Mercurial > octave
annotate libinterp/corefcn/svd.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 | ed17822e7662 |
children | aac27ad79be6 |
rev | line source |
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1 //////////////////////////////////////////////////////////////////////// |
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2 // |
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3 // Copyright (C) 1996-2022 The Octave Project Developers |
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4 // |
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5 // See the file COPYRIGHT.md in the top-level directory of this |
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6 // distribution or <https://octave.org/copyright/>. |
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7 // |
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8 // This file is part of Octave. |
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9 // |
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10 // Octave is free software: you can redistribute it and/or modify it |
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11 // under the terms of the GNU General Public License as published by |
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12 // the Free Software Foundation, either version 3 of the License, or |
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13 // (at your option) any later version. |
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14 // |
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15 // Octave is distributed in the hope that it will be useful, but |
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16 // WITHOUT ANY WARRANTY; without even the implied warranty of |
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17 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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18 // GNU General Public License for more details. |
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19 // |
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20 // You should have received a copy of the GNU General Public License |
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21 // along with Octave; see the file COPYING. If not, see |
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22 // <https://www.gnu.org/licenses/>. |
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23 // |
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24 //////////////////////////////////////////////////////////////////////// |
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26 #if defined (HAVE_CONFIG_H) |
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27 # include "config.h" |
2928 | 28 #endif |
29 | |
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30 #include "svd.h" |
2928 | 31 |
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32 #include "defun.h" |
2928 | 33 #include "error.h" |
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34 #include "errwarn.h" |
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35 #include "ovl.h" |
2928 | 36 #include "pr-output.h" |
37 #include "utils.h" | |
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38 #include "variables.h" |
2928 | 39 |
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40 OCTAVE_BEGIN_NAMESPACE(octave) |
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41 |
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42 static std::string Vsvd_driver = "gesvd"; |
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43 |
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44 template <typename T> |
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45 static typename math::svd<T>::Type |
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46 svd_type (int nargin, int nargout, const octave_value_list& args, const T& A) |
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47 { |
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48 if (nargout == 0 || nargout == 1) |
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49 return math::svd<T>::Type::sigma_only; |
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50 else if (nargin == 1) |
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51 return math::svd<T>::Type::std; |
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52 else if (! args(1).is_real_scalar ()) |
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53 return math::svd<T>::Type::economy; |
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54 else |
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55 { |
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56 if (A.rows () > A.columns ()) |
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57 return math::svd<T>::Type::economy; |
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58 else |
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59 return math::svd<T>::Type::std; |
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60 } |
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61 } |
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62 |
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63 template <typename T> |
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64 static typename math::svd<T>::Driver |
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65 svd_driver (void) |
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66 { |
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67 if (Vsvd_driver == "gejsv") |
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68 return math::svd<T>::Driver::GEJSV; |
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69 else if (Vsvd_driver == "gesdd") |
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70 return math::svd<T>::Driver::GESDD; |
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71 else |
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72 return math::svd<T>::Driver::GESVD; // default |
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73 } |
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75 DEFUN (svd, args, nargout, |
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76 classes: double single |
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77 doc: /* -*- texinfo -*- |
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78 @deftypefn {} {@var{s} =} svd (@var{A}) |
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79 @deftypefnx {} {[@var{U}, @var{S}, @var{V}] =} svd (@var{A}) |
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80 @deftypefnx {} {[@var{U}, @var{S}, @var{V}] =} svd (@var{A}, "econ") |
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81 @deftypefnx {} {[@var{U}, @var{S}, @var{V}] =} svd (@var{A}, 0) |
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82 @cindex singular value decomposition |
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83 Compute the singular value decomposition of @var{A}. |
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84 |
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85 The singular value decomposition is defined by the relation |
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86 |
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87 @tex |
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88 $$ |
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89 A = U S V^{\dagger} |
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90 $$ |
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91 @end tex |
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92 @ifnottex |
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93 |
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94 @example |
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95 A = U*S*V' |
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96 @end example |
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97 |
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98 @end ifnottex |
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99 |
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100 The function @code{svd} normally returns only the vector of singular values. |
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101 When called with three return values, it computes |
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102 @tex |
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103 $U$, $S$, and $V$. |
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104 @end tex |
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105 @ifnottex |
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106 @var{U}, @var{S}, and @var{V}. |
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107 @end ifnottex |
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108 For example, |
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109 |
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110 @example |
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111 svd (hilb (3)) |
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112 @end example |
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113 |
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114 @noindent |
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115 returns |
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116 |
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117 @example |
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118 @group |
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119 ans = |
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120 |
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121 1.4083189 |
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122 0.1223271 |
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123 0.0026873 |
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124 @end group |
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125 @end example |
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126 |
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127 @noindent |
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128 and |
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129 |
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130 @example |
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131 [u, s, v] = svd (hilb (3)) |
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132 @end example |
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133 |
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134 @noindent |
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135 returns |
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136 |
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137 @example |
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138 @group |
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139 u = |
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140 |
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141 -0.82704 0.54745 0.12766 |
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142 -0.45986 -0.52829 -0.71375 |
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143 -0.32330 -0.64901 0.68867 |
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144 |
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145 s = |
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146 |
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147 1.40832 0.00000 0.00000 |
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148 0.00000 0.12233 0.00000 |
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149 0.00000 0.00000 0.00269 |
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150 |
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151 v = |
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152 |
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153 -0.82704 0.54745 0.12766 |
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154 -0.45986 -0.52829 -0.71375 |
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155 -0.32330 -0.64901 0.68867 |
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156 @end group |
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157 @end example |
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158 |
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159 When given a second argument that is not 0, @code{svd} returns an economy-sized |
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160 decomposition, eliminating the unnecessary rows or columns of @var{U} or |
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161 @var{V}. |
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162 |
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163 If the second argument is exactly 0, then the choice of decomposition is based |
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164 on the matrix @var{A}. If @var{A} has more rows than columns then an |
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165 economy-sized decomposition is returned, otherwise a regular decomposition |
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166 is calculated. |
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167 |
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168 Algorithm Notes: When calculating the full decomposition (left and right |
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169 singular matrices in addition to singular values) there is a choice of two |
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170 routines in @sc{lapack}. The default routine used by Octave is @code{gesvd}. |
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171 The alternative is @code{gesdd} which is 5X faster, but may use more memory |
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172 and may be inaccurate for some input matrices. There is a third routine |
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173 @code{gejsv}, suitable for better accuracy at extreme scale. See the |
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174 documentation for @code{svd_driver} for more information on choosing a driver. |
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175 @seealso{svd_driver, svds, eig, lu, chol, hess, qr, qz} |
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176 @end deftypefn */) |
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178 int nargin = args.length (); | |
179 | |
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180 if (nargin < 1 || nargin > 2 || nargout > 3) |
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181 print_usage (); |
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183 octave_value arg = args(0); | |
184 | |
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185 if (arg.ndims () != 2) |
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186 error ("svd: A must be a 2-D matrix"); |
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187 |
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188 octave_value_list retval; |
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189 |
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190 bool isfloat = arg.is_single_type (); |
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191 |
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192 if (isfloat) |
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193 { |
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194 if (arg.isreal ()) |
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195 { |
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196 FloatMatrix tmp = arg.float_matrix_value (); |
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197 |
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198 if (tmp.any_element_is_inf_or_nan ()) |
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199 error ("svd: cannot take SVD of matrix containing Inf or NaN values"); |
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200 |
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201 math::svd<FloatMatrix> result |
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202 (tmp, |
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203 svd_type<FloatMatrix> (nargin, nargout, args, tmp), |
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204 svd_driver<FloatMatrix> ()); |
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205 |
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206 FloatDiagMatrix sigma = result.singular_values (); |
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207 |
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208 if (nargout == 0 || nargout == 1) |
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209 retval(0) = sigma.extract_diag (); |
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210 else if (nargout == 2) |
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211 retval = ovl (result.left_singular_matrix (), |
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212 sigma); |
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213 else |
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214 retval = ovl (result.left_singular_matrix (), |
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215 sigma, |
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216 result.right_singular_matrix ()); |
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217 } |
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218 else if (arg.iscomplex ()) |
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219 { |
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220 FloatComplexMatrix ctmp = arg.float_complex_matrix_value (); |
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221 |
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222 if (ctmp.any_element_is_inf_or_nan ()) |
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223 error ("svd: cannot take SVD of matrix containing Inf or NaN values"); |
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224 |
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225 math::svd<FloatComplexMatrix> result |
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226 (ctmp, |
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227 svd_type<FloatComplexMatrix> (nargin, nargout, args, ctmp), |
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228 svd_driver<FloatComplexMatrix> ()); |
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229 |
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230 FloatDiagMatrix sigma = result.singular_values (); |
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231 |
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232 if (nargout == 0 || nargout == 1) |
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233 retval(0) = sigma.extract_diag (); |
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234 else if (nargout == 2) |
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235 retval = ovl (result.left_singular_matrix (), |
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236 sigma); |
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237 else |
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238 retval = ovl (result.left_singular_matrix (), |
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239 sigma, |
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240 result.right_singular_matrix ()); |
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241 } |
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243 else | |
244 { | |
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245 if (arg.isreal ()) |
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246 { |
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247 Matrix tmp = arg.matrix_value (); |
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248 |
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249 if (tmp.any_element_is_inf_or_nan ()) |
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250 error ("svd: cannot take SVD of matrix containing Inf or NaN values"); |
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252 math::svd<Matrix> result |
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253 (tmp, |
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254 svd_type<Matrix> (nargin, nargout, args, tmp), |
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255 svd_driver<Matrix> ()); |
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256 |
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257 DiagMatrix sigma = result.singular_values (); |
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259 if (nargout == 0 || nargout == 1) |
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260 retval(0) = sigma.extract_diag (); |
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261 else if (nargout == 2) |
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262 retval = ovl (result.left_singular_matrix (), |
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263 sigma); |
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264 else |
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265 retval = ovl (result.left_singular_matrix (), |
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266 sigma, |
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267 result.right_singular_matrix ()); |
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268 } |
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269 else if (arg.iscomplex ()) |
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270 { |
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271 ComplexMatrix ctmp = arg.complex_matrix_value (); |
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273 if (ctmp.any_element_is_inf_or_nan ()) |
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274 error ("svd: cannot take SVD of matrix containing Inf or NaN values"); |
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276 math::svd<ComplexMatrix> result |
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277 (ctmp, |
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278 svd_type<ComplexMatrix> (nargin, nargout, args, ctmp), |
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279 svd_driver<ComplexMatrix> ()); |
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281 DiagMatrix sigma = result.singular_values (); |
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282 |
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283 if (nargout == 0 || nargout == 1) |
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284 retval(0) = sigma.extract_diag (); |
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285 else if (nargout == 2) |
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286 retval = ovl (result.left_singular_matrix (), |
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287 sigma); |
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288 else |
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289 retval = ovl (result.left_singular_matrix (), |
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290 sigma, |
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291 result.right_singular_matrix ()); |
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292 } |
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294 err_wrong_type_arg ("svd", arg); |
2928 | 295 } |
296 | |
297 return retval; | |
298 } | |
299 | |
300 /* | |
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301 %!assert (svd ([1, 2; 2, 1]), [3; 1], sqrt (eps)) |
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302 |
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303 %!test |
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304 %! a = [1, 2; 3, 4] + [5, 6; 7, 8]*i; |
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305 %! [u,s,v] = svd (a); |
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306 %! assert (a, u * s * v', 128 * eps); |
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307 |
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308 %!test |
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309 %! [u, s, v] = svd ([1, 2; 2, 1]); |
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310 %! x = 1 / sqrt (2); |
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311 %! assert (u, [-x, -x; -x, x], sqrt (eps)); |
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312 %! assert (s, [3, 0; 0, 1], sqrt (eps)); |
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313 %! assert (v, [-x, x; -x, -x], sqrt (eps)); |
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314 |
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315 %!test |
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316 %! a = [1, 2, 3; 4, 5, 6]; |
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317 %! [u, s, v] = svd (a); |
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318 %! assert (u * s * v', a, sqrt (eps)); |
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319 |
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320 %!test |
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321 %! a = [1, 2; 3, 4; 5, 6]; |
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322 %! [u, s, v] = svd (a); |
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323 %! assert (u * s * v', a, sqrt (eps)); |
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324 |
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325 %!test |
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326 %! a = [1, 2, 3; 4, 5, 6]; |
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327 %! [u, s, v] = svd (a, 1); |
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328 %! assert (u * s * v', a, sqrt (eps)); |
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329 |
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330 %!test |
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331 %! a = [1, 2; 3, 4; 5, 6]; |
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332 %! [u, s, v] = svd (a, 1); |
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333 %! assert (u * s * v', a, sqrt (eps)); |
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334 |
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335 %!assert (svd (single ([1, 2; 2, 1])), single ([3; 1]), sqrt (eps ("single"))) |
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336 |
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337 %!test |
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338 %! [u, s, v] = svd (single ([1, 2; 2, 1])); |
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339 %! x = single (1 / sqrt (2)); |
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340 %! assert (u, [-x, -x; -x, x], sqrt (eps ("single"))); |
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341 %! assert (s, single ([3, 0; 0, 1]), sqrt (eps ("single"))); |
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342 %! assert (v, [-x, x; -x, -x], sqrt (eps ("single"))); |
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343 |
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344 %!test |
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345 %! a = single ([1, 2, 3; 4, 5, 6]); |
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346 %! [u, s, v] = svd (a); |
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347 %! assert (u * s * v', a, sqrt (eps ("single"))); |
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348 |
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349 %!test |
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350 %! a = single ([1, 2; 3, 4; 5, 6]); |
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351 %! [u, s, v] = svd (a); |
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352 %! assert (u * s * v', a, sqrt (eps ("single"))); |
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353 |
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354 %!test |
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355 %! a = single ([1, 2, 3; 4, 5, 6]); |
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356 %! [u, s, v] = svd (a, 1); |
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357 %! assert (u * s * v', a, sqrt (eps ("single"))); |
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358 |
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359 %!test |
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360 %! a = single ([1, 2; 3, 4; 5, 6]); |
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361 %! [u, s, v] = svd (a, 1); |
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362 %! assert (u * s * v', a, sqrt (eps ("single"))); |
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363 |
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364 %!test |
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365 %! a = zeros (0, 5); |
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366 %! [u, s, v] = svd (a); |
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367 %! assert (size (u), [0, 0]); |
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368 %! assert (size (s), [0, 5]); |
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369 %! assert (size (v), [5, 5]); |
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370 |
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371 %!test |
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372 %! a = zeros (5, 0); |
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373 %! [u, s, v] = svd (a, 1); |
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374 %! assert (size (u), [5, 0]); |
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375 %! assert (size (s), [0, 0]); |
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376 %! assert (size (v), [0, 0]); |
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377 |
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378 %!test <*49309> |
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379 %! [~,~,v] = svd ([1, 1, 1], 0); |
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380 %! assert (size (v), [3 3]); |
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381 %! [~,~,v] = svd ([1, 1, 1], "econ"); |
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382 %! assert (size (v), [3 1]); |
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383 |
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384 %!assert <*55710> (1 / svd (-0), Inf) |
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385 |
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386 %!test |
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387 %! old_driver = svd_driver ("gejsv"); |
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388 %! s0 = [1e-20; 1e-10; 1]; # only gejsv can pass |
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389 %! q = sqrt (0.5); |
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390 %! a = s0 .* [q, 0, -q; -0.5, q, -0.5; 0.5, q, 0.5]; |
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391 %! s1 = svd (a); |
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392 %! svd_driver (old_driver); |
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393 %! assert (sort (s1), s0, -10 * eps); |
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394 |
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395 %!error svd () |
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396 %!error svd ([1, 2; 4, 5], 2, 3) |
2928 | 397 */ |
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399 DEFUN (svd_driver, args, nargout, |
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400 doc: /* -*- texinfo -*- |
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401 @deftypefn {} {@var{val} =} svd_driver () |
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402 @deftypefnx {} {@var{old_val} =} svd_driver (@var{new_val}) |
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403 @deftypefnx {} {@var{old_val} =} svd_driver (@var{new_val}, "local") |
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404 Query or set the underlying @sc{lapack} driver used by @code{svd}. |
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405 |
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406 Currently recognized values are @qcode{"gesdd"}, @qcode{"gesvd"}, and |
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407 @qcode{"gejsv"}. The default is @qcode{"gesvd"}. |
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408 |
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409 When called from inside a function with the @qcode{"local"} option, the |
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410 variable is changed locally for the function and any subroutines it calls. |
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411 The original variable value is restored when exiting the function. |
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412 |
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413 Algorithm Notes: The @sc{lapack} library routines @code{gesvd} and @code{gesdd} |
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414 are different only when calculating the full singular value decomposition (left |
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415 and right singular matrices as well as singular values). When calculating just |
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416 the singular values the following discussion is not relevant. |
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417 |
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418 The newer @code{gesdd} routine is based on a Divide-and-Conquer algorithm that |
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419 is 5X faster than the alternative @code{gesvd}, which is based on QR |
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420 factorization. However, the new algorithm can use significantly more memory. |
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421 For an @nospell{MxN} input matrix the memory usage is of order O(min(M,N) ^ 2), |
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422 whereas the alternative is of order O(max(M,N)). |
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423 |
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424 The routine @code{gejsv} uses a preconditioned Jacobi SVD algorithm. Unlike |
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425 @code{gesvd} and @code{gesdd}, in @code{gejsv}, there is no bidiagonalization |
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426 step that could contaminate accuracy in some extreme cases. Also, @code{gejsv} |
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427 is known to be optimally accurate in some sense. However, the speed is slower |
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428 (single threaded at its core) and uses more memory (O(min(M,N) ^ 2 + M + N)). |
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429 |
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430 Beyond speed and memory issues, there have been instances where some input |
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431 matrices were not accurately decomposed by @code{gesdd}. See currently active |
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432 bug @url{https://savannah.gnu.org/bugs/?55564}. Until these accuracy issues |
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433 are resolved in a new version of the @sc{lapack} library, the default driver |
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434 in Octave has been set to @qcode{"gesvd"}. |
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435 |
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436 @seealso{svd} |
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437 @end deftypefn */) |
10601 | 438 { |
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439 static const char *driver_names[] = { "gesvd", "gesdd", "gejsv", nullptr }; |
10601 | 440 |
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441 return set_internal_variable (Vsvd_driver, args, nargout, |
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442 "svd_driver", driver_names); |
10601 | 443 } |
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444 |
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445 /* |
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446 %!test |
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447 %! A = [1+1i, 1-1i, 0; 0, 2, 0; 1i, 1i, 1+2i]; |
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448 %! old_driver = svd_driver ("gesvd"); |
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449 %! [U1, S1, V1] = svd (A); |
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450 %! svd_driver ("gesdd"); |
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451 %! [U2, S2, V2] = svd (A); |
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452 %! svd_driver ("gejsv"); |
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453 %! [U3, S3, V3] = svd (A); |
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454 %! assert (svd_driver (), "gejsv"); |
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455 %! svd_driver (old_driver); |
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456 %! assert (U1, U2, 6*eps); |
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457 %! assert (S1, S2, 6*eps); |
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458 %! assert (V1, V2, 6*eps); |
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459 %! z = U1(1,:) ./ U3(1,:); |
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460 %! assert (U1, U3 .* z, 100*eps); |
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461 %! assert (S1, S3, 6*eps); |
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462 %! assert (V1, V3 .* z, 100*eps); |
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463 */ |
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464 |
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465 OCTAVE_END_NAMESPACE(octave) |