Mercurial > jwe > octave
view libinterp/corefcn/gsvd.cc @ 31120:d8d90ba892b0
maint: Merge stable to default.
author | Markus Mützel <markus.muetzel@gmx.de> |
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date | Mon, 04 Jul 2022 21:36:48 +0200 |
parents | 796f54d4ddbf |
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//////////////////////////////////////////////////////////////////////// // // Copyright (C) 1997-2022 The Octave Project Developers // // See the file COPYRIGHT.md in the top-level directory of this // distribution or <https://octave.org/copyright/>. // // 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 // <https://www.gnu.org/licenses/>. // //////////////////////////////////////////////////////////////////////// #ifdef HAVE_CONFIG_H # include <config.h> #endif #include "dMatrix.h" #include "CMatrix.h" #include "dDiagMatrix.h" #include "gsvd.h" #include "defun.h" #include "defun-int.h" #include "error.h" #include "errwarn.h" #include "utils.h" #include "ovl.h" #include "ov.h" OCTAVE_NAMESPACE_BEGIN template <typename T> static typename math::gsvd<T>::Type gsvd_type (int nargout, int nargin) { if (nargout == 0 || nargout == 1) return octave::math::gsvd<T>::Type::sigma_only; else if (nargin < 3) return octave::math::gsvd<T>::Type::std; else return octave::math::gsvd<T>::Type::economy; } // Named do_gsvd to avoid conflicts with the gsvd class itself. template <typename T> static octave_value_list do_gsvd (const T& A, const T& B, const octave_idx_type nargout, const octave_idx_type nargin, bool is_single = false) { math::gsvd<T> result (A, B, gsvd_type<T> (nargout, nargin)); octave_value_list retval (nargout); if (nargout <= 1) { if (is_single) { FloatMatrix sigA = result.singular_values_A (); FloatMatrix sigB = result.singular_values_B (); for (int i = sigA.rows () - 1; i >= 0; i--) sigA.xelem (i) /= sigB.xelem (i); retval(0) = sigA.sort (); } else { Matrix sigA = result.singular_values_A (); Matrix sigB = result.singular_values_B (); for (int i = sigA.rows () - 1; i >= 0; i--) sigA.xelem (i) /= sigB.xelem (i); retval(0) = sigA.sort (); } } else { switch (nargout) { case 5: retval(4) = result.singular_values_B (); OCTAVE_FALLTHROUGH; case 4: retval(3) = result.singular_values_A (); OCTAVE_FALLTHROUGH; case 3: retval(2) = result.right_singular_matrix (); } retval(1) = result.left_singular_matrix_B (); retval(0) = result.left_singular_matrix_A (); } return retval; } DEFUN (gsvd, args, nargout, doc: /* -*- texinfo -*- @deftypefn {} {@var{S} =} gsvd (@var{A}, @var{B}) @deftypefnx {} {[@var{U}, @var{V}, @var{X}, @var{C}, @var{S}] =} gsvd (@var{A}, @var{B}) @deftypefnx {} {[@var{U}, @var{V}, @var{X}, @var{C}, @var{S}] =} gsvd (@var{A}, @var{B}, 0) Compute the generalized singular value decomposition of (@var{A}, @var{B}). The generalized singular value decomposition is defined by the following relations: @tex $$ A = U C X^\dagger $$ $$ B = V S X^\dagger $$ $$ C^\dagger C + S^\dagger S = eye (columns (A)) $$ @end tex @ifnottex @example @group A = U*C*X' B = V*S*X' C'*C + S'*S = eye (columns (A)) @end group @end example @end ifnottex The function @code{gsvd} normally returns just the vector of generalized singular values @tex $$ \sqrt{{{diag (C^\dagger C)} \over {diag (S^\dagger S)}}} $$ @end tex @ifnottex @code{sqrt (diag (C'*C) ./ diag (S'*S))}. @end ifnottex If asked for five return values, it also computes @tex $U$, $V$, $X$, and $C$. @end tex @ifnottex U, V, X, and C. @end ifnottex If the optional third input is present, @code{gsvd} constructs the "economy-sized" decomposition where the number of columns of @var{U}, @var{V} and the number of rows of @var{C}, @var{S} is less than or equal to the number of columns of @var{A}. This option is not yet implemented. Programming Note: the code is a wrapper to the corresponding @sc{lapack} dggsvd and zggsvd routines. If matrices @var{A} and @var{B} are @emph{both} rank deficient then @sc{lapack} will return an incorrect factorization. Programmers should avoid this combination. @seealso{svd} @end deftypefn */) { int nargin = args.length (); if (nargin < 2 || nargin > 3) print_usage (); else if (nargin == 3) { // FIXME: when "economy" is implemented delete this code warning ("gsvd: economy-sized decomposition is not yet implemented, returning full decomposition"); nargin = 2; } octave_value_list retval; octave_value argA = args(0); octave_value argB = args(1); if (argA.columns () != argB.columns ()) error ("gsvd: A and B must have the same number of columns"); if (argA.is_single_type () || argB.is_single_type ()) { if (argA.isreal () && argB.isreal ()) { FloatMatrix tmpA = argA.xfloat_matrix_value ("gsvd: A must be a real or complex matrix"); FloatMatrix tmpB = argB.xfloat_matrix_value ("gsvd: B must be a real or complex matrix"); if (tmpA.any_element_is_inf_or_nan ()) error ("gsvd: A cannot have Inf or NaN values"); if (tmpB.any_element_is_inf_or_nan ()) error ("gsvd: B cannot have Inf or NaN values"); retval = do_gsvd (tmpA, tmpB, nargout, nargin, true); } else if (argA.iscomplex () || argB.iscomplex ()) { FloatComplexMatrix ctmpA = argA.xfloat_complex_matrix_value ("gsvd: A must be a real or complex matrix"); FloatComplexMatrix ctmpB = argB.xfloat_complex_matrix_value ("gsvd: B must be a real or complex matrix"); if (ctmpA.any_element_is_inf_or_nan ()) error ("gsvd: A cannot have Inf or NaN values"); if (ctmpB.any_element_is_inf_or_nan ()) error ("gsvd: B cannot have Inf or NaN values"); retval = do_gsvd (ctmpA, ctmpB, nargout, nargin, true); } else error ("gsvd: A and B must be real or complex matrices"); } else { if (argA.isreal () && argB.isreal ()) { Matrix tmpA = argA.xmatrix_value ("gsvd: A must be a real or complex matrix"); Matrix tmpB = argB.xmatrix_value ("gsvd: B must be a real or complex matrix"); if (tmpA.any_element_is_inf_or_nan ()) error ("gsvd: A cannot have Inf or NaN values"); if (tmpB.any_element_is_inf_or_nan ()) error ("gsvd: B cannot have Inf or NaN values"); retval = do_gsvd (tmpA, tmpB, nargout, nargin); } else if (argA.iscomplex () || argB.iscomplex ()) { ComplexMatrix ctmpA = argA.xcomplex_matrix_value ("gsvd: A must be a real or complex matrix"); ComplexMatrix ctmpB = argB.xcomplex_matrix_value ("gsvd: B must be a real or complex matrix"); if (ctmpA.any_element_is_inf_or_nan ()) error ("gsvd: A cannot have Inf or NaN values"); if (ctmpB.any_element_is_inf_or_nan ()) error ("gsvd: B cannot have Inf or NaN values"); retval = do_gsvd (ctmpA, ctmpB, nargout, nargin); } else error ("gsvd: A and B must be real or complex matrices"); } return retval; } /* ## Basic tests of decomposition %!test <60273> %! A = reshape (1:15,5,3); %! B = magic (3); %! [U,V,X,C,S] = gsvd (A,B); %! assert (size (U), [5, 5]); %! assert (size (V), [3, 3]); %! assert (size (X), [3, 3]); %! assert (size (C), [5, 3]); %! assert (C(4:5, :), zeros (2,3)); %! assert (size (S), [3, 3]); %! assert (U*C*X', A, 50*eps); %! assert (V*S*X', B, 50*eps); %! S0 = gsvd (A, B); %! assert (size (S0), [3, 1]); %! S1 = sort (svd (A / B)); %! assert (S0, S1, 10*eps); %!test <60273> %! A = reshape (1:15,3,5); %! B = magic (5); %! [U,V,X,C,S] = gsvd (A,B); %! assert (size (U), [3, 3]); %! assert (size (V), [5, 5]); %! assert (size (X), [5, 5]); %! assert (size (C), [3, 5]); %! assert (C(:, 4:5), zeros (3,2)); %! assert (size (S), [5, 5]); %! assert (U*C*X', A, 120*eps); # less accurate in this orientation %! assert (V*S*X', B, 150*eps); # for some reason. %! S0 = gsvd (A, B); %! assert (size (S0), [5, 1]); %! S0 = S0(3:end); %! S1 = sort (svd (A / B)); %! assert (S0, S1, 20*eps); ## a few tests for gsvd.m %!shared A, A0, B, B0, U, V, C, S, X, old_state, restore_state %! old_state = randn ("state"); %! restore_state = onCleanup (@() randn ("state", old_state)); %! randn ("state", 40); # initialize generator to make behavior reproducible %! A0 = randn (5, 3); %! B0 = diag ([1 2 4]); %! A = A0; %! B = B0; ## A (5x3) and B (3x3) are full rank %!test <48807> %! [U, V, X, C, S] = gsvd (A, B); %! assert (C'*C + S'*S, eye (3), 5*eps); %! assert (U*C*X', A, 10*eps); %! assert (V*S*X', B, 20*eps); ## A: 5x3 full rank, B: 3x3 rank deficient %!test <48807> %! B(2, 2) = 0; %! [U, V, X, C, S] = gsvd (A, B); %! assert (C'*C + S'*S, eye (3), 5*eps); %! assert (U*C*X', A, 10*eps); %! assert (V*S*X', B, 20*eps); ## A: 5x3 rank deficient, B: 3x3 full rank %!test <48807> %! B = B0; %! A(:, 3) = 2*A(:, 1) - A(:, 2); %! [U, V, X, C, S] = gsvd (A, B); %! assert (C'*C + S'*S, eye (3), 5*eps); %! assert (U*C*X', A, 10*eps); %! assert (V*S*X', B, 20*eps); ## A and B are both rank deficient ## FIXME: LAPACK seems to be completely broken for this case %!#test <48807> %! B(:, 3) = 2*B(:, 1) - B(:, 2); %! [U, V, X, C, S] = gsvd (A, B); %! assert (C'*C + S'*S, eye (3), 5*eps); %! assert (U*C*X', A, 10*eps); %! assert (V*S*X', B, 20*eps); ## A (now 3x5) and B (now 5x5) are full rank %!test <48807> %! A = A0.'; %! B0 = diag ([1 2 4 8 16]); %! B = B0; %! [U, V, X, C, S] = gsvd (A, B); %! assert (C'*C + S'*S, eye (5), 5*eps); %! assert (U*C*X', A, 15*eps); %! assert (V*S*X', B, 85*eps); ## A: 3x5 full rank, B: 5x5 rank deficient %!test <48807> %! B(2, 2) = 0; %! [U, V, X, C, S] = gsvd (A, B); %! assert (C'*C + S'*S, eye (5), 5*eps); %! assert (U*C*X', A, 15*eps); %! assert (V*S*X', B, 85*eps); ## A: 3x5 rank deficient, B: 5x5 full rank %!test <48807> %! B = B0; %! A(3, :) = 2*A(1, :) - A(2, :); %! [U, V, X, C, S] = gsvd (A, B); %! assert (C'*C + S'*S, eye (5), 5*eps); %! assert (U*C*X', A, 15*eps); %! assert (V*S*X', B, 85*eps); ## A and B are both rank deficient ## FIXME: LAPACK seems to be completely broken for this case %!#test <48807> %! A = A0.'; B = B0.'; %! A(:, 3) = 2*A(:, 1) - A(:, 2); %! B(:, 3) = 2*B(:, 1) - B(:, 2); %! [U, V, X, C, S] = gsvd (A, B); %! assert (C'*C + S'*S, eye (3), 5*eps); %! assert (U*C*X', A, 10*eps); %! assert (V*S*X', B, 20*eps); ## A: 5x3 complex full rank, B: 3x3 complex full rank %!test <48807> %! A0 = A0 + j*randn (5, 3); %! B0 = diag ([1 2 4]) + j*diag ([4 -2 -1]); %! A = A0; %! B = B0; %! [U, V, X, C, S] = gsvd (A, B); %! assert (C'*C + S'*S, eye (3), 5*eps); %! assert (U*C*X', A, 10*eps); %! assert (V*S*X', B, 25*eps); ## A: 5x3 complex full rank, B: 3x3 complex rank deficient %!test <48807> %! B(2, 2) = 0; %! [U, V, X, C, S] = gsvd (A, B); %! assert (C'*C + S'*S, eye (3), 5*eps); %! assert (U*C*X', A, 10*eps); %! assert (V*S*X', B, 25*eps); ## A: 5x3 complex rank deficient, B: 3x3 complex full rank %!test <48807> %! B = B0; %! A(:, 3) = 2*A(:, 1) - A(:, 2); %! [U, V, X, C, S] = gsvd (A, B); %! assert (C'*C + S'*S, eye (3), 5*eps); %! assert (U*C*X', A, 15*eps); %! assert (V*S*X', B, 25*eps); ## A (5x3) and B (3x3) are both complex rank deficient ## FIXME: LAPACK seems to be completely broken for this case %!#test <48807> %! B(:, 3) = 2*B(:, 1) - B(:, 2); %! [U, V, X, C, S] = gsvd (A, B); %! assert (C'*C + S'*S, eye (3), 5*eps); %! assert (U*C*X', A, 10*eps); %! assert (V*S*X', B, 20*eps); ## A (now 3x5) complex and B (now 5x5) complex are full rank ## now, A is 3x5 %!test <48807> %! A = A0.'; %! B0 = diag ([1 2 4 8 16]) + j*diag ([-5 4 -3 2 -1]); %! B = B0; %! [U, V, X, C, S] = gsvd (A, B); %! assert (C'*C + S'*S, eye (5), 5*eps); %! assert (U*C*X', A, 25*eps); %! assert (V*S*X', B, 85*eps); ## A: 3x5 complex full rank, B: 5x5 complex rank deficient %!test <48807> %! B(2, 2) = 0; %! [U, V, X, C, S] = gsvd (A, B); %! assert (C'*C + S'*S, eye (5), 5*eps); %! assert (U*C*X', A, 10*eps); %! assert (V*S*X', B, 85*eps); ## A: 3x5 complex rank deficient, B: 5x5 complex full rank %!test <48807> %! B = B0; %! A(3, :) = 2*A(1, :) - A(2, :); %! [U, V, X, C, S] = gsvd (A, B); %! assert (C'*C + S'*S, eye (5), 5*eps); %! assert (U*C*X', A, 10*eps); %! assert (V*S*X', B, 85*eps); ## A and B are both complex rank deficient ## FIXME: LAPACK seems to be completely broken for this case %!#test <48807> %! A = A0.'; %! B = B0.'; %! A(:, 3) = 2*A(:, 1) - A(:, 2); %! B(:, 3) = 2*B(:, 1) - B(:, 2); %! [U, V, X, C, S] = gsvd (A, B); %! assert (C'*C + S'*S, eye (5), 5*eps); %! assert (U*C*X', A, 10*eps); %! assert (V*S*X', B, 85*eps); ## Test that single inputs produce single outputs %!test %! s = gsvd (single (eye (5)), B); %! assert (class (s), "single"); %! [U,V,X,C,S] = gsvd (single (eye(5)), B); %! assert (class (U), "single"); %! assert (class (V), "single"); %! assert (class (X), "single"); %! assert (class (C), "single"); %! assert (class (S), "single"); %! %! s = gsvd (A, single (eye (5))); %! assert (class (s), "single"); %! [U,V,X,C,S] = gsvd (A, single (eye (5))); %! assert (class (U), "single"); %! assert (class (V), "single"); %! assert (class (X), "single"); %! assert (class (C), "single"); %! assert (class (S), "single"); ## Test input validation %!error <Invalid call> gsvd () %!error <Invalid call> gsvd (1) %!error <Invalid call> gsvd (1,2,3,4) %!warning <economy-sized decomposition is not yet implemented> gsvd (1,2,0); %!error <A and B must have the same number of columns> gsvd (1,[1, 2]) ## Test input validation for single (real and complex) inputs. %!error <A cannot have Inf or NaN values> gsvd (Inf, single (2)) %!error <A cannot have Inf or NaN values> gsvd (NaN, single (2)) %!error <B cannot have Inf or NaN values> gsvd (single (1), Inf) %!error <B cannot have Inf or NaN values> gsvd (single (1), NaN) %!error <A must be a real or complex matrix> gsvd ({1}, single (2i)) %!error <B must be a real or complex matrix> gsvd (single (i), {2}) %!error <A cannot have Inf or NaN values> gsvd (Inf, single (2i)) %!error <A cannot have Inf or NaN values> gsvd (NaN, single (2i)) %!error <B cannot have Inf or NaN values> gsvd (single (i), Inf) %!error <B cannot have Inf or NaN values> gsvd (single (i), NaN) ## Test input validation for single, but not real or complex, inputs. %!error <A and B must be real or complex matrices> gsvd ({1}, single (2)) %!error <A and B must be real or complex matrices> gsvd (single (1), {2}) ## Test input validation for double (real and complex) inputs. %!error <A cannot have Inf or NaN values> gsvd (Inf, 2) %!error <A cannot have Inf or NaN values> gsvd (NaN, 2) %!error <B cannot have Inf or NaN values> gsvd (1, Inf) %!error <B cannot have Inf or NaN values> gsvd (1, NaN) %!error <A must be a real or complex matrix> gsvd ({1}, 2i) %!error <B must be a real or complex matrix> gsvd (i, {2}) %!error <A cannot have Inf or NaN values> gsvd (Inf, 2i) %!error <A cannot have Inf or NaN values> gsvd (NaN, 2i) %!error <B cannot have Inf or NaN values> gsvd (i, Inf) %!error <B cannot have Inf or NaN values> gsvd (i, NaN) ## Test input validation for double, but not real or complex, inputs. %!error <A and B must be real or complex matrices> gsvd ({1}, double (2)) %!error <A and B must be real or complex matrices> gsvd (double (1), {2}) ## Test input validation in liboctave/numeric/gsvd.cc %!error <A and B cannot be empty matrices> gsvd (zeros (0,1), 1) %!error <A and B cannot be empty matrices> gsvd (1, zeros (0,1)) */ OCTAVE_NAMESPACE_END