Mercurial > octave
view libinterp/corefcn/eig.cc @ 21226:a55b8ece1ecd
reorganize octave_config_info again
* build-env-features.sh: Don't include ENABLE_ items in the output.
* toplev.cc (find_config_info): New static function.
(Foctave_config_info): Put Octave configuration info in the main
struct. Put the build system features and build environment info in
substructures. Allow searching of all elements by keyword.
* __have_feature__.m, doc/interpreter/testfun.txi:
Fix name of build features substructure element.
* geometryimages.m, interpimages.m, plotimages.m, sparseimages.m,
splineimages.m: Use __have_feature__ to check for OSMESA.
author | John W. Eaton <jwe@octave.org> |
---|---|
date | Mon, 08 Feb 2016 23:14:56 -0500 |
parents | fcac5dbbf9ed |
children | 40de9f8f23a6 |
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/* Copyright (C) 1996-2015 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/>. */ #ifdef HAVE_CONFIG_H # include <config.h> #endif #include "EIG.h" #include "fEIG.h" #include "defun.h" #include "error.h" #include "errwarn.h" #include "ovl.h" #include "utils.h" DEFUN (eig, args, nargout, "-*- texinfo -*-\n\ @deftypefn {} {@var{lambda} =} eig (@var{A})\n\ @deftypefnx {} {@var{lambda} =} eig (@var{A}, @var{B})\n\ @deftypefnx {} {[@var{V}, @var{lambda}] =} eig (@var{A})\n\ @deftypefnx {} {[@var{V}, @var{lambda}] =} eig (@var{A}, @var{B})\n\ Compute the eigenvalues (and optionally the eigenvectors) of a matrix\n\ or a pair of matrices\n\ \n\ The algorithm used depends on whether there are one or two input\n\ matrices, if they are real or complex, and if they are symmetric\n\ (Hermitian if complex) or non-symmetric.\n\ \n\ The eigenvalues returned by @code{eig} are not ordered.\n\ @seealso{eigs, svd}\n\ @end deftypefn") { int nargin = args.length (); if (nargin > 2 || nargin == 0) print_usage (); octave_value_list retval; octave_value arg_a, arg_b; octave_idx_type nr_a, nr_b, nc_a, nc_b; nr_a = nr_b = nc_a = nc_b = 0; arg_a = args(0); nr_a = arg_a.rows (); nc_a = arg_a.columns (); int arg_is_empty = empty_arg ("eig", nr_a, nc_a); if (arg_is_empty < 0) return retval; else if (arg_is_empty > 0) return octave_value_list (2, Matrix ()); if (! arg_a.is_double_type () && ! arg_a.is_single_type ()) err_wrong_type_arg ("eig", arg_a); if (nargin == 2) { arg_b = args(1); nr_b = arg_b.rows (); nc_b = arg_b.columns (); arg_is_empty = empty_arg ("eig", nr_b, nc_b); if (arg_is_empty < 0) return retval; else if (arg_is_empty > 0) return ovl (2, Matrix ()); if (! arg_b.is_single_type () && ! arg_b.is_double_type ()) err_wrong_type_arg ("eig", arg_b); } if (nr_a != nc_a) err_square_matrix_required ("eig", "A"); if (nargin == 2 && nr_b != nc_b) err_square_matrix_required ("eig", "B"); Matrix tmp_a, tmp_b; ComplexMatrix ctmp_a, ctmp_b; FloatMatrix ftmp_a, ftmp_b; FloatComplexMatrix fctmp_a, fctmp_b; if (arg_a.is_single_type ()) { FloatEIG result; if (nargin == 1) { if (arg_a.is_real_type ()) { ftmp_a = arg_a.float_matrix_value (); result = FloatEIG (ftmp_a, nargout > 1); } else { fctmp_a = arg_a.float_complex_matrix_value (); result = FloatEIG (fctmp_a, nargout > 1); } } else if (nargin == 2) { if (arg_a.is_real_type () && arg_b.is_real_type ()) { ftmp_a = arg_a.float_matrix_value (); ftmp_b = arg_b.float_matrix_value (); result = FloatEIG (ftmp_a, ftmp_b, nargout > 1); } else { fctmp_a = arg_a.float_complex_matrix_value (); fctmp_b = arg_b.float_complex_matrix_value (); result = FloatEIG (fctmp_a, fctmp_b, nargout > 1); } } if (nargout == 0 || nargout == 1) { retval = ovl (result.eigenvalues ()); } else { // Blame it on Matlab. FloatComplexDiagMatrix d (result.eigenvalues ()); retval = ovl (result.eigenvectors (), d); } } else { EIG result; if (nargin == 1) { if (arg_a.is_real_type ()) { tmp_a = arg_a.matrix_value (); result = EIG (tmp_a, nargout > 1); } else { ctmp_a = arg_a.complex_matrix_value (); result = EIG (ctmp_a, nargout > 1); } } else if (nargin == 2) { if (arg_a.is_real_type () && arg_b.is_real_type ()) { tmp_a = arg_a.matrix_value (); tmp_b = arg_b.matrix_value (); result = EIG (tmp_a, tmp_b, nargout > 1); } else { ctmp_a = arg_a.complex_matrix_value (); ctmp_b = arg_b.complex_matrix_value (); result = EIG (ctmp_a, ctmp_b, nargout > 1); } } if (nargout == 0 || nargout == 1) { retval = ovl (result.eigenvalues ()); } else { // Blame it on Matlab. ComplexDiagMatrix d (result.eigenvalues ()); retval = ovl (result.eigenvectors (), d); } } return retval; } /* %!assert (eig ([1, 2; 2, 1]), [-1; 3], sqrt (eps)) %!test %! [v, d] = eig ([1, 2; 2, 1]); %! x = 1 / sqrt (2); %! assert (d, [-1, 0; 0, 3], sqrt (eps)); %! assert (v, [-x, x; x, x], sqrt (eps)); %!assert (eig (single ([1, 2; 2, 1])), single ([-1; 3]), sqrt (eps ("single"))) %!test %! [v, d] = eig (single ([1, 2; 2, 1])); %! x = single (1 / sqrt (2)); %! assert (d, single ([-1, 0; 0, 3]), sqrt (eps ("single"))); %! assert (v, [-x, x; x, x], sqrt (eps ("single"))); %!test %! A = [1, 2; -1, 1]; B = [3, 3; 1, 2]; %! [v, d] = eig (A, B); %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps)); %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps)); %!test %! A = single ([1, 2; -1, 1]); B = single ([3, 3; 1, 2]); %! [v, d] = eig (A, B); %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps ("single"))); %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps ("single"))); %!test %! A = [1, 2; 2, 1]; B = [3, -2; -2, 3]; %! [v, d] = eig (A, B); %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps)); %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps)); %!test %! A = single ([1, 2; 2, 1]); B = single ([3, -2; -2, 3]); %! [v, d] = eig (A, B); %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps ("single"))); %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps ("single"))); %!test %! A = [1+3i, 2+i; 2-i, 1+3i]; B = [5+9i, 2+i; 2-i, 5+9i]; %! [v, d] = eig (A, B); %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps)); %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps)); %!test %! A = single ([1+3i, 2+i; 2-i, 1+3i]); B = single ([5+9i, 2+i; 2-i, 5+9i]); %! [v, d] = eig (A, B); %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps ("single"))); %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps ("single"))); %!test %! A = [1+3i, 2+3i; 3-8i, 8+3i]; B = [8+i, 3+i; 4-9i, 3+i]; %! [v, d] = eig (A, B); %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps)); %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps)); %!test %! A = single ([1+3i, 2+3i; 3-8i, 8+3i]); B = single ([8+i, 3+i; 4-9i, 3+i]); %! [v, d] = eig (A, B); %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps ("single"))); %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps ("single"))); %!test %! A = [1, 2; 3, 8]; B = [8, 3; 4, 3]; %! [v, d] = eig (A, B); %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps)); %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps)); %!test %! A = [1, 1+i; 1-i, 1]; B = [2, 0; 0, 2]; %! [v, d] = eig (A, B); %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps)); %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps)); %!test %! A = single ([1, 1+i; 1-i, 1]); B = single ([2, 0; 0, 2]); %! [v, d] = eig (A, B); %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps ("single"))); %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps ("single"))); %!error eig () %!error eig ([1, 2; 3, 4], [4, 3; 2, 1], 1) %!error <EIG requires same size matrices> eig ([1, 2; 3, 4], 2) %!error <must be a square matrix> eig ([1, 2; 3, 4; 5, 6]) %!error <wrong type argument> eig ("abcd") %!error <wrong type argument> eig ([1 2 ; 2 3], "abcd") %!error <wrong type argument> eig (false, [1 2 ; 2 3]) */