Mercurial > octave-nkf
view libinterp/corefcn/svd.cc @ 17281:bc924baa2c4e
doc: Add new @qcode macro for code samples which are quoted.
Macro handles options ("on") or properties ("position") more elegantly
than @code{"text"}.
* doc/interpreter/macros.texi: Add new @qcode macro.
* doc/interpreter/tips.txi: Add documentation about @qcode macro.
* doc/interpreter/basics.txi, doc/interpreter/container.txi,
doc/interpreter/emacs.txi, doc/interpreter/errors.txi,
doc/interpreter/eval.txi, doc/interpreter/expr.txi,
doc/interpreter/external.txi, doc/interpreter/func.txi,
doc/interpreter/grammar.txi, doc/interpreter/image.txi,
doc/interpreter/install.txi, doc/interpreter/interp.txi,
doc/interpreter/io.txi, doc/interpreter/matrix.txi,
doc/interpreter/numbers.txi, doc/interpreter/oop.txi,
doc/interpreter/package.txi, doc/interpreter/plot.txi,
doc/interpreter/quad.txi, doc/interpreter/sparse.txi,
doc/interpreter/strings.txi, doc/interpreter/system.txi,
doc/interpreter/vectorize.txi, libinterp/corefcn/balance.cc,
libinterp/corefcn/bitfcns.cc, libinterp/corefcn/cellfun.cc,
libinterp/corefcn/conv2.cc, libinterp/corefcn/data.cc,
libinterp/corefcn/debug.cc, libinterp/corefcn/defaults.cc,
libinterp/corefcn/dirfns.cc, libinterp/corefcn/dlmread.cc,
libinterp/corefcn/error.cc, libinterp/corefcn/file-io.cc,
libinterp/corefcn/find.cc, libinterp/corefcn/gammainc.cc,
libinterp/corefcn/graphics.cc, libinterp/corefcn/help.cc,
libinterp/corefcn/hex2num.cc, libinterp/corefcn/input.cc,
libinterp/corefcn/load-path.cc, libinterp/corefcn/load-save.cc,
libinterp/corefcn/ls-oct-ascii.cc, libinterp/corefcn/lu.cc,
libinterp/corefcn/luinc.cc, libinterp/corefcn/matrix_type.cc,
libinterp/corefcn/oct-hist.cc, libinterp/corefcn/pager.cc,
libinterp/corefcn/pr-output.cc, libinterp/corefcn/pt-jit.cc,
libinterp/corefcn/qz.cc, libinterp/corefcn/rand.cc,
libinterp/corefcn/regexp.cc, libinterp/corefcn/schur.cc,
libinterp/corefcn/sighandlers.cc, libinterp/corefcn/sparse.cc,
libinterp/corefcn/spparms.cc, libinterp/corefcn/str2double.cc,
libinterp/corefcn/svd.cc, libinterp/corefcn/symtab.cc,
libinterp/corefcn/syscalls.cc, libinterp/corefcn/toplev.cc,
libinterp/corefcn/tril.cc, libinterp/corefcn/typecast.cc,
libinterp/corefcn/utils.cc, libinterp/corefcn/variables.cc,
libinterp/dldfcn/__init_fltk__.cc, libinterp/dldfcn/chol.cc,
libinterp/dldfcn/colamd.cc, libinterp/dldfcn/fftw.cc, libinterp/dldfcn/qr.cc,
libinterp/dldfcn/symbfact.cc, libinterp/octave-value/ov-base.cc,
libinterp/octave-value/ov-fcn-handle.cc,
libinterp/octave-value/ov-fcn-inline.cc, libinterp/octave-value/ov-java.cc,
libinterp/octave-value/ov-range.cc, libinterp/octave-value/ov-struct.cc,
libinterp/octave-value/ov-usr-fcn.cc, libinterp/parse-tree/oct-parse.in.yy,
libinterp/parse-tree/pt-binop.cc, libinterp/parse-tree/pt-eval.cc,
libinterp/parse-tree/pt-mat.cc, scripts/@ftp/ftp.m,
scripts/deprecated/java_convert_matrix.m, scripts/deprecated/java_debug.m,
scripts/deprecated/java_unsigned_conversion.m, scripts/deprecated/shell_cmd.m,
scripts/general/dblquad.m, scripts/general/display.m,
scripts/general/genvarname.m, scripts/general/idivide.m,
scripts/general/interp1.m, scripts/general/interp2.m,
scripts/general/interp3.m, scripts/general/interpn.m, scripts/general/isa.m,
scripts/general/profexplore.m, scripts/general/profile.m,
scripts/general/quadgk.m, scripts/general/randi.m, scripts/general/structfun.m,
scripts/general/subsindex.m, scripts/general/triplequad.m,
scripts/geometry/griddata.m, scripts/geometry/griddata3.m,
scripts/geometry/griddatan.m, scripts/geometry/voronoi.m, scripts/help/help.m,
scripts/help/lookfor.m, scripts/image/cmpermute.m, scripts/image/colormap.m,
scripts/image/image.m, scripts/image/imagesc.m, scripts/image/imfinfo.m,
scripts/image/imformats.m, scripts/image/imread.m, scripts/image/imshow.m,
scripts/image/imwrite.m, scripts/image/ind2gray.m, scripts/image/lines.m,
scripts/image/rgb2ind.m, scripts/image/spinmap.m, scripts/io/dlmwrite.m,
scripts/io/strread.m, scripts/io/textread.m, scripts/io/textscan.m,
scripts/java/javaclasspath.m, scripts/java/usejava.m,
scripts/miscellaneous/bzip2.m, scripts/miscellaneous/computer.m,
scripts/miscellaneous/copyfile.m, scripts/miscellaneous/debug.m,
scripts/miscellaneous/dos.m, scripts/miscellaneous/edit.m,
scripts/miscellaneous/gzip.m, scripts/miscellaneous/license.m,
scripts/miscellaneous/mkoctfile.m, scripts/miscellaneous/movefile.m,
scripts/miscellaneous/parseparams.m, scripts/miscellaneous/unix.m,
scripts/optimization/fminbnd.m, scripts/optimization/fminsearch.m,
scripts/optimization/fminunc.m, scripts/optimization/fsolve.m,
scripts/optimization/fzero.m, scripts/optimization/glpk.m,
scripts/optimization/lsqnonneg.m, scripts/optimization/optimset.m,
scripts/optimization/pqpnonneg.m, scripts/pkg/pkg.m, scripts/plot/allchild.m,
scripts/plot/ancestor.m, scripts/plot/area.m, scripts/plot/axis.m,
scripts/plot/bar.m, scripts/plot/barh.m, scripts/plot/box.m,
scripts/plot/caxis.m, scripts/plot/cla.m, scripts/plot/clabel.m,
scripts/plot/clf.m, scripts/plot/close.m, scripts/plot/colorbar.m,
scripts/plot/daspect.m, scripts/plot/ezmesh.m, scripts/plot/ezmeshc.m,
scripts/plot/ezsurf.m, scripts/plot/ezsurfc.m, scripts/plot/findall.m,
scripts/plot/findobj.m, scripts/plot/gcbo.m, scripts/plot/gcf.m,
scripts/plot/gco.m, scripts/plot/grid.m, scripts/plot/guihandles.m,
scripts/plot/hdl2struct.m, scripts/plot/hidden.m, scripts/plot/hold.m,
scripts/plot/isonormals.m, scripts/plot/isosurface.m, scripts/plot/legend.m,
scripts/plot/mesh.m, scripts/plot/meshc.m, scripts/plot/meshz.m,
scripts/plot/newplot.m, scripts/plot/orient.m, scripts/plot/pareto.m,
scripts/plot/patch.m, scripts/plot/pbaspect.m, scripts/plot/pcolor.m,
scripts/plot/plot.m, scripts/plot/print.m,
scripts/plot/private/__add_default_menu__.m, scripts/plot/quiver.m,
scripts/plot/quiver3.m, scripts/plot/refreshdata.m, scripts/plot/saveas.m,
scripts/plot/scatter.m, scripts/plot/scatter3.m, scripts/plot/shading.m,
scripts/plot/shrinkfaces.m, scripts/plot/slice.m, scripts/plot/stem.m,
scripts/plot/stem3.m, scripts/plot/struct2hdl.m, scripts/plot/subplot.m,
scripts/plot/surf.m, scripts/plot/surfc.m, scripts/plot/surfl.m,
scripts/plot/tetramesh.m, scripts/plot/uigetfile.m, scripts/plot/uimenu.m,
scripts/plot/uiputfile.m, scripts/plot/waterfall.m, scripts/plot/whitebg.m,
scripts/plot/xlim.m, scripts/plot/ylim.m, scripts/plot/zlim.m,
scripts/polynomial/conv.m, scripts/polynomial/polyout.m,
scripts/polynomial/splinefit.m, scripts/set/ismember.m, scripts/set/powerset.m,
scripts/set/setdiff.m, scripts/set/union.m, scripts/set/unique.m,
scripts/signal/detrend.m, scripts/signal/filter2.m, scripts/signal/freqz.m,
scripts/signal/periodogram.m, scripts/signal/spectral_adf.m,
scripts/signal/spectral_xdf.m, scripts/sparse/eigs.m, scripts/sparse/svds.m,
scripts/specfun/legendre.m, scripts/special-matrix/gallery.m,
scripts/statistics/base/mean.m, scripts/statistics/base/moment.m,
scripts/statistics/tests/cor_test.m,
scripts/statistics/tests/kolmogorov_smirnov_test.m,
scripts/statistics/tests/kolmogorov_smirnov_test_2.m,
scripts/statistics/tests/kruskal_wallis_test.m,
scripts/statistics/tests/prop_test_2.m, scripts/statistics/tests/sign_test.m,
scripts/statistics/tests/t_test.m, scripts/statistics/tests/t_test_2.m,
scripts/statistics/tests/t_test_regression.m,
scripts/statistics/tests/u_test.m, scripts/statistics/tests/var_test.m,
scripts/statistics/tests/welch_test.m,
scripts/statistics/tests/wilcoxon_test.m, scripts/statistics/tests/z_test.m,
scripts/statistics/tests/z_test_2.m, scripts/strings/base2dec.m,
scripts/strings/index.m, scripts/strings/isstrprop.m,
scripts/strings/mat2str.m, scripts/strings/regexptranslate.m,
scripts/strings/rindex.m, scripts/strings/str2num.m, scripts/strings/strcat.m,
scripts/strings/strjust.m, scripts/strings/strmatch.m,
scripts/strings/validatestring.m, scripts/testfun/demo.m,
scripts/testfun/example.m, scripts/testfun/test.m, scripts/time/addtodate.m,
scripts/time/asctime.m, scripts/time/datestr.m, scripts/time/datetick.m,
scripts/time/weekday.m, scripts/ui/errordlg.m, scripts/ui/helpdlg.m,
scripts/ui/inputdlg.m, scripts/ui/listdlg.m, scripts/ui/msgbox.m,
scripts/ui/questdlg.m, scripts/ui/warndlg.m: Use new @qcode macro.
author | Rik <rik@octave.org> |
---|---|
date | Mon, 19 Aug 2013 20:46:38 -0700 |
parents | 53eaa83e4181 |
children | d63878346099 |
line wrap: on
line source
/* Copyright (C) 1996-2012 John W. Eaton This file is part of Octave. Octave is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version. Octave is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with Octave; see the file COPYING. If not, see <http://www.gnu.org/licenses/>. */ #ifdef HAVE_CONFIG_H #include <config.h> #endif #include "CmplxSVD.h" #include "dbleSVD.h" #include "fCmplxSVD.h" #include "floatSVD.h" #include "defun.h" #include "error.h" #include "gripes.h" #include "oct-obj.h" #include "pr-output.h" #include "utils.h" #include "variables.h" static int Vsvd_driver = SVD::GESVD; DEFUN (svd, args, nargout, "-*- texinfo -*-\n\ @deftypefn {Built-in Function} {@var{s} =} svd (@var{A})\n\ @deftypefnx {Built-in Function} {[@var{U}, @var{S}, @var{V}] =} svd (@var{A})\n\ @deftypefnx {Built-in Function} {[@var{U}, @var{S}, @var{V}] =} svd (@var{A}, @var{econ})\n\ @cindex singular value decomposition\n\ Compute the singular value decomposition of @var{A}\n\ @tex\n\ $$\n\ A = U S V^{\\dagger}\n\ $$\n\ @end tex\n\ @ifnottex\n\ \n\ @example\n\ A = U*S*V'\n\ @end example\n\ \n\ @end ifnottex\n\ \n\ The function @code{svd} normally returns only the vector of singular values.\n\ When called with three return values, it computes\n\ @tex\n\ $U$, $S$, and $V$.\n\ @end tex\n\ @ifnottex\n\ @var{U}, @var{S}, and @var{V}.\n\ @end ifnottex\n\ For example,\n\ \n\ @example\n\ svd (hilb (3))\n\ @end example\n\ \n\ @noindent\n\ returns\n\ \n\ @example\n\ @group\n\ ans =\n\ \n\ 1.4083189\n\ 0.1223271\n\ 0.0026873\n\ @end group\n\ @end example\n\ \n\ @noindent\n\ and\n\ \n\ @example\n\ [u, s, v] = svd (hilb (3))\n\ @end example\n\ \n\ @noindent\n\ returns\n\ \n\ @example\n\ @group\n\ u =\n\ \n\ -0.82704 0.54745 0.12766\n\ -0.45986 -0.52829 -0.71375\n\ -0.32330 -0.64901 0.68867\n\ \n\ s =\n\ \n\ 1.40832 0.00000 0.00000\n\ 0.00000 0.12233 0.00000\n\ 0.00000 0.00000 0.00269\n\ \n\ v =\n\ \n\ -0.82704 0.54745 0.12766\n\ -0.45986 -0.52829 -0.71375\n\ -0.32330 -0.64901 0.68867\n\ @end group\n\ @end example\n\ \n\ If given a second argument, @code{svd} returns an economy-sized\n\ decomposition, eliminating the unnecessary rows or columns of @var{U} or\n\ @var{V}.\n\ @seealso{svd_driver, svds, eig, lu, chol, hess, qr, qz}\n\ @end deftypefn") { octave_value_list retval; int nargin = args.length (); if (nargin < 1 || nargin > 2 || nargout == 2 || nargout > 3) { print_usage (); return retval; } octave_value arg = args(0); octave_idx_type nr = arg.rows (); octave_idx_type nc = arg.columns (); if (arg.ndims () != 2) { error ("svd: A must be a 2-D matrix"); return retval; } bool isfloat = arg.is_single_type (); SVD::type type = ((nargout == 0 || nargout == 1) ? SVD::sigma_only : (nargin == 2) ? SVD::economy : SVD::std); SVD::driver driver = static_cast<SVD::driver> (Vsvd_driver); if (nr == 0 || nc == 0) { if (isfloat) { switch (type) { case SVD::std: retval(2) = FloatDiagMatrix (nc, nc, 1.0f); retval(1) = FloatMatrix (nr, nc); retval(0) = FloatDiagMatrix (nr, nr, 1.0f); break; case SVD::economy: retval(2) = FloatDiagMatrix (0, nc, 1.0f); retval(1) = FloatMatrix (0, 0); retval(0) = FloatDiagMatrix (nr, 0, 1.0f); break; case SVD::sigma_only: default: retval(0) = FloatMatrix (0, 1); break; } } else { switch (type) { case SVD::std: retval(2) = DiagMatrix (nc, nc, 1.0); retval(1) = Matrix (nr, nc); retval(0) = DiagMatrix (nr, nr, 1.0); break; case SVD::economy: retval(2) = DiagMatrix (0, nc, 1.0); retval(1) = Matrix (0, 0); retval(0) = DiagMatrix (nr, 0, 1.0); break; case SVD::sigma_only: default: retval(0) = Matrix (0, 1); break; } } } else { if (isfloat) { if (arg.is_real_type ()) { FloatMatrix tmp = arg.float_matrix_value (); if (! error_state) { if (tmp.any_element_is_inf_or_nan ()) { error ("svd: cannot take SVD of matrix containing Inf or NaN values"); return retval; } FloatSVD result (tmp, type, driver); FloatDiagMatrix sigma = result.singular_values (); if (nargout == 0 || nargout == 1) { retval(0) = sigma.extract_diag (); } else { retval(2) = result.right_singular_matrix (); retval(1) = sigma; retval(0) = result.left_singular_matrix (); } } } else if (arg.is_complex_type ()) { FloatComplexMatrix ctmp = arg.float_complex_matrix_value (); if (! error_state) { if (ctmp.any_element_is_inf_or_nan ()) { error ("svd: cannot take SVD of matrix containing Inf or NaN values"); return retval; } FloatComplexSVD result (ctmp, type, driver); FloatDiagMatrix sigma = result.singular_values (); if (nargout == 0 || nargout == 1) { retval(0) = sigma.extract_diag (); } else { retval(2) = result.right_singular_matrix (); retval(1) = sigma; retval(0) = result.left_singular_matrix (); } } } } else { if (arg.is_real_type ()) { Matrix tmp = arg.matrix_value (); if (! error_state) { if (tmp.any_element_is_inf_or_nan ()) { error ("svd: cannot take SVD of matrix containing Inf or NaN values"); return retval; } SVD result (tmp, type, driver); DiagMatrix sigma = result.singular_values (); if (nargout == 0 || nargout == 1) { retval(0) = sigma.extract_diag (); } else { retval(2) = result.right_singular_matrix (); retval(1) = sigma; retval(0) = result.left_singular_matrix (); } } } else if (arg.is_complex_type ()) { ComplexMatrix ctmp = arg.complex_matrix_value (); if (! error_state) { if (ctmp.any_element_is_inf_or_nan ()) { error ("svd: cannot take SVD of matrix containing Inf or NaN values"); return retval; } ComplexSVD result (ctmp, type, driver); DiagMatrix sigma = result.singular_values (); if (nargout == 0 || nargout == 1) { retval(0) = sigma.extract_diag (); } else { retval(2) = result.right_singular_matrix (); retval(1) = sigma; retval(0) = result.left_singular_matrix (); } } } else { gripe_wrong_type_arg ("svd", arg); return retval; } } } return retval; } /* %!assert (svd ([1, 2; 2, 1]), [3; 1], sqrt (eps)) %!test %! [u, s, v] = svd ([1, 2; 2, 1]); %! x = 1 / sqrt (2); %! assert (u, [-x, -x; -x, x], sqrt (eps)); %! assert (s, [3, 0; 0, 1], sqrt (eps)); %! assert (v, [-x, x; -x, -x], sqrt (eps)); %!test %! a = [1, 2, 3; 4, 5, 6]; %! [u, s, v] = svd (a); %! assert (u * s * v', a, sqrt (eps)); %!test %! a = [1, 2; 3, 4; 5, 6]; %! [u, s, v] = svd (a); %! assert (u * s * v', a, sqrt (eps)); %!test %! a = [1, 2, 3; 4, 5, 6]; %! [u, s, v] = svd (a, 1); %! assert (u * s * v', a, sqrt (eps)); %!test %! a = [1, 2; 3, 4; 5, 6]; %! [u, s, v] = svd (a, 1); %! assert (u * s * v', a, sqrt (eps)); %!assert (svd (single ([1, 2; 2, 1])), single ([3; 1]), sqrt (eps ("single"))) %!test %! [u, s, v] = svd (single ([1, 2; 2, 1])); %! x = single (1 / sqrt (2)); %! assert (u, [-x, -x; -x, x], sqrt (eps ("single"))); %! assert (s, single ([3, 0; 0, 1]), sqrt (eps ("single"))); %! assert (v, [-x, x; -x, -x], sqrt (eps ("single"))); %!test %! a = single ([1, 2, 3; 4, 5, 6]); %! [u, s, v] = svd (a); %! assert (u * s * v', a, sqrt (eps ("single"))); %!test %! a = single ([1, 2; 3, 4; 5, 6]); %! [u, s, v] = svd (a); %! assert (u * s * v', a, sqrt (eps ("single"))); %!test %! a = single ([1, 2, 3; 4, 5, 6]); %! [u, s, v] = svd (a, 1); %! assert (u * s * v', a, sqrt (eps ("single"))); %!test %! a = single ([1, 2; 3, 4; 5, 6]); %! [u, s, v] = svd (a, 1); %! assert (u * s * v', a, sqrt (eps ("single"))); %!test %! a = zeros (0, 5); %! [u, s, v] = svd (a); %! assert (size (u), [0, 0]); %! assert (size (s), [0, 5]); %! assert (size (v), [5, 5]); %!test %! a = zeros (5, 0); %! [u, s, v] = svd (a, 1); %! assert (size (u), [5, 0]); %! assert (size (s), [0, 0]); %! assert (size (v), [0, 0]); %!error svd () %!error svd ([1, 2; 4, 5], 2, 3) %!error [u, v] = svd ([1, 2; 3, 4]) */ DEFUN (svd_driver, args, nargout, "-*- texinfo -*-\n\ @deftypefn {Built-in Function} {@var{val} =} svd_driver ()\n\ @deftypefnx {Built-in Function} {@var{old_val} =} svd_driver (@var{new_val})\n\ @deftypefnx {Built-in Function} {} svd_driver (@var{new_val}, \"local\")\n\ Query or set the underlying @sc{lapack} driver used by @code{svd}.\n\ Currently recognized values are @qcode{\"gesvd\"} and @qcode{\"gesdd\"}. \n\ The default is @qcode{\"gesvd\"}.\n\ \n\ When called from inside a function with the @qcode{\"local\"} option, the\n\ variable is changed locally for the function and any subroutines it calls. \n\ The original variable value is restored when exiting the function.\n\ @seealso{svd}\n\ @end deftypefn") { static const char *driver_names[] = { "gesvd", "gesdd", 0 }; return SET_INTERNAL_VARIABLE_CHOICES (svd_driver, driver_names); } /* %!test %! A = [1+1i, 1-1i, 0; 0, 2, 0; 1i, 1i, 1+2i]; %! old_driver = svd_driver ("gesvd"); %! [U1, S1, V1] = svd (A); %! svd_driver ("gesdd"); %! [U2, S2, V2] = svd (A); %! assert (U1, U2, 5*eps); %! assert (S1, S2, 5*eps); %! assert (V1, V2, 5*eps); %! svd_driver (old_driver); */