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clean up and vectorize code for dense output in ode45 * scripts/ode/private/ode_rk_interpolate.m: new file * scripts/ode/private/ode_rk_interpolate.m(hermite_quartic_interpolation): move to internal function, use vectorization and broadcasting. * scripts/ode/private/hermite_quartic_interpolation.m: remove file * scripts/ode/module.mk: list added and removed files * scripts/ode/private/integrate_adaptive.m: use new interpolation code.
author Carlo de Falco <carlo.defalco@polimi.it>
date Tue, 06 Oct 2015 19:28:59 +0200
parents f90c8372b7ba
children ba2b07c13913
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 \n\
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70 The Schur@tie{}decomposition is defined as\n\
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71 @tex\n\
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72 $$\n\
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73 S = U^T A U\n\
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74 $$\n\
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75 @end tex\n\
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76 @ifnottex\n\
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77 \n\
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78 @example\n\
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79 @code{@var{S} = @var{U}' * @var{A} * @var{U}}\n\
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80 @end example\n\
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81 \n\
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82 @end ifnottex\n\
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83 where @var{U} is a unitary matrix\n\
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84 @tex\n\
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85 ($U^T U$ is identity)\n\
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86 @end tex\n\
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87 @ifnottex\n\
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88 (@code{@var{U}'* @var{U}} is identity)\n\
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89 @end ifnottex\n\
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90 and @var{S} is upper triangular. The eigenvalues of @var{A} (and @var{S})\n\
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91 are the diagonal elements of @var{S}. If the matrix @var{A} is real, then\n\
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92 the real Schur@tie{}decomposition is computed, in which the matrix @var{U}\n\
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93 is orthogonal and @var{S} is block upper triangular with blocks of size at\n\
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94 most\n\
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95 @tex\n\
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96 $2 \\times 2$\n\
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97 @end tex\n\
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98 @ifnottex\n\
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99 @code{2 x 2}\n\
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100 @end ifnottex\n\
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101 along the diagonal. The diagonal elements of @var{S}\n\
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102 (or the eigenvalues of the\n\
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103 @tex\n\
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104 $2 \\times 2$\n\
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105 @end tex\n\
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106 @ifnottex\n\
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107 @code{2 x 2}\n\
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108 @end ifnottex\n\
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109 blocks, when appropriate) are the eigenvalues of @var{A} and @var{S}.\n\
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110 \n\
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111 The default for real matrices is a real Schur@tie{}decomposition.\n\
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112 A complex decomposition may be forced by passing the flag\n\
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113 @qcode{\"complex\"}.\n\
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114 \n\
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115 The eigenvalues are optionally ordered along the diagonal according to the\n\
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116 value of @var{opt}. @code{@var{opt} = \"a\"} indicates that all eigenvalues\n\
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117 with negative real parts should be moved to the leading block of @var{S}\n\
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118 (used in @code{are}), @code{@var{opt} = \"d\"} indicates that all\n\
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119 eigenvalues with magnitude less than one should be moved to the leading\n\
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120 block of @var{S} (used in @code{dare}), and @code{@var{opt} = \"u\"}, the\n\
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121 default, indicates that no ordering of eigenvalues should occur. The\n\
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122 leading @var{k} columns of @var{U} always span the @var{A}-invariant\n\
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123 subspace corresponding to the @var{k} leading eigenvalues of @var{S}.\n\
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124 \n\
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125 The Schur@tie{}decomposition is used to compute eigenvalues of a square\n\
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126 matrix, and has applications in the solution of algebraic Riccati equations\n\
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127 in control (see @code{are} and @code{dare}).\n\
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128 @seealso{rsf2csf, ordschur, lu, chol, hess, qr, qz, svd}\n\
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129 @end deftypefn")
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130 {
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131 octave_value_list retval;
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132
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133 int nargin = args.length ();
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134
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jwe
parents:
diff changeset
135 if (nargin < 1 || nargin > 2 || nargout > 2)
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
136 {
5823
080c08b192d8 [project @ 2006-05-19 05:32:17 by jwe]
jwe
parents: 5555
diff changeset
137 print_usage ();
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
138 return retval;
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
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
141 octave_value arg = args(0);
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
142
3523
b80bbb43a1a9 [project @ 2000-02-02 10:25:52 by jwe]
jwe
parents: 3372
diff changeset
143 std::string ord;
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
144
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
145 if (nargin == 2)
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
146 {
19600
03067dab10ca Use stricter input validation when looking for a string as input (bug #42651).
Rik <rik@octave.org>
parents: 19226
diff changeset
147 if (args(1).is_string ())
03067dab10ca Use stricter input validation when looking for a string as input (bug #42651).
Rik <rik@octave.org>
parents: 19226
diff changeset
148 ord = args(1).string_value ();
03067dab10ca Use stricter input validation when looking for a string as input (bug #42651).
Rik <rik@octave.org>
parents: 19226
diff changeset
149 else
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
150 {
11553
01f703952eff Improve docstrings for functions in DLD-FUNCTIONS directory.
Rik <octave@nomad.inbox5.com>
parents: 11523
diff changeset
151 error ("schur: second argument must be a string");
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
152 return retval;
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
153 }
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
154 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
155
10607
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Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
156 bool force_complex = false;
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
157
13224
0a67c717c652 Add support for additional argument "real" to schur() (Bug #34012).
Rik <octave@nomad.inbox5.com>
parents: 12642
diff changeset
158 if (ord == "real")
0a67c717c652 Add support for additional argument "real" to schur() (Bug #34012).
Rik <octave@nomad.inbox5.com>
parents: 12642
diff changeset
159 {
0a67c717c652 Add support for additional argument "real" to schur() (Bug #34012).
Rik <octave@nomad.inbox5.com>
parents: 12642
diff changeset
160 ord = std::string ();
0a67c717c652 Add support for additional argument "real" to schur() (Bug #34012).
Rik <octave@nomad.inbox5.com>
parents: 12642
diff changeset
161 }
0a67c717c652 Add support for additional argument "real" to schur() (Bug #34012).
Rik <octave@nomad.inbox5.com>
parents: 12642
diff changeset
162 else if (ord == "complex")
10607
f7501986e42d make schur more Matlab compatible
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parents: 10155
diff changeset
163 {
f7501986e42d make schur more Matlab compatible
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parents: 10155
diff changeset
164 force_complex = true;
f7501986e42d make schur more Matlab compatible
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parents: 10155
diff changeset
165 ord = std::string ();
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
166 }
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
167 else
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
168 {
10607
f7501986e42d make schur more Matlab compatible
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parents: 10155
diff changeset
169 char ord_char = ord.empty () ? 'U' : ord[0];
f7501986e42d make schur more Matlab compatible
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parents: 10155
diff changeset
170
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
171 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
172 && ord_char != 'u' && ord_char != 'a' && ord_char != 'd')
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
173 {
19208
b155fad47055 Fix error messages and %!fail tests for schur().
Rik <rik@octave.org>
parents: 17787
diff changeset
174 warning ("schur: incorrect ordered schur argument '%s'",
10607
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
175 ord.c_str ());
f7501986e42d make schur more Matlab compatible
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parents: 10155
diff changeset
176 return retval;
f7501986e42d make schur more Matlab compatible
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parents: 10155
diff changeset
177 }
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
178 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
179
5275
23b37da9fd5b [project @ 2005-04-08 16:07:35 by jwe]
jwe
parents: 5008
diff changeset
180 octave_idx_type nr = arg.rows ();
23b37da9fd5b [project @ 2005-04-08 16:07:35 by jwe]
jwe
parents: 5008
diff changeset
181 octave_idx_type nc = arg.columns ();
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
182
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
183 if (nr != nc)
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
184 {
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
185 gripe_square_matrix_required ("schur");
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
186 return retval;
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
187 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
188
10607
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
189 if (! arg.is_numeric_type ())
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
190 gripe_wrong_type_arg ("schur", arg);
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
191 else if (arg.is_single_type ())
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
192 {
10607
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
193 if (! force_complex && arg.is_real_type ())
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
194 {
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
195 FloatMatrix tmp = arg.float_matrix_value ();
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
196
20762
f90c8372b7ba eliminate many more simple uses of error_state
John W. Eaton <jwe@octave.org>
parents: 20382
diff changeset
197 if (nargout == 0 || nargout == 1)
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
198 {
20762
f90c8372b7ba eliminate many more simple uses of error_state
John W. Eaton <jwe@octave.org>
parents: 20382
diff changeset
199 FloatSCHUR result (tmp, ord, false);
f90c8372b7ba eliminate many more simple uses of error_state
John W. Eaton <jwe@octave.org>
parents: 20382
diff changeset
200 retval(0) = result.schur_matrix ();
f90c8372b7ba eliminate many more simple uses of error_state
John W. Eaton <jwe@octave.org>
parents: 20382
diff changeset
201 }
f90c8372b7ba eliminate many more simple uses of error_state
John W. Eaton <jwe@octave.org>
parents: 20382
diff changeset
202 else
f90c8372b7ba eliminate many more simple uses of error_state
John W. Eaton <jwe@octave.org>
parents: 20382
diff changeset
203 {
f90c8372b7ba eliminate many more simple uses of error_state
John W. Eaton <jwe@octave.org>
parents: 20382
diff changeset
204 FloatSCHUR result (tmp, ord, true);
f90c8372b7ba eliminate many more simple uses of error_state
John W. Eaton <jwe@octave.org>
parents: 20382
diff changeset
205 retval(1) = result.schur_matrix ();
f90c8372b7ba eliminate many more simple uses of error_state
John W. Eaton <jwe@octave.org>
parents: 20382
diff changeset
206 retval(0) = result.unitary_matrix ();
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
207 }
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
208 }
10607
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
209 else
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
210 {
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
211 FloatComplexMatrix ctmp = arg.float_complex_matrix_value ();
7789
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
212
20762
f90c8372b7ba eliminate many more simple uses of error_state
John W. Eaton <jwe@octave.org>
parents: 20382
diff changeset
213 if (nargout == 0 || nargout == 1)
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
214 {
20762
f90c8372b7ba eliminate many more simple uses of error_state
John W. Eaton <jwe@octave.org>
parents: 20382
diff changeset
215 FloatComplexSCHUR result (ctmp, ord, false);
f90c8372b7ba eliminate many more simple uses of error_state
John W. Eaton <jwe@octave.org>
parents: 20382
diff changeset
216 retval(0) = mark_upper_triangular (result.schur_matrix ());
f90c8372b7ba eliminate many more simple uses of error_state
John W. Eaton <jwe@octave.org>
parents: 20382
diff changeset
217 }
f90c8372b7ba eliminate many more simple uses of error_state
John W. Eaton <jwe@octave.org>
parents: 20382
diff changeset
218 else
f90c8372b7ba eliminate many more simple uses of error_state
John W. Eaton <jwe@octave.org>
parents: 20382
diff changeset
219 {
f90c8372b7ba eliminate many more simple uses of error_state
John W. Eaton <jwe@octave.org>
parents: 20382
diff changeset
220 FloatComplexSCHUR result (ctmp, ord, true);
f90c8372b7ba eliminate many more simple uses of error_state
John W. Eaton <jwe@octave.org>
parents: 20382
diff changeset
221 retval(1) = mark_upper_triangular (result.schur_matrix ());
f90c8372b7ba eliminate many more simple uses of error_state
John W. Eaton <jwe@octave.org>
parents: 20382
diff changeset
222 retval(0) = result.unitary_matrix ();
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
223 }
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
224 }
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
225 }
7789
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
226 else
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
227 {
10607
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
228 if (! force_complex && arg.is_real_type ())
10154
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 Matrix tmp = arg.matrix_value ();
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
231
20762
f90c8372b7ba eliminate many more simple uses of error_state
John W. Eaton <jwe@octave.org>
parents: 20382
diff changeset
232 if (nargout == 0 || nargout == 1)
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
233 {
20762
f90c8372b7ba eliminate many more simple uses of error_state
John W. Eaton <jwe@octave.org>
parents: 20382
diff changeset
234 SCHUR result (tmp, ord, false);
f90c8372b7ba eliminate many more simple uses of error_state
John W. Eaton <jwe@octave.org>
parents: 20382
diff changeset
235 retval(0) = result.schur_matrix ();
f90c8372b7ba eliminate many more simple uses of error_state
John W. Eaton <jwe@octave.org>
parents: 20382
diff changeset
236 }
f90c8372b7ba eliminate many more simple uses of error_state
John W. Eaton <jwe@octave.org>
parents: 20382
diff changeset
237 else
f90c8372b7ba eliminate many more simple uses of error_state
John W. Eaton <jwe@octave.org>
parents: 20382
diff changeset
238 {
f90c8372b7ba eliminate many more simple uses of error_state
John W. Eaton <jwe@octave.org>
parents: 20382
diff changeset
239 SCHUR result (tmp, ord, true);
f90c8372b7ba eliminate many more simple uses of error_state
John W. Eaton <jwe@octave.org>
parents: 20382
diff changeset
240 retval(1) = result.schur_matrix ();
f90c8372b7ba eliminate many more simple uses of error_state
John W. Eaton <jwe@octave.org>
parents: 20382
diff changeset
241 retval(0) = result.unitary_matrix ();
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
242 }
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
243 }
10607
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
244 else
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
245 {
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
246 ComplexMatrix ctmp = arg.complex_matrix_value ();
7789
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
247
20762
f90c8372b7ba eliminate many more simple uses of error_state
John W. Eaton <jwe@octave.org>
parents: 20382
diff changeset
248 if (nargout == 0 || nargout == 1)
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
249 {
20762
f90c8372b7ba eliminate many more simple uses of error_state
John W. Eaton <jwe@octave.org>
parents: 20382
diff changeset
250 ComplexSCHUR result (ctmp, ord, false);
f90c8372b7ba eliminate many more simple uses of error_state
John W. Eaton <jwe@octave.org>
parents: 20382
diff changeset
251 retval(0) = mark_upper_triangular (result.schur_matrix ());
f90c8372b7ba eliminate many more simple uses of error_state
John W. Eaton <jwe@octave.org>
parents: 20382
diff changeset
252 }
f90c8372b7ba eliminate many more simple uses of error_state
John W. Eaton <jwe@octave.org>
parents: 20382
diff changeset
253 else
f90c8372b7ba eliminate many more simple uses of error_state
John W. Eaton <jwe@octave.org>
parents: 20382
diff changeset
254 {
f90c8372b7ba eliminate many more simple uses of error_state
John W. Eaton <jwe@octave.org>
parents: 20382
diff changeset
255 ComplexSCHUR result (ctmp, ord, true);
f90c8372b7ba eliminate many more simple uses of error_state
John W. Eaton <jwe@octave.org>
parents: 20382
diff changeset
256 retval(1) = mark_upper_triangular (result.schur_matrix ());
f90c8372b7ba eliminate many more simple uses of error_state
John W. Eaton <jwe@octave.org>
parents: 20382
diff changeset
257 retval(0) = result.unitary_matrix ();
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
258 }
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
259 }
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
260 }
11586
12df7854fa7c strip trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 11553
diff changeset
261
12df7854fa7c strip trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 11553
diff changeset
262 return retval;
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
263 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
264
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
265 /*
7814
87865ed7405f Second set of single precision test code and fix of resulting bugs
David Bateman <dbateman@free.fr>
parents: 7789
diff changeset
266 %!test
87865ed7405f Second set of single precision test code and fix of resulting bugs
David Bateman <dbateman@free.fr>
parents: 7789
diff changeset
267 %! 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
268 %! [u, s] = schur (a);
14501
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14460
diff changeset
269 %! assert (u' * a * u, s, sqrt (eps));
7814
87865ed7405f Second set of single precision test code and fix of resulting bugs
David Bateman <dbateman@free.fr>
parents: 7789
diff changeset
270
87865ed7405f Second set of single precision test code and fix of resulting bugs
David Bateman <dbateman@free.fr>
parents: 7789
diff changeset
271 %!test
14501
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14460
diff changeset
272 %! a = single ([1, 2, 3; 4, 5, 9; 7, 8, 6]);
7814
87865ed7405f Second set of single precision test code and fix of resulting bugs
David Bateman <dbateman@free.fr>
parents: 7789
diff changeset
273 %! [u, s] = schur (a);
14501
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14460
diff changeset
274 %! assert (u' * a * u, s, sqrt (eps ("single")));
7814
87865ed7405f Second set of single precision test code and fix of resulting bugs
David Bateman <dbateman@free.fr>
parents: 7789
diff changeset
275
14501
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14460
diff changeset
276 %!error schur ()
19208
b155fad47055 Fix error messages and %!fail tests for schur().
Rik <rik@octave.org>
parents: 17787
diff changeset
277 %!error schur (1,2,3)
b155fad47055 Fix error messages and %!fail tests for schur().
Rik <rik@octave.org>
parents: 17787
diff changeset
278 %!error [a,b,c] = schur (1)
14501
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14460
diff changeset
279 %!error <argument must be a square matrix> schur ([1, 2, 3; 4, 5, 6])
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280 %!error <wrong type argument 'cell'> schur ({1})
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281 %!warning <incorrect ordered schur argument> schur ([1, 2; 3, 4], "bad_opt");
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282
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283 */
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284
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285 DEFUN (rsf2csf, args, nargout,
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286 "-*- texinfo -*-\n\
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287 @deftypefn {Function File} {[@var{U}, @var{T}] =} rsf2csf (@var{UR}, @var{TR})\n\
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288 Convert a real, upper quasi-triangular Schur@tie{}form @var{TR} to a complex,\n\
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289 upper triangular Schur@tie{}form @var{T}.\n\
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290 \n\
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291 Note that the following relations hold:\n\
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292 \n\
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293 @tex\n\
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294 $UR \\cdot TR \\cdot {UR}^T = U T U^{\\dagger}$ and\n\
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295 $U^{\\dagger} U$ is the identity matrix I.\n\
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296 @end tex\n\
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297 @ifnottex\n\
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298 @tcode{@var{UR} * @var{TR} * @var{UR}' = @var{U} * @var{T} * @var{U}'} and\n\
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299 @code{@var{U}' * @var{U}} is the identity matrix I.\n\
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300 @end ifnottex\n\
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301 \n\
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302 Note also that @var{U} and @var{T} are not unique.\n\
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303 @seealso{schur}\n\
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304 @end deftypefn")
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305 {
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306 octave_value_list retval;
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307
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308 if (args.length () == 2 && nargout <= 2)
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309 {
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310 if (! args(0).is_numeric_type ())
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311 gripe_wrong_type_arg ("rsf2csf", args(0));
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312 else if (! args(1).is_numeric_type ())
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313 gripe_wrong_type_arg ("rsf2csf", args(1));
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314 else if (args(0).is_complex_type () || args(1).is_complex_type ())
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315 error ("rsf2csf: UR and TR must be real matrices");
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316 else
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317 {
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318
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319 if (args(0).is_single_type () || args(1).is_single_type ())
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320 {
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321 FloatMatrix u = args(0).float_matrix_value ();
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322 FloatMatrix t = args(1).float_matrix_value ();
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323
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324 FloatComplexSCHUR cs (FloatSCHUR (t, u));
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325
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326 retval(1) = cs.schur_matrix ();
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327 retval(0) = cs.unitary_matrix ();
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328 }
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329 else
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330 {
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331 Matrix u = args(0).matrix_value ();
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332 Matrix t = args(1).matrix_value ();
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333
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334 ComplexSCHUR cs (SCHUR (t, u));
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335
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336 retval(1) = cs.schur_matrix ();
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337 retval(0) = cs.unitary_matrix ();
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338 }
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339 }
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340 }
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341 else
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342 print_usage ();
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343
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344 return retval;
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345 }
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346
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347 /*
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348 %!test
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349 %! A = [1, 1, 1, 2; 1, 2, 1, 1; 1, 1, 3, 1; -2, 1, 1, 1];
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350 %! [u, t] = schur (A);
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351 %! [U, T] = rsf2csf (u, t);
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352 %! assert (norm (u * t * u' - U * T * U'), 0, 1e-12);
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353 %! assert (norm (A - U * T * U'), 0, 1e-12);
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354
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355 %!test
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356 %! A = rand (10);
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357 %! [u, t] = schur (A);
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358 %! [U, T] = rsf2csf (u, t);
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359 %! assert (norm (tril (T, -1)), 0);
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360 %! assert (norm (U * U'), 1, 1e-14);
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361
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362 %!test
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363 %! A = [0, 1;-1, 0];
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364 %! [u, t] = schur (A);
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365 %! [U, T] = rsf2csf (u,t);
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366 %! assert (U * T * U', A, 1e-14);
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367 */