Mercurial > octave
view libinterp/corefcn/eig.cc @ 21747:61f3575250e4
rats: Fix round-off corner case for 32-bit systems (bug #47964)
* pr-output.cc (rational_approx): Invert convergence test to prevent
aborting early due to round-off error in 32-bit environments. Use std::abs
instead of fabs.
author | Mike Miller <mtmiller@octave.org> |
---|---|
date | Thu, 19 May 2016 15:47:24 -0700 |
parents | aba2e6293dd8 |
children | 112b20240c87 |
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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/>. */ #if defined (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]) */