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annotate libinterp/corefcn/ordschur.cc @ 31594:a3d8915b9f87 stable

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doc: more DOCSTRING changes ahead of 8.1 release. * ordschur.cc, stream-euler.cc, ov-class.cc, ov-classdef.cc, uigetfile.m, uiputfile.m, memory.m, compare_plot_demos.m, html_compare_plot_demos.m: More DOCSTRING changes ahead of 8.1 release.
author Rik <rik@octave.org>
date Tue, 29 Nov 2022 18:40:56 -0800
parents 796f54d4ddbf
children e88a07dec498
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
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1 ////////////////////////////////////////////////////////////////////////
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2 //
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3 // Copyright (C) 2016-2022 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 "defun.h"
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31 #include "error.h"
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32 #include "lo-lapack-proto.h"
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33 #include "ovl.h"
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34
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35 OCTAVE_NAMESPACE_BEGIN
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36
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37 DEFUN (ordschur, args, ,
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38 doc: /* -*- texinfo -*-
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39 @deftypefn {} {[@var{UR}, @var{SR}] =} ordschur (@var{U}, @var{S}, @var{select})
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40 Reorder the real Schur factorization (@var{U},@var{S}) obtained with the
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41 @code{schur} function, so that selected eigenvalues appear in the upper left
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42 diagonal blocks of the quasi triangular Schur matrix.
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43
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44 The logical vector @var{select} specifies the selected eigenvalues as they
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45 appear along @var{S}'s diagonal.
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46
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47 For example, given the matrix @code{@var{A} = [1, 2; 3, 4]}, and its Schur
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48 decomposition
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49
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50 @example
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51 [@var{U}, @var{S}] = schur (@var{A})
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52 @end example
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53
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54 @noindent
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55 which returns
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56
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57 @example
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58 @group
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59 @var{U} =
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60
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61 -0.82456 -0.56577
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62 0.56577 -0.82456
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63
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64 @var{S} =
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65
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66 -0.37228 -1.00000
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67 0.00000 5.37228
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68
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69 @end group
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70 @end example
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71
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72 It is possible to reorder the decomposition so that the positive eigenvalue
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73 is in the upper left corner, by doing:
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74
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75 @example
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76 [@var{U}, @var{S}] = ordschur (@var{U}, @var{S}, [0,1])
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77 @end example
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78
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79 @seealso{schur, ordeig, ordqz}
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80 @end deftypefn */)
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81 {
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82 if (args.length () != 3)
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83 print_usage ();
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84
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85 const Array<octave_idx_type> sel_arg = args(2).xoctave_idx_type_vector_value ("ordschur: SELECT must be an array of integers");
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86
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87 const octave_idx_type sel_n = sel_arg.numel ();
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88
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89 const dim_vector dimU = args(0).dims ();
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90 const dim_vector dimS = args(1).dims ();
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91
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92 if (sel_n != dimU(0))
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93 error ("ordschur: SELECT must have same length as the sides of U and S");
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94 else if (sel_n != dimU(0) || sel_n != dimS(0) || sel_n != dimU(1)
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95 || sel_n != dimS(1))
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96 error ("ordschur: U and S must be square and of equal sizes");
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97
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98 octave_value_list retval;
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99
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100 const bool double_type = args(0).is_double_type ()
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101 || args(1).is_double_type ();
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102 const bool complex_type = args(0).iscomplex ()
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103 || args(1).iscomplex ();
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104
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105 #define PREPARE_ARGS(TYPE, TYPE_M, TYPE_COND) \
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106 TYPE ## Matrix U = args(0).x ## TYPE_M ## _value \
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107 ("ordschur: U and S must be real or complex floating point matrices"); \
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108 TYPE ## Matrix S = args(1).x ## TYPE_M ## _value \
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109 ("ordschur: U and S must be real or complex floating point matrices"); \
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110 TYPE ## Matrix w (dim_vector (n, 1)); \
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111 TYPE ## Matrix work (dim_vector (n, 1)); \
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112 F77_INT m; \
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113 F77_INT info; \
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114 TYPE_COND cond1, cond2;
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115
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116 #define PREPARE_OUTPUT() \
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117 if (info != 0) \
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118 error ("ordschur: trsen failed"); \
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119 \
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120 retval = ovl (U, S);
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121
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122 F77_INT n = to_f77_int (sel_n);
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123 Array<F77_INT> sel (dim_vector (n, 1));
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124 for (F77_INT i = 0; i < n; i++)
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125 sel.xelem (i) = to_f77_int (sel_arg.xelem (i));
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126
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127 if (double_type)
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128 {
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129 if (complex_type)
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130 {
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131 PREPARE_ARGS (Complex, complex_matrix, double)
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132
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133 F77_XFCN (ztrsen, ztrsen,
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134 (F77_CONST_CHAR_ARG ("N"), F77_CONST_CHAR_ARG ("V"),
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135 sel.data (), n, F77_DBLE_CMPLX_ARG (S.fortran_vec ()), n,
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136 F77_DBLE_CMPLX_ARG (U.fortran_vec ()), n,
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137 F77_DBLE_CMPLX_ARG (w.fortran_vec ()), m, cond1, cond2,
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138 F77_DBLE_CMPLX_ARG (work.fortran_vec ()), n,
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139 info));
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140
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141 PREPARE_OUTPUT()
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142 }
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143 else
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144 {
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145 PREPARE_ARGS (, matrix, double)
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146 Matrix wi (dim_vector (n, 1));
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147 Array<F77_INT> iwork (dim_vector (n, 1));
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148
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149 F77_XFCN (dtrsen, dtrsen,
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150 (F77_CONST_CHAR_ARG ("N"), F77_CONST_CHAR_ARG ("V"),
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151 sel.data (), n, S.fortran_vec (), n, U.fortran_vec (), n,
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152 w.fortran_vec (), wi.fortran_vec (), m, cond1, cond2,
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153 work.fortran_vec (), n, iwork.fortran_vec (), n, info));
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154
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155 PREPARE_OUTPUT ()
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156 }
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157 }
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158 else
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159 {
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160 if (complex_type)
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161 {
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162 PREPARE_ARGS (FloatComplex, float_complex_matrix, float)
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163
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164 F77_XFCN (ctrsen, ctrsen,
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165 (F77_CONST_CHAR_ARG ("N"), F77_CONST_CHAR_ARG ("V"),
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166 sel.data (), n, F77_CMPLX_ARG (S.fortran_vec ()), n,
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167 F77_CMPLX_ARG (U.fortran_vec ()), n,
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168 F77_CMPLX_ARG (w.fortran_vec ()), m, cond1, cond2,
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169 F77_CMPLX_ARG (work.fortran_vec ()), n,
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170 info));
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171
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172 PREPARE_OUTPUT ()
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173 }
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174 else
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175 {
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176 PREPARE_ARGS (Float, float_matrix, float)
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177 FloatMatrix wi (dim_vector (n, 1));
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178 Array<F77_INT> iwork (dim_vector (n, 1));
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179
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180 F77_XFCN (strsen, strsen,
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181 (F77_CONST_CHAR_ARG ("N"), F77_CONST_CHAR_ARG ("V"),
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182 sel.data (), n, S.fortran_vec (), n, U.fortran_vec (), n,
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183 w.fortran_vec (), wi.fortran_vec (), m, cond1, cond2,
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184 work.fortran_vec (), n, iwork.fortran_vec (), n, info));
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185
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186 PREPARE_OUTPUT ()
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187 }
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188 }
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189
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190 #undef PREPARE_ARGS
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191 #undef PREPARE_OUTPUT
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192
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193 return retval;
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194 }
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195
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196 /*
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197
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198 %!test
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199 %! A = [1, 2, 3, -2; 4, 5, 6, -5 ; 7, 8, 9, -5; 10, 11, 12, 4 ];
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200 %! [U, T] = schur (A);
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201 %! [US, TS] = ordschur (U, T, [ 0, 0, 1, 1 ]);
21580
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202 %! assert (US*TS*US', A, sqrt (eps));
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203 %! assert (diag (T)(3:4), diag (TS)(1:2), sqrt (eps));
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204
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205 %!test
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206 %! A = [1, 2, 3, -2; 4, 5, 6, -5 ; 7, 8, 9, -5; 10, 11, 12, 4 ];
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207 %! [U, T] = schur (A);
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208 %! [US, TS] = ordschur (single (U), single (T), [ 0, 0, 1, 1 ]);
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209 %! assert (US*TS*US', A, sqrt (eps ("single")));
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210 %! assert (diag (T)(3:4), diag (TS)(1:2), sqrt (eps ("single")));
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211
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diff changeset
212 %!test
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213 %! A = [1, 2, 3, -2; 4, 5, 6, -5 ; 7, 8, 9, -5; 10, 11, 12, 4+3i ];
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214 %! [U, T] = schur (A);
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215 %! [US, TS] = ordschur (U, T, [ 0, 0, 1, 1 ]);
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216 %! assert (US*TS*US', A, sqrt (eps));
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217 %! assert (diag (T)(3:4), diag (TS)(1:2), sqrt (eps));
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218
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219 %!test
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220 %! A = [1, 2, 3, -2; 4, 5, 6, -5 ; 7, 8, 9, -5; 10, 11, 12, 4+3i ];
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221 %! [U, T] = schur (A);
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222 %! [US, TS] = ordschur (single (U), single (T), [ 0, 0, 1, 1 ]);
21580
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223 %! assert (US*TS*US', A, sqrt (eps ("single")));
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224 %! assert (diag (T)(3:4), diag (TS)(1:2), sqrt (eps ("single")));
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225
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diff changeset
226 */
29958
32c3a5805893 move DEFUN and DEFMETHOD functions inside octave namespace
John W. Eaton <jwe@octave.org>
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diff changeset
227
32c3a5805893 move DEFUN and DEFMETHOD functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29359
diff changeset
228 OCTAVE_NAMESPACE_END