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annotate libinterp/corefcn/schur.cc @ 17281:bc924baa2c4e

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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 1c21f264d26f
children d63878346099
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1 /*
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2
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3 Copyright (C) 1996-2012 John W. Eaton
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4
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5 This file is part of Octave.
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6
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7 Octave is free software; you can redistribute it and/or modify it
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8 under the terms of the GNU General Public License as published by the
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9 Free Software Foundation; either version 3 of the License, or (at your
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10 option) any later version.
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11
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12 Octave is distributed in the hope that it will be useful, but WITHOUT
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13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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15 for more details.
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16
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17 You should have received a copy of the GNU General Public License
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18 along with Octave; see the file COPYING. If not, see
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19 <http://www.gnu.org/licenses/>.
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20
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21 */
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22
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23 #ifdef HAVE_CONFIG_H
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24 #include <config.h>
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25 #endif
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26
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27 #include <string>
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28
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29 #include "CmplxSCHUR.h"
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30 #include "dbleSCHUR.h"
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31 #include "fCmplxSCHUR.h"
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32 #include "floatSCHUR.h"
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33
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34 #include "defun.h"
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35 #include "error.h"
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36 #include "gripes.h"
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37 #include "oct-obj.h"
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38 #include "utils.h"
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39
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40 template <class Matrix>
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41 static octave_value
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42 mark_upper_triangular (const Matrix& a)
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43 {
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44 octave_value retval = a;
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45
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46 octave_idx_type n = a.rows ();
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47 assert (a.columns () == n);
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48
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49 const typename Matrix::element_type zero = typename Matrix::element_type ();
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50
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51 for (octave_idx_type i = 0; i < n; i++)
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52 if (a(i,i) == zero)
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53 return retval;
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54
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55 retval.matrix_type (MatrixType::Upper);
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56
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57 return retval;
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58 }
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59
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60 DEFUN (schur, args, nargout,
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61 "-*- texinfo -*-\n\
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62 @deftypefn {Built-in Function} {@var{S} =} schur (@var{A})\n\
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63 @deftypefnx {Built-in Function} {@var{S} =} schur (@var{A}, \"real\")\n\
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64 @deftypefnx {Built-in Function} {@var{S} =} schur (@var{A}, \"complex\")\n\
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65 @deftypefnx {Built-in Function} {@var{S} =} schur (@var{A}, @var{opt})\n\
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66 @deftypefnx {Built-in Function} {[@var{U}, @var{S}] =} schur (@var{A}, @dots{})\n\
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67 @cindex Schur decomposition\n\
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68 Compute the Schur@tie{}decomposition of @var{A}\n\
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69 @tex\n\
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70 $$\n\
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71 S = U^T A U\n\
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72 $$\n\
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73 @end tex\n\
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74 @ifnottex\n\
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75 \n\
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76 @example\n\
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77 @code{@var{S} = @var{U}' * @var{A} * @var{U}}\n\
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78 @end example\n\
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79 \n\
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80 @end ifnottex\n\
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81 where @var{U} is a unitary matrix\n\
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82 @tex\n\
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83 ($U^T U$ is identity)\n\
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84 @end tex\n\
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85 @ifnottex\n\
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86 (@code{@var{U}'* @var{U}} is identity)\n\
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87 @end ifnottex\n\
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88 and @var{S} is upper triangular. The eigenvalues of @var{A} (and @var{S})\n\
7ef7e20057fa Improve documentation strings in Linear Algebra chapter.
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89 are the diagonal elements of @var{S}. If the matrix @var{A}\n\
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parents: 11523
diff changeset
90 is real, then the real Schur@tie{}decomposition is computed, in which the\n\
12584
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91 matrix @var{U} is orthogonal and @var{S} is block upper triangular\n\
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92 with blocks of size at most\n\
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93 @tex\n\
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94 $2 \\times 2$\n\
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95 @end tex\n\
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96 @ifnottex\n\
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97 @code{2 x 2}\n\
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98 @end ifnottex\n\
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99 along the diagonal. The diagonal elements of @var{S}\n\
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100 (or the eigenvalues of the\n\
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101 @tex\n\
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102 $2 \\times 2$\n\
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103 @end tex\n\
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104 @ifnottex\n\
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105 @code{2 x 2}\n\
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106 @end ifnottex\n\
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107 blocks, when appropriate) are the eigenvalues of @var{A} and @var{S}.\n\
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108 \n\
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109 The default for real matrices is a real Schur@tie{}decomposition.\n\
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Rik <rik@octave.org>
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diff changeset
110 A complex decomposition may be forced by passing the flag\n\
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Rik <rik@octave.org>
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diff changeset
111 @qcode{\"complex\"}.\n\
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112 \n\
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113 The eigenvalues are optionally ordered along the diagonal according to\n\
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114 the value of @var{opt}. @code{@var{opt} = \"a\"} indicates that all\n\
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115 eigenvalues with negative real parts should be moved to the leading\n\
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116 block of @var{S}\n\
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117 (used in @code{are}), @code{@var{opt} = \"d\"} indicates that all eigenvalues\n\
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118 with magnitude less than one should be moved to the leading block of @var{S}\n\
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119 (used in @code{dare}), and @code{@var{opt} = \"u\"}, the default, indicates\n\
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120 that no ordering of eigenvalues should occur. The leading @var{k}\n\
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121 columns of @var{U} always span the @var{A}-invariant\n\
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122 subspace corresponding to the @var{k} leading eigenvalues of @var{S}.\n\
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123 \n\
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124 The Schur@tie{}decomposition is used to compute eigenvalues of a\n\
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125 square matrix, and has applications in the solution of algebraic\n\
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126 Riccati equations in control (see @code{are} and @code{dare}).\n\
16920
53eaa83e4181 doc: Add seealso links between various factorization forms.
Rik <rik@octave.org>
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127 @seealso{rsf2csf, lu, chol, hess, qr, qz, svd}\n\
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128 @end deftypefn")
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129 {
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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130 octave_value_list retval;
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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131
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132 int nargin = args.length ();
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133
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134 if (nargin < 1 || nargin > 2 || nargout > 2)
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135 {
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136 print_usage ();
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137 return retval;
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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138 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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139
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140 octave_value arg = args(0);
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141
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142 std::string ord;
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143
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144 if (nargin == 2)
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145 {
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146 ord = args(1).string_value ();
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147
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148 if (error_state)
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149 {
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150 error ("schur: second argument must be a string");
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151 return retval;
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152 }
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153 }
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154
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155 bool force_complex = false;
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156
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157 if (ord == "real")
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158 {
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159 ord = std::string ();
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160 }
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161 else if (ord == "complex")
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162 {
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163 force_complex = true;
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164 ord = std::string ();
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165 }
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166 else
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167 {
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168 char ord_char = ord.empty () ? 'U' : ord[0];
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169
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170 if (ord_char != 'U' && ord_char != 'A' && ord_char != 'D'
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171 && ord_char != 'u' && ord_char != 'a' && ord_char != 'd')
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172 {
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173 warning ("schur: incorrect ordered schur argument '%c'",
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174 ord.c_str ());
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175 return retval;
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176 }
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177 }
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178
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179 octave_idx_type nr = arg.rows ();
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180 octave_idx_type nc = arg.columns ();
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181
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182 if (nr != nc)
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183 {
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184 gripe_square_matrix_required ("schur");
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185 return retval;
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186 }
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187
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188 if (! arg.is_numeric_type ())
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189 gripe_wrong_type_arg ("schur", arg);
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190 else if (arg.is_single_type ())
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191 {
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192 if (! force_complex && arg.is_real_type ())
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193 {
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194 FloatMatrix tmp = arg.float_matrix_value ();
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195
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196 if (! error_state)
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197 {
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198 if (nargout == 0 || nargout == 1)
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199 {
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200 FloatSCHUR result (tmp, ord, false);
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201 retval(0) = result.schur_matrix ();
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diff changeset
202 }
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
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diff changeset
203 else
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diff changeset
204 {
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diff changeset
205 FloatSCHUR result (tmp, ord, true);
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
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diff changeset
206 retval(1) = result.schur_matrix ();
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diff changeset
207 retval(0) = result.unitary_matrix ();
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diff changeset
208 }
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
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diff changeset
209 }
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210 }
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211 else
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212 {
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213 FloatComplexMatrix ctmp = arg.float_complex_matrix_value ();
7789
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
214
10154
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215 if (! error_state)
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216 {
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217
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218 if (nargout == 0 || nargout == 1)
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diff changeset
219 {
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diff changeset
220 FloatComplexSCHUR result (ctmp, ord, false);
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diff changeset
221 retval(0) = mark_upper_triangular (result.schur_matrix ());
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222 }
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
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diff changeset
223 else
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
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parents: 9758
diff changeset
224 {
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
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diff changeset
225 FloatComplexSCHUR result (ctmp, ord, true);
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diff changeset
226 retval(1) = mark_upper_triangular (result.schur_matrix ());
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diff changeset
227 retval(0) = result.unitary_matrix ();
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228 }
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229 }
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230 }
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231 }
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232 else
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233 {
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234 if (! force_complex && arg.is_real_type ())
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235 {
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236 Matrix tmp = arg.matrix_value ();
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237
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238 if (! error_state)
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239 {
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240 if (nargout == 0 || nargout == 1)
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241 {
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242 SCHUR result (tmp, ord, false);
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243 retval(0) = result.schur_matrix ();
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244 }
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245 else
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246 {
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247 SCHUR result (tmp, ord, true);
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248 retval(1) = result.schur_matrix ();
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249 retval(0) = result.unitary_matrix ();
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250 }
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251 }
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252 }
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253 else
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254 {
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255 ComplexMatrix ctmp = arg.complex_matrix_value ();
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256
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257 if (! error_state)
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258 {
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259
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260 if (nargout == 0 || nargout == 1)
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261 {
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262 ComplexSCHUR result (ctmp, ord, false);
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263 retval(0) = mark_upper_triangular (result.schur_matrix ());
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264 }
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265 else
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266 {
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267 ComplexSCHUR result (ctmp, ord, true);
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268 retval(1) = mark_upper_triangular (result.schur_matrix ());
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269 retval(0) = result.unitary_matrix ();
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270 }
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271 }
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272 }
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273 }
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274
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275 return retval;
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276 }
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277
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278 /*
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279 %!test
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280 %! a = [1, 2, 3; 4, 5, 9; 7, 8, 6];
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281 %! [u, s] = schur (a);
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282 %! assert (u' * a * u, s, sqrt (eps));
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283
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284 %!test
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285 %! a = single ([1, 2, 3; 4, 5, 9; 7, 8, 6]);
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286 %! [u, s] = schur (a);
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287 %! assert (u' * a * u, s, sqrt (eps ("single")));
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288
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289 %!test
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290 %! fail ("schur ([1, 2; 3, 4], 2)", "warning");
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291
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292 %!error schur ()
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293 %!error <argument must be a square matrix> schur ([1, 2, 3; 4, 5, 6])
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294 */
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295
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296 DEFUN (rsf2csf, args, nargout,
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297 "-*- texinfo -*-\n\
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298 @deftypefn {Function File} {[@var{U}, @var{T}] =} rsf2csf (@var{UR}, @var{TR})\n\
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299 Convert a real, upper quasi-triangular Schur@tie{}form @var{TR} to a complex,\n\
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300 upper triangular Schur@tie{}form @var{T}.\n\
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301 \n\
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302 Note that the following relations hold:\n\
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303 \n\
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304 @tex\n\
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305 $UR \\cdot TR \\cdot {UR}^T = U T U^{\\dagger}$ and\n\
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306 $U^{\\dagger} U$ is the identity matrix I.\n\
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307 @end tex\n\
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308 @ifnottex\n\
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309 @tcode{@var{UR} * @var{TR} * @var{UR}' = @var{U} * @var{T} * @var{U}'} and\n\
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310 @code{@var{U}' * @var{U}} is the identity matrix I.\n\
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311 @end ifnottex\n\
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312 \n\
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313 Note also that @var{U} and @var{T} are not unique.\n\
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314 @seealso{schur}\n\
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315 @end deftypefn")
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316 {
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317 octave_value_list retval;
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318
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319 if (args.length () == 2 && nargout <= 2)
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320 {
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321 if (! args(0).is_numeric_type ())
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322 gripe_wrong_type_arg ("rsf2csf", args(0));
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323 else if (! args(1).is_numeric_type ())
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324 gripe_wrong_type_arg ("rsf2csf", args(1));
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325 else if (args(0).is_complex_type () || args(1).is_complex_type ())
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326 error ("rsf2csf: UR and TR must be real matrices");
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327 else
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328 {
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329
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330 if (args(0).is_single_type () || args(1).is_single_type ())
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331 {
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332 FloatMatrix u = args(0).float_matrix_value ();
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333 FloatMatrix t = args(1).float_matrix_value ();
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334 if (! error_state)
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335 {
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336 FloatComplexSCHUR cs (FloatSCHUR (t, u));
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337
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338 retval(1) = cs.schur_matrix ();
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339 retval(0) = cs.unitary_matrix ();
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340 }
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341 }
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342 else
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343 {
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344 Matrix u = args(0).matrix_value ();
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345 Matrix t = args(1).matrix_value ();
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346 if (! error_state)
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347 {
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348 ComplexSCHUR cs (SCHUR (t, u));
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349
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350 retval(1) = cs.schur_matrix ();
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351 retval(0) = cs.unitary_matrix ();
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352 }
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353 }
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354 }
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355 }
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356 else
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357 print_usage ();
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358
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359 return retval;
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360 }
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361
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362 /*
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363 %!test
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364 %! A = [1, 1, 1, 2; 1, 2, 1, 1; 1, 1, 3, 1; -2, 1, 1, 1];
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365 %! [u, t] = schur (A);
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366 %! [U, T] = rsf2csf (u, t);
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367 %! assert (norm (u * t * u' - U * T * U'), 0, 1e-12);
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368 %! assert (norm (A - U * T * U'), 0, 1e-12);
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369
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Jaroslav Hajek <highegg@gmail.com>
parents: 10617
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370 %!test
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
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371 %! A = rand (10);
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
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372 %! [u, t] = schur (A);
23d2378512a0 implement rsf2csf
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parents: 10617
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373 %! [U, T] = rsf2csf (u, t);
14501
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14460
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374 %! assert (norm (tril (T, -1)), 0);
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Rik <octave@nomad.inbox5.com>
parents: 14460
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375 %! assert (norm (U * U'), 1, 1e-14);
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parents: 10617
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376
14460
6c3441f3146b Fix logm for complex matrix with real eigenvalues (bug #34893).
Marco Caliari <marco.caliari@univr.it>
parents: 14138
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377 %!test
6c3441f3146b Fix logm for complex matrix with real eigenvalues (bug #34893).
Marco Caliari <marco.caliari@univr.it>
parents: 14138
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378 %! A = [0, 1;-1, 0];
6c3441f3146b Fix logm for complex matrix with real eigenvalues (bug #34893).
Marco Caliari <marco.caliari@univr.it>
parents: 14138
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379 %! [u, t] = schur (A);
6c3441f3146b Fix logm for complex matrix with real eigenvalues (bug #34893).
Marco Caliari <marco.caliari@univr.it>
parents: 14138
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380 %! [U, T] = rsf2csf (u,t);
14501
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14460
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381 %! assert (U * T * U', A, 1e-14);
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parents: 10617
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382 */