 dict put def /arrowheadpath { newpath arrowHeight neg arrowWidth 2 div moveto 0 0 lineto arrowHeight neg arrowWidth 2 div neg lineto } def /leftarrow { 0 begin y exch get /taily exch def x exch get /tailx exch def y exch get /tipy exch def x exch get /tipx exch def brushLeftArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /rightarrow { 0 begin y exch get /tipy exch def x exch get /tipx exch def y exch get /taily exch def x exch get /tailx exch def brushRightArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def %%EndResource %%EndSetup %%Page: 1 1 %%PageResources: %%PageBoundingBox: 56 177 500 610 %%BeginPageSetup %I Idraw 8 Begin %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 1 0 0 1 0 0 ] concat /originalCTM matrix currentmatrix def /trueoriginalCTM matrix currentmatrix def %%EndPageSetup Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2564 10017 2564 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2578 10017 2578 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 2476 10017 2461 9930 2461 10017 2681 10017 2681 9930 2666 10017 6 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2520 9710 2622 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 2945 9973 2960 10017 2960 9930 2945 9973 2916 10003 2872 10017 2828 10017 2784 10003 2754 9973 2754 9944 2769 9915 2784 9900 2813 9886 2901 9856 2930 9842 2960 9812 16 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 2754 9944 2784 9915 2813 9900 2901 9871 2930 9856 2945 9842 2960 9812 2960 9754 2930 9724 2886 9710 2842 9710 2798 9724 2769 9754 2754 9798 2754 9710 2769 9754 16 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3077 10017 3077 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3092 10017 3092 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 3033 10017 3209 10017 3253 10003 3267 9988 3282 9959 3282 9915 3267 9886 3253 9871 3209 9856 3092 9856 10 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 3209 10017 3238 10003 3253 9988 3267 9959 3267 9915 3253 9886 3238 9871 3209 9856 8 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3033 9710 3136 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3619 9842 3883 9842 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 4264 9959 4294 9973 4338 10017 4338 9710 4 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4323 10003 4323 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4264 9710 4396 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 20 4528 9959 4543 9944 4528 9930 4514 9944 4514 9959 4528 9988 4543 10003 4587 10017 4646 10017 4690 10003 4704 9988 4719 9959 4719 9930 4704 9900 4660 9871 4587 9842 4558 9827 4528 9798 4514 9754 4514 9710 20 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 4646 10017 4675 10003 4690 9988 4704 9959 4704 9930 4690 9900 4646 9871 4587 9842 8 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 4514 9739 4528 9754 4558 9754 4631 9724 4675 9724 4704 9739 4719 9754 7 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 4558 9754 4631 9710 4690 9710 4704 9724 4719 9754 4719 9783 6 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 5188 9886 5203 9915 5203 9856 5188 9886 5174 9900 5144 9915 5086 9915 5056 9900 5042 9886 5042 9856 5056 9842 5086 9827 5159 9798 5188 9783 5203 9768 15 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 5042 9871 5056 9856 5086 9842 5159 9812 5188 9798 5203 9783 5203 9739 5188 9724 5159 9710 5100 9710 5071 9724 5056 9739 5042 9768 5042 9710 5056 9739 15 MLine End Begin %I Poly [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 5408 9915 5452 9900 5481 9871 5496 9827 5496 9798 5481 9754 5452 9724 5408 9710 5379 9710 5335 9724 5305 9754 5291 9798 5291 9827 5305 9871 5335 9900 5379 9915 16 Poly End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 5379 9915 5349 9900 5320 9871 5305 9827 5305 9798 5320 9754 5349 9724 5379 9710 8 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 5408 9710 5437 9724 5467 9754 5481 9798 5481 9827 5467 9871 5437 9900 5408 9915 8 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 5613 9915 5613 9754 5628 9724 5672 9710 5701 9710 5745 9724 5775 9754 7 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 5628 9915 5628 9754 5643 9724 5672 9710 4 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5775 9915 5775 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5789 9915 5789 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5569 9915 5628 9915 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5731 9915 5789 9915 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5775 9710 5833 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 5936 10017 5936 9768 5951 9724 5980 9710 6009 9710 6039 9724 6053 9754 7 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 5951 10017 5951 9768 5965 9724 5980 9710 4 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5892 9915 6009 9915 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6156 10017 6156 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6171 10017 6171 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 6171 9871 6200 9900 6244 9915 6273 9915 6317 9900 6332 9871 6332 9710 7 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 6273 9915 6302 9900 6317 9871 6317 9710 4 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6112 10017 6171 10017 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6112 9710 6215 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6273 9710 6376 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6464 9915 6522 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6478 9915 6522 9754 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6581 9915 6522 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6581 9915 6640 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6596 9915 6640 9754 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6698 9915 6640 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6420 9915 6522 9915 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6654 9915 6742 9915 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 17 6816 9827 6992 9827 6992 9856 6977 9886 6962 9900 6933 9915 6889 9915 6845 9900 6816 9871 6801 9827 6801 9798 6816 9754 6845 9724 6889 9710 6918 9710 6962 9724 6992 9754 17 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 6977 9827 6977 9871 6962 9900 3 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 6889 9915 6860 9900 6830 9871 6816 9827 6816 9798 6830 9754 6860 9724 6889 9710 8 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 7226 9886 7241 9915 7241 9856 7226 9886 7212 9900 7182 9915 7124 9915 7094 9900 7080 9886 7080 9856 7094 9842 7124 9827 7197 9798 7226 9783 7241 9768 15 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 7080 9871 7094 9856 7124 9842 7197 9812 7226 9798 7241 9783 7241 9739 7226 9724 7197 9710 7138 9710 7109 9724 7094 9739 7080 9768 7080 9710 7094 9739 15 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 7358 10017 7358 9768 7373 9724 7402 9710 7431 9710 7461 9724 7475 9754 7 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 7373 10017 7373 9768 7387 9724 7402 9710 4 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7314 9915 7431 9915 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 18 7959 9871 7945 9856 7959 9842 7974 9856 7974 9871 7945 9900 7915 9915 7871 9915 7827 9900 7798 9871 7783 9827 7783 9798 7798 9754 7827 9724 7871 9710 7901 9710 7945 9724 7974 9754 18 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 7871 9915 7842 9900 7813 9871 7798 9827 7798 9798 7813 9754 7842 9724 7871 9710 8 MLine End Begin %I Poly [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 8106 10003 8091 9988 8077 10003 8091 10017 4 Poly End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8091 9915 8091 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8106 9915 8106 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8047 9915 8106 9915 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8047 9710 8150 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 8253 10017 8253 9768 8267 9724 8296 9710 8326 9710 8355 9724 8370 9754 7 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 8267 10017 8267 9768 8282 9724 8296 9710 4 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8209 9915 8326 9915 2 MLine End Begin %I Poly [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 8487 10003 8472 9988 8458 10003 8472 10017 4 Poly End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8472 9915 8472 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8487 9915 8487 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8428 9915 8487 9915 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8428 9710 8531 9710 2 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 17 8619 9827 8795 9827 8795 9856 8780 9886 8766 9900 8736 9915 8692 9915 8648 9900 8619 9871 8604 9827 8604 9798 8619 9754 8648 9724 8692 9710 8722 9710 8766 9724 8795 9754 17 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 8780 9827 8780 9871 8766 9900 3 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 8692 9915 8663 9900 8634 9871 8619 9827 8619 9798 8634 9754 8663 9724 8692 9710 8 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 9030 9886 9044 9915 9044 9856 9030 9886 9015 9900 8986 9915 8927 9915 8898 9900 8883 9886 8883 9856 8898 9842 8927 9827 9000 9798 9030 9783 9044 9768 15 MLine End Begin %I MLine [1.040989 0 0 1.040989 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 8883 9871 8898 9856 8927 9842 9000 9812 9030 9798 9044 9783 9044 9739 9030 9724 9000 9710 8942 9710 8912 9724 8898 9739 8883 9768 8883 9710 8898 9739 15 MLine End Begin %I Rect [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2304 2304 9216 9216 Rect End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 2315 2151 2348 2140 2370 2107 2381 2052 2381 2019 2370 1964 2348 1931 2315 1920 2293 1920 2260 1931 2238 1964 2227 2019 2227 2052 2238 2107 2260 2140 2293 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 2293 2151 2271 2140 2260 2129 2249 2107 2238 2052 2238 2019 2249 1964 2260 1942 2271 1931 2293 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 2315 1920 2337 1931 2348 1942 2359 1964 2370 2019 2370 2052 2359 2107 2348 2129 2337 2140 2315 2151 10 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 9216 2304 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2304 2304 2442 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 3313 2107 3335 2118 3368 2151 3368 1920 4 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3357 2140 3357 1920 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3313 1920 3411 1920 2 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 3587 2151 3620 2140 3642 2107 3653 2052 3653 2019 3642 1964 3620 1931 3587 1920 3565 1920 3532 1931 3510 1964 3499 2019 3499 2052 3510 2107 3532 2140 3565 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 3565 2151 3543 2140 3532 2129 3521 2107 3510 2052 3510 2019 3521 1964 3532 1942 3543 1931 3565 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 3587 1920 3609 1931 3620 1942 3631 1964 3642 2019 3642 2052 3631 2107 3620 2129 3609 2140 3587 2151 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 3807 2151 3840 2140 3862 2107 3873 2052 3873 2019 3862 1964 3840 1931 3807 1920 3785 1920 3752 1931 3730 1964 3719 2019 3719 2052 3730 2107 3752 2140 3785 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 3785 2151 3763 2140 3752 2129 3741 2107 3730 2052 3730 2019 3741 1964 3752 1942 3763 1931 3785 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 3807 1920 3829 1931 3840 1942 3851 1964 3862 2019 3862 2052 3851 2107 3840 2129 3829 2140 3807 2151 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 4027 2151 4060 2140 4082 2107 4093 2052 4093 2019 4082 1964 4060 1931 4027 1920 4005 1920 3972 1931 3950 1964 3939 2019 3939 2052 3950 2107 3972 2140 4005 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 4005 2151 3983 2140 3972 2129 3961 2107 3950 2052 3950 2019 3961 1964 3972 1942 3983 1931 4005 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 4027 1920 4049 1931 4060 1942 4071 1964 4082 2019 4082 2052 4071 2107 4060 2129 4049 2140 4027 2151 10 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3686 9216 3686 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3686 2304 3686 2442 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 20 4673 2107 4684 2096 4673 2085 4662 2096 4662 2107 4673 2129 4684 2140 4717 2151 4761 2151 4794 2140 4805 2129 4816 2107 4816 2085 4805 2063 4772 2041 4717 2019 4695 2008 4673 1986 4662 1953 4662 1920 20 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 4761 2151 4783 2140 4794 2129 4805 2107 4805 2085 4794 2063 4761 2041 4717 2019 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 4662 1942 4673 1953 4695 1953 4750 1931 4783 1931 4805 1942 4816 1953 7 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 4695 1953 4750 1920 4794 1920 4805 1931 4816 1953 4816 1975 6 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 4970 2151 5003 2140 5025 2107 5036 2052 5036 2019 5025 1964 5003 1931 4970 1920 4948 1920 4915 1931 4893 1964 4882 2019 4882 2052 4893 2107 4915 2140 4948 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 4948 2151 4926 2140 4915 2129 4904 2107 4893 2052 4893 2019 4904 1964 4915 1942 4926 1931 4948 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 4970 1920 4992 1931 5003 1942 5014 1964 5025 2019 5025 2052 5014 2107 5003 2129 4992 2140 4970 2151 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 5190 2151 5223 2140 5245 2107 5256 2052 5256 2019 5245 1964 5223 1931 5190 1920 5168 1920 5135 1931 5113 1964 5102 2019 5102 2052 5113 2107 5135 2140 5168 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 5168 2151 5146 2140 5135 2129 5124 2107 5113 2052 5113 2019 5124 1964 5135 1942 5146 1931 5168 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 5190 1920 5212 1931 5223 1942 5234 1964 5245 2019 5245 2052 5234 2107 5223 2129 5212 2140 5190 2151 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 5410 2151 5443 2140 5465 2107 5476 2052 5476 2019 5465 1964 5443 1931 5410 1920 5388 1920 5355 1931 5333 1964 5322 2019 5322 2052 5333 2107 5355 2140 5388 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 5388 2151 5366 2140 5355 2129 5344 2107 5333 2052 5333 2019 5344 1964 5355 1942 5366 1931 5388 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 5410 1920 5432 1931 5443 1942 5454 1964 5465 2019 5465 2052 5454 2107 5443 2129 5432 2140 5410 2151 10 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5069 9216 5069 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5069 2304 5069 2442 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 6055 2107 6066 2096 6055 2085 6044 2096 6044 2107 6055 2129 6066 2140 6099 2151 6143 2151 6176 2140 6187 2118 6187 2085 6176 2063 6143 2052 6110 2052 15 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 6143 2151 6165 2140 6176 2118 6176 2085 6165 2063 6143 2052 6 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 6143 2052 6165 2041 6187 2019 6198 1997 6198 1964 6187 1942 6176 1931 6143 1920 6099 1920 6066 1931 6055 1942 6044 1964 6044 1975 6055 1986 6066 1975 6055 1964 16 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 6176 2030 6187 1997 6187 1964 6176 1942 6165 1931 6143 1920 6 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 6352 2151 6385 2140 6407 2107 6418 2052 6418 2019 6407 1964 6385 1931 6352 1920 6330 1920 6297 1931 6275 1964 6264 2019 6264 2052 6275 2107 6297 2140 6330 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 6330 2151 6308 2140 6297 2129 6286 2107 6275 2052 6275 2019 6286 1964 6297 1942 6308 1931 6330 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 6352 1920 6374 1931 6385 1942 6396 1964 6407 2019 6407 2052 6396 2107 6385 2129 6374 2140 6352 2151 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 6572 2151 6605 2140 6627 2107 6638 2052 6638 2019 6627 1964 6605 1931 6572 1920 6550 1920 6517 1931 6495 1964 6484 2019 6484 2052 6495 2107 6517 2140 6550 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 6550 2151 6528 2140 6517 2129 6506 2107 6495 2052 6495 2019 6506 1964 6517 1942 6528 1931 6550 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 6572 1920 6594 1931 6605 1942 6616 1964 6627 2019 6627 2052 6616 2107 6605 2129 6594 2140 6572 2151 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 6792 2151 6825 2140 6847 2107 6858 2052 6858 2019 6847 1964 6825 1931 6792 1920 6770 1920 6737 1931 6715 1964 6704 2019 6704 2052 6715 2107 6737 2140 6770 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 6770 2151 6748 2140 6737 2129 6726 2107 6715 2052 6715 2019 6726 1964 6737 1942 6748 1931 6770 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 6792 1920 6814 1931 6825 1942 6836 1964 6847 2019 6847 2052 6836 2107 6825 2129 6814 2140 6792 2151 10 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6451 9216 6451 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6451 2304 6451 2442 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7526 2129 7526 1920 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7537 2151 7537 1920 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 7537 2151 7416 1986 7592 1986 3 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7493 1920 7570 1920 2 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 7735 2151 7768 2140 7790 2107 7801 2052 7801 2019 7790 1964 7768 1931 7735 1920 7713 1920 7680 1931 7658 1964 7647 2019 7647 2052 7658 2107 7680 2140 7713 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 7713 2151 7691 2140 7680 2129 7669 2107 7658 2052 7658 2019 7669 1964 7680 1942 7691 1931 7713 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 7735 1920 7757 1931 7768 1942 7779 1964 7790 2019 7790 2052 7779 2107 7768 2129 7757 2140 7735 2151 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 7955 2151 7988 2140 8010 2107 8021 2052 8021 2019 8010 1964 7988 1931 7955 1920 7933 1920 7900 1931 7878 1964 7867 2019 7867 2052 7878 2107 7900 2140 7933 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 7933 2151 7911 2140 7900 2129 7889 2107 7878 2052 7878 2019 7889 1964 7900 1942 7911 1931 7933 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 7955 1920 7977 1931 7988 1942 7999 1964 8010 2019 8010 2052 7999 2107 7988 2129 7977 2140 7955 2151 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 8174 2151 8207 2140 8229 2107 8240 2052 8240 2019 8229 1964 8207 1931 8174 1920 8152 1920 8120 1931 8098 1964 8087 2019 8087 2052 8098 2107 8120 2140 8152 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 8152 2151 8131 2140 8120 2129 8109 2107 8098 2052 8098 2019 8109 1964 8120 1942 8131 1931 8152 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 8174 1920 8196 1931 8207 1942 8218 1964 8229 2019 8229 2052 8218 2107 8207 2129 8196 2140 8174 2151 10 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7834 9216 7834 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7834 2304 7834 2442 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8831 2151 8809 2041 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 19 8809 2041 8831 2063 8864 2074 8897 2074 8930 2063 8952 2041 8963 2008 8963 1986 8952 1953 8930 1931 8897 1920 8864 1920 8831 1931 8820 1942 8809 1964 8809 1975 8820 1986 8831 1975 8820 1964 19 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 8897 2074 8919 2063 8941 2041 8952 2008 8952 1986 8941 1953 8919 1931 8897 1920 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8831 2151 8941 2151 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 8831 2140 8886 2140 8941 2151 3 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 9117 2151 9150 2140 9172 2107 9183 2052 9183 2019 9172 1964 9150 1931 9117 1920 9095 1920 9062 1931 9040 1964 9029 2019 9029 2052 9040 2107 9062 2140 9095 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 9095 2151 9073 2140 9062 2129 9051 2107 9040 2052 9040 2019 9051 1964 9062 1942 9073 1931 9095 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 9117 1920 9139 1931 9150 1942 9161 1964 9172 2019 9172 2052 9161 2107 9150 2129 9139 2140 9117 2151 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 9337 2151 9370 2140 9392 2107 9403 2052 9403 2019 9392 1964 9370 1931 9337 1920 9315 1920 9282 1931 9260 1964 9249 2019 9249 2052 9260 2107 9282 2140 9315 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 9315 2151 9293 2140 9282 2129 9271 2107 9260 2052 9260 2019 9271 1964 9282 1942 9293 1931 9315 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 9337 1920 9359 1931 9370 1942 9381 1964 9392 2019 9392 2052 9381 2107 9370 2129 9359 2140 9337 2151 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 9557 2151 9590 2140 9612 2107 9623 2052 9623 2019 9612 1964 9590 1931 9557 1920 9535 1920 9502 1931 9480 1964 9469 2019 9469 2052 9480 2107 9502 2140 9535 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 9535 2151 9513 2140 9502 2129 9491 2107 9480 2052 9480 2019 9491 1964 9502 1942 9513 1931 9535 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 9557 1920 9579 1931 9590 1942 9601 1964 9612 2019 9612 2052 9601 2107 9590 2129 9579 2140 9557 2151 10 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 9216 9216 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2304 9216 2442 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 9216 2304 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2304 2304 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2580 9216 2580 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2580 2304 2580 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2857 9216 2857 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2857 2304 2857 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3133 9216 3133 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3133 2304 3133 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3410 9216 3410 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3410 2304 3410 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3686 9216 3686 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3686 2304 3686 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3963 9216 3963 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3963 2304 3963 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4239 9216 4239 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4239 2304 4239 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4516 9216 4516 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4516 2304 4516 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4792 9216 4792 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4792 2304 4792 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5069 9216 5069 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5069 2304 5069 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5345 9216 5345 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5345 2304 5345 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5622 9216 5622 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5622 2304 5622 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5898 9216 5898 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5898 2304 5898 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6175 9216 6175 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6175 2304 6175 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6451 9216 6451 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6451 2304 6451 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6728 9216 6728 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6728 2304 6728 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7004 9216 7004 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7004 2304 7004 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7281 9216 7281 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7281 2304 7281 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7557 9216 7557 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7557 2304 7557 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7834 9216 7834 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7834 2304 7834 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8110 9216 8110 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8110 2304 8110 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8387 9216 8387 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8387 2304 8387 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8663 9216 8663 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8663 2304 8663 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8940 9216 8940 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8940 2304 8940 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 9216 9216 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2304 9216 2359 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 1365 2824 1376 2813 1365 2802 1354 2813 1354 2824 1365 2846 1376 2857 1409 2868 1453 2868 1486 2857 1497 2835 1497 2802 1486 2780 1453 2769 1420 2769 15 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 1453 2868 1475 2857 1486 2835 1486 2802 1475 2780 1453 2769 6 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 1453 2769 1475 2758 1497 2736 1508 2714 1508 2681 1497 2659 1486 2648 1453 2637 1409 2637 1376 2648 1365 2659 1354 2681 1354 2692 1365 2703 1376 2692 1365 2681 16 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 1486 2747 1497 2714 1497 2681 1486 2659 1475 2648 1453 2637 6 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1596 2868 1574 2758 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 19 1574 2758 1596 2780 1629 2791 1661 2791 1694 2780 1716 2758 1727 2725 1727 2703 1716 2670 1694 2648 1661 2637 1629 2637 1596 2648 1585 2659 1574 2681 1574 2692 1585 2703 1596 2692 1585 2681 19 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 1661 2791 1683 2780 1705 2758 1716 2725 1716 2703 1705 2670 1683 2648 1661 2637 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1596 2868 1705 2868 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 1596 2857 1651 2857 1705 2868 3 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 1881 2868 1914 2857 1936 2824 1947 2769 1947 2736 1936 2681 1914 2648 1881 2637 1859 2637 1826 2648 1804 2681 1793 2736 1793 2769 1804 2824 1826 2857 1859 2868 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 1859 2868 1837 2857 1826 2846 1815 2824 1804 2769 1804 2736 1815 2681 1826 2659 1837 2648 1859 2637 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 1881 2637 1903 2648 1914 2659 1925 2681 1936 2736 1936 2769 1925 2824 1914 2846 1903 2857 1881 2868 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 2101 2868 2134 2857 2156 2824 2167 2769 2167 2736 2156 2681 2134 2648 2101 2637 2079 2637 2046 2648 2024 2681 2013 2736 2013 2769 2024 2824 2046 2857 2079 2868 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 2079 2868 2057 2857 2046 2846 2035 2824 2024 2769 2024 2736 2035 2681 2046 2659 2057 2648 2079 2637 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 2101 2637 2123 2648 2134 2659 2145 2681 2156 2736 2156 2769 2145 2824 2134 2846 2123 2857 2101 2868 10 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2736 9078 2736 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2736 2442 2736 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1453 3926 1453 3717 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1464 3948 1464 3717 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 1464 3948 1343 3783 1519 3783 3 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1420 3717 1497 3717 2 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 1661 3948 1694 3937 1716 3904 1727 3849 1727 3816 1716 3761 1694 3728 1661 3717 1640 3717 1607 3728 1585 3761 1574 3816 1574 3849 1585 3904 1607 3937 1640 3948 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 1640 3948 1618 3937 1607 3926 1596 3904 1585 3849 1585 3816 1596 3761 1607 3739 1618 3728 1640 3717 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 1661 3717 1683 3728 1694 3739 1705 3761 1716 3816 1716 3849 1705 3904 1694 3926 1683 3937 1661 3948 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 1881 3948 1914 3937 1936 3904 1947 3849 1947 3816 1936 3761 1914 3728 1881 3717 1859 3717 1826 3728 1804 3761 1793 3816 1793 3849 1804 3904 1826 3937 1859 3948 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 1859 3948 1837 3937 1826 3926 1815 3904 1804 3849 1804 3816 1815 3761 1826 3739 1837 3728 1859 3717 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 1881 3717 1903 3728 1914 3739 1925 3761 1936 3816 1936 3849 1925 3904 1914 3926 1903 3937 1881 3948 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 2101 3948 2134 3937 2156 3904 2167 3849 2167 3816 2156 3761 2134 3728 2101 3717 2079 3717 2046 3728 2024 3761 2013 3816 2013 3849 2024 3904 2046 3937 2079 3948 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 2079 3948 2057 3937 2046 3926 2035 3904 2024 3849 2024 3816 2035 3761 2046 3739 2057 3728 2079 3717 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 2101 3717 2123 3728 2134 3739 2145 3761 2156 3816 2156 3849 2145 3904 2134 3926 2123 3937 2101 3948 10 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 3816 9078 3816 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3816 2442 3816 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1453 5006 1453 4797 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1464 5028 1464 4797 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 1464 5028 1343 4863 1519 4863 3 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1420 4797 1497 4797 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1596 5028 1574 4918 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 19 1574 4918 1596 4940 1629 4951 1661 4951 1694 4940 1716 4918 1727 4885 1727 4863 1716 4830 1694 4808 1661 4797 1629 4797 1596 4808 1585 4819 1574 4841 1574 4852 1585 4863 1596 4852 1585 4841 19 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 1661 4951 1683 4940 1705 4918 1716 4885 1716 4863 1705 4830 1683 4808 1661 4797 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1596 5028 1705 5028 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 1596 5017 1651 5017 1705 5028 3 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 1881 5028 1914 5017 1936 4984 1947 4929 1947 4896 1936 4841 1914 4808 1881 4797 1859 4797 1826 4808 1804 4841 1793 4896 1793 4929 1804 4984 1826 5017 1859 5028 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 1859 5028 1837 5017 1826 5006 1815 4984 1804 4929 1804 4896 1815 4841 1826 4819 1837 4808 1859 4797 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 1881 4797 1903 4808 1914 4819 1925 4841 1936 4896 1936 4929 1925 4984 1914 5006 1903 5017 1881 5028 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 2101 5028 2134 5017 2156 4984 2167 4929 2167 4896 2156 4841 2134 4808 2101 4797 2079 4797 2046 4808 2024 4841 2013 4896 2013 4929 2024 4984 2046 5017 2079 5028 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 2079 5028 2057 5017 2046 5006 2035 4984 2024 4929 2024 4896 2035 4841 2046 4819 2057 4808 2079 4797 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 2101 4797 2123 4808 2134 4819 2145 4841 2156 4896 2156 4929 2145 4984 2134 5006 2123 5017 2101 5028 10 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 4896 9078 4896 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4896 2442 4896 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1376 6108 1354 5998 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 19 1354 5998 1376 6020 1409 6031 1442 6031 1475 6020 1497 5998 1508 5965 1508 5943 1497 5910 1475 5888 1442 5877 1409 5877 1376 5888 1365 5899 1354 5921 1354 5932 1365 5943 1376 5932 1365 5921 19 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 1442 6031 1464 6020 1486 5998 1497 5965 1497 5943 1486 5910 1464 5888 1442 5877 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1376 6108 1486 6108 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 1376 6097 1431 6097 1486 6108 3 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 1661 6108 1694 6097 1716 6064 1727 6009 1727 5976 1716 5921 1694 5888 1661 5877 1640 5877 1607 5888 1585 5921 1574 5976 1574 6009 1585 6064 1607 6097 1640 6108 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 1640 6108 1618 6097 1607 6086 1596 6064 1585 6009 1585 5976 1596 5921 1607 5899 1618 5888 1640 5877 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 1661 5877 1683 5888 1694 5899 1705 5921 1716 5976 1716 6009 1705 6064 1694 6086 1683 6097 1661 6108 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 1881 6108 1914 6097 1936 6064 1947 6009 1947 5976 1936 5921 1914 5888 1881 5877 1859 5877 1826 5888 1804 5921 1793 5976 1793 6009 1804 6064 1826 6097 1859 6108 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 1859 6108 1837 6097 1826 6086 1815 6064 1804 6009 1804 5976 1815 5921 1826 5899 1837 5888 1859 5877 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 1881 5877 1903 5888 1914 5899 1925 5921 1936 5976 1936 6009 1925 6064 1914 6086 1903 6097 1881 6108 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 2101 6108 2134 6097 2156 6064 2167 6009 2167 5976 2156 5921 2134 5888 2101 5877 2079 5877 2046 5888 2024 5921 2013 5976 2013 6009 2024 6064 2046 6097 2079 6108 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 2079 6108 2057 6097 2046 6086 2035 6064 2024 6009 2024 5976 2035 5921 2046 5899 2057 5888 2079 5877 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 2101 5877 2123 5888 2134 5899 2145 5921 2156 5976 2156 6009 2145 6064 2134 6086 2123 6097 2101 6108 10 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5976 9078 5976 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5976 2442 5976 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1376 7188 1354 7078 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 19 1354 7078 1376 7100 1409 7111 1442 7111 1475 7100 1497 7078 1508 7045 1508 7023 1497 6990 1475 6968 1442 6957 1409 6957 1376 6968 1365 6979 1354 7001 1354 7012 1365 7023 1376 7012 1365 7001 19 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 1442 7111 1464 7100 1486 7078 1497 7045 1497 7023 1486 6990 1464 6968 1442 6957 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1376 7188 1486 7188 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 1376 7177 1431 7177 1486 7188 3 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1596 7188 1574 7078 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 19 1574 7078 1596 7100 1629 7111 1661 7111 1694 7100 1716 7078 1727 7045 1727 7023 1716 6990 1694 6968 1661 6957 1629 6957 1596 6968 1585 6979 1574 7001 1574 7012 1585 7023 1596 7012 1585 7001 19 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 1661 7111 1683 7100 1705 7078 1716 7045 1716 7023 1705 6990 1683 6968 1661 6957 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1596 7188 1705 7188 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 1596 7177 1651 7177 1705 7188 3 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 1881 7188 1914 7177 1936 7144 1947 7089 1947 7056 1936 7001 1914 6968 1881 6957 1859 6957 1826 6968 1804 7001 1793 7056 1793 7089 1804 7144 1826 7177 1859 7188 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 1859 7188 1837 7177 1826 7166 1815 7144 1804 7089 1804 7056 1815 7001 1826 6979 1837 6968 1859 6957 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 1881 6957 1903 6968 1914 6979 1925 7001 1936 7056 1936 7089 1925 7144 1914 7166 1903 7177 1881 7188 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 2101 7188 2134 7177 2156 7144 2167 7089 2167 7056 2156 7001 2134 6968 2101 6957 2079 6957 2046 6968 2024 7001 2013 7056 2013 7089 2024 7144 2046 7177 2079 7188 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 2079 7188 2057 7177 2046 7166 2035 7144 2024 7089 2024 7056 2035 7001 2046 6979 2057 6968 2079 6957 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 2101 6957 2123 6968 2134 6979 2145 7001 2156 7056 2156 7089 2145 7144 2134 7166 2123 7177 2101 7188 10 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 7056 9078 7056 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 7056 2442 7056 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 28 1486 8235 1475 8224 1486 8213 1497 8224 1497 8235 1486 8257 1464 8268 1431 8268 1398 8257 1376 8235 1365 8213 1354 8169 1354 8103 1365 8070 1387 8048 1420 8037 1442 8037 1475 8048 1497 8070 1508 8103 1508 8114 1497 8147 1475 8169 1442 8180 1431 8180 1398 8169 1376 8147 1365 8114 28 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 9 1431 8268 1409 8257 1387 8235 1376 8213 1365 8169 1365 8103 1376 8070 1398 8048 1420 8037 9 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 1442 8037 1464 8048 1486 8070 1497 8103 1497 8114 1486 8147 1464 8169 1442 8180 8 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 1661 8268 1694 8257 1716 8224 1727 8169 1727 8136 1716 8081 1694 8048 1661 8037 1640 8037 1607 8048 1585 8081 1574 8136 1574 8169 1585 8224 1607 8257 1640 8268 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 1640 8268 1618 8257 1607 8246 1596 8224 1585 8169 1585 8136 1596 8081 1607 8059 1618 8048 1640 8037 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 1661 8037 1683 8048 1694 8059 1705 8081 1716 8136 1716 8169 1705 8224 1694 8246 1683 8257 1661 8268 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 1881 8268 1914 8257 1936 8224 1947 8169 1947 8136 1936 8081 1914 8048 1881 8037 1859 8037 1826 8048 1804 8081 1793 8136 1793 8169 1804 8224 1826 8257 1859 8268 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 1859 8268 1837 8257 1826 8246 1815 8224 1804 8169 1804 8136 1815 8081 1826 8059 1837 8048 1859 8037 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 1881 8037 1903 8048 1914 8059 1925 8081 1936 8136 1936 8169 1925 8224 1914 8246 1903 8257 1881 8268 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 2101 8268 2134 8257 2156 8224 2167 8169 2167 8136 2156 8081 2134 8048 2101 8037 2079 8037 2046 8048 2024 8081 2013 8136 2013 8169 2024 8224 2046 8257 2079 8268 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 2079 8268 2057 8257 2046 8246 2035 8224 2024 8169 2024 8136 2035 8081 2046 8059 2057 8048 2079 8037 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 2101 8037 2123 8048 2134 8059 2145 8081 2156 8136 2156 8169 2145 8224 2134 8246 2123 8257 2101 8268 10 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 8136 9078 8136 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 8136 2442 8136 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 28 1486 9315 1475 9304 1486 9293 1497 9304 1497 9315 1486 9337 1464 9348 1431 9348 1398 9337 1376 9315 1365 9293 1354 9249 1354 9183 1365 9150 1387 9128 1420 9117 1442 9117 1475 9128 1497 9150 1508 9183 1508 9194 1497 9227 1475 9249 1442 9260 1431 9260 1398 9249 1376 9227 1365 9194 28 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 9 1431 9348 1409 9337 1387 9315 1376 9293 1365 9249 1365 9183 1376 9150 1398 9128 1420 9117 9 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 1442 9117 1464 9128 1486 9150 1497 9183 1497 9194 1486 9227 1464 9249 1442 9260 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1596 9348 1574 9238 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 19 1574 9238 1596 9260 1629 9271 1661 9271 1694 9260 1716 9238 1727 9205 1727 9183 1716 9150 1694 9128 1661 9117 1629 9117 1596 9128 1585 9139 1574 9161 1574 9172 1585 9183 1596 9172 1585 9161 19 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 1661 9271 1683 9260 1705 9238 1716 9205 1716 9183 1705 9150 1683 9128 1661 9117 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1596 9348 1705 9348 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 1596 9337 1651 9337 1705 9348 3 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 1881 9348 1914 9337 1936 9304 1947 9249 1947 9216 1936 9161 1914 9128 1881 9117 1859 9117 1826 9128 1804 9161 1793 9216 1793 9249 1804 9304 1826 9337 1859 9348 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 1859 9348 1837 9337 1826 9326 1815 9304 1804 9249 1804 9216 1815 9161 1826 9139 1837 9128 1859 9117 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 1881 9117 1903 9128 1914 9139 1925 9161 1936 9216 1936 9249 1925 9304 1914 9326 1903 9337 1881 9348 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 2101 9348 2134 9337 2156 9304 2167 9249 2167 9216 2156 9161 2134 9128 2101 9117 2079 9117 2046 9128 2024 9161 2013 9216 2013 9249 2024 9304 2046 9337 2079 9348 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 2079 9348 2057 9337 2046 9326 2035 9304 2024 9249 2024 9216 2035 9161 2046 9139 2057 9128 2079 9117 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 2101 9117 2123 9128 2134 9139 2145 9161 2156 9216 2156 9249 2145 9304 2134 9326 2123 9337 2101 9348 10 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 9216 9078 9216 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 9216 2442 9216 2 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 4858 1621 4880 1610 4891 1599 4902 1577 4902 1555 4891 1533 4880 1522 4858 1511 4836 1511 4814 1522 4803 1533 4792 1555 4792 1577 4803 1599 4814 1610 4836 1621 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 4814 1610 4803 1588 4803 1544 4814 1522 4 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 4880 1522 4891 1544 4891 1588 4880 1610 4 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5 4891 1599 4902 1610 4924 1621 4924 1610 4902 1610 5 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 9 4803 1533 4792 1522 4781 1500 4781 1489 4792 1467 4825 1456 4880 1456 4913 1445 4924 1434 9 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 4781 1489 4792 1478 4825 1467 4880 1467 4913 1456 4924 1434 4924 1423 4913 1401 4880 1390 4814 1390 4781 1401 4770 1423 4770 1434 4781 1456 4814 1467 15 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 17 5001 1555 5133 1555 5133 1577 5122 1599 5111 1610 5089 1621 5056 1621 5023 1610 5001 1588 4990 1555 4990 1533 5001 1500 5023 1478 5056 1467 5078 1467 5111 1478 5133 1500 17 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 5122 1555 5122 1588 5111 1610 3 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 5056 1621 5034 1610 5012 1588 5001 1555 5001 1533 5012 1500 5034 1478 5056 1467 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5221 1621 5221 1467 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5232 1621 5232 1467 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 5232 1588 5254 1610 5287 1621 5309 1621 5342 1610 5353 1588 5353 1467 7 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 5309 1621 5331 1610 5342 1588 5342 1467 4 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5188 1621 5232 1621 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5188 1467 5265 1467 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5309 1467 5386 1467 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 17 5452 1555 5584 1555 5584 1577 5573 1599 5562 1610 5540 1621 5507 1621 5474 1610 5452 1588 5441 1555 5441 1533 5452 1500 5474 1478 5507 1467 5529 1467 5562 1478 5584 1500 17 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 5573 1555 5573 1588 5562 1610 3 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 5507 1621 5485 1610 5463 1588 5452 1555 5452 1533 5463 1500 5485 1478 5507 1467 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5672 1621 5672 1467 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5683 1621 5683 1467 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 5683 1555 5694 1588 5716 1610 5738 1621 5771 1621 5782 1610 5782 1599 5771 1588 5760 1599 5771 1610 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5639 1621 5683 1621 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5639 1467 5716 1467 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 13 5859 1599 5859 1588 5848 1588 5848 1599 5859 1610 5881 1621 5925 1621 5947 1610 5958 1599 5969 1577 5969 1500 5980 1478 5991 1467 13 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5 5958 1599 5958 1500 5969 1478 5991 1467 6002 1467 5 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 11 5958 1577 5947 1566 5881 1555 5848 1544 5837 1522 5837 1500 5848 1478 5881 1467 5914 1467 5936 1478 5958 1500 11 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 5881 1555 5859 1544 5848 1522 5848 1500 5859 1478 5881 1467 6 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 6079 1698 6079 1511 6090 1478 6112 1467 6134 1467 6156 1478 6167 1500 7 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 6090 1698 6090 1511 6101 1478 6112 1467 4 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6046 1621 6134 1621 2 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 6255 1687 6244 1676 6233 1687 6244 1698 4 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6244 1621 6244 1467 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6255 1621 6255 1467 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6211 1621 6255 1621 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6211 1467 6288 1467 2 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 6431 1621 6464 1610 6486 1588 6497 1555 6497 1533 6486 1500 6464 1478 6431 1467 6409 1467 6376 1478 6354 1500 6343 1533 6343 1555 6354 1588 6376 1610 6409 1621 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 6409 1621 6387 1610 6365 1588 6354 1555 6354 1533 6365 1500 6387 1478 6409 1467 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 6431 1467 6453 1478 6475 1500 6486 1533 6486 1555 6475 1588 6453 1610 6431 1621 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6585 1621 6585 1467 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6596 1621 6596 1467 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 6596 1588 6618 1610 6651 1621 6673 1621 6706 1610 6717 1588 6717 1467 7 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 6673 1621 6695 1610 6706 1588 6706 1467 4 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6552 1621 6596 1621 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6552 1467 6629 1467 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6673 1467 6750 1467 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 771 5133 1002 5133 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 771 5144 1002 5144 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 14 881 5133 859 5111 848 5089 848 5067 859 5034 881 5012 914 5001 936 5001 969 5012 991 5034 1002 5067 1002 5089 991 5111 969 5133 14 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 848 5067 859 5045 881 5023 914 5012 936 5012 969 5023 991 5045 1002 5067 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 771 5100 771 5144 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1002 5133 1002 5177 2 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 782 5265 793 5254 782 5243 771 5254 4 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 848 5254 1002 5254 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 848 5265 1002 5265 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 848 5221 848 5265 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1002 5221 1002 5298 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 870 5463 848 5474 892 5474 870 5463 859 5452 848 5430 848 5386 859 5364 870 5353 892 5353 903 5364 914 5386 936 5441 947 5463 958 5474 15 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 15 881 5353 892 5364 903 5386 925 5441 936 5463 947 5474 980 5474 991 5463 1002 5441 1002 5397 991 5375 980 5364 958 5353 1002 5353 980 5364 15 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 771 5562 958 5562 991 5573 1002 5595 1002 5617 991 5639 969 5650 7 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 771 5573 958 5573 991 5584 1002 5595 4 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 848 5529 848 5617 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 13 870 5727 881 5727 881 5716 870 5716 859 5727 848 5749 848 5793 859 5815 870 5826 892 5837 969 5837 991 5848 1002 5859 13 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5 870 5826 969 5826 991 5837 1002 5859 1002 5870 5 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 11 892 5826 903 5815 914 5749 925 5716 947 5705 969 5705 991 5716 1002 5749 1002 5782 991 5804 969 5826 11 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 914 5749 925 5727 947 5716 969 5716 991 5727 1002 5749 6 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 848 5947 1002 5947 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 848 5958 1002 5958 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 881 5958 859 5980 848 6013 848 6035 859 6068 881 6079 1002 6079 7 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 848 6035 859 6057 881 6068 1002 6068 4 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 848 5914 848 5958 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1002 5914 1002 5991 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1002 6035 1002 6112 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 18 881 6299 892 6288 903 6299 892 6310 881 6310 859 6288 848 6266 848 6233 859 6200 881 6178 914 6167 936 6167 969 6178 991 6200 1002 6233 1002 6255 991 6288 969 6310 18 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 848 6233 859 6211 881 6189 914 6178 936 6178 969 6189 991 6211 1002 6233 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 17 914 6387 914 6519 892 6519 870 6508 859 6497 848 6475 848 6442 859 6409 881 6387 914 6376 936 6376 969 6387 991 6409 1002 6442 1002 6464 991 6497 969 6519 17 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 914 6508 881 6508 859 6497 3 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 848 6442 859 6420 881 6398 914 6387 936 6387 969 6398 991 6420 1002 6442 8 MLine End Begin %I MLine [1 0 0 1 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 0 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 500 2304 5975 2305 7816 2307 4950 2308 6253 2310 6424 2311 7247 2312 7226 2314 7637 2315 5613 2316 5493 2318 6547 2319 6692 2321 5964 2322 7196 2323 5558 2325 5777 2326 5879 2328 6986 2329 6683 2330 6582 2332 7053 2333 6524 2334 7103 2336 6771 2337 6085 2339 6261 2340 7658 2341 6191 2343 5763 2344 5180 2345 6647 2347 6690 2348 6033 2350 5517 2351 6947 2352 6031 2354 7215 2355 5701 2357 6826 2358 4979 2359 7053 2361 7059 2362 6081 2363 5251 2365 6631 2366 7749 2368 7219 2369 7019 2370 5147 2372 6824 2373 7042 2375 5319 2376 6485 2377 6702 2379 7476 2380 6497 2381 5692 2383 7014 2384 6696 2386 7546 2387 6374 2388 7684 2390 5675 2391 6634 2392 5907 2394 6945 2395 4627 2397 5267 2398 7319 2399 6397 2401 6962 2402 6413 2404 5424 2405 4277 2406 7412 2408 5725 2409 5438 2410 7077 2412 7297 2413 6874 2415 5718 2416 7183 2417 6089 2419 6439 2420 5788 2422 7577 2423 7135 2424 4970 2426 4854 2427 7340 2428 6868 2430 7205 2431 4963 2433 5641 2434 6536 2435 4679 2437 6735 2438 4672 2439 8293 2441 6474 2442 7717 2444 7297 2445 5583 2446 7717 2448 6229 2449 7615 2451 5946 2452 7426 2453 7569 2455 7305 2456 7030 2457 5945 2459 6252 2460 6256 2462 5037 2463 7580 2464 6202 2466 6322 2467 7211 2469 6680 2470 7020 2471 7596 2473 6861 2474 6352 2475 6302 2477 6238 2478 5681 2480 7024 2481 7194 2482 7181 2484 5997 2485 7477 2486 6567 2488 5778 2489 7126 2491 7143 2492 4981 2493 7184 2495 6655 2496 6103 2498 7571 2499 7773 2500 4533 2502 7966 2503 6383 2504 5874 2506 6128 2507 7545 2509 7794 2510 5779 2511 6850 2513 6570 2514 6612 2516 6800 2517 7324 2518 6811 2520 6237 2521 5937 2522 7023 2524 5700 2525 6549 2527 5356 2528 4062 2529 5495 2531 7192 2532 7316 2533 6114 2535 7015 2536 6818 2538 6597 2539 7315 2540 6174 2542 5431 2543 4943 2545 7012 2546 6702 2547 7220 2549 6142 2550 7649 2551 6097 2553 7626 2554 5399 2556 6739 2557 5159 2558 6984 2560 6165 2561 6070 2563 7594 2564 6333 2565 6072 2567 6981 2568 6118 2569 8009 2571 6786 2572 3964 2574 7069 2575 6203 2576 7315 2578 6263 2579 6910 2580 7867 2582 7539 2583 6058 2585 7242 2586 7161 2587 4653 2589 5701 2590 5840 2592 7394 2593 6140 2594 6588 2596 7405 2597 7363 2598 6270 2600 6828 2601 6694 2603 6633 2604 5843 2605 6859 2607 7988 2608 8335 2610 6485 2611 6899 2612 6402 2614 6170 2615 6849 2616 6781 2618 5607 2619 7433 2621 6231 2622 6930 2623 6528 2625 5108 2626 5909 2627 6618 2629 6798 2630 7872 2632 6204 2633 5670 2634 6511 2636 7405 2637 7134 2639 6024 2640 5627 2641 7504 2643 6354 2644 6328 2645 6850 2647 6170 2648 5736 2650 5071 2651 7988 2652 5623 2654 7860 2655 8050 2657 6341 2658 6585 2659 7083 2661 6648 2662 6756 2663 5424 2665 6470 2666 7593 2668 5424 2669 6352 2670 6943 2672 6103 2673 5837 2674 7117 2676 6315 2677 5418 2679 6215 2680 6400 2681 6010 2683 7503 2684 7385 2686 6992 2687 6667 2688 6781 2690 5817 2691 5413 2692 5412 2694 5498 2695 4809 2697 6155 2698 6572 2699 5742 2701 6998 2702 7159 2704 5752 2705 6282 2706 7428 2708 6185 2709 5320 2710 5352 2712 7322 2713 6880 2715 5045 2716 8073 2717 6522 2719 6304 2720 6838 2721 7607 2723 6454 2724 4543 2726 5443 2727 4373 2728 6075 2730 4438 2731 6222 2733 6471 2734 6127 2735 4718 2737 6646 2738 7497 2739 6643 2741 6507 2742 7559 2744 5945 2745 6344 2746 5749 2748 3931 2749 5983 2751 5519 2752 7380 2753 6519 2755 6871 2756 6904 2757 4866 2759 6241 2760 6975 2762 6489 2763 6289 2764 7682 2766 6684 2767 7146 2768 4765 2770 6388 2771 5567 2773 6850 2774 7391 2775 6612 2777 6446 2778 6030 2780 4342 2781 4427 2782 6825 2784 5752 2785 6568 2786 7571 2788 6257 2789 6656 2791 6926 2792 6282 2793 6897 2795 6227 2796 5113 2798 7030 2799 7242 2800 5510 2802 7129 2803 6568 2804 6192 2806 6959 2807 5321 2809 4693 2810 6100 2811 6395 2813 6826 2814 5490 2815 6969 2817 6078 2818 7152 2820 6091 2821 7381 2822 6617 2824 7695 2825 5593 2827 6622 2828 6288 2829 6702 2831 6934 2832 6624 2833 5925 2835 7798 2836 4630 2838 6688 2839 7861 2840 6913 2842 6210 2843 6419 2845 6804 2846 7672 2847 7459 2849 7743 2850 6174 2851 7115 2853 7227 2854 6955 2856 4666 2857 5437 2858 7272 2860 7161 2861 6287 2862 6510 2864 7009 2865 6230 2867 8104 2868 5213 2869 7444 2871 5270 2872 6554 2874 8316 2875 6849 2876 7049 2878 7424 2879 5947 2880 7143 2882 4998 2883 6869 2885 6666 2886 5571 2887 4916 2889 7033 2890 7221 2892 6641 2893 5717 2894 5146 2896 5780 2897 6069 2898 5560 2900 6828 2901 6165 2903 5213 2904 7420 2905 5039 2907 6388 2908 7049 2909 6891 2911 6493 2912 7226 2914 7190 2915 6023 2916 7258 2918 7024 2919 7329 2921 5204 2922 6316 2923 7768 2925 5235 2926 3984 2927 4882 2929 5740 2930 6666 2932 5163 2933 6564 2934 7307 2936 5580 2937 7181 2939 6624 2940 7831 2941 7859 2943 5221 2944 7092 2945 7608 2947 5700 2948 6040 2950 7511 2951 5388 2952 7134 2954 6344 2955 7619 2956 5623 2958 5272 2959 5360 2961 6245 2962 6129 2963 6190 2965 6880 2966 6481 2968 6064 2969 5978 2970 5826 2972 6860 2973 7539 2974 5309 2976 5697 2977 6036 2979 5645 2980 7292 2981 7775 2983 5403 2984 7097 2986 6945 2987 6146 2988 5767 2990 6920 2991 6175 2992 6384 2994 6065 500 MLine End Begin %I MLine [1 0 0 1 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 0 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 500 2994 6065 2995 6508 2997 6632 2998 5605 2999 7427 3001 6132 3002 6997 3003 5107 3005 8057 3006 5980 3008 6607 3009 5047 3010 7159 3012 6130 3013 6326 3015 5480 3016 7144 3017 6460 3019 6057 3020 5236 3021 7111 3023 6834 3024 7882 3026 6138 3027 6672 3028 4868 3030 5932 3031 6708 3033 5904 3034 6156 3035 7098 3037 6948 3038 7216 3039 5263 3041 4902 3042 5075 3044 6038 3045 5928 3046 6721 3048 6916 3049 6175 3050 6186 3052 5165 3053 6628 3055 4563 3056 6825 3057 6994 3059 5837 3060 6024 3062 4145 3063 6181 3064 7149 3066 6230 3067 7353 3068 5027 3070 6784 3071 5176 3073 4734 3074 6185 3075 7018 3077 6738 3078 7112 3080 5657 3081 6499 3082 6577 3084 5404 3085 6748 3086 7088 3088 6050 3089 4645 3091 7826 3092 4502 3093 3982 3095 6140 3096 6906 3097 5287 3099 6297 3100 7275 3102 7638 3103 6758 3104 6217 3106 6206 3107 6472 3109 7863 3110 5915 3111 6128 3113 7946 3114 6022 3115 6673 3117 7093 3118 7403 3120 5984 3121 7523 3122 5666 3124 5830 3125 7180 3127 7926 3128 5279 3129 7104 3131 6301 3132 7283 3133 6673 3135 5524 3136 4270 3138 7139 3139 5666 3140 6830 3142 6505 3143 4847 3144 7208 3146 5955 3147 6739 3149 4931 3150 6824 3151 6430 3153 6334 3154 6755 3156 6898 3157 7908 3158 7316 3160 4991 3161 5627 3162 6798 3164 7575 3165 4947 3167 5466 3168 7527 3169 6864 3171 5942 3172 6255 3174 6357 3175 6552 3176 8008 3178 5726 3179 5386 3180 7356 3182 7055 3183 7835 3185 5904 3186 7610 3187 6764 3189 6366 3190 7155 3192 6349 3193 6661 3194 6692 3196 7036 3197 6412 3198 6167 3200 5942 3201 6170 3203 6511 3204 6497 3205 5323 3207 5020 3208 6034 3209 7502 3211 7104 3212 6304 3214 4423 3215 5941 3216 6554 3218 5133 3219 5137 3221 4899 3222 5826 3223 7202 3225 5999 3226 5980 3227 7764 3229 5558 3230 5769 3232 6808 3233 6655 3234 7062 3236 4576 3237 7493 3239 5320 3240 6538 3241 6106 3243 6974 3244 6782 3245 5881 3247 5960 3248 6582 3250 3852 3251 7165 3252 5777 3254 4462 3255 6883 3256 5868 3258 6677 3259 7032 3261 7121 3262 6284 3263 4604 3265 6944 3266 5429 3268 5106 3269 4632 3270 5302 3272 7407 3273 6297 3274 4845 3276 5363 3277 5750 3279 6514 3280 6256 3281 6940 3283 5749 3284 5088 3286 5680 3287 6105 3288 5626 3290 7455 3291 6419 3292 7427 3294 6426 3295 6968 3297 7535 3298 6764 3299 7084 3301 6368 3302 7328 3303 6864 3305 7209 3306 5261 3308 6392 3309 4682 3310 5981 3312 6751 3313 6832 3315 5489 3316 6844 3317 6692 3319 6347 3320 7442 3321 5362 3323 5816 3324 6621 3326 6946 3327 7012 3328 5654 3330 5382 3331 7440 3333 4981 3334 6342 3335 6539 3337 5497 3338 7107 3339 6330 3341 7525 3342 6899 3344 5995 3345 5421 3346 6763 3348 6741 3349 5918 3350 6332 3352 6261 3353 5289 3355 6792 3356 4720 3357 6069 3359 5393 3360 7078 3362 6579 3363 5048 3364 6334 3366 4833 3367 5472 3368 7092 3370 5130 3371 8076 3373 5672 3374 5522 3375 5711 3377 7683 3378 6997 3380 6467 3381 6152 3382 6038 3384 6242 3385 4935 3386 7055 3388 6717 3389 7209 3391 6157 3392 7196 3393 5341 3395 7441 3396 7034 3397 6058 3399 7014 3400 6908 3402 7481 3403 6465 3404 6024 3406 5161 3407 7598 3409 4797 3410 6655 3411 6232 3413 7690 3414 4949 3415 7138 3417 5030 3418 4984 3420 6002 3421 5609 3422 6021 3424 6210 3425 6712 3427 5799 3428 4447 3429 5318 3431 6674 3432 6104 3433 5491 3435 5034 3436 5408 3438 5728 3439 5729 3440 7040 3442 6414 3443 6618 3444 4612 3446 5057 3447 5917 3449 5631 3450 7749 3451 5845 3453 4696 3454 6539 3456 5306 3457 6940 3458 6095 3460 5522 3461 7480 3462 7401 3464 6061 3465 4705 3467 7143 3468 6591 3469 6361 3471 6358 3472 6579 3474 5328 3475 5058 3476 5359 3478 7628 3479 4818 3480 6228 3482 6697 3483 5229 3485 7214 3486 6968 3487 6231 3489 7966 3490 6855 3491 5392 3493 6562 3494 4965 3496 5518 3497 4392 3498 6042 3500 5510 3501 5253 3503 7226 3504 5400 3505 5482 3507 5709 3508 6324 3509 5405 3511 5800 3512 6493 3514 5151 3515 5342 3516 5332 3518 6004 3519 6017 3521 6112 3522 4149 3523 6556 3525 6055 3526 4613 3527 6550 3529 7414 3530 5444 3532 5983 3533 5153 3534 6227 3536 6975 3537 6840 3538 6669 3540 5521 3541 7013 3543 6924 3544 6700 3545 6718 3547 6761 3548 6997 3550 4070 3551 5336 3552 5382 3554 7298 3555 6985 3556 5151 3558 7633 3559 5992 3561 4105 3562 7280 3563 6925 3565 5363 3566 6286 3568 6211 3569 4586 3570 5155 3572 4908 3573 6782 3574 6281 3576 4295 3577 6229 3579 6564 3580 3982 3581 6056 3583 4917 3584 6610 3585 7452 3587 6288 3588 6866 3590 6604 3591 5803 3592 5523 3594 7327 3595 6162 3597 5427 3598 4539 3599 4636 3601 6353 3602 6531 3603 6937 3605 6264 3606 5553 3608 7460 3609 6216 3610 5923 3612 7448 3613 6211 3615 5896 3616 7463 3617 7677 3619 7453 3620 6312 3621 6029 3623 6315 3624 5449 3626 5130 3627 5696 3628 6288 3630 5038 3631 6149 3632 5816 3634 5556 3635 6803 3637 6792 3638 6528 3639 4853 3641 6032 3642 5143 3644 5579 3645 5671 3646 7076 3648 6538 3649 4431 3650 5194 3652 6770 3653 6072 3655 4156 3656 4607 3657 7255 3659 5704 3660 6602 3662 6843 3663 6291 3664 5185 3666 7251 3667 6110 3668 5283 3670 6565 3671 6153 3673 6825 3674 5929 3675 4326 3677 5884 3678 6694 3679 4817 3681 5716 3682 7328 3684 6636 500 MLine End Begin %I MLine [1 0 0 1 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 0 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 500 3684 6636 3685 6170 3686 5820 3688 5297 3689 5708 3691 4592 3692 4857 3693 6834 3695 7258 3696 6691 3697 6333 3699 7118 3700 5369 3702 6478 3703 6327 3704 6422 3706 5175 3707 6853 3709 6431 3710 5454 3711 5344 3713 6855 3714 5590 3715 7694 3717 6550 3718 7201 3720 6486 3721 4999 3722 7183 3724 5553 3725 6642 3726 4676 3728 6758 3729 4332 3731 5495 3732 5165 3733 5613 3735 5879 3736 4700 3738 4972 3739 4334 3740 6682 3742 7116 3743 5894 3744 6361 3746 5605 3747 6007 3749 5479 3750 5883 3751 5141 3753 7290 3754 6674 3756 4964 3757 5153 3758 7665 3760 4429 3761 4644 3762 4841 3764 6395 3765 5078 3767 4876 3768 6966 3769 5723 3771 7599 3772 7060 3773 5417 3775 3796 3776 5048 3778 6809 3779 5829 3780 6202 3782 5439 3783 7151 3785 5412 3786 6694 3787 4841 3789 7062 3790 5192 3791 4741 3793 4764 3794 4839 3796 6243 3797 5745 3798 5906 3800 7574 3801 4236 3803 6197 3804 7421 3805 3958 3807 6458 3808 7604 3809 5816 3811 4430 3812 5677 3814 5400 3815 5773 3816 6096 3818 3143 3819 5402 3820 7683 3822 5902 3823 6980 3825 4711 3826 4456 3827 6765 3829 6019 3830 5095 3832 4937 3833 5773 3834 5615 3836 6371 3837 6926 3838 6176 3840 6255 3841 6747 3843 7824 3844 6753 3845 6128 3847 5596 3848 3728 3850 5860 3851 5295 3852 5202 3854 5454 3855 5691 3856 5828 3858 6077 3859 4998 3861 7756 3862 6009 3863 5641 3865 4587 3866 5874 3867 5728 3869 5814 3870 6350 3872 6834 3873 5732 3874 5525 3876 5287 3877 5901 3879 6770 3880 5634 3881 6675 3883 5801 3884 6346 3885 6345 3887 3944 3888 6323 3890 7631 3891 5038 3892 5339 3894 5718 3895 6260 3897 4656 3898 5858 3899 5914 3901 5009 3902 6377 3903 6192 3905 3838 3906 5374 3908 6010 3909 6069 3910 4908 3912 6819 3913 5734 3914 5874 3916 3925 3917 6544 3919 7007 3920 4534 3921 4806 3923 6988 3924 4958 3926 4422 3927 6334 3928 4903 3930 7559 3931 6882 3932 7246 3934 7262 3935 6130 3937 3709 3938 5727 3939 6338 3941 4823 3942 6971 3944 6382 3945 5852 3946 5377 3948 6003 3949 6432 3950 5140 3952 5964 3953 6563 3955 4698 3956 7282 3957 5322 3959 6201 3960 5999 3961 7515 3963 7765 3964 6574 3966 6829 3967 5806 3968 6656 3970 6808 3971 6480 3973 4308 3974 5807 3975 4915 3977 5140 3978 5656 3979 6004 3981 7332 3982 6410 3984 5599 3985 5602 3986 5153 3988 4864 3989 5306 3991 5471 3992 5498 3993 5240 3995 6296 3996 5165 3997 7085 3999 4961 4000 4641 4002 6059 4003 5248 4004 6500 4006 5729 4007 6164 4008 4816 4010 4014 4011 5666 4013 4345 4014 4585 4015 5984 4017 4942 4018 4814 4020 5578 4021 4211 4022 7063 4024 4061 4025 4690 4026 5719 4028 6475 4029 7119 4031 4972 4032 5645 4033 7593 4035 5954 4036 6742 4038 4801 4039 6177 4040 7284 4042 6661 4043 5013 4044 4135 4046 4466 4047 4334 4049 3960 4050 4191 4051 5243 4053 7723 4054 6634 4056 5310 4057 5735 4058 7055 4060 6541 4061 7189 4062 5539 4064 6938 4065 4548 4067 4666 4068 6024 4069 5072 4071 5066 4072 4461 4073 5766 4075 4976 4076 4248 4078 6228 4079 6556 4080 6204 4082 4209 4083 7114 4085 6552 4086 6478 4087 6333 4089 5969 4090 5169 4091 7604 4093 6236 4094 6638 4096 5579 4097 6672 4098 6449 4100 5180 4101 6388 4103 4234 4104 4391 4105 4651 4107 6191 4108 6119 4109 5000 4111 5240 4112 6411 4114 5193 4115 7274 4116 4555 4118 5460 4119 3571 4120 6938 4122 6110 4123 4595 4125 5067 4126 5035 4127 7996 4129 4122 4130 6991 4132 4827 4133 4823 4134 5016 4136 5928 4137 4319 4138 5626 4140 5762 4141 5980 4143 5354 4144 7235 4145 5318 4147 6232 4148 5351 4150 5777 4151 5357 4152 5312 4154 4073 4155 5107 4156 6022 4158 3898 4159 5845 4161 4139 4162 7499 4163 6649 4165 5487 4166 6164 4167 5959 4169 5074 4170 5523 4172 5028 4173 6271 4174 5409 4176 7406 4177 5963 4179 5488 4180 4874 4181 5595 4183 4673 4184 4818 4185 4402 4187 5036 4188 5949 4190 5548 4191 4019 4192 4972 4194 4866 4195 6727 4197 5365 4198 4732 4199 6428 4201 3299 4202 4261 4203 5529 4205 5748 4206 3059 4208 5490 4209 4973 4210 6017 4212 4664 4213 3796 4214 4896 4216 4452 4217 6510 4219 4747 4220 5521 4221 4193 4223 4976 4224 4771 4226 4945 4227 4345 4228 5805 4230 5689 4231 4711 4232 6199 4234 4049 4235 5158 4237 3510 4238 5769 4239 5298 4241 5926 4242 4664 4244 6605 4245 5619 4246 4499 4248 5892 4249 5683 4250 5952 4252 6122 4253 4120 4255 6840 4256 4934 4257 5462 4259 3921 4260 6392 4261 3845 4263 4635 4264 5077 4266 5357 4267 5407 4268 4526 4270 5522 4271 5350 4273 6841 4274 5624 4275 6043 4277 6499 4278 6918 4279 7601 4281 5802 4282 4525 4284 5221 4285 6049 4286 4410 4288 4131 4289 3651 4291 6234 4292 5942 4293 5465 4295 3740 4296 4637 4297 5424 4299 5638 4300 5997 4302 5276 4303 5294 4304 5911 4306 5647 4307 3782 4308 5702 4310 6094 4311 6285 4313 5162 4314 6497 4315 5088 4317 5544 4318 4826 4320 4705 4321 5791 4322 3410 4324 5219 4325 5887 4326 7402 4328 4437 4329 4834 4331 3945 4332 5536 4333 4938 4335 4561 4336 4568 4338 4726 4339 4517 4340 4483 4342 4659 4343 5097 4344 4829 4346 6115 4347 4631 4349 4721 4350 6862 4351 6986 4353 4668 4354 6283 4355 3399 4357 4840 4358 4100 4360 3782 4361 5525 4362 5422 4364 5764 4365 4929 4367 4125 4368 4868 4369 6211 4371 5907 4372 4884 4373 4001 500 MLine End Begin %I MLine [1 0 0 1 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 0 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 500 4373 4001 4375 6307 4376 5989 4378 4968 4379 5533 4380 4396 4382 5916 4383 5373 4385 5302 4386 5738 4387 4804 4389 4709 4390 6196 4391 4473 4393 7109 4394 5018 4396 4731 4397 5907 4398 4788 4400 6437 4401 5667 4402 5365 4404 3650 4405 4945 4407 3976 4408 4879 4409 4407 4411 6014 4412 4096 4414 5222 4415 6216 4416 5301 4418 5797 4419 4803 4420 4612 4422 4215 4423 4238 4425 6240 4426 4646 4427 4413 4429 5132 4430 4949 4432 5271 4433 5711 4434 4627 4436 5084 4437 5256 4438 5503 4440 4790 4441 5481 4443 5128 4444 4624 4445 4050 4447 4813 4448 5188 4449 4801 4451 5200 4452 4263 4454 5300 4455 4722 4456 5144 4458 4835 4459 4681 4461 4219 4462 3599 4463 5365 4465 6045 4466 5993 4467 3658 4469 4438 4470 4802 4472 4337 4473 5162 4474 4701 4476 5821 4477 5553 4479 6380 4480 4313 4481 4448 4483 5026 4484 5513 4485 4882 4487 4593 4488 6002 4490 4918 4491 5307 4492 4385 4494 5196 4495 4424 4496 5074 4498 5191 4499 2876 4501 5532 4502 4186 4503 5173 4505 4020 4506 5470 4508 6183 4509 5789 4510 5566 4512 7397 4513 4030 4514 4571 4516 5151 4517 4024 4519 4736 4520 5770 4521 5857 4523 3621 4524 3999 4526 4367 4527 4136 4528 4411 4530 6602 4531 5130 4532 4375 4534 4136 4535 4354 4537 4480 4538 5302 4539 5085 4541 5188 4542 4070 4543 5418 4545 3478 4546 4261 4548 4781 4549 4659 4550 5145 4552 4164 4553 4856 4555 6950 4556 4181 4557 4789 4559 5802 4560 6507 4561 6295 4563 2845 4564 3797 4566 4108 4567 5561 4568 5758 4570 5495 4571 6497 4573 4735 4574 3843 4575 5613 4577 4142 4578 4111 4579 4694 4581 4239 4582 4944 4584 5527 4585 4880 4586 4081 4588 5156 4589 4686 4590 5033 4592 4636 4593 4331 4595 4534 4596 4100 4597 5606 4599 5805 4600 5260 4602 5058 4603 3519 4604 5371 4606 4458 4607 5803 4608 6090 4610 3593 4611 6145 4613 5581 4614 3785 4615 3642 4617 5094 4618 4028 4620 6271 4621 4236 4622 4135 4624 5583 4625 3876 4626 5511 4628 4542 4629 3819 4631 3291 4632 4485 4633 5821 4635 2945 4636 4217 4637 4247 4639 5298 4640 5690 4642 4138 4643 4686 4644 6049 4646 5350 4647 3809 4649 4497 4650 4178 4651 5365 4653 4685 4654 4860 4655 3455 4657 3674 4658 4198 4660 4522 4661 5279 4662 4441 4664 4086 4665 3529 4667 4959 4668 4313 4669 4104 4671 4460 4672 5557 4673 4769 4675 4642 4676 5072 4678 4229 4679 4214 4680 4135 4682 3574 4683 5016 4684 3918 4686 3988 4687 4638 4689 3379 4690 3912 4691 3752 4693 4410 4694 3841 4696 3147 4697 5088 4698 4660 4700 4743 4701 4963 4702 3857 4704 4519 4705 4511 4707 6638 4708 3514 4709 3953 4711 4098 4712 4830 4714 4213 4715 4801 4716 4252 4718 4835 4719 4799 4720 4029 4722 4666 4723 5112 4725 4237 4726 3929 4727 5011 4729 5031 4730 4380 4731 5397 4733 4341 4734 4368 4736 3439 4737 5105 4738 4054 4740 4108 4741 3825 4743 3774 4744 4465 4745 4408 4747 3875 4748 3327 4749 4335 4751 5010 4752 3419 4754 3467 4755 5674 4756 3545 4758 4611 4759 5626 4761 4621 4762 4163 4763 4579 4765 4164 4766 3478 4767 4734 4769 4378 4770 4729 4772 4792 4773 2917 4774 4123 4776 4701 4777 3921 4778 4556 4780 4234 4781 3942 4783 3896 4784 4881 4785 3423 4787 4234 4788 3534 4790 3747 4791 3514 4792 3246 4794 5988 4795 4811 4796 3302 4798 3206 4799 4655 4801 4662 4802 3633 4803 3951 4805 3603 4806 3966 4808 3180 4809 3612 4810 3946 4812 5075 4813 4119 4814 4512 4816 4386 4817 3565 4819 4355 4820 3819 4821 4626 4823 4929 4824 3337 4825 5396 4827 3200 4828 4573 4830 4451 4831 3233 4832 4307 4834 2969 4835 4928 4837 4062 4838 4411 4839 4053 4841 4414 4842 3122 4843 3562 4845 3344 4846 5002 4848 3488 4849 3619 4850 5116 4852 4652 4853 3643 4855 3366 4856 3762 4857 3847 4859 3509 4860 3357 4861 3683 4863 3601 4864 4759 4866 3734 4867 4163 4868 3625 4870 3684 4871 3988 4872 3739 4874 3013 4875 3886 4877 4262 4878 4208 4879 3747 4881 3695 4882 3499 4884 4756 4885 4083 4886 3708 4888 4346 4889 4228 4890 4875 4892 4302 4893 3129 4895 3595 4896 3206 4897 3657 4899 3897 4900 3714 4902 4546 4903 3941 4904 3987 4906 3399 4907 3728 4908 4032 4910 4304 4911 3607 4913 4106 4914 3293 4915 4661 4917 4094 4918 3563 4920 3370 4921 3443 4922 3681 4924 3064 4925 3626 4926 3979 4928 5253 4929 3296 4931 5318 4932 3374 4933 4219 4935 3011 4936 4587 4937 5470 4939 3823 4940 3979 4942 2946 4943 3030 4944 4637 4946 3945 4947 3750 4949 4495 4950 6040 4951 3667 4953 4144 4954 3213 4955 4001 4957 3328 4958 3290 4960 4729 4961 3859 4962 2930 4964 3991 4965 4481 4967 3328 4968 4332 4969 3967 4971 3367 4972 3517 4973 4507 4975 3048 4976 4018 4978 3168 4979 3484 4980 3019 4982 3981 4983 3219 4984 3418 4986 4245 4987 2792 4989 4461 4990 4808 4991 3574 4993 3264 4994 4046 4996 4112 4997 3535 4998 3439 5000 3694 5001 2853 5002 3746 5004 3686 5005 2864 5007 4195 5008 3154 5009 3880 5011 3566 5012 3762 5014 4567 5015 3416 5016 3373 5018 4005 5019 3810 5020 4561 5022 4018 5023 3856 5025 3308 5026 3627 5027 3297 5029 3280 5030 3243 5031 3710 5033 4076 5034 3332 5036 5182 5037 2777 5038 5224 5040 2786 5041 2890 5043 4560 5044 3147 5045 4228 5047 4021 5048 2970 5049 4851 5051 4002 5052 3527 5054 3231 5055 3118 5056 3904 5058 3773 5059 3850 5061 3070 5062 3773 5063 3879 500 MLine End Begin %I MLine [1 0 0 1 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 0 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 500 5063 3879 5065 3441 5066 4339 5067 3743 5069 4075 5070 3051 5072 4049 5073 4028 5074 3206 5076 3346 5077 3790 5078 3009 5080 3329 5081 3559 5083 4121 5084 3576 5085 3450 5087 2877 5088 3404 5090 3346 5091 3182 5092 2917 5094 3480 5095 2904 5096 3539 5098 4145 5099 3587 5101 4768 5102 2948 5103 3781 5105 2945 5106 3064 5108 4570 5109 3327 5110 4250 5112 2959 5113 3737 5114 3623 5116 3186 5117 3718 5119 2897 5120 2984 5121 4505 5123 3127 5124 3793 5125 4309 5127 3412 5128 3062 5130 3808 5131 2960 5132 3298 5134 3533 5135 3190 5137 3457 5138 2788 5139 3136 5141 3197 5142 3653 5143 3043 5145 3119 5146 3192 5148 3071 5149 3284 5150 3910 5152 3711 5153 3611 5155 3356 5156 3826 5157 2917 5159 3157 5160 3312 5161 4161 5163 3561 5164 3936 5166 3871 5167 3756 5168 3744 5170 3495 5171 3013 5172 3203 5174 4517 5175 3220 5177 3923 5178 3751 5179 3117 5181 4169 5182 3055 5184 3006 5185 3403 5186 2931 5188 3579 5189 3710 5190 3432 5192 3242 5193 4417 5195 3799 5196 3103 5197 2984 5199 4025 5200 4361 5202 3475 5203 3287 5204 3220 5206 4545 5207 3662 5208 3381 5210 3982 5211 2876 5213 3510 5214 3643 5215 4000 5217 2982 5218 3840 5219 3011 5221 3072 5222 2792 5224 3720 5225 2818 5226 3808 5228 3551 5229 3639 5231 2946 5232 3743 5233 3761 5235 3335 5236 3316 5237 2889 5239 3142 5240 2788 5242 3173 5243 2806 5244 3410 5246 3148 5247 3062 5249 3936 5250 2843 5251 4039 5253 3585 5254 3841 5255 2896 5257 3356 5258 3013 5260 4154 5261 3697 5262 2950 5264 3484 5265 3633 5266 3557 5268 3037 5269 3457 5271 3461 5272 3551 5273 4206 5275 3111 5276 3106 5278 3003 5279 3547 5280 3048 5282 3915 5283 2977 5284 3170 5286 3217 5287 3901 5289 3362 5290 2792 5291 3396 5293 3077 5294 3785 5296 3244 5297 3439 5298 3267 5300 3481 5301 3080 5302 3152 5304 3088 5305 3310 5307 3713 5308 3899 5309 3541 5311 3177 5312 3118 5313 3647 5315 2988 5316 2756 5318 2727 5319 2948 5320 3117 5322 3935 5323 2961 5325 3929 5326 3201 5327 3554 5329 3020 5330 3453 5331 3253 5333 3033 5334 4427 5336 2836 5337 2921 5338 4102 5340 2814 5341 3323 5343 2988 5344 3271 5345 3288 5347 2836 5348 3468 5349 2984 5351 2853 5352 2792 5354 3206 5355 2745 5356 3203 5358 3541 5359 3217 5360 2989 5362 3379 5363 3504 5365 3251 5366 3346 5367 3070 5369 3489 5370 2946 5372 3064 5373 3160 5374 2881 5376 3045 5377 3585 5378 2801 5380 3463 5381 3051 5383 3284 5384 3000 5385 3717 5387 2952 5388 3091 5390 3180 5391 3575 5392 3165 5394 3031 5395 2950 5396 2944 5398 3282 5399 3210 5401 3319 5402 3373 5403 2919 5405 2818 5406 2843 5407 3016 5409 2716 5410 2792 5412 2853 5413 2788 5414 2897 5416 3626 5417 3268 5419 2818 5420 3655 5421 3558 5423 3364 5424 3011 5425 2898 5427 2786 5428 2919 5430 3606 5431 3429 5432 2716 5434 2898 5435 2745 5437 3037 5438 2940 5439 3036 5441 2814 5442 3247 5443 2853 5445 2930 5446 2914 5448 2817 5449 2981 5450 2976 5452 2910 5453 2878 5454 2817 5456 2727 5457 3086 5459 2817 5460 2822 5461 3188 5463 3008 5464 2898 5466 2945 5467 2896 5468 2817 5470 2916 5471 2986 5472 3204 5474 2898 5475 2756 5477 3578 5478 2898 5479 3110 5481 2853 5482 2836 5484 3011 5485 3708 5486 3119 5488 3087 5489 3051 5490 3256 5492 2942 5493 3278 5495 2838 5496 2814 5497 3027 5499 3363 5500 2806 5501 2897 5503 3186 5504 2756 5506 2921 5507 3441 5508 2858 5510 2806 5511 2984 5513 3324 5514 2939 5515 3112 5517 2838 5518 2943 5519 2955 5521 3062 5522 3133 5524 3072 5525 2881 5526 2944 5528 2890 5529 3096 5531 3266 5532 3733 5533 2766 5535 2930 5536 2756 5537 3186 5539 2788 5540 2981 5542 2788 5543 3252 5544 2890 5546 3093 5547 3157 5548 3029 5550 3290 5551 2917 5553 2992 5554 2862 5555 2942 5557 3112 5558 2917 5560 2862 5561 3132 5562 2876 5564 2910 5565 2952 5566 2814 5568 2943 5569 2999 5571 2818 5572 2876 5573 3586 5575 3002 5576 3130 5578 3532 5579 3157 5580 2817 5582 2792 5583 3246 5584 2716 5586 3204 5587 2822 5589 3351 5590 3107 5591 3048 5593 3037 5594 3502 5595 3297 5597 3290 5598 3196 5600 3259 5601 2839 5602 3924 5604 2976 5605 2777 5607 3056 5608 2914 5609 2864 5611 2777 5612 2814 5613 3511 5615 2777 5616 3017 5618 3115 5619 2792 5620 3005 5622 2814 5623 2839 5625 2864 5626 2727 5627 3180 5629 2981 5630 2977 5631 3086 5633 2955 5634 2988 5636 2988 5637 2914 5638 2772 5640 3015 5641 3077 5642 2973 5644 3170 5645 3077 5647 2973 5648 2877 5649 3246 5651 2943 5652 2992 5654 2788 5655 3052 5656 2772 5658 2814 5659 2817 5660 2872 5662 2818 5663 2801 5665 3387 5666 2876 5667 3006 5669 2788 5670 2817 5672 2862 5673 2814 5674 2814 5676 2872 5677 2801 5678 3055 5680 2838 5681 2772 5683 2801 5684 2865 5685 2931 5687 3045 5688 2952 5689 2862 5691 2982 5692 2792 5694 2948 5695 2727 5696 2885 5698 3159 5699 3161 5701 3156 5702 2806 5703 2876 5705 2716 5706 2956 5707 2716 5709 2933 5710 3131 5712 2945 5713 2919 5714 2981 5716 2727 5717 2885 5719 3035 5720 2772 5721 2727 5723 2853 5724 2843 5725 2955 5727 2727 5728 2843 5730 2845 5731 2756 5732 2756 5734 2727 5735 3152 5736 3472 5738 2818 5739 2814 5741 3105 5742 3108 5743 2872 5745 3054 5746 2727 5748 2727 5749 2921 5750 2727 5752 2943 5753 2756 500 MLine End Begin %I MLine [1 0 0 1 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 0 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 500 5753 2756 5754 2756 5756 2857 5757 3025 5759 2814 5760 2727 5761 2945 5763 2756 5764 2843 5766 2756 5767 3115 5768 2777 5770 3071 5771 2916 5772 2727 5774 2788 5775 2756 5777 2981 5778 2902 5779 2838 5781 2992 5782 2942 5784 2986 5785 2772 5786 2872 5788 3157 5789 2772 5790 3007 5792 2801 5793 2788 5795 2910 5796 2772 5797 3196 5799 2950 5800 2872 5801 2788 5803 3064 5804 2788 5806 2801 5807 3006 5808 3215 5810 2788 5811 2872 5813 2772 5814 3046 5815 2986 5817 2942 5818 2788 5819 3016 5821 2817 5822 2897 5824 2878 5825 2955 5826 2727 5828 2792 5829 2745 5831 2716 5832 2766 5833 3071 5835 2806 5836 2745 5837 2889 5839 3368 5840 2986 5842 2890 5843 2961 5844 2982 5846 2716 5847 2898 5848 2982 5850 2745 5851 2836 5853 2745 5854 2858 5855 2766 5857 2745 5858 2745 5860 2745 5861 3028 5862 2806 5864 2716 5865 2845 5866 2716 5868 2876 5869 2912 5871 2839 5872 2843 5873 2946 5875 2756 5876 2857 5878 2939 5879 2916 5880 2777 5882 2777 5883 2864 5884 2792 5886 2777 5887 2727 5889 2727 5890 2885 5891 2843 5893 2727 5894 2756 5895 2727 5897 2788 5898 2885 5900 2843 5901 2727 5902 2864 5904 2727 5905 2792 5907 2864 5908 2727 5909 2756 5911 2727 5912 2756 5913 2727 5915 2916 5916 2756 5918 2727 5919 2756 5920 2792 5922 2853 5923 2727 5925 2727 5926 2839 5927 2792 5929 2857 5930 2914 5931 2976 5933 3013 5934 2766 5936 2745 5937 3064 5938 2836 5940 2961 5941 2919 5942 3050 5944 2716 5945 2716 5947 2766 5948 2786 5949 2716 5951 2786 5952 2836 5954 2716 5955 2716 5956 2716 5958 3048 5959 2815 5960 2766 5962 2786 5963 2716 5965 2990 5966 2766 5967 2716 5969 2806 5970 3096 5972 2766 5973 2716 5974 2836 5976 2745 5977 2902 5978 2960 5980 2889 5981 2745 5983 2716 5984 2945 5985 2916 5987 2845 5988 2806 5989 2716 5991 2786 5992 2815 5994 2806 5995 2716 5996 2745 5998 2806 5999 2766 6001 2716 6002 2853 6003 2815 6005 2933 6006 2786 6007 2912 6009 2716 6010 2716 6012 2716 6013 2766 6014 3028 6016 2716 6017 2716 6019 2745 6020 2841 6021 2745 6023 2836 6024 2815 6025 2961 6027 2845 6028 2745 6030 2841 6031 2836 6032 2716 6034 2766 6035 2716 6036 2716 6038 2836 6039 2716 6041 2786 6042 2766 6043 2745 6045 2716 6046 2716 6048 2745 6049 2716 6050 2716 6052 2766 6053 2786 6054 2716 6056 2845 6057 2716 6059 2745 6060 2876 6061 2766 6063 2766 6064 2786 6066 2716 6067 2716 6068 2933 6070 2716 6071 2716 6072 2716 6074 2745 6075 2716 6077 2716 6078 2786 6079 2716 6081 2745 6082 2716 6083 2853 6085 2806 6086 2716 6088 2766 6089 2845 6090 2876 6092 2786 6093 2716 6095 2836 6096 2841 6097 2745 6099 2845 6100 2874 6101 2940 6103 2845 6104 2876 6106 2766 6107 2806 6108 2806 6110 2716 6111 2841 6113 2716 6114 2745 6115 2766 6117 2716 6118 2716 6119 2716 6121 2986 6122 2853 6124 2845 6125 2745 6126 3047 6128 3093 6129 2745 6130 2716 6132 2745 6133 2716 6135 2745 6136 2716 6137 2858 6139 2716 6140 2766 6142 2716 6143 2806 6144 2745 6146 2745 6147 2766 6148 2806 6150 3020 6151 2716 6153 2876 6154 2845 6155 2766 6157 2786 6158 2786 6160 2716 6161 2745 6162 2806 6164 2716 6165 2716 6166 2745 6168 2716 6169 2745 6171 2745 6172 2745 6173 2716 6175 2716 6176 2745 6177 2716 6179 2716 6180 2716 6182 2766 6183 2716 6184 2815 6186 2745 6187 2716 6189 2745 6190 2716 6191 2716 6193 2766 6194 2944 6195 2919 6197 2716 6198 2745 6200 2845 6201 2716 6202 2716 6204 2716 6205 2716 6207 2716 6208 2786 6209 2716 6211 2716 6212 2745 6213 2815 6215 2806 6216 2716 6218 2836 6219 2716 6220 2786 6222 2836 6223 2716 6224 2716 6226 2716 6227 2786 6229 2845 6230 2716 6231 2716 6233 2916 6234 2745 6236 2716 6237 2786 6238 2745 6240 2786 6241 2806 6242 2745 6244 2716 6245 2716 6247 2786 6248 2766 6249 2853 6251 2716 6252 2716 6254 2766 6255 2766 6256 2716 6258 2745 6259 2745 6260 2716 6262 2815 6263 2766 6265 2919 6266 3047 6267 2944 6269 2944 6270 2766 6271 2766 6273 2716 6274 2716 6276 2815 6277 2716 6278 2716 6280 2716 6281 2716 6283 2845 6284 2815 6285 2716 6287 2716 6288 2766 6289 2836 6291 2716 6292 2716 6294 2716 6295 2745 6296 2716 6298 2766 6299 2716 6301 2815 6302 2745 6303 2716 6305 2745 6306 2716 6307 2786 6309 2716 6310 2858 6312 2766 6313 2786 6314 2745 6316 2745 6317 2766 6318 2786 6320 2716 6321 2716 6323 2716 6324 2716 6325 2806 6327 2716 6328 2716 6330 2745 6331 2836 6332 2716 6334 2716 6335 2745 6336 2716 6338 2716 6339 2716 6341 2716 6342 2716 6343 2786 6345 2745 6346 2845 6348 2716 6349 2745 6350 2716 6352 2845 6353 2716 6354 2716 6356 2841 6357 2766 6359 2766 6360 2806 6361 2745 6363 2745 6364 2716 6365 2766 6367 2766 6368 2716 6370 2874 6371 2858 6372 2815 6374 2716 6375 2745 6377 2716 6378 2716 6379 2716 6381 2716 6382 2786 6383 2745 6385 2766 6386 2815 6388 2716 6389 2716 6390 2716 6392 2786 6393 2745 6395 2766 6396 2716 6397 2766 6399 2716 6400 2716 6401 2806 6403 2716 6404 2716 6406 2716 6407 2716 6408 2716 6410 2716 6411 2716 6412 2766 6414 2716 6415 2716 6417 2716 6418 2716 6419 2766 6421 2874 6422 2745 6424 2836 6425 2745 6426 2716 6428 2766 6429 2716 6430 2716 6432 2716 6433 2716 6435 2766 6436 2745 6437 2786 6439 2745 6440 2876 6442 2766 6443 2766 500 MLine End Begin %I MLine [1 0 0 1 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 0 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 500 6443 2766 6444 2716 6446 2716 6447 2745 6448 2716 6450 2716 6451 2716 6453 2716 6454 2716 6455 2745 6457 2745 6458 2716 6459 2716 6461 2716 6462 2745 6464 2716 6465 2745 6466 2745 6468 2716 6469 2716 6471 2716 6472 2716 6473 2745 6475 2716 6476 2716 6477 2716 6479 2745 6480 2716 6482 2716 6483 2716 6484 2716 6486 2716 6487 2745 6489 2716 6490 2786 6491 2716 6493 2745 6494 2716 6495 2745 6497 2716 6498 2716 6500 2716 6501 2716 6502 2716 6504 2745 6505 2716 6506 2716 6508 2716 6509 2745 6511 2745 6512 2716 6513 2716 6515 2745 6516 2716 6518 2716 6519 2716 6520 2766 6522 2716 6523 2716 6524 2766 6526 2716 6527 2745 6529 2745 6530 2716 6531 2716 6533 2716 6534 2716 6536 2745 6537 2716 6538 2716 6540 2716 6541 2716 6542 2716 6544 2716 6545 2716 6547 2716 6548 2716 6549 2716 6551 2716 6552 2716 6553 2716 6555 2766 6556 2716 6558 2716 6559 2716 6560 2716 6562 2716 6563 2766 6565 2716 6566 2716 6567 2745 6569 2716 6570 2716 6571 2716 6573 2716 6574 2716 6576 2716 6577 2716 6578 2716 6580 2716 6581 2716 6583 2745 6584 2745 6585 2716 6587 2745 6588 2716 6589 2716 6591 2716 6592 2716 6594 2716 6595 2716 6596 2716 6598 2716 6599 2716 6600 2716 6602 2716 6603 2716 6605 2716 6606 2716 6607 2716 6609 2716 6610 2716 6612 2716 6613 2766 6614 2716 6616 2716 6617 2766 6618 2716 6620 2716 6621 2716 6623 2716 6624 2806 6625 2716 6627 2745 6628 2716 6630 2716 6631 2716 6632 2716 6634 2716 6635 2745 6636 2716 6638 2745 6639 2716 6641 2716 6642 2716 6643 2745 6645 2716 6646 2745 6648 2745 6649 2716 6650 2745 6652 2716 6653 2716 6654 2716 6656 2766 6657 2716 6659 2716 6660 2716 6661 2716 6663 2716 6664 2716 6665 2745 6667 2716 6668 2745 6670 2745 6671 2716 6672 2716 6674 2716 6675 2716 6677 2745 6678 2745 6679 2716 6681 2716 6682 2716 6683 2745 6685 2766 6686 2766 6688 2716 6689 2716 6690 2716 6692 2716 6693 2716 6695 2716 6696 2716 6697 2745 6699 2716 6700 2745 6701 2716 6703 2716 6704 2716 6706 2716 6707 2716 6708 2716 6710 2745 6711 2716 6712 2716 6714 2716 6715 2716 6717 2716 6718 2716 6719 2836 6721 2745 6722 2716 6724 2716 6725 2716 6726 2716 6728 2716 6729 2716 6730 2766 6732 2745 6733 2716 6735 2716 6736 2716 6737 2716 6739 2716 6740 2716 6742 2745 6743 2716 6744 2745 6746 2716 6747 2716 6748 2716 6750 2716 6751 2745 6753 2716 6754 2716 6755 2716 6757 2745 6758 2745 6759 2716 6761 2716 6762 2786 6764 2745 6765 2716 6766 2716 6768 2716 6769 2716 6771 2716 6772 2716 6773 2745 6775 2745 6776 2716 6777 2716 6779 2745 6780 2745 6782 2716 6783 2716 6784 2716 6786 2745 6787 2716 6789 2716 6790 2716 6791 2716 6793 2766 6794 2716 6795 2716 6797 2716 6798 2716 6800 2716 6801 2716 6802 2716 6804 2716 6805 2716 6806 2716 6808 2716 6809 2716 6811 2745 6812 2786 6813 2786 6815 2745 6816 2716 6818 2716 6819 2716 6820 2716 6822 2745 6823 2716 6824 2745 6826 2716 6827 2716 6829 2716 6830 2716 6831 2716 6833 2716 6834 2716 6836 2716 6837 2716 6838 2716 6840 2716 6841 2745 6842 2716 6844 2716 6845 2716 6847 2745 6848 2745 6849 2716 6851 2745 6852 2716 6853 2716 6855 2745 6856 2716 6858 2716 6859 2716 6860 2716 6862 2716 6863 2716 6865 2716 6866 2716 6867 2716 6869 2716 6870 2716 6871 2716 6873 2716 6874 2716 6876 2716 6877 2745 6878 2716 6880 2745 6881 2716 6883 2716 6884 2716 6885 2716 6887 2716 6888 2716 6889 2716 6891 2716 6892 2716 6894 2716 6895 2716 6896 2716 6898 2716 6899 2716 6900 2716 6902 2716 6903 2716 6905 2716 6906 2745 6907 2716 6909 2716 6910 2716 6912 2716 6913 2716 6914 2716 6916 2716 6917 2716 6918 2716 6920 2716 6921 2716 6923 2716 6924 2745 6925 2716 6927 2716 6928 2716 6930 2716 6931 2716 6932 2716 6934 2716 6935 2716 6936 2716 6938 2716 6939 2716 6941 2716 6942 2716 6943 2716 6945 2716 6946 2716 6947 2745 6949 2716 6950 2745 6952 2716 6953 2716 6954 2716 6956 2716 6957 2716 6959 2716 6960 2716 6961 2716 6963 2716 6964 2716 6965 2716 6967 2716 6968 2745 6970 2716 6971 2716 6972 2745 6974 2716 6975 2716 6977 2716 6978 2745 6979 2716 6981 2716 6982 2716 6983 2716 6985 2716 6986 2716 6988 2716 6989 2716 6990 2716 6992 2716 6993 2716 6994 2716 6996 2716 6997 2745 6999 2716 7000 2716 7001 2745 7003 2716 7004 2716 7006 2716 7007 2716 7008 2716 7010 2716 7011 2716 7012 2716 7014 2716 7015 2716 7017 2716 7018 2716 7019 2716 7021 2716 7022 2716 7024 2716 7025 2716 7026 2716 7028 2716 7029 2716 7030 2716 7032 2745 7033 2716 7035 2716 7036 2716 7037 2716 7039 2745 7040 2716 7041 2716 7043 2716 7044 2716 7046 2716 7047 2716 7048 2716 7050 2716 7051 2716 7053 2716 7054 2716 7055 2716 7057 2716 7058 2745 7059 2745 7061 2716 7062 2716 7064 2716 7065 2716 7066 2716 7068 2716 7069 2716 7071 2716 7072 2716 7073 2716 7075 2716 7076 2716 7077 2716 7079 2716 7080 2716 7082 2716 7083 2716 7084 2745 7086 2716 7087 2716 7088 2716 7090 2745 7091 2716 7093 2716 7094 2716 7095 2716 7097 2716 7098 2716 7100 2716 7101 2716 7102 2716 7104 2716 7105 2716 7106 2716 7108 2716 7109 2716 7111 2716 7112 2745 7113 2716 7115 2716 7116 2716 7118 2716 7119 2716 7120 2716 7122 2716 7123 2716 7124 2745 7126 2716 7127 2716 7129 2716 7130 2716 7131 2716 7133 2716 500 MLine End Begin %I MLine [1 0 0 1 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 0 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 500 7133 2716 7134 2716 7135 2716 7137 2716 7138 2716 7140 2716 7141 2716 7142 2716 7144 2716 7145 2716 7147 2716 7148 2745 7149 2745 7151 2745 7152 2716 7153 2716 7155 2716 7156 2716 7158 2716 7159 2716 7160 2716 7162 2716 7163 2716 7165 2716 7166 2716 7167 2716 7169 2716 7170 2716 7171 2716 7173 2716 7174 2716 7176 2716 7177 2716 7178 2716 7180 2716 7181 2716 7182 2716 7184 2716 7185 2716 7187 2716 7188 2716 7189 2716 7191 2716 7192 2716 7194 2716 7195 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2716 7749 2716 7751 2716 7752 2716 7753 2716 7755 2716 7756 2716 7758 2716 7759 2716 7760 2716 7762 2716 7763 2716 7764 2716 7766 2716 7767 2716 7769 2716 7770 2716 7771 2716 7773 2716 7774 2716 7776 2716 7777 2716 7778 2716 7780 2716 7781 2716 7782 2716 7784 2716 7785 2716 7787 2716 7788 2716 7789 2716 7791 2716 7792 2716 7794 2716 7795 2716 7796 2716 7798 2716 7799 2716 7800 2716 7802 2716 7803 2716 7805 2716 7806 2716 7807 2716 7809 2716 7810 2716 7811 2716 7813 2716 7814 2716 7816 2716 7817 2716 7818 2716 7820 2716 7821 2716 7823 2716 500 MLine End Begin %I MLine [1 0 0 1 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 0 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 500 7823 2716 7824 2716 7825 2716 7827 2716 7828 2716 7829 2716 7831 2716 7832 2716 7834 2716 7835 2716 7836 2716 7838 2716 7839 2716 7841 2716 7842 2716 7843 2716 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8398 2716 8399 2716 8400 2716 8402 2716 8403 2716 8405 2716 8406 2716 8407 2716 8409 2716 8410 2716 8411 2716 8413 2716 8414 2716 8416 2716 8417 2716 8418 2716 8420 2716 8421 2716 8423 2716 8424 2716 8425 2716 8427 2716 8428 2716 8429 2716 8431 2716 8432 2716 8434 2716 8435 2716 8436 2716 8438 2716 8439 2716 8440 2716 8442 2716 8443 2716 8445 2716 8446 2716 8447 2716 8449 2716 8450 2716 8452 2716 8453 2716 8454 2716 8456 2716 8457 2716 8458 2716 8460 2716 8461 2716 8463 2716 8464 2716 8465 2716 8467 2716 8468 2716 8470 2716 8471 2716 8472 2716 8474 2716 8475 2716 8476 2716 8478 2716 8479 2716 8481 2716 8482 2716 8483 2716 8485 2716 8486 2716 8487 2716 8489 2716 8490 2716 8492 2716 8493 2716 8494 2716 8496 2716 8497 2716 8499 2716 8500 2716 8501 2716 8503 2716 8504 2716 8505 2716 8507 2716 8508 2716 8510 2716 8511 2716 8512 2716 500 MLine End Begin %I MLine [1 0 0 1 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 0 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 119 8512 2716 8514 2716 8515 2716 8517 2716 8518 2716 8519 2716 8521 2716 8522 2716 8523 2716 8525 2716 8526 2716 8528 2716 8529 2716 8530 2716 8532 2716 8533 2716 8534 2716 8536 2716 8537 2716 8539 2716 8540 2716 8541 2716 8543 2716 8544 2716 8546 2716 8547 2716 8548 2716 8550 2716 8551 2716 8552 2716 8554 2716 8555 2716 8557 2716 8558 2716 8559 2716 8561 2716 8562 2716 8564 2716 8565 2716 8566 2716 8568 2716 8569 2716 8570 2716 8572 2716 8573 2716 8575 2716 8576 2716 8577 2716 8579 2716 8580 2716 8581 2716 8583 2716 8584 2716 8586 2716 8587 2716 8588 2716 8590 2716 8591 2716 8593 2716 8594 2716 8595 2716 8597 2716 8598 2716 8599 2716 8601 2716 8602 2716 8604 2716 8605 2716 8606 2716 8608 2716 8609 2716 8611 2716 8612 2716 8613 2716 8615 2716 8616 2716 8617 2716 8619 2716 8620 2716 8622 2716 8623 2716 8624 2716 8626 2716 8627 2716 8628 2716 8630 2716 8631 2716 8633 2716 8634 2716 8635 2716 8637 2716 8638 2716 8640 2716 8641 2716 8642 2716 8644 2716 8645 2716 8646 2716 8648 2716 8649 2716 8651 2716 8652 2716 8653 2716 8655 2716 8656 2716 8658 2716 8659 2716 8660 2716 8662 2716 8663 2716 8664 2716 8666 2716 8667 2716 8669 2716 8670 2716 8671 2716 8673 2716 8674 2716 8675 2716 119 MLine End %%PageTrailer End %I eop showpage %%Trailer end %%EOF %%EndDocument @endspecial 390 1922 a(Example)42 b(of)g(a)g(sim)m(ulated)g(annealing) h(run)d(for)i(the)f(12)i(south)m(w)m(estern)f(cities)h(Flying)390 2032 y(Salesman)30 b(Problem.)150 2264 y FJ(26.4)68 b(References)47 b(and)d(F)-11 b(urther)44 b(Reading)150 2424 y FK(F)-8 b(urther)30 b(information)h(is)f(a)m(v)-5 b(ailable)33 b(in)d(the)h(follo)m(wing)g(b)s(o)s(ok,)330 2558 y FD(Mo)s(dern)50 b(Heuristic)h(T)-8 b(ec)m(hniques)51 b(for)f(Com)m(binatorial)i (Problems)p FK(,)j(Colin)c(R.)f(Reev)m(es)i(\(ed.\),)330 2668 y(McGra)m(w-Hill,)33 b(1995)f(\(ISBN)f(0-07-709239-2\).)p eop end %%Page: 335 353 TeXDict begin 335 352 bop 150 -116 a FK(Chapter)30 b(27:)41 b(Ordinary)29 b(Di\013eren)m(tial)k(Equations)1690 b(335)150 299 y FG(27)80 b(Ordinary)54 b(Di\013eren)l(tial)d(Equations)150 513 y FK(This)41 b(c)m(hapter)h(describ)s(es)f(functions)h(for)f (solving)i(ordinary)e(di\013eren)m(tial)i(equation)f(\(ODE\))h(initial) 150 622 y(v)-5 b(alue)32 b(problems.)44 b(The)31 b(library)g(pro)m (vides)g(a)h(v)-5 b(ariet)m(y)33 b(of)f(lo)m(w-lev)m(el)i(metho)s(ds,)e (suc)m(h)f(as)h(Runge-Kutta)150 732 y(and)21 b(Bulirsc)m(h-Sto)s(er)h (routines,)i(and)d(higher-lev)m(el)i(comp)s(onen)m(ts)f(for)f(adaptiv)m (e)i(step-size)g(con)m(trol.)39 b(The)150 842 y(comp)s(onen)m(ts)c(can) g(b)s(e)f(com)m(bined)h(b)m(y)f(the)h(user)f(to)h(ac)m(hiev)m(e)i(the)e (desired)f(solution,)j(with)d(full)h(access)150 951 y(to)29 b(an)m(y)g(in)m(termediate)i(steps.)40 b(A)28 b(driv)m(er)h(ob)5 b(ject)29 b(can)g(b)s(e)f(used)g(as)h(a)g(high)f(lev)m(el)j(wrapp)s(er) c(for)h(easy)h(use)150 1061 y(of)i(lo)m(w)g(lev)m(el)h(functions.)275 1191 y(These)i(functions)h(are)g(declared)h(in)e(the)h(header)g(\014le) g FH(gsl_odeiv2.h)p FK(.)51 b(This)35 b(is)g(a)g(new)f(in)m(terface)150 1301 y(in)h(v)m(ersion)h(1.15)h(and)e(uses)g(the)g(pre\014x)g FH(gsl_odeiv2)d FK(for)k(all)g(functions.)55 b(It)36 b(is)g(recommended)f(o)m(v)m(er)150 1410 y(the)26 b(previous)e FH(gsl_odeiv)f FK(implemen)m(tation)k(de\014ned)d(in)h FH(gsl_odeiv.h)d FK(The)j(old)h(in)m(terface)h(has)e(b)s(een)150 1520 y(retained)31 b(under)e(the)h(original)i(name)e(for)g(bac)m(kw)m (ards)h(compatibilit)m(y)-8 b(.)150 1744 y FJ(27.1)68 b(De\014ning)45 b(the)h(ODE)f(System)150 1904 y FK(The)30 b(routines)g(solv)m(e)i(the)e(general)i FE(n)p FK(-dimensional)e (\014rst-order)g(system,)1400 2053 y FE(dy)1492 2067 y Fq(i)1519 2053 y FK(\()p FE(t)p FK(\))p 1400 2093 224 4 v 1471 2177 a FE(dt)1658 2114 y FK(=)25 b FE(f)1799 2128 y Fq(i)1826 2114 y FK(\()p FE(t;)15 b(y)1979 2128 y FB(1)2016 2114 y FK(\()p FE(t)p FK(\))p FE(;)g(:)g(:)g(:)j(y)2327 2128 y Fq(n)2371 2114 y FK(\()p FE(t)p FK(\)\))150 2303 y(for)24 b FE(i)i FK(=)f(1)p FE(;)15 b(:)g(:)g(:)i(;)e(n)p FK(.)38 b(The)24 b(stepping)h(functions)e(rely)i(on)f(the)h(v)m(ector)h (of)f(deriv)-5 b(ativ)m(es)25 b FE(f)3027 2317 y Fq(i)3079 2303 y FK(and)f(the)g(Jacobian)150 2413 y(matrix,)43 b FE(J)533 2427 y Fq(ij)633 2413 y FK(=)e FE(@)5 b(f)843 2427 y Fq(i)871 2413 y FK(\()p FE(t;)15 b(y)s FK(\()p FE(t)p FK(\)\))p FE(=@)5 b(y)1308 2427 y Fq(j)1344 2413 y FK(.)70 b(A)40 b(system)g(of)g(equations)h(is)f(de\014ned)e(using)i (the)g FH(gsl_odeiv2_)150 2522 y(system)29 b FK(datat)m(yp)s(e.)3269 2694 y([Data)j(T)m(yp)s(e])-3600 b Fv(gsl_odeiv2_system)390 2804 y FK(This)30 b(data)h(t)m(yp)s(e)f(de\014nes)g(a)g(general)i(ODE)e (system)h(with)f(arbitrary)g(parameters.)390 2955 y FH(int)f(\(*)h (function\))e(\(double)g(t,)i(const)f(double)g(y[],)g(double)g(dydt[],) f(void)h(*)390 3065 y(params\))870 3174 y FK(This)21 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b(all)g(of)g(the)f(stepp)s(er)f(algorithms)j(of)e FH(gsl_odeiv2)d FK(mak)m(e)45 b(use)e(of)g(the)h(Ja-)870 5121 y(cobian)35 b(matrix,)i(so)e(it)g(ma)m(y)g(not)g(b)s(e)g (necessary)g(to)g(pro)m(vide)g(this)g(function)f(\(the)870 5230 y FH(jacobian)22 b FK(elemen)m(t)j(of)g(the)f(struct)g(can)g(b)s (e)g(replaced)g(b)m(y)g(a)h(n)m(ull)f(p)s(oin)m(ter)g(for)f(those)870 5340 y(algorithms\).)p eop end %%Page: 336 354 TeXDict begin 336 353 bop 150 -116 a FK(Chapter)30 b(27:)41 b(Ordinary)29 b(Di\013eren)m(tial)k(Equations)1690 b(336)870 299 y(The)23 b(function)g(should)f(return)h FH(GSL_SUCCESS)d FK(if)j(the)h(calculation)h(w)m(as)f(completed)870 408 y(successfully)-8 b(.)44 b(An)m(y)32 b(other)f(return)g(v)-5 b(alue)32 b(indicates)g(an)f(error.)44 b(A)31 b(sp)s(ecial)h(return)870 518 y(v)-5 b(alue)47 b FH(GSL_EBADFUNC)42 b FK(causes)47 b FH(gsl_odeiv2)c FK(routines)j(to)h(immediately)h(stop)870 628 y(and)36 b(return.)59 b(If)37 b FH(jacobian)d FK(is)j(mo)s 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b (gsl_odeiv2_step_reset)f Fu(\()p FD(gsl)p 1650 3020 V 41 w(o)s(deiv2)p 1948 3020 V 41 w(step)30 b(*)h Ft(s)p Fu(\))390 3130 y FK(This)26 b(function)h(resets)h(the)g(stepping)f (function)g FD(s)p FK(.)39 b(It)28 b(should)e(b)s(e)h(used)f(whenev)m (er)h(the)h(next)f(use)390 3240 y(of)k FD(s)i FK(will)e(not)g(b)s(e)f (a)g(con)m(tin)m(uation)j(of)d(a)h(previous)f(step.)3350 3424 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_odeiv2_step_free)d Fu(\()p FD(gsl)p 1650 3424 V 41 w(o)s(deiv2)p 1948 3424 V 41 w(step)30 b(*)h Ft(s)p Fu(\))390 3533 y FK(This)f(function)g (frees)g(all)h(the)g(memory)f(asso)s(ciated)i(with)e(the)h(stepping)f (function)g FD(s)p FK(.)3350 3717 y([F)-8 b(unction])-3599 b Fv(const)54 b(char)f(*)g(gsl_odeiv2_step_name)e Fu(\()p FD(const)32 b(gsl)p 2307 3717 V 40 w(o)s(deiv2)p 2604 3717 V 41 w(step)e(*)h Ft(s)p Fu(\))390 3827 y FK(This)f(function)g (returns)f(a)i(p)s(oin)m(ter)f(to)h(the)g(name)f(of)h(the)f(stepping)g (function.)41 b(F)-8 b(or)31 b(example,)630 3961 y 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b(ailable,)3288 3120 y([Step)30 b(T)m(yp)s(e])-3600 b Fv(gsl_odeiv2_step_rk2)390 3229 y FK(Explicit)31 b(em)m(b)s(edded)e (Runge-Kutta)i(\(2,)h(3\))f(metho)s(d.)3288 3410 y([Step)f(T)m(yp)s(e]) -3600 b Fv(gsl_odeiv2_step_rk4)390 3520 y FK(Explicit)40 b(4th)f(order)g(\(classical\))i(Runge-Kutta.)68 b(Error)38 b(estimation)i(is)f(carried)h(out)f(b)m(y)g(the)390 3629 y(step)g(doubling)e(metho)s(d.)65 b(F)-8 b(or)39 b(more)g(e\016cien)m (t)h(estimate)g(of)f(the)g(error,)h(use)e(the)h(em)m(b)s(edded)390 3739 y(metho)s(ds)30 b(describ)s(ed)f(b)s(elo)m(w.)3288 3920 y([Step)h(T)m(yp)s(e])-3600 b Fv(gsl_odeiv2_step_rkf45)390 4030 y FK(Explicit)44 b(em)m(b)s(edded)d(Runge-Kutta-F)-8 b(ehlb)s(erg)44 b(\(4,)j(5\))d(metho)s(d.)78 b(This)42 b(metho)s(d)g(is)h(a)g(go)s(o)s(d)390 4139 y(general-purp)s(ose)30 b(in)m(tegrator.)3288 4320 y([Step)g(T)m(yp)s(e])-3600 b Fv(gsl_odeiv2_step_rkck)390 4430 y FK(Explicit)31 b(em)m(b)s(edded)e (Runge-Kutta)i(Cash-Karp)f(\(4,)h(5\))g(metho)s(d.)3288 4611 y([Step)f(T)m(yp)s(e])-3600 b Fv(gsl_odeiv2_step_rk8pd)390 4721 y FK(Explicit)31 b(em)m(b)s(edded)e(Runge-Kutta)i(Prince-Dormand)g (\(8,)g(9\))g(metho)s(d.)3288 4902 y([Step)f(T)m(yp)s(e])-3600 b Fv(gsl_odeiv2_step_rk1imp)390 5011 y FK(Implicit)26 b(Gaussian)f(\014rst)f(order)h(Runge-Kutta.)40 b(Also)25 b(kno)m(wn)g(as)g(implicit)i(Euler)d(or)h(bac)m(kw)m(ard)390 5121 y(Euler)37 b(metho)s(d.)61 b(Error)36 b(estimation)j(is)f(carried) f(out)h(b)m(y)f(the)h(step)f(doubling)g(metho)s(d.)61 b(This)390 5230 y(algorithm)44 b(requires)f(the)g(Jacobian)h(and)f (access)i(to)f(the)f(driv)m(er)g(ob)5 b(ject)44 b(via)g FH(gsl_odeiv2_)390 5340 y(step_set_driver)p FK(.)p eop end %%Page: 338 356 TeXDict begin 338 355 bop 150 -116 a FK(Chapter)30 b(27:)41 b(Ordinary)29 b(Di\013eren)m(tial)k(Equations)1690 b(338)3288 299 y([Step)30 b(T)m(yp)s(e])-3600 b Fv(gsl_odeiv2_step_rk2imp)390 408 y FK(Implicit)28 b(Gaussian)g(second)g(order)f(Runge-Kutta.)41 b(Also)28 b(kno)m(wn)g(as)g(implicit)g(mid-p)s(oin)m(t)g(rule.)390 518 y(Error)34 b(estimation)i(is)e(carried)h(out)g(b)m(y)f(the)h(step)f (doubling)g(metho)s(d.)53 b(This)34 b(stepp)s(er)f(requires)390 628 y(the)e(Jacobian)g(and)e(access)j(to)f(the)g(driv)m(er)f(ob)5 b(ject)31 b(via)g FH(gsl_odeiv2_step_set_drive)o(r)p FK(.)3288 829 y([Step)f(T)m(yp)s(e])-3600 b Fv(gsl_odeiv2_step_rk4imp) 390 938 y FK(Implicit)42 b(Gaussian)g(4th)f(order)g(Runge-Kutta.)74 b(Error)41 b(estimation)i(is)e(carried)h(out)f(b)m(y)h(the)390 1048 y(step)29 b(doubling)f(metho)s(d.)39 b(This)28 b(algorithm)i (requires)e(the)h(Jacobian)h(and)e(access)i(to)f(the)g(driv)m(er)390 1158 y(ob)5 b(ject)31 b(via)g FH(gsl_odeiv2_step_set_drive)o(r)p FK(.)3288 1359 y([Step)f(T)m(yp)s(e])-3600 b Fv(gsl_odeiv2_step_bsimp) 390 1468 y FK(Implicit)41 b(Bulirsc)m(h-Sto)s(er)g(metho)s(d)f(of)g (Bader)h(and)f(Deu\015hard.)70 b(The)40 b(metho)s(d)g(is)h(generally) 390 1578 y(suitable)31 b(for)f(sti\013)h(problems.)40 b(This)29 b(stepp)s(er)h(requires)g(the)g(Jacobian.)3288 1779 y([Step)g(T)m(yp)s(e])-3600 b Fv(gsl_odeiv2_step_msadam)q(s)390 1889 y FK(A)23 b(v)-5 b(ariable-co)s(e\016cien)m(t)26 b(linear)e(m)m(ultistep)g(Adams)e(metho)s(d)h(in)g(Nordsiec)m(k)h (form.)38 b(This)22 b(stepp)s(er)390 1998 y(uses)37 b(explicit)i (Adams-Bashforth)f(\(predictor\))h(and)e(implicit)h(Adams-Moulton)h (\(corrector\))390 2108 y(metho)s(ds)i(in)g FE(P)13 b FK(\()p FE(E)5 b(C)i FK(\))1170 2075 y Fq(m)1274 2108 y FK(functional)42 b(iteration)h(mo)s(de.)73 b(Metho)s(d)42 b(order)e(v)-5 b(aries)42 b(dynamically)390 2218 y(b)s(et)m(w)m(een)f (1)f(and)g(12.)71 b(This)40 b(stepp)s(er)f(requires)h(the)g(access)i (to)f(the)f(driv)m(er)g(ob)5 b(ject)41 b(via)g FH(gsl_)390 2327 y(odeiv2_step_set_driver)p FK(.)3288 2528 y([Step)30 b(T)m(yp)s(e])-3600 b Fv(gsl_odeiv2_step_msbdf)390 2638 y FK(A)20 b(v)-5 b(ariable-co)s(e\016cien)m(t)24 b(linear)d(m)m (ultistep)g(bac)m(kw)m(ard)g(di\013eren)m(tiation)h(form)m(ula)e (\(BDF\))i(metho)s(d)390 2748 y(in)43 b(Nordsiec)m(k)i(form.)79 b(This)43 b(stepp)s(er)f(uses)h(the)h(explicit)g(BDF)h(form)m(ula)e(as) h(predictor)g(and)390 2857 y(implicit)35 b(BDF)g(form)m(ula)g(as)f (corrector.)53 b(A)35 b(mo)s(di\014ed)e(Newton)h(iteration)i(metho)s(d) e(is)g(used)f(to)390 2967 y(solv)m(e)i(the)f(system)g(of)g(non-linear)g (equations.)52 b(Metho)s(d)33 b(order)h(v)-5 b(aries)34 b(dynamically)g(b)s(et)m(w)m(een)390 3076 y(1)h(and)g(5.)54 b(The)35 b(metho)s(d)f(is)h(generally)h(suitable)g(for)e(sti\013)i (problems.)53 b(This)34 b(stepp)s(er)g(requires)390 3186 y(the)d(Jacobian)g(and)e(the)i(access)h(to)f(the)f(driv)m(er)g(ob)5 b(ject)32 b(via)f FH(gsl_odeiv2_step_set_dri)o(ver)p FK(.)150 3431 y FJ(27.3)68 b(Adaptiv)l(e)46 b(Step-size)f(Con)l(trol) 150 3591 y FK(The)28 b(con)m(trol)h(function)f(examines)h(the)f(prop)s (osed)f(c)m(hange)i(to)g(the)f(solution)h(pro)s(duced)e(b)m(y)h(a)g (stepping)150 3700 y(function)h(and)g(attempts)i(to)f(determine)g(the)g (optimal)g(step-size)h(for)e(a)h(user-sp)s(eci\014ed)f(lev)m(el)i(of)f (error.)3350 3901 y([F)-8 b(unction])-3599 b Fv(gsl_odeiv2_control)58 b(*)52 b(gsl_odeiv2_control_st)q(and)q(ard)q(_new)565 4011 y Fu(\()p FD(double)30 b Ft(eps_abs)p FD(,)j(double)d Ft(eps_rel)p FD(,)j(double)d Ft(a_y)p FD(,)h(double)f Ft(a_dydt)p Fu(\))390 4121 y FK(The)44 b(standard)f(con)m(trol)j(ob)5 b(ject)45 b(is)f(a)h(four)e(parameter)i(heuristic)g(based)e(on)i (absolute)g(and)390 4230 y(relativ)m(e)29 b(errors)d FD(eps)p 1098 4230 28 4 v 40 w(abs)31 b FK(and)26 b FD(eps)p 1601 4230 V 40 w(rel)p FK(,)i(and)e(scaling)i(factors)g FD(a)p 2601 4230 V 40 w(y)35 b FK(and)26 b FD(a)p 2942 4230 V 41 w(dydt)i FK(for)f(the)g(system)390 4340 y(state)32 b FE(y)s FK(\()p FE(t)p FK(\))e(and)g(deriv)-5 b(ativ)m(es)32 b FE(y)1472 4307 y Fp(0)1495 4340 y FK(\()p FE(t)p FK(\))f(resp)s (ectiv)m(ely)-8 b(.)390 4483 y(The)27 b(step-size)i(adjustmen)m(t)f (pro)s(cedure)f(for)g(this)h(metho)s(d)f(b)s(egins)h(b)m(y)f(computing) h(the)g(desired)390 4592 y(error)i(lev)m(el)i FE(D)895 4606 y Fq(i)953 4592 y FK(for)e(eac)m(h)i(comp)s(onen)m(t,)1218 4768 y FE(D)1293 4782 y Fq(i)1347 4768 y FK(=)25 b FE(\017)1480 4782 y Fq(abs)1600 4768 y FK(+)20 b FE(\017)1728 4782 y Fq(r)r(el)1838 4768 y FI(\003)h FK(\()p FE(a)1987 4782 y Fq(y)2027 4768 y FI(j)p FE(y)2097 4782 y Fq(i)2124 4768 y FI(j)g FK(+)f FE(a)2309 4782 y Fq(dy)r(dt)2443 4768 y FE(h)p FI(j)p FE(y)s FI(0)2593 4782 y Fq(i)2621 4768 y FI(j)p FK(\))390 4945 y(and)44 b(comparing)g(it)h(with)f(the)g (observ)m(ed)h(error)e FE(E)2227 4959 y Fq(i)2303 4945 y FK(=)48 b FI(j)p FE(y)s(er)s(r)2622 4959 y Fq(i)2650 4945 y FI(j)p FK(.)83 b(If)43 b(the)i(observ)m(ed)f(error)g FD(E)390 5054 y FK(exceeds)f(the)f(desired)f(error)h(lev)m(el)i FD(D)j FK(b)m(y)41 b(more)i(than)e(10\045)i(for)f(an)m(y)g(comp)s(onen) m(t)g(then)g(the)390 5164 y(metho)s(d)30 b(reduces)g(the)g(step-size)i (b)m(y)e(an)h(appropriate)f(factor,)1400 5340 y FE(h)1452 5354 y Fq(new)1604 5340 y FK(=)25 b FE(h)1752 5354 y Fq(old)1865 5340 y FI(\003)c FE(S)k FI(\003)c FK(\()p FE(E)5 b(=D)s FK(\))2343 5302 y Fp(\000)p FB(1)p Fq(=q)p eop end %%Page: 339 357 TeXDict begin 339 356 bop 150 -116 a FK(Chapter)30 b(27:)41 b(Ordinary)29 b(Di\013eren)m(tial)k(Equations)1690 b(339)390 299 y(where)33 b FE(q)j FK(is)d(the)h(consistency)g(order)f(of)g(the)h (metho)s(d)e(\(e.g.)51 b FE(q)33 b FK(=)d(4)k(for)f(4\(5\))i(em)m(b)s (edded)d(RK\),)390 408 y(and)j FE(S)40 b FK(is)c(a)g(safet)m(y)h (factor)f(of)g(0.9.)58 b(The)35 b(ratio)h FE(E)5 b(=D)39 b FK(is)d(tak)m(en)h(to)f(b)s(e)f(the)h(maxim)m(um)f(of)h(the)390 518 y(ratios)31 b FE(E)710 532 y Fq(i)738 518 y FE(=D)858 532 y Fq(i)886 518 y FK(.)390 662 y(If)c(the)h(observ)m(ed)f(error)g FE(E)33 b FK(is)28 b(less)g(than)f(50\045)h(of)g(the)f(desired)g(error) g(lev)m(el)j FD(D)i FK(for)27 b(the)h(maxim)m(um)390 771 y(ratio)c FE(E)667 785 y Fq(i)695 771 y FE(=D)815 785 y Fq(i)866 771 y FK(then)f(the)g(algorithm)h(tak)m(es)g(the)g(opp)s (ortunit)m(y)e(to)i(increase)g(the)f(step-size)h(to)g(bring)390 881 y(the)31 b(error)f(in)g(line)g(with)g(the)h(desired)f(lev)m(el,) 1332 1058 y FE(h)1384 1072 y Fq(new)1536 1058 y FK(=)25 b FE(h)1684 1072 y Fq(old)1797 1058 y FI(\003)c FE(S)k FI(\003)c FK(\()p FE(E)5 b(=D)s FK(\))2275 1020 y Fp(\000)p FB(1)p Fq(=)p FB(\()p Fq(q)r FB(+1\))390 1234 y FK(This)44 b(encompasses)h(all)h(the)f(standard)f(error)g(scaling)i(metho)s(ds.)84 b(T)-8 b(o)45 b(a)m(v)m(oid)h(uncon)m(trolled)390 1344 y(c)m(hanges)31 b(in)f(the)h(stepsize,)h(the)e(o)m(v)m(erall)j(scaling) e(factor)h(is)e(limited)h(to)g(the)g(range)g(1)p FE(=)p FK(5)g(to)g(5.)3350 1546 y([F)-8 b(unction])-3599 b Fv (gsl_odeiv2_control)58 b(*)52 b(gsl_odeiv2_control_y_)q(new)g Fu(\()p FD(double)565 1656 y Ft(eps_abs)p FD(,)33 b(double)d Ft(eps_rel)p Fu(\))390 1766 y FK(This)38 b(function)g(creates)i(a)f (new)f(con)m(trol)i(ob)5 b(ject)40 b(whic)m(h)e(will)h(k)m(eep)g(the)g (lo)s(cal)h(error)e(on)h(eac)m(h)390 1875 y(step)31 b(within)g(an)g (absolute)h(error)f(of)g FD(eps)p 1815 1875 28 4 v 40 w(abs)k FK(and)c(relativ)m(e)i(error)e(of)g FD(eps)p 2979 1875 V 40 w(rel)k FK(with)c(resp)s(ect)g(to)390 1985 y(the)h(solution)g FE(y)938 1999 y Fq(i)965 1985 y FK(\()p FE(t)p FK(\).)45 b(This)31 b(is)g(equiv)-5 b(alen)m(t)33 b(to)f(the)g(standard)f(con)m(trol)i(ob)5 b(ject)32 b(with)g FD(a)p 3366 1985 V 40 w(y)8 b FK(=1)32 b(and)390 2094 y FD(a)p 441 2094 V 40 w(dydt)r FK(=0.)3350 2297 y([F)-8 b(unction])-3599 b Fv(gsl_odeiv2_control)58 b(*)52 b(gsl_odeiv2_control_yp)q(_ne)q(w)f Fu(\()p FD(double)565 2406 y Ft(eps_abs)p FD(,)33 b(double)d Ft(eps_rel)p Fu(\))390 2516 y FK(This)38 b(function)g(creates)i(a)f(new)f(con)m(trol)i(ob)5 b(ject)40 b(whic)m(h)e(will)h(k)m(eep)g(the)g(lo)s(cal)h(error)e(on)h (eac)m(h)390 2626 y(step)31 b(within)g(an)g(absolute)h(error)f(of)g FD(eps)p 1815 2626 V 40 w(abs)k FK(and)c(relativ)m(e)i(error)e(of)g FD(eps)p 2979 2626 V 40 w(rel)k FK(with)c(resp)s(ect)g(to)390 2735 y(the)e(deriv)-5 b(ativ)m(es)30 b(of)e(the)h(solution)g FE(y)1642 2702 y Fp(0)1639 2758 y Fq(i)1666 2735 y FK(\()p FE(t)p FK(\).)41 b(This)27 b(is)i(equiv)-5 b(alen)m(t)30 b(to)f(the)g(standard)e(con)m(trol)j(ob)5 b(ject)390 2845 y(with)30 b FD(a)p 648 2845 V 41 w(y)8 b FK(=0)30 b(and)g FD(a)p 1113 2845 V 40 w(dydt)r FK(=1.)3350 3047 y([F)-8 b(unction])-3599 b Fv(gsl_odeiv2_control)58 b(*)52 b(gsl_odeiv2_control_sc)q(ale)q(d_n)q(ew)g Fu(\()p FD(double)565 3157 y Ft(eps_abs)p FD(,)33 b(double)d Ft(eps_rel)p FD(,)i(double)e Ft(a_y)p FD(,)i(double)e Ft(a_dydt)p FD(,)i(const)f(double)565 3266 y Ft(scale_abs)p Fo([])p FD(,)i(size)p 1294 3266 V 41 w(t)e Ft(dim)p Fu(\))390 3376 y FK(This)37 b(function)g(creates)i (a)f(new)f(con)m(trol)j(ob)5 b(ject)38 b(whic)m(h)f(uses)h(the)f(same)i (algorithm)f(as)g FH(gsl_)390 3486 y(odeiv2_control_standard_)o(new)27 b FK(but)32 b(with)g(an)h(absolute)h(error)f(whic)m(h)f(is)h(scaled)h (for)f(eac)m(h)390 3595 y(comp)s(onen)m(t)e(b)m(y)f(the)g(arra)m(y)h FD(scale)p 1567 3595 V 42 w(abs)p FK(.)40 b(The)30 b(form)m(ula)h(for)f FE(D)2535 3609 y Fq(i)2593 3595 y FK(for)g(this)g(con)m(trol)i(ob)5 b(ject)31 b(is,)1183 3772 y FE(D)1258 3786 y Fq(i)1311 3772 y FK(=)25 b FE(\017)1444 3786 y Fq(abs)1545 3772 y FE(s)1588 3786 y Fq(i)1635 3772 y FK(+)20 b FE(\017)1763 3786 y Fq(r)r(el)1873 3772 y FI(\003)h FK(\()p FE(a)2022 3786 y Fq(y)2062 3772 y FI(j)p FE(y)2132 3786 y Fq(i)2159 3772 y FI(j)g FK(+)f FE(a)2344 3786 y Fq(dy)r(dt)2478 3772 y FE(h)p FI(j)p FE(y)s FI(0)2628 3786 y Fq(i)2656 3772 y FI(j)p FK(\))390 3949 y(where)i FE(s)688 3963 y Fq(i)739 3949 y FK(is)h(the)g FE(i)p FK(-th)g(comp)s(onen)m(t)g(of)g (the)g(arra)m(y)h FD(scale)p 2267 3949 V 41 w(abs)p FK(.)38 b(The)23 b(same)g(error)f(con)m(trol)j(heuristic)390 4058 y(is)30 b(used)g(b)m(y)g(the)h(Matlab)g FC(ode)f FK(suite.)3350 4261 y([F)-8 b(unction])-3599 b Fv(gsl_odeiv2_control)58 b(*)52 b(gsl_odeiv2_control_al)q(loc)g Fu(\()p FD(const)565 4370 y(gsl)p 677 4370 V 41 w(o)s(deiv2)p 975 4370 V 40 w(con)m(trol)p 1289 4370 V 42 w(t)m(yp)s(e)30 b(*)h Ft(T)p Fu(\))390 4480 y FK(This)e(function)g(returns)g(a)h(p)s(oin)m(ter)g(to) g(a)g(newly)g(allo)s(cated)i(instance)e(of)g(a)g(con)m(trol)h(function) f(of)390 4590 y(t)m(yp)s(e)g FD(T)p FK(.)40 b(This)28 b(function)h(is)h(only)f(needed)g(for)g(de\014ning)g(new)f(t)m(yp)s(es) i(of)f(con)m(trol)i(functions.)40 b(F)-8 b(or)390 4699 y(most)31 b(purp)s(oses)d(the)j(standard)e(con)m(trol)j(functions)e (describ)s(ed)f(ab)s(o)m(v)m(e)j(should)d(b)s(e)h(su\016cien)m(t.)3350 4902 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_odeiv2_control_in)q(it) f Fu(\()p FD(gsl)p 1755 4902 V 41 w(o)s(deiv2)p 2053 4902 V 40 w(con)m(trol)32 b(*)f Ft(c)p FD(,)g(double)565 5011 y Ft(eps_abs)p FD(,)i(double)d Ft(eps_rel)p FD(,)i(double)e Ft(a_y)p FD(,)i(double)e Ft(a_dydt)p Fu(\))390 5121 y FK(This)c(function)h(initializes)j(the)d(con)m(trol)i(function)e FD(c)33 b FK(with)27 b(the)h(parameters)f FD(eps)p 3189 5121 V 40 w(abs)k FK(\(absolute)390 5230 y(error\),)38 b FD(eps)p 814 5230 V 39 w(rel)i FK(\(relativ)m(e)f(error\),)e FD(a)p 1694 5230 V 41 w(y)44 b FK(\(scaling)37 b(factor)g(for)f(y\))g (and)g FD(a)p 2924 5230 V 40 w(dydt)h FK(\(scaling)h(factor)390 5340 y(for)30 b(deriv)-5 b(ativ)m(es\).)p eop end %%Page: 340 358 TeXDict begin 340 357 bop 150 -116 a FK(Chapter)30 b(27:)41 b(Ordinary)29 b(Di\013eren)m(tial)k(Equations)1690 b(340)3350 299 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_odeiv2_control_free)e Fu(\()p FD(gsl)p 1807 299 28 4 v 41 w(o)s(deiv2)p 2105 299 V 40 w(con)m(trol)32 b(*)f Ft(c)p Fu(\))390 408 y FK(This)f(function)g(frees)g(all)h(the)g(memory)f(asso)s(ciated)i(with) e(the)h(con)m(trol)g(function)f FD(c)p FK(.)3350 588 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_odeiv2_control_ha)q(djus)q (t)f Fu(\()p FD(gsl)p 1912 588 V 40 w(o)s(deiv2)p 2209 588 V 41 w(con)m(trol)32 b(*)f Ft(c)p FD(,)565 697 y(gsl)p 677 697 V 41 w(o)s(deiv2)p 975 697 V 40 w(step)f(*)h Ft(s)p FD(,)g(const)f(double)g Ft(y)p Fo([])p FD(,)h(const)f(double)g Ft(yerr)p Fo([])p FD(,)h(const)g(double)f Ft(dydt)p Fo([])p FD(,)565 807 y(double)g(*)h Ft(h)p Fu(\))390 917 y FK(This)38 b(function)g(adjusts)g(the)h(step-size)h FD(h)f FK(using)f(the)h(con)m (trol)h(function)f FD(c)p FK(,)i(and)d(the)h(curren)m(t)390 1026 y(v)-5 b(alues)35 b(of)h FD(y)p FK(,)g FD(y)m(err)42 b FK(and)34 b FD(dydt)p FK(.)55 b(The)34 b(stepping)h(function)g FD(step)j FK(is)d(also)h(needed)f(to)h(determine)390 1136 y(the)26 b(order)g(of)g(the)g(metho)s(d.)39 b(If)25 b(the)h(error)g(in)g(the)g(y-v)-5 b(alues)26 b FD(y)m(err)33 b FK(is)26 b(found)e(to)j(b)s(e)e(to)s(o)i(large)g(then)390 1245 y(the)g(step-size)h FD(h)e FK(is)h(reduced)f(and)g(the)h(function) g(returns)e FH(GSL_ODEIV_HADJ_DEC)p FK(.)35 b(If)26 b(the)h(error)390 1355 y(is)35 b(su\016cien)m(tly)h(small)f(then)g FD(h)f FK(ma)m(y)i(b)s(e)e(increased)h(and)g FH(GSL_ODEIV_HADJ_INC)30 b FK(is)35 b(returned.)390 1465 y(The)i(function)g(returns)e FH(GSL_ODEIV_HADJ_NIL)e FK(if)k(the)g(step-size)i(is)e(unc)m(hanged.)61 b(The)36 b(goal)390 1574 y(of)h(the)h(function)f(is)g(to)h(estimate)h (the)e(largest)i(step-size)f(whic)m(h)f(satis\014es)h(the)f(user-sp)s (eci\014ed)390 1684 y(accuracy)32 b(requiremen)m(ts)e(for)g(the)h (curren)m(t)f(p)s(oin)m(t.)3350 1863 y([F)-8 b(unction])-3599 b Fv(const)54 b(char)f(*)g(gsl_odeiv2_control_nam)q(e)e Fu(\()p FD(const)32 b(gsl)p 2464 1863 V 40 w(o)s(deiv2)p 2761 1863 V 41 w(con)m(trol)g(*)565 1973 y Ft(c)p Fu(\))390 2082 y FK(This)e(function)g(returns)f(a)i(p)s(oin)m(ter)f(to)h(the)g (name)f(of)h(the)f(con)m(trol)i(function.)40 b(F)-8 b(or)31 b(example,)630 2215 y FH(printf)46 b(\("control)f(method)h(is)i ('\045s'\\n",)1012 2325 y(gsl_odeiv2_control_name)41 b(\(c\)\);)390 2457 y FK(w)m(ould)30 b(prin)m(t)g(something)h(lik)m(e)h FH(control)c(method)h(is)g('standard')3350 2637 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_odeiv2_control_er)q(rlev)q(el)f Fu(\()p FD(gsl)p 1964 2637 V 41 w(o)s(deiv2)p 2262 2637 V 40 w(con)m(trol)32 b(*)f Ft(c)p FD(,)g(const)565 2746 y(double)f Ft(y)p FD(,)h(const)g(double)f Ft(dydt)p FD(,)h(const)g (double)f Ft(h)p FD(,)h(const)g(size)p 2785 2746 V 41 w(t)g Ft(ind)p FD(,)g(double)f(*)565 2856 y Ft(errlev)p Fu(\))390 2966 y FK(This)h(function)g(calculates)j(the)e(desired)f (error)g(lev)m(el)i(of)f(the)g FD(ind)p FK(-th)f(comp)s(onen)m(t)h(to)g FD(errlev)p FK(.)45 b(It)390 3075 y(requires)33 b(the)g(v)-5 b(alue)34 b(\()p FD(y)8 b FK(\))34 b(and)e(v)-5 b(alue)34 b(of)f(the)h(deriv)-5 b(ativ)m(e)35 b(\()p FD(dydt)r FK(\))e(of)g(the)h(comp)s(onen)m(t,)g(and)f(the)390 3185 y(curren)m(t)d(step)h(size)g FD(h)p FK(.)3350 3364 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_odeiv2_control_se)q(t_dr)q(ive)q(r)e Fu(\()p FD(gsl)p 2068 3364 V 41 w(o)s(deiv2)p 2366 3364 V 41 w(con)m(trol)32 b(*)f Ft(c)p FD(,)f(const)565 3474 y(gsl)p 677 3474 V 41 w(o)s(deiv2)p 975 3474 V 40 w(driv)m(er)g(*)h Ft(d)p Fu(\))390 3583 y FK(This)f(function)g(sets)g(a)h(p)s(oin)m(ter)g (of)f(the)h(driv)m(er)f(ob)5 b(ject)31 b FD(d)i FK(for)e(con)m(trol)g (ob)5 b(ject)32 b FD(c)p FK(.)150 3812 y FJ(27.4)68 b(Ev)l(olution)150 3972 y FK(The)30 b(ev)m(olution)j(function)d(com)m(bines)i(the)f (results)g(of)g(a)g(stepping)f(function)h(and)f(con)m(trol)j(function)d (to)150 4081 y(reliably)h(adv)-5 b(ance)31 b(the)g(solution)f(forw)m (ard)g(one)h(step)f(using)g(an)h(acceptable)h(step-size.)3350 4261 y([F)-8 b(unction])-3599 b Fv(gsl_odeiv2_evolve)57 b(*)c(gsl_odeiv2_evolve_allo)q(c)e Fu(\()p FD(size)p 2626 4261 V 42 w(t)30 b Ft(dim)p Fu(\))390 4370 y FK(This)c(function)h (returns)f(a)h(p)s(oin)m(ter)g(to)h(a)f(newly)g(allo)s(cated)i (instance)f(of)f(an)g(ev)m(olution)h(function)390 4480 y(for)i(a)h(system)f(of)h FD(dim)f FK(dimensions.)3350 4659 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_odeiv2_evolve_app)q(ly) f Fu(\()p FD(gsl)p 1755 4659 V 41 w(o)s(deiv2)p 2053 4659 V 40 w(ev)m(olv)m(e)33 b(*)e Ft(e)p FD(,)565 4769 y(gsl)p 677 4769 V 41 w(o)s(deiv2)p 975 4769 V 40 w(con)m(trol)h(*)f Ft(con)p FD(,)g(gsl)p 1715 4769 V 41 w(o)s(deiv2)p 2013 4769 V 40 w(step)g(*)g Ft(step)p FD(,)g(const)g(gsl)p 2930 4769 V 41 w(o)s(deiv2)p 3228 4769 V 40 w(system)g(*)565 4878 y Ft(sys)p FD(,)h(double)e(*)g Ft(t)p FD(,)h(double)f Ft(t1)p FD(,)h(double)f(*)h Ft(h)p FD(,)g(double)f Ft(y)p Fo([])p Fu(\))390 4988 y FK(This)42 b(function)g(adv)-5 b(ances)43 b(the)g(system)f(\()p FD(e)p FK(,)47 b FD(sys)t FK(\))42 b(from)g(time)h FD(t)i FK(and)d(p)s(osition)h FD(y)50 b FK(using)42 b(the)390 5098 y(stepping)30 b(function)g FD(step)p FK(.)41 b(The)30 b(new)g(time)h(and)f(p)s(osition)g(are)h (stored)f(in)g FD(t)j FK(and)d FD(y)38 b FK(on)30 b(output.)390 5230 y(The)21 b(initial)j(step-size)f(is)f(tak)m(en)h(as)f FD(h)p FK(.)38 b(The)21 b(con)m(trol)j(function)d FD(con)h FK(is)h(applied)e(to)i(c)m(hec)m(k)h(whether)390 5340 y(the)32 b(lo)s(cal)h(error)e(estimated)i(b)m(y)f(the)g(stepping)f (function)g FD(step)k FK(using)c(step-size)i FD(h)e FK(exceeds)i(the)p eop end %%Page: 341 359 TeXDict begin 341 358 bop 150 -116 a FK(Chapter)30 b(27:)41 b(Ordinary)29 b(Di\013eren)m(tial)k(Equations)1690 b(341)390 299 y(required)22 b(error)h(tolerance.)40 b(If)22 b(the)h(error)g(is)g (to)s(o)h(high,)g(the)f(step)g(is)g(retried)g(b)m(y)g(calling)h FD(step)i FK(with)390 408 y(a)h(decreased)f(step-size.)41 b(This)25 b(pro)s(cess)h(is)g(con)m(tin)m(ued)h(un)m(til)g(an)f (acceptable)i(step-size)g(is)e(found.)390 518 y(An)33 b(estimate)j(of)e(the)g(lo)s(cal)h(error)f(for)f(the)h(step)g(can)g(b)s (e)f(obtained)h(from)g(the)g(comp)s(onen)m(ts)g(of)390 628 y(the)d(arra)m(y)f FA(e)p FH(->yerr[])p FK(.)390 765 y(If)36 b(the)h(user-supplied)e(functions)h(de\014ned)f(in)h(the)h (system)g FD(sys)i FK(returns)d FH(GSL_EBADFUNC)p FK(,)f(the)390 874 y(function)48 b(returns)g(immediately)i(with)e(the)h(same)g(return) e(co)s(de.)96 b(In)48 b(this)g(case)i(the)f(user)390 984 y(m)m(ust)e(call)h FH(gsl_odeiv2_step_reset)42 b FK(and)k FH(gsl_odeiv2_evolve_reset)41 b FK(b)s(efore)46 b(calling)390 1093 y(this)30 b(function)g(again.)390 1230 y(Otherwise,)39 b(if)f(the)g(user-supplied)e(functions)h (de\014ned)f(in)h(the)h(system)g FD(sys)j FK(or)c(the)h(stepping)390 1340 y(function)43 b FD(step)j FK(return)c(a)h(status)h(other)f(than)g FH(GSL_SUCCESS)p FK(,)h(the)f(step)g(is)g(retried)h(with)f(a)390 1450 y(decreased)c(step-size.)66 b(If)38 b(the)h(step-size)g(decreases) h(b)s(elo)m(w)e(mac)m(hine)h(precision,)i(a)e(status)g(of)390 1559 y FH(GSL_FAILURE)28 b FK(is)i(returned)g(if)g(the)h(user)f (functions)g(returned)g FH(GSL_SUCCESS)p FK(.)38 b(Otherwise)31 b(the)390 1669 y(v)-5 b(alue)28 b(returned)e(b)m(y)i(user)e(function)h (is)h(returned.)39 b(If)27 b(no)g(acceptable)i(step)f(can)g(b)s(e)e (made,)j FD(t)h FK(and)390 1778 y FD(y)i FK(will)24 b(b)s(e)f(restored) h(to)h(their)e(pre-step)h(v)-5 b(alues)24 b(and)g FD(h)f FK(con)m(tains)i(the)f(\014nal)g(attempted)g(step-size.)390 1915 y(If)k(the)g(step)h(is)f(successful)g(the)h(function)f(returns)f (a)i(suggested)g(step-size)h(for)e(the)g(next)h(step)f(in)390 2025 y FD(h)p FK(.)40 b(The)28 b(maxim)m(um)g(time)h FD(t1)37 b FK(is)28 b(guaran)m(teed)i(not)f(to)g(b)s(e)f(exceeded)i(b)m (y)e(the)h(time-step.)41 b(On)28 b(the)390 2135 y(\014nal)i(time-step)i (the)e(v)-5 b(alue)31 b(of)f FD(t)j FK(will)e(b)s(e)f(set)g(to)i FD(t1)38 b FK(exactly)-8 b(.)3350 2324 y([F)g(unction])-3599 b Fv(int)53 b(gsl_odeiv2_evolve_app)q(ly_f)q(ixe)q(d_s)q(tep)f Fu(\()p FD(gsl)p 2330 2324 28 4 v 41 w(o)s(deiv2)p 2628 2324 V 40 w(ev)m(olv)m(e)33 b(*)e Ft(e)p FD(,)565 2434 y(gsl)p 677 2434 V 41 w(o)s(deiv2)p 975 2434 V 40 w(con)m(trol)h(*)f Ft(con)p FD(,)g(gsl)p 1715 2434 V 41 w(o)s(deiv2)p 2013 2434 V 40 w(step)g(*)g Ft(step)p FD(,)g(const)g(gsl)p 2930 2434 V 41 w(o)s(deiv2)p 3228 2434 V 40 w(system)g(*)565 2543 y Ft(sys)p FD(,)h(double)e(*)g Ft(t)p FD(,)h(const)g(double)f Ft(h)p FD(,)h(double)f Ft(y)p Fo([])p Fu(\))390 2653 y FK(This)40 b(function)h(adv)-5 b(ances)42 b(the)g(ODE-system)f(\()p FD(e)p FK(,)k FD(sys)p FK(,)f FD(con)p FK(\))e(from)f(time)h FD(t)h FK(and)e(p)s(osition)g FD(y)390 2762 y FK(using)25 b(the)h(stepping)f(function)g FD(step)k FK(b)m(y)c(a)h(sp)s(eci\014ed)f (step)h(size)g FD(h)p FK(.)39 b(If)25 b(the)h(lo)s(cal)g(error)g (estimated)390 2872 y(b)m(y)38 b(the)h(stepping)f(function)g(exceeds)h (the)g(desired)f(error)g(lev)m(el,)k(the)d(step)f(is)g(not)h(tak)m(en)h (and)390 2981 y(the)32 b(function)f(returns)f FH(GSL_FAILURE)p FK(.)42 b(Otherwise)31 b(the)h(v)-5 b(alue)32 b(returned)e(b)m(y)i (user)f(function)g(is)390 3091 y(returned.)3350 3280 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_odeiv2_evolve_res)q(et)f Fu(\()p FD(gsl)p 1755 3280 V 41 w(o)s(deiv2)p 2053 3280 V 40 w(ev)m(olv)m(e)33 b(*)e Ft(e)p Fu(\))390 3390 y FK(This)k(function)h(resets)g(the)g(ev)m(olution)h(function)f FD(e)p FK(.)57 b(It)36 b(should)f(b)s(e)g(used)g(whenev)m(er)h(the)g (next)390 3500 y(use)30 b(of)h FD(e)k FK(will)c(not)g(b)s(e)e(a)i(con)m (tin)m(uation)h(of)f(a)g(previous)f(step.)3350 3689 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_odeiv2_evolve_free)e Fu(\()p FD(gsl)p 1755 3689 V 41 w(o)s(deiv2)p 2053 3689 V 40 w(ev)m(olv)m(e)33 b(*)e Ft(e)p Fu(\))390 3799 y FK(This)f(function)g(frees)g(all)h(the)g(memory)f(asso)s(ciated)i(with) e(the)h(ev)m(olution)g(function)g FD(e)p FK(.)3350 3988 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_odeiv2_evolve_set)q(_dri)q (ver)f Fu(\()p FD(gsl)p 2016 3988 V 41 w(o)s(deiv2)p 2314 3988 V 41 w(ev)m(olv)m(e)32 b(*)f Ft(e)p FD(,)g(const)565 4097 y(gsl)p 677 4097 V 41 w(o)s(deiv2)p 975 4097 V 40 w(driv)m(er)f(*)h Ft(d)p Fu(\))390 4207 y FK(This)f(function)g(sets)g (a)h(p)s(oin)m(ter)g(of)f(the)h(driv)m(er)f(ob)5 b(ject)31 b FD(d)i FK(for)e(ev)m(olv)m(e)h(ob)5 b(ject)32 b FD(e)p FK(.)275 4396 y(If)c(a)h(system)g(has)g(discon)m(tin)m(uous)g(c)m (hanges)h(in)f(the)g(deriv)-5 b(ativ)m(es)30 b(at)g(kno)m(wn)f(p)s(oin) m(ts,)g(it)g(is)g(advisable)150 4506 y(to)g(ev)m(olv)m(e)i(the)e (system)f(b)s(et)m(w)m(een)i(eac)m(h)f(discon)m(tin)m(uit)m(y)h(in)e (sequence.)41 b(F)-8 b(or)29 b(example,)h(if)e(a)h(step-c)m(hange)150 4616 y(in)35 b(an)h(external)h(driving)e(force)h(o)s(ccurs)g(at)g (times)g FE(t)1975 4630 y Fq(a)2015 4616 y FE(;)15 b(t)2088 4630 y Fq(b)2158 4616 y FK(and)35 b FE(t)2373 4630 y Fq(c)2442 4616 y FK(then)h(ev)m(olution)h(should)e(b)s(e)g(carried)150 4725 y(out)c(o)m(v)m(er)i(the)e(ranges)g(\()p FE(t)1017 4739 y FB(0)1055 4725 y FE(;)15 b(t)1128 4739 y Fq(a)1168 4725 y FK(\),)32 b(\()p FE(t)1328 4739 y Fq(a)1368 4725 y FE(;)15 b(t)1441 4739 y Fq(b)1475 4725 y FK(\),)32 b(\()p FE(t)1635 4739 y Fq(b)1668 4725 y FE(;)15 b(t)1741 4739 y Fq(c)1775 4725 y FK(\),)32 b(and)f(\()p FE(t)2113 4739 y Fq(c)2147 4725 y FE(;)15 b(t)2220 4739 y FB(1)2257 4725 y FK(\))31 b(separately)i(and)d(not)i(directly)f(o)m(v)m(er)i(the) 150 4835 y(range)e(\()p FE(t)466 4849 y FB(0)503 4835 y FE(;)15 b(t)576 4849 y FB(1)614 4835 y FK(\).)150 5071 y FJ(27.5)68 b(Driv)l(er)150 5230 y FK(The)30 b(driv)m(er)g(ob)5 b(ject)32 b(is)f(a)g(high)f(lev)m(el)i(wrapp)s(er)d(that)i(com)m(bines) g(the)g(ev)m(olution,)i(con)m(trol)f(and)e(stepp)s(er)150 5340 y(ob)5 b(jects)31 b(for)f(easy)h(use.)p eop end %%Page: 342 360 TeXDict begin 342 359 bop 150 -116 a FK(Chapter)30 b(27:)41 b(Ordinary)29 b(Di\013eren)m(tial)k(Equations)1690 b(342)3350 299 y([F)-8 b(unction])-3599 b Fv(gsl_odeiv2_driver)57 b(*)c(gsl_odeiv2_driver_allo)q(c_y)q(_ne)q(w)e Fu(\()p FD(const)565 408 y(gsl)p 677 408 28 4 v 41 w(o)s(deiv2)p 975 408 V 40 w(system)31 b(*)g Ft(sys)p FD(,)g(const)g(gsl)p 1949 408 V 40 w(o)s(deiv2)p 2246 408 V 41 w(step)p 2449 408 V 40 w(t)m(yp)s(e)g(*)f Ft(T)p FD(,)h(const)g(double)f Ft(hstart)p FD(,)565 518 y(const)h(double)f Ft(epsabs)p FD(,)i(const)f(double)f Ft(epsrel)p Fu(\))3350 628 y FK([F)-8 b(unction])-3599 b Fv(gsl_odeiv2_driver)57 b(*)c (gsl_odeiv2_driver_allo)q(c_y)q(p_n)q(ew)f Fu(\()p FD(const)565 737 y(gsl)p 677 737 V 41 w(o)s(deiv2)p 975 737 V 40 w(system)31 b(*)g Ft(sys)p FD(,)g(const)g(gsl)p 1949 737 V 40 w(o)s(deiv2)p 2246 737 V 41 w(step)p 2449 737 V 40 w(t)m(yp)s(e)g(*)f Ft(T)p FD(,)h(const)g(double)f Ft(hstart)p FD(,)565 847 y(const)h(double)f Ft(epsabs)p FD(,)i(const)f(double)f Ft(epsrel)p Fu(\))3350 956 y FK([F)-8 b(unction])-3599 b Fv(gsl_odeiv2_driver)57 b(*)c(gsl_odeiv2_driver_allo)q(c_s)q(tan)q (dard)q(_ne)q(w)565 1066 y Fu(\()p FD(const)31 b(gsl)p 950 1066 V 41 w(o)s(deiv2)p 1248 1066 V 40 w(system)g(*)g Ft(sys)p FD(,)g(const)g(gsl)p 2222 1066 V 41 w(o)s(deiv2)p 2520 1066 V 40 w(step)p 2722 1066 V 40 w(t)m(yp)s(e)g(*)g Ft(T)p FD(,)g(const)f(double)565 1176 y Ft(hstart)p FD(,)i(const)f (double)f Ft(epsabs)p FD(,)j(const)e(double)e Ft(epsrel)p FD(,)k(const)e(double)f Ft(a_y)p FD(,)h(const)565 1285 y(double)f Ft(a_dydt)p Fu(\))3350 1395 y FK([F)-8 b(unction])-3599 b Fv(gsl_odeiv2_driver)57 b(*)c(gsl_odeiv2_driver_allo)q(c_s)q(cal)q (ed_n)q(ew)565 1504 y Fu(\()p FD(const)31 b(gsl)p 950 1504 V 41 w(o)s(deiv2)p 1248 1504 V 40 w(system)g(*)g Ft(sys)p FD(,)g(const)g(gsl)p 2222 1504 V 41 w(o)s(deiv2)p 2520 1504 V 40 w(step)p 2722 1504 V 40 w(t)m(yp)s(e)g(*)g Ft(T)p FD(,)g(const)f(double)565 1614 y Ft(hstart)p FD(,)i(const)f (double)f Ft(epsabs)p FD(,)j(const)e(double)e Ft(epsrel)p FD(,)k(const)e(double)f Ft(a_y)p FD(,)h(const)565 1724 y(double)f Ft(a_dydt)p FD(,)i(const)f(double)f Ft(scale_abs)p Fo([])p Fu(\))390 1833 y FK(These)c(functions)f(return)g(a)h(p)s(oin)m (ter)g(to)h(a)f(newly)g(allo)s(cated)i(instance)e(of)g(a)h(driv)m(er)e (ob)5 b(ject.)40 b(The)390 1943 y(functions)28 b(automatically)j(allo)s (cate)f(and)e(initialise)i(the)e(ev)m(olv)m(e,)k(con)m(trol)d(and)f (stepp)s(er)f(ob)5 b(jects)390 2052 y(for)25 b(ODE)h(system)f FD(sys)k FK(using)c(stepp)s(er)g(t)m(yp)s(e)h FD(T)p FK(.)38 b(The)25 b(initial)i(step)f(size)g(is)g(giv)m(en)g(in)f FD(hstart)p FK(.)39 b(The)390 2162 y(rest)34 b(of)g(the)g(argumen)m(ts) g(follo)m(w)h(the)g(syn)m(tax)f(and)f(seman)m(tics)i(of)f(the)g(con)m (trol)i(functions)d(with)390 2271 y(same)e(name)f(\()p FH(gsl_odeiv2_control_*_new)p FK(\).)3350 2506 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_odeiv2_driver_set)q(_hmi)q(n)f Fu(\()p FD(gsl)p 1912 2506 V 40 w(o)s(deiv2)p 2209 2506 V 41 w(driv)m(er)30 b(*)h Ft(d)p FD(,)g(const)g(double)565 2615 y Ft(hmin)p Fu(\))390 2725 y FK(The)i(function)g(sets)h(a)g(minim) m(um)f(for)g(allo)m(w)m(ed)i(step)f(size)g FD(hmin)f FK(for)g(driv)m(er)g FD(d)p FK(.)50 b(Default)34 b(v)-5 b(alue)390 2834 y(is)30 b(0.)3350 3068 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_odeiv2_driver_set)q(_hma)q(x)f Fu(\()p FD(gsl)p 1912 3068 V 40 w(o)s(deiv2)p 2209 3068 V 41 w(driv)m(er)30 b(*)h Ft(d)p FD(,)g(const)g(double)565 3178 y Ft(hmax)p Fu(\))390 3288 y FK(The)f(function)h(sets)g(a)h(maxim) m(um)e(for)h(allo)m(w)m(ed)i(step)e(size)h FD(hmax)k FK(for)31 b(driv)m(er)g FD(d)p FK(.)41 b(Default)32 b(v)-5 b(alue)390 3397 y(is)30 b FH(GSL_DBL_MAX)p FK(.)3350 3631 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_odeiv2_driver_set)q (_nma)q(x)f Fu(\()p FD(gsl)p 1912 3631 V 40 w(o)s(deiv2)p 2209 3631 V 41 w(driv)m(er)30 b(*)h Ft(d)p FD(,)g(const)565 3741 y(unsigned)e(long)i(in)m(t)g Ft(nmax)p Fu(\))390 3851 y FK(The)26 b(function)g(sets)g(a)h(maxim)m(um)f(for)g(allo)m(w)m (ed)i(n)m(um)m(b)s(er)d(of)i(steps)f FD(nmax)32 b FK(for)26 b(driv)m(er)g FD(d)p FK(.)39 b(Default)390 3960 y(v)-5 b(alue)31 b(of)f(0)h(sets)g(no)f(limit)h(for)f(steps.)3350 4194 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_odeiv2_driver_app)q(ly) f Fu(\()p FD(gsl)p 1755 4194 V 41 w(o)s(deiv2)p 2053 4194 V 40 w(driv)m(er)30 b(*)h Ft(d)p FD(,)g(double)f(*)h Ft(t)p FD(,)565 4304 y(const)g(double)f Ft(t1)p FD(,)h(double)f Ft(y)p Fo([])p Fu(\))390 4413 y FK(This)41 b(function)g(ev)m(olv)m(es)j (the)e(driv)m(er)g(system)f FD(d)k FK(from)c FD(t)j FK(to)f FD(t1)p FK(.)75 b(Initially)43 b(v)m(ector)h FD(y)49 b FK(should)390 4523 y(con)m(tain)43 b(the)e(v)-5 b(alues)42 b(of)f(dep)s(enden)m(t)f(v)-5 b(ariables)42 b(at)g(p)s(oin)m(t)f FD(t)p FK(.)74 b(If)41 b(the)g(function)g(is)g(unable)g(to)390 4633 y(complete)29 b(the)f(calculation,)j(an)d(error)f(co)s(de)h(from)g FH(gsl_odeiv2_evolve_apply)21 b FK(is)28 b(returned,)390 4742 y(and)i FD(t)i FK(and)e FD(y)38 b FK(con)m(tain)32 b(the)f(v)-5 b(alues)30 b(from)g(last)h(successful)f(step.)390 4902 y(If)40 b(maxim)m(um)h(n)m(um)m(b)s(er)f(of)h(steps)g(is)g(reac)m (hed,)j(a)d(v)-5 b(alue)42 b(of)f FH(GSL_EMAXITER)c FK(is)k(returned.) 71 b(If)390 5011 y(the)38 b(step)g(size)g(drops)f(b)s(elo)m(w)h(minim)m (um)e(v)-5 b(alue,)41 b(the)d(function)f(returns)f(with)i FH(GSL_ENOPROG)p FK(.)390 5121 y(If)e(the)h(user-supplied)e(functions)h (de\014ned)f(in)h(the)h(system)g FD(sys)i FK(returns)d FH(GSL_EBADFUNC)p FK(,)f(the)390 5230 y(function)d(returns)f (immediately)j(with)e(the)g(same)h(return)f(co)s(de.)46 b(In)32 b(this)g(case)i(the)e(user)g(m)m(ust)390 5340 y(call)g FH(gsl_odeiv2_driver_reset)24 b FK(b)s(efore)30 b(calling)i(this)e(function)g(again.)p eop end %%Page: 343 361 TeXDict begin 343 360 bop 150 -116 a FK(Chapter)30 b(27:)41 b(Ordinary)29 b(Di\013eren)m(tial)k(Equations)1690 b(343)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_odeiv2_driver_app)q (ly_f)q(ixe)q(d_s)q(tep)f Fu(\()p FD(gsl)p 2330 299 28 4 v 41 w(o)s(deiv2)p 2628 299 V 40 w(driv)m(er)31 b(*)f Ft(d)p FD(,)565 408 y(double)g(*)h Ft(t)p FD(,)g(const)g(double)e Ft(h)p FD(,)i(const)g(unsigned)e(long)i(in)m(t)g Ft(n)p FD(,)g(double)f Ft(y)p Fo([])p Fu(\))390 518 y FK(This)25 b(function)g(ev)m(olv)m(es)i(the)f(driv)m(er)f(system)g FD(d)k FK(from)c FD(t)i FK(with)e FD(n)g FK(steps)h(of)f(size)h FD(h)p FK(.)39 b(If)25 b(the)g(function)390 628 y(is)d(unable)g(to)h (complete)h(the)e(calculation,)k(an)d(error)e(co)s(de)i(from)f FH(gsl_odeiv2_evolve_apply)o(_)390 737 y(fixed_step)28 b FK(is)i(returned,)f(and)h FD(t)j FK(and)d FD(y)38 b FK(con)m(tain)31 b(the)g(v)-5 b(alues)31 b(from)f(last)h(successful)f (step.)3350 919 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_odeiv2_driver_res)q(et)f Fu(\()p FD(gsl)p 1755 919 V 41 w(o)s(deiv2)p 2053 919 V 40 w(driv)m(er)30 b(*)h Ft(d)p Fu(\))390 1028 y FK(This)f(function)g(resets)g(the)h(ev)m (olution)h(and)e(stepp)s(er)f(ob)5 b(jects.)3350 1209 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_odeiv2_driver_res)q(et_h)q (sta)q(rt)f Fu(\()p FD(gsl)p 2121 1209 V 41 w(o)s(deiv2)p 2419 1209 V 40 w(driv)m(er)30 b(*)h Ft(d)p FD(,)g(const)565 1319 y(double)f Ft(hstart)p Fu(\))390 1429 y FK(The)g(routine)g(resets) g(the)h(ev)m(olution)g(and)f(stepp)s(er)f(ob)5 b(jects)31 b(and)e(sets)i(new)f(initial)h(step)f(size)h(to)390 1538 y FD(hstart)p FK(.)41 b(This)29 b(function)h(can)h(b)s(e)f(used)f(e.g.) 42 b(to)31 b(c)m(hange)h(the)e(direction)h(of)g(in)m(tegration.)3350 1719 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_odeiv2_driver_fre)q(e)e Fu(\()p FD(gsl)p 1702 1719 V 41 w(o)s(deiv2)p 2000 1719 V 41 w(driv)m(er)30 b(*)h Ft(d)p Fu(\))390 1829 y FK(This)h(function)h (frees)h(the)f(driv)m(er)g(ob)5 b(ject,)35 b(and)e(the)g(related)i(ev)m (olution,)g(stepp)s(er)e(and)f(con)m(trol)390 1939 y(ob)5 b(jects.)150 2169 y FJ(27.6)68 b(Examples)150 2328 y FK(The)30 b(follo)m(wing)i(program)e(solv)m(es)h(the)g(second-order)f (nonlinear)h(V)-8 b(an)30 b(der)g(P)m(ol)i(oscillator)g(equation,)1252 2495 y FE(u)1304 2458 y Fp(00)1346 2495 y FK(\()p FE(t)p FK(\))21 b(+)f FE(\026u)1668 2458 y Fp(0)1691 2495 y FK(\()p FE(t)p FK(\)\()p FE(u)p FK(\()p FE(t)p FK(\))1984 2458 y FB(2)2043 2495 y FI(\000)g FK(1\))h(+)f FE(u)p FK(\()p FE(t)p FK(\))26 b(=)f(0)150 2662 y(This)j(can)i(b)s(e)f(con)m (v)m(erted)h(in)m(to)h(a)e(\014rst)g(order)f(system)i(suitable)g(for)f (use)g(with)f(the)i(routines)f(describ)s(ed)150 2771 y(in)h(this)g(c)m(hapter)h(b)m(y)g(in)m(tro)s(ducing)f(a)g(separate)i (v)-5 b(ariable)31 b(for)f(the)h(v)m(elo)s(cit)m(y)-8 b(,)33 b FE(v)c FK(=)c FE(u)3017 2738 y Fp(0)3040 2771 y FK(\()p FE(t)p FK(\),)1525 2938 y FE(u)1577 2901 y Fp(0)1626 2938 y FK(=)g FE(v)1530 3073 y(v)1577 3035 y Fp(0)1626 3073 y FK(=)g FI(\000)p FE(u)20 b FK(+)g FE(\026v)s FK(\(1)h FI(\000)f FE(u)2302 3035 y FB(2)2339 3073 y FK(\))150 3234 y(The)38 b(program)h(b)s(egins)f(b)m(y)g (de\014ning)g(functions)g(for)g(these)h(deriv)-5 b(ativ)m(es)41 b(and)d(their)g(Jacobian.)66 b(The)150 3343 y(main)37 b(function)f(uses)h(driv)m(er)f(lev)m(el)j(functions)d(to)h(solv)m(e)i (the)e(problem.)59 b(The)36 b(program)h(ev)m(olv)m(es)i(the)150 3453 y(solution)32 b(from)g(\()p FE(u;)15 b(v)s FK(\))29 b(=)e(\(1)p FE(;)15 b FK(0\))34 b(at)e FE(t)c FK(=)f(0)32 b(to)h FE(t)27 b FK(=)g(100.)47 b(The)31 b(step-size)i FE(h)f FK(is)g(automatically)j(adjusted)150 3563 y(b)m(y)25 b(the)g(con)m(troller)h(to)g(main)m(tain)f(an)g(absolute)h(accuracy)f (of)g(10)2337 3530 y Fp(\000)p FB(6)2452 3563 y FK(in)g(the)g(function) f(v)-5 b(alues)25 b(\()p FE(u;)15 b(v)s FK(\).)40 b(The)150 3672 y(lo)s(op)30 b(in)h(the)f(example)h(prin)m(ts)f(the)h(solution)g (at)g(the)f(p)s(oin)m(ts)g FE(t)2303 3686 y Fq(i)2356 3672 y FK(=)25 b(1)p FE(;)15 b FK(2)p FE(;)g(:)g(:)g(:)j(;)d FK(100.)390 3806 y FH(#include)46 b()390 3915 y(#include)g()390 4025 y(#include)g ()390 4134 y(#include)g()390 4354 y(int)390 4463 y(func)h(\(double)e(t,)j(const)e(double)g(y[],)h (double)f(f[],)676 4573 y(void)h(*params\))390 4682 y({)485 4792 y(\(void\)\(t\);)e(/*)j(avoid)e(unused)g(parameter)f(warning)h(*/) 485 4902 y(double)h(mu)g(=)g(*\(double)f(*\)params;)485 5011 y(f[0])h(=)h(y[1];)485 5121 y(f[1])f(=)h(-y[0])e(-)h (mu*y[1]*\(y[0]*y[0])c(-)48 b(1\);)485 5230 y(return)f(GSL_SUCCESS;)390 5340 y(})p eop end %%Page: 344 362 TeXDict begin 344 361 bop 150 -116 a FK(Chapter)30 b(27:)41 b(Ordinary)29 b(Di\013eren)m(tial)k(Equations)1690 b(344)390 408 y FH(int)390 518 y(jac)47 b(\(double)f(t,)h(const)f(double)g(y[],)h (double)f(*dfdy,)629 628 y(double)g(dfdt[],)g(void)g(*params\))390 737 y({)485 847 y(\(void\)\(t\);)f(/*)j(avoid)e(unused)g(parameter)f (warning)h(*/)485 956 y(double)h(mu)g(=)g(*\(double)f(*\)params;)485 1066 y(gsl_matrix_view)e(dfdy_mat)581 1176 y(=)j(gsl_matrix_view_array) 42 b(\(dfdy,)k(2,)i(2\);)485 1285 y(gsl_matrix)d(*)j(m)f(=)h (&dfdy_mat.matrix;)485 1395 y(gsl_matrix_set)c(\(m,)j(0,)g(0,)h(0.0\);) 485 1504 y(gsl_matrix_set)c(\(m,)j(0,)g(1,)h(1.0\);)485 1614 y(gsl_matrix_set)c(\(m,)j(1,)g(0,)h(-2.0*mu*y[0]*y[1])43 b(-)k(1.0\);)485 1724 y(gsl_matrix_set)d(\(m,)j(1,)g(1,)h (-mu*\(y[0]*y[0])c(-)j(1.0\)\);)485 1833 y(dfdt[0])f(=)i(0.0;)485 1943 y(dfdt[1])e(=)i(0.0;)485 2052 y(return)f(GSL_SUCCESS;)390 2162 y(})390 2381 y(int)390 2491 y(main)g(\(void\))390 2600 y({)485 2710 y(double)g(mu)g(=)g(10;)485 2819 y(gsl_odeiv2_system) d(sys)i(=)i({func,)e(jac,)h(2,)g(&mu};)485 3039 y(gsl_odeiv2_driver)d (*)j(d)g(=)581 3148 y(gsl_odeiv2_driver_alloc_)o(y_ne)o(w)42 b(\(&sys,)k(gsl_odeiv2_step_rk8pd,)2013 3258 y(1e-6,)g(1e-6,)g(0.0\);) 485 3367 y(int)h(i;)485 3477 y(double)g(t)g(=)g(0.0,)g(t1)g(=)h(100.0;) 485 3587 y(double)f(y[2])f(=)i({)f(1.0,)g(0.0)g(};)485 3806 y(for)g(\(i)h(=)f(1;)g(i)h(<=)f(100;)f(i++\))581 3915 y({)676 4025 y(double)g(ti)i(=)f(i)h(*)f(t1)g(/)h(100.0;)676 4134 y(int)f(status)f(=)i(gsl_odeiv2_driver_apply)41 b(\(d,)47 b(&t,)g(ti,)g(y\);)676 4354 y(if)h(\(status)d(!=)j (GSL_SUCCESS\))772 4463 y({)867 4573 y(printf)e(\("error,)g(return)g (value=\045d\\n",)e(status\);)867 4682 y(break;)772 4792 y(})676 5011 y(printf)i(\("\045.5e)h(\045.5e)f(\045.5e\\n",)g(t,)h (y[0],)f(y[1]\);)581 5121 y(})485 5340 y(gsl_odeiv2_driver_free)c (\(d\);)p eop end %%Page: 345 363 TeXDict begin 345 362 bop 150 -116 a FK(Chapter)30 b(27:)41 b(Ordinary)29 b(Di\013eren)m(tial)k(Equations)1690 b(345)485 299 y FH(return)47 b(0;)390 408 y(})150 555 y FK(The)33 b(user)f(can)i(w)m(ork)f(with)g(the)h(lo)m(w)m(er)g(lev)m(el)h (functions)e(directly)-8 b(,)35 b(as)f(in)f(the)g(follo)m(wing)i (example.)50 b(In)150 664 y(this)33 b(case)h(an)f(in)m(termediate)h (result)f(is)g(prin)m(ted)g(after)g(eac)m(h)h(successful)f(step)g (instead)g(of)g(equidistan)m(t)150 774 y(time)e(p)s(oin)m(ts.)390 920 y FH(int)390 1029 y(main)47 b(\(void\))390 1139 y({)485 1249 y(const)g(gsl_odeiv2_step_type)42 b(*)48 b(T)581 1358 y(=)f(gsl_odeiv2_step_rk8pd;)485 1577 y(gsl_odeiv2_step)d(*)k(s) 581 1687 y(=)f(gsl_odeiv2_step_alloc)42 b(\(T,)47 b(2\);)485 1797 y(gsl_odeiv2_control)c(*)48 b(c)581 1906 y(=)f (gsl_odeiv2_control_y_new)42 b(\(1e-6,)k(0.0\);)485 2016 y(gsl_odeiv2_evolve)e(*)j(e)581 2125 y(=)g(gsl_odeiv2_evolve_alloc)42 b(\(2\);)485 2345 y(double)47 b(mu)g(=)g(10;)485 2454 y(gsl_odeiv2_system)d(sys)i(=)i({func,)e(jac,)h(2,)g(&mu};)485 2673 y(double)g(t)g(=)g(0.0,)g(t1)g(=)h(100.0;)485 2783 y(double)f(h)g(=)g(1e-6;)485 2892 y(double)g(y[2])f(=)i({)f(1.0,)g(0.0) g(};)485 3112 y(while)g(\(t)g(<)g(t1\))581 3221 y({)676 3331 y(int)g(status)f(=)i(gsl_odeiv2_evolve_apply)41 b(\(e,)47 b(c,)g(s,)2442 3440 y(&sys,)2442 3550 y(&t,)g(t1,)2442 3660 y(&h,)g(y\);)676 3879 y(if)h(\(status)d(!=)j(GSL_SUCCESS\))867 3988 y(break;)676 4208 y(printf)e(\("\045.5e)h(\045.5e)f(\045.5e\\n",)g (t,)h(y[0],)f(y[1]\);)581 4317 y(})485 4536 y(gsl_odeiv2_evolve_free)c (\(e\);)485 4646 y(gsl_odeiv2_control_free)g(\(c\);)485 4755 y(gsl_odeiv2_step_free)h(\(s\);)485 4865 y(return)k(0;)390 4975 y(})150 5121 y FK(F)-8 b(or)48 b(functions)f(with)g(m)m(ultiple)h (parameters,)k(the)c(appropriate)f(information)h(can)g(b)s(e)e(passed)h (in)150 5230 y(through)35 b(the)h FD(params)j FK(argumen)m(t)d(in)f FH(gsl_odeiv2_system)c FK(de\014nition)36 b(\()p FD(m)m(u)f FK(in)h(this)f(example\))i(b)m(y)150 5340 y(using)30 b(a)h(p)s(oin)m(ter)f(to)h(a)g(struct.)p eop end %%Page: 346 364 TeXDict begin 346 363 bop 150 -116 a FK(Chapter)30 b(27:)41 b(Ordinary)29 b(Di\013eren)m(tial)k(Equations)1690 b(346)275 1528 y @beginspecial 50 @llx 50 @lly 410 @urx 302 @ury 2448 @rwi @setspecial %%BeginDocument: vdp.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: vdp.eps %%Creator: gnuplot 3.5 (pre 3.6) patchlevel beta 347 %%CreationDate: Mon Jun 11 17:56:56 2001 %%DocumentFonts: (atend) %%BoundingBox: 50 50 410 302 %%Orientation: Portrait %%EndComments /gnudict 120 dict def gnudict begin /Color false def /Solid false def /gnulinewidth 5.000 def /userlinewidth gnulinewidth def /vshift -46 def /dl {10 mul} def /hpt_ 31.5 def /vpt_ 31.5 def /hpt hpt_ def /vpt vpt_ def /M {moveto} bind def /L {lineto} bind def /R {rmoveto} bind def /V {rlineto} bind def /vpt2 vpt 2 mul def /hpt2 hpt 2 mul def /Lshow { currentpoint stroke M 0 vshift R show } def /Rshow { currentpoint stroke M dup stringwidth pop neg vshift R show } def /Cshow { currentpoint stroke M dup stringwidth pop -2 div vshift R show } def /UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def /DL { Color {setrgbcolor Solid {pop []} if 0 setdash } {pop pop pop Solid {pop []} if 0 setdash} ifelse } def /BL { stroke gnulinewidth 2 mul setlinewidth } def /AL { stroke gnulinewidth 2 div setlinewidth } def /UL { gnulinewidth mul /userlinewidth exch def } def /PL { stroke userlinewidth setlinewidth } def /LTb { BL [] 0 0 0 DL } def /LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def /LT0 { PL [] 1 0 0 DL } def /LT1 { PL [4 dl 2 dl] 0 1 0 DL } def /LT2 { PL [2 dl 3 dl] 0 0 1 DL } def /LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def /LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def /LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def /LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def /LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def /LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def /Pnt { stroke [] 0 setdash gsave 1 setlinecap M 0 0 V stroke grestore } def /Dia { stroke [] 0 setdash 2 copy vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke Pnt } def /Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V currentpoint stroke M hpt neg vpt neg R hpt2 0 V stroke } def /Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke Pnt } def /Crs { stroke [] 0 setdash exch hpt sub exch vpt add M hpt2 vpt2 neg V currentpoint stroke M hpt2 neg 0 R hpt2 vpt2 V stroke } def /TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke Pnt } def /Star { 2 copy Pls Crs } def /BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath fill } def /TriUF { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath fill } def /TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke Pnt } def /TriDF { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath fill} def /DiaF { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath fill } def /Pent { stroke [] 0 setdash 2 copy gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore Pnt } def /PentF { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath fill grestore } def /Circle { stroke [] 0 setdash 2 copy hpt 0 360 arc stroke Pnt } def /CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def /C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def /C1 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill vpt 0 360 arc closepath } bind def /C2 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath } bind def /C3 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill vpt 0 360 arc closepath } bind def /C4 { BL [] 0 setdash 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc closepath } bind def /C5 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc } bind def /C6 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 270 arc closepath fill vpt 0 360 arc closepath } bind def /C7 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 270 arc closepath fill vpt 0 360 arc closepath } bind def /C8 { BL [] 0 setdash 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath } bind def /C9 { BL [] 0 setdash 2 copy moveto 2 copy vpt 270 450 arc closepath fill vpt 0 360 arc closepath } bind def /C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath } bind def /C11 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath } bind def /C12 { BL [] 0 setdash 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath } bind def /C13 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath } bind def /C14 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 360 arc closepath fill vpt 0 360 arc } bind def /C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill vpt 0 360 arc closepath } bind def /Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath } bind def /Square { dup Rec } bind def /Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def /S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def /S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def /S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def /S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def /S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def /S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def /S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill 2 copy vpt Square fill Bsquare } bind def /S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def /S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def /S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def /S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def /S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy vpt Square fill Bsquare } bind def /S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def /D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def /D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def /D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def /D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def /D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def /D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def /D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def /D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def /D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def /D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def /D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def /D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def /D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def /D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def /D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def /D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def /DiaE { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke } def /BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke } def /TriUE { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke } def /TriDE { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke } def /PentE { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore } def /CircE { stroke [] 0 setdash hpt 0 360 arc stroke } def /Opaque { gsave closepath 1 setgray fill grestore 0 setgray closepath } def /DiaW { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V Opaque stroke } def /BoxW { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V Opaque stroke } def /TriUW { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V Opaque stroke } def /TriDW { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V Opaque stroke } def /PentW { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat Opaque stroke grestore } def /CircW { stroke [] 0 setdash hpt 0 360 arc Opaque stroke } def /BoxFill { gsave Rec 1 setgray fill grestore } def end %%EndProlog gnudict begin gsave 50 50 translate 0.050 0.050 scale 0 setgray newpath (Helvetica) findfont 140 scalefont setfont 1.000 UL LTb 336 739 M 63 0 V 6633 0 R -63 0 V 252 739 M (-4) Rshow 336 1658 M 63 0 V 6633 0 R -63 0 V -6717 0 R (-2) Rshow 336 2576 M 63 0 V 6633 0 R -63 0 V -6717 0 R (0) Rshow 336 3494 M 63 0 V 6633 0 R -63 0 V -6717 0 R (2) Rshow 336 4413 M 63 0 V 6633 0 R -63 0 V -6717 0 R (4) Rshow 336 280 M 0 63 V 0 4529 R 0 -63 V 336 140 M (0) Cshow 1006 280 M 0 63 V 0 4529 R 0 -63 V 0 -4669 R (10) Cshow 1675 280 M 0 63 V 0 4529 R 0 -63 V 0 -4669 R (20) Cshow 2345 280 M 0 63 V 0 4529 R 0 -63 V 0 -4669 R (30) Cshow 3014 280 M 0 63 V 0 4529 R 0 -63 V 0 -4669 R (40) Cshow 3684 280 M 0 63 V 0 4529 R 0 -63 V 0 -4669 R (50) Cshow 4354 280 M 0 63 V 0 4529 R 0 -63 V 0 -4669 R (60) Cshow 5023 280 M 0 63 V 0 4529 R 0 -63 V 0 -4669 R (70) Cshow 5693 280 M 0 63 V 0 4529 R 0 -63 V 0 -4669 R (80) Cshow 6362 280 M 0 63 V 0 4529 R 0 -63 V 0 -4669 R (90) Cshow 7032 280 M 0 63 V 0 4529 R 0 -63 V 0 -4669 R (100) Cshow 1.000 UL LTb 336 280 M 6696 0 V 0 4592 V -6696 0 V 336 280 L 1.000 UP 1.000 UL LT0 336 3035 Pls 336 3035 Pls 336 3035 Pls 336 3035 Pls 336 3035 Pls 336 3035 Pls 337 3035 Pls 343 3033 Pls 361 3002 Pls 371 2964 Pls 379 2914 Pls 385 2845 Pls 390 2743 Pls 393 2642 Pls 396 2508 Pls 399 2310 Pls 400 2140 Pls 402 1961 Pls 404 1832 Pls 406 1746 Pls 407 1698 Pls 409 1672 Pls 411 1660 Pls 413 1655 Pls 415 1654 Pls 418 1654 Pls 420 1655 Pls 424 1656 Pls 427 1658 Pls 432 1660 Pls 437 1662 Pls 444 1665 Pls 452 1669 Pls 463 1674 Pls 473 1679 Pls 483 1684 Pls 494 1689 Pls 504 1694 Pls 515 1699 Pls 525 1705 Pls 536 1710 Pls 546 1715 Pls 557 1721 Pls 568 1726 Pls 578 1732 Pls 589 1738 Pls 600 1744 Pls 611 1750 Pls 623 1756 Pls 634 1762 Pls 645 1769 Pls 657 1775 Pls 668 1782 Pls 680 1789 Pls 692 1796 Pls 704 1804 Pls 716 1811 Pls 728 1819 Pls 740 1827 Pls 753 1836 Pls 766 1845 Pls 779 1854 Pls 792 1864 Pls 805 1874 Pls 819 1885 Pls 833 1896 Pls 847 1908 Pls 862 1922 Pls 877 1936 Pls 892 1952 Pls 908 1969 Pls 925 1990 Pls 943 2015 Pls 962 2047 Pls 984 2095 Pls 998 2143 Pls 1007 2191 Pls 1014 2250 Pls 1020 2333 Pls 1024 2429 Pls 1027 2541 Pls 1029 2691 Pls 1032 2903 Pls 1034 3077 Pls 1036 3242 Pls 1037 3365 Pls 1039 3431 Pls 1041 3468 Pls 1042 3488 Pls 1044 3497 Pls 1046 3500 Pls 1049 3501 Pls 1051 3500 Pls 1054 3499 Pls 1057 3498 Pls 1061 3496 Pls 1066 3494 Pls 1072 3492 Pls 1079 3488 Pls 1089 3484 Pls 1099 3479 Pls 1109 3474 Pls 1119 3469 Pls 1130 3464 Pls 1140 3459 Pls 1150 3454 Pls 1161 3449 Pls 1171 3444 Pls 1182 3438 Pls 1193 3433 Pls 1203 3427 Pls 1214 3422 Pls 1225 3416 Pls 1236 3410 Pls 1247 3404 Pls 1258 3398 Pls 1269 3392 Pls 1281 3385 Pls 1292 3379 Pls 1304 3372 Pls 1315 3365 Pls 1327 3358 Pls 1339 3350 Pls 1351 3343 Pls 1363 3335 Pls 1376 3327 Pls 1388 3318 Pls 1401 3310 Pls 1414 3301 Pls 1427 3291 Pls 1440 3281 Pls 1454 3270 Pls 1468 3259 Pls 1482 3247 Pls 1496 3234 Pls 1511 3220 Pls 1526 3205 Pls 1542 3188 Pls 1559 3168 Pls 1576 3145 Pls 1595 3115 Pls 1616 3073 Pls 1634 3020 Pls 1643 2974 Pls 1651 2919 Pls 1657 2845 Pls 1662 2744 Pls 1665 2639 Pls 1667 2501 Pls 1670 2301 Pls 1672 2129 Pls 1674 1952 Pls 1675 1825 Pls 1677 1741 Pls 1679 1694 Pls 1681 1669 Pls 1682 1657 Pls 1684 1653 Pls 1687 1651 Pls 1689 1651 Pls 1692 1652 Pls 1695 1654 Pls 1699 1655 Pls 1703 1657 Pls 1708 1660 Pls 1715 1663 Pls 1724 1667 Pls 1734 1671 Pls 1744 1676 Pls 1755 1681 Pls 1765 1686 Pls 1775 1691 Pls 1786 1696 Pls 1796 1701 Pls 1807 1707 Pls 1817 1712 Pls 1828 1717 Pls 1838 1723 Pls 1849 1728 Pls 1860 1734 Pls 1871 1740 Pls 1882 1746 Pls 1893 1752 Pls 1904 1758 Pls 1916 1765 Pls 1927 1771 Pls 1938 1778 Pls 1950 1785 Pls 1962 1792 Pls 1974 1799 Pls 1986 1807 Pls 1998 1814 Pls 2010 1822 Pls 2023 1831 Pls 2035 1839 Pls 2048 1848 Pls 2061 1858 Pls 2074 1868 Pls 2088 1878 Pls 2101 1889 Pls 2116 1901 Pls 2130 1913 Pls 2145 1927 Pls 2160 1942 Pls 2176 1958 Pls 2192 1977 Pls 2209 1999 Pls 2227 2026 Pls 2247 2062 Pls 2270 2122 Pls 2279 2164 Pls 2288 2216 Pls 2294 2283 Pls 2301 2415 Pls 2304 2516 Pls 2306 2656 Pls 2309 2858 Pls 2311 3029 Pls 2313 3205 Pls 2314 3331 Pls 2316 3414 Pls 2318 3460 Pls 2319 3484 Pls 2321 3495 Pls 2323 3500 Pls 2325 3501 Pls 2328 3501 Pls 2331 3500 Pls 2334 3498 Pls 2338 3497 Pls 2342 3495 Pls 2347 3492 Pls 2354 3489 Pls 2363 3485 Pls 2373 3480 Pls 2383 3476 Pls 2394 3471 Pls 2404 3466 Pls 2414 3461 Pls 2425 3456 Pls 2435 3451 Pls 2446 3445 Pls 2456 3440 Pls 2467 3435 Pls 2477 3429 Pls 2488 3423 Pls 2499 3418 Pls 2510 3412 Pls 2521 3406 Pls 2532 3400 Pls 2543 3394 Pls 2555 3387 Pls 2566 3381 Pls 2577 3374 Pls 2589 3367 Pls 2601 3360 Pls 2613 3353 Pls 2625 3345 Pls 2637 3337 Pls 2649 3329 Pls 2662 3321 Pls 2674 3312 Pls 2687 3303 Pls 2700 3294 Pls 2713 3284 Pls 2727 3274 Pls 2741 3263 Pls 2755 3251 Pls 2769 3238 Pls 2784 3225 Pls 2799 3210 Pls 2815 3194 Pls 2831 3175 Pls 2848 3153 Pls 2867 3126 Pls 2887 3089 Pls 2909 3027 Pls 2919 2987 Pls 2927 2934 Pls 2933 2866 Pls 2940 2732 Pls 2942 2630 Pls 2945 2488 Pls 2948 2283 Pls 2950 2111 Pls 2951 1938 Pls 2953 1801 Pls 2955 1730 Pls 2957 1689 Pls 2958 1666 Pls 2960 1656 Pls 2962 1652 Pls 2965 1651 Pls 2967 1651 Pls 2970 1652 Pls 2973 1654 Pls 2977 1656 Pls 2982 1658 Pls 2987 1660 Pls 2994 1663 Pls 3004 1668 Pls 3014 1672 Pls 3024 1677 Pls 3034 1682 Pls 3044 1687 Pls 3055 1692 Pls 3065 1697 Pls 3075 1702 Pls 3086 1708 Pls 3096 1713 Pls 3107 1718 Pls 3118 1724 Pls 3129 1729 Pls 3139 1735 Pls 3150 1741 Pls 3161 1747 Pls 3173 1753 Pls 3184 1759 Pls 3195 1766 Pls 3206 1772 Pls 3218 1779 Pls 3230 1786 Pls 3241 1793 Pls 3253 1800 Pls 3265 1808 Pls 3277 1816 Pls 3290 1824 Pls 3302 1832 Pls 3315 1841 Pls 3328 1850 Pls 3341 1859 Pls 3354 1869 Pls 3368 1880 Pls 3381 1891 Pls 3396 1903 Pls 3410 1916 Pls 3425 1929 Pls 3440 1944 Pls 3456 1961 Pls 3472 1980 Pls 3490 2003 Pls 3508 2031 Pls 3529 2070 Pls 3548 2125 Pls 3558 2169 Pls 3566 2222 Pls 3572 2292 Pls 3578 2406 Pls 3581 2506 Pls 3583 2642 Pls 3586 2840 Pls 3588 3011 Pls 3590 3191 Pls 3592 3320 Pls 3593 3407 Pls 3595 3456 Pls 3597 3482 Pls 3599 3494 Pls 3600 3499 Pls 3603 3501 Pls 3605 3501 Pls 3608 3500 Pls 3611 3499 Pls 3615 3497 Pls 3619 3495 Pls 3624 3493 Pls 3630 3490 Pls 3639 3486 Pls 3649 3481 Pls 3660 3476 Pls 3670 3471 Pls 3681 3466 Pls 3691 3461 Pls 3702 3456 Pls 3712 3451 Pls 3723 3445 Pls 3733 3440 Pls 3744 3435 Pls 3755 3429 Pls 3765 3424 Pls 3776 3418 Pls 3787 3412 Pls 3798 3406 Pls 3809 3400 Pls 3821 3394 Pls 3832 3387 Pls 3843 3381 Pls 3855 3374 Pls 3866 3367 Pls 3878 3360 Pls 3890 3353 Pls 3902 3345 Pls 3914 3338 Pls 3926 3330 Pls 3939 3321 Pls 3951 3313 Pls 3964 3304 Pls 3977 3294 Pls 3991 3284 Pls 4004 3274 Pls 4018 3263 Pls 4032 3251 Pls 4046 3239 Pls 4061 3225 Pls 4076 3210 Pls 4092 3194 Pls 4108 3175 Pls 4125 3153 Pls 4144 3126 Pls 4164 3090 Pls 4186 3029 Pls 4196 2988 Pls 4204 2936 Pls 4210 2869 Pls 4217 2736 Pls 4220 2635 Pls 4222 2495 Pls 4225 2292 Pls 4227 2121 Pls 4229 1945 Pls 4231 1820 Pls 4232 1738 Pls 4234 1692 Pls 4236 1667 Pls 4238 1657 Pls 4240 1652 Pls 4242 1651 Pls 4244 1651 Pls 4247 1652 Pls 4250 1654 Pls 4254 1655 Pls 4258 1657 Pls 4264 1660 Pls 4270 1663 Pls 4279 1667 Pls 4290 1672 Pls 4300 1677 Pls 4310 1681 Pls 4320 1686 Pls 4331 1691 Pls 4341 1696 Pls 4351 1702 Pls 4362 1707 Pls 4373 1712 Pls 4383 1718 Pls 4394 1723 Pls 4405 1729 Pls 4415 1734 Pls 4426 1740 Pls 4437 1746 Pls 4448 1752 Pls 4460 1758 Pls 4471 1765 Pls 4482 1771 Pls 4494 1778 Pls 4506 1785 Pls 4517 1792 Pls 4529 1799 Pls 4541 1807 Pls 4553 1815 Pls 4566 1823 Pls 4578 1831 Pls 4591 1840 Pls 4604 1849 Pls 4617 1858 Pls 4630 1868 Pls 4643 1878 Pls 4657 1889 Pls 4671 1901 Pls 4685 1914 Pls 4700 1927 Pls 4715 1942 Pls 4731 1959 Pls 4748 1978 Pls 4765 2000 Pls 4783 2027 Pls 4803 2064 Pls 4826 2126 Pls 4835 2166 Pls 4843 2220 Pls 4849 2288 Pls 4856 2423 Pls 4859 2526 Pls 4861 2669 Pls 4864 2875 Pls 4866 3048 Pls 4868 3219 Pls 4870 3351 Pls 4871 3422 Pls 4873 3463 Pls 4875 3487 Pls 4877 3496 Pls 4879 3500 Pls 4881 3501 Pls 4883 3501 Pls 4886 3500 Pls 4890 3498 Pls 4893 3496 Pls 4898 3494 Pls 4903 3492 Pls 4910 3489 Pls 4920 3484 Pls 4930 3479 Pls 4940 3475 Pls 4950 3470 Pls 4961 3465 Pls 4971 3460 Pls 4981 3455 Pls 4992 3450 Pls 5002 3444 Pls 5013 3439 Pls 5024 3434 Pls 5034 3428 Pls 5045 3423 Pls 5056 3417 Pls 5067 3411 Pls 5078 3405 Pls 5089 3399 Pls 5100 3393 Pls 5111 3386 Pls 5123 3380 Pls 5134 3373 Pls 5146 3366 Pls 5158 3359 Pls 5170 3352 Pls 5182 3344 Pls 5194 3336 Pls 5206 3328 Pls 5219 3320 Pls 5231 3311 Pls 5244 3302 Pls 5257 3292 Pls 5271 3282 Pls 5284 3272 Pls 5298 3261 Pls 5312 3249 Pls 5326 3236 Pls 5341 3223 Pls 5357 3207 Pls 5372 3191 Pls 5389 3171 Pls 5406 3149 Pls 5425 3120 Pls 5445 3081 Pls 5464 3027 Pls 5474 2982 Pls 5482 2929 Pls 5488 2859 Pls 5494 2747 Pls 5497 2647 Pls 5500 2511 Pls 5502 2313 Pls 5504 2142 Pls 5506 1962 Pls 5508 1833 Pls 5509 1746 Pls 5511 1697 Pls 5513 1670 Pls 5515 1658 Pls 5517 1653 Pls 5519 1651 Pls 5521 1651 Pls 5524 1652 Pls 5527 1653 Pls 5531 1655 Pls 5535 1657 Pls 5540 1659 Pls 5547 1662 Pls 5555 1666 Pls 5566 1671 Pls 5576 1676 Pls 5587 1681 Pls 5597 1686 Pls 5608 1691 Pls 5618 1696 Pls 5629 1701 Pls 5639 1707 Pls 5650 1712 Pls 5660 1717 Pls 5671 1723 Pls 5682 1728 Pls 5693 1734 Pls 5704 1740 Pls 5715 1746 Pls 5726 1752 Pls 5737 1758 Pls 5748 1765 Pls 5760 1771 Pls 5771 1778 Pls 5783 1785 Pls 5794 1792 Pls 5806 1799 Pls 5818 1807 Pls 5830 1814 Pls 5843 1822 Pls 5855 1831 Pls 5868 1839 Pls 5881 1848 Pls 5894 1858 Pls 5907 1868 Pls 5920 1878 Pls 5934 1889 Pls 5948 1901 Pls 5963 1913 Pls 5977 1927 Pls 5993 1942 Pls 6008 1958 Pls 6025 1977 Pls 6042 1999 Pls 6060 2026 Pls 6080 2063 Pls 6103 2124 Pls 6112 2164 Pls 6120 2217 Pls 6127 2284 Pls 6133 2418 Pls 6136 2519 Pls 6139 2660 Pls 6141 2863 Pls 6143 3035 Pls 6145 3210 Pls 6147 3335 Pls 6148 3416 Pls 6150 3461 Pls 6152 3485 Pls 6154 3496 Pls 6156 3500 Pls 6158 3501 Pls 6161 3501 Pls 6163 3500 Pls 6167 3498 Pls 6170 3497 Pls 6175 3495 Pls 6180 3492 Pls 6187 3489 Pls 6196 3485 Pls 6206 3480 Pls 6217 3475 Pls 6227 3470 Pls 6237 3465 Pls 6247 3460 Pls 6258 3455 Pls 6268 3450 Pls 6279 3445 Pls 6289 3440 Pls 6300 3434 Pls 6310 3429 Pls 6321 3423 Pls 6332 3417 Pls 6343 3412 Pls 6354 3406 Pls 6365 3400 Pls 6376 3393 Pls 6388 3387 Pls 6399 3380 Pls 6411 3374 Pls 6422 3367 Pls 6434 3360 Pls 6446 3352 Pls 6458 3345 Pls 6470 3337 Pls 6482 3329 Pls 6495 3321 Pls 6507 3312 Pls 6520 3303 Pls 6533 3294 Pls 6547 3284 Pls 6560 3273 Pls 6574 3262 Pls 6588 3250 Pls 6602 3238 Pls 6617 3224 Pls 6632 3209 Pls 6648 3193 Pls 6664 3174 Pls 6682 3152 Pls 6700 3124 Pls 6720 3086 Pls 6743 3023 Pls 6752 2983 Pls 6760 2928 Pls 6766 2859 Pls 6772 2747 Pls 6775 2647 Pls 6777 2511 Pls 6780 2313 Pls 6782 2142 Pls 6784 1962 Pls 6785 1833 Pls 6787 1746 Pls 6789 1697 Pls 6790 1670 Pls 6792 1658 Pls 6794 1653 Pls 6796 1651 Pls 6799 1651 Pls 6801 1652 Pls 6805 1653 Pls 6808 1655 Pls 6812 1657 Pls 6818 1659 Pls 6824 1662 Pls 6833 1666 Pls 6843 1671 Pls 6854 1676 Pls 6864 1681 Pls 6875 1686 Pls 6885 1691 Pls 6896 1696 Pls 6906 1701 Pls 6917 1707 Pls 6927 1712 Pls 6938 1717 Pls 6949 1723 Pls 6959 1728 Pls 6970 1734 Pls 6981 1740 Pls 6992 1746 Pls 7003 1752 Pls 7014 1758 Pls 7026 1765 Pls 7032 1768 Pls stroke grestore end showpage %%Trailer %%DocumentFonts: Helvetica %%EndDocument @endspecial 812 1687 a(Numerical)31 b(solution)g(of)g(the)f(V)-8 b(an)31 b(der)f(P)m(ol)h(oscillator)i(equation)1014 1797 y(using)d(Prince-Dormand)h(8th)f(order)g(Runge-Kutta.)150 1924 y(It)22 b(is)g(also)g(p)s(ossible)f(to)i(w)m(ork)f(with)f(a)h (non-adaptiv)m(e)h(in)m(tegrator,)i(using)d(only)f(the)h(stepping)g (function)f(it-)150 2034 y(self,)32 b FH(gsl_odeiv2_driver_apply_)o (fixe)o(d_s)o(tep)25 b FK(or)31 b FH(gsl_odeiv2_evolve_apply_)o(fixe)o (d_st)o(ep)p FK(.)150 2144 y(The)f(follo)m(wing)i(program)e(uses)g(the) g(driv)m(er)g(lev)m(el)i(function,)e(with)h(fourth-order)e(Runge-Kutta) i(step-)150 2253 y(ping)f(function)g(with)g(a)h(\014xed)f(stepsize)h (of)f(0.001.)390 2381 y FH(int)390 2491 y(main)47 b(\(void\))390 2600 y({)485 2710 y(double)g(mu)g(=)g(10;)485 2819 y(gsl_odeiv2_system) d(sys)i(=)i({)f(func,)g(jac,)f(2,)i(&mu)e(};)485 3039 y(gsl_odeiv2_driver)e(*d)j(=)581 3148 y(gsl_odeiv2_driver_alloc_)o (y_ne)o(w)42 b(\(&sys,)k(gsl_odeiv2_step_rk4,)2060 3258 y(1e-3,)h(1e-8,)f(1e-8\);)485 3477 y(double)h(t)g(=)g(0.0;)485 3587 y(double)g(y[2])f(=)i({)f(1.0,)g(0.0)g(};)485 3696 y(int)g(i,)h(s;)485 3915 y(for)f(\(i)h(=)f(0;)g(i)h(<)f(100;)g(i++\)) 581 4025 y({)676 4134 y(s)h(=)f(gsl_odeiv2_driver_apply_f)o(ixed)o (_ste)o(p)42 b(\(d,)47 b(&t,)g(1e-3,)f(1000,)g(y\);)676 4354 y(if)i(\(s)f(!=)g(GSL_SUCCESS\))772 4463 y({)867 4573 y(printf)f(\("error:)94 b(driver)46 b(returned)f(\045d\\n",)h (s\);)867 4682 y(break;)772 4792 y(})676 5011 y(printf)g(\("\045.5e)h (\045.5e)f(\045.5e\\n",)g(t,)h(y[0],)f(y[1]\);)581 5121 y(})485 5340 y(gsl_odeiv2_driver_free)c(\(d\);)p eop end %%Page: 347 365 TeXDict begin 347 364 bop 150 -116 a FK(Chapter)30 b(27:)41 b(Ordinary)29 b(Di\013eren)m(tial)k(Equations)1690 b(347)485 299 y FH(return)47 b(s;)390 408 y(})150 641 y FJ(27.7)68 b(References)47 b(and)d(F)-11 b(urther)44 b(Reading)330 800 y FK(Asc)m(her,)69 b(U.M.,)g(P)m(etzold,)h(L.R.,)e FD(Computer)60 b(Metho)s(ds)g(for)h(Ordinary)e(Di\013eren)m(tial)k(and) 330 910 y(Di\013eren)m(tial-Algebraic)35 b(Equations)p FK(,)30 b(SIAM,)h(Philadelphia,)g(1998.)330 1044 y(Hairer,)50 b(E.,)g(Norsett,)g(S.)c(P)-8 b(.,)50 b(W)-8 b(anner,)49 b(G.,)h FD(Solving)c(Ordinary)e(Di\013eren)m(tial)k(Equations)e(I:)330 1154 y(Nonsti\013)31 b(Problems)p FK(,)f(Springer,)g(Berlin,)h(1993.) 330 1289 y(Hairer,)74 b(E.,)f(W)-8 b(anner,)74 b(G.,)g FD(Solving)64 b(Ordinary)f(Di\013eren)m(tial)k(Equations)e(I)s(I:)f (Sti\013)h(and)330 1398 y(Di\013eren)m(tial-Algebraic)35 b(Problems)p FK(,)30 b(Springer,)f(Berlin,)i(1996.)275 1557 y(Man)m(y)24 b(of)g(the)f(basic)h(Runge-Kutta)h(form)m(ulas)e(can) 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b(Math.)i(Soft)m(w)m(are,)31 b(1,)g(71{96,)i(1975.)330 2853 y(P)-8 b(.)30 b(N.)f(Bro)m(wn,)h(G.)f(D.)h(Byrne)f(and)f(A.)i(C.)f (Hindmarsh,)f(\\V)m(ODE:)i(A)f(V)-8 b(ariable-co)s(e\016cien)m(t)33 b(ODE)330 2962 y(Solv)m(er.",)f(SIAM)e(J.)g(Sci.)41 b(Stat.)h(Comput.)d (10,)32 b(1038{1051,)j(1989.)330 3097 y(A.)26 b(C.)g(Hindmarsh,)f(P)-8 b(.)26 b(N.)g(Bro)m(wn,)h(K.)f(E.)g(Gran)m(t,)h(S.)e(L.)h(Lee,)i(R.)d (Serban,)h(D.)g(E.)g(Sh)m(umak)m(er)g(and)330 3206 y(C.)f(S.)g(W)-8 b(o)s(o)s(dw)m(ard,)27 b(\\SUNDIALS:)f(Suite)f(of)h(Nonlinear)g(and)f (Di\013eren)m(tial/Algebraic)30 b(Equation)330 3316 y(Solv)m(ers.",)i (A)m(CM)f(T)-8 b(rans.)40 b(Math.)h(Soft)m(w)m(are)32 b(31,)f(363{396,)j(2005.)p eop end %%Page: 348 366 TeXDict begin 348 365 bop 150 -116 a FK(Chapter)30 b(28:)41 b(In)m(terp)s(olation)2437 b(348)150 299 y FG(28)80 b(In)l(terp)t (olation)150 570 y FK(This)22 b(c)m(hapter)h(describ)s(es)e(functions)h (for)h(p)s(erforming)e(in)m(terp)s(olation.)39 b(The)22 b(library)g(pro)m(vides)h(a)g(v)-5 b(ariet)m(y)150 679 y(of)35 b(in)m(terp)s(olation)i(metho)s(ds,)e(including)g(Cubic,)h (Akima,)h(and)d(Ste\013en)i(splines.)54 b(The)35 b(in)m(terp)s(olation) 150 789 y(t)m(yp)s(es)e(are)g(in)m(terc)m(hangeable,)k(allo)m(wing)d (di\013eren)m(t)g(metho)s(ds)e(to)i(b)s(e)e(used)g(without)h (recompiling.)49 b(In-)150 898 y(terp)s(olations)32 b(can)f(b)s(e)f (de\014ned)f(for)i(b)s(oth)f(normal)g(and)g(p)s(erio)s(dic)g(b)s (oundary)f(conditions.)42 b(Additional)150 1008 y(functions)37 b(are)g(a)m(v)-5 b(ailable)39 b(for)e(computing)g(deriv)-5 b(ativ)m(es)39 b(and)d(in)m(tegrals)j(of)e(in)m(terp)s(olating)h (functions.)150 1118 y(Routines)31 b(are)f(pro)m(vided)g(for)g(in)m (terp)s(olating)i(b)s(oth)e(one)g(and)g(t)m(w)m(o)i(dimensional)e (datasets.)275 1264 y(These)j(in)m(terp)s(olation)j(metho)s(ds)d(pro)s (duce)g(curv)m(es)h(that)h(pass)e(through)h(eac)m(h)h(datap)s(oin)m(t.) 52 b(T)-8 b(o)35 b(in-)150 1374 y(terp)s(olate)d(noisy)e(data)h(with)f 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(vior)g(at)h(the)f(end-p)s(oin)m(ts)f(is)h(determined)f(b)m(y)h(the)g (t)m(yp)s(e)g(of)g(in)m(terp)s(olation)h(used.)150 2511 y FJ(28.2)68 b(1D)46 b(In)l(terp)t(olation)g(F)-11 b(unctions)150 2670 y FK(The)30 b(in)m(terp)s(olation)h(function)f(for)g(a)g(giv)m(en) h(dataset)g(is)g(stored)f(in)f(a)i FH(gsl_interp)c FK(ob)5 b(ject.)42 b(These)30 b(are)150 2780 y(created)h(b)m(y)g(the)f(follo)m (wing)i(functions.)3350 2988 y([F)-8 b(unction])-3599 b Fv(gsl_interp)55 b(*)e(gsl_interp_alloc)d Fu(\()p FD(const)31 b(gsl)p 2097 2988 28 4 v 41 w(in)m(terp)p 2373 2988 V 40 w(t)m(yp)s(e)g(*)f Ft(T)p FD(,)h(size)p 2942 2988 V 41 w(t)565 3098 y Ft(size)p Fu(\))390 3207 y FK(This)j(function)h (returns)f(a)i(p)s(oin)m(ter)f(to)h(a)g(newly)f(allo)s(cated)i(in)m (terp)s(olation)g(ob)5 b(ject)36 b(of)f(t)m(yp)s(e)h FD(T)390 3317 y FK(for)30 b FD(size)36 b FK(data-p)s(oin)m(ts.)3350 3526 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_interp_init)d Fu(\()p FD(gsl)p 1336 3526 V 41 w(in)m(terp)31 b(*)f Ft(interp)p FD(,)j(const)e(double)e Ft(xa)p Fo([])p FD(,)i(const)565 3635 y(double)f Ft(ya)p Fo([])p FD(,)h(size)p 1221 3635 V 41 w(t)g Ft(size)p Fu(\))390 3745 y FK(This)d(function)h(initializes) i(the)e(in)m(terp)s(olation)h(ob)5 b(ject)29 b FD(in)m(terp)j FK(for)d(the)g(data)g(\()p FD(xa)p FK(,)p FD(y)m(a)p FK(\))i(where)e FD(xa)390 3855 y FK(and)j FD(y)m(a)i FK(are)g(arra)m(ys)f(of)h(size)g FD(size)p FK(.)49 b(The)33 b(in)m(terp)s(olation)h(ob)5 b(ject)34 b(\()p FH(gsl_interp)p FK(\))d(do)s(es)i(not)g(sa)m(v)m(e)390 3964 y(the)h(data)g(arra)m(ys)g FD(xa)f FK(and)g FD(y)m(a)h FK(and)f(only)h(stores)g(the)f(static)i (state)g(computed)e(from)g(the)h(data.)390 4074 y(The)28 b FD(xa)h FK(data)h(arra)m(y)f(is)g(alw)m(a)m(ys)h(assumed)e(to)h(b)s (e)g(strictly)g(ordered,)g(with)f(increasing)i FE(x)e FK(v)-5 b(alues;)390 4183 y(the)31 b(b)s(eha)m(vior)f(for)g(other)h (arrangemen)m(ts)g(is)f(not)h(de\014ned.)3350 4392 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_interp_free)c Fu(\()p FD(gsl)p 1389 4392 V 40 w(in)m(terp)31 b(*)g Ft(interp)p Fu(\))390 4502 y FK(This)f(function)g(frees)g(the)h(in)m(terp)s (olation)g(ob)5 b(ject)31 b FD(in)m(terp)p FK(.)150 4753 y FJ(28.3)68 b(1D)46 b(In)l(terp)t(olation)g(T)l(yp)t(es)150 4912 y FK(The)30 b(in)m(terp)s(olation)i(library)d(pro)m(vides)i(the)f (follo)m(wing)i(in)m(terp)s(olation)g(t)m(yp)s(es:)2947 5121 y([In)m(terp)s(olation)f(T)m(yp)s(e])-3600 b Fv(gsl_interp_linear) 390 5230 y FK(Linear)22 b(in)m(terp)s(olation.)40 b(This)21 b(in)m(terp)s(olation)j(metho)s(d)d(do)s(es)h(not)h(require)f(an)m(y)h (additional)g(mem-)390 5340 y(ory)-8 b(.)p eop end %%Page: 349 367 TeXDict begin 349 366 bop 150 -116 a FK(Chapter)30 b(28:)41 b(In)m(terp)s(olation)2437 b(349)2947 299 y([In)m(terp)s(olation)31 b(T)m(yp)s(e])-3600 b Fv(gsl_interp_polynomial)390 408 y FK(P)m(olynomial)37 b(in)m(terp)s(olation.)58 b(This)35 b(metho)s(d)g(should)g(only)g(b)s(e)g(used)g(for)h(in)m(terp)s(olating) g(small)390 518 y(n)m(um)m(b)s(ers)22 b(of)i(p)s(oin)m(ts)f(b)s(ecause) g(p)s(olynomial)h(in)m(terp)s(olation)h(in)m(tro)s(duces)e(large)i (oscillations,)i(ev)m(en)390 628 y(for)37 b(w)m(ell-b)s(eha)m(v)m(ed)h (datasets.)61 b(The)37 b(n)m(um)m(b)s(er)e(of)i(terms)g(in)g(the)g(in)m (terp)s(olating)h(p)s(olynomial)f(is)390 737 y(equal)31 b(to)g(the)g(n)m(um)m(b)s(er)e(of)h(p)s(oin)m(ts.)2947 918 y([In)m(terp)s(olation)h(T)m(yp)s(e])-3600 b Fv(gsl_interp_cspline) 390 1028 y FK(Cubic)44 b(spline)h(with)f(natural)h(b)s(oundary)e (conditions.)85 b(The)45 b(resulting)g(curv)m(e)g(is)g(piecewise)390 1137 y(cubic)c(on)f(eac)m(h)i(in)m(terv)-5 b(al,)45 b(with)c(matc)m (hing)h(\014rst)e(and)g(second)h(deriv)-5 b(ativ)m(es)42 b(at)f(the)g(supplied)390 1247 y(data-p)s(oin)m(ts.)65 b(The)38 b(second)g(deriv)-5 b(ativ)m(e)40 b(is)f(c)m(hosen)f(to)h(b)s (e)f(zero)h(at)g(the)g(\014rst)e(p)s(oin)m(t)h(and)g(last)390 1356 y(p)s(oin)m(t.)2947 1537 y([In)m(terp)s(olation)31 b(T)m(yp)s(e])-3600 b Fv(gsl_interp_cspline_per)q(iod)q(ic)390 1647 y FK(Cubic)42 b(spline)g(with)g(p)s(erio)s(dic)g(b)s(oundary)e (conditions.)77 b(The)42 b(resulting)h(curv)m(e)f(is)h(piecewise)390 1756 y(cubic)e(on)f(eac)m(h)i(in)m(terv)-5 b(al,)45 b(with)c(matc)m (hing)h(\014rst)e(and)g(second)h(deriv)-5 b(ativ)m(es)42 b(at)f(the)g(supplied)390 1866 y(data-p)s(oin)m(ts.)i(The)30 b(deriv)-5 b(ativ)m(es)32 b(at)f(the)g(\014rst)f(and)g(last)i(p)s(oin)m (ts)e(are)h(also)h(matc)m(hed.)42 b(Note)32 b(that)390 1975 y(the)27 b(last)g(p)s(oin)m(t)g(in)g(the)g(data)g(m)m(ust)g(ha)m (v)m(e)h(the)e(same)i(y-v)-5 b(alue)27 b(as)g(the)g(\014rst)f(p)s(oin)m (t,)i(otherwise)f(the)390 2085 y(resulting)j(p)s(erio)s(dic)g(in)m (terp)s(olation)i(will)f(ha)m(v)m(e)g(a)g(discon)m(tin)m(uit)m(y)h(at)f (the)g(b)s(oundary)-8 b(.)2947 2266 y([In)m(terp)s(olation)31 b(T)m(yp)s(e])-3600 b Fv(gsl_interp_akima)390 2375 y FK(Non-rounded)29 b(Akima)i(spline)f(with)g(natural)g(b)s(oundary)e (conditions.)41 b(This)29 b(metho)s(d)h(uses)g(the)390 2485 y(non-rounded)f(corner)h(algorithm)h(of)g(W)-8 b(o)s(dic)m(k)j(a.) 2947 2665 y([In)m(terp)s(olation)31 b(T)m(yp)s(e])-3600 b Fv(gsl_interp_akima_perio)q(dic)390 2775 y FK(Non-rounded)26 b(Akima)h(spline)g(with)g(p)s(erio)s(dic)f(b)s(oundary)f(conditions.)40 b(This)26 b(metho)s(d)g(uses)h(the)390 2885 y(non-rounded)i(corner)h (algorithm)h(of)g(W)-8 b(o)s(dic)m(k)j(a.)2947 3065 y([In)m(terp)s (olation)31 b(T)m(yp)s(e])-3600 b Fv(gsl_interp_steffen)390 3175 y FK(Ste\013en's)34 b(metho)s(d)f(guaran)m(tees)i(the)f (monotonicit)m(y)i(of)e(the)g(in)m(terp)s(olating)h(function)e(b)s(et)m (w)m(een)390 3284 y(the)e(giv)m(en)g(data)g(p)s(oin)m(ts.)41 b(Therefore,)30 b(minima)g(and)g(maxima)h(can)g(only)f(o)s(ccur)g (exactly)j(at)e(the)390 3394 y(data)36 b(p)s(oin)m(ts,)g(and)e(there)h (can)g(nev)m(er)g(b)s(e)f(spurious)f(oscillations)38 b(b)s(et)m(w)m(een)d(data)h(p)s(oin)m(ts.)53 b(The)390 3504 y(in)m(terp)s(olated)33 b(function)e(is)h(piecewise)h(cubic)e(in)h (eac)m(h)h(in)m(terv)-5 b(al.)45 b(The)32 b(resulting)f(curv)m(e)h(and) g(its)390 3613 y(\014rst)38 b(deriv)-5 b(ativ)m(e)39 b(are)g(guaran)m(teed)g(to)g(b)s(e)f(con)m(tin)m(uous,)j(but)d(the)g (second)h(deriv)-5 b(ativ)m(e)40 b(ma)m(y)f(b)s(e)390 3723 y(discon)m(tin)m(uous.)150 3904 y(The)30 b(follo)m(wing)i(related) f(functions)f(are)h(a)m(v)-5 b(ailable:)3350 4084 y([F)d(unction])-3599 b Fv(const)54 b(char)f(*)g(gsl_interp_name)d Fu(\()p FD(const)31 b(gsl)p 2045 4084 28 4 v 41 w(in)m(terp)f(*)h Ft(interp)p Fu(\))390 4194 y FK(This)24 b(function)g(returns)g(the)g (name)h(of)g(the)g(in)m(terp)s(olation)h(t)m(yp)s(e)e(used)g(b)m(y)h FD(in)m(terp)p FK(.)39 b(F)-8 b(or)25 b(example,)630 4327 y FH(printf)46 b(\("interp)g(uses)g('\045s')h(interpolation.\\n",) 1012 4437 y(gsl_interp_name)c(\(interp\)\);)390 4570 y FK(w)m(ould)30 b(prin)m(t)g(something)h(lik)m(e,)630 4703 y FH(interp)46 b(uses)h('cspline')e(interpolation.)3350 4884 y FK([F)-8 b(unction])-3599 b Fv(unsigned)55 b(int)e (gsl_interp_min_size)e Fu(\()p FD(const)31 b(gsl)p 2254 4884 V 41 w(in)m(terp)f(*)h Ft(interp)p Fu(\))3350 4994 y FK([F)-8 b(unction])-3599 b Fv(unsigned)55 b(int)e (gsl_interp_type_min_si)q(ze)f Fu(\()p FD(const)31 b(gsl)p 2516 4994 V 40 w(in)m(terp)p 2791 4994 V 41 w(t)m(yp)s(e)f(*)h Ft(T)p Fu(\))390 5103 y FK(These)42 b(functions)g(return)f(the)i(minim) m(um)f(n)m(um)m(b)s(er)f(of)h(p)s(oin)m(ts)g(required)g(b)m(y)g(the)h (in)m(terp)s(ola-)390 5213 y(tion)34 b(ob)5 b(ject)34 b FD(in)m(terp)h FK(or)f(in)m(terp)s(olation)g(t)m(yp)s(e)f FD(T)p FK(.)49 b(F)-8 b(or)33 b(example,)i(Akima)f(spline)f(in)m(terp)s (olation)390 5322 y(requires)d(a)h(minim)m(um)e(of)i(5)g(p)s(oin)m(ts.) p eop end %%Page: 350 368 TeXDict begin 350 367 bop 150 -116 a FK(Chapter)30 b(28:)41 b(In)m(terp)s(olation)2437 b(350)150 299 y FJ(28.4)68 b(1D)46 b(Index)e(Lo)t(ok-up)g(and)h(Acceleration)150 458 y FK(The)d(state)i(of)f(searc)m(hes)h(can)f(b)s(e)f(stored)h(in)g (a)g FH(gsl_interp_accel)38 b FK(ob)5 b(ject,)47 b(whic)m(h)c(is)g(a)g (kind)f(of)150 568 y(iterator)35 b(for)d(in)m(terp)s(olation)j(lo)s (okups.)48 b(It)33 b(cac)m(hes)i(the)e(previous)g(v)-5 b(alue)34 b(of)f(an)g(index)g(lo)s(okup.)48 b(When)150 677 y(the)27 b(subsequen)m(t)g(in)m(terp)s(olation)h(p)s(oin)m(t)f (falls)h(in)f(the)g(same)h(in)m(terv)-5 b(al)28 b(its)g(index)e(v)-5 b(alue)28 b(can)g(b)s(e)e(returned)150 787 y(immediately)-8 b(.)3350 948 y([F)g(unction])-3599 b Fv(size_t)54 b(gsl_interp_bsearch) d Fu(\()p FD(const)31 b(double)f Ft(x_array)p Fo([])p FD(,)j(double)d Ft(x)p FD(,)g(size)p 3094 948 28 4 v 41 w(t)565 1057 y Ft(index_lo)p FD(,)j(size)p 1186 1057 V 41 w(t)e Ft(index_hi)p Fu(\))390 1167 y FK(This)h(function)g(returns) f(the)i(index)f FE(i)h FK(of)g(the)g(arra)m(y)g FD(x)p 2303 1167 V 40 w(arra)m(y)41 b FK(suc)m(h)32 b(that)h FH(x_array[i])27 b(<=)j(x)g(<)390 1277 y(x_array[i+1])p FK(.)40 b(The)31 b(index)g(is)g(searc)m(hed)h(for)f(in)g(the)h(range)f ([)p FD(index)p 2824 1277 V 40 w(lo)p FK(,)p FD(index)p 3174 1277 V 41 w(hi)5 b FK(].)43 b(An)31 b(inline)390 1386 y(v)m(ersion)g(of)f(this)h(function)f(is)g(used)g(when)f FH(HAVE_INLINE)e FK(is)k(de\014ned.)3350 1547 y([F)-8 b(unction])-3599 b Fv(gsl_interp_accel)57 b(*)c(gsl_interp_accel_alloc) f Fu(\()p FD(v)m(oid)p Fu(\))390 1657 y FK(This)34 b(function)g (returns)g(a)h(p)s(oin)m(ter)f(to)i(an)e(accelerator)k(ob)5 b(ject,)37 b(whic)m(h)d(is)h(a)g(kind)f(of)h(iterator)390 1766 y(for)27 b(in)m(terp)s(olation)i(lo)s(okups.)39 b(It)28 b(trac)m(ks)g(the)g(state)h(of)e(lo)s(okups,)h(th)m(us)f(allo)m (wing)i(for)f(application)390 1876 y(of)j(v)-5 b(arious)30 b(acceleration)j(strategies.)3350 2036 y([F)-8 b(unction])-3599 b Fv(size_t)54 b(gsl_interp_accel_find)e Fu(\()p FD(gsl)p 1807 2036 V 41 w(in)m(terp)p 2083 2036 V 40 w(accel)32 b(*)f Ft(a)p FD(,)g(const)g(double)565 2146 y Ft(x_array)p Fo([])p FD(,)i(size)p 1190 2146 V 41 w(t)d Ft(size)p FD(,)i(double)e Ft(x)p Fu(\))390 2256 y FK(This)i(function)g(p)s (erforms)e(a)j(lo)s(okup)f(action)i(on)e(the)g(data)h(arra)m(y)g FD(x)p 2781 2256 V 40 w(arra)m(y)41 b FK(of)32 b(size)i FD(size)p FK(,)f(using)390 2365 y(the)44 b(giv)m(en)h(accelerator)h FD(a)p FK(.)82 b(This)43 b(is)g(ho)m(w)h(lo)s(okups)f(are)i(p)s (erformed)d(during)g(ev)-5 b(aluation)46 b(of)390 2475 y(an)37 b(in)m(terp)s(olation.)62 b(The)37 b(function)g(returns)f(an)h (index)f FE(i)i FK(suc)m(h)e(that)i FH(x_array[i])28 b(<=)h(x)i(<)f(x_)390 2584 y(array[i+1])p FK(.)37 b(An)29 b(inline)g(v)m(ersion)g(of)h(this)e(function)h(is)g(used)f(when)g FH(HAVE_INLINE)e FK(is)j(de\014ned.)3350 2745 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_interp_accel_rese)q(t)e Fu(\()p FD(gsl)p 1702 2745 V 41 w(in)m(terp)p 1978 2745 V 40 w(accel)33 b(*)d Ft(acc)p Fu(\))p FD(;)390 2855 y FK(This)40 b(function)h(reinitializes)i(the)f(accelerator)h(ob)5 b(ject)42 b FD(acc)p FK(.)75 b(It)41 b(should)f(b)s(e)g(used)h(when)f (the)390 2964 y(cac)m(hed)f(information)g(is)f(no)g(longer)h (applicable|for)g(example,)i(when)c(switc)m(hing)i(to)g(a)f(new)390 3074 y(dataset.)3350 3235 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_interp_accel_free)d Fu(\()p FD(gsl)p 1702 3235 V 41 w(in)m(terp)p 1978 3235 V 40 w(accel*)33 b Ft(acc)p Fu(\))390 3344 y FK(This)d(function)g(frees)g(the)h (accelerator)i(ob)5 b(ject)31 b FD(acc)p FK(.)150 3561 y FJ(28.5)68 b(1D)46 b(Ev)-7 b(aluation)46 b(of)f(In)l(terp)t(olating)h (F)-11 b(unctions)3350 3755 y FK([F)j(unction])-3599 b Fv(double)54 b(gsl_interp_eval)c Fu(\()p FD(const)31 b(gsl)p 1731 3755 V 41 w(in)m(terp)f(*)h Ft(interp)p FD(,)h(const)f(double)f Ft(xa)p Fo([])p FD(,)565 3864 y(const)h(double)f Ft(ya)p Fo([])p FD(,)h(double)f Ft(x)p FD(,)h(gsl)p 1825 3864 V 40 w(in)m(terp)p 2100 3864 V 40 w(accel)i(*)d Ft(acc)p Fu(\))3350 3974 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_interp_eval_e)e Fu(\()p FD(const)31 b(gsl)p 1679 3974 V 41 w(in)m(terp)f(*)h Ft(interp)p FD(,)h(const)f(double)f Ft(xa)p Fo([])p FD(,)565 4083 y(const)h(double)f Ft(ya)p Fo([])p FD(,)h(double)f Ft(x)p FD(,)h(gsl)p 1825 4083 V 40 w(in)m(terp)p 2100 4083 V 40 w(accel)i(*)d Ft(acc)p FD(,)i(double)e(*)g Ft(y)p Fu(\))390 4193 y FK(These)43 b(functions)f(return)g(the)h(in)m (terp)s(olated)h(v)-5 b(alue)43 b(of)g FD(y)51 b FK(for)42 b(a)h(giv)m(en)h(p)s(oin)m(t)f FD(x)p FK(,)j(using)d(the)390 4303 y(in)m(terp)s(olation)28 b(ob)5 b(ject)28 b FD(in)m(terp)p FK(,)g(data)g(arra)m(ys)f FD(xa)g FK(and)f FD(y)m(a)i FK(and)f(the)g(accelerator)i FD(acc)p FK(.)41 b(When)27 b FD(x)33 b FK(is)390 4412 y(outside)c(the)f(range)h(of)g FD(xa)p FK(,)g(the)g(error)f(co)s(de)h FH(GSL_EDOM)d FK(is)j(returned)e(with)h(a)h(v)-5 b(alue)29 b(of)g FH(GSL_NAN)390 4522 y FK(for)h FD(y)p FK(.)3350 4682 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_interp_eval_deriv)e Fu(\()p FD(const)31 b(gsl)p 2045 4682 V 41 w(in)m(terp)f(*)h Ft(interp)p FD(,)h(const)565 4792 y(double)e Ft(xa)p Fo([])p FD(,)h(const)g(double) f Ft(ya)p Fo([])p FD(,)h(double)f Ft(x)p FD(,)h(gsl)p 2334 4792 V 40 w(in)m(terp)p 2609 4792 V 40 w(accel)h(*)f Ft(acc)p Fu(\))3350 4902 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_interp_eval_deriv)q(_e)f Fu(\()p FD(const)31 b(gsl)p 1993 4902 V 40 w(in)m(terp)g(*)g Ft(interp)p FD(,)h(const)565 5011 y(double)e Ft(xa)p Fo([])p FD(,)h(const)g(double) f Ft(ya)p Fo([])p FD(,)h(double)f Ft(x)p FD(,)h(gsl)p 2334 5011 V 40 w(in)m(terp)p 2609 5011 V 40 w(accel)h(*)f Ft(acc)p FD(,)h(double)e(*)g Ft(d)p Fu(\))390 5121 y FK(These)h(functions)g(return)f(the)i(deriv)-5 b(ativ)m(e)33 b FD(d)h FK(of)e(an)f(in)m(terp)s(olated)i(function)e(for)g(a)h(giv)m (en)g(p)s(oin)m(t)390 5230 y FD(x)p FK(,)39 b(using)d(the)i(in)m(terp)s (olation)g(ob)5 b(ject)38 b FD(in)m(terp)p FK(,)h(data)f(arra)m(ys)f FD(xa)g FK(and)g FD(y)m(a)h FK(and)e(the)h(accelerator)390 5340 y FD(acc)p FK(.)p eop end %%Page: 351 369 TeXDict begin 351 368 bop 150 -116 a FK(Chapter)30 b(28:)41 b(In)m(terp)s(olation)2437 b(351)3350 299 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_interp_eval_deriv2)e Fu(\()p FD(const)31 b(gsl)p 2097 299 28 4 v 41 w(in)m(terp)f(*)h Ft(interp)p FD(,)i(const)565 408 y(double)d Ft(xa)p Fo([])p FD(,)h(const)g(double)f Ft(ya)p Fo([])p FD(,)h(double)f Ft(x)p FD(,)h(gsl)p 2334 408 V 40 w(in)m(terp)p 2609 408 V 40 w(accel)h(*)f Ft(acc)p Fu(\))3350 518 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_interp_eval_deriv)q(2_e)f Fu(\()p FD(const)31 b(gsl)p 2045 518 V 41 w(in)m(terp)f(*)h Ft(interp)p FD(,)h(const)565 628 y(double)e Ft(xa)p Fo([])p FD(,)h(const)g(double)f Ft(ya)p Fo([])p FD(,)h(double)f Ft(x)p FD(,)h(gsl)p 2334 628 V 40 w(in)m(terp)p 2609 628 V 40 w(accel)h(*)f Ft(acc)p FD(,)h(double)e(*)g Ft(d2)p Fu(\))390 737 y FK(These)42 b(functions)g(return)g(the)g(second)h(deriv)-5 b(ativ)m(e)44 b FD(d2)50 b FK(of)42 b(an)h(in)m(terp)s(olated)g(function)f(for)h(a) 390 847 y(giv)m(en)37 b(p)s(oin)m(t)e FD(x)p FK(,)i(using)e(the)h(in)m (terp)s(olation)h(ob)5 b(ject)36 b FD(in)m(terp)p FK(,)h(data)g(arra)m (ys)f FD(xa)f FK(and)g FD(y)m(a)i FK(and)e(the)390 956 y(accelerator)e FD(acc)p FK(.)3350 1118 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_interp_eval_integ)e Fu(\()p FD(const)31 b(gsl)p 2045 1118 V 41 w(in)m(terp)f(*)h Ft(interp)p FD(,)h(const)565 1228 y(double)e Ft(xa)p Fo([])p FD(,)h(const)g(double) f Ft(ya)p Fo([])p FD(,)h(double)f Ft(a)p FD(,)h(double)e Ft(b)p FD(,)i(gsl)p 2734 1228 V 41 w(in)m(terp)p 3010 1228 V 40 w(accel)h(*)f Ft(acc)p Fu(\))3350 1338 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_interp_eval_integ)q(_e)f Fu(\()p FD(const)31 b(gsl)p 1993 1338 V 40 w(in)m(terp)g(*)g Ft(interp)p FD(,)h(const)565 1447 y(double)e Ft(xa)p Fo([])p FD(,)h(const)g(double)f Ft(ya)p Fo([])p FD(,)h(double)f Ft(a)p FD(,)h(double)e Ft(b)p FD(,)i(gsl)p 2734 1447 V 41 w(in)m(terp)p 3010 1447 V 40 w(accel)h(*)f Ft(acc)p FD(,)565 1557 y(double)f(*)h Ft(result)p Fu(\))390 1666 y FK(These)g(functions)f(return)g(the)h(n)m(umerical)h(in)m(tegral)g FD(result)h FK(of)e(an)g(in)m(terp)s(olated)h(function)f(o)m(v)m(er)390 1776 y(the)f(range)g([)p FD(a)p FK(,)h FD(b)r FK(],)e(using)g(the)h(in) m(terp)s(olation)h(ob)5 b(ject)31 b FD(in)m(terp)p FK(,)f(data)g(arra)m (ys)g FD(xa)g FK(and)f FD(y)m(a)i FK(and)e(the)390 1886 y(accelerator)k FD(acc)p FK(.)150 2103 y FJ(28.6)68 b(1D)46 b(Higher-lev)l(el)h(In)l(terface)150 2263 y FK(The)27 b(functions)g(describ)s(ed)g(in)g(the)h(previous)f(sections)h(required) f(the)h(user)f(to)h(supply)e(p)s(oin)m(ters)h(to)i(the)150 2372 y FE(x)36 b FK(and)f FE(y)k FK(arra)m(ys)d(on)g(eac)m(h)h(call.)58 b(The)36 b(follo)m(wing)h(functions)f(are)g(equiv)-5 b(alen)m(t)37 b(to)g(the)f(corresp)s(onding)150 2482 y FH(gsl_interp)f FK(functions)j(but)g(main)m(tain)h(a)g(cop)m(y)g(of)f (this)g(data)h(in)f(the)h FH(gsl_spline)c FK(ob)5 b(ject.)66 b(This)150 2591 y(remo)m(v)m(es)29 b(the)e(need)g(to)i(pass)e(b)s(oth)f FD(xa)i FK(and)f FD(y)m(a)h FK(as)g(argumen)m(ts)f(on)g(eac)m(h)i(ev)-5 b(aluation.)41 b(These)27 b(functions)150 2701 y(are)k(de\014ned)e(in)h (the)h(header)f(\014le)g FH(gsl_spline.h)p FK(.)3350 2863 y([F)-8 b(unction])-3599 b Fv(gsl_spline)55 b(*)e (gsl_spline_alloc)d Fu(\()p FD(const)31 b(gsl)p 2097 2863 V 41 w(in)m(terp)p 2373 2863 V 40 w(t)m(yp)s(e)g(*)f Ft(T)p FD(,)h(size)p 2942 2863 V 41 w(t)565 2973 y Ft(size)p Fu(\))3350 3117 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_spline_init)d Fu(\()p FD(gsl)p 1336 3117 V 41 w(spline)30 b(*)h Ft(spline)p FD(,)h(const)f(double)f Ft(xa)p Fo([])p FD(,)h(const)565 3227 y(double)f Ft(ya)p Fo([])p FD(,)h(size)p 1221 3227 V 41 w(t)g Ft(size)p Fu(\))3350 3371 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_spline_free)c Fu(\()p FD(gsl)p 1389 3371 V 40 w(spline)31 b(*)f Ft(spline)p Fu(\))3350 3516 y FK([F)-8 b(unction])-3599 b Fv(const)54 b(char)f(*)g(gsl_spline_name)d Fu(\()p FD(const)31 b(gsl)p 2045 3516 V 41 w(spline)f(*)h Ft(spline)p Fu(\))3350 3661 y FK([F)-8 b(unction])-3599 b Fv(unsigned)55 b(int)e (gsl_spline_min_size)e Fu(\()p FD(const)31 b(gsl)p 2254 3661 V 41 w(spline)f(*)h Ft(spline)p Fu(\))3350 3805 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_spline_eval)c Fu(\()p FD(const)31 b(gsl)p 1731 3805 V 41 w(spline)f(*)h Ft(spline)p FD(,)h(double)e Ft(x)p FD(,)565 3915 y(gsl)p 677 3915 V 41 w(in)m(terp)p 953 3915 V 40 w(accel)i(*)f Ft(acc)p Fu(\))3350 4024 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_spline_eval_e)e Fu(\()p FD(const)31 b(gsl)p 1679 4024 V 41 w(spline)f(*)g Ft(spline)p FD(,)j(double)d Ft(x)p FD(,)565 4134 y(gsl)p 677 4134 V 41 w(in)m(terp)p 953 4134 V 40 w(accel)i(*)f Ft(acc)p FD(,)g(double)f(*)h Ft(y)p Fu(\))3350 4278 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_spline_eval_deriv)e Fu(\()p FD(const)31 b(gsl)p 2045 4278 V 41 w(spline)f(*)h Ft(spline)p FD(,)h(double)e Ft(x)p FD(,)565 4388 y(gsl)p 677 4388 V 41 w(in)m(terp)p 953 4388 V 40 w(accel)i(*)f Ft(acc)p Fu(\))3350 4498 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_spline_eval_deriv)q(_e)f Fu(\()p FD(const)31 b(gsl)p 1993 4498 V 40 w(spline)g(*)f Ft(spline)p FD(,)j(double)d Ft(x)p FD(,)565 4607 y(gsl)p 677 4607 V 41 w(in)m(terp)p 953 4607 V 40 w(accel)i(*)f Ft(acc)p FD(,)g(double)f(*)h Ft(d)p Fu(\))3350 4752 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_spline_eval_deriv2)e Fu(\()p FD(const)30 b(gsl)p 2096 4752 V 41 w(spline)f(*)g Ft(spline)p FD(,)j(double)d Ft(x)p FD(,)565 4861 y(gsl)p 677 4861 V 41 w(in)m(terp)p 953 4861 V 40 w(accel)j(*)f Ft(acc)p Fu(\))3350 4971 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_spline_eval_deriv)q(2_e)f Fu(\()p FD(const)31 b(gsl)p 2045 4971 V 41 w(spline)f(*)h Ft(spline)p FD(,)h(double)e Ft(x)p FD(,)565 5081 y(gsl)p 677 5081 V 41 w(in)m(terp)p 953 5081 V 40 w(accel)i(*)f Ft(acc)p FD(,)g(double)f(*)h Ft(d2)p Fu(\))3350 5225 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_spline_eval_integ)e Fu(\()p FD(const)31 b(gsl)p 2045 5225 V 41 w(spline)f(*)h Ft(spline)p FD(,)h(double)e Ft(a)p FD(,)565 5335 y(double)g Ft(b)p FD(,)h(gsl)p 1078 5335 V 40 w(in)m(terp)p 1353 5335 V 41 w(accel)h(*)f Ft(acc)p Fu(\))p eop end %%Page: 352 370 TeXDict begin 352 369 bop 150 -116 a FK(Chapter)30 b(28:)41 b(In)m(terp)s(olation)2437 b(352)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_spline_eval_integ)q(_e)f Fu(\()p FD(const)31 b(gsl)p 1993 299 28 4 v 40 w(spline)g(*)f Ft(spline)p FD(,)j(double)d Ft(a)p FD(,)565 408 y(double)g Ft(b)p FD(,)h(gsl)p 1078 408 V 40 w(in)m(terp)p 1353 408 V 41 w(accel)h(*)f Ft(acc)p FD(,)g(double)f(*)h Ft(result)p Fu(\))150 632 y FJ(28.7)68 b(Examples)46 b(of)g(1D)f(In)l(terp)t (olation)150 791 y FK(The)34 b(follo)m(wing)j(program)d(demonstrates)i (the)f(use)g(of)g(the)g(in)m(terp)s(olation)h(and)e(spline)h (functions.)54 b(It)150 901 y(computes)27 b(a)g(cubic)f(spline)g(in)m (terp)s(olation)i(of)f(the)g(10-p)s(oin)m(t)g(dataset)h(\()p FE(x)2656 915 y Fq(i)2684 901 y FE(;)15 b(y)2769 915 y Fq(i)2797 901 y FK(\))27 b(where)f FE(x)3170 915 y Fq(i)3222 901 y FK(=)f FE(i)13 b FK(+)g(sin)o(\()p FE(i)p FK(\))p FE(=)p FK(2)150 1010 y(and)30 b FE(y)372 1024 y Fq(i)424 1010 y FK(=)25 b FE(i)c FK(+)f(cos\()p FE(i)850 977 y FB(2)888 1010 y FK(\))31 b(for)f FE(i)c FK(=)f(0)15 b FE(:)g(:)g(:)h FK(9.)390 1176 y FH(#include)46 b()390 1285 y(#include)g()390 1395 y(#include)g()390 1504 y(#include)g()390 1614 y(#include)g ()390 1833 y(int)390 1943 y(main)h(\(void\))390 2052 y({)485 2162 y(int)g(i;)485 2271 y(double)g(xi,)f(yi,)h(x[10],)f (y[10];)485 2491 y(printf)h(\("#m=0,S=2\\n"\);)485 2710 y(for)g(\(i)h(=)f(0;)g(i)h(<)f(10;)g(i++\))581 2819 y({)676 2929 y(x[i])g(=)g(i)h(+)f(0.5)g(*)h(sin)f(\(i\);)676 3039 y(y[i])g(=)g(i)h(+)f(cos)g(\(i)g(*)h(i\);)676 3148 y(printf)e(\("\045g)h(\045g\\n",)f(x[i],)h(y[i]\);)581 3258 y(})485 3477 y(printf)g(\("#m=1,S=0\\n"\);)485 3696 y({)581 3806 y(gsl_interp_accel)c(*acc)676 3915 y(=)48 b(gsl_interp_accel_alloc)42 b(\(\);)581 4025 y(gsl_spline)j(*spline)676 4134 y(=)j(gsl_spline_alloc)43 b(\(gsl_interp_cspline,)f(10\);)581 4354 y(gsl_spline_init)i(\(spline,)h(x,)i(y,)g(10\);)581 4573 y(for)g(\(xi)g(=)g(x[0];)g(xi)g(<)g(x[9];)g(xi)g(+=)g(0.01\))676 4682 y({)772 4792 y(yi)g(=)g(gsl_spline_eval)d(\(spline,)i(xi,)h (acc\);)772 4902 y(printf)f(\("\045g)h(\045g\\n",)f(xi,)h(yi\);)676 5011 y(})581 5121 y(gsl_spline_free)d(\(spline\);)581 5230 y(gsl_interp_accel_free)e(\(acc\);)485 5340 y(})p eop end %%Page: 353 371 TeXDict begin 353 370 bop 150 -116 a FK(Chapter)30 b(28:)41 b(In)m(terp)s(olation)2437 b(353)485 299 y FH(return)47 b(0;)390 408 y(})150 553 y FK(The)30 b(output)g(is)g(designed)g(to)i(b) s(e)d(used)h(with)g(the)h FC(gnu)f FK(plotutils)h FH(graph)e FK(program,)390 697 y FH($)47 b(./a.out)f(>)i(interp.dat)390 806 y($)f(graph)g(-T)g(ps)g(<)h(interp.dat)d(>)i(interp.ps)275 2118 y @beginspecial 107 @llx 197 @lly 835 @urx 580 @ury 2448 @rwi @setspecial %%BeginDocument: interp2.eps %!PS-Adobe-3.0 EPSF-3.0 %%Creator: GNU libplot drawing library 4.1 %%Title: PostScript plot %%CreationDate: Thu Mar 17 17:03:59 2005 %%DocumentData: Clean7Bit %%LanguageLevel: 1 %%Pages: 1 %%PageOrder: Ascend %%Orientation: Portrait %%BoundingBox: 107 197 835 580 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} ifelse grestore end } dup 0 8 dict put def /istroke { gsave brushDashOffset -1 eq { [] 0 setdash 1 setgray } { brushDashArray brushDashOffset setdash fgred fggreen fgblue setrgbcolor } ifelse brushWidth 2 mul setlinewidth originalCTM setmatrix stroke grestore } def /ishow { 0 begin gsave fgred fggreen fgblue setrgbcolor /fontDict printFont findfont printSize scalefont dup setfont def /descender fontDict begin 0 /FontBBox load 1 get FontMatrix end transform exch pop def /vertoffset 1 printSize sub descender sub def { 0 vertoffset moveto show /vertoffset vertoffset printSize sub def } forall grestore end } dup 0 3 dict put def /patternproc { 0 begin /patternByteLength patternString length def /patternHeight patternByteLength 8 mul sqrt cvi def /patternWidth patternHeight def /patternByteWidth patternWidth 8 idiv def /imageByteMaxLength imageByteWidth imageHeight mul stringLimit patternByteWidth sub min def /imageMaxHeight imageByteMaxLength imageByteWidth idiv patternHeight idiv patternHeight mul patternHeight max def /imageHeight imageHeight imageMaxHeight sub store /imageString imageByteWidth imageMaxHeight mul patternByteWidth add string def 0 1 imageMaxHeight 1 sub { /y exch def /patternRow y patternByteWidth mul patternByteLength mod def /patternRowString patternString patternRow patternByteWidth getinterval def /imageRow y imageByteWidth mul def 0 patternByteWidth imageByteWidth 1 sub { /x exch def imageString imageRow x add patternRowString putinterval } for } for imageString end } dup 0 12 dict put def /min { dup 3 2 roll dup 4 3 roll lt { exch } if pop } def /max { dup 3 2 roll dup 4 3 roll gt { exch } if pop } def /midpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 x1 add 2 div y0 y1 add 2 div end } dup 0 4 dict put def /thirdpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 2 mul x1 add 3 div y0 2 mul y1 add 3 div end } dup 0 4 dict put def /subspline { 0 begin /movetoNeeded exch def y exch get /y3 exch def x exch get /x3 exch def y exch get /y2 exch def x exch get /x2 exch def y exch get /y1 exch def x exch get /x1 exch def y exch get /y0 exch def x exch get /x0 exch def x1 y1 x2 y2 thirdpoint /p1y exch def /p1x exch def x2 y2 x1 y1 thirdpoint /p2y exch def /p2x exch def x1 y1 x0 y0 thirdpoint p1x p1y midpoint /p0y exch def /p0x exch def x2 y2 x3 y3 thirdpoint p2x p2y midpoint /p3y exch def /p3x exch def movetoNeeded { p0x p0y moveto } if p1x p1y p2x p2y p3x p3y curveto end } dup 0 17 dict put def /storexyn { /n exch def /y n array def /x n array def n 1 sub -1 0 { /i exch def y i 3 2 roll put x i 3 2 roll put } for } def /arrowhead { 0 begin transform originalCTM itransform /taily exch def /tailx exch def transform originalCTM itransform /tipy exch def /tipx exch def /dy tipy taily sub def /dx tipx tailx sub def /angle dx 0 ne dy 0 ne or { dy dx atan } { 90 } ifelse def gsave originalCTM setmatrix tipx tipy translate angle rotate newpath arrowHeight neg arrowWidth 2 div moveto 0 0 lineto arrowHeight neg arrowWidth 2 div neg lineto patternNone not { originalCTM setmatrix /padtip arrowHeight 2 exp 0.25 arrowWidth 2 exp mul add sqrt brushWidth mul arrowWidth div def /padtail brushWidth 2 div def tipx tipy translate angle rotate padtip 0 translate arrowHeight padtip add padtail add arrowHeight div dup scale arrowheadpath ifill } if brushNone not { originalCTM setmatrix tipx tipy translate angle rotate arrowheadpath istroke } if grestore end } dup 0 9 dict put def /arrowheadpath { newpath arrowHeight neg arrowWidth 2 div moveto 0 0 lineto arrowHeight neg arrowWidth 2 div neg lineto } def /leftarrow { 0 begin y exch get /taily exch def x exch get /tailx exch def y exch get /tipy exch def x exch get /tipx exch def brushLeftArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /rightarrow { 0 begin y exch get /tipy exch def x exch get /tipx exch def y exch get /taily exch def x exch get /tailx exch def brushRightArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def %%EndResource %%EndSetup %%Page: 1 1 %%PageResources: font Helvetica %%PageBoundingBox: 107 197 835 580 %%BeginPageSetup %I Idraw 8 Begin %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 1 0 0 1 0 0 ] concat /originalCTM matrix currentmatrix def /trueoriginalCTM matrix currentmatrix def %%EndPageSetup Begin %I Rect [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2304 2304 16128 9216 Rect End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 128.156 214.1855 ] concat %I [ (0) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 9216 2304 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2304 2304 2442 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 266.396 214.1855 ] concat %I [ (2) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5069 9216 5069 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5069 2304 5069 2442 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 404.636 214.1855 ] concat %I [ (4) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7834 9216 7834 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7834 2304 7834 2442 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 542.876 214.1855 ] concat %I [ (6) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 10598 9216 10598 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 10598 2304 10598 2442 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 681.116 214.1855 ] concat %I [ (8) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 13363 9216 13363 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 13363 2304 13363 2442 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 814.3119 214.1855 ] concat %I [ (10) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 16128 9216 16128 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 16128 2304 16128 2442 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 9216 2304 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2304 2304 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3686 9216 3686 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3686 2304 3686 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5069 9216 5069 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5069 2304 5069 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6451 9216 6451 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6451 2304 6451 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7834 9216 7834 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7834 2304 7834 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 9216 9216 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2304 9216 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 10598 9216 10598 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 10598 2304 10598 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 11981 9216 11981 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 11981 2304 11981 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 13363 9216 13363 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 13363 2304 13363 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 14746 9216 14746 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 14746 2304 14746 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 16128 9216 16128 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 16128 2304 16128 2359 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 117.9279 229.8568 ] concat %I [ (0) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 16128 2304 15990 2304 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2304 2442 2304 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 117.9279 298.9768 ] concat %I [ (2) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 16128 3686 15990 3686 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3686 2442 3686 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 117.9279 368.0968 ] concat %I [ (4) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 16128 5069 15990 5069 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5069 2442 5069 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 117.9279 437.2168 ] concat %I [ (6) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 16128 6451 15990 6451 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 6451 2442 6451 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 117.9279 506.3368 ] concat %I [ (8) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 16128 7834 15990 7834 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 7834 2442 7834 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 107.8399 575.4568 ] concat %I [ (10) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 16128 9216 15990 9216 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 9216 2442 9216 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 16128 2304 16073 2304 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2304 2359 2304 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 16128 2995 16073 2995 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2995 2359 2995 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 16128 3686 16073 3686 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3686 2359 3686 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 16128 4378 16073 4378 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4378 2359 4378 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 16128 5069 16073 5069 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5069 2359 5069 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 16128 5760 16073 5760 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5760 2359 5760 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 16128 6451 16073 6451 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 6451 2359 6451 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 16128 7142 16073 7142 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 7142 2359 7142 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 16128 7834 16073 7834 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 7834 2359 7834 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 16128 8525 16073 8525 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 8525 2359 8525 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 16128 9216 16073 9216 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 9216 2359 9216 2 MLine End Begin %I Rect [0.54 0 0 0.54 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2196 2887 2412 3103 Rect End Begin %I Rect [0.54 0 0 0.54 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4160 3261 4376 3477 Rect End Begin %I Rect [0.54 0 0 0.54 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5589 3127 5805 3343 Rect End Begin %I Rect [0.54 0 0 0.54 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6441 3640 6657 3856 Rect End Begin %I Rect [0.54 0 0 0.54 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7202 4299 7418 4515 Rect End Begin %I Rect [0.54 0 0 0.54 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8445 6337 8661 6553 Rect End Begin %I Rect [0.54 0 0 0.54 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10297 6255 10513 6471 Rect End Begin %I Rect [0.54 0 0 0.54 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 12327 7242 12543 7458 Rect End Begin %I Rect [0.54 0 0 0.54 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 13939 7996 14155 8212 Rect End Begin %I Rect [0.54 0 0 0.54 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 14922 8954 15138 9170 Rect End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 500 2304 2995 2318 3000 2332 3005 2345 3010 2359 3015 2373 3019 2387 3024 2401 3029 2415 3034 2428 3039 2442 3043 2456 3048 2470 3053 2484 3058 2498 3063 2511 3067 2525 3072 2539 3077 2553 3082 2567 3086 2580 3091 2594 3096 2608 3100 2622 3105 2636 3110 2650 3114 2663 3119 2677 3123 2691 3128 2705 3133 2719 3137 2733 3142 2746 3146 2760 3151 2774 3155 2788 3160 2802 3164 2815 3168 2829 3173 2843 3177 2857 3181 2871 3186 2885 3190 2898 3194 2912 3198 2926 3203 2940 3207 2954 3211 2968 3215 2981 3219 2995 3223 3009 3227 3023 3231 3037 3235 3050 3239 3064 3243 3078 3247 3092 3250 3106 3254 3120 3258 3133 3261 3147 3265 3161 3269 3175 3272 3189 3276 3203 3279 3216 3283 3230 3286 3244 3289 3258 3293 3272 3296 3286 3299 3299 3302 3313 3305 3327 3308 3341 3311 3355 3314 3368 3317 3382 3320 3396 3323 3410 3326 3424 3328 3438 3331 3451 3334 3465 3336 3479 3339 3493 3341 3507 3344 3521 3346 3534 3348 3548 3350 3562 3353 3576 3355 3590 3357 3603 3359 3617 3361 3631 3362 3645 3364 3659 3366 3673 3368 3686 3369 3700 3371 3714 3372 3728 3374 3742 3375 3756 3376 3769 3377 3783 3378 3797 3379 3811 3380 3825 3381 3838 3382 3852 3383 3866 3384 3880 3384 3894 3385 3908 3385 3921 3386 3935 3386 3949 3386 3963 3386 3977 3386 3991 3386 4004 3386 4018 3386 4032 3386 4046 3386 4060 3385 4073 3385 4087 3384 4101 3383 4115 3383 4129 3382 4143 3381 4156 3380 4170 3379 4184 3378 4198 3376 4212 3375 4226 3374 4239 3372 4253 3371 4267 3369 4281 3367 4295 3365 4308 3363 4322 3361 4336 3359 4350 3357 4364 3354 4378 3352 4391 3349 4405 3347 4419 3344 4433 3342 4447 3339 4461 3336 4474 3333 4488 3331 4502 3328 4516 3325 4530 3322 4543 3319 4557 3316 4571 3313 4585 3309 4599 3306 4613 3303 4626 3300 4640 3297 4654 3294 4668 3290 4682 3287 4696 3284 4709 3281 4723 3277 4737 3274 4751 3271 4765 3268 4778 3265 4792 3261 4806 3258 4820 3255 4834 3252 4848 3249 4861 3246 4875 3243 4889 3240 4903 3237 4917 3234 4931 3231 4944 3228 4958 3226 4972 3223 4986 3220 5000 3218 5014 3215 5027 3213 5041 3210 5055 3208 5069 3206 5083 3204 5096 3202 5110 3200 5124 3198 5138 3196 5152 3194 5166 3193 5179 3191 5193 3190 5207 3189 5221 3187 5235 3186 5249 3185 5262 3184 5276 3184 5290 3183 5304 3183 5318 3182 5331 3182 5345 3182 5359 3182 5373 3182 5387 3183 5401 3183 5414 3184 5428 3185 5442 3185 5456 3187 5470 3188 5484 3189 5497 3191 5511 3193 5525 3195 5539 3197 5553 3199 5566 3201 5580 3204 5594 3207 5608 3210 5622 3213 5636 3217 5649 3220 5663 3224 5677 3228 5691 3233 5705 3237 5719 3242 5732 3247 5746 3252 5760 3257 5774 3262 5788 3268 5801 3274 5815 3280 5829 3286 5843 3293 5857 3299 5871 3306 5884 3313 5898 3320 5912 3327 5926 3334 5940 3342 5954 3350 5967 3357 5981 3365 5995 3373 6009 3381 6023 3390 6036 3398 6050 3406 6064 3415 6078 3424 6092 3432 6106 3441 6119 3450 6133 3459 6147 3468 6161 3478 6175 3487 6189 3496 6202 3505 6216 3515 6230 3524 6244 3534 6258 3544 6271 3553 6285 3563 6299 3572 6313 3582 6327 3592 6341 3602 6354 3611 6368 3621 6382 3631 6396 3641 6410 3651 6424 3660 6437 3670 6451 3680 6465 3690 6479 3699 6493 3709 6506 3719 6520 3728 6534 3738 6548 3747 6562 3757 6576 3766 6589 3776 6603 3785 6617 3794 6631 3804 6645 3813 6659 3822 6672 3832 6686 3841 6700 3850 6714 3860 6728 3869 6742 3879 6755 3888 6769 3898 6783 3908 6797 3917 6811 3927 6824 3937 6838 3947 6852 3957 6866 3968 6880 3978 6894 3988 6907 3999 6921 4010 6935 4021 6949 4032 6963 4043 6977 4055 6990 4067 7004 4078 7018 4091 7032 4103 7046 4115 7059 4128 7073 4141 7087 4154 7101 4168 7115 4181 7129 4195 7142 4209 7156 4224 7170 4239 7184 4254 7198 4269 7212 4285 7225 4301 7239 4317 7253 4334 7267 4351 7281 4368 7294 4386 7308 4404 7322 4422 7336 4441 7350 4460 7364 4480 7377 4500 7391 4520 7405 4540 7419 4561 7433 4582 7447 4603 7460 4625 7474 4647 7488 4669 7502 4692 7516 4714 7529 4737 7543 4760 7557 4784 7571 4807 7585 4831 7599 4855 7612 4879 7626 4903 7640 4928 7654 4952 7668 4977 7682 5002 7695 5027 7709 5052 7723 5078 7737 5103 7751 5128 7764 5154 7778 5179 7792 5205 7806 5231 7820 5257 7834 5282 7847 5308 7861 5334 7875 5360 7889 5386 7903 5411 7917 5437 7930 5463 7944 5489 7958 5514 7972 5540 7986 5566 7999 5591 8013 5616 8027 5642 8041 5667 8055 5692 8069 5717 8082 5742 8096 5767 8110 5791 8124 5816 8138 5840 8152 5864 8165 5888 8179 5911 8193 5935 8207 5958 8221 5981 8234 6004 8248 6027 8262 6049 8276 6071 8290 6093 8304 6114 8317 6136 8331 6156 8345 6177 8359 6197 8373 6217 8387 6237 8400 6257 8414 6276 8428 6294 8442 6312 8456 6330 8470 6348 8483 6365 8497 6382 8511 6398 8525 6414 8539 6429 8552 6444 8566 6459 8580 6473 8594 6487 8608 6500 8622 6513 8635 6525 8649 6537 8663 6549 8677 6560 8691 6571 8705 6581 8718 6591 8732 6600 8746 6610 8760 6618 8774 6627 8787 6635 8801 6642 8815 6650 8829 6657 8843 6663 8857 6670 8870 6676 8884 6681 8898 6686 8912 6691 8926 6696 8940 6700 8953 6704 8967 6708 8981 6711 8995 6714 9009 6717 9022 6720 9036 6722 9050 6724 9064 6725 9078 6727 9092 6728 9105 6729 9119 6729 9133 6730 9147 6730 9161 6730 9175 6729 9188 6729 9202 6728 500 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 422 9202 6728 9216 6727 9230 6726 9244 6724 9257 6723 9271 6721 9285 6719 9299 6717 9313 6714 9327 6712 9340 6709 9354 6706 9368 6703 9382 6700 9396 6696 9410 6693 9423 6689 9437 6685 9451 6681 9465 6677 9479 6673 9492 6668 9506 6664 9520 6659 9534 6655 9548 6650 9562 6645 9575 6640 9589 6635 9603 6630 9617 6625 9631 6619 9645 6614 9658 6609 9672 6603 9686 6598 9700 6592 9714 6587 9727 6581 9741 6575 9755 6570 9769 6564 9783 6558 9797 6552 9810 6547 9824 6541 9838 6535 9852 6529 9866 6524 9880 6518 9893 6512 9907 6507 9921 6501 9935 6495 9949 6490 9962 6484 9976 6479 9990 6474 10004 6468 10018 6463 10032 6458 10045 6453 10059 6448 10073 6443 10087 6438 10101 6433 10115 6428 10128 6424 10142 6419 10156 6415 10170 6411 10184 6407 10198 6403 10211 6399 10225 6395 10239 6392 10253 6389 10267 6385 10280 6382 10294 6379 10308 6377 10322 6374 10336 6372 10350 6370 10363 6368 10377 6366 10391 6364 10405 6363 10419 6362 10433 6361 10446 6360 10460 6359 10474 6359 10488 6359 10502 6359 10515 6359 10529 6359 10543 6360 10557 6361 10571 6362 10585 6363 10598 6364 10612 6366 10626 6368 10640 6370 10654 6372 10668 6374 10681 6376 10695 6379 10709 6382 10723 6385 10737 6388 10750 6391 10764 6394 10778 6398 10792 6402 10806 6405 10820 6409 10833 6414 10847 6418 10861 6422 10875 6427 10889 6432 10903 6437 10916 6442 10930 6447 10944 6452 10958 6457 10972 6463 10985 6468 10999 6474 11013 6480 11027 6486 11041 6492 11055 6499 11068 6505 11082 6511 11096 6518 11110 6525 11124 6531 11138 6538 11151 6545 11165 6552 11179 6560 11193 6567 11207 6574 11220 6582 11234 6589 11248 6597 11262 6605 11276 6612 11290 6620 11303 6628 11317 6636 11331 6645 11345 6653 11359 6661 11373 6669 11386 6678 11400 6686 11414 6695 11428 6703 11442 6712 11455 6721 11469 6729 11483 6738 11497 6747 11511 6756 11525 6765 11538 6774 11552 6783 11566 6792 11580 6801 11594 6810 11608 6819 11621 6828 11635 6838 11649 6847 11663 6856 11677 6865 11690 6875 11704 6884 11718 6893 11732 6903 11746 6912 11760 6922 11773 6931 11787 6940 11801 6950 11815 6959 11829 6969 11843 6978 11856 6987 11870 6997 11884 7006 11898 7016 11912 7025 11926 7034 11939 7044 11953 7053 11967 7062 11981 7072 11995 7081 12008 7090 12022 7099 12036 7108 12050 7117 12064 7127 12078 7136 12091 7145 12105 7154 12119 7163 12133 7171 12147 7180 12161 7189 12174 7198 12188 7206 12202 7215 12216 7224 12230 7232 12243 7241 12257 7249 12271 7257 12285 7266 12299 7274 12313 7282 12326 7290 12340 7298 12354 7306 12368 7314 12382 7321 12396 7329 12409 7336 12423 7344 12437 7351 12451 7359 12465 7366 12478 7373 12492 7380 12506 7387 12520 7394 12534 7400 12548 7407 12561 7414 12575 7420 12589 7427 12603 7433 12617 7439 12631 7446 12644 7452 12658 7458 12672 7464 12686 7470 12700 7476 12713 7482 12727 7488 12741 7494 12755 7499 12769 7505 12783 7511 12796 7516 12810 7522 12824 7527 12838 7533 12852 7538 12866 7544 12879 7549 12893 7555 12907 7560 12921 7565 12935 7571 12948 7576 12962 7581 12976 7586 12990 7592 13004 7597 13018 7602 13031 7607 13045 7612 13059 7618 13073 7623 13087 7628 13101 7633 13114 7638 13128 7644 13142 7649 13156 7654 13170 7659 13183 7665 13197 7670 13211 7675 13225 7680 13239 7686 13253 7691 13266 7696 13280 7702 13294 7707 13308 7713 13322 7718 13336 7724 13349 7729 13363 7735 13377 7741 13391 7746 13405 7752 13418 7758 13432 7764 13446 7770 13460 7775 13474 7781 13488 7788 13501 7794 13515 7800 13529 7806 13543 7812 13557 7819 13571 7825 13584 7832 13598 7838 13612 7845 13626 7852 13640 7858 13654 7865 13667 7872 13681 7879 13695 7887 13709 7894 13723 7901 13736 7909 13750 7916 13764 7924 13778 7931 13792 7939 13806 7947 13819 7955 13833 7963 13847 7972 13861 7980 13875 7988 13889 7997 13902 8006 13916 8015 13930 8024 13944 8033 13958 8042 13971 8051 13985 8061 13999 8070 14013 8080 14027 8090 14041 8100 14054 8110 14068 8120 14082 8131 14096 8141 14110 8152 14124 8163 14137 8174 14151 8185 14165 8196 14179 8207 14193 8219 14206 8230 14220 8242 14234 8254 14248 8265 14262 8277 14276 8290 14289 8302 14303 8314 14317 8327 14331 8339 14345 8352 14359 8365 14372 8377 14386 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(demonstrates)g(a)h(p)s(erio)s(dic)f(cubic)g(spline)g(with)g(4)h(data)g (p)s(oin)m(ts.)52 b(Note)35 b(that)150 2675 y(the)c(\014rst)e(and)h (last)h(p)s(oin)m(ts)f(m)m(ust)h(b)s(e)e(supplied)g(with)i(the)f(same)h (y-v)-5 b(alue)31 b(for)f(a)h(p)s(erio)s(dic)f(spline.)390 2819 y FH(#include)46 b()390 2929 y(#include)g()390 3039 y(#include)g()390 3148 y(#include)g()390 3258 y(#include)g()390 3477 y(int)390 3587 y(main)h(\(void\))390 3696 y({)485 3806 y(int)g(N)h(=)f(4;)485 3915 y(double)g(x[4])f(=)i({0.00,)e(0.10,)94 b(0.27,)g(0.30};)485 4025 y(double)47 b(y[4])f(=)i({0.15,)e(0.70,)g(-0.10,)94 b(0.15};)1010 4134 y(/*)48 b(Note:)94 b(y[0])46 b(==)i(y[3])e(for)h (periodic)f(data)g(*/)485 4354 y(gsl_interp_accel)e(*acc)i(=)i (gsl_interp_accel_alloc)42 b(\(\);)485 4463 y(const)47 b(gsl_interp_type)c(*t)48 b(=)f(gsl_interp_cspline_period)o(ic;)485 4573 y(gsl_spline)e(*spline)h(=)i(gsl_spline_alloc)43 b(\(t,)k(N\);)485 4792 y(int)g(i;)h(double)e(xi,)h(yi;)485 5011 y(printf)g(\("#m=0,S=5\\n"\);)485 5121 y(for)g(\(i)h(=)f(0;)g(i)h (<)f(N;)g(i++\))581 5230 y({)676 5340 y(printf)f(\("\045g)h(\045g\\n",) f(x[i],)h(y[i]\);)p eop end %%Page: 354 372 TeXDict begin 354 371 bop 150 -116 a FK(Chapter)30 b(28:)41 b(In)m(terp)s(olation)2437 b(354)581 299 y FH(})485 518 y(printf)47 b(\("#m=1,S=0\\n"\);)485 628 y(gsl_spline_init)d(\(spline,) i(x,)h(y,)g(N\);)485 847 y(for)g(\(i)h(=)f(0;)g(i)h(<=)f(100;)f(i++\)) 581 956 y({)676 1066 y(xi)i(=)f(\(1)g(-)h(i)f(/)h(100.0\))e(*)h(x[0])g (+)g(\(i)g(/)h(100.0\))e(*)h(x[N-1];)676 1176 y(yi)h(=)f (gsl_spline_eval)d(\(spline,)h(xi,)i(acc\);)676 1285 y(printf)f(\("\045g)h(\045g\\n",)f(xi,)h(yi\);)581 1395 y(})485 1614 y(gsl_spline_free)d(\(spline\);)485 1724 y(gsl_interp_accel_free)e(\(acc\);)485 1833 y(return)47 b(0;)390 1943 y(})275 2117 y FK(The)29 b(output)h(can)h(b)s(e)f (plotted)h(with)f FC(gnu)g FH(graph)p FK(.)390 2259 y FH($)47 b(./a.out)f(>)i(interp.dat)390 2368 y($)f(graph)g(-T)g(ps)g(<)h (interp.dat)d(>)i(interp.ps)275 4536 y @beginspecial 92 @llx 197 @lly 497 @urx 580 @ury 2448 @rwi @setspecial %%BeginDocument: interpp2.eps %!PS-Adobe-3.0 EPSF-3.0 %%Creator: GNU libplot drawing library 4.1 %%Title: PostScript plot %%CreationDate: Sat Dec 24 16:36:40 2005 %%DocumentData: Clean7Bit %%LanguageLevel: 1 %%Pages: 1 %%PageOrder: Ascend %%Orientation: Portrait %%BoundingBox: 92 197 497 580 %%DocumentNeededResources: font Helvetica %%DocumentSuppliedResources: procset GNU_libplot 1.0 0 %%EndComments %%BeginDefaults %%PageResources: font Helvetica %%EndDefaults %%BeginProlog %%EndProlog %%BeginSetup %%IncludeResource: font Helvetica /DrawDict 50 dict def DrawDict begin /ISOLatin1Encoding [ /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /space/exclam/quotedbl/numbersign/dollar/percent/ampersand/quoteright /parenleft/parenright/asterisk/plus/comma/minus/period/slash /zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon /less/equal/greater/question/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N /O/P/Q/R/S/T/U/V/W/X/Y/Z/bracketleft/backslash/bracketright /asciicircum/underscore/quoteleft/a/b/c/d/e/f/g/h/i/j/k/l/m /n/o/p/q/r/s/t/u/v/w/x/y/z/braceleft/bar/braceright/asciitilde /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/dotlessi/grave/acute/circumflex/tilde/macron/breve /dotaccent/dieresis/.notdef/ring/cedilla/.notdef/hungarumlaut /ogonek/caron/space/exclamdown/cent/sterling/currency/yen/brokenbar /section/dieresis/copyright/ordfeminine/guillemotleft/logicalnot /hyphen/registered/macron/degree/plusminus/twosuperior/threesuperior /acute/mu/paragraph/periodcentered/cedilla/onesuperior/ordmasculine /guillemotright/onequarter/onehalf/threequarters/questiondown /Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla /Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex /Idieresis/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis /multiply/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute /Thorn/germandbls/agrave/aacute/acircumflex/atilde/adieresis /aring/ae/ccedilla/egrave/eacute/ecircumflex/edieresis/igrave /iacute/icircumflex/idieresis/eth/ntilde/ograve/oacute/ocircumflex /otilde/odieresis/divide/oslash/ugrave/uacute/ucircumflex/udieresis /yacute/thorn/ydieresis ] def /reencodeISO { dup dup findfont dup length dict begin { 1 index /FID ne { def }{ pop pop } ifelse } forall /Encoding ISOLatin1Encoding def currentdict end definefont } def /Helvetica reencodeISO def %%BeginResource procset GNU_libplot 1.0 0 /none null def /numGraphicParameters 17 def /stringLimit 65535 def /arrowHeight 8 def /eoFillRule true def /Begin { save numGraphicParameters dict begin } def /End { end restore } def /SetB { dup type /nulltype eq { pop false /brushRightArrow idef false /brushLeftArrow idef true /brushNone idef } { /brushDashOffset idef /brushDashArray idef 0 ne /brushRightArrow idef 0 ne /brushLeftArrow idef /brushWidth idef false /brushNone idef } ifelse } def /SetCFg { /fgblue idef /fggreen idef /fgred idef } def /SetCBg { /bgblue idef /bggreen idef /bgred idef } def /SetF { /printSize idef /printFont idef } def /SetP { dup type /nulltype eq { pop true /patternNone idef } { /patternGrayLevel idef patternGrayLevel -1 eq { /patternString idef } if false /patternNone idef } ifelse } def /BSpl { 0 begin storexyn newpath n 1 gt { 0 0 0 0 0 0 1 1 true subspline n 2 gt { 0 0 0 0 1 1 2 2 false subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 2 copy false subspline } if n 2 sub dup n 1 sub dup 2 copy 2 copy false subspline patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup 1 sub dup rightarrow } if end } dup 0 4 dict put def /Circ { newpath 0 360 arc closepath patternNone not { ifill } if brushNone not { istroke } if } def /CBSpl { 0 begin dup 2 gt { storexyn newpath n 1 sub dup 0 0 1 1 2 2 true subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 0 0 false subspline n 2 sub dup n 1 sub dup 0 0 1 1 false subspline patternNone not { ifill } if brushNone not { istroke } if } { Poly } ifelse end } dup 0 4 dict put def /Elli { 0 begin newpath 4 2 roll translate scale 0 0 1 0 360 arc closepath patternNone not { ifill } if brushNone not { istroke } if end } dup 0 1 dict put def /Line { 0 begin 2 storexyn newpath x 0 get y 0 get moveto x 1 get y 1 get lineto brushNone not { istroke } if 0 0 1 1 leftarrow 0 0 1 1 rightarrow end } dup 0 4 dict put def /MLine { 0 begin storexyn newpath n 1 gt { x 0 get y 0 get moveto 1 1 n 1 sub { /i exch def x i get y i get lineto } for patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Poly { 3 1 roll newpath moveto -1 add { lineto } repeat closepath patternNone not { ifill } if brushNone not { istroke } if } def /Rect { 0 begin /t exch def /r exch def /b exch def /l exch def newpath l b moveto l t lineto r t lineto r b lineto closepath patternNone not { ifill } if brushNone not { istroke } if end } dup 0 4 dict put def /Text { ishow } def /idef { dup where { pop pop pop } { exch def } ifelse } def /ifill { 0 begin gsave patternGrayLevel -1 ne { fgred bgred fgred sub patternGrayLevel mul add fggreen bggreen fggreen sub patternGrayLevel mul add fgblue bgblue fgblue sub patternGrayLevel mul add setrgbcolor eoFillRule { eofill } { fill } ifelse } { eoFillRule { eoclip } { clip } ifelse originalCTM setmatrix pathbbox /t exch def /r exch def /b exch def /l exch def /w r l sub ceiling cvi def /h t b sub ceiling cvi def /imageByteWidth w 8 div ceiling cvi def /imageHeight h def bgred bggreen bgblue setrgbcolor eoFillRule { eofill } { fill } ifelse fgred fggreen fgblue setrgbcolor w 0 gt h 0 gt and { l b translate w h scale w h true [w 0 0 h neg 0 h] { patternproc } imagemask } if } ifelse grestore end } dup 0 8 dict put def /istroke { gsave brushDashOffset -1 eq { [] 0 setdash 1 setgray } { brushDashArray brushDashOffset setdash fgred fggreen fgblue setrgbcolor } ifelse brushWidth setlinewidth originalCTM setmatrix stroke grestore } def /ishow { 0 begin gsave fgred fggreen fgblue setrgbcolor /fontDict printFont findfont printSize scalefont dup setfont def /descender fontDict begin 0 /FontBBox load 1 get FontMatrix end transform exch pop def /vertoffset 1 printSize sub descender sub def { 0 vertoffset moveto show /vertoffset vertoffset printSize sub def } forall grestore end } dup 0 3 dict put def /patternproc { 0 begin /patternByteLength patternString length def /patternHeight patternByteLength 8 mul sqrt cvi def /patternWidth patternHeight def /patternByteWidth patternWidth 8 idiv def /imageByteMaxLength imageByteWidth imageHeight mul stringLimit patternByteWidth sub min def /imageMaxHeight imageByteMaxLength imageByteWidth idiv patternHeight idiv patternHeight mul patternHeight max def /imageHeight imageHeight imageMaxHeight sub store /imageString imageByteWidth imageMaxHeight mul patternByteWidth add string def 0 1 imageMaxHeight 1 sub { /y exch def /patternRow y patternByteWidth mul patternByteLength mod def /patternRowString patternString patternRow patternByteWidth getinterval def /imageRow y imageByteWidth mul def 0 patternByteWidth imageByteWidth 1 sub { /x exch def imageString imageRow x add patternRowString putinterval } for } for imageString end } dup 0 12 dict put def /min { dup 3 2 roll dup 4 3 roll lt { exch } if pop } def /max { dup 3 2 roll dup 4 3 roll gt { exch } if pop } def /midpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 x1 add 2 div y0 y1 add 2 div end } dup 0 4 dict put def /thirdpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 2 mul x1 add 3 div y0 2 mul y1 add 3 div end } dup 0 4 dict put def /subspline { 0 begin /movetoNeeded exch def y exch get /y3 exch def x exch get /x3 exch def y exch get /y2 exch def x exch get /x2 exch def y exch get /y1 exch def x exch get /x1 exch def y exch get /y0 exch def x exch get /x0 exch def x1 y1 x2 y2 thirdpoint /p1y exch def /p1x exch def x2 y2 x1 y1 thirdpoint /p2y exch def /p2x exch def x1 y1 x0 y0 thirdpoint p1x p1y midpoint /p0y exch def /p0x exch def x2 y2 x3 y3 thirdpoint p2x p2y midpoint /p3y exch def /p3x exch def movetoNeeded { p0x p0y moveto } if p1x p1y p2x p2y p3x p3y curveto end } dup 0 17 dict put def /storexyn { /n exch def /y n array def /x n array def n 1 sub -1 0 { /i exch def y i 3 2 roll put x i 3 2 roll put } for } def /arrowhead { 0 begin transform originalCTM itransform /taily exch def /tailx exch def transform originalCTM itransform /tipy exch def /tipx exch def /dy tipy taily sub def /dx tipx tailx sub def /angle dx 0 ne dy 0 ne or { dy dx atan } { 90 } ifelse def gsave originalCTM setmatrix tipx tipy translate angle rotate newpath arrowHeight neg arrowWidth 2 div moveto 0 0 lineto arrowHeight neg arrowWidth 2 div neg lineto patternNone not { originalCTM setmatrix /padtip arrowHeight 2 exp 0.25 arrowWidth 2 exp mul add sqrt brushWidth mul arrowWidth div def /padtail brushWidth 2 div def tipx tipy translate angle rotate padtip 0 translate arrowHeight padtip add padtail add arrowHeight div dup scale arrowheadpath ifill } if brushNone not { originalCTM setmatrix tipx tipy translate angle rotate arrowheadpath istroke } if grestore end } dup 0 9 dict put def /arrowheadpath { newpath arrowHeight neg arrowWidth 2 div moveto 0 0 lineto arrowHeight neg arrowWidth 2 div neg lineto } def /leftarrow { 0 begin y exch get /taily exch def x exch get /tailx exch def y exch get /tipy exch def x exch get /tipx exch def brushLeftArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /rightarrow { 0 begin y exch get /tipy exch def x exch get /tipx exch def y exch get /taily exch def x exch get /tailx exch def brushRightArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def %%EndResource %%EndSetup %%Page: 1 1 %%PageResources: font Helvetica %%PageBoundingBox: 92 197 497 580 %%BeginPageSetup %I Idraw 8 Begin %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 1 0 0 1 0 0 ] concat /originalCTM matrix currentmatrix def /trueoriginalCTM matrix currentmatrix def %%EndPageSetup Begin %I Rect [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2304 2304 9216 9216 Rect End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 115.5459 214.1855 ] concat %I [ (0.00) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 9216 2304 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2304 2304 2442 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 173.1459 214.1855 ] concat %I [ (0.05) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3456 9216 3456 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3456 2304 3456 2442 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 230.7459 214.1855 ] concat %I [ (0.10) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4608 9216 4608 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4608 2304 4608 2442 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 288.3459 214.1855 ] concat %I [ (0.15) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5760 9216 5760 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5760 2304 5760 2442 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 345.9459 214.1855 ] concat %I [ (0.20) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6912 9216 6912 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6912 2304 6912 2442 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 403.5459 214.1855 ] concat %I [ (0.25) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8064 9216 8064 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8064 2304 8064 2442 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 461.1459 214.1855 ] concat %I [ (0.30) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 9216 9216 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2304 9216 2442 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 92.19974 229.8568 ] concat %I [ (-0.2) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2304 9078 2304 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2304 2442 2304 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 102.7958 298.9768 ] concat %I [ (0.0) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 3686 9078 3686 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3686 2442 3686 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 102.7958 368.0968 ] concat %I [ (0.2) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5069 9078 5069 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5069 2442 5069 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 102.7958 437.2168 ] concat %I [ (0.4) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 6451 9078 6451 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 6451 2442 6451 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 102.7958 506.3368 ] concat %I [ (0.6) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 7834 9078 7834 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 7834 2442 7834 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 102.7958 575.4568 ] concat %I [ (0.8) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 9216 9078 9216 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 9216 2442 9216 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2304 9161 2304 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2304 2359 2304 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2995 9161 2995 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2995 2359 2995 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 3686 9161 3686 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3686 2359 3686 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 4378 9161 4378 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4378 2359 4378 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5069 9161 5069 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5069 2359 5069 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5760 9161 5760 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5760 2359 5760 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 6451 9161 6451 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 6451 2359 6451 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 7142 9161 7142 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 7142 2359 7142 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 7834 9161 7834 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 7834 2359 7834 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 8525 9161 8525 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 8525 2359 8525 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 9216 9161 9216 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 9216 2359 9216 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 34952 1 0 0 [ 1.48 4.43 ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3686 9216 3686 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2239 4658 2369 4788 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2369 4658 2239 4788 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4543 8460 4673 8590 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4673 8460 4543 8590 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8460 2930 8590 3060 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8590 2930 8460 3060 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9151 4658 9281 4788 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] 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5230 y FH(#include)46 b()390 5340 y(#include)g()p eop end %%Page: 355 373 TeXDict begin 355 372 bop 150 -116 a FK(Chapter)30 b(28:)41 b(In)m(terp)s(olation)2437 b(355)390 299 y FH(#include)46 b()390 518 y(#include)g()390 628 y(#include)g()390 847 y(int)390 956 y(main\(void\))390 1066 y({)485 1176 y(size_t)h(i;)485 1285 y(const)g(size_t)f(N)h(=)h(9;)485 1504 y(/*)g(this)e(dataset)g(is) h(taken)g(from)533 1614 y(*)h(J.)f(M.)g(Hyman,)f(Accurate)g (Monotonicity)e(preserving)h(cubic)h(interpolation,)533 1724 y(*)i(SIAM)e(J.)h(Sci.)95 b(Stat.)f(Comput.)f(4,)48 b(4,)f(1983.)94 b(*/)485 1833 y(const)47 b(double)f(x[])h(=)g({)h (7.99,)e(8.09,)g(8.19,)h(8.7,)f(9.2,)1488 1943 y(10.0,)g(12.0,)g(15.0,) h(20.0)f(};)485 2052 y(const)h(double)f(y[])h(=)g({)h(0.0,)e (2.76429e-5,)f(4.37498e-2,)1488 2162 y(0.169183,)g(0.469428,)g (0.943740,)1488 2271 y(0.998636,)g(0.999919,)g(0.999994)h(};)485 2491 y(gsl_interp_accel)e(*acc)i(=)i(gsl_interp_accel_alloc\(\))o(;)485 2600 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b(F)-8 b(or)25 b(example,)630 1605 y FH(printf)46 b(\("interp)g(uses)g('\045s')h(interpolation.\\n",) 1012 1715 y(gsl_interp2d_name)c(\(interp\)\);)390 1852 y FK(w)m(ould)30 b(prin)m(t)g(something)h(lik)m(e,)630 1990 y FH(interp)46 b(uses)h('bilinear')e(interpolation.)3350 2180 y FK([F)-8 b(unction])-3599 b Fv(unsigned)55 b(int)e (gsl_interp2d_min_size)f Fu(\()p FD(const)31 b(gsl)p 2359 2180 V 41 w(in)m(terp2d)f(*)h Ft(interp)p Fu(\))3350 2290 y FK([F)-8 b(unction])-3599 b Fv(unsigned)55 b(int)e (gsl_interp2d_type_min_)q(siz)q(e)e Fu(\()p FD(const)31 b(gsl)p 2620 2290 V 41 w(in)m(terp2d)p 2992 2290 V 40 w(t)m(yp)s(e)565 2399 y(*)g Ft(T)p Fu(\))390 2509 y FK(These)g (functions)f(return)g(the)h(minim)m(um)f(n)m(um)m(b)s(er)g(of)h(p)s (oin)m(ts)g(required)f(b)m(y)h(the)g(in)m(terp)s(olation)390 2618 y(ob)5 b(ject)35 b FD(in)m(terp)h FK(or)e(in)m(terp)s(olation)g(t) m(yp)s(e)g FD(T)p FK(.)50 b(F)-8 b(or)35 b(example,)g(bicubic)e(in)m (terp)s(olation)i(requires)f(a)390 2728 y(minim)m(um)c(of)g(4)h(p)s (oin)m(ts.)150 2965 y FJ(28.13)69 b(2D)45 b(Ev)-7 b(aluation)46 b(of)f(In)l(terp)t(olating)i(F)-11 b(unctions)3350 3177 y FK([F)j(unction])-3599 b Fv(double)54 b(gsl_interp2d_eval)d Fu(\()p FD(const)31 b(gsl)p 1836 3177 V 41 w(in)m(terp2d)f(*)h Ft(interp)p FD(,)h(const)f(double)565 3287 y Ft(xa)p Fo([])p FD(,)g(const)g(double)f Ft(ya)p Fo([])p FD(,)h(const)g(double)f Ft(za)p Fo([])p FD(,)h(const)f(double)g Ft(x)p FD(,)h(const)g(double)f Ft(y)p FD(,)565 3396 y(gsl)p 677 3396 V 41 w(in)m(terp)p 953 3396 V 40 w(accel)i(*)f Ft(xacc)p FD(,)h(gsl)p 1662 3396 V 40 w(in)m(terp)p 1937 3396 V 40 w(accel)g(*)f Ft(yacc)p Fu(\))3350 3506 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_interp2d_eval_e)e Fu(\()p FD(const)32 b(gsl)p 1784 3506 V 40 w(in)m(terp2d)f(*)f Ft(interp)p FD(,)j(const)e(double)565 3615 y Ft(xa)p Fo([])p FD(,)g(const)g(double) f Ft(ya)p Fo([])p FD(,)h(const)g(double)f Ft(za)p Fo([])p FD(,)h(const)f(double)g Ft(x)p FD(,)h(const)g(double)f Ft(y)p FD(,)565 3725 y(gsl)p 677 3725 V 41 w(in)m(terp)p 953 3725 V 40 w(accel)i(*)f Ft(xacc)p FD(,)h(gsl)p 1662 3725 V 40 w(in)m(terp)p 1937 3725 V 40 w(accel)g(*)f Ft(yacc)p FD(,)h(double)e(*)h Ft(z)p Fu(\))390 3835 y FK(These)i(functions)f(return)g(the)h(in)m(terp)s(olated)h(v)-5 b(alue)34 b(of)f FD(z)38 b FK(for)33 b(a)g(giv)m(en)h(p)s(oin)m(t)f(\() p FD(x)p FK(,)p FD(y)8 b FK(\),)34 b(using)f(the)390 3944 y(in)m(terp)s(olation)f(ob)5 b(ject)31 b FD(in)m(terp)p FK(,)f(data)h(arra)m(ys)g FD(xa)p FK(,)g FD(y)m(a)p FK(,)g(and)f FD(za)h FK(and)e(the)i(accelerators)i FD(xacc)k FK(and)390 4054 y FD(y)m(acc)p FK(.)k(When)26 b FD(x)32 b FK(is)26 b(outside)g(the)g(range)h(of)f FD(xa)g FK(or)g FD(y)34 b FK(is)26 b(outside)g(the)g(range)h(of)f FD(y)m(a)p FK(,)i(the)e(error)g(co)s(de)390 4163 y FH(GSL_EDOM)i FK(is)j(returned.)3350 4354 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_interp2d_eval_extr)q(ap)e Fu(\()p FD(const)31 b(gsl)p 2202 4354 V 41 w(in)m(terp2d)f(*)h Ft(interp)p FD(,)565 4463 y(const)g(double)f Ft(xa)p Fo([])p FD(,)h(const)g(double)f Ft(ya)p Fo([])p FD(,)h(const)g(double)e Ft(za)p Fo([])p FD(,)i(const)g(double)f Ft(x)p FD(,)h(const)565 4573 y(double)f Ft(y)p FD(,)h(gsl)p 1078 4573 V 40 w(in)m(terp)p 1353 4573 V 41 w(accel)h(*)f Ft(xacc)p FD(,)g(gsl)p 2062 4573 V 41 w(in)m(terp)p 2338 4573 V 40 w(accel)h(*)f Ft(yacc)p Fu(\))3350 4682 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_interp2d_eval_ext)q(rap_)q(e)f Fu(\()p FD(const)31 b(gsl)p 2150 4682 V 40 w(in)m(terp2d)g(*)f Ft(interp)p FD(,)j(const)565 4792 y(double)d Ft(xa)p Fo([])p FD(,)h(const)g(double)f Ft(ya)p Fo([])p FD(,)h(const)g(double)f Ft(za)p Fo([])p FD(,)h(const)f(double)g Ft(x)p FD(,)h(const)g(double) 565 4902 y Ft(y)p FD(,)g(gsl)p 785 4902 V 41 w(in)m(terp)p 1061 4902 V 40 w(accel)h(*)f Ft(xacc)p FD(,)g(gsl)p 1769 4902 V 41 w(in)m(terp)p 2045 4902 V 40 w(accel)h(*)f Ft(yacc)p FD(,)h(double)e(*)g Ft(z)p Fu(\))390 5011 y FK(These)j(functions)f(return)g(the)h(in)m(terp)s(olated)h(v)-5 b(alue)34 b(of)f FD(z)38 b FK(for)33 b(a)g(giv)m(en)h(p)s(oin)m(t)f(\() p FD(x)p FK(,)p FD(y)8 b FK(\),)34 b(using)f(the)390 5121 y(in)m(terp)s(olation)f(ob)5 b(ject)31 b FD(in)m(terp)p FK(,)f(data)h(arra)m(ys)g FD(xa)p FK(,)g FD(y)m(a)p FK(,)g(and)f FD(za)h FK(and)e(the)i(accelerators)i FD(xacc)k FK(and)390 5230 y FD(y)m(acc)p FK(.)52 b(The)33 b(functions)g(p)s(erform)f(no)h(b) s(ounds)e(c)m(hec)m(king,)36 b(so)e(when)f FD(x)39 b FK(is)34 b(outside)f(the)h(range)g(of)390 5340 y FD(xa)d FK(or)f FD(y)38 b FK(is)31 b(outside)f(the)h(range)g(of)f FD(y)m(a)p FK(,)i(extrap)s(olation)f(is)g(p)s(erformed.)p eop end %%Page: 359 377 TeXDict begin 359 376 bop 150 -116 a FK(Chapter)30 b(28:)41 b(In)m(terp)s(olation)2437 b(359)3350 299 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_interp2d_eval_deri)q(v_x)e Fu(\()p FD(const)31 b(gsl)p 2254 299 28 4 v 41 w(in)m(terp2d)f(*)h Ft(interp)p FD(,)565 408 y(const)g(double)f Ft(xa)p Fo([])p FD(,)h(const)g(double)f Ft(ya)p Fo([])p FD(,)h(const)g(double)e Ft(za)p Fo([])p FD(,)i(const)g(double)f Ft(x)p FD(,)h(const)565 518 y(double)f Ft(y)p FD(,)h(gsl)p 1078 518 V 40 w(in)m(terp)p 1353 518 V 41 w(accel)h(*)f Ft(xacc)p FD(,)g(gsl)p 2062 518 V 41 w(in)m(terp)p 2338 518 V 40 w(accel)h(*)f Ft(yacc)p Fu(\))3350 628 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_interp2d_eval_der)q(iv_x)q(_e)f Fu(\()p FD(const)31 b(gsl)p 2202 628 V 41 w(in)m(terp2d)f(*)h Ft(interp)p FD(,)565 737 y(const)g(double)f Ft(xa)p Fo([])p FD(,)h(const)g(double)f Ft(ya)p Fo([])p FD(,)h(const)g(double)e Ft(za)p Fo([])p FD(,)i(const)g(double)f Ft(x)p FD(,)h(const)565 847 y(double)f Ft(y)p FD(,)h(gsl)p 1078 847 V 40 w(in)m(terp)p 1353 847 V 41 w(accel)h(*)f Ft(xacc)p FD(,)g(gsl)p 2062 847 V 41 w(in)m(terp)p 2338 847 V 40 w(accel)h(*)f Ft(yacc)p FD(,)h(double)e(*)g Ft(d)p Fu(\))390 956 y FK(These)23 b(functions)g(return)g(the)g(in)m(terp)s(olated)i(v)-5 b(alue)24 b FD(d)i FK(=)f FE(@)5 b(z)t(=@)g(x)25 b FK(for)e(a)h(giv)m (en)g(p)s(oin)m(t)g(\()p FD(x)p FK(,)p FD(y)8 b FK(\),)25 b(using)390 1066 y(the)32 b(in)m(terp)s(olation)h(ob)5 b(ject)33 b FD(in)m(terp)p FK(,)f(data)g(arra)m(ys)g FD(xa)p FK(,)h FD(y)m(a)p FK(,)g(and)e FD(za)i FK(and)e(the)h (accelerators)i FD(xacc)390 1176 y FK(and)27 b FD(y)m(acc)p FK(.)42 b(When)27 b FD(x)34 b FK(is)28 b(outside)g(the)g(range)g(of)g FD(xa)h FK(or)e FD(y)36 b FK(is)28 b(outside)g(the)g(range)g(of)g FD(y)m(a)p FK(,)h(the)f(error)390 1285 y(co)s(de)j FH(GSL_EDOM)d FK(is)i(returned.)3350 1650 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_interp2d_eval_deri)q(v_y)e Fu(\()p FD(const)31 b(gsl)p 2254 1650 V 41 w(in)m(terp2d)f(*)h Ft(interp)p FD(,)565 1760 y(const)g(double)f Ft(xa)p Fo([])p FD(,)h(const)g(double)f Ft(ya)p Fo([])p FD(,)h(const)g(double)e Ft(za)p Fo([])p FD(,)i(const)g(double)f Ft(x)p FD(,)h(const)565 1870 y(double)f Ft(y)p FD(,)h(gsl)p 1078 1870 V 40 w(in)m(terp)p 1353 1870 V 41 w(accel)h(*)f Ft(xacc)p FD(,)g(gsl)p 2062 1870 V 41 w(in)m(terp)p 2338 1870 V 40 w(accel)h(*)f Ft(yacc)p Fu(\))3350 1979 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_interp2d_eval_der)q(iv_y)q(_e)f Fu(\()p FD(const)31 b(gsl)p 2202 1979 V 41 w(in)m(terp2d)f(*)h Ft(interp)p FD(,)565 2089 y(const)g(double)f Ft(xa)p Fo([])p FD(,)h(const)g(double)f Ft(ya)p Fo([])p FD(,)h(const)g(double)e Ft(za)p Fo([])p FD(,)i(const)g(double)f Ft(x)p FD(,)h(const)565 2198 y(double)f Ft(y)p FD(,)h(gsl)p 1078 2198 V 40 w(in)m(terp)p 1353 2198 V 41 w(accel)h(*)f Ft(xacc)p FD(,)g(gsl)p 2062 2198 V 41 w(in)m(terp)p 2338 2198 V 40 w(accel)h(*)f Ft(yacc)p FD(,)h(double)e(*)g Ft(d)p Fu(\))390 2308 y FK(These)24 b(functions)f(return)g(the)h(in)m(terp)s(olated)g(v)-5 b(alue)25 b FD(d)h FK(=)f FE(@)5 b(z)t(=@)g(y)28 b FK(for)c(a)g(giv)m (en)h(p)s(oin)m(t)e(\()p FD(x)p FK(,)p FD(y)8 b FK(\),)26 b(using)390 2418 y(the)32 b(in)m(terp)s(olation)h(ob)5 b(ject)33 b FD(in)m(terp)p FK(,)f(data)g(arra)m(ys)g FD(xa)p FK(,)h FD(y)m(a)p FK(,)g(and)e FD(za)i FK(and)e(the)h (accelerators)i FD(xacc)390 2527 y FK(and)27 b FD(y)m(acc)p FK(.)42 b(When)27 b FD(x)34 b FK(is)28 b(outside)g(the)g(range)g(of)g FD(xa)h FK(or)e FD(y)36 b FK(is)28 b(outside)g(the)g(range)g(of)g FD(y)m(a)p FK(,)h(the)f(error)390 2637 y(co)s(de)j FH(GSL_EDOM)d FK(is)i(returned.)3350 3002 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_interp2d_eval_deri)q(v_x)q(x)d Fu(\()p FD(const)32 b(gsl)p 2307 3002 V 40 w(in)m(terp2d)f(*)f Ft(interp)p FD(,)565 3112 y(const)h(double)f Ft(xa)p Fo([])p FD(,)h(const)g(double)f Ft(ya)p Fo([])p FD(,)h(const)g(double)e Ft(za)p Fo([])p FD(,)i(const)g(double)f Ft(x)p FD(,)h(const)565 3221 y(double)f Ft(y)p FD(,)h(gsl)p 1078 3221 V 40 w(in)m(terp)p 1353 3221 V 41 w(accel)h(*)f Ft(xacc)p FD(,)g(gsl)p 2062 3221 V 41 w(in)m(terp)p 2338 3221 V 40 w(accel)h(*)f Ft(yacc)p Fu(\))3350 3331 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_interp2d_eval_der)q(iv_x)q(x_e)f Fu(\()p FD(const)31 b(gsl)p 2254 3331 V 41 w(in)m(terp2d)f(*)h Ft(interp)p FD(,)565 3440 y(const)g(double)f Ft(xa)p Fo([])p FD(,)h(const)g(double)f Ft(ya)p Fo([])p FD(,)h(const)g(double)e Ft(za)p Fo([])p FD(,)i(const)g(double)f Ft(x)p FD(,)h(const)565 3550 y(double)f Ft(y)p FD(,)h(gsl)p 1078 3550 V 40 w(in)m(terp)p 1353 3550 V 41 w(accel)h(*)f Ft(xacc)p FD(,)g(gsl)p 2062 3550 V 41 w(in)m(terp)p 2338 3550 V 40 w(accel)h(*)f Ft(yacc)p FD(,)h(double)e(*)g Ft(d)p Fu(\))390 3660 y FK(These)36 b(functions)f(return)g(the)h(in)m(terp)s(olated)h(v)-5 b(alue)36 b FD(d)j FK(=)34 b FE(@)2506 3627 y FB(2)2543 3660 y FE(z)t(=@)5 b(x)2739 3627 y FB(2)2813 3660 y FK(for)36 b(a)g(giv)m(en)h(p)s(oin)m(t)f(\()p FD(x)p FK(,)p FD(y)8 b FK(\),)390 3769 y(using)29 b(the)h(in)m(terp)s(olation)h(ob)5 b(ject)30 b FD(in)m(terp)p FK(,)g(data)h(arra)m(ys)f FD(xa)p FK(,)g FD(y)m(a)p FK(,)h(and)e FD(za)h FK(and)g(the)f (accelerators)390 3879 y FD(xacc)35 b FK(and)28 b FD(y)m(acc)p FK(.)42 b(When)28 b FD(x)35 b FK(is)28 b(outside)h(the)g(range)g(of)g FD(xa)f FK(or)h FD(y)36 b FK(is)29 b(outside)f(the)h(range)g(of)g FD(y)m(a)p FK(,)h(the)390 3988 y(error)g(co)s(de)h FH(GSL_EDOM)d FK(is)i(returned.)3350 4354 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_interp2d_eval_deri)q(v_y)q(y)d Fu(\()p FD(const)32 b(gsl)p 2307 4354 V 40 w(in)m(terp2d)f(*)f Ft(interp)p FD(,)565 4463 y(const)h(double)f Ft(xa)p Fo([])p FD(,)h(const)g(double)f Ft(ya)p Fo([])p FD(,)h(const)g(double)e Ft(za)p Fo([])p FD(,)i(const)g(double)f Ft(x)p FD(,)h(const)565 4573 y(double)f Ft(y)p FD(,)h(gsl)p 1078 4573 V 40 w(in)m(terp)p 1353 4573 V 41 w(accel)h(*)f Ft(xacc)p FD(,)g(gsl)p 2062 4573 V 41 w(in)m(terp)p 2338 4573 V 40 w(accel)h(*)f Ft(yacc)p Fu(\))3350 4682 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_interp2d_eval_der)q(iv_y)q(y_e)f Fu(\()p FD(const)31 b(gsl)p 2254 4682 V 41 w(in)m(terp2d)f(*)h Ft(interp)p FD(,)565 4792 y(const)g(double)f Ft(xa)p Fo([])p FD(,)h(const)g(double)f Ft(ya)p Fo([])p FD(,)h(const)g(double)e Ft(za)p Fo([])p FD(,)i(const)g(double)f Ft(x)p FD(,)h(const)565 4902 y(double)f Ft(y)p FD(,)h(gsl)p 1078 4902 V 40 w(in)m(terp)p 1353 4902 V 41 w(accel)h(*)f Ft(xacc)p FD(,)g(gsl)p 2062 4902 V 41 w(in)m(terp)p 2338 4902 V 40 w(accel)h(*)f Ft(yacc)p FD(,)h(double)e(*)g Ft(d)p Fu(\))390 5011 y FK(These)36 b(functions)g(return)f(the)h(in)m(terp)s(olated)h(v)-5 b(alue)37 b FD(d)i FK(=)c FE(@)2509 4978 y FB(2)2546 5011 y FE(z)t(=@)5 b(y)2738 4978 y FB(2)2812 5011 y FK(for)36 b(a)h(giv)m(en)g(p)s(oin)m(t)f(\()p FD(x)p FK(,)p FD(y)8 b FK(\),)390 5121 y(using)29 b(the)h(in)m(terp)s(olation)h(ob)5 b(ject)30 b FD(in)m(terp)p FK(,)g(data)h(arra)m(ys)f FD(xa)p FK(,)g FD(y)m(a)p FK(,)h(and)e FD(za)h FK(and)g(the)f (accelerators)390 5230 y FD(xacc)35 b FK(and)28 b FD(y)m(acc)p FK(.)42 b(When)28 b FD(x)35 b FK(is)28 b(outside)h(the)g(range)g(of)g FD(xa)f FK(or)h FD(y)36 b FK(is)29 b(outside)f(the)h(range)g(of)g FD(y)m(a)p FK(,)h(the)390 5340 y(error)g(co)s(de)h FH(GSL_EDOM)d FK(is)i(returned.)p eop end %%Page: 360 378 TeXDict begin 360 377 bop 150 -116 a FK(Chapter)30 b(28:)41 b(In)m(terp)s(olation)2437 b(360)3350 299 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_interp2d_eval_deri)q(v_x)q(y)d Fu(\()p FD(const)32 b(gsl)p 2307 299 28 4 v 40 w(in)m(terp2d)f(*)f Ft(interp)p FD(,)565 408 y(const)h(double)f Ft(xa)p Fo([])p FD(,)h(const)g(double)f Ft(ya)p Fo([])p FD(,)h(const)g(double)e Ft(za)p Fo([])p FD(,)i(const)g(double)f Ft(x)p FD(,)h(const)565 518 y(double)f Ft(y)p FD(,)h(gsl)p 1078 518 V 40 w(in)m(terp)p 1353 518 V 41 w(accel)h(*)f Ft(xacc)p FD(,)g(gsl)p 2062 518 V 41 w(in)m(terp)p 2338 518 V 40 w(accel)h(*)f Ft(yacc)p Fu(\))3350 628 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_interp2d_eval_der)q(iv_x)q(y_e)f Fu(\()p FD(const)31 b(gsl)p 2254 628 V 41 w(in)m(terp2d)f(*)h Ft(interp)p FD(,)565 737 y(const)g(double)f Ft(xa)p Fo([])p FD(,)h(const)g(double)f Ft(ya)p Fo([])p FD(,)h(const)g(double)e Ft(za)p Fo([])p FD(,)i(const)g(double)f Ft(x)p FD(,)h(const)565 847 y(double)f Ft(y)p FD(,)h(gsl)p 1078 847 V 40 w(in)m(terp)p 1353 847 V 41 w(accel)h(*)f Ft(xacc)p FD(,)g(gsl)p 2062 847 V 41 w(in)m(terp)p 2338 847 V 40 w(accel)h(*)f Ft(yacc)p FD(,)h(double)e(*)g Ft(d)p Fu(\))390 956 y FK(These)h(functions)g (return)f(the)h(in)m(terp)s(olated)h(v)-5 b(alue)32 b FD(d)i FK(=)26 b FE(@)2465 923 y FB(2)2503 956 y FE(z)t(=@)5 b(x@)g(y)35 b FK(for)c(a)h(giv)m(en)g(p)s(oin)m(t)f(\()p FD(x)p FK(,)p FD(y)8 b FK(\),)390 1066 y(using)29 b(the)h(in)m(terp)s (olation)h(ob)5 b(ject)30 b FD(in)m(terp)p FK(,)g(data)h(arra)m(ys)f FD(xa)p FK(,)g FD(y)m(a)p FK(,)h(and)e FD(za)h FK(and)g(the)f (accelerators)390 1176 y FD(xacc)35 b FK(and)28 b FD(y)m(acc)p FK(.)42 b(When)28 b FD(x)35 b FK(is)28 b(outside)h(the)g(range)g(of)g FD(xa)f FK(or)h FD(y)36 b FK(is)29 b(outside)f(the)h(range)g(of)g FD(y)m(a)p FK(,)h(the)390 1285 y(error)g(co)s(de)h FH(GSL_EDOM)d FK(is)i(returned.)150 1508 y FJ(28.14)69 b(2D)45 b(Higher-lev)l(el)i (In)l(terface)150 1667 y FK(The)27 b(functions)g(describ)s(ed)g(in)g (the)h(previous)f(sections)h(required)f(the)h(user)f(to)h(supply)e(p)s (oin)m(ters)h(to)i(the)150 1777 y FE(x)p FK(,)f FE(y)s FK(,)g(and)f FE(z)32 b FK(arra)m(ys)c(on)g(eac)m(h)g(call.)42 b(The)27 b(follo)m(wing)i(functions)e(are)h(equiv)-5 b(alen)m(t)29 b(to)f(the)g(corresp)s(onding)150 1887 y FH(gsl_interp2d)21 b FK(functions)j(but)g(main)m(tain)i(a)e(cop)m(y)i (of)e(this)h(data)g(in)f(the)h FH(gsl_spline2d)c FK(ob)5 b(ject.)40 b(This)150 1996 y(remo)m(v)m(es)32 b(the)f(need)f(to)i(pass) e FD(xa)p FK(,)h FD(y)m(a)p FK(,)h(and)e FD(za)i FK(as)f(argumen)m(ts)f (on)h(eac)m(h)h(ev)-5 b(aluation.)43 b(These)30 b(functions)150 2106 y(are)h(de\014ned)e(in)h(the)h(header)f(\014le)g FH(gsl_spline2d.h)p FK(.)3350 2276 y([F)-8 b(unction])-3599 b Fv(gsl_spline2d)56 b(*)d(gsl_spline2d_alloc)d Fu(\()p FD(const)32 b(gsl)p 2307 2276 V 40 w(in)m(terp2d)p 2678 2276 V 40 w(t)m(yp)s(e)f(*)g Ft(T)p FD(,)565 2385 y(size)p 712 2385 V 41 w(t)g Ft(xsize)p FD(,)h(size)p 1277 2385 V 41 w(t)e Ft(ysize)p Fu(\))3350 2535 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_spline2d_init)e Fu(\()p FD(gsl)p 1441 2535 V 41 w(spline2d)30 b(*)h Ft(spline)p FD(,)h(const)f(double)f Ft(xa)p Fo([])p FD(,)565 2645 y(const)h(double)f Ft(ya)p Fo([])p FD(,)h(const)g(double)f Ft(za)p Fo([])p FD(,)h(size)p 2206 2645 V 41 w(t)f Ft(xsize)p FD(,)i(size)p 2770 2645 V 41 w(t)f Ft(ysize)p Fu(\))3350 2795 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_spline2d_free)c Fu(\()p FD(gsl)p 1493 2795 V 41 w(spline2d)30 b(*)h Ft(spline)p Fu(\))3350 2944 y FK([F)-8 b(unction])-3599 b Fv(const)54 b(char)f(*)g (gsl_spline2d_name)e Fu(\()p FD(const)31 b(gsl)p 2150 2944 V 40 w(spline2d)f(*)h Ft(spline)p Fu(\))3350 3094 y FK([F)-8 b(unction])-3599 b Fv(unsigned)55 b(int)e (gsl_spline2d_min_size)f Fu(\()p FD(const)31 b(gsl)p 2359 3094 V 41 w(spline2d)f(*)g Ft(spline)p Fu(\))3350 3244 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_spline2d_eval)d Fu(\()p FD(const)31 b(gsl)p 1836 3244 V 41 w(spline2d)f(*)g Ft(spline)p FD(,)j(const)e(double)565 3354 y Ft(x)p FD(,)g(const)g (double)f Ft(y)p FD(,)h(gsl)p 1424 3354 V 40 w(in)m(terp)p 1699 3354 V 40 w(accel)i(*)d Ft(xacc)p FD(,)i(gsl)p 2408 3354 V 41 w(in)m(terp)p 2684 3354 V 40 w(accel)g(*)f Ft(yacc)p Fu(\))3350 3463 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_spline2d_eval_e)e Fu(\()p FD(const)32 b(gsl)p 1784 3463 V 40 w(spline2d)e(*)h Ft(spline)p FD(,)h(const)f (double)565 3573 y Ft(x)p FD(,)g(const)g(double)f Ft(y)p FD(,)h(gsl)p 1424 3573 V 40 w(in)m(terp)p 1699 3573 V 40 w(accel)i(*)d Ft(xacc)p FD(,)i(gsl)p 2408 3573 V 41 w(in)m(terp)p 2684 3573 V 40 w(accel)g(*)f Ft(yacc)p FD(,)g(double)f(*)h Ft(z)p Fu(\))3350 3723 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_spline2d_eval_deri)q(v_x)e Fu(\()p FD(const)31 b(gsl)p 2254 3723 V 41 w(spline2d)f(*)h Ft(spline)p FD(,)565 3832 y(const)g(double)f Ft(x)p FD(,)h(const)g (double)f Ft(y)p FD(,)g(gsl)p 1954 3832 V 41 w(in)m(terp)p 2230 3832 V 40 w(accel)i(*)f Ft(xacc)p FD(,)h(gsl)p 2939 3832 V 40 w(in)m(terp)p 3214 3832 V 41 w(accel)g(*)565 3942 y Ft(yacc)p Fu(\))3350 4051 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_spline2d_eval_der)q(iv_x)q(_e)f 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1954 4859 V 41 w(in)m(terp)p 2230 4859 V 40 w(accel)i(*)f Ft(xacc)p FD(,)h(gsl)p 2939 4859 V 40 w(in)m(terp)p 3214 4859 V 41 w(accel)g(*)565 4968 y Ft(yacc)p FD(,)g(double)e(*)h Ft(d)p Fu(\))3350 5118 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_spline2d_eval_deri)q (v_x)q(x)d Fu(\()p FD(const)32 b(gsl)p 2307 5118 V 40 w(spline2d)e(*)h Ft(spline)p FD(,)565 5228 y(const)g(double)f Ft(x)p FD(,)h(const)g(double)f Ft(y)p FD(,)g(gsl)p 1954 5228 V 41 w(in)m(terp)p 2230 5228 V 40 w(accel)i(*)f Ft(xacc)p FD(,)h(gsl)p 2939 5228 V 40 w(in)m(terp)p 3214 5228 V 41 w(accel)g(*)565 5337 y Ft(yacc)p Fu(\))p eop end %%Page: 361 379 TeXDict begin 361 378 bop 150 -116 a FK(Chapter)30 b(28:)41 b(In)m(terp)s(olation)2437 b(361)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_spline2d_eval_der)q(iv_x)q(x_e)f Fu(\()p FD(const)31 b(gsl)p 2254 299 28 4 v 41 w(spline2d)f(*)h Ft(spline)p FD(,)565 408 y(const)g(double)f Ft(x)p FD(,)h(const)g (double)f Ft(y)p FD(,)g(gsl)p 1954 408 V 41 w(in)m(terp)p 2230 408 V 40 w(accel)i(*)f Ft(xacc)p FD(,)h(gsl)p 2939 408 V 40 w(in)m(terp)p 3214 408 V 41 w(accel)g(*)565 518 y Ft(yacc)p FD(,)g(double)e(*)h Ft(d)p Fu(\))3350 684 y FK([F)-8 b(unction])-3599 b Fv(double)54 b (gsl_spline2d_eval_deri)q(v_y)q(y)d Fu(\()p FD(const)32 b(gsl)p 2307 684 V 40 w(spline2d)e(*)h Ft(spline)p FD(,)565 793 y(const)g(double)f Ft(x)p FD(,)h(const)g(double)f Ft(y)p FD(,)g(gsl)p 1954 793 V 41 w(in)m(terp)p 2230 793 V 40 w(accel)i(*)f Ft(xacc)p FD(,)h(gsl)p 2939 793 V 40 w(in)m(terp)p 3214 793 V 41 w(accel)g(*)565 903 y Ft(yacc)p Fu(\))3350 1013 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_spline2d_eval_der)q(iv_y)q(y_e)f Fu(\()p FD(const)31 b(gsl)p 2254 1013 V 41 w(spline2d)f(*)h Ft(spline)p FD(,)565 1122 y(const)g(double)f Ft(x)p FD(,)h(const)g(double)f Ft(y)p FD(,)g(gsl)p 1954 1122 V 41 w(in)m(terp)p 2230 1122 V 40 w(accel)i(*)f Ft(xacc)p FD(,)h(gsl)p 2939 1122 V 40 w(in)m(terp)p 3214 1122 V 41 w(accel)g(*)565 1232 y Ft(yacc)p FD(,)g(double)e(*)h Ft(d)p Fu(\))3350 1398 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_spline2d_eval_deri)q (v_x)q(y)d Fu(\()p FD(const)32 b(gsl)p 2307 1398 V 40 w(spline2d)e(*)h Ft(spline)p FD(,)565 1507 y(const)g(double)f Ft(x)p FD(,)h(const)g(double)f Ft(y)p FD(,)g(gsl)p 1954 1507 V 41 w(in)m(terp)p 2230 1507 V 40 w(accel)i(*)f Ft(xacc)p FD(,)h(gsl)p 2939 1507 V 40 w(in)m(terp)p 3214 1507 V 41 w(accel)g(*)565 1617 y Ft(yacc)p Fu(\))3350 1726 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_spline2d_eval_der)q (iv_x)q(y_e)f Fu(\()p FD(const)31 b(gsl)p 2254 1726 V 41 w(spline2d)f(*)h Ft(spline)p FD(,)565 1836 y(const)g(double)f Ft(x)p FD(,)h(const)g(double)f Ft(y)p FD(,)g(gsl)p 1954 1836 V 41 w(in)m(terp)p 2230 1836 V 40 w(accel)i(*)f Ft(xacc)p FD(,)h(gsl)p 2939 1836 V 40 w(in)m(terp)p 3214 1836 V 41 w(accel)g(*)565 1946 y Ft(yacc)p FD(,)g(double)e(*)h Ft(d)p Fu(\))3350 2111 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_spline2d_set)e Fu(\()p FD(const)31 b(gsl)p 1627 2111 V 40 w(spline2d)f(*)h Ft(spline)p 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/MCshow { currentpoint stroke M exch dup MFwidth -2 div 3 -1 roll R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /XYsave { [( ) 1 2 true false 3 ()] } bind def /XYrestore { [( ) 1 2 true false 4 ()] } bind def Level1 SuppressPDFMark or {} { /SDict 10 dict def systemdict /pdfmark known not { userdict /pdfmark systemdict /cleartomark get put } if SDict begin [ /Title (interp2d.eps) /Subject (gnuplot plot) /Creator (gnuplot 4.6 patchlevel 5) /Author (palken) % /Producer (gnuplot) % /Keywords () /CreationDate (Thu May 1 10:20:59 2014) /DOCINFO pdfmark end } ifelse end %%EndProlog %%Page: 1 1 gnudict begin gsave doclip 50 50 translate 0.050 0.050 scale 0 setgray newpath (Helvetica) findfont 140 scalefont setfont BackgroundColor 0 lt 3 1 roll 0 lt exch 0 lt or or not {BackgroundColor C 1.000 0 0 7200.00 5040.00 BoxColFill} if gsave % colour palette begin /maxcolors 0 def /HSV2RGB { exch dup 0.0 eq {pop exch pop dup dup} % achromatic gray { /HSVs exch def /HSVv exch def 6.0 mul dup floor dup 3 1 roll sub /HSVf exch def /HSVi exch cvi def /HSVp HSVv 1.0 HSVs sub mul def /HSVq HSVv 1.0 HSVs HSVf mul sub mul def /HSVt HSVv 1.0 HSVs 1.0 HSVf sub mul sub mul def /HSVi HSVi 6 mod def 0 HSVi eq {HSVv HSVt HSVp} {1 HSVi eq {HSVq HSVv HSVp}{2 HSVi eq {HSVp HSVv HSVt} {3 HSVi eq {HSVp HSVq HSVv}{4 HSVi eq {HSVt HSVp HSVv} {HSVv HSVp HSVq} ifelse} ifelse} ifelse} ifelse} ifelse } ifelse} def /Constrain { dup 0 lt {0 exch pop}{dup 1 gt {1 exch pop} if} ifelse} def /YIQ2RGB { 3 copy -1.702 mul exch -1.105 mul add add Constrain 4 1 roll 3 copy -0.647 mul exch -0.272 mul add add Constrain 5 1 roll 0.621 mul exch -0.956 mul add add Constrain 3 1 roll } def /CMY2RGB { 1 exch sub exch 1 exch sub 3 2 roll 1 exch sub 3 1 roll exch } def /XYZ2RGB { 3 copy -0.9017 mul exch -0.1187 mul add exch 0.0585 mul exch add Constrain 4 1 roll 3 copy -0.0279 mul exch 1.999 mul add exch -0.9844 mul add Constrain 5 1 roll -0.2891 mul exch -0.5338 mul add exch 1.91 mul exch add Constrain 3 1 roll} def /SelectSpace {ColorSpace (HSV) eq {HSV2RGB}{ColorSpace (XYZ) eq { XYZ2RGB}{ColorSpace (CMY) eq {CMY2RGB}{ColorSpace (YIQ) eq {YIQ2RGB} if} ifelse} ifelse} ifelse} def /InterpolatedColor true def /grayindex {/gidx 0 def {GrayA gidx get grayv ge {exit} if /gidx gidx 1 add def} loop} def /dgdx {grayv GrayA gidx get sub GrayA gidx 1 sub get GrayA gidx get sub div} def /redvalue {RedA gidx get RedA gidx 1 sub get RedA gidx get sub dgdxval mul add} def /greenvalue {GreenA gidx get GreenA gidx 1 sub get GreenA gidx get sub dgdxval mul add} def /bluevalue {BlueA gidx get BlueA gidx 1 sub get BlueA gidx get sub dgdxval mul add} def /interpolate { grayindex grayv GrayA gidx get sub abs 1e-5 le {RedA gidx get GreenA gidx get BlueA gidx get} {/dgdxval dgdx def redvalue greenvalue bluevalue} ifelse} def /GrayA [0 .125 .25 .375 .5 .625 .75 .875 1 ] def /RedA [0 0 0 .0588 .5647 1 1 .9333 .498 ] def /GreenA [0 .0588 .5647 1 1 .9333 .4392 0 0 ] def /BlueA [.5647 1 1 .9333 .4392 0 0 0 0 ] def /pm3dround {maxcolors 0 gt {dup 1 ge {pop 1} {maxcolors mul floor maxcolors 1 sub div} ifelse} if} def /pm3dGamma 1.0 1.5 Gamma mul div def /ColorSpace (RGB) def Color InterpolatedColor or { % COLOUR vs. GRAY map InterpolatedColor { %% Interpolation vs. RGB-Formula /g {stroke pm3dround /grayv exch def interpolate SelectSpace setrgbcolor} bind def }{ /g {stroke pm3dround dup cF7 Constrain exch dup cF5 Constrain exch cF15 Constrain SelectSpace setrgbcolor} bind def } ifelse }{ /g {stroke pm3dround pm3dGamma exp setgray} bind def } ifelse 1.000 UL LTb LCb setrgbcolor 1.000 UP % Begin plot #1 LCb setrgbcolor /Helvetica findfont 140 scalefont setfont /vshift -46 def 5535 3979 M ('dat' us 1:2:3) Rshow 1.000 UL LT0 LC0 setrgbcolor %pm3d_map_begin 1.000 UL LT0 LC0 setrgbcolor .0101 g 1098 928 N -51 0 0 33 51 0 h .0201 g 1098 961 N -51 0 0 34 51 0 h .0301 g 1098 995 N -51 0 0 34 51 0 h .0401 g 1098 1029 N -51 0 0 33 51 0 h .0502 g 1098 1062 N -51 0 0 34 51 0 h .0602 g 1098 1096 N 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3077 N -50 0 0 33 50 0 h .6633 g 2160 3110 N -50 0 0 34 50 0 h .6701 g 2160 3144 N -50 0 0 33 50 0 h .6769 g 2160 3177 N -50 0 0 34 50 0 h .6837 g 2160 3211 N -50 0 0 34 50 0 h .6905 g 2160 3245 N -50 0 0 33 50 0 h .6973 g 2160 3278 N -50 0 0 34 50 0 h .7041 g 2160 3312 N -50 0 0 33 50 0 h .7109 g 2160 3345 N -50 0 0 34 50 0 h .7177 g 2160 3379 N -50 0 0 33 50 0 h .7246 g 2160 3412 N -50 0 0 34 50 0 h .7314 g 2160 3446 N -50 0 0 34 50 0 h .7382 g 2160 3480 N -50 0 0 33 50 0 h .745 g 2160 3513 N -50 0 0 34 50 0 h .7518 g 2160 3547 N -50 0 0 33 50 0 h .7586 g 2160 3580 N -50 0 0 34 50 0 h .7654 g 2160 3614 N -50 0 0 34 50 0 h .7722 g 2160 3648 N -50 0 0 33 50 0 h .779 g 2160 3681 N -50 0 0 34 50 0 h .7859 g 2160 3715 N -50 0 0 33 50 0 h .7927 g 2160 3748 N -50 0 0 34 50 0 h .7995 g 2160 3782 N -50 0 0 34 50 0 h .8063 g 2160 3816 N -50 0 0 33 50 0 h .8131 g 2160 3849 N -50 0 0 34 50 0 h .8199 g 2160 3883 N -50 0 0 33 50 0 h .8267 g 2160 3916 N -50 0 0 34 50 0 h .8335 g 2160 3950 N -50 0 0 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0 0 33 51 0 h .5302 g 2210 2439 N -51 0 0 34 51 0 h .5368 g 2210 2473 N -51 0 0 34 51 0 h .5435 g 2210 2507 N -51 0 0 33 51 0 h .5502 g 2210 2540 N -51 0 0 34 51 0 h .5568 g 2210 2574 N -51 0 0 32 51 0 h .5635 g 2210 2606 N -51 0 0 34 51 0 h .5701 g 2210 2640 N -51 0 0 33 51 0 h .5768 g 2210 2673 N -51 0 0 34 51 0 h .5834 g 2210 2707 N -51 0 0 34 51 0 h .5901 g 2210 2741 N -51 0 0 33 51 0 h .5968 g 2210 2774 N -51 0 0 34 51 0 h .6034 g 2210 2808 N -51 0 0 33 51 0 h .6101 g 2210 2841 N -51 0 0 34 51 0 h .6167 g 2210 2875 N -51 0 0 34 51 0 h .6234 g 2210 2909 N -51 0 0 33 51 0 h .6301 g 2210 2942 N -51 0 0 34 51 0 h .6367 g 2210 2976 N -51 0 0 33 51 0 h .6434 g 2210 3009 N -51 0 0 34 51 0 h .65 g 2210 3043 N -51 0 0 34 51 0 h .6567 g 2210 3077 N -51 0 0 33 51 0 h .6633 g 2210 3110 N -51 0 0 34 51 0 h .67 g 2210 3144 N -51 0 0 33 51 0 h .6767 g 2210 3177 N -51 0 0 34 51 0 h .6833 g 2210 3211 N -51 0 0 34 51 0 h .69 g 2210 3245 N -51 0 0 33 51 0 h .6966 g 2210 3278 N -51 0 0 34 51 0 h 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4185 N -51 0 0 34 51 0 h .883 g 2210 4219 N -51 0 0 33 51 0 h .2406 g 2261 928 N -50 0 0 33 50 0 h .2471 g 2261 961 N -50 0 0 34 50 0 h .2536 g 2261 995 N -50 0 0 34 50 0 h .2601 g 2261 1029 N -50 0 0 33 50 0 h .2666 g 2261 1062 N -50 0 0 34 50 0 h .2731 g 2261 1096 N -50 0 0 33 50 0 h .2797 g 2261 1129 N -50 0 0 34 50 0 h .2862 g 2261 1163 N -50 0 0 34 50 0 h .2927 g 2261 1197 N -50 0 0 33 50 0 h .2992 g 2261 1230 N -50 0 0 34 50 0 h .3057 g 2261 1264 N -50 0 0 33 50 0 h .3122 g 2261 1297 N -50 0 0 34 50 0 h .3187 g 2261 1331 N -50 0 0 33 50 0 h .3252 g 2261 1364 N -50 0 0 34 50 0 h .3317 g 2261 1398 N -50 0 0 34 50 0 h .3382 g 2261 1432 N -50 0 0 33 50 0 h .3447 g 2261 1465 N -50 0 0 34 50 0 h .3512 g 2261 1499 N -50 0 0 33 50 0 h .3577 g 2261 1532 N -50 0 0 34 50 0 h .3642 g 2261 1566 N -50 0 0 34 50 0 h .3707 g 2261 1600 N -50 0 0 33 50 0 h .3772 g 2261 1633 N -50 0 0 34 50 0 h .3837 g 2261 1667 N -50 0 0 33 50 0 h .3902 g 2261 1700 N -50 0 0 34 50 0 h .3967 g 2261 1734 N -50 0 0 34 50 0 h .4032 g 2261 1768 N -50 0 0 33 50 0 h .4097 g 2261 1801 N -50 0 0 34 50 0 h .4162 g 2261 1835 N -50 0 0 33 50 0 h .4228 g 2261 1868 N -50 0 0 34 50 0 h .4293 g 2261 1902 N -50 0 0 33 50 0 h .4358 g 2261 1935 N -50 0 0 34 50 0 h .4423 g 2261 1969 N -50 0 0 34 50 0 h .4488 g 2261 2003 N -50 0 0 33 50 0 h .4553 g 2261 2036 N -50 0 0 34 50 0 h .4618 g 2261 2070 N -50 0 0 33 50 0 h .4683 g 2261 2103 N -50 0 0 34 50 0 h .4748 g 2261 2137 N -50 0 0 34 50 0 h .4813 g 2261 2171 N -50 0 0 33 50 0 h .4878 g 2261 2204 N -50 0 0 34 50 0 h .4943 g 2261 2238 N -50 0 0 33 50 0 h .5008 g 2261 2271 N -50 0 0 34 50 0 h .5073 g 2261 2305 N -50 0 0 34 50 0 h .5138 g 2261 2339 N -50 0 0 33 50 0 h .5203 g 2261 2372 N -50 0 0 34 50 0 h .5268 g 2261 2406 N -50 0 0 33 50 0 h .5333 g 2261 2439 N -50 0 0 34 50 0 h .5398 g 2261 2473 N -50 0 0 34 50 0 h .5463 g 2261 2507 N -50 0 0 33 50 0 h .5528 g 2261 2540 N -50 0 0 34 50 0 h .5593 g 2261 2574 N -50 0 0 32 50 0 h .5658 g 2261 2606 N -50 0 0 34 50 0 h 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3513 N -50 0 0 34 50 0 h .748 g 2261 3547 N -50 0 0 33 50 0 h .7545 g 2261 3580 N -50 0 0 34 50 0 h .761 g 2261 3614 N -50 0 0 34 50 0 h .7675 g 2261 3648 N -50 0 0 33 50 0 h .774 g 2261 3681 N -50 0 0 34 50 0 h .7805 g 2261 3715 N -50 0 0 33 50 0 h .787 g 2261 3748 N -50 0 0 34 50 0 h .7935 g 2261 3782 N -50 0 0 34 50 0 h .8 g 2261 3816 N -50 0 0 33 50 0 h .8065 g 2261 3849 N -50 0 0 34 50 0 h .813 g 2261 3883 N -50 0 0 33 50 0 h .8195 g 2261 3916 N -50 0 0 34 50 0 h .826 g 2261 3950 N -50 0 0 33 50 0 h .8325 g 2261 3983 N -50 0 0 34 50 0 h .839 g 2261 4017 N -50 0 0 34 50 0 h .8455 g 2261 4051 N -50 0 0 33 50 0 h .852 g 2261 4084 N -50 0 0 34 50 0 h .8585 g 2261 4118 N -50 0 0 33 50 0 h .8651 g 2261 4151 N -50 0 0 34 50 0 h .8716 g 2261 4185 N -50 0 0 34 50 0 h .8781 g 2261 4219 N -50 0 0 33 50 0 h .2507 g 2311 928 N -51 0 0 33 51 0 h .257 g 2311 961 N -51 0 0 34 51 0 h .2634 g 2311 995 N -51 0 0 34 51 0 h .2697 g 2311 1029 N -51 0 0 33 51 0 h .2761 g 2311 1062 N -51 0 0 34 51 0 h 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N -50 0 0 33 50 0 h .6636 g 2362 3110 N -50 0 0 34 50 0 h .6698 g 2362 3144 N -50 0 0 33 50 0 h .676 g 2362 3177 N -50 0 0 34 50 0 h .6822 g 2362 3211 N -50 0 0 34 50 0 h .6884 g 2362 3245 N -50 0 0 33 50 0 h .6946 g 2362 3278 N -50 0 0 34 50 0 h .7008 g 2362 3312 N -50 0 0 33 50 0 h .707 g 2362 3345 N -50 0 0 34 50 0 h .7132 g 2362 3379 N -50 0 0 33 50 0 h .7194 g 2362 3412 N -50 0 0 34 50 0 h .7256 g 2362 3446 N -50 0 0 34 50 0 h .7317 g 2362 3480 N -50 0 0 33 50 0 h .7379 g 2362 3513 N -50 0 0 34 50 0 h .7441 g 2362 3547 N -50 0 0 33 50 0 h .7503 g 2362 3580 N -50 0 0 34 50 0 h .7565 g 2362 3614 N -50 0 0 34 50 0 h .7627 g 2362 3648 N -50 0 0 33 50 0 h .7689 g 2362 3681 N -50 0 0 34 50 0 h .7751 g 2362 3715 N -50 0 0 33 50 0 h .7813 g 2362 3748 N -50 0 0 34 50 0 h .7875 g 2362 3782 N -50 0 0 34 50 0 h .7937 g 2362 3816 N -50 0 0 33 50 0 h .7999 g 2362 3849 N -50 0 0 34 50 0 h .8061 g 2362 3883 N -50 0 0 33 50 0 h .8123 g 2362 3916 N -50 0 0 34 50 0 h .8185 g 2362 3950 N -50 0 0 33 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2640 N -51 0 0 33 51 0 h .5871 g 2463 2673 N -51 0 0 34 51 0 h .593 g 2463 2707 N -51 0 0 34 51 0 h .5989 g 2463 2741 N -51 0 0 33 51 0 h .6048 g 2463 2774 N -51 0 0 34 51 0 h .6107 g 2463 2808 N -51 0 0 33 51 0 h .6166 g 2463 2841 N -51 0 0 34 51 0 h .6225 g 2463 2875 N -51 0 0 34 51 0 h .6284 g 2463 2909 N -51 0 0 33 51 0 h .6343 g 2463 2942 N -51 0 0 34 51 0 h .6402 g 2463 2976 N -51 0 0 33 51 0 h .646 g 2463 3009 N -51 0 0 34 51 0 h .6519 g 2463 3043 N -51 0 0 34 51 0 h .6578 g 2463 3077 N -51 0 0 33 51 0 h .6637 g 2463 3110 N -51 0 0 34 51 0 h .6696 g 2463 3144 N -51 0 0 33 51 0 h .6755 g 2463 3177 N -51 0 0 34 51 0 h .6814 g 2463 3211 N -51 0 0 34 51 0 h .6873 g 2463 3245 N -51 0 0 33 51 0 h .6932 g 2463 3278 N -51 0 0 34 51 0 h .6991 g 2463 3312 N -51 0 0 33 51 0 h .705 g 2463 3345 N -51 0 0 34 51 0 h .7109 g 2463 3379 N -51 0 0 33 51 0 h .7168 g 2463 3412 N -51 0 0 34 51 0 h .7226 g 2463 3446 N -51 0 0 34 51 0 h .7285 g 2463 3480 N -51 0 0 33 51 0 h .7344 g 2463 3513 N -51 0 0 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2640 N -50 0 0 33 50 0 h .6202 g 3272 2673 N -50 0 0 34 50 0 h .6236 g 3272 2707 N -50 0 0 34 50 0 h .6271 g 3272 2741 N -50 0 0 33 50 0 h .6305 g 3272 2774 N -50 0 0 34 50 0 h .634 g 3272 2808 N -50 0 0 33 50 0 h .6374 g 3272 2841 N -50 0 0 34 50 0 h .6408 g 3272 2875 N -50 0 0 34 50 0 h .6443 g 3272 2909 N -50 0 0 33 50 0 h .6477 g 3272 2942 N -50 0 0 34 50 0 h .6512 g 3272 2976 N -50 0 0 33 50 0 h .6546 g 3272 3009 N -50 0 0 34 50 0 h .6581 g 3272 3043 N -50 0 0 34 50 0 h .6615 g 3272 3077 N -50 0 0 33 50 0 h .6649 g 3272 3110 N -50 0 0 34 50 0 h .6684 g 3272 3144 N -50 0 0 33 50 0 h .6718 g 3272 3177 N -50 0 0 34 50 0 h .6753 g 3272 3211 N -50 0 0 34 50 0 h .6787 g 3272 3245 N -50 0 0 33 50 0 h .6822 g 3272 3278 N -50 0 0 34 50 0 h .6856 g 3272 3312 N -50 0 0 33 50 0 h .689 g 3272 3345 N -50 0 0 34 50 0 h .6925 g 3272 3379 N -50 0 0 33 50 0 h .6959 g 3272 3412 N -50 0 0 34 50 0 h .6994 g 3272 3446 N -50 0 0 34 50 0 h .7028 g 3272 3480 N -50 0 0 33 50 0 h .7063 g 3272 3513 N -50 0 0 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0 0 34 51 0 h .5564 g 3322 2003 N -51 0 0 33 51 0 h .5597 g 3322 2036 N -51 0 0 34 51 0 h .563 g 3322 2070 N -51 0 0 33 51 0 h .5663 g 3322 2103 N -51 0 0 34 51 0 h .5696 g 3322 2137 N -51 0 0 34 51 0 h .5729 g 3322 2171 N -51 0 0 33 51 0 h .5762 g 3322 2204 N -51 0 0 34 51 0 h .5795 g 3322 2238 N -51 0 0 33 51 0 h .5828 g 3322 2271 N -51 0 0 34 51 0 h .5861 g 3322 2305 N -51 0 0 34 51 0 h .5893 g 3322 2339 N -51 0 0 33 51 0 h .5926 g 3322 2372 N -51 0 0 34 51 0 h .5959 g 3322 2406 N -51 0 0 33 51 0 h .5992 g 3322 2439 N -51 0 0 34 51 0 h .6025 g 3322 2473 N -51 0 0 34 51 0 h .6058 g 3322 2507 N -51 0 0 33 51 0 h .6091 g 3322 2540 N -51 0 0 34 51 0 h .6124 g 3322 2574 N -51 0 0 32 51 0 h .6157 g 3322 2606 N -51 0 0 34 51 0 h .619 g 3322 2640 N -51 0 0 33 51 0 h .6222 g 3322 2673 N -51 0 0 34 51 0 h .6255 g 3322 2707 N -51 0 0 34 51 0 h .6288 g 3322 2741 N -51 0 0 33 51 0 h .6321 g 3322 2774 N -51 0 0 34 51 0 h .6354 g 3322 2808 N -51 0 0 33 51 0 h .6387 g 3322 2841 N -51 0 0 34 51 0 h 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3748 N -51 0 0 34 51 0 h .7308 g 3322 3782 N -51 0 0 34 51 0 h .7341 g 3322 3816 N -51 0 0 33 51 0 h .7374 g 3322 3849 N -51 0 0 34 51 0 h .7407 g 3322 3883 N -51 0 0 33 51 0 h .744 g 3322 3916 N -51 0 0 34 51 0 h .7473 g 3322 3950 N -51 0 0 33 51 0 h .7506 g 3322 3983 N -51 0 0 34 51 0 h .7539 g 3322 4017 N -51 0 0 34 51 0 h .7572 g 3322 4051 N -51 0 0 33 51 0 h .7604 g 3322 4084 N -51 0 0 34 51 0 h .7637 g 3322 4118 N -51 0 0 33 51 0 h .767 g 3322 4151 N -51 0 0 34 51 0 h .7703 g 3322 4185 N -51 0 0 34 51 0 h .7736 g 3322 4219 N -51 0 0 33 51 0 h .4612 g 3373 928 N -51 0 0 33 51 0 h .4643 g 3373 961 N -51 0 0 34 51 0 h .4674 g 3373 995 N -51 0 0 34 51 0 h .4706 g 3373 1029 N -51 0 0 33 51 0 h .4737 g 3373 1062 N -51 0 0 34 51 0 h .4769 g 3373 1096 N -51 0 0 33 51 0 h .48 g 3373 1129 N -51 0 0 34 51 0 h .4831 g 3373 1163 N -51 0 0 34 51 0 h .4863 g 3373 1197 N -51 0 0 33 51 0 h .4894 g 3373 1230 N -51 0 0 34 51 0 h .4925 g 3373 1264 N -51 0 0 33 51 0 h .4957 g 3373 1297 N -51 0 0 34 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3373 2204 N -51 0 0 34 51 0 h .5835 g 3373 2238 N -51 0 0 33 51 0 h .5867 g 3373 2271 N -51 0 0 34 51 0 h .5898 g 3373 2305 N -51 0 0 34 51 0 h .5929 g 3373 2339 N -51 0 0 33 51 0 h .5961 g 3373 2372 N -51 0 0 34 51 0 h .5992 g 3373 2406 N -51 0 0 33 51 0 h .6023 g 3373 2439 N -51 0 0 34 51 0 h .6055 g 3373 2473 N -51 0 0 34 51 0 h .6086 g 3373 2507 N -51 0 0 33 51 0 h .6118 g 3373 2540 N -51 0 0 34 51 0 h .6149 g 3373 2574 N -51 0 0 32 51 0 h .618 g 3373 2606 N -51 0 0 34 51 0 h .6212 g 3373 2640 N -51 0 0 33 51 0 h .6243 g 3373 2673 N -51 0 0 34 51 0 h .6274 g 3373 2707 N -51 0 0 34 51 0 h .6306 g 3373 2741 N -51 0 0 33 51 0 h .6337 g 3373 2774 N -51 0 0 34 51 0 h .6369 g 3373 2808 N -51 0 0 33 51 0 h .64 g 3373 2841 N -51 0 0 34 51 0 h .6431 g 3373 2875 N -51 0 0 34 51 0 h .6463 g 3373 2909 N -51 0 0 33 51 0 h .6494 g 3373 2942 N -51 0 0 34 51 0 h .6525 g 3373 2976 N -51 0 0 33 51 0 h .6557 g 3373 3009 N -51 0 0 34 51 0 h .6588 g 3373 3043 N -51 0 0 34 51 0 h .662 g 3373 3077 N -51 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N -51 0 0 33 51 0 h .579 g 3675 1801 N -51 0 0 34 51 0 h .5812 g 3675 1835 N -51 0 0 33 51 0 h .5834 g 3675 1868 N -51 0 0 34 51 0 h .5857 g 3675 1902 N -51 0 0 33 51 0 h .5879 g 3675 1935 N -51 0 0 34 51 0 h .5901 g 3675 1969 N -51 0 0 34 51 0 h .5923 g 3675 2003 N -51 0 0 33 51 0 h .5945 g 3675 2036 N -51 0 0 34 51 0 h .5968 g 3675 2070 N -51 0 0 33 51 0 h .599 g 3675 2103 N -51 0 0 34 51 0 h .6012 g 3675 2137 N -51 0 0 34 51 0 h .6034 g 3675 2171 N -51 0 0 33 51 0 h .6056 g 3675 2204 N -51 0 0 34 51 0 h .6079 g 3675 2238 N -51 0 0 33 51 0 h .6101 g 3675 2271 N -51 0 0 34 51 0 h .6123 g 3675 2305 N -51 0 0 34 51 0 h .6145 g 3675 2339 N -51 0 0 33 51 0 h .6167 g 3675 2372 N -51 0 0 34 51 0 h .619 g 3675 2406 N -51 0 0 33 51 0 h .6212 g 3675 2439 N -51 0 0 34 51 0 h .6234 g 3675 2473 N -51 0 0 34 51 0 h .6256 g 3675 2507 N -51 0 0 33 51 0 h .6278 g 3675 2540 N -51 0 0 34 51 0 h .6301 g 3675 2574 N -51 0 0 32 51 0 h .6323 g 3675 2606 N -51 0 0 34 51 0 h .6345 g 3675 2640 N -51 0 0 33 51 0 h .6367 g 3675 2673 N -51 0 0 34 51 0 h .6389 g 3675 2707 N -51 0 0 34 51 0 h .6411 g 3675 2741 N -51 0 0 33 51 0 h .6434 g 3675 2774 N -51 0 0 34 51 0 h .6456 g 3675 2808 N -51 0 0 33 51 0 h .6478 g 3675 2841 N -51 0 0 34 51 0 h .65 g 3675 2875 N -51 0 0 34 51 0 h .6522 g 3675 2909 N -51 0 0 33 51 0 h .6545 g 3675 2942 N -51 0 0 34 51 0 h .6567 g 3675 2976 N -51 0 0 33 51 0 h .6589 g 3675 3009 N -51 0 0 34 51 0 h .6611 g 3675 3043 N -51 0 0 34 51 0 h .6633 g 3675 3077 N -51 0 0 33 51 0 h .6656 g 3675 3110 N -51 0 0 34 51 0 h .6678 g 3675 3144 N -51 0 0 33 51 0 h .67 g 3675 3177 N -51 0 0 34 51 0 h .6722 g 3675 3211 N -51 0 0 34 51 0 h .6744 g 3675 3245 N -51 0 0 33 51 0 h .6767 g 3675 3278 N -51 0 0 34 51 0 h .6789 g 3675 3312 N -51 0 0 33 51 0 h .6811 g 3675 3345 N -51 0 0 34 51 0 h .6833 g 3675 3379 N -51 0 0 33 51 0 h .6855 g 3675 3412 N -51 0 0 34 51 0 h .6877 g 3675 3446 N -51 0 0 34 51 0 h .69 g 3675 3480 N -51 0 0 33 51 0 h .6922 g 3675 3513 N -51 0 0 34 51 0 h .6944 g 3675 3547 N -51 0 0 33 51 0 h .6966 g 3675 3580 N -51 0 0 34 51 0 h .6988 g 3675 3614 N -51 0 0 34 51 0 h .7011 g 3675 3648 N -51 0 0 33 51 0 h .7033 g 3675 3681 N -51 0 0 34 51 0 h .7055 g 3675 3715 N -51 0 0 33 51 0 h .7077 g 3675 3748 N -51 0 0 34 51 0 h .7099 g 3675 3782 N -51 0 0 34 51 0 h .7122 g 3675 3816 N -51 0 0 33 51 0 h .7144 g 3675 3849 N -51 0 0 34 51 0 h .7166 g 3675 3883 N -51 0 0 33 51 0 h .7188 g 3675 3916 N -51 0 0 34 51 0 h .721 g 3675 3950 N -51 0 0 33 51 0 h .7233 g 3675 3983 N -51 0 0 34 51 0 h .7255 g 3675 4017 N -51 0 0 34 51 0 h .7277 g 3675 4051 N -51 0 0 33 51 0 h .7299 g 3675 4084 N -51 0 0 34 51 0 h .7321 g 3675 4118 N -51 0 0 33 51 0 h .7344 g 3675 4151 N -51 0 0 34 51 0 h .7366 g 3675 4185 N -51 0 0 34 51 0 h .7388 g 3675 4219 N -51 0 0 33 51 0 h .5313 g 3726 928 N -50 0 0 33 50 0 h .5334 g 3726 961 N -50 0 0 34 50 0 h .5355 g 3726 995 N -50 0 0 34 50 0 h .5375 g 3726 1029 N -50 0 0 33 50 0 h .5396 g 3726 1062 N -50 0 0 34 50 0 h .5417 g 3726 1096 N -50 0 0 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.5975 g 3726 2003 N -50 0 0 33 50 0 h .5995 g 3726 2036 N -50 0 0 34 50 0 h .6016 g 3726 2070 N -50 0 0 33 50 0 h .6037 g 3726 2103 N -50 0 0 34 50 0 h .6057 g 3726 2137 N -50 0 0 34 50 0 h .6078 g 3726 2171 N -50 0 0 33 50 0 h .6098 g 3726 2204 N -50 0 0 34 50 0 h .6119 g 3726 2238 N -50 0 0 33 50 0 h .614 g 3726 2271 N -50 0 0 34 50 0 h .616 g 3726 2305 N -50 0 0 34 50 0 h .6181 g 3726 2339 N -50 0 0 33 50 0 h .6202 g 3726 2372 N -50 0 0 34 50 0 h .6222 g 3726 2406 N -50 0 0 33 50 0 h .6243 g 3726 2439 N -50 0 0 34 50 0 h .6264 g 3726 2473 N -50 0 0 34 50 0 h .6284 g 3726 2507 N -50 0 0 33 50 0 h .6305 g 3726 2540 N -50 0 0 34 50 0 h .6326 g 3726 2574 N -50 0 0 32 50 0 h .6346 g 3726 2606 N -50 0 0 34 50 0 h .6367 g 3726 2640 N -50 0 0 33 50 0 h .6388 g 3726 2673 N -50 0 0 34 50 0 h .6408 g 3726 2707 N -50 0 0 34 50 0 h .6429 g 3726 2741 N -50 0 0 33 50 0 h .645 g 3726 2774 N -50 0 0 34 50 0 h .647 g 3726 2808 N -50 0 0 33 50 0 h .6491 g 3726 2841 N -50 0 0 34 50 0 h .6512 g 3726 2875 N -50 0 0 34 50 0 h .6532 g 3726 2909 N -50 0 0 33 50 0 h .6553 g 3726 2942 N -50 0 0 34 50 0 h .6574 g 3726 2976 N -50 0 0 33 50 0 h .6594 g 3726 3009 N -50 0 0 34 50 0 h .6615 g 3726 3043 N -50 0 0 34 50 0 h .6636 g 3726 3077 N -50 0 0 33 50 0 h .6656 g 3726 3110 N -50 0 0 34 50 0 h .6677 g 3726 3144 N -50 0 0 33 50 0 h .6698 g 3726 3177 N -50 0 0 34 50 0 h .6718 g 3726 3211 N -50 0 0 34 50 0 h .6739 g 3726 3245 N -50 0 0 33 50 0 h .676 g 3726 3278 N -50 0 0 34 50 0 h .678 g 3726 3312 N -50 0 0 33 50 0 h .6801 g 3726 3345 N -50 0 0 34 50 0 h .6822 g 3726 3379 N -50 0 0 33 50 0 h .6842 g 3726 3412 N -50 0 0 34 50 0 h .6863 g 3726 3446 N -50 0 0 34 50 0 h .6884 g 3726 3480 N -50 0 0 33 50 0 h .6904 g 3726 3513 N -50 0 0 34 50 0 h .6925 g 3726 3547 N -50 0 0 33 50 0 h .6946 g 3726 3580 N -50 0 0 34 50 0 h .6966 g 3726 3614 N -50 0 0 34 50 0 h .6987 g 3726 3648 N -50 0 0 33 50 0 h .7008 g 3726 3681 N -50 0 0 34 50 0 h .7028 g 3726 3715 N -50 0 0 33 50 0 h .7049 g 3726 3748 N -50 0 0 34 50 0 h .707 g 3726 3782 N -50 0 0 34 50 0 h .709 g 3726 3816 N -50 0 0 33 50 0 h .7111 g 3726 3849 N -50 0 0 34 50 0 h .7132 g 3726 3883 N -50 0 0 33 50 0 h .7152 g 3726 3916 N -50 0 0 34 50 0 h .7173 g 3726 3950 N -50 0 0 33 50 0 h .7194 g 3726 3983 N -50 0 0 34 50 0 h .7214 g 3726 4017 N -50 0 0 34 50 0 h .7235 g 3726 4051 N -50 0 0 33 50 0 h .7256 g 3726 4084 N -50 0 0 34 50 0 h .7276 g 3726 4118 N -50 0 0 33 50 0 h .7297 g 3726 4151 N -50 0 0 34 50 0 h .7317 g 3726 4185 N -50 0 0 34 50 0 h .7338 g 3726 4219 N -50 0 0 33 50 0 h .5414 g 3776 928 N -51 0 0 33 51 0 h .5433 g 3776 961 N -51 0 0 34 51 0 h .5452 g 3776 995 N -51 0 0 34 51 0 h .5471 g 3776 1029 N -51 0 0 33 51 0 h .549 g 3776 1062 N -51 0 0 34 51 0 h .5509 g 3776 1096 N -51 0 0 33 51 0 h .5528 g 3776 1129 N -51 0 0 34 51 0 h .5548 g 3776 1163 N -51 0 0 34 51 0 h .5567 g 3776 1197 N -51 0 0 33 51 0 h .5586 g 3776 1230 N -51 0 0 34 51 0 h .5605 g 3776 1264 N -51 0 0 33 51 0 h .5624 g 3776 1297 N -51 0 0 34 51 0 h .5643 g 3776 1331 N -51 0 0 33 51 0 h .5662 g 3776 1364 N -51 0 0 34 51 0 h .5681 g 3776 1398 N -51 0 0 34 51 0 h .5701 g 3776 1432 N -51 0 0 33 51 0 h .572 g 3776 1465 N -51 0 0 34 51 0 h .5739 g 3776 1499 N -51 0 0 33 51 0 h .5758 g 3776 1532 N -51 0 0 34 51 0 h .5777 g 3776 1566 N -51 0 0 34 51 0 h .5796 g 3776 1600 N -51 0 0 33 51 0 h .5815 g 3776 1633 N -51 0 0 34 51 0 h .5834 g 3776 1667 N -51 0 0 33 51 0 h .5854 g 3776 1700 N -51 0 0 34 51 0 h .5873 g 3776 1734 N -51 0 0 34 51 0 h .5892 g 3776 1768 N -51 0 0 33 51 0 h .5911 g 3776 1801 N -51 0 0 34 51 0 h .593 g 3776 1835 N -51 0 0 33 51 0 h .5949 g 3776 1868 N -51 0 0 34 51 0 h .5968 g 3776 1902 N -51 0 0 33 51 0 h .5988 g 3776 1935 N -51 0 0 34 51 0 h .6007 g 3776 1969 N -51 0 0 34 51 0 h .6026 g 3776 2003 N -51 0 0 33 51 0 h .6045 g 3776 2036 N -51 0 0 34 51 0 h .6064 g 3776 2070 N -51 0 0 33 51 0 h .6083 g 3776 2103 N -51 0 0 34 51 0 h .6102 g 3776 2137 N -51 0 0 34 51 0 h .6121 g 3776 2171 N -51 0 0 33 51 0 h .6141 g 3776 2204 N -51 0 0 34 51 0 h .616 g 3776 2238 N -51 0 0 33 51 0 h .6179 g 3776 2271 N -51 0 0 34 51 0 h .6198 g 3776 2305 N -51 0 0 34 51 0 h .6217 g 3776 2339 N -51 0 0 33 51 0 h .6236 g 3776 2372 N -51 0 0 34 51 0 h .6255 g 3776 2406 N -51 0 0 33 51 0 h .6274 g 3776 2439 N -51 0 0 34 51 0 h .6294 g 3776 2473 N -51 0 0 34 51 0 h .6313 g 3776 2507 N -51 0 0 33 51 0 h .6332 g 3776 2540 N -51 0 0 34 51 0 h .6351 g 3776 2574 N -51 0 0 32 51 0 h .637 g 3776 2606 N -51 0 0 34 51 0 h .6389 g 3776 2640 N -51 0 0 33 51 0 h .6408 g 3776 2673 N -51 0 0 34 51 0 h .6428 g 3776 2707 N -51 0 0 34 51 0 h .6447 g 3776 2741 N -51 0 0 33 51 0 h .6466 g 3776 2774 N -51 0 0 34 51 0 h .6485 g 3776 2808 N -51 0 0 33 51 0 h .6504 g 3776 2841 N -51 0 0 34 51 0 h .6523 g 3776 2875 N -51 0 0 34 51 0 h .6542 g 3776 2909 N -51 0 0 33 51 0 h .6561 g 3776 2942 N -51 0 0 34 51 0 h .6581 g 3776 2976 N -51 0 0 33 51 0 h .66 g 3776 3009 N -51 0 0 34 51 0 h .6619 g 3776 3043 N -51 0 0 34 51 0 h .6638 g 3776 3077 N -51 0 0 33 51 0 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3983 N -51 0 0 34 51 0 h .7174 g 3776 4017 N -51 0 0 34 51 0 h .7193 g 3776 4051 N -51 0 0 33 51 0 h .7212 g 3776 4084 N -51 0 0 34 51 0 h .7231 g 3776 4118 N -51 0 0 33 51 0 h .725 g 3776 4151 N -51 0 0 34 51 0 h .7269 g 3776 4185 N -51 0 0 34 51 0 h .7288 g 3776 4219 N -51 0 0 33 51 0 h .5514 g 3827 928 N -51 0 0 33 51 0 h .5531 g 3827 961 N -51 0 0 34 51 0 h .5549 g 3827 995 N -51 0 0 34 51 0 h .5567 g 3827 1029 N -51 0 0 33 51 0 h .5584 g 3827 1062 N -51 0 0 34 51 0 h .5602 g 3827 1096 N -51 0 0 33 51 0 h .5619 g 3827 1129 N -51 0 0 34 51 0 h .5637 g 3827 1163 N -51 0 0 34 51 0 h .5655 g 3827 1197 N -51 0 0 33 51 0 h .5672 g 3827 1230 N -51 0 0 34 51 0 h .569 g 3827 1264 N -51 0 0 33 51 0 h .5707 g 3827 1297 N -51 0 0 34 51 0 h .5725 g 3827 1331 N -51 0 0 33 51 0 h .5743 g 3827 1364 N -51 0 0 34 51 0 h .576 g 3827 1398 N -51 0 0 34 51 0 h .5778 g 3827 1432 N -51 0 0 33 51 0 h .5795 g 3827 1465 N -51 0 0 34 51 0 h .5813 g 3827 1499 N -51 0 0 33 51 0 h .5831 g 3827 1532 N -51 0 0 34 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3827 2439 N -51 0 0 34 51 0 h .6323 g 3827 2473 N -51 0 0 34 51 0 h .6341 g 3827 2507 N -51 0 0 33 51 0 h .6359 g 3827 2540 N -51 0 0 34 51 0 h .6376 g 3827 2574 N -51 0 0 32 51 0 h .6394 g 3827 2606 N -51 0 0 34 51 0 h .6411 g 3827 2640 N -51 0 0 33 51 0 h .6429 g 3827 2673 N -51 0 0 34 51 0 h .6447 g 3827 2707 N -51 0 0 34 51 0 h .6464 g 3827 2741 N -51 0 0 33 51 0 h .6482 g 3827 2774 N -51 0 0 34 51 0 h .6499 g 3827 2808 N -51 0 0 33 51 0 h .6517 g 3827 2841 N -51 0 0 34 51 0 h .6535 g 3827 2875 N -51 0 0 34 51 0 h .6552 g 3827 2909 N -51 0 0 33 51 0 h .657 g 3827 2942 N -51 0 0 34 51 0 h .6587 g 3827 2976 N -51 0 0 33 51 0 h .6605 g 3827 3009 N -51 0 0 34 51 0 h .6623 g 3827 3043 N -51 0 0 34 51 0 h .664 g 3827 3077 N -51 0 0 33 51 0 h .6658 g 3827 3110 N -51 0 0 34 51 0 h .6675 g 3827 3144 N -51 0 0 33 51 0 h .6693 g 3827 3177 N -51 0 0 34 51 0 h .6711 g 3827 3211 N -51 0 0 34 51 0 h .6728 g 3827 3245 N -51 0 0 33 51 0 h .6746 g 3827 3278 N -51 0 0 34 51 0 h .6763 g 3827 3312 N 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0 h .7239 g 3827 4219 N -51 0 0 33 51 0 h .5614 g 3878 928 N -50 0 0 33 50 0 h .563 g 3878 961 N -50 0 0 34 50 0 h .5646 g 3878 995 N -50 0 0 34 50 0 h .5662 g 3878 1029 N -50 0 0 33 50 0 h .5678 g 3878 1062 N -50 0 0 34 50 0 h .5694 g 3878 1096 N -50 0 0 33 50 0 h .5711 g 3878 1129 N -50 0 0 34 50 0 h .5727 g 3878 1163 N -50 0 0 34 50 0 h .5743 g 3878 1197 N -50 0 0 33 50 0 h .5759 g 3878 1230 N -50 0 0 34 50 0 h .5775 g 3878 1264 N -50 0 0 33 50 0 h .5791 g 3878 1297 N -50 0 0 34 50 0 h .5807 g 3878 1331 N -50 0 0 33 50 0 h .5823 g 3878 1364 N -50 0 0 34 50 0 h .5839 g 3878 1398 N -50 0 0 34 50 0 h .5855 g 3878 1432 N -50 0 0 33 50 0 h .5871 g 3878 1465 N -50 0 0 34 50 0 h .5887 g 3878 1499 N -50 0 0 33 50 0 h .5903 g 3878 1532 N -50 0 0 34 50 0 h .5919 g 3878 1566 N -50 0 0 34 50 0 h .5935 g 3878 1600 N -50 0 0 33 50 0 h .5952 g 3878 1633 N -50 0 0 34 50 0 h .5968 g 3878 1667 N -50 0 0 33 50 0 h .5984 g 3878 1700 N -50 0 0 34 50 0 h .6 g 3878 1734 N -50 0 0 34 50 0 h .6016 g 3878 1768 N -50 0 0 33 50 0 h .6032 g 3878 1801 N -50 0 0 34 50 0 h .6048 g 3878 1835 N -50 0 0 33 50 0 h .6064 g 3878 1868 N -50 0 0 34 50 0 h .608 g 3878 1902 N -50 0 0 33 50 0 h .6096 g 3878 1935 N -50 0 0 34 50 0 h .6112 g 3878 1969 N -50 0 0 34 50 0 h .6128 g 3878 2003 N -50 0 0 33 50 0 h .6144 g 3878 2036 N -50 0 0 34 50 0 h .616 g 3878 2070 N -50 0 0 33 50 0 h .6177 g 3878 2103 N -50 0 0 34 50 0 h .6193 g 3878 2137 N -50 0 0 34 50 0 h .6209 g 3878 2171 N -50 0 0 33 50 0 h .6225 g 3878 2204 N -50 0 0 34 50 0 h .6241 g 3878 2238 N -50 0 0 33 50 0 h .6257 g 3878 2271 N -50 0 0 34 50 0 h .6273 g 3878 2305 N -50 0 0 34 50 0 h .6289 g 3878 2339 N -50 0 0 33 50 0 h .6305 g 3878 2372 N -50 0 0 34 50 0 h .6321 g 3878 2406 N -50 0 0 33 50 0 h .6337 g 3878 2439 N -50 0 0 34 50 0 h .6353 g 3878 2473 N -50 0 0 34 50 0 h .6369 g 3878 2507 N -50 0 0 33 50 0 h .6385 g 3878 2540 N -50 0 0 34 50 0 h .6402 g 3878 2574 N -50 0 0 32 50 0 h .6418 g 3878 2606 N -50 0 0 34 50 0 h .6434 g 3878 2640 N -50 0 0 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g 3878 3547 N -50 0 0 33 50 0 h .6884 g 3878 3580 N -50 0 0 34 50 0 h .69 g 3878 3614 N -50 0 0 34 50 0 h .6916 g 3878 3648 N -50 0 0 33 50 0 h .6932 g 3878 3681 N -50 0 0 34 50 0 h .6948 g 3878 3715 N -50 0 0 33 50 0 h .6964 g 3878 3748 N -50 0 0 34 50 0 h .698 g 3878 3782 N -50 0 0 34 50 0 h .6996 g 3878 3816 N -50 0 0 33 50 0 h .7012 g 3878 3849 N -50 0 0 34 50 0 h .7028 g 3878 3883 N -50 0 0 33 50 0 h .7044 g 3878 3916 N -50 0 0 34 50 0 h .706 g 3878 3950 N -50 0 0 33 50 0 h .7076 g 3878 3983 N -50 0 0 34 50 0 h .7093 g 3878 4017 N -50 0 0 34 50 0 h .7109 g 3878 4051 N -50 0 0 33 50 0 h .7125 g 3878 4084 N -50 0 0 34 50 0 h .7141 g 3878 4118 N -50 0 0 33 50 0 h .7157 g 3878 4151 N -50 0 0 34 50 0 h .7173 g 3878 4185 N -50 0 0 34 50 0 h .7189 g 3878 4219 N -50 0 0 33 50 0 h .5714 g 3928 928 N -51 0 0 33 51 0 h .5729 g 3928 961 N -51 0 0 34 51 0 h .5743 g 3928 995 N -51 0 0 34 51 0 h .5758 g 3928 1029 N -51 0 0 33 51 0 h .5772 g 3928 1062 N -51 0 0 34 51 0 h .5787 g 3928 1096 N -51 0 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2875 N -51 0 0 34 51 0 h .6572 g 3928 2909 N -51 0 0 33 51 0 h .6587 g 3928 2942 N -51 0 0 34 51 0 h .6601 g 3928 2976 N -51 0 0 33 51 0 h .6616 g 3928 3009 N -51 0 0 34 51 0 h .663 g 3928 3043 N -51 0 0 34 51 0 h .6645 g 3928 3077 N -51 0 0 33 51 0 h .6659 g 3928 3110 N -51 0 0 34 51 0 h .6674 g 3928 3144 N -51 0 0 33 51 0 h .6688 g 3928 3177 N -51 0 0 34 51 0 h .6703 g 3928 3211 N -51 0 0 34 51 0 h .6718 g 3928 3245 N -51 0 0 33 51 0 h .6732 g 3928 3278 N -51 0 0 34 51 0 h .6747 g 3928 3312 N -51 0 0 33 51 0 h .6761 g 3928 3345 N -51 0 0 34 51 0 h .6776 g 3928 3379 N -51 0 0 33 51 0 h .679 g 3928 3412 N -51 0 0 34 51 0 h .6805 g 3928 3446 N -51 0 0 34 51 0 h .6819 g 3928 3480 N -51 0 0 33 51 0 h .6834 g 3928 3513 N -51 0 0 34 51 0 h .6848 g 3928 3547 N -51 0 0 33 51 0 h .6863 g 3928 3580 N -51 0 0 34 51 0 h .6877 g 3928 3614 N -51 0 0 34 51 0 h .6892 g 3928 3648 N -51 0 0 33 51 0 h .6907 g 3928 3681 N -51 0 0 34 51 0 h .6921 g 3928 3715 N -51 0 0 33 51 0 h .6936 g 3928 3748 N -51 0 0 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3979 1331 N -50 0 0 33 50 0 h .5984 g 3979 1364 N -50 0 0 34 50 0 h .5997 g 3979 1398 N -50 0 0 34 50 0 h .601 g 3979 1432 N -50 0 0 33 50 0 h .6023 g 3979 1465 N -50 0 0 34 50 0 h .6036 g 3979 1499 N -50 0 0 33 50 0 h .6049 g 3979 1532 N -50 0 0 34 50 0 h .6062 g 3979 1566 N -50 0 0 34 50 0 h .6075 g 3979 1600 N -50 0 0 33 50 0 h .6088 g 3979 1633 N -50 0 0 34 50 0 h .6101 g 3979 1667 N -50 0 0 33 50 0 h .6114 g 3979 1700 N -50 0 0 34 50 0 h .6127 g 3979 1734 N -50 0 0 34 50 0 h .614 g 3979 1768 N -50 0 0 33 50 0 h .6153 g 3979 1801 N -50 0 0 34 50 0 h .6166 g 3979 1835 N -50 0 0 33 50 0 h .6179 g 3979 1868 N -50 0 0 34 50 0 h .6192 g 3979 1902 N -50 0 0 33 50 0 h .6205 g 3979 1935 N -50 0 0 34 50 0 h .6218 g 3979 1969 N -50 0 0 34 50 0 h .6231 g 3979 2003 N -50 0 0 33 50 0 h .6244 g 3979 2036 N -50 0 0 34 50 0 h .6257 g 3979 2070 N -50 0 0 33 50 0 h .627 g 3979 2103 N -50 0 0 34 50 0 h .6283 g 3979 2137 N -50 0 0 34 50 0 h .6296 g 3979 2171 N -50 0 0 33 50 0 h .6309 g 3979 2204 N -50 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3983 N -50 0 0 34 50 0 h .7011 g 3979 4017 N -50 0 0 34 50 0 h .7024 g 3979 4051 N -50 0 0 33 50 0 h .7037 g 3979 4084 N -50 0 0 34 50 0 h .705 g 3979 4118 N -50 0 0 33 50 0 h .7063 g 3979 4151 N -50 0 0 34 50 0 h .7076 g 3979 4185 N -50 0 0 34 50 0 h .7089 g 3979 4219 N -50 0 0 33 50 0 h .5915 g 4029 928 N -51 0 0 33 51 0 h .5926 g 4029 961 N -51 0 0 34 51 0 h .5938 g 4029 995 N -51 0 0 34 51 0 h .5949 g 4029 1029 N -51 0 0 33 51 0 h .5961 g 4029 1062 N -51 0 0 34 51 0 h .5972 g 4029 1096 N -51 0 0 33 51 0 h .5984 g 4029 1129 N -51 0 0 34 51 0 h .5995 g 4029 1163 N -51 0 0 34 51 0 h .6007 g 4029 1197 N -51 0 0 33 51 0 h .6018 g 4029 1230 N -51 0 0 34 51 0 h .603 g 4029 1264 N -51 0 0 33 51 0 h .6041 g 4029 1297 N -51 0 0 34 51 0 h .6053 g 4029 1331 N -51 0 0 33 51 0 h .6064 g 4029 1364 N -51 0 0 34 51 0 h .6076 g 4029 1398 N -51 0 0 34 51 0 h .6087 g 4029 1432 N -51 0 0 33 51 0 h .6098 g 4029 1465 N -51 0 0 34 51 0 h .611 g 4029 1499 N -51 0 0 33 51 0 h .6121 g 4029 1532 N -51 0 0 34 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1768 N -50 0 0 33 50 0 h .6274 g 4080 1801 N -50 0 0 34 50 0 h .6284 g 4080 1835 N -50 0 0 33 50 0 h .6294 g 4080 1868 N -50 0 0 34 50 0 h .6304 g 4080 1902 N -50 0 0 33 50 0 h .6314 g 4080 1935 N -50 0 0 34 50 0 h .6323 g 4080 1969 N -50 0 0 34 50 0 h .6333 g 4080 2003 N -50 0 0 33 50 0 h .6343 g 4080 2036 N -50 0 0 34 50 0 h .6353 g 4080 2070 N -50 0 0 33 50 0 h .6363 g 4080 2103 N -50 0 0 34 50 0 h .6373 g 4080 2137 N -50 0 0 34 50 0 h .6383 g 4080 2171 N -50 0 0 33 50 0 h .6393 g 4080 2204 N -50 0 0 34 50 0 h .6403 g 4080 2238 N -50 0 0 33 50 0 h .6413 g 4080 2271 N -50 0 0 34 50 0 h .6423 g 4080 2305 N -50 0 0 34 50 0 h .6433 g 4080 2339 N -50 0 0 33 50 0 h .6443 g 4080 2372 N -50 0 0 34 50 0 h .6453 g 4080 2406 N -50 0 0 33 50 0 h .6463 g 4080 2439 N -50 0 0 34 50 0 h .6473 g 4080 2473 N -50 0 0 34 50 0 h .6483 g 4080 2507 N -50 0 0 33 50 0 h .6493 g 4080 2540 N -50 0 0 34 50 0 h .6503 g 4080 2574 N -50 0 0 32 50 0 h .6512 g 4080 2606 N -50 0 0 34 50 0 h .6522 g 4080 2640 N -50 0 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3547 N -51 0 0 33 51 0 h .6718 g 4282 3580 N -51 0 0 34 51 0 h .6722 g 4282 3614 N -51 0 0 34 51 0 h .6726 g 4282 3648 N -51 0 0 33 51 0 h .673 g 4282 3681 N -51 0 0 34 51 0 h .6734 g 4282 3715 N -51 0 0 33 51 0 h .6737 g 4282 3748 N -51 0 0 34 51 0 h .6741 g 4282 3782 N -51 0 0 34 51 0 h .6745 g 4282 3816 N -51 0 0 33 51 0 h .6749 g 4282 3849 N -51 0 0 34 51 0 h .6753 g 4282 3883 N -51 0 0 33 51 0 h .6757 g 4282 3916 N -51 0 0 34 51 0 h .676 g 4282 3950 N -51 0 0 33 51 0 h .6764 g 4282 3983 N -51 0 0 34 51 0 h .6768 g 4282 4017 N -51 0 0 34 51 0 h .6772 g 4282 4051 N -51 0 0 33 51 0 h .6776 g 4282 4084 N -51 0 0 34 51 0 h .678 g 4282 4118 N -51 0 0 33 51 0 h .6783 g 4282 4151 N -51 0 0 34 51 0 h .6787 g 4282 4185 N -51 0 0 34 51 0 h .6791 g 4282 4219 N -51 0 0 33 51 0 h .6516 g 4333 928 N -50 0 0 33 50 0 h .6519 g 4333 961 N -50 0 0 34 50 0 h .6521 g 4333 995 N -50 0 0 34 50 0 h .6523 g 4333 1029 N -50 0 0 33 50 0 h .6525 g 4333 1062 N -50 0 0 34 50 0 h .6528 g 4333 1096 N -50 0 0 33 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0 0 34 50 0 h .6652 g 4333 2909 N -50 0 0 33 50 0 h .6654 g 4333 2942 N -50 0 0 34 50 0 h .6656 g 4333 2976 N -50 0 0 33 50 0 h .6659 g 4333 3009 N -50 0 0 34 50 0 h .6661 g 4333 3043 N -50 0 0 34 50 0 h .6663 g 4333 3077 N -50 0 0 33 50 0 h .6666 g 4333 3110 N -50 0 0 34 50 0 h .6668 g 4333 3144 N -50 0 0 33 50 0 h .667 g 4333 3177 N -50 0 0 34 50 0 h .6672 g 4333 3211 N -50 0 0 34 50 0 h .6675 g 4333 3245 N -50 0 0 33 50 0 h .6677 g 4333 3278 N -50 0 0 34 50 0 h .6679 g 4333 3312 N -50 0 0 33 50 0 h .6682 g 4333 3345 N -50 0 0 34 50 0 h .6684 g 4333 3379 N -50 0 0 33 50 0 h .6686 g 4333 3412 N -50 0 0 34 50 0 h .6688 g 4333 3446 N -50 0 0 34 50 0 h .6691 g 4333 3480 N -50 0 0 33 50 0 h .6693 g 4333 3513 N -50 0 0 34 50 0 h .6695 g 4333 3547 N -50 0 0 33 50 0 h .6698 g 4333 3580 N -50 0 0 34 50 0 h .67 g 4333 3614 N -50 0 0 34 50 0 h .6702 g 4333 3648 N -50 0 0 33 50 0 h .6705 g 4333 3681 N -50 0 0 34 50 0 h .6707 g 4333 3715 N -50 0 0 33 50 0 h .6709 g 4333 3748 N -50 0 0 34 50 0 h .6711 g 4333 3782 N -50 0 0 34 50 0 h .6714 g 4333 3816 N -50 0 0 33 50 0 h .6716 g 4333 3849 N -50 0 0 34 50 0 h .6718 g 4333 3883 N -50 0 0 33 50 0 h .6721 g 4333 3916 N -50 0 0 34 50 0 h .6723 g 4333 3950 N -50 0 0 33 50 0 h .6725 g 4333 3983 N -50 0 0 34 50 0 h .6728 g 4333 4017 N -50 0 0 34 50 0 h .673 g 4333 4051 N -50 0 0 33 50 0 h .6732 g 4333 4084 N -50 0 0 34 50 0 h .6734 g 4333 4118 N -50 0 0 33 50 0 h .6737 g 4333 4151 N -50 0 0 34 50 0 h .6739 g 4333 4185 N -50 0 0 34 50 0 h .6741 g 4333 4219 N -50 0 0 33 50 0 h .6617 g 4383 928 N -51 0 0 33 51 0 h .6617 g 4383 961 N -51 0 0 34 51 0 h .6618 g 4383 995 N -51 0 0 34 51 0 h .6619 g 4383 1029 N -51 0 0 33 51 0 h .662 g 4383 1062 N -51 0 0 34 51 0 h .662 g 4383 1096 N -51 0 0 33 51 0 h .6621 g 4383 1129 N -51 0 0 34 51 0 h .6622 g 4383 1163 N -51 0 0 34 51 0 h .6623 g 4383 1197 N -51 0 0 33 51 0 h .6623 g 4383 1230 N -51 0 0 34 51 0 h .6624 g 4383 1264 N -51 0 0 33 51 0 h .6625 g 4383 1297 N -51 0 0 34 51 0 h .6626 g 4383 1331 N -51 0 0 33 51 0 h .6626 g 4383 1364 N -51 0 0 34 51 0 h .6627 g 4383 1398 N -51 0 0 34 51 0 h .6628 g 4383 1432 N -51 0 0 33 51 0 h .6629 g 4383 1465 N -51 0 0 34 51 0 h .663 g 4383 1499 N -51 0 0 33 51 0 h .663 g 4383 1532 N -51 0 0 34 51 0 h .6631 g 4383 1566 N -51 0 0 34 51 0 h .6632 g 4383 1600 N -51 0 0 33 51 0 h .6633 g 4383 1633 N -51 0 0 34 51 0 h .6633 g 4383 1667 N -51 0 0 33 51 0 h .6634 g 4383 1700 N -51 0 0 34 51 0 h .6635 g 4383 1734 N -51 0 0 34 51 0 h .6636 g 4383 1768 N -51 0 0 33 51 0 h .6636 g 4383 1801 N -51 0 0 34 51 0 h .6637 g 4383 1835 N -51 0 0 33 51 0 h .6638 g 4383 1868 N -51 0 0 34 51 0 h .6639 g 4383 1902 N -51 0 0 33 51 0 h .664 g 4383 1935 N -51 0 0 34 51 0 h .664 g 4383 1969 N -51 0 0 34 51 0 h .6641 g 4383 2003 N -51 0 0 33 51 0 h .6642 g 4383 2036 N -51 0 0 34 51 0 h .6643 g 4383 2070 N -51 0 0 33 51 0 h .6643 g 4383 2103 N -51 0 0 34 51 0 h .6644 g 4383 2137 N -51 0 0 34 51 0 h .6645 g 4383 2171 N -51 0 0 33 51 0 h .6646 g 4383 2204 N -51 0 0 34 51 0 h .6646 g 4383 2238 N -51 0 0 33 51 0 h .6647 g 4383 2271 N -51 0 0 34 51 0 h .6648 g 4383 2305 N -51 0 0 34 51 0 h .6649 g 4383 2339 N -51 0 0 33 51 0 h .6649 g 4383 2372 N -51 0 0 34 51 0 h .665 g 4383 2406 N -51 0 0 33 51 0 h .6651 g 4383 2439 N -51 0 0 34 51 0 h .6652 g 4383 2473 N -51 0 0 34 51 0 h .6653 g 4383 2507 N -51 0 0 33 51 0 h .6653 g 4383 2540 N -51 0 0 34 51 0 h .6654 g 4383 2574 N -51 0 0 32 51 0 h .6655 g 4383 2606 N -51 0 0 34 51 0 h .6656 g 4383 2640 N -51 0 0 33 51 0 h .6656 g 4383 2673 N -51 0 0 34 51 0 h .6657 g 4383 2707 N -51 0 0 34 51 0 h .6658 g 4383 2741 N -51 0 0 33 51 0 h .6659 g 4383 2774 N -51 0 0 34 51 0 h .6659 g 4383 2808 N -51 0 0 33 51 0 h .666 g 4383 2841 N -51 0 0 34 51 0 h .6661 g 4383 2875 N -51 0 0 34 51 0 h .6662 g 4383 2909 N -51 0 0 33 51 0 h .6662 g 4383 2942 N -51 0 0 34 51 0 h .6663 g 4383 2976 N -51 0 0 33 51 0 h .6664 g 4383 3009 N -51 0 0 34 51 0 h .6665 g 4383 3043 N -51 0 0 34 51 0 h .6666 g 4383 3077 N -51 0 0 33 51 0 h .6666 g 4383 3110 N -51 0 0 34 51 0 h .6667 g 4383 3144 N -51 0 0 33 51 0 h .6668 g 4383 3177 N -51 0 0 34 51 0 h .6669 g 4383 3211 N -51 0 0 34 51 0 h .6669 g 4383 3245 N -51 0 0 33 51 0 h .667 g 4383 3278 N -51 0 0 34 51 0 h .6671 g 4383 3312 N -51 0 0 33 51 0 h .6672 g 4383 3345 N -51 0 0 34 51 0 h .6672 g 4383 3379 N -51 0 0 33 51 0 h .6673 g 4383 3412 N -51 0 0 34 51 0 h .6674 g 4383 3446 N -51 0 0 34 51 0 h .6675 g 4383 3480 N -51 0 0 33 51 0 h .6675 g 4383 3513 N -51 0 0 34 51 0 h .6676 g 4383 3547 N -51 0 0 33 51 0 h .6677 g 4383 3580 N -51 0 0 34 51 0 h .6678 g 4383 3614 N -51 0 0 34 51 0 h .6679 g 4383 3648 N -51 0 0 33 51 0 h .6679 g 4383 3681 N -51 0 0 34 51 0 h .668 g 4383 3715 N -51 0 0 33 51 0 h .6681 g 4383 3748 N -51 0 0 34 51 0 h .6682 g 4383 3782 N -51 0 0 34 51 0 h .6682 g 4383 3816 N -51 0 0 33 51 0 h .6683 g 4383 3849 N -51 0 0 34 51 0 h .6684 g 4383 3883 N -51 0 0 33 51 0 h .6685 g 4383 3916 N -51 0 0 34 51 0 h .6685 g 4383 3950 N -51 0 0 33 51 0 h .6686 g 4383 3983 N 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2439 N -50 0 0 34 50 0 h .6682 g 4434 2473 N -50 0 0 34 50 0 h .6681 g 4434 2507 N -50 0 0 33 50 0 h .668 g 4434 2540 N -50 0 0 34 50 0 h .6679 g 4434 2574 N -50 0 0 32 50 0 h .6679 g 4434 2606 N -50 0 0 34 50 0 h .6678 g 4434 2640 N -50 0 0 33 50 0 h .6677 g 4434 2673 N -50 0 0 34 50 0 h .6676 g 4434 2707 N -50 0 0 34 50 0 h .6675 g 4434 2741 N -50 0 0 33 50 0 h .6675 g 4434 2774 N -50 0 0 34 50 0 h .6674 g 4434 2808 N -50 0 0 33 50 0 h .6673 g 4434 2841 N -50 0 0 34 50 0 h .6672 g 4434 2875 N -50 0 0 34 50 0 h .6672 g 4434 2909 N -50 0 0 33 50 0 h .6671 g 4434 2942 N -50 0 0 34 50 0 h .667 g 4434 2976 N -50 0 0 33 50 0 h .6669 g 4434 3009 N -50 0 0 34 50 0 h .6669 g 4434 3043 N -50 0 0 34 50 0 h .6668 g 4434 3077 N -50 0 0 33 50 0 h .6667 g 4434 3110 N -50 0 0 34 50 0 h .6666 g 4434 3144 N -50 0 0 33 50 0 h .6666 g 4434 3177 N -50 0 0 34 50 0 h .6665 g 4434 3211 N -50 0 0 34 50 0 h .6664 g 4434 3245 N -50 0 0 33 50 0 h .6663 g 4434 3278 N -50 0 0 34 50 0 h .6662 g 4434 3312 N -50 0 0 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N -51 0 0 33 51 0 h .6757 g 4484 1801 N -51 0 0 34 51 0 h .6755 g 4484 1835 N -51 0 0 33 51 0 h .6753 g 4484 1868 N -51 0 0 34 51 0 h .675 g 4484 1902 N -51 0 0 33 51 0 h .6748 g 4484 1935 N -51 0 0 34 51 0 h .6746 g 4484 1969 N -51 0 0 34 51 0 h .6744 g 4484 2003 N -51 0 0 33 51 0 h .6741 g 4484 2036 N -51 0 0 34 51 0 h .6739 g 4484 2070 N -51 0 0 33 51 0 h .6737 g 4484 2103 N -51 0 0 34 51 0 h .6734 g 4484 2137 N -51 0 0 34 51 0 h .6732 g 4484 2171 N -51 0 0 33 51 0 h .673 g 4484 2204 N -51 0 0 34 51 0 h .6728 g 4484 2238 N -51 0 0 33 51 0 h .6725 g 4484 2271 N -51 0 0 34 51 0 h .6723 g 4484 2305 N -51 0 0 34 51 0 h .6721 g 4484 2339 N -51 0 0 33 51 0 h .6718 g 4484 2372 N -51 0 0 34 51 0 h .6716 g 4484 2406 N -51 0 0 33 51 0 h .6714 g 4484 2439 N -51 0 0 34 51 0 h .6711 g 4484 2473 N -51 0 0 34 51 0 h .6709 g 4484 2507 N -51 0 0 33 51 0 h .6707 g 4484 2540 N -51 0 0 34 51 0 h .6705 g 4484 2574 N -51 0 0 32 51 0 h .6702 g 4484 2606 N -51 0 0 34 51 0 h .67 g 4484 2640 N -51 0 0 33 51 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2003 N -51 0 0 33 51 0 h .699 g 4737 2036 N -51 0 0 34 51 0 h .698 g 4737 2070 N -51 0 0 33 51 0 h .697 g 4737 2103 N -51 0 0 34 51 0 h .696 g 4737 2137 N -51 0 0 34 51 0 h .695 g 4737 2171 N -51 0 0 33 51 0 h .694 g 4737 2204 N -51 0 0 34 51 0 h .693 g 4737 2238 N -51 0 0 33 51 0 h .692 g 4737 2271 N -51 0 0 34 51 0 h .691 g 4737 2305 N -51 0 0 34 51 0 h .69 g 4737 2339 N -51 0 0 33 51 0 h .689 g 4737 2372 N -51 0 0 34 51 0 h .6881 g 4737 2406 N -51 0 0 33 51 0 h .6871 g 4737 2439 N -51 0 0 34 51 0 h .6861 g 4737 2473 N -51 0 0 34 51 0 h .6851 g 4737 2507 N -51 0 0 33 51 0 h .6841 g 4737 2540 N -51 0 0 34 51 0 h .6831 g 4737 2574 N -51 0 0 32 51 0 h .6821 g 4737 2606 N -51 0 0 34 51 0 h .6811 g 4737 2640 N -51 0 0 33 51 0 h .6801 g 4737 2673 N -51 0 0 34 51 0 h .6791 g 4737 2707 N -51 0 0 34 51 0 h .6781 g 4737 2741 N -51 0 0 33 51 0 h .6771 g 4737 2774 N -51 0 0 34 51 0 h .6761 g 4737 2808 N -51 0 0 33 51 0 h .6751 g 4737 2841 N -51 0 0 34 51 0 h .6741 g 4737 2875 N -51 0 0 34 51 0 h 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3782 N -51 0 0 34 51 0 h .6463 g 4737 3816 N -51 0 0 33 51 0 h .6453 g 4737 3849 N -51 0 0 34 51 0 h .6443 g 4737 3883 N -51 0 0 33 51 0 h .6433 g 4737 3916 N -51 0 0 34 51 0 h .6423 g 4737 3950 N -51 0 0 33 51 0 h .6413 g 4737 3983 N -51 0 0 34 51 0 h .6403 g 4737 4017 N -51 0 0 34 51 0 h .6393 g 4737 4051 N -51 0 0 33 51 0 h .6383 g 4737 4084 N -51 0 0 34 51 0 h .6373 g 4737 4118 N -51 0 0 33 51 0 h .6363 g 4737 4151 N -51 0 0 34 51 0 h .6353 g 4737 4185 N -51 0 0 34 51 0 h .6343 g 4737 4219 N -51 0 0 33 51 0 h .7419 g 4788 928 N -50 0 0 33 50 0 h .7407 g 4788 961 N -50 0 0 34 50 0 h .7396 g 4788 995 N -50 0 0 34 50 0 h .7384 g 4788 1029 N -50 0 0 33 50 0 h .7373 g 4788 1062 N -50 0 0 34 50 0 h .7361 g 4788 1096 N -50 0 0 33 50 0 h .735 g 4788 1129 N -50 0 0 34 50 0 h .7338 g 4788 1163 N -50 0 0 34 50 0 h .7327 g 4788 1197 N -50 0 0 33 50 0 h .7315 g 4788 1230 N -50 0 0 34 50 0 h .7304 g 4788 1264 N -50 0 0 33 50 0 h .7292 g 4788 1297 N -50 0 0 34 50 0 h .7281 g 4788 1331 N -50 0 0 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1566 N -51 0 0 34 51 0 h .7259 g 4838 1600 N -51 0 0 33 51 0 h .7246 g 4838 1633 N -51 0 0 34 51 0 h .7233 g 4838 1667 N -51 0 0 33 51 0 h .722 g 4838 1700 N -51 0 0 34 51 0 h .7207 g 4838 1734 N -51 0 0 34 51 0 h .7194 g 4838 1768 N -51 0 0 33 51 0 h .7181 g 4838 1801 N -51 0 0 34 51 0 h .7168 g 4838 1835 N -51 0 0 33 51 0 h .7155 g 4838 1868 N -51 0 0 34 51 0 h .7141 g 4838 1902 N -51 0 0 33 51 0 h .7128 g 4838 1935 N -51 0 0 34 51 0 h .7115 g 4838 1969 N -51 0 0 34 51 0 h .7102 g 4838 2003 N -51 0 0 33 51 0 h .7089 g 4838 2036 N -51 0 0 34 51 0 h .7076 g 4838 2070 N -51 0 0 33 51 0 h .7063 g 4838 2103 N -51 0 0 34 51 0 h .705 g 4838 2137 N -51 0 0 34 51 0 h .7037 g 4838 2171 N -51 0 0 33 51 0 h .7024 g 4838 2204 N -51 0 0 34 51 0 h .7011 g 4838 2238 N -51 0 0 33 51 0 h .6998 g 4838 2271 N -51 0 0 34 51 0 h .6985 g 4838 2305 N -51 0 0 34 51 0 h .6972 g 4838 2339 N -51 0 0 33 51 0 h .6959 g 4838 2372 N -51 0 0 34 51 0 h .6946 g 4838 2406 N -51 0 0 33 51 0 h .6933 g 4838 2439 N -51 0 0 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y FK(The)24 b(functions)f(describ)s(ed)g(in)h(this)g(c)m(hapter)g (compute)h(n)m(umerical)f(deriv)-5 b(ativ)m(es)26 b(b)m(y)d(\014nite)h (di\013erencing.)150 711 y(An)36 b(adaptiv)m(e)i(algorithm)f(is)f(used) g(to)h(\014nd)e(the)i(b)s(est)e(c)m(hoice)k(of)d(\014nite)g (di\013erence)h(and)f(to)h(estimate)150 821 y(the)31 b(error)f(in)g(the)g(deriv)-5 b(ativ)m(e.)42 b(These)31 b(functions)e(are)i(declared)g(in)f(the)h(header)f(\014le)g FH(gsl_deriv.h)p FK(.)150 1087 y FJ(29.1)68 b(F)-11 b(unctions)3350 1319 y FK([F)j(unction])-3599 b Fv(int)53 b(gsl_deriv_central)e Fu(\()p FD(const)31 b(gsl)p 1679 1319 28 4 v 41 w(function)f(*)g Ft(f)p FD(,)h(double)f Ft(x)p FD(,)h(double)f Ft(h)p FD(,)565 1429 y(double)g(*)h Ft(result)p FD(,)h(double)e(*)h Ft(abserr)p Fu(\))390 1539 y FK(This)41 b(function)h(computes)g(the)g (n)m(umerical)g(deriv)-5 b(ativ)m(e)44 b(of)e(the)g(function)g FD(f)59 b FK(at)43 b(the)f(p)s(oin)m(t)g FD(x)390 1648 y FK(using)28 b(an)g(adaptiv)m(e)h(cen)m(tral)h(di\013erence)f (algorithm)g(with)f(a)g(step-size)i(of)e FD(h)p FK(.)39 b(The)28 b(deriv)-5 b(ativ)m(e)30 b(is)390 1758 y(returned)f(in)h FD(result)j FK(and)c(an)i(estimate)h(of)e(its)h(absolute)g(error)f(is)g (returned)g(in)g FD(abserr)p FK(.)390 1915 y(The)d(initial)i(v)-5 b(alue)29 b(of)f FD(h)f FK(is)h(used)f(to)i(estimate)g(an)f(optimal)h (step-size,)h(based)d(on)h(the)g(scaling)h(of)390 2025 y(the)h(truncation)h(error)e(and)h(round-o\013)f(error)h(in)f(the)h (deriv)-5 b(ativ)m(e)32 b(calculation.)43 b(The)29 b(deriv)-5 b(ativ)m(e)390 2134 y(is)36 b(computed)g(using)f(a)h(5-p)s(oin)m(t)h (rule)e(for)h(equally)g(spaced)g(abscissae)h(at)g FE(x)23 b FI(\000)h FE(h)p FK(,)38 b FE(x)24 b FI(\000)f FE(h=)p FK(2,)39 b FE(x)p FK(,)390 2244 y FE(x)19 b FK(+)g FE(h=)p FK(2,)32 b FE(x)19 b FK(+)g FE(h)p FK(,)30 b(with)g(an)g(error)f (estimate)j(tak)m(en)f(from)e(the)h(di\013erence)h(b)s(et)m(w)m(een)f (the)g(5-p)s(oin)m(t)390 2353 y(rule)k(and)f(the)h(corresp)s(onding)f (3-p)s(oin)m(t)h(rule)g FE(x)23 b FI(\000)f FE(h)p FK(,)35 b FE(x)p FK(,)g FE(x)23 b FK(+)f FE(h)p FK(.)51 b(Note)36 b(that)e(the)g(v)-5 b(alue)35 b(of)f(the)390 2463 y(function)g(at)i FE(x)e FK(do)s(es)g(not)h(con)m(tribute)g(to)h(the)f(deriv)-5 b(ativ)m(e)36 b(calculation,)i(so)d(only)f(4-p)s(oin)m(ts)i(are)390 2573 y(actually)c(used.)3350 2803 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_deriv_forward)e Fu(\()p FD(const)31 b(gsl)p 1679 2803 V 41 w(function)f(*)g Ft(f)p FD(,)h(double)f Ft(x)p FD(,)h(double)f Ft(h)p FD(,)565 2912 y(double)g(*)h Ft(result)p FD(,)h(double)e(*)h Ft(abserr)p Fu(\))390 3022 y FK(This)41 b(function)h(computes)g(the)g(n)m(umerical)g(deriv)-5 b(ativ)m(e)44 b(of)e(the)g(function)g FD(f)59 b FK(at)43 b(the)f(p)s(oin)m(t)g FD(x)390 3131 y FK(using)36 b(an)h(adaptiv)m(e)i (forw)m(ard)d(di\013erence)h(algorithm)h(with)f(a)g(step-size)i(of)e FD(h)p FK(.)60 b(The)36 b(function)390 3241 y(is)h(ev)-5 b(aluated)39 b(only)e(at)h(p)s(oin)m(ts)f(greater)i(than)e FD(x)p FK(,)i(and)d(nev)m(er)i(at)g FD(x)43 b FK(itself.)62 b(The)37 b(deriv)-5 b(ativ)m(e)39 b(is)390 3351 y(returned)c(in)h FD(result)j FK(and)d(an)g(estimate)i(of)f(its)f(absolute)i(error)e(is)g (returned)f(in)h FD(abserr)p FK(.)59 b(This)390 3460 y(function)26 b(should)f(b)s(e)h(used)g(if)g FE(f)10 b FK(\()p FE(x)p FK(\))26 b(has)g(a)h(discon)m(tin)m(uit)m(y)h(at)f FD(x)p FK(,)g(or)f(is)h(unde\014ned)d(for)i(v)-5 b(alues)27 b(less)390 3570 y(than)j FD(x)p FK(.)390 3727 y(The)d(initial)i(v)-5 b(alue)29 b(of)f FD(h)f FK(is)h(used)f(to)i(estimate)g(an)f(optimal)h (step-size,)h(based)d(on)h(the)g(scaling)h(of)390 3837 y(the)h(truncation)h(error)e(and)h(round-o\013)f(error)h(in)f(the)h (deriv)-5 b(ativ)m(e)32 b(calculation.)43 b(The)29 b(deriv)-5 b(ativ)m(e)390 3946 y(at)26 b FE(x)g FK(is)f(computed)g(using)g(an)h (\\op)s(en")g(4-p)s(oin)m(t)g(rule)f(for)g(equally)i(spaced)e (abscissae)i(at)f FE(x)10 b FK(+)g FE(h=)p FK(4,)390 4056 y FE(x)22 b FK(+)h FE(h=)p FK(2,)36 b FE(x)22 b FK(+)g(3)p FE(h=)p FK(4,)37 b FE(x)22 b FK(+)g FE(h)p FK(,)35 b(with)f(an)f(error)h(estimate)h(tak)m(en)g(from)e(the)h (di\013erence)g(b)s(et)m(w)m(een)390 4165 y(the)d(4-p)s(oin)m(t)g(rule) f(and)g(the)g(corresp)s(onding)f(2-p)s(oin)m(t)j(rule)e FE(x)20 b FK(+)g FE(h=)p FK(2,)32 b FE(x)20 b FK(+)g FE(h)p FK(.)3350 4395 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_deriv_backward)e Fu(\()p FD(const)31 b(gsl)p 1731 4395 V 41 w(function)f(*)h Ft(f)p FD(,)g(double)f Ft(x)p FD(,)g(double)g Ft(h)p FD(,)565 4505 y(double)g(*)h Ft(result)p FD(,)h(double)e(*)h Ft(abserr)p Fu(\))390 4615 y FK(This)41 b(function)h(computes)g(the)g(n)m(umerical)g(deriv)-5 b(ativ)m(e)44 b(of)e(the)g(function)g FD(f)59 b FK(at)43 b(the)f(p)s(oin)m(t)g FD(x)390 4724 y FK(using)31 b(an)h(adaptiv)m(e)h (bac)m(kw)m(ard)f(di\013erence)g(algorithm)h(with)f(a)g(step-size)h(of) f FD(h)p FK(.)44 b(The)31 b(function)390 4834 y(is)23 b(ev)-5 b(aluated)24 b(only)g(at)g(p)s(oin)m(ts)f(less)g(than)g FD(x)p FK(,)i(and)d(nev)m(er)h(at)h FD(x)30 b FK(itself.)39 b(The)22 b(deriv)-5 b(ativ)m(e)25 b(is)e(returned)390 4943 y(in)37 b FD(result)i FK(and)e(an)g(estimate)i(of)e(its)h (absolute)g(error)f(is)g(returned)f(in)h FD(abserr)p FK(.)61 b(This)36 b(function)390 5053 y(should)26 b(b)s(e)f(used)h(if)h FE(f)10 b FK(\()p FE(x)p FK(\))26 b(has)g(a)h(discon)m(tin)m(uit)m(y)h (at)f FD(x)p FK(,)h(or)e(is)h(unde\014ned)d(for)j(v)-5 b(alues)26 b(greater)i(than)390 5162 y FD(x)p FK(.)390 5320 y(This)i(function)g(is)g(equiv)-5 b(alen)m(t)32 b(to)f(calling)h FH(gsl_deriv_forward)26 b FK(with)k(a)g(negativ)m(e)j (step-size.)p eop end %%Page: 365 383 TeXDict begin 365 382 bop 150 -116 a FK(Chapter)30 b(29:)41 b(Numerical)31 b(Di\013eren)m(tiation)1945 b(365)150 299 y FJ(29.2)68 b(Examples)150 458 y FK(The)36 b(follo)m(wing)j(co)s (de)e(estimates)h(the)f(deriv)-5 b(ativ)m(e)39 b(of)e(the)g(function)f FE(f)10 b FK(\()p FE(x)p FK(\))36 b(=)g FE(x)2950 425 y FB(3)p Fq(=)p FB(2)3091 458 y FK(at)i FE(x)e FK(=)g(2)h(and)f(at)150 568 y FE(x)f FK(=)f(0.)58 b(The)35 b(function)h FE(f)10 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b(gsl_cheb_calc_deriv)e Fu(\()p FD(gsl)p 1545 4107 V 41 w(c)m(heb)p 1765 4107 V 41 w(series)30 b(*)h Ft(deriv)p FD(,)h(const)565 4217 y(gsl)p 677 4217 V 41 w(c)m(heb)p 897 4217 V 40 w(series)f(*)f Ft(cs)p Fu(\))390 4327 y FK(This)35 b(function)h(computes)g(the)h(deriv)-5 b(ativ)m(e)37 b(of)g(the)f(series)h FD(cs)p FK(,)h(storing)e(the)g (deriv)-5 b(ativ)m(e)38 b(co)s(e\016-)390 4436 y(cien)m(ts)32 b(in)f(the)g(previously)f(allo)s(cated)j FD(deriv)p FK(.)42 b(The)31 b(t)m(w)m(o)h(series)f FD(cs)k FK(and)30 b FD(deriv)39 b FK(m)m(ust)31 b(ha)m(v)m(e)h(b)s(een)390 4546 y(allo)s(cated)g(with)e (the)h(same)g(order.)3350 4774 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_cheb_calc_integ)e Fu(\()p FD(gsl)p 1545 4774 V 41 w(c)m(heb)p 1765 4774 V 41 w(series)30 b(*)h Ft(integ)p FD(,)h(const)565 4884 y(gsl)p 677 4884 V 41 w(c)m(heb)p 897 4884 V 40 w(series)f(*)f Ft(cs)p Fu(\))390 4994 y FK(This)25 b(function)g(computes)h(the)g(in)m(tegral)i (of)e(the)g(series)g FD(cs)p FK(,)h(storing)f(the)g(in)m(tegral)i(co)s (e\016cien)m(ts)f(in)390 5103 y(the)j(previously)g(allo)s(cated)i FD(in)m(teg)p FK(.)42 b(The)29 b(t)m(w)m(o)i(series)g FD(cs)i FK(and)d FD(in)m(teg)39 b FK(m)m(ust)30 b(ha)m(v)m(e)h(b)s(een) e(allo)s(cated)390 5213 y(with)k(the)g(same)g(order.)48 b(The)32 b(lo)m(w)m(er)i(limit)g(of)f(the)g(in)m(tegration)i(is)e(tak)m (en)h(to)f(b)s(e)f(the)h(left)h(hand)390 5322 y(end)c(of)g(the)h(range) g FD(a)p FK(.)p eop end %%Page: 369 387 TeXDict begin 369 386 bop 150 -116 a FK(Chapter)30 b(30:)41 b(Cheb)m(yshev)30 b(Appro)m(ximations)1862 b(369)150 299 y FJ(30.6)68 b(Examples)150 458 y FK(The)37 b(follo)m(wing)j (example)e(program)g(computes)g(Cheb)m(yshev)f(appro)m(ximations)h(to)h (a)f(step)g(function.)150 568 y(This)24 b(is)h(an)g(extremely)i (di\016cult)e(appro)m(ximation)h(to)g(mak)m(e,)h(due)d(to)i(the)g (discon)m(tin)m(uit)m(y)-8 b(,)28 b(and)c(w)m(as)i(c)m(ho-)150 677 y(sen)21 b(as)h(an)f(example)h(where)f(appro)m(ximation)h(error)f (is)h(visible.)38 b(F)-8 b(or)22 b(smo)s(oth)f(functions)g(the)h(Cheb)m (yshev)150 787 y(appro)m(ximation)31 b(con)m(v)m(erges)i(extremely)e (rapidly)f(and)g(errors)g(w)m(ould)g(not)g(b)s(e)g(visible.)390 956 y FH(#include)46 b()390 1066 y(#include)g ()390 1176 y(#include)g()390 1395 y(double)390 1504 y(f)h(\(double)f(x,)h(void)g(*p\))390 1614 y({)485 1724 y(\(void\)\(p\);)e(/*)j(avoid)e(unused)g(parameter)f (warning)h(*/)485 1943 y(if)i(\(x)f(<)g(0.5\))581 2052 y(return)f(0.25;)485 2162 y(else)581 2271 y(return)g(0.75;)390 2381 y(})390 2600 y(int)390 2710 y(main)h(\(void\))390 2819 y({)485 2929 y(int)g(i,)h(n)f(=)g(10000;)485 3148 y(gsl_cheb_series)d(*cs)j(=)g(gsl_cheb_alloc)d(\(40\);)485 3367 y(gsl_function)h(F;)485 3587 y(F.function)g(=)j(f;)485 3696 y(F.params)e(=)h(0;)485 3915 y(gsl_cheb_init)e(\(cs,)h(&F,)h(0.0,) g(1.0\);)485 4134 y(for)g(\(i)h(=)f(0;)g(i)h(<)f(n;)g(i++\))581 4244 y({)676 4354 y(double)f(x)i(=)f(i)h(/)f(\(double\)n;)676 4463 y(double)f(r10)h(=)h(gsl_cheb_eval_n)43 b(\(cs,)k(10,)g(x\);)676 4573 y(double)f(r40)h(=)h(gsl_cheb_eval)c(\(cs,)j(x\);)676 4682 y(printf)f(\("\045g)h(\045g)g(\045g)g(\045g\\n",)1058 4792 y(x,)g(GSL_FN_EVAL)e(\(&F,)i(x\),)g(r10,)f(r40\);)581 4902 y(})485 5121 y(gsl_cheb_free)f(\(cs\);)485 5340 y(return)i(0;)p eop end %%Page: 370 388 TeXDict begin 370 387 bop 150 -116 a FK(Chapter)30 b(30:)41 b(Cheb)m(yshev)30 b(Appro)m(ximations)1862 b(370)390 299 y FH(})150 433 y FK(The)35 b(output)g(from)g(the)h(program)f(giv)m (es)i(the)e(original)i(function,)g(10-th)f(order)f(appro)m(ximation)i (and)150 543 y(40-th)31 b(order)f(appro)m(ximation,)i(all)f(sampled)f (at)h(in)m(terv)-5 b(als)32 b(of)e(0.001)j(in)d FE(x)p FK(.)275 2207 y @beginspecial 50 @llx 50 @lly 410 @urx 302 @ury 2448 @rwi @setspecial %%BeginDocument: cheb.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: cheb.eps %%Creator: gnuplot 3.5 (pre 3.6) patchlevel beta 347 %%CreationDate: Wed Apr 25 18:48:58 2001 %%DocumentFonts: (atend) %%BoundingBox: 50 50 410 302 %%Orientation: Portrait %%EndComments /gnudict 120 dict def gnudict begin /Color false def /Solid false def /gnulinewidth 5.000 def /userlinewidth gnulinewidth def /vshift -46 def /dl {10 mul} def /hpt_ 31.5 def /vpt_ 31.5 def /hpt hpt_ def /vpt vpt_ def /M {moveto} bind def /L {lineto} bind def /R {rmoveto} bind def /V {rlineto} bind def /vpt2 vpt 2 mul def /hpt2 hpt 2 mul def /Lshow { currentpoint stroke M 0 vshift R show } def /Rshow { currentpoint stroke M dup stringwidth pop neg vshift R show } def /Cshow { currentpoint stroke M dup stringwidth pop -2 div vshift R show } def /UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def /DL { Color {setrgbcolor Solid {pop []} if 0 setdash } {pop pop pop Solid {pop []} if 0 setdash} ifelse } def /BL { stroke gnulinewidth 2 mul setlinewidth } def /AL { stroke gnulinewidth 2 div setlinewidth } def /UL { gnulinewidth mul /userlinewidth exch def } def /PL { stroke userlinewidth setlinewidth } def /LTb { BL [] 0 0 0 DL } def /LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def /LT0 { PL [] 1 0 0 DL } def /LT1 { PL [4 dl 2 dl] 0 1 0 DL } def /LT2 { PL [2 dl 3 dl] 0 0 1 DL } def /LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def /LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def /LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def /LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def /LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def /LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def /Pnt { stroke [] 0 setdash gsave 1 setlinecap M 0 0 V stroke grestore } def /Dia { stroke [] 0 setdash 2 copy vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke Pnt } def /Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V currentpoint stroke M hpt neg vpt neg R hpt2 0 V stroke } def /Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke Pnt } def /Crs { stroke [] 0 setdash exch hpt sub exch vpt add M hpt2 vpt2 neg V currentpoint stroke M hpt2 neg 0 R hpt2 vpt2 V stroke } def /TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke Pnt } def /Star { 2 copy Pls Crs } def /BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath fill } def /TriUF { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath fill } def /TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke Pnt } def /TriDF { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath fill} def /DiaF { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath fill } def /Pent { stroke [] 0 setdash 2 copy gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore Pnt } def /PentF { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath fill grestore } def /Circle { stroke [] 0 setdash 2 copy hpt 0 360 arc stroke Pnt } def /CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def /C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def /C1 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill vpt 0 360 arc closepath } bind def /C2 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath } bind def /C3 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill vpt 0 360 arc closepath } bind def /C4 { BL [] 0 setdash 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc closepath } bind def /C5 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc } bind def /C6 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 270 arc closepath fill vpt 0 360 arc closepath } bind def /C7 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 270 arc closepath fill vpt 0 360 arc closepath } bind def /C8 { BL [] 0 setdash 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath } bind def /C9 { BL [] 0 setdash 2 copy moveto 2 copy vpt 270 450 arc closepath fill vpt 0 360 arc closepath } bind def /C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath } bind def /C11 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath } bind def /C12 { BL [] 0 setdash 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath } bind def /C13 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath } bind def /C14 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 360 arc closepath fill vpt 0 360 arc } bind def /C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill vpt 0 360 arc closepath } bind def /Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath } bind def /Square { dup Rec } bind def /Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def /S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def /S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def /S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def /S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def /S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def /S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def /S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill 2 copy vpt Square fill Bsquare } bind def /S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def /S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def /S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def /S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def /S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy vpt Square fill Bsquare } bind def /S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def /D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def /D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def /D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def /D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def /D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def /D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def /D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def /D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def /D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def /D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def /D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def /D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def /D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def /D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def /D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def /D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def /DiaE { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke } def /BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke } def /TriUE { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke } def /TriDE { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke } def /PentE { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore } def /CircE { stroke [] 0 setdash hpt 0 360 arc stroke } def /Opaque { gsave closepath 1 setgray fill grestore 0 setgray closepath } def /DiaW { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V Opaque stroke } def /BoxW { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V Opaque stroke } def /TriUW { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V Opaque stroke } def /TriDW { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V Opaque stroke } def /PentW { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat Opaque stroke grestore } def /CircW { stroke [] 0 setdash hpt 0 360 arc Opaque stroke } def /BoxFill { gsave Rec 1 setgray fill grestore } def end %%EndProlog gnudict begin gsave 50 50 translate 0.050 0.050 scale 0 setgray newpath (Helvetica) findfont 140 scalefont setfont 1.000 UL LTb 420 280 M 63 0 V 6549 0 R -63 0 V 336 280 M (0) Rshow 420 1198 M 63 0 V 6549 0 R -63 0 V -6633 0 R (0.2) Rshow 420 2117 M 63 0 V 6549 0 R -63 0 V -6633 0 R (0.4) Rshow 420 3035 M 63 0 V 6549 0 R -63 0 V -6633 0 R (0.6) Rshow 420 3954 M 63 0 V 6549 0 R -63 0 V -6633 0 R (0.8) Rshow 420 4872 M 63 0 V 6549 0 R -63 0 V -6633 0 R (1) Rshow 420 280 M 0 63 V 0 4529 R 0 -63 V 420 140 M (0) Cshow 1742 280 M 0 63 V 0 4529 R 0 -63 V 0 -4669 R (0.2) Cshow 3065 280 M 0 63 V 0 4529 R 0 -63 V 0 -4669 R (0.4) Cshow 4387 280 M 0 63 V 0 4529 R 0 -63 V 0 -4669 R (0.6) Cshow 5710 280 M 0 63 V 0 4529 R 0 -63 V 0 -4669 R (0.8) Cshow 7032 280 M 0 63 V 0 4529 R 0 -63 V 0 -4669 R (1) Cshow 1.000 UL LTb 420 280 M 6612 0 V 0 4592 V -6612 0 V 420 280 L 1.000 UL LT0 420 1428 M 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V currentpoint stroke M 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 2296 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V currentpoint stroke M 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 1.000 UL LT1 420 1331 M 7 20 V 6 19 V 7 17 V 6 16 V 7 15 V 7 14 V 6 12 V 7 12 V 7 10 V 6 10 V 7 8 V 6 8 V 7 7 V 7 6 V 6 5 V 7 5 V 6 3 V 7 4 V 7 2 V 6 2 V 7 1 V 6 1 V 7 1 V 7 -1 V 6 0 V 7 -1 V 7 -2 V 6 -1 V 7 -3 V 6 -2 V 7 -3 V 7 -3 V 6 -3 V 7 -4 V 6 -4 V 7 -4 V 7 -4 V 6 -4 V 7 -4 V 6 -5 V 7 -5 V 7 -4 V 6 -5 V 7 -5 V 7 -5 V 6 -5 V 7 -5 V 6 -5 V 7 -5 V 7 -5 V 6 -5 V 7 -5 V 6 -5 V 7 -5 V 7 -5 V 6 -5 V 7 -4 V 6 -5 V 7 -4 V 7 -5 V 6 -4 V 7 -4 V 7 -4 V 6 -4 V 7 -4 V 6 -4 V 7 -4 V 7 -3 V 6 -4 V 7 -3 V 6 -3 V 7 -3 V 7 -2 V 6 -3 V 7 -3 V 7 -2 V 6 -2 V 7 -2 V 6 -2 V 7 -2 V 7 -1 V 6 -1 V 7 -2 V 6 -1 V 7 -1 V 7 0 V 6 -1 V 7 -1 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 7 1 V 6 0 V 7 1 V 6 1 V 7 1 V 7 1 V 6 1 V 7 2 V 6 1 V 7 2 V 7 2 V 6 2 V 7 1 V 6 3 V 7 2 V 7 2 V 6 2 V 7 3 V 7 3 V 6 2 V 7 3 V 6 3 V 7 3 V 7 3 V 6 3 V 7 3 V 6 3 V 7 4 V 7 3 V 6 3 V 7 4 V 7 3 V 6 4 V 7 3 V 6 4 V 7 4 V 7 3 V 6 4 V 7 4 V 6 4 V 7 4 V 7 3 V 6 4 V 7 4 V 6 4 V 7 4 V 7 4 V 6 3 V 7 4 V 7 4 V 6 4 V 7 4 V 6 3 V 7 4 V 7 4 V 6 3 V 7 4 V 6 4 V 7 3 V 7 4 V 6 3 V 7 4 V 6 3 V 7 3 V 7 4 V 6 3 V 7 3 V 7 3 V 6 3 V 7 3 V 6 3 V 7 3 V 7 3 V 6 3 V 7 2 V 6 3 V 7 2 V 7 3 V 6 2 V 7 2 V 6 2 V 7 2 V 7 2 V 6 2 V 7 2 V 7 2 V 6 1 V 7 2 V 6 1 V 7 2 V 7 1 V 6 1 V 7 1 V 6 1 V 7 1 V 7 1 V 6 0 V 7 1 V 7 1 V 6 0 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 -1 V 7 0 V 6 -1 V 7 -1 V 6 -1 V 7 -1 V 7 -1 V 6 -1 V 7 -1 V 7 -1 V 6 -2 V 7 -1 V 6 -2 V 7 -1 V 7 -2 V 6 -2 V 7 -2 V 6 -2 V 7 -2 V 7 -3 V 6 -2 V 7 -2 V 6 -3 V 7 -2 V 7 -3 V 6 -3 V 7 -3 V 7 -2 V 6 -3 V 7 -3 V 6 -4 V 7 -3 V 7 -3 V 6 -3 V 7 -4 V 6 -3 V 7 -4 V 7 -3 V 6 -4 V 7 -4 V 6 -3 V 7 -4 V 7 -4 V 6 -4 V 7 -4 V 7 -4 V 6 -4 V 7 -4 V 6 -4 V 7 -4 V 7 -4 V 6 -5 V 7 -4 V 6 -4 V 7 -4 V 7 -5 V 6 -4 V 7 -4 V 7 -5 V 6 -4 V 7 -5 V 6 -4 V 7 -4 V 7 -5 V 6 -4 V 7 -5 V 6 -4 V 7 -5 V 7 -4 V 6 -4 V 7 -5 V 6 -4 V 7 -5 V 7 -4 V 6 -4 V 7 -5 V 7 -4 V 6 -4 V 7 -5 V 6 -4 V 7 -4 V 7 -4 V 6 -4 V 7 -4 V 6 -4 V 7 -4 V 7 -4 V 6 -4 V 7 -4 V 6 -4 V 7 -4 V 7 -3 V 6 -4 V 7 -4 V 7 -3 V 6 -4 V 7 -3 V 6 -3 V 7 -4 V 7 -3 V 6 -3 V 7 -3 V 6 -3 V 7 -3 V 7 -2 V 6 -3 V 7 -3 V 6 -2 V 7 -3 V 7 -2 V 6 -2 V 7 -2 V 7 -3 V 6 -1 V 7 -2 V 6 -2 V 7 -2 V 7 -1 V 6 -2 V 7 -1 V 6 -1 V 7 -1 V 7 -1 V 6 -1 V 7 -1 V 7 -1 V 6 0 V 7 0 V 6 -1 V 7 0 V 7 0 V 6 0 V 7 0 V 6 1 V 7 0 V 7 1 V 6 1 V 7 0 V 6 1 V 7 2 V 7 1 V 6 1 V 7 2 V 7 2 V 6 1 V 7 2 V 6 2 V 7 3 V 7 2 V 6 3 V 7 2 V 6 3 V 7 3 V 7 3 V 6 3 V 7 4 V 6 3 V 7 4 V 7 4 V 6 4 V 7 4 V 7 4 V 6 5 V 7 4 V 6 5 V 7 5 V 7 5 V 6 5 V 7 5 V 6 6 V 7 5 V 7 6 V 6 6 V 7 6 V 7 6 V 6 6 V 7 7 V 6 6 V 7 7 V 7 7 V 6 7 V 7 7 V 6 8 V 7 7 V 7 8 V 6 8 V 7 7 V 6 8 V 7 9 V 7 8 V 6 8 V 7 9 V 7 9 V 6 9 V 7 9 V 6 9 V 7 9 V 7 9 V 6 10 V currentpoint stroke M 7 10 V 6 9 V 7 10 V 7 10 V 6 11 V 7 10 V 6 10 V 7 11 V 7 11 V 6 10 V 7 11 V 7 11 V 6 11 V 7 12 V 6 11 V 7 12 V 7 11 V 6 12 V 7 12 V 6 12 V 7 12 V 7 12 V 6 12 V 7 12 V 6 13 V 7 12 V 7 13 V 6 13 V 7 12 V 7 13 V 6 13 V 7 13 V 6 13 V 7 14 V 7 13 V 6 13 V 7 14 V 6 13 V 7 14 V 7 14 V 6 14 V 7 13 V 7 14 V 6 14 V 7 14 V 6 14 V 7 15 V 7 14 V 6 14 V 7 14 V 6 15 V 7 14 V 7 15 V 6 14 V 7 15 V 6 14 V 7 15 V 7 15 V 6 14 V 7 15 V 7 15 V 6 15 V 7 15 V 6 14 V 7 15 V 7 15 V 6 15 V 7 15 V 6 15 V 7 15 V 7 15 V 6 15 V 7 15 V 6 15 V 7 15 V 7 15 V 6 15 V 7 15 V 7 15 V 6 15 V 7 15 V 6 15 V 7 15 V 7 15 V 6 15 V 7 15 V 6 15 V 7 15 V 7 14 V 6 15 V 7 15 V 6 15 V 7 15 V 7 14 V 6 15 V 7 15 V 7 14 V 6 15 V 7 14 V 6 15 V 7 14 V 7 14 V 6 15 V 7 14 V 6 14 V 7 14 V 7 14 V 6 14 V 7 14 V 7 14 V 6 14 V 7 14 V 6 13 V 7 14 V 7 14 V 6 13 V 7 14 V 6 13 V 7 13 V 7 13 V 6 13 V 7 13 V 6 13 V 7 13 V 7 13 V 6 13 V 7 12 V 7 13 V 6 12 V 7 12 V 6 13 V 7 12 V 7 12 V 6 12 V 7 11 V 6 12 V 7 12 V 7 11 V 6 12 V 7 11 V 6 11 V 7 11 V 7 11 V 6 11 V 7 11 V 7 10 V 6 11 V 7 10 V 6 11 V 7 10 V 7 10 V 6 10 V 7 10 V 6 9 V 7 10 V 7 9 V 6 10 V 7 9 V 6 9 V 7 9 V 7 9 V 6 9 V 7 8 V 7 9 V 6 8 V 7 8 V 6 8 V 7 8 V 7 8 V 6 8 V 7 8 V 6 7 V 7 7 V 7 8 V 6 7 V 7 7 V 7 7 V 6 6 V 7 7 V 6 6 V 7 7 V 7 6 V 6 6 V 7 6 V 6 6 V 7 5 V 7 6 V 6 5 V 7 6 V 6 5 V 7 5 V 7 5 V 6 4 V 7 5 V 7 5 V 6 4 V 7 4 V 6 5 V 7 4 V 7 3 V 6 4 V 7 4 V 6 3 V 7 4 V 7 3 V 6 3 V 7 3 V 6 3 V 7 3 V 7 3 V 6 2 V 7 3 V 7 2 V 6 2 V 7 2 V 6 2 V 7 2 V 7 2 V 6 2 V 7 1 V 6 2 V 7 1 V 7 1 V 6 1 V 7 1 V 7 1 V 6 1 V 7 1 V 6 0 V 7 1 V 7 0 V 6 1 V 7 0 V 6 0 V 7 0 V 7 0 V 6 0 V 7 0 V 6 -1 V 7 0 V 7 -1 V 6 0 V 7 -1 V 7 -1 V 6 -1 V 7 -1 V 6 -1 V 7 -1 V 7 -1 V 6 -1 V 7 -2 V 6 -1 V 7 -1 V 7 -2 V 6 -1 V 7 -2 V 6 -2 V 7 -2 V 7 -1 V 6 -2 V 7 -2 V 7 -2 V 6 -2 V 7 -3 V 6 -2 V 7 -2 V 7 -2 V 6 -3 V 7 -2 V 6 -2 V 7 -3 V 7 -2 V 6 -3 V 7 -3 V 6 -2 V 7 -3 V 7 -3 V 6 -2 V 7 -3 V 7 -3 V 6 -3 V 7 -3 V 6 -2 V 7 -3 V 7 -3 V 6 -3 V 7 -3 V 6 -3 V 7 -3 V 7 -3 V 6 -3 V 7 -3 V 7 -3 V 6 -3 V 7 -3 V 6 -3 V 7 -4 V 7 -3 V 6 -3 V 7 -3 V 6 -3 V 7 -3 V 7 -3 V 6 -3 V 7 -3 V 6 -3 V 7 -3 V 7 -3 V 6 -3 V 7 -3 V 7 -3 V 6 -3 V 7 -3 V 6 -3 V 7 -3 V 7 -3 V 6 -3 V 7 -2 V 6 -3 V 7 -3 V 7 -3 V 6 -3 V 7 -2 V 6 -3 V 7 -3 V 7 -2 V 6 -3 V 7 -2 V 7 -3 V 6 -2 V 7 -3 V 6 -2 V 7 -2 V 7 -3 V 6 -2 V 7 -2 V 6 -2 V 7 -2 V 7 -3 V 6 -2 V 7 -2 V 6 -2 V 7 -1 V 7 -2 V 6 -2 V 7 -2 V 7 -2 V 6 -1 V 7 -2 V 6 -1 V 7 -2 V 7 -1 V 6 -2 V 7 -1 V 6 -1 V 7 -2 V 7 -1 V 6 -1 V 7 -1 V 7 -1 V 6 -1 V 7 -1 V 6 -1 V 7 0 V 7 -1 V 6 -1 V 7 0 V 6 -1 V 7 -1 V 7 0 V 6 0 V 7 -1 V 6 0 V 7 0 V 7 0 V 6 0 V 7 -1 V 7 0 V 6 1 V 7 0 V 6 0 V 7 0 V 7 0 V 6 1 V 7 0 V 6 0 V 7 1 V 7 1 V 6 0 V 7 1 V 6 0 V 7 1 V 7 1 V 6 1 V 7 1 V 7 1 V 6 1 V 7 1 V 6 1 V 7 1 V currentpoint stroke M 7 1 V 6 1 V 7 1 V 6 2 V 7 1 V 7 1 V 6 2 V 7 1 V 6 2 V 7 1 V 7 2 V 6 1 V 7 2 V 7 2 V 6 1 V 7 2 V 6 2 V 7 2 V 7 1 V 6 2 V 7 2 V 6 2 V 7 2 V 7 2 V 6 2 V 7 2 V 7 1 V 6 2 V 7 2 V 6 2 V 7 2 V 7 2 V 6 2 V 7 2 V 6 2 V 7 2 V 7 3 V 6 2 V 7 2 V 6 2 V 7 2 V 7 2 V 6 2 V 7 2 V 7 2 V 6 2 V 7 2 V 6 2 V 7 2 V 7 1 V 6 2 V 7 2 V 6 2 V 7 2 V 7 2 V 6 2 V 7 1 V 6 2 V 7 2 V 7 2 V 6 1 V 7 2 V 7 2 V 6 1 V 7 2 V 6 1 V 7 2 V 7 1 V 6 1 V 7 2 V 6 1 V 7 1 V 7 2 V 6 1 V 7 1 V 7 1 V 6 1 V 7 1 V 6 1 V 7 1 V 7 0 V 6 1 V 7 1 V 6 1 V 7 0 V 7 1 V 6 0 V 7 1 V 6 0 V 7 0 V 7 0 V 6 1 V 7 0 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 -1 V 6 0 V 7 0 V 6 -1 V 7 0 V 7 -1 V 6 0 V 7 -1 V 6 -1 V 7 -1 V 7 0 V 6 -1 V 7 -1 V 7 -1 V 6 -1 V 7 -2 V 6 -1 V 7 -1 V 7 -1 V 6 -2 V 7 -1 V 6 -2 V 7 -1 V 7 -2 V 6 -1 V 7 -2 V 6 -2 V 7 -1 V 7 -2 V 6 -2 V 7 -2 V 7 -2 V 6 -1 V 7 -2 V 6 -2 V 7 -2 V 7 -2 V 6 -2 V 7 -2 V 6 -2 V 7 -3 V 7 -2 V 6 -2 V 7 -2 V 7 -2 V 6 -2 V 7 -2 V 6 -2 V 7 -2 V 7 -2 V 6 -2 V 7 -2 V 6 -2 V 7 -2 V 7 -2 V 6 -2 V 7 -2 V 6 -1 V 7 -2 V 7 -2 V 6 -1 V 7 -2 V 7 -1 V 6 -1 V 7 -2 V 6 -1 V 7 -1 V 7 -1 V 6 -1 V 7 0 V 6 -1 V 7 -1 V 7 0 V 6 0 V 7 0 V 6 0 V 7 0 V 7 1 V 6 0 V 7 1 V 7 1 V 6 1 V 7 1 V 6 2 V 7 2 V 7 1 V 6 3 V 7 2 V 6 3 V 7 3 V 7 3 V 6 3 V 7 4 V 6 4 V 7 4 V 7 5 V 6 5 V 7 5 V 7 6 V 6 6 V 7 6 V 6 7 V 7 7 V 1.000 UL LT2 420 1457 M 7 -54 V 6 0 V 7 19 V 6 19 V 7 13 V 7 3 V 6 -4 V 7 -11 V 7 -12 V 6 -12 V 7 -11 V 6 -6 V 7 -3 V 7 1 V 6 5 V 7 7 V 6 9 V 7 9 V 7 9 V 6 8 V 7 6 V 6 5 V 7 1 V 7 0 V 6 -2 V 7 -5 V 7 -6 V 6 -6 V 7 -8 V 6 -7 V 7 -7 V 7 -7 V 6 -5 V 7 -4 V 6 -3 V 7 -1 V 7 0 V 6 2 V 7 3 V 6 4 V 7 5 V 7 6 V 6 6 V 7 7 V 7 6 V 6 6 V 7 5 V 6 5 V 7 4 V 7 2 V 6 2 V 7 1 V 6 -1 V 7 -2 V 7 -2 V 6 -4 V 7 -4 V 6 -5 V 7 -5 V 7 -6 V 6 -5 V 7 -6 V 7 -6 V 6 -5 V 7 -4 V 6 -4 V 7 -3 V 7 -3 V 6 -1 V 7 -1 V 6 0 V 7 1 V 7 2 V 6 3 V 7 3 V 7 4 V 6 4 V 7 5 V 6 5 V 7 5 V 7 6 V 6 5 V 7 5 V 6 4 V 7 5 V 7 3 V 6 4 V 7 2 V 6 2 V 7 1 V 7 1 V 6 0 V 7 -1 V 7 -2 V 6 -2 V 7 -3 V 6 -4 V 7 -4 V 7 -4 V 6 -4 V 7 -5 V 6 -5 V 7 -5 V 7 -5 V 6 -5 V 7 -5 V 6 -4 V 7 -4 V 7 -3 V 6 -3 V 7 -2 V 7 -2 V 6 -1 V 7 -1 V 6 0 V 7 1 V 7 1 V 6 2 V 7 2 V 6 3 V 7 4 V 7 3 V 6 5 V 7 4 V 7 5 V 6 4 V 7 5 V 6 5 V 7 5 V 7 5 V 6 4 V 7 4 V 6 4 V 7 3 V 7 3 V 6 3 V 7 1 V 6 2 V 7 1 V 7 0 V 6 0 V 7 -1 V 7 -2 V 6 -2 V 7 -2 V 6 -3 V 7 -3 V 7 -4 V 6 -4 V 7 -5 V 6 -4 V 7 -5 V 7 -5 V 6 -4 V 7 -5 V 6 -5 V 7 -5 V 7 -4 V 6 -4 V 7 -4 V 7 -3 V 6 -3 V 7 -3 V 6 -2 V 7 -2 V 7 -1 V 6 0 V 7 0 V 6 0 V 7 1 V 7 2 V 6 2 V 7 2 V 6 3 V 7 3 V 7 4 V 6 4 V 7 4 V 7 5 V 6 5 V 7 5 V 6 5 V 7 5 V 7 4 V 6 5 V 7 5 V 6 4 V 7 5 V 7 4 V 6 3 V 7 3 V 7 3 V 6 3 V 7 1 V 6 2 V 7 1 V 7 0 V 6 0 V 7 -1 V 6 -1 V 7 -2 V 7 -2 V 6 -2 V 7 -3 V 6 -4 V 7 -4 V 7 -4 V 6 -4 V 7 -5 V 7 -5 V 6 -5 V 7 -5 V 6 -5 V 7 -6 V 7 -5 V 6 -5 V 7 -5 V 6 -4 V 7 -5 V 7 -4 V 6 -4 V 7 -3 V 6 -3 V 7 -3 V 7 -2 V 6 -1 V 7 -1 V 7 -1 V 6 0 V 7 0 V 6 1 V 7 2 V 7 2 V 6 2 V 7 3 V 6 4 V 7 3 V 7 5 V 6 4 V 7 5 V 6 5 V 7 5 V 7 6 V 6 5 V 7 6 V 7 5 V 6 6 V 7 6 V 6 5 V 7 5 V 7 5 V 6 5 V 7 4 V 6 4 V 7 4 V 7 3 V 6 3 V 7 2 V 7 1 V 6 2 V 7 0 V 6 0 V 7 0 V 7 -1 V 6 -2 V 7 -2 V 6 -2 V 7 -4 V 7 -3 V 6 -4 V 7 -5 V 6 -4 V 7 -6 V 7 -5 V 6 -6 V 7 -6 V 7 -6 V 6 -6 V 7 -6 V 6 -7 V 7 -6 V 7 -6 V 6 -6 V 7 -6 V 6 -5 V 7 -6 V 7 -5 V 6 -4 V 7 -4 V 6 -4 V 7 -3 V 7 -3 V 6 -2 V 7 -2 V 7 -1 V 6 0 V 7 0 V 6 1 V 7 2 V 7 2 V 6 2 V 7 3 V 6 4 V 7 4 V 7 5 V 6 5 V 7 6 V 6 6 V 7 6 V 7 7 V 6 7 V 7 7 V 7 7 V 6 8 V 7 7 V 6 7 V 7 8 V 7 7 V 6 6 V 7 7 V 6 6 V 7 6 V 7 6 V 6 5 V 7 5 V 7 4 V 6 3 V 7 3 V 6 2 V 7 2 V 7 1 V 6 0 V 7 0 V 6 -1 V 7 -2 V 7 -3 V 6 -3 V 7 -4 V 6 -4 V 7 -6 V 7 -5 V 6 -7 V 7 -7 V 7 -7 V 6 -8 V 7 -8 V 6 -8 V 7 -9 V 7 -9 V 6 -9 V 7 -9 V 6 -9 V 7 -9 V 7 -9 V 6 -9 V 7 -8 V 6 -8 V 7 -8 V 7 -7 V 6 -7 V 7 -6 V 7 -6 V 6 -5 V 7 -4 V 6 -3 V 7 -3 V 7 -2 V 6 -1 V 7 0 V 6 1 V 7 1 V 7 3 V 6 3 V 7 4 V 7 6 V 6 6 V 7 6 V 6 8 V 7 8 V 7 9 V 6 10 V 7 10 V 6 11 V 7 11 V 7 11 V 6 12 V 7 12 V 6 12 V 7 13 V 7 12 V 6 12 V 7 12 V 7 12 V 6 12 V 7 11 V 6 10 V 7 10 V 7 9 V 6 9 V currentpoint stroke M 7 7 V 6 7 V 7 5 V 7 5 V 6 4 V 7 2 V 6 1 V 7 1 V 7 -2 V 6 -2 V 7 -4 V 7 -5 V 6 -6 V 7 -8 V 6 -9 V 7 -10 V 7 -11 V 6 -12 V 7 -14 V 6 -14 V 7 -16 V 7 -16 V 6 -18 V 7 -18 V 6 -18 V 7 -19 V 7 -20 V 6 -20 V 7 -20 V 7 -20 V 6 -20 V 7 -20 V 6 -19 V 7 -19 V 7 -18 V 6 -18 V 7 -17 V 6 -15 V 7 -15 V 7 -13 V 6 -12 V 7 -10 V 7 -9 V 6 -7 V 7 -4 V 6 -3 V 7 -1 V 7 2 V 6 4 V 7 6 V 6 9 V 7 12 V 7 14 V 6 16 V 7 20 V 6 22 V 7 25 V 7 28 V 6 30 V 7 33 V 7 36 V 6 38 V 7 42 V 6 43 V 7 46 V 7 49 V 6 51 V 7 53 V 6 55 V 7 58 V 7 59 V 6 61 V 7 62 V 6 64 V 7 66 V 7 66 V 6 68 V 7 68 V 7 69 V 6 69 V 7 70 V 6 70 V 7 70 V 7 70 V 6 69 V 7 69 V 6 68 V 7 67 V 7 66 V 6 65 V 7 63 V 6 62 V 7 60 V 7 59 V 6 56 V 7 55 V 7 52 V 6 50 V 7 48 V 6 45 V 7 43 V 7 40 V 6 38 V 7 35 V 6 32 V 7 29 V 7 27 V 6 24 V 7 22 V 7 18 V 6 16 V 7 14 V 6 10 V 7 9 V 7 5 V 6 4 V 7 1 V 6 -1 V 7 -3 V 7 -6 V 6 -7 V 7 -8 V 6 -11 V 7 -12 V 7 -13 V 6 -15 V 7 -16 V 7 -16 V 6 -18 V 7 -18 V 6 -19 V 7 -19 V 7 -20 V 6 -20 V 7 -19 V 6 -20 V 7 -20 V 7 -19 V 6 -19 V 7 -18 V 6 -18 V 7 -17 V 7 -16 V 6 -15 V 7 -15 V 7 -13 V 6 -12 V 7 -11 V 6 -10 V 7 -9 V 7 -7 V 6 -7 V 7 -5 V 6 -4 V 7 -2 V 7 -1 V 6 0 V 7 1 V 6 2 V 7 3 V 7 5 V 6 5 V 7 6 V 7 8 V 6 8 V 7 9 V 6 9 V 7 10 V 7 11 V 6 11 V 7 11 V 6 12 V 7 12 V 7 12 V 6 12 V 7 12 V 7 12 V 6 12 V 7 11 V 6 11 V 7 11 V 7 10 V 6 10 V 7 9 V 6 8 V 7 8 V 7 7 V 6 6 V 7 6 V 6 4 V 7 4 V 7 3 V 6 2 V 7 2 V 7 0 V 6 0 V 7 -2 V 6 -2 V 7 -3 V 7 -3 V 6 -4 V 7 -5 V 6 -6 V 7 -6 V 7 -7 V 6 -7 V 7 -7 V 6 -8 V 7 -8 V 7 -9 V 6 -9 V 7 -8 V 7 -9 V 6 -9 V 7 -9 V 6 -8 V 7 -9 V 7 -8 V 6 -8 V 7 -7 V 6 -7 V 7 -7 V 7 -6 V 6 -6 V 7 -5 V 7 -5 V 6 -4 V 7 -3 V 6 -3 V 7 -2 V 7 -1 V 6 -1 V 7 0 V 6 0 V 7 2 V 7 2 V 6 2 V 7 3 V 6 4 V 7 4 V 7 4 V 6 5 V 7 6 V 7 6 V 6 6 V 7 6 V 6 7 V 7 7 V 7 7 V 6 7 V 7 7 V 6 7 V 7 7 V 7 7 V 6 6 V 7 7 V 6 6 V 7 6 V 7 5 V 6 5 V 7 5 V 7 4 V 6 4 V 7 3 V 6 3 V 7 2 V 7 1 V 6 1 V 7 1 V 6 0 V 7 -1 V 7 -1 V 6 -2 V 7 -2 V 6 -3 V 7 -3 V 7 -4 V 6 -4 V 7 -4 V 7 -5 V 6 -5 V 7 -5 V 6 -6 V 7 -6 V 7 -6 V 6 -6 V 7 -6 V 6 -6 V 7 -5 V 7 -6 V 6 -6 V 7 -5 V 7 -6 V 6 -5 V 7 -4 V 6 -5 V 7 -4 V 7 -3 V 6 -3 V 7 -3 V 6 -2 V 7 -2 V 7 -1 V 6 -1 V 7 0 V 6 0 V 7 1 V 7 1 V 6 2 V 7 2 V 7 3 V 6 3 V 7 3 V 6 4 V 7 4 V 7 4 V 6 5 V 7 5 V 6 5 V 7 5 V 7 5 V 6 5 V 7 6 V 6 5 V 7 5 V 7 5 V 6 5 V 7 5 V 7 4 V 6 4 V 7 4 V 6 3 V 7 4 V 7 2 V 6 2 V 7 2 V 6 2 V 7 1 V 7 0 V 6 0 V 7 -1 V 6 -1 V 7 -1 V 7 -2 V 6 -2 V 7 -3 V 7 -3 V 6 -3 V 7 -4 V 6 -4 V 7 -4 V 7 -5 V 6 -4 V 7 -5 V 6 -5 V 7 -5 V 7 -4 V 6 -5 V 7 -5 V 7 -4 V 6 -5 V 7 -4 V 6 -4 V 7 -4 V 7 -3 V 6 -3 V 7 -2 V 6 -3 V 7 -1 V 7 -2 V 6 0 V 7 -1 V 6 0 V 7 1 V 7 1 V 6 1 V 7 2 V 7 2 V 6 3 V 7 3 V 6 3 V 7 3 V 7 4 V 6 4 V 7 5 V 6 4 V 7 4 V 7 5 V 6 5 V 7 4 V 6 5 V 7 4 V 7 4 V 6 4 V 7 4 V 7 3 V 6 3 V 7 3 V 6 2 V 7 2 V currentpoint stroke M 7 1 V 6 2 V 7 0 V 6 0 V 7 0 V 7 -1 V 6 -1 V 7 -2 V 6 -2 V 7 -2 V 7 -3 V 6 -3 V 7 -4 V 7 -3 V 6 -4 V 7 -4 V 6 -5 V 7 -4 V 7 -4 V 6 -5 V 7 -4 V 6 -4 V 7 -4 V 7 -4 V 6 -4 V 7 -3 V 7 -3 V 6 -3 V 7 -2 V 6 -2 V 7 -1 V 7 -1 V 6 -1 V 7 0 V 6 1 V 7 1 V 7 1 V 6 2 V 7 3 V 6 2 V 7 3 V 7 4 V 6 3 V 7 4 V 7 4 V 6 5 V 7 4 V 6 4 V 7 5 V 7 4 V 6 4 V 7 4 V 6 3 V 7 4 V 7 3 V 6 2 V 7 3 V 6 1 V 7 2 V 7 1 V 6 0 V 7 0 V 7 -1 V 6 -1 V 7 -2 V 6 -2 V 7 -3 V 7 -3 V 6 -3 V 7 -4 V 6 -4 V 7 -4 V 7 -4 V 6 -5 V 7 -4 V 7 -4 V 6 -5 V 7 -4 V 6 -3 V 7 -4 V 7 -3 V 6 -3 V 7 -2 V 6 -2 V 7 -1 V 7 0 V 6 0 V 7 0 V 6 1 V 7 2 V 7 2 V 6 3 V 7 3 V 7 3 V 6 4 V 7 4 V 6 5 V 7 4 V 7 5 V 6 4 V 7 4 V 6 5 V 7 4 V 7 3 V 6 3 V 7 3 V 6 2 V 7 2 V 7 0 V 6 1 V 7 -1 V 7 -1 V 6 -2 V 7 -2 V 6 -3 V 7 -3 V 7 -4 V 6 -4 V 7 -5 V 6 -5 V 7 -5 V 7 -4 V 6 -5 V 7 -4 V 6 -4 V 7 -4 V 7 -3 V 6 -2 V 7 -2 V 7 -1 V 6 0 V 7 1 V 6 1 V 7 2 V 7 3 V 6 4 V 7 4 V 6 5 V 7 4 V 7 6 V 6 5 V 7 5 V 7 5 V 6 4 V 7 4 V 6 3 V 7 3 V 7 1 V 6 1 V 7 -1 V 6 -1 V 7 -3 V 7 -3 V 6 -4 V 7 -5 V 6 -6 V 7 -6 V 7 -5 V 6 -6 V 7 -6 V 7 -4 V 6 -4 V 7 -3 V 6 -2 V 7 0 V 7 1 V 6 3 V 7 4 V 6 5 V 7 5 V 7 7 V 6 7 V 7 7 V 6 6 V 7 5 V 7 4 V 6 3 V 7 0 V 7 -2 V 6 -4 V 7 -5 V 6 -8 V 7 -8 V 7 -9 V 6 -8 V 7 -6 V 6 -4 V 7 -2 V 7 3 V 6 6 V 7 9 V 6 12 V 7 11 V 7 10 V 6 4 V 7 -3 V 7 -12 V 6 -18 V 7 -17 V 6 0 V 7 50 V stroke grestore end showpage %%Trailer %%DocumentFonts: Helvetica %%EndDocument @endspecial 150 2489 a FJ(30.7)68 b(References)47 b(and)d(F)-11 b(urther)44 b(Reading)150 2649 y FK(The)30 b(follo)m(wing)i(pap)s(er)d (describ)s(es)h(the)g(use)g(of)h(Cheb)m(yshev)e(series,)330 2783 y(R.)37 b(Brouc)m(k)m(e,)k(\\T)-8 b(en)38 b(Subroutines)d(for)i (the)g(Manipulation)h(of)g(Cheb)m(yshev)e(Series)h([C1])h(\(Algo-)330 2893 y(rithm)30 b(446\)".)43 b FD(Comm)m(unications)31 b(of)f(the)h(A)m(CM)40 b FK(16\(4\),)33 b(254{256)h(\(1973\))p eop end %%Page: 371 389 TeXDict begin 371 388 bop 150 -116 a FK(Chapter)30 b(31:)41 b(Series)31 b(Acceleration)2205 b(371)150 299 y FG(31)80 b(Series)52 b(Acceleration)150 533 y FK(The)41 b(functions)g(describ)s (ed)f(in)h(this)h(c)m(hapter)g(accelerate)i(the)e(con)m(v)m(ergence)i (of)d(a)h(series)g(using)f(the)150 642 y(Levin)34 b FE(u)p FK(-transform.)50 b(This)33 b(metho)s(d)h(tak)m(es)h(a)f(small)g(n)m (um)m(b)s(er)f(of)h(terms)g(from)f(the)h(start)g(of)g(a)h(series)150 752 y(and)i(uses)h(a)g(systematic)i(appro)m(ximation)f(to)g(compute)f (an)g(extrap)s(olated)h(v)-5 b(alue)39 b(and)e(an)h(estimate)150 861 y(of)j(its)h(error.)72 b(The)40 b FE(u)p FK(-transform)h(w)m(orks)g (for)g(b)s(oth)f(con)m(v)m(ergen)m(t)j(and)e(div)m(ergen)m(t)h(series,) i(including)150 971 y(asymptotic)32 b(series.)275 1105 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b(di\013erence)g(b)s(et)m(w)m(een)g(these)h(t)m(w)m(o)g(v)-5 b(alues)31 b(is)g(used)f(as)h(estimate)i(of)e(the)390 3049 y(error)k(and)h(is)f(stored)h(in)g FD(abserr)p 1538 3049 V 39 w(trunc)p FK(.)56 b(T)-8 b(o)37 b(impro)m(v)m(e)f(the)g (reliabilit)m(y)i(of)e(the)g(algorithm)h(the)390 3159 y(extrap)s(olated)29 b(v)-5 b(alues)28 b(are)g(replaced)g(b)m(y)g(mo)m (ving)h(a)m(v)m(erages)h(when)d(calculating)j(the)e(truncation)390 3268 y(error,)i(smo)s(othing)h(out)f(an)m(y)h(\015uctuations.)150 3502 y FJ(31.3)68 b(Examples)150 3662 y FK(The)30 b(follo)m(wing)i(co)s (de)e(calculates)j(an)d(estimate)i(of)f FE(\020)7 b FK(\(2\))26 b(=)f FE(\031)2278 3629 y FB(2)2315 3662 y FE(=)p FK(6)31 b(using)f(the)h(series,)1250 3830 y FE(\020)7 b FK(\(2\))26 b(=)f(1)20 b(+)g(1)p FE(=)p FK(2)1825 3793 y FB(2)1884 3830 y FK(+)g(1)p FE(=)p FK(3)2110 3793 y FB(2)2169 3830 y FK(+)g(1)p FE(=)p FK(4)2395 3793 y FB(2)2453 3830 y FK(+)g FE(:)15 b(:)g(:)150 3999 y FK(After)43 b FD(N)52 b FK(terms)43 b(the)f(error)h(in)f(the)h(sum)e(is)i FE(O)s FK(\(1)p FE(=)-5 b(N)10 b FK(\),)47 b(making)c(direct)g(summation)f(of) h(the)g(series)150 4109 y(con)m(v)m(erge)32 b(slo)m(wly)-8 b(.)390 4244 y FH(#include)46 b()390 4354 y(#include)g ()390 4463 y(#include)g()390 4682 y(#define)g(N)h(20)390 4902 y(int)390 5011 y(main)g(\(void\))390 5121 y({)485 5230 y(double)g(t[N];)485 5340 y(double)g(sum_accel,)e (err;)p eop end %%Page: 373 391 TeXDict begin 373 390 bop 150 -116 a FK(Chapter)30 b(31:)41 b(Series)31 b(Acceleration)2205 b(373)485 299 y FH(double)47 b(sum)f(=)i(0;)485 408 y(int)f(n;)485 628 y(gsl_sum_levin_u_workspace) 41 b(*)48 b(w)581 737 y(=)f(gsl_sum_levin_u_alloc)42 b(\(N\);)485 956 y(const)47 b(double)f(zeta_2)g(=)h(M_PI)g(*)h(M_PI)e (/)i(6.0;)485 1176 y(/*)g(terms)e(for)h(zeta\(2\))f(=)h (\\sum_{n=1}^{\\infty})c(1/n^2)j(*/)485 1395 y(for)h(\(n)h(=)f(0;)g(n)h (<)f(N;)g(n++\))581 1504 y({)676 1614 y(double)f(np1)h(=)h(n)f(+)h (1.0;)676 1724 y(t[n])f(=)g(1.0)g(/)h(\(np1)e(*)i(np1\);)676 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b(for)f(Impro)m(ving)h(Con) m(v)m(ergence)i(of)330 1557 y(Sequences,)31 b FD(In)m(tern.)f(J.)g (Computer)g(Math.)41 b FK(B3:371{388,)35 b(1973.)150 1717 y(A)30 b(review)h(pap)s(er)e(on)i(the)f(Levin)g(T)-8 b(ransform)30 b(is)g(a)m(v)-5 b(ailable)33 b(online,)330 1851 y(Herb)s(ert)26 b(H.)h(H.)h(Homeier,)g(Scalar)g(Levin-T)m(yp)s(e)e (Sequence)h(T)-8 b(ransformations,)28 b FH(http://arxiv.)330 1961 y(org/abs/math/0005209)p FK(.)p eop end %%Page: 375 393 TeXDict begin 375 392 bop 150 -116 a FK(Chapter)30 b(32:)41 b(W)-8 b(a)m(v)m(elet)34 b(T)-8 b(ransforms)2161 b(375)150 299 y FG(32)80 b(W)-13 b(a)l(v)l(elet)52 b(T)-13 b(ransforms)150 501 y FK(This)24 b(c)m(hapter)i(describ)s(es)f(functions)g(for)g(p)s (erforming)f(Discrete)j(W)-8 b(a)m(v)m(elet)29 b(T)-8 b(ransforms)24 b(\(D)m(WTs\).)40 b(The)150 611 y(library)32 b(includes)f(w)m(a)m(v)m(elets)k(for)d(real)g(data)h(in)f(b)s(oth)f (one)h(and)g(t)m(w)m(o)h(dimensions.)45 b(The)32 b(w)m(a)m(v)m(elet)j (func-)150 721 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b(gsl_wavelet2d_nstrans)q(form)q(_ma)q(tri)q(x)e Fu(\()p FD(const)32 b(gsl)p 2464 2946 V 40 w(w)m(a)m(v)m(elet)h(*)e Ft(w)p FD(,)565 3055 y(gsl)p 677 3055 V 41 w(matrix)f(*)h Ft(m)p FD(,)g(gsl)p 1303 3055 V 41 w(w)m(a)m(v)m(elet)p 1634 3055 V 42 w(direction)h Ft(dir)p FD(,)f(gsl)p 2374 3055 V 41 w(w)m(a)m(v)m(elet)p 2705 3055 V 43 w(w)m(orkspace)g(*)f Ft(work)p Fu(\))3350 3165 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_wavelet2d_nstrans)q(form)q(_ma)q(tri)q(x_f)q(orwa)q (rd)f Fu(\()p FD(const)565 3274 y(gsl)p 677 3274 V 41 w(w)m(a)m(v)m(elet)33 b(*)e Ft(w)p FD(,)g(gsl)p 1331 3274 V 40 w(matrix)g(*)g Ft(m)p FD(,)f(gsl)p 1956 3274 V 41 w(w)m(a)m(v)m(elet)p 2287 3274 V 43 w(w)m(orkspace)h(*)g Ft(work)p Fu(\))3350 3384 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_wavelet2d_nstrans)q(form)q(_ma)q(tri)q(x_i)q(nver)q (se)f Fu(\()p FD(const)565 3494 y(gsl)p 677 3494 V 41 w(w)m(a)m(v)m(elet)33 b(*)e Ft(w)p FD(,)g(gsl)p 1331 3494 V 40 w(matrix)g(*)g Ft(m)p FD(,)f(gsl)p 1956 3494 V 41 w(w)m(a)m(v)m(elet)p 2287 3494 V 43 w(w)m(orkspace)h(*)g Ft(work)p Fu(\))390 3603 y FK(These)49 b(functions)f(compute)i(the)f (non-standard)f(form)h(of)g(the)g(t)m(w)m(o-dimensional)i(in-place)390 3713 y(w)m(a)m(v)m(elet)33 b(transform)d(on)g(a)h(matrix)g FD(a)p FK(.)150 3948 y FJ(32.4)68 b(Examples)150 4108 y FK(The)23 b(follo)m(wing)i(program)f(demonstrates)g(the)g(use)f(of)h (the)g(one-dimensional)h(w)m(a)m(v)m(elet)h(transform)e(func-)150 4217 y(tions.)40 b(It)29 b(computes)f(an)h(appro)m(ximation)g(to)g(an)f (input)f(signal)j(\(of)e(length)h(256\))h(using)e(the)g(20)i(largest) 150 4327 y(comp)s(onen)m(ts)h(of)f(the)h(w)m(a)m(v)m(elet)i(transform,) d(while)g(setting)i(the)e(others)h(to)g(zero.)390 4463 y FH(#include)46 b()390 4573 y(#include)g()390 4682 y(#include)g()390 4792 y(#include)g ()390 5011 y(int)390 5121 y(main)h(\(int)f(argc,)h (char)f(**argv\))390 5230 y({)485 5340 y(\(void\)\(argc\);)f(/*)i (avoid)f(unused)g(parameter)g(warning)f(*/)p eop end %%Page: 379 397 TeXDict begin 379 396 bop 150 -116 a FK(Chapter)30 b(32:)41 b(W)-8 b(a)m(v)m(elet)34 b(T)-8 b(ransforms)2161 b(379)485 299 y FH(int)47 b(i,)h(n)f(=)g(256,)g(nc)g(=)h(20;)485 408 y(double)f(*data)f(=)h(malloc)f(\(n)i(*)f(sizeof)f(\(double\)\);) 485 518 y(double)h(*abscoeff)e(=)i(malloc)f(\(n)i(*)f(sizeof)f (\(double\)\);)485 628 y(size_t)h(*p)g(=)g(malloc)f(\(n)h(*)h(sizeof)e (\(size_t\)\);)485 847 y(FILE)h(*)h(f;)485 956 y(gsl_wavelet)d(*w;)485 1066 y(gsl_wavelet_workspace)d(*work;)485 1285 y(w)48 b(=)f(gsl_wavelet_alloc)c(\(gsl_wavelet_daubechies,)f(4\);)485 1395 y(work)47 b(=)h(gsl_wavelet_workspace_a)o(llo)o(c)42 b(\(n\);)485 1614 y(f)48 b(=)f(fopen)g(\(argv[1],)e("r"\);)485 1724 y(for)i(\(i)h(=)f(0;)g(i)h(<)f(n;)g(i++\))581 1833 y({)676 1943 y(fscanf)f(\(f,)h("\045lg",)f(&data[i]\);)581 2052 y(})485 2162 y(fclose)h(\(f\);)485 2381 y (gsl_wavelet_transform_forw)o(ard)41 b(\(w,)47 b(data,)g(1,)g(n,)g (work\);)485 2600 y(for)g(\(i)h(=)f(0;)g(i)h(<)f(n;)g(i++\))581 2710 y({)676 2819 y(abscoeff[i])e(=)j(fabs)e(\(data[i]\);)581 2929 y(})485 3148 y(gsl_sort_index)e(\(p,)j(abscoeff,)f(1,)h(n\);)485 3367 y(for)g(\(i)h(=)f(0;)g(\(i)g(+)h(nc\))f(<)g(n;)g(i++\))581 3477 y(data[p[i]])e(=)i(0;)485 3696 y(gsl_wavelet_transform_inve)o(rse) 41 b(\(w,)47 b(data,)g(1,)g(n,)g(work\);)485 3915 y(for)g(\(i)h(=)f(0;) g(i)h(<)f(n;)g(i++\))581 4025 y({)676 4134 y(printf)f(\("\045g\\n",)g (data[i]\);)581 4244 y(})485 4463 y(gsl_wavelet_free)e(\(w\);)485 4573 y(gsl_wavelet_workspace_free)d(\(work\);)485 4792 y(free)47 b(\(data\);)485 4902 y(free)g(\(abscoeff\);)485 5011 y(free)g(\(p\);)485 5121 y(return)g(0;)390 5230 y(})p eop end %%Page: 380 398 TeXDict begin 380 397 bop 150 -116 a FK(Chapter)30 b(32:)41 b(W)-8 b(a)m(v)m(elet)34 b(T)-8 b(ransforms)2161 b(380)150 299 y(The)30 b(output)g(can)h(b)s(e)e(used)h(with)g(the)g FC(gnu)h FK(plotutils)g FH(graph)e FK(program,)390 426 y FH($)47 b(./a.out)f(ecg.dat)g(>)i(dwt.txt)390 536 y($)f(graph)g(-T)g 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/ogonek/caron/space/exclamdown/cent/sterling/currency/yen/brokenbar /section/dieresis/copyright/ordfeminine/guillemotleft/logicalnot /hyphen/registered/macron/degree/plusminus/twosuperior/threesuperior /acute/mu/paragraph/periodcentered/cedilla/onesuperior/ordmasculine /guillemotright/onequarter/onehalf/threequarters/questiondown /Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla /Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex /Idieresis/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis /multiply/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute /Thorn/germandbls/agrave/aacute/acircumflex/atilde/adieresis /aring/ae/ccedilla/egrave/eacute/ecircumflex/edieresis/igrave /iacute/icircumflex/idieresis/eth/ntilde/ograve/oacute/ocircumflex /otilde/odieresis/divide/oslash/ugrave/uacute/ucircumflex/udieresis /yacute/thorn/ydieresis ] def /reencodeISO { dup dup findfont dup length dict begin { 1 index /FID ne { def }{ pop pop } ifelse } forall /Encoding 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2 false subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 2 copy false subspline } if n 2 sub dup n 1 sub dup 2 copy 2 copy false subspline patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup 1 sub dup rightarrow } if end } dup 0 4 dict put def /Circ { newpath 0 360 arc closepath patternNone not { ifill } if brushNone not { istroke } if } def /CBSpl { 0 begin dup 2 gt { storexyn newpath n 1 sub dup 0 0 1 1 2 2 true subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 0 0 false subspline n 2 sub dup n 1 sub dup 0 0 1 1 false subspline patternNone not { ifill } if brushNone not { istroke } if } { Poly } ifelse end } dup 0 4 dict put def /Elli { 0 begin newpath 4 2 roll translate scale 0 0 1 0 360 arc closepath patternNone not { ifill } if brushNone not { istroke } if end } dup 0 1 dict put def /Line { 0 begin 2 storexyn newpath x 0 get y 0 get moveto x 1 get y 1 get lineto brushNone not { istroke } if 0 0 1 1 leftarrow 0 0 1 1 rightarrow end } dup 0 4 dict put def /MLine { 0 begin storexyn newpath n 1 gt { x 0 get y 0 get moveto 1 1 n 1 sub { /i exch def x i get y i get lineto } for patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Poly { 3 1 roll newpath moveto -1 add { lineto } repeat closepath patternNone not { ifill } if brushNone not { istroke } if } def /Rect { 0 begin /t exch def /r exch def /b exch def /l exch def newpath l b moveto l t lineto r t lineto r b lineto closepath patternNone not { ifill } if brushNone not { istroke } if end } dup 0 4 dict put def /Text { ishow } def /idef { dup where { pop pop pop } { exch def } ifelse } def /ifill { 0 begin gsave patternGrayLevel -1 ne { fgred bgred fgred sub patternGrayLevel mul add fggreen bggreen fggreen sub patternGrayLevel mul add fgblue bgblue fgblue sub patternGrayLevel mul add setrgbcolor eoFillRule { eofill } { fill } ifelse } { eoFillRule { eoclip } { clip } ifelse originalCTM setmatrix pathbbox /t exch def /r exch def /b exch def /l exch def /w r l sub ceiling cvi def /h t b sub ceiling cvi def /imageByteWidth w 8 div ceiling cvi def /imageHeight h def bgred bggreen bgblue setrgbcolor eoFillRule { eofill } { fill } ifelse fgred fggreen fgblue setrgbcolor w 0 gt h 0 gt and { l b translate w h scale w h true [w 0 0 h neg 0 h] { patternproc } imagemask } if } ifelse grestore end } dup 0 8 dict put def /istroke { gsave brushDashOffset -1 eq { [] 0 setdash 1 setgray } { brushDashArray brushDashOffset setdash fgred fggreen fgblue setrgbcolor } ifelse brushWidth setlinewidth originalCTM setmatrix stroke grestore } def /ishow { 0 begin gsave fgred fggreen fgblue setrgbcolor /fontDict printFont findfont printSize scalefont dup setfont def /descender fontDict begin 0 /FontBBox load 1 get FontMatrix end transform exch pop def /vertoffset 1 printSize sub descender sub def { 0 vertoffset moveto show /vertoffset vertoffset printSize sub def } forall grestore end } dup 0 3 dict put def /patternproc { 0 begin /patternByteLength patternString length def /patternHeight patternByteLength 8 mul sqrt cvi def /patternWidth patternHeight def /patternByteWidth patternWidth 8 idiv def /imageByteMaxLength imageByteWidth imageHeight mul stringLimit patternByteWidth sub min def /imageMaxHeight imageByteMaxLength imageByteWidth idiv patternHeight idiv patternHeight mul patternHeight max def /imageHeight imageHeight imageMaxHeight sub store /imageString imageByteWidth imageMaxHeight mul patternByteWidth add string def 0 1 imageMaxHeight 1 sub { /y exch def /patternRow y patternByteWidth mul patternByteLength mod def /patternRowString patternString patternRow patternByteWidth getinterval def /imageRow y imageByteWidth mul def 0 patternByteWidth imageByteWidth 1 sub { /x exch def imageString imageRow x add patternRowString putinterval } for } for imageString end } dup 0 12 dict put def /min { dup 3 2 roll dup 4 3 roll lt { exch } if pop } def /max { dup 3 2 roll dup 4 3 roll gt { exch } if pop } def /midpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 x1 add 2 div y0 y1 add 2 div end } dup 0 4 dict put def /thirdpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 2 mul x1 add 3 div y0 2 mul y1 add 3 div end } dup 0 4 dict put def /subspline { 0 begin /movetoNeeded exch def y exch get /y3 exch def x exch get /x3 exch def y exch get /y2 exch def x exch get /x2 exch def y exch get /y1 exch def x exch get /x1 exch def y exch get /y0 exch def x exch get /x0 exch def x1 y1 x2 y2 thirdpoint /p1y exch def /p1x exch def x2 y2 x1 y1 thirdpoint /p2y exch def /p2x exch def x1 y1 x0 y0 thirdpoint p1x p1y midpoint /p0y exch def /p0x exch def x2 y2 x3 y3 thirdpoint p2x p2y midpoint /p3y exch def /p3x exch def movetoNeeded { p0x p0y moveto } if p1x p1y p2x p2y p3x p3y curveto end } dup 0 17 dict put def /storexyn { /n exch def /y n array def /x n array def n 1 sub -1 0 { /i exch def y i 3 2 roll put x i 3 2 roll put } for } def /arrowhead { 0 begin transform originalCTM itransform /taily exch def /tailx exch def transform originalCTM itransform /tipy exch def /tipx exch def /dy tipy taily sub def /dx tipx tailx sub def /angle dx 0 ne dy 0 ne or { dy dx atan } { 90 } ifelse def gsave originalCTM setmatrix tipx tipy translate angle rotate newpath arrowHeight neg arrowWidth 2 div moveto 0 0 lineto arrowHeight neg arrowWidth 2 div neg lineto patternNone not { originalCTM setmatrix /padtip arrowHeight 2 exp 0.25 arrowWidth 2 exp mul add sqrt brushWidth mul arrowWidth div def /padtail brushWidth 2 div def tipx tipy translate angle rotate padtip 0 translate arrowHeight padtip add padtail add arrowHeight div dup scale arrowheadpath ifill } if brushNone not { originalCTM setmatrix tipx tipy translate angle rotate arrowheadpath istroke } if grestore end } dup 0 9 dict put def /arrowheadpath { newpath arrowHeight neg arrowWidth 2 div moveto 0 0 lineto arrowHeight neg arrowWidth 2 div neg lineto } def /leftarrow { 0 begin y exch get /taily exch def x exch get /tailx exch def y exch get /tipy exch def x exch get /tipx exch def brushLeftArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /rightarrow { 0 begin y exch get /tipy exch def x exch get /tipx exch def y exch get /taily exch def x exch get /tailx exch def brushRightArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def %%EndResource %%EndSetup %%Page: 1 1 %%PageResources: font Helvetica %%PageBoundingBox: 112 210 487 402 %%BeginPageSetup %I Idraw 8 Begin %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 1 0 0 1 0 0 ] concat /originalCTM matrix currentmatrix def /trueoriginalCTM matrix currentmatrix def %%EndPageSetup Begin %I 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SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2304 2304 2373 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-9-*-*-*-*-*-*-* /Helvetica 9.072000 SetF %I t [ 1 0 0 1 171.356 218.1928 ] concat %I [ (32) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3168 5760 3168 5691 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3168 2304 3168 2373 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-9-*-*-*-*-*-*-* /Helvetica 9.072000 SetF %I t [ 1 0 0 1 214.556 218.1928 ] concat %I [ (64) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4032 5760 4032 5691 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4032 2304 4032 2373 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-9-*-*-*-*-*-*-* /Helvetica 9.072000 SetF %I t [ 1 0 0 1 257.756 218.1928 ] concat %I [ (96) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4896 5760 4896 5691 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4896 2304 4896 2373 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-9-*-*-*-*-*-*-* /Helvetica 9.072000 SetF %I t [ 1 0 0 1 298.434 218.1928 ] concat %I [ (128) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5760 5760 5760 5691 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5760 2304 5760 2373 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-9-*-*-*-*-*-*-* /Helvetica 9.072000 SetF %I t [ 1 0 0 1 341.634 218.1928 ] concat %I [ (160) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6624 5760 6624 5691 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6624 2304 6624 2373 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-9-*-*-*-*-*-*-* /Helvetica 9.072000 SetF %I t [ 1 0 0 1 384.834 218.1928 ] concat %I [ (192) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7488 5760 7488 5691 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7488 2304 7488 2373 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-9-*-*-*-*-*-*-* /Helvetica 9.072000 SetF %I t [ 1 0 0 1 428.034 218.1928 ] concat %I [ (224) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8352 5760 8352 5691 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8352 2304 8352 2373 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-9-*-*-*-*-*-*-* /Helvetica 9.072000 SetF %I t [ 1 0 0 1 471.234 218.1928 ] concat %I [ (256) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5760 9216 5691 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2304 9216 2373 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-9-*-*-*-*-*-*-* /Helvetica 9.072000 SetF %I t [ 1 0 0 1 112.6999 226.0284 ] concat %I [ (-0.4) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2304 9147 2304 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2304 2373 2304 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-9-*-*-*-*-*-*-* /Helvetica 9.072000 SetF %I t [ 1 0 0 1 112.6999 245.2284 ] concat %I [ (-0.2) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2688 9147 2688 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2688 2373 2688 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-9-*-*-*-*-*-*-* /Helvetica 9.072000 SetF %I t [ 1 0 0 1 117.9979 264.4284 ] concat %I [ (0.0) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 3072 9147 3072 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3072 2373 3072 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-9-*-*-*-*-*-*-* /Helvetica 9.072000 SetF %I t [ 1 0 0 1 117.9979 283.6284 ] concat %I [ (0.2) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 3456 9147 3456 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3456 2373 3456 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-9-*-*-*-*-*-*-* /Helvetica 9.072000 SetF %I t [ 1 0 0 1 117.9979 302.8284 ] concat %I [ (0.4) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 3840 9147 3840 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3840 2373 3840 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-9-*-*-*-*-*-*-* /Helvetica 9.072000 SetF %I t [ 1 0 0 1 117.9979 322.0284 ] concat %I [ (0.6) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 4224 9147 4224 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4224 2373 4224 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-9-*-*-*-*-*-*-* /Helvetica 9.072000 SetF %I t [ 1 0 0 1 117.9979 341.2284 ] concat %I [ (0.8) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 4608 9147 4608 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4608 2373 4608 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-9-*-*-*-*-*-*-* /Helvetica 9.072000 SetF %I t [ 1 0 0 1 117.9979 360.4284 ] concat %I [ (1.0) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 4992 9147 4992 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4992 2373 4992 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-9-*-*-*-*-*-*-* /Helvetica 9.072000 SetF %I t [ 1 0 0 1 117.9979 379.6284 ] concat %I [ (1.2) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5376 9147 5376 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5376 2373 5376 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-9-*-*-*-*-*-*-* /Helvetica 9.072000 SetF %I t [ 1 0 0 1 117.9979 398.8284 ] concat %I [ (1.4) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5760 9147 5760 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5760 2373 5760 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2304 9188 2304 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2304 2332 2304 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2496 9188 2496 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2496 2332 2496 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2688 9188 2688 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2688 2332 2688 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2880 9188 2880 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2880 2332 2880 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 3072 9188 3072 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3072 2332 3072 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 3264 9188 3264 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3264 2332 3264 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 3456 9188 3456 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3456 2332 3456 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 3648 9188 3648 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3648 2332 3648 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 3840 9188 3840 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3840 2332 3840 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 4032 9188 4032 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4032 2332 4032 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 4224 9188 4224 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4224 2332 4224 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 4416 9188 4416 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4416 2332 4416 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 4608 9188 4608 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4608 2332 4608 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 4800 9188 4800 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4800 2332 4800 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 4992 9188 4992 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4992 2332 4992 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5184 9188 5184 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5184 2332 5184 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5376 9188 5376 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5376 2332 5376 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5568 9188 5568 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5568 2332 5568 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5760 9188 5760 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5760 2332 5760 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 34952 1 0 0 [ 1.48 4.43 ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3072 9216 3072 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 256 2304 3161 2331 3161 2358 3170 2385 3209 2412 3209 2439 3199 2466 3257 2493 3266 2520 3295 2547 3305 2574 3295 2601 3276 2628 3247 2655 3266 2682 3257 2709 3257 2736 3257 2763 3247 2790 3238 2817 3228 2844 3238 2871 3266 2898 3286 2925 3295 2952 3218 2979 3142 3006 3142 3033 3113 3060 3094 3087 3055 3114 3055 3141 3065 3168 3084 3195 3074 3222 3084 3249 3065 3276 3036 3303 3026 3330 3036 3357 3036 3384 3017 3411 3026 3438 3007 3465 3055 3492 3046 3519 3055 3546 3074 3573 3026 3600 3007 3627 3036 3654 3055 3681 3065 3708 3055 3735 3017 3762 2988 3789 2998 3816 2959 3843 2873 3870 2834 3897 2777 3924 2710 3951 2662 3978 2719 4005 2892 4032 3113 4059 3382 4086 3660 4113 4140 4140 4630 4167 5071 4194 5369 4221 5494 4248 5426 4275 5138 4302 4630 4329 4006 4356 3478 4383 3170 4410 2940 4437 2825 4464 2777 4491 2815 4518 2873 4545 2940 4572 2940 4599 2950 4626 2940 4653 2959 4680 2959 4707 2959 4734 2930 4761 2950 4788 2950 4815 2950 4842 2969 4869 2930 4896 2902 4923 2902 4950 2921 4977 2930 5004 2940 5031 2911 5058 2930 5085 2950 5112 2969 5139 2940 5166 2940 5193 2911 5220 2902 5247 2902 5274 2940 5301 2940 5328 2930 5355 2911 5382 2892 5409 2921 5436 2902 5463 2911 5490 2902 5517 2892 5544 2902 5571 2921 5598 2921 5625 2930 5652 2940 5679 2911 5706 2902 5733 2940 5760 2940 5787 2950 5814 2950 5841 2902 5868 2911 5895 2930 5922 2940 5949 2969 5976 2940 6003 2930 6030 2902 6057 2921 6084 2940 6111 2940 6138 2950 6165 2911 6192 2892 6219 2892 6246 2921 6273 2930 6300 2911 6327 2892 6354 2882 6381 2882 6408 2902 6435 2892 6462 2873 6489 2882 6516 2854 6543 2863 6570 2863 6597 2882 6624 2863 6651 2825 6678 2815 6705 2825 6732 2854 6759 2834 6786 2825 6813 2815 6840 2786 6867 2806 6894 2815 6921 2825 6948 2815 6975 2786 7002 2777 7029 2806 7056 2825 7083 2834 7110 2844 7137 2854 7164 2844 7191 2902 7218 2930 7245 2978 7272 2988 7299 2998 7326 2988 7353 3036 7380 3065 7407 3084 7434 3074 7461 3055 7488 3055 7515 3074 7542 3094 7569 3113 7596 3113 7623 3074 7650 3074 7677 3084 7704 3103 7731 3103 7758 3122 7785 3074 7812 3055 7839 3103 7866 3094 7893 3113 7920 3113 7947 3074 7974 3065 8001 3094 8028 3103 8055 3084 8082 3103 8109 3084 8136 3084 8163 3094 8190 3122 8217 3132 8244 3103 8271 3094 8298 3074 8325 3084 8352 3113 8379 3084 8406 3084 8433 3084 8460 3055 8487 3084 8514 3074 8541 3084 8568 3065 8595 3046 8622 3036 8649 3046 8676 3046 8703 3055 8730 3065 8757 3026 8784 3017 8811 3026 8838 3046 8865 3055 8892 3055 8919 3026 8946 3026 8973 3026 9000 3074 9027 3055 9054 3046 9081 3036 9108 3007 9135 3046 9162 3055 9189 3055 256 MLine End %%PageTrailer End %I eop showpage %%Trailer end %%EOF %%EndDocument @endspecial 1203 x @beginspecial 112 @llx 210 @lly 487 @urx 402 @ury 2448 @rwi @setspecial %%BeginDocument: dwt-samp.eps %!PS-Adobe-3.0 EPSF-3.0 %%Creator: GNU libplot drawing library 4.1 %%Title: PostScript plot %%CreationDate: Thu Jul 22 17:12:13 2004 %%DocumentData: Clean7Bit %%LanguageLevel: 1 %%Pages: 1 %%PageOrder: Ascend %%Orientation: Portrait %%BoundingBox: 112 210 487 402 %%DocumentNeededResources: font Helvetica %%DocumentSuppliedResources: procset GNU_libplot 1.0 0 %%EndComments %%BeginDefaults %%PageResources: font Helvetica %%EndDefaults %%BeginProlog %%EndProlog %%BeginSetup %%IncludeResource: font Helvetica /DrawDict 50 dict def DrawDict begin /ISOLatin1Encoding [ /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /space/exclam/quotedbl/numbersign/dollar/percent/ampersand/quoteright /parenleft/parenright/asterisk/plus/comma/minus/period/slash /zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon /less/equal/greater/question/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N /O/P/Q/R/S/T/U/V/W/X/Y/Z/bracketleft/backslash/bracketright /asciicircum/underscore/quoteleft/a/b/c/d/e/f/g/h/i/j/k/l/m /n/o/p/q/r/s/t/u/v/w/x/y/z/braceleft/bar/braceright/asciitilde /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/dotlessi/grave/acute/circumflex/tilde/macron/breve /dotaccent/dieresis/.notdef/ring/cedilla/.notdef/hungarumlaut /ogonek/caron/space/exclamdown/cent/sterling/currency/yen/brokenbar /section/dieresis/copyright/ordfeminine/guillemotleft/logicalnot /hyphen/registered/macron/degree/plusminus/twosuperior/threesuperior /acute/mu/paragraph/periodcentered/cedilla/onesuperior/ordmasculine /guillemotright/onequarter/onehalf/threequarters/questiondown /Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla /Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex /Idieresis/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis /multiply/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute /Thorn/germandbls/agrave/aacute/acircumflex/atilde/adieresis /aring/ae/ccedilla/egrave/eacute/ecircumflex/edieresis/igrave /iacute/icircumflex/idieresis/eth/ntilde/ograve/oacute/ocircumflex /otilde/odieresis/divide/oslash/ugrave/uacute/ucircumflex/udieresis /yacute/thorn/ydieresis ] def /reencodeISO { dup dup findfont dup length dict begin { 1 index /FID ne { def }{ pop pop } ifelse } forall /Encoding ISOLatin1Encoding def currentdict end definefont } def /Helvetica reencodeISO def %%BeginResource procset GNU_libplot 1.0 0 /none null def /numGraphicParameters 17 def /stringLimit 65535 def /arrowHeight 8 def /eoFillRule true def /Begin { save numGraphicParameters dict begin } def /End { end restore } def /SetB { dup type /nulltype eq { pop false /brushRightArrow idef false /brushLeftArrow idef true /brushNone idef } { /brushDashOffset idef /brushDashArray idef 0 ne /brushRightArrow idef 0 ne /brushLeftArrow idef /brushWidth idef false /brushNone idef } ifelse } def /SetCFg { /fgblue idef /fggreen idef /fgred idef } def /SetCBg { /bgblue idef /bggreen idef /bgred idef } def /SetF { /printSize idef /printFont idef } def /SetP { dup type /nulltype eq { pop true /patternNone idef } { /patternGrayLevel idef patternGrayLevel -1 eq { /patternString idef } if false /patternNone idef } ifelse } def /BSpl { 0 begin storexyn newpath n 1 gt { 0 0 0 0 0 0 1 1 true subspline n 2 gt { 0 0 0 0 1 1 2 2 false subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 2 copy false subspline } if n 2 sub dup n 1 sub dup 2 copy 2 copy false subspline patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup 1 sub dup rightarrow } if end } dup 0 4 dict put def /Circ { newpath 0 360 arc closepath patternNone not { ifill } if brushNone not { istroke } if } def /CBSpl { 0 begin dup 2 gt { storexyn newpath n 1 sub dup 0 0 1 1 2 2 true subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 0 0 false subspline n 2 sub dup n 1 sub dup 0 0 1 1 false subspline patternNone not { ifill } if brushNone not { istroke } if } { Poly } ifelse end } dup 0 4 dict put def /Elli { 0 begin newpath 4 2 roll translate scale 0 0 1 0 360 arc closepath patternNone not { ifill } if brushNone not { istroke } if end } dup 0 1 dict put def /Line { 0 begin 2 storexyn newpath x 0 get y 0 get moveto x 1 get y 1 get lineto brushNone not { istroke } if 0 0 1 1 leftarrow 0 0 1 1 rightarrow end } dup 0 4 dict put def /MLine { 0 begin storexyn newpath n 1 gt { x 0 get y 0 get moveto 1 1 n 1 sub { /i exch def x i get y i get lineto } for patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Poly { 3 1 roll newpath moveto -1 add { lineto } repeat closepath patternNone not { ifill } if brushNone not { istroke } if } def /Rect { 0 begin /t exch def /r exch def /b exch def /l exch def newpath l b moveto l t lineto r t lineto r b lineto closepath patternNone not { ifill } if brushNone not { istroke } if end } dup 0 4 dict put def /Text { ishow } def /idef { dup where { pop pop pop } { exch def } ifelse } def /ifill { 0 begin gsave patternGrayLevel -1 ne { fgred bgred fgred sub patternGrayLevel mul add fggreen bggreen fggreen sub patternGrayLevel mul add fgblue bgblue fgblue sub patternGrayLevel mul add setrgbcolor eoFillRule { eofill } { fill } ifelse } { eoFillRule { eoclip } { clip } ifelse originalCTM setmatrix pathbbox /t exch def /r exch def /b exch def /l exch def /w r l sub ceiling cvi def /h t b sub ceiling cvi def /imageByteWidth w 8 div ceiling cvi def /imageHeight h def bgred bggreen bgblue setrgbcolor eoFillRule { eofill } { fill } ifelse fgred fggreen fgblue setrgbcolor w 0 gt h 0 gt and { l b translate w h scale w h true [w 0 0 h neg 0 h] { patternproc } imagemask } if } ifelse grestore end } dup 0 8 dict put def /istroke { gsave brushDashOffset -1 eq { [] 0 setdash 1 setgray } { brushDashArray brushDashOffset setdash fgred fggreen fgblue setrgbcolor } ifelse brushWidth setlinewidth originalCTM setmatrix stroke grestore } def /ishow { 0 begin gsave fgred fggreen fgblue setrgbcolor /fontDict printFont findfont printSize scalefont dup setfont def /descender fontDict begin 0 /FontBBox load 1 get FontMatrix end transform exch pop def /vertoffset 1 printSize sub descender sub def { 0 vertoffset moveto show /vertoffset vertoffset printSize sub def } forall grestore end } dup 0 3 dict put def /patternproc { 0 begin /patternByteLength patternString length def /patternHeight patternByteLength 8 mul sqrt cvi def /patternWidth patternHeight def /patternByteWidth patternWidth 8 idiv def /imageByteMaxLength imageByteWidth imageHeight mul stringLimit patternByteWidth sub min def /imageMaxHeight imageByteMaxLength imageByteWidth idiv patternHeight idiv patternHeight mul patternHeight max def /imageHeight imageHeight imageMaxHeight sub store /imageString imageByteWidth imageMaxHeight mul patternByteWidth add string def 0 1 imageMaxHeight 1 sub { /y exch def /patternRow y patternByteWidth mul patternByteLength mod def /patternRowString patternString patternRow patternByteWidth getinterval def /imageRow y imageByteWidth mul def 0 patternByteWidth imageByteWidth 1 sub { /x exch def imageString imageRow x add patternRowString putinterval } for } for imageString end } dup 0 12 dict put def /min { dup 3 2 roll dup 4 3 roll lt { exch } if pop } def /max { dup 3 2 roll dup 4 3 roll gt { exch } if pop } def /midpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 x1 add 2 div y0 y1 add 2 div end } dup 0 4 dict put def /thirdpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 2 mul x1 add 3 div y0 2 mul y1 add 3 div end } dup 0 4 dict put def /subspline { 0 begin /movetoNeeded exch def y exch get /y3 exch def x exch get /x3 exch def y exch get /y2 exch def x exch get /x2 exch def y exch get /y1 exch def x exch get /x1 exch def y exch get /y0 exch def x exch get /x0 exch def x1 y1 x2 y2 thirdpoint /p1y exch def /p1x exch def x2 y2 x1 y1 thirdpoint /p2y exch def /p2x exch def x1 y1 x0 y0 thirdpoint p1x p1y midpoint /p0y exch def /p0x exch def x2 y2 x3 y3 thirdpoint p2x p2y midpoint /p3y exch def /p3x exch def movetoNeeded { p0x p0y moveto } if p1x p1y p2x p2y p3x p3y curveto end } dup 0 17 dict put def /storexyn { /n exch def /y n array def /x n array def n 1 sub -1 0 { /i exch def y i 3 2 roll put x i 3 2 roll put } for } def /arrowhead { 0 begin transform originalCTM itransform /taily exch def /tailx exch def transform originalCTM itransform /tipy exch def /tipx exch def /dy tipy taily sub def /dx tipx tailx sub def /angle dx 0 ne dy 0 ne or { dy dx atan } { 90 } ifelse def gsave originalCTM setmatrix tipx tipy translate angle rotate newpath arrowHeight neg arrowWidth 2 div moveto 0 0 lineto arrowHeight neg arrowWidth 2 div neg lineto patternNone not { originalCTM setmatrix /padtip arrowHeight 2 exp 0.25 arrowWidth 2 exp mul add sqrt brushWidth mul arrowWidth div def /padtail brushWidth 2 div def tipx tipy translate angle rotate padtip 0 translate arrowHeight padtip add padtail add arrowHeight div dup scale arrowheadpath ifill } if brushNone not { originalCTM setmatrix tipx tipy translate angle rotate arrowheadpath istroke } if grestore end } dup 0 9 dict put def /arrowheadpath { newpath arrowHeight neg arrowWidth 2 div moveto 0 0 lineto arrowHeight neg arrowWidth 2 div neg lineto } def /leftarrow { 0 begin y exch get /taily exch def x exch get /tailx exch def y exch get /tipy exch def x exch get /tipx exch def brushLeftArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /rightarrow { 0 begin y exch get /tipy exch def x exch get /tipx exch def y exch get /taily exch def x exch get /tailx exch def brushRightArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def %%EndResource %%EndSetup %%Page: 1 1 %%PageResources: font Helvetica %%PageBoundingBox: 112 210 487 402 %%BeginPageSetup %I Idraw 8 Begin %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 1 0 0 1 0 0 ] concat /originalCTM matrix currentmatrix def /trueoriginalCTM matrix currentmatrix def %%EndPageSetup Begin %I Rect [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2304 2304 9216 5760 Rect End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-9-*-*-*-*-*-*-* /Helvetica 9.072000 SetF %I t [ 1 0 0 1 130.678 218.1928 ] concat %I [ (0) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5760 2304 5691 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2304 2304 2373 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-9-*-*-*-*-*-*-* /Helvetica 9.072000 SetF %I t [ 1 0 0 1 171.356 218.1928 ] concat %I [ (32) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3168 5760 3168 5691 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3168 2304 3168 2373 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-9-*-*-*-*-*-*-* /Helvetica 9.072000 SetF %I t [ 1 0 0 1 214.556 218.1928 ] concat %I [ (64) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4032 5760 4032 5691 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4032 2304 4032 2373 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-9-*-*-*-*-*-*-* /Helvetica 9.072000 SetF %I t [ 1 0 0 1 257.756 218.1928 ] concat %I [ (96) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4896 5760 4896 5691 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4896 2304 4896 2373 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-9-*-*-*-*-*-*-* /Helvetica 9.072000 SetF %I t [ 1 0 0 1 298.434 218.1928 ] concat %I [ (128) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5760 5760 5760 5691 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5760 2304 5760 2373 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-9-*-*-*-*-*-*-* /Helvetica 9.072000 SetF %I t [ 1 0 0 1 341.634 218.1928 ] concat %I [ (160) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6624 5760 6624 5691 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6624 2304 6624 2373 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-9-*-*-*-*-*-*-* /Helvetica 9.072000 SetF %I t [ 1 0 0 1 384.834 218.1928 ] concat %I [ (192) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7488 5760 7488 5691 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7488 2304 7488 2373 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-9-*-*-*-*-*-*-* /Helvetica 9.072000 SetF %I t [ 1 0 0 1 428.034 218.1928 ] concat %I [ (224) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8352 5760 8352 5691 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8352 2304 8352 2373 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-9-*-*-*-*-*-*-* /Helvetica 9.072000 SetF %I t [ 1 0 0 1 471.234 218.1928 ] concat %I [ (256) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5760 9216 5691 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2304 9216 2373 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-9-*-*-*-*-*-*-* /Helvetica 9.072000 SetF %I t [ 1 0 0 1 112.6999 226.0284 ] concat %I [ (-0.4) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2304 9147 2304 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2304 2373 2304 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-9-*-*-*-*-*-*-* /Helvetica 9.072000 SetF %I t [ 1 0 0 1 112.6999 245.2284 ] concat %I [ (-0.2) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2688 9147 2688 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2688 2373 2688 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-9-*-*-*-*-*-*-* /Helvetica 9.072000 SetF %I t [ 1 0 0 1 117.9979 264.4284 ] concat %I [ (0.0) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 3072 9147 3072 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3072 2373 3072 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-9-*-*-*-*-*-*-* /Helvetica 9.072000 SetF %I t [ 1 0 0 1 117.9979 283.6284 ] concat %I [ (0.2) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 3456 9147 3456 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3456 2373 3456 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-9-*-*-*-*-*-*-* /Helvetica 9.072000 SetF %I t [ 1 0 0 1 117.9979 302.8284 ] concat %I [ (0.4) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 3840 9147 3840 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3840 2373 3840 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-9-*-*-*-*-*-*-* /Helvetica 9.072000 SetF %I t [ 1 0 0 1 117.9979 322.0284 ] concat %I [ (0.6) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 4224 9147 4224 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4224 2373 4224 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-9-*-*-*-*-*-*-* /Helvetica 9.072000 SetF %I t [ 1 0 0 1 117.9979 341.2284 ] concat %I [ (0.8) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 4608 9147 4608 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4608 2373 4608 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-9-*-*-*-*-*-*-* /Helvetica 9.072000 SetF %I t [ 1 0 0 1 117.9979 360.4284 ] concat %I [ (1.0) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 4992 9147 4992 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4992 2373 4992 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-9-*-*-*-*-*-*-* /Helvetica 9.072000 SetF %I t [ 1 0 0 1 117.9979 379.6284 ] concat %I [ (1.2) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5376 9147 5376 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5376 2373 5376 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-9-*-*-*-*-*-*-* /Helvetica 9.072000 SetF %I t [ 1 0 0 1 117.9979 398.8284 ] concat %I [ (1.4) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5760 9147 5760 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5760 2373 5760 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2304 9188 2304 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2304 2332 2304 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2496 9188 2496 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2496 2332 2496 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2688 9188 2688 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2688 2332 2688 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2880 9188 2880 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2880 2332 2880 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 3072 9188 3072 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3072 2332 3072 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 3264 9188 3264 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3264 2332 3264 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 3456 9188 3456 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3456 2332 3456 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 3648 9188 3648 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3648 2332 3648 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 3840 9188 3840 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3840 2332 3840 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 4032 9188 4032 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4032 2332 4032 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 4224 9188 4224 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4224 2332 4224 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 4416 9188 4416 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4416 2332 4416 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 4608 9188 4608 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4608 2332 4608 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 4800 9188 4800 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4800 2332 4800 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 4992 9188 4992 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4992 2332 4992 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5184 9188 5184 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5184 2332 5184 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5376 9188 5376 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5376 2332 5376 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5568 9188 5568 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5568 2332 5568 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5760 9188 5760 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5760 2332 5760 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 34952 1 0 0 [ 1.48 4.43 ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3072 9216 3072 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 256 2304 3104 2331 3133 2358 3151 2385 3172 2412 3182 2439 3195 2466 3211 2493 3226 2520 3230 2547 3238 2574 3248 2601 3257 2628 3269 2655 3280 2682 3291 2709 3302 2736 3272 2763 3253 2790 3244 2817 3233 2844 3233 2871 3230 2898 3224 2925 3219 2952 3170 2979 3133 3006 3107 3033 3079 3060 3062 3087 3042 3114 3018 3141 2996 3168 3041 3195 3068 3222 3077 3249 3091 3276 3087 3303 3088 3330 3093 3357 3097 3384 3083 3411 3074 3438 3070 3465 3064 3492 3064 3519 3062 3546 3059 3573 3056 3600 3044 3627 3036 3654 3029 3681 3022 3708 3016 3735 3011 3762 3004 3789 2998 3816 2918 3843 2858 3870 2817 3897 2771 3924 2760 3951 2739 3978 2709 4005 2681 4032 3062 4059 3334 4086 3727 4113 4088 4140 4611 4167 5091 4194 5289 4221 5563 4248 5317 4275 5210 4302 4533 4329 4009 4356 3548 4383 3070 4410 2955 4437 2743 4464 2875 4491 2915 4518 2863 4545 2836 4572 2893 4599 2928 4626 2940 4653 2958 4680 2933 4707 2920 4734 2918 4761 2913 4788 2920 4815 2924 4842 2924 4869 2925 4896 2920 4923 2917 4950 2916 4977 2913 5004 2913 5031 2912 5058 2911 5085 2910 5112 2910 5139 2910 5166 2910 5193 2910 5220 2909 5247 2908 5274 2908 5301 2907 5328 2907 5355 2907 5382 2907 5409 2906 5436 2906 5463 2905 5490 2905 5517 2905 5544 2904 5571 2904 5598 2903 5625 2903 5652 2902 5679 2902 5706 2902 5733 2901 5760 2901 5787 2901 5814 2900 5841 2900 5868 2900 5895 2900 5922 2899 5949 2899 5976 2899 6003 2898 6030 2898 6057 2898 6084 2897 6111 2897 6138 2897 6165 2896 6192 2896 6219 2895 6246 2895 6273 2895 6300 2894 6327 2894 6354 2894 6381 2893 6408 2893 6435 2892 6462 2892 6489 2892 6516 2891 6543 2891 6570 2891 6597 2890 6624 2873 6651 2860 6678 2852 6705 2843 6732 2838 6759 2832 6786 2824 6813 2817 6840 2815 6867 2811 6894 2806 6921 2802 6948 2796 6975 2791 7002 2785 7029 2780 7056 2839 7083 2881 7110 2906 7137 2935 7164 2947 7191 2964 7218 2985 7245 3005 7272 3008 7299 3015 7326 3027 7353 3038 7380 3053 7407 3067 7434 3080 7461 3093 7488 3068 7515 3052 7542 3048 7569 3040 7596 3043 7623 3043 7650 3040 7677 3038 7704 3046 7731 3052 7758 3055 7785 3058 7812 3059 7839 3061 7866 3063 7893 3065 7920 3077 7947 3087 7974 3094 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(original)h(lectures)f(b)m(y)150 4121 y(Daub)s(ec)m(hies,)330 4248 y(Ingrid)26 b(Daub)s(ec)m(hies.)40 b(T)-8 b(en)27 b(Lectures)g(on)g(W)-8 b(a)m(v)m(elets.)43 b FD(CBMS-NSF)27 b(Regional)i(Conference)e(Series)330 4358 y(in)j(Applied)g(Mathematics) 36 b FK(\(1992\),)d(SIAM,)e(ISBN)f(0898712742.)150 4503 y(An)39 b(easy)g(to)h(read)e(in)m(tro)s(duction)h(to)h(the)f(sub)5 b(ject)39 b(with)f(an)h(emphasis)g(on)f(the)h(application)i(of)e(the) 150 4612 y(w)m(a)m(v)m(elet)33 b(transform)d(in)g(v)-5 b(arious)30 b(branc)m(hes)g(of)h(science)g(is,)330 4739 y(P)m(aul)j(S.)g(Addison.)51 b FD(The)33 b(Illustrated)h(W)-8 b(a)m(v)m(elet)38 b(T)-8 b(ransform)33 b(Handb)s(o)s(ok)p FK(.)50 b(Institute)35 b(of)f(Ph)m(ysics)330 4849 y(Publishing)29 b(\(2002\),)k(ISBN)e(0750306920.)150 4994 y(F)-8 b(or)27 b(extensiv)m(e)i(co)m(v)m(erage)g(of)e(signal)g(analysis)h(b)m(y)e(w)m (a)m(v)m(elets,)31 b(w)m(a)m(v)m(elet)e(pac)m(k)m(ets)g(and)d(lo)s(cal) h(cosine)h(bases)150 5103 y(see,)330 5230 y(S.)36 b(G.)g(Mallat.)60 b FD(A)36 b(w)m(a)m(v)m(elet)j(tour)d(of)h(signal)f(pro)s(cessing)44 b FK(\(Second)36 b(edition\).)59 b(Academic)37 b(Press)330 5340 y(\(1999\),)c(ISBN)d(012466606X.)p eop end %%Page: 381 399 TeXDict begin 381 398 bop 150 -116 a FK(Chapter)30 b(32:)41 b(W)-8 b(a)m(v)m(elet)34 b(T)-8 b(ransforms)2161 b(381)150 299 y(The)30 b(concept)h(of)g(m)m(ultiresolution)g(analysis)g (underlying)e(the)i(w)m(a)m(v)m(elet)i(transform)d(is)g(describ)s(ed)g (in,)330 433 y(S.)45 b(G.)h(Mallat.)87 b(Multiresolution)46 b(Appro)m(ximations)g(and)e(W)-8 b(a)m(v)m(elet)49 b(Orthonormal)c (Bases)h(of)330 543 y(L)387 510 y FB(2)424 543 y FK(\(R\).)31 b FD(T)-8 b(ransactions)31 b(of)g(the)f(American)h(Mathematical)j(So)s (ciet)m(y)p FK(,)e(315\(1\),)h(1989,)f(69{87.)330 677 y(S.)21 b(G.)i(Mallat.)40 b(A)22 b(Theory)f(for)g(Multiresolution)j (Signal)e(Decomp)s(osition|The)g(W)-8 b(a)m(v)m(elet)26 b(Repre-)330 787 y(sen)m(tation.)42 b FD(IEEE)28 b(T)-8 b(ransactions)30 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b(F)-8 b(or)43 b(these)g(algorithms)g(the)f(initial)h (in)m(terv)-5 b(al)43 b(m)m(ust)f(con)m(tain)i(a)e(zero-crossing,)47 b(where)42 b(the)150 5340 y(function)35 b(is)h(negativ)m(e)h(at)g(one)e (end)g(of)h(the)f(in)m(terv)-5 b(al)37 b(and)e(p)s(ositiv)m(e)h(at)h (the)e(other)h(end.)55 b(Ro)s(ots)36 b(with)p eop end %%Page: 385 403 TeXDict begin 385 402 bop 150 -116 a FK(Chapter)30 b(34:)41 b(One)30 b(dimensional)h(Ro)s(ot-Finding)1729 b(385)150 299 y(ev)m(en-m)m(ultiplicit)m(y)31 b(do)d(not)g(cross)g(zero,)h(but)f (only)g(touc)m(h)g(it)h(instan)m(taneously)-8 b(.)41 b(Algorithms)28 b(based)g(on)150 408 y(ro)s(ot)38 b(brac)m(k)m(eting)h (will)f(still)h(w)m(ork)e(for)h(o)s(dd-m)m(ultiplicit)m(y)h(ro)s(ots)e (\(e.g.)64 b(cubic,)40 b(quin)m(tic,)46 b(.)22 b(.)g(.)12 b(\).)62 b(Ro)s(ot)150 518 y(p)s(olishing)36 b(algorithms)i(generally)f (w)m(ork)g(with)g(higher)f(m)m(ultiplicit)m(y)i(ro)s(ots,)h(but)d(at)h (a)g(reduced)f(rate)150 628 y(of)46 b(con)m(v)m(ergence.)88 b(In)44 b(these)i(cases)h(the)e FD(Ste\013enson)h(algorithm)g FK(can)g(b)s(e)f(used)f(to)i(accelerate)j(the)150 737 y(con)m(v)m(ergence)33 b(of)d(m)m(ultiple)h(ro)s(ots.)275 878 y(While)25 b(it)g(is)g(not)g(absolutely)g(required)f(that)i FE(f)33 b FK(ha)m(v)m(e)26 b(a)f(ro)s(ot)g(within)g(the)f(searc)m(h)i (region,)g(n)m(umerical)150 988 y(ro)s(ot)34 b(\014nding)e(functions)h (should)f(not)i(b)s(e)e(used)h(haphazardly)g(to)h(c)m(hec)m(k)h(for)e (the)h Fg(existenc)-5 b(e)40 b FK(of)33 b(ro)s(ots.)150 1097 y(There)22 b(are)h(b)s(etter)f(w)m(a)m(ys)h(to)g(do)f(this.)38 b(Because)24 b(it)f(is)f(easy)h(to)g(create)h(situations)f(where)f(n)m (umerical)h(ro)s(ot)150 1207 y(\014nders)28 b(can)i(fail,)g(it)g(is)g (a)f(bad)g(idea)h(to)g(thro)m(w)g(a)g(ro)s(ot)f(\014nder)f(at)j(a)e (function)h(y)m(ou)f(do)h(not)f(kno)m(w)h(m)m(uc)m(h)150 1316 y(ab)s(out.)55 b(In)34 b(general)j(it)e(is)g(b)s(est)g(to)h (examine)g(the)f(function)g(visually)h(b)m(y)f(plotting)h(b)s(efore)f (searc)m(hing)150 1426 y(for)30 b(a)h(ro)s(ot.)150 1668 y FJ(34.3)68 b(Initializing)47 b(the)e(Solv)l(er)3350 1884 y FK([F)-8 b(unction])-3599 b Fv(gsl_root_fsolver)57 b(*)c(gsl_root_fsolver_alloc)f Fu(\()p FD(const)565 1993 y(gsl)p 677 1993 28 4 v 41 w(ro)s(ot)p 882 1993 V 40 w(fsolv)m(er)p 1177 1993 V 41 w(t)m(yp)s(e)30 b(*)h Ft(T)p Fu(\))390 2103 y FK(This)j(function)h(returns)f(a)h(p)s(oin)m(ter)g(to) h(a)f(newly)g(allo)s(cated)i(instance)e(of)g(a)h(solv)m(er)g(of)f(t)m (yp)s(e)g FD(T)p FK(.)390 2213 y(F)-8 b(or)31 b(example,)g(the)g(follo) m(wing)h(co)s(de)e(creates)i(an)e(instance)i(of)e(a)h(bisection)g(solv) m(er,)630 2353 y FH(const)46 b(gsl_root_fsolver_type)c(*)48 b(T)725 2463 y(=)g(gsl_root_fsolver_bisecti)o(on;)630 2573 y(gsl_root_fsolver)43 b(*)48 b(s)725 2682 y(=)g (gsl_root_fsolver_alloc)42 b(\(T\);)390 2823 y FK(If)36 b(there)g(is)h(insu\016cien)m(t)f(memory)h(to)g(create)h(the)e(solv)m (er)i(then)e(the)g(function)g(returns)f(a)i(n)m(ull)390 2933 y(p)s(oin)m(ter)30 b(and)g(the)h(error)f(handler)f(is)i(in)m(v)m (ok)m(ed)g(with)g(an)f(error)g(co)s(de)g(of)h FH(GSL_ENOMEM)p FK(.)3350 3130 y([F)-8 b(unction])-3599 b Fv(gsl_root_fdfsolver)58 b(*)52 b(gsl_root_fdfsolver_al)q(loc)g Fu(\()p FD(const)565 3239 y(gsl)p 677 3239 V 41 w(ro)s(ot)p 882 3239 V 40 w(fdfsolv)m(er)p 1256 3239 V 40 w(t)m(yp)s(e)31 b(*)f Ft(T)p Fu(\))390 3349 y FK(This)37 b(function)g(returns)f(a)i(p)s(oin)m (ter)g(to)g(a)g(newly)g(allo)s(cated)h(instance)g(of)e(a)h(deriv)-5 b(ativ)m(e-based)390 3459 y(solv)m(er)36 b(of)e(t)m(yp)s(e)h FD(T)p FK(.)53 b(F)-8 b(or)35 b(example,)i(the)e(follo)m(wing)h(co)s (de)f(creates)h(an)e(instance)h(of)g(a)g(Newton-)390 3568 y(Raphson)30 b(solv)m(er,)630 3709 y FH(const)46 b(gsl_root_fdfsolver_type)c(*)47 b(T)725 3819 y(=)h (gsl_root_fdfsolver_newto)o(n;)630 3928 y(gsl_root_fdfsolver)43 b(*)k(s)725 4038 y(=)h(gsl_root_fdfsolver_alloc)41 b(\(T\);)390 4179 y FK(If)36 b(there)g(is)h(insu\016cien)m(t)f(memory)h(to)g(create) 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w(function)p 2968 5011 V 40 w(fdf)e(*)565 5121 y Ft(fdf)p FD(,)j(double)e Ft(root)p Fu(\))390 5230 y FK(This)i(function)g(initializes,)k(or)d(reinitializes,)i(an)e (existing)h(solv)m(er)f FD(s)j FK(to)e(use)e(the)h(function)g(and)390 5340 y(deriv)-5 b(ativ)m(e)32 b FD(fdf)47 b FK(and)30 b(the)g(initial)i(guess)e FD(ro)s(ot)p FK(.)p eop end %%Page: 386 404 TeXDict begin 386 403 bop 150 -116 a FK(Chapter)30 b(34:)41 b(One)30 b(dimensional)h(Ro)s(ot-Finding)1729 b(386)3350 299 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_root_fsolver_free)d Fu(\()p FD(gsl)p 1702 299 28 4 v 41 w(ro)s(ot)p 1907 299 V 41 w(fsolv)m(er)31 b(*)g Ft(s)p Fu(\))3350 408 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_root_fdfsolver_free)e Fu(\()p FD(gsl)p 1807 408 V 41 w(ro)s(ot)p 2012 408 V 40 w(fdfsolv)m(er)31 b(*)f Ft(s)p Fu(\))390 518 y FK(These)g(functions) g(free)h(all)g(the)f(memory)h(asso)s(ciated)g(with)g(the)f(solv)m(er)h FD(s)p FK(.)3350 698 y([F)-8 b(unction])-3599 b Fv(const)54 b(char)f(*)g(gsl_root_fsolver_name)f Fu(\()p FD(const)31 b(gsl)p 2359 698 V 41 w(ro)s(ot)p 2564 698 V 40 w(fsolv)m(er)g(*)g Ft(s)p Fu(\))3350 807 y FK([F)-8 b(unction])-3599 b Fv(const)54 b(char)f(*)g(gsl_root_fdfsolver_nam)q(e)e Fu(\()p FD(const)32 b(gsl)p 2464 807 V 40 w(ro)s(ot)p 2668 807 V 41 w(fdfsolv)m(er)e(*)565 917 y Ft(s)p Fu(\))390 1027 y FK(These)g(functions)g(return)f(a)i(p)s (oin)m(ter)f(to)i(the)e(name)h(of)f(the)h(solv)m(er.)41 b(F)-8 b(or)31 b(example,)630 1160 y FH(printf)46 b(\("s)h(is)g(a)h ('\045s')e(solver\\n",)1012 1269 y(gsl_root_fsolver_name)c(\(s\)\);)390 1402 y FK(w)m(ould)30 b(prin)m(t)g(something)h(lik)m(e)h FH(s)e(is)f(a)h('bisection')e(solver)p FK(.)150 1632 y FJ(34.4)68 b(Pro)l(viding)46 b(the)f(function)g(to)g(solv)l(e)150 1791 y FK(Y)-8 b(ou)32 b(m)m(ust)g(pro)m(vide)g(a)h(con)m(tin)m(uous)f (function)g(of)g(one)g(v)-5 b(ariable)33 b(for)f(the)g(ro)s(ot)g (\014nders)f(to)h(op)s(erate)h(on,)150 1901 y(and,)f(sometimes,)i(its)e (\014rst)g(deriv)-5 b(ativ)m(e.)47 b(In)32 b(order)f(to)i(allo)m(w)h (for)e(general)h(parameters)f(the)g(functions)150 2010 y(are)f(de\014ned)e(b)m(y)h(the)h(follo)m(wing)h(data)f(t)m(yp)s(es:) 3269 2190 y([Data)h(T)m(yp)s(e])-3600 b Fv(gsl_function)390 2300 y FK(This)30 b(data)h(t)m(yp)s(e)f(de\014nes)g(a)g(general)i (function)e(with)g(parameters.)390 2456 y FH(double)f(\(*)g(function\)) f(\(double)h FA(x)p FH(,)g(void)h(*)g FA(params)p FH(\))870 2566 y FK(this)39 b(function)f(should)g(return)g(the)h(v)-5 b(alue)39 b FE(f)10 b FK(\()p FE(x;)15 b Fg(p)-5 b(ar)g(ams)s FK(\))39 b(for)f(argumen)m(t)i FD(x)45 b FK(and)870 2675 y(parameters)31 b FD(params)390 2832 y FH(void)e(*)h(params)870 2941 y FK(a)h(p)s(oin)m(ter)f(to)h(the)g(parameters)g(of)f(the)h (function)275 3121 y(Here)f(is)h(an)f(example)h(for)f(the)h(general)g (quadratic)g(function,)1556 3287 y FE(f)10 b FK(\()p FE(x)p FK(\))25 b(=)g FE(ax)1954 3250 y FB(2)2012 3287 y FK(+)20 b FE(bx)g FK(+)g FE(c)150 3454 y FK(with)34 b FE(a)f FK(=)f(3,)k FE(b)d FK(=)f(2,)37 b FE(c)32 b FK(=)g(1.)55 b(The)34 b(follo)m(wing)i(co)s(de)f(de\014nes)f(a)h FH(gsl_function)c(F)j FK(whic)m(h)h(y)m(ou)g(could)150 3563 y(pass)30 b(to)h(a)g(ro)s(ot)g(\014nder)d(as)j(a)g(function)f(p)s (oin)m(ter:)390 3696 y FH(struct)46 b(my_f_params)f({)i(double)f(a;)i (double)e(b;)h(double)f(c;)h(};)390 3915 y(double)390 4025 y(my_f)g(\(double)e(x,)j(void)e(*)i(p\))f({)533 4134 y(struct)f(my_f_params)f(*)i(params)629 4244 y(=)g(\(struct)f (my_f_params)f(*\)p;)533 4354 y(double)h(a)i(=)f(\(params->a\);)533 4463 y(double)f(b)i(=)f(\(params->b\);)533 4573 y(double)f(c)i(=)f (\(params->c\);)533 4792 y(return)94 b(\(a)47 b(*)h(x)f(+)h(b\))f(*)g (x)h(+)f(c;)390 4902 y(})390 5121 y(gsl_function)d(F;)390 5230 y(struct)i(my_f_params)f(params)h(=)h({)h(3.0,)e(2.0,)h(1.0)g(};)p eop end %%Page: 387 405 TeXDict begin 387 404 bop 150 -116 a FK(Chapter)30 b(34:)41 b(One)30 b(dimensional)h(Ro)s(ot-Finding)1729 b(387)390 299 y FH(F.function)45 b(=)i(&my_f;)390 408 y(F.params)f(=)h(¶ms;) 150 547 y FK(The)33 b(function)g FE(f)10 b FK(\()p FE(x)p FK(\))33 b(can)g(b)s(e)g(ev)-5 b(aluated)34 b(using)f(the)g(macro)h FH(GSL_FN_EVAL\(&F,x\))28 b FK(de\014ned)k(in)h FH(gsl_)150 656 y(math.h)p FK(.)3269 848 y([Data)f(T)m(yp)s(e])-3600 b Fv(gsl_function_fdf)390 958 y FK(This)30 b(data)h(t)m(yp)s(e)f (de\014nes)g(a)g(general)i(function)e(with)g(parameters)h(and)e(its)i (\014rst)f(deriv)-5 b(ativ)m(e.)390 1123 y FH(double)29 b(\(*)g(f\))h(\(double)f FA(x)p FH(,)g(void)h(*)g FA(params)p FH(\))870 1233 y FK(this)e(function)h(should)e(return)h(the)h(v)-5 b(alue)29 b(of)g FE(f)10 b FK(\()p FE(x;)15 b Fg(p)-5 b(ar)g(ams)r FK(\))29 b(for)g(argumen)m(t)g FD(x)35 b FK(and)870 1342 y(parameters)c FD(params)390 1505 y FH(double)e(\(*)g (df\))h(\(double)e FA(x)p FH(,)i(void)f(*)h FA(params)p FH(\))870 1615 y FK(this)k(function)g(should)f(return)g(the)h(v)-5 b(alue)35 b(of)f(the)g(deriv)-5 b(ativ)m(e)36 b(of)e FD(f)51 b FK(with)34 b(resp)s(ect)870 1724 y(to)d FD(x)p FK(,)g FE(f)1140 1691 y Fp(0)1162 1724 y FK(\()p FE(x;)15 b Fg(p)-5 b(ar)g(ams)t FK(\),)31 b(for)f(argumen)m(t)h FD(x)36 b FK(and)30 b(parameters)h FD(params)390 1888 y FH(void)e(\(*)h(fdf\))f(\(double)g FA(x)p FH(,)g(void)h(*)g FA(params)p FH(,)e(double)h(*)h FA(f)p FH(,)f(double)g(*)h FA(df)p FH(\))870 1997 y FK(this)h(function)g(should)g(set)h(the)f(v)-5 b(alues)32 b(of)f(the)h(function)f FD(f)49 b FK(to)32 b FE(f)10 b FK(\()p FE(x;)15 b Fg(p)-5 b(ar)g(ams)s FK(\))32 b(and)870 2107 y(its)26 b(deriv)-5 b(ativ)m(e)28 b FD(df)43 b FK(to)26 b FE(f)1688 2074 y Fp(0)1711 2107 y FK(\()p FE(x;)15 b Fg(p)-5 b(ar)g(ams)t FK(\))26 b(for)g(argumen)m(t)g FD(x)32 b FK(and)26 b(parameters)g FD(params)p FK(.)870 2216 y(This)h(function)g(pro)m(vides)h(an)f(optimization)j(of)e(the)g (separate)g(functions)g(for)f FE(f)10 b FK(\()p FE(x)p FK(\))870 2326 y(and)30 b FE(f)1102 2293 y Fp(0)1125 2326 y FK(\()p FE(x)p FK(\)|it)i(is)f(alw)m(a)m(ys)h(faster)f(to)h (compute)f(the)g(function)g(and)f(its)h(deriv)-5 b(ativ)m(e)870 2436 y(at)31 b(the)g(same)f(time.)390 2599 y FH(void)f(*)h(params)870 2708 y FK(a)h(p)s(oin)m(ter)f(to)h(the)g(parameters)g(of)f(the)h (function)275 2900 y(Here)f(is)h(an)f(example)h(where)f FE(f)10 b FK(\()p FE(x)p FK(\))25 b(=)g(exp\(2)p FE(x)p FK(\):)390 3039 y FH(double)390 3148 y(my_f)47 b(\(double)e(x,)j(void)e (*)i(params\))390 3258 y({)533 3367 y(return)e(exp)h(\(2)g(*)h(x\);)390 3477 y(})390 3696 y(double)390 3806 y(my_df)e(\(double)g(x,)h(void)g(*) g(params\))390 3915 y({)533 4025 y(return)f(2)i(*)f(exp)g(\(2)g(*)h (x\);)390 4134 y(})390 4354 y(void)390 4463 y(my_fdf)e(\(double)g(x,)h (void)g(*)g(params,)772 4573 y(double)f(*)h(f,)h(double)e(*)h(df\))390 4682 y({)533 4792 y(double)f(t)i(=)f(exp)g(\(2)g(*)h(x\);)533 5011 y(*f)f(=)h(t;)533 5121 y(*df)f(=)h(2)f(*)g(t;)143 b(/*)47 b(uses)g(existing)e(value)i(*/)390 5230 y(})p eop end %%Page: 388 406 TeXDict begin 388 405 bop 150 -116 a FK(Chapter)30 b(34:)41 b(One)30 b(dimensional)h(Ro)s(ot-Finding)1729 b(388)390 299 y FH(gsl_function_fdf)43 b(FDF;)390 518 y(FDF.f)j(=)i(&my_f;)390 628 y(FDF.df)e(=)i(&my_df;)390 737 y(FDF.fdf)e(=)h(&my_fdf;)390 847 y(FDF.params)e(=)i(0;)150 977 y FK(The)26 b(function)g FE(f)10 b FK(\()p FE(x)p FK(\))27 b(can)g(b)s(e)f(ev)-5 b(aluated)28 b(using)e(the)h(macro)g FH(GSL_FN_FDF_EVAL_F\(&FDF,x)o(\)) 21 b FK(and)26 b(the)150 1087 y(deriv)-5 b(ativ)m(e)40 b FE(f)630 1054 y Fp(0)652 1087 y FK(\()p FE(x)p FK(\))f(can)g(b)s(e)e (ev)-5 b(aluated)39 b(using)f(the)h(macro)f FH (GSL_FN_FDF_EVAL_DF\(&FDF,x)o(\))p FK(.)58 b(Both)150 1196 y(the)39 b(function)g FE(y)k FK(=)d FE(f)10 b FK(\()p FE(x)p FK(\))39 b(and)g(its)g(deriv)-5 b(ativ)m(e)41 b FE(dy)i FK(=)d FE(f)2143 1163 y Fp(0)2166 1196 y FK(\()p FE(x)p FK(\))g(can)f(b)s(e)g(ev)-5 b(aluated)40 b(at)g(the)g(same)f (time)150 1306 y(using)d(the)h(macro)h FH(GSL_FN_FDF_EVAL_F_DF\(&F)o (DF,x)o(,y,d)o(y\))p FK(.)54 b(The)36 b(macro)i(stores)f FE(f)10 b FK(\()p FE(x)p FK(\))37 b(in)f(its)h FD(y)150 1415 y FK(argumen)m(t)31 b(and)f FE(f)789 1382 y Fp(0)811 1415 y FK(\()p FE(x)p FK(\))h(in)f(its)h FD(dy)38 b FK(argumen)m(t|b)s (oth)30 b(of)g(these)h(should)e(b)s(e)h(p)s(oin)m(ters)g(to)h FH(double)p FK(.)150 1639 y FJ(34.5)68 b(Searc)l(h)45 b(Bounds)f(and)h(Guesses)150 1799 y FK(Y)-8 b(ou)23 b(pro)m(vide)g (either)g(searc)m(h)g(b)s(ounds)d(or)i(an)h(initial)g(guess;)j(this)c (section)i(explains)f(ho)m(w)f(searc)m(h)h(b)s(ounds)150 1908 y(and)30 b(guesses)g(w)m(ork)h(and)f(ho)m(w)g(function)g(argumen)m (ts)h(con)m(trol)h(them.)275 2038 y(A)f(guess)h(is)g(simply)g(an)f FE(x)h FK(v)-5 b(alue)32 b(whic)m(h)g(is)g(iterated)h(un)m(til)f(it)g (is)g(within)f(the)h(desired)g(precision)g(of)150 2148 y(a)f(ro)s(ot.)41 b(It)30 b(tak)m(es)i(the)f(form)f(of)g(a)h FH(double)p FK(.)275 2278 y(Searc)m(h)g(b)s(ounds)f(are)i(the)g(endp)s (oin)m(ts)e(of)i(an)g(in)m(terv)-5 b(al)32 b(whic)m(h)g(is)f(iterated)i (un)m(til)f(the)g(length)g(of)g(the)150 2388 y(in)m(terv)-5 b(al)34 b(is)e(smaller)h(than)g(the)f(requested)h(precision.)47 b(The)32 b(in)m(terv)-5 b(al)34 b(is)e(de\014ned)g(b)m(y)g(t)m(w)m(o)i (v)-5 b(alues,)34 b(the)150 2497 y(lo)m(w)m(er)d(limit)g(and)f(the)g (upp)s(er)f(limit.)41 b(Whether)30 b(the)h(endp)s(oin)m(ts)e(are)i(in)m (tended)f(to)h(b)s(e)e(included)h(in)g(the)150 2607 y(in)m(terv)-5 b(al)32 b(or)e(not)h(dep)s(ends)d(on)i(the)h(con)m(text)h(in)e(whic)m (h)g(the)h(in)m(terv)-5 b(al)31 b(is)g(used.)150 2831 y FJ(34.6)68 b(Iteration)150 2990 y FK(The)32 b(follo)m(wing)i (functions)e(driv)m(e)g(the)h(iteration)h(of)e(eac)m(h)i(algorithm.)48 b(Eac)m(h)33 b(function)f(p)s(erforms)f(one)150 3100 y(iteration)45 b(to)e(up)s(date)g(the)g(state)h(of)g(an)m(y)f(solv)m (er)h(of)f(the)g(corresp)s(onding)g(t)m(yp)s(e.)78 b(The)43 b(same)h(func-)150 3209 y(tions)33 b(w)m(ork)g(for)g(all)g(solv)m(ers)h (so)f(that)h(di\013eren)m(t)f(metho)s(ds)f(can)h(b)s(e)f(substituted)h (at)g(run)m(time)g(without)150 3319 y(mo)s(di\014cations)e(to)g(the)f (co)s(de.)3350 3490 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_root_fsolver_iter)q(ate)f Fu(\()p FD(gsl)p 1807 3490 28 4 v 41 w(ro)s(ot)p 2012 3490 V 40 w(fsolv)m(er)31 b(*)g Ft(s)p Fu(\))3350 3600 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_root_fdfsolver_it)q(erat)q(e)f Fu(\()p FD(gsl)p 1912 3600 V 40 w(ro)s(ot)p 2116 3600 V 41 w(fdfsolv)m(er)30 b(*)h Ft(s)p Fu(\))390 3709 y FK(These)f(functions)h(p)s(erform)e(a)i (single)g(iteration)h(of)f(the)g(solv)m(er)h FD(s)p FK(.)41 b(If)30 b(the)h(iteration)i(encoun)m(ters)390 3819 y(an)d(unexp)s (ected)g(problem)g(then)g(an)g(error)g(co)s(de)h(will)f(b)s(e)g (returned,)390 3970 y FH(GSL_EBADFUNC)870 4079 y FK(the)22 b(iteration)h(encoun)m(tered)f(a)h(singular)e(p)s(oin)m(t)h(where)f (the)h(function)g(or)f(its)i(deriv)-5 b(a-)870 4189 y(tiv)m(e)32 b(ev)-5 b(aluated)31 b(to)g FH(Inf)f FK(or)g FH(NaN)p FK(.)390 4340 y FH(GSL_EZERODIV)870 4449 y FK(the)h(deriv)-5 b(ativ)m(e)32 b(of)f(the)g(function)f(v)-5 b(anished)30 b(at)h(the)g(iteration)h(p)s(oin)m(t,)f(prev)m(en)m(ting)870 4559 y(the)g(algorithm)g(from)f(con)m(tin)m(uing)h(without)g(a)f (division)h(b)m(y)f(zero.)275 4730 y(The)35 b(solv)m(er)i(main)m(tains) g(a)g(curren)m(t)f(b)s(est)g(estimate)i(of)e(the)g(ro)s(ot)h(at)g(all)g (times.)58 b(The)36 b(brac)m(k)m(eting)150 4840 y(solv)m(ers)28 b(also)g(k)m(eep)g(trac)m(k)h(of)e(the)h(curren)m(t)f(b)s(est)g(in)m (terv)-5 b(al)28 b(b)s(ounding)e(the)h(ro)s(ot.)40 b(This)27 b(information)h(can)150 4949 y(b)s(e)i(accessed)h(with)f(the)h(follo)m (wing)h(auxiliary)f(functions,)3350 5121 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_root_fsolver_root)e Fu(\()p FD(const)31 b(gsl)p 2045 5121 V 41 w(ro)s(ot)p 2250 5121 V 40 w(fsolv)m(er)g(*)g Ft(s)p Fu(\))3350 5230 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_root_fdfsolver_roo)q(t)e Fu(\()p FD(const)31 b(gsl)p 2150 5230 V 40 w(ro)s(ot)p 2354 5230 V 41 w(fdfsolv)m(er)f(*)h Ft(s)p Fu(\))390 5340 y FK(These)f(functions)g(return)f(the)i(curren)m (t)f(estimate)i(of)f(the)f(ro)s(ot)h(for)f(the)h(solv)m(er)g FD(s)p FK(.)p eop end %%Page: 389 407 TeXDict begin 389 406 bop 150 -116 a FK(Chapter)30 b(34:)41 b(One)30 b(dimensional)h(Ro)s(ot-Finding)1729 b(389)3350 299 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_root_fsolver_x_low)q (er)e Fu(\()p FD(const)31 b(gsl)p 2202 299 28 4 v 41 w(ro)s(ot)p 2407 299 V 40 w(fsolv)m(er)g(*)g Ft(s)p Fu(\))3350 408 y FK([F)-8 b(unction])-3599 b Fv(double)54 b (gsl_root_fsolver_x_upp)q(er)e Fu(\()p FD(const)31 b(gsl)p 2202 408 V 41 w(ro)s(ot)p 2407 408 V 40 w(fsolv)m(er)g(*)g Ft(s)p Fu(\))390 518 y FK(These)f(functions)g(return)f(the)i(curren)m (t)f(brac)m(k)m(eting)i(in)m(terv)-5 b(al)32 b(for)e(the)g(solv)m(er)i FD(s)p FK(.)150 747 y FJ(34.7)68 b(Searc)l(h)45 b(Stopping)g(P)l (arameters)150 906 y FK(A)30 b(ro)s(ot)h(\014nding)e(pro)s(cedure)g (should)h(stop)g(when)g(one)g(of)h(the)f(follo)m(wing)i(conditions)f (is)g(true:)225 1039 y FI(\017)60 b FK(A)30 b(ro)s(ot)h(has)f(b)s(een)g 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(terv)-5 b(al)42 b(also)g(implies)f(that)h(an)m(y)f(estimate)i(of)e (the)g(ro)s(ot)g FE(r)i FK(in)e(the)390 3089 y(in)m(terv)-5 b(al)32 b(satis\014es)e(the)h(same)g(condition)g(with)f(resp)s(ect)g (to)h(the)g(true)f(ro)s(ot)h FE(r)3054 3056 y Fp(\003)3091 3089 y FK(,)1400 3254 y FI(j)p FE(r)23 b FI(\000)d FE(r)1624 3217 y Fp(\003)1661 3254 y FI(j)26 b FE(<)f Fg(epsabs)c FK(+)f Fg(epsr)-5 b(el)26 b FE(r)2463 3217 y Fp(\003)390 3420 y FK(assuming)k(that)h(the)f(true)h(ro)s(ot)f FE(r)1569 3387 y Fp(\003)1637 3420 y FK(is)h(con)m(tained)g(within)f(the)h(in)m (terv)-5 b(al.)3350 3599 y([F)d(unction])-3599 b Fv(int)53 b(gsl_root_test_delta)e Fu(\()p FD(double)31 b Ft(x1)p FD(,)g(double)f Ft(x0)p FD(,)h(double)f Ft(epsabs)p FD(,)565 3708 y(double)g Ft(epsrel)p Fu(\))390 3818 y FK(This)40 b(function)g(tests)i(for)e(the)h(con)m(v)m(ergence)j(of)c(the)h (sequence)47 b(.)22 b(.)h(.)11 b(,)43 b FD(x0)p FK(,)h FD(x1)49 b FK(with)40 b(absolute)390 3928 y(error)30 b FD(epsabs)k FK(and)29 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(algorithm)i(uses)e(an)g(in)m(v)m(erse)h(quadratic)g(\014t)g(to)g(the)f (last)i(three)390 4735 y(p)s(oin)m(ts,)33 b(for)f(higher)g(accuracy)-8 b(.)48 b(The)32 b(in)m(tercept)h(of)g(the)f(in)m(terp)s(olating)i(curv) m(e)f(with)f(the)g FE(x)p FK(-axis)390 4844 y(is)k(tak)m(en)g(as)g(a)g (guess)g(for)g(the)f(ro)s(ot.)57 b(If)36 b(it)g(lies)g(within)f(the)h (b)s(ounds)e(of)h(the)h(curren)m(t)g(in)m(terv)-5 b(al)390 4954 y(then)34 b(the)g(in)m(terp)s(olating)h(p)s(oin)m(t)f(is)g (accepted,)i(and)e(used)f(to)i(generate)g(a)f(smaller)h(in)m(terv)-5 b(al.)52 b(If)390 5063 y(the)34 b(in)m(terp)s(olating)h(p)s(oin)m(t)f (is)g(not)g(accepted)h(then)f(the)g(algorithm)g(falls)h(bac)m(k)f(to)h (an)f(ordinary)390 5173 y(bisection)d(step.)390 5322 y(The)25 b(b)s(est)g(estimate)i(of)e(the)h(ro)s(ot)g(is)f(tak)m(en)h (from)f(the)h(most)f(recen)m(t)i(in)m(terp)s(olation)f(or)g(bisection.) p eop end %%Page: 391 409 TeXDict begin 391 408 bop 150 -116 a FK(Chapter)30 b(34:)41 b(One)30 b(dimensional)h(Ro)s(ot-Finding)1729 b(391)150 299 y FJ(34.9)68 b(Ro)t(ot)46 b(Finding)f(Algorithms)g(using)g(Deriv)-7 b(ativ)l(es)150 458 y FK(The)45 b(ro)s(ot)g(p)s(olishing)g(algorithms)h (describ)s(ed)e(in)h(this)g(section)i(require)e(an)g(initial)h(guess)g (for)f(the)150 568 y(lo)s(cation)33 b(of)e(the)g(ro)s(ot.)43 b(There)30 b(is)h(no)g(absolute)h(guaran)m(tee)g(of)f(con)m(v)m (ergence|the)j(function)d(m)m(ust)g(b)s(e)150 677 y(suitable)h(for)f (this)h(tec)m(hnique)g(and)f(the)g(initial)i(guess)e(m)m(ust)h(b)s(e)f (su\016cien)m(tly)h(close)h(to)f(the)f(ro)s(ot)h(for)f(it)150 787 y(to)g(w)m(ork.)41 b(When)30 b(these)h(conditions)g(are)g (satis\014ed)f(then)g(con)m(v)m(ergence)j(is)d(quadratic.)275 931 y(These)g(algorithms)h(mak)m(e)g(use)f(of)h(b)s(oth)f(the)g (function)g(and)g(its)h(deriv)-5 b(ativ)m(e.)3021 1135 y([Deriv)g(ativ)m(e)33 b(Solv)m(er])-3599 b Fv(gsl_root_fdfsolver_new)q (ton)390 1244 y FK(Newton's)41 b(Metho)s(d)g(is)g(the)g(standard)f(ro)s (ot-p)s(olishing)h(algorithm.)72 b(The)41 b(algorithm)g(b)s(egins)390 1354 y(with)29 b(an)g(initial)i(guess)e(for)g(the)h(lo)s(cation)h(of)e (the)h(ro)s(ot.)41 b(On)28 b(eac)m(h)j(iteration,)g(a)f(line)f(tangen)m (t)i(to)390 1463 y(the)e(function)f FE(f)38 b FK(is)29 b(dra)m(wn)f(at)i(that)f(p)s(osition.)40 b(The)28 b(p)s(oin)m(t)h (where)f(this)h(line)g(crosses)g(the)g FE(x)p FK(-axis)390 1573 y(b)s(ecomes)i(the)f(new)g(guess.)41 b(The)30 b(iteration)i(is)e (de\014ned)f(b)m(y)h(the)h(follo)m(wing)h(sequence,)1588 1797 y FE(x)1640 1811 y Fq(i)p FB(+1)1777 1797 y FK(=)25 b FE(x)1925 1811 y Fq(i)1973 1797 y FI(\000)2085 1736 y FE(f)10 b FK(\()p FE(x)2227 1750 y Fq(i)2255 1736 y FK(\))p 2074 1776 228 4 v 2074 1860 a FE(f)2129 1833 y Fp(0)2151 1860 y FK(\()p FE(x)2238 1874 y Fq(i)2266 1860 y FK(\))390 2022 y(Newton's)37 b(metho)s(d)e(con)m(v)m(erges)j (quadratically)g(for)e(single)g(ro)s(ots,)i(and)e(linearly)g(for)g(m)m (ultiple)390 2132 y(ro)s(ots.)3021 2335 y([Deriv)-5 b(ativ)m(e)33 b(Solv)m(er])-3599 b Fv(gsl_root_fdfsolver_sec)q(ant)390 2445 y FK(The)26 b FD(secan)m(t)h(metho)s(d)i FK(is)d(a)g(simpli\014ed) g(v)m(ersion)g(of)g(Newton's)h(metho)s(d)f(whic)m(h)f(do)s(es)h(not)g (require)390 2555 y(the)31 b(computation)g(of)f(the)h(deriv)-5 b(ativ)m(e)32 b(on)e(ev)m(ery)h(step.)390 2699 y(On)24 b(its)h(\014rst)f(iteration)i(the)f(algorithm)g(b)s(egins)f(with)h (Newton's)g(metho)s(d,)g(using)g(the)f(deriv)-5 b(ativ)m(e)390 2808 y(to)31 b(compute)g(a)g(\014rst)e(step,)1616 3033 y FE(x)1668 3047 y FB(1)1730 3033 y FK(=)c FE(x)1878 3047 y FB(0)1936 3033 y FI(\000)2048 2971 y FE(f)10 b FK(\()p FE(x)2190 2985 y FB(0)2227 2971 y FK(\))p 2037 3011 238 4 v 2037 3095 a FE(f)2092 3069 y Fp(0)2114 3095 y FK(\()p FE(x)2201 3109 y FB(0)2239 3095 y FK(\))390 3258 y(Subsequen)m(t)38 b(iterations)j(a)m(v)m(oid)f(the)g(ev)-5 b(aluation)40 b(of)g(the)f(deriv)-5 b(ativ)m(e)41 b(b)m(y)e(replacing)h (it)g(with)f(a)390 3367 y(n)m(umerical)31 b(estimate,)h(the)f(slop)s(e) f(of)h(the)f(line)h(through)f(the)g(previous)g(t)m(w)m(o)i(p)s(oin)m (ts,)1012 3591 y FE(x)1064 3605 y Fq(i)p FB(+1)1201 3591 y FK(=)25 b FE(x)1349 3605 y Fq(i)1397 3591 y FI(\000)1497 3530 y FE(f)10 b FK(\()p FE(x)1639 3544 y Fq(i)1667 3530 y FK(\))p 1497 3570 205 4 v 1531 3654 a FE(f)1586 3622 y Fp(0)1576 3671 y Fq(est)1742 3591 y FK(where)30 b FE(f)2060 3554 y Fp(0)2050 3614 y Fq(est)2167 3591 y FK(=)2273 3530 y FE(f)10 b FK(\()p FE(x)2415 3544 y Fq(i)2442 3530 y FK(\))21 b FI(\000)f FE(f)10 b FK(\()p FE(x)2731 3544 y Fq(i)p Fp(\000)p FB(1)2843 3530 y FK(\))p 2273 3570 606 4 v 2398 3654 a FE(x)2450 3668 y Fq(i)2498 3654 y FI(\000)20 b FE(x)2641 3668 y Fq(i)p Fp(\000)p FB(1)390 3814 y FK(When)44 b(the)g(deriv)-5 b(ativ)m(e)46 b(do)s(es)e(not)g(c)m (hange)i(signi\014can)m(tly)f(in)f(the)g(vicinit)m(y)i(of)e(the)g(ro)s (ot)h(the)390 3924 y(secan)m(t)28 b(metho)s(d)e(giv)m(es)j(a)e(useful)f (sa)m(ving.)40 b(Asymptotically)29 b(the)e(secan)m(t)h(metho)s(d)e(is)h (faster)g(than)390 4033 y(Newton's)38 b(metho)s(d)f(whenev)m(er)g(the)g (cost)h(of)g(ev)-5 b(aluating)38 b(the)g(deriv)-5 b(ativ)m(e)39 b(is)e(more)g(than)g(0.44)390 4143 y(times)c(the)f(cost)i(of)e(ev)-5 b(aluating)34 b(the)f(function)f(itself.)47 b(As)33 b(with)f(all)h (metho)s(ds)f(of)g(computing)h(a)390 4253 y(n)m(umerical)28 b(deriv)-5 b(ativ)m(e)29 b(the)f(estimate)h(can)f(su\013er)f(from)g (cancellation)k(errors)c(if)g(the)h(separation)390 4362 y(of)j(the)f(p)s(oin)m(ts)g(b)s(ecomes)h(to)s(o)g(small.)390 4506 y(On)j(single)i(ro)s(ots,)g(the)f(metho)s(d)f(has)h(a)g(con)m(v)m (ergence)j(of)d(order)f(\(1)24 b(+)2864 4431 y FI(p)p 2940 4431 46 4 v 75 x FK(5\))p FE(=)p FK(2)36 b(\(appro)m(ximately)390 4616 y(1)p FE(:)p FK(62\).)43 b(It)30 b(con)m(v)m(erges)i(linearly)f (for)g(m)m(ultiple)g(ro)s(ots.)3021 4819 y([Deriv)-5 b(ativ)m(e)33 b(Solv)m(er])-3599 b Fv(gsl_root_fdfsolver_ste)q(ffe)q (nson)390 4929 y FK(The)29 b FD(Ste\013enson)h(Metho)s(d)1320 4896 y FB(1)1387 4929 y FK(pro)m(vides)g(the)g(fastest)h(con)m(v)m (ergence)h(of)f(all)f(the)h(routines.)40 b(It)30 b(com-)390 5039 y(bines)c(the)g(basic)g(Newton)h(algorithm)g(with)f(an)g(Aitk)m (en)h(\\delta-squared")h(acceleration.)42 b(If)26 b(the)p 150 5154 1200 4 v 199 5221 a FB(1)275 5253 y Fx(J.F.)g(Ste\013ensen)f (\(1873{1961\).)37 b(The)26 b(sp)r(elling)h(used)e(in)g(the)g(name)g (of)i(the)d(function)i(is)g(sligh)n(tly)g(incorrect,)g(but)f(has)275 5340 y(b)r(een)g(preserv)n(ed)g(to)h(a)n(v)n(oid)g(incompatibilit)n(y) -6 b(.)p eop end %%Page: 392 410 TeXDict begin 392 409 bop 150 -116 a FK(Chapter)30 b(34:)41 b(One)30 b(dimensional)h(Ro)s(ot-Finding)1729 b(392)390 299 y(Newton)30 b(iterates)h(are)f FE(x)1251 313 y Fq(i)1309 299 y FK(then)f(the)h(acceleration)i(pro)s(cedure)d(generates)i(a)f (new)f(sequence)h FE(R)3697 313 y Fq(i)3725 299 y FK(,)1363 524 y FE(R)1432 538 y Fq(i)1485 524 y FK(=)25 b FE(x)1633 538 y Fq(i)1681 524 y FI(\000)1923 463 y FK(\()p FE(x)2010 477 y Fq(i)p FB(+1)2142 463 y FI(\000)20 b FE(x)2285 477 y Fq(i)2313 463 y FK(\))2348 430 y FB(2)p 1782 503 746 4 v 1782 586 a FK(\()p FE(x)1869 600 y Fq(i)p FB(+2)2001 586 y FI(\000)g FK(2)p FE(x)2189 600 y Fq(i)p FB(+1)2321 586 y FK(+)g FE(x)2464 600 y Fq(i)2492 586 y FK(\))390 748 y(whic)m(h)33 b(con)m(v)m(erges)j(faster)e(than)f(the)h(original)g (sequence)g(under)e(reasonable)j(conditions.)50 b(The)390 857 y(new)28 b(sequence)h(requires)f(three)h(terms)f(b)s(efore)g(it)h (can)g(pro)s(duce)e(its)i(\014rst)f(v)-5 b(alue)29 b(so)g(the)f(metho)s (d)390 967 y(returns)43 b(accelerated)k(v)-5 b(alues)45 b(on)f(the)g(second)h(and)e(subsequen)m(t)h(iterations.)84 b(On)43 b(the)i(\014rst)390 1077 y(iteration)23 b(it)g(returns)e(the)h (ordinary)f(Newton)h(estimate.)40 b(The)21 b(Newton)i(iterate)g(is)f (also)h(returned)390 1186 y(if)30 b(the)h(denominator)f(of)h(the)g (acceleration)i(term)d(ev)m(er)h(b)s(ecomes)g(zero.)390 1329 y(As)g(with)f(all)i(acceleration)h(pro)s(cedures)d(this)g(metho)s (d)g(can)h(b)s(ecome)g(unstable)g(if)f(the)h(function)390 1439 y(is)f(not)h(w)m(ell-b)s(eha)m(v)m(ed.)150 1684 y FJ(34.10)69 b(Examples)150 1843 y FK(F)-8 b(or)43 b(an)m(y)f(ro)s(ot) h(\014nding)e(algorithm)i(w)m(e)g(need)f(to)h(prepare)e(the)i(function) f(to)g(b)s(e)g(solv)m(ed.)77 b(F)-8 b(or)43 b(this)150 1953 y(example)i(w)m(e)h(will)f(use)f(the)h(general)h(quadratic)f (equation)h(describ)s(ed)d(earlier.)85 b(W)-8 b(e)46 b(\014rst)e(need)h(a)150 2062 y(header)30 b(\014le)h(\()p FH(demo_fn.h)p FK(\))d(to)j(de\014ne)f(the)h(function)f(parameters,)390 2205 y FH(struct)46 b(quadratic_params)485 2315 y({)581 2424 y(double)g(a,)h(b,)g(c;)485 2534 y(};)390 2753 y(double)f (quadratic)f(\(double)h(x,)h(void)g(*params\);)390 2863 y(double)f(quadratic_deriv)e(\(double)i(x,)h(void)f(*params\);)390 2972 y(void)h(quadratic_fdf)d(\(double)i(x,)h(void)f(*params,)1345 3082 y(double)g(*y,)h(double)f(*dy\);)150 3225 y FK(W)-8 b(e)32 b(place)f(the)f(function)h(de\014nitions)e(in)h(a)h(separate)h (\014le)e(\()p FH(demo_fn.c)p FK(\),)390 3367 y FH(double)390 3477 y(quadratic)45 b(\(double)h(x,)h(void)g(*params\))390 3587 y({)485 3696 y(struct)g(quadratic_params)c(*p)581 3806 y(=)k(\(struct)f(quadratic_params)e(*\))j(params;)485 4025 y(double)g(a)g(=)g(p->a;)485 4134 y(double)g(b)g(=)g(p->b;)485 4244 y(double)g(c)g(=)g(p->c;)485 4463 y(return)g(\(a)g(*)g(x)h(+)f (b\))g(*)h(x)f(+)h(c;)390 4573 y(})390 4792 y(double)390 4902 y(quadratic_deriv)c(\(double)h(x,)j(void)e(*params\))390 5011 y({)485 5121 y(struct)h(quadratic_params)c(*p)581 5230 y(=)k(\(struct)f(quadratic_params)e(*\))j(params;)p eop end %%Page: 393 411 TeXDict begin 393 410 bop 150 -116 a FK(Chapter)30 b(34:)41 b(One)30 b(dimensional)h(Ro)s(ot-Finding)1729 b(393)485 299 y FH(double)47 b(a)g(=)g(p->a;)485 408 y(double)g(b)g(=)g(p->b;)485 628 y(return)g(2.0)f(*)i(a)f(*)h(x)f(+)h(b;)390 737 y(})390 956 y(void)390 1066 y(quadratic_fdf)c(\(double)i(x,)h(void)g(*params,) 1106 1176 y(double)f(*y,)h(double)f(*dy\))390 1285 y({)485 1395 y(struct)h(quadratic_params)c(*p)581 1504 y(=)k(\(struct)f (quadratic_params)e(*\))j(params;)485 1724 y(double)g(a)g(=)g(p->a;)485 1833 y(double)g(b)g(=)g(p->b;)485 1943 y(double)g(c)g(=)g(p->c;)485 2162 y(*y)h(=)f(\(a)g(*)h(x)f(+)h(b\))f(*)g(x)h(+)f(c;)485 2271 y(*dy)g(=)h(2.0)f(*)g(a)h(*)f(x)h(+)f(b;)390 2381 y(})150 2529 y FK(The)36 b(\014rst)g(program)g(uses)h(the)f(function)h (solv)m(er)g FH(gsl_root_fsolver_brent)31 b FK(for)36 b(Bren)m(t's)h(metho)s(d)150 2638 y(and)30 b(the)g(general)i(quadratic) f(de\014ned)e(ab)s(o)m(v)m(e)i(to)g(solv)m(e)h(the)f(follo)m(wing)g (equation,)1744 2819 y FE(x)1796 2782 y FB(2)1853 2819 y FI(\000)20 b FK(5)26 b(=)f(0)150 3000 y(with)30 b(solution)h FE(x)25 b FK(=)874 2925 y FI(p)p 950 2925 46 4 v 75 x FK(5)h(=)f(2)p FE(:)p FK(236068)p FE(:::)390 3148 y FH(#include)46 b()390 3258 y(#include)g()390 3367 y(#include)g()390 3477 y(#include)g ()390 3696 y(#include)g("demo_fn.h")390 3806 y(#include)g("demo_fn.c")390 4025 y(int)390 4134 y(main)h(\(void\))390 4244 y({)485 4354 y(int)g(status;)485 4463 y(int)g(iter)g(=)g(0,)h(max_iter)d(=)j(100;)485 4573 y(const)f(gsl_root_fsolver_type)42 b(*T;)485 4682 y(gsl_root_fsolver)i(*s;)485 4792 y(double)j(r)g(=)g(0,)h(r_expected)d (=)i(sqrt)g(\(5.0\);)485 4902 y(double)g(x_lo)f(=)i(0.0,)e(x_hi)h(=)g (5.0;)485 5011 y(gsl_function)e(F;)485 5121 y(struct)i (quadratic_params)c(params)j(=)h({1.0,)g(0.0,)f(-5.0};)485 5340 y(F.function)f(=)j(&quadratic;)p eop end %%Page: 394 412 TeXDict begin 394 411 bop 150 -116 a FK(Chapter)30 b(34:)41 b(One)30 b(dimensional)h(Ro)s(ot-Finding)1729 b(394)485 299 y FH(F.params)46 b(=)h(¶ms;)485 518 y(T)h(=)f (gsl_root_fsolver_brent;)485 628 y(s)h(=)f(gsl_root_fsolver_alloc)42 b(\(T\);)485 737 y(gsl_root_fsolver_set)h(\(s,)k(&F,)g(x_lo,)f(x_hi\);) 485 956 y(printf)h(\("using)e(\045s)j(method\\n",)867 1066 y(gsl_root_fsolver_name)42 b(\(s\)\);)485 1285 y(printf)47 b(\("\0455s)f([\0459s,)g(\0459s])h(\0459s)g(\04510s)f(\0459s\\n",)867 1395 y("iter",)g("lower",)g("upper",)f("root",)867 1504 y("err",)h("err\(est\)"\);)485 1724 y(do)581 1833 y({)676 1943 y(iter++;)676 2052 y(status)g(=)i(gsl_root_fsolver_iterate)41 b(\(s\);)676 2162 y(r)48 b(=)f(gsl_root_fsolver_root)42 b(\(s\);)676 2271 y(x_lo)47 b(=)g(gsl_root_fsolver_x_lower)42 b(\(s\);)676 2381 y(x_hi)47 b(=)g(gsl_root_fsolver_x_upper)42 b(\(s\);)676 2491 y(status)k(=)i(gsl_root_test_interval)42 b(\(x_lo,)k(x_hi,)2251 2600 y(0,)i(0.001\);)676 2819 y(if)g(\(status)d(==)j(GSL_SUCCESS\))772 2929 y(printf)e (\("Converged:\\n"\);)676 3148 y(printf)g(\("\0455d)h([\045.7f,)f (\045.7f])g(\045.7f)h(\045+.7f)f(\045.7f\\n",)1058 3258 y(iter,)h(x_lo,)f(x_hi,)1058 3367 y(r,)h(r)h(-)f(r_expected,)1058 3477 y(x_hi)g(-)g(x_lo\);)581 3587 y(})485 3696 y(while)g(\(status)f (==)h(GSL_CONTINUE)d(&&)j(iter)g(<)h(max_iter\);)485 3915 y(gsl_root_fsolver_free)42 b(\(s\);)485 4134 y(return)47 b(status;)390 4244 y(})150 4411 y FK(Here)31 b(are)g(the)f(results)g (of)h(the)f(iterations,)390 4555 y Fz($)39 b(./a.out)390 4643 y(using)h(brent)h(method)429 4730 y(iter)f([)157 b(lower,)198 b(upper])237 b(root)314 b(err)80 b(err\(est\))547 4817 y(1)39 b([1.0000000,)j(5.0000000])g(1.0000000)f(-1.2360680)g (4.0000000)547 4904 y(2)e([1.0000000,)j(3.0000000])g(3.0000000)f (+0.7639320)g(2.0000000)547 4991 y(3)e([2.0000000,)j(3.0000000])g (2.0000000)f(-0.2360680)g(1.0000000)547 5078 y(4)e([2.2000000,)j (3.0000000])g(2.2000000)f(-0.0360680)g(0.8000000)547 5166 y(5)e([2.2000000,)j(2.2366300])g(2.2366300)f(+0.0005621)g (0.0366300)390 5253 y(Converged:)547 5340 y(6)e([2.2360634,)j (2.2366300])g(2.2360634)f(-0.0000046)g(0.0005666)p eop end %%Page: 395 413 TeXDict begin 395 412 bop 150 -116 a FK(Chapter)30 b(34:)41 b(One)30 b(dimensional)h(Ro)s(ot-Finding)1729 b(395)150 299 y(If)23 b(the)h(program)f(is)g(mo)s(di\014ed)g(to)h(use)f(the)h (bisection)g(solv)m(er)h(instead)e(of)h(Bren)m(t's)g(metho)s(d,)h(b)m (y)e(c)m(hanging)150 408 y FH(gsl_root_fsolver_brent)e FK(to)27 b FH(gsl_root_fsolver_bisectio)o(n)21 b FK(the)27 b(slo)m(w)m(er)h(con)m(v)m(ergence)h(of)e(the)150 518 y(Bisection)32 b(metho)s(d)e(can)h(b)s(e)e(observ)m(ed,)390 652 y Fz($)39 b(./a.out)390 739 y(using)h(bisection)i(method)429 826 y(iter)e([)157 b(lower,)198 b(upper])237 b(root)314 b(err)80 b(err\(est\))547 913 y(1)39 b([0.0000000,)j(2.5000000])g (1.2500000)f(-0.9860680)g(2.5000000)547 1000 y(2)e([1.2500000,)j (2.5000000])g(1.8750000)f(-0.3610680)g(1.2500000)547 1088 y(3)e([1.8750000,)j(2.5000000])g(2.1875000)f(-0.0485680)g (0.6250000)547 1175 y(4)e([2.1875000,)j(2.5000000])g(2.3437500)f (+0.1076820)g(0.3125000)547 1262 y(5)e([2.1875000,)j(2.3437500])g (2.2656250)f(+0.0295570)g(0.1562500)547 1349 y(6)e([2.1875000,)j (2.2656250])g(2.2265625)f(-0.0095055)g(0.0781250)547 1436 y(7)e([2.2265625,)j(2.2656250])g(2.2460938)f(+0.0100258)g (0.0390625)547 1523 y(8)e([2.2265625,)j(2.2460938])g(2.2363281)f (+0.0002601)g(0.0195312)547 1611 y(9)e([2.2265625,)j(2.2363281])g 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(-5.0};)485 4354 y(FDF.f)h(=)g(&quadratic;)485 4463 y(FDF.df)g(=)g (&quadratic_deriv;)485 4573 y(FDF.fdf)f(=)i(&quadratic_fdf;)485 4682 y(FDF.params)d(=)j(¶ms;)485 4902 y(T)g(=)f (gsl_root_fdfsolver_newton;)485 5011 y(s)h(=)f (gsl_root_fdfsolver_alloc)42 b(\(T\);)485 5121 y (gsl_root_fdfsolver_set)g(\(s,)47 b(&FDF,)f(x\);)485 5340 y(printf)h(\("using)e(\045s)j(method\\n",)p eop end %%Page: 396 414 TeXDict begin 396 413 bop 150 -116 a FK(Chapter)30 b(34:)41 b(One)30 b(dimensional)h(Ro)s(ot-Finding)1729 b(396)867 299 y FH(gsl_root_fdfsolver_name)42 b(\(s\)\);)485 518 y(printf)47 b(\("\045-5s)f(\04510s)g(\04510s)h(\04510s\\n",)867 628 y("iter",)f("root",)g("err",)g("err\(est\)"\);)485 737 y(do)581 847 y({)676 956 y(iter++;)676 1066 y(status)g(=)i (gsl_root_fdfsolver_itera)o(te)42 b(\(s\);)676 1176 y(x0)48 b(=)f(x;)676 1285 y(x)h(=)f(gsl_root_fdfsolver_root)42 b(\(s\);)676 1395 y(status)k(=)i(gsl_root_test_delta)42 b(\(x,)47 b(x0,)g(0,)g(1e-3\);)676 1614 y(if)h(\(status)d(==)j 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b(iterate)h(and)e(next)h(iterate)i (rather)d(than)h(the)g(previous)f(iterate.)40 b(The)21 b(other)h(deriv)-5 b(ativ)m(e)23 b(solv)m(ers)150 4100 y(can)39 b(b)s(e)f(in)m(v)m(estigated)j(b)m(y)e(c)m(hanging)g FH(gsl_root_fdfsolver_newton)32 b FK(to)39 b FH(gsl_root_fdfsolver_)150 4209 y(secant)29 b FK(or)h FH(gsl_root_fdfsolver_steff)o(enso)o(n)p FK(.)150 4442 y FJ(34.11)69 b(References)46 b(and)e(F)-11 b(urther)45 b(Reading)150 4601 y FK(F)-8 b(or)31 b(information)g(on)f (the)h(Bren)m(t-Dekk)m(er)h(algorithm)g(see)f(the)f(follo)m(wing)i(t)m (w)m(o)g(pap)s(ers,)330 4736 y(R.)h(P)-8 b(.)33 b(Bren)m(t,)h(\\An)f (algorithm)h(with)e(guaran)m(teed)i(con)m(v)m(ergence)h(for)e (\014nding)e(a)i(zero)h(of)e(a)i(func-)330 4845 y(tion",)e FD(Computer)d(Journal)p FK(,)h(14)h(\(1971\))i(422{425)330 4980 y(J.)22 b(C.)g(P)-8 b(.)22 b(Bus)g(and)f(T.)h(J.)g(Dekk)m(er,)j (\\Tw)m(o)d(E\016cien)m(t)h(Algorithms)g(with)e(Guaran)m(teed)i(Con)m (v)m(ergence)330 5089 y(for)31 b(Finding)h(a)g(Zero)g(of)f(a)i(F)-8 b(unction",)33 b FD(A)m(CM)f(T)-8 b(ransactions)33 b(of)e(Mathematical) k(Soft)m(w)m(are)p FK(,)e(V)-8 b(ol.)330 5199 y(1)31 b(No.)g(4)g(\(1975\))i(330{345)p eop end %%Page: 397 415 TeXDict begin 397 414 bop 150 -116 a FK(Chapter)30 b(35:)41 b(One)30 b(dimensional)h(Minimization)1735 b(397)150 299 y FG(35)80 b(One)53 b(dimensional)g(Minimization)150 535 y FK(This)31 b(c)m(hapter)h(describ)s(es)g(routines)f(for)h (\014nding)e(minima)i(of)g(arbitrary)g(one-dimensional)g(functions.)150 645 y(The)d(library)g(pro)m(vides)g(lo)m(w)h(lev)m(el)h(comp)s(onen)m (ts)e(for)g(a)h(v)-5 b(ariet)m(y)30 b(of)g(iterativ)m(e)i(minimizers)d (and)f(con)m(v)m(er-)150 755 y(gence)36 b(tests.)53 b(These)35 b(can)g(b)s(e)e(com)m(bined)i(b)m(y)f(the)h(user)f(to)h(ac)m(hiev)m(e)i (the)e(desired)f(solution,)i(with)e(full)150 864 y(access)k(to)g(the)f (in)m(termediate)i(steps)e(of)g(the)g(algorithms.)61 b(Eac)m(h)38 b(class)g(of)f(metho)s(ds)f(uses)g(the)i(same)150 974 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b(new)f(p)s(oin)m(t)h(also)h(allo)m(ws)g(the)f(size)h(of)f (the)g(b)s(ounded)e(in)m(terv)-5 b(al)150 4657 y(to)38 b(b)s(e)e(reduced,)j(b)m(y)d(c)m(ho)s(osing)i(the)g(most)f(compact)h (set)g(of)f(p)s(oin)m(ts)g(whic)m(h)g(satis\014es)h(the)f(constrain)m (t)150 4766 y FE(f)10 b FK(\()p FE(a)p FK(\))25 b FE(>)g(f)10 b FK(\()p FE(x)p FK(\))25 b FE(<)g(f)10 b FK(\()p FE(b)p FK(\).)40 b(The)27 b(in)m(terv)-5 b(al)28 b(is)g(reduced)e(un)m(til)i (it)f(encloses)i(the)e(true)g(minim)m(um)g(to)h(a)f(desired)150 4876 y(tolerance.)67 b(This)37 b(pro)m(vides)i(a)g(b)s(est)f(estimate)i (of)f(the)f(lo)s(cation)i(of)f(the)f(minim)m(um)g(and)g(a)h(rigorous) 150 4986 y(error)30 b(estimate.)275 5121 y(Sev)m(eral)25 b(brac)m(k)m(eting)i(algorithms)e(are)g(a)m(v)-5 b(ailable)27 b(within)d(a)i(single)f(framew)m(ork.)39 b(The)24 b(user)g(pro)m(vides) 150 5230 y(a)46 b(high-lev)m(el)h(driv)m(er)e(for)g(the)g(algorithm,)51 b(and)44 b(the)i(library)f(pro)m(vides)g(the)h(individual)e(functions) 150 5340 y(necessary)27 b(for)f(eac)m(h)h(of)g(the)f(steps.)39 b(There)26 b(are)h(three)f(main)h(phases)e(of)i(the)f(iteration.)41 b(The)26 b(steps)g(are,)p eop end %%Page: 398 416 TeXDict begin 398 415 bop 150 -116 a FK(Chapter)30 b(35:)41 b(One)30 b(dimensional)h(Minimization)1735 b(398)225 299 y FI(\017)60 b FK(initialize)33 b(minimizer)d(state,)i FD(s)p FK(,)f(for)f(algorithm)h FD(T)225 438 y FI(\017)60 b FK(up)s(date)30 b FD(s)j FK(using)d(the)h(iteration)h FD(T)225 577 y FI(\017)60 b FK(test)31 b FD(s)j FK(for)c(con)m(v)m (ergence,)j(and)d(rep)s(eat)h(iteration)h(if)e(necessary)150 751 y(The)j(state)h(for)f(the)g(minimizers)g(is)g(held)g(in)g(a)g FH(gsl_min_fminimizer)c FK(struct.)48 b(The)33 b(up)s(dating)f(pro-)150 861 y(cedure)e(uses)g(only)h(function)f(ev)-5 b(aluations)31 b(\(not)g(deriv)-5 b(ativ)m(es\).)150 1108 y FJ(35.2)68 b(Ca)l(v)l(eats)150 1267 y FK(Note)31 b(that)f(minimization)h (functions)e(can)h(only)g(searc)m(h)g(for)f(one)h(minim)m(um)f(at)h(a)g (time.)41 b(When)30 b(there)150 1377 y(are)41 b(sev)m(eral)h(minima)f (in)g(the)g(searc)m(h)g(area,)k(the)c(\014rst)f(minim)m(um)g(to)i(b)s (e)e(found)f(will)j(b)s(e)e(returned;)150 1486 y(ho)m(w)m(ev)m(er)33 b(it)g(is)f(di\016cult)g(to)h(predict)f(whic)m(h)g(of)g(the)g(minima)g (this)g(will)g(b)s(e.)45 b Fg(In)34 b(most)i(c)-5 b(ases,)35 b(no)f(err)-5 b(or)150 1596 y(wil)5 b(l)33 b(b)-5 b(e)32 b(r)-5 b(ep)g(orte)g(d)36 b(if)c(you)h(try)g(to)h(\014nd)f(a)g(minimum) g(in)f(an)i(ar)-5 b(e)g(a)34 b(wher)-5 b(e)34 b(ther)-5 b(e)33 b(is)g(mor)-5 b(e)33 b(than)h(one.)275 1740 y FK(With)40 b(all)i(minimization)f(algorithms)h(it)f(can)f(b)s(e)g (di\016cult)h(to)g(determine)f(the)h(lo)s(cation)h(of)f(the)150 1849 y(minim)m(um)e(to)i(full)e(n)m(umerical)i(precision.)69 b(The)39 b(b)s(eha)m(vior)h(of)g(the)g(function)g(in)f(the)h(region)h (of)f(the)150 1959 y(minim)m(um)30 b FE(x)609 1926 y Fp(\003)677 1959 y FK(can)h(b)s(e)e(appro)m(ximated)i(b)m(y)g(a)f(T)-8 b(a)m(ylor)32 b(expansion,)1360 2174 y FE(y)c FK(=)d FE(f)10 b FK(\()p FE(x)1671 2136 y Fp(\003)1709 2174 y FK(\))21 b(+)1866 2112 y(1)p 1866 2152 46 4 v 1866 2236 a(2)1921 2174 y FE(f)1976 2136 y Fp(00)2018 2174 y FK(\()p FE(x)2105 2136 y Fp(\003)2143 2174 y FK(\)\()p FE(x)g FI(\000)f FE(x)2429 2136 y Fp(\003)2467 2174 y FK(\))2502 2136 y FB(2)150 2376 y FK(and)36 b(the)g(second)g(term)h(of) f(this)g(expansion)g(can)h(b)s(e)e(lost)i(when)e(added)h(to)h(the)f (\014rst)g(term)g(at)h(\014nite)150 2485 y(precision.)69 b(This)39 b(magni\014es)h(the)g(error)g(in)f(lo)s(cating)i FE(x)2140 2452 y Fp(\003)2179 2485 y FK(,)h(making)e(it)g(prop)s (ortional)g(to)3330 2420 y FI(p)p 3405 2420 37 4 v 3405 2485 a FE(\017)g FK(\(where)150 2595 y FE(\017)35 b FK(is)g(the)g (relativ)m(e)i(accuracy)f(of)f(the)h(\015oating)f(p)s(oin)m(t)g(n)m(um) m(b)s(ers\).)54 b(F)-8 b(or)36 b(functions)e(with)h(higher)f(order)150 2705 y(minima,)c(suc)m(h)g(as)g FE(x)871 2672 y FB(4)909 2705 y FK(,)g(the)g(magni\014cation)i(of)e(the)g(error)g(is)g(corresp)s (ondingly)f(w)m(orse.)41 b(The)30 b(b)s(est)f(that)150 2814 y(can)38 b(b)s(e)e(ac)m(hiev)m(ed)j(is)f(to)g(con)m(v)m(erge)h(to) f(the)f(limit)h(of)g(n)m(umerical)g(accuracy)g(in)f(the)g(function)g(v) -5 b(alues,)150 2924 y(rather)30 b(than)g(the)h(lo)s(cation)h(of)e(the) h(minim)m(um)f(itself.)150 3171 y FJ(35.3)68 b(Initializing)47 b(the)e(Minimizer)3350 3389 y FK([F)-8 b(unction])-3599 b Fv(gsl_min_fminimizer)58 b(*)52 b(gsl_min_fminimizer_al)q(loc)g Fu(\()p FD(const)565 3499 y(gsl)p 677 3499 28 4 v 41 w(min)p 870 3499 V 39 w(fminimizer)p 1331 3499 V 40 w(t)m(yp)s(e)31 b(*)f Ft(T)p Fu(\))390 3609 y FK(This)h(function)h(returns)f(a)h(p)s (oin)m(ter)h(to)f(a)h(newly)f(allo)s(cated)i(instance)f(of)f(a)g (minimizer)g(of)h(t)m(yp)s(e)390 3718 y FD(T)p FK(.)39 b(F)-8 b(or)28 b(example,)h(the)e(follo)m(wing)i(co)s(de)e(creates)h (an)f(instance)h(of)f(a)h(golden)f(section)i(minimizer,)630 3862 y FH(const)46 b(gsl_min_fminimizer_type)c(*)47 b(T)725 3972 y(=)h(gsl_min_fminimizer_golde)o(nsec)o(tio)o(n;)630 4081 y(gsl_min_fminimizer)43 b(*)k(s)725 4191 y(=)h (gsl_min_fminimizer_alloc)41 b(\(T\);)390 4335 y FK(If)c(there)h(is)g (insu\016cien)m(t)g(memory)g(to)h(create)g(the)f(minimizer)g(then)f (the)h(function)g(returns)f(a)390 4445 y(n)m(ull)30 b(p)s(oin)m(ter)h (and)e(the)i(error)f(handler)g(is)g(in)m(v)m(ok)m(ed)i(with)e(an)g (error)g(co)s(de)h(of)f FH(GSL_ENOMEM)p FK(.)3350 4648 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_min_fminimizer_se)q(t)e Fu(\()p FD(gsl)p 1702 4648 V 41 w(min)p 1895 4648 V 40 w(fminimizer)30 b(*)h Ft(s)p FD(,)g(gsl)p 2677 4648 V 40 w(function)f(*)565 4758 y Ft(f)p FD(,)h(double)f Ft(x_minimum)p FD(,)j(double)d Ft(x_lower)p FD(,)j(double)d Ft(x_upper)p Fu(\))390 4867 y FK(This)35 b(function)h(sets,)i(or)e(resets,)i(an)e (existing)g(minimizer)h FD(s)i FK(to)e(use)e(the)i(function)e FD(f)53 b FK(and)36 b(the)390 4977 y(initial)25 b(searc)m(h)f(in)m (terv)-5 b(al)24 b([)p FD(x)p 1315 4977 V 40 w(lo)m(w)m(er)p FK(,)j FD(x)p 1661 4977 V 40 w(upp)s(er)7 b FK(],)23 b(with)g(a)g(guess)h(for)f(the)h(lo)s(cation)h(of)e(the)h(minim)m(um) 390 5086 y FD(x)p 444 5086 V 40 w(minim)m(um)p FK(.)390 5230 y(If)30 b(the)g(in)m(terv)-5 b(al)32 b(giv)m(en)f(do)s(es)f(not)h (con)m(tain)g(a)g(minim)m(um,)f(then)g(the)g(function)g(returns)f(an)h (error)390 5340 y(co)s(de)h(of)f FH(GSL_EINVAL)p FK(.)p eop end %%Page: 399 417 TeXDict begin 399 416 bop 150 -116 a FK(Chapter)30 b(35:)41 b(One)30 b(dimensional)h(Minimization)1735 b(399)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_min_fminimizer_se)q (t_wi)q(th_)q(val)q(ues)f Fu(\()p FD(gsl)p 2330 299 28 4 v 41 w(min)p 2523 299 V 39 w(fminimizer)31 b(*)f Ft(s)p FD(,)565 408 y(gsl)p 677 408 V 41 w(function)g(*)g Ft(f)p FD(,)h(double)f Ft(x_minimum)p FD(,)k(double)29 b Ft(f_minimum)p FD(,)34 b(double)c Ft(x_lower)p FD(,)565 518 y(double)g Ft(f_lower)p FD(,)j(double)d Ft(x_upper)p FD(,)i(double)e Ft(f_upper)p Fu(\))390 628 y FK(This)66 b(function)g(is)g(equiv)-5 b(alen)m(t)68 b(to)g FH(gsl_min_fminimizer_set)60 b FK(but)66 b(uses)g(the)h(v)-5 b(alues)390 737 y FD(f)p 424 737 V 40 w(minim)m(um)p FK(,)39 b FD(f)p 933 737 V 40 w(lo)m(w)m(er)46 b FK(and)37 b FD(f)p 1437 737 V 40 w(upp)s(er)42 b FK(instead)d(of)f (computing)g FH(f\(x_minimum\))p FK(,)f FH(f\(x_lower\))390 847 y FK(and)30 b FH(f\(x_upper\))p FK(.)3350 1032 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_min_fminimizer_free)e Fu(\()p FD(gsl)p 1807 1032 V 41 w(min)p 2000 1032 V 39 w(fminimizer)31 b(*)f Ft(s)p Fu(\))390 1142 y FK(This)g(function)g (frees)g(all)h(the)g(memory)f(asso)s(ciated)i(with)e(the)h(minimizer)f FD(s)p FK(.)3350 1327 y([F)-8 b(unction])-3599 b Fv(const)54 b(char)f(*)g(gsl_min_fminimizer_nam)q(e)e Fu(\()p FD(const)32 b(gsl)p 2464 1327 V 40 w(min)p 2656 1327 V 40 w(fminimizer)e(*)565 1437 y Ft(s)p Fu(\))390 1546 y FK(This)g(function)g(returns)f(a)i(p)s (oin)m(ter)f(to)h(the)g(name)f(of)h(the)f(minimizer.)41 b(F)-8 b(or)31 b(example,)630 1681 y FH(printf)46 b(\("s)h(is)g(a)h ('\045s')e(minimizer\\n",)1012 1791 y(gsl_min_fminimizer_name)41 b(\(s\)\);)390 1926 y FK(w)m(ould)30 b(prin)m(t)g(something)h(lik)m(e)h FH(s)e(is)f(a)h('brent')f(minimizer)p FK(.)150 2159 y FJ(35.4)68 b(Pro)l(viding)46 b(the)f(function)g(to)g(minimize)150 2318 y FK(Y)-8 b(ou)35 b(m)m(ust)f(pro)m(vide)g(a)g(con)m(tin)m(uous)h (function)f(of)g(one)g(v)-5 b(ariable)35 b(for)f(the)g(minimizers)g(to) h(op)s(erate)g(on.)150 2428 y(In)29 b(order)f(to)i(allo)m(w)h(for)e (general)h(parameters)g(the)f(functions)g(are)h(de\014ned)e(b)m(y)h(a)g FH(gsl_function)d FK(data)150 2537 y(t)m(yp)s(e)31 b(\(see)g(Section)g (34.4)h([Pro)m(viding)f(the)f(function)h(to)g(solv)m(e],)h(page)f (386\).)150 2771 y FJ(35.5)68 b(Iteration)150 2930 y FK(The)32 b(follo)m(wing)i(functions)e(driv)m(e)g(the)h(iteration)h(of) e(eac)m(h)i(algorithm.)48 b(Eac)m(h)33 b(function)f(p)s(erforms)f(one) 150 3040 y(iteration)23 b(to)e(up)s(date)f(the)i(state)g(of)f(an)m(y)g 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b(algorithm)h(could)f(not)h(impro)m(v)m(e)f(the)h (curren)m(t)e(b)s(est)h(appro)m(ximation)h(or)870 4422 y(b)s(ounding)29 b(in)m(terv)-5 b(al.)275 4607 y(The)31 b(minimizer)g(main)m(tains)h(a)g(curren)m(t)g(b)s(est)f(estimate)i(of)f (the)f(p)s(osition)h(of)f(the)h(minim)m(um)f(at)h(all)150 4716 y(times,)i(and)e(the)h(curren)m(t)g(in)m(terv)-5 b(al)34 b(b)s(ounding)d(the)i(minim)m(um.)47 b(This)32 b(information)h(can)g(b)s(e)f(accessed)150 4826 y(with)e(the)h(follo)m (wing)g(auxiliary)h(functions,)3350 5011 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_min_fminimizer_x_m)q(ini)q(mum)e Fu(\()p FD(const)31 b(gsl)p 2411 5011 V 41 w(min)p 2604 5011 V 39 w(fminimizer)g(*)565 5121 y Ft(s)p Fu(\))390 5230 y FK(This)38 b(function)g(returns)f(the)i(curren)m(t)g(estimate)h (of)f(the)f(p)s(osition)h(of)g(the)g(minim)m(um)e(for)i(the)390 5340 y(minimizer)30 b FD(s)p FK(.)p eop end %%Page: 400 418 TeXDict begin 400 417 bop 150 -116 a FK(Chapter)30 b(35:)41 b(One)30 b(dimensional)h(Minimization)1735 b(400)3350 299 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_min_fminimizer_x_u)q (ppe)q(r)d Fu(\()p FD(const)32 b(gsl)p 2307 299 28 4 v 40 w(min)p 2499 299 V 40 w(fminimizer)e(*)h Ft(s)p Fu(\))3350 408 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_min_fminimizer_x_l)q(owe)q(r)d Fu(\()p FD(const)32 b(gsl)p 2307 408 V 40 w(min)p 2499 408 V 40 w(fminimizer)e(*)h Ft(s)p Fu(\))390 518 y FK(These)41 b(functions)g(return)g(the)g(curren) m(t)h(upp)s(er)d(and)i(lo)m(w)m(er)i(b)s(ound)c(of)j(the)g(in)m(terv)-5 b(al)42 b(for)g(the)390 628 y(minimizer)30 b FD(s)p FK(.)3350 840 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_min_fminimizer_f_m)q (ini)q(mum)e Fu(\()p FD(const)31 b(gsl)p 2411 840 V 41 w(min)p 2604 840 V 39 w(fminimizer)g(*)565 950 y Ft(s)p Fu(\))3350 1059 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_min_fminimizer_f_u)q(ppe)q(r)d Fu(\()p FD(const)32 b(gsl)p 2307 1059 V 40 w(min)p 2499 1059 V 40 w(fminimizer)e(*)h Ft(s)p Fu(\))3350 1169 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_min_fminimizer_f_l)q(owe)q(r)d Fu(\()p FD(const)32 b(gsl)p 2307 1169 V 40 w(min)p 2499 1169 V 40 w(fminimizer)e(*)h Ft(s)p Fu(\))390 1279 y FK(These)f(functions)h (return)e(the)i(v)-5 b(alue)31 b(of)g(the)g(function)f(at)i(the)e (curren)m(t)h(estimate)h(of)f(the)g(mini-)390 1388 y(m)m(um)f(and)g(at) h(the)f(upp)s(er)f(and)g(lo)m(w)m(er)j(b)s(ounds)c(of)j(the)f(in)m (terv)-5 b(al)32 b(for)e(the)g(minimizer)h FD(s)p FK(.)150 1642 y FJ(35.6)68 b(Stopping)45 b(P)l(arameters)150 1801 y FK(A)30 b(minimization)i(pro)s(cedure)d(should)h(stop)g(when)f(one)i (of)g(the)f(follo)m(wing)i(conditions)f(is)f(true:)225 1950 y FI(\017)60 b FK(A)30 b(minim)m(um)g(has)g(b)s(een)g(found)f(to)i (within)f(the)g(user-sp)s(eci\014ed)g(precision.)225 2091 y FI(\017)60 b FK(A)30 b(user-sp)s(eci\014ed)g(maxim)m(um)g(n)m (um)m(b)s(er)f(of)i(iterations)g(has)g(b)s(een)e(reac)m(hed.)225 2233 y FI(\017)60 b FK(An)30 b(error)g(has)g(o)s(ccurred.)150 2414 y(The)f(handling)h(of)g(these)g(conditions)h(is)f(under)e(user)i (con)m(trol.)42 b(The)29 b(function)h(b)s(elo)m(w)g(allo)m(ws)h(the)g (user)150 2523 y(to)g(test)g(the)g(precision)f(of)h(the)g(curren)m(t)f (result.)3350 2736 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_min_test_interval)f Fu(\()p FD(double)30 b Ft(x_lower)p FD(,)j(double)d Ft(x_upper)p FD(,)565 2845 y(double)g Ft(epsabs)p FD(,)i(double)e Ft(epsrel)p Fu(\))390 2955 y FK(This)21 b(function)h(tests)h(for)f(the)h(con)m(v)m(ergence)h(of)f (the)f(in)m(terv)-5 b(al)24 b([)p FD(x)p 2560 2955 V 40 w(lo)m(w)m(er)p FK(,)h FD(x)p 2904 2955 V 40 w(upp)s(er)7 b FK(])20 b(with)i(absolute)390 3065 y(error)30 b FD(epsabs)k FK(and)29 b(relativ)m(e)k(error)d FD(epsrel)p FK(.)41 b(The)30 b(test)h(returns)e FH(GSL_SUCCESS)f FK(if)i(the)g(follo)m (wing)390 3174 y(condition)h(is)f(ac)m(hiev)m(ed,)1227 3356 y FI(j)p FE(a)20 b FI(\000)g FE(b)p FI(j)26 b FE(<)f Fg(epsabs)c FK(+)f Fg(epsr)-5 b(el)41 b FK(min)o(\()p FI(j)p FE(a)p FI(j)p FE(;)15 b FI(j)p FE(b)p FI(j)p FK(\))390 3538 y(when)33 b(the)i(in)m(terv)-5 b(al)36 b FE(x)c FK(=)g([)p FE(a;)15 b(b)p FK(])35 b(do)s(es)f(not)h(include)f(the)h (origin.)53 b(If)34 b(the)h(in)m(terv)-5 b(al)36 b(includes)e(the)390 3647 y(origin)h(then)f(min\()p FI(j)p FE(a)p FI(j)p FE(;)15 b FI(j)p FE(b)p FI(j)p FK(\))37 b(is)d(replaced)i(b)m(y)e(zero)i (\(whic)m(h)e(is)h(the)g(minim)m(um)f(v)-5 b(alue)35 b(of)g FI(j)p FE(x)p FI(j)g FK(o)m(v)m(er)390 3757 y(the)30 b(in)m(terv)-5 b(al\).)42 b(This)30 b(ensures)f(that)i(the)f(relativ)m (e)i(error)e(is)g(accurately)i(estimated)f(for)f(minima)390 3867 y(close)i(to)f(the)f(origin.)390 4015 y(This)i(condition)h(on)f (the)h(in)m(terv)-5 b(al)34 b(also)f(implies)g(that)g(an)m(y)g (estimate)i(of)d(the)h(minim)m(um)f FE(x)3579 4029 y Fq(m)3674 4015 y FK(in)390 4125 y(the)f(in)m(terv)-5 b(al)31 b(satis\014es)g(the)g(same)f(condition)h(with)f(resp)s(ect)h (to)g(the)f(true)h(minim)m(um)e FE(x)3430 4092 y Fp(\003)3430 4147 y Fq(m)3493 4125 y FK(,)1331 4307 y FI(j)p FE(x)1408 4321 y Fq(m)1491 4307 y FI(\000)20 b FE(x)1634 4269 y Fp(\003)1634 4329 y Fq(m)1697 4307 y FI(j)26 b FE(<)f Fg(epsabs)c FK(+)f Fg(epsr)-5 b(el)25 b FE(x)2506 4269 y Fp(\003)2506 4329 y Fq(m)390 4489 y FK(assuming)30 b(that)h(the)f(true)h(minim)m(um)e FE(x)1789 4456 y Fp(\003)1789 4511 y Fq(m)1883 4489 y FK(is)h(con)m(tained)i(within)d(the)i(in)m (terv)-5 b(al.)150 4742 y FJ(35.7)68 b(Minimization)46 b(Algorithms)150 4902 y FK(The)36 b(minimization)i(algorithms)g (describ)s(ed)e(in)h(this)g(section)h(require)e(an)h(initial)h(in)m (terv)-5 b(al)38 b(whic)m(h)f(is)150 5011 y(guaran)m(teed)31 b(to)g(con)m(tain)g(a)f(minim)m(um|if)f FE(a)h FK(and)f FE(b)h FK(are)g(the)h(endp)s(oin)m(ts)e(of)h(the)g(in)m(terv)-5 b(al)31 b(and)e FE(x)h FK(is)g(an)150 5121 y(estimate)35 b(of)f(the)f(minim)m(um)g(then)g FE(f)10 b FK(\()p FE(a)p FK(\))30 b FE(>)g(f)10 b FK(\()p FE(x)p FK(\))30 b FE(<)f(f)10 b FK(\()p FE(b)p FK(\).)50 b(This)32 b(ensures)h(that)h(the)f(function) g(has)g(at)150 5230 y(least)h(one)f(minim)m(um)f(somewhere)h(in)f(the)h (in)m(terv)-5 b(al.)50 b(If)32 b(a)h(v)-5 b(alid)33 b(initial)h(in)m (terv)-5 b(al)34 b(is)f(used)f(then)g(these)150 5340 y(algorithm)f(cannot)g(fail,)h(pro)m(vided)e(the)g(function)g(is)h(w)m (ell-b)s(eha)m(v)m(ed.)p eop end %%Page: 401 419 TeXDict begin 401 418 bop 150 -116 a FK(Chapter)30 b(35:)41 b(One)30 b(dimensional)h(Minimization)1735 b(401)3298 299 y([Minimizer])-3599 b Fv(gsl_min_fminimizer_gol)q(den)q(sect)q(ion) 390 408 y FK(The)28 b FD(golden)h(section)h(algorithm)f FK(is)g(the)g(simplest)f(metho)s(d)g(of)h(brac)m(k)m(eting)h(the)f (minim)m(um)f(of)h(a)390 518 y(function.)40 b(It)27 b(is)h(the)g(slo)m (w)m(est)i(algorithm)e(pro)m(vided)g(b)m(y)f(the)h(library)-8 b(,)29 b(with)e(linear)h(con)m(v)m(ergence.)390 657 y(On)23 b(eac)m(h)j(iteration,)h(the)d(algorithm)h(\014rst)f(compares)g(the)h (subin)m(terv)-5 b(als)24 b(from)f(the)i(endp)s(oin)m(ts)e(to)390 767 y(the)k(curren)m(t)f(minim)m(um.)38 b(The)26 b(larger)h(subin)m (terv)-5 b(al)26 b(is)h(divided)e(in)h(a)h(golden)g(section)h(\(using)e (the)390 877 y(famous)33 b(ratio)i(\(3)23 b FI(\000)1121 802 y(p)p 1197 802 46 4 v 75 x FK(5\))p FE(=)p FK(2)32 b(=)f(0)p FE(:)p FK(3819660)6 b(.)25 b(.)e(.)11 b(\))34 b(and)f(the)h(v)-5 b(alue)34 b(of)f(the)h(function)g(at)g(this)f(new) 390 986 y(p)s(oin)m(t)f(is)h(calculated.)49 b(The)32 b(new)g(v)-5 b(alue)33 b(is)f(used)g(with)g(the)h(constrain)m(t)h FE(f)10 b FK(\()p FE(a)3048 953 y Fp(0)3071 986 y FK(\))29 b FE(>)f(f)10 b FK(\()p FE(x)3376 953 y Fp(0)3399 986 y FK(\))29 b FE(<)g(f)10 b FK(\()p FE(b)3692 953 y Fp(0)3715 986 y FK(\))390 1096 y(to)28 b(a)f(select)i(new)d(in)m(terv)-5 b(al)28 b(con)m(taining)h(the)e(minim)m(um,)g(b)m(y)g(discarding)f(the) h(least)i(useful)d(p)s(oin)m(t.)390 1205 y(This)36 b(pro)s(cedure)g (can)i(b)s(e)e(con)m(tin)m(ued)i(inde\014nitely)f(un)m(til)h(the)f(in)m (terv)-5 b(al)38 b(is)f(su\016cien)m(tly)h(small.)390 1315 y(Cho)s(osing)25 b(the)h(golden)h(section)g(as)f(the)g(bisection)h (ratio)g(can)f(b)s(e)f(sho)m(wn)g(to)i(pro)m(vide)f(the)g(fastest)390 1425 y(con)m(v)m(ergence)33 b(for)d(this)g(t)m(yp)s(e)h(of)f (algorithm.)3298 1619 y([Minimizer])-3599 b Fv(gsl_min_fminimizer_bre)q (nt)390 1728 y FK(The)23 b FD(Bren)m(t)g(minimization)i(algorithm)f FK(com)m(bines)g(a)f(parab)s(olic)h(in)m(terp)s(olation)g(with)f(the)g (golden)390 1838 y(section)32 b(algorithm.)41 b(This)30 b(pro)s(duces)f(a)i(fast)f(algorithm)i(whic)m(h)e(is)g(still)i(robust.) 390 1977 y(The)27 b(outline)i(of)f(the)g(algorithm)h(can)f(b)s(e)g (summarized)f(as)h(follo)m(ws:)41 b(on)28 b(eac)m(h)h(iteration)g(Bren) m(t's)390 2087 y(metho)s(d)44 b(appro)m(ximates)i(the)e(function)h (using)f(an)g(in)m(terp)s(olating)i(parab)s(ola)f(through)f(three)390 2196 y(existing)33 b(p)s(oin)m(ts.)45 b(The)31 b(minim)m(um)g(of)h(the) g(parab)s(ola)g(is)g(tak)m(en)h(as)f(a)g(guess)g(for)f(the)h(minim)m (um.)390 2306 y(If)41 b(it)h(lies)h(within)e(the)h(b)s(ounds)d(of)j (the)g(curren)m(t)f(in)m(terv)-5 b(al)43 b(then)e(the)h(in)m(terp)s (olating)h(p)s(oin)m(t)f(is)390 2416 y(accepted,)e(and)c(used)h(to)g (generate)i(a)e(smaller)g(in)m(terv)-5 b(al.)62 b(If)36 b(the)i(in)m(terp)s(olating)g(p)s(oin)m(t)f(is)g(not)390 2525 y(accepted)f(then)f(the)g(algorithm)h(falls)f(bac)m(k)h(to)f(an)g (ordinary)f(golden)i(section)g(step.)54 b(The)34 b(full)390 2635 y(details)d(of)g(Bren)m(t's)g(metho)s(d)f(include)g(some)h (additional)g(c)m(hec)m(ks)h(to)f(impro)m(v)m(e)g(con)m(v)m(ergence.) 3298 2829 y([Minimizer])-3599 b Fv(gsl_min_fminimizer_qua)q(d_g)q(olde) q(n)390 2938 y FK(This)20 b(is)g(a)h(v)-5 b(arian)m(t)22 b(of)e(Bren)m(t's)i(algorithm)f(whic)m(h)f(uses)g(the)h(safeguarded)g (step-length)g(algorithm)390 3048 y(of)31 b(Gill)g(and)f(Murra)m(y)-8 b(.)150 3288 y FJ(35.8)68 b(Examples)150 3447 y FK(The)23 b(follo)m(wing)i(program)e(uses)g(the)g(Bren)m(t)h(algorithm)h(to)f 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FK(,)g(in)f FE(n)g FK(v)-5 b(ariables,)31 b FE(x)1171 2102 y Fq(i)1198 2088 y FK(,)1233 2263 y FE(f)1278 2277 y Fq(i)1306 2263 y FK(\()p FE(x)1393 2277 y FB(1)1430 2263 y FE(;)15 b(:)g(:)g(:)i(;)e (x)1684 2277 y Fq(n)1729 2263 y FK(\))26 b(=)f(0)182 b(for)30 b FE(i)c FK(=)f(1)15 b FE(:)g(:)g(:)i(n:)150 2439 y FK(In)25 b(general)i(there)f(are)g(no)f(brac)m(k)m(eting)j (metho)s(ds)d(a)m(v)-5 b(ailable)28 b(for)d FE(n)h FK(dimensional)f (systems,)i(and)e(no)h(w)m(a)m(y)150 2548 y(of)31 b(kno)m(wing)f (whether)g(an)m(y)h(solutions)g(exist.)42 b(All)31 b(algorithms)g(pro)s (ceed)g(from)f(an)g(initial)i(guess)e(using)150 2658 y(a)h(v)-5 b(arian)m(t)31 b(of)g(the)f(Newton)h(iteration,)1511 2833 y FE(x)25 b FI(!)g FE(x)1756 2796 y Fp(0)1805 2833 y FK(=)g FE(x)20 b FI(\000)g FE(J)2123 2796 y Fp(\000)p FB(1)2212 2833 y FE(f)10 b FK(\()p FE(x)p FK(\))150 3009 y(where)34 b FE(x)p FK(,)i FE(f)44 b FK(are)36 b(v)m(ector)g(quan)m (tities)g(and)e FE(J)44 b FK(is)35 b(the)g(Jacobian)g(matrix)g 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b(function)g(returns)g(a)h(p)s(oin)m(ter)f(to)i(a)f(newly)f(allo)s (cated)j(instance)e(of)g(a)g(deriv)-5 b(ativ)m(e)38 b(solv)m(er)390 2578 y(of)c(t)m(yp)s(e)f FD(T)40 b FK(for)33 b(a)h(system)g(of)f FD(n)g FK(dimensions.)49 b(F)-8 b(or)35 b(example,)g(the)f(follo)m (wing)g(co)s(de)g(creates)h(an)390 2688 y(instance)c(of)g(a)f (Newton-Raphson)h(solv)m(er,)g(for)f(a)h(2-dimensional)g(system)g(of)f (equations.)630 2832 y FH(const)46 b(gsl_multiroot_fdfsolver_ty)o(pe)41 b(*)48 b(T)821 2941 y(=)f(gsl_multiroot_fdfsolver_ne)o(wto)o(n;)630 3051 y(gsl_multiroot_fdfsolver)41 b(*)48 b(s)f(=)821 3161 y(gsl_multiroot_fdfsolver_)o(allo)o(c)42 b(\(T,)47 b(2\);)390 3305 y FK(If)36 b(there)g(is)h(insu\016cien)m(t)f(memory)h (to)g(create)h(the)e(solv)m(er)i(then)e(the)g(function)g(returns)f(a)i (n)m(ull)390 3414 y(p)s(oin)m(ter)30 b(and)g(the)h(error)f(handler)f (is)i(in)m(v)m(ok)m(ed)g(with)g(an)f(error)g(co)s(de)g(of)h FH(GSL_ENOMEM)p FK(.)3350 3618 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multiroot_fsolver)q(_set)f Fu(\()p FD(gsl)p 1859 3618 V 41 w(m)m(ultiro)s(ot)p 2273 3618 V 41 w(fsolv)m(er)31 b(*)g Ft(s)p FD(,)565 3727 y(gsl)p 677 3727 V 41 w(m)m(ultiro)s(ot)p 1091 3727 V 41 w(function)f(*)g Ft(f)p FD(,)h(const)g(gsl)p 2015 3727 V 41 w(v)m(ector)h(*)f Ft(x)p Fu(\))3350 3837 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multiroot_fdfsolv)q(er_s)q(et)f Fu(\()p FD(gsl)p 1964 3837 V 41 w(m)m(ultiro)s(ot)p 2378 3837 V 41 w(fdfsolv)m(er)30 b(*)h Ft(s)p FD(,)565 3947 y(gsl)p 677 3947 V 41 w(m)m(ultiro)s(ot)p 1091 3947 V 41 w(function)p 1458 3947 V 39 w(fdf)f(*)h Ft(fdf)p FD(,)g(const)g(gsl)p 2266 3947 V 40 w(v)m(ector)h(*)f Ft(x)p Fu(\))390 4056 y FK(These)25 b(functions)g(set,)i(or)f(reset,)h(an)e(existing)h(solv)m (er)h FD(s)i FK(to)d(use)f(the)g(function)g FD(f)43 b FK(or)25 b(function)h(and)390 4166 y(deriv)-5 b(ativ)m(e)31 b FD(fdf)p FK(,)e(and)g(the)h(initial)h(guess)e FD(x)p FK(.)41 b(Note)31 b(that)f(the)g(initial)g(p)s(osition)g(is)g(copied)g (from)f FD(x)p FK(,)390 4275 y(this)h(argumen)m(t)h(is)g(not)f(mo)s (di\014ed)f(b)m(y)i(subsequen)m(t)e(iterations.)3350 4479 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_multiroot_fsolver_fr)q (ee)e Fu(\()p FD(gsl)p 1964 4479 V 41 w(m)m(ultiro)s(ot)p 2378 4479 V 41 w(fsolv)m(er)31 b(*)g Ft(s)p Fu(\))3350 4589 y FK([F)-8 b(unction])-3599 b Fv(void)54 b (gsl_multiroot_fdfsolver_)q(fre)q(e)d Fu(\()p FD(gsl)p 2068 4589 V 41 w(m)m(ultiro)s(ot)p 2482 4589 V 41 w(fdfsolv)m(er)31 b(*)g Ft(s)p Fu(\))390 4698 y FK(These)f(functions)g(free)h(all)g(the)f (memory)h(asso)s(ciated)g(with)g(the)f(solv)m(er)h FD(s)p FK(.)3350 4902 y([F)-8 b(unction])-3599 b Fv(const)54 b(char)f(*)g(gsl_multiroot_fsolver_)q(nam)q(e)e Fu(\()p FD(const)565 5011 y(gsl)p 677 5011 V 41 w(m)m(ultiro)s(ot)p 1091 5011 V 41 w(fsolv)m(er)31 b(*)g Ft(s)p Fu(\))3350 5121 y FK([F)-8 b(unction])-3599 b Fv(const)54 b(char)f(*)g (gsl_multiroot_fdfsolve)q(r_n)q(ame)f Fu(\()p FD(const)565 5230 y(gsl)p 677 5230 V 41 w(m)m(ultiro)s(ot)p 1091 5230 V 41 w(fdfsolv)m(er)30 b(*)h Ft(s)p Fu(\))390 5340 y FK(These)f(functions)g(return)f(a)i(p)s(oin)m(ter)f(to)i(the)e(name)h (of)f(the)h(solv)m(er.)41 b(F)-8 b(or)31 b(example,)p eop end %%Page: 406 424 TeXDict begin 406 423 bop 150 -116 a FK(Chapter)30 b(36:)41 b(Multidimensional)32 b(Ro)s(ot-Finding)1701 b(406)630 299 y FH(printf)46 b(\("s)h(is)g(a)h('\045s')e(solver\\n",)1012 408 y(gsl_multiroot_fdfsolver_)o(nam)o(e)c(\(s\)\);)390 538 y FK(w)m(ould)30 b(prin)m(t)g(something)h(lik)m(e)h FH(s)e(is)f(a)h('newton')f(solver)p FK(.)150 760 y FJ(36.3)68 b(Pro)l(viding)46 b(the)f(function)g(to)g(solv)l(e)150 920 y FK(Y)-8 b(ou)31 b(m)m(ust)g(pro)m(vide)g FE(n)f FK(functions)g(of)h FE(n)f FK(v)-5 b(ariables)32 b(for)e(the)h(ro)s(ot) g(\014nders)e(to)j(op)s(erate)f(on.)42 b(In)30 b(order)g(to)150 1029 y(allo)m(w)i(for)e(general)h(parameters)g(the)g(functions)f(are)g (de\014ned)f(b)m(y)i(the)f(follo)m(wing)i(data)f(t)m(yp)s(es:)3269 1199 y([Data)h(T)m(yp)s(e])-3600 b Fv(gsl_multiroot_function)390 1308 y FK(This)30 b(data)h(t)m(yp)s(e)f(de\014nes)g(a)g(general)i (system)e(of)h(functions)f(with)g(parameters.)390 1458 y FH(int)f(\(*)h(f\))g(\(const)f(gsl_vector)e(*)j FA(x)p FH(,)g(void)f(*)h FA(params)p FH(,)f(gsl_vector)e(*)j FA(f)p FH(\))870 1567 y FK(this)24 b(function)f(should)g(store)h(the)g (v)m(ector)i(result)d FE(f)10 b FK(\()p FE(x;)15 b Fg(p)-5 b(ar)g(ams)s FK(\))24 b(in)g FD(f)41 b FK(for)23 b(argumen)m(t)870 1677 y FD(x)51 b FK(and)44 b(parameters)h FD(params)p FK(,)j(returning)43 b(an)i(appropriate)f(error)g(co)s(de)h(if)g(the)870 1787 y(function)30 b(cannot)h(b)s(e)f(computed.)390 1936 y FH(size_t)f(n)115 b FK(the)23 b(dimension)g(of)g(the)h(system,)h (i.e.)39 b(the)23 b(n)m(um)m(b)s(er)f(of)h(comp)s(onen)m(ts)h(of)f(the) g(v)m(ectors)870 2046 y FD(x)37 b FK(and)29 b FD(f)p FK(.)390 2195 y FH(void)g(*)h(params)870 2305 y FK(a)h(p)s(oin)m(ter)f (to)h(the)g(parameters)g(of)f(the)h(function.)150 2474 y(Here)g(is)f(an)h(example)g(using)f(P)m(o)m(w)m(ell's)i(test)g (function,)731 2637 y FE(f)776 2651 y FB(1)813 2637 y FK(\()p FE(x)p FK(\))26 b(=)f FE(Ax)1177 2651 y FB(0)1214 2637 y FE(x)1266 2651 y FB(1)1324 2637 y FI(\000)20 b FK(1)p FE(;)15 b(f)1545 2651 y FB(2)1582 2637 y FK(\()p FE(x)p FK(\))26 b(=)f(exp\()p FI(\000)p FE(x)2123 2651 y FB(0)2160 2637 y FK(\))c(+)f(exp\()p FI(\000)p FE(x)2604 2651 y FB(1)2641 2637 y FK(\))g FI(\000)g FK(\(1)h(+)f(1)p FE(=)-5 b(A)p FK(\))150 2800 y(with)29 b FE(A)d FK(=)f(10)636 2767 y FB(4)674 2800 y FK(.)40 b(The)30 b(follo)m(wing)h(co)s(de)f (de\014nes)f(a)h FH(gsl_multiroot_function)24 b FK(system)30 b FH(F)f FK(whic)m(h)h(y)m(ou)150 2909 y(could)g(pass)g(to)i(a)e(solv)m (er:)390 3039 y FH(struct)46 b(powell_params)e({)k(double)e(A;)h(};)390 3258 y(int)390 3367 y(powell)f(\(gsl_vector)f(*)i(x,)g(void)g(*)h(p,)f (gsl_vector)e(*)i(f\))g({)533 3477 y(struct)f(powell_params)e(*)k (params)629 3587 y(=)f(\(struct)f(powell_params)e(*\)p;)533 3696 y(const)j(double)f(A)h(=)h(\(params->A\);)533 3806 y(const)f(double)f(x0)h(=)g(gsl_vector_get\(x,0\);)533 3915 y(const)g(double)f(x1)h(=)g(gsl_vector_get\(x,1\);)533 4134 y(gsl_vector_set)d(\(f,)j(0,)g(A)h(*)f(x0)g(*)h(x1)f(-)g(1\);)533 4244 y(gsl_vector_set)d(\(f,)j(1,)g(\(exp\(-x0\))e(+)j(exp\(-x1\))1631 4354 y(-)f(\(1.0)g(+)g(1.0/A\)\)\);)533 4463 y(return)f(GSL_SUCCESS)390 4573 y(})390 4792 y(gsl_multiroot_function)c(F;)390 4902 y(struct)k(powell_params)e(params)i(=)i({)f(10000.0)f(};)390 5121 y(F.f)h(=)g(&powell;)390 5230 y(F.n)g(=)g(2;)390 5340 y(F.params)f(=)h(¶ms;)p eop end %%Page: 407 425 TeXDict begin 407 424 bop 150 -116 a FK(Chapter)30 b(36:)41 b(Multidimensional)32 b(Ro)s(ot-Finding)1701 b(407)3269 299 y([Data)32 b(T)m(yp)s(e])-3600 b Fv(gsl_multiroot_function)q(_fd)q (f)390 408 y FK(This)31 b(data)h(t)m(yp)s(e)g(de\014nes)f(a)h(general)h (system)f(of)g(functions)f(with)g(parameters)h(and)f(the)h(corre-)390 518 y(sp)s(onding)d(Jacobian)i(matrix)g(of)f(deriv)-5 b(ativ)m(es,)390 675 y FH(int)29 b(\(*)h(f\))g(\(const)f(gsl_vector)e (*)j FA(x)p FH(,)g(void)f(*)h FA(params)p FH(,)f(gsl_vector)e(*)j FA(f)p FH(\))870 784 y FK(this)24 b(function)f(should)g(store)h(the)g (v)m(ector)i(result)d FE(f)10 b FK(\()p FE(x;)15 b Fg(p)-5 b(ar)g(ams)s FK(\))24 b(in)g FD(f)41 b FK(for)23 b(argumen)m(t)870 894 y FD(x)51 b FK(and)44 b(parameters)h FD(params)p FK(,)j(returning)43 b(an)i(appropriate)f(error)g(co)s(de)h(if)g(the)870 1003 y(function)30 b(cannot)h(b)s(e)f(computed.)390 1160 y FH(int)f(\(*)h(df\))g(\(const)e(gsl_vector)g(*)i FA(x)p FH(,)g(void)f(*)h FA(params)p FH(,)e(gsl_matrix)g(*)i FA(J)p FH(\))870 1270 y FK(this)96 b(function)g(should)f(store)i(the)g FD(n)p FK(-b)m(y-)p FD(n)f FK(matrix)g(result)g FE(J)3485 1284 y Fq(ij)3679 1270 y FK(=)870 1379 y FE(@)5 b(f)968 1393 y Fq(i)995 1379 y FK(\()p FE(x;)15 b Fg(p)-5 b(ar)g(ams)t FK(\))p FE(=@)5 b(x)1588 1393 y Fq(j)1694 1379 y FK(in)69 b FD(J)76 b FK(for)70 b(argumen)m(t)g FD(x)75 b FK(and)69 b(parameters)h FD(params)p FK(,)870 1489 y(returning)29 b(an)i(appropriate)f(error)g(co)s(de)g(if)h(the)f(function)g(cannot)h (b)s(e)f(computed.)390 1645 y FH(int)f(\(*)h(fdf\))f(\(const)g (gsl_vector)f(*)i FA(x)p FH(,)f(void)h(*)g FA(params)p FH(,)e(gsl_vector)g(*)i FA(f)p FH(,)390 1755 y(gsl_matrix)e(*)i FA(J)p FH(\))870 1864 y FK(This)23 b(function)h(should)g(set)h(the)f(v) -5 b(alues)25 b(of)f(the)g FD(f)42 b FK(and)24 b FD(J)31 b FK(as)25 b(ab)s(o)m(v)m(e,)i(for)d(argumen)m(ts)870 1974 y FD(x)35 b FK(and)28 b(parameters)h FD(params)p FK(.)40 b(This)28 b(function)g(pro)m(vides)h(an)f(optimization)j(of)e (the)870 2084 y(separate)j(functions)e(for)g FE(f)10 b FK(\()p FE(x)p FK(\))31 b(and)f FE(J)9 b FK(\()p FE(x)p FK(\)|it)32 b(is)e(alw)m(a)m(ys)i(faster)f(to)h(compute)f(the)870 2193 y(function)f(and)g(its)h(deriv)-5 b(ativ)m(e)32 b(at)f(the)f(same)h(time.)390 2350 y FH(size_t)e(n)115 b FK(the)23 b(dimension)g(of)g(the)h(system,)h(i.e.)39 b(the)23 b(n)m(um)m(b)s(er)f(of)h(comp)s(onen)m(ts)h(of)f(the)g(v)m (ectors)870 2459 y FD(x)37 b FK(and)29 b FD(f)p FK(.)390 2616 y FH(void)g(*)h(params)870 2725 y FK(a)h(p)s(oin)m(ter)f(to)h(the) g(parameters)g(of)f(the)h(function.)150 2906 y(The)36 b(example)i(of)f(P)m(o)m(w)m(ell's)i(test)f(function)f(de\014ned)e(ab)s (o)m(v)m(e)k(can)e(b)s(e)f(extended)h(to)h(include)e(analytic)150 3015 y(deriv)-5 b(ativ)m(es)32 b(using)e(the)g(follo)m(wing)i(co)s(de,) 390 3148 y FH(int)390 3258 y(powell_df)45 b(\(gsl_vector)g(*)i(x,)h (void)e(*)i(p,)f(gsl_matrix)e(*)i(J\))390 3367 y({)533 3477 y(struct)f(powell_params)e(*)k(params)629 3587 y(=)f(\(struct)f (powell_params)e(*\)p;)533 3696 y(const)j(double)f(A)h(=)h (\(params->A\);)533 3806 y(const)f(double)f(x0)h(=)g (gsl_vector_get\(x,0\);)533 3915 y(const)g(double)f(x1)h(=)g (gsl_vector_get\(x,1\);)533 4025 y(gsl_matrix_set)d(\(J,)j(0,)g(0,)g(A) h(*)f(x1\);)533 4134 y(gsl_matrix_set)d(\(J,)j(0,)g(1,)g(A)h(*)f(x0\);) 533 4244 y(gsl_matrix_set)d(\(J,)j(1,)g(0,)g(-exp\(-x0\)\);)533 4354 y(gsl_matrix_set)d(\(J,)j(1,)g(1,)g(-exp\(-x1\)\);)533 4463 y(return)f(GSL_SUCCESS)390 4573 y(})390 4792 y(int)390 4902 y(powell_fdf)f(\(gsl_vector)g(*)i(x,)g(void)g(*)g(p,)963 5011 y(gsl_matrix)e(*)i(f,)g(gsl_matrix)e(*)j(J\))f({)533 5121 y(struct)f(powell_params)e(*)k(params)629 5230 y(=)f(\(struct)f (powell_params)e(*\)p;)533 5340 y(const)j(double)f(A)h(=)h (\(params->A\);)p eop end %%Page: 408 426 TeXDict begin 408 425 bop 150 -116 a FK(Chapter)30 b(36:)41 b(Multidimensional)32 b(Ro)s(ot-Finding)1701 b(408)533 299 y FH(const)47 b(double)f(x0)h(=)g(gsl_vector_get\(x,0\);)533 408 y(const)g(double)f(x1)h(=)g(gsl_vector_get\(x,1\);)533 628 y(const)g(double)f(u0)h(=)g(exp\(-x0\);)533 737 y(const)g(double)f (u1)h(=)g(exp\(-x1\);)533 956 y(gsl_vector_set)d(\(f,)j(0,)g(A)h(*)f (x0)g(*)h(x1)f(-)g(1\);)533 1066 y(gsl_vector_set)d(\(f,)j(1,)g(u0)g(+) h(u1)f(-)g(\(1)h(+)f(1/A\)\);)533 1285 y(gsl_matrix_set)d(\(J,)j(0,)g (0,)g(A)h(*)f(x1\);)533 1395 y(gsl_matrix_set)d(\(J,)j(0,)g(1,)g(A)h(*) f(x0\);)533 1504 y(gsl_matrix_set)d(\(J,)j(1,)g(0,)g(-u0\);)533 1614 y(gsl_matrix_set)d(\(J,)j(1,)g(1,)g(-u1\);)533 1724 y(return)f(GSL_SUCCESS)390 1833 y(})390 2052 y (gsl_multiroot_function_f)o(df)c(FDF;)390 2271 y(FDF.f)k(=)i (&powell_f;)390 2381 y(FDF.df)e(=)i(&powell_df;)390 2491 y(FDF.fdf)e(=)h(&powell_fdf;)390 2600 y(FDF.n)f(=)i(2;)390 2710 y(FDF.params)d(=)i(0;)150 2856 y FK(Note)33 b(that)e(the)h (function)f FH(powell_fdf)d FK(is)j(able)h(to)g(reuse)f(existing)h (terms)f(from)g(the)g(function)g(when)150 2965 y(calculating)i(the)d (Jacobian,)h(th)m(us)f(sa)m(ving)i(time.)150 3215 y FJ(36.4)68 b(Iteration)150 3374 y FK(The)32 b(follo)m(wing)i(functions)e(driv)m(e) g(the)h(iteration)h(of)e(eac)m(h)i(algorithm.)48 b(Eac)m(h)33 b(function)f(p)s(erforms)f(one)150 3484 y(iteration)45 b(to)e(up)s(date)g(the)g(state)h(of)g(an)m(y)f(solv)m(er)h(of)f(the)g (corresp)s(onding)g(t)m(yp)s(e.)78 b(The)43 b(same)h(func-)150 3593 y(tions)33 b(w)m(ork)g(for)g(all)g(solv)m(ers)h(so)f(that)h (di\013eren)m(t)f(metho)s(ds)f(can)h(b)s(e)f(substituted)h(at)g(run)m (time)g(without)150 3703 y(mo)s(di\014cations)e(to)g(the)f(co)s(de.) 3350 3910 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multiroot_fsolver) q(_ite)q(rat)q(e)e Fu(\()p FD(gsl)p 2068 3910 28 4 v 41 w(m)m(ultiro)s(ot)p 2482 3910 V 41 w(fsolv)m(er)31 b(*)g Ft(s)p Fu(\))3350 4019 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multiroot_fdfsolv)q(er_i)q(ter)q(ate)f Fu(\()p FD(gsl)p 2173 4019 V 41 w(m)m(ultiro)s(ot)p 2587 4019 V 41 w(fdfsolv)m(er)30 b(*)h Ft(s)p Fu(\))390 4129 y FK(These)f(functions)h(p)s(erform)e(a)i(single)g(iteration)h(of)f (the)g(solv)m(er)h FD(s)p FK(.)41 b(If)30 b(the)h(iteration)i(encoun)m (ters)390 4238 y(an)d(unexp)s(ected)g(problem)g(then)g(an)g(error)g(co) s(de)h(will)f(b)s(e)g(returned,)390 4415 y FH(GSL_EBADFUNC)870 4524 y FK(the)22 b(iteration)h(encoun)m(tered)f(a)h(singular)e(p)s(oin) m(t)h(where)f(the)h(function)g(or)f(its)i(deriv)-5 b(a-)870 4634 y(tiv)m(e)32 b(ev)-5 b(aluated)31 b(to)g FH(Inf)f FK(or)g FH(NaN)p FK(.)390 4804 y FH(GSL_ENOPROG)870 4914 y FK(the)j(iteration)i(is)e(not)g(making)g(an)m(y)g(progress,)h(prev)m (en)m(ting)f(the)g(algorithm)h(from)870 5024 y(con)m(tin)m(uing.)275 5230 y(The)k(solv)m(er)i(main)m(tains)g(a)g(curren)m(t)e(b)s(est)h (estimate)i(of)e(the)g(ro)s(ot)h FH(s->x)e FK(and)g(its)i(function)e(v) -5 b(alue)150 5340 y FH(s->f)29 b FK(at)i(all)g(times.)42 b(This)29 b(information)i(can)g(b)s(e)e(accessed)j(with)e(the)g(follo)m (wing)i(auxiliary)f(functions,)p eop end %%Page: 409 427 TeXDict begin 409 426 bop 150 -116 a FK(Chapter)30 b(36:)41 b(Multidimensional)32 b(Ro)s(ot-Finding)1701 b(409)3350 299 y([F)-8 b(unction])-3599 b Fv(gsl_vector)55 b(*)e (gsl_multiroot_fsolver_)q(roo)q(t)e Fu(\()p FD(const)565 408 y(gsl)p 677 408 28 4 v 41 w(m)m(ultiro)s(ot)p 1091 408 V 41 w(fsolv)m(er)31 b(*)g Ft(s)p Fu(\))3350 518 y FK([F)-8 b(unction])-3599 b Fv(gsl_vector)55 b(*)e (gsl_multiroot_fdfsolve)q(r_r)q(oot)f Fu(\()p FD(const)565 628 y(gsl)p 677 628 V 41 w(m)m(ultiro)s(ot)p 1091 628 V 41 w(fdfsolv)m(er)30 b(*)h Ft(s)p Fu(\))390 737 y FK(These)24 b(functions)g(return)f(the)i(curren)m(t)f(estimate)i(of)e(the)h(ro)s (ot)f(for)g(the)h(solv)m(er)g FD(s)p FK(,)g(giv)m(en)h(b)m(y)e FH(s->x)p FK(.)3350 930 y([F)-8 b(unction])-3599 b Fv(gsl_vector)55 b(*)e(gsl_multiroot_fsolver_)q(f)e Fu(\()p FD(const)32 b(gsl)p 2464 930 V 40 w(m)m(ultiro)s(ot)p 2877 930 V 41 w(fsolv)m(er)565 1040 y(*)f Ft(s)p Fu(\))3350 1149 y FK([F)-8 b(unction])-3599 b Fv(gsl_vector)55 b(*)e (gsl_multiroot_fdfsolve)q(r_f)f Fu(\()p FD(const)565 1259 y(gsl)p 677 1259 V 41 w(m)m(ultiro)s(ot)p 1091 1259 V 41 w(fdfsolv)m(er)30 b(*)h Ft(s)p Fu(\))390 1369 y FK(These)c(functions)g(return)g(the)h(function)f(v)-5 b(alue)28 b FE(f)10 b FK(\()p FE(x)p FK(\))27 b(at)i(the)e(curren)m(t)h (estimate)h(of)f(the)f(ro)s(ot)h(for)390 1478 y(the)j(solv)m(er)g FD(s)p FK(,)f(giv)m(en)i(b)m(y)e FH(s->f)p FK(.)3350 1671 y([F)-8 b(unction])-3599 b Fv(gsl_vector)55 b(*)e (gsl_multiroot_fsolver_)q(dx)f Fu(\()p FD(const)565 1781 y(gsl)p 677 1781 V 41 w(m)m(ultiro)s(ot)p 1091 1781 V 41 w(fsolv)m(er)31 b(*)g Ft(s)p Fu(\))3350 1890 y FK([F)-8 b(unction])-3599 b Fv(gsl_vector)55 b(*)e(gsl_multiroot_fdfsolve)q(r_d) q(x)e Fu(\()p FD(const)565 2000 y(gsl)p 677 2000 V 41 w(m)m(ultiro)s(ot)p 1091 2000 V 41 w(fdfsolv)m(er)30 b(*)h Ft(s)p Fu(\))390 2109 y FK(These)f(functions)g(return)f(the)i (last)g(step)g FE(dx)f FK(tak)m(en)i(b)m(y)e(the)g(solv)m(er)i FD(s)p FK(,)e(giv)m(en)i(b)m(y)e FH(s->dx)p FK(.)150 2348 y FJ(36.5)68 b(Searc)l(h)45 b(Stopping)g(P)l(arameters)150 2508 y FK(A)30 b(ro)s(ot)h(\014nding)e(pro)s(cedure)g(should)h(stop)g (when)g(one)g(of)h(the)f(follo)m(wing)i(conditions)f(is)g(true:)225 2646 y FI(\017)60 b FK(A)30 b(m)m(ultidimensional)i(ro)s(ot)e(has)g(b)s (een)g(found)f(to)i(within)f(the)h(user-sp)s(eci\014ed)e(precision.)225 2783 y FI(\017)60 b FK(A)30 b(user-sp)s(eci\014ed)g(maxim)m(um)g(n)m (um)m(b)s(er)f(of)i(iterations)g(has)g(b)s(een)e(reac)m(hed.)225 2920 y FI(\017)60 b FK(An)30 b(error)g(has)g(o)s(ccurred.)150 3086 y(The)f(handling)h(of)g(these)g(conditions)h(is)f(under)e(user)i (con)m(trol.)42 b(The)29 b(functions)h(b)s(elo)m(w)g(allo)m(w)h(the)g (user)150 3195 y(to)g(test)g(the)g(precision)f(of)h(the)g(curren)m(t)f (result)g(in)g(sev)m(eral)i(standard)d(w)m(a)m(ys.)3350 3388 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multiroot_test_de)q (lta)f Fu(\()p FD(const)31 b(gsl)p 2045 3388 V 41 w(v)m(ector)h(*)e Ft(dx)p FD(,)i(const)565 3498 y(gsl)p 677 3498 V 41 w(v)m(ector)g(*)e Ft(x)p FD(,)h(double)f Ft(epsabs)p FD(,)j(double)d Ft(epsrel)p Fu(\))390 3607 y FK(This)36 b(function)h(tests)h(for)e(the)i(con)m(v)m (ergence)h(of)e(the)g(sequence)h(b)m(y)f(comparing)g(the)g(last)h(step) 390 3717 y FD(dx)e FK(with)30 b(the)g(absolute)h(error)f FD(epsabs)k FK(and)29 b(relativ)m(e)j(error)e FD(epsrel)k FK(to)d(the)f(curren)m(t)g(p)s(osition)h FD(x)p FK(.)390 3826 y(The)f(test)h(returns)e FH(GSL_SUCCESS)f FK(if)i(the)g(follo)m (wing)i(condition)f(is)g(ac)m(hiev)m(ed,)1430 3998 y FI(j)p FE(dx)1554 4012 y Fq(i)1582 3998 y FI(j)26 b FE(<)f Fg(epsabs)c FK(+)f Fg(epsr)-5 b(el)26 b FI(j)p FE(x)2417 4012 y Fq(i)2444 3998 y FI(j)390 4170 y FK(for)k(eac)m(h)i(comp)s(onen) m(t)e(of)h FD(x)36 b FK(and)30 b(returns)f FH(GSL_CONTINUE)e FK(otherwise.)3350 4363 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multiroot_test_re)q(sidu)q(al)f Fu(\()p FD(const)31 b(gsl)p 2202 4363 V 41 w(v)m(ector)h(*)e Ft(f)p FD(,)h(double)565 4473 y Ft(epsabs)p Fu(\))390 4583 y FK(This)c(function)g(tests)h(the)g (residual)f(v)-5 b(alue)28 b FD(f)44 b FK(against)29 b(the)f(absolute)g(error)f(b)s(ound)e FD(epsabs)p FK(.)39 b(The)390 4692 y(test)31 b(returns)e FH(GSL_SUCCESS)f FK(if)i(the)h(follo)m(wing)g(condition)g(is)g(ac)m(hiev)m(ed,)1635 4783 y Fs(X)1683 4960 y Fq(i)1770 4864 y FI(j)p FE(f)1840 4878 y Fq(i)1868 4864 y FI(j)25 b FE(<)g Fg(epsabs)390 5103 y FK(and)33 b(returns)f FH(GSL_CONTINUE)e FK(otherwise.)51 b(This)32 b(criterion)i(is)g(suitable)g(for)f(situations)h(where)390 5213 y(the)41 b(precise)g(lo)s(cation)h(of)f(the)g(ro)s(ot,)j FE(x)p FK(,)f(is)e(unimp)s(ortan)m(t)f(pro)m(vided)g(a)h(v)-5 b(alue)41 b(can)g(b)s(e)f(found)390 5322 y(where)30 b(the)g(residual)h (is)f(small)h(enough.)p eop end %%Page: 410 428 TeXDict begin 410 427 bop 150 -116 a FK(Chapter)30 b(36:)41 b(Multidimensional)32 b(Ro)s(ot-Finding)1701 b(410)150 299 y FJ(36.6)68 b(Algorithms)46 b(using)f(Deriv)-7 b(ativ)l(es)150 458 y FK(The)28 b(ro)s(ot)i(\014nding)d(algorithms)j(describ)s(ed)e(in) g(this)h(section)h(mak)m(e)g(use)e(of)h(b)s(oth)g(the)g(function)f(and) h(its)150 568 y(deriv)-5 b(ativ)m(e.)40 b(They)24 b(require)h(an)f (initial)i(guess)e(for)h(the)g(lo)s(cation)h(of)e(the)h(ro)s(ot,)i(but) c(there)i(is)g(no)f(absolute)150 677 y(guaran)m(tee)34 b(of)f(con)m(v)m(ergence|the)i(function)d(m)m(ust)g(b)s(e)g(suitable)h (for)f(this)g(tec)m(hnique)h(and)f(the)h(initial)150 787 y(guess)27 b(m)m(ust)g(b)s(e)g(su\016cien)m(tly)h(close)g(to)g(the) f(ro)s(ot)h(for)f(it)h(to)f(w)m(ork.)40 b(When)27 b(the)h(conditions)f (are)h(satis\014ed)150 897 y(then)i(con)m(v)m(ergence)j(is)d (quadratic.)3021 1086 y([Deriv)-5 b(ativ)m(e)33 b(Solv)m(er])-3599 b Fv(gsl_multiroot_fdfsolve)q(r_h)q(ybri)q(dsj)390 1196 y FK(This)33 b(is)h(a)g(mo)s(di\014ed)f(v)m(ersion)h(of)g(P)m(o)m(w)m (ell's)i(Hybrid)d(metho)s(d)g(as)i(implemen)m(ted)f(in)f(the)h FC(hybrj)390 1305 y FK(algorithm)24 b(in)e FC(minp)-6 b(a)n(ck)p FK(.)37 b(Minpac)m(k)24 b(w)m(as)f(written)f(b)m(y)h(Jorge)g (J.)g(Mor)m(\023)-43 b(e,)26 b(Burton)d(S.)f(Garb)s(o)m(w)h(and)390 1415 y(Kenneth)f(E.)h(Hillstrom.)39 b(The)23 b(Hybrid)f(algorithm)i (retains)f(the)g(fast)h(con)m(v)m(ergence)h(of)e(Newton's)390 1525 y(metho)s(d)30 b(but)f(will)i(also)h(reduce)e(the)g(residual)g (when)g(Newton's)h(metho)s(d)f(is)g(unreliable.)390 1662 y(The)22 b(algorithm)h(uses)e(a)i(generalized)g(trust)f(region)g(to)h (k)m(eep)g(eac)m(h)g(step)f(under)f(con)m(trol.)39 b(In)21 b(order)390 1771 y(to)28 b(b)s(e)g(accepted)h(a)f(prop)s(osed)e(new)h (p)s(osition)h FE(x)2028 1738 y Fp(0)2079 1771 y FK(m)m(ust)g(satisfy)g (the)g(condition)g FI(j)p FE(D)s FK(\()p FE(x)3323 1738 y Fp(0)3362 1771 y FI(\000)15 b FE(x)p FK(\))p FI(j)25 b FE(<)g(\016)s FK(,)390 1881 y(where)43 b FE(D)k FK(is)d(a)h(diagonal) g(scaling)g(matrix)f(and)g FE(\016)j FK(is)d(the)h(size)f(of)h(the)f (trust)f(region.)82 b(The)390 1991 y(comp)s(onen)m(ts)35 b(of)g FE(D)i FK(are)f(computed)e(in)m(ternally)-8 b(,)38 b(using)c(the)h(column)f(norms)g(of)h(the)g(Jacobian)390 2100 y(to)30 b(estimate)g(the)f(sensitivit)m(y)h(of)f(the)g(residual)g (to)g(eac)m(h)h(comp)s(onen)m(t)f(of)g FE(x)p FK(.)40 b(This)28 b(impro)m(v)m(es)i(the)390 2210 y(b)s(eha)m(vior)g(of)h(the)g (algorithm)g(for)f(badly)g(scaled)h(functions.)390 2347 y(On)25 b(eac)m(h)j(iteration)f(the)g(algorithm)g(\014rst)e(determines) i(the)f(standard)f(Newton)i(step)f(b)m(y)g(solving)390 2456 y(the)h(system)f FE(J)9 b(dx)26 b FK(=)f FI(\000)p FE(f)10 b FK(.)38 b(If)26 b(this)g(step)g(falls)h(inside)f(the)h(trust) f(region)h(it)g(is)f(used)f(as)i(a)g(trial)g(step)390 2566 y(in)36 b(the)g(next)g(stage.)59 b(If)35 b(not,)j(the)e(algorithm) h(uses)f(the)g(linear)g(com)m(bination)h(of)f(the)g(Newton)390 2676 y(and)25 b(gradien)m(t)i(directions)g(whic)m(h)f(is)g(predicted)g (to)h(minimize)f(the)g(norm)g(of)g(the)g(function)g(while)390 2785 y(sta)m(ying)32 b(inside)e(the)g(trust)g(region,)1346 2956 y FE(dx)c FK(=)e FI(\000)p FE(\013J)1754 2918 y Fp(\000)p FB(1)1844 2956 y FE(f)10 b FK(\()p FE(x)p FK(\))20 b FI(\000)g FE(\014)5 b FI(rj)p FE(f)10 b FK(\()p FE(x)p FK(\))p FI(j)2491 2918 y FB(2)2529 2956 y FE(:)390 3126 y FK(This)30 b(com)m(bination)h(of)g(Newton)g(and)e(gradien)m(t)j (directions)f(is)f(referred)g(to)h(as)f(a)h FD(dogleg)h(step)p FK(.)390 3263 y(The)27 b(prop)s(osed)g(step)g(is)h(no)m(w)g(tested)h(b) m(y)e(ev)-5 b(aluating)29 b(the)f(function)g(at)g(the)g(resulting)g(p)s (oin)m(t,)g FE(x)3701 3230 y Fp(0)3725 3263 y FK(.)390 3373 y(If)e(the)i(step)f(reduces)f(the)h(norm)g(of)g(the)g(function)g (su\016cien)m(tly)g(then)g(it)g(is)g(accepted)i(and)d(size)i(of)390 3482 y(the)33 b(trust)f(region)h(is)g(increased.)47 b(If)32 b(the)h(prop)s(osed)e(step)i(fails)g(to)g(impro)m(v)m(e)g(the)g (solution)g(then)390 3592 y(the)e(size)g(of)f(the)h(trust)f(region)h (is)f(decreased)h(and)f(another)g(trial)i(step)e(is)h(computed.)390 3729 y(The)24 b(sp)s(eed)g(of)h(the)f(algorithm)i(is)f(increased)g(b)m (y)f(computing)h(the)g(c)m(hanges)g(to)h(the)e(Jacobian)i(ap-)390 3839 y(pro)m(ximately)-8 b(,)26 b(using)c(a)h(rank-1)g(up)s(date.)37 b(If)22 b(t)m(w)m(o)i(successiv)m(e)f(attempts)h(fail)f(to)g(reduce)f (the)h(resid-)390 3948 y(ual)33 b(then)g(the)h(full)e(Jacobian)i(is)g (recomputed.)49 b(The)32 b(algorithm)i(also)h(monitors)e(the)g (progress)390 4058 y(of)e(the)f(solution)h(and)f(returns)f(an)h(error)g (if)h(sev)m(eral)g(steps)g(fail)g(to)g(mak)m(e)g(an)m(y)g(impro)m(v)m (emen)m(t,)390 4221 y FH(GSL_ENOPROG)870 4331 y FK(the)i(iteration)i (is)e(not)g(making)g(an)m(y)g(progress,)h(prev)m(en)m(ting)f(the)g (algorithm)h(from)870 4440 y(con)m(tin)m(uing.)390 4602 y FH(GSL_ENOPROGJ)870 4712 y FK(re-ev)-5 b(aluations)37 b(of)f(the)g(Jacobian)g(indicate)g(that)g(the)g(iteration)h(is)f(not)g (making)870 4822 y(an)m(y)31 b(progress,)f(prev)m(en)m(ting)h(the)g (algorithm)g(from)f(con)m(tin)m(uing.)3021 5011 y([Deriv)-5 b(ativ)m(e)33 b(Solv)m(er])-3599 b Fv(gsl_multiroot_fdfsolve)q(r_h)q (ybri)q(dj)390 5121 y FK(This)38 b(algorithm)i(is)g(an)f(unscaled)f(v)m (ersion)i(of)f FH(hybridsj)p FK(.)65 b(The)38 b(steps)h(are)h(con)m (trolled)h(b)m(y)e(a)390 5230 y(spherical)29 b(trust)f(region)i FI(j)p FE(x)1338 5197 y Fp(0)1378 5230 y FI(\000)17 b FE(x)p FI(j)25 b FE(<)g(\016)s FK(,)30 b(instead)f(of)g(a)g (generalized)i(region.)41 b(This)28 b(can)h(b)s(e)f(useful)390 5340 y(if)i(the)h(generalized)h(region)f(estimated)g(b)m(y)g FH(hybridsj)d FK(is)i(inappropriate.)p eop end %%Page: 411 429 TeXDict begin 411 428 bop 150 -116 a FK(Chapter)30 b(36:)41 b(Multidimensional)32 b(Ro)s(ot-Finding)1701 b(411)3021 299 y([Deriv)-5 b(ativ)m(e)33 b(Solv)m(er])-3599 b Fv (gsl_multiroot_fdfsolve)q(r_n)q(ewto)q(n)390 408 y FK(Newton's)41 b(Metho)s(d)g(is)g(the)g(standard)f(ro)s(ot-p)s(olishing)h(algorithm.) 72 b(The)41 b(algorithm)g(b)s(egins)390 518 y(with)j(an)g(initial)h (guess)g(for)f(the)g(lo)s(cation)i(of)e(the)h(solution.)82 b(On)44 b(eac)m(h)h(iteration)h(a)f(linear)390 628 y(appro)m(ximation) 33 b(to)g(the)g(function)f FE(F)45 b FK(is)32 b(used)g(to)h(estimate)h (the)e(step)h(whic)m(h)f(will)g(zero)i(all)f(the)390 737 y(comp)s(onen)m(ts)e(of)f(the)h(residual.)40 b(The)30 b(iteration)i(is)e(de\014ned)f(b)m(y)i(the)f(follo)m(wing)i(sequence,) 1511 900 y FE(x)25 b FI(!)g FE(x)1756 862 y Fp(0)1805 900 y FK(=)g FE(x)20 b FI(\000)g FE(J)2123 862 y Fp(\000)p FB(1)2212 900 y FE(f)10 b FK(\()p FE(x)p FK(\))390 1062 y(where)31 b(the)h(Jacobian)g(matrix)g FE(J)41 b FK(is)31 b(computed)h(from)f(the)h(deriv)-5 b(ativ)m(e)33 b(functions)e(pro)m (vided)g(b)m(y)390 1172 y FD(f)p FK(.)40 b(The)30 b(step)h FE(dx)f FK(is)h(obtained)f(b)m(y)h(solving)g(the)f(linear)h(system,) 1679 1335 y FE(J)24 b(dx)i FK(=)f FI(\000)p FE(f)10 b FK(\()p FE(x)p FK(\))390 1497 y(using)22 b(LU)g(decomp)s(osition.)39 b(If)22 b(the)h(Jacobian)g(matrix)g(is)f(singular,)i(an)f(error)f(co)s (de)h(of)f FH(GSL_EDOM)390 1607 y FK(is)30 b(returned.)3021 1776 y([Deriv)-5 b(ativ)m(e)33 b(Solv)m(er])-3599 b Fv (gsl_multiroot_fdfsolve)q(r_g)q(newt)q(on)390 1885 y FK(This)41 b(is)g(a)h(mo)s(di\014ed)f(v)m(ersion)h(of)g(Newton's)g (metho)s(d)f(whic)m(h)g(attempts)i(to)f(impro)m(v)m(e)h(global)390 1995 y(con)m(v)m(ergence)e(b)m(y)e(requiring)g(ev)m(ery)h(step)f(to)g (reduce)g(the)g(Euclidean)g(norm)g(of)g(the)g(residual,)390 2104 y FI(j)p FE(f)10 b FK(\()p FE(x)p FK(\))p FI(j)p FK(.)57 b(If)35 b(the)h(Newton)g(step)g(leads)g(to)g(an)f(increase)i (in)e(the)h(norm)f(then)g(a)h(reduced)f(step)h(of)390 2214 y(relativ)m(e)c(size,)1496 2377 y FE(t)25 b FK(=)g(\()1685 2301 y FI(p)p 1761 2301 246 4 v 76 x FK(1)c(+)f(6)p FE(r)j FI(\000)d FK(1\))p FE(=)p FK(\(3)p FE(r)s FK(\))390 2539 y(is)36 b(prop)s(osed,)h(with)f FE(r)i FK(b)s(eing)e(the)g(ratio)h(of)g (norms)e FI(j)p FE(f)10 b FK(\()p FE(x)2391 2506 y Fp(0)2414 2539 y FK(\))p FI(j)2474 2506 y FB(2)2512 2539 y FE(=)p FI(j)p FE(f)g FK(\()p FE(x)p FK(\))p FI(j)2784 2506 y FB(2)2822 2539 y FK(.)58 b(This)36 b(pro)s(cedure)f(is)h(re-)390 2649 y(p)s(eated)30 b(un)m(til)h(a)g(suitable)g(step)f(size)h(is)g (found.)150 2871 y FJ(36.7)68 b(Algorithms)46 b(without)g(Deriv)-7 b(ativ)l(es)150 3030 y FK(The)37 b(algorithms)i(describ)s(ed)d(in)h (this)h(section)h(do)e(not)h(require)f(an)m(y)h(deriv)-5 b(ativ)m(e)39 b(information)f(to)h(b)s(e)150 3140 y(supplied)31 b(b)m(y)h(the)g(user.)45 b(An)m(y)32 b(deriv)-5 b(ativ)m(es)33 b(needed)f(are)g(appro)m(ximated)h(b)m(y)f(\014nite)g(di\013erences.)46 b(Note)150 3250 y(that)29 b(if)g(the)g(\014nite-di\013erencing)h(step)e (size)i(c)m(hosen)f(b)m(y)g(these)g(routines)g(is)g(inappropriate,)g (an)g(explicit)150 3359 y(user-supplied)e(n)m(umerical)i(deriv)-5 b(ativ)m(e)30 b(can)f(alw)m(a)m(ys)h(b)s(e)d(used)h(with)g(the)h (algorithms)g(describ)s(ed)f(in)g(the)150 3469 y(previous)i(section.) 3457 3638 y([Solv)m(er])-3599 b Fv(gsl_multiroot_fsolver_)q(hyb)q(rids) 390 3747 y FK(This)23 b(is)i(a)f(v)m(ersion)h(of)f(the)h(Hybrid)e (algorithm)i(whic)m(h)f(replaces)h(calls)g(to)g(the)f(Jacobian)h (function)390 3857 y(b)m(y)c(its)g(\014nite)h(di\013erence)f(appro)m (ximation.)39 b(The)20 b(\014nite)h(di\013erence)h(appro)m(ximation)g (is)f(computed)390 3966 y(using)40 b FH(gsl_multiroots_fdjac)35 b FK(with)41 b(a)g(relativ)m(e)i(step)e(size)g(of)g FH (GSL_SQRT_DBL_EPSILON)p FK(.)390 4076 y(Note)32 b(that)f(this)f(step)g 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FE(f)1706 5354 y Fq(i)1733 5340 y FK(\()p FE(x)c FK(+)f FE(\016)1972 5354 y Fq(j)2007 5340 y FK(\))h FI(\000)e FE(f)2198 5354 y Fq(i)2226 5340 y FK(\()p FE(x)p FK(\)\))p FE(=\016)2468 5354 y Fq(j)p eop end %%Page: 412 430 TeXDict begin 412 429 bop 150 -116 a FK(Chapter)30 b(36:)41 b(Multidimensional)32 b(Ro)s(ot-Finding)1701 b(412)390 299 y(where)26 b FE(\016)689 313 y Fq(j)750 299 y FK(is)g(a)h(step)f (of)g(size)1364 234 y FI(p)p 1440 234 37 4 v 65 x FE(\017)p FI(j)p FE(x)1554 313 y Fq(j)1589 299 y FI(j)h FK(with)f FE(\017)g FK(b)s(eing)f(the)i(mac)m(hine)g(precision)f(\()p FE(\017)f FI(\031)g FK(2)p FE(:)p FK(22)12 b FI(\002)g FK(10)3565 266 y Fp(\000)p FB(16)3689 299 y FK(\).)390 408 y(The)23 b(order)h(of)g(con)m(v)m(ergence)i(of)e(Newton's)g (algorithm)h(is)f(quadratic,)i(but)d(the)h(\014nite)g(di\013erences)390 518 y(require)d FE(n)742 485 y FB(2)801 518 y FK(function)g(ev)-5 b(aluations)23 b(on)f(eac)m(h)h(iteration.)39 b(The)21 b(algorithm)i(ma)m(y)f(b)s(ecome)g(unstable)390 628 y(if)30 b(the)h(\014nite)f(di\013erences)h(are)g(not)f(a)h(go)s(o)s(d)f(appro)m (ximation)i(to)f(the)f(true)g(deriv)-5 b(ativ)m(es.)3457 805 y([Solv)m(er])-3599 b Fv(gsl_multiroot_fsolver_)q(bro)q(yden)390 914 y FK(The)27 b FD(Bro)m(yden)g(algorithm)h FK(is)f(a)h(v)m(ersion)g (of)f(the)g(discrete)h(Newton)g(algorithm)g(whic)m(h)f(attempts)390 1024 y(to)f(a)m(v)m(oids)h(the)e(exp)s(ensiv)m(e)h(up)s(date)e(of)i (the)f(Jacobian)h(matrix)g(on)f(eac)m(h)i(iteration.)40 b(The)25 b(c)m(hanges)390 1133 y(to)31 b(the)g(Jacobian)g(are)f(also)i (appro)m(ximated,)f(using)f(a)h(rank-1)f(up)s(date,)1052 1299 y FE(J)1111 1261 y Fp(\000)p FB(1)1225 1299 y FI(!)25 b FE(J)1400 1261 y Fp(\000)p FB(1)1510 1299 y FI(\000)20 b FK(\()p FE(J)1695 1261 y Fp(\000)p FB(1)1784 1299 y FE(d)-15 b(f)30 b FI(\000)20 b FE(dx)p FK(\))p FE(dx)2215 1261 y Fq(T)2268 1299 y FE(J)2327 1261 y Fp(\000)p FB(1)2417 1299 y FE(=dx)2561 1261 y Fq(T)2614 1299 y FE(J)2673 1261 y Fp(\000)p FB(1)2762 1299 y FE(d)-15 b(f)390 1464 y FK(where)43 b(the)i(v)m(ectors)g FE(dx)f FK(and)g FE(d)-15 b(f)53 b FK(are)44 b(the)g(c)m(hanges)h(in)f FE(x)g FK(and)f FE(f)10 b FK(.)81 b(On)43 b(the)h(\014rst)f(iteration)390 1574 y(the)36 b(in)m(v)m(erse)g(Jacobian)h(is)e(estimated)i(using)e (\014nite)h(di\013erences,)h(as)f(in)f(the)h(discrete)g(Newton)390 1683 y(algorithm.)390 1815 y(This)27 b(appro)m(ximation)i(giv)m(es)h(a) e(fast)g(up)s(date)g(but)f(is)h(unreliable)g(if)g(the)g(c)m(hanges)h (are)g(not)f(small,)390 1925 y(and)22 b(the)i(estimate)g(of)g(the)f(in) m(v)m(erse)h(Jacobian)g(b)s(ecomes)f(w)m(orse)g(as)g(time)h(passes.)38 b(The)23 b(algorithm)390 2034 y(has)29 b(a)g(tendency)g(to)g(b)s(ecome) g(unstable)g(unless)f(it)i(starts)f(close)h(to)f(the)h(ro)s(ot.)40 b(The)28 b(Jacobian)i(is)390 2144 y(refreshed)f(if)i(this)f(instabilit) m(y)i(is)e(detected)i(\(consult)f(the)f(source)h(for)f(details\).)390 2276 y(This)c(algorithm)i(is)f(included)g(only)g(for)g(demonstration)g (purp)s(oses,)f(and)h(is)g(not)g(recommended)390 2386 y(for)j(serious)g(use.)150 2613 y FJ(36.8)68 b(Examples)150 2773 y FK(The)29 b(m)m(ultidimensional)g(solv)m(ers)h(are)f(used)g(in)f (a)i(similar)f(w)m(a)m(y)h(to)g(the)f(one-dimensional)h(ro)s(ot)f (\014nding)150 2882 y(algorithms.)57 b(This)35 b(\014rst)g(example)i (demonstrates)f(the)g FH(hybrids)d FK(scaled-h)m(ybrid)j(algorithm,)i (whic)m(h)150 2992 y(do)s(es)30 b(not)h(require)f(deriv)-5 b(ativ)m(es.)42 b(The)30 b(program)g(solv)m(es)h(the)g(Rosen)m(bro)s(c) m(k)g(system)f(of)h(equations,)1158 3157 y FE(f)1203 3171 y FB(1)1240 3157 y FK(\()p FE(x;)15 b(y)s FK(\))26 b(=)f FE(a)p FK(\(1)c FI(\000)f FE(x)p FK(\))p FE(;)46 b(f)2015 3171 y FB(2)2052 3157 y FK(\()p FE(x;)15 b(y)s FK(\))26 b(=)f FE(b)p FK(\()p FE(y)e FI(\000)d FE(x)2669 3120 y FB(2)2706 3157 y FK(\))150 3322 y(with)30 b FE(a)25 b FK(=)g(1)p FE(;)15 b(b)26 b FK(=)f(10.)42 b(The)30 b(solution)h(of)f(this)h(system)f(lies)h(at)g(\()p FE(x;)15 b(y)s FK(\))26 b(=)f(\(1)p FE(;)15 b FK(1\))33 b(in)d(a)h(narro)m(w)f (v)-5 b(alley)d(.)275 3454 y(The)29 b(\014rst)h(stage)i(of)e(the)h (program)f(is)h(to)g(de\014ne)e(the)i(system)f(of)h(equations,)390 3587 y FH(#include)46 b()390 3696 y(#include)g()390 3806 y(#include)g()390 3915 y(#include)g ()390 4134 y(struct)g(rparams)485 4244 y({)581 4354 y(double)g(a;)581 4463 y(double)g(b;)485 4573 y(};)390 4792 y(int)390 4902 y(rosenbrock_f)e(\(const)j (gsl_vector)e(*)i(x,)g(void)g(*params,)1058 5011 y(gsl_vector)e(*)j (f\))390 5121 y({)485 5230 y(double)f(a)g(=)g(\(\(struct)f(rparams)g (*\))h(params\)->a;)485 5340 y(double)g(b)g(=)g(\(\(struct)f(rparams)g (*\))h(params\)->b;)p eop end %%Page: 413 431 TeXDict begin 413 430 bop 150 -116 a FK(Chapter)30 b(36:)41 b(Multidimensional)32 b(Ro)s(ot-Finding)1701 b(413)485 408 y FH(const)47 b(double)f(x0)h(=)h(gsl_vector_get)43 b(\(x,)k(0\);)485 518 y(const)g(double)f(x1)h(=)h(gsl_vector_get)43 b(\(x,)k(1\);)485 737 y(const)g(double)f(y0)h(=)h(a)f(*)g(\(1)h(-)f (x0\);)485 847 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b(x)h(=)118 b(0.249)g(0.298)80 b(f\(x\))40 b(=)g(7.511e-01)80 b(2.359e+00)390 5253 y(iter)40 b(=)79 b(8)39 b(x)h(=)118 b(0.249)g(0.298)80 b(f\(x\))40 b(=)g(7.511e-01)80 b(2.359e+00)390 5340 y(iter)40 b(=)79 b(9)39 b(x)h(=)118 b(1.000)g(0.878)80 b(f\(x\))40 b(=)g(1.268e-10)h (-1.218e+00)p eop end %%Page: 415 433 TeXDict begin 415 432 bop 150 -116 a FK(Chapter)30 b(36:)41 b(Multidimensional)32 b(Ro)s(ot-Finding)1701 b(415)390 299 y Fz(iter)40 b(=)g(10)f(x)h(=)118 b(1.000)g(0.989)80 b(f\(x\))40 b(=)g(1.124e-11)h(-1.080e-01)390 386 y(iter)f(=)g(11)f(x)h (=)118 b(1.000)g(1.000)80 b(f\(x\))40 b(=)g(0.000e+00)80 b(0.000e+00)390 473 y(status)41 b(=)e(success)150 614 y FK(Note)c(that)f(the)g(algorithm)h(do)s(es)e(not)h(up)s(date)f(the)h (lo)s(cation)h(on)f(ev)m(ery)g(iteration.)53 b(Some)34 b(iterations)150 723 y(are)j(used)f(to)h(adjust)f(the)g(trust-region)h (parameter,)i(after)e(trying)g(a)g(step)f(whic)m(h)g(w)m(as)h(found)e (to)j(b)s(e)150 833 y(div)m(ergen)m(t,)32 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w(v)m(ector)i(*)f Ft(step_size)p Fu(\))390 3505 y FK(The)i(function)h FH (gsl_multimin_fdfminimizer)o(_set)27 b FK(initializes)36 b(the)f(minimizer)f FD(s)j FK(to)e(mini-)390 3614 y(mize)c(the)e (function)h FD(fdf)46 b FK(starting)31 b(from)e(the)h(initial)h(p)s (oin)m(t)f FD(x)p FK(.)40 b(The)30 b(size)g(of)g(the)g(\014rst)f(trial) i(step)390 3724 y(is)h(giv)m(en)i(b)m(y)e FD(step)p 1019 3724 V 40 w(size)p FK(.)48 b(The)32 b(accuracy)i(of)e(the)h(line)g (minimization)g(is)g(sp)s(eci\014ed)e(b)m(y)i FD(tol)p FK(.)47 b(The)390 3834 y(precise)36 b(meaning)g(of)g(this)f(parameter)i (dep)s(ends)c(on)j(the)g(metho)s(d)f(used.)56 b(T)m(ypically)37 b(the)f(line)390 3943 y(minimization)g(is)f(considered)g(successful)f (if)h(the)g(gradien)m(t)h(of)f(the)g(function)g FE(g)k FK(is)c(orthogonal)390 4053 y(to)e(the)f(curren)m(t)f(searc)m(h)i (direction)f FE(p)g FK(to)g(a)h(relativ)m(e)h(accuracy)f(of)f FD(tol)p FK(,)h(where)e FE(p)21 b FI(\001)h FE(g)31 b(<)d(tol)r FI(j)p FE(p)p FI(jj)p FE(g)s 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2173 5011 V 41 w(m)m(ultimin)p 2575 5011 V 40 w(fdfminimizer)30 b(*)565 5121 y Ft(s)p Fu(\))3350 5230 y FK([F)-8 b(unction])-3599 b Fv(void)54 b (gsl_multimin_fminimizer_)q(fre)q(e)d Fu(\()p FD(gsl)p 2068 5230 V 41 w(m)m(ultimin)p 2470 5230 V 40 w(fminimizer)31 b(*)g Ft(s)p Fu(\))390 5340 y FK(This)f(function)g(frees)g(all)h(the)g (memory)f(asso)s(ciated)i(with)e(the)h(minimizer)f FD(s)p FK(.)p eop end %%Page: 420 438 TeXDict begin 420 437 bop 150 -116 a FK(Chapter)30 b(37:)41 b(Multidimensional)32 b(Minimization)1707 b(420)3350 299 y([F)-8 b(unction])-3599 b Fv(const)54 b(char)f(*)g (gsl_multimin_fdfminimi)q(zer)q(_nam)q(e)e Fu(\()p FD(const)565 408 y(gsl)p 677 408 28 4 v 41 w(m)m(ultimin)p 1079 408 V 40 w(fdfminimizer)29 b(*)i Ft(s)p Fu(\))3350 518 y FK([F)-8 b(unction])-3599 b Fv(const)54 b(char)f(*)g (gsl_multimin_fminimize)q(r_n)q(ame)f Fu(\()p FD(const)565 628 y(gsl)p 677 628 V 41 w(m)m(ultimin)p 1079 628 V 40 w(fminimizer)30 b(*)h Ft(s)p Fu(\))390 737 y FK(This)f(function)g 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b FK(and)870 5230 y(parameters)33 b FD(params)p FK(.)48 b(If)33 b(the)g(function)g(cannot)g(b)s(e)f(computed,)i(an)f(error)f(v) -5 b(alue)870 5340 y(of)31 b FH(GSL_NAN)d FK(should)h(b)s(e)h (returned.)p eop end %%Page: 421 439 TeXDict begin 421 438 bop 150 -116 a FK(Chapter)30 b(37:)41 b(Multidimensional)32 b(Minimization)1707 b(421)390 299 y FH(size_t)29 b(n)115 b FK(the)23 b(dimension)g(of)g(the)h(system,)h (i.e.)39 b(the)23 b(n)m(um)m(b)s(er)f(of)h(comp)s(onen)m(ts)h(of)f(the) g(v)m(ectors)870 408 y FD(x)p FK(.)390 585 y FH(void)29 b(*)h(params)870 695 y FK(a)h(p)s(oin)m(ter)f(to)h(the)g(parameters)g (of)f(the)h(function.)150 914 y(The)i(follo)m(wing)i(example)f (function)g(de\014nes)e(a)i(simple)g(t)m(w)m(o-dimensional)h(parab)s (oloid)f(with)f(\014v)m(e)h(pa-)150 1024 y(rameters,)390 1176 y FH(/*)47 b(Paraboloid)e(centered)h(on)h(\(p[0],p[1]\),)d(with) 533 1285 y(scale)j(factors)e(\(p[2],p[3]\))g(and)i(minimum)f(p[4])g(*/) 390 1504 y(double)390 1614 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518 y(it)c(con)m(tracts)h(itself.)390 652 y(After)f(eac)m(h)g (iteration,)i(the)d(b)s(est)g(v)m(ertex)i(is)e(returned.)40 b(Note,)32 b(that)f(due)f(to)h(the)g(nature)f(of)h(the)390 761 y(algorithm)d(not)f(ev)m(ery)g(step)g(impro)m(v)m(es)g(the)g (curren)m(t)f(b)s(est)g(parameter)h(v)m(ector.)42 b(Usually)27 b(sev)m(eral)390 871 y(iterations)32 b(are)f(required.)390 1004 y(The)k(minimizer-sp)s(eci\014c)g(c)m(haracteristic)j(size)e(is)f (calculated)i(as)e(the)h(a)m(v)m(erage)i(distance)d(from)390 1114 y(the)40 b(geometrical)k(cen)m(ter)d(of)f(the)h(simplex)f(to)h (all)g(its)g(v)m(ertices.)72 b(This)40 b(size)h(can)g(b)s(e)e(used)h (as)390 1224 y(a)g(stopping)g(criteria,)j(as)d(the)g(simplex)g(con)m (tracts)i(itself)e(near)g(the)g(minim)m(um.)68 b(The)39 b(size)i(is)390 1333 y(returned)29 b(b)m(y)h(the)h(function)f FH(gsl_multimin_fminimizer_s)o(ize)o FK(.)390 1467 y(The)e FH(nmsimplex2)f FK(v)m(ersion)i(of)g(this)g(minimiser)g(is)g(a)g(new)g FE(O)s FK(\()p FE(N)10 b FK(\))29 b(op)s(erations)g(implemen)m(tation) 390 1576 y(of)36 b(the)g(earlier)h FE(O)s FK(\()p FE(N)1135 1543 y FB(2)1173 1576 y FK(\))f(op)s(erations)g FH(nmsimplex)e FK(minimiser.)57 b(It)36 b(uses)f(the)i(same)f(underlying)390 1686 y(algorithm,)24 b(but)c(the)h(simplex)g(up)s(dates)e(are)i (computed)g(more)g(e\016cien)m(tly)h(for)f(high-dimensional)390 1795 y(problems.)51 b(In)33 b(addition,)i(the)g(size)f(of)h(simplex)e (is)i(calculated)g(as)g(the)f FC(rms)f FK(distance)i(of)f(eac)m(h)390 1905 y(v)m(ertex)27 b(from)e(the)i(cen)m(ter)g(rather)e(than)h(the)g (mean)g(distance,)i(allo)m(wing)f(a)g(linear)f(up)s(date)f(of)h(this) 390 2015 y(quan)m(tit)m(y)32 b(on)e(eac)m(h)h(step.)41 b(The)30 b(memory)g(usage)h(is)g FE(O)s FK(\()p FE(N)2380 1982 y FB(2)2417 2015 y FK(\))g(for)f(b)s(oth)g(algorithms.)3298 2196 y([Minimizer])-3599 b Fv(gsl_multimin_fminimize)q(r_n)q(msim)q (ple)q(x2r)q(and)390 2306 y FK(This)42 b(metho)s(d)h(is)g(a)g(v)-5 b(arian)m(t)44 b(of)g FH(nmsimplex2)c FK(whic)m(h)j(initialises)h(the)g (simplex)f(around)f(the)390 2415 y(starting)c(p)s(oin)m(t)f FD(x)43 b FK(using)37 b(a)g(randomly-orien)m(ted)h(set)f(of)h(basis)e (v)m(ectors)j(instead)e(of)g(the)h(\014xed)390 2525 y(co)s(ordinate)31 b(axes.)41 b(The)30 b(\014nal)f(dimensions)g(of)i(the)f(simplex)g(are)g (scaled)h(along)g(the)f(co)s(ordinate)390 2635 y(axes)25 b(b)m(y)f(the)h(v)m(ector)h FD(step)p 1290 2635 28 4 v 40 w(size)p FK(.)40 b(The)24 b(randomisation)g(uses)g(a)h(simple)g (deterministic)g(generator)390 2744 y(so)e(that)h(rep)s(eated)f(calls)i (to)e FH(gsl_multimin_fminimizer_se)o(t)17 b FK(for)23 b(a)g(giv)m(en)i(solv)m(er)f(ob)5 b(ject)24 b(will)390 2854 y(v)-5 b(ary)30 b(the)h(orien)m(tation)h(in)e(a)h(w)m (ell-de\014ned)g(w)m(a)m(y)-8 b(.)150 3084 y FJ(37.9)68 b(Examples)150 3244 y FK(This)32 b(example)i(program)f(\014nds)f(the)h (minim)m(um)g(of)g(the)g(parab)s(oloid)g(function)g(de\014ned)f (earlier.)50 b(The)150 3353 y(lo)s(cation)32 b(of)e(the)g(minim)m(um)g 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y(gsl_vector_get)i(\(s->x,)d(0\),)939 2653 y(gsl_vector_get)j (\(s->x,)d(1\),)939 2740 y(s->f\);)547 2914 y(})468 3001 y(while)h(\(status)g(==)e(GSL_CONTINUE)j(&&)e(iter)g(<)g(100\);)468 3176 y(gsl_multimin_fdfminimizer_f)q(ree)46 b(\(s\);)468 3263 y(gsl_vector_free)d(\(x\);)468 3437 y(return)e(0;)390 3524 y(})150 3665 y FK(The)e(initial)i(step-size)g(is)f(c)m(hosen)g(as) g(0.01,)k(a)d(conserv)-5 b(ativ)m(e)41 b(estimate)h(in)d(this)h(case,)j (and)d(the)g(line)150 3775 y(minimization)d(parameter)g(is)g(set)g(at)g (0.0001.)61 b(The)35 b(program)i(terminates)g(when)e(the)i(norm)e(of)i (the)150 3884 y(gradien)m(t)31 b(has)f(b)s(een)g(reduced)g(b)s(elo)m(w) g(0.001.)43 b(The)30 b(output)g(of)g(the)h(program)f(is)h(sho)m(wn)e(b) s(elo)m(w,)820 4025 y FH(x)333 b(y)430 b(f)581 4134 y(1)47 b(4.99629)f(6.99072)94 b(687.84780)581 4244 y(2)47 b(4.98886)f(6.97215) 94 b(683.55456)581 4354 y(3)47 b(4.97400)f(6.93501)94 b(675.01278)581 4463 y(4)47 b(4.94429)f(6.86073)94 b(658.10798)581 4573 y(5)47 b(4.88487)f(6.71217)94 b(625.01340)581 4682 y(6)47 b(4.76602)f(6.41506)94 b(561.68440)581 4792 y(7)47 b(4.52833)f(5.82083)94 b(446.46694)581 4902 y(8)47 b(4.05295)f(4.63238) 94 b(261.79422)581 5011 y(9)47 b(3.10219)f(2.25548)141 b(75.49762)533 5121 y(10)47 b(2.85185)f(1.62963)141 b(67.03704)533 5230 y(11)47 b(2.19088)f(1.76182)141 b(45.31640)533 5340 y(12)47 b(0.86892)f(2.02622)141 b(30.18555)p eop end %%Page: 427 445 TeXDict begin 427 444 bop 150 -116 a FK(Chapter)30 b(37:)41 b(Multidimensional)32 b(Minimization)1707 b(427)390 299 y FH(Minimum)46 b(found)g(at:)533 408 y(13)h(1.00000)f(2.00000)141 b(30.00000)150 540 y FK(Note)31 b(that)f(the)g(algorithm)g(gradually)g (increases)g(the)g(step)f(size)i(as)f(it)g(successfully)f(mo)m(v)m(es)i (do)m(wnhill,)150 649 y(as)g(can)f(b)s(e)g(seen)g(b)m(y)h(plotting)g (the)g(successiv)m(e)g(p)s(oin)m(ts.)275 2934 y @beginspecial 50 @llx 50 @lly 301 @urx 302 @ury 2448 @rwi @setspecial %%BeginDocument: multimin.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: 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setlinewidth } def /AL { stroke gnulinewidth 2 div setlinewidth } def /UL { gnulinewidth mul /userlinewidth exch def } def /PL { stroke userlinewidth setlinewidth } def /LTb { BL [] 0 0 0 DL } def /LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def /LT0 { PL [] 1 0 0 DL } def /LT1 { PL [4 dl 2 dl] 0 1 0 DL } def /LT2 { PL [2 dl 3 dl] 0 0 1 DL } def /LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def /LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def /LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def /LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def /LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def /LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def /Pnt { stroke [] 0 setdash gsave 1 setlinecap M 0 0 V stroke grestore } def /Dia { stroke [] 0 setdash 2 copy vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke Pnt } def /Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V currentpoint stroke M hpt neg vpt neg R hpt2 0 V stroke } def /Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke Pnt } def /Crs { stroke [] 0 setdash exch hpt sub exch vpt add M hpt2 vpt2 neg V currentpoint stroke M hpt2 neg 0 R hpt2 vpt2 V stroke } def /TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke Pnt } def /Star { 2 copy Pls Crs } def /BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath fill } def /TriUF { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath fill } def /TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke Pnt } def /TriDF { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath fill} def /DiaF { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath fill } def /Pent { stroke [] 0 setdash 2 copy gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore Pnt } def /PentF { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath fill grestore } def /Circle { stroke [] 0 setdash 2 copy hpt 0 360 arc stroke Pnt } def /CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def /C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def /C1 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill vpt 0 360 arc closepath } bind def /C2 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath } bind def /C3 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill vpt 0 360 arc closepath } bind def /C4 { BL [] 0 setdash 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc closepath } bind def /C5 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc } bind def /C6 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 270 arc closepath fill vpt 0 360 arc closepath } bind def /C7 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 270 arc closepath fill vpt 0 360 arc closepath } bind def /C8 { BL [] 0 setdash 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath } bind def /C9 { BL [] 0 setdash 2 copy moveto 2 copy vpt 270 450 arc closepath fill vpt 0 360 arc closepath } bind def /C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath } bind def /C11 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath } bind def /C12 { BL [] 0 setdash 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath } bind def /C13 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath } bind def /C14 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 360 arc closepath fill vpt 0 360 arc } bind def /C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill vpt 0 360 arc closepath } bind def /Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath } bind def /Square { dup Rec } bind def /Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def /S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def /S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def /S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def /S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def /S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def /S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def /S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill 2 copy vpt Square fill Bsquare } bind def /S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def /S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def /S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def /S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def /S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy vpt Square fill Bsquare } bind def /S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def /D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def /D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def /D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def /D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def /D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def /D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def /D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def /D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def /D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def /D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def /D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def /D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def /D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def /D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def /D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def /D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def /DiaE { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke } def /BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke } def /TriUE { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke } def /TriDE { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke } def /PentE { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore } def /CircE { stroke [] 0 setdash hpt 0 360 arc stroke } def /Opaque { gsave closepath 1 setgray fill grestore 0 setgray closepath } def /DiaW { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V Opaque stroke } def /BoxW { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V Opaque stroke } def /TriUW 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(another)h(example)g(using)f(the)h(Nelder-Mead)h(Simplex)e(algorithm)h (to)h(minimize)f(the)g(same)150 3575 y(example)31 b(ob)5 b(ject)31 b(function,)g(as)f(ab)s(o)m(v)m(e.)390 3684 y Fz(int)390 3771 y(main\(void\))390 3858 y({)468 3945 y(double)41 b(par[5])g(=)e({1.0,)h(2.0,)h(10.0,)f(20.0,)g(30.0};)468 4120 y(const)h(gsl_multimin_fminimizer_type)k(*T)40 b(=)547 4207 y(gsl_multimin_fminimizer_nmsim)q(plex2)q(;)468 4294 y(gsl_multimin_fminimizer)45 b(*s)40 b(=)f(NULL;)468 4381 y(gsl_vector)j(*ss,)e(*x;)468 4468 y(gsl_multimin_function)k (minex_func;)468 4643 y(size_t)d(iter)f(=)g(0;)468 4730 y(int)g(status;)468 4817 y(double)h(size;)468 4991 y(/*)f(Starting)h (point)g(*/)468 5078 y(x)f(=)f(gsl_vector_alloc)k(\(2\);)468 5166 y(gsl_vector_set)g(\(x,)d(0,)f(5.0\);)468 5253 y(gsl_vector_set)k (\(x,)d(1,)f(7.0\);)p eop end %%Page: 428 446 TeXDict begin 428 445 bop 150 -116 a FK(Chapter)30 b(37:)41 b(Multidimensional)32 b(Minimization)1707 b(428)468 299 y Fz(/*)40 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2313 y FB(1)661 2299 y FE(X)38 b FK(at)31 b(the)f(p)s(oin)m(t)h FD(x)p FK(.)150 2520 y FJ(38.3)68 b(Multi-parameter)47 b(regression)150 2680 y FK(This)31 b(section)i(describ)s(es)e(routines)g(whic)m(h)h(p)s (erform)e(least)j(squares)e(\014ts)g(to)i(a)f(linear)g(mo)s(del)f(b)m (y)h(mini-)150 2789 y(mizing)f(the)f(cost)i(function)1122 2952 y FE(\037)1179 2914 y FB(2)1241 2952 y FK(=)1337 2871 y Fs(X)1386 3048 y Fq(i)1472 2952 y FE(w)1537 2966 y Fq(i)1565 2952 y FK(\()p FE(y)1645 2966 y Fq(i)1693 2952 y FI(\000)1784 2871 y Fs(X)1828 3048 y Fq(j)1919 2952 y FE(X)1994 2966 y Fq(ij)2053 2952 y FE(c)2092 2966 y Fq(j)2127 2952 y FK(\))2162 2914 y FB(2)2225 2952 y FK(=)25 b FI(jj)p FE(y)e FI(\000)d FE(X)7 b(c)p FI(jj)2701 2914 y FB(2)2701 2974 y Fq(W)150 3192 y FK(where)38 b FE(y)k FK(is)d(a)g(v)m(ector)h(of)f FE(n)f FK(observ)-5 b(ations,)42 b FE(X)k FK(is)39 b(an)g FE(n)p FK(-b)m(y-)p FE(p)f FK(matrix)h(of)g(predictor)g(v)-5 b(ariables,)42 b FE(c)d FK(is)150 3302 y(a)d(v)m(ector)h(of)e(the)h 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b FK(of)36 b(length)g FE(n)p FK(.)56 b(In)35 b(order)h(to)g(apply)f(this)h(transformation,)i FE(L)3210 4978 y Fp(\000)p FB(1)3335 5011 y FK(m)m(ust)d(exist)390 5121 y(and)c(so)h(none)g(of)g(the)g FE(l)1190 5135 y Fq(i)1249 5121 y FK(ma)m(y)h(b)s(e)e(zero.)46 b(After)32 b(the)g(standard)f(form)g(system)h(has)g(b)s(een)f(solv)m(ed,)390 5230 y(use)41 b FH(gsl_multifit_linear_gen)o(form)o(1)35 b FK(to)42 b(reco)m(v)m(er)h(the)e(original)h(solution)f(v)m(ector.)75 b(It)41 b(is)390 5340 y(allo)m(w)m(ed)31 b(to)f(ha)m(v)m(e)g FD(X)39 b FK(=)28 b FD(Xs)33 b FK(and)c FD(y)37 b FK(=)28 b FD(ys)33 b FK(for)c(an)g(in-place)h(transform.)40 b(In)28 b(order)h(to)h(p)s(erform)e(a)p eop end %%Page: 437 455 TeXDict begin 437 454 bop 150 -116 a FK(Chapter)30 b(38:)41 b(Least-Squares)31 b(Fitting)2098 b(437)390 299 y(w)m(eigh)m(ted)26 b(regularized)g(\014t)f(with)g FE(L)g FK(=)g FE(I)7 b FK(,)26 b(the)g(user)e(ma)m(y)i(call)g FH(gsl_multifit_linear_apply)o (W)390 408 y FK(to)31 b(con)m(v)m(ert)h(to)f(standard)f(form.)3350 600 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multifit_linear_L)q (_dec)q(omp)f Fu(\()p FD(gsl)p 2016 600 28 4 v 41 w(matrix)27 b(*)g Ft(L)p FD(,)h(gsl)p 2632 600 V 40 w(v)m(ector)h(*)e Ft(tau)p Fu(\))390 710 y FK(This)32 b(function)g(factors)h(the)g FE(m)p FK(-b)m(y-)p FE(p)g FK(regularization)h(matrix)f FD(L)g FK(in)m(to)g(a)g(form)f(needed)g(for)h(the)390 819 y(later)e(transformation)f(to)h(standard)e(form.)40 b FD(L)29 b FK(ma)m(y)i(ha)m(v)m(e)g(an)m(y)f(n)m(um)m(b)s(er)f(of)h (ro)m(ws)g FE(m)p FK(.)40 b(If)29 b FE(m)c FI(\025)g FE(p)390 929 y FK(the)36 b(QR)f(decomp)s(osition)i(of)f FD(L)g FK(is)f(computed)h(and)f(stored)h(in)g FD(L)f FK(on)h(output.)57 b(If)35 b FE(m)g(<)f(p)p FK(,)j(the)390 1039 y(QR)h(decomp)s(osition)h(of)g FE(L)1347 1006 y Fq(T)1437 1039 y FK(is)f(computed)h(and)e(stored)i(in)f FD(L)g FK(on)h(output.)64 b(On)37 b(output,)k(the)390 1148 y(Householder)34 b(scalars)h(are)g(stored)f(in)g(the)g(v)m(ector)h FD(tau)g 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FK(After)c(a)g(regularized)h(system)f(has)g(b)s(een)f(solv)m(ed) i(with)e FE(L)g FK(=)g(diag\()p FE(l)2712 5025 y FB(0)2750 5011 y FE(;)15 b(l)2817 5025 y FB(1)2855 5011 y FE(;)g(:::;)g(l)3037 5025 y Fq(p)p Fp(\000)p FB(1)3162 5011 y FK(\),)28 b(this)f(function) 390 5121 y(bac)m(ktransforms)h(the)h(standard)f(form)g(solution)h(v)m (ector)h FD(cs)i FK(to)e(reco)m(v)m(er)g(the)f(solution)g(v)m(ector)h (of)390 5230 y(the)e(original)h(problem)f FD(c)p FK(.)40 b(The)28 b(diagonal)h(matrix)f(elemen)m(ts)i FE(l)2563 5244 y Fq(i)2618 5230 y FK(are)f(pro)m(vided)e(in)h(the)g(v)m(ector)i FD(L)p FK(.)390 5340 y(It)g(is)h(allo)m(w)m(ed)h(to)f(ha)m(v)m(e)h FD(c)k FK(=)30 b FD(cs)k FK(for)d(an)f(in-place)h(transform.)p eop end %%Page: 438 456 TeXDict begin 438 455 bop 150 -116 a FK(Chapter)30 b(38:)41 b(Least-Squares)31 b(Fitting)2098 b(438)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multifit_linear_g)q(enfo)q(rm2)f Fu(\()p FD(const)31 b(gsl)p 2254 299 28 4 v 41 w(matrix)g(*)f Ft(LQR)p FD(,)i(const)565 408 y(gsl)p 677 408 V 41 w(v)m(ector)g(*)e Ft(Ltau)p FD(,)i(const)f(gsl)p 1675 408 V 41 w(matrix)f(*)h Ft(X)p FD(,)g(const)g(gsl)p 2539 408 V 40 w(v)m(ector)h(*)f Ft(y)p FD(,)g(const)g(gsl)p 3380 408 V 40 w(v)m(ector)h(*)565 518 y Ft(cs)p FD(,)f(const)g(gsl)p 1075 518 V 41 w(matrix)f(*)h Ft(M)p FD(,)g(gsl)p 1701 518 V 41 w(v)m(ector)h(*)e Ft(c)p FD(,)h(gsl)p 2304 518 V 41 w(m)m(ulti\014t)p 2640 518 V 40 w(linear)p 2902 518 V 41 w(w)m(orkspace)g(*)g Ft(work)p Fu(\))3350 628 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multifit_linear_w)q(genf)q(orm)q(2)e Fu(\()p FD(const)32 b(gsl)p 2307 628 V 40 w(matrix)f(*)g Ft(LQR)p FD(,)g(const)565 737 y(gsl)p 677 737 V 41 w(v)m(ector)h(*)e Ft(Ltau)p FD(,)i(const)f(gsl)p 1675 737 V 41 w(matrix)f(*)h Ft(X)p FD(,)g(const)g(gsl)p 2539 737 V 40 w(v)m(ector)h(*)f Ft(w)p FD(,)g(const)g(gsl)p 3380 737 V 40 w(v)m(ector)h(*)565 847 y Ft(y)p FD(,)f(const)g(gsl)p 1023 847 V 40 w(v)m(ector)h(*)f Ft(cs)p FD(,)g(const)g(gsl)p 1916 847 V 41 w(matrix)f(*)h Ft(M)p FD(,)g(gsl)p 2542 847 V 41 w(v)m(ector)h(*)e Ft(c)p FD(,)565 956 y(gsl)p 677 956 V 41 w(m)m(ulti\014t)p 1013 956 V 40 w(linear)p 1275 956 V 41 w(w)m(orkspace)h(*)f Ft(work)p Fu(\))390 1066 y FK(After)45 b(a)g(regularized)g(system)g (has)f(b)s(een)g(solv)m(ed)i(with)e(a)h(general)g(rectangular)h(matrix) f FE(L)p FK(,)390 1176 y(sp)s(eci\014ed)29 b(b)m(y)g(\()p FD(LQR)p FK(,)p FD(Ltau)p FK(\),)h(this)f(function)g(bac)m(ktransforms) g(the)h(standard)e(form)h(solution)h FD(cs)390 1285 y FK(to)i(reco)m(v)m(er)i(the)d(solution)i(v)m(ector)g(of)e(the)h (original)h(problem,)e(whic)m(h)h(is)f(stored)h(in)f FD(c)p FK(,)i(of)f(length)390 1395 y FE(p)p FK(.)57 b(The)36 b(original)h(least)g(squares)f(matrix)g(and)f(observ)-5 b(ation)37 b(v)m(ector)h(are)e(pro)m(vided)g(in)f FD(X)46 b FK(and)390 1504 y FD(y)38 b FK(resp)s(ectiv)m(ely)-8 b(.)43 b FD(M)e FK(is)31 b(the)g(matrix)g(computed)f(b)m(y)g FH(gsl_multifit_linear_stdfor)o(m2)p FK(.)35 b(F)-8 b(or)390 1614 y(w)m(eigh)m(ted)32 b(\014ts,)e(the)h(w)m(eigh)m(t)h(v)m(ector)f FD(w)38 b FK(m)m(ust)30 b(also)i(b)s(e)e(supplied.)3350 1833 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multifit_linear_a)q (pply)q(W)f Fu(\()p FD(const)31 b(gsl)p 2150 1833 V 40 w(matrix)g(*)g Ft(X)p FD(,)g(const)565 1943 y(gsl)p 677 1943 V 41 w(v)m(ector)h(*)e Ft(w)p FD(,)h(const)g(gsl)p 1518 1943 V 41 w(v)m(ector)h(*)e Ft(y)p FD(,)h(gsl)p 2121 1943 V 41 w(matrix)g(*)f Ft(WX)p FD(,)i(gsl)p 2800 1943 V 40 w(v)m(ector)g(*)f Ft(Wy)p Fu(\))390 2052 y FK(F)-8 b(or)30 b(w)m(eigh)m(ted)h(least)g(squares)e(systems)h(with)f FE(L)c FK(=)g FE(I)7 b FK(,)30 b(this)g(function)f(ma)m(y)h(b)s(e)f (used)g(to)h(con)m(v)m(ert)390 2162 y(the)41 b(system)g(to)h(standard)e (form)h(b)m(y)g(applying)f(the)h(w)m(eigh)m(t)i(matrix)e FE(W)56 b FK(=)40 b(diag\()p FD(w)8 b FK(\))42 b(to)g(the)390 2271 y(least)30 b(squares)d(matrix)i FD(X)37 b FK(and)28 b(observ)-5 b(ation)29 b(v)m(ector)h FD(y)p FK(.)40 b(On)27 b(output,)i FD(WX)38 b FK(is)28 b(equal)h(to)g FE(W)3564 2238 y FB(1)p Fq(=)p FB(2)3668 2271 y FE(X)390 2381 y FK(and)k FD(Wy)42 b FK(is)33 b(equal)h(to)g FE(W)1303 2348 y FB(1)p Fq(=)p FB(2)1407 2381 y FE(y)s FK(.)50 b(It)34 b(is)f(allo)m(w)m(ed)j(for)d FD(WX)43 b FK(=)33 b FD(X)43 b FK(and)33 b FD(Wy)42 b FK(=)33 b FD(y)41 b FK(for)34 b(an)f(in-place)390 2491 y(transform.)3350 2710 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multifit_linear_l)q (curv)q(e)f Fu(\()p FD(const)31 b(gsl)p 2150 2710 V 40 w(v)m(ector)h(*)f Ft(y)p FD(,)g(gsl)p 2753 2710 V 41 w(v)m(ector)g(*)565 2819 y Ft(reg_param)p FD(,)i(gsl)p 1203 2819 V 41 w(v)m(ector)f(*)f Ft(rho)p FD(,)g(gsl)p 1911 2819 V 41 w(v)m(ector)h(*)e Ft(eta)p FD(,)i(gsl)p 2619 2819 V 41 w(m)m(ulti\014t)p 2955 2819 V 40 w(linear)p 3217 2819 V 40 w(w)m(orkspace)g(*)565 2929 y Ft(work)p Fu(\))390 3039 y FK(This)h(function)g(computes)h(the)g(L-curv)m(e)g (for)g(a)g(least)h(squares)e(system)h(using)f(the)h(righ)m(t)g(hand)390 3148 y(side)c(v)m(ector)i FD(y)38 b FK(and)30 b(the)g(SVD)h(decomp)s (osition)f(of)h(the)f(least)i(squares)e(matrix)g FD(X)p FK(,)h(whic)m(h)f(m)m(ust)390 3258 y(b)s(e)d(pro)m(vided)h(to)h FH(gsl_multifit_linear_svd)22 b FK(prior)27 b(to)i(calling)g(this)f (function.)40 b(The)27 b(output)390 3367 y(v)m(ectors)46 b FD(reg)p 840 3367 V 41 w(param)p FK(,)i FD(rho)p FK(,)g(and)d FD(eta)h FK(m)m(ust)e(all)i(b)s(e)e(the)h(same)h(size,)j(and)44 b(will)i(con)m(tain)g(the)390 3477 y(regularization)39 b(parameters)f FE(\025)1504 3491 y Fq(i)1532 3477 y FK(,)h(residual)e (norms)f FI(jj)p FE(y)28 b FI(\000)d FE(X)7 b(c)2562 3491 y Fq(i)2590 3477 y FI(jj)p FK(,)40 b(and)d(solution)h(norms)e FI(jj)p FE(Lc)3671 3491 y Fq(i)3699 3477 y FI(jj)390 3587 y FK(whic)m(h)28 b(comp)s(ose)h(the)f(L-curv)m(e,)h(where)f FE(c)1820 3601 y Fq(i)1876 3587 y FK(is)h(the)f(regularized)h(solution) g(v)m(ector)h(corresp)s(onding)390 3696 y(to)f FE(\025)552 3710 y Fq(i)580 3696 y FK(.)40 b(The)28 b(user)g(ma)m(y)h(determine)g (the)g(n)m(um)m(b)s(er)e(of)i(p)s(oin)m(ts)g(on)f(the)h(L-curv)m(e)g(b) m(y)g(adjusting)f(the)390 3806 y(size)35 b(of)f(these)g(input)f(arra)m (ys.)51 b(The)33 b(regularization)j(parameters)e FE(\025)2771 3820 y Fq(i)2832 3806 y FK(are)g(estimated)h(from)f(the)390 3915 y(singular)24 b(v)-5 b(alues)25 b(of)g FD(X)p FK(,)h(and)d(c)m (hosen)i(to)g(represen)m(t)g(the)g(most)f(relev)-5 b(an)m(t)26 b(p)s(ortion)e(of)h(the)f(L-curv)m(e.)3350 4134 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multifit_linear_l)q(corn)q(er)f Fu(\()p FD(const)31 b(gsl)p 2202 4134 V 41 w(v)m(ector)h(*)e Ft(rho)p FD(,)i(const)565 4244 y(gsl)p 677 4244 V 41 w(v)m(ector)g(*)e Ft(eta)p FD(,)i(size)p 1420 4244 V 41 w(t)e(*)h Ft(idx)p Fu(\))390 4354 y FK(This)f(function)g(attempts)i (to)f(lo)s(cate)h(the)f(corner)g(of)f(the)h(L-curv)m(e)g(\()p FI(jj)p FE(y)24 b FI(\000)c FE(X)7 b(c)p FI(jj)p FE(;)15 b FI(jj)p FE(Lc)p FI(jj)p FK(\))34 b(de\014ned)390 4463 y(b)m(y)i(the)g FD(rho)k FK(and)35 b FD(eta)i FK(input)e(arra)m(ys)i (resp)s(ectiv)m(ely)-8 b(.)59 b(The)35 b(corner)h(is)g(de\014ned)f(as)h (the)g(p)s(oin)m(t)g(of)390 4573 y(maxim)m(um)f(curv)-5 b(ature)34 b(of)h(the)g(L-curv)m(e)h(in)e(log-log)j(scale.)56 b(The)34 b FD(rho)39 b FK(and)34 b FD(eta)i FK(arra)m(ys)f(can)h(b)s(e) 390 4682 y(outputs)h(of)h FH(gsl_multifit_linear_lcurv)o(e)p FK(.)57 b(The)37 b(algorithm)i(used)e(simply)g(\014ts)h(a)g(circle)390 4792 y(to)c(3)h(consecutiv)m(e)g(p)s(oin)m(ts)f(on)f(the)h(L-curv)m(e)g (and)f(uses)h(the)g(circle's)h(radius)d(to)j(determine)f(the)390 4902 y(curv)-5 b(ature)34 b(at)h(the)f(middle)g(p)s(oin)m(t.)52 b(Therefore,)35 b(the)f(input)g(arra)m(y)g(sizes)h(m)m(ust)f(b)s(e)g FI(\025)d FK(3.)52 b(With)390 5011 y(more)45 b(p)s(oin)m(ts)g(pro)m (vided)g(for)g(the)h(L-curv)m(e,)j(a)d(b)s(etter)f(estimate)i(of)f(the) f(curv)-5 b(ature)45 b(can)h(b)s(e)390 5121 y(obtained.)53 b(The)34 b(arra)m(y)h(index)f(corresp)s(onding)f(to)j(maxim)m(um)e (curv)-5 b(ature)34 b(\(ie:)50 b(the)34 b(corner\))h(is)390 5230 y(returned)f(in)h FD(idx)p FK(.)55 b(If)35 b(the)g(input)g(arra)m (ys)g(con)m(tain)i(colinear)f(p)s(oin)m(ts,)h(this)e(function)g(could)g (fail)390 5340 y(and)30 b(return)f FH(GSL_EINVAL)p FK(.)p eop end %%Page: 439 457 TeXDict begin 439 456 bop 150 -116 a FK(Chapter)30 b(38:)41 b(Least-Squares)31 b(Fitting)2098 b(439)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multifit_linear_l)q(corn)q(er2)f Fu(\()p FD(const)31 b(gsl)p 2254 299 28 4 v 41 w(v)m(ector)h(*)f Ft(reg_param)p FD(,)565 408 y(const)g(gsl)p 915 408 V 41 w(v)m(ector)h(*)e Ft(eta)p FD(,)i(size)p 1658 408 V 41 w(t)e(*)h Ft(idx)p Fu(\))390 518 y FK(This)d(function)h(attempts)h (to)g(lo)s(cate)g(the)g(corner)e(of)i(an)f(alternate)h(L-curv)m(e)g(\() p FE(\025)3166 485 y FB(2)3203 518 y FE(;)15 b FI(jj)p FE(Lc)p FI(jj)3444 485 y FB(2)3483 518 y FK(\))29 b(stud-)390 628 y(ied)24 b(b)m(y)g(Rezghi)h(and)e(Hosseini,)k(2009.)40 b(This)23 b(alternate)j(L-curv)m(e)f(can)f(pro)m(vide)g(b)s(etter)g (estimates)390 737 y(of)35 b(the)g(regularization)h(parameter)f(for)g (smo)s(oth)f(solution)h(v)m(ectors.)55 b(The)34 b(regularization)j(pa-) 390 847 y(rameters)i FE(\025)f FK(and)f(solution)i(norms)e FI(jj)p FE(Lc)p FI(jj)j FK(are)e(pro)m(vided)g(in)g(the)h FD(reg)p 2869 847 V 40 w(param)f FK(and)g FD(eta)h FK(input)390 956 y(arra)m(ys)31 b(resp)s(ectiv)m(ely)-8 b(.)43 b(The)30 b(corner)g(is)h(de\014ned)e(as)i(the)g(p)s(oin)m(t)f(of)h(maxim)m(um)f (curv)-5 b(ature)30 b(of)h(this)390 1066 y(alternate)39 b(L-curv)m(e)f(in)f(linear)g(scale.)63 b(The)37 b FD(reg)p 2085 1066 V 40 w(param)g FK(and)g FD(eta)h FK(arra)m(ys)g(can)f(b)s(e)g (outputs)g(of)390 1176 y FH(gsl_multifit_linear_lcur)o(ve)p FK(.)i(The)31 b(algorithm)i(used)e(simply)h(\014ts)f(a)i(circle)g(to)f (3)h(consec-)390 1285 y(utiv)m(e)k(p)s(oin)m(ts)g(on)f(the)h(L-curv)m (e)g(and)f(uses)g(the)g(circle's)i(radius)e(to)h(determine)g(the)f (curv)-5 b(ature)390 1395 y(at)44 b(the)g(middle)f(p)s(oin)m(t.)81 b(Therefore,)47 b(the)d(input)f(arra)m(y)h(sizes)g(m)m(ust)g(b)s(e)f FI(\025)k FK(3.)81 b(With)44 b(more)390 1504 y(p)s(oin)m(ts)32 b(pro)m(vided)g(for)g(the)h(L-curv)m(e,)g(a)g(b)s(etter)f(estimate)i (of)f(the)f(curv)-5 b(ature)32 b(can)h(b)s(e)e(obtained.)390 1614 y(The)e(arra)m(y)h(index)f(corresp)s(onding)g(to)h(maxim)m(um)f (curv)-5 b(ature)30 b(\(ie:)41 b(the)30 b(corner\))f(is)h(returned)e (in)390 1724 y FD(idx)p FK(.)59 b(If)36 b(the)h(input)f(arra)m(ys)g (con)m(tain)i(colinear)g(p)s(oin)m(ts,)g(this)f(function)f(could)h (fail)g(and)f(return)390 1833 y FH(GSL_EINVAL)p FK(.)3350 2107 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multifit_linear_g)q (cv_i)q(nit)q(\(co)q(nst)f FD(gsl)p 2295 2107 V 41 w(v)m(ector)32 b(*)e Ft(y)p FD(,)h(gsl)p 2898 2107 V 41 w(v)m(ector)565 2217 y(*)e Ft(reg_param)p FD(,)j(gsl)p 1276 2217 V 41 w(v)m(ector)e(*)f Ft(UTy)p FD(,)h(double)f(*)g Ft(delta0)p FD(,)i(gsl)p 2713 2217 V 40 w(m)m(ulti\014t)p 3048 2217 V 41 w(linear)p 3311 2217 V 40 w(w)m(orkspace)565 2326 y(*)g Ft(work)p Fu(\))390 2436 y FK(This)41 b(function)g(p)s(erforms)f (some)i(initialization)i(in)e(preparation)f(for)g(computing)h(the)g (GCV)390 2545 y(curv)m(e)d(and)f(its)i(minim)m(um.)65 b(The)38 b(righ)m(t)i(hand)e(side)h(v)m(ector)h(is)f(pro)m(vided)f(in)h FD(y)p FK(.)66 b(On)38 b(output,)390 2655 y FD(reg)p 517 2655 V 40 w(param)26 b FK(is)g(set)h(to)g(a)f(v)m(ector)i(of)e (regularization)i(parameters)f(in)e(decreasing)i(order)f(and)f(ma)m(y) 390 2765 y(b)s(e)38 b(of)h(an)m(y)h(size.)67 b(The)38 b(v)m(ector)j FD(UT)m(y)47 b FK(of)39 b(size)h FE(p)e FK(is)h(set)h(to)f FE(U)2570 2732 y Fq(T)2622 2765 y FE(y)s FK(.)67 b(The)38 b(parameter)h FD(delta0)48 b FK(is)390 2874 y(needed)30 b(for)g(subsequen)m(t)g(steps)g(of)h(the)f (GCV)h(calculation.)3350 3148 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multifit_linear_g)q(cv_c)q(urv)q(e\(c)q(ons)q(t)e FD(gsl)p 2347 3148 V 41 w(v)m(ector)32 b(*)565 3258 y Ft(reg_param)p FD(,)h(const)e(gsl)p 1441 3258 V 41 w(v)m(ector)h(*)f Ft(UTy)p FD(,)g(const)g(double)f Ft(delta0)p FD(,)i(gsl)p 3049 3258 V 41 w(v)m(ector)g(*)f Ft(G)p FD(,)565 3367 y(gsl)p 677 3367 V 41 w(m)m(ulti\014t)p 1013 3367 V 40 w(linear)p 1275 3367 V 41 w(w)m(orkspace)g(*)f Ft(work)p Fu(\))390 3477 y FK(This)24 b(fun)m(tion)h(calculates)j(the)d(GCV)h (curv)m(e)f FE(G)p FK(\()p FE(\025)p FK(\))h(and)f(stores)h(it)f(in)g FD(G)j FK(on)d(output,)h(whic)m(h)f(m)m(ust)390 3587 y(b)s(e)g(the)g(same)h(size)g(as)g FD(reg)p 1284 3587 V 40 w(param)p FK(.)39 b(The)25 b(inputs)f FD(reg)p 2217 3587 V 40 w(param)p FK(,)j FD(UT)m(y)33 b FK(and)25 b FD(delta0)33 b FK(are)26 b(computed)390 3696 y(in)k FH (gsl_multifit_linear_gcv_)o(init)o FK(.)3350 3970 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multifit_linear_g)q(cv_m)q(in\()q (con)q(st)f FD(gsl)p 2243 3970 V 40 w(v)m(ector)32 b(*)f Ft(reg_param)p FD(,)565 4080 y(const)g(gsl)p 915 4080 V 41 w(v)m(ector)h(*)e Ft(UTy)p FD(,)i(const)f(gsl)p 1861 4080 V 40 w(v)m(ector)h(*)f Ft(G)p FD(,)g(const)g(double)f Ft(delta0)p FD(,)i(double)e(*)565 4189 y Ft(lambda)p FD(,)i(gsl)p 1046 4189 V 41 w(m)m(ulti\014t)p 1382 4189 V 41 w(linear)p 1645 4189 V 40 w(w)m(orkspace)f(*)g Ft(work)p Fu(\))390 4299 y FK(This)37 b(function)h(computes)g(the)g(v)-5 b(alue)38 b(of)g(the)g(regularization)i(parameter)e(whic)m(h)g (minimizes)390 4408 y(the)h(GCV)f(curv)m(e)h FE(G)p FK(\()p FE(\025)p FK(\))h(and)d(stores)i(it)g(in)g FD(lam)m(b)s(da)p FK(.)64 b(The)38 b(input)g FD(G)j FK(is)d(calculated)j(b)m(y)d FH(gsl_)390 4518 y(multifit_linear_gcv_curv)o(e)29 b FK(and)k(the)i(inputs)e FD(reg)p 2368 4518 V 41 w(param)p FK(,)i FD(UT)m(y)42 b FK(and)34 b FD(delta0)43 b FK(are)35 b(com-)390 4628 y(puted)30 b(b)m(y)g FH(gsl_multifit_linear_gcv_)o(ini) o(t)p FK(.)3350 4902 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_multifit_linear_gc)q(v_c)q(alc)q(\(co)q(nst)e FD(double)30 b Ft(lambda)p FD(,)565 5011 y(const)h(gsl)p 915 5011 V 41 w(v)m(ector)h(*)e Ft(UTy)p FD(,)i(const)f(double)f Ft(delta0)p FD(,)i(gsl)p 2523 5011 V 41 w(m)m(ulti\014t)p 2859 5011 V 40 w(linear)p 3121 5011 V 40 w(w)m(orkspace)g(*)565 5121 y Ft(work)p Fu(\))390 5230 y FK(This)i(function)h(returns)f(the)i (v)-5 b(alue)35 b(of)h(the)f(GCV)g(curv)m(e)h FE(G)p FK(\()p FE(\025)p FK(\))g(corresp)s(onding)f(to)g(the)h(input)390 5340 y FD(lam)m(b)s(da)p FK(.)p eop end %%Page: 440 458 TeXDict begin 440 457 bop 150 -116 a FK(Chapter)30 b(38:)41 b(Least-Squares)31 b(Fitting)2098 b(440)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multifit_linear_g)q(cv\(c)q(ons)q(t) e FD(gsl)p 2033 299 28 4 v 41 w(v)m(ector)32 b(*)f Ft(y)p FD(,)g(gsl)p 2637 299 V 40 w(v)m(ector)h(*)565 408 y Ft(reg_param)p FD(,)h(gsl)p 1203 408 V 41 w(v)m(ector)f(*)f Ft(G)p FD(,)g(double)e(*)i Ft(lambda)p FD(,)i(double)d(*)g Ft(G_lambda)p FD(,)565 518 y(gsl)p 677 518 V 41 w(m)m(ulti\014t)p 1013 518 V 40 w(linear)p 1275 518 V 41 w(w)m(orkspace)h(*)f Ft(work)p Fu(\))390 628 y FK(This)h(function)h(com)m(bines)g(the)g (steps)g FH(gcv_init)p FK(,)e FH(gcv_curve)p FK(,)g(and)h 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Ft(L)p Fu(\))390 1469 y FK(This)i(function)g(computes)h(the)g(discrete)h(appro)m (ximation)g(to)f(the)g(deriv)-5 b(ativ)m(e)35 b(op)s(erator)f FE(L)3602 1483 y Fq(k)3677 1469 y FK(of)390 1579 y(order)k FD(k)44 b FK(on)38 b(a)h(regular)f(grid)h(of)f FD(p)j FK(p)s(oin)m(ts)d(and)g(stores)h(it)g(in)f FD(L)p FK(.)64 b(The)38 b(dimensions)g(of)g FD(L)h FK(are)390 1688 y(\()p FE(p)20 b FI(\000)g FE(k)s FK(\)-b)m(y-)p FE(p)p FK(.)3350 1872 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multifit_linear_L)q (sobo)q(lev)f Fu(\()p FD(const)31 b(size)p 2289 1872 V 41 w(t)g Ft(p)p FD(,)g(const)g(size)p 2883 1872 V 41 w(t)565 1982 y Ft(kmax)p FD(,)h(const)f(gsl)p 1180 1982 V 40 w(v)m(ector)h(*)f Ft(alpha)p FD(,)h(gsl)p 1992 1982 V 41 w(matrix)e(*)h Ft(L)p FD(,)g(gsl)p 2618 1982 V 41 w(m)m(ulti\014t)p 2954 1982 V 40 w(linear)p 3216 1982 V 41 w(w)m(orkspace)g(*)565 2091 y Ft(work)p Fu(\))390 2201 y FK(This)37 b(function)h(computes)g(the)g(regularization)i (matrix)e FD(L)g FK(corresp)s(onding)f(to)h(the)h(w)m(eigh)m(ted)390 2310 y(Sob)s(olo)m(v)31 b(norm)f FI(jj)p FE(Lc)p FI(jj)1170 2277 y FB(2)1233 2310 y FK(=)1329 2246 y Fs(P)1417 2333 y Fq(k)1473 2310 y FE(\013)1531 2277 y FB(2)1531 2333 y Fq(k)1572 2310 y FI(jj)p FE(L)1684 2324 y Fq(k)1725 2310 y FE(c)p FI(jj)1814 2277 y FB(2)1883 2310 y FK(where)g FE(L)2208 2324 y Fq(k)2279 2310 y FK(appro)m(ximates)h(the)g(deriv)-5 b(ativ)m(e)32 b(op)s(erator)390 2420 y(of)23 b(order)g FE(k)s FK(.)38 b(This)22 b(regularization)j(norm)d(can)h(b)s(e)g (useful)f(in)g(applications)j(where)d(it)i(is)f(necessary)390 2530 y(to)33 b(smo)s(oth)g(sev)m(eral)h(deriv)-5 b(ativ)m(es)34 b(of)f(the)g(solution.)48 b FD(p)35 b FK(is)e(the)g(n)m(um)m(b)s(er)e (of)i(mo)s(del)f(parameters,)390 2639 y FD(kmax)40 b FK(is)34 b(the)f(highest)h(deriv)-5 b(ativ)m(e)35 b(to)g(include)e(in)g (the)h(summation)g(ab)s(o)m(v)m(e,)h(and)e FD(alpha)h FK(is)g(the)390 2749 y(v)m(ector)d(of)e(w)m(eigh)m(ts)i(of)e(size)h FD(kmax)35 b FH(+)29 b FK(1,)h(where)f FD(alpha)p FK([k])h(=)e FE(\013)2553 2763 y Fq(k)2623 2749 y FK(is)i(the)f(w)m(eigh)m(t)i (assigned)e(to)h(the)390 2858 y(deriv)-5 b(ativ)m(e)32 b(of)e(order)g FE(k)s FK(.)41 b(The)30 b(output)g(matrix)h FD(L)f FK(is)g(size)h FD(p)p FK(-b)m(y-)p FD(p)i FK(and)d(upp)s(er)e (triangular.)3350 3042 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_multifit_linear_rc)q(ond)e Fu(\()p FD(const)565 3152 y(gsl)p 677 3152 V 41 w(m)m(ulti\014t)p 1013 3152 V 40 w(linear)p 1275 3152 V 41 w(w)m(orkspace)31 b(*)f Ft(work)p Fu(\))390 3261 y FK(This)e(function)g(returns)g(the)h (recipro)s(cal)g(condition)h(n)m(um)m(b)s(er)d(of)i(the)g(least)h (squares)e(matrix)h FE(X)7 b FK(,)390 3371 y(de\014ned)33 b(as)h(the)g(ratio)h(of)g(the)f(smallest)h(and)e(largest)j(singular)d (v)-5 b(alues,)36 b(rcond)d(=)h FE(\033)3363 3385 y Fq(min)3491 3371 y FE(=\033)3588 3385 y Fq(max)3725 3371 y FK(.)390 3481 y(The)d(routine)g FH(gsl_multifit_linear_svd)25 b FK(m)m(ust)31 b(\014rst)f(b)s(e)h(called)i(to)e(compute)h(the)f(SVD)h (of)390 3590 y FE(X)7 b FK(.)150 3822 y FJ(38.5)68 b(Robust)46 b(linear)f(regression)150 3982 y FK(Ordinary)21 b(least)j(squares)e (\(OLS\))g(mo)s(dels)g(are)h(often)g(hea)m(vily)h(in\015uenced)d(b)m(y) h(the)h(presence)f(of)h(outliers.)150 4091 y(Outliers)36 b(are)h(data)g(p)s(oin)m(ts)f(whic)m(h)g(do)h(not)f(follo)m(w)i(the)e (general)i(trend)d(of)i(the)f(other)h(observ)-5 b(ations,)150 4201 y(although)31 b(there)f(is)h(strictly)g(no)f(precise)h (de\014nition)f(of)g(an)h(outlier.)41 b(Robust)30 b(linear)h (regression)f(refers)150 4311 y(to)39 b(regression)f(algorithms)i(whic) m(h)d(are)i(robust)e(to)i(outliers.)65 b(The)38 b(most)h(common)f(t)m (yp)s(e)g(of)h(robust)150 4420 y(regression)31 b(is)f(M-estimation.)43 b(The)30 b(general)h(M-estimator)i(minimizes)d(the)h(ob)5 b(jectiv)m(e)32 b(function)1358 4507 y Fs(X)1407 4684 y Fq(i)1494 4588 y FE(\032)p FK(\()p FE(e)1618 4602 y Fq(i)1646 4588 y FK(\))25 b(=)1802 4507 y Fs(X)1851 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w(err)390 737 y FK(for)30 b(the)h(mo)s(del)f FE(y)e FK(=)d FE(x:c)31 b FK(at)g(the)f(p)s(oin)m(t) h FD(x)p FK(.)3350 911 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multifit_robust_r)q(esid)q(ual)q(s)e Fu(\()p FD(const)32 b(gsl)p 2307 911 V 40 w(matrix)f(*)g Ft(X)p FD(,)g(const)565 1020 y(gsl)p 677 1020 V 41 w(v)m(ector)h(*)e Ft(y)p FD(,)h(const)g(gsl) p 1518 1020 V 41 w(v)m(ector)h(*)e Ft(c)p FD(,)h(gsl)p 2121 1020 V 41 w(v)m(ector)h(*)f Ft(r)p FD(,)565 1130 y(gsl)p 677 1130 V 41 w(m)m(ulti\014t)p 1013 1130 V 40 w(robust)p 1307 1130 V 39 w(w)m(orkspace)h(*)e Ft(w)p Fu(\))390 1239 y FK(This)k(function)g(computes)h(the)g(v)m(ector)h(of)e (studen)m(tized)h(residuals)g FE(r)2824 1253 y Fq(i)2884 1239 y FK(=)2996 1197 y Fq(y)3030 1205 y Fl(i)3056 1197 y Fp(\000)p FB(\()p Fq(X)5 b(c)p FB(\))3249 1205 y Fl(i)p 2996 1218 279 4 v 3013 1273 a Fq(\033)3053 1227 y Fp(p)p 3108 1227 151 3 v 46 x FB(1)p Fp(\000)p Fq(h)3232 1281 y Fl(i)3320 1239 y FK(for)34 b(the)h(ob-)390 1349 y(serv)-5 b(ations)40 b 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390 847 y(v)m(ector.)42 b(It)31 b(is)f(allo)m(w)m(ed)i(to)g(ha)m(v)m(e) f FD(X)40 b FK(=)30 b FD(Xs)k FK(and)c FD(y)38 b FK(=)30 b FD(ys)k FK(for)c(an)g(in-place)h(transform.)3350 1022 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multilarge_linear)q(_L_d)q (eco)q(mp)f Fu(\()p FD(gsl)p 2121 1022 28 4 v 41 w(matrix)30 b(*)h Ft(L)p FD(,)g(gsl)p 2747 1022 V 41 w(v)m(ector)h(*)565 1132 y Ft(tau)p Fu(\))390 1241 y FK(This)i(function)g(calculates)j(the) e(QR)g(decomp)s(osition)g(of)g(the)g FE(m)p FK(-b)m(y-)p FE(p)g FK(regularization)i(matrix)390 1351 y FD(L)p FK(.)44 b FD(L)32 b FK(m)m(ust)f(ha)m(v)m(e)i FE(m)28 b FI(\025)f FE(p)p FK(.)44 b(On)31 b(output,)h(the)g(Householder)g(scalars)g(are)g (stored)g(in)f(the)h(v)m(ector)390 1461 y FD(tau)e FK(of)g(size)h FE(p)p FK(.)40 b(These)30 b(outputs)f(will)h(b)s(e)f(used)g(b)m(y)h FH(gsl_multilarge_linear_ws)o(tdfo)o(rm2)23 b FK(to)390 1570 y(complete)32 b(the)e(transformation)h(to)g(standard)f(form.)3350 1745 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multilarge_linear)q (_std)q(for)q(m2)f Fu(\()p FD(const)31 b(gsl)p 2359 1745 V 41 w(matrix)f(*)h Ft(LQR)p FD(,)h(const)565 1855 y(gsl)p 677 1855 V 41 w(v)m(ector)g(*)e Ft(Ltau)p FD(,)i(const)f(gsl)p 1675 1855 V 41 w(matrix)f(*)h Ft(X)p FD(,)g(const)g(gsl)p 2539 1855 V 40 w(v)m(ector)h(*)f Ft(y)p FD(,)g(gsl)p 3142 1855 V 41 w(matrix)f(*)h Ft(Xs)p FD(,)565 1965 y(gsl)p 677 1965 V 41 w(v)m(ector)h(*)e Ft(ys)p FD(,)i(gsl)p 1333 1965 V 40 w(m)m(ultilarge)p 1773 1965 V 42 w(linear)p 2037 1965 V 40 w(w)m(orkspace)f(*)g Ft(work)p Fu(\))3350 2074 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multilarge_linear)q (_wst)q(dfo)q(rm2)f Fu(\()p FD(const)31 b(gsl)p 2411 2074 V 41 w(matrix)g(*)f Ft(LQR)p FD(,)565 2184 y(const)h(gsl)p 915 2184 V 41 w(v)m(ector)h(*)e Ft(Ltau)p FD(,)i(const)f(gsl)p 1913 2184 V 41 w(matrix)f(*)h Ft(X)p FD(,)g(const)g(gsl)p 2777 2184 V 40 w(v)m(ector)h(*)f Ft(w)p FD(,)g(const)565 2293 y(gsl)p 677 2293 V 41 w(v)m(ector)g(*)f Ft(y)p FD(,)g(gsl)p 1278 2293 V 40 w(matrix)g(*)g Ft(Xs)p FD(,)g(gsl)p 1953 2293 V 41 w(v)m(ector)h(*)f Ft(ys)p FD(,)g(gsl)p 2606 2293 V 41 w(m)m(ultilarge)p 3047 2293 V 42 w(linear)p 3311 2293 V 40 w(w)m(orkspace)565 2403 y(*)h Ft(work)p Fu(\))390 2513 y FK(These)k(functions)h(con)m(v)m(ert)h(a)f(blo)s(c)m (k)g(of)g(ro)m(ws)g(\()p FD(X)p FK(,)p FD(y)p FK(,)p FD(w)8 b FK(\))37 b(to)f(standard)f(form)g(\()3155 2490 y(~)3136 2513 y FE(X)8 b FK(,)q(~)-46 b FE(y)s FK(\))36 b(whic)m(h)g(are)390 2622 y(stored)j(in)h FD(Xs)j FK(and)38 b FD(ys)43 b FK(resp)s(ectiv)m(ely)-8 b(.)70 b FD(X)p FK(,)42 b FD(y)p FK(,)g(and)c FD(w)47 b FK(m)m(ust)39 b(all)i(ha)m(v)m(e)f(the)g(same)g(n)m(um)m(b)s(er)e(of)390 2732 y(ro)m(ws.)45 b(The)31 b FE(m)p FK(-b)m(y-)p FE(p)h FK(regularization)i(matrix)e FD(L)g FK(is)g(sp)s(eci\014ed)f(b)m(y)g (the)h(inputs)f FD(LQR)g FK(and)h FD(Ltau)p FK(,)390 2841 y(whic)m(h)42 b(are)h(outputs)f(from)g FH (gsl_multilarge_linear_L_d)o(eco)o(mp)p FK(.)71 b FD(Xs)46 b FK(and)c FD(ys)k FK(ha)m(v)m(e)e(the)390 2951 y(same)35 b(dimensions)e(as)i FD(X)44 b FK(and)33 b FD(y)p FK(.)53 b(After)35 b(the)f(standard)g(form)g(system)g(has)g(b)s(een)g(solv)m (ed,)i(use)390 3061 y FH(gsl_multilarge_linear_ge)o(nfor)o(m2)22 b FK(to)30 b(reco)m(v)m(er)g(the)f(original)h(solution)g(v)m(ector.)42 b(Optional)390 3170 y(data)31 b(w)m(eigh)m(ts)h(ma)m(y)f(b)s(e)f (supplied)f(in)h(the)g(v)m(ector)i FD(w)p FK(,)e(where)g FE(W)38 b FK(=)30 b(diag\(w\).)3350 3345 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multilarge_linear)q(_acc)q(umu)q(lat)q(e)e Fu(\()p FD(gsl)p 2225 3345 V 41 w(matrix)30 b(*)g Ft(X)p FD(,)f(gsl)p 2848 3345 V 41 w(v)m(ector)i(*)565 3455 y Ft(y)p FD(,)g(gsl)p 785 3455 V 41 w(m)m(ultilarge)p 1226 3455 V 41 w(linear)p 1489 3455 V 41 w(w)m(orkspace)g(*)g Ft(w)p Fu(\))390 3565 y FK(This)47 b(function)g(accum)m(ulates)i(the)e (standard)g(form)f(blo)s(c)m(k)i(\()p FE(X)r(;)15 b(y)s FK(\))49 b(in)m(to)f(the)g(curren)m(t)f(least)390 3674 y(squares)39 b(system.)67 b FD(X)48 b FK(and)38 b FD(y)47 b FK(ha)m(v)m(e)41 b(the)e(same)g(n)m(um)m(b)s(er)f(of)h(ro)m(ws,)j (whic)m(h)d(can)g(b)s(e)g(arbitrary)-8 b(.)390 3784 y FD(X)42 b FK(m)m(ust)33 b(ha)m(v)m(e)h FE(p)f FK(columns.)48 b(F)-8 b(or)33 b(the)g(TSQR)f(metho)s(d,)h FD(X)42 b FK(and)33 b FD(y)40 b FK(are)33 b(destro)m(y)m(ed)h(on)f(output.)390 3893 y(F)-8 b(or)31 b(the)g(normal)f(equations)h(metho)s(d,)f(they)h (are)f(b)s(oth)g(unc)m(hanged.)3350 4069 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multilarge_linear)q(_sol)q(ve)f Fu(\()p FD(const)31 b(double)f Ft(lambda)p FD(,)i(gsl)p 2864 4069 V 41 w(v)m(ector)565 4178 y(*)f Ft(c)p FD(,)g(double)f(*)g Ft(rnorm)p FD(,)i(double)e(*)h Ft(snorm)p FD(,)h(gsl)p 2232 4178 V 41 w(m)m(ultilarge)p 2673 4178 V 42 w(linear)p 2937 4178 V 40 w(w)m(orkspace)f(*)g Ft(w)p Fu(\))390 4288 y FK(After)k(all)h(blo)s(c)m(ks)g(\()p FE(X)1154 4302 y Fq(i)1182 4288 y FE(;)15 b(y)1267 4302 y Fq(i)1295 4288 y FK(\))35 b(ha)m(v)m(e)i(b)s(een)d(accum)m(ulated)j(in)m(to)f 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FK(After)d(a)g(regularized)h(system)f(has)g(b)s(een)f(solv)m(ed) i(with)e FE(L)g FK(=)g(diag\()p FE(l)2712 5025 y FB(0)2750 5011 y FE(;)15 b(l)2817 5025 y FB(1)2855 5011 y FE(;)g(:::;)g(l)3037 5025 y Fq(p)p Fp(\000)p FB(1)3162 5011 y FK(\),)28 b(this)f(function) 390 5121 y(bac)m(ktransforms)h(the)h(standard)f(form)g(solution)h(v)m (ector)h FD(cs)i FK(to)e(reco)m(v)m(er)g(the)f(solution)g(v)m(ector)h (of)390 5230 y(the)e(original)h(problem)f FD(c)p FK(.)40 b(The)28 b(diagonal)h(matrix)f(elemen)m(ts)i FE(l)2563 5244 y Fq(i)2618 5230 y FK(are)f(pro)m(vided)e(in)h(the)g(v)m(ector)i FD(L)p FK(.)390 5340 y(It)g(is)h(allo)m(w)m(ed)h(to)f(ha)m(v)m(e)h FD(c)k FK(=)30 b FD(cs)k FK(for)d(an)f(in-place)h(transform.)p eop end %%Page: 449 467 TeXDict begin 449 466 bop 150 -116 a FK(Chapter)30 b(38:)41 b(Least-Squares)31 b(Fitting)2098 b(449)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multilarge_linear)q(_gen)q(for)q(m2) f Fu(\()p FD(const)31 b(gsl)p 2359 299 28 4 v 41 w(matrix)f(*)h Ft(LQR)p FD(,)h(const)565 408 y(gsl)p 677 408 V 41 w(v)m(ector)g(*)e Ft(Ltau)p FD(,)i(const)f(gsl)p 1675 408 V 41 w(v)m(ector)h(*)e Ft(cs)p FD(,)i(gsl)p 2331 408 V 40 w(v)m(ector)g(*)f Ft(c)p FD(,)565 518 y(gsl)p 677 518 V 41 w(m)m(ultilarge)p 1118 518 V 41 w(linear)p 1381 518 V 41 w(w)m(orkspace)g(*)g Ft(work)p Fu(\))390 628 y FK(After)h(a)h(regularized)g(system)f(has)g (b)s(een)f(solv)m(ed)i(with)f(a)h(regularization)h(matrix)e FE(L)p FK(,)h(sp)s(eci\014ed)390 737 y(b)m(y)24 b(\()p FD(LQR)p FK(,)p FD(Ltau)p FK(\),)i(this)e(function)g(bac)m(ktransforms) h(the)f(standard)f(form)h(solution)h FD(cs)j FK(to)d(reco)m(v)m(er)390 847 y(the)31 b(solution)g(v)m(ector)g(of)g(the)g(original)g(problem,)f (whic)m(h)g(is)h(stored)f(in)g FD(c)p FK(,)h(of)g(length)f FE(p)p FK(.)3350 1034 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multilarge_linear)q(_lcu)q(rve)f Fu(\()p FD(gsl)p 2016 1034 V 41 w(v)m(ector)32 b(*)f Ft(reg_param)p FD(,)565 1144 y(gsl)p 677 1144 V 41 w(v)m(ector)h(*)e Ft(rho)p FD(,)i(gsl)p 1385 1144 V 40 w(v)m(ector)g(*)f Ft(eta)p FD(,)h(gsl)p 2093 1144 V 40 w(m)m(ultilarge)p 2533 1144 V 42 w(linear)p 2797 1144 V 40 w(w)m(orkspace)g(*)e Ft(work)p Fu(\))390 1253 y FK(This)e(function)h(computes)g(the)g(L-curv)m(e)g (for)g(a)g(large)h(least)g(squares)f(system)g(after)h(it)f(has)g(b)s (een)390 1363 y(fully)g(accum)m(ulated)j(in)m(to)e(the)g(w)m(orkspace)h FD(w)m(ork)p FK(.)41 b(The)29 b(output)g(v)m(ectors)j FD(reg)p 3075 1363 V 40 w(param)p FK(,)e FD(rho)p FK(,)g(and)390 1473 y FD(eta)c FK(m)m(ust)f(all)g(b)s(e)g(the)g(same)g(size,)i(and)d (will)h(con)m(tain)h(the)f(regularization)i(parameters)e FE(\025)3453 1487 y Fq(i)3481 1473 y FK(,)h(resid-)390 1582 y(ual)34 b(norms)f FI(jj)p FE(y)26 b FI(\000)c FE(X)7 b(c)1157 1596 y Fq(i)1185 1582 y FI(jj)p FK(,)36 b(and)d(solution)i (norms)e FI(jj)p FE(Lc)2252 1596 y Fq(i)2280 1582 y FI(jj)h FK(whic)m(h)g(comp)s(ose)g(the)g(L-curv)m(e,)h(where)390 1692 y FE(c)429 1706 y Fq(i)484 1692 y FK(is)28 b(the)f(regularized)i (solution)f(v)m(ector)h(corresp)s(onding)d(to)i FE(\025)2542 1706 y Fq(i)2570 1692 y FK(.)40 b(The)26 b(user)h(ma)m(y)h(determine)g (the)390 1801 y(n)m(um)m(b)s(er)i(of)h(p)s(oin)m(ts)g(on)g(the)g (L-curv)m(e)g(b)m(y)g(adjusting)g(the)g(size)h(of)f(these)g(input)f (arra)m(ys.)43 b(F)-8 b(or)32 b(the)390 1911 y(TSQR)27 b(metho)s(d,)i(the)f(regularization)j(parameters)d FE(\025)2277 1925 y Fq(i)2334 1911 y FK(are)g(estimated)i(from)e(the)h(singular)f(v) -5 b(al-)390 2021 y(ues)29 b(of)h(the)g(triangular)g FE(R)g FK(factor.)41 b(F)-8 b(or)31 b(the)f(normal)f(equations)h(metho) s(d,)g(they)g(are)g(estimated)390 2130 y(from)g(the)g(eigen)m(v)-5 b(alues)33 b(of)d(the)h FE(X)1574 2097 y Fq(T)1627 2130 y FE(X)37 b FK(matrix.)3350 2317 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multilarge_linear)q(_rco)q(nd)f Fu(\()p FD(double)30 b(*)h Ft(rcond)p FD(,)565 2427 y(gsl)p 677 2427 V 41 w(m)m(ultilarge)p 1118 2427 V 41 w(linear)p 1381 2427 V 41 w(w)m(orkspace)g(*)g Ft(work)p Fu(\))390 2537 y FK(This)26 b(function)h(computes)h(the)f(recipro)s(cal)h (condition)g(n)m(um)m(b)s(er,)e(stored)i(in)f FD(rcond)p FK(,)g(of)g(the)h(least)390 2646 y(squares)c(matrix)g(after)h(it)g(has) f(b)s(een)g(accum)m(ulated)h(in)m(to)g(the)g(w)m(orkspace)g FD(w)m(ork)p FK(.)39 b(F)-8 b(or)25 b(the)f(TSQR)390 2756 y(algorithm,)k(this)e(is)g(accomplished)h(b)m(y)f(calculating)i (the)e(SVD)g(of)g(the)g FE(R)h FK(factor,)h(whic)m(h)e(has)g(the)390 2865 y(same)i(singular)f(v)-5 b(alues)27 b(as)h(the)f(matrix)h FE(X)7 b FK(.)40 b(F)-8 b(or)28 b(the)f(normal)g(equations)h(metho)s (d,)g(this)f(is)g(done)390 2975 y(b)m(y)k(computing)h(the)f(eigen)m(v) -5 b(alues)33 b(of)f FE(X)1783 2942 y Fq(T)1835 2975 y FE(X)7 b FK(,)33 b(whic)m(h)e(could)g(b)s(e)g(inaccurate)h(for)f (ill-conditioned)390 3085 y(matrices)g FE(X)7 b FK(.)150 3319 y FJ(38.7)68 b(T)-11 b(roublesho)t(oting)150 3479 y FK(When)42 b(using)g(mo)s(dels)f(based)h(on)g(p)s(olynomials,)k(care) d(should)e(b)s(e)h(tak)m(en)h(when)e(constructing)i(the)150 3588 y(design)27 b(matrix)h FE(X)7 b FK(.)40 b(If)26 b(the)i FE(x)f FK(v)-5 b(alues)27 b(are)h(large,)h(then)e(the)g(matrix) h FE(X)34 b FK(could)27 b(b)s(e)g(ill-conditioned)i(since)150 3698 y(its)i(columns)g(are)g(p)s(o)m(w)m(ers)f(of)h FE(x)p FK(,)g(leading)h(to)f(unstable)g(least-squares)h(solutions.)42 b(In)30 b(this)h(case)g(it)h(can)150 3808 y(often)f(help)f(to)h(cen)m (ter)g(and)f(scale)i(the)e FE(x)h FK(v)-5 b(alues)30 b(using)g(the)h(mean)f(and)g(standard)f(deviation:)1672 4024 y FE(x)1724 3986 y Fp(0)1772 4024 y FK(=)1878 3962 y FE(x)20 b FI(\000)g FE(\026)p FK(\()p FE(x)p FK(\))p 1878 4003 341 4 v 1959 4086 a FE(\033)s FK(\()p FE(x)p FK(\))150 4243 y(and)30 b(then)g(construct)h(the)f FE(X)38 b FK(matrix)31 b(using)e(the)i(transformed)f(v)-5 b(alues)30 b FE(x)2724 4210 y Fp(0)2748 4243 y FK(.)150 4478 y FJ(38.8)68 b(Examples)150 4637 y FK(The)30 b(example)h(programs)f(in)g(this)g (section)i(demonstrate)f(the)f(v)-5 b(arious)31 b(linear)f(regression)h (metho)s(ds.)150 4838 y Fy(38.8.1)63 b(Simple)42 b(Linear)e(Regression) j(Example)150 4985 y FK(The)35 b(follo)m(wing)i(program)e(computes)g(a) h(least)g(squares)f(straigh)m(t-line)i(\014t)e(to)i(a)e(simple)g (dataset,)k(and)150 5094 y(outputs)30 b(the)g(b)s(est-\014t)h(line)f (and)g(its)h(asso)s(ciated)h(one)e(standard-deviation)h(error)f(bars.) 390 5230 y FH(#include)46 b()390 5340 y(#include)g ()p eop end %%Page: 450 468 TeXDict begin 450 467 bop 150 -116 a FK(Chapter)30 b(38:)41 b(Least-Squares)31 b(Fitting)2098 b(450)390 408 y FH(int)390 518 y(main)47 b(\(void\))390 628 y({)485 737 y(int)g(i,)h(n)f(=)g(4;) 485 847 y(double)g(x[4])f(=)i({)f(1970,)f(1980,)h(1990,)f(2000)h(};)485 956 y(double)g(y[4])f(=)i({)143 b(12,)f(11,)g(14,)h(13)47 b(};)485 1066 y(double)g(w[4])f(=)i({)95 b(0.1,)f(0.2,)h(0.3,)f(0.4)47 b(};)485 1285 y(double)g(c0,)f(c1,)h(cov00,)f(cov01,)h(cov11,)f(chisq;) 485 1504 y(gsl_fit_wlinear)e(\(x,)j(1,)g(w,)g(1,)h(y,)f(1,)g(n,)1297 1614 y(&c0,)f(&c1,)h(&cov00,)f(&cov01,)g(&cov11,)1297 1724 y(&chisq\);)485 1943 y(printf)h(\("#)f(best)h(fit:)94 b(Y)48 b(=)f(\045g)h(+)f(\045g)g(X\\n",)g(c0,)f(c1\);)485 2052 y(printf)h(\("#)f(covariance)f(matrix:\\n"\);)485 2162 y(printf)i(\("#)f([)i(\045g,)f(\045g\\n#)142 b(\045g,)47 b(\045g]\\n",)867 2271 y(cov00,)f(cov01,)g(cov01,)h(cov11\);)485 2381 y(printf)g(\("#)f(chisq)h(=)g(\045g\\n",)f(chisq\);)485 2600 y(for)h(\(i)h(=)f(0;)g(i)h(<)f(n;)g(i++\))581 2710 y(printf)f(\("data:)94 b(\045g)47 b(\045g)g(\045g\\n",)1297 2819 y(x[i],)f(y[i],)h(1/sqrt\(w[i]\)\);)485 3039 y(printf)g (\("\\n"\);)485 3258 y(for)g(\(i)h(=)f(-30;)g(i)g(<)h(130;)e(i++\))581 3367 y({)676 3477 y(double)g(xf)i(=)f(x[0])g(+)g(\(i/100.0\))e(*)j (\(x[n-1])e(-)h(x[0]\);)676 3587 y(double)f(yf,)h(yf_err;)676 3806 y(gsl_fit_linear_est)c(\(xf,)1631 3915 y(c0,)k(c1,)1631 4025 y(cov00,)f(cov01,)g(cov11,)1631 4134 y(&yf,)h(&yf_err\);)676 4354 y(printf)f(\("fit:)94 b(\045g)47 b(\045g\\n",)g(xf,)f(yf\);)676 4463 y(printf)g(\("hi)h(:)95 b(\045g)47 b(\045g\\n",)g(xf,)f(yf)i(+)f (yf_err\);)676 4573 y(printf)f(\("lo)h(:)95 b(\045g)47 b(\045g\\n",)g(xf,)f(yf)i(-)f(yf_err\);)581 4682 y(})485 4792 y(return)g(0;)390 4902 y(})150 5066 y FK(The)35 b(follo)m(wing)h(commands)f(extract)h(the)f(data)h(from)f(the)g(output) g(of)g(the)g(program)g(and)f(displa)m(y)h(it)150 5176 y(using)30 b(the)g FC(gnu)h FK(plotutils)g FH(graph)e FK(utilit)m(y)-8 b(,)390 5340 y FH($)47 b(./demo)g(>)g(tmp)p eop end %%Page: 451 469 TeXDict begin 451 468 bop 150 -116 a FK(Chapter)30 b(38:)41 b(Least-Squares)31 b(Fitting)2098 b(451)390 299 y FH($)47 b(more)g(tmp)390 408 y(#)g(best)g(fit:)g(Y)g(=)h(-106.6)e(+)h(0.06)g(X) 390 518 y(#)g(covariance)e(matrix:)390 628 y(#)i([)h(39602,)e(-19.9)390 737 y(#)143 b(-19.9,)46 b(0.01])390 847 y(#)h(chisq)g(=)g(0.8)390 1066 y($)g(for)g(n)h(in)f(data)g(fit)g(hi)g(lo)g(;)533 1176 y(do)629 1285 y(grep)f("^$n")h(tmp)g(|)g(cut)g(-d:)g(-f2)g(>)g($n) g(;)533 1395 y(done)390 1504 y($)g(graph)g(-T)g(X)g(-X)h(x)f(-Y)g(y)h (-y)f(0)g(20)h(-m)f(0)g(-S)g(2)h(-Ie)f(data)629 1614 y(-S)g(0)g(-I)g(a)h(-m)f(1)h(fit)e(-m)i(2)f(hi)g(-m)g(2)h(lo)275 3550 y @beginspecial 85 @llx 180 @lly 500 @urx 576 @ury 2160 @rwi @setspecial %%BeginDocument: fit-wlinear.eps %!PS-Adobe-3.0 EPSF-3.0 %%Creator: GNU libplot drawing library 1.6 %%Title: PostScript plot %%CreationDate: Sun Aug 6 11:26:34 2000 %%DocumentData: Clean7Bit %%LanguageLevel: 1 %%Pages: 1 %%PageOrder: Ascend %%Orientation: Portrait %%BoundingBox: 85 180 500 576 %%DocumentNeededResources: %%DocumentSuppliedResources: procset GNU_libplot 1.0 0 %%EndComments %%BeginDefaults %%PageResources: %%EndDefaults %%BeginProlog %%EndProlog %%BeginSetup /DrawDict 50 dict def DrawDict begin %%BeginResource procset GNU_libplot 1.0 0 /none null def /numGraphicParameters 17 def /stringLimit 65535 def /arrowHeight 8 def /arrowWidth 4 def /Begin { save numGraphicParameters dict begin } def /End { end restore } def /SetB { dup type /nulltype eq { pop false /brushRightArrow idef false /brushLeftArrow idef true /brushNone idef } { /brushDashOffset idef /brushDashArray idef 0 ne /brushRightArrow idef 0 ne /brushLeftArrow idef /brushWidth idef false /brushNone idef } ifelse } def /SetCFg { /fgblue idef /fggreen idef /fgred idef } def /SetCBg { /bgblue idef /bggreen idef /bgred idef } def /SetF { /printSize idef /printFont idef } def /SetP { dup type /nulltype eq { pop true /patternNone idef } { /patternGrayLevel idef patternGrayLevel -1 eq { /patternString idef } if false /patternNone idef } ifelse } def /BSpl { 0 begin storexyn newpath n 1 gt { 0 0 0 0 0 0 1 1 true subspline n 2 gt { 0 0 0 0 1 1 2 2 false subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 2 copy false subspline } if n 2 sub dup n 1 sub dup 2 copy 2 copy false subspline patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup 1 sub dup rightarrow } if end } dup 0 4 dict put def /Circ { newpath 0 360 arc closepath patternNone not { ifill } if brushNone not { istroke } if } def /CBSpl { 0 begin dup 2 gt { storexyn newpath n 1 sub dup 0 0 1 1 2 2 true subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 0 0 false subspline n 2 sub dup n 1 sub dup 0 0 1 1 false subspline patternNone not { ifill } if brushNone not { istroke } if } { Poly } ifelse end } dup 0 4 dict put def /Elli { 0 begin newpath 4 2 roll translate scale 0 0 1 0 360 arc closepath patternNone not { ifill } if brushNone not { istroke } if end } dup 0 1 dict put def /Line { 0 begin 2 storexyn newpath x 0 get y 0 get moveto x 1 get y 1 get lineto brushNone not { istroke } if 0 0 1 1 leftarrow 0 0 1 1 rightarrow end } dup 0 4 dict put def /MLine { 0 begin storexyn newpath n 1 gt { x 0 get y 0 get moveto 1 1 n 1 sub { /i exch def x i get y i get lineto } for patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Poly { 3 1 roll newpath moveto -1 add { lineto } repeat closepath patternNone not { ifill } if brushNone not { istroke } if } def /Rect { 0 begin /t exch def /r exch def /b exch def /l exch def newpath l b moveto l t lineto r t lineto r b lineto closepath patternNone not { ifill } if brushNone not { istroke } if end } dup 0 4 dict put def /Text { ishow } def /idef { dup where { pop pop pop } { exch def } ifelse } def /ifill { 0 begin gsave patternGrayLevel -1 ne { fgred bgred fgred sub patternGrayLevel mul add fggreen bggreen fggreen sub patternGrayLevel mul add fgblue bgblue fgblue sub patternGrayLevel mul add setrgbcolor eofill } { eoclip originalCTM setmatrix pathbbox /t exch def /r exch def /b exch def /l exch def /w r l sub ceiling cvi def /h t b sub ceiling cvi def /imageByteWidth w 8 div ceiling cvi def /imageHeight h def bgred bggreen bgblue setrgbcolor eofill fgred fggreen fgblue setrgbcolor w 0 gt h 0 gt and { l b translate w h scale w h true [w 0 0 h neg 0 h] { patternproc } imagemask } if } ifelse grestore end } dup 0 8 dict put def /istroke { gsave brushDashOffset -1 eq { [] 0 setdash 1 setgray } { brushDashArray brushDashOffset setdash fgred fggreen fgblue setrgbcolor } ifelse brushWidth setlinewidth originalCTM setmatrix stroke grestore } def /ishow { 0 begin gsave fgred fggreen fgblue setrgbcolor /fontDict printFont findfont printSize scalefont dup setfont def /descender fontDict begin 0 /FontBBox load 1 get FontMatrix end transform exch pop def /vertoffset 1 printSize sub descender sub def { 0 vertoffset moveto show /vertoffset vertoffset printSize sub def } forall grestore end } dup 0 3 dict put def /patternproc { 0 begin /patternByteLength patternString length def /patternHeight patternByteLength 8 mul sqrt cvi def /patternWidth patternHeight def /patternByteWidth patternWidth 8 idiv def /imageByteMaxLength imageByteWidth imageHeight mul stringLimit patternByteWidth sub min def /imageMaxHeight imageByteMaxLength imageByteWidth idiv patternHeight idiv patternHeight mul patternHeight max def /imageHeight imageHeight imageMaxHeight sub store /imageString imageByteWidth imageMaxHeight mul patternByteWidth add string def 0 1 imageMaxHeight 1 sub { /y exch def /patternRow y patternByteWidth mul patternByteLength mod def /patternRowString patternString patternRow patternByteWidth getinterval def /imageRow y imageByteWidth mul def 0 patternByteWidth imageByteWidth 1 sub { /x exch def imageString imageRow x add patternRowString putinterval } for } for imageString end } dup 0 12 dict put def /min { dup 3 2 roll dup 4 3 roll lt { exch } if pop } def /max { dup 3 2 roll dup 4 3 roll gt { exch } if pop } def /midpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 x1 add 2 div y0 y1 add 2 div end } dup 0 4 dict put def /thirdpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 2 mul x1 add 3 div y0 2 mul y1 add 3 div end } dup 0 4 dict put def /subspline { 0 begin /movetoNeeded exch def y exch get /y3 exch def x exch get /x3 exch def y exch get /y2 exch def x exch get /x2 exch def y exch get /y1 exch def x exch get /x1 exch def y exch get /y0 exch def x exch get /x0 exch def x1 y1 x2 y2 thirdpoint /p1y exch def /p1x exch def x2 y2 x1 y1 thirdpoint /p2y exch def /p2x exch def x1 y1 x0 y0 thirdpoint p1x p1y midpoint /p0y exch def /p0x exch def x2 y2 x3 y3 thirdpoint p2x p2y midpoint /p3y exch def /p3x exch def movetoNeeded { p0x p0y moveto } if p1x p1y p2x p2y p3x p3y curveto end } dup 0 17 dict put def /storexyn { /n exch def /y n array def /x n array def n 1 sub -1 0 { /i exch def y i 3 2 roll put x i 3 2 roll put } for } def /arrowhead { 0 begin transform originalCTM itransform /taily exch def /tailx exch def transform originalCTM itransform /tipy exch def /tipx exch def /dy tipy taily sub def /dx tipx tailx sub def /angle dx 0 ne dy 0 ne or { dy dx atan } { 90 } ifelse def gsave originalCTM setmatrix tipx tipy translate angle rotate newpath arrowHeight neg arrowWidth 2 div moveto 0 0 lineto arrowHeight neg arrowWidth 2 div neg lineto patternNone not { originalCTM setmatrix /padtip arrowHeight 2 exp 0.25 arrowWidth 2 exp mul add sqrt brushWidth mul arrowWidth div def /padtail brushWidth 2 div def tipx tipy translate angle rotate padtip 0 translate arrowHeight padtip add padtail add arrowHeight div dup scale arrowheadpath ifill } if brushNone not { originalCTM setmatrix tipx tipy translate angle rotate arrowheadpath istroke } if grestore end } dup 0 9 dict put def /arrowheadpath { newpath arrowHeight neg arrowWidth 2 div moveto 0 0 lineto arrowHeight neg arrowWidth 2 div neg lineto } def /leftarrow { 0 begin y exch get /taily exch def x exch get /tailx exch def y exch get /tipy exch def x exch get /tipx exch def brushLeftArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /rightarrow { 0 begin y exch get /tipy exch def x exch get /tipx exch def y exch get /taily exch def x exch get /tailx exch def brushRightArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def %%EndResource %%EndSetup %%Page: 1 1 %%PageResources: %%PageBoundingBox: 85 180 500 576 %%BeginPageSetup %I Idraw 8 Begin %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 1 0 0 1 0 0 ] concat /originalCTM matrix currentmatrix def /trueoriginalCTM matrix currentmatrix def %%EndPageSetup Begin %I Poly [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 2304 2304 2304 9216 9216 9216 9216 2304 4 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 1930 2107 1952 2118 1985 2151 1985 1920 4 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1974 2140 1974 1920 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1930 1920 2029 1920 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 28 2260 2074 2249 2041 2227 2019 2194 2008 2183 2008 2150 2019 2128 2041 2117 2074 2117 2085 2128 2118 2150 2140 2183 2151 2205 2151 2238 2140 2260 2118 2271 2085 2271 2019 2260 1975 2249 1953 2227 1931 2194 1920 2161 1920 2139 1931 2128 1953 2128 1964 2139 1975 2150 1964 2139 1953 28 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 2183 2008 2161 2019 2139 2041 2128 2074 2128 2085 2139 2118 2161 2140 2183 2151 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 9 2205 2151 2227 2140 2249 2118 2260 2085 2260 2019 2249 1975 2238 1953 2216 1931 2194 1920 9 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 28 2469 2118 2458 2107 2469 2096 2480 2107 2480 2118 2469 2140 2447 2151 2414 2151 2381 2140 2359 2118 2348 2096 2337 2052 2337 1986 2348 1953 2370 1931 2403 1920 2425 1920 2458 1931 2480 1953 2491 1986 2491 1997 2480 2030 2458 2052 2425 2063 2414 2063 2381 2052 2359 2030 2348 1997 28 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 9 2414 2151 2392 2140 2370 2118 2359 2096 2348 2052 2348 1986 2359 1953 2381 1931 2403 1920 9 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 2425 1920 2447 1931 2469 1953 2480 1986 2480 1997 2469 2030 2447 2052 2425 2063 8 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 2623 2151 2590 2140 2568 2107 2557 2052 2557 2019 2568 1964 2590 1931 2623 1920 2645 1920 2678 1931 2700 1964 2711 2019 2711 2052 2700 2107 2678 2140 2645 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 2623 2151 2601 2140 2590 2129 2579 2107 2568 2052 2568 2019 2579 1964 2590 1942 2601 1931 2623 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 2645 1920 2667 1931 2678 1942 2689 1964 2700 2019 2700 2052 2689 2107 2678 2129 2667 2140 2645 2151 10 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 9216 2304 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2304 2304 2442 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 3313 2107 3335 2118 3368 2151 3368 1920 4 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3357 2140 3357 1920 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3313 1920 3411 1920 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 28 3642 2074 3631 2041 3609 2019 3576 2008 3565 2008 3532 2019 3510 2041 3499 2074 3499 2085 3510 2118 3532 2140 3565 2151 3587 2151 3620 2140 3642 2118 3653 2085 3653 2019 3642 1975 3631 1953 3609 1931 3576 1920 3543 1920 3521 1931 3510 1953 3510 1964 3521 1975 3532 1964 3521 1953 28 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 3565 2008 3543 2019 3521 2041 3510 2074 3510 2085 3521 2118 3543 2140 3565 2151 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 9 3587 2151 3609 2140 3631 2118 3642 2085 3642 2019 3631 1975 3620 1953 3598 1931 3576 1920 9 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3719 2151 3719 2085 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 3719 2107 3730 2129 3752 2151 3774 2151 3829 2118 3851 2118 3862 2129 3873 2151 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 3730 2129 3752 2140 3774 2140 3829 2118 4 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 3873 2151 3873 2118 3862 2085 3818 2030 3807 2008 3796 1975 3796 1920 7 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5 3862 2085 3807 2030 3796 2008 3785 1975 3785 1920 5 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 4005 2151 3972 2140 3950 2107 3939 2052 3939 2019 3950 1964 3972 1931 4005 1920 4027 1920 4060 1931 4082 1964 4093 2019 4093 2052 4082 2107 4060 2140 4027 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 4005 2151 3983 2140 3972 2129 3961 2107 3950 2052 3950 2019 3961 1964 3972 1942 3983 1931 4005 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 4027 1920 4049 1931 4060 1942 4071 1964 4082 2019 4082 2052 4071 2107 4060 2129 4049 2140 4027 2151 10 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3686 9216 3686 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3686 2304 3686 2442 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 4695 2107 4717 2118 4750 2151 4750 1920 4 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4739 2140 4739 1920 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4695 1920 4794 1920 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 28 5025 2074 5014 2041 4992 2019 4959 2008 4948 2008 4915 2019 4893 2041 4882 2074 4882 2085 4893 2118 4915 2140 4948 2151 4970 2151 5003 2140 5025 2118 5036 2085 5036 2019 5025 1975 5014 1953 4992 1931 4959 1920 4926 1920 4904 1931 4893 1953 4893 1964 4904 1975 4915 1964 4904 1953 28 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 4948 2008 4926 2019 4904 2041 4893 2074 4893 2085 4904 2118 4926 2140 4948 2151 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 9 4970 2151 4992 2140 5014 2118 5025 2085 5025 2019 5014 1975 5003 1953 4981 1931 4959 1920 9 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 12 5157 2151 5124 2140 5113 2118 5113 2085 5124 2063 5157 2052 5201 2052 5234 2063 5245 2085 5245 2118 5234 2140 5201 2151 12 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 5157 2151 5135 2140 5124 2118 5124 2085 5135 2063 5157 2052 6 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 5201 2052 5223 2063 5234 2085 5234 2118 5223 2140 5201 2151 6 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 5157 2052 5124 2041 5113 2030 5102 2008 5102 1964 5113 1942 5124 1931 5157 1920 5201 1920 5234 1931 5245 1942 5256 1964 5256 2008 5245 2030 5234 2041 5201 2052 16 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 5157 2052 5135 2041 5124 2030 5113 2008 5113 1964 5124 1942 5135 1931 5157 1920 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 5201 1920 5223 1931 5234 1942 5245 1964 5245 2008 5234 2030 5223 2041 5201 2052 8 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 5388 2151 5355 2140 5333 2107 5322 2052 5322 2019 5333 1964 5355 1931 5388 1920 5410 1920 5443 1931 5465 1964 5476 2019 5476 2052 5465 2107 5443 2140 5410 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 5388 2151 5366 2140 5355 2129 5344 2107 5333 2052 5333 2019 5344 1964 5355 1942 5366 1931 5388 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 5410 1920 5432 1931 5443 1942 5454 1964 5465 2019 5465 2052 5454 2107 5443 2129 5432 2140 5410 2151 10 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5069 9216 5069 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5069 2304 5069 2442 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 6077 2107 6099 2118 6132 2151 6132 1920 4 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6121 2140 6121 1920 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6077 1920 6176 1920 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 28 6407 2074 6396 2041 6374 2019 6341 2008 6330 2008 6297 2019 6275 2041 6264 2074 6264 2085 6275 2118 6297 2140 6330 2151 6352 2151 6385 2140 6407 2118 6418 2085 6418 2019 6407 1975 6396 1953 6374 1931 6341 1920 6308 1920 6286 1931 6275 1953 6275 1964 6286 1975 6297 1964 6286 1953 28 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 6330 2008 6308 2019 6286 2041 6275 2074 6275 2085 6286 2118 6308 2140 6330 2151 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 9 6352 2151 6374 2140 6396 2118 6407 2085 6407 2019 6396 1975 6385 1953 6363 1931 6341 1920 9 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 28 6627 2074 6616 2041 6594 2019 6561 2008 6550 2008 6517 2019 6495 2041 6484 2074 6484 2085 6495 2118 6517 2140 6550 2151 6572 2151 6605 2140 6627 2118 6638 2085 6638 2019 6627 1975 6616 1953 6594 1931 6561 1920 6528 1920 6506 1931 6495 1953 6495 1964 6506 1975 6517 1964 6506 1953 28 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 6550 2008 6528 2019 6506 2041 6495 2074 6495 2085 6506 2118 6528 2140 6550 2151 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 9 6572 2151 6594 2140 6616 2118 6627 2085 6627 2019 6616 1975 6605 1953 6583 1931 6561 1920 9 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 6770 2151 6737 2140 6715 2107 6704 2052 6704 2019 6715 1964 6737 1931 6770 1920 6792 1920 6825 1931 6847 1964 6858 2019 6858 2052 6847 2107 6825 2140 6792 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 6770 2151 6748 2140 6737 2129 6726 2107 6715 2052 6715 2019 6726 1964 6737 1942 6748 1931 6770 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 6792 1920 6814 1931 6825 1942 6836 1964 6847 2019 6847 2052 6836 2107 6825 2129 6814 2140 6792 2151 10 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6451 9216 6451 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6451 2304 6451 2442 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 20 7438 2107 7449 2096 7438 2085 7427 2096 7427 2107 7438 2129 7449 2140 7482 2151 7526 2151 7559 2140 7570 2129 7581 2107 7581 2085 7570 2063 7537 2041 7482 2019 7460 2008 7438 1986 7427 1953 7427 1920 20 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 7526 2151 7548 2140 7559 2129 7570 2107 7570 2085 7559 2063 7526 2041 7482 2019 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 7427 1942 7438 1953 7460 1953 7515 1931 7548 1931 7570 1942 7581 1953 7 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 7460 1953 7515 1920 7559 1920 7570 1931 7581 1953 7581 1975 6 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 7713 2151 7680 2140 7658 2107 7647 2052 7647 2019 7658 1964 7680 1931 7713 1920 7735 1920 7768 1931 7790 1964 7801 2019 7801 2052 7790 2107 7768 2140 7735 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 7713 2151 7691 2140 7680 2129 7669 2107 7658 2052 7658 2019 7669 1964 7680 1942 7691 1931 7713 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 7735 1920 7757 1931 7768 1942 7779 1964 7790 2019 7790 2052 7779 2107 7768 2129 7757 2140 7735 2151 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 7933 2151 7900 2140 7878 2107 7867 2052 7867 2019 7878 1964 7900 1931 7933 1920 7955 1920 7988 1931 8010 1964 8021 2019 8021 2052 8010 2107 7988 2140 7955 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 7933 2151 7911 2140 7900 2129 7889 2107 7878 2052 7878 2019 7889 1964 7900 1942 7911 1931 7933 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 7955 1920 7977 1931 7988 1942 7999 1964 8010 2019 8010 2052 7999 2107 7988 2129 7977 2140 7955 2151 10 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 8152 2151 8120 2140 8098 2107 8087 2052 8087 2019 8098 1964 8120 1931 8152 1920 8174 1920 8207 1931 8229 1964 8240 2019 8240 2052 8229 2107 8207 2140 8174 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 8152 2151 8131 2140 8120 2129 8109 2107 8098 2052 8098 2019 8109 1964 8120 1942 8131 1931 8152 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 8174 1920 8196 1931 8207 1942 8218 1964 8229 2019 8229 2052 8218 2107 8207 2129 8196 2140 8174 2151 10 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7834 9216 7834 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7834 2304 7834 2442 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 20 8820 2107 8831 2096 8820 2085 8809 2096 8809 2107 8820 2129 8831 2140 8864 2151 8908 2151 8941 2140 8952 2129 8963 2107 8963 2085 8952 2063 8919 2041 8864 2019 8842 2008 8820 1986 8809 1953 8809 1920 20 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 8908 2151 8930 2140 8941 2129 8952 2107 8952 2085 8941 2063 8908 2041 8864 2019 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 8809 1942 8820 1953 8842 1953 8897 1931 8930 1931 8952 1942 8963 1953 7 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 8842 1953 8897 1920 8941 1920 8952 1931 8963 1953 8963 1975 6 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 9095 2151 9062 2140 9040 2107 9029 2052 9029 2019 9040 1964 9062 1931 9095 1920 9117 1920 9150 1931 9172 1964 9183 2019 9183 2052 9172 2107 9150 2140 9117 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 9095 2151 9073 2140 9062 2129 9051 2107 9040 2052 9040 2019 9051 1964 9062 1942 9073 1931 9095 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 9117 1920 9139 1931 9150 1942 9161 1964 9172 2019 9172 2052 9161 2107 9150 2129 9139 2140 9117 2151 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 9282 2107 9304 2118 9337 2151 9337 1920 4 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9326 2140 9326 1920 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9282 1920 9381 1920 2 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 9535 2151 9502 2140 9480 2107 9469 2052 9469 2019 9480 1964 9502 1931 9535 1920 9557 1920 9590 1931 9612 1964 9623 2019 9623 2052 9612 2107 9590 2140 9557 2151 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 9535 2151 9513 2140 9502 2129 9491 2107 9480 2052 9480 2019 9491 1964 9502 1942 9513 1931 9535 1920 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 9557 1920 9579 1931 9590 1942 9601 1964 9612 2019 9612 2052 9601 2107 9590 2129 9579 2140 9557 2151 10 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 9216 9216 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2304 9216 2442 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 9216 2304 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2304 2304 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2580 9216 2580 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2580 2304 2580 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2857 9216 2857 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2857 2304 2857 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3133 9216 3133 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3133 2304 3133 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3410 9216 3410 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3410 2304 3410 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3686 9216 3686 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3686 2304 3686 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3963 9216 3963 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3963 2304 3963 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4239 9216 4239 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4239 2304 4239 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4516 9216 4516 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4516 2304 4516 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4792 9216 4792 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4792 2304 4792 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5069 9216 5069 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5069 2304 5069 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5345 9216 5345 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5345 2304 5345 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5622 9216 5622 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5622 2304 5622 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5898 9216 5898 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5898 2304 5898 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6175 9216 6175 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6175 2304 6175 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6451 9216 6451 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6451 2304 6451 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6728 9216 6728 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6728 2304 6728 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7004 9216 7004 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7004 2304 7004 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7281 9216 7281 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7281 2304 7281 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7557 9216 7557 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7557 2304 7557 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7834 9216 7834 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7834 2304 7834 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8110 9216 8110 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8110 2304 8110 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8387 9216 8387 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8387 2304 8387 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8663 9216 8663 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8663 2304 8663 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8940 9216 8940 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8940 2304 8940 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 9216 9216 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2304 9216 2359 2 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 2079 2436 2046 2425 2024 2392 2013 2337 2013 2304 2024 2249 2046 2216 2079 2205 2101 2205 2134 2216 2156 2249 2167 2304 2167 2337 2156 2392 2134 2425 2101 2436 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 2079 2436 2057 2425 2046 2414 2035 2392 2024 2337 2024 2304 2035 2249 2046 2227 2057 2216 2079 2205 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 2101 2205 2123 2216 2134 2227 2145 2249 2156 2304 2156 2337 2145 2392 2134 2414 2123 2425 2101 2436 10 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2304 9078 2304 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2304 2442 2304 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2035 4164 2013 4054 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 19 2013 4054 2035 4076 2068 4087 2101 4087 2134 4076 2156 4054 2167 4021 2167 3999 2156 3966 2134 3944 2101 3933 2068 3933 2035 3944 2024 3955 2013 3977 2013 3988 2024 3999 2035 3988 2024 3977 19 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 2101 4087 2123 4076 2145 4054 2156 4021 2156 3999 2145 3966 2123 3944 2101 3933 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2035 4164 2145 4164 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 2035 4153 2090 4153 2145 4164 3 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 4032 9078 4032 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4032 2442 4032 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 1826 5848 1848 5859 1881 5892 1881 5661 4 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1870 5881 1870 5661 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1826 5661 1925 5661 2 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 2079 5892 2046 5881 2024 5848 2013 5793 2013 5760 2024 5705 2046 5672 2079 5661 2101 5661 2134 5672 2156 5705 2167 5760 2167 5793 2156 5848 2134 5881 2101 5892 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 2079 5892 2057 5881 2046 5870 2035 5848 2024 5793 2024 5760 2035 5705 2046 5683 2057 5672 2079 5661 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 2101 5661 2123 5672 2134 5683 2145 5705 2156 5760 2156 5793 2145 5848 2134 5870 2123 5881 2101 5892 10 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5760 9078 5760 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5760 2442 5760 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 1826 7576 1848 7587 1881 7620 1881 7389 4 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1870 7609 1870 7389 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1826 7389 1925 7389 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2035 7620 2013 7510 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 19 2013 7510 2035 7532 2068 7543 2101 7543 2134 7532 2156 7510 2167 7477 2167 7455 2156 7422 2134 7400 2101 7389 2068 7389 2035 7400 2024 7411 2013 7433 2013 7444 2024 7455 2035 7444 2024 7433 19 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 2101 7543 2123 7532 2145 7510 2156 7477 2156 7455 2145 7422 2123 7400 2101 7389 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2035 7620 2145 7620 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3 2035 7609 2090 7609 2145 7620 3 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 7488 9078 7488 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 7488 2442 7488 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 20 1804 9304 1815 9293 1804 9282 1793 9293 1793 9304 1804 9326 1815 9337 1848 9348 1892 9348 1925 9337 1936 9326 1947 9304 1947 9282 1936 9260 1903 9238 1848 9216 1826 9205 1804 9183 1793 9150 1793 9117 20 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8 1892 9348 1914 9337 1925 9326 1936 9304 1936 9282 1925 9260 1892 9238 1848 9216 8 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7 1793 9139 1804 9150 1826 9150 1881 9128 1914 9128 1936 9139 1947 9150 7 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6 1826 9150 1881 9117 1925 9117 1936 9128 1947 9150 1947 9172 6 MLine End Begin %I Poly [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 16 2079 9348 2046 9337 2024 9304 2013 9249 2013 9216 2024 9161 2046 9128 2079 9117 2101 9117 2134 9128 2156 9161 2167 9216 2167 9249 2156 9304 2134 9337 2101 9348 16 Poly End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 2079 9348 2057 9337 2046 9326 2035 9304 2024 9249 2024 9216 2035 9161 2046 9139 2057 9128 2079 9117 10 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 10 2101 9117 2123 9128 2134 9139 2145 9161 2156 9216 2156 9249 2145 9304 2134 9326 2123 9337 2101 9348 10 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 9216 9078 9216 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 9216 2442 9216 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2304 9161 2304 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2304 2359 2304 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2650 9161 2650 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2650 2359 2650 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2995 9161 2995 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2995 2359 2995 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 3341 9161 3341 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3341 2359 3341 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 3686 9161 3686 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3686 2359 3686 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 4032 9161 4032 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4032 2359 4032 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 4378 9161 4378 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4378 2359 4378 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 4723 9161 4723 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4723 2359 4723 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5069 9161 5069 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5069 2359 5069 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5414 9161 5414 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5414 2359 5414 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5760 9161 5760 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5760 2359 5760 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 6106 9161 6106 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 6106 2359 6106 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 6451 9161 6451 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 6451 2359 6451 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 6797 9161 6797 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 6797 2359 6797 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 7142 9161 7142 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 7142 2359 7142 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 7488 9161 7488 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 7488 2359 7488 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 7834 9161 7834 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 7834 2359 7834 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 8179 9161 8179 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 8179 2359 8179 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 8525 9161 8525 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 8525 2359 8525 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 8870 9161 8870 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 8870 2359 8870 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 9216 9161 9216 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 9216 2359 9216 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5694 1621 5815 1467 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5705 1621 5826 1467 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5826 1621 5694 1467 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5672 1621 5738 1621 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5782 1621 5848 1621 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5672 1467 5738 1467 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5782 1467 5848 1467 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1354 5700 1508 5765 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1354 5711 1486 5765 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 9 1354 5831 1508 5765 1552 5744 1574 5722 1585 5700 1585 5689 1574 5678 1563 5689 1574 5700 9 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1354 5678 1354 5744 2 MLine End Begin %I MLine [0.7807418 0 0 0.7807418 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 1 setlinecap 1 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 1354 5787 1354 5853 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3583 5358 3790 5358 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3686 5358 3686 7544 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3583 7544 3790 7544 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3622 6451 3751 6451 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3686 6386 3686 6516 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4965 5333 5172 5333 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5069 5333 5069 6878 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4965 6878 5172 6878 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5004 6106 5134 6106 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5069 6041 5069 6170 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6348 6511 6555 6511 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6451 6511 6451 7773 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6348 7773 6555 7773 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6386 7142 6516 7142 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6451 7078 6451 7207 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7730 6250 7937 6250 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7834 6250 7834 7343 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7730 7343 7937 7343 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7769 6797 7898 6797 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7834 6732 7834 6862 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 160 2442 6126 2484 6133 2525 6139 2567 6145 2608 6151 2650 6157 2691 6164 2733 6170 2774 6176 2815 6182 2857 6189 2898 6195 2940 6201 2981 6207 3023 6213 3064 6220 3106 6226 3147 6232 3189 6238 3230 6245 3272 6251 3313 6257 3355 6263 3396 6269 3438 6276 3479 6282 3521 6288 3562 6294 3603 6301 3645 6307 3686 6313 3728 6319 3769 6325 3811 6332 3852 6338 3894 6344 3935 6350 3977 6357 4018 6363 4060 6369 4101 6375 4143 6381 4184 6388 4226 6394 4267 6400 4308 6406 4350 6412 4391 6419 4433 6425 4474 6431 4516 6437 4557 6444 4599 6450 4640 6456 4682 6462 4723 6468 4765 6475 4806 6481 4848 6487 4889 6493 4931 6500 4972 6506 5014 6512 5055 6518 5096 6524 5138 6531 5179 6537 5221 6543 5262 6549 5304 6556 5345 6562 5387 6568 5428 6574 5470 6580 5511 6587 5553 6593 5594 6599 5636 6605 5677 6612 5719 6618 5760 6624 5801 6630 5843 6636 5884 6643 5926 6649 5967 6655 6009 6661 6050 6668 6092 6674 6133 6680 6175 6686 6216 6692 6258 6699 6299 6705 6341 6711 6382 6717 6424 6724 6465 6730 6506 6736 6548 6742 6589 6748 6631 6755 6672 6761 6714 6767 6755 6773 6797 6780 6838 6786 6880 6792 6921 6798 6963 6804 7004 6811 7046 6817 7087 6823 7129 6829 7170 6836 7212 6842 7253 6848 7294 6854 7336 6860 7377 6867 7419 6873 7460 6879 7502 6885 7543 6891 7585 6898 7626 6904 7668 6910 7709 6916 7751 6923 7792 6929 7834 6935 7875 6941 7917 6947 7958 6954 7999 6960 8041 6966 8082 6972 8124 6979 8165 6985 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4557 7030 4599 7028 4640 7026 4682 7024 4723 7022 4765 7020 4806 7018 4848 7016 4889 7015 4931 7013 4972 7012 5014 7011 5055 7009 5096 7008 5138 7007 5179 7007 5221 7006 5262 7005 5304 7005 5345 7004 5387 7004 5428 7004 5470 7004 5511 7005 5553 7005 5594 7006 5636 7007 5677 7008 5719 7009 5760 7010 5801 7012 5843 7014 5884 7016 5926 7019 5967 7021 6009 7024 6050 7027 6092 7031 6133 7035 6175 7039 6216 7043 6258 7048 6299 7053 6341 7058 6382 7063 6424 7069 6465 7075 6506 7082 6548 7089 6589 7096 6631 7103 6672 7111 6714 7119 6755 7127 6797 7136 6838 7145 6880 7154 6921 7163 6963 7173 7004 7183 7046 7193 7087 7203 7129 7214 7170 7225 7212 7236 7253 7247 7294 7259 7336 7271 7377 7283 7419 7295 7460 7307 7502 7319 7543 7332 7585 7345 7626 7358 7668 7371 7709 7384 7751 7397 7792 7410 7834 7424 7875 7437 7917 7451 7958 7465 7999 7479 8041 7493 8082 7507 8124 7521 8165 7535 8207 7550 8248 7564 8290 7579 8331 7593 8373 7608 8414 7622 8456 7637 8497 7652 8539 7667 8580 7682 8622 7697 8663 7712 8705 7727 8746 7742 8787 7757 8829 7772 8870 7787 8912 7802 8953 7818 8995 7833 9036 7848 160 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 34952 1 0 0 [ 1 3 1 3 ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 160 2442 5066 2484 5082 2525 5098 2567 5114 2608 5130 2650 5146 2691 5162 2733 5178 2774 5194 2815 5210 2857 5226 2898 5242 2940 5258 2981 5273 3023 5289 3064 5305 3106 5321 3147 5337 3189 5352 3230 5368 3272 5384 3313 5400 3355 5415 3396 5431 3438 5447 3479 5462 3521 5478 3562 5494 3603 5509 3645 5525 3686 5540 3728 5556 3769 5571 3811 5587 3852 5602 3894 5617 3935 5633 3977 5648 4018 5663 4060 5678 4101 5694 4143 5709 4184 5724 4226 5739 4267 5754 4308 5769 4350 5784 4391 5799 4433 5813 4474 5828 4516 5843 4557 5857 4599 5872 4640 5886 4682 5901 4723 5915 4765 5930 4806 5944 4848 5958 4889 5972 4931 5986 4972 6000 5014 6013 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End %I eop showpage %%Trailer end %%EOF %%EndDocument @endspecial 150 3809 a Fy(38.8.2)63 b(Multi-parameter)41 b(Linear)g(Regression)h(Example)150 3956 y FK(The)32 b(follo)m(wing)i(program)f(p)s(erforms)e(a)i(quadratic)g(\014t)g FE(y)f FK(=)d FE(c)2296 3970 y FB(0)2355 3956 y FK(+)22 b FE(c)2487 3970 y FB(1)2524 3956 y FE(x)g FK(+)f FE(c)2729 3970 y FB(2)2767 3956 y FE(x)2819 3923 y FB(2)2889 3956 y FK(to)33 b(a)g(w)m(eigh)m(ted)i(dataset)150 4066 y(using)30 b(the)h(generalised)h(linear)f(\014tting)g(function)f FH(gsl_multifit_wlinear)p FK(.)36 b(The)30 b(mo)s(del)h(matrix)g FE(X)150 4175 y FK(for)f(a)h(quadratic)g(\014t)f(is)g(giv)m(en)i(b)m(y) -8 b(,)1510 4503 y FE(X)33 b FK(=)1714 4285 y Fs(0)1714 4431 y(B)1714 4481 y(B)1714 4534 y(@)1832 4339 y FK(1)130 b FE(x)2059 4353 y FB(0)2204 4339 y FE(x)2256 4306 y FB(2)2256 4361 y(0)1832 4448 y FK(1)g FE(x)2059 4462 y FB(1)2204 4448 y FE(x)2256 4415 y FB(2)2256 4471 y(1)1832 4558 y FK(1)g FE(x)2059 4572 y FB(2)2204 4558 y FE(x)2256 4525 y FB(2)2256 4581 y(2)1802 4668 y FE(:)15 b(:)g(:)92 b(:)15 b(:)g(:)92 b(:)15 b(:)g(:)2317 4285 y Fs(1)2317 4431 y(C)2317 4481 y(C)2317 4534 y(A)150 4831 y FK(where)27 b(the)g(column)g(of)g(ones)g(corresp)s(onds)f(to)i(the)f(constan)m(t)i (term)e FE(c)2551 4845 y FB(0)2588 4831 y FK(.)40 b(The)27 b(t)m(w)m(o)h(remaining)f(columns)150 4941 y(corresp)s(onds)i(to)i(the) g(terms)f FE(c)1209 4955 y FB(1)1247 4941 y FE(x)g FK(and)g FE(c)1545 4955 y FB(2)1582 4941 y FE(x)1634 4908 y FB(2)1671 4941 y FK(.)275 5086 y(The)20 b(program)h(reads)g FD(n)f FK(lines)h(of)h(data)f(in)g(the)g(format)h(\()p FD(x)p FK(,)h FD(y)p FK(,)g FD(err)7 b FK(\))21 b(where)f FD(err)27 b FK(is)22 b(the)f(error)f(\(standard)150 5195 y(deviation\))32 b(in)e(the)g(v)-5 b(alue)31 b FD(y)p FK(.)390 5340 y FH(#include)46 b()p eop end %%Page: 452 470 TeXDict begin 452 469 bop 150 -116 a FK(Chapter)30 b(38:)41 b(Least-Squares)31 b(Fitting)2098 b(452)390 299 y FH(#include)46 b()390 518 y(int)390 628 y(main)h(\(int)f(argc,)h (char)f(**argv\))390 737 y({)485 847 y(int)h(i,)h(n;)485 956 y(double)f(xi,)f(yi,)h(ei,)g(chisq;)485 1066 y(gsl_matrix)e(*X,)i (*cov;)485 1176 y(gsl_vector)e(*y,)i(*w,)g(*c;)485 1395 y(if)h(\(argc)e(!=)h(2\))581 1504 y({)676 1614 y(fprintf)f (\(stderr,"usage:)92 b(fit)46 b(n)i(<)f(data\\n"\);)676 1724 y(exit)g(\(-1\);)581 1833 y(})485 2052 y(n)h(=)f(atoi)g (\(argv[1]\);)485 2271 y(X)h(=)f(gsl_matrix_alloc)d(\(n,)j(3\);)485 2381 y(y)h(=)f(gsl_vector_alloc)d(\(n\);)485 2491 y(w)k(=)f (gsl_vector_alloc)d(\(n\);)485 2710 y(c)k(=)f(gsl_vector_alloc)d (\(3\);)485 2819 y(cov)j(=)h(gsl_matrix_alloc)43 b(\(3,)k(3\);)485 3039 y(for)g(\(i)h(=)f(0;)g(i)h(<)f(n;)g(i++\))581 3148 y({)676 3258 y(int)g(count)g(=)g(fscanf)f(\(stdin,)g("\045lg)h(\045lg)g (\045lg",)1631 3367 y(&xi,)g(&yi,)f(&ei\);)676 3587 y(if)i(\(count)e (!=)h(3\))772 3696 y({)867 3806 y(fprintf)f(\(stderr,)g("error)g (reading)g(file\\n"\);)867 3915 y(exit)h(\(-1\);)772 4025 y(})676 4244 y(printf)f(\("\045g)h(\045g)g(+/-)g(\045g\\n",)f(xi,) h(yi,)g(ei\);)676 4463 y(gsl_matrix_set)d(\(X,)j(i,)g(0,)h(1.0\);)676 4573 y(gsl_matrix_set)c(\(X,)j(i,)g(1,)h(xi\);)676 4682 y(gsl_matrix_set)c(\(X,)j(i,)g(2,)h(xi*xi\);)676 4902 y(gsl_vector_set)c(\(y,)j(i,)g(yi\);)676 5011 y(gsl_vector_set)d(\(w,)j (i,)g(1.0/\(ei*ei\)\);)581 5121 y(})485 5340 y({)p eop end %%Page: 453 471 TeXDict begin 453 470 bop 150 -116 a FK(Chapter)30 b(38:)41 b(Least-Squares)31 b(Fitting)2098 b(453)581 299 y FH (gsl_multifit_linear_work)o(spac)o(e)42 b(*)47 b(work)676 408 y(=)h(gsl_multifit_linear_allo)o(c)42 b(\(n,)47 b(3\);)581 518 y(gsl_multifit_wlinear)42 b(\(X,)47 b(w,)g(y,)g(c,)h(cov,)1631 628 y(&chisq,)e(work\);)581 737 y(gsl_multifit_linear_free)41 b(\(work\);)485 847 y(})390 1066 y(#define)46 b(C\(i\))g (\(gsl_vector_get\(c,\(i\)\)\))390 1176 y(#define)g(COV\(i,j\))f (\(gsl_matrix_get\(cov,\(i\),\(j)o(\)\)\))485 1395 y({)581 1504 y(printf)h(\("#)h(best)g(fit:)94 b(Y)47 b(=)h(\045g)f(+)g(\045g)h (X)f(+)h(\045g)f(X^2\\n",)963 1614 y(C\(0\),)f(C\(1\),)g(C\(2\)\);)581 1833 y(printf)g(\("#)h(covariance)e(matrix:\\n"\);)581 1943 y(printf)h(\("[)h(\045+.5e,)f(\045+.5e,)g(\045+.5e)94 b(\\n",)1106 2052 y(COV\(0,0\),)45 b(COV\(0,1\),)g(COV\(0,2\)\);)581 2162 y(printf)h(\(")95 b(\045+.5e,)46 b(\045+.5e,)g(\045+.5e)94 b(\\n",)1106 2271 y(COV\(1,0\),)45 b(COV\(1,1\),)g(COV\(1,2\)\);)581 2381 y(printf)h(\(")95 b(\045+.5e,)46 b(\045+.5e,)g(\045+.5e)g(]\\n",) 1106 2491 y(COV\(2,0\),)f(COV\(2,1\),)g(COV\(2,2\)\);)581 2600 y(printf)h(\("#)h(chisq)f(=)i(\045g\\n",)e(chisq\);)485 2710 y(})485 2929 y(gsl_matrix_free)e(\(X\);)485 3039 y(gsl_vector_free)g(\(y\);)485 3148 y(gsl_vector_free)g(\(w\);)485 3258 y(gsl_vector_free)g(\(c\);)485 3367 y(gsl_matrix_free)g(\(cov\);) 485 3587 y(return)j(0;)390 3696 y(})150 3861 y FK(A)31 b(suitable)h(set)g(of)f(data)h(for)f(\014tting)g(can)h(b)s(e)e (generated)j(using)d(the)i(follo)m(wing)g(program.)43 b(It)31 b(outputs)150 3970 y(a)g(set)g(of)f(p)s(oin)m(ts)g(with)h (gaussian)f(errors)g(from)g(the)g(curv)m(e)h FE(y)d FK(=)d FE(e)2400 3937 y Fq(x)2473 3970 y FK(in)30 b(the)g(region)h(0)26 b FE(<)f(x)g(<)g FK(2.)390 4134 y FH(#include)46 b()390 4244 y(#include)g()390 4354 y(#include)g() 390 4573 y(int)390 4682 y(main)h(\(void\))390 4792 y({)485 4902 y(double)g(x;)485 5011 y(const)g(gsl_rng_type)d(*)k(T;)485 5121 y(gsl_rng)e(*)i(r;)485 5340 y(gsl_rng_env_setup)c(\(\);)p eop end %%Page: 454 472 TeXDict begin 454 471 bop 150 -116 a FK(Chapter)30 b(38:)41 b(Least-Squares)31 b(Fitting)2098 b(454)485 408 y FH(T)48 b(=)f(gsl_rng_default;)485 518 y(r)h(=)f(gsl_rng_alloc)e(\(T\);)485 737 y(for)i(\(x)h(=)f(0.1;)g(x)g(<)h(2;)f(x+=)g(0.1\))581 847 y({)676 956 y(double)f(y0)i(=)f(exp)g(\(x\);)676 1066 y(double)f(sigma)h(=)g(0.1)g(*)h(y0;)676 1176 y(double)e(dy)i(=)f (gsl_ran_gaussian)c(\(r,)k(sigma\);)676 1395 y(printf)f(\("\045g)h (\045g)g(\045g\\n",)f(x,)i(y0)f(+)g(dy,)g(sigma\);)581 1504 y(})485 1724 y(gsl_rng_free\(r\);)485 1943 y(return)g(0;)390 2052 y(})150 2228 y FK(The)30 b(data)h(can)g(b)s(e)e(prepared)h(b)m(y)g (running)f(the)h(resulting)h(executable)h(program,)390 2403 y FH($)47 b(GSL_RNG_TYPE=mt19937_1999)41 b(./generate)k(>)j (exp.dat)390 2513 y($)f(more)g(exp.dat)390 2622 y(0.1)g(0.97935)f (0.110517)390 2732 y(0.2)h(1.3359)f(0.12214)390 2841 y(0.3)h(1.52573)f(0.134986)390 2951 y(0.4)h(1.60318)f(0.149182)390 3061 y(0.5)h(1.81731)f(0.164872)390 3170 y(0.6)h(1.92475)f(0.182212)390 3280 y(....)150 3455 y FK(T)-8 b(o)30 b(\014t)f(the)g(data)h(use)f(the) g(previous)g(program,)g(with)g(the)h(n)m(um)m(b)s(er)d(of)j(data)g(p)s (oin)m(ts)f(giv)m(en)h(as)f(the)h(\014rst)150 3565 y(argumen)m(t.)41 b(In)30 b(this)g(case)i(there)e(are)h(19)g(data)g(p)s(oin)m(ts.)390 3740 y FH($)47 b(./fit)g(19)g(<)g(exp.dat)390 3850 y(0.1)g(0.97935)f (+/-)h(0.110517)390 3959 y(0.2)g(1.3359)f(+/-)h(0.12214)390 4069 y(...)390 4178 y(#)g(best)g(fit:)g(Y)g(=)h(1.02318)d(+)j(0.956201) d(X)j(+)f(0.876796)f(X^2)390 4288 y(#)h(covariance)e(matrix:)390 4398 y([)i(+1.25612e-02,)e(-3.64387e-02,)f(+1.94389e-02)485 4507 y(-3.64387e-02,)h(+1.42339e-01,)f(-8.48761e-02)485 4617 y(+1.94389e-02,)h(-8.48761e-02,)f(+5.60243e-02)g(])390 4726 y(#)j(chisq)g(=)g(23.0987)150 4902 y FK(The)36 b(parameters)h(of)g (the)g(quadratic)h(\014t)e(matc)m(h)i(the)f(co)s(e\016cien)m(ts)i(of)e (the)g(expansion)f(of)h FE(e)3394 4869 y Fq(x)3436 4902 y FK(,)i(taking)150 5011 y(in)m(to)27 b(accoun)m(t)h(the)e(errors)f(on) h(the)h(parameters)f(and)f(the)i FE(O)s FK(\()p FE(x)2293 4978 y FB(3)2330 5011 y FK(\))f(di\013erence)h(b)s(et)m(w)m(een)g(the)f (exp)s(onen)m(tial)150 5121 y(and)31 b(quadratic)h(functions)f(for)h (the)f(larger)i(v)-5 b(alues)32 b(of)f FE(x)p FK(.)45 b(The)31 b(errors)g(on)g(the)h(parameters)g(are)g(giv)m(en)150 5230 y(b)m(y)j(the)h(square-ro)s(ot)f(of)h(the)f(corresp)s(onding)g (diagonal)h(elemen)m(ts)h(of)e(the)h(co)m(v)-5 b(ariance)38 b(matrix.)55 b(The)150 5340 y(c)m(hi-squared)31 b(p)s(er)e(degree)i(of) g(freedom)f(is)g(1.4,)i(indicating)f(a)g(reasonable)g(\014t)f(to)h(the) g(data.)p eop end %%Page: 455 473 TeXDict begin 455 472 bop 150 -116 a FK(Chapter)30 b(38:)41 b(Least-Squares)31 b(Fitting)2098 b(455)275 1948 y @beginspecial 117 @llx 195 @lly 492 @urx 580 @ury 2160 @rwi @setspecial %%BeginDocument: fit-wlinear2.eps %!PS-Adobe-3.0 EPSF-3.0 %%Creator: GNU libplot drawing library 1.6 %%Title: PostScript plot %%CreationDate: Sun Jul 29 14:10:38 2001 %%DocumentData: Clean7Bit %%LanguageLevel: 1 %%Pages: 1 %%PageOrder: Ascend %%Orientation: Portrait %%BoundingBox: 117 195 492 580 %%DocumentNeededResources: font Helvetica %%DocumentSuppliedResources: procset GNU_libplot 1.0 0 %%EndComments %%BeginDefaults %%PageResources: font Helvetica %%EndDefaults %%BeginProlog %%EndProlog %%BeginSetup %%IncludeResource: font Helvetica /DrawDict 50 dict def DrawDict begin /ISOLatin1Encoding [ /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /space/exclam/quotedbl/numbersign/dollar/percent/ampersand/quoteright /parenleft/parenright/asterisk/plus/comma/minus/period/slash /zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon /less/equal/greater/question/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N /O/P/Q/R/S/T/U/V/W/X/Y/Z/bracketleft/backslash/bracketright /asciicircum/underscore/quoteleft/a/b/c/d/e/f/g/h/i/j/k/l/m /n/o/p/q/r/s/t/u/v/w/x/y/z/braceleft/bar/braceright/asciitilde /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/dotlessi/grave/acute/circumflex/tilde/macron/breve /dotaccent/dieresis/.notdef/ring/cedilla/.notdef/hungarumlaut /ogonek/caron/space/exclamdown/cent/sterling/currency/yen/brokenbar /section/dieresis/copyright/ordfeminine/guillemotleft/logicalnot /hyphen/registered/macron/degree/plusminus/twosuperior/threesuperior /acute/mu/paragraph/periodcentered/cedilla/onesuperior/ordmasculine /guillemotright/onequarter/onehalf/threequarters/questiondown /Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla /Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex /Idieresis/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis /multiply/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute /Thorn/germandbls/agrave/aacute/acircumflex/atilde/adieresis /aring/ae/ccedilla/egrave/eacute/ecircumflex/edieresis/igrave /iacute/icircumflex/idieresis/eth/ntilde/ograve/oacute/ocircumflex /otilde/odieresis/divide/oslash/ugrave/uacute/ucircumflex/udieresis /yacute/thorn/ydieresis ] def /reencodeISO { dup dup findfont dup length dict begin { 1 index /FID ne { def }{ pop pop } ifelse } forall /Encoding ISOLatin1Encoding def currentdict end definefont } def /Helvetica reencodeISO def %%BeginResource procset GNU_libplot 1.0 0 /none null def /numGraphicParameters 17 def /stringLimit 65535 def /arrowHeight 8 def /arrowWidth 4 def /Begin { save numGraphicParameters dict begin } def /End { end restore } def /SetB { dup type /nulltype eq { pop false /brushRightArrow idef false /brushLeftArrow idef true /brushNone idef } { /brushDashOffset idef /brushDashArray idef 0 ne /brushRightArrow idef 0 ne /brushLeftArrow idef /brushWidth idef false /brushNone idef } ifelse } def /SetCFg { /fgblue idef /fggreen idef /fgred idef } def /SetCBg { /bgblue idef /bggreen idef /bgred idef } def /SetF { /printSize idef /printFont idef } def /SetP { dup type /nulltype eq { pop true /patternNone idef } { /patternGrayLevel idef patternGrayLevel -1 eq { /patternString idef } if false /patternNone idef } ifelse } def /BSpl { 0 begin storexyn newpath n 1 gt { 0 0 0 0 0 0 1 1 true subspline n 2 gt { 0 0 0 0 1 1 2 2 false subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 2 copy false subspline } if n 2 sub dup n 1 sub dup 2 copy 2 copy false subspline patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup 1 sub dup rightarrow } if end } dup 0 4 dict put def /Circ { newpath 0 360 arc closepath patternNone not { ifill } if brushNone not { istroke } if } def /CBSpl { 0 begin dup 2 gt { storexyn newpath n 1 sub dup 0 0 1 1 2 2 true subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 0 0 false subspline n 2 sub dup n 1 sub dup 0 0 1 1 false subspline patternNone not { ifill } if brushNone not { istroke } if } { Poly } ifelse end } dup 0 4 dict put def /Elli { 0 begin newpath 4 2 roll translate scale 0 0 1 0 360 arc closepath patternNone not { ifill } if brushNone not { istroke } if end } dup 0 1 dict put def /Line { 0 begin 2 storexyn newpath x 0 get y 0 get moveto x 1 get y 1 get lineto brushNone not { istroke } if 0 0 1 1 leftarrow 0 0 1 1 rightarrow end } dup 0 4 dict put def /MLine { 0 begin storexyn newpath n 1 gt { x 0 get y 0 get moveto 1 1 n 1 sub { /i exch def x i get y i get lineto } for patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Poly { 3 1 roll newpath moveto -1 add { lineto } repeat closepath patternNone not { ifill } if brushNone not { istroke } if } def /Rect { 0 begin /t exch def /r exch def /b exch def /l exch def newpath l b moveto l t lineto r t lineto r b lineto closepath patternNone not { ifill } if brushNone not { istroke } if end } dup 0 4 dict put def /Text { ishow } def /idef { dup where { pop pop pop } { exch def } ifelse } def /ifill { 0 begin gsave patternGrayLevel -1 ne { fgred bgred fgred sub patternGrayLevel mul add fggreen bggreen fggreen sub patternGrayLevel mul add fgblue bgblue fgblue sub patternGrayLevel mul add setrgbcolor eofill } { eoclip originalCTM setmatrix pathbbox /t exch def /r exch def /b exch def /l exch def /w r l sub ceiling cvi def /h t b sub ceiling cvi def /imageByteWidth w 8 div ceiling cvi def /imageHeight h def bgred bggreen bgblue setrgbcolor eofill fgred fggreen fgblue setrgbcolor w 0 gt h 0 gt and { l b translate w h scale w h true [w 0 0 h neg 0 h] { patternproc } imagemask } if } ifelse grestore end } dup 0 8 dict put def /istroke { gsave brushDashOffset -1 eq { [] 0 setdash 1 setgray } { brushDashArray brushDashOffset setdash fgred fggreen fgblue setrgbcolor } ifelse brushWidth setlinewidth originalCTM setmatrix stroke grestore } def /ishow { 0 begin gsave fgred fggreen fgblue setrgbcolor /fontDict printFont findfont printSize scalefont dup setfont def /descender fontDict begin 0 /FontBBox load 1 get FontMatrix end transform exch pop def /vertoffset 1 printSize sub descender sub def { 0 vertoffset moveto show /vertoffset vertoffset printSize sub def } forall grestore end } dup 0 3 dict put def /patternproc { 0 begin /patternByteLength patternString length def /patternHeight patternByteLength 8 mul sqrt cvi def /patternWidth patternHeight def /patternByteWidth patternWidth 8 idiv def /imageByteMaxLength imageByteWidth imageHeight mul stringLimit patternByteWidth sub min def /imageMaxHeight imageByteMaxLength imageByteWidth idiv patternHeight idiv patternHeight mul patternHeight max def /imageHeight imageHeight imageMaxHeight sub store /imageString imageByteWidth imageMaxHeight mul patternByteWidth add string def 0 1 imageMaxHeight 1 sub { /y exch def /patternRow y patternByteWidth mul patternByteLength mod def /patternRowString patternString patternRow patternByteWidth getinterval def /imageRow y imageByteWidth mul def 0 patternByteWidth imageByteWidth 1 sub { /x exch def imageString imageRow x add patternRowString putinterval } for } for imageString end } dup 0 12 dict put def /min { dup 3 2 roll dup 4 3 roll lt { exch } if pop } def /max { dup 3 2 roll dup 4 3 roll gt { exch } if pop } def /midpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 x1 add 2 div y0 y1 add 2 div end } dup 0 4 dict put def /thirdpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 2 mul x1 add 3 div y0 2 mul y1 add 3 div end } dup 0 4 dict put def /subspline { 0 begin /movetoNeeded exch def y exch get /y3 exch def x exch get /x3 exch def y exch get /y2 exch def x exch get /x2 exch def y exch get /y1 exch def x exch get /x1 exch def y exch get /y0 exch def x exch get /x0 exch def x1 y1 x2 y2 thirdpoint /p1y exch def /p1x exch def x2 y2 x1 y1 thirdpoint /p2y exch def /p2x exch def x1 y1 x0 y0 thirdpoint p1x p1y midpoint /p0y exch def /p0x exch def x2 y2 x3 y3 thirdpoint p2x p2y midpoint /p3y exch def /p3x exch def movetoNeeded { p0x p0y moveto } if p1x p1y p2x p2y p3x p3y curveto end } dup 0 17 dict put def /storexyn { /n exch def /y n array def /x n array def n 1 sub -1 0 { /i exch def y i 3 2 roll put x i 3 2 roll put } for } def /arrowhead { 0 begin transform originalCTM itransform /taily exch def /tailx exch def transform originalCTM itransform /tipy exch def /tipx exch def /dy tipy taily sub def /dx tipx tailx sub def /angle dx 0 ne dy 0 ne or { dy dx atan } { 90 } ifelse def gsave originalCTM setmatrix tipx tipy translate angle rotate newpath arrowHeight neg arrowWidth 2 div moveto 0 0 lineto arrowHeight neg arrowWidth 2 div neg lineto patternNone not { originalCTM setmatrix /padtip arrowHeight 2 exp 0.25 arrowWidth 2 exp mul add sqrt brushWidth mul arrowWidth div def /padtail brushWidth 2 div def tipx tipy translate angle rotate padtip 0 translate arrowHeight padtip add padtail add arrowHeight div dup scale arrowheadpath ifill } if brushNone not { originalCTM setmatrix tipx tipy translate angle rotate arrowheadpath istroke } if grestore end } dup 0 9 dict put def /arrowheadpath { newpath arrowHeight neg arrowWidth 2 div moveto 0 0 lineto arrowHeight neg arrowWidth 2 div neg lineto } def /leftarrow { 0 begin y exch get /taily exch def x exch get /tailx exch def y exch get /tipy exch def x exch get /tipx exch def brushLeftArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /rightarrow { 0 begin y exch get /tipy exch def x exch get /tipx exch def y exch get /taily exch def x exch get /tailx exch def brushRightArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def %%EndResource %%EndSetup %%Page: 1 1 %%PageResources: font Helvetica %%PageBoundingBox: 117 195 492 580 %%BeginPageSetup %I Idraw 8 Begin %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 1 0 0 1 0 0 ] concat /originalCTM matrix currentmatrix def /trueoriginalCTM matrix currentmatrix def %%EndPageSetup Begin %I Poly [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4 2304 2304 2304 9216 9216 9216 9216 2304 4 Poly End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 120.5899 213.1332 ] concat %I [ (0.0) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 9216 2304 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2304 2304 2442 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 206.9899 213.1332 ] concat %I [ (0.5) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4032 9216 4032 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4032 2304 4032 2442 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 293.3899 213.1332 ] concat %I [ (1.0) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5760 9216 5760 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5760 2304 5760 2442 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 379.7899 213.1332 ] concat %I [ (1.5) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7488 9216 7488 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7488 2304 7488 2442 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 466.1899 213.1332 ] concat %I [ (2.0) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 9216 9216 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2304 9216 2442 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 9216 2304 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2304 2304 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2650 9216 2650 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2650 2304 2650 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2995 9216 2995 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2995 2304 2995 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3341 9216 3341 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3341 2304 3341 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3686 9216 3686 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3686 2304 3686 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4032 9216 4032 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4032 2304 4032 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4378 9216 4378 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4378 2304 4378 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4723 9216 4723 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4723 2304 4723 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5069 9216 5069 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5069 2304 5069 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5414 9216 5414 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5414 2304 5414 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5760 9216 5760 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5760 2304 5760 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6106 9216 6106 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6106 2304 6106 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6451 9216 6451 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6451 2304 6451 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6797 9216 6797 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6797 2304 6797 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7142 9216 7142 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7142 2304 7142 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7488 9216 7488 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7488 2304 7488 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7834 9216 7834 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7834 2304 7834 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8179 9216 8179 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8179 2304 8179 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8525 9216 8525 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8525 2304 8525 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8870 9216 8870 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8870 2304 8870 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 9216 9216 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2304 9216 2359 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 117.9279 229.3306 ] concat %I [ (0) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2304 9078 2304 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2304 2442 2304 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 117.9279 278.702 ] concat %I [ (1) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 3291 9078 3291 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3291 2442 3291 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 117.9279 328.0734 ] concat %I [ (2) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 4279 9078 4279 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4279 2442 4279 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 117.9279 377.4449 ] concat %I [ (3) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5266 9078 5266 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5266 2442 5266 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 117.9279 426.8163 ] concat %I [ (4) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 6254 9078 6254 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 6254 2442 6254 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 117.9279 476.1877 ] concat %I [ (5) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 7241 9078 7241 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 7241 2442 7241 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 117.9279 525.5592 ] concat %I [ (6) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 8229 9078 8229 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 8229 2442 8229 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 117.9279 574.9306 ] concat %I [ (7) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 9216 9078 9216 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 9216 2442 9216 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2304 9161 2304 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2304 2359 2304 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2798 9161 2798 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2798 2359 2798 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 3291 9161 3291 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3291 2359 3291 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 3785 9161 3785 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3785 2359 3785 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 4279 9161 4279 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4279 2359 4279 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 4773 9161 4773 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4773 2359 4773 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5266 9161 5266 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5266 2359 5266 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5760 9161 5760 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5760 2359 5760 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 6254 9161 6254 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 6254 2359 6254 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 6747 9161 6747 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 6747 2359 6747 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 7241 9161 7241 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 7241 2359 7241 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 7735 9161 7735 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 7735 2359 7735 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 8229 9161 8229 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 8229 2359 8229 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 8722 9161 8722 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 8722 2359 8722 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 9216 9161 9216 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 9216 2359 9216 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2546 3162 2753 3162 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2650 3162 2650 3380 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2546 3380 2753 3380 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2650 3206 2650 3336 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2650 3271 2706 3303 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2650 3271 2593 3239 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2650 3271 2706 3239 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2650 3271 2593 3303 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2892 3503 3099 3503 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2995 3503 2995 3744 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2892 3744 3099 3744 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2995 3558 2995 3688 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2995 3623 3051 3656 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2995 3623 2939 3591 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2995 3623 3051 3591 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2995 3623 2939 3656 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3237 3677 3444 3677 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3341 3677 3341 3944 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3237 3944 3444 3944 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3341 3746 3341 3875 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3341 3811 3397 3843 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3341 3811 3285 3778 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3341 3811 3397 3778 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3341 3811 3285 3843 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3583 3740 3790 3740 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3686 3740 3686 4034 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3583 4034 3790 4034 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3686 3822 3686 3952 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3686 3887 3743 3919 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3686 3887 3630 3855 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3686 3887 3743 3855 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3686 3887 3630 3919 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3928 3936 4136 3936 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4032 3936 4032 4261 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3928 4261 4136 4261 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4032 4034 4032 4163 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4032 4098 4088 4131 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4032 4098 3976 4066 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4032 4098 4088 4066 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4032 4098 3976 4131 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4274 4025 4481 4025 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4378 4025 4378 4384 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4274 4384 4481 4384 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4378 4140 4378 4269 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4378 4205 4434 4237 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4378 4205 4321 4172 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4378 4205 4434 4172 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4378 4205 4321 4237 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4620 4013 4827 4013 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4723 4013 4723 4411 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4620 4411 4827 4411 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4723 4147 4723 4277 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4723 4212 4779 4245 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4723 4212 4667 4180 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4723 4212 4779 4180 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4723 4212 4667 4245 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4965 4563 5172 4563 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5069 4563 5069 5003 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4965 5003 5172 5003 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5069 4718 5069 4848 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5069 4783 5125 4816 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5069 4783 5013 4751 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5069 4783 5125 4751 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5069 4783 5013 4816 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5311 4481 5518 4481 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5414 4481 5414 4967 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5311 4967 5518 4967 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5414 4659 5414 4789 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5414 4724 5471 4756 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5414 4724 5358 4692 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5414 4724 5471 4692 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5414 4724 5358 4756 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5656 4257 5864 4257 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5760 4257 5760 4794 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5656 4794 5864 4794 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5760 4460 5760 4590 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5760 4525 5816 4558 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5760 4525 5704 4493 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5760 4525 5816 4493 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5760 4525 5704 4558 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6002 5058 6209 5058 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6106 5058 6106 5651 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6002 5651 6209 5651 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6106 5290 6106 5420 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6106 5355 6162 5387 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6106 5355 6049 5322 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6106 5355 6162 5322 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6106 5355 6049 5387 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6348 5751 6555 5751 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6451 5751 6451 6407 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6348 6407 6555 6407 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6451 6014 6451 6144 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6451 6079 6507 6111 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6451 6079 6395 6047 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6451 6079 6507 6047 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6451 6079 6395 6111 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6693 6156 6900 6156 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6797 6156 6797 6880 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6693 6880 6900 6880 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6797 6453 6797 6583 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6797 6518 6853 6550 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6797 6518 6741 6486 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6797 6518 6853 6486 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6797 6518 6741 6550 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7039 5122 7246 5122 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7142 5122 7142 5923 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7039 5923 7246 5923 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7142 5458 7142 5588 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7142 5523 7199 5555 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7142 5523 7086 5490 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7142 5523 7199 5490 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7142 5523 7086 5555 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7384 6788 7592 6788 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7488 6788 7488 7673 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7384 7673 7592 7673 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7488 7166 7488 7295 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7488 7230 7544 7263 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7488 7230 7432 7198 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7488 7230 7544 7198 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7488 7230 7432 7263 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7730 5908 7937 5908 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7834 5908 7834 6886 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7730 6886 7937 6886 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7834 6332 7834 6462 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7834 6397 7890 6430 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7834 6397 7777 6365 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7834 6397 7890 6365 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7834 6397 7777 6430 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8076 6922 8283 6922 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8179 6922 8179 8003 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8076 8003 8283 8003 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8179 7397 8179 7527 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8179 7462 8235 7495 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8179 7462 8123 7430 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8179 7462 8235 7430 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8179 7462 8123 7495 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8421 8010 8628 8010 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8525 8010 8525 9205 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8421 9205 8628 9205 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8525 8543 8525 8672 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8525 8608 8581 8640 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8525 8608 8469 8575 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8525 8608 8581 8575 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8525 8608 8469 8640 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8767 7571 8974 7571 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8870 7571 8870 8891 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8767 8891 8974 8891 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8870 8167 8870 8296 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8870 8231 8927 8264 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8870 8231 8814 8199 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8870 8231 8927 8199 2 MLine End Begin %I MLine [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8870 8231 8814 8264 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 200 2304 3314 2339 3324 2373 3334 2408 3343 2442 3353 2477 3364 2511 3374 2546 3385 2580 3395 2615 3406 2650 3417 2684 3429 2719 3440 2753 3452 2788 3463 2822 3475 2857 3488 2892 3500 2926 3512 2961 3525 2995 3538 3030 3551 3064 3564 3099 3577 3133 3591 3168 3604 3203 3618 3237 3632 3272 3647 3306 3661 3341 3675 3375 3690 3410 3705 3444 3720 3479 3735 3514 3751 3548 3766 3583 3782 3617 3798 3652 3814 3686 3831 3721 3847 3756 3864 3790 3880 3825 3897 3859 3915 3894 3932 3928 3949 3963 3967 3997 3985 4032 4003 4067 4021 4101 4039 4136 4058 4170 4077 4205 4096 4239 4115 4274 4134 4308 4153 4343 4173 4378 4193 4412 4212 4447 4233 4481 4253 4516 4273 4550 4294 4585 4315 4620 4336 4654 4357 4689 4378 4723 4399 4758 4421 4792 4443 4827 4465 4861 4487 4896 4509 4931 4532 4965 4555 5000 4578 5034 4601 5069 4624 5103 4647 5138 4671 5172 4694 5207 4718 5242 4742 5276 4767 5311 4791 5345 4816 5380 4840 5414 4865 5449 4890 5484 4916 5518 4941 5553 4967 5587 4993 5622 5019 5656 5045 5691 5071 5725 5098 5760 5124 5795 5151 5829 5178 5864 5205 5898 5233 5933 5260 5967 5288 6002 5316 6036 5344 6071 5372 6106 5401 6140 5429 6175 5458 6209 5487 6244 5516 6278 5545 6313 5575 6348 5604 6382 5634 6417 5664 6451 5694 6486 5724 6520 5755 6555 5785 6589 5816 6624 5847 6659 5878 6693 5910 6728 5941 6762 5973 6797 6005 6831 6037 6866 6069 6900 6102 6935 6134 6970 6167 7004 6200 7039 6233 7073 6266 7108 6299 7142 6333 7177 6367 7212 6401 7246 6435 7281 6469 7315 6504 7350 6538 7384 6573 7419 6608 7453 6643 7488 6679 7523 6714 7557 6750 7592 6786 7626 6822 7661 6858 7695 6894 7730 6931 7764 6967 7799 7004 7834 7041 7868 7079 7903 7116 7937 7154 7972 7191 8006 7229 8041 7267 8076 7306 8110 7344 8145 7383 8179 7422 8214 7460 8248 7500 8283 7539 8317 7578 8352 7618 8387 7658 8421 7698 8456 7738 8490 7778 8525 7819 8559 7860 8594 7901 8628 7942 8663 7983 8698 8024 8732 8066 8767 8107 8801 8149 8836 8191 8870 8234 8905 8276 8940 8319 8974 8362 9009 8404 9043 8448 9078 8491 9112 8534 9147 8578 9181 8622 200 MLine End %%PageTrailer End %I eop showpage %%Trailer end %%EOF %%EndDocument @endspecial 150 2182 a Fy(38.8.3)63 b(Regularized)41 b(Linear)f(Regression)j(Example)d(1)150 2329 y FK(The)48 b(next)h(program)f(demonstrates)h(the)g(di\013erence)g(b)s(et)m(w)m (een)g(ordinary)f(and)g(regularized)i(least)150 2438 y(squares)38 b(when)g(the)h(design)f(matrix)h(is)g(near-singular.)65 b(In)38 b(this)g(program,)j(w)m(e)e(generate)h(t)m(w)m(o)g(ran-)150 2548 y(dom)29 b(normally)h(distributed)f(v)-5 b(ariables)30 b FE(u)g FK(and)f FE(v)s FK(,)h(with)f FE(v)g FK(=)c FE(u)18 b FK(+)h FE(noise)29 b FK(so)h(that)g FE(u)g FK(and)f FE(v)k FK(are)d(nearly)150 2657 y(colinear.)42 b(W)-8 b(e)30 b(then)e(set)i(a)f(third)f(dep)s(enden)m(t)g(v)-5 b(ariable)30 b FE(y)e FK(=)d FE(u)17 b FK(+)g FE(v)k FK(+)c FE(noise)29 b FK(and)f(solv)m(e)i(for)f(the)g(co)s(e\016-)150 2767 y(cien)m(ts)j FE(c)445 2781 y FB(1)483 2767 y FE(;)15 b(c)562 2781 y FB(2)630 2767 y FK(of)31 b(the)g(mo)s(del)g FE(Y)20 b FK(\()p FE(c)1309 2781 y FB(1)1347 2767 y FE(;)15 b(c)1426 2781 y FB(2)1464 2767 y FK(\))26 b(=)f FE(c)1660 2781 y FB(1)1698 2767 y FE(u)c FK(+)f FE(c)1901 2781 y FB(2)1938 2767 y FE(v)s FK(.)42 b(Since)31 b FE(u)26 b FI(\031)g FE(v)s FK(,)31 b(the)g(design)g(matrix)g FE(X)38 b FK(is)31 b(nearly)150 2877 y(singular,)f(leading)i(to)f (unstable)f(ordinary)f(least)j(squares)e(solutions.)150 3004 y(Here)h(is)f(the)h(program)f(output:)390 3131 y FH(matrix)46 b(condition)f(number)h(=)i(1.025113e+04)390 3240 y(===)f(Unregularized)d(fit)j(===)390 3350 y(best)g(fit:)f(y)i(=)f (-43.6588)f(u)h(+)h(45.6636)d(v)390 3460 y(residual)h(norm)g(=)i (31.6248)390 3569 y(solution)e(norm)g(=)i(63.1764)390 3679 y(chisq/dof)d(=)j(1.00213)390 3788 y(===)f(Regularized)e(fit)i (\(L-curve\))e(===)390 3898 y(optimal)h(lambda:)g(4.51103)390 4007 y(best)h(fit:)f(y)i(=)f(1.00113)f(u)h(+)h(1.0032)e(v)390 4117 y(residual)g(norm)g(=)i(31.6547)390 4227 y(solution)e(norm)g(=)i (1.41728)390 4336 y(chisq/dof)d(=)j(1.04499)390 4446 y(===)f(Regularized)e(fit)i(\(GCV\))f(===)390 4555 y(optimal)g(lambda:) g(0.0232029)390 4665 y(best)h(fit:)f(y)i(=)f(-19.8367)f(u)h(+)h (21.8417)d(v)390 4775 y(residual)h(norm)g(=)i(31.6332)390 4884 y(solution)e(norm)g(=)i(29.5051)390 4994 y(chisq/dof)d(=)j (1.00314)150 5121 y FK(W)-8 b(e)43 b(see)g(that)g(the)g(ordinary)e (least)j(squares)e(solution)g(is)h(completely)h(wrong,)h(while)d(the)h (L-curv)m(e)150 5230 y(regularized)37 b(metho)s(d)f(with)g(the)g (optimal)h FE(\025)e FK(=)g(4)p FE(:)p FK(51103)k(\014nds)34 b(the)j(correct)g(solution)g FE(c)3284 5244 y FB(1)3356 5230 y FI(\031)e FE(c)3501 5244 y FB(2)3574 5230 y FI(\031)f FK(1.)150 5340 y(The)c(GCV)h(regularized)g(metho)s(d)f(\014nds)f(a)i (regularization)i(parameter)e FE(\025)25 b FK(=)h(0)p FE(:)p FK(0232029)34 b(whic)m(h)d(is)f(to)s(o)p eop end %%Page: 456 474 TeXDict begin 456 473 bop 150 -116 a FK(Chapter)30 b(38:)41 b(Least-Squares)31 b(Fitting)2098 b(456)150 299 y(small)29 b(to)h(giv)m(e)g(an)e(accurate)i(solution,)g(although)f(it)g(p)s (erforms)e(b)s(etter)i(than)f(OLS.)g(The)g(L-curv)m(e)i(and)150 408 y(its)h(computed)f(corner,)g(as)h(w)m(ell)g(as)g(the)g(GCV)f(curv)m (e)h(and)f(its)g(minim)m(um)g(are)h(plotted)g(b)s(elo)m(w.)275 2144 y @beginspecial 50 @llx 50 @lly 626 @urx 338 @ury 3600 @rwi @setspecial %%BeginDocument: regularized.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: regularized.eps %%Creator: gnuplot 4.6 patchlevel 2 %%CreationDate: Wed 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3915 y({)772 4025 y(printf\("\045e)g(\045e)i(\045e)g(\045e\\n",)1106 4134 y(gsl_vector_get\(reg_param)o(,)42 b(i\),)1106 4244 y(gsl_vector_get\(rho,)g(i\),)1106 4354 y(gsl_vector_get\(eta,)g(i\),) 1106 4463 y(gsl_vector_get\(G,)h(i\)\);)676 4573 y(})581 4792 y(/*)k(output)f(L-curve)g(corner)g(point)g(*/)581 4902 y(printf\("\\n\\n\045f)e(\045f\\n",)915 5011 y (gsl_vector_get\(rho,)f(reg_idx\),)915 5121 y(gsl_vector_get\(eta,)g (reg_idx\)\);)581 5340 y(/*)k(output)f(GCV)h(curve)f(corner)h(minimum)e (*/)p eop end %%Page: 459 477 TeXDict begin 459 476 bop 150 -116 a FK(Chapter)30 b(38:)41 b(Least-Squares)31 b(Fitting)2098 b(459)581 299 y FH (printf\("\\n\\n\045e)44 b(\045e\\n",)915 408 y(lambda_gcv,)915 518 y(G_gcv\);)581 737 y(gsl_multifit_linear_free)o(\(w\);)581 847 y(gsl_vector_free\(c\);)581 956 y(gsl_vector_free\(c_lcurve)o(\);) 581 1066 y(gsl_vector_free\(reg_para)o(m\);)581 1176 y(gsl_vector_free\(rho\);)581 1285 y(gsl_vector_free\(eta\);)581 1395 y(gsl_vector_free\(G\);)485 1504 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vpt2 Square} bind def /S0 {BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare} bind def /S1 {BL [] 0 setdash 2 copy vpt Square fill Bsquare} bind def /S2 {BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare} bind def /S3 {BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare} bind def /S4 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare} bind def /S5 {BL [] 0 setdash 2 copy 2 copy vpt Square fill exch vpt sub exch vpt sub vpt Square fill Bsquare} bind def /S6 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare} bind def /S7 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill 2 copy vpt Square fill Bsquare} bind def /S8 {BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare} bind def /S9 {BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare} bind def /S10 {BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill Bsquare} bind def /S11 {BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare} bind def /S12 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare} bind def /S13 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy vpt Square fill Bsquare} bind def /S14 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy exch vpt sub exch vpt Square fill Bsquare} bind def /S15 {BL [] 0 setdash 2 copy Bsquare fill Bsquare} bind def /D0 {gsave translate 45 rotate 0 0 S0 stroke grestore} bind def /D1 {gsave translate 45 rotate 0 0 S1 stroke grestore} bind def /D2 {gsave translate 45 rotate 0 0 S2 stroke grestore} bind def /D3 {gsave translate 45 rotate 0 0 S3 stroke grestore} bind def /D4 {gsave translate 45 rotate 0 0 S4 stroke grestore} bind def /D5 {gsave translate 45 rotate 0 0 S5 stroke grestore} bind def /D6 {gsave translate 45 rotate 0 0 S6 stroke grestore} bind def /D7 {gsave translate 45 rotate 0 0 S7 stroke grestore} bind def /D8 {gsave translate 45 rotate 0 0 S8 stroke grestore} bind def /D9 {gsave translate 45 rotate 0 0 S9 stroke grestore} bind def /D10 {gsave translate 45 rotate 0 0 S10 stroke grestore} bind def /D11 {gsave translate 45 rotate 0 0 S11 stroke grestore} bind def /D12 {gsave translate 45 rotate 0 0 S12 stroke grestore} bind def /D13 {gsave translate 45 rotate 0 0 S13 stroke grestore} bind def /D14 {gsave translate 45 rotate 0 0 S14 stroke grestore} bind def /D15 {gsave translate 45 rotate 0 0 S15 stroke grestore} bind def /DiaE {stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke} def /BoxE {stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke} def /TriUE {stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke} def /TriDE {stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke} def /PentE {stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore} def /CircE {stroke [] 0 setdash hpt 0 360 arc stroke} def /Opaque {gsave closepath 1 setgray fill grestore 0 setgray closepath} def /DiaW {stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V Opaque stroke} def /BoxW {stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V Opaque stroke} def /TriUW {stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V Opaque stroke} def /TriDW {stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V Opaque stroke} def /PentW {stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat Opaque stroke grestore} def /CircW {stroke [] 0 setdash hpt 0 360 arc Opaque stroke} def /BoxFill {gsave Rec 1 setgray fill grestore} def /Density { /Fillden exch def currentrgbcolor /ColB exch def /ColG exch def /ColR exch def /ColR ColR Fillden mul Fillden sub 1 add def /ColG ColG Fillden mul Fillden sub 1 add def /ColB ColB Fillden mul Fillden sub 1 add def ColR ColG ColB setrgbcolor} def /BoxColFill {gsave Rec PolyFill} def /PolyFill {gsave Density fill grestore grestore} def /h {rlineto rlineto rlineto gsave closepath fill grestore} bind def % % PostScript Level 1 Pattern Fill routine for rectangles % Usage: x y w h s a XX PatternFill % x,y = lower left corner of box to be filled % w,h = width and height of box % a = angle in degrees between lines and x-axis % XX = 0/1 for no/yes cross-hatch % /PatternFill {gsave /PFa [ 9 2 roll ] def PFa 0 get PFa 2 get 2 div add PFa 1 get PFa 3 get 2 div add translate PFa 2 get -2 div PFa 3 get -2 div PFa 2 get PFa 3 get Rec TransparentPatterns {} {gsave 1 setgray fill grestore} ifelse clip currentlinewidth 0.5 mul setlinewidth /PFs PFa 2 get dup mul PFa 3 get dup mul add sqrt def 0 0 M PFa 5 get rotate PFs -2 div dup translate 0 1 PFs PFa 4 get div 1 add floor cvi {PFa 4 get mul 0 M 0 PFs V} for 0 PFa 6 get ne { 0 1 PFs PFa 4 get div 1 add floor cvi {PFa 4 get mul 0 2 1 roll M PFs 0 V} for } if stroke grestore} def % /languagelevel where {pop languagelevel} {1} ifelse 2 lt {/InterpretLevel1 true def} {/InterpretLevel1 Level1 def} ifelse % % PostScript level 2 pattern fill definitions % /Level2PatternFill { /Tile8x8 {/PaintType 2 /PatternType 1 /TilingType 1 /BBox [0 0 8 8] /XStep 8 /YStep 8} bind def /KeepColor {currentrgbcolor [/Pattern /DeviceRGB] setcolorspace} bind def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 0 M 8 8 L 0 8 M 8 0 L stroke} >> matrix makepattern /Pat1 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 0 M 8 8 L 0 8 M 8 0 L stroke 0 4 M 4 8 L 8 4 L 4 0 L 0 4 L stroke} >> matrix makepattern /Pat2 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 0 M 0 8 L 8 8 L 8 0 L 0 0 L fill} >> matrix makepattern /Pat3 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -4 8 M 8 -4 L 0 12 M 12 0 L stroke} >> matrix makepattern /Pat4 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -4 0 M 8 12 L 0 -4 M 12 8 L stroke} >> matrix makepattern /Pat5 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -2 8 M 4 -4 L 0 12 M 8 -4 L 4 12 M 10 0 L stroke} >> matrix makepattern /Pat6 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -2 0 M 4 12 L 0 -4 M 8 12 L 4 -4 M 10 8 L stroke} >> matrix makepattern /Pat7 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 8 -2 M -4 4 L 12 0 M -4 8 L 12 4 M 0 10 L stroke} >> matrix makepattern /Pat8 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 -2 M 12 4 L -4 0 M 12 8 L -4 4 M 8 10 L stroke} >> matrix makepattern /Pat9 exch def /Pattern1 {PatternBgnd KeepColor Pat1 setpattern} bind def /Pattern2 {PatternBgnd KeepColor Pat2 setpattern} bind def /Pattern3 {PatternBgnd KeepColor Pat3 setpattern} bind def /Pattern4 {PatternBgnd KeepColor Landscape {Pat5} {Pat4} ifelse setpattern} bind def /Pattern5 {PatternBgnd KeepColor Landscape {Pat4} {Pat5} ifelse setpattern} bind def /Pattern6 {PatternBgnd KeepColor Landscape {Pat9} {Pat6} ifelse setpattern} bind def /Pattern7 {PatternBgnd KeepColor Landscape {Pat8} {Pat7} ifelse setpattern} bind def } def % % %End of PostScript Level 2 code % /PatternBgnd { TransparentPatterns {} {gsave 1 setgray fill grestore} ifelse } def % % Substitute for Level 2 pattern fill codes with % grayscale if Level 2 support is not selected. % /Level1PatternFill { /Pattern1 {0.250 Density} bind def /Pattern2 {0.500 Density} bind def /Pattern3 {0.750 Density} bind def /Pattern4 {0.125 Density} bind def /Pattern5 {0.375 Density} bind def /Pattern6 {0.625 Density} bind def /Pattern7 {0.875 Density} bind def } def % % Now test for support of Level 2 code % Level1 {Level1PatternFill} {Level2PatternFill} ifelse % /Symbol-Oblique /Symbol findfont [1 0 .167 1 0 0] makefont dup length dict begin {1 index /FID eq {pop pop} {def} ifelse} forall currentdict end definefont pop /MFshow { { dup 5 get 3 ge { 5 get 3 eq {gsave} {grestore} ifelse } {dup dup 0 get findfont exch 1 get scalefont setfont [ currentpoint ] exch dup 2 get 0 exch R dup 5 get 2 ne {dup dup 6 get exch 4 get {Gshow} {stringwidth pop 0 R} ifelse }if dup 5 get 0 eq {dup 3 get {2 get neg 0 exch R pop} {pop aload pop M} ifelse} {dup 5 get 1 eq {dup 2 get exch dup 3 get exch 6 get stringwidth pop -2 div dup 0 R} {dup 6 get stringwidth pop -2 div 0 R 6 get show 2 index {aload pop M neg 3 -1 roll neg R pop pop} {pop pop pop pop aload pop M} ifelse }ifelse }ifelse } ifelse } forall} def /Gswidth {dup type /stringtype eq {stringwidth} {pop (n) stringwidth} ifelse} def /MFwidth {0 exch { dup 5 get 3 ge { 5 get 3 eq { 0 } { pop } ifelse } {dup 3 get{dup dup 0 get findfont exch 1 get scalefont setfont 6 get Gswidth pop add} {pop} ifelse} ifelse} forall} def /MLshow { currentpoint stroke M 0 exch R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /MRshow { currentpoint stroke M exch dup MFwidth neg 3 -1 roll R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /MCshow { currentpoint stroke M exch dup MFwidth -2 div 3 -1 roll R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /XYsave { [( ) 1 2 true false 3 ()] } bind def /XYrestore { [( ) 1 2 true false 4 ()] } bind def Level1 SuppressPDFMark or {} { /SDict 10 dict def systemdict /pdfmark known not { userdict /pdfmark systemdict /cleartomark get put } if SDict begin [ /Title (regularized2.eps) /Subject (gnuplot plot) /Creator (gnuplot 4.6 patchlevel 2) /Author (palken) % /Producer (gnuplot) % /Keywords () /CreationDate (Wed Oct 26 06:04:23 2016) /DOCINFO pdfmark end } ifelse end %%EndProlog %%Page: 1 1 gnudict begin gsave doclip 50 50 translate 0.050 0.050 scale 0 setgray newpath (Helvetica) findfont 140 scalefont setfont BackgroundColor 0 lt 3 1 roll 0 lt exch 0 lt or or not {BackgroundColor C 1.000 0 0 11520.00 5760.00 BoxColFill} if 1.000 UL LTb LCb setrgbcolor 602 448 M 63 0 V 4842 0 R -63 0 V stroke 518 448 M [ [(Helvetica) 140.0 0.0 true true 0 (10)] [(Helvetica) 112.0 70.0 true true 0 (-1)] ] -60.7 MRshow 1.000 UL LTb LCb setrgbcolor 602 893 M 63 0 V 4842 0 R -63 0 V stroke 518 893 M [ [(Helvetica) 140.0 0.0 true true 0 (10)] [(Helvetica) 112.0 70.0 true true 0 (0)] ] -60.7 MRshow 1.000 UL LTb LCb setrgbcolor 602 1337 M 63 0 V 4842 0 R -63 0 V stroke 518 1337 M [ [(Helvetica) 140.0 0.0 true true 0 (10)] [(Helvetica) 112.0 70.0 true true 0 (1)] ] -60.7 MRshow 1.000 UL LTb LCb setrgbcolor 602 1782 M 63 0 V 4842 0 R -63 0 V stroke 518 1782 M [ [(Helvetica) 140.0 0.0 true true 0 (10)] [(Helvetica) 112.0 70.0 true true 0 (2)] ] -60.7 MRshow 1.000 UL LTb LCb setrgbcolor 602 2227 M 63 0 V 4842 0 R -63 0 V stroke 518 2227 M [ [(Helvetica) 140.0 0.0 true true 0 (10)] [(Helvetica) 112.0 70.0 true true 0 (3)] ] -60.7 MRshow 1.000 UL LTb LCb setrgbcolor 602 2671 M 63 0 V 4842 0 R -63 0 V stroke 518 2671 M [ [(Helvetica) 140.0 0.0 true true 0 (10)] 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63 0 V 4842 0 R -63 0 V stroke 518 5339 M [ [(Helvetica) 140.0 0.0 true true 0 (10)] [(Helvetica) 112.0 70.0 true true 0 (10)] ] -60.7 MRshow 1.000 UL LTb LCb setrgbcolor 602 448 M 0 63 V 0 4828 R 0 -63 V stroke 602 308 M [ [(Helvetica) 140.0 0.0 true true 0 (2.3)] ] -46.7 MCshow 1.000 UL LTb LCb setrgbcolor 5507 448 M 0 63 V 0 4828 R 0 -63 V stroke 5507 308 M [ [(Helvetica) 140.0 0.0 true true 0 (3.2)] ] -46.7 MCshow 1.000 UL LTb LCb setrgbcolor 1.000 UL LTb LCb setrgbcolor 602 5339 N 602 448 L 4905 0 V 0 4891 V -4905 0 V Z stroke LCb setrgbcolor 112 2893 M currentpoint gsave translate -270 rotate 0 0 moveto [ [(Helvetica) 140.0 0.0 true true 0 (solution norm ||c||)] ] -46.7 MCshow grestore LTb LCb setrgbcolor 3054 98 M [ [(Helvetica) 140.0 0.0 true true 0 (residual norm ||y - X c||)] ] -46.7 MCshow LTb 3054 5549 M [ [(Helvetica) 140.0 0.0 true true 0 (L-curve)] ] -46.7 MCshow 0.300 UP 1.000 UL LTb LCb setrgbcolor % Begin plot #1 0.300 UP 2.000 UL LTb LCb setrgbcolor /Helvetica 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2199 4332 CircleF 2179 4373 CircleF 2155 4414 CircleF 2126 4455 CircleF 2089 4496 CircleF 2045 4536 CircleF 1991 4576 CircleF 1926 4616 CircleF 1849 4655 CircleF 1758 4693 CircleF 1652 4730 CircleF 1529 4765 CircleF 1391 4800 CircleF 1239 4833 CircleF 1074 4864 CircleF 900 4893 CircleF 724 4920 CircleF % End plot #1 % Begin plot #2 3.000 UP 2.000 UL LT6 0.90 0.17 0.09 C /Helvetica findfont 140 scalefont setfont 2445 3395 Circle % End plot #2 1.000 UL LTb LCb setrgbcolor 602 5339 N 602 448 L 4905 0 V 0 4891 V -4905 0 V Z stroke 0.300 UP 1.000 UL LTb LCb setrgbcolor 1.000 UL LTb LCb setrgbcolor 6362 448 M 63 0 V 4842 0 R -63 0 V stroke 6278 448 M [ [(Helvetica) 140.0 0.0 true true 0 (10)] [(Helvetica) 112.0 70.0 true true 0 (-1)] ] -60.7 MRshow 1.000 UL LTb LCb setrgbcolor 6362 1920 M 31 0 V 4874 0 R -31 0 V 6362 2782 M 31 0 V 4874 0 R -31 0 V 6362 3393 M 31 0 V 4874 0 R -31 0 V 6362 3867 M 31 0 V 4874 0 R -31 0 V 6362 4254 M 31 0 V 4874 0 R -31 0 V 6362 4581 M 31 0 V 4874 0 R -31 0 V 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moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath} bind def /C3 {BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill vpt 0 360 arc closepath} bind def /C4 {BL [] 0 setdash 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc closepath} bind def /C5 {BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc} bind def /C6 {BL [] 0 setdash 2 copy moveto 2 copy vpt 90 270 arc closepath fill vpt 0 360 arc closepath} bind def /C7 {BL [] 0 setdash 2 copy moveto 2 copy vpt 0 270 arc closepath fill vpt 0 360 arc closepath} bind def /C8 {BL [] 0 setdash 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath} bind def /C9 {BL [] 0 setdash 2 copy moveto 2 copy vpt 270 450 arc closepath fill vpt 0 360 arc closepath} bind def /C10 {BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath} bind def /C11 {BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath} bind def /C12 {BL [] 0 setdash 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath} bind def /C13 {BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath} bind def /C14 {BL [] 0 setdash 2 copy moveto 2 copy vpt 90 360 arc closepath fill vpt 0 360 arc} bind def /C15 {BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill vpt 0 360 arc closepath} bind def /Rec {newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath} bind def /Square {dup Rec} bind def /Bsquare {vpt sub exch vpt sub exch vpt2 Square} bind def /S0 {BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare} bind def /S1 {BL [] 0 setdash 2 copy vpt Square fill Bsquare} bind def /S2 {BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare} bind def /S3 {BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare} bind def /S4 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare} bind def /S5 {BL [] 0 setdash 2 copy 2 copy vpt Square fill exch vpt sub exch vpt sub vpt Square fill Bsquare} bind def /S6 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare} bind def /S7 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill 2 copy vpt Square fill Bsquare} bind def /S8 {BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare} bind def /S9 {BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare} bind def /S10 {BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill Bsquare} bind def /S11 {BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare} bind def /S12 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare} bind def /S13 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy vpt Square fill Bsquare} bind def /S14 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy exch vpt sub exch vpt Square fill Bsquare} bind def /S15 {BL [] 0 setdash 2 copy Bsquare fill Bsquare} bind def /D0 {gsave translate 45 rotate 0 0 S0 stroke grestore} bind def /D1 {gsave translate 45 rotate 0 0 S1 stroke grestore} bind def /D2 {gsave translate 45 rotate 0 0 S2 stroke grestore} bind def /D3 {gsave translate 45 rotate 0 0 S3 stroke grestore} bind def /D4 {gsave translate 45 rotate 0 0 S4 stroke grestore} bind def /D5 {gsave translate 45 rotate 0 0 S5 stroke grestore} bind def /D6 {gsave translate 45 rotate 0 0 S6 stroke grestore} bind def /D7 {gsave translate 45 rotate 0 0 S7 stroke grestore} bind def /D8 {gsave translate 45 rotate 0 0 S8 stroke grestore} bind def /D9 {gsave translate 45 rotate 0 0 S9 stroke grestore} bind def /D10 {gsave translate 45 rotate 0 0 S10 stroke grestore} bind def /D11 {gsave translate 45 rotate 0 0 S11 stroke grestore} bind def /D12 {gsave translate 45 rotate 0 0 S12 stroke grestore} bind def /D13 {gsave translate 45 rotate 0 0 S13 stroke grestore} bind def /D14 {gsave translate 45 rotate 0 0 S14 stroke grestore} bind def /D15 {gsave translate 45 rotate 0 0 S15 stroke grestore} bind def /DiaE {stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke} def /BoxE {stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke} def /TriUE {stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke} def /TriDE {stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke} def /PentE {stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore} def /CircE {stroke [] 0 setdash hpt 0 360 arc stroke} def /Opaque {gsave closepath 1 setgray fill grestore 0 setgray closepath} def /DiaW {stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V Opaque stroke} def /BoxW {stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V Opaque stroke} def /TriUW {stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V Opaque stroke} def /TriDW {stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V Opaque stroke} def /PentW {stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat Opaque stroke grestore} def /CircW {stroke [] 0 setdash hpt 0 360 arc Opaque stroke} def /BoxFill {gsave Rec 1 setgray fill grestore} def /Density { /Fillden exch def currentrgbcolor /ColB exch def /ColG exch def /ColR exch def /ColR ColR Fillden mul Fillden sub 1 add def /ColG ColG Fillden mul Fillden sub 1 add def /ColB ColB Fillden mul Fillden sub 1 add def ColR ColG ColB setrgbcolor} def /BoxColFill {gsave Rec PolyFill} def /PolyFill {gsave Density fill grestore grestore} def /h {rlineto rlineto rlineto gsave closepath fill grestore} bind def % % PostScript Level 1 Pattern Fill routine for rectangles % Usage: x y w h s a XX PatternFill % x,y = lower left corner of box to be filled % w,h = width and height of box % a = angle in degrees between lines and x-axis % XX = 0/1 for no/yes cross-hatch % /PatternFill {gsave /PFa [ 9 2 roll ] def PFa 0 get PFa 2 get 2 div add PFa 1 get PFa 3 get 2 div add translate PFa 2 get -2 div PFa 3 get -2 div PFa 2 get PFa 3 get Rec TransparentPatterns {} {gsave 1 setgray fill grestore} ifelse clip currentlinewidth 0.5 mul setlinewidth /PFs PFa 2 get dup mul PFa 3 get dup mul add sqrt def 0 0 M PFa 5 get rotate PFs -2 div dup translate 0 1 PFs PFa 4 get div 1 add floor cvi {PFa 4 get mul 0 M 0 PFs V} for 0 PFa 6 get ne { 0 1 PFs PFa 4 get div 1 add floor cvi {PFa 4 get mul 0 2 1 roll M PFs 0 V} for } if stroke grestore} def % /languagelevel where {pop languagelevel} {1} ifelse 2 lt {/InterpretLevel1 true def} {/InterpretLevel1 Level1 def} ifelse % % PostScript level 2 pattern fill definitions % /Level2PatternFill { /Tile8x8 {/PaintType 2 /PatternType 1 /TilingType 1 /BBox [0 0 8 8] /XStep 8 /YStep 8} bind def /KeepColor {currentrgbcolor [/Pattern /DeviceRGB] setcolorspace} bind def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 0 M 8 8 L 0 8 M 8 0 L stroke} >> matrix makepattern /Pat1 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 0 M 8 8 L 0 8 M 8 0 L stroke 0 4 M 4 8 L 8 4 L 4 0 L 0 4 L stroke} >> matrix makepattern /Pat2 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 0 M 0 8 L 8 8 L 8 0 L 0 0 L fill} >> matrix makepattern /Pat3 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -4 8 M 8 -4 L 0 12 M 12 0 L stroke} >> matrix makepattern /Pat4 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -4 0 M 8 12 L 0 -4 M 12 8 L stroke} >> matrix makepattern /Pat5 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -2 8 M 4 -4 L 0 12 M 8 -4 L 4 12 M 10 0 L stroke} >> matrix makepattern /Pat6 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -2 0 M 4 12 L 0 -4 M 8 12 L 4 -4 M 10 8 L stroke} >> matrix makepattern /Pat7 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 8 -2 M -4 4 L 12 0 M -4 8 L 12 4 M 0 10 L stroke} >> matrix makepattern /Pat8 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 -2 M 12 4 L -4 0 M 12 8 L -4 4 M 8 10 L stroke} >> matrix makepattern /Pat9 exch def /Pattern1 {PatternBgnd KeepColor Pat1 setpattern} bind def /Pattern2 {PatternBgnd KeepColor Pat2 setpattern} bind def /Pattern3 {PatternBgnd KeepColor Pat3 setpattern} bind def /Pattern4 {PatternBgnd KeepColor Landscape {Pat5} {Pat4} ifelse setpattern} bind def /Pattern5 {PatternBgnd KeepColor Landscape {Pat4} {Pat5} ifelse setpattern} bind def /Pattern6 {PatternBgnd KeepColor Landscape {Pat9} {Pat6} ifelse setpattern} bind def /Pattern7 {PatternBgnd KeepColor Landscape {Pat8} {Pat7} ifelse setpattern} bind def } def % % %End of PostScript Level 2 code % /PatternBgnd { TransparentPatterns {} {gsave 1 setgray fill grestore} ifelse } def % % Substitute for Level 2 pattern fill codes with % grayscale if Level 2 support is not selected. % /Level1PatternFill { /Pattern1 {0.250 Density} bind def /Pattern2 {0.500 Density} bind def /Pattern3 {0.750 Density} bind def /Pattern4 {0.125 Density} bind def /Pattern5 {0.375 Density} bind def /Pattern6 {0.625 Density} bind def /Pattern7 {0.875 Density} bind def } def % % Now test for support of Level 2 code % Level1 {Level1PatternFill} {Level2PatternFill} ifelse % /Symbol-Oblique /Symbol findfont [1 0 .167 1 0 0] makefont dup length dict begin {1 index /FID eq {pop pop} {def} ifelse} forall currentdict end definefont pop /MFshow { { dup 5 get 3 ge { 5 get 3 eq {gsave} {grestore} ifelse } {dup dup 0 get findfont exch 1 get scalefont setfont [ currentpoint ] exch dup 2 get 0 exch R dup 5 get 2 ne {dup dup 6 get exch 4 get {Gshow} {stringwidth pop 0 R} ifelse }if dup 5 get 0 eq {dup 3 get {2 get neg 0 exch R pop} {pop aload pop M} ifelse} {dup 5 get 1 eq {dup 2 get exch dup 3 get exch 6 get stringwidth pop -2 div dup 0 R} {dup 6 get stringwidth pop -2 div 0 R 6 get show 2 index {aload pop M neg 3 -1 roll neg R pop pop} {pop pop pop pop aload pop M} ifelse }ifelse }ifelse } ifelse } forall} def /Gswidth {dup type /stringtype eq {stringwidth} {pop (n) stringwidth} ifelse} def /MFwidth {0 exch { dup 5 get 3 ge { 5 get 3 eq { 0 } { pop } ifelse } {dup 3 get{dup dup 0 get findfont exch 1 get scalefont setfont 6 get Gswidth pop add} {pop} ifelse} ifelse} forall} def /MLshow { currentpoint stroke M 0 exch R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /MRshow { currentpoint stroke M exch dup MFwidth neg 3 -1 roll R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /MCshow { currentpoint stroke M exch dup MFwidth -2 div 3 -1 roll R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /XYsave { [( ) 1 2 true false 3 ()] } bind def /XYrestore { [( ) 1 2 true false 4 ()] } bind def Level1 SuppressPDFMark or {} { /SDict 10 dict def systemdict /pdfmark known not { userdict /pdfmark systemdict /cleartomark get put } if SDict begin [ /Title (multilarge.eps) /Subject (gnuplot plot) /Creator (gnuplot 4.6 patchlevel 2) /Author (palken) % /Producer (gnuplot) % /Keywords () /CreationDate (Fri Aug 12 11:55:12 2016) /DOCINFO pdfmark end } ifelse end %%EndProlog %%Page: 1 1 gnudict begin gsave doclip 50 50 translate 0.050 0.050 scale 0 setgray newpath (Helvetica) findfont 140 scalefont setfont BackgroundColor 0 lt 3 1 roll 0 lt exch 0 lt or or not {BackgroundColor C 1.000 0 0 10080.00 8640.00 BoxColFill} if 1.000 UL LTb LCb setrgbcolor 686 4768 M 63 0 V 4038 0 R -63 0 V stroke 602 4768 M [ [(Helvetica) 140.0 0.0 true true 0 ( 0)] ] -46.7 MRshow 1.000 UL LTb LCb setrgbcolor 686 5199 M 63 0 V 4038 0 R -63 0 V stroke 602 5199 M [ [(Helvetica) 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4185 0 V 0 3452 V -4185 0 V Z stroke 0.300 UP 1.000 UL LTb LCb setrgbcolor stroke grestore end showpage %%Trailer %%DocumentFonts: Symbol Helvetica %%EndDocument @endspecial 390 4134 a FH(#include)46 b()390 4244 y(#include)g()390 4354 y(#include)g ()390 4463 y(#include)g()390 4573 y(#include)g()390 4682 y(#include)g ()390 4792 y(#include)g()390 4902 y(#include)g()390 5121 y(/*)h(function)f(to)h(be)g (fitted)f(*/)390 5230 y(double)390 5340 y(func\(const)f(double)h(t\))p eop end %%Page: 468 486 TeXDict begin 468 485 bop 150 -116 a FK(Chapter)30 b(38:)41 b(Least-Squares)31 b(Fitting)2098 b(468)390 299 y FH({)485 408 y(double)47 b(x)g(=)g(sin\(10.0)f(*)h(t\);)485 518 y(return)g(exp\(x*x*x\);)390 628 y(})390 847 y(/*)g(construct)e(a)j (row)f(of)g(the)g(least)f(squares)g(matrix)g(*/)390 956 y(int)390 1066 y(build_row\(const)e(double)i(t,)h(gsl_vector)e(*row\)) 390 1176 y({)485 1285 y(const)i(size_t)f(p)h(=)h(row->size;)485 1395 y(double)f(Xj)g(=)g(1.0;)485 1504 y(size_t)g(j;)485 1724 y(for)g(\(j)h(=)f(0;)g(j)h(<)f(p;)g(++j\))581 1833 y({)676 1943 y(gsl_vector_set\(row,)c(j,)k(Xj\);)676 2052 y(Xj)h(*=)f(t;)581 2162 y(})485 2381 y(return)g(0;)390 2491 y(})390 2710 y(int)390 2819 y(solve_system\(const)c(int)k (print_data,)d(const)j(gsl_multilarge_linear_ty)o(pe)41 b(*)48 b(T,)1010 2929 y(const)f(double)f(lambda,)g(const)g(size_t)g(n,) h(const)g(size_t)f(p,)1010 3039 y(gsl_vector)f(*)j(c\))390 3148 y({)485 3258 y(const)f(size_t)f(nblock)g(=)h(5;)429 b(/*)48 b(number)e(of)h(blocks)f(to)h(accumulate)e(*/)485 3367 y(const)i(size_t)f(nrows)g(=)i(n)f(/)h(nblock;)d(/*)j(number)e(of) h(rows)g(per)f(block)h(*/)485 3477 y(gsl_multilarge_linear_work)o(spac) o(e)42 b(*)47 b(w)h(=)581 3587 y(gsl_multilarge_linear_al)o(loc\()o(T,) 41 b(p\);)485 3696 y(gsl_matrix)k(*X)j(=)f(gsl_matrix_alloc\(nrows,)42 b(p\);)485 3806 y(gsl_vector)j(*y)j(=)f(gsl_vector_alloc\(nrows\);)485 3915 y(gsl_rng)f(*r)h(=)h(gsl_rng_alloc\(gsl_rng_de)o(faul)o(t\);)485 4025 y(const)f(size_t)f(nlcurve)g(=)h(200;)485 4134 y(gsl_vector)e (*reg_param)g(=)j(gsl_vector_alloc\(nlcurve)o(\);)485 4244 y(gsl_vector)d(*rho)i(=)h(gsl_vector_alloc\(nlcurv)o(e\);)485 4354 y(gsl_vector)d(*eta)i(=)h(gsl_vector_alloc\(nlcurv)o(e\);)485 4463 y(size_t)f(rowidx)f(=)h(0;)485 4573 y(double)g(rnorm,)f(snorm,)g (rcond;)485 4682 y(double)h(t)g(=)g(0.0;)485 4792 y(double)g(dt)g(=)g (1.0)g(/)h(\(n)f(-)g(1.0\);)485 5011 y(while)g(\(rowidx)f(<)h(n\))581 5121 y({)676 5230 y(size_t)f(nleft)h(=)g(n)h(-)f(rowidx;)428 b(/*)47 b(number)f(of)h(rows)g(left)g(to)g(accumulate)e(*/)676 5340 y(size_t)h(nr)i(=)f(GSL_MIN\(nrows,)d(nleft\);)i(/*)h(number)f(of) h(rows)g(in)g(this)g(block)f(*/)p eop end %%Page: 469 487 TeXDict begin 469 486 bop 150 -116 a FK(Chapter)30 b(38:)41 b(Least-Squares)31 b(Fitting)2098 b(469)676 299 y FH(gsl_matrix_view)44 b(Xv)j(=)h(gsl_matrix_submatrix\(X,)41 b(0,)47 b(0,)g(nr,)g(p\);)676 408 y(gsl_vector_view)d(yv)j(=)h(gsl_vector_subvector\(y,)41 b(0,)47 b(nr\);)676 518 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4053 y(to)33 b(the)f(ob)5 b(jectiv)m(e)34 b(function)d(\010\()p FE(x)1319 4067 y Fq(k)1381 4053 y FK(+)21 b FE(\016)s FK(\).)47 b(In)31 b(other)h(w)m(ords,)g(w)m(e)g (seek)h(a)f(solution)h(of)f(the)g(trust)f(region)150 4163 y(subproblem)e(\(TRS\))769 4374 y(min)764 4428 y Fq(\016)r Fp(2)p Fq(R)891 4412 y Fl(p)941 4374 y FE(m)1021 4388 y Fq(k)1062 4374 y FK(\()p FE(\016)s FK(\))e(=)e(\010\()p FE(x)1451 4388 y Fq(k)1492 4374 y FK(\))20 b(+)g FE(g)1684 4337 y Fq(T)1681 4397 y(k)1737 4374 y FE(\016)k FK(+)1902 4313 y(1)p 1902 4353 V 1902 4436 a(2)1957 4374 y FE(\016)2000 4337 y Fq(T)2054 4374 y FE(B)2123 4388 y Fq(k)2163 4374 y FE(\016)n(;)198 b FK(s.t.)92 b FI(jj)p FE(D)2762 4388 y Fq(k)2804 4374 y FE(\016)s FI(jj)26 b(\024)f FK(\001)3095 4388 y Fq(k)150 4573 y FK(where)f(\001)483 4587 y Fq(k)548 4573 y FE(>)h FK(0)g(is)f(the)g(trust)g(region)h(radius)e(and)h FE(D)1946 4587 y Fq(k)2011 4573 y FK(is)g(a)g(scaling)i(matrix.)39 b(If)23 b FE(D)2946 4587 y Fq(k)3013 4573 y FK(=)i FE(I)7 b 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FK(ma)m(y)h(b)s(e)e(a)i(p)s(o)s(or)e(appro)m(ximation)i(to)g (\010)f(along)h(the)g(rapidly)f(c)m(hanging)h(directions.)50 b(In)150 5340 y(suc)m(h)30 b(problems,)g(it)g(ma)m(y)h(b)s(e)f(b)s(est) g(to)h(use)f(an)g(elliptical)i(trust)e(region,)h(b)m(y)f(setting)i FE(D)3159 5354 y Fq(k)3230 5340 y FK(to)f(a)g(diagonal)p eop end %%Page: 474 492 TeXDict begin 474 491 bop 150 -116 a FK(Chapter)30 b(39:)41 b(Nonlinear)31 b(Least-Squares)g(Fitting)1681 b(474)150 299 y(matrix)29 b(whose)g(en)m(tries)h(are)g(designed)f(so)g(that)h (the)f(scaled)h(step)f FE(D)2514 313 y Fq(k)2556 299 y FE(\016)j FK(has)d(en)m(tries)h(of)g(appro)m(ximately)150 408 y(the)h(same)f(order)g(of)h(magnitude.)275 540 y(The)i(trust)h (region)h(subproblem)d(ab)s(o)m(v)m(e)k(normally)e(amoun)m(ts)h(to)g (solving)g(a)f(linear)h(least)g(squares)150 650 y(system)e(\(or)f(m)m (ultiple)h(systems\))g(for)f(the)h(step)g FE(\016)s FK(.)47 b(Once)33 b FE(\016)j FK(is)c(computed,)h(it)g(is)g(c)m(hec)m(k)m(ed)h (whether)e(or)150 760 y(not)e(it)h(reduces)f(the)g(ob)5 b(jectiv)m(e)32 b(function)e(\010\()p FE(x)p FK(\).)41 b(A)30 b(useful)g(statistic)i(for)e(this)g(is)g(to)h(lo)s(ok)g(at)g (the)f(ratio)1455 977 y FE(\032)1502 991 y Fq(k)1568 977 y FK(=)1674 915 y(\010\()p FE(x)1827 929 y Fq(k)1867 915 y FK(\))21 b FI(\000)f FK(\010\()p FE(x)2167 929 y Fq(k)2228 915 y FK(+)g FE(\016)2359 929 y Fq(k)2400 915 y FK(\))p 1674 956 762 4 v 1744 1039 a FE(m)1824 1053 y Fq(k)1865 1039 y FK(\(0\))h FI(\000)f FE(m)2172 1053 y Fq(k)2213 1039 y FK(\()p FE(\016)2288 1053 y Fq(k)2329 1039 y FK(\))150 1190 y(where)j(the)h(n)m(umerator)g(is)g(the)g(actual) h(reduction)f(of)g(the)f(ob)5 b(jectiv)m(e)26 b(function)e(due)f(to)h (the)g(step)g FE(\016)3512 1204 y Fq(k)3553 1190 y FK(,)i(and)150 1299 y(the)h(denominator)f(is)h(the)g(predicted)f(reduction)h(due)f(to) h(the)g(mo)s(del)f FE(m)2640 1313 y Fq(k)2681 1299 y FK(.)39 b(If)26 b FE(\032)2879 1313 y Fq(k)2947 1299 y FK(is)g(negativ)m(e,)k(it)d(means)150 1409 y(that)i(the)f(step)g FE(\016)729 1423 y Fq(k)798 1409 y FK(increased)h(the)f(ob)5 b(jectiv)m(e)30 b(function)e(and)f(so)h(it)h(is)f(rejected.)41 b(If)28 b FE(\032)3056 1423 y Fq(k)3124 1409 y FK(is)g(p)s(ositiv)m(e,) i(then)150 1518 y(w)m(e)d(ha)m(v)m(e)g(found)e(a)i(step)f(whic)m(h)g (reduced)g(the)g(ob)5 b(jectiv)m(e)28 b(function)e(and)g(it)h(is)f (accepted.)41 b(F)-8 b(urthermore,)150 1628 y(if)34 b FE(\032)284 1642 y Fq(k)358 1628 y FK(is)g(close)h(to)f(1,)h(then)f (this)f(indicates)i(that)f(the)g(mo)s(del)g(function)f(is)h(a)g(go)s(o) s(d)g(appro)m(ximation)g(to)150 1738 y(the)g(ob)5 b(jectiv)m(e)36 b(function)e(in)g(the)g(trust)f(region,)j(and)d(so)i(on)f(the)g(next)g (iteration)i(the)e(trust)f(region)i(is)150 1847 y(enlarged)29 b(in)f(order)g(to)h(tak)m(e)h(more)f(am)m(bitious)g(steps.)40 b(When)28 b(a)h(step)g(is)f(rejected,)i(the)f(trust)f(region)h(is)150 1957 y(made)h(smaller)h(and)e(the)i(TRS)e(is)h(solv)m(ed)h(again.)42 b(An)30 b(outline)h(for)e(the)i(general)g(trust)f(region)g(metho)s(d) 150 2066 y(used)g(b)m(y)g(GSL)g(can)g(no)m(w)h(b)s(e)f(giv)m(en.)150 2198 y Fk(T)-8 b(rust)31 b(Region)g(Algorithm)199 2330 y FK(1.)61 b(Initialize:)43 b(giv)m(en)31 b FE(x)1031 2344 y FB(0)1068 2330 y FK(,)g(construct)f FE(m)1603 2344 y FB(0)1641 2330 y FK(\()p FE(\016)s FK(\),)i FE(D)1886 2344 y FB(0)1953 2330 y FK(and)e(\001)2206 2344 y FB(0)2269 2330 y FE(>)24 b FK(0)199 2462 y(2.)61 b(F)-8 b(or)31 b(k)f(=)g(0,)h(1,)g(2,)g(...)379 2594 y(a.)61 b(If)30 b(con)m(v)m(erged,)i(then)e(stop)374 2726 y(b.)60 b(Solv)m(e)31 b(TRS)f(for)g(trial)h(step)g FE(\016)1530 2740 y Fq(k)384 2858 y FK(c.)61 b(Ev)-5 b(aluate)32 b(trial)f(step)f(b)m(y)g(computing) h FE(\032)1900 2872 y Fq(k)559 2990 y FK(1.)61 b(if)30 b(step)h(is)f(accepted,)i(set)f FE(x)1650 3004 y Fq(k)q FB(+1)1800 2990 y FK(=)25 b FE(x)1948 3004 y Fq(k)2009 2990 y FK(+)20 b FE(\016)2140 3004 y Fq(k)2212 2990 y FK(and)29 b(increase)j(radius,)d(\001)3107 3004 y Fq(k)q FB(+1)3257 2990 y FK(=)c FE(\013)p FK(\001)3487 3004 y Fq(k)559 3122 y FK(2.)61 b(if)30 b(step)h(is)f(rejected,)i(set)f FE(x)1618 3136 y Fq(k)q FB(+1)1768 3122 y FK(=)25 b FE(x)1916 3136 y Fq(k)1987 3122 y FK(and)k(decrease)j(radius,)e(\001)2898 3136 y Fq(k)q FB(+1)3047 3122 y FK(=)3153 3086 y FB(\001)3208 3095 y Fl(k)p 3153 3101 91 4 v 3178 3154 a Fq(\014)3254 3122 y FK(;)h(goto)h(2\(b\))374 3265 y(d.)60 b(Construct)30 b FE(m)1015 3279 y Fq(k)q FB(+1)1140 3265 y FK(\()p FE(\016)s FK(\))i(and)d FE(D)1536 3279 y Fq(k)q FB(+1)150 3419 y FK(GSL)c(o\013ers)g(the)g(user)f(a)h(n)m(um)m(b)s(er)f(of)h (di\013eren)m(t)g(algorithms)h(for)f(solving)g(the)h(trust)e(region)i (subproblem)150 3528 y(in)f(2\(b\),)i(as)f(w)m(ell)g(as)f(di\013eren)m (t)h(c)m(hoices)h(of)f(scaling)g(matrices)g FE(D)2342 3542 y Fq(k)2409 3528 y FK(and)e(di\013eren)m(t)i(metho)s(ds)f(of)g(up) s(dating)150 3638 y(the)32 b(trust)g(region)g(radius)f(\001)1158 3652 y Fq(k)1199 3638 y FK(.)45 b(Therefore,)32 b(while)g(reasonable)h (default)f(metho)s(ds)f(are)i(pro)m(vided,)f(the)150 3748 y(user)37 b(has)h(a)g(lot)h(of)f(con)m(trol)i(to)e(\014ne-tune)g (the)g(v)-5 b(arious)38 b(steps)f(of)h(the)h(algorithm)f(for)g(their)g (sp)s(eci\014c)150 3857 y(problem.)150 4085 y FJ(39.2)68 b(Solving)46 b(the)f(T)-11 b(rust)44 b(Region)i(Subproblem)f(\(TRS\)) 150 4244 y FK(Belo)m(w)f(w)m(e)f(describ)s(e)f(the)g(metho)s(ds)g(a)m (v)-5 b(ailable)45 b(for)d(solving)h(the)f(trust)g(region)h (subproblem.)75 b(The)150 4354 y(metho)s(ds)37 b(a)m(v)-5 b(ailable)41 b(pro)m(vide)d(either)g(exact)h(or)f(appro)m(ximate)i (solutions)e(to)h(the)f(trust)f(region)i(sub-)150 4463 y(problem.)53 b(In)34 b(all)i(algorithms)f(b)s(elo)m(w,)h(the)f (Hessian)g(matrix)g FE(B)2409 4477 y Fq(k)2485 4463 y FK(is)f(appro)m(ximated)i(as)f FE(B)3346 4477 y Fq(k)3419 4463 y FI(\031)d FE(J)3581 4430 y Fq(T)3572 4486 y(k)3633 4463 y FE(J)3683 4477 y Fq(k)3725 4463 y FK(,)150 4573 y(where)i FE(J)467 4587 y Fq(k)539 4573 y FK(=)d FE(J)9 b FK(\()p FE(x)787 4587 y Fq(k)829 4573 y FK(\).)52 b(In)33 b(all)i(metho)s(ds,)g(the)f(solution)g(of)h(the)f(TRS)f(in)m(v)m(olv)m (es)j(solving)f(a)f(linear)h(least)150 4682 y(squares)27 b(system)h(in)m(v)m(olving)h(the)e(Jacobian)i(matrix.)40 b(F)-8 b(or)28 b(small)g(to)g(mo)s(derate)g(sized)g(problems)f(\()p FH(gsl_)150 4792 y(multifit_nlinear)32 b FK(in)m(terface\),)39 b(this)d(is)g(accomplished)h(b)m(y)f(factoring)h(the)f(full)g(Jacobian) g(matrix,)150 4902 y(whic)m(h)d(is)h(pro)m(vided)f(b)m(y)h(the)g(user,) g(with)f(the)h(Cholesky)-8 b(,)35 b(QR,)f(or)g(SVD)f(decomp)s (ositions.)51 b(F)-8 b(or)35 b(large)150 5011 y(systems)j(\()p FH(gsl_multilarge_nlinear)33 b FK(in)m(terface\),)43 b(the)38 b(user)g(has)g(t)m(w)m(o)i(c)m(hoices.)66 b(One)38 b(is)g(to)i(solv)m(e)150 5121 y(the)31 b(system)g(iterativ)m(ely)-8 b(,)34 b(without)d(needing)f(to)i(store)f(the)g(full)g(Jacobian)g (matrix)g(in)f(memory)-8 b(.)42 b(With)150 5230 y(this)28 b(metho)s(d,)g(the)g(user)f(m)m(ust)h(pro)m(vide)g(a)g(routine)g(to)g (calculate)i(the)e(matrix-v)m(ector)j(pro)s(ducts)26 b FE(J)9 b(u)28 b FK(or)150 5340 y FE(J)209 5307 y Fq(T)261 5340 y FE(u)g FK(for)f(a)g(giv)m(en)i(v)m(ector)g FE(u)p FK(.)39 b(This)27 b(iterativ)m(e)i(metho)s(d)e(is)g(particularly)h (useful)f(for)g(systems)g(where)g(the)p eop end %%Page: 475 493 TeXDict begin 475 492 bop 150 -116 a FK(Chapter)30 b(39:)41 b(Nonlinear)31 b(Least-Squares)g(Fitting)1681 b(475)150 299 y(Jacobian)35 b(has)e(sparse)h(structure,)h(since)f(forming)g (matrix-v)m(ector)i(pro)s(ducts)d(can)h(b)s(e)g(done)f(c)m(heaply)-8 b(.)150 408 y(The)26 b(second)g(option)h(for)e(large)j(systems)e(in)m (v)m(olv)m(es)i(forming)e(the)g(normal)g(equations)h(matrix)g FE(J)3466 375 y Fq(T)3518 408 y FE(J)36 b FK(and)150 518 y(then)c(factoring)h(it)f(using)f(a)h(Cholesky)g(decomp)s(osition.) 46 b(The)31 b(normal)h(equations)h(matrix)f(is)g FE(p)p FK(-b)m(y-)p FE(p)p FK(,)150 628 y(t)m(ypically)e(m)m(uc)m(h)f(smaller) g(than)f(the)h(full)f FE(n)p FK(-b)m(y-)p FE(p)g FK(Jacobian,)i(and)e (can)g(usually)h(b)s(e)e(stored)i(in)f(memory)150 737 y(ev)m(en)i(if)f(the)g(full)g(Jacobian)h(matrix)f(cannot.)41 b(This)28 b(option)i(is)f(useful)f(for)h(large,)i(dense)d(systems,)i (or)f(if)150 847 y(the)i(iterativ)m(e)h(metho)s(d)e(has)g(di\016cult)m (y)h(con)m(v)m(erging.)150 1056 y Fy(39.2.1)63 b(Lev)m(en)m(b)s (erg-Marquardt)150 1203 y FK(There)26 b(is)g(a)h(theorem)g(whic)m(h)f (states)i(that)f(if)f FE(\016)1741 1217 y Fq(k)1809 1203 y FK(is)g(a)h(solution)g(to)g(the)g(trust)f(region)h(subproblem)e(giv)m (en)150 1312 y(ab)s(o)m(v)m(e,)32 b(then)e(there)g(exists)h FE(\026)1178 1326 y Fq(k)1244 1312 y FI(\025)25 b FK(0)31 b(suc)m(h)f(that)1444 1421 y Fs(\000)1482 1490 y FE(B)1551 1504 y Fq(k)1612 1490 y FK(+)20 b FE(\026)1758 1504 y Fq(k)1799 1490 y FE(D)1877 1452 y Fq(T)1874 1512 y(k)1929 1490 y FE(D)2004 1504 y Fq(k)2045 1421 y Fs(\001)2098 1490 y FE(\016)2138 1504 y Fq(k)2205 1490 y FK(=)25 b FI(\000)p FE(g)2415 1504 y Fq(k)150 1667 y FK(with)34 b FE(\026)416 1681 y Fq(k)457 1667 y FK(\(\001)568 1681 y Fq(k)632 1667 y FI(\000)22 b(jj)p FE(D)850 1681 y Fq(k)892 1667 y FE(\016)932 1681 y Fq(k)973 1667 y FI(jj)p FK(\))33 b(=)f(0.)54 b(This)33 b(forms)h(the)h(basis)f(of)h(the)g(Lev)m(en)m(b)s (erg-Marquardt)g(algorithm,)150 1777 y(whic)m(h)f(con)m(trols)h(the)f (trust)f(region)h(size)h(b)m(y)f(adjusting)f(the)h(parameter)g FE(\026)2780 1791 y Fq(k)2855 1777 y FK(rather)f(than)h(the)g(radius) 150 1887 y(\001)226 1901 y Fq(k)305 1887 y FK(directly)-8 b(.)67 b(F)-8 b(or)39 b(eac)m(h)h(radius)d(\001)1430 1901 y Fq(k)1471 1887 y FK(,)k(there)d(is)h(a)g(unique)f(parameter)h FE(\026)2763 1901 y Fq(k)2842 1887 y FK(whic)m(h)f(solv)m(es)i(the)f (TRS,)150 1996 y(and)26 b(they)h(ha)m(v)m(e)h(an)f(in)m(v)m(erse)h (relationship,)g(so)f(that)h(large)g(v)-5 b(alues)27 b(of)g FE(\026)2612 2010 y Fq(k)2680 1996 y FK(corresp)s(ond)e(to)j (smaller)f(trust)150 2106 y(regions,)k(while)f(small)h(v)-5 b(alues)31 b(of)g FE(\026)1389 2120 y Fq(k)1460 2106 y FK(corresp)s(ond)e(to)i(larger)g(trust)f(regions.)150 2250 y(With)37 b(the)f(appro)m(ximation)h FE(B)1234 2264 y Fq(k)1310 2250 y FI(\031)e FE(J)1475 2217 y Fq(T)1466 2273 y(k)1527 2250 y FE(J)1577 2264 y Fq(k)1619 2250 y FK(,)i(on)g(eac)m(h)g(iteration,)j(in)35 b(order)h(to)h(calculate)i (the)d(step)g FE(\016)3683 2264 y Fq(k)3725 2250 y FK(,)150 2360 y(the)31 b(follo)m(wing)g(linear)g(least)h(squares)e(problem)g(is) g(solv)m(ed:)1494 2458 y Fs(\024)1651 2523 y FE(J)1701 2537 y Fq(k)1553 2576 y FI(p)p 1629 2576 96 4 v 56 x FE(\026)1684 2646 y Fq(k)1724 2632 y FE(D)1799 2646 y Fq(k)1856 2458 y Fs(\025)1914 2577 y FE(\016)1954 2591 y Fq(k)2021 2577 y FK(=)25 b FI(\000)2203 2458 y Fs(\024)2262 2523 y FE(f)2307 2537 y Fq(k)2282 2632 y FK(0)2362 2458 y Fs(\025)150 2795 y FK(If)39 b(the)h(step)g FE(\016)658 2809 y Fq(k)739 2795 y FK(is)f(accepted,)44 b(then)39 b FE(\026)1521 2809 y Fq(k)1602 2795 y FK(is)g(decreased)i(on)e(the)h (next)g(iteration)h(in)f(order)f(to)h(tak)m(e)i(a)150 2905 y(larger)h(step,)i(otherwise)d(it)g(is)g(increased)h(to)f(tak)m(e) i(a)e(smaller)h(step.)75 b(The)41 b(Lev)m(en)m(b)s(erg-Marquardt)150 3014 y(algorithm)e(pro)m(vides)f(an)f(exact)j(solution)e(of)g(the)g (trust)g(region)g(subproblem,)g(but)f(t)m(ypically)j(has)e(a)150 3124 y(higher)i(computational)h(cost)g(p)s(er)e(iteration)j(than)e(the) g(appro)m(ximate)h(metho)s(ds)e(discussed)g(b)s(elo)m(w,)150 3233 y(since)32 b(it)f(ma)m(y)h(need)f(to)h(solv)m(e)h(the)e(least)i (squares)e(system)g(ab)s(o)m(v)m(e)h(sev)m(eral)h(times)f(for)f (di\013eren)m(t)h(v)-5 b(alues)150 3343 y(of)31 b FE(\026)309 3357 y Fq(k)349 3343 y FK(.)150 3552 y Fy(39.2.2)63 b(Lev)m(en)m(b)s (erg-Marquardt)41 b(with)f(Geo)s(desic)j(Acceleration)150 3699 y FK(This)25 b(metho)s(d)g(applies)h(a)g(so-called)h(geo)s(desic)g (acceleration)i(correction)e(to)f(the)g(standard)f(Lev)m(en)m(b)s(erg-) 150 3809 y(Marquardt)34 b(step)g FE(\016)850 3823 y Fq(k)925 3809 y FK(\(T)-8 b(ranstrum)33 b(et)i(al,)h(2011\).)53 b(By)35 b(in)m(terpreting)f FE(\016)2639 3823 y Fq(k)2714 3809 y FK(as)h(a)f(\014rst)f(order)h(step)g(along)150 3918 y(a)e(geo)s(desic)g(in)f(the)h(mo)s(del)f(parameter)h(space)g (\(ie:)44 b(a)31 b(v)m(elo)s(cit)m(y)j FE(\016)2422 3932 y Fq(k)2490 3918 y FK(=)27 b FE(v)2632 3932 y Fq(k)2673 3918 y FK(\),)32 b(the)f(geo)s(desic)i(acceleration)150 4028 y FE(a)198 4042 y Fq(k)267 4028 y FK(is)28 b(a)g(second)g(order)g (correction)h(along)g(the)f(geo)s(desic)h(whic)m(h)f(is)g(determined)g (b)m(y)g(solving)g(the)h(linear)150 4137 y(least)j(squares)e(system) 1391 4236 y Fs(\024)1548 4300 y FE(J)1598 4314 y Fq(k)1450 4353 y FI(p)p 1526 4353 V 57 x FE(\026)1581 4424 y Fq(k)1622 4410 y FE(D)1697 4424 y Fq(k)1753 4236 y Fs(\025)1812 4355 y FE(a)1860 4369 y Fq(k)1926 4355 y FK(=)25 b FI(\000)2108 4236 y Fs(\024)2167 4300 y FE(f)2212 4314 y Fq(v)r(v)2286 4300 y FK(\()p FE(x)2373 4314 y Fq(k)2414 4300 y FK(\))2286 4410 y(0)2465 4236 y Fs(\025)150 4573 y FK(where)i FE(f)455 4587 y Fq(v)r(v)557 4573 y 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y(with)33 b(a)h(mo)s(dest)f(additional)h(cost,)h(and)e(has)g(b)s (een)g(sho)m(wn)f(to)i(dramatically)h(reduce)e(the)h(n)m(um)m(b)s(er)e (of)150 5011 y(iterations)g(\(and)e(exp)s(ensiv)m(e)h(Jacobian)g(ev)-5 b(aluations\))33 b(required)c(to)j(reac)m(h)f(con)m(v)m(ergence)i(on)e (a)g(v)-5 b(ariet)m(y)150 5121 y(of)37 b(di\013eren)m(t)h(problems.)60 b(In)37 b(order)f(to)i(utilize)h(the)e(geo)s(desic)i(acceleration,)j (the)37 b(user)f(m)m(ust)h(supply)150 5230 y(a)e(function)g(whic)m(h)g (pro)m(vides)g(the)g(second)g(directional)i(deriv)-5 b(ativ)m(e)36 b(v)m(ector)h FE(f)2878 5244 y Fq(v)r(v)2952 5230 y FK(\()p FE(x)p FK(\),)g(or)e(alternativ)m(ely)150 5340 y(the)h(library)g(can)g(use)g(a)h(\014nite)f(di\013erence)g(metho) s(d)g(to)g(estimate)i(this)e(v)m(ector)i(with)e(one)g(additional)p eop end %%Page: 476 494 TeXDict begin 476 493 bop 150 -116 a FK(Chapter)30 b(39:)41 b(Nonlinear)31 b(Least-Squares)g(Fitting)1681 b(476)150 299 y(function)34 b(ev)-5 b(aluation)37 b(of)e FE(f)10 b FK(\()p FE(x)22 b FK(+)h FE(hv)s FK(\))36 b(where)e FE(h)h FK(is)g(a)g(tunable)g(step)g(size)g(\(see)h(the)f FH(h_fvv)e FK(parameter)150 408 y(description\).)150 592 y Fy(39.2.3)63 b(Dogleg)150 739 y FK(This)38 b(is)g(P)m(o)m(w)m (ell's)j(dogleg)f(metho)s(d,)g(whic)m(h)e(\014nds)f(an)i(appro)m (ximate)g(solution)g(to)h(the)e(trust)g(region)150 849 y(subproblem,)31 b(b)m(y)i(restricting)g(its)g(searc)m(h)g(to)g(a)g (piecewise)g(linear)g(\\dogleg")i(path,)e(comp)s(osed)f(of)h(the)150 959 y(origin,)g(the)f(Cauc)m(h)m(y)h(p)s(oin)m(t)f(whic)m(h)g(represen) m(ts)g(the)g(mo)s(del)g(minimizer)g(along)h(the)f(steep)s(est)h(descen) m(t)150 1068 y(direction,)28 b(and)e(the)h(Gauss-Newton)g(p)s(oin)m(t,) h(whic)m(h)e(is)g(the)h(o)m(v)m(erall)i(minimizer)d(of)h(the)g (unconstrained)150 1178 y(mo)s(del.)41 b(The)29 b(Gauss-Newton)j(step)e (is)g(calculated)j(b)m(y)d(solving)1706 1338 y FE(J)1756 1352 y Fq(k)1797 1338 y FE(\016)1837 1352 y Fq(g)r(n)1942 1338 y FK(=)25 b FI(\000)p FE(f)2154 1352 y 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(the)h(Gauss-Newton)g(p)s(oin)m(t)f(outside,)j(the)d(metho)s(d)g(uses)g (a)h(dogleg)h(step,)g(whic)m(h)e(is)h(a)150 2265 y(linear)c(com)m (bination)i(of)e(the)g(gradien)m(t)h(direction)g(and)e(the)i (Gauss-Newton)f(direction,)i(stopping)e(at)150 2375 y(the)d(trust)f (region)h(b)s(oundary)-8 b(.)150 2559 y Fy(39.2.4)63 b(Double)42 b(Dogleg)150 2706 y FK(This)g(metho)s(d)g(is)g(an)h(impro)m (v)m(emen)m(t)h(o)m(v)m(er)g(the)f(classical)h(dogleg)g(algorithm,)j (whic)m(h)c(attempts)g(to)150 2815 y(include)35 b(information)h(ab)s (out)g(the)f(Gauss-Newton)i(step)e(while)h(the)g(iteration)h(is)f (still)g(far)g(from)f(the)150 2925 y(minim)m(um.)45 b(When)32 b(the)g(Cauc)m(h)m(y)h(p)s(oin)m(t)f(is)g(inside)g(the)g(trust)g (region)g(and)g(the)g(Gauss-Newton)h(p)s(oin)m(t)150 3034 y(is)27 b(outside,)h(the)g(metho)s(d)e(computes)h(a)h(scaled)f (Gauss-Newton)h(p)s(oin)m(t)f(and)g(then)f(tak)m(es)j(a)e(dogleg)i (step)150 3144 y(b)s(et)m(w)m(een)f(the)g(Cauc)m(h)m(y)f(p)s(oin)m(t)h (and)e(the)i(scaled)g(Gauss-Newton)g(p)s(oin)m(t.)40 b(The)27 b(scaling)h(is)g(calculated)h(to)150 3253 y(ensure)g(that)i (the)f(reduction)h(in)e(the)i(mo)s(del)f FE(m)1803 3267 y Fq(k)1873 3253 y FK(is)h(ab)s(out)f(the)g(same)g(as)h(the)f (reduction)g(pro)m(vided)g(b)m(y)150 3363 y(the)h(Cauc)m(h)m(y)f(p)s (oin)m(t.)150 3547 y Fy(39.2.5)63 b(Tw)m(o)41 b(Dimensional)h(Subspace) 150 3694 y FK(The)31 b(dogleg)j(metho)s(ds)d(restrict)h(the)g(searc)m (h)h(for)e(the)i(TRS)d(solution)j(to)f(a)h(1D)f(curv)m(e)g(de\014ned)f (b)m(y)h(the)150 3804 y(Cauc)m(h)m(y)27 b(and)g(Gauss-Newton)h(p)s(oin) m(ts.)39 b(An)27 b(impro)m(v)m(emen)m(t)h(to)g(this)f(is)g(to)h(searc)m (h)g(for)e(a)i(solution)f(using)150 3913 y(the)38 b(full)f(t)m(w)m(o)i (dimensional)e(subspace)g(spanned)f(b)m(y)i(the)f(Cauc)m(h)m(y)h(and)f (Gauss-Newton)h(directions.)150 4023 y(The)e(dogleg)i(path)e(is)g(of)h (course)g(inside)f(this)g(subspace,)i(and)e(so)g(this)h(metho)s(d)e (solv)m(es)j(the)f(TRS)e(at)150 4132 y(least)k(as)e(accurately)i(as)f (the)f(dogleg)i(metho)s(ds.)61 b(Since)37 b(this)h(metho)s(d)e(searc)m (hes)j(a)e(larger)i(subspace)150 4242 y(for)d(a)h(solution,)i(it)e(can) f(con)m(v)m(erge)j(more)d(quic)m(kly)i(than)e(dogleg)i(on)e(some)h (problems.)58 b(Because)38 b(the)150 4352 y(subspace)33 b(is)g(only)g(t)m(w)m(o)h(dimensional,)g(this)f(metho)s(d)g(is)g(v)m (ery)h(e\016cien)m(t)g(and)f(the)g(main)g(computation)150 4461 y(p)s(er)c(iteration)j(is)f(to)g(determine)f(the)h(Gauss-Newton)g (p)s(oin)m(t.)150 4645 y Fy(39.2.6)63 b(Steihaug-T)-10 b(oin)m(t)41 b(Conjugate)h(Gradien)m(t)150 4792 y FK(One)20 b(di\016cult)m(y)h(of)f(the)h(dogleg)h(metho)s(ds)e(is)g(calculating)j (the)d(Gauss-Newton)i(step)e(when)g(the)g(Jacobian)150 4902 y(matrix)38 b(is)g(singular.)63 b(The)37 b(Steihaug-T)-8 b(oin)m(t)40 b(metho)s(d)d(also)i(computes)f(a)g(generalized)h(dogleg)h (step,)150 5011 y(but)29 b(a)m(v)m(oids)i(solving)f(for)g(the)g (Gauss-Newton)g(step)g(directly)-8 b(,)31 b(instead)f(using)f(an)h (iterativ)m(e)i(conjugate)150 5121 y(gradien)m(t)37 b(algorithm.)58 b(This)35 b(metho)s(d)g(p)s(erforms)g(w)m(ell)i(at)f(p)s(oin)m(ts)g (where)f(the)h(Jacobian)h(is)f(singular,)150 5230 y(and)c(is)h(also)g (suitable)g(for)g(large-scale)i(problems)d(where)g(factoring)i(the)f (Jacobian)g(matrix)g(could)g(b)s(e)150 5340 y(prohibitiv)m(ely)e(exp)s (ensiv)m(e.)p eop end %%Page: 477 495 TeXDict begin 477 494 bop 150 -116 a FK(Chapter)30 b(39:)41 b(Nonlinear)31 b(Least-Squares)g(Fitting)1681 b(477)150 299 y FJ(39.3)68 b(W)-11 b(eigh)l(ted)46 b(Nonlinear)g(Least-Squares) 150 458 y FK(W)-8 b(eigh)m(ted)33 b(nonlinear)d(least-squares)h (\014tting)g(minimizes)g(the)f(function)1152 680 y(\010\()p FE(x)p FK(\))25 b(=)1471 618 y(1)p 1471 658 46 4 v 1471 742 a(2)1526 680 y FI(jj)p FE(f)10 b FI(jj)1681 642 y FB(2)1681 702 y Fq(W)1783 680 y FK(=)1888 618 y(1)p 1888 658 V 1888 742 a(2)1998 574 y Fq(n)1959 599 y Fs(X)1965 776 y Fq(i)p FB(=1)2094 680 y FE(w)2159 694 y Fq(i)2187 680 y FE(f)2232 694 y Fq(i)2259 680 y FK(\()p FE(x)2346 694 y FB(1)2384 680 y FE(;)15 b(:)g(:)g(:)h(;)f(x)2637 694 y Fq(p)2676 680 y FK(\))2711 642 y FB(2)150 921 y FK(where)31 b FE(W)39 b FK(=)27 b FE(diag)s FK(\()p FE(w)909 935 y FB(1)948 921 y FE(;)15 b(w)1053 935 y FB(2)1091 921 y FE(;)g(:::;)g(w)1311 935 y Fq(n)1358 921 y FK(\))31 b(is)h(the)g(w)m(eigh)m(ting)h(matrix,)f(and)f FI(jj)p FE(f)10 b FI(jj)2740 888 y FB(2)2740 943 y Fq(W)2843 921 y FK(=)26 b FE(f)2995 888 y Fq(T)3047 921 y FE(W)13 b(f)d FK(.)43 b(The)31 b(w)m(eigh)m(ts)150 1031 y FE(w)215 1045 y Fq(i)278 1031 y FK(are)k(commonly)h(de\014ned)e(as)i FE(w)1376 1045 y Fq(i)1437 1031 y FK(=)d(1)p FE(=\033)1686 998 y FB(2)1683 1053 y Fq(i)1724 1031 y FK(,)k(where)d FE(\033)2105 1045 y Fq(i)2168 1031 y FK(is)h(the)h(error)f(in)f(the)i FE(i)p FK(th)f(measuremen)m(t.)56 b(A)150 1140 y(simple)36 b(c)m(hange)i(of)f(v)-5 b(ariables)1243 1116 y(~)1239 1140 y FE(f)44 b FK(=)35 b FE(W)1543 1085 y Fn(1)p 1543 1094 29 4 v 1543 1127 a(2)1585 1140 y FE(f)46 b FK(yields)36 b(\010\()p FE(x)p FK(\))g(=)2277 1104 y FB(1)p 2277 1119 34 4 v 2277 1172 a(2)2320 1140 y FI(jj)2374 1116 y FK(~)2370 1140 y FE(f)10 b FI(jj)2475 1107 y FB(2)2513 1140 y FK(,)38 b(whic)m(h)e(is)g(in)g(the)h(same)g(form)f(as)150 1250 y(the)30 b(un)m(w)m(eigh)m(ted)h(case.)42 b(The)29 b(user)g(can)i (either)f(p)s(erform)f(this)g(transform)h(directly)g(on)g(their)g (function)150 1359 y(residuals)25 b(and)f(Jacobian,)j(or)f(use)e(the)i FH(gsl_multifit_nlinear_win)o(it)19 b FK(in)m(terface)26 b(whic)m(h)f(automat-)150 1469 y(ically)31 b(p)s(erforms)d(the)i (correct)g(scaling.)42 b(T)-8 b(o)30 b(man)m(ually)g(p)s(erform)e(this) h(transformation,)i(the)e(residuals)150 1579 y(and)h(Jacobian)h(should) e(b)s(e)h(mo)s(di\014ed)f(according)i(to)1521 1761 y(~)1517 1785 y FE(f)1562 1799 y Fq(i)1614 1785 y FK(=)1710 1722 y FI(p)p 1786 1722 93 4 v 63 x FE(w)1851 1799 y Fq(i)1879 1785 y FE(f)1924 1799 y Fq(i)1976 1785 y FK(=)2086 1724 y FE(f)2131 1738 y Fq(i)p 2082 1764 80 4 v 2082 1848 a FE(\033)2134 1862 y Fq(i)1487 1997 y FK(~)1480 2020 y FE(J)1530 2034 y Fq(ij)1614 2020 y FK(=)1710 1957 y FI(p)p 1786 1957 93 4 v 63 x FE(w)1851 2034 y Fq(i)1896 1958 y FE(@)5 b(f)1994 1972 y Fq(i)p 1889 1999 141 4 v 1889 2082 a FE(@)g(x)1994 2096 y Fq(j)2064 2020 y FK(=)2187 1958 y(1)p 2170 1999 80 4 v 2170 2082 a FE(\033)2222 2096 y Fq(i)2277 1958 y FE(@)g(f)2375 1972 y Fq(i)p 2270 1999 141 4 v 2270 2082 a FE(@)g(x)2375 2096 y Fq(j)150 2257 y FK(F)-8 b(or)31 b(large)h(systems,)e(the)h(user)e(m)m(ust)i(p)s (erform)e(their)h(o)m(wn)g(w)m(eigh)m(ting.)150 2484 y FJ(39.4)68 b(T)-11 b(unable)45 b(P)l(arameters)150 2643 y FK(The)57 b(user)h(can)g(tune)f(nearly)h(all)h(asp)s(ects)f(of)g (the)g(iteration)i(at)e(allo)s(cation)i(time.)124 b(F)-8 b(or)59 b(the)150 2753 y FH(gsl_multifit_nlinear)54 b FK(in)m(terface,)68 b(the)60 b(user)f(ma)m(y)h(mo)s(dify)e(the)i FH(gsl_multifit_nlinear_)150 2863 y(parameters)28 b FK(structure,)i 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y(})g(gsl_multifit_nlinear_param)o(eter)o(s;)150 4332 y FK(F)-8 b(or)40 b(the)f FH(gsl_multilarge_nlinear)33 b FK(in)m(terface,)44 b(the)39 b(user)g(ma)m(y)g(mo)s(dify)g(the)g FH(gsl_multilarge_)150 4441 y(nlinear_parameters)25 b FK(structure,)31 b(whic)m(h)f(is)g(de\014ned)f(as)i(follo)m(ws:)390 4573 y FH(typedef)46 b(struct)390 4682 y({)485 4792 y(const)h (gsl_multilarge_nlinear_t)o(rs)41 b(*trs;)333 b(/*)47 b(trust)g(region)f(subproblem)f(method)h(*/)485 4902 y(const)h(gsl_multilarge_nlinear_s)o(cal)o(e)42 b(*scale;)141 b(/*)47 b(scaling)f(method)g(*/)485 5011 y(const)h (gsl_multilarge_nlinear_s)o(olv)o(er)42 b(*solver;)j(/*)i(solver)f (method)h(*/)485 5121 y(gsl_multilarge_nlinear_fdt)o(ype)41 b(fdtype;)380 b(/*)47 b(finite)f(difference)f(method)i(*/)485 5230 y(double)g(factor_up;)1333 b(/*)47 b(factor)f(for)h(increasing)e (trust)i(radius)f(*/)485 5340 y(double)h(factor_down;)1237 b(/*)47 b(factor)f(for)h(decreasing)e(trust)i(radius)f(*/)p eop end %%Page: 478 496 TeXDict begin 478 495 bop 150 -116 a FK(Chapter)30 b(39:)41 b(Nonlinear)31 b(Least-Squares)g(Fitting)1681 b(478)485 299 y FH(double)47 b(avmax;)1525 b(/*)47 b(max)g(allowed)f(|a|/|v|)g (*/)485 408 y(double)h(h_df;)1573 b(/*)47 b(step)g(size)g(for)g(finite) f(difference)f(Jacobian)g(*/)485 518 y(double)i(h_fvv;)1525 b(/*)47 b(step)g(size)g(for)g(finite)f(difference)f(fvv)h(*/)485 628 y(size_t)h(max_iter;)1381 b(/*)47 b(maximum)f(iterations)f(for)i (trs)g(method)f(*/)485 737 y(double)h(tol;)1621 b(/*)47 b(tolerance)f(for)h(solving)e(trs)i(*/)390 847 y(})g (gsl_multilarge_nlinear_par)o(amet)o(ers)o(;)150 980 y FK(Eac)m(h)31 b(of)g(these)f(parameters)h(is)f(discussed)g(in)g (further)f(detail)j(b)s(elo)m(w.)3286 1160 y([P)m(arameter])-3598 b Fv(const)54 b(gsl_multifit_nlinear_tr)q(s)k(*)53 b(trs)3286 1270 y FK([P)m(arameter])-3598 b Fv(const)54 b(gsl_multilarge_nlinear_) q(trs)59 b(*)53 b(trs)390 1379 y FK(This)38 b(parameter)h(determines)f (the)h(metho)s(d)f(used)g(to)h(solv)m(e)h(the)f(trust)f(region)h (subproblem,)390 1489 y(and)30 b(ma)m(y)h(b)s(e)e(selected)j(from)e (the)h(follo)m(wing)h(c)m(hoices,)3405 1669 y([Default])-3358 b Fv(gsl_multifit_nlinear_t)q(rs_)q(lm)3405 1778 y FK([Default])g Fv(gsl_multilarge_nlinear)q(_tr)q(s_lm)630 1888 y FK(This)30 b(selects)h(the)g(Lev)m(en)m(b)s(erg-Marquardt)g(algorithm.)3422 2068 y([Option])-3360 b Fv(gsl_multifit_nlinear_t)q(rs_)q(lmac)q(cel) 3422 2178 y FK([Option])g Fv(gsl_multilarge_nlinear)q(_tr)q(s_lm)q(acc) q(el)630 2287 y FK(This)30 b(selects)h(the)g(Lev)m(en)m(b)s (erg-Marquardt)g(algorithm)g(with)f(geo)s(desic)i(acceleration.)3422 2467 y([Option])-3360 b Fv(gsl_multifit_nlinear_t)q(rs_)q(dogl)q(eg) 3422 2577 y FK([Option])g Fv(gsl_multilarge_nlinear)q(_tr)q(s_do)q(gle) q(g)630 2686 y FK(This)30 b(selects)h(the)g(dogleg)h(algorithm.)3422 2866 y([Option])-3360 b Fv(gsl_multifit_nlinear_t)q(rs_)q(ddog)q(leg) 3422 2976 y FK([Option])g Fv(gsl_multilarge_nlinear)q(_tr)q(s_dd)q(ogl) q(eg)630 3086 y FK(This)30 b(selects)h(the)g(double)f(dogleg)i (algorithm.)3422 3266 y([Option])-3360 b Fv(gsl_multifit_nlinear_t)q (rs_)q(subs)q(pac)q(e2D)3422 3375 y FK([Option])g Fv (gsl_multilarge_nlinear)q(_tr)q(s_su)q(bsp)q(ace)q(2D)630 3485 y FK(This)30 b(selects)h(the)g(2D)g(subspace)f(algorithm.)3422 3665 y([Option])-3360 b Fv(gsl_multilarge_nlinear)q(_tr)q(s_cg)q(st)630 3774 y FK(This)33 b(selects)i(the)g(Steihaug-T)-8 b(oin)m(t)35 b(conjugate)g(gradien)m(t)g(algorithm.)52 b(This)34 b(metho)s(d)f(is) 630 3884 y(a)m(v)-5 b(ailable)33 b(only)d(for)g(large)i(systems.)3286 4064 y([P)m(arameter])-3598 b Fv(const)54 b(gsl_multifit_nlinear_sc)q (ale)59 b(*)53 b(scale)3286 4174 y FK([P)m(arameter])-3598 b Fv(const)54 b(gsl_multilarge_nlinear_)q(sca)q(le)59 b(*)52 b(scale)390 4283 y FK(This)31 b(parameter)h(determines)f(the)h (diagonal)h(scaling)f(matrix)g FE(D)i FK(and)d(ma)m(y)h(b)s(e)f (selected)i(from)390 4393 y(the)e(follo)m(wing)g(c)m(hoices,)3405 4573 y([Default])-3358 b Fv(gsl_multifit_nlinear_s)q(cal)q(e_mo)q(re) 3405 4682 y FK([Default])g Fv(gsl_multilarge_nlinear)q(_sc)q(ale_)q (mor)q(e)630 4792 y FK(This)40 b(damping)g(strategy)i(w)m(as)g (suggested)f(b)m(y)g(Mor)m(\023)-43 b(e,)45 b(and)c(corresp)s(onds)e (to)j FE(D)3507 4759 y Fq(T)3559 4792 y FE(D)j FK(=)630 4902 y(max\(diag\()p FE(J)1094 4869 y Fq(T)1148 4902 y FE(J)9 b FK(\)\),)33 b(in)e(other)g(w)m(ords)g(the)h(maxim)m(um)f (elemen)m(ts)i(of)f(diag\()p FE(J)3263 4869 y Fq(T)3316 4902 y FE(J)9 b FK(\))32 b(encoun-)630 5011 y(tered)43 b(th)m(us)g(far)g(in)g(the)g(iteration.)80 b(This)43 b(c)m(hoice)i(of)e FE(D)j FK(mak)m(es)e(the)f(problem)f(scale-)630 5121 y(in)m(v)-5 b(arian)m(t,)39 b(so)e(that)g(if)f(the)h(mo)s(del)f (parameters)h FE(x)2422 5135 y Fq(i)2486 5121 y FK(are)g(eac)m(h)g (scaled)h(b)m(y)e(an)g(arbitrary)630 5230 y(constan)m(t,)43 b(~)-48 b FE(x)1082 5244 y Fq(i)1145 5230 y FK(=)35 b FE(a)1299 5244 y Fq(i)1327 5230 y FE(x)1379 5244 y Fq(i)1406 5230 y FK(,)j(then)f(the)f(sequence)h(of)g(iterates)h(pro)s(duced)d(b)m (y)h(the)h(algorithm)630 5340 y(w)m(ould)25 b(b)s(e)g(unc)m(hanged.)39 b(This)24 b(metho)s(d)h(can)h(w)m(ork)f(v)m(ery)h(w)m(ell)g(in)f(cases) i(where)e(the)g(mo)s(del)p eop end %%Page: 479 497 TeXDict begin 479 496 bop 150 -116 a FK(Chapter)30 b(39:)41 b(Nonlinear)31 b(Least-Squares)g(Fitting)1681 b(479)630 299 y(parameters)27 b(ha)m(v)m(e)h(widely)f(di\013eren)m(t)g(scales)h (\(ie:)39 b(if)27 b(some)g(parameters)g(are)g(measured)f(in)630 408 y(nanometers,)37 b(while)f(others)g(are)g(measured)f(in)g(degrees)h (Kelvin\).)57 b(This)35 b(strategy)i(has)630 518 y(b)s(een)23 b(pro)m(v)m(en)i(e\013ectiv)m(e)h(on)e(a)g(large)h(class)g(of)f (problems)g(and)f(so)h(it)h(is)f(the)g(library)f(default,)630 628 y(but)30 b(it)h(ma)m(y)g(not)f(b)s(e)g(the)g(b)s(est)g(c)m(hoice)j (for)d(all)h(problems.)3422 816 y([Option])-3360 b Fv (gsl_multifit_nlinear_s)q(cal)q(e_le)q(ven)q(ber)q(g)3422 925 y FK([Option])g Fv(gsl_multilarge_nlinear)q(_sc)q(ale_)q(lev)q(enb) q(erg)630 1035 y FK(This)26 b(damping)g(strategy)i(w)m(as)f(originally) h(suggested)g(b)m(y)e(Lev)m(en)m(b)s(erg,)i(and)e(corresp)s(onds)630 1145 y(to)e FE(D)812 1112 y Fq(T)864 1145 y FE(D)k FK(=)d FE(I)7 b FK(.)38 b(This)23 b(metho)s(d)f(has)h(also)i(pro)m(v)m(en)e (e\013ectiv)m(e)j(on)d(a)h(large)g(class)g(of)f(problems,)630 1254 y(but)30 b(is)g(not)h(scale-in)m(v)-5 b(arian)m(t.)44 b(Ho)m(w)m(ev)m(er,)33 b(some)e(authors)f(\(e.g.)43 b(T)-8 b(ranstrum)29 b(and)h(Sethna)630 1364 y(2012\))44 b(argue)e(that)g (this)g(c)m(hoice)h(is)f(b)s(etter)g(for)g(problems)f(whic)m(h)g(are)h (susceptible)g(to)630 1473 y(parameter)31 b(ev)-5 b(ap)s(oration)31 b(\(ie:)42 b(parameters)30 b(go)i(to)f(in\014nit)m(y\))3422 1662 y([Option])-3360 b Fv(gsl_multifit_nlinear_s)q(cal)q(e_ma)q(rqu)q (ard)q(t)3422 1771 y FK([Option])g Fv(gsl_multilarge_nlinear)q(_sc)q (ale_)q(mar)q(qua)q(rdt)630 1881 y FK(This)55 b(damping)g(strategy)i(w) m(as)f(suggested)g(b)m(y)g(Marquardt,)62 b(and)55 b(corresp)s(onds)f (to)630 1990 y FE(D)708 1957 y Fq(T)760 1990 y FE(D)74 b FK(=)57 b(diag\()p FE(J)1297 1957 y Fq(T)1350 1990 y FE(J)9 b FK(\).)123 b(This)57 b(metho)s(d)g(is)h(scale-in)m(v)-5 b(arian)m(t,)68 b(but)57 b(it)h(is)g(generally)630 2100 y(considered)42 b(inferior)g(to)i(b)s(oth)d(the)i(Lev)m(en)m(b)s(erg)g (and)f(Mor)m(\023)-43 b(e)44 b(strategies,)j(though)42 b(ma)m(y)630 2209 y(w)m(ork)30 b(w)m(ell)i(on)e(certain)h(classes)h(of) e(problems.)3286 2398 y([P)m(arameter])-3598 b Fv(const)54 b(gsl_multifit_nlinear_so)q(lve)q(r)k(*)53 b(solver)3286 2507 y FK([P)m(arameter])-3598 b Fv(const)54 b(gsl_multilarge_nlinear_) q(sol)q(ver)59 b(*)53 b(solver)390 2617 y FK(Solving)44 b(the)f(trust)g(region)i(subproblem)c(on)j(eac)m(h)g(iteration)h (almost)g(alw)m(a)m(ys)g(requires)e(the)390 2726 y(solution)31 b(of)f(the)h(follo)m(wing)h(linear)f(least)g(squares)f(system)1568 2817 y Fs(\024)1701 2881 y FE(J)1627 2935 y FI(p)p 1702 2935 55 4 v 1702 2991 a FE(\026D)1850 2817 y Fs(\025)1909 2936 y FE(\016)f FK(=)c FI(\000)2160 2817 y Fs(\024)2219 2881 y FE(f)2223 2991 y FK(0)2288 2817 y Fs(\025)390 3173 y FK(The)31 b FD(solv)m(er)38 b FK(parameter)32 b(determines)f(ho)m(w)g(the)h(system)f(is)g(solv)m(ed)h(and)f(can)g(b)s (e)g(selected)h(from)390 3282 y(the)f(follo)m(wing)g(c)m(hoices:)3405 3471 y([Default])-3358 b Fv(gsl_multifit_nlinear_s)q(olv)q(er_q)q(r)630 3580 y FK(This)40 b(metho)s(d)h(solv)m(es)h(the)f(system)g(using)g(a)g (rank)g(rev)m(ealing)i(QR)d(decomp)s(osition)i(of)630 3690 y(the)29 b(Jacobian)g FE(J)9 b FK(.)40 b(This)28 b(metho)s(d)g(will)h(pro)s(duce)f(reliable)i(solutions)f(in)f(cases)i (where)e(the)630 3799 y(Jacobian)c(is)g(rank)f(de\014cien)m(t)h(or)g (near-singular)f(but)g(do)s(es)g(require)h(ab)s(out)f(t)m(wice)i(as)f (man)m(y)630 3909 y(op)s(erations)31 b(as)f(the)h(Cholesky)f(metho)s(d) g(discussed)g(b)s(elo)m(w.)3422 4097 y([Option])-3360 b Fv(gsl_multifit_nlinear_s)q(olv)q(er_c)q(hol)q(esk)q(y)3405 4207 y FK([Default])i Fv(gsl_multilarge_nlinear)q(_so)q(lver)q(_ch)q (ole)q(sky)630 4316 y FK(This)30 b(metho)s(d)f(solv)m(es)j(the)f (alternate)h(normal)e(equations)h(problem)1431 4417 y Fs(\000)1469 4486 y FE(J)1528 4448 y Fq(T)1581 4486 y FE(J)e FK(+)20 b FE(\026D)1884 4448 y Fq(T)1936 4486 y FE(D)2014 4417 y Fs(\001)2067 4486 y FE(\016)29 b FK(=)c FI(\000)p FE(J)2362 4448 y Fq(T)2414 4486 y FE(f)630 4682 y FK(b)m(y)g(using)g(a)g(Cholesky)h(decomp)s(osition)g(of)f(the)g (matrix)h FE(J)2632 4649 y Fq(T)2684 4682 y FE(J)20 b FK(+)10 b FE(\026D)2968 4649 y Fq(T)3019 4682 y FE(D)s FK(.)39 b(This)24 b(metho)s(d)h(is)630 4792 y(faster)g(than)g(the)g(QR) f(approac)m(h,)j(ho)m(w)m(ev)m(er)f(it)f(is)g(susceptible)g(to)h(n)m (umerical)f(instabilities)630 4902 y(if)41 b(the)g(Jacobian)h(matrix)g (is)f(rank)f(de\014cien)m(t)i(or)f(near-singular.)73 b(In)41 b(these)g(cases,)k(an)630 5011 y(attempt)40 b(is)f(made)g(to)h 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b(is)f(set)h(to)1543 1206 y FI(p)p 1619 1206 37 4 v 66 x FE(\017)f FK(b)m(y)h(default,)f (where)g FE(\017)g FK(is)h FH(GSL_DBL_EPSILON)p FK(.)3286 1477 y([P)m(arameter])-3598 b Fv(double)54 b(h_fvv)390 1587 y FK(When)27 b(using)f(geo)s(desic)i(acceleration,)j(the)c(user)g (m)m(ust)g(either)g(supply)f(a)h(function)g(to)h(calculate)390 1696 y FE(f)435 1710 y Fq(v)r(v)509 1696 y FK(\()p FE(x)p FK(\))43 b(or)f(the)g(library)g(can)g(estimate)i(this)e(second)g (directional)h(deriv)-5 b(ativ)m(e)44 b(using)e(a)g(\014nite)390 1806 y(di\013erence)26 b(metho)s(d.)39 b(When)25 b(using)h(\014nite)f (di\013erences,)j(the)e(library)f(m)m(ust)h(calculate)i FE(f)10 b FK(\()p FE(x)h FK(+)g FE(hv)s FK(\))390 1916 y(where)24 b FE(h)g FK(represen)m(ts)h(a)f(small)h(step)f(in)g(the)h(v) m(elo)s(cit)m(y)i(direction.)39 b(The)24 b(parameter)h FD(h)p 3293 1916 28 4 v 39 w(fvv)32 b FK(de\014nes)390 2025 y(this)e(step)h(size)g(and)f(is)g(set)h(to)g(0.02)h(b)m(y)e (default.)150 2274 y FJ(39.5)68 b(Initializing)47 b(the)e(Solv)l(er) 3350 2494 y FK([F)-8 b(unction])-3599 b Fv(gsl_multifit_nlinear_w)q (ork)q(spac)q(e)58 b(*)565 2603 y(gsl_multifit_nlinear_a)q(llo)q(c)51 b Fu(\()p FD(const)32 b(gsl)p 2356 2603 V 40 w(m)m(ulti\014t)p 2691 2603 V 41 w(nlinear)p 3005 2603 V 40 w(t)m(yp)s(e)e(*)h Ft(T)p FD(,)g(const)565 2713 y(gsl)p 677 2713 V 41 w(m)m(ulti\014t)p 1013 2713 V 40 w(nlinear)p 1326 2713 V 40 w(parameters)g(*)g Ft(params)p FD(,)h(const)f(size)p 2661 2713 V 41 w(t)f Ft(n)p FD(,)h(const)g(size)p 3254 2713 V 41 w(t)g Ft(p)p Fu(\))3350 2822 y FK([F)-8 b(unction])-3599 b Fv (gsl_multilarge_nlinear)q(_wo)q(rksp)q(ace)59 b(*)565 2932 y(gsl_multilarge_nlinear)q(_al)q(loc)52 b Fu(\()p FD(const)31 b(gsl)p 2460 2932 V 41 w(m)m(ultilarge)p 2901 2932 V 42 w(nlinear)p 3216 2932 V 40 w(t)m(yp)s(e)f(*)h Ft(T)p FD(,)565 3041 y(const)g(gsl)p 915 3041 V 41 w(m)m(ultilarge)p 1356 3041 V 41 w(nlinear)p 1670 3041 V 40 w(parameters)g(*)g Ft(params)p FD(,)h(const)f(size)p 3005 3041 V 41 w(t)g 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b(Section)f(39.4)i([Nonlinear)e(Least-Squares)390 4028 y(T)-8 b(unable)50 b(P)m(arameters],)58 b(page)51 b(477)h(for)f(descriptions)f(of)h(the)g(v)-5 b(arious)51 b(parameters.)102 b(F)-8 b(or)390 4137 y(example,)32 b(the)e(follo)m(wing)i(co)s(de)f(creates)h(an)f(instance)g(of)g(a)f (Lev)m(en)m(b)s(erg-Marquardt)i(solv)m(er)f(for)390 4247 y(100)h(data)f(p)s(oin)m(ts)f(and)g(3)g(parameters,)h(using)f (suggested)h(defaults:)630 4392 y FH(const)46 b (gsl_multifit_nlinear_type)41 b(*)48 b(T)821 4502 y(=)f (gsl_multifit_nlinear_lm;)630 4611 y(gsl_multifit_nlinear_par)o(amet)o (ers)41 b(params)821 4721 y(=)47 b(gsl_multifit_nlinear_defau)o(lt_)o (para)o(mete)o(rs\()o(\);)630 4830 y(gsl_multifit_nlinear_wor)o(kspa)o (ce)42 b(*)47 b(w)821 4940 y(=)g(gsl_multifit_nlinear_alloc)41 b(\(T,)47 b(¶ms,)e(100,)i(3\);)390 5085 y FK(The)30 b(n)m(um)m(b)s(er)f(of)h(observ)-5 b(ations)31 b FD(n)f FK(m)m(ust)g(b)s(e)g(greater)i(than)e(or)g(equal)h(to)g(parameters)g FD(p)p FK(.)390 5230 y(If)36 b(there)g(is)h(insu\016cien)m(t)f(memory)h (to)g(create)h(the)e(solv)m(er)i(then)e(the)g(function)g(returns)f(a)i (n)m(ull)390 5340 y(p)s(oin)m(ter)30 b(and)g(the)h(error)f(handler)f (is)i(in)m(v)m(ok)m(ed)g(with)g(an)f(error)g(co)s(de)g(of)h FH(GSL_ENOMEM)p FK(.)p eop end %%Page: 482 500 TeXDict begin 482 499 bop 150 -116 a FK(Chapter)30 b(39:)41 b(Nonlinear)31 b(Least-Squares)g(Fitting)1681 b(482)3350 299 y([F)-8 b(unction])-3599 b Fv(gsl_multifit_nlinear_p)q(ara)q(mete)q (rs)565 408 y(gsl_multifit_nlinear_d)q(efa)q(ult)q(_pa)q(rame)q(ter)q (s)51 b Fu(\()p FD(v)m(oid)p Fu(\))3350 518 y FK([F)-8 b(unction])-3599 b Fv(gsl_multilarge_nlinear)q(_pa)q(rame)q(ter)q(s)565 628 y(gsl_multilarge_nlinear)q(_de)q(fau)q(lt_)q(para)q(met)q(ers)52 b Fu(\()p FD(v)m(oid)p Fu(\))390 737 y FK(These)36 b(functions)h (return)e(a)i(set)g(of)g(recommended)f(default)h(parameters)g(for)g (use)f(in)g(solving)390 847 y(nonlinear)c(least)h(squares)f(problems.) 46 b(The)31 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41 w(m)m(ulti\014t)p 2940 1559 V 40 w(nlinear)p 3253 1559 V 40 w(w)m(orkspace)565 1668 y(*)g Ft(w)p Fu(\))3350 1778 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multilarge_nlinea)q (r_in)q(it)f Fu(\()p FD(const)31 b(gsl)p 2202 1778 V 41 w(v)m(ector)h(*)e Ft(x)p FD(,)565 1888 y(gsl)p 677 1888 V 41 w(m)m(ultilarge)p 1118 1888 V 41 w(nlinear)p 1432 1888 V 40 w(fdf)g(*)h Ft(fdf)p FD(,)g(gsl)p 2003 1888 V 41 w(m)m(ultilarge)p 2444 1888 V 41 w(nlinear)p 2758 1888 V 40 w(w)m(orkspace)g(*)g Ft(w)p Fu(\))3350 1997 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multilarge_nlinea)q (r_wi)q(nit)f Fu(\()p FD(const)31 b(gsl)p 2254 1997 V 41 w(v)m(ector)h(*)f Ft(x)p FD(,)g(const)565 2107 y(gsl)p 677 2107 V 41 w(v)m(ector)h(*)e Ft(wts)p FD(,)i(gsl)p 1385 2107 V 40 w(m)m(ultilarge)p 1825 2107 V 42 w(nlinear)p 2140 2107 V 40 w(fdf)e(*)g Ft(fdf)p FD(,)565 2216 y(gsl)p 677 2216 V 41 w(m)m(ultilarge)p 1118 2216 V 41 w(nlinear)p 1432 2216 V 40 w(w)m(orkspace)i(*)e Ft(w)p Fu(\))390 2326 y FK(These)42 b(functions)h(initialize,)48 b(or)43 b(reinitialize,)48 b(an)42 b(existing)i(w)m(orkspace)f FD(w)50 b FK(to)44 b(use)e(the)h(sys-)390 2436 y(tem)33 b FD(fdf)49 b FK(and)32 b(the)h(initial)h(guess)f FD(x)p FK(.)47 b(See)33 b(Section)h(39.6)g([Nonlinear)f(Least-Squares)g(F)-8 b(unction)390 2545 y(De\014nition],)31 b(page)h(483)f(for)f(a)h (description)g(of)f(the)h FD(fdf)47 b FK(structure.)390 2673 y(Optionally)-8 b(,)31 b(a)e(w)m(eigh)m(t)i(v)m(ector)f FD(wts)j FK(can)c(b)s(e)f(giv)m(en)i(to)g(p)s(erform)e(a)h(w)m(eigh)m (ted)h(nonlinear)f(regres-)390 2782 y(sion.)41 b(Here,)31 b(the)f(w)m(eigh)m(ting)j(matrix)d(is)h FE(W)37 b FK(=)25 b FE(diag)s FK(\()p FE(w)2297 2796 y FB(1)2336 2782 y FE(;)15 b(w)2441 2796 y FB(2)2479 2782 y FE(;)g(:::;)g(w)2699 2796 y Fq(n)2746 2782 y FK(\).)3350 2946 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_multifit_nlinear_fre)q(e)e Fu(\()p FD(gsl)p 1912 2946 V 40 w(m)m(ulti\014t)p 2247 2946 V 41 w(nlinear)p 2561 2946 V 40 w(w)m(orkspace)31 b(*)g Ft(w)p Fu(\))3350 3056 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_multilarge_nlinear_f)q(ree)565 3166 y Fu(\()p FD(gsl)p 712 3166 V 41 w(m)m(ultilarge)p 1153 3166 V 42 w(nlinear)p 1468 3166 V 40 w(w)m(orkspace)31 b(*)g Ft(w)p Fu(\))390 3275 y FK(These)f(functions)g(free)h(all)g(the)f (memory)h(asso)s(ciated)g(with)g(the)f(w)m(orkspace)h FD(w)p FK(.)3350 3439 y([F)-8 b(unction])-3599 b Fv(const)54 b(char)f(*)g(gsl_multifit_nlinear_n)q(ame)f Fu(\()p FD(const)565 3549 y(gsl)p 677 3549 V 41 w(m)m(ulti\014t)p 1013 3549 V 40 w(nlinear)p 1326 3549 V 40 w(w)m(orkspace)31 b(*)g Ft(w)p Fu(\))3350 3658 y FK([F)-8 b(unction])-3599 b Fv(const)54 b(char)f(*)g(gsl_multilarge_nlinear)q(_na)q(me)f Fu(\()p FD(const)565 3768 y(gsl)p 677 3768 V 41 w(m)m(ultilarge)p 1118 3768 V 41 w(nlinear)p 1432 3768 V 40 w(w)m(orkspace)32 b(*)e Ft(w)p Fu(\))390 3878 y FK(These)g(functions)g(return)f(a)i(p)s (oin)m(ter)f(to)i(the)e(name)h(of)f(the)h(solv)m(er.)41 b(F)-8 b(or)31 b(example,)630 4005 y FH(printf)46 b(\("w)h(is)g(a)h ('\045s')e(solver\\n",)1012 4115 y(gsl_multifit_nlinear_nam)o(e)c (\(w\)\);)390 4243 y FK(w)m(ould)30 b(prin)m(t)g(something)h(lik)m(e)h FH(w)e(is)f(a)h('trust-region')d(solver)p FK(.)3350 4407 y([F)-8 b(unction])-3599 b Fv(const)54 b(char)f(*)g (gsl_multifit_nlinear_t)q(rs_)q(name)f Fu(\()p FD(const)565 4516 y(gsl)p 677 4516 V 41 w(m)m(ulti\014t)p 1013 4516 V 40 w(nlinear)p 1326 4516 V 40 w(w)m(orkspace)31 b(*)g Ft(w)p Fu(\))3350 4626 y FK([F)-8 b(unction])-3599 b Fv(const)54 b(char)f(*)g(gsl_multilarge_nlinear)q(_tr)q(s_na)q(me)f Fu(\()p FD(const)565 4736 y(gsl)p 677 4736 V 41 w(m)m(ultilarge)p 1118 4736 V 41 w(nlinear)p 1432 4736 V 40 w(w)m(orkspace)32 b(*)e Ft(w)p Fu(\))390 4845 y FK(These)d(functions)f(return)g(a)h(p)s (oin)m(ter)g(to)h(the)f(name)g(of)g(the)g(trust)g(region)g(subproblem)e (metho)s(d.)390 4955 y(F)-8 b(or)31 b(example,)630 5082 y FH(printf)46 b(\("w)h(is)g(a)h('\045s')e(solver\\n",)1012 5192 y(gsl_multifit_nlinear_trs)o(_na)o(me)c(\(w\)\);)390 5320 y FK(w)m(ould)30 b(prin)m(t)g(something)h(lik)m(e)h FH(w)e(is)f(a)h('levenberg-marquardt')25 b(solver)p FK(.)p eop end %%Page: 483 501 TeXDict begin 483 500 bop 150 -116 a FK(Chapter)30 b(39:)41 b(Nonlinear)31 b(Least-Squares)g(Fitting)1681 b(483)150 299 y FJ(39.6)68 b(Pro)l(viding)46 b(the)f(F)-11 b(unction)44 b(to)h(b)t(e)g(Minimized)150 458 y FK(The)28 b(user)f(m)m(ust)i(pro)m (vide)f FE(n)g FK(functions)g(of)g FE(p)g FK(v)-5 b(ariables)29 b(for)f(the)h(minimization)g(algorithm)g(to)g(op)s(erate)150 568 y(on.)58 b(In)36 b(order)g(to)h(allo)m(w)g(for)f(arbitrary)g (parameters)h(the)f(functions)g(are)h(de\014ned)e(b)m(y)h(the)g(follo)m (wing)150 677 y(data)31 b(t)m(yp)s(es:)3269 885 y([Data)h(T)m(yp)s(e]) -3600 b Fv(gsl_multifit_nlinear_f)q(df)390 995 y FK(This)33 b(data)h(t)m(yp)s(e)g(de\014nes)f(a)h(general)g(system)g(of)g (functions)f(with)g(arbitrary)h(parameters,)h(the)390 1104 y(corresp)s(onding)f(Jacobian)i(matrix)g(of)f(deriv)-5 b(ativ)m(es,)38 b(and)d(optionally)i(the)e(second)h(directional)390 1214 y(deriv)-5 b(ativ)m(e)32 b(of)e(the)h(functions)f(for)g(geo)s (desic)i(acceleration.)390 1391 y FH(int)d(\(*)h(f\))g(\(const)f (gsl_vector)e(*)j FA(x)p FH(,)g(void)f(*)h FA(params)p FH(,)f(gsl_vector)e(*)j FA(f)p FH(\))870 1501 y FK(This)i(function)h (should)e(store)j(the)f FE(n)f FK(comp)s(onen)m(ts)h(of)g(the)g(v)m (ector)i FE(f)10 b FK(\()p FE(x)p FK(\))32 b(in)h FD(f)50 b FK(for)870 1610 y(argumen)m(t)34 b FD(x)39 b FK(and)33 b(arbitrary)g(parameters)h FD(params)p FK(,)f(returning)g(an)g (appropriate)870 1720 y(error)d(co)s(de)h(if)f(the)g(function)h(cannot) g(b)s(e)e(computed.)390 1891 y FH(int)g(\(*)h(df\))g(\(const)e (gsl_vector)g(*)i FA(x)p FH(,)g(void)f(*)h FA(params)p FH(,)e(gsl_matrix)g(*)i FA(J)p FH(\))870 2001 y FK(This)25 b(function)g(should)g(store)i(the)f FD(n)p FK(-b)m(y-)p FD(p)i FK(matrix)e(result)g FE(J)2955 2015 y Fq(ij)3039 2001 y FK(=)f FE(@)5 b(f)3233 2015 y Fq(i)3260 2001 y FK(\()p FE(x)p FK(\))p FE(=@)g(x)3532 2015 y Fq(j)3594 2001 y FK(in)26 b FD(J)870 2110 y FK(for)h(argumen)m(t)h FD(x)34 b FK(and)27 b(arbitrary)h(parameters)g FD(params)p FK(,)g(returning)e(an)i(appropri-)870 2220 y(ate)h(error)e(co)s(de)h (if)g(the)g(matrix)g(cannot)h(b)s(e)e(computed.)40 b(If)27 b(an)h(analytic)h(Jacobian)870 2329 y(is)39 b(una)m(v)-5 b(ailable,)43 b(or)c(to)s(o)g(exp)s(ensiv)m(e)h(to)f(compute,)j(this)d (function)f(p)s(oin)m(ter)h(ma)m(y)870 2439 y(b)s(e)30 b(set)i(to)g(NULL,)f(in)g(whic)m(h)g(case)h(the)f(Jacobian)h(will)g(b)s (e)e(in)m(ternally)i(computed)870 2549 y(using)e(\014nite)g (di\013erence)h(appro)m(ximations)g(of)g(the)f(function)g FD(f)p FK(.)390 2720 y FH(int)f(\(*)h(fvv\))f(\(const)g(gsl_vector)f(*) i FA(x)p FH(,)f(const)g(gsl_vector)f(*)i FA(v)p FH(,)g(void)f(*)h FA(params)p FH(,)390 2829 y(gsl_vector)e(*)i FA(fvv)p FH(\))870 2939 y FK(When)35 b(geo)s(desic)i(acceleration)h(is)e (enabled,)h(this)e(function)g(should)g(store)h(the)f FE(n)870 3049 y FK(comp)s(onen)m(ts)45 b(of)f(the)h(v)m(ector)h FE(f)2005 3063 y Fq(v)r(v)2080 3049 y FK(\()p FE(x)p FK(\))j(=)2371 2984 y Fs(P)2459 3071 y Fq(\013\014)2562 3049 y FE(v)2606 3063 y Fq(\013)2653 3049 y FE(v)2697 3063 y Fq(\014)2792 3013 y(@)p 2752 3028 119 4 v 2752 3080 a(@)t(x)2829 3088 y Fl(\013)2929 3013 y Fq(@)p 2891 3028 116 4 v 2891 3080 a(@)t(x)2968 3089 y Fl(\014)3016 3049 y FE(f)10 b FK(\()p FE(x)p FK(\),)49 b(represen)m(ting)870 3169 y(second)36 b(directional)h(deriv)-5 b(ativ)m(es)38 b(of)e(the)g(function)g(to)h(b)s(e)e(minimized,)j(in)m(to)f(the)870 3279 y(output)31 b FD(fvv)p FK(.)44 b(The)31 b(parameter)h(v)m(ector)h (is)f(pro)m(vided)f(in)g FD(x)38 b FK(and)31 b(the)g(v)m(elo)s(cit)m(y) j(v)m(ec-)870 3388 y(tor)39 b(is)f(pro)m(vided)g(in)g FD(v)p FK(,)j(b)s(oth)d(of)g(whic)m(h)g(ha)m(v)m(e)i FE(p)e FK(comp)s(onen)m(ts.)65 b(The)38 b(arbitrary)870 3498 y(parameters)i(are)h(giv)m(en)g(in)f FD(params)p FK(.)69 b(If)40 b(analytic)h(expressions)f(for)g FE(f)3392 3512 y Fq(v)r(v)3466 3498 y FK(\()p FE(x)p FK(\))h(are)870 3607 y(una)m(v)-5 b(ailable)33 b(or)f(to)s(o)h(di\016cult)f(to)g (compute,)h(this)f(function)g(p)s(oin)m(ter)g(ma)m(y)g(b)s(e)f(set)870 3717 y(to)g(NULL,)e(in)h(whic)m(h)f(case)i FE(f)1887 3731 y Fq(v)r(v)1962 3717 y FK(\()p FE(x)p FK(\))f(will)g(b)s(e)f (computed)h(in)m(ternally)h(using)e(a)h(\014nite)870 3827 y(di\013erence)h(appro)m(ximation.)390 3998 y FH(size_t)e(n)115 b FK(the)31 b(n)m(um)m(b)s(er)e(of)h(functions,)g(i.e.)42 b(the)30 b(n)m(um)m(b)s(er)g(of)g(comp)s(onen)m(ts)h(of)f(the)h(v)m (ector)h FD(f)p FK(.)390 4169 y FH(size_t)d(p)115 b FK(the)35 b(n)m(um)m(b)s(er)e(of)h(indep)s(enden)m(t)g(v)-5 b(ariables,)36 b(i.e.)54 b(the)34 b(n)m(um)m(b)s(er)g(of)g(comp)s(onen)m(ts)h(of)870 4279 y(the)c(v)m(ector)h FD(x)p FK(.)390 4450 y FH(void)d(*)h(params) 870 4559 y FK(a)h(p)s(oin)m(ter)f(to)h(the)g(arbitrary)f(parameters)h (of)f(the)h(function.)390 4730 y FH(size_t)e(nevalf)870 4840 y FK(This)23 b(do)s(es)g(not)h(need)g(to)g(b)s(e)f(set)i(b)m(y)e (the)h(user.)38 b(It)24 b(coun)m(ts)g(the)g(n)m(um)m(b)s(er)e(of)i (function)870 4950 y(ev)-5 b(aluations)32 b(and)d(is)i(initialized)h(b) m(y)e(the)h FH(_init)e FK(function.)390 5121 y FH(size_t)g(nevaldf)870 5230 y FK(This)21 b(do)s(es)h(not)g(need)g(to)h(b)s(e)e(set)i(b)m(y)f (the)g(user.)37 b(It)23 b(coun)m(ts)f(the)g(n)m(um)m(b)s(er)f(of)h (Jacobian)870 5340 y(ev)-5 b(aluations)32 b(and)d(is)i(initialized)h(b) m(y)e(the)h FH(_init)e FK(function.)p eop end %%Page: 484 502 TeXDict begin 484 501 bop 150 -116 a FK(Chapter)30 b(39:)41 b(Nonlinear)31 b(Least-Squares)g(Fitting)1681 b(484)390 299 y FH(size_t)29 b(nevalfvv)870 408 y FK(This)g(do)s(es)g(not)h(need) f(to)h(b)s(e)f(set)i(b)m(y)e(the)h(user.)40 b(It)29 b(coun)m(ts)h(the)g (n)m(um)m(b)s(er)e(of)i FE(f)3553 422 y Fq(v)r(v)3627 408 y FK(\()p FE(x)p FK(\))870 518 y(ev)-5 b(aluations)32 b(and)d(is)i(initialized)h(b)m(y)e(the)h FH(_init)e FK(function.)3269 726 y([Data)j(T)m(yp)s(e])-3600 b Fv(gsl_multilarge_nlinear)q(_fd)q(f) 390 836 y FK(This)39 b(data)i(t)m(yp)s(e)g(de\014nes)e(a)i(general)g (system)f(of)h(functions)e(with)h(arbitrary)g(parameters,)k(a)390 945 y(function)38 b(to)g(compute)g FE(J)9 b(u)38 b FK(or)g FE(J)1575 912 y Fq(T)1628 945 y FE(u)g FK(for)f(a)i(giv)m(en)g(v)m (ector)g FE(u)p FK(,)h(the)e(normal)g(equations)h(matrix)390 1055 y FE(J)449 1022 y Fq(T)501 1055 y FE(J)9 b FK(,)42 b(and)c(optionally)i(the)g(second)f(directional)h(deriv)-5 b(ativ)m(e)40 b(of)f(the)h(functions)e(for)h(geo)s(desic)390 1165 y(acceleration.)390 1342 y FH(int)29 b(\(*)h(f\))g(\(const)f (gsl_vector)e(*)j FA(x)p FH(,)g(void)f(*)h FA(params)p FH(,)f(gsl_vector)e(*)j FA(f)p FH(\))870 1452 y FK(This)i(function)h (should)e(store)j(the)f FE(n)f FK(comp)s(onen)m(ts)h(of)g(the)g(v)m (ector)i FE(f)10 b FK(\()p FE(x)p FK(\))32 b(in)h FD(f)50 b FK(for)870 1561 y(argumen)m(t)34 b FD(x)39 b FK(and)33 b(arbitrary)g(parameters)h FD(params)p FK(,)f(returning)g(an)g (appropriate)870 1671 y(error)d(co)s(de)h(if)f(the)g(function)h(cannot) g(b)s(e)e(computed.)390 1842 y FH(int)g(\(*)h(df\))g (\(CBLAS_TRANSPOSE_t)25 b FA(TransJ)p FH(,)j(const)h(gsl_vector)f(*)i FA(x)p FH(,)g(const)390 1952 y(gsl_vector)e(*)i FA(u)p FH(,)f(void)h(*)g FA(params)p FH(,)e(gsl_vector)g(*)i FA(v)p FH(,)f(gsl_matrix)f(*)i FA(JTJ)p FH(\))870 2061 y FK(If)k FD(T)-8 b(ransJ)41 b FK(is)34 b(equal)h(to)g FH(CblasNoTrans)p FK(,)e(then)h(this)g(function)g(should)g(compute)870 2171 y(the)43 b(matrix-v)m(ector)j(pro)s(duct)c FE(J)9 b(u)44 b FK(and)e(store)i(the)g(result)f(in)g FD(v)p FK(.)79 b(If)43 b FD(T)-8 b(ransJ)50 b FK(is)870 2280 y(equal)d(to)g FH(CblasTrans)p FK(,)g(then)f(this)g(function)g(should)f (compute)i(the)f(matrix-)870 2390 y(v)m(ector)37 b(pro)s(duct)d FE(J)1553 2357 y Fq(T)1605 2390 y FE(u)i FK(and)e(store)i(the)g(result) f(in)g FD(v)p FK(.)55 b(Additionally)-8 b(,)38 b(the)e(normal)870 2500 y(equations)30 b(matrix)g FE(J)1630 2467 y Fq(T)1683 2500 y FE(J)38 b FK(should)29 b(b)s(e)g(stored)g(in)h(the)f(lo)m(w)m (er)i(half)f(of)f FD(JTJ)p FK(.)40 b(The)29 b(in-)870 2609 y(put)f(matrix)h FD(JTJ)35 b FK(could)29 b(b)s(e)f(set)h(to)g (NULL,)g(for)g(example)g(b)m(y)g(iterativ)m(e)i(metho)s(ds)870 2719 y(whic)m(h)h(do)g(not)h(require)e(this)i(matrix,)g(so)f(the)h (user)e(should)h(c)m(hec)m(k)h(for)f(this)h(prior)870 2828 y(to)44 b(constructing)f(the)g(matrix.)79 b(The)43 b(input)f FD(params)k FK(con)m(tains)e(the)f(arbitrary)870 2938 y(parameters.)390 3109 y FH(int)29 b(\(*)h(fvv\))f(\(const)g (gsl_vector)f(*)i FA(x)p FH(,)f(const)g(gsl_vector)f(*)i FA(v)p FH(,)g(void)f(*)h FA(params)p FH(,)390 3219 y(gsl_vector)e(*)i FA(fvv)p FH(\))870 3329 y FK(When)35 b(geo)s(desic)i(acceleration)h(is) e(enabled,)h(this)e(function)g(should)g(store)h(the)f FE(n)870 3438 y FK(comp)s(onen)m(ts)45 b(of)f(the)h(v)m(ector)h FE(f)2005 3452 y Fq(v)r(v)2080 3438 y FK(\()p FE(x)p FK(\))j(=)2371 3374 y Fs(P)2459 3461 y Fq(\013\014)2562 3438 y FE(v)2606 3452 y Fq(\013)2653 3438 y FE(v)2697 3452 y Fq(\014)2792 3402 y(@)p 2752 3417 119 4 v 2752 3469 a(@)t(x)2829 3477 y Fl(\013)2929 3402 y Fq(@)p 2891 3417 116 4 v 2891 3469 a(@)t(x)2968 3478 y Fl(\014)3016 3438 y FE(f)10 b FK(\()p FE(x)p FK(\),)49 b(represen)m(ting)870 3559 y(second)36 b(directional)h(deriv)-5 b(ativ)m(es)38 b(of)e(the)g(function)g(to)h(b)s(e)e(minimized,)j(in)m(to)f(the)870 3668 y(output)31 b FD(fvv)p FK(.)44 b(The)31 b(parameter)h(v)m(ector)h (is)f(pro)m(vided)f(in)g FD(x)38 b FK(and)31 b(the)g(v)m(elo)s(cit)m(y) j(v)m(ec-)870 3778 y(tor)39 b(is)f(pro)m(vided)g(in)g FD(v)p FK(,)j(b)s(oth)d(of)g(whic)m(h)g(ha)m(v)m(e)i FE(p)e FK(comp)s(onen)m(ts.)65 b(The)38 b(arbitrary)870 3887 y(parameters)i(are)h(giv)m(en)g(in)f FD(params)p FK(.)69 b(If)40 b(analytic)h(expressions)f(for)g FE(f)3392 3901 y Fq(v)r(v)3466 3887 y FK(\()p FE(x)p FK(\))h(are)870 3997 y(una)m(v)-5 b(ailable)33 b(or)f(to)s(o)h(di\016cult)f(to)g (compute,)h(this)f(function)g(p)s(oin)m(ter)g(ma)m(y)g(b)s(e)f(set)870 4107 y(to)g(NULL,)e(in)h(whic)m(h)f(case)i FE(f)1887 4121 y Fq(v)r(v)1962 4107 y FK(\()p FE(x)p FK(\))f(will)g(b)s(e)f (computed)h(in)m(ternally)h(using)e(a)h(\014nite)870 4216 y(di\013erence)h(appro)m(ximation.)390 4388 y FH(size_t)e(n)115 b FK(the)31 b(n)m(um)m(b)s(er)e(of)h(functions,)g(i.e.)42 b(the)30 b(n)m(um)m(b)s(er)g(of)g(comp)s(onen)m(ts)h(of)f(the)h(v)m (ector)h FD(f)p FK(.)390 4559 y FH(size_t)d(p)115 b FK(the)35 b(n)m(um)m(b)s(er)e(of)h(indep)s(enden)m(t)g(v)-5 b(ariables,)36 b(i.e.)54 b(the)34 b(n)m(um)m(b)s(er)g(of)g(comp)s(onen)m(ts)h(of)870 4668 y(the)c(v)m(ector)h FD(x)p FK(.)390 4840 y FH(void)d(*)h(params) 870 4949 y FK(a)h(p)s(oin)m(ter)f(to)h(the)g(arbitrary)f(parameters)h (of)f(the)h(function.)390 5121 y FH(size_t)e(nevalf)870 5230 y FK(This)23 b(do)s(es)g(not)h(need)g(to)g(b)s(e)f(set)i(b)m(y)e (the)h(user.)38 b(It)24 b(coun)m(ts)g(the)g(n)m(um)m(b)s(er)e(of)i (function)870 5340 y(ev)-5 b(aluations)32 b(and)d(is)i(initialized)h(b) m(y)e(the)h FH(_init)e 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w(nlinear)p 2666 2697 V 40 w(w)m(orkspace)31 b(*)565 2806 y Ft(w)p Fu(\))3350 2916 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multilarge_nlinea)q(r_it)q(era)q(te)565 3025 y Fu(\()p FD(gsl)p 712 3025 V 41 w(m)m(ultilarge)p 1153 3025 V 42 w(nlinear)p 1468 3025 V 40 w(w)m(orkspace)31 b(*)g Ft(w)p Fu(\))390 3135 y FK(These)d(functions)g(p)s(erform)f(a)i (single)f(iteration)i(of)f(the)f(solv)m(er)i FD(w)p FK(.)39 b(If)28 b(the)h(iteration)h(encoun)m(ters)390 3245 y(an)36 b(unexp)s(ected)g(problem)g(then)g(an)g(error)g(co)s(de)h(will)g(b)s(e) e(returned.)58 b(The)36 b(solv)m(er)h(w)m(orkspace)390 3354 y(main)m(tains)31 b(a)g(curren)m(t)f(estimate)i(of)f(the)f(b)s (est-\014t)g(parameters)h(at)g(all)h(times.)150 3598 y(The)42 b(solv)m(er)i(w)m(orkspace)f FD(w)50 b FK(con)m(tains)44 b(the)f(follo)m(wing)h(en)m(tries,)i(whic)m(h)d(can)g(b)s(e)f(used)g (to)h(trac)m(k)h(the)150 3707 y(progress)30 b(of)h(the)f(solution:)150 3911 y FH(gsl_vector)e(*)i(x)630 4021 y FK(The)g(curren)m(t)g(p)s (osition,)h(length)g FE(p)p FK(.)150 4210 y FH(gsl_vector)d(*)i(f)630 4320 y FK(The)g(function)g(residual)g(v)m(ector)i(at)f(the)g(curren)m (t)f(p)s(osition)g FE(f)10 b FK(\()p FE(x)p FK(\),)31 b(length)g FE(n)p FK(.)150 4509 y FH(gsl_matrix)d(*)i(J)630 4618 y FK(The)35 b(Jacobian)i(matrix)f(at)g(the)g(curren)m(t)g(p)s (osition)f FE(J)9 b FK(\()p FE(x)p FK(\),)38 b(size)f FE(n)p FK(-b)m(y-)p FE(p)e FK(\(only)i(for)e FH(gsl_)630 4728 y(multifit_nlinear)26 b FK(in)m(terface\).)150 4917 y FH(gsl_vector)i(*)i(dx)630 5026 y FK(The)g(di\013erence)i(b)s(et)m(w) m(een)f(the)g(curren)m(t)g(p)s(osition)g(and)f(the)h(previous)f(p)s (osition,)i(i.e.)43 b(the)630 5136 y(last)31 b(step)g FE(\016)s FK(,)g(tak)m(en)h(as)e(a)h(v)m(ector,)h(length)f FE(p)p FK(.)150 5340 y(These)f(quan)m(tities)i(can)e(b)s(e)g(accessed)i (with)e(the)g(follo)m(wing)i(functions,)p eop end %%Page: 486 504 TeXDict begin 486 503 bop 150 -116 a FK(Chapter)30 b(39:)41 b(Nonlinear)31 b(Least-Squares)g(Fitting)1681 b(486)3350 299 y([F)-8 b(unction])-3599 b Fv(gsl_vector)55 b(*)e (gsl_multifit_nlinear_p)q(osi)q(tion)f Fu(\()p FD(const)565 408 y(gsl)p 677 408 28 4 v 41 w(m)m(ulti\014t)p 1013 408 V 40 w(nlinear)p 1326 408 V 40 w(w)m(orkspace)31 b(*)g Ft(w)p Fu(\))3350 518 y FK([F)-8 b(unction])-3599 b Fv(gsl_vector)55 b(*)e(gsl_multilarge_nlinear)q(_po)q(siti)q(on)f Fu(\()p FD(const)565 628 y(gsl)p 677 628 V 41 w(m)m(ultilarge)p 1118 628 V 41 w(nlinear)p 1432 628 V 40 w(w)m(orkspace)32 b(*)e Ft(w)p Fu(\))390 737 y FK(These)i(functions)g(return)f(the)i (curren)m(t)f(p)s(osition)h FE(x)f FK(\(i.e.)48 b(b)s(est-\014t)32 b(parameters\))h(of)f(the)h(solv)m(er)390 847 y FD(w)p FK(.)3350 1041 y([F)-8 b(unction])-3599 b Fv(gsl_vector)55 b(*)e(gsl_multifit_nlinear_r)q(esi)q(dual)f Fu(\()p FD(const)565 1150 y(gsl)p 677 1150 V 41 w(m)m(ulti\014t)p 1013 1150 V 40 w(nlinear)p 1326 1150 V 40 w(w)m(orkspace)31 b(*)g Ft(w)p Fu(\))3350 1260 y FK([F)-8 b(unction])-3599 b Fv(gsl_vector)55 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b(gsl_multifit_nlinear_)q(rcon)q(d)f Fu(\()p FD(double)30 b(*)h Ft(rcond)p FD(,)h(const)565 3375 y(gsl)p 677 3375 V 41 w(m)m(ulti\014t)p 1013 3375 V 40 w(nlinear)p 1326 3375 V 40 w(w)m(orkspace)f(*)g Ft(w)p Fu(\))3350 3485 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multilarge_nlinea)q(r_rc) q(ond)f Fu(\()p FD(double)30 b(*)h Ft(rcond)p FD(,)h(const)565 3594 y(gsl)p 677 3594 V 41 w(m)m(ultilarge)p 1118 3594 V 41 w(nlinear)p 1432 3594 V 40 w(w)m(orkspace)g(*)e Ft(w)p Fu(\))390 3704 y FK(This)36 b(function)h(estimates)i(the)f (recipro)s(cal)g(condition)g(n)m(um)m(b)s(er)e(of)h(the)h(Jacobian)g (matrix)f(at)390 3814 y(the)27 b(curren)m(t)f(p)s(osition)h FE(x)f FK(and)g(stores)h(it)h(in)e FD(rcond)p FK(.)39 b(The)26 b(computed)g(v)-5 b(alue)27 b(is)g(only)g(an)f(estimate)390 3923 y(to)39 b(giv)m(e)g(the)f(user)f(a)h(guideline)h(as)f(to)g(the)h (conditioning)f(of)g(their)g(particular)g(problem.)63 b(Its)390 4033 y(calculation)33 b(is)d(based)g(on)g(whic)m(h)g 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y(to)g(test)g(the)g(curren)m(t)f(estimate)i(of)f(the)f (b)s(est-\014t)g(parameters)h(in)f(sev)m(eral)i(standard)e(w)m(a)m(ys.) 3350 1382 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multifit_nlinear_) q(test)f Fu(\()p FD(const)31 b(double)f Ft(xtol)p FD(,)i(const)f (double)565 1492 y Ft(gtol)p FD(,)h(const)f(double)f Ft(ftol)p FD(,)h(in)m(t)g(*)g Ft(info)p FD(,)h(const)f(gsl)p 2455 1492 28 4 v 40 w(m)m(ulti\014t)p 2790 1492 V 41 w(nlinear)p 3104 1492 V 40 w(w)m(orkspace)g(*)g Ft(w)p Fu(\))3350 1601 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multilarge_nlinea)q(r_te)q(st)f Fu(\()p FD(const)31 b(double)f Ft(xtol)p FD(,)i(const)f(double)565 1711 y Ft(gtol)p FD(,)h(const)f(double)f Ft(ftol)p FD(,)h(in)m(t)g(*)g Ft(info)p FD(,)h(const)f(gsl)p 2455 1711 V 40 w(m)m(ultilarge)p 2895 1711 V 42 w(nlinear)p 3210 1711 V 40 w(w)m(orkspace)g(*)565 1820 y Ft(w)p Fu(\))390 1930 y FK(These)f(functions)f(test)i(for)f(con) m(v)m(ergence)j(of)d(the)g(minimization)h(metho)s(d)f(using)f(the)h (follo)m(wing)390 2040 y(criteria:)465 2186 y FI(\017)60 b FK(T)-8 b(esting)31 b(for)f(a)h(small)g(step)f(size)i(relativ)m(e)g (to)f(the)g(curren)m(t)f(parameter)h(v)m(ector)1516 2366 y FI(j)p FE(\016)1581 2380 y Fq(i)1610 2366 y FI(j)25 b(\024)g FE(xtol)r FK(\()p FI(j)p FE(x)2026 2380 y Fq(i)2054 2366 y FI(j)c FK(+)e FE(xtol)r FK(\))570 2546 y(for)37 b(eac)m(h)i(0)e FE(<)p FK(=)f FE(i)h(<)g(p)p FK(.)61 b(Eac)m(h)38 b(elemen)m(t)h(of)f(the)f(step)h(v)m(ector)h FE(\016)i FK(is)c(tested)h(individually)570 2656 y(in)30 b(case)i(the)f(di\013eren)m(t)g(parameters)g(ha)m(v)m(e)g(widely)g (di\013eren)m(t)g(scales.)43 b(Adding)29 b FD(xtol)36 b FK(to)31 b FI(j)p FE(x)3697 2670 y Fq(i)3725 2656 y FI(j)570 2765 y FK(helps)37 b(the)g(test)h(a)m(v)m(oid)g(breaking)g(do) m(wn)e(in)h(situations)h(where)f(the)g(true)g(solution)g(v)-5 b(alue)570 2875 y FE(x)622 2889 y Fq(i)675 2875 y FK(=)25 b(0.)38 b(If)20 b(this)h(test)h(succeeds,)h FD(info)i FK(is)c(set)h(to)f(1)g(and)g(the)g(function)f(returns)g 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V 42 w(nlinear)p 2752 1066 V 40 w(w)m(orkspace)f(*)g Ft(w)p Fu(\))390 1176 y FK(These)23 b(functions)g(iterate)i(the)f(nonlinear)f(least)i (squares)e(solv)m(er)h FD(w)31 b FK(for)23 b(a)h(maxim)m(um)f(of)h FD(maxiter)390 1285 y FK(iterations.)56 b(After)36 b(eac)m(h)g (iteration,)i(the)d(system)h(is)f(tested)h(for)f(con)m(v)m(ergence)i (with)e(the)g(error)390 1395 y(tolerances)f FD(xtol)p FK(,)h FD(gtol)j FK(and)32 b FD(ftol)p FK(.)48 b(Additionally)-8 b(,)35 b(the)e(user)f(ma)m(y)h(supply)e(a)i(callbac)m(k)i(function)390 1504 y FD(callbac)m(k)30 b FK(whic)m(h)22 b(is)h(called)h(after)f(eac)m (h)g(iteration,)j(so)d(that)g(the)g(user)f(ma)m(y)h(sa)m(v)m(e)h(or)e (prin)m(t)h(relev)-5 b(an)m(t)390 1614 y(quan)m(tities)24 b(for)e(eac)m(h)i(iteration.)39 b(The)22 b(parameter)h FD(callbac)m(k)p 2459 1614 V 42 w(params)j FK(is)d(passed)e(to)j(the)e FD(callbac)m(k)390 1724 y FK(function.)78 b(The)43 b(parameters)g FD(callbac)m(k)51 b FK(and)42 b FD(callbac)m(k)p 2380 1724 V 43 w(params)k 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b(page)g(489)h(for)e(further)f(guidance.)150 2728 y FJ(39.10)69 b(Co)l(v)-7 b(ariance)45 b(matrix)h(of)g(b)t(est)f(\014t)f(parameters) 3350 2941 y FK([F)-8 b(unction])-3599 b Fv(int)53 b (gsl_multifit_nlinear_)q(cova)q(r)f Fu(\()p FD(const)31 b(gsl)p 2150 2941 V 40 w(matrix)g(*)g Ft(J)p FD(,)g(const)g(double)565 3051 y Ft(epsrel)p FD(,)h(gsl)p 1046 3051 V 41 w(matrix)f(*)g Ft(covar)p Fu(\))3350 3160 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multilarge_nlinea)q(r_co)q(var)f Fu(\()p FD(gsl)p 2016 3160 V 41 w(matrix)31 b(*)g Ft(covar)p FD(,)565 3270 y(gsl)p 677 3270 V 41 w(m)m(ultilarge)p 1118 3270 V 41 w(nlinear)p 1432 3270 V 40 w(w)m(orkspace)h(*)e Ft(w)p Fu(\))390 3379 y FK(This)38 b(function)h(computes)h(the)f(co)m (v)-5 b(ariance)42 b(matrix)d(of)h(b)s(est-\014t)f(parameters)g(using)g (the)h(Ja-)390 3489 y(cobian)k(matrix)g FD(J)51 b FK(and)43 b(stores)h(it)g(in)f FD(co)m(v)-5 b(ar)p FK(.)82 b(The)43 b(parameter)h FD(epsrel)k FK(is)43 b(used)g(to)h(remo)m(v)m(e)390 3599 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y(gsl_multifit_nlinear_covar)41 b(\(J,)47 b(0.0,)g(covar\);) 485 4134 y(/*)h(compute)d(final)i(cost)f(*/)485 4244 y(gsl_blas_ddot\(f,)e(f,)j(&chisq\);)390 4463 y(#define)f(FIT\(i\))g (gsl_vector_get\(w->x,)c(i\))390 4573 y(#define)k(ERR\(i\))g (sqrt\(gsl_matrix_get\(cova)o(r,i,)o(i\)\))485 4792 y(fprintf\(stderr,) e("summary)i(from)g(method)g('\045s/\045s'\\n",)867 4902 y(gsl_multifit_nlinear_name)o(\(w\),)867 5011 y (gsl_multifit_nlinear_trs_)o(name)o(\(w\)\))o(;)485 5121 y(fprintf\(stderr,)e("number)i(of)h(iterations:)93 b(\045zu\\n",)867 5230 y(gsl_multifit_nlinear_nite)o(r\(w\))o(\);)485 5340 y(fprintf\(stderr,)44 b("function)h(evaluations:)93 b(\045zu\\n",)45 b(fdf.nevalf\);)p eop end %%Page: 495 513 TeXDict begin 495 512 bop 150 -116 a FK(Chapter)30 b(39:)41 b(Nonlinear)31 b(Least-Squares)g(Fitting)1681 b(495)485 299 y FH(fprintf\(stderr,)44 b("Jacobian)h(evaluations:)93 b(\045zu\\n",)45 b(fdf.nevaldf\);)485 408 y(fprintf\(stderr,)f("reason) i(for)h(stopping:)93 b(\045s\\n",)867 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/Pattern1 {0.250 Density} bind def /Pattern2 {0.500 Density} bind def /Pattern3 {0.750 Density} bind def /Pattern4 {0.125 Density} bind def /Pattern5 {0.375 Density} bind def /Pattern6 {0.625 Density} bind def /Pattern7 {0.875 Density} bind def } def % % Now test for support of Level 2 code % Level1 {Level1PatternFill} {Level2PatternFill} ifelse % /Symbol-Oblique /Symbol findfont [1 0 .167 1 0 0] makefont dup length dict begin {1 index /FID eq {pop pop} {def} ifelse} forall currentdict end definefont pop /MFshow { { dup 5 get 3 ge { 5 get 3 eq {gsave} {grestore} ifelse } {dup dup 0 get findfont exch 1 get scalefont setfont [ currentpoint ] exch dup 2 get 0 exch R dup 5 get 2 ne {dup dup 6 get exch 4 get {Gshow} {stringwidth pop 0 R} ifelse }if dup 5 get 0 eq {dup 3 get {2 get neg 0 exch R pop} {pop aload pop M} ifelse} {dup 5 get 1 eq {dup 2 get exch dup 3 get exch 6 get stringwidth pop -2 div dup 0 R} {dup 6 get stringwidth pop -2 div 0 R 6 get show 2 index {aload pop M neg 3 -1 roll neg R pop pop} {pop pop pop pop aload pop M} ifelse }ifelse }ifelse } ifelse } forall} def /Gswidth {dup type /stringtype eq {stringwidth} {pop (n) stringwidth} ifelse} def /MFwidth {0 exch { dup 5 get 3 ge { 5 get 3 eq { 0 } { pop } ifelse } {dup 3 get{dup dup 0 get findfont exch 1 get scalefont setfont 6 get Gswidth pop add} {pop} ifelse} ifelse} forall} def /MLshow { currentpoint stroke M 0 exch R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /MRshow { currentpoint stroke M exch dup MFwidth neg 3 -1 roll R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /MCshow { currentpoint stroke M exch dup MFwidth -2 div 3 -1 roll R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /XYsave { [( ) 1 2 true false 3 ()] } bind def /XYrestore { [( ) 1 2 true false 4 ()] } bind def Level1 SuppressPDFMark or {} { /SDict 10 dict def systemdict /pdfmark known not { userdict /pdfmark systemdict /cleartomark get put } if SDict begin [ /Title (nlfit2.eps) /Subject (gnuplot plot) /Creator (gnuplot 4.6 patchlevel 2) /Author (palken) % /Producer (gnuplot) % /Keywords () /CreationDate (Wed Jun 8 08:50:03 2016) /DOCINFO pdfmark end } ifelse end %%EndProlog %%Page: 1 1 gnudict begin gsave doclip 50 50 translate 0.050 0.050 scale 0 setgray newpath (Helvetica) findfont 140 scalefont setfont BackgroundColor 0 lt 3 1 roll 0 lt exch 0 lt or or not {BackgroundColor C 1.000 0 0 7200.00 5040.00 BoxColFill} if gsave % colour palette begin /maxcolors 0 def /HSV2RGB { exch dup 0.0 eq {pop exch pop dup dup} % achromatic gray { /HSVs exch def /HSVv exch def 6.0 mul dup floor dup 3 1 roll sub /HSVf exch def /HSVi exch cvi def /HSVp HSVv 1.0 HSVs sub mul def /HSVq HSVv 1.0 HSVs HSVf mul sub mul def /HSVt HSVv 1.0 HSVs 1.0 HSVf sub mul sub mul def /HSVi HSVi 6 mod def 0 HSVi eq {HSVv HSVt HSVp} {1 HSVi eq {HSVq HSVv HSVp}{2 HSVi eq {HSVp HSVv HSVt} {3 HSVi eq {HSVp HSVq HSVv}{4 HSVi eq {HSVt HSVp HSVv} {HSVv HSVp HSVq} ifelse} ifelse} ifelse} ifelse} ifelse } ifelse} def /Constrain { dup 0 lt {0 exch pop}{dup 1 gt {1 exch pop} if} ifelse} def /YIQ2RGB { 3 copy -1.702 mul exch -1.105 mul add add Constrain 4 1 roll 3 copy -0.647 mul exch -0.272 mul add add Constrain 5 1 roll 0.621 mul exch -0.956 mul add add Constrain 3 1 roll } def /CMY2RGB { 1 exch sub exch 1 exch sub 3 2 roll 1 exch sub 3 1 roll exch } def /XYZ2RGB { 3 copy -0.9017 mul exch -0.1187 mul add exch 0.0585 mul exch add Constrain 4 1 roll 3 copy -0.0279 mul exch 1.999 mul add exch -0.9844 mul add Constrain 5 1 roll -0.2891 mul exch -0.5338 mul add exch 1.91 mul exch add Constrain 3 1 roll} def /SelectSpace {ColorSpace (HSV) eq {HSV2RGB}{ColorSpace (XYZ) eq { XYZ2RGB}{ColorSpace (CMY) eq {CMY2RGB}{ColorSpace (YIQ) eq {YIQ2RGB} if} ifelse} ifelse} ifelse} def /InterpolatedColor true def /grayindex {/gidx 0 def {GrayA gidx get grayv ge {exit} if /gidx gidx 1 add def} loop} def /dgdx {grayv GrayA gidx get sub GrayA gidx 1 sub get GrayA gidx get sub div} def /redvalue {RedA gidx get RedA gidx 1 sub get RedA gidx get sub dgdxval mul add} def /greenvalue {GreenA gidx get GreenA gidx 1 sub get GreenA gidx get sub dgdxval mul add} def /bluevalue {BlueA gidx get BlueA gidx 1 sub get BlueA gidx get sub dgdxval mul add} def /interpolate { grayindex grayv GrayA gidx get sub abs 1e-5 le {RedA gidx get GreenA gidx get BlueA gidx get} {/dgdxval dgdx def redvalue greenvalue bluevalue} ifelse} def /GrayA [0 .125 .25 .375 .5 .625 .75 .875 1 ] def /RedA [0 0 0 0 .5 1 1 1 .5 ] def /GreenA [0 0 .5 1 1 1 .5 0 0 ] def /BlueA [.5 1 1 1 .5 0 0 0 0 ] def /pm3dround {maxcolors 0 gt {dup 1 ge {pop 1} {maxcolors mul floor maxcolors 1 sub div} ifelse} if} def /pm3dGamma 1.0 1.5 Gamma mul div def /ColorSpace (RGB) def Color InterpolatedColor or { % COLOUR vs. GRAY map InterpolatedColor { %% Interpolation vs. RGB-Formula /g {stroke pm3dround /grayv exch def interpolate SelectSpace setrgbcolor} bind def }{ /g {stroke pm3dround dup cF7 Constrain exch dup cF5 Constrain exch cF15 Constrain SelectSpace setrgbcolor} bind def } ifelse }{ /g {stroke pm3dround pm3dGamma exp setgray} bind def } ifelse 1.000 UL LTb LCb setrgbcolor 686 588 M 63 0 V 5311 0 R -63 0 V stroke 602 588 M [ [(Helvetica) 140.0 0.0 true true 0 (-0.5)] ] -46.7 MRshow 1.000 UL LTb LCb setrgbcolor 686 1445 M 63 0 V 5311 0 R -63 0 V stroke 602 1445 M [ [(Helvetica) 140.0 0.0 true true 0 ( 0)] ] -46.7 MRshow 1.000 UL LTb LCb setrgbcolor 686 2301 M 63 0 V 5311 0 R -63 0 V stroke 602 2301 M [ [(Helvetica) 140.0 0.0 true true 0 ( 0.5)] ] -46.7 MRshow 1.000 UL LTb LCb setrgbcolor 686 3158 M 63 0 V 5311 0 R -63 0 V stroke 602 3158 M [ [(Helvetica) 140.0 0.0 true true 0 ( 1)] ] -46.7 MRshow 1.000 UL LTb LCb setrgbcolor 686 4014 M 63 0 V 5311 0 R -63 0 V stroke 602 4014 M [ [(Helvetica) 140.0 0.0 true true 0 ( 1.5)] ] -46.7 MRshow 1.000 UL LTb LCb setrgbcolor 686 4871 M 63 0 V 5311 0 R -63 0 V stroke 602 4871 M [ [(Helvetica) 140.0 0.0 true true 0 ( 2)] ] -46.7 MRshow 1.000 UL LTb LCb setrgbcolor 1134 588 M 0 63 V 0 4220 R 0 -63 V stroke 1134 448 M [ [(Helvetica) 140.0 0.0 true true 0 (-1)] ] -46.7 MCshow 1.000 UL LTb LCb setrgbcolor 2253 588 M 0 63 V 0 4220 R 0 -63 V stroke 2253 448 M [ [(Helvetica) 140.0 0.0 true true 0 (-0.5)] ] -46.7 MCshow 1.000 UL LTb LCb setrgbcolor 3373 588 M 0 63 V 0 4220 R 0 -63 V stroke 3373 448 M [ [(Helvetica) 140.0 0.0 true true 0 ( 0)] ] -46.7 MCshow 1.000 UL LTb LCb setrgbcolor 4493 588 M 0 63 V 0 4220 R 0 -63 V stroke 4493 448 M [ [(Helvetica) 140.0 0.0 true true 0 ( 0.5)] ] -46.7 MCshow 1.000 UL LTb LCb setrgbcolor 5612 588 M 0 63 V 0 4220 R 0 -63 V stroke 5612 448 M [ [(Helvetica) 140.0 0.0 true true 0 ( 1)] ] -46.7 MCshow 1.000 UL LTb LCb setrgbcolor 1.000 UL LTb LCb setrgbcolor 686 4871 N 686 588 L 5374 0 V 0 4283 V -5374 0 V Z stroke LCb setrgbcolor 112 2729 M currentpoint gsave translate -270 rotate 0 0 moveto [ [(Helvetica) 140.0 0.0 true true 0 (x)] [(Helvetica) 112.0 -42.0 true true 0 (2)] ] -32.7 MCshow grestore LTb LCb setrgbcolor 3373 238 M [ [(Helvetica) 140.0 0.0 true true 0 (x)] [(Helvetica) 112.0 -42.0 true true 0 (1)] ] -32.7 MCshow LTb 0.300 UP 1.000 UL LTb LCb setrgbcolor % Begin plot #1 2.000 UL LT0 0 g 1 g 3374 4871 M 1 g 3374 4871 M -1 0 V 1 g 3373 4871 M -1 0 V 0 g .975 g 3711 4871 M .975 g 3711 4871 M -114 -27 V .975 g 3597 4844 M -224 -17 V .975 g 3373 4827 M -224 17 V .975 g 3149 4844 M -114 27 V 0 g .95 g 3869 4871 M .95 g 3869 4871 M -48 -19 V .95 g 3821 4852 M -224 -52 V .95 g 3597 4800 M -224 -17 V .95 g 3373 4783 M -224 17 V .95 g 3149 4800 M -224 52 V .95 g 2925 4852 M -48 19 V 0 g .925 g 703 588 M .925 g 703 588 M -17 29 V 0 g .925 g 3985 4871 M .925 g 3985 4871 M -164 -64 V .925 g 3821 4807 M -224 -51 V .925 g 3597 4756 M -224 -17 V .925 g 3373 4739 M -224 17 V .925 g 3149 4756 M -224 51 V .925 g 2925 4807 M -164 64 V 0 g .925 g 6060 617 M .925 g 6060 617 M -17 -29 V 0 g .9 g 730 588 M .9 g 730 588 M -44 74 V 0 g .9 g 4086 4871 M .9 g 4086 4871 M -41 -22 V .9 g 4045 4849 M -224 -86 V .9 g 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4045 4252 M -175 -66 V .6 g 3870 4186 M -49 -19 V .6 g 3821 4167 M -224 -53 V .6 g 3597 4114 M -224 -17 V .6 g 3373 4097 M -224 17 V .6 g 3149 4114 M -224 53 V .6 g 2925 4167 M -49 19 V .6 g 2876 4186 M -175 65 V .6 g 2701 4251 M -195 106 V .6 g 2506 4357 M -29 15 V .6 g 2477 4372 M -224 155 V .6 g 2253 4527 M -1 1 V .6 g 2252 4528 M -205 172 V .6 g 2047 4700 M -17 15 V .6 g 2030 4715 M -159 156 V 0 g .6 g 6060 1258 M .6 g 6060 1258 M -92 -156 V .6 g 5968 1102 M 5872 931 L .6 g 5872 931 M -36 -66 V .6 g 5836 865 M 5768 759 L .6 g 5768 759 M 5662 588 L 0 g .575 g 1117 588 M .575 g 1117 588 M 1014 759 L .575 g 1014 759 M 910 920 L .575 g 910 920 M -6 11 V .575 g 904 931 M -94 171 V .575 g 810 1102 M -99 171 V .575 g 711 1273 M -25 42 V 0 g .575 g 4930 4871 M .575 g 4930 4871 M 4758 4700 L .575 g 4758 4700 M -41 -41 V .575 g 4717 4659 M 4562 4528 L .575 g 4562 4528 M -69 -58 V .575 g 4493 4470 M 4328 4357 L .575 g 4328 4357 M -59 -41 V .575 g 4269 4316 M 4045 4197 L .575 g 4045 4197 M -29 -11 V .575 g 4016 4186 M -195 -76 V .575 g 3821 4110 M -224 -51 V .575 g 3597 4059 M -224 -17 V .575 g 3373 4042 M -224 17 V .575 g 3149 4059 M -224 51 V .575 g 2925 4110 M -195 76 V .575 g 2730 4186 M -29 11 V .575 g 2701 4197 M -224 119 V .575 g 2477 4316 M -59 41 V .575 g 2418 4357 M -165 113 V .575 g 2253 4470 M -70 58 V .575 g 2183 4528 M -153 130 V .575 g 2030 4658 M -42 42 V .575 g 1988 4700 M -172 171 V 0 g .575 g 6060 1314 M .575 g 6060 1314 M -24 -41 V .575 g 6036 1273 M 5936 1102 L .575 g 5936 1102 M 5842 931 L .575 g 5842 931 M -6 -11 V .575 g 5836 920 M 5733 759 L .575 g 5733 759 M 5629 588 L 0 g .55 g 1155 588 M .55 g 1155 588 M -21 30 V .55 g 1134 618 M -85 141 V .55 g 1049 759 M 940 931 L .55 g 940 931 M -30 47 V .55 g 910 978 M -68 124 V .55 g 842 1102 M -97 171 V .55 g 745 1273 M -59 99 V 0 g .55 g 4982 4871 M .55 g 4982 4871 M -42 -47 V .55 g 4940 4824 M 4817 4700 L .55 g 4817 4700 M -100 -99 V .55 g 4717 4601 M -87 -73 V .55 g 4630 4528 M 4493 4413 L .55 g 4493 4413 M -82 -56 V .55 g 4411 4357 M -142 -99 V .55 g 4269 4258 M -137 -72 V .55 g 4132 4186 M -87 -47 V .55 g 4045 4139 M -224 -86 V .55 g 3821 4053 M -173 -39 V .55 g 3648 4014 M -51 -12 V .55 g 3597 4002 M -224 -17 V .55 g 3373 3985 M -224 17 V .55 g 3149 4002 M -51 12 V .55 g 3098 4014 M -173 39 V .55 g 2925 4053 M -224 86 V .55 g 2701 4139 M -87 47 V .55 g 2614 4186 M -137 72 V .55 g 2477 4258 M -143 99 V .55 g 2334 4357 M -81 56 V .55 g 2253 4413 M -138 115 V .55 g 2115 4528 M -85 73 V .55 g 2030 4601 M -101 99 V .55 g 1929 4700 M -123 124 V .55 g 1806 4824 M -42 47 V 0 g .55 g 6060 1372 M .55 g 6060 1372 M -59 -99 V .55 g 6001 1273 M -97 -171 V .55 g 5904 1102 M 5836 978 L .55 g 5836 978 M -30 -47 V .55 g 5806 931 M 5697 759 L .55 g 5697 759 M 5612 618 L .55 g 5612 618 M -21 -30 V 0 g .525 g 1197 588 M .525 g 1197 588 M -63 89 V .525 g 1134 677 M -50 82 V .525 g 1084 759 M 978 931 L .525 g 978 931 M -68 106 V .525 g 910 1037 M -36 65 V .525 g 874 1102 M -95 171 V .525 g 779 1273 M -93 157 V 0 g .525 g 5034 4871 M .525 g 5034 4871 M -94 -106 V .525 g 4940 4765 M -65 -65 V .525 g 4875 4700 M 4717 4544 L .525 g 4717 4544 M -18 -16 V .525 g 4699 4528 M 4494 4357 L .525 g 4494 4357 M -1 -2 V .525 g 4493 4355 M 4269 4201 L .525 g 4269 4201 M -29 -15 V .525 g 4240 4186 M 4045 4080 L .525 g 4045 4080 M -175 -66 V .525 g 3870 4014 M -49 -19 V .525 g 3821 3995 M -224 -52 V .525 g 3597 3943 M -224 -17 V .525 g 3373 3926 M -224 17 V .525 g 3149 3943 M -224 52 V .525 g 2925 3995 M -49 19 V .525 g 2876 4014 M -175 66 V .525 g 2701 4080 M -195 106 V .525 g 2506 4186 M -29 15 V .525 g 2477 4201 M -224 154 V .525 g 2253 4355 M -2 2 V .525 g 2251 4357 M -204 171 V .525 g 2047 4528 M -17 15 V .525 g 2030 4543 M -159 157 V .525 g 1871 4700 M -65 65 V .525 g 1806 4765 M -94 106 V 0 g .525 g 6060 1429 M .525 g 6060 1429 M -93 -156 V .525 g 5967 1273 M -95 -171 V .525 g 5872 1102 M -36 -66 V .525 g 5836 1036 M 5768 931 L .525 g 5768 931 M 5662 759 L .525 g 5662 759 M -50 -82 V .525 g 5612 677 M -63 -89 V 0 g .5 g 1239 588 M .5 g 1239 588 M 1134 736 L .5 g 1134 736 M -14 23 V .5 g 1120 759 M 1016 931 L .5 g 1016 931 M 910 1095 L .5 g 910 1095 M -4 7 V .5 g 906 1102 M -93 171 V .5 g 813 1273 M 713 1445 L .5 g 713 1445 M -27 45 V 0 g .5 g 5086 4871 M .5 g 5086 4871 M 4940 4707 L .5 g 4940 4707 M -7 -7 V .5 g 4933 4700 M 4763 4528 L .5 g 4763 4528 M -46 -45 V .5 g 4717 4483 M 4567 4357 L .5 g 4567 4357 M -74 -63 V .5 g 4493 4294 M 4334 4186 L .5 g 4334 4186 M -65 -46 V .5 g 4269 4140 M 4045 4021 L .5 g 4045 4021 M -19 -7 V .5 g 4026 4014 M -205 -80 V .5 g 3821 3934 M -224 -51 V .5 g 3597 3883 M -224 -16 V .5 g 3373 3867 M -224 16 V .5 g 3149 3883 M -224 51 V .5 g 2925 3934 M -205 80 V .5 g 2720 4014 M -19 7 V .5 g 2701 4021 M -224 119 V .5 g 2477 4140 M -65 46 V .5 g 2412 4186 M -159 108 V .5 g 2253 4294 M -75 63 V .5 g 2178 4357 M -148 126 V .5 g 2030 4483 M -47 45 V .5 g 1983 4528 M -171 172 V .5 g 1812 4700 M -6 6 V .5 g 1806 4706 M -146 165 V 0 g .5 g 6060 1490 M .5 g 6060 1490 M -27 -45 V .5 g 6033 1445 M 5933 1273 L .5 g 5933 1273 M -93 -171 V .5 g 5840 1102 M -4 -7 V .5 g 5836 1095 M 5730 931 L .5 g 5730 931 M 5626 759 L .5 g 5626 759 M -14 -23 V .5 g 5612 736 M 5507 588 L 0 g .475 g 1281 588 M .475 g 1281 588 M 1161 759 L .475 g 1161 759 M -27 39 V .475 g 1134 798 M -80 133 V .475 g 1054 931 M 946 1102 L .475 g 946 1102 M -36 56 V .475 g 910 1158 M -63 115 V .475 g 847 1273 M -97 172 V .475 g 750 1445 M -64 107 V 0 g .475 g 5138 4871 M .475 g 5138 4871 M 4990 4700 L .475 g 4990 4700 M -50 -56 V .475 g 4940 4644 M 4825 4528 L .475 g 4825 4528 M 4717 4421 L .475 g 4717 4421 M -77 -64 V .475 g 4640 4357 M 4493 4233 L .475 g 4493 4233 M -70 -47 V .475 g 4423 4186 M 4269 4079 L .475 g 4269 4079 M -122 -65 V .475 g 4147 4014 M -102 -55 V .475 g 4045 3959 M -224 -85 V .475 g 3821 3874 M -137 -31 V .475 g 3684 3843 M -87 -20 V .475 g 3597 3823 M -224 -18 V .475 g 3373 3805 M -224 17 V .475 g 3149 3822 M -87 21 V .475 g 3062 3843 M -137 31 V .475 g 2925 3874 M -224 85 V .475 g 2701 3959 M -102 55 V .475 g 2599 4014 M -122 65 V .475 g 2477 4079 M -155 107 V .475 g 2322 4186 M -69 47 V .475 g 2253 4233 M -148 124 V .475 g 2105 4357 M -75 64 V .475 g 2030 4421 M -109 107 V .475 g 1921 4528 M -115 116 V .475 g 1806 4644 M -50 56 V .475 g 1756 4700 M -148 171 V 0 g .475 g 6060 1552 M .475 g 6060 1552 M -64 -107 V .475 g 5996 1445 M -97 -172 V .475 g 5899 1273 M -63 -116 V .475 g 5836 1157 M -36 -55 V .475 g 5800 1102 M 5692 931 L .475 g 5692 931 M 5612 797 L .475 g 5612 797 M -27 -38 V .475 g 5585 759 M 5465 588 L 0 g .45 g 1323 588 M .45 g 1323 588 M 1206 759 L .45 g 1206 759 M -72 102 V .45 g 1134 861 M -42 70 V .45 g 1092 931 M 987 1102 L .45 g 987 1102 M -77 119 V .45 g 910 1221 M -29 52 V .45 g 881 1273 M -94 172 V .45 g 787 1445 M 686 1614 L 0 g .45 g 5190 4871 M .45 g 5190 4871 M -26 -32 V .45 g 5164 4839 M 5046 4700 L .45 g 5046 4700 M 4940 4581 L .45 g 4940 4581 M -52 -53 V .45 g 4888 4528 M 4717 4360 L .45 g 4717 4360 M -4 -3 V .45 g 4713 4357 M 4510 4186 L .45 g 4510 4186 M -17 -15 V .45 g 4493 4171 M 4269 4017 L .45 g 4269 4017 M -5 -3 V .45 g 4264 4014 M 4045 3896 L .45 g 4045 3896 M -141 -53 V .45 g 3904 3843 M -83 -32 V .45 g 3821 3811 M -224 -52 V .45 g 3597 3759 M -224 -18 V .45 g 3373 3741 M -224 18 V .45 g 3149 3759 M -224 52 V .45 g 2925 3811 M -83 32 V .45 g 2842 3843 M -141 53 V .45 g 2701 3896 M -219 118 V .45 g 2482 4014 M -5 3 V .45 g 2477 4017 M -224 154 V .45 g 2253 4171 M -17 15 V .45 g 2236 4186 M -203 171 V .45 g 2033 4357 M -3 3 V .45 g 2030 4360 M -172 168 V .45 g 1858 4528 M -52 53 V .45 g 1806 4581 M -106 119 V .45 g 1700 4700 M -118 138 V .45 g 1582 4838 M -26 33 V 0 g .45 g 6060 1613 M .45 g 6060 1613 M 5959 1445 L .45 g 5959 1445 M -94 -172 V .45 g 5865 1273 M -29 -53 V .45 g 5836 1220 M -77 -118 V .45 g 5759 1102 M 5654 931 L .45 g 5654 931 M -42 -70 V .45 g 5612 861 M 5540 759 L .45 g 5540 759 M 5423 588 L 0 g .425 g 1367 588 M .425 g 1367 588 M -9 11 V .425 g 1358 599 M 1251 759 L .425 g 1251 759 M 1134 925 L .425 g 1134 925 M -4 6 V .425 g 1130 931 M -102 171 V .425 g 1028 1102 M 917 1273 L .425 g 917 1273 M -7 12 V .425 g 910 1285 M -87 160 V .425 g 823 1445 M -99 171 V .425 g 724 1616 M -38 64 V 0 g .425 g 5242 4871 M .425 g 5242 4871 M -78 -98 V .425 g 5164 4773 M -63 -73 V .425 g 5101 4700 M 4950 4528 L .425 g 4950 4528 M -10 -11 V .425 g 4940 4517 M 4781 4357 L .425 g 4781 4357 M -64 -63 V .425 g 4717 4294 M 4589 4186 L .425 g 4589 4186 M -96 -81 V .425 g 4493 4105 M -132 -91 V .425 g 4361 4014 M -92 -63 V .425 g 4269 3951 M 4065 3843 L .425 g 4065 3843 M -20 -11 V .425 g 4045 3832 M -224 -87 V .425 g 3821 3745 M -224 -50 V .425 g 3597 3695 M -224 -17 V .425 g 3373 3678 M -224 17 V .425 g 3149 3695 M -224 50 V .425 g 2925 3745 M -224 87 V .425 g 2701 3832 M -20 11 V .425 g 2681 3843 M -204 108 V .425 g 2477 3951 M -92 63 V .425 g 2385 4014 M -132 91 V .425 g 2253 4105 M -96 81 V .425 g 2157 4186 M -127 107 V .425 g 2030 4293 M -65 64 V .425 g 1965 4357 M -159 160 V .425 g 1806 4517 M -10 11 V .425 g 1796 4528 M -152 172 V .425 g 1644 4700 M -62 73 V .425 g 1582 4773 M -78 98 V 0 g .425 g 6060 1679 M .425 g 6060 1679 M -38 -63 V .425 g 6022 1616 M -99 -171 V .425 g 5923 1445 M -87 -161 V .425 g 5836 1284 M -7 -11 V .425 g 5829 1273 M 5718 1102 L .425 g 5718 1102 M 5616 931 L .425 g 5616 931 M -4 -7 V .425 g 5612 924 M 5495 759 L .425 g 5495 759 M 5388 599 L .425 g 5388 599 M -8 -11 V 0 g .4 g 1420 588 M .4 g 1420 588 M -62 79 V .4 g 1358 667 M -61 92 V .4 g 1297 759 M 1178 931 L .4 g 1178 931 M -44 62 V .4 g 1134 993 M -65 109 V .4 g 1069 1102 M 961 1273 L .4 g 961 1273 M -51 80 V .4 g 910 1353 M -50 92 V .4 g 860 1445 M -96 171 V .4 g 764 1616 M -78 130 V 0 g .4 g 5293 4871 M .4 g 5293 4871 M 5164 4708 L .4 g 5164 4708 M -7 -8 V .4 g 5157 4700 M 5011 4528 L .4 g 5011 4528 M -71 -79 V .4 g 4940 4449 M -91 -92 V .4 g 4849 4357 M 4717 4227 L .4 g 4717 4227 M -50 -41 V .4 g 4667 4186 M 4493 4039 L .4 g 4493 4039 M -36 -25 V .4 g 4457 4014 M 4269 3884 L .4 g 4269 3884 M -79 -41 V .4 g 4190 3843 M -145 -79 V .4 g 4045 3764 M -224 -84 V .4 g 3821 3680 M -36 -8 V .4 g 3785 3672 M -188 -45 V .4 g 3597 3627 M -224 -17 V .4 g 3373 3610 M -224 17 V .4 g 3149 3627 M -188 45 V .4 g 2961 3672 M -36 8 V .4 g 2925 3680 M -224 84 V .4 g 2701 3764 M -146 79 V .4 g 2555 3843 M -78 41 V .4 g 2477 3884 M -188 130 V .4 g 2289 4014 M -36 25 V .4 g 2253 4039 M -175 147 V .4 g 2078 4186 M -48 41 V .4 g 2030 4227 M -133 130 V .4 g 1897 4357 M -91 92 V .4 g 1806 4449 M -71 79 V .4 g 1735 4528 M -147 172 V .4 g 1588 4700 M -6 8 V .4 g 1582 4708 M -129 163 V 0 g .4 g 6060 1746 M .4 g 6060 1746 M -78 -130 V .4 g 5982 1616 M -96 -171 V .4 g 5886 1445 M -50 -93 V .4 g 5836 1352 M -51 -79 V .4 g 5785 1273 M 5678 1102 L .4 g 5678 1102 M 5612 992 L .4 g 5612 992 M -44 -61 V .4 g 5568 931 M 5450 759 L .4 g 5450 759 M -62 -92 V .4 g 5388 667 M -62 -79 V 0 g .375 g 1474 588 M .375 g 1474 588 M 1358 735 L .375 g 1358 735 M -16 24 V .375 g 1342 759 M 1227 931 L .375 g 1227 931 M -93 130 V .375 g 1134 1061 M -25 41 V .375 g 1109 1102 M -103 171 V .375 g 1006 1273 M -96 147 V .375 g 910 1420 M -13 25 V .375 g 897 1445 M -93 171 V .375 g 804 1616 M 702 1787 L .375 g 702 1787 M -16 28 V 0 g .375 g 5345 4871 M .375 g 5345 4871 M 5213 4700 L .375 g 5213 4700 M -49 -62 V .375 g 5164 4638 M -93 -110 V .375 g 5071 4528 M 4940 4381 L .375 g 4940 4381 M -24 -24 V .375 g 4916 4357 M 4744 4186 L .375 g 4744 4186 M -27 -27 V .375 g 4717 4159 M 4546 4014 L .375 g 4546 4014 M -53 -44 V .375 g 4493 3970 M 4308 3843 L .375 g 4308 3843 M -39 -27 V .375 g 4269 3816 M 4045 3696 L .375 g 4045 3696 M -65 -24 V .375 g 3980 3672 M -159 -62 V .375 g 3821 3610 M -224 -52 V .375 g 3597 3558 M -224 -17 V .375 g 3373 3541 M -224 17 V .375 g 3149 3558 M -224 52 V .375 g 2925 3610 M -159 62 V .375 g 2766 3672 M -65 24 V .375 g 2701 3696 M -224 120 V .375 g 2477 3816 M -39 27 V .375 g 2438 3843 M -185 127 V .375 g 2253 3970 M -53 44 V .375 g 2200 4014 M -170 144 V .375 g 2030 4158 M -28 28 V .375 g 2002 4186 M -172 171 V .375 g 1830 4357 M -24 24 V .375 g 1806 4381 M -131 147 V .375 g 1675 4528 M -93 109 V .375 g 1582 4637 M -50 63 V .375 g 1532 4700 M -131 171 V 0 g .375 g 6060 1814 M .375 g 6060 1814 M -16 -27 V .375 g 6044 1787 M 5943 1616 L .375 g 5943 1616 M -94 -171 V .375 g 5849 1445 M -13 -25 V .375 g 5836 1420 M -96 -147 V .375 g 5740 1273 M 5637 1102 L .375 g 5637 1102 M -25 -41 V .375 g 5612 1061 M 5519 931 L .375 g 5519 931 M 5404 759 L .375 g 5404 759 M -16 -24 V .375 g 5388 735 M 5272 588 L 0 g .35 g 1528 588 M .35 g 1528 588 M 1395 759 L .35 g 1395 759 M -37 48 V .35 g 1358 807 M -82 124 V .35 g 1276 931 M -121 171 V .35 g 1155 1102 M -21 30 V .35 g 1134 1132 M -84 141 V .35 g 1050 1273 M 941 1445 L .35 g 941 1445 M -31 47 V .35 g 910 1492 M -67 124 V .35 g 843 1616 M -97 171 V .35 g 746 1787 M -60 100 V 0 g .35 g 5397 4871 M .35 g 5397 4871 M -9 -12 V .35 g 5388 4859 M 5269 4700 L .35 g 5269 4700 M 5164 4567 L .35 g 5164 4567 M -33 -39 V .35 g 5131 4528 M 4983 4357 L .35 g 4983 4357 M -43 -47 V .35 g 4940 4310 M 4817 4186 L .35 g 4817 4186 M -100 -99 V .35 g 4717 4087 M -86 -73 V .35 g 4631 4014 M 4493 3898 L .35 g 4493 3898 M -81 -55 V .35 g 4412 3843 M -143 -99 V .35 g 4269 3744 M -137 -72 V .35 g 4132 3672 M -87 -48 V .35 g 4045 3624 M -224 -85 V .35 g 3821 3539 M -173 -39 V .35 g 3648 3500 M -51 -12 V .35 g 3597 3488 M -224 -17 V .35 g 3373 3471 M -224 17 V .35 g 3149 3488 M -51 12 V .35 g 3098 3500 M -173 39 V .35 g 2925 3539 M -224 85 V .35 g 2701 3624 M -87 48 V .35 g 2614 3672 M -137 72 V .35 g 2477 3744 M -143 99 V .35 g 2334 3843 M -81 55 V .35 g 2253 3898 M -138 116 V .35 g 2115 4014 M -85 72 V .35 g 2030 4086 M -102 100 V .35 g 1928 4186 M -122 123 V .35 g 1806 4309 M -43 48 V .35 g 1763 4357 M -149 171 V .35 g 1614 4528 M -32 39 V .35 g 1582 4567 M -106 133 V .35 g 1476 4700 M -118 159 V .35 g 1358 4859 M -9 12 V 0 g .35 g 6060 1886 M .35 g 6060 1886 M -60 -99 V .35 g 6000 1787 M -97 -171 V .35 g 5903 1616 M -67 -124 V .35 g 5836 1492 M -31 -47 V .35 g 5805 1445 M 5696 1273 L .35 g 5696 1273 M -84 -141 V .35 g 5612 1132 M -21 -30 V .35 g 5591 1102 M 5470 931 L .35 g 5470 931 M 5388 807 L .35 g 5388 807 M -37 -48 V .35 g 5351 759 M 5218 588 L 0 g .325 g 1582 588 M .325 g 1582 588 M 1454 759 L .325 g 1454 759 M -96 122 V .325 g 1358 881 M -33 50 V .325 g 1325 931 M -116 171 V .325 g 1209 1102 M -75 105 V .325 g 1134 1207 M -40 66 V .325 g 1094 1273 M 989 1445 L .325 g 989 1445 M -79 121 V .325 g 910 1566 M -27 50 V .325 g 883 1616 M -94 171 V .325 g 789 1787 M 686 1959 L .325 g 0 g .325 g 5451 4871 M .325 g 5451 4871 M -63 -87 V .325 g 5388 4784 M -62 -84 V .325 g 5326 4700 M 5192 4528 L .325 g 5192 4528 M -28 -35 V .325 g 5164 4493 M 5048 4357 L .325 g 5048 4357 M 4940 4236 L .325 g 4940 4236 M -49 -50 V .325 g 4891 4186 M 4717 4015 L .325 g 4717 4015 M -1 -1 V .325 g 4716 4014 M 4514 3843 L .325 g 4514 3843 M -21 -17 V .325 g 4493 3826 M 4269 3672 L .325 g 4269 3672 M -1 0 V .325 g 4268 3672 M 4045 3551 L .325 g 4045 3551 M -134 -51 V .325 g 3911 3500 M -90 -35 V .325 g 3821 3465 M -224 -52 V .325 g 3597 3413 M -224 -17 V .325 g 3373 3396 M -224 17 V .325 g 3149 3413 M -224 52 V .325 g 2925 3465 M -90 35 V .325 g 2835 3500 M -134 50 V .325 g 2701 3550 M -223 122 V .325 g 2478 3672 M -1 0 V .325 g 2477 3672 M -224 153 V .325 g 2253 3825 M -21 18 V .325 g 2232 3843 M -202 171 V .325 g 2030 4014 M 0 1 V .325 g 2030 4015 M -175 171 V .325 g 1855 4186 M -49 50 V .325 g 1806 4236 M -109 121 V .325 g 1697 4357 M -115 136 V .325 g 1582 4493 M -28 35 V .325 g 1554 4528 M -134 172 V .325 g 1420 4700 M -62 83 V .325 g 1358 4783 M -63 88 V 0 g .325 g 6060 1958 M .325 g 6060 1958 M 5957 1787 L .325 g 5957 1787 M -94 -171 V .325 g 5863 1616 M -27 -50 V .325 g 5836 1566 M -79 -121 V .325 g 5757 1445 M 5652 1273 L .325 g 5652 1273 M -40 -67 V .325 g 5612 1206 M -74 -104 V .325 g 5538 1102 M 5421 931 L .325 g 5421 931 M -33 -51 V .325 g 5388 880 M 5292 759 L .325 g 5292 759 M 5165 588 L 0 g .3 g 1652 588 M .3 g 1652 588 M -70 79 V .3 g 1582 667 M -69 92 V .3 g 1513 759 M 1379 931 L .3 g 1379 931 M -21 26 V .3 g 1358 957 M -96 145 V .3 g 1262 1102 M -122 171 V .3 g 1140 1273 M -6 9 V .3 g 1134 1282 M -96 163 V .3 g 1038 1445 M 927 1616 L .3 g 927 1616 M -17 26 V .3 g 910 1642 M -78 145 V .3 g 832 1787 M -98 172 V .3 g 734 1959 M -48 78 V 0 g .3 g 5505 4871 M .3 g 5505 4871 M 5388 4709 L .3 g 5388 4709 M -6 -9 V .3 g 5382 4700 M 5254 4528 L .3 g 5254 4528 M -90 -112 V .3 g 5164 4416 M -50 -59 V .3 g 5114 4357 M 4964 4186 L .3 g 4964 4186 M -24 -26 V .3 g 4940 4160 M 4796 4014 L .3 g 4796 4014 M -79 -78 V .3 g 4717 3936 M -111 -93 V .3 g 4606 3843 M -113 -95 V .3 g 4493 3748 M -111 -76 V .3 g 4382 3672 M -113 -79 V .3 g 4269 3593 M -176 -93 V .3 g 4093 3500 M -48 -26 V .3 g 4045 3474 M -224 -86 V .3 g 3821 3388 M -224 -50 V .3 g 3597 3338 M -121 -9 V .3 g 3476 3329 M -103 -8 V .3 g 3373 3321 M -103 8 V .3 g 3270 3329 M -121 9 V .3 g 3149 3338 M -224 50 V .3 g 2925 3388 M -224 86 V .3 g 2701 3474 M -48 26 V .3 g 2653 3500 M -176 93 V .3 g 2477 3593 M -113 79 V .3 g 2364 3672 M -111 76 V .3 g 2253 3748 M -114 95 V .3 g 2139 3843 M -109 93 V .3 g 2030 3936 M -81 78 V .3 g 1949 4014 M -143 146 V .3 g 1806 4160 M -24 26 V .3 g 1782 4186 M -150 171 V .3 g 1632 4357 M -50 59 V .3 g 1582 4416 M -90 112 V .3 g 1492 4528 M -128 172 V .3 g 1364 4700 M -6 8 V .3 g 1358 4708 M -117 163 V 0 g .3 g 6060 2037 M .3 g 6060 2037 M -47 -78 V .3 g 6013 1959 M -99 -172 V .3 g 5914 1787 M -78 -145 V .3 g 5836 1642 M -17 -26 V .3 g 5819 1616 M 5709 1445 L .3 g 5709 1445 M -97 -164 V .3 g 5612 1281 M -6 -8 V .3 g 5606 1273 M 5484 1102 L .3 g 5484 1102 M 5388 957 L .3 g 5388 957 M -20 -26 V .3 g 5368 931 M 5234 759 L .3 g 5234 759 M -70 -93 V .3 g 5164 666 M -69 -78 V 0 g .275 g 1722 588 M .275 g 1722 588 M 1582 745 L .275 g 1582 745 M -11 14 V .275 g 1571 759 M 1443 931 L .275 g 1443 931 M -85 107 V .275 g 1358 1038 M -43 64 V .275 g 1315 1102 M -116 171 V .275 g 1199 1273 M -65 90 V .275 g 1134 1363 M -48 82 V .275 g 1086 1445 M 980 1616 L .275 g 980 1616 M -70 107 V .275 g 910 1723 M -34 64 V .275 g 876 1787 M -95 172 V .275 g 781 1959 M -95 157 V 0 g .275 g 5558 4871 M .275 g 5558 4871 M 5440 4700 L .275 g 5440 4700 M -52 -73 V .275 g 5388 4627 M -73 -99 V .275 g 5315 4528 M 5180 4357 L .275 g 5180 4357 M -16 -20 V .275 g 5164 4337 M 5036 4186 L .275 g 5036 4186 M -96 -107 V .275 g 4940 4079 M -64 -65 V .275 g 4876 4014 M 4717 3858 L .275 g 4717 3858 M -18 -15 V .275 g 4699 3843 M 4495 3672 L .275 g 4495 3672 M -2 -2 V .275 g 4493 3670 M 4269 3515 L .275 g 4269 3515 M -28 -15 V .275 g 4241 3500 M 4045 3394 L .275 g 4045 3394 M -173 -65 V .275 g 3872 3329 M -51 -20 V .275 g 3821 3309 M -224 -53 V .275 g 3597 3256 M -224 -17 V .275 g 3373 3239 M -224 17 V .275 g 3149 3256 M -224 53 V .275 g 2925 3309 M -51 20 V .275 g 2874 3329 M -173 65 V .275 g 2701 3394 M -197 106 V .275 g 2504 3500 M -27 15 V .275 g 2477 3515 M -224 154 V .275 g 2253 3669 M -2 3 V .275 g 2251 3672 M -205 171 V .275 g 2046 3843 M -16 14 V .275 g 2030 3857 M -161 157 V .275 g 1869 4014 M -63 65 V .275 g 1806 4079 M -96 107 V .275 g 1710 4186 M -128 151 V .275 g 1582 4337 M -16 20 V .275 g 1566 4357 M -135 171 V .275 g 1431 4528 M -73 99 V .275 g 1358 4627 M -53 73 V .275 g 1305 4700 M -118 171 V 0 g .275 g 6060 2115 M .275 g 6060 2115 M -95 -156 V .275 g 5965 1959 M -94 -172 V .275 g 5871 1787 M -35 -64 V .275 g 5836 1723 M -70 -107 V .275 g 5766 1616 M 5660 1445 L .275 g 5660 1445 M -48 -82 V .275 g 5612 1363 M -64 -90 V .275 g 5548 1273 M 5431 1102 L .275 g 5431 1102 M -43 -65 V .275 g 5388 1037 M 5303 931 L .275 g 5303 931 M 5175 759 L .275 g 5175 759 M -11 -14 V .275 g 5164 745 M 5024 588 L 0 g .25 g 1792 588 M .25 g 1792 588 M 1645 759 L .25 g 1645 759 M -63 71 V .25 g 1582 830 M -75 101 V .25 g 1507 931 M -135 171 V .25 g 1372 1102 M -14 18 V .25 g 1358 1120 M -101 153 V .25 g 1257 1273 M -123 172 V .25 g .25 g 1134 1445 M -101 171 V .25 g 1033 1616 M 922 1787 L .25 g 922 1787 M -12 19 V .25 g 910 1806 M -81 153 V .25 g 829 1959 M 729 2130 L .25 g 729 2130 M -43 71 V 0 g .25 g 5612 4871 M .25 g 5612 4871 M 5500 4700 L .25 g 5500 4700 M 5388 4545 L .25 g 5388 4545 M -12 -17 V .25 g 5376 4528 M 5248 4357 L .25 g 5248 4357 M -84 -105 V .25 g 5164 4252 M -56 -66 V .25 g 5108 4186 M 4956 4014 L .25 g 4956 4014 M -16 -18 V .25 g 4940 3996 M 4789 3843 L .25 g 4789 3843 M -72 -71 V .25 g 4717 3772 M 4597 3672 L .25 g 4597 3672 M -104 -88 V .25 g 4493 3584 M -122 -84 V .25 g 4371 3500 M -102 -70 V .25 g 4269 3430 M 4078 3329 L .25 g 4078 3329 M -33 -18 V .25 g 4045 3311 M -224 -87 V .25 g 3821 3224 M -224 -50 V .25 g 3597 3174 M -223 -16 V .25 g 3374 3158 M -1 0 V .25 g 3373 3158 M -1 0 V .25 g 3372 3158 M -223 16 V .25 g 3149 3174 M -224 50 V .25 g 2925 3224 M -224 87 V .25 g 2701 3311 M -33 18 V .25 g 2668 3329 M -191 101 V .25 g 2477 3430 M -102 70 V .25 g 2375 3500 M -122 84 V .25 g 2253 3584 M -105 88 V .25 g 2148 3672 M -118 100 V .25 g 2030 3772 M -73 71 V .25 g 1957 3843 M -151 153 V .25 g 1806 3996 M -17 18 V .25 g 1789 4014 M -151 172 V .25 g 1638 4186 M -56 66 V .25 g 1582 4252 M -84 105 V .25 g 1498 4357 M -128 171 V .25 g 1370 4528 M -12 16 V .25 g 1358 4544 M -112 156 V .25 g 1246 4700 M -112 171 V .25 g 0 g .25 g 6060 2200 M .25 g 6060 2200 M -43 -70 V .25 g 6017 2130 M -99 -171 V .25 g 5918 1959 M -82 -154 V .25 g 5836 1805 M -12 -18 V .25 g 5824 1787 M 5713 1616 L .25 g 5713 1616 M 5612 1445 L .25 g 5612 1445 M 5489 1273 L .25 g 5489 1273 M 5388 1120 L .25 g 5388 1120 M -14 -18 V .25 g 5374 1102 M 5239 931 L .25 g 5239 931 M 5164 830 L .25 g 5164 830 M -63 -71 V .25 g 5101 759 M 4954 588 L 0 g .225 g 1880 588 M .225 g 1880 588 M -74 73 V .225 g 1806 661 M -84 98 V .225 g 1722 759 M 1582 917 L .225 g 1582 917 M -11 14 V .225 g 1571 931 M -127 171 V .225 g 1444 1102 M -86 107 V .225 g 1358 1209 M -42 64 V .225 g 1316 1273 M -117 172 V .225 g 1199 1445 M -65 90 V .225 g 1134 1535 M -48 81 V .225 g 1086 1616 M 981 1787 L .225 g 981 1787 M -71 108 V .225 g 910 1895 M -34 64 V .225 g 876 1959 M -94 171 V .225 g 782 2130 M -96 157 V 0 g .225 g 5672 4871 M .225 g 5672 4871 M -60 -90 V .225 g 5612 4781 M -53 -81 V .225 g 5559 4700 M 5441 4528 L .225 g 5441 4528 M -53 -73 V .225 g 5388 4455 M -73 -98 V .225 g 5315 4357 M 5181 4186 L .225 g 5181 4186 M -17 -21 V .225 g 5164 4165 M 5036 4014 L .225 g 5036 4014 M -96 -107 V .225 g 4940 3907 M -63 -64 V .225 g 4877 3843 M 4717 3686 L .225 g 4717 3686 M -17 -14 V .225 g 4700 3672 M 4495 3500 L .225 g 4495 3500 M -2 -2 V .225 g 4493 3498 M 4269 3343 L .225 g 4269 3343 M -27 -14 V .225 g 4242 3329 M 4045 3222 L .225 g 4045 3222 M -172 -64 V .225 g 3873 3158 M -52 -21 V .225 g 3821 3137 M -224 -52 V .225 g 3597 3085 M -224 -17 V .225 g 3373 3068 M -224 17 V .225 g 3149 3085 M -224 52 V .225 g 2925 3137 M -52 21 V .225 g 2873 3158 M -172 64 V .225 g 2701 3222 M -197 107 V .225 g 2504 3329 M -27 14 V .225 g 2477 3343 M -224 155 V .225 g 2253 3498 M -3 2 V .225 g 2250 3500 M -204 172 V .225 g 2046 3672 M -16 14 V .225 g 2030 3686 M -161 157 V .225 g 1869 3843 M -63 64 V .225 g 1806 3907 M -97 107 V .225 g 1709 4014 M -127 151 V .225 g 1582 4165 M -17 21 V .225 g 1565 4186 M -135 171 V .225 g 1430 4357 M -72 98 V .225 g 1358 4455 M -53 73 V .225 g 1305 4528 M -118 172 V .225 g 1187 4700 M -53 80 V .225 g 1134 4780 M -60 91 V 0 g .225 g 6060 2287 M .225 g 6060 2287 M -96 -157 V .225 g 5964 2130 M -94 -171 V .225 g 5870 1959 M -34 -65 V .225 g 5836 1894 M -71 -107 V .225 g 5765 1787 M 5660 1616 L .225 g 5660 1616 M -48 -81 V .225 g 5612 1535 M -65 -90 V .225 g 5547 1445 M 5430 1273 L .225 g 5430 1273 M -42 -64 V .225 g 5388 1209 M -85 -107 V .225 g 5303 1102 M 5175 931 L .225 g 5175 931 M -11 -15 V .225 g 5164 916 M 5024 759 L .225 g 5024 759 M -84 -98 V .225 g 4940 661 M -74 -73 V 0 g .2 g 1974 588 M .2 g 1974 588 M 1806 752 L .2 g 1806 752 M -6 7 V .2 g 1800 759 M 1654 931 L .2 g 1654 931 M -72 80 V .2 g 1582 1011 M -67 91 V .2 g 1515 1102 M -135 171 V .2 g 1380 1273 M -22 29 V .2 g 1358 1302 M -94 143 V .2 g 1264 1445 M -123 171 V .2 g 1141 1616 M -7 10 V .2 g 1134 1626 M -94 161 V .2 g 1040 1787 M 929 1959 L .2 g 929 1959 M -19 28 V .2 g 910 1987 M -76 143 V .2 g 834 2130 M -98 171 V .2 g 736 2301 M -50 81 V 0 g .2 g 5731 4871 M .2 g 5731 4871 M 5619 4700 L .2 g 5619 4700 M -7 -10 V .2 g 5612 4690 M 5507 4528 L .2 g 5507 4528 M 5388 4364 L .2 g 5388 4364 M -5 -7 V .2 g 5383 4357 M 5256 4186 L .2 g 5256 4186 M -92 -115 V .2 g 5164 4071 M -48 -57 V .2 g 5116 4014 M 4966 3843 L .2 g 4966 3843 M -26 -28 V .2 g 4940 3815 M 4799 3672 L .2 g 4799 3672 M -82 -81 V .2 g 4717 3591 M -108 -91 V .2 g 4609 3500 M -116 -97 V .2 g 4493 3403 M -108 -74 V .2 g 4385 3329 M -116 -80 V .2 g 4269 3249 M -173 -91 V .2 g 4096 3158 M -51 -28 V .2 g 4045 3130 M -224 -87 V .2 g 3821 3043 M -224 -49 V .2 g 3597 2994 M -98 -8 V .2 g 3499 2986 M -126 -10 V .2 g 3373 2976 M -126 10 V .2 g 3247 2986 M -98 8 V .2 g 3149 2994 M -224 49 V .2 g 2925 3043 M -224 87 V .2 g 2701 3130 M -51 28 V .2 g 2650 3158 M -173 90 V .2 g 2477 3248 M -116 81 V .2 g 2361 3329 M -108 74 V .2 g 2253 3403 M -116 97 V .2 g 2137 3500 M -107 91 V .2 g 2030 3591 M -83 81 V .2 g 1947 3672 M -141 143 V .2 g 1806 3815 M -26 28 V .2 g 1780 3843 M -150 171 V .2 g 1630 4014 M -48 57 V .2 g 1582 4071 M -92 115 V .2 g 1490 4186 M -127 171 V .2 g 1363 4357 M -5 7 V .2 g 1358 4364 M -119 164 V .2 g 1239 4528 M -105 161 V .2 g 1134 4689 M -7 11 V .2 g 1127 4700 M -113 171 V 0 g .2 g 6060 2382 M .2 g 6060 2382 M -49 -81 V .2 g 6011 2301 M -99 -171 V .2 g 5912 2130 M -76 -143 V .2 g 5836 1987 M -19 -28 V .2 g 5817 1959 M 5706 1787 L .2 g 5706 1787 M -94 -161 V .2 g 5612 1626 M -7 -10 V .2 g 5605 1616 M 5482 1445 L .2 g 5482 1445 M -94 -144 V .2 g 5388 1301 M -22 -28 V .2 g 5366 1273 M 5232 1102 L .2 g 5232 1102 M -68 -91 V .2 g 5164 1011 M -72 -80 V .2 g 5092 931 M 4947 759 L .2 g 4947 759 M -7 -7 V .2 g 4940 752 M 4773 588 L 0 g .175 g 2080 588 M .175 g 2080 588 M -50 42 V .175 g 2030 630 M 1902 759 L .175 g 1902 759 M -96 95 V .175 g 1806 854 M -66 77 V .175 g 1740 931 M -153 171 V .175 g 1587 1102 M -5 6 V .175 g 1582 1108 M -122 165 V .175 g 1460 1273 M -102 128 V .175 g 1358 1401 M -29 44 V .175 g 1329 1445 M -114 171 V .175 g 1215 1616 M -81 111 V .175 g 1134 1727 M -35 60 V .175 g 1099 1787 M 995 1959 L .175 g 995 1959 M -85 128 V .175 g 910 2087 M -23 43 V .175 g 887 2130 M -92 171 V .175 g 795 2301 M 690 2473 L .175 g 690 2473 M -4 6 V 0 g .175 g 5791 4871 M .175 g 5791 4871 M 5686 4700 L .175 g 5686 4700 M -74 -111 V .175 g 5612 4589 M -39 -61 V .175 g 5573 4528 M 5457 4357 L .175 g 5457 4357 M -69 -94 V .175 g 5388 4263 M -57 -77 V .175 g 5331 4186 M 5198 4014 L .175 g 5198 4014 M -34 -41 V .175 g 5164 3973 M 5055 3843 L .175 g 5055 3843 M 4940 3715 L .175 g 4940 3715 M -43 -43 V .175 g 4897 3672 M 4723 3500 L .175 g 4723 3500 M -6 -6 V .175 g 4717 3494 M 4521 3329 L .175 g 4521 3329 M -28 -24 V .175 g 4493 3305 M 4277 3158 L .175 g 4277 3158 M -8 -6 V .175 g 4269 3152 M 4045 3030 L .175 g 4045 3030 M -118 -44 V .175 g 3927 2986 M -106 -41 V .175 g 3821 2945 M -224 -53 V .175 g 3597 2892 M -224 -16 V .175 g 3373 2876 M -224 16 V .175 g 3149 2892 M -224 52 V .175 g 2925 2944 M -106 42 V .175 g 2819 2986 M -118 44 V .175 g 2701 3030 M -224 122 V .175 g 2477 3152 M -9 6 V .175 g 2468 3158 M -215 147 V .175 g 2253 3305 M -29 24 V .175 g 2224 3329 M -194 165 V .175 g 2030 3494 M -7 6 V .175 g 2023 3500 M -174 172 V .175 g 1849 3672 M -43 43 V .175 g 1806 3715 M -115 128 V .175 g 1691 3843 M -109 129 V .175 g 1582 3972 M -34 42 V .175 g 1548 4014 M -133 172 V .175 g 1415 4186 M -57 77 V .175 g 1358 4263 M -69 94 V .175 g 1289 4357 M -116 171 V .175 g 1173 4528 M -39 60 V .175 g 1134 4588 M -74 112 V .175 g 1060 4700 M 955 4871 L 0 g .175 g 6060 2479 M .175 g 6060 2479 M -4 -6 V .175 g 6056 2473 M 5952 2301 L .175 g 5952 2301 M -93 -171 V .175 g 5859 2130 M -23 -44 V .175 g 5836 2086 M -85 -127 V .175 g 5751 1959 M 5648 1787 L .175 g 5648 1787 M -36 -60 V .175 g 5612 1727 M -80 -111 V .175 g 5532 1616 M 5417 1445 L .175 g 5417 1445 M -29 -44 V .175 g 5388 1401 M 5286 1273 L .175 g 5286 1273 M 5164 1108 L .175 g 5164 1108 M -5 -6 V .175 g 5159 1102 M 5006 931 L .175 g 5006 931 M -66 -78 V .175 g 4940 853 M -96 -94 V .175 g 4844 759 M 4717 630 L .175 g 4717 630 M -51 -42 V 0 g .15 g 2206 588 M .15 g 2206 588 M 2030 736 L .15 g 2030 736 M -24 23 V .15 g 2006 759 M 1835 931 L .15 g 1835 931 M -29 28 V .15 g 1806 959 M -121 143 V .15 g 1685 1102 M -103 115 V .15 g 1582 1217 M -42 56 V .15 g 1540 1273 M -131 172 V .15 g 1409 1445 M -51 63 V .15 g 1358 1508 M -70 108 V .15 g 1288 1616 M -120 171 V .15 g 1168 1787 M -34 46 V .15 g 1134 1833 M -73 126 V .15 g 1061 1959 M 953 2130 L .15 g 953 2130 M -43 64 V .15 g 910 2194 M -56 107 V .15 g 854 2301 M -97 172 V .15 g 757 2473 M -71 115 V 0 g .15 g 5853 4871 M .15 g 5853 4871 M -17 -28 V .15 g 5836 4843 M -83 -143 V .15 g 5753 4700 M 5643 4528 L .15 g 5643 4528 M -31 -45 V .15 g 5612 4483 M -81 -126 V .15 g 5531 4357 M 5409 4186 L .15 g 5409 4186 M -21 -28 V .15 g 5388 4158 M 5283 4014 L .15 g 5283 4014 M 5164 3867 L .15 g 5164 3867 M -20 -24 V .15 g 5144 3843 M 4997 3672 L .15 g 4997 3672 M -57 -63 V .15 g 4940 3609 M 4834 3500 L .15 g 4834 3500 M 4717 3386 L .15 g 4717 3386 M -68 -57 V .15 g 4649 3329 M 4493 3198 L .15 g 4493 3198 M -59 -40 V .15 g 4434 3158 M 4269 3043 L .15 g 4269 3043 M -108 -57 V .15 g 4161 2986 M -116 -63 V .15 g 4045 2923 M -224 -84 V .15 g 3821 2839 M -108 -24 V .15 g 3713 2815 M -116 -28 V .15 g 3597 2787 M -224 -18 V .15 g 3373 2769 M -224 18 V .15 g 3149 2787 M -117 28 V .15 g 3032 2815 M -107 24 V .15 g 2925 2839 M -224 84 V .15 g 2701 2923 M -116 63 V .15 g 2585 2986 M -108 57 V .15 g 2477 3043 M -165 115 V .15 g 2312 3158 M -59 40 V .15 g 2253 3198 M -157 131 V .15 g 2096 3329 M -66 57 V .15 g 2030 3386 M -118 114 V .15 g 1912 3500 M -106 108 V .15 g 1806 3608 M -58 64 V .15 g 1748 3672 M -147 171 V .15 g 1601 3843 M -19 23 V .15 g 1582 3866 M -119 148 V .15 g 1463 4014 M -105 143 V .15 g 1358 4157 M -21 29 V .15 g 1337 4186 M -122 171 V .15 g 1215 4357 M -81 125 V .15 g 1134 4482 M -31 46 V .15 g 1103 4528 M 993 4700 L .15 g 993 4700 M -83 143 V .15 g 910 4843 M -18 28 V 0 g .15 g 6060 2587 M .15 g 6060 2587 M -71 -114 V .15 g 5989 2473 M -96 -172 V .15 g 5893 2301 M -57 -108 V .15 g 5836 2193 M -42 -63 V .15 g 5794 2130 M 5685 1959 L .15 g 5685 1959 M -73 -126 V .15 g 5612 1833 M -33 -46 V .15 g 5579 1787 M 5458 1616 L .15 g 5458 1616 M -70 -108 V .15 g 5388 1508 M -51 -63 V .15 g 5337 1445 M 5206 1273 L .15 g 5206 1273 M -42 -57 V .15 g 5164 1216 M 5061 1102 L .15 g 5061 1102 M 4940 959 L .15 g 4940 959 M -28 -28 V .15 g 4912 931 M 4740 759 L .15 g 4740 759 M -23 -23 V .15 g 4717 736 M 4540 588 L 0 g .125 g 2364 588 M .125 g 2364 588 M -111 77 V .125 g 2253 665 M -111 94 V .125 g 2142 759 M -112 94 V .125 g 2030 853 M -77 78 V .125 g 1953 931 M -147 144 V .125 g 1806 1075 M -23 27 V .125 g 1783 1102 M -148 171 V .125 g 1635 1273 M -53 60 V .125 g 1582 1333 M -82 112 V .125 g 1500 1445 M -138 171 V .125 g 1362 1616 M -4 6 V .125 g 1358 1622 M -107 165 V .125 g 1251 1787 M -117 161 V .125 g 1134 1948 M -7 11 V .125 g 1127 1959 M -99 171 V .125 g 1028 2130 M 914 2301 L .125 g 914 2301 M -4 6 V .125 g 910 2307 M -86 166 V .125 g 824 2473 M 723 2644 L .125 g 723 2644 M -37 60 V 0 g .125 g 5926 4871 M .125 g 5926 4871 M -90 -144 V .125 g 5836 4727 M -16 -27 V .125 g 5820 4700 M 5720 4528 L .125 g 5720 4528 M 5612 4368 L .125 g 5612 4368 M -7 -11 V .125 g 5605 4357 M 5493 4186 L .125 g 5493 4186 M 5388 4042 L .125 g 5388 4042 M -20 -28 V .125 g 5368 4014 M 5240 3843 L .125 g 5240 3843 M -76 -94 V .125 g 5164 3749 M -65 -77 V .125 g 5099 3672 M 4945 3500 L .125 g 4945 3500 M -5 -5 V .125 g 4940 3495 M 4777 3329 L .125 g 4777 3329 M -60 -59 V .125 g 4717 3270 M 4584 3158 L .125 g 4584 3158 M -91 -77 V .125 g 4493 3081 M -139 -95 V .125 g 4354 2986 M -85 -59 V .125 g 4269 2927 M 4055 2815 L .125 g 4055 2815 M -10 -5 V .125 g 4045 2810 M -224 -89 V .125 g 3821 2721 M -224 -50 V .125 g 3597 2671 M -224 -16 V .125 g 3373 2655 M -224 16 V .125 g 3149 2671 M -224 50 V .125 g 2925 2721 M -224 89 V .125 g 2701 2810 M -10 5 V .125 g 2691 2815 M -214 112 V .125 g 2477 2927 M -85 59 V .125 g 2392 2986 M -139 95 V .125 g 2253 3081 M -91 77 V .125 g 2162 3158 M -132 112 V .125 g 2030 3270 M -62 59 V .125 g 1968 3329 M -162 166 V .125 g 1806 3495 M -6 5 V .125 g 1800 3500 M -153 172 V .125 g 1647 3672 M -65 77 V .125 g 1582 3749 M -76 94 V .125 g 1506 3843 M -128 171 V .125 g 1378 4014 M -20 28 V .125 g 1358 4042 M -106 144 V .125 g 1252 4186 M -111 171 V .125 g 1141 4357 M -7 11 V .125 g 1134 4368 M -108 160 V .125 g 1026 4528 M 926 4700 L .125 g 926 4700 M -16 27 V .125 g 910 4727 M -90 144 V 0 g .125 g 6060 2703 M .125 g 6060 2703 M -37 -59 V .125 g 6023 2644 M 5922 2473 L .125 g 5922 2473 M -86 -166 V .125 g 5836 2307 M -4 -6 V .125 g 5832 2301 M 5718 2130 L .125 g 5718 2130 M -99 -171 V .125 g 5619 1959 M -7 -12 V .125 g 5612 1947 M 5495 1787 L .125 g 5495 1787 M 5388 1621 L .125 g 5388 1621 M -4 -5 V .125 g 5384 1616 M 5246 1445 L .125 g 5246 1445 M -82 -113 V .125 g 5164 1332 M -53 -59 V .125 g 5111 1273 M 4964 1102 L .125 g 4964 1102 M -24 -28 V .125 g 4940 1074 M 4793 931 L .125 g 4793 931 M -76 -78 V .125 g 4717 853 M 4604 759 L .125 g 4604 759 M 4493 665 L .125 g 4493 665 M 4382 588 L 0 g .1 g 2569 588 M .1 g 2569 588 M -92 50 V .1 g 2477 638 M 2300 759 L .1 g 2300 759 M -47 33 V .1 g 2253 792 M 2090 931 L .1 g 2090 931 M -60 50 V .1 g 2030 981 M -119 121 V .1 g 1911 1102 M -105 102 V .1 g 1806 1204 M -58 69 V .1 g 1748 1273 M -153 172 V .1 g 1595 1445 M -13 14 V .1 g 1582 1459 M -114 157 V .1 g 1468 1616 M -110 135 V .1 g 1358 1751 M -23 36 V .1 g 1335 1787 M -113 172 V .1 g 1222 1959 M -88 119 V .1 g 1134 2078 M -30 52 V .1 g 1104 2130 M -102 171 V .1 g 1002 2301 M -92 136 V .1 g 910 2437 M -19 36 V .1 g 891 2473 M -90 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DL} def /LT7 {PL [1 dl1 2 dl2 6 dl1 2 dl2 1 dl1 2 dl2] LC7 DL} def /LT8 {PL [2 dl1 2 dl2 2 dl1 2 dl2 2 dl1 2 dl2 2 dl1 4 dl2] LC8 DL} def /Pnt {stroke [] 0 setdash gsave 1 setlinecap M 0 0 V stroke grestore} def /Dia {stroke [] 0 setdash 2 copy vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke Pnt} def /Pls {stroke [] 0 setdash vpt sub M 0 vpt2 V currentpoint stroke M hpt neg vpt neg R hpt2 0 V stroke } def /Box {stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke Pnt} def /Crs {stroke [] 0 setdash exch hpt sub exch vpt add M hpt2 vpt2 neg V currentpoint stroke M hpt2 neg 0 R hpt2 vpt2 V stroke} def /TriU {stroke [] 0 setdash 2 copy vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke Pnt} def /Star {2 copy Pls Crs} def /BoxF {stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath fill} def /TriUF {stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath fill} def /TriD {stroke [] 0 setdash 2 copy vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke Pnt} def /TriDF {stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath fill} def /DiaF {stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath fill} def /Pent {stroke [] 0 setdash 2 copy gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore Pnt} def /PentF {stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath fill grestore} def /Circle {stroke [] 0 setdash 2 copy hpt 0 360 arc stroke Pnt} def /CircleF {stroke [] 0 setdash hpt 0 360 arc fill} def /C0 {BL [] 0 setdash 2 copy moveto vpt 90 450 arc} bind def /C1 {BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill vpt 0 360 arc closepath} bind def /C2 {BL [] 0 setdash 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath} bind def /C3 {BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill vpt 0 360 arc closepath} bind def /C4 {BL [] 0 setdash 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc closepath} bind def /C5 {BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc} bind def /C6 {BL [] 0 setdash 2 copy moveto 2 copy vpt 90 270 arc closepath fill vpt 0 360 arc closepath} bind def /C7 {BL [] 0 setdash 2 copy moveto 2 copy vpt 0 270 arc closepath fill vpt 0 360 arc closepath} bind def /C8 {BL [] 0 setdash 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath} bind def /C9 {BL [] 0 setdash 2 copy moveto 2 copy vpt 270 450 arc closepath fill vpt 0 360 arc closepath} bind def /C10 {BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath} bind def /C11 {BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath} bind def /C12 {BL [] 0 setdash 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath} bind def /C13 {BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath} bind def /C14 {BL [] 0 setdash 2 copy moveto 2 copy vpt 90 360 arc closepath fill vpt 0 360 arc} bind def /C15 {BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill vpt 0 360 arc closepath} bind def /Rec {newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath} bind def /Square {dup Rec} bind def /Bsquare {vpt sub exch vpt sub exch vpt2 Square} bind def /S0 {BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare} bind def /S1 {BL [] 0 setdash 2 copy vpt Square fill Bsquare} bind def /S2 {BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare} bind def /S3 {BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare} bind def /S4 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare} bind def /S5 {BL [] 0 setdash 2 copy 2 copy vpt Square fill exch vpt sub exch vpt sub vpt Square fill Bsquare} bind def /S6 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare} bind def /S7 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill 2 copy vpt Square fill Bsquare} bind def /S8 {BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare} bind def /S9 {BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare} bind def /S10 {BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill Bsquare} bind def /S11 {BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare} bind def /S12 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare} bind def /S13 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy vpt Square fill Bsquare} bind def /S14 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy exch vpt sub exch vpt Square fill Bsquare} bind def /S15 {BL [] 0 setdash 2 copy Bsquare fill Bsquare} bind def /D0 {gsave translate 45 rotate 0 0 S0 stroke grestore} bind def /D1 {gsave translate 45 rotate 0 0 S1 stroke grestore} bind def /D2 {gsave translate 45 rotate 0 0 S2 stroke grestore} bind def /D3 {gsave translate 45 rotate 0 0 S3 stroke grestore} bind def /D4 {gsave translate 45 rotate 0 0 S4 stroke grestore} bind def /D5 {gsave translate 45 rotate 0 0 S5 stroke grestore} bind def /D6 {gsave translate 45 rotate 0 0 S6 stroke grestore} bind def /D7 {gsave translate 45 rotate 0 0 S7 stroke grestore} bind def /D8 {gsave translate 45 rotate 0 0 S8 stroke grestore} bind def /D9 {gsave translate 45 rotate 0 0 S9 stroke grestore} bind def /D10 {gsave translate 45 rotate 0 0 S10 stroke grestore} bind def /D11 {gsave translate 45 rotate 0 0 S11 stroke grestore} bind def /D12 {gsave translate 45 rotate 0 0 S12 stroke grestore} bind def /D13 {gsave translate 45 rotate 0 0 S13 stroke grestore} bind def /D14 {gsave translate 45 rotate 0 0 S14 stroke grestore} bind def /D15 {gsave translate 45 rotate 0 0 S15 stroke grestore} bind def /DiaE {stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke} def /BoxE {stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke} def /TriUE {stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke} def /TriDE {stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke} def /PentE {stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore} def /CircE {stroke [] 0 setdash hpt 0 360 arc stroke} def /Opaque {gsave closepath 1 setgray fill grestore 0 setgray closepath} def /DiaW {stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V Opaque stroke} def /BoxW {stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V Opaque stroke} def /TriUW {stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V Opaque stroke} def /TriDW {stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V Opaque stroke} def /PentW {stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat Opaque stroke grestore} def /CircW {stroke [] 0 setdash hpt 0 360 arc Opaque stroke} def /BoxFill {gsave Rec 1 setgray fill grestore} def /Density { /Fillden exch def currentrgbcolor /ColB exch def /ColG exch def /ColR exch def /ColR ColR Fillden mul Fillden sub 1 add def /ColG ColG Fillden mul Fillden sub 1 add def /ColB ColB Fillden mul Fillden sub 1 add def ColR ColG ColB setrgbcolor} def /BoxColFill {gsave Rec PolyFill} def /PolyFill {gsave Density fill grestore grestore} def /h {rlineto rlineto rlineto gsave closepath fill grestore} bind def % % PostScript Level 1 Pattern Fill routine for rectangles % Usage: x y w h s a XX PatternFill % x,y = lower left corner of box to be filled % w,h = width and height of box % a = angle in degrees between lines and x-axis % XX = 0/1 for no/yes cross-hatch % /PatternFill {gsave /PFa [ 9 2 roll ] def PFa 0 get PFa 2 get 2 div add PFa 1 get PFa 3 get 2 div add translate PFa 2 get -2 div PFa 3 get -2 div PFa 2 get PFa 3 get Rec TransparentPatterns {} {gsave 1 setgray fill grestore} ifelse clip currentlinewidth 0.5 mul setlinewidth /PFs PFa 2 get dup mul PFa 3 get dup mul add sqrt def 0 0 M PFa 5 get rotate PFs -2 div dup translate 0 1 PFs PFa 4 get div 1 add floor cvi {PFa 4 get mul 0 M 0 PFs V} for 0 PFa 6 get ne { 0 1 PFs PFa 4 get div 1 add floor cvi {PFa 4 get mul 0 2 1 roll M PFs 0 V} for } if stroke grestore} def % /languagelevel where {pop languagelevel} {1} ifelse 2 lt {/InterpretLevel1 true def} {/InterpretLevel1 Level1 def} ifelse % % PostScript level 2 pattern fill definitions % /Level2PatternFill { /Tile8x8 {/PaintType 2 /PatternType 1 /TilingType 1 /BBox [0 0 8 8] /XStep 8 /YStep 8} bind def /KeepColor {currentrgbcolor [/Pattern /DeviceRGB] setcolorspace} bind def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 0 M 8 8 L 0 8 M 8 0 L stroke} >> matrix makepattern /Pat1 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 0 M 8 8 L 0 8 M 8 0 L stroke 0 4 M 4 8 L 8 4 L 4 0 L 0 4 L stroke} >> matrix makepattern /Pat2 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 0 M 0 8 L 8 8 L 8 0 L 0 0 L fill} >> matrix makepattern /Pat3 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -4 8 M 8 -4 L 0 12 M 12 0 L stroke} >> matrix makepattern /Pat4 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -4 0 M 8 12 L 0 -4 M 12 8 L stroke} >> matrix makepattern /Pat5 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -2 8 M 4 -4 L 0 12 M 8 -4 L 4 12 M 10 0 L stroke} >> matrix makepattern /Pat6 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -2 0 M 4 12 L 0 -4 M 8 12 L 4 -4 M 10 8 L stroke} >> matrix makepattern /Pat7 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 8 -2 M -4 4 L 12 0 M -4 8 L 12 4 M 0 10 L stroke} >> matrix makepattern /Pat8 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 -2 M 12 4 L -4 0 M 12 8 L -4 4 M 8 10 L stroke} >> matrix makepattern /Pat9 exch def /Pattern1 {PatternBgnd KeepColor Pat1 setpattern} bind def /Pattern2 {PatternBgnd KeepColor Pat2 setpattern} bind def /Pattern3 {PatternBgnd KeepColor Pat3 setpattern} bind def /Pattern4 {PatternBgnd KeepColor Landscape {Pat5} {Pat4} ifelse setpattern} bind def /Pattern5 {PatternBgnd KeepColor Landscape {Pat4} {Pat5} ifelse setpattern} bind def /Pattern6 {PatternBgnd KeepColor Landscape {Pat9} {Pat6} ifelse setpattern} bind def /Pattern7 {PatternBgnd KeepColor Landscape {Pat8} {Pat7} ifelse setpattern} bind def } def % % %End of PostScript Level 2 code % /PatternBgnd { TransparentPatterns {} {gsave 1 setgray fill grestore} ifelse } def % % Substitute for Level 2 pattern fill codes with % grayscale if Level 2 support is not selected. % /Level1PatternFill { /Pattern1 {0.250 Density} bind def /Pattern2 {0.500 Density} bind def /Pattern3 {0.750 Density} bind def /Pattern4 {0.125 Density} bind def /Pattern5 {0.375 Density} bind def /Pattern6 {0.625 Density} bind def /Pattern7 {0.875 Density} bind def } def % % Now test for support of Level 2 code % Level1 {Level1PatternFill} {Level2PatternFill} ifelse % /Symbol-Oblique /Symbol findfont [1 0 .167 1 0 0] makefont dup length dict begin {1 index /FID eq {pop pop} {def} ifelse} forall currentdict end definefont pop /MFshow { { dup 5 get 3 ge { 5 get 3 eq {gsave} {grestore} ifelse } {dup dup 0 get findfont exch 1 get scalefont setfont [ currentpoint ] exch dup 2 get 0 exch R dup 5 get 2 ne {dup dup 6 get exch 4 get {Gshow} {stringwidth pop 0 R} ifelse }if dup 5 get 0 eq {dup 3 get {2 get neg 0 exch R pop} {pop aload pop M} ifelse} {dup 5 get 1 eq {dup 2 get exch dup 3 get exch 6 get stringwidth pop -2 div dup 0 R} {dup 6 get stringwidth pop -2 div 0 R 6 get show 2 index {aload pop M neg 3 -1 roll neg R pop pop} {pop pop pop pop aload pop M} ifelse }ifelse }ifelse } ifelse } forall} def /Gswidth {dup type /stringtype eq {stringwidth} {pop (n) stringwidth} ifelse} def /MFwidth {0 exch { dup 5 get 3 ge { 5 get 3 eq { 0 } { pop } ifelse } {dup 3 get{dup dup 0 get findfont exch 1 get scalefont setfont 6 get Gswidth pop add} {pop} ifelse} ifelse} forall} def /MLshow { currentpoint stroke M 0 exch R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /MRshow { currentpoint stroke M exch dup MFwidth neg 3 -1 roll R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /MCshow { currentpoint stroke M exch dup MFwidth -2 div 3 -1 roll R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /XYsave { [( ) 1 2 true false 3 ()] } bind def /XYrestore { [( ) 1 2 true false 4 ()] } bind def Level1 SuppressPDFMark or {} { /SDict 10 dict def systemdict /pdfmark known not { userdict /pdfmark systemdict /cleartomark get put } if SDict begin [ /Title (nlfit3.eps) /Subject (gnuplot plot) /Creator (gnuplot 4.6 patchlevel 2) /Author (palken) % /Producer (gnuplot) % /Keywords () /CreationDate (Sat Jul 2 12:39:50 2016) /DOCINFO pdfmark end } ifelse end %%EndProlog %%Page: 1 1 gnudict begin gsave doclip 50 50 translate 0.050 0.050 scale 0 setgray newpath (Helvetica) findfont 140 scalefont setfont BackgroundColor 0 lt 3 1 roll 0 lt exch 0 lt or or not {BackgroundColor C 1.000 0 0 7200.00 5040.00 BoxColFill} if gsave % colour palette begin /maxcolors 0 def /HSV2RGB { exch dup 0.0 eq {pop exch pop dup dup} % achromatic gray { /HSVs exch def /HSVv exch def 6.0 mul dup floor dup 3 1 roll sub /HSVf exch def /HSVi exch cvi def /HSVp HSVv 1.0 HSVs sub mul def /HSVq HSVv 1.0 HSVs HSVf mul sub mul def /HSVt HSVv 1.0 HSVs 1.0 HSVf sub mul sub mul def /HSVi HSVi 6 mod def 0 HSVi eq {HSVv HSVt HSVp} {1 HSVi eq {HSVq HSVv HSVp}{2 HSVi eq {HSVp HSVv HSVt} {3 HSVi eq {HSVp HSVq HSVv}{4 HSVi eq {HSVt HSVp HSVv} {HSVv HSVp HSVq} ifelse} ifelse} ifelse} ifelse} ifelse } ifelse} def /Constrain { dup 0 lt {0 exch pop}{dup 1 gt {1 exch pop} if} ifelse} def /YIQ2RGB { 3 copy -1.702 mul exch -1.105 mul add add Constrain 4 1 roll 3 copy -0.647 mul exch -0.272 mul add add Constrain 5 1 roll 0.621 mul exch -0.956 mul add add Constrain 3 1 roll } def /CMY2RGB { 1 exch sub exch 1 exch sub 3 2 roll 1 exch sub 3 1 roll exch } def /XYZ2RGB { 3 copy -0.9017 mul exch -0.1187 mul add exch 0.0585 mul exch add Constrain 4 1 roll 3 copy -0.0279 mul exch 1.999 mul add exch -0.9844 mul add Constrain 5 1 roll -0.2891 mul exch -0.5338 mul add exch 1.91 mul exch add Constrain 3 1 roll} def /SelectSpace {ColorSpace (HSV) eq {HSV2RGB}{ColorSpace (XYZ) eq { XYZ2RGB}{ColorSpace (CMY) eq {CMY2RGB}{ColorSpace (YIQ) eq {YIQ2RGB} if} ifelse} ifelse} ifelse} def /InterpolatedColor true def /grayindex {/gidx 0 def {GrayA gidx get grayv ge {exit} if /gidx gidx 1 add def} loop} def /dgdx {grayv GrayA gidx get sub GrayA gidx 1 sub get GrayA gidx get sub div} def /redvalue {RedA gidx get RedA gidx 1 sub get RedA gidx get sub dgdxval mul add} def /greenvalue {GreenA gidx get GreenA gidx 1 sub get GreenA gidx get sub dgdxval mul add} def /bluevalue {BlueA gidx get BlueA gidx 1 sub get BlueA gidx get sub dgdxval mul add} def /interpolate { grayindex grayv GrayA gidx get sub abs 1e-5 le {RedA gidx get GreenA gidx get BlueA gidx get} {/dgdxval dgdx def redvalue greenvalue bluevalue} ifelse} def /GrayA [0 .125 .25 .375 .5 .625 .75 .875 1 ] def /RedA [0 0 0 0 .5 1 1 1 .5 ] def /GreenA [0 0 .5 1 1 1 .5 0 0 ] def /BlueA [.5 1 1 1 .5 0 0 0 0 ] def /pm3dround {maxcolors 0 gt {dup 1 ge {pop 1} {maxcolors mul floor maxcolors 1 sub div} ifelse} if} def /pm3dGamma 1.0 1.5 Gamma mul div def /ColorSpace (RGB) def Color InterpolatedColor or { % COLOUR vs. GRAY map InterpolatedColor { %% Interpolation vs. RGB-Formula /g {stroke pm3dround /grayv exch def interpolate SelectSpace setrgbcolor} bind def }{ /g {stroke pm3dround dup cF7 Constrain exch dup cF5 Constrain exch cF15 Constrain SelectSpace setrgbcolor} bind def } ifelse }{ /g {stroke pm3dround pm3dGamma exp setgray} bind def } ifelse 1.000 UL LTb LCb setrgbcolor 602 588 M 63 0 V 5387 0 R -63 0 V stroke 518 588 M [ [(Helvetica) 140.0 0.0 true true 0 (-5)] ] -46.7 MRshow 1.000 UL LTb LCb setrgbcolor 602 1596 M 63 0 V 5387 0 R -63 0 V stroke 518 1596 M [ [(Helvetica) 140.0 0.0 true true 0 ( 0)] ] -46.7 MRshow 1.000 UL LTb LCb setrgbcolor 602 2604 M 63 0 V 5387 0 R -63 0 V stroke 518 2604 M [ [(Helvetica) 140.0 0.0 true true 0 ( 5)] ] -46.7 MRshow 1.000 UL LTb LCb setrgbcolor 602 3611 M 63 0 V 5387 0 R -63 0 V stroke 518 3611 M [ [(Helvetica) 140.0 0.0 true true 0 ( 10)] ] -46.7 MRshow 1.000 UL LTb LCb setrgbcolor 602 4619 M 63 0 V 5387 0 R -63 0 V stroke 518 4619 M [ [(Helvetica) 140.0 0.0 true true 0 ( 15)] ] -46.7 MRshow 1.000 UL LTb LCb setrgbcolor 602 588 M 0 63 V 0 3968 R 0 -63 V stroke 602 448 M [ [(Helvetica) 140.0 0.0 true true 0 (-5)] ] -46.7 MCshow 1.000 UL LTb LCb setrgbcolor 1965 588 M 0 63 V 0 3968 R 0 -63 V stroke 1965 448 M [ [(Helvetica) 140.0 0.0 true true 0 ( 0)] ] -46.7 MCshow 1.000 UL LTb LCb setrgbcolor 3327 588 M 0 63 V 0 3968 R 0 -63 V stroke 3327 448 M [ [(Helvetica) 140.0 0.0 true true 0 ( 5)] ] -46.7 MCshow 1.000 UL LTb LCb setrgbcolor 4690 588 M 0 63 V 0 3968 R 0 -63 V stroke 4690 448 M [ [(Helvetica) 140.0 0.0 true true 0 ( 10)] ] -46.7 MCshow 1.000 UL LTb LCb setrgbcolor 6052 588 M 0 63 V 0 3968 R 0 -63 V stroke 6052 448 M [ [(Helvetica) 140.0 0.0 true true 0 ( 15)] ] -46.7 MCshow 1.000 UL LTb LCb setrgbcolor 1.000 UL LTb LCb setrgbcolor 602 4619 N 602 588 L 5450 0 V 0 4031 V -5450 0 V Z stroke LCb setrgbcolor 112 2603 M currentpoint gsave translate -270 rotate 0 0 moveto [ [(Helvetica) 140.0 0.0 true true 0 (x)] [(Helvetica) 112.0 -42.0 true true 0 (2)] ] -32.7 MCshow grestore LTb LCb setrgbcolor 3327 238 M [ [(Helvetica) 140.0 0.0 true true 0 (x)] [(Helvetica) 112.0 -42.0 true true 0 (1)] ] -32.7 MCshow LTb 3327 4829 M [ [(Helvetica) 140.0 0.0 true true 0 (Minimizing the Branin function)] ] -46.7 MCshow 0.300 UP 1.000 UL LTb LCb setrgbcolor % Begin plot #1 2.000 UL LT0 0 g 1 g 612 588 M 1 g 612 588 M -9 20 V 1 g 603 608 M -1 3 V 0 g .98 g 632 588 M .98 g 632 588 M -3 7 V .98 g 629 595 M -6 13 V .98 g 623 608 M -9 20 V .98 g 614 628 M -8 20 V .98 g 606 648 M -4 9 V 0 g .96 g 653 588 M .96 g 653 588 M -9 20 V .96 g 644 608 M -9 20 V .96 g 635 628 M -6 13 V .96 g 629 641 M -3 7 V .96 g 626 648 M -9 21 V .96 g 617 669 M -9 20 V .96 g 608 689 M -6 14 V 0 g .94 g 673 588 M .94 g 673 588 M -9 20 V .94 g 664 608 M -7 18 V .94 g 657 626 M -2 2 V .94 g 655 628 M -8 20 V .94 g 647 648 M -9 21 V .94 g 638 669 M -9 19 V .94 g 629 688 M 0 1 V .94 g 629 689 M -9 20 V .94 g 620 709 M -9 20 V .94 g 611 729 M -9 20 V .94 g 602 749 M 0 1 V 0 g .92 g 694 588 M .92 g 694 588 M -9 20 V .92 g 685 608 M -1 4 V .92 g 684 612 M -8 16 V .92 g 676 628 M -9 20 V .92 g 667 648 M -8 21 V .92 g 659 669 M -2 4 V .92 g 657 673 M -7 16 V .92 g 650 689 M -9 20 V .92 g 641 709 M -9 20 V .92 g 632 729 M -3 6 V .92 g 629 735 M -6 14 V .92 g 623 749 M -9 20 V .92 g 614 769 M -9 21 V .92 g 605 790 M -3 7 V 0 g .9 g 716 588 M .9 g 716 588 M -5 11 V .9 g 711 599 M -4 9 V .9 g 707 608 M -9 20 V .9 g 698 628 M -9 20 V .9 g 689 648 M -5 12 V .9 g 684 660 M -4 9 V .9 g 680 669 M -9 20 V .9 g 671 689 M -9 20 V .9 g 662 709 M -5 12 V .9 g 657 721 M -4 8 V .9 g 653 729 M -9 20 V stroke 644 749 M .9 g 644 749 M -9 20 V .9 g 635 769 M -6 14 V .9 g 629 783 M -3 7 V .9 g 626 790 M -8 20 V .9 g 618 810 M -9 20 V .9 g 609 830 M -7 15 V 0 g .88 g 738 588 M .88 g 738 588 M -9 20 V .88 g 729 608 M -10 20 V .88 g 719 628 M -8 19 V .88 g 711 647 M -1 1 V .88 g 710 648 M -9 21 V .88 g 701 669 M -9 20 V .88 g 692 689 M -8 19 V .88 g 684 708 M -1 1 V .88 g 683 709 M -9 20 V .88 g 674 729 M -9 20 V .88 g 665 749 M -8 20 V .88 g 657 769 M -1 0 V .88 g 656 769 M -8 21 V .88 g 648 790 M -9 20 V .88 g 639 810 M -9 20 V .88 g 630 830 M -1 1 V .88 g 629 831 M -8 19 V .88 g 621 850 M -9 20 V .88 g 612 870 M -9 20 V .88 g 603 890 M -1 4 V 0 g .86 g 760 588 M .86 g 760 588 M -9 20 V .86 g 751 608 M -10 20 V .86 g 741 628 M -3 7 V .86 g 738 635 M -6 13 V .86 g 732 648 M -9 21 V .86 g 723 669 M -9 20 V .86 g 714 689 M -3 7 V .86 g 711 696 M -6 13 V .86 g 705 709 M -9 20 V .86 g 696 729 M -9 20 V .86 g 687 749 M -3 8 V .86 g 684 757 M -6 12 V .86 g 678 769 M -9 21 V .86 g 669 790 M -9 20 V .86 g 660 810 M -3 8 V .86 g 657 818 M -6 12 V .86 g 651 830 M -8 20 V .86 g 643 850 M -9 20 V .86 g 634 870 M -5 10 V .86 g 629 880 M -4 10 V .86 g 625 890 M -9 20 V .86 g 616 910 M -9 21 V .86 g 607 931 M -5 12 V 0 g .84 g 782 588 M .84 g 782 588 M -9 20 V .84 g 773 608 M -8 17 V stroke 765 625 M .84 g 765 625 M -1 3 V .84 g 764 628 M -9 20 V .84 g 755 648 M -9 21 V .84 g 746 669 M -8 16 V .84 g 738 685 M -2 4 V .84 g 736 689 M -9 20 V .84 g 727 709 M -9 20 V .84 g 718 729 M -7 16 V .84 g 711 745 M -2 4 V .84 g 709 749 M -9 20 V .84 g 700 769 M -9 21 V .84 g 691 790 M -7 16 V .84 g 684 806 M -2 4 V .84 g 682 810 M -9 20 V .84 g 673 830 M -9 20 V .84 g 664 850 M -7 18 V .84 g 657 868 M -2 2 V .84 g 655 870 M -8 20 V .84 g 647 890 M -9 20 V .84 g 638 910 M -9 20 V .84 g 629 930 M 0 1 V .84 g 629 931 M -9 20 V .84 g 620 951 M -9 20 V .84 g 611 971 M -8 20 V .84 g 603 991 M -1 1 V 0 g .82 g 806 588 M .82 g 806 588 M -10 20 V .82 g 796 608 M -3 7 V .82 g 793 615 M -6 13 V .82 g 787 628 M -9 20 V .82 g 778 648 M -10 21 V .82 g 768 669 M -3 6 V .82 g 765 675 M -6 14 V .82 g 759 689 M -9 20 V .82 g 750 709 M -9 20 V .82 g 741 729 M -3 6 V .82 g 738 735 M -6 14 V .82 g 732 749 M -9 20 V .82 g 723 769 M -9 21 V .82 g 714 790 M -3 5 V .82 g 711 795 M -6 15 V .82 g 705 810 M -9 20 V .82 g 696 830 M -9 20 V .82 g 687 850 M -3 6 V .82 g 684 856 M -6 14 V .82 g 678 870 M -9 20 V .82 g 669 890 M -9 20 V .82 g 660 910 M -3 8 V .82 g 657 918 M -6 13 V .82 g 651 931 M -9 20 V .82 g 642 951 M -9 20 V .82 g 633 971 M -4 9 V .82 g 629 980 M -5 11 V stroke 624 991 M .82 g 624 991 M -8 20 V .82 g 616 1011 M -9 20 V .82 g 607 1031 M -5 12 V 0 g .8 g 829 588 M .8 g 829 588 M -9 19 V .8 g 820 607 M 0 1 V .8 g 820 608 M -10 20 V .8 g 810 628 M -9 20 V .8 g 801 648 M -8 18 V .8 g 793 666 M -1 3 V .8 g 792 669 M -10 20 V .8 g 782 689 M -9 20 V .8 g 773 709 M -8 16 V .8 g 765 725 M -1 4 V .8 g 764 729 M -9 20 V .8 g 755 749 M -10 20 V .8 g 745 769 M -7 16 V .8 g 738 785 M -2 5 V .8 g 736 790 M -9 20 V .8 g 727 810 M -9 20 V .8 g 718 830 M -7 16 V .8 g 711 846 M -2 4 V .8 g 709 850 M -9 20 V .8 g 700 870 M -9 20 V .8 g 691 890 M -7 17 V .8 g 684 907 M -2 3 V .8 g 682 910 M -9 21 V .8 g 673 931 M -9 20 V .8 g 664 951 M -7 18 V .8 g 657 969 M -1 2 V .8 g 656 971 M -9 20 V .8 g 647 991 M -9 20 V .8 g 638 1011 M -9 20 V .8 g .8 g 629 1031 M -9 21 V .8 g 620 1052 M -8 20 V .8 g 612 1072 M -9 20 V .8 g 603 1092 M -1 1 V 0 g .78 g 853 588 M .78 g 853 588 M -6 13 V .78 g 847 601 M -3 7 V .78 g 844 608 M -10 20 V .78 g 834 628 M -9 20 V .78 g 825 648 M -5 10 V .78 g 820 658 M -5 11 V .78 g 815 669 M -9 20 V .78 g 806 689 M -9 20 V .78 g 797 709 M -4 8 V .78 g 793 717 M -6 12 V .78 g 787 729 M -9 20 V .78 g 778 749 M -9 20 V .78 g 769 769 M -4 7 V .78 g 765 776 M -5 14 V .78 g 760 790 M -10 20 V stroke 750 810 M .78 g 750 810 M -9 20 V .78 g 741 830 M -3 6 V .78 g 738 836 M -6 14 V .78 g 732 850 M -9 20 V .78 g 723 870 M -9 20 V .78 g 714 890 M -3 7 V .78 g 711 897 M -6 13 V .78 g 705 910 M -9 21 V .78 g 696 931 M -9 20 V .78 g 687 951 M -3 7 V .78 g 684 958 M -6 13 V .78 g 678 971 M -9 20 V .78 g 669 991 M -9 20 V .78 g 660 1011 M -3 9 V .78 g 657 1020 M -5 11 V .78 g 652 1031 M -9 21 V .78 g 643 1052 M -9 20 V .78 g 634 1072 M -5 10 V .78 g 629 1082 M -4 10 V .78 g 625 1092 M -9 20 V .78 g 616 1112 M -8 20 V .78 g 608 1132 M -6 13 V 0 g .76 g 878 588 M .76 g 878 588 M -3 7 V .76 g 875 595 M -7 13 V .76 g 868 608 M -9 20 V .76 g 859 628 M -10 20 V .76 g 849 648 M -2 4 V .76 g 847 652 M -7 17 V .76 g 840 669 M -10 20 V .76 g 830 689 M -9 20 V .76 g 821 709 M -1 1 V .76 g 820 710 M -9 19 V .76 g 811 729 M -9 20 V .76 g 802 749 M -9 20 V .76 g 793 769 M -1 0 V .76 g 792 769 M -9 21 V .76 g 783 790 M -9 20 V .76 g 774 810 M -9 18 V .76 g 765 828 M 0 2 V .76 g 765 830 M -9 20 V .76 g 756 850 M -9 20 V .76 g 747 870 M -9 18 V .76 g 738 888 M -1 2 V .76 g 737 890 M -9 20 V .76 g 728 910 M -9 21 V .76 g 719 931 M -8 18 V .76 g 711 949 M -1 2 V .76 g 710 951 M -9 20 V .76 g 701 971 M -9 20 V .76 g 692 991 M -8 19 V .76 g 684 1010 M -1 1 V .76 g 683 1011 M -8 20 V stroke 675 1031 M .76 g 675 1031 M -9 21 V .76 g 666 1052 M -9 20 V .76 g .76 g 657 1072 M -9 20 V .76 g 648 1092 M -9 20 V .76 g 639 1112 M -9 20 V .76 g 630 1132 M -1 3 V .76 g 629 1135 M -7 17 V .76 g 622 1152 M -9 20 V .76 g 613 1172 M -9 21 V .76 g 604 1193 M -2 4 V 0 g .74 g 903 588 M .74 g 903 588 M -1 3 V .74 g 902 591 M -8 17 V .74 g 894 608 M -10 20 V .74 g 884 628 M -9 19 V .74 g 875 647 M -1 1 V .74 g 874 648 M -10 21 V .74 g 864 669 M -9 20 V .74 g 855 689 M -8 16 V .74 g 847 705 M -2 4 V .74 g 845 709 M -9 20 V .74 g 836 729 M -10 20 V .74 g 826 749 M -6 14 V .74 g 820 763 M -3 6 V .74 g 817 769 M -9 21 V .74 g 808 790 M -10 20 V .74 g 798 810 M -5 11 V .74 g 793 821 M -4 9 V .74 g 789 830 M -9 20 V .74 g 780 850 M -10 20 V .74 g 770 870 M -5 11 V .74 g 765 881 M -4 9 V .74 g 761 890 M -9 20 V .74 g 752 910 M -9 21 V .74 g 743 931 M -5 10 V .74 g 738 941 M -4 10 V .74 g 734 951 M -9 20 V .74 g 725 971 M -9 20 V .74 g 716 991 M -5 11 V .74 g 711 1002 M -4 9 V .74 g 707 1011 M -9 20 V .74 g 698 1031 M -9 21 V .74 g 689 1052 M -5 11 V .74 g 684 1063 M -4 9 V .74 g 680 1072 M -9 20 V .74 g 671 1092 M -9 20 V .74 g 662 1112 M -5 13 V .74 g 657 1125 M -4 7 V .74 g 653 1132 M -8 20 V .74 g 645 1152 M -9 20 V .74 g 636 1172 M -7 15 V .74 g 629 1187 M -2 6 V .74 g 627 1193 M -9 20 V stroke 618 1213 M .74 g 618 1213 M -8 20 V .74 g 610 1233 M -8 17 V 0 g .72 g 929 588 M .72 g 929 588 M 0 1 V .72 g 929 589 M -10 19 V .72 g 919 608 M -9 20 V .72 g 910 628 M -8 16 V .72 g 902 644 M -2 4 V .72 g 900 648 M -10 21 V .72 g 890 669 M -10 20 V .72 g 880 689 M -5 11 V .72 g 875 700 M -5 9 V .72 g 870 709 M -9 20 V .72 g 861 729 M -10 20 V .72 g 851 749 M -4 9 V .72 g 847 758 M -5 11 V .72 g 842 769 M -10 21 V .72 g 832 790 M -9 20 V .72 g 823 810 M -3 6 V .72 g 820 816 M -7 14 V .72 g 813 830 M -9 20 V .72 g 804 850 M -9 20 V .72 g 795 870 M -2 4 V .72 g 793 874 M -7 16 V .72 g 786 890 M -10 20 V .72 g 776 910 M -9 21 V .72 g 767 931 M -2 3 V .72 g 765 934 M -7 17 V .72 g 758 951 M -9 20 V .72 g 749 971 M -9 20 V .72 g 740 991 M -2 3 V .72 g 738 994 M -7 17 V .72 g 731 1011 M -9 20 V .72 g 722 1031 M -9 21 V .72 g 713 1052 M -2 3 V .72 g 711 1055 M -7 17 V .72 g 704 1072 M -9 20 V .72 g 695 1092 M -9 20 V .72 g 686 1112 M -2 5 V .72 g 684 1117 M -7 15 V .72 g 677 1132 M -9 20 V .72 g 668 1152 M -9 20 V .72 g 659 1172 M -2 7 V .72 g 657 1179 M -7 14 V .72 g 650 1193 M -8 20 V .72 g 642 1213 M -9 20 V .72 g 633 1233 M -4 8 V .72 g 629 1241 M -5 12 V .72 g 624 1253 M -9 20 V .72 g 615 1273 M -8 20 V .72 g 607 1293 M -5 11 V 0 g .7 g 956 588 M .7 g 956 588 M -10 20 V stroke 946 608 M .7 g 946 608 M -10 20 V .7 g 936 628 M -7 14 V .7 g 929 642 M -3 6 V .7 g 926 648 M -10 21 V .7 g 916 669 M -10 20 V .7 g 906 689 M -4 9 V .7 g 902 698 M -6 11 V .7 g 896 709 M -9 20 V .7 g 887 729 M -10 20 V .7 g 877 749 M -2 5 V .7 g 875 754 M -8 15 V .7 g 867 769 M -9 21 V .7 g 858 790 M -10 20 V .7 g 848 810 M -1 1 V .7 g 847 811 M -8 19 V .7 g 839 830 M -10 20 V .7 g 829 850 M -9 20 V .7 g .7 g 820 870 M -10 20 V .7 g 810 890 M -9 20 V .7 g 801 910 M -8 18 V .7 g 793 928 M -1 3 V .7 g 792 931 M -9 20 V .7 g 783 951 M -10 20 V .7 g 773 971 M -8 17 V .7 g 765 988 M -1 3 V .7 g 764 991 M -9 20 V .7 g 755 1011 M -9 20 V .7 g 746 1031 M -8 17 V .7 g 738 1048 M -1 4 V .7 g 737 1052 M -9 20 V .7 g 728 1072 M -9 20 V .7 g 719 1092 M -8 17 V .7 g 711 1109 M -1 3 V .7 g 710 1112 M -9 20 V .7 g 701 1132 M -9 20 V .7 g 692 1152 M -8 19 V .7 g 684 1171 M -1 1 V .7 g 683 1172 M -9 21 V .7 g 674 1193 M -9 20 V .7 g 665 1213 M -8 20 V .7 g 657 1233 M -1 0 V .7 g 656 1233 M -8 20 V .7 g 648 1253 M -9 20 V .7 g 639 1273 M -9 20 V .7 g 630 1293 M -1 2 V .7 g 629 1295 M -8 19 V .7 g 621 1314 M -8 20 V .7 g 613 1334 M -9 20 V .7 g 604 1354 M -2 4 V 0 g .68 g 984 588 M .68 g .68 g 984 588 M -10 20 V .68 g 974 608 M -11 20 V .68 g 963 628 M -7 14 V stroke 956 642 M .68 g 956 642 M -3 6 V .68 g 953 648 M -10 21 V .68 g 943 669 M -10 20 V .68 g 933 689 M -4 8 V .68 g 929 697 M -6 12 V .68 g 923 709 M -10 20 V .68 g 913 729 M -10 20 V .68 g 903 749 M -1 3 V .68 g 902 752 M -8 17 V .68 g 894 769 M -10 21 V .68 g 884 790 M -9 19 V .68 g 875 809 M -1 1 V .68 g 874 810 M -9 20 V .68 g 865 830 M -10 20 V .68 g 855 850 M -8 16 V .68 g 847 866 M -2 4 V .68 g 845 870 M -9 20 V .68 g 836 890 M -10 20 V .68 g 826 910 M -6 14 V .68 g 820 924 M -3 7 V .68 g 817 931 M -9 20 V .68 g 808 951 M -10 20 V .68 g 798 971 M -5 12 V .68 g 793 983 M -4 8 V .68 g 789 991 M -9 20 V .68 g 780 1011 M -9 20 V .68 g 771 1031 M -6 12 V .68 g 765 1043 M -3 9 V .68 g 762 1052 M -9 20 V .68 g 753 1072 M -10 20 V .68 g 743 1092 M -5 11 V .68 g 738 1103 M -4 9 V .68 g 734 1112 M -9 20 V .68 g 725 1132 M -9 20 V .68 g 716 1152 M -5 12 V .68 g 711 1164 M -4 8 V .68 g 707 1172 M -9 21 V .68 g 698 1193 M -8 20 V .68 g 690 1213 M -6 13 V .68 g 684 1226 M -3 7 V .68 g 681 1233 M -9 20 V .68 g 672 1253 M -9 20 V .68 g 663 1273 M -6 15 V .68 g 657 1288 M -3 5 V .68 g 654 1293 M -9 21 V .68 g 645 1314 M -8 20 V .68 g 637 1334 M -8 17 V .68 g 629 1351 M -1 3 V .68 g 628 1354 M -9 20 V .68 g 619 1374 M -9 20 V .68 g 610 1394 M -8 20 V 0 g .66 g 1012 588 M .66 g 1012 588 M -1 3 V stroke 1011 591 M .66 g 1011 591 M -9 17 V .66 g 1002 608 M -11 20 V .66 g 991 628 M -7 16 V .66 g 984 644 M -3 4 V .66 g 981 648 M -10 21 V .66 g 971 669 M -10 20 V .66 g 961 689 M -5 8 V .66 g 956 697 M -5 12 V .66 g 951 709 M -11 20 V .66 g 940 729 M -10 20 V .66 g 930 749 M -1 3 V .66 g 929 752 M -8 17 V .66 g 921 769 M -10 21 V .66 g 911 790 M -9 18 V .66 g 902 808 M -1 2 V .66 g 901 810 M -10 20 V .66 g 891 830 M -10 20 V .66 g 881 850 M -6 14 V .66 g 875 864 M -3 6 V .66 g 872 870 M -10 20 V .66 g 862 890 M -9 20 V .66 g 853 910 M -6 12 V .66 g 847 922 M -4 9 V .66 g 843 931 M -9 20 V .66 g 834 951 M -10 20 V .66 g 824 971 M -4 9 V .66 g 820 980 M -5 11 V .66 g 815 991 M -10 20 V .66 g 805 1011 M -9 20 V .66 g 796 1031 M -3 8 V .66 g 793 1039 M -6 13 V .66 g 787 1052 M -9 20 V .66 g 778 1072 M -9 20 V .66 g 769 1092 M -4 7 V .66 g 765 1099 M -6 13 V .66 g 759 1112 M -9 20 V .66 g 750 1132 M -9 20 V .66 g 741 1152 M -3 7 V .66 g 738 1159 M -6 13 V .66 g 732 1172 M -9 21 V .66 g 723 1193 M -9 20 V .66 g 714 1213 M -3 7 V .66 g 711 1220 M -6 13 V .66 g 705 1233 M -9 20 V .66 g 696 1253 M -8 20 V .66 g 688 1273 M -4 9 V .66 g 684 1282 M -5 11 V .66 g 679 1293 M -9 21 V .66 g 670 1314 M -9 20 V .66 g 661 1334 M -4 10 V .66 g 657 1344 M -5 10 V .66 g 652 1354 M -9 20 V stroke 643 1374 M .66 g 643 1374 M -8 20 V .66 g 635 1394 M -6 13 V .66 g 629 1407 M -3 7 V .66 g 626 1414 M -9 21 V .66 g 617 1435 M -8 20 V .66 g 609 1455 M -7 15 V 0 g .64 g 1042 588 M .64 g 1042 588 M -4 7 V .64 g 1038 595 M -7 13 V .64 g 1031 608 M -10 20 V .64 g 1021 628 M -10 19 V .64 g 1011 647 M -1 1 V .64 g 1010 648 M -10 21 V .64 g 1000 669 M -11 20 V .64 g 989 689 M -5 11 V .64 g 984 700 M -5 9 V .64 g 979 709 M -10 20 V .64 g 969 729 M -11 20 V .64 g 958 749 M -2 4 V .64 g 956 753 M -8 16 V .64 g 948 769 M -10 21 V .64 g 938 790 M -9 18 V .64 g 929 808 M -1 2 V .64 g 928 810 M -10 20 V .64 g 918 830 M -9 20 V .64 g 909 850 M -7 14 V .64 g 902 864 M -3 6 V .64 g 899 870 M -10 20 V .64 g 889 890 M -10 20 V .64 g 879 910 M -4 10 V .64 g 875 920 M -5 11 V .64 g 870 931 M -10 20 V .64 g 860 951 M -9 20 V .64 g 851 971 M -4 7 V .64 g 847 978 M -6 13 V .64 g 841 991 M -9 20 V .64 g 832 1011 M -10 20 V .64 g 822 1031 M -2 5 V .64 g 820 1036 M -7 16 V .64 g 813 1052 M -9 20 V .64 g 804 1072 M -10 20 V .64 g 794 1092 M -1 3 V .64 g 793 1095 M -8 17 V .64 g 785 1112 M -9 20 V .64 g 776 1132 M -9 20 V .64 g 767 1152 M -2 3 V .64 g 765 1155 M -7 17 V .64 g 758 1172 M -9 21 V .64 g 749 1193 M -9 20 V .64 g 740 1213 M -2 3 V .64 g 738 1216 M -7 17 V .64 g 731 1233 M -9 20 V .64 g 722 1253 M -9 20 V stroke 713 1273 M .64 g 713 1273 M -2 4 V .64 g 711 1277 M -7 16 V .64 g 704 1293 M -9 21 V .64 g 695 1314 M -9 20 V .64 g 686 1334 M -2 5 V .64 g 684 1339 M -7 15 V .64 g 677 1354 M -9 20 V .64 g 668 1374 M -9 20 V .64 g 659 1394 M -2 7 V .64 g 657 1401 M -6 13 V .64 g 651 1414 M -9 21 V .64 g 642 1435 M -9 20 V .64 g 633 1455 M -4 9 V .64 g 629 1464 M -5 11 V .64 g 624 1475 M -8 20 V .64 g 616 1495 M -9 20 V .64 g 607 1515 M -5 12 V 0 g .62 g 1073 588 M .62 g 1073 588 M -8 13 V .62 g 1065 601 M -3 7 V .62 g 1062 608 M -11 20 V .62 g 1051 628 M -11 20 V .62 g 1040 648 M -2 4 V .62 g 1038 652 M -9 17 V .62 g 1029 669 M -10 20 V .62 g 1019 689 M -8 15 V .62 g 1011 704 M -3 5 V .62 g 1008 709 M -10 20 V .62 g 998 729 M -11 20 V .62 g 987 749 M -3 8 V .62 g 984 757 M -7 12 V .62 g 977 769 M -10 21 V .62 g 967 790 M -10 20 V .62 g 957 810 M -1 0 V .62 g 956 810 M -9 20 V .62 g 947 830 M -10 20 V .62 g 937 850 M -8 15 V .62 g 929 865 M -2 5 V .62 g 927 870 M -10 20 V .62 g 917 890 M -10 20 V .62 g 907 910 M -5 11 V .62 g 902 921 M -5 10 V .62 g 897 931 M -10 20 V .62 g 887 951 M -9 20 V .62 g 878 971 M -3 6 V .62 g 875 977 M -7 14 V .62 g 868 991 M -9 20 V .62 g 859 1011 M -10 20 V .62 g 849 1031 M -2 4 V .62 g 847 1035 M -7 17 V .62 g 840 1052 M -10 20 V .62 g 830 1072 M -9 20 V .62 g 821 1092 M -1 1 V stroke 820 1093 M .62 g 820 1093 M -9 19 V .62 g 811 1112 M -9 20 V .62 g 802 1132 M -9 20 V .62 g 793 1152 M 0 1 V .62 g 793 1153 M -9 19 V .62 g 784 1172 M -9 21 V .62 g 775 1193 M -10 19 V .62 g 765 1212 M 0 1 V .62 g 765 1213 M -9 20 V .62 g 756 1233 M -9 20 V .62 g 747 1253 M -9 20 V .62 g .62 g 738 1273 M -9 20 V .62 g 729 1293 M -9 21 V .62 g 720 1314 M -9 20 V .62 g .62 g 711 1334 M -9 20 V .62 g 702 1354 M -8 20 V .62 g 694 1374 M -9 20 V .62 g 685 1394 M -1 2 V .62 g 684 1396 M -8 18 V .62 g 676 1414 M -9 21 V .62 g 667 1435 M -9 20 V .62 g 658 1455 M -1 4 V .62 g 657 1459 M -7 16 V .62 g 650 1475 M -9 20 V .62 g 641 1495 M -9 20 V .62 g 632 1515 M -3 7 V .62 g 629 1522 M -6 13 V .62 g 623 1535 M -8 20 V .62 g 615 1555 M -9 21 V .62 g 606 1576 M -4 9 V 0 g .6 g 1105 588 M .6 g 1105 588 M -12 20 V .6 g 1093 608 M 0 2 V .6 g 1093 610 M -11 18 V .6 g 1082 628 M -11 20 V .6 g 1071 648 M -6 11 V .6 g 1065 659 M -5 10 V .6 g 1060 669 M -11 20 V .6 g 1049 689 M -10 20 V .6 g 1039 709 M -1 1 V .6 g 1038 710 M -10 19 V .6 g 1028 729 M -11 20 V .6 g 1017 749 M -6 13 V .6 g 1011 762 M -4 7 V .6 g 1007 769 M -11 21 V .6 g 996 790 M -10 20 V .6 g 986 810 M -2 4 V .6 g 984 814 M -8 16 V .6 g 976 830 M -10 20 V .6 g 966 850 M -10 18 V .6 g 956 868 M -1 2 V .6 g 955 870 M -10 20 V .6 g 945 890 M -10 20 V stroke 935 910 M .6 g 935 910 M -6 13 V .6 g 929 923 M -4 8 V .6 g 925 931 M -10 20 V .6 g 915 951 M -9 20 V .6 g 906 971 M -4 8 V .6 g 902 979 M -6 12 V .6 g 896 991 M -10 20 V .6 g 886 1011 M -10 20 V .6 g 876 1031 M -1 5 V .6 g 875 1036 M -8 16 V .6 g 867 1052 M -10 20 V .6 g 857 1072 M -9 20 V .6 g 848 1092 M -1 1 V .6 g 847 1093 M -9 19 V .6 g 838 1112 M -9 20 V .6 g 829 1132 M -9 20 V .6 g .6 g 820 1152 M -10 20 V .6 g 810 1172 M -9 21 V .6 g 801 1193 M -8 18 V .6 g 793 1211 M -1 2 V .6 g 792 1213 M -9 20 V .6 g 783 1233 M -9 20 V .6 g 774 1253 M -9 18 V .6 g 765 1271 M -1 2 V .6 g 764 1273 M -9 20 V .6 g 755 1293 M -9 21 V .6 g 746 1314 M -8 18 V .6 g 738 1332 M -1 2 V .6 g 737 1334 M -9 20 V .6 g 728 1354 M -9 20 V .6 g 719 1374 M -8 19 V .6 g 711 1393 M -1 1 V .6 g 710 1394 M -8 20 V .6 g 702 1414 M -9 21 V .6 g 693 1435 M -9 20 V .6 g .6 g 684 1455 M -9 20 V .6 g 675 1475 M -9 20 V .6 g 666 1495 M -9 20 V .6 g 657 1515 M 0 2 V .6 g 657 1517 M -8 18 V .6 g 649 1535 M -9 20 V .6 g 640 1555 M -9 21 V .6 g 631 1576 M -2 4 V .6 g 629 1580 M -6 16 V .6 g 623 1596 M -9 20 V .6 g 614 1616 M -9 20 V .6 g 605 1636 M -3 8 V 0 g .58 g 1138 588 M .58 g 1138 588 M -12 20 V .58 g 1126 608 M -6 12 V .58 g 1120 620 M -5 8 V .58 g 1115 628 M -11 20 V .58 g 1104 648 M -11 20 V stroke 1093 668 M .58 g 1093 668 M -1 1 V .58 g 1092 669 M -11 20 V .58 g 1081 689 M -11 20 V .58 g 1070 709 M -5 9 V .58 g 1065 718 M -6 11 V .58 g 1059 729 M -11 20 V .58 g 1048 749 M -10 20 V .58 g .58 g 1038 769 M -11 21 V .58 g 1027 790 M -11 20 V .58 g 1016 810 M -5 10 V .58 g 1011 820 M -5 10 V .58 g 1006 830 M -10 20 V .58 g 996 850 M -11 20 V .58 g 985 870 M -1 3 V .58 g 984 873 M -9 17 V .58 g 975 890 M -10 20 V .58 g 965 910 M -9 17 V .58 g 956 927 M -1 4 V .58 g 955 931 M -10 20 V .58 g 945 951 M -10 20 V .58 g 935 971 M -6 11 V .58 g 929 982 M -4 9 V .58 g 925 991 M -10 20 V .58 g 915 1011 M -10 20 V .58 g 905 1031 M -3 7 V .58 g 902 1038 M -7 14 V .58 g 895 1052 M -9 20 V .58 g 886 1072 M -10 20 V .58 g 876 1092 M -1 3 V .58 g 875 1095 M -9 17 V .58 g 866 1112 M -9 20 V .58 g 857 1132 M -10 20 V .58 g .58 g 847 1152 M -9 20 V .58 g 838 1172 M -10 21 V .58 g 828 1193 M -8 18 V .58 g 820 1211 M -1 2 V .58 g 819 1213 M -9 20 V .58 g 810 1233 M -9 20 V .58 g 801 1253 M -8 17 V .58 g 793 1270 M -2 3 V .58 g 791 1273 M -9 20 V .58 g 782 1293 M -9 21 V .58 g 773 1314 M -8 16 V .58 g 765 1330 M -1 4 V .58 g 764 1334 M -9 20 V .58 g 755 1354 M -9 20 V .58 g 746 1374 M -8 17 V .58 g 738 1391 M -1 3 V .58 g 737 1394 M -9 20 V .58 g 728 1414 M -9 21 V .58 g 719 1435 M -8 18 V .58 g 711 1453 M -1 2 V stroke 710 1455 M .58 g 710 1455 M -9 20 V .58 g 701 1475 M -9 20 V .58 g 692 1495 M -8 20 V .58 g .58 g 684 1515 M -9 20 V .58 g 675 1535 M -9 20 V .58 g 666 1555 M -9 21 V .58 g 657 1576 M 0 1 V .58 g 657 1577 M -8 19 V .58 g 649 1596 M -9 20 V .58 g 640 1616 M -9 20 V .58 g 631 1636 M -2 4 V .58 g 629 1640 M -7 16 V .58 g 622 1656 M -8 20 V .58 g 614 1676 M -9 21 V .58 g 605 1697 M -3 7 V 0 g .56 g 1173 588 M .56 g 1173 588 M -12 20 V .56 g 1161 608 M -12 20 V .56 g 1149 628 M -2 4 V .56 g 1147 632 M -9 16 V .56 g 1138 648 M -12 21 V .56 g 1126 669 M -6 11 V .56 g 1120 680 M -5 9 V .56 g 1115 689 M -12 20 V .56 g 1103 709 M -10 19 V .56 g 1093 728 M -1 1 V .56 g 1092 729 M -11 20 V .56 g 1081 749 M -11 20 V .56 g 1070 769 M -5 9 V .56 g 1065 778 M -6 12 V .56 g 1059 790 M -11 20 V .56 g 1048 810 M -10 18 V .56 g 1038 828 M -1 2 V .56 g 1037 830 M -10 20 V .56 g 1027 850 M -11 20 V .56 g 1016 870 M -5 10 V .56 g 1011 880 M -5 10 V .56 g 1006 890 M -11 20 V .56 g 995 910 M -10 21 V .56 g 985 931 M -1 2 V .56 g 984 933 M -9 18 V .56 g 975 951 M -11 20 V .56 g 964 971 M -8 16 V .56 g 956 987 M -2 4 V .56 g 954 991 M -10 20 V .56 g 944 1011 M -10 20 V .56 g 934 1031 M -5 11 V .56 g 929 1042 M -5 10 V .56 g 924 1052 M -9 20 V .56 g 915 1072 M -10 20 V .56 g 905 1092 M -3 6 V .56 g 902 1098 M -7 14 V .56 g 895 1112 M -10 20 V stroke 885 1132 M .56 g 885 1132 M -9 20 V .56 g 876 1152 M -1 3 V .56 g 875 1155 M -9 17 V .56 g 866 1172 M -9 21 V .56 g 857 1193 M -10 19 V .56 g 847 1212 M 0 1 V .56 g 847 1213 M -9 20 V .56 g 838 1233 M -10 20 V .56 g 828 1253 M -8 18 V .56 g 820 1271 M -1 2 V .56 g 819 1273 M -9 20 V .56 g 810 1293 M -9 21 V .56 g 801 1314 M -8 17 V .56 g 793 1331 M -2 3 V .56 g 791 1334 M -9 20 V .56 g 782 1354 M -9 20 V .56 g 773 1374 M -8 17 V .56 g 765 1391 M -1 3 V .56 g 764 1394 M -9 20 V .56 g 755 1414 M -9 21 V .56 g 746 1435 M -8 17 V .56 g 738 1452 M -1 3 V .56 g 737 1455 M -9 20 V .56 g 728 1475 M -9 20 V .56 g 719 1495 M -8 18 V .56 g 711 1513 M -1 2 V .56 g 710 1515 M -9 20 V .56 g 701 1535 M -8 20 V .56 g 693 1555 M -9 20 V .56 g 684 1575 M 0 1 V .56 g 684 1576 M -9 20 V .56 g 675 1596 M -9 20 V .56 g 666 1616 M -9 20 V .56 g 657 1636 M 0 2 V .56 g 657 1638 M -8 18 V .56 g 649 1656 M -9 20 V .56 g 640 1676 M -9 21 V .56 g 631 1697 M -2 4 V .56 g 629 1701 M -6 16 V .56 g 623 1717 M -9 20 V .56 g 614 1737 M -9 20 V .56 g 605 1757 M -3 8 V 0 g .54 g 1210 588 M .54 g 1210 588 M -8 13 V .54 g 1202 601 M -5 7 V .54 g 1197 608 M -12 20 V .54 g 1185 628 M -11 19 V .54 g 1174 647 M -1 1 V .54 g 1173 648 M -12 21 V .54 g 1161 669 M -12 20 V .54 g 1149 689 M -2 4 V .54 g 1147 693 M -9 16 V .54 g 1138 709 M -12 20 V stroke 1126 729 M .54 g 1126 729 M -6 11 V .54 g 1120 740 M -5 9 V .54 g 1115 749 M -12 20 V .54 g 1103 769 M -10 20 V .54 g 1093 789 M -1 1 V .54 g 1092 790 M -11 20 V .54 g 1081 810 M -11 20 V .54 g 1070 830 M -5 9 V .54 g 1065 839 M -6 11 V .54 g 1059 850 M -11 20 V .54 g 1048 870 M -10 19 V .54 g 1038 889 M -1 1 V .54 g 1037 890 M -10 20 V .54 g 1027 910 M -11 21 V .54 g 1016 931 M -5 10 V .54 g 1011 941 M -5 10 V .54 g 1006 951 M -11 20 V .54 g 995 971 M -10 20 V .54 g 985 991 M -1 3 V .54 g 984 994 M -9 17 V .54 g 975 1011 M -10 20 V .54 g 965 1031 M -9 17 V .54 g 956 1048 M -2 4 V .54 g 954 1052 M -9 20 V .54 g 945 1072 M -10 20 V .54 g 935 1092 M -6 11 V .54 g 929 1103 M -4 9 V .54 g 925 1112 M -10 20 V .54 g 915 1132 M -10 20 V .54 g 905 1152 M -3 7 V .54 g 902 1159 M -7 13 V .54 g 895 1172 M -9 21 V .54 g 886 1193 M -10 20 V .54 g 876 1213 M -1 3 V .54 g 875 1216 M -9 17 V .54 g 866 1233 M -9 20 V .54 g 857 1253 M -10 20 V .54 g 847 1273 M 0 1 V .54 g 847 1274 M -9 19 V .54 g 838 1293 M -9 21 V .54 g 829 1314 M -9 18 V .54 g 820 1332 M -1 2 V .54 g 819 1334 M -9 20 V .54 g 810 1354 M -9 20 V .54 g 801 1374 M -8 18 V .54 g 793 1392 M -1 2 V .54 g 792 1394 M -9 20 V .54 g 783 1414 M -9 21 V .54 g 774 1435 M -9 17 V .54 g 765 1452 M -1 3 V .54 g 764 1455 M -9 20 V .54 g 755 1475 M -9 20 V stroke 746 1495 M .54 g 746 1495 M -8 18 V .54 g 738 1513 M -1 2 V .54 g 737 1515 M -8 20 V .54 g 729 1535 M -9 20 V .54 g 720 1555 M -9 20 V .54 g 711 1575 M 0 1 V .54 g 711 1576 M -9 20 V .54 g 702 1596 M -9 20 V .54 g 693 1616 M -9 20 V .54 g 684 1636 M 0 1 V .54 g 684 1637 M -8 19 V .54 g 676 1656 M -9 20 V .54 g 667 1676 M -9 21 V .54 g 658 1697 M -1 3 V .54 g 657 1700 M -8 17 V .54 g 649 1717 M -8 20 V .54 g 641 1737 M -9 20 V .54 g 632 1757 M -3 6 V .54 g 629 1763 M -6 14 V .54 g 623 1777 M -8 20 V .54 g 615 1797 M -9 20 V .54 g 606 1817 M -4 10 V 0 g .52 g 1249 588 M .52 g 1249 588 M -13 20 V .52 g 1236 608 M -7 11 V .52 g 1229 619 M -6 9 V .52 g 1223 628 M -12 20 V .52 g 1211 648 M -9 15 V .52 g 1202 663 M -4 6 V .52 g 1198 669 M -12 20 V .52 g 1186 689 M -12 20 V .52 g .52 g 1174 709 M -12 20 V .52 g 1162 729 M -12 20 V .52 g 1150 749 M -3 6 V .52 g 1147 755 M -8 14 V .52 g 1139 769 M -12 21 V .52 g 1127 790 M -7 12 V .52 g 1120 802 M -4 8 V .52 g 1116 810 M -12 20 V .52 g 1104 830 M -11 20 V .52 g 1093 850 M 0 1 V .52 g 1093 851 M -11 19 V .52 g 1082 870 M -11 20 V .52 g 1071 890 M -6 11 V .52 g 1065 901 M -5 9 V .52 g 1060 910 M -11 21 V .52 g 1049 931 M -11 20 V .52 g .52 g 1038 951 M -10 20 V .52 g 1028 971 M -11 20 V .52 g 1017 991 M -6 12 V .52 g 1011 1003 M -4 8 V .52 g 1007 1011 M -11 20 V .52 g 996 1031 M -10 21 V stroke 986 1052 M .52 g 986 1052 M -2 4 V .52 g 984 1056 M -8 16 V .52 g 976 1072 M -11 20 V .52 g 965 1092 M -9 18 V .52 g 956 1110 M -1 2 V .52 g 955 1112 M -10 20 V .52 g 945 1132 M -10 20 V .52 g 935 1152 M -6 13 V .52 g 929 1165 M -4 7 V .52 g 925 1172 M -9 21 V .52 g 916 1193 M -10 20 V .52 g 906 1213 M -4 8 V .52 g 902 1221 M -6 12 V .52 g 896 1233 M -9 20 V .52 g 887 1253 M -10 20 V .52 g 877 1273 M -2 5 V .52 g 875 1278 M -8 15 V .52 g 867 1293 M -9 21 V .52 g 858 1314 M -10 20 V .52 g 848 1334 M -1 2 V .52 g 847 1336 M -8 18 V .52 g 839 1354 M -9 20 V .52 g 830 1374 M -10 20 V .52 g 820 1394 M 0 1 V .52 g 820 1395 M -9 19 V .52 g 811 1414 M -9 21 V .52 g 802 1435 M -9 20 V .52 g .52 g 793 1455 M -9 20 V .52 g 784 1475 M -9 20 V .52 g 775 1495 M -10 20 V .52 g .52 g 765 1515 M -8 20 V .52 g 757 1535 M -9 20 V .52 g 748 1555 M -10 21 V .52 g .52 g 738 1576 M -8 20 V .52 g 730 1596 M -9 20 V .52 g 721 1616 M -9 20 V .52 g 712 1636 M -1 2 V .52 g 711 1638 M -8 18 V .52 g 703 1656 M -9 20 V .52 g 694 1676 M -9 21 V .52 g 685 1697 M -1 3 V .52 g 684 1700 M -7 17 V .52 g 677 1717 M -9 20 V .52 g 668 1737 M -9 20 V .52 g 659 1757 M -2 6 V .52 g 657 1763 M -6 14 V .52 g 651 1777 M -9 20 V .52 g 642 1797 M -9 20 V .52 g 633 1817 M -4 10 V .52 g 629 1827 M -4 11 V .52 g 625 1838 M -9 20 V .52 g 616 1858 M -9 20 V stroke 607 1878 M .52 g 607 1878 M -5 12 V 0 g .52 g 6052 619 M .52 g 6052 619 M -7 -11 V .52 g 6045 608 M -13 -20 V 0 g .5 g 1290 588 M .5 g 1290 588 M -7 10 V .5 g 1283 598 M -7 10 V .5 g 1276 608 M -13 20 V .5 g 1263 628 M -7 12 V .5 g 1256 640 M -6 8 V .5 g 1250 648 M -12 21 V .5 g 1238 669 M -9 14 V .5 g 1229 683 M -4 6 V .5 g 1225 689 M -12 20 V .5 g 1213 709 M -11 18 V .5 g 1202 727 M -2 2 V .5 g 1200 729 M -12 20 V .5 g 1188 749 M -12 20 V .5 g 1176 769 M -2 3 V .5 g 1174 772 M -10 18 V .5 g 1164 790 M -12 20 V .5 g 1152 810 M -5 8 V .5 g 1147 818 M -7 12 V .5 g 1140 830 M -11 20 V .5 g 1129 850 M -9 15 V .5 g 1120 865 M -3 5 V .5 g 1117 870 M -11 20 V .5 g 1106 890 M -12 20 V .5 g 1094 910 M -1 4 V .5 g 1093 914 M -10 17 V .5 g 1083 931 M -11 20 V .5 g 1072 951 M -7 13 V .5 g 1065 964 M -4 7 V .5 g 1061 971 M -10 20 V .5 g 1051 991 M -11 20 V .5 g 1040 1011 M -2 3 V .5 g 1038 1014 M -9 17 V .5 g 1029 1031 M -10 21 V .5 g 1019 1052 M -8 14 V .5 g 1011 1066 M -3 6 V .5 g 1008 1072 M -10 20 V .5 g 998 1092 M -11 20 V .5 g 987 1112 M -3 7 V .5 g 984 1119 M -7 13 V .5 g 977 1132 M -10 20 V .5 g 967 1152 M -10 20 V .5 g 957 1172 M -1 1 V .5 g 956 1173 M -9 20 V .5 g 947 1193 M -10 20 V .5 g 937 1213 M -8 16 V .5 g 929 1229 M -2 4 V .5 g 927 1233 M -10 20 V .5 g 917 1253 M -10 20 V stroke 907 1273 M .5 g 907 1273 M -5 12 V .5 g 902 1285 M -4 8 V .5 g 898 1293 M -10 21 V .5 g 888 1314 M -10 20 V .5 g 878 1334 M -3 8 V .5 g 875 1342 M -6 12 V .5 g 869 1354 M -10 20 V .5 g 859 1374 M -9 20 V .5 g 850 1394 M -3 6 V .5 g 847 1400 M -6 14 V .5 g 841 1414 M -10 21 V .5 g 831 1435 M -9 20 V .5 g 822 1455 M -2 4 V .5 g 820 1459 M -7 16 V .5 g 813 1475 M -9 20 V .5 g 804 1495 M -10 20 V .5 g 794 1515 M -1 3 V .5 g 793 1518 M -8 17 V .5 g 785 1535 M -9 20 V .5 g 776 1555 M -9 21 V .5 g 767 1576 M -2 3 V .5 g 765 1579 M -7 17 V .5 g 758 1596 M -9 20 V .5 g 749 1616 M -9 20 V .5 g 740 1636 M -2 4 V .5 g 738 1640 M -7 16 V .5 g 731 1656 M -9 20 V .5 g 722 1676 M -8 21 V .5 g 714 1697 M -3 5 V .5 g 711 1702 M -6 15 V .5 g 705 1717 M -9 20 V .5 g 696 1737 M -9 20 V .5 g 687 1757 M -3 8 V .5 g 684 1765 M -6 12 V .5 g 678 1777 M -8 20 V .5 g 670 1797 M -9 20 V .5 g 661 1817 M -4 11 V .5 g 657 1828 M -5 10 V .5 g 652 1838 M -8 20 V .5 g 644 1858 M -9 20 V .5 g 635 1878 M -6 13 V .5 g 629 1891 M -3 7 V .5 g 626 1898 M -8 20 V .5 g 618 1918 M -9 20 V .5 g 609 1938 M -7 17 V 0 g .5 g 6052 682 M .5 g 6052 682 M -9 -13 V .5 g 6043 669 M -13 -21 V .5 g 6030 648 M -5 -7 V .5 g 6025 641 M -9 -13 V .5 g 6016 628 M -13 -20 V .5 g 6003 608 M -5 -8 V .5 g 5998 600 M -9 -12 V stroke 5989 588 M 0 g .48 g 1333 588 M .48 g 1333 588 M -13 20 V .48 g 1320 608 M -9 14 V .48 g 1311 622 M -5 6 V .48 g 1306 628 M -13 20 V .48 g 1293 648 M -10 14 V .48 g 1283 662 M -4 7 V .48 g 1279 669 M -13 20 V .48 g 1266 689 M -10 15 V .48 g 1256 704 M -3 5 V .48 g 1253 709 M -13 20 V .48 g 1240 729 M -11 18 V .48 g 1229 747 M -2 2 V .48 g 1227 749 M -12 20 V .48 g 1215 769 M -12 21 V .48 g 1203 790 M -1 1 V .48 g 1202 791 M -12 19 V .48 g 1190 810 M -12 20 V .48 g 1178 830 M -4 6 V .48 g 1174 836 M -8 14 V .48 g 1166 850 M -12 20 V .48 g 1154 870 M -7 13 V .48 g 1147 883 M -4 7 V .48 g 1143 890 M -12 20 V .48 g 1131 910 M -11 20 V .48 g 1120 930 M -1 1 V .48 g 1119 931 M -11 20 V .48 g 1108 951 M -11 20 V .48 g 1097 971 M -4 7 V .48 g 1093 978 M -7 13 V .48 g 1086 991 M -11 20 V .48 g 1075 1011 M -10 17 V .48 g 1065 1028 M -1 3 V .48 g 1064 1031 M -11 21 V .48 g 1053 1052 M -11 20 V .48 g 1042 1072 M -4 7 V .48 g 1038 1079 M -7 13 V .48 g 1031 1092 M -10 20 V .48 g 1021 1112 M -10 19 V .48 g 1011 1131 M -1 1 V .48 g 1010 1132 M -10 20 V .48 g 1000 1152 M -11 20 V .48 g 989 1172 M -5 12 V .48 g 984 1184 M -5 9 V .48 g 979 1193 M -10 20 V .48 g 969 1213 M -10 20 V .48 g 959 1233 M -3 5 V .48 g 956 1238 M -7 15 V .48 g 949 1253 M -10 20 V .48 g 939 1273 M -10 20 V .48 g .48 g 929 1293 M -10 21 V .48 g 919 1314 M -10 20 V .48 g 909 1334 M -7 15 V stroke 902 1349 M .48 g 902 1349 M -2 5 V .48 g 900 1354 M -10 20 V .48 g 890 1374 M -10 20 V .48 g 880 1394 M -5 13 V .48 g 875 1407 M -4 7 V .48 g 871 1414 M -9 21 V .48 g 862 1435 M -10 20 V .48 g 852 1455 M -5 10 V .48 g 847 1465 M -4 10 V .48 g 843 1475 M -10 20 V .48 g 833 1495 M -9 20 V .48 g 824 1515 M -4 9 V .48 g 820 1524 M -5 11 V .48 g 815 1535 M -9 20 V .48 g 806 1555 M -10 21 V .48 g 796 1576 M -3 8 V .48 g 793 1584 M -6 12 V .48 g 787 1596 M -9 20 V .48 g 778 1616 M -9 20 V .48 g 769 1636 M -4 8 V .48 g 765 1644 M -5 12 V .48 g 760 1656 M -9 20 V .48 g 751 1676 M -9 21 V .48 g 742 1697 M -4 9 V .48 g 738 1706 M -5 11 V .48 g 733 1717 M -8 20 V .48 g 725 1737 M -9 20 V .48 g 716 1757 M -5 11 V .48 g 711 1768 M -4 9 V .48 g 707 1777 M -9 20 V .48 g 698 1797 M -9 20 V .48 g 689 1817 M -5 13 V .48 g 684 1830 M -3 8 V .48 g 681 1838 M -9 20 V .48 g 672 1858 M -9 20 V .48 g 663 1878 M -6 16 V .48 g 657 1894 M -2 4 V .48 g 655 1898 M -9 20 V .48 g 646 1918 M -9 20 V .48 g 637 1938 M -8 19 V .48 g 629 1957 M 0 2 V .48 g 629 1959 M -9 20 V .48 g 620 1979 M -8 20 V .48 g 612 1999 M -9 20 V .48 g 603 2019 M -1 2 V 0 g .48 g 6052 747 M .48 g 6052 747 M -12 -18 V .48 g 6040 729 M -13 -20 V .48 g 6027 709 M -2 -3 V .48 g 6025 706 M -12 -17 V .48 g 6013 689 M -13 -20 V .48 g 6000 669 M -2 -4 V .48 g 5998 665 M -12 -17 V stroke 5986 648 M .48 g 5986 648 M -14 -20 V .48 g 5972 628 M -2 -3 V .48 g 5970 625 M -12 -17 V .48 g 5958 608 M -14 -20 V 0 g .46 g 632 2019 M .46 g 632 2019 M -3 6 V .46 g 629 2025 M -6 14 V .46 g 623 2039 M -8 20 V .46 g 615 2059 M -9 20 V .46 g 606 2079 M -4 10 V 0 g .46 g 1380 588 M .46 g 1380 588 M -14 20 V .46 g 1366 608 M -1 1 V .46 g 1365 609 M -13 19 V .46 g 1352 628 M -14 20 V .46 g 1338 648 M -1 0 V .46 g 1337 648 M -13 21 V .46 g 1324 669 M -13 19 V .46 g 1311 688 M -1 1 V .46 g 1310 689 M -14 20 V .46 g 1296 709 M -13 19 V .46 g 1283 728 M 0 1 V .46 g 1283 729 M -13 20 V .46 g 1270 749 M -13 20 V .46 g 1257 769 M -1 1 V .46 g 1256 770 M -12 20 V .46 g 1244 790 M -13 20 V .46 g 1231 810 M -2 3 V .46 g 1229 813 M -11 17 V .46 g 1218 830 M -12 20 V .46 g 1206 850 M -4 7 V .46 g 1202 857 M -8 13 V .46 g 1194 870 M -13 20 V .46 g 1181 890 M -7 12 V .46 g 1174 902 M -5 8 V .46 g 1169 910 M -12 21 V .46 g 1157 931 M -10 17 V .46 g 1147 948 M -1 3 V .46 g 1146 951 M -12 20 V .46 g 1134 971 M -12 20 V .46 g 1122 991 M -2 5 V .46 g 1120 996 M -9 15 V .46 g 1111 1011 M -11 20 V .46 g 1100 1031 M -7 13 V .46 g 1093 1044 M -4 8 V .46 g 1089 1052 M -12 20 V .46 g 1077 1072 M -11 20 V .46 g 1066 1092 M -1 2 V .46 g 1065 1094 M -9 18 V .46 g 1056 1112 M -11 20 V .46 g 1045 1132 M -7 13 V .46 g 1038 1145 M -4 7 V .46 g 1034 1152 M -10 20 V stroke 1024 1172 M .46 g 1024 1172 M -11 21 V .46 g 1013 1193 M -2 4 V .46 g 1011 1197 M -8 16 V .46 g 1003 1213 M -11 20 V .46 g 992 1233 M -8 17 V .46 g 984 1250 M -2 3 V .46 g 982 1253 M -10 20 V .46 g 972 1273 M -10 20 V .46 g 962 1293 M -6 11 V .46 g 956 1304 M -4 10 V .46 g 952 1314 M -10 20 V .46 g 942 1334 M -10 20 V .46 g 932 1354 M -3 5 V .46 g 929 1359 M -7 15 V .46 g 922 1374 M -10 20 V .46 g 912 1394 M -10 20 V .46 g 902 1414 M 0 2 V .46 g 902 1416 M -9 19 V .46 g 893 1435 M -10 20 V .46 g 883 1455 M -8 18 V .46 g 875 1473 M -1 2 V .46 g 874 1475 M -10 20 V .46 g 864 1495 M -9 20 V .46 g 855 1515 M -8 16 V .46 g 847 1531 M -2 4 V .46 g 845 1535 M -9 20 V .46 g 836 1555 M -9 21 V .46 g 827 1576 M -7 14 V .46 g 820 1590 M -2 6 V .46 g 818 1596 M -10 20 V .46 g 808 1616 M -9 20 V .46 g 799 1636 M -6 14 V .46 g 793 1650 M -3 6 V .46 g 790 1656 M -9 20 V .46 g 781 1676 M -9 21 V .46 g 772 1697 M -7 14 V .46 g 765 1711 M -2 6 V .46 g 763 1717 M -9 20 V .46 g 754 1737 M -9 20 V .46 g 745 1757 M -7 16 V .46 g 738 1773 M -2 4 V .46 g 736 1777 M -9 20 V .46 g 727 1797 M -8 20 V .46 g 719 1817 M -8 18 V .46 g 711 1835 M -1 3 V .46 g 710 1838 M -9 20 V .46 g 701 1858 M -9 20 V .46 g 692 1878 M -8 20 V .46 g .46 g 684 1898 M -9 20 V .46 g 675 1918 M -9 20 V .46 g 666 1938 M -8 21 V .46 g 658 1959 M -1 2 V stroke 657 1961 M .46 g 657 1961 M -8 18 V .46 g 649 1979 M -9 20 V .46 g 640 1999 M -8 20 V 0 g .46 g 6052 813 M .46 g 6052 813 M -2 -3 V .46 g 6050 810 M -14 -20 V .46 g 6036 790 M -11 -18 V .46 g 6025 772 M -2 -3 V .46 g 6023 769 M -14 -20 V .46 g 6009 749 M -11 -18 V .46 g 5998 731 M -2 -2 V .46 g 5996 729 M -14 -20 V .46 g 5982 709 M -12 -17 V .46 g 5970 692 M -2 -3 V .46 g 5968 689 M -14 -20 V .46 g 5954 669 M -11 -16 V .46 g 5943 653 M -4 -5 V .46 g 5939 648 M -14 -20 V .46 g 5925 628 M -9 -12 V .46 g 5916 616 M -6 -8 V .46 g 5910 608 M -15 -20 V 0 g .44 g 670 1999 M .44 g 670 1999 M -9 20 V .44 g 661 2019 M -4 11 V .44 g 657 2030 M -4 9 V .44 g 653 2039 M -9 20 V .44 g 644 2059 M -9 20 V .44 g 635 2079 M -6 15 V .44 g 629 2094 M -2 6 V .44 g 627 2100 M -9 20 V .44 g 618 2120 M -8 20 V .44 g 610 2140 M -8 18 V 0 g .44 g 1430 588 M .44 g 1430 588 M -10 14 V .44 g 1420 602 M -5 6 V .44 g 1415 608 M -15 20 V .44 g 1400 628 M -8 11 V .44 g 1392 639 M -6 9 V .44 g 1386 648 M -15 21 V .44 g 1371 669 M -6 8 V .44 g 1365 677 M -8 12 V .44 g 1357 689 M -14 20 V .44 g 1343 709 M -5 7 V .44 g 1338 716 M -9 13 V .44 g 1329 729 M -14 20 V .44 g 1315 749 M -4 6 V .44 g 1311 755 M -10 14 V .44 g 1301 769 M -13 21 V .44 g 1288 790 M -5 6 V .44 g 1283 796 M -9 14 V .44 g 1274 810 M -13 20 V .44 g 1261 830 M -5 8 V .44 g 1256 838 M -8 12 V .44 g 1248 850 M -13 20 V stroke 1235 870 M .44 g 1235 870 M -6 10 V .44 g 1229 880 M -6 10 V .44 g 1223 890 M -13 20 V .44 g 1210 910 M -8 14 V .44 g 1202 924 M -4 7 V .44 g 1198 931 M -12 20 V .44 g 1186 951 M -12 18 V .44 g 1174 969 M -1 2 V .44 g 1173 971 M -11 20 V .44 g 1162 991 M -12 20 V .44 g 1150 1011 M -3 5 V .44 g 1147 1016 M -9 15 V .44 g 1138 1031 M -12 21 V .44 g 1126 1052 M -6 11 V .44 g 1120 1063 M -5 9 V .44 g 1115 1072 M -11 20 V .44 g 1104 1092 M -11 20 V .44 g 1093 1112 M -1 0 V .44 g 1092 1112 M -11 20 V .44 g 1081 1132 M -11 20 V .44 g 1070 1152 M -5 9 V .44 g 1065 1161 M -6 11 V .44 g 1059 1172 M -11 21 V .44 g 1048 1193 M -10 19 V .44 g 1038 1212 M 0 1 V .44 g 1038 1213 M -11 20 V .44 g 1027 1233 M -10 20 V .44 g 1017 1253 M -6 11 V .44 g 1011 1264 M -5 9 V .44 g 1006 1273 M -10 20 V .44 g 996 1293 M -11 21 V .44 g 985 1314 M -1 3 V .44 g 984 1317 M -9 17 V .44 g 975 1334 M -10 20 V .44 g 965 1354 M -9 18 V .44 g 956 1372 M -1 2 V .44 g 955 1374 M -10 20 V .44 g 945 1394 M -10 20 V .44 g 935 1414 M -6 13 V .44 g 929 1427 M -4 8 V .44 g 925 1435 M -9 20 V .44 g 916 1455 M -10 20 V .44 g 906 1475 M -4 8 V .44 g 902 1483 M -6 12 V .44 g 896 1495 M -9 20 V .44 g 887 1515 M -10 20 V .44 g 877 1535 M -2 6 V .44 g 875 1541 M -7 14 V .44 g 868 1555 M -10 21 V .44 g 858 1576 M -9 20 V .44 g 849 1596 M -2 3 V .44 g 847 1599 M -7 17 V stroke 840 1616 M .44 g 840 1616 M -10 20 V .44 g 830 1636 M -9 20 V .44 g 821 1656 M -1 2 V .44 g 820 1658 M -8 18 V .44 g 812 1676 M -9 21 V .44 g 803 1697 M -9 20 V .44 g 794 1717 M -1 1 V .44 g 793 1718 M -8 19 V .44 g 785 1737 M -9 20 V .44 g 776 1757 M -10 20 V .44 g 766 1777 M -1 2 V .44 g 765 1779 M -7 18 V .44 g 758 1797 M -9 20 V .44 g 749 1817 M -9 21 V .44 g 740 1838 M -2 3 V .44 g 738 1841 M -7 17 V .44 g 731 1858 M -9 20 V .44 g 722 1878 M -9 20 V .44 g 713 1898 M -2 5 V .44 g 711 1903 M -6 15 V .44 g 705 1918 M -9 20 V .44 g 696 1938 M -9 21 V .44 g 687 1959 M -3 7 V .44 g 684 1966 M -6 13 V .44 g 678 1979 M -8 20 V 0 g .44 g 6052 881 M .44 g 6052 881 M -7 -11 V .44 g 6045 870 M -13 -20 V .44 g 6032 850 M -7 -11 V .44 g 6025 839 M -7 -9 V .44 g 6018 830 M -13 -20 V .44 g 6005 810 M -7 -11 V .44 g 5998 799 M -7 -9 V .44 g 5991 790 M -14 -21 V .44 g 5977 769 M -7 -9 V .44 g 5970 760 M -7 -11 V .44 g 5963 749 M -15 -20 V .44 g 5948 729 M -5 -8 V .44 g 5943 721 M -9 -12 V .44 g 5934 709 M -15 -20 V .44 g 5919 689 M -3 -5 V .44 g 5916 684 M -12 -15 V .44 g 5904 669 M -14 -21 V .44 g 5890 648 M -1 -1 V .44 g 5889 647 M -15 -19 V .44 g 5874 628 M -13 -17 V .44 g 5861 611 M -2 -3 V .44 g 5859 608 M -15 -20 V 0 g .42 g 709 1979 M .42 g 709 1979 M -9 20 V .42 g 700 1999 M -9 20 V .42 g 691 2019 M -7 18 V .42 g 684 2037 M -1 2 V stroke 683 2039 M .42 g 683 2039 M -9 20 V .42 g 674 2059 M -9 20 V .42 g 665 2079 M -8 21 V .42 g .42 g 657 2100 M -9 20 V .42 g 648 2120 M -8 20 V .42 g 640 2140 M -9 20 V .42 g 631 2160 M -2 4 V .42 g 629 2164 M -6 16 V .42 g 623 2180 M -9 20 V .42 g 614 2200 M -8 21 V .42 g 606 2221 M -4 8 V 0 g .42 g 1484 588 M .42 g 1484 588 M -10 13 V .42 g 1474 601 M -6 7 V .42 g 1468 608 M -15 20 V .42 g 1453 628 M -6 8 V .42 g 1447 636 M -10 12 V .42 g 1437 648 M -15 21 V .42 g 1422 669 M -2 3 V .42 g 1420 672 M -13 17 V .42 g 1407 689 M -15 20 V .42 g .42 g 1392 709 M -14 20 V .42 g 1378 729 M -13 17 V .42 g 1365 746 M -2 3 V .42 g 1363 749 M -14 20 V .42 g 1349 769 M -11 16 V .42 g 1338 785 M -3 5 V .42 g 1335 790 M -14 20 V .42 g 1321 810 M -10 15 V .42 g 1311 825 M -4 5 V .42 g 1307 830 M -14 20 V .42 g 1293 850 M -10 15 V .42 g 1283 865 M -3 5 V .42 g 1280 870 M -13 20 V .42 g 1267 890 M -11 17 V .42 g 1256 907 M -2 3 V .42 g 1254 910 M -13 21 V .42 g 1241 931 M -12 18 V .42 g 1229 949 M -1 2 V .42 g 1228 951 M -13 20 V .42 g 1215 971 M -12 20 V .42 g 1203 991 M -1 2 V .42 g 1202 993 M -11 18 V .42 g 1191 1011 M -13 20 V .42 g 1178 1031 M -4 7 V .42 g 1174 1038 M -8 14 V .42 g 1166 1052 M -11 20 V .42 g 1155 1072 M -8 12 V .42 g 1147 1084 M -4 8 V .42 g 1143 1092 M -12 20 V .42 g 1131 1112 M -11 20 V .42 g .42 g 1120 1132 M -12 20 V .42 g 1108 1152 M -11 20 V stroke 1097 1172 M .42 g 1097 1172 M -4 8 V .42 g 1093 1180 M -7 13 V .42 g 1086 1193 M -11 20 V .42 g 1075 1213 M -10 17 V .42 g 1065 1230 M -1 3 V .42 g 1064 1233 M -11 20 V .42 g 1053 1253 M -11 20 V .42 g 1042 1273 M -4 8 V .42 g 1038 1281 M -6 12 V .42 g 1032 1293 M -11 21 V .42 g 1021 1314 M -10 19 V .42 g 1011 1333 M -1 1 V .42 g 1010 1334 M -10 20 V .42 g 1000 1354 M -10 20 V .42 g 990 1374 M -6 12 V .42 g 984 1386 M -4 8 V .42 g 980 1394 M -11 20 V .42 g 969 1414 M -10 21 V .42 g 959 1435 M -3 6 V .42 g 956 1441 M -7 14 V .42 g 949 1455 M -10 20 V .42 g 939 1475 M -9 20 V .42 g 930 1495 M -1 1 V .42 g 929 1496 M -9 19 V .42 g 920 1515 M -10 20 V .42 g 910 1535 M -8 18 V .42 g 902 1553 M -2 2 V .42 g 900 1555 M -9 21 V .42 g 891 1576 M -10 20 V .42 g 881 1596 M -6 14 V .42 g 875 1610 M -3 6 V .42 g 872 1616 M -10 20 V .42 g 862 1636 M -9 20 V .42 g 853 1656 M -6 13 V .42 g 847 1669 M -3 7 V .42 g 844 1676 M -10 21 V .42 g 834 1697 M -9 20 V .42 g 825 1717 M -5 11 V .42 g 820 1728 M -4 9 V .42 g 816 1737 M -9 20 V .42 g 807 1757 M -9 20 V .42 g 798 1777 M -5 11 V .42 g 793 1788 M -4 9 V .42 g 789 1797 M -9 20 V .42 g 780 1817 M -9 21 V .42 g 771 1838 M -6 11 V .42 g 765 1849 M -3 9 V .42 g 762 1858 M -9 20 V .42 g 753 1878 M -9 20 V .42 g 744 1898 M -6 13 V .42 g 738 1911 M -3 7 V .42 g 735 1918 M -9 20 V stroke 726 1938 M .42 g 726 1938 M -8 21 V .42 g 718 1959 M -7 15 V .42 g 711 1974 M -2 5 V 0 g .42 g 3821 4619 M .42 g 3821 4619 M -3 -1 V .42 g 3818 4618 M -28 -6 V .42 g 3790 4612 M -27 -5 V .42 g 3763 4607 M -27 -4 V .42 g 3736 4603 M -27 -3 V .42 g 3709 4600 M -24 -1 V .42 g 3685 4599 M -4 0 V .42 g 3681 4599 M -27 -1 V .42 g 3654 4598 M -12 1 V .42 g 3642 4599 M -15 0 V .42 g 3627 4599 M -27 3 V .42 g 3600 4602 M -28 3 V .42 g 3572 4605 M -27 5 V .42 g 3545 4610 M -27 5 V .42 g 3518 4615 M -15 4 V 0 g .42 g 6052 950 M .42 g 6052 950 M -13 -19 V .42 g 6039 931 M -13 -21 V .42 g 6026 910 M -1 -1 V .42 g 6025 909 M -13 -19 V .42 g 6012 890 M -13 -20 V .42 g 5999 870 M -1 -1 V .42 g 5998 869 M -13 -19 V .42 g 5985 850 M -14 -20 V .42 g 5971 830 M -1 -1 V .42 g 5970 829 M -14 -19 V .42 g 5956 810 M -13 -19 V .42 g 5943 791 M -1 -1 V .42 g 5942 790 M -15 -21 V .42 g 5927 769 M -11 -15 V .42 g 5916 754 M -3 -5 V .42 g 5913 749 M -15 -20 V .42 g 5898 729 M -9 -12 V .42 g 5889 717 M -7 -8 V .42 g 5882 709 M -15 -20 V .42 g 5867 689 M -6 -8 V .42 g 5861 681 M -9 -12 V .42 g 5852 669 M -16 -21 V .42 g 5836 648 M -2 -2 V .42 g 5834 646 M -14 -18 V .42 g 5820 628 M -13 -17 V .42 g 5807 611 M -2 -3 V .42 g 5805 608 M -16 -20 V 0 g .4 g 740 1979 M .4 g 740 1979 M -2 4 V .4 g 738 1983 M -7 16 V .4 g 731 1999 M -8 20 V .4 g 723 2019 M -9 20 V .4 g 714 2039 M -3 7 V .4 g 711 2046 M -6 13 V stroke 705 2059 M .4 g 705 2059 M -9 20 V .4 g 696 2079 M -8 21 V .4 g 688 2100 M -4 9 V .4 g 684 2109 M -5 11 V .4 g 679 2120 M -8 20 V .4 g 671 2140 M -9 20 V .4 g 662 2160 M -5 13 V .4 g 657 2173 M -4 7 V .4 g 653 2180 M -8 20 V .4 g 645 2200 M -9 21 V .4 g 636 2221 M -7 16 V .4 g 629 2237 M -1 4 V .4 g 628 2241 M -9 20 V .4 g 619 2261 M -8 20 V .4 g 611 2281 M -9 20 V .4 g 602 2301 M 0 1 V 0 g .4 g 1542 588 M .4 g 1542 588 M -13 17 V .4 g 1529 605 M -3 3 V .4 g 1526 608 M -17 20 V .4 g 1509 628 M -8 10 V .4 g 1501 638 M -8 10 V .4 g 1493 648 M -16 21 V .4 g 1477 669 M -3 4 V .4 g 1474 673 M -12 16 V .4 g 1462 689 M -15 19 V .4 g 1447 708 M -1 1 V .4 g 1446 709 M -15 20 V .4 g 1431 729 M -11 15 V .4 g 1420 744 M -5 5 V .4 g 1415 749 M -15 20 V .4 g 1400 769 M -8 11 V .4 g 1392 780 M -7 10 V .4 g 1385 790 M -14 20 V .4 g 1371 810 M -6 8 V .4 g 1365 818 M -9 12 V .4 g 1356 830 M -14 20 V .4 g 1342 850 M -4 6 V .4 g 1338 856 M -10 14 V .4 g 1328 870 M -14 20 V .4 g 1314 890 M -3 5 V .4 g 1311 895 M -11 15 V .4 g 1300 910 M -13 21 V .4 g 1287 931 M -4 5 V .4 g 1283 936 M -9 15 V .4 g 1274 951 M -14 20 V .4 g 1260 971 M -4 6 V .4 g 1256 977 M -9 14 V .4 g 1247 991 M -13 20 V .4 g 1234 1011 M -5 9 V .4 g 1229 1020 M -7 11 V .4 g 1222 1031 M -13 21 V .4 g 1209 1052 M -7 12 V stroke 1202 1064 M .4 g 1202 1064 M -5 8 V .4 g 1197 1072 M -12 20 V .4 g 1185 1092 M -11 17 V .4 g 1174 1109 M -2 3 V .4 g 1172 1112 M -12 20 V .4 g 1160 1132 M -11 20 V .4 g 1149 1152 M -2 3 V .4 g 1147 1155 M -10 17 V .4 g 1137 1172 M -12 21 V .4 g 1125 1193 M -5 9 V .4 g 1120 1202 M -6 11 V .4 g 1114 1213 M -11 20 V .4 g 1103 1233 M -10 18 V .4 g 1093 1251 M -2 2 V .4 g 1091 1253 M -11 20 V .4 g 1080 1273 M -11 20 V .4 g 1069 1293 M -4 8 V .4 g 1065 1301 M -7 13 V .4 g 1058 1314 M -10 20 V .4 g 1048 1334 M -10 17 V .4 g 1038 1351 M -1 3 V .4 g 1037 1354 M -11 20 V .4 g 1026 1374 M -10 20 V .4 g 1016 1394 M -5 10 V .4 g 1011 1404 M -6 10 V .4 g 1005 1414 M -10 21 V .4 g 995 1435 M -10 20 V .4 g 985 1455 M -1 2 V .4 g 984 1457 M -9 18 V .4 g 975 1475 M -11 20 V .4 g 964 1495 M -8 16 V .4 g 956 1511 M -2 4 V .4 g 954 1515 M -9 20 V .4 g 945 1535 M -10 20 V .4 g 935 1555 M -6 12 V .4 g 929 1567 M -4 9 V .4 g 925 1576 M -10 20 V .4 g 915 1596 M -10 20 V .4 g 905 1616 M -3 7 V .4 g 902 1623 M -6 13 V .4 g 896 1636 M -10 20 V .4 g 886 1656 M -9 20 V .4 g 877 1676 M -2 5 V .4 g 875 1681 M -8 16 V .4 g 867 1697 M -9 20 V .4 g 858 1717 M -9 20 V .4 g 849 1737 M -2 3 V .4 g 847 1740 M -8 17 V .4 g 839 1757 M -9 20 V .4 g 830 1777 M -9 20 V .4 g 821 1797 M -1 2 V .4 g 820 1799 M -8 18 V stroke 812 1817 M .4 g 812 1817 M -9 21 V .4 g 803 1838 M -9 20 V .4 g 794 1858 M -1 2 V .4 g 793 1860 M -8 18 V .4 g 785 1878 M -9 20 V .4 g 776 1898 M -9 20 V .4 g 767 1918 M -2 3 V .4 g 765 1921 M -7 17 V .4 g 758 1938 M -9 21 V .4 g 749 1959 M -9 20 V 0 g .4 g 4011 4619 M .4 g 4011 4619 M -3 -1 V .4 g 4008 4618 M -27 -14 V .4 g 3981 4604 M -12 -5 V .4 g 3969 4599 M -15 -7 V .4 g 3954 4592 M -27 -12 V .4 g 3927 4580 M -5 -1 V .4 g 3922 4579 M -23 -9 V .4 g 3899 4570 M -27 -10 V .4 g 3872 4560 M -5 -1 V .4 g 3867 4559 M -22 -7 V .4 g 3845 4552 M -27 -8 V .4 g 3818 4544 M -26 -6 V .4 g 3792 4538 M -2 0 V .4 g 3790 4538 M -27 -5 V .4 g 3763 4533 M -27 -4 V .4 g 3736 4529 M -27 -3 V .4 g 3709 4526 M -28 -1 V .4 g 3681 4525 M -27 -1 V .4 g 3654 4524 M -27 1 V .4 g 3627 4525 M -27 3 V .4 g 3600 4528 M -28 3 V .4 g 3572 4531 M -27 5 V .4 g 3545 4536 M -12 2 V .4 g 3533 4538 M -15 4 V .4 g 3518 4542 M -27 6 V .4 g 3491 4548 M -28 8 V .4 g 3463 4556 M -6 3 V .4 g 3457 4559 M -21 6 V .4 g 3436 4565 M -27 10 V .4 g 3409 4575 M -9 4 V .4 g 3400 4579 M -18 7 V .4 g 3382 4586 M -28 12 V .4 g 3354 4598 M -2 1 V .4 g 3352 4599 M -25 11 V .4 g 3327 4610 M -18 9 V 0 g .4 g 6052 1021 M .4 g 6052 1021 M -6 -10 V .4 g 6046 1011 M -14 -20 V .4 g 6032 991 M -7 -11 V .4 g 6025 980 M -6 -9 V .4 g 6019 971 M -14 -20 V .4 g 6005 951 M -7 -11 V stroke 5998 940 M .4 g 5998 940 M -7 -9 V .4 g 5991 931 M -14 -21 V .4 g 5977 910 M -7 -9 V .4 g 5970 901 M -7 -11 V .4 g 5963 890 M -15 -20 V .4 g 5948 870 M -5 -8 V .4 g 5943 862 M -9 -12 V .4 g 5934 850 M -15 -20 V .4 g 5919 830 M -3 -5 V .4 g 5916 825 M -12 -15 V .4 g 5904 810 M -15 -20 V .4 g 5889 790 M 0 -1 V .4 g 5889 789 M -15 -20 V .4 g 5874 769 M -13 -16 V .4 g 5861 753 M -2 -4 V .4 g 5859 749 M -16 -20 V .4 g 5843 729 M -9 -11 V .4 g 5834 718 M -7 -9 V .4 g 5827 709 M -16 -20 V .4 g 5811 689 M -4 -6 V .4 g 5807 683 M -12 -14 V .4 g 5795 669 M -15 -20 V .4 g 5780 649 M -1 -1 V .4 g 5779 648 M -16 -20 V .4 g 5763 628 M -11 -13 V .4 g 5752 615 M -6 -7 V .4 g 5746 608 M -16 -20 V 0 g .38 g 781 1959 M .38 g 781 1959 M -8 20 V .38 g 773 1979 M -8 15 V .38 g 765 1994 M -1 5 V .38 g 764 1999 M -9 20 V .38 g 755 2019 M -9 20 V .38 g 746 2039 M -8 18 V .38 g 738 2057 M -1 2 V .38 g 737 2059 M -9 20 V .38 g 728 2079 M -8 21 V .38 g 720 2100 M -9 19 V .38 g 711 2119 M 0 1 V .38 g 711 2120 M -9 20 V .38 g 702 2140 M -8 20 V .38 g 694 2160 M -9 20 V .38 g 685 2180 M -1 3 V .38 g 684 2183 M -8 17 V .38 g 676 2200 M -8 21 V .38 g 668 2221 M -9 20 V .38 g 659 2241 M -2 6 V .38 g 657 2247 M -6 14 V .38 g 651 2261 M -9 20 V .38 g 642 2281 M -8 20 V .38 g 634 2301 M -5 10 V .38 g 629 2311 M -4 10 V .38 g 625 2321 M -8 20 V stroke 617 2341 M .38 g 617 2341 M -9 21 V .38 g 608 2362 M -6 14 V 0 g .38 g 1605 588 M .38 g 1605 588 M -18 20 V .38 g 1587 608 M -4 5 V .38 g 1583 613 M -12 15 V .38 g 1571 628 M -15 18 V .38 g 1556 646 M -2 2 V .38 g 1554 648 M -17 21 V .38 g 1537 669 M -8 10 V .38 g 1529 679 M -9 10 V .38 g 1520 689 M -16 20 V .38 g 1504 709 M -3 3 V .38 g 1501 712 M -13 17 V .38 g 1488 729 M -14 17 V .38 g 1474 746 M -2 3 V .38 g 1472 749 M -16 20 V .38 g 1456 769 M -9 12 V .38 g 1447 781 M -7 9 V .38 g 1440 790 M -15 20 V .38 g 1425 810 M -5 7 V .38 g 1420 817 M -10 13 V .38 g 1410 830 M -15 20 V .38 g 1395 850 M -3 3 V .38 g 1392 853 M -12 17 V .38 g 1380 870 M -15 20 V .38 g 1365 890 M 0 1 V .38 g 1365 891 M -14 19 V .38 g 1351 910 M -13 19 V .38 g 1338 929 M -1 2 V .38 g 1337 931 M -14 20 V .38 g 1323 951 M -12 17 V .38 g 1311 968 M -2 3 V .38 g 1309 971 M -14 20 V .38 g 1295 991 M -12 17 V .38 g 1283 1008 M -2 3 V .38 g 1281 1011 M -13 20 V .38 g 1268 1031 M -12 19 V .38 g 1256 1050 M -1 2 V .38 g 1255 1052 M -13 20 V .38 g 1242 1072 M -13 20 V .38 g .38 g 1229 1092 M -12 20 V .38 g 1217 1112 M -13 20 V .38 g 1204 1132 M -2 4 V .38 g 1202 1136 M -10 16 V .38 g 1192 1152 M -13 20 V .38 g 1179 1172 M -5 9 V .38 g 1174 1181 M -7 12 V .38 g 1167 1193 M -11 20 V .38 g 1156 1213 M -9 14 V .38 g 1147 1227 M -3 6 V .38 g 1144 1233 M -12 20 V .38 g 1132 1253 M -12 20 V stroke 1120 1273 M .38 g 1120 1273 M 0 1 V .38 g 1120 1274 M -11 19 V .38 g 1109 1293 M -11 21 V .38 g 1098 1314 M -5 9 V .38 g 1093 1323 M -6 11 V .38 g 1087 1334 M -11 20 V .38 g 1076 1354 M -11 19 V .38 g 1065 1373 M 0 1 V .38 g 1065 1374 M -11 20 V .38 g 1054 1394 M -11 20 V .38 g 1043 1414 M -5 10 V .38 g 1038 1424 M -6 11 V .38 g 1032 1435 M -10 20 V .38 g 1022 1455 M -11 20 V .38 g 1011 1475 M 0 1 V .38 g 1011 1476 M -10 19 V .38 g 1001 1495 M -10 20 V .38 g 991 1515 M -7 14 V .38 g 984 1529 M -3 6 V .38 g 981 1535 M -11 20 V .38 g 970 1555 M -10 21 V .38 g 960 1576 M -4 8 V .38 g 956 1584 M -6 12 V .38 g 950 1596 M -9 20 V .38 g 941 1616 M -10 20 V .38 g 931 1636 M -2 3 V .38 g 929 1639 M -8 17 V .38 g 921 1656 M -10 20 V .38 g 911 1676 M -9 20 V .38 g 902 1696 M 0 1 V .38 g 902 1697 M -10 20 V .38 g 892 1717 M -9 20 V .38 g 883 1737 M -8 17 V .38 g 875 1754 M -2 3 V .38 g 873 1757 M -9 20 V .38 g 864 1777 M -10 20 V .38 g 854 1797 M -7 16 V .38 g 847 1813 M -2 4 V .38 g 845 1817 M -9 21 V .38 g 836 1838 M -9 20 V .38 g 827 1858 M -7 14 V .38 g 820 1872 M -2 6 V .38 g 818 1878 M -9 20 V .38 g 809 1898 M -10 20 V .38 g 799 1918 M -6 15 V .38 g 793 1933 M -3 5 V .38 g 790 1938 M -9 21 V 0 g .38 g 4143 4619 M .38 g 4143 4619 M -26 -16 V .38 g 4117 4603 M -7 -4 V .38 g 4110 4599 M -20 -12 V .38 g 4090 4587 M -15 -8 V .38 g 4075 4579 M -12 -7 V stroke 4063 4572 M .38 g 4063 4572 M -25 -13 V .38 g 4038 4559 M -2 -2 V .38 g 4036 4557 M -28 -14 V .38 g 4008 4543 M -9 -5 V .38 g 3999 4538 M -18 -9 V .38 g 3981 4529 M -24 -11 V .38 g 3957 4518 M -3 -1 V .38 g 3954 4517 M -27 -12 V .38 g 3927 4505 M -18 -7 V .38 g 3909 4498 M -10 -4 V .38 g 3899 4494 M -27 -9 V .38 g 3872 4485 M -21 -7 V .38 g 3851 4478 M -6 -2 V .38 g 3845 4476 M -27 -8 V .38 g 3818 4468 M -28 -6 V .38 g 3790 4462 M -22 -4 V .38 g 3768 4458 M -5 -1 V .38 g 3763 4457 M -27 -4 V .38 g 3736 4453 M -27 -3 V .38 g 3709 4450 M -28 -1 V .38 g 3681 4449 M -27 -1 V .38 g 3654 4448 M -27 1 V .38 g 3627 4449 M -27 3 V .38 g 3600 4452 M -28 3 V .38 g 3572 4455 M -15 3 V .38 g 3557 4458 M -12 2 V .38 g 3545 4460 M -27 6 V .38 g 3518 4466 M -27 7 V .38 g 3491 4473 M -18 5 V .38 g 3473 4478 M -10 3 V .38 g 3463 4481 M -27 9 V .38 g 3436 4490 M -22 8 V .38 g 3414 4498 M -5 2 V .38 g 3409 4500 M -27 11 V .38 g 3382 4511 M -17 7 V .38 g 3365 4518 M -11 5 V .38 g 3354 4523 M -27 13 V .38 g 3327 4536 M -6 2 V .38 g 3321 4538 M -21 11 V .38 g 3300 4549 M -19 10 V .38 g 3281 4559 M -8 4 V .38 g 3273 4563 M -28 15 V .38 g 3245 4578 M -2 1 V .38 g 3243 4579 M -25 14 V .38 g 3218 4593 M -11 6 V .38 g 3207 4599 M -16 9 V .38 g 3191 4608 M -19 11 V 0 g .38 g 6052 1093 M .38 g 6052 1093 M -1 -1 V .38 g 6051 1092 M -14 -20 V .38 g 6037 1072 M -12 -19 V .38 g 6025 1053 M -1 -1 V .38 g 6024 1052 M -14 -21 V stroke 6010 1031 M .38 g 6010 1031 M -12 -18 V .38 g 5998 1013 M -1 -2 V .38 g 5997 1011 M -15 -20 V .38 g 5982 991 M -12 -17 V .38 g 5970 974 M -2 -3 V .38 g 5968 971 M -14 -20 V .38 g 5954 951 M -11 -15 V .38 g 5943 936 M -4 -5 V .38 g 5939 931 M -15 -21 V .38 g 5924 910 M -8 -11 V .38 g 5916 899 M -6 -9 V .38 g 5910 890 M -16 -20 V .38 g 5894 870 M -5 -8 V .38 g 5889 862 M -10 -12 V .38 g 5879 850 M -15 -20 V .38 g 5864 830 M -3 -3 V .38 g 5861 827 M -13 -17 V .38 g 5848 810 M -14 -18 V .38 g 5834 792 M -2 -2 V .38 g 5832 790 M -16 -21 V .38 g 5816 769 M -9 -12 V .38 g 5807 757 M -7 -8 V .38 g 5800 749 M -16 -20 V .38 g 5784 729 M -4 -6 V .38 g 5780 723 M -12 -14 V .38 g 5768 709 M -16 -19 V .38 g 5752 690 M -1 -1 V .38 g 5751 689 M -16 -20 V .38 g 5735 669 M -10 -12 V .38 g 5725 657 M -7 -9 V .38 g 5718 648 M -17 -20 V .38 g 5701 628 M -3 -4 V .38 g 5698 624 M -14 -16 V .38 g 5684 608 M -13 -17 V .38 g 5671 591 M -3 -3 V 0 g .36 g 824 1938 M .36 g 824 1938 M -4 10 V .36 g 820 1948 M -5 11 V .36 g 815 1959 M -9 20 V .36 g 806 1979 M -9 20 V .36 g 797 1999 M -4 9 V .36 g 793 2008 M -5 11 V .36 g 788 2019 M -9 20 V .36 g 779 2039 M -9 20 V .36 g 770 2059 M -5 11 V .36 g 765 2070 M -4 9 V .36 g 761 2079 M -8 21 V .36 g 753 2100 M -9 20 V .36 g 744 2120 M -6 12 V .36 g 738 2132 M -3 8 V .36 g 735 2140 M -9 20 V .36 g 726 2160 M -8 20 V .36 g 718 2180 M -7 15 V stroke 711 2195 M .36 g 711 2195 M -2 5 V .36 g 709 2200 M -9 21 V .36 g 700 2221 M -8 20 V .36 g 692 2241 M -8 18 V .36 g 684 2259 M -1 2 V .36 g 683 2261 M -9 20 V .36 g 674 2281 M -8 20 V .36 g 666 2301 M -9 20 V .36 g 657 2321 M 0 2 V .36 g 657 2323 M -8 18 V .36 g 649 2341 M -9 21 V .36 g 640 2362 M -8 20 V .36 g 632 2382 M -3 6 V .36 g 629 2388 M -6 14 V .36 g 623 2402 M -8 20 V .36 g 615 2422 M -8 20 V .36 g 607 2442 M -5 11 V 0 g .36 g 1671 588 M .36 g 1671 588 M -6 7 V .36 g 1665 595 M -11 13 V .36 g 1654 608 M -16 19 V .36 g 1638 627 M -2 1 V .36 g 1636 628 M -17 20 V .36 g 1619 648 M -9 10 V .36 g 1610 658 M -9 11 V .36 g 1601 669 M -17 20 V .36 g 1584 689 M -1 1 V .36 g 1583 690 M -16 19 V .36 g 1567 709 M -11 13 V .36 g 1556 722 M -6 7 V .36 g 1550 729 M -17 20 V .36 g 1533 749 M -4 6 V .36 g 1529 755 M -12 14 V .36 g 1517 769 M -16 19 V .36 g 1501 788 M -1 2 V .36 g 1500 790 M -16 20 V .36 g 1484 810 M -10 12 V .36 g 1474 822 M -6 8 V .36 g 1468 830 M -16 20 V .36 g 1452 850 M -5 7 V .36 g 1447 857 M -11 13 V .36 g 1436 870 M -15 20 V .36 g 1421 890 M -1 2 V .36 g 1420 892 M -14 18 V .36 g 1406 910 M -14 18 V .36 g 1392 928 M -1 3 V .36 g 1391 931 M -15 20 V .36 g 1376 951 M -11 15 V .36 g 1365 966 M -4 5 V .36 g 1361 971 M -14 20 V .36 g 1347 991 M -9 13 V .36 g 1338 1004 M -5 7 V .36 g 1333 1011 M -14 20 V stroke 1319 1031 M .36 g 1319 1031 M -8 12 V .36 g 1311 1043 M -6 9 V .36 g 1305 1052 M -14 20 V .36 g 1291 1072 M -8 11 V .36 g 1283 1083 M -6 9 V .36 g 1277 1092 M -13 20 V .36 g 1264 1112 M -8 12 V .36 g 1256 1124 M -5 8 V .36 g 1251 1132 M -13 20 V .36 g 1238 1152 M -9 15 V .36 g 1229 1167 M -4 5 V .36 g 1225 1172 M -12 21 V .36 g 1213 1193 M -11 17 V .36 g 1202 1210 M -2 3 V .36 g 1200 1213 M -12 20 V .36 g 1188 1233 M -12 20 V .36 g 1176 1253 M -2 2 V .36 g 1174 1255 M -10 18 V .36 g 1164 1273 M -12 20 V .36 g 1152 1293 M -5 8 V .36 g 1147 1301 M -7 13 V .36 g 1140 1314 M -12 20 V .36 g 1128 1334 M -8 15 V .36 g 1120 1349 M -3 5 V .36 g 1117 1354 M -11 20 V .36 g 1106 1374 M -12 20 V .36 g 1094 1394 M -1 3 V .36 g 1093 1397 M -10 17 V .36 g 1083 1414 M -11 21 V .36 g 1072 1435 M -7 12 V .36 g 1065 1447 M -4 8 V .36 g 1061 1455 M -11 20 V .36 g 1050 1475 M -10 20 V .36 g 1040 1495 M -2 3 V .36 g 1038 1498 M -9 17 V .36 g 1029 1515 M -10 20 V .36 g 1019 1535 M -8 15 V .36 g 1011 1550 M -3 5 V .36 g 1008 1555 M -10 21 V .36 g 998 1576 M -10 20 V .36 g 988 1596 M -4 8 V .36 g 984 1604 M -7 12 V .36 g 977 1616 M -10 20 V .36 g 967 1636 M -10 20 V .36 g 957 1656 M -1 2 V .36 g 956 1658 M -9 18 V .36 g 947 1676 M -9 21 V .36 g 938 1697 M -9 17 V .36 g 929 1714 M -1 3 V .36 g 928 1717 M -10 20 V .36 g 918 1737 M -10 20 V .36 g 908 1757 M -6 14 V stroke 902 1771 M .36 g 902 1771 M -3 6 V .36 g 899 1777 M -10 20 V .36 g 889 1797 M -9 20 V .36 g 880 1817 M -5 12 V .36 g 875 1829 M -5 9 V .36 g 870 1838 M -9 20 V .36 g 861 1858 M -9 20 V .36 g 852 1878 M -5 10 V .36 g 847 1888 M -4 10 V .36 g 843 1898 M -10 20 V .36 g 833 1918 M -9 20 V 0 g .36 g 4261 4619 M .36 g 4261 4619 M -7 -5 V .36 g 4254 4614 M -23 -15 V .36 g 4231 4599 M -5 -3 V .36 g 4226 4596 M -26 -17 V .36 g 4200 4579 M -1 -1 V .36 g 4199 4578 M -27 -17 V .36 g 4172 4561 M -4 -2 V .36 g 4168 4559 M -23 -15 V .36 g 4145 4544 M -9 -6 V .36 g 4136 4538 M -19 -11 V .36 g 4117 4527 M -15 -9 V .36 g 4102 4518 M -12 -7 V .36 g 4090 4511 M -22 -13 V .36 g 4068 4498 M -5 -3 V .36 g 4063 4495 M -27 -15 V .36 g 4036 4480 M -5 -2 V .36 g 4031 4478 M -23 -12 V .36 g 4008 4466 M -16 -8 V .36 g 3992 4458 M -11 -6 V .36 g 3981 4452 M -27 -13 V .36 g 3954 4439 M -4 -1 V .36 g 3950 4438 M -23 -10 V .36 g 3927 4428 M -26 -11 V .36 g 3901 4417 M -2 0 V .36 g 3899 4417 M -27 -10 V .36 g 3872 4407 M -27 -9 V .36 g 3845 4398 M -3 -1 V .36 g 3842 4397 M -24 -7 V .36 g 3818 4390 M -28 -6 V .36 g 3790 4384 M -27 -6 V .36 g 3763 4378 M -9 -1 V .36 g 3754 4377 M -18 -3 V .36 g 3736 4374 M -27 -2 V .36 g 3709 4372 M -28 -2 V .36 g 3681 4370 M -27 0 V .36 g 3654 4370 M -27 1 V .36 g 3627 4371 M -27 2 V .36 g 3600 4373 M -28 4 V .36 g 3572 4377 M -1 0 V .36 g 3571 4377 M -26 5 V .36 g 3545 4382 M -27 6 V stroke 3518 4388 M .36 g 3518 4388 M -27 7 V .36 g 3491 4395 M -8 2 V .36 g 3483 4397 M -20 6 V .36 g 3463 4403 M -27 9 V .36 g 3436 4412 M -13 5 V .36 g 3423 4417 M -14 6 V .36 g 3409 4423 M -27 11 V .36 g 3382 4434 M -9 4 V .36 g 3373 4438 M -19 8 V .36 g 3354 4446 M -25 12 V .36 g 3329 4458 M -2 1 V .36 g 3327 4459 M -27 13 V .36 g 3300 4472 M -11 6 V .36 g 3289 4478 M -16 9 V .36 g 3273 4487 M -22 11 V .36 g 3251 4498 M -6 3 V .36 g 3245 4501 M -27 16 V .36 g 3218 4517 M -3 1 V .36 g 3215 4518 M -24 14 V .36 g 3191 4532 M -11 6 V .36 g 3180 4538 M -16 10 V .36 g 3164 4548 M -18 11 V .36 g 3146 4559 M -10 6 V .36 g 3136 4565 M -23 14 V .36 g 3113 4579 M -4 2 V .36 g 3109 4581 M -27 17 V .36 g 3082 4598 M -2 1 V .36 g 3080 4599 M -25 15 V .36 g 3055 4614 M -8 5 V 0 g .36 g 6052 1168 M .36 g 6052 1168 M -11 -16 V .36 g 6041 1152 M -13 -20 V .36 g 6028 1132 M -3 -5 V .36 g 6025 1127 M -11 -15 V .36 g 6014 1112 M -14 -20 V .36 g 6000 1092 M -2 -4 V .36 g 5998 1088 M -12 -16 V .36 g 5986 1072 M -14 -20 V .36 g 5972 1052 M -2 -3 V .36 g 5970 1049 M -12 -18 V .36 g 5958 1031 M -15 -20 V .36 g .36 g 5943 1011 M -15 -20 V .36 g 5928 991 M -12 -17 V .36 g 5916 974 M -3 -3 V .36 g 5913 971 M -15 -20 V .36 g 5898 951 M -9 -13 V .36 g 5889 938 M -6 -7 V .36 g 5883 931 M -16 -21 V .36 g 5867 910 M -6 -8 V .36 g 5861 902 M -9 -12 V .36 g 5852 890 M -16 -20 V .36 g 5836 870 M -2 -2 V .36 g 5834 868 M -14 -18 V stroke 5820 850 M .36 g 5820 850 M -13 -17 V .36 g 5807 833 M -3 -3 V .36 g 5804 830 M -16 -20 V .36 g 5788 810 M -8 -10 V .36 g 5780 800 M -9 -10 V .36 g 5771 790 M -16 -21 V .36 g 5755 769 M -3 -2 V .36 g 5752 767 M -14 -18 V .36 g 5738 749 M -13 -15 V .36 g 5725 734 M -4 -5 V .36 g 5721 729 M -17 -20 V .36 g 5704 709 M -6 -8 V .36 g 5698 701 M -11 -12 V .36 g 5687 689 M -16 -20 V .36 g 5671 669 M -1 0 V .36 g 5670 669 M -17 -21 V .36 g 5653 648 M -10 -12 V .36 g 5643 636 M -7 -8 V .36 g 5636 628 M -17 -20 V .36 g 5619 608 M -3 -4 V .36 g 5616 604 M -14 -16 V 0 g .34 g 869 1918 M .34 g 869 1918 M -9 20 V .34 g 860 1938 M -10 21 V .34 g 850 1959 M -3 6 V .34 g 847 1965 M -6 14 V .34 g 841 1979 M -9 20 V .34 g 832 1999 M -9 20 V .34 g 823 2019 M -3 6 V .34 g 820 2025 M -6 14 V .34 g 814 2039 M -9 20 V .34 g 805 2059 M -9 20 V .34 g 796 2079 M -3 7 V .34 g 793 2086 M -6 14 V .34 g 787 2100 M -9 20 V .34 g 778 2120 M -9 20 V .34 g 769 2140 M -4 8 V .34 g 765 2148 M -5 12 V .34 g 760 2160 M -9 20 V .34 g 751 2180 M -8 20 V .34 g 743 2200 M -5 10 V .34 g 738 2210 M -4 11 V .34 g 734 2221 M -9 20 V .34 g 725 2241 M -8 20 V .34 g 717 2261 M -6 13 V .34 g 711 2274 M -3 7 V .34 g 708 2281 M -9 20 V .34 g 699 2301 M -8 20 V .34 g 691 2321 M -7 16 V .34 g 684 2337 M -2 4 V .34 g 682 2341 M -8 21 V .34 g 674 2362 M -9 20 V .34 g 665 2382 M -8 20 V stroke 657 2402 M .34 g 657 2402 M -9 20 V .34 g 648 2422 M -8 20 V .34 g 640 2442 M -9 20 V .34 g 631 2462 M -2 5 V .34 g 629 2467 M -6 16 V .34 g 623 2483 M -9 20 V .34 g 614 2503 M -8 20 V .34 g 606 2523 M -4 9 V 0 g .34 g 1742 588 M .34 g 1742 588 M -18 20 V .34 g 1724 608 M -5 5 V .34 g 1719 613 M -13 15 V .34 g 1706 628 M -14 16 V .34 g 1692 644 M -4 4 V .34 g 1688 648 M -18 21 V .34 g 1670 669 M -5 6 V .34 g 1665 675 M -12 14 V .34 g 1653 689 M -15 17 V .34 g 1638 706 M -3 3 V .34 g 1635 709 M -18 20 V .34 g 1617 729 M -7 8 V .34 g 1610 737 M -10 12 V .34 g 1600 749 M -17 20 V .34 g 1583 769 M -1 0 V .34 g 1582 769 M -17 21 V .34 g 1565 790 M -9 11 V .34 g 1556 801 M -8 9 V .34 g 1548 810 M -17 20 V .34 g 1531 830 M -2 3 V .34 g 1529 833 M -14 17 V .34 g 1515 850 M -14 16 V .34 g 1501 866 M -3 4 V .34 g 1498 870 M -16 20 V .34 g 1482 890 M -8 10 V .34 g 1474 900 M -8 10 V .34 g 1466 910 M -16 21 V .34 g 1450 931 M -3 3 V .34 g 1447 934 M -13 17 V .34 g 1434 951 M -14 19 V .34 g 1420 970 M -1 1 V .34 g 1419 971 M -16 20 V .34 g 1403 991 M -11 15 V .34 g 1392 1006 M -4 5 V .34 g 1388 1011 M -15 20 V .34 g 1373 1031 M -8 12 V .34 g 1365 1043 M -6 9 V .34 g 1359 1052 M -15 20 V .34 g 1344 1072 M -6 9 V .34 g 1338 1081 M -8 11 V .34 g 1330 1092 M -14 20 V .34 g 1316 1112 M -5 8 V .34 g 1311 1120 M -9 12 V .34 g 1302 1132 M -14 20 V stroke 1288 1152 M .34 g 1288 1152 M -5 8 V .34 g 1283 1160 M -8 12 V .34 g 1275 1172 M -13 21 V .34 g 1262 1193 M -6 8 V .34 g 1256 1201 M -8 12 V .34 g 1248 1213 M -13 20 V .34 g 1235 1233 M -6 10 V .34 g 1229 1243 M -6 10 V .34 g 1223 1253 M -13 20 V .34 g 1210 1273 M -8 14 V .34 g 1202 1287 M -4 6 V .34 g 1198 1293 M -13 21 V .34 g 1185 1314 M -11 18 V .34 g 1174 1332 M -1 2 V .34 g 1173 1334 M -12 20 V .34 g 1161 1354 M -12 20 V .34 g 1149 1374 M -2 4 V .34 g 1147 1378 M -9 16 V .34 g 1138 1394 M -12 20 V .34 g 1126 1414 M -6 11 V .34 g 1120 1425 M -6 10 V .34 g 1114 1435 M -11 20 V .34 g 1103 1455 M -10 18 V .34 g 1093 1473 M -1 2 V .34 g 1092 1475 M -11 20 V .34 g 1081 1495 M -11 20 V .34 g 1070 1515 M -5 8 V .34 g 1065 1523 M -6 12 V .34 g 1059 1535 M -11 20 V .34 g 1048 1555 M -10 19 V .34 g 1038 1574 M -1 2 V .34 g 1037 1576 M -10 20 V .34 g 1027 1596 M -11 20 V .34 g 1016 1616 M -5 11 V .34 g 1011 1627 M -5 9 V .34 g 1006 1636 M -10 20 V .34 g 996 1656 M -11 20 V .34 g 985 1676 M -1 4 V .34 g 984 1680 M -9 17 V .34 g 975 1697 M -10 20 V .34 g 965 1717 M -9 18 V .34 g 956 1735 M -1 2 V .34 g 955 1737 M -9 20 V .34 g 946 1757 M -10 20 V .34 g 936 1777 M -7 14 V .34 g 929 1791 M -3 6 V .34 g 926 1797 M -10 20 V .34 g 916 1817 M -9 21 V .34 g 907 1838 M -5 10 V .34 g 902 1848 M -5 10 V .34 g 897 1858 M -9 20 V .34 g 888 1878 M -10 20 V stroke 878 1898 M .34 g 878 1898 M -3 8 V .34 g 875 1906 M -6 12 V 0 g .34 g 4377 4619 M .34 g 4377 4619 M -14 -10 V .34 g 4363 4609 M -16 -10 V .34 g 4347 4599 M -12 -8 V .34 g 4335 4591 M -18 -12 V .34 g 4317 4579 M -9 -6 V .34 g 4308 4573 M -22 -14 V .34 g 4286 4559 M -5 -4 V .34 g 4281 4555 M -25 -17 V .34 g 4256 4538 M -2 -1 V .34 g 4254 4537 M -28 -18 V .34 g 4226 4519 M 0 -1 V .34 g 4226 4518 M -27 -17 V .34 g 4199 4501 M -4 -3 V .34 g 4195 4498 M -23 -15 V .34 g 4172 4483 M -8 -5 V .34 g 4164 4478 M -19 -12 V .34 g 4145 4466 M -13 -8 V .34 g 4132 4458 M -15 -9 V .34 g 4117 4449 M -18 -11 V .34 g 4099 4438 M -9 -6 V .34 g 4090 4432 M -26 -15 V .34 g 4064 4417 M -1 -1 V .34 g 4063 4416 M -27 -15 V .34 g 4036 4401 M -8 -4 V .34 g 4028 4397 M -20 -10 V .34 g 4008 4387 M -18 -10 V .34 g 3990 4377 M -9 -4 V .34 g 3981 4373 M -27 -13 V .34 g 3954 4360 M -7 -3 V .34 g 3947 4357 M -20 -9 V .34 g 3927 4348 M -27 -11 V .34 g 3900 4337 M -1 0 V .34 g 3899 4337 M -27 -11 V .34 g 3872 4326 M -27 -8 V .34 g 3845 4318 M -3 -1 V .34 g 3842 4317 M -24 -7 V .34 g 3818 4310 M -28 -7 V .34 g 3790 4303 M -27 -5 V .34 g 3763 4298 M -8 -1 V .34 g 3755 4297 M -19 -3 V .34 g 3736 4294 M -27 -3 V .34 g 3709 4291 M -28 -2 V .34 g 3681 4289 M -27 0 V .34 g 3654 4289 M -27 1 V .34 g 3627 4290 M -27 3 V .34 g 3600 4293 M -28 3 V .34 g 3572 4296 M -1 1 V .34 g 3571 4297 M -26 4 V .34 g 3545 4301 M -27 6 V .34 g 3518 4307 M -27 8 V stroke 3491 4315 M .34 g 3491 4315 M -7 2 V .34 g 3484 4317 M -21 6 V .34 g 3463 4323 M -27 9 V .34 g 3436 4332 M -11 5 V .34 g 3425 4337 M -16 6 V .34 g 3409 4343 M -27 11 V .34 g 3382 4354 M -6 3 V .34 g 3376 4357 M -22 10 V .34 g 3354 4367 M -22 10 V .34 g 3332 4377 M -5 3 V .34 g 3327 4380 M -27 14 V .34 g 3300 4394 M -7 3 V .34 g 3293 4397 M -20 11 V .34 g 3273 4408 M -18 9 V .34 g 3255 4417 M -10 6 V .34 g 3245 4423 M -26 15 V .34 g 3219 4438 M -1 0 V .34 g 3218 4438 M -27 16 V .34 g 3191 4454 M -6 4 V .34 g 3185 4458 M -21 13 V .34 g 3164 4471 M -13 7 V .34 g 3151 4478 M -15 9 V .34 g 3136 4487 M -18 11 V .34 g 3118 4498 M -9 6 V .34 g 3109 4504 M -23 14 V .34 g 3086 4518 M -4 3 V .34 g 3082 4521 M -27 16 V .34 g 3055 4537 M -2 1 V .34 g 3053 4538 M -26 16 V .34 g 3027 4554 M -6 5 V .34 g 3021 4559 M -21 12 V .34 g 3000 4571 M -12 8 V .34 g 2988 4579 M -15 9 V .34 g 2973 4588 M -18 11 V .34 g 2955 4599 M -9 6 V .34 g 2946 4605 M -24 14 V 0 g .34 g 6052 1245 M .34 g 6052 1245 M -8 -12 V .34 g 6044 1233 M -14 -20 V .34 g 6030 1213 M -5 -9 V .34 g 6025 1204 M -8 -11 V .34 g 6017 1193 M -14 -21 V .34 g 6003 1172 M -5 -7 V .34 g 5998 1165 M -9 -13 V .34 g 5989 1152 M -14 -20 V .34 g 5975 1132 M -5 -6 V .34 g 5970 1126 M -10 -14 V .34 g 5960 1112 M -15 -20 V .34 g 5945 1092 M -2 -4 V .34 g 5943 1088 M -12 -16 V .34 g 5931 1072 M -15 -20 V .34 g .34 g 5916 1052 M -16 -21 V .34 g 5900 1031 M -11 -15 V stroke 5889 1016 M .34 g 5889 1016 M -4 -5 V .34 g 5885 1011 M -16 -20 V .34 g 5869 991 M -8 -11 V .34 g 5861 980 M -7 -9 V .34 g 5854 971 M -16 -20 V .34 g 5838 951 M -4 -5 V .34 g 5834 946 M -12 -15 V .34 g 5822 931 M -15 -19 V .34 g 5807 912 M -1 -2 V .34 g 5806 910 M -17 -20 V .34 g 5789 890 M -9 -11 V .34 g 5780 879 M -7 -9 V .34 g 5773 870 M -17 -20 V .34 g 5756 850 M -4 -4 V .34 g 5752 846 M -13 -16 V .34 g 5739 830 M -14 -17 V .34 g 5725 813 M -3 -3 V .34 g 5722 810 M -17 -20 V .34 g 5705 790 M -7 -9 V .34 g 5698 781 M -10 -12 V .34 g 5688 769 M -17 -20 V .34 g 5671 749 M 0 -1 V .34 g 5671 748 M -17 -19 V .34 g 5654 729 M -11 -13 V .34 g 5643 716 M -6 -7 V .34 g 5637 709 M -17 -20 V .34 g 5620 689 M -4 -5 V .34 g 5616 684 M -14 -15 V .34 g 5602 669 M -13 -17 V .34 g 5589 652 M -4 -4 V .34 g 5585 648 M -17 -20 V .34 g 5568 628 M -6 -7 V .34 g 5562 621 M -11 -13 V .34 g 5551 608 M -17 -20 V .34 g 0 g .32 g 916 1898 M .32 g 916 1898 M -10 20 V .32 g 906 1918 M -4 9 V .32 g 902 1927 M -6 11 V .32 g 896 1938 M -9 21 V .32 g 887 1959 M -9 20 V .32 g 878 1979 M -3 6 V .32 g 875 1985 M -7 14 V .32 g 868 1999 M -9 20 V .32 g 859 2019 M -9 20 V .32 g 850 2039 M -3 5 V .32 g 847 2044 M -6 15 V .32 g 841 2059 M -10 20 V .32 g 831 2079 M -9 21 V .32 g 822 2100 M -2 5 V .32 g 820 2105 M -7 15 V .32 g 813 2120 M -9 20 V .32 g 804 2140 M -9 20 V .32 g 795 2160 M -2 6 V stroke 793 2166 M .32 g 793 2166 M -7 14 V .32 g 786 2180 M -8 20 V .32 g 778 2200 M -9 21 V .32 g 769 2221 M -4 7 V .32 g 765 2228 M -5 13 V .32 g 760 2241 M -9 20 V .32 g 751 2261 M -9 20 V .32 g 742 2281 M -4 10 V .32 g 738 2291 M -4 10 V .32 g 734 2301 M -9 20 V .32 g 725 2321 M -8 20 V .32 g 717 2341 M -6 13 V .32 g 711 2354 M -3 8 V .32 g 708 2362 M -9 20 V .32 g 699 2382 M -8 20 V .32 g 691 2402 M -7 16 V .32 g 684 2418 M -2 4 V .32 g 682 2422 M -8 20 V .32 g 674 2442 M -9 20 V .32 g 665 2462 M -8 21 V .32 g .32 g 657 2483 M -9 20 V .32 g 648 2503 M -8 20 V .32 g 640 2523 M -9 20 V .32 g 631 2543 M -2 5 V .32 g 629 2548 M -6 15 V .32 g 623 2563 M -8 20 V .32 g 615 2583 M -9 21 V .32 g 606 2604 M -4 10 V 0 g .32 g 1816 588 M .32 g 1816 588 M -15 17 V .32 g 1801 605 M -3 3 V .32 g 1798 608 M -18 20 V .32 g 1780 628 M -6 7 V .32 g 1774 635 M -12 13 V .32 g 1762 648 M -15 18 V .32 g 1747 666 M -3 3 V .32 g 1744 669 M -18 20 V .32 g 1726 689 M -7 7 V .32 g 1719 696 M -11 13 V .32 g 1708 709 M -16 17 V .32 g 1692 726 M -2 3 V .32 g 1690 729 M -18 20 V .32 g 1672 749 M -7 8 V .32 g 1665 757 M -11 12 V .32 g 1654 769 M -16 19 V .32 g 1638 788 M -2 2 V .32 g 1636 790 M -18 20 V .32 g 1618 810 M -8 9 V .32 g 1610 819 M -9 11 V .32 g 1601 830 M -18 20 V .32 g .32 g 1583 850 M -17 20 V .32 g 1566 870 M -10 12 V .32 g 1556 882 M -7 8 V stroke 1549 890 M .32 g 1549 890 M -17 20 V .32 g 1532 910 M -3 4 V .32 g 1529 914 M -14 17 V .32 g 1515 931 M -14 16 V .32 g 1501 947 M -3 4 V .32 g 1498 951 M -16 20 V .32 g 1482 971 M -8 9 V .32 g 1474 980 M -8 11 V .32 g 1466 991 M -17 20 V .32 g 1449 1011 M -2 4 V .32 g 1447 1015 M -13 16 V .32 g 1434 1031 M -14 19 V .32 g 1420 1050 M -2 2 V .32 g 1418 1052 M -15 20 V .32 g 1403 1072 M -11 13 V .32 g 1392 1085 M -4 7 V .32 g 1388 1092 M -15 20 V .32 g 1373 1112 M -8 10 V .32 g 1365 1122 M -7 10 V .32 g 1358 1132 M -15 20 V .32 g 1343 1152 M -5 8 V .32 g 1338 1160 M -9 12 V .32 g 1329 1172 M -14 21 V .32 g 1315 1193 M -4 6 V .32 g 1311 1199 M -10 14 V .32 g 1301 1213 M -14 20 V .32 g 1287 1233 M -4 6 V .32 g 1283 1239 M -9 14 V .32 g 1274 1253 M -14 20 V .32 g 1260 1273 M -4 7 V .32 g 1256 1280 M -9 13 V .32 g 1247 1293 M -13 21 V .32 g 1234 1314 M -5 8 V .32 g 1229 1322 M -8 12 V .32 g 1221 1334 M -12 20 V .32 g 1209 1354 M -7 12 V .32 g 1202 1366 M -6 8 V .32 g 1196 1374 M -12 20 V .32 g 1184 1394 M -10 16 V .32 g 1174 1410 M -2 4 V .32 g 1172 1414 M -12 21 V .32 g 1160 1435 M -12 20 V .32 g 1148 1455 M -1 1 V .32 g 1147 1456 M -11 19 V .32 g 1136 1475 M -11 20 V .32 g 1125 1495 M -5 9 V .32 g 1120 1504 M -7 11 V .32 g 1113 1515 M -11 20 V .32 g 1102 1535 M -9 17 V .32 g 1093 1552 M -2 3 V .32 g 1091 1555 M -11 21 V .32 g 1080 1576 M -11 20 V stroke 1069 1596 M .32 g 1069 1596 M -4 6 V .32 g 1065 1602 M -7 14 V .32 g 1058 1616 M -11 20 V .32 g 1047 1636 M -9 17 V .32 g 1038 1653 M -2 3 V .32 g 1036 1656 M -10 20 V .32 g 1026 1676 M -11 21 V .32 g 1015 1697 M -4 8 V .32 g 1011 1705 M -6 12 V .32 g 1005 1717 M -10 20 V .32 g 995 1737 M -10 20 V .32 g 985 1757 M -1 2 V .32 g 984 1759 M -9 18 V .32 g 975 1777 M -11 20 V .32 g 964 1797 M -8 17 V .32 g 956 1814 M -2 3 V .32 g 954 1817 M -9 21 V .32 g 945 1838 M -10 20 V .32 g 935 1858 M -6 12 V .32 g 929 1870 M -4 8 V .32 g 925 1878 M -9 20 V 0 g .32 g 2864 4575 M .32 g 2864 4575 M -6 4 V .32 g 2858 4579 M -21 12 V .32 g 2837 4591 M -14 8 V .32 g 2823 4599 M -14 8 V .32 g 2809 4607 M -21 12 V 0 g .32 g 4498 4619 M .32 g 4498 4619 M -26 -17 V .32 g 4472 4602 M -5 -3 V .32 g 4467 4599 M -23 -15 V .32 g 4444 4584 M -8 -5 V .32 g 4436 4579 M -19 -13 V .32 g 4417 4566 M -12 -7 V .32 g 4405 4559 M -15 -11 V .32 g 4390 4548 M -15 -10 V .32 g 4375 4538 M -12 -8 V .32 g 4363 4530 M -18 -12 V .32 g 4345 4518 M -10 -6 V .32 g 4335 4512 M -20 -14 V .32 g 4315 4498 M -7 -4 V .32 g 4308 4494 M -23 -16 V .32 g 4285 4478 M -4 -3 V .32 g 4281 4475 M -26 -17 V .32 g 4255 4458 M -1 -1 V .32 g 4254 4457 M -28 -18 V .32 g 4226 4439 M -1 -1 V .32 g 4225 4438 M -26 -17 V .32 g 4199 4421 M -5 -4 V .32 g 4194 4417 M -22 -14 V .32 g 4172 4403 M -9 -6 V .32 g 4163 4397 M -18 -12 V .32 g 4145 4385 M -13 -8 V stroke 4132 4377 M .32 g 4132 4377 M -15 -9 V .32 g 4117 4368 M -18 -11 V .32 g 4099 4357 M -9 -6 V .32 g 4090 4351 M -24 -14 V .32 g 4066 4337 M -3 -2 V .32 g 4063 4335 M -27 -15 V .32 g 4036 4320 M -6 -3 V .32 g 4030 4317 M -22 -12 V .32 g 4008 4305 M -16 -8 V .32 g 3992 4297 M -11 -6 V .32 g 3981 4291 M -27 -14 V .32 g 3954 4277 M -3 -1 V .32 g 3951 4276 M -24 -11 V .32 g 3927 4265 M -22 -9 V .32 g 3905 4256 M -6 -2 V .32 g 3899 4254 M -27 -10 V .32 g 3872 4244 M -23 -8 V .32 g 3849 4236 M -4 -2 V .32 g 3845 4234 M -27 -7 V .32 g 3818 4227 M -28 -7 V .32 g 3790 4220 M -19 -4 V .32 g 3771 4216 M -8 -2 V .32 g 3763 4214 M -27 -4 V .32 g 3736 4210 M -27 -3 V .32 g 3709 4207 M -28 -1 V .32 g 3681 4206 M -27 0 V .32 g 3654 4206 M -27 1 V .32 g 3627 4207 M -27 2 V .32 g 3600 4209 M -28 4 V .32 g 3572 4213 M -16 3 V .32 g 3556 4216 M -11 2 V .32 g 3545 4218 M -27 6 V .32 g 3518 4224 M -27 8 V .32 g 3491 4232 M -14 4 V .32 g 3477 4236 M -14 4 V .32 g 3463 4240 M -27 10 V .32 g 3436 4250 M -16 6 V .32 g 3420 4256 M -11 5 V .32 g 3409 4261 M -27 11 V .32 g 3382 4272 M -10 4 V .32 g 3372 4276 M -18 9 V .32 g 3354 4285 M -24 12 V .32 g 3330 4297 M -3 1 V .32 g 3327 4298 M -27 14 V .32 g 3300 4312 M -9 5 V .32 g 3291 4317 M -18 10 V .32 g 3273 4327 M -18 10 V .32 g 3255 4337 M -10 5 V .32 g 3245 4342 M -26 15 V .32 g 3219 4357 M -1 1 V .32 g 3218 4358 M -27 16 V .32 g 3191 4374 M -6 3 V stroke 3185 4377 M .32 g 3185 4377 M -21 13 V .32 g 3164 4390 M -12 7 V .32 g 3152 4397 M -16 10 V .32 g 3136 4407 M -16 10 V .32 g 3120 4417 M -11 7 V .32 g 3109 4424 M -22 14 V .32 g 3087 4438 M -5 3 V .32 g 3082 4441 M -27 17 V .32 g .32 g 3055 4458 M -28 17 V .32 g 3027 4475 M -4 3 V .32 g 3023 4478 M -23 14 V .32 g 3000 4492 M -9 6 V .32 g 2991 4498 M -18 11 V .32 g 2973 4509 M -15 9 V .32 g 2958 4518 M -12 8 V .32 g 2946 4526 M -21 12 V .32 g 2925 4538 M -7 5 V .32 g 2918 4543 M -26 16 V .32 g 2892 4559 M -1 0 V .32 g 2891 4559 M -27 16 V 0 g .32 g 6052 1324 M .32 g 6052 1324 M -7 -10 V .32 g 6045 1314 M -14 -21 V .32 g 6031 1293 M -6 -9 V .32 g 6025 1284 M -7 -11 V .32 g 6018 1273 M -14 -20 V .32 g 6004 1253 M -6 -9 V .32 g 5998 1244 M -8 -11 V .32 g 5990 1233 M -15 -20 V .32 g 5975 1213 M -5 -7 V .32 g 5970 1206 M -9 -13 V .32 g 5961 1193 M -15 -21 V .32 g 5946 1172 M -3 -4 V .32 g 5943 1168 M -12 -16 V .32 g 5931 1152 M -15 -20 V .32 g .32 g 5916 1132 M -15 -20 V .32 g 5901 1112 M -12 -16 V .32 g 5889 1096 M -4 -4 V .32 g 5885 1092 M -15 -20 V .32 g 5870 1072 M -9 -11 V .32 g 5861 1061 M -7 -9 V .32 g 5854 1052 M -16 -21 V .32 g 5838 1031 M -4 -4 V .32 g 5834 1027 M -13 -16 V .32 g 5821 1011 M -14 -18 V .32 g 5807 993 M -2 -2 V .32 g 5805 991 M -16 -20 V .32 g 5789 971 M -9 -11 V .32 g 5780 960 M -8 -9 V .32 g 5772 951 M -17 -20 V .32 g 5755 931 M -3 -4 V .32 g 5752 927 M -14 -17 V .32 g 5738 910 M -13 -15 V stroke 5725 895 M .32 g 5725 895 M -4 -5 V .32 g 5721 890 M -17 -20 V .32 g 5704 870 M -6 -7 V .32 g 5698 863 M -11 -13 V .32 g 5687 850 M -16 -19 V .32 g 5671 831 M -1 -1 V .32 g 5670 830 M -17 -20 V .32 g 5653 810 M -10 -11 V .32 g 5643 799 M -8 -9 V .32 g 5635 790 M -17 -21 V .32 g 5618 769 M -2 -2 V .32 g 5616 767 M -15 -18 V .32 g 5601 749 M -12 -14 V .32 g 5589 735 M -6 -6 V .32 g 5583 729 M -17 -20 V .32 g 5566 709 M -4 -5 V .32 g 5562 704 M -13 -15 V .32 g 5549 689 M -15 -17 V .32 g 5534 672 M -2 -3 V .32 g 5532 669 M -17 -21 V .32 g 5515 648 M -8 -8 V .32 g 5507 640 M -10 -12 V .32 g 5497 628 M -16 -20 V .32 g 5481 608 M -1 -1 V .32 g 5480 607 M -16 -19 V 0 g .3 g 956 1895 M .3 g 956 1895 M -1 3 V .3 g 955 1898 M -10 20 V .3 g 945 1918 M -10 20 V .3 g 935 1938 M -6 13 V .3 g 929 1951 M -3 8 V .3 g 926 1959 M -10 20 V .3 g 916 1979 M -10 20 V .3 g 906 1999 M -4 10 V .3 g 902 2009 M -5 10 V .3 g 897 2019 M -9 20 V .3 g 888 2039 M -10 20 V .3 g 878 2059 M -3 8 V .3 g 875 2067 M -6 12 V .3 g 869 2079 M -9 21 V .3 g 860 2100 M -10 20 V .3 g 850 2120 M -3 7 V .3 g 847 2127 M -6 13 V .3 g 841 2140 M -9 20 V .3 g 832 2160 M -9 20 V .3 g 823 2180 M -3 7 V .3 g 820 2187 M -6 13 V .3 g 814 2200 M -9 21 V .3 g 805 2221 M -9 20 V .3 g 796 2241 M -3 8 V .3 g 793 2249 M -6 12 V .3 g 787 2261 M -8 20 V .3 g 779 2281 M -9 20 V stroke 770 2301 M .3 g 770 2301 M -5 10 V .3 g 765 2311 M -4 10 V .3 g 761 2321 M -9 20 V .3 g 752 2341 M -8 21 V .3 g 744 2362 M -6 12 V .3 g 738 2374 M -3 8 V .3 g 735 2382 M -9 20 V .3 g 726 2402 M -8 20 V .3 g 718 2422 M -7 16 V .3 g 711 2438 M -2 4 V .3 g 709 2442 M -8 20 V .3 g 701 2462 M -9 21 V .3 g 692 2483 M -8 19 V .3 g 684 2502 M -1 1 V .3 g 683 2503 M -8 20 V .3 g 675 2523 M -8 20 V .3 g 667 2543 M -9 20 V .3 g 658 2563 M -1 4 V .3 g 657 2567 M -7 16 V .3 g 650 2583 M -9 21 V .3 g 641 2604 M -8 20 V .3 g 633 2624 M -4 9 V .3 g 629 2633 M -4 11 V .3 g 625 2644 M -9 20 V .3 g 616 2664 M -8 20 V .3 g 608 2684 M -6 14 V 0 g .3 g 1892 588 M .3 g 1892 588 M -9 10 V .3 g 1883 598 M -9 10 V .3 g 1874 608 M -18 20 V .3 g 1856 628 M 0 1 V .3 g 1856 629 M -17 19 V .3 g 1839 648 M -11 12 V .3 g 1828 660 M -7 9 V .3 g 1821 669 M -18 20 V .3 g 1803 689 M -2 2 V .3 g 1801 691 M -16 18 V .3 g 1785 709 M -11 12 V .3 g 1774 721 M -8 8 V .3 g 1766 729 M -18 20 V .3 g 1748 749 M -1 2 V .3 g 1747 751 M -17 18 V .3 g 1730 769 M -11 12 V .3 g 1719 781 M -7 9 V .3 g 1712 790 M -18 20 V .3 g 1694 810 M -2 2 V .3 g 1692 812 M -16 18 V .3 g 1676 830 M -11 12 V .3 g 1665 842 M -7 8 V .3 g 1658 850 M -18 20 V .3 g 1640 870 M -2 3 V .3 g 1638 873 M -16 17 V .3 g 1622 890 M -12 13 V stroke 1610 903 M .3 g 1610 903 M -6 7 V .3 g 1604 910 M -18 21 V .3 g 1586 931 M -3 3 V .3 g 1583 934 M -14 17 V .3 g 1569 951 M -13 15 V .3 g 1556 966 M -5 5 V .3 g 1551 971 M -17 20 V .3 g 1534 991 M -5 7 V .3 g 1529 998 M -12 13 V .3 g 1517 1011 M -16 19 V .3 g 1501 1030 M -1 1 V .3 g 1500 1031 M -16 21 V .3 g 1484 1052 M -10 12 V .3 g 1474 1064 M -7 8 V .3 g 1467 1072 M -16 20 V .3 g 1451 1092 M -4 5 V .3 g 1447 1097 M -12 15 V .3 g 1435 1112 M -15 20 V .3 g 1420 1132 M -16 20 V .3 g 1404 1152 M -12 16 V .3 g 1392 1168 M -3 4 V .3 g 1389 1172 M -15 21 V .3 g 1374 1193 M -9 11 V .3 g 1365 1204 M -6 9 V .3 g 1359 1213 M -15 20 V .3 g 1344 1233 M -6 9 V .3 g 1338 1242 M -8 11 V .3 g 1330 1253 M -14 20 V .3 g 1316 1273 M -5 8 V .3 g 1311 1281 M -9 12 V .3 g 1302 1293 M -14 21 V .3 g 1288 1314 M -5 6 V .3 g 1283 1320 M -9 14 V .3 g 1274 1334 M -13 20 V .3 g 1261 1354 M -5 7 V .3 g 1256 1361 M -8 13 V .3 g 1248 1374 M -13 20 V .3 g 1235 1394 M -6 9 V .3 g 1229 1403 M -7 11 V .3 g 1222 1414 M -13 21 V .3 g 1209 1435 M -7 12 V .3 g 1202 1447 M -5 8 V .3 g 1197 1455 M -13 20 V .3 g 1184 1475 M -10 16 V .3 g 1174 1491 M -2 4 V .3 g 1172 1495 M -12 20 V .3 g 1160 1515 M -12 20 V .3 g 1148 1535 M -1 2 V .3 g 1147 1537 M -10 18 V .3 g 1137 1555 M -12 21 V .3 g 1125 1576 M -5 9 V .3 g 1120 1585 M -6 11 V stroke 1114 1596 M .3 g 1114 1596 M -12 20 V .3 g 1102 1616 M -9 17 V .3 g 1093 1633 M -2 3 V .3 g 1091 1636 M -11 20 V .3 g 1080 1656 M -11 20 V .3 g 1069 1676 M -4 7 V .3 g 1065 1683 M -7 14 V .3 g 1058 1697 M -11 20 V .3 g 1047 1717 M -9 17 V .3 g 1038 1734 M -1 3 V .3 g 1037 1737 M -11 20 V .3 g 1026 1757 M -10 20 V .3 g 1016 1777 M -5 10 V .3 g 1011 1787 M -6 10 V .3 g 1005 1797 M -10 20 V .3 g 995 1817 M -10 21 V .3 g 985 1838 M -1 2 V .3 g 984 1840 M -9 18 V .3 g 975 1858 M -10 20 V .3 g 965 1878 M -9 17 V 0 g .3 g 2989 4417 M .3 g 2989 4417 M -16 11 V .3 g 2973 4428 M -16 10 V .3 g 2957 4438 M -11 7 V .3 g 2946 4445 M -22 13 V .3 g 2924 4458 M -6 3 V .3 g 2918 4461 M -27 17 V .3 g .3 g 2891 4478 M -27 16 V .3 g 2864 4494 M -7 4 V .3 g 2857 4498 M -20 12 V .3 g 2837 4510 M -14 8 V .3 g 2823 4518 M -14 8 V .3 g 2809 4526 M -22 12 V .3 g 2787 4538 M -5 3 V .3 g 2782 4541 M -27 16 V .3 g 2755 4557 M -4 2 V .3 g 2751 4559 M -23 13 V .3 g 2728 4572 M -14 7 V .3 g 2714 4579 M -14 7 V .3 g 2700 4586 M -23 13 V .3 g 2677 4599 M -4 2 V .3 g 2673 4601 M -27 14 V .3 g 2646 4615 M -7 4 V 0 g .3 g 4630 4619 M .3 g 4630 4619 M -22 -13 V .3 g 4608 4606 M -11 -7 V .3 g 4597 4599 M -16 -10 V .3 g 4581 4589 M -18 -10 V .3 g 4563 4579 M -10 -7 V .3 g 4553 4572 M -22 -13 V .3 g 4531 4559 M -5 -3 V .3 g 4526 4556 M -27 -18 V .3 g 4499 4538 M -27 -17 V stroke 4472 4521 M .3 g 4472 4521 M -5 -3 V .3 g 4467 4518 M -23 -15 V .3 g 4444 4503 M -7 -5 V .3 g 4437 4498 M -20 -13 V .3 g 4417 4485 M -11 -7 V .3 g 4406 4478 M -16 -11 V .3 g 4390 4467 M -14 -9 V .3 g 4376 4458 M -13 -9 V .3 g 4363 4449 M -17 -11 V .3 g 4346 4438 M -11 -8 V .3 g 4335 4430 M -19 -13 V .3 g 4316 4417 M -8 -5 V .3 g 4308 4412 M -21 -15 V .3 g 4287 4397 M -6 -4 V .3 g 4281 4393 M -24 -16 V .3 g 4257 4377 M -3 -2 V .3 g 4254 4375 M -26 -18 V .3 g 4228 4357 M -2 -1 V .3 g 4226 4356 M -27 -18 V .3 g 4199 4338 M -1 -1 V .3 g 4198 4337 M -26 -17 V .3 g 4172 4320 M -5 -3 V .3 g 4167 4317 M -22 -15 V .3 g 4145 4302 M -9 -5 V .3 g 4136 4297 M -19 -13 V .3 g 4117 4284 M -13 -8 V .3 g 4104 4276 M -14 -9 V .3 g 4090 4267 M -19 -11 V .3 g 4071 4256 M -8 -5 V .3 g 4063 4251 M -26 -15 V .3 g 4037 4236 M -1 -1 V .3 g 4036 4235 M -28 -15 V .3 g 4008 4220 M -8 -4 V .3 g 4000 4216 M -19 -10 V .3 g 3981 4206 M -20 -10 V .3 g 3961 4196 M -7 -4 V .3 g 3954 4192 M -27 -12 V .3 g 3927 4180 M -10 -4 V .3 g 3917 4176 M -18 -8 V .3 g 3899 4168 M -27 -10 V .3 g 3872 4158 M -7 -3 V .3 g 3865 4155 M -20 -7 V .3 g 3845 4148 M -27 -8 V .3 g 3818 4140 M -20 -5 V .3 g 3798 4135 M -8 -2 V .3 g 3790 4133 M -27 -5 V .3 g 3763 4128 M -27 -4 V .3 g 3736 4124 M -27 -3 V .3 g 3709 4121 M -28 -2 V .3 g 3681 4119 M -27 0 V .3 g 3654 4119 M -27 1 V .3 g 3627 4120 M -27 3 V stroke 3600 4123 M .3 g 3600 4123 M -28 3 V .3 g 3572 4126 M -27 6 V .3 g 3545 4132 M -15 3 V .3 g 3530 4135 M -12 3 V .3 g 3518 4138 M -27 8 V .3 g 3491 4146 M -28 8 V .3 g 3463 4154 M -2 1 V .3 g 3461 4155 M -25 9 V .3 g 3436 4164 M -27 11 V .3 g 3409 4175 M -1 1 V .3 g 3408 4176 M -26 11 V .3 g 3382 4187 M -19 9 V .3 g 3363 4196 M -9 4 V .3 g 3354 4200 M -27 14 V .3 g 3327 4214 M -4 2 V .3 g 3323 4216 M -23 12 V .3 g 3300 4228 M -15 8 V .3 g 3285 4236 M -12 7 V .3 g 3273 4243 M -24 13 V .3 g 3249 4256 M -4 2 V .3 g 3245 4258 M -27 16 V .3 g 3218 4274 M -3 2 V .3 g 3215 4276 M -24 15 V .3 g 3191 4291 M -10 6 V .3 g 3181 4297 M -17 10 V .3 g 3164 4307 M -15 10 V .3 g 3149 4317 M -13 7 V .3 g 3136 4324 M -19 13 V .3 g 3117 4337 M -8 5 V .3 g 3109 4342 M -24 15 V .3 g 3085 4357 M -3 2 V .3 g 3082 4359 M -27 17 V .3 g 3055 4376 M -2 1 V .3 g 3053 4377 M -26 16 V .3 g 3027 4393 M -6 4 V .3 g 3021 4397 M -21 14 V .3 g 3000 4411 M -11 6 V 0 g .3 g 6052 1406 M .3 g 6052 1406 M -8 -12 V .3 g 6044 1394 M -13 -20 V .3 g 6031 1374 M -6 -9 V .3 g 6025 1365 M -8 -11 V .3 g 6017 1354 M -14 -20 V .3 g 6003 1334 M -5 -8 V .3 g 5998 1326 M -10 -12 V .3 g 5988 1314 M -14 -21 V .3 g 5974 1293 M -4 -5 V .3 g 5970 1288 M -11 -15 V .3 g 5959 1273 M -14 -20 V .3 g 5945 1253 M -2 -2 V .3 g 5943 1251 M -13 -18 V .3 g 5930 1233 M -14 -19 V .3 g 5916 1214 M -2 -1 V stroke 5914 1213 M .3 g 5914 1213 M -15 -20 V .3 g 5899 1193 M -10 -14 V .3 g 5889 1179 M -6 -7 V .3 g 5883 1172 M -15 -20 V .3 g 5868 1152 M -7 -8 V .3 g 5861 1144 M -10 -12 V .3 g 5851 1132 M -16 -20 V .3 g 5835 1112 M -1 -2 V .3 g 5834 1110 M -15 -18 V .3 g 5819 1092 M -12 -15 V .3 g 5807 1077 M -5 -5 V .3 g 5802 1072 M -16 -20 V .3 g 5786 1052 M -6 -8 V .3 g 5780 1044 M -11 -13 V .3 g 5769 1031 M -17 -20 V .3 g .3 g 5752 1011 M -17 -20 V .3 g 5735 991 M -10 -12 V .3 g 5725 979 M -7 -8 V .3 g 5718 971 M -17 -20 V .3 g 5701 951 M -3 -4 V .3 g 5698 947 M -15 -16 V .3 g 5683 931 M -12 -15 V .3 g 5671 916 M -5 -6 V .3 g 5666 910 M -18 -20 V .3 g 5648 890 M -5 -6 V .3 g 5643 884 M -12 -14 V .3 g 5631 870 M -15 -17 V .3 g 5616 853 M -2 -3 V .3 g 5614 850 M -18 -20 V .3 g 5596 830 M -7 -9 V .3 g 5589 821 M -10 -11 V .3 g 5579 810 M -17 -20 V .3 g 5562 790 M -18 -21 V .3 g 5544 769 M -10 -11 V .3 g 5534 758 M -7 -9 V .3 g 5527 749 M -17 -20 V .3 g 5510 729 M -3 -3 V .3 g 5507 726 M -14 -17 V .3 g 5493 709 M -13 -15 V .3 g 5480 694 M -4 -5 V .3 g 5476 689 M -17 -20 V .3 g 5459 669 M -6 -8 V .3 g 5453 661 M -11 -13 V .3 g 5442 648 M -17 -20 V .3 g .3 g 5425 628 M -16 -20 V .3 g 5409 608 M -11 -13 V .3 g 5398 595 M -6 -7 V 0 g .28 g 1011 1871 M .28 g 1011 1871 M -4 7 V .28 g 1007 1878 M -10 20 V .28 g 997 1898 M -10 20 V .28 g 987 1918 M -3 6 V .28 g 984 1924 M -7 14 V stroke 977 1938 M .28 g 977 1938 M -10 21 V .28 g 967 1959 M -10 20 V .28 g 957 1979 M -1 0 V .28 g 956 1979 M -9 20 V .28 g 947 1999 M -10 20 V .28 g 937 2019 M -8 17 V .28 g 929 2036 M -2 3 V .28 g 927 2039 M -9 20 V .28 g 918 2059 M -10 20 V .28 g 908 2079 M -6 14 V .28 g 902 2093 M -3 7 V .28 g 899 2100 M -10 20 V .28 g 889 2120 M -9 20 V .28 g 880 2140 M -5 12 V .28 g 875 2152 M -4 8 V .28 g 871 2160 M -9 20 V .28 g 862 2180 M -10 20 V .28 g 852 2200 M -5 12 V .28 g 847 2212 M -4 9 V .28 g 843 2221 M -9 20 V .28 g 834 2241 M -9 20 V .28 g 825 2261 M -5 11 V .28 g 820 2272 M -4 9 V .28 g 816 2281 M -9 20 V .28 g 807 2301 M -9 20 V .28 g 798 2321 M -5 13 V .28 g 793 2334 M -3 7 V .28 g 790 2341 M -9 21 V .28 g 781 2362 M -9 20 V .28 g 772 2382 M -7 15 V .28 g 765 2397 M -2 5 V .28 g 763 2402 M -8 20 V .28 g 755 2422 M -9 20 V .28 g 746 2442 M -8 18 V .28 g 738 2460 M -1 2 V .28 g 737 2462 M -8 21 V .28 g 729 2483 M -9 20 V .28 g 720 2503 M -8 20 V .28 g 712 2523 M -1 1 V .28 g 711 2524 M -8 19 V .28 g 703 2543 M -8 20 V .28 g 695 2563 M -9 20 V .28 g 686 2583 M -2 6 V .28 g 684 2589 M -6 15 V .28 g 678 2604 M -9 20 V .28 g 669 2624 M -8 20 V .28 g 661 2644 M -4 10 V .28 g 657 2654 M -5 10 V .28 g 652 2664 M -8 20 V .28 g 644 2684 M -8 20 V .28 g 636 2704 M -7 16 V .28 g 629 2720 M -2 4 V stroke 627 2724 M .28 g 627 2724 M -8 21 V .28 g 619 2745 M -8 20 V .28 g 611 2765 M -9 20 V .28 g 602 2785 M 0 1 V 0 g .28 g 1969 588 M .28 g 1969 588 M -4 6 V .28 g 1965 594 M -13 14 V .28 g 1952 608 M -15 17 V .28 g 1937 625 M -2 3 V .28 g 1935 628 M -18 20 V .28 g 1917 648 M -7 9 V .28 g 1910 657 M -10 12 V .28 g 1900 669 M -17 19 V .28 g 1883 688 M -1 1 V .28 g 1882 689 M -18 20 V .28 g 1864 709 M -8 10 V .28 g 1856 719 M -9 10 V .28 g 1847 729 M -18 20 V .28 g 1829 749 M -1 1 V .28 g 1828 750 M -17 19 V .28 g 1811 769 M -10 11 V .28 g 1801 780 M -9 10 V .28 g 1792 790 M -18 20 V .28 g .28 g 1774 810 M -18 20 V .28 g 1756 830 M -9 10 V .28 g 1747 840 M -9 10 V .28 g 1738 850 M -19 20 V .28 g 1719 870 M -18 20 V .28 g 1701 890 M -9 10 V .28 g 1692 900 M -9 10 V .28 g 1683 910 M -18 20 V .28 g 1665 930 M -1 1 V .28 g 1664 931 M -18 20 V .28 g 1646 951 M -8 9 V .28 g 1638 960 M -10 11 V .28 g 1628 971 M -18 20 V .28 g .28 g 1610 991 M -18 20 V .28 g 1592 1011 M -9 11 V .28 g 1583 1022 M -8 9 V .28 g 1575 1031 M -18 21 V .28 g 1557 1052 M -1 1 V .28 g 1556 1053 M -16 19 V .28 g 1540 1072 M -11 12 V .28 g 1529 1084 M -7 8 V .28 g 1522 1092 M -17 20 V .28 g 1505 1112 M -4 5 V .28 g 1501 1117 M -13 15 V .28 g 1488 1132 M -14 18 V .28 g 1474 1150 M -2 2 V .28 g 1472 1152 M -16 20 V .28 g 1456 1172 M -9 11 V .28 g 1447 1183 M -8 10 V .28 g 1439 1193 M -16 20 V stroke 1423 1213 M .28 g 1423 1213 M -3 5 V .28 g 1420 1218 M -12 15 V .28 g 1408 1233 M -16 20 V .28 g .28 g 1392 1253 M -15 20 V .28 g 1377 1273 M -12 16 V .28 g 1365 1289 M -3 4 V .28 g 1362 1293 M -15 21 V .28 g 1347 1314 M -9 13 V .28 g 1338 1327 M -5 7 V .28 g 1333 1334 M -14 20 V .28 g 1319 1354 M -8 11 V .28 g 1311 1365 M -7 9 V .28 g 1304 1374 M -13 20 V .28 g 1291 1394 M -8 11 V .28 g 1283 1405 M -6 9 V .28 g 1277 1414 M -14 21 V .28 g 1263 1435 M -7 10 V .28 g 1256 1445 M -6 10 V .28 g 1250 1455 M -13 20 V .28 g 1237 1475 M -8 12 V .28 g 1229 1487 M -5 8 V .28 g 1224 1495 M -13 20 V .28 g 1211 1515 M -9 16 V .28 g 1202 1531 M -3 4 V .28 g 1199 1535 M -13 20 V .28 g 1186 1555 M -12 20 V .28 g 1174 1575 M 0 1 V .28 g 1174 1576 M -12 20 V .28 g 1162 1596 M -12 20 V .28 g 1150 1616 M -3 5 V .28 g 1147 1621 M -9 15 V .28 g 1138 1636 M -11 20 V .28 g 1127 1656 M -7 12 V .28 g 1120 1668 M -5 8 V .28 g 1115 1676 M -11 21 V .28 g 1104 1697 M -11 20 V .28 g .28 g 1093 1717 M -11 20 V .28 g 1082 1737 M -11 20 V .28 g 1071 1757 M -6 10 V .28 g 1065 1767 M -5 10 V .28 g 1060 1777 M -11 20 V .28 g 1049 1797 M -11 20 V .28 g 1038 1817 M 0 1 V .28 g 1038 1818 M -10 20 V .28 g 1028 1838 M -11 20 V .28 g 1017 1858 M -6 13 V 0 g .28 g 3173 4216 M .28 g 3173 4216 M -9 6 V .28 g 3164 4222 M -23 14 V .28 g 3141 4236 M -5 3 V .28 g 3136 4239 M -27 17 V .28 g .28 g 3109 4256 M -27 18 V .28 g 3082 4274 M -4 2 V stroke 3078 4276 M .28 g 3078 4276 M -23 15 V .28 g 3055 4291 M -9 6 V .28 g 3046 4297 M -19 12 V .28 g 3027 4309 M -12 8 V .28 g 3015 4317 M -15 9 V .28 g 3000 4326 M -17 11 V .28 g 2983 4337 M -10 7 V .28 g 2973 4344 M -22 13 V .28 g 2951 4357 M -5 4 V .28 g 2946 4361 M -27 16 V .28 g 2919 4377 M -1 0 V .28 g 2918 4377 M -27 17 V .28 g 2891 4394 M -5 3 V .28 g 2886 4397 M -22 13 V .28 g 2864 4410 M -12 7 V .28 g 2852 4417 M -15 9 V .28 g 2837 4426 M -20 12 V .28 g 2817 4438 M -8 4 V .28 g 2809 4442 M -27 16 V .28 g .28 g 2782 4458 M -27 15 V .28 g 2755 4473 M -10 5 V .28 g 2745 4478 M -17 10 V .28 g 2728 4488 M -20 10 V .28 g 2708 4498 M -8 4 V .28 g 2700 4502 M -27 15 V .28 g 2673 4517 M -3 1 V .28 g 2670 4518 M -24 13 V .28 g 2646 4531 M -15 7 V .28 g 2631 4538 M -12 7 V .28 g 2619 4545 M -27 14 V .28 g 2592 4559 M -1 0 V .28 g 2591 4559 M -27 14 V .28 g 2564 4573 M -12 6 V .28 g 2552 4579 M -15 8 V .28 g 2537 4587 M -24 12 V .28 g 2513 4599 M -3 2 V .28 g 2510 4601 M -28 14 V .28 g 2482 4615 M -8 4 V 0 g .28 g 4778 4619 M .28 g 4778 4619 M -7 -4 V .28 g 4771 4615 M -27 -15 V .28 g 4744 4600 M -2 -1 V .28 g 4742 4599 M -25 -14 V .28 g 4717 4585 M -11 -6 V .28 g 4706 4579 M -16 -10 V .28 g 4690 4569 M -19 -10 V .28 g 4671 4559 M -9 -5 V .28 g 4662 4554 M -26 -16 V .28 g 4636 4538 M -1 0 V .28 g 4635 4538 M -27 -16 V .28 g 4608 4522 M -6 -4 V .28 g 4602 4518 M -21 -13 V .28 g 4581 4505 M -12 -7 V stroke 4569 4498 M .28 g 4569 4498 M -16 -9 V .28 g 4553 4489 M -17 -11 V .28 g 4536 4478 M -10 -6 V .28 g 4526 4472 M -22 -14 V .28 g 4504 4458 M -5 -3 V .28 g 4499 4455 M -27 -17 V .28 g 4472 4438 M 0 -1 V .28 g 4472 4437 M -28 -18 V .28 g 4444 4419 M -2 -2 V .28 g 4442 4417 M -25 -16 V .28 g 4417 4401 M -6 -4 V .28 g 4411 4397 M -21 -14 V .28 g 4390 4383 M -9 -6 V .28 g 4381 4377 M -18 -13 V .28 g 4363 4364 M -11 -7 V .28 g 4352 4357 M -17 -11 V .28 g 4335 4346 M -13 -9 V .28 g 4322 4337 M -14 -10 V .28 g 4308 4327 M -15 -10 V .28 g 4293 4317 M -12 -9 V .28 g 4281 4308 M -17 -11 V .28 g 4264 4297 M -10 -8 V .28 g 4254 4289 M -19 -13 V .28 g 4235 4276 M -9 -5 V .28 g 4226 4271 M -21 -15 V .28 g 4205 4256 M -6 -4 V .28 g 4199 4252 M -24 -16 V .28 g 4175 4236 M -3 -2 V .28 g 4172 4234 M -27 -18 V .28 g .28 g 4145 4216 M -28 -18 V .28 g 4117 4198 M -3 -2 V .28 g 4114 4196 M -24 -15 V .28 g 4090 4181 M -8 -5 V .28 g 4082 4176 M -19 -12 V .28 g 4063 4164 M -14 -9 V .28 g 4049 4155 M -13 -7 V .28 g 4036 4148 M -22 -13 V .28 g 4014 4135 M -6 -3 V .28 g 4008 4132 M -27 -14 V .28 g 3981 4118 M -5 -3 V .28 g 3976 4115 M -22 -11 V .28 g 3954 4104 M -19 -9 V .28 g 3935 4095 M -8 -4 V .28 g 3927 4091 M -28 -12 V .28 g 3899 4079 M -11 -4 V .28 g 3888 4075 M -16 -6 V .28 g 3872 4069 M -27 -10 V .28 g 3845 4059 M -15 -4 V .28 g 3830 4055 M -12 -4 V .28 g 3818 4051 M -28 -7 V .28 g 3790 4044 M -27 -6 V .28 g 3763 4038 M -22 -3 V stroke 3741 4035 M .28 g 3741 4035 M -5 -1 V .28 g 3736 4034 M -27 -3 V .28 g 3709 4031 M -28 -2 V .28 g 3681 4029 M -27 0 V .28 g 3654 4029 M -27 1 V .28 g 3627 4030 M -27 3 V .28 g 3600 4033 M -12 2 V .28 g 3588 4035 M -16 2 V .28 g 3572 4037 M -27 5 V .28 g 3545 4042 M -27 7 V .28 g 3518 4049 M -21 6 V .28 g 3497 4055 M -6 1 V .28 g 3491 4056 M -28 9 V .28 g 3463 4065 M -25 10 V .28 g 3438 4075 M -2 1 V .28 g 3436 4076 M -27 11 V .28 g 3409 4087 M -19 8 V .28 g 3390 4095 M -8 4 V .28 g 3382 4099 M -28 13 V .28 g 3354 4112 M -6 3 V .28 g 3348 4115 M -21 11 V .28 g 3327 4126 M -17 9 V .28 g 3310 4135 M -10 6 V .28 g 3300 4141 M -27 14 V .28 g 3273 4155 M 0 1 V .28 g 3273 4156 M -28 16 V .28 g 3245 4172 M -6 4 V .28 g 3239 4176 M -21 12 V .28 g 3218 4188 M -13 8 V .28 g 3205 4196 M -14 9 V .28 g 3191 4205 M -18 11 V 0 g .28 g 6052 1490 M .28 g 6052 1490 M -10 -15 V .28 g 6042 1475 M -14 -20 V .28 g 6028 1455 M -3 -5 V .28 g 6025 1450 M -11 -15 V .28 g 6014 1435 M -14 -21 V .28 g 6000 1414 M -2 -3 V .28 g 5998 1411 M -13 -17 V .28 g 5985 1394 M -14 -20 V .28 g 5971 1374 M -1 -1 V .28 g 5970 1373 M -14 -19 V .28 g 5956 1354 M -13 -18 V .28 g 5943 1336 M -2 -2 V .28 g 5941 1334 M -15 -20 V .28 g 5926 1314 M -10 -14 V .28 g 5916 1300 M -6 -7 V .28 g 5910 1293 M -15 -20 V .28 g 5895 1273 M -6 -8 V .28 g 5889 1265 M -10 -12 V .28 g 5879 1253 M -16 -20 V .28 g 5863 1233 M -2 -2 V .28 g 5861 1231 M -14 -18 V stroke 5847 1213 M .28 g 5847 1213 M -13 -16 V .28 g 5834 1197 M -3 -4 V .28 g 5831 1193 M -17 -21 V .28 g 5814 1172 M -7 -8 V .28 g 5807 1164 M -10 -12 V .28 g 5797 1152 M -17 -20 V .28 g 5780 1132 M 0 -1 V .28 g 5780 1131 M -17 -19 V .28 g 5763 1112 M -11 -13 V .28 g 5752 1099 M -6 -7 V .28 g 5746 1092 M -17 -20 V .28 g 5729 1072 M -4 -5 V .28 g 5725 1067 M -13 -15 V .28 g 5712 1052 M -14 -16 V .28 g 5698 1036 M -4 -5 V .28 g 5694 1031 M -17 -20 V .28 g 5677 1011 M -6 -7 V .28 g 5671 1004 M -12 -13 V .28 g 5659 991 M -16 -18 V .28 g 5643 973 M -1 -2 V .28 g 5642 971 M -18 -20 V .28 g 5624 951 M -8 -9 V .28 g 5616 942 M -10 -11 V .28 g 5606 931 M -17 -21 V .28 g .28 g 5589 910 M -18 -20 V .28 g 5571 890 M -9 -11 V .28 g 5562 879 M -8 -9 V .28 g 5554 870 M -17 -20 V .28 g 5537 850 M -3 -3 V .28 g 5534 847 M -15 -17 V .28 g 5519 830 M -12 -14 V .28 g 5507 816 M -5 -6 V .28 g 5502 810 M -17 -20 V .28 g 5485 790 M -5 -6 V .28 g 5480 784 M -12 -15 V .28 g 5468 769 M -15 -18 V .28 g 5453 751 M -2 -2 V .28 g 5451 749 M -17 -20 V .28 g 5434 729 M -9 -11 V .28 g 5425 718 M -8 -9 V .28 g 5417 709 M -16 -20 V .28 g 5401 689 M -3 -4 V .28 g 5398 685 M -14 -16 V .28 g 5384 669 M -13 -17 V .28 g 5371 652 M -3 -4 V .28 g 5368 648 M -16 -20 V .28 g 5352 628 M -8 -10 V .28 g 5344 618 M -9 -10 V .28 g 5335 608 M -16 -20 V 0 g .26 g 1074 1838 M .26 g 1074 1838 M -9 16 V .26 g 1065 1854 M -2 4 V .26 g 1063 1858 M -11 20 V stroke 1052 1878 M .26 g 1052 1878 M -10 20 V .26 g 1042 1898 M -4 7 V .26 g 1038 1905 M -7 13 V .26 g 1031 1918 M -10 20 V .26 g 1021 1938 M -10 20 V .26 g 1011 1958 M -1 1 V .26 g 1010 1959 M -10 20 V .26 g 1000 1979 M -10 20 V .26 g 990 1999 M -6 13 V .26 g 984 2012 M -4 7 V .26 g 980 2019 M -10 20 V .26 g 970 2039 M -10 20 V .26 g 960 2059 M -4 8 V .26 g 956 2067 M -6 12 V .26 g 950 2079 M -10 21 V .26 g 940 2100 M -9 20 V .26 g 931 2120 M -2 3 V .26 g 929 2123 M -8 17 V .26 g 921 2140 M -9 20 V .26 g 912 2160 M -10 20 V .26 g 902 2180 M 0 1 V .26 g 902 2181 M -9 19 V .26 g 893 2200 M -9 21 V .26 g 884 2221 M -9 19 V .26 g 875 2240 M -1 1 V .26 g 874 2241 M -9 20 V .26 g 865 2261 M -9 20 V .26 g 856 2281 M -9 19 V .26 g 847 2300 M 0 1 V .26 g 847 2301 M -9 20 V .26 g 838 2321 M -9 20 V .26 g 829 2341 M -9 20 V .26 g 820 2361 M 0 1 V .26 g 820 2362 M -9 20 V .26 g 811 2382 M -9 20 V .26 g 802 2402 M -9 20 V .26 g 793 2422 M 0 1 V .26 g 793 2423 M -9 19 V .26 g 784 2442 M -8 20 V .26 g 776 2462 M -9 21 V .26 g 767 2483 M -2 3 V .26 g 765 2486 M -7 17 V .26 g 758 2503 M -8 20 V .26 g 750 2523 M -9 20 V .26 g 741 2543 M -3 6 V .26 g 738 2549 M -6 14 V .26 g 732 2563 M -8 20 V .26 g 724 2583 M -9 21 V .26 g 715 2604 M -4 10 V .26 g 711 2614 M -4 10 V .26 g 707 2624 M -8 20 V .26 g 699 2644 M -9 20 V stroke 690 2664 M .26 g 690 2664 M -6 15 V .26 g 684 2679 M -2 5 V .26 g 682 2684 M -9 20 V .26 g 673 2704 M -8 20 V .26 g 665 2724 M -8 21 V .26 g 657 2745 M -9 20 V .26 g 648 2765 M -8 20 V .26 g 640 2785 M -8 20 V .26 g 632 2805 M -3 6 V .26 g 629 2811 M -6 14 V .26 g 623 2825 M -8 20 V .26 g 615 2845 M -8 21 V .26 g 607 2866 M -5 11 V 0 g .26 g 2047 588 M .26 g 2047 588 M -1 1 V .26 g 2046 589 M -15 19 V .26 g 2031 608 M -12 14 V .26 g 2019 622 M -5 6 V .26 g 2014 628 M -17 20 V .26 g 1997 648 M -5 7 V .26 g 1992 655 M -12 14 V .26 g 1980 669 M -15 18 V .26 g 1965 687 M -2 2 V .26 g 1963 689 M -17 20 V .26 g 1946 709 M -9 10 V .26 g 1937 719 M -8 10 V .26 g 1929 729 M -18 20 V .26 g 1911 749 M -1 2 V .26 g 1910 751 M -16 18 V .26 g 1894 769 M -11 13 V .26 g 1883 782 M -7 8 V .26 g 1876 790 M -18 20 V .26 g 1858 810 M -2 3 V .26 g 1856 813 M -16 17 V .26 g 1840 830 M -12 13 V .26 g 1828 843 M -6 7 V .26 g 1822 850 M -18 20 V .26 g 1804 870 M -3 3 V .26 g 1801 873 M -16 17 V .26 g 1785 890 M -11 13 V .26 g 1774 903 M -7 7 V .26 g 1767 910 M -18 21 V .26 g 1749 931 M -2 2 V .26 g 1747 933 M -17 18 V .26 g 1730 951 M -11 12 V .26 g 1719 963 M -7 8 V .26 g 1712 971 M -19 20 V .26 g 1693 991 M -1 1 V .26 g 1692 992 M -17 19 V .26 g 1675 1011 M -10 11 V .26 g 1665 1022 M -9 9 V .26 g 1656 1031 M -18 21 V .26 g .26 g 1638 1052 M -18 20 V stroke 1620 1072 M .26 g 1620 1072 M -10 10 V .26 g 1610 1082 M -9 10 V .26 g 1601 1092 M -18 20 V .26 g .26 g 1583 1112 M -17 20 V .26 g 1566 1132 M -10 11 V .26 g 1556 1143 M -8 9 V .26 g 1548 1152 M -18 20 V .26 g 1530 1172 M -1 3 V .26 g 1529 1175 M -16 18 V .26 g 1513 1193 M -12 13 V .26 g 1501 1206 M -5 7 V .26 g 1496 1213 M -17 20 V .26 g 1479 1233 M -5 6 V .26 g 1474 1239 M -12 14 V .26 g 1462 1253 M -15 19 V .26 g 1447 1272 M -1 1 V .26 g 1446 1273 M -16 20 V .26 g 1430 1293 M -10 13 V .26 g 1420 1306 M -6 8 V .26 g 1414 1314 M -16 20 V .26 g 1398 1334 M -6 8 V .26 g 1392 1342 M -9 12 V .26 g 1383 1354 M -15 20 V .26 g 1368 1374 M -3 4 V .26 g 1365 1378 M -12 16 V .26 g 1353 1394 M -15 20 V .26 g 1338 1414 M 0 1 V .26 g 1338 1415 M -14 20 V .26 g 1324 1435 M -13 18 V .26 g 1311 1453 M -2 2 V .26 g 1309 1455 M -14 20 V .26 g 1295 1475 M -12 17 V .26 g 1283 1492 M -2 3 V .26 g 1281 1495 M -13 20 V .26 g 1268 1515 M -12 18 V .26 g 1256 1533 M -2 2 V .26 g 1254 1535 M -13 20 V .26 g 1241 1555 M -12 20 V .26 g 1229 1575 M -1 1 V .26 g 1228 1576 M -13 20 V .26 g 1215 1596 M -12 20 V .26 g 1203 1616 M -1 2 V .26 g 1202 1618 M -12 18 V .26 g 1190 1636 M -12 20 V .26 g 1178 1656 M -4 6 V .26 g 1174 1662 M -8 14 V .26 g 1166 1676 M -12 21 V .26 g 1154 1697 M -7 11 V .26 g 1147 1708 M -5 9 V .26 g 1142 1717 M -12 20 V .26 g 1130 1737 M -10 18 V .26 g 1120 1755 M -1 2 V stroke 1119 1757 M .26 g 1119 1757 M -11 20 V .26 g 1108 1777 M -12 20 V .26 g 1096 1797 M -3 7 V .26 g 1093 1804 M -8 13 V .26 g 1085 1817 M -11 21 V 0 g .26 g 3327 4035 M .26 g 3327 4035 M -27 15 V .26 g 3300 4050 M -9 5 V .26 g 3291 4055 M -18 10 V .26 g 3273 4065 M -16 10 V .26 g 3257 4075 M -12 7 V .26 g 3245 4082 M -22 13 V .26 g 3223 4095 M -5 3 V .26 g 3218 4098 M -27 17 V .26 g .26 g 3191 4115 M -27 18 V .26 g 3164 4133 M -5 2 V .26 g 3159 4135 M -23 15 V .26 g 3136 4150 M -8 5 V .26 g 3128 4155 M -19 13 V .26 g 3109 4168 M -12 8 V .26 g 3097 4176 M -15 10 V .26 g 3082 4186 M -16 10 V .26 g 3066 4196 M -11 7 V .26 g 3055 4203 M -20 13 V .26 g 3035 4216 M -8 5 V .26 g 3027 4221 M -23 15 V .26 g 3004 4236 M -4 3 V .26 g 3000 4239 M -27 17 V .26 g 2973 4256 M -27 17 V .26 g 2946 4273 M -5 3 V .26 g 2941 4276 M -23 14 V .26 g 2918 4290 M -10 7 V .26 g 2908 4297 M -17 10 V .26 g 2891 4307 M -16 10 V .26 g 2875 4317 M -11 6 V .26 g 2864 4323 M -23 14 V .26 g 2841 4337 M -4 3 V .26 g 2837 4340 M -28 15 V .26 g 2809 4355 M -3 2 V .26 g 2806 4357 M -24 14 V .26 g 2782 4371 M -12 6 V .26 g 2770 4377 M -15 9 V .26 g 2755 4386 M -21 11 V .26 g 2734 4397 M -6 4 V .26 g 2728 4401 M -28 14 V .26 g 2700 4415 M -4 2 V .26 g 2696 4417 M -23 12 V .26 g 2673 4429 M -16 9 V .26 g 2657 4438 M -11 5 V .26 g 2646 4443 M -27 14 V .26 g 2619 4457 M -2 1 V .26 g 2617 4458 M -26 13 V .26 g 2591 4471 M -14 7 V stroke 2577 4478 M .26 g 2577 4478 M -13 7 V .26 g 2564 4485 M -27 13 V .26 g .26 g 2537 4498 M -27 14 V .26 g 2510 4512 M -13 6 V .26 g 2497 4518 M -15 8 V .26 g 2482 4526 M -24 12 V .26 g 2458 4538 M -3 2 V .26 g 2455 4540 M -27 14 V .26 g 2428 4554 M -8 5 V .26 g 2420 4559 M -19 10 V .26 g 2401 4569 M -18 10 V .26 g 2383 4579 M -10 5 V .26 g 2373 4584 M -25 15 V .26 g 2348 4599 M -2 1 V .26 g 2346 4600 M -27 16 V .26 g 2319 4616 M -5 3 V 0 g .26 g 4936 4619 M .26 g 4936 4619 M -1 -1 V .26 g 4935 4618 M -27 -15 V .26 g 4908 4603 M -7 -4 V .26 g 4901 4599 M -21 -12 V .26 g 4880 4587 M -15 -8 V .26 g 4865 4579 M -12 -7 V .26 g 4853 4572 M -24 -13 V .26 g 4829 4559 M -3 -2 V .26 g 4826 4557 M -27 -15 V .26 g 4799 4542 M -7 -4 V .26 g 4792 4538 M -21 -11 V .26 g 4771 4527 M -16 -9 V .26 g 4755 4518 M -11 -6 V .26 g 4744 4512 M -25 -14 V .26 g 4719 4498 M -2 -1 V .26 g 4717 4497 M -27 -15 V .26 g 4690 4482 M -7 -4 V .26 g 4683 4478 M -21 -12 V .26 g 4662 4466 M -15 -8 V .26 g 4647 4458 M -12 -7 V .26 g 4635 4451 M -22 -13 V .26 g 4613 4438 M -5 -3 V .26 g 4608 4435 M -27 -17 V .26 g 4581 4418 M -2 -1 V .26 g 4579 4417 M -26 -15 V .26 g 4553 4402 M -7 -5 V .26 g 4546 4397 M -20 -12 V .26 g 4526 4385 M -12 -8 V .26 g 4514 4377 M -15 -9 V .26 g 4499 4368 M -17 -11 V .26 g 4482 4357 M -10 -7 V .26 g 4472 4350 M -21 -13 V .26 g 4451 4337 M -7 -5 V .26 g 4444 4332 M -23 -15 V .26 g 4421 4317 M -4 -3 V .26 g 4417 4314 M -26 -17 V stroke 4391 4297 M .26 g 4391 4297 M -1 -1 V .26 g 4390 4296 M -27 -19 V .26 g 4363 4277 M -1 -1 V .26 g 4362 4276 M -27 -18 V .26 g 4335 4258 M -2 -2 V .26 g 4333 4256 M -25 -17 V .26 g 4308 4239 M -4 -3 V .26 g 4304 4236 M -23 -16 V .26 g 4281 4220 M -6 -4 V .26 g 4275 4216 M -21 -15 V .26 g 4254 4201 M -8 -5 V .26 g 4246 4196 M -20 -14 V .26 g 4226 4182 M -9 -6 V .26 g 4217 4176 M -18 -13 V .26 g 4199 4163 M -11 -8 V .26 g 4188 4155 M -16 -11 V .26 g 4172 4144 M -14 -9 V .26 g 4158 4135 M -13 -9 V .26 g 4145 4126 M -17 -11 V .26 g 4128 4115 M -11 -7 V .26 g 4117 4108 M -20 -13 V .26 g 4097 4095 M -7 -5 V .26 g 4090 4090 M -25 -15 V .26 g 4065 4075 M -2 -2 V .26 g 4063 4073 M -27 -16 V .26 g 4036 4057 M -4 -2 V .26 g 4032 4055 M -24 -14 V .26 g 4008 4041 M -11 -6 V .26 g 3997 4035 M -16 -9 V .26 g 3981 4026 M -22 -12 V .26 g 3959 4014 M -5 -2 V .26 g 3954 4012 M -27 -13 V .26 g 3927 3999 M -11 -5 V .26 g 3916 3994 M -17 -7 V .26 g 3899 3987 M -27 -11 V .26 g 3872 3976 M -5 -2 V .26 g 3867 3974 M -22 -8 V .26 g 3845 3966 M -27 -9 V .26 g 3818 3957 M -14 -3 V .26 g 3804 3954 M -14 -4 V .26 g 3790 3950 M -27 -6 V .26 g 3763 3944 M -27 -4 V .26 g 3736 3940 M -27 -3 V .26 g 3709 3937 M -28 -2 V .26 g 3681 3935 M -27 0 V .26 g 3654 3935 M -27 1 V .26 g 3627 3936 M -27 3 V .26 g 3600 3939 M -28 4 V .26 g 3572 3943 M -27 6 V .26 g 3545 3949 M -21 5 V .26 g 3524 3954 M -6 1 V .26 g 3518 3955 M -27 8 V stroke 3491 3963 M .26 g 3491 3963 M -28 10 V .26 g 3463 3973 M -3 1 V .26 g 3460 3974 M -24 9 V .26 g 3436 3983 M -26 11 V .26 g 3410 3994 M -1 1 V .26 g 3409 3995 M -27 12 V .26 g 3382 4007 M -15 7 V .26 g 3367 4014 M -13 7 V .26 g 3354 4021 M -27 14 V .26 g 0 g .26 g 6052 1578 M .26 g 6052 1578 M -1 -2 V .26 g 6051 1576 M -14 -21 V .26 g 6037 1555 M -12 -17 V .26 g 6025 1538 M -2 -3 V .26 g 6023 1535 M -14 -20 V .26 g 6009 1515 M -11 -16 V .26 g 5998 1499 M -4 -4 V .26 g 5994 1495 M -14 -20 V .26 g 5980 1475 M -10 -13 V .26 g 5970 1462 M -5 -7 V .26 g 5965 1455 M -15 -20 V .26 g 5950 1435 M -7 -10 V .26 g 5943 1425 M -8 -11 V .26 g 5935 1414 M -15 -20 V .26 g 5920 1394 M -4 -5 V .26 g 5916 1389 M -12 -15 V .26 g 5904 1374 M -15 -20 V .26 g 5889 1354 M -1 0 V .26 g 5888 1354 M -16 -20 V .26 g 5872 1334 M -11 -14 V .26 g 5861 1320 M -5 -6 V .26 g 5856 1314 M -17 -21 V .26 g 5839 1293 M -5 -6 V .26 g 5834 1287 M -11 -14 V .26 g 5823 1273 M -16 -19 V .26 g 5807 1254 M -1 -1 V .26 g 5806 1253 M -17 -20 V .26 g 5789 1233 M -9 -11 V .26 g 5780 1222 M -8 -9 V .26 g 5772 1213 M -17 -20 V .26 g 5755 1193 M -3 -3 V .26 g 5752 1190 M -15 -18 V .26 g 5737 1172 M -12 -14 V .26 g 5725 1158 M -5 -6 V .26 g 5720 1152 M -18 -20 V .26 g 5702 1132 M -4 -5 V .26 g 5698 1127 M -14 -15 V .26 g 5684 1112 M -13 -16 V .26 g 5671 1096 M -4 -4 V .26 g 5667 1092 M -18 -20 V .26 g 5649 1072 M -6 -7 V .26 g 5643 1065 M -12 -13 V .26 g 5631 1052 M -15 -18 V stroke 5616 1034 M .26 g 5616 1034 M -2 -3 V .26 g 5614 1031 M -18 -20 V .26 g 5596 1011 M -7 -8 V .26 g 5589 1003 M -11 -12 V .26 g 5578 991 M -16 -19 V .26 g 5562 972 M -1 -1 V .26 g 5561 971 M -18 -20 V .26 g 5543 951 M -9 -10 V .26 g 5534 941 M -8 -10 V .26 g 5526 931 M -18 -21 V .26 g 5508 910 M -1 -1 V .26 g 5507 909 M -16 -19 V .26 g 5491 890 M -11 -13 V .26 g 5480 877 M -6 -7 V .26 g 5474 870 M -17 -20 V .26 g 5457 850 M -4 -5 V .26 g 5453 845 M -13 -15 V .26 g 5440 830 M -15 -18 V .26 g 5425 812 M -2 -2 V .26 g 5423 810 M -16 -20 V .26 g 5407 790 M -9 -11 V .26 g 5398 779 M -8 -10 V .26 g 5390 769 M -16 -20 V .26 g 5374 749 M -3 -3 V .26 g 5371 746 M -14 -17 V .26 g 5357 729 M -13 -17 V .26 g 5344 712 M -3 -3 V .26 g 5341 709 M -16 -20 V .26 g 5325 689 M -9 -11 V .26 g 5316 678 M -7 -9 V .26 g 5309 669 M -16 -21 V .26 g 5293 648 M -4 -5 V .26 g 5289 643 M -12 -15 V .26 g 5277 628 M -15 -20 V .26 g .26 g 5262 608 M -16 -20 V 0 g .24 g 1124 1838 M .24 g 1124 1838 M -4 8 V .24 g 1120 1846 M -7 12 V .24 g 1113 1858 M -11 20 V .24 g 1102 1878 M -9 16 V .24 g 1093 1894 M -3 4 V .24 g 1090 1898 M -11 20 V .24 g 1079 1918 M -11 20 V .24 g 1068 1938 M -3 6 V .24 g 1065 1944 M -7 15 V .24 g 1058 1959 M -11 20 V .24 g 1047 1979 M -9 16 V .24 g 1038 1995 M -2 4 V .24 g 1036 1999 M -10 20 V .24 g 1026 2019 M -11 20 V .24 g 1015 2039 M -4 9 V .24 g 1011 2048 M -6 11 V .24 g 1005 2059 M -10 20 V stroke 995 2079 M .24 g 995 2079 M -10 21 V .24 g 985 2100 M -1 2 V .24 g 984 2102 M -9 18 V .24 g 975 2120 M -10 20 V .24 g 965 2140 M -9 18 V .24 g 956 2158 M -1 2 V .24 g 955 2160 M -10 20 V .24 g 945 2180 M -9 20 V .24 g 936 2200 M -7 14 V .24 g 929 2214 M -3 7 V .24 g 926 2221 M -9 20 V .24 g 917 2241 M -10 20 V .24 g 907 2261 M -5 11 V .24 g 902 2272 M -4 9 V .24 g 898 2281 M -9 20 V .24 g 889 2301 M -10 20 V .24 g 879 2321 M -4 10 V .24 g 875 2331 M -5 10 V .24 g 870 2341 M -9 21 V .24 g 861 2362 M -9 20 V .24 g 852 2382 M -5 10 V .24 g 847 2392 M -4 10 V .24 g 843 2402 M -9 20 V .24 g 834 2422 M -9 20 V .24 g 825 2442 M -5 11 V .24 g 820 2453 M -4 9 V .24 g 816 2462 M -9 21 V .24 g 807 2483 M -9 20 V .24 g 798 2503 M -5 12 V .24 g 793 2515 M -3 8 V .24 g 790 2523 M -9 20 V .24 g 781 2543 M -9 20 V .24 g 772 2563 M -7 16 V .24 g 765 2579 M -2 4 V .24 g 763 2583 M -8 21 V .24 g 755 2604 M -9 20 V .24 g 746 2624 M -8 19 V .24 g 738 2643 M 0 1 V .24 g 738 2644 M -9 20 V .24 g 729 2664 M -8 20 V .24 g 721 2684 M -9 20 V .24 g 712 2704 M -1 3 V .24 g 711 2707 M -7 17 V .24 g 704 2724 M -8 21 V .24 g 696 2745 M -9 20 V .24 g 687 2765 M -3 8 V .24 g 684 2773 M -5 12 V .24 g 679 2785 M -8 20 V .24 g 671 2805 M -9 20 V .24 g 662 2825 M -5 14 V .24 g 657 2839 M -3 6 V .24 g 654 2845 M -8 21 V stroke 646 2866 M .24 g 646 2866 M -9 20 V .24 g 637 2886 M -8 19 V .24 g 629 2905 M 0 1 V .24 g 629 2906 M -8 20 V .24 g 621 2926 M -8 20 V .24 g 613 2946 M -9 20 V .24 g 604 2966 M -2 6 V 0 g .24 g 2126 588 M .24 g 2126 588 M -16 20 V .24 g 2110 608 M -9 12 V .24 g 2101 620 M -7 8 V .24 g 2094 628 M -16 20 V .24 g 2078 648 M -4 6 V .24 g 2074 654 M -12 15 V .24 g 2062 669 M -16 18 V .24 g 2046 687 M -1 2 V .24 g 2045 689 M -16 20 V .24 g 2029 709 M -10 12 V .24 g 2019 721 M -7 8 V .24 g 2012 729 M -17 20 V .24 g 1995 749 M -3 4 V .24 g 1992 753 M -14 16 V .24 g 1978 769 M -13 17 V .24 g 1965 786 M -4 4 V .24 g 1961 790 M -17 20 V .24 g 1944 810 M -7 7 V .24 g 1937 817 M -11 13 V .24 g 1926 830 M -16 19 V .24 g 1910 849 M -1 1 V .24 g 1909 850 M -18 20 V .24 g 1891 870 M -8 10 V .24 g 1883 880 M -10 10 V .24 g 1873 890 M -17 20 V .24 g 1856 910 M -1 0 V .24 g 1855 910 M -18 21 V .24 g 1837 931 M -9 10 V .24 g 1828 941 M -9 10 V .24 g 1819 951 M -18 20 V .24 g .24 g 1801 971 M -19 20 V .24 g 1782 991 M -8 9 V .24 g 1774 1000 M -10 11 V .24 g 1764 1011 M -17 19 V .24 g 1747 1030 M -2 1 V .24 g 1745 1031 M -19 21 V .24 g 1726 1052 M -7 7 V .24 g 1719 1059 M -11 13 V .24 g 1708 1072 M -16 16 V .24 g 1692 1088 M -3 4 V .24 g 1689 1092 M -19 20 V .24 g 1670 1112 M -5 6 V .24 g 1665 1118 M -13 14 V .24 g 1652 1132 M -14 15 V .24 g 1638 1147 M -5 5 V stroke 1633 1152 M .24 g 1633 1152 M -19 20 V .24 g 1614 1172 M -4 5 V .24 g 1610 1177 M -14 16 V .24 g 1596 1193 M -13 14 V .24 g 1583 1207 M -5 6 V .24 g 1578 1213 M -18 20 V .24 g 1560 1233 M -4 4 V .24 g 1556 1237 M -14 16 V .24 g 1542 1253 M -13 15 V .24 g 1529 1268 M -5 5 V .24 g 1524 1273 M -17 20 V .24 g 1507 1293 M -6 7 V .24 g 1501 1300 M -11 14 V .24 g 1490 1314 M -16 18 V .24 g 1474 1332 M -1 2 V .24 g 1473 1334 M -17 20 V .24 g 1456 1354 M -9 11 V .24 g 1447 1365 M -7 9 V .24 g 1440 1374 M -17 20 V .24 g 1423 1394 M -3 5 V .24 g 1420 1399 M -13 15 V .24 g 1407 1414 M -15 20 V .24 g 1392 1434 M 0 1 V .24 g 1392 1435 M -16 20 V .24 g 1376 1455 M -11 14 V .24 g 1365 1469 M -4 6 V .24 g 1361 1475 M -15 20 V .24 g 1346 1495 M -8 11 V .24 g 1338 1506 M -7 9 V .24 g 1331 1515 M -14 20 V .24 g 1317 1535 M -6 9 V .24 g 1311 1544 M -8 11 V .24 g 1303 1555 M -14 21 V .24 g 1289 1576 M -6 7 V .24 g 1283 1583 M -8 13 V .24 g 1275 1596 M -14 20 V .24 g 1261 1616 M -5 8 V .24 g 1256 1624 M -8 12 V .24 g 1248 1636 M -13 20 V .24 g 1235 1656 M -6 9 V .24 g 1229 1665 M -7 11 V .24 g 1222 1676 M -13 21 V .24 g 1209 1697 M -7 11 V .24 g 1202 1708 M -6 9 V .24 g 1196 1717 M -12 20 V .24 g 1184 1737 M -10 16 V .24 g 1174 1753 M -2 4 V .24 g 1172 1757 M -12 20 V .24 g 1160 1777 M -12 20 V .24 g 1148 1797 M -1 1 V .24 g 1147 1798 M -11 19 V .24 g 1136 1817 M -12 21 V stroke 1124 1838 M 0 g .24 g 3491 3866 M .24 g 3491 3866 M -20 7 V .24 g 3471 3873 M -8 3 V .24 g 3463 3876 M -27 11 V .24 g 3436 3887 M -16 6 V .24 g 3420 3893 M -11 5 V .24 g 3409 3898 M -27 13 V .24 g 3382 3911 M -5 3 V .24 g 3377 3914 M -23 11 V .24 g 3354 3925 M -16 9 V .24 g 3338 3934 M -11 6 V .24 g 3327 3940 M -25 14 V .24 g 3302 3954 M -2 1 V .24 g 3300 3955 M -27 16 V .24 g 3273 3971 M -5 3 V .24 g 3268 3974 M -23 14 V .24 g 3245 3988 M -10 6 V .24 g 3235 3994 M -17 11 V .24 g 3218 4005 M -15 9 V .24 g 3203 4014 M -12 8 V .24 g 3191 4022 M -19 13 V .24 g 3172 4035 M -8 5 V .24 g 3164 4040 M -23 15 V .24 g 3141 4055 M -5 3 V .24 g 3136 4058 M -26 17 V .24 g 3110 4075 M -1 1 V .24 g 3109 4076 M -27 18 V .24 g 3082 4094 M -2 1 V .24 g 3080 4095 M -25 17 V .24 g 3055 4112 M -5 3 V .24 g 3050 4115 M -23 15 V .24 g 3027 4130 M -8 5 V .24 g 3019 4135 M -19 13 V .24 g 3000 4148 M -12 7 V .24 g 2988 4155 M -15 10 V .24 g 2973 4165 M -16 11 V .24 g 2957 4176 M -11 7 V .24 g 2946 4183 M -21 13 V .24 g 2925 4196 M -7 4 V .24 g 2918 4200 M -26 16 V .24 g 2892 4216 M -1 1 V .24 g 2891 4217 M -27 16 V .24 g 2864 4233 M -5 3 V .24 g 2859 4236 M -22 13 V .24 g 2837 4249 M -13 7 V .24 g 2824 4256 M -15 9 V .24 g 2809 4265 M -20 11 V .24 g 2789 4276 M -7 4 V .24 g 2782 4280 M -27 15 V .24 g 2755 4295 M -2 2 V .24 g 2753 4297 M -25 13 V .24 g 2728 4310 M -13 7 V .24 g 2715 4317 M -15 7 V stroke 2700 4324 M .24 g 2700 4324 M -24 13 V .24 g 2676 4337 M -3 2 V .24 g 2673 4339 M -27 13 V .24 g 2646 4352 M -9 5 V .24 g 2637 4357 M -18 9 V .24 g 2619 4366 M -23 11 V .24 g 2596 4377 M -5 2 V .24 g 2591 4379 M -27 14 V .24 g 2564 4393 M -9 4 V .24 g 2555 4397 M -18 9 V .24 g 2537 4406 M -23 11 V .24 g 2514 4417 M -4 3 V .24 g 2510 4420 M -28 13 V .24 g 2482 4433 M -9 5 V .24 g 2473 4438 M -18 9 V .24 g 2455 4447 M -22 11 V .24 g 2433 4458 M -5 3 V .24 g 2428 4461 M -27 14 V .24 g 2401 4475 M -6 3 V .24 g 2395 4478 M -22 12 V .24 g 2373 4490 M -15 8 V .24 g 2358 4498 M -12 7 V .24 g 2346 4505 M -22 13 V .24 g 2324 4518 M -5 3 V .24 g 2319 4521 M -27 17 V .24 g 2292 4538 M -1 0 V .24 g 2291 4538 M -27 17 V .24 g 2264 4555 M -5 4 V .24 g 2259 4559 M -22 15 V .24 g 2237 4574 M -7 5 V .24 g 2230 4579 M -20 14 V .24 g 2210 4593 M -8 6 V .24 g 2202 4599 M -19 15 V .24 g 2183 4614 M -7 5 V 0 g .24 g 5085 4619 M .24 g 5085 4619 M -14 -10 V .24 g 5071 4609 M -15 -10 V .24 g 5056 4599 M -12 -8 V .24 g 5044 4591 M -19 -12 V .24 g 5025 4579 M -8 -6 V .24 g 5017 4573 M -25 -14 V .24 g 4992 4559 M -3 -2 V .24 g 4989 4557 M -27 -17 V .24 g 4962 4540 M -4 -2 V .24 g 4958 4538 M -23 -13 V .24 g 4935 4525 M -12 -7 V .24 g 4923 4518 M -15 -9 V .24 g 4908 4509 M -21 -11 V .24 g 4887 4498 M -7 -4 V .24 g 4880 4494 M -27 -15 V .24 g 4853 4479 M -3 -1 V .24 g 4850 4478 M -24 -13 V .24 g 4826 4465 M -13 -7 V stroke 4813 4458 M .24 g 4813 4458 M -14 -8 V .24 g 4799 4450 M -24 -12 V .24 g 4775 4438 M -4 -2 V .24 g 4771 4436 M -27 -15 V .24 g 4744 4421 M -6 -4 V .24 g 4738 4417 M -21 -11 V .24 g 4717 4406 M -16 -9 V .24 g 4701 4397 M -11 -6 V .24 g 4690 4391 M -25 -14 V .24 g 4665 4377 M -3 -1 V .24 g 4662 4376 M -27 -16 V .24 g 4635 4360 M -5 -3 V .24 g 4630 4357 M -22 -13 V .24 g 4608 4344 M -13 -7 V .24 g 4595 4337 M -14 -9 V .24 g 4581 4328 M -19 -11 V .24 g 4562 4317 M -9 -6 V .24 g 4553 4311 M -24 -14 V .24 g 4529 4297 M -3 -2 V .24 g 4526 4295 M -27 -18 V .24 g 4499 4277 M -2 -1 V .24 g 4497 4276 M -25 -16 V .24 g 4472 4260 M -6 -4 V .24 g 4466 4256 M -22 -14 V .24 g 4444 4242 M -8 -6 V .24 g 4436 4236 M -19 -13 V .24 g 4417 4223 M -11 -7 V .24 g 4406 4216 M -16 -11 V .24 g 4390 4205 M -13 -9 V .24 g 4377 4196 M -14 -10 V .24 g 4363 4186 M -15 -10 V .24 g 4348 4176 M -13 -9 V .24 g 4335 4167 M -16 -12 V .24 g 4319 4155 M -11 -7 V .24 g 4308 4148 M -17 -13 V .24 g 4291 4135 M -10 -7 V .24 g 4281 4128 M -19 -13 V .24 g 4262 4115 M -8 -6 V .24 g 4254 4109 M -20 -14 V .24 g 4234 4095 M -8 -5 V .24 g 4226 4090 M -21 -15 V .24 g 4205 4075 M -6 -5 V .24 g 4199 4070 M -22 -15 V .24 g 4177 4055 M -5 -4 V .24 g 4172 4051 M -25 -16 V .24 g 4147 4035 M -2 -3 V .24 g 4145 4032 M -27 -18 V .24 g 4118 4014 M -1 0 V .24 g 4117 4014 M -27 -18 V .24 g 4090 3996 M -3 -2 V .24 g 4087 3994 M -24 -16 V .24 g 4063 3978 M -7 -4 V stroke 4056 3974 M .24 g 4056 3974 M -20 -12 V .24 g 4036 3962 M -14 -8 V .24 g 4022 3954 M -14 -9 V .24 g 4008 3945 M -21 -11 V .24 g 3987 3934 M -6 -4 V .24 g 3981 3930 M -27 -14 V .24 g 3954 3916 M -4 -2 V .24 g 3950 3914 M -23 -12 V .24 g 3927 3902 M -20 -9 V .24 g 3907 3893 M -8 -3 V .24 g 3899 3890 M -27 -11 V .24 g 3872 3879 M -14 -6 V .24 g 3858 3873 M -13 -4 V .24 g 3845 3869 M -27 -9 V .24 g 3818 3860 M -25 -7 V .24 g 3793 3853 M -3 -1 V .24 g 3790 3852 M -27 -6 V .24 g 3763 3846 M -27 -4 V .24 g 3736 3842 M -27 -3 V .24 g 3709 3839 M -28 -2 V .24 g 3681 3837 M -27 0 V .24 g 3654 3837 M -27 1 V .24 g 3627 3838 M -27 3 V .24 g 3600 3841 M -28 4 V .24 g 3572 3845 M -27 6 V .24 g 3545 3851 M -8 2 V .24 g 3537 3853 M -19 5 V .24 g 3518 3858 M -27 8 V 0 g .24 g 6052 1669 M .24 g 6052 1669 M -9 -13 V .24 g 6043 1656 M -14 -20 V .24 g 6029 1636 M -4 -7 V .24 g 6025 1629 M -10 -13 V .24 g 6015 1616 M -14 -20 V .24 g 6001 1596 M -3 -5 V .24 g 5998 1591 M -12 -15 V .24 g 5986 1576 M -14 -21 V .24 g 5972 1555 M -2 -2 V .24 g 5970 1553 M -13 -18 V .24 g 5957 1535 M -14 -18 V .24 g 5943 1517 M -2 -2 V .24 g 5941 1515 M -15 -20 V .24 g 5926 1495 M -10 -13 V .24 g 5916 1482 M -6 -7 V .24 g 5910 1475 M -16 -20 V .24 g 5894 1455 M -5 -8 V .24 g 5889 1447 M -11 -12 V .24 g 5878 1435 M -16 -21 V .24 g 5862 1414 M -1 0 V .24 g 5861 1414 M -16 -20 V .24 g 5845 1394 M -11 -13 V .24 g 5834 1381 M -5 -7 V .24 g 5829 1374 M -17 -20 V stroke 5812 1354 M .24 g 5812 1354 M -5 -6 V .24 g 5807 1348 M -13 -14 V .24 g 5794 1334 M -14 -18 V .24 g 5780 1316 M -3 -2 V .24 g 5777 1314 M -17 -21 V .24 g 5760 1293 M -8 -8 V .24 g 5752 1285 M -10 -12 V .24 g 5742 1273 M -17 -19 V .24 g 5725 1254 M -1 -1 V .24 g 5724 1253 M -17 -20 V .24 g 5707 1233 M -9 -10 V .24 g 5698 1223 M -9 -10 V .24 g 5689 1213 M -18 -20 V .24 g 5671 1193 M 0 -1 V .24 g 5671 1192 M -18 -20 V .24 g 5653 1172 M -10 -10 V .24 g 5643 1162 M -8 -10 V .24 g 5635 1152 M -18 -20 V .24 g 5617 1132 M -1 -1 V .24 g 5616 1131 M -17 -19 V .24 g 5599 1112 M -10 -12 V .24 g 5589 1100 M -8 -8 V .24 g 5581 1092 M -17 -20 V .24 g 5564 1072 M -2 -3 V .24 g 5562 1069 M -16 -17 V .24 g 5546 1052 M -12 -14 V .24 g 5534 1038 M -6 -7 V .24 g 5528 1031 M -17 -20 V .24 g 5511 1011 M -4 -4 V .24 g 5507 1007 M -14 -16 V .24 g 5493 991 M -13 -16 V .24 g 5480 975 M -4 -4 V .24 g 5476 971 M -17 -20 V .24 g 5459 951 M -6 -8 V .24 g 5453 943 M -11 -12 V .24 g 5442 931 M -17 -21 V .24 g .24 g 5425 910 M -16 -20 V .24 g 5409 890 M -11 -13 V .24 g 5398 877 M -6 -7 V .24 g 5392 870 M -16 -20 V .24 g 5376 850 M -5 -6 V .24 g 5371 844 M -12 -14 V .24 g 5359 830 M -15 -20 V .24 g 5344 810 M -1 0 V .24 g 5343 810 M -16 -20 V .24 g 5327 790 M -11 -14 V .24 g 5316 776 M -5 -7 V .24 g 5311 769 M -16 -20 V .24 g 5295 749 M -6 -8 V .24 g 5289 741 M -9 -12 V .24 g 5280 729 M -16 -20 V .24 g 5264 709 M -2 -3 V stroke 5262 706 M .24 g 5262 706 M -14 -17 V .24 g 5248 689 M -13 -18 V .24 g 5235 671 M -2 -2 V .24 g 5233 669 M -15 -21 V .24 g 5218 648 M -11 -13 V .24 g 5207 635 M -5 -7 V .24 g 5202 628 M -15 -20 V .24 g 5187 608 M -7 -9 V .24 g 5180 599 M -8 -11 V 0 g .22 g 1192 1817 M .22 g 1192 1817 M -12 21 V .22 g 1180 1838 M -6 9 V .22 g 1174 1847 M -6 11 V .22 g 1168 1858 M -12 20 V .22 g 1156 1878 M -9 15 V .22 g 1147 1893 M -3 5 V .22 g 1144 1898 M -12 20 V .22 g 1132 1918 M -11 20 V .22 g 1121 1938 M -1 2 V .22 g 1120 1940 M -11 19 V .22 g 1109 1959 M -11 20 V .22 g 1098 1979 M -5 9 V .22 g 1093 1988 M -6 11 V .22 g 1087 1999 M -11 20 V .22 g 1076 2019 M -11 19 V .22 g 1065 2038 M 0 1 V .22 g 1065 2039 M -11 20 V .22 g 1054 2059 M -11 20 V .22 g 1043 2079 M -5 11 V .22 g 1038 2090 M -5 10 V .22 g 1033 2100 M -10 20 V .22 g 1023 2120 M -11 20 V .22 g 1012 2140 M -1 3 V .22 g 1011 2143 M -9 17 V .22 g 1002 2160 M -10 20 V .22 g 992 2180 M -8 17 V .22 g 984 2197 M -2 3 V .22 g 982 2200 M -10 21 V .22 g 972 2221 M -10 20 V .22 g 962 2241 M -6 11 V .22 g 956 2252 M -4 9 V .22 g 952 2261 M -9 20 V .22 g 943 2281 M -10 20 V .22 g 933 2301 M -4 8 V .22 g 929 2309 M -6 12 V .22 g 923 2321 M -9 20 V .22 g 914 2341 M -9 21 V .22 g 905 2362 M -3 6 V .22 g 902 2368 M -7 14 V .22 g 895 2382 M -9 20 V .22 g 886 2402 M -9 20 V .22 g 877 2422 M -2 5 V .22 g 875 2427 M -7 15 V stroke 868 2442 M .22 g 868 2442 M -9 20 V .22 g 859 2462 M -9 21 V .22 g 850 2483 M -3 5 V .22 g 847 2488 M -6 15 V .22 g 841 2503 M -9 20 V .22 g 832 2523 M -9 20 V .22 g 823 2543 M -3 6 V .22 g 820 2549 M -6 14 V .22 g 814 2563 M -9 20 V .22 g 805 2583 M -9 21 V .22 g 796 2604 M -3 8 V .22 g 793 2612 M -5 12 V .22 g 788 2624 M -9 20 V .22 g 779 2644 M -9 20 V .22 g 770 2664 M -5 12 V .22 g 765 2676 M -3 8 V .22 g 762 2684 M -9 20 V .22 g 753 2704 M -8 20 V .22 g 745 2724 M -7 16 V .22 g 738 2740 M -2 5 V .22 g 736 2745 M -8 20 V .22 g 728 2765 M -8 20 V .22 g 720 2785 M -9 20 V .22 g .22 g 711 2805 M -8 20 V .22 g 703 2825 M -9 20 V .22 g 694 2845 M -8 21 V .22 g 686 2866 M -2 5 V .22 g 684 2871 M -6 15 V .22 g 678 2886 M -8 20 V .22 g 670 2906 M -9 20 V .22 g 661 2926 M -4 12 V .22 g 657 2938 M -4 8 V .22 g 653 2946 M -8 20 V .22 g 645 2966 M -8 20 V .22 g 637 2986 M -8 19 V .22 g 629 3005 M -1 2 V .22 g 628 3007 M -8 20 V .22 g 620 3027 M -8 20 V .22 g 612 3047 M -8 20 V .22 g 604 3067 M -2 5 V 0 g .22 g 2206 588 M .22 g 2206 588 M -16 20 V .22 g 2190 608 M -7 10 V .22 g 2183 618 M -8 10 V .22 g 2175 628 M -16 20 V .22 g 2159 648 M -4 5 V .22 g 2155 653 M -12 16 V .22 g 2143 669 M -15 19 V .22 g 2128 688 M -1 1 V .22 g 2127 689 M -16 20 V .22 g 2111 709 M -10 13 V .22 g 2101 722 M -6 7 V .22 g 2095 729 M -16 20 V stroke 2079 749 M .22 g 2079 749 M -5 8 V .22 g 2074 757 M -11 12 V .22 g 2063 769 M -16 21 V .22 g 2047 790 M -1 0 V .22 g 2046 790 M -16 20 V .22 g 2030 810 M -11 14 V .22 g 2019 824 M -5 6 V .22 g 2014 830 M -17 20 V .22 g 1997 850 M -5 6 V .22 g 1992 856 M -12 14 V .22 g 1980 870 M -15 19 V .22 g 1965 889 M -2 1 V .22 g 1963 890 M -17 20 V .22 g 1946 910 M -9 11 V .22 g 1937 921 M -8 10 V .22 g 1929 931 M -18 20 V .22 g 1911 951 M -1 1 V .22 g 1910 952 M -17 19 V .22 g 1893 971 M -10 12 V .22 g 1883 983 M -8 8 V .22 g 1875 991 M -18 20 V .22 g 1857 1011 M -1 2 V .22 g 1856 1013 M -17 18 V .22 g 1839 1031 M -11 12 V .22 g 1828 1043 M -7 9 V .22 g 1821 1052 M -19 20 V .22 g 1802 1072 M -1 1 V .22 g 1801 1073 M -18 19 V .22 g 1783 1092 M -9 10 V .22 g 1774 1102 M -9 10 V .22 g 1765 1112 M -18 19 V .22 g 1747 1131 M -1 1 V .22 g 1746 1132 M -19 20 V .22 g 1727 1152 M -8 8 V .22 g 1719 1160 M -11 12 V .22 g 1708 1172 M -16 17 V .22 g 1692 1189 M -3 4 V .22 g 1689 1193 M -19 20 V .22 g 1670 1213 M -5 5 V .22 g 1665 1218 M -14 15 V .22 g 1651 1233 M -13 14 V .22 g 1638 1247 M -6 6 V .22 g 1632 1253 M -19 20 V .22 g 1613 1273 M -3 4 V .22 g 1610 1277 M -15 16 V .22 g 1595 1293 M -12 13 V .22 g 1583 1306 M -7 8 V .22 g 1576 1314 M -18 20 V .22 g 1558 1334 M -2 2 V .22 g 1556 1336 M -16 18 V .22 g 1540 1354 M -11 13 V .22 g 1529 1367 M -7 7 V stroke 1522 1374 M .22 g 1522 1374 M -18 20 V .22 g 1504 1394 M -3 4 V .22 g 1501 1398 M -14 16 V .22 g 1487 1414 M -13 15 V .22 g 1474 1429 M -4 6 V .22 g 1470 1435 M -17 20 V .22 g 1453 1455 M -6 7 V .22 g 1447 1462 M -11 13 V .22 g 1436 1475 M -16 20 V .22 g .22 g 1420 1495 M -16 20 V .22 g 1404 1515 M -12 15 V .22 g 1392 1530 M -4 5 V .22 g 1388 1535 M -15 20 V .22 g 1373 1555 M -8 10 V .22 g 1365 1565 M -8 11 V .22 g 1357 1576 M -15 20 V .22 g 1342 1596 M -4 6 V .22 g 1338 1602 M -11 14 V .22 g 1327 1616 M -14 20 V .22 g 1313 1636 M -2 3 V .22 g 1311 1639 M -12 17 V .22 g 1299 1656 M -14 20 V .22 g 1285 1676 M -2 2 V .22 g 1283 1678 M -12 19 V .22 g 1271 1697 M -14 20 V .22 g 1257 1717 M -1 1 V .22 g 1256 1718 M -12 19 V .22 g 1244 1737 M -13 20 V .22 g 1231 1757 M -2 3 V .22 g 1229 1760 M -11 17 V .22 g 1218 1777 M -13 20 V .22 g 1205 1797 M -3 6 V .22 g 1202 1803 M -10 14 V 0 g .22 g 2149 4538 M .22 g 2149 4538 M -21 18 V .22 g 2128 4556 M -3 3 V .22 g 2125 4559 M -23 20 V .22 g 2102 4579 M -1 1 V .22 g 2101 4580 M -21 19 V .22 g 2080 4599 M -6 6 V .22 g 2074 4605 M -15 14 V 0 g .22 g 3736 3739 M .22 g 3736 3739 M -27 -3 V .22 g 3709 3736 M -28 -2 V .22 g 3681 3734 M -27 0 V .22 g 3654 3734 M -27 1 V .22 g 3627 3735 M -27 3 V .22 g 3600 3738 M -28 4 V .22 g 3572 3742 M -27 6 V .22 g 3545 3748 M -15 4 V .22 g 3530 3752 M -12 4 V .22 g 3518 3756 M -27 8 V .22 g 3491 3764 M -23 8 V stroke 3468 3772 M .22 g 3468 3772 M -5 2 V .22 g 3463 3774 M -27 11 V .22 g 3436 3785 M -17 8 V .22 g 3419 3793 M -10 4 V .22 g 3409 3797 M -27 14 V .22 g 3382 3811 M -5 2 V .22 g 3377 3813 M -23 12 V .22 g 3354 3825 M -14 8 V .22 g 3340 3833 M -13 7 V .22 g 3327 3840 M -23 13 V .22 g 3304 3853 M -4 3 V .22 g 3300 3856 M -27 16 V .22 g 3273 3872 M -2 1 V .22 g 3271 3873 M -26 16 V .22 g 3245 3889 M -6 4 V .22 g 3239 3893 M -21 14 V .22 g 3218 3907 M -10 7 V .22 g 3208 3914 M -17 11 V .22 g 3191 3925 M -14 9 V .22 g 3177 3934 M -13 9 V .22 g 3164 3943 M -17 11 V .22 g 3147 3954 M -11 7 V .22 g 3136 3961 M -19 13 V .22 g 3117 3974 M -8 5 V .22 g 3109 3979 M -22 15 V .22 g 3087 3994 M -5 4 V .22 g 3082 3998 M -25 16 V .22 g 3057 4014 M -2 2 V .22 g 3055 4016 M -28 19 V .22 g .22 g 3027 4035 M -27 18 V .22 g 3000 4053 M -3 2 V .22 g 2997 4055 M -24 16 V .22 g 2973 4071 M -7 4 V .22 g 2966 4075 M -20 13 V .22 g 2946 4088 M -11 7 V .22 g 2935 4095 M -17 10 V .22 g 2918 4105 M -15 10 V .22 g 2903 4115 M -12 7 V .22 g 2891 4122 M -21 13 V .22 g 2870 4135 M -6 4 V .22 g 2864 4139 M -27 16 V .22 g 2837 4155 M -1 0 V .22 g 2836 4155 M -27 16 V .22 g 2809 4171 M -8 5 V .22 g 2801 4176 M -19 10 V .22 g 2782 4186 M -17 10 V .22 g 2765 4196 M -10 5 V .22 g 2755 4201 M -27 15 V .22 g 2728 4216 M -1 0 V .22 g 2727 4216 M -27 14 V .22 g 2700 4230 M -12 6 V .22 g 2688 4236 M -15 8 V stroke 2673 4244 M .22 g 2673 4244 M -25 12 V .22 g 2648 4256 M -2 1 V .22 g 2646 4257 M -27 14 V .22 g 2619 4271 M -12 5 V .22 g 2607 4276 M -16 8 V .22 g 2591 4284 M -26 13 V .22 g 2565 4297 M -1 0 V .22 g 2564 4297 M -27 13 V .22 g 2537 4310 M -14 7 V .22 g 2523 4317 M -13 6 V .22 g 2510 4323 M -28 13 V .22 g 2482 4336 M -1 1 V .22 g 2481 4337 M -26 12 V .22 g 2455 4349 M -15 8 V .22 g 2440 4357 M -12 6 V .22 g 2428 4363 M -27 14 V .22 g 2401 4377 M -1 0 V .22 g 2400 4377 M -27 14 V .22 g 2373 4391 M -11 6 V .22 g 2362 4397 M -16 9 V .22 g 2346 4406 M -20 11 V .22 g 2326 4417 M -7 4 V .22 g 2319 4421 M -27 17 V .22 g .22 g 2292 4438 M -28 17 V .22 g 2264 4455 M -4 3 V .22 g 2260 4458 M -23 15 V .22 g 2237 4473 M -7 5 V .22 g 2230 4478 M -20 14 V .22 g 2210 4492 M -9 6 V .22 g 2201 4498 M -18 14 V .22 g 2183 4512 M -8 6 V .22 g 2175 4518 M -20 15 V .22 g 2155 4533 M -6 5 V 0 g .22 g 5214 4619 M .22 g 5214 4619 M -7 -6 V .22 g 5207 4613 M -16 -14 V .22 g 5191 4599 M -11 -9 V .22 g 5180 4590 M -14 -11 V .22 g 5166 4579 M -13 -11 V .22 g 5153 4568 M -13 -9 V .22 g 5140 4559 M -14 -12 V .22 g 5126 4547 M -13 -9 V .22 g 5113 4538 M -15 -10 V .22 g 5098 4528 M -14 -10 V .22 g 5084 4518 M -13 -9 V .22 g 5071 4509 M -17 -11 V .22 g 5054 4498 M -10 -7 V .22 g 5044 4491 M -22 -13 V .22 g 5022 4478 M -5 -4 V .22 g 5017 4474 M -28 -16 V .22 g .22 g 4989 4458 M -27 -16 V .22 g 4962 4442 M -8 -4 V .22 g 4954 4438 M -19 -11 V stroke 4935 4427 M .22 g 4935 4427 M -17 -10 V .22 g 4918 4417 M -10 -5 V .22 g 4908 4412 M -28 -15 V .22 g .22 g 4880 4397 M -27 -14 V .22 g 4853 4383 M -11 -6 V .22 g 4842 4377 M -16 -9 V .22 g 4826 4368 M -22 -11 V .22 g 4804 4357 M -5 -3 V .22 g 4799 4354 M -28 -14 V .22 g 4771 4340 M -6 -3 V .22 g 4765 4337 M -21 -12 V .22 g 4744 4325 M -16 -8 V .22 g 4728 4317 M -11 -6 V .22 g 4717 4311 M -27 -14 V .22 g 4690 4297 M 0 -1 V .22 g 4690 4296 M -28 -15 V .22 g 4662 4281 M -8 -5 V .22 g 4654 4276 M -19 -10 V .22 g 4635 4266 M -16 -10 V .22 g 4619 4256 M -11 -6 V .22 g 4608 4250 M -24 -14 V .22 g 4584 4236 M -3 -2 V .22 g 4581 4234 M -28 -17 V .22 g 4553 4217 M -2 -1 V .22 g 4551 4216 M -25 -16 V .22 g 4526 4200 M -7 -4 V .22 g 4519 4196 M -20 -13 V .22 g 4499 4183 M -12 -7 V .22 g 4487 4176 M -15 -11 V .22 g 4472 4165 M -16 -10 V .22 g 4456 4155 M -12 -8 V .22 g 4444 4147 M -18 -12 V .22 g 4426 4135 M -9 -6 V .22 g 4417 4129 M -20 -14 V .22 g 4397 4115 M -7 -5 V .22 g 4390 4110 M -22 -15 V .22 g 4368 4095 M -5 -4 V .22 g 4363 4091 M -23 -16 V .22 g 4340 4075 M -5 -3 V .22 g 4335 4072 M -24 -17 V .22 g 4311 4055 M -3 -3 V .22 g 4308 4052 M -25 -17 V .22 g 4283 4035 M -2 -2 V .22 g 4281 4033 M -25 -19 V .22 g 4256 4014 M -2 -1 V .22 g 4254 4013 M -26 -19 V .22 g 4228 3994 M -2 -1 V .22 g 4226 3993 M -26 -19 V .22 g 4200 3974 M -1 -1 V .22 g 4199 3973 M -27 -19 V .22 g .22 g 4172 3954 M -27 -19 V .22 g 4145 3935 M -2 -1 V stroke 4143 3934 M .22 g 4143 3934 M -26 -18 V .22 g 4117 3916 M -3 -2 V .22 g 4114 3914 M -24 -17 V .22 g 4090 3897 M -6 -4 V .22 g 4084 3893 M -21 -14 V .22 g 4063 3879 M -10 -6 V .22 g 4053 3873 M -17 -11 V .22 g 4036 3862 M -15 -9 V .22 g 4021 3853 M -13 -8 V .22 g 4008 3845 M -21 -12 V .22 g 3987 3833 M -6 -3 V .22 g 3981 3830 M -27 -15 V .22 g 3954 3815 M -4 -2 V .22 g 3950 3813 M -23 -12 V .22 g 3927 3801 M -18 -8 V .22 g 3909 3793 M -10 -5 V .22 g 3899 3788 M -27 -11 V .22 g 3872 3777 M -11 -5 V .22 g 3861 3772 M -16 -6 V .22 g 3845 3766 M -27 -9 V .22 g 3818 3757 M -18 -5 V .22 g 3800 3752 M -10 -2 V .22 g 3790 3750 M -27 -7 V .22 g 3763 3743 M -27 -4 V 0 g .22 g 6052 1764 M .22 g 6052 1764 M -5 -7 V .22 g 6047 1757 M -14 -20 V .22 g 6033 1737 M -8 -12 V .22 g 6025 1725 M -6 -8 V .22 g 6019 1717 M -14 -20 V .22 g 6005 1697 M -7 -10 V .22 g 5998 1687 M -8 -11 V .22 g 5990 1676 M -15 -20 V .22 g 5975 1656 M -5 -6 V .22 g 5970 1650 M -10 -14 V .22 g 5960 1636 M -15 -20 V .22 g 5945 1616 M -2 -2 V .22 g 5943 1614 M -14 -18 V .22 g 5929 1596 M -13 -17 V .22 g 5916 1579 M -3 -3 V .22 g 5913 1576 M -16 -21 V .22 g 5897 1555 M -8 -11 V .22 g 5889 1544 M -8 -9 V .22 g 5881 1535 M -17 -20 V .22 g 5864 1515 M -3 -4 V .22 g 5861 1511 M -13 -16 V .22 g 5848 1495 M -14 -16 V .22 g 5834 1479 M -3 -4 V .22 g 5831 1475 M -17 -20 V .22 g 5814 1455 M -7 -8 V .22 g 5807 1447 M -11 -12 V .22 g 5796 1435 M -16 -20 V .22 g 5780 1415 M -1 -1 V stroke 5779 1414 M .22 g 5779 1414 M -18 -20 V .22 g 5761 1394 M -9 -10 V .22 g 5752 1384 M -9 -10 V .22 g 5743 1374 M -18 -20 V .22 g .22 g 5725 1354 M -18 -20 V .22 g 5707 1334 M -9 -11 V .22 g 5698 1323 M -9 -9 V .22 g 5689 1314 M -18 -21 V .22 g .22 g 5671 1293 M -18 -20 V .22 g 5653 1273 M -10 -10 V .22 g 5643 1263 M -8 -10 V .22 g 5635 1253 M -19 -20 V .22 g .22 g 5616 1233 M -18 -20 V .22 g 5598 1213 M -9 -11 V .22 g 5589 1202 M -9 -9 V .22 g 5580 1193 M -18 -21 V .22 g .22 g 5562 1172 M -18 -20 V .22 g 5544 1152 M -10 -11 V .22 g 5534 1141 M -7 -9 V .22 g 5527 1132 M -18 -20 V .22 g 5509 1112 M -2 -2 V .22 g 5507 1110 M -15 -18 V .22 g 5492 1092 M -12 -14 V .22 g 5480 1078 M -6 -6 V .22 g 5474 1072 M -17 -20 V .22 g 5457 1052 M -4 -6 V .22 g 5453 1046 M -13 -15 V .22 g 5440 1031 M -15 -17 V .22 g 5425 1014 M -2 -3 V .22 g 5423 1011 M -16 -20 V .22 g 5407 991 M -9 -10 V .22 g 5398 981 M -8 -10 V .22 g 5390 971 M -16 -20 V .22 g 5374 951 M -3 -4 V .22 g 5371 947 M -14 -16 V .22 g 5357 931 M -13 -18 V .22 g 5344 913 M -3 -3 V .22 g 5341 910 M -16 -20 V .22 g 5325 890 M -9 -11 V .22 g 5316 879 M -7 -9 V .22 g 5309 870 M -15 -20 V .22 g 5294 850 M -5 -6 V .22 g 5289 844 M -11 -14 V .22 g 5278 830 M -15 -20 V .22 g 5263 810 M -1 -1 V .22 g 5262 809 M -15 -19 V .22 g 5247 790 M -12 -17 V .22 g 5235 773 M -3 -4 V .22 g 5232 769 M -16 -20 V .22 g 5216 749 M -9 -12 V .22 g 5207 737 M -6 -8 V .22 g 5201 729 M -15 -20 V stroke 5186 709 M .22 g 5186 709 M -6 -8 V .22 g 5180 701 M -9 -12 V .22 g 5171 689 M -15 -20 V .22 g 5156 669 M -3 -5 V .22 g 5153 664 M -12 -16 V .22 g 5141 648 M -15 -20 V .22 g .22 g 5126 628 M -15 -20 V .22 g 5111 608 M -13 -17 V .22 g 5098 591 M -2 -3 V 0 g .2 g 1256 1817 M .2 g 1256 1817 M 0 1 V .2 g 1256 1818 M -13 20 V .2 g 1243 1838 M -14 20 V .2 g 1229 1858 M 0 1 V .2 g 1229 1859 M -12 19 V .2 g 1217 1878 M -13 20 V .2 g 1204 1898 M -2 3 V .2 g 1202 1901 M -11 17 V .2 g 1191 1918 M -12 20 V .2 g 1179 1938 M -5 8 V .2 g 1174 1946 M -7 13 V .2 g 1167 1959 M -12 20 V .2 g 1155 1979 M -8 12 V .2 g 1147 1991 M -4 8 V .2 g 1143 1999 M -12 20 V .2 g 1131 2019 M -11 19 V .2 g 1120 2038 M -1 1 V .2 g 1119 2039 M -11 20 V .2 g 1108 2059 M -11 20 V .2 g 1097 2079 M -4 8 V .2 g 1093 2087 M -7 13 V .2 g 1086 2100 M -11 20 V .2 g 1075 2120 M -10 17 V .2 g 1065 2137 M -1 3 V .2 g 1064 2140 M -11 20 V .2 g 1053 2160 M -11 20 V .2 g 1042 2180 M -4 8 V .2 g 1038 2188 M -6 12 V .2 g 1032 2200 M -10 21 V .2 g 1022 2221 M -11 20 V .2 g .2 g 1011 2241 M -10 20 V .2 g 1001 2261 M -10 20 V .2 g 991 2281 M -7 15 V .2 g 984 2296 M -3 5 V .2 g 981 2301 M -10 20 V .2 g 971 2321 M -10 20 V .2 g 961 2341 M -5 11 V .2 g 956 2352 M -4 10 V .2 g 952 2362 M -10 20 V .2 g 942 2382 M -10 20 V .2 g 932 2402 M -3 7 V .2 g 929 2409 M -6 13 V .2 g 923 2422 M -9 20 V stroke 914 2442 M .2 g 914 2442 M -10 20 V .2 g 904 2462 M -2 5 V .2 g 902 2467 M -7 16 V .2 g 895 2483 M -9 20 V .2 g 886 2503 M -10 20 V .2 g 876 2523 M -1 4 V .2 g 875 2527 M -8 16 V .2 g 867 2543 M -9 20 V .2 g 858 2563 M -9 20 V .2 g 849 2583 M -2 5 V .2 g 847 2588 M -6 16 V .2 g 841 2604 M -9 20 V .2 g 832 2624 M -9 20 V .2 g 823 2644 M -3 6 V .2 g 820 2650 M -6 14 V .2 g 814 2664 M -9 20 V .2 g 805 2684 M -8 20 V .2 g 797 2704 M -4 9 V .2 g 793 2713 M -5 11 V .2 g 788 2724 M -8 21 V .2 g 780 2745 M -9 20 V .2 g 771 2765 M -6 12 V .2 g 765 2777 M -3 8 V .2 g 762 2785 M -8 20 V .2 g 754 2805 M -8 20 V .2 g 746 2825 M -8 17 V .2 g 738 2842 M -1 3 V .2 g 737 2845 M -8 21 V .2 g 729 2866 M -9 20 V .2 g 720 2886 M -8 20 V .2 g 712 2906 M -1 2 V .2 g 711 2908 M -7 18 V .2 g 704 2926 M -9 20 V .2 g 695 2946 M -8 20 V .2 g 687 2966 M -3 9 V .2 g 684 2975 M -5 11 V .2 g 679 2986 M -8 21 V .2 g 671 3007 M -8 20 V .2 g 663 3027 M -6 15 V .2 g 657 3042 M -3 5 V .2 g 654 3047 M -8 20 V .2 g 646 3067 M -8 20 V .2 g 638 3087 M -8 20 V .2 g 630 3107 M -1 2 V .2 g 629 3109 M -7 19 V .2 g 622 3128 M -8 20 V .2 g 614 3148 M -8 20 V .2 g 606 3168 M -4 9 V 0 g .2 g 2288 588 M .2 g 2288 588 M -16 20 V .2 g 2272 608 M -8 10 V .2 g 2264 618 M -7 10 V .2 g 2257 628 M -16 20 V stroke 2241 648 M .2 g 2241 648 M -4 6 V .2 g 2237 654 M -11 15 V .2 g 2226 669 M -15 20 V .2 g 2211 689 M -1 1 V .2 g 2210 690 M -15 19 V .2 g 2195 709 M -12 16 V .2 g 2183 725 M -3 4 V .2 g 2180 729 M -16 20 V .2 g 2164 749 M -9 12 V .2 g 2155 761 M -6 8 V .2 g 2149 769 M -16 21 V .2 g 2133 790 M -5 6 V .2 g 2128 796 M -11 14 V .2 g 2117 810 M -15 20 V .2 g 2102 830 M -1 1 V .2 g 2101 831 M -15 19 V .2 g 2086 850 M -12 15 V .2 g 2074 865 M -4 5 V .2 g 2070 870 M -17 20 V .2 g 2053 890 M -7 9 V .2 g 2046 899 M -9 11 V .2 g 2037 910 M -16 21 V .2 g 2021 931 M -2 2 V .2 g 2019 933 M -15 18 V .2 g 2004 951 M -12 15 V .2 g 1992 966 M -5 5 V .2 g 1987 971 M -17 20 V .2 g 1970 991 M -5 7 V .2 g 1965 998 M -12 13 V .2 g 1953 1011 M -16 19 V .2 g 1937 1030 M -1 1 V .2 g 1936 1031 M -18 21 V .2 g 1918 1052 M -8 9 V .2 g 1910 1061 M -10 11 V .2 g 1900 1072 M -17 20 V .2 g .2 g 1883 1092 M -19 20 V .2 g 1864 1112 M -8 10 V .2 g 1856 1122 M -10 10 V .2 g 1846 1132 M -18 20 V .2 g .2 g 1828 1152 M -19 20 V .2 g 1809 1172 M -8 9 V .2 g 1801 1181 M -11 12 V .2 g 1790 1193 M -16 17 V .2 g 1774 1210 M -3 3 V .2 g 1771 1213 M -19 20 V .2 g 1752 1233 M -5 6 V .2 g 1747 1239 M -14 14 V .2 g 1733 1253 M -14 14 V .2 g 1719 1267 M -5 6 V .2 g 1714 1273 M -20 20 V .2 g 1694 1293 M -2 3 V .2 g 1692 1296 M -17 18 V stroke 1675 1314 M .2 g 1675 1314 M -10 10 V .2 g 1665 1324 M -9 10 V .2 g 1656 1334 M -18 19 V .2 g 1638 1353 M -2 1 V .2 g 1636 1354 M -19 20 V .2 g 1617 1374 M -7 7 V .2 g 1610 1381 M -12 13 V .2 g 1598 1394 M -15 17 V .2 g 1583 1411 M -4 3 V .2 g 1579 1414 M -18 21 V .2 g 1561 1435 M -5 5 V .2 g 1556 1440 M -14 15 V .2 g 1542 1455 M -13 15 V .2 g 1529 1470 M -5 5 V .2 g 1524 1475 M -18 20 V .2 g 1506 1495 M -5 5 V .2 g 1501 1500 M -12 15 V .2 g 1489 1515 M -15 17 V .2 g 1474 1532 M -3 3 V .2 g 1471 1535 M -17 20 V .2 g 1454 1555 M -7 9 V .2 g 1447 1564 M -10 12 V .2 g 1437 1576 M -17 20 V .2 g 1420 1596 M 0 1 V .2 g 1420 1597 M -16 19 V .2 g 1404 1616 M -12 15 V .2 g 1392 1631 M -4 5 V .2 g 1388 1636 M -16 20 V .2 g 1372 1656 M -7 10 V .2 g 1365 1666 M -8 10 V .2 g 1357 1676 M -15 21 V .2 g 1342 1697 M -4 5 V .2 g 1338 1702 M -11 15 V .2 g 1327 1717 M -15 20 V .2 g 1312 1737 M -1 2 V .2 g 1311 1739 M -13 18 V .2 g 1298 1757 M -14 20 V .2 g 1284 1777 M -1 1 V .2 g 1283 1778 M -13 19 V .2 g 1270 1797 M -14 20 V 0 g .2 g 2292 4332 M .2 g 2292 4332 M -8 5 V .2 g 2284 4337 M -20 12 V .2 g 2264 4349 M -12 8 V .2 g 2252 4357 M -15 9 V .2 g 2237 4366 M -16 11 V .2 g 2221 4377 M -11 8 V .2 g 2210 4385 M -17 12 V .2 g 2193 4397 M -10 8 V .2 g 2183 4405 M -17 12 V .2 g 2166 4417 M -11 9 V .2 g 2155 4426 M -14 12 V .2 g 2141 4438 M -13 10 V stroke 2128 4448 M .2 g 2128 4448 M -11 10 V .2 g 2117 4458 M -16 14 V .2 g 2101 4472 M -7 6 V .2 g 2094 4478 M -20 19 V .2 g 2074 4497 M -2 1 V .2 g 2072 4498 M -21 20 V .2 g 2051 4518 M -5 5 V .2 g 2046 4523 M -15 15 V .2 g 2031 4538 M -12 13 V .2 g 2019 4551 M -7 8 V .2 g 2012 4559 M -18 20 V .2 g 1994 4579 M -2 2 V .2 g 1992 4581 M -16 18 V .2 g 1976 4599 M -11 13 V .2 g 1965 4612 M -6 7 V 0 g .2 g 3922 3692 M .2 g 3922 3692 M -23 -11 V .2 g 3899 3681 M -21 -9 V .2 g 3878 3672 M -6 -3 V .2 g 3872 3669 M -27 -11 V .2 g 3845 3658 M -20 -6 V .2 g 3825 3652 M -7 -3 V .2 g 3818 3649 M -28 -8 V .2 g 3790 3641 M -27 -6 V .2 g 3763 3635 M -18 -4 V .2 g 3745 3631 M -9 -1 V .2 g 3736 3630 M -27 -4 V .2 g 3709 3626 M -28 -1 V .2 g 3681 3625 M -27 0 V .2 g 3654 3625 M -27 1 V .2 g 3627 3626 M -27 3 V .2 g 3600 3629 M -13 2 V .2 g 3587 3631 M -15 3 V .2 g 3572 3634 M -27 6 V .2 g 3545 3640 M -27 7 V .2 g 3518 3647 M -13 5 V .2 g 3505 3652 M -14 4 V .2 g 3491 3656 M -28 11 V .2 g 3463 3667 M -11 5 V .2 g 3452 3672 M -16 6 V .2 g 3436 3678 M -27 13 V .2 g 3409 3691 M -2 1 V .2 g 3407 3692 M -25 13 V .2 g 3382 3705 M -14 7 V .2 g 3368 3712 M -14 7 V .2 g 3354 3719 M -22 13 V .2 g 3332 3732 M -5 3 V .2 g 3327 3735 M -27 16 V .2 g 3300 3751 M -2 1 V .2 g 3298 3752 M -25 16 V .2 g 3273 3768 M -7 4 V .2 g 3266 3772 M -21 14 V .2 g 3245 3786 M -10 7 V stroke 3235 3793 M .2 g 3235 3793 M -17 11 V .2 g 3218 3804 M -13 9 V .2 g 3205 3813 M -14 9 V .2 g 3191 3822 M -16 11 V .2 g 3175 3833 M -11 8 V .2 g 3164 3841 M -18 12 V .2 g 3146 3853 M -10 7 V .2 g 3136 3860 M -19 13 V .2 g 3117 3873 M -8 6 V .2 g 3109 3879 M -22 14 V .2 g 3087 3893 M -5 4 V .2 g 3082 3897 M -24 17 V .2 g 3058 3914 M -3 2 V .2 g 3055 3916 M -26 18 V .2 g 3029 3934 M -2 1 V .2 g 3027 3935 M -27 18 V .2 g 3000 3953 M -1 1 V .2 g 2999 3954 M -26 17 V .2 g 2973 3971 M -4 3 V .2 g 2969 3974 M -23 15 V .2 g 2946 3989 M -8 5 V .2 g 2938 3994 M -20 13 V .2 g 2918 4007 M -12 7 V .2 g 2906 4014 M -15 10 V .2 g 2891 4024 M -18 11 V .2 g 2873 4035 M -9 5 V .2 g 2864 4040 M -24 15 V .2 g 2840 4055 M -3 1 V .2 g 2837 4056 M -28 16 V .2 g 2809 4072 M -4 3 V .2 g 2805 4075 M -23 13 V .2 g 2782 4088 M -14 7 V .2 g 2768 4095 M -13 7 V .2 g 2755 4102 M -24 13 V .2 g 2731 4115 M -3 2 V .2 g 2728 4117 M -28 14 V .2 g 2700 4131 M -8 4 V .2 g 2692 4135 M -19 10 V .2 g 2673 4145 M -22 10 V .2 g 2651 4155 M -5 3 V .2 g 2646 4158 M -27 13 V .2 g 2619 4171 M -10 5 V .2 g 2609 4176 M -18 8 V .2 g 2591 4184 M -25 12 V .2 g 2566 4196 M -2 1 V .2 g 2564 4197 M -27 12 V .2 g 2537 4209 M -15 7 V .2 g 2522 4216 M -12 6 V .2 g 2510 4222 M -28 12 V .2 g 2482 4234 M -3 2 V .2 g 2479 4236 M -24 11 V .2 g 2455 4247 M -19 9 V stroke 2436 4256 M .2 g 2436 4256 M -8 4 V .2 g 2428 4260 M -27 14 V .2 g 2401 4274 M -6 2 V .2 g 2395 4276 M -22 11 V .2 g 2373 4287 M -17 10 V .2 g 2356 4297 M -10 5 V .2 g 2346 4302 M -27 15 V .2 g .2 g 2319 4317 M -27 15 V 0 g .2 g 5325 4619 M .2 g 5325 4619 M -9 -9 V .2 g 5316 4610 M -10 -11 V .2 g 5306 4599 M -17 -18 V .2 g 5289 4581 M -3 -2 V .2 g 5286 4579 M -20 -20 V .2 g 5266 4559 M -4 -5 V .2 g 5262 4554 M -17 -16 V .2 g 5245 4538 M -10 -9 V .2 g 5235 4529 M -13 -11 V .2 g 5222 4518 M -15 -13 V .2 g 5207 4505 M -8 -7 V .2 g 5199 4498 M -19 -16 V .2 g 5180 4482 M -6 -4 V .2 g 5174 4478 M -21 -17 V .2 g 5153 4461 M -5 -3 V .2 g 5148 4458 M -22 -17 V .2 g 5126 4441 M -5 -3 V .2 g 5121 4438 M -23 -16 V .2 g 5098 4422 M -6 -5 V .2 g 5092 4417 M -21 -14 V .2 g 5071 4403 M -10 -6 V .2 g 5061 4397 M -17 -11 V .2 g 5044 4386 M -15 -9 V .2 g 5029 4377 M -12 -7 V .2 g 5017 4370 M -22 -13 V .2 g 4995 4357 M -6 -3 V .2 g 4989 4354 M -27 -15 V .2 g 4962 4339 M -3 -2 V .2 g 4959 4337 M -24 -13 V .2 g 4935 4324 M -14 -7 V .2 g 4921 4317 M -13 -8 V .2 g 4908 4309 M -25 -12 V .2 g 4883 4297 M -3 -2 V .2 g 4880 4295 M -27 -14 V .2 g 4853 4281 M -10 -5 V .2 g 4843 4276 M -17 -9 V .2 g 4826 4267 M -22 -11 V .2 g 4804 4256 M -5 -2 V .2 g 4799 4254 M -28 -14 V .2 g 4771 4240 M -7 -4 V .2 g 4764 4236 M -20 -10 V .2 g 4744 4226 M -19 -10 V .2 g 4725 4216 M -8 -5 V .2 g 4717 4211 M -27 -14 V stroke 4690 4197 M .2 g 4690 4197 M -2 -1 V .2 g 4688 4196 M -26 -14 V .2 g 4662 4182 M -11 -6 V .2 g 4651 4176 M -16 -9 V .2 g 4635 4167 M -20 -12 V .2 g 4615 4155 M -7 -4 V .2 g 4608 4151 M -27 -16 V .2 g .2 g 4581 4135 M -28 -16 V .2 g 4553 4119 M -6 -4 V .2 g 4547 4115 M -21 -13 V .2 g 4526 4102 M -11 -7 V .2 g 4515 4095 M -16 -11 V .2 g 4499 4084 M -15 -9 V .2 g 4484 4075 M -12 -8 V .2 g 4472 4067 M -19 -12 V .2 g 4453 4055 M -9 -6 V .2 g 4444 4049 M -20 -14 V .2 g 4424 4035 M -7 -5 V .2 g 4417 4030 M -22 -16 V .2 g 4395 4014 M -5 -3 V .2 g 4390 4011 M -24 -17 V .2 g 4366 3994 M -3 -2 V .2 g 4363 3992 M -25 -18 V .2 g 4338 3974 M -3 -2 V .2 g 4335 3972 M -25 -18 V .2 g 4310 3954 M -2 -2 V .2 g 4308 3952 M -25 -18 V .2 g 4283 3934 M -2 -2 V .2 g 4281 3932 M -25 -18 V .2 g 4256 3914 M -2 -2 V .2 g 4254 3912 M -26 -19 V .2 g 4228 3893 M -2 -1 V .2 g 4226 3892 M -25 -19 V .2 g 4201 3873 M -2 -1 V .2 g 4199 3872 M -25 -19 V .2 g 4174 3853 M -2 -1 V .2 g 4172 3852 M -26 -19 V .2 g 4146 3833 M -1 -1 V .2 g 4145 3832 M -28 -19 V .2 g .2 g 4117 3813 M -27 -19 V .2 g 4090 3794 M -1 -1 V .2 g 4089 3793 M -26 -18 V .2 g 4063 3775 M -4 -3 V .2 g 4059 3772 M -23 -15 V .2 g 4036 3757 M -8 -5 V .2 g 4028 3752 M -20 -12 V .2 g 4008 3740 M -13 -8 V .2 g 3995 3732 M -14 -8 V .2 g 3981 3724 M -21 -12 V .2 g 3960 3712 M -6 -3 V .2 g 3954 3709 M -27 -15 V .2 g 3927 3694 M -5 -2 V stroke 3922 3692 M 0 g .2 g 5047 628 M .2 g 5047 628 M -3 -4 V .2 g 5044 624 M -12 -16 V .2 g 5032 608 M -15 -20 V 0 g .2 g 6052 1864 M .2 g 6052 1864 M -4 -6 V .2 g 6048 1858 M -14 -20 V .2 g 6034 1838 M -9 -13 V .2 g 6025 1825 M -6 -8 V .2 g 6019 1817 M -14 -20 V .2 g 6005 1797 M -7 -10 V .2 g 5998 1787 M -8 -10 V .2 g 5990 1777 M -15 -20 V .2 g 5975 1757 M -5 -7 V .2 g 5970 1750 M -10 -13 V .2 g 5960 1737 M -16 -20 V .2 g 5944 1717 M -1 -2 V .2 g 5943 1715 M -14 -18 V .2 g 5929 1697 M -13 -17 V .2 g 5916 1680 M -3 -4 V .2 g 5913 1676 M -17 -20 V .2 g 5896 1656 M -7 -9 V .2 g 5889 1647 M -9 -11 V .2 g 5880 1636 M -17 -20 V .2 g 5863 1616 M -2 -2 V .2 g 5861 1614 M -15 -18 V .2 g 5846 1596 M -12 -14 V .2 g 5834 1582 M -5 -6 V .2 g 5829 1576 M -18 -21 V .2 g 5811 1555 M -4 -5 V .2 g 5807 1550 M -14 -15 V .2 g 5793 1535 M -13 -16 V .2 g 5780 1519 M -4 -4 V .2 g 5776 1515 M -18 -20 V .2 g 5758 1495 M -6 -6 V .2 g 5752 1489 M -13 -14 V .2 g 5739 1475 M -14 -16 V .2 g 5725 1459 M -4 -4 V .2 g 5721 1455 M -18 -20 V .2 g 5703 1435 M -5 -6 V .2 g 5698 1429 M -14 -15 V .2 g 5684 1414 M -13 -15 V .2 g 5671 1399 M -5 -5 V .2 g 5666 1394 M -19 -20 V .2 g 5647 1374 M -4 -5 V .2 g 5643 1369 M -14 -15 V .2 g 5629 1354 M -13 -14 V .2 g 5616 1340 M -5 -6 V .2 g 5611 1334 M -19 -20 V .2 g 5592 1314 M -3 -4 V .2 g 5589 1310 M -15 -17 V .2 g 5574 1293 M -12 -13 V .2 g 5562 1280 M -6 -7 V stroke 5556 1273 M .2 g 5556 1273 M -18 -20 V .2 g 5538 1253 M -4 -4 V .2 g 5534 1249 M -14 -16 V .2 g 5520 1233 M -13 -15 V .2 g 5507 1218 M -5 -5 V .2 g 5502 1213 M -17 -20 V .2 g 5485 1193 M -5 -6 V .2 g 5480 1187 M -13 -15 V .2 g 5467 1172 M -14 -17 V .2 g 5453 1155 M -3 -3 V .2 g 5450 1152 M -17 -20 V .2 g 5433 1132 M -8 -9 V .2 g 5425 1123 M -9 -11 V .2 g 5416 1112 M -16 -20 V .2 g 5400 1092 M -2 -2 V .2 g 5398 1090 M -15 -18 V .2 g 5383 1072 M -12 -16 V .2 g 5371 1056 M -4 -4 V .2 g 5367 1052 M -16 -21 V .2 g 5351 1031 M -7 -9 V .2 g 5344 1022 M -9 -11 V .2 g 5335 1011 M -16 -20 V .2 g 5319 991 M -3 -3 V .2 g 5316 988 M -13 -17 V .2 g 5303 971 M -14 -18 V .2 g 5289 953 M -1 -2 V .2 g 5288 951 M -16 -20 V .2 g 5272 931 M -10 -14 V .2 g 5262 917 M -5 -7 V .2 g 5257 910 M -16 -20 V .2 g 5241 890 M -6 -9 V .2 g 5235 881 M -9 -11 V .2 g 5226 870 M -15 -20 V .2 g 5211 850 M -4 -5 V .2 g 5207 845 M -11 -15 V .2 g 5196 830 M -15 -20 V .2 g 5181 810 M -1 -2 V .2 g 5180 808 M -14 -18 V .2 g 5166 790 M -13 -19 V .2 g 5153 771 M -2 -2 V .2 g 5151 769 M -15 -20 V .2 g 5136 749 M -10 -15 V .2 g 5126 734 M -4 -5 V .2 g 5122 729 M -15 -20 V .2 g 5107 709 M -9 -12 V .2 g 5098 697 M -6 -8 V .2 g 5092 689 M -15 -20 V .2 g 5077 669 M -6 -8 V .2 g 5071 661 M -9 -13 V .2 g 5062 648 M -15 -20 V 0 g .18 g 618 3248 M .18 g 618 3248 M -8 21 V .18 g 610 3269 M -8 19 V stroke 602 3288 M 0 g .18 g 1338 1807 M .18 g 1338 1807 M -8 10 V .18 g 1330 1817 M -15 21 V .18 g 1315 1838 M -4 6 V .18 g 1311 1844 M -10 14 V .18 g 1301 1858 M -15 20 V .18 g 1286 1878 M -3 4 V .18 g 1283 1882 M -11 16 V .18 g 1272 1898 M -13 20 V .18 g 1259 1918 M -3 4 V .18 g 1256 1922 M -11 16 V .18 g 1245 1938 M -13 21 V .18 g 1232 1959 M -3 4 V .18 g 1229 1963 M -10 16 V .18 g 1219 1979 M -13 20 V .18 g 1206 1999 M -4 6 V .18 g 1202 2005 M -9 14 V .18 g 1193 2019 M -12 20 V .18 g 1181 2039 M -7 10 V .18 g 1174 2049 M -6 10 V .18 g 1168 2059 M -12 20 V .18 g 1156 2079 M -9 16 V .18 g 1147 2095 M -3 5 V .18 g 1144 2100 M -11 20 V .18 g 1133 2120 M -12 20 V .18 g 1121 2140 M -1 2 V .18 g 1120 2142 M -10 18 V .18 g 1110 2160 M -12 20 V .18 g 1098 2180 M -5 11 V .18 g 1093 2191 M -6 9 V .18 g 1087 2200 M -11 21 V .18 g 1076 2221 M -11 20 V .18 g .18 g 1065 2241 M -10 20 V .18 g 1055 2261 M -11 20 V .18 g 1044 2281 M -6 11 V .18 g 1038 2292 M -5 9 V .18 g 1033 2301 M -10 20 V .18 g 1023 2321 M -10 20 V .18 g 1013 2341 M -2 4 V .18 g 1011 2345 M -8 17 V .18 g 1003 2362 M -10 20 V .18 g 993 2382 M -9 18 V .18 g 984 2400 M -1 2 V .18 g 983 2402 M -10 20 V .18 g 973 2422 M -10 20 V .18 g 963 2442 M -7 14 V .18 g 956 2456 M -3 6 V .18 g 953 2462 M -9 21 V .18 g 944 2483 M -10 20 V .18 g 934 2503 M -5 11 V .18 g 929 2514 M -4 9 V .18 g 925 2523 M -10 20 V .18 g 915 2543 M -9 20 V stroke 906 2563 M .18 g 906 2563 M -4 10 V .18 g 902 2573 M -5 10 V .18 g 897 2583 M -9 21 V .18 g 888 2604 M -9 20 V .18 g 879 2624 M -4 9 V .18 g 875 2633 M -5 11 V .18 g 870 2644 M -9 20 V .18 g 861 2664 M -9 20 V .18 g 852 2684 M -5 10 V .18 g 847 2694 M -4 10 V .18 g 843 2704 M -9 20 V .18 g 834 2724 M -9 21 V .18 g 825 2745 M -5 12 V .18 g 820 2757 M -3 8 V .18 g 817 2765 M -9 20 V .18 g 808 2785 M -9 20 V .18 g 799 2805 M -6 15 V .18 g 793 2820 M -2 5 V .18 g 791 2825 M -9 20 V .18 g 782 2845 M -8 21 V .18 g 774 2866 M -9 19 V .18 g 765 2885 M 0 1 V .18 g 765 2886 M -8 20 V .18 g 757 2906 M -9 20 V .18 g 748 2926 M -8 20 V .18 g 740 2946 M -2 4 V .18 g 738 2950 M -6 16 V .18 g 732 2966 M -8 20 V .18 g 724 2986 M -9 21 V .18 g 715 3007 M -4 10 V .18 g 711 3017 M -4 10 V .18 g 707 3027 M -8 20 V .18 g 699 3047 M -8 20 V .18 g 691 3067 M -7 17 V .18 g 684 3084 M -2 3 V .18 g 682 3087 M -8 20 V .18 g 674 3107 M -8 21 V .18 g 666 3128 M -8 20 V .18 g 658 3148 M -1 3 V .18 g 657 3151 M -7 17 V .18 g 650 3168 M -8 20 V .18 g 642 3188 M -8 20 V .18 g 634 3208 M -5 12 V .18 g 629 3220 M -3 8 V .18 g 626 3228 M -8 20 V 0 g .18 g 2373 588 M .18 g 2373 588 M -16 20 V .18 g 2357 608 M -11 15 V .18 g 2346 623 M -4 5 V .18 g 2342 628 M -16 20 V .18 g 2326 648 M -7 11 V .18 g 2319 659 M -8 10 V .18 g 2311 669 M -15 20 V stroke 2296 689 M .18 g 2296 689 M -4 6 V .18 g 2292 695 M -11 14 V .18 g 2281 709 M -15 20 V .18 g 2266 729 M -2 2 V .18 g 2264 731 M -14 18 V .18 g 2250 749 M -13 18 V .18 g 2237 767 M -2 2 V .18 g 2235 769 M -15 21 V .18 g 2220 790 M -10 13 V .18 g 2210 803 M -5 7 V .18 g 2205 810 M -15 20 V .18 g 2190 830 M -7 9 V .18 g 2183 839 M -9 11 V .18 g 2174 850 M -15 20 V .18 g 2159 870 M -4 5 V .18 g 2155 875 M -11 15 V .18 g 2144 890 M -16 20 V .18 g 2128 910 M 0 1 V .18 g 2128 911 M -15 20 V .18 g 2113 931 M -12 15 V .18 g 2101 946 M -4 5 V .18 g 2097 951 M -16 20 V .18 g 2081 971 M -7 10 V .18 g 2074 981 M -9 10 V .18 g 2065 991 M -16 20 V .18 g 2049 1011 M -3 4 V .18 g 2046 1015 M -13 16 V .18 g 2033 1031 M -14 18 V .18 g 2019 1049 M -2 3 V .18 g 2017 1052 M -17 20 V .18 g 2000 1072 M -8 10 V .18 g 1992 1082 M -9 10 V .18 g 1983 1092 M -17 20 V .18 g 1966 1112 M -1 2 V .18 g 1965 1114 M -16 18 V .18 g 1949 1132 M -12 14 V .18 g 1937 1146 M -5 6 V .18 g 1932 1152 M -18 20 V .18 g 1914 1172 M -4 5 V .18 g 1910 1177 M -14 16 V .18 g 1896 1193 M -13 14 V .18 g 1883 1207 M -5 6 V .18 g 1878 1213 M -18 20 V .18 g 1860 1233 M -4 4 V .18 g 1856 1237 M -15 16 V .18 g 1841 1253 M -13 14 V .18 g 1828 1267 M -6 6 V .18 g 1822 1273 M -19 20 V .18 g 1803 1293 M -2 3 V .18 g 1801 1296 M -17 18 V .18 g 1784 1314 M -10 10 V .18 g 1774 1324 M -9 10 V stroke 1765 1334 M .18 g 1765 1334 M -18 19 V .18 g 1747 1353 M -2 1 V .18 g 1745 1354 M -19 20 V .18 g 1726 1374 M -7 7 V .18 g 1719 1381 M -13 13 V .18 g 1706 1394 M -14 15 V .18 g 1692 1409 M -6 5 V .18 g 1686 1414 M -19 21 V .18 g 1667 1435 M -2 1 V .18 g 1665 1436 M -18 19 V .18 g 1647 1455 M -9 9 V .18 g 1638 1464 M -11 11 V .18 g 1627 1475 M -17 18 V .18 g 1610 1493 M -2 2 V .18 g 1608 1495 M -19 20 V .18 g 1589 1515 M -6 6 V .18 g 1583 1521 M -13 14 V .18 g 1570 1535 M -14 15 V .18 g 1556 1550 M -5 5 V .18 g 1551 1555 M -19 21 V .18 g 1532 1576 M -3 3 V .18 g 1529 1579 M -16 17 V .18 g 1513 1596 M -12 13 V .18 g 1501 1609 M -6 7 V .18 g 1495 1616 M -18 20 V .18 g 1477 1636 M -3 4 V .18 g 1474 1640 M -14 16 V .18 g 1460 1656 M -13 15 V .18 g 1447 1671 M -5 5 V .18 g 1442 1676 M -17 21 V .18 g 1425 1697 M -5 7 V .18 g 1420 1704 M -11 13 V .18 g 1409 1717 M -17 20 V .18 g .18 g 1392 1737 M -15 20 V .18 g 1377 1757 M -12 15 V .18 g 1365 1772 M -4 5 V .18 g 1361 1777 M -16 20 V .18 g 1345 1797 M -7 10 V 0 g .18 g 2455 4139 M .18 g 2455 4139 M -27 13 V .18 g 2428 4152 M -9 3 V .18 g 2419 4155 M -18 9 V .18 g 2401 4164 M -24 12 V .18 g 2377 4176 M -4 2 V .18 g 2373 4178 M -27 13 V .18 g 2346 4191 M -9 5 V .18 g 2337 4196 M -18 10 V .18 g 2319 4206 M -19 10 V .18 g 2300 4216 M -8 5 V .18 g 2292 4221 M -27 15 V .18 g 2265 4236 M -1 1 V .18 g 2264 4237 M -27 17 V .18 g 2237 4254 M -4 2 V stroke 2233 4256 M .18 g 2233 4256 M -23 16 V .18 g 2210 4272 M -7 4 V .18 g 2203 4276 M -20 15 V .18 g 2183 4291 M -8 6 V .18 g 2175 4297 M -20 14 V .18 g 2155 4311 M -7 6 V .18 g 2148 4317 M -20 16 V .18 g 2128 4333 M -4 4 V .18 g 2124 4337 M -23 19 V .18 g 2101 4356 M -1 1 V .18 g 2100 4357 M -22 20 V .18 g 2078 4377 M -4 4 V .18 g 2074 4381 M -17 16 V .18 g 2057 4397 M -11 10 V .18 g 2046 4407 M -10 10 V .18 g 2036 4417 M -17 18 V .18 g 2019 4435 M -2 3 V .18 g 2017 4438 M -19 20 V .18 g 1998 4458 M -6 7 V .18 g 1992 4465 M -12 13 V .18 g 1980 4478 M -15 18 V .18 g 1965 4496 M -2 2 V .18 g 1963 4498 M -17 20 V .18 g 1946 4518 M -9 11 V .18 g 1937 4529 M -7 9 V .18 g 1930 4538 M -16 21 V .18 g 1914 4559 M -4 5 V .18 g 1910 4564 M -11 15 V .18 g 1899 4579 M -16 20 V .18 g 1883 4599 M 0 1 V .18 g 1883 4600 M -14 19 V 0 g .18 g 4043 3652 M .18 g 4043 3652 M -7 -6 V .18 g 4036 3646 M -23 -15 V .18 g 4013 3631 M -5 -2 V .18 g 4008 3629 M -27 -17 V .18 g 3981 3612 M -1 -1 V .18 g 3980 3611 M -26 -15 V .18 g 3954 3596 M -9 -5 V .18 g 3945 3591 M -18 -10 V .18 g 3927 3581 M -20 -10 V .18 g 3907 3571 M -8 -4 V .18 g 3899 3567 M -27 -12 V .18 g 3872 3555 M -9 -4 V .18 g 3863 3551 M -18 -8 V .18 g 3845 3543 M -27 -9 V .18 g 3818 3534 M -11 -3 V .18 g 3807 3531 M -17 -5 V .18 g 3790 3526 M -27 -7 V .18 g 3763 3519 M -27 -5 V .18 g 3736 3514 M -27 -4 V .18 g .18 g 3709 3510 M -28 -1 V .18 g 3681 3509 M -27 0 V stroke 3654 3509 M .18 g 3654 3509 M -27 1 V .18 g 3627 3510 M -3 0 V .18 g 3624 3510 M -24 3 V .18 g 3600 3513 M -28 5 V .18 g 3572 3518 M -27 7 V .18 g 3545 3525 M -20 6 V .18 g 3525 3531 M -7 2 V .18 g 3518 3533 M -27 9 V .18 g 3491 3542 M -23 9 V .18 g 3468 3551 M -5 2 V .18 g 3463 3553 M -27 12 V .18 g 3436 3565 M -13 6 V .18 g 3423 3571 M -14 7 V .18 g 3409 3578 M -25 13 V .18 g 3384 3591 M -2 1 V .18 g 3382 3592 M -28 16 V .18 g 3354 3608 M -6 3 V .18 g 3348 3611 M -21 13 V .18 g 3327 3624 M -12 7 V .18 g 3315 3631 M -15 10 V .18 g 3300 3641 M -17 11 V .18 g 3283 3652 M -10 6 V .18 g 3273 3658 M -20 14 V .18 g 3253 3672 M -8 5 V .18 g 3245 3677 M -22 15 V .18 g 3223 3692 M -5 3 V .18 g 3218 3695 M -24 17 V .18 g 3194 3712 M -3 2 V .18 g 3191 3714 M -26 18 V .18 g 3165 3732 M -1 1 V .18 g 3164 3733 M -27 19 V .18 g 3137 3752 M -1 1 V .18 g 3136 3753 M -27 19 V .18 g 3109 3772 M -1 0 V .18 g 3108 3772 M -26 19 V .18 g 3082 3791 M -2 2 V .18 g 3080 3793 M -25 18 V .18 g 3055 3811 M -4 2 V .18 g 3051 3813 M -24 17 V .18 g 3027 3830 M -5 3 V .18 g 3022 3833 M -22 15 V .18 g 3000 3848 M -7 5 V .18 g 2993 3853 M -20 14 V .18 g 2973 3867 M -10 6 V .18 g 2963 3873 M -17 12 V .18 g 2946 3885 M -14 8 V .18 g 2932 3893 M -14 10 V .18 g 2918 3903 M -17 11 V .18 g 2901 3914 M -10 6 V .18 g 2891 3920 M -23 14 V .18 g 2868 3934 M -4 3 V .18 g 2864 3937 M -27 16 V stroke 2837 3953 M .18 g 2837 3953 M -2 1 V .18 g 2835 3954 M -26 15 V .18 g 2809 3969 M -9 5 V .18 g 2800 3974 M -18 10 V .18 g 2782 3984 M -19 10 V .18 g 2763 3994 M -8 5 V .18 g 2755 3999 M -27 14 V .18 g 2728 4013 M -3 1 V .18 g 2725 4014 M -25 13 V .18 g 2700 4027 M -15 8 V .18 g 2685 4035 M -12 5 V .18 g 2673 4040 M -27 13 V .18 g 2646 4053 M -3 2 V .18 g 2643 4055 M -24 11 V .18 g 2619 4066 M -20 9 V .18 g 2599 4075 M -8 3 V .18 g 2591 4078 M -27 13 V .18 g 2564 4091 M -10 4 V .18 g 2554 4095 M -17 8 V .18 g 2537 4103 M -27 12 V .18 g 2510 4115 M -1 0 V .18 g 2509 4115 M -27 12 V .18 g 2482 4127 M -18 8 V .18 g 2464 4135 M -9 4 V 0 g .18 g 5422 4619 M .18 g 5422 4619 M -15 -20 V .18 g 5407 4599 M -9 -11 V .18 g 5398 4588 M -8 -9 V .18 g 5390 4579 M -16 -20 V .18 g 5374 4559 M -3 -4 V .18 g 5371 4555 M -15 -17 V .18 g 5356 4538 M -12 -14 V .18 g 5344 4524 M -5 -6 V .18 g 5339 4518 M -19 -20 V .18 g 5320 4498 M -4 -4 V .18 g 5316 4494 M -15 -16 V .18 g 5301 4478 M -12 -12 V .18 g 5289 4466 M -8 -8 V .18 g 5281 4458 M -19 -19 V .18 g 5262 4439 M -2 -1 V .18 g 5260 4438 M -22 -21 V .18 g 5238 4417 M -3 -3 V .18 g 5235 4414 M -20 -17 V .18 g 5215 4397 M -8 -7 V .18 g 5207 4390 M -16 -13 V .18 g 5191 4377 M -11 -9 V .18 g 5180 4368 M -15 -11 V .18 g 5165 4357 M -12 -10 V .18 g 5153 4347 M -15 -10 V .18 g 5138 4337 M -12 -9 V .18 g 5126 4328 M -17 -11 V .18 g 5109 4317 M -11 -8 V .18 g 5098 4309 M -19 -12 V stroke 5079 4297 M .18 g 5079 4297 M -8 -5 V .18 g 5071 4292 M -25 -16 V .18 g 5046 4276 M -2 -1 V .18 g 5044 4275 M -27 -16 V .18 g 5017 4259 M -6 -3 V .18 g 5011 4256 M -22 -12 V .18 g 4989 4244 M -14 -8 V .18 g 4975 4236 M -13 -7 V .18 g 4962 4229 M -26 -13 V .18 g 4936 4216 M -1 -1 V .18 g 4935 4215 M -27 -14 V .18 g 4908 4201 M -12 -5 V .18 g 4896 4196 M -16 -8 V .18 g 4880 4188 M -24 -12 V .18 g 4856 4176 M -3 -2 V .18 g 4853 4174 M -27 -13 V .18 g 4826 4161 M -11 -6 V .18 g 4815 4155 M -16 -7 V .18 g 4799 4148 M -25 -13 V .18 g 4774 4135 M -3 -1 V .18 g 4771 4134 M -27 -14 V .18 g 4744 4120 M -10 -5 V .18 g 4734 4115 M -17 -9 V .18 g 4717 4106 M -22 -11 V .18 g 4695 4095 M -5 -3 V .18 g 4690 4092 M -28 -14 V .18 g 4662 4078 M -5 -3 V .18 g 4657 4075 M -22 -12 V .18 g 4635 4063 M -14 -8 V .18 g 4621 4055 M -13 -8 V .18 g 4608 4047 M -22 -12 V .18 g 4586 4035 M -5 -4 V .18 g 4581 4031 M -28 -16 V .18 g 4553 4015 M -1 -1 V .18 g 4552 4014 M -26 -16 V .18 g 4526 3998 M -6 -4 V .18 g 4520 3994 M -21 -13 V .18 g 4499 3981 M -11 -7 V .18 g 4488 3974 M -16 -11 V .18 g 4472 3963 M -14 -9 V .18 g 4458 3954 M -14 -9 V .18 g 4444 3945 M -15 -11 V .18 g 4429 3934 M -12 -8 V .18 g 4417 3926 M -17 -12 V .18 g 4400 3914 M -10 -7 V .18 g 4390 3907 M -19 -14 V .18 g 4371 3893 M -8 -6 V .18 g 4363 3887 M -19 -14 V .18 g 4344 3873 M -9 -6 V .18 g 4335 3867 M -18 -14 V .18 g 4317 3853 M -9 -6 V .18 g 4308 3847 M -18 -14 V stroke 4290 3833 M .18 g 4290 3833 M -9 -7 V .18 g 4281 3826 M -18 -13 V .18 g 4263 3813 M -9 -7 V .18 g 4254 3806 M -18 -13 V .18 g 4236 3793 M -10 -8 V .18 g 4226 3785 M -16 -13 V .18 g 4210 3772 M -11 -8 V .18 g 4199 3764 M -16 -12 V .18 g 4183 3752 M -11 -8 V .18 g 4172 3744 M -16 -12 V .18 g 4156 3732 M -11 -8 V .18 g 4145 3724 M -16 -12 V .18 g 4129 3712 M -12 -8 V .18 g 4117 3704 M -16 -12 V .18 g 4101 3692 M -11 -8 V .18 g 4090 3684 M -17 -12 V .18 g 4073 3672 M -10 -7 V .18 g 4063 3665 M -20 -13 V 0 g .18 g 5039 729 M .18 g 5039 729 M -14 -20 V .18 g 5025 709 M -8 -11 V .18 g 5017 698 M -7 -9 V .18 g 5010 689 M -15 -20 V .18 g 4995 669 M -6 -8 V .18 g 4989 661 M -9 -13 V .18 g 4980 648 M -15 -20 V .18 g 4965 628 M -3 -3 V .18 g 4962 625 M -13 -17 V .18 g 4949 608 M -14 -19 V .18 g 4935 589 M -1 -1 V 0 g .18 g 6052 1969 M .18 g 6052 1969 M -7 -10 V .18 g 6045 1959 M -14 -21 V .18 g 6031 1938 M -6 -8 V .18 g 6025 1930 M -9 -12 V .18 g 6016 1918 M -15 -20 V .18 g 6001 1898 M -3 -5 V .18 g 5998 1893 M -12 -15 V .18 g 5986 1878 M -15 -20 V .18 g 5971 1858 M -1 -2 V .18 g 5970 1856 M -14 -18 V .18 g 5956 1838 M -13 -17 V .18 g 5943 1821 M -3 -4 V .18 g 5940 1817 M -16 -20 V .18 g 5924 1797 M -8 -10 V .18 g 5916 1787 M -9 -10 V .18 g 5907 1777 M -16 -20 V .18 g 5891 1757 M -2 -3 V .18 g 5889 1754 M -15 -17 V .18 g 5874 1737 M -13 -15 V .18 g 5861 1722 M -5 -5 V .18 g 5856 1717 M -17 -20 V .18 g 5839 1697 M -5 -6 V stroke 5834 1691 M .18 g 5834 1691 M -13 -15 V .18 g 5821 1676 M -14 -16 V .18 g 5807 1660 M -4 -4 V .18 g 5803 1656 M -18 -20 V .18 g 5785 1636 M -5 -6 V .18 g 5780 1630 M -13 -14 V .18 g 5767 1616 M -15 -16 V .18 g 5752 1600 M -4 -4 V .18 g 5748 1596 M -18 -20 V .18 g 5730 1576 M -5 -6 V .18 g 5725 1570 M -14 -15 V .18 g 5711 1555 M -13 -14 V .18 g 5698 1541 M -6 -6 V .18 g 5692 1535 M -18 -20 V .18 g 5674 1515 M -3 -3 V .18 g 5671 1512 M -16 -17 V .18 g 5655 1495 M -12 -12 V .18 g 5643 1483 M -7 -8 V .18 g 5636 1475 M -19 -20 V .18 g 5617 1455 M -1 -2 V .18 g 5616 1453 M -18 -18 V .18 g 5598 1435 M -9 -11 V .18 g 5589 1424 M -9 -10 V .18 g 5580 1414 M -18 -20 V .18 g 5562 1394 M -19 -20 V .18 g 5543 1374 M -9 -10 V .18 g 5534 1364 M -9 -10 V .18 g 5525 1354 M -18 -20 V .18 g .18 g 5507 1334 M -18 -20 V .18 g 5489 1314 M -9 -12 V .18 g 5480 1302 M -8 -9 V .18 g 5472 1293 M -17 -20 V .18 g 5455 1273 M -2 -2 V .18 g 5453 1271 M -16 -18 V .18 g 5437 1253 M -12 -14 V .18 g 5425 1239 M -4 -6 V .18 g 5421 1233 M -17 -20 V .18 g 5404 1213 M -6 -7 V .18 g 5398 1206 M -11 -13 V .18 g 5387 1193 M -16 -21 V .18 g .18 g 5371 1172 M -16 -20 V .18 g 5355 1152 M -11 -14 V .18 g 5344 1138 M -5 -6 V .18 g 5339 1132 M -16 -20 V .18 g 5323 1112 M -7 -8 V .18 g 5316 1104 M -9 -12 V .18 g 5307 1092 M -15 -20 V .18 g 5292 1072 M -3 -4 V .18 g 5289 1068 M -13 -16 V .18 g 5276 1052 M -14 -20 V .18 g 5262 1032 M -1 -1 V .18 g 5261 1031 M -15 -20 V stroke 5246 1011 M .18 g 5246 1011 M -11 -15 V .18 g 5235 996 M -4 -5 V .18 g 5231 991 M -15 -20 V .18 g 5216 971 M -9 -12 V .18 g 5207 959 M -6 -8 V .18 g 5201 951 M -15 -20 V .18 g 5186 931 M -6 -9 V .18 g 5180 922 M -9 -12 V .18 g 5171 910 M -14 -20 V .18 g 5157 890 M -4 -5 V .18 g 5153 885 M -11 -15 V .18 g 5142 870 M -15 -20 V .18 g 5127 850 M -1 -3 V .18 g 5126 847 M -13 -17 V .18 g 5113 830 M -15 -20 V .18 g .18 g 5098 810 M -15 -20 V .18 g 5083 790 M -12 -18 V .18 g 5071 772 M -2 -3 V .18 g 5069 769 M -15 -20 V .18 g 5054 749 M -10 -14 V .18 g 5044 735 M -5 -6 V 0 g .16 g 681 3208 M .16 g 681 3208 M -8 20 V .16 g 673 3228 M -8 20 V .16 g 665 3248 M -8 21 V .16 g 657 3269 M -1 0 V .16 g 656 3269 M -7 20 V .16 g 649 3289 M -8 20 V .16 g 641 3309 M -8 20 V .16 g 633 3329 M -4 8 V .16 g 629 3337 M -4 12 V .16 g 625 3349 M -8 20 V .16 g 617 3369 M -8 21 V .16 g 609 3390 M -7 17 V 0 g .16 g 1437 1797 M .16 g 1437 1797 M -17 20 V .16 g 1420 1817 M -1 0 V .16 g 1419 1817 M -17 21 V .16 g 1402 1838 M -10 12 V .16 g 1392 1850 M -6 8 V .16 g 1386 1858 M -16 20 V .16 g 1370 1878 M -5 6 V .16 g 1365 1884 M -11 14 V .16 g 1354 1898 M -16 20 V .16 g 1338 1918 M 0 1 V .16 g 1338 1919 M -15 19 V .16 g 1323 1938 M -12 17 V .16 g 1311 1955 M -3 4 V .16 g 1308 1959 M -14 20 V .16 g 1294 1979 M -11 14 V .16 g 1283 1993 M -4 6 V .16 g 1279 1999 M -14 20 V .16 g 1265 2019 M -9 13 V stroke 1256 2032 M .16 g 1256 2032 M -4 7 V .16 g 1252 2039 M -14 20 V .16 g 1238 2059 M -9 14 V .16 g 1229 2073 M -4 6 V .16 g 1225 2079 M -13 21 V .16 g 1212 2100 M -10 15 V .16 g 1202 2115 M -3 5 V .16 g 1199 2120 M -13 20 V .16 g 1186 2140 M -12 19 V .16 g 1174 2159 M 0 1 V .16 g 1174 2160 M -12 20 V .16 g 1162 2180 M -12 20 V .16 g 1150 2200 M -3 5 V .16 g 1147 2205 M -9 16 V .16 g 1138 2221 M -12 20 V .16 g 1126 2241 M -6 11 V .16 g 1120 2252 M -5 9 V .16 g 1115 2261 M -12 20 V .16 g 1103 2281 M -10 19 V .16 g 1093 2300 M -1 1 V .16 g 1092 2301 M -11 20 V .16 g 1081 2321 M -11 20 V .16 g 1070 2341 M -5 9 V .16 g 1065 2350 M -6 12 V .16 g 1059 2362 M -10 20 V .16 g 1049 2382 M -11 20 V .16 g .16 g 1038 2402 M -10 20 V .16 g 1028 2422 M -10 20 V .16 g 1018 2442 M -7 13 V .16 g 1011 2455 M -4 7 V .16 g 1007 2462 M -10 21 V .16 g 997 2483 M -10 20 V .16 g 987 2503 M -3 7 V .16 g 984 2510 M -7 13 V .16 g 977 2523 M -9 20 V .16 g 968 2543 M -10 20 V .16 g 958 2563 M -2 4 V .16 g 956 2567 M -8 16 V .16 g 948 2583 M -9 21 V .16 g 939 2604 M -10 20 V .16 g 929 2624 M 0 1 V .16 g 929 2625 M -9 19 V .16 g 920 2644 M -9 20 V .16 g 911 2664 M -9 20 V .16 g .16 g 902 2684 M -9 20 V .16 g 893 2704 M -9 20 V .16 g 884 2724 M -9 20 V .16 g 875 2744 M -1 1 V .16 g 874 2745 M -8 20 V .16 g 866 2765 M -9 20 V .16 g 857 2785 M -9 20 V .16 g 848 2805 M -1 1 V stroke 847 2806 M .16 g 847 2806 M -8 19 V .16 g 839 2825 M -8 20 V .16 g 831 2845 M -9 21 V .16 g 822 2866 M -2 4 V .16 g 820 2870 M -7 16 V .16 g 813 2886 M -8 20 V .16 g 805 2906 M -9 20 V .16 g 796 2926 M -3 8 V .16 g 793 2934 M -5 12 V .16 g 788 2946 M -9 20 V .16 g 779 2966 M -8 20 V .16 g 771 2986 M -6 13 V .16 g 765 2999 M -3 8 V .16 g 762 3007 M -8 20 V .16 g 754 3027 M -8 20 V .16 g 746 3047 M -8 18 V .16 g 738 3065 M 0 2 V .16 g 738 3067 M -9 20 V .16 g 729 3087 M -8 20 V .16 g 721 3107 M -8 21 V .16 g 713 3128 M -2 4 V .16 g 711 3132 M -6 16 V .16 g 705 3148 M -8 20 V .16 g 697 3168 M -8 20 V .16 g 689 3188 M -5 12 V .16 g 684 3200 M -3 8 V 0 g .16 g 2465 588 M .16 g 2465 588 M -10 12 V .16 g 2455 600 M -7 8 V .16 g 2448 608 M -16 20 V .16 g 2432 628 M -4 6 V .16 g 2428 634 M -12 14 V .16 g 2416 648 M -15 21 V .16 g .16 g 2401 669 M -16 20 V .16 g 2385 689 M -12 15 V .16 g 2373 704 M -3 5 V .16 g 2370 709 M -15 20 V .16 g 2355 729 M -9 12 V .16 g 2346 741 M -7 8 V .16 g 2339 749 M -15 20 V .16 g 2324 769 M -5 8 V .16 g 2319 777 M -10 13 V .16 g 2309 790 M -14 20 V .16 g 2295 810 M -3 4 V .16 g 2292 814 M -12 16 V .16 g 2280 830 M -15 20 V .16 g 2265 850 M -1 1 V .16 g 2264 851 M -14 19 V .16 g 2250 870 M -13 18 V .16 g 2237 888 M -2 2 V .16 g 2235 890 M -15 20 V .16 g 2220 910 M -10 15 V .16 g 2210 925 M -5 6 V stroke 2205 931 M .16 g 2205 931 M -15 20 V .16 g 2190 951 M -7 10 V .16 g 2183 961 M -8 10 V .16 g 2175 971 M -15 20 V .16 g 2160 991 M -5 7 V .16 g 2155 998 M -10 13 V .16 g 2145 1011 M -15 20 V .16 g 2130 1031 M -2 3 V .16 g 2128 1034 M -13 18 V .16 g 2115 1052 M -14 18 V .16 g 2101 1070 M -2 2 V .16 g 2099 1072 M -15 20 V .16 g 2084 1092 M -10 13 V .16 g 2074 1105 M -6 7 V .16 g 2068 1112 M -16 20 V .16 g 2052 1132 M -6 7 V .16 g 2046 1139 M -10 13 V .16 g 2036 1152 M -17 20 V .16 g 2019 1172 M 0 1 V .16 g 2019 1173 M -16 20 V .16 g 2003 1193 M -11 13 V .16 g 1992 1206 M -6 7 V .16 g 1986 1213 M -17 20 V .16 g 1969 1233 M -4 6 V .16 g 1965 1239 M -13 14 V .16 g 1952 1253 M -15 17 V .16 g 1937 1270 M -2 3 V .16 g 1935 1273 M -18 20 V .16 g 1917 1293 M -7 8 V .16 g 1910 1301 M -11 13 V .16 g 1899 1314 M -16 18 V .16 g 1883 1332 M -2 2 V .16 g 1881 1334 M -19 20 V .16 g 1862 1354 M -6 7 V .16 g 1856 1361 M -12 13 V .16 g 1844 1374 M -16 16 V .16 g 1828 1390 M -3 4 V .16 g 1825 1394 M -20 20 V .16 g 1805 1414 M -4 5 V .16 g 1801 1419 M -15 16 V .16 g 1786 1435 M -12 12 V .16 g 1774 1447 M -8 8 V .16 g 1766 1455 M -19 20 V .16 g 1747 1475 M -1 0 V .16 g 1746 1475 M -20 20 V .16 g 1726 1495 M -7 7 V .16 g 1719 1502 M -13 13 V .16 g 1706 1515 M -14 14 V .16 g 1692 1529 M -6 6 V .16 g 1686 1535 M -20 20 V .16 g 1666 1555 M -1 1 V .16 g 1665 1556 M -19 20 V stroke 1646 1576 M .16 g 1646 1576 M -8 8 V .16 g 1638 1584 M -12 12 V .16 g 1626 1596 M -16 15 V .16 g 1610 1611 M -5 5 V .16 g 1605 1616 M -19 20 V .16 g 1586 1636 M -3 3 V .16 g 1583 1639 M -17 17 V .16 g 1566 1656 M -10 11 V .16 g 1556 1667 M -9 9 V .16 g 1547 1676 M -18 19 V .16 g 1529 1695 M -2 2 V .16 g 1527 1697 M -18 20 V .16 g 1509 1717 M -8 8 V .16 g 1501 1725 M -11 12 V .16 g 1490 1737 M -16 17 V .16 g 1474 1754 M -2 3 V .16 g 1472 1757 M -18 20 V .16 g 1454 1777 M -7 8 V .16 g 1447 1785 M -10 12 V 0 g .16 g 2619 3955 M .16 g 2619 3955 M -28 12 V .16 g 2591 3967 M -17 7 V .16 g 2574 3974 M -10 4 V .16 g 2564 3978 M -27 12 V .16 g 2537 3990 M -10 4 V .16 g 2527 3994 M -17 7 V .16 g 2510 4001 M -28 12 V .16 g 2482 4013 M -3 1 V .16 g 2479 4014 M -24 10 V .16 g 2455 4024 M -24 11 V .16 g 2431 4035 M -3 1 V .16 g 2428 4036 M -27 12 V .16 g 2401 4048 M -15 7 V .16 g 2386 4055 M -13 6 V .16 g 2373 4061 M -27 13 V .16 g 2346 4074 M -3 1 V .16 g 2343 4075 M -24 12 V .16 g 2319 4087 M -15 8 V .16 g 2304 4095 M -12 6 V .16 g 2292 4101 M -25 14 V .16 g 2267 4115 M -3 2 V .16 g 2264 4117 M -27 16 V .16 g 2237 4133 M -4 2 V .16 g 2233 4135 M -23 15 V .16 g 2210 4150 M -8 5 V .16 g 2202 4155 M -19 14 V .16 g 2183 4169 M -10 7 V .16 g 2173 4176 M -18 13 V .16 g 2155 4189 M -9 7 V .16 g 2146 4196 M -18 14 V .16 g 2128 4210 M -7 6 V .16 g 2121 4216 M -20 17 V .16 g 2101 4233 M -4 3 V stroke 2097 4236 M .16 g 2097 4236 M -23 20 V .16 g 2074 4256 M 0 1 V .16 g 2074 4257 M -21 19 V .16 g 2053 4276 M -7 7 V .16 g 2046 4283 M -13 14 V .16 g 2033 4297 M -14 14 V .16 g 2019 4311 M -5 6 V .16 g 2014 4317 M -19 20 V .16 g 1995 4337 M -3 3 V .16 g 1992 4340 M -15 17 V .16 g 1977 4357 M -12 14 V .16 g 1965 4371 M -5 6 V .16 g 1960 4377 M -17 20 V .16 g 1943 4397 M -6 7 V .16 g 1937 4404 M -10 13 V .16 g 1927 4417 M -16 21 V .16 g 1911 4438 M -1 1 V .16 g 1910 4439 M -14 19 V .16 g 1896 4458 M -13 18 V .16 g 1883 4476 M -2 2 V .16 g 1881 4478 M -14 20 V .16 g 1867 4498 M -11 16 V .16 g 1856 4514 M -4 4 V .16 g 1852 4518 M -13 20 V .16 g 1839 4538 M -11 15 V .16 g 1828 4553 M -3 6 V .16 g 1825 4559 M -13 20 V .16 g 1812 4579 M -11 16 V .16 g 1801 4595 M -3 4 V .16 g 1798 4599 M -12 20 V 0 g .16 g 4174 3631 M .16 g 4174 3631 M -2 -2 V .16 g 4172 3629 M -24 -18 V .16 g 4148 3611 M -3 -3 V .16 g 4145 3608 M -23 -17 V .16 g 4122 3591 M -5 -4 V .16 g 4117 3587 M -22 -16 V .16 g 4095 3571 M -5 -4 V .16 g 4090 3567 M -22 -16 V .16 g 4068 3551 M -5 -4 V .16 g 4063 3547 M -24 -16 V .16 g 4039 3531 M -3 -3 V .16 g 4036 3528 M -26 -18 V .16 g 4010 3510 M -2 0 V .16 g 4008 3510 M -27 -18 V .16 g 3981 3492 M -3 -2 V .16 g 3978 3490 M -24 -15 V .16 g 3954 3475 M -9 -5 V .16 g 3945 3470 M -18 -10 V .16 g 3927 3460 M -19 -10 V .16 g 3908 3450 M -9 -5 V .16 g 3899 3445 M -27 -13 V .16 g 3872 3432 M -5 -2 V stroke 3867 3430 M .16 g 3867 3430 M -22 -10 V .16 g 3845 3420 M -27 -10 V .16 g 3818 3410 M -2 0 V .16 g 3816 3410 M -26 -8 V .16 g 3790 3402 M -27 -7 V .16 g 3763 3395 M -26 -5 V .16 g 3737 3390 M -1 -1 V .16 g 3736 3389 M -27 -3 V .16 g 3709 3386 M -28 -2 V .16 g 3681 3384 M -27 0 V .16 g 3654 3384 M -27 2 V .16 g 3627 3386 M -27 3 V .16 g 3600 3389 M -3 1 V .16 g 3597 3390 M -25 4 V .16 g 3572 3394 M -27 7 V .16 g 3545 3401 M -27 8 V .16 g 3518 3409 M -1 1 V .16 g 3517 3410 M -26 9 V .16 g 3491 3419 M -26 11 V .16 g 3465 3430 M -2 1 V .16 g 3463 3431 M -27 12 V .16 g 3436 3443 M -13 7 V .16 g 3423 3450 M -14 7 V .16 g 3409 3457 M -24 13 V .16 g 3385 3470 M -3 2 V .16 g 3382 3472 M -28 16 V .16 g 3354 3488 M -3 2 V .16 g 3351 3490 M -24 15 V .16 g 3327 3505 M -8 5 V .16 g 3319 3510 M -19 13 V .16 g 3300 3523 M -12 8 V .16 g 3288 3531 M -15 10 V .16 g 3273 3541 M -14 10 V .16 g 3259 3551 M -14 9 V .16 g 3245 3560 M -15 11 V .16 g 3230 3571 M -12 9 V .16 g 3218 3580 M -16 11 V .16 g 3202 3591 M -11 8 V .16 g 3191 3599 M -17 12 V .16 g 3174 3611 M -10 8 V .16 g 3164 3619 M -17 12 V .16 g 3147 3631 M -11 8 V .16 g 3136 3639 M -17 13 V .16 g 3119 3652 M -10 7 V .16 g 3109 3659 M -17 13 V .16 g 3092 3672 M -10 7 V .16 g 3082 3679 M -18 13 V .16 g 3064 3692 M -9 7 V .16 g 3055 3699 M -19 13 V .16 g 3036 3712 M -9 6 V .16 g 3027 3718 M -19 14 V .16 g 3008 3732 M -8 5 V stroke 3000 3737 M .16 g 3000 3737 M -22 15 V .16 g 2978 3752 M -5 4 V .16 g 2973 3756 M -24 16 V .16 g 2949 3772 M -3 3 V .16 g 2946 3775 M -28 18 V .16 g 2918 3793 M -27 17 V .16 g 2891 3810 M -4 3 V .16 g 2887 3813 M -23 14 V .16 g 2864 3827 M -10 6 V .16 g 2854 3833 M -17 10 V .16 g 2837 3843 M -18 10 V .16 g 2819 3853 M -10 6 V .16 g 2809 3859 M -25 14 V .16 g 2784 3873 M -2 1 V .16 g 2782 3874 M -27 15 V .16 g 2755 3889 M -9 4 V .16 g 2746 3893 M -18 10 V .16 g 2728 3903 M -22 11 V .16 g 2706 3914 M -6 3 V .16 g 2700 3917 M -27 13 V .16 g 2673 3930 M -9 4 V .16 g 2664 3934 M -18 8 V .16 g 2646 3942 M -26 12 V .16 g 2620 3954 M -1 1 V 0 g .16 g 5511 4619 M .16 g 5511 4619 M -4 -6 V .16 g 5507 4613 M -10 -14 V .16 g 5497 4599 M -13 -20 V .16 g 5484 4579 M -4 -6 V .16 g 5480 4573 M -11 -14 V .16 g 5469 4559 M -14 -21 V .16 g 5455 4538 M -2 -3 V .16 g 5453 4535 M -13 -17 V .16 g 5440 4518 M -15 -20 V .16 g .16 g 5425 4498 M -16 -20 V .16 g 5409 4478 M -11 -15 V .16 g 5398 4463 M -5 -5 V .16 g 5393 4458 M -16 -20 V .16 g 5377 4438 M -6 -8 V .16 g 5371 4430 M -11 -13 V .16 g 5360 4417 M -16 -18 V .16 g 5344 4399 M -2 -2 V .16 g 5342 4397 M -19 -20 V .16 g 5323 4377 M -7 -8 V .16 g 5316 4369 M -12 -12 V .16 g 5304 4357 M -15 -15 V .16 g 5289 4342 M -5 -5 V .16 g 5284 4337 M -21 -20 V .16 g 5263 4317 M -1 -2 V .16 g 5262 4315 M -21 -18 V .16 g 5241 4297 M -6 -6 V .16 g 5235 4291 M -17 -15 V .16 g 5218 4276 M -11 -8 V stroke 5207 4268 M .16 g 5207 4268 M -14 -12 V .16 g 5193 4256 M -13 -10 V .16 g 5180 4246 M -13 -10 V .16 g 5167 4236 M -14 -10 V .16 g 5153 4226 M -14 -10 V .16 g 5139 4216 M -13 -9 V .16 g 5126 4207 M -17 -11 V .16 g 5109 4196 M -11 -7 V .16 g 5098 4189 M -21 -13 V .16 g 5077 4176 M -6 -4 V .16 g 5071 4172 M -27 -16 V .16 g 5044 4156 M -2 -1 V .16 g 5042 4155 M -25 -14 V .16 g 5017 4141 M -11 -6 V .16 g 5006 4135 M -17 -8 V .16 g 4989 4127 M -22 -12 V .16 g 4967 4115 M -5 -2 V .16 g 4962 4113 M -27 -14 V .16 g 4935 4099 M -9 -4 V .16 g 4926 4095 M -18 -9 V .16 g 4908 4086 M -25 -11 V .16 g 4883 4075 M -3 -2 V .16 g 4880 4073 M -27 -12 V .16 g 4853 4061 M -13 -6 V .16 g 4840 4055 M -14 -7 V .16 g 4826 4048 M -27 -13 V .16 g 4799 4035 M -2 0 V .16 g 4797 4035 M -26 -13 V .16 g 4771 4022 M -16 -8 V .16 g 4755 4014 M -11 -5 V .16 g 4744 4009 M -27 -13 V .16 g 4717 3996 M -3 -2 V .16 g 4714 3994 M -24 -12 V .16 g 4690 3982 M -15 -8 V .16 g 4675 3974 M -13 -7 V .16 g 4662 3967 M -25 -13 V .16 g 4637 3954 M -2 -1 V .16 g 4635 3953 M -27 -16 V .16 g 4608 3937 M -7 -3 V .16 g 4601 3934 M -20 -12 V .16 g 4581 3922 M -14 -8 V .16 g 4567 3914 M -14 -9 V .16 g 4553 3905 M -19 -12 V .16 g 4534 3893 M -8 -4 V .16 g 4526 3889 M -24 -16 V .16 g 4502 3873 M -3 -2 V .16 g 4499 3871 M -27 -18 V .16 g 4472 3853 M -1 0 V .16 g 4471 3853 M -27 -18 V .16 g 4444 3835 M -2 -2 V .16 g 4442 3833 M -25 -17 V .16 g 4417 3816 M -4 -3 V stroke 4413 3813 M .16 g 4413 3813 M -23 -17 V .16 g 4390 3796 M -5 -3 V .16 g 4385 3793 M -22 -17 V .16 g 4363 3776 M -5 -4 V .16 g 4358 3772 M -23 -16 V .16 g 4335 3756 M -4 -4 V .16 g 4331 3752 M -23 -17 V .16 g 4308 3735 M -4 -3 V .16 g 4304 3732 M -23 -18 V .16 g 4281 3714 M -3 -2 V .16 g 4278 3712 M -24 -19 V .16 g 4254 3693 M -2 -1 V .16 g 4252 3692 M -26 -20 V .16 g .16 g 4226 3672 M -26 -20 V .16 g 4200 3652 M -1 -2 V .16 g 4199 3650 M -25 -19 V 0 g .16 g 5044 854 M .16 g 5044 854 M -3 -4 V .16 g 5041 850 M -14 -20 V .16 g 5027 830 M -10 -14 V .16 g 5017 816 M -5 -6 V .16 g 5012 810 M -15 -20 V .16 g 4997 790 M -8 -12 V .16 g 4989 778 M -6 -9 V .16 g 4983 769 M -15 -20 V .16 g 4968 749 M -6 -8 V .16 g 4962 741 M -9 -12 V .16 g 4953 729 M -15 -20 V .16 g 4938 709 M -3 -4 V .16 g 4935 705 M -12 -16 V .16 g 4923 689 M -15 -20 V .16 g 4908 669 M -1 0 V .16 g 4907 669 M -16 -21 V .16 g 4891 648 M -11 -14 V .16 g 4880 634 M -4 -6 V .16 g 4876 628 M -17 -20 V .16 g 4859 608 M -6 -8 V .16 g 4853 600 M -10 -12 V 0 g .16 g 6052 2080 M .16 g 6052 2080 M 0 -1 V .16 g 6052 2079 M -15 -20 V .16 g 6037 2059 M -12 -17 V .16 g 6025 2042 M -2 -3 V .16 g 6023 2039 M -15 -20 V .16 g 6008 2019 M -10 -14 V .16 g 5998 2005 M -5 -6 V .16 g 5993 1999 M -15 -20 V .16 g 5978 1979 M -8 -10 V .16 g 5970 1969 M -8 -10 V .16 g 5962 1959 M -16 -21 V .16 g 5946 1938 M -3 -3 V .16 g 5943 1935 M -13 -17 V .16 g 5930 1918 M -14 -17 V stroke 5916 1901 M .16 g 5916 1901 M -3 -3 V .16 g 5913 1898 M -17 -20 V .16 g 5896 1878 M -7 -9 V .16 g 5889 1869 M -10 -11 V .16 g 5879 1858 M -18 -20 V .16 g 5861 1838 M 0 -1 V .16 g 5861 1837 M -17 -20 V .16 g 5844 1817 M -10 -10 V .16 g 5834 1807 M -9 -10 V .16 g 5825 1797 M -18 -20 V .16 g .16 g 5807 1777 M -18 -20 V .16 g 5789 1757 M -9 -10 V .16 g 5780 1747 M -10 -10 V .16 g 5770 1737 M -18 -19 V .16 g 5752 1718 M -1 -1 V .16 g 5751 1717 M -19 -20 V .16 g 5732 1697 M -7 -8 V .16 g 5725 1689 M -12 -13 V .16 g 5713 1676 M -15 -15 V .16 g 5698 1661 M -5 -5 V .16 g 5693 1656 M -19 -20 V .16 g 5674 1636 M -3 -4 V .16 g 5671 1632 M -16 -16 V .16 g 5655 1616 M -12 -12 V .16 g 5643 1604 M -8 -8 V .16 g 5635 1596 M -19 -20 V .16 g 5616 1576 M 0 -1 V .16 g 5616 1575 M -19 -20 V .16 g 5597 1555 M -8 -9 V .16 g 5589 1546 M -11 -11 V .16 g 5578 1535 M -16 -18 V .16 g 5562 1517 M -2 -2 V .16 g 5560 1515 M -19 -20 V .16 g 5541 1495 M -7 -7 V .16 g 5534 1488 M -11 -13 V .16 g 5523 1475 M -16 -18 V .16 g 5507 1457 M -2 -2 V .16 g 5505 1455 M -18 -20 V .16 g 5487 1435 M -7 -8 V .16 g 5480 1427 M -11 -13 V .16 g 5469 1414 M -16 -19 V .16 g 5453 1395 M -1 -1 V .16 g 5452 1394 M -18 -20 V .16 g 5434 1374 M -9 -11 V .16 g 5425 1363 M -8 -9 V .16 g 5417 1354 M -16 -20 V .16 g 5401 1334 M -3 -4 V .16 g 5398 1330 M -14 -16 V .16 g 5384 1314 M -13 -17 V .16 g 5371 1297 M -3 -4 V .16 g 5368 1293 M -16 -20 V .16 g 5352 1273 M -8 -10 V stroke 5344 1263 M .16 g 5344 1263 M -8 -10 V .16 g 5336 1253 M -16 -20 V .16 g 5320 1233 M -4 -5 V .16 g 5316 1228 M -11 -15 V .16 g 5305 1213 M -16 -20 V .16 g 5289 1193 M 0 -1 V .16 g 5289 1192 M -15 -20 V .16 g 5274 1172 M -12 -16 V .16 g 5262 1156 M -3 -4 V .16 g 5259 1152 M -15 -20 V .16 g 5244 1132 M -9 -13 V .16 g 5235 1119 M -6 -7 V .16 g 5229 1112 M -15 -20 V .16 g 5214 1092 M -7 -10 V .16 g 5207 1082 M -7 -10 V .16 g 5200 1072 M -15 -20 V .16 g 5185 1052 M -5 -7 V .16 g 5180 1045 M -9 -14 V .16 g 5171 1031 M -15 -20 V .16 g 5156 1011 M -3 -4 V .16 g 5153 1007 M -11 -16 V .16 g 5142 991 M -15 -20 V .16 g 5127 971 M -1 -3 V .16 g 5126 968 M -13 -17 V .16 g 5113 951 M -14 -20 V .16 g 5099 931 M -1 -1 V .16 g 5098 930 M -14 -20 V .16 g 5084 910 M -13 -18 V .16 g 5071 892 M -1 -2 V .16 g 5070 890 M -15 -20 V .16 g 5055 870 M -11 -16 V 0 g .14 g 738 3188 M .14 g 738 3188 M -8 20 V .14 g 730 3208 M -8 20 V .14 g 722 3228 M -8 20 V .14 g 714 3248 M -3 8 V .14 g 711 3256 M -5 13 V .14 g 706 3269 M -8 20 V .14 g 698 3289 M -8 20 V .14 g 690 3309 M -6 16 V .14 g 684 3325 M -2 4 V .14 g 682 3329 M -8 20 V .14 g 674 3349 M -8 20 V .14 g 666 3369 M -8 21 V .14 g 658 3390 M -1 4 V .14 g 657 3394 M -6 16 V .14 g 651 3410 M -8 20 V .14 g 643 3430 M -8 20 V .14 g 635 3450 M -6 14 V .14 g 629 3464 M -2 6 V .14 g 627 3470 M -8 20 V .14 g 619 3490 M -8 20 V .14 g 611 3510 M -7 21 V stroke 604 3531 M .14 g 604 3531 M -2 4 V 0 g .14 g 1551 1797 M .14 g 1551 1797 M -20 20 V .14 g 1531 1817 M -2 3 V .14 g 1529 1820 M -17 18 V .14 g 1512 1838 M -11 10 V .14 g 1501 1848 M -8 10 V .14 g 1493 1858 M -19 19 V .14 g 1474 1877 M 0 1 V .14 g 1474 1878 M -19 20 V .14 g 1455 1898 M -8 9 V .14 g 1447 1907 M -10 11 V .14 g 1437 1918 M -17 20 V .14 g 1420 1938 M -18 21 V .14 g 1402 1959 M -10 11 V .14 g 1392 1970 M -6 9 V .14 g 1386 1979 M -17 20 V .14 g 1369 1999 M -4 5 V .14 g 1365 2004 M -12 15 V .14 g 1353 2019 M -15 19 V .14 g 1338 2038 M -1 1 V .14 g 1337 2039 M -15 20 V .14 g 1322 2059 M -11 15 V .14 g 1311 2074 M -4 5 V .14 g 1307 2079 M -15 21 V .14 g 1292 2100 M -9 11 V .14 g 1283 2111 M -6 9 V .14 g 1277 2120 M -14 20 V .14 g 1263 2140 M -7 10 V .14 g 1256 2150 M -7 10 V .14 g 1249 2160 M -13 20 V .14 g 1236 2180 M -7 11 V .14 g 1229 2191 M -7 9 V .14 g 1222 2200 M -13 21 V .14 g 1209 2221 M -7 12 V .14 g 1202 2233 M -6 8 V .14 g 1196 2241 M -12 20 V .14 g 1184 2261 M -10 15 V .14 g 1174 2276 M -3 5 V .14 g 1171 2281 M -12 20 V .14 g 1159 2301 M -12 20 V .14 g .14 g 1147 2321 M -12 20 V .14 g 1135 2341 M -11 21 V .14 g 1124 2362 M -4 6 V .14 g 1120 2368 M -8 14 V .14 g 1112 2382 M -11 20 V .14 g 1101 2402 M -8 15 V .14 g 1093 2417 M -3 5 V .14 g 1090 2422 M -11 20 V .14 g 1079 2442 M -11 20 V .14 g 1068 2462 M -3 5 V .14 g 1065 2467 M -8 16 V .14 g 1057 2483 M -10 20 V stroke 1047 2503 M .14 g 1047 2503 M -9 16 V .14 g 1038 2519 M -2 4 V .14 g 1036 2523 M -10 20 V .14 g 1026 2543 M -10 20 V .14 g 1016 2563 M -5 10 V .14 g 1011 2573 M -5 10 V .14 g 1006 2583 M -10 21 V .14 g 996 2604 M -10 20 V .14 g 986 2624 M -2 4 V .14 g 984 2628 M -8 16 V .14 g 976 2644 M -10 20 V .14 g 966 2664 M -10 20 V .14 g 956 2684 M 0 1 V .14 g 956 2685 M -9 19 V .14 g 947 2704 M -9 20 V .14 g 938 2724 M -9 19 V .14 g 929 2743 M -1 2 V .14 g 928 2745 M -9 20 V .14 g 919 2765 M -9 20 V .14 g 910 2785 M -8 18 V .14 g 902 2803 M -1 2 V .14 g 901 2805 M -9 20 V .14 g 892 2825 M -9 20 V .14 g 883 2845 M -8 19 V .14 g 875 2864 M -1 2 V .14 g 874 2866 M -9 20 V .14 g 865 2886 M -9 20 V .14 g 856 2906 M -9 20 V .14 g .14 g 847 2926 M -8 20 V .14 g 839 2946 M -9 20 V .14 g 830 2966 M -8 20 V .14 g 822 2986 M -2 4 V .14 g 820 2990 M -7 17 V .14 g 813 3007 M -8 20 V .14 g 805 3027 M -9 20 V .14 g 796 3047 M -3 8 V .14 g 793 3055 M -5 12 V .14 g 788 3067 M -8 20 V .14 g 780 3087 M -9 20 V .14 g 771 3107 M -6 14 V .14 g 765 3121 M -2 7 V .14 g 763 3128 M -8 20 V .14 g 755 3148 M -8 20 V .14 g 747 3168 M -9 20 V .14 g 0 g .14 g 2568 588 M .14 g 2568 588 M -4 4 V .14 g 2564 592 M -14 16 V .14 g 2550 608 M -13 15 V .14 g 2537 623 M -5 5 V .14 g 2532 628 M -17 20 V .14 g 2515 648 M -5 7 V .14 g 2510 655 M -11 14 V .14 g 2499 669 M -17 19 V stroke 2482 688 M .14 g 2482 688 M 0 1 V .14 g 2482 689 M -16 20 V .14 g 2466 709 M -11 14 V .14 g 2455 723 M -5 6 V .14 g 2450 729 M -16 20 V .14 g 2434 749 M -6 9 V .14 g 2428 758 M -9 11 V .14 g 2419 769 M -15 21 V .14 g 2404 790 M -3 4 V .14 g 2401 794 M -12 16 V .14 g 2389 810 M -16 20 V .14 g .14 g 2373 830 M -14 20 V .14 g 2359 850 M -13 17 V .14 g 2346 867 M -2 3 V .14 g 2344 870 M -15 20 V .14 g 2329 890 M -10 15 V .14 g 2319 905 M -4 5 V .14 g 2315 910 M -15 21 V .14 g 2300 931 M -8 11 V .14 g 2292 942 M -7 9 V .14 g 2285 951 M -14 20 V .14 g 2271 971 M -7 9 V .14 g 2264 980 M -8 11 V .14 g 2256 991 M -14 20 V .14 g 2242 1011 M -5 7 V .14 g 2237 1018 M -10 13 V .14 g 2227 1031 M -14 21 V .14 g 2213 1052 M -3 4 V .14 g 2210 1056 M -12 16 V .14 g 2198 1072 M -14 20 V .14 g 2184 1092 M -1 2 V .14 g 2183 1094 M -14 18 V .14 g 2169 1112 M -14 19 V .14 g 2155 1131 M -1 1 V .14 g 2154 1132 M -15 20 V .14 g 2139 1152 M -11 16 V .14 g 2128 1168 M -4 4 V .14 g 2124 1172 M -15 21 V .14 g 2109 1193 M -8 11 V .14 g 2101 1204 M -7 9 V .14 g 2094 1213 M -16 20 V .14 g 2078 1233 M -4 6 V .14 g 2074 1239 M -11 14 V .14 g 2063 1253 M -16 20 V .14 g 2047 1273 M -1 1 V .14 g 2046 1274 M -15 19 V .14 g 2031 1293 M -12 15 V .14 g 2019 1308 M -4 6 V .14 g 2015 1314 M -17 20 V .14 g 1998 1334 M -6 8 V .14 g 1992 1342 M -10 12 V .14 g 1982 1354 M -17 20 V stroke 1965 1374 M .14 g .14 g 1965 1374 M -18 20 V .14 g 1947 1394 M -10 12 V .14 g 1937 1406 M -7 8 V .14 g 1930 1414 M -18 21 V .14 g 1912 1435 M -2 2 V .14 g 1910 1437 M -16 18 V .14 g 1894 1455 M -11 12 V .14 g 1883 1467 M -8 8 V .14 g 1875 1475 M -19 20 V .14 g 1856 1495 M 0 1 V .14 g 1856 1496 M -19 19 V .14 g 1837 1515 M -9 10 V .14 g 1828 1525 M -10 10 V .14 g 1818 1535 M -17 17 V .14 g 1801 1552 M -3 3 V .14 g 1798 1555 M -20 21 V .14 g 1778 1576 M -4 4 V .14 g 1774 1580 M -16 16 V .14 g 1758 1596 M -11 11 V .14 g 1747 1607 M -10 9 V .14 g 1737 1616 M -18 17 V .14 g 1719 1633 M -3 3 V .14 g 1716 1636 M -20 20 V .14 g 1696 1656 M -4 4 V .14 g 1692 1660 M -17 16 V .14 g 1675 1676 M -10 10 V .14 g 1665 1686 M -11 11 V .14 g 1654 1697 M -16 15 V .14 g 1638 1712 M -5 5 V .14 g 1633 1717 M -21 20 V .14 g 1612 1737 M -2 2 V .14 g 1610 1739 M -18 18 V .14 g 1592 1757 M -9 8 V .14 g 1583 1765 M -12 12 V .14 g 1571 1777 M -15 15 V .14 g 1556 1792 M -5 5 V .0005 g .14 g 2809 3742 M .14 g 2809 3742 M -18 10 V .14 g 2791 3752 M -9 5 V .14 g 2782 3757 M -27 15 V .14 g 2755 3772 M -1 0 V .14 g 2754 3772 M -26 14 V .14 g 2728 3786 M -15 7 V .14 g 2713 3793 M -13 6 V .14 g 2700 3799 M -27 13 V .14 g 2673 3812 M -2 1 V .14 g 2671 3813 M -25 11 V .14 g 2646 3824 M -21 9 V .14 g 2625 3833 M -6 3 V .14 g 2619 3836 M -28 11 V .14 g 2591 3847 M -14 6 V .14 g 2577 3853 M -13 5 V .14 g 2564 3858 M -27 11 V stroke 2537 3869 M .14 g 2537 3869 M -10 4 V .14 g 2527 3873 M -17 7 V .14 g 2510 3880 M -28 11 V .14 g 2482 3891 M -7 2 V .14 g 2475 3893 M -20 8 V .14 g 2455 3901 M -27 11 V .14 g 2428 3912 M -4 2 V .14 g 2424 3914 M -23 9 V .14 g 2401 3923 M -25 11 V .14 g 2376 3934 M -3 1 V .14 g 2373 3935 M -27 12 V .14 g 2346 3947 M -15 7 V .14 g 2331 3954 M -12 5 V .14 g 2319 3959 M -27 14 V .14 g 2292 3973 M -3 1 V .14 g 2289 3974 M -25 13 V .14 g 2264 3987 M -12 7 V .14 g 2252 3994 M -15 8 V .14 g 2237 4002 M -20 12 V .14 g 2217 4014 M -7 5 V .14 g 2210 4019 M -24 16 V .14 g 2186 4035 M -3 2 V .14 g 2183 4037 M -26 18 V .14 g 2157 4055 M -2 1 V .14 g 2155 4056 M -25 19 V .14 g 2130 4075 M -2 1 V .14 g 2128 4076 M -23 19 V .14 g 2105 4095 M -4 4 V .14 g 2101 4099 M -19 16 V .14 g 2082 4115 M -8 7 V .14 g 2074 4122 M -14 13 V .14 g 2060 4135 M -14 13 V .14 g 2046 4148 M -7 7 V .14 g 2039 4155 M -20 20 V .14 g 2019 4175 M 0 1 V .14 g 2019 4176 M -19 20 V .14 g 2000 4196 M -8 9 V .14 g 1992 4205 M -10 11 V .14 g 1982 4216 M -17 20 V .14 g 1965 4236 M -1 0 V .14 g 1964 4236 M -16 20 V .14 g 1948 4256 M -11 13 V .14 g 1937 4269 M -6 7 V .14 g 1931 4276 M -15 21 V .14 g 1916 4297 M -6 7 V .14 g 1910 4304 M -10 13 V .14 g 1900 4317 M -15 20 V .14 g 1885 4337 M -2 4 V .14 g 1883 4341 M -12 16 V .14 g 1871 4357 M -14 20 V .14 g 1857 4377 M -1 2 V .14 g 1856 4379 M -13 18 V stroke 1843 4397 M .14 g 1843 4397 M -13 20 V .14 g 1830 4417 M -2 2 V .14 g 1828 4419 M -12 19 V .14 g 1816 4438 M -13 20 V .14 g 1803 4458 M -2 3 V .14 g 1801 4461 M -10 17 V .14 g 1791 4478 M -13 20 V .14 g 1778 4498 M -4 7 V .14 g 1774 4505 M -8 13 V .14 g 1766 4518 M -13 20 V .14 g 1753 4538 M -6 12 V .14 g 1747 4550 M -6 9 V .14 g 1741 4559 M -11 20 V .14 g 1730 4579 M -11 17 V .14 g 1719 4596 M -1 3 V .14 g 1718 4599 M -12 20 V 0 g .14 g 4302 3611 M .14 g 4302 3611 M -21 -17 V .14 g 4281 3594 M -4 -3 V .14 g 4277 3591 M -23 -19 V .14 g 4254 3572 M -2 -1 V .14 g 4252 3571 M -25 -20 V .14 g 4227 3551 M -1 -1 V .14 g 4226 3550 M -24 -19 V .14 g 4202 3531 M -3 -3 V .14 g 4199 3528 M -22 -18 V .14 g 4177 3510 M -5 -4 V .14 g 4172 3506 M -20 -16 V .14 g 4152 3490 M -7 -6 V .14 g 4145 3484 M -19 -14 V .14 g 4126 3470 M -9 -7 V .14 g 4117 3463 M -16 -13 V .14 g 4101 3450 M -11 -8 V .14 g 4090 3442 M -15 -12 V .14 g 4075 3430 M -12 -9 V .14 g 4063 3421 M -15 -11 V .14 g 4048 3410 M -12 -9 V .14 g 4036 3401 M -16 -11 V .14 g 4020 3390 M -12 -9 V .14 g 4008 3381 M -17 -12 V .14 g 3991 3369 M -10 -7 V .14 g 3981 3362 M -21 -13 V .14 g 3960 3349 M -6 -4 V .14 g 3954 3345 M -27 -16 V .14 g 3927 3329 M 0 -1 V .14 g 3927 3328 M -28 -15 V .14 g 3899 3313 M -8 -4 V .14 g 3891 3309 M -19 -10 V .14 g 3872 3299 M -23 -10 V .14 g 3849 3289 M -4 -2 V .14 g 3845 3287 M -27 -11 V .14 g 3818 3276 M -23 -7 V .14 g 3795 3269 M -5 -2 V stroke 3790 3267 M .14 g 3790 3267 M -27 -7 V .14 g 3763 3260 M -27 -6 V .14 g 3736 3254 M -27 -4 V .14 g 3709 3250 M -27 -2 V .14 g 3682 3248 M -1 0 V .14 g 3681 3248 M -27 0 V .14 g 3654 3248 M -1 0 V .14 g 3653 3248 M -26 2 V .14 g 3627 3250 M -27 4 V .14 g 3600 3254 M -28 5 V .14 g 3572 3259 M -27 8 V .14 g 3545 3267 M -6 2 V .14 g 3539 3269 M -21 7 V .14 g 3518 3276 M -27 10 V .14 g 3491 3286 M -6 3 V .14 g 3485 3289 M -22 9 V .14 g 3463 3298 M -21 11 V .14 g 3442 3309 M -6 3 V .14 g 3436 3312 M -27 15 V .14 g 3409 3327 M -4 2 V .14 g 3405 3329 M -23 14 V .14 g 3382 3343 M -11 6 V .14 g 3371 3349 M -17 11 V .14 g 3354 3360 M -15 9 V .14 g 3339 3369 M -12 8 V .14 g 3327 3377 M -18 13 V .14 g 3309 3390 M -9 6 V .14 g 3300 3396 M -19 14 V .14 g 3281 3410 M -8 5 V .14 g 3273 3415 M -20 15 V .14 g 3253 3430 M -8 5 V .14 g 3245 3435 M -20 15 V .14 g 3225 3450 M -7 6 V .14 g 3218 3456 M -19 14 V .14 g 3199 3470 M -8 6 V .14 g 3191 3476 M -19 14 V .14 g 3172 3490 M -8 7 V .14 g 3164 3497 M -18 13 V .14 g 3146 3510 M -10 8 V .14 g 3136 3518 M -17 13 V .14 g 3119 3531 M -10 7 V .14 g 3109 3538 M -16 13 V .14 g 3093 3551 M -11 8 V .14 g 3082 3559 M -16 12 V .14 g 3066 3571 M -11 8 V .14 g 3055 3579 M -16 12 V .14 g 3039 3591 M -12 8 V .14 g 3027 3599 M -16 12 V .14 g 3011 3611 M -11 8 V .14 g 3000 3619 M -17 12 V .14 g 2983 3631 M -10 7 V .14 g 2973 3638 M -19 14 V stroke 2954 3652 M .14 g 2954 3652 M -8 5 V .14 g 2946 3657 M -22 15 V .14 g 2924 3672 M -6 3 V .14 g 2918 3675 M -25 17 V .14 g 2893 3692 M -2 1 V .14 g 2891 3693 M -27 17 V .14 g 2864 3710 M -4 2 V .14 g 2860 3712 M -23 14 V .14 g 2837 3726 M -10 6 V .14 g 2827 3732 M -18 10 V 0 g .14 g 5594 4619 M .14 g 5594 4619 M -5 -9 V .14 g 5589 4610 M -7 -11 V .14 g 5582 4599 M -12 -20 V .14 g 5570 4579 M -8 -14 V .14 g 5562 4565 M -4 -6 V .14 g 5558 4559 M -13 -21 V .14 g 5545 4538 M -11 -17 V .14 g 5534 4521 M -1 -3 V .14 g 5533 4518 M -13 -20 V .14 g 5520 4498 M -13 -19 V .14 g 5507 4479 M 0 -1 V .14 g 5507 4478 M -14 -20 V .14 g 5493 4458 M -13 -20 V .14 g 5480 4438 M -1 0 V .14 g 5479 4438 M -14 -21 V .14 g 5465 4417 M -12 -17 V .14 g 5453 4400 M -2 -3 V .14 g 5451 4397 M -15 -20 V .14 g 5436 4377 M -11 -14 V .14 g 5425 4363 M -4 -6 V .14 g 5421 4357 M -16 -20 V .14 g 5405 4337 M -7 -9 V .14 g 5398 4328 M -9 -11 V .14 g 5389 4317 M -17 -20 V .14 g 5372 4297 M -1 -2 V .14 g 5371 4295 M -16 -19 V .14 g 5355 4276 M -11 -12 V .14 g 5344 4264 M -7 -8 V .14 g 5337 4256 M -19 -20 V .14 g 5318 4236 M -2 -2 V .14 g 5316 4234 M -18 -18 V .14 g 5298 4216 M -9 -9 V .14 g 5289 4207 M -12 -11 V .14 g 5277 4196 M -15 -15 V .14 g 5262 4181 M -6 -5 V .14 g 5256 4176 M -21 -19 V .14 g 5235 4157 M -2 -2 V .14 g 5233 4155 M -25 -20 V .14 g 5208 4135 M -1 0 V .14 g 5207 4135 M -25 -20 V .14 g 5182 4115 M -2 -1 V .14 g 5180 4114 M -26 -19 V stroke 5154 4095 M .14 g 5154 4095 M -1 -1 V .14 g 5153 4094 M -27 -18 V .14 g 5126 4076 M -3 -1 V .14 g 5123 4075 M -25 -16 V .14 g 5098 4059 M -7 -4 V .14 g 5091 4055 M -20 -12 V .14 g 5071 4043 M -16 -8 V .14 g 5055 4035 M -11 -7 V .14 g 5044 4028 M -27 -14 V .14 g .14 g 5017 4014 M -28 -13 V .14 g 4989 4001 M -13 -7 V .14 g 4976 3994 M -14 -6 V .14 g 4962 3988 M -27 -13 V .14 g 4935 3975 M -3 -1 V .14 g 4932 3974 M -24 -11 V .14 g 4908 3963 M -21 -9 V .14 g 4887 3954 M -7 -3 V .14 g 4880 3951 M -27 -12 V .14 g 4853 3939 M -12 -5 V .14 g 4841 3934 M -15 -7 V .14 g 4826 3927 M -27 -12 V .14 g 4799 3915 M -3 -1 V .14 g 4796 3914 M -25 -11 V .14 g 4771 3903 M -20 -10 V .14 g 4751 3893 M -7 -3 V .14 g 4744 3890 M -27 -13 V .14 g 4717 3877 M -8 -4 V .14 g 4709 3873 M -19 -9 V .14 g 4690 3864 M -21 -11 V .14 g 4669 3853 M -7 -3 V .14 g 4662 3850 M -27 -15 V .14 g 4635 3835 M -5 -2 V .14 g 4630 3833 M -22 -13 V .14 g 4608 3820 M -14 -7 V .14 g 4594 3813 M -13 -8 V .14 g 4581 3805 M -21 -12 V .14 g 4560 3793 M -7 -4 V .14 g 4553 3789 M -26 -17 V .14 g 4527 3772 M -1 0 V .14 g 4526 3772 M -27 -18 V .14 g 4499 3754 M -3 -2 V .14 g 4496 3752 M -24 -16 V .14 g 4472 3736 M -6 -4 V .14 g 4466 3732 M -22 -14 V .14 g 4444 3718 M -7 -6 V .14 g 4437 3712 M -20 -14 V .14 g 4417 3698 M -9 -6 V .14 g 4408 3692 M -18 -14 V .14 g 4390 3678 M -9 -6 V .14 g 4381 3672 M -18 -14 V .14 g 4363 3658 M -9 -6 V .14 g 4354 3652 M -19 -15 V stroke 4335 3637 M .14 g 4335 3637 M -7 -6 V .14 g 4328 3631 M -20 -15 V .14 g 4308 3616 M -6 -5 V 0 g .14 g 5022 951 M .14 g 5022 951 M -5 -8 V .14 g 5017 943 M -9 -12 V .14 g 5008 931 M -14 -21 V .14 g 4994 910 M -5 -6 V .14 g 4989 904 M -10 -14 V .14 g 4979 890 M -14 -20 V .14 g 4965 870 M -3 -4 V .14 g 4962 866 M -12 -16 V .14 g 4950 850 M -15 -20 V .14 g 4935 830 M 0 -1 V .14 g 4935 829 M -15 -19 V .14 g 4920 810 M -12 -18 V .14 g 4908 792 M -3 -2 V .14 g 4905 790 M -15 -21 V .14 g 4890 769 M -10 -12 V .14 g 4880 757 M -5 -8 V .14 g 4875 749 M -16 -20 V .14 g 4859 729 M -6 -7 V .14 g 4853 722 M -10 -13 V .14 g 4843 709 M -17 -20 V .14 g 4826 689 M 0 -1 V .14 g 4826 688 M -16 -19 V .14 g 4810 669 M -11 -14 V .14 g 4799 655 M -7 -7 V .14 g 4792 648 M -17 -20 V .14 g 4775 628 M -4 -4 V .14 g 4771 624 M -14 -16 V .14 g 4757 608 M -13 -14 V .14 g 4744 594 M -6 -6 V 0 g .14 g 6052 2198 M .14 g 6052 2198 M -13 -18 V .14 g 6039 2180 M -14 -19 V .14 g 6025 2161 M -1 -1 V .14 g 6024 2160 M -15 -20 V .14 g 6009 2140 M -11 -16 V .14 g 5998 2124 M -4 -4 V .14 g 5994 2120 M -16 -20 V .14 g 5978 2100 M -8 -10 V .14 g 5970 2090 M -8 -11 V .14 g 5962 2079 M -16 -20 V .14 g 5946 2059 M -3 -3 V .14 g 5943 2056 M -14 -17 V .14 g 5929 2039 M -13 -16 V .14 g 5916 2023 M -4 -4 V .14 g 5912 2019 M -17 -20 V .14 g 5895 1999 M -6 -7 V .14 g 5889 1992 M -12 -13 V .14 g 5877 1979 M -16 -18 V .14 g 5861 1961 M -2 -2 V stroke 5859 1959 M .14 g 5859 1959 M -18 -21 V .14 g 5841 1938 M -7 -7 V .14 g 5834 1931 M -12 -13 V .14 g 5822 1918 M -15 -16 V .14 g 5807 1902 M -4 -4 V .14 g 5803 1898 M -19 -20 V .14 g 5784 1878 M -4 -5 V .14 g 5780 1873 M -16 -15 V .14 g 5764 1858 M -12 -13 V .14 g 5752 1845 M -7 -7 V .14 g 5745 1838 M -20 -20 V .14 g 5725 1818 M 0 -1 V .14 g 5725 1817 M -20 -20 V .14 g 5705 1797 M -7 -7 V .14 g 5698 1790 M -13 -13 V .14 g 5685 1777 M -14 -15 V .14 g 5671 1762 M -6 -5 V .14 g 5665 1757 M -20 -20 V .14 g 5645 1737 M -2 -2 V .14 g 5643 1735 M -18 -18 V .14 g 5625 1717 M -9 -10 V .14 g 5616 1707 M -10 -10 V .14 g 5606 1697 M -17 -18 V .14 g 5589 1679 M -3 -3 V .14 g 5586 1676 M -19 -20 V .14 g 5567 1656 M -5 -6 V .14 g 5562 1650 M -14 -14 V .14 g 5548 1636 M -14 -15 V .14 g 5534 1621 M -5 -5 V .14 g 5529 1616 M -18 -20 V .14 g 5511 1596 M -4 -4 V .14 g 5507 1592 M -15 -16 V .14 g 5492 1576 M -12 -14 V .14 g 5480 1562 M -6 -7 V .14 g 5474 1555 M -17 -20 V .14 g 5457 1535 M -4 -4 V .14 g 5453 1531 M -14 -16 V .14 g 5439 1515 M -14 -16 V .14 g 5425 1499 M -3 -4 V .14 g 5422 1495 M -17 -20 V .14 g 5405 1475 M -7 -9 V .14 g 5398 1466 M -9 -11 V .14 g 5389 1455 M -17 -20 V .14 g 5372 1435 M -1 -2 V .14 g 5371 1433 M -15 -19 V .14 g 5356 1414 M -12 -16 V .14 g 5344 1398 M -4 -4 V .14 g 5340 1394 M -15 -20 V .14 g 5325 1374 M -9 -11 V .14 g 5316 1363 M -7 -9 V .14 g 5309 1354 M -15 -20 V .14 g 5294 1334 M -5 -7 V stroke 5289 1327 M .14 g 5289 1327 M -10 -13 V .14 g 5279 1314 M -15 -21 V .14 g 5264 1293 M -2 -3 V .14 g 5262 1290 M -13 -17 V .14 g 5249 1273 M -14 -20 V .14 g 5235 1253 M -15 -20 V .14 g 5220 1233 M -13 -18 V .14 g 5207 1215 M -1 -2 V .14 g 5206 1213 M -15 -20 V .14 g 5191 1193 M -11 -16 V .14 g 5180 1177 M -3 -5 V .14 g 5177 1172 M -14 -20 V .14 g 5163 1152 M -10 -14 V .14 g 5153 1138 M -4 -6 V .14 g 5149 1132 M -14 -20 V .14 g 5135 1112 M -9 -13 V .14 g 5126 1099 M -6 -7 V .14 g 5120 1092 M -14 -20 V .14 g 5106 1072 M -8 -12 V .14 g 5098 1060 M -6 -8 V .14 g 5092 1052 M -14 -21 V .14 g 5078 1031 M -7 -10 V .14 g 5071 1021 M -7 -10 V .14 g 5064 1011 M -14 -20 V .14 g 5050 991 M -6 -9 V .14 g 5044 982 M -8 -11 V .14 g 5036 971 M -14 -20 V 0 g .12 g 809 3148 M .12 g 809 3148 M -8 20 V .12 g 801 3168 M -8 19 V .12 g 793 3187 M -1 1 V .12 g 792 3188 M -8 20 V .12 g 784 3208 M -8 20 V .12 g 776 3228 M -8 20 V .12 g 768 3248 M -3 6 V .12 g 765 3254 M -5 15 V .12 g 760 3269 M -8 20 V .12 g 752 3289 M -8 20 V .12 g 744 3309 M -6 13 V .12 g 738 3322 M -2 7 V .12 g 736 3329 M -8 20 V .12 g 728 3349 M -8 20 V .12 g 720 3369 M -8 21 V .12 g 712 3390 M -1 1 V .12 g 711 3391 M -7 19 V .12 g 704 3410 M -8 20 V .12 g 696 3430 M -8 20 V .12 g 688 3450 M -4 11 V .12 g 684 3461 M -4 9 V .12 g 680 3470 M -7 20 V .12 g 673 3490 M -8 20 V .12 g 665 3510 M -8 21 V .12 g 657 3531 M 0 1 V stroke 657 3532 M .12 g 657 3532 M -8 19 V .12 g 649 3551 M -8 20 V .12 g 641 3571 M -7 20 V .12 g 634 3591 M -5 12 V .12 g 629 3603 M -3 8 V .12 g 626 3611 M -8 20 V .12 g 618 3631 M -7 21 V .12 g 611 3652 M -8 20 V .12 g 603 3672 M -1 2 V 0 g .12 g 1676 1817 M .12 g 1676 1817 M -11 11 V .12 g 1665 1828 M -11 10 V .12 g 1654 1838 M -16 15 V .12 g 1638 1853 M -6 5 V .12 g 1632 1858 M -22 20 V .12 g .12 g 1610 1878 M -21 20 V .12 g 1589 1898 M -6 5 V .12 g 1583 1903 M -15 15 V .12 g 1568 1918 M -12 11 V .12 g 1556 1929 M -9 9 V .12 g 1547 1938 M -18 18 V .12 g 1529 1956 M -3 3 V .12 g 1526 1959 M -20 20 V .12 g 1506 1979 M -5 4 V .12 g 1501 1983 M -15 16 V .12 g 1486 1999 M -12 12 V .12 g 1474 2011 M -8 8 V .12 g 1466 2019 M -19 20 V .12 g 1447 2039 M 0 1 V .12 g 1447 2040 M -18 19 V .12 g 1429 2059 M -9 11 V .12 g 1420 2070 M -9 9 V .12 g 1411 2079 M -18 21 V .12 g 1393 2100 M -1 1 V .12 g 1392 2101 M -16 19 V .12 g 1376 2120 M -11 13 V .12 g 1365 2133 M -5 7 V .12 g 1360 2140 M -17 20 V .12 g 1343 2160 M -5 7 V .12 g 1338 2167 M -10 13 V .12 g 1328 2180 M -16 20 V .12 g 1312 2200 M -1 2 V .12 g 1311 2202 M -14 19 V .12 g 1297 2221 M -14 18 V .12 g 1283 2239 M -1 2 V .12 g 1282 2241 M -14 20 V .12 g 1268 2261 M -12 16 V .12 g 1256 2277 M -3 4 V .12 g 1253 2281 M -13 20 V .12 g 1240 2301 M -11 16 V .12 g 1229 2317 M -3 4 V .12 g 1226 2321 M -13 20 V .12 g 1213 2341 M -11 18 V stroke 1202 2359 M .12 g 1202 2359 M -2 3 V .12 g 1200 2362 M -13 20 V .12 g 1187 2382 M -13 20 V .12 g .12 g 1174 2402 M -12 20 V .12 g 1162 2422 M -12 20 V .12 g 1150 2442 M -3 5 V .12 g 1147 2447 M -9 15 V .12 g 1138 2462 M -12 21 V .12 g 1126 2483 M -6 11 V .12 g 1120 2494 M -5 9 V .12 g 1115 2503 M -11 20 V .12 g 1104 2523 M -11 19 V .12 g 1093 2542 M -1 1 V .12 g 1092 2543 M -11 20 V .12 g 1081 2563 M -11 20 V .12 g 1070 2583 M -5 10 V .12 g 1065 2593 M -5 11 V .12 g 1060 2604 M -11 20 V .12 g 1049 2624 M -10 20 V .12 g 1039 2644 M -1 1 V .12 g 1038 2645 M -10 19 V .12 g 1028 2664 M -10 20 V .12 g 1018 2684 M -7 15 V .12 g 1011 2699 M -3 5 V .12 g 1008 2704 M -10 20 V .12 g 998 2724 M -10 21 V .12 g 988 2745 M -4 9 V .12 g 984 2754 M -5 11 V .12 g 979 2765 M -10 20 V .12 g 969 2785 M -10 20 V .12 g 959 2805 M -3 7 V .12 g 956 2812 M -6 13 V .12 g 950 2825 M -9 20 V .12 g 941 2845 M -10 21 V .12 g 931 2866 M -2 4 V .12 g 929 2870 M -7 16 V .12 g 922 2886 M -9 20 V .12 g 913 2906 M -9 20 V .12 g 904 2926 M -2 5 V .12 g 902 2931 M -7 15 V .12 g 895 2946 M -9 20 V .12 g 886 2966 M -9 20 V .12 g 877 2986 M -2 7 V .12 g 875 2993 M -6 14 V .12 g 869 3007 M -9 20 V .12 g 860 3027 M -9 20 V .12 g 851 3047 M -4 9 V .12 g 847 3056 M -4 11 V .12 g 843 3067 M -9 20 V .12 g 834 3087 M -8 20 V .12 g 826 3107 M -6 14 V .12 g 820 3121 M -3 7 V stroke 817 3128 M .12 g 817 3128 M -8 20 V 0 g .12 g 2697 588 M .12 g 2697 588 M -23 20 V .12 g 2674 608 M -1 1 V .12 g 2673 609 M -20 19 V .12 g 2653 628 M -7 7 V .12 g 2646 635 M -14 13 V .12 g 2632 648 M -13 14 V .12 g 2619 662 M -6 7 V .12 g 2613 669 M -19 20 V .12 g 2594 689 M -3 2 V .12 g 2591 691 M -15 18 V .12 g 2576 709 M -12 13 V .12 g 2564 722 M -6 7 V .12 g 2558 729 M -18 20 V .12 g 2540 749 M -3 5 V .12 g 2537 754 M -13 15 V .12 g 2524 769 M -14 18 V .12 g 2510 787 M -3 3 V .12 g 2507 790 M -16 20 V .12 g 2491 810 M -9 11 V .12 g 2482 821 M -7 9 V .12 g 2475 830 M -15 20 V .12 g 2460 850 M -5 6 V .12 g 2455 856 M -11 14 V .12 g 2444 870 M -15 20 V .12 g 2429 890 M -1 2 V .12 g 2428 892 M -14 18 V .12 g 2414 910 M -13 19 V .12 g 2401 929 M -1 2 V .12 g 2400 931 M -15 20 V .12 g 2385 951 M -12 16 V .12 g 2373 967 M -3 4 V .12 g 2370 971 M -14 20 V .12 g 2356 991 M -10 14 V .12 g 2346 1005 M -4 6 V .12 g 2342 1011 M -14 20 V .12 g 2328 1031 M -9 13 V .12 g 2319 1044 M -6 8 V .12 g 2313 1052 M -14 20 V .12 g 2299 1072 M -7 11 V .12 g 2292 1083 M -7 9 V .12 g 2285 1092 M -14 20 V .12 g 2271 1112 M -7 10 V .12 g 2264 1122 M -7 10 V .12 g 2257 1132 M -14 20 V .12 g 2243 1152 M -6 9 V .12 g 2237 1161 M -8 11 V .12 g 2229 1172 M -14 21 V .12 g 2215 1193 M -5 7 V .12 g 2210 1200 M -9 13 V .12 g 2201 1213 M -14 20 V .12 g 2187 1233 M -4 6 V stroke 2183 1239 M .12 g 2183 1239 M -11 14 V .12 g 2172 1253 M -14 20 V .12 g 2158 1273 M -3 4 V .12 g 2155 1277 M -12 16 V .12 g 2143 1293 M -14 21 V .12 g 2129 1314 M -1 1 V .12 g 2128 1315 M -14 19 V .12 g 2114 1334 M -13 18 V .12 g 2101 1352 M -2 2 V .12 g 2099 1354 M -15 20 V .12 g 2084 1374 M -10 14 V .12 g 2074 1388 M -5 6 V .12 g 2069 1394 M -16 20 V .12 g 2053 1414 M -7 9 V .12 g 2046 1423 M -9 12 V .12 g 2037 1435 M -15 20 V .12 g 2022 1455 M -3 3 V .12 g 2019 1458 M -14 17 V .12 g 2005 1475 M -13 16 V .12 g 1992 1491 M -3 4 V .12 g 1989 1495 M -17 20 V .12 g 1972 1515 M -7 9 V .12 g 1965 1524 M -10 11 V .12 g 1955 1535 M -18 20 V .12 g 1937 1555 M 0 1 V .12 g 1937 1556 M -17 20 V .12 g 1920 1576 M -10 10 V .12 g 1910 1586 M -9 10 V .12 g 1901 1596 M -18 20 V .12 g .12 g 1883 1616 M -19 20 V .12 g 1864 1636 M -8 9 V .12 g 1856 1645 M -12 11 V .12 g 1844 1656 M -16 16 V .12 g 1828 1672 M -4 4 V .12 g 1824 1676 M -20 21 V .12 g 1804 1697 M -3 3 V .12 g 1801 1700 M -18 17 V .12 g 1783 1717 M -9 9 V .12 g 1774 1726 M -12 11 V .12 g 1762 1737 M -15 15 V .12 g 1747 1752 M -6 5 V .12 g 1741 1757 M -21 20 V .12 g 1720 1777 M -1 0 V .12 g 1719 1777 M -21 20 V .12 g 1698 1797 M -6 6 V .12 g 1692 1803 M -16 14 V 0 g .12 g 1672 4538 M .12 g 1672 4538 M -7 13 V .12 g 1665 4551 M -4 8 V .12 g 1661 4559 M -11 20 V .12 g 1650 4579 M -11 20 V .12 g 1639 4599 M -1 3 V .12 g 1638 4602 M -9 17 V stroke 1629 4619 M 0 g .12 g 2973 3511 M .12 g 2973 3511 M -27 20 V .12 g .12 g 2946 3531 M -28 18 V .12 g 2918 3549 M -2 2 V .12 g 2916 3551 M -25 16 V .12 g 2891 3567 M -6 4 V .12 g 2885 3571 M -21 13 V .12 g 2864 3584 M -11 7 V .12 g 2853 3591 M -16 10 V .12 g 2837 3601 M -18 10 V .12 g 2819 3611 M -10 6 V .12 g 2809 3617 M -26 14 V .12 g 2783 3631 M -1 1 V .12 g 2782 3632 M -27 14 V .12 g 2755 3646 M -11 6 V .12 g 2744 3652 M -16 8 V .12 g 2728 3660 M -26 12 V .12 g 2702 3672 M -2 1 V .12 g 2700 3673 M -27 12 V .12 g 2673 3685 M -16 7 V .12 g 2657 3692 M -11 5 V .12 g 2646 3697 M -27 11 V .12 g 2619 3708 M -11 4 V .12 g 2608 3712 M -17 7 V .12 g 2591 3719 M -27 10 V .12 g 2564 3729 M -9 3 V .12 g 2555 3732 M -18 7 V .12 g 2537 3739 M -27 10 V .12 g 2510 3749 M -11 3 V .12 g 2499 3752 M -17 6 V .12 g 2482 3758 M -27 10 V .12 g 2455 3768 M -13 4 V .12 g 2442 3772 M -14 6 V .12 g 2428 3778 M -27 10 V .12 g 2401 3788 M -14 5 V .12 g 2387 3793 M -14 5 V .12 g 2373 3798 M -27 11 V .12 g 2346 3809 M -10 4 V .12 g 2336 3813 M -17 7 V .12 g 2319 3820 M -27 12 V .12 g 2292 3832 M -2 1 V .12 g 2290 3833 M -26 12 V .12 g 2264 3845 M -15 8 V .12 g 2249 3853 M -12 6 V .12 g 2237 3859 M -24 14 V .12 g 2213 3873 M -3 2 V .12 g 2210 3875 M -27 16 V .12 g 2183 3891 M -3 2 V .12 g 2180 3893 M -25 17 V .12 g 2155 3910 M -5 4 V .12 g 2150 3914 M -22 15 V .12 g 2128 3929 M -6 5 V .12 g 2122 3934 M -21 17 V stroke 2101 3951 M .12 g 2101 3951 M -4 3 V .12 g 2097 3954 M -23 20 V .12 g 2074 3974 M -1 0 V .12 g 2073 3974 M -22 20 V .12 g 2051 3994 M -5 5 V .12 g 2046 3999 M -15 15 V .12 g 2031 4014 M -12 12 V .12 g 2019 4026 M -8 9 V .12 g 2011 4035 M -19 20 V .12 g .12 g 1992 4055 M -18 20 V .12 g 1974 4075 M -9 11 V .12 g 1965 4086 M -8 9 V .12 g 1957 4095 M -16 20 V .12 g 1941 4115 M -4 4 V .12 g 1937 4119 M -12 16 V .12 g 1925 4135 M -15 19 V .12 g 1910 4154 M -1 1 V .12 g 1909 4155 M -15 21 V .12 g 1894 4176 M -11 15 V .12 g 1883 4191 M -3 5 V .12 g 1880 4196 M -14 20 V .12 g 1866 4216 M -10 14 V .12 g 1856 4230 M -4 6 V .12 g 1852 4236 M -14 20 V .12 g 1838 4256 M -10 15 V .12 g 1828 4271 M -3 5 V .12 g 1825 4276 M -13 21 V .12 g 1812 4297 M -11 17 V .12 g 1801 4314 M -2 3 V .12 g 1799 4317 M -12 20 V .12 g 1787 4337 M -12 20 V .12 g 1775 4357 M -1 2 V .12 g 1774 4359 M -11 18 V .12 g 1763 4377 M -12 20 V .12 g 1751 4397 M -4 8 V .12 g 1747 4405 M -8 12 V .12 g 1739 4417 M -11 21 V .12 g 1728 4438 M -9 14 V .12 g 1719 4452 M -3 6 V .12 g 1716 4458 M -11 20 V .12 g 1705 4478 M -11 20 V .12 g 1694 4498 M -2 3 V .12 g 1692 4501 M -9 17 V .12 g 1683 4518 M -11 20 V 0 g .12 g 4417 3572 M .12 g 4417 3572 M -1 -1 V .12 g 4416 3571 M -26 -19 V .12 g 4390 3552 M -1 -1 V .12 g 4389 3551 M -26 -20 V .12 g 4363 3531 M -1 0 V .12 g 4362 3531 M -25 -21 V .12 g 4337 3510 M -2 -1 V .12 g 4335 3509 M -23 -19 V stroke 4312 3490 M .12 g 4312 3490 M -4 -3 V .12 g 4308 3487 M -21 -17 V .12 g 4287 3470 M -6 -5 V .12 g 4281 3465 M -18 -15 V .12 g 4263 3450 M -9 -8 V .12 g 4254 3442 M -15 -12 V .12 g 4239 3430 M -13 -11 V .12 g 4226 3419 M -11 -9 V .12 g 4215 3410 M -16 -14 V .12 g 4199 3396 M -8 -6 V .12 g 4191 3390 M -19 -17 V .12 g 4172 3373 M -5 -4 V .12 g 4167 3369 M -22 -19 V .12 g 4145 3350 M -2 -1 V .12 g 4143 3349 M -24 -20 V .12 g 4119 3329 M -2 -2 V .12 g 4117 3327 M -22 -18 V .12 g 4095 3309 M -5 -4 V .12 g 4090 3305 M -20 -16 V .12 g 4070 3289 M -7 -6 V .12 g 4063 3283 M -18 -14 V .12 g 4045 3269 M -9 -8 V .12 g 4036 3261 M -18 -13 V .12 g 4018 3248 M -10 -7 V .12 g 4008 3241 M -17 -13 V .12 g 3991 3228 M -10 -7 V .12 g 3981 3221 M -19 -13 V .12 g 3962 3208 M -8 -6 V .12 g 3954 3202 M -22 -14 V .12 g 3932 3188 M -5 -3 V .12 g 3927 3185 M -28 -17 V .12 g 3899 3168 M -1 0 V .12 g 3898 3168 M -26 -15 V .12 g 3872 3153 M -12 -5 V .12 g 3860 3148 M -15 -8 V .12 g 3845 3140 M -27 -12 V .12 g 3818 3128 M -3 0 V .12 g 3815 3128 M -25 -9 V .12 g 3790 3119 M -27 -8 V .12 g 3763 3111 M -15 -4 V .12 g 3748 3107 M -12 -2 V .12 g 3736 3105 M -27 -4 V .12 g 3709 3101 M -28 -2 V .12 g 3681 3099 M -27 0 V .12 g 3654 3099 M -27 2 V .12 g 3627 3101 M -27 4 V .12 g 3600 3105 M -12 2 V .12 g 3588 3107 M -16 4 V .12 g 3572 3111 M -27 8 V .12 g 3545 3119 M -24 9 V .12 g 3521 3128 M -3 1 V .12 g 3518 3129 M -27 11 V stroke 3491 3140 M .12 g 3491 3140 M -17 8 V .12 g 3474 3148 M -11 5 V .12 g 3463 3153 M -27 15 V .12 g .12 g 3436 3168 M -27 15 V .12 g 3409 3183 M -7 5 V .12 g 3402 3188 M -20 13 V .12 g 3382 3201 M -12 7 V .12 g 3370 3208 M -16 11 V .12 g 3354 3219 M -13 9 V .12 g 3341 3228 M -14 10 V .12 g 3327 3238 M -14 10 V .12 g 3313 3248 M -13 10 V .12 g 3300 3258 M -15 11 V .12 g 3285 3269 M -12 9 V .12 g 3273 3278 M -14 11 V .12 g 3259 3289 M -14 10 V .12 g 3245 3299 M -12 10 V .12 g 3233 3309 M -15 12 V .12 g 3218 3321 M -10 8 V .12 g 3208 3329 M -17 14 V .12 g 3191 3343 M -9 6 V .12 g 3182 3349 M -18 15 V .12 g 3164 3364 M -7 5 V .12 g 3157 3369 M -21 17 V .12 g 3136 3386 M -4 4 V .12 g 3132 3390 M -23 18 V .12 g 3109 3408 M -2 2 V .12 g 3107 3410 M -25 19 V .12 g 3082 3429 M -1 1 V .12 g 3081 3430 M -26 20 V .12 g 3055 3450 M 0 1 V .12 g 3055 3451 M -26 19 V .12 g 3029 3470 M -2 1 V .12 g 3027 3471 M -25 19 V .12 g 3002 3490 M -2 2 V .12 g 3000 3492 M -26 18 V .12 g 2974 3510 M -1 1 V 0 g .12 g 5674 4619 M .12 g 5674 4619 M -3 -7 V .12 g 5671 4612 M -7 -13 V .12 g 5664 4599 M -11 -20 V .12 g 5653 4579 M -10 -18 V .12 g 5643 4561 M -1 -2 V .12 g 5642 4559 M -11 -21 V .12 g 5631 4538 M -11 -20 V .12 g 5620 4518 M -4 -6 V .12 g 5616 4512 M -8 -14 V .12 g 5608 4498 M -11 -20 V .12 g 5597 4478 M -8 -14 V .12 g 5589 4464 M -4 -6 V .12 g 5585 4458 M -12 -20 V .12 g 5573 4438 M -11 -20 V .12 g 5562 4418 M -1 -1 V stroke 5561 4417 M .12 g 5561 4417 M -12 -20 V .12 g 5549 4397 M -12 -20 V .12 g 5537 4377 M -3 -4 V .12 g 5534 4373 M -10 -16 V .12 g 5524 4357 M -13 -20 V .12 g 5511 4337 M -4 -7 V .12 g 5507 4330 M -9 -13 V .12 g 5498 4317 M -13 -20 V .12 g 5485 4297 M -5 -8 V .12 g 5480 4289 M -9 -13 V .12 g 5471 4276 M -14 -20 V .12 g 5457 4256 M -4 -6 V .12 g 5453 4250 M -11 -14 V .12 g 5442 4236 M -15 -20 V .12 g 5427 4216 M -2 -3 V .12 g 5425 4213 M -13 -17 V .12 g 5412 4196 M -14 -18 V .12 g 5398 4178 M -2 -2 V .12 g 5396 4176 M -17 -21 V .12 g 5379 4155 M -8 -10 V .12 g 5371 4145 M -9 -10 V .12 g 5362 4135 M -18 -20 V .12 g 5344 4115 M 0 -1 V .12 g 5344 4114 M -18 -19 V .12 g 5326 4095 M -10 -10 V .12 g 5316 4085 M -10 -10 V .12 g 5306 4075 M -17 -17 V .12 g 5289 4058 M -4 -3 V .12 g 5285 4055 M -22 -20 V .12 g 5263 4035 M -1 -2 V .12 g 5262 4033 M -22 -19 V .12 g 5240 4014 M -5 -4 V .12 g 5235 4010 M -20 -16 V .12 g 5215 3994 M -8 -6 V .12 g 5207 3988 M -19 -14 V .12 g 5188 3974 M -8 -6 V .12 g 5180 3968 M -21 -14 V .12 g 5159 3954 M -6 -4 V .12 g 5153 3950 M -26 -16 V .12 g 5127 3934 M -1 -1 V .12 g 5126 3933 M -28 -16 V .12 g 5098 3917 M -6 -3 V .12 g 5092 3914 M -21 -12 V .12 g 5071 3902 M -17 -9 V .12 g 5054 3893 M -10 -5 V .12 g 5044 3888 M -27 -12 V .12 g 5017 3876 M -6 -3 V .12 g 5011 3873 M -22 -10 V .12 g 4989 3863 M -23 -10 V .12 g 4966 3853 M -4 -1 V .12 g 4962 3852 M -27 -12 V .12 g 4935 3840 M -18 -7 V stroke 4917 3833 M .12 g 4917 3833 M -9 -4 V .12 g 4908 3829 M -28 -11 V .12 g 4880 3818 M -13 -5 V .12 g 4867 3813 M -14 -6 V .12 g 4853 3807 M -27 -11 V .12 g 4826 3796 M -9 -3 V .12 g 4817 3793 M -18 -8 V .12 g 4799 3785 M -28 -11 V .12 g 4771 3774 M -2 -2 V .12 g 4769 3772 M -25 -10 V .12 g 4744 3762 M -21 -10 V .12 g 4723 3752 M -6 -3 V .12 g 4717 3749 M -27 -12 V .12 g 4690 3737 M -10 -5 V .12 g 4680 3732 M -18 -9 V .12 g 4662 3723 M -22 -11 V .12 g 4640 3712 M -5 -3 V .12 g 4635 3709 M -27 -14 V .12 g 4608 3695 M -5 -3 V .12 g 4603 3692 M -22 -13 V .12 g 4581 3679 M -13 -7 V .12 g 4568 3672 M -15 -9 V .12 g 4553 3663 M -19 -11 V .12 g 4534 3652 M -8 -6 V .12 g 4526 3646 M -23 -15 V .12 g 4503 3631 M -4 -2 V .12 g 4499 3629 M -26 -18 V .12 g 4473 3611 M -1 0 V .12 g 4472 3611 M -28 -19 V .12 g 4444 3592 M 0 -1 V .12 g 4444 3591 M -27 -19 V 0 g .12 g 5037 1112 M .12 g 5037 1112 M -13 -20 V .12 g 5024 1092 M -7 -11 V .12 g 5017 1081 M -7 -9 V .12 g 5010 1072 M -14 -20 V .12 g 4996 1052 M -7 -10 V .12 g 4989 1042 M -7 -11 V .12 g 4982 1031 M -14 -20 V .12 g 4968 1011 M -6 -9 V .12 g 4962 1002 M -8 -11 V .12 g 4954 991 M -14 -20 V .12 g 4940 971 M -5 -7 V .12 g 4935 964 M -10 -13 V .12 g 4925 951 M -14 -20 V .12 g 4911 931 M -3 -5 V .12 g 4908 926 M -12 -16 V .12 g 4896 910 M -15 -20 V .12 g 4881 890 M -1 -1 V .12 g 4880 889 M -14 -19 V .12 g 4866 870 M -13 -17 V .12 g 4853 853 M -3 -3 V .12 g 4850 850 M -15 -20 V stroke 4835 830 M .12 g 4835 830 M -9 -11 V .12 g 4826 819 M -8 -9 V .12 g 4818 810 M -16 -20 V .12 g 4802 790 M -3 -5 V .12 g 4799 785 M -14 -16 V .12 g 4785 769 M -14 -16 V .12 g 4771 753 M -3 -4 V .12 g 4768 749 M -18 -20 V .12 g 4750 729 M -6 -7 V .12 g 4744 722 M -12 -13 V .12 g 4732 709 M -15 -16 V .12 g 4717 693 M -4 -4 V .12 g 4713 689 M -20 -20 V .12 g 4693 669 M -3 -4 V .12 g 4690 665 M -18 -17 V .12 g 4672 648 M -10 -9 V .12 g 4662 639 M -12 -11 V .12 g 4650 628 M -15 -13 V .12 g 4635 615 M -8 -7 V .12 g 4627 608 M -19 -16 V .12 g 4608 592 M -6 -4 V 0 g .12 g 6052 2326 M .12 g 6052 2326 M -4 -5 V .12 g 6048 2321 M -15 -20 V .12 g 6033 2301 M -8 -12 V .12 g 6025 2289 M -7 -8 V .12 g 6018 2281 M -15 -20 V .12 g 6003 2261 M -5 -7 V .12 g 5998 2254 M -11 -13 V .12 g 5987 2241 M -16 -20 V .12 g 5971 2221 M -1 -1 V .12 g 5970 2220 M -16 -20 V .12 g 5954 2200 M -11 -13 V .12 g 5943 2187 M -6 -7 V .12 g 5937 2180 M -17 -20 V .12 g 5920 2160 M -4 -5 V .12 g 5916 2155 M -14 -15 V .12 g 5902 2140 M -13 -15 V .12 g 5889 2125 M -5 -5 V .12 g 5884 2120 M -19 -20 V .12 g 5865 2100 M -4 -5 V .12 g 5861 2095 M -15 -16 V .12 g 5846 2079 M -12 -13 V .12 g 5834 2066 M -7 -7 V .12 g 5827 2059 M -20 -20 V .12 g 5807 2039 M 0 -1 V .12 g 5807 2038 M -20 -19 V .12 g 5787 2019 M -7 -8 V .12 g 5780 2011 M -13 -12 V .12 g 5767 1999 M -15 -15 V .12 g 5752 1984 M -6 -5 V .12 g 5746 1979 M -20 -20 V .12 g 5726 1959 M -1 -1 V stroke 5725 1958 M .12 g 5725 1958 M -20 -20 V .12 g 5705 1938 M -7 -7 V .12 g 5698 1931 M -14 -13 V .12 g 5684 1918 M -13 -13 V .12 g 5671 1905 M -8 -7 V .12 g 5663 1898 M -20 -19 V .12 g 5643 1879 M 0 -1 V .12 g 5643 1878 M -21 -20 V .12 g 5622 1858 M -6 -6 V .12 g 5616 1852 M -14 -14 V .12 g 5602 1838 M -13 -13 V .12 g 5589 1825 M -8 -8 V .12 g 5581 1817 M -19 -20 V .12 g .12 g 5562 1797 M -20 -20 V .12 g 5542 1777 M -8 -8 V .12 g 5534 1769 M -11 -12 V .12 g 5523 1757 M -16 -17 V .12 g 5507 1740 M -3 -3 V .12 g 5504 1737 M -19 -20 V .12 g 5485 1717 M -5 -7 V .12 g 5480 1710 M -13 -13 V .12 g 5467 1697 M -14 -17 V .12 g 5453 1680 M -4 -4 V .12 g 5449 1676 M -17 -20 V .12 g 5432 1656 M -7 -8 V .12 g 5425 1648 M -10 -12 V .12 g 5415 1636 M -17 -20 V .12 g .12 g 5398 1616 M -16 -20 V .12 g 5382 1596 M -11 -14 V .12 g 5371 1582 M -6 -6 V .12 g 5365 1576 M -15 -21 V .12 g 5350 1555 M -6 -7 V .12 g 5344 1548 M -10 -13 V .12 g 5334 1535 M -16 -20 V .12 g 5318 1515 M -2 -3 V .12 g 5316 1512 M -13 -17 V .12 g 5303 1495 M -14 -19 V .12 g 5289 1476 M -1 -1 V .12 g 5288 1475 M -15 -20 V .12 g 5273 1455 M -11 -16 V .12 g 5262 1439 M -3 -4 V .12 g 5259 1435 M -15 -21 V .12 g 5244 1414 M -9 -13 V .12 g 5235 1401 M -5 -7 V .12 g 5230 1394 M -14 -20 V .12 g 5216 1374 M -9 -12 V .12 g 5207 1362 M -5 -8 V .12 g 5202 1354 M -14 -20 V .12 g 5188 1334 M -8 -12 V .12 g 5180 1322 M -6 -8 V .12 g 5174 1314 M -14 -21 V .12 g 5160 1293 M -7 -10 V stroke 5153 1283 M .12 g 5153 1283 M -7 -10 V .12 g 5146 1273 M -13 -20 V .12 g 5133 1253 M -7 -11 V .12 g 5126 1242 M -7 -9 V .12 g 5119 1233 M -14 -20 V .12 g 5105 1213 M -7 -11 V .12 g 5098 1202 M -6 -9 V .12 g 5092 1193 M -14 -21 V .12 g 5078 1172 M -7 -10 V .12 g 5071 1162 M -6 -10 V .12 g 5065 1152 M -14 -20 V .12 g 5051 1132 M -7 -11 V .12 g 5044 1121 M -7 -9 V 0 g .1 g 912 3047 M .1 g 912 3047 M -9 20 V .1 g 903 3067 M -1 4 V .1 g 902 3071 M -7 16 V .1 g 895 3087 M -9 20 V .1 g 886 3107 M -9 21 V .1 g 877 3128 M -2 6 V .1 g 875 3134 M -6 14 V .1 g 869 3148 M -9 20 V .1 g 860 3168 M -8 20 V .1 g 852 3188 M -5 10 V .1 g 847 3198 M -4 10 V .1 g 843 3208 M -8 20 V .1 g 835 3228 M -9 20 V .1 g 826 3248 M -6 16 V .1 g 820 3264 M -2 5 V .1 g 818 3269 M -8 20 V .1 g 810 3289 M -8 20 V .1 g 802 3309 M -8 20 V .1 g 794 3329 M -1 2 V .1 g 793 3331 M -7 18 V .1 g 786 3349 M -8 20 V .1 g 778 3369 M -8 21 V .1 g 770 3390 M -5 10 V .1 g 765 3400 M -3 10 V .1 g 762 3410 M -8 20 V .1 g 754 3430 M -8 20 V .1 g 746 3450 M -8 19 V .1 g 738 3469 M 0 1 V .1 g 738 3470 M -8 20 V .1 g 730 3490 M -8 20 V .1 g 722 3510 M -7 21 V .1 g 715 3531 M -4 9 V .1 g 711 3540 M -4 11 V .1 g 707 3551 M -8 20 V .1 g 699 3571 M -7 20 V .1 g 692 3591 M -8 20 V .1 g 684 3611 M -8 20 V .1 g 676 3631 M -7 21 V .1 g 669 3652 M -8 20 V stroke 661 3672 M .1 g 661 3672 M -4 11 V .1 g 657 3683 M -4 9 V .1 g 653 3692 M -7 20 V .1 g 646 3712 M -8 20 V .1 g 638 3732 M -7 20 V .1 g 631 3752 M -2 4 V .1 g 629 3756 M -6 16 V .1 g 623 3772 M -7 21 V .1 g 616 3793 M -8 20 V .1 g 608 3813 M -6 16 V 0 g .1 g 1883 1785 M .1 g 1883 1785 M -13 12 V .1 g 1870 1797 M -14 16 V .1 g 1856 1813 M -5 4 V .1 g 1851 1817 M -21 21 V .1 g 1830 1838 M -2 1 V .1 g 1828 1839 M -19 19 V .1 g 1809 1858 M -8 7 V .1 g 1801 1865 M -13 13 V .1 g 1788 1878 M -14 13 V .1 g 1774 1891 M -8 7 V .1 g 1766 1898 M -19 17 V .1 g 1747 1915 M -4 3 V .1 g 1743 1918 M -23 20 V .1 g 1720 1938 M -1 1 V .1 g 1719 1939 M -22 20 V .1 g 1697 1959 M -5 4 V .1 g 1692 1963 M -19 16 V .1 g 1673 1979 M -8 7 V .1 g 1665 1986 M -15 13 V .1 g 1650 1999 M -12 11 V .1 g 1638 2010 M -11 9 V .1 g 1627 2019 M -17 14 V .1 g 1610 2033 M -7 6 V .1 g 1603 2039 M -20 18 V .1 g 1583 2057 M -3 2 V .1 g 1580 2059 M -23 20 V .1 g 1557 2079 M -1 2 V .1 g 1556 2081 M -21 19 V .1 g 1535 2100 M -6 6 V .1 g 1529 2106 M -15 14 V .1 g 1514 2120 M -13 11 V .1 g 1501 2131 M -8 9 V .1 g 1493 2140 M -19 18 V .1 g 1474 2158 M -2 2 V .1 g 1472 2160 M -20 20 V .1 g 1452 2180 M -5 5 V .1 g 1447 2185 M -15 15 V .1 g 1432 2200 M -12 14 V .1 g 1420 2214 M -6 7 V .1 g 1414 2221 M -19 20 V .1 g 1395 2241 M -3 3 V .1 g 1392 2244 M -15 17 V stroke 1377 2261 M .1 g 1377 2261 M -12 14 V .1 g 1365 2275 M -5 6 V .1 g 1360 2281 M -17 20 V .1 g 1343 2301 M -5 7 V .1 g 1338 2308 M -11 13 V .1 g 1327 2321 M -16 20 V .1 g 1311 2341 M 0 1 V .1 g 1311 2342 M -15 20 V .1 g 1296 2362 M -13 16 V .1 g 1283 2378 M -3 4 V .1 g 1280 2382 M -14 20 V .1 g 1266 2402 M -10 13 V .1 g 1256 2415 M -5 7 V .1 g 1251 2422 M -14 20 V .1 g 1237 2442 M -8 13 V .1 g 1229 2455 M -5 7 V .1 g 1224 2462 M -14 21 V .1 g 1210 2483 M -8 13 V .1 g 1202 2496 M -5 7 V .1 g 1197 2503 M -13 20 V .1 g 1184 2523 M -10 16 V .1 g 1174 2539 M -2 4 V .1 g 1172 2543 M -12 20 V .1 g 1160 2563 M -13 20 V .1 g 1147 2583 M 0 1 V .1 g 1147 2584 M -11 20 V .1 g 1136 2604 M -12 20 V .1 g 1124 2624 M -4 6 V .1 g 1120 2630 M -8 14 V .1 g 1112 2644 M -11 20 V .1 g 1101 2664 M -8 15 V .1 g 1093 2679 M -3 5 V .1 g 1090 2684 M -11 20 V .1 g 1079 2704 M -11 20 V .1 g 1068 2724 M -3 5 V .1 g 1065 2729 M -8 16 V .1 g 1057 2745 M -10 20 V .1 g 1047 2765 M -9 17 V .1 g 1038 2782 M -2 3 V .1 g 1036 2785 M -10 20 V .1 g 1026 2805 M -10 20 V .1 g 1016 2825 M -5 11 V .1 g 1011 2836 M -5 9 V .1 g 1006 2845 M -9 21 V .1 g 997 2866 M -10 20 V .1 g 987 2886 M -3 6 V .1 g 984 2892 M -7 14 V .1 g 977 2906 M -9 20 V .1 g 968 2926 M -10 20 V .1 g 958 2946 M -2 4 V .1 g 956 2950 M -7 16 V .1 g 949 2966 M -9 20 V stroke 940 2986 M .1 g 940 2986 M -10 21 V .1 g 930 3007 M -1 3 V .1 g 929 3010 M -8 17 V .1 g 921 3027 M -9 20 V 0 g .1 g 2927 588 M .1 g 2927 588 M -9 3 V .1 g 2918 591 M -27 10 V .1 g 2891 601 M -18 7 V .1 g 2873 608 M -9 4 V .1 g 2864 612 M -27 14 V .1 g 2837 626 M -5 2 V .1 g 2832 628 M -23 14 V .1 g 2809 642 M -11 6 V .1 g 2798 648 M -16 11 V .1 g 2782 659 M -14 10 V .1 g 2768 669 M -13 9 V .1 g 2755 678 M -14 11 V .1 g 2741 689 M -13 11 V .1 g 2728 700 M -12 9 V .1 g 2716 709 M -16 14 V .1 g 2700 723 M -7 6 V .1 g 2693 729 M -20 18 V .1 g 2673 747 M -2 2 V .1 g 2671 749 M -21 20 V .1 g 2650 769 M -4 5 V .1 g 2646 774 M -15 16 V .1 g 2631 790 M -12 12 V .1 g 2619 802 M -7 8 V .1 g 2612 810 M -19 20 V .1 g 2593 830 M -2 2 V .1 g 2591 832 M -15 18 V .1 g 2576 850 M -12 14 V .1 g 2564 864 M -5 6 V .1 g 2559 870 M -17 20 V .1 g 2542 890 M -5 7 V .1 g 2537 897 M -11 13 V .1 g 2526 910 M -16 21 V .1 g .1 g 2510 931 M -16 20 V .1 g 2494 951 M -12 15 V .1 g 2482 966 M -3 5 V .1 g 2479 971 M -15 20 V .1 g 2464 991 M -9 12 V .1 g 2455 1003 M -6 8 V .1 g 2449 1011 M -15 20 V .1 g 2434 1031 M -6 10 V .1 g 2428 1041 M -8 11 V .1 g 2420 1052 M -14 20 V .1 g 2406 1072 M -5 7 V .1 g 2401 1079 M -9 13 V .1 g 2392 1092 M -14 20 V .1 g 2378 1112 M -5 7 V .1 g 2373 1119 M -9 13 V .1 g 2364 1132 M -14 20 V stroke 2350 1152 M .1 g 2350 1152 M -4 7 V .1 g 2346 1159 M -9 13 V .1 g 2337 1172 M -14 21 V .1 g 2323 1193 M -4 6 V .1 g 2319 1199 M -10 14 V .1 g 2309 1213 M -13 20 V .1 g 2296 1233 M -4 7 V .1 g 2292 1240 M -10 13 V .1 g 2282 1253 M -13 20 V .1 g 2269 1273 M -5 7 V .1 g 2264 1280 M -8 13 V .1 g 2256 1293 M -14 21 V .1 g 2242 1314 M -5 7 V .1 g 2237 1321 M -8 13 V .1 g 2229 1334 M -14 20 V .1 g 2215 1354 M -5 8 V .1 g 2210 1362 M -9 12 V .1 g 2201 1374 M -13 20 V .1 g 2188 1394 M -5 8 V .1 g 2183 1402 M -9 12 V .1 g 2174 1414 M -14 21 V .1 g 2160 1435 M -5 7 V .1 g 2155 1442 M -9 13 V .1 g 2146 1455 M -14 20 V .1 g 2132 1475 M -4 6 V .1 g 2128 1481 M -10 14 V .1 g 2118 1495 M -15 20 V .1 g 2103 1515 M -2 4 V .1 g 2101 1519 M -12 16 V .1 g 2089 1535 M -15 20 V .1 g 2074 1555 M 0 1 V .1 g 2074 1556 M -15 20 V .1 g 2059 1576 M -13 16 V .1 g 2046 1592 M -3 4 V .1 g 2043 1596 M -15 20 V .1 g 2028 1616 M -9 11 V .1 g 2019 1627 M -7 9 V .1 g 2012 1636 M -16 20 V .1 g 1996 1656 M -4 5 V .1 g 1992 1661 M -13 15 V .1 g 1979 1676 M -14 18 V .1 g 1965 1694 M -3 3 V .1 g 1962 1697 M -17 20 V .1 g 1945 1717 M -8 8 V .1 g 1937 1725 M -10 12 V .1 g 1927 1737 M -17 19 V .1 g 1910 1756 M -1 1 V .1 g 1909 1757 M -19 20 V .1 g 1890 1777 M -7 8 V 0 g .1 g 1761 4216 M .1 g 1761 4216 M -11 20 V .1 g 1750 4236 M -3 6 V .1 g 1747 4242 M -9 14 V stroke 1738 4256 M .1 g 1738 4256 M -11 20 V .1 g 1727 4276 M -8 15 V .1 g 1719 4291 M -3 6 V .1 g 1716 4297 M -11 20 V .1 g 1705 4317 M -11 20 V .1 g 1694 4337 M -2 4 V .1 g 1692 4341 M -8 16 V .1 g 1684 4357 M -11 20 V .1 g 1673 4377 M -8 16 V .1 g 1665 4393 M -3 4 V .1 g 1662 4397 M -10 20 V .1 g 1652 4417 M -10 21 V .1 g 1642 4438 M -4 7 V .1 g 1638 4445 M -7 13 V .1 g 1631 4458 M -10 20 V .1 g 1621 4478 M -10 20 V .1 g 1611 4498 M -1 1 V .1 g 1610 4499 M -9 19 V .1 g 1601 4518 M -10 20 V .1 g 1591 4538 M -8 16 V .1 g 1583 4554 M -2 5 V .1 g 1581 4559 M -10 20 V .1 g 1571 4579 M -10 20 V .1 g 1561 4599 M -5 10 V .1 g 1556 4609 M -5 10 V 0 g .1 g 3128 3248 M .1 g 3128 3248 M -19 17 V .1 g 3109 3265 M -5 4 V .1 g 3104 3269 M -22 18 V .1 g 3082 3287 M -2 2 V .1 g 3080 3289 M -25 20 V .1 g 3055 3309 M 0 1 V .1 g 3055 3310 M -25 19 V .1 g 3030 3329 M -3 2 V .1 g 3027 3331 M -23 18 V .1 g 3004 3349 M -4 4 V .1 g 3000 3353 M -22 16 V .1 g 2978 3369 M -5 4 V .1 g 2973 3373 M -23 17 V .1 g 2950 3390 M -4 3 V .1 g 2946 3393 M -24 17 V .1 g 2922 3410 M -4 2 V .1 g 2918 3412 M -26 18 V .1 g 2892 3430 M -1 0 V .1 g 2891 3430 M -27 18 V .1 g 2864 3448 M -4 2 V .1 g 2860 3450 M -23 14 V .1 g 2837 3464 M -10 6 V .1 g 2827 3470 M -18 10 V .1 g 2809 3480 M -18 10 V .1 g 2791 3490 M -9 5 V .1 g 2782 3495 M -27 14 V .1 g 2755 3509 M -3 1 V stroke 2752 3510 M .1 g 2752 3510 M -24 13 V .1 g 2728 3523 M -18 8 V .1 g 2710 3531 M -10 4 V .1 g 2700 3535 M -27 12 V .1 g 2673 3547 M -10 4 V .1 g 2663 3551 M -17 7 V .1 g 2646 3558 M -27 10 V .1 g 2619 3568 M -8 3 V .1 g 2611 3571 M -20 7 V .1 g 2591 3578 M -27 9 V .1 g 2564 3587 M -12 4 V .1 g 2552 3591 M -15 5 V .1 g 2537 3596 M -27 8 V .1 g 2510 3604 M -23 7 V .1 g 2487 3611 M -5 2 V .1 g 2482 3613 M -27 8 V .1 g 2455 3621 M -27 8 V .1 g 2428 3629 M -7 2 V .1 g 2421 3631 M -20 7 V .1 g 2401 3638 M -28 8 V .1 g 2373 3646 M -16 6 V .1 g 2357 3652 M -11 3 V .1 g 2346 3655 M -27 10 V .1 g 2319 3665 M -17 7 V .1 g 2302 3672 M -10 4 V .1 g 2292 3676 M -28 11 V .1 g 2264 3687 M -10 5 V .1 g 2254 3692 M -17 7 V .1 g 2237 3699 M -25 13 V .1 g 2212 3712 M -2 1 V .1 g 2210 3713 M -27 15 V .1 g 2183 3728 M -7 4 V .1 g 2176 3732 M -21 13 V .1 g 2155 3745 M -11 7 V .1 g 2144 3752 M -16 11 V .1 g 2128 3763 M -12 9 V .1 g 2116 3772 M -15 12 V .1 g 2101 3784 M -11 9 V .1 g 2090 3793 M -16 13 V .1 g 2074 3806 M -8 7 V .1 g 2066 3813 M -20 17 V .1 g 2046 3830 M -3 3 V .1 g 2043 3833 M -20 20 V .1 g 2023 3853 M -4 4 V .1 g 2019 3857 M -16 16 V .1 g 2003 3873 M -11 12 V .1 g 1992 3885 M -7 8 V .1 g 1985 3893 M -18 21 V .1 g 1967 3914 M -2 2 V .1 g 1965 3916 M -15 18 V .1 g 1950 3934 M -13 15 V .1 g 1937 3949 M -3 5 V stroke 1934 3954 M .1 g 1934 3954 M -16 20 V .1 g 1918 3974 M -8 11 V .1 g 1910 3985 M -7 9 V .1 g 1903 3994 M -14 20 V .1 g 1889 4014 M -6 9 V .1 g 1883 4023 M -8 12 V .1 g 1875 4035 M -14 20 V .1 g 1861 4055 M -5 7 V .1 g 1856 4062 M -9 13 V .1 g 1847 4075 M -13 20 V .1 g 1834 4095 M -6 9 V .1 g 1828 4104 M -6 11 V .1 g 1822 4115 M -13 20 V .1 g 1809 4135 M -8 13 V .1 g 1801 4148 M -4 7 V .1 g 1797 4155 M -12 21 V .1 g 1785 4176 M -11 18 V .1 g 1774 4194 M -1 2 V .1 g 1773 4196 M -12 20 V 0 g .1 g 4560 3531 M .1 g 4560 3531 M -7 -4 V .1 g 4553 3527 M -26 -17 V .1 g 4527 3510 M -1 0 V .1 g 4526 3510 M -27 -18 V .1 g 4499 3492 M -3 -2 V .1 g 4496 3490 M -24 -16 V .1 g 4472 3474 M -5 -4 V .1 g 4467 3470 M -23 -16 V .1 g 4444 3454 M -6 -4 V .1 g 4438 3450 M -21 -16 V .1 g 4417 3434 M -6 -4 V .1 g 4411 3430 M -21 -17 V .1 g 4390 3413 M -5 -3 V .1 g 4385 3410 M -22 -18 V .1 g 4363 3392 M -3 -2 V .1 g 4360 3390 M -25 -20 V .1 g 4335 3370 M 0 -1 V .1 g 4335 3369 M -24 -20 V .1 g 4311 3349 M -3 -2 V .1 g 4308 3347 M -21 -18 V .1 g 4287 3329 M -6 -6 V .1 g 4281 3323 M -17 -14 V .1 g 4264 3309 M -10 -9 V .1 g 4254 3300 M -13 -11 V .1 g 4241 3289 M -15 -14 V .1 g 4226 3275 M -7 -6 V .1 g 4219 3269 M -20 -18 V .1 g 4199 3251 M -3 -3 V .1 g 4196 3248 M -22 -20 V .1 g 4174 3228 M -2 -2 V .1 g 4172 3226 M -21 -18 V .1 g 4151 3208 M -6 -6 V .1 g 4145 3202 M -16 -14 V stroke 4129 3188 M .1 g 4129 3188 M -12 -10 V .1 g 4117 3178 M -11 -10 V .1 g 4106 3168 M -16 -15 V .1 g 4090 3153 M -7 -5 V .1 g 4083 3148 M -20 -18 V .1 g 4063 3130 M -3 -2 V .1 g 4060 3128 M -24 -21 V .1 g .1 g 4036 3107 M -24 -20 V .1 g 4012 3087 M -4 -3 V .1 g 4008 3084 M -22 -17 V .1 g 3986 3067 M -5 -4 V .1 g 3981 3063 M -21 -16 V .1 g 3960 3047 M -6 -5 V .1 g 3954 3042 M -22 -15 V .1 g 3932 3027 M -5 -4 V .1 g 3927 3023 M -26 -16 V .1 g 3901 3007 M -2 -2 V .1 g 3899 3005 M -27 -16 V .1 g 3872 2989 M -5 -3 V .1 g 3867 2986 M -22 -12 V .1 g 3845 2974 M -18 -8 V .1 g 3827 2966 M -9 -4 V .1 g 3818 2962 M -28 -11 V .1 g 3790 2951 M -14 -5 V .1 g 3776 2946 M -13 -4 V .1 g 3763 2942 M -27 -7 V .1 g 3736 2935 M -27 -4 V .1 g 3709 2931 M -28 -2 V .1 g 3681 2929 M -27 0 V .1 g 3654 2929 M -27 2 V .1 g 3627 2931 M -27 5 V .1 g 3600 2936 M -28 7 V .1 g 3572 2943 M -10 3 V .1 g 3562 2946 M -17 6 V .1 g 3545 2952 M -27 10 V .1 g 3518 2962 M -8 4 V .1 g 3510 2966 M -19 9 V .1 g 3491 2975 M -22 11 V .1 g 3469 2986 M -6 4 V .1 g 3463 2990 M -27 16 V .1 g 3436 3006 M -1 1 V .1 g 3435 3007 M -26 16 V .1 g 3409 3023 M -5 4 V .1 g 3404 3027 M -22 15 V .1 g 3382 3042 M -7 5 V .1 g 3375 3047 M -21 15 V .1 g 3354 3062 M -7 5 V .1 g 3347 3067 M -20 16 V .1 g 3327 3083 M -6 4 V .1 g 3321 3087 M -21 17 V .1 g 3300 3104 M -4 3 V .1 g 3296 3107 M -23 19 V stroke 3273 3126 M .1 g 3273 3126 M -2 2 V .1 g 3271 3128 M -24 20 V .1 g 3247 3148 M -2 1 V .1 g 3245 3149 M -22 19 V .1 g 3223 3168 M -5 4 V .1 g 3218 3172 M -19 16 V .1 g 3199 3188 M -8 7 V .1 g 3191 3195 M -15 13 V .1 g 3176 3208 M -12 11 V .1 g 3164 3219 M -12 9 V .1 g 3152 3228 M -16 14 V .1 g 3136 3242 M -8 6 V 0 g .1 g 5754 4619 M .1 g 5754 4619 M -2 -4 V .1 g 5752 4615 M -8 -16 V .1 g 5744 4599 M -10 -20 V .1 g 5734 4579 M -9 -19 V .1 g 5725 4560 M -1 -1 V .1 g 5724 4559 M -10 -21 V .1 g 5714 4538 M -10 -20 V .1 g 5704 4518 M -6 -13 V .1 g 5698 4505 M -4 -7 V .1 g 5694 4498 M -10 -20 V .1 g 5684 4478 M -11 -20 V .1 g 5673 4458 M -2 -6 V .1 g 5671 4452 M -8 -14 V .1 g 5663 4438 M -11 -21 V .1 g 5652 4417 M -9 -17 V .1 g 5643 4400 M -1 -3 V .1 g 5642 4397 M -11 -20 V .1 g 5631 4377 M -11 -20 V .1 g 5620 4357 M -4 -8 V .1 g 5616 4349 M -7 -12 V .1 g 5609 4337 M -11 -20 V .1 g 5598 4317 M -9 -17 V .1 g 5589 4300 M -2 -3 V .1 g 5587 4297 M -12 -21 V .1 g 5575 4276 M -11 -20 V .1 g 5564 4256 M -2 -4 V .1 g 5562 4252 M -10 -16 V .1 g 5552 4236 M -12 -20 V .1 g 5540 4216 M -6 -10 V .1 g 5534 4206 M -6 -10 V .1 g 5528 4196 M -13 -20 V .1 g 5515 4176 M -8 -13 V .1 g 5507 4163 M -5 -8 V .1 g 5502 4155 M -13 -20 V .1 g 5489 4135 M -9 -14 V .1 g 5480 4121 M -4 -6 V .1 g 5476 4115 M -14 -20 V .1 g 5462 4095 M -9 -14 V .1 g 5453 4081 M -5 -6 V .1 g 5448 4075 M -15 -20 V stroke 5433 4055 M .1 g 5433 4055 M -8 -12 V .1 g 5425 4043 M -7 -8 V .1 g 5418 4035 M -15 -21 V .1 g 5403 4014 M -5 -6 V .1 g 5398 4008 M -11 -14 V .1 g 5387 3994 M -16 -19 V .1 g 5371 3975 M -1 -1 V .1 g 5370 3974 M -18 -20 V .1 g 5352 3954 M -8 -10 V .1 g 5344 3944 M -11 -10 V .1 g 5333 3934 M -17 -18 V .1 g 5316 3916 M -2 -2 V .1 g 5314 3914 M -21 -21 V .1 g 5293 3893 M -4 -3 V .1 g 5289 3890 M -18 -17 V .1 g 5271 3873 M -9 -7 V .1 g 5262 3866 M -15 -13 V .1 g 5247 3853 M -12 -10 V .1 g 5235 3843 M -14 -10 V .1 g 5221 3833 M -14 -10 V .1 g 5207 3823 M -15 -10 V .1 g 5192 3813 M -12 -8 V .1 g 5180 3805 M -19 -12 V .1 g 5161 3793 M -8 -5 V .1 g 5153 3788 M -27 -16 V .1 g .1 g 5126 3772 M -28 -14 V .1 g 5098 3758 M -12 -6 V .1 g 5086 3752 M -15 -7 V .1 g 5071 3745 M -27 -12 V .1 g 5044 3733 M -2 -1 V .1 g 5042 3732 M -25 -10 V .1 g 5017 3722 M -25 -10 V .1 g 4992 3712 M -3 -1 V .1 g 4989 3711 M -27 -10 V .1 g 4962 3701 M -26 -9 V .1 g 4936 3692 M -1 -1 V .1 g 4935 3691 M -27 -9 V .1 g 4908 3682 M -28 -10 V .1 g 4880 3672 M -1 0 V .1 g 4879 3672 M -26 -9 V .1 g 4853 3663 M -27 -10 V .1 g 4826 3653 M -4 -1 V .1 g 4822 3652 M -23 -9 V .1 g 4799 3643 M -28 -10 V .1 g 4771 3633 M -3 -2 V .1 g 4768 3631 M -24 -9 V .1 g 4744 3622 M -25 -11 V .1 g 4719 3611 M -2 -1 V .1 g 4717 3610 M -27 -12 V .1 g 4690 3598 M -16 -7 V .1 g 4674 3591 M -12 -6 V .1 g 4662 3585 M -27 -13 V stroke 4635 3572 M .1 g 4635 3572 M -2 -1 V .1 g 4633 3571 M -25 -13 V .1 g 4608 3558 M -13 -7 V .1 g 4595 3551 M -14 -8 V .1 g 4581 3543 M -21 -12 V 0 g .1 g 3436 659 M .1 g 3436 659 M -27 -10 V .1 g 3409 649 M -3 -1 V .1 g 3406 648 M -24 -8 V .1 g 3382 640 M -28 -9 V .1 g 3354 631 M -7 -3 V .1 g 3347 628 M -20 -6 V .1 g 3327 622 M -27 -9 V .1 g 3300 613 M -14 -5 V .1 g 3286 608 M -13 -4 V .1 g 3273 604 M -28 -8 V .1 g 3245 596 M -27 -7 V .1 g 3218 589 M -3 -1 V 0 g .1 g 5028 1253 M .1 g 5028 1253 M -11 -18 V .1 g 5017 1235 M -2 -2 V .1 g 5015 1233 M -13 -20 V .1 g 5002 1213 M -13 -19 V .1 g 4989 1194 M -1 -1 V .1 g 4988 1193 M -13 -21 V .1 g 4975 1172 M -13 -19 V .1 g 4962 1153 M 0 -1 V .1 g 4962 1152 M -14 -20 V .1 g 4948 1132 M -13 -19 V .1 g 4935 1113 M -1 -1 V .1 g 4934 1112 M -14 -20 V .1 g 4920 1092 M -12 -18 V .1 g 4908 1074 M -2 -2 V .1 g 4906 1072 M -14 -20 V .1 g 4892 1052 M -12 -17 V .1 g 4880 1035 M -3 -4 V .1 g 4877 1031 M -14 -20 V .1 g 4863 1011 M -10 -13 V .1 g 4853 998 M -5 -7 V .1 g 4848 991 M -15 -20 V .1 g 4833 971 M -7 -9 V .1 g 4826 962 M -9 -11 V .1 g 4817 951 M -16 -20 V .1 g 4801 931 M -2 -4 V .1 g 4799 927 M -14 -17 V .1 g 4785 910 M -14 -16 V .1 g 4771 894 M -3 -4 V .1 g 4768 890 M -17 -20 V .1 g 4751 870 M -7 -8 V .1 g 4744 862 M -11 -12 V .1 g 4733 850 M -16 -18 V .1 g 4717 832 M -3 -2 V .1 g 4714 830 M -19 -20 V stroke 4695 810 M .1 g 4695 810 M -5 -6 V .1 g 4690 804 M -15 -14 V .1 g 4675 790 M -13 -13 V .1 g 4662 777 M -8 -8 V .1 g 4654 769 M -19 -17 V .1 g 4635 752 M -3 -3 V .1 g 4632 749 M -24 -20 V .1 g .1 g 4608 729 M -26 -20 V .1 g 4582 709 M -1 -1 V .1 g 4581 708 M -27 -19 V .1 g 4554 689 M -1 -1 V .1 g 4553 688 M -27 -17 V .1 g 4526 671 M -4 -2 V .1 g 4522 669 M -23 -14 V .1 g 4499 655 M -14 -7 V .1 g 4485 648 M -13 -6 V .1 g 4472 642 M -28 -12 V .1 g 4444 630 M -4 -2 V .1 g 4440 628 M -23 -8 V .1 g 4417 620 M -27 -8 V .1 g 4390 612 M -15 -4 V .1 g 4375 608 M -12 -3 V .1 g 4363 605 M -28 -4 V .1 g 4335 601 M -27 -4 V .1 g 4308 597 M -27 -1 V .1 g 4281 596 M -27 0 V .1 g 4254 596 M -28 1 V .1 g 4226 597 M -27 3 V .1 g 4199 600 M -27 4 V .1 g 4172 604 M -26 4 V .1 g 4146 608 M -1 0 V .1 g 4145 608 M -28 6 V .1 g 4117 614 M -27 7 V .1 g 4090 621 M -27 7 V .1 g 4063 628 M -2 0 V .1 g 4061 628 M -25 7 V .1 g 4036 635 M -28 8 V .1 g 4008 643 M -17 5 V .1 g 3991 648 M -10 3 V .1 g 3981 651 M -27 8 V .1 g 3954 659 M -27 8 V .1 g 3927 667 M -5 2 V .1 g 3922 669 M -23 6 V .1 g 3899 675 M -27 7 V .1 g 3872 682 M -27 6 V .1 g 3845 688 M -3 1 V .1 g 3842 689 M -24 5 V .1 g 3818 694 M -28 5 V .1 g 3790 699 M -27 3 V .1 g 3763 702 M -27 3 V .1 g 3736 705 M -27 1 V .1 g 3709 706 M -28 0 V stroke 3681 706 M .1 g 3681 706 M -27 -1 V .1 g 3654 705 M -27 -2 V .1 g 3627 703 M -27 -3 V .1 g 3600 700 M -28 -5 V .1 g 3572 695 M -27 -6 V .1 g 3545 689 M -2 0 V .1 g 3543 689 M -25 -6 V .1 g 3518 683 M -27 -8 V .1 g 3491 675 M -23 -6 V .1 g 3468 669 M -5 -2 V .1 g 3463 667 M -27 -8 V 0 g .1 g 6052 2466 M .1 g 6052 2466 M -3 -4 V .1 g 6049 2462 M -15 -20 V .1 g 6034 2442 M -9 -12 V .1 g 6025 2430 M -6 -8 V .1 g 6019 2422 M -16 -20 V .1 g 6003 2402 M -5 -7 V .1 g 5998 2395 M -12 -13 V .1 g 5986 2382 M -16 -20 V .1 g .1 g 5970 2362 M -18 -21 V .1 g 5952 2341 M -9 -10 V .1 g 5943 2331 M -8 -10 V .1 g 5935 2321 M -18 -20 V .1 g 5917 2301 M -1 -1 V .1 g 5916 2300 M -18 -19 V .1 g 5898 2281 M -9 -10 V .1 g 5889 2271 M -11 -10 V .1 g 5878 2261 M -17 -18 V .1 g 5861 2243 M -2 -2 V .1 g 5859 2241 M -20 -20 V .1 g 5839 2221 M -5 -5 V .1 g 5834 2216 M -16 -16 V .1 g 5818 2200 M -11 -10 V .1 g 5807 2190 M -10 -10 V .1 g 5797 2180 M -17 -16 V .1 g 5780 2164 M -5 -4 V .1 g 5775 2160 M -21 -20 V .1 g 5754 2140 M -2 -1 V .1 g 5752 2139 M -21 -19 V .1 g 5731 2120 M -6 -6 V .1 g 5725 2114 M -16 -14 V .1 g 5709 2100 M -11 -11 V .1 g 5698 2089 M -11 -10 V .1 g 5687 2079 M -16 -15 V .1 g 5671 2064 M -6 -5 V .1 g 5665 2059 M -22 -19 V .1 g 5643 2040 M 0 -1 V .1 g 5643 2039 M -22 -20 V .1 g 5621 2019 M -5 -4 V .1 g 5616 2015 M -17 -16 V .1 g 5599 1999 M -10 -10 V .1 g 5589 1989 M -11 -10 V stroke 5578 1979 M .1 g 5578 1979 M -16 -16 V .1 g 5562 1963 M -5 -4 V .1 g 5557 1959 M -20 -21 V .1 g 5537 1938 M -3 -2 V .1 g 5534 1936 M -17 -18 V .1 g 5517 1918 M -10 -10 V .1 g 5507 1908 M -9 -10 V .1 g 5498 1898 M -18 -19 V .1 g 5480 1879 M -1 -1 V .1 g 5479 1878 M -19 -20 V .1 g 5460 1858 M -7 -9 V .1 g 5453 1849 M -11 -11 V .1 g 5442 1838 M -17 -20 V .1 g 5425 1818 M 0 -1 V .1 g 5425 1817 M -17 -20 V .1 g 5408 1797 M -10 -11 V .1 g 5398 1786 M -7 -9 V .1 g 5391 1777 M -16 -20 V .1 g 5375 1757 M -4 -5 V .1 g 5371 1752 M -12 -15 V .1 g 5359 1737 M -15 -20 V .1 g 5344 1717 M -1 0 V .1 g 5343 1717 M -15 -20 V .1 g 5328 1697 M -12 -16 V .1 g 5316 1681 M -3 -5 V .1 g 5313 1676 M -15 -20 V .1 g 5298 1656 M -9 -12 V .1 g 5289 1644 M -6 -8 V .1 g 5283 1636 M -14 -20 V .1 g 5269 1616 M -7 -10 V .1 g 5262 1606 M -7 -10 V .1 g 5255 1596 M -14 -20 V .1 g 5241 1576 M -6 -9 V .1 g 5235 1567 M -8 -12 V .1 g 5227 1555 M -14 -20 V .1 g 5213 1535 M -6 -8 V .1 g 5207 1527 M -8 -12 V .1 g 5199 1515 M -13 -20 V .1 g 5186 1495 M -6 -9 V .1 g 5180 1486 M -7 -11 V .1 g 5173 1475 M -14 -20 V .1 g 5159 1455 M -6 -10 V .1 g 5153 1445 M -7 -10 V .1 g 5146 1435 M -13 -21 V .1 g 5133 1414 M -7 -11 V .1 g 5126 1403 M -6 -9 V .1 g 5120 1394 M -13 -20 V .1 g 5107 1374 M -9 -13 V .1 g 5098 1361 M -4 -7 V .1 g 5094 1354 M -13 -20 V .1 g 5081 1334 M -10 -15 V .1 g 5071 1319 M -4 -5 V stroke 5067 1314 M .1 g 5067 1314 M -13 -21 V .1 g 5054 1293 M -10 -16 V .1 g 5044 1277 M -3 -4 V .1 g 5041 1273 M -13 -20 V 0 g .08 g 1863 3853 M .08 g 1863 3853 M -7 12 V .08 g 1856 3865 M -6 8 V .08 g 1850 3873 M -13 20 V .08 g 1837 3893 M -9 15 V .08 g 1828 3908 M -3 6 V .08 g 1825 3914 M -12 20 V .08 g 1813 3934 M -12 20 V .08 g 1801 3954 M -12 20 V .08 g 1789 3974 M -11 20 V .08 g 1778 3994 M -4 8 V .08 g 1774 4002 M -7 12 V .08 g 1767 4014 M -11 21 V .08 g 1756 4035 M -9 16 V .08 g 1747 4051 M -2 4 V .08 g 1745 4055 M -11 20 V .08 g 1734 4075 M -11 20 V .08 g 1723 4095 M -4 8 V .08 g 1719 4103 M -6 12 V .08 g 1713 4115 M -10 20 V .08 g 1703 4135 M -11 20 V .08 g 1692 4155 M 0 1 V .08 g 1692 4156 M -10 20 V .08 g 1682 4176 M -10 20 V .08 g 1672 4196 M -7 14 V .08 g 1665 4210 M -3 6 V .08 g 1662 4216 M -10 20 V .08 g 1652 4236 M -10 20 V .08 g 1642 4256 M -4 9 V .08 g 1638 4265 M -6 11 V .08 g 1632 4276 M -10 21 V .08 g 1622 4297 M -9 20 V .08 g 1613 4317 M -3 5 V .08 g 1610 4322 M -7 15 V .08 g 1603 4337 M -10 20 V .08 g 1593 4357 M -9 20 V .08 g 1584 4377 M -1 2 V .08 g 1583 4379 M -9 18 V .08 g 1574 4397 M -9 20 V .08 g 1565 4417 M -9 19 V .08 g 1556 4436 M -1 2 V .08 g 1555 4438 M -9 20 V .08 g 1546 4458 M -10 20 V .08 g 1536 4478 M -7 16 V .08 g 1529 4494 M -2 4 V .08 g 1527 4498 M -10 20 V .08 g 1517 4518 M -9 20 V .08 g 1508 4538 M -7 14 V .08 g 1501 4552 M -3 7 V stroke 1498 4559 M .08 g 1498 4559 M -9 20 V .08 g 1489 4579 M -10 20 V .08 g 1479 4599 M -5 11 V .08 g 1474 4610 M -4 9 V 0 g .08 g 3303 2926 M .08 g 3303 2926 M -3 3 V .08 g 3300 2929 M -19 17 V .08 g 3281 2946 M -8 8 V .08 g 3273 2954 M -14 12 V .08 g 3259 2966 M -14 13 V .08 g 3245 2979 M -8 7 V .08 g 3237 2986 M -19 18 V .08 g 3218 3004 M -3 3 V .08 g 3215 3007 M -21 20 V .08 g 3194 3027 M -3 2 V .08 g 3191 3029 M -19 18 V .08 g 3172 3047 M -8 8 V .08 g 3164 3055 M -14 12 V .08 g 3150 3067 M -14 13 V .08 g 3136 3080 M -8 7 V .08 g 3128 3087 M -19 17 V .08 g 3109 3104 M -3 3 V .08 g 3106 3107 M -23 21 V .08 g 3083 3128 M -1 1 V .08 g 3082 3129 M -22 19 V .08 g 3060 3148 M -5 4 V .08 g 3055 3152 M -19 16 V .08 g 3036 3168 M -9 7 V .08 g 3027 3175 M -15 13 V .08 g 3012 3188 M -12 10 V .08 g 3000 3198 M -13 10 V .08 g 2987 3208 M -14 11 V .08 g 2973 3219 M -12 9 V .08 g 2961 3228 M -15 12 V .08 g 2946 3240 M -12 8 V .08 g 2934 3248 M -16 12 V .08 g 2918 3260 M -12 9 V .08 g 2906 3269 M -15 10 V .08 g 2891 3279 M -16 10 V .08 g 2875 3289 M -11 7 V .08 g 2864 3296 M -20 13 V .08 g 2844 3309 M -7 4 V .08 g 2837 3313 M -28 16 V .08 g 2809 3329 M -27 15 V .08 g 2782 3344 M -11 5 V .08 g 2771 3349 M -16 9 V .08 g 2755 3358 M -25 11 V .08 g 2730 3369 M -2 1 V .08 g 2728 3370 M -28 12 V .08 g 2700 3382 M -18 8 V .08 g 2682 3390 M -9 3 V .08 g 2673 3393 M -27 10 V .08 g 2646 3403 M -19 7 V stroke 2627 3410 M .08 g 2627 3410 M -8 2 V .08 g 2619 3412 M -28 9 V .08 g 2591 3421 M -27 8 V .08 g 2564 3429 M -4 1 V .08 g 2560 3430 M -23 6 V .08 g 2537 3436 M -27 7 V .08 g 2510 3443 M -28 6 V .08 g 2482 3449 M -3 1 V .08 g 2479 3450 M -24 5 V .08 g 2455 3455 M -27 6 V .08 g 2428 3461 M -27 7 V .08 g 2401 3468 M -12 2 V .08 g 2389 3470 M -16 4 V .08 g 2373 3474 M -27 6 V .08 g 2346 3480 M -27 8 V .08 g 2319 3488 M -10 2 V .08 g 2309 3490 M -17 6 V .08 g 2292 3496 M -28 8 V .08 g 2264 3504 M -17 6 V .08 g 2247 3510 M -10 4 V .08 g 2237 3514 M -27 11 V .08 g 2210 3525 M -11 6 V .08 g 2199 3531 M -16 7 V .08 g 2183 3538 M -24 13 V .08 g 2159 3551 M -4 2 V .08 g 2155 3553 M -27 16 V .08 g 2128 3569 M -3 2 V .08 g 2125 3571 M -24 16 V .08 g 2101 3587 M -5 4 V .08 g 2096 3591 M -22 17 V .08 g 2074 3608 M -4 3 V .08 g 2070 3611 M -24 20 V .08 g .08 g 2046 3631 M -22 21 V .08 g 2024 3652 M -5 4 V .08 g 2019 3656 M -15 16 V .08 g 2004 3672 M -12 13 V .08 g 1992 3685 M -7 7 V .08 g 1985 3692 M -18 20 V .08 g 1967 3712 M -2 3 V .08 g 1965 3715 M -14 17 V .08 g 1951 3732 M -14 17 V .08 g 1937 3749 M -3 3 V .08 g 1934 3752 M -15 20 V .08 g 1919 3772 M -9 13 V .08 g 1910 3785 M -6 8 V .08 g 1904 3793 M -14 20 V .08 g 1890 3813 M -7 10 V .08 g 1883 3823 M -7 10 V .08 g 1876 3833 M -13 20 V 0 g .08 g 4744 3466 M .08 g 4744 3466 M -27 -11 V .08 g 4717 3455 M -13 -5 V .08 g 4704 3450 M -14 -6 V stroke 4690 3444 M .08 g 4690 3444 M -28 -12 V .08 g 4662 3432 M -5 -2 V .08 g 4657 3430 M -22 -10 V .08 g 4635 3420 M -20 -10 V .08 g 4615 3410 M -7 -4 V .08 g 4608 3406 M -27 -15 V .08 g 4581 3391 M -3 -1 V .08 g 4578 3390 M -25 -15 V .08 g 4553 3375 M -10 -6 V .08 g 4543 3369 M -17 -10 V .08 g 4526 3359 M -14 -10 V .08 g 4512 3349 M -13 -8 V .08 g 4499 3341 M -17 -12 V .08 g 4482 3329 M -10 -7 V .08 g 4472 3322 M -19 -13 V .08 g 4453 3309 M -9 -7 V .08 g 4444 3302 M -18 -13 V .08 g 4426 3289 M -9 -7 V .08 g 4417 3282 M -16 -13 V .08 g 4401 3269 M -11 -9 V .08 g 4390 3260 M -14 -12 V .08 g 4376 3248 M -13 -11 V .08 g 4363 3237 M -11 -9 V .08 g 4352 3228 M -17 -14 V .08 g 4335 3214 M -7 -6 V .08 g 4328 3208 M -20 -18 V .08 g 4308 3190 M -2 -2 V .08 g 4306 3188 M -22 -20 V .08 g 4284 3168 M -3 -3 V .08 g 4281 3165 M -19 -17 V .08 g 4262 3148 M -8 -8 V .08 g 4254 3140 M -13 -12 V .08 g 4241 3128 M -15 -14 V .08 g 4226 3114 M -7 -7 V .08 g 4219 3107 M -20 -19 V .08 g 4199 3088 M -1 -1 V .08 g 4198 3087 M -20 -20 V .08 g 4178 3067 M -6 -6 V .08 g 4172 3061 M -15 -14 V .08 g 4157 3047 M -12 -12 V .08 g 4145 3035 M -9 -8 V .08 g 4136 3027 M -19 -19 V .08 g 4117 3008 M -1 -1 V .08 g 4116 3007 M -21 -21 V .08 g 4095 2986 M -5 -5 V .08 g 4090 2981 M -16 -15 V .08 g 4074 2966 M -11 -11 V .08 g 4063 2955 M -10 -9 V .08 g 4053 2946 M -17 -16 V .08 g 4036 2930 M -5 -4 V .08 g 4031 2926 M -22 -20 V .08 g 4009 2906 M -1 -1 V stroke 4008 2905 M .08 g 4008 2905 M -21 -19 V .08 g 3987 2886 M -6 -5 V .08 g 3981 2881 M -18 -15 V .08 g 3963 2866 M -9 -8 V .08 g 3954 2858 M -16 -13 V .08 g 3938 2845 M -11 -9 V .08 g 3927 2836 M -15 -11 V .08 g 3912 2825 M -13 -9 V .08 g 3899 2816 M -15 -11 V .08 g 3884 2805 M -12 -8 V .08 g 3872 2797 M -20 -12 V .08 g 3852 2785 M -7 -5 V .08 g 3845 2780 M -27 -14 V .08 g 3818 2766 M -2 -1 V .08 g 3816 2765 M -26 -12 V .08 g 3790 2753 M -23 -8 V .08 g 3767 2745 M -4 -2 V .08 g 3763 2743 M -27 -8 V .08 g 3736 2735 M -27 -5 V .08 g 3709 2730 M -28 -2 V .08 g 3681 2728 M -27 0 V .08 g 3654 2728 M -27 3 V .08 g 3627 2731 M -27 5 V .08 g 3600 2736 M -28 9 V .08 g .08 g 3572 2745 M -27 10 V .08 g 3545 2755 M -21 10 V .08 g 3524 2765 M -6 3 V .08 g 3518 2768 M -27 14 V .08 g 3491 2782 M -5 3 V .08 g 3486 2785 M -23 14 V .08 g 3463 2799 M -9 6 V .08 g 3454 2805 M -18 12 V .08 g 3436 2817 M -10 8 V .08 g 3426 2825 M -17 12 V .08 g 3409 2837 M -10 8 V .08 g 3399 2845 M -17 14 V .08 g 3382 2859 M -9 7 V .08 g 3373 2866 M -19 15 V .08 g 3354 2881 M -5 5 V .08 g 3349 2886 M -22 19 V .08 g 3327 2905 M -1 1 V .08 g 3326 2906 M -23 20 V 0 g .08 g 5836 4619 M .08 g 5836 4619 M -2 -4 V .08 g 5834 4615 M -7 -16 V .08 g 5827 4599 M -10 -20 V .08 g 5817 4579 M -9 -20 V .08 g 5808 4559 M -1 -3 V .08 g 5807 4556 M -8 -18 V .08 g 5799 4538 M -10 -20 V .08 g 5789 4518 M -9 -20 V .08 g 5780 4498 M 0 -1 V .08 g 5780 4497 M -9 -19 V stroke 5771 4478 M .08 g 5771 4478 M -10 -20 V .08 g 5761 4458 M -9 -20 V .08 g .08 g 5752 4438 M -10 -21 V .08 g 5742 4417 M -9 -20 V .08 g 5733 4397 M -8 -16 V .08 g 5725 4381 M -2 -4 V .08 g 5723 4377 M -9 -20 V .08 g 5714 4357 M -10 -20 V .08 g 5704 4337 M -6 -13 V .08 g 5698 4324 M -4 -7 V .08 g 5694 4317 M -9 -20 V .08 g 5685 4297 M -10 -21 V .08 g 5675 4276 M -4 -8 V .08 g 5671 4268 M -6 -12 V .08 g 5665 4256 M -10 -20 V .08 g 5655 4236 M -10 -20 V .08 g 5645 4216 M -2 -3 V .08 g 5643 4213 M -9 -17 V .08 g 5634 4196 M -10 -20 V .08 g 5624 4176 M -8 -16 V .08 g 5616 4160 M -2 -5 V .08 g 5614 4155 M -11 -20 V .08 g 5603 4135 M -11 -20 V .08 g 5592 4115 M -3 -7 V .08 g 5589 4108 M -7 -13 V .08 g 5582 4095 M -11 -20 V .08 g 5571 4075 M -9 -17 V .08 g 5562 4058 M -3 -3 V .08 g 5559 4055 M -11 -20 V .08 g 5548 4035 M -12 -21 V .08 g 5536 4014 M -2 -3 V .08 g 5534 4011 M -10 -17 V .08 g 5524 3994 M -12 -20 V .08 g 5512 3974 M -5 -9 V .08 g 5507 3965 M -7 -11 V .08 g 5500 3954 M -13 -20 V .08 g 5487 3934 M -7 -12 V .08 g 5480 3922 M -6 -8 V .08 g 5474 3914 M -13 -21 V .08 g 5461 3893 M -8 -12 V .08 g 5453 3881 M -6 -8 V .08 g 5447 3873 M -14 -20 V .08 g 5433 3853 M -8 -10 V .08 g 5425 3843 M -7 -10 V .08 g 5418 3833 M -16 -20 V .08 g 5402 3813 M -4 -6 V .08 g 5398 3807 M -12 -14 V .08 g 5386 3793 M -15 -19 V .08 g 5371 3774 M -2 -2 V .08 g 5369 3772 M -18 -20 V .08 g 5351 3752 M -7 -8 V .08 g 5344 3744 M -12 -12 V stroke 5332 3732 M .08 g 5332 3732 M -16 -16 V .08 g 5316 3716 M -4 -4 V .08 g 5312 3712 M -22 -20 V .08 g 5290 3692 M -1 -1 V .08 g 5289 3691 M -23 -19 V .08 g 5266 3672 M -4 -3 V .08 g 5262 3669 M -23 -17 V .08 g 5239 3652 M -4 -4 V .08 g 5235 3648 M -26 -17 V .08 g 5209 3631 M -2 -1 V .08 g 5207 3630 M -27 -16 V .08 g 5180 3614 M -4 -3 V .08 g 5176 3611 M -23 -12 V .08 g 5153 3599 M -17 -8 V .08 g 5136 3591 M -10 -5 V .08 g 5126 3586 M -28 -12 V .08 g 5098 3574 M -9 -3 V .08 g 5089 3571 M -18 -7 V .08 g 5071 3564 M -27 -9 V .08 g 5044 3555 M -12 -4 V .08 g 5032 3551 M -15 -5 V .08 g 5017 3546 M -28 -8 V .08 g 4989 3538 M -25 -7 V .08 g 4964 3531 M -2 -1 V .08 g 4962 3530 M -27 -7 V .08 g 4935 3523 M -27 -8 V .08 g 4908 3515 M -18 -5 V .08 g 4890 3510 M -10 -2 V .08 g 4880 3508 M -27 -8 V .08 g 4853 3500 M -27 -8 V .08 g 4826 3492 M -7 -2 V .08 g 4819 3490 M -20 -6 V .08 g 4799 3484 M -28 -9 V .08 g 4771 3475 M -14 -5 V .08 g 4757 3470 M -13 -4 V 0 g .08 g 1107 2805 M .08 g 1107 2805 M -12 20 V .08 g 1095 2825 M -2 5 V .08 g 1093 2830 M -9 15 V .08 g 1084 2845 M -10 21 V .08 g 1074 2866 M -9 15 V .08 g 1065 2881 M -2 5 V .08 g 1063 2886 M -11 20 V .08 g 1052 2906 M -10 20 V .08 g 1042 2926 M -4 7 V .08 g 1038 2933 M -6 13 V .08 g 1032 2946 M -10 20 V .08 g 1022 2966 M -10 20 V .08 g 1012 2986 M -1 2 V .08 g 1011 2988 M -9 19 V .08 g 1002 3007 M -10 20 V .08 g 992 3027 M -8 18 V .08 g 984 3045 M -1 2 V stroke 983 3047 M .08 g 983 3047 M -10 20 V .08 g 973 3067 M -9 20 V .08 g 964 3087 M -8 17 V .08 g 956 3104 M -1 3 V .08 g 955 3107 M -9 21 V .08 g 946 3128 M -9 20 V .08 g 937 3148 M -8 16 V .08 g 929 3164 M -2 4 V .08 g 927 3168 M -8 20 V .08 g 919 3188 M -9 20 V .08 g 910 3208 M -8 19 V .08 g 902 3227 M -1 1 V .08 g 901 3228 M -8 20 V .08 g 893 3248 M -9 21 V .08 g 884 3269 M -9 20 V .08 g 875 3289 M 0 2 V .08 g 875 3291 M -8 18 V .08 g 867 3309 M -8 20 V .08 g 859 3329 M -9 20 V .08 g 850 3349 M -3 8 V .08 g 847 3357 M -5 12 V .08 g 842 3369 M -8 21 V .08 g 834 3390 M -8 20 V .08 g 826 3410 M -6 14 V .08 g 820 3424 M -2 6 V .08 g 818 3430 M -8 20 V .08 g 810 3450 M -8 20 V .08 g 802 3470 M -8 20 V .08 g 794 3490 M -1 3 V .08 g 793 3493 M -7 17 V .08 g 786 3510 M -8 21 V .08 g 778 3531 M -7 20 V .08 g 771 3551 M -6 13 V .08 g 765 3564 M -2 7 V .08 g 763 3571 M -8 20 V .08 g 755 3591 M -8 20 V .08 g 747 3611 M -7 20 V .08 g 740 3631 M -2 4 V .08 g 738 3635 M -6 17 V .08 g 732 3652 M -7 20 V .08 g 725 3672 M -8 20 V .08 g 717 3692 M -6 16 V .08 g 711 3708 M -1 4 V .08 g 710 3712 M -8 20 V .08 g 702 3732 M -7 20 V .08 g 695 3752 M -8 20 V .08 g 687 3772 M -3 10 V .08 g 684 3782 M -4 11 V .08 g 680 3793 M -7 20 V .08 g 673 3813 M -8 20 V .08 g 665 3833 M -7 20 V .08 g 658 3853 M -1 3 V stroke 657 3856 M .08 g 657 3856 M -7 17 V .08 g 650 3873 M -7 20 V .08 g 643 3893 M -7 21 V .08 g 636 3914 M -7 18 V .08 g 629 3932 M -1 2 V .08 g 628 3934 M -7 20 V .08 g 621 3954 M -7 20 V .08 g 614 3974 M -7 20 V .08 g 607 3994 M -5 13 V 0 g .08 g 2167 1616 M .08 g 2167 1616 M -12 18 V .08 g 2155 1634 M -1 2 V .08 g 2154 1636 M -13 20 V .08 g 2141 1656 M -13 19 V .08 g 2128 1675 M -1 1 V .08 g 2127 1676 M -14 21 V .08 g 2113 1697 M -12 18 V .08 g 2101 1715 M -1 2 V .08 g 2100 1717 M -14 20 V .08 g 2086 1737 M -12 17 V .08 g 2074 1754 M -3 3 V .08 g 2071 1757 M -14 20 V .08 g 2057 1777 M -11 14 V .08 g 2046 1791 M -4 6 V .08 g 2042 1797 M -15 20 V .08 g 2027 1817 M -8 10 V .08 g 2019 1827 M -8 11 V .08 g 2011 1838 M -16 20 V .08 g 1995 1858 M -3 4 V .08 g 1992 1862 M -13 16 V .08 g 1979 1878 M -14 17 V .08 g 1965 1895 M -3 3 V .08 g 1962 1898 M -18 20 V .08 g 1944 1918 M -7 8 V .08 g 1937 1926 M -11 12 V .08 g 1926 1938 M -16 18 V .08 g 1910 1956 M -3 3 V .08 g 1907 1959 M -19 20 V .08 g 1888 1979 M -5 5 V .08 g 1883 1984 M -15 15 V .08 g 1868 1999 M -12 12 V .08 g 1856 2011 M -10 8 V .08 g 1846 2019 M -18 17 V .08 g 1828 2036 M -3 3 V .08 g 1825 2039 M -23 20 V .08 g 1802 2059 M -1 1 V .08 g 1801 2060 M -23 19 V .08 g 1778 2079 M -4 4 V .08 g 1774 2083 M -20 17 V .08 g 1754 2100 M -7 5 V .08 g 1747 2105 M -19 15 V .08 g 1728 2120 M -9 7 V .08 g 1719 2127 M -17 13 V stroke 1702 2140 M .08 g 1702 2140 M -10 8 V .08 g 1692 2148 M -16 12 V .08 g 1676 2160 M -11 9 V .08 g 1665 2169 M -15 11 V .08 g 1650 2180 M -12 10 V .08 g 1638 2190 M -14 10 V .08 g 1624 2200 M -14 10 V .08 g 1610 2210 M -13 11 V .08 g 1597 2221 M -14 11 V .08 g 1583 2232 M -11 9 V .08 g 1572 2241 M -16 12 V .08 g 1556 2253 M -9 8 V .08 g 1547 2261 M -18 15 V .08 g 1529 2276 M -6 5 V .08 g 1523 2281 M -22 18 V .08 g 1501 2299 M -2 2 V .08 g 1499 2301 M -23 20 V .08 g 1476 2321 M -2 2 V .08 g 1474 2323 M -19 18 V .08 g 1455 2341 M -8 8 V .08 g 1447 2349 M -13 13 V .08 g 1434 2362 M -14 14 V .08 g 1420 2376 M -6 6 V .08 g 1414 2382 M -20 20 V .08 g 1394 2402 M -2 2 V .08 g 1392 2404 M -17 18 V .08 g 1375 2422 M -10 11 V .08 g 1365 2433 M -8 9 V .08 g 1357 2442 M -17 20 V .08 g 1340 2462 M -2 3 V .08 g 1338 2465 M -15 18 V .08 g 1323 2483 M -12 15 V .08 g 1311 2498 M -4 5 V .08 g 1307 2503 M -16 20 V .08 g 1291 2523 M -8 9 V .08 g 1283 2532 M -8 11 V .08 g 1275 2543 M -15 20 V .08 g 1260 2563 M -4 6 V .08 g 1256 2569 M -10 14 V .08 g 1246 2583 M -14 21 V .08 g 1232 2604 M -3 3 V .08 g 1229 2607 M -11 17 V .08 g 1218 2624 M -14 20 V .08 g 1204 2644 M -2 4 V .08 g 1202 2648 M -11 16 V .08 g 1191 2664 M -13 20 V .08 g 1178 2684 M -4 6 V .08 g 1174 2690 M -8 14 V .08 g 1166 2704 M -12 20 V .08 g 1154 2724 M -7 11 V .08 g 1147 2735 M -6 10 V .08 g 1141 2745 M -11 20 V stroke 1130 2765 M .08 g 1130 2765 M -10 16 V .08 g 1120 2781 M -2 4 V .08 g 1118 2785 M -11 20 V 0 g .08 g 3463 858 M .08 g 3463 858 M -19 -8 V .08 g 3444 850 M -8 -3 V .08 g 3436 847 M -27 -12 V .08 g 3409 835 M -12 -5 V .08 g 3397 830 M -15 -7 V .08 g 3382 823 M -28 -12 V .08 g 3354 811 M -3 -1 V .08 g 3351 810 M -24 -10 V .08 g 3327 800 M -23 -10 V .08 g 3304 790 M -4 -2 V .08 g 3300 788 M -27 -11 V .08 g 3273 777 M -20 -8 V .08 g 3253 769 M -8 -3 V .08 g 3245 766 M -27 -9 V .08 g 3218 757 M -24 -8 V .08 g 3194 749 M -3 -1 V .08 g 3191 748 M -27 -7 V .08 g 3164 741 M -28 -6 V .08 g 3136 735 M -27 -5 V .08 g 3109 730 M -5 -1 V .08 g 3104 729 M -22 -3 V .08 g 3082 726 M -27 -1 V .08 g 3055 725 M -28 0 V .08 g 3027 725 M -27 1 V .08 g 3000 726 M -21 3 V .08 g 2979 729 M -6 1 V .08 g 2973 730 M -27 5 V .08 g 2946 735 M -28 8 V .08 g 2918 743 M -19 6 V .08 g 2899 749 M -8 3 V .08 g 2891 752 M -27 12 V .08 g 2864 764 M -12 5 V .08 g 2852 769 M -15 8 V .08 g 2837 777 M -22 13 V .08 g 2815 790 M -6 3 V .08 g 2809 793 M -26 17 V .08 g 2783 810 M -1 0 V .08 g 2782 810 M -27 20 V .08 g 2755 830 M -26 20 V .08 g 2729 850 M -1 2 V .08 g 2728 852 M -22 18 V .08 g 2706 870 M -6 5 V .08 g 2700 875 M -16 15 V .08 g 2684 890 M -11 11 V .08 g 2673 901 M -9 9 V .08 g 2664 910 M -18 18 V .08 g 2646 928 M -2 3 V .08 g 2644 931 M -19 20 V .08 g 2625 951 M -6 7 V stroke 2619 958 M .08 g 2619 958 M -12 13 V .08 g 2607 971 M -16 18 V .08 g 2591 989 M -1 2 V .08 g 2590 991 M -17 20 V .08 g 2573 1011 M -9 11 V .08 g 2564 1022 M -7 9 V .08 g 2557 1031 M -16 21 V .08 g 2541 1052 M -4 4 V .08 g 2537 1056 M -12 16 V .08 g 2525 1072 M -15 20 V .08 g .08 g 2510 1092 M -15 20 V .08 g 2495 1112 M -13 18 V .08 g 2482 1130 M -1 2 V .08 g 2481 1132 M -15 20 V .08 g 2466 1152 M -11 17 V .08 g 2455 1169 M -3 3 V .08 g 2452 1172 M -13 21 V .08 g 2439 1193 M -11 16 V .08 g 2428 1209 M -3 4 V .08 g 2425 1213 M -14 20 V .08 g 2411 1233 M -10 16 V .08 g 2401 1249 M -3 4 V .08 g 2398 1253 M -13 20 V .08 g 2385 1273 M -12 18 V .08 g 2373 1291 M -1 2 V .08 g 2372 1293 M -13 21 V .08 g 2359 1314 M -13 20 V .08 g .08 g 2346 1334 M -13 20 V .08 g 2333 1354 M -13 20 V .08 g 2320 1374 M -1 2 V .08 g 2319 1376 M -11 18 V .08 g 2308 1394 M -13 20 V .08 g 2295 1414 M -3 6 V .08 g 2292 1420 M -10 15 V .08 g 2282 1435 M -12 20 V .08 g 2270 1455 M -6 8 V .08 g 2264 1463 M -7 12 V .08 g 2257 1475 M -13 20 V .08 g 2244 1495 M -7 11 V .08 g 2237 1506 M -6 9 V .08 g 2231 1515 M -12 20 V .08 g 2219 1535 M -9 14 V .08 g 2210 1549 M -4 6 V .08 g 2206 1555 M -13 21 V .08 g 2193 1576 M -10 16 V .08 g 2183 1592 M -3 4 V .08 g 2180 1596 M -13 20 V 0 g .08 g 5017 1411 M .08 g 5017 1411 M -11 -17 V .08 g 5006 1394 M -12 -20 V .08 g 4994 1374 M -5 -7 V .08 g 4989 1367 M -8 -13 V .08 g 4981 1354 M -13 -20 V stroke 4968 1334 M .08 g 4968 1334 M -6 -10 V .08 g 4962 1324 M -7 -10 V .08 g 4955 1314 M -13 -21 V .08 g 4942 1293 M -7 -12 V .08 g 4935 1281 M -6 -8 V .08 g 4929 1273 M -13 -20 V .08 g 4916 1253 M -8 -13 V .08 g 4908 1240 M -5 -7 V .08 g 4903 1233 M -14 -20 V .08 g 4889 1213 M -9 -13 V .08 g 4880 1200 M -5 -7 V .08 g 4875 1193 M -14 -21 V .08 g 4861 1172 M -8 -12 V .08 g 4853 1160 M -6 -8 V .08 g 4847 1152 M -14 -20 V .08 g 4833 1132 M -7 -9 V .08 g 4826 1123 M -8 -11 V .08 g 4818 1112 M -15 -20 V .08 g 4803 1092 M -4 -6 V .08 g 4799 1086 M -12 -14 V .08 g 4787 1072 M -16 -20 V .08 g 4771 1052 M 0 -1 V .08 g 4771 1051 M -16 -20 V .08 g 4755 1031 M -11 -13 V .08 g 4744 1018 M -6 -7 V .08 g 4738 1011 M -18 -20 V .08 g 4720 991 M -3 -4 V .08 g 4717 987 M -15 -16 V .08 g 4702 971 M -12 -13 V .08 g 4690 958 M -7 -7 V .08 g 4683 951 M -20 -20 V .08 g 4663 931 M -1 -1 V .08 g 4662 930 M -21 -20 V .08 g 4641 910 M -6 -6 V .08 g 4635 904 M -16 -14 V .08 g 4619 890 M -11 -9 V .08 g 4608 881 M -14 -11 V .08 g 4594 870 M -13 -11 V .08 g 4581 859 M -13 -9 V .08 g 4568 850 M -15 -10 V .08 g 4553 840 M -15 -10 V .08 g 4538 830 M -12 -8 V .08 g 4526 822 M -22 -12 V .08 g 4504 810 M -5 -3 V .08 g 4499 807 M -27 -14 V .08 g 4472 793 M -9 -3 V .08 g 4463 790 M -19 -8 V .08 g 4444 782 M -27 -10 V .08 g 4417 772 M -11 -3 V .08 g 4406 769 M -16 -4 V .08 g 4390 765 M -27 -5 V .08 g 4363 760 M -28 -4 V stroke 4335 756 M .08 g 4335 756 M -27 -2 V .08 g 4308 754 M -27 0 V .08 g 4281 754 M -27 2 V .08 g 4254 756 M -28 3 V .08 g 4226 759 M -27 4 V .08 g 4199 763 M -27 6 V .08 g 4172 769 M -2 0 V .08 g 4170 769 M -25 7 V .08 g 4145 776 M -28 8 V .08 g 4117 784 M -17 6 V .08 g 4100 790 M -10 3 V .08 g 4090 793 M -27 9 V .08 g 4063 802 M -20 8 V .08 g 4043 810 M -7 2 V .08 g 4036 812 M -28 11 V .08 g 4008 823 M -18 7 V .08 g 3990 830 M -9 4 V .08 g 3981 834 M -27 10 V .08 g 3954 844 M -16 6 V .08 g 3938 850 M -11 5 V .08 g 3927 855 M -28 10 V .08 g 3899 865 M -16 5 V .08 g 3883 870 M -11 4 V .08 g 3872 874 M -27 8 V .08 g 3845 882 M -27 8 V .08 g 3818 890 M -2 0 V .08 g 3816 890 M -26 6 V .08 g 3790 896 M -27 5 V .08 g 3763 901 M -27 4 V .08 g 3736 905 M -27 2 V .08 g 3709 907 M -28 0 V .08 g 3681 907 M -27 -1 V .08 g 3654 906 M -27 -3 V .08 g 3627 903 M -27 -4 V .08 g 3600 899 M -28 -6 V .08 g 3572 893 M -10 -3 V .08 g 3562 890 M -17 -4 V .08 g 3545 886 M -27 -8 V .08 g 3518 878 M -21 -8 V .08 g 3497 870 M -6 -2 V .08 g 3491 868 M -28 -10 V 0 g .08 g 6052 2621 M .08 g 6052 2621 M -14 -17 V .08 g 6038 2604 M -13 -18 V .08 g 6025 2586 M -3 -3 V .08 g 6022 2583 M -16 -20 V .08 g 6006 2563 M -8 -10 V .08 g 5998 2553 M -9 -10 V .08 g 5989 2543 M -18 -20 V .08 g 5971 2523 M -1 -1 V .08 g 5970 2522 M -17 -19 V .08 g 5953 2503 M -10 -11 V .08 g 5943 2492 M -9 -9 V stroke 5934 2483 M .08 g 5934 2483 M -18 -20 V .08 g 5916 2463 M -1 -1 V .08 g 5915 2462 M -20 -20 V .08 g 5895 2442 M -6 -6 V .08 g 5889 2436 M -15 -14 V .08 g 5874 2422 M -13 -12 V .08 g 5861 2410 M -9 -8 V .08 g 5852 2402 M -18 -17 V .08 g 5834 2385 M -4 -3 V .08 g 5830 2382 M -23 -20 V .08 g 5807 2362 M 0 -1 V .08 g 5807 2361 M -23 -20 V .08 g 5784 2341 M -4 -3 V .08 g 5780 2338 M -21 -17 V .08 g 5759 2321 M -7 -6 V .08 g 5752 2315 M -17 -14 V .08 g 5735 2301 M -10 -8 V .08 g 5725 2293 M -15 -12 V .08 g 5710 2281 M -12 -10 V .08 g 5698 2271 M -13 -10 V .08 g 5685 2261 M -14 -12 V .08 g 5671 2249 M -11 -8 V .08 g 5660 2241 M -17 -14 V .08 g 5643 2227 M -7 -6 V .08 g 5636 2221 M -20 -17 V .08 g 5616 2204 M -4 -4 V .08 g 5612 2200 M -23 -19 V .08 g 5589 2181 M -1 -1 V .08 g 5588 2180 M -23 -20 V .08 g 5565 2160 M -3 -3 V .08 g 5562 2157 M -19 -17 V .08 g 5543 2140 M -9 -8 V .08 g 5534 2132 M -12 -12 V .08 g 5522 2120 M -15 -15 V .08 g 5507 2105 M -6 -5 V .08 g 5501 2100 M -20 -21 V .08 g 5481 2079 M -1 -1 V .08 g 5480 2078 M -18 -19 V .08 g 5462 2059 M -9 -10 V .08 g 5453 2049 M -9 -10 V .08 g 5444 2039 M -18 -20 V .08 g 5426 2019 M -1 0 V .08 g 5425 2019 M -17 -20 V .08 g 5408 1999 M -10 -12 V .08 g 5398 1987 M -6 -8 V .08 g 5392 1979 M -17 -20 V .08 g 5375 1959 M -4 -6 V .08 g 5371 1953 M -12 -15 V .08 g 5359 1938 M -15 -20 V .08 g .08 g 5344 1918 M -15 -20 V .08 g 5329 1898 M -13 -17 V .08 g 5316 1881 M -2 -3 V stroke 5314 1878 M .08 g 5314 1878 M -14 -20 V .08 g 5300 1858 M -11 -15 V .08 g 5289 1843 M -3 -5 V .08 g 5286 1838 M -14 -21 V .08 g 5272 1817 M -10 -14 V .08 g 5262 1803 M -4 -6 V .08 g 5258 1797 M -13 -20 V .08 g 5245 1777 M -10 -15 V .08 g 5235 1762 M -4 -5 V .08 g 5231 1757 M -13 -20 V .08 g 5218 1737 M -11 -17 V .08 g 5207 1720 M -2 -3 V .08 g 5205 1717 M -13 -20 V .08 g 5192 1697 M -12 -20 V .08 g 5180 1677 M 0 -1 V .08 g 5180 1676 M -13 -20 V .08 g 5167 1656 M -13 -20 V .08 g 5154 1636 M -1 -3 V .08 g 5153 1633 M -11 -17 V .08 g 5142 1616 M -12 -20 V .08 g 5130 1596 M -4 -7 V .08 g 5126 1589 M -9 -13 V .08 g 5117 1576 M -12 -21 V .08 g 5105 1555 M -7 -10 V .08 g 5098 1545 M -5 -10 V .08 g 5093 1535 M -13 -20 V .08 g 5080 1515 M -9 -15 V .08 g 5071 1500 M -3 -5 V .08 g 5068 1495 M -12 -20 V .08 g 5056 1475 M -12 -20 V .08 g 5044 1455 M -1 0 V .08 g 5043 1455 M -12 -20 V .08 g 5031 1435 M -12 -21 V .08 g 5019 1414 M -2 -3 V 0 g .06 g 2028 3390 M .06 g 2028 3390 M -9 8 V .06 g 2019 3398 M -12 12 V .06 g 2007 3410 M -15 15 V .06 g 1992 3425 M -5 5 V .06 g 1987 3430 M -18 20 V .06 g 1969 3450 M -4 5 V .06 g 1965 3455 M -13 15 V .06 g 1952 3470 M -15 19 V .06 g 1937 3489 M -1 1 V .06 g 1936 3490 M -15 20 V .06 g 1921 3510 M -11 16 V .06 g 1910 3526 M -3 5 V .06 g 1907 3531 M -14 20 V .06 g 1893 3551 M -10 16 V .06 g 1883 3567 M -3 4 V .06 g 1880 3571 M -12 20 V .06 g 1868 3591 M -12 20 V .06 g 1856 3611 M -1 0 V stroke 1855 3611 M .06 g 1855 3611 M -12 20 V .06 g 1843 3631 M -11 21 V .06 g 1832 3652 M -4 6 V .06 g 1828 3658 M -8 14 V .06 g 1820 3672 M -11 20 V .06 g 1809 3692 M -8 15 V .06 g 1801 3707 M -3 5 V .06 g 1798 3712 M -10 20 V .06 g 1788 3732 M -11 20 V .06 g 1777 3752 M -3 7 V .06 g 1774 3759 M -7 13 V .06 g 1767 3772 M -10 21 V .06 g 1757 3793 M -10 20 V .06 g 1747 3813 M 0 1 V .06 g 1747 3814 M -10 19 V .06 g 1737 3833 M -10 20 V .06 g 1727 3853 M -8 17 V .06 g 1719 3870 M -1 3 V .06 g 1718 3873 M -10 20 V .06 g 1708 3893 M -9 21 V .06 g 1699 3914 M -7 14 V .06 g 1692 3928 M -3 6 V .06 g 1689 3934 M -9 20 V .06 g 1680 3954 M -9 20 V .06 g 1671 3974 M -6 13 V .06 g 1665 3987 M -4 7 V .06 g 1661 3994 M -9 20 V .06 g 1652 4014 M -9 21 V .06 g 1643 4035 M -5 12 V .06 g 1638 4047 M -4 8 V .06 g 1634 4055 M -9 20 V .06 g 1625 4075 M -9 20 V .06 g 1616 4095 M -6 13 V .06 g 1610 4108 M -3 7 V .06 g 1607 4115 M -9 20 V .06 g 1598 4135 M -9 20 V .06 g 1589 4155 M -6 14 V .06 g 1583 4169 M -3 7 V .06 g 1580 4176 M -9 20 V .06 g 1571 4196 M -9 20 V .06 g 1562 4216 M -6 15 V .06 g 1556 4231 M -3 5 V .06 g 1553 4236 M -9 20 V .06 g 1544 4256 M -8 20 V .06 g 1536 4276 M -7 17 V .06 g 1529 4293 M -2 4 V .06 g 1527 4297 M -9 20 V .06 g 1518 4317 M -9 20 V .06 g 1509 4337 M -8 17 V .06 g 1501 4354 M -1 3 V .06 g 1500 4357 M -9 20 V .06 g 1491 4377 M -9 20 V stroke 1482 4397 M .06 g 1482 4397 M -8 19 V .06 g 1474 4416 M -1 1 V .06 g 1473 4417 M -9 21 V .06 g 1464 4438 M -9 20 V .06 g 1455 4458 M -8 19 V .06 g 1447 4477 M -1 1 V .06 g 1446 4478 M -9 20 V .06 g 1437 4498 M -9 20 V .06 g 1428 4518 M -8 20 V .06 g 1420 4538 M -1 0 V .06 g 1419 4538 M -9 21 V .06 g 1410 4559 M -9 20 V .06 g 1401 4579 M -9 19 V .06 g 1392 4598 M 0 1 V .06 g 1392 4599 M -9 20 V 0 g .06 g 3545 2504 M .06 g 3545 2504 M -27 16 V .06 g 3518 2520 M -4 3 V .06 g 3514 2523 M -23 16 V .06 g 3491 2539 M -5 4 V .06 g 3486 2543 M -23 18 V .06 g 3463 2561 M -3 2 V .06 g 3460 2563 M -24 20 V .06 g 3436 2583 M 0 1 V .06 g 3436 2584 M -22 20 V .06 g 3414 2604 M -5 4 V .06 g 3409 2608 M -16 16 V .06 g 3393 2624 M -11 11 V .06 g 3382 2635 M -10 9 V .06 g 3372 2644 M -18 18 V .06 g 3354 2662 M -2 2 V .06 g 3352 2664 M -19 20 V .06 g 3333 2684 M -6 6 V .06 g 3327 2690 M -14 14 V .06 g 3313 2704 M -13 14 V .06 g 3300 2718 M -6 6 V .06 g 3294 2724 M -19 21 V .06 g 3275 2745 M -2 2 V .06 g 3273 2747 M -17 18 V .06 g 3256 2765 M -11 12 V .06 g 3245 2777 M -7 8 V .06 g 3238 2785 M -19 20 V .06 g 3219 2805 M -1 1 V .06 g 3218 2806 M -18 19 V .06 g 3200 2825 M -9 10 V .06 g 3191 2835 M -10 10 V .06 g 3181 2845 M -17 18 V .06 g 3164 2863 M -3 3 V .06 g 3161 2866 M -19 20 V .06 g 3142 2886 M -6 5 V .06 g 3136 2891 M -14 15 V .06 g 3122 2906 M -13 13 V .06 g 3109 2919 M -7 7 V stroke 3102 2926 M .06 g 3102 2926 M -20 20 V .06 g 3082 2946 M -1 0 V .06 g 3081 2946 M -21 20 V .06 g 3060 2966 M -5 6 V .06 g 3055 2972 M -17 14 V .06 g 3038 2986 M -11 11 V .06 g 3027 2997 M -11 10 V .06 g 3016 3007 M -16 14 V .06 g 3000 3021 M -7 6 V .06 g 2993 3027 M -20 17 V .06 g 2973 3044 M -4 3 V .06 g 2969 3047 M -23 19 V .06 g 2946 3066 M -2 1 V .06 g 2944 3067 M -26 20 V .06 g 2918 3087 M -1 0 V .06 g 2917 3087 M -26 19 V .06 g 2891 3106 M -2 1 V .06 g 2889 3107 M -25 17 V .06 g 2864 3124 M -5 4 V .06 g 2859 3128 M -22 13 V .06 g 2837 3141 M -11 7 V .06 g 2826 3148 M -17 9 V .06 g 2809 3157 M -20 11 V .06 g 2789 3168 M -7 4 V .06 g 2782 3172 M -27 13 V .06 g 2755 3185 M -7 3 V .06 g 2748 3188 M -20 9 V .06 g 2728 3197 M -28 11 V .06 g 2700 3208 M -27 10 V .06 g 2673 3218 M -27 8 V .06 g 2646 3226 M -7 2 V .06 g 2639 3228 M -20 6 V .06 g 2619 3234 M -28 6 V .06 g 2591 3240 M -27 6 V .06 g 2564 3246 M -13 2 V .06 g 2551 3248 M -14 3 V .06 g 2537 3251 M -27 4 V .06 g 2510 3255 M -28 3 V .06 g 2482 3258 M -27 3 V .06 g 2455 3261 M -27 3 V .06 g 2428 3264 M -27 2 V .06 g 2401 3266 M -28 2 V .06 g 2373 3268 M -2 1 V .06 g 2371 3269 M -25 2 V .06 g 2346 3271 M -27 2 V .06 g 2319 3273 M -27 4 V .06 g 2292 3277 M -28 4 V .06 g 2264 3281 M -27 5 V .06 g 2237 3286 M -12 3 V .06 g 2225 3289 M -15 3 V .06 g 2210 3292 M -27 8 V .06 g 2183 3300 M -24 9 V stroke 2159 3309 M .06 g 2159 3309 M -4 1 V .06 g 2155 3310 M -27 12 V .06 g 2128 3322 M -13 7 V .06 g 2115 3329 M -14 8 V .06 g 2101 3337 M -20 12 V .06 g 2081 3349 M -7 5 V .06 g 2074 3354 M -21 15 V .06 g 2053 3369 M -7 5 V .06 g 2046 3374 M -18 16 V 0 g .06 g 4989 3331 M .06 g 4989 3331 M -14 -2 V .06 g 4975 3329 M -13 -2 V .06 g 4962 3327 M -27 -3 V .06 g 4935 3324 M -27 -4 V .06 g 4908 3320 M -28 -4 V .06 g 4880 3316 M -27 -4 V .06 g 4853 3312 M -14 -3 V .06 g 4839 3309 M -13 -3 V .06 g 4826 3306 M -27 -5 V .06 g 4799 3301 M -28 -7 V .06 g 4771 3294 M -19 -5 V .06 g 4752 3289 M -8 -2 V .06 g 4744 3287 M -27 -9 V .06 g 4717 3278 M -27 -9 V .06 g .06 g 4690 3269 M -28 -11 V .06 g 4662 3258 M -22 -10 V .06 g 4640 3248 M -5 -2 V .06 g 4635 3246 M -27 -13 V .06 g 4608 3233 M -10 -5 V .06 g 4598 3228 M -17 -9 V .06 g 4581 3219 M -20 -11 V .06 g 4561 3208 M -8 -4 V .06 g 4553 3204 M -25 -16 V .06 g 4528 3188 M -2 -1 V .06 g 4526 3187 M -27 -18 V .06 g 4499 3169 M -2 -1 V .06 g 4497 3168 M -25 -18 V .06 g 4472 3150 M -3 -2 V .06 g 4469 3148 M -25 -19 V .06 g 4444 3129 M -2 -1 V .06 g 4442 3128 M -25 -20 V .06 g 4417 3108 M 0 -1 V .06 g 4417 3107 M -25 -20 V .06 g 4392 3087 M -2 -2 V .06 g 4390 3085 M -21 -18 V .06 g 4369 3067 M -6 -6 V .06 g 4363 3061 M -16 -14 V .06 g 4347 3047 M -12 -11 V .06 g 4335 3036 M -9 -9 V .06 g 4326 3027 M -18 -17 V .06 g 4308 3010 M -3 -3 V .06 g 4305 3007 M -21 -21 V .06 g 4284 2986 M -3 -3 V stroke 4281 2983 M .06 g 4281 2983 M -17 -17 V .06 g 4264 2966 M -10 -11 V .06 g 4254 2955 M -9 -9 V .06 g 4245 2946 M -19 -19 V .06 g 4226 2927 M 0 -1 V .06 g 4226 2926 M -19 -20 V .06 g 4207 2906 M -8 -9 V .06 g 4199 2897 M -11 -11 V .06 g 4188 2886 M -16 -18 V .06 g 4172 2868 M -2 -2 V .06 g 4170 2866 M -18 -21 V .06 g 4152 2845 M -7 -8 V .06 g 4145 2837 M -12 -12 V .06 g 4133 2825 M -16 -18 V .06 g 4117 2807 M -2 -2 V .06 g 4115 2805 M -18 -20 V .06 g 4097 2785 M -7 -8 V .06 g 4090 2777 M -11 -12 V .06 g 4079 2765 M -16 -19 V .06 g 4063 2746 M -2 -1 V .06 g 4061 2745 M -18 -21 V .06 g 4043 2724 M -7 -8 V .06 g 4036 2716 M -12 -12 V .06 g 4024 2704 M -16 -17 V .06 g 4008 2687 M -2 -3 V .06 g 4006 2684 M -19 -20 V .06 g 3987 2664 M -6 -6 V .06 g 3981 2658 M -14 -14 V .06 g 3967 2644 M -13 -14 V .06 g 3954 2630 M -7 -6 V .06 g 3947 2624 M -20 -20 V .06 g 3927 2604 M -1 0 V .06 g 3926 2604 M -22 -21 V .06 g 3904 2583 M -5 -4 V .06 g 3899 2579 M -18 -16 V .06 g 3881 2563 M -9 -8 V .06 g 3872 2555 M -16 -12 V .06 g 3856 2543 M -11 -9 V .06 g 3845 2534 M -17 -11 V .06 g 3828 2523 M -10 -7 V .06 g 3818 2516 M -23 -13 V .06 g 3795 2503 M -5 -3 V .06 g 3790 2500 M -27 -13 V .06 g 3763 2487 M -12 -4 V .06 g 3751 2483 M -15 -6 V .06 g 3736 2477 M -27 -7 V .06 g 3709 2470 M -28 -3 V .06 g 3681 2467 M -27 1 V .06 g 3654 2468 M -27 4 V .06 g 3627 2472 M -27 7 V .06 g 3600 2479 M -8 4 V .06 g 3592 2483 M -20 7 V stroke 3572 2490 M .06 g 3572 2490 M -25 13 V .06 g 3547 2503 M -2 1 V 0 g .06 g 5923 4619 M .06 g 5923 4619 M -7 -16 V .06 g 5916 4603 M -2 -4 V .06 g 5914 4599 M -9 -20 V .06 g 5905 4579 M -9 -20 V .06 g 5896 4559 M -7 -18 V .06 g 5889 4541 M -2 -3 V .06 g 5887 4538 M -8 -20 V .06 g 5879 4518 M -9 -20 V .06 g 5870 4498 M -9 -20 V .06 g .06 g 5861 4478 M -8 -20 V .06 g 5853 4458 M -9 -20 V .06 g 5844 4438 M -9 -21 V .06 g 5835 4417 M -1 -2 V .06 g 5834 4415 M -8 -18 V .06 g 5826 4397 M -8 -20 V .06 g 5818 4377 M -9 -20 V .06 g 5809 4357 M -2 -5 V .06 g 5807 4352 M -7 -15 V .06 g 5800 4337 M -8 -20 V .06 g 5792 4317 M -9 -20 V .06 g 5783 4297 M -3 -8 V .06 g 5780 4289 M -6 -13 V .06 g 5774 4276 M -9 -20 V .06 g 5765 4256 M -8 -20 V .06 g 5757 4236 M -5 -10 V .06 g 5752 4226 M -4 -10 V .06 g 5748 4216 M -9 -20 V .06 g 5739 4196 M -9 -20 V .06 g 5730 4176 M -5 -13 V .06 g 5725 4163 M -4 -8 V .06 g 5721 4155 M -8 -20 V .06 g 5713 4135 M -9 -20 V .06 g 5704 4115 M -6 -13 V .06 g 5698 4102 M -3 -7 V .06 g 5695 4095 M -9 -20 V .06 g 5686 4075 M -9 -20 V .06 g 5677 4055 M -6 -14 V .06 g 5671 4041 M -4 -6 V .06 g 5667 4035 M -9 -21 V .06 g 5658 4014 M -9 -20 V .06 g 5649 3994 M -6 -12 V .06 g 5643 3982 M -3 -8 V .06 g 5640 3974 M -10 -20 V .06 g 5630 3954 M -9 -20 V .06 g 5621 3934 M -5 -10 V .06 g 5616 3924 M -5 -10 V .06 g 5611 3914 M -10 -21 V .06 g 5601 3893 M -9 -20 V .06 g 5592 3873 M -3 -6 V .06 g 5589 3867 M -7 -14 V stroke 5582 3853 M .06 g 5582 3853 M -10 -20 V .06 g 5572 3833 M -10 -20 V .06 g 5562 3813 M -1 0 V .06 g 5561 3813 M -10 -20 V .06 g 5551 3793 M -11 -21 V .06 g 5540 3772 M -6 -11 V .06 g 5534 3761 M -5 -9 V .06 g 5529 3752 M -11 -20 V .06 g 5518 3732 M -11 -20 V .06 g .06 g 5507 3712 M -12 -20 V .06 g 5495 3692 M -12 -20 V .06 g 5483 3672 M -3 -6 V .06 g 5480 3666 M -9 -14 V .06 g 5471 3652 M -13 -21 V .06 g 5458 3631 M -5 -8 V .06 g 5453 3623 M -8 -12 V .06 g 5445 3611 M -14 -20 V .06 g 5431 3591 M -6 -8 V .06 g 5425 3583 M -9 -12 V .06 g 5416 3571 M -15 -20 V .06 g 5401 3551 M -3 -4 V .06 g 5398 3547 M -13 -16 V .06 g 5385 3531 M -14 -17 V .06 g 5371 3514 M -4 -4 V .06 g 5367 3510 M -18 -20 V .06 g 5349 3490 M -5 -5 V .06 g 5344 3485 M -16 -15 V .06 g 5328 3470 M -12 -11 V .06 g 5316 3459 M -10 -9 V .06 g 5306 3450 M -17 -14 V .06 g 5289 3436 M -9 -6 V .06 g 5280 3430 M -18 -13 V .06 g 5262 3417 M -12 -7 V .06 g 5250 3410 M -15 -10 V .06 g 5235 3400 M -21 -10 V .06 g 5214 3390 M -7 -4 V .06 g 5207 3386 M -27 -12 V .06 g 5180 3374 M -13 -5 V .06 g 5167 3369 M -14 -5 V .06 g 5153 3364 M -27 -8 V .06 g 5126 3356 M -28 -7 V .06 g 5098 3349 M -1 0 V .06 g 5097 3349 M -26 -5 V .06 g 5071 3344 M -27 -5 V .06 g 5044 3339 M -27 -4 V .06 g 5017 3335 M -28 -4 V 0 g .06 g 1173 2866 M .06 g 1173 2866 M -13 20 V .06 g 1160 2886 M -12 20 V .06 g 1148 2906 M -1 1 V .06 g 1147 2907 M -11 19 V .06 g 1136 2926 M -12 20 V .06 g 1124 2946 M -4 7 V stroke 1120 2953 M .06 g 1120 2953 M -7 13 V .06 g 1113 2966 M -12 20 V .06 g 1101 2986 M -8 16 V .06 g 1093 3002 M -3 5 V .06 g 1090 3007 M -11 20 V .06 g 1079 3027 M -11 20 V .06 g 1068 3047 M -3 6 V .06 g 1065 3053 M -7 14 V .06 g 1058 3067 M -10 20 V .06 g 1048 3087 M -10 19 V .06 g 1038 3106 M -1 1 V .06 g 1037 3107 M -9 21 V .06 g 1028 3128 M -10 20 V .06 g 1018 3148 M -7 14 V .06 g 1011 3162 M -3 6 V .06 g 1008 3168 M -10 20 V .06 g 998 3188 M -9 20 V .06 g 989 3208 M -5 11 V .06 g 984 3219 M -5 9 V .06 g 979 3228 M -9 20 V .06 g 970 3248 M -9 21 V .06 g 961 3269 M -5 10 V .06 g 956 3279 M -4 10 V .06 g 952 3289 M -9 20 V .06 g 943 3309 M -9 20 V .06 g 934 3329 M -5 12 V .06 g 929 3341 M -3 8 V .06 g 926 3349 M -9 20 V .06 g 917 3369 M -8 21 V .06 g 909 3390 M -7 15 V .06 g 902 3405 M -2 5 V .06 g 900 3410 M -8 20 V .06 g 892 3430 M -9 20 V .06 g 883 3450 M -8 20 V .06 g 875 3470 M 0 2 V .06 g 875 3472 M -8 18 V .06 g 867 3490 M -8 20 V .06 g 859 3510 M -8 21 V .06 g 851 3531 M -4 9 V .06 g 847 3540 M -4 11 V .06 g 843 3551 M -8 20 V .06 g 835 3571 M -8 20 V .06 g 827 3591 M -7 19 V .06 g 820 3610 M -1 1 V .06 g 819 3611 M -7 20 V .06 g 812 3631 M -8 21 V .06 g 804 3652 M -7 20 V .06 g 797 3672 M -4 10 V .06 g 793 3682 M -4 10 V .06 g 789 3692 M -7 20 V .06 g 782 3712 M -8 20 V .06 g 774 3732 M -8 20 V stroke 766 3752 M .06 g 766 3752 M -1 3 V .06 g 765 3755 M -6 17 V .06 g 759 3772 M -7 21 V .06 g 752 3793 M -7 20 V .06 g 745 3813 M -7 17 V .06 g 738 3830 M -1 3 V .06 g 737 3833 M -7 20 V .06 g 730 3853 M -7 20 V .06 g 723 3873 M -7 20 V .06 g 716 3893 M -5 13 V .06 g 711 3906 M -3 8 V .06 g 708 3914 M -7 20 V .06 g 701 3934 M -7 20 V .06 g 694 3954 M -7 20 V .06 g 687 3974 M -3 10 V .06 g 684 3984 M -4 10 V .06 g 680 3994 M -7 20 V .06 g 673 4014 M -7 21 V .06 g 666 4035 M -7 20 V .06 g 659 4055 M -2 8 V .06 g 657 4063 M -5 12 V .06 g 652 4075 M -7 20 V .06 g 645 4095 M -6 20 V .06 g 639 4115 M -7 20 V .06 g 632 4135 M -3 7 V .06 g 629 4142 M -4 13 V .06 g 625 4155 M -7 21 V .06 g 618 4176 M -7 20 V .06 g 611 4196 M -7 20 V .06 g 604 4216 M -2 6 V 0 g .06 g 2259 1697 M .06 g 2259 1697 M -12 20 V .06 g 2247 1717 M -10 18 V .06 g 2237 1735 M -1 2 V .06 g 2236 1737 M -12 20 V .06 g 2224 1757 M -11 20 V .06 g 2213 1777 M -3 6 V .06 g 2210 1783 M -9 14 V .06 g 2201 1797 M -11 20 V .06 g 2190 1817 M -7 13 V .06 g 2183 1830 M -5 8 V .06 g 2178 1838 M -12 20 V .06 g 2166 1858 M -11 18 V .06 g 2155 1876 M -1 2 V .06 g 2154 1878 M -12 20 V .06 g 2142 1898 M -12 20 V .06 g 2130 1918 M -2 4 V .06 g 2128 1922 M -10 16 V .06 g 2118 1938 M -13 21 V .06 g 2105 1959 M -4 7 V .06 g 2101 1966 M -9 13 V .06 g 2092 1979 M -13 20 V .06 g 2079 1999 M -5 9 V stroke 2074 2008 M .06 g 2074 2008 M -8 11 V .06 g 2066 2019 M -14 20 V .06 g 2052 2039 M -6 9 V .06 g 2046 2048 M -8 11 V .06 g 2038 2059 M -14 20 V .06 g 2024 2079 M -5 7 V .06 g 2019 2086 M -10 14 V .06 g 2009 2100 M -16 20 V .06 g 1993 2120 M -1 2 V .06 g 1992 2122 M -15 18 V .06 g 1977 2140 M -12 15 V .06 g 1965 2155 M -5 5 V .06 g 1960 2160 M -18 20 V .06 g 1942 2180 M -5 6 V .06 g 1937 2186 M -13 14 V .06 g 1924 2200 M -14 14 V .06 g 1910 2214 M -6 7 V .06 g 1904 2221 M -21 19 V .06 g 1883 2240 M -1 1 V .06 g 1882 2241 M -22 20 V .06 g 1860 2261 M -4 3 V .06 g 1856 2264 M -21 17 V .06 g 1835 2281 M -7 5 V .06 g 1828 2286 M -20 15 V .06 g 1808 2301 M -7 6 V .06 g 1801 2307 M -21 14 V .06 g 1780 2321 M -6 4 V .06 g 1774 2325 M -25 16 V .06 g 1749 2341 M -2 2 V .06 g 1747 2343 M -28 17 V .06 g 1719 2360 M -3 2 V .06 g 1716 2362 M -24 14 V .06 g 1692 2376 M -9 6 V .06 g 1683 2382 M -18 10 V .06 g 1665 2392 M -17 10 V .06 g 1648 2402 M -10 6 V .06 g 1638 2408 M -23 14 V .06 g 1615 2422 M -5 3 V .06 g 1610 2425 M -27 16 V .06 g 1583 2441 M -1 1 V .06 g 1582 2442 M -26 17 V .06 g 1556 2459 M -5 3 V .06 g 1551 2462 M -22 15 V .06 g 1529 2477 M -8 6 V .06 g 1521 2483 M -20 14 V .06 g 1501 2497 M -7 6 V .06 g 1494 2503 M -20 15 V .06 g 1474 2518 M -6 5 V .06 g 1468 2523 M -21 17 V .06 g 1447 2540 M -4 3 V .06 g 1443 2543 M -23 20 V .06 g .06 g 1420 2563 M -22 20 V stroke 1398 2583 M .06 g 1398 2583 M -6 6 V .06 g 1392 2589 M -14 15 V .06 g 1378 2604 M -13 12 V .06 g 1365 2616 M -7 8 V .06 g 1358 2624 M -19 20 V .06 g 1339 2644 M -1 1 V .06 g 1338 2645 M -17 19 V .06 g 1321 2664 M -10 12 V .06 g 1311 2676 M -7 8 V .06 g 1304 2684 M -17 20 V .06 g 1287 2704 M -4 5 V .06 g 1283 2709 M -11 15 V .06 g 1272 2724 M -16 20 V .06 g 1256 2744 M 0 1 V .06 g 1256 2745 M -15 20 V .06 g 1241 2765 M -12 17 V .06 g 1229 2782 M -2 3 V .06 g 1227 2785 M -14 20 V .06 g 1213 2805 M -11 16 V .06 g 1202 2821 M -3 4 V .06 g 1199 2825 M -13 20 V .06 g 1186 2845 M -12 18 V .06 g 1174 2863 M -1 3 V 0 g .06 g 3534 1132 M .06 g 3534 1132 M -16 -7 V .06 g 3518 1125 M -26 -13 V .06 g 3492 1112 M -1 -1 V .06 g 3491 1111 M -28 -15 V .06 g 3463 1096 M -7 -4 V .06 g 3456 1092 M -20 -11 V .06 g 3436 1081 M -15 -9 V .06 g 3421 1072 M -12 -8 V .06 g 3409 1064 M -21 -12 V .06 g 3388 1052 M -6 -4 V .06 g 3382 1048 M -27 -17 V .06 g 3355 1031 M -1 0 V .06 g 3354 1031 M -27 -17 V .06 g 3327 1014 M -5 -3 V .06 g 3322 1011 M -22 -13 V .06 g 3300 998 M -13 -7 V .06 g 3287 991 M -14 -8 V .06 g 3273 983 M -23 -12 V .06 g 3250 971 M -5 -2 V .06 g 3245 969 M -27 -14 V .06 g 3218 955 M -10 -4 V .06 g 3208 951 M -17 -8 V .06 g 3191 943 M -27 -11 V .06 g 3164 932 M -5 -1 V .06 g 3159 931 M -23 -8 V .06 g 3136 923 M -27 -8 V .06 g 3109 915 M -22 -5 V .06 g 3087 910 M -5 -1 V .06 g 3082 909 M -27 -4 V stroke 3055 905 M .06 g 3055 905 M -28 -2 V .06 g 3027 903 M -27 0 V .06 g 3000 903 M -27 2 V .06 g 2973 905 M -27 5 V .06 g 2946 910 M -4 0 V .06 g 2942 910 M -24 6 V .06 g 2918 916 M -27 9 V .06 g 2891 925 M -15 6 V .06 g 2876 931 M -12 5 V .06 g 2864 936 M -27 13 V .06 g 2837 949 M -4 2 V .06 g 2833 951 M -24 13 V .06 g 2809 964 M -10 7 V .06 g 2799 971 M -17 11 V .06 g 2782 982 M -12 9 V .06 g 2770 991 M -15 11 V .06 g 2755 1002 M -11 9 V .06 g 2744 1011 M -16 14 V .06 g 2728 1025 M -8 6 V .06 g 2720 1031 M -20 18 V .06 g 2700 1049 M -2 3 V .06 g 2698 1052 M -20 20 V .06 g 2678 1072 M -5 4 V .06 g 2673 1076 M -15 16 V .06 g 2658 1092 M -12 13 V .06 g 2646 1105 M -6 7 V .06 g 2640 1112 M -18 20 V .06 g 2622 1132 M -3 4 V .06 g 2619 1136 M -14 16 V .06 g 2605 1152 M -14 17 V .06 g 2591 1169 M -2 3 V .06 g 2589 1172 M -16 21 V .06 g 2573 1193 M -9 12 V .06 g 2564 1205 M -6 8 V .06 g 2558 1213 M -15 20 V .06 g 2543 1233 M -6 9 V .06 g 2537 1242 M -8 11 V .06 g 2529 1253 M -15 20 V .06 g 2514 1273 M -4 7 V .06 g 2510 1280 M -9 13 V .06 g 2501 1293 M -14 21 V .06 g 2487 1314 M -5 7 V .06 g 2482 1321 M -8 13 V .06 g 2474 1334 M -13 20 V .06 g 2461 1354 M -6 9 V .06 g 2455 1363 M -7 11 V .06 g 2448 1374 M -13 20 V .06 g 2435 1394 M -7 12 V .06 g 2428 1406 M -5 8 V .06 g 2423 1414 M -13 21 V .06 g 2410 1435 M -9 16 V .06 g 2401 1451 M -3 4 V stroke 2398 1455 M .06 g 2398 1455 M -12 20 V .06 g 2386 1475 M -12 20 V .06 g 2374 1495 M -1 2 V .06 g 2373 1497 M -11 18 V .06 g 2362 1515 M -11 20 V .06 g 2351 1535 M -5 8 V .06 g 2346 1543 M -7 12 V .06 g 2339 1555 M -12 21 V .06 g 2327 1576 M -8 15 V .06 g 2319 1591 M -3 5 V .06 g 2316 1596 M -12 20 V .06 g 2304 1616 M -11 20 V .06 g 2293 1636 M -1 2 V .06 g 2292 1638 M -11 18 V .06 g 2281 1656 M -11 20 V .06 g 2270 1676 M -6 11 V .06 g 2264 1687 M -5 10 V 0 g .06 g 5002 1596 M .06 g 5002 1596 M -12 -20 V .06 g 4990 1576 M -1 -2 V .06 g 4989 1574 M -10 -19 V .06 g 4979 1555 M -12 -20 V .06 g 4967 1535 M -5 -8 V .06 g 4962 1527 M -7 -12 V .06 g 4955 1515 M -12 -20 V .06 g 4943 1495 M -8 -15 V .06 g 4935 1480 M -4 -5 V .06 g 4931 1475 M -12 -20 V .06 g 4919 1455 M -11 -20 V .06 g 4908 1435 M -1 0 V .06 g 4907 1435 M -12 -21 V .06 g 4895 1414 M -13 -20 V .06 g 4882 1394 M -2 -3 V .06 g 4880 1391 M -11 -17 V .06 g 4869 1374 M -13 -20 V .06 g 4856 1354 M -3 -5 V .06 g 4853 1349 M -10 -15 V .06 g 4843 1334 M -14 -20 V .06 g 4829 1314 M -3 -5 V .06 g 4826 1309 M -11 -16 V .06 g 4815 1293 M -14 -20 V .06 g 4801 1273 M -2 -3 V .06 g 4799 1270 M -13 -17 V .06 g 4786 1253 M -14 -20 V .06 g 4772 1233 M -1 0 V .06 g 4771 1233 M -15 -20 V .06 g 4756 1213 M -12 -15 V .06 g 4744 1198 M -4 -5 V .06 g 4740 1193 M -17 -21 V .06 g 4723 1172 M -6 -8 V .06 g 4717 1164 M -11 -12 V .06 g 4706 1152 M -16 -19 V .06 g 4690 1133 M -2 -1 V stroke 4688 1132 M .06 g 4688 1132 M -19 -20 V .06 g 4669 1112 M -7 -7 V .06 g 4662 1105 M -13 -13 V .06 g 4649 1092 M -14 -14 V .06 g 4635 1078 M -7 -6 V .06 g 4628 1072 M -20 -19 V .06 g 4608 1053 M -3 -1 V .06 g 4605 1052 M -24 -21 V .06 g .06 g 4581 1031 M -28 -20 V .06 g .06 g 4553 1011 M -27 -17 V .06 g 4526 994 M -5 -3 V .06 g 4521 991 M -22 -12 V .06 g 4499 979 M -16 -8 V .06 g 4483 971 M -11 -5 V .06 g 4472 966 M -28 -11 V .06 g 4444 955 M -13 -4 V .06 g 4431 951 M -14 -5 V .06 g 4417 946 M -27 -6 V .06 g 4390 940 M -27 -4 V .06 g 4363 936 M -28 -2 V .06 g 4335 934 M -27 0 V .06 g 4308 934 M -27 2 V .06 g 4281 936 M -27 4 V .06 g 4254 940 M -28 6 V .06 g 4226 946 M -17 5 V .06 g 4209 951 M -10 2 V .06 g 4199 953 M -27 10 V .06 g 4172 963 M -22 8 V .06 g 4150 971 M -5 2 V .06 g 4145 973 M -28 12 V .06 g 4117 985 M -14 6 V .06 g 4103 991 M -13 7 V .06 g 4090 998 M -27 13 V .06 g 4063 1011 M -27 15 V .06 g 4036 1026 M -11 5 V .06 g 4025 1031 M -17 10 V .06 g 4008 1041 M -19 11 V .06 g 3989 1052 M -8 4 V .06 g 3981 1056 M -27 16 V .06 g .06 g 3954 1072 M -27 15 V .06 g 3927 1087 M -10 5 V .06 g 3917 1092 M -18 10 V .06 g 3899 1102 M -20 10 V .06 g 3879 1112 M -7 3 V .06 g 3872 1115 M -27 13 V .06 g 3845 1128 M -10 4 V .06 g 3835 1132 M -17 8 V .06 g 3818 1140 M -28 10 V .06 g 3790 1150 M -10 2 V .06 g 3780 1152 M -17 5 V .06 g 3763 1157 M -27 6 V .06 g 3736 1163 M -27 4 V stroke 3709 1167 M .06 g 3709 1167 M -28 1 V .06 g 3681 1168 M -27 -2 V .06 g 3654 1166 M -27 -4 V .06 g 3627 1162 M -27 -6 V .06 g 3600 1156 M -12 -4 V .06 g 3588 1152 M -16 -4 V .06 g 3572 1148 M -27 -11 V .06 g 3545 1137 M -11 -5 V 0 g .06 g 6052 2799 M .06 g 6052 2799 M -12 -14 V .06 g 6040 2785 M -15 -19 V .06 g 6025 2766 M -1 -1 V .06 g 6024 2765 M -18 -20 V .06 g 6006 2745 M -8 -10 V .06 g 5998 2735 M -10 -11 V .06 g 5988 2724 M -18 -18 V .06 g 5970 2706 M -1 -2 V .06 g 5969 2704 M -21 -20 V .06 g 5948 2684 M -5 -5 V .06 g 5943 2679 M -16 -15 V .06 g 5927 2664 M -11 -11 V .06 g 5916 2653 M -11 -9 V .06 g 5905 2644 M -16 -15 V .06 g 5889 2629 M -7 -5 V .06 g 5882 2624 M -21 -17 V .06 g 5861 2607 M -4 -3 V .06 g 5857 2604 M -23 -19 V .06 g 5834 2585 M -3 -2 V .06 g 5831 2583 M -24 -18 V .06 g 5807 2565 M -3 -2 V .06 g 5804 2563 M -24 -17 V .06 g 5780 2546 M -5 -3 V .06 g 5775 2543 M -23 -15 V .06 g 5752 2528 M -8 -5 V .06 g 5744 2523 M -19 -13 V .06 g 5725 2510 M -12 -7 V .06 g 5713 2503 M -15 -10 V .06 g 5698 2493 M -17 -10 V .06 g 5681 2483 M -10 -7 V .06 g 5671 2476 M -21 -14 V .06 g 5650 2462 M -7 -4 V .06 g 5643 2458 M -24 -16 V .06 g 5619 2442 M -3 -2 V .06 g 5616 2440 M -26 -18 V .06 g 5590 2422 M -1 -1 V .06 g 5589 2421 M -27 -19 V .06 g .06 g 5562 2402 M -26 -20 V .06 g 5536 2382 M -2 -1 V .06 g 5534 2381 M -23 -19 V .06 g 5511 2362 M -4 -4 V .06 g 5507 2358 M -19 -17 V .06 g 5488 2341 M -8 -7 V .06 g 5480 2334 M -13 -13 V stroke 5467 2321 M .06 g 5467 2321 M -14 -14 V .06 g 5453 2307 M -6 -6 V .06 g 5447 2301 M -19 -20 V .06 g 5428 2281 M -3 -3 V .06 g 5425 2278 M -15 -17 V .06 g 5410 2261 M -12 -14 V .06 g 5398 2247 M -5 -6 V .06 g 5393 2241 M -16 -20 V .06 g 5377 2221 M -6 -8 V .06 g 5371 2213 M -10 -13 V .06 g 5361 2200 M -15 -20 V .06 g 5346 2180 M -2 -3 V .06 g 5344 2177 M -12 -17 V .06 g 5332 2160 M -15 -20 V .06 g 5317 2140 M -1 -2 V .06 g 5316 2138 M -12 -18 V .06 g 5304 2120 M -14 -20 V .06 g 5290 2100 M -1 -3 V .06 g 5289 2097 M -11 -18 V .06 g 5278 2079 M -13 -20 V .06 g 5265 2059 M -3 -4 V .06 g 5262 2055 M -10 -16 V .06 g 5252 2039 M -12 -20 V .06 g 5240 2019 M -5 -9 V .06 g 5235 2010 M -7 -11 V .06 g 5228 1999 M -12 -20 V .06 g 5216 1979 M -9 -15 V .06 g 5207 1964 M -3 -5 V .06 g 5204 1959 M -11 -21 V .06 g 5193 1938 M -12 -20 V .06 g 5181 1918 M -1 -2 V .06 g 5180 1916 M -10 -18 V .06 g 5170 1898 M -12 -20 V .06 g 5158 1878 M -5 -10 V .06 g 5153 1868 M -6 -10 V .06 g 5147 1858 M -11 -20 V .06 g 5136 1838 M -10 -19 V .06 g 5126 1819 M -1 -2 V .06 g 5125 1817 M -11 -20 V .06 g 5114 1797 M -12 -20 V .06 g 5102 1777 M -4 -7 V .06 g 5098 1770 M -7 -13 V .06 g 5091 1757 M -11 -20 V .06 g 5080 1737 M -9 -17 V .06 g 5071 1720 M -2 -3 V .06 g 5069 1717 M -11 -20 V .06 g 5058 1697 M -11 -21 V .06 g 5047 1676 M -3 -5 V .06 g 5044 1671 M -9 -15 V .06 g 5035 1656 M -11 -20 V .06 g 5024 1636 M -7 -14 V .06 g 5017 1622 M -4 -6 V stroke 5013 1616 M .06 g 5013 1616 M -11 -20 V 0 g .04 g 1708 3551 M .04 g 1708 3551 M -8 20 V .04 g 1700 3571 M -7 20 V .04 g 1693 3591 M -1 3 V .04 g 1692 3594 M -6 17 V .04 g 1686 3611 M -8 20 V .04 g 1678 3631 M -7 21 V .04 g 1671 3652 M -6 16 V .04 g 1665 3668 M -2 4 V .04 g 1663 3672 M -7 20 V .04 g 1656 3692 M -7 20 V .04 g 1649 3712 M -8 20 V .04 g 1641 3732 M -3 10 V .04 g 1638 3742 M -4 10 V .04 g 1634 3752 M -8 20 V .04 g 1626 3772 M -7 21 V .04 g 1619 3793 M -8 20 V .04 g 1611 3813 M -1 2 V .04 g 1610 3815 M -6 18 V .04 g 1604 3833 M -8 20 V .04 g 1596 3853 M -7 20 V .04 g 1589 3873 M -6 15 V .04 g 1583 3888 M -2 5 V .04 g 1581 3893 M -8 21 V .04 g 1573 3914 M -7 20 V .04 g 1566 3934 M -8 20 V .04 g 1558 3954 M -2 6 V .04 g 1556 3960 M -6 14 V .04 g 1550 3974 M -7 20 V .04 g 1543 3994 M -8 20 V .04 g 1535 4014 M -6 17 V .04 g 1529 4031 M -2 4 V .04 g 1527 4035 M -8 20 V .04 g 1519 4055 M -8 20 V .04 g 1511 4075 M -7 20 V .04 g 1504 4095 M -3 6 V .04 g 1501 4101 M -5 14 V .04 g 1496 4115 M -8 20 V .04 g 1488 4135 M -8 20 V .04 g 1480 4155 M -6 15 V .04 g 1474 4170 M -2 6 V .04 g 1472 4176 M -8 20 V .04 g 1464 4196 M -8 20 V .04 g 1456 4216 M -8 20 V .04 g 1448 4236 M -1 2 V .04 g 1447 4238 M -8 18 V .04 g 1439 4256 M -8 20 V .04 g 1431 4276 M -8 21 V .04 g 1423 4297 M -3 8 V .04 g 1420 4305 M -6 12 V .04 g 1414 4317 M -8 20 V .04 g 1406 4337 M -8 20 V stroke 1398 4357 M .04 g 1398 4357 M -6 13 V .04 g 1392 4370 M -3 7 V .04 g 1389 4377 M -8 20 V .04 g 1381 4397 M -9 20 V .04 g 1372 4417 M -7 17 V .04 g 1365 4434 M -2 4 V .04 g 1363 4438 M -8 20 V .04 g 1355 4458 M -9 20 V .04 g 1346 4478 M -8 19 V .04 g 1338 4497 M -1 1 V .04 g 1337 4498 M -9 20 V .04 g 1328 4518 M -9 20 V .04 g 1319 4538 M -8 20 V .04 g 1311 4558 M -1 1 V .04 g 1310 4559 M -9 20 V .04 g 1301 4579 M -9 20 V .04 g 1292 4599 M -9 18 V .04 g 1283 4617 M 0 2 V 0 g .04 g 3023 2785 M .04 g 3023 2785 M -21 20 V .04 g 3002 2805 M -2 2 V .04 g 3000 2807 M -19 18 V .04 g 2981 2825 M -8 8 V .04 g 2973 2833 M -14 12 V .04 g 2959 2845 M -13 12 V .04 g 2946 2857 M -11 9 V .04 g 2935 2866 M -17 14 V .04 g 2918 2880 M -8 6 V .04 g 2910 2886 M -19 14 V .04 g 2891 2900 M -8 6 V .04 g 2883 2906 M -19 14 V .04 g 2864 2920 M -10 6 V .04 g 2854 2926 M -17 11 V .04 g 2837 2937 M -16 9 V .04 g 2821 2946 M -12 7 V .04 g 2809 2953 M -25 13 V .04 g 2784 2966 M -2 1 V .04 g 2782 2967 M -27 13 V .04 g 2755 2980 M -17 6 V .04 g 2738 2986 M -10 5 V .04 g 2728 2991 M -28 9 V .04 g 2700 3000 M -24 7 V .04 g 2676 3007 M -3 1 V .04 g 2673 3008 M -27 6 V .04 g 2646 3014 M -27 4 V .04 g 2619 3018 M -28 3 V .04 g 2591 3021 M -27 2 V .04 g 2564 3023 M -27 0 V .04 g 2537 3023 M -27 -1 V .04 g 2510 3022 M -28 -3 V .04 g 2482 3019 M -27 -4 V .04 g 2455 3015 M -27 -4 V .04 g 2428 3011 M -19 -4 V stroke 2409 3007 M .04 g 2409 3007 M -8 -2 V .04 g 2401 3005 M -28 -7 V .04 g 2373 2998 M -27 -8 V .04 g 2346 2990 M -12 -4 V .04 g 2334 2986 M -15 -5 V .04 g 2319 2981 M -27 -9 V .04 g 2292 2972 M -18 -6 V .04 g 2274 2966 M -10 -4 V .04 g 2264 2962 M -27 -10 V .04 g 2237 2952 M -17 -6 V .04 g 2220 2946 M -10 -4 V .04 g 2210 2942 M -27 -10 V .04 g 2183 2932 M -17 -6 V .04 g 2166 2926 M -11 -4 V .04 g 2155 2922 M -27 -10 V .04 g 2128 2912 M -22 -6 V .04 g 2106 2906 M -5 -2 V .04 g 2101 2904 M -27 -7 V .04 g 2074 2897 M -28 -3 V .04 g 2046 2894 M -27 2 V .04 g 2019 2896 M -23 10 V .04 g 1996 2906 M -4 2 V .04 g 1992 2908 M -21 18 V .04 g 1971 2926 M -6 6 V .04 g 1965 2932 M -11 14 V .04 g 1954 2946 M -13 20 V .04 g 1941 2966 M -4 6 V .04 g 1937 2972 M -7 14 V .04 g 1930 2986 M -11 21 V .04 g 1919 3007 M -9 18 V .04 g 1910 3025 M -1 2 V .04 g 1909 3027 M -9 20 V .04 g 1900 3047 M -9 20 V .04 g 1891 3067 M -8 20 V .04 g .04 g 1883 3087 M -9 20 V .04 g 1874 3107 M -8 21 V .04 g 1866 3128 M -8 20 V .04 g 1858 3148 M -2 6 V .04 g 1856 3154 M -6 14 V .04 g 1850 3168 M -8 20 V .04 g 1842 3188 M -7 20 V .04 g 1835 3208 M -7 17 V .04 g 1828 3225 M -1 3 V .04 g 1827 3228 M -8 20 V .04 g 1819 3248 M -7 21 V .04 g 1812 3269 M -8 20 V .04 g 1804 3289 M -3 8 V .04 g 1801 3297 M -4 12 V .04 g 1797 3309 M -8 20 V .04 g 1789 3329 M -7 20 V .04 g 1782 3349 M -8 20 V .04 g 1774 3369 M 0 2 V stroke 1774 3371 M .04 g 1774 3371 M -7 19 V .04 g 1767 3390 M -8 20 V .04 g 1759 3410 M -7 20 V .04 g 1752 3430 M -5 15 V .04 g 1747 3445 M -2 5 V .04 g 1745 3450 M -8 20 V .04 g 1737 3470 M -7 20 V .04 g 1730 3490 M -7 20 V .04 g 1723 3510 M -4 9 V .04 g 1719 3519 M -4 12 V .04 g 1715 3531 M -7 20 V 0 g .04 g 3993 2362 M .04 g 3993 2362 M -12 -20 V .04 g 3981 2342 M 0 -1 V .04 g 3981 2341 M -13 -20 V .04 g 3968 2321 M -13 -20 V .04 g 3955 2301 M -1 -2 V .04 g 3954 2299 M -12 -18 V .04 g 3942 2281 M -13 -20 V .04 g 3929 2261 M -2 -5 V .04 g 3927 2256 M -11 -15 V .04 g 3916 2241 M -12 -20 V .04 g 3904 2221 M -5 -8 V .04 g 3899 2213 M -8 -13 V .04 g 3891 2200 M -13 -20 V .04 g 3878 2180 M -6 -10 V .04 g 3872 2170 M -7 -10 V .04 g 3865 2160 M -13 -20 V .04 g 3852 2140 M -7 -12 V .04 g 3845 2128 M -6 -8 V .04 g 3839 2120 M -13 -20 V .04 g 3826 2100 M -8 -13 V .04 g 3818 2087 M -6 -8 V .04 g 3812 2079 M -14 -20 V .04 g 3798 2059 M -8 -12 V .04 g 3790 2047 M -6 -8 V .04 g 3784 2039 M -15 -20 V .04 g 3769 2019 M -6 -9 V .04 g 3763 2010 M -11 -11 V .04 g 3752 1999 M -16 -20 V .04 g 3736 1979 M -1 0 V .04 g 3735 1979 M -23 -20 V .04 g 3712 1959 M -3 -3 V .04 g 3709 1956 M -28 -11 V .04 g 3681 1945 M -27 4 V .04 g 3654 1949 M -13 10 V .04 g 3641 1959 M -14 8 V .04 g 3627 1967 M -10 12 V .04 g 3617 1979 M -17 17 V .04 g 3600 1996 M -3 3 V .04 g 3597 1999 M -16 20 V .04 g 3581 2019 M -9 10 V .04 g 3572 2029 M -6 10 V stroke 3566 2039 M .04 g 3566 2039 M -15 20 V .04 g 3551 2059 M -6 8 V .04 g 3545 2067 M -8 12 V .04 g 3537 2079 M -14 21 V .04 g 3523 2100 M -5 6 V .04 g 3518 2106 M -9 14 V .04 g 3509 2120 M -13 20 V .04 g 3496 2140 M -5 7 V .04 g 3491 2147 M -9 13 V .04 g 3482 2160 M -13 20 V .04 g 3469 2180 M -6 9 V .04 g 3463 2189 M -7 11 V .04 g 3456 2200 M -13 21 V .04 g 3443 2221 M -7 9 V .04 g 3436 2230 M -7 11 V .04 g 3429 2241 M -13 20 V .04 g 3416 2261 M -7 11 V .04 g 3409 2272 M -6 9 V .04 g 3403 2281 M -13 20 V .04 g 3390 2301 M -8 13 V .04 g 3382 2314 M -5 7 V .04 g 3377 2321 M -14 20 V .04 g 3363 2341 M -9 14 V .04 g 3354 2355 M -4 7 V .04 g 3350 2362 M -13 20 V .04 g 3337 2382 M -10 14 V .04 g 3327 2396 M -4 6 V .04 g 3323 2402 M -14 20 V .04 g 3309 2422 M -9 14 V .04 g 3300 2436 M -5 6 V .04 g 3295 2442 M -14 20 V .04 g 3281 2462 M -8 13 V .04 g 3273 2475 M -6 8 V .04 g 3267 2483 M -14 20 V .04 g 3253 2503 M -8 11 V .04 g 3245 2514 M -6 9 V .04 g 3239 2523 M -15 20 V .04 g 3224 2543 M -6 8 V .04 g 3218 2551 M -9 12 V .04 g 3209 2563 M -15 20 V .04 g 3194 2583 M -3 5 V .04 g 3191 2588 M -12 16 V .04 g 3179 2604 M -15 19 V .04 g 3164 2623 M -1 1 V .04 g 3163 2624 M -16 20 V .04 g 3147 2644 M -11 13 V .04 g 3136 2657 M -5 7 V .04 g 3131 2664 M -17 20 V .04 g 3114 2684 M -5 6 V .04 g 3109 2690 M -12 14 V .04 g 3097 2704 M -15 18 V .04 g 3082 2722 M -3 2 V stroke 3079 2724 M .04 g 3079 2724 M -18 21 V .04 g 3061 2745 M -6 7 V .04 g 3055 2752 M -13 13 V .04 g 3042 2765 M -15 15 V .04 g 3027 2780 M -4 5 V 0 g .04 g 5425 3071 M .04 g 5425 3071 M -2 -4 V .04 g 5423 3067 M -11 -20 V .04 g 5412 3047 M -13 -20 V .04 g 5399 3027 M -1 -2 V .04 g 5398 3025 M -15 -18 V .04 g 5383 3007 M -12 -13 V .04 g 5371 2994 M -12 -8 V .04 g 5359 2986 M -15 -9 V .04 g 5344 2977 M -28 -6 V .04 g 5316 2971 M -27 1 V .04 g 5289 2972 M -27 4 V .04 g 5262 2976 M -27 7 V .04 g 5235 2983 M -13 3 V .04 g 5222 2986 M -15 4 V .04 g 5207 2990 M -27 9 V .04 g 5180 2999 M -22 8 V .04 g 5158 3007 M -5 1 V .04 g 5153 3008 M -27 9 V .04 g 5126 3017 M -28 9 V .04 g 5098 3026 M -2 1 V .04 g 5096 3027 M -25 8 V .04 g 5071 3035 M -27 8 V .04 g 5044 3043 M -15 4 V .04 g 5029 3047 M -12 3 V .04 g 5017 3050 M -28 7 V .04 g 4989 3057 M -27 6 V .04 g 4962 3063 M -22 4 V .04 g 4940 3067 M -5 1 V .04 g 4935 3068 M -27 4 V .04 g 4908 3072 M -28 3 V .04 g 4880 3075 M -27 1 V .04 g 4853 3076 M -27 1 V .04 g 4826 3077 M -27 -1 V .04 g 4799 3076 M -28 -3 V .04 g 4771 3073 M -27 -3 V .04 g 4744 3070 M -13 -3 V .04 g 4731 3067 M -14 -3 V .04 g 4717 3064 M -27 -7 V .04 g 4690 3057 M -28 -8 V .04 g 4662 3049 M -6 -2 V .04 g 4656 3047 M -21 -8 V .04 g 4635 3039 M -27 -12 V .04 g 4608 3027 M -2 0 V .04 g 4606 3027 M -25 -13 V .04 g 4581 3014 M -14 -7 V .04 g 4567 3007 M -14 -8 V .04 g 4553 2999 M -21 -13 V stroke 4532 2986 M .04 g 4532 2986 M -6 -3 V .04 g 4526 2983 M -24 -17 V .04 g 4502 2966 M -3 -2 V .04 g 4499 2964 M -25 -18 V .04 g 4474 2946 M -2 -1 V .04 g 4472 2945 M -24 -19 V .04 g 4448 2926 M -4 -3 V .04 g 4444 2923 M -20 -17 V .04 g 4424 2906 M -7 -6 V .04 g 4417 2900 M -15 -14 V .04 g 4402 2886 M -12 -11 V .04 g 4390 2875 M -10 -9 V .04 g 4380 2866 M -17 -17 V .04 g 4363 2849 M -4 -4 V .04 g 4359 2845 M -19 -20 V .04 g 4340 2825 M -5 -4 V .04 g 4335 2821 M -14 -16 V .04 g 4321 2805 M -13 -14 V .04 g 4308 2791 M -6 -6 V .04 g 4302 2785 M -17 -20 V .04 g 4285 2765 M -4 -5 V .04 g 4281 2760 M -14 -15 V .04 g 4267 2745 M -13 -17 V .04 g 4254 2728 M -3 -4 V .04 g 4251 2724 M -17 -20 V .04 g 4234 2704 M -8 -10 V .04 g 4226 2694 M -8 -10 V .04 g 4218 2684 M -15 -20 V .04 g 4203 2664 M -4 -5 V .04 g 4199 2659 M -12 -15 V .04 g 4187 2644 M -15 -20 V .04 g 4172 2624 M 0 -1 V .04 g 4172 2623 M -15 -19 V .04 g 4157 2604 M -12 -18 V .04 g 4145 2586 M -2 -3 V .04 g 4143 2583 M -15 -20 V .04 g 4128 2563 M -11 -16 V .04 g 4117 2547 M -3 -4 V .04 g 4114 2543 M -14 -20 V .04 g 4100 2523 M -10 -15 V .04 g 4090 2508 M -3 -5 V .04 g 4087 2503 M -14 -20 V .04 g 4073 2483 M -10 -16 V .04 g 4063 2467 M -4 -5 V .04 g 4059 2462 M -13 -20 V .04 g 4046 2442 M -10 -16 V .04 g 4036 2426 M -3 -4 V .04 g 4033 2422 M -13 -20 V .04 g 4020 2402 M -12 -18 V .04 g 4008 2384 M -1 -2 V .04 g 4007 2382 M -14 -20 V 0 g .04 g 6021 4619 M .04 g 6021 4619 M -9 -20 V stroke 6012 4599 M .04 g 6012 4599 M -8 -20 V .04 g 6004 4579 M -6 -14 V .04 g 5998 4565 M -3 -6 V .04 g 5995 4559 M -8 -21 V .04 g 5987 4538 M -9 -20 V .04 g 5978 4518 M -8 -18 V .04 g 5970 4500 M 0 -2 V .04 g 5970 4498 M -9 -20 V .04 g 5961 4478 M -8 -20 V .04 g 5953 4458 M -8 -20 V .04 g 5945 4438 M -2 -4 V .04 g 5943 4434 M -6 -17 V .04 g 5937 4417 M -9 -20 V .04 g 5928 4397 M -8 -20 V .04 g 5920 4377 M -4 -11 V .04 g 5916 4366 M -4 -9 V .04 g 5912 4357 M -8 -20 V .04 g 5904 4337 M -8 -20 V .04 g 5896 4317 M -7 -20 V .04 g 5889 4297 M -1 0 V .04 g 5888 4297 M -8 -21 V .04 g 5880 4276 M -7 -20 V .04 g 5873 4256 M -8 -20 V .04 g 5865 4236 M -4 -9 V .04 g 5861 4227 M -4 -11 V .04 g 5857 4216 M -8 -20 V .04 g 5849 4196 M -8 -20 V .04 g 5841 4176 M -7 -20 V .04 g 5834 4156 M 0 -1 V .04 g 5834 4155 M -8 -20 V .04 g 5826 4135 M -8 -20 V .04 g 5818 4115 M -7 -20 V .04 g 5811 4095 M -4 -11 V .04 g 5807 4084 M -4 -9 V .04 g 5803 4075 M -7 -20 V .04 g 5796 4055 M -8 -20 V .04 g 5788 4035 M -7 -21 V .04 g 5781 4014 M -1 -3 V .04 g 5780 4011 M -7 -17 V .04 g 5773 3994 M -7 -20 V .04 g 5766 3974 M -8 -20 V .04 g 5758 3954 M -6 -16 V .04 g 5752 3938 M -1 -4 V .04 g 5751 3934 M -8 -20 V .04 g 5743 3914 M -7 -21 V .04 g 5736 3893 M -7 -20 V .04 g 5729 3873 M -4 -10 V .04 g 5725 3863 M -4 -10 V .04 g 5721 3853 M -7 -20 V .04 g 5714 3833 M -7 -20 V .04 g 5707 3813 M -8 -20 V .04 g 5699 3793 M -1 -5 V stroke 5698 3788 M .04 g 5698 3788 M -6 -16 V .04 g 5692 3772 M -7 -20 V .04 g 5685 3752 M -8 -20 V .04 g 5677 3732 M -6 -19 V .04 g 5671 3713 M -1 -1 V .04 g 5670 3712 M -7 -20 V .04 g 5663 3692 M -7 -20 V .04 g 5656 3672 M -8 -20 V .04 g 5648 3652 M -5 -15 V .04 g 5643 3637 M -2 -6 V .04 g 5641 3631 M -7 -20 V .04 g 5634 3611 M -7 -20 V .04 g 5627 3591 M -8 -20 V .04 g 5619 3571 M -3 -10 V .04 g 5616 3561 M -4 -10 V .04 g 5612 3551 M -7 -20 V .04 g 5605 3531 M -7 -21 V .04 g 5598 3510 M -8 -20 V .04 g 5590 3490 M -1 -4 V .04 g 5589 3486 M -6 -16 V .04 g 5583 3470 M -7 -20 V .04 g 5576 3450 M -8 -20 V .04 g 5568 3430 M -6 -19 V .04 g 5562 3411 M -1 -1 V .04 g 5561 3410 M -7 -20 V .04 g 5554 3390 M -8 -21 V .04 g 5546 3369 M -7 -20 V .04 g 5539 3349 M -5 -13 V .04 g 5534 3336 M -3 -7 V .04 g 5531 3329 M -7 -20 V .04 g 5524 3309 M -8 -20 V .04 g 5516 3289 M -7 -20 V .04 g 5509 3269 M -2 -5 V .04 g 5507 3264 M -6 -16 V .04 g 5501 3248 M -8 -20 V .04 g 5493 3228 M -8 -20 V .04 g 5485 3208 M -5 -14 V .04 g 5480 3194 M -3 -6 V .04 g 5477 3188 M -8 -20 V .04 g 5469 3168 M -8 -20 V .04 g 5461 3148 M -8 -19 V .04 g 5453 3129 M -1 -1 V .04 g 5452 3128 M -9 -21 V .04 g 5443 3107 M -10 -20 V .04 g 5433 3087 M -8 -16 V 0 g .04 g 739 4075 M .04 g 739 4075 M -1 2 V .04 g 738 4077 M -6 18 V .04 g 732 4095 M -6 20 V .04 g 726 4115 M -7 20 V .04 g 719 4135 M -6 20 V .04 g 713 4155 M -2 6 V .04 g 711 4161 M -5 15 V stroke 706 4176 M .04 g 706 4176 M -6 20 V .04 g 700 4196 M -6 20 V .04 g 694 4216 M -7 20 V .04 g 687 4236 M -3 11 V .04 g 684 4247 M -3 9 V .04 g 681 4256 M -6 20 V .04 g 675 4276 M -7 21 V .04 g 668 4297 M -6 20 V .04 g 662 4317 M -5 18 V .04 g 657 4335 M -1 2 V .04 g 656 4337 M -6 20 V .04 g 650 4357 M -6 20 V .04 g 644 4377 M -6 20 V .04 g 638 4397 M -7 20 V .04 g 631 4417 M -2 8 V .04 g 629 4425 M -4 13 V .04 g 625 4438 M -5 20 V .04 g 620 4458 M -6 20 V .04 g 614 4478 M -7 20 V .04 g 607 4498 M -5 18 V 0 g .04 g 1583 2722 M .04 g 1583 2722 M -8 2 V .04 g 1575 2724 M -19 6 V .04 g 1556 2730 M -27 9 V .04 g 1529 2739 M -14 6 V .04 g 1515 2745 M -14 5 V .04 g 1501 2750 M -27 13 V .04 g 1474 2763 M -2 2 V .04 g 1472 2765 M -25 14 V .04 g 1447 2779 M -9 6 V .04 g 1438 2785 M -18 12 V .04 g 1420 2797 M -11 8 V .04 g 1409 2805 M -17 12 V .04 g 1392 2817 M -10 8 V .04 g 1382 2825 M -17 14 V .04 g 1365 2839 M -6 6 V .04 g 1359 2845 M -21 19 V .04 g 1338 2864 M -1 2 V .04 g 1337 2866 M -20 20 V .04 g 1317 2886 M -6 6 V .04 g 1311 2892 M -13 14 V .04 g 1298 2906 M -15 16 V .04 g 1283 2922 M -3 4 V .04 g 1280 2926 M -17 20 V .04 g 1263 2946 M -7 9 V .04 g 1256 2955 M -9 11 V .04 g 1247 2966 M -16 20 V .04 g 1231 2986 M -2 4 V .04 g 1229 2990 M -12 17 V .04 g 1217 3007 M -15 20 V .04 g 1202 3027 M 0 1 V .04 g 1202 3028 M -13 19 V .04 g 1189 3047 M -14 20 V stroke 1175 3067 M .04 g 1175 3067 M -1 1 V .04 g 1174 3068 M -11 19 V .04 g 1163 3087 M -13 20 V .04 g 1150 3107 M -3 5 V .04 g 1147 3112 M -9 16 V .04 g 1138 3128 M -12 20 V .04 g 1126 3148 M -6 10 V .04 g 1120 3158 M -6 10 V .04 g 1114 3168 M -11 20 V .04 g 1103 3188 M -10 18 V .04 g 1093 3206 M -2 2 V .04 g 1091 3208 M -10 20 V .04 g 1081 3228 M -11 20 V .04 g 1070 3248 M -5 10 V .04 g 1065 3258 M -5 11 V .04 g 1060 3269 M -10 20 V .04 g 1050 3289 M -11 20 V .04 g 1039 3309 M -1 3 V .04 g 1038 3312 M -8 17 V .04 g 1030 3329 M -10 20 V .04 g 1020 3349 M -9 19 V .04 g 1011 3368 M -1 1 V .04 g 1010 3369 M -9 21 V .04 g 1001 3390 M -9 20 V .04 g 992 3410 M -8 18 V .04 g 984 3428 M -1 2 V .04 g 983 3430 M -9 20 V .04 g 974 3450 M -9 20 V .04 g 965 3470 M -9 20 V .04 g .04 g 956 3490 M -8 20 V .04 g 948 3510 M -9 21 V .04 g 939 3531 M -8 20 V .04 g 931 3551 M -2 4 V .04 g 929 3555 M -7 16 V .04 g 922 3571 M -8 20 V .04 g 914 3591 M -8 20 V .04 g 906 3611 M -4 11 V .04 g 902 3622 M -4 9 V .04 g 898 3631 M -8 21 V .04 g 890 3652 M -8 20 V .04 g 882 3672 M -7 20 V .04 g 875 3692 M -1 0 V .04 g 874 3692 M -7 20 V .04 g 867 3712 M -8 20 V .04 g 859 3732 M -7 20 V .04 g 852 3752 M -5 12 V .04 g 847 3764 M -3 8 V .04 g 844 3772 M -7 21 V .04 g 837 3793 M -7 20 V .04 g 830 3813 M -8 20 V .04 g 822 3833 M -2 6 V .04 g 820 3839 M -5 14 V stroke 815 3853 M .04 g 815 3853 M -7 20 V .04 g 808 3873 M -7 20 V .04 g 801 3893 M -7 21 V .04 g 794 3914 M -1 2 V .04 g 793 3916 M -6 18 V .04 g 787 3934 M -7 20 V .04 g 780 3954 M -7 20 V .04 g 773 3974 M -7 20 V .04 g 766 3994 M -1 1 V .04 g 765 3995 M -6 19 V .04 g 759 4014 M -6 21 V .04 g 753 4035 M -7 20 V .04 g 746 4055 M -7 20 V 0 g .04 g 2547 1455 M .04 g 2547 1455 M -10 15 V .04 g 2537 1470 M -3 5 V .04 g 2534 1475 M -13 20 V .04 g 2521 1495 M -11 19 V .04 g 2510 1514 M -1 1 V .04 g 2509 1515 M -12 20 V .04 g 2497 1535 M -12 20 V .04 g 2485 1555 M -3 5 V .04 g 2482 1560 M -9 16 V .04 g 2473 1576 M -11 20 V .04 g 2462 1596 M -7 13 V .04 g 2455 1609 M -4 7 V .04 g 2451 1616 M -11 20 V .04 g 2440 1636 M -11 20 V .04 g 2429 1656 M -1 3 V .04 g 2428 1659 M -9 17 V .04 g 2419 1676 M -10 21 V .04 g 2409 1697 M -8 15 V .04 g 2401 1712 M -3 5 V .04 g 2398 1717 M -10 20 V .04 g 2388 1737 M -10 20 V .04 g 2378 1757 M -5 10 V .04 g 2373 1767 M -5 10 V .04 g 2368 1777 M -9 20 V .04 g 2359 1797 M -10 20 V .04 g 2349 1817 M -3 7 V .04 g 2346 1824 M -6 14 V .04 g 2340 1838 M -10 20 V .04 g 2330 1858 M -9 20 V .04 g 2321 1878 M -2 5 V .04 g 2319 1883 M -7 15 V .04 g 2312 1898 M -9 20 V .04 g 2303 1918 M -9 20 V .04 g 2294 1938 M -2 5 V .04 g 2292 1943 M -7 16 V .04 g 2285 1959 M -9 20 V .04 g 2276 1979 M -9 20 V .04 g 2267 1999 M -3 6 V .04 g 2264 2005 M -6 14 V stroke 2258 2019 M .04 g 2258 2019 M -9 20 V .04 g 2249 2039 M -8 20 V .04 g 2241 2059 M -4 9 V .04 g 2237 2068 M -5 11 V .04 g 2232 2079 M -8 21 V .04 g 2224 2100 M -9 20 V .04 g 2215 2120 M -5 13 V .04 g 2210 2133 M -3 7 V .04 g 2207 2140 M -9 20 V .04 g 2198 2160 M -8 20 V .04 g 2190 2180 M -7 18 V .04 g 2183 2198 M -1 2 V .04 g 2182 2200 M -9 21 V .04 g 2173 2221 M -8 20 V .04 g 2165 2241 M -8 20 V .04 g 2157 2261 M -2 4 V .04 g 2155 2265 M -6 16 V .04 g 2149 2281 M -9 20 V .04 g 2140 2301 M -8 20 V .04 g 2132 2321 M -4 11 V .04 g 2128 2332 M -4 9 V .04 g 2124 2341 M -8 21 V .04 g 2116 2362 M -9 20 V .04 g 2107 2382 M -6 16 V .04 g 2101 2398 M -2 4 V .04 g 2099 2402 M -8 20 V .04 g 2091 2422 M -8 20 V .04 g 2083 2442 M -9 20 V .04 g 2074 2462 M 0 2 V .04 g 2074 2464 M -8 19 V .04 g 2066 2483 M -9 20 V .04 g 2057 2503 M -9 20 V .04 g 2048 2523 M -2 5 V .04 g 2046 2528 M -7 15 V .04 g 2039 2543 M -9 20 V .04 g 2030 2563 M -9 20 V .04 g 2021 2583 M -2 4 V .04 g 2019 2587 M -8 17 V .04 g 2011 2604 M -11 20 V .04 g 2000 2624 M -8 15 V .04 g 1992 2639 M -4 5 V .04 g 1988 2644 M -13 20 V .04 g 1975 2664 M -10 14 V .04 g 1965 2678 M -7 6 V .04 g 1958 2684 M -21 19 V .04 g 1937 2703 M -2 1 V .04 g 1935 2704 M -25 12 V .04 g 1910 2716 M -27 5 V .04 g 1883 2721 M -27 0 V .04 g 1856 2721 M -28 -2 V .04 g 1828 2719 M -27 -2 V .04 g 1801 2717 M -27 -3 V stroke 1774 2714 M .04 g 1774 2714 M -27 -2 V .04 g 1747 2712 M -28 -2 V .04 g 1719 2710 M -27 0 V .04 g 1692 2710 M -27 1 V .04 g 1665 2711 M -27 2 V .04 g 1638 2713 M -28 4 V .04 g 1610 2717 M -27 5 V 0 g .04 g 3828 1555 M .04 g 3828 1555 M -10 14 V .04 g 3818 1569 M -7 7 V .04 g 3811 1576 M -16 20 V .04 g 3795 1596 M -5 6 V .04 g 3790 1602 M -12 14 V .04 g 3778 1616 M -15 18 V .04 g 3763 1634 M -3 2 V .04 g 3760 1636 M -20 20 V .04 g 3740 1656 M -4 5 V .04 g 3736 1661 M -21 15 V .04 g 3715 1676 M -6 6 V .04 g 3709 1682 M -28 9 V .04 g 3681 1691 M -27 -6 V .04 g 3654 1685 M -12 -9 V .04 g 3642 1676 M -15 -9 V .04 g 3627 1667 M -10 -11 V .04 g 3617 1656 M -17 -16 V .04 g 3600 1640 M -3 -4 V .04 g 3597 1636 M -17 -20 V .04 g 3580 1616 M -8 -8 V .04 g 3572 1608 M -9 -12 V .04 g 3563 1596 M -16 -20 V .04 g 3547 1576 M -2 -2 V .04 g 3545 1574 M -14 -19 V .04 g 3531 1555 M -13 -16 V .04 g 3518 1539 M -3 -4 V .04 g 3515 1535 M -15 -20 V .04 g 3500 1515 M -9 -12 V .04 g 3491 1503 M -7 -8 V .04 g 3484 1495 M -15 -20 V .04 g 3469 1475 M -6 -7 V .04 g 3463 1468 M -10 -13 V .04 g 3453 1455 M -16 -20 V .04 g 3437 1435 M -1 -1 V .04 g 3436 1434 M -16 -20 V .04 g 3420 1414 M -11 -13 V .04 g 3409 1401 M -5 -7 V .04 g 3404 1394 M -17 -20 V .04 g 3387 1374 M -5 -6 V .04 g 3382 1368 M -13 -14 V .04 g 3369 1354 M -15 -16 V .04 g 3354 1338 M -3 -4 V .04 g 3351 1334 M -19 -20 V .04 g 3332 1314 M -5 -6 V .04 g 3327 1308 M -15 -15 V stroke 3312 1293 M .04 g 3312 1293 M -12 -12 V .04 g 3300 1281 M -8 -8 V .04 g 3292 1273 M -19 -18 V .04 g 3273 1255 M -3 -2 V .04 g 3270 1253 M -23 -20 V .04 g 3247 1233 M -2 -2 V .04 g 3245 1231 M -23 -18 V .04 g 3222 1213 M -4 -3 V .04 g 3218 1210 M -23 -17 V .04 g 3195 1193 M -4 -3 V .04 g 3191 1190 M -27 -18 V .04 g .04 g 3164 1172 M -28 -15 V .04 g 3136 1157 M -10 -5 V .04 g 3126 1152 M -17 -8 V .04 g 3109 1144 M -27 -10 V .04 g 3082 1134 M -5 -2 V .04 g 3077 1132 M -22 -7 V .04 g 3055 1125 M -28 -5 V .04 g 3027 1120 M -27 -3 V .04 g 3000 1117 M -27 -1 V .04 g 2973 1116 M -27 2 V .04 g 2946 1118 M -28 5 V .04 g 2918 1123 M -27 7 V .04 g 2891 1130 M -5 2 V .04 g 2886 1132 M -22 8 V .04 g 2864 1140 M -26 12 V .04 g 2838 1152 M -1 1 V .04 g 2837 1153 M -28 16 V .04 g 2809 1169 M -5 3 V .04 g 2804 1172 M -22 15 V .04 g 2782 1187 M -7 6 V .04 g 2775 1193 M -20 15 V .04 g 2755 1208 M -6 5 V .04 g 2749 1213 M -21 18 V .04 g 2728 1231 M -2 2 V .04 g 2726 1233 M -21 20 V .04 g 2705 1253 M -5 5 V .04 g 2700 1258 M -14 15 V .04 g 2686 1273 M -13 14 V .04 g 2673 1287 M -6 6 V .04 g 2667 1293 M -17 21 V .04 g 2650 1314 M -4 4 V .04 g 2646 1318 M -13 16 V .04 g 2633 1334 M -14 18 V .04 g 2619 1352 M -2 2 V .04 g 2617 1354 M -15 20 V .04 g 2602 1374 M -11 15 V .04 g 2591 1389 M -3 5 V .04 g 2588 1394 M -14 20 V .04 g 2574 1414 M -10 14 V .04 g 2564 1428 M -4 7 V .04 g 2560 1435 M -13 20 V stroke 2547 1455 M 0 g .04 g 4989 1848 M .04 g 4989 1848 M -5 -10 V .04 g 4984 1838 M -9 -21 V .04 g 4975 1817 M -10 -20 V .04 g 4965 1797 M -3 -6 V .04 g 4962 1791 M -7 -14 V .04 g 4955 1777 M -10 -20 V .04 g 4945 1757 M -10 -20 V .04 g 4935 1737 M 0 -1 V .04 g 4935 1736 M -10 -19 V .04 g 4925 1717 M -11 -20 V .04 g 4914 1697 M -6 -14 V .04 g 4908 1683 M -4 -7 V .04 g 4904 1676 M -11 -20 V .04 g 4893 1656 M -11 -20 V .04 g 4882 1636 M -2 -3 V .04 g 4880 1633 M -9 -17 V .04 g 4871 1616 M -12 -20 V .04 g 4859 1596 M -6 -12 V .04 g 4853 1584 M -5 -8 V .04 g 4848 1576 M -12 -21 V .04 g 4836 1555 M -10 -17 V .04 g 4826 1538 M -2 -3 V .04 g 4824 1535 M -13 -20 V .04 g 4811 1515 M -12 -20 V .04 g .04 g 4799 1495 M -14 -20 V .04 g 4785 1475 M -13 -20 V .04 g 4772 1455 M -1 -2 V .04 g 4771 1453 M -13 -18 V .04 g 4758 1435 M -14 -21 V .04 g .04 g 4744 1414 M -15 -20 V .04 g 4729 1394 M -12 -16 V .04 g 4717 1378 M -4 -4 V .04 g 4713 1374 M -16 -20 V .04 g 4697 1354 M -7 -9 V .04 g 4690 1345 M -10 -11 V .04 g 4680 1334 M -18 -20 V .04 g 4662 1314 M 0 -1 V .04 g 4662 1313 M -19 -20 V .04 g 4643 1293 M -8 -8 V .04 g 4635 1285 M -12 -12 V .04 g 4623 1273 M -15 -14 V .04 g 4608 1259 M -8 -6 V .04 g 4600 1253 M -19 -17 V .04 g 4581 1236 M -5 -3 V .04 g 4576 1233 M -23 -17 V .04 g 4553 1216 M -4 -3 V .04 g 4549 1213 M -23 -15 V .04 g 4526 1198 M -10 -5 V .04 g 4516 1193 M -17 -10 V .04 g 4499 1183 M -24 -11 V .04 g 4475 1172 M -3 -1 V .04 g 4472 1171 M -28 -10 V stroke 4444 1161 M .04 g 4444 1161 M -27 -7 V .04 g 4417 1154 M -13 -2 V .04 g 4404 1152 M -14 -2 V .04 g 4390 1150 M -27 -1 V .04 g 4363 1149 M -28 0 V .04 g 4335 1149 M -22 3 V .04 g 4313 1152 M -5 1 V .04 g 4308 1153 M -27 6 V .04 g 4281 1159 M -27 9 V .04 g 4254 1168 M -13 4 V .04 g 4241 1172 M -15 6 V .04 g 4226 1178 M -27 14 V .04 g 4199 1192 M -2 1 V .04 g 4197 1193 M -25 14 V .04 g 4172 1207 M -9 6 V .04 g 4163 1213 M -18 12 V .04 g 4145 1225 M -12 8 V .04 g 4133 1233 M -16 12 V .04 g 4117 1245 M -11 8 V .04 g 4106 1253 M -16 14 V .04 g 4090 1267 M -8 6 V .04 g 4082 1273 M -19 17 V .04 g 4063 1290 M -4 3 V .04 g 4059 1293 M -21 21 V .04 g 4038 1314 M -2 2 V .04 g 4036 1316 M -19 18 V .04 g 4017 1334 M -9 9 V .04 g 4008 1343 M -10 11 V .04 g 3998 1354 M -17 18 V .04 g 3981 1372 M -2 2 V .04 g 3979 1374 M -18 20 V .04 g 3961 1394 M -7 9 V .04 g 3954 1403 M -11 11 V .04 g 3943 1414 M -16 20 V .04 g 3927 1434 M -1 1 V .04 g 3926 1435 M -17 20 V .04 g 3909 1455 M -10 12 V .04 g 3899 1467 M -6 8 V .04 g 3893 1475 M -17 20 V .04 g 3876 1495 M -4 6 V .04 g 3872 1501 M -12 14 V .04 g 3860 1515 M -15 20 V .04 g 3845 1535 M -1 0 V .04 g 3844 1535 M -16 20 V 0 g .04 g 6052 3014 M .04 g 6052 3014 M -7 -7 V .04 g 6045 3007 M -18 -21 V .04 g 6027 2986 M -2 -2 V .04 g 6025 2984 M -18 -18 V .04 g 6007 2966 M -9 -9 V .04 g 5998 2957 M -13 -11 V .04 g 5985 2946 M -15 -14 V .04 g 5970 2932 M -8 -6 V stroke 5962 2926 M .04 g 5962 2926 M -19 -16 V .04 g 5943 2910 M -6 -4 V .04 g 5937 2906 M -21 -16 V .04 g 5916 2890 M -7 -4 V .04 g 5909 2886 M -20 -13 V .04 g 5889 2873 M -13 -7 V .04 g 5876 2866 M -15 -9 V .04 g 5861 2857 M -24 -12 V .04 g 5837 2845 M -3 -1 V .04 g 5834 2844 M -27 -11 V .04 g 5807 2833 M -22 -8 V .04 g 5785 2825 M -5 -2 V .04 g 5780 2823 M -28 -7 V .04 g 5752 2816 M -27 -6 V .04 g 5725 2810 M -27 -4 V .04 g 5698 2806 M -14 -1 V .04 g 5684 2805 M -13 -1 V .04 g 5671 2804 M -28 -1 V .04 g 5643 2803 M -27 -1 V .04 g 5616 2802 M -27 1 V .04 g 5589 2803 M -27 1 V .04 g 5562 2804 M -14 1 V .04 g 5548 2805 M -14 1 V .04 g 5534 2806 M -27 1 V .04 g 5507 2807 M -27 -1 V .04 g 5480 2806 M -6 -1 V .04 g 5474 2805 M -21 -3 V .04 g 5453 2802 M -28 -11 V .04 g 5425 2791 M -8 -6 V .04 g 5417 2785 M -19 -16 V .04 g 5398 2769 M -4 -4 V .04 g 5394 2765 M -15 -20 V .04 g 5379 2745 M -8 -11 V .04 g 5371 2734 M -5 -10 V .04 g 5366 2724 M -12 -20 V .04 g 5354 2704 M -10 -20 V .04 g 5344 2684 M -10 -20 V .04 g 5334 2664 M -9 -20 V .04 g 5325 2644 M -9 -18 V .04 g 5316 2626 M -1 -2 V .04 g 5315 2624 M -8 -20 V .04 g 5307 2604 M -9 -21 V .04 g 5298 2583 M -8 -20 V .04 g 5290 2563 M -1 -1 V .04 g 5289 2562 M -8 -19 V .04 g 5281 2543 M -8 -20 V .04 g 5273 2523 M -8 -20 V .04 g 5265 2503 M -3 -8 V .04 g 5262 2495 M -5 -12 V .04 g 5257 2483 M -8 -21 V .04 g 5249 2462 M -9 -20 V .04 g 5240 2442 M -5 -14 V stroke 5235 2428 M .04 g 5235 2428 M -3 -6 V .04 g 5232 2422 M -8 -20 V .04 g 5224 2402 M -8 -20 V .04 g 5216 2382 M -8 -20 V .04 g 5208 2362 M -1 -3 V .04 g 5207 2359 M -7 -18 V .04 g 5200 2341 M -8 -20 V .04 g 5192 2321 M -8 -20 V .04 g 5184 2301 M -4 -9 V .04 g 5180 2292 M -4 -11 V .04 g 5176 2281 M -8 -20 V .04 g 5168 2261 M -9 -20 V .04 g 5159 2241 M -6 -17 V .04 g 5153 2224 M -2 -3 V .04 g 5151 2221 M -8 -21 V .04 g 5143 2200 M -8 -20 V .04 g 5135 2180 M -9 -20 V .04 g 5126 2160 M 0 -2 V .04 g 5126 2158 M -8 -18 V .04 g 5118 2140 M -8 -20 V .04 g 5110 2120 M -9 -20 V .04 g 5101 2100 M -3 -7 V .04 g 5098 2093 M -5 -14 V .04 g 5093 2079 M -9 -20 V .04 g 5084 2059 M -9 -20 V .04 g 5075 2039 M -4 -10 V .04 g 5071 2029 M -4 -10 V .04 g 5067 2019 M -9 -20 V .04 g 5058 1999 M -9 -20 V .04 g 5049 1979 M -5 -12 V .04 g 5044 1967 M -4 -8 V .04 g 5040 1959 M -9 -21 V .04 g 5031 1938 M -9 -20 V .04 g 5022 1918 M -5 -11 V .04 g 5017 1907 M -4 -9 V .04 g 5013 1898 M -10 -20 V .04 g 5003 1878 M -9 -20 V .04 g 4994 1858 M -5 -10 V 0 g .02 g 2394 2321 M .02 g 2394 2321 M -1 20 V .02 g 2393 2341 M 0 21 V .02 g 2393 2362 M 0 20 V .02 g 2393 2382 M 1 20 V .02 g 2394 2402 M 1 20 V .02 g 2395 2422 M 2 20 V .02 g 2397 2442 M 3 20 V .02 g 2400 2462 M 1 3 V .02 g 2401 2465 M 3 18 V .02 g 2404 2483 M 5 20 V .02 g 2409 2503 M 5 20 V .02 g 2414 2523 M 7 20 V .02 g 2421 2543 M 7 16 V .02 g 2428 2559 M 2 4 V stroke 2430 2563 M .02 g 2430 2563 M 10 20 V .02 g 2440 2583 M 11 21 V .02 g 2451 2604 M 4 6 V .02 g 2455 2610 M 10 14 V .02 g 2465 2624 M 16 20 V .02 g 2481 2644 M 1 1 V .02 g 2482 2645 M 20 19 V .02 g 2502 2664 M 8 6 V .02 g 2510 2670 M 18 14 V .02 g 2528 2684 M 9 6 V .02 g 2537 2690 M 27 14 V .02 g .02 g 2564 2704 M 27 11 V .02 g 2591 2715 M 28 6 V .02 g 2619 2721 M 23 3 V .02 g 2642 2724 M 4 1 V .02 g 2646 2725 M 27 0 V .02 g 2673 2725 M 8 -1 V .02 g 2681 2724 M 19 -1 V .02 g 2700 2723 M 28 -6 V .02 g 2728 2717 M 27 -8 V .02 g 2755 2709 M 12 -5 V .02 g 2767 2704 M 15 -6 V .02 g 2782 2698 M 27 -13 V .02 g 2809 2685 M 2 -1 V .02 g 2811 2684 M 26 -15 V .02 g 2837 2669 M 7 -5 V .02 g 2844 2664 M 20 -13 V .02 g 2864 2651 M 9 -7 V .02 g 2873 2644 M 18 -15 V .02 g 2891 2629 M 7 -5 V .02 g 2898 2624 M 20 -18 V .02 g 2918 2606 M 2 -2 V .02 g 2920 2604 M 21 -21 V .02 g 2941 2583 M 5 -4 V .02 g 2946 2579 M 14 -16 V .02 g 2960 2563 M 13 -13 V .02 g 2973 2550 M 5 -7 V .02 g 2978 2543 M 18 -20 V .02 g 2996 2523 M 4 -6 V .02 g 3000 2517 M 11 -14 V .02 g 3011 2503 M 16 -20 V .02 g 3027 2483 M 0 -1 V .02 g 3027 2482 M 14 -20 V .02 g 3041 2462 M 14 -19 V .02 g 3055 2443 M 0 -1 V .02 g 3055 2442 M 13 -20 V .02 g 3068 2422 M 13 -20 V .02 g 3081 2402 M 1 -1 V .02 g 3082 2401 M 11 -19 V .02 g 3093 2382 M 12 -20 V .02 g 3105 2362 M 4 -8 V .02 g 3109 2354 M 7 -13 V stroke 3116 2341 M .02 g 3116 2341 M 11 -20 V .02 g 3127 2321 M 9 -19 V .02 g 3136 2302 M 1 -1 V .02 g 3137 2301 M 10 -20 V .02 g 3147 2281 M 9 -20 V .02 g 3156 2261 M 8 -17 V .02 g 3164 2244 M 1 -3 V .02 g 3165 2241 M 8 -20 V .02 g 3173 2221 M 8 -21 V .02 g 3181 2200 M 8 -20 V .02 g 3189 2180 M 2 -5 V .02 g 3191 2175 M 5 -15 V .02 g 3196 2160 M 7 -20 V .02 g 3203 2140 M 6 -20 V .02 g 3209 2120 M 6 -20 V .02 g 3215 2100 M 3 -11 V .02 g 3218 2089 M 3 -10 V .02 g 3221 2079 M 5 -20 V .02 g 3226 2059 M 4 -20 V .02 g 3230 2039 M 4 -20 V .02 g 3234 2019 M 4 -20 V .02 g 3238 1999 M 3 -20 V .02 g 3241 1979 M 3 -20 V .02 g 3244 1959 M 1 -17 V .02 g 3245 1942 M 1 -4 V .02 g 3246 1938 M 1 -20 V .02 g 3247 1918 M 1 -20 V .02 g 3248 1898 M 1 -20 V .02 g 3249 1878 M -1 -20 V .02 g 3248 1858 M 0 -20 V .02 g 3248 1838 M -1 -21 V 0 g .02 g 3247 1817 M .02 g 3247 1817 M -2 -13 V .02 g 3245 1804 M 0 -7 V .02 g 3245 1797 M -3 -20 V .02 g 3242 1777 M -3 -20 V .02 g 3239 1757 M -4 -20 V .02 g 3235 1737 M -4 -20 V .02 g 3231 1717 M -6 -20 V .02 g 3225 1697 M -5 -21 V .02 g 3220 1676 M -2 -5 V .02 g 3218 1671 M -5 -15 V .02 g 3213 1656 M -8 -20 V .02 g 3205 1636 M -8 -20 V .02 g 3197 1616 M -6 -14 V .02 g 3191 1602 M -3 -6 V .02 g 3188 1596 M -11 -20 V .02 g 3177 1576 M -11 -21 V .02 g 3166 1555 M -2 -3 V .02 g 3164 1552 M -11 -17 V .02 g 3153 1535 M -14 -20 V .02 g 3139 1515 M -3 -3 V .02 g 3136 1512 M -14 -17 V stroke 3122 1495 M .02 g 3122 1495 M -13 -15 V .02 g 3109 1480 M -5 -5 V .02 g 3104 1475 M -22 -20 V .02 g 3082 1455 M 0 -1 V .02 g 3082 1454 M -26 -19 V .02 g 3056 1435 M -1 -1 V .02 g 3055 1434 M -28 -16 V .02 g 3027 1418 M -8 -4 V .02 g 3019 1414 M -19 -7 V .02 g 3000 1407 M -27 -7 V .02 g 2973 1400 M -27 -4 V .02 g 2946 1396 M -28 1 V .02 g 2918 1397 M -27 4 V .02 g 2891 1401 M -27 8 V .02 g 2864 1409 M -12 5 V .02 g 2852 1414 M -15 7 V .02 g 2837 1421 M -24 14 V .02 g 2813 1435 M -4 2 V .02 g 2809 1437 M -26 18 V .02 g 2783 1455 M -1 1 V .02 g 2782 1456 M -23 19 V .02 g 2759 1475 M -4 3 V .02 g 2755 1478 M -17 17 V .02 g 2738 1495 M -10 10 V .02 g 2728 1505 M -10 10 V .02 g 2718 1515 M -18 20 V .02 g .02 g 2700 1535 M -16 20 V .02 g 2684 1555 M -11 14 V .02 g 2673 1569 M -5 7 V .02 g 2668 1576 M -14 20 V .02 g 2654 1596 M -8 11 V .02 g 2646 1607 M -6 9 V .02 g 2640 1616 M -13 20 V .02 g 2627 1636 M -8 13 V .02 g 2619 1649 M -5 7 V .02 g 2614 1656 M -12 20 V .02 g 2602 1676 M -11 19 V .02 g 2591 1695 M 0 2 V .02 g 2591 1697 M -11 20 V .02 g 2580 1717 M -11 20 V .02 g 2569 1737 M -5 9 V .02 g 2564 1746 M -5 11 V .02 g 2559 1757 M -10 20 V .02 g 2549 1777 M -10 20 V .02 g 2539 1797 M -2 6 V .02 g 2537 1803 M -7 14 V .02 g 2530 1817 M -9 21 V .02 g 2521 1838 M -9 20 V .02 g 2512 1858 M -2 7 V .02 g 2510 1865 M -6 13 V .02 g 2504 1878 M -8 20 V .02 g 2496 1898 M -8 20 V stroke 2488 1918 M .02 g 2488 1918 M -6 17 V .02 g 2482 1935 M -1 3 V .02 g 2481 1938 M -7 21 V .02 g 2474 1959 M -7 20 V .02 g 2467 1979 M -7 20 V .02 g 2460 1999 M -5 15 V .02 g 2455 2014 M -1 5 V .02 g 2454 2019 M -7 20 V .02 g 2447 2039 M -5 20 V .02 g 2442 2059 M -6 20 V .02 g 2436 2079 M -5 21 V .02 g 2431 2100 M -3 11 V .02 g 2428 2111 M -2 9 V .02 g 2426 2120 M -5 20 V .02 g 2421 2140 M -5 20 V .02 g 2416 2160 M -4 20 V .02 g 2412 2180 M -3 20 V .02 g 2409 2200 M -4 21 V .02 g 2405 2221 M -3 20 V .02 g 2402 2241 M -1 11 V .02 g 2401 2252 M -2 9 V .02 g 2399 2261 M -2 20 V .02 g 2397 2281 M -2 20 V .02 g 2395 2301 M -1 20 V 0 g .02 g 4110 1979 M .02 g 4110 1979 M 2 20 V .02 g 4112 1999 M 3 20 V .02 g 4115 2019 M 2 10 V .02 g 4117 2029 M 2 10 V .02 g 4119 2039 M 4 20 V .02 g 4123 2059 M 4 20 V .02 g 4127 2079 M 5 21 V .02 g 4132 2100 M 6 20 V .02 g 4138 2120 M 5 20 V .02 g 4143 2140 M 2 3 V .02 g 4145 2143 M 5 17 V .02 g 4150 2160 M 6 20 V .02 g 4156 2180 M 7 20 V .02 g 4163 2200 M 8 21 V .02 g 4171 2221 M 1 2 V .02 g 4172 2223 M 7 18 V .02 g 4179 2241 M 8 20 V .02 g 4187 2261 M 8 20 V .02 g 4195 2281 M 4 8 V .02 g 4199 2289 M 6 12 V .02 g 4205 2301 M 9 20 V .02 g 4214 2321 M 10 20 V .02 g 4224 2341 M 2 5 V .02 g 4226 2346 M 8 16 V .02 g 4234 2362 M 11 20 V .02 g 4245 2382 M 9 16 V .02 g 4254 2398 M 2 4 V .02 g 4256 2402 M 12 20 V stroke 4268 2422 M .02 g 4268 2422 M 12 20 V .02 g 4280 2442 M 1 2 V .02 g 4281 2444 M 11 18 V .02 g 4292 2462 M 13 21 V .02 g 4305 2483 M 3 4 V .02 g 4308 2487 M 11 16 V .02 g 4319 2503 M 14 20 V .02 g 4333 2523 M 2 2 V .02 g 4335 2525 M 14 18 V .02 g 4349 2543 M 14 18 V .02 g 4363 2561 M 1 2 V .02 g 4364 2563 M 17 20 V .02 g 4381 2583 M 9 10 V .02 g 4390 2593 M 9 11 V .02 g 4399 2604 M 18 19 V .02 g 4417 2623 M 0 1 V .02 g 4417 2624 M 21 20 V .02 g 4438 2644 M 6 6 V .02 g 4444 2650 M 16 14 V .02 g 4460 2664 M 12 10 V .02 g 4472 2674 M 12 10 V .02 g 4484 2684 M 15 12 V .02 g 4499 2696 M 12 8 V .02 g 4511 2704 M 15 11 V .02 g 4526 2715 M 16 9 V .02 g 4542 2724 M 11 7 V .02 g 4553 2731 M 27 14 V .02 g 4580 2745 M 1 0 V .02 g 4581 2745 M 27 11 V .02 g 4608 2756 M 27 8 V .02 g 4635 2764 M 1 1 V .02 g 4636 2765 M 26 5 V .02 g 4662 2770 M 28 3 V .02 g 4690 2773 M 27 0 V .02 g 4717 2773 M 27 -3 V .02 g 4744 2770 M 21 -5 V .02 g 4765 2765 M 6 -2 V .02 g 4771 2763 M 28 -10 V .02 g 4799 2753 M 15 -8 V .02 g 4814 2745 M 12 -7 V .02 g 4826 2738 M 19 -14 V .02 g 4845 2724 M 8 -6 V .02 g 4853 2718 M 14 -14 V .02 g 4867 2704 M 13 -13 V .02 g 4880 2691 M 6 -7 V .02 g 4886 2684 M 14 -20 V .02 g 4900 2664 M 8 -11 V .02 g 4908 2653 M 5 -9 V .02 g 4913 2644 M 10 -20 V .02 g 4923 2624 M 9 -20 V .02 g 4932 2604 M 3 -9 V .02 g 4935 2595 M 4 -12 V stroke 4939 2583 M .02 g 4939 2583 M 5 -20 V .02 g 4944 2563 M 5 -20 V .02 g 4949 2543 M 4 -20 V .02 g 4953 2523 M 3 -20 V .02 g 4956 2503 M 2 -20 V .02 g 4958 2483 M 2 -21 V .02 g 4960 2462 M 1 -20 V .02 g 4961 2442 M 0 -20 V .02 g 4961 2422 M -1 -20 V .02 g 4960 2402 M -1 -20 V .02 g 4959 2382 M -1 -20 V .02 g 4958 2362 M -2 -21 V .02 g 4956 2341 M -2 -20 V .02 g 4954 2321 M -3 -20 V .02 g 4951 2301 M -3 -20 V .02 g 4948 2281 M -3 -20 V .02 g 4945 2261 M -4 -20 V .02 g 4941 2241 M -4 -20 V 0 g .02 g 4937 2221 M .02 g 4937 2221 M -2 -12 V .02 g 4935 2209 M -2 -9 V .02 g 4933 2200 M -5 -20 V .02 g 4928 2180 M -5 -20 V .02 g 4923 2160 M -5 -20 V .02 g 4918 2140 M -6 -20 V .02 g 4912 2120 M -4 -18 V .02 g 4908 2102 M -1 -2 V .02 g 4907 2100 M -6 -21 V .02 g 4901 2079 M -7 -20 V .02 g 4894 2059 M -6 -20 V .02 g 4888 2039 M -7 -20 V .02 g 4881 2019 M -1 -2 V .02 g 4880 2017 M -6 -18 V .02 g 4874 1999 M -7 -20 V .02 g 4867 1979 M -8 -20 V .02 g 4859 1959 M -6 -16 V .02 g 4853 1943 M -2 -5 V .02 g 4851 1938 M -8 -20 V .02 g 4843 1918 M -8 -20 V .02 g 4835 1898 M -9 -20 V .02 g 4826 1878 M 0 -1 V .02 g 4826 1877 M -9 -19 V .02 g 4817 1858 M -9 -20 V .02 g 4808 1838 M -9 -21 V .02 g .02 g 4799 1817 M -11 -20 V .02 g 4788 1797 M -10 -20 V .02 g 4778 1777 M -7 -14 V .02 g 4771 1763 M -3 -6 V .02 g 4768 1757 M -11 -20 V .02 g 4757 1737 M -12 -20 V .02 g 4745 1717 M -1 -3 V .02 g 4744 1714 M -11 -17 V .02 g 4733 1697 M -12 -21 V stroke 4721 1676 M .02 g 4721 1676 M -4 -6 V .02 g 4717 1670 M -9 -14 V .02 g 4708 1656 M -14 -20 V .02 g 4694 1636 M -4 -7 V .02 g 4690 1629 M -10 -13 V .02 g 4680 1616 M -15 -20 V .02 g 4665 1596 M -3 -4 V .02 g 4662 1592 M -14 -16 V .02 g 4648 1576 M -13 -16 V .02 g 4635 1560 M -4 -5 V .02 g 4631 1555 M -19 -20 V .02 g 4612 1535 M -4 -4 V .02 g 4608 1531 M -17 -16 V .02 g 4591 1515 M -10 -9 V .02 g 4581 1506 M -14 -11 V .02 g 4567 1495 M -14 -11 V .02 g 4553 1484 M -14 -9 V .02 g 4539 1475 M -13 -9 V .02 g 4526 1466 M -22 -11 V .02 g 4504 1455 M -5 -3 V .02 g 4499 1452 M -27 -11 V .02 g 4472 1441 M -26 -6 V .02 g 4446 1435 M -2 -1 V .02 g 4444 1434 M -27 -3 V .02 g 4417 1431 M -27 1 V .02 g 4390 1432 M -18 3 V .02 g 4372 1435 M -9 1 V .02 g 4363 1436 M -28 9 V .02 g 4335 1445 M -21 10 V .02 g 4314 1455 M -6 3 V .02 g 4308 1458 M -27 17 V .02 g .02 g 4281 1475 M -24 20 V .02 g 4257 1495 M -3 3 V .02 g 4254 1498 M -18 17 V .02 g 4236 1515 M -10 11 V .02 g 4226 1526 M -7 9 V .02 g 4219 1535 M -15 20 V .02 g 4204 1555 M -5 7 V .02 g 4199 1562 M -9 14 V .02 g 4190 1576 M -12 20 V .02 g 4178 1596 M -6 11 V .02 g 4172 1607 M -5 9 V .02 g 4167 1616 M -9 20 V .02 g 4158 1636 M -9 20 V .02 g 4149 1656 M -4 11 V .02 g 4145 1667 M -4 9 V .02 g 4141 1676 M -7 21 V .02 g 4134 1697 M -6 20 V .02 g 4128 1717 M -5 20 V .02 g 4123 1737 M -5 20 V .02 g 4118 1757 M -1 5 V .02 g 4117 1762 M -3 15 V stroke 4114 1777 M .02 g 4114 1777 M -3 20 V .02 g 4111 1797 M -2 20 V .02 g 4109 1817 M -2 21 V .02 g 4107 1838 M -1 20 V .02 g 4106 1858 M -1 20 V .02 g 4105 1878 M 0 20 V .02 g 4105 1898 M 0 20 V .02 g 4105 1918 M 1 20 V .02 g 4106 1938 M 2 21 V .02 g 4108 1959 M 2 20 V 0 g .02 g 1287 3208 M .02 g 1287 3208 M -4 3 V .02 g 1283 3211 M -18 17 V .02 g 1265 3228 M -9 9 V .02 g 1256 3237 M -10 11 V .02 g 1246 3248 M -17 19 V .02 g 1229 3267 M -1 2 V .02 g 1228 3269 M -16 20 V .02 g 1212 3289 M -10 12 V .02 g 1202 3301 M -6 8 V .02 g 1196 3309 M -14 20 V .02 g 1182 3329 M -8 10 V .02 g 1174 3339 M -6 10 V .02 g 1168 3349 M -14 20 V .02 g 1154 3369 M -7 11 V .02 g 1147 3380 M -5 10 V .02 g 1142 3390 M -13 20 V .02 g 1129 3410 M -9 15 V .02 g 1120 3425 M -3 5 V .02 g 1117 3430 M -11 20 V .02 g 1106 3450 M -11 20 V .02 g 1095 3470 M -2 4 V .02 g 1093 3474 M -9 16 V .02 g 1084 3490 M -10 20 V .02 g 1074 3510 M -9 17 V .02 g 1065 3527 M -2 4 V .02 g 1063 3531 M -9 20 V .02 g 1054 3551 M -10 20 V .02 g 1044 3571 M -6 12 V .02 g 1038 3583 M -4 8 V .02 g 1034 3591 M -9 20 V .02 g 1025 3611 M -9 20 V .02 g 1016 3631 M -5 11 V .02 g 1011 3642 M -4 10 V .02 g 1007 3652 M -9 20 V .02 g 998 3672 M -8 20 V .02 g 990 3692 M -6 14 V .02 g 984 3706 M -3 6 V .02 g 981 3712 M -8 20 V .02 g 973 3732 M -8 20 V .02 g 965 3752 M -8 20 V .02 g 957 3772 M -1 1 V .02 g 956 3773 M -7 20 V stroke 949 3793 M .02 g 949 3793 M -8 20 V .02 g 941 3813 M -7 20 V .02 g 934 3833 M -5 12 V .02 g 929 3845 M -3 8 V .02 g 926 3853 M -7 20 V .02 g 919 3873 M -7 20 V .02 g 912 3893 M -8 21 V .02 g 904 3914 M -2 6 V .02 g 902 3920 M -5 14 V .02 g 897 3934 M -7 20 V .02 g 890 3954 M -7 20 V .02 g 883 3974 M -7 20 V .02 g 876 3994 M -1 6 V .02 g 875 4000 M -5 14 V .02 g 870 4014 M -7 21 V .02 g 863 4035 M -6 20 V .02 g 857 4055 M -7 20 V .02 g 850 4075 M -3 10 V .02 g 847 4085 M -3 10 V .02 g 844 4095 M -6 20 V .02 g 838 4115 M -6 20 V .02 g 832 4135 M -6 20 V .02 g 826 4155 M -6 19 V .02 g 820 4174 M 0 2 V .02 g 820 4176 M -6 20 V .02 g 814 4196 M -6 20 V .02 g 808 4216 M -5 20 V .02 g 803 4236 M -6 20 V .02 g 797 4256 M -4 15 V .02 g 793 4271 M -2 5 V .02 g 791 4276 M -5 21 V .02 g 786 4297 M -5 20 V .02 g 781 4317 M -6 20 V .02 g 775 4337 M -5 20 V .02 g 770 4357 M -5 17 V .02 g 765 4374 M 0 3 V .02 g 765 4377 M -5 20 V .02 g 760 4397 M -5 20 V .02 g 755 4417 M -5 21 V .02 g 750 4438 M -4 20 V .02 g 746 4458 M -5 20 V .02 g 741 4478 M -3 11 V .02 g 738 4489 M -2 9 V .02 g 736 4498 M -4 20 V .02 g 732 4518 M -4 20 V .02 g 728 4538 M -4 21 V .02 g 724 4559 M -4 20 V .02 g 720 4579 M -4 20 V .02 g 716 4599 M -4 20 V 0 g .02 g 1149 4619 M .02 g 1149 4619 M 10 -20 V .02 g 1159 4599 M 11 -20 V .02 g 1170 4579 M 4 -9 V stroke 1174 4570 M .02 g 1174 4570 M 6 -11 V .02 g 1180 4559 M 9 -21 V .02 g 1189 4538 M 10 -20 V .02 g 1199 4518 M 3 -4 V .02 g 1202 4514 M 7 -16 V .02 g 1209 4498 M 9 -20 V .02 g 1218 4478 M 9 -20 V .02 g 1227 4458 M 2 -3 V .02 g 1229 4455 M 7 -17 V .02 g 1236 4438 M 9 -21 V .02 g 1245 4417 M 9 -20 V .02 g 1254 4397 M 2 -4 V .02 g 1256 4393 M 7 -16 V .02 g 1263 4377 M 8 -20 V .02 g 1271 4357 M 9 -20 V .02 g 1280 4337 M 3 -8 V .02 g 1283 4329 M 5 -12 V .02 g 1288 4317 M 8 -20 V .02 g 1296 4297 M 8 -21 V .02 g 1304 4276 M 7 -15 V .02 g 1311 4261 M 1 -5 V .02 g 1312 4256 M 8 -20 V .02 g 1320 4236 M 8 -20 V .02 g 1328 4216 M 8 -20 V .02 g 1336 4196 M 2 -6 V .02 g 1338 4190 M 5 -14 V .02 g 1343 4176 M 7 -21 V .02 g 1350 4155 M 8 -20 V .02 g 1358 4135 M 7 -19 V .02 g 1365 4116 M 0 -1 V .02 g 1365 4115 M 7 -20 V .02 g 1372 4095 M 7 -20 V .02 g 1379 4075 M 7 -20 V .02 g 1386 4055 M 6 -18 V .02 g 1392 4037 M 1 -2 V .02 g 1393 4035 M 7 -21 V .02 g 1400 4014 M 6 -20 V .02 g 1406 3994 M 7 -20 V .02 g 1413 3974 M 6 -20 V .02 g 1419 3954 M 1 0 V .02 g 1420 3954 M 6 -20 V .02 g 1426 3934 M 6 -20 V .02 g 1432 3914 M 6 -21 V .02 g 1438 3893 M 6 -20 V .02 g 1444 3873 M 3 -10 V .02 g 1447 3863 M 3 -10 V .02 g 1450 3853 M 5 -20 V .02 g 1455 3833 M 6 -20 V .02 g 1461 3813 M 5 -20 V .02 g 1466 3793 M 6 -21 V .02 g 1472 3772 M 2 -8 V .02 g 1474 3764 M 3 -12 V stroke 1477 3752 M .02 g 1477 3752 M 5 -20 V .02 g 1482 3732 M 5 -20 V .02 g 1487 3712 M 5 -20 V .02 g 1492 3692 M 4 -20 V .02 g 1496 3672 M 5 -20 V .02 g 1501 3652 M 0 -2 V .02 g 1501 3650 M 4 -19 V .02 g 1505 3631 M 4 -20 V .02 g 1509 3611 M 4 -20 V .02 g 1513 3591 M 3 -20 V .02 g 1516 3571 M 4 -20 V .02 g 1520 3551 M 3 -20 V .02 g 1523 3531 M 3 -21 V .02 g 1526 3510 M 3 -18 V .02 g 1529 3492 M 0 -2 V .02 g 1529 3490 M 2 -20 V .02 g 1531 3470 M 2 -20 V .02 g 1533 3450 M 1 -20 V .02 g 1534 3430 M 1 -20 V .02 g 1535 3410 M 1 -20 V .02 g 1536 3390 M 0 -21 V .02 g 1536 3369 M 0 -20 V .02 g 1536 3349 M -1 -20 V .02 g 1535 3329 M -2 -20 V .02 g 1533 3309 M -3 -20 V .02 g 1530 3289 M -1 -10 V .02 g 1529 3279 M -3 -10 V .02 g 1526 3269 M -5 -21 V .02 g 1521 3248 M -7 -20 V .02 g 1514 3228 M -9 -20 V .02 g 1505 3208 M -4 -6 V .02 g 1501 3202 M -10 -14 V .02 g 1491 3188 M -17 -19 V .02 g 1474 3169 M -2 -1 V .02 g 1472 3168 M -25 -14 V .02 g 1447 3154 M -27 -6 V .02 g 1420 3148 M -28 2 V .02 g 1392 3150 M -27 8 V .02 g 1365 3158 M -21 10 V .02 g 1344 3168 M -6 3 V .02 g 1338 3171 M -27 17 V .02 g 1311 3188 M 0 1 V .02 g 1311 3189 M -24 19 V 0 g .02 g 6052 3307 M .02 g 6052 3307 M -25 -18 V .02 g 6027 3289 M -2 -2 V .02 g 6025 3287 M -27 -16 V .02 g 5998 3271 M -6 -2 V .02 g 5992 3269 M -22 -9 V .02 g 5970 3260 M -27 -5 V .02 g 5943 3255 M -27 1 V .02 g 5916 3256 M -27 11 V .02 g 5889 3267 M -3 2 V stroke 5886 3269 M .02 g 5886 3269 M -23 20 V .02 g 5863 3289 M -2 2 V .02 g 5861 3291 M -11 18 V .02 g 5850 3309 M -10 20 V .02 g 5840 3329 M -6 15 V .02 g 5834 3344 M -2 5 V .02 g 5832 3349 M -5 20 V .02 g 5827 3369 M -4 21 V .02 g 5823 3390 M -2 20 V .02 g 5821 3410 M -2 20 V .02 g 5819 3430 M -1 20 V .02 g 5818 3450 M -1 20 V .02 g 5817 3470 M 0 20 V .02 g 5817 3490 M 1 20 V .02 g 5818 3510 M 1 21 V .02 g 5819 3531 M 2 20 V .02 g 5821 3551 M 2 20 V .02 g 5823 3571 M 2 20 V .02 g 5825 3591 M 2 20 V .02 g 5827 3611 M 3 20 V .02 g 5830 3631 M 3 21 V .02 g 5833 3652 M 1 4 V .02 g 5834 3656 M 3 16 V .02 g 5837 3672 M 3 20 V .02 g 5840 3692 M 4 20 V .02 g 5844 3712 M 4 20 V .02 g 5848 3732 M 4 20 V .02 g 5852 3752 M 5 20 V .02 g 5857 3772 M 4 21 V .02 g 5861 3793 M 0 1 V .02 g 5861 3794 M 5 19 V .02 g 5866 3813 M 5 20 V .02 g 5871 3833 M 5 20 V .02 g 5876 3853 M 5 20 V .02 g 5881 3873 M 5 20 V .02 g 5886 3893 M 3 10 V .02 g 5889 3903 M 2 11 V .02 g 5891 3914 M 6 20 V .02 g 5897 3934 M 6 20 V .02 g 5903 3954 M 5 20 V .02 g 5908 3974 M 6 20 V .02 g 5914 3994 M 2 6 V .02 g 5916 4000 M 4 14 V .02 g 5920 4014 M 6 21 V .02 g 5926 4035 M 6 20 V .02 g 5932 4055 M 7 20 V .02 g 5939 4075 M 4 14 V .02 g 5943 4089 M 2 6 V .02 g 5945 4095 M 7 20 V .02 g 5952 4115 M 6 20 V .02 g 5958 4135 M 7 20 V .02 g 5965 4155 M 5 17 V stroke 5970 4172 M .02 g 5970 4172 M 1 4 V .02 g 5971 4176 M 8 20 V .02 g 5979 4196 M 7 20 V .02 g 5986 4216 M 6 20 V .02 g 5992 4236 M 6 15 V .02 g 5998 4251 M 2 5 V .02 g 6000 4256 M 7 20 V .02 g 6007 4276 M 7 21 V .02 g 6014 4297 M 8 20 V .02 g 6022 4317 M 3 8 V .02 g 6025 4325 M 4 12 V .02 g 6029 4337 M 8 20 V .02 g 6037 4357 M 8 20 V .02 g 6045 4377 M 7 19 V % End plot #1 % Begin plot #2 1.500 UP stroke 6.000 UL LT0 0.55 0.10 0.05 C 3600 4518 M 1299 3219 L -57 460 V -117 320 V -35 91 V 26 -27 V -12 11 V 6 -6 V -2 2 V 1 0 V -1 0 V 3600 4518 CircleF 1299 3219 CircleF 1242 3679 CircleF 1125 3999 CircleF 1090 4090 CircleF 1116 4063 CircleF 1104 4074 CircleF 1110 4068 CircleF 1108 4070 CircleF 1109 4070 CircleF 1108 4070 CircleF 1108 4070 CircleF 1108 4070 CircleF 1108 4070 CircleF 1108 4070 CircleF 1108 4070 CircleF 1108 4070 CircleF 1108 4070 CircleF 1108 4070 CircleF 1108 4070 CircleF 1108 4070 CircleF % End plot #2 % Begin plot #3 1.500 UP 6.000 UL LT1 0.37 0.61 0.21 C 3600 4518 M -155 -79 V 3289 4222 L 3077 3729 L 2848 2964 L 2525 2442 L 223 -256 V 136 -138 V -92 15 V 55 -16 V -30 5 V 5 1 V -2 1 V 1 0 V 3600 4518 TriUF 3445 4439 TriUF 3289 4222 TriUF 3077 3729 TriUF 2848 2964 TriUF 2525 2442 TriUF 2748 2186 TriUF 2884 2048 TriUF 2792 2063 TriUF 2847 2047 TriUF 2817 2052 TriUF 2822 2053 TriUF 2820 2054 TriUF 2821 2054 TriUF 2821 2054 TriUF 2821 2054 TriUF 2821 2054 TriUF 2821 2054 TriUF 2821 2054 TriUF 2821 2054 TriUF 2821 2054 TriUF 2821 2054 TriUF 2821 2054 TriUF 2821 2054 TriUF 2821 2054 TriUF 2821 2054 TriUF 2821 2054 TriUF 2821 2054 TriUF % End plot #3 % Begin plot #4 1.500 UP 6.000 UL LT2 0.00 0.38 0.68 C 3600 4518 M 1988 3715 L 3160 1440 L -415 600 V 158 -40 V -158 91 V 137 -41 V -69 -20 V 12 17 V -7 6 V 4 2 V -2 -1 V 1 1 V 0 -1 V 3600 4518 Circle 1988 3715 Circle 3160 1440 Circle 2745 2040 Circle 2903 2000 Circle 2745 2091 Circle 2882 2050 Circle 2813 2030 Circle 2825 2047 Circle 2818 2053 Circle 2822 2055 Circle 2820 2054 Circle 2821 2055 Circle 2821 2054 Circle 2821 2054 Circle 2821 2054 Circle 2821 2054 Circle 2821 2054 Circle 2821 2054 Circle 2821 2054 Circle 2821 2054 Circle 2821 2054 Circle 2821 2054 Circle 2821 2054 Circle % End plot #4 % Begin plot #5 1.500 UP 6.000 UL LT3 0.95 0.35 0.00 C 3600 4518 M 1988 3715 L 3198 1467 L -475 568 V 163 -26 V -66 7 V 7 21 V -16 28 V 12 -6 V -5 -5 V 3 1 V -1 -1 V 1 0 V -1 0 V 1 0 V 3600 4518 Crs 1988 3715 Crs 3198 1467 Crs 2723 2035 Crs 2886 2009 Crs 2820 2016 Crs 2827 2037 Crs 2811 2065 Crs 2823 2059 Crs 2818 2054 Crs 2821 2055 Crs 2820 2054 Crs 2821 2054 Crs 2820 2054 Crs 2821 2054 Crs 2821 2054 Crs 2821 2054 Crs 2821 2054 Crs 2821 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end showpage %%Trailer %%DocumentFonts: Arial-Bold Helvetica %%EndDocument @endspecial 150 2799 a(The)30 b(program)g(is)g(giv)m(en)i(b)s(elo)m (w.)390 2929 y FH(#include)46 b()390 3039 y(#include)g ()390 3148 y(#include)g()390 3258 y(#include)g()390 3367 y(#include)g ()390 3477 y(#include)g()390 3696 y(/*)h(parameters)e(to)i(model)g(*/)390 3806 y(struct)f(model_params)390 3915 y({)485 4025 y(double)h(a1;)485 4134 y(double)g(a2;)485 4244 y(double)g(a3;)485 4354 y(double)g(a4;)485 4463 y(double)g(a5;)390 4573 y(};)390 4792 y(/*)g(Branin)f(function)g(*/)390 4902 y(int)390 5011 y(func_f)g(\(const)g(gsl_vector)f(*)j(x,)f(void)f(*params,)g (gsl_vector)f(*)i(f\))390 5121 y({)485 5230 y(struct)g(model_params)d (*par)j(=)g(\(struct)f(model_params)e(*\))k(params;)485 5340 y(double)f(x1)g(=)g(gsl_vector_get\(x,)c(0\);)p eop end %%Page: 503 521 TeXDict begin 503 520 bop 150 -116 a FK(Chapter)30 b(39:)41 b(Nonlinear)31 b(Least-Squares)g(Fitting)1681 b(503)485 299 y FH(double)47 b(x2)g(=)g(gsl_vector_get\(x,)c(1\);)485 408 y(double)k(f1)g(=)g(x2)g(+)h(par->a1)e(*)h(x1)g(*)h(x1)f(+)g (par->a2)f(*)i(x1)f(+)g(par->a3;)485 518 y(double)g(f2)g(=)g (sqrt\(par->a4\))d(*)k(sqrt\(1.0)d(+)j(\(1.0)e(-)i(par->a5\))d(*)j (cos\(x1\)\);)485 737 y(gsl_vector_set\(f,)c(0,)j(f1\);)485 847 y(gsl_vector_set\(f,)d(1,)j(f2\);)485 1066 y(return)g(GSL_SUCCESS;) 390 1176 y(})390 1395 y(int)390 1504 y(func_df)f(\(const)g(gsl_vector)f (*)i(x,)h(void)e(*params,)g(gsl_matrix)f(*)i(J\))390 1614 y({)485 1724 y(struct)g(model_params)d(*par)j(=)g(\(struct)f (model_params)e(*\))k(params;)485 1833 y(double)f(x1)g(=)g (gsl_vector_get\(x,)c(0\);)485 1943 y(double)k(f2)g(=)g (sqrt\(par->a4\))d(*)k(sqrt\(1.0)d(+)j(\(1.0)e(-)i(par->a5\))d(*)j (cos\(x1\)\);)485 2162 y(gsl_matrix_set\(J,)c(0,)j(0,)g(2.0)g(*)g (par->a1)f(*)i(x1)f(+)g(par->a2\);)485 2271 y(gsl_matrix_set\(J,)d(0,)j (1,)g(1.0\);)485 2491 y(gsl_matrix_set\(J,)d(1,)j(0,)g(-0.5)g(*)g (par->a4)f(/)h(f2)g(*)h(\(1.0)f(-)g(par->a5\))f(*)h(sin\(x1\)\);)485 2600 y(gsl_matrix_set\(J,)d(1,)j(1,)g(0.0\);)485 2819 y(return)g(GSL_SUCCESS;)390 2929 y(})390 3148 y(int)390 3258 y(func_fvv)f(\(const)g(gsl_vector)f(*)i(x,)g(const)g(gsl_vector)e (*)i(v,)867 3367 y(void)g(*params,)e(gsl_vector)g(*)j(fvv\))390 3477 y({)485 3587 y(struct)f(model_params)d(*par)j(=)g(\(struct)f (model_params)e(*\))k(params;)485 3696 y(double)f(x1)g(=)g (gsl_vector_get\(x,)c(0\);)485 3806 y(double)k(v1)g(=)g (gsl_vector_get\(v,)c(0\);)485 3915 y(double)k(c)g(=)g(cos\(x1\);)485 4025 y(double)g(s)g(=)g(sin\(x1\);)485 4134 y(double)g(f2)g(=)g (sqrt\(par->a4\))d(*)k(sqrt\(1.0)d(+)j(\(1.0)e(-)i(par->a5\))d(*)j (c\);)485 4244 y(double)f(t)g(=)g(0.5)g(*)h(par->a4)e(*)h(\(1.0)g(-)g (par->a5\))f(/)h(f2;)485 4463 y(gsl_vector_set\(fvv,)c(0,)k(2.0)g(*)h (par->a1)d(*)j(v1)f(*)g(v1\);)485 4573 y(gsl_vector_set\(fvv,)c(1,)k (-t)g(*)h(\(c)f(+)g(s*s/f2\))f(*)i(v1)f(*)g(v1\);)485 4792 y(return)g(GSL_SUCCESS;)390 4902 y(})390 5121 y(void)390 5230 y(callback\(const)d(size_t)i(iter,)g(void)h(*params,)820 5340 y(const)f(gsl_multifit_nlinear_wor)o(kspa)o(ce)41 b(*w\))p eop end %%Page: 504 522 TeXDict begin 504 521 bop 150 -116 a FK(Chapter)30 b(39:)41 b(Nonlinear)31 b(Least-Squares)g(Fitting)1681 b(504)390 299 y FH({)485 408 y(gsl_vector)45 b(*)j(x)f(=)h (gsl_multifit_nlinear_pos)o(iti)o(on\(w)o(\);)485 518 y(double)f(x1)g(=)g(gsl_vector_get\(x,)c(0\);)485 628 y(double)k(x2)g(=)g(gsl_vector_get\(x,)c(1\);)485 847 y(/*)48 b(print)e(out)h(current)f(location)f(*/)485 956 y(printf\("\045f)g(\045f\\n",)i(x1,)f(x2\);)390 1066 y(})390 1285 y(void)390 1395 y(solve_system\(gsl_vector)41 b(*x0,)47 b(gsl_multifit_nlinear_fdf)41 b(*fdf,)1010 1504 y(gsl_multifit_nlinear_param)o(eter)o(s)h(*params\))390 1614 y({)485 1724 y(const)47 b(gsl_multifit_nlinear_typ)o(e)42 b(*T)47 b(=)g(gsl_multifit_nlinear_trust)o(;)485 1833 y(const)g(size_t)f(max_iter)f(=)j(200;)485 1943 y(const)f(double)f (xtol)h(=)g(1.0e-8;)485 2052 y(const)g(double)f(gtol)h(=)g(1.0e-8;)485 2162 y(const)g(double)f(ftol)h(=)g(1.0e-8;)485 2271 y(const)g(size_t)f (n)h(=)h(fdf->n;)485 2381 y(const)f(size_t)f(p)h(=)h(fdf->p;)485 2491 y(gsl_multifit_nlinear_works)o(pace)41 b(*work)46 b(=)581 2600 y(gsl_multifit_nlinear_all)o(oc\(T)o(,)c(params,)k(n,)h (p\);)485 2710 y(gsl_vector)e(*)j(f)f(=)h(gsl_multifit_nlinear_res)o (idu)o(al\(w)o(ork\))o(;)485 2819 y(gsl_vector)d(*)j(x)f(=)h (gsl_multifit_nlinear_pos)o(iti)o(on\(w)o(ork\))o(;)485 2929 y(int)f(info;)485 3039 y(double)g(chisq0,)e(chisq,)h(rcond;)485 3258 y(printf\("#)g(\045s/\045s\\n",)820 3367 y (gsl_multifit_nlinear_na)o(me\()o(work)o(\),)820 3477 y(gsl_multifit_nlinear_tr)o(s_n)o(ame\()o(work)o(\)\);)485 3696 y(/*)i(initialize)d(solver)h(*/)485 3806 y (gsl_multifit_nlinear_init\()o(x0,)41 b(fdf,)47 b(work\);)485 4025 y(/*)h(store)e(initial)g(cost)g(*/)485 4134 y(gsl_blas_ddot\(f,)e (f,)j(&chisq0\);)485 4354 y(/*)h(iterate)d(until)i(convergence)e(*/)485 4463 y(gsl_multifit_nlinear_drive)o(r\(ma)o(x_i)o(ter,)c(xtol,)46 b(gtol,)h(ftol,)1822 4573 y(callback,)e(NULL,)h(&info,)h(work\);)485 4792 y(/*)h(store)e(final)g(cost)h(*/)485 4902 y(gsl_blas_ddot\(f,)d (f,)j(&chisq\);)485 5121 y(/*)h(store)e(cond\(J\(x\)\))f(*/)485 5230 y(gsl_multifit_nlinear_rcond)o(\(&rc)o(ond)o(,)d(work\);)p eop end %%Page: 505 523 TeXDict begin 505 522 bop 150 -116 a FK(Chapter)30 b(39:)41 b(Nonlinear)31 b(Least-Squares)g(Fitting)1681 b(505)485 299 y FH(/*)48 b(print)e(summary)g(*/)485 408 y(fprintf\(stderr,)e ("\045-25s)i(\045-6zu)h(\045-5zu)f(\045-5zu)g(\045-13.4e)g(\045-12.4e)g (\045-13.4e)g(\(\045.2e,)g(\045.2e\)\\n",)867 518 y (gsl_multifit_nlinear_trs_)o(name)o(\(wor)o(k\),)867 628 y(gsl_multifit_nlinear_nite)o(r\(wo)o(rk\),)867 737 y(fdf->nevalf,)867 847 y(fdf->nevaldf,)867 956 y(chisq0,)867 1066 y(chisq,)867 1176 y(1.0)h(/)h(rcond,)867 1285 y (gsl_vector_get\(x,)43 b(0\),)867 1395 y(gsl_vector_get\(x,)g(1\)\);) 485 1614 y(printf\("\\n\\n"\);)485 1833 y(gsl_multifit_nlinear_free\()o (work)o(\);)390 1943 y(})390 2162 y(int)390 2271 y(main)k(\(void\))390 2381 y({)485 2491 y(const)g(size_t)f(n)h(=)h(2;)485 2600 y(const)f(size_t)f(p)h(=)h(2;)485 2710 y(gsl_vector)d(*f)j(=)f (gsl_vector_alloc\(n\);)485 2819 y(gsl_vector)e(*x)j(=)f (gsl_vector_alloc\(p\);)485 2929 y(gsl_multifit_nlinear_fdf)42 b(fdf;)485 3039 y(gsl_multifit_nlinear_param)o(eter)o(s)g(fdf_params)j (=)581 3148 y(gsl_multifit_nlinear_def)o(ault)o(_pa)o(rame)o(ters)o (\(\);)485 3258 y(struct)i(model_params)d(params;)485 3477 y(params.a1)i(=)h(-5.1)g(/)g(\(4.0)g(*)g(M_PI)g(*)g(M_PI\);)485 3587 y(params.a2)f(=)h(5.0)g(/)h(M_PI;)485 3696 y(params.a3)e(=)h (-6.0;)485 3806 y(params.a4)f(=)h(10.0;)485 3915 y(params.a5)f(=)h(1.0) g(/)h(\(8.0)e(*)i(M_PI\);)485 4134 y(/*)g(print)e(map)h(of)g(Phi\(x1,)f (x2\))h(*/)485 4244 y({)581 4354 y(double)f(x1,)h(x2,)g(chisq;)581 4573 y(for)g(\(x1)g(=)g(-5.0;)g(x1)g(<)g(15.0;)g(x1)g(+=)g(0.1\))676 4682 y({)772 4792 y(for)g(\(x2)g(=)g(-5.0;)f(x2)i(<)f(15.0;)f(x2)i(+=)f (0.1\))867 4902 y({)963 5011 y(gsl_vector_set\(x,)c(0,)k(x1\);)963 5121 y(gsl_vector_set\(x,)c(1,)k(x2\);)963 5230 y(func_f\(x,)e (¶ms,)h(f\);)p eop end %%Page: 506 524 TeXDict begin 506 523 bop 150 -116 a FK(Chapter)30 b(39:)41 b(Nonlinear)31 b(Least-Squares)g(Fitting)1681 b(506)963 299 y FH(gsl_blas_ddot\(f,)43 b(f,)k(&chisq\);)963 518 y(printf\("\045f)e(\045f)i(\045f\\n",)f(x1,)h(x2,)g(chisq\);)867 628 y(})772 737 y(printf\("\\n"\);)676 847 y(})581 956 y(printf\("\\n\\n"\);)485 1066 y(})485 1285 y(/*)h(define)e(function)f (to)i(be)h(minimized)d(*/)485 1395 y(fdf.f)i(=)g(func_f;)485 1504 y(fdf.df)g(=)g(func_df;)485 1614 y(fdf.fvv)f(=)i(func_fvv;)485 1724 y(fdf.n)f(=)g(n;)485 1833 y(fdf.p)g(=)g(p;)485 1943 y(fdf.params)e(=)j(¶ms;)485 2162 y(/*)g(starting)d(point)i(*/)485 2271 y(gsl_vector_set\(x,)d(0,)j(6.0\);)485 2381 y(gsl_vector_set\(x,)d (1,)j(14.5\);)485 2600 y(fprintf\(stderr,)d("\045-25s)i(\045-6s)h 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bop 150 -116 a FK(Chapter)30 b(39:)41 b(Nonlinear)31 b(Least-Squares)g(Fitting)1681 b(507)150 299 y Fy(39.12.4)63 b(Large)41 b(Nonlinear)h(Least)e(Squares)h(Example) 150 446 y FK(The)27 b(follo)m(wing)h(program)f(illustrates)h(the)f (large)i(nonlinear)e(least)h(squares)f(solv)m(ers)h(on)f(a)g(system)g (with)150 555 y(signi\014can)m(t)k(sparse)f(structure)g(in)g(the)h (Jacobian.)41 b(The)30 b(cost)h(function)g(is)f(giv)m(en)h(b)m(y)1327 793 y(\010\()p FE(x)p FK(\))25 b(=)1646 732 y(1)p 1646 772 46 4 v 1646 856 a(2)1717 684 y Fq(p)p FB(+1)1717 712 y Fs(X)1723 889 y Fq(i)p FB(=1)1852 793 y FE(f)1907 756 y FB(2)1897 816 y Fq(i)1443 1009 y FE(f)1488 1023 y Fq(i)1540 1009 y FK(=)1636 939 y FI(p)p 1712 939 59 4 v 70 x FE(\013)p FK(\()p FE(x)1857 1023 y Fq(i)1905 1009 y FI(\000)20 b FK(1\))p FE(;)108 b FK(1)25 b FI(\024)g FE(i)h FI(\024)f FE(p)1348 1195 y(f)1393 1209 y Fq(p)p FB(+1)1540 1195 y FK(=)g FI(jj)p FE(x)p FI(jj)1788 1158 y FB(2)1846 1195 y FI(\000)1947 1134 y FK(1)p 1947 1174 46 4 v 1947 1258 a(4)150 1393 y(with)35 b FE(\013)f FK(=)f(10)648 1360 y Fp(\000)p FB(5)738 1393 y FK(.)56 b(The)35 b(residual)g FE(f)1400 1407 y Fq(p)p FB(+1)1557 1393 y FK(imp)s(oses)g(a)h (constrain)m(t)g(on)g(the)f FE(p)g FK(parameters)h FE(x)p FK(,)h(to)f(ensure)150 1502 y(that)31 b FI(jj)p FE(x)p FI(jj)499 1469 y FB(2)562 1502 y FI(\031)668 1467 y FB(1)p 668 1482 34 4 v 668 1534 a(4)711 1502 y FK(.)41 b(The)30 b(\()p FE(p)20 b FK(+)g(1\)-b)m(y-)p FE(p)32 b FK(Jacobian)f(for)f (this)g(system)h(is)f(giv)m(en)h(b)m(y)1616 1721 y FE(J)9 b FK(\()p FE(x)p FK(\))26 b(=)1919 1602 y Fs(\022)1995 1601 y FI(p)p 2071 1601 59 4 v 66 x FE(\013I)2169 1681 y Fq(p)2027 1776 y FK(2)p FE(x)2124 1743 y Fq(T)2223 1602 y Fs(\023)150 1927 y FK(and)k(the)g(normal)h(equations)g(matrix)f (is)h(giv)m(en)g(b)m(y)1579 2092 y FE(J)1638 2054 y Fq(T)1691 2092 y FE(J)j FK(=)25 b FE(\013I)1969 2106 y Fq(p)2028 2092 y FK(+)20 b(4)p FE(xx)2268 2054 y Fq(T)150 2257 y FK(Finally)-8 b(,)31 b(the)f(second)f(directional)i(deriv)-5 b(ativ)m(e)31 b(of)e FE(f)39 b FK(for)29 b(the)g(geo)s(desic)i (acceleration)h(metho)s(d)d(is)g(giv)m(en)150 2367 y(b)m(y)1493 2572 y FE(f)1538 2586 y Fq(v)r(v)1637 2572 y FK(=)c FE(D)1811 2534 y FB(2)1808 2594 y Fq(v)1848 2572 y FE(f)35 b FK(=)2024 2453 y Fs(\022)2193 2517 y FK(0)2100 2627 y(2)p FI(jj)p FE(v)s FI(jj)2292 2594 y FB(2)2346 2453 y Fs(\023)150 2777 y FK(Since)e(the)f(upp)s(er)f FE(p)p FK(-b)m(y-)p FE(p)h FK(blo)s(c)m(k)i(of)e FE(J)42 b FK(is)33 b(diagonal,)h(this)f (sparse)f(structure)g(should)g(b)s(e)g(exploited)h(in)150 2887 y(the)28 b(nonlinear)g(solv)m(er.)41 b(F)-8 b(or)28 b(comparison,)h(the)f(follo)m(wing)i(program)d(solv)m(es)i(the)g (system)f(for)f FE(p)e FK(=)g(2000)150 2996 y(using)31 b(the)g(dense)g(direct)h(Cholesky)f(solv)m(er)i(based)e(on)g(the)g (normal)g(equations)h(matrix)g FE(J)3315 2964 y Fq(T)3368 2996 y FE(J)9 b FK(,)31 b(as)h(w)m(ell)150 3106 y(as)c(the)g(iterativ)m (e)i(Steihaug-T)-8 b(oin)m(t)29 b(solv)m(er,)g(based)f(on)f(sparse)g (matrix-v)m(ector)j(pro)s(ducts)d FE(J)9 b(u)27 b FK(and)g FE(J)3620 3073 y Fq(T)3673 3106 y FE(u)p FK(.)150 3216 y(The)j(program)g(output)g(is)g(sho)m(wn)g(b)s(elo)m(w.)150 3325 y Fz(Method)786 b(NITER)40 b(NFEV)g(NJUEV)h(NJTJEV)f(NAEV)h(Init)f (Cost)79 b(Final)40 b(cost)h(cond\(J\))f(Final)h(|x|^2)f(Time)g(\(s\)) 150 3412 y(levenberg-marquardt)279 b(25)157 b(31)118 b(26)158 b(26)196 b(0)158 b(7.1218e+18)41 b(1.9555e-02)h(447.50)79 b(2.5044e-01)i(46.28)150 3500 y(levenberg-marquardt+accel)45 b(22)157 b(23)118 b(45)158 b(23)196 b(22)119 b(7.1218e+18)41 b(1.9555e-02)h(447.64)79 b(2.5044e-01)i(33.92)150 3587 y(dogleg)786 b(37)157 b(87)118 b(36)158 b(36)196 b(0)158 b(7.1218e+18)41 b(1.9555e-02)h(447.59)79 b(2.5044e-01)i(56.05)150 3674 y(double-dogleg)513 b(35)157 b(88)118 b(34)158 b(34)196 b(0)158 b(7.1218e+18)41 b(1.9555e-02)h(447.62)79 b(2.5044e-01)i(52.65) 150 3761 y(2D-subspace)591 b(37)157 b(88)118 b(36)158 b(36)196 b(0)158 b(7.1218e+18)41 b(1.9555e-02)h(447.71)79 b(2.5044e-01)i(59.75)150 3848 y(steihaug-toint)474 b(35)157 b(88)118 b(345)h(0)235 b(0)158 b(7.1218e+18)41 b(1.9555e-02)h(inf)196 b(2.5044e-01)81 b(0.09)150 3980 y FK(The)38 b(\014rst)g(\014v)m(e)i(ro) m(ws)e(use)h(metho)s(ds)f(based)g(on)h(factoring)h(the)f(dense)g FE(J)2743 3947 y Fq(T)2795 3980 y FE(J)48 b FK(matrix)39 b(while)g(the)g(last)150 4090 y(ro)m(w)27 b(uses)f(the)g(iterativ)m(e)j (Steihaug-T)-8 b(oin)m(t)29 b(metho)s(d.)39 b(While)27 b(the)g(n)m(um)m(b)s(er)e(of)h(Jacobian)i(matrix-v)m(ector)150 4199 y(pro)s(ducts)34 b(\(NJUEV\))h(is)g(less)h(for)e(the)h(dense)g (metho)s(ds,)h(the)f(added)f(time)i(to)f(construct)h(and)e(factor)150 4309 y(the)28 b FE(J)363 4276 y Fq(T)416 4309 y FE(J)37 b FK(matrix)28 b(\(NJTJEV\))g(results)f(in)h(a)g(m)m(uc)m(h)g(larger)h (run)m(time)f(than)f(the)h(iterativ)m(e)j(metho)s(d)c(\(see)150 4419 y(last)k(column\).)150 4550 y(The)f(program)g(is)g(giv)m(en)i(b)s (elo)m(w.)390 4682 y FH(#include)46 b()390 4792 y(#include)g()390 4902 y(#include)g()390 5011 y(#include)g()390 5121 y(#include)g ()390 5230 y(#include)g()390 5340 y(#include)g()p eop end %%Page: 508 526 TeXDict begin 508 525 bop 150 -116 a FK(Chapter)30 b(39:)41 b(Nonlinear)31 b(Least-Squares)g(Fitting)1681 b(508)390 299 y FH(#include)46 b()390 408 y(#include)g ()390 628 y(/*)h(parameters)e(for)i(functions)e(*/) 390 737 y(struct)h(model_params)390 847 y({)485 956 y(double)h(alpha;) 485 1066 y(gsl_spmatrix)e(*J;)390 1176 y(};)390 1395 y(/*)i(penalty)f(function)g(*/)390 1504 y(int)390 1614 y(penalty_f)f(\(const)h(gsl_vector)f(*)j(x,)f(void)g(*params,)e (gsl_vector)g(*)j(f\))390 1724 y({)485 1833 y(struct)f(model_params)d (*par)j(=)g(\(struct)f(model_params)e(*\))k(params;)485 1943 y(const)f(double)f(sqrt_alpha)f(=)i(sqrt\(par->alpha\);)485 2052 y(const)g(size_t)f(p)h(=)h(x->size;)485 2162 y(size_t)f(i;)485 2271 y(double)g(sum)f(=)i(0.0;)485 2491 y(for)f(\(i)h(=)f(0;)g(i)h(<)f (p;)g(++i\))581 2600 y({)676 2710 y(double)f(xi)i(=)f (gsl_vector_get\(x,)c(i\);)676 2929 y(gsl_vector_set\(f,)g(i,)48 b(sqrt_alpha*\(xi)c(-)j(1.0\)\);)676 3148 y(sum)g(+=)g(xi)h(*)f(xi;)581 3258 y(})485 3477 y(gsl_vector_set\(f,)d(p,)j(sum)g(-)g(0.25\);)485 3696 y(return)g(GSL_SUCCESS;)390 3806 y(})390 4025 y(int)390 4134 y(penalty_df)e(\(CBLAS_TRANSPOSE_t)e(TransJ,)j(const)g(gsl_vector) f(*)i(x,)963 4244 y(const)f(gsl_vector)f(*)j(u,)f(void)f(*)i(params,)e (gsl_vector)f(*)i(v,)963 4354 y(gsl_matrix)e(*)i(JTJ\))390 4463 y({)485 4573 y(struct)g(model_params)d(*par)j(=)g(\(struct)f (model_params)e(*\))k(params;)485 4682 y(const)f(size_t)f(p)h(=)h (x->size;)485 4792 y(size_t)f(j;)485 5011 y(/*)h(store)e(2*x)h(in)g (last)g(row)g(of)g(J)g(*/)485 5121 y(for)g(\(j)h(=)f(0;)g(j)h(<)f(p;)g (++j\))581 5230 y({)676 5340 y(double)f(xj)i(=)f(gsl_vector_get\(x,)c (j\);)p eop end %%Page: 509 527 TeXDict begin 509 526 bop 150 -116 a FK(Chapter)30 b(39:)41 b(Nonlinear)31 b(Least-Squares)g(Fitting)1681 b(509)676 299 y FH(gsl_spmatrix_set\(par->J,)42 b(p,)47 b(j,)g(2.0)g(*)g(xj\);) 581 408 y(})485 628 y(/*)h(compute)d(v)j(=)f(op\(J\))g(u)g(*/)485 737 y(if)h(\(v\))581 847 y(gsl_spblas_dgemv\(TransJ,)41 b(1.0,)47 b(par->J,)f(u,)h(0.0,)f(v\);)485 1066 y(if)i(\(JTJ\))581 1176 y({)676 1285 y(gsl_vector_view)c(diag)j(=)g (gsl_matrix_diagonal\(JTJ\);)676 1504 y(/*)h(compute)d(J^T)i(J)h(=)f([) h(alpha*I_p)d(+)i(4)h(x)f(x^T)g(])h(*/)676 1614 y (gsl_matrix_set_zero\(JTJ\);)676 1833 y(/*)g(store)e(4)h(x)h(x^T)f(in)g (lower)f(half)h(of)g(JTJ)g(*/)676 1943 y(gsl_blas_dsyr\(CblasLower,)41 b(4.0,)47 b(x,)g(JTJ\);)676 2162 y(/*)h(add)e(alpha)h(to)g(diag\(JTJ\)) e(*/)676 2271 y(gsl_vector_add_constant\(&d)o(iag)o(.vec)o(tor,)c (par->alpha\);)581 2381 y(})485 2600 y(return)47 b(GSL_SUCCESS;)390 2710 y(})390 2929 y(int)390 3039 y(penalty_fvv)e(\(const)h(gsl_vector)f (*)i(x,)g(const)g(gsl_vector)e(*)i(v,)1010 3148 y(void)g(*params,)f (gsl_vector)f(*)i(fvv\))390 3258 y({)485 3367 y(const)g(size_t)f(p)h(=) h(x->size;)485 3477 y(double)f(normv)f(=)h(gsl_blas_dnrm2\(v\);)485 3696 y(gsl_vector_set_zero\(fvv\);)485 3806 y(gsl_vector_set\(fvv,)c (p,)k(2.0)g(*)h(normv)e(*)h(normv\);)485 4025 y(\(void\)params;)e(/*)i (avoid)f(unused)g(parameter)g(warning)f(*/)485 4244 y(return)i (GSL_SUCCESS;)390 4354 y(})390 4573 y(void)390 4682 y (solve_system\(const)c(gsl_vector)i(*x0,)h(gsl_multilarge_nlinear_fdf) 41 b(*fdf,)1010 4792 y(gsl_multilarge_nlinear_par)o(amet)o(ers)g (*params\))390 4902 y({)485 5011 y(const)47 b(gsl_multilarge_nlinear_t) o(ype)41 b(*T)47 b(=)h(gsl_multilarge_nlinear_t)o(rus)o(t;)485 5121 y(const)f(size_t)f(max_iter)f(=)j(200;)485 5230 y(const)f(double)f(xtol)h(=)g(1.0e-8;)485 5340 y(const)g(double)f(gtol) h(=)g(1.0e-8;)p eop end %%Page: 510 528 TeXDict begin 510 527 bop 150 -116 a FK(Chapter)30 b(39:)41 b(Nonlinear)31 b(Least-Squares)g(Fitting)1681 b(510)485 299 y FH(const)47 b(double)f(ftol)h(=)g(1.0e-8;)485 408 y(const)g(size_t)f(n)h(=)h(fdf->n;)485 518 y(const)f(size_t)f(p)h(=)h (fdf->p;)485 628 y(gsl_multilarge_nlinear_wor)o(kspa)o(ce)41 b(*work)47 b(=)581 737 y(gsl_multilarge_nlinear_a)o(lloc)o(\(T,)41 b(params,)46 b(n,)h(p\);)485 847 y(gsl_vector)e(*)j(f)f(=)h (gsl_multilarge_nlinear_r)o(esi)o(dual)o(\(wor)o(k\);)485 956 y(gsl_vector)d(*)j(x)f(=)h(gsl_multilarge_nlinear_p)o(osi)o(tion)o (\(wor)o(k\);)485 1066 y(int)f(info;)485 1176 y(double)g(chisq0,)e (chisq,)h(rcond,)h(xsq;)485 1285 y(struct)g(timeval)e(tv0,)i(tv1;)485 1504 y(gettimeofday\(&tv0,)c(NULL\);)485 1724 y(/*)48 b(initialize)d(solver)h(*/)485 1833 y(gsl_multilarge_nlinear_ini)o (t\(x0)o(,)c(fdf,)k(work\);)485 2052 y(/*)i(store)e(initial)g(cost)g (*/)485 2162 y(gsl_blas_ddot\(f,)e(f,)j(&chisq0\);)485 2381 y(/*)h(iterate)d(until)i(convergence)e(*/)485 2491 y(gsl_multilarge_nlinear_dri)o(ver\()o(max)o(_ite)o(r,)d(xtol,)k(gtol,) g(ftol,)1917 2600 y(NULL,)h(NULL,)f(&info,)g(work\);)485 2819 y(gettimeofday\(&tv1,)d(NULL\);)485 3039 y(/*)48 b(store)e(final)g(cost)h(*/)485 3148 y(gsl_blas_ddot\(f,)d(f,)j (&chisq\);)485 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b(Least-Squares)g(Fitting)1681 b(512)485 299 y FH(fdf_params.trs)44 b(=)k(gsl_multilarge_nlinear_t)o(rs_)o(lm;) 485 408 y(solve_system\(x,)c(&fdf,)i(&fdf_params\);)485 628 y(fdf_params.trs)e(=)k(gsl_multilarge_nlinear_t)o(rs_)o(lmac)o (cel;)485 737 y(solve_system\(x,)c(&fdf,)i(&fdf_params\);)485 956 y(fdf_params.trs)e(=)k(gsl_multilarge_nlinear_t)o(rs_)o(dogl)o(eg;) 485 1066 y(solve_system\(x,)c(&fdf,)i(&fdf_params\);)485 1285 y(fdf_params.trs)e(=)k(gsl_multilarge_nlinear_t)o(rs_)o(ddog)o (leg;)485 1395 y(solve_system\(x,)c(&fdf,)i(&fdf_params\);)485 1614 y(fdf_params.trs)e(=)k(gsl_multilarge_nlinear_t)o(rs_)o(subs)o (pace)o(2D;)485 1724 y(solve_system\(x,)c(&fdf,)i(&fdf_params\);)485 1943 y(fdf_params.trs)e(=)k(gsl_multilarge_nlinear_t)o(rs_)o(cgst)o(;) 485 2052 y(solve_system\(x,)c(&fdf,)i(&fdf_params\);)485 2271 y(gsl_vector_free\(f\);)485 2381 y(gsl_vector_free\(x\);)485 2491 y(gsl_spmatrix_free\(J\);)485 2710 y(return)h(0;)390 2819 y(})150 3052 y FJ(39.13)69 b(References)46 b(and)e(F)-11 b(urther)45 b(Reading)150 3211 y FK(The)30 b(follo)m(wing)i (publications)e(are)h(relev)-5 b(an)m(t)32 b(to)f(the)f(algorithms)i (describ)s(ed)d(in)h(this)g(section,)330 3346 y(J.J.)24 b(Mor)m(\023)-43 b(e,)27 b FD(The)d(Lev)m(en)m(b)s(erg-Marquardt)h (Algorithm:)38 b(Implemen)m(tation)26 b(and)d(Theory)p FK(,)j(Lecture)330 3455 y(Notes)32 b(in)e(Mathematics,)i(v630)g (\(1978\),)h(ed)d(G.)h(W)-8 b(atson.)330 3590 y(H.)41 b(B.)g(Nielsen,)j(\\Damping)e(P)m(arameter)f(in)g(Marquardt's)f(Metho)s (d",)k(IMM)d(Departmen)m(t)h(of)330 3699 y(Mathematical)33 b(Mo)s(deling,)f(DTU,)e(T)-8 b(ec)m(h.)42 b(Rep)s(ort)30 b(IMM-REP-1999-05)k(\(1999\).)330 3834 y(K.)28 b(Madsen)g(and)g(H.)h (B.)g(Nielsen,)g(\\In)m(tro)s(duction)g(to)g(Optimization)g(and)f(Data) i(Fitting",)h(IMM)330 3944 y(Departmen)m(t)h(of)e(Mathematical)j(Mo)s (deling,)f(DTU,)e(2010.)330 4078 y(J.)f(E.)h(Dennis)f(and)g(R.)g(B.)h (Sc)m(hnab)s(el,)g(Numerical)g(Metho)s(ds)f(for)g(Unconstrained)h (Optimization)330 4188 y(and)g(Nonlinear)h(Equations,)f(SIAM,)h(1996.) 330 4322 y(M.)26 b(K.)g(T)-8 b(ranstrum,)26 b(B.)g(B.)g(Mac)m(h)m(ta,)k (and)25 b(J.)h(P)-8 b(.)26 b(Sethna,)h(Geometry)g(of)f(nonlinear)f (least)i(squares)330 4432 y(with)j(applications)i(to)f(slopp)m(y)f(mo)s (dels)g(and)g(optimization,)i(Ph)m(ys.)41 b(Rev.)g(E)30 b(83,)h(036701,)j(2011.)330 4566 y(M.)g(K.)g(T)-8 b(ranstrum)33 b(and)g(J.)h(P)-8 b(.)34 b(Sethna,)h(Impro)m(v)m(emen)m(ts)g(to)f(the)h (Lev)m(en)m(b)s(erg-Marquardt)f(algo-)330 4676 y(rithm)c(for)g (nonlinear)g(least-squares)i(minimization,)g(arXiv:1201.5885,)j(2012.) 330 4810 y(J.J.)i(Mor)m(\023)-43 b(e,)40 b(B.S.)d(Garb)s(o)m(w,)i(K.E.) e(Hillstrom,)j(\\T)-8 b(esting)38 b(Unconstrained)f(Optimization)h (Soft-)330 4920 y(w)m(are",)32 b(A)m(CM)f(T)-8 b(ransactions)31 b(on)f(Mathematical)j(Soft)m(w)m(are,)f(V)-8 b(ol)32 b(7,)f(No)f(1)h(\(1981\),)i(p)d(17{41.)330 5054 y(H.)g(B.)g(Nielsen,)g (\\UCTP)f(T)-8 b(est)30 b(Problems)f(for)g(Unconstrained)h 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b(declarations.)150 1388 y FJ(40.1)68 b(Ov)l(erview)150 1548 y FK(B-splines)33 b(are)f(commonly)h(used)e(as)i (basis)f(functions)g(to)h(\014t)f(smo)s(othing)g(curv)m(es)h(to)g (large)g(data)g(sets.)150 1657 y(T)-8 b(o)37 b(do)g(this,)h(the)f (abscissa)g(axis)g(is)f(brok)m(en)h(up)e(in)m(to)j(some)f(n)m(um)m(b)s (er)e(of)i(in)m(terv)-5 b(als,)39 b(where)e(the)f(end-)150 1767 y(p)s(oin)m(ts)41 b(of)f(eac)m(h)i(in)m(terv)-5 b(al)42 b(are)f(called)h FD(breakp)s(oin)m(ts)p FK(.)72 b(These)40 b(breakp)s(oin)m(ts)h(are)g(then)f(con)m(v)m(erted)i(to)150 1876 y FD(knots)32 b FK(b)m(y)c(imp)s(osing)f(v)-5 b(arious)28 b(con)m(tin)m(uit)m(y)i(and)d(smo)s(othness)h(conditions)g(at)h(eac)m (h)g(in)m(terface.)42 b(Giv)m(en)29 b(a)150 1986 y(nondecreasing)g (knot)g(v)m(ector)i FE(t)25 b FK(=)g FI(f)p FE(t)1447 2000 y FB(0)1484 1986 y FE(;)15 b(t)1557 2000 y FB(1)1595 1986 y FE(;)g(:)g(:)g(:)h(;)f(t)1829 2000 y Fq(n)p FB(+)p Fq(k)q Fp(\000)p FB(1)2047 1986 y FI(g)p FK(,)30 b(the)f FE(n)f FK(basis)h(splines)g(of)g(order)f FE(k)k FK(are)d(de\014ned)150 2096 y(b)m(y)1372 2313 y FE(B)1441 2327 y Fq(i;)p FB(1)1521 2313 y FK(\()p FE(x)p FK(\))d(=)1765 2193 y Fs(\032)1842 2258 y FK(1)p FE(;)92 b(t)2037 2272 y Fq(i)2090 2258 y FI(\024)25 b FE(x)g(<)g(t)2392 2272 y Fq(i)p FB(+1)1842 2367 y FK(0)p FE(;)264 b(el)r(se)798 2663 y(B)867 2677 y Fq(i;k)951 2663 y FK(\()p FE(x)p FK(\))26 b(=)1296 2602 y(\()p FE(x)20 b FI(\000)g FE(t)1527 2616 y Fq(i)1555 2602 y FK(\))p 1205 2642 476 4 v 1205 2726 a(\()p FE(t)1273 2740 y Fq(i)p FB(+)p Fq(k)q Fp(\000)p FB(1)1494 2726 y FI(\000)g FE(t)1618 2740 y Fq(i)1645 2726 y FK(\))1691 2663 y FE(B)1760 2677 y Fq(i;k)q Fp(\000)p FB(1)1929 2663 y FK(\()p FE(x)p FK(\))h(+)2219 2602 y(\()p FE(t)2287 2616 y Fq(i)p FB(+)p Fq(k)2422 2602 y FI(\000)f FE(x)p FK(\))p 2172 2642 475 4 v 2172 2726 a(\()p FE(t)2240 2740 y Fq(i)p FB(+)p Fq(k)2376 2726 y FI(\000)g FE(t)2500 2740 y Fq(i)p FB(+1)2612 2726 y FK(\))2657 2663 y FE(B)2726 2677 y Fq(i)p FB(+1)p Fq(;k)q Fp(\000)p FB(1)2979 2663 y FK(\()p FE(x)p FK(\))150 2888 y(for)37 b FE(i)f FK(=)f(0)p FE(;)15 b(:)g(:)g(:)i(;)e(n)25 b FI(\000)f FK(1.)60 b(The)37 b(common)g(case)g(of)g(cubic)g(B-splines)g(is)g(giv)m(en)h(b)m(y)e FE(k)k FK(=)35 b(4.)60 b(The)37 b(ab)s(o)m(v)m(e)150 2997 y(recurrence)28 b(relation)i(can)f(b)s(e)e(ev)-5 b(aluated)30 b(in)e(a)h(n)m(umerically)g(stable)g(w)m(a)m(y)h(b)m(y)e (the)h(de)f(Bo)s(or)h(algorithm.)275 3141 y(If)d(w)m(e)h(de\014ne)e (appropriate)i(knots)g(on)f(an)h(in)m(terv)-5 b(al)27 b([)p FE(a;)15 b(b)p FK(])28 b(then)e(the)h(B-spline)g(basis)f (functions)g(form)150 3251 y(a)31 b(complete)h(set)f(on)f(that)h(in)m (terv)-5 b(al.)42 b(Therefore)30 b(w)m(e)h(can)f(expand)g(a)h(smo)s (othing)f(function)g(as)1559 3496 y FE(f)10 b FK(\()p FE(x)p FK(\))25 b(=)1857 3390 y Fq(n)p Fp(\000)p FB(1)1860 3415 y Fs(X)1866 3592 y Fq(i)p FB(=0)1998 3496 y FE(c)2037 3510 y Fq(i)2065 3496 y FE(B)2134 3510 y Fq(i;k)2218 3496 y FK(\()p FE(x)p FK(\))150 3745 y(giv)m(en)43 b(enough)f(\()p FE(x)811 3759 y Fq(j)846 3745 y FE(;)15 b(f)10 b FK(\()p FE(x)1028 3759 y Fq(j)1063 3745 y FK(\)\))43 b(data)f(pairs.)76 b(The)41 b(co)s(e\016cien)m(ts)j FE(c)2397 3759 y Fq(i)2467 3745 y FK(can)e(b)s(e)f(readily)i(obtained)f(from)g(a)150 3854 y(least-squares)32 b(\014t.)150 4100 y FJ(40.2)68 b(Initializing)47 b(the)e(B-splines)g(solv)l(er)150 4260 y FK(The)g(computation)i(of)f(B-spline)g(functions)g(requires)f(a)h (preallo)s(cated)i(w)m(orkspace)e(of)g(t)m(yp)s(e)g FH(gsl_)150 4369 y(bspline_workspace)p FK(.)3350 4572 y([F)-8 b(unction])-3599 b Fv(gsl_bspline_workspace)59 b(*)52 b(gsl_bspline_alloc)f Fu(\()p FD(const)31 b(size)p 2760 4572 28 4 v 41 w(t)g Ft(k)p FD(,)g(const)565 4681 y(size)p 712 4681 V 41 w(t)g Ft(nbreak)p Fu(\))390 4791 y FK(This)21 b(function)g(allo)s(cates)j(a)e (w)m(orkspace)g(for)f(computing)h(B-splines)f(of)h(order)f FD(k)p FK(.)38 b(The)21 b(n)m(um)m(b)s(er)f(of)390 4901 y(breakp)s(oin)m(ts)i(is)f(giv)m(en)i(b)m(y)f FD(n)m(break)p FK(.)37 b(This)21 b(leads)h(to)h FE(n)i FK(=)g FE(nbr)s(eak)6 b FK(+)s FE(k)g FI(\000)s FK(2)21 b(basis)g(functions.)38 b(Cubic)390 5010 y(B-splines)31 b(are)f(sp)s(eci\014ed)g(b)m(y)g FE(k)f FK(=)c(4.)41 b(The)30 b(size)h(of)f(the)h(w)m(orkspace)g(is)g FE(O)s FK(\(2)p FE(k)3054 4977 y FB(2)3112 5010 y FK(+)20 b(5)p FE(k)k FK(+)c FE(nbr)s(eak)s FK(\).)3350 5213 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_bspline_free)c Fu(\()p FD(gsl)p 1441 5213 V 41 w(bspline)p 1761 5213 V 39 w(w)m(orkspace)31 b(*)g Ft(w)p Fu(\))390 5322 y FK(This)f(function)g(frees)g(the)h (memory)f(asso)s(ciated)i(with)e(the)g(w)m(orkspace)h FD(w)p FK(.)p eop end %%Page: 514 532 TeXDict begin 514 531 bop 150 -116 a FK(Chapter)30 b(40:)41 b(Basis)31 b(Splines)2438 b(514)150 299 y FJ(40.3)68 b(Constructing)46 b(the)f(knots)g(v)l(ector)3350 526 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_bspline_knots)e Fu(\()p FD(const)31 b(gsl)p 1679 526 28 4 v 41 w(v)m(ector)h(*)e Ft(breakpts)p FD(,)565 636 y(gsl)p 677 636 V 41 w(bspline)p 997 636 V 39 w(w)m(orkspace)h(*)g Ft(w)p Fu(\))390 745 y FK(This)k(function)g(computes)h(the)g(knots)f(asso)s(ciated)i(with)f (the)f(giv)m(en)i(breakp)s(oin)m(ts)e(and)g(stores)390 855 y(them)30 b(in)m(ternally)i(in)e FH(w->knots)p FK(.)3350 1076 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_bspline_knots_uni)q (form)f Fu(\()p FD(const)31 b(double)f Ft(a)p FD(,)h(const)g(double)f Ft(b)p FD(,)565 1185 y(gsl)p 677 1185 V 41 w(bspline)p 997 1185 V 39 w(w)m(orkspace)h(*)g Ft(w)p Fu(\))390 1295 y FK(This)e(function)g(assumes)g(uniformly)f(spaced)i(breakp)s(oin)m (ts)f(on)h([)p FE(a;)15 b(b)p FK(])30 b(and)f(constructs)h(the)f(cor-) 390 1404 y(resp)s(onding)j(knot)j(v)m(ector)g(using)e(the)i(previously) e(sp)s(eci\014ed)g FD(n)m(break)40 b FK(parameter.)51 b(The)34 b(knots)390 1514 y(are)d(stored)f(in)g FH(w->knots)p FK(.)150 1774 y FJ(40.4)68 b(Ev)-7 b(aluation)46 b(of)g(B-splines)3350 2001 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_bspline_eval)e Fu(\()p FD(const)31 b(double)f Ft(x)p FD(,)h(gsl)p 2028 2001 V 40 w(v)m(ector)h(*)f Ft(B)p FD(,)565 2110 y(gsl)p 677 2110 V 41 w(bspline)p 997 2110 V 39 w(w)m(orkspace)g(*)g Ft(w)p Fu(\))390 2220 y FK(This)d(function)g(ev)-5 b(aluates)30 b(all)f(B-spline)g(basis)f(functions)g(at)h(the)f(p)s(osition)h FD(x)34 b FK(and)28 b(stores)h(them)390 2330 y(in)35 b(the)g(v)m(ector)i FD(B)p FK(,)f(so)g(that)f(the)g FE(i)p FK(-th)h(elemen)m(t)g(is)f FE(B)2232 2344 y Fq(i)2260 2330 y FK(\()p FE(x)p FK(\).)55 b(The)35 b(v)m(ector)h FD(B)41 b FK(m)m(ust)35 b(b)s(e)f(of)i(length)390 2439 y FE(n)46 b FK(=)g FE(nbr)s(eak)32 b FK(+)c FE(k)k FI(\000)c FK(2.)80 b(This)42 b(v)-5 b(alue)44 b(ma)m(y)g(also)g(b)s(e)e(obtained) i(b)m(y)f(calling)h FH(gsl_bspline_)390 2549 y(ncoeffs)p FK(.)38 b(Computing)29 b(all)g(the)g(basis)g(functions)g(at)g(once)h (is)f(more)g(e\016cien)m(t)h(than)f(computing)390 2658 y(them)h(individually)-8 b(,)31 b(due)f(to)h(the)f(nature)h(of)f(the)h (de\014ning)e(recurrence)h(relation.)3350 2879 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_bspline_eval_nonz)q(ero)f Fu(\()p FD(const)30 b(double)f Ft(x)p FD(,)h(gsl)p 2443 2879 V 40 w(v)m(ector)h(*)f Ft(Bk)p FD(,)g(size)p 3130 2879 V 41 w(t)565 2989 y(*)h Ft(istart)p FD(,)h(size)p 1157 2989 V 41 w(t)f(*)g Ft(iend)p FD(,)g(gsl)p 1710 2989 V 41 w(bspline)p 2030 2989 V 39 w(w)m(orkspace)g(*)g Ft(w)p Fu(\))390 3098 y FK(This)23 b(function)h(ev)-5 b(aluates)26 b(all)f(p)s(oten)m(tially)g(nonzero)g(B-spline)f(basis)g (functions)g(at)h(the)f(p)s(osition)390 3208 y FD(x)33 b FK(and)26 b(stores)h(them)g(in)f(the)h(v)m(ector)h FD(Bk)p FK(,)g(so)f(that)g(the)g FE(i)p FK(-th)g(elemen)m(t)h(is)f FE(B)2934 3222 y FB(\()p Fq(istar)r(t)p FB(+)p Fq(i)p FB(\))3238 3208 y FK(\()p FE(x)p FK(\).)40 b(The)26 b(last)390 3317 y(elemen)m(t)k(of)e FD(Bk)34 b FK(is)28 b FE(B)1129 3331 y Fq(iend)1264 3317 y FK(\()p FE(x)p FK(\).)40 b(The)28 b(v)m(ector)i FD(Bk)j FK(m)m(ust)28 b(b)s(e)g(of)g(length)h FE(k)s FK(.)40 b(By)28 b(returning)g(only)g(the)390 3427 y(nonzero)i(basis)f(functions,)h(this)f(function)g(allo)m(ws)i(quan)m (tities)g(in)m(v)m(olving)g(linear)f(com)m(binations)390 3537 y(of)38 b(the)g FE(B)734 3551 y Fq(i)762 3537 y FK(\()p FE(x)p FK(\))h(to)f(b)s(e)g(computed)g(without)g(unnecessary)f (terms)h(\(suc)m(h)g(linear)h(com)m(binations)390 3646 y(o)s(ccur,)30 b(for)h(example,)g(when)e(ev)-5 b(aluating)32 b(an)e(in)m(terp)s(olated)i(function\).)3350 3867 y([F)-8 b(unction])-3599 b Fv(size_t)54 b(gsl_bspline_ncoeffs)d Fu(\()p FD(gsl)p 1702 3867 V 41 w(bspline)p 2022 3867 V 40 w(w)m(orkspace)31 b(*)f Ft(w)p Fu(\))390 3976 y FK(This)25 b(function)h(returns)e(the)i(n)m(um)m(b)s(er)f(of)h (B-spline)g(co)s(e\016cien)m(ts)h(giv)m(en)g(b)m(y)f FE(n)f FK(=)g FE(nbr)s(eak)14 b FK(+)d FE(k)j FI(\000)d FK(2.)150 4236 y FJ(40.5)68 b(Ev)-7 b(aluation)46 b(of)g(B-spline)e (deriv)-7 b(ativ)l(es)3350 4463 y FK([F)f(unction])-3599 b Fv(int)53 b(gsl_bspline_deriv_eva)q(l)e Fu(\()p FD(const)32 b(double)e Ft(x)p FD(,)g(const)h(size)p 2614 4463 V 41 w(t)g Ft(nderiv)p FD(,)565 4573 y(gsl)p 677 4573 V 41 w(matrix)f(*)h Ft(dB)p FD(,)g(gsl)p 1355 4573 V 41 w(bspline)p 1675 4573 V 39 w(w)m(orkspace)g(*)g Ft(w)p Fu(\))390 4682 y FK(This)41 b(function)h(ev)-5 b(aluates)43 b(all)g(B-spline)f (basis)g(function)g(deriv)-5 b(ativ)m(es)43 b(of)f(orders)f(0)i (through)390 4792 y FE(nder)s(iv)36 b FK(\(inclusiv)m(e\))d(at)g(the)g (p)s(osition)f FD(x)38 b FK(and)32 b(stores)h(them)f(in)g(the)g(matrix) h FD(dB)p FK(.)46 b(The)32 b(\()p FE(i;)15 b(j)5 b FK(\)-th)390 4902 y(elemen)m(t)37 b(of)f FD(dB)k FK(is)c FE(d)1139 4869 y Fq(j)1174 4902 y FE(B)1243 4916 y Fq(i)1271 4902 y FK(\()p FE(x)p FK(\))p FE(=dx)1537 4869 y Fq(j)1573 4902 y FK(.)56 b(The)35 b(matrix)h FD(dB)41 b FK(m)m(ust)35 b(b)s(e)g(of)g(size)i FE(n)c FK(=)h FE(nbr)s(eak)26 b FK(+)d FE(k)k FI(\000)d FK(2)390 5011 y(b)m(y)31 b FE(nder)s(iv)25 b FK(+)20 b(1.)45 b(The)31 b(v)-5 b(alue)32 b FE(n)f FK(ma)m(y)h(also)g(b)s(e)f(obtained)h(b)m(y)f(calling)i FH(gsl_bspline_ncoeffs)p FK(.)390 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b(=)f(gsl_vector_alloc\(ncoeffs\);)485 3477 y(w)h(=)f(gsl_vector_alloc\(n\);)485 3587 y(cov)g(=)h (gsl_matrix_alloc\(ncoeffs)o(,)42 b(ncoeffs\);)485 3696 y(mw)48 b(=)f(gsl_multifit_linear_alloc)o(\(n,)41 b(ncoeffs\);)485 3915 y(printf\("#m=0,S=0\\n"\);)485 4025 y(/*)48 b(this)e(is)h(the)g (data)g(to)g(be)g(fitted)f(*/)485 4134 y(for)h(\(i)h(=)f(0;)g(i)h(<)f (n;)g(++i\))581 4244 y({)676 4354 y(double)f(sigma;)676 4463 y(double)g(xi)i(=)f(\(15.0)f(/)i(\(N)f(-)h(1\)\))e(*)i(i;)676 4573 y(double)e(yi)i(=)f(cos\(xi\))f(*)h(exp\(-0.1)f(*)h(xi\);)676 4792 y(sigma)g(=)g(0.1)g(*)h(yi;)676 4902 y(dy)g(=)f (gsl_ran_gaussian\(r,)c(sigma\);)676 5011 y(yi)48 b(+=)f(dy;)676 5230 y(gsl_vector_set\(x,)c(i,)48 b(xi\);)676 5340 y (gsl_vector_set\(y,)43 b(i,)48 b(yi\);)p eop end %%Page: 517 535 TeXDict begin 517 534 bop 150 -116 a FK(Chapter)30 b(40:)41 b(Basis)31 b(Splines)2438 b(517)676 299 y FH(gsl_vector_set\(w,)43 b(i,)48 b(1.0)f(/)g(\(sigma)f(*)i(sigma\)\);)676 518 y(printf\("\045f)d(\045f\\n",)h(xi,)h(yi\);)581 628 y(})485 847 y(/*)h(use)f(uniform)e(breakpoints)g(on)i([0,)g(15])g(*/)485 956 y(gsl_bspline_knots_uniform\()o(0.0,)41 b(15.0,)46 b(bw\);)485 1176 y(/*)i(construct)d(the)i(fit)g(matrix)f(X)h(*/)485 1285 y(for)g(\(i)h(=)f(0;)g(i)h(<)f(n;)g(++i\))581 1395 y({)676 1504 y(double)f(xi)i(=)f(gsl_vector_get\(x,)c(i\);)676 1724 y(/*)48 b(compute)d(B_j\(xi\))h(for)h(all)g(j)g(*/)676 1833 y(gsl_bspline_eval\(xi,)c(B,)k(bw\);)676 2052 y(/*)h(fill)e(in)h (row)g(i)h(of)f(X)g(*/)676 2162 y(for)g(\(j)g(=)h(0;)f(j)h(<)f (ncoeffs;)f(++j\))772 2271 y({)867 2381 y(double)g(Bj)i(=)f (gsl_vector_get\(B,)c(j\);)867 2491 y(gsl_matrix_set\(X,)g(i,)48 b(j,)f(Bj\);)772 2600 y(})581 2710 y(})485 2929 y(/*)h(do)f(the)g(fit)g (*/)485 3039 y(gsl_multifit_wlinear\(X,)42 b(w,)47 b(y,)g(c,)g(cov,)g (&chisq,)f(mw\);)485 3258 y(dof)h(=)h(n)f(-)h(ncoeffs;)485 3367 y(tss)f(=)h(gsl_stats_wtss\(w->data,)41 b(1,)47 b(y->data,)f(1,)h(y->size\);)485 3477 y(Rsq)g(=)h(1.0)f(-)g(chisq)g(/)g (tss;)485 3696 y(fprintf\(stderr,)d("chisq/dof)h(=)j(\045e,)e(Rsq)h(=)h (\045f\\n",)1297 3806 y(chisq)e(/)i(dof,)e(Rsq\);)485 4025 y(/*)i(output)e(the)h(smoothed)e(curve)i(*/)485 4134 y({)581 4244 y(double)f(xi,)h(yi,)g(yerr;)581 4463 y(printf\("#m=1,S=0\\n"\);)581 4573 y(for)g(\(xi)g(=)g(0.0;)g(xi)g(<)g (15.0;)g(xi)g(+=)g(0.1\))676 4682 y({)772 4792 y(gsl_bspline_eval\(xi,) 42 b(B,)47 b(bw\);)772 4902 y(gsl_multifit_linear_est\()o(B,)41 b(c,)48 b(cov,)e(&yi,)h(&yerr\);)772 5011 y(printf\("\045f)e (\045f\\n",)h(xi,)h(yi\);)676 5121 y(})485 5230 y(})p eop end %%Page: 518 536 TeXDict begin 518 535 bop 150 -116 a FK(Chapter)30 b(40:)41 b(Basis)31 b(Splines)2438 b(518)485 299 y FH(gsl_rng_free\(r\);)485 408 y(gsl_bspline_free\(bw\);)485 518 y(gsl_vector_free\(B\);)485 628 y(gsl_vector_free\(x\);)485 737 y(gsl_vector_free\(y\);)485 847 y(gsl_matrix_free\(X\);)485 956 y(gsl_vector_free\(c\);)485 1066 y(gsl_vector_free\(w\);)485 1176 y(gsl_matrix_free\(cov\);)485 1285 y(gsl_multifit_linear_free\(m)o(w\);)485 1504 y(return)47 b(0;)390 1614 y(})g(/*)h(main\(\))e(*/)275 1769 y FK(The)29 b(output)h(can)h(b)s(e)f(plotted)h(with)f FC(gnu)g FH(graph)p FK(.)390 1923 y FH($)47 b(./a.out)f(>)i(bspline.txt)390 2033 y(chisq/dof)d(=)j(1.118217e+00,)c(Rsq)j(=)g(0.989771)390 2142 y($)g(graph)g(-T)g(ps)g(-X)g(x)h(-Y)f(y)g(-x)h(0)f(15)g(-y)g(-1)h (1.3)f(<)g(bspline.txt)e(>)i(bspline.ps)275 4304 y @beginspecial 60 @llx 174 @lly 480 @urx 570 @ury 2448 @rwi @setspecial %%BeginDocument: bspline.eps %!PS-Adobe-3.0 EPSF-3.0 %%Creator: GNU libplot drawing library 4.2 %%Title: PostScript plot %%CreationDate: Fri Nov 2 13:18:54 2007 %%DocumentData: Clean7Bit %%LanguageLevel: 1 %%Pages: 1 %%PageOrder: Ascend %%Orientation: Portrait %%BoundingBox: 60 174 480 570 %%DocumentNeededResources: font Helvetica %%DocumentSuppliedResources: procset GNU_libplot 1.1 0 %%EndComments %%BeginDefaults %%PageResources: font Helvetica %%EndDefaults %%BeginProlog %%EndProlog %%BeginSetup %%IncludeResource: font Helvetica /DrawDict 50 dict def DrawDict begin /ISOLatin1Encoding [ /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /space/exclam/quotedbl/numbersign/dollar/percent/ampersand/quoteright /parenleft/parenright/asterisk/plus/comma/minus/period/slash /zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon /less/equal/greater/question/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N /O/P/Q/R/S/T/U/V/W/X/Y/Z/bracketleft/backslash/bracketright /asciicircum/underscore/quoteleft/a/b/c/d/e/f/g/h/i/j/k/l/m /n/o/p/q/r/s/t/u/v/w/x/y/z/braceleft/bar/braceright/asciitilde /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/dotlessi/grave/acute/circumflex/tilde/macron/breve /dotaccent/dieresis/.notdef/ring/cedilla/.notdef/hungarumlaut /ogonek/caron/space/exclamdown/cent/sterling/currency/yen/brokenbar /section/dieresis/copyright/ordfeminine/guillemotleft/logicalnot /hyphen/registered/macron/degree/plusminus/twosuperior/threesuperior /acute/mu/paragraph/periodcentered/cedilla/onesuperior/ordmasculine /guillemotright/onequarter/onehalf/threequarters/questiondown /Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla /Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex /Idieresis/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis /multiply/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute /Thorn/germandbls/agrave/aacute/acircumflex/atilde/adieresis /aring/ae/ccedilla/egrave/eacute/ecircumflex/edieresis/igrave /iacute/icircumflex/idieresis/eth/ntilde/ograve/oacute/ocircumflex /otilde/odieresis/divide/oslash/ugrave/uacute/ucircumflex/udieresis /yacute/thorn/ydieresis ] def /reencodeISO { dup dup findfont dup length dict begin { 1 index /FID ne { def }{ pop pop } ifelse } forall /Encoding ISOLatin1Encoding def currentdict end definefont } def /Helvetica reencodeISO def %%BeginResource procset GNU_libplot 1.1 0 /none null def /numGraphicParameters 17 def /stringLimit 65535 def /arrowHeight 8 def /eoFillRule true def /Begin { save numGraphicParameters dict begin } def /End { end restore } def /SetB { dup type /nulltype eq { pop false /brushRightArrow idef false /brushLeftArrow idef true /brushNone idef } { /brushDashOffset idef /brushDashArray idef 0 ne /brushRightArrow idef 0 ne /brushLeftArrow idef /brushWidth idef false /brushNone idef } ifelse } def /SetCFg { /fgblue idef /fggreen idef /fgred idef } def /SetCBg { /bgblue idef /bggreen idef /bgred idef } def /SetF { /printSize idef /printFont idef } def /SetP { dup type /nulltype eq { pop true /patternNone idef } { /patternGrayLevel idef patternGrayLevel -1 eq { /patternString idef } if false /patternNone idef } ifelse } def /BSpl { 0 begin storexyn newpath n 1 gt { 0 0 0 0 0 0 1 1 true subspline n 2 gt { 0 0 0 0 1 1 2 2 false subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 2 copy false subspline } if n 2 sub dup n 1 sub dup 2 copy 2 copy false subspline patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup 1 sub dup rightarrow } if end } dup 0 4 dict put def /Circ { newpath 0 360 arc closepath patternNone not { ifill } if brushNone not { istroke } if } def /CBSpl { 0 begin dup 2 gt { storexyn newpath n 1 sub dup 0 0 1 1 2 2 true subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 0 0 false subspline n 2 sub dup n 1 sub dup 0 0 1 1 false subspline patternNone not { ifill } if brushNone not { istroke } if } { Poly } ifelse end } dup 0 4 dict put def /Elli { 0 begin newpath 4 2 roll translate scale 0 0 1 0 360 arc closepath patternNone not { ifill } if brushNone not { istroke } if end } dup 0 1 dict put def /Line { 0 begin 2 storexyn newpath x 0 get y 0 get moveto x 1 get y 1 get lineto brushNone not { istroke } if 0 0 1 1 leftarrow 0 0 1 1 rightarrow end } dup 0 4 dict put def /MLine { 0 begin storexyn newpath n 1 gt { x 0 get y 0 get moveto 1 1 n 1 sub { /i exch def x i get y i get lineto } for patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Poly { 3 1 roll newpath moveto -1 add { lineto } repeat closepath patternNone not { ifill } if brushNone not { istroke } if } def /Rect { 0 begin /t exch def /r exch def /b exch def /l exch def newpath l b moveto l t lineto r t lineto r b lineto closepath patternNone not { ifill } if brushNone not { istroke } if end } dup 0 4 dict put def /Text { ishow } def /idef { dup where { pop pop pop } { exch def } ifelse } def /ifill { 0 begin gsave patternGrayLevel -1 ne { fgred bgred fgred sub patternGrayLevel mul add fggreen bggreen fggreen sub patternGrayLevel mul add fgblue bgblue fgblue sub patternGrayLevel mul add setrgbcolor eoFillRule { eofill } { fill } ifelse } { eoFillRule { eoclip } { clip } ifelse originalCTM setmatrix pathbbox /t exch def /r exch def /b exch def /l exch def /w r l sub ceiling cvi def /h t b sub ceiling cvi def /imageByteWidth w 8 div ceiling cvi def /imageHeight h def bgred bggreen bgblue setrgbcolor eoFillRule { eofill } { fill } ifelse fgred fggreen fgblue setrgbcolor w 0 gt h 0 gt and { l b translate w h scale w h true [w 0 0 h neg 0 h] { patternproc } imagemask } if } ifelse grestore end } dup 0 8 dict put def /istroke { gsave brushDashOffset -1 eq { [] 0 setdash 1 setgray } { brushDashArray brushDashOffset setdash fgred fggreen fgblue setrgbcolor } ifelse brushWidth setlinewidth originalCTM setmatrix stroke grestore } def /ishow { 0 begin gsave fgred fggreen fgblue setrgbcolor /fontDict printFont findfont printSize scalefont dup setfont def /descender fontDict begin 0 /FontBBox load 1 get FontMatrix end transform exch pop def /vertoffset 1 printSize sub descender sub def { 0 vertoffset moveto show /vertoffset vertoffset printSize sub def } forall grestore end } dup 0 3 dict put def /patternproc { 0 begin /patternByteLength patternString length def /patternHeight patternByteLength 8 mul sqrt cvi def /patternWidth patternHeight def /patternByteWidth patternWidth 8 idiv def /imageByteMaxLength imageByteWidth imageHeight mul stringLimit patternByteWidth sub min def /imageMaxHeight imageByteMaxLength imageByteWidth idiv patternHeight idiv patternHeight mul patternHeight max def /imageHeight imageHeight imageMaxHeight sub store /imageString imageByteWidth imageMaxHeight mul patternByteWidth add string def 0 1 imageMaxHeight 1 sub { /y exch def /patternRow y patternByteWidth mul patternByteLength mod def /patternRowString patternString patternRow patternByteWidth getinterval def /imageRow y imageByteWidth mul def 0 patternByteWidth imageByteWidth 1 sub { /x exch def imageString imageRow x add patternRowString putinterval } for } for imageString end } dup 0 12 dict put def /min { dup 3 2 roll dup 4 3 roll lt { exch } if pop } def /max { dup 3 2 roll dup 4 3 roll gt { exch } if pop } def /midpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 x1 add 2 div y0 y1 add 2 div end } dup 0 4 dict put def /thirdpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 2 mul x1 add 3 div y0 2 mul y1 add 3 div end } dup 0 4 dict put def /subspline { 0 begin /movetoNeeded exch def y exch get /y3 exch def x exch get /x3 exch def y exch get /y2 exch def x exch get /x2 exch def y exch get /y1 exch def x exch get /x1 exch def y exch get /y0 exch def x exch get /x0 exch def x1 y1 x2 y2 thirdpoint /p1y exch def /p1x exch def x2 y2 x1 y1 thirdpoint /p2y exch def /p2x exch def x1 y1 x0 y0 thirdpoint p1x p1y midpoint /p0y exch def /p0x exch def x2 y2 x3 y3 thirdpoint p2x p2y midpoint /p3y exch def /p3x exch def movetoNeeded { p0x p0y moveto } if p1x p1y p2x p2y p3x p3y curveto end } dup 0 17 dict put def /storexyn { /n exch def /y n array def /x n array def n 1 sub -1 0 { /i exch def y i 3 2 roll put x i 3 2 roll put } for } def /arrowhead { 0 begin transform originalCTM itransform /taily exch def /tailx exch def transform originalCTM itransform /tipy exch def /tipx exch def /dy tipy taily sub def /dx tipx tailx sub def /angle dx 0 ne dy 0 ne or { dy dx atan } { 90 } ifelse def gsave originalCTM setmatrix tipx tipy translate angle rotate newpath arrowHeight neg arrowWidth 2 div moveto 0 0 lineto arrowHeight neg arrowWidth 2 div neg lineto patternNone not { originalCTM setmatrix /padtip arrowHeight 2 exp 0.25 arrowWidth 2 exp mul add sqrt brushWidth mul arrowWidth div def /padtail brushWidth 2 div def tipx tipy translate angle rotate padtip 0 translate arrowHeight padtip add padtail add arrowHeight div dup scale arrowheadpath ifill } if brushNone not { originalCTM setmatrix tipx tipy translate angle rotate arrowheadpath istroke } if grestore end } dup 0 9 dict put def /arrowheadpath { newpath arrowHeight neg arrowWidth 2 div moveto 0 0 lineto arrowHeight neg arrowWidth 2 div neg lineto } def /leftarrow { 0 begin y exch get /taily exch def x exch get /tailx exch def y exch get /tipy exch def x exch get /tipx exch def brushLeftArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /rightarrow { 0 begin y exch get /tipy exch def x exch get /tipx exch def y exch get /taily exch def x exch get /tailx exch def brushRightArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def %%EndResource %%EndSetup %%Page: 1 1 %%PageResources: font Helvetica %%PageBoundingBox: 60 174 480 570 %%BeginPageSetup %I Idraw 8 Begin %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 1 0 0 1 0 0 ] concat /originalCTM matrix currentmatrix def /trueoriginalCTM matrix currentmatrix def %%EndPageSetup Begin %I Rect [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2304 2304 9216 9216 Rect End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 128.156 214.1855 ] concat %I [ (0) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 9216 2304 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2304 2304 2442 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 174.236 214.1855 ] concat %I [ (2) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3226 9216 3226 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3226 2304 3226 2442 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 220.316 214.1855 ] concat %I [ (4) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4147 9216 4147 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4147 2304 4147 2442 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 266.396 214.1855 ] concat %I [ (6) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5069 9216 5069 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5069 2304 5069 2442 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 312.476 214.1855 ] concat %I [ (8) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5990 9216 5990 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5990 2304 5990 2442 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 353.5119 214.1855 ] concat %I [ (10) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6912 9216 6912 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6912 2304 6912 2442 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 399.5919 214.1855 ] concat %I [ (12) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7834 9216 7834 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7834 2304 7834 2442 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 445.6719 214.1855 ] concat %I [ (14) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8755 9216 8755 9078 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8755 2304 8755 2442 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 9216 2304 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2304 2304 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2765 9216 2765 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2765 2304 2765 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3226 9216 3226 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3226 2304 3226 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3686 9216 3686 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 3686 2304 3686 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4147 9216 4147 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4147 2304 4147 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4608 9216 4608 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 4608 2304 4608 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5069 9216 5069 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5069 2304 5069 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5530 9216 5530 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5530 2304 5530 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5990 9216 5990 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 5990 2304 5990 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6451 9216 6451 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6451 2304 6451 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6912 9216 6912 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 6912 2304 6912 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7373 9216 7373 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7373 2304 7373 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7834 9216 7834 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 7834 2304 7834 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8294 9216 8294 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8294 2304 8294 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8755 9216 8755 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 8755 2304 8755 2359 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 9216 9216 9161 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2304 9216 2359 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 92.19974 229.8568 ] concat %I [ (-1.0) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2304 9078 2304 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2304 2442 2304 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 92.19974 304.9872 ] concat %I [ (-0.5) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 3807 9078 3807 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3807 2442 3807 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 102.7958 380.1176 ] concat %I [ (0.0) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5309 9078 5309 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5309 2442 5309 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 102.7958 455.2481 ] concat %I [ (0.5) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 6812 9078 6812 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 6812 2442 6812 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 102.7958 530.3785 ] concat %I [ (1.0) ] Text End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 8314 9078 8314 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 8314 2442 8314 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2304 9161 2304 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2304 2359 2304 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2605 9161 2605 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2605 2359 2605 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 2905 9161 2905 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 2905 2359 2905 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 3206 9161 3206 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3206 2359 3206 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 3506 9161 3506 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3506 2359 3506 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 3807 9161 3807 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 3807 2359 3807 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 4107 9161 4107 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4107 2359 4107 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 4408 9161 4408 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4408 2359 4408 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 4708 9161 4708 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 4708 2359 4708 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5009 9161 5009 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5009 2359 5009 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5309 9161 5309 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5309 2359 5309 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5610 9161 5610 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5610 2359 5610 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 5910 9161 5910 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5910 2359 5910 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 6211 9161 6211 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 6211 2359 6211 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 6511 9161 6511 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 6511 2359 6511 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 6812 9161 6812 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 6812 2359 6812 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 7112 9161 7112 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 7112 2359 7112 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 7413 9161 7413 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 7413 2359 7413 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 7713 9161 7713 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 7713 2359 7713 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 8014 9161 8014 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 8014 2359 8014 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 8314 9161 8314 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 8314 2359 8314 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 8615 9161 8615 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 8615 2359 8615 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 8915 9161 8915 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 8915 2359 8915 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 9216 9216 9161 9216 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 9216 2359 9216 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 34952 1 0 0 [ 1.48 4.43 ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2 2304 5309 9216 5309 2 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 1 0 0 1 301.464 191.5487 ] concat %I [ (x) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-helvetica-medium-r-normal-*-18-*-*-*-*-*-*-* /Helvetica 18.144000 SetF %I t [ 6.123234e-17 1 -1 6.123234e-17 64.69371 391.464 ] concat %I [ (y) ] Text End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2304 8355 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2339 8257 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2373 8726 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2408 8382 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2443 8371 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2478 7656 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2512 7274 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2547 7605 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2582 7630 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2617 7691 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2651 7338 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2686 6935 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2721 6893 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2756 6855 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2790 6753 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2825 6390 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2860 6199 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2894 6064 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2929 5829 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2964 5639 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 2999 5483 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3033 5279 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3068 5093 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3103 4937 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3138 4752 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3172 4536 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3207 4368 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3242 4294 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3277 4077 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3311 3710 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3346 3814 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3381 3703 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3415 3573 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3450 3923 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3485 3250 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3520 3295 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3554 3272 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3589 3023 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3624 2796 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3659 3201 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3693 2843 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3728 2711 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3763 3280 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3798 3283 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3832 2745 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3867 3422 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3902 2947 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3936 3099 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 3971 3519 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4006 3594 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4041 3431 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4075 3791 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4110 3869 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4145 3878 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4180 4047 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4214 4234 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4249 4254 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4284 4518 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4319 4612 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4353 4884 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4388 4957 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4423 5085 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4457 5236 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4492 5373 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4527 5488 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4562 5710 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4596 5803 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4631 6002 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4666 6082 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4701 6098 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4735 6382 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4770 6272 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4805 6543 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4840 6442 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4874 6608 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4909 6895 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4944 6807 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 4978 7300 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5013 7121 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5048 7153 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5083 7007 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5117 6747 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5152 6974 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5187 6989 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5222 6529 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5256 6784 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5291 6517 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5326 6660 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5361 6696 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5395 6594 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5430 6672 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5465 6528 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5499 6304 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5534 6318 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5569 6338 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5604 6356 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5638 6312 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5673 6064 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5708 5967 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5743 5923 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5777 5774 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5812 5628 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5847 5549 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5882 5459 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5916 5334 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5951 5230 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 5986 5140 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6021 5064 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6055 4985 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6090 4859 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6125 4671 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6159 4756 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6194 4667 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6229 4531 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6264 4437 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6298 4176 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6333 4301 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6368 4248 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6403 4321 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6437 4018 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6472 4221 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6507 3938 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6542 4095 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6576 4252 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6611 4099 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6646 4177 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6680 4045 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6715 4018 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6750 4104 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6785 4266 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6819 4199 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6854 4365 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6889 4399 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6924 4330 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6958 4439 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 6993 4551 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7028 4543 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7063 4677 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7097 4713 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7132 4761 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7167 4734 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7201 4961 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7236 5032 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7271 5051 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7306 5145 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7340 5241 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7375 5319 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7410 5392 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7445 5428 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7479 5515 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7514 5605 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7549 5671 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7584 5729 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7618 5800 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7653 5888 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7688 5862 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7722 5946 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7757 5983 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7792 6033 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7827 6170 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7861 5989 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7896 6199 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7931 6052 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 7966 6206 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8000 6191 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8035 6193 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8070 6229 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8105 6143 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8139 6168 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8174 6220 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8209 6082 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8243 6040 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8278 5967 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8313 6104 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8348 5976 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8382 5899 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8417 5996 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8452 5780 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8487 5888 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8521 5780 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8556 5743 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8591 5754 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8626 5663 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8660 5558 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8695 5498 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8730 5432 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8764 5389 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8799 5340 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8834 5287 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8869 5221 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8903 5180 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8938 5136 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 8973 5095 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 9008 5015 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 9042 4917 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 9077 4909 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 9112 4914 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 9147 4849 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 9181 4839 10 Circ End Begin %I Circ [0.324 0 0 0.324 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg Black 0 0 0 SetCBg %I p 0.000000 SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 9216 4819 10 Circ End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 151 2304 8375 2350 8317 2396 8230 2442 8114 2488 7974 2534 7812 2580 7629 2627 7429 2673 7213 2719 6985 2765 6747 2811 6500 2857 6249 2903 5994 2949 5739 2995 5486 3041 5237 3087 4996 3133 4763 3180 4539 3226 4327 3272 4127 3318 3940 3364 3768 3410 3611 3456 3470 3502 3347 3548 3242 3594 3158 3640 3094 3686 3052 3732 3033 3779 3038 3825 3069 3871 3125 3917 3207 3963 3311 4009 3436 4055 3579 4101 3737 4147 3909 4193 4091 4239 4283 4285 4480 4332 4682 4378 4884 4424 5087 4470 5285 4516 5479 4562 5664 4608 5839 4654 6002 4700 6152 4746 6289 4792 6413 4838 6523 4884 6620 4931 6704 4977 6773 5023 6828 5069 6869 5115 6896 5161 6908 5207 6905 5253 6887 5299 6854 5345 6805 5391 6742 5437 6663 5484 6570 5530 6466 5576 6351 5622 6227 5668 6097 5714 5960 5760 5820 5806 5677 5852 5533 5898 5390 5944 5249 5990 5113 6036 4981 6083 4857 6129 4741 6175 4636 6221 4541 6267 4457 6313 4384 6359 4321 6405 4268 6451 4226 6497 4195 6543 4174 6589 4163 6636 4162 6682 4172 6728 4191 6774 4221 6820 4261 6866 4310 6912 4370 6958 4439 7004 4517 7050 4603 7096 4694 7142 4791 7188 4892 7235 4996 7281 5102 7327 5208 7373 5313 7419 5416 7465 5517 7511 5613 7557 5704 7603 5789 7649 5865 7695 5933 7741 5992 7788 6041 7834 6081 7880 6112 7926 6135 7972 6150 8018 6156 8064 6155 8110 6146 8156 6130 8202 6108 8248 6078 8294 6042 8340 6000 8387 5952 8433 5898 8479 5839 8525 5775 8571 5707 8617 5636 8663 5563 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b(are)150 1946 y(three)i(supp)s (orted)d(storage)k(formats)f(for)f(sparse)g(matrices:)39 b(the)25 b(triplet,)h(compressed)e(column)g(storage)150 2055 y(\(CCS\))e(and)g(compressed)h(ro)m(w)g(storage)h(\(CRS\))f (formats.)38 b(The)22 b(triplet)i(format)f(stores)g(triplets)h(\()p FE(i;)15 b(j;)g(x)p FK(\))150 2165 y(for)28 b(eac)m(h)i(non-zero)g (elemen)m(t)g(of)f(the)g(matrix.)40 b(This)28 b(notation)i(means)f (that)g(the)g(\()p FE(i;)15 b(j)5 b FK(\))31 b(elemen)m(t)f(of)f(the) 150 2274 y(matrix)37 b FE(A)h FK(is)f FE(A)724 2288 y Fq(ij)819 2274 y FK(=)f FE(x)p FK(.)61 b(Compressed)36 b(column)g(storage)j(stores)f(eac)m(h)g(column)f(of)g(non-zero)h(v)-5 b(alues)150 2384 y(in)36 b(the)g(sparse)f(matrix)i(in)e(a)i(con)m(tin)m (uous)f(memory)g(blo)s(c)m(k,)i(k)m(eeping)f(p)s(oin)m(ters)f(to)g(the) h(b)s(eginning)e(of)150 2494 y(eac)m(h)f(column)f(in)g(that)h(memory)f (blo)s(c)m(k,)i(and)d(storing)i(the)f(ro)m(w)g(indices)h(of)f(eac)m(h)h (non-zero)g(elemen)m(t.)150 2603 y(Compressed)29 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FK(con)m(taining)d(the)e(ro)m(w)h(indices)150 5340 y(and)i(elemen)m(t)i(v)-5 b(alues,)33 b(iden)m(tical)h(to)g(the)e (triplet)h(case.)48 b FD(p)35 b FK(is)d(an)h(arra)m(y)g(of)f(size)i FE(siz)t(e)p FK(2)22 b(+)f(1)33 b(where)f FE(p)p FK([)p FE(j)5 b FK(])p eop end %%Page: 521 539 TeXDict begin 521 538 bop 150 -116 a FK(Chapter)30 b(41:)41 b(Sparse)30 b(Matrices)2325 b(521)150 299 y(p)s(oin)m(ts)28 b(to)h(the)g(index)f(in)g FD(data)h FK(of)g(the)f(start)h(of)g(column)f FD(j)p FK(.)40 b(Th)m(us,)28 b(if)g FE(data)p FK([)p FE(k)s FK(])e(=)f FE(A)p FK(\()p FE(i;)15 b(j)5 b FK(\),)31 b(then)d FE(i)e FK(=)f FE(i)p FK([)p FE(k)s FK(])150 408 y(and)30 b FE(p)p FK([)p FE(j)5 b FK(])26 b FE(<)p FK(=)f FE(k)j(<)d(p)p FK([)p FE(j)h FK(+)20 b(1].)150 553 y(F)-8 b(or)30 b(compressed)f(ro)m(w)h(storage,)h FD(i)k FK(and)28 b FD(data)i FK(are)g(arra)m(ys)g(of)g(size)g FD(nz)k FK(con)m(taining)d(the)f(column)f(indices)150 663 y(and)j(elemen)m(t)j(v)-5 b(alues,)34 b(iden)m(tical)h(to)f(the)f 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2160 4069 V 41 w(t)g Ft(sptype)p Fu(\))390 4179 y FK(This)d(function)h (allo)s(cates)j(a)e(sparse)f(matrix)g(of)h(size)g FD(n1)p FK(-b)m(y-)p FD(n2)37 b FK(and)29 b(initializes)i(it)f(to)g(all)g (zeros.)390 4289 y(If)38 b(the)g(size)h(of)f(the)h(matrix)f(is)h(not)f (kno)m(wn)g(at)h(allo)s(cation)h(time,)h(b)s(oth)d FD(n1)45 b FK(and)37 b FD(n2)46 b FK(ma)m(y)39 b(b)s(e)390 4398 y(set)45 b(to)g(1,)j(and)c(they)h(will)f(automatically)j(gro)m(w)e(as)g (elemen)m(ts)g(are)g(added)f(to)h(the)f(matrix.)390 4508 y(The)c(parameter)h FD(nzmax)48 b FK(sp)s(eci\014es)40 b(the)h(maxim)m(um)f(n)m(um)m(b)s(er)g(of)h(non-zero)g(elemen)m(ts)h (whic)m(h)390 4617 y(will)f(b)s(e)g(added)f(to)h(the)h(matrix.)72 b(It)41 b(do)s(es)g(not)g(need)g(to)g(b)s(e)g(precisely)g(kno)m(wn)f (in)h(adv)-5 b(ance,)390 4727 y(since)36 b(storage)g(space)g(will)f (automatically)j(gro)m(w)e(using)f FH(gsl_spmatrix_realloc)30 b FK(if)35 b FD(nzmax)390 4837 y FK(is)j(not)h(large)g(enough.)64 b(Accurate)39 b(kno)m(wledge)h(of)e(this)g(parameter)h(reduces)e(the)i (n)m(um)m(b)s(er)e(of)390 4946 y(reallo)s(cation)c(calls)f(required.)42 b(The)30 b(parameter)i FD(spt)m(yp)s(e)j FK(sp)s(eci\014es)c(the)g (storage)h(format)g(of)f(the)390 5056 y(sparse)f(matrix.)41 b(P)m(ossible)31 b(v)-5 b(alues)31 b(are)390 5230 y FH (GSL_SPMATRIX_TRIPLET)870 5340 y FK(This)f(\015ag)g(sp)s(eci\014es)g (triplet)h(storage.)p eop end %%Page: 522 540 TeXDict begin 522 539 bop 150 -116 a FK(Chapter)30 b(41:)41 b(Sparse)30 b(Matrices)2325 b(522)390 299 y FH(GSL_SPMATRIX_CCS)870 408 y FK(This)30 b(\015ag)g(sp)s(eci\014es)g(compressed)g(column)h (storage.)390 574 y FH(GSL_SPMATRIX_CRS)870 683 y FK(This)f(\015ag)g (sp)s(eci\014es)g(compressed)g(ro)m(w)h(storage.)390 852 y(The)f(allo)s(cated)i FH(gsl_spmatrix)27 b FK(structure)j(is)h(of) f(size)h FE(O)s FK(\()p FE(nz)t(max)p FK(\).)3350 1048 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_spmatrix_realloc)f Fu(\()p FD(const)31 b(size)p 1871 1048 28 4 v 41 w(t)g Ft(nzmax)p FD(,)h(gsl)p 2401 1048 V 40 w(spmatrix)e(*)h Ft(m)p Fu(\))390 1158 y FK(This)43 b(function)g(reallo)s(cates)j(the)e (storage)h(space)f(for)g FD(m)f FK(to)i(accomo)s(date)g FD(nzmax)50 b FK(non-zero)390 1267 y(elemen)m(ts.)f(It)33 b(is)g(t)m(ypically)h(called)g(in)m(ternally)g(b)m(y)f FH(gsl_spmatrix_set)28 b FK(if)33 b(the)g(user)f(w)m(an)m(ts)h(to)390 1377 y(add)d(more)g(elemen)m(ts)i(to)f(the)g(sparse)f(matrix)g(than)h (the)f(previously)g(sp)s(eci\014ed)g FD(nzmax)p FK(.)3350 1573 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_spmatrix_free)c Fu(\()p FD(gsl)p 1493 1573 V 41 w(spmatrix)30 b(*)h Ft(m)p Fu(\))390 1683 y FK(This)f(function)g(frees)g(the)h(memory)f(asso)s (ciated)i(with)e(the)g(sparse)g(matrix)h FD(m)p FK(.)150 1925 y FJ(41.3)68 b(Accessing)45 b(Matrix)g(Elemen)l(ts)3350 2140 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_spmatrix_get)c Fu(\()p FD(const)32 b(gsl)p 1784 2140 V 40 w(spmatrix)e(*)h Ft(m)p FD(,)g(const)g(size)p 2769 2140 V 41 w(t)f Ft(i)p FD(,)h(const)565 2249 y(size)p 712 2249 V 41 w(t)g Ft(j)p Fu(\))390 2359 y FK(This)e(function)h(returns)f(elemen)m(t)j(\()p FD(i)p FK(,)p FD(j)s FK(\))f(of)g(the)f(matrix)h FD(m)p FK(.)40 b(The)30 b(matrix)h(ma)m(y)f(b)s(e)g(in)g(triplet)h(or)390 2469 y(compressed)f(format.)3350 2665 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_spmatrix_set)e Fu(\()p FD(gsl)p 1389 2665 V 40 w(spmatrix)31 b(*)f Ft(m)p FD(,)h(const)g(size)p 2374 2665 V 41 w(t)g Ft(i)p FD(,)f(const)h(size)p 2967 2665 V 41 w(t)g Ft(j)p FD(,)565 2775 y(const)g(double)f Ft(x)p Fu(\))390 2884 y FK(This)h(function)g(sets)h(elemen)m(t)h(\()p FD(i)p FK(,)p FD(j)s FK(\))g(of)e(the)h(matrix)g FD(m)f FK(to)h(the)g(v)-5 b(alue)32 b FD(x)p FK(.)44 b(The)31 b(matrix)h(m)m(ust)g(b)s(e)390 2994 y(in)e(triplet)h(represen)m (tation.)3350 3190 y([F)-8 b(unction])-3599 b Fv(double)54 b(*)f(gsl_spmatrix_ptr)d Fu(\()p FD(gsl)p 1650 3190 V 41 w(spmatrix)30 b(*)h Ft(m)p FD(,)g(const)g(size)p 2636 3190 V 40 w(t)g Ft(i)p FD(,)g(const)565 3300 y(size)p 712 3300 V 41 w(t)g Ft(j)p Fu(\))390 3409 y FK(This)21 b(function)h(returns)f(a)i(p)s(oin)m(ter)f(to)h(the)f(\()p FD(i)p FK(,)p FD(j)s FK(\))i(elemen)m(t)f(of)g(the)f(matrix)g FD(m)p FK(.)38 b(If)22 b(the)g(\()p FD(i)p FK(,)p FD(j)s FK(\))h(elemen)m(t)390 3519 y(is)30 b(not)h(explicitly)h(stored)e(in)h (the)f(matrix,)h(a)g(n)m(ull)f(p)s(oin)m(ter)g(is)h(returned.)150 3760 y FJ(41.4)68 b(Initializing)47 b(Matrix)f(Elemen)l(ts)150 3920 y FK(Since)36 b(the)g(sparse)f(matrix)i(format)f(only)g(stores)g (the)g(non-zero)h(elemen)m(ts,)i(it)d(is)g(automatically)j(ini-)150 4029 y(tialized)i(to)f(zero)f(up)s(on)f(allo)s(cation.)69 b(The)38 b(function)h FH(gsl_spmatrix_set_zero)33 b FK(ma)m(y)40 b(b)s(e)e(used)g(to)150 4139 y(re-initialize)33 b(a)e(matrix)f(to)i (zero)f(after)g(elemen)m(ts)g(ha)m(v)m(e)h(b)s(een)e(added)f(to)i(it.) 3350 4335 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_spmatrix_set_zero) f Fu(\()p FD(gsl)p 1650 4335 V 41 w(spmatrix)30 b(*)h Ft(m)p Fu(\))390 4445 y FK(This)f(function)g(sets)g(\(or)h(resets\))g (all)h(the)e(elemen)m(ts)i(of)e(the)h(matrix)g FD(m)f FK(to)h(zero.)150 4686 y FJ(41.5)68 b(Reading)46 b(and)f(W)-11 b(riting)45 b(Matrices)3350 4902 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_spmatrix_fwrite)e Fu(\()p FD(FILE)31 b(*)g Ft(stream)p FD(,)h(const)f(gsl)p 2470 4902 V 41 w(spmatrix)f(*)g Ft(m)p Fu(\))390 5011 y FK(This)38 b(function)g (writes)g(the)g(elemen)m(ts)i(of)f(the)f(matrix)h FD(m)f FK(to)h(the)f(stream)h FD(stream)g FK(in)f(binary)390 5121 y(format.)58 b(The)36 b(return)f(v)-5 b(alue)36 b(is)g(0)h(for)f(success)g(and)f FH(GSL_EFAILED)e FK(if)j(there)h(w)m (as)f(a)h(problem)390 5230 y(writing)c(to)h(the)f(\014le.)50 b(Since)33 b(the)g(data)h(is)f(written)h(in)e(the)i(nativ)m(e)g(binary) f(format)g(it)h(ma)m(y)g(not)390 5340 y(b)s(e)c(p)s(ortable)g(b)s(et)m (w)m(een)h(di\013eren)m(t)g(arc)m(hitectures.)p eop end %%Page: 523 541 TeXDict begin 523 540 bop 150 -116 a FK(Chapter)30 b(41:)41 b(Sparse)30 b(Matrices)2325 b(523)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_spmatrix_fread)e Fu(\()p FD(FILE)31 b(*)f Ft(stream)p FD(,)j(gsl)p 2180 299 28 4 v 40 w(spmatrix)d(*)h Ft(m)p Fu(\))390 408 y FK(This)26 b(function)g(reads)g(in)m(to)h(the)g (matrix)g FD(m)f FK(from)g(the)g(op)s(en)g(stream)h FD(stream)g FK(in)f(binary)f(format.)390 518 y(The)k(matrix)i FD(m)e FK(m)m(ust)h(b)s(e)g(preallo)s(cated)h(with)f(the)g(correct)h(storage)h (format,)e(dimensions)g(and)390 628 y(ha)m(v)m(e)e(a)f(su\016cien)m (tly)h(large)f FH(nzmax)f FK(in)g(order)g(to)i(read)f(in)f(all)i (matrix)f(elemen)m(ts,)i(otherwise)e FH(GSL_)390 737 y(EBADLEN)h FK(is)h(returned.)40 b(The)29 b(return)g(v)-5 b(alue)30 b(is)g(0)g(for)f(success)h(and)f FH(GSL_EFAILED)e FK(if)j(there)g(w)m(as)390 847 y(a)38 b(problem)e(reading)i(from)f(the) g(\014le.)62 b(The)36 b(data)i(is)g(assumed)e(to)i(ha)m(v)m(e)h(b)s (een)d(written)i(in)f(the)390 956 y(nativ)m(e)32 b(binary)d(format)i (on)f(the)h(same)g(arc)m(hitecture.)3350 1142 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_spmatrix_fprintf)f Fu(\()p FD(FILE)30 b(*)h Ft(stream)p FD(,)h(const)f(gsl)p 2522 1142 V 41 w(spmatrix)f(*)h Ft(m)p FD(,)565 1251 y(const)g(c)m(har)g(*)f Ft(format)p Fu(\))390 1361 y FK(This)i(function)h(writes)g(the)g(elemen)m(ts)h(of)f(the)g(matrix)h FD(m)e FK(line-b)m(y-line)i(to)g(the)f(stream)h FD(stream)390 1470 y FK(using)26 b(the)h(format)g(sp)s(eci\014er)g FD(format)p FK(,)h(whic)m(h)e(should)g(b)s(e)g(one)h(of)g(the)g FH(\045g)p FK(,)g FH(\045e)f FK(or)h FH(\045f)f FK(formats)h(for)390 1580 y(\015oating)k(p)s(oin)m(t)e(n)m(um)m(b)s(ers.)39 b(The)30 b(function)f(returns)g(0)h(for)f(success)h(and)f FH(GSL_EFAILED)e FK(if)j(there)390 1690 y(w)m(as)e(a)g(problem)f (writing)h(to)g(the)g(\014le.)40 b(The)27 b(input)g(matrix)h FD(m)f FK(ma)m(y)i(b)s(e)e(in)g(an)m(y)h(storage)h(format,)390 1799 y(and)h(the)g(output)g(\014le)h(will)f(b)s(e)g(written)h(in)f (MatrixMark)m(et)j(format.)3350 1984 y([F)-8 b(unction])-3599 b Fv(gsl_spmatrix)56 b(*)d(gsl_spmatrix_fscanf)e Fu(\()p FD(FILE)30 b(*)h Ft(stream)p Fu(\))390 2094 y FK(This)e(function)h (reads)f(sparse)h(matrix)g(data)h(in)e(the)h(MatrixMark)m(et)j(format)d (from)f(the)i(stream)390 2203 y FD(stream)h FK(and)f(stores)h(it)g(in)f (a)h(newly)f(allo)s(cated)i(matrix)f(whic)m(h)f(is)h(returned)e(in)h (triplet)h(format.)390 2313 y(The)g(function)h(returns)f(0)h(for)g (success)g(and)f FH(GSL_EFAILED)e FK(if)j(there)g(w)m(as)g(a)g(problem) g(reading)390 2423 y(from)d(the)g(\014le.)41 b(The)30 b(user)g(should)f(free)i(the)f(returned)f(matrix)i(when)f(it)g(is)h(no) f(longer)h(needed.)150 2656 y FJ(41.6)68 b(Cop)l(ying)46 b(Matrices)3350 2865 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_spmatrix_memcpy)e Fu(\()p FD(gsl)p 1545 2865 V 41 w(spmatrix)30 b(*)h Ft(dest)p FD(,)h(const)f(gsl)p 2653 2865 V 40 w(spmatrix)f(*)565 2975 y Ft(src)p Fu(\))390 3085 y FK(This)23 b(function)h(copies)h(the)g(elemen)m(ts)g(of)g(the)f (sparse)g(matrix)g FD(src)30 b FK(in)m(to)25 b FD(dest)p FK(.)39 b(The)23 b(t)m(w)m(o)j(matrices)390 3194 y(m)m(ust)k(ha)m(v)m (e)i(the)e(same)h(dimensions)f(and)g(b)s(e)f(in)h(the)h(same)g(storage) h(format.)150 3427 y FJ(41.7)68 b(Exc)l(hanging)46 b(Ro)l(ws)g(and)e (Columns)3350 3637 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_spmatrix_transpos)q(e_me)q(mcp)q(y)e Fu(\()p FD(gsl)p 2068 3637 V 41 w(spmatrix)30 b(*)h Ft(dest)p FD(,)h(const)565 3746 y(gsl)p 677 3746 V 41 w(spmatrix)e(*)h Ft(src)p Fu(\))390 3856 y FK(This)26 b(function)g(copies)h(the)g(transp)s(ose)f (of)g(the)h(sparse)f(matrix)h FD(src)32 b FK(in)m(to)27 b FD(dest)p FK(.)40 b(The)26 b(dimensions)390 3966 y(of)h FD(dest)h FK(m)m(ust)f(matc)m(h)g(the)g(transp)s(ose)f(of)h(the)f (matrix)h FD(src)p FK(.)39 b(Also,)29 b(b)s(oth)d(matrices)h(m)m(ust)f (use)h(the)390 4075 y(same)k(sparse)f(storage)i(format.)3350 4260 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_spmatrix_transpos)q(e)e Fu(\()p FD(gsl)p 1702 4260 V 41 w(spmatrix)30 b(*)h Ft(m)p Fu(\))390 4370 y FK(This)h(function)h(replaces)h(the)f(matrix)h FD(m)f FK(b)m(y)g(its)g(transp)s(ose,)h(preserving)f(the)g(storage)i (format)390 4480 y(of)c(the)f(input)g(matrix.)41 b(Curren)m(tly)-8 b(,)30 b(only)g(triplet)h(matrix)g(inputs)e(are)i(supp)s(orted.)3350 4665 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_spmatrix_transpos)q(e2) f Fu(\()p FD(gsl)p 1755 4665 V 41 w(spmatrix)30 b(*)g Ft(m)p Fu(\))390 4774 y FK(This)d(function)h(replaces)h(the)f(matrix)g FD(m)g FK(b)m(y)f(its)i(transp)s(ose,)f(but)f(c)m(hanges)i(the)f (storage)i(format)390 4884 y(for)k(compressed)g(matrix)h(inputs.)51 b(Since)34 b(compressed)g(column)g(storage)i(is)f(the)f(transp)s(ose)g (of)390 4994 y(compressed)26 b(ro)m(w)g(storage,)j(this)d(function)g (simply)f(con)m(v)m(erts)j(a)e(CCS)f(matrix)i(to)f(CRS)f(and)h(vice)390 5103 y(v)m(ersa.)51 b(This)32 b(is)i(the)f(most)h(e\016cien)m(t)h(w)m (a)m(y)f(to)g(transp)s(ose)f(a)h(compressed)f(storage)i(matrix,)g(but) 390 5213 y(the)d(user)f(should)g(note)h(that)g(the)g(storage)i(format)e (of)f(their)h(compressed)g(matrix)g(will)g(c)m(hange)390 5322 y(on)e(output.)41 b(F)-8 b(or)31 b(triplet)g(matrices,)g(the)g (output)f(matrix)h(is)f(also)h(in)f(triplet)h(storage.)p eop end %%Page: 524 542 TeXDict begin 524 541 bop 150 -116 a FK(Chapter)30 b(41:)41 b(Sparse)30 b(Matrices)2325 b(524)150 299 y FJ(41.8)68 b(Matrix)46 b(Op)t(erations)3350 533 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_spmatrix_add)e Fu(\()p FD(gsl)p 1389 533 28 4 v 40 w(spmatrix)31 b(*)f Ft(c)p FD(,)h(const)g(gsl)p 2339 533 V 41 w(spmatrix)f(*)g Ft(a)p FD(,)h(const)565 643 y(gsl)p 677 643 V 41 w(spmatrix)f(*)h Ft(b)p Fu(\))390 752 y FK(This)h(function)h(computes)g(the)g(sum)e FE(c)f FK(=)f FE(a)22 b FK(+)g FE(b)p FK(.)48 b(The)32 b(three)h(matrices)h(m) m(ust)e(ha)m(v)m(e)j(the)e(same)390 862 y(dimensions)d(and)f(b)s(e)h (stored)h(in)f(a)g(compressed)h(format.)3350 1097 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_spmatrix_scale)e Fu(\()p 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FD(b)h FK(are)f(equal)h(\(b)m(y)f (comparison)g(of)g(elemen)m(t)390 2494 y(v)-5 b(alues\))36 b(and)e(0)h(otherwise.)55 b(The)35 b(matrices)h FD(a)f FK(and)f FD(b)j FK(m)m(ust)d(b)s(e)h(in)f(the)i(same)f(sparse)f (storage)390 2603 y(format)d(for)f(comparison.)150 2874 y FJ(41.10)69 b(Finding)44 b(Maxim)l(um)h(and)g(Minim)l(um)g(Elemen)l (ts)3350 3108 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_spmatrix_minmax)e Fu(\()p FD(const)32 b(gsl)p 1784 3108 V 40 w(spmatrix)e(*)h Ft(m)p FD(,)g(double)f(*)h Ft(min_out)p FD(,)565 3218 y(double)f(*)h Ft(max_out)p Fu(\))390 3327 y FK(This)d(function)h(returns)f(the)i(minim)m(um)e(and) g(maxim)m(um)h(elemen)m(ts)i(of)e(the)h(matrix)f FD(m)p FK(,)h(storing)390 3437 y(them)g(in)g FD(min)p 886 3437 V 40 w(out)i FK(and)e FD(max)p 1435 3437 V 40 w(out)p FK(,)h(and)f(searc)m(hing)h(only)g(the)f(non-zero)h(v)-5 b(alues.)150 3707 y FJ(41.11)69 b(Compressed)45 b(F)-11 b(ormat)150 3867 y FK(GSL)35 b(supp)s(orts)e(compressed)i(column)g (storage)i(\(CCS\))d(and)h(compressed)g(ro)m(w)g(storage)i(\(CRS\))e (for-)150 3976 y(mats.)3350 4211 y([F)-8 b(unction])-3599 b Fv(gsl_spmatrix)56 b(*)d(gsl_spmatrix_ccs)d Fu(\()p FD(const)31 b(gsl)p 2202 4211 V 41 w(spmatrix)f(*)g Ft(T)p Fu(\))390 4320 y FK(This)35 b(function)g(creates)i(a)f(sparse)f(matrix) h(in)f(compressed)h(column)f(format)h(from)f(the)h(input)390 4430 y(sparse)j(matrix)h FD(T)46 b FK(whic)m(h)39 b(m)m(ust)h(b)s(e)f (in)g(triplet)i(format.)69 b(A)39 b(p)s(oin)m(ter)h(to)g(a)h(newly)e (allo)s(cated)390 4540 y(matrix)28 b(is)g(returned.)38 b(The)27 b(calling)i(function)f(should)e(free)i(the)g(newly)f(allo)s (cated)j(matrix)e(when)390 4649 y(it)j(is)f(no)h(longer)g(needed.)3350 4884 y([F)-8 b(unction])-3599 b Fv(gsl_spmatrix)56 b(*)d (gsl_spmatrix_crs)d Fu(\()p FD(const)31 b(gsl)p 2202 4884 V 41 w(spmatrix)f(*)g Ft(T)p Fu(\))390 4994 y FK(This)24 b(function)h(creates)i(a)e(sparse)g(matrix)h(in)e(compressed)h(ro)m(w)h (format)f(from)g(the)g(input)f(sparse)390 5103 y(matrix)33 b FD(T)38 b FK(whic)m(h)33 b(m)m(ust)f(b)s(e)g(in)g(triplet)h(format.) 47 b(A)33 b(p)s(oin)m(ter)f(to)i(a)e(newly)h(allo)s(cated)h(matrix)f (is)390 5213 y(returned.)49 b(The)33 b(calling)i(function)e(should)g (free)g(the)h(newly)f(allo)s(cated)j(matrix)e(when)e(it)i(is)g(no)390 5322 y(longer)d(needed.)p eop end %%Page: 525 543 TeXDict begin 525 542 bop 150 -116 a FK(Chapter)30 b(41:)41 b(Sparse)30 b(Matrices)2325 b(525)150 299 y FJ(41.12)69 b(Con)l(v)l(ersion)46 b(Bet)l(w)l(een)g(Sparse)f(and)g(Dense)g (Matrices)150 458 y FK(The)29 b FH(gsl_spmatrix)e FK(structure)j(can)g (b)s(e)f(con)m(v)m(erted)j(in)m(to)e(the)h(dense)e FH(gsl_matrix)e FK(format)k(and)e(vice)150 568 y(v)m(ersa)i(with)f(the)h(follo)m(wing)h (routines.)3350 767 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_spmatrix_d2sp)e Fu(\()p FD(gsl)p 1441 767 28 4 v 41 w(spmatrix)30 b(*)h Ft(S)p FD(,)f(const)h(gsl)p 2391 767 V 41 w(matrix)g(*)f Ft(A)p Fu(\))390 877 y FK(This)j(function) h(con)m(v)m(erts)h(the)f(dense)g(matrix)g FD(A)g FK(in)m(to)h(sparse)f (triplet)h(format)f(and)f(stores)i(the)390 986 y(result)30 b(in)g FD(S)p FK(.)3350 1186 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_spmatrix_sp2d)e Fu(\()p FD(gsl)p 1441 1186 V 41 w(matrix)30 b(*)h Ft(A)p FD(,)g(const)g(gsl)p 2305 1186 V 41 w(spmatrix)f(*)g Ft(S)p Fu(\))390 1295 y FK(This)g(function)h(con)m(v)m(erts)h(the)f(sparse)g(matrix)g FD(S)36 b FK(in)m(to)c(a)f(dense)g(matrix)g(and)f(stores)i(the)f (result)390 1405 y(in)f FD(A)p FK(.)41 b FD(S)35 b FK(m)m(ust)30 b(b)s(e)g(in)g(triplet)h(format.)150 1649 y FJ(41.13)69 b(Examples)150 1808 y FK(The)29 b(follo)m(wing)i(example)f(program)f (builds)g(a)h(5-b)m(y-4)g(sparse)g(matrix)f(and)g(prin)m(ts)g(it)h(in)g (triplet,)g(com-)150 1918 y(pressed)f(column,)i(and)f(compressed)g(ro)m (w)g(format.)41 b(The)30 b(matrix)h(whic)m(h)f(is)g(constructed)h(is) 1494 2029 y Fs(0)1494 2175 y(B)1494 2225 y(B)1494 2275 y(B)1494 2325 y(B)1494 2378 y(@)1617 2078 y FK(0)162 b(0)126 b(3)p FE(:)p FK(1)93 b(4)p FE(:)p FK(6)1617 2188 y(1)162 b(0)126 b(7)p FE(:)p FK(2)i(0)1617 2298 y(0)162 b(0)g(0)g(0)1581 2407 y(2)p FE(:)p FK(1)92 b(2)p FE(:)p FK(9)128 b(0)f(8)p FE(:)p FK(5)1581 2517 y(4)p FE(:)p FK(1)h(0)162 b(0)g(0)2334 2029 y Fs(1)2334 2175 y(C)2334 2225 y(C)2334 2275 y(C)2334 2325 y(C)2334 2378 y(A)150 2677 y FK(The)30 b(output)g(of)g(the)h(program)f(is)390 2819 y FH(printing)46 b(all)g(matrix)h(elements:)390 2929 y(A\(0,0\))f(=)i(0)390 3039 y(A\(0,1\))e(=)i(0)390 3148 y(A\(0,2\))e(=)i(3.1)390 3258 y(A\(0,3\))e(=)i(4.6)390 3367 y(A\(1,0\))e(=)i(1)390 3477 y(.)390 3587 y(.)390 3696 y(.)390 3806 y(A\(4,0\))e(=)i(4.1)390 3915 y(A\(4,1\))e(=)i(0)390 4025 y(A\(4,2\))e(=)i(0)390 4134 y(A\(4,3\))e(=)i(0)390 4244 y(matrix)e(in)h(triplet)f(format)g(\(i,j,Aij\):)390 4354 y(\(0,)h(2,)g(3.1\))390 4463 y(\(0,)g(3,)g(4.6\))390 4573 y(\(1,)g(0,)g(1.0\))390 4682 y(\(1,)g(2,)g(7.2\))390 4792 y(\(3,)g(0,)g(2.1\))390 4902 y(\(3,)g(1,)g(2.9\))390 5011 y(\(3,)g(3,)g(8.5\))390 5121 y(\(4,)g(0,)g(4.1\))390 5230 y(matrix)f(in)h(compressed)e(column)h(format:)390 5340 y(i)h(=)h([)f(1,)h(3,)f(4,)g(3,)g(0,)g(1,)g(0,)h(3,)f(])p eop end %%Page: 526 544 TeXDict begin 526 543 bop 150 -116 a FK(Chapter)30 b(41:)41 b(Sparse)30 b(Matrices)2325 b(526)390 299 y FH(p)47 b(=)h([)f(0,)h(3,)f (4,)g(6,)g(8,)g(])390 408 y(d)g(=)h([)f(1,)h(2.1,)e(4.1,)h(2.9,)f(3.1,) h(7.2,)g(4.6,)f(8.5,)h(])390 518 y(matrix)f(in)h(compressed)e(row)i (format:)390 628 y(i)g(=)h([)f(2,)h(3,)f(0,)g(2,)g(0,)g(1,)g(3,)h(0,)f (])390 737 y(p)g(=)h([)f(0,)h(2,)f(4,)g(4,)g(7,)g(8,)g(])390 847 y(d)g(=)h([)f(3.1,)g(4.6,)g(1,)g(7.2,)f(2.1,)h(2.9,)g(8.5,)f(4.1,)h (])150 1011 y FK(W)-8 b(e)33 b(see)f(in)f(the)h(compressed)f(column)g (output,)h(the)g(data)g(arra)m(y)g(stores)g(eac)m(h)h(column)e(con)m (tiguously)-8 b(,)150 1121 y(the)32 b(arra)m(y)g FE(i)g FK(stores)g(the)g(ro)m(w)g(index)f(of)h(the)f(corresp)s(onding)g(data)h (elemen)m(t,)i(and)d(the)h(arra)m(y)g FE(p)f FK(stores)150 1230 y(the)h(index)g(of)h(the)f(start)h(of)f(eac)m(h)i(column)e(in)f (the)i(data)g(arra)m(y)-8 b(.)47 b(Similarly)-8 b(,)34 b(for)e(the)g(compressed)g(ro)m(w)150 1340 y(output,)d(the)h(data)g (arra)m(y)g(stores)g(eac)m(h)h(ro)m(w)e(con)m(tiguously)-8 b(,)32 b(the)d(arra)m(y)h FE(i)g FK(stores)g(the)g(column)f(index)g(of) 150 1450 y(the)34 b(corresp)s(onding)e(data)j(elemen)m(t,)h(and)d(the)h FE(p)f FK(arra)m(y)h(stores)g(the)g(index)f(of)h(the)g(start)g(of)g (eac)m(h)h(ro)m(w)150 1559 y(in)30 b(the)h(data)g(arra)m(y)-8 b(.)390 1724 y FH(#include)46 b()390 1833 y(#include)g ()390 2052 y(#include)g()390 2271 y(int)390 2381 y(main\(\))390 2491 y({)485 2600 y(gsl_spmatrix)f(*A)i(=)h(gsl_spmatrix_alloc\(5,)42 b(4\);)k(/*)i (triplet)d(format)i(*/)485 2710 y(gsl_spmatrix)e(*B,)i(*C;)485 2819 y(size_t)g(i,)g(j;)485 3039 y(/*)h(build)e(the)h(sparse)f(matrix)g (*/)485 3148 y(gsl_spmatrix_set\(A,)d(0,)k(2,)g(3.1\);)485 3258 y(gsl_spmatrix_set\(A,)c(0,)k(3,)g(4.6\);)485 3367 y(gsl_spmatrix_set\(A,)c(1,)k(0,)g(1.0\);)485 3477 y (gsl_spmatrix_set\(A,)c(1,)k(2,)g(7.2\);)485 3587 y (gsl_spmatrix_set\(A,)c(3,)k(0,)g(2.1\);)485 3696 y (gsl_spmatrix_set\(A,)c(3,)k(1,)g(2.9\);)485 3806 y (gsl_spmatrix_set\(A,)c(3,)k(3,)g(8.5\);)485 3915 y (gsl_spmatrix_set\(A,)c(4,)k(0,)g(4.1\);)485 4134 y(printf\("printing)d (all)j(matrix)f(elements:\\n"\);)485 4244 y(for)h(\(i)h(=)f(0;)g(i)h(<) f(5;)g(++i\))581 4354 y(for)g(\(j)g(=)g(0;)h(j)f(<)h(4;)f(++j\))676 4463 y(printf\("A\(\045zu,\045zu\))c(=)48 b(\045g\\n",)e(i,)h(j,)1010 4573 y(gsl_spmatrix_get\(A,)c(i,)k(j\)\);)485 4792 y(/*)h(print)e(out)h (elements)e(in)j(triplet)d(format)i(*/)485 4902 y(printf\("matrix)d(in) k(triplet)d(format)h(\(i,j,Aij\):\\n"\);)485 5011 y (gsl_spmatrix_fprintf\(stdou)o(t,)c(A,)47 b("\045.1f"\);)485 5230 y(/*)h(convert)d(to)j(compressed)d(column)h(format)g(*/)485 5340 y(B)i(=)f(gsl_spmatrix_ccs\(A\);)p eop end %%Page: 527 545 TeXDict begin 527 544 bop 150 -116 a FK(Chapter)30 b(41:)41 b(Sparse)30 b(Matrices)2325 b(527)485 408 y FH(printf\("matrix)44 b(in)k(compressed)d(column)h(format:\\n"\);)485 518 y(printf\("i)g(=)h ([)h("\);)485 628 y(for)f(\(i)h(=)f(0;)g(i)h(<)f(B->nz;)f(++i\))581 737 y(printf\("\045zu,)e(",)k(B->i[i]\);)485 847 y(printf\("]\\n"\);) 485 1066 y(printf\("p)e(=)h([)h("\);)485 1176 y(for)f(\(i)h(=)f(0;)g(i) h(<)f(B->size2)f(+)h(1;)g(++i\))581 1285 y(printf\("\045zu,)d(",)k (B->p[i]\);)485 1395 y(printf\("]\\n"\);)485 1614 y(printf\("d)e(=)h([) h("\);)485 1724 y(for)f(\(i)h(=)f(0;)g(i)h(<)f(B->nz;)f(++i\))581 1833 y(printf\("\045g,)f(",)i(B->data[i]\);)485 1943 y(printf\("]\\n"\);)485 2162 y(/*)h(convert)d(to)j(compressed)d(row)i (format)f(*/)485 2271 y(C)i(=)f(gsl_spmatrix_crs\(A\);)485 2491 y(printf\("matrix)d(in)k(compressed)d(row)h(format:\\n"\);)485 2600 y(printf\("i)g(=)h([)h("\);)485 2710 y(for)f(\(i)h(=)f(0;)g(i)h(<) f(C->nz;)f(++i\))581 2819 y(printf\("\045zu,)e(",)k(C->i[i]\);)485 2929 y(printf\("]\\n"\);)485 3148 y(printf\("p)e(=)h([)h("\);)485 3258 y(for)f(\(i)h(=)f(0;)g(i)h(<)f(C->size1)f(+)h(1;)g(++i\))581 3367 y(printf\("\045zu,)d(",)k(C->p[i]\);)485 3477 y(printf\("]\\n"\);) 485 3696 y(printf\("d)e(=)h([)h("\);)485 3806 y(for)f(\(i)h(=)f(0;)g(i) h(<)f(C->nz;)f(++i\))581 3915 y(printf\("\045g,)f(",)i(C->data[i]\);) 485 4025 y(printf\("]\\n"\);)485 4244 y(gsl_spmatrix_free\(A\);)485 4354 y(gsl_spmatrix_free\(B\);)485 4463 y(gsl_spmatrix_free\(C\);)485 4682 y(return)g(0;)390 4792 y(})150 5037 y FJ(41.14)69 b(References)46 b(and)e(F)-11 b(urther)45 b(Reading)150 5197 y FK(The)30 b(algorithms)h(used)f(b)m(y)g(these)h(functions)f(are) g(describ)s(ed)g(in)g(the)g(follo)m(wing)i(sources:)330 5340 y(T.)e(A.)h(Da)m(vis,)h(Direct)g(Metho)s(ds)e(for)g(Sparse)g (Linear)g(Systems,)g(SIAM,)h(2006.)p eop end %%Page: 528 546 TeXDict begin 528 545 bop 150 -116 a FK(Chapter)30 b(41:)41 b(Sparse)30 b(Matrices)2325 b(528)330 299 y(CSparse)29 b(soft)m(w)m(are)j(library)-8 b(,)31 b FH(https://www.cise.ufl.ed)o (u/re)o(sear)o(ch/)o(spar)o(se/C)o(Spa)o(rse)p eop end %%Page: 529 547 TeXDict begin 529 546 bop 150 -116 a FK(Chapter)30 b(42:)41 b(Sparse)30 b(BLAS)g(Supp)s(ort)2072 b(529)150 299 y FG(42)80 b(Sparse)53 b(BLAS)g(Supp)t(ort)150 533 y FK(The)38 b(Sparse)f(Basic)j(Linear)e(Algebra)h(Subprograms)d(\()p FC(blas)p FK(\))i(de\014ne)f(a)i(set)g(of)f(fundamen)m(tal)g(op)s(er-) 150 643 y(ations)f(on)e(v)m(ectors)j(and)d(sparse)g(matrices)i(whic)m (h)e(can)i(b)s(e)e(used)g(to)h(create)i(optimized)e(higher-lev)m(el)150 752 y(linear)28 b(algebra)h(functionalit)m(y)-8 b(.)42 b(GSL)28 b(supp)s(orts)e(a)i(limited)h(n)m(um)m(b)s(er)d(of)j(BLAS)e (op)s(erations)i(for)e(sparse)150 862 y(matrices.)150 996 y(The)32 b(header)g(\014le)h FH(gsl_spblas.h)c FK(con)m(tains)34 b(the)f(protot)m(yp)s(es)g(for)f(the)h(sparse)f(BLAS)g(functions)h(and) 150 1106 y(related)e(declarations.)150 1338 y FJ(42.1)68 b(Sparse)45 b(BLAS)f(op)t(erations)3350 1548 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_spblas_dgemv)e Fu(\()p FD(const)31 b(CBLAS)p 1827 1548 28 4 v 39 w(TRANSPOSE)p 2432 1548 V 39 w(t)f(T)-8 b(ransA,)31 b(const)565 1657 y(double)f Ft(alpha)p FD(,)i(const)f(gsl)p 1525 1657 V 41 w(spmatrix)f(*)g Ft(A)p FD(,)h(const)g(gsl)p 2475 1657 V 41 w(v)m(ector)h(*)e Ft(x)p FD(,)h(const)g(double)f Ft(beta)p FD(,)565 1767 y(gsl)p 677 1767 V 41 w(v)m(ector)i(*)e Ft(y)p Fu(\))390 1876 y FK(This)24 b(function)g(computes)g(the)h (matrix-v)m(ector)i(pro)s(duct)c(and)h(sum)g FE(y)k FI( )d FE(\013op)p FK(\()p FE(A)p FK(\))p FE(x)8 b FK(+)g FE(\014)d(y)s FK(,)27 b(where)390 1986 y FE(op)p FK(\()p FE(A)p FK(\))f(=)f FE(A)p FK(,)i FE(A)928 1953 y Fq(T)1007 1986 y FK(for)f FD(T)-8 b(ransA)26 b FK(=)f FH(CblasNoTrans)p FK(,)f FH(CblasTrans)p FK(.)37 b(In-place)27 b(computations)g(are)390 2095 y(not)k(supp)s(orted,)f(so)h FD(x)37 b FK(and)30 b FD(y)39 b FK(m)m(ust)30 b(b)s(e)g(distinct)i(v)m(ectors.)43 b(The)31 b(matrix)g FD(A)g FK(ma)m(y)g(b)s(e)g(in)f(triplet)390 2205 y(or)g(compressed)g(format.)3350 2389 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_spblas_dgemm)e Fu(\()p FD(const)31 b(double)f Ft(alpha)p FD(,)i(const)f(gsl)p 2475 2389 V 40 w(spmatrix)f(*)h Ft(A)p FD(,)565 2499 y(const)g(gsl)p 915 2499 V 41 w(spmatrix)f(*)g Ft(B)p FD(,)h(gsl)p 1627 2499 V 41 w(spmatrix)f(*)h Ft(C)p Fu(\))390 2609 y FK(This)i(function)g (computes)h(the)g(sparse)g(matrix-matrix)h(pro)s(duct)d FE(C)38 b FK(=)30 b FE(\013AB)5 b FK(.)52 b(The)33 b(matrices)390 2718 y(m)m(ust)d(b)s(e)g(in)g(compressed)g(format.)150 2951 y FJ(42.2)68 b(References)47 b(and)d(F)-11 b(urther)44 b(Reading)150 3110 y FK(The)30 b(algorithms)h(used)f(b)m(y)g(these)h (functions)f(are)g(describ)s(ed)g(in)g(the)g(follo)m(wing)i(sources:) 330 3244 y(T.)e(A.)h(Da)m(vis,)h(Direct)g(Metho)s(ds)e(for)g(Sparse)g (Linear)g(Systems,)g(SIAM,)h(2006.)330 3379 y(CSparse)e(soft)m(w)m(are) j(library)-8 b(,)31 b FH(https://www.cise.ufl.ed)o(u/re)o(sear)o(ch/)o (spar)o(se/C)o(Spa)o(rse)p eop end %%Page: 530 548 TeXDict begin 530 547 bop 150 -116 a 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b(:)g(:)97 b(:)15 b(:)g(:)127 b FK(1)g FI(\000)p FK(2)2158 1922 y Fs(1)2158 2068 y(C)2158 2117 y(C)2158 2167 y(C)2158 2217 y(C)2158 2267 y(C)2158 2317 y(C)2158 2367 y(C)2158 2420 y(A)2246 1922 y(0)2246 2068 y(B)2246 2117 y(B)2246 2167 y(B)2246 2217 y(B)2246 2267 y(B)2246 2317 y(B)2246 2367 y(B)2246 2420 y(@)2389 1971 y FE(u)2441 1985 y FB(1)2389 2081 y FE(u)2441 2095 y FB(2)2389 2190 y FE(u)2441 2204 y FB(3)2421 2273 y FK(.)2421 2306 y(.)2421 2339 y(.)2334 2449 y FE(u)2386 2463 y Fq(N)6 b Fp(\000)p FB(3)2334 2558 y FE(u)2386 2572 y Fq(N)g Fp(\000)p FB(2)2549 1922 y Fs(1)2549 2068 y(C)2549 2117 y(C)2549 2167 y(C)2549 2217 y(C)2549 2267 y(C)2549 2317 y(C)2549 2367 y(C)2549 2420 y(A)2647 2265 y FK(=)2743 1922 y Fs(0)2743 2068 y(B)2743 2117 y(B)2743 2167 y(B)2743 2217 y(B)2743 2267 y(B)2743 2317 y(B)2743 2367 y(B)2743 2420 y(@)2886 1969 y FE(f)2931 1983 y FB(1)2886 2079 y FE(f)2931 2093 y FB(2)2886 2188 y FE(f)2931 2202 y FB(3)2914 2275 y FK(.)2914 2308 y(.)2914 2341 y(.)2831 2451 y FE(f)2876 2465 y Fq(N)g Fp(\000)p FB(3)2831 2560 y FE(f)2876 2574 y Fq(N)g Fp(\000)p FB(2)3038 1922 y Fs(1)3038 2068 y(C)3038 2117 y(C)3038 2167 y(C)3038 2217 y(C)3038 2267 y(C)3038 2317 y(C)3038 2367 y(C)3038 2420 y(A)150 2713 y FK(An)33 b(example)h(program)e(whic)m(h)h(constructs)h (and)e(solv)m(es)i(this)f(system)h(is)f(giv)m(en)h(b)s(elo)m(w.)49 b(The)33 b(system)150 2823 y(is)d(solv)m(ed)i(using)e(the)g(iterativ)m (e)j(GMRES)d(solv)m(er.)42 b(Here)31 b(is)f(the)h(output)f(of)g(the)h (program:)390 2957 y FH(iter)47 b(0)g(residual)f(=)h (4.297275996844e-11)390 3067 y(Converged)150 3201 y FK(sho)m(wing)31 b(that)h(the)f(metho)s(d)g(con)m(v)m(erged)h(in)f(a)h(single)g (iteration.)44 b(The)31 b(calculated)i(solution)e(is)h(sho)m(wn)150 3311 y(in)e(the)h(follo)m(wing)g(plot.)p eop end %%Page: 533 551 TeXDict begin 533 550 bop 150 -116 a FK(Chapter)30 b(43:)41 b(Sparse)30 b(Linear)g(Algebra)2071 b(533)275 2620 y @beginspecial 50 @llx 50 @lly 410 @urx 302 @ury 4320 @rwi @setspecial 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b(c)m(hapter)i(describ)s(es)f(macros)g(for)g(the)h(v)-5 b(alues)39 b(of)h(ph)m(ysical)g(constan)m(ts,)j(suc)m(h)38 b(as)i(the)f(sp)s(eed)g(of)150 651 y(ligh)m(t,)d FE(c)p FK(,)g(and)d(gra)m(vitational)k(constan)m(t,)g FE(G)p FK(.)52 b(The)33 b(v)-5 b(alues)34 b(are)h(a)m(v)-5 b(ailable)36 b(in)e(di\013eren)m(t)g(unit)g(systems,)150 760 y(including)22 b(the)i(standard)e(MKSA)g(system)h(\(meters,)j(kilograms,)f(seconds,)g (amp)s(eres\))e(and)f(the)h(CGSM)150 870 y(system)31 b(\(cen)m(timeters,)h(grams,)f(seconds,)f(gauss\),)h(whic)m(h)g(is)f (commonly)h(used)e(in)h(Astronom)m(y)-8 b(.)275 1007 y(The)34 b(de\014nitions)h(of)h(constan)m(ts)g(in)f(the)g(MKSA)g (system)h(are)f(a)m(v)-5 b(ailable)38 b(in)d(the)g(\014le)h FH(gsl_const_)150 1117 y(mksa.h)p FK(.)59 b(The)37 b(constan)m(ts)h(in) f(the)g(CGSM)g(system)h(are)f(de\014ned)f(in)h FH(gsl_const_cgsm.h)p FK(.)56 b(Dimen-)150 1226 y(sionless)31 b(constan)m(ts,)h(suc)m(h)e(as) g(the)h(\014ne)e(structure)h(constan)m(t,)i(whic)m(h)e(are)h(pure)e(n)m (um)m(b)s(ers)g(are)i(de\014ned)150 1336 y(in)f FH(gsl_const_num.h)p FK(.)275 1473 y(The)g(full)h(list)g(of)g(constan)m(ts)h(is)f(describ)s (ed)f(brie\015y)g(b)s(elo)m(w.)43 b(Consult)30 b(the)h(header)g (\014les)g(themselv)m(es)150 1583 y(for)f(the)h(v)-5 b(alues)30 b(of)h(the)g(constan)m(ts)g(used)f(in)g(the)g(library)-8 b(.)150 1819 y FJ(44.1)68 b(F)-11 b(undamen)l(tal)46 b(Constan)l(ts)150 2005 y FH(GSL_CONST_MKSA_SPEED_OF_)o(LIGH)o(T)630 2114 y FK(The)30 b(sp)s(eed)f(of)i(ligh)m(t)h(in)e(v)-5 b(acuum,)30 b FE(c)p FK(.)150 2277 y FH(GSL_CONST_MKSA_VACUUM_PE)o (RMEA)o(BILI)o(TY)630 2386 y FK(The)43 b(p)s(ermeabilit)m(y)h(of)g (free)f(space,)48 b FE(\026)2015 2400 y FB(0)2052 2386 y FK(.)80 b(This)43 b(constan)m(t)i(is)e(de\014ned)f(in)i(the)f(MKSA) 630 2496 y(system)31 b(only)-8 b(.)150 2658 y FH (GSL_CONST_MKSA_VACUUM_PE)o(RMIT)o(TIVI)o(TY)630 2767 y FK(The)23 b(p)s(ermittivit)m(y)i(of)f(free)g(space,)i FE(\017)1879 2781 y FB(0)1916 2767 y FK(.)39 b(This)23 b(constan)m(t)i(is)f(de\014ned)f(in)g(the)h(MKSA)g(system)630 2877 y(only)-8 b(.)150 3039 y FH(GSL_CONST_MKSA_PLANCKS_C)o(ONST)o (ANT_)o(H)630 3149 y FK(Planc)m(k's)31 b(constan)m(t,)h FE(h)p FK(.)150 3311 y FH(GSL_CONST_MKSA_PLANCKS_C)o(ONST)o(ANT_)o(HBA) o(R)630 3420 y FK(Planc)m(k's)f(constan)m(t)h(divided)e(b)m(y)g(2)p FE(\031)s FK(,)h(\026)-45 b FE(h)p FK(.)150 3583 y FH (GSL_CONST_NUM_AVOGADRO)630 3692 y FK(Av)m(ogadro's)32 b(n)m(um)m(b)s(er,)d FE(N)1532 3706 y Fq(a)1573 3692 y FK(.)150 3854 y FH(GSL_CONST_MKSA_FARADAY)630 3964 y FK(The)h(molar)h(c)m(harge)g(of)g(1)g(F)-8 b(arada)m(y)g(.)150 4126 y FH(GSL_CONST_MKSA_BOLTZMANN)630 4236 y FK(The)30 b(Boltzmann)h(constan)m(t,)h FE(k)s FK(.)150 4398 y FH (GSL_CONST_MKSA_MOLAR_GAS)630 4507 y FK(The)e(molar)h(gas)g(constan)m (t,)h FE(R)1693 4521 y FB(0)1730 4507 y FK(.)150 4669 y FH(GSL_CONST_MKSA_STANDARD_)o(GAS_)o(VOLU)o(ME)630 4779 y FK(The)e(standard)f(gas)i(v)m(olume,)h FE(V)1745 4793 y FB(0)1782 4779 y FK(.)150 4941 y FH(GSL_CONST_MKSA_STEFAN_BO)o (LTZM)o(ANN_)o(CON)o(STAN)o(T)630 5051 y FK(The)e(Stefan-Boltzmann)i (radiation)f(constan)m(t,)h FE(\033)s FK(.)150 5213 y FH(GSL_CONST_MKSA_GAUSS)630 5322 y FK(The)e(magnetic)i(\014eld)e(of)g (1)h(Gauss.)p eop end %%Page: 537 555 TeXDict begin 537 554 bop 150 -116 a FK(Chapter)30 b(44:)41 b(Ph)m(ysical)32 b(Constan)m(ts)2196 b(537)150 299 y FJ(44.2)68 b(Astronom)l(y)46 b(and)e(Astroph)l(ysics)150 485 y FH(GSL_CONST_MKSA_ASTRONOMI)o(CAL_)o(UNIT)630 595 y FK(The)30 b(length)h(of)f(1)h(astronomical)h(unit)e(\(mean)h (earth-sun)f(distance\),)h FE(au)p FK(.)150 759 y FH (GSL_CONST_MKSA_GRAVITATI)o(ONAL)o(_CON)o(STA)o(NT)630 868 y FK(The)f(gra)m(vitational)j(constan)m(t,)f FE(G)p FK(.)150 1032 y FH(GSL_CONST_MKSA_LIGHT_YEA)o(R)630 1142 y FK(The)e(distance)h(of)f(1)h(ligh)m(t-y)m(ear,)i FE(l)r(y)s FK(.)150 1305 y FH(GSL_CONST_MKSA_PARSEC)630 1415 y FK(The)d(distance)h (of)f(1)h(parsec,)g FE(pc)p FK(.)150 1579 y FH (GSL_CONST_MKSA_GRAV_ACCE)o(L)630 1688 y FK(The)f(standard)f(gra)m (vitational)34 b(acceleration)f(on)e(Earth,)f FE(g)s FK(.)150 1852 y FH(GSL_CONST_MKSA_SOLAR_MAS)o(S)630 1962 y FK(The)g(mass)g(of)h(the)f(Sun.)150 2201 y FJ(44.3)68 b(A)l(tomic)46 b(and)e(Nuclear)i(Ph)l(ysics)150 2387 y FH(GSL_CONST_MKSA_ELECTRON_)o(CHAR)o(GE)630 2497 y FK(The)30 b(c)m(harge)h(of)g(the)g(electron,)h FE(e)p FK(.)150 2661 y FH(GSL_CONST_MKSA_ELECTRON_)o(VOLT)630 2770 y FK(The)e(energy)h(of)f(1)h(electron)h(v)m(olt,)g FE(eV)20 b FK(.)150 2934 y FH(GSL_CONST_MKSA_UNIFIED_A)o(TOMI)o(C_MA)o (SS)630 3044 y FK(The)30 b(uni\014ed)f(atomic)j(mass,)e FE(amu)p FK(.)150 3207 y FH(GSL_CONST_MKSA_MASS_ELEC)o(TRON)630 3317 y FK(The)g(mass)g(of)h(the)f(electron,)i FE(m)1749 3331 y Fq(e)1785 3317 y FK(.)150 3481 y FH(GSL_CONST_MKSA_MASS_MUON)630 3590 y FK(The)e(mass)g(of)h(the)f(m)m(uon,)g FE(m)1655 3604 y Fq(\026)1700 3590 y FK(.)150 3754 y FH(GSL_CONST_MKSA_MASS_PROT) o(ON)630 3864 y FK(The)g(mass)g(of)h(the)f(proton,)h FE(m)1699 3878 y Fq(p)1737 3864 y FK(.)150 4027 y FH (GSL_CONST_MKSA_MASS_NEUT)o(RON)630 4137 y FK(The)f(mass)g(of)h(the)f (neutron,)g FE(m)1744 4151 y Fq(n)1789 4137 y FK(.)150 4301 y FH(GSL_CONST_NUM_FINE_STRUC)o(TURE)630 4410 y FK(The)g(electromagnetic)k(\014ne)29 b(structure)h(constan)m(t)i FE(\013)p FK(.)150 4574 y FH(GSL_CONST_MKSA_RYDBERG)630 4684 y FK(The)g(Rydb)s(erg)f(constan)m(t,)k FE(R)q(y)s FK(,)d(in)h(units)e(of)i(energy)-8 b(.)48 b(This)31 b(is)i(related)g (to)g(the)g(Rydb)s(erg)630 4793 y(in)m(v)m(erse)e(w)m(a)m(v)m(elength)i FE(R)1470 4807 y Fp(1)1571 4793 y FK(b)m(y)d FE(R)q(y)e FK(=)d FE(hcR)2096 4807 y Fp(1)2167 4793 y FK(.)150 4957 y FH(GSL_CONST_MKSA_BOHR_RADI)o(US)630 5067 y FK(The)30 b(Bohr)g(radius,)g FE(a)1390 5081 y FB(0)1427 5067 y FK(.)150 5230 y FH(GSL_CONST_MKSA_ANGSTROM)630 5340 y FK(The)g(length)h(of)f(1)h(angstrom.)p eop end %%Page: 538 556 TeXDict begin 538 555 bop 150 -116 a FK(Chapter)30 b(44:)41 b(Ph)m(ysical)32 b(Constan)m(ts)2196 b(538)150 299 y FH(GSL_CONST_MKSA_BARN)630 408 y FK(The)30 b(area)h(of)g(1)f(barn.)150 583 y FH(GSL_CONST_MKSA_BOHR_MAGN)o(ETON)630 692 y FK(The)g(Bohr)g (Magneton,)i FE(\026)1550 706 y Fq(B)1607 692 y FK(.)150 866 y FH(GSL_CONST_MKSA_NUCLEAR_M)o(AGNE)o(TON)630 976 y FK(The)e(Nuclear)h(Magneton,)h FE(\026)1660 990 y Fq(N)1723 976 y FK(.)150 1150 y FH(GSL_CONST_MKSA_ELECTRON_)o(MAGN)o(ETIC)o(_MO)o (MENT)630 1259 y FK(The)h(absolute)i(v)-5 b(alue)34 b(of)g(the)g (magnetic)h(momen)m(t)g(of)f(the)g(electron,)i FE(\026)3130 1273 y Fq(e)3165 1259 y FK(.)51 b(The)33 b(ph)m(ysical)630 1369 y(magnetic)f(momen)m(t)f(of)f(the)h(electron)h(is)e(negativ)m(e.) 150 1543 y FH(GSL_CONST_MKSA_PROTON_MA)o(GNET)o(IC_M)o(OME)o(NT)630 1653 y FK(The)g(magnetic)i(momen)m(t)f(of)f(the)h(proton,)f FE(\026)2190 1667 y Fq(p)2228 1653 y FK(.)150 1827 y FH(GSL_CONST_MKSA_THOMSON_C)o(ROSS)o(_SEC)o(TIO)o(N)630 1936 y FK(The)g(Thomson)f(cross)i(section,)h FE(\033)1821 1950 y Fq(T)1873 1936 y FK(.)150 2111 y FH(GSL_CONST_MKSA_DEBYE)630 2220 y FK(The)e(electric)i(dip)s(ole)e(momen)m(t)h(of)g(1)g(Deb)m(y)m (e,)h FE(D)s FK(.)150 2475 y FJ(44.4)68 b(Measuremen)l(t)46 b(of)f(Time)150 2666 y FH(GSL_CONST_MKSA_MINUTE)630 2776 y FK(The)30 b(n)m(um)m(b)s(er)f(of)h(seconds)h(in)f(1)h(min)m(ute.)150 2950 y FH(GSL_CONST_MKSA_HOUR)630 3059 y FK(The)f(n)m(um)m(b)s(er)f(of) h(seconds)h(in)f(1)h(hour.)150 3234 y FH(GSL_CONST_MKSA_DAY)630 3343 y FK(The)f(n)m(um)m(b)s(er)f(of)h(seconds)h(in)f(1)h(da)m(y)-8 b(.)150 3517 y FH(GSL_CONST_MKSA_WEEK)630 3627 y FK(The)30 b(n)m(um)m(b)s(er)f(of)h(seconds)h(in)f(1)h(w)m(eek.)150 3881 y FJ(44.5)68 b(Imp)t(erial)46 b(Units)150 4073 y FH(GSL_CONST_MKSA_INCH)630 4183 y FK(The)30 b(length)h(of)f(1)h(inc)m (h.)150 4357 y FH(GSL_CONST_MKSA_FOOT)630 4466 y FK(The)f(length)h(of)f (1)h(fo)s(ot.)150 4640 y FH(GSL_CONST_MKSA_YARD)630 4750 y FK(The)f(length)h(of)f(1)h(y)m(ard.)150 4924 y FH (GSL_CONST_MKSA_MILE)630 5034 y FK(The)f(length)h(of)f(1)h(mile.)150 5208 y FH(GSL_CONST_MKSA_MIL)630 5317 y FK(The)f(length)h(of)f(1)h(mil) g(\(1/1000th)i(of)d(an)h(inc)m(h\).)p eop end %%Page: 539 557 TeXDict begin 539 556 bop 150 -116 a FK(Chapter)30 b(44:)41 b(Ph)m(ysical)32 b(Constan)m(ts)2196 b(539)150 299 y FJ(44.6)68 b(Sp)t(eed)45 b(and)f(Nautical)j(Units)150 488 y FH(GSL_CONST_MKSA_KILOMETER)o(S_PE)o(R_HO)o(UR)630 598 y FK(The)30 b(sp)s(eed)f(of)i(1)g(kilometer)g(p)s(er)f(hour.)150 768 y FH(GSL_CONST_MKSA_MILES_PER)o(_HOU)o(R)630 877 y FK(The)g(sp)s(eed)f(of)i(1)g(mile)g(p)s(er)e(hour.)150 1047 y FH(GSL_CONST_MKSA_NAUTICAL_)o(MILE)630 1156 y FK(The)h(length)h(of)f(1)h(nautical)g(mile.)150 1326 y FH(GSL_CONST_MKSA_FATHOM)630 1436 y FK(The)f(length)h(of)f(1)h (fathom.)150 1605 y FH(GSL_CONST_MKSA_KNOT)630 1715 y FK(The)f(sp)s(eed)f(of)i(1)g(knot.)150 1963 y FJ(44.7)68 b(Prin)l(ters)46 b(Units)150 2152 y FH(GSL_CONST_MKSA_POINT)630 2262 y FK(The)30 b(length)h(of)f(1)h(prin)m(ter's)f(p)s(oin)m(t)g (\(1/72)j(inc)m(h\).)150 2432 y FH(GSL_CONST_MKSA_TEXPOINT)630 2541 y FK(The)d(length)h(of)f(1)h(T)-8 b(eX)31 b(p)s(oin)m(t)f (\(1/72.27)k(inc)m(h\).)150 2789 y FJ(44.8)68 b(V)-11 b(olume,)46 b(Area)f(and)f(Length)150 2979 y FH(GSL_CONST_MKSA_MICRON) 630 3088 y FK(The)30 b(length)h(of)f(1)h(micron.)150 3258 y FH(GSL_CONST_MKSA_HECTARE)630 3367 y FK(The)f(area)h(of)g(1)f (hectare.)150 3537 y FH(GSL_CONST_MKSA_ACRE)630 3647 y FK(The)g(area)h(of)g(1)f(acre.)150 3816 y FH(GSL_CONST_MKSA_LITER)630 3926 y FK(The)g(v)m(olume)h(of)g(1)f(liter.)150 4096 y FH(GSL_CONST_MKSA_US_GALLON)630 4205 y FK(The)g(v)m(olume)h(of)g(1)f (US)g(gallon.)150 4375 y FH(GSL_CONST_MKSA_CANADIAN_)o(GALL)o(ON)630 4484 y FK(The)g(v)m(olume)h(of)g(1)f(Canadian)g(gallon.)150 4654 y FH(GSL_CONST_MKSA_UK_GALLON)630 4764 y FK(The)g(v)m(olume)h(of)g (1)f(UK)g(gallon.)150 4933 y FH(GSL_CONST_MKSA_QUART)630 5043 y FK(The)g(v)m(olume)h(of)g(1)f(quart.)150 5213 y FH(GSL_CONST_MKSA_PINT)630 5322 y FK(The)g(v)m(olume)h(of)g(1)f(pin)m (t.)p eop end %%Page: 540 558 TeXDict begin 540 557 bop 150 -116 a FK(Chapter)30 b(44:)41 b(Ph)m(ysical)32 b(Constan)m(ts)2196 b(540)150 299 y FJ(44.9)68 b(Mass)45 b(and)g(W)-11 b(eigh)l(t)150 481 y FH(GSL_CONST_MKSA_POUND_MAS)o(S)630 591 y FK(The)30 b(mass)g(of)h(1)f(p)s(ound.)150 746 y FH(GSL_CONST_MKSA_OUNCE_MAS)o(S) 630 856 y FK(The)g(mass)g(of)h(1)f(ounce.)150 1011 y FH(GSL_CONST_MKSA_TON)630 1121 y FK(The)g(mass)g(of)h(1)f(ton.)150 1276 y FH(GSL_CONST_MKSA_METRIC_TO)o(N)630 1385 y FK(The)g(mass)g(of)h (1)f(metric)h(ton)g(\(1000)i(kg\).)150 1541 y FH(GSL_CONST_MKSA_UK_TON) 630 1650 y FK(The)d(mass)g(of)h(1)f(UK)h(ton.)150 1806 y FH(GSL_CONST_MKSA_TROY_OUNC)o(E)630 1915 y FK(The)f(mass)g(of)h(1)f (tro)m(y)i(ounce.)150 2071 y FH(GSL_CONST_MKSA_CARAT)630 2180 y FK(The)e(mass)g(of)h(1)f(carat.)150 2336 y FH (GSL_CONST_MKSA_GRAM_FORC)o(E)630 2445 y FK(The)g(force)h(of)f(1)h (gram)g(w)m(eigh)m(t.)150 2600 y FH(GSL_CONST_MKSA_POUND_FOR)o(CE)630 2710 y FK(The)f(force)h(of)f(1)h(p)s(ound)d(w)m(eigh)m(t.)150 2865 y FH(GSL_CONST_MKSA_KILOPOUND)o(_FOR)o(CE)630 2975 y FK(The)i(force)h(of)f(1)h(kilop)s(ound)e(w)m(eigh)m(t.)150 3130 y FH(GSL_CONST_MKSA_POUNDAL)630 3240 y FK(The)h(force)h(of)f(1)h (p)s(oundal.)150 3468 y FJ(44.10)69 b(Thermal)45 b(Energy)g(and)g(P)l (o)l(w)l(er)150 3651 y FH(GSL_CONST_MKSA_CALORIE)630 3760 y FK(The)30 b(energy)h(of)f(1)h(calorie.)150 3915 y FH(GSL_CONST_MKSA_BTU)630 4025 y FK(The)f(energy)h(of)f(1)h(British)f (Thermal)g(Unit,)h FE(btu)p FK(.)150 4180 y FH(GSL_CONST_MKSA_THERM)630 4290 y FK(The)f(energy)h(of)f(1)h(Therm.)150 4445 y FH (GSL_CONST_MKSA_HORSEPOWE)o(R)630 4555 y FK(The)f(p)s(o)m(w)m(er)g(of)h (1)g(horsep)s(o)m(w)m(er.)150 4783 y FJ(44.11)69 b(Pressure)150 4965 y FH(GSL_CONST_MKSA_BAR)630 5075 y FK(The)30 b(pressure)f(of)h(1)h (bar.)150 5230 y FH(GSL_CONST_MKSA_STD_ATMOS)o(PHER)o(E)630 5340 y FK(The)f(pressure)f(of)h(1)h(standard)f(atmosphere.)p eop end %%Page: 541 559 TeXDict begin 541 558 bop 150 -116 a FK(Chapter)30 b(44:)41 b(Ph)m(ysical)32 b(Constan)m(ts)2196 b(541)150 299 y FH(GSL_CONST_MKSA_TORR)630 408 y FK(The)30 b(pressure)f(of)h(1)h(torr.) 150 560 y FH(GSL_CONST_MKSA_METER_OF_)o(MERC)o(URY)630 669 y FK(The)f(pressure)f(of)h(1)h(meter)g(of)g(mercury)-8 b(.)150 820 y FH(GSL_CONST_MKSA_INCH_OF_M)o(ERCU)o(RY)630 930 y FK(The)30 b(pressure)f(of)h(1)h(inc)m(h)g(of)f(mercury)-8 b(.)150 1081 y FH(GSL_CONST_MKSA_INCH_OF_W)o(ATER)630 1191 y FK(The)30 b(pressure)f(of)h(1)h(inc)m(h)g(of)f(w)m(ater.)150 1342 y FH(GSL_CONST_MKSA_PSI)630 1451 y FK(The)g(pressure)f(of)h(1)h(p) s(ound)e(p)s(er)g(square)h(inc)m(h.)150 1676 y FJ(44.12)69 b(Viscosit)l(y)150 1856 y FH(GSL_CONST_MKSA_POISE)630 1965 y FK(The)30 b(dynamic)g(viscosit)m(y)i(of)f(1)f(p)s(oise.)150 2117 y FH(GSL_CONST_MKSA_STOKES)630 2226 y FK(The)g(kinematic)i (viscosit)m(y)g(of)e(1)h(stok)m(es.)150 2450 y FJ(44.13)69 b(Ligh)l(t)45 b(and)g(Illumination)150 2631 y FH(GSL_CONST_MKSA_STILB) 630 2740 y FK(The)30 b(luminance)g(of)h(1)g(stilb.)150 2891 y FH(GSL_CONST_MKSA_LUMEN)630 3001 y FK(The)f(luminous)f(\015ux)h (of)g(1)h(lumen.)150 3152 y FH(GSL_CONST_MKSA_LUX)630 3262 y FK(The)f(illuminance)h(of)f(1)h(lux.)150 3413 y FH(GSL_CONST_MKSA_PHOT)630 3522 y FK(The)f(illuminance)h(of)f(1)h (phot.)150 3673 y FH(GSL_CONST_MKSA_FOOTCANDL)o(E)630 3783 y FK(The)f(illuminance)h(of)f(1)h(fo)s(otcandle.)150 3934 y FH(GSL_CONST_MKSA_LAMBERT)630 4044 y FK(The)f(luminance)g(of)h (1)g(lam)m(b)s(ert.)150 4195 y FH(GSL_CONST_MKSA_FOOTLAMBE)o(RT)630 4305 y FK(The)f(luminance)g(of)h(1)g(fo)s(otlam)m(b)s(ert.)150 4529 y FJ(44.14)69 b(Radioactivit)l(y)150 4709 y FH (GSL_CONST_MKSA_CURIE)630 4819 y FK(The)30 b(activit)m(y)j(of)d(1)h (curie.)150 4970 y FH(GSL_CONST_MKSA_ROENTGEN)630 5079 y FK(The)f(exp)s(osure)f(of)i(1)g(ro)s(en)m(tgen.)150 5230 y FH(GSL_CONST_MKSA_RAD)630 5340 y FK(The)f(absorb)s(ed)f(dose)i (of)f(1)h(rad.)p eop end %%Page: 542 560 TeXDict begin 542 559 bop 150 -116 a FK(Chapter)30 b(44:)41 b(Ph)m(ysical)32 b(Constan)m(ts)2196 b(542)150 299 y FJ(44.15)69 b(F)-11 b(orce)44 b(and)h(Energy)150 485 y FH(GSL_CONST_MKSA_NEWTON)630 594 y FK(The)30 b(SI)g(unit)f(of)i (force,)g(1)g(Newton.)150 756 y FH(GSL_CONST_MKSA_DYNE)630 866 y FK(The)f(force)h(of)f(1)h(Dyne)g(=)f(10)1646 833 y Fp(\000)p FB(5)1766 866 y FK(Newton.)150 1028 y FH (GSL_CONST_MKSA_JOULE)630 1138 y FK(The)g(SI)g(unit)f(of)i(energy)-8 b(,)31 b(1)g(Joule.)150 1300 y FH(GSL_CONST_MKSA_ERG)630 1409 y FK(The)f(energy)h(1)f(erg)h(=)f(10)1526 1376 y Fp(\000)p FB(7)1646 1409 y FK(Joule.)150 1646 y FJ(44.16)69 b(Pre\014xes)150 1806 y FK(These)30 b(constan)m(ts)i(are)e (dimensionless)h(scaling)g(factors.)150 1969 y FH(GSL_CONST_NUM_YOTTA) 630 2079 y FK(10)720 2046 y FB(24)150 2241 y FH(GSL_CONST_NUM_ZETTA)630 2350 y FK(10)720 2317 y FB(21)150 2513 y FH(GSL_CONST_NUM_EXA)630 2622 y FK(10)720 2589 y FB(18)150 2784 y FH(GSL_CONST_NUM_PETA)630 2894 y FK(10)720 2861 y FB(15)150 3056 y FH(GSL_CONST_NUM_TERA)630 3166 y FK(10)720 3133 y FB(12)150 3328 y FH(GSL_CONST_NUM_GIGA)630 3438 y FK(10)720 3405 y FB(9)150 3600 y FH(GSL_CONST_NUM_MEGA)630 3709 y FK(10)720 3676 y FB(6)150 3872 y FH(GSL_CONST_NUM_KILO)630 3981 y FK(10)720 3948 y FB(3)150 4143 y FH(GSL_CONST_NUM_MILLI)630 4253 y FK(10)720 4220 y Fp(\000)p FB(3)150 4415 y FH (GSL_CONST_NUM_MICRO)630 4525 y FK(10)720 4492 y Fp(\000)p FB(6)150 4687 y FH(GSL_CONST_NUM_NANO)630 4796 y FK(10)720 4763 y Fp(\000)p FB(9)150 4959 y FH(GSL_CONST_NUM_PICO)630 5068 y FK(10)720 5035 y Fp(\000)p FB(12)150 5230 y FH (GSL_CONST_NUM_FEMTO)630 5340 y FK(10)720 5307 y Fp(\000)p FB(15)p eop end %%Page: 543 561 TeXDict begin 543 560 bop 150 -116 a FK(Chapter)30 b(44:)41 b(Ph)m(ysical)32 b(Constan)m(ts)2196 b(543)150 299 y FH(GSL_CONST_NUM_ATTO)630 408 y FK(10)720 375 y Fp(\000)p FB(18)150 559 y FH(GSL_CONST_NUM_ZEPTO)630 669 y FK(10)720 636 y Fp(\000)p FB(21)150 820 y FH(GSL_CONST_NUM_YOCTO)630 929 y FK(10)720 896 y Fp(\000)p FB(24)150 1153 y FJ(44.17)69 b(Examples)150 1312 y FK(The)31 b(follo)m(wing)j(program)d (demonstrates)i(the)f(use)f(of)i(the)f(ph)m(ysical)g(constan)m(ts)h(in) f(a)g(calculation.)48 b(In)150 1422 y(this)30 b(case,)i(the)f(goal)g (is)g(to)g(calculate)i(the)d(range)h(of)g(ligh)m(t-tra)m(v)m(el)i (times)e(from)f(Earth)g(to)i(Mars.)275 1552 y(The)h(required)g(data)h (is)g(the)f(a)m(v)m(erage)k(distance)d(of)g(eac)m(h)h(planet)f(from)f (the)h(Sun)e(in)h(astronomical)150 1662 y(units)e(\(the)i(eccen)m (tricities)i(and)c(inclinations)i(of)f(the)g(orbits)f(will)i(b)s(e)e (neglected)i(for)f(the)g(purp)s(oses)e(of)150 1771 y(this)25 b(calculation\).)42 b(The)25 b(a)m(v)m(erage)j(radius)d(of)h(the)f (orbit)h(of)g(Mars)f(is)h(1.52)h(astronomical)g(units,)f(and)f(for)150 1881 y(the)j(orbit)g(of)h(Earth)e(it)i(is)f(1)h(astronomical)g(unit)f (\(b)m(y)g(de\014nition\).)40 b(These)28 b(v)-5 b(alues)29 b(are)f(com)m(bined)g(with)150 1991 y(the)j(MKSA)f(v)-5 b(alues)30 b(of)h(the)g(constan)m(ts)g(for)g(the)f(sp)s(eed)g(of)g (ligh)m(t)i(and)e(the)g(length)h(of)g(an)f(astronomical)150 2100 y(unit)40 b(to)h(pro)s(duce)e(a)i(result)g(for)f(the)g(shortest)h (and)f(longest)i(ligh)m(t-tra)m(v)m(el)i(times)d(in)f(seconds.)70 b(The)150 2210 y(\014gures)30 b(are)g(con)m(v)m(erted)i(in)m(to)g(min)m (utes)e(b)s(efore)g(b)s(eing)g(displa)m(y)m(ed.)390 2340 y FH(#include)46 b()390 2449 y(#include)g ()390 2669 y(int)390 2778 y(main)h(\(void\))390 2888 y({)485 2997 y(double)g(c)95 b(=)47 b(GSL_CONST_MKSA_SPEED_OF_L)o (IGHT)o(;)485 3107 y(double)g(au)g(=)g(GSL_CONST_MKSA_ASTRONOMIC)o (AL_U)o(NIT)o(;)485 3217 y(double)g(minutes)e(=)j (GSL_CONST_MKSA_MINUTE;)485 3436 y(/*)g(distance)d(stored)h(in)h (meters)g(*/)485 3545 y(double)g(r_earth)e(=)j(1.00)e(*)i(au;)485 3655 y(double)f(r_mars)93 b(=)48 b(1.52)e(*)i(au;)485 3874 y(double)f(t_min,)f(t_max;)485 4093 y(t_min)h(=)g(\(r_mars)f(-)i (r_earth\))d(/)j(c;)485 4203 y(t_max)f(=)g(\(r_mars)f(+)i(r_earth\))d (/)j(c;)485 4422 y(printf)f(\("light)e(travel)h(time)h(from)g(Earth)f (to)h(Mars:\\n"\);)485 4532 y(printf)g(\("minimum)e(=)i(\045.1f)g (minutes\\n",)e(t_min)h(/)h(minutes\);)485 4641 y(printf)g(\("maximum)e (=)i(\045.1f)g(minutes\\n",)e(t_max)h(/)h(minutes\);)485 4860 y(return)g(0;)390 4970 y(})150 5100 y FK(Here)31 b(is)f(the)h(output)f(from)g(the)g(program,)390 5230 y FH(light)46 b(travel)g(time)h(from)g(Earth)f(to)h(Mars:)390 5340 y(minimum)f(=)h(4.3)g(minutes)p eop end %%Page: 544 562 TeXDict begin 544 561 bop 150 -116 a FK(Chapter)30 b(44:)41 b(Ph)m(ysical)32 b(Constan)m(ts)2196 b(544)390 299 y FH(maximum)46 b(=)h(21.0)g(minutes)150 531 y FJ(44.18)69 b(References)46 b(and)e(F)-11 b(urther)45 b(Reading)150 691 y FK(The)30 b(authoritativ)m(e)j(sources)d(for)h(ph)m(ysical)g (constan)m(ts)g(are)g(the)g(2006)h(COD)m(A)-8 b(T)g(A)32 b(recommended)e(v)-5 b(al-)150 800 y(ues,)29 b(published)d(in)i(the)g (article)i(b)s(elo)m(w.)40 b(F)-8 b(urther)28 b(information)h(on)f(the) g(v)-5 b(alues)29 b(of)f(ph)m(ysical)h(constan)m(ts)150 910 y(is)h(also)i(a)m(v)-5 b(ailable)32 b(from)e(the)h(NIST)e(w)m (ebsite.)330 1044 y(P)-8 b(.J.)32 b(Mohr,)f(B.N.)h(T)-8 b(a)m(ylor,)33 b(D.B.)g(New)m(ell,)g(\\COD)m(A)-8 b(T)g(A)33 b(Recommended)e(V)-8 b(alues)32 b(of)g(the)f(F)-8 b(unda-)330 1154 y(men)m(tal)40 b(Ph)m(ysical)g(Constan)m(ts:)59 b(2006",)44 b(Reviews)39 b(of)g(Mo)s(dern)g(Ph)m(ysics,)i(80\(2\),)j (pp.)66 b(633{730)330 1264 y(\(2008\).)330 1398 y FH (http://www.physics.nist.)o(gov/)o(cuu/)o(Con)o(stan)o(ts/i)o(nde)o (x.ht)o(ml)330 1533 y(http://physics.nist.gov/)o(Pubs)o(/SP8)o(11/)o (appe)o(nB9.)o(htm)o(l)p eop end %%Page: 545 563 TeXDict begin 545 562 bop 150 -116 a FK(Chapter)30 b(45:)41 b(IEEE)30 b(\015oating-p)s(oin)m(t)i(arithmetic)1731 b(545)150 299 y FG(45)80 b(IEEE)54 b(\015oating-p)t(oin)l(t)d (arithmetic)150 541 y FK(This)25 b(c)m(hapter)i(describ)s(es)f (functions)f(for)h(examining)h(the)f(represen)m(tation)i(of)e (\015oating)h(p)s(oin)m(t)f(n)m(um)m(b)s(ers)150 651 y(and)35 b(con)m(trolling)i(the)f(\015oating)g(p)s(oin)m(t)f(en)m (vironmen)m(t)h(of)g(y)m(our)f(program.)55 b(The)35 b(functions)g (describ)s(ed)150 761 y(in)30 b(this)g(c)m(hapter)h(are)g(declared)g (in)f(the)h(header)f(\014le)g FH(gsl_ieee_utils.h)p FK(.)150 997 y FJ(45.1)68 b(Represen)l(tation)48 b(of)d(\015oating)h(p)t(oin)l (t)f(n)l(um)l(b)t(ers)150 1157 y FK(The)29 b(IEEE)f(Standard)g(for)h (Binary)g(Floating-P)m(oin)m(t)k(Arithmetic)d(de\014nes)e(binary)g (formats)h(for)g(single)150 1266 y(and)h(double)g(precision)h(n)m(um)m (b)s(ers.)41 b(Eac)m(h)31 b(n)m(um)m(b)s(er)f(is)g(comp)s(osed)h(of)g (three)g(parts:)41 b(a)31 b FD(sign)g(bit)i FK(\()p FE(s)p FK(\),)e(an)150 1376 y FD(exp)s(onen)m(t)g FK(\()p FE(E)5 b FK(\))31 b(and)e(a)h FD(fraction)g FK(\()p FE(f)10 b FK(\).)40 b(The)29 b(n)m(umerical)h(v)-5 b(alue)30 b(of)g(the)f(com)m(bination)i(\()p FE(s;)15 b(E)5 b(;)15 b(f)10 b FK(\))30 b(is)g(giv)m(en)150 1485 y(b)m(y)g(the)h(follo)m (wing)h(form)m(ula,)1501 1656 y(\()p FI(\000)p FK(1\))1687 1618 y Fq(s)1723 1656 y FK(\(1)21 b FI(\001)g FE(f)10 b(f)g(f)g(f)g(f)21 b(:)15 b(:)g(:)q FK(\)2)2342 1618 y Fq(E)150 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b(the)g(leading)h(digit)f(is)g(alw)m(a)m(ys)i(1)e(for)g(normalized)g(n) m(um)m(b)s(ers)f(it)h(is)g(assumed)g(implicitly)150 2484 y(and)j(do)s(es)h(not)h(ha)m(v)m(e)g(to)g(b)s(e)e(stored.)40 b(Num)m(b)s(ers)27 b(smaller)i(than)e(2)2383 2451 y Fq(E)2432 2459 y Fl(min)2579 2484 y FK(are)h(b)s(e)g(stored)g(in)f FD(denormalized)150 2593 y(form)j FK(with)g(a)h(leading)g(zero,)1445 2764 y(\()p FI(\000)p FK(1\))1631 2726 y Fq(s)1668 2764 y FK(\(0)21 b FI(\001)f FE(f)10 b(f)g(f)g(f)g(f)22 b(:)15 b(:)g(:)q FK(\)2)2287 2726 y Fq(E)2336 2734 y Fl(min)150 2934 y FK(This)34 b(allo)m(ws)j(gradual)e(under\015o)m(w)f(do)m(wn)h (to)h(2)1799 2901 y Fq(E)1848 2909 y Fl(min)1962 2901 y Fp(\000)p Fq(p)2088 2934 y FK(for)f FE(p)f FK(bits)i(of)f(precision.) 56 b(A)35 b(zero)h(is)f(enco)s(ded)150 3044 y(with)30 b(the)h(sp)s(ecial)g(exp)s(onen)m(t)f(of)h(2)1350 3011 y Fq(E)1399 3019 y Fl(min)1513 3011 y Fp(\000)p FB(1)1632 3044 y FK(and)f(in\014nities)g(with)g(the)h(exp)s(onen)m(t)f(of)h(2) 3082 3011 y Fq(E)3131 3019 y Fl(max)3251 3011 y FB(+1)3339 3044 y FK(.)150 3181 y(The)f(format)h(for)f(single)h(precision)f(n)m (um)m(b)s(ers)f(uses)h(32)h(bits)g(divided)e(in)h(the)h(follo)m(wing)h (w)m(a)m(y)-8 b(,)390 3296 y Fz(seeeeeeeeffffffffffffffffffff)q(fff)390 3471 y(s)39 b(=)h(sign)g(bit,)g(1)g(bit)390 3558 y(e)f(=)h(exponent,)h (8)f(bits)79 b(\(E_min=-126,)42 b(E_max=127,)f(bias=127\))390 3645 y(f)e(=)h(fraction,)h(23)f(bits)150 3782 y FK(The)30 b(format)h(for)f(double)g(precision)g(n)m(um)m(b)s(ers)f(uses)h(64)h (bits)g(divided)e(in)h(the)h(follo)m(wing)h(w)m(a)m(y)-8 b(,)390 3897 y Fz(seeeeeeeeeeefffffffffffffffff)q(ffff)q(fffff)q(ffff)q (fffff)q(ffff)q(ffff)q(fffff)q(ffff)390 4071 y(s)39 b(=)h(sign)g(bit,)g (1)g(bit)390 4159 y(e)f(=)h(exponent,)h(11)f(bits)79 b(\(E_min=-1022,)42 b(E_max=1023,)g(bias=1023\))390 4246 y(f)d(=)h(fraction,)h(52)f(bits)150 4383 y FK(It)30 b(is)h(often)g (useful)e(to)i(b)s(e)f(able)h(to)g(in)m(v)m(estigate)j(the)c(b)s(eha)m 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b(output)f(tak)m(es)i(one)g(of)f (the)390 5340 y(follo)m(wing)f(forms,)p eop end %%Page: 546 564 TeXDict begin 546 563 bop 150 -116 a FK(Chapter)30 b(45:)41 b(IEEE)30 b(\015oating-p)s(oin)m(t)i(arithmetic)1731 b(546)390 299 y FH(NaN)336 b FK(the)31 b(Not-a-Num)m(b)s(er)g(sym)m(b)s (ol)390 461 y FH(Inf,)e(-Inf)67 b FK(p)s(ositiv)m(e)31 b(or)g(negativ)m(e)h(in\014nit)m(y)390 623 y FH(1.fffff...*2^E,)26 b(-1.fffff...*2^E)870 732 y FK(a)31 b(normalized)g(\015oating)g(p)s (oin)m(t)f(n)m(um)m(b)s(er)390 894 y FH(0.fffff...*2^E,)c (-0.fffff...*2^E)870 1004 y FK(a)31 b(denormalized)g(\015oating)g(p)s (oin)m(t)f(n)m(um)m(b)s(er)390 1166 y FH(0,)g(-0)258 b FK(p)s(ositiv)m(e)31 b(or)g(negativ)m(e)h(zero)390 1329 y(The)g(output)g(can)h(b)s(e)f(used)f(directly)i(in)g(GNU)g(Emacs) f(Calc)i(mo)s(de)e(b)m(y)g(preceding)g(it)h(with)g FH(2#)390 1439 y FK(to)e(indicate)h(binary)-8 b(.)3350 1628 y([F)g(unction])-3599 b Fv(void)54 b(gsl_ieee_printf_float)d Fu(\()p FD(const)32 b(\015oat)f(*)f Ft(x)p Fu(\))3350 1738 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_ieee_printf_double)e Fu(\()p FD(const)31 b(double)f(*)h Ft(x)p Fu(\))390 1848 y FK(These)21 b(functions)f (output)h(a)g(formatted)h(v)m(ersion)f(of)h(the)f(IEEE)f(\015oating-p)s (oin)m(t)i(n)m(um)m(b)s(er)e(p)s(oin)m(ted)390 1957 y(to)31 b(b)m(y)f FD(x)37 b FK(to)31 b(the)g(stream)f FH(stdout)p FK(.)150 2147 y(The)39 b(follo)m(wing)h(program)f(demonstrates)h(the)f (use)g(of)g(the)h(functions)e(b)m(y)h(prin)m(ting)g(the)h(single)g(and) 150 2256 y(double)32 b(precision)h(represen)m(tations)h(of)f(the)g (fraction)g(1)p FE(=)p FK(3.)50 b(F)-8 b(or)33 b(comparison)g(the)g (represen)m(tation)h(of)150 2366 y(the)d(v)-5 b(alue)30 b(promoted)h(from)f(single)h(to)g(double)f(precision)g(is)h(also)g (prin)m(ted.)390 2503 y FH(#include)46 b()390 2613 y(#include)g()390 2832 y(int)390 2941 y(main)h(\(void\))390 3051 y({)485 3160 y(float)g(f)g(=)h (1.0/3.0;)485 3270 y(double)f(d)g(=)g(1.0/3.0;)485 3489 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-116 a FK(Chapter)30 b(45:)41 b(IEEE)30 b(\015oating-p)s(oin)m(t)i(arithmetic)1731 b(547)150 299 y(The)34 b(output)h(also)h(sho)m(ws)f(that)g(a)h (single-precision)g(n)m(um)m(b)s(er)d(is)i(promoted)g(to)h (double-precision)f(b)m(y)150 408 y(adding)30 b(zeros)h(in)f(the)h (binary)e(represen)m(tation.)150 643 y FJ(45.2)68 b(Setting)46 b(up)e(y)l(our)h(IEEE)h(en)l(vironmen)l(t)150 802 y FK(The)c(IEEE)g (standard)f(de\014nes)h(sev)m(eral)i FD(mo)s(des)h FK(for)d(con)m (trolling)j(the)d(b)s(eha)m(vior)h(of)g(\015oating)g(p)s(oin)m(t)150 912 y(op)s(erations.)77 b(These)42 b(mo)s(des)f(sp)s(ecify)h(the)g(imp) s(ortan)m(t)h(prop)s(erties)f(of)g(computer)g(arithmetic:)66 b(the)150 1022 y(direction)34 b(used)f(for)g(rounding)f(\(e.g.)52 b(whether)33 b(n)m(um)m(b)s(ers)f(should)h(b)s(e)f(rounded)g(up,)i(do)m (wn)f(or)g(to)i(the)150 1131 y(nearest)k(n)m(um)m(b)s(er\),)i(the)e (rounding)f(precision)h(and)f(ho)m(w)h(the)g(program)g(should)f(handle) h(arithmetic)150 1241 y(exceptions,)32 b(suc)m(h)e(as)g(division)h(b)m (y)f(zero.)275 1377 y(Man)m(y)23 b(of)g(these)g(features)g(can)g(no)m (w)g(b)s(e)f(con)m(trolled)i(via)g(standard)e(functions)g(suc)m(h)g(as) h FH(fpsetround)p FK(,)150 1486 y(whic)m(h)i(should)f(b)s(e)g(used)g (whenev)m(er)h(they)g(are)g(a)m(v)-5 b(ailable.)42 b(Unfortunately)25 b(in)g(the)g(past)g(there)g(has)g(b)s(een)150 1596 y(no)j(univ)m(ersal) g(API)g(for)g(con)m(trolling)h(their)f(b)s(eha)m(vior|eac)m(h)i(system) e(has)f(had)h(its)g(o)m(wn)g(lo)m(w-lev)m(el)j(w)m(a)m(y)150 1705 y(of)h(accessing)i(them.)46 b(T)-8 b(o)33 b(help)e(y)m(ou)i(write) f(p)s(ortable)g(programs)g(GSL)g(allo)m(ws)h(y)m(ou)g(to)g(sp)s(ecify)e (mo)s(des)150 1815 y(in)25 b(a)g(platform-indep)s(enden)m(t)f(w)m(a)m (y)i(using)f(the)g(en)m(vironmen)m(t)h(v)-5 b(ariable)26 b FH(GSL_IEEE_MODE)p FK(.)35 b(The)24 b(library)150 1925 y(then)37 b(tak)m(es)h(care)f(of)g(all)h(the)f(necessary)g(mac)m (hine-sp)s(eci\014c)h(initializations)i(for)c(y)m(ou)i(when)d(y)m(ou)j (call)150 2034 y(the)31 b(function)f FH(gsl_ieee_env_setup)p FK(.)3350 2221 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_ieee_env_setup)c Fu(\(\))390 2331 y FK(This)27 b(function)g(reads)h(the)g(en)m(vironmen)m(t)g(v)-5 b(ariable)29 b FH(GSL_IEEE_MODE)24 b FK(and)j(attempts)i(to)g(set)f(up)390 2440 y(the)33 b(corresp)s(onding)e(sp)s(eci\014ed)h(IEEE)g(mo)s(des.)46 b(The)32 b(en)m(vironmen)m(t)h(v)-5 b(ariable)33 b(should)f(b)s(e)f(a)i (list)390 2550 y(of)e(k)m(eyw)m(ords,)f(separated)h(b)m(y)g(commas,)g (lik)m(e)h(this,)630 2686 y FH(GSL_IEEE_MODE)27 b FK(=)j FH(")p FD(k)m(eyw)m(ord)p FK(,)p FD(k)m(eyw)m(ord)p FK(,...)p FH(")390 2822 y FK(where)g FD(k)m(eyw)m(ord)k FK(is)d(one)f(of)h(the)f (follo)m(wing)i(mo)s(de-names,)570 2957 y FH(single-precision)570 3093 y(double-precision)570 3228 y(extended-precision)570 3363 y(round-to-nearest)570 3498 y(round-down)570 3633 y(round-up)570 3768 y(round-to-zero)570 3904 y(mask-all)570 4039 y(mask-invalid)570 4174 y(mask-denormalized)570 4309 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y(double)g(x)g(=)g(1,)h (oldsum)e(=)h(0,)g(sum)g(=)h(0;)485 4244 y(int)f(i)h(=)f(0;)485 4463 y(gsl_ieee_env_setup)c(\(\);)k(/*)g(read)g(GSL_IEEE_MODE)d(*/)485 4682 y(do)581 4792 y({)676 4902 y(i++;)676 5121 y(oldsum)i(=)i(sum;)676 5230 y(sum)f(+=)g(x;)676 5340 y(x)h(=)f(x)h(/)f(i;)p eop end %%Page: 549 567 TeXDict begin 549 566 bop 150 -116 a FK(Chapter)30 b(45:)41 b(IEEE)30 b(\015oating-p)s(oin)m(t)i(arithmetic)1731 b(549)676 408 y FH(printf)46 b(\("i=\0452d)g(sum=\045.18f)g (error=\045g\\n",)1058 518 y(i,)h(sum,)g(sum)g(-)g(M_E\);)676 737 y(if)h(\(i)f(>)g(30\))820 847 y(break;)581 956 y(})485 1066 y(while)g(\(sum)f(!=)i(oldsum\);)485 1285 y(return)f(0;)390 1395 y(})150 1541 y FK(Here)29 b(are)f(the)h(results)f(of)g(running)e (the)j(program)f(in)f FH(round-to-nearest)d FK(mo)s(de.)40 b(This)27 b(is)h(the)h(IEEE)150 1650 y(default)i(so)f(it)h(isn't)g (really)g(necessary)g(to)g(sp)s(ecify)f(it)h(here,)390 1797 y FH($)47 b(GSL_IEEE_MODE="round-to-ne)o(ares)o(t")41 b(./a.out)390 1906 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b(error=1.5587e-07)150 5121 y FK(with)33 b(an)g(error)f(of)i FE(O)s FK(\(10)1018 5088 y Fp(\000)p FB(7)1108 5121 y FK(\),)g(whic)m(h)f(corresp)s(onds)f(to)i(single)f(precision)g (accuracy)i(\(ab)s(out)e(1)g(part)g(in)150 5230 y(10)240 5197 y FB(7)278 5230 y FK(\).)54 b(Con)m(tin)m(uing)35 b(the)g(iterations)h(further)e(do)s(es)g(not)h(decrease)h(the)f(error)f (b)s(ecause)h(all)h(the)f(subse-)150 5340 y(quen)m(t)c(results)f(are)g (rounded)f(to)i(the)g(same)g(v)-5 b(alue.)p eop end %%Page: 550 568 TeXDict begin 550 567 bop 150 -116 a FK(Chapter)30 b(45:)41 b(IEEE)30 b(\015oating-p)s(oin)m(t)i(arithmetic)1731 b(550)150 299 y FJ(45.3)68 b(References)47 b(and)d(F)-11 b(urther)44 b(Reading)150 458 y FK(The)30 b(reference)h(for)f(the)g (IEEE)g(standard)g(is,)330 593 y(ANSI/IEEE)g(Std)g(754-1985,)k(IEEE)29 b(Standard)h(for)g(Binary)g(Floating-P)m(oin)m(t)k(Arithmetic.)150 752 y(A)c(more)h(p)s(edagogical)h(in)m(tro)s(duction)f(to)g(the)g 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b(detailed)h(textb)s(o)s(ok)f(on)g(IEEE)f(arithmetic)i(and)f(its)g (practical)i(use)d(is)h(a)m(v)-5 b(ailable)40 b(from)c(SIAM)150 1753 y(Press,)330 1888 y(Mic)m(hael)50 b(L.)d(Ov)m(erton,)53 b FD(Numerical)48 b(Computing)f(with)g(IEEE)g(Floating)j(P)m(oin)m(t)f (Arithmetic)p FK(,)330 1998 y(SIAM)30 b(Press,)g(ISBN)h(0898715717.)p eop end %%Page: 551 569 TeXDict begin 551 568 bop 150 -116 a FK(App)s(endix)29 b(A:)h(Debugging)i(Numerical)f(Programs)1652 b(551)150 299 y FG(App)t(endix)52 b(A)81 b(Debugging)51 b(Numerical)j(Programs) 150 535 y FK(This)36 b(c)m(hapter)g(describ)s(es)g(some)h(tips)f(and)g (tric)m(ks)h(for)f(debugging)g(n)m(umerical)h(programs)f(whic)m(h)g (use)150 645 y(GSL.)150 878 y FJ(A.1)67 b(Using)46 b(gdb)150 1038 y FK(An)m(y)29 b(errors)g(rep)s(orted)f(b)m(y)h(the)h(library)e (are)i(passed)e(to)i(the)g(function)e FH(gsl_error)p FK(.)38 b(By)30 b(running)d(y)m(our)150 1147 y(programs)j(under)e(gdb)i (and)f(setting)i(a)g(breakp)s(oin)m(t)f(in)g(this)g(function)g(y)m(ou)g (can)g(automatically)j(catc)m(h)150 1257 y(an)m(y)e(library)f(errors.) 40 b(Y)-8 b(ou)31 b(can)f(add)g(a)h(breakp)s(oin)m(t)f(for)g(ev)m(ery)i (session)e(b)m(y)g(putting)390 1392 y FH(break)46 b(gsl_error)150 1527 y FK(in)m(to)31 b(y)m(our)g FH(.gdbinit)d FK(\014le)i(in)g(the)h (directory)g(where)f(y)m(our)g(program)g(is)h(started.)275 1663 y(If)c(the)h(breakp)s(oin)m(t)g(catc)m(hes)i(an)e(error)g(then)g (y)m(ou)g(can)g(use)g(a)g(bac)m(ktrace)i(\()p FH(bt)p FK(\))f(to)f(see)h(the)f(call-tree,)150 1772 y(and)f(the)g(argumen)m (ts)h(whic)m(h)f(p)s(ossibly)f(caused)i(the)f(error.)40 b(By)27 b(mo)m(ving)h(up)f(in)m(to)h(the)f(calling)i(function)150 1882 y(y)m(ou)42 b(can)g(in)m(v)m(estigate)j(the)c(v)-5 b(alues)42 b(of)g(v)-5 b(ariables)42 b(at)h(that)f(p)s(oin)m(t.)74 b(Here)42 b(is)g(an)f(example)i(from)e(the)150 1992 y(program)30 b FH(fft/test_trap)p FK(,)d(whic)m(h)j(con)m(tains)i(the)e(follo)m (wing)i(line,)390 2104 y Fz(status)41 b(=)e (gsl_fft_complex_wavetable_all)q(oc)45 b(\(0,)40 b (&complex_wavetable\);)150 2240 y FK(The)33 b(function)h FH(gsl_fft_complex_wavetable)o(_all)o(oc)28 b FK(tak)m(es)35 b(the)f(length)h(of)f(an)g(FFT)g(as)g(its)h(\014rst)150 2349 y(argumen)m(t.)49 b(When)33 b(this)g(line)h(is)f(executed)h(an)f (error)g(will)g(b)s(e)g(generated)h(b)s(ecause)f(the)g(length)h(of)f (an)150 2459 y(FFT)e(is)f(not)h(allo)m(w)m(ed)h(to)f(b)s(e)f(zero.)275 2594 y(T)-8 b(o)34 b(debug)f(this)h(problem)g(w)m(e)h(start)f FH(gdb)p FK(,)h(using)e(the)i(\014le)f FH(.gdbinit)e FK(to)i(de\014ne)g(a)g(breakp)s(oin)m(t)g(in)150 2704 y FH(gsl_error)p FK(,)390 2816 y Fz($)39 b(gdb)h(test_trap)390 2991 y(GDB)g(is)g(free)g(software)h(and)f(you)g(are)g(welcome)g(to)g (distribute)i(copies)390 3078 y(of)e(it)f(under)i(certain)g (conditions;)g(type)f("show)h(copying")g(to)f(see)390 3165 y(the)g(conditions.)81 b(There)40 b(is)g(absolutely)h(no)f (warranty)h(for)f(GDB;)390 3252 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b(bt)390 4817 y(#0)79 b(gsl_error)41 b(\(reason=0x8052b0d)547 4904 y("length)g(n)e(must)h(be)g(positive)h(integer",)547 4991 y(file=0x8052b04)h("c_init.c",)g(line=108,)f(gsl_errno=1\))547 5078 y(at)f(error.c:14)390 5166 y(#1)79 b(0x8049376)41 b(in)f(gsl_fft_complex_wavetable_allo)q(c)45 b(\(n=0,)547 5253 y(wavetable=0xbffff778\))f(at)c(c_init.c:108)390 5340 y(#2)79 b(0x8048a00)41 b(in)f(main)g(\(argc=1,)h (argv=0xbffff9bc\))p eop end %%Page: 552 570 TeXDict begin 552 569 bop 150 -116 a FK(App)s(endix)29 b(A:)h(Debugging)i(Numerical)f(Programs)1652 b(552)547 299 y Fz(at)40 b(test_trap.c:94)390 386 y(#3)79 b(0x80488be)41 b(in)f(___crt_dummy__)i(\(\))150 534 y FK(W)-8 b(e)41 b(can)f(see)h(that)f(the)g(error)g(w)m(as)g(generated)h(in)e(the)i (function)e FH(gsl_fft_complex_wavetable)o(_)150 644 y(alloc)29 b FK(when)g(it)i(w)m(as)f(called)h(with)f(an)g(argumen)m(t)h (of)f FD(n=0)p FK(.)41 b(The)29 b(original)j(call)f(came)g(from)f(line) g(94)h(in)150 753 y(the)g(\014le)f FH(test_trap.c)p FK(.)275 902 y(By)f(mo)m(ving)h(up)e(to)i(the)f(lev)m(el)i(of)e(the)h(original)g (call)g(w)m(e)g(can)f(\014nd)f(the)h(line)h(that)g(caused)f(the)g (error,)390 1027 y Fz(\(gdb\))40 b(up)390 1114 y(#1)79 b(0x8049376)41 b(in)f(gsl_fft_complex_wavetable_allo)q(c)45 b(\(n=0,)547 1202 y(wavetable=0xbffff778\))f(at)c(c_init.c:108)390 1289 y(108)118 b(GSL_ERROR)42 b(\("length)f(n)e(must)h(be)g(positive)h (integer",)g(GSL_EDOM\);)390 1376 y(\(gdb\))f(up)390 1463 y(#2)79 b(0x8048a00)41 b(in)f(main)g(\(argc=1,)h (argv=0xbffff9bc\))547 1550 y(at)f(test_trap.c:94)390 1637 y(94)157 b(status)41 b(=)e(gsl_fft_complex_wavetable_a)q(lloc)46 b(\(0,)704 1725 y(&complex_wavetable\);)150 1873 y FK(Th)m(us)29 b(w)m(e)i(ha)m(v)m(e)h(found)d(the)h(line)h(that)g(caused)f(the)h (problem.)40 b(F)-8 b(rom)31 b(this)f(p)s(oin)m(t)h(w)m(e)g(could)f (also)h(prin)m(t)150 1982 y(out)g(the)f(v)-5 b(alues)31 b(of)f(other)h(v)-5 b(ariables)31 b(suc)m(h)f(as)h FH (complex_wavetable)p FK(.)150 2235 y FJ(A.2)67 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y(-Wmissing-prototypes)c(-Wstrict-prototypes)485 2249 y(-Wconversion)i(-Wshadow)g(-Wpointer-arith)485 2358 y(-Wcast-qual)g(-Wcast-align)485 2468 y(-Wwrite-strings)f (-Wnested-externs)485 2577 y(-fshort-enums)h(-fno-common)f(-Dinline=)i (-g)h(-O2)150 2710 y FK(F)-8 b(or)30 b(details)g(of)f(eac)m(h)h(option) g(consult)f(the)g(man)m(ual)h FD(Using)f(and)f(P)m(orting)i(GCC)p FK(.)f(The)g(follo)m(wing)h(table)150 2820 y(giv)m(es)i(a)e(brief)g (explanation)i(of)e(what)h(t)m(yp)s(es)f(of)h(errors)e(these)i(options) g(catc)m(h.)150 2976 y FH(-ansi)e(-pedantic)630 3086 y FK(Use)j(ANSI)f(C,)h(and)f(reject)i(an)m(y)f(non-ANSI)f(extensions.) 45 b(These)31 b(\015ags)h(help)g(in)f(writing)630 3196 y(p)s(ortable)f(programs)g(that)h(will)g(compile)g(on)g(other)f (systems.)150 3352 y FH(-Werror)144 b FK(Consider)27 b(w)m(arnings)g(to)i(b)s(e)e(errors,)h(so)g(that)g(compilation)h (stops.)40 b(This)27 b(prev)m(en)m(ts)h(w)m(arn-)630 3462 y(ings)k(from)f(scrolling)i(o\013)g(the)f(top)g(of)g(the)g(screen) g(and)f(b)s(eing)h(lost.)46 b(Y)-8 b(ou)33 b(w)m(on't)f(b)s(e)f(able) 630 3571 y(to)g(compile)g(the)g(program)f(un)m(til)h(it)g(is)f (completely)i(w)m(arning-free.)150 3728 y FH(-Wall)240 b FK(This)28 b(turns)g(on)i(a)f(set)h(of)f(w)m(arnings)g(for)g(common)h (programming)f(problems.)39 b(Y)-8 b(ou)30 b(need)630 3837 y FH(-Wall)p FK(,)f(but)h(it)h(is)f(not)h(enough)f(on)g(its)h(o)m (wn.)150 3994 y FH(-O2)336 b FK(T)-8 b(urn)35 b(on)i(optimization.)61 b(The)36 b(w)m(arnings)g(for)g(uninitialized)h(v)-5 b(ariables)38 b(in)e FH(-Wall)f FK(rely)630 4103 y(on)j(the)g(optimizer)h(to)f (analyze)i(the)e(co)s(de.)64 b(If)37 b(there)h(is)g(no)g(optimization)i (then)d(these)630 4213 y(w)m(arnings)30 b(aren't)h(generated.)150 4369 y FH(-W)384 b FK(This)21 b(turns)f(on)i(some)g(extra)g(w)m (arnings)g(not)g(included)f(in)g FH(-Wall)p FK(,)h(suc)m(h)g(as)f (missing)h(return)630 4479 y(v)-5 b(alues)31 b(and)e(comparisons)i(b)s (et)m(w)m(een)g(signed)f(and)g(unsigned)f(in)m(tegers.)150 4636 y FH(-Wmissing-prototypes)c(-Wstrict-prototypes)630 4745 y FK(W)-8 b(arn)33 b(if)f(there)g(are)h(an)m(y)f(missing)g(or)h (inconsisten)m(t)g(protot)m(yp)s(es.)47 b(Without)33 b(protot)m(yp)s(es)630 4855 y(it)e(is)f(harder)g(to)h(detect)h (problems)d(with)h(incorrect)i(argumen)m(ts.)150 5011 y FH(-Wconversion)630 5121 y FK(The)20 b(main)h(use)f(of)h(this)g (option)g(is)g(to)h(w)m(arn)e(ab)s(out)h(con)m(v)m(ersions)g(from)g (signed)f(to)i(unsigned)630 5230 y(in)m(tegers.)67 b(F)-8 b(or)40 b(example,)i FH(unsigned)28 b(int)h(x)h(=)g(-1)p FK(.)66 b(If)38 b(y)m(ou)h(need)g(to)h(p)s(erform)d(suc)m(h)i(a)630 5340 y(con)m(v)m(ersion)32 b(y)m(ou)e(can)h(use)f(an)g(explicit)i (cast.)p eop end %%Page: 554 572 TeXDict begin 554 571 bop 150 -116 a FK(App)s(endix)29 b(A:)h(Debugging)i(Numerical)f(Programs)1652 b(554)150 299 y FH(-Wshadow)96 b FK(This)38 b(w)m(arns)g(whenev)m(er)g(a)h(lo)s (cal)h(v)-5 b(ariable)39 b(shado)m(ws)g(another)g(lo)s(cal)g(v)-5 b(ariable.)66 b(If)39 b(t)m(w)m(o)630 408 y(v)-5 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b(ARISING)g(IN)g(ANY)e(W)-8 b(A)i(Y)24 b(OUT)f(OF)g(THE)g(USE)g(OF)g(THIS)h(SOFTW)-8 b(ARE,)23 b(EVEN)g(IF)390 4530 y(AD)n(VISED)h(OF)f(THE)g(POSSIBILITY)i (OF)f(SUCH)f(D)n(AMA)n(GE.)p eop end %%Page: 557 575 TeXDict begin 557 574 bop 150 -116 a FK(App)s(endix)29 b(C:)h(Auto)s(conf)g(Macros)2245 b(557)150 299 y FG(App)t(endix)52 b(C)81 b(Auto)t(conf)52 b(Macros)150 524 y FK(F)-8 b(or)24 b(applications)g(using)e FH(autoconf)f FK(the)i(standard)g(macro)g FH(AC_CHECK_LIB)d FK(can)j(b)s(e)f(used)h(to)g(link)g(with)150 633 y(GSL)30 b(automatically)k(from)c(a)h FH(configure)d FK(script.)41 b(The)30 b(library)h(itself)g(dep)s(ends)e(on)h(the)h (presence)g(of)150 743 y(a)38 b FC(cblas)e FK(and)g(math)i(library)f (as)g(w)m(ell,)k(so)c(these)h(m)m(ust)f(also)i(b)s(e)d(lo)s(cated)j(b)s (efore)e(linking)h(with)f(the)150 853 y(main)e FH(libgsl)e FK(\014le.)54 b(The)34 b(follo)m(wing)i(commands)e(should)g(b)s(e)g (placed)i(in)e(the)h FH(configure.ac)c FK(\014le)k(to)150 962 y(p)s(erform)29 b(these)i(tests,)390 1095 y FH (AC_CHECK_LIB\([m],[cos]\))390 1204 y(AC_CHECK_LIB\([gslcblas],)o([cbl) o(as_d)o(gem)o(m]\))390 1314 y(AC_CHECK_LIB\([gsl],[gsl_)o(blas)o(_dge) o(mm])o(\))150 1447 y FK(It)g(is)f(imp)s(ortan)m(t)h(to)g(c)m(hec)m(k)h (for)e FH(libm)f FK(and)h FH(libgslcblas)e FK(b)s(efore)i FH(libgsl)p FK(,)f(otherwise)i(the)f(tests)i(will)150 1556 y(fail.)41 b(Assuming)29 b(the)g(libraries)h(are)g(found)e(the)h (output)g(during)g(the)g(con\014gure)g(stage)i(lo)s(oks)f(lik)m(e)h (this,)390 1689 y FH(checking)46 b(for)g(cos)h(in)h(-lm...)e(yes)390 1799 y(checking)g(for)g(cblas_dgemm)f(in)i(-lgslcblas...)e(yes)390 1908 y(checking)h(for)g(gsl_blas_dgemm)e(in)k(-lgsl...)d(yes)150 2041 y FK(If)61 b(the)h(library)f(is)h(found)e(then)i(the)f(tests)i (will)f(de\014ne)f(the)h(macros)g FH(HAVE_LIBGSL)p FK(,)k FH(HAVE_)150 2150 y(LIBGSLCBLAS)p FK(,)55 b FH(HAVE_LIBM)50 b FK(and)h(add)h(the)g(options)h FH(-lgsl)29 b(-lgslcblas)e(-lm)52 b FK(to)h(the)f(v)-5 b(ariable)150 2260 y FH(LIBS)p FK(.)275 2393 y(The)34 b(tests)h(ab)s(o)m(v)m(e)g(will)g(\014nd)e(an)m(y)i(v)m (ersion)g(of)g(the)f(library)-8 b(.)53 b(They)34 b(are)h(suitable)g (for)f(general)i(use,)150 2502 y(where)29 b(the)h(v)m(ersions)f(of)h (the)g(functions)f(are)h(not)f(imp)s(ortan)m(t.)41 b(An)29 b(alternativ)m(e)j(macro)e(is)f(a)m(v)-5 b(ailable)32 b(in)150 2612 y(the)j(\014le)g FH(gsl.m4)f FK(to)i(test)g(for)f(a)g(sp) s(eci\014c)g(v)m(ersion)g(of)h(the)f(library)-8 b(.)55 b(T)-8 b(o)35 b(use)g(this)g(macro)h(simply)f(add)150 2721 y(the)c(follo)m(wing)g(line)g(to)g(y)m(our)g FH(configure.in)c FK(\014le)j(instead)h(of)f(the)h(tests)g(ab)s(o)m(v)m(e:)390 2854 y FH(AX_PATH_GSL\(GSL_VERSION,)915 2964 y([action-if-found],)915 3073 y([action-if-not-found]\))150 3206 y FK(The)73 b(argumen)m(t)h FH(GSL_VERSION)d FK(should)h(b)s(e)h(the)h(t)m(w)m(o)h(or)f(three)g (digit)g FC(major.minor)e FK(or)150 3315 y FC(major.minor.micr)n(o)43 b FK(v)m(ersion)i(n)m(um)m(b)s(er)f(of)h(the)h(release)g(y)m(ou)f (require.)85 b(A)45 b(suitable)g(c)m(hoice)i(for)150 3425 y FH(action-if-not-found)25 b FK(is,)390 3558 y FH(AC_MSG_ERROR\(could)43 b(not)k(find)f(required)g(version)g(of)h (GSL\))150 3690 y FK(Then)39 b(y)m(ou)i(can)f(add)g(the)g(v)-5 b(ariables)41 b FH(GSL_LIBS)d FK(and)i FH(GSL_CFLAGS)d FK(to)k(y)m(our)g(Mak)m(e\014le.am)h(\014les)e(to)150 3800 y(obtain)c(the)f(correct)i(compiler)e(\015ags.)56 b FH(GSL_LIBS)33 b FK(is)i(equal)h(to)g(the)f(output)g(of)h(the)f FH(gsl-config)28 b(--)150 3910 y(libs)c FK(command)i(and)f FH(GSL_CFLAGS)d FK(is)k(equal)g(to)g FH(gsl-config)i(--cflags)23 b FK(command.)39 b(F)-8 b(or)26 b(example,)390 4042 y FH(libfoo_la_LDFLAGS)43 b(=)48 b(-lfoo)e($\(GSL_LIBS\))f(-lgslcblas)150 4175 y FK(Note)34 b(that)f(the)g(macro)g FH(AX_PATH_GSL)d FK(needs)i(to)i(use)e(the)h(C)f(compiler)h(so)g(it)h(should)d(app)s (ear)h(in)h(the)150 4284 y FH(configure.in)27 b FK(\014le)j(b)s(efore)g (the)h(macro)g FH(AC_LANG_CPLUSPLUS)26 b FK(for)k(programs)g(that)h (use)f(C)p FH(++)p FK(.)275 4417 y(T)-8 b(o)30 b(test)i(for)e FH(inline)e FK(the)j(follo)m(wing)h(test)f(should)f(b)s(e)f(placed)i (in)f(y)m(our)g FH(configure.in)d FK(\014le,)390 4550 y FH(AC_C_INLINE)390 4769 y(if)47 b(test)g("$ac_cv_c_inline")c(!=)k(no) g(;)h(then)485 4879 y(AC_DEFINE\(HAVE_INLINE,1\))485 4988 y(AC_SUBST\(HAVE_INLINE\))390 5098 y(fi)150 5230 y FK(and)23 b(the)h(macro)h(will)f(then)g(b)s(e)f(de\014ned)g(in)g(the) h(compilation)i(\015ags)e(or)g(b)m(y)g(including)f(the)h(\014le)g FH(config.h)150 5340 y FK(b)s(efore)30 b(an)m(y)h(library)f(headers.)p eop end %%Page: 558 576 TeXDict begin 558 575 bop 150 -116 a FK(App)s(endix)29 b(C:)h(Auto)s(conf)g(Macros)2245 b(558)275 299 y(The)29 b(follo)m(wing)j(auto)s(conf)f(test)g(will)g(c)m(hec)m(k)h(for)e FH(extern)f(inline)p FK(,)390 411 y Fz(dnl)40 b(Check)g(for)g("extern)h (inline",)g(using)f(a)g(modified)h(version)390 498 y(dnl)f(of)g(the)f (test)i(for)f(AC_C_INLINE)h(from)f(acspecific.mt)390 585 y(dnl)390 672 y(AC_CACHE_CHECK\([for)k(extern)c(inline],)h (ac_cv_c_extern_inline,)390 760 y([ac_cv_c_extern_inline=no)390 847 y(AC_TRY_COMPILE\([extern)j($ac_cv_c_inline)f(double)d(foo\(double) i(x\);)390 934 y(extern)f($ac_cv_c_inline)h(double)f(foo\(double)g(x\)) f({)f(return)i(x+1.0;)g(};)390 1021 y(double)g(foo)e(\(double)i(x\))f ({)f(return)i(x)f(+)f(1.0;)h(};],)390 1108 y([)79 b(foo\(1.0\))h(],)390 1196 y([ac_cv_c_extern_inline="yes"])q(\))390 1283 y(]\))390 1457 y(if)40 b(test)g("$ac_cv_c_extern_inline")45 b(!=)39 b(no)h(;)f(then)468 1544 y(AC_DEFINE\(HAVE_INLINE,1\))468 1631 y(AC_SUBST\(HAVE_INLINE\))390 1719 y(fi)275 1853 y FK(The)22 b(substitution)g(of)h(p)s(ortabilit)m(y)h(functions)f(can)g (b)s(e)f(made)h(automatically)i(if)e(y)m(ou)g(use)g FH(autoconf)p FK(.)150 1963 y(F)-8 b(or)44 b(example,)j(to)c(test)h(whether)f(the)g (BSD)g(function)g FH(hypot)e FK(is)i(a)m(v)-5 b(ailable)45 b(y)m(ou)f(can)f(include)g(the)150 2072 y(follo)m(wing)32 b(line)f(in)f(the)g(con\014gure)g(\014le)h FH(configure.in)c FK(for)j(y)m(our)g(application,)390 2207 y FH(AC_CHECK_FUNCS\(hypot\)) 150 2341 y FK(and)g(place)h(the)g(follo)m(wing)g(macro)g(de\014nitions) f(in)g(the)h(\014le)f FH(config.h.in)p FK(,)390 2476 y FH(/*)47 b(Substitute)e(gsl_hypot)g(for)i(missing)f(system)g(hypot)h (*/)390 2695 y(#ifndef)f(HAVE_HYPOT)390 2804 y(#define)g(hypot)g (gsl_hypot)390 2914 y(#endif)150 3049 y FK(The)36 b(application)i (source)e(\014les)h(can)g(then)f(use)g(the)h(include)f(command)g FH(#include)28 b()34 b FK(to)150 3158 y(substitute)c FH(gsl_hypot)e FK(for)i(eac)m(h)i(o)s(ccurrence)e(of)h FH(hypot)e FK(when)g FH(hypot)g FK(is)i(not)f(a)m(v)-5 b(ailable.)p eop end %%Page: 559 577 TeXDict begin 559 576 bop 150 -116 a FK(App)s(endix)29 b(D:)i(GSL)f(CBLAS)f(Library)2080 b(559)150 299 y FG(App)t(endix)52 b(D)81 b(GSL)53 b(CBLAS)g(Library)150 550 y FK(The)42 b(protot)m(yp)s(es)i(for)e(the)i(lo)m(w-lev)m(el)h FC(cblas)d FK(functions)g(are)i(declared)f(in)g(the)g(\014le)g FH(gsl_cblas.h)p FK(.)150 660 y(F)-8 b(or)41 b(the)f(de\014nition)g(of)g(the)h (functions)e(consult)i(the)f(do)s(cumen)m(tation)h(a)m(v)-5 b(ailable)42 b(from)e(Netlib)h(\(see)150 769 y(Section)31 b(13.3)h([BLAS)f(References)g(and)e(F)-8 b(urther)30 b(Reading],)i(page)f(136\).)150 1010 y FJ(D.1)68 b(Lev)l(el)46 b(1)3350 1225 y FK([F)-8 b(unction])-3599 b Fv(float)54 b(cblas_sdsdot)49 b Fu(\()p FD(const)31 b(in)m(t)g Ft(N)p FD(,)g(const)g(\015oat)g Ft(alpha)p FD(,)h(const)f(\015oat)g(*)g Ft(x)p FD(,)565 1335 y(const)g(in)m(t)g Ft(incx)p FD(,)h(const)f (\015oat)g(*)f Ft(y)p FD(,)h(const)g(in)m(t)g Ft(incy)p Fu(\))3350 1500 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(cblas_dsdot)49 b Fu(\()p FD(const)31 b(in)m(t)g Ft(N)p FD(,)g(const)g(\015oat)g(*)g Ft(x)p FD(,)f(const)h(in)m(t)g Ft(incx)p FD(,)h(const)565 1609 y(\015oat)f(*)g Ft(y)p FD(,)g(const)g(in)m(t)g Ft(incy)p Fu(\))3350 1774 y FK([F)-8 b(unction])-3599 b Fv(float)54 b(cblas_sdot)48 b Fu(\()p FD(const)32 b(in)m(t)e Ft(N)p FD(,)h(const)g(\015oat)g(*)g Ft(x)p FD(,)g(const)g(in)m(t)g Ft(incx)p FD(,)g(const)565 1884 y(\015oat)g(*)g Ft(y)p FD(,)g(const)g(in)m(t)g Ft(incy)p Fu(\))3350 2049 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(cblas_ddot)49 b Fu(\()p FD(const)31 b(in)m(t)g Ft(N)p FD(,)g(const)f(double)g(*)h Ft(x)p FD(,)g(const)g(in)m(t)g Ft(incx)p FD(,)h(const)565 2159 y(double)e(*)h Ft(y)p FD(,)g(const)g(in)m(t)f Ft(incy)p Fu(\))3350 2324 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_cdotu_sub)c Fu(\()p FD(const)31 b(in)m(t)g Ft(N)p FD(,)g(const)f(v)m(oid)h(*)g Ft(x)p FD(,)g(const)g(in)m(t)g Ft(incx)p FD(,)565 2433 y(const)g(v)m(oid)g(*)g Ft(y)p FD(,)g(const)f(in)m(t)h Ft(incy)p FD(,)h(v)m(oid)f(*)g Ft(dotu)p Fu(\))3350 2598 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_cdotc_sub)c Fu(\()p FD(const)31 b(in)m(t)g Ft(N)p FD(,)g(const)f(v)m(oid)h(*)g Ft(x)p FD(,)g(const)g(in)m(t)g Ft(incx)p FD(,)565 2708 y(const)g(v)m(oid)g(*)g Ft(y)p FD(,)g(const)f(in)m(t)h Ft(incy)p FD(,)h(v)m(oid)f(*)g Ft(dotc)p Fu(\))3350 2873 y FK([F)-8 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b(cblas_dnrm2)49 b Fu(\()p FD(const)31 b(in)m(t)g Ft(N)p FD(,)g(const)g(double)f(*)g Ft(x)p FD(,)h(const)g(in)m(t)g Ft(incx)p Fu(\))3350 3918 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(cblas_dasum)49 b Fu(\()p FD(const)31 b(in)m(t)g Ft(N)p FD(,)g(const)g(double)f(*)g Ft(x)p FD(,)h(const)g(in)m(t)g Ft(incx)p Fu(\))3350 4083 y FK([F)-8 b(unction])-3599 b Fv(float)54 b(cblas_scnrm2)49 b Fu(\()p FD(const)31 b(in)m(t)g Ft(N)p FD(,)g(const)g(v)m(oid)g(*)g Ft(x)p FD(,)f(const)h(in)m(t)g Ft(incx)p Fu(\))3350 4248 y FK([F)-8 b(unction])-3599 b Fv(float)54 b(cblas_scasum)49 b Fu(\()p FD(const)31 b(in)m(t)g Ft(N)p FD(,)g(const)g(v)m(oid)g(*)g Ft(x)p FD(,)f(const)h(in)m(t)g Ft(incx)p Fu(\))3350 4413 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(cblas_dznrm2)49 b Fu(\()p FD(const)31 b(in)m(t)g Ft(N)p FD(,)g(const)g(v)m(oid)g(*)g Ft(x)p FD(,)g(const)g(in)m(t)f Ft(incx)p Fu(\))3350 4578 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(cblas_dzasum)49 b Fu(\()p FD(const)31 b(in)m(t)g Ft(N)p FD(,)g(const)g(v)m(oid)g(*)g Ft(x)p FD(,)g(const)g(in)m(t)f Ft(incx)p Fu(\))3350 4743 y FK([F)-8 b(unction])-3599 b Fv(CBLAS_INDEX)56 b(cblas_isamax)49 b Fu(\()p FD(const)29 b(in)m(t)f Ft(N)p FD(,)h(const)f(\015oat)h(*)g Ft(x)p FD(,)g(const)f(in)m(t)h Ft(incx)p Fu(\))3350 4908 y FK([F)-8 b(unction])-3599 b Fv(CBLAS_INDEX)56 b(cblas_idamax)49 b Fu(\()p FD(const)31 b(in)m(t)g Ft(N)p FD(,)g(const)g(double)f(*)g Ft(x)p FD(,)h(const)g(in)m(t)565 5018 y Ft(incx)p Fu(\))3350 5183 y FK([F)-8 b(unction])-3599 b Fv(CBLAS_INDEX)56 b(cblas_icamax)49 b Fu(\()p FD(const)30 b(in)m(t)g Ft(N)p FD(,)f(const)h(v)m(oid)g(*)f Ft(x)p FD(,)h(const)g(in)m(t)g Ft(incx)p Fu(\))3350 5348 y FK([F)-8 b(unction])-3599 b Fv(CBLAS_INDEX)56 b(cblas_izamax)49 b Fu(\()p FD(const)30 b(in)m(t)g Ft(N)p FD(,)f(const)h(v)m(oid)g(*)f Ft(x)p FD(,)h(const)g(in)m(t)g Ft(incx)p Fu(\))p eop end %%Page: 560 578 TeXDict begin 560 577 bop 150 -116 a FK(App)s(endix)29 b(D:)i(GSL)f(CBLAS)f(Library)2080 b(560)3350 299 y([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_sswap)48 b Fu(\()p FD(const)32 b(in)m(t)e Ft(N)p FD(,)h(\015oat)g(*)g Ft(x)p FD(,)g(const)g(in)m(t)g Ft(incx)p FD(,)h(\015oat)f(*)f Ft(y)p FD(,)h(const)565 408 y(in)m(t)g Ft(incy)p Fu(\))3350 556 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_scopy)48 b Fu(\()p FD(const)32 b(in)m(t)e Ft(N)p FD(,)h(const)g(\015oat)g(*)g Ft(x)p FD(,)g(const)g(in)m(t)g Ft(incx)p FD(,)g(\015oat)g(*)g Ft(y)p FD(,)565 666 y(const)g(in)m(t)g Ft(incy)p Fu(\))3350 814 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_saxpy)48 b Fu(\()p FD(const)32 b(in)m(t)e Ft(N)p FD(,)h(const)g(\015oat)g Ft(alpha)p FD(,)h(const)f(\015oat)g(*)g Ft(x)p FD(,)g(const)565 923 y(in)m(t)g Ft(incx)p FD(,)h(\015oat)f(*)g Ft(y)p FD(,)f(const)h(in)m(t)g Ft(incy)p Fu(\))3350 1071 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_dswap)48 b Fu(\()p FD(const)32 b(in)m(t)e Ft(N)p FD(,)h(double)f(*)h Ft(x)p FD(,)g(const)g(in)m(t)g Ft(incx)p FD(,)g(double)f(*)h Ft(y)p FD(,)565 1181 y(const)g(in)m(t)g Ft(incy)p Fu(\))3350 1328 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_dcopy)48 b Fu(\()p FD(const)32 b(in)m(t)e Ft(N)p FD(,)h(const)g(double)f(*)h Ft(x)p FD(,)g(const)g(in)m(t)f Ft(incx)p FD(,)i(double)565 1438 y(*)f Ft(y)p FD(,)g(const)g(in)m(t)f Ft(incy)p Fu(\))3350 1586 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_daxpy)48 b Fu(\()p FD(const)32 b(in)m(t)e Ft(N)p FD(,)h(const)g(double)f Ft(alpha)p FD(,)i(const)f(double)f(*)h Ft(x)p FD(,)565 1695 y(const)g(in)m(t)g Ft(incx)p FD(,)h(double)e(*)g Ft(y)p FD(,)h(const)g(in)m(t)g Ft(incy)p Fu(\))3350 1843 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_cswap)48 b Fu(\()p FD(const)32 b(in)m(t)e Ft(N)p FD(,)h(v)m(oid)g(*)g Ft(x)p FD(,)g(const)g(in)m(t)g Ft(incx)p FD(,)g(v)m(oid)g(*)g Ft(y)p FD(,)g(const)565 1953 y(in)m(t)g Ft(incy)p Fu(\))3350 2100 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_ccopy)48 b Fu(\()p FD(const)32 b(in)m(t)e Ft(N)p FD(,)h(const)g(v)m(oid)g(*)g Ft(x)p FD(,)g(const)g(in)m(t)g Ft(incx)p FD(,)g(v)m(oid)g(*)g Ft(y)p FD(,)565 2210 y(const)g(in)m(t)g Ft(incy)p Fu(\))3350 2358 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_caxpy)48 b Fu(\()p FD(const)31 b(in)m(t)f Ft(N)p FD(,)h(const)f(v)m(oid)g(*)h Ft(alpha)p FD(,)g(const)g(v)m(oid)f(*)g Ft(x)p FD(,)h(const)565 2467 y(in)m(t)g Ft(incx)p FD(,)h(v)m(oid)f(*)f Ft(y)p FD(,)h(const)g(in)m(t)g Ft(incy)p Fu(\))3350 2615 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_zswap)48 b Fu(\()p FD(const)32 b(in)m(t)e Ft(N)p FD(,)h(v)m(oid)g(*)g Ft(x)p FD(,)g(const)g(in)m(t)g Ft(incx)p FD(,)g(v)m(oid)g(*)g Ft(y)p FD(,)g(const)565 2725 y(in)m(t)g Ft(incy)p Fu(\))3350 2872 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_zcopy)48 b Fu(\()p FD(const)32 b(in)m(t)e Ft(N)p FD(,)h(const)g(v)m(oid)g(*)g Ft(x)p FD(,)g(const)g(in)m(t)g Ft(incx)p FD(,)g(v)m(oid)g(*)g Ft(y)p FD(,)565 2982 y(const)g(in)m(t)g Ft(incy)p Fu(\))3350 3130 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_zaxpy)48 b Fu(\()p FD(const)31 b(in)m(t)f Ft(N)p FD(,)h(const)f(v)m(oid)g(*)h Ft(alpha)p FD(,)g(const)g(v)m(oid)f(*)g Ft(x)p FD(,)h(const)565 3239 y(in)m(t)g Ft(incx)p FD(,)h(v)m(oid)f(*)f Ft(y)p FD(,)h(const)g(in)m(t)g Ft(incy)p Fu(\))3350 3387 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_srotg)48 b Fu(\()p FD(\015oat)32 b(*)e Ft(a)p FD(,)h(\015oat)g(*)g Ft(b)p FD(,)g(\015oat)g(*)g Ft(c)p FD(,)g(\015oat)g(*)g Ft(s)p Fu(\))3350 3535 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_srotmg)49 b Fu(\()p FD(\015oat)31 b(*)g Ft(d1)p FD(,)g(\015oat)g(*)g Ft(d2)p FD(,)g(\015oat)g(*)g Ft(b1)p FD(,)g(const)g(\015oat)g Ft(b2)p FD(,)565 3644 y(\015oat)g(*)g Ft(P)p Fu(\))3350 3792 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_srot)48 b Fu(\()p FD(const)31 b(in)m(t)g Ft(N)p FD(,)g(\015oat)g(*)g Ft(x)p FD(,)g(const)g(in)m(t)f Ft(incx)p FD(,)i(\015oat)f(*)g Ft(y)p FD(,)g(const)565 3902 y(in)m(t)g Ft(incy)p FD(,)h(const)f(\015oat)g Ft(c)p FD(,)g(const)f(\015oat)i Ft(s)p Fu(\))3350 4050 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_srotm)48 b Fu(\()p FD(const)32 b(in)m(t)e Ft(N)p FD(,)h(\015oat)g(*)g Ft(x)p FD(,)g(const)g(in)m(t)g Ft(incx)p FD(,)h(\015oat)f(*)f Ft(y)p FD(,)h(const)565 4159 y(in)m(t)g Ft(incy)p FD(,)h(const)f (\015oat)g(*)f Ft(P)p Fu(\))3350 4307 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_drotg)48 b Fu(\()p FD(double)31 b(*)f Ft(a)p FD(,)h(double)f(*)h Ft(b)p FD(,)g(double)f(*)g Ft(c)p FD(,)h(double)f(*)h Ft(s)p Fu(\))3350 4455 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_drotmg)49 b Fu(\()p FD(double)29 b(*)h Ft(d1)p FD(,)h(double)e(*)h Ft(d2)p FD(,)h(double)e(*)h Ft(b1)p FD(,)h(const)f(double)565 4564 y Ft(b2)p FD(,)h(double)f(*)h Ft(P)p Fu(\))3350 4712 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_drot)48 b Fu(\()p FD(const)31 b(in)m(t)g Ft(N)p FD(,)g(double)f(*)h Ft(x)p FD(,)g(const)f(in)m(t)h Ft(incx)p FD(,)h(double)e(*)h Ft(y)p FD(,)565 4822 y(const)g(in)m(t)g Ft(incy)p FD(,)h(const)f (double)e Ft(c)p FD(,)i(const)g(double)f Ft(s)p Fu(\))3350 4969 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_drotm)48 b Fu(\()p FD(const)32 b(in)m(t)e Ft(N)p FD(,)h(double)f(*)h Ft(x)p FD(,)g(const)g(in)m(t)g Ft(incx)p FD(,)g(double)f(*)h Ft(y)p FD(,)565 5079 y(const)g(in)m(t)g Ft(incy)p FD(,)h(const)f (double)e(*)i Ft(P)p Fu(\))3350 5227 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_sscal)48 b Fu(\()p FD(const)32 b(in)m(t)e Ft(N)p FD(,)h(const)g(\015oat)g Ft(alpha)p FD(,)h(\015oat)f(*)g Ft(x)p FD(,)g(const)g(in)m(t)565 5336 y Ft(incx)p Fu(\))p eop end %%Page: 561 579 TeXDict begin 561 578 bop 150 -116 a FK(App)s(endix)29 b(D:)i(GSL)f(CBLAS)f(Library)2080 b(561)3350 299 y([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_dscal)48 b Fu(\()p FD(const)32 b(in)m(t)e Ft(N)p FD(,)h(const)g(double)f Ft(alpha)p FD(,)i(double)e(*)h Ft(x)p FD(,)g(const)565 408 y(in)m(t)g Ft(incx)p Fu(\))3350 561 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_cscal)48 b Fu(\()p FD(const)32 b(in)m(t)e Ft(N)p FD(,)h(const)g(v)m(oid)g(*)g Ft(alpha)p FD(,)h(v)m(oid)f(*)g Ft(x)p FD(,)g(const)f(in)m(t)565 670 y Ft(incx)p Fu(\))3350 823 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_zscal)48 b Fu(\()p FD(const)32 b(in)m(t)e Ft(N)p FD(,)h(const)g(v)m(oid)g(*)g Ft(alpha)p FD(,)h(v)m(oid)f(*)g Ft(x)p FD(,)g(const)f(in)m(t)565 932 y Ft(incx)p Fu(\))3350 1084 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_csscal)49 b Fu(\()p FD(const)31 b(in)m(t)g Ft(N)p FD(,)g(const)f(\015oat)i Ft(alpha)p FD(,)g(v)m(oid)f(*)f Ft(x)p FD(,)h(const)g(in)m(t)565 1194 y Ft(incx)p Fu(\))3350 1346 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_zdscal)49 b Fu(\()p FD(const)31 b(in)m(t)g Ft(N)p FD(,)g(const)f(double)g Ft(alpha)p FD(,)i(v)m(oid)f(*)g Ft(x)p FD(,)g(const)g(in)m(t)565 1456 y Ft(incx)p Fu(\))150 1660 y FJ(D.2)68 b(Lev)l(el)46 b(2)3350 1862 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_sgemv)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 1862 28 4 v 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 1971 y(CBLAS)p 877 1971 V 40 w(TRANSPOSE)d Ft(TransA)p FD(,)33 b(const)e(in)m(t)g Ft(M)p FD(,)f(const)h(in)m(t)g Ft(N)p FD(,)g(const)g(\015oat)g Ft(alpha)p FD(,)565 2081 y(const)g(\015oat)g(*)g Ft(A)p FD(,)g(const)g(in)m(t)f Ft(lda)p FD(,)i(const)f(\015oat)g(*)g Ft(x)p FD(,)f(const)h(in)m(t)g Ft(incx)p FD(,)h(const)f(\015oat)g Ft(beta)p FD(,)565 2191 y(\015oat)g(*)g Ft(y)p FD(,)g(const)g(in)m(t)g Ft(incy)p Fu(\))3350 2343 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_sgbmv)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 2343 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 2452 y(CBLAS)p 877 2452 V 40 w(TRANSPOSE)d Ft(TransA)p FD(,)33 b(const)e(in)m(t)g Ft(M)p FD(,)f(const)h(in)m(t)g Ft(N)p FD(,)g(const)g(in)m(t)g Ft(KL)p FD(,)g(const)g(in)m(t)565 2562 y Ft(KU)p FD(,)g(const)g(\015oat)g Ft(alpha)p FD(,)h(const)f (\015oat)g(*)g Ft(A)p FD(,)g(const)g(in)m(t)g Ft(lda)p FD(,)g(const)g(\015oat)g(*)g Ft(x)p FD(,)g(const)g(in)m(t)565 2672 y Ft(incx)p FD(,)h(const)f(\015oat)g Ft(beta)p FD(,)h(\015oat)f(*) f Ft(y)p FD(,)h(const)g(in)m(t)g Ft(incy)p Fu(\))3350 2824 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_strmv)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 2824 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 2933 y(CBLAS)p 877 2933 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(en)m(um)f (CBLAS)p 2258 2933 V 40 w(TRANSPOSE)e Ft(TransA)p FD(,)33 b(const)e(en)m(um)565 3043 y(CBLAS)p 877 3043 V 40 w(DIA)m(G)g Ft(Diag)p FD(,)h(const)f(in)m(t)g Ft(N)p FD(,)g(const)g(\015oat)g(*)f Ft(A)p FD(,)h(const)g(in)m(t)g Ft(lda)p FD(,)g(\015oat)h(*)e Ft(x)p FD(,)h(const)565 3153 y(in)m(t)g Ft(incx)p Fu(\))3350 3305 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_stbmv)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 3305 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 3415 y(CBLAS)p 877 3415 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(en)m(um)f (CBLAS)p 2258 3415 V 40 w(TRANSPOSE)e Ft(TransA)p FD(,)33 b(const)e(en)m(um)565 3524 y(CBLAS)p 877 3524 V 40 w(DIA)m(G)g Ft(Diag)p FD(,)h(const)f(in)m(t)g Ft(N)p FD(,)g(const)g(in)m(t)f Ft(K)p FD(,)h(const)g(\015oat)g(*)g Ft(A)p FD(,)g(const)g(in)m(t)g Ft(lda)p FD(,)565 3634 y(\015oat)g(*)g Ft(x)p FD(,)g(const)g(in)m(t)g Ft(incx)p Fu(\))3350 3786 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_stpmv)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 3786 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 3896 y(CBLAS)p 877 3896 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(en)m(um) f(CBLAS)p 2258 3896 V 40 w(TRANSPOSE)e Ft(TransA)p FD(,)33 b(const)e(en)m(um)565 4005 y(CBLAS)p 877 4005 V 40 w(DIA)m(G)g Ft(Diag)p FD(,)h(const)f(in)m(t)g Ft(N)p FD(,)g(const)g(\015oat)g(*)f Ft(Ap)p FD(,)i(\015oat)f(*)f Ft(x)p FD(,)h(const)g(in)m(t)g Ft(incx)p Fu(\))3350 4157 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_strsv)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 4157 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 4267 y(CBLAS)p 877 4267 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(en)m(um) f(CBLAS)p 2258 4267 V 40 w(TRANSPOSE)e Ft(TransA)p FD(,)33 b(const)e(en)m(um)565 4377 y(CBLAS)p 877 4377 V 40 w(DIA)m(G)g Ft(Diag)p FD(,)h(const)f(in)m(t)g Ft(N)p FD(,)g(const)g(\015oat)g(*)f Ft(A)p FD(,)h(const)g(in)m(t)g Ft(lda)p FD(,)g(\015oat)h(*)e Ft(x)p FD(,)h(const)565 4486 y(in)m(t)g Ft(incx)p Fu(\))3350 4638 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_stbsv)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 4638 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 4748 y(CBLAS)p 877 4748 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(en)m(um)f (CBLAS)p 2258 4748 V 40 w(TRANSPOSE)e Ft(TransA)p FD(,)33 b(const)e(en)m(um)565 4858 y(CBLAS)p 877 4858 V 40 w(DIA)m(G)g Ft(Diag)p FD(,)h(const)f(in)m(t)g Ft(N)p FD(,)g(const)g(in)m(t)f Ft(K)p FD(,)h(const)g(\015oat)g(*)g Ft(A)p FD(,)g(const)g(in)m(t)g Ft(lda)p FD(,)565 4967 y(\015oat)g(*)g Ft(x)p FD(,)g(const)g(in)m(t)g Ft(incx)p Fu(\))3350 5119 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_stpsv)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 5119 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 5229 y(CBLAS)p 877 5229 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(en)m(um) f(CBLAS)p 2258 5229 V 40 w(TRANSPOSE)e Ft(TransA)p FD(,)33 b(const)e(en)m(um)565 5339 y(CBLAS)p 877 5339 V 40 w(DIA)m(G)g Ft(Diag)p FD(,)h(const)f(in)m(t)g Ft(N)p FD(,)g(const)g(\015oat)g(*)f Ft(Ap)p FD(,)i(\015oat)f(*)f Ft(x)p FD(,)h(const)g(in)m(t)g Ft(incx)p Fu(\))p eop end %%Page: 562 580 TeXDict begin 562 579 bop 150 -116 a FK(App)s(endix)29 b(D:)i(GSL)f(CBLAS)f(Library)2080 b(562)3350 299 y([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_dgemv)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 299 28 4 v 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 408 y(CBLAS)p 877 408 V 40 w(TRANSPOSE)d Ft(TransA)p FD(,)33 b(const)e(in)m(t)g Ft(M)p FD(,)f(const)h(in)m(t)g Ft(N)p FD(,)g(const)g(double)f Ft(alpha)p FD(,)565 518 y(const)h(double)f(*)h Ft(A)p FD(,)g(const)f(in)m(t)h Ft(lda)p FD(,)h(const)f(double)f(*)g Ft(x)p FD(,)h(const)g(in)m(t)g Ft(incx)p FD(,)h(const)f(double)565 628 y Ft(beta)p FD(,)h(double)e(*)h Ft(y)p FD(,)f(const)h(in)m(t)g Ft(incy)p Fu(\))3350 793 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_dgbmv)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 793 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 902 y(CBLAS)p 877 902 V 40 w(TRANSPOSE)d Ft(TransA)p FD(,)33 b(const)e(in)m(t)g Ft(M)p FD(,)f(const)h(in)m(t)g Ft(N)p FD(,)g(const)g(in)m(t)g Ft(KL)p FD(,)g(const)g(in)m(t)565 1012 y Ft(KU)p FD(,)g(const)g(double)f Ft(alpha)p FD(,)i(const)f (double)f(*)h Ft(A)p FD(,)g(const)f(in)m(t)h Ft(lda)p FD(,)h(const)f(double)f(*)g Ft(x)p FD(,)565 1122 y(const)h(in)m(t)g Ft(incx)p FD(,)h(const)f(double)e Ft(beta)p FD(,)j(double)e(*)h Ft(y)p FD(,)g(const)g(in)m(t)g Ft(incy)p Fu(\))3350 1287 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_dtrmv)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 1287 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 1396 y(CBLAS)p 877 1396 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(en)m(um)f (CBLAS)p 2258 1396 V 40 w(TRANSPOSE)e Ft(TransA)p FD(,)33 b(const)e(en)m(um)565 1506 y(CBLAS)p 877 1506 V 40 w(DIA)m(G)g Ft(Diag)p FD(,)h(const)f(in)m(t)g Ft(N)p FD(,)g(const)g(double)e(*)i Ft(A)p FD(,)g(const)g(in)m(t)g Ft(lda)p FD(,)g(double)f(*)h Ft(x)p FD(,)565 1616 y(const)g(in)m(t)g Ft(incx)p Fu(\))3350 1781 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_dtbmv)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 1781 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 1890 y(CBLAS)p 877 1890 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(en)m(um)f (CBLAS)p 2258 1890 V 40 w(TRANSPOSE)e Ft(TransA)p FD(,)33 b(const)e(en)m(um)565 2000 y(CBLAS)p 877 2000 V 40 w(DIA)m(G)g Ft(Diag)p FD(,)h(const)f(in)m(t)g Ft(N)p FD(,)g(const)g(in)m(t)f Ft(K)p FD(,)h(const)g(double)f(*)h Ft(A)p FD(,)g(const)g(in)m(t)f Ft(lda)p FD(,)565 2109 y(double)g(*)h Ft(x)p FD(,)g(const)g(in)m(t)f Ft(incx)p Fu(\))3350 2275 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_dtpmv)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 2275 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 2384 y(CBLAS)p 877 2384 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(en)m(um) f(CBLAS)p 2258 2384 V 40 w(TRANSPOSE)e Ft(TransA)p FD(,)33 b(const)e(en)m(um)565 2494 y(CBLAS)p 877 2494 V 40 w(DIA)m(G)d Ft(Diag)p FD(,)h(const)f(in)m(t)f Ft(N)p FD(,)h(const)f(double)g(*)g Ft(Ap)p FD(,)i(double)e(*)g Ft(x)p FD(,)h(const)g(in)m(t)f Ft(incx)p Fu(\))3350 2659 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_dtrsv)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 2659 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 2769 y(CBLAS)p 877 2769 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(en)m(um) f(CBLAS)p 2258 2769 V 40 w(TRANSPOSE)e Ft(TransA)p FD(,)33 b(const)e(en)m(um)565 2878 y(CBLAS)p 877 2878 V 40 w(DIA)m(G)g Ft(Diag)p FD(,)h(const)f(in)m(t)g Ft(N)p FD(,)g(const)g(double)e(*)i Ft(A)p FD(,)g(const)g(in)m(t)g Ft(lda)p FD(,)g(double)f(*)h Ft(x)p FD(,)565 2988 y(const)g(in)m(t)g Ft(incx)p Fu(\))3350 3153 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_dtbsv)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 3153 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 3263 y(CBLAS)p 877 3263 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(en)m(um)f (CBLAS)p 2258 3263 V 40 w(TRANSPOSE)e Ft(TransA)p FD(,)33 b(const)e(en)m(um)565 3372 y(CBLAS)p 877 3372 V 40 w(DIA)m(G)g Ft(Diag)p FD(,)h(const)f(in)m(t)g Ft(N)p FD(,)g(const)g(in)m(t)f Ft(K)p FD(,)h(const)g(double)f(*)h Ft(A)p FD(,)g(const)g(in)m(t)f Ft(lda)p FD(,)565 3482 y(double)g(*)h Ft(x)p FD(,)g(const)g(in)m(t)f Ft(incx)p Fu(\))3350 3647 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_dtpsv)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 3647 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 3757 y(CBLAS)p 877 3757 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(en)m(um) f(CBLAS)p 2258 3757 V 40 w(TRANSPOSE)e Ft(TransA)p FD(,)33 b(const)e(en)m(um)565 3866 y(CBLAS)p 877 3866 V 40 w(DIA)m(G)d Ft(Diag)p FD(,)h(const)f(in)m(t)f Ft(N)p FD(,)h(const)f(double)g(*)g Ft(Ap)p FD(,)i(double)e(*)g Ft(x)p FD(,)h(const)g(in)m(t)f Ft(incx)p Fu(\))3350 4031 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_cgemv)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 4031 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 4141 y(CBLAS)p 877 4141 V 40 w(TRANSPOSE)d Ft(TransA)p FD(,)33 b(const)e(in)m(t)g Ft(M)p FD(,)f(const)h(in)m(t)g Ft(N)p FD(,)g(const)g(v)m(oid)g(*)g Ft(alpha)p FD(,)565 4250 y(const)e(v)m(oid)h(*)f Ft(A)p FD(,)g(const)g(in)m(t)g Ft(lda)p FD(,)h(const)f(v)m(oid)h(*)f Ft(x)p FD(,)g(const)g(in)m(t)h Ft(incx)p FD(,)g(const)f(v)m(oid)g(*)h Ft(beta)p FD(,)565 4360 y(v)m(oid)h(*)g Ft(y)p FD(,)g(const)g(in)m(t)f Ft(incy)p Fu(\))3350 4525 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_cgbmv)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 4525 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 4635 y(CBLAS)p 877 4635 V 40 w(TRANSPOSE)d Ft(TransA)p FD(,)33 b(const)e(in)m(t)g Ft(M)p FD(,)f(const)h(in)m(t)g Ft(N)p FD(,)g(const)g(in)m(t)g Ft(KL)p FD(,)g(const)g(in)m(t)565 4744 y Ft(KU)p FD(,)g(const)g(v)m(oid)g(*)g Ft(alpha)p FD(,)h(const)f(v)m(oid)g(*)g Ft(A)p FD(,)f(const)h(in)m(t)g Ft(lda)p FD(,)h(const)f(v)m(oid)f(*)h Ft(x)p FD(,)g(const)g(in)m(t)565 4854 y Ft(incx)p FD(,)h(const)f(v)m(oid)g(*)f Ft(beta)p FD(,)i(v)m(oid)f(*)g Ft(y)p FD(,)g(const)g(in)m(t)g Ft(incy)p Fu(\))3350 5019 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_ctrmv)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 5019 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 5129 y(CBLAS)p 877 5129 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(en)m(um) f(CBLAS)p 2258 5129 V 40 w(TRANSPOSE)e Ft(TransA)p FD(,)33 b(const)e(en)m(um)565 5238 y(CBLAS)p 877 5238 V 40 w(DIA)m(G)g Ft(Diag)p FD(,)h(const)f(in)m(t)g Ft(N)p FD(,)g(const)g(v)m(oid)f(*)h Ft(A)p FD(,)g(const)g(in)m(t)g Ft(lda)p FD(,)g(v)m(oid)g(*)g Ft(x)p FD(,)g(const)565 5348 y(in)m(t)g Ft(incx)p Fu(\))p eop end %%Page: 563 581 TeXDict begin 563 580 bop 150 -116 a FK(App)s(endix)29 b(D:)i(GSL)f(CBLAS)f(Library)2080 b(563)3350 299 y([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_ctbmv)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 299 28 4 v 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 408 y(CBLAS)p 877 408 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(en)m(um)f(CBLAS)p 2258 408 V 40 w(TRANSPOSE)e Ft(TransA)p FD(,)33 b(const)e(en)m(um)565 518 y(CBLAS)p 877 518 V 40 w(DIA)m(G)g Ft(Diag)p FD(,)h(const)f(in)m(t) g Ft(N)p FD(,)g(const)g(in)m(t)f Ft(K)p FD(,)h(const)g(v)m(oid)g(*)g Ft(A)p FD(,)g(const)g(in)m(t)f Ft(lda)p FD(,)565 628 y(v)m(oid)h(*)g Ft(x)p FD(,)g(const)g(in)m(t)f Ft(incx)p Fu(\))3350 868 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_ctpmv)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 868 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 978 y(CBLAS)p 877 978 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(en)m(um)f (CBLAS)p 2258 978 V 40 w(TRANSPOSE)e Ft(TransA)p FD(,)33 b(const)e(en)m(um)565 1087 y(CBLAS)p 877 1087 V 40 w(DIA)m(G)g Ft(Diag)p FD(,)h(const)f(in)m(t)g Ft(N)p FD(,)g(const)g(v)m(oid)f(*)h Ft(Ap)p FD(,)g(v)m(oid)g(*)g Ft(x)p FD(,)g(const)g(in)m(t)g Ft(incx)p Fu(\))3350 1328 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_ctrsv)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 1328 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 1438 y(CBLAS)p 877 1438 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(en)m(um) f(CBLAS)p 2258 1438 V 40 w(TRANSPOSE)e Ft(TransA)p FD(,)33 b(const)e(en)m(um)565 1547 y(CBLAS)p 877 1547 V 40 w(DIA)m(G)g Ft(Diag)p FD(,)h(const)f(in)m(t)g Ft(N)p FD(,)g(const)g(v)m(oid)f(*)h Ft(A)p FD(,)g(const)g(in)m(t)g Ft(lda)p FD(,)g(v)m(oid)g(*)g Ft(x)p FD(,)g(const)565 1657 y(in)m(t)g Ft(incx)p Fu(\))3350 1897 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_ctbsv)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 1897 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 2007 y(CBLAS)p 877 2007 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(en)m(um)f (CBLAS)p 2258 2007 V 40 w(TRANSPOSE)e Ft(TransA)p FD(,)33 b(const)e(en)m(um)565 2117 y(CBLAS)p 877 2117 V 40 w(DIA)m(G)g Ft(Diag)p FD(,)h(const)f(in)m(t)g Ft(N)p FD(,)g(const)g(in)m(t)f Ft(K)p FD(,)h(const)g(v)m(oid)g(*)g Ft(A)p FD(,)g(const)g(in)m(t)f Ft(lda)p FD(,)565 2226 y(v)m(oid)h(*)g Ft(x)p FD(,)g(const)g(in)m(t)f Ft(incx)p Fu(\))3350 2467 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_ctpsv)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 2467 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 2576 y(CBLAS)p 877 2576 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(en)m(um) f(CBLAS)p 2258 2576 V 40 w(TRANSPOSE)e Ft(TransA)p FD(,)33 b(const)e(en)m(um)565 2686 y(CBLAS)p 877 2686 V 40 w(DIA)m(G)g Ft(Diag)p FD(,)h(const)f(in)m(t)g Ft(N)p FD(,)g(const)g(v)m(oid)f(*)h Ft(Ap)p FD(,)g(v)m(oid)g(*)g Ft(x)p FD(,)g(const)g(in)m(t)g Ft(incx)p Fu(\))3350 2927 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_zgemv)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 2927 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 3036 y(CBLAS)p 877 3036 V 40 w(TRANSPOSE)d Ft(TransA)p FD(,)33 b(const)e(in)m(t)g Ft(M)p FD(,)f(const)h(in)m(t)g Ft(N)p FD(,)g(const)g(v)m(oid)g(*)g Ft(alpha)p FD(,)565 3146 y(const)e(v)m(oid)h(*)f Ft(A)p FD(,)g(const)g(in)m(t)g Ft(lda)p FD(,)h(const)f(v)m(oid)h(*)f Ft(x)p FD(,)g(const)g(in)m(t)h Ft(incx)p FD(,)g(const)f(v)m(oid)g(*)h Ft(beta)p FD(,)565 3255 y(v)m(oid)h(*)g Ft(y)p FD(,)g(const)g(in)m(t)f Ft(incy)p Fu(\))3350 3496 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_zgbmv)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 3496 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 3606 y(CBLAS)p 877 3606 V 40 w(TRANSPOSE)d Ft(TransA)p FD(,)33 b(const)e(in)m(t)g Ft(M)p FD(,)f(const)h(in)m(t)g Ft(N)p FD(,)g(const)g(in)m(t)g Ft(KL)p FD(,)g(const)g(in)m(t)565 3715 y Ft(KU)p FD(,)g(const)g(v)m(oid)g(*)g Ft(alpha)p FD(,)h(const)f(v)m(oid)g(*)g Ft(A)p FD(,)f(const)h(in)m(t)g Ft(lda)p FD(,)h(const)f(v)m(oid)f(*)h Ft(x)p FD(,)g(const)g(in)m(t)565 3825 y Ft(incx)p FD(,)h(const)f(v)m(oid)g(*)f Ft(beta)p FD(,)i(v)m(oid)f(*)g Ft(y)p FD(,)g(const)g(in)m(t)g Ft(incy)p Fu(\))3350 4065 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_ztrmv)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 4065 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 4175 y(CBLAS)p 877 4175 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(en)m(um) f(CBLAS)p 2258 4175 V 40 w(TRANSPOSE)e Ft(TransA)p FD(,)33 b(const)e(en)m(um)565 4285 y(CBLAS)p 877 4285 V 40 w(DIA)m(G)g Ft(Diag)p FD(,)h(const)f(in)m(t)g Ft(N)p FD(,)g(const)g(v)m(oid)f(*)h Ft(A)p FD(,)g(const)g(in)m(t)g Ft(lda)p FD(,)g(v)m(oid)g(*)g Ft(x)p FD(,)g(const)565 4394 y(in)m(t)g Ft(incx)p Fu(\))3350 4635 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_ztbmv)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 4635 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 4744 y(CBLAS)p 877 4744 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(en)m(um)f (CBLAS)p 2258 4744 V 40 w(TRANSPOSE)e Ft(TransA)p FD(,)33 b(const)e(en)m(um)565 4854 y(CBLAS)p 877 4854 V 40 w(DIA)m(G)g Ft(Diag)p FD(,)h(const)f(in)m(t)g Ft(N)p FD(,)g(const)g(in)m(t)f Ft(K)p FD(,)h(const)g(v)m(oid)g(*)g Ft(A)p FD(,)g(const)g(in)m(t)f Ft(lda)p FD(,)565 4964 y(v)m(oid)h(*)g Ft(x)p FD(,)g(const)g(in)m(t)f Ft(incx)p Fu(\))3350 5204 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_ztpmv)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 5204 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 5314 y(CBLAS)p 877 5314 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(en)m(um) f(CBLAS)p 2258 5314 V 40 w(TRANSPOSE)e Ft(TransA)p FD(,)33 b(const)e(en)m(um)565 5423 y(CBLAS)p 877 5423 V 40 w(DIA)m(G)g Ft(Diag)p FD(,)h(const)f(in)m(t)g Ft(N)p FD(,)g(const)g(v)m(oid)f(*)h Ft(Ap)p FD(,)g(v)m(oid)g(*)g Ft(x)p FD(,)g(const)g(in)m(t)g Ft(incx)p Fu(\))p eop end %%Page: 564 582 TeXDict begin 564 581 bop 150 -116 a FK(App)s(endix)29 b(D:)i(GSL)f(CBLAS)f(Library)2080 b(564)3350 299 y([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_ztrsv)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 299 28 4 v 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 408 y(CBLAS)p 877 408 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(en)m(um)f(CBLAS)p 2258 408 V 40 w(TRANSPOSE)e Ft(TransA)p FD(,)33 b(const)e(en)m(um)565 518 y(CBLAS)p 877 518 V 40 w(DIA)m(G)g Ft(Diag)p FD(,)h(const)f(in)m(t) g Ft(N)p FD(,)g(const)g(v)m(oid)f(*)h Ft(A)p FD(,)g(const)g(in)m(t)g Ft(lda)p FD(,)g(v)m(oid)g(*)g Ft(x)p FD(,)g(const)565 628 y(in)m(t)g Ft(incx)p Fu(\))3350 809 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_ztbsv)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 809 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 919 y(CBLAS)p 877 919 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(en)m(um)f (CBLAS)p 2258 919 V 40 w(TRANSPOSE)e Ft(TransA)p FD(,)33 b(const)e(en)m(um)565 1028 y(CBLAS)p 877 1028 V 40 w(DIA)m(G)g Ft(Diag)p FD(,)h(const)f(in)m(t)g Ft(N)p FD(,)g(const)g(in)m(t)f Ft(K)p FD(,)h(const)g(v)m(oid)g(*)g Ft(A)p FD(,)g(const)g(in)m(t)f Ft(lda)p FD(,)565 1138 y(v)m(oid)h(*)g Ft(x)p FD(,)g(const)g(in)m(t)f Ft(incx)p Fu(\))3350 1319 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_ztpsv)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 1319 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 1429 y(CBLAS)p 877 1429 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(en)m(um) f(CBLAS)p 2258 1429 V 40 w(TRANSPOSE)e Ft(TransA)p FD(,)33 b(const)e(en)m(um)565 1539 y(CBLAS)p 877 1539 V 40 w(DIA)m(G)g Ft(Diag)p FD(,)h(const)f(in)m(t)g Ft(N)p FD(,)g(const)g(v)m(oid)f(*)h Ft(Ap)p FD(,)g(v)m(oid)g(*)g Ft(x)p FD(,)g(const)g(in)m(t)g Ft(incx)p Fu(\))3350 1720 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_ssymv)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 1720 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 1830 y(CBLAS)p 877 1830 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(in)m(t)g Ft(N)p FD(,)g(const)g(\015oat)g Ft(alpha)p FD(,)h(const)f(\015oat)g(*)g Ft(A)p FD(,)g(const)f(in)m(t)565 1939 y Ft(lda)p FD(,)h(const)e (\015oat)h(*)f Ft(x)p FD(,)h(const)g(in)m(t)f Ft(incx)p FD(,)i(const)f(\015oat)f Ft(beta)p FD(,)i(\015oat)f(*)f Ft(y)p FD(,)h(const)g(in)m(t)f Ft(incy)p Fu(\))3350 2121 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_ssbmv)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 2121 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 2231 y(CBLAS)p 877 2231 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(in)m(t)g Ft(N)p FD(,)g(const)g(in)m(t)g Ft(K)p FD(,)g(const)f(\015oat)i Ft(alpha)p FD(,)g(const)e(\015oat)i(*)565 2340 y Ft(A)p FD(,)f(const)g(in)m(t)g Ft(lda)p FD(,)g(const)g(\015oat)g(*)g Ft(x)p FD(,)g(const)g(in)m(t)g Ft(incx)p FD(,)g(const)g(\015oat)g Ft(beta)p FD(,)h(\015oat)f(*)g Ft(y)p FD(,)565 2450 y(const)g(in)m(t)g Ft(incy)p Fu(\))3350 2631 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_sspmv)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 2631 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 2741 y(CBLAS)p 877 2741 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(in)m(t)g Ft(N)p FD(,)g(const)g(\015oat)g Ft(alpha)p FD(,)h(const)f(\015oat)g(*)g Ft(Ap)p FD(,)g(const)565 2850 y(\015oat)g(*)g Ft(x)p FD(,)g(const)g(in)m(t)g Ft(incx)p FD(,)g(const)g(\015oat)g Ft(beta)p FD(,)h(\015oat)f(*)g Ft(y)p FD(,)g(const)g(in)m(t)g Ft(incy)p Fu(\))3350 3032 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_sger)48 b Fu(\()p FD(const)31 b(en)m(um)f(CBLAS)p 1810 3032 V 40 w(ORDER)g Ft(order)p FD(,)i(const)f(in)m(t)g Ft(M)p FD(,)565 3142 y(const)g(in)m(t)g Ft(N)p FD(,)g(const)g(\015oat)g Ft(alpha)p FD(,)h(const)f(\015oat)g(*)f Ft(x)p FD(,)h(const)g(in)m(t)g Ft(incx)p FD(,)h(const)f(\015oat)g(*)g Ft(y)p FD(,)565 3251 y(const)g(in)m(t)g Ft(incy)p FD(,)h(\015oat)f(*)f Ft(A)p FD(,)h(const)g(in)m(t)g Ft(lda)p Fu(\))3350 3433 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_ssyr)48 b Fu(\()p FD(const)31 b(en)m(um)f(CBLAS)p 1810 3433 V 40 w(ORDER)g Ft(order)p FD(,)i(const)f(en)m(um)565 3542 y(CBLAS)p 877 3542 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(in)m(t)g Ft(N)p FD(,)g(const)g(\015oat)g Ft(alpha)p FD(,)h(const)f(\015oat)g(*)g Ft(x)p FD(,)g(const)f(in)m(t)565 3652 y Ft(incx)p FD(,)i(\015oat)f(*)g Ft(A)p FD(,)g(const)f(in)m(t)h Ft(lda)p Fu(\))3350 3833 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_sspr)48 b Fu(\()p FD(const)31 b(en)m(um)f(CBLAS)p 1810 3833 V 40 w(ORDER)g Ft(order)p FD(,)i(const)f(en)m(um)565 3943 y(CBLAS)p 877 3943 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(in)m(t)g Ft(N)p FD(,)g(const)g(\015oat)g Ft(alpha)p FD(,)h(const)f(\015oat)g(*)g Ft(x)p FD(,)g(const)f(in)m(t)565 4053 y Ft(incx)p FD(,)i(\015oat)f(*)g Ft(Ap)p Fu(\))3350 4234 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_ssyr2)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 4234 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 4344 y(CBLAS)p 877 4344 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(in)m(t)g Ft(N)p FD(,)g(const)g(\015oat)g Ft(alpha)p FD(,)h(const)f(\015oat)g(*)g Ft(x)p FD(,)g(const)f(in)m(t)565 4453 y Ft(incx)p FD(,)i(const)f (\015oat)g(*)g Ft(y)p FD(,)f(const)h(in)m(t)g Ft(incy)p FD(,)h(\015oat)f(*)g Ft(A)p FD(,)g(const)g(in)m(t)f Ft(lda)p Fu(\))3350 4635 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_sspr2)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 4635 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 4744 y(CBLAS)p 877 4744 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(in)m(t)g Ft(N)p FD(,)g(const)g(\015oat)g Ft(alpha)p FD(,)h(const)f(\015oat)g(*)g Ft(x)p FD(,)g(const)f(in)m(t)565 4854 y Ft(incx)p FD(,)i(const)f (\015oat)g(*)g Ft(y)p FD(,)f(const)h(in)m(t)g Ft(incy)p FD(,)h(\015oat)f(*)g Ft(A)p Fu(\))3350 5036 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_dsymv)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 5036 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 5145 y(CBLAS)p 877 5145 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(in)m(t)g Ft(N)p FD(,)g(const)g(double)f Ft(alpha)p FD(,)i(const)f(double)f(*)g Ft(A)p FD(,)h(const)565 5255 y(in)m(t)g Ft(lda)p FD(,)g(const)g(double) f(*)g Ft(x)p FD(,)h(const)g(in)m(t)g Ft(incx)p FD(,)g(const)g(double)f Ft(beta)p FD(,)h(double)f(*)h Ft(y)p FD(,)f(const)565 5364 y(in)m(t)h Ft(incy)p Fu(\))p eop end %%Page: 565 583 TeXDict begin 565 582 bop 150 -116 a FK(App)s(endix)29 b(D:)i(GSL)f(CBLAS)f(Library)2080 b(565)3350 299 y([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_dsbmv)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 299 28 4 v 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 408 y(CBLAS)p 877 408 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(in)m(t)g Ft(N)p FD(,)g(const)g(in)m(t)g Ft(K)p FD(,)g(const)f(double)g Ft(alpha)p FD(,)i(const)565 518 y(double)e(*)h Ft(A)p FD(,)f(const)h(in)m(t)g Ft(lda)p FD(,)g(const)g(double)f(*)g Ft(x)p FD(,)h(const)g(in)m(t)f Ft(incx)p FD(,)i(const)f(double)f Ft(beta)p FD(,)565 628 y(double)g(*)h Ft(y)p FD(,)g(const)g(in)m(t)f Ft(incy)p Fu(\))3350 820 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_dspmv)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 820 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 930 y(CBLAS)p 877 930 V 40 w(UPLO)d Ft(Uplo)p FD(,)i(const)f(in)m(t)g Ft(N)p FD(,)g(const)h(double)e Ft(alpha)p FD(,)i(const)g(double)e(*)h Ft(Ap)p FD(,)g(const)565 1039 y(double)h(*)h Ft(x)p FD(,)g(const)g(in)m (t)f Ft(incx)p FD(,)i(const)f(double)f Ft(beta)p FD(,)i(double)e(*)g Ft(y)p FD(,)h(const)g(in)m(t)g Ft(incy)p Fu(\))3350 1232 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_dger)48 b Fu(\()p FD(const)31 b(en)m(um)f(CBLAS)p 1810 1232 V 40 w(ORDER)g Ft(order)p FD(,)i(const)f(in)m(t)g Ft(M)p FD(,)565 1341 y(const)g(in)m(t)f Ft(N)p FD(,)h(const)f(double)g Ft(alpha)p FD(,)i(const)e(double)g(*)h Ft(x)p FD(,)f(const)h(in)m(t)f Ft(incx)p FD(,)i(const)e(double)565 1451 y(*)h Ft(y)p FD(,)g(const)g(in)m(t)f Ft(incy)p FD(,)i(double)e(*)h Ft(A)p FD(,)g(const)g(in)m(t)g Ft(lda)p Fu(\))3350 1643 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_dsyr)48 b Fu(\()p FD(const)31 b(en)m(um)f(CBLAS)p 1810 1643 V 40 w(ORDER)g Ft(order)p FD(,)i(const)f(en)m(um)565 1753 y(CBLAS)p 877 1753 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(in)m(t)g Ft(N)p FD(,)g(const)g(double)f Ft(alpha)p FD(,)i(const)f(double)f(*)g Ft(x)p FD(,)h(const)565 1863 y(in)m(t)g Ft(incx)p FD(,)h(double)e(*)g Ft(A)p FD(,)h(const)g(in)m(t)g Ft(lda)p Fu(\))3350 2055 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_dspr)48 b Fu(\()p FD(const)31 b(en)m(um)f(CBLAS)p 1810 2055 V 40 w(ORDER)g Ft(order)p FD(,)i(const)f(en)m(um)565 2165 y(CBLAS)p 877 2165 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(in)m(t)g Ft(N)p FD(,)g(const)g(double)f Ft(alpha)p FD(,)i(const)f(double)f(*)g Ft(x)p FD(,)h(const)565 2274 y(in)m(t)g Ft(incx)p FD(,)h(double)e(*)g Ft(Ap)p Fu(\))3350 2467 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_dsyr2)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 2467 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 2576 y(CBLAS)p 877 2576 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(in)m(t)g Ft(N)p FD(,)g(const)g(double)f Ft(alpha)p FD(,)i(const)f(double)f(*)g Ft(x)p FD(,)h(const)565 2686 y(in)m(t)g Ft(incx)p FD(,)h(const)f (double)f(*)g Ft(y)p FD(,)h(const)g(in)m(t)g Ft(incy)p FD(,)h(double)e(*)g Ft(A)p FD(,)h(const)g(in)m(t)g Ft(lda)p Fu(\))3350 2879 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_dspr2)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 2879 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 2988 y(CBLAS)p 877 2988 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(in)m(t)g Ft(N)p FD(,)g(const)g(double)f Ft(alpha)p FD(,)i(const)f(double)f(*)g Ft(x)p FD(,)h(const)565 3098 y(in)m(t)g Ft(incx)p FD(,)h(const)f (double)f(*)g Ft(y)p FD(,)h(const)g(in)m(t)g Ft(incy)p FD(,)h(double)e(*)g Ft(A)p Fu(\))3350 3290 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_chemv)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 3290 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 3400 y(CBLAS)p 877 3400 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(in)m(t)g Ft(N)p FD(,)g(const)g(v)m(oid)g(*)g Ft(alpha)p FD(,)h(const)f(v)m(oid)f (*)h Ft(A)p FD(,)g(const)g(in)m(t)565 3509 y Ft(lda)p FD(,)h(const)e(v)m(oid)h(*)g Ft(x)p FD(,)g(const)g(in)m(t)g Ft(incx)p FD(,)h(const)e(v)m(oid)h(*)g Ft(beta)p FD(,)h(v)m(oid)f(*)g Ft(y)p FD(,)g(const)f(in)m(t)565 3619 y Ft(incy)p Fu(\))3350 3811 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_chbmv)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 3811 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 3921 y(CBLAS)p 877 3921 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(in)m(t)g Ft(N)p FD(,)g(const)g(in)m(t)g Ft(K)p FD(,)g(const)f(v)m(oid)h(*)g Ft(alpha)p FD(,)h(const)f(v)m(oid)g(*)565 4031 y Ft(A)p FD(,)g(const)g(in)m(t)g Ft(lda)p FD(,)g(const)g(v)m(oid)g(*)g Ft(x)p FD(,)g(const)g(in)m(t)f Ft(incx)p FD(,)i(const)f(v)m(oid)g(*)g Ft(beta)p FD(,)h(v)m(oid)f(*)f Ft(y)p FD(,)565 4140 y(const)h(in)m(t)g Ft(incy)p Fu(\))3350 4333 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_chpmv)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 4333 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 4442 y(CBLAS)p 877 4442 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(in)m(t)g Ft(N)p FD(,)g(const)g(v)m(oid)g(*)g Ft(alpha)p FD(,)h(const)f(v)m(oid)f (*)h Ft(Ap)p FD(,)g(const)565 4552 y(v)m(oid)g(*)g Ft(x)p FD(,)g(const)g(in)m(t)f Ft(incx)p FD(,)i(const)f(v)m(oid)g(*)g Ft(beta)p FD(,)h(v)m(oid)f(*)f Ft(y)p FD(,)h(const)g(in)m(t)g Ft(incy)p Fu(\))3350 4744 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_cgeru)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 4744 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(in)m(t)g Ft(M)p FD(,)565 4854 y(const)g(in)m(t)g Ft(N)p FD(,)g(const)g(v)m(oid)g (*)f Ft(alpha)p FD(,)i(const)f(v)m(oid)g(*)g Ft(x)p FD(,)g(const)g(in)m (t)g Ft(incx)p FD(,)g(const)g(v)m(oid)g(*)g Ft(y)p FD(,)565 4964 y(const)g(in)m(t)g Ft(incy)p FD(,)h(v)m(oid)f(*)f Ft(A)p FD(,)h(const)g(in)m(t)g Ft(lda)p Fu(\))3350 5156 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_cgerc)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 5156 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(in)m(t)g Ft(M)p FD(,)565 5266 y(const)g(in)m(t)g Ft(N)p FD(,)g(const)g(v)m(oid)g(*)f Ft(alpha)p FD(,)i(const)f(v)m(oid)g(*)g Ft(x)p FD(,)g(const)g(in)m(t)g Ft(incx)p FD(,)g(const)g(v)m(oid)g(*)g Ft(y)p FD(,)565 5375 y(const)g(in)m(t)g Ft(incy)p FD(,)h(v)m(oid)f(*)f Ft(A)p FD(,)h(const)g(in)m(t)g Ft(lda)p Fu(\))p eop end %%Page: 566 584 TeXDict begin 566 583 bop 150 -116 a FK(App)s(endix)29 b(D:)i(GSL)f(CBLAS)f(Library)2080 b(566)3350 299 y([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_cher)48 b Fu(\()p FD(const)31 b(en)m(um)f(CBLAS)p 1810 299 28 4 v 40 w(ORDER)g Ft(order)p FD(,)i(const)f(en)m(um)565 408 y(CBLAS)p 877 408 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(in)m(t)g Ft(N)p FD(,)g(const)g(\015oat)g Ft(alpha)p FD(,)h(const)f(v)m(oid)g(*)g Ft(x)p FD(,)f(const)h(in)m(t)565 518 y Ft(incx)p FD(,)h(v)m(oid)f(*)g Ft(A)p FD(,)f(const)h(in)m(t)g Ft(lda)p Fu(\))3350 683 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_chpr)48 b Fu(\()p FD(const)31 b(en)m(um)f(CBLAS)p 1810 683 V 40 w(ORDER)g Ft(order)p FD(,)i(const)f(en)m(um)565 793 y(CBLAS)p 877 793 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(in)m(t)g Ft(N)p FD(,)g(const)g(\015oat)g Ft(alpha)p FD(,)h(const)f(v)m(oid)g(*)g Ft(x)p FD(,)f(const)h(in)m(t)565 902 y Ft(incx)p FD(,)h(v)m(oid)f(*)g Ft(A)p Fu(\))3350 1067 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_cher2)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 1067 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 1177 y(CBLAS)p 877 1177 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(in)m(t)g Ft(N)p FD(,)g(const)g(v)m(oid)g(*)g Ft(alpha)p FD(,)h(const)f(v)m(oid)f (*)h Ft(x)p FD(,)g(const)g(in)m(t)565 1286 y Ft(incx)p FD(,)h(const)f(v)m(oid)g(*)f Ft(y)p FD(,)h(const)g(in)m(t)g Ft(incy)p FD(,)h(v)m(oid)f(*)g Ft(A)p FD(,)f(const)h(in)m(t)g Ft(lda)p Fu(\))3350 1452 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_chpr2)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 1452 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 1561 y(CBLAS)p 877 1561 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(in)m(t)g Ft(N)p FD(,)g(const)g(v)m(oid)g(*)g Ft(alpha)p FD(,)h(const)f(v)m(oid)f (*)h Ft(x)p FD(,)g(const)g(in)m(t)565 1671 y Ft(incx)p FD(,)h(const)f(v)m(oid)g(*)f Ft(y)p FD(,)h(const)g(in)m(t)g Ft(incy)p FD(,)h(v)m(oid)f(*)g Ft(Ap)p Fu(\))3350 1836 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_zhemv)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 1836 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 1945 y(CBLAS)p 877 1945 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(in)m(t)g Ft(N)p FD(,)g(const)g(v)m(oid)g(*)g Ft(alpha)p FD(,)h(const)f(v)m(oid)f (*)h Ft(A)p FD(,)g(const)g(in)m(t)565 2055 y Ft(lda)p FD(,)h(const)e(v)m(oid)h(*)g Ft(x)p FD(,)g(const)g(in)m(t)g Ft(incx)p FD(,)h(const)e(v)m(oid)h(*)g Ft(beta)p FD(,)h(v)m(oid)f(*)g Ft(y)p FD(,)g(const)f(in)m(t)565 2164 y Ft(incy)p Fu(\))3350 2330 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_zhbmv)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 2330 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 2439 y(CBLAS)p 877 2439 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(in)m(t)g Ft(N)p FD(,)g(const)g(in)m(t)g Ft(K)p FD(,)g(const)f(v)m(oid)h(*)g Ft(alpha)p FD(,)h(const)f(v)m(oid)g(*)565 2549 y Ft(A)p FD(,)g(const)g(in)m(t)g Ft(lda)p FD(,)g(const)g(v)m(oid)g(*)g Ft(x)p FD(,)g(const)g(in)m(t)f Ft(incx)p FD(,)i(const)f(v)m(oid)g(*)g Ft(beta)p FD(,)h(v)m(oid)f(*)f Ft(y)p FD(,)565 2658 y(const)h(in)m(t)g Ft(incy)p Fu(\))3350 2823 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_zhpmv)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 2823 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 2933 y(CBLAS)p 877 2933 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(in)m(t)g Ft(N)p FD(,)g(const)g(v)m(oid)g(*)g Ft(alpha)p FD(,)h(const)f(v)m(oid)f (*)h Ft(Ap)p FD(,)g(const)565 3043 y(v)m(oid)g(*)g Ft(x)p FD(,)g(const)g(in)m(t)f Ft(incx)p FD(,)i(const)f(v)m(oid)g(*)g Ft(beta)p FD(,)h(v)m(oid)f(*)f Ft(y)p FD(,)h(const)g(in)m(t)g Ft(incy)p Fu(\))3350 3208 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_zgeru)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 3208 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(in)m(t)g Ft(M)p FD(,)565 3317 y(const)g(in)m(t)g Ft(N)p FD(,)g(const)g(v)m(oid)g (*)f Ft(alpha)p FD(,)i(const)f(v)m(oid)g(*)g Ft(x)p FD(,)g(const)g(in)m (t)g Ft(incx)p FD(,)g(const)g(v)m(oid)g(*)g Ft(y)p FD(,)565 3427 y(const)g(in)m(t)g Ft(incy)p FD(,)h(v)m(oid)f(*)f Ft(A)p FD(,)h(const)g(in)m(t)g Ft(lda)p Fu(\))3350 3592 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_zgerc)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 3592 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(in)m(t)g Ft(M)p FD(,)565 3701 y(const)g(in)m(t)g Ft(N)p FD(,)g(const)g(v)m(oid)g(*)f Ft(alpha)p FD(,)i(const)f(v)m(oid)g(*)g Ft(x)p FD(,)g(const)g(in)m(t)g Ft(incx)p FD(,)g(const)g(v)m(oid)g(*)g Ft(y)p FD(,)565 3811 y(const)g(in)m(t)g Ft(incy)p FD(,)h(v)m(oid)f(*)f Ft(A)p FD(,)h(const)g(in)m(t)g Ft(lda)p Fu(\))3350 3976 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_zher)48 b Fu(\()p FD(const)31 b(en)m(um)f(CBLAS)p 1810 3976 V 40 w(ORDER)g Ft(order)p FD(,)i(const)f(en)m(um)565 4086 y(CBLAS)p 877 4086 V 40 w(UPLO)e Ft(Uplo)p FD(,)i(const)f(in)m(t)g Ft(N)p FD(,)g(const)g(double)f Ft(alpha)p FD(,)i(const)f(v)m(oid)g(*)g Ft(x)p FD(,)g(const)g(in)m(t)565 4195 y Ft(incx)p FD(,)i(v)m(oid)f(*)g Ft(A)p FD(,)f(const)h(in)m(t)g Ft(lda)p Fu(\))3350 4360 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_zhpr)48 b Fu(\()p FD(const)31 b(en)m(um)f(CBLAS)p 1810 4360 V 40 w(ORDER)g Ft(order)p FD(,)i(const)f(en)m(um)565 4470 y(CBLAS)p 877 4470 V 40 w(UPLO)e Ft(Uplo)p FD(,)i(const)f(in)m(t)g Ft(N)p FD(,)g(const)g(double)f Ft(alpha)p FD(,)i(const)f(v)m(oid)g(*)g Ft(x)p FD(,)g(const)g(in)m(t)565 4579 y Ft(incx)p FD(,)i(v)m(oid)f(*)g Ft(A)p Fu(\))3350 4744 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_zher2)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 4744 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 4854 y(CBLAS)p 877 4854 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(in)m(t)g Ft(N)p FD(,)g(const)g(v)m(oid)g(*)g Ft(alpha)p FD(,)h(const)f(v)m(oid)f (*)h Ft(x)p FD(,)g(const)g(in)m(t)565 4964 y Ft(incx)p FD(,)h(const)f(v)m(oid)g(*)f Ft(y)p FD(,)h(const)g(in)m(t)g Ft(incy)p FD(,)h(v)m(oid)f(*)g Ft(A)p FD(,)f(const)h(in)m(t)g Ft(lda)p Fu(\))3350 5129 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_zhpr2)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 5129 V 40 w(ORDER)h Ft(order)p FD(,)i(const)f(en)m(um)565 5238 y(CBLAS)p 877 5238 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(in)m(t)g Ft(N)p FD(,)g(const)g(v)m(oid)g(*)g Ft(alpha)p FD(,)h(const)f(v)m(oid)f (*)h Ft(x)p FD(,)g(const)g(in)m(t)565 5348 y Ft(incx)p FD(,)h(const)f(v)m(oid)g(*)f Ft(y)p FD(,)h(const)g(in)m(t)g Ft(incy)p FD(,)h(v)m(oid)f(*)g Ft(Ap)p Fu(\))p eop end %%Page: 567 585 TeXDict begin 567 584 bop 150 -116 a FK(App)s(endix)29 b(D:)i(GSL)f(CBLAS)f(Library)2080 b(567)150 299 y FJ(D.3)68 b(Lev)l(el)46 b(3)3350 617 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_sgemm)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 617 28 4 v 40 w(ORDER)h Ft(Order)p FD(,)i(const)f(en)m(um)565 726 y(CBLAS)p 877 726 V 40 w(TRANSPOSE)d Ft(TransA)p FD(,)33 b(const)e(en)m(um)f(CBLAS)p 2670 726 V 39 w(TRANSPOSE)f Ft(TransB)p FD(,)565 836 y(const)i(in)m(t)f Ft(M)p FD(,)h(const)f(in)m (t)h Ft(N)p FD(,)f(const)h(in)m(t)f Ft(K)p FD(,)h(const)f(\015oat)h Ft(alpha)p FD(,)h(const)e(\015oat)h(*)f Ft(A)p FD(,)h(const)f(in)m(t) 565 945 y Ft(lda)p FD(,)i(const)e(\015oat)i(*)e Ft(B)p FD(,)h(const)g(in)m(t)g Ft(ldb)p FD(,)g(const)g(\015oat)g Ft(beta)p FD(,)h(\015oat)f(*)g Ft(C)p FD(,)g(const)g(in)m(t)g Ft(ldc)p Fu(\))3350 1213 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_ssymm)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 1213 V 40 w(ORDER)h Ft(Order)p FD(,)i(const)f(en)m(um)565 1323 y(CBLAS)p 877 1323 V 40 w(SIDE)f Ft(Side)p FD(,)h(const)g(en)m(um) f(CBLAS)p 2215 1323 V 40 w(UPLO)g Ft(Uplo)p FD(,)h(const)g(in)m(t)g Ft(M)p FD(,)g(const)g(in)m(t)g Ft(N)p FD(,)565 1432 y(const)g(\015oat)g Ft(alpha)p FD(,)h(const)f(\015oat)g(*)g Ft(A)p FD(,)g(const)g(in)m(t)f Ft(lda)p FD(,)i(const)f(\015oat)g(*)g Ft(B)p FD(,)f(const)h(in)m(t)g Ft(ldb)p FD(,)565 1542 y(const)g(\015oat)g Ft(beta)p FD(,)h(\015oat)f(*)g Ft(C)p FD(,)g(const)f(in)m(t)h Ft(ldc)p Fu(\))3350 1810 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_ssyrk)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 1810 V 40 w(ORDER)h Ft(Order)p FD(,)i(const)f(en)m(um)565 1919 y(CBLAS)p 877 1919 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(en)m(um) f(CBLAS)p 2258 1919 V 40 w(TRANSPOSE)e Ft(Trans)p FD(,)k(const)f(in)m (t)g Ft(N)p FD(,)565 2029 y(const)g(in)m(t)g Ft(K)p FD(,)g(const)g (\015oat)g Ft(alpha)p FD(,)h(const)f(\015oat)g(*)f Ft(A)p FD(,)h(const)g(in)m(t)g Ft(lda)p FD(,)h(const)e(\015oat)i Ft(beta)p FD(,)565 2139 y(\015oat)f(*)g Ft(C)p FD(,)g(const)g(in)m(t)g Ft(ldc)p Fu(\))3350 2407 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_ssyr2k)49 b Fu(\()p FD(const)31 b(en)m(um)f(CBLAS)p 1915 2407 V 39 w(ORDER)h Ft(Order)p FD(,)h(const)e(en)m(um)565 2516 y(CBLAS)p 877 2516 V 40 w(UPLO)g Ft(Uplo)p FD(,)h(const)g(en)m(um)f(CBLAS)p 2258 2516 V 40 w(TRANSPOSE)e Ft(Trans)p FD(,)k(const)f(in)m(t)g Ft(N)p FD(,)565 2626 y(const)g(in)m(t)g Ft(K)p FD(,)g(const)g(\015oat)g Ft(alpha)p FD(,)h(const)f(\015oat)g(*)f Ft(A)p FD(,)h(const)g(in)m(t)g Ft(lda)p FD(,)h(const)e(\015oat)i(*)e Ft(B)p FD(,)565 2735 y(const)h(in)m(t)g Ft(ldb)p FD(,)g(const)g(\015oat)g Ft(beta)p FD(,)h(\015oat)f(*)g Ft(C)p FD(,)g(const)g(in)m(t)g Ft(ldc)p Fu(\))3350 3003 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_strmm)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 3003 V 40 w(ORDER)h Ft(Order)p FD(,)i(const)f(en)m(um)565 3113 y(CBLAS)p 877 3113 V 40 w(SIDE)f Ft(Side)p FD(,)h(const)g(en)m(um) f(CBLAS)p 2215 3113 V 40 w(UPLO)g Ft(Uplo)p FD(,)h(const)g(en)m(um)565 3222 y(CBLAS)p 877 3222 V 40 w(TRANSPOSE)d Ft(TransA)p FD(,)33 b(const)e(en)m(um)f(CBLAS)p 2670 3222 V 39 w(DIA)m(G)i Ft(Diag)p FD(,)f(const)g(in)m(t)g Ft(M)p FD(,)565 3332 y(const)f(in)m(t)g Ft(N)p FD(,)g(const)g(\015oat)g Ft(alpha)p FD(,)h(const)f(\015oat)g(*)g Ft(A)p FD(,)f(const)h(in)m(t)g Ft(lda)p FD(,)h(\015oat)f(*)g Ft(B)p FD(,)g(const)f(in)m(t)565 3442 y Ft(ldb)p Fu(\))3350 3709 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_strsm)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 3709 V 40 w(ORDER)h Ft(Order)p FD(,)i(const)f(en)m(um)565 3819 y(CBLAS)p 877 3819 V 40 w(SIDE)f Ft(Side)p FD(,)h(const)g(en)m(um) f(CBLAS)p 2215 3819 V 40 w(UPLO)g Ft(Uplo)p FD(,)h(const)g(en)m(um)565 3929 y(CBLAS)p 877 3929 V 40 w(TRANSPOSE)d Ft(TransA)p FD(,)33 b(const)e(en)m(um)f(CBLAS)p 2670 3929 V 39 w(DIA)m(G)i Ft(Diag)p FD(,)f(const)g(in)m(t)g Ft(M)p FD(,)565 4038 y(const)f(in)m(t)g Ft(N)p FD(,)g(const)g(\015oat)g Ft(alpha)p FD(,)h(const)f(\015oat)g(*)g Ft(A)p FD(,)f(const)h(in)m(t)g Ft(lda)p FD(,)h(\015oat)f(*)g Ft(B)p FD(,)g(const)f(in)m(t)565 4148 y Ft(ldb)p Fu(\))3350 4416 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_dgemm)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 4416 V 40 w(ORDER)h Ft(Order)p FD(,)i(const)f(en)m(um)565 4525 y(CBLAS)p 877 4525 V 40 w(TRANSPOSE)d Ft(TransA)p FD(,)33 b(const)e(en)m(um)f(CBLAS)p 2670 4525 V 39 w(TRANSPOSE)f Ft(TransB)p FD(,)565 4635 y(const)i(in)m(t)g Ft(M)p FD(,)g(const)g(in)m (t)g Ft(N)p FD(,)f(const)h(in)m(t)g Ft(K)p FD(,)g(const)g(double)f Ft(alpha)p FD(,)i(const)f(double)f(*)g Ft(A)p FD(,)565 4744 y(const)h(in)m(t)g Ft(lda)p FD(,)g(const)g(double)f(*)h Ft(B)p FD(,)g(const)g(in)m(t)g Ft(ldb)p FD(,)g(const)g(double)f Ft(beta)p FD(,)i(double)e(*)g Ft(C)p FD(,)565 4854 y(const)h(in)m(t)g Ft(ldc)p Fu(\))3350 5122 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_dsymm)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 5122 V 40 w(ORDER)h Ft(Order)p FD(,)i(const)f(en)m(um)565 5231 y(CBLAS)p 877 5231 V 40 w(SIDE)f Ft(Side)p FD(,)h(const)g(en)m(um) f(CBLAS)p 2215 5231 V 40 w(UPLO)g Ft(Uplo)p FD(,)h(const)g(in)m(t)g Ft(M)p FD(,)g(const)g(in)m(t)g Ft(N)p FD(,)565 5341 y(const)g(double)f Ft(alpha)p FD(,)i(const)f(double)f(*)h Ft(A)p FD(,)f(const)h(in)m(t)g Ft(lda)p FD(,)h(const)f(double)e(*)i Ft(B)p FD(,)g(const)565 5451 y(in)m(t)g Ft(ldb)p FD(,)g(const)g(double)f Ft(beta)p FD(,)i(double)e(*)h Ft(C)p FD(,)g(const)f(in)m(t)h Ft(ldc)p Fu(\))p eop end %%Page: 568 586 TeXDict begin 568 585 bop 150 -116 a FK(App)s(endix)29 b(D:)i(GSL)f(CBLAS)f(Library)2080 b(568)3350 299 y([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_dsyrk)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 299 28 4 v 40 w(ORDER)h Ft(Order)p FD(,)i(const)f(en)m(um)565 408 y(CBLAS)p 877 408 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(en)m(um)f(CBLAS)p 2258 408 V 40 w(TRANSPOSE)e Ft(Trans)p FD(,)k(const)f(in)m(t)g Ft(N)p FD(,)565 518 y(const)g(in)m(t)g Ft(K)p FD(,)g(const)g(double)f Ft(alpha)p FD(,)i(const)e(double)g(*)h Ft(A)p FD(,)g(const)g(in)m(t)g Ft(lda)p FD(,)g(const)g(double)565 628 y Ft(beta)p FD(,)h(double)e(*)h Ft(C)p FD(,)f(const)h(in)m(t)g Ft(ldc)p Fu(\))3350 856 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_dsyr2k)49 b Fu(\()p FD(const)31 b(en)m(um)f(CBLAS)p 1915 856 V 39 w(ORDER)h Ft(Order)p FD(,)h(const)e(en)m(um)565 965 y(CBLAS)p 877 965 V 40 w(UPLO)g Ft(Uplo)p FD(,)h(const)g(en)m(um)f (CBLAS)p 2258 965 V 40 w(TRANSPOSE)e Ft(Trans)p FD(,)k(const)f(in)m(t)g Ft(N)p FD(,)565 1075 y(const)g(in)m(t)g Ft(K)p FD(,)g(const)g(double)f Ft(alpha)p FD(,)i(const)e(double)g(*)h Ft(A)p FD(,)g(const)g(in)m(t)g Ft(lda)p FD(,)g(const)g(double)565 1184 y(*)g Ft(B)p FD(,)g(const)g(in)m(t)f Ft(ldb)p FD(,)i(const)f(double)f Ft(beta)p FD(,)i(double)d(*)i Ft(C)p FD(,)g(const)g(in)m(t)g Ft(ldc)p Fu(\))3350 1412 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_dtrmm)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 1412 V 40 w(ORDER)h Ft(Order)p FD(,)i(const)f(en)m(um)565 1522 y(CBLAS)p 877 1522 V 40 w(SIDE)f Ft(Side)p FD(,)h(const)g(en)m(um) f(CBLAS)p 2215 1522 V 40 w(UPLO)g Ft(Uplo)p FD(,)h(const)g(en)m(um)565 1632 y(CBLAS)p 877 1632 V 40 w(TRANSPOSE)d Ft(TransA)p FD(,)33 b(const)e(en)m(um)f(CBLAS)p 2670 1632 V 39 w(DIA)m(G)i Ft(Diag)p FD(,)f(const)g(in)m(t)g Ft(M)p FD(,)565 1741 y(const)g(in)m(t)g Ft(N)p FD(,)g(const)g(double)f Ft(alpha)p FD(,)i(const)e(double)g(*)h Ft(A)p FD(,)g(const)g(in)m(t)g Ft(lda)p FD(,)g(double)f(*)h Ft(B)p FD(,)565 1851 y(const)g(in)m(t)g Ft(ldb)p Fu(\))3350 2079 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_dtrsm)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 2079 V 40 w(ORDER)h Ft(Order)p FD(,)i(const)f(en)m(um)565 2188 y(CBLAS)p 877 2188 V 40 w(SIDE)f Ft(Side)p FD(,)h(const)g(en)m(um) f(CBLAS)p 2215 2188 V 40 w(UPLO)g Ft(Uplo)p FD(,)h(const)g(en)m(um)565 2298 y(CBLAS)p 877 2298 V 40 w(TRANSPOSE)d Ft(TransA)p FD(,)33 b(const)e(en)m(um)f(CBLAS)p 2670 2298 V 39 w(DIA)m(G)i Ft(Diag)p FD(,)f(const)g(in)m(t)g Ft(M)p FD(,)565 2408 y(const)g(in)m(t)g Ft(N)p FD(,)g(const)g(double)f Ft(alpha)p FD(,)i(const)e(double)g(*)h Ft(A)p FD(,)g(const)g(in)m(t)g Ft(lda)p FD(,)g(double)f(*)h Ft(B)p FD(,)565 2517 y(const)g(in)m(t)g Ft(ldb)p Fu(\))3350 2745 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_cgemm)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 2745 V 40 w(ORDER)h Ft(Order)p FD(,)i(const)f(en)m(um)565 2855 y(CBLAS)p 877 2855 V 40 w(TRANSPOSE)d Ft(TransA)p FD(,)33 b(const)e(en)m(um)f(CBLAS)p 2670 2855 V 39 w(TRANSPOSE)f Ft(TransB)p FD(,)565 2964 y(const)f(in)m(t)f Ft(M)p FD(,)g(const)h(in)m (t)f Ft(N)p FD(,)h(const)f(in)m(t)g Ft(K)p FD(,)h(const)f(v)m(oid)h(*)f Ft(alpha)p FD(,)i(const)f(v)m(oid)f(*)h Ft(A)p FD(,)f(const)g(in)m(t) 565 3074 y Ft(lda)p FD(,)32 b(const)e(v)m(oid)h(*)g Ft(B)p FD(,)g(const)g(in)m(t)g Ft(ldb)p FD(,)g(const)g(v)m(oid)g(*)g Ft(beta)p FD(,)h(v)m(oid)f(*)f Ft(C)p FD(,)h(const)g(in)m(t)g Ft(ldc)p Fu(\))3350 3302 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_csymm)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 3302 V 40 w(ORDER)h Ft(Order)p FD(,)i(const)f(en)m(um)565 3412 y(CBLAS)p 877 3412 V 40 w(SIDE)f Ft(Side)p FD(,)h(const)g(en)m(um) f(CBLAS)p 2215 3412 V 40 w(UPLO)g Ft(Uplo)p FD(,)h(const)g(in)m(t)g Ft(M)p FD(,)g(const)g(in)m(t)g Ft(N)p FD(,)565 3521 y(const)e(v)m(oid)h (*)f Ft(alpha)p FD(,)h(const)g(v)m(oid)f(*)g Ft(A)p FD(,)g(const)g(in)m (t)h Ft(lda)p FD(,)g(const)f(v)m(oid)g(*)g Ft(B)p FD(,)g(const)h(in)m (t)f Ft(ldb)p FD(,)565 3631 y(const)i(v)m(oid)g(*)g Ft(beta)p FD(,)g(v)m(oid)g(*)g Ft(C)p FD(,)g(const)g(in)m(t)g Ft(ldc)p Fu(\))3350 3859 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_csyrk)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 3859 V 40 w(ORDER)h Ft(Order)p FD(,)i(const)f(en)m(um)565 3968 y(CBLAS)p 877 3968 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(en)m(um) f(CBLAS)p 2258 3968 V 40 w(TRANSPOSE)e Ft(Trans)p FD(,)k(const)f(in)m (t)g Ft(N)p FD(,)565 4078 y(const)g(in)m(t)g Ft(K)p FD(,)g(const)g(v)m (oid)g(*)f Ft(alpha)p FD(,)i(const)f(v)m(oid)g(*)g Ft(A)p FD(,)g(const)g(in)m(t)g Ft(lda)p FD(,)g(const)g(v)m(oid)g(*)565 4188 y Ft(beta)p FD(,)h(v)m(oid)f(*)g Ft(C)p FD(,)f(const)h(in)m(t)g Ft(ldc)p Fu(\))3350 4416 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_csyr2k)49 b Fu(\()p FD(const)31 b(en)m(um)f(CBLAS)p 1915 4416 V 39 w(ORDER)h Ft(Order)p FD(,)h(const)e(en)m(um)565 4525 y(CBLAS)p 877 4525 V 40 w(UPLO)g Ft(Uplo)p FD(,)h(const)g(en)m(um)f(CBLAS)p 2258 4525 V 40 w(TRANSPOSE)e Ft(Trans)p FD(,)k(const)f(in)m(t)g Ft(N)p FD(,)565 4635 y(const)g(in)m(t)g Ft(K)p FD(,)g(const)g(v)m(oid)g (*)f Ft(alpha)p FD(,)i(const)f(v)m(oid)g(*)g Ft(A)p FD(,)g(const)g(in)m (t)g Ft(lda)p FD(,)g(const)g(v)m(oid)g(*)g Ft(B)p FD(,)565 4744 y(const)g(in)m(t)g Ft(ldb)p FD(,)g(const)g(v)m(oid)g(*)g Ft(beta)p FD(,)h(v)m(oid)f(*)f Ft(C)p FD(,)h(const)g(in)m(t)g Ft(ldc)p Fu(\))3350 4972 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_ctrmm)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 4972 V 40 w(ORDER)h Ft(Order)p FD(,)i(const)f(en)m(um)565 5082 y(CBLAS)p 877 5082 V 40 w(SIDE)f Ft(Side)p FD(,)h(const)g(en)m(um) f(CBLAS)p 2215 5082 V 40 w(UPLO)g Ft(Uplo)p FD(,)h(const)g(en)m(um)565 5192 y(CBLAS)p 877 5192 V 40 w(TRANSPOSE)d Ft(TransA)p FD(,)33 b(const)e(en)m(um)f(CBLAS)p 2670 5192 V 39 w(DIA)m(G)i Ft(Diag)p FD(,)f(const)g(in)m(t)g Ft(M)p FD(,)565 5301 y(const)g(in)m(t)g Ft(N)p FD(,)g(const)g(v)m(oid)g(*)f Ft(alpha)p FD(,)i(const)f(v)m(oid)g(*)g Ft(A)p FD(,)g(const)g(in)m(t)g Ft(lda)p FD(,)g(v)m(oid)g(*)g Ft(B)p FD(,)g(const)565 5411 y(in)m(t)g Ft(ldb)p Fu(\))p eop end %%Page: 569 587 TeXDict begin 569 586 bop 150 -116 a FK(App)s(endix)29 b(D:)i(GSL)f(CBLAS)f(Library)2080 b(569)3350 299 y([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_ctrsm)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 299 28 4 v 40 w(ORDER)h Ft(Order)p FD(,)i(const)f(en)m(um)565 408 y(CBLAS)p 877 408 V 40 w(SIDE)f Ft(Side)p FD(,)h(const)g(en)m(um)f(CBLAS)p 2215 408 V 40 w(UPLO)g Ft(Uplo)p FD(,)h(const)g(en)m(um)565 518 y(CBLAS)p 877 518 V 40 w(TRANSPOSE)d Ft(TransA)p FD(,)33 b(const)e(en)m(um)f(CBLAS)p 2670 518 V 39 w(DIA)m(G)i Ft(Diag)p FD(,)f(const)g(in)m(t)g Ft(M)p FD(,)565 628 y(const)g(in)m(t)g Ft(N)p FD(,)g(const)g(v)m(oid)g(*)f Ft(alpha)p FD(,)i(const)f(v)m(oid)g(*)g Ft(A)p FD(,)g(const)g(in)m(t)g Ft(lda)p FD(,)g(v)m(oid)g(*)g Ft(B)p FD(,)g(const)565 737 y(in)m(t)g Ft(ldb)p Fu(\))3350 965 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_zgemm)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 965 V 40 w(ORDER)h Ft(Order)p FD(,)i(const)f(en)m(um)565 1075 y(CBLAS)p 877 1075 V 40 w(TRANSPOSE)d Ft(TransA)p FD(,)33 b(const)e(en)m(um)f(CBLAS)p 2670 1075 V 39 w(TRANSPOSE)f Ft(TransB)p FD(,)565 1184 y(const)f(in)m(t)f Ft(M)p FD(,)g(const)h(in)m (t)f Ft(N)p FD(,)h(const)f(in)m(t)g Ft(K)p FD(,)h(const)f(v)m(oid)h(*)f Ft(alpha)p FD(,)i(const)f(v)m(oid)f(*)h Ft(A)p FD(,)f(const)g(in)m(t) 565 1294 y Ft(lda)p FD(,)32 b(const)e(v)m(oid)h(*)g Ft(B)p FD(,)g(const)g(in)m(t)g Ft(ldb)p FD(,)g(const)g(v)m(oid)g(*)g Ft(beta)p FD(,)h(v)m(oid)f(*)f Ft(C)p FD(,)h(const)g(in)m(t)g Ft(ldc)p Fu(\))3350 1522 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_zsymm)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 1522 V 40 w(ORDER)h Ft(Order)p FD(,)i(const)f(en)m(um)565 1632 y(CBLAS)p 877 1632 V 40 w(SIDE)f Ft(Side)p FD(,)h(const)g(en)m(um) f(CBLAS)p 2215 1632 V 40 w(UPLO)g Ft(Uplo)p FD(,)h(const)g(in)m(t)g Ft(M)p FD(,)g(const)g(in)m(t)g Ft(N)p FD(,)565 1741 y(const)e(v)m(oid)h (*)f Ft(alpha)p FD(,)h(const)g(v)m(oid)f(*)g Ft(A)p FD(,)g(const)g(in)m (t)h Ft(lda)p FD(,)g(const)f(v)m(oid)g(*)g Ft(B)p FD(,)g(const)h(in)m (t)f Ft(ldb)p FD(,)565 1851 y(const)i(v)m(oid)g(*)g Ft(beta)p FD(,)g(v)m(oid)g(*)g Ft(C)p FD(,)g(const)g(in)m(t)g Ft(ldc)p Fu(\))3350 2079 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_zsyrk)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 2079 V 40 w(ORDER)h Ft(Order)p FD(,)i(const)f(en)m(um)565 2188 y(CBLAS)p 877 2188 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(en)m(um) f(CBLAS)p 2258 2188 V 40 w(TRANSPOSE)e Ft(Trans)p FD(,)k(const)f(in)m (t)g Ft(N)p FD(,)565 2298 y(const)g(in)m(t)g Ft(K)p FD(,)g(const)g(v)m (oid)g(*)f Ft(alpha)p FD(,)i(const)f(v)m(oid)g(*)g Ft(A)p FD(,)g(const)g(in)m(t)g Ft(lda)p FD(,)g(const)g(v)m(oid)g(*)565 2408 y Ft(beta)p FD(,)h(v)m(oid)f(*)g Ft(C)p FD(,)f(const)h(in)m(t)g Ft(ldc)p Fu(\))3350 2636 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_zsyr2k)49 b Fu(\()p FD(const)31 b(en)m(um)f(CBLAS)p 1915 2636 V 39 w(ORDER)h Ft(Order)p FD(,)h(const)e(en)m(um)565 2745 y(CBLAS)p 877 2745 V 40 w(UPLO)g Ft(Uplo)p FD(,)h(const)g(en)m(um)f(CBLAS)p 2258 2745 V 40 w(TRANSPOSE)e Ft(Trans)p FD(,)k(const)f(in)m(t)g Ft(N)p FD(,)565 2855 y(const)g(in)m(t)g Ft(K)p FD(,)g(const)g(v)m(oid)g (*)f Ft(alpha)p FD(,)i(const)f(v)m(oid)g(*)g Ft(A)p FD(,)g(const)g(in)m (t)g Ft(lda)p FD(,)g(const)g(v)m(oid)g(*)g Ft(B)p FD(,)565 2964 y(const)g(in)m(t)g Ft(ldb)p FD(,)g(const)g(v)m(oid)g(*)g Ft(beta)p FD(,)h(v)m(oid)f(*)f Ft(C)p FD(,)h(const)g(in)m(t)g Ft(ldc)p Fu(\))3350 3192 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_ztrmm)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 3192 V 40 w(ORDER)h Ft(Order)p FD(,)i(const)f(en)m(um)565 3302 y(CBLAS)p 877 3302 V 40 w(SIDE)f Ft(Side)p FD(,)h(const)g(en)m(um) f(CBLAS)p 2215 3302 V 40 w(UPLO)g Ft(Uplo)p FD(,)h(const)g(en)m(um)565 3412 y(CBLAS)p 877 3412 V 40 w(TRANSPOSE)d Ft(TransA)p FD(,)33 b(const)e(en)m(um)f(CBLAS)p 2670 3412 V 39 w(DIA)m(G)i Ft(Diag)p FD(,)f(const)g(in)m(t)g Ft(M)p FD(,)565 3521 y(const)g(in)m(t)g Ft(N)p FD(,)g(const)g(v)m(oid)g(*)f Ft(alpha)p FD(,)i(const)f(v)m(oid)g(*)g Ft(A)p FD(,)g(const)g(in)m(t)g Ft(lda)p FD(,)g(v)m(oid)g(*)g Ft(B)p FD(,)g(const)565 3631 y(in)m(t)g Ft(ldb)p Fu(\))3350 3859 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_ztrsm)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 3859 V 40 w(ORDER)h Ft(Order)p FD(,)i(const)f(en)m(um)565 3968 y(CBLAS)p 877 3968 V 40 w(SIDE)f Ft(Side)p FD(,)h(const)g(en)m(um) f(CBLAS)p 2215 3968 V 40 w(UPLO)g Ft(Uplo)p FD(,)h(const)g(en)m(um)565 4078 y(CBLAS)p 877 4078 V 40 w(TRANSPOSE)d Ft(TransA)p FD(,)33 b(const)e(en)m(um)f(CBLAS)p 2670 4078 V 39 w(DIA)m(G)i Ft(Diag)p FD(,)f(const)g(in)m(t)g Ft(M)p FD(,)565 4188 y(const)g(in)m(t)g Ft(N)p FD(,)g(const)g(v)m(oid)g(*)f Ft(alpha)p FD(,)i(const)f(v)m(oid)g(*)g Ft(A)p FD(,)g(const)g(in)m(t)g Ft(lda)p FD(,)g(v)m(oid)g(*)g Ft(B)p FD(,)g(const)565 4297 y(in)m(t)g Ft(ldb)p Fu(\))3350 4525 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_chemm)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 4525 V 40 w(ORDER)h Ft(Order)p FD(,)i(const)f(en)m(um)565 4635 y(CBLAS)p 877 4635 V 40 w(SIDE)f Ft(Side)p FD(,)h(const)g(en)m(um) f(CBLAS)p 2215 4635 V 40 w(UPLO)g Ft(Uplo)p FD(,)h(const)g(in)m(t)g Ft(M)p FD(,)g(const)g(in)m(t)g Ft(N)p FD(,)565 4744 y(const)e(v)m(oid)h (*)f Ft(alpha)p FD(,)h(const)g(v)m(oid)f(*)g Ft(A)p FD(,)g(const)g(in)m (t)h Ft(lda)p FD(,)g(const)f(v)m(oid)g(*)g Ft(B)p FD(,)g(const)h(in)m (t)f Ft(ldb)p FD(,)565 4854 y(const)i(v)m(oid)g(*)g Ft(beta)p FD(,)g(v)m(oid)g(*)g Ft(C)p FD(,)g(const)g(in)m(t)g Ft(ldc)p Fu(\))3350 5082 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_cherk)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 5082 V 40 w(ORDER)h Ft(Order)p FD(,)i(const)f(en)m(um)565 5192 y(CBLAS)p 877 5192 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(en)m(um) f(CBLAS)p 2258 5192 V 40 w(TRANSPOSE)e Ft(Trans)p FD(,)k(const)f(in)m (t)g Ft(N)p FD(,)565 5301 y(const)g(in)m(t)g Ft(K)p FD(,)g(const)g (\015oat)g Ft(alpha)p FD(,)h(const)f(v)m(oid)g(*)f Ft(A)p FD(,)h(const)g(in)m(t)g Ft(lda)p FD(,)g(const)g(\015oat)g Ft(beta)p FD(,)565 5411 y(v)m(oid)g(*)g Ft(C)p FD(,)g(const)g(in)m(t)f Ft(ldc)p Fu(\))p eop end %%Page: 570 588 TeXDict begin 570 587 bop 150 -116 a FK(App)s(endix)29 b(D:)i(GSL)f(CBLAS)f(Library)2080 b(570)3350 299 y([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_cher2k)49 b Fu(\()p FD(const)31 b(en)m(um)f(CBLAS)p 1915 299 28 4 v 39 w(ORDER)h Ft(Order)p FD(,)h(const)e(en)m(um)565 408 y(CBLAS)p 877 408 V 40 w(UPLO)g Ft(Uplo)p FD(,)h(const)g(en)m(um)f(CBLAS)p 2258 408 V 40 w(TRANSPOSE)e Ft(Trans)p FD(,)k(const)f(in)m(t)g Ft(N)p FD(,)565 518 y(const)g(in)m(t)g Ft(K)p FD(,)g(const)g(v)m(oid)g (*)f Ft(alpha)p FD(,)i(const)f(v)m(oid)g(*)g Ft(A)p FD(,)g(const)g(in)m (t)g Ft(lda)p FD(,)g(const)g(v)m(oid)g(*)g Ft(B)p FD(,)565 628 y(const)g(in)m(t)g Ft(ldb)p FD(,)g(const)g(\015oat)g Ft(beta)p FD(,)h(v)m(oid)f(*)g Ft(C)p FD(,)g(const)g(in)m(t)f Ft(ldc)p Fu(\))3350 784 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_zhemm)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 784 V 40 w(ORDER)h Ft(Order)p FD(,)i(const)f(en)m(um)565 893 y(CBLAS)p 877 893 V 40 w(SIDE)f Ft(Side)p FD(,)h(const)g(en)m(um)f (CBLAS)p 2215 893 V 40 w(UPLO)g Ft(Uplo)p FD(,)h(const)g(in)m(t)g Ft(M)p FD(,)g(const)g(in)m(t)g Ft(N)p FD(,)565 1003 y(const)e(v)m(oid)h (*)f Ft(alpha)p FD(,)h(const)g(v)m(oid)f(*)g Ft(A)p FD(,)g(const)g(in)m (t)h Ft(lda)p FD(,)g(const)f(v)m(oid)g(*)g Ft(B)p FD(,)g(const)h(in)m (t)f Ft(ldb)p FD(,)565 1112 y(const)i(v)m(oid)g(*)g Ft(beta)p FD(,)g(v)m(oid)g(*)g Ft(C)p FD(,)g(const)g(in)m(t)g Ft(ldc)p Fu(\))3350 1268 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_zherk)48 b Fu(\()p FD(const)32 b(en)m(um)d(CBLAS)p 1862 1268 V 40 w(ORDER)h Ft(Order)p FD(,)i(const)f(en)m(um)565 1378 y(CBLAS)p 877 1378 V 40 w(UPLO)f Ft(Uplo)p FD(,)h(const)g(en)m(um) f(CBLAS)p 2258 1378 V 40 w(TRANSPOSE)e Ft(Trans)p FD(,)k(const)f(in)m (t)g Ft(N)p FD(,)565 1488 y(const)g(in)m(t)g Ft(K)p FD(,)g(const)g (double)f Ft(alpha)p FD(,)i(const)e(v)m(oid)h(*)g Ft(A)p FD(,)g(const)g(in)m(t)g Ft(lda)p FD(,)g(const)g(double)565 1597 y Ft(beta)p FD(,)h(v)m(oid)f(*)g Ft(C)p FD(,)f(const)h(in)m(t)g Ft(ldc)p Fu(\))3350 1753 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_zher2k)49 b Fu(\()p FD(const)31 b(en)m(um)f(CBLAS)p 1915 1753 V 39 w(ORDER)h Ft(Order)p FD(,)h(const)e(en)m(um)565 1863 y(CBLAS)p 877 1863 V 40 w(UPLO)g Ft(Uplo)p FD(,)h(const)g(en)m(um)f(CBLAS)p 2258 1863 V 40 w(TRANSPOSE)e Ft(Trans)p FD(,)k(const)f(in)m(t)g Ft(N)p FD(,)565 1972 y(const)g(in)m(t)g Ft(K)p FD(,)g(const)g(v)m(oid)g (*)f Ft(alpha)p FD(,)i(const)f(v)m(oid)g(*)g Ft(A)p FD(,)g(const)g(in)m (t)g Ft(lda)p FD(,)g(const)g(v)m(oid)g(*)g Ft(B)p FD(,)565 2082 y(const)g(in)m(t)g Ft(ldb)p FD(,)g(const)g(double)f Ft(beta)p FD(,)i(v)m(oid)f(*)g Ft(C)p FD(,)g(const)f(in)m(t)h Ft(ldc)p Fu(\))3350 2238 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(cblas_xerbla)49 b Fu(\()p FD(in)m(t)31 b Ft(p)p FD(,)g(const)g(c)m(har)f(*)h Ft(rout)p FD(,)h(const)f(c)m(har) f(*)h Ft(form)p FD(,)h(...)p Fu(\))150 2444 y FJ(D.4)68 b(Examples)150 2603 y FK(The)29 b(follo)m(wing)i(program)e(computes)h (the)f(pro)s(duct)g(of)g(t)m(w)m(o)i(matrices)f(using)f(the)h(Lev)m (el-3)h FC(blas)e FK(func-)150 2713 y(tion)i FC(sgemm)p FK(,)783 2855 y Fs(\022)859 2919 y FK(0)p FE(:)p FK(11)93 b(0)p FE(:)p FK(12)f(0)p FE(:)p FK(13)859 3028 y(0)p FE(:)p FK(21)h(0)p FE(:)p FK(22)f(0)p FE(:)p FK(23)1541 2855 y Fs(\023)1617 2805 y(0)1617 2954 y(@)1705 2864 y FK(1011)h(1012)1705 2974 y(1021)g(1022)1705 3083 y(1031)g(1032)2175 2805 y Fs(1)2175 2954 y(A)2273 2974 y FK(=)2369 2855 y Fs(\022)2445 2919 y FK(367)p FE(:)p FK(76)g(368)p FE(:)p FK(12)2445 3028 y(674)p FE(:)p FK(06)g(674)p FE(:)p FK(72)3056 2855 y Fs(\023)150 3235 y FK(The)33 b(matrices)i(are)f(stored)g(in)f (ro)m(w)h(ma)5 b(jor)34 b(order)f(but)g(could)g(b)s(e)g(stored)h(in)g (column)f(ma)5 b(jor)34 b(order)f(if)150 3344 y(the)e(\014rst)e (argumen)m(t)i(of)g(the)f(call)i(to)f FH(cblas_sgemm)c FK(w)m(as)k(c)m(hanged)g(to)g FH(CblasColMajor)p FK(.)390 3477 y FH(#include)46 b()390 3587 y(#include)g ()390 3806 y(int)390 3915 y(main)h(\(void\))390 4025 y({)485 4134 y(int)g(lda)g(=)h(3;)485 4354 y(float)f(A[])g(=)g({)h (0.11,)e(0.12,)g(0.13,)1154 4463 y(0.21,)g(0.22,)g(0.23)h(};)485 4682 y(int)g(ldb)g(=)h(2;)485 4902 y(float)f(B[])g(=)g({)h(1011,)e (1012,)1154 5011 y(1021,)g(1022,)1154 5121 y(1031,)g(1032)h(};)485 5340 y(int)g(ldc)g(=)h(2;)p eop end %%Page: 571 589 TeXDict begin 571 588 bop 150 -116 a FK(App)s(endix)29 b(D:)i(GSL)f(CBLAS)f(Library)2080 b(571)485 408 y FH(float)47 b(C[])g(=)g({)h(0.00,)e(0.00,)1154 518 y(0.00,)g(0.00)h(};)485 737 y(/*)h(Compute)d(C)j(=)f(A)h(B)f(*/)485 956 y(cblas_sgemm)e (\(CblasRowMajor,)1106 1066 y(CblasNoTrans,)f(CblasNoTrans,)g(2,)j(2,)h (3,)1106 1176 y(1.0,)f(A,)g(lda,)f(B,)i(ldb,)e(0.0,)h(C,)g(ldc\);)485 1395 y(printf)g(\("[)f(\045g,)h(\045g\\n",)f(C[0],)h(C[1]\);)485 1504 y(printf)g(\(")94 b(\045g,)47 b(\045g)h(]\\n",)e(C[2],)g(C[3]\);) 485 1724 y(return)h(0;)390 1833 y(})150 1968 y FK(T)-8 b(o)31 b(compile)g(the)g(program)f(use)g(the)h(follo)m(wing)g(command)f (line,)390 2102 y FH($)47 b(gcc)g(-Wall)g(demo.c)f(-lgslcblas)150 2237 y FK(There)27 b(is)h(no)g(need)g(to)g(link)g(with)g(the)g(main)g (library)f FH(-lgsl)g FK(in)g(this)h(case)h(as)f(the)g FC(cblas)f FK(library)g(is)h(an)150 2346 y(indep)s(enden)m(t)h(unit.)40 b(Here)31 b(is)g(the)f(output)g(from)g(the)h(program,)390 2481 y FH($)47 b(./a.out)390 2590 y([)g(367.76,)f(368.12)485 2700 y(674.06,)g(674.72)g(])p eop end %%Page: 572 590 TeXDict begin 572 589 bop 150 -116 a FK(GNU)31 b(General)g(Public)f (License)2314 b(572)150 299 y FG(GNU)54 b(General)f(Public)f(License) 1477 509 y FK(V)-8 b(ersion)31 b(3,)g(29)g(June)e(2007)390 613 y Ff(Cop)n(yrigh)n(t)741 611 y(c)721 613 y Fe(\015)23 b Ff(2007)i(F)-6 b(ree)24 b(Soft)n(w)n(are)g(F)-6 b(oundation,)25 b(Inc.)f Fd(http://fsf.org/)390 770 y Ff(Ev)n(ery)n(one)h(is)e(p)r (ermitted)h(to)g(cop)n(y)h(and)f(distribute)g(v)n(erbatim)g(copies)g (of)g(this)390 849 y(license)g(do)r(cumen)n(t,)h(but)f(c)n(hanging)h (it)f(is)f(not)h(allo)n(w)n(ed.)150 1082 y FJ(Pream)l(ble)150 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(whic)n(h)g(is)f(not)i(part)f(of)g(that)h(Ma)t(jor)e(Comp)r(onen)n(t,) 330 1596 y(and)g(\(b\))h(serv)n(es)f(only)g(to)g(enable)g(use)g(of)g (the)g(w)n(ork)g(with)g(that)h(Ma)t(jor)d(Comp)r(onen)n(t,)k(or)d(to)i (implemen)n(t)f(a)g(Standard)g(In)n(terface)330 1675 y(for)29 b(whic)n(h)h(an)g(implemen)n(tation)h(is)e(a)n(v)l(ailable)h (to)h(the)f(public)g(in)g(source)g(co)r(de)h(form.)48 b(A)30 b(\\Ma)t(jor)f(Comp)r(onen)n(t",)j(in)e(this)330 1754 y(con)n(text,)39 b(means)c(a)g(ma)t(jor)f(essen)n(tial)h(comp)r (onen)n(t)i(\(k)n(ernel,)g(windo)n(w)e(system,)i(and)f(so)e(on\))i(of)e (the)h(sp)r(eci\014c)h(op)r(erating)330 1833 y(system)25 b(\(if)f(an)n(y\))h(on)g(whic)n(h)g(the)g(executable)i(w)n(ork)e(runs,) e(or)i(a)f(compiler)g(used)h(to)g(pro)r(duce)h(the)f(w)n(ork,)f(or)g (an)h(ob)t(ject)h(co)r(de)330 1911 y(in)n(terpreter)e(used)g(to)g(run)g (it.)330 2013 y(The)31 b(\\Corresp)r(onding)h(Source")g(for)e(a)h(w)n (ork)g(in)g(ob)t(ject)h(co)r(de)g(form)e(means)i(all)e(the)i(source)f 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b(to)g(require,)g(suc)n(h)f(as)h(b)n(y)f(in)n (timate)h(data)h(comm)n(unication)f(or)f(con)n(trol)h(\015o)n(w)g(b)r (et)n(w)n(een)h(those)f(subprograms)f(and)330 2565 y(other)d(parts)g (of)f(the)i(w)n(ork.)330 2667 y(The)f(Corresp)r(onding)f(Source)h(need) g(not)g(include)g(an)n(ything)g(that)h(users)e(can)g(regenerate)i (automatically)g(from)d(other)i(parts)330 2746 y(of)f(the)i(Corresp)r (onding)f(Source.)330 2847 y(The)g(Corresp)r(onding)g(Source)g(for)f(a) h(w)n(ork)g(in)f(source)h(co)r(de)h(form)d(is)h(that)i(same)f(w)n(ork.) 215 2949 y(2.)60 b(Basic)24 b(P)n(ermissions.)330 3051 y(All)d(righ)n(ts)i(gran)n(ted)g(under)g(this)f(License)h(are)g(gran)n (ted)g(for)f(the)h(term)g(of)f(cop)n(yrigh)n(t)h(on)g(the)g(Program,)f (and)h(are)g(irrev)n(o)r(cable)330 3130 y(pro)n(vided)29 b(the)g(stated)h(conditions)g(are)e(met.)46 b(This)28 b(License)h(explicitly)g(a\016rms)e(y)n(our)i(unlimited)f(p)r (ermission)g(to)h(run)f(the)330 3209 y(unmo)r(di\014ed)18 b(Program.)28 b(The)17 b(output)i(from)d(running)h(a)g(co)n(v)n(ered)h (w)n(ork)f(is)f(co)n(v)n(ered)i(b)n(y)g(this)e(License)i(only)f(if)f (the)i(output,)h(giv)n(en)330 3287 y(its)26 b(con)n(ten)n(t,)j (constitutes)f(a)e(co)n(v)n(ered)i(w)n(ork.)39 b(This)26 b(License)h(ac)n(kno)n(wledges)h(y)n(our)e(righ)n(ts)g(of)g(fair)f(use) i(or)f(other)h(equiv)l(alen)n(t,)330 3366 y(as)d(pro)n(vided)g(b)n(y)g (cop)n(yrigh)n(t)h(la)n(w.)330 3468 y(Y)-6 b(ou)27 b(ma)n(y)f(mak)n(e,) i(run)e(and)h(propagate)h(co)n(v)n(ered)g(w)n(orks)e(that)h(y)n(ou)g (do)g(not)g(con)n(v)n(ey)-6 b(,)29 b(without)e(conditions)g(so)g(long)f (as)h(y)n(our)330 3547 y(license)22 b(otherwise)f(remains)g(in)g (force.)31 b(Y)-6 b(ou)21 b(ma)n(y)h(con)n(v)n(ey)h(co)n(v)n(ered)g(w)n (orks)e(to)h(others)g(for)e(the)j(sole)e(purp)r(ose)h(of)f(ha)n(ving)h (them)330 3626 y(mak)n(e)f(mo)r(di\014cations)h(exclusiv)n(ely)f(for)f (y)n(ou,)h(or)f(pro)n(vide)h(y)n(ou)g(with)g(facilities)f(for)g (running)g(those)i(w)n(orks,)e(pro)n(vided)h(that)h(y)n(ou)330 3705 y(comply)j(with)g(the)g(terms)f(of)h(this)f(License)h(in)g(con)n (v)n(eying)h(all)e(material)g(for)g(whic)n(h)h(y)n(ou)g(do)g(not)g(con) n(trol)g(cop)n(yrigh)n(t.)35 b(Those)330 3783 y(th)n(us)25 b(making)g(or)f(running)h(the)g(co)n(v)n(ered)h(w)n(orks)e(for)g(y)n (ou)h(m)n(ust)g(do)g(so)g(exclusiv)n(ely)g(on)g(y)n(our)f(b)r(ehalf,)h (under)g(y)n(our)f(direction)330 3862 y(and)29 b(con)n(trol,)h(on)f (terms)f(that)i(prohibit)f(them)g(from)f(making)h(an)n(y)g(copies)g(of) f(y)n(our)h(cop)n(yrigh)n(ted)h(material)e(outside)i(their)330 3941 y(relationship)24 b(with)f(y)n(ou.)330 4043 y(Con)n(v)n(eying)k (under)f(an)n(y)h(other)g(circumstances)g(is)e(p)r(ermitted)h(solely)g (under)g(the)h(conditions)g(stated)g(b)r(elo)n(w.)38 b(Sublicensing)330 4122 y(is)23 b(not)h(allo)n(w)n(ed;)g(section)h(10)f (mak)n(es)g(it)f(unnecessary)-6 b(.)215 4223 y(3.)60 b(Protecting)25 b(Users')e(Legal)h(Righ)n(ts)g(F)-6 b(rom)23 b(An)n(ti-Circum)n(v)n(en)n(tion)h(La)n(w.)330 4325 y(No)h(co)n(v)n (ered)h(w)n(ork)f(shall)f(b)r(e)h(deemed)i(part)e(of)f(an)i(e\013ectiv) n(e)g(tec)n(hnological)h(measure)e(under)g(an)n(y)h(applicable)f(la)n (w)g(ful\014lling)330 4404 y(obligations)35 b(under)h(article)e(11)i (of)e(the)i(WIPO)g(cop)n(yrigh)n(t)g(treat)n(y)g(adopted)g(on)g(20)f (Decem)n(b)r(er)g(1996,)k(or)34 b(similar)f(la)n(ws)330 4483 y(prohibiting)24 b(or)f(restricting)h(circum)n(v)n(en)n(tion)g(of) g(suc)n(h)g(measures.)330 4585 y(When)g(y)n(ou)f(con)n(v)n(ey)i(a)e(co) n(v)n(ered)h(w)n(ork,)e(y)n(ou)i(w)n(aiv)n(e)f(an)n(y)g(legal)g(p)r(o)n (w)n(er)g(to)h(forbid)e(circum)n(v)n(en)n(tion)i(of)e(tec)n(hnological) j(measures)330 4663 y(to)g(the)g(exten)n(t)h(suc)n(h)f(circum)n(v)n(en) n(tion)g(is)f(e\013ected)i(b)n(y)e(exercising)h(righ)n(ts)f(under)g (this)h(License)f(with)h(resp)r(ect)g(to)g(the)g(co)n(v)n(ered)330 4742 y(w)n(ork,)j(and)g(y)n(ou)h(disclaim)d(an)n(y)j(in)n(ten)n(tion)g (to)f(limit)e(op)r(eration)j(or)e(mo)r(di\014cation)i(of)e(the)i(w)n (ork)e(as)h(a)g(means)g(of)f(enforcing,)330 4821 y(against)d(the)h(w)n (ork's)e(users,)g(y)n(our)h(or)f(third)g(parties')h(legal)f(righ)n(ts)h (to)g(forbid)f(circum)n(v)n(en)n(tion)i(of)e(tec)n(hnological)j (measures.)215 4923 y(4.)60 b(Con)n(v)n(eying)25 b(V)-6 b(erbatim)24 b(Copies.)330 5024 y(Y)-6 b(ou)33 b(ma)n(y)f(con)n(v)n(ey) i(v)n(erbatim)f(copies)g(of)f(the)h(Program's)e(source)i(co)r(de)g(as)g (y)n(ou)f(receiv)n(e)h(it,)h(in)e(an)n(y)h(medium,)h(pro)n(vided)330 5103 y(that)24 b(y)n(ou)g(conspicuously)g(and)f(appropriately)h (publish)f(on)g(eac)n(h)h(cop)n(y)g(an)f(appropriate)h(cop)n(yrigh)n(t) g(notice;)g(k)n(eep)g(in)n(tact)h(all)330 5182 y(notices)c(stating)g (that)g(this)f(License)g(and)h(an)n(y)f(non-p)r(ermissiv)n(e)g(terms)f (added)i(in)f(accord)h(with)f(section)h(7)f(apply)g(to)g(the)h(co)r (de;)330 5261 y(k)n(eep)26 b(in)n(tact)g(all)e(notices)h(of)f(the)i (absence)g(of)e(an)n(y)i(w)n(arran)n(t)n(y;)f(and)g(giv)n(e)g(all)f (recipien)n(ts)h(a)g(cop)n(y)g(of)g(this)f(License)i(along)f(with)330 5340 y(the)g(Program.)p eop end %%Page: 574 592 TeXDict begin 574 591 bop 150 -116 a FK(GNU)31 b(General)g(Public)f (License)2314 b(574)330 299 y Ff(Y)-6 b(ou)27 b(ma)n(y)h(c)n(harge)g (an)n(y)g(price)f(or)g(no)g(price)g(for)g(eac)n(h)h(cop)n(y)g(that)g(y) n(ou)g(con)n(v)n(ey)-6 b(,)30 b(and)d(y)n(ou)h(ma)n(y)g(o\013er)f(supp) r(ort)h(or)e(w)n(arran)n(t)n(y)330 378 y(protection)f(for)e(a)h(fee.) 215 483 y(5.)60 b(Con)n(v)n(eying)25 b(Mo)r(di\014ed)f(Source)g(V)-6 b(ersions.)330 587 y(Y)g(ou)28 b(ma)n(y)h(con)n(v)n(ey)h(a)e(w)n(ork)g (based)h(on)f(the)h(Program,)f(or)g(the)h(mo)r(di\014cations)g(to)g (pro)r(duce)g(it)f(from)f(the)i(Program,)f(in)g(the)330 666 y(form)23 b(of)g(source)h(co)r(de)h(under)f(the)g(terms)g(of)f (section)i(4,)e(pro)n(vided)h(that)h(y)n(ou)g(also)e(meet)i(all)e(of)g (these)i(conditions:)395 771 y(a.)60 b(The)24 b(w)n(ork)g(m)n(ust)f (carry)h(prominen)n(t)g(notices)h(stating)f(that)h(y)n(ou)g(mo)r (di\014ed)f(it,)f(and)h(giving)g(a)g(relev)l(an)n(t)g(date.)391 876 y(b.)60 b(The)25 b(w)n(ork)g(m)n(ust)h(carry)f(prominen)n(t)g (notices)h(stating)g(that)h(it)e(is)f(released)h(under)h(this)f (License)h(and)f(an)n(y)h(conditions)510 955 y(added)21 b(under)f(section)h(7.)30 b(This)19 b(requiremen)n(t)h(mo)r(di\014es)g (the)h(requiremen)n(t)f(in)g(section)g(4)g(to)h(\\k)n(eep)g(in)n(tact)g (all)e(notices".)399 1059 y(c.)60 b(Y)-6 b(ou)30 b(m)n(ust)f(license)g (the)h(en)n(tire)g(w)n(ork,)g(as)f(a)g(whole,)i(under)e(this)h(License) f(to)h(an)n(y)n(one)h(who)e(comes)h(in)n(to)g(p)r(ossession)510 1138 y(of)25 b(a)g(cop)n(y)-6 b(.)36 b(This)24 b(License)i(will)d (therefore)j(apply)-6 b(,)25 b(along)g(with)g(an)n(y)h(applicable)f (section)h(7)f(additional)h(terms,)e(to)i(the)510 1217 y(whole)21 b(of)f(the)h(w)n(ork,)f(and)h(all)f(its)g(parts,)h (regardless)f(of)g(ho)n(w)h(they)g(are)f(pac)n(k)l(aged.)33 b(This)19 b(License)j(giv)n(es)e(no)h(p)r(ermission)510 1296 y(to)29 b(license)g(the)g(w)n(ork)g(in)f(an)n(y)h(other)g(w)n(a)n (y)-6 b(,)30 b(but)g(it)e(do)r(es)h(not)g(in)n(v)l(alidate)h(suc)n(h)f (p)r(ermission)f(if)f(y)n(ou)i(ha)n(v)n(e)h(separately)510 1375 y(receiv)n(ed)25 b(it.)391 1480 y(d.)60 b(If)26 b(the)h(w)n(ork)f(has)g(in)n(teractiv)n(e)h(user)f(in)n(terfaces,)h (eac)n(h)g(m)n(ust)f(displa)n(y)g(Appropriate)g(Legal)g(Notices;)i(ho)n (w)n(ev)n(er,)f(if)e(the)510 1559 y(Program)k(has)i(in)n(teractiv)n(e)g (in)n(terfaces)f(that)i(do)e(not)h(displa)n(y)f(Appropriate)g(Legal)g (Notices,)i(y)n(our)e(w)n(ork)g(need)h(not)510 1637 y(mak)n(e)24 b(them)h(do)f(so.)330 1768 y(A)29 b(compilation)h(of)g(a)f(co)n(v)n (ered)i(w)n(ork)f(with)f(other)i(separate)f(and)h(indep)r(enden)n(t)g (w)n(orks,)g(whic)n(h)f(are)f(not)i(b)n(y)e(their)h(nature)330 1847 y(extensions)g(of)e(the)h(co)n(v)n(ered)h(w)n(ork,)f(and)g(whic)n (h)g(are)g(not)g(com)n(bined)g(with)g(it)f(suc)n(h)h(as)g(to)g(form)e (a)i(larger)f(program,)h(in)f(or)330 1926 y(on)f(a)f(v)n(olume)g(of)g (a)h(storage)g(or)f(distribution)g(medium,)g(is)g(called)g(an)h (\\aggregate")h(if)d(the)j(compilation)e(and)h(its)f(resulting)330 2005 y(cop)n(yrigh)n(t)f(are)f(not)h(used)g(to)f(limit)g(the)h(access)g (or)e(legal)h(righ)n(ts)g(of)g(the)h(compilation's)f(users)g(b)r(ey)n (ond)h(what)g(the)g(individual)330 2084 y(w)n(orks)j(p)r(ermit.)44 b(Inclusion)28 b(of)g(a)g(co)n(v)n(ered)i(w)n(ork)e(in)f(an)i (aggregate)h(do)r(es)e(not)h(cause)g(this)f(License)h(to)f(apply)h(to)f (the)h(other)330 2163 y(parts)24 b(of)f(the)i(aggregate.)215 2267 y(6.)60 b(Con)n(v)n(eying)25 b(Non-Source)f(F)-6 b(orms.)330 2372 y(Y)g(ou)22 b(ma)n(y)f(con)n(v)n(ey)i(a)e(co)n(v)n (ered)i(w)n(ork)e(in)g(ob)t(ject)h(co)r(de)h(form)d(under)i(the)g (terms)f(of)g(sections)h(4)f(and)h(5,)g(pro)n(vided)g(that)g(y)n(ou)g (also)330 2451 y(con)n(v)n(ey)j(the)g(mac)n(hine-readable)g(Corresp)r (onding)f(Source)g(under)g(the)h(terms)e(of)g(this)h(License,)g(in)f (one)i(of)e(these)i(w)n(a)n(ys:)395 2556 y(a.)60 b(Con)n(v)n(ey)21 b(the)g(ob)t(ject)g(co)r(de)g(in,)f(or)f(em)n(b)r(o)r(died)i(in,)f(a)g (ph)n(ysical)g(pro)r(duct)h(\(including)g(a)f(ph)n(ysical)g (distribution)g(medium\),)510 2635 y(accompanied)37 b(b)n(y)e(the)h (Corresp)r(onding)g(Source)g(\014xed)g(on)f(a)g(durable)h(ph)n(ysical)f (medium)g(customarily)g(used)h(for)510 2714 y(soft)n(w)n(are)24 b(in)n(terc)n(hange.)391 2818 y(b.)60 b(Con)n(v)n(ey)21 b(the)g(ob)t(ject)g(co)r(de)g(in,)f(or)f(em)n(b)r(o)r(died)i(in,)f(a)g (ph)n(ysical)g(pro)r(duct)h(\(including)g(a)f(ph)n(ysical)g (distribution)g(medium\),)510 2897 y(accompanied)33 b(b)n(y)f(a)g (written)g(o\013er,)h(v)l(alid)f(for)f(at)h(least)g(three)g(y)n(ears)g (and)g(v)l(alid)f(for)g(as)h(long)f(as)h(y)n(ou)g(o\013er)g(spare)510 2976 y(parts)c(or)f(customer)h(supp)r(ort)g(for)e(that)j(pro)r(duct)f 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(only)g(o)r(ccasionally)g(and)h(noncommercially)-6 b(,)27 b(and)g(only)g(if)f(y)n(ou)h(receiv)n(ed)h(the)510 3554 y(ob)t(ject)d(co)r(de)f(with)g(suc)n(h)g(an)g(o\013er,)g(in)f(accord)i (with)e(subsection)i(6b.)391 3659 y(d.)60 b(Con)n(v)n(ey)34 b(the)g(ob)t(ject)g(co)r(de)g(b)n(y)f(o\013ering)g(access)h(from)e(a)g (designated)j(place)f(\(gratis)f(or)f(for)g(a)h(c)n(harge\),)j(and)e (o\013er)510 3738 y(equiv)l(alen)n(t)f(access)f(to)g(the)g(Corresp)r (onding)f(Source)h(in)f(the)h(same)g(w)n(a)n(y)f(through)h(the)h(same)e (place)h(at)g(no)f(further)510 3817 y(c)n(harge.)i(Y)-6 b(ou)25 b(need)g(not)g(require)e(recipien)n(ts)i(to)g(cop)n(y)g(the)g (Corresp)r(onding)f(Source)h(along)f(with)h(the)g(ob)t(ject)g(co)r(de.) 33 b(If)510 3895 y(the)c(place)g(to)g(cop)n(y)g(the)g(ob)t(ject)h(co)r (de)f(is)f(a)g(net)n(w)n(ork)h(serv)n(er,)g(the)g(Corresp)r(onding)g (Source)g(ma)n(y)f(b)r(e)h(on)g(a)f(di\013eren)n(t)510 3974 y(serv)n(er)18 b(\(op)r(erated)i(b)n(y)f(y)n(ou)f(or)g(a)h(third)f (part)n(y\))h(that)g(supp)r(orts)g(equiv)l(alen)n(t)h(cop)n(ying)f (facilities,)f(pro)n(vided)h(y)n(ou)g(main)n(tain)510 4053 y(clear)g(directions)g(next)h(to)f(the)h(ob)t(ject)g(co)r(de)g(sa) n(ying)f(where)g(to)g(\014nd)h(the)f(Corresp)r(onding)g(Source.)31 b(Regardless)19 b(of)f(what)510 4132 y(serv)n(er)26 b(hosts)g(the)h (Corresp)r(onding)f(Source,)g(y)n(ou)h(remain)e(obligated)i(to)g (ensure)f(that)h(it)f(is)f(a)n(v)l(ailable)h(for)f(as)h(long)g(as)510 4211 y(needed)f(to)f(satisfy)g(these)h(requiremen)n(ts.)399 4316 y(e.)60 b(Con)n(v)n(ey)21 b(the)g(ob)t(ject)g(co)r(de)g(using)f(p) r(eer-to-p)r(eer)h(transmission,)f(pro)n(vided)g(y)n(ou)h(inform)e (other)h(p)r(eers)h(where)f(the)h(ob)t(ject)510 4395 y(co)r(de)30 b(and)f(Corresp)r(onding)g(Source)g(of)f(the)i(w)n(ork)e (are)h(b)r(eing)g(o\013ered)g(to)g(the)g(general)g(public)g(at)g(no)g (c)n(harge)h(under)510 4474 y(subsection)25 b(6d.)330 4604 y(A)31 b(separable)g(p)r(ortion)g(of)g(the)h(ob)t(ject)g(co)r(de,) h(whose)f(source)f(co)r(de)h(is)f(excluded)h(from)e(the)i(Corresp)r (onding)f(Source)h(as)f(a)330 4683 y(System)24 b(Library)-6 b(,)23 b(need)i(not)f(b)r(e)g(included)h(in)e(con)n(v)n(eying)i(the)g (ob)t(ject)f(co)r(de)h(w)n(ork.)330 4788 y(A)k(\\User)f(Pro)r(duct")i (is)e(either)h(\(1\))h(a)f(\\consumer)h(pro)r(duct",)h(whic)n(h)e (means)g(an)n(y)g(tangible)h(p)r(ersonal)f(prop)r(ert)n(y)g(whic)n(h)h (is)330 4867 y(normally)d(used)h(for)f(p)r(ersonal,)h(family)-6 b(,)28 b(or)f(household)i(purp)r(oses,)f(or)f(\(2\))i(an)n(ything)g (designed)g(or)e(sold)g(for)g(incorp)r(oration)330 4946 y(in)n(to)g(a)g(dw)n(elling.)40 b(In)27 b(determining)h(whether)f(a)g (pro)r(duct)h(is)e(a)h(consumer)g(pro)r(duct,)h(doubtful)g(cases)f (shall)f(b)r(e)h(resolv)n(ed)g(in)330 5024 y(fa)n(v)n(or)c(of)g(co)n(v) n(erage.)33 b(F)-6 b(or)23 b(a)h(particular)f(pro)r(duct)i(receiv)n(ed) f(b)n(y)g(a)g(particular)f(user,)g(\\normally)g(used")h(refers)e(to)j (a)e(t)n(ypical)h(or)330 5103 y(common)h(use)h(of)e(that)i(class)f(of)f (pro)r(duct,)i(regardless)f(of)f(the)i(status)g(of)e(the)i(particular)f (user)f(or)h(of)f(the)i(w)n(a)n(y)f(in)g(whic)n(h)g(the)330 5182 y(particular)h(user)g(actually)h(uses,)f(or)g(exp)r(ects)i(or)e (is)f(exp)r(ected)k(to)d(use,)h(the)g(pro)r(duct.)40 b(A)25 b(pro)r(duct)j(is)d(a)h(consumer)h(pro)r(duct)330 5261 y(regardless)20 b(of)h(whether)g(the)h(pro)r(duct)g(has)f(substan) n(tial)g(commercial,)g(industrial)f(or)g(non-consumer)i(uses,)f(unless) g(suc)n(h)g(uses)330 5340 y(represen)n(t)j(the)h(only)f(signi\014can)n (t)g(mo)r(de)g(of)g(use)g(of)f(the)i(pro)r(duct.)p eop end %%Page: 575 593 TeXDict begin 575 592 bop 150 -116 a FK(GNU)31 b(General)g(Public)f (License)2314 b(575)330 299 y Ff(\\Installation)32 b(Information")g (for)e(a)h(User)f(Pro)r(duct)h(means)g(an)n(y)h(metho)r(ds,)h(pro)r (cedures,)g(authorization)f(k)n(eys,)h(or)d(other)330 378 y(information)i(required)g(to)h(install)f(and)g(execute)j(mo)r (di\014ed)e(v)n(ersions)f(of)g(a)g(co)n(v)n(ered)i(w)n(ork)e(in)g(that) h(User)f(Pro)r(duct)h(from)330 457 y(a)f(mo)r(di\014ed)g(v)n(ersion)f (of)g(its)h(Corresp)r(onding)g(Source.)55 b(The)32 b(information)f(m)n (ust)h(su\016ce)g(to)g(ensure)g(that)h(the)f(con)n(tin)n(ued)330 535 y(functioning)c(of)f(the)h(mo)r(di\014ed)g(ob)t(ject)g(co)r(de)g (is)f(in)f(no)i(case)g(prev)n(en)n(ted)h(or)e(in)n(terfered)g(with)g (solely)g(b)r(ecause)i(mo)r(di\014cation)330 614 y(has)24 b(b)r(een)g(made.)330 722 y(If)f(y)n(ou)h(con)n(v)n(ey)h(an)f(ob)t (ject)g(co)r(de)g(w)n(ork)f(under)h(this)f(section)h(in,)f(or)g(with,)g (or)g(sp)r(eci\014cally)h(for)e(use)i(in,)e(a)i(User)f(Pro)r(duct,)g (and)330 801 y(the)28 b(con)n(v)n(eying)h(o)r(ccurs)e(as)g(part)h(of)f (a)g(transaction)h(in)f(whic)n(h)g(the)h(righ)n(t)f(of)g(p)r(ossession) g(and)h(use)f(of)g(the)h(User)f(Pro)r(duct)h(is)330 880 y(transferred)20 b(to)i(the)f(recipien)n(t)g(in)g(p)r(erp)r(etuit)n(y)h (or)e(for)g(a)h(\014xed)h(term)e(\(regardless)h(of)f(ho)n(w)h(the)h (transaction)g(is)e(c)n(haracterized\),)330 959 y(the)29 b(Corresp)r(onding)f(Source)h(con)n(v)n(ey)n(ed)h(under)e(this)g (section)h(m)n(ust)f(b)r(e)h(accompanied)h(b)n(y)e(the)h(Installation)g (Information.)330 1037 y(But)f(this)g(requiremen)n(t)g(do)r(es)h(not)f (apply)h(if)d(neither)j(y)n(ou)f(nor)g(an)n(y)g(third)g(part)n(y)g (retains)g(the)h(abilit)n(y)f(to)g(install)f(mo)r(di\014ed)330 1116 y(ob)t(ject)e(co)r(de)f(on)g(the)h(User)e(Pro)r(duct)h(\(for)g (example,)g(the)g(w)n(ork)g(has)g(b)r(een)g(installed)g(in)f(R)n(OM\).) 330 1224 y(The)33 b(requiremen)n(t)g(to)g(pro)n(vide)f(Installation)i (Information)f(do)r(es)f(not)i(include)e(a)h(requiremen)n(t)g(to)g(con) n(tin)n(ue)h(to)f(pro)n(vide)330 1303 y(supp)r(ort)d(service,)g(w)n (arran)n(t)n(y)-6 b(,)31 b(or)e(up)r(dates)i(for)e(a)g(w)n(ork)g(that)i (has)e(b)r(een)i(mo)r(di\014ed)e(or)g(installed)h(b)n(y)g(the)g (recipien)n(t,)h(or)e(for)330 1382 y(the)i(User)f(Pro)r(duct)g(in)g (whic)n(h)h(it)f(has)g(b)r(een)h(mo)r(di\014ed)g(or)e(installed.)51 b(Access)30 b(to)h(a)f(net)n(w)n(ork)h(ma)n(y)g(b)r(e)f(denied)h(when)g (the)330 1460 y(mo)r(di\014cation)18 b(itself)d(materially)h(and)h(adv) n(ersely)g(a\013ects)h(the)g(op)r(eration)f(of)f(the)i(net)n(w)n(ork)f (or)f(violates)h(the)g(rules)f(and)h(proto)r(cols)330 1539 y(for)23 b(comm)n(unication)i(across)f(the)g(net)n(w)n(ork.)330 1647 y(Corresp)r(onding)d(Source)h(con)n(v)n(ey)n(ed,)i(and)d (Installation)h(Information)g(pro)n(vided,)g(in)e(accord)i(with)f(this) g(section)h(m)n(ust)g(b)r(e)f(in)g(a)330 1726 y(format)j(that)i(is)e (publicly)g(do)r(cumen)n(ted)j(\(and)f(with)e(an)h(implemen)n(tation)h (a)n(v)l(ailable)f(to)g(the)g(public)g(in)f(source)h(co)r(de)h(form\),) 330 1805 y(and)e(m)n(ust)g(require)f(no)h(sp)r(ecial)g(passw)n(ord)g (or)f(k)n(ey)i(for)d(unpac)n(king,)j(reading)f(or)f(cop)n(ying.)215 1912 y(7.)60 b(Additional)24 b(T)-6 b(erms.)330 2020 y(\\Additional)26 b(p)r(ermissions")f(are)h(terms)f(that)i(supplemen)n (t)g(the)f(terms)g(of)f(this)h(License)g(b)n(y)g(making)g(exceptions)h (from)e(one)330 2099 y(or)f(more)g(of)h(its)f(conditions.)34 b(Additional)25 b(p)r(ermissions)e(that)j(are)e(applicable)h(to)g(the)h (en)n(tire)e(Program)g(shall)g(b)r(e)h(treated)h(as)330 2178 y(though)f(they)g(w)n(ere)e(included)h(in)g(this)f(License,)h(to)g (the)g(exten)n(t)i(that)f(they)f(are)g(v)l(alid)f(under)h(applicable)g (la)n(w.)31 b(If)23 b(additional)330 2256 y(p)r(ermissions)f(apply)i (only)g(to)g(part)g(of)f(the)i(Program,)e(that)h(part)g(ma)n(y)g(b)r(e) g(used)g(separately)h(under)f(those)g(p)r(ermissions,)e(but)330 2335 y(the)j(en)n(tire)f(Program)f(remains)g(go)n(v)n(erned)i(b)n(y)f (this)g(License)g(without)h(regard)e(to)h(the)h(additional)f(p)r (ermissions.)330 2443 y(When)k(y)n(ou)f(con)n(v)n(ey)i(a)e(cop)n(y)h (of)e(a)i(co)n(v)n(ered)g(w)n(ork,)f(y)n(ou)g(ma)n(y)g(at)h(y)n(our)f (option)h(remo)n(v)n(e)f(an)n(y)h(additional)f(p)r(ermissions)f(from) 330 2522 y(that)21 b(cop)n(y)-6 b(,)20 b(or)f(from)g(an)n(y)h(part)f (of)g(it.)30 b(\(Additional)20 b(p)r(ermissions)e(ma)n(y)i(b)r(e)f (written)h(to)g(require)f(their)g(o)n(wn)h(remo)n(v)l(al)f(in)g (certain)330 2601 y(cases)i(when)f(y)n(ou)h(mo)r(dify)f(the)h(w)n (ork.\))30 b(Y)-6 b(ou)20 b(ma)n(y)g(place)h(additional)g(p)r (ermissions)e(on)h(material,)g(added)i(b)n(y)e(y)n(ou)h(to)f(a)h(co)n (v)n(ered)330 2680 y(w)n(ork,)i(for)g(whic)n(h)h(y)n(ou)g(ha)n(v)n(e)h (or)e(can)i(giv)n(e)f(appropriate)g(cop)n(yrigh)n(t)h(p)r(ermission.) 330 2787 y(Not)n(withstanding)35 b(an)n(y)g(other)f(pro)n(vision)f(of)h (this)f(License,)k(for)c(material)g(y)n(ou)h(add)h(to)f(a)g(co)n(v)n (ered)h(w)n(ork,)g(y)n(ou)f(ma)n(y)g(\(if)330 2866 y(authorized)25 b(b)n(y)f(the)h(cop)n(yrigh)n(t)f(holders)g(of)f(that)i(material\))f (supplemen)n(t)h(the)f(terms)g(of)f(this)h(License)g(with)g(terms:)395 2974 y(a.)60 b(Disclaiming)23 b(w)n(arran)n(t)n(y)h(or)f(limiting)f (liabilit)n(y)h(di\013eren)n(tly)h(from)f(the)h(terms)g(of)f(sections)i (15)f(and)g(16)g(of)f(this)h(License;)510 3052 y(or)391 3160 y(b.)60 b(Requiring)27 b(preserv)l(ation)g(of)g(sp)r(eci\014ed)h (reasonable)g(legal)e(notices)i(or)f(author)g(attributions)h(in)f(that) h(material)f(or)f(in)510 3239 y(the)f(Appropriate)f(Legal)g(Notices)g (displa)n(y)n(ed)g(b)n(y)g(w)n(orks)f(con)n(taining)j(it;)d(or)399 3346 y(c.)60 b(Prohibiting)27 b(misrepresen)n(tation)i(of)e(the)h (origin)f(of)g(that)i(material,)f(or)f(requiring)g(that)i(mo)r (di\014ed)f(v)n(ersions)f(of)g(suc)n(h)510 3425 y(material)c(b)r(e)h (mark)n(ed)g(in)g(reasonable)g(w)n(a)n(ys)g(as)g(di\013eren)n(t)g(from) f(the)h(original)f(v)n(ersion;)h(or)391 3533 y(d.)60 b(Limiting)23 b(the)i(use)f(for)e(publicit)n(y)j(purp)r(oses)e(of)h (names)g(of)f(licensors)g(or)h(authors)g(of)f(the)i(material;)e(or)399 3640 y(e.)60 b(Declining)21 b(to)i(gran)n(t)f(righ)n(ts)f(under)h (trademark)g(la)n(w)f(for)g(use)g(of)g(some)h(trade)g(names,)g (trademarks,)g(or)f(service)h(marks;)510 3719 y(or)409 3827 y(f.)59 b(Requiring)26 b(indemni\014cation)h(of)e(licensors)g(and) i(authors)f(of)g(that)h(material)e(b)n(y)i(an)n(y)n(one)g(who)f(con)n (v)n(eys)h(the)g(material)510 3906 y(\(or)22 b(mo)r(di\014ed)h(v)n (ersions)f(of)g(it\))g(with)g(con)n(tractual)i(assumptions)f(of)f (liabilit)n(y)f(to)i(the)g(recipien)n(t,)f(for)g(an)n(y)g(liabilit)n(y) g(that)510 3985 y(these)j(con)n(tractual)g(assumptions)f(directly)g (imp)r(ose)g(on)g(those)g(licensors)g(and)g(authors.)330 4121 y(All)j(other)i(non-p)r(ermissiv)n(e)e(additional)i(terms)f(are)g (considered)h(\\further)e(restrictions")i(within)f(the)g(meaning)h(of)f (section)330 4200 y(10.)45 b(If)28 b(the)h(Program)f(as)g(y)n(ou)h (receiv)n(ed)g(it,)f(or)g(an)n(y)h(part)f(of)g(it,)h(con)n(tains)g(a)g (notice)g(stating)g(that)g(it)f(is)g(go)n(v)n(erned)h(b)n(y)g(this)330 4279 y(License)19 b(along)h(with)e(a)h(term)g(that)h(is)e(a)h(further)f (restriction,)h(y)n(ou)h(ma)n(y)e(remo)n(v)n(e)i(that)g(term.)29 b(If)19 b(a)f(license)h(do)r(cumen)n(t)i(con)n(tains)330 4358 y(a)28 b(further)f(restriction)g(but)i(p)r(ermits)e(relicensing)g (or)g(con)n(v)n(eying)i(under)f(this)g(License,)g(y)n(ou)h(ma)n(y)e (add)h(to)h(a)e(co)n(v)n(ered)i(w)n(ork)330 4436 y(material)22 b(go)n(v)n(erned)j(b)n(y)e(the)g(terms)g(of)f(that)i(license)f(do)r (cumen)n(t,)h(pro)n(vided)g(that)g(the)f(further)f(restriction)h(do)r (es)g(not)h(surviv)n(e)330 4515 y(suc)n(h)g(relicensing)g(or)f(con)n(v) n(eying.)330 4623 y(If)j(y)n(ou)h(add)g(terms)g(to)g(a)f(co)n(v)n(ered) i(w)n(ork)f(in)f(accord)h(with)g(this)f(section,)i(y)n(ou)f(m)n(ust)g (place,)g(in)f(the)i(relev)l(an)n(t)f(source)g(\014les,)g(a)330 4702 y(statemen)n(t)h(of)d(the)i(additional)f(terms)f(that)i(apply)f (to)h(those)f(\014les,)g(or)f(a)h(notice)h(indicating)f(where)g(to)h (\014nd)f(the)g(applicable)330 4781 y(terms.)330 4888 y(Additional)i(terms,)f(p)r(ermissiv)n(e)g(or)g(non-p)r(ermissiv)n(e,)g (ma)n(y)h(b)r(e)g(stated)h(in)e(the)h(form)e(of)h(a)h(separately)g (written)g(license,)g(or)330 4967 y(stated)d(as)f(exceptions;)h(the)f (ab)r(o)n(v)n(e)h(requiremen)n(ts)f(apply)g(either)g(w)n(a)n(y)-6 b(.)215 5075 y(8.)60 b(T)-6 b(ermination.)330 5182 y(Y)g(ou)21 b(ma)n(y)f(not)i(propagate)g(or)e(mo)r(dify)g(a)g(co)n(v)n(ered)i(w)n (ork)e(except)j(as)d(expressly)h(pro)n(vided)g(under)f(this)h(License.) 30 b(An)n(y)21 b(attempt)330 5261 y(otherwise)30 b(to)g(propagate)h(or) e(mo)r(dify)g(it)h(is)e(v)n(oid,)j(and)f(will)e(automatically)j (terminate)f(y)n(our)g(righ)n(ts)f(under)h(this)f(License)330 5340 y(\(including)24 b(an)n(y)h(paten)n(t)g(licenses)f(gran)n(ted)h (under)f(the)g(third)g(paragraph)g(of)f(section)i(11\).)p eop end %%Page: 576 594 TeXDict begin 576 593 bop 150 -116 a FK(GNU)31 b(General)g(Public)f (License)2314 b(576)330 299 y Ff(Ho)n(w)n(ev)n(er,)37 b(if)d(y)n(ou)h(cease)h(all)e(violation)h(of)f(this)g(License,)k(then)d (y)n(our)g(license)g(from)e(a)i(particular)f(cop)n(yrigh)n(t)i(holder)f (is)330 378 y(reinstated)25 b(\(a\))g(pro)n(visionally)-6 b(,)22 b(unless)i(and)g(un)n(til)g(the)g(cop)n(yrigh)n(t)h(holder)f (explicitly)g(and)g(\014nally)g(terminates)g(y)n(our)g(license,)330 457 y(and)f(\(b\))g(p)r(ermanen)n(tly)-6 b(,)24 b(if)d(the)j(cop)n (yrigh)n(t)f(holder)f(fails)g(to)h(notify)f(y)n(ou)h(of)f(the)i (violation)f(b)n(y)f(some)h(reasonable)g(means)g(prior)330 535 y(to)h(60)g(da)n(ys)g(after)g(the)h(cessation.)330 634 y(Moreo)n(v)n(er,)35 b(y)n(our)d(license)h(from)f(a)g(particular)h (cop)n(yrigh)n(t)g(holder)g(is)f(reinstated)h(p)r(ermanen)n(tly)h(if)e (the)h(cop)n(yrigh)n(t)h(holder)330 713 y(noti\014es)21 b(y)n(ou)g(of)f(the)h(violation)f(b)n(y)h(some)f(reasonable)h(means,)g (this)f(is)f(the)i(\014rst)f(time)g(y)n(ou)h(ha)n(v)n(e)g(receiv)n(ed)g (notice)h(of)d(violation)330 791 y(of)j(this)f(License)i(\(for)e(an)n (y)i(w)n(ork\))f(from)f(that)i(cop)n(yrigh)n(t)g(holder,)e(and)i(y)n (ou)f(cure)g(the)h(violation)f(prior)f(to)h(30)h(da)n(ys)f(after)g(y)n (our)330 870 y(receipt)i(of)g(the)g(notice.)330 968 y(T)-6 b(ermination)21 b(of)f(y)n(our)h(righ)n(ts)f(under)h(this)f(section)i (do)r(es)f(not)g(terminate)h(the)f(licenses)g(of)f(parties)g(who)h(ha)n (v)n(e)h(receiv)n(ed)f(copies)330 1047 y(or)g(righ)n(ts)h(from)f(y)n (ou)h(under)h(this)e(License.)32 b(If)21 b(y)n(our)h(righ)n(ts)g(ha)n (v)n(e)h(b)r(een)f(terminated)h(and)g(not)f(p)r(ermanen)n(tly)h (reinstated,)g(y)n(ou)330 1126 y(do)h(not)g(qualify)g(to)g(receiv)n(e)g (new)g(licenses)g(for)f(the)i(same)e(material)h(under)g(section)g(10.) 215 1224 y(9.)60 b(Acceptance)26 b(Not)e(Required)g(for)f(Ha)n(ving)h (Copies.)330 1323 y(Y)-6 b(ou)35 b(are)g(not)h(required)f(to)g(accept)i (this)e(License)h(in)e(order)h(to)h(receiv)n(e)f(or)g(run)g(a)g(cop)n (y)h(of)e(the)i(Program.)65 b(Ancillary)330 1401 y(propagation)28 b(of)f(a)g(co)n(v)n(ered)h(w)n(ork)f(o)r(ccurring)g(solely)g(as)g(a)g (consequence)i(of)e(using)g(p)r(eer-to-p)r(eer)g(transmission)g(to)g (receiv)n(e)330 1480 y(a)g(cop)n(y)h(lik)n(ewise)f(do)r(es)g(not)h (require)f(acceptance.)44 b(Ho)n(w)n(ev)n(er,)28 b(nothing)g(other)g (than)g(this)f(License)h(gran)n(ts)f(y)n(ou)h(p)r(ermission)330 1559 y(to)f(propagate)i(or)d(mo)r(dify)h(an)n(y)g(co)n(v)n(ered)h(w)n (ork.)40 b(These)28 b(actions)f(infringe)f(cop)n(yrigh)n(t)i(if)e(y)n (ou)h(do)h(not)f(accept)i(this)e(License.)330 1638 y(Therefore,)c(b)n (y)h(mo)r(difying)g(or)f(propagating)i(a)f(co)n(v)n(ered)h(w)n(ork,)e (y)n(ou)h(indicate)h(y)n(our)f(acceptance)i(of)e(this)f(License)i(to)f (do)g(so.)180 1736 y(10.)60 b(Automatic)25 b(Licensing)f(of)f(Do)n (wnstream)h(Recipien)n(ts.)330 1834 y(Eac)n(h)19 b(time)f(y)n(ou)h(con) n(v)n(ey)h(a)f(co)n(v)n(ered)g(w)n(ork,)g(the)g(recipien)n(t)g (automatically)g(receiv)n(es)g(a)g(license)f(from)f(the)i(original)f (licensors,)g(to)330 1913 y(run,)k(mo)r(dify)f(and)h(propagate)i(that)f (w)n(ork,)f(sub)t(ject)g(to)h(this)e(License.)32 b(Y)-6 b(ou)22 b(are)g(not)g(resp)r(onsible)g(for)f(enforcing)h(compliance)330 1992 y(b)n(y)i(third)f(parties)h(with)g(this)g(License.)330 2090 y(An)29 b(\\en)n(tit)n(y)i(transaction")f(is)f(a)g(transaction)i (transferring)d(con)n(trol)i(of)f(an)g(organization,)i(or)e(substan)n (tially)h(all)f(assets)g(of)330 2169 y(one,)g(or)f(sub)r(dividing)f(an) h(organization,)i(or)d(merging)h(organizations.)45 b(If)27 b(propagation)i(of)f(a)g(co)n(v)n(ered)h(w)n(ork)e(results)h(from)330 2248 y(an)h(en)n(tit)n(y)h(transaction,)i(eac)n(h)e(part)n(y)f(to)h (that)g(transaction)g(who)f(receiv)n(es)h(a)f(cop)n(y)h(of)f(the)g(w)n (ork)g(also)g(receiv)n(es)h(whatev)n(er)330 2327 y(licenses)25 b(to)g(the)h(w)n(ork)f(the)g(part)n(y's)g(predecessor)h(in)e(in)n (terest)i(had)f(or)g(could)g(giv)n(e)g(under)g(the)h(previous)f (paragraph,)g(plus)g(a)330 2406 y(righ)n(t)e(to)h(p)r(ossession)g(of)f (the)i(Corresp)r(onding)e(Source)i(of)e(the)h(w)n(ork)f(from)g(the)h (predecessor)g(in)g(in)n(terest,)f(if)g(the)h(predecessor)330 2485 y(has)g(it)f(or)h(can)g(get)h(it)e(with)h(reasonable)g(e\013orts.) 330 2583 y(Y)-6 b(ou)21 b(ma)n(y)f(not)i(imp)r(ose)e(an)n(y)h(further)f (restrictions)h(on)f(the)i(exercise)f(of)f(the)h(righ)n(ts)f(gran)n (ted)i(or)e(a\016rmed)g(under)h(this)g(License.)330 2662 y(F)-6 b(or)30 b(example,)h(y)n(ou)f(ma)n(y)g(not)h(imp)r(ose)f(a)g (license)f(fee,)i(ro)n(y)n(alt)n(y)-6 b(,)32 b(or)d(other)i(c)n(harge)f (for)f(exercise)i(of)e(righ)n(ts)h(gran)n(ted)h(under)330 2741 y(this)25 b(License,)g(and)g(y)n(ou)h(ma)n(y)f(not)g(initiate)g (litigation)g(\(including)h(a)f(cross-claim)e(or)i(coun)n(terclaim)g (in)g(a)g(la)n(wsuit\))g(alleging)330 2819 y(that)g(an)n(y)g(paten)n(t) h(claim)e(is)g(infringed)f(b)n(y)i(making,)f(using,)g(selling,)f (o\013ering)i(for)e(sale,)h(or)g(imp)r(orting)g(the)h(Program)e(or)h (an)n(y)330 2898 y(p)r(ortion)g(of)f(it.)180 2996 y(11.)60 b(P)n(aten)n(ts.)330 3095 y(A)21 b(\\con)n(tributor")j(is)d(a)h(cop)n (yrigh)n(t)g(holder)g(who)g(authorizes)h(use)f(under)g(this)g(License)g (of)g(the)g(Program)g(or)f(a)h(w)n(ork)g(on)g(whic)n(h)330 3174 y(the)j(Program)e(is)g(based.)32 b(The)24 b(w)n(ork)f(th)n(us)h (licensed)g(is)f(called)h(the)h(con)n(tributor's)f(\\con)n(tributor)h (v)n(ersion".)330 3272 y(A)e(con)n(tributor's)h(\\essen)n(tial)g(paten) n(t)h(claims")e(are)g(all)g(paten)n(t)i(claims)e(o)n(wned)h(or)f(con)n (trolled)h(b)n(y)g(the)g(con)n(tributor,)g(whether)330 3351 y(already)h(acquired)g(or)f(hereafter)h(acquired,)g(that)g(w)n (ould)g(b)r(e)g(infringed)e(b)n(y)i(some)g(manner,)f(p)r(ermitted)h(b)n (y)g(this)f(License,)h(of)330 3429 y(making,)k(using,)f(or)g(selling)f (its)g(con)n(tributor)i(v)n(ersion,)f(but)h(do)f(not)g(include)h (claims)e(that)i(w)n(ould)f(b)r(e)g(infringed)f(only)h(as)g(a)330 3508 y(consequence)21 b(of)d(further)h(mo)r(di\014cation)g(of)g(the)g (con)n(tributor)h(v)n(ersion.)29 b(F)-6 b(or)18 b(purp)r(oses)h(of)f (this)h(de\014nition,)h(\\con)n(trol")g(includes)330 3587 y(the)25 b(righ)n(t)e(to)h(gran)n(t)h(paten)n(t)g(sublicenses)f (in)f(a)h(manner)g(consisten)n(t)h(with)f(the)h(requiremen)n(ts)f(of)f (this)h(License.)330 3685 y(Eac)n(h)34 b(con)n(tributor)h(gran)n(ts)f (y)n(ou)h(a)f(non-exclusiv)n(e,)i(w)n(orldwide,)g(ro)n(y)n(alt)n (y-free)d(paten)n(t)j(license)e(under)g(the)g(con)n(tributor's)330 3764 y(essen)n(tial)27 b(paten)n(t)h(claims,)e(to)h(mak)n(e,)g(use,)g (sell,)f(o\013er)g(for)g(sale,)g(imp)r(ort)g(and)h(otherwise)g(run,)f (mo)r(dify)g(and)h(propagate)h(the)330 3843 y(con)n(ten)n(ts)e(of)d (its)h(con)n(tributor)g(v)n(ersion.)330 3941 y(In)31 b(the)g(follo)n(wing)f(three)h(paragraphs,)h(a)e(\\paten)n(t)i (license")f(is)f(an)n(y)h(express)f(agreemen)n(t)i(or)e(commitmen)n(t,) j(ho)n(w)n(ev)n(er)e(de-)330 4020 y(nominated,)26 b(not)g(to)g(enforce) f(a)g(paten)n(t)i(\(suc)n(h)f(as)f(an)g(express)h(p)r(ermission)e(to)h (practice)h(a)f(paten)n(t)i(or)e(co)n(v)n(enan)n(t)i(not)f(to)g(sue)330 4099 y(for)j(paten)n(t)i(infringemen)n(t\).)50 b(T)-6 b(o)30 b(\\gran)n(t")h(suc)n(h)f(a)g(paten)n(t)i(license)e(to)g(a)g (part)n(y)g(means)g(to)g(mak)n(e)h(suc)n(h)f(an)g(agreemen)n(t)h(or)330 4178 y(commitmen)n(t)25 b(not)f(to)g(enforce)h(a)e(paten)n(t)j(against) e(the)h(part)n(y)-6 b(.)330 4276 y(If)19 b(y)n(ou)g(con)n(v)n(ey)i(a)d (co)n(v)n(ered)j(w)n(ork,)e(kno)n(wingly)g(relying)g(on)g(a)g(paten)n (t)h(license,)g(and)f(the)h(Corresp)r(onding)f(Source)h(of)e(the)i(w)n (ork)f(is)330 4355 y(not)j(a)n(v)l(ailable)g(for)e(an)n(y)n(one)j(to)f (cop)n(y)-6 b(,)22 b(free)f(of)g(c)n(harge)i(and)e(under)h(the)g(terms) f(of)g(this)h(License,)g(through)g(a)f(publicly)g(a)n(v)l(ailable)330 4434 y(net)n(w)n(ork)27 b(serv)n(er)e(or)g(other)i(readily)e (accessible)i(means,)f(then)h(y)n(ou)f(m)n(ust)g(either)g(\(1\))h (cause)f(the)h(Corresp)r(onding)f(Source)g(to)330 4513 y(b)r(e)h(so)g(a)n(v)l(ailable,)g(or)f(\(2\))i(arrange)f(to)g(depriv)n (e)g(y)n(ourself)f(of)g(the)i(b)r(ene\014t)g(of)e(the)h(paten)n(t)i (license)e(for)e(this)i(particular)f(w)n(ork,)330 4592 y(or)i(\(3\))i(arrange,)f(in)f(a)h(manner)f(consisten)n(t)i(with)f(the) g(requiremen)n(ts)g(of)f(this)g(License,)i(to)f(extend)h(the)f(paten)n (t)i(license)d(to)330 4670 y(do)n(wnstream)c(recipien)n(ts.)31 b(\\Kno)n(wingly)23 b(relying")g(means)g(y)n(ou)g(ha)n(v)n(e)h(actual)g (kno)n(wledge)g(that,)f(but)h(for)e(the)h(paten)n(t)i(license,)330 4749 y(y)n(our)h(con)n(v)n(eying)i(the)f(co)n(v)n(ered)g(w)n(ork)f(in)f (a)i(coun)n(try)-6 b(,)27 b(or)f(y)n(our)g(recipien)n(t's)g(use)g(of)g (the)g(co)n(v)n(ered)i(w)n(ork)e(in)f(a)h(coun)n(try)-6 b(,)28 b(w)n(ould)330 4828 y(infringe)23 b(one)h(or)g(more)f(iden)n (ti\014able)i(paten)n(ts)g(in)e(that)i(coun)n(try)g(that)g(y)n(ou)f(ha) n(v)n(e)h(reason)f(to)g(b)r(eliev)n(e)g(are)g(v)l(alid.)330 4926 y(If,)c(pursuan)n(t)h(to)f(or)f(in)h(connection)i(with)e(a)g (single)f(transaction)j(or)d(arrangemen)n(t,)i(y)n(ou)g(con)n(v)n(ey)-6 b(,)22 b(or)d(propagate)j(b)n(y)e(pro)r(curing)330 5005 y(con)n(v)n(ey)n(ance)32 b(of,)e(a)g(co)n(v)n(ered)h(w)n(ork,)f(and)g (gran)n(t)g(a)f(paten)n(t)i(license)f(to)g(some)g(of)f(the)h(parties)f (receiving)h(the)g(co)n(v)n(ered)h(w)n(ork)330 5084 y(authorizing)20 b(them)f(to)h(use,)f(propagate,)i(mo)r(dify)e(or)f(con)n(v)n(ey)j(a)d (sp)r(eci\014c)i(cop)n(y)g(of)e(the)i(co)n(v)n(ered)g(w)n(ork,)f(then)h (the)g(paten)n(t)h(license)330 5163 y(y)n(ou)j(gran)n(t)h(is)e (automatically)i(extended)g(to)g(all)e(recipien)n(ts)h(of)f(the)i(co)n (v)n(ered)g(w)n(ork)e(and)h(w)n(orks)g(based)g(on)g(it.)330 5261 y(A)d(paten)n(t)i(license)e(is)f(\\discriminatory")h(if)f(it)h(do) r(es)h(not)f(include)h(within)f(the)h(scop)r(e)f(of)g(its)g(co)n(v)n (erage,)i(prohibits)d(the)i(exercise)330 5340 y(of,)29 b(or)f(is)g(conditioned)i(on)f(the)g(non-exercise)g(of)g(one)g(or)f 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y(section)h(\\En)n(titled) f(XYZ")g(according)h(to)f(this)f(de\014nition.)330 1012 y(The)j(Do)r(cumen)n(t)h(ma)n(y)f(include)g(W)-6 b(arran)n(t)n(y)27 b(Disclaimers)d(next)j(to)f(the)h(notice)g(whic)n(h)f(states)h(that)g (this)e(License)i(applies)e(to)330 1091 y(the)d(Do)r(cumen)n(t.)32 b(These)22 b(W)-6 b(arran)n(t)n(y)22 b(Disclaimers)e(are)h(considered)h (to)g(b)r(e)g(included)g(b)n(y)g(reference)f(in)g(this)h(License,)g (but)g(only)330 1169 y(as)g(regards)h(disclaiming)f(w)n(arran)n(ties:) 30 b(an)n(y)23 b(other)g(implication)g(that)g(these)h(W)-6 b(arran)n(t)n(y)23 b(Disclaimers)f(ma)n(y)g(ha)n(v)n(e)i(is)e(v)n(oid)g (and)330 1248 y(has)i(no)g(e\013ect)h(on)f(the)h(meaning)f(of)f(this)h (License.)215 1354 y(2.)60 b(VERBA)-6 b(TIM)23 b(COPYING)330 1461 y(Y)-6 b(ou)23 b(ma)n(y)h(cop)n(y)g(and)f(distribute)h(the)g(Do)r (cumen)n(t)g(in)f(an)n(y)h(medium,)e(either)i(commercially)e(or)h (noncommercially)-6 b(,)23 b(pro)n(vided)330 1539 y(that)32 b(this)f(License,)i(the)f(cop)n(yrigh)n(t)g(notices,)i(and)d(the)h (license)f(notice)h(sa)n(ying)g(this)e(License)i(applies)f(to)h(the)f (Do)r(cumen)n(t)330 1618 y(are)d(repro)r(duced)i(in)e(all)f(copies,)j (and)f(that)g(y)n(ou)g(add)g(no)g(other)g(conditions)g(whatso)r(ev)n (er)g(to)g(those)h(of)e(this)g(License.)46 b(Y)-6 b(ou)330 1697 y(ma)n(y)28 b(not)h(use)f(tec)n(hnical)h(measures)e(to)i(obstruct) g(or)e(con)n(trol)h(the)h(reading)f(or)f(further)h(cop)n(ying)h(of)e (the)i(copies)f(y)n(ou)g(mak)n(e)330 1776 y(or)d(distribute.)35 b(Ho)n(w)n(ev)n(er,)25 b(y)n(ou)h(ma)n(y)f(accept)h(comp)r(ensation)h (in)e(exc)n(hange)i(for)d(copies.)35 b(If)25 b(y)n(ou)g(distribute)h(a) f(large)f(enough)330 1855 y(n)n(um)n(b)r(er)g(of)f(copies)h(y)n(ou)h(m) n(ust)f(also)f(follo)n(w)g(the)h(conditions)h(in)e(section)i(3.)330 1961 y(Y)-6 b(ou)24 b(ma)n(y)g(also)f(lend)h(copies,)g(under)g(the)h (same)e(conditions)i(stated)g(ab)r(o)n(v)n(e,)g(and)f(y)n(ou)g(ma)n(y)g (publicly)g(displa)n(y)f(copies.)215 2067 y(3.)60 b(COPYING)24 b(IN)g(QUANTITY)330 2173 y(If)16 b(y)n(ou)h(publish)f(prin)n(ted)h (copies)g(\(or)f(copies)h(in)f(media)h(that)g(commonly)g(ha)n(v)n(e)g (prin)n(ted)g(co)n(v)n(ers\))g(of)g(the)g(Do)r(cumen)n(t,)i(n)n(um)n(b) r(ering)330 2252 y(more)25 b(than)h(100,)g(and)g(the)g(Do)r(cumen)n (t's)g(license)f(notice)h(requires)f(Co)n(v)n(er)h(T)-6 b(exts,)26 b(y)n(ou)f(m)n(ust)h(enclose)g(the)g(copies)f(in)g(co)n(v)n (ers)330 2331 y(that)30 b(carry)-6 b(,)30 b(clearly)f(and)h(legibly)-6 b(,)30 b(all)f(these)h(Co)n(v)n(er)f(T)-6 b(exts:)43 b(F)-6 b(ron)n(t-Co)n(v)n(er)30 b(T)-6 b(exts)30 b(on)f(the)i(fron)n(t) e(co)n(v)n(er,)h(and)g(Bac)n(k-Co)n(v)n(er)330 2410 y(T)-6 b(exts)23 b(on)g(the)g(bac)n(k)g(co)n(v)n(er.)31 b(Both)23 b(co)n(v)n(ers)g(m)n(ust)f(also)g(clearly)g(and)h(legibly)f(iden)n (tify)h(y)n(ou)f(as)h(the)g(publisher)f(of)f(these)j(copies.)330 2489 y(The)c(fron)n(t)f(co)n(v)n(er)h(m)n(ust)g(presen)n(t)g(the)g (full)e(title)i(with)g(all)e(w)n(ords)h(of)g(the)i(title)e(equally)h (prominen)n(t)g(and)g(visible.)29 b(Y)-6 b(ou)20 b(ma)n(y)f(add)330 2568 y(other)26 b(material)e(on)i(the)f(co)n(v)n(ers)h(in)f(addition.) 35 b(Cop)n(ying)26 b(with)f(c)n(hanges)h(limited)f(to)g(the)h(co)n(v)n (ers,)f(as)g(long)h(as)f(they)h(preserv)n(e)330 2647 y(the)f(title)f(of)f(the)h(Do)r(cumen)n(t)h(and)g(satisfy)e(these)i (conditions,)f(can)g(b)r(e)g(treated)i(as)d(v)n(erbatim)h(cop)n(ying)h (in)e(other)i(resp)r(ects.)330 2753 y(If)i(the)h(required)e(texts)j (for)d(either)h(co)n(v)n(er)h(are)f(to)r(o)h(v)n(oluminous)f(to)g (\014t)h(legibly)-6 b(,)27 b(y)n(ou)h(should)f(put)g(the)h(\014rst)f (ones)h(listed)e(\(as)330 2832 y(man)n(y)e(as)g(\014t)g(reasonably\))h (on)f(the)g(actual)h(co)n(v)n(er,)f(and)g(con)n(tin)n(ue)h(the)g(rest)f (on)n(to)g(adjacen)n(t)i(pages.)330 2938 y(If)c(y)n(ou)i(publish)e(or)g (distribute)h(Opaque)g(copies)g(of)g(the)g(Do)r(cumen)n(t)h(n)n(um)n(b) r(ering)f(more)f(than)i(100,)f(y)n(ou)g(m)n(ust)g(either)f(include)330 3017 y(a)29 b(mac)n(hine-readable)h(T)-6 b(ransparen)n(t)29 b(cop)n(y)h(along)f(with)g(eac)n(h)g(Opaque)h(cop)n(y)-6 b(,)31 b(or)d(state)i(in)e(or)h(with)g(eac)n(h)g(Opaque)h(cop)n(y)g(a) 330 3095 y(computer-net)n(w)n(ork)e(lo)r(cation)g(from)d(whic)n(h)i (the)h(general)f(net)n(w)n(ork-using)g(public)g(has)f(access)i(to)f(do) n(wnload)h(using)e(public-)330 3174 y(standard)h(net)n(w)n(ork)g(proto) r(cols)f(a)g(complete)i(T)-6 b(ransparen)n(t)26 b(cop)n(y)h(of)f(the)h (Do)r(cumen)n(t,)g(free)f(of)f(added)j(material.)37 b(If)26 b(y)n(ou)h(use)330 3253 y(the)j(latter)g(option,)h(y)n(ou)f(m)n(ust)g (tak)n(e)g(reasonably)g(pruden)n(t)g(steps,)h(when)f(y)n(ou)g(b)r(egin) g(distribution)f(of)g(Opaque)h(copies)g(in)330 3332 y(quan)n(tit)n(y)-6 b(,)28 b(to)f(ensure)f(that)h(this)f(T)-6 b(ransparen)n(t)27 b(cop)n(y)g(will)e(remain)h(th)n(us)g(accessible)h(at)g(the)f(stated)i (lo)r(cation)f(un)n(til)f(at)g(least)330 3411 y(one)d(y)n(ear)f(after)g (the)g(last)g(time)g(y)n(ou)h(distribute)f(an)g(Opaque)h(cop)n(y)g (\(directly)f(or)g(through)h(y)n(our)f(agen)n(ts)h(or)e(retailers\))h (of)g(that)330 3490 y(edition)i(to)g(the)h(public.)330 3596 y(It)h(is)e(requested,)i(but)g(not)g(required,)f(that)h(y)n(ou)g (con)n(tact)h(the)f(authors)g(of)e(the)i(Do)r(cumen)n(t)h(w)n(ell)d(b)r (efore)h(redistributing)g(an)n(y)330 3675 y(large)f(n)n(um)n(b)r(er)f (of)h(copies,)g(to)g(giv)n(e)g(them)g(a)g(c)n(hance)h(to)g(pro)n(vide)f (y)n(ou)g(with)g(an)g(up)r(dated)h(v)n(ersion)f(of)f(the)i(Do)r(cumen)n (t.)215 3781 y(4.)60 b(MODIFICA)-6 b(TIONS)330 3887 y(Y)g(ou)31 b(ma)n(y)f(cop)n(y)h(and)g(distribute)f(a)h(Mo)r(di\014ed)f(V)-6 b(ersion)30 b(of)g(the)h(Do)r(cumen)n(t)h(under)e(the)i(conditions)f (of)f(sections)h(2)f(and)h(3)330 3966 y(ab)r(o)n(v)n(e,)c(pro)n(vided)f (that)h(y)n(ou)f(release)g(the)h(Mo)r(di\014ed)f(V)-6 b(ersion)25 b(under)h(precisely)g(this)f(License,)i(with)f(the)g(Mo)r (di\014ed)g(V)-6 b(ersion)330 4045 y(\014lling)20 b(the)h(role)f(of)g (the)h(Do)r(cumen)n(t,)h(th)n(us)f(licensing)f(distribution)h(and)g(mo) r(di\014cation)g(of)f(the)h(Mo)r(di\014ed)g(V)-6 b(ersion)20 b(to)h(who)r(ev)n(er)330 4124 y(p)r(ossesses)j(a)g(cop)n(y)g(of)g(it.) 31 b(In)24 b(addition,)g(y)n(ou)g(m)n(ust)g(do)g(these)h(things)f(in)f (the)i(Mo)r(di\014ed)f(V)-6 b(ersion:)378 4230 y(A.)59 b(Use)19 b(in)g(the)h(Title)f(P)n(age)h(\(and)g(on)g(the)g(co)n(v)n (ers,)g(if)e(an)n(y\))j(a)e(title)g(distinct)h(from)e(that)j(of)e(the)h (Do)r(cumen)n(t,)h(and)f(from)e(those)510 4309 y(of)26 b(previous)g(v)n(ersions)g(\(whic)n(h)h(should,)f(if)f(there)i(w)n(ere) f(an)n(y)-6 b(,)28 b(b)r(e)e(listed)g(in)g(the)h(History)f(section)h (of)e(the)i(Do)r(cumen)n(t\).)510 4388 y(Y)-6 b(ou)22 b(ma)n(y)g(use)g(the)h(same)f(title)g(as)g(a)g(previous)f(v)n(ersion)h (if)f(the)i(original)e(publisher)g(of)g(that)i(v)n(ersion)f(giv)n(es)g (p)r(ermission.)380 4494 y(B.)60 b(List)33 b(on)h(the)h(Title)e(P)n (age,)j(as)e(authors,)i(one)e(or)f(more)h(p)r(ersons)f(or)g(en)n (tities)i(resp)r(onsible)e(for)g(authorship)h(of)f(the)510 4573 y(mo)r(di\014cations)21 b(in)f(the)i(Mo)r(di\014ed)e(V)-6 b(ersion,)21 b(together)h(with)e(at)h(least)g(\014v)n(e)g(of)f(the)h (principal)f(authors)h(of)f(the)h(Do)r(cumen)n(t)510 4652 y(\(all)i(of)h(its)f(principal)g(authors,)h(if)f(it)g(has)h(few)n (er)g(than)g(\014v)n(e\),)h(unless)e(they)i(release)f(y)n(ou)g(from)f (this)h(requiremen)n(t.)379 4758 y(C.)60 b(State)25 b(on)f(the)h(Title) e(page)i(the)g(name)f(of)f(the)i(publisher)e(of)g(the)i(Mo)r(di\014ed)f (V)-6 b(ersion,)23 b(as)g(the)i(publisher.)377 4864 y(D.)59 b(Preserv)n(e)24 b(all)f(the)h(cop)n(yrigh)n(t)h(notices)g(of)e(the)i (Do)r(cumen)n(t.)382 4970 y(E.)60 b(Add)24 b(an)g(appropriate)g(cop)n (yrigh)n(t)h(notice)g(for)e(y)n(our)g(mo)r(di\014cations)i(adjacen)n(t) g(to)g(the)f(other)g(cop)n(yrigh)n(t)h(notices.)384 5076 y(F.)60 b(Include,)26 b(immediately)g(after)f(the)h(cop)n(yrigh)n(t)g 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b(an)n(y)f(section)h(En)n(titled)g (\\Endorsemen)n(ts".)31 b(Suc)n(h)22 b(a)f(section)h(ma)n(y)f(not)h(b)r (e)f(included)g(in)g(the)g(Mo)r(di\014ed)h(V)-6 b(ersion.)378 1773 y(N.)59 b(Do)21 b(not)h(retitle)g(an)n(y)g(existing)g(section)g (to)g(b)r(e)f(En)n(titled)h(\\Endorsemen)n(ts")h(or)e(to)h(con\015ict)h (in)e(title)g(with)h(an)n(y)g(In)n(v)l(arian)n(t)510 1852 y(Section.)376 1953 y(O.)59 b(Preserv)n(e)24 b(an)n(y)g(W)-6 b(arran)n(t)n(y)25 b(Disclaimers.)330 2076 y(If)20 b(the)i(Mo)r (di\014ed)f(V)-6 b(ersion)20 b(includes)h(new)g(fron)n(t-matter)f (sections)i(or)e(app)r(endices)i(that)g(qualify)e(as)h(Secondary)h (Sections)f(and)330 2155 y(con)n(tain)k(no)f(material)g(copied)g(from)f (the)i(Do)r(cumen)n(t,)g(y)n(ou)f(ma)n(y)g(at)g(y)n(our)g(option)h (designate)g(some)f(or)g(all)f(of)g(these)i(sections)330 2234 y(as)c(in)n(v)l(arian)n(t.)31 b(T)-6 b(o)22 b(do)g(this,)f(add)h (their)g(titles)g(to)g(the)g(list)f(of)g(In)n(v)l(arian)n(t)i(Sections) f(in)g(the)g(Mo)r(di\014ed)g(V)-6 b(ersion's)20 b(license)i(notice.)330 2313 y(These)i(titles)g(m)n(ust)g(b)r(e)g(distinct)g(from)f(an)n(y)h (other)h(section)f(titles.)330 2414 y(Y)-6 b(ou)17 b(ma)n(y)g(add)g(a)g (section)h(En)n(titled)f(\\Endorsemen)n(ts",)i(pro)n(vided)f(it)e(con)n (tains)i(nothing)g(but)f(endorsemen)n(ts)h(of)f(y)n(our)g(Mo)r (di\014ed)330 2493 y(V)-6 b(ersion)27 b(b)n(y)g(v)l(arious)g (parties|for)f(example,)i(statemen)n(ts)h(of)e(p)r(eer)g(review)g(or)f (that)j(the)e(text)i(has)e(b)r(een)h(appro)n(v)n(ed)g(b)n(y)g(an)330 2572 y(organization)d(as)f(the)g(authoritativ)n(e)i(de\014nition)e(of)g (a)f(standard.)330 2673 y(Y)-6 b(ou)24 b(ma)n(y)h(add)f(a)h(passage)g (of)e(up)i(to)f(\014v)n(e)h(w)n(ords)f(as)g(a)g(F)-6 b(ron)n(t-Co)n(v)n(er)25 b(T)-6 b(ext,)24 b(and)h(a)f(passage)h(of)f (up)g(to)h(25)g(w)n(ords)e(as)h(a)h(Bac)n(k-)330 2752 y(Co)n(v)n(er)k(T)-6 b(ext,)31 b(to)f(the)f(end)h(of)f(the)g(list)g(of) f(Co)n(v)n(er)i(T)-6 b(exts)29 b(in)g(the)h(Mo)r(di\014ed)f(V)-6 b(ersion.)47 b(Only)28 b(one)i(passage)g(of)e(F)-6 b(ron)n(t-Co)n(v)n (er)330 2831 y(T)g(ext)26 b(and)f(one)h(of)e(Bac)n(k-Co)n(v)n(er)i(T)-6 b(ext)26 b(ma)n(y)f(b)r(e)g(added)h(b)n(y)f(\(or)g(through)h (arrangemen)n(ts)g(made)f(b)n(y\))h(an)n(y)g(one)f(en)n(tit)n(y)-6 b(.)36 b(If)25 b(the)330 2909 y(Do)r(cumen)n(t)i(already)e(includes)h (a)f(co)n(v)n(er)h(text)h(for)d(the)j(same)e(co)n(v)n(er,)h(previously) f(added)i(b)n(y)e(y)n(ou)h(or)f(b)n(y)h(arrangemen)n(t)g(made)330 2988 y(b)n(y)e(the)h(same)f(en)n(tit)n(y)h(y)n(ou)g(are)e(acting)i(on)g (b)r(ehalf)e(of,)h(y)n(ou)g(ma)n(y)g(not)h(add)f(another;)h(but)g(y)n (ou)f(ma)n(y)g(replace)h(the)f(old)g(one,)h(on)330 3067 y(explicit)f(p)r(ermission)f(from)f(the)j(previous)f(publisher)f(that)i (added)g(the)f(old)g(one.)330 3168 y(The)h(author\(s\))h(and)f (publisher\(s\))g(of)f(the)h(Do)r(cumen)n(t)h(do)f(not)g(b)n(y)g(this)g (License)g(giv)n(e)g(p)r(ermission)e(to)j(use)e(their)h(names)g(for)330 3247 y(publicit)n(y)f(for)f(or)g(to)h(assert)g(or)g(imply)f(endorsemen) n(t)i(of)e(an)n(y)h(Mo)r(di\014ed)g(V)-6 b(ersion.)215 3348 y(5.)60 b(COMBINING)24 b(DOCUMENTS)330 3449 y(Y)-6 b(ou)24 b(ma)n(y)f(com)n(bine)h(the)g(Do)r(cumen)n(t)h(with)e(other)h (do)r(cumen)n(ts)h(released)e(under)h(this)f(License,)h(under)f(the)h (terms)g(de\014ned)g(in)330 3528 y(section)e(4)g(ab)r(o)n(v)n(e)h(for)e (mo)r(di\014ed)h(v)n(ersions,)f(pro)n(vided)h(that)h(y)n(ou)f(include)g (in)f(the)i(com)n(bination)f(all)f(of)h(the)g(In)n(v)l(arian)n(t)h (Sections)330 3607 y(of)j(all)f(of)g(the)i(original)e(do)r(cumen)n(ts,) j(unmo)r(di\014ed,)f(and)f(list)f(them)i(all)e(as)h(In)n(v)l(arian)n(t) h(Sections)g(of)f(y)n(our)g(com)n(bined)g(w)n(ork)g(in)330 3686 y(its)d(license)h(notice,)h(and)f(that)h(y)n(ou)f(preserv)n(e)g (all)f(their)h(W)-6 b(arran)n(t)n(y)24 b(Disclaimers.)330 3787 y(The)c(com)n(bined)h(w)n(ork)f(need)h(only)f(con)n(tain)i(one)e (cop)n(y)h(of)f(this)g(License,)h(and)g(m)n(ultiple)e(iden)n(tical)i (In)n(v)l(arian)n(t)g(Sections)g(ma)n(y)f(b)r(e)330 3866 y(replaced)k(with)f(a)g(single)f(cop)n(y)-6 b(.)32 b(If)23 b(there)h(are)f(m)n(ultiple)f(In)n(v)l(arian)n(t)i(Sections)h(with)e (the)g(same)g(name)h(but)g(di\013eren)n(t)f(con)n(ten)n(ts,)330 3945 y(mak)n(e)j(the)g(title)g(of)f(eac)n(h)i(suc)n(h)e(section)i (unique)f(b)n(y)g(adding)g(at)g(the)g(end)g(of)f(it,)g(in)g(paren)n (theses,)i(the)f(name)g(of)f(the)i(original)330 4024 y(author)22 b(or)f(publisher)f(of)h(that)h(section)h(if)d(kno)n(wn,)i (or)e(else)i(a)f(unique)h(n)n(um)n(b)r(er.)30 b(Mak)n(e)22 b(the)g(same)f(adjustmen)n(t)h(to)g(the)g(section)330 4102 y(titles)i(in)f(the)i(list)e(of)g(In)n(v)l(arian)n(t)i(Sections)g (in)e(the)i(license)e(notice)i(of)f(the)g(com)n(bined)h(w)n(ork.)330 4204 y(In)17 b(the)h(com)n(bination,)h(y)n(ou)f(m)n(ust)f(com)n(bine)h (an)n(y)f(sections)h(En)n(titled)g(\\History")f(in)f(the)i(v)l(arious)f (original)f(do)r(cumen)n(ts,)k(forming)330 4282 y(one)27 b(section)f(En)n(titled)h(\\History";)g(lik)n(ewise)e(com)n(bine)i(an)n (y)f(sections)h(En)n(titled)f(\\Ac)n(kno)n(wledgemen)n(ts",)j(and)e(an) n(y)f(sections)330 4361 y(En)n(titled)e(\\Dedications".)33 b(Y)-6 b(ou)24 b(m)n(ust)g(delete)h(all)e(sections)h(En)n(titled)h (\\Endorsemen)n(ts.")215 4462 y(6.)60 b(COLLECTIONS)24 b(OF)f(DOCUMENTS)330 4563 y(Y)-6 b(ou)26 b(ma)n(y)g(mak)n(e)h(a)f (collection)h(consisting)f(of)g(the)h(Do)r(cumen)n(t)g(and)f(other)h (do)r(cumen)n(ts)g(released)g(under)f(this)g(License,)g(and)330 4642 y(replace)e(the)f(individual)g(copies)h(of)e(this)h(License)h(in)f (the)h(v)l(arious)e(do)r(cumen)n(ts)j(with)e(a)g(single)g(cop)n(y)h (that)g(is)f(included)g(in)g(the)330 4721 y(collection,)j(pro)n(vided)g (that)h(y)n(ou)f(follo)n(w)f(the)h(rules)f(of)g(this)g(License)h(for)f (v)n(erbatim)h(cop)n(ying)g(of)f(eac)n(h)i(of)e(the)h(do)r(cumen)n(ts)h (in)330 4800 y(all)c(other)h(resp)r(ects.)330 4901 y(Y)-6 b(ou)29 b(ma)n(y)g(extract)h(a)f(single)g(do)r(cumen)n(t)h(from)e(suc)n (h)h(a)g(collection,)i(and)e(distribute)g(it)g(individually)f(under)h (this)g(License,)330 4980 y(pro)n(vided)i(y)n(ou)g(insert)f(a)g(cop)n (y)h(of)f(this)h(License)g(in)n(to)f(the)i(extracted)g(do)r(cumen)n(t,) h(and)e(follo)n(w)e(this)i(License)g(in)f(all)f(other)330 5059 y(resp)r(ects)24 b(regarding)g(v)n(erbatim)g(cop)n(ying)h(of)e (that)i(do)r(cumen)n(t.)215 5160 y(7.)60 b(A)n(GGREGA)-6 b(TION)25 b(WITH)f(INDEPENDENT)f(W)n(ORKS)330 5261 y(A)h(compilation)g (of)f(the)i(Do)r(cumen)n(t)g(or)f(its)f(deriv)l(ativ)n(es)i(with)e (other)i(separate)g(and)f(indep)r(enden)n(t)i(do)r(cumen)n(ts)g(or)d(w) n(orks,)g(in)330 5340 y(or)f(on)h(a)g(v)n(olume)g(of)f(a)h(storage)g (or)g(distribution)f(medium,)g(is)g(called)h(an)g(\\aggregate")i(if)d (the)h(cop)n(yrigh)n(t)h(resulting)e(from)g(the)p eop end %%Page: 582 600 TeXDict begin 582 599 bop 150 -116 a FK(GNU)31 b(F)-8 b(ree)31 b(Do)s(cumen)m(tation)i(License)2098 b(582)330 299 y 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(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) g(.)h(.)f(.)g(.)g(.)g(.)52 b Fj(18)p eop %%Page: -2 4 -2 3 bop 3699 -116 a Fj(ii)449 83 y(3.35)92 b(Thread-safet)m(y)15 b Ff(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g (.)g(.)g(.)g(.)g(.)h(.)f(.)44 b Fj(18)449 193 y(3.36)92 b(Legal)31 b(issues)13 b Ff(.)h(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g (.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)h(.) f(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)42 b Fj(18)449 302 y(3.37)92 b(Non-UNIX)32 b(p)s(ortabilit)m(y)20 b Ff(.)12 b(.)j(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g (.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)49 b Fj(19)449 412 y(3.38)92 b(Compatibilit)m(y)28 b(with)h(other)i (libraries)23 b Ff(.)15 b(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g (.)h(.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)55 b Fj(19)449 521 y(3.39)92 b(P)m(arallelism)25 b Ff(.)15 b(.)g(.)g(.)h(.)f(.)g(.)g (.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g (.)56 b Fj(20)449 631 y(3.40)92 b(Precision)22 b Ff(.)15 b(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)g (.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) g(.)g(.)g(.)g(.)g(.)g(.)g(.)h(.)f(.)52 b Fj(20)449 741 y(3.41)92 b(Miscellaneous)18 b Ff(.)c(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g (.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)g(.)g(.) g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)47 b Fj(20)150 983 y Fk(Cop)l(ying)23 b Fg(.)d(.)f(.)g(.)h(.)f(.)h(.)f(.)h (.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.) g(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)67 b Fk(21)p eop %%Page: 1 5 1 4 bop 150 -116 a Fj(Ab)s(out)30 b(GSL)3093 b(1)150 299 y Fh(Ab)t(out)53 b(GSL)150 533 y Fj(The)42 b Ff(GNU)i(Scienti\014c) g(Libr)-5 b(ary)52 b Fj(is)42 b(a)h(library)e(of)i(scien)m(ti\014c)f (subroutines.)77 b(It)43 b(aims)f(to)h(pro)m(vide)g(a)150 643 y(con)m(v)m(enien)m(t)32 b(in)m(terface)f(to)g(routines)e(that)i (do)g(standard)e(\(and)i(not)f(so)h(standard\))f(tasks)h(that)g(arise)f (in)150 752 y(scien)m(ti\014c)37 b(researc)m(h.)64 b(More)39 b(than)f(that,)i(it)e(also)g(pro)m(vides)e(the)i(source)h(co)s(de.)63 b(Users)38 b(are)g(w)m(elcome)150 862 y(to)e(alter,)h(adjust,)f(mo)s (dify)-8 b(,)36 b(and)f(impro)m(v)m(e)g(the)h(in)m(terfaces)g(and/or)f (implemen)m(tations)f(of)h(whic)m(hev)m(er)150 971 y(routines)29 b(migh)m(t)h(b)s(e)g(needed)g(for)g(a)h(particular)e(purp)s(ose.)275 1106 y(GSL)j(is)f(in)m(tended)h(to)h(pro)m(vide)e(a)i(free)g(equiv)-5 b(alen)m(t)32 b(to)h(existing)f(proprietary)f(n)m(umerical)g(libraries) 150 1215 y(written)e(in)g(C)h(or)h(F)-8 b(ortran,)31 b(suc)m(h)f(as)h(NA)m(G,)h(IMSL's)d(CNL,)i(IBM's)g(ESSL,)e(and)h(SGI's) g(SCSL.)275 1350 y(The)d(target)i(platform)e(is)g(a)i(lo)m(w-end)e (desktop)h(w)m(orkstation.)40 b(The)27 b(goal)i(is)e(to)h(pro)m(vide)f (something)150 1460 y(whic)m(h)i(is)h(generally)f(useful,)g(and)h(the)g (library)e(is)i(aimed)f(at)i(general)g(users)e(rather)i(than)f(sp)s (ecialists.)p eop %%Page: 2 6 2 5 bop 150 -116 a Fj(Chapter)30 b(1:)41 b(Motiv)-5 b(ation)2656 b(2)150 299 y Fh(1)80 b(Motiv)-9 b(ation)150 552 y Fj(There)30 b(is)f(a)i(need)f(for)g(scien)m(tists)g(and)g(engineers)g(to)h(ha)m(v)m (e)g(a)g(n)m(umerical)e(library)f(that:)225 693 y Fi(\017)60 b Fj(is)28 b(free)h(\(in)f(the)g(sense)h(of)g(freedom,)g(not)g(in)f (the)h(sense)f(of)h(gratis;)h(see)f(the)g(GNU)h(General)e(Public)330 803 y(License\),)j(so)f(that)h(p)s(eople)e(can)i(use)f(that)h(library) -8 b(,)29 b(redistribute)f(it,)i(mo)s(dify)e(it)36 b(.)22 b(.)g(.)225 941 y Fi(\017)60 b Fj(is)29 b(written)h(in)f(C)h(using)f (mo)s(dern)g(co)s(ding)g(con)m(v)m(en)m(tions,)j(calling)d(con)m(v)m (en)m(tions,)i(scoping)36 b(.)22 b(.)g(.)225 1078 y Fi(\017)60 b Fj(is)25 b(clearly)g(and)g(p)s(edagogically)f(do)s(cumen)m(ted;)k (preferably)c(with)g(T)-8 b(eXinfo,)26 b(so)g(as)g(to)h(allo)m(w)e (online)330 1188 y(info,)30 b(WWW)h(and)f(T)-8 b(eX)31 b(output.)225 1326 y Fi(\017)60 b Fj(uses)30 b(top)h(qualit)m(y)e (state-of-the-art)34 b(algorithms.)225 1463 y Fi(\017)60 b Fj(is)29 b(p)s(ortable)h(and)g(con\014gurable)f(using)g Ff(auto)-5 b(c)g(onf)51 b Fj(and)30 b Ff(automake)p Fj(.)225 1601 y Fi(\017)60 b Fj(basically)-8 b(,)29 b(is)h(GNUlitically)e (correct.)275 1770 y(There)h(are)i(strengths)f(and)g(w)m(eaknesses)h (with)e(existing)h(libraries:)275 1911 y Ff(Netlib)42 b Fj(\(h)m(ttp://www.netlib.org/\))c(is)f(probably)e(the)j(most)g(adv) -5 b(anced)37 b(set)h(of)g(n)m(umerical)e(algo-)150 2021 y(rithms)e(a)m(v)-5 b(ailable)34 b(on)i(the)f(net,)j(main)m(tained)c(b) m(y)h(A)-8 b(T&T.)35 b(Unfortunately)g(most)h(of)f(the)h(soft)m(w)m (are)h(is)150 2130 y(written)27 b(in)g(F)-8 b(ortran,)30 b(with)d(strange)i(calling)e(con)m(v)m(en)m(tions)i(in)e(man)m(y)i (places.)40 b(It)28 b(is)f(also)i(not)f(v)m(ery)h(w)m(ell)150 2240 y(collected,)i(so)g(it)f(is)f(a)i(lot)f(of)h(w)m(ork)f(to)h(get)h (started)f(with)e(netlib.)275 2381 y Ff(GAMS)k Fj(\(h)m (ttp://gams.nist.go)m(v/\))26 b(is)c(an)h(extremely)g(w)m(ell)f (organized)h(set)g(of)g(p)s(oin)m(ters)f(to)i(scien)m(ti\014c)150 2490 y(soft)m(w)m(are,)46 b(but)41 b(lik)m(e)g(netlib,)i(the)f (individual)37 b(routines)j(v)-5 b(ary)42 b(in)e(their)h(qualit)m(y)g (and)g(their)f(lev)m(el)i(of)150 2600 y(do)s(cumen)m(tation.)275 2741 y Ff(Numeric)-5 b(al)34 b(R)-5 b(e)g(cip)g(es)41 b Fj(\(h)m(ttp://www.nr.com,)34 b(h)m(ttp://cfata2.harv)-5 b(ard.edu/nr/\))35 b(is)c(an)i(excellen)m(t)150 2850 y(b)s(o)s(ok:)38 b(it)24 b(explains)g(the)h(algorithms)f(in)g(a)i(v)m (ery)g(clear)f(w)m(a)m(y)-8 b(.)41 b(Unfortunately)24 b(the)i(authors)f(released)g(the)150 2960 y(source)g(co)s(de)g(under)e 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y(a)f(mo)s(dern)e(v)m(ersion)h(of)g(SLA)-8 b(TEC.)275 3899 y Ff(NSWC)34 b Fj(is)21 b(the)h(Na)m(v)-5 b(al)23 b(Surface)f(W)-8 b(arfare)23 b(Cen)m(ter)f(n)m(umerical)f(library)-8 b(.)36 b(It)22 b(is)f(a)h(large)g(public-domain)150 4009 y(F)-8 b(ortran)26 b(library)-8 b(,)25 b(con)m(taining)g(a)h(lot)f(of)h (high-qualit)m(y)e(co)s(de.)39 b(Do)s(cumen)m(tation)26 b(for)g(the)f(library)e(is)i(hard)150 4119 y(to)31 b(\014nd,)e(only)h (a)g(few)h(photo)s(copies)f(of)g(the)h(prin)m(ted)e(man)m(ual)g(are)i (still)d(in)h(circulation.)275 4260 y Ff(NA)n(G)34 b Fj(and)27 b Ff(IMSL)g Fj(b)s(oth)g(sell)f(high-qualit)m(y)g(libraries)f (whic)m(h)h(are)i(proprietary)-8 b(.)39 b(The)27 b(NA)m(G)h(library)150 4369 y(is)34 b(more)h(adv)-5 b(anced)34 b(and)g(has)h(wider)e(scop)s(e) i(than)f(IMSL.)h(The)f(IMSL)g(library)e(leans)i(more)h(to)m(w)m(ards) 150 4479 y(ease-of-use)i(and)d(mak)m(es)i(extensiv)m(e)g(use)e(of)h(v) -5 b(ariable)34 b(length)h(argumen)m(t)g(lists)f(to)h(em)m(ulate)h Fe(")p Fj(default)150 4588 y(argumen)m(ts)p Fe(")p Fj(.)275 4729 y Ff(ESSL)30 b Fj(and)g Ff(SCSL)g Fj(are)h(proprietary)e (libraries)e(from)j(IBM)h(and)f(SGI.)275 4870 y Ff(F)-7 b(orth)70 b(Scienti\014c)f(Libr)-5 b(ary)79 b Fj([see)70 b(the)g(URL)g(h)m(ttp://www.ta)m(ygeta.com/fsl/sciforth.h)m(tml].)150 4980 y(Mainly)29 b(of)i(in)m(terest)f(to)h(F)-8 b(orth)31 b(users.)275 5121 y Ff(Numeric)-5 b(al)41 b(A)n(lgorithms)g(with)h(C)52 b Fj(G.)39 b(Engeln-Mullges,)h(F.)f(Uhlig.)65 b(A)39 b(nice)g(n)m(umerical)e(library)150 5230 y(written)24 b(in)g(ANSI)h(C)f(with)g(an)h(accompan)m(ying)h(textb)s(o)s(ok.)39 b(Source)25 b(co)s(de)g(is)f(a)m(v)-5 b(ailable)25 b(but)f(the)h (library)150 5340 y(is)k(not)i(free)g(soft)m(w)m(are.)p eop %%Page: 3 7 3 6 bop 150 -116 a Fj(Chapter)30 b(1:)41 b(Motiv)-5 b(ation)2656 b(3)275 299 y Ff(NUMAL)42 b Fj(A)j(C)f(v)m(ersion)g(of)h(the)f(NUMAL)i (library)c(has)i(b)s(een)g(written)f(b)m(y)i(H.T.)g(Lau)f(and)g(is)150 408 y(published)30 b(as)k(a)g(b)s(o)s(ok)f(and)h(disk)e(with)h(the)h (title)f Fe(")p Fj(A)h(Numerical)e(Library)g(in)h(C)g(for)h(Scien)m (tists)f(and)150 518 y(Engineers)p Fe(")p Fj(.)39 b(Source)30 b(co)s(de)h(is)e(a)m(v)-5 b(ailable)30 b(but)g(the)g(library)e(is)i (not)g(free)h(soft)m(w)m(are.)275 653 y Ff(C)k(Mathematic)-5 b(al)38 b(F)-7 b(unction)36 b(Handb)-5 b(o)g(ok)45 b Fj(b)m(y)34 b(Louis)e(Bak)m(er.)51 b(A)34 b(library)d(of)j(function)e (appro)m(xima-)150 762 y(tions)h(and)g(metho)s(ds)g(corresp)s(onding)e (to)k(those)f(in)e(the)i Fe(")p Fj(Handb)s(o)s(ok)e(of)i(Mathematical)h (F)-8 b(unctions)p Fe(")150 872 y Fj(b)m(y)30 b(Abramo)m(witz)h(and)e (Stegun.)41 b(Source)30 b(co)s(de)h(is)e(a)m(v)-5 b(ailable)30 b(but)f(the)i(library)d(is)h(not)i(free)f(soft)m(w)m(are.)275 1006 y Ff(CCMA)-7 b(TH)40 b Fj(b)m(y)27 b(Daniel)f(A.)h(A)m(tkinson.)39 b(A)27 b(C)f(n)m(umerical)g(library)e(co)m(v)m(ering)k(similar)c(areas) k(to)f(GSL.)150 1116 y(The)41 b(co)s(de)h(is)f(quite)g(terse.)75 b(Earlier)40 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y(the)32 b(argumen)m(t)h(list)d(gets)j(to)s(o)g(long)f(and)f(confusing,)h(with)e (\(size1,)k(size2,)f(tda\))f(for)g(eac)m(h)h(matrix)f(and)150 4989 y(p)s(oten)m(tial)42 b(am)m(biguities)e(o)m(v)m(er)k(ro)m(w)e(vs)h (column)e(ordering.)75 b(In)41 b(this)g(case,)47 b(it)42 b(mak)m(es)h(sense)f(to)h(use)150 5099 y(gsl)p 263 5099 V 40 w(v)m(ector)32 b(and)d(gsl)p 859 5099 V 40 w(matrix,)h(whic)m(h)f (tak)m(e)j(care)f(of)g(this)e(for)h(the)h(user.)275 5230 y(So)i(really)f(the)i(library)d(has)j(t)m(w)m(o)h(lev)m(els)e({)h(a)g (lo)m(w)m(er)g(lev)m(el)f(based)g(on)h(C)f(t)m(yp)s(es)h(for)f(1d)g(op) s(erations,)150 5340 y(and)d(a)h(higher)e(lev)m(el)h(based)g(on)g(gsl)p 1380 5340 V 39 w(matrix)g(and)g(gsl)p 1999 5340 V 40 w(v)m(ector)i(for)e(general)g(linear)f(algebra.)p eop %%Page: 13 17 13 16 bop 150 -116 a Fj(Chapter)30 b(3:)41 b(Design)2777 b(13)275 299 y(Of)25 b(course,)j(it)e(w)m(ould)g(b)s(e)f(p)s(ossible)f (to)k(de\014ne)e(a)g(v)m(ector)j(v)m(ersion)d(of)g(the)h(lo)m(w)m(er)g 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b(Constan)l(ts)150 1286 y Fj(Av)m(oid)30 b(arbitrary)f(constan)m(ts.)275 1425 y(F)-8 b(or)50 b(example,)k(don't) 49 b(hard)f(co)s(de)i Fe(")p Fj(small)p Fe(")d Fj(v)-5 b(alues)49 b(lik)m(e)g('1e-30',)56 b('1e-100')d(or)c Fe(10*GSL_DBL_)150 1535 y(EPSILON)28 b Fj(in)m(to)j(the)f(routines.)40 b(This)28 b(is)i(not)h(appropriate)e(for)h(a)h(general)f(purp)s(ose)f (library)-8 b(.)275 1674 y(Compute)34 b(v)-5 b(alues)34 b(accurately)h(using)e(IEEE)h(arithmetic.)53 b(If)34 b(errors)h(are)g(p)s(oten)m(tially)e(signi\014can)m(t)150 1784 y(then)41 b(error)g(terms)g(should)f(b)s(e)h(estimated)g(reliably) e(and)i(returned)g(to)h(the)f(user,)j(b)m(y)d(analytically)150 1893 y(deriving)28 b(an)j(error)f(propagation)g(form)m(ula,)g(not)g (using)f(guessw)m(ork.)275 2033 y(A)i(careful)f(consideration)g(of)h (the)h(algorithm)e(usually)f(sho)m(ws)h(that)i(arbitrary)e(constan)m (ts)i(are)g(un-)150 2142 y(necessary)-8 b(,)31 b(and)f(represen)m(t)h 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y(of)j(these)g(righ)m(ts.)40 b(F)-8 b(or)31 b(example,)f(if)f(y)m(ou)h(distribute)d(copies)j(of)g (the)g Ff(GNU)i(Scienti\014c)f(Libr)-5 b(ary)8 b Fj(-related)150 2007 y(co)s(de,)35 b(y)m(ou)f(m)m(ust)f(giv)m(e)h(the)f(recipien)m(ts)g (all)f(the)i(righ)m(ts)f(that)h(y)m(ou)g(ha)m(v)m(e.)51 b(Y)-8 b(ou)34 b(m)m(ust)f(mak)m(e)i(sure)d(that)150 2117 y(they)-8 b(,)31 b(to)s(o,)h(receiv)m(e)f(or)f(can)h(get)g(the)g (source)f(co)s(de.)41 b(And)30 b(y)m(ou)h(m)m(ust)f(tell)f(them)i (their)e(righ)m(ts.)275 2252 y(Also,)e(for)g(our)g(o)m(wn)g (protection,)i(w)m(e)e(m)m(ust)g(mak)m(e)i(certain)e(that)h(ev)m(ery)m (one)h(\014nds)c(out)j(that)f(there)h(is)150 2361 y(no)h(w)m(arran)m(t) m(y)i(for)e(the)h(programs)f(that)h(relate)g(to)h Ff(GNU)g (Scienti\014c)g(Libr)-5 b(ary)8 b Fj(.)42 b(If)29 b(these)h(programs)g (are)150 2471 y(mo)s(di\014ed)g(b)m(y)h(someone)i(else)e(and)h(passed)f (on,)h(w)m(e)g(w)m(an)m(t)h(their)e(recipien)m(ts)f(to)j(kno)m(w)f (that)g(what)g(they)150 2580 y(ha)m(v)m(e)f(is)d(not)i(what)f(w)m(e)h (distributed,)d(so)i(that)h(an)m(y)g(problems)d(in)m(tro)s(duced)h(b)m (y)i(others)f(will)e(not)i(re\015ect)150 2690 y(on)h(our)g(reputation.) 275 2824 y(The)g(precise)h(conditions)e(of)i(the)h(licenses)e(for)g (the)i(programs)e(curren)m(tly)h(b)s(eing)e(distributed)f(that)150 2934 y(relate)i(to)g Ff(GNU)h(Scienti\014c)h(Libr)-5 b(ary)38 b Fj(are)30 b(found)e(in)h(the)g(General)g(Public)f(Licenses)h (that)h(accompan)m(y)150 3044 y(them.)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF