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maint: Merge default to bytecode-interpreter.
author Markus Mützel <markus.muetzel@gmx.de>
date Tue, 21 May 2024 18:29:03 +0200
parents a258493e726a
children
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1 ////////////////////////////////////////////////////////////////////////
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2 //
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3 // Copyright (C) 1996-2024 The Octave Project Developers
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4 //
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5 // See the file COPYRIGHT.md in the top-level directory of this
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6 // distribution or <https://octave.org/copyright/>.
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7 //
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8 // This file is part of Octave.
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9 //
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10 // Octave is free software: you can redistribute it and/or modify it
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11 // under the terms of the GNU General Public License as published by
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12 // the Free Software Foundation, either version 3 of the License, or
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13 // (at your option) any later version.
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14 //
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15 // Octave is distributed in the hope that it will be useful, but
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16 // WITHOUT ANY WARRANTY; without even the implied warranty of
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17 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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18 // GNU General Public License for more details.
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19 //
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20 // You should have received a copy of the GNU General Public License
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21 // along with Octave; see the file COPYING. If not, see
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22 // <https://www.gnu.org/licenses/>.
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23 //
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24 ////////////////////////////////////////////////////////////////////////
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25
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26 #if defined (HAVE_CONFIG_H)
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27 # include "config.h"
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28 #endif
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29
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30 #include <string>
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31
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32 #include "schur.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 "errwarn.h"
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37 #include "ovl.h"
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38 #include "utils.h"
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39
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40 OCTAVE_BEGIN_NAMESPACE(octave)
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41
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42 template <typename Matrix>
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43 static octave_value
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44 mark_upper_triangular (const Matrix& a)
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45 {
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46 octave_value retval = a;
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47
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48 octave_idx_type n = a.rows ();
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49 panic_unless (a.columns () == n);
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50
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51 const typename Matrix::element_type zero = typename Matrix::element_type ();
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52
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53 for (octave_idx_type i = 0; i < n; i++)
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54 if (a(i, i) == zero)
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55 return retval;
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56
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57 retval.matrix_type (MatrixType::Upper);
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58
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59 return retval;
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60 }
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61
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62 DEFUN (schur, args, nargout,
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63 doc: /* -*- texinfo -*-
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64 @deftypefn {} {@var{S} =} schur (@var{A})
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65 @deftypefnx {} {@var{S} =} schur (@var{A}, "real")
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66 @deftypefnx {} {@var{S} =} schur (@var{A}, "complex")
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67 @deftypefnx {} {@var{S} =} schur (@var{A}, @var{opt})
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68 @deftypefnx {} {[@var{U}, @var{S}] =} schur (@dots{})
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69 @cindex Schur decomposition
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70 Compute the Schur@tie{}decomposition of @var{A}.
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71
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72 The Schur@tie{}decomposition of a square matrix @var{A} is defined as
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73 @tex
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74 $$
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75 S = U^T A U
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76 $$
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77 @end tex
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78 @ifnottex
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79
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80 @example
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81 @code{@var{S} = @var{U}' * @var{A} * @var{U}}
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82 @end example
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83
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84 @end ifnottex
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85 where @var{U} is a unitary matrix
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86 @tex
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87 ($U^T U$ is identity)
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88 @end tex
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89 @ifnottex
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90 (@code{@var{U}'* @var{U}} is identity)
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91 @end ifnottex
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92 and @var{S} is upper triangular. The eigenvalues of @var{A} (and @var{S})
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93 are the diagonal elements of @var{S}. If the matrix @var{A} is real, then
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94 the real Schur@tie{}decomposition is computed, in which the matrix @var{U}
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95 is orthogonal and @var{S} is block upper triangular with blocks of size at
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96 most
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97 @tex
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98 $2 \times 2$
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99 @end tex
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100 @ifnottex
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101 @code{2 x 2}
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102 @end ifnottex
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103 along the diagonal.
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104
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105 The default for real matrices is a real Schur@tie{}decomposition. A complex
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106 decomposition may be forced by passing the flag @qcode{"complex"}.
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107
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108 The eigenvalues are optionally ordered along the diagonal according to the
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109 value of @var{opt}:
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110
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111 @table @asis
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112 @item @qcode{@var{opt} = "a"}
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113 Move eigenvalues with negative real parts to the leading block of @var{S}.
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114 Mnemonic: @qcode{"a"} for Algebraic @nospell{Riccati} Equations, where this
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115 ordering is useful.
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116
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117 @item @qcode{@var{opt} = "d"}
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118 Move eigenvalues with magnitude less than one to the leading block of @var{S}.
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119 Mnemonic: @qcode{"d"} for Discrete Algebraic @nospell{Riccati} Equations,
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120 where this ordering is useful.
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121
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122 @item @qcode{@var{opt} = "u"}
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123 Unordered. No particular ordering of eigenvalues (default).
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124 @end table
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125
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126 The leading @var{k} columns of @var{U} always span the @var{A}-invariant
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127 subspace corresponding to the @var{k} leading eigenvalues of @var{S}.
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128 @seealso{rsf2csf, ordschur, ordeig, lu, chol, hess, qr, qz, svd, eig}
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129 @end deftypefn */)
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130 {
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131 int nargin = args.length ();
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132
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133 if (nargin < 1 || nargin > 2 || nargout > 2)
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134 print_usage ();
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135
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136 octave_value arg = args(0);
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137
3523
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parents: 3372
diff changeset
138 std::string ord;
2928
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diff changeset
139 if (nargin == 2)
20700
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parents: 20582
diff changeset
140 ord = args(1).xstring_value ("schur: second argument must be a string");
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141
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diff changeset
142 bool force_complex = false;
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143
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parents: 12642
diff changeset
144 if (ord == "real")
0a67c717c652 Add support for additional argument "real" to schur() (Bug #34012).
Rik <octave@nomad.inbox5.com>
parents: 12642
diff changeset
145 {
21017
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Rik <rik@octave.org>
parents: 20941
diff changeset
146 ord = "";
13224
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Rik <octave@nomad.inbox5.com>
parents: 12642
diff changeset
147 }
0a67c717c652 Add support for additional argument "real" to schur() (Bug #34012).
Rik <octave@nomad.inbox5.com>
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diff changeset
148 else if (ord == "complex")
10607
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diff changeset
149 {
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diff changeset
150 force_complex = true;
21017
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diff changeset
151 ord = "";
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152 }
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diff changeset
153 else
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jwe
parents:
diff changeset
154 {
23450
855122b993da maint: Wrap tertiary operator in parentheses "(COND ? x : y)".
Rik <rik@octave.org>
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diff changeset
155 char ord_char = (ord.empty () ? 'U' : ord[0]);
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diff changeset
156
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diff changeset
157 if (ord_char != 'U' && ord_char != 'A' && ord_char != 'D'
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158 && ord_char != 'u' && ord_char != 'a' && ord_char != 'd')
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diff changeset
159 {
19016
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diff changeset
160 warning ("schur: incorrect ordered schur argument '%s'",
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diff changeset
161 ord.c_str ());
20941
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diff changeset
162 return ovl ();
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diff changeset
163 }
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parents:
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164 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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parents:
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165
5275
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parents: 5008
diff changeset
166 octave_idx_type nr = arg.rows ();
23b37da9fd5b [project @ 2005-04-08 16:07:35 by jwe]
jwe
parents: 5008
diff changeset
167 octave_idx_type nc = arg.columns ();
2928
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168
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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parents:
diff changeset
169 if (nr != nc)
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diff changeset
170 err_square_matrix_required ("schur", "A");
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171
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diff changeset
172 if (! arg.isnumeric ())
21120
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parents: 21110
diff changeset
173 err_wrong_type_arg ("schur", arg);
499b851fbfae Replace pattern if/err_XXX/else/code with if/err_XXX/ code.
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diff changeset
174
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parents: 20898
diff changeset
175 octave_value_list retval;
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diff changeset
176
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diff changeset
177 if (arg.is_single_type ())
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jwe
parents:
diff changeset
178 {
23582
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parents: 23581
diff changeset
179 if (! force_complex && arg.isreal ())
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180 {
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diff changeset
181 FloatMatrix tmp = arg.float_matrix_value ();
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182
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diff changeset
183 if (nargout <= 1)
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diff changeset
184 {
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diff changeset
185 math::schur<FloatMatrix> result (tmp, ord, false);
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diff changeset
186 retval = ovl (result.schur_matrix ());
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diff changeset
187 }
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parents: 20172
diff changeset
188 else
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parents: 20172
diff changeset
189 {
29961
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diff changeset
190 math::schur<FloatMatrix> result (tmp, ord, true);
30073
1e277c6b6626 maint: rename schur member function from "unitary_matrix" to "unitary_schur_matrix"
Rik <rik@octave.org>
parents: 29961
diff changeset
191 retval = ovl (result.unitary_schur_matrix (),
20892
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Rik <rik@octave.org>
parents: 20853
diff changeset
192 result.schur_matrix ());
10154
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parents: 9758
diff changeset
193 }
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
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parents: 9758
diff changeset
194 }
10607
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Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
195 else
10154
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parents: 9758
diff changeset
196 {
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
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parents: 9758
diff changeset
197 FloatComplexMatrix ctmp = arg.float_complex_matrix_value ();
7789
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diff changeset
198
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diff changeset
199 if (nargout <= 1)
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parents: 9758
diff changeset
200 {
29961
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parents: 29958
diff changeset
201 math::schur<FloatComplexMatrix> result (ctmp, ord, false);
20892
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parents: 20853
diff changeset
202 retval = ovl (mark_upper_triangular (result.schur_matrix ()));
20555
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parents: 20172
diff changeset
203 }
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parents: 20172
diff changeset
204 else
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parents: 20172
diff changeset
205 {
29961
7d6709900da7 eliminate octave:: namespace tags in DEFUN and DEFMETHOD and more
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parents: 29958
diff changeset
206 math::schur<FloatComplexMatrix> result (ctmp, ord, true);
30073
1e277c6b6626 maint: rename schur member function from "unitary_matrix" to "unitary_schur_matrix"
Rik <rik@octave.org>
parents: 29961
diff changeset
207 retval = ovl (result.unitary_schur_matrix (),
20892
c07bee629973 2015 Code Sprint: use ovl ().
Rik <rik@octave.org>
parents: 20853
diff changeset
208 mark_upper_triangular (result.schur_matrix ()));
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
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parents: 9758
diff changeset
209 }
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
210 }
2928
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jwe
parents:
diff changeset
211 }
7789
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
212 else
2928
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jwe
parents:
diff changeset
213 {
23582
0cc2011d800e maint: Deprecate is_real_type and replace with isreal.
Rik <rik@octave.org>
parents: 23581
diff changeset
214 if (! force_complex && arg.isreal ())
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
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parents: 9758
diff changeset
215 {
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
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parents: 9758
diff changeset
216 Matrix tmp = arg.matrix_value ();
2928
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jwe
parents:
diff changeset
217
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parents: 20853
diff changeset
218 if (nargout <= 1)
10154
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parents: 9758
diff changeset
219 {
29961
7d6709900da7 eliminate octave:: namespace tags in DEFUN and DEFMETHOD and more
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parents: 29958
diff changeset
220 math::schur<Matrix> result (tmp, ord, false);
20892
c07bee629973 2015 Code Sprint: use ovl ().
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parents: 20853
diff changeset
221 retval = ovl (result.schur_matrix ());
20555
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parents: 20172
diff changeset
222 }
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John W. Eaton <jwe@octave.org>
parents: 20172
diff changeset
223 else
f90c8372b7ba eliminate many more simple uses of error_state
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parents: 20172
diff changeset
224 {
29961
7d6709900da7 eliminate octave:: namespace tags in DEFUN and DEFMETHOD and more
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parents: 29958
diff changeset
225 math::schur<Matrix> result (tmp, ord, true);
30073
1e277c6b6626 maint: rename schur member function from "unitary_matrix" to "unitary_schur_matrix"
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parents: 29961
diff changeset
226 retval = ovl (result.unitary_schur_matrix (),
20892
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parents: 20853
diff changeset
227 result.schur_matrix ());
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
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parents: 9758
diff changeset
228 }
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
229 }
10607
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
230 else
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
231 {
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
232 ComplexMatrix ctmp = arg.complex_matrix_value ();
7789
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parents: 7017
diff changeset
233
20892
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parents: 20853
diff changeset
234 if (nargout <= 1)
10154
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John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
235 {
29961
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parents: 29958
diff changeset
236 math::schur<ComplexMatrix> result (ctmp, ord, false);
20892
c07bee629973 2015 Code Sprint: use ovl ().
Rik <rik@octave.org>
parents: 20853
diff changeset
237 retval = ovl (mark_upper_triangular (result.schur_matrix ()));
20555
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parents: 20172
diff changeset
238 }
f90c8372b7ba eliminate many more simple uses of error_state
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parents: 20172
diff changeset
239 else
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parents: 20172
diff changeset
240 {
29961
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parents: 29958
diff changeset
241 math::schur<ComplexMatrix> result (ctmp, ord, true);
30073
1e277c6b6626 maint: rename schur member function from "unitary_matrix" to "unitary_schur_matrix"
Rik <rik@octave.org>
parents: 29961
diff changeset
242 retval = ovl (result.unitary_schur_matrix (),
20892
c07bee629973 2015 Code Sprint: use ovl ().
Rik <rik@octave.org>
parents: 20853
diff changeset
243 mark_upper_triangular (result.schur_matrix ()));
10154
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parents: 9758
diff changeset
244 }
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
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parents: 9758
diff changeset
245 }
2928
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jwe
parents:
diff changeset
246 }
11586
12df7854fa7c strip trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 11553
diff changeset
247
12df7854fa7c strip trailing whitespace from source files
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parents: 11553
diff changeset
248 return retval;
2928
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jwe
parents:
diff changeset
249 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
250
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
251 /*
7814
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David Bateman <dbateman@free.fr>
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diff changeset
252 %!test
87865ed7405f Second set of single precision test code and fix of resulting bugs
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diff changeset
253 %! a = [1, 2, 3; 4, 5, 9; 7, 8, 6];
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parents: 7789
diff changeset
254 %! [u, s] = schur (a);
14501
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
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diff changeset
255 %! assert (u' * a * u, s, sqrt (eps));
7814
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diff changeset
256
87865ed7405f Second set of single precision test code and fix of resulting bugs
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parents: 7789
diff changeset
257 %!test
14501
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
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diff changeset
258 %! a = single ([1, 2, 3; 4, 5, 9; 7, 8, 6]);
7814
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parents: 7789
diff changeset
259 %! [u, s] = schur (a);
14501
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
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parents: 14460
diff changeset
260 %! assert (u' * a * u, s, sqrt (eps ("single")));
7814
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parents: 7789
diff changeset
261
14501
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14460
diff changeset
262 %!error schur ()
19016
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Rik <rik@octave.org>
parents: 17787
diff changeset
263 %!error schur (1,2,3)
b155fad47055 Fix error messages and %!fail tests for schur().
Rik <rik@octave.org>
parents: 17787
diff changeset
264 %!error [a,b,c] = schur (1)
21110
3d0d84305600 Use err_square_matrix_required more widely.
Rik <rik@octave.org>
parents: 21100
diff changeset
265 %!error <must be a square matrix> schur ([1, 2, 3; 4, 5, 6])
19016
b155fad47055 Fix error messages and %!fail tests for schur().
Rik <rik@octave.org>
parents: 17787
diff changeset
266 %!error <wrong type argument 'cell'> schur ({1})
19034
f707835af867 Rewrite schur built-in test as a %!warning to stop failure during 'make check'
Rik <rik@octave.org>
parents: 19016
diff changeset
267 %!warning <incorrect ordered schur argument> schur ([1, 2; 3, 4], "bad_opt");
f707835af867 Rewrite schur built-in test as a %!warning to stop failure during 'make check'
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parents: 19016
diff changeset
268
2928
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jwe
parents:
diff changeset
269 */
10822
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parents: 10617
diff changeset
270
15039
e753177cde93 maint: Move non-dynamically linked functions from DLD-FUNCTIONS/ to corefcn/ directory
Rik <rik@octave.org>
parents: 14854
diff changeset
271 DEFUN (rsf2csf, args, nargout,
21966
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John W. Eaton <jwe@octave.org>
parents: 21724
diff changeset
272 doc: /* -*- texinfo -*-
112b20240c87 move docstrings in C++ files out of C strings and into comments
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diff changeset
273 @deftypefn {} {[@var{U}, @var{T}] =} rsf2csf (@var{UR}, @var{TR})
112b20240c87 move docstrings in C++ files out of C strings and into comments
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parents: 21724
diff changeset
274 Convert a real, upper quasi-triangular Schur@tie{}form @var{TR} to a
112b20240c87 move docstrings in C++ files out of C strings and into comments
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parents: 21724
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275 complex, upper triangular Schur@tie{}form @var{T}.
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276
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277 Note that the following relations hold:
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278
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279 @tex
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280 $UR \cdot TR \cdot {UR}^T = U T U^{\dagger}$ and
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281 $U^{\dagger} U$ is the identity matrix I.
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282 @end tex
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283 @ifnottex
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284 @tcode{@var{UR} * @var{TR} * @var{UR}' = @var{U} * @var{T} * @var{U}'} and
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285 @code{@var{U}' * @var{U}} is the identity matrix I.
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286 @end ifnottex
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287
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288 Note also that @var{U} and @var{T} are not unique.
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289 @seealso{schur}
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290 @end deftypefn */)
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291 {
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292 if (args.length () != 2 || nargout > 2)
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293 print_usage ();
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294
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295 if (! args(0).isnumeric ())
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296 err_wrong_type_arg ("rsf2csf", args(0));
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297 if (! args(1).isnumeric ())
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298 err_wrong_type_arg ("rsf2csf", args(1));
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299 if (args(0).iscomplex () || args(1).iscomplex ())
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300 error ("rsf2csf: UR and TR must be real matrices");
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301
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302 if (args(0).is_single_type () || args(1).is_single_type ())
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303 {
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304 FloatMatrix u = args(0).float_matrix_value ();
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305 FloatMatrix t = args(1).float_matrix_value ();
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306
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307 math::schur<FloatComplexMatrix> cs
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308 = math::rsf2csf<FloatComplexMatrix, FloatMatrix> (t, u);
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309
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310 return ovl (cs.unitary_schur_matrix (), cs.schur_matrix ());
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311 }
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312 else
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313 {
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314 Matrix u = args(0).matrix_value ();
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315 Matrix t = args(1).matrix_value ();
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316
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317 math::schur<ComplexMatrix> cs
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318 = math::rsf2csf<ComplexMatrix, Matrix> (t, u);
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319
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320 return ovl (cs.unitary_schur_matrix (), cs.schur_matrix ());
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321 }
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322 }
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323
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324 /*
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325 %!test
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326 %! A = [1, 1, 1, 2; 1, 2, 1, 1; 1, 1, 3, 1; -2, 1, 1, 1];
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327 %! [u, t] = schur (A);
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328 %! [U, T] = rsf2csf (u, t);
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329 %! assert (norm (u * t * u' - U * T * U'), 0, 1e-12);
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330 %! assert (norm (A - U * T * U'), 0, 1e-12);
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331
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332 %!test
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333 %! A = rand (10);
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334 %! [u, t] = schur (A);
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335 %! [U, T] = rsf2csf (u, t);
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336 %! assert (norm (tril (T, -1)), 0);
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337 %! assert (norm (U * U'), 1, 1e-14);
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338
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339 %!test
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340 %! A = [0, 1;-1, 0];
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341 %! [u, t] = schur (A);
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342 %! [U, T] = rsf2csf (u,t);
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343 %! assert (U * T * U', A, 1e-14);
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344 */
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345
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346 OCTAVE_END_NAMESPACE(octave)