Mercurial > jwe > octave
view libinterp/corefcn/gsvd.cc @ 29963:32c3a5805893
move DEFUN and DEFMETHOD functions inside octave namespace
* mk-opts.pl: Surround emitted function definitions with
OCTAVE_NAMESPACE_BEGIN and OCTAVE_NAMESPACE_END tags.
* mk-builtins.pl: Surround emitted function declarations with
OCTAVE_NAMESPACE_BEGIN and OCTAVE_NAMESPACE_END tags. Emit deprecated
global inline functions.
* __betainc__.cc, __contourc__.cc, __dsearchn__.cc, __eigs__.cc,
__expint__.cc, __ftp__.cc, __gammainc__.cc, __ichol__.cc, __ilu__.cc,
__lin_interpn__.cc, __magick_read__.cc, __pchip_deriv__.cc, __qp__.cc,
amd.cc, balance.cc, besselj.cc, bitfcns.cc, bsxfun.cc, call-stack.cc,
ccolamd.cc, cellfun.cc, chol.cc, colamd.cc, colloc.cc, conv2.cc,
daspk.cc, dasrt.cc, dassl.cc, data.cc, debug.cc, defaults.cc,
defun.cc, det.cc, dirfns.cc, display.cc, dlmread.cc, dmperm.cc,
dot.cc, eig.cc, ellipj.cc, environment.cc, error.cc, event-manager.cc,
fcn-info.cc, fft.cc, fft2.cc, fftn.cc, file-io.cc, filter.cc, find.cc,
gcd.cc, getgrent.cc, getpwent.cc, getrusage.cc, givens.cc,
graphics.cc, gsvd.cc, hash.cc, help.cc, hess.cc, hex2num.cc, input.cc,
interpreter.cc, inv.cc, jsondecode.cc, jsonencode.cc, kron.cc,
load-path.cc, load-save.cc, lookup.cc, ls-oct-text.cc, lsode.cc,
lu.cc, mappers.cc, matrix_type.cc, max.cc, mgorth.cc, nproc.cc,
oct-hist.cc, ordqz.cc, ordschur.cc, pager.cc, pinv.cc, pr-flt-fmt.cc,
pr-output.cc, psi.cc, qr.cc, quad.cc, quadcc.cc, qz.cc, rand.cc,
rcond.cc, regexp.cc, schur.cc, settings.cc, sighandlers.cc, sparse.cc,
spparms.cc, sqrtm.cc, stream-euler.cc, strfind.cc, strfns.cc,
sub2ind.cc, svd.cc, sylvester.cc, symbfact.cc, symrcm.cc, symtab.cc,
syscalls.cc, sysdep.cc, time.cc, toplev.cc, tril.cc, tsearch.cc,
typecast.cc, urlwrite.cc, utils.cc, variables.cc, __delaunayn__.cc,
__fltk_uigetfile__.cc, __glpk__.cc, __init_gnuplot__.cc, __ode15__.cc,
__voronoi__.cc, audiodevinfo.cc, audioread.cc, convhulln.cc, fftw.cc,
gzip.cc, ov-base.cc, ov-bool-mat.cc, ov-cell.cc, ov-class.cc,
ov-classdef.cc, ov-fcn-handle.cc, ov-java.cc, ov-null-mat.cc,
ov-oncleanup.cc, ov-struct.cc, ov-typeinfo.cc, ov-usr-fcn.cc, ov.cc,
octave.cc, lex.ll, oct-parse.yy, profiler.cc, pt-eval.cc: Surround
DEFUN and DEFMETHOD function defnitions with OCTAVE_NAMESPACE_BEGIN
and OCTAVE_NAMESPACE_END tags.
author | John W. Eaton <jwe@octave.org> |
---|---|
date | Fri, 13 Aug 2021 21:53:51 -0400 |
parents | 7854d5752dd2 |
children | 7d6709900da7 |
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line source
//////////////////////////////////////////////////////////////////////// // // Copyright (C) 1997-2021 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 octave::math::gsvd<T>::Type gsvd_type (int nargout) { return ((nargout == 0 || nargout == 1) ? octave::math::gsvd<T>::Type::sigma_only : (nargout > 5) ? octave::math::gsvd<T>::Type::std : octave::math::gsvd<T>::Type::economy); } // Named like this to avoid conflicts with the gsvd class. template <typename T> static octave_value_list do_gsvd (const T& A, const T& B, const octave_idx_type nargout, bool is_single = false) { octave::math::gsvd<T> result (A, B, gsvd_type<T> (nargout)); octave_value_list retval (nargout); if (nargout < 2) { if (is_single) { FloatDiagMatrix sigA = result.singular_values_A (); FloatDiagMatrix sigB = result.singular_values_B (); for (int i = sigA.rows () - 1; i >= 0; i--) sigA.dgxelem(i) /= sigB.dgxelem(i); retval(0) = sigA.diag (); } else { DiagMatrix sigA = result.singular_values_A (); DiagMatrix sigB = result.singular_values_B (); for (int i = sigA.rows () - 1; i >= 0; i--) sigA.dgxelem(i) /= sigB.dgxelem(i); retval(0) = sigA.diag (); } } else { retval(0) = result.left_singular_matrix_A (); retval(1) = result.left_singular_matrix_B (); if (nargout > 2) retval(2) = result.right_singular_matrix (); if (nargout > 3) retval(3) = result.singular_values_A (); if (nargout > 4) retval(4) = result.singular_values_B (); if (nargout > 5) retval(5) = result.R_matrix (); } 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. @seealso{svd} @end deftypefn */) { int nargin = args.length (); if (nargin < 2 || nargin > 3) print_usage (); else if (nargin == 3) warning ("gsvd: economy-sized decomposition is not yet implemented, returning full decomposition"); octave_value_list retval; octave_value argA = args(0); octave_value argB = args(1); octave_idx_type nr = argA.rows (); octave_idx_type nc = argA.columns (); octave_idx_type np = argB.columns (); // FIXME: This "special" case should be handled in the gsvd class, not here if (nr == 0 || nc == 0) { retval = octave_value_list (nargout); if (nargout < 2) // S = gsvd (A, B) { if (argA.is_single_type () || argB.is_single_type ()) retval(0) = FloatMatrix (0, 1); else retval(0) = Matrix (0, 1); } else // [U, V, X, C, S, R] = gsvd (A, B) { if (argA.is_single_type () || argB.is_single_type ()) { retval(0) = octave::float_identity_matrix (nc, nc); retval(1) = octave::float_identity_matrix (nc, nc); if (nargout > 2) retval(2) = octave::float_identity_matrix (nr, nr); if (nargout > 3) retval(3) = FloatMatrix (nr, nc); if (nargout > 4) retval(4) = octave::float_identity_matrix (nr, nr); if (nargout > 5) retval(5) = octave::float_identity_matrix (nr, nr); } else { retval(0) = octave::identity_matrix (nc, nc); retval(1) = octave::identity_matrix (nc, nc); if (nargout > 2) retval(2) = octave::identity_matrix (nr, nr); if (nargout > 3) retval(3) = Matrix (nr, nc); if (nargout > 4) retval(4) = octave::identity_matrix (nr, nr); if (nargout > 5) retval(5) = octave::identity_matrix (nr, nr); } } } else { if (nc != np) print_usage (); 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, 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, 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); } 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); } else error ("gsvd: A and B must be real or complex matrices"); } } return retval; } /* ## Basic test of decomposition %!test <48807> %! A = reshape (1:15,5,3); %! B = magic (3); %! [U,V,X,C,S] = gsvd (A,B); %! assert (U*C*X', A, 50*eps); %! assert (V*S*X', B, 50*eps); %! S0 = gsvd (A, B); %! S1 = svd (A / B); %! assert (S0, S1, 10*eps); ## a few tests for gsvd.m %!shared A, A0, B, B0, U, V, C, S, X, R, D1, D2 %! 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, R] = gsvd (A, B); %! D1 = zeros (5, 3); D1(1:3, 1:3) = C; %! D2 = S; %! assert (norm (diag (C).^2 + diag (S).^2 - ones (3, 1)) <= 1e-6); %! assert (norm ((U'*A*X) - D1*R) <= 1e-6); %! assert (norm ((V'*B*X) - D2*R) <= 1e-6); ## A: 5x3 full rank, B: 3x3 rank deficient %!test <48807> %! B(2, 2) = 0; %! [U, V, X, C, S, R] = gsvd (A, B); %! D1 = zeros (5, 3); D1(1, 1) = 1; D1(2:3, 2:3) = C; %! D2 = [zeros(2, 1) S; zeros(1, 3)]; %! assert (norm (diag (C).^2 + diag (S).^2 - ones (2, 1)) <= 1e-6); %! assert (norm ((U'*A*X) - D1*R) <= 1e-6); %! assert (norm ((V'*B*X) - D2*R) <= 1e-6); ## A: 5x3 rank deficient, B: 3x3 full rank %!test <48807> %! B = B0; %! A(:, 3) = 2*A(:, 1) - A(:, 2); %! [U, V, X, C, S, R] = gsvd (A, B); %! D1 = zeros (5, 3); D1(1:3, 1:3) = C; %! D2 = S; %! assert (norm (diag (C).^2 + diag (S).^2 - ones (3, 1)) <= 1e-6); %! assert (norm ((U'*A*X) - D1*R) <= 1e-6); %! assert (norm ((V'*B*X) - D2*R) <= 1e-6); ## A and B are both rank deficient %!test <48807> %! B(:, 3) = 2*B(:, 1) - B(:, 2); %! [U, V, X, C, S, R] = gsvd (A, B); %! D1 = zeros (5, 2); D1(1:2, 1:2) = C; %! D2 = [S; zeros(1, 2)]; %! assert (norm (diag (C).^2 + diag (S).^2 - ones (2, 1)) <= 1e-6); %! assert (norm ((U'*A*X) - D1*[zeros(2, 1) R]) <= 1e-6); %! assert (norm ((V'*B*X) - D2*[zeros(2, 1) R]) <= 1e-6); ## 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, R] = gsvd (A, B); %! D1 = [C zeros(3,2)]; %! D2 = [S zeros(3,2); zeros(2, 3) eye(2)]; %! assert (norm (diag (C).^2 + diag (S).^2 - ones (3, 1)) <= 1e-6); %! assert (norm ((U'*A*X) - D1*R) <= 1e-6); %! assert (norm ((V'*B*X) - D2*R) <= 1e-6); ## A: 3x5 full rank, B: 5x5 rank deficient %!test <48807> %! B(2, 2) = 0; %! [U, V, X, C, S, R] = gsvd (A, B); %! D1 = zeros (3, 5); D1(1, 1) = 1; D1(2:3, 2:3) = C; %! D2 = zeros (5, 5); D2(1:2, 2:3) = S; D2(3:4, 4:5) = eye (2); %! assert (norm (diag (C).^2 + diag (S).^2 - ones (2, 1)) <= 1e-6); %! assert (norm ((U'*A*X) - D1*R) <= 1e-6); %! assert (norm ((V'*B*X) - D2*R) <= 1e-6); ## A: 3x5 rank deficient, B: 5x5 full rank %!test <48807> %! B = B0; %! A(3, :) = 2*A(1, :) - A(2, :); %! [U, V, X, C, S, R] = gsvd (A, B); %! D1 = zeros (3, 5); D1(1:3, 1:3) = C; %! D2 = zeros (5, 5); D2(1:3, 1:3) = S; D2(4:5, 4:5) = eye (2); %! assert (norm (diag (C).^2 + diag (S).^2 - ones (3, 1)) <= 1e-6); %! assert (norm ((U'*A*X) - D1*R) <= 1e-6); %! assert (norm ((V'*B*X) - D2*R) <= 1e-6); ## A and B are both rank deficient %!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, R]=gsvd (A, B); %! D1 = zeros (3, 4); D1(1:3, 1:3) = C; %! D2 = eye (4); D2(1:3, 1:3) = S; D2(5,:) = 0; %! assert (norm (diag (C).^2 + diag (S).^2 - ones (3, 1)) <= 1e-6); %! assert (norm ((U'*A*X) - D1*[zeros(4, 1) R]) <= 1e-6); %! assert (norm ((V'*B*X) - D2*[zeros(4, 1) R]) <= 1e-6); ## 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, R] = gsvd (A, B); %! D1 = zeros (5, 3); D1(1:3, 1:3) = C; %! D2 = S; %! assert (norm (diag (C).^2 + diag (S).^2 - ones (3, 1)) <= 1e-6); %! assert (norm ((U'*A*X) - D1*R) <= 1e-6); %! assert (norm ((V'*B*X) - D2*R) <= 1e-6); ## A: 5x3 complex full rank, B: 3x3 complex rank deficient %!test <48807> %! B(2, 2) = 0; %! [U, V, X, C, S, R] = gsvd (A, B); %! D1 = zeros (5, 3); D1(1, 1) = 1; D1(2:3, 2:3) = C; %! D2 = [zeros(2, 1) S; zeros(1, 3)]; %! assert (norm (diag (C).^2 + diag (S).^2 - ones (2, 1)) <= 1e-6); %! assert (norm ((U'*A*X) - D1*R) <= 1e-6); %! assert (norm ((V'*B*X) - D2*R) <= 1e-6); ## 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, R] = gsvd (A, B); %! D1 = zeros (5, 3); D1(1:3, 1:3) = C; %! D2 = S; %! assert (norm (diag (C).^2 + diag (S).^2 - ones (3, 1)) <= 1e-6); %! assert (norm ((U'*A*X) - D1*R) <= 1e-6); %! assert (norm ((V'*B*X) - D2*R) <= 1e-6); ## A (5x3) and B (3x3) are both complex rank deficient %!test <48807> %! B(:, 3) = 2*B(:, 1) - B(:, 2); %! [U, V, X, C, S, R] = gsvd (A, B); %! D1 = zeros (5, 2); D1(1:2, 1:2) = C; %! D2 = [S; zeros(1, 2)]; %! assert (norm (diag (C).^2 + diag (S).^2 - ones (2, 1)) <= 1e-6); %! assert (norm ((U'*A*X) - D1*[zeros(2, 1) R]) <= 1e-6); %! assert (norm ((V'*B*X) - D2*[zeros(2, 1) R]) <= 1e-6); ## 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, R] = gsvd (A, B); %! D1 = [C zeros(3,2)]; %! D2 = [S zeros(3,2); zeros(2, 3) eye(2)]; %! assert (norm (diag (C).^2 + diag (S).^2 - ones (3, 1)) <= 1e-6); %! assert (norm ((U'*A*X) - D1*R) <= 1e-6); %! assert (norm ((V'*B*X) - D2*R) <= 1e-6); ## A: 3x5 complex full rank, B: 5x5 complex rank deficient %!test <48807> %! B(2, 2) = 0; %! [U, V, X, C, S, R] = gsvd (A, B); %! D1 = zeros (3, 5); D1(1, 1) = 1; D1(2:3, 2:3) = C; %! D2 = zeros (5,5); D2(1:2, 2:3) = S; D2(3:4, 4:5) = eye (2); %! assert (norm (diag (C).^2 + diag (S).^2 - ones (2, 1)) <= 1e-6); %! assert (norm ((U'*A*X) - D1*R) <= 1e-6); %! assert (norm ((V'*B*X) - D2*R) <= 1e-6); ## 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, R] = gsvd (A, B); %! D1 = zeros (3, 5); D1(1:3, 1:3) = C; %! D2 = zeros (5,5); D2(1:3, 1:3) = S; D2(4:5, 4:5) = eye (2); %! assert (norm (diag (C).^2 + diag (S).^2 - ones (3, 1)) <= 1e-6); %! assert (norm ((U'*A*X) - D1*R) <= 1e-6); %! assert (norm ((V'*B*X) - D2*R) <= 1e-6); ## A and B are both complex rank deficient %!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, R] = gsvd (A, B); %! D1 = zeros (3, 4); D1(1:3, 1:3) = C; %! D2 = eye (4); D2(1:3, 1:3) = S; D2(5,:) = 0; %! assert (norm (diag (C).^2 + diag (S).^2 - ones (3, 1)) <= 1e-6); %! assert (norm ((U'*A*X) - D1*[zeros(4, 1) R]) <= 1e-6); %! assert (norm ((V'*B*X) - D2*[zeros(4, 1) R]) <= 1e-6); ## Test that single inputs produce single outputs %!test %! s = gsvd (single (ones (0,1)), B); %! assert (class (s), "single"); %! s = gsvd (single (ones (1,0)), B); %! assert (class (s), "single"); %! s = gsvd (single (ones (1,0)), B); %! [U,V,X,C,S,R] = gsvd (single ([]), B); %! assert (class (U), "single"); %! assert (class (V), "single"); %! assert (class (X), "single"); %! assert (class (C), "single"); %! assert (class (S), "single"); %! assert (class (R), "single"); %! %! s = gsvd (single (A), B); %! assert (class (s), "single"); %! [U,V,X,C,S,R] = gsvd (single (A), B); %! assert (class (U), "single"); %! assert (class (V), "single"); %! assert (class (X), "single"); %! assert (class (C), "single"); %! assert (class (S), "single"); %! assert (class (R), "single"); */ OCTAVE_NAMESPACE_END