Mercurial > octave
annotate libinterp/corefcn/ordschur.cc @ 29359:7854d5752dd2
maint: merge stable to default.
author | John W. Eaton <jwe@octave.org> |
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date | Wed, 10 Feb 2021 10:10:40 -0500 |
parents | 69ec8d9e769b 0a5b15007766 |
children | 32c3a5805893 |
rev | line source |
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1 //////////////////////////////////////////////////////////////////////// |
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2 // |
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3 // Copyright (C) 2016-2021 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 DEFUN (ordschur, args, , |
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36 doc: /* -*- texinfo -*- |
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37 @deftypefn {} {[@var{UR}, @var{SR}] =} ordschur (@var{U}, @var{S}, @var{select}) |
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38 Reorders the real Schur factorization (@var{U},@var{S}) obtained with the |
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39 @code{schur} function, so that selected eigenvalues appear in the upper left |
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40 diagonal blocks of the quasi triangular Schur matrix. |
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41 |
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42 The logical vector @var{select} specifies the selected eigenvalues as they |
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43 appear along @var{S}'s diagonal. |
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44 |
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45 For example, given the matrix @code{@var{A} = [1, 2; 3, 4]}, and its Schur |
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46 decomposition |
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47 |
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48 @example |
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49 [@var{U}, @var{S}] = schur (@var{A}) |
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50 @end example |
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51 |
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52 @noindent |
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53 which returns |
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54 |
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55 @example |
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56 @group |
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57 @var{U} = |
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58 |
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59 -0.82456 -0.56577 |
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60 0.56577 -0.82456 |
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61 |
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62 @var{S} = |
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63 |
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64 -0.37228 -1.00000 |
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65 0.00000 5.37228 |
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66 |
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67 @end group |
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68 @end example |
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69 |
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70 It is possible to reorder the decomposition so that the positive eigenvalue |
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71 is in the upper left corner, by doing: |
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72 |
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73 @example |
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74 [@var{U}, @var{S}] = ordschur (@var{U}, @var{S}, [0,1]) |
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75 @end example |
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76 |
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77 @seealso{schur, ordeig, ordqz} |
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78 @end deftypefn */) |
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79 { |
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80 if (args.length () != 3) |
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81 print_usage (); |
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82 |
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83 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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84 |
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85 const octave_idx_type sel_n = sel_arg.numel (); |
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86 |
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87 const dim_vector dimU = args(0).dims (); |
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88 const dim_vector dimS = args(1).dims (); |
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89 |
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90 if (sel_n != dimU(0)) |
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91 error ("ordschur: SELECT must have same length as the sides of U and S"); |
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92 else if (sel_n != dimU(0) || sel_n != dimS(0) || sel_n != dimU(1) |
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93 || sel_n != dimS(1)) |
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94 error ("ordschur: U and S must be square and of equal sizes"); |
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95 |
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96 octave_value_list retval; |
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97 |
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98 const bool double_type = args(0).is_double_type () |
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99 || args(1).is_double_type (); |
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100 const bool complex_type = args(0).iscomplex () |
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101 || args(1).iscomplex (); |
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102 |
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103 #define PREPARE_ARGS(TYPE, TYPE_M, TYPE_COND) \ |
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104 TYPE ## Matrix U = args(0).x ## TYPE_M ## _value \ |
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105 ("ordschur: U and S must be real or complex floating point matrices"); \ |
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106 TYPE ## Matrix S = args(1).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 w (dim_vector (n, 1)); \ |
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109 TYPE ## Matrix work (dim_vector (n, 1)); \ |
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110 F77_INT m; \ |
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111 F77_INT info; \ |
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112 TYPE_COND cond1, cond2; |
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113 |
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114 #define PREPARE_OUTPUT() \ |
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115 if (info != 0) \ |
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116 error ("ordschur: trsen failed"); \ |
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117 \ |
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118 retval = ovl (U, S); |
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119 |
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120 F77_INT n = octave::to_f77_int (sel_n); |
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121 Array<F77_INT> sel (dim_vector (n, 1)); |
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122 for (F77_INT i = 0; i < n; i++) |
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123 sel.xelem (i) = octave::to_f77_int (sel_arg.xelem (i)); |
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124 |
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125 if (double_type) |
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126 { |
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127 if (complex_type) |
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128 { |
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129 PREPARE_ARGS (Complex, complex_matrix, double) |
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130 |
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131 F77_XFCN (ztrsen, ztrsen, |
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132 (F77_CONST_CHAR_ARG ("N"), F77_CONST_CHAR_ARG ("V"), |
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133 sel.data (), n, F77_DBLE_CMPLX_ARG (S.fortran_vec ()), n, |
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134 F77_DBLE_CMPLX_ARG (U.fortran_vec ()), n, |
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135 F77_DBLE_CMPLX_ARG (w.fortran_vec ()), m, cond1, cond2, |
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136 F77_DBLE_CMPLX_ARG (work.fortran_vec ()), n, |
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137 info)); |
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138 |
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139 PREPARE_OUTPUT() |
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140 } |
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141 else |
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142 { |
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143 PREPARE_ARGS (, matrix, double) |
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144 Matrix wi (dim_vector (n, 1)); |
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145 Array<F77_INT> iwork (dim_vector (n, 1)); |
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146 |
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147 F77_XFCN (dtrsen, dtrsen, |
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148 (F77_CONST_CHAR_ARG ("N"), F77_CONST_CHAR_ARG ("V"), |
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149 sel.data (), n, S.fortran_vec (), n, U.fortran_vec (), n, |
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150 w.fortran_vec (), wi.fortran_vec (), m, cond1, cond2, |
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151 work.fortran_vec (), n, iwork.fortran_vec (), n, info)); |
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152 |
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153 PREPARE_OUTPUT () |
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154 } |
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155 } |
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156 else |
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157 { |
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158 if (complex_type) |
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159 { |
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160 PREPARE_ARGS (FloatComplex, float_complex_matrix, float) |
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161 |
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162 F77_XFCN (ctrsen, ctrsen, |
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163 (F77_CONST_CHAR_ARG ("N"), F77_CONST_CHAR_ARG ("V"), |
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164 sel.data (), n, F77_CMPLX_ARG (S.fortran_vec ()), n, |
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165 F77_CMPLX_ARG (U.fortran_vec ()), n, |
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166 F77_CMPLX_ARG (w.fortran_vec ()), m, cond1, cond2, |
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167 F77_CMPLX_ARG (work.fortran_vec ()), n, |
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168 info)); |
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169 |
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170 PREPARE_OUTPUT () |
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171 } |
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172 else |
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173 { |
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174 PREPARE_ARGS (Float, float_matrix, float) |
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175 FloatMatrix wi (dim_vector (n, 1)); |
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176 Array<F77_INT> iwork (dim_vector (n, 1)); |
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177 |
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178 F77_XFCN (strsen, strsen, |
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179 (F77_CONST_CHAR_ARG ("N"), F77_CONST_CHAR_ARG ("V"), |
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180 sel.data (), n, S.fortran_vec (), n, U.fortran_vec (), n, |
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181 w.fortran_vec (), wi.fortran_vec (), m, cond1, cond2, |
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182 work.fortran_vec (), n, iwork.fortran_vec (), n, info)); |
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183 |
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184 PREPARE_OUTPUT () |
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185 } |
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186 } |
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187 |
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188 #undef PREPARE_ARGS |
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189 #undef PREPARE_OUTPUT |
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190 |
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191 return retval; |
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192 } |
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193 |
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194 /* |
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195 |
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196 %!test |
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197 %! A = [1, 2, 3, -2; 4, 5, 6, -5 ; 7, 8, 9, -5; 10, 11, 12, 4 ]; |
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198 %! [U, T] = schur (A); |
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199 %! [US, TS] = ordschur (U, T, [ 0, 0, 1, 1 ]); |
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200 %! assert (US*TS*US', A, sqrt (eps)); |
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201 %! assert (diag (T)(3:4), diag (TS)(1:2), sqrt (eps)); |
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202 |
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203 %!test |
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204 %! A = [1, 2, 3, -2; 4, 5, 6, -5 ; 7, 8, 9, -5; 10, 11, 12, 4 ]; |
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205 %! [U, T] = schur (A); |
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206 %! [US, TS] = ordschur (single (U), single (T), [ 0, 0, 1, 1 ]); |
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207 %! assert (US*TS*US', A, sqrt (eps ("single"))); |
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208 %! assert (diag (T)(3:4), diag (TS)(1:2), sqrt (eps ("single"))); |
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209 |
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210 %!test |
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211 %! A = [1, 2, 3, -2; 4, 5, 6, -5 ; 7, 8, 9, -5; 10, 11, 12, 4+3i ]; |
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212 %! [U, T] = schur (A); |
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213 %! [US, TS] = ordschur (U, T, [ 0, 0, 1, 1 ]); |
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214 %! assert (US*TS*US', A, sqrt (eps)); |
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215 %! assert (diag (T)(3:4), diag (TS)(1:2), sqrt (eps)); |
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216 |
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217 %!test |
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218 %! A = [1, 2, 3, -2; 4, 5, 6, -5 ; 7, 8, 9, -5; 10, 11, 12, 4+3i ]; |
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219 %! [U, T] = schur (A); |
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220 %! [US, TS] = ordschur (single (U), single (T), [ 0, 0, 1, 1 ]); |
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221 %! assert (US*TS*US', A, sqrt (eps ("single"))); |
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222 %! assert (diag (T)(3:4), diag (TS)(1:2), sqrt (eps ("single"))); |
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223 |
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224 */ |