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author | John W. Eaton <jwe@octave.org> |
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date | Fri, 20 Jan 2017 12:19:08 -0500 |
parents | ee0df00e12d6 |
children | ef4d915df748 3ac9f9ecfae5 |
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/* Copyright (C) 1996-2016 John W. Eaton This file is part of Octave. Octave 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. Octave 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 Octave; see the file COPYING. If not, see <http://www.gnu.org/licenses/>. */ #if defined (HAVE_CONFIG_H) # include "config.h" #endif #include "svd.h" #include "defun.h" #include "error.h" #include "errwarn.h" #include "ovl.h" #include "pr-output.h" #include "utils.h" #include "variables.h" static std::string Vsvd_driver = "gesvd"; template <typename T> static typename octave::math::svd<T>::Type svd_type (int nargin, int nargout) { return ((nargout == 0 || nargout == 1) ? octave::math::svd<T>::Type::sigma_only : ((nargin == 2) ? octave::math::svd<T>::Type::economy : octave::math::svd<T>::Type::std)); } template <typename T> static typename octave::math::svd<T>::Driver svd_driver (void) { return (Vsvd_driver == "gesvd" ? octave::math::svd<T>::Driver::GESVD : octave::math::svd<T>::Driver::GESDD); } DEFUN (svd, args, nargout, doc: /* -*- texinfo -*- @deftypefn {} {@var{s} =} svd (@var{A}) @deftypefnx {} {[@var{U}, @var{S}, @var{V}] =} svd (@var{A}) @deftypefnx {} {[@var{U}, @var{S}, @var{V}] =} svd (@var{A}, @var{econ}) @cindex singular value decomposition Compute the singular value decomposition of @var{A} @tex $$ A = U S V^{\dagger} $$ @end tex @ifnottex @example A = U*S*V' @end example @end ifnottex The function @code{svd} normally returns only the vector of singular values. When called with three return values, it computes @tex $U$, $S$, and $V$. @end tex @ifnottex @var{U}, @var{S}, and @var{V}. @end ifnottex For example, @example svd (hilb (3)) @end example @noindent returns @example @group ans = 1.4083189 0.1223271 0.0026873 @end group @end example @noindent and @example [u, s, v] = svd (hilb (3)) @end example @noindent returns @example @group u = -0.82704 0.54745 0.12766 -0.45986 -0.52829 -0.71375 -0.32330 -0.64901 0.68867 s = 1.40832 0.00000 0.00000 0.00000 0.12233 0.00000 0.00000 0.00000 0.00269 v = -0.82704 0.54745 0.12766 -0.45986 -0.52829 -0.71375 -0.32330 -0.64901 0.68867 @end group @end example If given a second argument, @code{svd} returns an economy-sized decomposition, eliminating the unnecessary rows or columns of @var{U} or @var{V}. @seealso{svd_driver, svds, eig, lu, chol, hess, qr, qz} @end deftypefn */) { int nargin = args.length (); if (nargin < 1 || nargin > 2 || nargout == 2 || nargout > 3) print_usage (); octave_value arg = args(0); if (arg.ndims () != 2) error ("svd: A must be a 2-D matrix"); octave_value_list retval; bool isfloat = arg.is_single_type (); if (isfloat) { if (arg.is_real_type ()) { FloatMatrix tmp = arg.float_matrix_value (); if (tmp.any_element_is_inf_or_nan ()) error ("svd: cannot take SVD of matrix containing Inf or NaN values"); octave::math::svd<FloatMatrix> result (tmp, svd_type<FloatMatrix> (nargin, nargout), svd_driver<FloatMatrix> ()); FloatDiagMatrix sigma = result.singular_values (); if (nargout == 0 || nargout == 1) retval(0) = sigma.extract_diag (); else retval = ovl (result.left_singular_matrix (), sigma, result.right_singular_matrix ()); } else if (arg.is_complex_type ()) { FloatComplexMatrix ctmp = arg.float_complex_matrix_value (); if (ctmp.any_element_is_inf_or_nan ()) error ("svd: cannot take SVD of matrix containing Inf or NaN values"); octave::math::svd<FloatComplexMatrix> result (ctmp, svd_type<FloatComplexMatrix> (nargin, nargout), svd_driver<FloatComplexMatrix> ()); FloatDiagMatrix sigma = result.singular_values (); if (nargout == 0 || nargout == 1) retval(0) = sigma.extract_diag (); else retval = ovl (result.left_singular_matrix (), sigma, result.right_singular_matrix ()); } } else { if (arg.is_real_type ()) { Matrix tmp = arg.matrix_value (); if (tmp.any_element_is_inf_or_nan ()) error ("svd: cannot take SVD of matrix containing Inf or NaN values"); octave::math::svd<Matrix> result (tmp, svd_type<Matrix> (nargin, nargout), svd_driver<Matrix> ()); DiagMatrix sigma = result.singular_values (); if (nargout == 0 || nargout == 1) retval(0) = sigma.extract_diag (); else retval = ovl (result.left_singular_matrix (), sigma, result.right_singular_matrix ()); } else if (arg.is_complex_type ()) { ComplexMatrix ctmp = arg.complex_matrix_value (); if (ctmp.any_element_is_inf_or_nan ()) error ("svd: cannot take SVD of matrix containing Inf or NaN values"); octave::math::svd<ComplexMatrix> result (ctmp, svd_type<ComplexMatrix> (nargin, nargout), svd_driver<ComplexMatrix> ()); DiagMatrix sigma = result.singular_values (); if (nargout == 0 || nargout == 1) retval(0) = sigma.extract_diag (); else retval = ovl (result.left_singular_matrix (), sigma, result.right_singular_matrix ()); } else err_wrong_type_arg ("svd", arg); } return retval; } /* %!assert (svd ([1, 2; 2, 1]), [3; 1], sqrt (eps)) %!test a = [1, 2; 3, 4] + [5, 6; 7, 8]*i; [u,s,v] = svd (a); assert (a, u * s * v', 128 * eps); %!test %! [u, s, v] = svd ([1, 2; 2, 1]); %! x = 1 / sqrt (2); %! assert (u, [-x, -x; -x, x], sqrt (eps)); %! assert (s, [3, 0; 0, 1], sqrt (eps)); %! assert (v, [-x, x; -x, -x], sqrt (eps)); %!test %! a = [1, 2, 3; 4, 5, 6]; %! [u, s, v] = svd (a); %! assert (u * s * v', a, sqrt (eps)); %!test %! a = [1, 2; 3, 4; 5, 6]; %! [u, s, v] = svd (a); %! assert (u * s * v', a, sqrt (eps)); %!test %! a = [1, 2, 3; 4, 5, 6]; %! [u, s, v] = svd (a, 1); %! assert (u * s * v', a, sqrt (eps)); %!test %! a = [1, 2; 3, 4; 5, 6]; %! [u, s, v] = svd (a, 1); %! assert (u * s * v', a, sqrt (eps)); %!assert (svd (single ([1, 2; 2, 1])), single ([3; 1]), sqrt (eps ("single"))) %!test %! [u, s, v] = svd (single ([1, 2; 2, 1])); %! x = single (1 / sqrt (2)); %! assert (u, [-x, -x; -x, x], sqrt (eps ("single"))); %! assert (s, single ([3, 0; 0, 1]), sqrt (eps ("single"))); %! assert (v, [-x, x; -x, -x], sqrt (eps ("single"))); %!test %! a = single ([1, 2, 3; 4, 5, 6]); %! [u, s, v] = svd (a); %! assert (u * s * v', a, sqrt (eps ("single"))); %!test %! a = single ([1, 2; 3, 4; 5, 6]); %! [u, s, v] = svd (a); %! assert (u * s * v', a, sqrt (eps ("single"))); %!test %! a = single ([1, 2, 3; 4, 5, 6]); %! [u, s, v] = svd (a, 1); %! assert (u * s * v', a, sqrt (eps ("single"))); %!test %! a = single ([1, 2; 3, 4; 5, 6]); %! [u, s, v] = svd (a, 1); %! assert (u * s * v', a, sqrt (eps ("single"))); %!test %! a = zeros (0, 5); %! [u, s, v] = svd (a); %! assert (size (u), [0, 0]); %! assert (size (s), [0, 5]); %! assert (size (v), [5, 5]); %!test %! a = zeros (5, 0); %! [u, s, v] = svd (a, 1); %! assert (size (u), [5, 0]); %! assert (size (s), [0, 0]); %! assert (size (v), [0, 0]); %!error svd () %!error svd ([1, 2; 4, 5], 2, 3) %!error [u, v] = svd ([1, 2; 3, 4]) */ DEFUN (svd_driver, args, nargout, doc: /* -*- texinfo -*- @deftypefn {} {@var{val} =} svd_driver () @deftypefnx {} {@var{old_val} =} svd_driver (@var{new_val}) @deftypefnx {} {} svd_driver (@var{new_val}, "local") Query or set the underlying @sc{lapack} driver used by @code{svd}. Currently recognized values are @qcode{"gesvd"} and @qcode{"gesdd"}. The default is @qcode{"gesvd"}. When called from inside a function with the @qcode{"local"} option, the variable is changed locally for the function and any subroutines it calls. The original variable value is restored when exiting the function. @seealso{svd} @end deftypefn */) { static const char *driver_names[] = { "gesvd", "gesdd", 0 }; return SET_INTERNAL_VARIABLE_CHOICES (svd_driver, driver_names); } /* %!test %! A = [1+1i, 1-1i, 0; 0, 2, 0; 1i, 1i, 1+2i]; %! old_driver = svd_driver ("gesvd"); %! [U1, S1, V1] = svd (A); %! svd_driver ("gesdd"); %! [U2, S2, V2] = svd (A); %! assert (U1, U2, 5*eps); %! assert (S1, S2, 5*eps); %! assert (V1, V2, 5*eps); %! svd_driver (old_driver); */