Mercurial > octave
view libinterp/corefcn/gsvd.cc @ 31605:e88a07dec498 stable
maint: Use macros to begin/end C++ namespaces.
* oct-conf-post-public.in.h: Define two macros (OCTAVE_BEGIN_NAMESPACE,
OCTAVE_END_NAMESPACE) that can be used to start/end a namespace.
* mk-opts.pl, build-env.h, build-env.in.cc, __betainc__.cc, __contourc__.cc,
__dsearchn__.cc, __eigs__.cc, __expint__.cc, __ftp__.cc, __gammainc__.cc,
__ichol__.cc, __ilu__.cc, __isprimelarge__.cc, __lin_interpn__.cc,
__magick_read__.cc, __pchip_deriv__.cc, __qp__.cc, amd.cc, auto-shlib.cc,
auto-shlib.h, balance.cc, base-text-renderer.cc, base-text-renderer.h,
besselj.cc, bitfcns.cc, bsxfun.cc, c-file-ptr-stream.cc, c-file-ptr-stream.h,
call-stack.cc, call-stack.h, ccolamd.cc, cellfun.cc, chol.cc, colamd.cc,
colloc.cc, conv2.cc, daspk.cc, dasrt.cc, dassl.cc, data.cc, data.h, debug.cc,
defaults.cc, defaults.h, defun-int.h, defun.cc, det.cc, dirfns.cc, display.cc,
display.h, dlmread.cc, dmperm.cc, dot.cc, dynamic-ld.cc, dynamic-ld.h, eig.cc,
ellipj.cc, environment.cc, environment.h, error.cc, error.h, errwarn.h,
event-manager.cc, event-manager.h, event-queue.cc, event-queue.h, fcn-info.cc,
fcn-info.h, fft.cc, fft2.cc, fftn.cc, file-io.cc, filter.cc, find.cc,
ft-text-renderer.cc, ft-text-renderer.h, gcd.cc, getgrent.cc, getpwent.cc,
getrusage.cc, givens.cc, gl-render.cc, gl-render.h, gl2ps-print.cc,
gl2ps-print.h, graphics-toolkit.cc, graphics-toolkit.h, graphics.cc,
graphics.in.h, gsvd.cc, gtk-manager.cc, gtk-manager.h, hash.cc, help.cc,
help.h, hess.cc, hex2num.cc, hook-fcn.cc, hook-fcn.h, input.cc, input.h,
interpreter-private.cc, interpreter-private.h, interpreter.cc, interpreter.h,
inv.cc, jsondecode.cc, jsonencode.cc, kron.cc, latex-text-renderer.cc,
latex-text-renderer.h, load-path.cc, load-path.h, load-save.cc, load-save.h,
lookup.cc, ls-ascii-helper.cc, ls-ascii-helper.h, ls-oct-text.cc, ls-utils.cc,
ls-utils.h, lsode.cc, lu.cc, mappers.cc, matrix_type.cc, max.cc, mex-private.h,
mex.cc, mgorth.cc, nproc.cc, oct-fstrm.cc, oct-fstrm.h, oct-hdf5-types.cc,
oct-hdf5-types.h, oct-hist.cc, oct-hist.h, oct-iostrm.cc, oct-iostrm.h,
oct-opengl.h, oct-prcstrm.cc, oct-prcstrm.h, oct-procbuf.cc, oct-procbuf.h,
oct-process.cc, oct-process.h, oct-stdstrm.h, oct-stream.cc, oct-stream.h,
oct-strstrm.cc, oct-strstrm.h, oct-tex-lexer.in.ll, oct-tex-parser.yy,
ordqz.cc, ordschur.cc, pager.cc, pager.h, pinv.cc, pow2.cc, pr-flt-fmt.cc,
pr-output.cc, procstream.cc, procstream.h, psi.cc, qr.cc, quad.cc, quadcc.cc,
qz.cc, rand.cc, rcond.cc, regexp.cc, schur.cc, settings.cc, settings.h,
sighandlers.cc, sighandlers.h, sparse-xdiv.cc, sparse-xdiv.h, sparse-xpow.cc,
sparse-xpow.h, sparse.cc, spparms.cc, sqrtm.cc, stack-frame.cc, stack-frame.h,
stream-euler.cc, strfind.cc, strfns.cc, sub2ind.cc, svd.cc, sylvester.cc,
symbfact.cc, syminfo.cc, syminfo.h, symrcm.cc, symrec.cc, symrec.h,
symscope.cc, symscope.h, symtab.cc, symtab.h, syscalls.cc, sysdep.cc, sysdep.h,
text-engine.cc, text-engine.h, text-renderer.cc, text-renderer.h, time.cc,
toplev.cc, tril.cc, tsearch.cc, typecast.cc, url-handle-manager.cc,
url-handle-manager.h, urlwrite.cc, utils.cc, utils.h, variables.cc,
variables.h, xdiv.cc, xdiv.h, xnorm.cc, xnorm.h, xpow.cc, xpow.h,
__delaunayn__.cc, __fltk_uigetfile__.cc, __glpk__.cc, __init_fltk__.cc,
__init_gnuplot__.cc, __ode15__.cc, __voronoi__.cc, audiodevinfo.cc,
audioread.cc, convhulln.cc, fftw.cc, gzip.cc, mk-build-env-features.sh,
mk-builtins.pl, cdef-class.cc, cdef-class.h, cdef-fwd.h, cdef-manager.cc,
cdef-manager.h, cdef-method.cc, cdef-method.h, cdef-object.cc, cdef-object.h,
cdef-package.cc, cdef-package.h, cdef-property.cc, cdef-property.h,
cdef-utils.cc, cdef-utils.h, ov-base.cc, ov-base.h, ov-bool-mat.cc,
ov-builtin.h, ov-cell.cc, ov-class.cc, ov-class.h, ov-classdef.cc,
ov-classdef.h, ov-complex.cc, ov-fcn-handle.cc, ov-fcn-handle.h, ov-fcn.h,
ov-java.cc, ov-java.h, ov-mex-fcn.h, ov-null-mat.cc, ov-oncleanup.cc,
ov-struct.cc, ov-typeinfo.cc, ov-typeinfo.h, ov-usr-fcn.cc, ov-usr-fcn.h,
ov.cc, ov.h, octave.cc, octave.h, mk-ops.sh, op-b-b.cc, op-b-bm.cc,
op-b-sbm.cc, op-bm-b.cc, op-bm-bm.cc, op-bm-sbm.cc, op-cdm-cdm.cc, op-cell.cc,
op-chm.cc, op-class.cc, op-cm-cm.cc, op-cm-cs.cc, op-cm-m.cc, op-cm-s.cc,
op-cm-scm.cc, op-cm-sm.cc, op-cs-cm.cc, op-cs-cs.cc, op-cs-m.cc, op-cs-s.cc,
op-cs-scm.cc, op-cs-sm.cc, op-dm-dm.cc, op-dm-scm.cc, op-dm-sm.cc,
op-dm-template.cc, op-dms-template.cc, op-fcdm-fcdm.cc, op-fcm-fcm.cc,
op-fcm-fcs.cc, op-fcm-fm.cc, op-fcm-fs.cc, op-fcn.cc, op-fcs-fcm.cc,
op-fcs-fcs.cc, op-fcs-fm.cc, op-fcs-fs.cc, op-fdm-fdm.cc, op-fm-fcm.cc,
op-fm-fcs.cc, op-fm-fm.cc, op-fm-fs.cc, op-fs-fcm.cc, op-fs-fcs.cc,
op-fs-fm.cc, op-fs-fs.cc, op-i16-i16.cc, op-i32-i32.cc, op-i64-i64.cc,
op-i8-i8.cc, op-int-concat.cc, op-m-cm.cc, op-m-cs.cc, op-m-m.cc, op-m-s.cc,
op-m-scm.cc, op-m-sm.cc, op-mi.cc, op-pm-pm.cc, op-pm-scm.cc, op-pm-sm.cc,
op-pm-template.cc, op-range.cc, op-s-cm.cc, op-s-cs.cc, op-s-m.cc, op-s-s.cc,
op-s-scm.cc, op-s-sm.cc, op-sbm-b.cc, op-sbm-bm.cc, op-sbm-sbm.cc,
op-scm-cm.cc, op-scm-cs.cc, op-scm-m.cc, op-scm-s.cc, op-scm-scm.cc,
op-scm-sm.cc, op-sm-cm.cc, op-sm-cs.cc, op-sm-m.cc, op-sm-s.cc, op-sm-scm.cc,
op-sm-sm.cc, op-str-m.cc, op-str-s.cc, op-str-str.cc, op-struct.cc,
op-ui16-ui16.cc, op-ui32-ui32.cc, op-ui64-ui64.cc, op-ui8-ui8.cc, ops.h,
anon-fcn-validator.cc, anon-fcn-validator.h, bp-table.cc, bp-table.h,
comment-list.cc, comment-list.h, filepos.h, lex.h, lex.ll, oct-lvalue.cc,
oct-lvalue.h, oct-parse.yy, parse.h, profiler.cc, profiler.h,
pt-anon-scopes.cc, pt-anon-scopes.h, pt-arg-list.cc, pt-arg-list.h,
pt-args-block.cc, pt-args-block.h, pt-array-list.cc, pt-array-list.h,
pt-assign.cc, pt-assign.h, pt-binop.cc, pt-binop.h, pt-bp.cc, pt-bp.h,
pt-cbinop.cc, pt-cbinop.h, pt-cell.cc, pt-cell.h, pt-check.cc, pt-check.h,
pt-classdef.cc, pt-classdef.h, pt-cmd.h, pt-colon.cc, pt-colon.h, pt-const.cc,
pt-const.h, pt-decl.cc, pt-decl.h, pt-eval.cc, pt-eval.h, pt-except.cc,
pt-except.h, pt-exp.cc, pt-exp.h, pt-fcn-handle.cc, pt-fcn-handle.h, pt-id.cc,
pt-id.h, pt-idx.cc, pt-idx.h, pt-jump.h, pt-loop.cc, pt-loop.h, pt-mat.cc,
pt-mat.h, pt-misc.cc, pt-misc.h, pt-pr-code.cc, pt-pr-code.h, pt-select.cc,
pt-select.h, pt-spmd.cc, pt-spmd.h, pt-stmt.cc, pt-stmt.h, pt-tm-const.cc,
pt-tm-const.h, pt-unop.cc, pt-unop.h, pt-vm-eval.cc, pt-walk.cc, pt-walk.h,
pt.cc, pt.h, token.cc, token.h, Range.cc, Range.h, idx-vector.cc, idx-vector.h,
range-fwd.h, CollocWt.cc, CollocWt.h, aepbalance.cc, aepbalance.h, chol.cc,
chol.h, gepbalance.cc, gepbalance.h, gsvd.cc, gsvd.h, hess.cc, hess.h,
lo-mappers.cc, lo-mappers.h, lo-specfun.cc, lo-specfun.h, lu.cc, lu.h,
oct-convn.cc, oct-convn.h, oct-fftw.cc, oct-fftw.h, oct-norm.cc, oct-norm.h,
oct-rand.cc, oct-rand.h, oct-spparms.cc, oct-spparms.h, qr.cc, qr.h, qrp.cc,
qrp.h, randgamma.cc, randgamma.h, randmtzig.cc, randmtzig.h, randpoisson.cc,
randpoisson.h, schur.cc, schur.h, sparse-chol.cc, sparse-chol.h, sparse-lu.cc,
sparse-lu.h, sparse-qr.cc, sparse-qr.h, svd.cc, svd.h, child-list.cc,
child-list.h, dir-ops.cc, dir-ops.h, file-ops.cc, file-ops.h, file-stat.cc,
file-stat.h, lo-sysdep.cc, lo-sysdep.h, lo-sysinfo.cc, lo-sysinfo.h,
mach-info.cc, mach-info.h, oct-env.cc, oct-env.h, oct-group.cc, oct-group.h,
oct-password.cc, oct-password.h, oct-syscalls.cc, oct-syscalls.h, oct-time.cc,
oct-time.h, oct-uname.cc, oct-uname.h, action-container.cc, action-container.h,
base-list.h, cmd-edit.cc, cmd-edit.h, cmd-hist.cc, cmd-hist.h, f77-fcn.h,
file-info.cc, file-info.h, lo-array-errwarn.cc, lo-array-errwarn.h, lo-hash.cc,
lo-hash.h, lo-ieee.h, lo-regexp.cc, lo-regexp.h, lo-utils.cc, lo-utils.h,
oct-base64.cc, oct-base64.h, oct-glob.cc, oct-glob.h, oct-inttypes.h,
oct-mutex.cc, oct-mutex.h, oct-refcount.h, oct-shlib.cc, oct-shlib.h,
oct-sparse.cc, oct-sparse.h, oct-string.h, octave-preserve-stream-state.h,
pathsearch.cc, pathsearch.h, quit.cc, quit.h, unwind-prot.cc, unwind-prot.h,
url-transfer.cc, url-transfer.h : Use new macros to begin/end C++ namespaces.
author | Rik <rik@octave.org> |
---|---|
date | Thu, 01 Dec 2022 14:23:45 -0800 |
parents | 796f54d4ddbf |
children | aac27ad79be6 |
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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_BEGIN_NAMESPACE(octave) 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_END_NAMESPACE(octave)