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annotate libinterp/corefcn/ordschur.cc @ 22323:bac0d6f07a3e

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maint: Update copyright notices for 2016.
author John W. Eaton <jwe@octave.org>
date Wed, 17 Aug 2016 01:05:19 -0400
parents 93b3cdd36854
children 34ce5be04942
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) 2016 Sébastien Villemot <sebastien@debian.org>
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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 #if defined (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 "defun.h"
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28 #include "error.h"
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29 #include "lo-lapack-proto.h"
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30 #include "ovl.h"
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31
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32 DEFUN (ordschur, args, ,
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33 doc: /* -*- texinfo -*-
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34 @deftypefn {} {[@var{UR}, @var{SR}] =} ordschur (@var{U}, @var{S}, @var{select})
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35 Reorders the real Schur factorization (@var{U},@var{S}) obtained with the
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36 @code{schur} function, so that selected eigenvalues appear in the upper left
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37 diagonal blocks of the quasi triangular Schur matrix.
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38
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39 The logical vector @var{select} specifies the selected eigenvalues as they
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40 appear along @var{S}'s diagonal.
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41
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42 For example, given the matrix @code{@var{A} = [1, 2; 3, 4]}, and its Schur
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43 decomposition
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44
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45 @example
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46 [@var{U}, @var{S}] = schur (@var{A})
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47 @end example
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48
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49 @noindent
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50 which returns
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51
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52 @example
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53 @group
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54 @var{U} =
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55
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56 -0.82456 -0.56577
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57 0.56577 -0.82456
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58
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59 @var{S} =
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60
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61 -0.37228 -1.00000
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62 0.00000 5.37228
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63
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64 @end group
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65 @end example
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66
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67 It is possible to reorder the decomposition so that the positive eigenvalue
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68 is in the upper left corner, by doing:
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69
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70 @example
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71 [@var{U}, @var{S}] = ordschur (@var{U}, @var{S}, [0,1])
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72 @end example
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73
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74 @seealso{schur}
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75 @end deftypefn */)
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76 {
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77 if (args.length () != 3)
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78 print_usage ();
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79
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80 const Array<octave_idx_type> sel = args(2).octave_idx_type_vector_value ("ordschur: SELECT must be an array of integers");
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81
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82 const octave_idx_type n = sel.numel ();
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83
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84 const dim_vector dimU = args(0).dims ();
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85 const dim_vector dimS = args(1).dims ();
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86
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87 if (n != dimU(0))
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88 error ("ordschur: SELECT must have same length as the sides of U and S");
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89 else if (n != dimU(0) || n != dimS(0) || n != dimU(1) || n != dimS(1))
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90 error ("ordschur: U and S must be square and of equal sizes");
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91
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92 octave_value_list retval;
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93
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94 const bool double_type = args(0).is_double_type ()
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95 || args(1).is_double_type ();
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96 const bool complex_type = args(0).is_complex_type ()
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97 || args(1).is_complex_type ();
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98
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99 #define PREPARE_ARGS(TYPE, TYPE_M, TYPE_COND) \
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100 TYPE ## Matrix U = args(0).x ## TYPE_M ## _value ("ordschur: U and S must be real or complex floating point matrices"); \
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101 TYPE ## Matrix S = args(1).x ## TYPE_M ## _value ("ordschur: U and S must be real or complex floating point matrices"); \
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102 TYPE ## Matrix w (dim_vector (n, 1)); \
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103 TYPE ## Matrix work (dim_vector (n, 1)); \
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104 octave_idx_type m; \
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105 octave_idx_type info; \
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106 TYPE_COND cond1, cond2;
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107
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108 #define PREPARE_OUTPUT() \
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109 if (info != 0) \
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110 error ("ordschur: trsen failed"); \
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111 \
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112 retval = ovl (U, S);
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113
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114 if (double_type)
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115 {
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116 if (complex_type)
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117 {
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118 PREPARE_ARGS (Complex, complex_matrix, double)
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119
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120 F77_XFCN (ztrsen, ztrsen,
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121 (F77_CONST_CHAR_ARG ("N"), F77_CONST_CHAR_ARG ("V"),
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122 sel.data (), n, F77_DBLE_CMPLX_ARG (S.fortran_vec ()), n, F77_DBLE_CMPLX_ARG (U.fortran_vec ()), n,
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123 F77_DBLE_CMPLX_ARG (w.fortran_vec ()), m, cond1, cond2, F77_DBLE_CMPLX_ARG (work.fortran_vec ()), n,
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124 info));
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125
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126 PREPARE_OUTPUT()
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127 }
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128 else
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129 {
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130 PREPARE_ARGS (, matrix, double)
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131 Matrix wi (dim_vector (n, 1));
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132 Array<octave_idx_type> iwork (dim_vector (n, 1));
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133
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134 F77_XFCN (dtrsen, dtrsen,
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135 (F77_CONST_CHAR_ARG ("N"), F77_CONST_CHAR_ARG ("V"),
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136 sel.data (), n, S.fortran_vec (), n, U.fortran_vec (), n,
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137 w.fortran_vec (), wi.fortran_vec (), m, cond1, cond2,
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138 work.fortran_vec (), n, iwork.fortran_vec (), n, info));
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139
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140 PREPARE_OUTPUT ()
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141 }
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142 }
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143 else
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144 {
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145 if (complex_type)
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146 {
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147 PREPARE_ARGS (FloatComplex, float_complex_matrix, float)
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148
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149 F77_XFCN (ctrsen, ctrsen,
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150 (F77_CONST_CHAR_ARG ("N"), F77_CONST_CHAR_ARG ("V"),
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151 sel.data (), n, F77_CMPLX_ARG (S.fortran_vec ()), n, F77_CMPLX_ARG (U.fortran_vec ()), n,
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152 F77_CMPLX_ARG (w.fortran_vec ()), m, cond1, cond2, F77_CMPLX_ARG (work.fortran_vec ()), n,
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153 info));
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154
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155 PREPARE_OUTPUT ()
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156 }
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157 else
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158 {
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159 PREPARE_ARGS (Float, float_matrix, float)
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160 FloatMatrix wi (dim_vector (n, 1));
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161 Array<octave_idx_type> iwork (dim_vector (n, 1));
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162
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163 F77_XFCN (strsen, strsen,
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164 (F77_CONST_CHAR_ARG ("N"), F77_CONST_CHAR_ARG ("V"),
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165 sel.data (), n, S.fortran_vec (), n, U.fortran_vec (), n,
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166 w.fortran_vec (), wi.fortran_vec (), m, cond1, cond2,
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167 work.fortran_vec (), n, iwork.fortran_vec (), n, info));
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168
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169 PREPARE_OUTPUT ()
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170 }
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171 }
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172
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173 #undef PREPARE_ARGS
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174 #undef PREPARE_OUTPUT
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175
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176 return retval;
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177 }
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178
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179 /*
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180
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181 %!test
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182 %! A = [1, 2, 3, -2; 4, 5, 6, -5 ; 7, 8, 9, -5; 10, 11, 12, 4 ];
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183 %! [U, T] = schur (A);
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184 %! [US, TS] = ordschur (U, T, [ 0, 0, 1, 1 ]);
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185 %! assert (US*TS*US', A, sqrt (eps));
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186 %! assert (diag (T)(3:4), diag (TS)(1:2), sqrt (eps));
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187
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188 %!test
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189 %! A = [1, 2, 3, -2; 4, 5, 6, -5 ; 7, 8, 9, -5; 10, 11, 12, 4 ];
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190 %! [U, T] = schur (A);
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191 %! [US, TS] = ordschur (single (U), single (T), [ 0, 0, 1, 1 ]);
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192 %! assert (US*TS*US', A, sqrt (eps ("single")));
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193 %! assert (diag (T)(3:4), diag (TS)(1:2), sqrt (eps ("single")));
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194
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195 %!test
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196 %! A = [1, 2, 3, -2; 4, 5, 6, -5 ; 7, 8, 9, -5; 10, 11, 12, 4+3i ];
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197 %! [U, T] = schur (A);
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198 %! [US, TS] = ordschur (U, T, [ 0, 0, 1, 1 ]);
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199 %! assert (US*TS*US', A, sqrt (eps));
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200 %! assert (diag (T)(3:4), diag (TS)(1:2), sqrt (eps));
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201
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202 %!test
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203 %! A = [1, 2, 3, -2; 4, 5, 6, -5 ; 7, 8, 9, -5; 10, 11, 12, 4+3i ];
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204 %! [U, T] = schur (A);
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205 %! [US, TS] = ordschur (single (U), single (T), [ 0, 0, 1, 1 ]);
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206 %! assert (US*TS*US', A, sqrt (eps ("single")));
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207 %! assert (diag (T)(3:4), diag (TS)(1:2), sqrt (eps ("single")));
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208
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209 */