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cleartomark %%EndFont %%BeginFont: CMSL8 %!PS-AdobeFont-1.1: CMSL8 1.0 %%CreationDate: 1991 Aug 20 16:41:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSL8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -9.46 def /isFixedPitch false def end readonly def /FontName /CMSL8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 101 /e put dup 102 /f put dup 114 /r put readonly def /FontBBox{-57 -250 1183 750}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSLTT10 %!PS-AdobeFont-1.1: CMSLTT10 1.0 %%CreationDate: 1991 Aug 20 16:41:43 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSLTT10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -9.46 def /isFixedPitch true def end readonly def /FontName /CMSLTT10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 39 /quoteright put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two 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 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 88 /X put dup 90 /Z put dup 95 /underscore put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q 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 readonly def /FontBBox{-20 -233 617 696}readonly def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMTT8 %!PS-AdobeFont-1.1: CMTT8 1.0 %%CreationDate: 1991 Aug 20 16:46:05 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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1E150BB09E04F6CFC6D0F8FD0604D937272AAB79C76BC23116D291F300A1FAEF ED9E98434A8CB0473494217CCB99F044B293AE9530437EC29074F7C33CFE36C3 D2A50D9335539AD958DCAB84452E7FE7EF4050109F3FFACA6F8FF911822FF740 73C39DFAFD0010ACECD331C084CE068F360195E329D1C267CD4546CBB04394D8 D5CF5D195E6A5230739349CE9F196C4FCEBEAEADFBAD4E17806BFA134D474169 A6527B4A7FADD2B9FEAE0BF509544A2755865F37D42982BDDB6BA6608F453419 53566FD8B7B8137345BEC470D12E07087CFB6F96F5FC5560B597C273C7234D83 89E15868F8257918930A5655C9E2413E4C222483EDB530561D771EF87C9842E7 ABD968A67383C8D85BA3AA67173F56CEBD09E72F75334542EA7E361F85E37C21 10BDD4D35D9C8E9EEA6E0CD5E17F11916EFA38588A2C36C0760A1990F2010069 003E036DEB64DC24745C5481EEF26FA103D061EB450C9032716B5BFF13A13CB4 029E1B680E8A685ADFD409A9884D51A7878876616EFADD10EF5CE36BA85361CB CA2A8B8E9C928AF8BCB980C26DE4283F8C4C8C8E960ACBC28B0111B77B7D7265 EAA78F42306C 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY8 %!PS-AdobeFont-1.1: CMSY8 1.0 %%CreationDate: 1991 Aug 15 07:22:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 13 /circlecopyrt put dup 15 /bullet put readonly def /FontBBox{-30 -955 1185 779}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964 7D53359E51216774A4EAA1E2B58EC3176BD1184A633B951372B4198D4E8C5EF4 A213ACB58AA0A658908035BF2ED8531779838A960DFE2B27EA49C37156989C85 E21B3ABF72E39A89232CD9F4237FC80C9E64E8425AA3BEF7DED60B122A52922A 221A37D9A807DD01161779DDE7D5FC1B2109839E5B52DFBB2A7C1B5D8E7E8AA0 5B10EA43D6A8ED61AF5B23D49920D8F79DAB6A59062134D84AC0100187A6CD1F 80F5DDD9D222ACB1C23326A7656A635C4A241CCD32CBFDF8363206B8AA36E107 1477F5496111E055C7491002AFF272E46ECC46422F0380D093284870022523FB DA1716CC4F2E2CCAD5F173FCBE6EDDB874AD255CD5E5C0F86214393FCB5F5C20 9C3C2BB5886E36FC3CCC21483C3AC193485A46E9D22BD7201894E4D45ADD9BF1 CC5CF6A5010B5654AC0BE0DA903DB563B13840BA3015F72E51E3BC80156388BA F83C7D393392BCBC227771CDCB976E93302530FA3F4BEF341997D4302A48384A CEFFC1559A8B405E037AF56B9DE3809EFA62660A93C351BCFB7718678227EBCE D9FB011FC3673F73458233A0F54B99B69BED915B1B67B75846A626E7C4177F3F 48EBB7746A8DDD48CEFB60B3D6444B8A776DDD77A1B09157EB20EAA79EE8A3AE 0FCCBA37BE84B859EFFFC62B880B973A7E11DE7E1B5668834F24E8BBB653007B F267CFD50A6AC9DF8585D21ADA5B74693E304E93E7025BF1AFE5BDA9F6F06AF0 30B064EBBECD6D3ED312AB01883FA0B9529DF8FBEB77B7BD347F2B42A2261BD4 33E016C90648426E807F83801345F5BC6EF2FB98BBC3F1EC8BE4190C521D11AA 58111D12E4CF3D03C9680A5E87DF449186BD1C7E51273008486025027E082494 C044078710D13202567B4EE4138EF610BBAF66842AACEB230F4B050BA61DB7F3 DF296335C8254B7EAC55629D91571010A2D6C836AB85906B2008650C7874322F 250FC38FC78E4318CFD0B8D7F9A7EF0CD4C791E806F2003D 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR8 %!PS-AdobeFont-1.1: CMR8 1.0 %%CreationDate: 1991 Aug 20 16:39:40 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 34 /quotedblright put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon 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 81 /Q 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 92 /quotedblleft put dup 96 /quoteleft put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q 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 123 /endash put dup 124 /emdash put readonly def /FontBBox{-36 -250 1070 750}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF4E9D2405B169CD5365D6ECED5D768D66D6C 68618B8C482B341F8CA38E9BB9BAFCFAAD9C2F3FD033B62690986ED43D9C9361 3645B82392D5CAE11A7CB49D7E2E82DCD485CBA1772CE422BB1D7283AD675B65 48A7EA0069A883EC1DAA3E1F9ECE7586D6CF0A128CD557C7E5D7AA3EA97EBAD3 9619D1BFCF4A6D64768741EDEA0A5B0EFBBF347CDCBE2E03D756967A16B613DB 0FC45FA2A3312E0C46A5FD0466AB097C58FFEEC40601B8395E52775D0AFCD7DB 8AB317333110531E5C44A4CB4B5ACD571A1A60960B15E450948A5EEA14DD330F EA209265DB8E1A1FC80DCD3860323FD26C113B041A88C88A21655878680A4466 FA10403D24BB97152A49B842C180E4D258C9D48F21D057782D90623116830BA3 9902B3C5F2F2DD01433B0D7099C07DBDE268D0FFED5169BCD03D48B2F058AD62 D8678C626DC7A3F352152C99BA963EF95F8AD11DB8B0D351210A17E4C2C55AD8 9EB64172935D3C20A398F3EEEEC31551966A7438EF3FEE422C6D4E05337620D5 ACC7B52BED984BFAAD36EF9D20748B05D07BE4414A63975125D272FAD83F76E6 10FFF8363014BE526D580873C5A42B70FA911EC7B86905F13AFE55EB0273F582 83158793B8CC296B8DE1DCCF1250FD57CB0E035C7EDA3B0092ED940D37A05493 2EC54E09B984FCA4AB7D2EA182BCF1263AA244B07EC0EA912A2BCC6CA6105B29 044005DDBEAF88E0F05541BBD233977A447B469F013D8535A9D7023CC0FB7B49 A95CD2B6F18935C37F49E9A73E97A8602C5C26EE13D7A04A188336FCAB4CDEE0 23DE9D803FD6E8D846B3F729BD36137E834E016242CD2F7BF048959DD45AD413 19B985D05E5D422F3D0968375EA6A90FBEBF8B42B15F15280469D69629C08A42 1C298CC027CC288B9C984239ABB96B6A891C1360D08F9ECC22202861E4CE9B39 8BFC6F94072527A7506414355537169B83AF8A09EF6E5E1EA5EC41D89148FFAE 325AC2F60AB8D3E72737173A1375FE631213F18492C9EA9F233CF098315D2953 EB45BCB8A5E505517BC98363E8FA90A4A2B26132DFF09DE1F2E18084D5666AF0 A425F5D1E604D3CEA844C4C4A6E79B10D07621B33E7F4997BC27D23179BF0FB6 CBB600AC2958DA3A2C5E9257EB71BB04D95870FE625CCE9CF39B27E942E6C18A A8899321A338212B6B57C83CC7E4EA2CF7DD78FBC786AFAEE7E3873DAC601E2C 0EFD4427F00ADDB644BCCDEE912A7742385C0FEBA5E620B6B7CAD9A091D6F2FB 8554FE30807276B7A3668ED70F983F811E5DB36252F80757B40BA46079C7E9C5 24D7C5B0540B73A5C02692AD851521654C152958717943ACC0BA498E0B06E4AD 172C07D0526F1C4285A2CF706AC95E79064F431646E42C17DD3F6674F45C7607 5BDA780DC42942E08045624ABE2A9DEAAD9FD3343C7AC9BEC858FF3F9EEF9EB3 32521CB097C2DB21EBA7480610C470525C637E5DFC85B9A4FCA49F4F26D5A669 46E4C672C55DB0BD77BB706780F063813B811AE9E0C954FB0A84521EB322585D 95A35892067A9E28F689C4AD66E5090989CBB8C756E1B6CDE1E58E82CADD4ADE 71FD101003E18F035963697CE88C531E90625C75B493DD048B4D5DA5240E0BF4 675B3710C62A8F68C2CF41C5CD99D0F031A0FA261C734520D120081872D2DBF7 06D5EA5BB547692857A53D311FAFCA6E7A95157AB322E46E84A4E61916213755 EBEE588F5872330967869E1C3522293D72C27D4B4BF65207729F7A2099B83AAD 9EADC23D128358606580EFE39B896DB12208DD59C0F77756DCCE3797FA7816C8 C1D8875F92DF17F1871D85AF7DC34081D01B38363ECAE2C880028E85025952C7 F9826D29D72070C886D883F82426C99E50C6691306F5A21631A104F8C6865437 7C6E95C014CE169EBA1C33BF73D0CF559F9137664BC2546B7938197BF69DF210 390ECCF9F4BD5EEB65AEE60C3A0A0E8B1460EB08C967CF23A7293383169C4207 32AF91815682D2E4C34E2959E9F9C07DEEA1969AA619B8D5B0568E8D2FCC89AF BFDAE9C5C102F92618AFB13CAEFEA217E7097FCA60C439218825FA32D6DA02E4 AC78B4F50622A87A7066E747A3CD042CF1CBA3E93F8D5CB15228A4A04DA3ABAF 5655D4D816576CE429E220F2D2363EED3F8E2900E13AE5F53E1049D1AE9F1A71 948929CFCFE2AE6AF9D4991E2F87EAC26724B2282590F08AE4286B2299DADAC9 B1C85844A790C7AE357B8449AB08E3C46ED0D61BA40362D3D3209E9A9BBE64A3 1EE31AC4CEFB415DB57578A2943A26CDC9C572CD0741A216AFECFC3D17AC25A2 299D589DAEC96D3B82CFED5CF48C085F63E6C65E7ACEF039F6D2255B6C57FE77 EFBBF9DE94913E471539D0784A52C5988914676388F7B3B3D644E255267C510A A0D1F7BA69D35C251C9DB5FA4FE11DB5F048E8A8EECAD0D057689126193C467F E6F22122672599AB8CD83553D14D070FE00AA381644BD20897E35EC0084DA30A 344545C10A274220C6ECBB87D4A0D319614D234DCF434396737046E1B77F53AB 50DA821DE01CD6826541E6C4AE974EAAB6D5BEEA30B910E5A4D3CD9E4A40134F 98BF023C31722C3061CE4B24B9A7468727BE50EF1E10C06F3EE9BB8C5F636380 6701CF5C14FF798239877B45DB0EB518E5453F7B5DB48136A870D42534D51E74 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All Rights Reserved) readonly def /FullName (CMSY5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put readonly def /FontBBox{21 -944 1448 791}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964 7D53359E51216774A4EAA1E2B58EC3176BD1184A633B951372B4198D4E8C5EF4 A213ACB58AA0A658908035BF2ED8531779838A960DFE2B27EA49C37156989C85 E21B3ABF72E39A89232CD9F4237FC80C9E64E8425AA3BEF7DED60B122A52922A 221A37D9A807DD01161779DDE7D5FC1B2109839E5B52DFBAF552B11EFFB6A16C F03FB920C15AE724EFDF0CCBF00A838D34440FF9FED532F44036AD22561184C5 283722DDFA7285E62754372D716D704AC0E00B2F6AB67154241C7449AA047833 94CEDB08E8C92907FE72A0B05AE36A7B9226ACD6E7890A0B528FDDE84A950FC6 801DE75CF2E739E9121149CCB8B1C87A106822648D84A3D3FBF295EE6C4BF403 BBE9A1C1F6DAEDD1E642ACC486E609703D7612BFFD10C324F5DC710811F7F614 3691B400E3773987424C0D2B0D8A736873C6371DDB2442F05E018A2B5CA9A4AA 17AABB95D09E5890CFFFED5AC01495D89A53D3C89F3D8DBAC85E06561646557A B16BAE67D1C3D5F6EC51F05178B6CBC34F9F491056E5ADE1256277DB904A7F75 6105D774449D6CBB70F2F539D739D011BDBE27A9674A5CA3D5BD42B7FBFBBA35 89966597639DE60F2A4812AFAEFBBBB26C9E24F72439F3AF2A7D5C0D2AFB5146 58112FC60E9307B9FE29090D81441A1C3B7E371656A3321A0031038D54BB6670 0594C9C72FDDE3DE50EE1CFBDEEE5B6DDBA17B1D6328651FE1EFD1E2B8376949 5353E35A988064FDB6CE37ED4570B49903AF26304DE40164903476EC2F4830D6 4995CEE9B37B 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY9 %!PS-AdobeFont-1.1: CMSY9 1.0 %%CreationDate: 1991 Aug 15 07:22:27 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 3 /asteriskmath put dup 106 /bar put readonly def /FontBBox{-30 -958 1146 777}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI9 %!PS-AdobeFont-1.1: CMMI9 1.100 %%CreationDate: 1996 Jul 23 07:53:55 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 58 /period put dup 59 /comma put dup 60 /less put dup 78 /N put dup 99 /c put dup 101 /e put dup 105 /i put dup 110 /n put dup 113 /q put dup 115 /s put dup 120 /x put readonly def /FontBBox{-29 -250 1075 750}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D5993DFC0930297866E1CD0A319B6B1FD958 9E394A533A081C36D6F5CA5FED4F9AC9ADE41E04F9FC52E758C9F45A92BED935 86F9CFDB57732045913A6422AD4206418610C81D882EE493DE9523CC1BFE1505 DD1390B19BC1947A01B93BC668BE9B2A0E69A968554239B88C00AF9FBDF09CCD 67D3B2094C11A04762FE8CC1E91D020A28B3C122D24BEAACF82313F4604F2FEF 6E176D730A879BE45DD0D4996EF0247AEB1CA0AB08FF374D99F06D47B36F9554 FAD9A2D3CE451B7791C3709D8A1DDDEFBD840C1B42AB824D5A0DFF0E0F15B0B7 22AEEB877FF489581DA6FA8DA64944555101EB16F7AB0B717E148B7B98D8DBFD 730C52937E226545CF8DC3E07C5BA30739BAFCD0F2B44275A6D503F582C0FB4F 449963D0AD2FAFDE33BA3D77BCA9D1DF878DDAFCA2E22CC4BACD542B282164C7 97C2BDE318AF9D501CA21F6E662E7AAB75A5F24D2C182E598D175D44E88AB19A E7CD59584F95B389183EE21B525BF52A3F23C0FE5383A5565A19361D716F508C AAB78411CA5A4D27552CC1C435760D5A89D535B71C593E755C616661363308DA A683F54ED0C23FB2C225A008392B0B719F66F11A946A090B7C00B662A3C69599 B4ECB0CC70C85C4BBBF207E0026F6C7A19F2ACFB7A60804FC98A4BFFD7BFFF2B 9529E6D9D4238002BBC255BC62959D6F3381FE06E0621B879D5FE5B541D45A1E 759A6E7DC32B1D1632368D09A97039DF255B6492B1B2B7E2C1434E8306ECA7D3 5A79B6D614B4979F10988BC76ED53A5F45315CD7DA216221F842FD0F3E050DD2 BAC23C984D506D8F7D614BCB6B244F5F41321549BB0BD041FBF3053307168680 3435E9C947D7F87B5D967FC8414668CB404B346CF11EA3EBF562EAE366BEC299 8A4CAA3DC1CD553679340364AA090D81D254D9AE44A8A34C52CBBA85E65AA3BC 2978BB13D0B9D00F2B1931CBD17D0BADC8300EBACE22647F5029F38B2CB4A883 2777DBBD5706D890D68F9A780A6A2796C2B5F2F2DD3694CE8DC5C3FC6E1C4582 78DF3097CF62D17BA2E8B7F17230ED2CC2CD28D7F527C1CD9D2F0EA5752590B9 7CE625CF516F9D1E8F506F459C9FA3D09E530FFBE8D45AE08841C4CB8AB09F8E 875DD6548C0A027ADC45090031D86122E655261D0A312BA1A6148A5190FEF3B4 D017964FF16FCB03B1BAAD9A2499A8C11B665EA726EEFC696AE2FC019FE2125F 4895C3AED0E724DF0CB98549BD69CC09B6258DC6AC81DC04E03FBE6DDB53167C EDB515A36828FFBB50DF302B333E4D2B57D2E4D378AD481876E3798DE20CC333 456A2B0E93DDF69FDD2C57D17057063AD58E778E2D1CC0DB4D7E266B31863769 95418AAEF32C30E2D448ABDCA6DD424FCB4D272166AB6E7ECF097668FFB94633 0C5CA95246E79EF0B42139B9FFF1E8125C411C6FE4678A6026EC28E14037A117 0FC019C2A2DB5DE5A453A1523CB3240C137327705F32BC32BB2F12CAB1A9E53D BF371C627D2CE50F7C24A15E2771B0F3FA1B4ACD91D453FF97B6A2035B4B7FBA 43A4EB219687A41974FC8E9D4CAC0A06E7EAC67384BBCA056E964E86AAF34D10 C5DBC210F0786EBACB5D61E4454E5DB2A6DA258DA948B64953132DED14ECE61F 9F8EEDBD95C2F739CFC949548233F4EC4C0AFC4146013F9E8E3D5369BDA7D984 BAFD6AA00F81890189973A0B21EE68C90EEFC092B3383BDC2157C34F88C5E90F 9FE4660E85104523E0CF73FBC680C3FB3096FF26E5F1E7EEC4574B401C31C79D 0E3B149B3B93BC7B443ADDE50C532E8A39106D8E323ED6E54661A855BE83E83A A1DDD368514138BFF4283CB90B282C94F179208FA0E86EAA6B9D2E3C5F922360 8215D43057DA7DD6388DFE96AA412000AEC55F98A9BF39C2333DA41DA5AFD0D6 65642F25CAD576E30CD9C213D9A905384D29A9C7C53DADB04603B8BB2B199393 25CE251767AF27AAF6D0032954EF262DC62EBF176AB894E620AD43635B32A388 FD58B2DF2CC2826BA7C768475AC33A9EC2534C27584293E63490193AE03FF9EE 79AE25DE07F0AF2230A599A715BEBD032F675D35199A45A250F631E95B3DA12E 7FA4B7004FA53446FF462EF3479344A6F2B989B23E571AB4995A1FBF0D0090CE 2CBEFDE67472DCB740999EB96D86E9292C2F1DC2639F32D78B14CEA2CBA06514 BFC16D9E50870E16BA4D87B33F8E5824A382EDE8EA9554E0403A44C3776D7A12 AFA510E115D0BBCA69ADB8C4E43A382566D2BB09CFFC1EED0E305D83A1455DF6 AF58110882D2534AFD5E67DA5D734C2090D1A7E9757EA3CC61D98892A5DB9F84 498749148940D6E816979FE17DAE00137A7CEF126CA77F7C8625718F719D6FEF 62C053701965BE1B1059060575569494A20CD3C1B49D543E57B71215B4D0B0F2 25E7560788C66DC23A3D3BE87ECC1843B7AE46F573CE9074F1A404CC7A05C1B5 8AFB921092892F89AD8FAECBD46F9337C9696B9A98377560F63F95B7655BBEE5 03A4C0B17E1FBDD9BF6DAFFC44E3A40FB794A4370BD9E0EE42D3350000526AE0 38F607E2CD21E6B4B48321E0DB23427342921542CCD51796FFA72ED47139B833 D02D3B88937FBDEA7D132707F39EEDD2DFBB7F97DD6A3F3F3A466C46E8B08D04 FA7BD3F218D45CE2FE47D0010A4B996A33CB0AF81B883CD2C178C9B48B49D7F9 B8537D554CFEE340BB6719E9584F19EB48D53D36DC7430AC8268A8A888B901B5 F28395063A1F713367A02DEFC16620D3A422D9F9086FE16DC9B6D76411E7CA9D EF8A5F1E68033263937064A6BC4ACE649081256AE1927A2200DFCCC271D74083 D13B9A9133A2348809B926F35D2AA9F70066C50014B2356D68764D9F28843691 5A2CAC8A663F1948DEF8A000C5A03A1A21DCB38FE6D567D58B8027B44A80F2BF 5A535019A81D6ECFF0C3805B5A1956BE619B73DDD3BB0374DE1E0C3677D00D43 0C29F856B0A472BB405706E2CF214C9C37734B91DC2629C3A998308046914FA7 40E54313CE25886108462087F37AC8373C750FEB9A511C94C244F09079D5ECA6 7F74E966A4080B507BF3FF7AD8851A94DD12CC682B2714BBF5C2EE2EC5488979 EB600E249DE5A35882E3AD98665BBBA4E83B3A8D4F33DD4306B3BF06E56F97ED 55979666C868754D40DFD5F861A29DBD036453C64798058A1817C984E2743F02 C1A6722781F0ACABF6283ECBA64099B44E0B6C7E8B52818D7100B51672A793F5 0D56CDDE3F9CBE3483DB12EB07EA9FBC2BC3290D99C54033E294A2CD9F34BF2B C375C7CD7F72062850785DD94C4D6EC3F4F7A8B1FF3C4412E9183AB690248BDF 21E99169C40F90D74C41FCA18D17985C327B4B68ADBBFE1C313ECA7298E6BF25 EA2A56A773B1FC6F079A777A993EC37872D1AC1CFC0E111231C621E43CFF58BC B95BC6559AA0A5809183712C7AC3868ACF93427B26C2C8FBD79B9DC0EB565B70 B40F3C5334B8F1405D97F5738ED490798FDDA718369BA21FE6A1EBAA4F3A5CD0 445E86104E128C0B37615EBB8DB14F05EA55BFA9B14954BC3AB908F10EF99F99 6A4584B35FAB7ABD8BBD25C778CC323C87F7A7924BF06E7CD906CE77E0A4ADF2 874C1F32649AB213D5B1A2FFE3799ACDE418115D5828C0AF77522393C67F8B8F 1744E3B985537B506B8C18F4166245737638794D10FA2F702E570B09B37A26BD 989C3FD725880B0989196D342AE3B6818C7E710A8EBDB1EAC5C92222D5196361 8D9DB894AC1FD65B24BF4AABFD27238F423AB3B12A8B17B702E78CF13E0BF388 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMB10 %!PS-AdobeFont-1.1: CMB10 1.0 %%CreationDate: 1991 Aug 20 16:34:36 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMB10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMB10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] 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 /FontBBox{-62 -250 1011 750}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI5 %!PS-AdobeFont-1.1: CMMI5 1.100 %%CreationDate: 1996 Aug 02 08:21:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 74 /J put dup 75 /K put dup 97 /a put dup 105 /i put dup 108 /l put dup 109 /m put dup 110 /n put dup 117 /u put dup 120 /x put readonly def /FontBBox{37 -250 1349 750}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMTI10 %!PS-AdobeFont-1.1: CMTI10 1.00B %%CreationDate: 1992 Feb 19 19:56:16 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /ff put dup 12 /fi put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 65 /A put dup 66 /B put dup 69 /E put dup 73 /I put dup 76 /L put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 119 /w put dup 120 /x put dup 121 /y put readonly def /FontBBox{-163 -250 1146 969}readonly def currentdict end currentfile eexec 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1985191275371E1DF231E91C026E5996397242E49B449B15F6F56EB8A29BC170 ABBB528914C3933907DC484BE9C622E7F1F237F730F204D84FBB35C73BFD6ADC 86771F624B0CB43E6A411014DC0B5BF7482A6F87CFBB69DB54961B6548C69A05 BF86EABB6EC2C8130439D33335CA94D9C6CE16834F2464001FACCB73C4A84A8C A854827F6ADA031FE2595BA69D180D871CC3DAADC04C5464D302B42A88FB42A6 8BB9B40B2608613931910A6C548FFC8C4A453DFA838F92CB006EC14782FE0168 CA058414C09AC62F3BB8ECB590DC323D3EB1ABBDA2B6EB0005D43F9F40D2A5FA DEE712CD6AF65F19FA8785F9AD059D8A040C1E4A5C16D89F6814EC2F5D0770EF 823CE5FA26EE31C9CBEA8501C5DAE591227BD4838278F09D6045BC2326C65395 4BB12FD8A38B5CDDA42BE43E63D2B3A61C123AB18D6EEE79F10106C49572F34E 2C66FFD08115C71B0EA26694DEC48FF8148F83BE1E0438EC1875F66549583FC4 1D96A78AB50FCA2FD901AA80F313EB042839BF530F0A5A7EC2F52830660D35A7 22AFFFAF76B69686E48D38BC1F24E73C98F4478B1FBEDB81684E149F0EF2ACEF 56571FEF8A6FA6CAD40C86C83E746AF1440025AFEA39D4266C5F985E05EF3476 58080D968742657A322D5CC781DC01AC9EB0F0DC68491DC3D9B5DD31F5DA5D1A F4A4596B16355BDFEFC8B5E6DD73A4EF4F79F20A5175DE9C7156D3CE6D96C035 AA09F254D68A7AD080440A39AD616C5C06E40F5C3A12A6152A6F84BA68D83725 615F0BB10F9CA014AFCC4845D06917CCB86597F72134CE520BA424E3874E4F2E 741A215A54C9A168193771360D102338F08C2490E36DB7855CAD5779D9B32E32 E0A31DDBF9C3E693CBDF758BE2C68A4214FD3C38B17C0014EB9E05DD8BE25B7A E266AA3AF44F85658FB1C3C2FC1C7521C00ECA844094D1091FF2A0993FAFFAD3 4A61E5FDDF5E3C98 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR5 %!PS-AdobeFont-1.1: CMR5 1.00B %%CreationDate: 1992 Feb 19 19:55:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 43 /plus put dup 49 /one put dup 50 /two put dup 51 /three put readonly def /FontBBox{-341 -250 1304 965}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY7 %!PS-AdobeFont-1.1: CMSY7 1.0 %%CreationDate: 1991 Aug 15 07:21:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 3 /asteriskmath put dup 20 /lessequal put dup 33 /arrowright put dup 48 /prime put dup 49 /infinity put dup 106 /bar put dup 121 /dagger put readonly def /FontBBox{-15 -951 1252 782}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI7 %!PS-AdobeFont-1.1: CMMI7 1.100 %%CreationDate: 1996 Jul 23 07:53:53 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /alpha put dup 12 /beta put dup 15 /epsilon1 put dup 18 /theta put dup 21 /lambda put dup 22 /mu put dup 23 /nu put dup 25 /pi put dup 28 /tau put dup 30 /phi put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater 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 82 /R put dup 84 /T 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 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{0 -250 1171 750}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSL9 %!PS-AdobeFont-1.1: CMSL9 1.0 %%CreationDate: 1991 Aug 20 16:41:23 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSL9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -9.46 def /isFixedPitch false def end readonly def /FontName /CMSL9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 120 /x put readonly def /FontBBox{-61 -250 1150 750}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D5993DFC0930297866E1CD0A319B6B1FD958 9429B9D40924DC059325D9D4CC0344F3F997A99E6CC0676735EBCD685AAC9142 08DAFEC78BB41AFC2F1C219910BDF41D6279284EF600B69776CA15BC8A34347C 30783C5D479C203738F62EFD2B5B2E4411A9E9B1B2D1062E3E115E0B0A27F7D4 B189B800FD287297D86CAC19A7E78541E5DB5B518DD757D0412CFA5CCA38AD55 111D0E1D779819A83100AD907EE41C6039B64502BD92D4E720EE46DA8C5FFB58 DD34C4123DBF588726E01FB3EB389F02B041F752811ECBB8A808008A4E48EA11 C1D6C0351461EE08AADEBC932102C6DC259F56B14D408A4A565061B547A1D97E 41E364802889380AE998A80611C1906D5187732BE0BF0FB1E460B6F569C6E1DD 7C627D6577387FAD7A819AA83868916F251DCC25C015EC27CD8943A81511F9FB 34B8BE2AB72AD659A61EFB9BCF0502DE0A99C24BE1119B6D1C8E6E305187D1FD 353F808B8425E04C04C5C64A87289DECF8BD576E9A57627938BCF7681BA7D1DB 953556F92472A07851F01AAA08139761939C4D79BF3910BF10434729D6461061 C3C76F898F8322B982CEA71F5E4F385CD457F84F58EA00F5F560C815D62C2B78 96A5F48BF55B2FA5437B7ECB49CD6D72355A2B401945E1CBFB0F203E19CD384E C1555EB30C93FD7EE042F4BC7A85B5A9D8A9F9244093919954F5874C627A6E3C 819DF33C5A46E851536CDDC8F125D8700496D3FB5AC1DF7E809C01EA71DA655F 2B2974626D7EC1D4B56E0E8FAC5B739A2DE69A90A733DF8E98FBB11D9AA75DC4 B7C084AB034878D9A72C83F80BF014B243B2FD2432035FA2828A2B260F63FCDC F00F3348B84B73D7387D5C11BDE845374074D31F709D9C9D7315B0A68EC17D30 7B3A0F41B290FE84A6243A04F8AC00BAA164D40355717A204AA7039F7627D088 E0DEAEDD42A818AB2E2A674EB678809E8A1F896B19DFC046C5BA296044478CD4 5B60635CB3653580A348EFAB67A98E2586EB3F8FDB4E70291A6E226C099F050D B5F85D3F6633D9D7F6F63C7E28BC645F228BC0D2AE4F6072CC4F62F6921E7A61 864209CF0DC11FE4BDBCCBDE8781BDFCEF65FDC998E7B1402D2629DFC37E5BAD FFFD62C5E682A414649F87C0F9782870CBEA9D128D4492FBFBCF81AD4C5B8CD4 A435A15A2A9F45FD6D67E5DFE2A38DAEFD311F708A163E8302C9C8A4B6752A82 3E31CAE574D2B6F2AA04A7B6FB380DBA0C78793A228120DCF4FA4E5DF668538B 1DF00E396A62DEAF77ECBCBB8382C24FA3434BEFF71769B68AE4F4BD049BBE21 D4AA52CB4DC31401779343D08D9FF8B234C8DF7D95C707C63F7EE8012F783C79 4308E7B99F31AD9FC16B6633F71A2322752ABA2F2739E3ADA0DF5542041CBBDA 9BE7823EEC42ED3BF9C8A1C78C36082B65960D889AA94A 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMEX10 %!PS-AdobeFont-1.1: CMEX10 1.00 %%CreationDate: 1992 Jul 23 21:22:48 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMEX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMEX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /parenleftbig put dup 1 /parenrightbig put dup 18 /parenleftbigg put dup 19 /parenrightbigg put dup 26 /braceleftbigg put dup 27 /bracerightbigg put dup 32 /parenleftBigg put dup 33 /parenrightBigg put dup 40 /braceleftBigg put dup 41 /bracerightBigg put dup 48 /parenlefttp put dup 49 /parenrighttp put dup 56 /bracelefttp put dup 57 /bracerighttp put dup 58 /braceleftbt put dup 59 /bracerightbt put dup 60 /braceleftmid put dup 61 /bracerightmid put dup 64 /parenleftbt put dup 65 /parenrightbt put dup 66 /parenleftex put dup 67 /parenrightex put dup 80 /summationtext put dup 81 /producttext put dup 82 /integraltext put dup 88 /summationdisplay put dup 89 /productdisplay put dup 90 /integraldisplay put dup 112 /radicalbig put dup 113 /radicalBig put dup 114 /radicalbigg put dup 115 /radicalBigg put readonly def /FontBBox{-24 -2960 1454 772}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSS10 %!PS-AdobeFont-1.1: CMSS10 1.0 %%CreationDate: 1991 Aug 20 17:33:34 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSS10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMSS10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 40 /parenleft put dup 41 /parenright put readonly def /FontBBox{-61 -250 999 759}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMTT10 %!PS-AdobeFont-1.1: CMTT10 1.00B %%CreationDate: 1992 Apr 26 10:42:42 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTT10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch true def end readonly def /FontName /CMTT10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 33 /exclam put dup 34 /quotedbl put dup 35 /numbersign put dup 36 /dollar put dup 37 /percent put dup 38 /ampersand put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 60 /less put dup 61 /equal put dup 62 /greater put dup 63 /question put dup 64 /at 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 81 /Q 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 92 /backslash put dup 93 /bracketright put dup 94 /asciicircum put dup 95 /underscore put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q 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 123 /braceleft put dup 124 /bar put dup 125 /braceright put dup 126 /asciitilde put readonly def /FontBBox{-4 -235 731 800}readonly def currentdict end 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cleartomark %%EndFont %%BeginFont: CMTT12 %!PS-AdobeFont-1.1: CMTT12 1.0 %%CreationDate: 1991 Aug 20 16:45:46 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTT12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch true def end readonly def /FontName /CMTT12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 43 /plus put readonly def /FontBBox{-1 -234 524 695}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5F0364CD5660FE13FF01BC20148F9C480BCD0E C81D5BFC66F04993DD73F0BE0AB13F53B1BA79FE5F618A4F672B16C06BE3251E 3BCB599BFA0E6041FBD558475370D693A959259A2699BA6E97CF40435B8E8A4B 426343E145DF14E59028D4E0941AB537E34024E6CDE0EA9AF8038A3260A0358D D5B1DB53582F0DAB7ADE29CF8DBA0992D5A94672DFF91573F38D9BFD1A57E161 E52DA1B41433C82261E47F79997DF603935D2A187A95F7A25D148FB3C2B6AA32 6B982C32C6B25867871ED7B38E150031A3DE568C8D3731A779EAAF09AC5CE6C5 A129C4147E56882B8068DF37C97C761694F1316AF93E33FF7E0B2F1F252735CE 0D9F7BCE136B06EE967ABE0C8DF24DCBBF99874702ED252B677F407CB39678CC 85DDFC2F45C552BA967E4158165ED16FECC4E32AC4D3B3EB8046DCDD37C92FDF F1F3710BB8EF5CA358ABACA33C7E5ACAD6BF5DC58BDFC3CF09BA2A38291D45A4 C15FF1916FE2EC47FDC80911EB9C61F5D355BEDFC9DB17588547763AC5F0B1CC 12D2FFB32E0803D37E3281DA9CE36C5433655526ACFB3A301C56FAB09DF07B5D 048B47687348DEB96F3F9C53CE56DDD312B93D3918CD92AF53FB9461864D11B8 0138918D0B1270C54873C4012CDE6F886DB11BCEA04B023EBB43E0D0A06BE725 741D08B9DB688731A6C9886C15A83C28DADCC81385EA239E045E8F3670CE03DB 9EE77ED067036595C9F3B1854343BE3A12E486B6E5A2F8AC44FA5378D28DCCEE 306B0E283AA444423F9A4FF38E2B56DCF67A39CEB2C643DAE86865517D5D0371 CB8797208ADEC637330A3A57902C9A88EDB75A7C16FA9850075D9F19578EC666 1353CC1FC512D59DFF847ACCD058E2058E262194FA3370E876BBB803BCC86390 9DA3AF2A74FFCDE3DC525731B9C696BAB3E0CD0D3DB061CA1B00E3BD9C5AF268 97ECE57F738B592F4F7F9515A29D0D76E93E3C8765020B7840312BE5E4602B75 A3AAF16F492451ADE4CBF379D22CD167959C5A79679B23E907925A671FB3B63C D7E7437162FFF1E33A17492409A1AFDC7C5932260B241507BBB215E4716878F5 FDA295E8DB5EF28BA26B1E3CF65CEBFADF173782520615E6D8792E366579CFFF C35A09C850EB339C2A263183D305C861EF5B39159BA628D036861B66C3D3FE2A A7BC6EBE272A0F53E20A4CDE5ADC4D8480096DD7E6EF44F7540A0C47FC17FF5C B2149ACFE568B3B8C1AB270C71A5D3072921 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR9 %!PS-AdobeFont-1.1: CMR9 1.0 %%CreationDate: 1991 Aug 20 16:39:59 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 61 /equal 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 81 /Q 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 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q 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 123 /endash put dup 124 /emdash put readonly def /FontBBox{-39 -250 1036 750}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX12 %!PS-AdobeFont-1.1: CMBX12 1.0 %%CreationDate: 1991 Aug 20 16:34:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 15 /ffl put dup 36 /dollar put dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon 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 81 /Q 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 89 /Y put dup 90 /Z put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q 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 124 /emdash put readonly def /FontBBox{-53 -251 1139 750}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5F0364CD5660F74BEE96790DE35AFA90CCF712 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CD9804AA436376AADABCBAD1476E98F5DBE800498B2F04E24AC802543467D3A5 7BC13B4C98E19730D4B862D6011A60CF3AF17D4B685FD587483A04F4BD7CE33F 036E89F7C42A695D3A57983D564727FA531C7F99286B3140D548274C4EFD767C 9BDF380577FD568ECFB41B712A72B0 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMTT9 %!PS-AdobeFont-1.1: CMTT9 1.0 %%CreationDate: 1991 Aug 20 16:46:24 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTT9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch true def end readonly def /FontName /CMTT9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 33 /exclam put dup 34 /quotedbl put dup 35 /numbersign put dup 36 /dollar put dup 37 /percent put dup 38 /ampersand put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 60 /less put dup 61 /equal put dup 62 /greater put dup 63 /question 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 81 /Q 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 92 /backslash put dup 93 /bracketright put dup 94 /asciicircum put dup 95 /underscore put dup 96 /quoteleft put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q 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 123 /braceleft put dup 124 /bar put dup 125 /braceright put readonly def /FontBBox{-6 -233 542 698}readonly def currentdict end currentfile eexec 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cleartomark %%EndFont %%BeginFont: CMR7 %!PS-AdobeFont-1.1: CMR7 1.0 %%CreationDate: 1991 Aug 20 16:39:21 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 61 /equal put readonly def /FontBBox{-27 -250 1122 750}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSL10 %!PS-AdobeFont-1.1: CMSL10 1.0 %%CreationDate: 1991 Aug 20 16:40:20 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSL10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -9.46 def /isFixedPitch false def end readonly def /FontName /CMSL10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 34 /quotedblright put dup 36 /dollar put dup 38 /ampersand put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 61 /equal 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 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cleartomark %%EndFont %%BeginFont: CMMI10 %!PS-AdobeFont-1.1: CMMI10 1.100 %%CreationDate: 1996 Jul 23 07:53:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /alpha put dup 12 /beta put dup 13 /gamma put dup 14 /delta put dup 15 /epsilon1 put dup 16 /zeta put dup 17 /eta put dup 18 /theta put dup 21 /lambda put dup 22 /mu put dup 23 /nu put dup 25 /pi put dup 26 /rho put dup 27 /sigma put dup 28 /tau put dup 30 /phi put dup 31 /chi put dup 32 /psi put dup 33 /omega put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 64 /partialdiff 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 81 /Q 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 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q 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 126 /vector put readonly def /FontBBox{-32 -250 1048 750}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE 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cleartomark %%EndFont %%BeginFont: CMMI12 %!PS-AdobeFont-1.1: CMMI12 1.100 %%CreationDate: 1996 Jul 27 08:57:55 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 58 /period put readonly def /FontBBox{-30 -250 1026 750}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 1 /periodcentered put dup 2 /multiply put dup 3 /asteriskmath put dup 6 /plusminus put dup 8 /circleplus put dup 13 /circlecopyrt put dup 15 /bullet put dup 20 /lessequal put dup 21 /greaterequal put dup 24 /similar put dup 25 /approxequal put dup 28 /lessmuch put dup 29 /greatermuch put dup 32 /arrowleft put dup 33 /arrowright put dup 48 /prime put dup 49 /infinity put dup 54 /negationslash put dup 98 /floorleft put dup 99 /floorright put dup 102 /braceleft put dup 103 /braceright put dup 104 /angbracketleft put dup 105 /angbracketright put dup 106 /bar put dup 112 /radical put dup 114 /nabla put readonly def /FontBBox{-29 -960 1116 775}readonly def currentdict end currentfile eexec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85BABD43642CAF8F03BB1DB5F3A9D84DB9F1C581264D 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR10 %!PS-AdobeFont-1.1: CMR10 1.00B %%CreationDate: 1992 Feb 19 19:54:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /Gamma put dup 1 /Delta put dup 5 /Pi put dup 8 /Phi put dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 15 /ffl put dup 19 /acute put dup 20 /caron put dup 22 /macron put dup 33 /exclam put dup 34 /quotedblright put dup 37 /percent put dup 38 /ampersand put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 61 /equal 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 81 /Q 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 92 /quotedblleft put dup 93 /bracketright put dup 94 /circumflex put dup 96 /quoteleft put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q 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 123 /endash put dup 124 /emdash put dup 127 /dieresis put readonly def /FontBBox{-251 -250 1009 969}readonly def currentdict end currentfile eexec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39 39 1[39 39 50[39 6[39 39[{}22 74.7198 /CMSLTT10 rf /Fd 134[35 1[35 1[35 35 35 35 1[35 35 35 35 35 2[35 35 35 35 35 1[35 40[35 10[35 35 35 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 255[45{}1 41.511 /CMSY5 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 6[37 51 20 2[22 7[32 21[47 32 74[{}9 41.511 /CMMI5 rf /Fm 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 /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 14[20 56[66 19 14[66 12[52 16[34 2[52{}8 58.1154 /CMSY7 rf /Fq 133[32 34 38 48 1[39 25 31 31 30 34 33 41 59 21 35 27 23 1[32 1[31 35 30 29 36 12[39 1[50 3[53 63 46 56 37 29 54 52 42 49 54 48 50 50 2[52 34 52 20 28[40 1[31 2[39 1[33 40 39 2[32 2[28 2[38 43 11[{}53 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 6[61 61 16[38 38{}32 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 1[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[{}54 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 42[{}64 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 1[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 1[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[{}61 109.091 /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 4[48 48 1[48 48 48 48 3[48 1[48 48 48 48 48 1[48 1[48 20[48 25[48 48[{}17 90.9091 /CMSLTT10 rf /FB 194[51 3[33 33 33 33 33 33 33 33 33 33 4[51 1[26 26 40[{}14 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 43[0 4[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{}28 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 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y(di\013eren)m(t)e(c)m (haracter.)275 4759 y(The)43 b(examples)i(assume)g(the)f(use)g(of)h (the)g(GNU)g(op)s(erating)g(system.)83 b(There)44 b(ma)m(y)h(b)s(e)e (minor)150 4868 y(di\013erences)23 b(in)g(the)g(output)g(on)f(other)i (systems.)38 b(The)22 b(commands)h(for)g(setting)h(en)m(vironmen)m(t)f (v)-5 b(ariables)150 4978 y(use)30 b(the)h(Bourne)f(shell)g(syn)m(tax)h (of)g(the)f(standard)g(GNU)h(shell)g(\()p FH(bash)p FK(\).)p 150 5241 1200 4 v 199 5308 a FB(1)275 5340 y Fz (http://savannah.gnu.org/bugs/?g)q(roup=)q(gsl)p eop end %%Page: 4 20 TeXDict begin 4 19 bop 150 -116 a FK(Chapter)30 b(2:)41 b(Using)30 b(the)h(library)2412 b(4)150 299 y FG(2)80 b(Using)53 b(the)g(library)150 551 y FK(This)31 b(c)m(hapter)h(describ) s(es)e(ho)m(w)h(to)i(compile)f(programs)f(that)h(use)f(GSL,)g(and)g(in) m(tro)s(duces)g(its)g(con)m(v)m(en-)150 661 y(tions.)150 903 y FJ(2.1)68 b(An)44 b(Example)i(Program)150 1062 y FK(The)27 b(follo)m(wing)j(short)d(program)h(demonstrates)g(the)g (use)g(of)g(the)g(library)g(b)m(y)f(computing)h(the)g(v)-5 b(alue)29 b(of)150 1172 y(the)i(Bessel)g(function)f FE(J)985 1186 y FB(0)1023 1172 y FK(\()p FE(x)p FK(\))h(for)f FE(x)25 b FK(=)g(5,)390 1312 y FH(#include)46 b()390 1422 y(#include)g()390 1641 y(int)390 1751 y(main)h(\(void\))390 1860 y({)485 1970 y(double)g(x)g(=)g(5.0;) 485 2080 y(double)g(y)g(=)g(gsl_sf_bessel_J0)d(\(x\);)485 2189 y(printf)j(\("J0\(\045g\))e(=)j(\045.18e\\n",)d(x,)i(y\);)485 2299 y(return)g(0;)390 2408 y(})150 2549 y FK(The)30 b(output)g(is)g(sho)m(wn)g(b)s(elo)m(w,)h(and)f(should)f(b)s(e)h (correct)h(to)g(double-precision)g(accuracy)-8 b(,)3323 2516 y FB(1)390 2690 y FH(J0\(5\))46 b(=)i(-1.775967713143382920e-0)o (1)150 2830 y FK(The)30 b(steps)g(needed)g(to)h(compile)h(this)e (program)g(are)h(describ)s(ed)e(in)h(the)h(follo)m(wing)h(sections.)150 3072 y FJ(2.2)68 b(Compiling)46 b(and)f(Linking)150 3231 y FK(The)c(library)g(header)g(\014les)g(are)h(installed)g(in)f(their)g (o)m(wn)h FH(gsl)e 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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 21 TeXDict begin 5 20 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(121.)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 22 TeXDict begin 6 21 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 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b(.)59 b(The)36 b FH(long)150 568 y(double)29 b FK(t)m(yp)s(e)h(is)h (not)f(supp)s(orted)f(for)h(actual)i(computation.)275 738 y(One)h(reason)i(for)f(this)g(c)m(hoice)i(is)e(that)h(the)g (precision)f(of)g FH(long)c(double)i FK(is)i(platform)h(dep)s(enden)m (t.)150 847 y(The)g(IEEE)g(standard)g(only)h(sp)s(eci\014es)g(the)g (minim)m(um)f(precision)h(of)f(extended)h(precision)g(n)m(um)m(b)s (ers,)150 957 y(while)30 b(the)h(precision)f(of)h FH(double)e FK(is)h(the)h(same)f(on)h(all)g(platforms.)275 1127 y(Ho)m(w)m(ev)m (er,)e(it)f(is)f(sometimes)h(necessary)f(to)h(in)m(teract)g(with)f (external)h(data)f(in)g(long-double)g(format,)150 1236 y(so)k(the)f(v)m(ector)i(and)e(matrix)h(datat)m(yp)s(es)g(include)f (long-double)h(v)m(ersions.)275 1406 y(It)k(should)g(b)s(e)g(noted)g (that)i(in)e(some)h(system)g(libraries)f(the)h FH(stdio.h)e FK(formatted)i(input/output)150 1515 y(functions)29 b FH(printf)f FK(and)h FH(scanf)f FK(are)i(not)g(implemen)m(ted)g (correctly)h(for)f FH(long)f(double)p 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(otherwise,)h(since)f(this)g(allo)m(ws)i(y)m(our)e(application)150 5230 y(to)h(tak)m(e)i(adv)-5 b(an)m(tage)33 b(of)f(an)m(y)g (platform-sp)s(eci\014c)g(optimizations)i(in)d(the)h(system)g(library) -8 b(.)45 b(This)31 b(is)h(the)150 5340 y(strategy)g(used)d(within)h (GSL)g(itself.)p eop end %%Page: 8 24 TeXDict begin 8 23 bop 150 -116 a FK(Chapter)30 b(2:)41 b(Using)30 b(the)h(library)2412 b(8)150 299 y FJ(2.8)68 b(Alternativ)l(e)47 b(optimized)f(functions)150 458 y FK(The)37 b(main)g(implemen)m(tation)h(of)g(some)f(functions)g(in)f (the)i(library)e(will)i(not)f(b)s(e)g(optimal)h(on)f(all)h(ar-)150 568 y(c)m(hitectures.)65 b(F)-8 b(or)39 b(example,)i(there)d(are)g(sev) m(eral)i(w)m(a)m(ys)f(to)f(compute)h(a)f(Gaussian)g(random)g(v)-5 b(ariate)150 677 y(and)39 b(their)h(relativ)m(e)i(sp)s(eeds)c(are)i (platform-dep)s(enden)m(t.)69 b(In)39 b(cases)h(lik)m(e)h(this)f(the)g (library)f(pro)m(vides)150 787 y(alternativ)m(e)e(implemen)m(tations)g (of)e(these)g(functions)g(with)f(the)i(same)f(in)m(terface.)56 b(If)35 b(y)m(ou)g(write)g(y)m(our)150 897 y(application)j(using)e (calls)i(to)f(the)g(standard)f(implemen)m(tation)i(y)m(ou)f(can)g (select)h(an)e(alternativ)m(e)j(v)m(er-)150 1006 y(sion)30 b(later)h(via)g(a)f(prepro)s(cessor)g(de\014nition.)40 b(It)30 b(is)g(also)h(p)s(ossible)f(to)h(in)m(tro)s(duce)f(y)m(our)g(o) m(wn)g(optimized)150 1116 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 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g(inserted)g(in)m(to)h(the)f(function)g(name)g(after)h(the)f(initial)i (mo)s(dule)150 3141 y(pre\014x.)52 b(The)34 b(follo)m(wing)h(table)h (sho)m(ws)e(the)h(function)f(names)g(de\014ned)f(for)h(all)i(the)e(n)m (umeric)g(t)m(yp)s(es)h(of)150 3251 y(an)30 b(imaginary)h(mo)s(dule)f FH(gsl_foo)e FK(with)i(function)h FH(fn)p FK(,)390 3399 y FH(gsl_foo_fn)713 b(double)390 3509 y(gsl_foo_long_double_fn)137 b(long)47 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 25 TeXDict begin 9 24 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 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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 29 TeXDict begin 13 28 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 30 TeXDict begin 14 29 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(\(stderr,)f("failed,)h(gsl_errno=\045d\\n",)p eop end %%Page: 15 31 TeXDict begin 15 30 bop 150 -116 a FK(Chapter)30 b(3:)41 b(Error)29 b(Handling)2439 b(15)1535 299 y FH(status\);)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 32 TeXDict begin 16 31 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 33 TeXDict begin 17 32 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 34 TeXDict begin 18 33 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 35 TeXDict begin 19 34 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 b(platforms)h(where)g(inline)g(functions)f(are)i (not)f(a)m(v)-5 b(ailable)43 b(the)e(macros)390 3733 y FH(GSL_MAX)28 b FK(or)j FH(GSL_MIN)d FK(will)j(b)s(e)f(automatically) j(substituted.)3350 3943 y([F)-8 b(unction])-3599 b Fv(extern)54 b(inline)g(long)g(double)g(GSL_MAX_LDBL)49 b Fu(\()p FD(long)31 b(double)f Ft(a)p FD(,)h(long)565 4052 y(double)f Ft(b)p Fu(\))3350 4162 y FK([F)-8 b(unction])-3599 b Fv(extern)54 b(inline)g(long)g(double)g(GSL_MIN_LDBL)49 b Fu(\()p FD(long)31 b(double)f Ft(a)p FD(,)h(long)565 4271 y(double)f Ft(b)p Fu(\))390 4381 y FK(These)g(functions)g(return)f (the)i(maxim)m(um)f(or)g(minim)m(um)g(of)g(the)h(long)g(doubles)e FD(a)i FK(and)f FD(b)h FK(using)390 4490 y(an)g(inline)g(function.)43 b(On)31 b(platforms)g(where)f(inline)i(functions)e(are)i(not)g(a)m(v)-5 b(ailable)33 b(the)e(macros)390 4600 y FH(GSL_MAX)d FK(or)j FH(GSL_MIN)d FK(will)j(b)s(e)f(automatically)j(substituted.)150 4852 y FJ(4.8)68 b(Appro)l(ximate)46 b(Comparison)g(of)f(Floating)h(P)l (oin)l(t)g(Num)l(b)t(ers)150 5011 y FK(It)39 b(is)h(sometimes)g(useful) f(to)h(b)s(e)f(able)h(to)g(compare)g(t)m(w)m(o)g(\015oating)h(p)s(oin)m (t)e(n)m(um)m(b)s(ers)f(appro)m(ximately)-8 b(,)150 5121 y(to)40 b(allo)m(w)g(for)f(rounding)f(and)h(truncation)g(errors.)67 b(The)38 b(follo)m(wing)j(function)e(implemen)m(ts)g(the)h(ap-)150 5230 y(pro)m(ximate)30 b(\015oating-p)s(oin)m(t)g(comparison)f (algorithm)h(prop)s(osed)e(b)m(y)h(D.E.)h(Kn)m(uth)e(in)g(Section)i (4.2.2)h(of)150 5340 y FD(Semin)m(umerical)g(Algorithms)k FK(\(3rd)30 b(edition\).)p eop end %%Page: 20 36 TeXDict begin 20 35 bop 150 -116 a FK(Chapter)30 b(4:)41 b(Mathematical)33 b(F)-8 b(unctions)2081 b(20)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_fcmp)48 b Fu(\()p FD(double)30 b Ft(x)p FD(,)h(double)f Ft(y)p FD(,)h(double)f Ft(epsilon)p Fu(\))390 408 y FK(This)45 b(function)g(determines)g(whether)g FE(x)g FK(and)g FE(y)j FK(are)d(appro)m(ximately)i(equal)f(to)g(a)g(relativ)m(e)390 518 y(accuracy)32 b FD(epsilon)p FK(.)390 653 y(The)27 b(relativ)m(e)j(accuracy)g(is)e(measured)f(using)g(an)h(in)m(terv)-5 b(al)29 b(of)f(size)h(2)p FE(\016)s FK(,)h(where)d FE(\016)i FK(=)c(2)3330 620 y Fq(k)3372 653 y FE(\017)j FK(and)f FE(k)k FK(is)390 762 y(the)g(maxim)m(um)f(base-2)h(exp)s(onen)m(t)g(of) f FE(x)g FK(and)g FE(y)j FK(as)e(computed)f(b)m(y)g(the)h(function)f FH(frexp)p FK(.)390 897 y(If)k FE(x)g FK(and)f FE(y)k FK(lie)e(within)f(this)g(in)m(terv)-5 b(al,)36 b(they)f(are)f 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FH(typedef)46 b(struct)390 2571 y({)485 2681 y(double)h(dat[2];)390 2790 y(})g(gsl_complex;)150 2926 y FK(The)26 b(real)i(and)e(imaginary)i(part)e(are)i(stored)f(in)f (con)m(tiguous)i(elemen)m(ts)g(of)f(a)h(t)m(w)m(o)g(elemen)m(t)g(arra)m (y)-8 b(.)41 b(This)150 3036 y(eliminates)27 b(an)m(y)f(padding)e(b)s (et)m(w)m(een)i(the)g(real)g(and)e(imaginary)j(parts,)f FH(dat[0])e FK(and)g FH(dat[1])p FK(,)h(allo)m(wing)150 3145 y(the)31 b(struct)f(to)h(b)s(e)f(mapp)s(ed)f(correctly)j(on)m(to)f (pac)m(k)m(ed)h(complex)f(arra)m(ys.)3350 3332 y([F)-8 b(unction])-3599 b Fv(gsl_complex)56 b(gsl_complex_rect)50 b Fu(\()p FD(double)30 b Ft(x)p FD(,)h(double)f Ft(y)p Fu(\))390 3442 y FK(This)25 b(function)h(uses)g(the)h(rectangular)g (Cartesian)f(comp)s(onen)m(ts)h(\()p FD(x)p FK(,)p FD(y)8 b FK(\))27 b(to)g(return)e(the)h(complex)390 3552 y(n)m(um)m(b)s(er)32 b FE(z)j FK(=)30 b FE(x)22 b FK(+)g FE(iy)s FK(.)51 b(An)33 b(inline)g(v)m(ersion)h(of)g(this)f(function)h(is)f(used)g(when)f 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b(to)h(set)g(the)f(real)h(and)e(imaginary)i(parts)390 4880 y(of)g(the)f(complex)h(n)m(um)m(b)s(er)e(p)s(oin)m(ted)i(to)g(b)m (y)f FD(zp)p FK(.)40 b(F)-8 b(or)32 b(example,)630 5016 y FH(GSL_SET_COMPLEX\(&z,)43 b(3,)k(4\))390 5152 y FK(sets)31 b FD(z)k FK(to)d(b)s(e)d(3)21 b(+)f(4)p FE(i)p FK(.)p 150 5241 1200 4 v 199 5308 a FB(1)275 5340 y Fx(Note)25 b(that)h(the)f(\014rst)g(edition)h(uses)g(di\013eren)n(t)f (de\014nitions.)p eop end %%Page: 22 38 TeXDict begin 22 37 bop 150 -116 a FK(Chapter)30 b(5:)41 b(Complex)30 b(Num)m(b)s(ers)2305 b(22)3449 299 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 FH(log\(gsl_complex_abs\(z\)\))29 b FK(w)m(ould)36 b(lead)g(to)g(a)h (loss)f(of)f(precision)h(in)390 2572 y(this)30 b(case.)150 2817 y FJ(5.3)68 b(Complex)46 b(arithmetic)g(op)t(erators)3350 3035 y FK([F)-8 b(unction])-3599 b Fv(gsl_complex)56 b(gsl_complex_add)50 b Fu(\()p FD(gsl)p 1755 3035 V 41 w(complex)31 b Ft(a)p FD(,)f(gsl)p 2365 3035 V 41 w(complex)h Ft(b)p Fu(\))390 3145 y FK(This)f(function)g(returns)f(the)h(sum)g(of)g (the)h(complex)g(n)m(um)m(b)s(ers)e FD(a)i FK(and)e FD(b)p FK(,)h FE(z)g FK(=)25 b FE(a)20 b FK(+)g FE(b)p FK(.)3350 3346 y([F)-8 b(unction])-3599 b Fv(gsl_complex)56 b(gsl_complex_sub)50 b Fu(\()p FD(gsl)p 1755 3346 V 41 w(complex)31 b Ft(a)p FD(,)f(gsl)p 2365 3346 V 41 w(complex)h Ft(b)p Fu(\))390 3456 y FK(This)f(function)g(returns)f(the)h(di\013erence)h(of)g(the)f (complex)h(n)m(um)m(b)s(ers)e FD(a)i FK(and)f FD(b)p FK(,)g FE(z)f FK(=)c FE(a)c FI(\000)e FE(b)p FK(.)3350 3657 y([F)-8 b(unction])-3599 b Fv(gsl_complex)56 b(gsl_complex_mul)50 b Fu(\()p FD(gsl)p 1755 3657 V 41 w(complex)31 b Ft(a)p FD(,)f(gsl)p 2365 3657 V 41 w(complex)h Ft(b)p Fu(\))390 3767 y FK(This)f(function)g(returns)f(the)h(pro)s(duct)g(of)g(the)h (complex)g(n)m(um)m(b)s(ers)e FD(a)h FK(and)g FD(b)p FK(,)g FE(z)g FK(=)25 b FE(ab)p FK(.)3350 3968 y([F)-8 b(unction])-3599 b Fv(gsl_complex)56 b(gsl_complex_div)50 b Fu(\()p FD(gsl)p 1755 3968 V 41 w(complex)31 b Ft(a)p FD(,)f(gsl)p 2365 3968 V 41 w(complex)h Ft(b)p 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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 39 TeXDict begin 23 38 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 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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 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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 41 TeXDict begin 25 40 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 FD(z)p FK(,)k(arccos)q(\()p FE(z)t FK(\).)57 b(F)-8 b(or)37 b FE(z)390 913 y FK(b)s(et)m(w)m(een)h FI(\000)p FK(1)f(and)g(1,)j(the) d(function)g(returns)f(a)i(real)g(v)-5 b(alue)37 b(in)g(the)h(range)f ([0)p FE(;)15 b(\031)s FK(].)63 b(F)-8 b(or)38 b FE(z)k FK(less)390 1023 y(than)30 b FI(\000)p FK(1)h(the)f(result)h(has)f(a)h (real)g(part)f(of)h FE(\031)i FK(and)d(a)h(negativ)m(e)i(imaginary)e (part.)41 b(F)-8 b(or)31 b FE(z)k FK(greater)390 1133 y(than)30 b(1)h(the)f(result)h(is)f(purely)g(imaginary)h(and)e(p)s (ositiv)m(e.)3350 1309 y([F)-8 b(unction])-3599 b Fv(gsl_complex)56 b(gsl_complex_arctan)51 b Fu(\()p FD(gsl)p 1912 1309 V 40 w(complex)32 b Ft(z)p Fu(\))390 1418 y FK(This)37 b(function)g(returns)f(the)h(complex)i(arctangen)m(t)g(of)e(the)h (complex)g(n)m(um)m(b)s(er)e FD(z)p FK(,)k(arctan)q(\()p FE(z)t FK(\).)390 1528 y(The)30 b(branc)m(h)g(cuts)g(are)h(on)f(the)h (imaginary)g(axis,)g(b)s(elo)m(w)f FI(\000)p FE(i)h FK(and)e(ab)s(o)m (v)m(e)j FE(i)p FK(.)3350 1704 y([F)-8 b(unction])-3599 b Fv(gsl_complex)56 b(gsl_complex_arcsec)51 b Fu(\()p FD(gsl)p 1912 1704 V 40 w(complex)32 b Ft(z)p Fu(\))390 1813 y FK(This)k(function)g(returns)f(the)i(complex)g(arcsecan)m(t)h (of)e(the)h(complex)g(n)m(um)m(b)s(er)e FD(z)p FK(,)k(arcsec)q(\()p FE(z)t FK(\))d(=)390 1923 y(arccos)q(\(1)p FE(=z)t FK(\).)3350 2099 y([F)-8 b(unction])-3599 b Fv(gsl_complex)56 b (gsl_complex_arcsec_real)c Fu(\()p FD(double)30 b Ft(z)p Fu(\))390 2209 y FK(This)103 b(function)h(returns)f(the)i(complex)g (arcsecan)m(t)h(of)e(the)h(real)f(n)m(um)m(b)s(er)f FD(z)p FK(,)390 2318 y(arcsec)q(\()p FE(z)t FK(\))26 b(=)f(arccos)r(\(1)p FE(=z)t FK(\).)3350 2494 y([F)-8 b(unction])-3599 b Fv(gsl_complex)56 b(gsl_complex_arccsc)51 b Fu(\()p FD(gsl)p 1912 2494 V 40 w(complex)32 b Ft(z)p Fu(\))390 2604 y FK(This)d(function)g (returns)g(the)g(complex)i(arccosecan)m(t)h(of)e(the)g(complex)g(n)m (um)m(b)s(er)f FD(z)p FK(,)h(arccsc)q(\()p FE(z)t FK(\))c(=)390 2714 y(arcsin\(1)p FE(=z)t FK(\).)3350 2890 y([F)-8 b(unction])-3599 b Fv(gsl_complex)56 b(gsl_complex_arccsc_real)c Fu(\()p FD(double)30 b Ft(z)p Fu(\))390 2999 y FK(This)43 b(function)g(returns) g(the)g(complex)i(arccosecan)m(t)h(of)e(the)g(real)g(n)m(um)m(b)s(er)e FD(z)p FK(,)48 b(arccsc)q(\()p FE(z)t FK(\))g(=)390 3109 y(arcsin\(1)p FE(=z)t FK(\).)3350 3285 y([F)-8 b(unction])-3599 b Fv(gsl_complex)56 b(gsl_complex_arccot)51 b Fu(\()p FD(gsl)p 1912 3285 V 40 w(complex)32 b Ft(z)p Fu(\))390 3395 y FK(This)23 b(function)h(returns)f(the)h(complex)h(arccotangen)m (t)i(of)d(the)h(complex)g(n)m(um)m(b)s(er)d FD(z)p FK(,)k(arccot)r(\()p FE(z)t FK(\))g(=)390 3504 y(arctan)q(\(1)p FE(=z)t FK(\).)150 3731 y FJ(5.7)68 b(Complex)46 b(Hyp)t(erb)t(olic)f(F)-11 b(unctions)3350 3935 y FK([F)j(unction])-3599 b Fv(gsl_complex)56 b(gsl_complex_sinh)50 b Fu(\()p FD(gsl)p 1807 3935 V 41 w(complex)31 b Ft(z)p Fu(\))390 4045 y FK(This)23 b(function)h(returns)f(the)h(complex)g(h)m(yp)s(erb)s(olic)g(sine)g(of) g(the)g(complex)g(n)m(um)m(b)s(er)f FD(z)p FK(,)j(sinh)o(\()p FE(z)t FK(\))g(=)390 4154 y(\(exp\()p FE(z)t FK(\))21 b FI(\000)f FK(exp\()p FI(\000)p FE(z)t FK(\)\))p FE(=)p FK(2.)3350 4330 y([F)-8 b(unction])-3599 b Fv(gsl_complex)56 b(gsl_complex_cosh)50 b Fu(\()p FD(gsl)p 1807 4330 V 41 w(complex)31 b Ft(z)p Fu(\))390 4440 y FK(This)52 b(function)g(returns)f(the)i(complex)g(h)m(yp)s(erb)s(olic)f(cosine)h (of)g(the)g(complex)g(n)m(um)m(b)s(er)e FD(z)p FK(,)390 4549 y(cosh\()p FE(z)t 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y([F)-8 b(unction])-3599 b Fv(gsl_complex)56 b(gsl_complex_csch)50 b Fu(\()p FD(gsl)p 1807 299 28 4 v 41 w(complex)31 b Ft(z)p Fu(\))390 408 y FK(This)43 b(function)h(returns)f(the)h(complex) h(h)m(yp)s(erb)s(olic)e(cosecan)m(t)j(of)f(the)f(complex)h(n)m(um)m(b)s (er)d FD(z)p FK(,)390 518 y(csc)m(h)q(\()p FE(z)t FK(\))26 b(=)f(1)p FE(=)15 b FK(sinh\()p FE(z)t FK(\).)3350 689 y([F)-8 b(unction])-3599 b Fv(gsl_complex)56 b(gsl_complex_coth)50 b Fu(\()p FD(gsl)p 1807 689 V 41 w(complex)31 b Ft(z)p Fu(\))390 798 y FK(This)38 b(function)h(returns)f(the)h(complex)h(h)m (yp)s(erb)s(olic)e(cotangen)m(t)j(of)f(the)f(complex)h(n)m(um)m(b)s(er) d FD(z)p FK(,)390 908 y(coth)q(\()p FE(z)t FK(\))26 b(=)f(1)p FE(=)15 b FK(tanh)q(\()p FE(z)t FK(\).)150 1131 y FJ(5.8)68 b(In)l(v)l(erse)46 b(Complex)g(Hyp)t(erb)t(olic)f(F)-11 b(unctions)3350 1331 y FK([F)j(unction])-3599 b Fv(gsl_complex)56 b(gsl_complex_arcsinh)51 b Fu(\()p FD(gsl)p 1964 1331 V 41 w(complex)31 b Ft(z)p Fu(\))390 1441 y FK(This)49 b(function)f(returns)h(the)g(complex)h(h)m(yp)s(erb)s(olic)f(arcsine)g (of)h(the)f(complex)h(n)m(um)m(b)s(er)e FD(z)p FK(,)390 1551 y(arcsinh\()p FE(z)t FK(\).)41 b(The)30 b(branc)m(h)g(cuts)g(are)h (on)f(the)h(imaginary)g(axis,)g(b)s(elo)m(w)g FI(\000)p FE(i)f FK(and)g(ab)s(o)m(v)m(e)h FE(i)p FK(.)3350 1721 y([F)-8 b(unction])-3599 b Fv(gsl_complex)56 b(gsl_complex_arccosh)51 b Fu(\()p FD(gsl)p 1964 1721 V 41 w(complex)31 b Ft(z)p Fu(\))390 1831 y FK(This)41 b(function)g(returns)f(the)i(complex)g(h)m (yp)s(erb)s(olic)f(arccosine)i(of)e(the)h(complex)g(n)m(um)m(b)s(er)e FD(z)p FK(,)390 1940 y(arccosh)q(\()p FE(z)t FK(\).)60 b(The)36 b(branc)m(h)g(cut)h(is)f(on)h(the)f(real)i(axis,)g(less)f (than)g(1.)59 b(Note)38 b(that)f(in)f(this)h(case)390 2050 y(w)m(e)i(use)g(the)f(negativ)m(e)j(square)e(ro)s(ot)g(in)f(form)m (ula)h(4.6.21)i(of)e(Abramo)m(witz)g(&)g(Stegun)f(giving)390 2160 y(arccosh)q(\()p FE(z)t FK(\))26 b(=)f(log)r(\()p FE(z)g FI(\000)1232 2086 y(p)p 1308 2086 241 4 v 74 x FE(z)1354 2133 y FB(2)1412 2160 y FI(\000)19 b FK(1)q(\).)3350 2330 y([F)-8 b(unction])-3599 b Fv(gsl_complex)56 b (gsl_complex_arccosh_rea)q(l)51 b Fu(\()p FD(double)31 b Ft(z)p Fu(\))390 2440 y FK(This)57 b(function)g(returns)g(the)h (complex)g(h)m(yp)s(erb)s(olic)g(arccosine)h(of)e(the)h(real)h(n)m(um)m (b)s(er)d FD(z)p FK(,)390 2549 y(arccosh)q(\()p FE(z)t FK(\).)3350 2720 y([F)-8 b(unction])-3599 b Fv(gsl_complex)56 b(gsl_complex_arctanh)51 b Fu(\()p FD(gsl)p 1964 2720 28 4 v 41 w(complex)31 b Ft(z)p Fu(\))390 2830 y FK(This)k(function)g (returns)g(the)h(complex)h(h)m(yp)s(erb)s(olic)e(arctangen)m(t)i(of)f (the)g(complex)h(n)m(um)m(b)s(er)d FD(z)p FK(,)390 2939 y(arctanh\()p FE(z)t FK(\).)42 b(The)30 b(branc)m(h)g(cuts)g(are)h(on)f (the)h(real)g(axis,)g(less)f(than)g FI(\000)p FK(1)h(and)f(greater)h (than)f(1.)3350 3110 y([F)-8 b(unction])-3599 b Fv(gsl_complex)56 b(gsl_complex_arctanh_rea)q(l)51 b Fu(\()p FD(double)31 b Ft(z)p Fu(\))390 3219 y FK(This)51 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5281 y Fq(k)q Fp(\000)p FB(1)3220 5267 y FK(\))p eop end %%Page: 29 45 TeXDict begin 29 44 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 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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 46 TeXDict begin 30 45 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 b(to)h(rounding)e(and)h(cancellation)j(errors)d(when)f(computed)i(in)f (double)g(precision,)j(and)390 760 y(will)33 b(also)g(b)s(e)f(sub)5 b(ject)32 b(to)h(errors)e(if)i(the)f(co)s(e\016cien)m(ts)i(of)f(the)f (p)s(olynomial)h(are)f(inexact.)48 b(These)390 870 y(errors)28 b(ma)m(y)i(cause)f(a)g(discrete)h(c)m(hange)g(in)f(the)g(n)m(um)m(b)s (er)e(of)i(ro)s(ots.)41 b(Ho)m(w)m(ev)m(er,)31 b(for)e(p)s(olynomials) 390 979 y(with)h(small)h(in)m(teger)h(co)s(e\016cien)m(ts)g(the)e (discriminan)m(t)h(can)g(alw)m(a)m(ys)g(b)s(e)f(computed)g(exactly)-8 b(.)3350 1157 y([F)g(unction])-3599 b Fv(int)53 b (gsl_poly_complex_solv)q(e_qu)q(adr)q(ati)q(c)e Fu(\()p FD(double)31 b Ft(a)p FD(,)g(double)e Ft(b)p FD(,)i(double)565 1266 y Ft(c)p FD(,)g(gsl)p 785 1266 28 4 v 41 w(complex)g(*)f Ft(z0)p FD(,)i(gsl)p 1524 1266 V 40 w(complex)f(*)g Ft(z1)p Fu(\))390 1376 y FK(This)f(function)g(\014nds)e(the)j(complex)g(ro)s (ots)f(of)h(the)g(quadratic)f(equation,)1627 1542 y FE(az)1721 1504 y FB(2)1779 1542 y 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 (of)h(the)g(cubic)f(equation,)1522 2854 y FE(x)1574 2816 y FB(3)1631 2854 y FK(+)20 b FE(ax)1822 2816 y FB(2)1879 2854 y FK(+)g FE(bx)g FK(+)g FE(c)26 b FK(=)f(0)390 3019 y(with)33 b(a)g(leading)g(co)s(e\016cien)m(t)i(of)e(unit)m(y)-8 b(.)49 b(The)32 b(n)m(um)m(b)s(er)f(of)i(real)h(ro)s(ots)f(\(either)h (one)f(or)f(three\))i(is)390 3129 y(returned,)i(and)f(their)h(lo)s (cations)h(are)f(stored)f(in)h FD(x0)p FK(,)h FD(x1)44 b FK(and)35 b FD(x2)p FK(.)56 b(If)35 b(one)h(real)h(ro)s(ot)f(is)f (found)390 3238 y(then)d(only)g FD(x0)39 b FK(is)32 b(mo)s(di\014ed.)44 b(When)31 b(three)h(real)h(ro)s(ots)f(are)g(found)f(they)h(are)g (stored)g(in)f FD(x0)p FK(,)i FD(x1)390 3348 y FK(and)26 b FD(x2)34 b FK(in)26 b(ascending)h(order.)39 b(The)26 b(case)h(of)g(coinciden)m(t)h(ro)s(ots)f(is)f(not)h(considered)f(sp)s (ecial.)40 b(F)-8 b(or)390 3457 y(example,)37 b(the)d(equation)i(\()p FE(x)23 b FI(\000)g FK(1\))1597 3424 y FB(3)1667 3457 y FK(=)32 b(0)j(will)g(ha)m(v)m(e)h(three)f(ro)s(ots)g(with)f(exactly)i (equal)f(v)-5 b(alues.)390 3567 y(As)28 b(in)g(the)h(quadratic)g(case,) h(\014nite)e(precision)g(ma)m(y)h(cause)g(equal)g(or)f(closely-spaced)j (real)e(ro)s(ots)390 3677 y(to)k(mo)m(v)m(e)h(o\013)f(the)g(real)g (axis)g(in)m(to)h(the)e(complex)i(plane,)f(leading)g(to)h(a)f(discrete) g(c)m(hange)h(in)e(the)390 3786 y(n)m(um)m(b)s(er)d(of)i(real)g(ro)s (ots.)3350 3964 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_poly_complex_solv)q(e_cu)q(bic)f Fu(\()p FD(double)30 b Ft(a)p FD(,)h(double)f Ft(b)p FD(,)h(double)f Ft(c)p FD(,)565 4073 y(gsl)p 677 4073 V 41 w(complex)h(*)f Ft(z0)p FD(,)i(gsl)p 1416 4073 V 40 w(complex)f(*)g Ft(z1)p FD(,)g(gsl)p 2154 4073 V 41 w(complex)g(*)g Ft(z2)p Fu(\))390 4183 y FK(This)f(function)g(\014nds)e(the)j(complex)g(ro)s(ots)f(of)h(the)g (cubic)f(equation,)1530 4349 y FE(z)1576 4311 y FB(3)1634 4349 y FK(+)20 b FE(az)1819 4311 y FB(2)1877 4349 y FK(+)f FE(bz)25 b FK(+)20 b FE(c)25 b FK(=)g(0)390 4514 y(The)f(n)m(um)m(b)s (er)g(of)h(complex)g(ro)s(ots)g(is)g(returned)e(\(alw)m(a)m(ys)k (three\))e(and)g(the)g(lo)s(cations)h(of)f(the)g(ro)s(ots)390 4624 y(are)j(stored)f(in)h FD(z0)p FK(,)h FD(z1)35 b FK(and)27 b FD(z2)p FK(.)40 b(The)27 b(ro)s(ots)h(are)g(returned)e(in)h (ascending)h(order,)g(sorted)f(\014rst)g(b)m(y)390 4733 y(their)j(real)h(comp)s(onen)m(ts)g(and)f(then)g(b)m(y)g(their)g (imaginary)h(comp)s(onen)m(ts.)150 4961 y FJ(6.5)68 b(General)46 b(P)l(olynomial)g(Equations)150 5121 y FK(The)27 b(ro)s(ots)h(of)g(p)s (olynomial)g(equations)h(cannot)f(b)s(e)f(found)g(analytically)j(b)s (ey)m(ond)d(the)h(sp)s(ecial)g(cases)h(of)150 5230 y(the)i(quadratic,)g (cubic)f(and)g(quartic)h(equation.)41 b(The)30 b(algorithm)i(describ)s (ed)d(in)h(this)h(section)g(uses)f(an)150 5340 y(iterativ)m(e)j(metho)s (d)d(to)h(\014nd)e(the)h(appro)m(ximate)i(lo)s(cations)f(of)g(ro)s(ots) g(of)f(higher)g(order)g(p)s(olynomials.)p eop end %%Page: 31 47 TeXDict begin 31 46 bop 150 -116 a FK(Chapter)30 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(\()p FD(gsl)p 712 1285 V 41 w(p)s(oly)p 925 1285 V 40 w(complex)p 1290 1285 V 41 w(w)m(orkspace)31 b(*)f Ft(w)p Fu(\))390 1395 y FK(This)g(function)g(frees)g(all)h(the)g (memory)f(asso)s(ciated)i(with)e(the)h(w)m(orkspace)g FD(w)p FK(.)3350 1586 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_poly_complex_solv)q(e)e Fu(\()p FD(const)32 b(double)e(*)g Ft(a)p FD(,)h(size)p 2452 1586 V 41 w(t)g Ft(n)p FD(,)565 1695 y(gsl)p 677 1695 V 41 w(p)s(oly)p 890 1695 V 39 w(complex)p 1254 1695 V 41 w(w)m(orkspace)g(*)g Ft(w)p FD(,)g(gsl)p 2020 1695 V 40 w(complex)p 2385 1695 V 41 w(pac)m(k)m(ed)p 2695 1695 V 41 w(ptr)f Ft(z)p Fu(\))390 1805 y FK(This)c(function)h(computes)g(the)g(ro)s(ots)h(of)f(the)g (general)h(p)s(olynomial)f FE(P)13 b FK(\()p FE(x)p FK(\))26 b(=)f FE(a)3121 1819 y FB(0)3172 1805 y FK(+)14 b FE(a)3305 1819 y FB(1)3342 1805 y FE(x)g FK(+)g FE(a)3541 1819 y FB(2)3577 1805 y FE(x)3629 1772 y FB(2)3679 1805 y FK(+)390 1914 y FE(:::)e FK(+)g FE(a)608 1928 y Fq(n)p Fp(\000)p FB(1)739 1914 y FE(x)791 1881 y Fq(n)p Fp(\000)p FB(1)948 1914 y FK(using)26 b(balanced-QR)h(reduction)f(of)g(the)h (companion)g(matrix.)40 b(The)25 b(parameter)390 2024 y FD(n)g FK(sp)s(eci\014es)g(the)g(length)h(of)g(the)f(co)s(e\016cien)m (t)i(arra)m(y)-8 b(.)40 b(The)25 b(co)s(e\016cien)m(t)i(of)f(the)f (highest)h(order)f(term)390 2134 y(m)m(ust)30 b(b)s(e)f(non-zero.)41 b(The)29 b(function)g(requires)h(a)g(w)m(orkspace)g FD(w)37 b FK(of)30 b(the)g(appropriate)g(size.)41 b(The)390 2243 y FE(n)14 b FI(\000)g FK(1)27 b(ro)s(ots)g(are)h(returned)e(in)h(the)h (pac)m(k)m(ed)g(complex)g(arra)m(y)g FD(z)k 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b(30,)h(Issue)e(2)g(\(2004\),)j(pp)d(218{236\).)150 3386 y FJ(6.6)68 b(Examples)150 3545 y FK(T)-8 b(o)25 b(demonstrate)f(the)g(use)g(of)g(the)h(general)g(p)s(olynomial)f(solv)m (er)h(w)m(e)g(will)f(tak)m(e)i(the)e(p)s(olynomial)g FE(P)13 b FK(\()p FE(x)p FK(\))26 b(=)150 3655 y FE(x)202 3622 y FB(5)259 3655 y FI(\000)20 b FK(1)31 b(whic)m(h)f(has)g(the)h (follo)m(wing)h(ro)s(ots,)1424 3826 y(1)p FE(;)15 b(e)1551 3788 y FB(2)p Fq(\031)r(i=)p FB(5)1721 3826 y FE(;)g(e)1803 3788 y FB(4)p Fq(\031)r(i=)p FB(5)1973 3826 y FE(;)g(e)2055 3788 y FB(6)p Fq(\031)r(i=)p FB(5)2224 3826 y FE(;)g(e)2306 3788 y FB(8)p Fq(\031)r(i=)p FB(5)150 3997 y FK(The)30 b(follo)m(wing)i(program)e(will)h(\014nd)d(these)j(ro)s(ots.)390 4134 y FH(#include)46 b()390 4244 y(#include)g ()390 4463 y(int)390 4573 y(main)h(\(void\))390 4682 y({)485 4792 y(int)g(i;)485 4902 y(/*)h(coefficients)c(of)j (P\(x\))g(=)95 b(-1)47 b(+)h(x^5)94 b(*/)485 5011 y(double)47 b(a[6])f(=)i({)f(-1,)g(0,)g(0,)g(0,)h(0,)f(1)g(};)485 5121 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w(t)g Ft(mode)p Fu(\))3350 5121 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_airy_Ai_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1790 5121 V 40 w(mo)s(de)p 2045 5121 V 40 w(t)g Ft(mode)p FD(,)g(gsl)p 2521 5121 V 41 w(sf)p 2626 5121 V 40 w(result)f(*)565 5230 y Ft(result)p Fu(\))390 5340 y FK(These)d(routines)g(compute)h(the)g(Airy)f(function) g FE(Ai)p FK(\()p FE(x)p FK(\))h(with)f(an)h(accuracy)g(sp)s(eci\014ed) f(b)m(y)g FD(mo)s(de)p FK(.)p eop end %%Page: 35 51 TeXDict begin 35 50 bop 150 -116 a FK(Chapter)30 b(7:)41 b(Sp)s(ecial)31 b(F)-8 b(unctions)2348 b(35)3350 299 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_airy_Bi)c Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1842 299 28 4 v 41 w(mo)s(de)p 2098 299 V 39 w(t)g Ft(mode)p Fu(\))3350 408 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_airy_Bi_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1790 408 V 40 w(mo)s(de)p 2045 408 V 40 w(t)g Ft(mode)p FD(,)g(gsl)p 2521 408 V 41 w(sf)p 2626 408 V 40 w(result)f(*)565 518 y 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FE(x)1961 1239 y FB(3)p Fq(=)p FB(2)2068 1272 y FK(\),)g(and)f(is)g(1)h(for)f FE(x)25 b(<)g FK(0.)3350 1477 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_airy_Bi_scaled)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 2208 1477 V 41 w(mo)s(de)p 2464 1477 V 39 w(t)g Ft(mode)p Fu(\))3350 1587 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_airy_Bi_scaled)q (_e)f Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 2156 1587 V 40 w(mo)s(de)p 2411 1587 V 40 w(t)g Ft(mode)p FD(,)565 1696 y(gsl)p 677 1696 V 41 w(sf)p 782 1696 V 39 w(result)g(*)f Ft(result)p Fu(\))390 1806 y FK(These)f(routines)h (compute)g(a)g(scaled)h(v)m(ersion)f(of)g(the)f(Airy)h(function)f FE(S)2896 1820 y Fq(B)2953 1806 y FK(\()p FE(x)p FK(\))p FE(B)5 b(i)p FK(\()p FE(x)p FK(\).)42 b(F)-8 b(or)30 b FE(x)c(>)f FK(0)390 1916 y(the)31 b(scaling)g(factor)g FE(S)1161 1930 y Fq(B)1218 1916 y FK(\()p FE(x)p FK(\))g(is)g(exp\()p FI(\000)p FK(\(2)p FE(=)p FK(3\))p FE(x)1965 1883 y FB(3)p Fq(=)p FB(2)2071 1916 y FK(\),)g(and)f(is)g(1)h(for)f FE(x)25 b(<)g FK(0.)150 2126 y Fy(7.4.2)63 b(Deriv)-7 b(ativ)m(es)40 b(of)i(Airy)e(F)-10 b(unctions)3350 2333 y FK([F)i(unction])-3599 b Fv(double)54 b(gsl_sf_airy_Ai_deriv)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 2156 2333 V 40 w(mo)s(de)p 2411 2333 V 40 w(t)g Ft(mode)p Fu(\))3350 2443 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_airy_Ai_deriv_)q (e)e Fu(\()p FD(double)31 b Ft(x)p FD(,)f(gsl)p 2103 2443 V 41 w(mo)s(de)p 2359 2443 V 40 w(t)g Ft(mode)p FD(,)i(gsl)p 2835 2443 V 41 w(sf)p 2940 2443 V 39 w(result)565 2552 y(*)f Ft(result)p Fu(\))390 2662 y FK(These)23 b(routines)g (compute)g(the)h(Airy)f(function)f(deriv)-5 b(ativ)m(e)25 b FE(Ai)2556 2629 y Fp(0)2580 2662 y FK(\()p FE(x)p FK(\))f(with)e(an)h (accuracy)i(sp)s(eci\014ed)390 2771 y(b)m(y)30 b FD(mo)s(de)p FK(.)3350 2977 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_airy_Bi_deriv)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 2156 2977 V 40 w(mo)s(de)p 2411 2977 V 40 w(t)g Ft(mode)p Fu(\))3350 3087 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_airy_Bi_deriv_)q(e)e Fu(\()p FD(double)31 b Ft(x)p FD(,)f(gsl)p 2103 3087 V 41 w(mo)s(de)p 2359 3087 V 40 w(t)g Ft(mode)p FD(,)i(gsl)p 2835 3087 V 41 w(sf)p 2940 3087 V 39 w(result)565 3196 y(*)f Ft(result)p Fu(\))390 3306 y FK(These)22 b(routines)h(compute)g(the)g(Airy)f (function)h(deriv)-5 b(ativ)m(e)24 b FE(B)5 b(i)2559 3273 y Fp(0)2582 3306 y FK(\()p FE(x)p FK(\))23 b(with)f(an)h(accuracy) h(sp)s(eci\014ed)390 3415 y(b)m(y)30 b FD(mo)s(de)p FK(.)3350 3621 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_airy_Ai_deriv_s)q (cal)q(ed)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 2522 3621 V 40 w(mo)s(de)p 2777 3621 V 40 w(t)g Ft(mode)p Fu(\))3350 3731 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_airy_Ai_deriv_)q(scal)q(ed_)q(e)e Fu(\()p FD(double)31 b Ft(x)p FD(,)g(gsl)p 2470 3731 V 40 w(mo)s(de)p 2725 3731 V 40 w(t)f Ft(mode)p FD(,)565 3840 y(gsl)p 677 3840 V 41 w(sf)p 782 3840 V 39 w(result)h(*)f Ft(result)p Fu(\))390 3950 y FK(These)j(routines)h(compute)g(the)f(scaled)i(Airy)e (function)g(deriv)-5 b(ativ)m(e)35 b FE(S)2857 3964 y Fq(A)2911 3950 y FK(\()p FE(x)p FK(\))p FE(Ai)3132 3917 y Fp(0)3157 3950 y FK(\()p FE(x)p FK(\).)51 b(F)-8 b(or)34 b FE(x)c(>)h FK(0)390 4059 y(the)g(scaling)g(factor)g FE(S)1161 4073 y Fq(A)1215 4059 y FK(\()p FE(x)p FK(\))g(is)g(exp)o (\(+\(2)p FE(=)p FK(3\))p FE(x)1961 4026 y FB(3)p Fq(=)p FB(2)2068 4059 y FK(\),)g(and)f(is)g(1)h(for)f FE(x)25 b(<)g FK(0.)3350 4265 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_airy_Bi_deriv_s)q(cal)q(ed)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 2522 4265 V 40 w(mo)s(de)p 2777 4265 V 40 w(t)g Ft(mode)p Fu(\))3350 4375 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_airy_Bi_deriv_)q(scal)q(ed_)q(e)e Fu(\()p FD(double)31 b Ft(x)p FD(,)g(gsl)p 2470 4375 V 40 w(mo)s(de)p 2725 4375 V 40 w(t)f Ft(mode)p FD(,)565 4484 y(gsl)p 677 4484 V 41 w(sf)p 782 4484 V 39 w(result)h(*)f Ft(result)p Fu(\))390 4594 y FK(These)j(routines)g(compute)g(the)g (scaled)h(Airy)f(function)g(deriv)-5 b(ativ)m(e)34 b FE(S)2853 4608 y Fq(B)2910 4594 y FK(\()p FE(x)p FK(\))p FE(B)5 b(i)3137 4561 y Fp(0)3161 4594 y FK(\()p FE(x)p FK(\).)49 b(F)-8 b(or)34 b FE(x)29 b(>)h FK(0)390 4703 y(the)h(scaling)g(factor)g FE(S)1161 4717 y Fq(B)1218 4703 y FK(\()p FE(x)p FK(\))g(is)g(exp\()p FI(\000)p FK(\(2)p FE(=)p FK(3\))p FE(x)1965 4670 y FB(3)p Fq(=)p FB(2)2071 4703 y 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 52 TeXDict begin 36 51 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 53 TeXDict begin 37 52 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 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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 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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 b(routines)g(compute)g(the)g(regular)g(spherical)g(Bessel)h(function)f (of)g(second)g(order,)h FE(j)3494 4228 y FB(2)3531 4214 y FK(\()p FE(x)p FK(\))f(=)390 4324 y(\(\(3)p FE(=x)602 4291 y FB(2)661 4324 y FI(\000)20 b FK(1\))15 b(sin)q(\()p FE(x)p FK(\))20 b FI(\000)g FK(3)15 b(cos)r(\()p FE(x)p FK(\))p FE(=x)p FK(\))p FE(=x)p FK(.)3350 4503 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_bessel_jl)c Fu(\()p FD(in)m(t)32 b Ft(l)p FD(,)f(double)e Ft(x)p Fu(\))3350 4613 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_jl_e)e Fu(\()p FD(in)m(t)31 b Ft(l)p FD(,)g(double)f Ft(x)p FD(,)h(gsl)p 2141 4613 V 41 w(sf)p 2246 4613 V 39 w(result)g(*)f Ft(result)p Fu(\))390 4722 y FK(These)41 b(routines)g(compute)g(the)g(regular)h(spherical)f (Bessel)h(function)f(of)g(order)g FD(l)p FK(,)j FE(j)3424 4736 y Fq(l)3450 4722 y FK(\()p FE(x)p FK(\),)g(for)390 4832 y FE(l)27 b FI(\025)e FK(0)31 b(and)f FE(x)25 b FI(\025)g FK(0.)3350 5011 y([F)-8 b(unction])-3599 b Fv(int)53 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 56 TeXDict begin 40 55 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 57 TeXDict begin 41 56 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)40 b(routine)h(computes)g(the)g(v)-5 b(alues)41 b(of)g(the)g(scaled)h (regular)f(mo)s(di\014ed)e(cylindrical)j(Bessel)390 2367 y(functions)f(exp\()p FI(\000j)p FE(x)p FI(j)p FK(\))p FE(i)1206 2381 y Fq(l)1233 2367 y FK(\()p FE(x)p FK(\))h(for)f FE(l)j FK(from)d(0)h(to)g FD(lmax)48 b FK(inclusiv)m(e)43 b(for)e FE(l)r(max)j FI(\025)g FK(0,)h(storing)d(the)390 2477 y(results)29 b(in)g(the)g(arra)m(y)h FD(result)p 1404 2477 V 40 w(arra)m(y)p FK(.)41 b(The)29 b(v)-5 b(alues)29 b(are)h(computed)f(using)g(recurrence)g(relations)390 2586 y(for)h(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 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 58 TeXDict begin 42 57 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 (y)g(di\013er)f(sligh)m(tly)i(from)e(the)g(exact)i(v)-5 b(alues.)150 1066 y Fy(7.5.9)63 b(Regular)40 b(Bessel)j(F)-10 b(unction|F)g(ractional)40 b(Order)3350 1283 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_bessel_Jnu)d Fu(\()p FD(double)30 b Ft(nu)p FD(,)h(double)f Ft(x)p Fu(\))3350 1392 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_Jnu_e)e Fu(\()p FD(double)28 b Ft(nu)p FD(,)h(double)e Ft(x)p FD(,)i(gsl)p 2390 1392 V 40 w(sf)p 2494 1392 V 40 w(result)e(*)h Ft(result)p Fu(\))390 1502 y FK(These)k(routines)g(compute)g(the)g(regular)h(cylindrical)g(Bessel) g(function)f(of)g(fractional)h(order)f FE(\027)6 b FK(,)390 1611 y FE(J)440 1625 y Fq(\027)482 1611 y FK(\()p FE(x)p FK(\).)3350 1836 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_bessel_sequenc)q(e_Jn)q(u_e)f Fu(\()p FD(double)30 b Ft(nu)p FD(,)i(gsl)p 2470 1836 V 40 w(mo)s(de)p 2725 1836 V 40 w(t)e Ft(mode)p FD(,)565 1945 y(size)p 712 1945 V 41 w(t)h Ft(size)p FD(,)g(double)f Ft(v)p Fo([])p Fu(\))390 2055 y 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 59 TeXDict begin 43 58 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 60 TeXDict begin 44 59 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 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w(exp)s(onen)m(t)p FK(.)p eop end %%Page: 45 61 TeXDict begin 45 60 bop 150 -116 a FK(Chapter)30 b(7:)41 b(Sp)s(ecial)31 b(F)-8 b(unctions)2348 b(45)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_coulomb_wave_F)q(G_ar)q (ray)f Fu(\()p FD(double)30 b Ft(L_min)p FD(,)j(in)m(t)d Ft(kmax)p FD(,)i(double)565 408 y Ft(eta)p FD(,)g(double)e Ft(x)p FD(,)g(double)g Ft(fc_array)p Fo([])p FD(,)j(double)d Ft(gc_array)p Fo([])p FD(,)j(double)d(*)g Ft(F_exponent)p FD(,)565 518 y(double)g(*)h Ft(G_exponent)p Fu(\))390 628 y FK(This)38 b(function)g(computes)h(the)g(functions)f FE(F)2006 642 y Fq(L)2056 628 y FK(\()p FE(\021)s(;)15 b(x)p FK(\),)42 b FE(G)2404 642 y Fq(L)2454 628 y FK(\()p FE(\021)s(;)15 b(x)p FK(\))40 b(for)f FE(L)f FK(=)h FE(Lmin)15 b(:)g(:)g(:)h(Lmin)25 b FK(+)390 737 y FE(k)s(max)32 b FK(storing)g(the)g(results)f(in)g FD(fc)p 1586 737 28 4 v 41 w(arra)m(y)39 b FK(and)32 b FD(gc)p 2137 737 V 40 w(arra)m(y)p FK(.)46 b(In)30 b(the)i(case)h(of)f(o)m(v)m(er\015o)m 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1578 y FK(\()p FE(\021)s(;)15 b(x)p FK(\))43 b(for)e FE(L)i FK(=)g FE(Lmin)15 b(:)g(:)g(:)h(Lmin)27 b FK(+)g FE(k)s(max)41 b FK(storing)h(the)f (results)g(in)g FD(fc)p 3483 1578 V 40 w(arra)m(y)p FK(,)390 1688 y FD(gc)p 481 1688 V 41 w(arra)m(y)p FK(,)35 b FD(fcp)p 908 1688 V 39 w(arra)m(y)42 b FK(and)33 b FD(gcp)p 1512 1688 V 40 w(arra)m(y)p FK(.)50 b(In)32 b(the)i(case)g(of)g(o)m(v)m (er\015o)m(w)g(the)g(exp)s(onen)m(ts)f(are)h(stored)390 1797 y(in)c FD(F)p 561 1797 V 40 w(exp)s(onen)m(t)j FK(and)d FD(G)p 1243 1797 V 40 w(exp)s(onen)m(t)p FK(.)3350 1981 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_coulomb_wave_s)q(phF_)q (arr)q(ay)f Fu(\()p FD(double)30 b Ft(L_min)p FD(,)i(in)m(t)f Ft(kmax)p FD(,)565 2090 y(double)f Ft(eta)p FD(,)i(double)d Ft(x)p FD(,)i(double)f Ft(fc_array)p Fo([])p FD(,)j(double)d Ft(F_exponent)p Fo([])p Fu(\))390 2200 y FK(This)59 b(function)g (computes)g(the)h(Coulom)m(b)f(w)m(a)m(v)m(e)j(function)d(divided)g(b)m (y)g(the)g(argumen)m(t)390 2309 y FE(F)448 2323 y Fq(L)498 2309 y FK(\()p FE(\021)s(;)15 b(x)p FK(\))p FE(=x)40 b FK(for)e FE(L)g FK(=)h FE(Lmin)15 b(:)g(:)g(:)h(Lmin)25 b FK(+)g FE(k)s(max)p FK(,)40 b(storing)f(the)f(results)g(in)g FD(fc)p 3171 2309 V 40 w(arra)m(y)p FK(.)65 b(In)38 b(the)390 2419 y(case)45 b(of)g(o)m(v)m(er\015o)m(w)h(the)f(exp)s(onen)m(t)f(is)g (stored)h(in)f FD(F)p 2236 2419 V 40 w(exp)s(onen)m(t)p FK(.)83 b(This)44 b(function)g(reduces)g(to)390 2529 y(spherical)31 b(Bessel)g(functions)f(in)g(the)h(limit)g FE(\021)d FI(!)e FK(0.)150 2727 y Fy(7.7.3)63 b(Coulom)m(b)41 b(W)-10 b(a)m(v)m(e)39 b(F)-10 b(unction)41 b(Normalization)g(Constan)m (t)150 2874 y FK(The)30 b(Coulom)m(b)g(w)m(a)m(v)m(e)i(function)f (normalization)h(constan)m(t)f(is)g(de\014ned)e(in)h(Abramo)m(witz)h (14.1.7.)3350 3057 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_coulomb_CL_e)e Fu(\()p FD(double)31 b Ft(L)p FD(,)g(double)f Ft(eta)p FD(,)h(gsl)p 2452 3057 V 41 w(sf)p 2557 3057 V 39 w(result)f(*)565 3167 y Ft(result)p Fu(\))390 3277 y 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b(7:)41 b(Sp)s(ecial)31 b(F)-8 b(unctions)2348 b(46)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_coupling_3j_e)f Fu(\()p FD(in)m(t)31 b Ft(two_ja)p FD(,)h(in)m(t)f Ft(two_jb)p FD(,)i(in)m(t)e Ft(two_jc)p FD(,)h(in)m(t)565 408 y Ft(two_ma)p FD(,)g(in)m(t)f Ft(two_mb)p FD(,)i(in)m(t)e Ft(two_mc)p FD(,)h(gsl)p 2063 408 28 4 v 41 w(sf)p 2168 408 V 39 w(result)f(*)f Ft(result)p Fu(\))390 518 y FK(These)g(routines)g (compute)h(the)g(Wigner)g(3-j)f(co)s(e\016cien)m(t,)1600 630 y Fs(\022)1695 694 y FE(j)5 b(a)129 b(j)5 b(b)128 b(j)5 b(c)1676 804 y(ma)91 b(mb)g(mc)2239 630 y Fs(\023)390 985 y FK(where)27 b(the)h(argumen)m(ts)h(are)f(giv)m(en)h(in)e(half-in) m(teger)j(units,)e FE(j)5 b(a)28 b FK(=)g FD(t)m(w)m(o)p 2824 985 V 41 w(ja)p FK(/2,)i FE(ma)e FK(=)f FD(t)m(w)m(o)p 3477 985 V 42 w(ma)p FK(/2,)390 1094 y(etc.)150 1317 y Fy(7.8.2)63 b(6-j)41 b(Sym)m(b)s(ols)3350 1537 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_coupling_6j)d Fu(\()p FD(in)m(t)31 b Ft(two_ja)p FD(,)i(in)m(t)e Ft(two_jb)p FD(,)h(in)m(t)f Ft(two_jc)p FD(,)h(in)m(t)565 1646 y Ft(two_jd)p FD(,)g(in)m(t)f Ft(two_je)p FD(,)i(in)m(t)e Ft(two_jf)p Fu(\))3350 1756 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_coupling_6j_e)f Fu(\()p FD(in)m(t)31 b Ft(two_ja)p FD(,)h(in)m(t)f Ft(two_jb)p FD(,)i(in)m(t)e Ft(two_jc)p FD(,)h(in)m(t)565 1865 y Ft(two_jd)p FD(,)g(in)m(t)f Ft(two_je)p FD(,)i(in)m(t)e Ft(two_jf)p FD(,)h(gsl)p 2063 1865 V 41 w(sf)p 2168 1865 V 39 w(result)f(*)f Ft(result)p Fu(\))390 1975 y FK(These)g(routines)g(compute)h(the)g(Wigner)g(6-j)f (co)s(e\016cien)m(t,)1645 2087 y Fs(\032)1723 2151 y FE(j)5 b(a)93 b(j)5 b(b)101 b(j)5 b(c)1723 2261 y(j)g(d)92 b(j)5 b(e)92 b(j)5 b(f)2192 2087 y Fs(\033)390 2442 y FK(where)27 b(the)h(argumen)m(ts)h(are)f(giv)m(en)h(in)e(half-in)m (teger)j(units,)e FE(j)5 b(a)28 b FK(=)g FD(t)m(w)m(o)p 2824 2442 V 41 w(ja)p FK(/2,)i FE(ma)e FK(=)f FD(t)m(w)m(o)p 3477 2442 V 42 w(ma)p FK(/2,)390 2551 y(etc.)150 2774 y Fy(7.8.3)63 b(9-j)41 b(Sym)m(b)s(ols)3350 2993 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_coupling_9j)d Fu(\()p FD(in)m(t)31 b Ft(two_ja)p FD(,)i(in)m(t)e Ft(two_jb)p FD(,)h(in)m(t)f Ft(two_jc)p FD(,)h(in)m(t)565 3103 y Ft(two_jd)p FD(,)g(in)m(t)f Ft(two_je)p FD(,)i(in)m(t)e Ft(two_jf)p FD(,)h(in)m(t)f Ft(two_jg)p FD(,)h(in)m(t)f Ft(two_jh)p FD(,)i(in)m(t)d Ft(two_ji)p Fu(\))3350 3212 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_coupling_9j_e)f Fu(\()p FD(in)m(t)31 b Ft(two_ja)p FD(,)h(in)m(t)f Ft(two_jb)p FD(,)i(in)m(t)e Ft(two_jc)p FD(,)h(in)m(t)565 3322 y Ft(two_jd)p FD(,)g(in)m(t)f Ft(two_je)p FD(,)i(in)m(t)e Ft(two_jf)p FD(,)h(in)m(t)f Ft(two_jg)p FD(,)h(in)m(t)f Ft(two_jh)p FD(,)i(in)m(t)d Ft(two_ji)p FD(,)565 3432 y(gsl)p 677 3432 V 41 w(sf)p 782 3432 V 39 w(result)h(*)f Ft(result)p Fu(\))390 3541 y FK(These)g(routines)g(compute)h(the)g (Wigner)g(9-j)f(co)s(e\016cien)m(t,)1629 3655 y Fs(8)1629 3729 y(<)1629 3879 y(:)1718 3717 y FE(j)5 b(a)98 b(j)5 b(b)106 b(j)5 b(c)1718 3827 y(j)g(d)97 b(j)5 b(e)97 b(j)5 b(f)1718 3937 y(j)g(g)96 b(j)5 b(h)104 b(j)5 b(i)2197 3655 y Fs(9)2197 3729 y(=)2197 3879 y(;)390 4118 y FK(where)27 b(the)h(argumen)m(ts)h(are)f(giv)m(en)h(in)e(half-in)m(teger)j(units,)e FE(j)5 b(a)28 b FK(=)g FD(t)m(w)m(o)p 2824 4118 V 41 w(ja)p FK(/2,)i FE(ma)e FK(=)f FD(t)m(w)m(o)p 3477 4118 V 42 w(ma)p FK(/2,)390 4227 y(etc.)150 4494 y FJ(7.9)68 b(Da)l(wson)46 b(F)-11 b(unction)150 4654 y FK(The)28 b(Da)m(wson)h(in)m(tegral)h(is)e(de\014ned)f(b)m(y)h(exp\()p FI(\000)p FE(x)1823 4621 y FB(2)1860 4654 y FK(\))1910 4585 y Fs(R)1966 4605 y Fq(x)1950 4681 y FB(0)2023 4654 y FE(dt)15 b FK(exp\()p FE(t)2325 4621 y FB(2)2363 4654 y FK(\).)40 b(A)28 b(table)h(of)g(Da)m(wson's)g(in)m(tegral)h(can)150 4763 y(b)s(e)k(found)g(in)h(Abramo)m(witz)h(&)f(Stegun,)h(T)-8 b(able)36 b(7.5.)56 b(The)34 b(Da)m(wson)i(functions)f(are)g(declared)h (in)f(the)150 4873 y(header)30 b(\014le)h FH(gsl_sf_dawson.h)p FK(.)3350 5103 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_dawson)c Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 5213 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_dawson_e)d Fu(\()p FD(double)31 b Ft(x)p FD(,)f(gsl)p 1737 5213 V 41 w(sf)p 1842 5213 V 40 w(result)g(*)h Ft(result)p Fu(\))390 5322 y FK(These)f(routines)g(compute)h(the)g(v)-5 b(alue)30 b(of)h(Da)m(wson's)g(in)m(tegral)h(for)e FD(x)p FK(.)p eop end %%Page: 47 63 TeXDict begin 47 62 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 (ed)f(in)h(this)g(section)i(are)f(declared)g(in)f(the)g(header)g (\014le)h FH(gsl_sf_dilog.h)p FK(.)150 4352 y Fy(7.11.1)63 b(Real)40 b(Argumen)m(t)3350 4533 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_dilog)49 b Fu(\()p FD(double)31 b Ft(x)p Fu(\))3350 4643 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_dilog_e)d Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1685 4643 V 41 w(sf)p 1790 4643 V 39 w(result)g(*)f Ft(result)p Fu(\))390 4752 y FK(These)25 b(routines)g(compute)h(the)g(dilogarithm)g(for)f(a)h(real)g(argumen)m (t.)40 b(In)24 b(Lewin's)h(notation)i(this)390 4862 y(is)37 b FE(Li)581 4876 y FB(2)618 4862 y FK(\()p FE(x)p FK(\),)i(the)e(real)g (part)f(of)h(the)g(dilogarithm)g(of)g(a)f(real)i FE(x)p FK(.)59 b(It)36 b(is)h(de\014ned)e(b)m(y)i(the)f(in)m(tegral)390 4971 y(represen)m(tation)c FE(Li)1078 4985 y FB(2)1115 4971 y FK(\()p FE(x)p FK(\))27 b(=)f FI(\000)p FK(Re)1554 4903 y Fs(R)1610 4923 y Fq(x)1594 4999 y FB(0)1667 4971 y FE(ds)15 b FK(log)r(\(1)21 b FI(\000)g FE(s)p FK(\))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 64 TeXDict begin 48 63 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(\()p FD(double)31 b Ft(r)p FD(,)f(double)g Ft(theta)p FD(,)i(gsl)p 2713 557 28 4 v 41 w(sf)p 2818 557 V 40 w(result)e(*)565 666 y Ft(result_re)p FD(,)j(gsl)p 1203 666 V 41 w(sf)p 1308 666 V 40 w(result)d(*)h Ft(result_im)p Fu(\))390 776 y FK(This)21 b(function)h(computes)g(the)g(full)g (complex-v)-5 b(alued)23 b(dilogarithm)g(for)f(the)g(complex)g(argumen) m(t)390 885 y FE(z)37 b FK(=)32 b FE(r)18 b FK(exp\()p FE(i\022)s FK(\).)54 b(The)34 b(real)i(and)e(imaginary)h(parts)g(of)g (the)g(result)f(are)i(returned)d(in)i FD(result)p 3615 885 V 40 w(re)p FK(,)390 995 y FD(result)p 619 995 V 40 w(im)p FK(.)150 1319 y FJ(7.12)68 b(Elemen)l(tary)47 b(Op)t(erations)150 1478 y FK(The)34 b(follo)m(wing)i(functions)e(allo) m(w)i(for)e(the)h(propagation)g(of)g(errors)f(when)f(com)m(bining)i 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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 (this)h(section)h(are)f(declared)h(in)e(the)h(header)g(\014le)g FH(gsl_sf_ellint.h)p FK(.)150 3232 y(F)-8 b(urther)41 b(information)g(ab)s(out)g(the)h(elliptic)g(in)m(tegrals)h(can)f(b)s(e) e(found)g(in)h(Abramo)m(witz)h(&)f(Stegun,)150 3341 y(Chapter)30 b(17.)150 3602 y Fy(7.13.1)63 b(De\014nition)42 b(of)g(Legendre)f(F)-10 b(orms)150 3748 y FK(The)30 b(Legendre)g(forms)g(of)h(elliptic)h(in)m (tegrals)f FE(F)13 b FK(\()p FE(\036;)i(k)s FK(\),)33 b FE(E)5 b FK(\()p FE(\036;)15 b(k)s FK(\))32 b(and)d(\005\()p FE(\036;)15 b(k)s(;)g(n)p FK(\))32 b(are)f(de\014ned)e(b)m(y)-8 b(,)1099 4034 y FE(F)13 b FK(\()p FE(\036;)i(k)s FK(\))27 b(=)1507 3919 y 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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 65 TeXDict begin 49 64 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 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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 66 TeXDict begin 50 65 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 1049 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_ellint_P)c Fu(\()p FD(double)30 b Ft(phi)p FD(,)i(double)e Ft(k)p FD(,)h(double)f Ft(n)p FD(,)g(gsl)p 2800 1049 V 41 w(mo)s(de)p 3056 1049 V 40 w(t)565 1159 y Ft(mode)p Fu(\))3350 1268 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_ellint_P_e)e Fu(\()p FD(double)30 b Ft(phi)p FD(,)i(double)e Ft(k)p FD(,)g(double)g Ft(n)p FD(,)h(gsl)p 2748 1268 V 41 w(mo)s(de)p 3004 1268 V 39 w(t)565 1378 y Ft(mode)p FD(,)h(gsl)p 942 1378 V 40 w(sf)p 1046 1378 V 40 w(result)e(*)h Ft(result)p Fu(\))390 1487 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 1597 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 1707 y(function)26 b(in)h(terms)f(of)h(the)f(parameters)h FE(m)e FK(=)g FE(k)2064 1674 y FB(2)2128 1707 y FK(and)h(sin)2413 1666 y FB(2)2450 1707 y FK(\()p FE(\013)p FK(\))h(=)e FE(k)2751 1674 y FB(2)2788 1707 y FK(,)i(with)g(the)g(c)m(hange)g(of)g(sign)390 1816 y FE(n)e FI(!)g(\000)p FE(n)p FK(.)3350 2018 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_ellint_D)c Fu(\()p FD(double)30 b Ft(phi)p FD(,)i(double)e Ft(k)p FD(,)h(double)f Ft(n)p FD(,)g(gsl)p 2800 2018 V 41 w(mo)s(de)p 3056 2018 V 40 w(t)565 2128 y Ft(mode)p Fu(\))3350 2238 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_ellint_D_e)e Fu(\()p FD(double)30 b Ft(phi)p FD(,)i(double)e Ft(k)p FD(,)g(double)g Ft(n)p FD(,)h(gsl)p 2748 2238 V 41 w(mo)s(de)p 3004 2238 V 39 w(t)565 2347 y Ft(mode)p FD(,)h(gsl)p 942 2347 V 40 w(sf)p 1046 2347 V 40 w(result)e(*)h Ft(result)p Fu(\))390 2457 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 2566 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,)852 2785 y FE(D)s FK(\()p FE(\036;)15 b(k)s(;)g(n)p FK(\))26 b(=)1371 2724 y(1)p 1371 2764 46 4 v 1371 2848 a(3)1427 2785 y(\(sin)15 b FE(\036)p FK(\))1678 2748 y FB(3)1715 2785 y FE(R)q(D)s FK(\(1)21 b FI(\000)f FK(sin)2166 2745 y FB(2)2204 2785 y FK(\()p FE(\036)p FK(\))p FE(;)15 b FK(1)22 b FI(\000)e FE(k)2576 2748 y FB(2)2628 2785 y FK(sin)2740 2745 y FB(2)2777 2785 y FK(\()p FE(\036)p FK(\))p FE(;)15 b FK(1\))p FE(:)390 2987 y FK(The)30 b(argumen)m(t)h FD(n)e FK(is)i(not)g(used)e(and)h(will)h(b)s(e)e(remo)m(v)m(ed)j(in)e(a)h (future)e(release.)150 3195 y Fy(7.13.5)63 b(Carlson)41 b(F)-10 b(orms)3350 3401 y FK([F)i(unction])-3599 b Fv(double)54 b(gsl_sf_ellint_RC)c Fu(\()p FD(double)31 b Ft(x)p FD(,)g(double)f Ft(y)p FD(,)g(gsl)p 2347 3401 28 4 v 41 w(mo)s(de)p 2603 3401 V 40 w(t)g Ft(mode)p Fu(\))3350 3511 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_ellint_RC_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(double)f Ft(y)p FD(,)h(gsl)p 2295 3511 V 41 w(mo)s(de)p 2551 3511 V 39 w(t)g Ft(mode)p FD(,)565 3620 y(gsl)p 677 3620 V 41 w(sf)p 782 3620 V 39 w(result)g(*)f Ft(result)p Fu(\))390 3730 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 3840 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 4042 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_ellint_RD)c Fu(\()p FD(double)31 b Ft(x)p FD(,)g(double)f Ft(y)p FD(,)g(double)g Ft(z)p FD(,)h(gsl)p 2748 4042 V 41 w(mo)s(de)p 3004 4042 V 39 w(t)565 4151 y Ft(mode)p Fu(\))3350 4261 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_ellint_RD_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(double)f Ft(y)p FD(,)h(double)f Ft(z)p FD(,)h(gsl)p 2696 4261 V 40 w(mo)s(de)p 2951 4261 V 40 w(t)565 4371 y Ft(mode)p FD(,)h(gsl)p 942 4371 V 40 w(sf)p 1046 4371 V 40 w(result)e(*)h Ft(result)p Fu(\))390 4480 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 4590 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 67 TeXDict begin 51 66 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 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Fy(7.15.1)63 b(Error)41 b(F)-10 b(unction)3350 2683 y FK([F)i(unction])-3599 b Fv(double)54 b(gsl_sf_erf)49 b Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 2792 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_erf_e)c Fu(\()p FD(double)31 b Ft(x)p FD(,)f(gsl)p 1580 2792 V 41 w(sf)p 1685 2792 V 40 w(result)g(*)h Ft(result)p Fu(\))390 2902 y FK(These)108 b(routines)h(compute)g(the)g(error)f(function)g(erf\()p FE(x)p FK(\),)129 b(where)108 b(erf\()p FE(x)p FK(\))156 b(=)390 3011 y(\(2)p FE(=)515 2946 y FI(p)p 592 2946 56 4 v 592 3011 a FE(\031)s FK(\))697 2943 y Fs(R)753 2963 y Fq(x)737 3039 y FB(0)810 3011 y FE(dt)15 b FK(exp\()p FI(\000)p FE(t)1183 2978 y FB(2)1220 3011 y FK(\).)150 3197 y Fy(7.15.2)63 b(Complemen)m(tary)41 b(Error)g(F)-10 b(unction)3350 3380 y FK([F)i(unction])-3599 b Fv(double)54 b(gsl_sf_erfc)49 b Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 3489 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_erfc_e)d Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1633 3489 28 4 v 40 w(sf)p 1737 3489 V 40 w(result)f(*)h Ft(result)p Fu(\))390 3599 y FK(These)41 b(routines)f(compute)h(the)h(complemen)m (tary)g(error)e(function)h(erfc\()p FE(x)p FK(\))i(=)g(1)27 b FI(\000)g FK(erf\()p FE(x)p FK(\))43 b(=)390 3709 y(\(2)p FE(=)515 3643 y FI(p)p 592 3643 56 4 v 592 3709 a FE(\031)s FK(\))697 3640 y Fs(R)753 3660 y Fp(1)737 3736 y Fq(x)838 3709 y FK(exp\()p FI(\000)p FE(t)1116 3676 y FB(2)1153 3709 y FK(\).)150 3894 y Fy(7.15.3)63 b(Log)41 b(Complemen)m(tary)g (Error)g(F)-10 b(unction)3350 4077 y FK([F)i(unction])-3599 b Fv(double)54 b(gsl_sf_log_erfc)c Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 4187 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_log_erfc_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1842 4187 28 4 v 41 w(sf)p 1947 4187 V 39 w(result)f(*)h Ft(result)p Fu(\))390 4296 y FK(These)70 b(routines)h(compute)g(the)g(logarithm)g(of)g(the)g (complemen)m(tary)h(error)e(function)390 4406 y(log)r(\(erfc)q(\()p FE(x)p FK(\)\).)150 4591 y Fy(7.15.4)63 b(Probabilit)m(y)41 b(functions)150 4738 y FK(The)58 b(probabilit)m(y)h(functions)e(for)i (the)f(Normal)h(or)f(Gaussian)h(distribution)e(are)i(describ)s(ed)e(in) 150 4848 y(Abramo)m(witz)31 b(&)f(Stegun,)h(Section)g(26.2.)3350 5011 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_erf_Z)49 b Fu(\()p FD(double)31 b Ft(x)p Fu(\))3350 5121 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_erf_Z_e)d Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1685 5121 V 41 w(sf)p 1790 5121 V 39 w(result)g(*)f Ft(result)p Fu(\))390 5230 y FK(These)134 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 68 TeXDict begin 52 67 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 FK(exp\()p FI(\000)p FE(t)1257 595 y FB(2)1294 628 y FE(=)p FK(2\).)275 833 y(The)30 b FD(hazard)h(function)f FK(for)h(the)g(normal)g(distribution,)f(also)i(kno)m(wn)f(as)g(the)g (in)m(v)m(erse)h(Mills')g(ratio,)150 942 y(is)e(de\014ned)g(as,)1315 1177 y FE(h)p FK(\()p FE(x)p FK(\))c(=)1623 1116 y FE(Z)7 b FK(\()p FE(x)p FK(\))p 1621 1156 195 4 v 1621 1240 a FE(Q)p FK(\()p FE(x)p FK(\))1851 1177 y(=)1947 1044 y Fs(r)p 2030 1044 76 4 v 2045 1116 a FK(2)p 2040 1156 56 4 v 2040 1240 a FE(\031)2115 1116 y FK(exp\()p FI(\000)p FE(x)2412 1083 y FB(2)2449 1116 y FE(=)p FK(2\))p 2115 1156 461 4 v 2128 1249 a(erfc\()p FE(x=)2404 1174 y FI(p)p 2481 1174 46 4 v 2481 1249 a FK(2\))150 1417 y(It)27 b(decreases)g(rapidly)f(as)h FE(x)g FK(approac)m(hes)g FI(\0001)f FK(and)h(asymptotes)g(to)h FE(h)p FK(\()p FE(x)p FK(\))e FI(\030)f FE(x)h FK(as)h FE(x)g FK(approac)m(hes)g(+)p FI(1)p FK(.)3350 1622 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_hazard)c Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 1731 y 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 b(routines)g(exp)s(onen)m (tiate)h FD(x)44 b FK(and)38 b(m)m(ultiply)g(b)m(y)g(the)g(factor)h FD(y)45 b FK(to)39 b(return)e(the)h(pro)s(duct)390 4061 y FE(y)18 b FK(exp\()p FE(x)p FK(\).)3350 4266 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_exp_mult_e10_e)f Fu(\()p FD(const)31 b(double)f Ft(x)p FD(,)h(const)g(double)f Ft(y)p FD(,)565 4375 y(gsl)p 677 4375 V 41 w(sf)p 782 4375 V 39 w(result)p 1044 4375 V 40 w(e10)i(*)f Ft(result)p Fu(\))390 4485 y FK(This)g(function)h(computes)h(the)f(pro)s(duct)f FE(y)18 b FK(exp\()p FE(x)p FK(\))32 b(using)g(the)g FH(gsl_sf_result_e10)c FK(t)m(yp)s(e)k(to)390 4595 y(return)d(a)i (result)f(with)g(extended)h(n)m(umeric)f(range.)150 4804 y Fy(7.16.2)63 b(Relativ)m(e)39 b(Exp)s(onen)m(tial)i(F)-10 b(unctions)3350 5011 y FK([F)i(unction])-3599 b Fv(double)54 b(gsl_sf_expm1)49 b Fu(\()p FD(double)31 b Ft(x)p Fu(\))3350 5121 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_expm1_e)d Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1685 5121 V 41 w(sf)p 1790 5121 V 39 w(result)g(*)f Ft(result)p Fu(\))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 69 TeXDict begin 53 68 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 FE(=x)26 b FK(=)390 737 y(1)21 b(+)f FE(x=)p FK(2)h(+)f FE(x)853 704 y FB(2)890 737 y FE(=)p FK(\(2)h FI(\003)g FK(3\))g(+)f FE(x)1346 704 y FB(3)1383 737 y FE(=)p FK(\(2)h FI(\003)g FK(3)g FI(\003)f FK(4\))h(+)f FE(:)15 b(:)g(:)q FK(.)3350 938 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_exprel_2)c Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 1047 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_exprel_2_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1842 1047 V 41 w(sf)p 1947 1047 V 39 w(result)f(*)h Ft(result)p Fu(\))390 1157 y FK(These)d(routines)g (compute)g(the)h(quan)m(tit)m(y)g(2\(exp)q(\()p FE(x)p FK(\))16 b FI(\000)g FK(1)g FI(\000)f FE(x)p FK(\))p FE(=x)2656 1124 y FB(2)2722 1157 y FK(using)28 b(an)g(algorithm)h(that) g(is)390 1266 y(accurate)h(for)d(small)i FE(x)p FK(.)40 b(F)-8 b(or)29 b(small)f FE(x)g FK(the)g(algorithm)h(is)g(based)e(on)h (the)g(expansion)g(2\(exp)q(\()p FE(x)p FK(\))16 b FI(\000)390 1376 y FK(1)21 b FI(\000)f FE(x)p FK(\))p FE(=x)731 1343 y FB(2)794 1376 y FK(=)25 b(1)20 b(+)g FE(x=)p FK(3)h(+)f FE(x)1352 1343 y FB(2)1389 1376 y FE(=)p FK(\(3)i FI(\003)f FK(4\))g(+)f FE(x)1846 1343 y FB(3)1883 1376 y FE(=)p FK(\(3)h FI(\003)g FK(4)g FI(\003)f FK(5\))h(+)f FE(:)15 b(:)g(:)q FK(.)3350 1576 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_exprel_n)c Fu(\()p FD(in)m(t)31 b Ft(n)p FD(,)g(double)f Ft(x)p Fu(\))3350 1686 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_exprel_n_e)e Fu(\()p FD(in)m(t)31 b Ft(n)p FD(,)g(double)f Ft(x)p FD(,)h(gsl)p 2089 1686 V 40 w(sf)p 2193 1686 V 40 w(result)f(*)h Ft(result)p Fu(\))390 1796 y FK(These)h(routines)g(compute)g(the)g FE(N)10 b FK(-relativ)m(e)35 b(exp)s(onen)m(tial,)e(whic)m(h)f(is)g (the)h FD(n)p FK(-th)e(generalization)390 1905 y(of)h(the)h(functions)e FH(gsl_sf_exprel)e FK(and)j FH(gsl_sf_exprel_2)p FK(.)42 b(The)31 b FE(N)10 b FK(-relativ)m(e)35 b(exp)s(onen)m(tial)390 2015 y(is)30 b(giv)m(en)i(b)m(y)-8 b(,)817 2262 y(exprel)1058 2283 y Fq(N)1120 2262 y FK(\()p FE(x)p FK(\))26 b(=)f 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 FD(dx)p FK(.)3350 3330 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_exp_err_e10_e)f Fu(\()p FD(double)30 b Ft(x)p FD(,)h(double)f Ft(dx)p FD(,)h(gsl)p 2452 3330 V 41 w(sf)p 2557 3330 V 39 w(result)p 2819 3330 V 40 w(e10)h(*)565 3439 y Ft(result)p Fu(\))390 3549 y FK(This)e(function)h(exp)s(onen)m (tiates)h(a)g(quan)m(tit)m(y)g FD(x)37 b FK(with)31 b(an)g(asso)s (ciated)h(absolute)g(error)f FD(dx)36 b FK(using)390 3658 y(the)31 b FH(gsl_sf_result_e10)25 b FK(t)m(yp)s(e)31 b(to)g(return)e(a)i(result)f(with)g(extended)h(range.)3350 3859 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_exp_mult_err_e)f Fu(\()p FD(double)30 b Ft(x)p FD(,)h(double)f Ft(dx)p FD(,)h(double)f Ft(y)p FD(,)h(double)565 3968 y Ft(dy)p FD(,)g(gsl)p 837 3968 V 41 w(sf)p 942 3968 V 39 w(result)g(*)g Ft(result)p Fu(\))390 4078 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 4188 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 70 TeXDict begin 54 69 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 71 TeXDict begin 55 70 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 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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 72 TeXDict begin 56 71 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 b(routines)h(compute)g(the)f(incomplete)i(F)-8 b(ermi-Dirac)38 b(in)m(tegral)f(with)f(an)f(index)g(of)h(zero,)390 3157 y FE(F)448 3171 y FB(0)486 3157 y FK(\()p FE(x;)15 b(b)p FK(\))26 b(=)f(ln\(1)c(+)f FE(e)1119 3124 y Fq(b)p Fp(\000)p Fq(x)1242 3157 y FK(\))g FI(\000)g FK(\()p FE(b)h FI(\000)f FE(x)p FK(\).)150 3383 y FJ(7.19)68 b(Gamma)46 b(and)e(Beta)i(F)-11 b(unctions)150 3542 y FK(This)26 b(follo)m(wing)i(routines)f(compute)g(the)g(gamma)h(and)e(b) s(eta)h(functions)g(in)f(their)h(full)f(and)h(incomplete)150 3652 y(forms,)41 b(as)f(w)m(ell)g(as)f(v)-5 b(arious)40 b(kinds)e(of)h(factorials.)69 b(The)39 b(functions)g(describ)s(ed)f(in) h(this)g(section)i(are)150 3761 y(declared)31 b(in)f(the)g(header)h (\014le)f FH(gsl_sf_gamma.h)p FK(.)150 3954 y Fy(7.19.1)63 b(Gamma)41 b(F)-10 b(unctions)150 4101 y FK(The)30 b(Gamma)h(function)f (is)g(de\014ned)g(b)m(y)g(the)g(follo)m(wing)i(in)m(tegral,)1424 4302 y(\000\()p FE(x)p FK(\))26 b(=)1724 4187 y Fs(Z)1808 4208 y Fp(1)1771 4376 y 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 73 TeXDict begin 57 72 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 FK(0)f(the)g(real)h(part)e(of)h(log)r(\(\000\()p FE(x)p FK(\)\))h(is)f(returned,)390 737 y(whic)m(h)33 b(is)g(equiv)-5 b(alen)m(t)35 b(to)f(log)s(\()p FI(j)p FK(\000\()p FE(x)p FK(\))p FI(j)p FK(\).)51 b(The)33 b(function)g(is)g(computed)h(using)f (the)g(real)h(Lanczos)390 847 y(metho)s(d.)3350 1110 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_lngamma_sgn_e)f Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1999 1110 V 40 w(sf)p 2103 1110 V 40 w(result)f(*)h Ft(result_lg)p FD(,)565 1219 y(double)f(*)h Ft(sgn)p Fu(\))390 1329 y FK(This)d(routine)h(computes)g(the)h(sign)f(of)g(the)g(gamma)h (function)f(and)f(the)h(logarithm)h(of)g(its)f(mag-)390 1438 y(nitude,)k(sub)5 b(ject)33 b(to)g FE(x)g FK(not)g(b)s(eing)f(a)h (negativ)m(e)i(in)m(teger)f(or)f(zero.)49 b(The)32 b(function)g(is)h (computed)390 1548 y(using)h(the)g(real)g(Lanczos)h(metho)s(d.)51 b(The)34 b(v)-5 b(alue)34 b(of)g(the)h(gamma)g(function)e(and)h(its)g (error)g(can)390 1658 y(b)s(e)d(reconstructed)h(using)f(the)h(relation) 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 b(will)i(result)e(in)h(a)h FH(GSL_ELOSS)c FK(error)j(when)f(it)h(o)s (ccurs.)46 b(The)31 b(absolute)i(v)-5 b(alue)32 b(part)g(\()p FD(lnr)7 b FK(\),)390 4626 y(ho)m(w)m(ev)m(er,)32 b(nev)m(er)f (su\013ers)e(from)h(loss)h(of)f(precision.)150 4864 y Fy(7.19.2)63 b(F)-10 b(actorials)150 5011 y FK(Although)37 b(factorials)i(can)f(b)s(e)f(computed)g(from)g(the)g(Gamma)h(function,) h(using)e(the)g(relation)i FE(n)p FK(!)d(=)150 5121 y(\000\()p FE(n)28 b FK(+)g(1\))43 b(for)f(non-negativ)m(e)i(in)m(teger)g FE(n)p FK(,)h(it)e(is)g(usually)f(more)g(e\016cien)m(t)i(to)f(call)h (the)e(functions)g(in)150 5230 y(this)f(section,)k(particularly)d(for)f (small)g(v)-5 b(alues)42 b(of)f FE(n)p FK(,)i(whose)e(factorial)i(v)-5 b(alues)42 b(are)f(main)m(tained)h(in)150 5340 y(hardco)s(ded)29 b(tables.)p eop end %%Page: 58 74 TeXDict begin 58 73 bop 150 -116 a FK(Chapter)30 b(7:)41 b(Sp)s(ecial)31 b(F)-8 b(unctions)2348 b(58)3350 299 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_fact)49 b Fu(\()p FD(unsigned)30 b(in)m(t)g Ft(n)p Fu(\))3350 408 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_fact_e)d Fu(\()p FD(unsigned)29 b(in)m(t)i Ft(n)p FD(,)g(gsl)p 1858 408 28 4 v 41 w(sf)p 1963 408 V 39 w(result)f(*)h Ft(result)p Fu(\))390 518 y FK(These)45 b(routines)f(compute)h(the)g (factorial)i FE(n)p FK(!.)83 b(The)45 b(factorial)h(is)f(related)h(to)f (the)g(Gamma)390 628 y(function)33 b(b)m(y)g FE(n)p FK(!)d(=)g(\000\()p FE(n)22 b FK(+)g(1\).)50 b(The)33 b(maxim)m(um)g(v)-5 b(alue)34 b(of)f FE(n)g FK(suc)m(h)g(that)h FE(n)p FK(!)f(is)h(not)f (considered)390 737 y(an)d(o)m(v)m(er\015o)m(w)i(is)e(giv)m(en)i(b)m(y) e(the)h(macro)g FH(GSL_SF_FACT_NMAX)26 b FK(and)j(is)i(170.)3350 916 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_doublefact)d Fu(\()p FD(unsigned)29 b(in)m(t)i Ft(n)p Fu(\))3350 1026 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_doublefact_e)e Fu(\()p FD(unsigned)30 b(in)m(t)h Ft(n)p FD(,)g(gsl)p 2172 1026 V 40 w(sf)p 2276 1026 V 40 w(result)f(*)h Ft(result)p Fu(\))390 1136 y FK(These)d(routines)f(compute)h(the)g(double)g (factorial)i FE(n)p FK(!!)25 b(=)g FE(n)p FK(\()p FE(n)15 b FI(\000)g FK(2\)\()p FE(n)g FI(\000)g FK(4\))g FE(:)g(:)g(:)r FK(.)40 b(The)27 b(maxim)m(um)390 1245 y(v)-5 b(alue)31 b(of)g FE(n)f FK(suc)m(h)g(that)h FE(n)p FK(!!)g(is)f(not)h(considered) f(an)h(o)m(v)m(er\015o)m(w)h(is)e(giv)m(en)i(b)m(y)e(the)h(macro)g FH(GSL_SF_)390 1355 y(DOUBLEFACT_NMAX)26 b FK(and)k(is)g(297.)3350 1534 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_lnfact)c Fu(\()p FD(unsigned)29 b(in)m(t)i Ft(n)p Fu(\))3350 1644 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_lnfact_e)d Fu(\()p FD(unsigned)30 b(in)m(t)h Ft(n)p FD(,)g(gsl)p 1963 1644 V 40 w(sf)p 2067 1644 V 40 w(result)f(*)h Ft(result)p Fu(\))390 1753 y FK(These)e(routines)g(compute)h(the)f(logarithm)h(of)g (the)f(factorial)i(of)f FD(n)p FK(,)f(log)r(\()p FE(n)p FK(!\).)41 b(The)29 b(algorithm)h(is)390 1863 y(faster)k(than)e (computing)i(ln)o(\(\000\()p FE(n)23 b FK(+)e(1\)\))35 b(via)e FH(gsl_sf_lngamma)d FK(for)j FE(n)c(<)h FK(170,)35 b(but)e(defers)f(for)390 1972 y(larger)f FD(n)p FK(.)3350 2152 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_lndoublefact)d Fu(\()p FD(unsigned)30 b(in)m(t)h Ft(n)p Fu(\))3350 2261 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_lndoublefact_e)f Fu(\()p FD(unsigned)30 b(in)m(t)h Ft(n)p FD(,)f(gsl)p 2276 2261 V 41 w(sf)p 2381 2261 V 40 w(result)g(*)h Ft(result)p Fu(\))390 2371 y FK(These)f(routines)g(compute)h(the)g(logarithm)g(of)g (the)f(double)g(factorial)i(of)f FD(n)p FK(,)f(log)r(\()p FE(n)p FK(!!\).)3350 2550 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_choose)c Fu(\()p FD(unsigned)29 b(in)m(t)i Ft(n)p FD(,)g(unsigned)e(in)m(t)i Ft(m)p Fu(\))3350 2660 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_choose_e)d Fu(\()p FD(unsigned)30 b(in)m(t)h Ft(n)p FD(,)g(unsigned)e(in)m(t)i Ft(m)p FD(,)g(gsl)p 2589 2660 V 40 w(sf)p 2693 2660 V 40 w(result)f(*)565 2769 y Ft(result)p Fu(\))390 2879 y FK(These)g(routines)g(compute)h(the)g(com)m(binatorial)h(factor)f FH(n)f(choose)f(m)h FK(=)25 b FE(n)p FK(!)p FE(=)p FK(\()p FE(m)p FK(!\()p FE(n)c FI(\000)f FE(m)p FK(\)!\))3350 3058 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_lnchoose)c Fu(\()p FD(unsigned)30 b(in)m(t)h Ft(n)p FD(,)g(unsigned)e(in)m(t)i Ft(m)p Fu(\))3350 3168 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_lnchoose_e)e Fu(\()p FD(unsigned)29 b(in)m(t)i Ft(n)p FD(,)g(unsigned)f(in)m(t)g Ft(m)p FD(,)h(gsl)p 2693 3168 V 41 w(sf)p 2798 3168 V 39 w(result)g(*)565 3277 y Ft(result)p Fu(\))390 3387 y FK(These)i(routines)f(compute)i (the)f(logarithm)h(of)f FH(n)d(choose)f(m)p FK(.)48 b(This)32 b(is)h(equiv)-5 b(alen)m(t)34 b(to)g(the)f(sum)390 3496 y(log)r(\()p FE(n)p FK(!\))21 b FI(\000)f FK(log)r(\()p FE(m)p FK(!\))h FI(\000)f FK(log)s(\(\()p FE(n)g FI(\000)g FE(m)p FK(\)!\).)3350 3676 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_taylorcoeff)d Fu(\()p FD(in)m(t)31 b Ft(n)p FD(,)g(double)f Ft(x)p Fu(\))3350 3785 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_taylorcoeff_e)f Fu(\()p FD(in)m(t)31 b Ft(n)p FD(,)g(double)f Ft(x)p FD(,)h(gsl)p 2246 3785 V 40 w(sf)p 2350 3785 V 40 w(result)f(*)h Ft(result)p Fu(\))390 3895 y FK(These)f(routines)g(compute)h(the)g(T)-8 b(a)m(ylor)31 b(co)s(e\016cien)m(t)h FE(x)2289 3862 y Fq(n)2335 3895 y FE(=n)p FK(!)e(for)g FE(x)c FI(\025)f FK(0,)31 b FE(n)24 b FI(\025)h FK(0.)150 4091 y Fy(7.19.3)63 b(P)m(o)s(c)m(hhammer)41 b(Sym)m(b)s(ol)3350 4284 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_poch)49 b Fu(\()p FD(double)30 b Ft(a)p FD(,)h(double)f Ft(x)p Fu(\))3350 4394 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_poch_e)d Fu(\()p FD(double)30 b Ft(a)p FD(,)h(double)f Ft(x)p FD(,)h(gsl)p 2034 4394 V 40 w(sf)p 2138 4394 V 40 w(result)f(*)h Ft(result)p Fu(\))390 4503 y FK(These)52 b(routines)g(compute)g(the)h (P)m(o)s(c)m(hhammer)f(sym)m(b)s(ol)g(\()p FE(a)p FK(\))2637 4517 y Fq(x)2741 4503 y FK(=)62 b(\000\()p FE(a)35 b FK(+)f FE(x)p FK(\))p FE(=)p FK(\000\()p FE(a)p FK(\).)107 b(The)390 4613 y(P)m(o)s(c)m(hhammer)39 b(sym)m(b)s(ol)f(is)h(also)g (kno)m(wn)g(as)f(the)h(Ap)s(ell)g(sym)m(b)s(ol)f(and)g(sometimes)i (written)f(as)390 4722 y(\()p FE(a;)15 b(x)p FK(\).)41 b(When)29 b FE(a)f FK(and)g FE(a)17 b FK(+)g FE(x)28 b FK(are)h(negativ)m(e)i(in)m(tegers)f(or)f(zero,)h(the)e(limiting)i(v) -5 b(alue)29 b(of)g(the)g(ratio)390 4832 y(is)h(returned.)3350 5011 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_lnpoch)c Fu(\()p FD(double)30 b Ft(a)p FD(,)h(double)f Ft(x)p Fu(\))3350 5121 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_lnpoch_e)d Fu(\()p FD(double)31 b Ft(a)p FD(,)f(double)g Ft(x)p FD(,)h(gsl)p 2138 5121 V 41 w(sf)p 2243 5121 V 39 w(result)g(*)f Ft(result)p Fu(\))390 5230 y FK(These)117 b(routines)f(compute)i(the)f(logarithm)h(of)f(the)g(P)m(o)s(c)m (hhammer)g(sym)m(b)s(ol,)390 5340 y(log)r(\(\()p FE(a)p FK(\))660 5354 y Fq(x)703 5340 y FK(\))26 b(=)f(log)r(\(\000\()p FE(a)c FK(+)f FE(x)p FK(\))p FE(=)p FK(\000\()p FE(a)p FK(\)\).)p eop end %%Page: 59 75 TeXDict begin 59 74 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 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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 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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 FB(\()p Fq(\025)p FB(\))2593 2394 y Fq(n)2695 2372 y FK(\()p FE(x)p FK(\))h(using)e(explicit)i(represen-) 390 2481 y(tations)32 b(for)e FE(n)24 b FK(=)h(1)p FE(;)15 b FK(2)p FE(;)g FK(3.)3350 2707 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_gegenpoly_n)d Fu(\()p FD(in)m(t)31 b Ft(n)p FD(,)g(double)f Ft(lambda)p FD(,)i(double)e Ft(x)p Fu(\))3350 2816 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_gegenpoly_n_e)f Fu(\()p FD(in)m(t)31 b 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y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_hyperg_1F1_int)e Fu(\()p FD(in)m(t)31 b Ft(m)p FD(,)g(in)m(t)g Ft(n)p FD(,)g(double)f Ft(x)p Fu(\))3350 5011 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_hyperg_1F1_int)q(_e)f Fu(\()p FD(in)m(t)31 b Ft(m)p FD(,)g(in)m(t)g Ft(n)p FD(,)f(double)g Ft(x)p FD(,)h(gsl)p 2649 5011 V 41 w(sf)p 2754 5011 V 39 w(result)g(*)565 5121 y Ft(result)p Fu(\))390 5230 y FK(These)61 b(routines)g(compute)h (the)g(con\015uen)m(t)f(h)m(yp)s(ergeometric)h(function)3132 5244 y FB(1)3169 5230 y FE(F)3227 5244 y FB(1)3265 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 77 TeXDict begin 61 76 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 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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 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b(o)s(ccurs)g(in)g(the)g(region)h(of)g FE(x)25 b FK(=)g(1,)31 b FE(c)20 b FI(\000)g FE(a)h FI(\000)f FE(b)25 b FK(=)g FE(m)30 b FK(for)g(in)m(teger)i(m.)3350 4075 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_hyperg_2F1_conj)e Fu(\()p FD(double)31 b Ft(aR)p FD(,)g(double)f Ft(aI)p FD(,)h(double)f Ft(c)p FD(,)565 4184 y(double)g Ft(x)p Fu(\))3350 4294 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_hyperg_2F1_con)q(j_e)f Fu(\()p FD(double)30 b Ft(aR)p FD(,)h(double)f Ft(aI)p FD(,)h(double)f Ft(c)p FD(,)565 4403 y(double)g Ft(x)p FD(,)h(gsl)p 1078 4403 V 40 w(sf)p 1182 4403 V 40 w(result)f(*)h Ft(result)p Fu(\))390 4513 y FK(These)20 b(routines)h(compute)g(the)g(Gauss)g(h)m (yp)s(ergeometric)g(function)2725 4527 y FB(2)2762 4513 y FE(F)2820 4527 y FB(1)2858 4513 y FK(\()p FE(a)2941 4527 y Fq(R)2996 4513 y FK(+)q FE(ia)3147 4527 y Fq(I)3185 4513 y FE(;)15 b(aR)r FI(\000)q FE(iaI)7 b(;)15 b(c;)g(x)p FK(\))390 4623 y(with)30 b(complex)h(parameters)g(for)f FI(j)p FE(x)p FI(j)c FE(<)f 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FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_hyperg_2F0_e)e Fu(\()p FD(double)31 b Ft(a)p FD(,)g(double)f Ft(b)p FD(,)g(double)g Ft(x)p FD(,)h(gsl)p 2748 1175 V 41 w(sf)p 2853 1175 V 39 w(result)g(*)565 1285 y Ft(result)p Fu(\))390 1394 y FK(These)24 b(routines)g(compute)g (the)g(h)m(yp)s(ergeometric)i(function)2485 1408 y FB(2)2523 1394 y FE(F)2581 1408 y FB(0)2618 1394 y FK(\()p FE(a;)15 b(b;)g(x)p FK(\).)40 b(The)24 b(series)g(represen-)390 1504 y(tation)k(is)g(a)f(div)m(ergen)m(t)i(h)m(yp)s(ergeometric)f (series.)40 b(Ho)m(w)m(ev)m(er,)30 b(for)d FE(x)e(<)g FK(0)j(w)m(e)f(ha)m(v)m(e)3231 1518 y FB(2)3268 1504 y FE(F)3326 1518 y FB(0)3363 1504 y FK(\()p FE(a;)15 b(b;)g(x)p FK(\))27 b(=)390 1614 y(\()p FI(\000)p FK(1)p FE(=x)p FK(\))673 1581 y Fq(a)714 1614 y FE(U)10 b FK(\()p FE(a;)15 b FK(1)22 b(+)e FE(a)g FI(\000)g FE(b;)15 b FI(\000)p FK(1)p FE(=x)p FK(\))150 1872 y FJ(7.22)68 b(Laguerre)46 b(F)-11 b(unctions)150 2031 y FK(The)43 b(generalized)i(Laguerre)e(p)s(olynomials)g(are)h(de\014ned)e(in)h (terms)g(of)h(con\015uen)m(t)f(h)m(yp)s(ergeometric)150 2141 y(functions)i(as)g FE(L)745 2108 y Fq(a)745 2163 y(n)790 2141 y FK(\()p FE(x)p FK(\))50 b(=)g(\(\()p FE(a)31 b FK(+)e(1\))1412 2155 y Fq(n)1458 2141 y FE(=n)p FK(!\))1618 2155 y FB(1)1656 2141 y FE(F)1714 2155 y FB(1)1752 2141 y FK(\()p FI(\000)p FE(n;)15 b(a)30 b FK(+)g(1)p FE(;)15 b(x)p FK(\),)50 b(and)44 b(are)i(sometimes)g(referred)e(to)i(as)150 2251 y(the)34 b(asso)s(ciated)i(Laguerre)e(p)s(olynomials.)52 b(They)34 b(are)g(related)h(to)g(the)f(plain)g(Laguerre)h(p)s (olynomials)150 2360 y FE(L)212 2374 y Fq(n)257 2360 y FK(\()p FE(x)p FK(\))g(b)m(y)f FE(L)606 2327 y FB(0)606 2383 y Fq(n)652 2360 y FK(\()p FE(x)p FK(\))e(=)g FE(L)971 2374 y Fq(n)1016 2360 y FK(\()p FE(x)p FK(\))j(and)f FE(L)1416 2327 y Fq(k)1416 2383 y(n)1461 2360 y FK(\()p FE(x)p FK(\))f(=)e(\()p FI(\000)p FK(1\))1904 2327 y Fq(k)1946 2360 y FK(\()p FE(d)2028 2327 y Fq(k)2070 2360 y FE(=dx)2214 2327 y Fq(k)2255 2360 y FK(\))p FE(L)2352 2374 y FB(\()p Fq(n)p FB(+)p Fq(k)q FB(\))2537 2360 y FK(\()p FE(x)p FK(\).)54 b(F)-8 b(or)35 b(more)g(information)f(see)150 2470 y(Abramo)m(witz)d(&)f(Stegun,)h(Chapter)e(22.)275 2622 y(The)59 b(functions)h(describ)s(ed)g(in)g(this)g(section)i(are)f (declared)f(in)h(the)f(header)g(\014le)h FH(gsl_sf_)150 2731 y(laguerre.h)p FK(.)3350 2950 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_laguerre_1)d Fu(\()p FD(double)30 b Ft(a)p FD(,)h(double)f Ft(x)p Fu(\))3350 3060 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_laguerre_2)d Fu(\()p FD(double)30 b Ft(a)p FD(,)h(double)f Ft(x)p Fu(\))3350 3169 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_laguerre_3)d Fu(\()p FD(double)30 b Ft(a)p FD(,)h(double)f Ft(x)p Fu(\))3350 3279 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_laguerre_1_e)e Fu(\()p FD(double)31 b Ft(a)p FD(,)g(double)f Ft(x)p FD(,)g(gsl)p 2347 3279 V 41 w(sf)p 2452 3279 V 40 w(result)g(*)h Ft(result)p Fu(\))3350 3388 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_laguerre_2_e)e Fu(\()p FD(double)31 b Ft(a)p FD(,)g(double)f Ft(x)p FD(,)g(gsl)p 2347 3388 V 41 w(sf)p 2452 3388 V 40 w(result)g(*)h Ft(result)p Fu(\))3350 3498 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_laguerre_3_e)e Fu(\()p FD(double)31 b Ft(a)p FD(,)g(double)f Ft(x)p FD(,)g(gsl)p 2347 3498 V 41 w(sf)p 2452 3498 V 40 w(result)g(*)h Ft(result)p Fu(\))390 3607 y FK(These)40 b(routines)g(ev)-5 b(aluate)42 b(the)e(generalized)i(Laguerre)f(p)s(olynomials)f FE(L)3002 3574 y Fq(a)3002 3630 y FB(1)3042 3607 y FK(\()p FE(x)p FK(\),)k FE(L)3295 3574 y Fq(a)3295 3630 y FB(2)3335 3607 y FK(\()p FE(x)p FK(\),)f FE(L)3587 3574 y Fq(a)3587 3630 y FB(3)3627 3607 y FK(\()p FE(x)p FK(\))390 3717 y(using)30 b(explicit)i(represen)m(tations.)3350 3936 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_laguerre_n)d Fu(\()p FD(const)31 b(in)m(t)g Ft(n)p FD(,)g(const)g(double)f Ft(a)p FD(,)g(const)h(double)565 4045 y Ft(x)p Fu(\))3350 4155 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_laguerre_n_e)e Fu(\()p FD(in)m(t)32 b Ft(n)p FD(,)f(double)e Ft(a)p FD(,)i(double)f Ft(x)p FD(,)h(gsl)p 2594 4155 V 41 w(sf)p 2699 4155 V 39 w(result)g(*)565 4265 y Ft(result)p Fu(\))390 4374 y FK(These)44 b(routines)g(ev)-5 b(aluate)46 b(the)e(generalized)h (Laguerre)g(p)s(olynomials)f FE(L)3029 4341 y Fq(a)3029 4397 y(n)3074 4374 y FK(\()p FE(x)p FK(\))h(for)f FE(a)k(>)g FI(\000)p FK(1,)390 4484 y FE(n)25 b FI(\025)g FK(0.)150 4742 y FJ(7.23)68 b(Lam)l(b)t(ert)46 b(W)f(F)-11 b(unctions)150 4902 y FK(Lam)m(b)s(ert's)89 b(W)g(functions,)103 b FE(W)13 b FK(\()p FE(x)p FK(\),)103 b(are)89 b(de\014ned)f(to)h(b)s(e)f (solutions)h(of)g(the)g(equation)150 5011 y FE(W)13 b FK(\()p FE(x)p FK(\))i(exp\()p FE(W)e FK(\()p FE(x)p FK(\)\))28 b(=)f FE(x)p FK(.)45 b(This)31 b(function)g(has)g(m)m (ultiple)i(branc)m(hes)e(for)g FE(x)d(<)f FK(0;)33 b(ho)m(w)m(ev)m(er,) g(it)f(has)g(only)150 5121 y(t)m(w)m(o)h(real-v)-5 b(alued)33 b(branc)m(hes.)44 b(W)-8 b(e)33 b(de\014ne)e FE(W)1711 5135 y FB(0)1748 5121 y FK(\()p FE(x)p FK(\))h(to)g(b)s(e)f(the)h (principal)g(branc)m(h,)f(where)g FE(W)40 b(>)27 b FI(\000)p FK(1)32 b(for)150 5230 y FE(x)g(<)g FK(0,)k(and)e FE(W)710 5244 y Fp(\000)p FB(1)799 5230 y FK(\()p FE(x)p FK(\))h(to)g(b)s(e)f (the)h(other)g(real)g(branc)m(h,)g(where)f FE(W)45 b(<)32 b FI(\000)p FK(1)i(for)h FE(x)d(<)g FK(0.)53 b(The)34 b(Lam)m(b)s(ert)150 5340 y(functions)c(are)h(declared)g(in)f(the)g (header)g(\014le)h FH(gsl_sf_lambert.h)p FK(.)p eop end %%Page: 63 79 TeXDict begin 63 78 bop 150 -116 a FK(Chapter)30 b(7:)41 b(Sp)s(ecial)31 b(F)-8 b(unctions)2348 b(63)3350 299 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_lambert_W0)d 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_lambert_W0_e)e Fu(\()p FD(double)31 b Ft(x)p FD(,)g(gsl)p 1947 408 28 4 v 40 w(sf)p 2051 408 V 40 w(result)f(*)h Ft(result)p Fu(\))390 518 y FK(These)f(compute)h(the)f(principal)g(branc)m(h)g(of)h (the)f(Lam)m(b)s(ert)g(W)h(function,)g FE(W)3080 532 y FB(0)3117 518 y FK(\()p FE(x)p FK(\).)3350 738 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_lambert_Wm1)d Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 847 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_lambert_Wm1_e)f Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1999 847 V 40 w(sf)p 2103 847 V 40 w(result)f(*)h Ft(result)p Fu(\))390 957 y FK(These)23 b(compute)h(the)g(secondary)g(real-v)-5 b(alued)25 b(branc)m(h)e(of)h(the)g(Lam)m(b)s(ert)f(W)h(function,)h FE(W)3513 971 y Fp(\000)p FB(1)3602 957 y FK(\()p FE(x)p FK(\).)150 1216 y FJ(7.24)68 b(Legendre)46 b(F)-11 b(unctions)44 b(and)g(Spherical)i(Harmonics)150 1376 y FK(The)26 b(Legendre)g(F)-8 b(unctions)26 b(and)g(Legendre)g(P)m(olynomials)i(are)e(describ)s(ed)f (in)h(Abramo)m(witz)h(&)f(Stegun,)150 1485 y(Chapter)k(8.)41 b(These)30 b(functions)g(are)h(declared)g(in)f(the)g(header)g(\014le)h FH(gsl_sf_legendre.h)p FK(.)150 1702 y Fy(7.24.1)63 b(Legendre)41 b(P)m(olynomials)3350 1917 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_legendre_P1)d Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 2026 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_legendre_P2)d Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 2136 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_legendre_P3)d Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 2245 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_legendre_P1_e)f Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1999 2245 V 40 w(sf)p 2103 2245 V 40 w(result)f(*)h Ft(result)p Fu(\))3350 2355 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_legendre_P2_e)f Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1999 2355 V 40 w(sf)p 2103 2355 V 40 w(result)f(*)h Ft(result)p Fu(\))3350 2465 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_legendre_P3_e)f Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1999 2465 V 40 w(sf)p 2103 2465 V 40 w(result)f(*)h Ft(result)p Fu(\))390 2574 y FK(These)37 b(functions)g(ev)-5 b(aluate)39 b(the)f(Legendre)f(p)s(olynomials)h FE(P)2554 2588 y Fq(l)2580 2574 y FK(\()p FE(x)p FK(\))g(using)e(explicit)j (represen)m(ta-)390 2684 y(tions)31 b(for)f FE(l)d FK(=)e(1)p FE(;)15 b FK(2)p FE(;)g FK(3.)3350 2904 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_legendre_Pl)d Fu(\()p FD(in)m(t)31 b Ft(l)p FD(,)g(double)f Ft(x)p Fu(\))3350 3013 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_legendre_Pl_e)f Fu(\()p FD(in)m(t)31 b Ft(l)p FD(,)g(double)f Ft(x)p FD(,)h(gsl)p 2246 3013 V 40 w(sf)p 2350 3013 V 40 w(result)f(*)h Ft(result)p Fu(\))390 3123 y FK(These)37 b(functions)g(ev)-5 b(aluate)39 b(the)e(Legendre)g(p)s(olynomial)h FE(P)2517 3137 y Fq(l)2543 3123 y FK(\()p FE(x)p FK(\))g(for)f(a)g(sp)s(eci\014c) g(v)-5 b(alue)38 b(of)f FD(l)p FK(,)j FD(x)390 3232 y FK(sub)5 b(ject)30 b(to)h FE(l)c FI(\025)e FK(0,)31 b FI(j)p FE(x)p FI(j)26 b(\024)f FK(1)3350 3452 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_legendre_Pl_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)565 3562 y Ft(result_array)p Fo([])p 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FE(Q)2346 4453 y FB(0)2383 4439 y FK(\()p FE(x)p FK(\))h(for)f FE(x)c(>)e FI(\000)p FK(1,)31 b FE(x)25 b FI(6)p FK(=)g(1.)3350 4659 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_legendre_Q1)d Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 4769 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_legendre_Q1_e)f Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1999 4769 V 40 w(sf)p 2103 4769 V 40 w(result)f(*)h Ft(result)p Fu(\))390 4878 y FK(These)f(routines)g (compute)h(the)g(Legendre)f(function)g FE(Q)2346 4892 y FB(1)2383 4878 y FK(\()p FE(x)p FK(\))h(for)f FE(x)c(>)e FI(\000)p FK(1,)31 b FE(x)25 b FI(6)p FK(=)g(1.)3350 5098 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_legendre_Ql)d Fu(\()p FD(in)m(t)31 b Ft(l)p FD(,)g(double)f Ft(x)p Fu(\))3350 5208 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_legendre_Ql_e)f Fu(\()p FD(in)m(t)31 b Ft(l)p FD(,)g(double)f Ft(x)p FD(,)h(gsl)p 2246 5208 V 40 w(sf)p 2350 5208 V 40 w(result)f(*)h Ft(result)p Fu(\))390 5317 y FK(These)f(routines)g(compute)h(the)g(Legendre)f(function)g FE(Q)2346 5331 y Fq(l)2371 5317 y FK(\()p FE(x)p FK(\))h(for)g FE(x)25 b(>)g FI(\000)p FK(1,)30 b FE(x)c FI(6)p FK(=)f(1)30 b(and)g FE(l)d FI(\025)e FK(0.)p eop end %%Page: 64 80 TeXDict begin 64 79 bop 150 -116 a FK(Chapter)30 b(7:)41 b(Sp)s(ecial)31 b(F)-8 b(unctions)2348 b(64)150 299 y Fy(7.24.2)63 b(Asso)s(ciated)41 b(Legendre)h(P)m(olynomials)f(and)g (Spherical)g(Harmonics)150 446 y FK(The)36 b(follo)m(wing)h(functions)f (compute)g(the)g(asso)s(ciated)i(Legendre)e(P)m(olynomials)i FE(P)3090 413 y Fq(m)3077 468 y(l)3153 446 y FK(\()p FE(x)p FK(\).)58 b(Note)37 b(that)150 555 y(this)h(function)g(gro)m(ws) h(com)m(binatorially)h(with)e FE(l)i FK(and)e(can)h(o)m(v)m(er\015o)m (w)g(for)f FE(l)i FK(larger)f(than)f(ab)s(out)g(150.)150 665 y(There)30 b(is)h(no)g(trouble)g(for)g(small)g FE(m)p FK(,)g(but)f(o)m(v)m(er\015o)m(w)j(o)s(ccurs)d(when)g FE(m)h FK(and)f FE(l)j FK(are)e(b)s(oth)f(large.)44 b(Rather)150 775 y(than)39 b(allo)m(w)h(o)m(v)m(er\015o)m(ws,)i(these)e(functions)e (refuse)h(to)g(calculate)i FE(P)2528 742 y Fq(m)2515 797 y(l)2592 775 y FK(\()p FE(x)p FK(\))e(and)f(return)g FH(GSL_EOVRFLW)150 884 y FK(when)29 b(they)i(can)g(sense)f(that)h FE(l)h FK(and)e FE(m)g FK(are)h(to)s(o)g(big.)275 1036 y(If)41 b(y)m(ou)i(w)m(an)m(t)g(to)g(calculate)h(a)f(spherical)f (harmonic,)j(then)d Fm(do)j(not)51 b FK(use)42 b(these)h(functions.)75 b(In-)150 1145 y(stead)40 b(use)e FH(gsl_sf_legendre_sphPlm)33 b FK(b)s(elo)m(w,)42 b(whic)m(h)c(uses)h(a)g(similar)h(recursion,)h (but)d(with)h(the)150 1255 y(normalized)31 b(functions.)3350 1473 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_legendre_Plm)d Fu(\()p FD(in)m(t)32 b Ft(l)p FD(,)e(in)m(t)h Ft(m)p FD(,)g(double)f Ft(x)p Fu(\))3350 1583 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_legendre_Plm_e)f Fu(\()p FD(in)m(t)31 b Ft(l)p FD(,)g(in)m(t)g Ft(m)p FD(,)g(double)f Ft(x)p FD(,)h(gsl)p 2545 1583 28 4 v 40 w(sf)p 2649 1583 V 40 w(result)f(*)565 1692 y Ft(result)p Fu(\))390 1802 y FK(These)25 b(routines)f(compute)i(the)f(asso)s(ciated)h(Legendre)f(p)s (olynomial)g FE(P)2853 1769 y Fq(m)2840 1824 y(l)2916 1802 y FK(\()p FE(x)p FK(\))h(for)e FE(m)h FI(\025)g FK(0,)i FE(l)g FI(\025)e FE(m)p FK(,)390 1912 y FI(j)p FE(x)p FI(j)h(\024)f FK(1.)3350 2130 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_legendre_Plm_a)q(rray)f Fu(\()p FD(in)m(t)31 b Ft(lmax)p FD(,)h(in)m(t)f Ft(m)p FD(,)g(double)f Ft(x)p FD(,)h(double)565 2240 y Ft(result_array)p Fo([])p Fu(\))3350 2349 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_legendre_Plm_d)q(eriv)q(_ar)q(ray)f Fu(\()p FD(in)m(t)31 b Ft(lmax)p FD(,)h(in)m(t)f Ft(m)p FD(,)g(double)f Ft(x)p FD(,)565 2459 y(double)g Ft(result_array)p Fo([])p FD(,)k(double)c Ft(result_deriv_array)p Fo([])p Fu(\))390 2568 y FK(These)50 b(functions)f(compute)i(arra)m(ys)f(of)g(Legendre)g (p)s(olynomials)g FE(P)2895 2535 y Fq(m)2882 2591 y(l)2959 2568 y FK(\()p FE(x)p FK(\))g(and)g(deriv)-5 b(ativ)m(es)390 2678 y FE(dP)508 2645 y Fq(m)495 2700 y(l)571 2678 y FK(\()p FE(x)p FK(\))p FE(=dx)p FK(,)32 b(for)e FE(m)c FI(\025)e FK(0,)31 b FE(l)d FK(=)d FI(j)p FE(m)p FI(j)p FE(;)15 b(:)g(:)g(:)i(;)e(l)r(max)p FK(,)30 b FI(j)p FE(x)p FI(j)c(\024)f FK(1.)3350 2896 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_legendre_sphPlm)e Fu(\()p FD(in)m(t)31 b Ft(l)p FD(,)g(in)m(t)g Ft(m)p FD(,)g(double)f Ft(x)p Fu(\))3350 3006 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_legendre_sphPl)q(m_e)f Fu(\()p FD(in)m(t)31 b Ft(l)p FD(,)g(in)m(t)g Ft(m)p FD(,)g(double)f Ft(x)p FD(,)h(gsl)p 2702 3006 V 40 w(sf)p 2806 3006 V 40 w(result)f(*)565 3115 y Ft(result)p Fu(\))390 3225 y FK(These)101 b(routines)g(compute)g (the)g(normalized)h(asso)s(ciated)h(Legendre)e(p)s(olynomial)390 3262 y Fs(p)p 473 3262 519 4 v 73 x FK(\(2)p FE(l)23 b FK(+)d(1\))p FE(=)p FK(\(4)p FE(\031)s FK(\))991 3262 y Fs(p)p 1074 3262 678 4 v 73 x FK(\()p FE(l)j FI(\000)d FE(m)p FK(\)!)p FE(=)p FK(\()p FE(l)j FK(+)d FE(m)p FK(\)!)p FE(P)1822 3302 y Fq(m)1809 3357 y(l)1885 3335 y FK(\()p FE(x)p FK(\))58 b(suitable)g(for)f(use)g(in)g(spherical)g(harmonics.) 390 3444 y(The)41 b(parameters)h(m)m(ust)g(satisfy)g FE(m)i FI(\025)g FK(0,)i FE(l)g FI(\025)e FE(m)p FK(,)g FI(j)p FE(x)p FI(j)h(\024)f FK(1.)75 b(Theses)42 b(routines)f(a)m(v)m (oid)j(the)390 3554 y(o)m(v)m(er\015o)m(ws)32 b(that)f(o)s(ccur)f(for)g (the)h(standard)e(normalization)j(of)f FE(P)2648 3521 y Fq(m)2635 3576 y(l)2711 3554 y FK(\()p FE(x)p FK(\).)3350 3772 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_legendre_sphPl)q (m_ar)q(ray)f Fu(\()p FD(in)m(t)31 b Ft(lmax)p FD(,)h(in)m(t)f Ft(m)p FD(,)g(double)f Ft(x)p FD(,)565 3882 y(double)g Ft(result_array)p Fo([])p Fu(\))3350 3991 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_legendre_sphPl)q(m_de)q(riv)q (_ar)q(ray)f Fu(\()p FD(in)m(t)31 b Ft(lmax)p FD(,)h(in)m(t)f Ft(m)p FD(,)g(double)565 4101 y Ft(x)p FD(,)g(double)f Ft(result_array)p Fo([])p FD(,)k(double)c Ft(result_deriv_array)p Fo([])p Fu(\))390 4210 y FK(These)89 b(functions)g(compute)g(arra)m(ys) h(of)g(normalized)f(asso)s(ciated)i(Legendre)f(func-)390 4320 y(tions)658 4247 y Fs(p)p 741 4247 519 4 v 73 x FK(\(2)p FE(l)23 b FK(+)d(1\))p FE(=)p FK(\(4)p FE(\031)s FK(\))1259 4247 y Fs(p)p 1342 4247 678 4 v 73 x FK(\()p FE(l)j FI(\000)d FE(m)p FK(\)!)p FE(=)p FK(\()p FE(l)j FK(+)d FE(m)p FK(\)!)p FE(P)2090 4287 y Fq(m)2077 4343 y(l)2153 4320 y FK(\()p FE(x)p FK(\),)88 b(and)75 b(deriv)-5 b(ativ)m(es,)88 b(for)75 b FE(m)100 b FI(\025)g FK(0,)390 4430 y FE(l)27 b FK(=)e FI(j)p FE(m)p FI(j)p FE(;)15 b(:)g(:)g(:)i(;)e(l)r(max)p FK(,)31 b FI(j)p FE(x)p FI(j)25 b(\024)g FK(1)3350 4648 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_legendre_array)q(_siz)q(e)f Fu(\()p FD(const)31 b(in)m(t)g Ft(lmax)p FD(,)g(const)g(in)m(t)g Ft(m)p Fu(\))390 4758 y FK(This)24 b(function)g(returns)f(the)i(size)g(of)g FD(result)p 1894 4758 28 4 v 40 w(arra)m(y)8 b FK([])25 b(needed)f(for)h(the)f(arra)m(y)h(v)m(ersions)g(of)g FE(P)3539 4725 y Fq(m)3526 4780 y(l)3602 4758 y FK(\()p FE(x)p FK(\),)390 4867 y FD(lmax)18 b FI(\000)12 b FD(m)g FK(+)g(1.)38 b(An)26 b(inline)g(v)m(ersion)g(of)h(this)f(function)f(is) h(used)g(when)f FH(HAVE_INLINE)e FK(is)j(de\014ned.)150 5083 y Fy(7.24.3)63 b(Conical)40 b(F)-10 b(unctions)150 5230 y FK(The)26 b(Conical)i(F)-8 b(unctions)27 b FE(P)1141 5188 y Fq(\026)1128 5256 y Fp(\000)p FB(\(1)p Fq(=)p FB(2\)+)p Fq(i\025)1451 5230 y FK(\()p FE(x)p FK(\))g(and)f FE(Q)1845 5188 y Fq(\026)1845 5256 y Fp(\000)p FB(\(1)p Fq(=)p FB(2\)+)p Fq(i\025)2194 5230 y FK(are)h(describ)s(ed)e(in)i (Abramo)m(witz)h(&)e(Stegun,)150 5340 y(Section)31 b(8.12.)p eop end %%Page: 65 81 TeXDict begin 65 80 bop 150 -116 a FK(Chapter)30 b(7:)41 b(Sp)s(ecial)31 b(F)-8 b(unctions)2348 b(65)3350 299 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_conicalP_half)e Fu(\()p FD(double)30 b Ft(lambda)p FD(,)i(double)e Ft(x)p Fu(\))3350 408 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_conicalP_half_)q(e)e Fu(\()p FD(double)30 b Ft(lambda)p FD(,)i(double)d 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FI(\000)p FK(1.)3350 1580 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_conicalP_0)d Fu(\()p FD(double)30 b Ft(lambda)p FD(,)i(double)e Ft(x)p Fu(\))3350 1689 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_conicalP_0_e)e Fu(\()p FD(double)31 b Ft(lambda)p FD(,)h(double)e Ft(x)p FD(,)h(gsl)p 2609 1689 V 40 w(sf)p 2713 1689 V 40 w(result)f(*)565 1799 y Ft(result)p Fu(\))390 1908 y FK(These)g(routines)g(compute)h(the)g (conical)h(function)e FE(P)2258 1875 y FB(0)2245 1932 y Fp(\000)p FB(1)p Fq(=)p FB(2+)p Fq(i\025)2515 1908 y FK(\()p FE(x)p FK(\))h(for)f FE(x)25 b(>)g FI(\000)p FK(1.)3350 2099 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_conicalP_1)d Fu(\()p FD(double)30 b Ft(lambda)p FD(,)i(double)e Ft(x)p Fu(\))3350 2208 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_conicalP_1_e)e Fu(\()p FD(double)31 b Ft(lambda)p FD(,)h(double)e Ft(x)p FD(,)h(gsl)p 2609 2208 V 40 w(sf)p 2713 2208 V 40 w(result)f(*)565 2318 y Ft(result)p Fu(\))390 2428 y FK(These)g(routines)g(compute)h(the)g (conical)h(function)e FE(P)2258 2395 y FB(1)2245 2451 y Fp(\000)p FB(1)p Fq(=)p FB(2+)p Fq(i\025)2515 2428 y FK(\()p FE(x)p FK(\))h(for)f FE(x)25 b(>)g FI(\000)p FK(1.)3350 2618 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_conicalP_sph_re)q(g)e Fu(\()p FD(in)m(t)31 b Ft(l)p FD(,)g(double)f Ft(lambda)p FD(,)i(double)e Ft(x)p Fu(\))3350 2727 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_conicalP_sph_r)q(eg_e)f Fu(\()p FD(in)m(t)31 b Ft(l)p FD(,)g(double)f Ft(lambda)p FD(,)j(double)d Ft(x)p FD(,)565 2837 y(gsl)p 677 2837 V 41 w(sf)p 782 2837 V 39 w(result)h(*)f Ft(result)p Fu(\))390 2958 y FK(These)h(routines)g(compute)h(the)g(Regular)f(Spherical)h(Conical)g (F)-8 b(unction)32 b FE(P)3049 2912 y Fp(\000)p FB(1)p Fq(=)p FB(2)p Fp(\000)p Fq(l)3036 2984 y Fp(\000)p FB(1)p Fq(=)p FB(2+)p Fq(i\025)3306 2958 y FK(\()p FE(x)p FK(\))g(for)f FE(x)c(>)390 3068 y FI(\000)p FK(1,)k FE(l)c FI(\025)e(\000)p FK(1.)3350 3258 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_conicalP_cyl_re)q(g)e Fu(\()p FD(in)m(t)31 b Ft(m)p FD(,)g(double)f Ft(lambda)p FD(,)i(double)e Ft(x)p Fu(\))3350 3368 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_conicalP_cyl_r)q(eg_e)f Fu(\()p FD(in)m(t)31 b Ft(m)p FD(,)g(double)f Ft(lambda)p FD(,)j(double)d Ft(x)p FD(,)565 3477 y(gsl)p 677 3477 V 41 w(sf)p 782 3477 V 39 w(result)h(*)f Ft(result)p Fu(\))390 3587 y FK(These)43 b(routines)g(compute)h(the)f(Regular)h(Cylindrical)g (Conical)g(F)-8 b(unction)44 b FE(P)3218 3549 y Fp(\000)p Fq(m)3205 3613 y Fp(\000)p FB(1)p Fq(=)p FB(2+)p Fq(i\025)3475 3587 y FK(\()p FE(x)p FK(\))g(for)390 3697 y FE(x)25 b(>)g FI(\000)p FK(1,)31 b FE(m)25 b FI(\025)g(\000)p FK(1.)150 3899 y Fy(7.24.4)63 b(Radial)40 b(F)-10 b(unctions)42 b(for)g(Hyp)s(erb)s(olic)g(Space)150 4046 y FK(The)34 b(follo)m(wing)i(spherical)f(functions)f(are)i(sp)s(ecializations)g(of) f(Legendre)g(functions)f(whic)m(h)h(giv)m(e)h(the)150 4155 y(regular)c(eigenfunctions)h(of)f(the)g(Laplacian)i(on)e(a)g 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FE(\025)15 b FK(sinh)o(\()p FE(\021)s FK(\))420 5340 y(for)30 b FE(\021)f FI(\025)c FK(0.)41 b(In)30 b(the)g(\015at)h(limit)g(this)f(tak)m(es)i(the)f(form) f FE(L)2333 5307 y Fq(H)t FB(3)p Fq(d)2333 5362 y FB(0)2463 5340 y FK(\()p FE(\025;)15 b(\021)s FK(\))27 b(=)e FE(j)2834 5354 y FB(0)2872 5340 y FK(\()p FE(\025\021)s FK(\).)p eop end %%Page: 66 82 TeXDict begin 66 81 bop 150 -116 a FK(Chapter)30 b(7:)41 b(Sp)s(ecial)31 b(F)-8 b(unctions)2348 b(66)3350 299 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_legendre_H3d_1)e Fu(\()p FD(double)30 b Ft(lambda)p FD(,)j(double)d Ft(eta)p Fu(\))3350 408 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_legendre_H3d_1)q(_e)f Fu(\()p FD(double)30 b Ft(lambda)p FD(,)i(double)e Ft(eta)p FD(,)565 518 y(gsl)p 677 518 28 4 v 41 w(sf)p 782 518 V 39 w(result)h(*)f Ft(result)p Fu(\))390 628 y FK(These)46 b(routines)f(compute)h(the)g (\014rst)f(radial)h(eigenfunction)h(of)f(the)g(Laplacian)h(on)e(the)h (3-)390 737 y(dimensional)31 b(h)m(yp)s(erb)s(olic)e(space,)833 956 y FE(L)895 918 y Fq(H)t FB(3)p Fq(d)895 978 y FB(1)1025 956 y FK(\()p FE(\025;)15 b(\021)s FK(\))27 b(:=)1533 894 y(1)p 1394 935 323 4 v 1394 952 a FI(p)p 1470 952 247 4 v 74 x FE(\025)1523 999 y FB(2)1580 1026 y FK(+)20 b(1)1727 837 y Fs(\022)1830 894 y FK(sin\()p FE(\025\021)s FK(\))p 1798 935 350 4 v 1798 1018 a FE(\025)15 b FK(sinh)o(\()p FE(\021)s FK(\))2157 837 y Fs(\023)2233 956 y FK(\()q(coth\()p FE(\021)s FK(\))22 b FI(\000)e FE(\025)15 b FK(cot)q(\()p FE(\025\021)s FK(\)\))420 1185 y(for)30 b FE(\021)f FI(\025)c FK(0.)41 b(In)30 b(the)g(\015at)h(limit)g(this)f(tak)m(es)i(the)f(form) f FE(L)2333 1152 y Fq(H)t FB(3)p Fq(d)2333 1208 y FB(1)2463 1185 y FK(\()p FE(\025;)15 b(\021)s FK(\))27 b(=)e FE(j)2834 1199 y FB(1)2872 1185 y FK(\()p FE(\025\021)s FK(\).)3350 1378 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_legendre_H3d)d Fu(\()p FD(in)m(t)32 b Ft(l)p FD(,)e(double)g Ft(lambda)p FD(,)j(double)d Ft(eta)p Fu(\))3350 1487 y FK([F)-8 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y(The)41 b(radial)h(Mathieu)g(functions)f FE(M)10 b(c)1654 1698 y FB(\()p Fq(j)s FB(\))1654 1753 y Fq(r)1741 1731 y FK(\()p FE(z)t(;)15 b(q)s FK(\),)46 b FE(M)10 b(s)2153 1698 y FB(\()p Fq(j)s FB(\))2153 1753 y Fq(r)2240 1731 y FK(\()p FE(z)t(;)15 b(q)s FK(\))43 b(are)f(the)f(solutions)h(of)g (the)g(second)150 1840 y(equation,)26 b(whic)m(h)d(is)h(referred)f(to)h (as)g(Mathieu's)h(mo)s(di\014ed)d(equation.)40 b(The)23 b(radial)h(Mathieu)g(functions)150 1950 y(of)30 b(the)g(\014rst,)g (second,)g(third)f(and)h(fourth)f(kind)g(are)h(denoted)g(b)m(y)g(the)g (parameter)h FE(j)5 b FK(,)31 b(whic)m(h)e(tak)m(es)j(the)150 2060 y(v)-5 b(alue)31 b(1,)g(2,)g(3)g(or)f(4.)275 2213 y(F)-8 b(or)34 b(more)g(information)g(on)g(the)g(Mathieu)h(functions,)f (see)h(Abramo)m(witz)g(and)e(Stegun,)i(Chapter)150 2323 y(20.)42 b(These)30 b(functions)g(are)g(de\014ned)g(in)g(the)g(header)g (\014le)h FH(gsl_sf_mathieu.h)p FK(.)150 2541 y Fy(7.26.1)63 b(Mathieu)41 b(F)-10 b(unction)41 b(W)-10 b(orkspace)150 2688 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w(w)m(orkspace)31 b(*)f Ft(work)p Fu(\))390 3790 y FK(This)g(function)g(frees)g(the)h(w)m(orkspace)g FD(w)m(ork)p FK(.)150 4008 y Fy(7.26.2)63 b(Mathieu)41 b(F)-10 b(unction)41 b(Characteristic)f(V)-10 b(alues)3350 4223 y FK([F)i(unction])-3599 b Fv(int)53 b(gsl_sf_mathieu_a)e Fu(\()p FD(in)m(t)31 b Ft(n)p FD(,)g(double)f Ft(q)p FD(,)g(gsl)p 2036 4223 V 41 w(sf)p 2141 4223 V 40 w(result)g(*)h Ft(result)p Fu(\))3350 4333 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_mathieu_b)e Fu(\()p FD(in)m(t)31 b Ft(n)p FD(,)g(double)f Ft(q)p FD(,)g(gsl)p 2036 4333 V 41 w(sf)p 2141 4333 V 40 w(result)g(*)h Ft(result)p Fu(\))390 4443 y FK(These)22 b(routines)h(compute)g(the)g(c)m (haracteristic)i(v)-5 b(alues)23 b FE(a)2359 4457 y Fq(n)2405 4443 y FK(\()p FE(q)s FK(\),)i FE(b)2608 4457 y Fq(n)2653 4443 y FK(\()p FE(q)s FK(\))e(of)g(the)g(Mathieu)g(functions)390 4552 y FE(ce)471 4566 y Fq(n)517 4552 y FK(\()p FE(q)s(;)15 b(x)p FK(\))31 b(and)f FE(se)1016 4566 y Fq(n)1061 4552 y FK(\()p FE(q)s(;)15 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5121 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_synchrotron_1)e Fu(\()p FD(double)30 b Ft(x)p Fu(\))3350 5230 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_synchrotron_1_)q(e)e Fu(\()p FD(double)31 b Ft(x)p FD(,)f(gsl)p 2103 5230 V 41 w(sf)p 2208 5230 V 40 w(result)g(*)h Ft(result)p Fu(\))390 5340 y FK(These)f(routines)g(compute)h(the)g(\014rst)e(sync)m (hrotron)h(function)g FE(x)2639 5271 y Fs(R)2695 5292 y Fp(1)2679 5368 y Fq(x)2780 5340 y FE(dtK)2937 5354 y FB(5)p Fq(=)p FB(3)3042 5340 y FK(\()p FE(t)p FK(\))h(for)f FE(x)25 b FI(\025)g FK(0.)p eop end %%Page: 70 86 TeXDict begin 70 85 bop 150 -116 a FK(Chapter)30 b(7:)41 b(Sp)s(ecial)31 b(F)-8 b(unctions)2348 b(70)3350 299 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_synchrotron_2)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_synchrotron_2_)q(e)e Fu(\()p FD(double)31 b Ft(x)p FD(,)f(gsl)p 2103 408 28 4 v 41 w(sf)p 2208 408 V 40 w(result)g(*)h Ft(result)p Fu(\))390 518 y 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FK(\).)3350 2483 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 2593 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_transport_5_e)f Fu(\()p FD(double)30 b Ft(x)p FD(,)h(gsl)p 1999 2593 V 40 w(sf)p 2103 2593 V 40 w(result)f(*)h Ft(result)p Fu(\))390 2702 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 2946 y FJ(7.31)68 b(T)-11 b(rigonometric)46 b(F)-11 b(unctions)150 3105 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 3215 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 3324 y(sf_trig.h)p FK(.)150 3531 y Fy(7.31.1)63 b(Circular)40 b(T)-10 b(rigonometric)43 b(F)-10 b(unctions)3350 3735 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 3844 y 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b(unction])-3599 b Fv(int)53 b(gsl_sf_complex_sin_e)f Fu(\()p FD(double)30 b Ft(zr)p FD(,)h(double)f Ft(zi)p FD(,)h(gsl)p 2504 494 28 4 v 41 w(sf)p 2609 494 V 39 w(result)g(*)g Ft(szr)p FD(,)565 603 y(gsl)p 677 603 V 41 w(sf)p 782 603 V 39 w(result)g(*)f Ft(szi)p Fu(\))390 713 y FK(This)d(function)g(computes)g (the)h(complex)g(sine,)g(sin\()p FE(z)2250 727 y Fq(r)2302 713 y FK(+)14 b FE(iz)2460 727 y Fq(i)2488 713 y FK(\))28 b(storing)g(the)f(real)h(and)f(imaginary)390 822 y(parts)j(in)g FD(szr)p FK(,)h FD(szi)p FK(.)3350 1004 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_complex_cos_e)f Fu(\()p FD(double)30 b Ft(zr)p FD(,)h(double)f Ft(zi)p FD(,)h(gsl)p 2504 1004 V 41 w(sf)p 2609 1004 V 39 w(result)g(*)g Ft(czr)p FD(,)565 1113 y(gsl)p 677 1113 V 41 w(sf)p 782 1113 V 39 w(result)g(*)f Ft(czi)p Fu(\))390 1223 y FK(This)20 b(function)h(computes)g(the)g (complex)h(cosine,)i(cos\()p FE(z)2308 1237 y Fq(r)2347 1223 y FK(+)q FE(iz)2492 1237 y Fq(i)2521 1223 y FK(\))d(storing)g(the) g(real)h(and)e(imaginary)390 1333 y(parts)30 b(in)g FD(czr)p FK(,)h FD(czi)p FK(.)3350 1514 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_complex_logsin)q(_e)f Fu(\()p FD(double)30 b Ft(zr)p FD(,)h(double)f Ft(zi)p FD(,)h(gsl)p 2661 1514 V 41 w(sf)p 2766 1514 V 39 w(result)g(*)565 1623 y Ft(lszr)p FD(,)h(gsl)p 942 1623 V 40 w(sf)p 1046 1623 V 40 w(result)e(*)h Ft(lszi)p Fu(\))390 1733 y FK(This)h(function)h(computes)g(the)h (logarithm)g(of)f(the)g(complex)h(sine,)g(log)r(\(sin\()p FE(z)3119 1747 y Fq(r)3179 1733 y FK(+)22 b FE(iz)3345 1747 y Fq(i)3373 1733 y FK(\)\))34 b(storing)390 1843 y(the)d(real)g(and)e(imaginary)i(parts)f(in)h FD(lszr)p FK(,)f FD(lszi)p FK(.)150 2040 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 2235 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 2344 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_lnsinh_e)d Fu(\()p FD(double)31 b Ft(x)p FD(,)f(gsl)p 1737 2344 V 41 w(sf)p 1842 2344 V 40 w(result)g(*)h Ft(result)p Fu(\))390 2454 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 2635 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 2745 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_lncosh_e)d Fu(\()p FD(double)31 b Ft(x)p FD(,)f(gsl)p 1737 2745 V 41 w(sf)p 1842 2745 V 40 w(result)g(*)h Ft(result)p Fu(\))390 2854 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 3052 y Fy(7.31.4)63 b(Con)m(v)m(ersion)41 b(F)-10 b(unctions)3350 3246 y FK([F)i(unction])-3599 b Fv(int)53 b(gsl_sf_polar_to_rect)f Fu(\()p FD(double)30 b Ft(r)p FD(,)h(double)f Ft(theta)p FD(,)i(gsl)p 2609 3246 V 40 w(sf)p 2713 3246 V 40 w(result)e(*)h Ft(x)p FD(,)565 3356 y(gsl)p 677 3356 V 41 w(sf)p 782 3356 V 39 w(result)g(*)f Ft(y)p Fu(\))p FD(;)390 3466 y FK(This)24 b(function)h(con)m(v)m(erts)i(the)e(p)s(olar)g(co)s(ordinates)g(\()p 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Fy(7.31.5)63 b(Restriction)41 b(F)-10 b(unctions)3350 4477 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 4587 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 4696 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 4830 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 4939 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 5121 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 5230 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 5340 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(\).)p eop end %%Page: 72 88 TeXDict begin 72 87 bop 150 -116 a FK(Chapter)30 b(7:)41 b(Sp)s(ecial)31 b(F)-8 b(unctions)2348 b(72)390 299 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)390 408 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.)150 608 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 805 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_sin_err_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(double)f Ft(dx)p FD(,)h(gsl)p 2243 805 28 4 v 40 w(sf)p 2347 805 V 40 w(result)f(*)h Ft(result)p Fu(\))390 914 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 1024 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 1134 y(its)i(purp)s(ose)d(is)j(to)g(compute)g(the)f(propagated)h (error.)3350 1318 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_cos_err_e)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(double)f Ft(dx)p FD(,)h(gsl)p 2243 1318 V 40 w(sf)p 2347 1318 V 40 w(result)f(*)h Ft(result)p Fu(\))390 1428 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 1538 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 1647 y(its)j(purp)s(ose)d(is)j(to)g(compute)g(the)f(propagated)h (error.)150 1880 y FJ(7.32)68 b(Zeta)46 b(F)-11 b(unctions)150 2039 y FK(The)24 b(Riemann)h(zeta)h(function)e(is)h(de\014ned)e(in)i (Abramo)m(witz)g(&)g(Stegun,)g(Section)h(23.2.)40 b(The)24 b(functions)150 2149 y(describ)s(ed)29 b(in)h(this)h(section)g(are)g (declared)g(in)f(the)g(header)h(\014le)f FH(gsl_sf_zeta.h)p FK(.)150 2348 y Fy(7.32.1)63 b(Riemann)41 b(Zeta)f(F)-10 b(unction)150 2495 y FK(The)30 b(Riemann)g(zeta)i(function)e(is)g (de\014ned)f(b)m(y)i(the)f(in\014nite)g(sum)g FE(\020)7 b FK(\()p FE(s)p FK(\))25 b(=)2739 2431 y Fs(P)2826 2452 y Fp(1)2826 2518 y Fq(k)q FB(=1)2967 2495 y FE(k)3017 2462 y Fp(\000)p Fq(s)3104 2495 y FK(.)3350 2680 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_zeta_int)c Fu(\()p FD(in)m(t)31 b Ft(n)p Fu(\))3350 2790 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_zeta_int_e)e Fu(\()p FD(in)m(t)31 b Ft(n)p FD(,)g(gsl)p 1688 2790 V 40 w(sf)p 1792 2790 V 40 w(result)f(*)h Ft(result)p Fu(\))390 2899 y FK(These)f(routines)g (compute)h(the)g(Riemann)f(zeta)i(function)e FE(\020)7 b FK(\()p FE(n)p FK(\))30 b(for)g(in)m(teger)i FD(n)p FK(,)e FE(n)25 b FI(6)p FK(=)g(1.)3350 3084 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 3194 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_zeta_e)d Fu(\()p FD(double)30 b Ft(s)p FD(,)h(gsl)p 1633 3194 V 40 w(sf)p 1737 3194 V 40 w(result)f(*)h Ft(result)p Fu(\))390 3303 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 3503 y Fy(7.32.2)63 b(Riemann)41 b(Zeta)f(F)-10 b(unction)41 b(Min)m(us)h(One)150 3650 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 3759 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 3944 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 4053 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_zetam1_int_e)e Fu(\()p FD(in)m(t)32 b Ft(n)p FD(,)f(gsl)p 1793 4053 V 40 w(sf)p 1897 4053 V 40 w(result)f(*)h Ft(result)p Fu(\))390 4163 y FK(These)f(routines)g (compute)h FE(\020)7 b FK(\()p FE(n)p FK(\))20 b FI(\000)g FK(1)31 b(for)f(in)m(teger)i FD(n)p FK(,)e FE(n)24 b FI(6)p FK(=)h(1.)3350 4348 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_zetam1)c Fu(\()p FD(double)30 b Ft(s)p Fu(\))3350 4457 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_zetam1_e)d Fu(\()p FD(double)31 b Ft(s)p FD(,)f(gsl)p 1737 4457 V 41 w(sf)p 1842 4457 V 40 w(result)g(*)h Ft(result)p Fu(\))390 4567 y FK(These)f(routines)g (compute)h FE(\020)7 b FK(\()p FE(s)p FK(\))20 b FI(\000)g FK(1)31 b(for)f(arbitrary)g FD(s)p FK(,)g FE(s)25 b FI(6)p FK(=)g(1.)150 4766 y Fy(7.32.3)63 b(Hurwitz)40 b(Zeta)g(F)-10 b(unction)150 4913 y FK(The)30 b(Hurwitz)g(zeta)i(function)e(is)h (de\014ned)e(b)m(y)h FE(\020)7 b FK(\()p FE(s;)15 b(q)s FK(\))25 b(=)2132 4849 y Fs(P)2220 4870 y Fp(1)2220 4936 y FB(0)2290 4913 y FK(\()p FE(k)f FK(+)c FE(q)s FK(\))2566 4880 y Fp(\000)p Fq(s)2653 4913 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: 73 89 TeXDict begin 73 88 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 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(\()p FE(s)p FK(\).)3350 642 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_eta_int)c Fu(\()p FD(in)m(t)31 b Ft(n)p Fu(\))3350 752 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_eta_int_e)e Fu(\()p FD(in)m(t)31 b Ft(n)p FD(,)g(gsl)p 1636 752 28 4 v 40 w(sf)p 1740 752 V 40 w(result)f(*)h Ft(result)p Fu(\))390 861 y FK(These)f(routines)g (compute)h(the)g(eta)g(function)f FE(\021)s FK(\()p FE(n)p FK(\))h(for)f(in)m(teger)i FD(n)p FK(.)3350 1058 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_sf_eta)49 b Fu(\()p FD(double)30 b Ft(s)p Fu(\))3350 1168 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sf_eta_e)c Fu(\()p FD(double)31 b Ft(s)p FD(,)f(gsl)p 1580 1168 V 41 w(sf)p 1685 1168 V 40 w(result)g(*)h Ft(result)p Fu(\))390 1277 y FK(These)f(routines)g(compute)h(the)g(eta) g(function)f FE(\021)s FK(\()p FE(s)p FK(\))h(for)f(arbitrary)g FD(s)p FK(.)150 1519 y FJ(7.33)68 b(Examples)150 1678 y FK(The)28 b(follo)m(wing)i(example)g(demonstrates)f(the)f(use)h(of)g (the)f(error)h(handling)f(form)g(of)g(the)h(sp)s(ecial)h(func-)150 1788 y(tions,)h(in)f(this)g(case)i(to)f(compute)g(the)f(Bessel)i (function)e FE(J)2189 1802 y FB(0)2226 1788 y FK(\(5)p FE(:)p FK(0\),)390 1928 y FH(#include)46 b()390 2038 y(#include)g()390 2148 y(#include)g ()390 2367 y(int)390 2476 y(main)h(\(void\))390 2586 y({)485 2695 y(double)g(x)g(=)g(5.0;)485 2805 y(gsl_sf_result)e (result;)485 3024 y(double)i(expected)e(=)j(-0.17759677131433830434)o (739)o(701;)485 3243 y(int)f(status)f(=)i(gsl_sf_bessel_J0_e)43 b(\(x,)k(&result\);)485 3463 y(printf)g(\("status)93 b(=)47 b(\045s\\n",)f(gsl_strerror\(status\)\);)485 3572 y(printf)h(\("J0\(5.0\))e(=)i(\045.18f\\n")867 3682 y(")286 b(+/-)47 b(\045)h(.18f\\n",)867 3791 y(result.val,)d(result.err\);)485 3901 y(printf)i(\("exact)141 b(=)47 b(\045.18f\\n",)f(expected\);)485 4011 y(return)h(status;)390 4120 y(})150 4261 y FK(Here)31 b(are)g(the)f(results)g(of)h(running)e(the)h(program,)390 4401 y FH($)47 b(./a.out)390 4511 y(status)94 b(=)47 b(success)390 4620 y(J0\(5.0\))f(=)h(-0.177596771314338292)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: 74 90 TeXDict begin 74 89 bop 150 -116 a FK(Chapter)30 b(7:)41 b(Sp)s(ecial)31 b(F)-8 b(unctions)2348 b(74)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 FK(The)30 b(results)g(of)h(the)f(function)g(are)h (the)g(same,)390 1883 y FH($)47 b(./a.out)390 1993 y(J0\(5.0\))f(=)h (-0.177596771314338292)390 2102 y(exact)142 b(=)47 b 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b(Nemeth,)i(Mathematical)g(Appro)m(ximations)e(of)g(Sp)s(ecial)g(F)-8 b(unctions,)26 b(No)m(v)-5 b(a)27 b(Science)e(Publish-)330 3630 y(ers,)30 b(ISBN)h(1-56072-052-2)330 3764 y(B.C.)g(Carlson,)f(Sp)s (ecial)h(F)-8 b(unctions)31 b(of)f(Applied)g(Mathematics)j(\(1977\))330 3899 y(N.)28 b(M.)g(T)-8 b(emme,)28 b(Sp)s(ecial)g(F)-8 b(unctions:)39 b(An)27 b(In)m(tro)s(duction)g(to)h(the)g(Classical)h(F) -8 b(unctions)28 b(of)f(Math-)330 4008 y(ematical)33 b(Ph)m(ysics)d(\(1996\),)j(ISBN)d(978-0471113133)q(.)330 4143 y(W.J.)36 b(Thompson,)h(A)m(tlas)g(for)f(Computing)f(Mathematical) k(F)-8 b(unctions,)38 b(John)d(Wiley)i(&)e(Sons,)330 4252 y(New)c(Y)-8 b(ork)30 b(\(1997\).)330 4387 y(Y.Y.)44 b(Luk)m(e,)i(Algorithms)e(for)f(the)g(Computation)g(of)h(Mathematical)i (F)-8 b(unctions,)47 b(Academic)330 4496 y(Press,)30 b(New)h(Y)-8 b(ork)31 b(\(1977\).)p eop end %%Page: 75 91 TeXDict begin 75 90 bop 150 -116 a FK(Chapter)30 b(8:)41 b(V)-8 b(ectors)32 b(and)e(Matrices)2203 b(75)150 299 y FG(8)80 b(V)-13 b(ectors)52 b(and)i(Matrices)150 550 y FK(The)40 b(functions)g(describ)s(ed)f(in)i(this)f(c)m(hapter)h(pro)m (vide)g(a)g(simple)f(v)m(ector)i(and)e(matrix)h(in)m(terface)h(to)150 660 y(ordinary)28 b(C)h(arra)m(ys.)40 b(The)29 b(memory)f(managemen)m (t)j(of)e(these)g(arra)m(ys)g(is)g(implemen)m(ted)h(using)e(a)h(single) 150 769 y(underlying)41 b(t)m(yp)s(e,)46 b(kno)m(wn)c(as)g(a)h(blo)s(c) m(k.)77 b(By)43 b(writing)f(y)m(our)g(functions)g(in)g(terms)g(of)h(v)m (ectors)h(and)150 879 y(matrices)21 b(y)m(ou)g(can)g(pass)f(a)h(single) g(structure)e(con)m(taining)j(b)s(oth)e(data)h(and)f(dimensions)g(as)g (an)g(argumen)m(t)150 989 y(without)37 b(needing)f(additional)i (function)e(parameters.)60 b(The)36 b(structures)g(are)h(compatible)g (with)g(the)150 1098 y(v)m(ector)32 b(and)e(matrix)g(formats)h(used)f (b)m(y)g FC(blas)f FK(routines.)150 1339 y FJ(8.1)68 b(Data)46 b(t)l(yp)t(es)150 1499 y FK(All)28 b(the)f(functions)f(are)h (a)m(v)-5 b(ailable)30 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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: 77 93 TeXDict begin 77 92 bop 150 -116 a FK(Chapter)30 b(8:)41 b(V)-8 b(ectors)32 b(and)e(Matrices)2203 b(77)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(\("length)e(of)i(block) g(=)g(\045u\\n",)f(b->size\);)485 1899 y(printf)h(\("block)e(data)i (address)f(=)h(\045#x\\n",)f(b->data\);)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: 78 94 TeXDict begin 78 93 bop 150 -116 a FK(Chapter)30 b(8:)41 b(V)-8 b(ectors)32 b(and)e(Matrices)2203 b(78)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 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(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 (disabling)g(range)h(c)m(hec)m(king)h(here)f(than)f(for)g(inline)g (functions.)3350 1154 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_vector_get)c Fu(\()p FD(const)31 b(gsl)p 1679 1154 28 4 v 41 w(v)m(ector)h(*)e Ft(v)p FD(,)h(size)p 2317 1154 V 41 w(t)g Ft(i)p Fu(\))390 1263 y FK(This)25 b(function)h (returns)f(the)h FD(i)p FK(-th)g(elemen)m(t)i(of)e(a)g(v)m(ector)i FD(v)p FK(.)39 b(If)26 b FD(i)31 b FK(lies)26 b(outside)h(the)f(allo)m (w)m(ed)i(range)390 1373 y(of)h(0)g(to)h FD(n)16 b FI(\000)h FK(1)29 b(then)g(the)g(error)f(handler)g(is)h(in)m(v)m(ok)m(ed)h(and)e (0)h(is)g(returned.)39 b(An)29 b(inline)g(v)m(ersion)g(of)390 1482 y(this)h(function)g(is)h(used)e(when)h FH(HAVE_INLINE)d FK(is)j(de\014ned.)3350 1658 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_vector_set)49 b Fu(\()p FD(gsl)p 1336 1658 V 41 w(v)m(ector)32 b(*)f Ft(v)p FD(,)g(size)p 1975 1658 V 41 w(t)f Ft(i)p FD(,)h(double)f Ft(x)p Fu(\))390 1767 y FK(This)35 b(function)g(sets)h(the)g(v)-5 b(alue)36 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: 80 96 TeXDict begin 80 95 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(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 FK(for)g(in)m(tegers.)59 b(The)35 b(function)h(returns)f(0)h (for)g(success)h(and)390 1239 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 1413 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_vector_fscanf)e Fu(\()p FD(FILE)30 b(*)h Ft(stream)p FD(,)h(gsl)p 2127 1413 V 41 w(v)m(ector)g(*)f Ft(v)p Fu(\))390 1522 y FK(This)k(function) g(reads)g(formatted)h(data)g(from)f(the)h(stream)g FD(stream)f FK(in)m(to)i(the)f(v)m(ector)h FD(v)p FK(.)55 b(The)390 1632 y(v)m(ector)30 b FD(v)35 b FK(m)m(ust)28 b(b)s(e)g(preallo)s (cated)h(with)f(the)g(correct)h(length)g(since)f(the)h(function)e(uses) h(the)g(size)390 1741 y(of)f FD(v)35 b FK(to)28 b(determine)f(ho)m(w)h (man)m(y)f(n)m(um)m(b)s(ers)f(to)i(read.)39 b(The)27 b(function)g(returns)f(0)h(for)g(success)h(and)390 1851 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 2043 y Fy(8.3.5)63 b(V)-10 b(ector)40 b(views)150 2190 y FK(In)33 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: 81 97 TeXDict begin 81 96 bop 150 -116 a FK(Chapter)30 b(8:)41 b(V)-8 b(ectors)32 b(and)e(Matrices)2203 b(81)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: 82 98 TeXDict begin 82 97 bop 150 -116 a FK(Chapter)30 b(8:)41 b(V)-8 b(ectors)32 b(and)e(Matrices)2203 b(82)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(\(see)i(Chapter)e(13)i([BLAS)f(Supp)s(ort],)f(page)i(121\).) 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: 83 99 TeXDict begin 83 98 bop 150 -116 a FK(Chapter)30 b(8:)41 b(V)-8 b(ectors)32 b(and)e(Matrices)2203 b(83)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: 84 100 TeXDict begin 84 99 bop 150 -116 a FK(Chapter)30 b(8:)41 b(V)-8 b(ectors)32 b(and)e(Matrices)2203 b(84)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: 85 101 TeXDict begin 85 100 bop 150 -116 a FK(Chapter)30 b(8:)41 b(V)-8 b(ectors)32 b(and)e(Matrices)2203 b(85)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: 86 102 TeXDict begin 86 101 bop 150 -116 a FK(Chapter)30 b(8:)41 b(V)-8 b(ectors)32 b(and)e(Matrices)2203 b(86)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: 87 103 TeXDict begin 87 102 bop 150 -116 a FK(Chapter)30 b(8:)41 b(V)-8 b(ectors)32 b(and)e(Matrices)2203 b(87)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: 88 104 TeXDict begin 88 103 bop 150 -116 a FK(Chapter)30 b(8:)41 b(V)-8 b(ectors)32 b(and)e(Matrices)2203 b(88)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)390 649 y FH(m->data[i)45 b(*)j(m->tda)e(+)h(j])150 779 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 952 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_matrix_get)c Fu(\()p FD(const)31 b(gsl)p 1679 952 28 4 v 41 w(matrix)f(*)h Ft(m)p FD(,)g(size)p 2340 952 V 41 w(t)g Ft(i)p FD(,)f(size)p 2695 952 V 41 w(t)h Ft(j)p Fu(\))390 1062 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 1172 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 1281 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 1454 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_matrix_set)49 b Fu(\()p FD(gsl)p 1336 1454 V 41 w(matrix)31 b(*)g Ft(m)p FD(,)f(size)p 1997 1454 V 41 w(t)h Ft(i)p FD(,)g(size)p 2353 1454 V 41 w(t)f Ft(j)p FD(,)h(double)f Ft(x)p Fu(\))390 1564 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 1673 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 1783 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 1956 y([F)-8 b(unction])-3599 b Fv(double)54 b(*)f(gsl_matrix_ptr)c Fu(\()p FD(gsl)p 1545 1956 V 41 w(matrix)31 b(*)g Ft(m)p FD(,)g(size)p 2207 1956 V 41 w(t)f Ft(i)p FD(,)h(size)p 2562 1956 V 41 w(t)g Ft(j)p Fu(\))3350 2066 y FK([F)-8 b(unction])-3599 b Fv(const)54 b(double)g(*)f(gsl_matrix_const_ptr)e Fu(\()p FD(const)31 b(gsl)p 2411 2066 V 41 w(matrix)g(*)f Ft(m)p FD(,)h(size)p 3072 2066 V 41 w(t)565 2175 y Ft(i)p FD(,)g(size)p 820 2175 V 41 w(t)g Ft(j)p Fu(\))390 2285 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 2394 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 2504 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 2613 y(when)29 b FH(HAVE_INLINE)f FK(is)i(de\014ned.)150 2805 y Fy(8.4.3)63 b(Initializing)40 b(matrix)h(elemen)m(ts)3350 2994 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_matrix_set_all)c Fu(\()p FD(gsl)p 1545 2994 V 41 w(matrix)31 b(*)g Ft(m)p FD(,)g(double)f Ft(x)p Fu(\))390 3104 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 3277 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_matrix_set_zero)d Fu(\()p FD(gsl)p 1598 3277 V 41 w(matrix)30 b(*)h Ft(m)p Fu(\))390 3387 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 3559 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_matrix_set_identity)e Fu(\()p FD(gsl)p 1807 3559 V 41 w(matrix)31 b(*)f Ft(m)p Fu(\))390 3669 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 3779 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 3888 y(zero.)k(This)29 b(applies)i(to)g(b)s(oth)e(square)i(and)e(rectangular)j(matrices.)150 4080 y Fy(8.4.4)63 b(Reading)41 b(and)f(writing)i(matrices)150 4227 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 4336 y(formatted)e(text.)3350 4509 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_matrix_fwrite)e Fu(\()p FD(FILE)30 b(*)h Ft(stream)p FD(,)h(const)f(gsl)p 2365 4509 V 41 w(matrix)g(*)f Ft(m)p Fu(\))390 4619 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 4729 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 4838 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 4948 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_matrix_fread)e Fu(\()p FD(FILE)30 b(*)h Ft(stream)p FD(,)h(gsl)p 2075 5121 V 41 w(matrix)e(*)h Ft(m)p Fu(\))390 5230 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 5340 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)p eop end %%Page: 89 105 TeXDict begin 89 104 bop 150 -116 a FK(Chapter)30 b(8:)41 b(V)-8 b(ectors)32 b(and)e(Matrices)2203 b(89)390 299 y(uses)35 b(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)390 408 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)390 518 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 695 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_matrix_fprintf)e Fu(\()p FD(FILE)31 b(*)f Ft(stream)p FD(,)j(const)e(gsl)p 2418 695 28 4 v 40 w(matrix)g(*)g Ft(m)p FD(,)g(const)565 805 y(c)m(har)g(*)g Ft(format)p Fu(\))390 915 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 1024 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 1134 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 1243 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 1421 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_matrix_fscanf)e Fu(\()p FD(FILE)30 b(*)h Ft(stream)p FD(,)h(gsl)p 2127 1421 V 41 w(matrix)f(*)g Ft(m)p Fu(\))390 1530 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 1640 y(matrix)36 b FD(m)g FK(m)m(ust)f(b)s(e)h 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b(In)150 2639 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 2748 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 2858 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 2968 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 3145 y([F)-8 b(unction])-3599 b Fv(gsl_matrix_view)57 b(gsl_matrix_submatrix)51 b Fu(\()p FD(gsl)p 2225 3145 V 41 w(matrix)31 b(*)g Ft(m)p FD(,)g(size)p 2887 3145 V 41 w(t)f Ft(k1)p FD(,)565 3255 y(size)p 712 3255 V 41 w(t)h Ft(k2)p FD(,)g(size)p 1120 3255 V 41 w(t)f Ft(n1)p FD(,)i(size)p 1528 3255 V 41 w(t)e Ft(n2)p Fu(\))3350 3364 y FK([F)-8 b(unction])-3599 b Fv(gsl_matrix_const_view)59 b(gsl_matrix_const_submat)q(rix)52 b Fu(\()p FD(const)565 3474 y(gsl)p 677 3474 V 41 w(matrix)30 b(*)h Ft(m)p FD(,)g(size)p 1338 3474 V 41 w(t)g Ft(k1)p FD(,)g(size)p 1746 3474 V 41 w(t)f Ft(k2)p FD(,)h(size)p 2153 3474 V 41 w(t)g Ft(n1)p FD(,)g(size)p 2561 3474 V 41 w(t)g Ft(n2)p Fu(\))390 3583 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 3693 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 3802 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 3912 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 4022 y(b)m(y)-8 b(,)630 4154 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 4286 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 4418 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 4528 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 4660 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 4769 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 4879 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)390 4989 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 5098 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 5230 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 5340 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(.)p eop end %%Page: 90 106 TeXDict begin 90 105 bop 150 -116 a FK(Chapter)30 b(8:)41 b(V)-8 b(ectors)32 b(and)e(Matrices)2203 b(90)3350 299 y([F)-8 b(unction])-3599 b Fv(gsl_matrix_view)57 b (gsl_matrix_view_array)52 b Fu(\()p FD(double)30 b(*)h Ft(base)p FD(,)g(size)p 2946 299 28 4 v 41 w(t)g Ft(n1)p FD(,)565 408 y(size)p 712 408 V 41 w(t)g Ft(n2)p Fu(\))3350 518 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(\()p FD(const)565 628 y(double)30 b(*)h Ft(base)p FD(,)h(size)p 1346 628 V 40 w(t)f Ft(n1)p FD(,)g(size)p 1753 628 V 41 w(t)g Ft(n2)p Fu(\))390 737 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)390 847 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(.)390 956 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 1102 y FH(m'\(i,j\))46 b(=)h(base[i*n2)f(+)h(j])390 1247 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 1392 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 1502 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 1611 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 1721 y(deallo)s(cated)g(while)f(the)f(view)h(is)f(still)h(in)g (use.)390 1866 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 1975 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 2181 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(\()p FD(double)31 b(*)565 2291 y Ft(base)p FD(,)h(size)p 977 2291 V 41 w(t)e Ft(n1)p FD(,)i(size)p 1385 2291 V 41 w(t)e Ft(n2)p FD(,)h(size)p 1792 2291 V 41 w(t)g Ft(tda)p Fu(\))3350 2400 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 2510 y Fu(\()p FD(const)31 b(double)f(*)h Ft(base)p FD(,)h(size)p 1619 2510 V 41 w(t)e Ft(n1)p FD(,)i(size)p 2027 2510 V 40 w(t)f Ft(n2)p FD(,)g(size)p 2434 2510 V 41 w(t)g Ft(tda)p Fu(\))390 2619 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 2729 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 2839 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 2948 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 3093 y FH(m'\(i,j\))46 b(=)h(base[i*tda)e(+)j(j])390 3239 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 3384 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 3493 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 3603 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 3713 y(deallo)s(cated)g(while)f(the)f(view)h(is)f(still)h(in)g (use.)390 3858 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 3967 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 4077 y FH(const)p FK(.)3350 4283 y([F)-8 b(unction])-3599 b Fv(gsl_matrix_view)57 b(gsl_matrix_view_vector)52 b Fu(\()p FD(gsl)p 2330 4283 V 41 w(v)m(ector)32 b(*)f Ft(v)p FD(,)g(size)p 2969 4283 V 40 w(t)g Ft(n1)p FD(,)565 4392 y(size)p 712 4392 V 41 w(t)g Ft(n2)p Fu(\))3350 4502 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(\()p FD(const)565 4611 y(gsl)p 677 4611 V 41 w(v)m(ector)32 b(*)e Ft(v)p FD(,)h(size)p 1315 4611 V 41 w(t)g Ft(n1)p FD(,)g(size)p 1723 4611 V 41 w(t)g Ft(n2)p Fu(\))390 4721 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 4830 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 4940 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 5050 y(is)f(giv)m(en)i(b)m(y)-8 b(,)630 5195 y FH(m'\(i,j\))46 b(=)h(v->data[i*n2)e(+)i(j])390 5340 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(.)p eop end %%Page: 91 107 TeXDict begin 91 106 bop 150 -116 a FK(Chapter)30 b(8:)41 b(V)-8 b(ectors)32 b(and)e(Matrices)2203 b(91)390 299 y(The)30 b(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)390 408 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)390 518 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)390 628 y(while)30 b(the)h(view)g(is)f(still)h(in)f(use.)390 766 y(The)39 b(function)f FH(gsl_matrix_const_view_vect)o(or)33 b FK(is)39 b(equiv)-5 b(alen)m(t)41 b(to)e FH(gsl_matrix_view_)390 875 y(vector)29 b 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(only)h(b)s(e)e(deallo)s(cated)390 2687 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 2796 y(while)30 b(the)h(view)g(is)f(still)h(in)f(use.)390 2935 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 3044 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 3154 y(declared)31 b FH(const)p FK(.)150 3357 y Fy(8.4.6)63 b(Creating)40 b(ro)m(w)h(and)g(column)g(views)150 3504 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 3613 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 3723 y(matrix)29 b(b)m(y)f(reference.)41 b(Mo)s(difying)28 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b(the)g(real)h(and)f(imaginary)h(parts)f(m)m(ust)g (satisfy)h(the)g(conditions.)3350 3249 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_matrix_isnull)e Fu(\()p FD(const)31 b(gsl)p 1679 3249 V 41 w(matrix)f(*)h Ft(m)p Fu(\))3350 3358 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_matrix_ispos)e Fu(\()p FD(const)31 b(gsl)p 1627 3358 V 40 w(matrix)g(*)g Ft(m)p Fu(\))3350 3468 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_matrix_isneg)e Fu(\()p FD(const)31 b(gsl)p 1627 3468 V 40 w(matrix)g(*)g Ft(m)p Fu(\))3350 3578 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_matrix_isnonneg)e Fu(\()p FD(const)32 b(gsl)p 1784 3578 V 40 w(matrix)f(*)g Ft(m)p Fu(\))390 3687 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 3797 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 3906 y(matrix)21 b(is)h(p)s(ositiv)m (e-de\014nite,)i(use)d(the)g(Cholesky)g(decomp)s(osition)h(\(see)g (Section)g(14.5)h([Cholesky)390 4016 y(Decomp)s(osition],)32 b(page)g(139\).)3350 4201 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_matrix_equal)e Fu(\()p FD(const)31 b(gsl)p 1627 4201 V 40 w(matrix)g(*)g Ft(a)p FD(,)g(const)g(gsl)p 2491 4201 V 40 w(matrix)g(*)g Ft(b)p Fu(\))390 4311 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(\(b)m(y)f(comparison)g(of)g (elemen)m(t)390 4420 y(v)-5 b(alues\))31 b(and)f(0)h(otherwise.)150 4620 y Fy(8.4.13)63 b(Example)40 b(programs)j(for)f(matrices)150 4767 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 4876 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 5011 y FH(#include)46 b()390 5121 y(#include)g ()390 5340 y(int)p eop end %%Page: 96 112 TeXDict begin 96 111 bop 150 -116 a FK(Chapter)30 b(8:)41 b(V)-8 b(ectors)32 b(and)e(Matrices)2203 b(96)390 299 y FH(main)47 b(\(void\))390 408 y({)485 518 y(int)g(i,)h(j;)485 628 y(gsl_matrix)d(*)j(m)f(=)h(gsl_matrix_alloc)43 b(\(10,)k(3\);)485 847 y(for)g(\(i)h(=)f(0;)g(i)h(<)f(10;)g(i++\))581 956 y(for)g(\(j)g(=)g(0;)h(j)f(<)h(3;)f(j++\))676 1066 y(gsl_matrix_set)d (\(m,)j(i,)g(j,)h(0.23)e(+)i(100*i)e(+)h(j\);)485 1285 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 1395 y(for)h(\(j)g(=)g(0;)h(j)f(<)h (3;)f(j++\))676 1504 y(printf)f(\("m\(\045d,\045d\))f(=)j(\045g\\n",)e (i,)h(j,)1058 1614 y(gsl_matrix_get)d(\(m,)j(i,)g(j\)\);)485 1833 y(gsl_matrix_free)d(\(m\);)485 2052 y(return)j(0;)390 2162 y(})150 2299 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 2408 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 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y(for)g(\(j)g(=)g(0;)h(j)f(<)h(100;)e(j++\))676 5340 y(gsl_matrix_set)e(\(m,)j(i,)g(j,)h(0.23)e(+)i(i)f(+)h(j\);)p eop end %%Page: 97 113 TeXDict begin 97 112 bop 150 -116 a FK(Chapter)30 b(8:)41 b(V)-8 b(ectors)32 b(and)e(Matrices)2203 b(97)485 408 y FH({)629 518 y(FILE)46 b(*)i(f)f(=)h(fopen)e(\("test.dat",)e("wb"\);) 629 628 y(gsl_matrix_fwrite)f(\(f,)k(m\);)629 737 y(fclose)f(\(f\);)485 847 y(})485 1066 y({)629 1176 y(FILE)g(*)i(f)f(=)h(fopen)e (\("test.dat",)e("rb"\);)629 1285 y(gsl_matrix_fread)f(\(f,)k(a\);)629 1395 y(fclose)f(\(f\);)485 1504 y(})485 1724 y(for)h(\(i)h(=)f(0;)g(i)h (<)f(100;)g(i++\))581 1833 y(for)g(\(j)g(=)g(0;)h(j)f(<)h(100;)e(j++\)) 676 1943 y({)772 2052 y(double)g(mij)h(=)g(gsl_matrix_get)d(\(m,)j(i,)g (j\);)772 2162 y(double)f(aij)h(=)g(gsl_matrix_get)d(\(a,)j(i,)g(j\);) 772 2271 y(if)g(\(mij)g(!=)g(aij\))f(k++;)676 2381 y(})485 2600 y(gsl_matrix_free)e(\(m\);)485 2710 y(gsl_matrix_free)g(\(a\);)485 2929 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y(for)g(\(j)g(=)g(0;)h(j)f(<)h(10;)e(j++\))p eop end %%Page: 98 114 TeXDict begin 98 113 bop 150 -116 a FK(Chapter)30 b(8:)41 b(V)-8 b(ectors)32 b(and)e(Matrices)2203 b(98)676 299 y FH(gsl_matrix_set)44 b(\(m,)j(i,)g(j,)h(sin)e(\(i\))h(+)h(cos)f (\(j\)\);)485 518 y(for)g(\(j)h(=)f(0;)g(j)h(<)f(10;)g(j++\))581 628 y({)676 737 y(gsl_vector_view)d(column)i(=)i(gsl_matrix_column)43 b(\(m,)k(j\);)676 847 y(double)f(d;)676 1066 y(d)i(=)f(gsl_blas_dnrm2)d (\(&column.vector\);)676 1285 y(printf)i(\("matrix)g(column)g(\045d,)h (norm)g(=)g(\045g\\n",)f(j,)h(d\);)581 1395 y(})485 1614 y(gsl_matrix_free)d(\(m\);)485 1833 y(return)j(0;)390 1943 y(})150 2077 y FK(Here)31 b(is)f(the)h(output)f(of)g(the)h (program,)390 2212 y FH($)47 b(./a.out)390 2321 y(matrix)f(column)g(0,) h(norm)g(=)g(4.31461)390 2431 y(matrix)f(column)g(1,)h(norm)g(=)g (3.1205)390 2540 y(matrix)f(column)g(2,)h(norm)g(=)g(2.19316)390 2650 y(matrix)f(column)g(3,)h(norm)g(=)g(3.26114)390 2760 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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 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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: 100 116 TeXDict begin 100 115 bop 150 -116 a FK(Chapter)30 b(9:)41 b(P)m(erm)m(utations)2468 b(100)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(\()p FD(const)31 b(gsl)p 2097 2394 V 41 w(p)s(erm)m(utation)g(*)f Ft(p)p Fu(\))390 2504 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(p)s(erm)m(utation)h FD(p)p FK(.)3350 2729 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_permutation_valid)f Fu(\()p FD(const)31 b(gsl)p 1888 2729 V 41 w(p)s(erm)m(utation)f(*)h Ft(p)p Fu(\))390 2839 y FK(This)e(function)h(c)m(hec)m(ks)h(that)f(the)g(p)s(erm)m (utation)g FD(p)i FK(is)e(v)-5 b(alid.)41 b(The)29 b FD(n)h FK(elemen)m(ts)h(should)e(con)m(tain)390 2948 y(eac)m(h)j(of)e(the)h(n)m(um)m(b)s(ers)e(0)h(to)h FD(n)20 b FI(\000)g FK(1)31 b(once)g(and)f(only)g(once.)150 3211 y FJ(9.5)68 b(P)l(erm)l(utation)47 b(functions)3350 3441 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_permutation_reverse)e Fu(\()p FD(gsl)p 1807 3441 V 41 w(p)s(erm)m(utation)30 b(*)h Ft(p)p Fu(\))390 3551 y FK(This)f(function)g(rev)m(erses)h(the)f (elemen)m(ts)i(of)e(the)h(p)s(erm)m(utation)f FD(p)p FK(.)3350 3776 y([F)-8 b(unction])-3599 b Fv(int)53 b (gsl_permutation_inver)q(se)f Fu(\()p FD(gsl)p 1755 3776 V 41 w(p)s(erm)m(utation)30 b(*)h Ft(inv)p FD(,)g(const)565 3885 y(gsl)p 677 3885 V 41 w(p)s(erm)m(utation)f(*)h Ft(p)p Fu(\))390 3995 y FK(This)f(function)g(computes)g(the)h(in)m(v)m (erse)g(of)g(the)f(p)s(erm)m(utation)h FD(p)p FK(,)f(storing)g(the)h (result)f(in)g FD(in)m(v)p FK(.)3350 4220 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_permutation_next)f Fu(\()p FD(gsl)p 1598 4220 V 41 w(p)s(erm)m(utation)30 b(*)h Ft(p)p Fu(\))390 4330 y FK(This)i(function)g(adv)-5 b(ances)35 b(the)f(p)s(erm)m (utation)f FD(p)j FK(to)f(the)f(next)g(p)s(erm)m(utation)g(in)f (lexicographic)390 4439 y(order)i(and)f(returns)g FH(GSL_SUCCESS)p FK(.)51 b(If)35 b(no)g(further)f(p)s(erm)m(utations)h(are)g(a)m(v)-5 b(ailable)38 b(it)d(returns)390 4549 y FH(GSL_FAILURE)d FK(and)i(lea)m(v)m(es)k FD(p)f FK(unmo)s(di\014ed.)52 b(Starting)36 b(with)f(the)g(iden)m(tit)m(y)h(p)s(erm)m(utation)g(and) 390 4659 y(rep)s(eatedly)e(applying)f(this)g(function)h(will)f(iterate) i(through)e(all)i(p)s(ossible)e(p)s(erm)m(utations)g(of)h(a)390 4768 y(giv)m(en)d(order.)3350 4994 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_permutation_prev)f Fu(\()p FD(gsl)p 1598 4994 V 41 w(p)s(erm)m(utation)30 b(*)h Ft(p)p Fu(\))390 5103 y FK(This)23 b(function)h(steps)g(bac)m(kw)m(ards)g(from)g(the)g (p)s(erm)m(utation)g FD(p)j FK(to)d(the)h(previous)e(p)s(erm)m(utation) h(in)390 5213 y(lexicographic)34 b(order,)f(returning)f FH(GSL_SUCCESS)p FK(.)44 b(If)32 b(no)g(previous)g(p)s(erm)m(utation)h (is)g(a)m(v)-5 b(ailable)390 5322 y(it)31 b(returns)e FH(GSL_FAILURE)e FK(and)j(lea)m(v)m(es)j FD(p)f FK(unmo)s(di\014ed.)p eop end %%Page: 101 117 TeXDict begin 101 116 bop 150 -116 a FK(Chapter)30 b(9:)41 b(P)m(erm)m(utations)2468 b(101)150 299 y FJ(9.6)68 b(Applying)45 b(P)l(erm)l(utations)3350 511 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_permute)c Fu(\()p FD(const)31 b(size)p 1400 511 28 4 v 41 w(t)g(*)g Ft(p)p FD(,)f(double)g(*)h Ft(data)p FD(,)h(size)p 2465 511 V 41 w(t)e Ft(stride)p FD(,)j(size)p 3082 511 V 41 w(t)565 621 y Ft(n)p Fu(\))390 730 y FK(This)27 b(function)g(applies)g(the)h(p)s(erm)m(utation)f FD(p)j FK(to)e(the)f(arra)m(y)h FD(data)g FK(of)g(size)g FD(n)e FK(with)i(stride)f FD(stride)p FK(.)3350 921 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_permute_inverse)e Fu(\()p FD(const)32 b(size)p 1819 921 V 41 w(t)e(*)h Ft(p)p FD(,)g(double)f(*)h Ft(data)p FD(,)g(size)p 2883 921 V 41 w(t)565 1031 y Ft(stride)p FD(,)h(size)p 1081 1031 V 41 w(t)f Ft(n)p Fu(\))390 1140 y FK(This)25 b(function)g (applies)h(the)g(in)m(v)m(erse)h(of)e(the)h(p)s(erm)m(utation)g FD(p)i FK(to)e(the)g(arra)m(y)g FD(data)h FK(of)f(size)g FD(n)f FK(with)390 1250 y(stride)30 b FD(stride)p FK(.)3350 1441 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_permute_vector)e Fu(\()p FD(const)31 b(gsl)p 1731 1441 V 41 w(p)s(erm)m(utation)f(*)h Ft(p)p FD(,)g(gsl)p 2582 1441 V 41 w(v)m(ector)h(*)e Ft(v)p Fu(\))390 1550 y FK(This)j(function)g(applies)h(the)f(p)s(erm)m (utation)h FD(p)h FK(to)g(the)e(elemen)m(ts)i(of)f(the)g(v)m(ector)h FD(v)p FK(,)f(considered)390 1660 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 1627 y Fp(0)3124 1660 y FK(=)25 b FE(v)s(P)13 b FK(.)41 b(The)30 b FE(j)5 b FK(-th)390 1769 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 1783 y Fq(j)2681 1769 y FK(-th)g(column)g(of)g(the)g(iden)m(tit)m(y)390 1879 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 2070 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_permute_vector_in)q(vers)q(e)f Fu(\()p FD(const)31 b(gsl)p 2150 2070 V 40 w(p)s(erm)m(utation)g(*)g Ft(p)p FD(,)565 2179 y(gsl)p 677 2179 V 41 w(v)m(ector)h(*)e Ft(v)p Fu(\))390 2289 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 2399 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 2508 y(righ)m(t,)48 b FE(v)699 2475 y Fp(0)769 2508 y FK(=)f FE(v)s(P)1005 2475 y Fq(T)1058 2508 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 2618 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 2632 y Fq(j)3634 2618 y FK(-th)390 2727 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 2837 y(same)31 b(length.)3350 3028 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_permutation_mul)e Fu(\()p FD(gsl)p 1545 3028 V 41 w(p)s(erm)m(utation)31 b(*)g Ft(p)p FD(,)f(const)h(gsl)p 2634 3028 V 41 w(p)s(erm)m(utation) 565 3137 y(*)g Ft(pa)p FD(,)g(const)g(gsl)p 1151 3137 V 40 w(p)s(erm)m(utation)g(*)g Ft(pb)p Fu(\))390 3247 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 3356 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 3594 y FJ(9.7)68 b(Reading)46 b(and)f(writing)h(p)t(erm)l(utations)150 3753 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 3863 y(or)k(formatted)h(text.)3350 4053 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_permutation_fwrit)q(e)e Fu(\()p FD(FILE)31 b(*)g Ft(stream)p FD(,)h(const)f(gsl)p 2627 4053 V 40 w(p)s(erm)m(utation)565 4163 y(*)g Ft(p)p Fu(\))390 4273 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 4382 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 4492 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 4601 y(di\013eren)m(t)i(arc)m(hitectures.)3350 4792 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_permutation_fread)f Fu(\()p FD(FILE)31 b(*)f Ft(stream)p FD(,)j(gsl)p 2337 4792 V 40 w(p)s(erm)m(utation)e(*)f Ft(p)p Fu(\))390 4902 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 5011 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 5121 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 5230 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 5340 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.)p eop end %%Page: 102 118 TeXDict begin 102 117 bop 150 -116 a FK(Chapter)30 b(9:)41 b(P)m(erm)m(utations)2468 b(102)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_permutation_fprin)q(tf)f Fu(\()p FD(FILE)29 b(*)h Ft(stream)p FD(,)i(const)e(gsl)p 2676 299 28 4 v 40 w(p)s(erm)m(utation)565 408 y(*)h Ft(p)p FD(,)g(const)g(c)m(har)f (*)h Ft(format)p Fu(\))390 518 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)390 628 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)390 737 y FD(size)p 537 737 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)390 847 y(format.)680 814 y FB(1)757 847 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 1019 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_permutation_fscan) q(f)e Fu(\()p FD(FILE)31 b(*)g Ft(stream)p FD(,)h(gsl)p 2389 1019 V 41 w(p)s(erm)m(utation)e(*)h Ft(p)p Fu(\))390 1129 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 1238 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 1348 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 1458 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 1682 y FJ(9.8)68 b(P)l(erm)l(utations)47 b(in)e(cyclic)g(form)150 1841 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 1951 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 2061 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 2170 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 2301 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 2410 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 2520 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 2629 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 2739 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 2870 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 2979 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 3089 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 3198 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 (Section)f(1.3.3,)i(p.178.)275 3329 y(The)c(pro)s(cedure)h(for)g (obtaining)h(the)f(canonical)i(form)e(giv)m(en)i(b)m(y)e(Kn)m(uth)f (is,)199 3459 y(1.)61 b(W)-8 b(rite)32 b(all)f(singleton)g(cycles)h (explicitly)199 3590 y(2.)61 b(Within)31 b(eac)m(h)g(cycle,)h(put)e (the)g(smallest)i(n)m(um)m(b)s(er)d(\014rst)199 3720 y(3.)61 b(Order)29 b(the)i(cycles)g(in)f(decreasing)i(order)d(of)i(the) f(\014rst)g(n)m(um)m(b)s(er)f(in)h(the)h(cycle.)150 3872 y(F)-8 b(or)27 b(example,)h(the)e(linear)h(represen)m(tation)g(\(2)g(4) g(3)f(0)h(1\))g(is)f(represen)m(ted)g(as)g(\(1)h(4\))g(\(0)g(2)g(3\))f (in)g(canonical)150 3981 y(form.)57 b(The)35 b(p)s(erm)m(utation)h (corresp)s(onds)f(to)h(an)g(exc)m(hange)h(of)g(elemen)m(ts)g(1)f(and)f (4,)j(and)e(rotation)h(of)150 4091 y(elemen)m(ts)32 b(0,)f(2)f(and)g (3.)275 4222 y(The)i(imp)s(ortan)m(t)h(prop)s(ert)m(y)f(of)h(the)h (canonical)g(form)f(is)g(that)g(it)h(can)f(b)s(e)f(reconstructed)h (from)g(the)150 4331 y(con)m(ten)m(ts)28 b(of)e(eac)m(h)h(cycle)h (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)150 4441 y(considered)e(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 4550 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 4660 y(in)j(the)h(theory)f(of)h(p)s(erm)m(utations.)3350 4832 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(\()p FD(gsl)p 2382 4832 V 41 w(p)s(erm)m(utation)31 b(*)f Ft(q)p FD(,)565 4942 y(const)h(gsl)p 915 4942 V 41 w(p)s(erm)m(utation)f(*)h Ft(p)p Fu(\))390 5051 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 5161 y(output)g(argumen)m(t)h FD(q)p FK(.)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: 103 119 TeXDict begin 103 118 bop 150 -116 a FK(Chapter)30 b(9:)41 b(P)m(erm)m(utations)2468 b(103)3350 299 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(\()p FD(gsl)p 2382 299 28 4 v 41 w(p)s(erm)m(utation)31 b(*)f Ft(p)p FD(,)565 408 y(const)h(gsl)p 915 408 V 41 w(p)s(erm)m(utation)f(*)h Ft(q)p Fu(\))390 518 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)390 628 y(it)31 b(in)f(the)h(output)f(argumen)m(t)g FD(p)p FK(.)3350 816 y([F)-8 b(unction])-3599 b Fv(size_t)54 b(gsl_permutation_invers)q(ion)q(s)d Fu(\()p FD(const)32 b(gsl)p 2307 816 V 40 w(p)s(erm)m(utation)f(*)f Ft(p)p Fu(\))390 925 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 1035 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 1145 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 1254 y(p)s(erm)m(utation)30 b(has)h(no)f(in)m(v)m(ersions.)3350 1442 y([F)-8 b(unction])-3599 b Fv(size_t)54 b(gsl_permutation_linear)q(_cy)q(cle)q(s)d Fu(\()p FD(const)32 b(gsl)p 2464 1442 V 40 w(p)s(erm)m(utation)f(*)f Ft(p)p Fu(\))390 1552 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 1740 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(\()p FD(const)32 b(gsl)p 2621 1740 V 40 w(p)s(erm)m(utation)565 1850 y(*)f Ft(q)p Fu(\))390 1959 y FK(This)j(function)h(coun)m(ts)g(the)g(n)m(um)m(b)s(er)f(of)h (cycles)h(in)f(the)g(p)s(erm)m(utation)g FD(q)p FK(,)h(giv)m(en)g(in)e (canonical)390 2069 y(form.)150 2304 y FJ(9.9)68 b(Examples)150 2464 y FK(The)36 b(example)i(program)e(b)s(elo)m(w)h(creates)i(a)e (random)f(p)s(erm)m(utation)h(\(b)m(y)g(sh)m(u\017ing)f(the)h(elemen)m (ts)h(of)150 2573 y(the)31 b(iden)m(tit)m(y\))h(and)e(\014nds)e(its)j (in)m(v)m(erse.)390 2710 y FH(#include)46 b()390 2819 y(#include)g()390 2929 y(#include)g ()390 3039 y(#include)g()390 3258 y(int)390 3367 y(main)h(\(void\))390 3477 y({)485 3587 y(const)g(size_t)f(N)h(=)h(10;)485 3696 y(const)f(gsl_rng_type)d (*)k(T;)485 3806 y(gsl_rng)e(*)i(r;)485 4025 y(gsl_permutation)c(*)k(p) f(=)g(gsl_permutation_alloc)42 b(\(N\);)485 4134 y(gsl_permutation)i(*) k(q)f(=)g(gsl_permutation_alloc)42 b(\(N\);)485 4354 y(gsl_rng_env_setup\(\);)485 4463 y(T)48 b(=)f(gsl_rng_default;)485 4573 y(r)h(=)f(gsl_rng_alloc)e(\(T\);)485 4792 y(printf)i(\("initial)e (permutation:"\);)485 4902 y(gsl_permutation_init)e(\(p\);)485 5011 y(gsl_permutation_fprintf)f(\(stdout,)j(p,)j(")f(\045u"\);)485 5121 y(printf)g(\("\\n"\);)485 5340 y(printf)g(\(")g(random)f (permutation:"\);)p eop end %%Page: 104 120 TeXDict begin 104 119 bop 150 -116 a FK(Chapter)30 b(9:)41 b(P)m(erm)m(utations)2468 b(104)485 299 y FH(gsl_ran_shuffle)44 b(\(r,)j(p->data,)f(N,)h(sizeof\(size_t\)\);)485 408 y(gsl_permutation_fprintf)42 b(\(stdout,)j(p,)j(")f(\045u"\);)485 518 y(printf)g(\("\\n"\);)485 737 y(printf)g(\("inverse)e (permutation:"\);)485 847 y(gsl_permutation_inverse)d(\(q,)47 b(p\);)485 956 y(gsl_permutation_fprintf)42 b(\(stdout,)j(q,)j(")f (\045u"\);)485 1066 y(printf)g(\("\\n"\);)485 1285 y (gsl_permutation_free)c(\(p\);)485 1395 y(gsl_permutation_free)g (\(q\);)485 1504 y(gsl_rng_free)i(\(r\);)485 1724 y(return)i(0;)390 1833 y(})150 1961 y FK(Here)31 b(is)f(the)h(output)f(from)g(the)g (program,)390 2089 y FH($)47 b(./a.out)390 2198 y(initial)f (permutation:)e(0)k(1)f(2)h(3)f(4)h(5)f(6)g(7)h(8)f(9)438 2308 y(random)f(permutation:)e(1)k(3)f(5)h(2)f(7)h(6)f(0)g(4)h(9)f(8) 390 2418 y(inverse)f(permutation:)e(6)k(0)f(3)h(1)f(7)h(2)f(5)g(4)h(9)f (8)150 2545 y FK(The)21 b(random)g(p)s(erm)m(utation)h FH(p[i])e FK(and)h(its)h(in)m(v)m(erse)h FH(q[i])d FK(are)i(related)h (through)e(the)h(iden)m(tit)m(y)h FH(p[q[i]])150 2655 y(=)30 b(i)p FK(,)g(whic)m(h)g(can)h(b)s(e)f(v)m(eri\014ed)g(from)g (the)h(output.)275 2783 y(The)24 b(next)h(example)g(program)f(steps)h (forw)m(ards)f(through)g(all)i(p)s(ossible)e(third)g(order)g(p)s(erm)m (utations,)150 2892 y(starting)31 b(from)f(the)h(iden)m(tit)m(y)-8 b(,)390 3020 y FH(#include)46 b()390 3130 y(#include)g ()390 3349 y(int)390 3459 y(main)h(\(void\))390 3568 y({)485 3678 y(gsl_permutation)d(*)k(p)f(=)g (gsl_permutation_alloc)42 b(\(3\);)485 3897 y(gsl_permutation_init)h (\(p\);)485 4116 y(do)533 4226 y({)676 4335 y(gsl_permutation_fprintf)f (\(stdout,)j(p,)j(")f(\045u"\);)676 4445 y(printf)f(\("\\n"\);)533 4555 y(})485 4664 y(while)h(\(gsl_permutation_next\(p\))41 b(==)47 b(GSL_SUCCESS\);)485 4883 y(gsl_permutation_free)c(\(p\);)485 5103 y(return)k(0;)390 5212 y(})150 5340 y FK(Here)31 b(is)f(the)h(output)f(from)g(the)g(program,)p eop end %%Page: 105 121 TeXDict begin 105 120 bop 150 -116 a FK(Chapter)30 b(9:)41 b(P)m(erm)m(utations)2468 b(105)390 299 y FH($)47 b(./a.out)438 408 y(0)g(1)h(2)438 518 y(0)f(2)h(1)438 628 y(1)f(0)h(2)438 737 y(1)f(2)h(0)438 847 y(2)f(0)h(1)438 956 y(2)f(1)h(0)150 1091 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 1200 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 1310 y(next)f FK(with)h FH(gsl_permutation_prev)p FK(.)150 1543 y FJ(9.10)68 b(References)47 b(and)d(F)-11 b(urther)44 b(Reading)150 1702 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 1836 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(\(V)-8 b(ol)31 b(3,)330 1946 y(3rd)f(Ed,)g(1997\),)j(Addison-W)-8 b(esley)g(,)32 b(ISBN)e(0201896850.)150 2105 y(F)-8 b(or)31 b(the)g(de\014nition)f(of) g(the)h FD(canonical)h(form)e FK(see,)330 2240 y(Donald)f(E.)g(Kn)m (uth,)f 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y(size_t)g(*data;)390 2596 y(})g(gsl_combination;)150 2848 y FJ(10.2)68 b(Com)l(bination)47 b(allo)t(cation)3350 3071 y FK([F)-8 b(unction])-3599 b Fv(gsl_combination)57 b(*)52 b(gsl_combination_allo)q(c)f Fu(\()p FD(size)p 2417 3071 28 4 v 42 w(t)30 b Ft(n)p FD(,)h(size)p 2773 3071 V 41 w(t)g Ft(k)p Fu(\))390 3181 y FK(This)37 b(function)g(allo)s(cates)i(memory)f(for)f(a)h(new)e(com)m (bination)j(with)e(parameters)h FD(n)p FK(,)h FD(k)p 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: 107 123 TeXDict begin 107 122 bop 150 -116 a FK(Chapter)30 b(10:)41 b(Com)m(binations)2406 b(107)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 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(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: 108 124 TeXDict begin 108 123 bop 150 -116 a FK(Chapter)30 b(10:)41 b(Com)m(binations)2406 b(108)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 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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: 109 125 TeXDict begin 109 124 bop 150 -116 a FK(Chapter)30 b(10:)41 b(Com)m(binations)2406 b(109)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 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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: 111 127 TeXDict begin 111 126 bop 150 -116 a FK(Chapter)30 b(11:)41 b(Multisets)2588 b(111)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 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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 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b(determine)g(ho)m (w)f(man)m(y)h(n)m(um)m(b)s(ers)e(to)i(read.)67 b(The)39 b(function)g(returns)390 2846 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 3084 y FJ(11.7)68 b(Examples)150 3244 y FK(The)32 b(example)i(program)e (b)s(elo)m(w)h(prin)m(ts)f(all)i(m)m(ultisets)g(elemen)m(ts)g(con)m (taining)g(the)f(v)-5 b(alues)33 b FI(f)p FK(0)p FE(;)15 b FK(1)p FE(;)g FK(2)p FE(;)g FK(3)p FI(g)150 3353 y FK(ordered)30 b(b)m(y)g(size.)42 b(Multiset)31 b(elemen)m(ts)h(of)e (the)h(same)g(size)g(are)g(ordered)f(lexicographically)-8 b(.)390 3491 y FH(#include)46 b()390 3601 y(#include)g ()390 3820 y(int)390 3930 y(main)h(\(void\))390 4039 y({)485 4149 y(gsl_multiset)e(*)i(c;)485 4259 y(size_t)g(i;)485 4478 y(printf)g(\("All)f(multisets)f(of)i({0,1,2,3})f(by)h(size:\\n"\)) e(;)485 4587 y(for)i(\(i)h(=)f(0;)g(i)h(<=)f(4;)g(i++\))581 4697 y({)676 4806 y(c)h(=)f(gsl_multiset_calloc)c(\(4,)k(i\);)676 4916 y(do)772 5026 y({)867 5135 y(printf)f(\("{"\);)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: 113 129 TeXDict begin 113 128 bop 150 -116 a FK(Chapter)30 b(11:)41 b(Multisets)2588 b(113)867 299 y FH(gsl_multiset_fprintf)43 b(\(stdout,)i(c,)i(")h(\045u"\);)867 408 y(printf)e(\(")i(}\\n"\);)772 518 y(})676 628 y(while)f(\(gsl_multiset_next)c(\(c\))j(==)i (GSL_SUCCESS\);)676 737 y(gsl_multiset_free)43 b(\(c\);)581 847 y(})485 1066 y(return)k(0;)390 1176 y(})150 1340 y FK(Here)31 b(is)f(the)h(output)f(from)g(the)g(program,)390 1504 y FH($)47 b(./a.out)390 1614 y(all)g(multisets)e(of)i({0,1,2,3})f (by)h(size:)390 1724 y({)g(})390 1833 y({)g(0)h(})390 1943 y({)f(1)h(})390 2052 y({)f(2)h(})390 2162 y({)f(3)h(})390 2271 y({)f(0)h(0)f(})390 2381 y({)g(0)h(1)f(})390 2491 y({)g(0)h(2)f(})390 2600 y({)g(0)h(3)f(})390 2710 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FK(All)31 b(70)g(m)m(ultisets)h (are)e(generated)i(and)e(sorted)g(lexicographically)-8 b(.)p eop end %%Page: 115 131 TeXDict begin 115 130 bop 150 -116 a FK(Chapter)30 b(12:)41 b(Sorting)2666 b(115)150 299 y FG(12)80 b(Sorting)150 558 y FK(This)39 b(c)m(hapter)h(describ)s(es)f(functions)g(for)g (sorting)h(data,)j(b)s(oth)c(directly)i(and)e(indirectly)h(\(using)f (an)150 667 y(index\).)h(All)29 b(the)f(functions)g(use)g(the)g FD(heapsort)i FK(algorithm.)41 b(Heapsort)29 b(is)g(an)f FE(O)s FK(\()p FE(N)d FK(log)17 b FE(N)10 b FK(\))29 b(algorithm)150 777 y(whic)m(h)c(op)s(erates)h(in-place)g(and)e(do)s (es)h(not)h(require)f(an)m(y)g(additional)h(storage.)41 b(It)25 b(also)h(pro)m(vides)f(consis-)150 886 y(ten)m(t)k(p)s (erformance,)f(the)g(running)e(time)i(for)g(its)g(w)m(orst-case)i (\(ordered)d(data\))i(b)s(eing)f(not)g(signi\014can)m(tly)150 996 y(longer)f(than)f(the)h(a)m(v)m(erage)i(and)d(b)s(est)g(cases.)41 b(Note)28 b(that)f(the)g(heapsort)f(algorithm)i(do)s(es)e(not)h (preserv)m(e)150 1106 y(the)i(relativ)m(e)j(ordering)c(of)i(equal)f (elemen)m(ts|it)i(is)e(an)g FD(unstable)34 b FK(sort.)41 b(Ho)m(w)m(ev)m(er)31 b(the)e(resulting)g(order)150 1215 y(of)i(equal)f(elemen)m(ts)i(will)f(b)s(e)f(consisten)m(t)h(across)g (di\013eren)m(t)g(platforms)f(when)g(using)g(these)h(functions.)150 1460 y FJ(12.1)68 b(Sorting)46 b(ob)7 b(jects)150 1619 y FK(The)25 b(follo)m(wing)h(function)f(pro)m(vides)g(a)h(simple)f (alternativ)m(e)i(to)f(the)f(standard)g(library)f(function)h FH(qsort)p FK(.)150 1729 y(It)34 b(is)f(in)m(tended)h(for)f(systems)h (lac)m(king)h FH(qsort)p FK(,)f(not)f(as)h(a)g(replacemen)m(t)h(for)f (it.)51 b(The)33 b(function)g FH(qsort)150 1839 y FK(should)j(b)s(e)h (used)f(whenev)m(er)h(p)s(ossible,)h(as)g(it)f(will)h(b)s(e)e(faster)i (and)e(can)i(pro)m(vide)f(stable)h(ordering)f(of)150 1948 y(equal)j(elemen)m(ts.)71 b(Do)s(cumen)m(tation)42 b(for)d FH(qsort)g FK(is)g(a)m(v)-5 b(ailable)43 b(in)c(the)h FD(GNU)h(C)e(Library)g(Reference)150 2058 y(Man)m(ual)p FK(.)275 2201 y(The)29 b(functions)h(describ)s(ed)g(in)g(this)g (section)h(are)g(de\014ned)e(in)h(the)h(header)f(\014le)h FH(gsl_heapsort.h)p FK(.)3350 2401 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_heapsort)49 b Fu(\()p FD(v)m(oid)31 b(*)g Ft(array)p FD(,)h(size)p 1857 2401 28 4 v 41 w(t)e Ft(count)p FD(,)i(size)p 2421 2401 V 41 w(t)f Ft(size)p FD(,)565 2511 y(gsl)p 677 2511 V 41 w(comparison)p 1168 2511 V 40 w(fn)p 1287 2511 V 39 w(t)g Ft(compare)p Fu(\))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 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(sizeof\(double\),)1298 5340 y(compare_doubles\);)p eop end %%Page: 116 132 TeXDict begin 116 131 bop 150 -116 a FK(Chapter)30 b(12:)41 b(Sorting)2666 b(116)390 299 y(Note)32 b(that)f(unlik)m(e)f FH(qsort)f FK(the)i(heapsort)f(algorithm)i(cannot)f(b)s(e)f(made)g(in)m (to)h(a)g(stable)g(sort)g(b)m(y)390 408 y(p)s(oin)m(ter)k(arithmetic.) 57 b(The)35 b(tric)m(k)h(of)g(comparing)g(p)s(oin)m(ters)f(for)g(equal) h(elemen)m(ts)h(in)e(the)g(com-)390 518 y(parison)e(function)g(do)s(es) g(not)h(w)m(ork)g(for)f(the)h(heapsort)f(algorithm.)51 b(The)33 b(heapsort)h(algorithm)390 628 y(p)s(erforms)29 b(an)h(in)m(ternal)h(rearrangemen)m(t)g(of)g(the)g(data)g(whic)m(h)f (destro)m(ys)h(its)f(initial)i(ordering.)3350 798 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_heapsort_index)e Fu(\()p FD(size)p 1528 798 28 4 v 41 w(t)31 b(*)g Ft(p)p FD(,)g(const)g(v)m (oid)g(*)f Ft(array)p FD(,)i(size)p 2787 798 V 41 w(t)f Ft(count)p FD(,)565 908 y(size)p 712 908 V 41 w(t)g Ft(size)p FD(,)g(gsl)p 1189 908 V 41 w(comparison)p 1680 908 V 40 w(fn)p 1799 908 V 40 w(t)f Ft(compare)p Fu(\))390 1017 y FK(This)43 b(function)h(indirectly)g(sorts)g(the)g FD(coun)m(t)j FK(elemen)m(ts)e(of)f(the)g(arra)m(y)h FD(arra)m(y)p FK(,)j(eac)m(h)d(of)f(size)390 1127 y FD(size)p FK(,)k(in)m(to)d(ascending)f(order)f(using)h(the)g(comparison)g (function)f FD(compare)p FK(.)82 b(The)43 b(resulting)390 1236 y(p)s(erm)m(utation)36 b(is)g(stored)f(in)h FD(p)p FK(,)g(an)g(arra)m(y)g(of)g(length)g FD(n)p FK(.)56 b(The)35 b(elemen)m(ts)j(of)d FD(p)j FK(giv)m(e)f(the)f(index)390 1346 y(of)c(the)h(arra)m(y)g(elemen)m(t)h(whic)m(h)e(w)m(ould)g(ha)m(v) m(e)h(b)s(een)f(stored)g(in)h(that)f(p)s(osition)h(if)f(the)h(arra)m(y) g(had)390 1455 y(b)s(een)i(sorted)g(in)h(place.)57 b(The)35 b(\014rst)f(elemen)m(t)j(of)f FD(p)i FK(giv)m(es)e(the)g(index)f(of)h (the)g(least)g(elemen)m(t)h(in)390 1565 y FD(arra)m(y)p FK(,)29 b(and)f(the)h(last)g(elemen)m(t)g(of)g FD(p)h FK(giv)m(es)g(the)e(index)g(of)h(the)f(greatest)i(elemen)m(t)g(in)e FD(arra)m(y)p FK(.)40 b(The)390 1675 y(arra)m(y)31 b(itself)g(is)f(not) h(c)m(hanged.)150 1898 y FJ(12.2)68 b(Sorting)46 b(v)l(ectors)150 2057 y FK(The)e(follo)m(wing)j(functions)d(will)i(sort)f(the)g(elemen)m (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: 117 133 TeXDict begin 117 132 bop 150 -116 a FK(Chapter)30 b(12:)41 b(Sorting)2666 b(117)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 (total)h(size)g(of)f(the)g(dataset.)52 b(F)-8 b(or)35 b(example,)h(the)e(routines)g(are)150 2009 y(useful)29 b(for)h(selecting)h(the)f(10)h(largest)g(v)-5 b(alues)31 b(from)e(one)h(million)h(data)f(p)s(oin)m(ts,)g(but)f(not)h(for)g (selecting)150 2118 y(the)38 b(largest)i(100,000)h(v)-5 b(alues.)64 b(If)38 b(the)g(subset)f(is)h(a)h(signi\014can)m(t)g(part)f (of)g(the)g(total)i(dataset)g(it)e(ma)m(y)150 2228 y(b)s(e)29 b(faster)h(to)g(sort)g(all)g(the)g(elemen)m(ts)h(of)e(the)h(dataset)h (directly)f(with)f(an)g FE(O)s FK(\()p FE(N)d FK(log)17 b FE(N)10 b FK(\))30 b(algorithm)h(and)150 2338 y(obtain)g(the)f (smallest)i(or)e(largest)i(v)-5 b(alues)31 b(that)g(w)m(a)m(y)-8 b(.)3350 2544 y([F)g(unction])-3599 b Fv(int)53 b(gsl_sort_smallest)e Fu(\()p FD(double)30 b(*)h Ft(dest)p FD(,)h(size)p 2110 2544 V 41 w(t)e Ft(k)p FD(,)h(const)g(double)f(*)h Ft(src)p FD(,)565 2653 y(size)p 712 2653 V 41 w(t)g Ft(stride)p FD(,)h(size)p 1329 2653 V 41 w(t)f Ft(n)p Fu(\))390 2763 y FK(This)39 b(function)h(copies)g(the)g FD(k)46 b FK(smallest)41 b(elemen)m(ts)g(of)f(the)g(arra)m(y)g FD(src)p FK(,)j(of)d(size)g FD(n)g FK(and)f(stride)390 2872 y FD(stride)p FK(,)j(in)d(ascending)h (n)m(umerical)g(order)f(in)m(to)h(the)g(arra)m(y)g FD(dest)p FK(.)68 b(The)39 b(size)h FD(k)45 b FK(of)40 b(the)g(subset)390 2982 y(m)m(ust)30 b(b)s(e)g(less)h(than)f(or)g(equal)h(to)g FD(n)p FK(.)40 b(The)30 b(data)h FD(src)36 b FK(is)30 b(not)h(mo)s(di\014ed)e(b)m(y)h(this)h(op)s(eration.)3350 3188 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sort_largest)e Fu(\()p FD(double)30 b(*)h Ft(dest)p FD(,)g(size)p 2057 3188 V 41 w(t)g Ft(k)p FD(,)g(const)g(double)f(*)g Ft(src)p FD(,)565 3297 y(size)p 712 3297 V 41 w(t)h Ft(stride)p FD(,)h(size)p 1329 3297 V 41 w(t)f Ft(n)p Fu(\))390 3407 y FK(This)25 b(function)g(copies)h(the)g FD(k)31 b FK(largest)26 b(elemen)m(ts)h(of)f(the)f(arra)m(y)h FD(src)p FK(,)h(of)e(size)i FD(n)e FK(and)f(stride)i FD(stride)p FK(,)390 3517 y(in)j(descending)g (n)m(umerical)h(order)e(in)m(to)i(the)g(arra)m(y)f FD(dest)p FK(.)41 b FD(k)34 b FK(m)m(ust)29 b(b)s(e)g(less)h(than)e(or)i(equal)f (to)h FD(n)p FK(.)390 3626 y(The)g(data)h FD(src)36 b FK(is)30 b(not)h(mo)s(di\014ed)e(b)m(y)h(this)g(op)s(eration.)3350 3832 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sort_vector_small)q (est)f Fu(\()p FD(double)30 b(*)h Ft(dest)p FD(,)h(size)p 2476 3832 V 41 w(t)e Ft(k)p FD(,)h(const)565 3942 y(gsl)p 677 3942 V 41 w(v)m(ector)h(*)e Ft(v)p Fu(\))3350 4051 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sort_vector_large)q(st)f Fu(\()p FD(double)30 b(*)h Ft(dest)p FD(,)g(size)p 2423 4051 V 41 w(t)g Ft(k)p FD(,)g(const)565 4161 y(gsl)p 677 4161 V 41 w(v)m(ector)h(*)e Ft(v)p Fu(\))390 4271 y FK(These)d(functions)h(cop)m(y)g(the)g FD(k)33 b FK(smallest)28 b(or)g(largest)h(elemen)m(ts)g(of)f(the)g(v)m(ector)h FD(v)35 b FK(in)m(to)29 b(the)e(arra)m(y)390 4380 y FD(dest)p FK(.)41 b FD(k)36 b FK(m)m(ust)30 b(b)s(e)g(less)g(than)g(or)h(equal)g (to)g(the)f(length)h(of)g(the)f(v)m(ector)i FD(v)p FK(.)275 4586 y(The)24 b(follo)m(wing)i(functions)e(\014nd)g(the)h(indices)g(of) f(the)h FE(k)j FK(smallest)e(or)f(largest)h(elemen)m(ts)g(of)f(a)g (dataset,)3350 4792 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_sort_smallest_ind)q(ex)f Fu(\()p FD(size)p 1790 4792 V 41 w(t)31 b(*)f Ft(p)p FD(,)h(size)p 2221 4792 V 41 w(t)g Ft(k)p FD(,)g(const)g(double)e(*)565 4902 y Ft(src)p FD(,)j(size)p 925 4902 V 40 w(t)f Ft(stride)p FD(,)i(size)p 1542 4902 V 40 w(t)e Ft(n)p Fu(\))390 5011 y FK(This)g(function)h(stores)g(the)g(indices)g(of)h(the)f FD(k)37 b FK(smallest)c(elemen)m(ts)g(of)g(the)f(arra)m(y)g FD(src)p FK(,)h(of)f(size)g FD(n)390 5121 y FK(and)j(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 5230 y(data)28 b(is)f(in)g(ascending)g(n)m(umerical)h (order.)39 b FD(k)32 b FK(m)m(ust)27 b(b)s(e)g(less)g(than)g(or)g (equal)g(to)h FD(n)p FK(.)39 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: 118 134 TeXDict begin 118 133 bop 150 -116 a FK(Chapter)30 b(12:)41 b(Sorting)2666 b(118)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: 119 135 TeXDict begin 119 134 bop 150 -116 a FK(Chapter)30 b(12:)41 b(Sorting)2666 b(119)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(\("\045d)f(smallest)g(values)g(from)g(\045d\\n",)h (k,)g(N\);)485 4792 y(for)g(\(i)h(=)f(0;)g(i)h(<)f(k;)g(i++\))581 4902 y({)676 5011 y(printf)f(\("\045d:)95 b(\045.18f\\n",)45 b(i,)i(small[i]\);)581 5121 y(})485 5340 y(free)g(\(x\);)p eop end %%Page: 120 136 TeXDict begin 120 135 bop 150 -116 a FK(Chapter)30 b(12:)41 b(Sorting)2666 b(120)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: 121 137 TeXDict begin 121 136 bop 150 -116 a FK(Chapter)30 b(13:)41 b(BLAS)31 b(Supp)s(ort)2360 b(121)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 b(and)e(matrices)h(whic)m(h)f(can)h(b)s(e)e(used)h(to)h(create)h (optimized)f(higher-lev)m(el)h(linear)f(algebra)150 745 y(functionalit)m(y)-8 b(.)275 878 y(The)24 b(library)h(pro)m(vides)g(a) g(lo)m(w-lev)m(el)j(la)m(y)m(er)f(whic)m(h)e(corresp)s(onds)f(directly) i(to)f(the)h(C-language)g FC(blas)150 987 y FK(standard,)34 b(referred)f(to)i(here)f(as)g(\\)p FC(cblas)p FK(",)h(and)e(a)h (higher-lev)m(el)i(in)m(terface)g(for)d(op)s(erations)h(on)g(GSL)150 1097 y(v)m(ectors)40 b(and)e(matrices.)66 b(Users)38 b(who)g(are)h(in)m(terested)g(in)f(simple)h(op)s(erations)f(on)h(GSL)f (v)m(ector)i(and)150 1207 y(matrix)32 b(ob)5 b(jects)32 b(should)e(use)h(the)h(high-lev)m(el)h(la)m(y)m(er)g(describ)s(ed)d(in) h(this)g(c)m(hapter.)45 b(The)31 b(functions)g(are)150 1316 y(declared)g(in)f(the)g(\014le)h FH(gsl_blas.h)d FK(and)h(should)h(satisfy)g(the)h(needs)f(of)h(most)f(users.)275 1449 y(Note)36 b(that)f(GSL)g(matrices)g(are)h(implemen)m(ted)f(using)f (dense-storage)j(so)e(the)g(in)m(terface)h(only)f(in-)150 1559 y(cludes)43 b(the)h(corresp)s(onding)e(dense-storage)j FC(blas)d FK(functions.)79 b(The)42 b(full)h FC(blas)f FK(functionalit)m(y)j(for)150 1668 y(band-format)c(and)f(pac)m(k)m (ed-format)j(matrices)f(is)f(a)m(v)-5 b(ailable)44 b(through)c(the)i (lo)m(w-lev)m(el)i FC(cblas)39 b FK(in)m(ter-)150 1778 y(face.)45 b(Similarly)-8 b(,)33 b(GSL)e(v)m(ectors)i(are)f(restricted) g(to)h(p)s(ositiv)m(e)f(strides,)g(whereas)f(the)h(lo)m(w-lev)m(el)i FC(cblas)150 1887 y FK(in)m(terface)e(supp)s(orts)c(negativ)m(e)33 b(strides)d(as)h(sp)s(eci\014ed)e(in)h(the)h FC(blas)e FK(standard.)2882 1854 y FB(1)275 2020 y FK(The)c(in)m(terface)i(for)e (the)h FH(gsl_cblas)d FK(la)m(y)m(er)k(is)e(sp)s(eci\014ed)g(in)g(the)h (\014le)g FH(gsl_cblas.h)p FK(.)36 b(This)24 b(in)m(terface)150 2130 y(corresp)s(onds)39 b(to)i(the)f FC(blas)f FK(T)-8 b(ec)m(hnical)42 b(F)-8 b(orum's)41 b(standard)e(for)h(the)g(C)g(in)m (terface)i(to)f(legacy)h FC(blas)150 2240 y FK(implemen)m(tations.)52 b(Users)34 b(who)f(ha)m(v)m(e)i(access)g(to)f(other)g(conforming)g FC(cblas)e FK(implemen)m(tations)k(can)150 2349 y(use)g(these)h(in)f (place)h(of)f(the)h(v)m(ersion)g(pro)m(vided)e(b)m(y)i(the)f(library)-8 b(.)59 b(Note)37 b(that)g(users)e(who)h(ha)m(v)m(e)i(only)150 2459 y(a)h(F)-8 b(ortran)39 b FC(blas)e FK(library)h(can)h(use)f(a)h FC(cblas)d FK(conforman)m(t)k(wrapp)s(er)c(to)j(con)m(v)m(ert)h(it)f (in)m(to)h(a)e FC(cblas)150 2568 y FK(library)-8 b(.)61 b(A)38 b(reference)f FC(cblas)f FK(wrapp)s(er)g(for)h(legacy)i(F)-8 b(ortran)38 b(implemen)m(tations)g(exists)g(as)g(part)f(of)150 2678 y(the)27 b FC(cblas)f FK(standard)g(and)h(can)h(b)s(e)e(obtained)i (from)f(Netlib.)40 b(The)27 b(complete)i(set)e(of)h FC(cblas)d FK(functions)150 2788 y(is)30 b(listed)h(in)f(an)h(app)s(endix)e(\(see) i(App)s(endix)e(D)h([GSL)h(CBLAS)e(Library],)h(page)i(463\).)275 2921 y(There)d(are)i(three)g(lev)m(els)h(of)e FC(blas)f FK(op)s(erations,)150 3077 y 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: 122 138 TeXDict begin 122 137 bop 150 -116 a FK(Chapter)30 b(13:)41 b(BLAS)31 b(Supp)s(ort)2360 b(122)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 FK(hermitian)150 947 y Fk(HB)344 b FK(hermitian)30 b(band)150 1109 y Fk(HP)347 b FK(hermitian)30 b(pac)m(k)m(ed)150 1271 y Fk(TR)348 b FK(triangular)150 1433 y Fk(TB)k FK(triangular)31 b(band)150 1596 y Fk(TP)355 b FK(triangular)31 b(pac)m(k)m(ed)150 1759 y(Eac)m(h)g(op)s(eration)g (is)f(de\014ned)f(for)i(four)e(precisions,)150 1922 y Fk(S)429 b FK(single)31 b(real)150 2084 y Fk(D)410 b FK(double)30 b(real)150 2247 y Fk(C)414 b FK(single)31 b(complex)150 2409 y Fk(Z)424 b FK(double)30 b(complex)150 2572 y(Th)m(us,)45 b(for)e(example,)k(the)d(name)f FC(sgemm)f FK(stands)g(for)h(\\single-precision)i(general)f(matrix-matrix)150 2682 y(m)m(ultiply")31 b(and)f FC(zgemm)g FK(stands)f(for)i (\\double-precision)f(complex)i(matrix-matrix)f(m)m(ultiply".)275 2819 y(Note)i(that)g(the)f(v)m(ector)i(and)d(matrix)i(argumen)m(ts)f (to)h(BLAS)f(functions)g(m)m(ust)g(not)g(b)s(e)g(aliased,)i(as)150 2928 y(the)d(results)g(are)h(unde\014ned)d(when)h(the)h(underlying)f (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: 123 139 TeXDict begin 123 138 bop 150 -116 a FK(Chapter)30 b(13:)41 b(BLAS)31 b(Supp)s(ort)2360 b(123)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: 124 140 TeXDict begin 124 139 bop 150 -116 a FK(Chapter)30 b(13:)41 b(BLAS)31 b(Supp)s(ort)2360 b(124)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: 125 141 TeXDict begin 125 140 bop 150 -116 a FK(Chapter)30 b(13:)41 b(BLAS)31 b(Supp)s(ort)2360 b(125)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: 126 142 TeXDict begin 126 141 bop 150 -116 a FK(Chapter)30 b(13:)41 b(BLAS)31 b(Supp)s(ort)2360 b(126)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: 127 143 TeXDict begin 127 142 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_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: 128 144 TeXDict begin 128 143 bop 150 -116 a FK(Chapter)30 b(13:)41 b(BLAS)31 b(Supp)s(ort)2360 b(128)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: 129 145 TeXDict begin 129 144 bop 150 -116 a FK(Chapter)30 b(13:)41 b(BLAS)31 b(Supp)s(ort)2360 b(129)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(\()p FD(CBLAS)p 1484 1943 V 40 w(SIDE)p 1739 1943 V 39 w(t)31 b Ft(Side)p FD(,)h(CBLAS)p 2415 1943 V 39 w(UPLO)p 2712 1943 V 40 w(t)f Ft(Uplo)p FD(,)565 2052 y(CBLAS)p 877 2052 V 40 w(TRANSPOSE)p 1483 2052 V 38 w(t)g Ft(TransA)p FD(,)h(CBLAS)p 2262 2052 V 40 w(DIA)m(G)p 2540 2052 V 41 w(t)f Ft(Diag)p FD(,)g(const)g(gsl)p 3255 2052 V 41 w(complex)565 2162 y Ft(alpha)p FD(,)h(const)f(gsl)p 1232 2162 V 41 w(matrix)p 1538 2162 V 40 w(complex)g(*)g Ft(A)p FD(,)g(gsl)p 2224 2162 V 40 w(matrix)p 2529 2162 V 41 w(complex)g(*)g Ft(B)p Fu(\))390 2271 y FK(These)51 b(functions)g(compute)h(the)f(matrix-matrix)i(pro)s(duct)d FE(B)65 b FK(=)60 b FE(\013op)p FK(\()p FE(A)p FK(\))p FE(B)d FK(for)51 b FD(Side)56 b FK(is)390 2381 y FH(CblasLeft)34 b FK(and)h FE(B)40 b FK(=)34 b FE(\013B)5 b(op)p FK(\()p FE(A)p FK(\))37 b(for)f FD(Side)41 b FK(is)36 b FH(CblasRight)p FK(.)56 b(The)35 b(matrix)i FD(A)f FK(is)h(triangular)390 2491 y(and)24 b FE(op)p FK(\()p FE(A)p FK(\))i(=)f FE(A)p FK(,)h FE(A)1098 2458 y Fq(T)1151 2491 y FK(,)g FE(A)1270 2458 y Fq(H)1357 2491 y FK(for)f FD(T)-8 b(ransA)24 b FK(=)h FH(CblasNoTrans)p FK(,)d FH(CblasTrans)p FK(,)i FH(CblasConjTrans)p FK(.)390 2600 y(When)36 b FD(Uplo)41 b FK(is)36 b FH(CblasUpper)e FK(then)h(the)i(upp)s(er)d(triangle)j(of)g FD(A)f FK(is)g(used,)h(and)f(when)f FD(Uplo)41 b FK(is)390 2710 y FH(CblasLower)30 b FK(then)i(the)h(lo)m(w)m(er)i(triangle)f(of)f FD(A)f FK(is)h(used.)47 b(If)33 b FD(Diag)42 b FK(is)33 b FH(CblasNonUnit)c FK(then)k(the)390 2819 y(diagonal)39 b(of)f FD(A)h FK(is)f(used,)h(but)e(if)h FD(Diag)48 b FK(is)38 b FH(CblasUnit)d FK(then)j(the)g(diagonal)h(elemen)m(ts)h(of)e (the)390 2929 y(matrix)31 b FD(A)f FK(are)h(tak)m(en)g(as)g(unit)m(y)f (and)g(are)h(not)g(referenced.)3350 3258 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_strsm)d Fu(\()p FD(CBLAS)p 1484 3258 V 40 w(SIDE)p 1739 3258 V 39 w(t)31 b Ft(Side)p FD(,)h(CBLAS)p 2415 3258 V 39 w(UPLO)p 2712 3258 V 40 w(t)f Ft(Uplo)p FD(,)565 3367 y(CBLAS)p 877 3367 V 40 w(TRANSPOSE)p 1483 3367 V 38 w(t)g Ft(TransA)p FD(,)h(CBLAS)p 2262 3367 V 40 w(DIA)m(G)p 2540 3367 V 41 w(t)f Ft(Diag)p FD(,)g(\015oat)g Ft(alpha)p FD(,)h(const)565 3477 y(gsl)p 677 3477 V 41 w(matrix)p 983 3477 V 40 w(\015oat)f(*)g Ft(A)p FD(,)g(gsl)p 1520 3477 V 40 w(matrix)p 1825 3477 V 41 w(\015oat)g(*)g Ft(B)p Fu(\))3350 3587 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_dtrsm)d Fu(\()p FD(CBLAS)p 1484 3587 V 40 w(SIDE)p 1739 3587 V 39 w(t)31 b Ft(Side)p FD(,)h(CBLAS)p 2415 3587 V 39 w(UPLO)p 2712 3587 V 40 w(t)f Ft(Uplo)p FD(,)565 3696 y(CBLAS)p 877 3696 V 40 w(TRANSPOSE)p 1483 3696 V 38 w(t)g Ft(TransA)p FD(,)h(CBLAS)p 2262 3696 V 40 w(DIA)m(G)p 2540 3696 V 41 w(t)f Ft(Diag)p FD(,)g(double)f Ft(alpha)p FD(,)i(const)565 3806 y(gsl)p 677 3806 V 41 w(matrix)e(*)h Ft(A)p FD(,)g(gsl)p 1303 3806 V 41 w(matrix)f(*)h Ft(B)p Fu(\))3350 3915 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_ctrsm)d Fu(\()p FD(CBLAS)p 1484 3915 V 40 w(SIDE)p 1739 3915 V 39 w(t)31 b Ft(Side)p FD(,)h(CBLAS)p 2415 3915 V 39 w(UPLO)p 2712 3915 V 40 w(t)f Ft(Uplo)p FD(,)565 4025 y(CBLAS)p 877 4025 V 40 w(TRANSPOSE)p 1483 4025 V 38 w(t)g Ft(TransA)p FD(,)h(CBLAS)p 2262 4025 V 40 w(DIA)m(G)p 2540 4025 V 41 w(t)f Ft(Diag)p FD(,)g(const)565 4134 y(gsl)p 677 4134 V 41 w(complex)p 1043 4134 V 40 w(\015oat)h Ft(alpha)p FD(,)g(const)e(gsl)p 1951 4134 V 41 w(matrix)p 2257 4134 V 40 w(complex)p 2622 4134 V 41 w(\015oat)h(*)g Ft(A)p FD(,)565 4244 y(gsl)p 677 4244 V 41 w(matrix)p 983 4244 V 40 w(complex)p 1348 4244 V 41 w(\015oat)g(*)g Ft(B)p Fu(\))3350 4354 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_ztrsm)d Fu(\()p FD(CBLAS)p 1484 4354 V 40 w(SIDE)p 1739 4354 V 39 w(t)31 b Ft(Side)p FD(,)h(CBLAS)p 2415 4354 V 39 w(UPLO)p 2712 4354 V 40 w(t)f Ft(Uplo)p FD(,)565 4463 y(CBLAS)p 877 4463 V 40 w(TRANSPOSE)p 1483 4463 V 38 w(t)g Ft(TransA)p FD(,)h(CBLAS)p 2262 4463 V 40 w(DIA)m(G)p 2540 4463 V 41 w(t)f Ft(Diag)p FD(,)g(const)g(gsl)p 3255 4463 V 41 w(complex)565 4573 y Ft(alpha)p FD(,)h(const)f(gsl)p 1232 4573 V 41 w(matrix)p 1538 4573 V 40 w(complex)g(*)g Ft(A)p FD(,)g(gsl)p 2224 4573 V 40 w(matrix)p 2529 4573 V 41 w(complex)g(*)g Ft(B)p Fu(\))390 4682 y FK(These)j(functions)g(compute)h(the)g(in)m(v)m (erse-matrix)h(matrix)f(pro)s(duct)e FE(B)k FK(=)32 b FE(\013op)p FK(\()p FE(inv)s FK(\()p FE(A)p FK(\)\))p FE(B)41 b FK(for)390 4792 y FD(Side)h FK(is)37 b FH(CblasLeft)e FK(and)i FE(B)k FK(=)c FE(\013B)5 b(op)p FK(\()p FE(inv)s FK(\()p FE(A)p FK(\)\))39 b(for)e FD(Side)42 b FK(is)37 b FH(CblasRight)p FK(.)59 b(The)37 b(matrix)h FD(A)390 4902 y FK(is)k(triangular)g(and)f FE(op)p FK(\()p FE(A)p FK(\))k(=)f FE(A)p FK(,)h FE(A)1711 4869 y Fq(T)1764 4902 y FK(,)g FE(A)1902 4869 y Fq(H)2006 4902 y FK(for)d FD(T)-8 b(ransA)41 b FK(=)h FH(CblasNoTrans)p FK(,)f FH(CblasTrans)p FK(,)390 5011 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 5121 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 5230 y FH(CblasNonUnit)37 b FK(then)j(the)h(diagonal)h(of)f FD(A)f FK(is)h(used,)i(but)c(if)i FD(Diag)50 b FK(is)40 b FH(CblasUnit)e FK(then)j(the)390 5340 y(diagonal)32 b(elemen)m(ts)f(of)g(the)f(matrix)h FD(A)g FK(are)f(tak)m(en)i(as)f(unit)m(y)f(and)g(are)g(not)h (referenced.)p eop end %%Page: 130 146 TeXDict begin 130 145 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_ssyrk)d Fu(\()p FD(CBLAS)p 1484 299 28 4 v 40 w(UPLO)p 1782 299 V 39 w(t)31 b Ft(Uplo)p FD(,)h(CBLAS)p 2458 299 V 39 w(TRANSPOSE)p 3063 299 V 39 w(t)565 408 y Ft(Trans)p FD(,)e(\015oat)e Ft(alpha)p FD(,)i(const)d(gsl)p 1745 408 V 41 w(matrix)p 2051 408 V 40 w(\015oat)h(*)g Ft(A)p FD(,)g(\015oat)g Ft(beta)p FD(,)i(gsl)p 3046 408 V 40 w(matrix)p 3351 408 V 41 w(\015oat)e(*)f Ft(C)p Fu(\))3350 518 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_dsyrk)d Fu(\()p FD(CBLAS)p 1484 518 V 40 w(UPLO)p 1782 518 V 39 w(t)31 b Ft(Uplo)p FD(,)h(CBLAS)p 2458 518 V 39 w(TRANSPOSE)p 3063 518 V 39 w(t)565 628 y Ft(Trans)p FD(,)g(double)e Ft(alpha)p FD(,)i(const)f(gsl)p 1842 628 V 41 w(matrix)f(*)h Ft(A)p FD(,)g(double)f Ft(beta)p FD(,)i(gsl)p 3026 628 V 40 w(matrix)f(*)g Ft(C)p Fu(\))3350 737 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_csyrk)d Fu(\()p FD(CBLAS)p 1484 737 V 40 w(UPLO)p 1782 737 V 39 w(t)31 b Ft(Uplo)p FD(,)h(CBLAS)p 2458 737 V 39 w(TRANSPOSE)p 3063 737 V 39 w(t)565 847 y Ft(Trans)p FD(,)g(const)f(gsl)p 1232 847 V 41 w(complex)p 1598 847 V 40 w(\015oat)g Ft(alpha)p FD(,)i(const)d(gsl)p 2506 847 V 41 w(matrix)p 2812 847 V 40 w(complex)p 3177 847 V 41 w(\015oat)h(*)g Ft(A)p FD(,)565 956 y(const)g(gsl)p 915 956 V 41 w(complex)p 1281 956 V 40 w(\015oat)g Ft(beta)p FD(,)h(gsl)p 1899 956 V 41 w(matrix)p 2205 956 V 40 w(complex)p 2570 956 V 41 w(\015oat)f(*)g Ft(C)p Fu(\))3350 1066 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_zsyrk)d Fu(\()p FD(CBLAS)p 1484 1066 V 40 w(UPLO)p 1782 1066 V 39 w(t)31 b Ft(Uplo)p FD(,)h(CBLAS)p 2458 1066 V 39 w(TRANSPOSE)p 3063 1066 V 39 w(t)565 1176 y Ft(Trans)p FD(,)g(const)f(gsl)p 1232 1176 V 41 w(complex)g Ft(alpha)p FD(,)h(const)f(gsl)p 2290 1176 V 40 w(matrix)p 2595 1176 V 41 w(complex)g(*)f Ft(A)p FD(,)h(const)565 1285 y(gsl)p 677 1285 V 41 w(complex)g Ft(beta)p FD(,)h(gsl)p 1445 1285 V 40 w(matrix)p 1750 1285 V 40 w(complex)g(*)e Ft(C)p Fu(\))390 1395 y FK(These)21 b(functions)g(compute)h(a)g(rank-k)f(up)s(date)g(of)h(the)f(symmetric)h (matrix)g FD(C)p FK(,)h FE(C)32 b FK(=)25 b FE(\013AA)3494 1362 y Fq(T)3549 1395 y FK(+)r FE(\014)5 b(C)390 1504 y FK(when)25 b FD(T)-8 b(rans)30 b FK(is)c FH(CblasNoTrans)d FK(and)i FE(C)32 b FK(=)25 b FE(\013A)2056 1471 y Fq(T)2109 1504 y FE(A)12 b FK(+)g FE(\014)5 b(C)33 b FK(when)25 b FD(T)-8 b(rans)29 b FK(is)d FH(CblasTrans)p FK(.)37 b(Since)390 1614 y(the)30 b(matrix)f FD(C)37 b FK(is)30 b(symmetric)f(only)h(its)g(upp)s(er)d(half)i(or)h(lo)m(w)m(er)g(half)g (need)f(to)h(b)s(e)f(stored.)40 b(When)390 1724 y FD(Uplo)g FK(is)35 b FH(CblasUpper)d FK(then)i(the)h(upp)s(er)e(triangle)j(and)e (diagonal)i(of)f FD(C)42 b FK(are)35 b(used,)h(and)e(when)390 1833 y FD(Uplo)h FK(is)c FH(CblasLower)c FK(then)j(the)h(lo)m(w)m(er)h (triangle)f(and)f(diagonal)h(of)g FD(C)38 b FK(are)31 b(used.)3350 1998 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_cherk)d Fu(\()p FD(CBLAS)p 1484 1998 V 40 w(UPLO)p 1782 1998 V 39 w(t)31 b Ft(Uplo)p FD(,)h(CBLAS)p 2458 1998 V 39 w(TRANSPOSE)p 3063 1998 V 39 w(t)565 2107 y Ft(Trans)p FD(,)g(\015oat)f Ft(alpha)p FD(,)h(const)f(gsl)p 1756 2107 V 41 w(matrix)p 2062 2107 V 40 w(complex)p 2427 2107 V 41 w(\015oat)g(*)g Ft(A)p FD(,)g(\015oat)g Ft(beta)p FD(,)565 2217 y(gsl)p 677 2217 V 41 w(matrix)p 983 2217 V 40 w(complex)p 1348 2217 V 41 w(\015oat)g(*)g Ft(C)p Fu(\))3350 2326 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_zherk)d Fu(\()p FD(CBLAS)p 1484 2326 V 40 w(UPLO)p 1782 2326 V 39 w(t)31 b Ft(Uplo)p FD(,)h(CBLAS)p 2458 2326 V 39 w(TRANSPOSE)p 3063 2326 V 39 w(t)565 2436 y Ft(Trans)p FD(,)g(double)e Ft(alpha)p FD(,)i(const)f(gsl)p 1842 2436 V 41 w(matrix)p 2148 2436 V 40 w(complex)g(*)g Ft(A)p FD(,)g(double)f Ft(beta)p FD(,)565 2545 y(gsl)p 677 2545 V 41 w(matrix)p 983 2545 V 40 w(complex)h(*)g Ft(C)p Fu(\))390 2655 y FK(These)22 b(functions)h(compute)g(a)g(rank-k)f(up)s(date)g(of)h(the)g(hermitian)f (matrix)h FD(C)p FK(,)h FE(C)32 b FK(=)25 b FE(\013AA)3478 2622 y Fq(H)3547 2655 y FK(+)5 b FE(\014)g(C)390 2765 y FK(when)29 b FD(T)-8 b(rans)32 b FK(is)e FH(CblasNoTrans)c FK(and)j FE(C)j FK(=)25 b FE(\013A)2073 2732 y Fq(H)2137 2765 y FE(A)19 b FK(+)f FE(\014)5 b(C)36 b FK(when)29 b FD(T)-8 b(rans)33 b FK(is)d FH(CblasConjTrans)p FK(.)390 2874 y(Since)k(the)f(matrix)h FD(C)41 b FK(is)34 b(hermitian)f(only)h (its)g(upp)s(er)e(half)h(or)h(lo)m(w)m(er)h(half)e(need)g(to)i(b)s(e)e (stored.)390 2984 y(When)g FD(Uplo)k FK(is)c FH(CblasUpper)d FK(then)j(the)g(upp)s(er)e(triangle)j(and)e(diagonal)i(of)f FD(C)40 b FK(are)34 b(used,)f(and)390 3093 y(when)g FD(Uplo)40 b FK(is)34 b FH(CblasLower)e FK(then)i(the)h(lo)m(w)m(er)h(triangle)f (and)f(diagonal)i(of)e FD(C)42 b FK(are)35 b(used.)52 b(The)390 3203 y(imaginary)31 b(elemen)m(ts)h(of)e(the)h(diagonal)g (are)g(automatically)i(set)e(to)h(zero.)3350 3367 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_ssyr2k)d Fu(\()p FD(CBLAS)p 1536 3367 V 40 w(UPLO)p 1834 3367 V 40 w(t)30 b Ft(Uplo)p FD(,)i(CBLAS)p 2510 3367 V 40 w(TRANSPOSE)p 3116 3367 V 38 w(t)565 3477 y Ft(Trans)p FD(,)g(\015oat)f Ft(alpha)p FD(,)h(const)f(gsl)p 1756 3477 V 41 w(matrix)p 2062 3477 V 40 w(\015oat)g(*)g Ft(A)p FD(,)g(const)g(gsl)p 2837 3477 V 40 w(matrix)p 3142 3477 V 41 w(\015oat)g(*)g Ft(B)p FD(,)f(\015oat)565 3587 y Ft(beta)p FD(,)i(gsl)p 942 3587 V 40 w(matrix)p 1247 3587 V 41 w(\015oat)f(*)g Ft(C)p Fu(\))3350 3696 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_dsyr2k)d Fu(\()p FD(CBLAS)p 1536 3696 V 40 w(UPLO)p 1834 3696 V 40 w(t)30 b Ft(Uplo)p FD(,)i(CBLAS)p 2510 3696 V 40 w(TRANSPOSE)p 3116 3696 V 38 w(t)565 3806 y Ft(Trans)p FD(,)g(double)e Ft(alpha)p FD(,)i(const)f(gsl)p 1842 3806 V 41 w(matrix)f(*)h Ft(A)p FD(,)g(const)g(gsl)p 2706 3806 V 40 w(matrix)g(*)g Ft(B)p FD(,)g(double)f Ft(beta)p FD(,)565 3915 y(gsl)p 677 3915 V 41 w(matrix)g(*)h Ft(C)p Fu(\))3350 4025 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_csyr2k)d Fu(\()p FD(CBLAS)p 1536 4025 V 40 w(UPLO)p 1834 4025 V 40 w(t)30 b Ft(Uplo)p FD(,)i(CBLAS)p 2510 4025 V 40 w(TRANSPOSE)p 3116 4025 V 38 w(t)565 4134 y Ft(Trans)p FD(,)g(const)f(gsl)p 1232 4134 V 41 w(complex)p 1598 4134 V 40 w(\015oat)g Ft(alpha)p FD(,)i(const)d(gsl)p 2506 4134 V 41 w(matrix)p 2812 4134 V 40 w(complex)p 3177 4134 V 41 w(\015oat)h(*)g Ft(A)p FD(,)565 4244 y(const)g(gsl)p 915 4244 V 41 w(matrix)p 1221 4244 V 40 w(complex)p 1586 4244 V 41 w(\015oat)g(*)g Ft(B)p FD(,)f(const)h(gsl)p 2361 4244 V 41 w(complex)p 2727 4244 V 41 w(\015oat)g Ft(beta)p FD(,)565 4354 y(gsl)p 677 4354 V 41 w(matrix)p 983 4354 V 40 w(complex)p 1348 4354 V 41 w(\015oat)g(*)g Ft(C)p Fu(\))3350 4463 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_zsyr2k)d Fu(\()p FD(CBLAS)p 1536 4463 V 40 w(UPLO)p 1834 4463 V 40 w(t)30 b Ft(Uplo)p FD(,)i(CBLAS)p 2510 4463 V 40 w(TRANSPOSE)p 3116 4463 V 38 w(t)565 4573 y Ft(Trans)p FD(,)g(const)f(gsl)p 1232 4573 V 41 w(complex)g Ft(alpha)p FD(,)h(const)f(gsl)p 2290 4573 V 40 w(matrix)p 2595 4573 V 41 w(complex)g(*)f Ft(A)p FD(,)h(const)565 4682 y(gsl)p 677 4682 V 41 w(matrix)p 983 4682 V 40 w(complex)g(*)g Ft(B)p FD(,)g(const)g(gsl)p 1907 4682 V 40 w(complex)g Ft(beta)p FD(,)h(gsl)p 2674 4682 V 41 w(matrix)p 2980 4682 V 40 w(complex)f(*)g Ft(C)p Fu(\))390 4792 y FK(These)c(functions)h(compute)g(a)g(rank-2k)g(up)s (date)e(of)i(the)g(symmetric)g(matrix)g FD(C)p FK(,)g FE(C)k FK(=)25 b FE(\013AB)3612 4759 y Fq(T)3679 4792 y FK(+)390 4902 y FE(\013B)5 b(A)590 4869 y Fq(T)655 4902 y FK(+)13 b FE(\014)5 b(C)33 b FK(when)26 b FD(T)-8 b(rans)30 b FK(is)c FH(CblasNoTrans)e FK(and)i FE(C)31 b FK(=)25 b FE(\013A)2561 4869 y Fq(T)2614 4902 y FE(B)18 b FK(+)13 b FE(\013B)2917 4869 y Fq(T)2968 4902 y FE(A)g FK(+)g FE(\014)5 b(C)33 b FK(when)26 b FD(T)-8 b(rans)390 5011 y FK(is)39 b FH(CblasTrans)p FK(.)63 b(Since)39 b(the)g(matrix)g FD(C)46 b FK(is)39 b(symmetric)g(only)g(its)g(upp)s (er)e(half)h(or)h(lo)m(w)m(er)h(half)390 5121 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 5230 y(of)c FD(C)37 b FK(are)29 b(used,)g(and)g(when)f FD(Uplo)34 b FK(is)29 b FH(CblasLower)e FK(then)i(the)g(lo)m(w)m(er)h (triangle)h(and)d(diagonal)j(of)390 5340 y FD(C)38 b FK(are)31 b(used.)p eop end %%Page: 131 147 TeXDict begin 131 146 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_cher2k)d Fu(\()p FD(CBLAS)p 1536 299 28 4 v 40 w(UPLO)p 1834 299 V 40 w(t)30 b Ft(Uplo)p FD(,)i(CBLAS)p 2510 299 V 40 w(TRANSPOSE)p 3116 299 V 38 w(t)565 408 y Ft(Trans)p FD(,)g(const)f(gsl)p 1232 408 V 41 w(complex)p 1598 408 V 40 w(\015oat)g Ft(alpha)p FD(,)i(const)d(gsl)p 2506 408 V 41 w(matrix)p 2812 408 V 40 w(complex)p 3177 408 V 41 w(\015oat)h(*)g Ft(A)p FD(,)565 518 y(const)g(gsl)p 915 518 V 41 w(matrix)p 1221 518 V 40 w(complex)p 1586 518 V 41 w(\015oat)g(*)g Ft(B)p FD(,)f(\015oat)h Ft(beta)p FD(,)h(gsl)p 2595 518 V 41 w(matrix)p 2901 518 V 40 w(complex)p 3266 518 V 41 w(\015oat)f(*)g Ft(C)p Fu(\))3350 628 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_blas_zher2k)d Fu(\()p FD(CBLAS)p 1536 628 V 40 w(UPLO)p 1834 628 V 40 w(t)30 b Ft(Uplo)p FD(,)i(CBLAS)p 2510 628 V 40 w(TRANSPOSE)p 3116 628 V 38 w(t)565 737 y Ft(Trans)p FD(,)g(const)f(gsl)p 1232 737 V 41 w(complex)g Ft(alpha)p FD(,)h(const)f(gsl)p 2290 737 V 40 w(matrix)p 2595 737 V 41 w(complex)g(*)f Ft(A)p FD(,)h(const)565 847 y(gsl)p 677 847 V 41 w(matrix)p 983 847 V 40 w(complex)g(*)g Ft(B)p FD(,)g(double)f Ft(beta)p FD(,)h(gsl)p 2226 847 V 41 w(matrix)p 2532 847 V 40 w(complex)g(*)g Ft(C)p Fu(\))390 956 y FK(These)e(functions)f(compute)i(a)f(rank-2k)h(up)s (date)e(of)h(the)g(hermitian)g(matrix)h FD(C)p FK(,)f FE(C)j FK(=)25 b FE(\013AB)3599 923 y Fq(H)3679 956 y FK(+)390 1066 y FE(\013)448 1033 y Fp(\003)487 1066 y FE(B)5 b(A)629 1033 y Fq(H)715 1066 y FK(+)24 b FE(\014)5 b(C)42 b FK(when)35 b FD(T)-8 b(rans)39 b FK(is)c FH(CblasNoTrans)e FK(and)i FE(C)41 b FK(=)34 b FE(\013A)2705 1033 y Fq(H)2768 1066 y FE(B)28 b FK(+)c FE(\013)3018 1033 y Fp(\003)3057 1066 y FE(B)3131 1033 y Fq(H)3193 1066 y FE(A)g FK(+)g FE(\014)5 b(C)42 b FK(when)390 1176 y FD(T)-8 b(rans)42 b FK(is)d FH(CblasConjTrans)p FK(.)63 b(Since)39 b(the)g(matrix)g FD(C)47 b FK(is)39 b(hermitian)g(only)g(its)g(upp)s(er)e(half)i(or)390 1285 y(lo)m(w)m(er)31 b(half)f(need)g(to)h(b)s(e)e(stored.)41 b(When)29 b FD(Uplo)35 b FK(is)30 b FH(CblasUpper)e FK(then)h(the)h (upp)s(er)e(triangle)k(and)390 1395 y(diagonal)38 b(of)e FD(C)44 b FK(are)37 b(used,)g(and)f(when)f FD(Uplo)42 b FK(is)36 b FH(CblasLower)e FK(then)i(the)g(lo)m(w)m(er)i(triangle)g (and)390 1504 y(diagonal)27 b(of)g FD(C)33 b FK(are)27 b(used.)39 b(The)25 b(imaginary)i(elemen)m(ts)h(of)e(the)g(diagonal)i (are)e(automatically)j(set)390 1614 y(to)i(zero.)150 1861 y FJ(13.2)68 b(Examples)150 2021 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 2130 y(tion)i FC(dgemm)p FK(,)783 2284 y Fs(\022)859 2348 y FK(0)p FE(:)p FK(11)93 b(0)p FE(:)p FK(12)f(0)p FE(:)p FK(13)859 2457 y(0)p FE(:)p FK(21)h(0)p FE(:)p FK(22)f(0)p FE(:)p FK(23)1541 2284 y Fs(\023)1617 2234 y(0)1617 2383 y(@)1705 2293 y FK(1011)h(1012)1705 2403 y(1021)g(1022)1705 2512 y(1031)g(1031)2175 2234 y Fs(1)2175 2383 y(A)2273 2403 y FK(=)2369 2284 y Fs(\022)2445 2348 y FK(367)p FE(:)p FK(76)g(368)p FE(:)p FK(12)2445 2457 y(674)p FE(:)p FK(06)g(674)p FE(:)p FK(72)3056 2284 y Fs(\023)150 2675 y FK(The)30 b(matrices)h(are)g(stored)g(in)f(ro)m(w)g(ma)5 b(jor)30 b(order,)h(according)g(to)g(the)g(C)f(con)m(v)m(en)m(tion)i (for)e(arra)m(ys.)390 2819 y FH(#include)46 b()390 2929 y(#include)g()390 3148 y(int)390 3258 y(main)h(\(void\))390 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(\(CblasNoTrans,)g(CblasNoTrans,)1249 5340 y(1.0,)j(&A.matrix,)e(&B.matrix,)p eop end %%Page: 132 148 TeXDict begin 132 147 bop 150 -116 a FK(Chapter)30 b(13:)41 b(BLAS)31 b(Supp)s(ort)2360 b(132)1249 299 y FH(0.0,)47 b(&C.matrix\);)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;)390 956 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)390 1335 y([)g(367.76,)f(368.12)485 1445 y(674.06,)g(674.72)g(])150 1677 y FJ(13.3)68 b(References)47 b(and)d(F)-11 b(urther)44 b(Reading)150 1836 y FK(Information)31 b(on)g(the)g FC(blas)f FK(standards,)h(including)g(b)s(oth)f(the)h (legacy)i(and)e(up)s(dated)f(in)m(terface)j(stan-)150 1946 y(dards,)c(is)i(a)m(v)-5 b(ailable)33 b(online)d(from)g(the)h FC(blas)e FK(Homepage)j(and)e FC(blas)f FK(T)-8 b(ec)m(hnical)32 b(F)-8 b(orum)30 b(w)m(eb-site.)330 2081 y FD(BLAS)g(Homepage)330 2190 y FH(http://www.netlib.org/bl)o(as/)330 2325 y FD(BLAS)g(T)-8 b(ec)m(hnical)32 b(F)-8 b(orum)330 2434 y FH(http://www.netlib.org/bl)o (as/b)o(last)o(-fo)o(rum/)150 2594 y FK(The)30 b(follo)m(wing)i(pap)s 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b(on)f(Mathematical)k(Soft)m(w)m(are)p FK(,)d(V)-8 b(ol.)31 b(16)f(\(1990\),)330 3655 y(P)m(ages)i(1{28.)150 3814 y(P)m(ostscript)j(v)m(ersions)g(of)g(the)f(latter)i(t)m(w)m(o)g (pap)s(ers)d(are)i(a)m(v)-5 b(ailable)37 b(from)d FH(http:)s(/)s(/)s (www)s(.)s(netlib)s(.)s(org)s(/)150 3924 y(blas/)p FK(.)39 b(A)31 b FC(cblas)e FK(wrapp)s(er)f(for)i(F)-8 b(ortran)31 b FC(blas)e FK(libraries)i(is)f(a)m(v)-5 b(ailable)33 b(from)d(the)h(same)f(lo)s(cation.)p eop end %%Page: 133 149 TeXDict begin 133 148 bop 150 -116 a FK(Chapter)30 b(14:)41 b(Linear)31 b(Algebra)2359 b(133)150 299 y FG(14)80 b(Linear)53 b(Algebra)150 659 y FK(This)41 b(c)m(hapter)i(describ)s(es)e(functions) h(for)g(solving)g(linear)h(systems.)75 b(The)42 b(library)g(pro)m (vides)g(linear)150 769 y(algebra)k(op)s(erations)e(whic)m(h)g(op)s (erate)i(directly)f(on)f(the)h FH(gsl_vector)c FK(and)j FH(gsl_matrix)e FK(ob)5 b(jects.)150 878 y(These)23 b(routines)g(use)g (the)g(standard)g(algorithms)h(from)f(Golub)g(&)g(V)-8 b(an)23 b(Loan's)h FD(Matrix)g(Computations)150 988 y FK(with)30 b(Lev)m(el-1)i(and)e(Lev)m(el-2)j(BLAS)d(calls)h(for)f (e\016ciency)-8 b(.)275 1165 y(The)29 b(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_linalg.h)p FK(.)150 1460 y FJ(14.1)68 b(LU)45 b(Decomp)t(osition)150 1619 y FK(A)32 b(general)h(square)e(matrix)i FE(A)f FK(has)f(an)h FE(LU)42 b FK(decomp)s(osition)32 b(in)m(to)h(upp)s(er)d(and)h(lo)m(w)m(er)i(triangular)f(ma-)150 1729 y(trices,)1753 1939 y FE(P)13 b(A)25 b FK(=)g FE(LU)150 2149 y FK(where)d FE(P)35 b FK(is)22 b(a)g(p)s(erm)m(utation)g(matrix,) i FE(L)e FK(is)g(unit)g(lo)m(w)m(er)h(triangular)g(matrix)f(and)f FE(U)32 b FK(is)23 b(upp)s(er)d(triangular)150 2258 y(matrix.)55 b(F)-8 b(or)35 b(square)g(matrices)h(this)f(decomp)s(osition)g(can)h(b) s(e)e(used)g(to)i(con)m(v)m(ert)g(the)f(linear)h(system)150 2368 y FE(Ax)25 b FK(=)g FE(b)f FK(in)m(to)g(a)g(pair)g(of)f (triangular)h(systems)g(\()p FE(Ly)k FK(=)d FE(P)13 b(b)p FK(,)25 b FE(U)10 b(x)25 b FK(=)g FE(y)s FK(\),)h(whic)m(h)d(can)h(b)s (e)f(solv)m(ed)h(b)m(y)f(forw)m(ard)150 2477 y(and)30 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 2746 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_LU_decomp)f Fu(\()p FD(gsl)p 1598 2746 28 4 v 41 w(matrix)30 b(*)h Ft(A)p FD(,)g(gsl)p 2224 2746 V 41 w(p)s(erm)m(utation)f(*)h Ft(p)p FD(,)g(in)m(t)g(*)565 2855 y Ft(signum)p Fu(\))3350 2965 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_complex_LU)q(_dec)q(omp)f Fu(\()p FD(gsl)p 2016 2965 V 41 w(matrix)p 2322 2965 V 40 w(complex)32 b(*)e Ft(A)p FD(,)565 3075 y(gsl)p 677 3075 V 41 w(p)s(erm)m(utation)g (*)h Ft(p)p FD(,)g(in)m(t)g(*)f Ft(signum)p Fu(\))390 3184 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 3294 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 3403 y(matrix)39 b FE(U)10 b FK(.)65 b(The)38 b(lo)m(w)m(er)i (triangular)f(part)f(of)h(the)g(input)f(matrix)g(\(excluding)i(the)e (diagonal\))390 3513 y(con)m(tains)32 b FE(L)p FK(.)40 b(The)30 b(diagonal)i(elemen)m(ts)f(of)g FE(L)f FK(are)h(unit)m(y)-8 b(,)31 b(and)f(are)g(not)h(stored.)390 3689 y(The)e(p)s(erm)m(utation)h (matrix)g FE(P)42 b FK(is)30 b(enco)s(ded)f(in)h(the)f(p)s(erm)m (utation)h FD(p)p FK(.)40 b(The)29 b FE(j)5 b FK(-th)31 b(column)e(of)h(the)390 3799 y(matrix)k FE(P)46 b FK(is)34 b(giv)m(en)g(b)m(y)g(the)g FE(k)s FK(-th)f(column)h(of)g(the)f(iden)m (tit)m(y)i(matrix,)g(where)e FE(k)h FK(=)c FE(p)3363 3813 y Fq(j)3431 3799 y FK(the)k FE(j)5 b FK(-th)390 3909 y(elemen)m(t)33 b(of)f(the)g(p)s(erm)m(utation)g(v)m(ector.)46 b(The)31 b(sign)h(of)f(the)h(p)s(erm)m(utation)g(is)g(giv)m(en)g(b)m(y) g FD(sign)m(um)p FK(.)390 4018 y(It)e(has)h(the)f(v)-5 b(alue)31 b(\()p FI(\000)p FK(1\))1228 3985 y Fq(n)1274 4018 y FK(,)g(where)f FE(n)f FK(is)i(the)f(n)m(um)m(b)s(er)f(of)i(in)m (terc)m(hanges)h(in)e(the)h(p)s(erm)m(utation.)390 4195 y(The)d(algorithm)h(used)f(in)g(the)h(decomp)s(osition)g(is)f(Gaussian) h(Elimination)g(with)f(partial)i(piv)m(ot-)390 4304 y(ing)h(\(Golub)f (&)g(V)-8 b(an)31 b(Loan,)g FD(Matrix)g(Computations)p FK(,)g(Algorithm)g(3.4.1\).)3350 4573 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_LU_solve)e Fu(\()p FD(const)32 b(gsl)p 1784 4573 V 40 w(matrix)f(*)g Ft(LU)p FD(,)g(const)565 4682 y(gsl)p 677 4682 V 41 w(p)s(erm)m(utation)f(*)h Ft(p)p FD(,)g(const)g(gsl)p 1766 4682 V 40 w(v)m(ector)h(*)f Ft(b)p FD(,)g(gsl)p 2369 4682 V 40 w(v)m(ector)h(*)f Ft(x)p Fu(\))3350 4792 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_complex_LU)q(_sol)q(ve)f Fu(\()p FD(const)31 b(gsl)p 2202 4792 V 41 w(matrix)p 2508 4792 V 40 w(complex)g(*)g Ft(LU)p FD(,)565 4902 y(const)g(gsl)p 915 4902 V 41 w(p)s(erm)m(utation)f(*)h Ft(p)p FD(,)g(const)g(gsl)p 2004 4902 V 40 w(v)m(ector)p 2285 4902 V 42 w(complex)g(*)g Ft(b)p FD(,)f(gsl)p 2972 4902 V 41 w(v)m(ector)p 3254 4902 V 42 w(complex)h(*)565 5011 y Ft(x)p Fu(\))390 5121 y FK(These)37 b(functions)f(solv)m(e)i(the)f(square)f(system)h FE(Ax)f FK(=)g FE(b)h FK(using)f(the)h FE(LU)47 b FK(decomp)s(osition) 37 b(of)g FE(A)390 5230 y FK(in)m(to)g(\()p FD(LU)p FK(,)i FD(p)s FK(\))d(giv)m(en)i(b)m(y)e FH(gsl_linalg_LU_decomp)31 b FK(or)37 b FH(gsl_linalg_complex_LU_d)o(ecom)o(p)390 5340 y FK(as)31 b(input.)p eop end %%Page: 134 150 TeXDict begin 134 149 bop 150 -116 a FK(Chapter)30 b(14:)41 b(Linear)31 b(Algebra)2359 b(134)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_LU_svx)e Fu(\()p FD(const)31 b(gsl)p 1679 299 28 4 v 41 w(matrix)f(*)h Ft(LU)p FD(,)g(const)g(gsl)p 2595 299 V 41 w(p)s(erm)m(utation)f(*)565 408 y Ft(p)p FD(,)h(gsl)p 785 408 V 41 w(v)m(ector)h(*)e Ft(x)p Fu(\))3350 518 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_complex_LU)q (_svx)f Fu(\()p FD(const)31 b(gsl)p 2097 518 V 41 w(matrix)p 2403 518 V 40 w(complex)h(*)e Ft(LU)p FD(,)565 628 y(const)h(gsl)p 915 628 V 41 w(p)s(erm)m(utation)f(*)h Ft(p)p FD(,)g(gsl)p 1766 628 V 40 w(v)m(ector)p 2047 628 V 42 w(complex)g(*)g Ft(x)p Fu(\))390 737 y FK(These)g(functions)g(solv)m(e)i(the)f(square)f (system)g FE(Ax)c FK(=)g FE(b)k FK(in-place)i(using)e(the)g (precomputed)g FE(LU)390 847 y FK(decomp)s(osition)37 b(of)g FE(A)g FK(in)m(to)h(\()p FD(LU)p FK(,)p FD(p)s FK(\).)60 b(On)36 b(input)g FD(x)43 b FK(should)36 b(con)m(tain)i(the)f (righ)m(t-hand)g(side)g FE(b)p FK(,)390 956 y(whic)m(h)30 b(is)h(replaced)f(b)m(y)h(the)f(solution)h(on)f(output.)3350 1149 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_LU_refine)f Fu(\()p FD(const)31 b(gsl)p 1836 1149 V 41 w(matrix)f(*)h Ft(A)p FD(,)g(const)g(gsl)p 2700 1149 V 40 w(matrix)g(*)565 1259 y Ft(LU)p FD(,)g(const)g(gsl)p 1075 1259 V 41 w(p)s(erm)m(utation) f(*)h Ft(p)p FD(,)g(const)g(gsl)p 2164 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w(v)m(ector)h(*)f Ft(x)p Fu(\))390 5213 y FK(This)22 b(function)g(solv)m(es)i(the)f(triangular)g(system)f FE(R)q(x)j FK(=)g FE(b)e FK(in-place.)39 b(On)22 b(input)f FD(x)29 b FK(should)22 b(con)m(tain)390 5322 y(the)31 b(righ)m(t-hand)f(side)g FE(b)p FK(,)h(whic)m(h)f(is)g(replaced)h(b)m (y)f(the)h(solution)g(on)f(output.)p eop end %%Page: 137 153 TeXDict begin 137 152 bop 150 -116 a FK(Chapter)30 b(14:)41 b(Linear)31 b(Algebra)2359 b(137)150 299 y FJ(14.3)68 b(QR)46 b(Decomp)t(osition)g(with)f(Column)g(Piv)l(oting)150 458 y FK(The)27 b FE(QR)h FK(decomp)s(osition)g(can)g(b)s(e)f(extended) g(to)h(the)g(rank)f(de\014cien)m(t)h(case)h(b)m(y)e(in)m(tro)s(ducing)g (a)h(column)150 568 y(p)s(erm)m(utation)i FE(P)13 b FK(,)1749 729 y FE(AP)38 b FK(=)25 b FE(QR)150 889 y FK(The)34 b(\014rst)g FE(r)j FK(columns)d(of)g FE(Q)h FK(form)f(an)g(orthonormal) h(basis)f(for)h(the)f(range)h(of)g FE(A)f FK(for)h(a)f(matrix)h(with) 150 999 y(column)e(rank)f FE(r)s FK(.)49 b(This)32 b(decomp)s(osition)i 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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 2806 y(length)c FD(N)40 b FK(used)30 b(for)g(column)g(piv)m(oting.)390 2933 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 3043 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 3206 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_QRPT_decom)q(p2) f Fu(\()p FD(const)31 b(gsl)p 1993 3206 V 40 w(matrix)g(*)g Ft(A)p FD(,)g(gsl)p 2619 3206 V 40 w(matrix)g(*)g Ft(q)p FD(,)565 3316 y(gsl)p 677 3316 V 41 w(matrix)f(*)h Ft(r)p FD(,)g(gsl)p 1303 3316 V 41 w(v)m(ector)h(*)e Ft(tau)p FD(,)i(gsl)p 2011 3316 V 40 w(p)s(erm)m(utation)f(*)g Ft(p)p FD(,)f(in)m(t)h(*)g Ft(signum)p FD(,)h(gsl)p 3445 3316 V 41 w(v)m(ector)565 3425 y(*)f Ft(norm)p Fu(\))390 3535 y FK(This)38 b(function)g(factorizes)j(the)e(matrix)g FD(A)g 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w(matrix)565 5121 y(*)g Ft(R)p FD(,)g(const)g(gsl)p 1099 5121 V 40 w(p)s(erm)m(utation)g(*)f Ft(p)p FD(,)h(const)g(gsl)p 2187 5121 V 41 w(v)m(ector)h(*)e Ft(b)p FD(,)h(gsl)p 2790 5121 V 41 w(v)m(ector)h(*)f Ft(x)p Fu(\))390 5230 y FK(This)g(function)g(solv)m(es)h(the)g(square)f(system)h FE(R)q(P)2104 5197 y Fq(T)2156 5230 y FE(x)27 b FK(=)g FE(Q)2405 5197 y Fq(T)2457 5230 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 5340 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(\()p FD(Q)p FK(,)h FD(R)p FK(\).)p eop end %%Page: 138 154 TeXDict begin 138 153 bop 150 -116 a FK(Chapter)30 b(14:)41 b(Linear)31 b(Algebra)2359 b(138)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_QRPT_updat)q(e)e Fu(\()p FD(gsl)p 1702 299 28 4 v 41 w(matrix)31 b(*)g Ft(Q)p FD(,)g(gsl)p 2329 299 V 40 w(matrix)g(*)g Ft(R)p FD(,)f(const)565 408 y(gsl)p 677 408 V 41 w(p)s(erm)m(utation)g(*)h Ft(p)p FD(,)g(gsl)p 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y(This)g(routine)g(uses)g(the)g(Golub-Reinsc)m(h)h(SVD)g (algorithm.)3350 733 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_SV_decomp_)q(mod)f Fu(\()p FD(gsl)p 1807 733 28 4 v 41 w(matrix)31 b(*)f Ft(A)p FD(,)h(gsl)p 2433 733 V 41 w(matrix)f(*)h Ft(X)p FD(,)565 842 y(gsl)p 677 842 V 41 w(matrix)f(*)h Ft(V)p FD(,)g(gsl)p 1303 842 V 41 w(v)m(ector)h(*)e Ft(S)p FD(,)h(gsl)p 1906 842 V 41 w(v)m(ector)h(*)e Ft(work)p Fu(\))390 952 y FK(This)d(function)g (computes)g(the)h(SVD)f(using)g(the)h(mo)s(di\014ed)e(Golub-Reinsc)m(h) i(algorithm,)h(whic)m(h)390 1061 y(is)e(faster)g(for)g FE(M)36 b FI(\035)25 b FE(N)10 b FK(.)39 b(It)27 b(requires)g(the)g(v)m (ector)i FD(w)m(ork)j FK(of)27 b(length)h FD(N)37 b FK(and)26 b(the)h FE(N)10 b FK(-b)m(y-)p FE(N)38 b FK(matrix)390 1171 y FD(X)i FK(as)30 b(additional)h(w)m(orking)g(space.)3350 1359 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_SV_decomp_)q (jaco)q(bi)f Fu(\()p FD(gsl)p 1964 1359 V 41 w(matrix)30 b(*)h Ft(A)p FD(,)g(gsl)p 2590 1359 V 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y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_SV_leverag)q(e)e Fu(\()p FD(const)32 b(gsl)p 1941 3103 V 40 w(matrix)f(*)g Ft(U)p FD(,)f(gsl)p 2566 3103 V 41 w(v)m(ector)i(*)f Ft(h)p Fu(\))390 3213 y FK(This)44 b(function)g(computes)g(the)h(statistical)i(lev)m(erage)g (v)-5 b(alues)45 b FE(h)2700 3227 y Fq(i)2772 3213 y FK(of)g(a)f(matrix)h FE(A)g FK(using)f(its)390 3323 y(singular)35 b(v)-5 b(alue)35 b(decomp)s(osition)g(\()p FD(U)p FK(,)i FD(S)p FK(,)e FD(V)12 b FK(\))35 b(previously)g(computed)f(with)h FH(gsl_linalg_SV_)390 3432 y(decomp)p FK(.)48 b FE(h)803 3446 y Fq(i)864 3432 y FK(are)34 b(the)f(diagonal)i(v)-5 b(alues)33 b(of)h(the)f(matrix)h FE(A)p FK(\()p FE(A)2554 3399 y Fq(T)2607 3432 y FE(A)p FK(\))2710 3399 y Fp(\000)p FB(1)2800 3432 y FE(A)2868 3399 y Fq(T)2953 3432 y FK(and)f(dep)s(end)f (only)h(on)390 3542 y(the)e(matrix)f FD(U)41 b FK(whic)m(h)30 b(is)g(the)h(input)e(to)i(this)f(function.)150 3777 y FJ(14.5)68 b(Cholesky)46 b(Decomp)t(osition)150 3936 y FK(A)22 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(e)f(solv)m(ed)h(b)m(y)f(forw)m(ard)g(and)g(bac)m(k-substitution.)3350 4902 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_cholesky_d)q (ecom)q(p)f Fu(\()p FD(gsl)p 1912 4902 V 40 w(matrix)31 b(*)g Ft(A)p Fu(\))3350 5011 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_complex_ch)q(oles)q(ky_)q(dec)q(omp)f Fu(\()p FD(gsl)p 2330 5011 V 41 w(matrix)p 2636 5011 V 40 w(complex)31 b(*)g Ft(A)p Fu(\))390 5121 y FK(These)36 b(functions)g(factorize)j(the)e(symmetric,)i(p)s(ositiv)m(e-de\014nite) e(square)g(matrix)g FD(A)f FK(in)m(to)i(the)390 5230 y(Cholesky)g(decomp)s(osition)h FE(A)g FK(=)f FE(LL)1734 5197 y Fq(T)1824 5230 y FK(\(or)h FE(A)f FK(=)g FE(LL)2318 5197 y Fp(y)2391 5230 y FK(for)g(the)g(complex)h(case\).)66 b(On)38 b(input,)390 5340 y(the)30 b(v)-5 b(alues)29 b(from)g(the)h(diagonal)g(and)f(lo)m(w)m(er-triangular)j(part)d(of)g (the)h(matrix)g FD(A)f FK(are)h(used)e(\(the)p eop end %%Page: 140 156 TeXDict begin 140 155 bop 150 -116 a FK(Chapter)30 b(14:)41 b(Linear)31 b(Algebra)2359 b(140)390 299 y(upp)s(er)21 b(triangular)j(part)f(is)g(ignored\).)39 b(On)23 b(output)g(the)g (diagonal)i(and)d(lo)m(w)m(er)j(triangular)f(part)f(of)390 408 y(the)j(input)e(matrix)i FD(A)g FK(con)m(tain)h(the)e(matrix)h FE(L)p FK(,)h(while)e(the)h(upp)s(er)d(triangular)j(part)g(of)f(the)h (input)390 518 y(matrix)f(is)g(o)m(v)m(erwritten)h(with)e FE(L)1506 485 y Fq(T)1583 518 y FK(\(the)i(diagonal)g(terms)e(b)s(eing) h(iden)m(tical)h(for)f(b)s(oth)f FE(L)g FK(and)g FE(L)3637 485 y Fq(T)3689 518 y FK(\).)390 628 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)390 737 y(error)30 b(co)s(de)h FH(GSL_EDOM)p FK(.)390 884 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)390 994 y(a)m(v)m(oid)h(triggering)g(an)e(error.)3350 1203 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_cholesky_s)q (olve)f Fu(\()p FD(const)31 b(gsl)p 2097 1203 28 4 v 41 w(matrix)g(*)g Ft(cholesky)p FD(,)i(const)565 1312 y(gsl)p 677 1312 V 41 w(v)m(ector)f(*)e Ft(b)p FD(,)h(gsl)p 1280 1312 V 41 w(v)m(ector)h(*)f Ft(x)p Fu(\))3350 1422 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_complex_ch)q(oles) q(ky_)q(sol)q(ve)f Fu(\()p FD(const)31 b(gsl)p 2516 1422 V 40 w(matrix)p 2821 1422 V 41 w(complex)565 1531 y(*)g Ft(cholesky)p FD(,)i(const)e(gsl)p 1465 1531 V 40 w(v)m(ector)p 1746 1531 V 42 w(complex)g(*)g Ft(b)p FD(,)g(gsl)p 2434 1531 V 40 w(v)m(ector)p 2715 1531 V 42 w(complex)g(*)g Ft(x)p Fu(\))390 1641 y FK(These)c(functions)g(solv)m(e)h(the)g(system) f FE(Ax)e FK(=)g FE(b)j FK(using)e(the)i(Cholesky)f(decomp)s(osition)h (of)f FE(A)g FK(held)390 1751 y(in)32 b(the)g(matrix)g FD(c)m(holesky)41 b FK(whic)m(h)32 b(m)m(ust)f(ha)m(v)m(e)j(b)s(een)d (previously)g(computed)h(b)m(y)g FH(gsl_linalg_)390 1860 y(cholesky_decomp)26 b FK(or)31 b FH(gsl_linalg_complex_chol)o(esk)o (y_de)o(comp)o FK(.)3350 2069 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_cholesky_s)q(vx)f Fu(\()p FD(const)31 b(gsl)p 1993 2069 V 40 w(matrix)g(*)g Ft(cholesky)p FD(,)565 2179 y(gsl)p 677 2179 V 41 w(v)m(ector)h(*)e Ft(x)p Fu(\))3350 2288 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_complex_ch)q (oles)q(ky_)q(svx)f Fu(\()p FD(const)31 b(gsl)p 2411 2288 V 41 w(matrix)p 2717 2288 V 40 w(complex)g(*)565 2398 y Ft(cholesky)p FD(,)i(gsl)p 1151 2398 V 41 w(v)m(ector)p 1433 2398 V 41 w(complex)e(*)g Ft(x)p Fu(\))390 2508 y FK(These)h(functions)f(solv)m(e)j(the)e(system)g FE(Ax)d FK(=)e FE(b)32 b FK(in-place)h(using)f(the)g(Cholesky)g(decomp)s (osition)390 2617 y(of)27 b FE(A)g FK(held)g(in)f(the)i(matrix)f FD(c)m(holesky)36 b FK(whic)m(h)27 b(m)m(ust)f(ha)m(v)m(e)j(b)s(een)d (previously)g(computed)h(b)m(y)g FH(gsl_)390 2727 y (linalg_cholesky_decomp)i FK(or)35 b FH(gsl_linalg_complex_chol)o(esky) o(_dec)o(omp)o FK(.)49 b(On)34 b(input)g FD(x)390 2836 y FK(should)29 b(con)m(tain)j(the)f(righ)m(t-hand)f(side)g FE(b)p 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w(v)m(ector)i(*)f Ft(tau_U)p FD(,)565 3173 y(gsl)p 677 3173 V 41 w(v)m(ector)h(*)e Ft(tau_V)p FD(,)i(gsl)p 1489 3173 V 41 w(matrix)f(*)g Ft(V)p Fu(\))390 3282 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 3392 y(bidiag_decomp)p FK(,)d(\()p FD(A)p FK(,)33 b FD(tau)p 1365 3392 V 40 w(U)p FK(,)f FD(tau)p 1661 3392 V 41 w(V)12 b FK(\))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 3502 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 3611 y(in)30 b FD(A)p FK(.)3350 3814 y([F)-8 b(unction])-3599 b Fv(int)53 b (gsl_linalg_bidiag_unp)q(ack_)q(B)f Fu(\()p FD(const)31 b(gsl)p 2150 3814 V 40 w(matrix)g(*)g Ft(A)p FD(,)g(gsl)p 2776 3814 V 40 w(v)m(ector)h(*)565 3923 y Ft(diag)p FD(,)g(gsl)p 942 3923 V 40 w(v)m(ector)g(*)f Ft(superdiag)p Fu(\))390 4033 y 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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 1683 y FD(A)p FK(.)3350 1861 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_householde)q (r_mh)f Fu(\()p FD(double)31 b Ft(tau)p FD(,)g(const)g(gsl)p 2603 1861 V 40 w(v)m(ector)h(*)f Ft(v)p FD(,)565 1970 y(gsl)p 677 1970 V 41 w(matrix)f(*)h Ft(A)p Fu(\))3350 2080 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(\()p FD(gsl)p 2278 2080 V 41 w(complex)31 b Ft(tau)p FD(,)g(const)565 2190 y(gsl)p 677 2190 V 41 w(v)m(ector)p 959 2190 V 41 w(complex)g(*)g Ft(v)p FD(,)g(gsl)p 1646 2190 V 41 w(matrix)p 1952 2190 V 40 w(complex)g(*)g Ft(A)p Fu(\))390 2299 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 2409 y(v)m(ector)d FD(v)41 b FK(to)34 b(the)f(righ)m(t-hand)g(side)g 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FK(is)d(stored)h(in)f FD(w)p FK(.)150 3473 y FJ(14.12)69 b(Householder)45 b(solv)l(er)h(for)f(linear)h (systems)3350 3678 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_HH_solve)e Fu(\()p FD(gsl)p 1545 3678 V 41 w(matrix)31 b(*)g Ft(A)p FD(,)g(const)g(gsl)p 2410 3678 V 40 w(v)m(ector)h(*)f Ft(b)p FD(,)565 3788 y(gsl)p 677 3788 V 41 w(v)m(ector)h(*)e Ft(x)p Fu(\))390 3897 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 4007 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 4116 y(b)m(y)30 b(the)h(Householder)f(transformations.)3350 4295 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_HH_svx)e Fu(\()p FD(gsl)p 1441 4295 V 41 w(matrix)30 b(*)h Ft(A)p FD(,)g(gsl)p 2067 4295 V 41 w(v)m(ector)h(*)e Ft(x)p Fu(\))390 4404 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 4514 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 4623 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 4852 y FJ(14.13)69 b(T)-11 b(ridiagonal)45 b(Systems)150 5011 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 5121 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 5230 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 5340 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(.)p eop end %%Page: 145 161 TeXDict begin 145 160 bop 150 -116 a FK(Chapter)30 b(14:)41 b(Linear)31 b(Algebra)2359 b(145)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_solve_trid)q(iag)f Fu(\()p FD(const)31 b(gsl)p 2045 299 28 4 v 41 w(v)m(ector)h(*)e Ft(diag)p FD(,)i(const)565 408 y(gsl)p 677 408 V 41 w(v)m(ector)g(*)e Ft(e)p FD(,)h(const)g(gsl)p 1518 408 V 41 w(v)m(ector)h(*)e Ft(f)p FD(,)h(const)g(gsl)p 2359 408 V 41 w(v)m(ector)h(*)f Ft(b)p FD(,)f(gsl)p 2962 408 V 41 w(v)m(ector)i(*)f Ft(x)p Fu(\))390 518 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(\()p FE(N)35 b FI(\025)390 628 y FK(2\).)40 b(The)25 b(sup)s(er-diagonal)h (and)f(sub-diagonal)h(v)m(ectors)h FD(e)k FK(and)25 b FD(f)43 b FK(m)m(ust)26 b(b)s(e)f(one)h(elemen)m(t)h(shorter)390 737 y(than)j(the)h(diagonal)g(v)m(ector)h FD(diag)p FK(.)42 b(The)29 b(form)h(of)h FD(A)f 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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 1759 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)390 1868 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 2195 y FE(A)25 b FK(=)1651 1976 y Fs(0)1651 2122 y(B)1651 2172 y(B)1651 2225 y(@)1739 2031 y FE(d)1786 2045 y FB(0)1917 2031 y FE(e)1959 2045 y FB(0)2110 2031 y FK(0)130 b(0)1742 2140 y FE(e)1784 2154 y FB(0)1915 2140 y FE(d)1962 2154 y FB(1)2093 2140 y FE(e)2135 2154 y FB(1)2285 2140 y FK(0)1759 2250 y(0)113 b FE(e)1959 2264 y FB(1)2090 2250 y FE(d)2137 2264 y FB(2)2268 2250 y FE(e)2310 2264 y FB(2)1759 2359 y FK(0)130 b(0)114 b FE(e)2135 2373 y FB(2)2266 2359 y FE(d)2313 2373 y FB(3)2365 1976 y Fs(1)2365 2122 y(C)2365 2172 y(C)2365 2225 y(A)3350 2561 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_linalg_solve_cyc_)q(trid)q(iag)f Fu(\()p FD(const)31 b(gsl)p 2254 2561 V 41 w(v)m(ector)h(*)f Ft(diag)p FD(,)g(const)565 2671 y(gsl)p 677 2671 V 41 w(v)m(ector)h(*)e Ft(e)p FD(,)h(const)g(gsl)p 1518 2671 V 41 w(v)m(ector)h(*)e Ft(f)p FD(,)h(const)g(gsl)p 2359 2671 V 41 w(v)m(ector)h(*)f Ft(b)p FD(,)f(gsl)p 2962 2671 V 41 w(v)m(ector)i(*)f Ft(x)p Fu(\))390 2780 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 2890 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 2999 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 3109 y(case)d(is)g(sho)m(wn)f(b)s(elo)m(w,)1462 3436 y FE(A)25 b FK(=)1651 3217 y Fs(0)1651 3363 y(B)1651 3413 y(B)1651 3466 y(@)1739 3271 y FE(d)1786 3285 y FB(0)1917 3271 y FE(e)1959 3285 y FB(0)2110 3271 y FK(0)112 b FE(f)2312 3285 y FB(3)1741 3381 y FE(f)1786 3395 y FB(0)1915 3381 y FE(d)1962 3395 y FB(1)2093 3381 y FE(e)2135 3395 y FB(1)2285 3381 y FK(0)1759 3490 y(0)g FE(f)1961 3504 y FB(1)2090 3490 y FE(d)2137 3504 y FB(2)2268 3490 y FE(e)2310 3504 y FB(2)1742 3600 y FE(e)1784 3614 y FB(3)1934 3600 y FK(0)h FE(f)2137 3614 y FB(2)2266 3600 y FE(d)2313 3614 y FB(3)2365 3217 y Fs(1)2365 3363 y(C)2365 3413 y(C)2365 3466 y(A)3350 3802 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(\()p FD(const)31 b(gsl)p 2516 3802 V 40 w(v)m(ector)h(*)f Ft(diag)p FD(,)565 3911 y(const)g(gsl)p 915 3911 V 41 w(v)m(ector)h(*)e Ft(e)p FD(,)h(const)g(gsl)p 1756 3911 V 41 w(v)m(ector)h(*)e Ft(b)p FD(,)h(gsl)p 2359 3911 V 41 w(v)m(ector)h(*)f Ft(x)p Fu(\))390 4021 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 4130 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 4240 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 4350 y(b)s(elo)m(w,)1462 4676 y FE(A)25 b FK(=)1651 4458 y Fs(0)1651 4604 y(B)1651 4654 y(B)1651 4707 y(@)1739 4512 y FE(d)1786 4526 y FB(0)1917 4512 y FE(e)1959 4526 y FB(0)2110 4512 y FK(0)113 b FE(e)2310 4526 y FB(3)1742 4621 y FE(e)1784 4635 y FB(0)1915 4621 y FE(d)1962 4635 y FB(1)2093 4621 y FE(e)2135 4635 y FB(1)2285 4621 y FK(0)1759 4731 y(0)g FE(e)1959 4745 y FB(1)2090 4731 y FE(d)2137 4745 y FB(2)2268 4731 y FE(e)2310 4745 y FB(2)1742 4841 y FE(e)1784 4855 y FB(3)1934 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b(gsl_eigen_nonsymm_params)e Fu(\()p FD(const)31 b(in)m(t)g Ft(compute_t)p FD(,)j(const)d(in)m(t)565 1761 y Ft(balance)p FD(,)i(gsl)p 1099 1761 V 40 w(eigen)p 1340 1761 V 41 w(nonsymm)p 1764 1761 V 39 w(w)m(orkspace)e(*)g Ft(w)p Fu(\))390 1871 y FK(This)i(function)h(sets)g(some)h(parameters)f (whic)m(h)g(determine)g(ho)m(w)g(the)g(eigen)m(v)-5 b(alue)36 b(problem)e(is)390 1980 y(solv)m(ed)d(in)f(subsequen)m(t)g(calls)h(to)h FH(gsl_eigen_nonsymm)p FK(.)390 2120 y(If)42 b FD(compute)p 837 2120 V 40 w(t)j FK(is)d(set)g(to)h(1,)j(the)d(full)e(Sc)m(h)m(ur)h (form)g FE(T)55 b FK(will)42 b(b)s(e)g(computed)g(b)m(y)g FH(gsl_eigen_)390 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 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(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: 152 168 TeXDict begin 152 167 bop 150 -116 a FK(Chapter)30 b(15:)41 b(Eigensystems)2424 b(152)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: 153 169 TeXDict begin 153 168 bop 150 -116 a FK(Chapter)30 b(15:)41 b(Eigensystems)2424 b(153)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: 154 170 TeXDict begin 154 169 bop 150 -116 a FK(Chapter)30 b(15:)41 b(Eigensystems)2424 b(154)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 FK(This)h(function)g(computes)h(the)g(eigen)m (v)-5 b(alues)35 b(and)d(eigen)m(v)m(ectors)k(of)d(the)g(complex)g (generalized)390 3426 y(hermitian-de\014nite)d(matrix)h(pair)e(\()p FD(A)p FK(,)i FD(B)5 b FK(\),)31 b(and)f(stores)g(them)g(in)g FD(ev)-5 b(al)34 b FK(and)c FD(ev)m(ec)37 b FK(resp)s(ectiv)m(ely)-8 b(.)390 3535 y(The)36 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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 3185 y FK(This)i(function)h (sets)g(some)h(parameters)f(whic)m(h)g(determine)g(ho)m(w)g(the)g (eigen)m(v)-5 b(alue)36 b(problem)e(is)390 3295 y(solv)m(ed)d(in)f (subsequen)m(t)g(calls)h(to)h FH(gsl_eigen_gen)p FK(.)390 3436 y(If)f FD(compute)p 826 3436 V 40 w(s)k FK(is)c(set)h(to)g(1,)g 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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 FK(This)k(function)h(computes)g(eigen)m(v)-5 b(alues)36 b(and)e(righ)m(t)i(eigen)m(v)m(ectors)i(of)d(the)g FD(n)p FK(-b)m(y-)p FD(n)f FK(real)h(gener-)390 2796 y(alized)c(nonsymmetric)f (matrix)g(pair)g(\()p FD(A)p FK(,)g FD(B)5 b FK(\).)42 b(The)29 b(eigen)m(v)-5 b(alues)32 b(are)e(stored)g(in)g(\()p FD(alpha)p FK(,)g FD(b)s(eta)p FK(\))390 2906 y(and)42 b(the)g(eigen)m(v)m(ectors)j(are)e(stored)f(in)g FD(ev)m(ec)p FK(.)78 b(It)42 b(\014rst)g(calls)h FH(gsl_eigen_gen)c FK(to)k(compute)390 3015 y(the)c(eigen)m(v)-5 b(alues,)43 b(Sc)m(h)m(ur)38 b(forms,)i(and)f(Sc)m(h)m(ur)f(v)m(ectors.)67 b(Then)38 b(it)h(\014nds)e(eigen)m(v)m(ectors)42 b(of)d(the)390 3125 y(Sc)m(h)m(ur)f(forms)f(and)h(bac)m(ktransforms)g(them)g(using)g (the)h(Sc)m(h)m(ur)e(v)m(ectors.)66 b(The)38 b(Sc)m(h)m(ur)f(v)m (ectors)390 3235 y(are)g(destro)m(y)m(ed)i(in)d(the)i(pro)s(cess,)g (but)f(can)g(b)s(e)f(sa)m(v)m(ed)j(b)m(y)e(using)f FH (gsl_eigen_genv_QZ)p FK(.)56 b(The)390 3344 y(computed)36 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: 157 173 TeXDict begin 157 172 bop 150 -116 a FK(Chapter)30 b(15:)41 b(Eigensystems)2424 b(157)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: 158 174 TeXDict begin 158 173 bop 150 -116 a FK(Chapter)30 b(15:)41 b(Eigensystems)2424 b(158)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: 159 175 TeXDict begin 159 174 bop 150 -116 a FK(Chapter)30 b(15:)41 b(Eigensystems)2424 b(159)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 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%%Page: 160 176 TeXDict begin 160 175 bop 150 -116 a FK(Chapter)30 b(15:)41 b(Eigensystems)2424 b(160)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: 161 177 TeXDict begin 161 176 bop 150 -116 a FK(Chapter)30 b(15:)41 b(Eigensystems)2424 b(161)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 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b(ourier)34 b(T)-8 b(ransforms)32 b(are)i(e\016cien)m(t)h(algorithms)g(for)e(calculating)j(the)e (discrete)g(F)-8 b(ourier)34 b(trans-)150 1927 y(form)c(\(DFT\),)1424 2172 y FE(x)1476 2186 y Fq(j)1536 2172 y FK(=)1632 2066 y Fq(n)p Fp(\000)p FB(1)1635 2091 y Fs(X)1634 2270 y Fq(k)q FB(=0)1773 2172 y FE(z)1815 2186 y Fq(k)1871 2172 y FK(exp\()p FI(\000)p FK(2)p FE(\031)s(ij)5 b(k)s(=n)p FK(\))275 2440 y(The)29 b(DFT)i(usually)f(arises)g(as)h(an)f(appro)m (ximation)h(to)g(the)f(con)m(tin)m(uous)h(F)-8 b(ourier)30 b(transform)g(when)150 2550 y(functions)36 b(are)h(sampled)f(at)i (discrete)f(in)m(terv)-5 b(als)37 b(in)g(space)g(or)f(time.)60 b(The)36 b(naiv)m(e)i(ev)-5 b(aluation)38 b(of)f(the)150 2659 y(discrete)f(F)-8 b(ourier)35 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 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b(in)m(v)m(erse)g(and)f(bac)m(kw)m (ards,)150 3455 y(based)j(on)h(the)f(same)h(mathematical)i (de\014nitions.)52 b(The)34 b(de\014nition)h(of)f(the)h FD(forw)m(ard)f(F)-8 b(ourier)35 b(trans-)150 3564 y(form)p FK(,)30 b FE(x)25 b FK(=)g(FFT)q(\()p FE(z)t FK(\),)31 b(is,)1424 3809 y FE(x)1476 3823 y Fq(j)1536 3809 y FK(=)1632 3704 y Fq(n)p Fp(\000)p FB(1)1635 3729 y Fs(X)1634 3907 y Fq(k)q FB(=0)1773 3809 y FE(z)1815 3823 y Fq(k)1871 3809 y FK(exp\()p FI(\000)p FK(2)p FE(\031)s(ij)5 b(k)s(=n)p FK(\))150 4054 y(and)30 b(the)g(de\014nition)g(of)h(the)f FD(in)m(v)m(erse)i(F)-8 b(ourier)31 b(transform)p FK(,)f FE(x)25 b FK(=)g(IFFT\()p FE(z)t FK(\),)31 b(is,)1402 4299 y FE(z)1444 4313 y Fq(j)1504 4299 y FK(=)1615 4238 y(1)p 1610 4278 55 4 v 1610 4362 a FE(n)1690 4194 y Fq(n)p Fp(\000)p FB(1)1693 4219 y Fs(X)1692 4397 y Fq(k)q FB(=0)1831 4299 y FE(x)1883 4313 y Fq(k)1939 4299 y FK(exp\(2)p FE(\031)s(ij)5 b(k)s(=n)p FK(\))p FE(:)150 4544 y FK(The)40 b(factor)h(of)f(1)p FE(=n)g 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y(uses)f(the)g(opp)s(osite)h(con)m (v)m(en)m(tion,)i(a)e(p)s(ositiv)m(e)g(exp)s(onen)m(tial)g(in)f(the)h (forw)m(ard)f(transform.)p eop end %%Page: 164 180 TeXDict begin 164 179 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(164)275 299 y(The)37 b FD(bac)m(kw)m(ards)i(FFT)45 b FK(is)38 b(simply)g(our)g(terminology)i(for)e(an)g(unscaled)g(v)m (ersion)h(of)g(the)f(in)m(v)m(erse)150 408 y(FFT,)1302 644 y FE(z)1348 606 y Fq(back)q(w)r(ar)r(ds)1344 666 y(j)1693 644 y FK(=)1789 538 y Fq(n)p Fp(\000)p FB(1)1792 563 y Fs(X)1792 741 y Fq(k)q FB(=0)1930 644 y FE(x)1982 658 y Fq(k)2038 644 y FK(exp\(2)p FE(\031)s(ij)5 b(k)s(=n)p FK(\))p FE(:)150 879 y FK(When)32 b(the)h(o)m(v)m(erall)i(scale)f(of)f (the)g(result)f(is)h(unimp)s(ortan)m(t)f(it)h(is)g(often)g(con)m(v)m (enien)m(t)h(to)g(use)e(the)h(bac)m(k-)150 988 y(w)m(ards)d(FFT)h (instead)f(of)h(the)f(in)m(v)m(erse)i(to)f(sa)m(v)m(e)h(unnecessary)d (divisions.)150 1218 y FJ(16.2)68 b(Ov)l(erview)47 b(of)e(complex)g (data)h(FFTs)150 1378 y FK(The)33 b(inputs)f(and)g(outputs)h(for)g(the) h(complex)f(FFT)h(routines)f(are)h FD(pac)m(k)m(ed)g(arra)m(ys)j FK(of)d(\015oating)g(p)s(oin)m(t)150 1487 y(n)m(um)m(b)s(ers.)j(In)23 b(a)g(pac)m(k)m(ed)i(arra)m(y)f(the)f(real)h(and)f(imaginary)h(parts)f (of)h(eac)m(h)h(complex)f(n)m(um)m(b)s(er)e(are)h(placed)150 1597 y(in)32 b(alternate)j(neigh)m(b)s(oring)d(elemen)m(ts.)49 b(F)-8 b(or)33 b(example,)h(the)f(follo)m(wing)h(de\014nition)e(of)h(a) g(pac)m(k)m(ed)g(arra)m(y)150 1707 y(of)e(length)f(6,)390 1840 y FH(double)46 b(x[3*2];)390 1949 y(gsl_complex_packed_array)41 b(data)47 b(=)g(x;)150 2083 y FK(can)31 b(b)s(e)e(used)h(to)h(hold)f (an)g(arra)m(y)h(of)g(three)f(complex)h(n)m(um)m(b)s(ers,)f FH(z[3])p FK(,)f(in)h(the)h(follo)m(wing)h(w)m(a)m(y)-8 b(,)390 2216 y FH(data[0])46 b(=)h(Re\(z[0]\))390 2325 y(data[1])f(=)h(Im\(z[0]\))390 2435 y(data[2])f(=)h(Re\(z[1]\))390 2545 y(data[3])f(=)h(Im\(z[1]\))390 2654 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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 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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: 170 186 TeXDict begin 170 185 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(170)390 299 y(algorithm.)41 b(There)27 b(is)h(no)f(restriction)i(on)f(the)g(length)g FD(n)p FK(.)39 b(E\016cien)m(t)29 b(mo)s(dules)e(are)h(pro)m(vided)f(for)390 408 y(subtransforms)e(of)j(length)f(2,)i(3,)f(4,)h(5,)f(6)g(and)f(7.)40 b(An)m(y)27 b(remaining)g(factors)i(are)e(computed)g(with)390 518 y(a)k(slo)m(w,)g FE(O)s FK(\()p FE(n)853 485 y FB(2)890 518 y FK(\),)g(general-)p FE(n)g FK(mo)s(dule.)41 b(The)30 b(caller)h(m)m(ust)g(supply)e(a)h FD(w)m(a)m(v)m(etable)39 b FK(con)m(taining)32 b(the)390 628 y(trigonometric)d(lo)s(okup)f (tables)g(and)f(a)h(w)m(orkspace)h FD(w)m(ork)p FK(.)39 b(F)-8 b(or)29 b(the)f FH(transform)d FK(v)m(ersion)j(of)g(the)390 737 y(function)i(the)h FD(sign)f FK(argumen)m(t)h(can)f(b)s(e)g(either) h FH(forward)d FK(\()p FI(\000)p FK(1\))k(or)e FH(backward)e FK(\(+1\).)390 871 y(The)d(functions)g(return)f(a)i(v)-5 b(alue)26 b(of)f FH(0)g FK(if)h(no)f(errors)g(w)m(ere)g(detected.)41 b(The)25 b(follo)m(wing)h FH(gsl_errno)390 981 y FK(conditions)31 b(are)g(de\014ned)e(for)h(these)h(functions:)390 1139 y FH(GSL_EDOM)96 b FK(The)30 b(length)h(of)f(the)h(data)g FD(n)f FK(is)g(not)h(a)f(p)s(ositiv)m(e)i(in)m(teger)g(\(i.e.)41 b FD(n)30 b FK(is)h(zero\).)390 1297 y FH(GSL_EINVAL)870 1407 y FK(The)46 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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: 171 187 TeXDict begin 171 186 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(171)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 y(printf)g(\("\\n"\);)485 956 y(wavetable)f(=)h(gsl_fft_complex_wavetable)o(_all)o(oc)41 b(\(n\);)485 1066 y(workspace)46 b(=)h(gsl_fft_complex_workspace)o (_all)o(oc)41 b(\(n\);)485 1285 y(for)47 b(\(i)h(=)f(0;)g(i)h(<)f (wavetable->nf;)d(i++\))581 1395 y({)724 1504 y(printf)i(\("#)h(factor) f(\045d:)95 b(\045d\\n",)46 b(i,)1106 1614 y(wavetable->factor[i]\);) 581 1724 y(})485 1943 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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: 173 189 TeXDict begin 173 188 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(173)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 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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: 174 190 TeXDict begin 174 189 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(174)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 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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: 175 191 TeXDict begin 175 190 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(175)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 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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: 176 192 TeXDict begin 176 191 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(176)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: 177 193 TeXDict begin 177 192 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)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 b(generates)h(a)e(real)i(signal)f(in)f(the)h(shap)s(e)f(of)h(a) f(square)h(pulse.)39 b(The)28 b(pulse)150 2995 y(is)f(F)-8 b(ourier)27 b(transformed)g(to)g(frequency)g(space,)h(and)e(all)i(but)e (the)h(lo)m(w)m(est)i(ten)e(frequency)g(comp)s(onen)m(ts)150 3104 y(are)k(remo)m(v)m(ed)g(from)f(the)h(arra)m(y)f(of)h(F)-8 b(ourier)31 b(co)s(e\016cien)m(ts)h(returned)d(b)m(y)h FH(gsl_fft_real_transform)p FK(.)275 3236 y(The)j(remaining)i(F)-8 b(ourier)35 b(co)s(e\016cien)m(ts)h(are)f(transformed)f(bac)m(k)h(to)g (the)g(time-domain,)h(to)g(giv)m(e)g(a)150 3345 y(\014ltered)41 b(v)m(ersion)g(of)g(the)g(square)g(pulse.)71 b(Since)41 b(F)-8 b(ourier)42 b(co)s(e\016cien)m(ts)g(are)f(stored)g(using)g(the)g (half-)150 3455 y(complex)26 b(symmetry)f(b)s(oth)g(p)s(ositiv)m(e)h (and)f(negativ)m(e)j(frequencies)d(are)h(remo)m(v)m(ed)g(and)f(the)h (\014nal)f(\014ltered)150 3565 y(signal)31 b(is)f(also)i(real.)390 3696 y FH(#include)46 b()390 3806 y(#include)g()390 3915 y(#include)g()390 4025 y(#include)g ()390 4134 y(#include)g()390 4354 y(int)390 4463 y(main)h(\(void\))390 4573 y({)485 4682 y(int)g(i,)h(n)f(=)g(100;)485 4792 y(double)g(data[n];)485 5011 y(gsl_fft_real_wavetable)42 b(*)48 b(real;)485 5121 y(gsl_fft_halfcomplex_waveta)o(ble)41 b(*)48 b(hc;)485 5230 y(gsl_fft_real_workspace)42 b(*)48 b(work;)p eop end %%Page: 178 194 TeXDict begin 178 193 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(178)485 299 y FH(for)47 b(\(i)h(=)f(0;)g(i)h(<)f(n;)g (i++\))581 408 y({)676 518 y(data[i])f(=)i(0.0;)581 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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: 182 198 TeXDict begin 182 197 bop 150 -116 a FK(Chapter)30 b(17:)41 b(Numerical)31 b(In)m(tegration)2079 b(182)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 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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 b(the)h(Cheb)m(yshev)f (appro)m(ximation.)48 b(The)32 b(mo)s(di\014ed)g(Clensha)m(w-Curtis)g (rules)g(used)g(in)g FC(quadp)-6 b(a)n(ck)150 4046 y FK(separate)31 b(out)g(sev)m(eral)h(common)e(w)m(eigh)m(t)i(functions)e (whic)m(h)g(cause)h(slo)m(w)g(con)m(v)m(ergence.)275 4225 y(These)24 b(w)m(eigh)m(t)i(functions)f(are)g(in)m(tegrated)i (analytically)g(against)f(the)f(Cheb)m(yshev)f(p)s(olynomials)h(to)150 4334 y(precompute)35 b FD(mo)s(di\014ed)g(Cheb)m(yshev)g(momen)m(ts)p 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b(In)m(tegration)2079 b(183)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: 184 200 TeXDict begin 184 199 bop 150 -116 a FK(Chapter)30 b(17:)41 b(Numerical)31 b(In)m(tegration)2079 b(184)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: 185 201 TeXDict begin 185 200 bop 150 -116 a FK(Chapter)30 b(17:)41 b(Numerical)31 b(In)m(tegration)2079 b(185)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: 186 202 TeXDict begin 186 201 bop 150 -116 a FK(Chapter)30 b(17:)41 b(Numerical)31 b(In)m(tegration)2079 b(186)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: 187 203 TeXDict begin 187 202 bop 150 -116 a FK(Chapter)30 b(17:)41 b(Numerical)31 b(In)m(tegration)2079 b(187)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: 188 204 TeXDict begin 188 203 bop 150 -116 a FK(Chapter)30 b(17:)41 b(Numerical)31 b(In)m(tegration)2079 b(188)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: 189 205 TeXDict begin 189 204 bop 150 -116 a FK(Chapter)30 b(17:)41 b(Numerical)31 b(In)m(tegration)2079 b(189)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 Fm(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 Fm(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: 191 207 TeXDict begin 191 206 bop 150 -116 a FK(Chapter)30 b(17:)41 b(Numerical)31 b(In)m(tegration)2079 b(191)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: 192 208 TeXDict begin 192 207 bop 150 -116 a FK(Chapter)30 b(17:)41 b(Numerical)31 b(In)m(tegration)2079 b(192)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(\("intervals)d(=)95 b(\045d\\n",)47 b(w->size\);)485 737 y(gsl_integration_workspace_)o (free)41 b(\(w\);)485 956 y(return)47 b(0;)390 1066 y(})150 1200 y FK(The)30 b(results)g(b)s(elo)m(w)h(sho)m(w)f(that)h(the)f (desired)g(accuracy)i(is)e(ac)m(hiev)m(ed)i(after)f(8)g(sub)s (divisions.)390 1335 y FH($)47 b(./a.out)390 1445 y(result)476 b(=)47 b(-3.999999999999973799)390 1554 y(exact)f(result)190 b(=)47 b(-4.000000000000000000)390 1664 y(estimated)e(error)i(=)95 b(0.000000000000246025)390 1773 y(actual)46 b(error)190 b(=)95 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b(suc)m(h)g(as)g(the)h(Gaussian,)g(log-normal)g(or)g(P)m(oisson)g (distributions.)275 1375 y(These)f(functions)g(are)g(declared)h(in)f (the)h(header)f(\014le)g FH(gsl_rng.h)p FK(.)150 1626 y FJ(18.1)68 b(General)46 b(commen)l(ts)g(on)f(random)f(n)l(um)l(b)t (ers)150 1786 y FK(In)34 b(1988,)k(P)m(ark)d(and)f(Miller)i(wrote)f(a)g (pap)s(er)f(en)m(titled)i(\\Random)e(n)m(um)m(b)s(er)g(generators:)50 b(go)s(o)s(d)35 b(ones)150 1895 y(are)h(hard)f(to)i(\014nd.")57 b([Comm)m(un.)35 b(A)m(CM,)i(31,)h(1192{1201].)62 b(F)-8 b(ortunately)g(,)40 b(some)c(excellen)m(t)j(random)150 2005 y(n)m(um)m(b)s(er)k(generators)i(are)g(a)m(v)-5 b(ailable,)50 b(though)44 b(p)s(o)s(or)f(ones)h(are)h(still)g(in)f (common)g(use.)82 b(Y)-8 b(ou)44 b(ma)m(y)150 2115 y(b)s(e)33 b(happ)m(y)g(with)g(the)h(system-supplied)f(random)f(n)m(um)m(b)s(er)h (generator)h(on)g(y)m(our)f(computer,)i(but)e(y)m(ou)150 2224 y(should)d(b)s(e)h(a)m(w)m(are)i(that)f(as)f(computers)g(get)i 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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 (obtain)h(\(they)f(require)f(real)i(math!\),)h(but)d(one)h(prefers)150 3614 y(a)d(random)f(n)m(um)m(b)s(er)f(generator)j(with)e(a)h(long)g(p)s (erio)s(d,)f(lo)m(w)h(serial)h(correlation,)h(and)d(a)h(tendency)f Fm(not)150 3724 y FK(to)i(\\fall)f(mainly)g(on)g(the)g(planes.")46 b(Statistical)34 b(tests)e(are)h(p)s(erformed)d(with)h(n)m(umerical)i (sim)m(ulations.)150 3833 y(Generally)-8 b(,)45 b(a)c(random)e(n)m(um)m 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FH(gsl_rng_type)37 b FK(whic)m(h)150 408 y(holds)43 b(static)i(information)f(ab)s(out)g (eac)m(h)h(t)m(yp)s(e)e(of)h(generator)h(and)e FH(gsl_rng)f FK(whic)m(h)h(describ)s(es)g(an)150 518 y(instance)31 b(of)g(a)f(generator)i(created)f(from)f(a)h(giv)m(en)g FH(gsl_rng_type)p FK(.)275 670 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_rng.h)p FK(.)150 930 y FJ(18.3)68 b(Random)46 b(n)l(um)l(b)t(er)e(generator)j(initialization)3350 1157 y FK([F)-8 b(unction])-3599 b Fv(gsl_rng)54 b(*)f(gsl_rng_alloc)c Fu(\()p FD(const)32 b(gsl)p 1784 1157 28 4 v 40 w(rng)p 1956 1157 V 40 w(t)m(yp)s(e)e(*)h Ft(T)p Fu(\))390 1266 y FK(This)43 b(function)g(returns)g(a)h(p)s(oin)m(ter)g(to)g(a)g (newly-created)h(instance)f(of)g(a)g(random)f(n)m(um)m(b)s(er)390 1376 y(generator)i(of)f(t)m(yp)s(e)g FD(T)p FK(.)82 b(F)-8 b(or)44 b(example,)49 b(the)44 b(follo)m(wing)h(co)s(de)g(creates)g(an) f(instance)h(of)f(the)390 1485 y(T)-8 b(ausw)m(orthe)31 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b(unction])-3599 b Fv(void)54 b(gsl_rng_set)48 b Fu(\()p FD(const)32 b(gsl)p 1418 2753 V 40 w(rng)e(*)h Ft(r)p FD(,)g(unsigned)e(long)i(in)m(t)g Ft(s)p Fu(\))390 2863 y FK(This)i(function)g(initializes)j(\(or)e (`seeds'\))h(the)f(random)e(n)m(um)m(b)s(er)h(generator.)52 b(If)33 b(the)h(generator)390 2972 y(is)d(seeded)g(with)f(the)h(same)g (v)-5 b(alue)31 b(of)g FD(s)j FK(on)d(t)m(w)m(o)h(di\013eren)m(t)f (runs,)f(the)h(same)g(stream)g(of)g(random)390 3082 y(n)m(um)m(b)s(ers) 44 b(will)h(b)s(e)f(generated)i(b)m(y)f(successiv)m(e)h(calls)g(to)g (the)f(routines)g(b)s(elo)m(w.)85 b(If)44 b(di\013eren)m(t)390 3191 y(v)-5 b(alues)33 b(of)g FD(s)g FI(\025)c FK(1)k(are)h(supplied,)e (then)h(the)g(generated)g(streams)g(of)g(random)g(n)m(um)m(b)s(ers)e (should)390 3301 y(b)s(e)d(completely)i(di\013eren)m(t.)41 b(If)28 b(the)h(seed)g FD(s)j FK(is)d(zero)h(then)e(the)h(standard)f (seed)h(from)f(the)h(original)390 3410 y(implemen)m(tation)e(is)f(used) f(instead.)40 b(F)-8 b(or)27 b(example,)g(the)f(original)h(F)-8 b(ortran)27 b(source)f(co)s(de)g(for)g(the)390 3520 y FH(ranlux)21 b FK(generator)i(used)f(a)h(seed)g(of)f(314159265,)29 b(and)22 b(so)g(c)m(ho)s(osing)i FD(s)i FK(equal)d(to)g(zero)g(repro)s (duces)390 3630 y(this)30 b(when)g(using)g FH(gsl_rng_ranlux)p FK(.)390 3782 y(When)g(using)g(m)m(ultiple)h(seeds)f(with)g(the)h(same) f(generator,)i(c)m(ho)s(ose)g(seed)e(v)-5 b(alues)31 b(greater)g(than)390 3892 y(zero)g(to)g(a)m(v)m(oid)h(collisions)g (with)e(the)h(default)f(setting.)390 4044 y(Note)44 b(that)f(the)g (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(213.)p eop end %%Page: 195 211 TeXDict begin 195 210 bop 150 -116 a FK(Chapter)30 b(18:)41 b(Random)30 b(Num)m(b)s(er)g(Generation)1798 b(195)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: 196 212 TeXDict begin 196 211 bop 150 -116 a FK(Chapter)30 b(18:)41 b(Random)30 b(Num)m(b)s(er)g(Generation)1798 b(196)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: 197 213 TeXDict begin 197 212 bop 150 -116 a FK(Chapter)30 b(18:)41 b(Random)30 b(Num)m(b)s(er)g(Generation)1798 b(197)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: 198 214 TeXDict begin 198 213 bop 150 -116 a FK(Chapter)30 b(18:)41 b(Random)30 b(Num)m(b)s(er)g(Generation)1798 b(198)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: 199 215 TeXDict begin 199 214 bop 150 -116 a FK(Chapter)30 b(18:)41 b(Random)30 b(Num)m(b)s(er)g(Generation)1798 b(199)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: 200 216 TeXDict begin 200 215 bop 150 -116 a FK(Chapter)30 b(18:)41 b(Random)30 b(Num)m(b)s(er)g(Generation)1798 b(200)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: 201 217 TeXDict begin 201 216 bop 150 -116 a FK(Chapter)30 b(18:)41 b(Random)30 b(Num)m(b)s(er)g(Generation)1798 b(201)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: 202 218 TeXDict begin 202 217 bop 150 -116 a FK(Chapter)30 b(18:)41 b(Random)30 b(Num)m(b)s(er)g(Generation)1798 b(202)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: 203 219 TeXDict begin 203 218 bop 150 -116 a FK(Chapter)30 b(18:)41 b(Random)30 b(Num)m(b)s(er)g(Generation)1798 b(203)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: 204 220 TeXDict begin 204 219 bop 150 -116 a FK(Chapter)30 b(18:)41 b(Random)30 b(Num)m(b)s(er)g(Generation)1798 b(204)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: 205 221 TeXDict begin 205 220 bop 150 -116 a FK(Chapter)30 b(18:)41 b(Random)30 b(Num)m(b)s(er)g(Generation)1798 b(205)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: 206 222 TeXDict begin 206 221 bop 150 -116 a FK(Chapter)30 b(18:)41 b(Random)30 b(Num)m(b)s(er)g(Generation)1798 b(206)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: 207 223 TeXDict begin 207 222 bop 150 -116 a FK(Chapter)30 b(18:)41 b(Random)30 b(Num)m(b)s(er)g(Generation)1798 b(207)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(GSL_RNG_TYPE=mrg)390 4573 y(GSL_RNG_SEED=123)390 4682 y(0.33050)390 4792 y(0.86631)390 4902 y(0.32982)390 5011 y(0.67620)390 5121 y(0.53391)390 5230 y(0.06457)390 5340 y(0.16847)p eop end %%Page: 208 224 TeXDict begin 208 223 bop 150 -116 a FK(Chapter)30 b(18:)41 b(Random)30 b(Num)m(b)s(er)g(Generation)1798 b(208)390 299 y FH(0.70229)390 408 y(0.04371)390 518 y(0.86374)150 751 y FJ(18.14)69 b(References)46 b(and)e(F)-11 b(urther)45 b(Reading)150 910 y FK(The)35 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b(ailable)40 b(under)150 3489 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 3598 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: 209 225 TeXDict begin 209 224 bop 150 -116 a FK(Chapter)30 b(19:)41 b(Quasi-Random)30 b(Sequences)1934 b(209)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: 210 226 TeXDict begin 210 225 bop 150 -116 a FK(Chapter)30 b(19:)41 b(Quasi-Random)30 b(Sequences)1934 b(210)150 166 y FJ(19.4)68 b(Sa)l(ving)46 b(and)e(resorting)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: 211 227 TeXDict begin 211 226 bop 150 -116 a FK(Chapter)30 b(19:)41 b(Quasi-Random)30 b(Sequences)1934 b(211)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 /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 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 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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 3034 3998 Pls 4182 554 Pls 1886 2850 Pls 2460 1128 Pls 4756 3424 Pls 3608 2276 Pls 1312 4572 Pls 1025 841 Pls 3321 3137 Pls 4469 1989 Pls 2173 4285 Pls 1599 2563 Pls 3895 4859 Pls 2747 1415 Pls 451 3711 Pls 442 1423 Pls 2738 3719 Pls 3886 2571 Pls 1590 4867 Pls 2164 1997 Pls 4460 4293 Pls 3312 849 Pls 1016 3145 Pls 1303 2284 Pls 3599 4580 Pls 4747 1136 Pls 2451 3432 Pls 1877 562 Pls 4173 2858 Pls 3025 1710 Pls 729 4006 Pls 873 1567 Pls 3169 3863 Pls 4317 419 Pls 2021 2715 Pls 2595 993 Pls 4891 3289 Pls 3743 2141 Pls 1447 4437 Pls 1160 706 Pls 3456 3002 Pls 4604 1854 Pls 2308 4150 Pls 1734 2428 Pls 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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 y FK(The)36 b(implemen)m(tations)i(of)e(the)h(quasi-random)f(sequence)g(routines)h (are)f(based)g(on)h(the)f(algorithms)150 5340 y(describ)s(ed)29 b(in)h(the)h(follo)m(wing)h(pap)s(er,)p eop end %%Page: 212 228 TeXDict begin 212 227 bop 150 -116 a FK(Chapter)30 b(19:)41 b(Quasi-Random)30 b(Sequences)1934 b(212)330 299 y(P)-8 b(.)41 b(Bratley)g(and)f(B.L.)g(F)-8 b(o)m(x)42 b(and)e(H.)g (Niederreiter,)k(\\Algorithm)d(738:)61 b(Programs)41 b(to)f(Gener-)330 408 y(ate)g(Niederreiter's)h(Lo)m(w-discrepancy)e (Sequences",)j FD(A)m(CM)e(T)-8 b(ransactions)40 b(on)f(Mathematical) 330 518 y(Soft)m(w)m(are)p FK(,)32 b(V)-8 b(ol.)32 b(20,)f(No.)g(4,)g (Decem)m(b)s(er,)h(1994,)g(p.)e(494{495.)p eop end %%Page: 213 229 TeXDict begin 213 228 bop 150 -116 a FK(Chapter)30 b(20:)41 b(Random)30 b(Num)m(b)s(er)g(Distributions)1717 b(213)150 299 y FG(20)80 b(Random)54 b(Num)l(b)t(er)g(Distributions)150 543 y FK(This)27 b(c)m(hapter)i(describ)s(es)f(functions)g(for)g (generating)h(random)f(v)-5 b(ariates)29 b(and)f(computing)g(their)h (prob-)150 653 y(abilit)m(y)36 b(distributions.)54 b(Samples)35 b(from)g(the)g(distributions)f(describ)s(ed)g(in)h(this)f(c)m(hapter)i (can)f(b)s(e)g(ob-)150 762 y(tained)f(using)g(an)m(y)g(of)g(the)h (random)e(n)m(um)m(b)s(er)f(generators)j(in)f(the)g(library)g(as)g(an)g (underlying)f(source)150 872 y(of)e(randomness.)275 1010 y(In)h(the)i(simplest)g(cases)g(a)g(non-uniform)e(distribution)h(can)h (b)s(e)f(obtained)h(analytically)i(from)d(the)150 1119 y(uniform)h(distribution)i(of)f(a)h(random)f(n)m(um)m(b)s(er)g 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g(of)g(parameters)g(\(where)f(there)h(is)g(a)g(negligible)h(probabilit) m(y)f(of)g(a)150 2848 y(v)-5 b(ariate)32 b(exceeding)f(this)g(limit\))g (to)g(prev)m(en)m(t)g(incorrect)h(results)e(due)f(to)j(o)m(v)m(er\015o) m(w.)150 3085 y FJ(20.1)68 b(In)l(tro)t(duction)150 3245 y FK(Con)m(tin)m(uous)43 b(random)f(n)m(um)m(b)s(er)g(distributions)g (are)i(de\014ned)e(b)m(y)h(a)g(probabilit)m(y)h(densit)m(y)f(function,) 150 3354 y FE(p)p FK(\()p FE(x)p FK(\),)30 b(suc)m(h)f(that)h(the)f (probabilit)m(y)h(of)f FE(x)g FK(o)s(ccurring)g(in)g(the)g (in\014nitesimal)g(range)h FE(x)f FK(to)h FE(x)18 b FK(+)f FE(dx)29 b FK(is)h FE(p)15 b(dx)p FK(.)275 3492 y(The)29 b(cum)m(ulativ)m(e)k(distribution)c(function)h(for)g(the)h(lo)m(w)m(er) h(tail)f FE(P)13 b FK(\()p FE(x)p FK(\))31 b(is)g(de\014ned)e(b)m(y)h (the)h(in)m(tegral,)1544 3705 y FE(P)13 b FK(\()p FE(x)p FK(\))26 b(=)1859 3590 y Fs(Z)1942 3610 y Fq(x)1905 3779 y Fp(\0001)2042 3705 y FE(dx)2141 3667 y Fp(0)2165 3705 y FE(p)p FK(\()p FE(x)2298 3667 y Fp(0)2321 3705 y FK(\))150 3919 y(and)k(giv)m(es)h(the)g(probabilit)m(y)g(of)f(a)h(v)-5 b(ariate)32 b(taking)f(a)g(v)-5 b(alue)31 b(less)g(than)f FE(x)p FK(.)275 4057 y(The)f(cum)m(ulativ)m(e)k(distribution)c (function)h(for)g(the)h(upp)s(er)d(tail)k FE(Q)p FK(\()p FE(x)p FK(\))f(is)f(de\014ned)f(b)m(y)i(the)f(in)m(tegral,)1525 4281 y FE(Q)p FK(\()p FE(x)p FK(\))c(=)1841 4166 y Fs(Z)1924 4186 y FB(+)p Fp(1)1887 4354 y Fq(x)2060 4281 y FE(dx)2159 4243 y Fp(0)2183 4281 y FE(p)p FK(\()p FE(x)2316 4243 y Fp(0)2339 4281 y FK(\))150 4488 y(and)k(giv)m(es)h(the)g(probabilit)m (y)g(of)f(a)h(v)-5 b(ariate)32 b(taking)f(a)g(v)-5 b(alue)31 b(greater)h(than)e FE(x)p FK(.)275 4626 y(The)h(upp)s(er)e(and)i(lo)m (w)m(er)i(cum)m(ulativ)m(e)g(distribution)e(functions)g(are)h(related)g (b)m(y)g FE(P)13 b FK(\()p FE(x)p FK(\))21 b(+)g FE(Q)p FK(\()p FE(x)p FK(\))28 b(=)f(1)150 4736 y(and)j(satisfy)h(0)25 b FI(\024)g FE(P)13 b FK(\()p FE(x)p FK(\))26 b FI(\024)f FK(1,)31 b(0)26 b FI(\024)f FE(Q)p 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TeXDict begin 224 239 bop 150 -116 a FK(Chapter)30 b(20:)41 b(Random)30 b(Num)m(b)s(er)g(Distributions)1717 b(224)150 299 y FJ(20.9)68 b(The)45 b(Ra)l(yleigh)i(Distribution)3350 508 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_ran_rayleigh)c Fu(\()p FD(const)32 b(gsl)p 1784 508 28 4 v 40 w(rng)e(*)h Ft(r)p FD(,)g(double)f Ft(sigma)p Fu(\))390 618 y FK(This)42 b(function)g(returns)g(a)h(random)f(v)-5 b(ariate)44 b(from)e(the)h(Ra)m(yleigh)h(distribution)e(with)h(scale)390 727 y(parameter)31 b FD(sigma)p FK(.)41 b(The)30 b(distribution)g(is,) 1330 913 y FE(p)p FK(\()p FE(x)p FK(\))p FE(dx)c FK(=)1749 851 y FE(x)p 1729 892 93 4 v 1729 975 a(\033)1784 949 y FB(2)1847 913 y FK(exp\()p FI(\000)p FE(x)2144 875 y FB(2)2181 913 y FE(=)p FK(\(2)p FE(\033)2361 875 y FB(2)2400 913 y FK(\)\))p FE(dx)390 1106 y FK(for)k FE(x)25 b(>)g FK(0.)3350 1290 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_ran_rayleigh_pdf)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(double)f Ft(sigma)p Fu(\))390 1399 y 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V 20 -5 V 19 -4 V 20 -4 V 19 -5 V 20 -4 V 19 -5 V 19 -4 V 20 -4 V 19 -5 V 20 -4 V 19 -4 V 20 -4 V 19 -4 V 19 -5 V 20 -4 V 19 -4 V 20 -4 V 19 -4 V 20 -4 V 19 -4 V 19 -4 V 20 -4 V 19 -4 V 20 -4 V 19 -3 V 20 -4 V 19 -4 V 19 -4 V 20 -4 V 19 -3 V 20 -4 V 19 -4 V 20 -3 V 19 -4 V 19 -4 V 20 -3 V 19 -4 V 20 -3 V 19 -4 V 20 -3 V 19 -4 V 19 -3 V 20 -3 V 19 -4 V 20 -3 V 19 -4 V 20 -3 V 19 -3 V 19 -3 V 20 -4 V 19 -3 V 20 -3 V 19 -3 V 20 -4 V 19 -3 V 19 -3 V 20 -3 V 19 -3 V 20 -3 V 19 -3 V 20 -3 V 19 -3 V 19 -3 V 20 -3 V 19 -3 V 20 -3 V 19 -3 V 20 -3 V 19 -3 V 19 -3 V 20 -2 V 19 -3 V 20 -3 V 19 -3 V 20 -2 V 19 -3 V 19 -3 V 20 -3 V 19 -2 V 20 -3 V 19 -3 V 20 -2 V 19 -3 V stroke LT1 LTb LT1 6077 4581 M 543 0 V 1051 631 M 19 38 V 20 39 V 19 38 V 20 39 V 19 38 V 20 38 V 19 39 V 19 38 V 20 38 V 19 38 V 20 38 V 19 38 V 20 37 V 19 38 V 19 37 V 20 37 V 19 38 V 20 36 V 19 37 V 20 37 V 19 36 V 19 36 V 20 36 V 19 36 V 20 35 V 19 35 V 20 35 V 19 35 V 19 34 V 20 34 V 19 34 V 20 34 V 19 33 V 20 33 V 19 33 V 19 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20 9 V 19 9 V 19 9 V 20 10 V 19 9 V 20 9 V 19 9 V 20 10 V 19 9 V 19 10 V 20 9 V 19 10 V 20 9 V 19 10 V 20 10 V 19 9 V 19 10 V 20 10 V 19 10 V 20 10 V 19 10 V 20 10 V 19 10 V 19 10 V 20 10 V 19 10 V 20 10 V 19 10 V 20 10 V 19 10 V 19 11 V 20 10 V 19 10 V 20 10 V 19 11 V 20 10 V 19 10 V 19 11 V 20 10 V 19 10 V 20 11 V 19 10 V 20 10 V 19 11 V 19 10 V 20 10 V 19 11 V 20 10 V 19 10 V 19 11 V 20 10 V 19 10 V 20 11 V 19 10 V 20 10 V 19 10 V 19 11 V 20 10 V 19 10 V 20 10 V 19 10 V 20 10 V 19 10 V 19 10 V 20 10 V 19 10 V 20 10 V 19 10 V 20 10 V 19 10 V 19 9 V 20 10 V 19 10 V 20 9 V 19 10 V 20 9 V 19 10 V 19 9 V 20 9 V 19 10 V 20 9 V 19 9 V 20 9 V 19 9 V 19 9 V 20 9 V 19 8 V 20 9 V 19 9 V 20 8 V 19 9 V 19 8 V 20 8 V 19 9 V 20 8 V 19 8 V 20 8 V 19 7 V 19 8 V 20 8 V 19 7 V 20 8 V 19 7 V 20 7 V 5092 2122 L 19 7 V 20 7 V 19 6 V 20 7 V 19 7 V 20 6 V 19 7 V 19 6 V 20 6 V 19 6 V 20 6 V 19 6 V 20 5 V 19 6 V 19 5 V 20 6 V 19 5 V 20 5 V 19 5 V 20 5 V 19 4 V 19 5 V 20 4 V 19 5 V 20 4 V 19 4 V 20 4 V 19 3 V 19 4 V 20 3 V 19 4 V 20 3 V 19 3 V 20 3 V 19 2 V 19 3 V 20 2 V 19 3 V 20 2 V 19 2 V 20 2 V 19 2 V 19 1 V 20 2 V 19 1 V 20 1 V 19 1 V 20 1 V 19 1 V 19 0 V 20 1 V 19 0 V 20 0 V 19 0 V 20 0 V 19 -1 V 19 0 V 20 -1 V 19 -1 V 20 -1 V 19 -1 V 20 -1 V 19 -1 V 19 -2 V 20 -1 V 19 -2 V 20 -2 V 19 -2 V 20 -3 V 19 -2 V 19 -3 V 20 -2 V 19 -3 V 20 -3 V 19 -3 V 20 -3 V 19 -4 V 19 -3 V 20 -4 V 19 -4 V 20 -4 V 19 -4 V 20 -4 V 19 -4 V 19 -5 V 20 -4 V 19 -5 V 20 -5 V 19 -5 V 20 -5 V 19 -5 V stroke 0.500 UL LTb 1051 4944 M 0 -4313 V 5809 0 V 0 4313 V -5809 0 V 1.000 UP stroke grestore end showpage @endspecial 2471 2227 a FE(a)26 b FK(=)f(2)p FE(;)15 b(b)26 b FK(=)f(3)2471 2143 y FE(a)h FK(=)f(1)p FE(;)15 b(b)26 b FK(=)f(2)2471 2060 y FE(a)h FK(=)f(1)p FE(;)15 b(b)26 b FK(=)f(1)1689 1867 y(W)-8 b(eibull)31 b(Distribution)2072 4010 y FE(x)533 2868 y gsave currentpoint currentpoint translate 270 rotate neg exch neg exch translate 533 2868 a 449 2891 a FE(p)p FK(\()p FE(x)p FK(\))533 2868 y currentpoint 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b(distribution)f(with)g(scale)i FD(a)e FK(and)g(exp)s(onen) m(t)h FD(b)p FK(.)p eop end %%Page: 243 259 TeXDict begin 243 258 bop 150 -116 a FK(Chapter)30 b(20:)41 b(Random)30 b(Num)m(b)s(er)g(Distributions)1717 b(243)150 299 y FJ(20.25)69 b(The)44 b(T)l(yp)t(e-1)h(Gum)l(b)t(el)f (Distribution)3350 508 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_ran_gumbel1)c Fu(\()p FD(const)31 b(gsl)p 1731 508 28 4 v 41 w(rng)f(*)h Ft(r)p FD(,)f(double)g Ft(a)p FD(,)h(double)f Ft(b)p Fu(\))390 618 y FK(This)k(function)h (returns)e(a)i(random)g(v)-5 b(ariate)36 b(from)e(the)h(T)m(yp)s(e-1)g (Gum)m(b)s(el)g(distribution.)53 b(The)390 727 y(T)m(yp)s(e-1)31 b(Gum)m(b)s(el)f(distribution)f(function)h(is,)1157 895 y FE(p)p FK(\()p FE(x)p FK(\))p FE(dx)25 b FK(=)g FE(ab)15 b FK(exp\()p FI(\000)p FK(\()p FE(b)g FK(exp)q(\()p FI(\000)p FE(ax)p FK(\))21 b(+)f FE(ax)p FK(\)\))p FE(dx)390 1063 y FK(for)30 b FI(\0001)25 b FE(<)g(x)g(<)g FI(1)p FK(.)3350 1247 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_ran_gumbel1_pdf)d Fu(\()p FD(double)31 b Ft(x)p FD(,)f(double)g Ft(a)p FD(,)h(double)f Ft(b)p Fu(\))390 1357 y FK(This)j(function)h(computes)h (the)f(probabilit)m(y)h(densit)m(y)g FE(p)p FK(\()p FE(x)p FK(\))f(at)h FD(x)41 b FK(for)34 b(a)h(T)m(yp)s(e-1)f(Gum)m(b)s(el)g (dis-)390 1466 y(tribution)c(with)g(parameters)h FD(a)g FK(and)e FD(b)p FK(,)h(using)g(the)h(form)m(ula)f(giv)m(en)i(ab)s(o)m (v)m(e.)450 3962 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-gumbel1.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 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y(A)25 b(m)m(uc)m(h)h(b)s(etter)g(approac)m(h) g(is)g(due)f(to)i(Alastair)g(J.)f(W)-8 b(alk)m(er)28 b(\(An)d(e\016cien)m(t)j(metho)s(d)d(for)h(generating)150 2588 y(discrete)e(random)f(v)-5 b(ariables)24 b(with)f(general)h (distributions,)g(A)m(CM)g(T)-8 b(rans)23 b(on)h(Mathematical)i(Soft)m (w)m(are)150 2698 y(3,)40 b(253{256)i(\(1977\);)i(see)39 b(also)f(Kn)m(uth,)i(v2,)g(3rd)d(ed,)j(p120{121,139\).)68 b(This)38 b(requires)f(t)m(w)m(o)i(lo)s(okup)150 2808 y(tables,)g(one)f(\015oating)f(p)s(oin)m(t)g(and)f(one)i(in)m(teger,)i (but)c(b)s(oth)g(only)h(of)g(size)h FE(K)7 b FK(.)59 b(After)37 b(prepro)s(cessing,)150 2917 y(the)42 b(random)g(n)m(um)m(b) s(ers)f(are)i(generated)g(in)f(O\(1\))h(time,)j(ev)m(en)d(for)f(large)i FE(K)7 b FK(.)76 b(The)42 b(prepro)s(cessing)150 3027 y(suggested)i(b)m(y)e(W)-8 b(alk)m(er)45 b(requires)d FE(O)s FK(\()p FE(K)1577 2994 y FB(2)1615 3027 y FK(\))h(e\013ort,)k (but)42 b(that)h(is)g(not)g(actually)i(necessary)-8 b(,)47 b(and)42 b(the)150 3136 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y([F)-8 b(unction])-3599 b Fv(gsl_ran_discrete_t)58 b(*)52 b(gsl_ran_discrete_prep)q(roc)g Fu(\()p FD(size)p 2731 4037 28 4 v 41 w(t)31 b Ft(K)p FD(,)g(const)565 4147 y(double)f(*)h Ft(P)p Fu(\))390 4256 y FK(This)g(function)g(returns)f(a)i(p)s(oin)m(ter)f(to)i(a)f (structure)f(that)h(con)m(tains)g(the)g(lo)s(okup)f(table)h(for)g(the) 390 4366 y(discrete)38 b(random)e(n)m(um)m(b)s(er)f(generator.)62 b(The)36 b(arra)m(y)i FD(P)5 b FK([])37 b(con)m(tains)h(the)f (probabilities)h(of)f(the)390 4475 y(discrete)f(ev)m(en)m(ts;)k(these)d (arra)m(y)f(elemen)m(ts)h(m)m(ust)e(all)i(b)s(e)e(p)s(ositiv)m(e,)j (but)d(they)h(needn't)g(add)f(up)390 4585 y(to)28 b(one)g(\(so)g(y)m (ou)g(can)g(think)f(of)g(them)h(more)f(generally)i(as)f(\\w)m(eigh)m (ts"\)|the)i(prepro)s(cessor)d(will)390 4695 y(normalize)32 b(appropriately)-8 b(.)44 b(This)31 b(return)f(v)-5 b(alue)32 b(is)f(used)f(as)i(an)f(argumen)m(t)h(for)f(the)g FH(gsl_ran_)390 4804 y(discrete)d FK(function)i(b)s(elo)m(w.)3350 5011 y([F)-8 b(unction])-3599 b Fv(size_t)54 b(gsl_ran_discrete)c Fu(\()p FD(const)32 b(gsl)p 1784 5011 V 40 w(rng)e(*)h Ft(r)p FD(,)g(const)g(gsl)p 2514 5011 V 40 w(ran)p 2686 5011 V 40 w(discrete)p 3029 5011 V 41 w(t)f(*)565 5121 y Ft(g)p Fu(\))390 5230 y FK(After)22 b(the)h(prepro)s(cessor,)g(ab)s (o)m(v)m(e,)i(has)d(b)s(een)f(called,)k(y)m(ou)e(use)e(this)h(function) g(to)h(get)g(the)f(discrete)390 5340 y(random)30 b(n)m(um)m(b)s(ers.)p eop end %%Page: 247 263 TeXDict begin 247 262 bop 150 -116 a FK(Chapter)30 b(20:)41 b(Random)30 b(Num)m(b)s(er)g(Distributions)1717 b(247)3350 299 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_ran_discrete_pdf)e Fu(\()p FD(size)p 1790 299 28 4 v 41 w(t)31 b Ft(k)p FD(,)f(const)h(gsl)p 2348 299 V 41 w(ran)p 2521 299 V 39 w(discrete)p 2863 299 V 41 w(t)g(*)g Ft(g)p Fu(\))390 408 y FK(Returns)g(the)h(probabilit)m(y)g FE(P)13 b FK([)p FE(k)s FK(])32 b(of)g(observing)g(the)g(v)-5 b(ariable)32 b FD(k)p FK(.)45 b(Since)32 b FE(P)13 b FK([)p FE(k)s FK(])32 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FD(p)p FK(,)f(using)g(the)g(form)m(ula)h(giv)m(en)g(ab)s(o)m(v)m(e.)450 3932 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-bernoulli.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 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b FK(b)s(e)27 b(less)h(than)g(or)f(equal)i(to)f FH(n)p FK(.)40 b(The)27 b(ob)5 b(jects)29 b(in)e FD(dest)j FK(will)f(b)s(e)390 4011 y(in)f(the)g(same)g(relativ)m(e)i(order)e(as)g(those)g(in)g FD(src)p FK(.)40 b(Y)-8 b(ou)28 b(will)g(need)g(to)h(call)g FH(gsl_ran_shuffle\(r,)390 4120 y(dest,)g(n,)h(size\))f FK(if)h(y)m(ou)h(w)m(an)m(t)g(to)g(randomize)g(the)f(order.)390 4292 y(The)37 b(follo)m(wing)h(co)s(de)g(sho)m(ws)f(ho)m(w)g(to)h (select)h(a)e(random)g(sample)g(of)h(three)f(unique)f(n)m(um)m(b)s(ers) 390 4401 y(from)30 b(the)g(set)h(0)g(to)g(99,)630 4573 y FH(double)46 b(a[3],)g(b[100];)630 4792 y(for)h(\(i)g(=)h(0;)f(i)g(<) h(100;)e(i++\))725 4902 y({)821 5011 y(b[i])h(=)g(\(double\))f(i;)725 5121 y(})630 5340 y(gsl_ran_choose)e(\(r,)j(a,)g(3,)g(b,)g(100,)g (sizeof)f(\(double\)\);)p eop end %%Page: 258 274 TeXDict begin 258 273 bop 150 -116 a FK(Chapter)30 b(20:)41 b(Random)30 b(Num)m(b)s(er)g(Distributions)1717 b(258)3350 299 y([F)-8 b(unction])-3599 b Fv(void)54 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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: 264 280 TeXDict begin 264 279 bop 150 -116 a FK(Chapter)30 b(21:)41 b(Statistics)2591 b(264)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: 265 281 TeXDict begin 265 280 bop 150 -116 a FK(Chapter)30 b(21:)41 b(Statistics)2591 b(265)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(=1)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 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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 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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: 266 282 TeXDict begin 266 281 bop 150 -116 a FK(Chapter)30 b(21:)41 b(Statistics)2591 b(266)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: 267 283 TeXDict begin 267 282 bop 150 -116 a FK(Chapter)30 b(21:)41 b(Statistics)2591 b(267)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 Fm(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: 268 284 TeXDict begin 268 283 bop 150 -116 a FK(Chapter)30 b(21:)41 b(Statistics)2591 b(268)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 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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: 269 285 TeXDict begin 269 284 bop 150 -116 a FK(Chapter)30 b(21:)41 b(Statistics)2591 b(269)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: 270 286 TeXDict begin 270 285 bop 150 -116 a FK(Chapter)30 b(21:)41 b(Statistics)2591 b(270)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 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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: 276 292 TeXDict begin 276 291 bop 150 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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(22.5)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 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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: 277 293 TeXDict begin 277 292 bop 150 -116 a FK(Chapter)30 b(22:)41 b(Histograms)2507 b(277)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(22.7)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 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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 Fm(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 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b(The)33 b(histogram)390 1664 y(output)e(is)h(formatted)g(in)f(three)h(columns,) f(and)g(the)h(columns)f(are)h(separated)g(b)m(y)f(spaces,)i(lik)m(e)390 1774 y(this,)630 1900 y FH(range[0])46 b(range[1])f(bin[0])630 2010 y(range[1])h(range[2])f(bin[1])630 2120 y(range[2])h(range[3])f (bin[2])630 2229 y(....)630 2339 y(range[n-1])g(range[n])h(bin[n-1])390 2465 y FK(The)30 b(v)-5 b(alues)31 b(of)f(the)h(ranges)g(are)g (formatted)g(using)f FD(range)p 2427 2465 V 40 w(format)j FK(and)d(the)h(v)-5 b(alue)31 b(of)f(the)h(bins)390 2575 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) 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(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(22.10)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: 279 295 TeXDict begin 279 294 bop 150 -116 a FK(Chapter)30 b(22:)41 b(Histograms)2507 b(279)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: 280 296 TeXDict begin 280 295 bop 150 -116 a FK(Chapter)30 b(22:)41 b(Histograms)2507 b(280)150 299 y FJ(22.11)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: 281 297 TeXDict begin 281 296 bop 150 -116 a FK(Chapter)30 b(22:)41 b(Histograms)2507 b(281)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 @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 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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: 97 195 494 580 %%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 1 112.7699 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 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 1 204.2139 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 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 4328 4274 4081 4308 4081 4308 4773 4343 4773 4343 5168 4378 5168 4378 4032 4412 4032 4412 4229 4447 4229 4447 4476 4481 4476 4481 4921 4516 4921 4516 4180 4550 4180 4550 4378 4585 4378 4585 4871 4620 4871 4620 4921 4654 4921 4654 4180 4689 4180 4689 4526 4723 4526 4723 5464 4758 5464 4758 5711 4792 5711 4792 5563 4827 5563 4827 5316 4861 5316 4861 5217 4896 5217 4896 5908 4931 5908 4931 4921 4965 4921 4965 6106 5000 6106 5000 5612 5034 5612 5034 6056 5069 6056 5069 5908 5103 5908 5103 6204 5138 6204 5138 6698 5172 6698 5172 6994 5207 6994 5207 7044 5242 7044 5242 6994 5276 6994 5276 6599 5311 6599 5311 6846 5345 6846 5345 7093 5380 7093 5380 7636 5414 7636 5414 6056 5449 6056 5449 7340 5484 7340 5484 6994 5518 6994 5518 7439 5553 7439 5553 7241 5587 7241 5587 7192 5622 7192 5622 7932 5656 7932 5656 7389 5691 7389 5691 7192 5725 7192 5725 7340 5760 7340 5760 6550 5795 6550 5795 8278 5829 8278 5829 6994 5864 6994 5864 7291 5898 7291 5898 7636 5933 7636 5933 7241 5967 7241 5967 6945 6002 6945 6002 7537 6036 7537 6036 7587 6071 7587 6071 7241 6106 7241 6106 6599 6140 6599 6140 7587 6175 7587 6175 7932 6209 7932 6209 5859 6244 5859 6244 7340 6278 7340 6278 5661 6313 5661 6313 6352 6348 6352 6348 6303 6382 6303 6382 6254 6417 6254 6417 5957 6451 5957 6451 6106 6486 6106 6486 5414 6520 5414 6520 4773 6555 4773 6555 5019 6589 5019 6589 5563 6624 5563 6624 5661 6659 5661 6659 4822 6693 4822 6693 5266 6728 5266 6728 5266 6762 5266 6762 5069 6797 5069 6797 5168 6831 5168 6831 4229 6866 4229 6866 4526 6900 4526 6900 4674 6935 4674 6935 4921 6970 4921 6970 3835 7004 3835 7004 4229 7039 4229 7039 3983 7073 3983 7073 3835 7108 3835 7108 4279 7142 4279 7142 4229 7177 4229 7177 3884 7212 3884 7212 4427 7246 4427 7246 3637 7281 3637 7281 3983 7315 3983 7315 3637 7350 3637 7350 3686 7384 3686 7384 3884 7419 3884 7419 3538 7453 3538 7453 3637 7488 3637 7488 3785 7523 3785 7523 3291 7557 3291 7557 3835 7592 3835 7592 3045 7626 3045 7626 3390 7661 3390 7661 3736 7695 3736 7695 3785 7730 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(22.12)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(22.13)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: 282 298 TeXDict begin 282 297 bop 150 -116 a FK(Chapter)30 b(22:)41 b(Histograms)2507 b(282)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 Fm(xr)-5 b(ange)q FK([)p FE(i)p FK(])26 b FI(\024)f FE(x)g(<)g Fm(xr)-5 b(ange)q FK([)p FE(i)21 b FK(+)f(1])1256 1640 y(and)460 b Fm(yr)-5 b(ange)q FK([)p FE(j)5 b FK(])26 b FI(\024)f FE(y)j(<)d Fm(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(22.14)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: 283 299 TeXDict begin 283 298 bop 150 -116 a FK(Chapter)30 b(22:)41 b(Histograms)2507 b(283)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(22.15)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(22.16)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: 284 300 TeXDict begin 284 299 bop 150 -116 a FK(Chapter)30 b(22:)41 b(Histograms)2507 b(284)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(\(i.e.)60 b(ev)m(en)m(ts)390 518 y(with)31 b(the)g(v)-5 b(alue)32 b(of)f(the)g(upp)s(er)e(limit)j(are)f (not)h(included)e(and)h(fall)g(in)g(the)g(neigh)m(b)s(oring)g(higher) 390 628 y(bin,)h(if)f(it)h(exists\).)46 b(The)32 b(functions)f(return)f (0)j(to)f(indicate)h(success.)45 b(If)31 b FD(i)37 b FK(or)32 b FD(j)i FK(lies)f(outside)f(the)390 737 y(v)-5 b(alid)29 b(range)h(of)f(indices)g(for)g(the)g(histogram)h(then)e(the)i (error)e(handler)g(is)h(called)i(with)d(an)h(error)390 847 y(co)s(de)i(of)f FH(GSL_EDOM)p FK(.)3350 1062 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_histogram2d_xmax)e Fu(\()p FD(const)31 b(gsl)p 1993 1062 28 4 v 40 w(histogram2d)g(*)g Ft(h)p Fu(\))3350 1172 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_histogram2d_xmin)e Fu(\()p FD(const)31 b(gsl)p 1993 1172 V 40 w(histogram2d)g(*)g Ft(h)p Fu(\))3350 1281 y FK([F)-8 b(unction])-3599 b Fv(size_t)54 b(gsl_histogram2d_nx)d Fu(\()p FD(const)31 b(gsl)p 1888 1281 V 41 w(histogram2d)g(*)g Ft(h)p Fu(\))3350 1391 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_histogram2d_ymax)e Fu(\()p FD(const)31 b(gsl)p 1993 1391 V 40 w(histogram2d)g(*)g Ft(h)p Fu(\))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 FK(to)h(zero.)150 2520 y FJ(22.17)69 b(Searc)l(hing)45 b(2D)g(histogram)h(ranges)150 2679 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 2789 y(corresp)s(onds)h(to)i(a)g(giv)m(en)g(\()p FE(x;)15 b(y)s FK(\))31 b(co)s(ordinate.)3350 3004 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_histogram2d_find)f Fu(\()p FD(const)31 b(gsl)p 1836 3004 V 41 w(histogram2d)f(*)h Ft(h)p FD(,)g(double)f Ft(x)p FD(,)565 3114 y(double)g Ft(y)p FD(,)h(size)p 1113 3114 V 41 w(t)f(*)h Ft(i)p FD(,)g(size)p 1544 3114 V 41 w(t)g(*)f Ft(j)p Fu(\))390 3223 y FK(This)24 b(function)g(\014nds)f(and)h(sets)g(the)h(indices)g FD(i)k FK(and)24 b FD(j)k FK(to)d(the)g(bin)e(whic)m(h)h(co)m(v)m(ers)j (the)d(co)s(ordinates)390 3333 y(\()p FD(x)p FK(,)p FD(y)8 b FK(\).)41 b(The)30 b(bin)f(is)h(lo)s(cated)h(using)f(a)g(binary)f (searc)m(h.)41 b(The)30 b(searc)m(h)h(includes)e(an)h(optimization)390 3442 y(for)36 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(22.18)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: 285 301 TeXDict begin 285 300 bop 150 -116 a FK(Chapter)30 b(22:)41 b(Histograms)2507 b(285)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(22.19)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: 286 302 TeXDict begin 286 301 bop 150 -116 a FK(Chapter)30 b(22:)41 b(Histograms)2507 b(286)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 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-)390 628 y(ing)33 b(bins)e(of)i(histogram)h FD(h1)p FK(,)f(i.e.)48 b FE(h)1641 595 y Fp(0)1641 650 y FB(1)1679 628 y FK(\()p FE(i;)15 b(j)5 b FK(\))31 b(=)e FE(h)2045 642 y FB(1)2082 628 y FK(\()p FE(i;)15 b(j)5 b FK(\))24 b FI(\000)e FE(h)2434 642 y FB(2)2471 628 y FK(\()p FE(i;)15 b(j)5 b FK(\).)50 b(The)32 b(t)m(w)m(o)i(histograms) f(m)m(ust)390 737 y(ha)m(v)m(e)f(iden)m(tical)g(bin)d(ranges.)3350 917 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_histogram2d_mul)e Fu(\()p FD(gsl)p 1545 917 V 41 w(histogram2d)31 b(*)g Ft(h1)p FD(,)g(const)565 1026 y(gsl)p 677 1026 V 41 w(histogram2d)g(*)f Ft(h2)p Fu(\))390 1136 y FK(This)i(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 1245 y(the)40 b(corresp)s(onding)e(bins)h(in)g(histogram)h FD(h2)p FK(,)i(i.e.)68 b FE(h)2298 1212 y Fp(0)2298 1268 y FB(1)2336 1245 y FK(\()p FE(i;)15 b(j)5 b FK(\))42 b(=)e FE(h)2724 1259 y FB(1)2762 1245 y FK(\()p FE(i;)15 b(j)5 b FK(\))28 b FI(\003)f FE(h)3097 1259 y FB(2)3135 1245 y FK(\()p FE(i;)15 b(j)5 b FK(\).)70 b(The)39 b(t)m(w)m(o)390 1355 y(histograms)31 b(m)m(ust)f(ha)m(v)m(e)i(iden)m(tical)g(bin)d (ranges.)3350 1534 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_histogram2d_div)e Fu(\()p FD(gsl)p 1545 1534 V 41 w(histogram2d)31 b(*)g Ft(h1)p FD(,)g(const)565 1644 y(gsl)p 677 1644 V 41 w(histogram2d)g(*)f Ft(h2)p Fu(\))390 1753 y FK(This)40 b(function)g(divides)h(the)g(con)m(ten)m(ts)h(of)f (the)g(bins)f(of)h(histogram)g FD(h1)48 b FK(b)m(y)40 b(the)h(con)m(ten)m(ts)i(of)390 1863 y(the)g(corresp)s(onding)e(bins)h (in)g(histogram)i FD(h2)p FK(,)h(i.e.)79 b FE(h)2328 1830 y Fp(0)2328 1885 y FB(1)2365 1863 y FK(\()p FE(i;)15 b(j)5 b FK(\))48 b(=)d FE(h)2764 1877 y FB(1)2802 1863 y FK(\()p FE(i;)15 b(j)5 b FK(\))p FE(=h)3082 1877 y FB(2)3122 1863 y FK(\()p FE(i;)15 b(j)5 b FK(\).)79 b(The)43 b(t)m(w)m(o)390 1973 y(histograms)31 b(m)m(ust)f(ha)m(v)m(e)i(iden)m (tical)g(bin)d(ranges.)3350 2152 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_histogram2d_scale)f Fu(\()p FD(gsl)p 1650 2152 V 41 w(histogram2d)31 b(*)g Ft(h)p FD(,)g(double)e Ft(scale)p Fu(\))390 2262 y FK(This)c(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 2371 y(i.e.)42 b FE(h)599 2338 y Fp(0)599 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Fv(int)53 b(gsl_histogram2d_fwrit)q(e)e Fu(\()p FD(FILE)31 b(*)g Ft(stream)p FD(,)h(const)f(gsl)p 2627 3447 V 40 w(histogram2d)565 3557 y(*)g Ft(h)p Fu(\))390 3666 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 3776 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 3885 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 3995 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.)3350 4174 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_histogram2d_fread)f Fu(\()p FD(FILE)31 b(*)f Ft(stream)p FD(,)j(gsl)p 2337 4174 V 40 w(histogram2d)e(*)g Ft(h)p Fu(\))390 4284 y FK(This)j(function)h(reads)g(in)m(to)h(the)f(histogram)g FD(h)g FK(from)f(the)i(stream)f FD(stream)g FK(in)g(binary)f(format.) 390 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FK(line-b)m(y-line)h(to)h(the)f(stream)390 5340 y FD(stream)e FK(using)g(the)g(format)g(sp)s(eci\014ers)f FD(range)p 1962 5340 V 40 w(format)j FK(and)e FD(bin)p 2593 5340 V 39 w(format)p FK(.)39 b(These)25 b(should)e(b)s(e)i(one)p eop end %%Page: 287 303 TeXDict begin 287 302 bop 150 -116 a FK(Chapter)30 b(22:)41 b(Histograms)2507 b(287)390 299 y(of)37 b(the)f FH(\045g)p FK(,)i FH(\045e)e FK(or)g FH(\045f)g FK(formats)h(for)f(\015oating)i(p) s(oin)m(t)e(n)m(um)m(b)s(ers.)58 b(The)36 b(function)g(returns)f(0)i (for)390 408 y(success)d(and)g FH(GSL_EFAILED)c FK(if)k(there)g(w)m(as) h(a)f(problem)f(writing)h(to)h(the)f(\014le.)52 b(The)33 b(histogram)390 518 y(output)j(is)g(formatted)h(in)f(\014v)m(e)h (columns,)h(and)e(the)g(columns)g(are)h(separated)g(b)m(y)f(spaces,)j (lik)m(e)390 628 y(this,)630 733 y Fz(xrange[0])i(xrange[1])h (yrange[0])f(yrange[1])g(bin\(0,0\))630 820 y(xrange[0])g(xrange[1])h (yrange[1])f(yrange[2])g(bin\(0,1\))630 907 y(xrange[0])g(xrange[1])h (yrange[2])f(yrange[3])g(bin\(0,2\))630 995 y(....)630 1082 y(xrange[0])g(xrange[1])h(yrange[ny-1])f(yrange[ny])h (bin\(0,ny-1\))630 1256 y(xrange[1])f(xrange[2])h(yrange[0])f (yrange[1])g(bin\(1,0\))630 1343 y(xrange[1])g(xrange[2])h(yrange[1])f (yrange[2])g(bin\(1,1\))630 1430 y(xrange[1])g(xrange[2])h(yrange[1])f (yrange[2])g(bin\(1,2\))630 1518 y(....)630 1605 y(xrange[1])g (xrange[2])h(yrange[ny-1])f(yrange[ny])h(bin\(1,ny-1\))630 1779 y(....)630 1953 y(xrange[nx-1])g(xrange[nx])f(yrange[0])h (yrange[1])f(bin\(nx-1,0\))630 2041 y(xrange[nx-1])h(xrange[nx])f (yrange[1])h(yrange[2])f(bin\(nx-1,1\))630 2128 y(xrange[nx-1])h (xrange[nx])f(yrange[1])h(yrange[2])f(bin\(nx-1,2\))630 2215 y(....)630 2302 y(xrange[nx-1])h(xrange[nx])f(yrange[ny-1])h (yrange[ny])g(bin\(nx-1,ny-1\))390 2430 y FK(Eac)m(h)31 b(line)g(con)m(tains)g(the)g(lo)m(w)m(er)h(and)d(upp)s(er)g(limits)i (of)g(the)f(bin)g(and)g(the)g(con)m(ten)m(ts)i(of)f(the)f(bin.)390 2540 y(Since)38 b(the)g(upp)s(er)e(limits)j(of)f(the)g(eac)m(h)i(bin)d (are)h(the)h(lo)m(w)m(er)g(limits)g(of)f(the)g(neigh)m(b)s(oring)g (bins)390 2649 y(there)33 b(is)f(duplication)h(of)g(these)g(v)-5 b(alues)33 b(but)f(this)g(allo)m(ws)i(the)f(histogram)g(to)g(b)s(e)f (manipulated)390 2759 y(with)e(line-orien)m(ted)i(to)s(ols.)3350 2923 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_histogram2d_fscan)q(f)e Fu(\()p FD(FILE)31 b(*)g Ft(stream)p FD(,)h(gsl)p 2389 2923 28 4 v 41 w(histogram2d)f(*)f Ft(h)p Fu(\))390 3032 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 3142 y(data)28 b(is)f(assumed)f(to)h(b)s(e)g (in)f(the)h(\014v)m(e-column)h(format)f(used)f(b)m(y)h FH(gsl_histogram2d_fprintf)p FK(.)390 3252 y(The)d(histogram)i FD(h)e FK(m)m(ust)g(b)s(e)g(preallo)s(cated)j(with)d(the)h(correct)h (lengths)f(since)g(the)g(function)f(uses)390 3361 y(the)35 b(sizes)h(of)g FD(h)e 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4449 y FE(p)p FK(\()p FE(x;)15 b(y)s FK(\))26 b(=)f FE(n)1975 4463 y Fq(ij)2033 4449 y FE(=)p FK(\()p FE(N)10 b(A)2264 4463 y Fq(ij)2323 4449 y FK(\))150 4610 y(In)28 b(this)g(equation)h FE(n)861 4624 y Fq(ij)947 4610 y FK(is)f(the)h(n)m(um)m(b)s(er)e(of)h(ev)m(en)m (ts)i(in)e(the)g(bin)f(whic)m(h)h(con)m(tains)i(\()p FE(x;)15 b(y)s FK(\),)30 b FE(A)3253 4624 y Fq(ij)3339 4610 y FK(is)f(the)f(area)150 4719 y(of)j(the)g(bin)f(and)g FE(N)41 b FK(is)30 b(the)h(total)i(n)m(um)m(b)s(er)c(of)i(ev)m(en)m (ts.)43 b(The)31 b(distribution)f(of)h(ev)m(en)m(ts)h(within)e(eac)m(h) i(bin)150 4829 y(is)e(assumed)g(to)h(b)s(e)f(uniform.)3269 4993 y([Data)i(T)m(yp)s(e])-3600 b Fv(gsl_histogram2d_pdf)390 5121 y FH(size_t)29 b(nx,)g(ny)870 5230 y FK(This)24 b(is)h(the)f(n)m(um)m(b)s(er)g(of)h(histogram)g(bins)f(used)f(to)j (appro)m(ximate)g(the)e(probabilit)m(y)870 5340 y(distribution)30 b(function)g(in)g(the)g(x)h(and)e(y)i(directions.)p eop end %%Page: 288 304 TeXDict begin 288 303 bop 150 -116 a FK(Chapter)30 b(22:)41 b(Histograms)2507 b(288)390 299 y FH(double)29 b(*)h(xrange)870 408 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)870 518 y(elemen)m(ts)32 b(p)s(oin)m(ted)e(to)h(b)m(y)f FD(xrange)p FK(.)390 677 y FH(double)f(*)h(yrange)870 787 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)870 897 y(p)s(oin)m(ted)30 b(to)h(b)m(y)g FD(yrange)p FK(.)390 1056 y FH(double)e(*)h(sum)870 1166 y FK(The)37 b(cum)m(ulativ)m(e)i(probabilit)m(y)f(for)f(the)h(bins)f(is)g(stored)h (in)f(an)g(arra)m(y)h(of)g FD(nx)6 b FK(*)p FD(n)m(y)870 1275 y FK(elemen)m(ts)32 b(p)s(oin)m(ted)e(to)h(b)m(y)f FD(sum)p FK(.)150 1460 y(The)22 b(follo)m(wing)j(functions)d(allo)m(w)i (y)m(ou)g(to)f(create)i(a)e FH(gsl_histogram2d_pdf)18 b FK(struct)k(whic)m(h)h(represen)m(ts)150 1569 y(a)31 b(t)m(w)m(o)g(dimensional)g(probabilit)m(y)g(distribution)f(and)f (generate)j(random)e(samples)g(from)g(it.)3350 1753 y([F)-8 b(unction])-3599 b Fv(gsl_histogram2d_pdf)58 b(*)53 b (gsl_histogram2d_pdf_all)q(oc)f Fu(\()p FD(size)p 2836 1753 28 4 v 41 w(t)31 b Ft(nx)p FD(,)565 1863 y(size)p 712 1863 V 41 w(t)g Ft(ny)p Fu(\))390 1973 y FK(This)d(function)g(allo) s(cates)i(memory)f(for)f(a)h(t)m(w)m(o-dimensional)h(probabilit)m(y)f (distribution)f(of)g(size)390 2082 y FD(nx)p FK(-b)m(y-)p FD(n)m(y)41 b FK(and)33 b(returns)f(a)h(p)s(oin)m(ter)h(to)g(a)f(newly) h(initialized)h FH(gsl_histogram2d_pdf)28 b FK(struct.)390 2192 y(If)j(insu\016cien)m(t)h(memory)g(is)g(a)m(v)-5 b(ailable)34 b(a)e(n)m(ull)g(p)s(oin)m(ter)g(is)g(returned)e(and)h(the) i(error)e(handler)g(is)390 2301 y(in)m(v)m(ok)m(ed)h(with)e(an)g(error) g(co)s(de)h(of)f FH(GSL_ENOMEM)p FK(.)3350 2486 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_histogram2d_pdf_i)q(nit)f Fu(\()p FD(gsl)p 1807 2486 V 41 w(histogram2d)p 2338 2486 V 41 w(p)s(df)28 b(*)j Ft(p)p FD(,)g(const)565 2595 y(gsl)p 677 2595 V 41 w(histogram2d)g(*)f Ft(h)p Fu(\))390 2705 y FK(This)45 b(function)g(initializes)i(the)f(t)m(w)m (o-dimensional)h(probabilit)m(y)f(distribution)e(calculated)k FD(p)390 2814 y FK(from)38 b(the)h(histogram)h FD(h)p FK(.)66 b(If)38 b(an)m(y)h(of)g(the)g(bins)f(of)h FD(h)f FK(are)i(negativ)m(e)h(then)d(the)h(error)g(handler)390 2924 y(is)32 b(in)m(v)m(ok)m(ed)h(with)e(an)h(error)f(co)s(de)h(of)g FH(GSL_EDOM)d FK(b)s(ecause)j(a)g(probabilit)m(y)g(distribution)f (cannot)390 3034 y(con)m(tain)h(negativ)m(e)g(v)-5 b(alues.)3350 3218 y([F)d(unction])-3599 b Fv(void)54 b(gsl_histogram2d_pdf_free)e Fu(\()p FD(gsl)p 1859 3218 V 41 w(histogram2d)p 2390 3218 V 41 w(p)s(df)28 b(*)j Ft(p)p Fu(\))390 3328 y FK(This)d(function) g(frees)h(the)g(t)m(w)m(o-dimensional)h(probabilit)m(y)f(distribution)f (function)g FD(p)j FK(and)d(all)i(of)390 3437 y(the)h(memory)f(asso)s (ciated)i(with)e(it.)3350 3621 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_histogram2d_pdf_s)q(ampl)q(e)f Fu(\()p FD(const)31 b(gsl)p 2150 3621 V 40 w(histogram2d)p 2680 3621 V 41 w(p)s(df)e(*)h Ft(p)p FD(,)565 3731 y(double)g Ft(r1)p FD(,)h(double)f Ft(r2)p FD(,)h(double)f(*)h Ft(x)p FD(,)g(double)f(*)h Ft(y)p Fu(\))390 3841 y FK(This)c(function)h(uses)f (t)m(w)m(o)i(uniform)e(random)g(n)m(um)m(b)s(ers)f(b)s(et)m(w)m(een)j (zero)f(and)f(one,)i FD(r1)35 b FK(and)28 b FD(r2)p FK(,)g(to)390 3950 y(compute)36 b(a)h(single)g(random)e(sample)h(from)g(the)g(t)m(w)m (o-dimensional)i(probabilit)m(y)f(distribution)390 4060 y FD(p)p FK(.)p eop end %%Page: 289 305 TeXDict begin 289 304 bop 150 -116 a FK(Chapter)30 b(22:)41 b(Histograms)2507 b(289)150 299 y FJ(22.22)69 b(Example)46 b(programs)f(for)g(2D)g(histograms)150 458 y FK(This)34 b(program)g(demonstrates)h(t)m(w)m(o)h(features)f(of)g(t)m(w)m (o-dimensional)h(histograms.)54 b(First)35 b(a)g(10-b)m(y-10)150 568 y(t)m(w)m(o-dimensional)29 b(histogram)f(is)f(created)h(with)f(x)g (and)g(y)g(running)e(from)i(0)g(to)h(1.)40 b(Then)26 b(a)i(few)f(sample)150 677 y(p)s(oin)m(ts)h(are)g(added)f(to)i(the)f (histogram,)h(at)g(\(0.3,0.3\))i(with)d(a)g(heigh)m(t)h(of)f(1,)h(at)g (\(0.8,0.1\))i(with)d(a)g(heigh)m(t)150 787 y(of)41 b(5)h(and)e(at)i (\(0.7,0.9\))i(with)d(a)g(heigh)m(t)h(of)g(0.5.)73 b(This)41 b(histogram)g(with)g(three)g(ev)m(en)m(ts)i(is)e(used)f(to)150 897 y(generate)32 b(a)f(random)e(sample)i(of)f(1000)i(sim)m(ulated)g (ev)m(en)m(ts,)g(whic)m(h)e(are)g(prin)m(ted)g(out.)390 1066 y FH(#include)46 b()390 1176 y(#include)g ()390 1285 y(#include)g()390 1504 y(int)390 1614 y(main)h(\(void\))390 1724 y({)485 1833 y(const)g(gsl_rng_type)d(*)k(T;)485 1943 y(gsl_rng)e(*)i(r;)485 2162 y(gsl_histogram2d)c(*)k(h)f(=)g(gsl_histogram2d_alloc)42 b(\(10,)47 b(10\);)485 2381 y(gsl_histogram2d_set_ranges)o(_uni)o(for)o (m)42 b(\(h,)2204 2491 y(0.0,)k(1.0,)2204 2600 y(0.0,)g(1.0\);)485 2819 y(gsl_histogram2d_accumulate)41 b(\(h,)47 b(0.3,)g(0.3,)f(1\);)485 2929 y(gsl_histogram2d_accumulate)41 b(\(h,)47 b(0.8,)g(0.1,)f(5\);)485 3039 y(gsl_histogram2d_accumulate)41 b(\(h,)47 b(0.7,)g(0.9,)f(0.5\);) 485 3258 y(gsl_rng_env_setup)e(\(\);)485 3477 y(T)k(=)f (gsl_rng_default;)485 3587 y(r)h(=)f(gsl_rng_alloc)e(\(T\);)485 3806 y({)581 3915 y(int)i(i;)581 4025 y(gsl_histogram2d_pdf)42 b(*)48 b(p)676 4134 y(=)g(gsl_histogram2d_pdf_allo)o(c)42 b(\(h->nx,)k(h->ny\);)581 4354 y(gsl_histogram2d_pdf_init)41 b(\(p,)47 b(h\);)581 4573 y(for)g(\(i)g(=)g(0;)h(i)f(<)h(1000;)e(i++\)) h({)676 4682 y(double)f(x,)i(y;)676 4792 y(double)e(u)i(=)f (gsl_rng_uniform)d(\(r\);)676 4902 y(double)i(v)i(=)f(gsl_rng_uniform)d (\(r\);)676 5121 y(gsl_histogram2d_pdf_sample)d(\(p,)47 b(u,)g(v,)g(&x,)g(&y\);)676 5340 y(printf)f(\("\045g)h(\045g\\n",)f(x,) h(y\);)p eop end %%Page: 290 306 TeXDict begin 290 305 bop 150 -116 a FK(Chapter)30 b(22:)41 b(Histograms)2507 b(290)581 299 y FH(})581 518 y (gsl_histogram2d_pdf_free)41 b(\(p\);)485 628 y(})485 847 y(gsl_histogram2d_free)i(\(h\);)485 956 y(gsl_rng_free)i(\(r\);)485 1176 y(return)i(0;)390 1285 y(})150 1420 y FK(The)26 b(follo)m(wing)h(plot)g(sho)m(ws)e(the)i(distribution)e(of)h(the)g(sim) m(ulated)h(ev)m(en)m(ts.)41 b(Using)26 b(a)h(higher)e(resolution)150 1529 y(grid)e(w)m(e)i(can)f(see)g(the)g(original)h(underlying)d (histogram)j(and)e(also)i(the)f(statistical)i(\015uctuations)e(caused) 150 1639 y(b)m(y)30 b(the)h(ev)m(en)m(ts)h(b)s(eing)e(uniformly)f (distributed)g(o)m(v)m(er)j(the)f(area)g(of)f(the)h(original)g(bins.) 275 3915 y @beginspecial 0 @llx 0 @lly 567 @urx 567 @ury 2448 @rwi @setspecial %%BeginDocument: histogram2d.eps %!PS-Adobe-2.0 EPSF-2.0 %%BoundingBox: 0 0 567 567 %%Title: paw.eps %%Creator: HIGZ Version 1.23/07 %%CreationDate: 98/05/04 19.25 %%EndComments %%BeginProlog 80 dict begin /s {stroke} def /l {lineto} def /m {moveto} def /t {translate} def /sw {stringwidth} def /r {rotate} def /rl {roll} def /R {repeat} def /d {rlineto} def /rm {rmoveto} def /gr 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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 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m 39 10 d s 761 599 m 22 -16 d s 723 590 m 38 9 d s 799 609 m 22 -17 d s 761 599 m 38 10 d s 838 619 m 22 -17 d s 799 609 m 39 10 d s 876 629 m 22 -17 d s 838 619 m 38 10 d s 914 638 m 22 -16 d s 876 629 m 38 9 d s 953 648 m 17 -13 d s 914 638 m 39 10 d s 953 648 m 17 5 d s 953 648 m 12 -9 d s 1075 679 m 16 4 d s 1144 697 m 22 -17 d s 1136 695 m 8 2 d s 1183 707 m 22 -17 d s 1144 697 m 39 10 d s 1221 717 m 22 -17 d s 1183 707 m 38 10 d s 1259 726 m 22 -17 d s 1221 717 m 38 9 d s 1298 736 m 22 -17 d s 1259 726 m 39 10 d s 1336 746 m 22 -17 d s 1298 736 m 38 10 d s 1374 756 m 22 -17 d s 1336 746 m 38 10 d s 1413 765 m 22 -17 d s 1374 756 m 39 9 d s 1451 775 m 22 -17 d s 1413 765 m 38 10 d s 1489 785 m 22 -17 d s 1451 775 m 38 10 d s 1528 795 m 22 -17 d s 1489 785 m 39 10 d s 1566 804 m 22 -16 d s 1528 795 m 38 9 d s 1604 814 m 23 -17 d s 1566 804 m 38 10 d s 1643 824 m 22 -17 d s 1604 814 m 39 10 d s 492 531 m s 509 558 m 22 -17 d s 470 548 m 39 10 d s 470 548 m 22 -17 d s 547 568 m 22 -17 d s 509 558 m 38 10 d s 585 577 m 22 -17 d s 547 568 m 38 9 d s 624 587 m 22 -17 d s 585 577 m 39 10 d s 662 597 m 22 -17 d s 624 587 m 38 10 d s 700 607 m 23 -17 d s 662 597 m 38 10 d s 739 616 m 22 -17 d s 700 607 m 39 9 d s 777 626 m 22 -17 d s 739 616 m 38 10 d s 815 636 m 23 -17 d s 777 626 m 38 10 d s 854 646 m 22 -17 d s 815 636 m 39 10 d s 892 655 m 22 -17 d s 854 646 m 38 9 d s 930 665 m 23 -17 d s 892 655 m 38 10 d s 930 665 m 39 10 d s 930 665 m 9 -6 d s 941 657 m 6 -5 d s 1084 704 m 15 -12 d s 1068 700 m 16 4 d s 1122 714 m 22 -17 d s 1084 704 m 38 10 d s 1160 724 m 23 -17 d s 1122 714 m 38 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: 291 307 TeXDict begin 291 306 bop 150 -116 a FK(Chapter)30 b(23:)41 b(N-tuples)2618 b(291)150 299 y FG(23)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 (included)h(in)g(the)150 1588 y(subset)35 b(to)g(b)s(e)g(analyzed)h(or) f(not.)55 b(The)35 b(v)-5 b(alue)35 b(function)g(computes)g(the)h(en)m (try)f(to)h(b)s(e)e(added)h(to)h(the)150 1697 y(histogram)31 b(for)f(eac)m(h)i(ev)m(en)m(t.)275 1857 y(All)f(the)f(n)m(tuple)g (functions)g(are)h(de\014ned)e(in)h(the)h(header)f(\014le)g FH(gsl_ntuple.h)150 2128 y FJ(23.1)68 b(The)45 b(n)l(tuple)g(struct)150 2288 y FK(Ntuples)27 b(are)h(manipulated)g(using)f(the)g FH(gsl_ntuple)e FK(struct.)40 b(This)26 b(struct)i(con)m(tains)g (information)g(on)150 2397 y(the)34 b(\014le)g(where)g(the)g(n)m(tuple) g(data)g(is)g(stored,)i(a)e(p)s(oin)m(ter)g(to)h(the)f(curren)m(t)g(n)m (tuple)g(data)g(ro)m(w)g(and)g(the)150 2507 y(size)d(of)g(the)f (user-de\014ned)f(n)m(tuple)h(data)i(struct.)390 2667 y FH(typedef)46 b(struct)g({)581 2777 y(FILE)h(*)g(file;)581 2886 y(void)g(*)g(ntuple_data;)581 2996 y(size_t)f(size;)390 3105 y(})h(gsl_ntuple;)150 3376 y FJ(23.2)68 b(Creating)47 b(n)l(tuples)3350 3611 y FK([F)-8 b(unction])-3599 b Fv(gsl_ntuple)55 b(*)e(gsl_ntuple_create)e Fu(\()p FD(c)m(har)31 b(*)f Ft(filename)p FD(,)j(v)m(oid)e(*)565 3721 y Ft(ntuple_data)p FD(,)j(size)p 1343 3721 28 4 v 41 w(t)d Ft(size)p Fu(\))390 3830 y FK(This)40 b(function)g(creates)h(a)g(new)f(write-only)h(n)m (tuple)f(\014le)g FD(\014lename)46 b FK(for)40 b(n)m(tuples)g(of)h (size)g FD(size)390 3940 y FK(and)33 b(returns)e(a)j(p)s(oin)m(ter)f (to)h(the)f(newly)g(created)h(n)m(tuple)f(struct.)49 b(An)m(y)34 b(existing)g(\014le)f(with)g(the)390 4049 y(same)28 b(name)g(is)g(truncated)h(to)f(zero)h(length)f(and)g(o)m(v)m (erwritten.)41 b(A)28 b(p)s(oin)m(ter)g(to)h(memory)f(for)g(the)390 4159 y(curren)m(t)f(n)m(tuple)g(ro)m(w)g FD(n)m(tuple)p 1407 4159 V 40 w(data)g FK(m)m(ust)g(b)s(e)f(supplied|this)g(is)h(used) f(to)i(cop)m(y)f(n)m(tuples)g(in)g(and)390 4269 y(out)k(of)f(the)h (\014le.)150 4540 y FJ(23.3)68 b(Op)t(ening)45 b(an)g(existing)h(n)l (tuple)f(\014le)3350 4774 y FK([F)-8 b(unction])-3599 b Fv(gsl_ntuple)55 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: 292 308 TeXDict begin 292 307 bop 150 -116 a FK(Chapter)30 b(23:)41 b(N-tuples)2618 b(292)150 299 y FJ(23.4)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(\()p FD(gsl)p 1389 493 28 4 v 40 w(n)m(tuple)31 b(*)g Ft(ntuple)p Fu(\))390 603 y FK(This)38 b(function)h(writes)g(the)h(curren)m(t)f(n)m(tuple)g FD(n)m(tuple-)p FH(>)p FD(n)m(tuple)p 2612 603 V 40 w(data)h FK(of)f(size)h FD(n)m(tuple-)p FH(>)p FD(size)45 b FK(to)390 712 y(the)31 b(corresp)s(onding)e(\014le.)3350 874 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_ntuple_bookdata)e Fu(\()p FD(gsl)p 1545 874 V 41 w(n)m(tuple)31 b(*)f Ft(ntuple)p Fu(\))390 984 y FK(This)g(function)g(is)g(a)h(synon)m(ym)f(for)g FH(gsl_ntuple_write)p FK(.)150 1201 y FJ(23.5)68 b(Reading)46 b(n)l(tuples)3350 1396 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_ntuple_read)d Fu(\()p FD(gsl)p 1336 1396 V 41 w(n)m(tuple)30 b(*)h Ft(ntuple)p Fu(\))390 1505 y FK(This)c(function)h(reads)g(the)h(curren)m(t)f(ro)m(w)g(of)g(the)h (n)m(tuple)f(\014le)g(for)g FD(n)m(tuple)33 b FK(and)28 b(stores)g(the)h(v)-5 b(alues)390 1615 y(in)30 b FD(n)m(tuple-)p FH(>)p FD(data)p FK(.)150 1832 y FJ(23.6)68 b(Closing)46 b(an)f(n)l(tuple)h(\014le)3350 2027 y 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(23.7)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 y(argumen)m(t.)275 3078 y(The)d FD(selection)j (function)e FK(determines)g(whic)m(h)g(n)m(tuple)g(ro)m(ws)g(are)g (selected)i(for)e(histogramming.)41 b(It)150 3188 y(is)30 b(de\014ned)g(b)m(y)g(the)g(follo)m(wing)i(struct,)390 3293 y Fz(typedef)41 b(struct)f({)468 3380 y(int)g(\(*)g(function\))h (\(void)g(*)e(ntuple_data,)j(void)e(*)g(params\);)468 3467 y(void)h(*)e(params;)390 3554 y(})g(gsl_ntuple_select_fn;)150 3681 y FK(The)32 b(struct)g(comp)s(onen)m(t)h FD(function)e FK(should)h(return)f(a)i(non-zero)f(v)-5 b(alue)33 b(for)f(eac)m(h)h(n) m(tuple)g(ro)m(w)f(that)h(is)150 3791 y(to)e(b)s(e)f(included)f(in)i (the)f(histogram.)275 3918 y(The)24 b FD(v)-5 b(alue)26 b(function)g FK(computes)f(scalar)i(v)-5 b(alues)25 b(for)g(those)h(n)m (tuple)g(ro)m(ws)f(selected)i(b)m(y)e(the)h(selection)150 4027 y(function,)390 4132 y Fz(typedef)41 b(struct)f({)468 4219 y(double)h(\(*)f(function\))h(\(void)f(*)g(ntuple_data,)i(void)e (*)f(params\);)468 4306 y(void)i(*)e(params;)390 4394 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: 293 309 TeXDict begin 293 308 bop 150 -116 a FK(Chapter)30 b(23:)41 b(N-tuples)2618 b(293)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(23.8)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: 294 310 TeXDict begin 294 309 bop 150 -116 a FK(Chapter)30 b(23:)41 b(N-tuples)2618 b(294)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: 295 311 TeXDict begin 295 310 bop 150 -116 a FK(Chapter)30 b(23:)41 b(N-tuples)2618 b(295)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(struct)g(data)f(*)i(data)e(=) i(\(struct)e(data)g(*\))h(ntuple_data;)485 3258 y(double)g(x,)g(y,)g (z;)485 3477 y(x)h(=)f(data->x;)485 3587 y(y)h(=)f(data->y;)485 3696 y(z)h(=)f(data->z;)485 3915 y(return)g(x)g(*)g(x)h(+)f(y)h(*)f(y)h (+)f(z)h(*)f(z;)390 4025 y(})p eop end %%Page: 296 312 TeXDict begin 296 311 bop 150 -116 a FK(Chapter)30 b(23:)41 b(N-tuples)2618 b(296)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 %%CreationDate: Mon Jan 22 20:12:36 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 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FK(and)g FC(hbook)f FK(\(a)m(v)-5 b(ailable)33 b(online\).)p eop end %%Page: 297 313 TeXDict begin 297 312 bop 150 -116 a FK(Chapter)30 b(24:)41 b(Mon)m(te)32 b(Carlo)f(In)m(tegration)1985 b(297)150 299 y FG(24)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 FK(whic)m(h)g(use)g(imp)s (ortance)g(sampling)h(and)f(strati\014ed)g(sampling)h(tec)m(hniques.)44 b(Eac)m(h)32 b(algorithm)150 866 y(computes)f(an)f(estimate)i(of)e(a)h (m)m(ultidimensional)g(de\014nite)g(in)m(tegral)h(of)e(the)h(form,)1340 1072 y FE(I)h FK(=)1508 957 y Fs(Z)1591 977 y Fq(x)1629 985 y Fl(u)1555 1145 y Fq(x)1593 1154 y Fl(l)1688 1072 y FE(dx)1817 957 y Fs(Z)1900 977 y Fq(y)1934 985 y Fl(u)1863 1145 y Fq(y)1897 1154 y Fl(l)1992 1072 y FE(dy)19 b(:::f)10 b FK(\()p FE(x;)15 b(y)s(;)g(:::)p FK(\))150 1294 y(o)m(v)m(er)35 b(a)f(h)m(yp)s(ercubic)f(region)h(\(\()p FE(x)1291 1308 y Fq(l)1317 1294 y FE(;)15 b(x)1409 1308 y Fq(u)1453 1294 y FK(\),)35 b(\()p FE(y)1628 1308 y Fq(l)1653 1294 y FE(;)15 b(y)1738 1308 y Fq(u)1782 1294 y FK(\))p FE(;)g(:::)p FK(\))35 b(using)e(a)h(\014xed)f(n)m(um)m(b)s(er)g(of)g(function)h (calls.)51 b(The)150 1403 y(routines)35 b(also)g(pro)m(vide)g(a)h (statistical)h(estimate)g(of)e(the)g(error)f(on)h(the)g(result.)54 b(This)34 b(error)g(estimate)150 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(24.1)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 (automatically)k(a)m(v)m(oided.)275 3546 y(The)42 b(function)g(to)h(b)s (e)f(in)m(tegrated)j(has)d(its)h(o)m(wn)g(datat)m(yp)s(e,)j(de\014ned)c (in)g(the)h(header)f(\014le)h FH(gsl_)150 3656 y(monte.h)p FK(.)3269 3843 y([Data)32 b(T)m(yp)s(e])-3600 b Fv(gsl_monte_function) 390 3953 y FK(This)21 b(data)h(t)m(yp)s(e)f(de\014nes)g(a)h(general)g (function)f(with)g(parameters)h(for)f(Mon)m(te)i(Carlo)f(in)m (tegration.)390 4114 y FH(double)29 b(\(*)g(f\))h(\(double)f(*)h FA(x)p FH(,)f(size_t)g FA(dim)p FH(,)g(void)g(*)h FA(params)p FH(\))870 4224 y FK(this)24 b(function)f(should)g(return)g(the)h(v)-5 b(alue)24 b FE(f)10 b FK(\()p FE(x;)15 b Fm(p)-5 b(ar)g(ams)s FK(\))24 b(for)f(the)h(argumen)m(t)h FD(x)30 b FK(and)870 4333 y(parameters)24 b FD(params)p FK(,)h(where)f FD(x)30 b FK(is)24 b(an)g(arra)m(y)h(of)f(size)h FD(dim)e FK(giving)i(the)f(co) s(ordinates)870 4443 y(of)31 b(the)f(p)s(oin)m(t)g(where)g(the)h (function)f(is)g(to)i(b)s(e)d(ev)-5 b(aluated.)390 4604 y FH(size_t)29 b(dim)870 4713 y FK(the)i(n)m(um)m(b)s(er)e(of)h (dimensions)g(for)g FD(x)p FK(.)390 4874 y FH(void)f(*)h(params)870 4984 y FK(a)h(p)s(oin)m(ter)f(to)h(the)g(parameters)g(of)f(the)h (function.)150 5171 y(Here)g(is)f(an)h(example)g(for)f(a)h(quadratic)f (function)g(in)g(t)m(w)m(o)i(dimensions,)1445 5340 y FE(f)10 b FK(\()p FE(x;)15 b(y)s FK(\))26 b(=)f FE(ax)1932 5302 y FB(2)1989 5340 y FK(+)20 b FE(bxy)j FK(+)d FE(cy)2417 5302 y FB(2)p eop end %%Page: 298 314 TeXDict begin 298 313 bop 150 -116 a FK(Chapter)30 b(24:)41 b(Mon)m(te)32 b(Carlo)f(In)m(tegration)1985 b(298)150 299 y(with)33 b FE(a)d FK(=)f(3,)34 b FE(b)c FK(=)g(2,)k FE(c)c FK(=)g(1.)49 b(The)32 b(follo)m(wing)j(co)s(de)e(de\014nes)f(a)i FH(gsl_monte_function)28 b(F)33 b FK(whic)m(h)g(y)m(ou)150 408 y(could)d(pass)g(to)i(an)e(in)m(tegrator:)390 543 y FH(struct)46 b(my_f_params)f({)i(double)f(a;)i(double)e(b;)h(double)f (c;)h(};)390 762 y(double)390 872 y(my_f)g(\(double)e(x[],)i(size_t)f (dim,)h(void)f(*)i(p\))f({)533 981 y(struct)f(my_f_params)f(*)i(fp)h(=) f(\(struct)f(my_f_params)f(*\)p;)533 1201 y(if)i(\(dim)g(!=)g(2\))676 1310 y({)772 1420 y(fprintf)f(\(stderr,)f("error:)h(dim)h(!=)g(2"\);) 772 1529 y(abort)f(\(\);)676 1639 y(})533 1858 y(return)94 b(fp->a)46 b(*)i(x[0])e(*)i(x[0])1010 1968 y(+)g(fp->b)e(*)i(x[0])e(*)i (x[1])1106 2077 y(+)f(fp->c)g(*)g(x[1])g(*)g(x[1];)390 2187 y(})390 2406 y(gsl_monte_function)c(F;)390 2516 y(struct)j(my_f_params)f(params)h(=)h({)h(3.0,)e(2.0,)h(1.0)g(};)390 2735 y(F.f)g(=)g(&my_f;)390 2844 y(F.dim)f(=)i(2;)390 2954 y(F.params)e(=)h(¶ms;)150 3089 y FK(The)30 b(function)g FE(f)10 b FK(\()p FE(x)p FK(\))30 b(can)h(b)s(e)f(ev)-5 b(aluated)31 b(using)f(the)h(follo)m(wing)g(macro,)390 3223 y FH(#define)46 b(GSL_MONTE_FN_EVAL\(F,x\))581 3333 y(\(*\(\(F\)->f\)\)\(x,\(F\)->dim,\()o(F\)->)o(par)o(ams\))150 3566 y FJ(24.2)68 b(PLAIN)45 b(Mon)l(te)g(Carlo)150 3725 y FK(The)33 b(plain)g(Mon)m(te)h(Carlo)g(algorithm)g(samples)f(p)s(oin) 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: 299 315 TeXDict begin 299 314 bop 150 -116 a FK(Chapter)30 b(24:)41 b(Mon)m(te)32 b(Carlo)f(In)m(tegration)1985 b(299)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 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 1928 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 2037 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 2147 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 2256 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 2434 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_monte_plain_free)d Fu(\()p FD(gsl)p 1650 2434 V 41 w(mon)m(te)p 1935 2434 V 41 w(plain)p 2173 2434 V 40 w(state)32 b(*)e Ft(s)p Fu(\))390 2544 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(.)150 2772 y FJ(24.3)68 b(MISER)150 2931 y FK(The)36 b FC(miser)g FK(algorithm)i(of)f(Press)f(and)g(F)-8 b(arrar)37 b(is)g(based)f(on)g(recursiv)m(e)h(strati\014ed)g(sampling.) 60 b(This)150 3041 y(tec)m(hnique)35 b(aims)g(to)h(reduce)e(the)h(o)m (v)m(erall)i(in)m(tegration)f(error)e(b)m(y)h(concen)m(trating)h(in)m (tegration)h(p)s(oin)m(ts)150 3150 y(in)30 b(the)h(regions)f(of)h (highest)g(v)-5 b(ariance.)275 3283 y(The)28 b(idea)i(of)g (strati\014ed)f(sampling)h(b)s(egins)e(with)h(the)h(observ)-5 b(ation)30 b(that)g(for)f(t)m(w)m(o)i(disjoin)m(t)e(regions)150 3392 y FE(a)35 b FK(and)f FE(b)g FK(with)h(Mon)m(te)h(Carlo)f (estimates)i(of)d(the)h(in)m(tegral)i FE(E)2314 3406 y Fq(a)2354 3392 y FK(\()p FE(f)10 b FK(\))35 b(and)f FE(E)2762 3406 y Fq(b)2795 3392 y FK(\()p FE(f)10 b FK(\))35 b(and)f(v)-5 b(ariances)36 b FE(\033)3588 3359 y FB(2)3585 3415 y Fq(a)3625 3392 y FK(\()p FE(f)10 b FK(\))150 3502 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: 300 316 TeXDict begin 300 315 bop 150 -116 a FK(Chapter)30 b(24:)41 b(Mon)m(te)32 b(Carlo)f(In)m(tegration)1985 b(300)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 Fu(\()p FD(gsl)p 1598 1509 V 41 w(mon)m(te)p 1883 1509 V 41 w(miser)p 2137 1509 V 39 w(state*)33 b Ft(s)p Fu(\))390 1619 y FK(This)g(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 1728 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 1932 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_monte_miser_integ)q(rate)f Fu(\()p FD(gsl)p 1859 1932 V 41 w(mon)m(te)p 2144 1932 V 41 w(function)30 b(*)h Ft(f)p FD(,)g(const)565 2042 y(double)f Ft(xl)p Fo([])p FD(,)h(const)g(double)f Ft(xu)p Fo([])p FD(,)h(size)p 1968 2042 V 41 w(t)f Ft(dim)p FD(,)i(size)p 2428 2042 V 41 w(t)e Ft(calls)p FD(,)i(gsl)p 2957 2042 V 41 w(rng)e(*)h Ft(r)p FD(,)565 2152 y(gsl)p 677 2152 V 41 w(mon)m(te)p 962 2152 V 41 w(miser)p 1216 2152 V 40 w(state)g(*)g Ft(s)p FD(,)g(double)f(*)h Ft(result)p FD(,)h(double)e(*)h Ft(abserr)p Fu(\))390 2261 y FK(This)e(routines)g(uses)h(the)f FC(miser)g 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: 301 317 TeXDict begin 301 316 bop 150 -116 a FK(Chapter)30 b(24:)41 b(Mon)m(te)32 b(Carlo)f(In)m(tegration)1985 b(301)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(24.4)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: 302 318 TeXDict begin 302 317 bop 150 -116 a FK(Chapter)30 b(24:)41 b(Mon)m(te)32 b(Carlo)f(In)m(tegration)1985 b(302)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 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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: 303 319 TeXDict begin 303 318 bop 150 -116 a FK(Chapter)30 b(24:)41 b(Mon)m(te)32 b(Carlo)f(In)m(tegration)1985 b(303)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 (ccasionally)i(pro)s(duce)d(an)g(estimate)i(where)150 628 y(the)30 b(error)g(is)g(zero,)i(particularly)e(if)g(the)h(function) e(is)i(constan)m(t)g(in)f(some)g(regions.)42 b(An)29 b(estimate)j(with)150 737 y(zero)43 b(error)f(causes)h(the)f(w)m(eigh)m (ted)i(a)m(v)m(erage)h(to)d(break)h(do)m(wn)e(and)h(m)m(ust)g(b)s(e)g (handled)f(separately)-8 b(.)150 847 y(In)33 b(the)i(original)g(F)-8 b(ortran)35 b(implemen)m(tations)g(of)f FC(vegas)f FK(the)i(error)e (estimate)j(is)e(made)g(non-zero)h(b)m(y)150 956 y(substituting)c(a)h (small)g(v)-5 b(alue)32 b(\(t)m(ypically)i FH(1e-30)p FK(\).)43 b(The)31 b(implemen)m(tation)i(in)e(GSL)g(di\013ers)g(from)g (this)150 1066 y(and)41 b(a)m(v)m(oids)h(the)g(use)e(of)i(an)f (arbitrary)g(constan)m(t|it)i(either)e(assigns)h(the)f(v)-5 b(alue)42 b(a)g(w)m(eigh)m(t)g(whic)m(h)150 1176 y(is)37 b(the)f(a)m(v)m(erage)j(w)m(eigh)m(t)f(of)f(the)g(preceding)f (estimates)j(or)d(discards)g(it)h(according)g(to)h(the)e(follo)m(wing) 150 1285 y(pro)s(cedure,)150 1464 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: 304 320 TeXDict begin 304 319 bop 150 -116 a FK(Chapter)30 b(24:)41 b(Mon)m(te)32 b(Carlo)f(In)m(tegration)1985 b(304)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(24.5)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: 305 321 TeXDict begin 305 320 bop 150 -116 a FK(Chapter)30 b(24:)41 b(Mon)m(te)32 b(Carlo)f(In)m(tegration)1985 b(305)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 (en)m(t)f(at)h(the)g(origin)g(b)m(y)g(a)150 518 y(random)30 b(w)m(alk)h(on)f(a)h(b)s(o)s(dy-cen)m(tered)f(cubic)g(lattice)j(in)d (three)h(dimensions.)275 672 y(F)-8 b(or)45 b(simplicit)m(y)h(w)m(e)g (will)f(compute)g(the)g(in)m(tegral)i(o)m(v)m(er)f(the)f(region)h(\(0)p FE(;)15 b FK(0)p FE(;)g FK(0\))47 b(to)f(\()p FE(\031)s(;)15 b(\031)s(;)g(\031)s FK(\))47 b(and)150 782 y(m)m(ultiply)33 b(b)m(y)f(8)h(to)g(obtain)g(the)g(full)f(result.)47 b(The)32 b(in)m(tegral)i(is)e(slo)m(wly)i(v)-5 b(arying)32 b(in)g(the)h(middle)f (of)h(the)150 892 y(region)25 b(but)g(has)f(in)m(tegrable)i (singularities)g(at)g(the)f(corners)f(\(0)p FE(;)15 b FK(0)p FE(;)g FK(0\),)29 b(\(0)p FE(;)15 b(\031)s(;)g(\031)s FK(\),)29 b(\()p FE(\031)s(;)15 b FK(0)p FE(;)g(\031)s FK(\))26 b(and)f(\()p FE(\031)s(;)15 b(\031)s(;)g FK(0\).)150 1001 y(The)26 b(Mon)m(te)h(Carlo)g(routines)f(only)g(select)i(p)s(oin)m (ts)e(whic)m(h)g(are)g(strictly)h(within)f(the)g(in)m(tegration)i (region)150 1111 y(and)i(so)g(no)h(sp)s(ecial)g(measures)f(are)h (needed)f(to)h(a)m(v)m(oid)h(these)e(singularities.)390 1243 y Fz(#include)41 b()390 1330 y(#include)g ()390 1417 y(#include)g()390 1504 y(#include)g()390 1592 y(#include)g ()390 1679 y(#include)g() 390 1853 y(/*)f(Computation)h(of)f(the)g(integral,)625 2027 y(I)g(=)f(int)h(\(dx)g(dy)g(dz\)/\(2pi\)^3)81 b (1/\(1-cos\(x\)cos\(y\)cos\(z\)\))508 2202 y(over)40 b(\(-pi,-pi,-pi\))i(to)e(\(+pi,)g(+pi,)g(+pi\).)158 b(The)40 b(exact)h(answer)508 2289 y(is)e(Gamma\(1/4\)^4/\(4)k(pi^3\).)158 b(This)40 b(example)h(is)f(taken)g(from)508 2376 y(C.Itzykson,)h (J.M.Drouffe,)h("Statistical)g(Field)f(Theory)f(-)508 2463 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b(transition)h(can)f(still)h(o)s(ccur,)h(and)d(its)i(lik)m (eliho)s(o)s(d)f(is)h(prop)s(ortional)f(to)g(the)h(temp)s(erature)f FE(T)47 b FK(and)150 2858 y(in)m(v)m(ersely)31 b(prop)s(ortional)g(to)g (the)f(energy)h(di\013erence)g FE(E)2080 2872 y Fq(i)p FB(+1)2212 2858 y FI(\000)20 b FE(E)2370 2872 y Fq(i)2398 2858 y FK(.)275 2991 y(The)38 b(temp)s(erature)g FE(T)51 b FK(is)38 b(initially)i(set)f(to)h(a)f(high)f(v)-5 b(alue,)41 b(and)d(a)h(random)e(w)m(alk)j(is)e(carried)h(out)150 3101 y(at)32 b(that)g(temp)s(erature.)42 b(Then)31 b(the)g(temp)s (erature)g(is)g(lo)m(w)m(ered)h(v)m(ery)g(sligh)m(tly)g(according)g(to) g(a)g FD(co)s(oling)150 3210 y(sc)m(hedule)p FK(,)f(for)f(example:)41 b FE(T)d FI(!)26 b FE(T)10 b(=\026)1438 3224 y Fq(T)1521 3210 y FK(where)30 b FE(\026)1839 3224 y Fq(T)1921 3210 y FK(is)g(sligh)m(tly)i(greater)g(than)e(1.)275 3344 y(The)d(sligh)m(t)i(probabilit)m(y)g(of)f(taking)h(a)f(step)g(that)h (giv)m(es)g(higher)f(energy)g(is)g(what)g(allo)m(ws)h(sim)m(ulated)150 3454 y(annealing)i(to)g(frequen)m(tly)g(get)g(out)g(of)f(lo)s(cal)i (minima.)150 3684 y FJ(25.2)68 b(Sim)l(ulated)46 b(Annealing)g (functions)3350 3891 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_siman_solve)c Fu(\()p FD(const)31 b(gsl)p 1627 3891 28 4 v 40 w(rng)f(*)h Ft(r)p FD(,)g(v)m(oid)g(*)g Ft(x0_p)p FD(,)565 4001 y(gsl)p 677 4001 V 41 w(siman)p 951 4001 V 40 w(Efunc)p 1223 4001 V 39 w(t)f Ft(Ef)p FD(,)h(gsl)p 1593 4001 V 41 w(siman)p 1867 4001 V 40 w(step)p 2069 4001 V 40 w(t)g Ft(take_step)p FD(,)i(gsl)p 2807 4001 V 40 w(siman)p 3080 4001 V 40 w(metric)p 3372 4001 V 41 w(t)565 4111 y Ft(distance)p FD(,)g(gsl)p 1151 4111 V 41 w(siman)p 1425 4111 V 39 w(prin)m(t)p 1659 4111 V 40 w(t)e Ft(print_position)p FD(,)k(gsl)p 2659 4111 V 40 w(siman)p 2932 4111 V 40 w(cop)m(y)p 3153 4111 V 41 w(t)c Ft(copyfunc)p FD(,)565 4220 y(gsl)p 677 4220 V 41 w(siman)p 951 4220 V 40 w(cop)m(y)p 1172 4220 V 40 w(construct)p 1581 4220 V 41 w(t)f Ft(copy_constructor)p FD(,)36 b(gsl)p 2686 4220 V 40 w(siman)p 2959 4220 V 40 w(destro)m(y)p 3287 4220 V 41 w(t)565 4330 y Ft(destructor)p FD(,)e(size)p 1291 4330 V 41 w(t)c Ft(element_size)p FD(,)k(gsl)p 2186 4330 V 41 w(siman)p 2460 4330 V 40 w(params)p 2789 4330 V 40 w(t)c Ft(params)p Fu(\))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 (con\014gurations,)j(a)e(\014xed-size)h(mo)s(de)e(and)h(a)g(v)-5 b(ariable-size)37 b(mo)s(de.)390 5011 y(In)30 b(the)g(\014xed-size)h (mo)s(de)f(the)h(con\014guration)f(is)h(stored)f(as)h(a)g(single)g(blo) s(c)m(k)g(of)f(memory)h(of)f(size)390 5121 y FD(elemen)m(t)p 700 5121 V 42 w(size)p FK(.)39 b(Copies)24 b(of)g(this)g (con\014guration)g(are)g(created,)j(copied)d(and)f(destro)m(y)m(ed)i (in)m(ternally)390 5230 y(using)f(the)h(standard)g(library)f(functions) g FH(malloc)p FK(,)h FH(memcpy)e FK(and)h FH(free)p FK(.)38 b(The)24 b(function)h(p)s(oin)m(ters)390 5340 y FD(cop)m(yfunc)p FK(,)h FD(cop)m(y)p 979 5340 V 41 w(constructor)32 b FK(and)24 b FD(destructor)32 b FK(should)24 b(b)s(e)g(n)m(ull)h(p)s (oin)m(ters)g(in)g(\014xed-size)g(mo)s(de.)p eop end %%Page: 310 326 TeXDict begin 310 325 bop 150 -116 a FK(Chapter)30 b(25:)41 b(Sim)m(ulated)31 b(Annealing)2126 b(310)390 299 y(In)22 b(the)h(v)-5 b(ariable-size)25 b(mo)s(de)e(the)g(functions)f FD(cop)m(yfunc)p FK(,)j FD(cop)m(y)p 2510 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 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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 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y(gsl_siman_params_t)j(params) p eop end %%Page: 312 328 TeXDict begin 312 327 bop 150 -116 a FK(Chapter)30 b(25:)41 b(Sim)m(ulated)31 b(Annealing)2126 b(312)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\(int)h (argc,)f(char)h(*argv[]\))390 3524 y({)468 3611 y(const)g(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: 313 329 TeXDict begin 313 328 bop 150 -116 a FK(Chapter)30 b(25:)41 b(Sim)m(ulated)31 b(Annealing)2126 b(313)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 FK(in)i(the)g(follo)m(wing)150 565 y(w)m(a)m(y:)390 837 y FH($)47 b(./siman_test)e(|)i(awk)g('!/^#/)f ({print)g($1,)h($4}')438 947 y(|)g(graph)g(-y)g(1.34)f(1.4)h(-W0)g(-X)g (generation)e(-Y)j(position)438 1056 y(|)f(plot)g(-Tps)f(>)i (siman-test.eps)390 1166 y($)f(./siman_test)e(|)i(awk)g('!/^#/)f ({print)g($1,)h($5}')438 1276 y(|)g(graph)g(-y)g(-0.88)f(-0.83)g(-W0)h (-X)h(generation)d(-Y)i(energy)438 1385 y(|)g(plot)g(-Tps)f(>)i (siman-energy.eps)275 3154 y @beginspecial 62 @llx 177 @lly 500 @urx 576 @ury 2016 @rwi @setspecial %%BeginDocument: siman-test.eps %!PS-Adobe-3.0 EPSF-3.0 %%Creator: GNU libplot drawing library 4.1 %%Title: PostScript plot %%CreationDate: Wed Dec 20 22:05:02 2006 %%DocumentData: Clean7Bit %%LanguageLevel: 1 %%Pages: 1 %%PageOrder: Ascend %%Orientation: Portrait %%BoundingBox: 62 177 500 576 %%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: 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 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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 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bop 150 -116 a FK(Chapter)30 b(25:)41 b(Sim)m(ulated)31 b(Annealing)2126 b(314)150 299 y Fy(25.3.2)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: 315 331 TeXDict begin 315 330 bop 150 -116 a FK(Chapter)30 b(25:)41 b(Sim)m(ulated)31 b(Annealing)2126 b(315)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: 316 332 TeXDict begin 316 331 bop 150 -116 a FK(Chapter)30 b(25:)41 b(Sim)m(ulated)31 b(Annealing)2126 b(316)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 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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 7845 2716 7846 2716 7847 2716 7849 2716 7850 2716 7852 2716 7853 2716 7854 2716 7856 2716 7857 2716 7858 2716 7860 2716 7861 2716 7863 2716 7864 2716 7865 2716 7867 2716 7868 2716 7870 2716 7871 2716 7872 2716 7874 2716 7875 2716 7876 2716 7878 2716 7879 2716 7881 2716 7882 2716 7883 2716 7885 2716 7886 2716 7888 2716 7889 2716 7890 2716 7892 2716 7893 2716 7894 2716 7896 2716 7897 2716 7899 2716 7900 2716 7901 2716 7903 2716 7904 2716 7905 2716 7907 2716 7908 2716 7910 2716 7911 2716 7912 2716 7914 2716 7915 2716 7917 2716 7918 2716 7919 2716 7921 2716 7922 2716 7923 2716 7925 2716 7926 2716 7928 2716 7929 2716 7930 2716 7932 2716 7933 2716 7935 2716 7936 2716 7937 2716 7939 2716 7940 2716 7941 2716 7943 2716 7944 2716 7946 2716 7947 2716 7948 2716 7950 2716 7951 2716 7952 2716 7954 2716 7955 2716 7957 2716 7958 2716 7959 2716 7961 2716 7962 2716 7964 2716 7965 2716 7966 2716 7968 2716 7969 2716 7970 2716 7972 2716 7973 2716 7975 2716 7976 2716 7977 2716 7979 2716 7980 2716 7982 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(25.4)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: 317 333 TeXDict begin 317 332 bop 150 -116 a FK(Chapter)30 b(26:)41 b(Ordinary)29 b(Di\013eren)m(tial)k(Equations)1690 b(317)150 299 y FG(26)80 b(Ordinary)54 b(Di\013eren)l(tial)d(Equations)150 541 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) 150 650 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)150 760 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)150 869 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)150 979 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 1088 y(of)i(lo)m(w)g(lev)m(el)h(functions.)275 1225 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 1335 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 1445 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 1554 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 1790 y FJ(26.1)68 b(De\014ning)45 b(the)h(ODE)f(System)150 1950 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 2106 y FE(dy)1492 2120 y Fq(i)1519 2106 y FK(\()p FE(t)p FK(\))p 1400 2146 224 4 v 1471 2229 a FE(dt)1658 2167 y FK(=)25 b FE(f)1799 2181 y Fq(i)1826 2167 y FK(\()p FE(t;)15 b(y)1979 2181 y FB(1)2016 2167 y FK(\()p FE(t)p FK(\))p 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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: 320 336 TeXDict begin 320 335 bop 150 -116 a FK(Chapter)30 b(26:)41 b(Ordinary)29 b(Di\013eren)m(tial)k(Equations)1690 b(320)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(26.3)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: 321 337 TeXDict begin 321 336 bop 150 -116 a FK(Chapter)30 b(26:)41 b(Ordinary)29 b(Di\013eren)m(tial)k(Equations)1690 b(321)390 299 y(where)33 b FE(q)j 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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: 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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 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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: 323 339 TeXDict begin 323 338 bop 150 -116 a FK(Chapter)30 b(26:)41 b(Ordinary)29 b(Di\013eren)m(tial)k(Equations)1690 b(323)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 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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 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b(Di\013eren)m(tial)k(Equations)1690 b(324)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 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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 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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 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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 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(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(double)g(mu)g(=)g(*\(double)f(*\)params;)485 4902 y(f[0])h(=)h(y[1];)485 5011 y(f[1])f(=)h(-y[0])e(-)h (mu*y[1]*\(y[0]*y[0])c(-)48 b(1\);)485 5121 y(return)f(GSL_SUCCESS;)390 5230 y(})p eop end %%Page: 326 342 TeXDict begin 326 341 bop 150 -116 a FK(Chapter)30 b(26:)41 b(Ordinary)29 b(Di\013eren)m(tial)k(Equations)1690 b(326)390 299 y FH(int)390 408 y(jac)47 b(\(double)f(t,)h(const)f(double)g(y[],)h (double)f(*dfdy,)629 518 y(double)g(dfdt[],)g(void)g(*params\))390 628 y({)485 737 y(double)h(mu)g(=)g(*\(double)f(*\)params;)485 847 y(gsl_matrix_view)e(dfdy_mat)581 956 y(=)j(gsl_matrix_view_array)42 b(\(dfdy,)k(2,)i(2\);)485 1066 y(gsl_matrix)d(*)j(m)f(=)h (&dfdy_mat.matrix;)485 1176 y(gsl_matrix_set)c(\(m,)j(0,)g(0,)h(0.0\);) 485 1285 y(gsl_matrix_set)c(\(m,)j(0,)g(1,)h(1.0\);)485 1395 y(gsl_matrix_set)c(\(m,)j(1,)g(0,)h(-2.0*mu*y[0]*y[1])43 b(-)k(1.0\);)485 1504 y(gsl_matrix_set)d(\(m,)j(1,)g(1,)h (-mu*\(y[0]*y[0])c(-)j(1.0\)\);)485 1614 y(dfdt[0])f(=)i(0.0;)485 1724 y(dfdt[1])e(=)i(0.0;)485 1833 y(return)f(GSL_SUCCESS;)390 1943 y(})390 2162 y(int)390 2271 y(main)g(\(void\))390 2381 y({)485 2491 y(double)g(mu)g(=)g(10;)485 2600 y(gsl_odeiv2_system) d(sys)i(=)i({func,)e(jac,)h(2,)g(&mu};)485 2819 y(gsl_odeiv2_driver)d (*)j(d)g(=)581 2929 y(gsl_odeiv2_driver_alloc_)o(y_ne)o(w)42 b(\(&sys,)k(gsl_odeiv2_step_rk8pd,)2013 3039 y(1e-6,)g(1e-6,)g(0.0\);) 485 3148 y(int)h(i;)485 3258 y(double)g(t)g(=)g(0.0,)g(t1)g(=)h(100.0;) 485 3367 y(double)f(y[2])f(=)i({)f(1.0,)g(0.0)g(};)485 3587 y(for)g(\(i)h(=)f(1;)g(i)h(<=)f(100;)f(i++\))581 3696 y({)676 3806 y(double)g(ti)i(=)f(i)h(*)f(t1)g(/)h(100.0;)676 3915 y(int)f(status)f(=)i(gsl_odeiv2_driver_apply)41 b(\(d,)47 b(&t,)g(ti,)g(y\);)676 4134 y(if)h(\(status)d(!=)j (GSL_SUCCESS\))772 4244 y({)867 4354 y(printf)e(\("error,)g(return)g (value=\045d\\n",)e(status\);)867 4463 y(break;)772 4573 y(})676 4792 y(printf)i(\("\045.5e)h(\045.5e)f(\045.5e\\n",)g(t,)h (y[0],)f(y[1]\);)581 4902 y(})485 5121 y(gsl_odeiv2_driver_free)c (\(d\);)485 5230 y(return)47 b(0;)390 5340 y(})p eop end %%Page: 327 343 TeXDict begin 327 342 bop 150 -116 a FK(Chapter)30 b(26:)41 b(Ordinary)29 b(Di\013eren)m(tial)k(Equations)1690 b(327)150 299 y(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)150 408 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)150 518 y(time)e(p)s(oin)m(ts.)390 792 y FH(int)390 902 y(main)47 b(\(void\))390 1011 y({)485 1121 y(const)g(gsl_odeiv2_step_type)42 b(*)48 b(T)581 1230 y(=)f(gsl_odeiv2_step_rk8pd;)485 1450 y(gsl_odeiv2_step)d(*)k(s) 581 1559 y(=)f(gsl_odeiv2_step_alloc)42 b(\(T,)47 b(2\);)485 1669 y(gsl_odeiv2_control)c(*)48 b(c)581 1778 y(=)f (gsl_odeiv2_control_y_new)42 b(\(1e-6,)k(0.0\);)485 1888 y(gsl_odeiv2_evolve)e(*)j(e)581 1998 y(=)g(gsl_odeiv2_evolve_alloc)42 b(\(2\);)485 2217 y(double)47 b(mu)g(=)g(10;)485 2326 y(gsl_odeiv2_system)d(sys)i(=)i({func,)e(jac,)h(2,)g(&mu};)485 2545 y(double)g(t)g(=)g(0.0,)g(t1)g(=)h(100.0;)485 2655 y(double)f(h)g(=)g(1e-6;)485 2765 y(double)g(y[2])f(=)i({)f(1.0,)g(0.0) g(};)485 2984 y(while)g(\(t)g(<)g(t1\))581 3093 y({)676 3203 y(int)g(status)f(=)i(gsl_odeiv2_evolve_apply)41 b(\(e,)47 b(c,)g(s,)2442 3313 y(&sys,)2442 3422 y(&t,)g(t1,)2442 3532 y(&h,)g(y\);)676 3751 y(if)h(\(status)d(!=)j(GSL_SUCCESS\))867 3861 y(break;)676 4080 y(printf)e(\("\045.5e)h(\045.5e)f(\045.5e\\n",)g (t,)h(y[0],)f(y[1]\);)581 4189 y(})485 4408 y(gsl_odeiv2_evolve_free)c (\(e\);)485 4518 y(gsl_odeiv2_control_free)g(\(c\);)485 4628 y(gsl_odeiv2_step_free)h(\(s\);)485 4737 y(return)k(0;)390 4847 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: 328 344 TeXDict begin 328 343 bop 150 -116 a FK(Chapter)30 b(26:)41 b(Ordinary)29 b(Di\013eren)m(tial)k(Equations)1690 b(328)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: 329 345 TeXDict begin 329 344 bop 150 -116 a FK(Chapter)30 b(26:)41 b(Ordinary)29 b(Di\013eren)m(tial)k(Equations)1690 b(329)485 299 y FH(return)47 b(s;)390 408 y(})150 641 y FJ(26.7)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) h(b)s(e)f(found)f(in)i(the)g(Handb)s(o)s(ok)e(of)i(Mathematical)150 1667 y(F)-8 b(unctions,)330 1802 y(Abramo)m(witz)31 b(&)f(Stegun)g (\(eds.\),)i FD(Handb)s(o)s(ok)d(of)i(Mathematical)i(F)-8 b(unctions)p FK(,)31 b(Section)g(25.5.)150 1961 y(The)f(implicit)h (Bulirsc)m(h-Sto)s(er)g(algorithm)g FH(bsimp)e FK(is)i(describ)s(ed)e (in)h(the)h(follo)m(wing)g(pap)s(er,)330 2095 y(G.)46 b(Bader)f(and)f(P)-8 b(.)46 b(Deu\015hard,)h(\\A)f(Semi-Implicit)g (Mid-P)m(oin)m(t)g(Rule)f(for)g(Sti\013)g(Systems)g(of)330 2205 y(Ordinary)29 b(Di\013eren)m(tial)k(Equations.",)e(Numer.)f(Math.) h(41,)h(373{398,)i(1983.)150 2364 y(The)j(Adams)f(and)h(BDF)h(m)m (ultistep)g(metho)s(ds)e FH(msadams)f FK(and)h FH(msbdf)g FK(are)i(based)e(on)h(the)g(follo)m(wing)150 2474 y(articles,)330 2609 y(G.)g(D.)h(Byrne)e(and)h(A.)g(C.)g(Hindmarsh,)g(\\A)g(P)m(oly)m (algorithm)j(for)c(the)h(Numerical)h(Solution)f(of)330 2718 y(Ordinary)29 b(Di\013eren)m(tial)k(Equations.",)e(A)m(CM)g(T)-8 b(rans.)40 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: 330 346 TeXDict begin 330 345 bop 150 -116 a FK(Chapter)30 b(27:)41 b(In)m(terp)s(olation)2437 b(330)150 299 y FG(27)80 b(In)l(terp)t (olation)150 519 y FK(This)30 b(c)m(hapter)i(describ)s(es)e(functions)h (for)g(p)s(erforming)f(in)m(terp)s(olation.)44 b(The)30 b(library)h(pro)m(vides)g(a)g(v)-5 b(ari-)150 628 y(et)m(y)28 b(of)f(in)m(terp)s(olation)i(metho)s(ds,)e(including)f(Cubic)h(splines) f(and)g(Akima)i(splines.)39 b(The)27 b(in)m(terp)s(olation)150 738 y(t)m(yp)s(es)33 b(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-)150 848 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)150 957 y(functions)30 b(are)h(a)m(v)-5 b(ailable)32 b(for)f(computing)f(deriv)-5 b(ativ)m(es)32 b(and)e(in)m(tegrals)i(of)e(in)m(terp)s(olating)i (functions.)275 1089 y(These)h(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 1198 y(terp)s(olate)d(noisy)e(data)h(with)f (a)h(smo)s(othing)f(curv)m(e)h(see)g(Chapter)f(39)h([Basis)g(Splines],) f(page)i(433.)275 1330 y(The)37 b(functions)g(describ)s(ed)f(in)h(this) h(section)h(are)e(declared)h(in)g(the)f(header)h(\014les)f FH(gsl_interp.h)150 1440 y FK(and)30 b FH(gsl_spline.h)p FK(.)150 1666 y FJ(27.1)68 b(In)l(tro)t(duction)150 1826 y FK(Giv)m(en)28 b(a)f(set)h(of)f(data)g(p)s(oin)m(ts)g(\()p FE(x)1281 1840 y FB(1)1319 1826 y FE(;)15 b(y)1404 1840 y FB(1)1441 1826 y FK(\))g FE(:)g(:)g(:)i FK(\()p FE(x)1700 1840 y Fq(n)1745 1826 y FE(;)e(y)1830 1840 y Fq(n)1875 1826 y FK(\))27 b(the)h(routines)e(describ)s(ed)g(in)h(this)g(section)h (compute)150 1935 y(a)c(con)m(tin)m(uous)g(in)m(terp)s(olating)h (function)e FE(y)s FK(\()p FE(x)p FK(\))h(suc)m(h)f(that)h FE(y)s FK(\()p FE(x)2267 1949 y Fq(i)2295 1935 y FK(\))i(=)f FE(y)2497 1949 y Fq(i)2524 1935 y FK(.)38 b(The)23 b(in)m(terp)s (olation)i(is)f(piecewise)150 2045 y(smo)s(oth,)k(and)g(its)g(b)s(eha)m (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 2272 y FJ(27.2)68 b(In)l(terp)t(olation)47 b(F)-11 b(unctions)150 2431 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 2541 y(created)h(b)m(y)g(the)f(follo)m (wing)i(functions.)3350 2716 y([F)-8 b(unction])-3599 b Fv(gsl_interp)55 b(*)e(gsl_interp_alloc)d Fu(\()p FD(const)31 b(gsl)p 2097 2716 28 4 v 41 w(in)m(terp)p 2373 2716 V 40 w(t)m(yp)s(e)g(*)f Ft(T)p FD(,)h(size)p 2942 2716 V 41 w(t)565 2826 y Ft(size)p Fu(\))390 2936 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 3045 y FK(for)30 b FD(size)36 b FK(data-p)s(oin)m(ts.)3350 3221 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_interp_init)d Fu(\()p FD(gsl)p 1336 3221 V 41 w(in)m(terp)31 b(*)f Ft(interp)p FD(,)j(const)e(double)e Ft(xa)p Fo([])p FD(,)i(const)565 3331 y(double)f Ft(ya)p Fo([])p FD(,)h(size)p 1221 3331 V 41 w(t)g Ft(size)p Fu(\))390 3440 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 3550 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 3659 y(the)h(data)g(arra)m(ys)g FD(xa)f FK(and)g FD(y)m(a)h 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5121 y([In)m(terp)s(olation)31 b(T)m(yp)s(e])-3600 b Fv(gsl_interp_polynomial)390 5230 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 5340 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)p eop end %%Page: 331 347 TeXDict begin 331 346 bop 150 -116 a FK(Chapter)30 b(27:)41 b(In)m(terp)s(olation)2437 b(331)390 299 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)390 408 y(equal)31 b(to)g(the)g(n)m(um)m(b)s(er)e(of)h(p)s(oin)m(ts.)2947 573 y([In)m(terp)s(olation)h(T)m(yp)s(e])-3600 b Fv(gsl_interp_cspline) 390 683 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)390 793 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)390 902 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 1012 y(p)s(oin)m(t.)2947 1177 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 1286 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 1396 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 1505 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 1615 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 1725 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 1889 y([In)m(terp)s(olation)31 b(T)m(yp)s(e])-3600 b Fv(gsl_interp_akima)390 1999 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 2109 y(non-rounded)f(corner)h(algorithm)h(of)g(W)-8 b(o)s(dic)m(k)j(a.) 2947 2274 y([In)m(terp)s(olation)31 b(T)m(yp)s(e])-3600 b Fv(gsl_interp_akima_perio)q(dic)390 2383 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 2493 y(non-rounded)i(corner)h (algorithm)h(of)g(W)-8 b(o)s(dic)m(k)j(a.)275 2658 y(The)29 b(follo)m(wing)j(related)g(functions)d(are)i(a)m(v)-5 b(ailable:)3350 2823 y([F)d(unction])-3599 b Fv(const)54 b(char)f(*)g(gsl_interp_name)d Fu(\()p FD(const)31 b(gsl)p 2045 2823 28 4 v 41 w(in)m(terp)f(*)h Ft(interp)p Fu(\))390 2932 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 3060 y FH(printf)46 b(\("interp)g(uses)g('\045s')h(interpolation.\\n",)1012 3170 y(gsl_interp_name)c(\(interp\)\);)390 3298 y FK(w)m(ould)30 b(prin)m(t)g(something)h(lik)m(e,)630 3426 y FH(interp)46 b(uses)h('cspline')e(interpolation.)3350 3591 y FK([F)-8 b(unction])-3599 b Fv(unsigned)55 b(int)e(gsl_interp_min_size)e Fu(\()p FD(const)31 b(gsl)p 2254 3591 V 41 w(in)m(terp)f(*)h Ft(interp)p Fu(\))3350 3700 y FK([F)-8 b(unction])-3599 b Fv(unsigned)55 b(int)e(gsl_interp_type_min_si)q(ze)f Fu(\()p FD(const)31 b(gsl)p 2516 3700 V 40 w(in)m(terp)p 2791 3700 V 41 w(t)m(yp)s(e)f(*)h Ft(T)p Fu(\))390 3810 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 3919 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 4029 y(requires)d(a)h(minim)m(um)e(of)i(5)g(p)s(oin)m(ts.)150 4249 y FJ(27.4)68 b(Index)45 b(Lo)t(ok-up)f(and)h(Acceleration)150 4408 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 4518 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 4627 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 4737 y(immediately)-8 b(.)3350 4902 y([F)g(unction])-3599 b Fv(size_t)54 b (gsl_interp_bsearch)d Fu(\()p FD(const)31 b(double)f Ft(x_array)p Fo([])p FD(,)j(double)d Ft(x)p FD(,)g(size)p 3094 4902 V 41 w(t)565 5011 y Ft(index_lo)p FD(,)j(size)p 1186 5011 V 41 w(t)e Ft(index_hi)p Fu(\))390 5121 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 5121 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 5230 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 5230 V 40 w(lo)p FK(,)p FD(index)p 3174 5230 V 41 w(hi)5 b FK(].)43 b(An)31 b(inline)390 5340 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.)p eop end %%Page: 332 348 TeXDict begin 332 347 bop 150 -116 a FK(Chapter)30 b(27:)41 b(In)m(terp)s(olation)2437 b(332)3350 299 y([F)-8 b(unction])-3599 b Fv(gsl_interp_accel)57 b(*)c(gsl_interp_accel_alloc)f Fu(\()p FD(v)m(oid)p Fu(\))390 408 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)390 518 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) 390 628 y(of)j(v)-5 b(arious)30 b(acceleration)j(strategies.)3350 857 y([F)-8 b(unction])-3599 b Fv(size_t)54 b(gsl_interp_accel_find)e Fu(\()p FD(gsl)p 1807 857 28 4 v 41 w(in)m(terp)p 2083 857 V 40 w(accel)32 b(*)f Ft(a)p FD(,)g(const)g(double)565 966 y Ft(x_array)p Fo([])p FD(,)i(size)p 1190 966 V 41 w(t)d Ft(size)p FD(,)i(double)e Ft(x)p Fu(\))390 1076 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 1076 V 40 w(arra)m(y)41 b FK(of)32 b(size)i FD(size)p FK(,)f(using)390 1186 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 1295 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 1405 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 1634 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_interp_accel_rese)q(t)e Fu(\()p FD(gsl)p 1702 1634 V 41 w(in)m(terp)p 1978 1634 V 40 w(accel)33 b(*)d Ft(acc)p Fu(\))p FD(;)390 1744 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 1853 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 1963 y(dataset.)3350 2192 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_interp_accel_free)d Fu(\()p FD(gsl)p 1702 2192 V 41 w(in)m(terp)p 1978 2192 V 40 w(accel*)33 b Ft(acc)p Fu(\))390 2302 y FK(This)d(function)g(frees)g(the)h (accelerator)i(ob)5 b(ject)31 b FD(acc)p FK(.)150 2568 y FJ(27.5)68 b(Ev)-7 b(aluation)46 b(of)g(In)l(terp)t(olating)g(F)-11 b(unctions)3350 2799 y FK([F)j(unction])-3599 b Fv(double)54 b(gsl_interp_eval)c Fu(\()p FD(const)31 b(gsl)p 1731 2799 V 41 w(in)m(terp)f(*)h Ft(interp)p FD(,)h(const)f(double)f Ft(xa)p Fo([])p FD(,)565 2909 y(const)h(double)f Ft(ya)p Fo([])p FD(,)h(double)f Ft(x)p FD(,)h(gsl)p 1825 2909 V 40 w(in)m(terp)p 2100 2909 V 40 w(accel)i(*)d Ft(acc)p Fu(\))3350 3019 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_interp_eval_e)e Fu(\()p FD(const)31 b(gsl)p 1679 3019 V 41 w(in)m(terp)f(*)h Ft(interp)p FD(,)h(const)f(double)f Ft(xa)p Fo([])p FD(,)565 3128 y(const)h(double)f Ft(ya)p Fo([])p FD(,)h(double)f Ft(x)p FD(,)h(gsl)p 1825 3128 V 40 w(in)m(terp)p 2100 3128 V 40 w(accel)i(*)d Ft(acc)p FD(,)i(double)e(*)g Ft(y)p Fu(\))390 3238 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 3347 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 3457 y(outside)c(the)f(range)h(of)g FD(xa)p 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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(a)p FD(,)h(double)e Ft(b)p FD(,)i(gsl)p 2734 628 V 41 w(in)m(terp)p 3010 628 V 40 w(accel)h(*)f Ft(acc)p FD(,)565 737 y(double)f(*)h Ft(result)p Fu(\))390 847 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)390 956 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 1066 y(accelerator)k FD(acc)p FK(.)150 1286 y FJ(27.6)68 b(Higher-lev)l(el) 47 b(In)l(terface)150 1445 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 1555 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 1665 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 1774 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 1884 y(are)k(de\014ned)e(in)h (the)h(header)f(\014le)g FH(gsl_spline.h)p FK(.)3350 2050 y([F)-8 b(unction])-3599 b Fv(gsl_spline)55 b(*)e (gsl_spline_alloc)d Fu(\()p FD(const)31 b(gsl)p 2097 2050 V 41 w(in)m(terp)p 2373 2050 V 40 w(t)m(yp)s(e)g(*)f Ft(T)p FD(,)h(size)p 2942 2050 V 41 w(t)565 2159 y Ft(size)p Fu(\))3350 2306 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_spline_init)d Fu(\()p FD(gsl)p 1336 2306 V 41 w(spline)30 b(*)h Ft(spline)p FD(,)h(const)f(double)f Ft(xa)p Fo([])p FD(,)h(const)565 2416 y(double)f Ft(ya)p Fo([])p FD(,)h(size)p 1221 2416 V 41 w(t)g Ft(size)p Fu(\))3350 2563 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_spline_free)c Fu(\()p FD(gsl)p 1389 2563 V 40 w(spline)31 b(*)f Ft(spline)p Fu(\))3350 2710 y FK([F)-8 b(unction])-3599 b Fv(const)54 b(char)f(*)g(gsl_spline_name)d Fu(\()p FD(const)31 b(gsl)p 2045 2710 V 41 w(spline)f(*)h Ft(spline)p Fu(\))3350 2857 y FK([F)-8 b(unction])-3599 b Fv(unsigned)55 b(int)e (gsl_spline_min_size)e Fu(\()p FD(const)31 b(gsl)p 2254 2857 V 41 w(spline)f(*)h Ft(spline)p Fu(\))3350 3004 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_spline_eval)c Fu(\()p FD(const)31 b(gsl)p 1731 3004 V 41 w(spline)f(*)h Ft(spline)p FD(,)h(double)e Ft(x)p FD(,)565 3113 y(gsl)p 677 3113 V 41 w(in)m(terp)p 953 3113 V 40 w(accel)i(*)f Ft(acc)p Fu(\))3350 3223 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_spline_eval_e)e Fu(\()p FD(const)31 b(gsl)p 1679 3223 V 41 w(spline)f(*)g Ft(spline)p FD(,)j(double)d Ft(x)p FD(,)565 3333 y(gsl)p 677 3333 V 41 w(in)m(terp)p 953 3333 V 40 w(accel)i(*)f Ft(acc)p FD(,)g(double)f(*)h Ft(y)p Fu(\))3350 3480 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_spline_eval_deriv)e Fu(\()p FD(const)31 b(gsl)p 2045 3480 V 41 w(spline)f(*)h Ft(spline)p FD(,)h(double)e Ft(x)p FD(,)565 3589 y(gsl)p 677 3589 V 41 w(in)m(terp)p 953 3589 V 40 w(accel)i(*)f Ft(acc)p Fu(\))3350 3699 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_spline_eval_deriv)q(_e)f Fu(\()p FD(const)31 b(gsl)p 1993 3699 V 40 w(spline)g(*)f Ft(spline)p FD(,)j(double)d Ft(x)p FD(,)565 3808 y(gsl)p 677 3808 V 41 w(in)m(terp)p 953 3808 V 40 w(accel)i(*)f Ft(acc)p FD(,)g(double)f(*)h Ft(d)p Fu(\))3350 3955 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_spline_eval_deriv2)e Fu(\()p FD(const)30 b(gsl)p 2096 3955 V 41 w(spline)f(*)g Ft(spline)p FD(,)j(double)d Ft(x)p FD(,)565 4065 y(gsl)p 677 4065 V 41 w(in)m(terp)p 953 4065 V 40 w(accel)j(*)f Ft(acc)p Fu(\))3350 4175 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_spline_eval_deriv)q(2_e)f Fu(\()p FD(const)31 b(gsl)p 2045 4175 V 41 w(spline)f(*)h Ft(spline)p FD(,)h(double)e Ft(x)p FD(,)565 4284 y(gsl)p 677 4284 V 41 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5244 y Fq(i)2684 5230 y FE(;)15 b(y)2769 5244 y Fq(i)2797 5230 y FK(\))27 b(where)f FE(x)3170 5244 y Fq(i)3222 5230 y FK(=)f FE(i)13 b FK(+)g(sin)o(\()p FE(i)p FK(\))p FE(=)p FK(2)150 5340 y(and)30 b FE(y)372 5354 y Fq(i)424 5340 y FK(=)25 b FE(i)c FK(+)f(cos\()p FE(i)850 5307 y FB(2)888 5340 y FK(\))31 b(for)f FE(i)c FK(=)f(0)15 b FE(:)g(:)g(:)h FK(9.)p eop end %%Page: 334 350 TeXDict begin 334 349 bop 150 -116 a FK(Chapter)30 b(27:)41 b(In)m(terp)s(olation)2437 b(334)390 299 y FH(#include)46 b()390 408 y(#include)g()390 518 y(#include)g ()390 628 y(#include)g()390 737 y(#include)g()390 956 y(int)390 1066 y(main)h(\(void\))390 1176 y({)485 1285 y(int)g(i;)485 1395 y(double)g(xi,)f(yi,)h(x[10],)f(y[10];)485 1614 y(printf)h(\("#m=0,S=2\\n"\);)485 1833 y(for)g(\(i)h(=)f(0;)g(i)h(<)f (10;)g(i++\))581 1943 y({)676 2052 y(x[i])g(=)g(i)h(+)f(0.5)g(*)h(sin)f (\(i\);)676 2162 y(y[i])g(=)g(i)h(+)f(cos)g(\(i)g(*)h(i\);)676 2271 y(printf)e(\("\045g)h(\045g\\n",)f(x[i],)h(y[i]\);)581 2381 y(})485 2600 y(printf)g(\("#m=1,S=0\\n"\);)485 2819 y({)581 2929 y(gsl_interp_accel)c(*acc)676 3039 y(=)48 b(gsl_interp_accel_alloc)42 b(\(\);)581 3148 y(gsl_spline)j(*spline)676 3258 y(=)j(gsl_spline_alloc)43 b(\(gsl_interp_cspline,)f(10\);)581 3477 y(gsl_spline_init)i(\(spline,)h(x,)i(y,)g(10\);)581 3696 y(for)g(\(xi)g(=)g(x[0];)g(xi)g(<)g(x[9];)g(xi)g(+=)g(0.01\))676 3806 y({)772 3915 y(yi)g(=)g(gsl_spline_eval)d(\(spline,)i(xi,)h (acc\);)772 4025 y(printf)f(\("\045g)h(\045g\\n",)f(xi,)h(yi\);)676 4134 y(})581 4244 y(gsl_spline_free)d(\(spline\);)581 4354 y(gsl_interp_accel_free)e(\(acc\);)485 4463 y(})485 4573 y(return)47 b(0;)390 4682 y(})150 4956 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 5230 y FH($)47 b(./a.out)f(>)i(interp.dat)390 5340 y($)f(graph)g(-T)g(ps)g (<)h(interp.dat)d(>)i(interp.ps)p eop end %%Page: 335 351 TeXDict begin 335 350 bop 150 -116 a FK(Chapter)30 b(27:)41 b(In)m(terp)s(olation)2437 b(335)275 1173 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 %%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 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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 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 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b(result)h(sho)m(ws)g(a)g(smo)s(oth)g (in)m(terp)s(olation)h(of)f(the)g(original)i(p)s(oin)m(ts.)48 b(The)32 b(in)m(terp)s(olation)i(metho)s(d)150 1463 y(can)d(b)s(e)e(c)m (hanged)i(simply)f(b)m(y)h(v)-5 b(arying)30 b(the)h(\014rst)e(argumen)m (t)i(of)g FH(gsl_spline_alloc)p FK(.)275 1593 y(The)i(next)i(program)f (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 1703 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 1833 y FH(#include)46 b()390 1943 y(#include)g()390 2052 y(#include)g()390 2162 y(#include)g()390 2271 y(#include)g()390 2491 y(int)390 2600 y(main)h(\(void\))390 2710 y({)485 2819 y(int)g(N)h(=)f(4;)485 2929 y(double)g(x[4])f(=)i({0.00,)e(0.10,)94 b(0.27,)g(0.30};)485 3039 y(double)47 b(y[4])f(=)i({0.15,)e(0.70,)g(-0.10,)94 b(0.15};)1010 3148 y(/*)48 b(Note:)94 b(y[0])46 b(==)i(y[3])e(for)h (periodic)f(data)g(*/)485 3367 y(gsl_interp_accel)e(*acc)i(=)i (gsl_interp_accel_alloc)42 b(\(\);)485 3477 y(const)47 b(gsl_interp_type)c(*t)48 b(=)f(gsl_interp_cspline_period)o(ic;)485 3587 y(gsl_spline)e(*spline)h(=)i(gsl_spline_alloc)43 b(\(t,)k(N\);)485 3806 y(int)g(i;)h(double)e(xi,)h(yi;)485 4025 y(printf)g(\("#m=0,S=5\\n"\);)485 4134 y(for)g(\(i)h(=)f(0;)g(i)h (<)f(N;)g(i++\))581 4244 y({)676 4354 y(printf)f(\("\045g)h(\045g\\n",) f(x[i],)h(y[i]\);)581 4463 y(})485 4682 y(printf)g(\("#m=1,S=0\\n"\);) 485 4792 y(gsl_spline_init)d(\(spline,)i(x,)h(y,)g(N\);)485 5011 y(for)g(\(i)h(=)f(0;)g(i)h(<=)f(100;)f(i++\))581 5121 y({)676 5230 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 5340 y(yi)h(=)f(gsl_spline_eval)d (\(spline,)h(xi,)i(acc\);)p eop end %%Page: 336 352 TeXDict begin 336 351 bop 150 -116 a FK(Chapter)30 b(27:)41 b(In)m(terp)s(olation)2437 b(336)676 299 y FH(printf)46 b(\("\045g)h(\045g\\n",)f(xi,)h(yi\);)581 408 y(})485 628 y(gsl_spline_free)d(\(spline\);)485 737 y(gsl_interp_accel_free)e (\(acc\);)485 847 y(return)47 b(0;)390 956 y(})275 1116 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 1250 y FH($)47 b(./a.out)f(>)i(interp.dat) 390 1360 y($)f(graph)g(-T)g(ps)g(<)h(interp.dat)d(>)i(interp.ps)275 3528 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 [ 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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 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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 ] concat %I 2 9281 4658 9151 4788 2 MLine End Begin %I MLine [0.6776471 0 0 0.6776471 0 0 ] trueoriginalCTM originalCTM concatmatrix pop 0 setlinecap 0 setlinejoin 10.43 setmiterlimit /eoFillRule true def %I b 65535 1 0 0 [ ] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p none SetP %I t [0.05 0 0 0.05 18 108 ] concat %I 101 2304 4723 2373 4920 2442 5115 2511 5308 2580 5499 2650 5687 2719 5872 2788 6054 2857 6232 2926 6406 2995 6576 3064 6741 3133 6901 3203 7056 3272 7205 3341 7348 3410 7485 3479 7616 3548 7739 3617 7855 3686 7964 3756 8065 3825 8157 3894 8241 3963 8316 4032 8381 4101 8437 4170 8484 4239 8519 4308 8545 4378 8559 4447 8563 4516 8554 4585 8534 4654 8502 4723 8458 4792 8402 4861 8335 4931 8258 5000 8171 5069 8075 5138 7970 5207 7857 5276 7736 5345 7608 5414 7473 5484 7332 5553 7185 5622 7033 5691 6876 5760 6716 5829 6552 5898 6385 5967 6215 6036 6043 6106 5870 6175 5696 6244 5522 6313 5348 6382 5174 6451 5002 6520 4831 6589 4663 6659 4497 6728 4335 6797 4177 6866 4022 6935 3873 7004 3729 7073 3591 7142 3460 7212 3335 7281 3218 7350 3109 7419 3009 7488 2918 7557 2836 7626 2764 7695 2703 7764 2654 7834 2615 7903 2590 7972 2577 8041 2577 8110 2591 8179 2619 8248 2663 8317 2721 8387 2796 8456 2887 8525 2995 8594 3120 8663 3261 8732 3416 8801 3582 8870 3758 8940 3943 9009 4133 9078 4328 9147 4525 9216 4723 101 MLine End %%PageTrailer End %I eop showpage %%Trailer end %%EOF %%EndDocument @endspecial 150 3712 a FK(The)39 b(result)h(sho)m(ws)f(a)h(p)s(erio)s (dic)f(in)m(terp)s(olation)i(of)e(the)h(original)h(p)s(oin)m(ts.)68 b(The)39 b(slop)s(e)g(of)h(the)g(\014tted)150 3822 y(curv)m(e)31 b(is)f(the)h(same)f(at)i(the)e(b)s(eginning)g(and)g(end)f(of)i(the)f (data,)i(and)d(the)i(second)f(deriv)-5 b(ativ)m(e)32 b(is)f(also.)150 4054 y FJ(27.8)68 b(References)47 b(and)d(F)-11 b(urther)44 b(Reading)150 4213 y FK(Descriptions)g(of)f(the)g(in)m (terp)s(olation)h(algorithms)g(and)e(further)g(references)h(can)g(b)s (e)g(found)e(in)i(the)150 4323 y(follo)m(wing)32 b(b)s(o)s(oks:)330 4457 y(C.W.)43 b(Ueb)s(erh)m(ub)s(er,)h FD(Numerical)f(Computation)g (\(V)-8 b(olume)44 b(1\),)i(Chapter)c(9)h(\\In)m(terp)s(olation")p FK(,)330 4567 y(Springer)29 b(\(1997\),)k(ISBN)d(3-540-62058-3.)330 4702 y(D.M.)i(Y)-8 b(oung,)32 b(R.T.)f(Gregory)g FD(A)g(Surv)m(ey)g(of) g(Numerical)g(Mathematics)i(\(V)-8 b(olume)33 b(1\),)f(Chapter)330 4811 y(6.8)p FK(,)g(Do)m(v)m(er)g(\(1988\),)h(ISBN)d(0-486-65691-8.)p eop end %%Page: 337 353 TeXDict begin 337 352 bop 150 -116 a FK(Chapter)30 b(28:)41 b(Numerical)31 b(Di\013eren)m(tiation)1945 b(337)150 299 y FG(28)80 b(Numerical)54 b(Di\013eren)l(tiation)150 601 y FK(The)24 b(functions)f(describ)s(ed)g(in)h(this)g(c)m(hapter)g 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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: 338 354 TeXDict begin 338 353 bop 150 -116 a FK(Chapter)30 b(28:)41 b(Numerical)31 b(Di\013eren)m(tiation)1945 b(338)150 299 y FJ(28.2)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 b FK(\()p FE(x)p FK(\))36 b(is)g(unde\014ned)e(for)i FE(x)e(<)h FK(0)h(so)g(the)g(deriv)-5 b(ativ)m(e)38 b(at)f FE(x)d FK(=)h(0)h(is)g(computed)150 677 y(using)30 b FH(gsl_deriv_forward)p FK(.)390 807 y FH(#include)46 b()390 917 y(#include)g()390 1026 y(#include)g()390 1245 y(double)g(f)i(\(double)d (x,)j(void)e(*)i(params\))390 1355 y({)485 1465 y(return)f(pow)f(\(x,)h (1.5\);)390 1574 y(})390 1793 y(int)390 1903 y(main)g(\(void\))390 2012 y({)485 2122 y(gsl_function)e(F;)485 2232 y(double)i(result,)e (abserr;)485 2451 y(F.function)g(=)j(&f;)485 2560 y(F.params)e(=)h(0;) 485 2780 y(printf)g(\("f\(x\))f(=)h(x^\(3/2\)\\n"\);)485 2999 y(gsl_deriv_central)d(\(&F,)i(2.0,)h(1e-8,)f(&result,)g (&abserr\);)485 3108 y(printf)h(\("x)f(=)i(2.0\\n"\);)485 3218 y(printf)f(\("f'\(x\))e(=)j(\045.10f)e(+/-)h(\045.10f\\n",)e (result,)h(abserr\);)485 3328 y(printf)h(\("exact)e(=)j (\045.10f\\n\\n",)d(1.5)h(*)i(sqrt\(2.0\)\);)485 3547 y(gsl_deriv_forward)c(\(&F,)i(0.0,)h(1e-8,)f(&result,)g(&abserr\);)485 3656 y(printf)h(\("x)f(=)i(0.0\\n"\);)485 3766 y(printf)f(\("f'\(x\))e (=)j(\045.10f)e(+/-)h(\045.10f\\n",)e(result,)h(abserr\);)485 3875 y(printf)h(\("exact)e(=)j(\045.10f\\n",)d(0.0\);)485 4095 y(return)i(0;)390 4204 y(})150 4334 y FK(Here)31 b(is)f(the)h(output)f(of)g(the)h(program,)390 4463 y FH($)47 b(./a.out)390 4573 y(f\(x\))g(=)g(x^\(3/2\))390 4682 y(x)g(=)h(2.0)390 4792 y(f'\(x\))e(=)i(2.1213203120)c(+/-)j (0.0000004064)390 4902 y(exact)f(=)i(2.1213203436)390 5121 y(x)f(=)h(0.0)390 5230 y(f'\(x\))e(=)i(0.0000000160)c(+/-)j (0.0000000339)390 5340 y(exact)f(=)i(0.0000000000)p eop end %%Page: 339 355 TeXDict begin 339 354 bop 150 -116 a FK(Chapter)30 b(28:)41 b(Numerical)31 b(Di\013eren)m(tiation)1945 b(339)150 299 y FJ(28.3)68 b(References)47 b(and)d(F)-11 b(urther)44 b(Reading)150 458 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:) 330 593 y(Abramo)m(witz)40 b(and)f(Stegun,)i FD(Handb)s(o)s(ok)d(of)h (Mathematical)j(F)-8 b(unctions)p FK(,)42 b(Section)e(25.3.4,)k(and)330 702 y(T)-8 b(able)31 b(25.5)h(\(Co)s(e\016cien)m(ts)g(for)e(Di\013eren) m(tiation\).)330 837 y(S.D.)37 b(Con)m(te)h(and)e(Carl)h(de)g(Bo)s(or,) i FD(Elemen)m(tary)f(Numerical)g(Analysis:)54 b(An)37 b(Algorithmic)h(Ap-)330 946 y(proac)m(h)p FK(,)31 b(McGra)m(w-Hill,)i (1972.)p eop end %%Page: 340 356 TeXDict begin 340 355 bop 150 -116 a FK(Chapter)30 b(29:)41 b(Cheb)m(yshev)30 b(Appro)m(ximations)1862 b(340)150 299 y FG(29)80 b(Cheb)l(yshev)51 b(Appro)l(ximations)150 514 y FK(This)44 b(c)m(hapter)i(describ)s(es)f(routines)g(for)g (computing)g(Cheb)m(yshev)f(appro)m(ximations)i(to)g(univ)-5 b(ariate)150 624 y(functions.)72 b(A)41 b(Cheb)m(yshev)f(appro)m (ximation)i(is)f(a)h(truncation)f(of)g(the)h(series)f FE(f)10 b FK(\()p FE(x)p FK(\))43 b(=)3316 560 y Fs(P)3419 624 y FE(c)3458 638 y Fq(n)3504 624 y FE(T)3557 638 y Fq(n)3602 624 y FK(\()p FE(x)p FK(\),)150 734 y(where)36 b(the)g(Cheb)m(yshev)f(p)s(olynomials)i 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1418 y FJ(29.1)68 b(De\014nitions)150 1578 y FK(A)30 b(Cheb)m(yshev)g(series)h(is)f(stored)h(using)f(the)g(follo)m (wing)i(structure,)390 1708 y FH(typedef)46 b(struct)390 1818 y({)485 1927 y(double)h(*)g(c;)143 b(/*)47 b(coefficients)92 b(c[0])47 b(..)g(c[order])e(*/)485 2037 y(int)i(order;)190 b(/*)47 b(order)f(of)h(expansion)618 b(*/)485 2147 y(double)47 b(a;)238 b(/*)47 b(lower)f(interval)g(point)523 b(*/)485 2256 y(double)47 b(b;)238 b(/*)47 b(upper)f(interval)g(point)523 b(*/)485 2366 y(...)390 2475 y(})47 b(gsl_cheb_series)150 2606 y FK(The)32 b(appro)m(ximation)h(is)g(made)f(o)m(v)m(er)i(the)e (range)h([)p FE(a;)15 b(b)p FK(])33 b(using)f FD(order)7 b FH(+)p FK(1)32 b(terms,)h(including)f(the)g(co)s(e\016-)150 2716 y(cien)m(t)g FE(c)p FK([0].)42 b(The)30 b(series)g(is)h(computed)f (using)g(the)g(follo)m(wing)i(con)m(v)m(en)m(tion,)1474 2903 y FE(f)10 b FK(\()p FE(x)p FK(\))25 b(=)1782 2841 y FE(c)1821 2855 y FB(0)p 1782 2882 77 4 v 1798 2965 a FK(2)1889 2903 y(+)1983 2822 y Fs(X)1980 2998 y Fq(n)p FB(=1)2120 2903 y FE(c)2159 2917 y Fq(n)2205 2903 y FE(T)2258 2917 y Fq(n)2303 2903 y FK(\()p FE(x)p FK(\))150 3133 y(whic)m(h)30 b(is)h(needed)f(when)f(accessing)j(the)e(co)s(e\016cien)m (ts)i(directly)-8 b(.)150 3358 y FJ(29.2)68 b(Creation)47 b(and)d(Calculation)j(of)e(Cheb)l(yshev)g(Series)3350 3559 y FK([F)-8 b(unction])-3599 b Fv(gsl_cheb_series)57 b(*)52 b(gsl_cheb_alloc)e Fu(\()p FD(const)31 b(size)p 2289 3559 28 4 v 41 w(t)g Ft(n)p Fu(\))390 3669 y FK(This)e(function)h (allo)s(cates)i(space)e(for)g(a)g(Cheb)m(yshev)g(series)g(of)g(order)f FD(n)h FK(and)f(returns)g(a)h(p)s(oin)m(ter)390 3779 y(to)h(a)g(new)f FH(gsl_cheb_series)c FK(struct.)3350 3952 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_cheb_free)49 b Fu(\()p FD(gsl)p 1284 3952 V 41 w(c)m(heb)p 1504 3952 V 40 w(series)31 b(*)g Ft(cs)p Fu(\))390 4061 y FK(This)f(function)g (frees)g(a)h(previously)f(allo)s(cated)i(Cheb)m(yshev)e(series)g FD(cs)p FK(.)3350 4234 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_cheb_init)d Fu(\()p FD(gsl)p 1232 4234 V 41 w(c)m(heb)p 1452 4234 V 40 w(series)31 b(*)f Ft(cs)p FD(,)h(const)g(gsl)p 2315 4234 V 41 w(function)f(*)h Ft(f)p FD(,)g(const)565 4344 y(double)f Ft(a)p FD(,)h(const)g(double)f Ft(b)p Fu(\))390 4454 y FK(This)h(function)g(computes)g(the)h(Cheb)m(yshev)f (appro)m(ximation)h FD(cs)j FK(for)d(the)f(function)g FD(f)49 b FK(o)m(v)m(er)33 b(the)390 4563 y(range)41 b(\()p FE(a;)15 b(b)p FK(\))42 b(to)g(the)f(previously)g(sp)s (eci\014ed)f(order.)71 b(The)41 b(computation)h(of)f(the)g(Cheb)m (yshev)390 4673 y(appro)m(ximation)31 b(is)g(an)f FE(O)s FK(\()p FE(n)1376 4640 y FB(2)1413 4673 y FK(\))h(pro)s(cess,)f(and)g (requires)g FE(n)f FK(function)h(ev)-5 b(aluations.)150 4898 y FJ(29.3)68 b(Auxiliary)46 b(F)-11 b(unctions)150 5057 y FK(The)30 b(follo)m(wing)i(functions)e(pro)m(vide)g(information) h(ab)s(out)f(an)g(existing)i(Cheb)m(yshev)d(series.)3350 5230 y([F)-8 b(unction])-3599 b Fv(size_t)54 b(gsl_cheb_order)c Fu(\()p FD(const)31 b(gsl)p 1679 5230 V 41 w(c)m(heb)p 1899 5230 V 40 w(series)g(*)f Ft(cs)p Fu(\))390 5340 y FK(This)g(function)g(returns)f(the)h(order)g(of)h(Cheb)m(yshev)e (series)i FD(cs)p FK(.)p eop end %%Page: 341 357 TeXDict begin 341 356 bop 150 -116 a FK(Chapter)30 b(29:)41 b(Cheb)m(yshev)30 b(Appro)m(ximations)1862 b(341)3350 299 y([F)-8 b(unction])-3599 b Fv(size_t)54 b(gsl_cheb_size)c Fu(\()p FD(const)31 b(gsl)p 1627 299 28 4 v 40 w(c)m(heb)p 1846 299 V 41 w(series)f(*)h Ft(cs)p Fu(\))3350 408 y FK([F)-8 b(unction])-3599 b Fv(double)54 b(*)f(gsl_cheb_coeffs)d Fu(\()p FD(const)31 b(gsl)p 1836 408 V 41 w(c)m(heb)p 2056 408 V 40 w(series)g(*)f Ft(cs)p Fu(\))390 518 y FK(These)h(functions)f(return)g(the)i(size)g(of)f(the)g(Cheb)m(yshev)f (co)s(e\016cien)m(t)j(arra)m(y)f FH(c[])e FK(and)g(a)i(p)s(oin)m(ter) 390 628 y(to)f(its)g(lo)s(cation)h(in)e(memory)g(for)g(the)h(Cheb)m (yshev)e(series)i FD(cs)p FK(.)150 893 y FJ(29.4)68 b(Cheb)l(yshev)45 b(Series)h(Ev)-7 b(aluation)3350 1125 y FK([F)f(unction])-3599 b Fv(double)54 b(gsl_cheb_eval)c Fu(\()p FD(const)31 b(gsl)p 1627 1125 V 40 w(c)m(heb)p 1846 1125 V 41 w(series)f(*)h Ft(cs)p FD(,)g(double)f Ft(x)p Fu(\))390 1234 y FK(This)g(function)g (ev)-5 b(aluates)32 b(the)e(Cheb)m(yshev)g(series)g FD(cs)35 b FK(at)c(a)g(giv)m(en)g(p)s(oin)m(t)f FD(x)p FK(.)3350 1463 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_cheb_eval_err)e Fu(\()p FD(const)31 b(gsl)p 1679 1463 V 41 w(c)m(heb)p 1899 1463 V 40 w(series)g(*)f Ft(cs)p FD(,)i(const)e(double)g Ft(x)p FD(,)565 1572 y(double)g(*)h Ft(result)p FD(,)h(double)e(*)h Ft(abserr)p Fu(\))390 1682 y FK(This)h(function)g(computes)h(the)g (Cheb)m(yshev)e(series)i FD(cs)k FK(at)c(a)g(giv)m(en)h(p)s(oin)m(t)e FD(x)p FK(,)h(estimating)i(b)s(oth)390 1791 y(the)f(series)h FD(result)h FK(and)d(its)i(absolute)g(error)f FD(abserr)p FK(.)51 b(The)34 b(error)g(estimate)i(is)e(made)g(from)g(the)390 1901 y(\014rst)c(neglected)i(term)e(in)g(the)h(series.)3350 2130 y([F)-8 b(unction])-3599 b Fv(double)54 b(gsl_cheb_eval_n)c Fu(\()p FD(const)31 b(gsl)p 1731 2130 V 41 w(c)m(heb)p 1951 2130 V 40 w(series)g(*)g Ft(cs)p FD(,)g(size)p 2612 2130 V 41 w(t)f Ft(order)p FD(,)565 2239 y(double)g Ft(x)p Fu(\))390 2349 y FK(This)h(function)h(ev)-5 b(aluates)34 b(the)f(Cheb)m(yshev)e(series)i FD(cs)j FK(at)d(a)g(giv)m(en)g(p)s(oin) m(t)f FD(x)p FK(,)h(to)g(\(at)h(most\))f(the)390 2458 y(giv)m(en)e(order)f FD(order)p FK(.)3350 2687 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_cheb_eval_n_err)e Fu(\()p FD(const)32 b(gsl)p 1784 2687 V 40 w(c)m(heb)p 2003 2687 V 41 w(series)e(*)h Ft(cs)p FD(,)g(const)g(size)p 2902 2687 V 41 w(t)565 2796 y Ft(order)p FD(,)h(const)f(double)f Ft(x)p FD(,)h(double)f(*)h Ft(result)p FD(,)h(double)e(*)h Ft(abserr)p Fu(\))390 2906 y FK(This)c(function)h(ev)-5 b(aluates)29 b(a)f(Cheb)m(yshev)g(series)g FD(cs)k FK(at)c(a)h(giv)m (en)g(p)s(oin)m(t)e FD(x)p FK(,)i(estimating)h(b)s(oth)d(the)390 3016 y(series)37 b FD(result)h FK(and)e(its)h(absolute)g(error)f FD(abserr)p 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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: 342 358 TeXDict begin 342 357 bop 150 -116 a FK(Chapter)30 b(29:)41 b(Cheb)m(yshev)30 b(Appro)m(ximations)1862 b(342)150 299 y FJ(29.6)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 1066 y FH(#include)46 b()390 1176 y(#include)g ()390 1285 y(#include)g()390 1504 y(double)390 1614 y(f)h(\(double)f(x,)h(void)g(*p\))390 1724 y({)485 1833 y(if)h(\(x)f(<)g(0.5\))581 1943 y(return)f(0.25;)485 2052 y(else)581 2162 y(return)g(0.75;)390 2271 y(})390 2491 y(int)390 2600 y(main)h(\(void\))390 2710 y({)485 2819 y(int)g(i,)h(n)f(=)g(10000;)485 3039 y(gsl_cheb_series)d(*cs)j(=)g (gsl_cheb_alloc)d(\(40\);)485 3258 y(gsl_function)h(F;)485 3477 y(F.function)g(=)j(f;)485 3587 y(F.params)e(=)h(0;)485 3806 y(gsl_cheb_init)e(\(cs,)h(&F,)h(0.0,)g(1.0\);)485 4025 y(for)g(\(i)h(=)f(0;)g(i)h(<)f(n;)g(i++\))581 4134 y({)676 4244 y(double)f(x)i(=)f(i)h(/)f(\(double\)n;)676 4354 y(double)f(r10)h(=)h(gsl_cheb_eval_n)43 b(\(cs,)k(10,)g(x\);)676 4463 y(double)f(r40)h(=)h(gsl_cheb_eval)c(\(cs,)j(x\);)676 4573 y(printf)f(\("\045g)h(\045g)g(\045g)g(\045g\\n",)1058 4682 y(x,)g(GSL_FN_EVAL)e(\(&F,)i(x\),)g(r10,)f(r40\);)581 4792 y(})485 5011 y(gsl_cheb_free)f(\(cs\);)485 5230 y(return)i(0;)390 5340 y(})p eop end %%Page: 343 359 TeXDict begin 343 358 bop 150 -116 a FK(Chapter)30 b(29:)41 b(Cheb)m(yshev)30 b(Appro)m(ximations)1862 b(343)150 299 y(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)150 408 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 2072 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 2355 a FJ(29.7)68 b(References)47 b(and)d(F)-11 b(urther)44 b(Reading)150 2514 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 2649 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(\(Algo-)330 2758 y(rithm)30 b(446\)".)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: 344 360 TeXDict begin 344 359 bop 150 -116 a FK(Chapter)30 b(30:)41 b(Series)31 b(Acceleration)2205 b(344)150 299 y FG(30)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 y(These)e(functions)g(are)g(declared)h(in)f(the)h(header)f(\014le)g FH(gsl_sum.h)p FK(.)150 1338 y FJ(30.1)68 b(Acceleration)46 b(functions)150 1497 y FK(The)20 b(follo)m(wing)i(functions)e(compute)h (the)g(full)f(Levin)h FE(u)p FK(-transform)f(of)h(a)g(series)f(with)h (its)g(error)f(estimate.)150 1607 y(The)28 b(error)h(estimate)h(is)f (computed)g(b)m(y)f(propagating)i(rounding)e(errors)g(from)g(eac)m(h)i (term)f(through)f(to)150 1716 y(the)j(\014nal)f(extrap)s(olation.)275 1851 y(These)i(functions)h(are)g(in)m(tended)g(for)g(summing)f (analytic)j(series)e(where)f(eac)m(h)j(term)e(is)g(kno)m(wn)f(to)150 1960 y(high)26 b(accuracy)-8 b(,)29 b(and)d(the)h(rounding)f(errors)g (are)h(assumed)f(to)h(originate)h(from)e(\014nite)h(precision.)39 b(They)150 2070 y(are)31 b(tak)m(en)g(to)g(b)s(e)f(relativ)m(e)j (errors)c(of)i(order)f FH(GSL_DBL_EPSILON)c FK(for)k(eac)m(h)i(term.) 275 2204 y(The)39 b(calculation)k(of)e(the)f(error)h(in)f(the)g(extrap) s(olated)i(v)-5 b(alue)41 b(is)f(an)h FE(O)s FK(\()p FE(N)2951 2171 y FB(2)2988 2204 y FK(\))g(pro)s(cess,)i(whic)m(h)d(is) 150 2314 y(exp)s(ensiv)m(e)29 b(in)g(time)g(and)f(memory)-8 b(.)41 b(A)29 b(faster)g(but)f(less)h(reliable)h(metho)s(d)e(whic)m(h)h (estimates)h(the)f(error)150 2423 y(from)37 b(the)g(con)m(v)m(ergence)j (of)e(the)f(extrap)s(olated)i(v)-5 b(alue)37 b(is)h(describ)s(ed)e(in)h (the)g(next)h(section.)63 b(F)-8 b(or)38 b(the)150 2533 y(metho)s(d)29 b(describ)s(ed)g(here)h(a)h(full)e(table)i(of)f(in)m (termediate)i(v)-5 b(alues)31 b(and)e(deriv)-5 b(ativ)m(es)31 b(through)f(to)g FE(O)s FK(\()p FE(N)10 b FK(\))150 2643 y(m)m(ust)30 b(b)s(e)g(computed)g(and)g(stored,)h(but)e(this)i(do)s(es) f(giv)m(e)i(a)e(reliable)i(error)e(estimate.)3350 2827 y([F)-8 b(unction])-3599 b Fv(gsl_sum_levin_u_worksp)q(ace)59 b(*)52 b(gsl_sum_levin_u_allo)q(c)f Fu(\()p FD(size)p 2940 2827 28 4 v 42 w(t)30 b Ft(n)p Fu(\))390 2936 y FK(This)i(function)h(allo)s(cates)i(a)f(w)m(orkspace)f(for)g(a)h(Levin) f FE(u)p FK(-transform)f(of)h FD(n)g FK(terms.)48 b(The)33 b(size)h(of)390 3046 y(the)d(w)m(orkspace)g(is)f FE(O)s FK(\(2)p FE(n)1280 3013 y FB(2)1338 3046 y FK(+)20 b(3)p FE(n)p FK(\).)3350 3230 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_sum_levin_u_free)d Fu(\()p FD(gsl)p 1650 3230 V 41 w(sum)p 1854 3230 V 39 w(levin)p 2082 3230 V 40 w(u)p 2173 3230 V 40 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FE(f)10 b FK(\()p FE(t)p FK(\))20 b FI(\003)h FE( )2254 1260 y Fp(\003)2251 1320 y Fq(s;\034)2344 1298 y FK(\()p FE(t)p FK(\))p FE(dt)150 1502 y FK(and,)1227 1701 y FE(f)10 b FK(\()p FE(t)p FK(\))25 b(=)1506 1586 y Fs(Z)1589 1606 y Fp(1)1552 1774 y FB(0)1675 1701 y FE(ds)1780 1586 y Fs(Z)1863 1606 y Fp(1)1826 1774 y(\0001)1963 1701 y FE(w)r FK(\()p FE(s;)15 b(\034)10 b FK(\))22 b FI(\003)e FE( )2379 1715 y Fq(s;\034)2472 1701 y FK(\()p FE(t)p FK(\))p FE(d\034)150 1905 y FK(where)j(the)g(basis)h(functions)e FE( )1215 1919 y Fq(s;\034)1331 1905 y FK(are)i(obtained)g(b)m(y)f(scaling)h(and) f(translation)h(from)f(a)h(single)g(function,)150 2015 y(referred)30 b(to)h(as)f(the)h FD(mother)f(w)m(a)m(v)m(elet)p FK(.)275 2143 y(The)c(discrete)i(v)m(ersion)g(of)f(the)h(w)m(a)m(v)m (elet)i(transform)d(acts)h(on)f(equally-spaced)h(samples,)h(with)e (\014xed)150 2253 y(scaling)f(and)e(translation)i(steps)f(\()p FE(s)p FK(,)h FE(\034)10 b FK(\).)39 b(The)25 b(frequency)f(and)g(time) i(axes)f(are)g(sampled)g FD(dy)m(adically)34 b FK(on)150 2362 y(scales)26 b(of)f(2)541 2329 y Fq(j)601 2362 y FK(through)f(a)h(lev)m(el)i(parameter)e FE(j)5 b FK(.)39 b(The)24 b(resulting)h(family)h(of)e(functions)h FI(f)p FE( )3157 2376 y Fq(j;n)3250 2362 y FI(g)g FK(constitutes)150 2472 y(an)30 b(orthonormal)h(basis)f(for)g(square-in)m(tegrable)i (signals.)275 2600 y(The)d(discrete)h(w)m(a)m(v)m(elet)j(transform)c (is)g(an)h FE(O)s FK(\()p FE(N)10 b FK(\))30 b(algorithm,)h(and)e(is)h (also)g(referred)f(to)i(as)f(the)g FD(fast)150 2709 y(w)m(a)m(v)m(elet) j(transform)p FK(.)150 2929 y FJ(31.2)68 b(Initialization)150 3089 y FK(The)42 b FH(gsl_wavelet)e FK(structure)i(con)m(tains)i(the)f (\014lter)g(co)s(e\016cien)m(ts)h(de\014ning)e(the)h(w)m(a)m(v)m(elet)i (and)e(an)m(y)150 3198 y(asso)s(ciated)32 b(o\013set)f(parameters.)3350 3364 y([F)-8 b(unction])-3599 b Fv(gsl_wavelet)56 b(*)c (gsl_wavelet_alloc)f Fu(\()p FD(const)31 b(gsl)p 2202 3364 28 4 v 41 w(w)m(a)m(v)m(elet)p 2533 3364 V 43 w(t)m(yp)s(e)f(*)h Ft(T)p FD(,)g(size)p 3105 3364 V 41 w(t)565 3473 y Ft(k)p Fu(\))390 3583 y FK(This)39 b(function)h(allo)s(cates)j(and)d (initializes)i(a)f(w)m(a)m(v)m(elet)i(ob)5 b(ject)41 b(of)f(t)m(yp)s(e)h FD(T)p FK(.)70 b(The)39 b(parameter)390 3692 y FD(k)47 b FK(selects)c(the)e(sp)s(eci\014c)h(mem)m(b)s(er)e(of)i (the)g(w)m(a)m(v)m(elet)i(family)-8 b(.)75 b(A)41 b(n)m(ull)h(p)s(oin)m (ter)f(is)h(returned)e(if)390 3802 y(insu\016cien)m(t)31 b(memory)f(is)g(a)m(v)-5 b(ailable)33 b(or)d(if)h(a)f(unsupp)s(orted)e (mem)m(b)s(er)i(is)g(selected.)275 3967 y(The)f(follo)m(wing)j(w)m(a)m (v)m(elet)h(t)m(yp)s(es)e(are)g(implemen)m(ted:)3384 4133 y([W)-8 b(a)m(v)m(elet])-3596 b Fv(gsl_wavelet_daubechies)3384 4242 y FK([W)-8 b(a)m(v)m(elet])-3596 b Fv(gsl_wavelet_daubechies)q (_ce)q(nter)q(ed)390 4352 y FK(This)20 b(is)g(the)h(Daub)s(ec)m(hies)g (w)m(a)m(v)m(elet)i(family)e(of)g(maxim)m(um)f(phase)g(with)h FE(k)s(=)p FK(2)g(v)-5 b(anishing)20 b(momen)m(ts.)390 4461 y(The)30 b(implemen)m(ted)h(w)m(a)m(v)m(elets)i(are)e FE(k)d FK(=)d(4)p FE(;)15 b FK(6)p FE(;)g(:)g(:)g(:)j(;)d FK(20,)32 b(with)e FD(k)36 b FK(ev)m(en.)3384 4627 y([W)-8 b(a)m(v)m(elet])-3596 b Fv(gsl_wavelet_haar)3384 4736 y FK([W)-8 b(a)m(v)m(elet])-3596 b Fv(gsl_wavelet_haar_cente)q(red)390 4846 y FK(This)30 b(is)g(the)h(Haar)g(w)m(a)m(v)m(elet.)43 b(The)30 b(only)h(v)-5 b(alid)30 b(c)m(hoice)i(of)f FE(k)i FK(for)e(the)f(Haar)h(w)m(a)m(v)m(elet)i(is)e FE(k)d FK(=)d(2.)3384 5011 y([W)-8 b(a)m(v)m(elet])-3596 b Fv (gsl_wavelet_bspline)3384 5121 y FK([W)-8 b(a)m(v)m(elet])-3596 b Fv(gsl_wavelet_bspline_ce)q(nte)q(red)390 5230 y FK(This)40 b(is)h(the)f(biorthogonal)i(B-spline)f(w)m(a)m(v)m(elet)j(family)d(of)g (order)f(\()p FE(i;)15 b(j)5 b FK(\).)73 b(The)40 b(implemen)m(ted)390 5340 y(v)-5 b(alues)31 b(of)f FE(k)f FK(=)c(100)c FI(\003)g FE(i)f FK(+)g FE(j)36 b FK(are)31 b(103,)h(105,)g(202,)g(204,)g(206,)g (208,)g(301,)f(303,)h(305)g(307,)g(309.)p eop end %%Page: 349 365 TeXDict begin 349 364 bop 150 -116 a FK(Chapter)30 b(31:)41 b(W)-8 b(a)m(v)m(elet)34 b(T)-8 b(ransforms)2161 b(349)150 299 y(The)28 b(cen)m(tered)i(forms)e(of)h(the)g(w)m(a)m(v)m(elets)i (align)f(the)f(co)s(e\016cien)m(ts)h(of)f(the)g(v)-5 b(arious)29 b(sub-bands)d(on)j(edges.)150 408 y(Th)m(us)37 b(the)i(resulting)f(visualization)j(of)d(the)h(co)s(e\016cien)m(ts)h (of)e(the)h(w)m(a)m(v)m(elet)i(transform)d(in)g(the)g(phase)150 518 y(plane)30 b(is)h(easier)g(to)g(understand.)3350 720 y([F)-8 b(unction])-3599 b Fv(const)54 b(char)f(*)g (gsl_wavelet_name)d Fu(\()p FD(const)31 b(gsl)p 2097 720 28 4 v 41 w(w)m(a)m(v)m(elet)i(*)e Ft(w)p Fu(\))390 830 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(w)m(a)m(v)m(elet)j(family)e(for)f FD(w)p FK(.)3350 1032 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_wavelet_free)c Fu(\()p FD(gsl)p 1441 1032 V 41 w(w)m(a)m(v)m(elet)33 b(*)e Ft(w)p Fu(\))390 1141 y FK(This)f(function) g(frees)g(the)h(w)m(a)m(v)m(elet)i(ob)5 b(ject)31 b FD(w)p FK(.)275 1343 y(The)k FH(gsl_wavelet_workspace)29 b FK(structure)35 b(con)m(tains)i(scratc)m(h)g(space)f(of)g(the)f(same)h(size)h(as)f(the) 150 1453 y(input)29 b(data)i(and)f(is)h(used)e(to)i(hold)f(in)m (termediate)i(results)f(during)e(the)h(transform.)3350 1655 y([F)-8 b(unction])-3599 b Fv(gsl_wavelet_workspace)59 b(*)52 b(gsl_wavelet_workspace)q(_al)q(loc)g Fu(\()p FD(size)p 3045 1655 V 41 w(t)565 1765 y Ft(n)p Fu(\))390 1874 y FK(This)28 b(function)h(allo)s(cates)i(a)f(w)m(orkspace)f(for)g (the)g(discrete)h(w)m(a)m(v)m(elet)i(transform.)40 b(T)-8 b(o)29 b(p)s(erform)f(a)390 1984 y(one-dimensional)c(transform)e(on)h FD(n)g FK(elemen)m(ts,)j(a)e(w)m(orkspace)g(of)f(size)h FD(n)f FK(m)m(ust)g(b)s(e)f(pro)m(vided.)38 b(F)-8 b(or)390 2093 y(t)m(w)m(o-dimensional)31 b(transforms)d(of)i FD(n)p FK(-b)m(y-)p FD(n)e FK(matrices)j(it)e(is)g(su\016cien)m(t)h(to)g(allo) s(cate)i(a)d(w)m(orkspace)390 2203 y(of)c(size)h FD(n)p FK(,)g(since)f(the)g(transform)f(op)s(erates)i(on)f(individual)f(ro)m (ws)h(and)f(columns.)39 b(A)25 b(n)m(ull)g(p)s(oin)m(ter)390 2313 y(is)30 b(returned)g(if)g(insu\016cien)m(t)h(memory)f(is)g(a)m(v) -5 b(ailable.)3350 2515 y([F)d(unction])-3599 b Fv(void)54 b(gsl_wavelet_workspace_fr)q(ee)e Fu(\()p FD(gsl)p 1964 2515 V 41 w(w)m(a)m(v)m(elet)p 2295 2515 V 43 w(w)m(orkspace)31 b(*)g Ft(work)p Fu(\))390 2624 y FK(This)f(function)g(frees)g(the)h (allo)s(cated)h(w)m(orkspace)f FD(w)m(ork)p FK(.)150 2870 y FJ(31.3)68 b(T)-11 b(ransform)45 b(F)-11 b(unctions)150 3029 y FK(This)22 b(sections)i(describ)s(es)e(the)h(actual)h(functions) f(p)s(erforming)f(the)h(discrete)g(w)m(a)m(v)m(elet)j(transform.)38 b(Note)150 3139 y(that)d(the)g(transforms)f(use)g(p)s(erio)s(dic)g(b)s (oundary)f(conditions.)54 b(If)34 b(the)h(signal)g(is)g(not)f(p)s(erio) s(dic)g(in)h(the)150 3249 y(sample)c(length)g(then)f(spurious)f(co)s (e\016cien)m(ts)j(will)f(app)s(ear)f(at)h(the)f(b)s(eginning)g(and)g (end)g(of)h(eac)m(h)g(lev)m(el)150 3358 y(of)g(the)f(transform.)150 3566 y Fy(31.3.1)63 b(W)-10 b(a)m(v)m(elet)39 b(transforms)k(in)e(one)g (dimension)3350 3772 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_wavelet_transform)f Fu(\()p FD(const)31 b(gsl)p 1888 3772 V 41 w(w)m(a)m(v)m(elet)i(*)e Ft(w)p FD(,)g(double)f(*)g Ft(data)p FD(,)565 3882 y(size)p 712 3882 V 41 w(t)h Ft(stride)p FD(,)h(size)p 1329 3882 V 41 w(t)f Ft(n)p FD(,)f(gsl)p 1649 3882 V 41 w(w)m(a)m(v)m(elet)p 1980 3882 V 43 w(direction)h Ft(dir)p FD(,)h(gsl)p 2721 3882 V 40 w(w)m(a)m(v)m(elet)p 3051 3882 V 43 w(w)m(orkspace)f(*)565 3991 y Ft(work)p Fu(\))3350 4101 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_wavelet_transform)q(_for)q(war)q(d)e Fu(\()p FD(const)32 b(gsl)p 2307 4101 V 40 w(w)m(a)m(v)m(elet)h(*)e Ft(w)p FD(,)g(double)f(*)565 4210 y Ft(data)p FD(,)i(size)p 977 4210 V 41 w(t)e Ft(stride)p FD(,)j(size)p 1594 4210 V 41 w(t)d Ft(n)p FD(,)h(gsl)p 1914 4210 V 41 w(w)m(a)m(v)m(elet)p 2245 4210 V 43 w(w)m(orkspace)g(*)g Ft(work)p Fu(\))3350 4320 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_wavelet_transform)q (_inv)q(ers)q(e)e Fu(\()p FD(const)32 b(gsl)p 2307 4320 V 40 w(w)m(a)m(v)m(elet)h(*)e Ft(w)p FD(,)g(double)f(*)565 4429 y Ft(data)p FD(,)i(size)p 977 4429 V 41 w(t)e Ft(stride)p FD(,)j(size)p 1594 4429 V 41 w(t)d Ft(n)p FD(,)h(gsl)p 1914 4429 V 41 w(w)m(a)m(v)m(elet)p 2245 4429 V 43 w(w)m(orkspace)g(*)g Ft(work)p Fu(\))390 4539 y FK(These)42 b(functions)f(compute)i (in-place)g(forw)m(ard)f(and)f(in)m(v)m(erse)i(discrete)g(w)m(a)m(v)m (elet)i(transforms)390 4649 y(of)38 b(length)g FD(n)f FK(with)g(stride)h FD(stride)43 b FK(on)37 b(the)h(arra)m(y)g FD(data)p FK(.)64 b(The)37 b(length)h(of)g(the)g(transform)f FD(n)g FK(is)390 4758 y(restricted)31 b(to)f(p)s(o)m(w)m(ers)g(of)g(t)m (w)m(o.)42 b(F)-8 b(or)31 b(the)f FH(transform)d FK(v)m(ersion)k(of)f (the)g(function)f(the)h(argumen)m(t)390 4868 y FD(dir)43 b FK(can)38 b(b)s(e)f(either)h FH(forward)d FK(\(+1\))j(or)g FH(backward)d FK(\()p FI(\000)p FK(1\).)62 b(A)38 b(w)m(orkspace)g FD(w)m(ork)43 b FK(of)38 b(length)f FD(n)390 4977 y FK(m)m(ust)30 b(b)s(e)g(pro)m(vided.)390 5121 y(F)-8 b(or)42 b(the)g(forw)m(ard)e (transform,)k(the)e(elemen)m(ts)g(of)g(the)g(original)g(arra)m(y)g(are) g(replaced)f(b)m(y)h(the)390 5230 y(discrete)30 b(w)m(a)m(v)m(elet)h (transform)d FE(f)1505 5244 y Fq(i)1558 5230 y FI(!)d FE(w)1739 5244 y Fq(j;k)1856 5230 y FK(in)j(a)h(pac)m(k)m(ed)h (triangular)f(storage)i(la)m(y)m(out,)g(where)d FD(j)k FK(is)390 5340 y(the)f(index)f(of)h(the)g(lev)m(el)h FE(j)f FK(=)26 b(0)15 b FE(:)g(:)g(:)h(J)30 b FI(\000)20 b FK(1)31 b(and)f FD(k)36 b FK(is)31 b(the)f(index)h(of)f(the)h(co)s (e\016cien)m(t)i(within)d(eac)m(h)p eop end %%Page: 350 366 TeXDict begin 350 365 bop 150 -116 a FK(Chapter)30 b(31:)41 b(W)-8 b(a)m(v)m(elet)34 b(T)-8 b(ransforms)2161 b(350)390 299 y(lev)m(el,)38 b FE(k)f FK(=)c(0)15 b FE(:)g(:)g(:)h FK(2)1042 266 y Fq(j)1101 299 y FI(\000)23 b FK(1.)56 b(The)35 b(total)h(n)m(um)m(b)s(er)e(of)i(lev)m(els)g(is)g FE(J)42 b FK(=)33 b(log)2836 321 y FB(2)2874 299 y FK(\()p FE(n)p FK(\).)55 b(The)34 b(output)h(data)390 408 y(has)30 b(the)h(follo)m(wing)h(form,)982 591 y(\()p FE(s)1060 605 y Fp(\000)p FB(1)p Fq(;)p FB(0)1202 591 y FE(;)15 b(d)1289 605 y FB(0)p Fq(;)p FB(0)1380 591 y FE(;)g(d)1467 605 y FB(1)p Fq(;)p FB(0)1558 591 y FE(;)g(d)1645 605 y FB(1)p Fq(;)p FB(1)1736 591 y FE(;)g(d)1823 605 y FB(2)p Fq(;)p FB(0)1913 591 y FE(;)g FI(\001)g(\001)g(\001)i FE(;)e(d)2162 605 y Fq(j;k)2250 591 y FE(;)g FI(\001)g(\001)g(\001)i FE(;)e(d)2499 605 y Fq(J)5 b Fp(\000)p FB(1)p Fq(;)p FB(2)2679 588 y Fl(J)t Fg(\000)p Fn(1)2793 605 y Fp(\000)p FB(1)2882 591 y FK(\))390 773 y(where)34 b(the)h(\014rst)g(elemen)m(t)h (is)f(the)g(smo)s(othing)g(co)s(e\016cien)m(t)i FE(s)2527 787 y Fp(\000)p FB(1)p Fq(;)p FB(0)2668 773 y FK(,)f(follo)m(w)m(ed)h (b)m(y)e(the)g(detail)h(co-)390 882 y(e\016cien)m(ts)i FE(d)815 896 y Fq(j;k)939 882 y FK(for)e(eac)m(h)h(lev)m(el)h FE(j)5 b FK(.)59 b(The)36 b(bac)m(kw)m(ard)h(transform)e(in)m(v)m(erts) 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b(functions)h(compute)f(t)m(w)m (o-dimensional)j(in-place)f(forw)m(ard)e(and)g(in)m(v)m(erse)h (discrete)390 4682 y(w)m(a)m(v)m(elet)46 b(transforms)c(in)h(standard)f (form)g(on)h(the)g(arra)m(y)h FD(data)f FK(stored)g(in)g(ro)m(w-ma)5 b(jor)43 b(form)390 4792 y(with)33 b(dimensions)f FD(size1)42 b FK(and)32 b FD(size2)42 b FK(and)32 b(ph)m(ysical)i(ro)m(w)f(length)h FD(tda)p FK(.)49 b(The)33 b(dimensions)f(m)m(ust)390 4902 y(b)s(e)39 b(equal)h(\(square)g(matrix\))g(and)f(are)h(restricted) g(to)g(p)s(o)m(w)m(ers)g(of)g(t)m(w)m(o.)69 b(F)-8 b(or)41 b(the)e FH(transform)390 5011 y FK(v)m(ersion)g(of)f(the)g(function)g (the)g(argumen)m(t)h FD(dir)44 b FK(can)38 b(b)s(e)g(either)g FH(forward)e FK(\(+1\))j(or)f FH(backward)390 5121 y FK(\()p FI(\000)p FK(1\).)73 b(A)41 b(w)m(orkspace)h FD(w)m(ork)47 b FK(of)41 b(the)g(appropriate)g(size)h(m)m(ust)e(b)s(e)h (pro)m(vided.)72 b(On)40 b(exit,)45 b(the)390 5230 y(appropriate)28 b(elemen)m(ts)h(of)f(the)h(arra)m(y)f FD(data)h 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Ft(work)p Fu(\))3350 925 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_wavelet2d_transfo)q (rm_m)q(atr)q(ix_)q(for)q(ward)f Fu(\()p FD(const)31 b(gsl)p 2777 925 V 41 w(w)m(a)m(v)m(elet)i(*)565 1035 y Ft(w)p FD(,)e(gsl)p 785 1035 V 41 w(matrix)f(*)h Ft(m)p FD(,)g(gsl)p 1411 1035 V 40 w(w)m(a)m(v)m(elet)p 1741 1035 V 43 w(w)m(orkspace)g(*)g Ft(work)p Fu(\))3350 1145 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_wavelet2d_transfo)q(rm_m) q(atr)q(ix_)q(inv)q(erse)f Fu(\()p FD(const)31 b(gsl)p 2777 1145 V 41 w(w)m(a)m(v)m(elet)i(*)565 1254 y Ft(w)p FD(,)e(gsl)p 785 1254 V 41 w(matrix)f(*)h Ft(m)p FD(,)g(gsl)p 1411 1254 V 40 w(w)m(a)m(v)m(elet)p 1741 1254 V 43 w(w)m(orkspace)g(*)g Ft(work)p Fu(\))390 1364 y FK(These)26 b(functions)g(compute)h(the)g(t) m(w)m(o-dimensional)h(in-place)f(w)m(a)m(v)m(elet)j(transform)25 b(on)i(a)g(matrix)390 1473 y FD(a)p FK(.)3350 1662 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_wavelet2d_nstrans)q(form)f Fu(\()p FD(const)31 b(gsl)p 2097 1662 V 41 w(w)m(a)m(v)m(elet)i(*)e Ft(w)p FD(,)g(double)f(*)565 1771 y Ft(data)p FD(,)i(size)p 977 1771 V 41 w(t)e Ft(tda)p FD(,)i(size)p 1437 1771 V 41 w(t)e Ft(size1)p FD(,)j(size)p 2002 1771 V 40 w(t)e Ft(size2)p FD(,)h(gsl)p 2531 1771 V 41 w(w)m(a)m(v)m(elet)p 2862 1771 V 43 w(direction)f Ft(dir)p FD(,)565 1881 y(gsl)p 677 1881 V 41 w(w)m(a)m(v)m(elet)p 1008 1881 V 43 w(w)m(orkspace)g(*)f Ft(work)p Fu(\))3350 1990 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_wavelet2d_nstrans)q(form)q(_fo)q(rwa)q(rd)f Fu(\()p FD(const)31 b(gsl)p 2516 1990 V 40 w(w)m(a)m(v)m(elet)j(*)c Ft(w)p FD(,)565 2100 y(double)g(*)h Ft(data)p FD(,)h(size)p 1346 2100 V 40 w(t)f Ft(tda)p FD(,)h(size)p 1806 2100 V 41 w(t)e Ft(size1)p FD(,)i(size)p 2370 2100 V 41 w(t)f Ft(size2)p FD(,)h(gsl)p 2900 2100 V 40 w(w)m(a)m(v)m(elet)p 3230 2100 V 43 w(w)m(orkspace)g(*)565 2210 y Ft(work)p Fu(\))3350 2319 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_wavelet2d_nstrans)q(form)q(_in)q(ver)q(se)f Fu(\()p FD(const)31 b(gsl)p 2516 2319 V 40 w(w)m(a)m(v)m(elet)j(*)c Ft(w)p FD(,)565 2429 y(double)g(*)h Ft(data)p FD(,)h(size)p 1346 2429 V 40 w(t)f Ft(tda)p FD(,)h(size)p 1806 2429 V 41 w(t)e Ft(size1)p FD(,)i(size)p 2370 2429 V 41 w(t)f Ft(size2)p FD(,)h(gsl)p 2900 2429 V 40 w(w)m(a)m(v)m(elet)p 3230 2429 V 43 w(w)m(orkspace)g(*)565 2538 y Ft(work)p Fu(\))390 2648 y FK(These)47 b(functions)g(compute)g(the)h(t)m(w)m (o-dimensional)h(w)m(a)m(v)m(elet)h(transform)c(in)h(non-standard)390 2758 y(form.)3350 2946 y([F)-8 b(unction])-3599 b Fv(int)53 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 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EPSF-3.0 %%Creator: GNU libplot drawing library 4.1 %%Title: PostScript plot %%CreationDate: Thu Jul 22 17:12:05 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 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/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 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 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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 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3069 9081 3068 9108 3067 9135 3066 9162 3065 9189 3064 256 MLine End %%PageTrailer End %I eop showpage %%Trailer end %%EOF %%EndDocument @endspecial 390 3422 a(Original)43 b(\(upp)s(er\))e(and)h(w)m(a)m(v)m (elet-compressed)j(\(lo)m(w)m(er\))g(ECG)d(signals,)k(using)c(the)h(20) 390 3532 y(largest)32 b(comp)s(onen)m(ts)e(of)h(the)f(Daub)s(ec)m (hies\(4\))i(discrete)g(w)m(a)m(v)m(elet)h(transform.)150 3771 y FJ(31.5)68 b(References)47 b(and)d(F)-11 b(urther)44 b(Reading)150 3931 y FK(The)32 b(mathematical)j(bac)m(kground)d(to)h(w) m(a)m(v)m(elet)j(transforms)31 b(is)i(co)m(v)m(ered)h(in)e(the)h (original)h(lectures)f(b)m(y)150 4040 y(Daub)s(ec)m(hies,)330 4180 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 4289 y(in)j(Applied)g(Mathematics) 36 b FK(\(1992\),)d(SIAM,)e(ISBN)f(0898712742.)150 4456 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 4566 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 4705 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 4815 y(Publishing)29 b(\(2002\),)k(ISBN)e(0750306920.)150 4981 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 5091 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: 354 370 TeXDict begin 354 369 bop 150 -116 a FK(Chapter)30 b(31:)41 b(W)-8 b(a)m(v)m(elet)34 b(T)-8 b(ransforms)2161 b(354)150 299 y(The)30 b(concept)h(of)g(m)m(ultiresolution)g(analysis)g 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(form)m(ula)h(giv)m(en)g(ab)s(o)m(v)m(e.)74 b(Therefore,)44 b(this)e(transform)150 4393 y(corresp)s(onds)32 b(to)h(an)g(orthogonal) i(expansion)e(in)f(eigenfunctions)i(of)f(the)h(Diric)m(hlet)g(problem)f (for)g(the)150 4503 y(Bessel)e(di\013eren)m(tial)h(equation.)150 4733 y FJ(32.2)68 b(F)-11 b(unctions)3350 4940 y FK([F)j(unction])-3599 b Fv(gsl_dht)54 b(*)f(gsl_dht_alloc)c Fu(\()p FD(size)p 1580 4940 28 4 v 42 w(t)30 b Ft(size)p Fu(\))390 5050 y FK(This)g(function)g(allo)s(cates)i(a)f(Discrete)h(Hank)m(el)g (transform)d(ob)5 b(ject)32 b(of)e(size)h FD(size)p FK(.)3350 5230 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_dht_init)c Fu(\()p FD(gsl)p 1179 5230 V 41 w(dh)m(t)30 b(*)h Ft(t)p FD(,)g(double)f Ft(nu)p FD(,)h(double)f Ft(xmax)p Fu(\))390 5340 y FK(This)g(function)g(initializes)i(the)f(transform)e FD(t)k FK(for)d(the)h(giv)m(en)g(v)-5 b(alues)31 b(of)f FD(n)m(u)g FK(and)g FD(xmax)p FK(.)p eop end %%Page: 356 372 TeXDict begin 356 371 bop 150 -116 a FK(Chapter)30 b(32:)41 b(Discrete)32 b(Hank)m(el)g(T)-8 b(ransforms)1848 b(356)3350 299 y([F)-8 b(unction])-3599 b Fv(gsl_dht)54 b(*)f(gsl_dht_new)c Fu(\()p FD(size)p 1476 299 28 4 v 41 w(t)31 b Ft(size)p FD(,)h(double)d Ft(nu)p FD(,)j(double)e Ft(xmax)p Fu(\))390 408 y FK(This)f(function)h(allo)s(cates)i(a)e(Discrete)h(Hank)m(el)g (transform)e(ob)5 b(ject)31 b(of)f(size)h FD(size)36 b FK(and)29 b(initializes)390 518 y(it)i(for)f(the)h(giv)m(en)g(v)-5 b(alues)31 b(of)f FD(n)m(u)g FK(and)g FD(xmax)p FK(.)3350 702 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_dht_free)49 b Fu(\()p FD(gsl)p 1232 702 V 41 w(dh)m(t)30 b(*)g Ft(t)p Fu(\))390 812 y FK(This)g(function)g(frees)g(the)h(transform)e FD(t)p FK(.)3350 996 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_dht_apply)d Fu(\()p FD(const)31 b(gsl)p 1470 996 V 40 w(dh)m(t)g(*)f Ft(t)p FD(,)h(double)f(*)h Ft(f_in)p FD(,)h(double)e(*)g Ft(f_out)p Fu(\))390 1106 y FK(This)f(function)g (applies)h(the)g(transform)f FD(t)j FK(to)f(the)f(arra)m(y)g FD(f)p 2433 1106 V 40 w(in)f 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FK(Chapter)30 b(33:)41 b(One)30 b(dimensional)h(Ro)s(ot-Finding)1729 b(358)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 Fm(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(33.3)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) h(the)e(solv)m(er)i(then)e(the)g(function)g(returns)f(a)i(n)m(ull)390 4288 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 4485 y([F)-8 b(unction])-3599 b Fv(int)53 b (gsl_root_fsolver_set)f Fu(\()p FD(gsl)p 1598 4485 V 41 w(ro)s(ot)p 1803 4485 V 40 w(fsolv)m(er)31 b(*)g Ft(s)p FD(,)g(gsl)p 2419 4485 V 40 w(function)f(*)h Ft(f)p FD(,)565 4595 y(double)f Ft(x_lower)p FD(,)j(double)d Ft(x_upper)p Fu(\))390 4705 y FK(This)c(function)h(initializes,)j(or)d (reinitializes,)k(an)c(existing)h(solv)m(er)g FD(s)i FK(to)e(use)f(the)g(function)g FD(f)45 b FK(and)390 4814 y(the)31 b(initial)g(searc)m(h)g(in)m(terv)-5 b(al)32 b([)p FD(x)p 1493 4814 V 40 w(lo)m(w)m(er)p FK(,)g FD(x)p 1844 4814 V 40 w(upp)s(er)7 b FK(].)3350 5011 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_root_fdfsolver_se)q(t)e Fu(\()p FD(gsl)p 1702 5011 V 41 w(ro)s(ot)p 1907 5011 V 41 w(fdfsolv)m(er)30 b(*)h Ft(s)p FD(,)g(gsl)p 2602 5011 V 40 w(function)p 2968 5011 V 40 w(fdf)e(*)565 5121 y Ft(fdf)p FD(,)j(double)e Ft(root)p Fu(\))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: 359 375 TeXDict begin 359 374 bop 150 -116 a FK(Chapter)30 b(33:)41 b(One)30 b(dimensional)h(Ro)s(ot-Finding)1729 b(359)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 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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(\()p FE(x;)15 b Fm(p)-5 b(ar)g(ams)s FK(\))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: 360 376 TeXDict begin 360 375 bop 150 -116 a FK(Chapter)30 b(33:)41 b(One)30 b(dimensional)h(Ro)s(ot-Finding)1729 b(360)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(\()p FE(x;)15 b Fm(p)-5 b(ar)g(ams)r FK(\))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(\()p FE(x;)15 b Fm(p)-5 b(ar)g(ams)t FK(\),)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(\()p FE(x;)15 b Fm(p)-5 b(ar)g(ams)s FK(\))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(\()p FE(x;)15 b Fm(p)-5 b(ar)g(ams)t FK(\))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: 361 377 TeXDict begin 361 376 bop 150 -116 a FK(Chapter)30 b(33:)41 b(One)30 b(dimensional)h(Ro)s(ot-Finding)1729 b(361)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 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(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: 362 378 TeXDict begin 362 377 bop 150 -116 a FK(Chapter)30 b(33:)41 b(One)30 b(dimensional)h(Ro)s(ot-Finding)1729 b(362)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(33.7)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 (found)f(to)i(within)f(the)h(user-sp)s(eci\014ed)e(precision.)225 1171 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 1304 y FI(\017)60 b FK(An)30 b(error)g(has)g(o)s(ccurred.)150 1459 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 1569 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 1748 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_root_test_interva)q(l)e Fu(\()p FD(double)31 b Ft(x_lower)p FD(,)h(double)e Ft(x_upper)p FD(,)565 1857 y(double)g Ft(epsabs)p FD(,)i(double)e Ft(epsrel)p Fu(\))390 1967 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 1967 V 40 w(lo)m(w)m(er)p FK(,)h FD(x)p 2904 1967 V 40 w(upp)s(er)7 b FK(])20 b(with)i(absolute)390 2076 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 2186 y(condition)h(is)f(ac)m(hiev)m(ed,) 1227 2352 y FI(j)p FE(a)20 b FI(\000)g FE(b)p FI(j)26 b FE(<)f Fm(epsabs)c FK(+)f Fm(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 2518 y(when)33 b(the)i(in)m(terv)-5 b(al)36 b FE(x)c FK(=)g([)p FE(a;)15 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4547 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_root_test_residua)q(l)e Fu(\()p FD(double)31 b Ft(f)p FD(,)f(double)g Ft(epsabs)p Fu(\))390 4657 y FK(This)d(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 4766 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,)1712 4932 y FI(j)p FE(f)10 b FI(j)25 b FE(<)g Fm(epsabs)390 5098 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 5208 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 5317 y(where)30 b(the)g(residual,)h FI(j)p FE(f)10 b FK(\()p FE(x)p FK(\))p FI(j)p FK(,)31 b(is)f(small)h(enough.)p eop end %%Page: 363 379 TeXDict begin 363 378 bop 150 -116 a FK(Chapter)30 b(33:)41 b(One)30 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y(lation)i(strategy) g(with)f(the)g(bisection)g(algorithm.)42 b(This)28 b(pro)s(duces)f(a)i (fast)h(algorithm)f(whic)m(h)g(is)390 4257 y(still)i(robust.)390 4406 y(On)j(eac)m(h)h(iteration)h(Bren)m(t's)f(metho)s(d)f(appro)m (ximates)i(the)e(function)g(using)g(an)h(in)m(terp)s(olating)390 4516 y(curv)m(e.)52 b(On)33 b(the)h(\014rst)f(iteration)j(this)e(is)g (a)g(linear)g(in)m(terp)s(olation)i(of)e(the)g(t)m(w)m(o)h(endp)s(oin)m (ts.)51 b(F)-8 b(or)390 4625 y(subsequen)m(t)41 b(iterations)i(the)e (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: 364 380 TeXDict begin 364 379 bop 150 -116 a FK(Chapter)30 b(33:)41 b(One)30 b(dimensional)h(Ro)s(ot-Finding)1729 b(364)150 299 y FJ(33.9)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: 365 381 TeXDict begin 365 380 bop 150 -116 a FK(Chapter)30 b(33:)41 b(One)30 b(dimensional)h(Ro)s(ot-Finding)1729 b(365)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(33.10)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: 366 382 TeXDict begin 366 381 bop 150 -116 a FK(Chapter)30 b(33:)41 b(One)30 b(dimensional)h(Ro)s(ot-Finding)1729 b(366)485 299 y FH(double)47 b(a)g(=)g(p->a;)485 408 y(double)g(b)g(=)g(p->b;)485 518 y(double)g(c)g(=)g(p->c;)485 737 y(return)g(2.0)f(*)i(a)f(*)h(x)f (+)h(b;)390 847 y(})390 1066 y(void)390 1176 y(quadratic_fdf)c (\(double)i(x,)h(void)g(*params,)1106 1285 y(double)f(*y,)h(double)f (*dy\))390 1395 y({)485 1504 y(struct)h(quadratic_params)c(*p)581 1614 y(=)k(\(struct)f(quadratic_params)e(*\))j(params;)485 1833 y(double)g(a)g(=)g(p->a;)485 1943 y(double)g(b)g(=)g(p->b;)485 2052 y(double)g(c)g(=)g(p->c;)485 2271 y(*y)h(=)f(\(a)g(*)h(x)f(+)h (b\))f(*)g(x)h(+)f(c;)485 2381 y(*dy)g(=)h(2.0)f(*)g(a)h(*)f(x)h(+)f (b;)390 2491 y(})150 2638 y FK(The)36 b(\014rst)g(program)g(uses)h(the) 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y(struct)i(quadratic_params)c(params)j(=)h({1.0,)g(0.0,)f(-5.0};)p eop end %%Page: 367 383 TeXDict begin 367 382 bop 150 -116 a FK(Chapter)30 b(33:)41 b(One)30 b(dimensional)h(Ro)s(ot-Finding)1729 b(367)485 299 y FH(F.function)45 b(=)j(&quadratic;)485 408 y(F.params)e(=)h (¶ms;)485 628 y(T)h(=)f(gsl_root_fsolver_brent;)485 737 y(s)h(=)f(gsl_root_fsolver_alloc)42 b(\(T\);)485 847 y(gsl_root_fsolver_set)h(\(s,)k(&F,)g(x_lo,)f(x_hi\);)485 1066 y(printf)h(\("using)e(\045s)j(method\\n",)867 1176 y(gsl_root_fsolver_name)42 b(\(s\)\);)485 1395 y(printf)47 b(\("\0455s)f([\0459s,)g(\0459s])h(\0459s)g(\04510s)f(\0459s\\n",)867 1504 y("iter",)g("lower",)g("upper",)f("root",)867 1614 y("err",)h("err\(est\)"\);)485 1833 y(do)581 1943 y({)676 2052 y(iter++;)676 2162 y(status)g(=)i(gsl_root_fsolver_iterate)41 b(\(s\);)676 2271 y(r)48 b(=)f(gsl_root_fsolver_root)42 b(\(s\);)676 2381 y(x_lo)47 b(=)g(gsl_root_fsolver_x_lower)42 b(\(s\);)676 2491 y(x_hi)47 b(=)g(gsl_root_fsolver_x_upper)42 b(\(s\);)676 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(using)g(a)h(deriv)-5 b(ativ)m(e)32 b(solv)m(er)f(instead.)390 2381 y FH(#include)46 b()390 2491 y(#include)g ()390 2600 y(#include)g()390 2710 y(#include)g()390 2929 y(#include)g("demo_fn.h") 390 3039 y(#include)g("demo_fn.c")390 3258 y(int)390 3367 y(main)h(\(void\))390 3477 y({)485 3587 y(int)g(status;)485 3696 y(int)g(iter)g(=)g(0,)h(max_iter)d(=)j(100;)485 3806 y(const)f(gsl_root_fdfsolver_type)41 b(*T;)485 3915 y(gsl_root_fdfsolver)i(*s;)485 4025 y(double)k(x0,)f(x)i(=)f(5.0,)g (r_expected)e(=)i(sqrt)g(\(5.0\);)485 4134 y(gsl_function_fdf)d(FDF;) 485 4244 y(struct)j(quadratic_params)c(params)j(=)h({1.0,)g(0.0,)f (-5.0};)485 4463 y(FDF.f)h(=)g(&quadratic;)485 4573 y(FDF.df)g(=)g (&quadratic_deriv;)485 4682 y(FDF.fdf)f(=)i(&quadratic_fdf;)485 4792 y(FDF.params)d(=)j(¶ms;)485 5011 y(T)g(=)f (gsl_root_fdfsolver_newton;)485 5121 y(s)h(=)f (gsl_root_fdfsolver_alloc)42 b(\(T\);)485 5230 y (gsl_root_fdfsolver_set)g(\(s,)47 b(&FDF,)f(x\);)p eop end %%Page: 369 385 TeXDict begin 369 384 bop 150 -116 a FK(Chapter)30 b(33:)41 b(One)30 b(dimensional)h(Ro)s(ot-Finding)1729 b(369)485 299 y FH(printf)47 b(\("using)e(\045s)j(method\\n",)867 408 y(gsl_root_fdfsolver_name)42 b(\(s\)\);)485 628 y(printf)47 b(\("\045-5s)f(\04510s)g(\04510s)h(\04510s\\n",)867 737 y("iter",)f("root",)g("err",)g("err\(est\)"\);)485 847 y(do)581 956 y({)676 1066 y(iter++;)676 1176 y(status)g(=)i (gsl_root_fdfsolver_itera)o(te)42 b(\(s\);)676 1285 y(x0)48 b(=)f(x;)676 1395 y(x)h(=)f(gsl_root_fdfsolver_root)42 b(\(s\);)676 1504 y(status)k(=)i(gsl_root_test_delta)42 b(\(x,)47 b(x0,)g(0,)g(1e-3\);)676 1724 y(if)h(\(status)d(==)j (GSL_SUCCESS\))772 1833 y(printf)e(\("Converged:\\n"\);)676 2052 y(printf)g(\("\0455d)h(\04510.7f)f(\045+10.7f)g(\04510.7f\\n",) 1058 2162 y(iter,)h(x,)g(x)g(-)h(r_expected,)c(x)k(-)f(x0\);)581 2271 y(})485 2381 y(while)g(\(status)f(==)h(GSL_CONTINUE)d(&&)j(iter)g (<)h(max_iter\);)485 2600 y(gsl_root_fdfsolver_free)42 b(\(s\);)485 2710 y(return)47 b(status;)390 2819 y(})150 2952 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b(and)e(F)-11 b(urther)45 b(Reading)150 4701 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 4833 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 4943 y(tion",)e FD(Computer)d(Journal)p FK(,)h(14)h(\(1971\))i(422{425)330 5075 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 5185 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 5294 y(1)31 b(No.)g(4)g(\(1975\))i(330{345)p eop end %%Page: 370 386 TeXDict begin 370 385 bop 150 -116 a FK(Chapter)30 b(34:)41 b(One)30 b(dimensional)h(Minimization)1735 b(370)150 299 y FG(34)80 b(One)53 b(dimensional)g(Minimization)150 535 y FK(This)31 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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: 371 387 TeXDict begin 371 386 bop 150 -116 a FK(Chapter)30 b(34:)41 b(One)30 b(dimensional)h(Minimization)1735 b(371)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(34.2)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 Fm(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) 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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 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(algorithm)150 677 y(and)30 b(can)g(b)s(e)g(reused)g(for)g(di\013eren)m (t)h(problems.)3350 881 y([F)-8 b(unction])-3599 b Fv (gsl_multiroot_fsolver)59 b(*)52 b(gsl_multiroot_fsolver)q(_al)q(loc)g Fu(\()p FD(const)565 991 y(gsl)p 677 991 28 4 v 41 w(m)m(ultiro)s(ot)p 1091 991 V 41 w(fsolv)m(er)p 1387 991 V 40 w(t)m(yp)s(e)31 b(*)g Ft(T)p FD(,)g(size)p 1957 991 V 41 w(t)f Ft(n)p Fu(\))390 1100 y FK(This)c(function)h(returns)f(a)i(p)s(oin)m(ter)f(to) h(a)f(newly)g(allo)s(cated)i(instance)f(of)g(a)f(solv)m(er)h(of)g(t)m (yp)s(e)f FD(T)33 b FK(for)390 1210 y(a)i(system)g(of)g FD(n)f FK(dimensions.)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)i(of)f(a)390 1319 y(h)m(ybrid)29 b(solv)m(er,)j(to)f(solv)m(e)h(a)e(3-dimensional)i (system)e(of)h(equations.)630 1463 y FH(const)46 b (gsl_multiroot_fsolver_type)41 b(*)47 b(T)821 1573 y(=)g (gsl_multiroot_fsolver_hybr)o(id;)630 1683 y(gsl_multiroot_fsolver)42 b(*)47 b(s)821 1792 y(=)g(gsl_multiroot_fsolver_allo)o(c)42 b(\(T,)47 b(3\);)390 1936 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 2046 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 2249 y([F)-8 b(unction])-3599 b Fv(gsl_multiroot_fdfsolve)q(r)58 b(*)53 b(gsl_multiroot_fdfsolve)q (r_al)q(loc)565 2359 y Fu(\()p FD(const)31 b(gsl)p 950 2359 V 41 w(m)m(ultiro)s(ot)p 1364 2359 V 41 w(fdfsolv)m(er)p 1739 2359 V 40 w(t)m(yp)s(e)g(*)f Ft(T)p FD(,)h(size)p 2308 2359 V 41 w(t)g Ft(n)p Fu(\))390 2469 y FK(This)36 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: 379 395 TeXDict begin 379 394 bop 150 -116 a FK(Chapter)30 b(35:)41 b(Multidimensional)32 b(Ro)s(ot-Finding)1701 b(379)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(35.3)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(\()p FE(x;)15 b Fm(p)-5 b(ar)g(ams)s FK(\))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 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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: 380 396 TeXDict begin 380 395 bop 150 -116 a FK(Chapter)30 b(35:)41 b(Multidimensional)32 b(Ro)s(ot-Finding)1701 b(380)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(\()p FE(x;)15 b Fm(p)-5 b(ar)g(ams)s FK(\))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 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(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: 384 400 TeXDict begin 384 399 bop 150 -116 a FK(Chapter)30 b(35:)41 b(Multidimensional)32 b(Ro)s(ot-Finding)1701 b(384)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(35.7)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 (size)i(will)e(not)h(b)s(e)f(suitable)h(for)f(all)h(problems.)3457 4245 y([Solv)m(er])-3599 b Fv(gsl_multiroot_fsolver_)q(hyb)q(rid)390 4355 y FK(This)30 b(is)g(a)h(\014nite)f(di\013erence)h(v)m(ersion)g(of) f(the)h(Hybrid)e(algorithm)j(without)e(in)m(ternal)h(scaling.)3457 4523 y([Solv)m(er])-3599 b Fv(gsl_multiroot_fsolver_)q(dne)q(wton)390 4633 y FK(The)29 b FD(discrete)h(Newton)g(algorithm)h FK(is)e(the)h(simplest)g(metho)s(d)e(of)i(solving)g(a)g(m)m (ultidimensional)390 4743 y(system.)41 b(It)30 b(uses)g(the)h(Newton)g (iteration)1609 4905 y FE(x)25 b FI(!)h FE(x)20 b FI(\000)g FE(J)2025 4868 y Fp(\000)p FB(1)2114 4905 y FE(f)10 b FK(\()p FE(x)p FK(\))390 5068 y(where)27 b(the)h(Jacobian)h(matrix)f FE(J)37 b FK(is)28 b(appro)m(ximated)g(b)m(y)g(taking)h(\014nite)e (di\013erences)i(of)e(the)i(func-)390 5177 y(tion)i FD(f)p FK(.)40 b(The)30 b(appro)m(ximation)h(sc)m(heme)h(used)d(b)m(y)h(this)h (implemen)m(tation)h(is,)1396 5340 y FE(J)1446 5354 y Fq(ij)1530 5340 y FK(=)25 b(\()p 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: 385 401 TeXDict begin 385 400 bop 150 -116 a FK(Chapter)30 b(35:)41 b(Multidimensional)32 b(Ro)s(ot-Finding)1701 b(385)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(35.8)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: 386 402 TeXDict begin 386 401 bop 150 -116 a FK(Chapter)30 b(35:)41 b(Multidimensional)32 b(Ro)s(ot-Finding)1701 b(386)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 y(const)g(double)f(y1)h(=)h(b)f(*)g(\(x1)g(-)h(x0)f(*)g (x0\);)485 1066 y(gsl_vector_set)d(\(f,)j(0,)g(y0\);)485 1176 y(gsl_vector_set)d(\(f,)j(1,)g(y1\);)485 1395 y(return)g (GSL_SUCCESS;)390 1504 y(})150 1669 y FK(The)40 b(main)g(program)g(b)s (egins)f(b)m(y)h(creating)i(the)e(function)g(ob)5 b(ject)41 b FH(f)p FK(,)i(with)d(the)g(argumen)m(ts)g FH(\(x,y\))150 1778 y FK(and)35 b(parameters)i FH(\(a,b\))p FK(.)55 b(The)36 b(solv)m(er)h FH(s)e FK(is)h(initialized)i(to)f(use)e(this)h (function,)h(with)f(the)g FH(hybrids)150 1888 y FK(metho)s(d.)390 2052 y FH(int)390 2162 y(main)47 b(\(void\))390 2271 y({)485 2381 y(const)g(gsl_multiroot_fsolver_ty)o(pe)41 b(*T;)485 2491 y(gsl_multiroot_fsolver)h(*s;)485 2710 y(int)47 b(status;)485 2819 y(size_t)g(i,)g(iter)f(=)i(0;)485 3039 y(const)f(size_t)f(n)h(=)h(2;)485 3148 y(struct)f(rparams)e(p)j(=) f({1.0,)g(10.0};)485 3258 y(gsl_multiroot_function)42 b(f)48 b(=)f({&rosenbrock_f,)d(n,)j(&p};)485 3477 y(double)g(x_init[2]) e(=)i({-10.0,)f(-5.0};)485 3587 y(gsl_vector)f(*x)j(=)f (gsl_vector_alloc)c(\(n\);)485 3806 y(gsl_vector_set)h(\(x,)j(0,)g (x_init[0]\);)485 3915 y(gsl_vector_set)d(\(x,)j(1,)g(x_init[1]\);)485 4134 y(T)h(=)f(gsl_multiroot_fsolver_hybr)o(ids)o(;)485 4244 y(s)h(=)f(gsl_multiroot_fsolver_allo)o(c)42 b(\(T,)47 b(2\);)485 4354 y(gsl_multiroot_fsolver_set)41 b(\(s,)47 b(&f,)g(x\);)485 4573 y(print_state)e(\(iter,)h(s\);)485 4792 y(do)581 4902 y({)676 5011 y(iter++;)676 5121 y(status)g(=)i (gsl_multiroot_fsolver_it)o(erat)o(e)42 b(\(s\);)676 5340 y(print_state)j(\(iter,)h(s\);)p eop end %%Page: 387 403 TeXDict begin 387 402 bop 150 -116 a FK(Chapter)30 b(35:)41 b(Multidimensional)32 b(Ro)s(ot-Finding)1701 b(387)676 408 y FH(if)48 b(\(status\))141 b(/*)47 b(check)f(if)h(solver)f(is)i (stuck)e(*/)772 518 y(break;)676 737 y(status)g(=)772 847 y(gsl_multiroot_test_resid)o(ual)41 b(\(s->f,)46 b(1e-7\);)581 956 y(})485 1066 y(while)h(\(status)f(==)h(GSL_CONTINUE)d (&&)j(iter)g(<)h(1000\);)485 1285 y(printf)f(\("status)e(=)j (\045s\\n",)e(gsl_strerror)e(\(status\)\);)485 1504 y (gsl_multiroot_fsolver_free)d(\(s\);)485 1614 y(gsl_vector_free)j (\(x\);)485 1724 y(return)j(0;)390 1833 y(})150 1966 y FK(Note)25 b(that)f(it)h(is)e(imp)s(ortan)m(t)h(to)h(c)m(hec)m(k)g (the)f(return)f(status)h(of)g(eac)m(h)h(solv)m(er)f(step,)i(in)d(case)i (the)f(algorithm)150 2075 y(b)s(ecomes)44 b(stuc)m(k.)80 b(If)43 b(an)g(error)g(condition)h(is)g(detected,)k(indicating)c(that)g (the)g(algorithm)g(cannot)150 2185 y(pro)s(ceed,)j(then)d(the)g(error)f (can)h(b)s(e)g(rep)s(orted)f(to)h(the)g(user,)j(a)d(new)g(starting)g(p) s(oin)m(t)g(c)m(hosen)h(or)f(a)150 2294 y(di\013eren)m(t)31 b(algorithm)g(used.)275 2427 y(The)c(in)m(termediate)j(state)f(of)g (the)f(solution)h(is)f(displa)m(y)m(ed)h(b)m(y)f(the)g(follo)m(wing)i (function.)39 b(The)28 b(solv)m(er)150 2536 y(state)44 b(con)m(tains)f(the)g(v)m(ector)g FH(s->x)f FK(whic)m(h)g(is)g(the)g (curren)m(t)g(p)s(osition,)k(and)c(the)g(v)m(ector)i FH(s->f)d FK(with)150 2646 y(corresp)s(onding)29 b(function)h(v)-5 b(alues.)390 2779 y FH(int)390 2888 y(print_state)45 b(\(size_t)h(iter,)g(gsl_multiroot_fsolver)c(*)47 b(s\))390 2998 y({)485 3107 y(printf)g(\("iter)f(=)h(\0453u)g(x)g(=)h(\045)f(.3f) g(\045)h(.3f)f(")867 3217 y("f\(x\))g(=)g(\045)h(.3e)e(\045)i(.3e\\n",) 867 3327 y(iter,)867 3436 y(gsl_vector_get)c(\(s->x,)i(0\),)867 3546 y(gsl_vector_get)e(\(s->x,)i(1\),)867 3655 y(gsl_vector_get)e (\(s->f,)i(0\),)867 3765 y(gsl_vector_get)e(\(s->f,)i(1\)\);)390 3874 y(})150 4007 y FK(Here)26 b(are)g(the)g(results)g(of)g(running)e (the)i(program.)39 b(The)25 b(algorithm)i(is)f(started)g(at)g(\()p FI(\000)p FK(10)p FE(;)15 b FI(\000)p FK(5\))28 b(far)d(from)150 4117 y(the)37 b(solution.)59 b(Since)37 b(the)f(solution)h(is)g(hidden) e(in)h(a)h(narro)m(w)f(v)-5 b(alley)38 b(the)f(earliest)h(steps)e (follo)m(w)i(the)150 4226 y(gradien)m(t)c(of)g(the)g(function)f(do)m (wnhill,)h(in)g(an)f(attempt)i(to)f(reduce)f(the)h(large)h(v)-5 b(alue)34 b(of)f(the)h(residual.)150 4336 y(Once)f(the)g(ro)s(ot)h(has) f(b)s(een)f(appro)m(ximately)j(lo)s(cated,)g(on)e(iteration)i(8,)f(the) g(Newton)f(b)s(eha)m(vior)g(tak)m(es)150 4445 y(o)m(v)m(er)f(and)d(con) m(v)m(ergence)k(is)e(v)m(ery)f(rapid.)390 4555 y Fz(iter)40 b(=)79 b(0)39 b(x)h(=)f(-10.000)80 b(-5.000)g(f\(x\))40 b(=)g(1.100e+01)h(-1.050e+03)390 4643 y(iter)f(=)79 b(1)39 b(x)h(=)f(-10.000)80 b(-5.000)g(f\(x\))40 b(=)g(1.100e+01)h(-1.050e+03) 390 4730 y(iter)f(=)79 b(2)39 b(x)h(=)78 b(-3.976)i(24.827)g(f\(x\))40 b(=)g(4.976e+00)80 b(9.020e+01)390 4817 y(iter)40 b(=)79 b(3)39 b(x)h(=)78 b(-3.976)i(24.827)g(f\(x\))40 b(=)g(4.976e+00)80 b(9.020e+01)390 4904 y(iter)40 b(=)79 b(4)39 b(x)h(=)78 b(-3.976)i(24.827)g(f\(x\))40 b(=)g(4.976e+00)80 b(9.020e+01)390 4991 y(iter)40 b(=)79 b(5)39 b(x)h(=)78 b(-1.274)i(-5.680)g(f\(x\))40 b(=)g(2.274e+00)h(-7.302e+01)390 5078 y(iter)f(=)79 b(6)39 b(x)h(=)78 b(-1.274)i(-5.680)g(f\(x\))40 b(=)g(2.274e+00)h(-7.302e+01) 390 5166 y(iter)f(=)79 b(7)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 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: 388 404 TeXDict begin 388 403 bop 150 -116 a FK(Chapter)30 b(35:)41 b(Multidimensional)32 b(Ro)s(ot-Finding)1701 b(388)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 b(or)e(to)h(recompute)g(the)g (Jacobian,)g(when)e(p)s(o)s(or)h(con)m(v)m(ergence)j(b)s(eha)m(vior)d (is)g(detected.)275 973 y(The)f(next)i(example)f(program)g(adds)g (deriv)-5 b(ativ)m(e)32 b(information,)e(in)g(order)g(to)h(accelerate)i (the)e(solu-)150 1083 y(tion.)45 b(There)31 b(are)h(t)m(w)m(o)h(deriv) -5 b(ativ)m(e)33 b(functions)e FH(rosenbrock_df)d FK(and)j FH(rosenbrock_fdf)p FK(.)40 b(The)32 b(latter)150 1193 y(computes)27 b(b)s(oth)g(the)g(function)g(and)g(its)h(deriv)-5 b(ativ)m(e)29 b(sim)m(ultaneously)-8 b(.)40 b(This)27 b(allo)m(ws)i(the)e(optimization)150 1302 y(of)h(an)m(y)g(common)g (terms.)40 b(F)-8 b(or)29 b(simplicit)m(y)g(w)m(e)f(substitute)g(calls) h(to)g(the)f(separate)g FH(f)g FK(and)f FH(df)g FK(functions)150 1412 y(at)k(this)f(p)s(oin)m(t)h(in)f(the)g(co)s(de)h(b)s(elo)m(w.)390 1552 y FH(int)390 1662 y(rosenbrock_df)44 b(\(const)i(gsl_vector)f(*)j (x,)f(void)g(*params,)1106 1771 y(gsl_matrix)e(*)i(J\))390 1881 y({)485 1991 y(const)g(double)f(a)h(=)h(\(\(struct)d(rparams)h (*\))h(params\)->a;)485 2100 y(const)g(double)f(b)h(=)h(\(\(struct)d (rparams)h(*\))h(params\)->b;)485 2319 y(const)g(double)f(x0)h(=)h (gsl_vector_get)43 b(\(x,)k(0\);)485 2538 y(const)g(double)f(df00)h(=)g (-a;)485 2648 y(const)g(double)f(df01)h(=)g(0;)485 2758 y(const)g(double)f(df10)h(=)g(-2)g(*)h(b)95 b(*)47 b(x0;)485 2867 y(const)g(double)f(df11)h(=)g(b;)485 3086 y(gsl_matrix_set)d(\(J,) j(0,)g(0,)h(df00\);)485 3196 y(gsl_matrix_set)c(\(J,)j(0,)g(1,)h (df01\);)485 3306 y(gsl_matrix_set)c(\(J,)j(1,)g(0,)h(df10\);)485 3415 y(gsl_matrix_set)c(\(J,)j(1,)g(1,)h(df11\);)485 3634 y(return)f(GSL_SUCCESS;)390 3744 y(})390 3963 y(int)390 4073 y(rosenbrock_fdf)d(\(const)i(gsl_vector)f(*)i(x,)h(void)e (*params,)1154 4182 y(gsl_vector)f(*)i(f,)g(gsl_matrix)e(*)j(J\))390 4292 y({)485 4401 y(rosenbrock_f)d(\(x,)i(params,)f(f\);)485 4511 y(rosenbrock_df)f(\(x,)i(params,)e(J\);)485 4730 y(return)i(GSL_SUCCESS;)390 4840 y(})150 4980 y FK(The)33 b(main)g(program)h(no)m(w)f(mak)m(es)h(calls)h(to)f(the)g(corresp)s (onding)e FH(fdfsolver)f FK(v)m(ersions)j(of)g(the)g(func-)150 5090 y(tions,)390 5230 y FH(int)390 5340 y(main)47 b(\(void\))p eop end %%Page: 389 405 TeXDict begin 389 404 bop 150 -116 a FK(Chapter)30 b(35:)41 b(Multidimensional)32 b(Ro)s(ot-Finding)1701 b(389)390 299 y FH({)485 408 y(const)47 b(gsl_multiroot_fdfsolver_)o(typ)o(e)42 b(*T;)485 518 y(gsl_multiroot_fdfsolver)g(*s;)485 737 y(int)47 b(status;)485 847 y(size_t)g(i,)g(iter)f(=)i(0;)485 1066 y(const)f(size_t)f(n)h(=)h(2;)485 1176 y(struct)f(rparams)e(p)j(=) f({1.0,)g(10.0};)485 1285 y(gsl_multiroot_function_fdf)41 b(f)48 b(=)f({&rosenbrock_f,)2013 1395 y(&rosenbrock_df,)2013 1504 y(&rosenbrock_fdf,)2013 1614 y(n,)g(&p};)485 1833 y(double)g(x_init[2])e(=)i({-10.0,)f(-5.0};)485 1943 y(gsl_vector)f(*x)j(=)f(gsl_vector_alloc)c(\(n\);)485 2162 y(gsl_vector_set)h(\(x,)j(0,)g(x_init[0]\);)485 2271 y(gsl_vector_set)d(\(x,)j(1,)g(x_init[1]\);)485 2491 y(T)h(=)f(gsl_multiroot_fdfsolver_gn)o(ewt)o(on;)485 2600 y(s)h(=)f(gsl_multiroot_fdfsolver_al)o(loc)41 b(\(T,)47 b(n\);)485 2710 y(gsl_multiroot_fdfsolver_se)o(t)42 b(\(s,)47 b(&f,)g(x\);)485 2929 y(print_state)e(\(iter,)h(s\);)485 3148 y(do)581 3258 y({)676 3367 y(iter++;)676 3587 y(status)g(=)i (gsl_multiroot_fdfsolver_)o(iter)o(ate)41 b(\(s\);)676 3806 y(print_state)k(\(iter,)h(s\);)676 4025 y(if)i(\(status\))772 4134 y(break;)676 4354 y(status)e(=)i(gsl_multiroot_test_resid)o(ual)41 b(\(s->f,)46 b(1e-7\);)581 4463 y(})485 4573 y(while)h(\(status)f(==)h (GSL_CONTINUE)d(&&)j(iter)g(<)h(1000\);)485 4792 y(printf)f(\("status)e (=)j(\045s\\n",)e(gsl_strerror)e(\(status\)\);)485 5011 y(gsl_multiroot_fdfsolver_fr)o(ee)e(\(s\);)485 5121 y(gsl_vector_free)i (\(x\);)485 5230 y(return)j(0;)390 5340 y(})p eop end %%Page: 390 406 TeXDict begin 390 405 bop 150 -116 a FK(Chapter)30 b(35:)41 b(Multidimensional)32 b(Ro)s(ot-Finding)1701 b(390)150 299 y(The)38 b(addition)i(of)f(deriv)-5 b(ativ)m(e)40 b(information)g(to)f(the)h FH(hybrids)d FK(solv)m(er)j(do)s(es)e(not)i (mak)m(e)g(an)m(y)f(signi\014-)150 408 y(can)m(t)33 b(di\013erence)e (to)h(its)g(b)s(eha)m(vior,)g(since)g(it)g(able)g(to)g(appro)m(ximate)g (the)g(Jacobian)g(n)m(umerically)g(with)150 518 y(su\016cien)m(t)j (accuracy)-8 b(.)54 b(T)-8 b(o)34 b(illustrate)i(the)e(b)s(eha)m(vior)h (of)f(a)h(di\013eren)m(t)g(deriv)-5 b(ativ)m(e)35 b(solv)m(er)h(w)m(e)e (switc)m(h)h(to)150 628 y FH(gnewton)p FK(.)j(This)25 b(is)i(a)g(traditional)i(Newton)e(solv)m(er)g(with)g(the)g(constrain)m (t)h(that)f(it)g(scales)h(bac)m(k)g(its)f(step)150 737 y(if)j(the)h(full)f(step)g(w)m(ould)h(lead)f(\\uphill".)41 b(Here)31 b(is)g(the)f(output)g(for)g(the)h FH(gnewton)d FK(algorithm,)390 849 y Fz(iter)40 b(=)g(0)f(x)g(=)h(-10.000)80 b(-5.000)41 b(f\(x\))f(=)78 b(1.100e+01)42 b(-1.050e+03)390 936 y(iter)e(=)g(1)f(x)g(=)79 b(-4.231)41 b(-65.317)g(f\(x\))f(=)78 b(5.231e+00)42 b(-8.321e+02)390 1024 y(iter)e(=)g(2)f(x)g(=)118 b(1.000)41 b(-26.358)g(f\(x\))f(=)f(-8.882e-16)j(-2.736e+02)390 1111 y(iter)e(=)g(3)f(x)g(=)118 b(1.000)h(1.000)41 b(f\(x\))f(=)f (-2.220e-16)j(-4.441e-15)390 1198 y(status)f(=)e(success)150 1333 y FK(The)55 b(con)m(v)m(ergence)j(is)e(m)m(uc)m(h)g(more)f(rapid,) 62 b(but)55 b(tak)m(es)i(a)f(wide)f(excursion)h(out)g(to)g(the)g(p)s (oin)m(t)150 1442 y(\()p FI(\000)p FK(4)p FE(:)p FK(23)p FE(;)15 b FI(\000)p FK(65)p FE(:)p FK(3\).)46 b(This)29 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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 (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,)630 871 y FH(printf)46 b(\("s)h(is)g(a)h ('\045s')e(minimizer\\n",)1012 981 y(gsl_multimin_fdfminimize)o(r_n)o (ame)41 b(\(s\)\);)390 1115 y FK(w)m(ould)30 b(prin)m(t)g(something)h (lik)m(e)h FH(s)e(is)f(a)h('conjugate_pr')d(minimizer)p FK(.)150 1346 y FJ(36.4)68 b(Pro)l(viding)46 b(a)f(function)g(to)g (minimize)150 1505 y FK(Y)-8 b(ou)37 b(m)m(ust)g(pro)m(vide)g(a)h (parametric)g(function)e(of)h FE(n)g FK(v)-5 b(ariables)38 b(for)e(the)h(minimizers)g(to)h(op)s(erate)g(on.)150 1615 y(Y)-8 b(ou)29 b(ma)m(y)g(also)h(need)e(to)i(pro)m(vide)e(a)h (routine)g(whic)m(h)f(calculates)j(the)e(gradien)m(t)h(of)e(the)h (function)g(and)f(a)150 1724 y(third)j(routine)g(whic)m(h)g(calculates) j(b)s(oth)d(the)h(function)f(v)-5 b(alue)32 b(and)f(the)h(gradien)m(t)g (together.)46 b(In)30 b(order)150 1834 y(to)h(allo)m(w)h(for)e(general) h(parameters)g(the)g(functions)f(are)g(de\014ned)g(b)m(y)g(the)g(follo) m(wing)i(data)f(t)m(yp)s(es:)3269 2017 y([Data)h(T)m(yp)s(e])-3600 b Fv(gsl_multimin_function_)q(fdf)390 2126 y FK(This)41 b(data)i(t)m(yp)s(e)f(de\014nes)f(a)h(general)h(function)f(of)g FE(n)g FK(v)-5 b(ariables)42 b(with)g(parameters)g(and)g(the)390 2236 y(corresp)s(onding)29 b(gradien)m(t)j(v)m(ector)g(of)e(deriv)-5 b(ativ)m(es,)390 2394 y FH(double)29 b(\(*)g(f\))h(\(const)f (gsl_vector)e(*)j FA(x)p FH(,)g(void)f(*)h FA(params)p FH(\))870 2503 y FK(this)37 b(function)f(should)g(return)g(the)h (result)g FE(f)10 b FK(\()p FE(x;)15 b Fm(p)-5 b(ar)g(ams)s FK(\))37 b(for)g(argumen)m(t)g FD(x)44 b FK(and)870 2613 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 2723 y(of)31 b FH(GSL_NAN)d FK(should)h(b)s(e)h(returned.)390 2881 y FH(void)f(\(*)h(df\))f(\(const)g(gsl_vector)f(*)i FA(x)p FH(,)f(void)h(*)g FA(params)p FH(,)e(gsl_vector)g(*)i FA(g)p FH(\))870 2990 y FK(this)159 b(function)f(should)g(store)i(the)f FD(n)p FK(-dimensional)g(gradien)m(t)870 3100 y FE(g)913 3114 y Fq(i)1045 3100 y FK(=)103 b FE(@)5 b(f)10 b FK(\()p FE(x;)15 b Fm(p)-5 b(ar)g(ams)s FK(\))p FE(=@)5 b(x)1919 3114 y Fq(i)2025 3100 y FK(in)77 b(the)h(v)m(ector)h FD(g)85 b FK(for)77 b(argumen)m(t)h FD(x)84 b FK(and)870 3210 y(parameters)36 b FD(params)p FK(,)h(returning)e(an)h(appropriate) g(error)f(co)s(de)h(if)g(the)g(function)870 3319 y(cannot)31 b(b)s(e)f(computed.)390 3477 y FH(void)f(\(*)h(fdf\))f(\(const)g (gsl_vector)e(*)j FA(x)p FH(,)g(void)f(*)h FA(params)p FH(,)f(double)f(*)j(f,)e(gsl_vector)f(*)390 3587 y FA(g)p FH(\))870 3697 y FK(This)c(function)g(should)f(set)i(the)f(v)-5 b(alues)25 b(of)g(the)f FD(f)42 b FK(and)23 b FD(g)33 b FK(as)25 b(ab)s(o)m(v)m(e,)i(for)d(argumen)m(ts)870 3806 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 3916 y(separate)k(functions)e(for)h FE(f)10 b FK(\()p FE(x)p FK(\))31 b(and)g FE(g)s FK(\()p FE(x)p FK(\)|it)j(is)e(alw)m(a)m(ys)h(faster)f(to)h(compute)f(the)870 4025 y(function)e(and)g(its)h(deriv)-5 b(ativ)m(e)32 b(at)f(the)f(same)h(time.)390 4184 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 4293 y FD(x)p FK(.)390 4451 y FH(void)29 b(*)h(params)870 4561 y FK(a)h(p)s(oin)m(ter)f(to)h(the)g(parameters)g (of)f(the)h(function.)3269 4743 y([Data)h(T)m(yp)s(e])-3600 b Fv(gsl_multimin_function)390 4853 y FK(This)30 b(data)h(t)m(yp)s(e)f (de\014nes)g(a)g(general)i(function)e(of)g FE(n)g FK(v)-5 b(ariables)31 b(with)f(parameters,)390 5011 y FH(double)f(\(*)g(f\))h (\(const)f(gsl_vector)e(*)j FA(x)p FH(,)g(void)f(*)h FA(params)p FH(\))870 5121 y FK(this)37 b(function)f(should)g(return)g (the)h(result)g FE(f)10 b FK(\()p FE(x;)15 b Fm(p)-5 b(ar)g(ams)s FK(\))37 b(for)g(argumen)m(t)g FD(x)44 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: 394 410 TeXDict begin 394 409 bop 150 -116 a FK(Chapter)30 b(36:)41 b(Multidimensional)32 b(Minimization)1707 b(394)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 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y(double)i(x,)g(y;)485 3587 y(double)g(*p)g(=)g(\(double)f (*\)params;)485 3806 y(x)i(=)f(gsl_vector_get\(v,)c(0\);)485 3915 y(y)48 b(=)f(gsl_vector_get\(v,)c(1\);)485 4134 y(gsl_vector_set\(df,)g(0,)k(2.0)g(*)h(p[2])e(*)i(\(x)f(-)h(p[0]\)\);) 485 4244 y(gsl_vector_set\(df,)43 b(1,)k(2.0)g(*)h(p[3])e(*)i(\(y)f(-)h (p[1]\)\);)390 4354 y(})390 4573 y(/*)f(Compute)f(both)h(f)g(and)g(df)g (together.)93 b(*/)390 4682 y(void)390 4792 y(my_fdf)46 b(\(const)g(gsl_vector)f(*x,)i(void)g(*params,)772 4902 y(double)f(*f,)h(gsl_vector)e(*df\))390 5011 y({)485 5121 y(*f)j(=)f(my_f\(x,)f(params\);)485 5230 y(my_df\(x,)g(params,)g (df\);)390 5340 y(})p eop end %%Page: 395 411 TeXDict begin 395 410 bop 150 -116 a FK(Chapter)30 b(36:)41 b(Multidimensional)32 b(Minimization)1707 b(395)150 299 y(The)30 b(function)g(can)h(b)s(e)e(initialized)k(using)c(the)i(follo)m (wing)h(co)s(de,)390 448 y FH(gsl_multimin_function_fd)o(f)42 b(my_func;)390 667 y(/*)47 b(Paraboloid)e(center)h(at)h(\(1,2\),)g 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v 41 w(m)m(ultimin)p 1114 2501 V 40 w(fdfminimizer)30 b(*)g Ft(s)p Fu(\))3350 2611 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multimin_fminimiz)q (er_i)q(ter)q(ate)f Fu(\()p FD(gsl)p 2173 2611 V 41 w(m)m(ultimin)p 2575 2611 V 40 w(fminimizer)30 b(*)565 2720 y Ft(s)p Fu(\))390 2830 y FK(These)39 b(functions)h(p)s(erform)e(a)i(single)g (iteration)i(of)d(the)h(minimizer)g FD(s)p FK(.)68 b(If)40 b(the)g(iteration)h(en-)390 2939 y(coun)m(ters)30 b(an)e(unexp)s(ected) h(problem)f(then)h(an)g(error)g(co)s(de)g(will)g(b)s(e)f(returned.)40 b(The)28 b(error)h(co)s(de)390 3049 y FH(GSL_ENOPROG)36 b FK(signi\014es)k(that)g(the)g(minimizer)f(is)h(unable)f(to)h(impro)m (v)m(e)g(on)g(its)g(curren)m(t)f(esti-)390 3159 y(mate,)28 b(either)f(due)f(to)h(n)m(umerical)g(di\016cult)m(y)g(or)f(b)s(ecause)h (a)f(gen)m(uine)h(lo)s(cal)h(minim)m(um)e(has)g(b)s(een)390 3268 y(reac)m(hed.)150 3482 y(The)31 b(minimizer)g(main)m(tains)h(a)g (curren)m(t)f(b)s(est)g(estimate)i(of)f(the)f(minim)m(um)g(at)h(all)g 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y(to)g(test)g(the)g(precision)f(of)h(the)g(curren)m(t)f(result.) 3350 1785 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multimin_test_gra) q(dien)q(t)f Fu(\()p FD(const)31 b(gsl)p 2150 1785 V 40 w(v)m(ector)h(*)f Ft(g)p FD(,)g(double)565 1895 y Ft(epsabs)p Fu(\))390 2005 y FK(This)e(function)g(tests)h(the)f(norm)g (of)g(the)h(gradien)m(t)g FD(g)38 b FK(against)30 b(the)g(absolute)g (tolerance)h FD(epsabs)p FK(.)390 2114 y(The)37 b(gradien)m(t)h(of)g(a) g(m)m(ultidimensional)g(function)f(go)s(es)h(to)g(zero)g(at)g(a)g (minim)m(um.)61 b(The)37 b(test)390 2224 y(returns)29 b FH(GSL_SUCCESS)e FK(if)k(the)f(follo)m(wing)i(condition)f(is)g(ac)m (hiev)m(ed,)1715 2394 y FI(j)p FE(g)s FI(j)c FE(<)e Fm(epsabs)390 2565 y FK(and)30 b(returns)g FH(GSL_CONTINUE)d FK(otherwise.)42 b(A)31 b(suitable)g(c)m(hoice)i(of)e FD(epsabs)j FK(can)d(b)s(e)f(made) g(from)390 2674 y(the)21 b(desired)f(accuracy)h(in)f(the)h(function)f (for)g(small)h(v)-5 b(ariations)22 b(in)e FE(x)p FK(.)38 b(The)19 b(relationship)i(b)s(et)m(w)m(een)390 2784 y(these)31 b(quan)m(tities)h(is)e(giv)m(en)h(b)m(y)g FE(\016)s(f)k FK(=)25 b FE(g)19 b(\016)s(x)p FK(.)3350 2973 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multimin_test_siz)q(e)e Fu(\()p FD(const)32 b(double)e Ft(size)p FD(,)h(double)f Ft(epsabs)p Fu(\))390 3083 y FK(This)c(function)h(tests)h(the)g (minimizer)f(sp)s(eci\014c)g(c)m(haracteristic)j(size)e(\(if)f (applicable)h(to)g(the)g(used)390 3193 y(minimizer\))37 b(against)g(absolute)g(tolerance)h FD(epsabs)p FK(.)58 b(The)36 b(test)h(returns)e FH(GSL_SUCCESS)e FK(if)k(the)390 3302 y(size)31 b(is)g(smaller)g(than)f(tolerance,)i(otherwise)f FH(GSL_CONTINUE)c FK(is)j(returned.)150 3539 y FJ(36.7)68 b(Algorithms)46 b(with)f(Deriv)-7 b(ativ)l(es)150 3698 y FK(There)35 b(are)h(sev)m(eral)h(minimization)g(metho)s(ds)e(a)m(v)-5 b(ailable.)59 b(The)35 b(b)s(est)h(c)m(hoice)h(of)f(algorithm)h(dep)s (ends)150 3808 y(on)30 b(the)g(problem.)39 b(The)30 b(algorithms)g 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(eci\014ed)g(b)m(y)390 4902 y(the)f(parameter)h FD(tol)p FK(.)54 b(The)34 b(minim)m(um)f(along)i(this)g(line)f(o)s(ccurs)g(when) g(the)g(function)g(gradien)m(t)390 5011 y FD(g)k FK(and)30 b(the)g(searc)m(h)h(direction)f FD(p)i FK(are)f(orthogonal.)42 b(The)29 b(line)i(minimization)g(terminates)g(when)390 5121 y FE(p)23 b FI(\001)h FE(g)36 b(<)d(tol)r FI(j)p FE(p)p FI(jj)p FE(g)s FI(j)p FK(.)56 b(The)35 b(searc)m(h)h(direction)f (is)h(up)s(dated)d(using)i(the)g(Fletc)m(her-Reev)m(es)k(form)m(ula)390 5230 y FE(p)436 5197 y Fp(0)484 5230 y FK(=)25 b FE(g)626 5197 y Fp(0)665 5230 y FI(\000)15 b FE(\014)5 b(g)31 b FK(where)c FE(\014)k FK(=)25 b FI(\000j)p FE(g)1461 5197 y Fp(0)1485 5230 y FI(j)1510 5197 y FB(2)1547 5230 y FE(=)p FI(j)p FE(g)s FI(j)1688 5197 y FB(2)1727 5230 y FK(,)j(and)f(the)h(line)g(minimization)h(is)f(then)f(rep)s(eated)h (for)g(the)390 5340 y(new)i(searc)m(h)h(direction.)p eop end %%Page: 397 413 TeXDict begin 397 412 bop 150 -116 a FK(Chapter)30 b(36:)41 b(Multidimensional)32 b(Minimization)1707 b(397)3298 299 y([Minimizer])-3599 b Fv(gsl_multimin_fdfminimi)q(zer)q(_con)q(jug) q(ate)q(_pr)390 408 y FK(This)30 b(is)h(the)g(P)m(olak-Ribiere)i (conjugate)f(gradien)m(t)g(algorithm.)43 b(It)31 b(is)g(similar)g(to)h (the)f(Fletc)m(her-)390 518 y(Reev)m(es)i(metho)s(d,)f(di\013ering)g (only)g(in)g(the)g(c)m(hoice)i(of)e(the)g(co)s(e\016cien)m(t)i FE(\014)5 b FK(.)46 b(Both)33 b(metho)s(ds)e(w)m(ork)390 628 y(w)m(ell)46 b(when)f(the)g(ev)-5 b(aluation)47 b(p)s(oin)m(t)e(is) h(close)h(enough)e(to)h(the)f(minim)m(um)g(of)g(the)h(ob)5 b(jectiv)m(e)390 737 y(function)30 b(that)h(it)g(is)f(w)m(ell)i(appro)m (ximated)f(b)m(y)f(a)h(quadratic)g(h)m(yp)s(ersurface.)3298 905 y([Minimizer])-3599 b Fv(gsl_multimin_fdfminimi)q(zer)q(_vec)q(tor) q(_bf)q(gs2)3298 1014 y FK([Minimizer])g Fv(gsl_multimin_fdfminimi)q (zer)q(_vec)q(tor)q(_bf)q(gs)390 1124 y FK(These)25 b(metho)s(ds)g(use) h(the)g(v)m(ector)h(Bro)m(yden-Fletc)m(her-Goldfarb-Shanno)g(\(BF)m 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b(sup)s(ersedes)e (the)j(original)390 2020 y FH(bfgs)e FK(routine)h(and)g(requires)f (substan)m(tially)i(few)m(er)g(function)f(and)f(gradien)m(t)i(ev)-5 b(aluations.)41 b(The)390 2129 y(user-supplied)26 b(tolerance)j FD(tol)j FK(corresp)s(onds)25 b(to)j(the)g(parameter)g FE(\033)i FK(used)d(b)m(y)g(Fletc)m(her.)41 b(A)27 b(v)-5 b(alue)390 2239 y(of)33 b(0.1)i(is)e(recommended)g(for)g(t)m(ypical)i (use)e(\(larger)h(v)-5 b(alues)33 b(corresp)s(ond)f(to)i(less)g (accurate)h(line)390 2348 y(searc)m(hes\).)3298 2516 y([Minimizer])-3599 b Fv(gsl_multimin_fdfminimi)q(zer)q(_ste)q(epe)q (st_)q(des)q(cent)390 2625 y FK(The)31 b(steep)s(est)h(descen)m(t)g (algorithm)g(follo)m(ws)h(the)e(do)m(wnhill)g(gradien)m(t)i(of)e(the)h (function)f(at)h(eac)m(h)390 2735 y(step.)41 b(When)29 b(a)h(do)m(wnhill)f(step)h(is)f(successful)h(the)f(step-size)i(is)f (increased)g(b)m(y)f(a)h(factor)h(of)e(t)m(w)m(o.)390 2845 y(If)35 b(the)i(do)m(wnhill)e(step)h(leads)h(to)f(a)h(higher)e (function)h(v)-5 b(alue)36 b(then)g(the)g(algorithm)h(bac)m(ktrac)m(ks) 390 2954 y(and)h(the)g(step)h(size)g(is)f(decreased)h(using)f(the)g (parameter)h FD(tol)p FK(.)66 b(A)38 b(suitable)h(v)-5 b(alue)39 b(of)f FD(tol)43 b FK(for)390 3064 y(most)36 b(applications)g(is)f(0.1.)57 b(The)34 b(steep)s(est)i(descen)m(t)g (metho)s(d)f(is)g(ine\016cien)m(t)i(and)d(is)i(included)390 3173 y(only)30 b(for)h(demonstration)f(purp)s(oses.)150 3395 y FJ(36.8)68 b(Algorithms)46 b(without)g(Deriv)-7 b(ativ)l(es)150 3554 y FK(The)22 b(algorithms)i(describ)s(ed)e(in)g (this)h(section)h(use)f(only)g(the)g(v)-5 b(alue)23 b(of)g(the)g (function)g(at)g(eac)m(h)h(ev)-5 b(aluation)150 3664 y(p)s(oin)m(t.)3298 3831 y([Minimizer])-3599 b Fv (gsl_multimin_fminimize)q(r_n)q(msim)q(ple)q(x2)3298 3940 y FK([Minimizer])g Fv(gsl_multimin_fminimize)q(r_n)q(msim)q(ple)q (x)390 4050 y FK(These)38 b(metho)s(ds)f(use)g(the)h(Simplex)g (algorithm)h(of)f(Nelder)g(and)f(Mead.)64 b(Starting)38 b(from)g(the)390 4160 y(initial)f(v)m(ector)h FD(x)j FK(=)34 b FE(p)1177 4174 y FB(0)1214 4160 y FK(,)j(the)f(algorithm)h (constructs)g(an)e(additional)i FE(n)f FK(v)m(ectors)h FE(p)3317 4174 y Fq(i)3380 4160 y FK(using)f(the)390 4269 y(step)30 b(size)i(v)m(ector)g FE(s)24 b FK(=)h FD(step)p 1362 4269 28 4 v 43 w(size)37 b FK(as)30 b(follo)m(ws:)1466 4426 y FE(p)1512 4440 y FB(0)1574 4426 y FK(=)25 b(\()p FE(x)1757 4440 y FB(0)1794 4426 y FE(;)15 b(x)1886 4440 y FB(1)1924 4426 y FE(;)g FI(\001)g(\001)g(\001)i FE(;)e(x)2178 4440 y Fq(n)2223 4426 y FK(\))1466 4561 y FE(p)1512 4575 y FB(1)1574 4561 y FK(=)25 b(\()p FE(x)1757 4575 y FB(0)1815 4561 y FK(+)20 b FE(s)1949 4575 y FB(0)1985 4561 y FE(;)15 b(x)2077 4575 y FB(1)2115 4561 y FE(;)g FI(\001)g(\001)g(\001)i FE(;)e(x)2369 4575 y Fq(n)2414 4561 y FK(\))1466 4695 y FE(p)1512 4709 y FB(2)1574 4695 y FK(=)25 b(\()p FE(x)1757 4709 y FB(0)1794 4695 y FE(;)15 b(x)1886 4709 y FB(1)1944 4695 y FK(+)20 b FE(s)2078 4709 y FB(1)2115 4695 y FE(;)15 b FI(\001)g(\001)g(\001)i FE(;)e(x)2369 4709 y Fq(n)2414 4695 y FK(\))1443 4830 y FE(:)g(:)g(:)26 b FK(=)f FE(:)15 b(:)g(:)1458 4964 y(p)1504 4978 y Fq(n)1574 4964 y FK(=)25 b(\()p FE(x)1757 4978 y FB(0)1794 4964 y FE(;)15 b(x)1886 4978 y FB(1)1924 4964 y FE(;)g FI(\001)g(\001)g(\001)i FE(;)e(x)2178 4978 y Fq(n)2243 4964 y FK(+)20 b FE(s)2377 4978 y Fq(n)2422 4964 y FK(\))390 5121 y(These)27 b(v)m(ectors)i(form)e (the)h FE(n)14 b FK(+)g(1)27 b(v)m(ertices)i(of)f(a)g(simplex)f(in)g FE(n)g FK(dimensions.)39 b(On)27 b(eac)m(h)h(iteration)390 5230 y(the)40 b(algorithm)i(uses)d(simple)h(geometrical)j (transformations)e(to)g(up)s(date)e(the)h(v)m(ector)i(corre-)390 5340 y(sp)s(onding)25 b(to)j(the)f(highest)g(function)g(v)-5 b(alue.)40 b(The)26 b(geometric)j(transformations)f(are)f (re\015ection,)p eop end %%Page: 398 414 TeXDict begin 398 413 bop 150 -116 a FK(Chapter)30 b(36:)41 b(Multidimensional)32 b(Minimization)1707 b(398)390 299 y(re\015ection)36 b(follo)m(w)m(ed)i(b)m(y)d(expansion,)j(con)m (traction)f(and)e(m)m(ultiple)i(con)m(traction.)59 b(Using)35 b(these)390 408 y(transformations)g(the)f(simplex)h(mo)m(v)m(es)h (through)e(the)g(space)h(to)m(w)m(ards)h(the)e(minim)m(um,)h(where)390 518 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(36.9)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 (is)g(o\013set)h(from)f(the)g(origin)h(in)f FE(x)g FK(and)f FE(y)s FK(,)h(and)g(the)g(function)g(v)-5 b(alue)31 b(at)g(the)150 3463 y(minim)m(um)h(is)h(non-zero.)48 b(The)33 b(main)f(program)h(is)g (giv)m(en)g(b)s(elo)m(w,)h(it)f(requires)g(the)g(example)g(function)150 3573 y(giv)m(en)e(earlier)h(in)e(this)g(c)m(hapter.)390 3684 y Fz(int)390 3771 y(main)40 b(\(void\))390 3858 y({)468 3945 y(size_t)h(iter)f(=)g(0;)468 4032 y(int)g(status;)468 4207 y(const)h(gsl_multimin_fdfminimizer_type)46 b(*T;)468 4294 y(gsl_multimin_fdfminimizer)f(*s;)468 4468 y(/*)40 b(Position)h(of)f(the)g(minimum)h(\(1,2\),)f(scale)h(factors)586 4555 y(10,20,)g(height)f(30.)79 b(*/)468 4643 y(double)41 b(par[5])g(=)e({)h(1.0,)g(2.0,)g(10.0,)g(20.0,)h(30.0)f(};)468 4817 y(gsl_vector)i(*x;)468 4904 y(gsl_multimin_function_fdf)j (my_func;)468 5078 y(my_func.n)d(=)d(2;)468 5166 y(my_func.f)j(=)d (my_f;)468 5253 y(my_func.df)j(=)d(my_df;)468 5340 y(my_func.fdf)j(=)e (my_fdf;)p eop end %%Page: 399 415 TeXDict begin 399 414 bop 150 -116 a FK(Chapter)30 b(36:)41 b(Multidimensional)32 b(Minimization)1707 b(399)468 299 y Fz(my_func.params)43 b(=)c(par;)468 473 y(/*)h(Starting)h(point,)g(x) e(=)h(\(5,7\))g(*/)468 560 y(x)g(=)f(gsl_vector_alloc)k(\(2\);)468 648 y(gsl_vector_set)g(\(x,)d(0,)f(5.0\);)468 735 y(gsl_vector_set)k (\(x,)d(1,)f(7.0\);)468 909 y(T)h(=)f(gsl_multimin_fdfminimizer_c)q (onjug)q(ate_)q(fr;)468 996 y(s)h(=)f(gsl_multimin_fdfminimizer_a)q (lloc)46 b(\(T,)40 b(2\);)468 1171 y(gsl_multimin_fdfminimizer_s)q(et) 45 b(\(s,)40 b(&my_func,)h(x,)f(0.01,)h(1e-4\);)468 1345 y(do)547 1432 y({)625 1519 y(iter++;)625 1606 y(status)g(=)e (gsl_multimin_fdfminimizer_i)q(terat)q(e)45 b(\(s\);)625 1781 y(if)40 b(\(status\))704 1868 y(break;)625 2042 y(status)h(=)e(gsl_multimin_test_gradient)46 b(\(s->gradient,)c (1e-3\);)625 2217 y(if)e(\(status)h(==)f(GSL_SUCCESS\))704 2304 y(printf)g(\("Minimum)i(found)e(at:\\n"\);)625 2478 y(printf)h(\("\0455d)f(\045.5f)g(\045.5f)h(\04510.5f\\n",)g(iter,)939 2565 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: 400 416 TeXDict begin 400 415 bop 150 -116 a FK(Chapter)30 b(36:)41 b(Multidimensional)32 b(Minimization)1707 b(400)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: minplot.eps %%Creator: gnuplot 3.5 (pre 3.6) patchlevel beta 347 %%CreationDate: Thu Oct 25 17:40:53 2001 %%DocumentFonts: (atend) %%BoundingBox: 50 50 301 302 %%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 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b(unction])-3599 b Fv(int)53 b(gsl_fit_linear_est)e Fu(\()p FD(double)30 b Ft(x)p FD(,)h(double)f Ft(c0)p FD(,)h(double)f Ft(c1)p FD(,)h(double)565 3558 y Ft(cov00)p FD(,)h(double)e Ft(cov01)p FD(,)i(double)e Ft(cov11)p FD(,)i(double)e(*)h Ft(y)p FD(,)g(double)f(*)g Ft(y_err)p Fu(\))390 3667 y FK(This)24 b(function)g(uses)h(the)g(b)s(est-\014t)f(linear)h(regression)g(co)s (e\016cien)m(ts)i FD(c0)p FK(,)g FD(c1)33 b FK(and)24 b(their)h(co)m(v)-5 b(ariance)390 3777 y FD(co)m(v00)p FK(,)29 b FD(co)m(v01)p FK(,)g FD(co)m(v11)35 b FK(to)26 b(compute)g(the)f(\014tted)h(function)f FD(y)33 b FK(and)25 b(its)h(standard)e(deviation)j FD(y)p 3598 3777 V 40 w(err)390 3887 y FK(for)j(the)h(mo)s(del)f FE(Y)45 b FK(=)25 b FE(c)1189 3901 y FB(0)1247 3887 y FK(+)20 b FE(c)1377 3901 y FB(1)1414 3887 y FE(X)38 b FK(at)31 b(the)g(p)s(oin)m(t)f FD(x)p FK(.)150 4119 y FJ(37.3)68 b(Linear)46 b(\014tting)f(without)h(a)f(constan)l(t)h(term)150 4279 y FK(The)23 b(functions)g(describ)s(ed)g(in)g(this)h(section)h 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41 w(t)f Ft(n)p FD(,)565 518 y(double)f(*)h Ft(c1)p FD(,)g(double)f(*)h Ft(cov11)p FD(,)h(double)e(*)g Ft(sumsq)p Fu(\))390 628 y FK(This)g(function)g (computes)h(the)g(b)s(est-\014t)f(linear)h(regression)g(co)s(e\016cien) m(t)i FD(c1)38 b FK(of)31 b(the)g(mo)s(del)g FE(Y)45 b FK(=)390 737 y FE(c)429 751 y FB(1)467 737 y FE(X)35 b FK(for)28 b(the)g(w)m(eigh)m(ted)h(datasets)g(\()p FD(x)p FK(,)g FD(y)8 b FK(\),)29 b(t)m(w)m(o)g(v)m(ectors)g(of)g (length)f FD(n)f FK(with)h(strides)g FD(xstride)33 b FK(and)390 847 y FD(ystride)p FK(.)65 b(The)37 b(v)m(ector)j FD(w)p FK(,)h(of)d(length)h FD(n)f FK(and)f(stride)i FD(wstride)p FK(,)h(sp)s(eci\014es)e(the)g(w)m(eigh)m(t)i(of)f(eac)m(h) 390 956 y(datap)s(oin)m(t.)i(The)30 b(w)m(eigh)m(t)i(is)f(the)f (recipro)s(cal)h(of)g(the)f(v)-5 b(ariance)32 b(for)e(eac)m(h)h(datap)s (oin)m(t)h(in)e FD(y)p FK(.)390 1086 y(The)c(v)-5 b(ariance)28 b(of)f(the)g(parameter)g FD(c1)34 b FK(is)27 b(computed)g(using)f(the)h 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Fv(int)53 b(gsl_multifit_wlinear_)q(svd)f Fu(\()p FD(const)31 b(gsl)p 2045 3865 V 41 w(matrix)f(*)h Ft(X)p FD(,)g(const)g(gsl)p 2909 3865 V 41 w(v)m(ector)565 3974 y(*)e Ft(w)p FD(,)h(const)f(gsl)p 1094 3974 V 40 w(v)m(ector)i(*)e Ft(y)p FD(,)g(double)f Ft(tol)p FD(,)i(size)p 2229 3974 V 41 w(t)f(*)g Ft(rank)p FD(,)i(gsl)p 2778 3974 V 40 w(v)m(ector)f(*)g Ft(c)p FD(,)f(gsl)p 3376 3974 V 41 w(matrix)g(*)565 4084 y Ft(cov)p FD(,)j(double)e(*)g Ft(chisq)p FD(,)i(gsl)p 1575 4084 V 41 w(m)m(ulti\014t)p 1911 4084 V 40 w(linear)p 2173 4084 V 41 w(w)m(orkspace)f(*)g Ft(work)p Fu(\))390 4194 y FK(In)i(these)h(functions)f(comp)s(onen)m(ts)g(of)h(the)f(\014t)h (are)f(discarded)g(if)h(the)f(ratio)i(of)e(singular)h(v)-5 b(alues)390 4303 y FE(s)433 4317 y Fq(i)460 4303 y FE(=s)548 4317 y FB(0)615 4303 y FK(falls)30 b(b)s(elo)m(w)g(the)g(user-sp)s (eci\014ed)e(tolerance)j FD(tol)p FK(,)g(and)e(the)h(e\013ectiv)m(e)i (rank)d(is)h(returned)e(in)390 4413 y FD(rank)p FK(.)3350 4682 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multifit_linear_u)q (svd)f Fu(\()p FD(const)31 b(gsl)p 2045 4682 V 41 w(matrix)f(*)h Ft(X)p FD(,)g(const)g(gsl)p 2909 4682 V 41 w(v)m(ector)565 4792 y(*)g Ft(y)p FD(,)g(double)f Ft(tol)p FD(,)h(size)p 1401 4792 V 41 w(t)g(*)f Ft(rank)p FD(,)i(gsl)p 1954 4792 V 41 w(v)m(ector)g(*)f Ft(c)p FD(,)f(gsl)p 2557 4792 V 41 w(matrix)h(*)f Ft(cov)p FD(,)i(double)e(*)565 4902 y Ft(chisq)p FD(,)i(gsl)p 994 4902 V 41 w(m)m(ulti\014t)p 1330 4902 V 40 w(linear)p 1592 4902 V 41 w(w)m(orkspace)f(*)g Ft(work)p Fu(\))3350 5011 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multifit_wlinear_)q(usvd)f Fu(\()p FD(const)31 b(gsl)p 2097 5011 V 41 w(matrix)g(*)g Ft(X)p FD(,)f(const)565 5121 y(gsl)p 677 5121 V 41 w(v)m(ector)i(*)e Ft(w)p FD(,)h(const)g(gsl)p 1518 5121 V 41 w(v)m(ector)h(*)e Ft(y)p FD(,)h(double)f Ft(tol)p FD(,)i(size)p 2662 5121 V 41 w(t)e(*)h Ft(rank)p FD(,)h(gsl)p 3215 5121 V 40 w(v)m(ector)g(*)f Ft(c)p FD(,)565 5230 y(gsl)p 677 5230 V 41 w(matrix)f(*)h Ft(cov)p FD(,)h(double)e(*)g Ft(chisq)p FD(,)i(gsl)p 2093 5230 V 41 w(m)m(ulti\014t)p 2429 5230 V 40 w(linear)p 2691 5230 V 41 w(w)m(orkspace)f(*)g Ft(work)p Fu(\))390 5340 y FK(These)f(functions)g(compute)h(the)f(\014t)g(using)g (an)h(SVD)f(without)g(column)h(scaling.)p eop end %%Page: 407 423 TeXDict begin 407 422 bop 150 -116 a FK(Chapter)30 b(37:)41 b(Least-Squares)31 b(Fitting)2098 b(407)3350 299 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multifit_linear_e)q(st)f Fu(\()p FD(const)31 b(gsl)p 1993 299 28 4 v 40 w(v)m(ector)h(*)f Ft(x)p FD(,)g(const)g(gsl)p 2834 299 V 40 w(v)m(ector)h(*)565 408 y Ft(c)p FD(,)f(const)g(gsl)p 1023 408 V 40 w(matrix)g(*)g Ft(cov)p FD(,)g(double)f(*)h Ft(y)p FD(,)g(double)f(*)h Ft(y_err)p Fu(\))390 518 y FK(This)22 b(function)g(uses)g(the)g(b)s (est-\014t)h(m)m(ultilinear)g(regression)g(co)s(e\016cien)m(ts)h FD(c)k FK(and)22 b(their)h(co)m(v)-5 b(ariance)390 628 y(matrix)35 b FD(co)m(v)43 b FK(to)36 b(compute)e(the)h(\014tted)g (function)f(v)-5 b(alue)35 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FB(2)2253 2689 y FK(\))630 2856 y(and)30 b(the)g(default)h(tuning)f(constan)m(t)h(is)g FE(t)25 b FK(=)g(2)p FE(:)p FK(985.)3350 3039 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_multifit_robust_free)e Fu(\()p FD(gsl)p 1859 3039 28 4 v 41 w(m)m(ulti\014t)p 2195 3039 V 41 w(robust)p 2490 3039 V 39 w(w)m(orkspace)31 b(*)g Ft(w)p Fu(\))390 3149 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 3331 y([F)-8 b(unction])-3599 b Fv(const)54 b(char)f(*)g(gsl_multifit_robust_na)q(me)f Fu(\()p FD(const)565 3441 y(gsl)p 677 3441 V 41 w(m)m(ulti\014t)p 1013 3441 V 40 w(robust)p 1307 3441 V 39 w(w)m(orkspace)32 b(*)e Ft(w)p Fu(\))390 3550 y FK(This)41 b(function)g(returns)f(the)i(name)g (of)f(the)h(robust)f(t)m(yp)s(e)h FD(T)47 b FK(sp)s(eci\014ed)41 b(to)i FH(gsl_multifit_)390 3660 y(robust_alloc)p FK(.)3350 3842 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multifit_robust_t)q (une)f Fu(\()p FD(const)31 b(double)f Ft(tune)p FD(,)565 3952 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4244 y(double)f(yf,)h(yf_err;)676 4463 y(gsl_fit_linear_est)c(\(xf,)1631 4573 y(c0,)k(c1,)1631 4682 y(cov00,)f(cov01,)g(cov11,)1631 4792 y(&yf,)h(&yf_err\);)676 5011 y(printf)f(\("fit:)94 b(\045g)47 b(\045g\\n",)g(xf,)f(yf\);)676 5121 y(printf)g(\("hi)h(:)95 b(\045g)47 b(\045g\\n",)g(xf,)f(yf)i(+)f (yf_err\);)676 5230 y(printf)f(\("lo)h(:)95 b(\045g)47 b(\045g\\n",)g(xf,)f(yf)i(-)f(yf_err\);)581 5340 y(})p eop end %%Page: 412 428 TeXDict begin 412 427 bop 150 -116 a FK(Chapter)30 b(37:)41 b(Least-Squares)31 b(Fitting)2098 b(412)485 299 y FH(return)47 b(0;)390 408 y(})150 552 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)150 661 y(using)30 b(the)g FC(gnu)h FK(plotutils)g FH(graph)e FK(utilit)m(y)-8 b(,)390 805 y FH($)47 b(./demo)g(>)g(tmp)390 914 y($)g(more)g(tmp)390 1024 y(#)g(best)g(fit:)g(Y)g(=)h(-106.6)e(+)h(0.06)g(X)390 1134 y(#)g(covariance)e(matrix:)390 1243 y(#)i([)h(39602,)e(-19.9)390 1353 y(#)143 b(-19.9,)46 b(0.01])390 1462 y(#)h(chisq)g(=)g(0.8)390 1681 y($)g(for)g(n)h(in)f(data)g(fit)g(hi)g(lo)g(;)533 1791 y(do)629 1901 y(grep)f("^$n")h(tmp)g(|)g(cut)g(-d:)g(-f2)g(>)g($n) g(;)533 2010 y(done)390 2120 y($)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 2229 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 4165 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 8207 6991 8248 6997 8290 7003 8331 7010 8373 7016 8414 7022 8456 7028 8497 7035 8539 7041 8580 7047 8622 7053 8663 7059 8705 7066 8746 7072 8787 7078 8829 7084 8870 7091 8912 7097 8953 7103 8995 7109 9036 7115 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 7186 2484 7183 2525 7179 2567 7176 2608 7172 2650 7169 2691 7165 2733 7162 2774 7158 2815 7155 2857 7151 2898 7148 2940 7144 2981 7141 3023 7138 3064 7134 3106 7131 3147 7127 3189 7124 3230 7121 3272 7118 3313 7114 3355 7111 3396 7108 3438 7105 3479 7101 3521 7098 3562 7095 3603 7092 3645 7089 3686 7086 3728 7083 3769 7080 3811 7077 3852 7074 3894 7071 3935 7068 3977 7065 4018 7062 4060 7060 4101 7057 4143 7054 4184 7051 4226 7049 4267 7046 4308 7044 4350 7041 4391 7039 4433 7037 4474 7034 4516 7032 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 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FK(1)g FE(x)2059 4863 y FB(1)2204 4849 y FE(x)2256 4816 y FB(2)2256 4872 y(1)1832 4959 y FK(1)g FE(x)2059 4973 y FB(2)2204 4959 y FE(x)2256 4926 y FB(2)2256 4981 y(2)1802 5068 y FE(:)15 b(:)g(:)92 b(:)15 b(:)g(:)92 b(:)15 b(:)g(:)2317 4685 y Fs(1)2317 4832 y(C)2317 4881 y(C)2317 4934 y(A)150 5230 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 5244 y FB(0)2588 5230 y FK(.)40 b(The)27 b(t)m(w)m(o)h(remaining)f(columns)150 5340 y(corresp)s(onds)i(to)i(the) g(terms)f FE(c)1209 5354 y FB(1)1247 5340 y FE(x)g FK(and)g FE(c)1545 5354 y FB(2)1582 5340 y FE(x)1634 5307 y FB(2)1671 5340 y FK(.)p eop end %%Page: 413 429 TeXDict begin 413 428 bop 150 -116 a FK(Chapter)30 b(37:)41 b(Least-Squares)31 b(Fitting)2098 b(413)275 299 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(\(standard)150 408 y(deviation\))32 b(in)e(the)g(v)-5 b(alue)31 b FD(y)p FK(.)390 628 y FH(#include)46 b()390 737 y(#include)g ()390 956 y(int)390 1066 y(main)h(\(int)f(argc,)h (char)f(**argv\))390 1176 y({)485 1285 y(int)h(i,)h(n;)485 1395 y(double)f(xi,)f(yi,)h(ei,)g(chisq;)485 1504 y(gsl_matrix)e(*X,)i (*cov;)485 1614 y(gsl_vector)e(*y,)i(*w,)g(*c;)485 1833 y(if)h(\(argc)e(!=)h(2\))581 1943 y({)676 2052 y(fprintf)f (\(stderr,"usage:)92 b(fit)46 b(n)i(<)f(data\\n"\);)676 2162 y(exit)g(\(-1\);)581 2271 y(})485 2491 y(n)h(=)f(atoi)g (\(argv[1]\);)485 2710 y(X)h(=)f(gsl_matrix_alloc)d(\(n,)j(3\);)485 2819 y(y)h(=)f(gsl_vector_alloc)d(\(n\);)485 2929 y(w)k(=)f (gsl_vector_alloc)d(\(n\);)485 3148 y(c)k(=)f(gsl_vector_alloc)d (\(3\);)485 3258 y(cov)j(=)h(gsl_matrix_alloc)43 b(\(3,)k(3\);)485 3477 y(for)g(\(i)h(=)f(0;)g(i)h(<)f(n;)g(i++\))581 3587 y({)676 3696 y(int)g(count)g(=)g(fscanf)f(\(stdin,)g("\045lg)h(\045lg)g (\045lg",)1631 3806 y(&xi,)g(&yi,)f(&ei\);)676 4025 y(if)i(\(count)e (!=)h(3\))772 4134 y({)867 4244 y(fprintf)f(\(stderr,)g("error)g (reading)g(file\\n"\);)867 4354 y(exit)h(\(-1\);)772 4463 y(})676 4682 y(printf)f(\("\045g)h(\045g)g(+/-)g(\045g\\n",)f(xi,) h(yi,)g(ei\);)676 4902 y(gsl_matrix_set)d(\(X,)j(i,)g(0,)h(1.0\);)676 5011 y(gsl_matrix_set)c(\(X,)j(i,)g(1,)h(xi\);)676 5121 y(gsl_matrix_set)c(\(X,)j(i,)g(2,)h(xi*xi\);)676 5340 y(gsl_vector_set)c(\(y,)j(i,)g(yi\);)p eop end %%Page: 414 430 TeXDict begin 414 429 bop 150 -116 a FK(Chapter)30 b(37:)41 b(Least-Squares)31 b(Fitting)2098 b(414)676 299 y FH(gsl_vector_set)44 b(\(w,)j(i,)g(1.0/\(ei*ei\)\);)581 408 y(})485 628 y({)581 737 y(gsl_multifit_linear_work)o(spac)o(e)42 b(*)47 b(work)676 847 y(=)h(gsl_multifit_linear_allo)o(c)42 b(\(n,)47 b(3\);)581 956 y(gsl_multifit_wlinear)42 b(\(X,)47 b(w,)g(y,)g(c,)h(cov,)1631 1066 y(&chisq,)e(work\);)581 1176 y(gsl_multifit_linear_free)41 b(\(work\);)485 1285 y(})390 1504 y(#define)46 b(C\(i\))g (\(gsl_vector_get\(c,\(i\)\)\))390 1614 y(#define)g(COV\(i,j\))f 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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 4408 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 4375 y Fq(x)2473 4408 y FK(in)30 b(the)g(region)h(0)26 b FE(<)f(x)g(<)g FK(2.)390 4573 y FH(#include)46 b()390 4682 y(#include)g()390 4792 y(#include)g() 390 5011 y(int)390 5121 y(main)h(\(void\))390 5230 y({)485 5340 y(double)g(x;)p eop end %%Page: 415 431 TeXDict begin 415 430 bop 150 -116 a FK(Chapter)30 b(37:)41 b(Least-Squares)31 b(Fitting)2098 b(415)485 299 y FH(const)47 b(gsl_rng_type)d(*)k(T;)485 408 y(gsl_rng)e(*)i(r;)485 628 y(gsl_rng_env_setup)c(\(\);)485 847 y(T)k(=)f(gsl_rng_default;)485 956 y(r)h(=)f(gsl_rng_alloc)e(\(T\);)485 1176 y(for)i(\(x)h(=)f(0.1;)g (x)g(<)h(2;)f(x+=)g(0.1\))581 1285 y({)676 1395 y(double)f(y0)i(=)f (exp)g(\(x\);)676 1504 y(double)f(sigma)h(=)g(0.1)g(*)h(y0;)676 1614 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y(0.1)g(0.97935)f (+/-)h(0.110517)390 4222 y(0.2)g(1.3359)f(+/-)h(0.12214)390 4332 y(...)390 4441 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 4551 y(#)h(covariance)e(matrix:)390 4661 y([)i(+1.25612e-02,)e(-3.64387e-02,)f(+1.94389e-02)485 4770 y(-3.64387e-02,)h(+1.42339e-01,)f(-8.48761e-02)485 4880 y(+1.94389e-02,)h(-8.48761e-02,)f(+5.60243e-02)g(])390 4989 y(#)j(chisq)g(=)g(23.0987)150 5121 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 5088 y Fq(x)3436 5121 y FK(,)i(taking)150 5230 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(\()p FE(x)2293 5197 y FB(3)2330 5230 y FK(\))f(di\013erence)h(b)s(et)m(w)m(een)g(the)f (exp)s(onen)m(tial)150 5340 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)p eop end %%Page: 416 432 TeXDict begin 416 431 bop 150 -116 a FK(Chapter)30 b(37:)41 b(Least-Squares)31 b(Fitting)2098 b(416)150 299 y(b)m(y)35 b(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)150 408 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.)275 2492 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 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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 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FE(x;)15 b(y)s FK(\))32 b(data)g(pairs)f(on)g(the)g(line)h FE(y)e FK(=)c(1)p FE(:)p FK(45)p FE(x)d FK(+)d(3)p FE(:)p FK(88,)34 b(adds)150 2900 y(some)g(random)e(noise,)j(and)d(inserts)h(3) h(outliers)f(in)m(to)i(the)e(dataset.)50 b(Both)34 b(the)g(robust)e (and)h(ordinary)150 3010 y(least)f(squares)e(\(OLS\))g(co)s(e\016cien)m (ts)i(are)f(computed)f(for)g(comparison.)390 3148 y FH(#include)46 b()390 3258 y(#include)g()390 3367 y(#include)g()390 3587 y(int)390 3696 y(dofit\(const)f(gsl_multifit_robust_typ)o(e)d(*T,)676 3806 y(const)47 b(gsl_matrix)e(*X,)i(const)f(gsl_vector)f(*y,)676 3915 y(gsl_vector)g(*c,)i(gsl_matrix)e(*cov\))390 4025 y({)485 4134 y(int)i(s;)485 4244 y(gsl_multifit_robust_worksp)o(ace)41 b(*)48 b(work)581 4354 y(=)f(gsl_multifit_robust_alloc)41 b(\(T,)47 b(X->size1,)e(X->size2\);)485 4573 y(s)j(=)f (gsl_multifit_robust)c(\(X,)k(y,)g(c,)g(cov,)g(work\);)485 4682 y(gsl_multifit_robust_free)42 b(\(work\);)485 4902 y(return)47 b(s;)390 5011 y(})390 5230 y(int)390 5340 y(main)g(\(int)f(argc,)h(char)f(**argv\))p eop end %%Page: 417 433 TeXDict begin 417 432 bop 150 -116 a FK(Chapter)30 b(37:)41 b(Least-Squares)31 b(Fitting)2098 b(417)390 299 y FH({)485 408 y(int)47 b(i;)485 518 y(size_t)g(n;)485 628 y(const)g(size_t)f(p)h (=)h(2;)f(/*)g(linear)f(fit)h(*/)485 737 y(gsl_matrix)e(*X,)i(*cov;)485 847 y(gsl_vector)e(*x,)i(*y,)g(*c,)g(*c_ols;)485 956 y(const)g(double)f(a)h(=)h(1.45;)e(/*)h(slope)g(*/)485 1066 y(const)g(double)f(b)h(=)h(3.88;)e(/*)h(intercept)f(*/)485 1176 y(gsl_rng)g(*r;)485 1395 y(if)i(\(argc)e(!=)h(2\))581 1504 y({)676 1614 y(fprintf)f(\(stderr,"usage:)92 b(robfit)46 b(n\\n"\);)676 1724 y(exit)h(\(-1\);)581 1833 y(})485 2052 y(n)h(=)f(atoi)g(\(argv[1]\);)485 2271 y(X)h(=)f(gsl_matrix_alloc) d(\(n,)j(p\);)485 2381 y(x)h(=)f(gsl_vector_alloc)d(\(n\);)485 2491 y(y)k(=)f(gsl_vector_alloc)d(\(n\);)485 2710 y(c)k(=)f (gsl_vector_alloc)d(\(p\);)485 2819 y(c_ols)j(=)g(gsl_vector_alloc)d (\(p\);)485 2929 y(cov)j(=)h(gsl_matrix_alloc)43 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y(gsl_vector_set\(y,)c(n)j(-)g(1,)h(-6.0\);)485 628 y(/*)g(construct)d (design)h(matrix)g(X)i(for)e(linear)h(fit)f(*/)485 737 y(for)h(\(i)h(=)f(0;)g(i)h(<)f(n;)g(++i\))581 847 y({)676 956 y(double)f(xi)i(=)f(gsl_vector_get\(x,)c(i\);)676 1176 y(gsl_matrix_set)h(\(X,)j(i,)g(0,)h(1.0\);)676 1285 y(gsl_matrix_set)c(\(X,)j(i,)g(1,)h(xi\);)581 1395 y(})485 1614 y(/*)g(perform)d(robust)i(and)f(OLS)h(fit)g(*/)485 1724 y(dofit\(gsl_multifit_robust_)o(ols,)41 b(X,)47 b(y,)g(c_ols,)f(cov\);)485 1833 y(dofit\(gsl_multifit_robust_)o(bisq)o (uar)o(e,)c(X,)47 b(y,)g(c,)g(cov\);)485 2052 y(/*)h(output)e(data)g (and)h(model)g(*/)485 2162 y(for)g(\(i)h(=)f(0;)g(i)h(<)f(n;)g(++i\)) 581 2271 y({)676 2381 y(double)f(xi)i(=)f(gsl_vector_get\(x,)c(i\);)676 2491 y(double)j(yi)i(=)f(gsl_vector_get\(y,)c(i\);)676 2600 y(gsl_vector_view)h(v)j(=)h(gsl_matrix_row\(X,)43 b(i\);)676 2710 y(double)j(y_ols,)h(y_rob,)f(y_err;)676 2929 y(gsl_multifit_robust_est\(&v)o(.ve)o(ctor)o(,)c(c,)47 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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 3.8 setmiterlimit % Default Line colors /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 % Default Line Types /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 [] 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 (robust.eps) /Subject (gnuplot plot) /Creator (gnuplot 4.6 patchlevel 3) /Author (palken) % /Producer (gnuplot) % /Keywords () /CreationDate (Fri May 10 14:35:06 2013) /DOCINFO pdfmark end } ifelse end %%EndProlog 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792 240 M [ [(Helvetica) 240.0 0.0 true true 0 (-5)] ] -80.0 MCshow 1.000 UL LTb LCb setrgbcolor 1390 480 M 0 63 V 0 4208 R 0 -63 V stroke 1390 240 M [ [(Helvetica) 240.0 0.0 true true 0 (-4)] ] -80.0 MCshow 1.000 UL LTb LCb setrgbcolor 1987 480 M 0 63 V 0 4208 R 0 -63 V stroke 1987 240 M [ [(Helvetica) 240.0 0.0 true true 0 (-3)] ] -80.0 MCshow 1.000 UL LTb LCb setrgbcolor 2585 480 M 0 63 V 0 4208 R 0 -63 V stroke 2585 240 M [ [(Helvetica) 240.0 0.0 true true 0 (-2)] ] -80.0 MCshow 1.000 UL LTb LCb setrgbcolor 3182 480 M 0 63 V 0 4208 R 0 -63 V stroke 3182 240 M [ [(Helvetica) 240.0 0.0 true true 0 (-1)] ] -80.0 MCshow 1.000 UL LTb LCb setrgbcolor 3780 480 M 0 63 V 0 4208 R 0 -63 V stroke 3780 240 M [ [(Helvetica) 240.0 0.0 true true 0 ( 0)] ] -80.0 MCshow 1.000 UL LTb LCb setrgbcolor 4377 480 M 0 63 V 0 4208 R 0 -63 V stroke 4377 240 M [ [(Helvetica) 240.0 0.0 true true 0 ( 1)] ] -80.0 MCshow 1.000 UL LTb LCb setrgbcolor 4975 480 M 0 63 V 0 4208 R 0 -63 V stroke 4975 240 M [ [(Helvetica) 240.0 0.0 true true 0 ( 2)] ] -80.0 MCshow 1.000 UL LTb LCb setrgbcolor 5572 480 M 0 63 V 0 4208 R 0 -63 V stroke 5572 240 M [ [(Helvetica) 240.0 0.0 true true 0 ( 3)] ] -80.0 MCshow 1.000 UL LTb LCb setrgbcolor 6170 480 M 0 63 V 0 4208 R 0 -63 V stroke 6170 240 M [ [(Helvetica) 240.0 0.0 true true 0 ( 4)] ] -80.0 MCshow 1.000 UL LTb LCb setrgbcolor 6767 480 M 0 63 V 0 4208 R 0 -63 V stroke 6767 240 M [ [(Helvetica) 240.0 0.0 true true 0 ( 5)] ] -80.0 MCshow 1.000 UL LTb LCb setrgbcolor 1.000 UL LTb LCb setrgbcolor 792 4751 N 792 480 L 5975 0 V 0 4271 V -5975 0 V Z stroke 1.000 UP 1.000 UL LTb LCb setrgbcolor % Begin plot #1 4.000 UL LT0 LC0 setrgbcolor LCb setrgbcolor 1800 4568 M [ [(Helvetica) 240.0 0.0 true true 0 (Robust)] ] -80.0 MRshow LT0 1944 4568 M 639 0 V 792 1886 M 122 56 V 122 56 V 122 57 V 122 56 V 122 56 V 122 56 V 122 56 V 122 56 V 121 56 V 122 56 V 122 57 V 122 56 V 122 56 V 122 56 V 122 56 V 122 56 V 122 56 V 122 56 V 122 57 V 122 56 V 122 56 V 122 56 V 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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 1528 y FK(this)24 b(function)f(should)g(store)h(the)g (v)m(ector)i(result)d FE(f)10 b FK(\()p FE(x;)15 b Fm(p)-5 b(ar)g(ams)s FK(\))24 b(in)g FD(f)41 b FK(for)23 b(argumen)m(t)870 1637 y FD(x)36 b FK(and)30 b(arbitrary)g(parameters)g FD(params)p FK(,)g(returning)g(an)g(appropriate)g(error)g(co)s(de)870 1747 y(if)g(the)h(function)f(cannot)h(b)s(e)f(computed.)390 1910 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 2019 y FK(this)96 b(function)g(should)f(store)h(the)g FD(n)p FK(-b)m(y-)p FD(p)j FK(matrix)d(result)g FE(J)3486 2033 y Fq(ij)3679 2019 y FK(=)870 2129 y FE(@)5 b(f)968 2143 y Fq(i)995 2129 y FK(\()p FE(x;)15 b Fm(p)-5 b(ar)g(ams)t FK(\))p FE(=@)5 b(x)1588 2143 y Fq(j)1688 2129 y FK(in)64 b FD(J)71 b FK(for)64 b(argumen)m(t)h FD(x)70 b FK(and)64 b(arbitrary)g(parameters)870 2238 y FD(params)p FK(,)c(returning)54 b(an)g(appropriate)h(error)f(co)s(de)h(if)f(the)h(function)f(cannot)870 2348 y(b)s(e)39 b(computed.)70 b(If)39 b(an)h(analytic)h(Jacobian)g(is) f(una)m(v)-5 b(ailable,)44 b(or)c(to)s(o)h(exp)s(ensiv)m(e)870 2457 y(to)59 b(compute,)66 b(this)58 b(function)g(p)s(oin)m(ter)g(ma)m (y)h(b)s(e)e(set)i(to)g(NULL,)f(in)g(whic)m(h)870 2567 y(case)51 b(the)g(Jacobian)g(will)g(b)s(e)f(in)m(ternally)h(computed)f (using)g(\014nite)g(di\013erence)870 2677 y(appro)m(ximations)31 b(of)g(the)f(function)g FD(f)p FK(.)390 2839 y FH(int)f(\(*)h(fdf\))f (\(const)g(gsl_vector)f(*)i FA(x)p FH(,)f(void)h(*)g FA(params)p FH(,)e(gsl_vector)g(*)i FA(f)p FH(,)390 2949 y(gsl_matrix)e(*)i FA(J)p FH(\))870 3059 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 3168 y FD(x)35 b FK(and)27 b(arbitrary)i(parameters)f FD(params)p FK(.)40 b(This)28 b(function)g(pro)m(vides)g(an)g (optimiza-)870 3278 y(tion)38 b(of)f(the)g(separate)h(functions)f(for)g FE(f)10 b FK(\()p FE(x)p FK(\))37 b(and)f FE(J)9 b FK(\()p FE(x)p FK(\)|it)39 b(is)e(alw)m(a)m(ys)i(faster)e(to)870 3387 y(compute)42 b(the)f(function)g(and)f(its)i(deriv)-5 b(ativ)m(e)43 b(at)f(the)f(same)h(time.)73 b(If)41 b(an)g(ana-)870 3497 y(lytic)33 b(Jacobian)g(is)f(una)m(v)-5 b(ailable,)33 b(or)f(to)s(o)h(exp)s(ensiv)m(e)f(to)h(compute,)f(this)g(function)870 3606 y(p)s(oin)m(ter)24 b(ma)m(y)h(b)s(e)e(set)i(to)f(NULL,)h(in)e (whic)m(h)h(case)h(the)f(Jacobian)h(will)g(b)s(e)e(in)m(ternally)870 3716 y(computed)30 b(using)g(\014nite)g(di\013erence)h(appro)m (ximations)g(of)g(the)f(function)h FD(f)p FK(.)390 3879 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 4042 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 4151 y(the)c(v)m(ector)h FD(x)p FK(.)390 4314 y FH(void)d(*)h(params)870 4423 y FK(a)h(p)s(oin)m(ter)f(to)h(the) g(arbitrary)f(parameters)h(of)f(the)h(function.)275 4614 y(Note)e(that)g(when)e(\014tting)h(a)h(non-linear)f(mo)s(del)g(against) h(exp)s(erimen)m(tal)g(data,)g(the)g(data)f(is)g(passed)150 4724 y(to)e(the)f(functions)g(ab)s(o)m(v)m(e)i(using)d(the)i FD(params)i FK(argumen)m(t)e(and)f(the)g(trial)h(b)s(est-\014t)f (parameters)h(through)150 4834 y(the)31 b FD(x)36 b FK(argumen)m(t.)150 5071 y FJ(38.4)68 b(Finite)46 b(Di\013erence)g(Jacobian)150 5230 y FK(F)-8 b(or)28 b(the)g(algorithms)g(whic)m(h)g(require)f(a)h (Jacobian)g(matrix)g(of)f(deriv)-5 b(ativ)m(es)29 b(of)f(the)g(\014t)f (functions,)h(there)150 5340 y(are)43 b(times)h(when)e(an)h(analytic)i (Jacobian)f(ma)m(y)f(b)s(e)g(una)m(v)-5 b(ailable)44 b(or)f(to)s(o)h(exp)s(ensiv)m(e)g(to)f(compute.)p eop end %%Page: 423 439 TeXDict begin 423 438 bop 150 -116 a FK(Chapter)30 b(38:)41 b(Nonlinear)31 b(Least-Squares)g(Fitting)1681 b(423)150 299 y(Therefore)29 b(GSL)g(supp)s(orts)e(appro)m(ximating)j(the)f (Jacobian)h(n)m(umerically)g(using)e(\014nite)h(di\013erences)h(of)150 408 y(the)40 b(\014t)g(functions.)69 b(This)39 b(is)h(t)m(ypically)h (done)f(b)m(y)g(setting)h(the)f(relev)-5 b(an)m(t)41 b(function)f(p)s(oin)m(ters)g(of)g(the)150 518 y FH (gsl_multifit_function_fd)o(f)31 b FK(data)38 b(t)m(yp)s(e)g(to)g (NULL,)g(ho)m(w)m(ev)m(er)g(the)g(follo)m(wing)h(functions)d(allo)m(w) 150 628 y(the)31 b(user)e(to)i(access)h(the)f(appro)m(ximate)g (Jacobian)g(directly)g(if)g(needed.)3350 818 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multifit_fdfsolve)q(r_di)q(f_d)q(f)e Fu(\()p FD(const)32 b(gsl)p 2307 818 28 4 v 40 w(v)m(ector)g(*)f Ft(x)p FD(,)565 928 y(gsl)p 677 928 V 41 w(m)m(ulti\014t)p 1013 928 V 40 w(function)p 1379 928 V 40 w(fdf)e(*)i Ft(fdf)p FD(,)g(const)g(gsl)p 2187 928 V 41 w(v)m(ector)h(*)f Ft(f)p FD(,)g(gsl)p 2791 928 V 40 w(matrix)g(*)g Ft(J)p Fu(\))390 1037 y FK(This)39 b(function)h(tak)m(es)h(as)f(input)f(the)h (curren)m(t)g(p)s(osition)g FD(x)46 b FK(with)39 b(the)h(function)g(v) -5 b(alues)40 b(com-)390 1147 y(puted)c(at)i(the)g(curren)m(t)f(p)s (osition)g FD(f)p FK(,)i(along)f(with)f FD(fdf)54 b FK(whic)m(h)37 b(sp)s(eci\014es)g(the)h(\014t)f(function)g(and)390 1256 y(parameters)30 b(and)g(appro)m(ximates)h(the)f FD(n)p FK(-b)m(y-)p FD(p)j FK(Jacobian)e FD(J)37 b FK(using)30 b(forw)m(ard)f(\014nite)h(di\013erences:)390 1366 y FE(J)440 1380 y Fq(ij)531 1366 y FK(=)i FE(@)5 b(f)732 1380 y Fq(i)760 1366 y FK(\()p FE(x;)15 b Fm(p)-5 b(ar)g(ams)s FK(\))p FE(=@)5 b(x)1352 1380 y Fq(j)1420 1366 y FI(\031)32 b FK(\()p FE(f)1603 1380 y Fq(i)1631 1366 y FK(\()p FE(x)1718 1333 y Fp(\003)1756 1366 y FE(;)15 b Fm(p)-5 b(ar)g(ams)t FK(\))23 b FI(\000)g FE(f)2274 1380 y Fq(i)2301 1366 y FK(\()p FE(x;)15 b Fm(p)-5 b(ar)g(ams)t FK(\)\))p FE(=)p FK(\001)p FE(x)2952 1380 y Fq(j)2987 1366 y FK(.)54 b(where)34 b FE(x)3385 1333 y Fp(\003)3457 1366 y FK(has)h(the)390 1475 y FE(j)5 b FK(th)39 b(elemen)m(t)h(p)s(erturb)s(ed)c(b)m(y)i(\001) p FE(x)1596 1489 y Fq(j)1669 1475 y FK(and)g(\001)p FE(x)1982 1489 y Fq(j)2055 1475 y FK(=)h FE(\017)p FI(j)p FE(x)2279 1489 y Fq(j)2314 1475 y FI(j)p FK(,)i(where)d FE(\017)g FK(is)h(the)f(square)g(ro)s(ot)h(of)g(the)390 1585 y(mac)m(hine)31 b(precision)g FH(GSL_DBL_EPSILON)p FK(.)3350 1775 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multifit_fdfsolve)q(r_di)q(f_f)q(df) f Fu(\()p FD(const)31 b(gsl)p 2359 1775 V 41 w(v)m(ector)h(*)e Ft(x)p FD(,)565 1885 y(gsl)p 677 1885 V 41 w(m)m(ulti\014t)p 1013 1885 V 40 w(function)p 1379 1885 V 40 w(fdf)f(*)i Ft(fdf)p FD(,)g(gsl)p 1949 1885 V 41 w(v)m(ector)h(*)f Ft(f)p FD(,)g(gsl)p 2553 1885 V 40 w(matrix)g(*)g Ft(J)p Fu(\))390 1995 y FK(This)25 b(function)h(computes)g(the)g(v)m(ector)i (of)e(function)g(v)-5 b(alues)26 b FD(f)43 b FK(and)26 b(the)g(appro)m(ximate)h(Jacobian)390 2104 y FD(J)47 b FK(at)41 b(the)f(p)s(osition)h(v)m(ector)g FD(x)46 b FK(using)40 b(the)g(system)h(describ)s(ed)e(in)g FD(fdf)p FK(.)69 b(See)41 b FH(gsl_multifit_)390 2214 y(fdfsolver_dif_df)26 b FK(for)k(a)h(description)f(of)h(ho)m(w)f(the)h(Jacobian)g(is)f (computed.)150 2451 y FJ(38.5)68 b(Iteration)150 2610 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 2720 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 2829 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 2939 y(mo)s(di\014cations) e(to)g(the)f(co)s(de.)3350 3129 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multifit_fsolver_)q(iter)q(ate)f Fu(\()p FD(gsl)p 2016 3129 V 41 w(m)m(ulti\014t)p 2352 3129 V 41 w(fsolv)m(er)31 b(*)f Ft(s)p Fu(\))3350 3239 y FK([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multifit_fdfsolve)q(r_it)q(era)q(te) f Fu(\()p FD(gsl)p 2121 3239 V 41 w(m)m(ulti\014t)p 2457 3239 V 40 w(fdfsolv)m(er)31 b(*)f Ft(s)p Fu(\))390 3348 y FK(These)g(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 3458 y(an)f(unexp)s(ected)g(problem)f(then)h(an)g(error)g(co) s(de)g(will)h(b)s(e)e(returned.)45 b(The)32 b(solv)m(er)h(main)m(tains) g(a)390 3568 y(curren)m(t)d(estimate)i(of)f(the)f(b)s(est-\014t)h (parameters)f(at)h(all)h(times.)275 3758 y(The)23 b(solv)m(er)h(struct) g FD(s)j FK(con)m(tains)e(the)f(follo)m(wing)h(en)m(tries,)h(whic)m(h)d (can)h(b)s(e)f(used)g(to)i(trac)m(k)f(the)g(progress)150 3867 y(of)31 b(the)f(solution:)150 4031 y FH(gsl_vector)e(*)i(x)630 4141 y FK(The)g(curren)m(t)g(p)s(osition.)150 4303 y FH(gsl_vector)e(*)i(f)630 4413 y FK(The)g(function)g(v)-5 b(alue)31 b(at)g(the)f(curren)m(t)h(p)s(osition.)150 4575 y FH(gsl_vector)d(*)i(dx)630 4685 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 4794 y(last)31 b(step,)g(tak)m(en)g (as)g(a)g(v)m(ector.)150 4957 y FH(gsl_matrix)d(*)i(J)630 5066 y FK(The)24 b(Jacobian)h(matrix)g(at)g(the)f(curren)m(t)g(p)s (osition)h(\(for)f(the)h FH(gsl_multifit_fdfsolver)630 5176 y FK(struct)30 b(only\))275 5340 y(The)f(b)s(est-\014t)i (information)f(also)i(can)e(b)s(e)g(accessed)i(with)e(the)g(follo)m (wing)i(auxiliary)f(functions,)p eop end %%Page: 424 440 TeXDict begin 424 439 bop 150 -116 a FK(Chapter)30 b(38:)41 b(Nonlinear)31 b(Least-Squares)g(Fitting)1681 b(424)3350 299 y([F)-8 b(unction])-3599 b Fv(gsl_vector)55 b(*)e (gsl_multifit_fsolver_p)q(osi)q(tion)f Fu(\()p FD(const)565 408 y(gsl)p 677 408 28 4 v 41 w(m)m(ulti\014t)p 1013 408 V 40 w(fsolv)m(er)31 b(*)g Ft(s)p Fu(\))3350 518 y FK([F)-8 b(unction])-3599 b Fv(gsl_vector)55 b(*)e (gsl_multifit_fdfsolver)q(_po)q(siti)q(on)f Fu(\()p FD(const)565 628 y(gsl)p 677 628 V 41 w(m)m(ulti\014t)p 1013 628 V 40 w(fdfsolv)m(er)31 b(*)f Ft(s)p Fu(\))390 737 y FK(These)41 b(functions)h(return)e(the)i(curren)m(t)g(p)s(osition)g(\(i.e.)75 b(b)s(est-\014t)42 b(parameters\))g FH(s->x)f FK(of)h(the)390 847 y(solv)m(er)31 b FD(s)p FK(.)150 1099 y FJ(38.6)68 b(Searc)l(h)45 b(Stopping)g(P)l(arameters)150 1258 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 1405 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 1546 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 1687 y FI(\017)60 b FK(An)30 b(error)g(has)g(o)s(ccurred.)150 1866 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 1975 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 2185 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_multifit_test_del) q(ta)f Fu(\()p FD(const)31 b(gsl)p 1993 2185 V 40 w(v)m(ector)h(*)f Ft(dx)p FD(,)g(const)g(gsl)p 2886 2185 V 41 w(v)m(ector)565 2295 y(*)g Ft(x)p FD(,)g(double)f Ft(epsabs)p FD(,)i(double)e Ft(epsrel)p Fu(\))390 2405 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 2514 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 2624 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 2804 y FI(j)p FE(dx)1554 2818 y Fq(i)1582 2804 y FI(j)26 b FE(<)f Fm(epsabs)c FK(+)f Fm(epsr)-5 b(el)26 b FI(j)p FE(x)2417 2818 y Fq(i)2444 2804 y FI(j)390 2985 y 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FK(\()p FE(x;)15 b(t)922 4819 y Fq(i)951 4805 y FK(\)\))1021 4772 y FB(2)1059 4805 y FE(=)p FK(\()p FE(n)i FI(\000)f FE(p)p FK(\))29 b(to)g(giv)m(e)h(the)f (v)-5 b(ariance-co)m(v)g(ariance)32 b(matrix)d FE(\033)3000 4772 y FB(2)3038 4805 y FE(C)7 b FK(.)39 b(This)28 b(estimates)390 4915 y(the)c(statistical)j(error)c(on)h(the)g(b)s(est-\014t)g (parameters)g(from)g(the)g(scatter)h(of)f(the)g(underlying)f(data.)390 5046 y(F)-8 b(or)31 b(more)g(information)g(ab)s(out)f(co)m(v)-5 b(ariance)33 b(matrices)e(see)g(Section)h(37.1)g([Fitting)g(Ov)m (erview],)390 5156 y(page)f(403.)p 150 5241 1200 4 v 199 5308 a FB(1)275 5340 y Fx(The)25 b(return)g(co)r(de)i Fz(GSL_CONTINUE)h Fx(w)n(as)e(used)g(for)g(this)g(case)h(in)e(v)n (ersions)h(prior)h(to)e(1.14.)p eop end %%Page: 427 443 TeXDict begin 427 442 bop 150 -116 a FK(Chapter)30 b(38:)41 b(Nonlinear)31 b(Least-Squares)g(Fitting)1681 b(427)150 299 y FJ(38.11)69 b(Examples)150 458 y FK(The)45 b(follo)m(wing)i 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b(resp)s(ect)g(to)i(the)e(three)h(parameters)f(\()p FE(A)p FK(,)h FE(\025)p FK(,)g FE(b)p FK(\).)41 b(It)31 b(is)f(giv)m(en)h(b)m (y)-8 b(,)1755 1467 y FE(J)1805 1481 y Fq(ij)1889 1467 y FK(=)2002 1406 y FE(@)5 b(f)2100 1420 y Fq(i)p 1995 1446 141 4 v 1995 1530 a FE(@)g(x)2100 1544 y Fq(j)150 1692 y FK(where)30 b FE(x)465 1706 y FB(0)527 1692 y FK(=)25 b FE(A)p FK(,)31 b FE(x)799 1706 y FB(1)861 1692 y FK(=)25 b FE(\025)31 b FK(and)f FE(x)1270 1706 y FB(2)1332 1692 y FK(=)25 b FE(b)p FK(.)390 1833 y FH(/*)47 b(expfit.c)f(--)h (model)f(functions)g(for)g(exponential)f(+)j(background)d(*/)390 2052 y(struct)h(data)h({)485 2162 y(size_t)g(n;)485 2271 y(double)g(*)g(y;)485 2381 y(double)g(*)g(sigma;)390 2491 y(};)390 2710 y(int)390 2819 y(expb_f)f(\(const)g(gsl_vector)f(*)j (x,)f(void)f(*data,)772 2929 y(gsl_vector)f(*)i(f\))390 3039 y({)485 3148 y(size_t)g(n)g(=)g(\(\(struct)f(data)h(*\)data\)->n;) 485 3258 y(double)g(*y)g(=)g(\(\(struct)f(data)g(*\)data\)->y;)485 3367 y(double)h(*sigma)f(=)h(\(\(struct)f(data)g(*\))h(data\)->sigma;) 485 3587 y(double)g(A)g(=)g(gsl_vector_get)d(\(x,)j(0\);)485 3696 y(double)g(lambda)f(=)h(gsl_vector_get)d(\(x,)j(1\);)485 3806 y(double)g(b)g(=)g(gsl_vector_get)d(\(x,)j(2\);)485 4025 y(size_t)g(i;)485 4244 y(for)g(\(i)h(=)f(0;)g(i)h(<)f(n;)g(i++\)) 581 4354 y({)676 4463 y(/*)h(Model)e(Yi)h(=)h(A)f(*)g(exp\(-lambda)e(*) j(i\))f(+)g(b)h(*/)676 4573 y(double)e(t)i(=)f(i;)676 4682 y(double)f(Yi)i(=)f(A)h(*)f(exp)g(\(-lambda)e(*)j(t\))f(+)h(b;)676 4792 y(gsl_vector_set)c(\(f,)j(i,)g(\(Yi)g(-)h(y[i]\)/sigma[i]\);)581 4902 y(})485 5121 y(return)f(GSL_SUCCESS;)390 5230 y(})p eop end %%Page: 428 444 TeXDict begin 428 443 bop 150 -116 a FK(Chapter)30 b(38:)41 b(Nonlinear)31 b(Least-Squares)g(Fitting)1681 b(428)390 299 y FH(int)390 408 y(expb_df)46 b(\(const)g(gsl_vector)f(*)i(x,)h (void)e(*data,)820 518 y(gsl_matrix)f(*)i(J\))390 628 y({)485 737 y(size_t)g(n)g(=)g(\(\(struct)f(data)h(*\)data\)->n;)485 847 y(double)g(*sigma)f(=)h(\(\(struct)f(data)g(*\))h(data\)->sigma;) 485 1066 y(double)g(A)g(=)g(gsl_vector_get)d(\(x,)j(0\);)485 1176 y(double)g(lambda)f(=)h(gsl_vector_get)d(\(x,)j(1\);)485 1395 y(size_t)g(i;)485 1614 y(for)g(\(i)h(=)f(0;)g(i)h(<)f(n;)g(i++\)) 581 1724 y({)676 1833 y(/*)h(Jacobian)d(matrix)h(J\(i,j\))g(=)i(dfi)f (/)g(dxj,)g(*/)676 1943 y(/*)h(where)e(fi)h(=)h(\(Yi)e(-)i (yi\)/sigma[i],)283 b(*/)676 2052 y(/*)334 b(Yi)47 b(=)h(A)f(*)g (exp\(-lambda)e(*)j(i\))f(+)g(b)95 b(*/)676 2162 y(/*)48 b(and)e(the)h(xj)h(are)e(the)h(parameters)e(\(A,lambda,b\))g(*/)676 2271 y(double)h(t)i(=)f(i;)676 2381 y(double)f(s)i(=)f(sigma[i];)676 2491 y(double)f(e)i(=)f(exp\(-lambda)e(*)j(t\);)676 2600 y(gsl_matrix_set)c(\(J,)j(i,)g(0,)h(e/s\);)676 2710 y(gsl_matrix_set)c (\(J,)j(i,)g(1,)h(-t)f(*)g(A)h(*)f(e/s\);)676 2819 y(gsl_matrix_set)d (\(J,)j(i,)g(2,)h(1/s\);)581 2929 y(})485 3039 y(return)f(GSL_SUCCESS;) 390 3148 y(})390 3367 y(int)390 3477 y(expb_fdf)f(\(const)g(gsl_vector) 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y(iter:)e(5)g(x=5.04520433)i(0.10405523)f(1.01941607)h (|f\(x\)|=5.44398)390 3519 y(status=success)390 3606 y(iter:)e(6)g(x=5.04535782)i(0.10404906)f(1.01924871)h (|f\(x\)|=5.44397)390 3694 y(chisq/dof)f(=)f(0.800996)390 3781 y(A)236 b(=)39 b(5.04536)i(+/-)f(0.06028)390 3868 y(lambda)h(=)e(0.10405)i(+/-)f(0.00316)390 3955 y(b)236 b(=)39 b(1.01925)i(+/-)f(0.03782)390 4042 y(status)h(=)e(success)150 4308 y FK(The)c(appro)m(ximate)i(v)-5 b(alues)36 b(of)g(the)g (parameters)g(are)h(found)d(correctly)-8 b(,)39 b(and)c(the)h(c)m (hi-squared)g(v)-5 b(alue)150 4417 y(indicates)40 b(a)g(go)s(o)s(d)f (\014t)h(\(the)g(c)m(hi-squared)f(p)s(er)g(degree)h(of)f(freedom)h(is)f (appro)m(ximately)i(1\).)68 b(In)39 b(this)150 4527 y(case)c(the)f (errors)f(on)h(the)g(parameters)g(can)g(b)s(e)g(estimated)h(from)e(the) h(square)g(ro)s(ots)g(of)g(the)g(diagonal)150 4636 y(elemen)m(ts)e(of)e (the)h(co)m(v)-5 b(ariance)32 b(matrix.)275 4902 y(If)f(the)h(c)m (hi-squared)f(v)-5 b(alue)32 b(sho)m(ws)g(a)g(p)s(o)s(or)e(\014t)i (\(i.e.)46 b FE(\037)2166 4869 y FB(2)2203 4902 y FE(=)p FK(\()p FE(n)21 b FI(\000)g FE(p)p FK(\))27 b FI(\035)h FK(1\))k(then)f(the)h(error)f(estimates)150 5011 y(obtained)j(from)f (the)h(co)m(v)-5 b(ariance)36 b(matrix)e(will)g(b)s(e)f(to)s(o)h (small.)51 b(In)33 b(the)h(example)g(program)g(the)f(error)150 5121 y(estimates)26 b(are)f(m)m(ultiplied)f(b)m(y)1236 5048 y Fs(p)p 1319 5048 422 4 v 73 x FE(\037)1376 5095 y FB(2)1413 5121 y FE(=)p FK(\()p FE(n)c FI(\000)g FE(p)p FK(\))25 b(in)f(this)g(case,)j(a)e(common)f(w)m(a)m(y)h(of)g (increasing)g(the)f(errors)150 5230 y(for)k(a)g(p)s(o)s(or)f(\014t.)39 b(Note)29 b(that)g(a)f(p)s(o)s(or)f(\014t)g(will)h(result)g(from)f(the) h(use)g(an)g(inappropriate)f(mo)s(del,)i(and)e(the)150 5340 y(scaled)k(error)f(estimates)i(ma)m(y)f(then)f(b)s(e)g(outside)h (the)f(range)h(of)f(v)-5 b(alidit)m(y)32 b(for)e(Gaussian)h(errors.)p eop end %%Page: 432 448 TeXDict begin 432 447 bop 150 -116 a FK(Chapter)30 b(38:)41 b(Nonlinear)31 b(Least-Squares)g(Fitting)1681 b(432)275 1528 y @beginspecial 50 @llx 50 @lly 410 @urx 302 @ury 2448 @rwi @setspecial %%BeginDocument: fit-exp.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: tmp.eps %%Creator: gnuplot 3.5 (pre 3.6) patchlevel beta 347 %%CreationDate: Sun Sep 24 21:06:38 2000 %%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 392 420 M 63 0 V 6577 0 R -63 0 V 308 420 M (0) Rshow 392 1056 M 63 0 V 6577 0 R -63 0 V -6661 0 R (1) Rshow 392 1692 M 63 0 V 6577 0 R -63 0 V -6661 0 R (2) Rshow 392 2328 M 63 0 V 6577 0 R -63 0 V 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135 -72 R 0 127 V -31 -127 R 62 0 V -62 127 R 62 0 V 135 -86 R 0 128 V -31 -128 R 62 0 V -62 128 R 62 0 V 135 -159 R 0 128 V -31 -128 R 62 0 V -62 128 R 62 0 V 392 4164 Pls 558 3993 Pls 724 3742 Pls 890 3459 Pls 1056 3253 Pls 1222 3021 Pls 1388 2776 Pls 1554 2717 Pls 1720 2483 Pls 1886 2239 Pls 2052 2244 Pls 2218 2211 Pls 2384 2118 Pls 2550 1798 Pls 2716 1912 Pls 2882 1662 Pls 3048 1669 Pls 3214 1672 Pls 3380 1517 Pls 3546 1575 Pls 3712 1429 Pls 3878 1384 Pls 4044 1463 Pls 4210 1342 Pls 4376 1411 Pls 4542 1261 Pls 4708 1301 Pls 4874 1273 Pls 5040 1327 Pls 5206 1104 Pls 5372 1290 Pls 5538 1158 Pls 5704 1139 Pls 5870 1228 Pls 6036 1136 Pls 6202 1129 Pls 6368 1100 Pls 6534 1156 Pls 6700 1197 Pls 6866 1166 Pls 6664 4739 Pls 1.000 UL LT1 6381 4599 M (f\(x\)) Rshow 6465 4599 M 399 0 V 392 4251 M 67 -127 V 67 -122 V 67 -117 V 67 -112 V 67 -108 V 67 -104 V 67 -99 V 68 -96 V 67 -92 V 67 -88 V 67 -84 V 67 -81 V 67 -78 V 67 -75 V 67 -72 V 67 -69 V 67 -66 V 67 -64 V 67 -61 V 67 -59 V 67 -56 V 68 -54 V 67 -52 V 67 -50 V 67 -48 V 67 -46 V 67 -44 V 67 -42 V 67 -41 V 67 -39 V 67 -38 V 67 -36 V 67 -34 V 67 -33 V 67 -32 V 68 -31 V 67 -29 V 67 -29 V 67 -27 V 67 -26 V 67 -25 V 67 -24 V 67 -23 V 67 -22 V 67 -21 V 67 -20 V 67 -20 V 67 -19 V 67 -18 V 68 -17 V 67 -17 V 67 -16 V 67 -15 V 67 -15 V 67 -14 V 67 -14 V 67 -13 V 67 -12 V 67 -12 V 67 -12 V 67 -11 V 67 -11 V 67 -10 V 68 -10 V 67 -9 V 67 -9 V 67 -9 V 67 -8 V 67 -8 V 67 -8 V 67 -7 V 67 -7 V 67 -7 V 67 -7 V 67 -6 V 67 -6 V 67 -6 V 68 -5 V 67 -6 V 67 -5 V 67 -5 V 67 -4 V 67 -5 V 67 -4 V 67 -4 V 67 -4 V 67 -4 V 67 -4 V 67 -4 V 67 -3 V 67 -3 V 68 -3 V 67 -3 V 67 -3 V 67 -3 V 67 -3 V 67 -2 V 67 -3 V 67 -2 V stroke grestore end showpage %%Trailer %%DocumentFonts: Helvetica %%EndDocument @endspecial 150 1810 a FJ(38.12)69 b(References)46 b(and)e(F)-11 b(urther)45 b(Reading)150 1969 y FK(The)30 b FC(minp)-6 b(a)n(ck)29 b FK(algorithm)j(is)e(describ)s(ed)f(in)h(the)h(follo)m (wing)h(article,)330 2104 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 2213 y(Notes)32 b(in)e(Mathematics,)i(v630)g(\(1978\),)h(ed)d(G.)h(W)-8 b(atson.)150 2373 y(The)30 b(follo)m(wing)i(pap)s(er)d(is)h(also)i (relev)-5 b(an)m(t)31 b(to)h(the)e(algorithms)h(describ)s(ed)f(in)g (this)g(section,)330 2507 y(J.J.)37 b(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 2617 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.)p eop end %%Page: 433 449 TeXDict begin 433 448 bop 150 -116 a FK(Chapter)30 b(39:)41 b(Basis)31 b(Splines)2438 b(433)150 299 y FG(39)80 b(Basis)53 b(Splines)150 545 y FK(This)24 b(c)m(hapter)i(describ)s(es)f(functions) g(for)g(the)g(computation)h(of)g(smo)s(othing)f(basis)g(splines)g (\(B-splines\).)150 654 y(A)37 b(smo)s(othing)g(spline)f(di\013ers)h 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b(gsl_bspline_free)c Fu(\()p FD(gsl)p 1441 5230 V 41 w(bspline)p 1761 5230 V 39 w(w)m(orkspace)31 b(*)g Ft(w)p Fu(\))390 5340 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: 434 450 TeXDict begin 434 449 bop 150 -116 a FK(Chapter)30 b(39:)41 b(Basis)31 b(Splines)2438 b(434)3350 299 y([F)-8 b(unction])-3599 b Fv(gsl_bspline_deriv_work)q(spa)q(ce)58 b(*)53 b (gsl_bspline_deriv_allo)q(c)565 408 y Fu(\()p FD(const)31 b(size)p 985 408 28 4 v 41 w(t)g Ft(k)p Fu(\))390 518 y FK(This)e(function)g(allo)s(cates)j(a)e(w)m(orkspace)g(for)g (computing)f(the)h(deriv)-5 b(ativ)m(es)31 b(of)f(a)g(B-spline)g(basis) 390 628 y(function)g(of)h(order)e FD(k)p FK(.)41 b(The)30 b(size)h(of)g(the)f(w)m(orkspace)h(is)g FE(O)s FK(\(2)p FE(k)2549 595 y FB(2)2587 628 y FK(\).)3350 801 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_bspline_deriv_free)e Fu(\()p FD(gsl)p 1755 801 V 41 w(bspline)p 2075 801 V 39 w(deriv)p 2314 801 V 40 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w(w)m(orkspace)31 b(*)f Ft(w)p Fu(\))390 4584 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 4809 y FJ(39.5)68 b(Ev)-7 b(aluation)46 b(of)g(B-spline)e (deriv)-7 b(ativ)l(es)3350 5011 y FK([F)f(unction])-3599 b Fv(int)53 b(gsl_bspline_deriv_eva)q(l)e Fu(\()p FD(const)32 b(double)e Ft(x)p FD(,)g(const)h(size)p 2614 5011 V 41 w(t)g Ft(nderiv)p FD(,)565 5121 y(gsl)p 677 5121 V 41 w(matrix)f(*)h Ft(dB)p FD(,)g(gsl)p 1355 5121 V 41 w(bspline)p 1675 5121 V 39 w(w)m(orkspace)g(*)g Ft(w)p FD(,)g(gsl)p 2439 5121 V 40 w(bspline)p 2758 5121 V 40 w(deriv)p 2998 5121 V 39 w(w)m(orkspace)h(*)e Ft(dw)p Fu(\))390 5230 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 5340 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)p eop end %%Page: 435 451 TeXDict begin 435 450 bop 150 -116 a FK(Chapter)30 b(39:)41 b(Basis)31 b(Splines)2438 b(435)390 299 y(elemen)m(t)37 b(of)f FD(dB)k FK(is)c FE(d)1139 266 y Fq(j)1174 299 y FE(B)1243 313 y Fq(i)1271 299 y FK(\()p FE(x)p FK(\))p FE(=dx)1537 266 y Fq(j)1573 299 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)390 408 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(.)390 518 y(Note)41 b(that)g(function)f(ev)-5 b(aluations)41 b(are)g(included)e(as)h(the)g (zeroth)h(order)f(deriv)-5 b(ativ)m(es)41 b(in)f FD(dB)p FK(.)390 628 y(Computing)27 b(all)h(the)g(basis)f(function)h(deriv)-5 b(ativ)m(es)29 b(at)f(once)g(is)g(more)f(e\016cien)m(t)j(than)d (computing)390 737 y(them)j(individually)-8 b(,)31 b(due)f(to)h(the)f (nature)h(of)f(the)h(de\014ning)e(recurrence)h(relation.)3350 929 y([F)-8 b(unction])-3599 b Fv(int)53 b(gsl_bspline_deriv_eva)q (l_no)q(nze)q(ro)f Fu(\()p FD(const)31 b(double)f Ft(x)p FD(,)h(const)g(size)p 3033 929 28 4 v 41 w(t)565 1038 y Ft(nderiv)p FD(,)g(gsl)p 1045 1038 V 41 w(matrix)e(*)h Ft(dB)p FD(,)f(size)p 1754 1038 V 41 w(t)h(*)f Ft(istart)p FD(,)i(size)p 2443 1038 V 41 w(t)e(*)h Ft(iend)p FD(,)g(gsl)p 2992 1038 V 41 w(bspline)p 3312 1038 V 39 w(w)m(orkspace)565 1148 y(*)h Ft(w)p FD(,)g(gsl)p 861 1148 V 40 w(bspline)p 1180 1148 V 40 w(deriv)p 1420 1148 V 39 w(w)m(orkspace)g(*)g Ft(dw)p Fu(\))390 1257 y FK(This)h(function)h(ev)-5 b(aluates)34 b(all)g(p)s(oten)m(tially)g(nonzero)f(B-spline)g(basis)g(function)g (deriv)-5 b(ativ)m(es)34 b(of)390 1367 y(orders)e(0)i(through)e FE(nder)s(iv)k FK(\(inclusiv)m(e\))e(at)g(the)f(p)s(osition)g FD(x)39 b FK(and)33 b(stores)g(them)g(in)f(the)i(matrix)390 1477 y FD(dB)p FK(.)48 b(The)32 b(\()p FE(i;)15 b(j)5 b FK(\)-th)35 b(elemen)m(t)g(of)e FD(dB)38 b FK(is)33 b FE(d)1840 1444 y Fq(j)1875 1477 y FE(B)1944 1491 y FB(\()p Fq(istar)r(t)p FB(+)p Fq(i)p FB(\))2248 1477 y FK(\()p FE(x)p FK(\))p FE(=dx)2514 1444 y Fq(j)2550 1477 y FK(.)49 b(The)32 b(last)i(ro)m(w)f(of)g FD(dB)38 b FK(con)m(tains)390 1586 y FE(d)437 1553 y Fq(j)472 1586 y FE(B)541 1600 y Fq(iend)676 1586 y FK(\()p FE(x)p FK(\))p FE(=dx)942 1553 y Fq(j)978 1586 y FK(.)48 b(The)32 b(matrix)h FD(dB)k FK(m)m(ust)c(b)s(e)f(of)g(size)i FE(k)i FK(b)m(y)c(at)h(least)h FE(nder)s(iv)25 b FK(+)d(1.)47 b(Note)34 b(that)390 1696 y(function)h(ev)-5 b(aluations)37 b(are)f(included)f(as)g(the)h(zeroth)g(order)f(deriv)-5 b(ativ)m(es)37 b(in)e FD(dB)p FK(.)56 b(By)36 b(return-)390 1805 y(ing)e(only)g(the)g(nonzero)g(basis)f(functions,)i(this)f (function)f(allo)m(ws)i(quan)m(tities)g(in)m(v)m(olving)h(linear)390 1915 y(com)m(binations)30 b(of)f(the)g FE(B)1268 1929 y Fq(i)1296 1915 y FK(\()p FE(x)p 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(bsc)q(iss)q(a)d Fu(\()p FD(size)p 2260 3051 V 42 w(t)30 b Ft(i)p FD(,)565 3161 y(gsl)p 677 3161 V 41 w(bspline)p 997 3161 V 39 w(w)m(orkspace)h(*)p Ft(w)p Fu(\))p FD(;)390 3271 y FK(Returns)26 b(the)h(lo)s(cation)i(of)e(the)g FE(i)p FK(-th)g(Greville)h(abscissa)g(for)e(the)h(giv)m(en)h(B-spline)g (basis.)39 b(F)-8 b(or)28 b(the)390 3380 y(ill-de\014ned)e(case)i(when) e FE(k)i FK(=)d(1,)j(the)f(implemen)m(tation)i(c)m(ho)s(oses)e(to)h (return)d(breakp)s(oin)m(t)i(in)m(terv)-5 b(al)390 3490 y(midp)s(oin)m(ts.)150 3727 y FJ(39.7)68 b(Examples)150 3887 y FK(The)43 b(follo)m(wing)h(program)f(computes)g(a)h(linear)f (least)i(squares)d(\014t)h(to)h(data)g(using)e(cubic)i(B-spline)150 3996 y(basis)38 b(functions)g(with)h(uniform)e(breakp)s(oin)m(ts.)65 b(The)38 b(data)h(is)g(generated)g(from)f(the)h(curv)m(e)g FE(y)s FK(\()p FE(x)p FK(\))g(=)150 4106 y(cos)16 b(\()p FE(x)p FK(\))g(exp)f(\()p FI(\000)p FE(x=)p FK(10\))32 b(on)e(the)h(in)m(terv)-5 b(al)31 b([0)p FE(;)15 b FK(15])33 b(with)d(Gaussian)g(noise)h(added.)390 4244 y FH(#include)46 b()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 5011 y(#include)g()390 5230 y(/*)h(number)f(of)h (data)g(points)f(to)h(fit)g(*/)390 5340 y(#define)f(N)381 b(200)p eop end %%Page: 436 452 TeXDict begin 436 451 bop 150 -116 a FK(Chapter)30 b(39:)41 b(Basis)31 b(Splines)2438 b(436)390 408 y FH(/*)47 b(number)f(of)h(fit) g(coefficients)e(*/)390 518 y(#define)h(NCOEFFS)93 b(12)390 737 y(/*)47 b(nbreak)f(=)i(ncoeffs)e(+)h(2)g(-)h(k)f(=)h(ncoeffs)e(-)h (2)h(since)e(k)h(=)h(4)f(*/)390 847 y(#define)f(NBREAK)141 b(\(NCOEFFS)46 b(-)h(2\))390 1066 y(int)390 1176 y(main)g(\(void\))390 1285 y({)485 1395 y(const)g(size_t)f(n)h(=)h(N;)485 1504 y(const)f(size_t)f(ncoeffs)g(=)h(NCOEFFS;)485 1614 y(const)g(size_t)f (nbreak)g(=)h(NBREAK;)485 1724 y(size_t)g(i,)g(j;)485 1833 y(gsl_bspline_workspace)42 b(*bw;)485 1943 y(gsl_vector)j(*B;)485 2052 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(data)g(to)g(be)g(fitted)f(*/)485 4792 y(for)h(\(i)h(=)f(0;)g(i)h(<)f (n;)g(++i\))581 4902 y({)676 5011 y(double)f(sigma;)676 5121 y(double)g(xi)i(=)f(\(15.0)f(/)i(\(N)f(-)h(1\)\))e(*)i(i;)676 5230 y(double)e(yi)i(=)f(cos\(xi\))f(*)h(exp\(-0.1)f(*)h(xi\);)p eop end %%Page: 437 453 TeXDict begin 437 452 bop 150 -116 a FK(Chapter)30 b(39:)41 b(Basis)31 b(Splines)2438 b(437)676 299 y FH(sigma)47 b(=)g(0.1)g(*)h(yi;)676 408 y(dy)g(=)f(gsl_ran_gaussian\(r,)c(sigma\);) 676 518 y(yi)48 b(+=)f(dy;)676 737 y(gsl_vector_set\(x,)c(i,)48 b(xi\);)676 847 y(gsl_vector_set\(y,)43 b(i,)48 b(yi\);)676 956 y(gsl_vector_set\(w,)43 b(i,)48 b(1.0)f(/)g(\(sigma)f(*)i (sigma\)\);)676 1176 y(printf\("\045f)d(\045f\\n",)h(xi,)h(yi\);)581 1285 y(})485 1504 y(/*)h(use)f(uniform)e(breakpoints)g(on)i([0,)g(15])g (*/)485 1614 y(gsl_bspline_knots_uniform\()o(0.0,)41 b(15.0,)46 b(bw\);)485 1833 y(/*)i(construct)d(the)i(fit)g(matrix)f(X)h (*/)485 1943 y(for)g(\(i)h(=)f(0;)g(i)h(<)f(n;)g(++i\))581 2052 y({)676 2162 y(double)f(xi)i(=)f(gsl_vector_get\(x,)c(i\);)676 2381 y(/*)48 b(compute)d(B_j\(xi\))h(for)h(all)g(j)g(*/)676 2491 y(gsl_bspline_eval\(xi,)c(B,)k(bw\);)676 2710 y(/*)h(fill)e(in)h (row)g(i)h(of)f(X)g(*/)676 2819 y(for)g(\(j)g(=)h(0;)f(j)h(<)f (ncoeffs;)f(++j\))772 2929 y({)867 3039 y(double)g(Bj)i(=)f (gsl_vector_get\(B,)c(j\);)867 3148 y(gsl_matrix_set\(X,)g(i,)48 b(j,)f(Bj\);)772 3258 y(})581 3367 y(})485 3587 y(/*)h(do)f(the)g(fit)g (*/)485 3696 y(gsl_multifit_wlinear\(X,)42 b(w,)47 b(y,)g(c,)g(cov,)g (&chisq,)f(mw\);)485 3915 y(dof)h(=)h(n)f(-)h(ncoeffs;)485 4025 y(tss)f(=)h(gsl_stats_wtss\(w->data,)41 b(1,)47 b(y->data,)f(1,)h(y->size\);)485 4134 y(Rsq)g(=)h(1.0)f(-)g(chisq)g(/)g (tss;)485 4354 y(fprintf\(stderr,)d("chisq/dof)h(=)j(\045e,)e(Rsq)h(=)h (\045f\\n",)1297 4463 y(chisq)e(/)i(dof,)e(Rsq\);)485 4682 y(/*)i(output)e(the)h(smoothed)e(curve)i(*/)485 4792 y({)581 4902 y(double)f(xi,)h(yi,)g(yerr;)581 5121 y(printf\("#m=1,S=0\\n"\);)581 5230 y(for)g(\(xi)g(=)g(0.0;)g(xi)g(<)g (15.0;)g(xi)g(+=)g(0.1\))676 5340 y({)p eop end %%Page: 438 454 TeXDict begin 438 453 bop 150 -116 a FK(Chapter)30 b(39:)41 b(Basis)31 b(Splines)2438 b(438)772 299 y FH(gsl_bspline_eval\(xi,)42 b(B,)47 b(bw\);)772 408 y(gsl_multifit_linear_est\()o(B,)41 b(c,)48 b(cov,)e(&yi,)h(&yerr\);)772 518 y(printf\("\045f)e(\045f\\n",) h(xi,)h(yi\);)676 628 y(})485 737 y(})485 956 y(gsl_rng_free\(r\);)485 1066 y(gsl_bspline_free\(bw\);)485 1176 y(gsl_vector_free\(B\);)485 1285 y(gsl_vector_free\(x\);)485 1395 y(gsl_vector_free\(y\);)485 1504 y(gsl_matrix_free\(X\);)485 1614 y(gsl_vector_free\(c\);)485 1724 y(gsl_vector_free\(w\);)485 1833 y(gsl_matrix_free\(cov\);)485 1943 y(gsl_multifit_linear_free\(m)o(w\);)485 2162 y(return)g(0;)390 2271 y(})g(/*)h(main\(\))e(*/)275 2590 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 2909 y FH($)47 b(./a.out)f(>)i(bspline.dat)390 3019 y(chisq/dof)d(=)j (1.118217e+00,)c(Rsq)j(=)g(0.989771)390 3128 y($)g(graph)g(-T)g(ps)g 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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 8709 5488 8755 5413 8801 5337 8847 5263 8893 5190 8940 5121 8986 5054 9032 4992 9078 4935 9124 4884 9170 4840 9216 4803 151 MLine End %%PageTrailer End %I eop showpage %%Trailer end %%EOF %%EndDocument @endspecial eop end %%Page: 439 455 TeXDict begin 439 454 bop 150 -116 a FK(Chapter)30 b(39:)41 b(Basis)31 b(Splines)2438 b(439)150 299 y FJ(39.8)68 b(References)47 b(and)d(F)-11 b(urther)44 b(Reading)150 458 y FK(F)-8 b(urther)22 b(information)i(on)e(the)h(algorithms)h (describ)s(ed)d(in)i(this)g(section)g(can)g(b)s(e)g(found)e(in)i(the)f (follo)m(wing)150 568 y(b)s(o)s(ok,)330 702 y(C.)k(de)g(Bo)s(or,)h FD(A)g(Practical)h(Guide)e(to)h(Splines)i FK(\(1978\),)g(Springer-V)-8 b(erlag,)28 b(ISBN)e(0-387-90356-9.)275 862 y(F)-8 b(urther)34 b(information)i(of)f(Greville)i(abscissae)f(and)f(B-spline)g(collo)s (cation)j(can)d(b)s(e)g(found)f(in)h(the)150 971 y(follo)m(wing)d(pap)s (er,)330 1106 y(Ric)m(hard)g(W.)h(Johnson,)f(Higher)h(order)f(B-spline) g(collo)s(cation)j(at)e(the)g(Greville)h(abscissae.)47 b FD(Ap-)330 1215 y(plied)30 b(Numerical)h(Mathematics)p FK(.)43 b(v)m(ol.)32 b(52,)f(2005,)i(63{75.)150 1375 y(A)22 b(large)i(collection)g(of)f(B-spline)f(routines)g(is)h(a)m(v)-5 b(ailable)24 b(in)e(the)g FC(ppp)-6 b(a)n(ck)21 b FK(library)g(a)m(v)-5 b(ailable)25 b(at)e FH(http://)150 1484 y(www.netlib.org/pppack)p FK(,)i(whic)m(h)30 b(is)g(also)i(part)e(of)g FC(sla)-6 b(tec)p FK(.)p eop end %%Page: 440 456 TeXDict begin 440 455 bop 150 -116 a FK(Chapter)30 b(40:)41 b(Ph)m(ysical)32 b(Constan)m(ts)2196 b(440)150 299 y FG(40)80 b(Ph)l(ysical)53 b(Constan)l(ts)150 541 y FK(This)38 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(40.1)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: 441 457 TeXDict begin 441 456 bop 150 -116 a FK(Chapter)30 b(40:)41 b(Ph)m(ysical)32 b(Constan)m(ts)2196 b(441)150 299 y FJ(40.2)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(40.3)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: 442 458 TeXDict begin 442 457 bop 150 -116 a FK(Chapter)30 b(40:)41 b(Ph)m(ysical)32 b(Constan)m(ts)2196 b(442)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(40.4)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(40.5)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: 443 459 TeXDict begin 443 458 bop 150 -116 a FK(Chapter)30 b(40:)41 b(Ph)m(ysical)32 b(Constan)m(ts)2196 b(443)150 299 y FJ(40.6)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(40.7)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(40.8)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: 444 460 TeXDict begin 444 459 bop 150 -116 a FK(Chapter)30 b(40:)41 b(Ph)m(ysical)32 b(Constan)m(ts)2196 b(444)150 299 y FJ(40.9)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(40.10)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(40.11)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: 445 461 TeXDict begin 445 460 bop 150 -116 a FK(Chapter)30 b(40:)41 b(Ph)m(ysical)32 b(Constan)m(ts)2196 b(445)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(40.12)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(40.13)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(40.14)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: 446 462 TeXDict begin 446 461 bop 150 -116 a FK(Chapter)30 b(40:)41 b(Ph)m(ysical)32 b(Constan)m(ts)2196 b(446)150 299 y FJ(40.15)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(40.16)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: 447 463 TeXDict begin 447 462 bop 150 -116 a FK(Chapter)30 b(40:)41 b(Ph)m(ysical)32 b(Constan)m(ts)2196 b(447)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(40.17)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 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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: 448 464 TeXDict begin 448 463 bop 150 -116 a FK(Chapter)30 b(40:)41 b(Ph)m(ysical)32 b(Constan)m(ts)2196 b(448)390 299 y FH(maximum)46 b(=)h(21.0)g(minutes)150 531 y FJ(40.18)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: 449 465 TeXDict begin 449 464 bop 150 -116 a FK(Chapter)30 b(41:)41 b(IEEE)30 b(\015oating-p)s(oin)m(t)i(arithmetic)1731 b(449)150 299 y FG(41)80 b(IEEE)54 b(\015oating-p)t(oin)l(t)d (arithmetic)150 541 y FK(This)25 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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 1826 y FK(The)37 b(sign)h(bit)f(is)h(either)g(zero)g(or)g (one.)63 b(The)37 b(exp)s(onen)m(t)g(ranges)h(from)f(a)h(minim)m(um)f (v)-5 b(alue)38 b FE(E)3504 1840 y Fq(min)3669 1826 y FK(to)150 1936 y(a)45 b(maxim)m(um)f(v)-5 b(alue)44 b FE(E)993 1950 y Fq(max)1174 1936 y FK(dep)s(ending)f(on)h(the)h (precision.)82 b(The)44 b(exp)s(onen)m(t)g(is)g(con)m(v)m(erted)i(to)f (an)150 2046 y(unsigned)27 b(n)m(um)m(b)s(er)f FE(e)p FK(,)j(kno)m(wn)f(as)g(the)g FD(biased)g(exp)s(onen)m(t)p FK(,)h(for)e(storage)j(b)m(y)e(adding)f(a)i FD(bias)i FK(parameter,)150 2155 y FE(e)j FK(=)g FE(E)29 b FK(+)23 b Fm(bias)p FK(.)57 b(The)35 b(sequence)h FE(f)10 b(f)g(f)g(f)g(f)5 b(:::)32 b FK(represen)m(ts)k(the)f(digits)i(of)e(the)h(binary)f (fraction)h FE(f)10 b FK(.)55 b(The)150 2265 y(binary)37 b(digits)h(are)g(stored)g(in)f FD(normalized)h(form)p FK(,)h(b)m(y)e(adjusting)h(the)f(exp)s(onen)m(t)h(to)g(giv)m(e)h(a)f (leading)150 2374 y(digit)25 b(of)f(1.)39 b(Since)24 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 (vior)h(of)f(a)h(calculation)h(at)g(the)e(bit-lev)m(el)j(and)150 4493 y(the)j(library)f(pro)m(vides)h(functions)f(for)h(prin)m(ting)g (the)f(IEEE)h(represen)m(tations)g(in)g(a)g(h)m(uman-readable)150 4602 y(form.)3350 4792 y([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_ieee_fprintf_float)e Fu(\()p FD(FILE)30 b(*)h Ft(stream)p FD(,)h(const)f(\015oat)g(*)g Ft(x)p Fu(\))3350 4902 y FK([F)-8 b(unction])-3599 b Fv(void)54 b(gsl_ieee_fprintf_double)e Fu(\()p FD(FILE)30 b(*)h Ft(stream)p FD(,)i(const)d(double)g(*)h Ft(x)p Fu(\))390 5011 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 5121 y(to)38 b(b)m(y)f FD(x)43 b FK(to)38 b(the)g(stream)f FD(stream)p FK(.)62 b(A)37 b(p)s(oin)m(ter)g(is)h(used)e(to)i(pass)f(the)g(n)m(um)m(b)s(er) f(indirectly)-8 b(,)40 b(to)390 5230 y(a)m(v)m(oid)34 b(an)m(y)g(undesired)d(promotion)i(from)g FH(float)e FK(to)j FH(double)p FK(.)46 b(The)33 b(output)f(tak)m(es)i(one)g(of)f (the)390 5340 y(follo)m(wing)f(forms,)p eop end %%Page: 450 466 TeXDict begin 450 465 bop 150 -116 a FK(Chapter)30 b(41:)41 b(IEEE)30 b(\015oating-p)s(oin)m(t)i(arithmetic)1731 b(450)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 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FK(Chapter)30 b(41:)41 b(IEEE)30 b(\015oating-p)s(oin)m(t)i(arithmetic)1731 b(452)390 299 y(If)22 b(the)g(requested)h(mo)s(des)e(are)i(not)g(supp)s (orted)d(b)m(y)i(the)h(platform)f(b)s(eing)g(used)g(then)g(the)g (function)390 408 y(calls)32 b(the)e(error)g(handler)g(and)f(returns)h (an)g(error)g(co)s(de)g(of)h FH(GSL_EUNSUP)p FK(.)390 551 y(When)22 b(options)h(are)f(sp)s(eci\014ed)g(using)g(this)g(metho)s (d,)i(the)e(resulting)h(mo)s(de)f(is)g(based)g(on)g(a)h(default)390 660 y(setting)32 b(of)f(the)f(highest)h(a)m(v)-5 b(ailable)33 b(precision)e(\(double)g(precision)f(or)h(extended)g(precision,)g(de-) 390 770 y(p)s(ending)23 b(on)i(the)g(platform\))g(in)f (round-to-nearest)i(mo)s(de,)f(with)g(all)g(exceptions)h(enabled)f (apart)390 879 y(from)e(the)g FC(inexa)n(ct)f FK(exception.)39 b(The)23 b FC(inexa)n(ct)f FK(exception)i(is)f(generated)h(whenev)m(er) f(rounding)390 989 y(o)s(ccurs,)39 b(so)e(it)h(m)m(ust)g(generally)g(b) 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y(1)p 1582 3154 V 1582 3237 a(3!)1683 3175 y(+)1797 3113 y(1)p 1784 3154 V 1784 3237 a(4!)1885 3175 y(+)f FE(:)15 b(:)g(:)26 b FK(=)f(2)p FE(:)p FK(71828182846)p FE(:::)390 3367 y FH(#include)46 b()390 3477 y(#include)g()390 3587 y(#include)g()390 3806 y(int)390 3915 y(main)h(\(void\))390 4025 y({)485 4134 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: 453 469 TeXDict begin 453 468 bop 150 -116 a FK(Chapter)30 b(41:)41 b(IEEE)30 b(\015oating-p)s(oin)m(t)i(arithmetic)1731 b(453)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 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(e)i(w)m(ould)e(need)h(to)h(use)e(a)h(safer)g(con)m(v)m(erge)i (criterion,)h(suc)m(h)c(as)i FH(while)28 b(\(fabs\(sum)150 3915 y(-)i(oldsum\))e(>)i(epsilon\))p FK(,)f(with)h(a)h(suitably)f(c)m (hosen)h(v)-5 b(alue)31 b(of)f(epsilon.)275 4061 y(Finally)36 b(w)m(e)f(can)h(see)g(the)f(e\013ect)i(of)e(computing)h(the)f(sum)g (using)f(single-precision)j(rounding,)e(in)150 4171 y(the)25 b(default)g FH(round-to-nearest)20 b FK(mo)s(de.)38 b(In)24 b(this)h(case)g(the)g(program)g(thinks)f(it)h(is)g(still)g(using)f (double)150 4281 y(precision)j(n)m(um)m(b)s(ers)e(but)i(the)g(CPU)f (rounds)f(the)j(result)e(of)h(eac)m(h)h(\015oating)g(p)s(oin)m(t)f(op)s (eration)g(to)h(single-)150 4390 y(precision)33 b(accuracy)-8 b(.)51 b(This)33 b(sim)m(ulates)h(the)f(e\013ect)i(of)e(writing)h(the)f (program)g(using)g(single-precision)150 4500 y FH(float)21 b FK(v)-5 b(ariables)24 b(instead)f(of)g FH(double)e FK(v)-5 b(ariables.)39 b(The)22 b(iteration)j(stops)e(after)g(ab)s(out) f(half)h(the)g(n)m(um)m(b)s(er)150 4609 y(of)31 b(iterations)g(and)f (the)h(\014nal)f(result)g(is)g(m)m(uc)m(h)h(less)f(accurate,)390 4756 y FH($)47 b(GSL_IEEE_MODE="single-prec)o(isio)o(n")41 b(./a.out)390 4865 y(....)390 4975 y(i=12)47 b(sum=2.71828198432922363) o(3)42 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: 454 470 TeXDict begin 454 469 bop 150 -116 a FK(Chapter)30 b(41:)41 b(IEEE)30 b(\015oating-p)s(oin)m(t)i(arithmetic)1731 b(454)150 299 y FJ(41.3)68 b(References)47 b(and)d(F)-11 b(urther)44 b(Reading)150 458 y FK(The)30 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y(Signal)80 b(Stop)f(Print)h(Pass)40 b(to)g(program)g(Description) 390 803 y(SIGFPE)80 b(Yes)118 b(Yes)158 b(No)549 b(Arithmetic)42 b(exception)150 936 y FK(Dep)s(ending)34 b(on)h(the)g(platform)g(it)g (ma)m(y)h(b)s(e)e(necessary)h(to)h(instruct)e(the)h(k)m(ernel)g(to)h (generate)g(signals)150 1046 y(for)29 b(\015oating)i(p)s(oin)m(t)e (exceptions.)42 b(F)-8 b(or)30 b(programs)f(using)g(GSL)g(this)g(can)h (b)s(e)f(ac)m(hiev)m(ed)i(using)e(the)h FH(GSL_)150 1155 y(IEEE_MODE)c FK(en)m(vironmen)m(t)k(v)-5 b(ariable)30 b(in)e(conjunction)h(with)g(the)g(function)g FH(gsl_ieee_env_setup)24 b FK(as)150 1265 y(describ)s(ed)29 b(in)h(see)h(Chapter)f(41)h([IEEE)f (\015oating-p)s(oin)m(t)i(arithmetic],)g(page)f(449.)390 1398 y FH(\(gdb\))46 b(set)h(env)g(GSL_IEEE_MODE=double-prec)o(isio)o (n)150 1627 y FJ(A.4)67 b(GCC)45 b(w)l(arning)h(options)f(for)g(n)l (umerical)h(programs)150 1787 y FK(W)-8 b(riting)32 b(reliable)g(n)m (umerical)g(programs)e(in)h(C)f(requires)h(great)h(care.)43 b(The)30 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b(A:)h(Debugging)i(Numerical)f(Programs)1652 b(458)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 b(ariables)31 b(ha)m(v)m(e)h(the)e(same)h(name)f(then)g(it)h(is)g(a)g(p)s(oten)m (tial)g(source)g(of)f(confusion.)150 568 y FH(-Wpointer-arith)c (-Wcast-qual)i(-Wcast-align)630 677 y FK(These)36 b(options)g(w)m(arn)f (if)h(y)m(ou)g(try)g(to)h(do)f(p)s(oin)m(ter)g(arithmetic)h(for)e(t)m (yp)s(es)h(whic)m(h)g(don't)630 787 y(ha)m(v)m(e)c(a)g(size,)g(suc)m(h) e(as)i FH(void)p FK(,)e(if)h(y)m(ou)g(remo)m(v)m(e)i(a)e FH(const)e FK(cast)j(from)f(a)g(p)s(oin)m(ter,)h(or)f(if)g(y)m(ou)630 897 y(cast)c(a)f(p)s(oin)m(ter)g(to)h(a)f(t)m(yp)s(e)g(whic)m(h)g(has)f (a)i(di\013eren)m(t)f(size,)i(causing)e(an)g(in)m(v)-5 b(alid)26 b(alignmen)m(t.)150 1056 y FH(-Wwrite-strings)630 1166 y FK(This)g(option)h(giv)m(es)h(string)e(constan)m(ts)i(a)f FH(const)e 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b(.)150 3729 y FJ(A.5)67 b(References)47 b(and)d(F)-11 b(urther)44 b(Reading)150 3889 y FK(The)28 b(follo)m(wing)j(b)s(o)s(oks)d(are)i(essen)m(tial)g(reading)f(for)g(an) m(y)m(one)h(writing)f(and)g(debugging)g(n)m(umerical)g(pro-)150 3998 y(grams)h(with)h FC(gcc)f FK(and)f FC(gdb)p FK(.)330 4133 y(R.M.)60 b(Stallman,)67 b FD(Using)60 b(and)e(P)m(orting)i(GNU)g (CC)p FK(,)f(F)-8 b(ree)60 b(Soft)m(w)m(are)h(F)-8 b(oundation,)67 b(ISBN)330 4242 y(1882114388)330 4377 y(R.M.)31 b(Stallman,)h(R.H.)f(P) m(esc)m(h,)h FD(Debugging)g(with)e(GDB:)i(The)e(GNU)i(Source-Lev)m(el)g (Debugger)p FK(,)330 4487 y(F)-8 b(ree)31 b(Soft)m(w)m(are)h(F)-8 b(oundation,)31 b(ISBN)f(1882114779)150 4646 y(F)-8 b(or)31 b(a)g(tutorial)g(in)m(tro)s(duction)g(to)g(the)g(GNU)g(C)f(Compiler)g (and)f(related)j(programs,)e(see)330 4780 y(B.J.)h(Gough,)g FD(An)f(In)m(tro)s(duction)g(to)h(GCC)8 b FK(,)30 b(Net)m(w)m(ork)i (Theory)e(Ltd,)g(ISBN)g(0954161793)p eop end %%Page: 459 475 TeXDict begin 459 474 bop 150 -116 a FK(App)s(endix)29 b(B:)i(Con)m(tributors)f(to)h(GSL)2098 b(459)150 299 y FG(App)t(endix)52 b(B)81 b(Con)l(tributors)50 b(to)j(GSL)150 542 y FK(\(See)31 b(the)g(A)m(UTHORS)f(\014le)g(in)g(the)h (distribution)e(for)i(up-to-date)g(information.\))150 706 y Fk(Mark)g(Galassi)630 816 y FK(Conceiv)m(ed)k(GSL)g(\(with)f (James)h(Theiler\))g(and)e(wrote)i(the)g(design)f(do)s(cumen)m(t.)53 b(W)-8 b(rote)630 926 y(the)31 b(sim)m(ulated)g(annealing)g(pac)m(k)-5 b(age)32 b(and)e(the)g(relev)-5 b(an)m(t)32 b(c)m(hapter)f(in)f(the)h (man)m(ual.)150 1088 y Fk(James)g(Theiler)630 1198 y FK(Conceiv)m(ed)41 b(GSL)e(\(with)g(Mark)h(Galassi\).)71 b(W)-8 b(rote)41 b(the)f(random)f(n)m(um)m(b)s(er)f(generators)630 1307 y(and)30 b(the)g(relev)-5 b(an)m(t)32 b(c)m(hapter)f(in)f(this)g (man)m(ual.)150 1470 y Fk(Jim)g(Da)m(vies)630 1580 y FK(W)-8 b(rote)32 b(the)f(statistical)i(routines)d(and)g(the)g(relev)-5 b(an)m(t)32 b(c)m(hapter)f(in)f(this)g(man)m(ual.)150 1742 y Fk(Brian)g(Gough)630 1852 y FK(FFTs,)24 b(n)m(umerical)e(in)m (tegration,)k(random)21 b(n)m(um)m(b)s(er)g(generators)h(and)g (distributions,)h(ro)s(ot)630 1961 y(\014nding,)28 b(minimization)j (and)d(\014tting,)i(p)s(olynomial)g(solv)m(ers,)g(complex)g(n)m(um)m(b) s(ers,)e(ph)m(ysi-)630 2071 y(cal)c(constan)m(ts,)i(p)s(erm)m (utations,)e(v)m(ector)g(and)f(matrix)g(functions,)h(histograms,)h (statistics,)630 2180 y(ieee-utils,)30 b(revised)d FC(cblas)f FK(Lev)m(el)i(2)g(&)e(3,)j(matrix)e(decomp)s(ositions,)i(eigensystems,) g(cu-)630 2290 y(m)m(ulativ)m(e)j(distribution)e(functions,)g(testing,) i(do)s(cumen)m(tation)f(and)f(releases.)150 2453 y Fk(Reid)h (Priedhorsky)630 2562 y FK(W)-8 b(rote)33 b(and)d(do)s(cumen)m(ted)h (the)g(initial)h(v)m(ersion)f(of)g(the)h(ro)s(ot)f(\014nding)e (routines)i(while)g(at)630 2672 y(Los)26 b(Alamos)g(National)i(Lab)s (oratory)-8 b(,)27 b(Mathematical)h(Mo)s(deling)f(and)d(Analysis)i (Group.)150 2834 y Fk(Gerard)31 b(Jungman)630 2944 y FK(Sp)s(ecial)c(F)-8 b(unctions,)28 b(Series)e(acceleration,)k(ODEs,)d (BLAS,)g(Linear)f(Algebra,)j(Eigensys-)630 3053 y(tems,)i(Hank)m(el)g (T)-8 b(ransforms.)150 3216 y Fk(Mik)m(e)32 b(Bo)s(oth)630 3326 y FK(W)-8 b(rote)32 b(the)f(Mon)m(te)g(Carlo)g(library)-8 b(.)150 3488 y Fk(Jorma)31 b(Ola)m(vi)g(T)o(\177)-45 b(ah)m(tinen)630 3598 y FK(W)-8 b(rote)32 b(the)f(initial)g(complex)g (arithmetic)h(functions.)150 3760 y Fk(Thomas)e(W)-8 b(alter)630 3870 y FK(W)g(rote)32 b(the)f(initial)g(heapsort)g (routines)f(and)g(Cholesky)g(decomp)s(osition.)150 4032 y Fk(F)-8 b(abrice)31 b(Rossi)630 4142 y FK(Multidimensional)g (minimization.)150 4304 y Fk(Carlo)g(P)m(erassi)630 4414 y FK(Implemen)m(tation)40 b(of)f(the)g(random)f(n)m(um)m(b)s(er)f (generators)j(in)f(Kn)m(uth's)e FD(Semin)m(umerical)630 4524 y(Algorithms)p FK(,)31 b(3rd)f(Ed.)150 4686 y Fk(Szymon)g (Jaroszewicz)630 4796 y FK(W)-8 b(rote)32 b(the)f(routines)f(for)g (generating)i(com)m(binations.)150 4958 y Fk(Nicolas)g(Darnis)630 5068 y FK(W)-8 b(rote)29 b(the)f(cyclic)h(functions)e(and)g(the)h (initial)g(functions)f(for)h(canonical)h(p)s(erm)m(utations.)150 5230 y Fk(Jason)h(H.)h(Sto)m(v)m(er)630 5340 y FK(W)-8 b(rote)32 b(the)f(ma)5 b(jor)30 b(cum)m(ulativ)m(e)i(distribution)e (functions.)p eop end %%Page: 460 476 TeXDict begin 460 475 bop 150 -116 a FK(App)s(endix)29 b(B:)i(Con)m(tributors)f(to)h(GSL)2098 b(460)150 299 y Fk(Iv)m(o)31 b(Alxneit)630 408 y FK(W)-8 b(rote)32 b(the)f(routines)f(for)g(w)m(a)m(v)m(elet)j(transforms.)150 568 y Fk(T)-8 b(uomo)31 b(Keskitalo)630 677 y FK(Impro)m(v)m(ed)38 b(the)f(implemen)m(tation)j(of)d(the)h(ODE)g(solv)m(ers)g(and)f(wrote)i (the)e(o)s(de-initv)-5 b(al2)630 787 y(routines.)150 946 y Fk(Lo)m(w)m(ell)32 b(Johnson)630 1056 y FK(Implemen)m(tation)g (of)e(the)h(Mathieu)g(functions.)150 1215 y Fk(P)m(atric)m(k)i(Alk)m (en)630 1325 y FK(Implemen)m(tation)e(of)g(nonsymmetric)f(and)f (generalized)j(eigensystems,)g(B-splines,)f(and)630 1435 y(robust)f(linear)g(regression.)150 1594 y Fk(Rh)m(ys)g(Uleric)m(h)630 1704 y FK(W)-8 b(rote)32 b(the)f(m)m(ultiset)g(routines.)150 1863 y Fk(P)m(a)m(v)m(el)i(Holob)s(oro)s(dk)m(o)630 1973 y FK(W)-8 b(rote)32 b(the)f(\014xed)e(order)h(Gauss-Legendre)h (quadrature)f(routines.)150 2132 y Fk(P)m(edro)h(Gonnet)630 2242 y FK(W)-8 b(rote)32 b(the)f FC(cquad)e FK(in)m(tegration)j (routines.)275 2401 y(Thanks)d(to)i(Nigel)h(Lo)m(wry)e(for)g(help)g(in) g(pro)s(ofreading)g(the)h(man)m(ual.)275 2535 y(The)37 b(non-symmetric)i(eigensystems)g(routines)g(con)m(tain)g(co)s(de)g (based)f(on)g(the)h(LAP)-8 b(A)m(CK)39 b(linear)150 2645 y(algebra)31 b(library)-8 b(.)41 b(LAP)-8 b(A)m(CK)31 b(is)f(distributed)g(under)e(the)j(follo)m(wing)h(license:)390 2828 y Ff(Cop)n(yrigh)n(t)24 b(\(c\))h(1992-2006)g(The)f(Univ)n(ersit)n (y)g(of)f(T)-6 b(ennessee.)33 b(All)23 b(righ)n(ts)g(reserv)n(ed.)390 2932 y(Redistribution)i(and)g(use)g(in)g(source)g(and)g(binary)g (forms,)e(with)i(or)g(without)g(mo)r(di\014cation,)h(are)f(p)r (ermitted)g(pro-)390 3010 y(vided)f(that)h(the)g(follo)n(wing)e (conditions)h(are)g(met:)390 3114 y Fe(\017)d Ff(Redistributions)g(of)g (source)g(co)r(de)h(m)n(ust)g(retain)f(the)h(ab)r(o)n(v)n(e)g(cop)n (yrigh)n(t)g(notice,)g(this)f(list)g(of)g(conditions)g(and)h(the)390 3193 y(follo)n(wing)h(disclaimer.)390 3297 y Fe(\017)d Ff(Redistributions)g(in)g(binary)g(form)e(m)n(ust)j(repro)r(duce)f(the) h(ab)r(o)n(v)n(e)g(cop)n(yrigh)n(t)g(notice,)h(this)e(list)f(of)g (conditions)i(and)390 3376 y(the)29 b(follo)n(wing)e(disclaimer)g (listed)h(in)g(this)f(license)i(in)e(the)i(do)r(cumen)n(tation)i (and/or)d(other)h(materials)e(pro)n(vided)390 3455 y(with)d(the)g (distribution.)390 3558 y Fe(\017)e Ff(Neither)h(the)g(name)f(of)g(the) h(cop)n(yrigh)n(t)h(holders)e(nor)g(the)h(names)f(of)g(its)g(con)n (tributors)h(ma)n(y)f(b)r(e)h(used)f(to)h(endorse)390 3637 y(or)g(promote)i(pro)r(ducts)f(deriv)n(ed)g(from)f(this)h(soft)n (w)n(are)f(without)i(sp)r(eci\014c)g(prior)d(written)i(p)r(ermission.) 390 3741 y(THIS)34 b(SOFTW)-8 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e(STRICT)h(LIABILITY,)h(OR)f(TOR)-6 b(T)21 b(\(INCLUDING)h(NEGLIGENCE) 390 4451 y(OR)h(OTHER)-8 b(WISE\))24 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: 461 477 TeXDict begin 461 476 bop 150 -116 a FK(App)s(endix)29 b(C:)h(Auto)s(conf)g(Macros)2245 b(461)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 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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: 462 478 TeXDict begin 462 477 bop 150 -116 a FK(App)s(endix)29 b(C:)h(Auto)s(conf)g(Macros)2245 b(462)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 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Fu(\))p eop end %%Page: 464 480 TeXDict begin 464 479 bop 150 -116 a FK(App)s(endix)29 b(D:)i(GSL)f(CBLAS)f(Library)2080 b(464)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: 465 481 TeXDict begin 465 480 bop 150 -116 a FK(App)s(endix)29 b(D:)i(GSL)f(CBLAS)f(Library)2080 b(465)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: 466 482 TeXDict begin 466 481 bop 150 -116 a FK(App)s(endix)29 b(D:)i(GSL)f(CBLAS)f(Library)2080 b(466)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: 467 483 TeXDict begin 467 482 bop 150 -116 a FK(App)s(endix)29 b(D:)i(GSL)f(CBLAS)f(Library)2080 b(467)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: 468 484 TeXDict begin 468 483 bop 150 -116 a FK(App)s(endix)29 b(D:)i(GSL)f(CBLAS)f(Library)2080 b(468)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: 469 485 TeXDict begin 469 484 bop 150 -116 a FK(App)s(endix)29 b(D:)i(GSL)f(CBLAS)f(Library)2080 b(469)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: 470 486 TeXDict begin 470 485 bop 150 -116 a FK(App)s(endix)29 b(D:)i(GSL)f(CBLAS)f(Library)2080 b(470)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: 471 487 TeXDict begin 471 486 bop 150 -116 a FK(App)s(endix)29 b(D:)i(GSL)f(CBLAS)f(Library)2080 b(471)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: 472 488 TeXDict begin 472 487 bop 150 -116 a FK(App)s(endix)29 b(D:)i(GSL)f(CBLAS)f(Library)2080 b(472)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: 473 489 TeXDict begin 473 488 bop 150 -116 a FK(App)s(endix)29 b(D:)i(GSL)f(CBLAS)f(Library)2080 b(473)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: 474 490 TeXDict begin 474 489 bop 150 -116 a FK(App)s(endix)29 b(D:)i(GSL)f(CBLAS)f(Library)2080 b(474)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 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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: 476 492 TeXDict begin 476 491 bop 150 -116 a FK(GNU)31 b(General)g(Public)f (License)2314 b(476)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 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(License)g(for)e(most)i(of)f(our)g(soft)n(w)n(are;)h(it)f(applies)h (also)f(to)h(an)n(y)g(other)g(w)n(ork)f(released)150 1630 y(this)h(w)n(a)n(y)g(b)n(y)g(its)f(authors.)32 b(Y)-6 b(ou)24 b(can)g(apply)g(it)g(to)g(y)n(our)g(programs,)f(to)r(o.)275 1734 y(When)f(w)n(e)g(sp)r(eak)h(of)e(free)g(soft)n(w)n(are,)h(w)n(e)g (are)f(referring)g(to)h(freedom,)g(not)g(price.)30 b(Our)22 b(General)g(Public)f(Licenses)h(are)g(designed)150 1813 y(to)j(mak)n(e)h(sure)e(that)i(y)n(ou)f(ha)n(v)n(e)h(the)g(freedom)e (to)i(distribute)f(copies)g(of)f(free)h(soft)n(w)n(are)f(\(and)i(c)n (harge)g(for)e(them)h(if)f(y)n(ou)h(wish\),)g(that)150 1892 y(y)n(ou)h(receiv)n(e)g(source)g(co)r(de)g(or)f(can)h(get)g(it)g (if)e(y)n(ou)i(w)n(an)n(t)g(it,)f(that)i(y)n(ou)f(can)g(c)n(hange)h (the)f(soft)n(w)n(are)g(or)f(use)g(pieces)h(of)f(it)g(in)g(new)h(free) 150 1971 y(programs,)d(and)h(that)h(y)n(ou)f(kno)n(w)h(y)n(ou)f(can)g (do)g(these)h(things.)275 2075 y(T)-6 b(o)33 b(protect)i(y)n(our)e (righ)n(ts,)i(w)n(e)e(need)h(to)g(prev)n(en)n(t)h(others)e(from)f(den)n (ying)j(y)n(ou)e(these)i(righ)n(ts)d(or)h(asking)h(y)n(ou)g(to)f (surrender)150 2154 y(the)c(righ)n(ts.)44 b(Therefore,)29 b(y)n(ou)f(ha)n(v)n(e)h(certain)g(resp)r(onsibilities)e(if)g(y)n(ou)i (distribute)f(copies)h(of)e(the)i(soft)n(w)n(are,)g(or)f(if)f(y)n(ou)i (mo)r(dify)e(it:)150 2233 y(resp)r(onsibilities)c(to)h(resp)r(ect)g (the)h(freedom)f(of)f(others.)275 2337 y(F)-6 b(or)29 b(example,)j(if)d(y)n(ou)h(distribute)g(copies)g(of)g(suc)n(h)g(a)g (program,)h(whether)f(gratis)g(or)f(for)g(a)h(fee,)h(y)n(ou)g(m)n(ust)f (pass)f(on)i(to)f(the)150 2415 y(recipien)n(ts)f(the)g(same)g(freedoms) f(that)i(y)n(ou)f(receiv)n(ed.)47 b(Y)-6 b(ou)28 b(m)n(ust)h(mak)n(e)g (sure)g(that)g(they)-6 b(,)31 b(to)r(o,)f(receiv)n(e)f(or)f(can)i(get)f (the)g(source)150 2494 y(co)r(de.)j(And)24 b(y)n(ou)g(m)n(ust)g(sho)n (w)g(them)g(these)h(terms)f(so)f(they)i(kno)n(w)f(their)g(righ)n(ts.) 275 2598 y(Dev)n(elop)r(ers)g(that)h(use)g(the)g(GNU)f(GPL)g(protect)i (y)n(our)e(righ)n(ts)g(with)g(t)n(w)n(o)h(steps:)32 b(\(1\))25 b(assert)g(cop)n(yrigh)n(t)g(on)f(the)h(soft)n(w)n(are,)f(and)150 2677 y(\(2\))h(o\013er)f(y)n(ou)g(this)f(License)i(giving)f(y)n(ou)g (legal)f(p)r(ermission)g(to)h(cop)n(y)-6 b(,)25 b(distribute)f(and/or)g (mo)r(dify)f(it.)275 2781 y(F)-6 b(or)32 b(the)h(dev)n(elop)r(ers')f (and)h(authors')f(protection,)k(the)d(GPL)f(clearly)g(explains)h(that)g (there)g(is)f(no)g(w)n(arran)n(t)n(y)h(for)e(this)h(free)150 2860 y(soft)n(w)n(are.)h(F)-6 b(or)24 b(b)r(oth)i(users')d(and)i (authors')f(sak)n(e,)h(the)g(GPL)g(requires)f(that)h(mo)r(di\014ed)g(v) n(ersions)f(b)r(e)h(mark)n(ed)f(as)g(c)n(hanged,)i(so)f(that)150 2939 y(their)f(problems)f(will)f(not)j(b)r(e)f(attributed)h (erroneously)f(to)g(authors)g(of)g(previous)g(v)n(ersions.)275 3043 y(Some)k(devices)h(are)f(designed)g(to)h(den)n(y)g(users)e(access) i(to)f(install)g(or)f(run)h(mo)r(di\014ed)g(v)n(ersions)g(of)f(the)i (soft)n(w)n(are)f(inside)g(them,)150 3122 y(although)e(the)f(man)n (ufacturer)g(can)g(do)g(so.)33 b(This)24 b(is)f(fundamen)n(tally)j (incompatible)f(with)f(the)h(aim)f(of)g(protecting)i(users')e(freedom) 150 3201 y(to)j(c)n(hange)h(the)f(soft)n(w)n(are.)39 b(The)27 b(systematic)g(pattern)h(of)e(suc)n(h)h(abuse)g(o)r(ccurs)g (in)f(the)h(area)g(of)f(pro)r(ducts)h(for)e(individuals)h(to)h(use,)150 3280 y(whic)n(h)i(is)e(precisely)h(where)h(it)f(is)g(most)g (unacceptable.)48 b(Therefore,)29 b(w)n(e)f(ha)n(v)n(e)i(designed)f (this)f(v)n(ersion)g(of)g(the)i(GPL)e(to)h(prohibit)150 3358 y(the)c(practice)f(for)f(those)i(pro)r(ducts.)32 b(If)23 b(suc)n(h)i(problems)e(arise)g(substan)n(tially)i(in)e(other)h (domains,)g(w)n(e)g(stand)g(ready)g(to)h(extend)g(this)150 3437 y(pro)n(vision)e(to)i(those)f(domains)g(in)f(future)h(v)n(ersions) g(of)f(the)h(GPL,)g(as)g(needed)h(to)f(protect)h(the)g(freedom)e(of)h (users.)275 3541 y(Finally)-6 b(,)25 b(ev)n(ery)h(program)g(is)f 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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: 478 494 TeXDict begin 478 493 bop 150 -116 a FK(GNU)31 b(General)g(Public)f (License)2314 b(478)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 (mo)r(del,)g(to)g(giv)n(e)g(an)n(y)n(one)h(who)f(p)r(ossesses)f(the)i (ob)t(ject)f(co)r(de)h(either)510 3055 y(\(1\))23 b(a)f(cop)n(y)i(of)d (the)i(Corresp)r(onding)g(Source)g(for)e(all)h(the)h(soft)n(w)n(are)f (in)g(the)h(pro)r(duct)g(that)g(is)f(co)n(v)n(ered)h(b)n(y)g(this)f (License,)510 3134 y(on)27 b(a)g(durable)f(ph)n(ysical)h(medium)f (customarily)h(used)g(for)f(soft)n(w)n(are)h(in)n(terc)n(hange,)h(for)e (a)h(price)f(no)h(more)f(than)i(y)n(our)510 3213 y(reasonable)22 b(cost)h(of)e(ph)n(ysically)h(p)r(erforming)f(this)h(con)n(v)n(eying)h (of)e(source,)h(or)g(\(2\))g(access)h(to)f(cop)n(y)h(the)g(Corresp)r (onding)510 3292 y(Source)h(from)f(a)h(net)n(w)n(ork)h(serv)n(er)e(at)h (no)g(c)n(harge.)399 3396 y(c.)60 b(Con)n(v)n(ey)23 b(individual)f (copies)g(of)g(the)h(ob)t(ject)g(co)r(de)g(with)f(a)g(cop)n(y)h(of)f (the)g(written)h(o\013er)f(to)g(pro)n(vide)h(the)g(Corresp)r(onding)510 3475 y(Source.)41 b(This)26 b(alternativ)n(e)i(is)e(allo)n(w)n(ed)h (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: 479 495 TeXDict begin 479 494 bop 150 -116 a FK(GNU)31 b(General)g(Public)f (License)2314 b(479)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 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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 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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 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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 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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 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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 (more)g(of)h(the)g(righ)n(ts)f(that)i(are)e(sp)r(eci\014cally)h(gran)n (ted)h(under)f(this)p eop end %%Page: 481 497 TeXDict begin 481 496 bop 150 -116 a FK(GNU)31 b(General)g(Public)f (License)2314 b(481)330 299 y Ff(License.)50 b(Y)-6 b(ou)30 b(ma)n(y)g(not)h(con)n(v)n(ey)g(a)f(co)n(v)n(ered)h(w)n(ork)f(if)f(y)n (ou)h(are)g(a)g(part)n(y)g(to)h(an)f(arrangemen)n(t)h(with)f(a)g(third) f(part)n(y)i(that)330 378 y(is)f(in)h(the)h(business)f(of)g (distributing)g(soft)n(w)n(are,)i(under)e(whic)n(h)h(y)n(ou)f(mak)n(e)h (pa)n(ymen)n(t)h(to)e(the)h(third)f(part)n(y)h(based)g(on)f(the)330 457 y(exten)n(t)23 b(of)e(y)n(our)g(activit)n(y)h(of)f(con)n(v)n(eying) i(the)f(w)n(ork,)f(and)g(under)h(whic)n(h)f(the)h(third)f(part)n(y)h (gran)n(ts,)f(to)h(an)n(y)g(of)e(the)i(parties)g(who)330 535 y(w)n(ould)27 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y(with)j(the)h(relationship)f(of)g (the)h(publishers)e(or)h(authors)g(of)g(the)h(Do)r(cumen)n(t)g(to)g (the)g(Do)r(cumen)n(t's)g(o)n(v)n(erall)e(sub)t(ject)i(\(or)f(to)330 3148 y(related)18 b(matters\))h(and)f(con)n(tains)h(nothing)f(that)h (could)f(fall)f(directly)h(within)f(that)i(o)n(v)n(erall)f(sub)t(ject.) 29 b(\(Th)n(us,)19 b(if)e(the)h(Do)r(cumen)n(t)330 3227 y(is)i(in)h(part)h(a)f(textb)r(o)r(ok)j(of)c(mathematics,)j(a)e (Secondary)i(Section)g(ma)n(y)e(not)h(explain)f(an)n(y)h (mathematics.\))32 b(The)22 b(relationship)330 3306 y(could)30 b(b)r(e)f(a)h(matter)g(of)f(historical)g(connection)i(with)e(the)h(sub) t(ject)g(or)f(with)h(related)g(matters,)g(or)f(of)g(legal,)h (commercial,)330 3385 y(philosophical,)23 b(ethical)i(or)e(p)r (olitical)h(p)r(osition)g(regarding)f(them.)330 3492 y(The)f(\\In)n(v)l(arian)n(t)h(Sections")g(are)f(certain)g(Secondary)h (Sections)g(whose)f(titles)f(are)h(designated,)h(as)f(b)r(eing)g(those) g(of)g(In)n(v)l(arian)n(t)330 3571 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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 (notices,)g(a)g(license)f(notice)h(giving)f(the)h(public)g(p)r (ermission)e(to)i(use)f(the)510 5155 y(Mo)r(di\014ed)f(V)-6 b(ersion)23 b(under)h(the)h(terms)e(of)h(this)f(License,)h(in)g(the)g (form)f(sho)n(wn)h(in)f(the)i(Addendum)f(b)r(elo)n(w.)375 5261 y(G.)60 b(Preserv)n(e)28 b(in)f(that)i(license)f(notice)h(the)f (full)f(lists)g(of)g(In)n(v)l(arian)n(t)i(Sections)g(and)f(required)g (Co)n(v)n(er)g(T)-6 b(exts)28 b(giv)n(en)h(in)e(the)510 5340 y(Do)r(cumen)n(t's)e(license)e(notice.)p eop end %%Page: 485 501 TeXDict begin 485 500 bop 150 -116 a FK(GNU)31 b(F)-8 b(ree)31 b(Do)s(cumen)m(tation)i(License)2098 b(485)378 299 y Ff(H.)59 b(Include)25 b(an)f(unaltered)h(cop)n(y)f(of)g(this)f (License.)405 400 y(I.)60 b(Preserv)n(e)31 b(the)i(section)f(En)n (titled)g(\\History",)h(Preserv)n(e)f(its)f(Title,)i(and)f(add)f(to)h (it)g(an)f(item)h(stating)g(at)g(least)g(the)510 479 y(title,)25 b(y)n(ear,)h(new)f(authors,)h(and)f(publisher)g(of)g(the)h (Mo)r(di\014ed)f(V)-6 b(ersion)25 b(as)g(giv)n(en)g(on)h(the)g(Title)e (P)n(age.)37 b(If)24 b(there)i(is)f(no)510 558 y(section)i(En)n(titled) f(\\History")g(in)g(the)h(Do)r(cumen)n(t,)g(create)g(one)g(stating)f (the)h(title,)f(y)n(ear,)h(authors,)f(and)h(publisher)e(of)510 637 y(the)h(Do)r(cumen)n(t)h(as)f(giv)n(en)g(on)f(its)h(Title)f(P)n (age,)h(then)h(add)f(an)g(item)f(describing)h(the)g(Mo)r(di\014ed)g(V) -6 b(ersion)25 b(as)g(stated)i(in)510 715 y(the)e(previous)e(sen)n (tence.)394 817 y(J.)60 b(Preserv)n(e)19 b(the)i(net)n(w)n(ork)f(lo)r (cation,)h(if)d(an)n(y)-6 b(,)21 b(giv)n(en)f(in)f(the)h(Do)r(cumen)n (t)h(for)e(public)g(access)i(to)f(a)f(T)-6 b(ransparen)n(t)20 b(cop)n(y)h(of)e(the)510 895 y(Do)r(cumen)n(t,)27 b(and)g(lik)n(ewise)e 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(arian)n(t)h(Sections)f(of)g(the)g(Do)r(cumen)n(t,)i(unaltered)e(in)f (their)h(text)h(and)f(in)f(their)h(titles.)43 b(Section)510 1571 y(n)n(um)n(b)r(ers)24 b(or)f(the)i(equiv)l(alen)n(t)g(are)e(not)i (considered)f(part)g(of)g(the)g(section)h(titles.)366 1672 y(M.)59 b(Delete)22 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: 486 502 TeXDict begin 486 501 bop 150 -116 a FK(GNU)31 b(F)-8 b(ree)31 b(Do)s(cumen)m(tation)i(License)2098 b(486)330 299 y Ff(compilation)29 b(is)e(not)i(used)g(to)g(limit)e(the)i(legal)f (righ)n(ts)g(of)g(the)h(compilation's)f(users)g(b)r(ey)n(ond)h(what)g (the)g(individual)f(w)n(orks)330 378 y(p)r(ermit.)j(When)24 b(the)g(Do)r(cumen)n(t)g(is)e(included)i(in)e(an)i(aggregate,)g(this)f (License)h(do)r(es)f(not)h(apply)g(to)f(the)h(other)g(w)n(orks)e(in)h (the)330 457 y(aggregate)j(whic)n(h)e(are)f(not)i(themselv)n(es)f (deriv)l(ativ)n(e)h(w)n(orks)e(of)h(the)g(Do)r(cumen)n(t.)330 560 y(If)f(the)h(Co)n(v)n(er)f(T)-6 b(ext)25 b(requiremen)n(t)e(of)g (section)h(3)f(is)g(applicable)g(to)h(these)g(copies)g(of)f(the)h(Do)r (cumen)n(t,)g(then)g(if)e(the)i(Do)r(cumen)n(t)330 639 y(is)e(less)h(than)h(one)g(half)f(of)f(the)i(en)n(tire)g(aggregate,)h (the)f(Do)r(cumen)n(t's)g(Co)n(v)n(er)f(T)-6 b(exts)24 b(ma)n(y)f(b)r(e)h(placed)g(on)f(co)n(v)n(ers)h(that)h(brac)n(k)n(et) 330 718 y(the)e(Do)r(cumen)n(t)g(within)f(the)g(aggregate,)i(or)d(the)i (electronic)g(equiv)l(alen)n(t)g(of)f(co)n(v)n(ers)g(if)f(the)i(Do)r (cumen)n(t)g(is)e(in)g(electronic)i(form.)330 797 y(Otherwise)h(they)g (m)n(ust)g(app)r(ear)h(on)f(prin)n(ted)g(co)n(v)n(ers)g(that)h(brac)n (k)n(et)g(the)f(whole)g(aggregate.)215 901 y(8.)60 b(TRANSLA)-6 b(TION)330 1005 y(T)g(ranslation)31 b(is)f(considered)h(a)g(kind)g(of)f (mo)r(di\014cation,)k(so)c(y)n(ou)i(ma)n(y)e(distribute)h(translations) g(of)g(the)g(Do)r(cumen)n(t)i(under)330 1083 y(the)d(terms)g(of)f (section)h(4.)49 b(Replacing)30 b(In)n(v)l(arian)n(t)g(Sections)h(with) f(translations)f(requires)g(sp)r(ecial)h(p)r(ermission)e(from)h(their) 330 1162 y(cop)n(yrigh)n(t)24 b(holders,)e(but)h(y)n(ou)h(ma)n(y)f 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(\\History",)i(the)f(requiremen)n(t)330 1660 y(\(section)25 b(4\))f(to)h(Preserv)n(e)e(its)h(Title)f(\(section)i(1\))g(will)d(t)n (ypically)i(require)f(c)n(hanging)i(the)g(actual)g(title.)215 1764 y(9.)60 b(TERMINA)-6 b(TION)330 1868 y(Y)g(ou)32 b(ma)n(y)h(not)g(cop)n(y)-6 b(,)35 b(mo)r(dify)-6 b(,)33 b(sublicense,)h(or)e(distribute)g(the)h(Do)r(cumen)n(t)h(except)g(as)e (expressly)g(pro)n(vided)g(under)h(this)330 1947 y(License.)53 b(An)n(y)31 b(attempt)i(otherwise)e(to)h(cop)n(y)-6 b(,)33 b(mo)r(dify)-6 b(,)32 b(sublicense,)h(or)d(distribute)h(it)g(is)f(v)n (oid,)j(and)e(will)f(automatically)330 2026 y(terminate)25 b(y)n(our)e(righ)n(ts)h(under)g(this)f(License.)330 2130 y(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 2208 y(reinstated)25 b(\(a\))g(pro)n(visionally)-6 b(,)22 b(unless)i(and)g(un)n(til)g(the)g 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Ff(.)13 b(.)i(.)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(.)52 b Fj(14)449 4546 y(3.27)92 b(size)p 849 4546 28 4 v 40 w(t)9 b Ff(.)16 b(.)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(.)g(.)g(.)g(.)g(.)g(.) g(.)g(.)g(.)g(.)38 b Fj(15)449 4656 y(3.28)92 b(Arra)m(ys)31 b(vs)f(P)m(oin)m(ters)f Ff(.)16 b(.)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(.)58 b Fj(15)449 4765 y(3.29)92 b(P)m(oin)m(ters)19 b Ff(.)d(.)f(.)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(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)49 b Fj(15)449 4875 y(3.30)92 b(Constness)27 b Ff(.)15 b(.)g(.)g(.)g(.)g 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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 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y(suc)m(h)i(as)h(the)f(man)m(y)h(recurrence)f (relations)f(found)g(in)h(Abramo)m(witz)g(and)g(Stegun.)39 b(While)28 b(suc)m(h)g(meth-)150 1863 y(o)s(ds)33 b(migh)m(t)h(b)s(e)f (acceptable)i(for)e Fb(n)e Fj(=)f Fb(O)s Fj(\(10)24 b Fi(\000)e Fj(100\))36 b(they)e(will)d(not)j(b)s(e)f(satisfactory)i(for) e(a)h(user)f(who)150 1972 y(needs)d(to)h(compute)g(the)f(same)h (function)e(for)h Fb(n)25 b Fj(=)g(1000000.)275 2107 y(Similarly)-8 b(,)32 b(do)i(not)g(mak)m(e)h(the)f(implicit)e (assumption)g(that)j(m)m(ultiv)-5 b(ariate)33 b(data)i(has)f(b)s(een)f (scaled)150 2217 y(to)28 b(ha)m(v)m(e)h(comp)s(onen)m(ts)e(of)h(the)f (same)h(size)f(or)g(O\(1\).)41 b(Algorithms)26 b(should)f(tak)m(e)k (care)f(of)g(an)m(y)g(necessary)150 2326 y(scaling)d(or)g(balancing)g (in)m(ternally)-8 b(,)25 b(and)g(use)g(appropriate)g(norms)g(\(e.g.)40 b Fe(|)p Fj(Dx)p Fe(|)26 b Fj(where)f(D)h(is)f(a)h(diagonal)150 2436 y(scaling)j(matrix,)h(rather)h(than)f Fe(|)p Fj(x)p Fe(|)p Fj(\).)150 2694 y Fk(3.10)68 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b(suites)150 3935 y Fj(The)30 b(implemen)m(tor)f(of)h(eac)m(h)i(mo)s(dule)d(should)f(pro) m(vide)i(a)g(reasonable)h(test)g(suite)e(for)i(the)f(routines.)275 4075 y(The)j(test)h(suite)f(should)f(b)s(e)h(a)h(program)f(that)h(uses) f(the)h(library)d(and)i(c)m(hec)m(ks)i(the)f(result)f(against)150 4184 y(kno)m(wn)38 b(results,)g(or)g(in)m(v)m(ok)m(es)h(the)f(library)e (sev)m(eral)i(times)g(and)f(do)s(es)h(a)g(statistical)g(analysis)f(on)h (the)150 4294 y(results)29 b(\(for)i(example)f(in)f(the)h(case)i(of)e (random)g(n)m(um)m(b)s(er)f(generators\).)275 4433 y(Ideally)36 b(the)j(one)g(test)g(program)f(p)s(er)f(directory)h(should)f(aim)g(for) h(100\045)i(path)e(co)m(v)m(erage)j(of)e(the)150 4543 y(co)s(de.)63 b(Ob)m(viously)36 b(it)h(w)m(ould)g(b)s(e)g(a)h(lot)g(of) g(w)m(ork)f(to)i(really)e(ac)m(hiev)m(e)i(this,)f(so)g(prioritize)e (testing)i(on)150 4653 y(the)31 b(critical)e(parts)h(and)g(use)g(insp)s (ection)f(for)h(the)h(rest.)41 b(T)-8 b(est)31 b(all)e(the)i(error)f 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