quaternion/0000755000076500000240000000000012505453300012242 5ustar lukasstaffquaternion/COPYING0000644000076500000240000010451312505453300013301 0ustar lukasstaff GNU GENERAL PUBLIC LICENSE Version 3, 29 June 2007 Copyright (C) 2007 Free Software Foundation, Inc. Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. Preamble The GNU General Public License is a free, copyleft license for software and other kinds of works. The licenses for most software and other practical works are designed to take away your freedom to share and change the works. By contrast, the GNU General Public License is intended to guarantee your freedom to share and change all versions of a program--to make sure it remains free software for all its users. We, the Free Software Foundation, use the GNU General Public License for most of our software; it applies also to any other work released this way by its authors. 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But first, please read . quaternion/DESCRIPTION0000644000076500000240000000054312505453357013766 0ustar lukasstaffName: quaternion Version: 2.4.0 Date: 2015-03-21 Author: Lukas Reichlin Maintainer: Lukas Reichlin Title: Quaternion Description: Quaternion package for GNU Octave, includes a quaternion class with overloaded operators Depends: octave (>= 3.8.0) Autoload: no License: GPLv3+ Url: http://octave.sf.net quaternion/doc/0000755000076500000240000000000012505453300013007 5ustar lukasstaffquaternion/doc/functions.texi0000644000076500000240000006115612505453300015723 0ustar lukasstaff@chapter Quaternion Constructors @section quaternion @findex quaternion @deftypefn {Function File} {@var{q} =} quaternion (@var{w}) @deftypefnx {Function File} {@var{q} =} quaternion (@var{x}, @var{y}, @var{z}) @deftypefnx {Function File} {@var{q} =} quaternion (@var{w}, @var{x}, @var{y}, @var{z}) Constructor for quaternions - create or convert to quaternion. @example q = w + x*i + y*j + z*k @end example Arguments @var{w}, @var{x}, @var{y} and @var{z} can be scalars, matrices or n-dimensional arrays, but they must be real-valued and of equal size. If scalar part @var{w} or components @var{x}, @var{y} and @var{z} of the vector part are not specified, zero matrices of appropriate size are assumed. @strong{Example} @example @group octave:1> q = quaternion (2) q = 2 + 0i + 0j + 0k octave:2> q = quaternion (3, 4, 5) q = 0 + 3i + 4j + 5k octave:3> q = quaternion (2, 3, 4, 5) q = 2 + 3i + 4j + 5k @end group @end example @example @group octave:4> w = [2, 6, 10; 14, 18, 22]; octave:5> x = [3, 7, 11; 15, 19, 23]; octave:6> y = [4, 8, 12; 16, 20, 24]; octave:7> z = [5, 9, 13; 17, 21, 25]; octave:8> q = quaternion (w, x, y, z) q.w = 2 6 10 14 18 22 q.x = 3 7 11 15 19 23 q.y = 4 8 12 16 20 24 q.z = 5 9 13 17 21 25 octave:9> @end group @end example @end deftypefn @section qi @findex qi @deftypefn {Function File} {} qi Create x-component of a quaternion's vector part. @example q = w + x*qi + y*qj + z*qk @end example @strong{Example} @example @group octave:1> q1 = quaternion (1, 2, 3, 4) q1 = 1 + 2i + 3j + 4k octave:2> q2 = 1 + 2*qi + 3*qj + 4*qk q2 = 1 + 2i + 3j + 4k octave:3> @end group @end example @end deftypefn @section qj @findex qj @deftypefn {Function File} {} qj Create y-component of a quaternion's vector part. @example q = w + x*qi + y*qj + z*qk @end example @strong{Example} @example @group octave:1> q1 = quaternion (1, 2, 3, 4) q1 = 1 + 2i + 3j + 4k octave:2> q2 = 1 + 2*qi + 3*qj + 4*qk q2 = 1 + 2i + 3j + 4k octave:3> @end group @end example @end deftypefn @section qk @findex qk @deftypefn {Function File} {} qk Create z-component of a quaternion's vector part. @example q = w + x*qi + y*qj + z*qk @end example @strong{Example} @example @group octave:1> q1 = quaternion (1, 2, 3, 4) q1 = 1 + 2i + 3j + 4k octave:2> q2 = 1 + 2*qi + 3*qj + 4*qk q2 = 1 + 2i + 3j + 4k octave:3> @end group @end example @end deftypefn @chapter Conversions @section q2rot @findex q2rot @deftypefn {Function File} {[@var{axis}, @var{angle}] =} q2rot (@var{q}) @deftypefnx {Function File} {[@var{axis}, @var{angle}, @var{qn}] =} q2rot (@var{q}) Extract vector/angle form of a unit quaternion @var{q}. @strong{Inputs} @table @var @item q Unit quaternion describing the rotation. Quaternion @var{q} can be a scalar or an array. In the latter case, @var{q} is reshaped to a row vector and the return values @var{axis} and @var{angle} are concatenated horizontally, accordingly. @end table @strong{Outputs} @table @var @item axis Eigenaxis as a 3-d unit vector @code{[x; y; z]}. If input argument @var{q} is a quaternion array, @var{axis} becomes a matrix where @var{axis(:,i)} corresponds to @var{q(i)}. @item angle Rotation angle in radians. The positive direction is determined by the right-hand rule applied to @var{axis}. The angle lies in the interval [0, 2*pi]. If input argument @var{q} is a quaternion array, @var{angle} becomes a row vector where @var{angle(i)} corresponds to @var{q(i)}. @item qn Optional output of diagnostic nature. @code{qn = reshape (q, 1, [])} or, if needed, @code{qn = reshape (unit (q), 1, [])}. @end table @strong{Example} @example @group octave:1> axis = [0; 0; 1] axis = 0 0 1 octave:2> angle = pi/4 angle = 0.78540 octave:3> q = rot2q (axis, angle) q = 0.9239 + 0i + 0j + 0.3827k octave:4> [vv, th] = q2rot (q) vv = 0 0 1 th = 0.78540 octave:5> theta = th*180/pi theta = 45.000 octave:6> @end group @end example @end deftypefn @section rot2q @findex rot2q @deftypefn {Function File} {@var{q} =} rot2q (@var{axis}, @var{angle}) Create unit quaternion @var{q} which describes a rotation of @var{angle} radians about the vector @var{axis}. This function uses the active convention where the vector @var{axis} is rotated by @var{angle} radians. If the coordinate frame should be rotated by @var{angle} radians, also called the passive convention, this is equivalent to rotating the @var{axis} by @var{-angle} radians. @strong{Inputs} @table @var @item axis Vector @code{[x, y, z]} or @code{[x; y; z]} describing the axis of rotation. @item angle Rotation angle in radians. The positive direction is determined by the right-hand rule applied to @var{axis}. If @var{angle} is a real-valued array, a quaternion array @var{q} of the same size is returned. @end table @strong{Outputs} @table @var @item q Unit quaternion describing the rotation. If @var{angle} is an array, @var{q(i,j)} corresponds to the rotation angle @var{angle(i,j)}. @end table @strong{Example} @example @group octave:1> axis = [0, 0, 1]; octave:2> angle = pi/4; octave:3> q = rot2q (axis, angle) q = 0.9239 + 0i + 0j + 0.3827k octave:4> v = quaternion (1, 1, 0) v = 0 + 1i + 1j + 0k octave:5> vr = q * v * conj (q) vr = 0 + 0i + 1.414j + 0k octave:6> @end group @end example @end deftypefn @section rotm2q @findex rotm2q @deftypefn {Function File} {@var{q} =} rotm2q (@var{R}) Convert 3x3 rotation matrix @var{R} to unit quaternion @var{q}. @end deftypefn @chapter Quaternion Methods @section @@quaternion/abs @findex abs @deftypefn {Function File} {@var{qabs} =} abs (@var{q}) Modulus of a quaternion. @example q = w + x*i + y*j + z*k abs (q) = sqrt (w.^2 + x.^2 + y.^2 + z.^2) @end example @end deftypefn @section @@quaternion/arg @findex arg @deftypefn {Function File} {@var{theta} =} arg (@var{q}) Compute the argument or phase of quaternion @var{q} in radians. @var{theta} is defined as @code{atan2 (sqrt (q.x.^2 + q.y.^2 + q.z.^2), q.w)}. The argument @var{theta} lies in the range (0, pi). @end deftypefn @section @@quaternion/blkdiag @findex blkdiag @deftypefn {Function File} {@var{q} =} blkdiag (@var{q1}, @var{q2}, @dots{}) Block-diagonal concatenation of quaternions. @end deftypefn @section @@quaternion/cast @findex cast @deftypefn {Function File} {@var{q} =} cast (@var{q}, @var{'type'}) Convert the components of quaternion @var{q} to data type @var{type}. Valid types are int8, uint8, int16, uint16, int32, uint32, int64, uint64, double, single and logical. @end deftypefn @section @@quaternion/cat @findex cat @deftypefn {Function File} {@var{q} =} cat (@var{dim}, @var{q1}, @var{q2}, @dots{}) Concatenation of quaternions along dimension @var{dim}. @end deftypefn @section @@quaternion/ceil @findex ceil @deftypefn {Function File} {@var{q} =} ceil (@var{q}) Round quaternion @var{q} towards positive infinity. @end deftypefn @section @@quaternion/columns @findex columns @deftypefn {Function File} {@var{nc} =} columns (@var{q}) Return number of columns @var{nc} of quaternion array @var{q}. @end deftypefn @section @@quaternion/conj @findex conj @deftypefn {Function File} {@var{q} =} conj (@var{q}) Return conjugate of a quaternion. @example q = w + x*i + y*j + z*k conj (q) = w - x*i - y*j - z*k @end example @end deftypefn @section @@quaternion/cumsum @findex cumsum @deftypefn {Function File} {@var{q} =} cumsum (@var{q}) @deftypefnx {Function File} {@var{q} =} cumsum (@var{q}, @var{dim}) @deftypefnx {Function File} {@var{q} =} cumsum (@dots{}, @var{'native'}) @deftypefnx {Function File} {@var{q} =} cumsum (@dots{}, @var{'double'}) @deftypefnx {Function File} {@var{q} =} cumsum (@dots{}, @var{'extra'}) Cumulative sum of elements along dimension @var{dim}. If @var{dim} is omitted, it defaults to the first non-singleton dimension. See @code{help cumsum} for more information. @end deftypefn @section @@quaternion/diag @findex diag @deftypefn {Function File} {@var{q} =} diag (@var{v}) @deftypefnx {Function File} {@var{q} =} diag (@var{v}, @var{k}) Return a diagonal quaternion matrix with quaternion vector V on diagonal K. The second argument is optional. If it is positive, the vector is placed on the K-th super-diagonal. If it is negative, it is placed on the -K-th sub-diagonal. The default value of K is 0, and the vector is placed on the main diagonal. Given a matrix argument, instead of a vector, @command{diag} extracts the @var{K}-th diagonal of the matrix. @end deftypefn @section @@quaternion/diff @findex diff @deftypefn {Function File} {@var{qdot} =} diff (@var{q}, @var{omega}) Derivative of a quaternion. Let Q be a quaternion to transform a vector from a fixed frame to a rotating frame. If the rotating frame is rotating about the [x, y, z] axes at angular rates [wx, wy, wz], then the derivative of Q is given by @example Q' = diff(Q, omega) @end example If the passive convention is used (rotate the frame, not the vector), then @example Q' = diff(Q,-omega) @end example @end deftypefn @section @@quaternion/exp @findex exp @deftypefn {Function File} {@var{qexp} =} exp (@var{q}) Exponential of a quaternion. @end deftypefn @section @@quaternion/fix @findex fix @deftypefn {Function File} {@var{q} =} fix (@var{q}) Round quaternion @var{q} towards zero. @end deftypefn @section @@quaternion/floor @findex floor @deftypefn {Function File} {@var{q} =} floor (@var{q}) Round quaternion @var{q} towards negative infinity. @end deftypefn @section @@quaternion/full @findex full @deftypefn {Function File} {@var{fq} =} full (@var{sq}) Return a full storage quaternion representation @var{fq} from sparse or diagonal quaternion @var{sq}. @end deftypefn @section @@quaternion/get @findex get @deftypefn {Function File} {} get (@var{q}) @deftypefnx {Function File} {@var{value} =} get (@var{q}, @var{"key"}) @deftypefnx {Function File} {[@var{val1}, @var{val2}, @dots{}] =} get (@var{q}, @var{"key1"}, @var{"key2"}, @dots{}) Access key values of quaternion objects. @strong{Keys} @table @var @item w Return scalar part @var{w} of quaternion @var{q} as a built-in type. @item x, y, z Return component @var{x}, @var{y} or @var{z} of the vector part of quaternion @var{q} as a built-in type. @item s Return scalar part of quaternion @var{q}. The vector part of @var{q} is set to zero. @item v Return vector part of quaternion @var{q}. The scalar part of @var{q} is set to zero. @end table @end deftypefn @section @@quaternion/inv @findex inv @deftypefn {Function File} {@var{qinv} =} inv (@var{q}) Return inverse of a quaternion. @end deftypefn @section @@quaternion/isempty @findex isempty @deftypefn {Function File} {@var{bool} =} isempty (@var{q}) Return true if quaternion @var{q} is empty and false otherwise. @end deftypefn @section @@quaternion/isfinite @findex isfinite @deftypefn {Function File} {@var{bool} =} isfinite (@var{q}) Return a logical array which is true where the elements of @var{q} are finite values and false where they are not. @end deftypefn @section @@quaternion/isinf @findex isinf @deftypefn {Function File} {@var{bool} =} isinf (@var{q}) Return a logical array which is true where the elements of @var{q} are infinite and false where they are not. @end deftypefn @section @@quaternion/isnan @findex isnan @deftypefn {Function File} {@var{bool} =} isnan (@var{q}) Return a logical array which is true where the elements of @var{q} are NaN values and false where they are not. @end deftypefn @section @@quaternion/ispure @findex ispure @deftypefn {Function File} {@var{bool} =} ispure (@var{q}) Return true if scalar part of quaternion is zero, otherwise return false. @end deftypefn @section @@quaternion/isreal @findex isreal @deftypefn {Function File} {@var{bool} =} isreal (@var{q}) Return true if the vector part of quaternion @var{q} is zero and false otherwise. @end deftypefn @section @@quaternion/length @findex length @deftypefn {Function File} {@var{l} =} length (@var{q}) Return the "length" @var{l} of the quaternion array @var{q}. For quaternion matrices, the length is the number of rows or columns, whichever is greater (this odd definition is used for compatibility with @acronym{MATLAB}). @end deftypefn @section @@quaternion/log @findex log @deftypefn {Function File} {@var{qlog} =} log (@var{q}) Logarithmus naturalis of a quaternion. @end deftypefn @section @@quaternion/mean @findex mean @deftypefn {Function File} {@var{q} =} mean (@var{q}) @deftypefnx {Function File} {@var{q} =} mean (@var{q}, @var{dim}) @deftypefnx {Function File} {@var{q} =} mean (@var{q}, @var{opt}) @deftypefnx {Function File} {@var{q} =} mean (@var{q}, @var{dim}, @var{opt}) Compute the mean of the elements of the quaternion array @var{q}. @example mean (q) = mean (q.w) + mean (q.x)*i + mean (q.y)*j + mean (q.z)*k @end example See @code{help mean} for more information and a description of the parameters @var{dim} and @var{opt}. @end deftypefn @section @@quaternion/ndims @findex ndims @deftypefn {Function File} {@var{n} =} ndims (@var{q}) Return the number of dimensions of quaternion @var{q}. For any array, the result will always be larger than or equal to 2. Trailing singleton dimensions are not counted. @end deftypefn @section @@quaternion/norm @findex norm @deftypefn {Function File} {@var{n} =} norm (@var{q}) Norm of a quaternion. @end deftypefn @section @@quaternion/numel @findex numel @deftypefn {Function File} {@var{n} =} numel (@var{q}) @deftypefnx {Function File} {@var{n} =} numel (@var{q}, @var{idx1}, @var{idx2}, @dots{}) For internal use only, use @code{prod(size(q))} or @code{numel (q.w)} instead. For technical reasons, this method must return the number of elements which are returned from cs-list indexing, no matter whether it is called with one or more arguments. @end deftypefn @section @@quaternion/repmat @findex repmat @deftypefn {Function File} {@var{qret} =} repmat (@var{q}, @var{m}) @deftypefnx {Function File} {@var{qret} =} repmat (@var{q}, @var{m}, @var{n}) @deftypefnx {Function File} {@var{qret} =} repmat (@var{q}, [@var{m} @var{n}]) @deftypefnx {Function File} {@var{qret} =} repmat (@var{q}, [@var{m} @var{n} @var{p} @dots{}]) Form a block quaternion matrix @var{qret} of size @var{m} by @var{n}, with a copy of quaternion matrix @var{q} as each element. If @var{n} is not specified, form an @var{m} by @var{m} block matrix. @end deftypefn @section @@quaternion/reshape @findex reshape @deftypefn {Function File} {@var{q} =} reshape (@var{q}, @var{m}, @var{n}, @dots{}) @deftypefnx {Function File} {@var{q} =} reshape (@var{q}, [@var{m} @var{n} @dots{}]) @deftypefnx {Function File} {@var{q} =} reshape (@var{q}, @dots{}, [], @dots{}) @deftypefnx {Function File} {@var{q} =} reshape (@var{q}, @var{size}) Return a quaternion array with the specified dimensions (@var{m}, @var{n}, @dots{}) whose elements are taken from the quaternion array @var{q}. The elements of the quaternion are accessed in column-major order (like Fortran arrays are stored). @end deftypefn @section @@quaternion/round @findex round @deftypefn {Function File} {@var{q} =} round (@var{q}) Round the components of quaternion @var{q} towards the nearest integers. @end deftypefn @section @@quaternion/rows @findex rows @deftypefn {Function File} {@var{nr} =} rows (@var{q}) Return number of rows @var{nr} of quaternion array @var{q}. @end deftypefn @section @@quaternion/set @findex set @deftypefn {Function File} {} set (@var{q}) @deftypefnx {Function File} {} set (@var{q}, @var{"key"}, @var{value}, @dots{}) @deftypefnx {Function File} {@var{qret} =} set (@var{q}, @var{"key"}, @var{value}, @dots{}) Set or modify properties of quaternion objects. If no return argument @var{qret} is specified, the modified quaternion object is stored in input argument @var{q}. @command{set} can handle multiple keys in one call: @code{set (q, 'key1', val1, 'key2', val2, 'key3', val3)}. @code{set (q)} prints a list of the object's key names. @strong{Keys} @table @var @item w Assign real-valued array @var{val} to scalar part @var{w} of quaternion @var{q}. @item x, y, z Assign real-valued array @var{val} to component @var{x}, @var{y} or @var{z} of the vector part of quaternion @var{q}. @item s Assign scalar part of quaternion @var{val} to scalar part of quaternion @var{q}. The vector part of @var{q} is left untouched. @item v Assign vector part of quaternion @var{val} to vector part of quaternion @var{q}. The scalar part of @var{q} is left untouched. @end table @end deftypefn @section @@quaternion/size @findex size @deftypefn {Function File} {@var{nvec} =} size (@var{q}) @deftypefnx {Function File} {@var{n} =} size (@var{q}, @var{dim}) @deftypefnx {Function File} {[@var{nx}, @var{ny}, @dots{}] =} size (@var{q}) Return size of quaternion arrays. @strong{Inputs} @table @var @item q Quaternion object. @item dim If given a second argument, @command{size} will return the size of the corresponding dimension. @end table @strong{Outputs} @table @var @item nvec Row vector. The first element is the number of rows and the second element the number of columns. If @var{q} is an n-dimensional array of quaternions, the n-th element of @var{nvec} corresponds to the size of the n-th dimension of @var{q}. @item n Scalar value. The size of the dimension @var{dim}. @item nx Number of rows. @item ny Number of columns. @item @dots{} Sizes of the 3rd to n-th dimensions. @end table @end deftypefn @section @@quaternion/size_equal @findex size_equal @deftypefn {Function File} {@var{bool} =} size_equal (@var{a}, @var{b}, @dots{}) Return true if quaternions (and matrices) @var{a}, @var{b}, @dots{} are of equal size and false otherwise. @end deftypefn @section @@quaternion/sparse @findex sparse @deftypefn {Function File} {@var{sq} =} sparse (@var{fq}) Return a sparse quaternion representation @var{sq} from full quaternion @var{fq}. @end deftypefn @section @@quaternion/squeeze @findex squeeze @deftypefn {Function File} {@var{qret} =} squeeze (@var{q}) Remove singleton dimensions from quaternion @var{q} and return the result. Note that for compatibility with @acronym{MATLAB}, all objects have a minimum of two dimensions and row vectors are left unchanged. @end deftypefn @section @@quaternion/sum @findex sum @deftypefn {Function File} {@var{q} =} sum (@var{q}) @deftypefnx {Function File} {@var{q} =} sum (@var{q}, @var{dim}) @deftypefnx {Function File} {@var{q} =} sum (@dots{}, @var{'native'}) @deftypefnx {Function File} {@var{q} =} sum (@dots{}, @var{'double'}) @deftypefnx {Function File} {@var{q} =} sum (@dots{}, @var{'extra'}) Sum of elements along dimension @var{dim}. If @var{dim} is omitted, it defaults to the first non-singleton dimension. See @code{help sum} for more information. @end deftypefn @section @@quaternion/tril @findex tril @deftypefn {Function File} {@var{q} =} tril (@var{q}) @deftypefnx {Function File} {@var{q} =} tril (@var{q}, @var{k}) @deftypefnx {Function File} {@var{q} =} tril (@var{q}, @var{k}, @var{'pack'}) Return a new quaternion matrix formed by extracting the lower triangular part of the quaternion @var{q}, and setting all other elements to zero. The second argument @var{k} is optional, and specifies how many diagonals above or below the main diagonal should also be included. Default value for @var{k} is zero. If the option "pack" is given as third argument, the extracted elements are not inserted into a matrix, but rather stacked column-wise one above other. @end deftypefn @section @@quaternion/triu @findex triu @deftypefn {Function File} {@var{q} =} triu (@var{q}) @deftypefnx {Function File} {@var{q} =} triu (@var{q}, @var{k}) @deftypefnx {Function File} {@var{q} =} triu (@var{q}, @var{k}, @var{'pack'}) Return a new quaternion matrix formed by extracting the upper triangular part of the quaternion @var{q}, and setting all other elements to zero. The second argument @var{k} is optional, and specifies how many diagonals above or below the main diagonal should also be included. Default value for @var{k} is zero. If the option "pack" is given as third argument, the extracted elements are not inserted into a matrix, but rather stacked column-wise one above other. @end deftypefn @section @@quaternion/unit @findex unit @deftypefn {Function File} {@var{qn} =} unit (@var{q}) Normalize quaternion to length 1 (unit quaternion). @example q = w + x*i + y*j + z*k unit (q) = q ./ sqrt (w.^2 + x.^2 + y.^2 + z.^2) @end example @end deftypefn @chapter Overloaded Quaternion Operators @section @@quaternion/ctranspose @findex ctranspose Conjugate transpose of a quaternion. Used by Octave for "q'". @section @@quaternion/end @findex end End indexing for quaternions. Used by Octave for "q(1:end)". @section @@quaternion/eq @findex eq Equal to operator for two quaternions. Used by Octave for "q1 == q2". @section @@quaternion/ge @findex ge Greater-than-or-equal-to operator for two quaternions. Used by Octave for "q1 >= q2". The ordering is lexicographic. @section @@quaternion/gt @findex gt Greater-than operator for two quaternions. Used by Octave for "q1 > q2". The ordering is lexicographic. @section @@quaternion/horzcat @findex horzcat Horizontal concatenation of quaternions. Used by Octave for "[q1, q2]". @section @@quaternion/ldivide @findex ldivide Element-wise left division for quaternions. Used by Octave for "q1 .\ q2". @section @@quaternion/le @findex le Less-than-or-equal-to operator for two quaternions. Used by Octave for "q1 <= q2". The ordering is lexicographic. @section @@quaternion/lt @findex lt Less-than operator for two quaternions. Used by Octave for "q1 < q2". The ordering is lexicographic. @section @@quaternion/minus @findex minus Subtraction of two quaternions. Used by Octave for "q1 - q2". @section @@quaternion/mldivide @findex mldivide Matrix left division for quaternions. Used by Octave for "q1 \ q2". @section @@quaternion/mpower @findex mpower Matrix power operator of quaternions. Used by Octave for "q^x". @section @@quaternion/mrdivide @findex mrdivide Matrix right division for quaternions. Used by Octave for "q1 / q2". @section @@quaternion/mtimes @findex mtimes Matrix multiplication of two quaternions. Used by Octave for "q1 * q2". @section @@quaternion/ne @findex ne Not-equal-to operator for two quaternions. Used by Octave for "q1 != q2". @section @@quaternion/plus @findex plus Addition of two quaternions. Used by Octave for "q1 + q2". @section @@quaternion/power @findex power Power operator of quaternions. Used by Octave for "q.^x". Exponent x can be scalar or of appropriate size. @section @@quaternion/rdivide @findex rdivide Element-wise right division for quaternions. Used by Octave for "q1 ./ q2". @section @@quaternion/subsasgn @findex subsasgn Subscripted assignment for quaternions. Used by Octave for "q.key = value". @strong{Subscripts} @table @var @item q.w Assign real-valued array @var{val} to scalar part @var{w} of quaternion @var{q}. @item q.x, q.y, q.z Assign real-valued array @var{val} to component @var{x}, @var{y} or @var{z} of the vector part of quaternion @var{q}. @item q.s Assign scalar part of quaternion @var{val} to scalar part of quaternion @var{q}. The vector part of @var{q} is left untouched. @item q.v Assign vector part of quaternion @var{val} to vector part of quaternion @var{q}. The scalar part of @var{q} is left untouched. @item q(@dots{}) Assign @var{val} to certain elements of quaternion array @var{q}, e.g. @code{q(3, 2:end) = val}. @end table @section @@quaternion/subsref @findex subsref Subscripted reference for quaternions. Used by Octave for "q.w". @strong{Subscripts} @table @var @item q.w Return scalar part @var{w} of quaternion @var{q} as a built-in type. @item q.x, q.y, q.z Return component @var{x}, @var{y} or @var{z} of the vector part of quaternion @var{q} as a built-in type. @item q.s Return scalar part of quaternion @var{q}. The vector part of @var{q} is set to zero. @item q.v Return vector part of quaternion @var{q}. The scalar part of @var{q} is set to zero. @item q(@dots{}) Extract certain elements of quaternion array @var{q}, e.g. @code{q(3, 2:end)}. @end table @section @@quaternion/times @findex times Element-wise multiplication of two quaternions. Used by Octave for "q1 .* q2". @section @@quaternion/transpose @findex transpose Transpose of a quaternion. Used by Octave for "q.'". @section @@quaternion/uminus @findex uminus Unary minus of a quaternion. Used by Octave for "-q". @section @@quaternion/uplus @findex uplus Unary plus of a quaternion. 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Reichlin @author Juan Pablo Carbajal @page @vskip 0pt plus 1filll Copyright @copyright{} 2010-2015, Lukas F. Reichlin @email{lukas.reichlin@@gmail.com} This manual is generated automatically from the texinfo help strings of the package's functions. Permission is granted to make and distribute verbatim copies of this manual provided the copyright notice and this permission notice are preserved on all copies. Permission is granted to copy and distribute modified versions of this manual under the conditions for verbatim copying, provided that the entire resulting derived work is distributed under the terms of a permission notice identical to this one. Permission is granted to copy and distribute translations of this manual into another language, under the same conditions as for modified versions. @page @paragraphindent 0 @chapheading Preface The @acronym{GNU} Octave quaternion package from version 2 onwards was developed by Lukas F. Reichlin with important contributions by Juan Pablo Carbajal. This new package is intended as a replacement for quaternion-1.0.0 by A. Scottedward Hodel. It is loosely based on ideas from the Quaternion Toolbox for Matlab by Steve Sangwine and Nicolas Le Bihan with a special focus on code simplicity and vectorization. Its main features are: @itemize @item Matrices and n-dimensional arrays of quaternions. @item Overloaded operators due to the use of classes introduced with Octave 3.2. @item Operator semantics similar to Octave's built-in complex numbers. @item Fully vectorized code for crunching large quaternion arrays in a speedy manner. @end itemize @sp 5 @subheading Using the help function Some functions of the quaternion package are listed with the somewhat cryptic prefix @code{@@quaternion/}. This prefix is only needed to view the help text of the function, e.g. @w{@code{help norm}} shows the built-in function while @w{@code{help @@quaternion/norm}} shows the overloaded function for quaternions. Note that there are quaternion functions like @code{unit} that have no built-in equivalent. When just using the function, the leading @code{@@quaternion/} must @strong{not} be typed. Octave selects the right function automatically. So one can type @w{@code{norm (q)}} and @w{@code{norm (matrix)}} regardless of the class of the argument. @end titlepage @c %*** End of TITLEPAGE @headings double @contents @c @chapter Function Reference @include functions.texi @end @node Function Index @unnumbered Function Index @printindex fn @bye quaternion/INDEX0000644000076500000240000000274212505453300013041 0ustar lukasstaffquaternion >> Quaternion Quaternion Constructors quaternion qi qj qk Conversions q2rot rot2q rotm2q Quaternion Methods @quaternion/abs @quaternion/arg @quaternion/blkdiag @quaternion/cast @quaternion/cat @quaternion/ceil @quaternion/columns @quaternion/conj @quaternion/cumsum @quaternion/diag @quaternion/diff @quaternion/exp @quaternion/fix @quaternion/floor @quaternion/full @quaternion/get @quaternion/inv @quaternion/isempty @quaternion/isfinite @quaternion/isinf @quaternion/isnan @quaternion/ispure @quaternion/isreal @quaternion/length @quaternion/log @quaternion/mean @quaternion/ndims @quaternion/norm @quaternion/numel @quaternion/repmat @quaternion/reshape @quaternion/round @quaternion/rows @quaternion/set @quaternion/size @quaternion/size_equal @quaternion/sparse @quaternion/squeeze @quaternion/sum @quaternion/tril @quaternion/triu @quaternion/unit Overloaded Quaternion Operators @quaternion/ctranspose @quaternion/end @quaternion/eq @quaternion/ge @quaternion/gt @quaternion/horzcat @quaternion/ldivide @quaternion/le @quaternion/lt @quaternion/minus @quaternion/mldivide @quaternion/mpower @quaternion/mrdivide @quaternion/mtimes @quaternion/ne @quaternion/plus @quaternion/power @quaternion/rdivide @quaternion/subsasgn @quaternion/subsref @quaternion/times @quaternion/transpose @quaternion/uminus @quaternion/uplus @quaternion/vertcat quaternion/inst/0000755000076500000240000000000012505453300013217 5ustar lukasstaffquaternion/inst/@quaternion/0000755000076500000240000000000012505453300015504 5ustar lukasstaffquaternion/inst/@quaternion/abs.m0000644000076500000240000000214712505453300016433 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{qabs} =} abs (@var{q}) ## Modulus of a quaternion. ## ## @example ## q = w + x*i + y*j + z*k ## abs (q) = sqrt (w.^2 + x.^2 + y.^2 + z.^2) ## @end example ## @end deftypefn ## Author: Lukas Reichlin ## Created: August 2010 ## Version: 0.2 function b = abs (a) if (nargin != 1) print_usage (); endif b = sqrt (norm2 (a)); endfunction quaternion/inst/@quaternion/arg.m0000644000076500000240000000231112505453300016430 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{theta} =} arg (@var{q}) ## Compute the argument or phase of quaternion @var{q} in radians. ## @var{theta} is defined as @code{atan2 (sqrt (q.x.^2 + q.y.^2 + q.z.^2), q.w)}. ## The argument @var{theta} lies in the range (0, pi). ## @end deftypefn ## Author: Lukas Reichlin ## Created: December 2013 ## Version: 0.1 function theta = arg (q) if (nargin != 1) print_usage (); endif theta = arg (complex (q.w, normv (q))); endfunction quaternion/inst/@quaternion/blkdiag.m0000644000076500000240000000324412505453300017262 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{q} =} blkdiag (@var{q1}, @var{q2}, @dots{}) ## Block-diagonal concatenation of quaternions. ## @end deftypefn ## Author: Lukas Reichlin ## Created: December 2011 ## Version: 0.1 function q = blkdiag (varargin) tmp = cellfun (@quaternion, varargin); # uniformoutput = true ! w = blkdiag (tmp.w); x = blkdiag (tmp.x); y = blkdiag (tmp.y); z = blkdiag (tmp.z); q = quaternion (w, x, y, z); endfunction %!shared C, D %! Aw = [2, 6; 10, 14]; %! Ax = [3, 7; 11, 15]; %! Ay = [4, 8; 12, 16]; %! Az = [5, 9; 13, 17]; %! A = quaternion (Aw, Ax, Ay, Az); %! %! Bw = [2, 6, 10; 14, 18, 22]; %! Bx = [3, 7, 11; 15, 19, 23]; %! By = [4, 8, 12; 16, 20, 24]; %! Bz = [5, 9, 13; 17, 21, 25]; %! B = quaternion (Bw, Bx, By, Bz); %! %! C = blkdiag (A, B); %! %! Dw = blkdiag (Aw, Bw); %! Dx = blkdiag (Ax, Bx); %! Dy = blkdiag (Ay, By); %! Dz = blkdiag (Az, Bz); %! D = quaternion (Dw, Dx, Dy, Dz); %!assert (C == D); quaternion/inst/@quaternion/cast.m0000644000076500000240000000344012505453300016615 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{q} =} cast (@var{q}, @var{'type'}) ## Convert the components of quaternion @var{q} to data type @var{type}. ## Valid types are int8, uint8, int16, uint16, int32, uint32, int64, ## uint64, double, single and logical. ## @end deftypefn ## Author: Lukas Reichlin ## Created: December 2013 ## Version: 0.1 function qret = cast (q, typ) if (nargin != 2 || ! ischar (typ)) # q is always a quaternion, no need to test print_usage (); endif if (! any (strcmp (typ, {"int8"; "uint8"; "int16"; "uint16"; "int32"; "uint32"; "int64"; "uint64"; "double"; "single"; "logical"}))) error ("quaternion: cast: type name '%s' is not a built-in type", typ); endif ## NOTE: Without strcmp, cast could be used to apply any function to the ## components of a quaternion. Shall I create such a method with ## a different name? w = feval (typ, q.w); x = feval (typ, q.x); y = feval (typ, q.y); z = feval (typ, q.z); qret = quaternion (w, x, y, z); endfunction quaternion/inst/@quaternion/cat.m0000644000076500000240000000230412505453300016430 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{q} =} cat (@var{dim}, @var{q1}, @var{q2}, @dots{}) ## Concatenation of quaternions along dimension @var{dim}. ## @end deftypefn ## Author: Lukas Reichlin ## Created: November 2011 ## Version: 0.1 function q = cat (dim, varargin) tmp = cellfun (@quaternion, varargin); # uniformoutput = true ! w = cat (dim, tmp.w); x = cat (dim, tmp.x); y = cat (dim, tmp.y); z = cat (dim, tmp.z); q = quaternion (w, x, y, z); endfunction quaternion/inst/@quaternion/ceil.m0000644000076500000240000000212512505453300016576 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{q} =} ceil (@var{q}) ## Round quaternion @var{q} towards positive infinity. ## @end deftypefn ## Author: Lukas Reichlin ## Created: December 2013 ## Version: 0.1 function q = ceil (q) if (nargin != 1) print_usage (); endif q.w = ceil (q.w); q.x = ceil (q.x); q.y = ceil (q.y); q.z = ceil (q.z); endfunction quaternion/inst/@quaternion/columns.m0000644000076500000240000000204512505453300017343 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{nc} =} columns (@var{q}) ## Return number of columns @var{nc} of quaternion array @var{q}. ## @end deftypefn ## Author: Lukas Reichlin ## Created: May 2010 ## Version: 0.1 function c = columns (a) if (nargin != 1) print_usage (); endif c = columns (a.w); endfunction quaternion/inst/@quaternion/conj.m0000644000076500000240000000216212505453300016614 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{q} =} conj (@var{q}) ## Return conjugate of a quaternion. ## ## @example ## q = w + x*i + y*j + z*k ## conj (q) = w - x*i - y*j - z*k ## @end example ## @end deftypefn ## Author: Lukas Reichlin ## Created: May 2010 ## Version: 0.1 function a = conj (a) if (nargin != 1) print_usage (); endif a.x = -a.x; a.y = -a.y; a.z = -a.z; endfunction quaternion/inst/@quaternion/ctranspose.m0000644000076500000240000000174012505453300020045 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## Conjugate transpose of a quaternion. Used by Octave for "q'". ## Author: Lukas Reichlin ## Created: May 2010 ## Version: 0.1 function a = ctranspose (a) if (nargin != 1) print_usage (); endif a = conj (transpose (a)); endfunction quaternion/inst/@quaternion/cumsum.m0000644000076500000240000000312412505453300017173 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{q} =} cumsum (@var{q}) ## @deftypefnx {Function File} {@var{q} =} cumsum (@var{q}, @var{dim}) ## @deftypefnx {Function File} {@var{q} =} cumsum (@dots{}, @var{'native'}) ## @deftypefnx {Function File} {@var{q} =} cumsum (@dots{}, @var{'double'}) ## @deftypefnx {Function File} {@var{q} =} cumsum (@dots{}, @var{'extra'}) ## Cumulative sum of elements along dimension @var{dim}. If @var{dim} is omitted, ## it defaults to the first non-singleton dimension. ## See @code{help cumsum} for more information. ## @end deftypefn ## Author: Lukas Reichlin ## Created: December 2013 ## Version: 0.1 function q = cumsum (q, varargin) if (! isa (q, "quaternion")) print_usage (); endif q.w = cumsum (q.w, varargin{:}); q.x = cumsum (q.x, varargin{:}); q.y = cumsum (q.y, varargin{:}); q.z = cumsum (q.z, varargin{:}); endfunction quaternion/inst/@quaternion/diag.m0000644000076500000240000000350512505453300016571 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{q} =} diag (@var{v}) ## @deftypefnx {Function File} {@var{q} =} diag (@var{v}, @var{k}) ## Return a diagonal quaternion matrix with quaternion vector V on diagonal K. ## The second argument is optional. If it is positive, ## the vector is placed on the K-th super-diagonal. ## If it is negative, it is placed on the -K-th sub-diagonal. ## The default value of K is 0, and the vector is placed ## on the main diagonal. ## Given a matrix argument, instead of a vector, @command{diag} ## extracts the @var{K}-th diagonal of the matrix. ## @end deftypefn ## Author: Lukas Reichlin ## Created: May 2010 ## Version: 0.2 function a = diag (a, b = 0) if (nargin > 2) print_usage (); endif a.w = diag (a.w, b); a.x = diag (a.x, b); a.y = diag (a.y, b); a.z = diag (a.z, b); endfunction %!shared R, S, T, U %! Q = quaternion (2, 3, 4, 5); %! R = diag ([Q, Q, Q]); %! W = diag ([2, 2, 2]); %! X = diag ([3, 3, 3]); %! Y = diag ([4, 4, 4]); %! Z = diag ([5, 5, 5]); %! S = quaternion (W, X, Y, Z); %! T = diag (R); %! U = [Q; Q; Q]; %!assert (R == S); %!assert (T == U); quaternion/inst/@quaternion/diff.m0000644000076500000240000000371212505453300016575 0ustar lukasstaff## Copyright (c) 1998, 2000, 2005, 2007 Auburn University. ## Copyright (c) 2011 Juan Pablo Carbajal ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{qdot} =} diff (@var{q}, @var{omega}) ## Derivative of a quaternion. ## ## Let Q be a quaternion to transform a vector from a fixed frame to ## a rotating frame. If the rotating frame is rotating about the ## [x, y, z] axes at angular rates [wx, wy, wz], then the derivative ## of Q is given by ## ## @example ## Q' = diff(Q, omega) ## @end example ## ## If the passive convention is used (rotate the frame, not the vector), ## then ## ## @example ## Q' = diff(Q,-omega) ## @end example ## @end deftypefn ## Adapted from: qderiv by A. S. Hodel function qd = diff (q, Omega) if (nargin != 2) print_usage (); endif if (! isa (q, "quaternion") || ! isscalar (q.w)) error ("quaternion: first argument '%s' must be a scalar quaternion", inputname(1)); endif Omega = vec (Omega); if (length (Omega) != 3) error ("quaternion: second argument '%s' must be a length 3 vector", inputname(2)); endif qd = 0.5 * quaternion (Omega(1), Omega(2), Omega(3)) * q; endfunction %!shared q %! q = quaternion(3,1,0,0); %!assert(quaternion(0,0,0.5,1.5) == diff(q,[0 0 1])) %!assert(quaternion(0,0,2,1) == diff(q,[0 1 1])) quaternion/inst/@quaternion/display.m0000644000076500000240000000313312505453300017327 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## Display routine for quaternions. Used by Octave internally. ## Author: Lukas Reichlin ## Created: May 2010 ## Version: 0.2 function display (q) name = inputname (1); s = size (q); if (length (s) == 2 && all (s == 1)) # scalar quaternion w = num2str (q.w, 4); x = __num2str__ (q.x); y = __num2str__ (q.y); z = __num2str__ (q.z); disp ([name, " = ", w, x, "i" y, "j", z, "k"]); else # non-scalar quaternion disp ([name, ".w ="]); disp (q.w); disp (""); disp ([name, ".x ="]); disp (q.x); disp (""); disp ([name, ".y ="]); disp (q.y); disp (""); disp ([name, ".z ="]); disp (q.z); disp (""); endif endfunction function str = __num2str__ (num) if (num < 0) str = " - "; else str = " + "; endif str = [str, num2str(abs (num), 4)]; endfunction quaternion/inst/@quaternion/end.m0000644000076500000240000000274712505453300016442 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## End indexing for quaternions. ## Used by Octave for "q(1:end)". ## Author: Lukas Reichlin ## Created: December 2013 ## Version: 0.1 function ret = end (q, k, n) ## error: end: no method for class double ## octave 3.6.4 raises an error for the following 4 variants: ## ret = end (q.w, k, n); ## ret = feval ("end", q.w, k, n); ## ret = feval (@end, q.w, k, n); ## ret = builtin ("end", q.w, k, n); if (n == 1) # q(idx), note that ndims (q.w) >= 2 ret = numel (q.w); else # q(idx1, idx2), q(idx1, idx2, idx3), ... ret = size (q.w, k); endif endfunction %!test %! w = eye (3); %! q = quaternion (w); %! assert (q(end).w, w(end)); %! assert (q(end,1).w, w(end,1)); %! assert (q(1,end).w, w(1,end)); quaternion/inst/@quaternion/eq.m0000644000076500000240000000233712505453300016274 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## Equal to operator for two quaternions. Used by Octave for "q1 == q2". ## Author: Lukas Reichlin ## Created: May 2010 ## Version: 0.4 function bool = eq (a, b) if (nargin != 2) error ("quaternion: eq: this is a binary operator"); endif a = quaternion (a); b = quaternion (b); bool = (a.w == b.w) & (a.x == b.x) & (a.y == b.y) & (a.z == b.z); endfunction %!test %! a = quaternion (2, 3, 4, 5); %! b = quaternion (2, -3, 4, 5); %! assert (a == a, true); %! assert (a == b, false); quaternion/inst/@quaternion/exp.m0000644000076500000240000000230612505453300016457 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{qexp} =} exp (@var{q}) ## Exponential of a quaternion. ## @end deftypefn ## Author: Lukas Reichlin ## Created: November 2011 ## Version: 0.1 function q = exp (q) if (nargin != 1) print_usage (); endif normv = normv (q); exps = exp (q.w); sinv = sin (normv); q.w = exps .* cos (normv); q.x = exps .* (q.x ./ normv) .* sinv; q.y = exps .* (q.y ./ normv) .* sinv; q.z = exps .* (q.z ./ normv) .* sinv; endfunction quaternion/inst/@quaternion/fix.m0000644000076500000240000000210212505453300016443 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{q} =} fix (@var{q}) ## Round quaternion @var{q} towards zero. ## @end deftypefn ## Author: Lukas Reichlin ## Created: December 2013 ## Version: 0.1 function q = fix (q) if (nargin != 1) print_usage (); endif q.w = fix (q.w); q.x = fix (q.x); q.y = fix (q.y); q.z = fix (q.z); endfunction quaternion/inst/@quaternion/floor.m0000644000076500000240000000213312505453300017002 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{q} =} floor (@var{q}) ## Round quaternion @var{q} towards negative infinity. ## @end deftypefn ## Author: Lukas Reichlin ## Created: December 2013 ## Version: 0.1 function q = floor (q) if (nargin != 1) print_usage (); endif q.w = floor (q.w); q.x = floor (q.x); q.y = floor (q.y); q.z = floor (q.z); endfunction quaternion/inst/@quaternion/full.m0000644000076500000240000000221412505453300016623 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{fq} =} full (@var{sq}) ## Return a full storage quaternion representation @var{fq} ## from sparse or diagonal quaternion @var{sq}. ## @end deftypefn ## Author: Lukas Reichlin ## Created: December 2013 ## Version: 0.1 function q = full (q) if (nargin != 1) print_usage (); endif q.w = full (q.w); q.x = full (q.x); q.y = full (q.y); q.z = full (q.z); endfunction quaternion/inst/@quaternion/ge.m0000644000076500000240000000227512505453300016263 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## Greater-than-or-equal-to operator for two quaternions. ## Used by Octave for "q1 >= q2". ## The ordering is lexicographic. ## Author: Lukas Reichlin ## Created: December 2013 ## Version: 0.1 function bool = ge (a, b) if (nargin != 2) error ("quaternion: ge: this is a binary operator"); endif bool = ! lt (a, b); endfunction %!test %! a = quaternion (2, 3, 4, 5); %! b = quaternion (2, -3, 4, 5); %! assert (a >= b, true); %! assert (b >= a, false); quaternion/inst/@quaternion/get.m0000644000076500000240000000430712505453300016445 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {} get (@var{q}) ## @deftypefnx {Function File} {@var{value} =} get (@var{q}, @var{"key"}) ## @deftypefnx {Function File} {[@var{val1}, @var{val2}, @dots{}] =} get (@var{q}, @var{"key1"}, @var{"key2"}, @dots{}) ## Access key values of quaternion objects. ## ## @strong{Keys} ## @table @var ## @item w ## Return scalar part @var{w} of quaternion @var{q} as a built-in type. ## ## @item x, y, z ## Return component @var{x}, @var{y} or @var{z} of the vector part of ## quaternion @var{q} as a built-in type. ## ## @item s ## Return scalar part of quaternion @var{q}. The vector part of @var{q} ## is set to zero. ## ## @item v ## Return vector part of quaternion @var{q}. The scalar part of @var{q} ## is set to zero. ## @end table ## @end deftypefn ## Author: Lukas Reichlin ## Created: April 2014 ## Version: 0.1 function varargout = get (q, varargin) if (! isa (q, "quaternion")) error ("quaternion: get: first argument must be a quaternion"); endif if (! all (cellfun (@ischar, varargin))) error ("quaternion: get: key names must be strings"); endif if (nargin == 1) [keys, vals] = keys_vals (q); nrows = numel (keys); str = strjust (strvcat (keys), "right"); str = horzcat (repmat (" ", nrows, 1), str, repmat (": ", nrows, 1), strvcat (vals)); disp (str); else for k = 1 : (nargin-1) key = varargin{k}; idx = substruct (".", key); varargout{k} = subsref (q, idx); endfor endif endfunction quaternion/inst/@quaternion/gt.m0000644000076500000240000000260612505453300016300 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## Greater-than operator for two quaternions. ## Used by Octave for "q1 > q2". ## The ordering is lexicographic. ## Author: Lukas Reichlin ## Created: December 2013 ## Version: 0.1 function bool = gt (a, b) if (nargin != 2) error ("quaternion: gt: this is a binary operator"); endif a = quaternion (a); b = quaternion (b); bool = (a.w > b.w) ... | (a.w == b.w & a.x > b.x) ... | (a.w == b.w & a.x == b.x & a.y > b.y) ... | (a.w == b.w & a.x == b.x & a.y == b.y & a.z > b.z); endfunction %!test %! a = quaternion (2, 3, 4, 5); %! b = quaternion (2, -3, 4, 5); %! assert (a > b, true); %! assert (b > a, false); quaternion/inst/@quaternion/horzcat.m0000644000076500000240000000214212505453300017333 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## Horizontal concatenation of quaternions. Used by Octave for "[q1, q2]". ## Author: Lukas Reichlin ## Created: May 2010 ## Version: 0.1 function q = horzcat (varargin) tmp = cellfun (@quaternion, varargin); # uniformoutput = true ! w = horzcat (tmp.w); x = horzcat (tmp.x); y = horzcat (tmp.y); z = horzcat (tmp.z); q = quaternion (w, x, y, z); endfunction quaternion/inst/@quaternion/inv.m0000644000076500000240000000341312505453300016457 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{qinv} =} inv (@var{q}) ## Return inverse of a quaternion. ## @end deftypefn ## Author: Lukas Reichlin ## Created: May 2010 ## Version: 0.4 function a = inv (a) if (nargin != 1) print_usage (); endif if (isscalar (a.w)) norm2 = norm2 (a); a.w = a.w / norm2; a.x = -a.x / norm2; a.y = -a.y / norm2; a.z = -a.z / norm2; elseif (issquare (a.w)) ## blockwise inversion, use recursion ## the formula is well-known from linear algebra n = rows (a.w); # a is square m1 = fix (n/2); m2 = m1 + 1; A = subsref (a, substruct ("()", {1:m1, 1:m1})); B = subsref (a, substruct ("()", {1:m1, m2:n})); C = subsref (a, substruct ("()", {m2:n, 1:m1})); D = subsref (a, substruct ("()", {m2:n, m2:n})); iA = inv (A); iAB = iA * B; CiA = C * iA; X = inv (D - C * iAB); Y = X * CiA; a = [iA + iAB*Y, -iAB*X; -Y, X]; else error ("quaternion: inv: require square matrices of quaternions"); endif endfunction quaternion/inst/@quaternion/isempty.m0000644000076500000240000000206312505453300017355 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{bool} =} isempty (@var{q}) ## Return true if quaternion @var{q} is empty and false otherwise. ## @end deftypefn ## Author: Lukas Reichlin ## Created: December 2013 ## Version: 0.1 function bool = isempty (q) if (nargin != 1) print_usage (); endif bool = isempty (q.w); endfunction quaternion/inst/@quaternion/isfinite.m0000644000076500000240000000223712505453300017500 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{bool} =} isfinite (@var{q}) ## Return a logical array which is true where the elements of ## @var{q} are finite values and false where they are not. ## @end deftypefn ## Author: Lukas Reichlin ## Created: December 2013 ## Version: 0.1 function bool = isfinite (q) if (nargin != 1) print_usage (); endif bool = isfinite (q.w) & isfinite (q.x) & isfinite (q.y) & isfinite (q.z); endfunction quaternion/inst/@quaternion/isinf.m0000644000076500000240000000221012505453300016765 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{bool} =} isinf (@var{q}) ## Return a logical array which is true where the elements of ## @var{q} are infinite and false where they are not. ## @end deftypefn ## Author: Lukas Reichlin ## Created: December 2013 ## Version: 0.1 function bool = isinf (q) if (nargin != 1) print_usage (); endif bool = isinf (q.w) | isinf (q.x) | isinf (q.y) | isinf (q.z); endfunction quaternion/inst/@quaternion/isnan.m0000644000076500000240000000221212505453300016767 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{bool} =} isnan (@var{q}) ## Return a logical array which is true where the elements of ## @var{q} are NaN values and false where they are not. ## @end deftypefn ## Author: Lukas Reichlin ## Created: December 2013 ## Version: 0.1 function bool = isnan (q) if (nargin != 1) print_usage (); endif bool = isnan (q.w) | isnan (q.x) | isnan (q.y) | isnan (q.z); endfunction quaternion/inst/@quaternion/ispure.m0000644000076500000240000000210312505453300017165 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{bool} =} ispure (@var{q}) ## Return true if scalar part of quaternion is zero, otherwise return false. ## @end deftypefn ## Author: Lukas Reichlin ## Created: May 2010 ## Version: 0.1 function bool = ispure (a) if (nargin != 1) print_usage (); endif bool = all ((abs (a.w) < eps)(:)); endfunction quaternion/inst/@quaternion/isreal.m0000644000076500000240000000226312505453300017144 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{bool} =} isreal (@var{q}) ## Return true if the vector part of quaternion @var{q} is zero ## and false otherwise. ## @end deftypefn ## Author: Lukas Reichlin ## Created: December 2013 ## Version: 0.1 function bool = isreal (q) if (nargin != 1) print_usage (); endif ## bool = all ((abs(q.x) < eps & abs(q.y) < eps & abs(q.z) < eps)(:)); bool = all ((q.x == 0 & q.y == 0 & q.z == 0)(:)); endfunction quaternion/inst/@quaternion/ldivide.m0000644000076500000240000000201612505453300017301 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## Element-wise left division for quaternions. Used by Octave for "q1 .\\ q2". ## Author: Lukas Reichlin ## Created: May 2010 ## Version: 0.2 function q = ldivide (a, b) if (nargin != 2) error ("quaternion: ldivide: this is a binary operator"); endif q = a.^-1 .* b; endfunction quaternion/inst/@quaternion/le.m0000644000076500000240000000227212505453300016265 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## Less-than-or-equal-to operator for two quaternions. ## Used by Octave for "q1 <= q2". ## The ordering is lexicographic. ## Author: Lukas Reichlin ## Created: December 2013 ## Version: 0.1 function bool = le (a, b) if (nargin != 2) error ("quaternion: le: this is a binary operator"); endif bool = ! gt (a, b); endfunction %!test %! a = quaternion (2, 3, 4, 5); %! b = quaternion (2, -3, 4, 5); %! assert (a <= b, false); %! assert (b <= a, true); quaternion/inst/@quaternion/length.m0000644000076500000240000000231712505453300017146 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{l} =} length (@var{q}) ## Return the "length" @var{l} of the quaternion array @var{q}. ## For quaternion matrices, the length is the number of rows or columns, ## whichever is greater (this odd definition is used for compatibility ## with @acronym{MATLAB}). ## @end deftypefn ## Author: Lukas Reichlin ## Created: December 2013 ## Version: 0.1 function l = length (q) if (nargin != 1) print_usage (); endif l = length (q.w); endfunction quaternion/inst/@quaternion/log.m0000644000076500000240000000335212505453300016446 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{qlog} =} log (@var{q}) ## Logarithmus naturalis of a quaternion. ## @end deftypefn ## Author: Lukas Reichlin ## Created: November 2011 ## Version: 0.1 function q = log (q) if (nargin != 1) print_usage (); endif normq = abs (q); normv = normv (q); acossq = acos (q.w ./ normq); q.w = log (normq); q.x = (q.x ./ normv) .* acossq; q.y = (q.y ./ normv) .* acossq; q.z = (q.z ./ normv) .* acossq; ## FIXME: q = quaternion (2, 3, 4, 5) ## p = log (exp (q)) ## p.v is wrong, probably somehow related to acos ## NOTE: p = exp (log (q)) is calculated correctly ## NOTE: qtfm 1.9 returns the same "wrong" result endfunction %!shared A, B %! Aw = [2, 6, 10; 14, 18, 22]; %! Ax = [3, 7, 11; 15, 19, 23]; %! Ay = [4, 8, 12; 16, 20, 24]; %! Az = [5, 9, 13; 17, 21, 25]; %! A = quaternion (Aw, Ax, Ay, Az); %! %! B = exp (log (A)); %! %!assert (A.w, B.w, 1e-4); %!assert (A.x, B.x, 1e-4); %!assert (A.y, B.y, 1e-4); %!assert (A.z, B.z, 1e-4); quaternion/inst/@quaternion/lt.m0000644000076500000240000000260712505453300016306 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## Less-than operator for two quaternions. ## Used by Octave for "q1 < q2". ## The ordering is lexicographic. ## Author: Lukas Reichlin ## Created: December 2013 ## Version: 0.1 function bool = lt (a, b) if (nargin != 2) error ("quaternion: lt: this is a binary operator"); endif a = quaternion (a); b = quaternion (b); bool = (a.w < b.w) ... | (a.w == b.w & a.x < b.x) ... | (a.w == b.w & a.x == b.x & a.y < b.y) ... | (a.w == b.w & a.x == b.x & a.y == b.y & a.z < b.z); endfunction %!test %! a = quaternion (2, 3, 4, 5); %! b = quaternion (2, -3, 4, 5); %! assert (a < b, false); %! assert (b < a, true); quaternion/inst/@quaternion/mean.m0000644000076500000240000000315312505453300016604 0ustar lukasstaff## Copyright (C) 2013 Willem Atsma ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{q} =} mean (@var{q}) ## @deftypefnx {Function File} {@var{q} =} mean (@var{q}, @var{dim}) ## @deftypefnx {Function File} {@var{q} =} mean (@var{q}, @var{opt}) ## @deftypefnx {Function File} {@var{q} =} mean (@var{q}, @var{dim}, @var{opt}) ## Compute the mean of the elements of the quaternion array @var{q}. ## ## @example ## mean (q) = mean (q.w) + mean (q.x)*i + mean (q.y)*j + mean (q.z)*k ## @end example ## ## See @code{help mean} for more information and a description of the ## parameters @var{dim} and @var{opt}. ## @end deftypefn ## Author: Willem Atsma ## Created: June 2013 ## Version: 0.1 function q = mean (q, varargin) if (! isa (q, "quaternion")) print_usage (); endif w = mean (q.w, varargin{:}); x = mean (q.x, varargin{:}); y = mean (q.y, varargin{:}); z = mean (q.z, varargin{:}); q = quaternion (w, x, y, z); endfunction quaternion/inst/@quaternion/minus.m0000644000076500000240000000217312505453300017020 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## Subtraction of two quaternions. Used by Octave for "q1 - q2". ## Author: Lukas Reichlin ## Created: May 2010 ## Version: 0.2 function q = minus (a, b) if (nargin != 2) error ("quaternion: minus: this is a binary operator"); endif a = quaternion (a); b = quaternion (b); w = a.w - b.w; x = a.x - b.x; y = a.y - b.y; z = a.z - b.z; q = quaternion (w, x, y, z); endfunction quaternion/inst/@quaternion/mldivide.m0000644000076500000240000000201212505453300017452 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## Matrix left division for quaternions. Used by Octave for "q1 \\ q2". ## Author: Lukas Reichlin ## Created: May 2010 ## Version: 0.2 function q = mldivide (a, b) if (nargin != 2) error ("quaternion: mldivide: this is a binary operator"); endif q = inv (a) * b; endfunction quaternion/inst/@quaternion/mpower.m0000644000076500000240000000367412505453300017205 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## Matrix power operator of quaternions. Used by Octave for "q^x". ## Author: Lukas Reichlin ## Created: May 2010 ## Version: 0.2 function q = mpower (a, b) if (nargin != 2) error ("quaternion: mpower: this is a binary operator"); endif [r, c] = size (a); if (r != c) error ("quaternion: mpower: quaternion matrix must be square"); endif if (r == 1 && c == 1) # a scalar, b? q = a .^ b; # b could be a quaternion elseif (is_real_array (b) && isscalar (b) && fix (b) == b) e = fix (abs (b)); switch (sign (b)) case -1 # q^-e a = inv (a); q = a; case 0 # q^0 q = eye (r); # alternative: q = quaternion (eye (r)) return; case 1; # q^e q = a; endswitch for k = 2 : e q *= a; # improvement?: q^8 = ((q^2)^2)^2, q^9 = (((q^2)^2)^2)*q endfor else error ("quaternion: mpower: case not implemented yet"); q = expm (logm (a) * b); # don't know whether this formula is correct endif ## TODO: - q1 ^ q2 ## - arrays endfunction quaternion/inst/@quaternion/mrdivide.m0000644000076500000240000000201212505453300017460 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## Matrix right division for quaternions. Used by Octave for "q1 / q2". ## Author: Lukas Reichlin ## Created: May 2010 ## Version: 0.2 function q = mrdivide (a, b) if (nargin != 2) error ("quaternion: mrdivide: this is a binary operator"); endif q = a * inv (b); endfunction quaternion/inst/@quaternion/mtimes.m0000644000076500000240000000236612505453300017167 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## Matrix multiplication of two quaternions. Used by Octave for "q1 * q2". ## Author: Lukas Reichlin ## Created: May 2010 ## Version: 0.2 function q = mtimes (a, b) if (nargin != 2) error ("quaternion: mtimes: this is a binary operator"); endif a = quaternion (a); b = quaternion (b); w = a.w*b.w - a.x*b.x - a.y*b.y - a.z*b.z; x = a.y*b.z - a.z*b.y + a.w*b.x + a.x*b.w; y = a.z*b.x - a.x*b.z + a.w*b.y + a.y*b.w; z = a.x*b.y - a.y*b.x + a.w*b.z + a.z*b.w; q = quaternion (w, x, y, z); endfunction quaternion/inst/@quaternion/ndims.m0000644000076500000240000000232412505453300016775 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{n} =} ndims (@var{q}) ## Return the number of dimensions of quaternion @var{q}. ## For any array, the result will always be larger than or equal to 2. ## Trailing singleton dimensions are not counted. ## @end deftypefn ## Author: Lukas Reichlin ## Created: December 2013 ## Version: 0.1 function n = ndims (q) if (nargin != 1) print_usage (); endif n = ndims (q.w); endfunction %!test %! assert (ndims (quaternion (ones (4, 1, 2, 1))), 3); quaternion/inst/@quaternion/ne.m0000644000076500000240000000221512505453300016264 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## Not-equal-to operator for two quaternions. Used by Octave for "q1 != q2". ## Author: Lukas Reichlin ## Created: December 2013 ## Version: 0.1 function bool = ne (a, b) if (nargin != 2) error ("quaternion: ne: this is a binary operator"); endif bool = ! eq (a, b); endfunction %!test %! a = quaternion (2, 3, 4, 5); %! b = quaternion (2, -3, 4, 5); %! assert (a != a, false); %! assert (a != b, true); quaternion/inst/@quaternion/norm.m0000644000076500000240000000227212505453300016640 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{n} =} norm (@var{q}) ## Norm of a quaternion. ## @end deftypefn ## Author: Lukas Reichlin ## Created: November 2011 ## Version: 0.1 function n = norm (a) if (nargin != 1) print_usage (); endif if (! isscalar (a.w)) warning ("norm: use 'abs' to calculate the lengths of quaternion arrays"); error ("norm: only the 2-norm of scalar quaternions is implemented until now"); endif n = abs (a); endfunction quaternion/inst/@quaternion/numel.m0000644000076500000240000000255512505453300017011 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{n} =} numel (@var{q}) ## @deftypefnx {Function File} {@var{n} =} numel (@var{q}, @var{idx1}, @var{idx2}, @dots{}) ## For internal use only, use @code{prod(size(q))} or @code{numel (q.w)} instead. ## For technical reasons, this method must return the number of elements which are ## returned from cs-list indexing, no matter whether it is called with one or more ## arguments. ## @end deftypefn ## Author: Lukas Reichlin ## Created: February 2015 ## Version: 0.1 function ret = numel (q, varargin) ret = builtin ("numel", q, varargin{:}); endfunction %!test %! assert (numel (quaternion (eye (3))), 1); quaternion/inst/@quaternion/plus.m0000644000076500000240000000210612505453300016644 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## Addition of two quaternions. Used by Octave for "q1 + q2". ## Author: Lukas Reichlin ## Created: May 2010 ## Version: 0.2 function q = plus (varargin) tmp = cellfun (@quaternion, varargin); # uniformoutput = true ! w = plus (tmp.w); x = plus (tmp.x); y = plus (tmp.y); z = plus (tmp.z); q = quaternion (w, x, y, z); endfunction quaternion/inst/@quaternion/power.m0000644000076500000240000000373612505453300017027 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## Copyright (c) 2011 Juan Pablo Carbajal ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## Power operator of quaternions. Used by Octave for "q.^x". ## Exponent x can be scalar or of appropriate size. ## Author: Lukas Reichlin ## Created: May 2010 ## Version: 0.4 function a = power (a, b) if (nargin != 2) error ("quaternion: power: this is a binary operator"); endif if (isa (b, "quaternion")) # exponent is a quaternion a = exp (log (a) .* b); # a could be real, but log doesn't care elseif (! isreal (b)) error ("quaternion:invalidArgument", "quaternion: power: invalid exponent"); elseif (b == -1) # special case for ldivide and rdivide norm2 = norm2 (a); # a is quaternion because b is not, a.w = a.w ./ norm2; # otherwise octave wouldn't call a.x = -a.x ./ norm2; # quaternion's power operator. a.y = -a.y ./ norm2; a.z = -a.z ./ norm2; else # exponent is real na = abs (a); nv = normv (a); th = acos (a.w ./ na); nab = na.^b; snt = sin (b.*th); a.w = nab .* cos (b.*th); a.x = (a.x ./ nv) .* nab .* snt; a.y = (a.y ./ nv) .* nab .* snt; a.z = (a.z ./ nv) .* nab .* snt; endif endfunction quaternion/inst/@quaternion/private/0000755000076500000240000000000012505453300017156 5ustar lukasstaffquaternion/inst/@quaternion/private/keys_vals.m0000644000076500000240000000334112505453300021335 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{keys}, @var{vals}] =} keys_vals (@var{q}) ## Return the list of keys as well as the assignable values for a quaternion q. ## @end deftypefn ## Author: Lukas Reichlin ## Created: April 2014 ## Version: 0.1 function [keys, vals] = keys_vals (q) str = num2str (size (q), "%d "); str = regexprep (str, " ", "x"); ## cell vector of keys keys = {"w"; "x"; "y"; "z"; "s"; "v"}; ## cell vector of values vals = {sprintf("real-valued array of type '%s', dimensions (%s)", class (q.w), str); sprintf("real-valued array of type '%s', dimensions (%s)", class (q.x), str); sprintf("real-valued array of type '%s', dimensions (%s)", class (q.y), str); sprintf("real-valued array of type '%s', dimensions (%s)", class (q.z), str); sprintf("scalar part of type 'quaternion', dimensions (%s)", str); sprintf("vector part of type 'quaternion', dimensions (%s)", str)}; endfunction quaternion/inst/@quaternion/private/norm2.m0000644000076500000240000000176712505453300020404 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{norm2} =} norm2 (@var{q}) ## Return squared norm of a quaternion. ## @end deftypefn ## Author: Lukas Reichlin ## Created: November 2011 ## Version: 0.1 function ret = norm2 (a) ret = a.w.^2 + a.x.^2 + a.y.^2 + a.z.^2; endfunction quaternion/inst/@quaternion/private/normv.m0000644000076500000240000000176012505453300020501 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{normv} =} normv (@var{q}) ## Return norm of the vector part. ## @end deftypefn ## Author: Lukas Reichlin ## Created: November 2011 ## Version: 0.1 function ret = normv (a) ret = sqrt (a.x.^2 + a.y.^2 + a.z.^2); endfunction quaternion/inst/@quaternion/quaternion.m0000644000076500000240000000620312505453300020050 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{q} =} quaternion (@var{w}) ## @deftypefnx {Function File} {@var{q} =} quaternion (@var{x}, @var{y}, @var{z}) ## @deftypefnx {Function File} {@var{q} =} quaternion (@var{w}, @var{x}, @var{y}, @var{z}) ## Constructor for quaternions - create or convert to quaternion. ## ## @example ## q = w + x*i + y*j + z*k ## @end example ## ## Arguments @var{w}, @var{x}, @var{y} and @var{z} can be scalars, ## matrices or n-dimensional arrays, but they must be real-valued ## and of equal size. ## If scalar part @var{w} or components @var{x}, @var{y} and @var{z} ## of the vector part are not specified, zero matrices of appropriate ## size are assumed. ## ## @strong{Example} ## @example ## @group ## octave:1> q = quaternion (2) ## q = 2 + 0i + 0j + 0k ## ## octave:2> q = quaternion (3, 4, 5) ## q = 0 + 3i + 4j + 5k ## ## octave:3> q = quaternion (2, 3, 4, 5) ## q = 2 + 3i + 4j + 5k ## @end group ## @end example ## @example ## @group ## octave:4> w = [2, 6, 10; 14, 18, 22]; ## octave:5> x = [3, 7, 11; 15, 19, 23]; ## octave:6> y = [4, 8, 12; 16, 20, 24]; ## octave:7> z = [5, 9, 13; 17, 21, 25]; ## octave:8> q = quaternion (w, x, y, z) ## q.w = ## 2 6 10 ## 14 18 22 ## ## q.x = ## 3 7 11 ## 15 19 23 ## ## q.y = ## 4 8 12 ## 16 20 24 ## ## q.z = ## 5 9 13 ## 17 21 25 ## ## octave:9> ## @end group ## @end example ## ## @end deftypefn ## Author: Lukas Reichlin ## Created: May 2010 ## Version: 0.3 function q = quaternion (a, b, c, d) switch (nargin) case 1 if (isa (a, "quaternion")) # quaternion (q) q = a; return; elseif (is_real_array (a)) # quaternion (w) b = c = d = zeros (size (a), class (a)); else print_usage (); endif case 3 # quaternion (x, y, z) d = c; c = b; b = a; a = zeros (size (a), class (a)); case 4 # quaternion (w, x, y, z) ## nothing to do here, just prevent case "otherwise" otherwise print_usage (); endswitch if (! is_real_array (a, b, c, d)) error ("quaternion: arguments must be real-valued scalars, matrices or n-dimensional arrays"); endif if (! size_equal (a, b, c, d)); error ("quaternion: arguments must have identical sizes"); endif q = class (struct ("w", a, "x", b, "y", c, "z", d), "quaternion"); endfunction quaternion/inst/@quaternion/rdivide.m0000644000076500000240000000201612505453300017307 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## Element-wise right division for quaternions. Used by Octave for "q1 ./ q2". ## Author: Lukas Reichlin ## Created: May 2010 ## Version: 0.2 function q = rdivide (a, b) if (nargin != 2) error ("quaternion: rdivide: this is a binary operator"); endif q = a .* b.^-1; endfunction quaternion/inst/@quaternion/repmat.m0000644000076500000240000000315112505453300017152 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{qret} =} repmat (@var{q}, @var{m}) ## @deftypefnx {Function File} {@var{qret} =} repmat (@var{q}, @var{m}, @var{n}) ## @deftypefnx {Function File} {@var{qret} =} repmat (@var{q}, [@var{m} @var{n}]) ## @deftypefnx {Function File} {@var{qret} =} repmat (@var{q}, [@var{m} @var{n} @var{p} @dots{}]) ## Form a block quaternion matrix @var{qret} of size @var{m} by @var{n}, ## with a copy of quaternion matrix @var{q} as each element. ## If @var{n} is not specified, form an @var{m} by @var{m} block matrix. ## @end deftypefn ## Author: Lukas Reichlin ## Created: July 2014 ## Version: 0.1 function q = repmat (a, varargin) if (! isa (a, "quaternion")) print_usage (); endif w = repmat (a.w, varargin{:}); x = repmat (a.x, varargin{:}); y = repmat (a.y, varargin{:}); z = repmat (a.z, varargin{:}); q = quaternion (w, x, y, z); endfunction quaternion/inst/@quaternion/reshape.m0000644000076500000240000000320512505453300017311 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{q} =} reshape (@var{q}, @var{m}, @var{n}, @dots{}) ## @deftypefnx {Function File} {@var{q} =} reshape (@var{q}, [@var{m} @var{n} @dots{}]) ## @deftypefnx {Function File} {@var{q} =} reshape (@var{q}, @dots{}, [], @dots{}) ## @deftypefnx {Function File} {@var{q} =} reshape (@var{q}, @var{size}) ## Return a quaternion array with the specified dimensions (@var{m}, @var{n}, @dots{}) ## whose elements are taken from the quaternion array @var{q}. The elements of the ## quaternion are accessed in column-major order (like Fortran arrays are stored). ## @end deftypefn ## Author: Lukas Reichlin ## Created: December 2013 ## Version: 0.1 function q = reshape (q, varargin) if (! isa (q, "quaternion")) print_usage (); endif q.w = reshape (q.w, varargin{:}); q.x = reshape (q.x, varargin{:}); q.y = reshape (q.y, varargin{:}); q.z = reshape (q.z, varargin{:}); endfunction quaternion/inst/@quaternion/round.m0000644000076500000240000000216012505453300017010 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{q} =} round (@var{q}) ## Round the components of quaternion @var{q} towards the nearest integers. ## @end deftypefn ## Author: Lukas Reichlin ## Created: December 2013 ## Version: 0.1 function q = round (q) if (nargin != 1) print_usage (); endif q.w = round (q.w); q.x = round (q.x); q.y = round (q.y); q.z = round (q.z); endfunction quaternion/inst/@quaternion/rows.m0000644000076500000240000000203112505453300016650 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{nr} =} rows (@var{q}) ## Return number of rows @var{nr} of quaternion array @var{q}. ## @end deftypefn ## Author: Lukas Reichlin ## Created: May 2010 ## Version: 0.1 function r = rows (a) if (nargin != 1) print_usage (); endif r = rows (a.w); endfunction quaternion/inst/@quaternion/set.m0000644000076500000240000000576712505453300016474 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {} set (@var{q}) ## @deftypefnx {Function File} {} set (@var{q}, @var{"key"}, @var{value}, @dots{}) ## @deftypefnx {Function File} {@var{qret} =} set (@var{q}, @var{"key"}, @var{value}, @dots{}) ## Set or modify properties of quaternion objects. ## If no return argument @var{qret} is specified, the modified quaternion object is stored ## in input argument @var{q}. @command{set} can handle multiple keys in one call: ## @code{set (q, 'key1', val1, 'key2', val2, 'key3', val3)}. ## @code{set (q)} prints a list of the object's key names. ## ## @strong{Keys} ## @table @var ## @item w ## Assign real-valued array @var{val} to scalar part @var{w} of quaternion @var{q}. ## ## @item x, y, z ## Assign real-valued array @var{val} to component @var{x}, @var{y} or @var{z} ## of the vector part of quaternion @var{q}. ## ## @item s ## Assign scalar part of quaternion @var{val} to scalar part of quaternion @var{q}. ## The vector part of @var{q} is left untouched. ## ## @item v ## Assign vector part of quaternion @var{val} to vector part of quaternion @var{q}. ## The scalar part of @var{q} is left untouched. ## @end table ## @end deftypefn ## Author: Lukas Reichlin ## Created: April 2014 ## Version: 0.1 function qret = set (q, varargin) if (! isa (q, "quaternion")) error ("quaternion: set: first argument must be a quaternion"); endif if (nargin == 1) # set (q) [keys, vals] = keys_vals (q); nrows = numel (keys); str = strjust (strvcat (keys), "right"); str = horzcat (repmat (" ", nrows, 1), str, repmat (": ", nrows, 1), strvcat (vals)); disp (str); if (nargout != 0) qret = q; endif else # set (q, "key", val, ...) if (rem (nargin-1, 2)) error ("quaternion: set: keys and values must come in pairs"); endif if (! all (cellfun (@ischar, varargin(1:2:end)))) error ("quaternion: set: key names must be strings"); endif for k = 1 : 2: (nargin-1) key = varargin{k}; val = varargin{k+1}; idx = substruct (".", key); q = subsasgn (q, idx, val); endfor if (nargout == 0) # set (q, "key1", val1, ...) assignin ("caller", inputname (1), q); else # q = set (q, "key1", val1, ...) qret = q; endif endif endfunction quaternion/inst/@quaternion/size.m0000644000076500000240000000442212505453300016636 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{nvec} =} size (@var{q}) ## @deftypefnx {Function File} {@var{n} =} size (@var{q}, @var{dim}) ## @deftypefnx {Function File} {[@var{nx}, @var{ny}, @dots{}] =} size (@var{q}) ## Return size of quaternion arrays. ## ## @strong{Inputs} ## @table @var ## @item q ## Quaternion object. ## @item dim ## If given a second argument, @command{size} will return the size of the ## corresponding dimension. ## @end table ## ## @strong{Outputs} ## @table @var ## @item nvec ## Row vector. The first element is the number of rows and the second ## element the number of columns. If @var{q} is an n-dimensional array ## of quaternions, the n-th element of @var{nvec} corresponds to the ## size of the n-th dimension of @var{q}. ## @item n ## Scalar value. The size of the dimension @var{dim}. ## @item nx ## Number of rows. ## @item ny ## Number of columns. ## @item @dots{} ## Sizes of the 3rd to n-th dimensions. ## @end table ## @end deftypefn ## Author: Lukas Reichlin ## Created: May 2010 ## Version: 0.2 function varargout = size (a, b) switch (nargout) case {0, 1} switch (nargin) case 1 # nvec = size (q) varargout{1} = size (a.w); case 2 # n = size (q, dim) varargout{1} = size (a.w, b); otherwise print_usage (); endswitch otherwise if (nargin == 1) # [nx, ny, ...] = size (q) varargout = num2cell (size (a.w)); else print_usage (); endif endswitch endfunction quaternion/inst/@quaternion/size_equal.m0000644000076500000240000000236212505453300020026 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{bool} =} size_equal (@var{a}, @var{b}, @dots{}) ## Return true if quaternions (and matrices) @var{a}, @var{b}, @dots{} ## are of equal size and false otherwise. ## @end deftypefn ## Author: Lukas Reichlin ## Created: October 2012 ## Version: 0.1 function bool = size_equal (varargin) s = cellfun (@size, varargin, "uniformoutput", false); bool = (nargin == 1 || isequal (s{:})); # isequal errors out with only 1 argument, nargin==0 handled by built-in size_equal endfunction quaternion/inst/@quaternion/sparse.m0000644000076500000240000000220412505453300017155 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{sq} =} sparse (@var{fq}) ## Return a sparse quaternion representation @var{sq} from ## full quaternion @var{fq}. ## @end deftypefn ## Author: Lukas Reichlin ## Created: December 2013 ## Version: 0.1 function q = sparse (q) if (nargin != 1) print_usage (); endif q.w = sparse (q.w); q.x = sparse (q.x); q.y = sparse (q.y); q.z = sparse (q.z); endfunction quaternion/inst/@quaternion/squeeze.m0000644000076500000240000000244512505453300017350 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{qret} =} squeeze (@var{q}) ## Remove singleton dimensions from quaternion @var{q} and return the result. ## Note that for compatibility with @acronym{MATLAB}, all objects have a minimum ## of two dimensions and row vectors are left unchanged. ## @end deftypefn ## Author: Lukas Reichlin ## Created: December 2013 ## Version: 0.1 function ret = squeeze (q) if (nargin != 1) print_usage (); endif w = squeeze (q.w); x = squeeze (q.x); y = squeeze (q.y); z = squeeze (q.z); ret = quaternion (w, x, y, z); endfunction quaternion/inst/@quaternion/subsasgn.m0000644000076500000240000001017712505453300017515 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## Subscripted assignment for quaternions. ## Used by Octave for "q.key = value". ## ## @strong{Subscripts} ## @table @var ## @item q.w ## Assign real-valued array @var{val} to scalar part @var{w} of quaternion @var{q}. ## ## @item q.x, q.y, q.z ## Assign real-valued array @var{val} to component @var{x}, @var{y} or @var{z} ## of the vector part of quaternion @var{q}. ## ## @item q.s ## Assign scalar part of quaternion @var{val} to scalar part of quaternion @var{q}. ## The vector part of @var{q} is left untouched. ## ## @item q.v ## Assign vector part of quaternion @var{val} to vector part of quaternion @var{q}. ## The scalar part of @var{q} is left untouched. ## ## @item q(@dots{}) ## Assign @var{val} to certain elements of quaternion array @var{q}, e.g. @code{q(3, 2:end) = val}. ## @end table ## Author: Lukas Reichlin ## Created: November 2011 ## Version: 0.3 function q = subsasgn (q, idx, val) switch (idx(1).type) case "()" # q(...) = val if (length (idx(1).subs) == 1 && isa (val, "quaternion")) # required by horzcat, vertcat, cat, ... q(idx(1).subs{:}) = val; # q = cellfun (@quaternion, varargin) else # general case val = quaternion (val); w = subsasgn (q.w, idx, val.w); x = subsasgn (q.x, idx, val.x); y = subsasgn (q.y, idx, val.y); z = subsasgn (q.z, idx, val.z); q = quaternion (w, x, y, z); endif case "." # q.w = val if (is_real_array (val)) if (! size_equal (subsref (q.w, idx(2:end)), val)) error ("quaternion: subsasgn: invalid argument size (%s), require dimensions (%s)", ... regexprep (num2str (size (val), "%d "), " ", "x"), ... regexprep (num2str (size (subsref (q.w, idx(2:end))), "%d "), " ", "x")); endif switch (tolower (idx(1).subs)) case {"w", "e"} q.w = subsasgn (q.w, idx(2:end), val); case {"x", "i"} q.x = subsasgn (q.x, idx(2:end), val); case {"y", "j"} q.y = subsasgn (q.y, idx(2:end), val); case {"z", "k"} q.z = subsasgn (q.z, idx(2:end), val); otherwise error ("quaternion: subsasgn: invalid subscript name '%s'", idx(1).subs); endswitch elseif (isa (val, "quaternion")) if (! size_equal (subsref (q.w, idx(2:end)), val.w)) error ("quaternion: subsasgn: invalid argument size (%s), require dimensions (%s)", ... regexprep (num2str (size (val), "%d "), " ", "x"), ... regexprep (num2str (size (subsref (q.w, idx(2:end))), "%d "), " ", "x")); endif switch (tolower (idx(1).subs)) case "s" q.w = subsasgn (q.w, idx(2:end), val.w); case "v" q.x = subsasgn (q.x, idx(2:end), val.x); q.y = subsasgn (q.y, idx(2:end), val.y); q.z = subsasgn (q.z, idx(2:end), val.z); otherwise error ("quaternion: subsasgn: invalid subscript name '%s'", idx(1).subs); endswitch else error ("quaternion: subsasgn: invalid argument type, require real-valued array"); endif otherwise error ("quaternion: subsasgn: invalid subscript type '%s'", idx(1).type); endswitch endfunction quaternion/inst/@quaternion/subsref.m0000644000076500000240000000540112505453300017333 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## Subscripted reference for quaternions. Used by Octave for "q.w". ## ## @strong{Subscripts} ## @table @var ## @item q.w ## Return scalar part @var{w} of quaternion @var{q} as a built-in type. ## ## @item q.x, q.y, q.z ## Return component @var{x}, @var{y} or @var{z} of the vector part of ## quaternion @var{q} as a built-in type. ## ## @item q.s ## Return scalar part of quaternion @var{q}. The vector part of @var{q} ## is set to zero. ## ## @item q.v ## Return vector part of quaternion @var{q}. The scalar part of @var{q} ## is set to zero. ## ## @item q(@dots{}) ## Extract certain elements of quaternion array @var{q}, e.g. @code{q(3, 2:end)}. ## @end table ## Author: Lukas Reichlin ## Created: May 2010 ## Version: 0.6 function ret = subsref (q, s) if (numel (s) == 0) ret = q; return; endif switch (s(1).type) case "." # q.w switch (tolower (s(1).subs)) case {"w", "e"} # scalar part, returned as built-in type ret = subsref (q.w, s(2:end)); case {"x", "i"} ret = subsref (q.x, s(2:end)); case {"y", "j"} ret = subsref (q.y, s(2:end)); case {"z", "k"} ret = subsref (q.z, s(2:end)); case "s" # scalar part, vector part set to zero q.x = q.y = q.z = zeros (size (q.w), class (q.w)); ret = subsref (q, s(2:end)); case "v" # vector part, scalar part set to zero q.w = zeros (size (q.w), class (q.w)); ret = subsref (q, s(2:end)); otherwise error ("quaternion: invalid subscript name '%s'", s(1).subs); endswitch case "()" # q(...) w = subsref (q.w, s(1)); x = subsref (q.x, s(1)); y = subsref (q.y, s(1)); z = subsref (q.z, s(1)); tmp = quaternion (w, x, y, z); ret = subsref (tmp, s(2:end)); otherwise error ("quaternion: invalid subscript type '%s'", s(1).type); endswitch endfunction quaternion/inst/@quaternion/sum.m0000644000076500000240000000305012505453300016464 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{q} =} sum (@var{q}) ## @deftypefnx {Function File} {@var{q} =} sum (@var{q}, @var{dim}) ## @deftypefnx {Function File} {@var{q} =} sum (@dots{}, @var{'native'}) ## @deftypefnx {Function File} {@var{q} =} sum (@dots{}, @var{'double'}) ## @deftypefnx {Function File} {@var{q} =} sum (@dots{}, @var{'extra'}) ## Sum of elements along dimension @var{dim}. If @var{dim} is omitted, ## it defaults to the first non-singleton dimension. ## See @code{help sum} for more information. ## @end deftypefn ## Author: Lukas Reichlin ## Created: December 2013 ## Version: 0.1 function q = sum (q, varargin) if (! isa (q, "quaternion")) print_usage (); endif q.w = sum (q.w, varargin{:}); q.x = sum (q.x, varargin{:}); q.y = sum (q.y, varargin{:}); q.z = sum (q.z, varargin{:}); endfunction quaternion/inst/@quaternion/times.m0000644000076500000240000000245412505453300017010 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## Element-wise multiplication of two quaternions. Used by Octave for "q1 .* q2". ## Author: Lukas Reichlin ## Created: May 2010 ## Version: 0.2 function q = times (a, b) if (nargin != 2) error ("quaternion: times: this is a binary operator"); endif a = quaternion (a); b = quaternion (b); w = a.w .* b.w - a.x .* b.x - a.y .* b.y - a.z .* b.z; x = a.y .* b.z - a.z .* b.y + a.w .* b.x + a.x .* b.w; y = a.z .* b.x - a.x .* b.z + a.w .* b.y + a.y .* b.w; z = a.x .* b.y - a.y .* b.x + a.w .* b.z + a.z .* b.w; q = quaternion (w, x, y, z); endfunction quaternion/inst/@quaternion/transpose.m0000644000076500000240000000203612505453300017701 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## Transpose of a quaternion. Used by Octave for "q.'". ## Author: Lukas Reichlin ## Created: May 2010 ## Version: 0.1 function a = transpose (a) if (nargin != 1) print_usage (); endif a.w = transpose (a.w); a.x = transpose (a.x); a.y = transpose (a.y); a.z = transpose (a.z); endfunction quaternion/inst/@quaternion/tril.m0000644000076500000240000000334412505453300016640 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{q} =} tril (@var{q}) ## @deftypefnx {Function File} {@var{q} =} tril (@var{q}, @var{k}) ## @deftypefnx {Function File} {@var{q} =} tril (@var{q}, @var{k}, @var{'pack'}) ## Return a new quaternion matrix formed by extracting the lower ## triangular part of the quaternion @var{q}, and setting all ## other elements to zero. The second argument @var{k} is optional, ## and specifies how many diagonals above or below the main diagonal ## should also be included. Default value for @var{k} is zero. ## If the option "pack" is given as third argument, the extracted ## elements are not inserted into a matrix, but rather stacked ## column-wise one above other. ## @end deftypefn ## Author: Lukas Reichlin ## Created: December 2013 ## Version: 0.1 function q = tril (q, varargin) if (! isa (q, "quaternion")) print_usage (); endif q.w = tril (q.w, varargin{:}); q.x = tril (q.x, varargin{:}); q.y = tril (q.y, varargin{:}); q.z = tril (q.z, varargin{:}); endfunction quaternion/inst/@quaternion/triu.m0000644000076500000240000000334412505453300016651 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{q} =} triu (@var{q}) ## @deftypefnx {Function File} {@var{q} =} triu (@var{q}, @var{k}) ## @deftypefnx {Function File} {@var{q} =} triu (@var{q}, @var{k}, @var{'pack'}) ## Return a new quaternion matrix formed by extracting the upper ## triangular part of the quaternion @var{q}, and setting all ## other elements to zero. The second argument @var{k} is optional, ## and specifies how many diagonals above or below the main diagonal ## should also be included. Default value for @var{k} is zero. ## If the option "pack" is given as third argument, the extracted ## elements are not inserted into a matrix, but rather stacked ## column-wise one above other. ## @end deftypefn ## Author: Lukas Reichlin ## Created: December 2013 ## Version: 0.1 function q = triu (q, varargin) if (! isa (q, "quaternion")) print_usage (); endif q.w = triu (q.w, varargin{:}); q.x = triu (q.x, varargin{:}); q.y = triu (q.y, varargin{:}); q.z = triu (q.z, varargin{:}); endfunction quaternion/inst/@quaternion/uminus.m0000644000076500000240000000203112505453300017176 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## Unary minus of a quaternion. Used by Octave for "-q". ## Author: Lukas Reichlin ## Created: May 2010 ## Version: 0.2 function a = uminus (a) if (nargin != 1) error ("quaternion: uminus: this is an unary operator"); endif a.w = -a.w; a.x = -a.x; a.y = -a.y; a.z = -a.z; endfunction quaternion/inst/@quaternion/unit.m0000644000076500000240000000220612505453300016641 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{qn} =} unit (@var{q}) ## Normalize quaternion to length 1 (unit quaternion). ## ## @example ## q = w + x*i + y*j + z*k ## unit (q) = q ./ sqrt (w.^2 + x.^2 + y.^2 + z.^2) ## @end example ## @end deftypefn ## Author: Lukas Reichlin ## Created: November 2011 ## Version: 0.1 function q = unit (a) if (nargin != 1) print_usage (); endif q = a ./ abs (a); endfunction quaternion/inst/@quaternion/uplus.m0000644000076500000240000000177312505453300017042 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## Unary plus of a quaternion. Used by Octave for "+q". ## Author: Lukas Reichlin ## Created: November 2011 ## Version: 0.2 function a = uplus (a) if (nargin != 1) error ("quaternion: uplus: this is an unary operator"); endif ## nothing to do here endfunction quaternion/inst/@quaternion/vertcat.m0000644000076500000240000000214012505453300017327 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## Vertical concatenation of quaternions. Used by Octave for "[q1; q2]". ## Author: Lukas Reichlin ## Created: May 2010 ## Version: 0.1 function q = vertcat (varargin) tmp = cellfun (@quaternion, varargin); # uniformoutput = true ! w = vertcat (tmp.w); x = vertcat (tmp.x); y = vertcat (tmp.y); z = vertcat (tmp.z); q = quaternion (w, x, y, z); endfunction quaternion/inst/q2rot.m0000644000076500000240000001000212505453300014435 0ustar lukasstaff## Copyright (C) 1998, 1999, 2000, 2002, 2005, 2006, 2007 Auburn University ## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{axis}, @var{angle}] =} q2rot (@var{q}) ## @deftypefnx {Function File} {[@var{axis}, @var{angle}, @var{qn}] =} q2rot (@var{q}) ## Extract vector/angle form of a unit quaternion @var{q}. ## ## @strong{Inputs} ## @table @var ## @item q ## Unit quaternion describing the rotation. ## Quaternion @var{q} can be a scalar or an array. ## In the latter case, @var{q} is reshaped to a row vector ## and the return values @var{axis} and @var{angle} are ## concatenated horizontally, accordingly. ## @end table ## ## @strong{Outputs} ## @table @var ## @item axis ## Eigenaxis as a 3-d unit vector @code{[x; y; z]}. ## If input argument @var{q} is a quaternion array, ## @var{axis} becomes a matrix where ## @var{axis(:,i)} corresponds to @var{q(i)}. ## @item angle ## Rotation angle in radians. The positive direction is ## determined by the right-hand rule applied to @var{axis}. ## The angle lies in the interval [0, 2*pi]. ## If input argument @var{q} is a quaternion array, ## @var{angle} becomes a row vector where ## @var{angle(i)} corresponds to @var{q(i)}. ## @item qn ## Optional output of diagnostic nature. ## @code{qn = reshape (q, 1, [])} or, if needed, ## @code{qn = reshape (unit (q), 1, [])}. ## @end table ## ## @strong{Example} ## @example ## @group ## octave:1> axis = [0; 0; 1] ## axis = ## ## 0 ## 0 ## 1 ## ## octave:2> angle = pi/4 ## angle = 0.78540 ## octave:3> q = rot2q (axis, angle) ## q = 0.9239 + 0i + 0j + 0.3827k ## octave:4> [vv, th] = q2rot (q) ## vv = ## ## 0 ## 0 ## 1 ## ## th = 0.78540 ## octave:5> theta = th*180/pi ## theta = 45.000 ## octave:6> ## @end group ## @end example ## ## @end deftypefn ## Adapted from: quaternion by A. S. Hodel ## Author: Lukas Reichlin ## Created: May 2010 ## Version: 0.4 function [vv, theta, q] = q2rot (q) if (nargin != 1 || nargout > 3) print_usage (); endif if (! isa (q, "quaternion")) error ("q2rot: require quaternion as input"); endif if (any (abs (abs (q) - 1) > 1e-12)) warning ("q2rot:normalizing", "q2rot: abs(q) != 1, normalizing"); q = unit (q); # do we still need this with the atan2 formula? endif q = reshape (q, 1, []); # row vector ## According to Wikipedia, ## ## the formula using atan2 ## theta = 2 * atan2 (||x||, s) ## should be numerically more stable than ## theta = 2 * acos (s) ## Possibly it helps if the quaternion has not exactly unit length. vv = [q.x; q.y; q.z]; norm_vv = norm (vv, 2, "cols"); theta = 2 * atan2 (norm_vv, q.w); ## NOTE: sin (theta/2) = norm (vv) idx = (norm_vv != 0); if (any (idx)) vv(:, idx) ./= ones (3, 1) * norm_vv(idx); # normalize vectors, prevent division by zero endif idx = ! idx; if (any (idx)) vv(:, idx) = [1; 0; 0] * ones (1, nnz (idx)); # set real-valued quaternions to default value endif endfunction %!test %! q = quaternion (2, 0, 0, 0); %! w = warning ("query", "q2rot:normalizing"); %! warning ("off", w.identifier); %! [vv, th, qn] = q2rot (q); %! warning (w.identifier, w.state); %! assert (vv, [1; 0; 0], 1e-4); %! assert (th, 0, 1e-4); %! assert (qn == quaternion (1), true); quaternion/inst/qi.m0000644000076500000240000000243612505453300014013 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {} qi ## Create x-component of a quaternion's vector part. ## ## @example ## q = w + x*qi + y*qj + z*qk ## @end example ## ## @strong{Example} ## @example ## @group ## octave:1> q1 = quaternion (1, 2, 3, 4) ## q1 = 1 + 2i + 3j + 4k ## octave:2> q2 = 1 + 2*qi + 3*qj + 4*qk ## q2 = 1 + 2i + 3j + 4k ## octave:3> ## @end group ## @end example ## ## @end deftypefn ## Author: Lukas Reichlin ## Created: May 2010 ## Version: 0.1 function q = qi if (nargin != 0) print_usage (); endif q = quaternion (0, 1, 0, 0); endfunction quaternion/inst/qj.m0000644000076500000240000000243612505453300014014 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {} qj ## Create y-component of a quaternion's vector part. ## ## @example ## q = w + x*qi + y*qj + z*qk ## @end example ## ## @strong{Example} ## @example ## @group ## octave:1> q1 = quaternion (1, 2, 3, 4) ## q1 = 1 + 2i + 3j + 4k ## octave:2> q2 = 1 + 2*qi + 3*qj + 4*qk ## q2 = 1 + 2i + 3j + 4k ## octave:3> ## @end group ## @end example ## ## @end deftypefn ## Author: Lukas Reichlin ## Created: May 2010 ## Version: 0.1 function q = qj if (nargin != 0) print_usage (); endif q = quaternion (0, 0, 1, 0); endfunction quaternion/inst/qk.m0000644000076500000240000000243612505453300014015 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {} qk ## Create z-component of a quaternion's vector part. ## ## @example ## q = w + x*qi + y*qj + z*qk ## @end example ## ## @strong{Example} ## @example ## @group ## octave:1> q1 = quaternion (1, 2, 3, 4) ## q1 = 1 + 2i + 3j + 4k ## octave:2> q2 = 1 + 2*qi + 3*qj + 4*qk ## q2 = 1 + 2i + 3j + 4k ## octave:3> ## @end group ## @end example ## ## @end deftypefn ## Author: Lukas Reichlin ## Created: May 2010 ## Version: 0.1 function q = qk if (nargin != 0) print_usage (); endif q = quaternion (0, 0, 0, 1); endfunction quaternion/inst/rot2q.m0000644000076500000240000000650112505453300014446 0ustar lukasstaff## Copyright (C) 1998, 1999, 2000, 2002, 2005, 2006, 2007 Auburn University ## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{q} =} rot2q (@var{axis}, @var{angle}) ## Create unit quaternion @var{q} which describes a rotation of ## @var{angle} radians about the vector @var{axis}. This function uses ## the active convention where the vector @var{axis} is rotated by @var{angle} ## radians. If the coordinate frame should be rotated by @var{angle} ## radians, also called the passive convention, this is equivalent ## to rotating the @var{axis} by @var{-angle} radians. ## ## @strong{Inputs} ## @table @var ## @item axis ## Vector @code{[x, y, z]} or @code{[x; y; z]} describing the axis of rotation. ## @item angle ## Rotation angle in radians. The positive direction is ## determined by the right-hand rule applied to @var{axis}. ## If @var{angle} is a real-valued array, a quaternion array ## @var{q} of the same size is returned. ## @end table ## ## @strong{Outputs} ## @table @var ## @item q ## Unit quaternion describing the rotation. ## If @var{angle} is an array, @var{q(i,j)} corresponds to ## the rotation angle @var{angle(i,j)}. ## @end table ## ## @strong{Example} ## @example ## @group ## octave:1> axis = [0, 0, 1]; ## octave:2> angle = pi/4; ## octave:3> q = rot2q (axis, angle) ## q = 0.9239 + 0i + 0j + 0.3827k ## octave:4> v = quaternion (1, 1, 0) ## v = 0 + 1i + 1j + 0k ## octave:5> vr = q * v * conj (q) ## vr = 0 + 0i + 1.414j + 0k ## octave:6> ## @end group ## @end example ## ## @end deftypefn ## Adapted from: quaternion by A. S. Hodel ## Author: Lukas Reichlin ## Created: May 2010 ## Version: 0.2 function q = rot2q (vv, theta) if (nargin != 2 || nargout > 1) print_usage (); endif if (! is_real_array (vv) || ! isvector (vv) || length (vv) != 3) error ("rot2q: first argument 'axis' must be a length three vector"); endif if (! is_real_array (theta)) error ("rot2q: second argument 'angle' must be a scalar"); endif if (norm (vv) == 0) error ("rot2q: first argument 'axis' is zero"); endif if (abs (norm (vv) - 1) > 1e-12) warning ("rot2q:axis", "rot2q: ||axis|| != 1, normalizing") vv = vv / norm (vv); endif if (any ((abs (theta) > 2*pi)(:))) warning ("rot2q:angle", "rot2q: |angle| > 2 pi, normalizing") theta = rem (theta, 2*pi); endif w = cos (theta ./ 2); st2 = sin (theta ./ 2); x = vv(1) .* st2; y = vv(2) .* st2; z = vv(3) .* st2; q = quaternion (w, x, y, z); endfunction %!shared ax, an %! q = rot2q ([1;0;0], -1.2*pi); %! [ax, an] = q2rot (q); %!assert (abs (ax(1)), 1, 1e-4); %!assert (an*ax(1), -1.2*pi, 1e-4); quaternion/inst/rotm2q.m0000644000076500000240000000443512505453300014627 0ustar lukasstaff## Copyright (C) 2013 Willem Atsma ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{q} =} rotm2q (@var{R}) ## Convert 3x3 rotation matrix @var{R} to unit quaternion @var{q}. ## @end deftypefn ## Author: Willem Atsma ## Based on C code from ## Created: May 2013 ## Version: 0.1 function q = rotm2q (R) if (nargin != 1) print_usage (); endif if (! is_real_array (R) || ! isequal (size (R), [3, 3])) error ("rotm2q: require a (3x3) rotation matrix"); endif T = trace (R); if (T > 0) s = 0.5 / sqrt (T+1); w = 0.25 / s; x = (R(3,2) - R(2,3)) * s; y = (R(1,3) - R(3,1)) * s; z = (R(2,1) - R(1,2)) * s; else if (R(1,1) > R(2,2) && R(1,1) > R(3,3)) s = 2 * sqrt (1 + R(1,1) - R(2,2) - R(3,3)); w = (R(3,2) - R(2,3)) / s; x = 0.25 * s; y = (R(1,2) + R(2,1)) / s; z = (R(1,3) + R(3,1)) / s; elseif (R(2,2) > R(3,3)) s = 2 * sqrt (1 + R(2,2) - R(1,1) - R(3,3)); w = (R(1,3) - R(3,1)) / s; x = (R(1,2) + R(2,1)) / s; y = 0.25 * s; z = (R(2,3) + R(3,2) ) / s; else s = 2 * sqrt (1 + R(3,3) - R(1,1) - R(2,2)); w = (R(2,1) - R(1,2)) / s; x = (R(1,3) + R(3,1)) / s; y = (R(2,3) + R(3,2)) / s; z = 0.25 * s; endif endif q = quaternion (w, x, y, z); endfunction %!test %! R = eye (3); %! q = rotm2q (R); %! assert (q.w, 1, 1e-4); %! assert (q.x, 0, 1e-4); %! assert (q.y, 0, 1e-4); %! assert (q.z, 0, 1e-4); %!test %! R = [[1;0;0], [0;0;1], [0;-1;0]]; %! q = rotm2q (R); %! [ax, an] = q2rot (q); %! assert (ax(:), [1;0;0], 1e-4); %! assert (an, pi/2, 1e-4); quaternion/inst/test_quaternion.m0000644000076500000240000000231612505453300016623 0ustar lukasstaff## Copyright (C) 2010-2015 Lukas F. Reichlin ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Script File} {} test_quaternion ## Execute all available tests at once. ## @end deftypefn ## Author: Lukas Reichlin ## Created: December 2011 ## Version: 0.1 test @quaternion/blkdiag test @quaternion/diag test @quaternion/diff test @quaternion/end test @quaternion/eq test @quaternion/ge test @quaternion/gt test @quaternion/le test @quaternion/log test @quaternion/lt test @quaternion/ndims test @quaternion/ne test @quaternion/numel test q2rot test rot2q test rotm2q quaternion/NEWS0000644000076500000240000001465512505454256012767 0ustar lukasstaffSummary of important user-visible changes for releases of the quaternion package =============================================================================== quaternion-2.4.0 Release Date: 2015-03-21 Release Manager: Lukas Reichlin =============================================================================== ** q2rot -- Vectorized code to support the input of multiple quaternions. -- Return axis as a column vector. -- Add test. ** rot2q -- Support for multiple rotation angles (vectorized code). -- Improved error messages. -- Add test. ** The following functions are new: rotm2q ** The following functions are now overloaded for quaternions: mean numel (Thanks to Willem Atsma for all the changes above) ** The quaternion package now depends on Octave version 3.8.0 or beyond. ** In order to comply with modified Octave Forge rules, the package no longer auto-loads. See "help pkg" for details on auto-loading. =============================================================================== quaternion-2.2.2 Release Date: 2014-07-20 Release Manager: Lukas Reichlin =============================================================================== ** q2rot Fixed bug #42666. The function no longer errors out. The bug has been introduced with the changes in quaternion-2.2.1. (Thanks to Kjell Andersen) ** The following functions are now overloaded for quaternions: repmat =============================================================================== quaternion-2.2.1 Release Date: 2014-05-05 Release Manager: Lukas Reichlin =============================================================================== ** The following functions are now overloaded for quaternions: get set While they offer no new editing features compared to subscripted assignment and reference, they can display the types and dimensions of the quaternion's components if called with one argument: get (q) set (q) ** subsasgn, subsref -- Improved documentation. -- Support assignment of scalar and vector part from other quaternions: q1.v = q2 # assign components x, y and z, leave w untouched =============================================================================== quaternion-2.2.0 Release Date: 2014-01-04 Release Manager: Lukas Reichlin =============================================================================== ** eq Changed operator semantics of "==" to match those of complex numbers and other built-in types. Quaternion arrays are now compared element-wise. The old behavior can be restored by the expression bool = size_equal (a, b) && all (eq (a, b)(:)) ** end "end" indexing for quaternions works now as expected. ** The following functions are now overloaded for quaternions: arg isempty reshape cast isfinite round ceil isinf sparse cumsum isnan squeeze fix isreal sum floor length tril full ndims triu ** The following operators are now overloaded for quaternions: ge (>=) le (<=) ne (!=, ~=) gt (>) lt (<) Since there is no ordering that makes quaternions an ordered field, several definitions are possible. The ordering chosen here is the lexicographic one. ** quaternion -- Allow logicals as quaternion components. -- When called with one or three arguments, fill missing vector or scalar part with zeros of the same class as the given arguments. Before, always doubles were used. =============================================================================== quaternion-2.0.3 Release Date: 2013-10-28 Release Manager: Lukas Reichlin =============================================================================== ** Compatibility to GNU Octave 3.8 Replaced line continuation marker "\" by "..." to avoid deprecated syntax warning. ** q2rot -- The rotation angle now lies in the interval [0, 2*pi]. -- Fixed bug #39521. (Thanks to Juan Pablo Carbajal and Max Katsev) http://savannah.gnu.org/bugs/?39521 =============================================================================== quaternion-2.0.2 Release Date: 2012-10-25 Release Manager: Lukas Reichlin =============================================================================== ** eq -- Fix typo bug which gave false positives for the k-component. -- Avoid error if arguments are non-conformant. ** size_equal Add overloaded method because the built-in function gives false positives for quaternions. ** ldivide, mldivide, mpower Show error message if the number of input arguments is not 2. =============================================================================== quaternion-2.0.1 Release Date: 2012-10-14 Release Manager: Lukas Reichlin =============================================================================== ** inv Support for the inversion of quaternion matrices. Right and left division operators (/ and \) profit from this change and support quaternion matrices as well. ** Check number of arguments when operators are called by their function names, e.g. plus (q1, q2, q3). Function plus supports now more than two arguments. ** doc/quaternion.pdf Revised PDF manual. There is now a function index at the end of the manual. ** The TeX-files quaternion.tex and functions.texi for generating quaternion.pdf are included in the doc folder, next to quaternion.pdf. Note that functions.texi is generated automatically by the scripts in the quaternion/devel folder and the package generate_html. They are not included in the quaternion package and can be found on the OctaveForge SVN server. =============================================================================== quaternion-2.0.0 Release Date: 2012-03-28 Release Manager: Lukas Reichlin =============================================================================== ** First official release. Its main features are: -- Matrices and n-dimensional arrays of quaternions. -- Overloaded operators due to the use of classes. -- Operator semantics similar to Octave’s built-in complex numbers. -- Vectorized code for crunching large quaternion arrays in a speedy manner. =============================================================================== quaternion/src/0000755000076500000240000000000012505453300013031 5ustar lukasstaffquaternion/src/is_real_array.cc0000644000076500000240000000327112505453300016157 0ustar lukasstaff/* Copyright (C) 2010-2015 Lukas F. Reichlin This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program. If not, see . Return true if all arguments are real-valued arrays and false otherwise. Author: Lukas Reichlin Created: November 2011 Version: 0.3 */ #include DEFUN_DLD (is_real_array, args, nargout, "-*- texinfo -*-\n\ @deftypefn {Loadable Function} {} is_real_array (@var{a}, @dots{})\n\ Return true if all arguments are real-valued arrays and false otherwise.\n\ @var{[]} is a valid array.\n\ Avoid nasty stuff like @code{true = isreal (\"a\")}.\n\ @end deftypefn") { octave_value retval = true; octave_idx_type nargin = args.length (); if (nargin == 0) { print_usage (); } else { for (octave_idx_type i = 0; i < nargin; i++) { // args(i).ndims () should be always >= 2 if (args(i).ndims () < 2 || ! ((args(i).is_numeric_type () && args(i).is_real_type ()) || args(i).is_bool_type ())) { retval = false; break; } } } return retval; } quaternion/src/Makefile0000644000076500000240000000025412505453300014472 0ustar lukasstaffall: is_real_array.oct # helper is_real_array.oct: is_real_array.cc mkoctfile is_real_array.cc clean: rm -rf *.o core octave-core *.oct *~ realclean: clean rm -rf *.a