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annotate libinterp/corefcn/schur.cc @ 19781:56157a7505ed

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Add new ordschur function. * libinterp/corefcn/ordschur.cc: New file. * libinterp/corefcn/module.mk: Include it in the list of source files. * scripts/help/__unimplemented__.m: Remove ordschur from the list of unimplemented functions. * doc/interpreter/linalg.txi: Add it to the interpreter manual. * NEWS: Mention it. * libinterp/corefcn/schur.cc (schur): Reference it from the documentation of the schur function. Thanks to Carnë Draug for improving the original patch, and to Mike Miller for reviewing it and suggesting improvements.
author Sébastien Villemot <sebastien@debian.org>
date Sat, 07 Feb 2015 21:51:20 +0100
parents 4197fc428c7d
children 4f45eaf83908
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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1 /*
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2
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3 Copyright (C) 1996-2015 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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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 (@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\
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89 are the diagonal elements of @var{S}. If the matrix @var{A}\n\
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90 is real, then the real Schur@tie{}decomposition is computed, in which the\n\
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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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110 A complex decomposition may be forced by passing the flag\n\
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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\
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127 @seealso{rsf2csf, ordschur, lu, chol, hess, qr, qz, svd}\n\
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128 @end deftypefn")
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129 {
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130 octave_value_list retval;
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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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diff changeset
135 {
5823
080c08b192d8 [project @ 2006-05-19 05:32:17 by jwe]
jwe
parents: 5555
diff changeset
136 print_usage ();
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
137 return retval;
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
138 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
139
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
140 octave_value arg = args(0);
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
141
3523
b80bbb43a1a9 [project @ 2000-02-02 10:25:52 by jwe]
jwe
parents: 3372
diff changeset
142 std::string ord;
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
143
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
144 if (nargin == 2)
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
145 {
19437
03067dab10ca Use stricter input validation when looking for a string as input (bug #42651).
Rik <rik@octave.org>
parents: 19068
diff changeset
146 if (args(1).is_string ())
03067dab10ca Use stricter input validation when looking for a string as input (bug #42651).
Rik <rik@octave.org>
parents: 19068
diff changeset
147 ord = args(1).string_value ();
03067dab10ca Use stricter input validation when looking for a string as input (bug #42651).
Rik <rik@octave.org>
parents: 19068
diff changeset
148 else
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
149 {
11553
01f703952eff Improve docstrings for functions in DLD-FUNCTIONS directory.
Rik <octave@nomad.inbox5.com>
parents: 11523
diff changeset
150 error ("schur: second argument must be a string");
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
151 return retval;
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
152 }
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
153 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
154
10607
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
155 bool force_complex = false;
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
156
13224
0a67c717c652 Add support for additional argument "real" to schur() (Bug #34012).
Rik <octave@nomad.inbox5.com>
parents: 12642
diff changeset
157 if (ord == "real")
0a67c717c652 Add support for additional argument "real" to schur() (Bug #34012).
Rik <octave@nomad.inbox5.com>
parents: 12642
diff changeset
158 {
0a67c717c652 Add support for additional argument "real" to schur() (Bug #34012).
Rik <octave@nomad.inbox5.com>
parents: 12642
diff changeset
159 ord = std::string ();
0a67c717c652 Add support for additional argument "real" to schur() (Bug #34012).
Rik <octave@nomad.inbox5.com>
parents: 12642
diff changeset
160 }
0a67c717c652 Add support for additional argument "real" to schur() (Bug #34012).
Rik <octave@nomad.inbox5.com>
parents: 12642
diff changeset
161 else if (ord == "complex")
10607
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
162 {
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
163 force_complex = true;
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
164 ord = std::string ();
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
165 }
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
166 else
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
167 {
10607
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
168 char ord_char = ord.empty () ? 'U' : ord[0];
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
169
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
170 if (ord_char != 'U' && ord_char != 'A' && ord_char != 'D'
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
171 && ord_char != 'u' && ord_char != 'a' && ord_char != 'd')
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
172 {
19050
b155fad47055 Fix error messages and %!fail tests for schur().
Rik <rik@octave.org>
parents: 17787
diff changeset
173 warning ("schur: incorrect ordered schur argument '%s'",
10607
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
174 ord.c_str ());
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
175 return retval;
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
176 }
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
177 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
178
5275
23b37da9fd5b [project @ 2005-04-08 16:07:35 by jwe]
jwe
parents: 5008
diff changeset
179 octave_idx_type nr = arg.rows ();
23b37da9fd5b [project @ 2005-04-08 16:07:35 by jwe]
jwe
parents: 5008
diff changeset
180 octave_idx_type nc = arg.columns ();
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
181
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
182 if (nr != nc)
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
183 {
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
184 gripe_square_matrix_required ("schur");
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
185 return retval;
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
186 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
187
10607
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
188 if (! arg.is_numeric_type ())
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
189 gripe_wrong_type_arg ("schur", arg);
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
190 else if (arg.is_single_type ())
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
191 {
10607
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
192 if (! force_complex && arg.is_real_type ())
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
193 {
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
194 FloatMatrix tmp = arg.float_matrix_value ();
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
195
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
196 if (! error_state)
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
197 {
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
198 if (nargout == 0 || nargout == 1)
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
199 {
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
200 FloatSCHUR result (tmp, ord, false);
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
201 retval(0) = result.schur_matrix ();
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
202 }
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
203 else
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
204 {
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
205 FloatSCHUR result (tmp, ord, true);
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
206 retval(1) = result.schur_matrix ();
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
207 retval(0) = result.unitary_matrix ();
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
208 }
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
209 }
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
210 }
10607
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
211 else
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
212 {
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
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
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
215 if (! error_state)
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
216 {
11586
12df7854fa7c strip trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 11553
diff changeset
217
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
218 if (nargout == 0 || nargout == 1)
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
219 {
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
220 FloatComplexSCHUR result (ctmp, ord, false);
10617
9c9e07f5eb1c make schur mark triangular matrices on output
Jaroslav Hajek <highegg@gmail.com>
parents: 10607
diff changeset
221 retval(0) = mark_upper_triangular (result.schur_matrix ());
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
222 }
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
223 else
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
224 {
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
225 FloatComplexSCHUR result (ctmp, ord, true);
10617
9c9e07f5eb1c make schur mark triangular matrices on output
Jaroslav Hajek <highegg@gmail.com>
parents: 10607
diff changeset
226 retval(1) = mark_upper_triangular (result.schur_matrix ());
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
227 retval(0) = result.unitary_matrix ();
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
228 }
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
229 }
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
230 }
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
231 }
7789
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
232 else
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
233 {
10607
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
234 if (! force_complex && arg.is_real_type ())
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
235 {
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
236 Matrix tmp = arg.matrix_value ();
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
237
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
238 if (! error_state)
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
239 {
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
240 if (nargout == 0 || nargout == 1)
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
241 {
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
242 SCHUR result (tmp, ord, false);
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
243 retval(0) = result.schur_matrix ();
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
244 }
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
245 else
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
246 {
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
247 SCHUR result (tmp, ord, true);
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
248 retval(1) = result.schur_matrix ();
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
249 retval(0) = result.unitary_matrix ();
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
250 }
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
251 }
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
252 }
10607
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
253 else
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
254 {
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
255 ComplexMatrix ctmp = arg.complex_matrix_value ();
7789
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
256
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
257 if (! error_state)
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
258 {
11586
12df7854fa7c strip trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 11553
diff changeset
259
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
260 if (nargout == 0 || nargout == 1)
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
261 {
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
262 ComplexSCHUR result (ctmp, ord, false);
10617
9c9e07f5eb1c make schur mark triangular matrices on output
Jaroslav Hajek <highegg@gmail.com>
parents: 10607
diff changeset
263 retval(0) = mark_upper_triangular (result.schur_matrix ());
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
264 }
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
265 else
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
266 {
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
267 ComplexSCHUR result (ctmp, ord, true);
10617
9c9e07f5eb1c make schur mark triangular matrices on output
Jaroslav Hajek <highegg@gmail.com>
parents: 10607
diff changeset
268 retval(1) = mark_upper_triangular (result.schur_matrix ());
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
269 retval(0) = result.unitary_matrix ();
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
270 }
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
271 }
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
272 }
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
273 }
11586
12df7854fa7c strip trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 11553
diff changeset
274
12df7854fa7c strip trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 11553
diff changeset
275 return retval;
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
276 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
277
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
278 /*
7814
87865ed7405f Second set of single precision test code and fix of resulting bugs
David Bateman <dbateman@free.fr>
parents: 7789
diff changeset
279 %!test
87865ed7405f Second set of single precision test code and fix of resulting bugs
David Bateman <dbateman@free.fr>
parents: 7789
diff changeset
280 %! a = [1, 2, 3; 4, 5, 9; 7, 8, 6];
87865ed7405f Second set of single precision test code and fix of resulting bugs
David Bateman <dbateman@free.fr>
parents: 7789
diff changeset
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 %!error schur ()
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290 %!error schur (1,2,3)
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291 %!error [a,b,c] = schur (1)
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292 %!error <argument must be a square matrix> schur ([1, 2, 3; 4, 5, 6])
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293 %!error <wrong type argument 'cell'> schur ({1})
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294 %!warning <incorrect ordered schur argument> schur ([1, 2; 3, 4], "bad_opt");
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295
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296 */
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297
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298 DEFUN (rsf2csf, args, nargout,
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299 "-*- texinfo -*-\n\
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300 @deftypefn {Function File} {[@var{U}, @var{T}] =} rsf2csf (@var{UR}, @var{TR})\n\
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301 Convert a real, upper quasi-triangular Schur@tie{}form @var{TR} to a complex,\n\
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302 upper triangular Schur@tie{}form @var{T}.\n\
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303 \n\
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304 Note that the following relations hold:\n\
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305 \n\
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306 @tex\n\
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307 $UR \\cdot TR \\cdot {UR}^T = U T U^{\\dagger}$ and\n\
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308 $U^{\\dagger} U$ is the identity matrix I.\n\
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309 @end tex\n\
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310 @ifnottex\n\
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311 @tcode{@var{UR} * @var{TR} * @var{UR}' = @var{U} * @var{T} * @var{U}'} and\n\
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312 @code{@var{U}' * @var{U}} is the identity matrix I.\n\
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313 @end ifnottex\n\
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314 \n\
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315 Note also that @var{U} and @var{T} are not unique.\n\
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316 @seealso{schur}\n\
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317 @end deftypefn")
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318 {
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319 octave_value_list retval;
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320
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321 if (args.length () == 2 && nargout <= 2)
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322 {
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323 if (! args(0).is_numeric_type ())
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324 gripe_wrong_type_arg ("rsf2csf", args(0));
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325 else if (! args(1).is_numeric_type ())
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326 gripe_wrong_type_arg ("rsf2csf", args(1));
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327 else if (args(0).is_complex_type () || args(1).is_complex_type ())
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328 error ("rsf2csf: UR and TR must be real matrices");
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329 else
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330 {
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331
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332 if (args(0).is_single_type () || args(1).is_single_type ())
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333 {
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334 FloatMatrix u = args(0).float_matrix_value ();
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335 FloatMatrix t = args(1).float_matrix_value ();
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336 if (! error_state)
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337 {
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338 FloatComplexSCHUR cs (FloatSCHUR (t, u));
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339
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340 retval(1) = cs.schur_matrix ();
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341 retval(0) = cs.unitary_matrix ();
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342 }
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343 }
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344 else
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345 {
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346 Matrix u = args(0).matrix_value ();
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347 Matrix t = args(1).matrix_value ();
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348 if (! error_state)
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349 {
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350 ComplexSCHUR cs (SCHUR (t, u));
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351
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352 retval(1) = cs.schur_matrix ();
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353 retval(0) = cs.unitary_matrix ();
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354 }
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355 }
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356 }
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357 }
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358 else
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359 print_usage ();
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360
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361 return retval;
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362 }
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363
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364 /*
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365 %!test
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366 %! A = [1, 1, 1, 2; 1, 2, 1, 1; 1, 1, 3, 1; -2, 1, 1, 1];
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367 %! [u, t] = schur (A);
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368 %! [U, T] = rsf2csf (u, t);
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369 %! assert (norm (u * t * u' - U * T * U'), 0, 1e-12);
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370 %! assert (norm (A - U * T * U'), 0, 1e-12);
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371
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372 %!test
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373 %! A = rand (10);
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374 %! [u, t] = schur (A);
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375 %! [U, T] = rsf2csf (u, t);
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376 %! assert (norm (tril (T, -1)), 0);
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377 %! assert (norm (U * U'), 1, 1e-14);
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378
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379 %!test
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380 %! A = [0, 1;-1, 0];
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381 %! [u, t] = schur (A);
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382 %! [U, T] = rsf2csf (u,t);
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383 %! assert (U * T * U', A, 1e-14);
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384 */