Mercurial > octave
annotate liboctave/numeric/schur.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 | 5c14f81e0937 0a5b15007766 |
children | ae47678c76e8 |
rev | line source |
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1 //////////////////////////////////////////////////////////////////////// |
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2 // |
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3 // Copyright (C) 1994-2021 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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26 #if defined (HAVE_CONFIG_H) |
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27 # include "config.h" |
457 | 28 #endif |
29 | |
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30 #include "Array.h" |
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31 #include "CMatrix.h" |
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32 #include "dMatrix.h" |
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33 #include "fCMatrix.h" |
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34 #include "fMatrix.h" |
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36 #include "lo-lapack-proto.h" |
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37 #include "oct-locbuf.h" |
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38 #include "schur.h" |
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39 |
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40 namespace octave |
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41 { |
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42 namespace math |
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43 { |
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44 // For real types. |
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45 |
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46 static F77_INT |
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47 select_ana (const double& a, const double&) |
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48 { |
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49 return (a < 0.0); |
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50 } |
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51 |
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52 static F77_INT |
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53 select_dig (const double& a, const double& b) |
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54 { |
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55 return (hypot (a, b) < 1.0); |
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56 } |
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57 |
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58 static F77_INT |
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59 select_ana (const float& a, const float&) |
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60 { |
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61 return (a < 0.0); |
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62 } |
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63 |
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64 static F77_INT |
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65 select_dig (const float& a, const float& b) |
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66 { |
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67 return (hypot (a, b) < 1.0); |
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68 } |
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69 |
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70 // For complex types. |
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71 |
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72 static F77_INT |
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73 select_ana (const F77_DBLE_CMPLX& a_arg) |
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74 { |
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75 const Complex a = reinterpret_cast<const Complex&> (a_arg); |
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76 return a.real () < 0.0; |
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77 } |
1929 | 78 |
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79 static F77_INT |
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80 select_dig (const F77_DBLE_CMPLX& a_arg) |
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81 { |
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82 const Complex& a = reinterpret_cast<const Complex&> (a_arg); |
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83 return (abs (a) < 1.0); |
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84 } |
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85 |
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86 static F77_INT |
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87 select_ana (const F77_CMPLX& a_arg) |
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88 { |
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89 const FloatComplex& a = reinterpret_cast<const FloatComplex&> (a_arg); |
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90 return a.real () < 0.0; |
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91 } |
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92 |
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93 static F77_INT |
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94 select_dig (const F77_CMPLX& a_arg) |
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95 { |
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96 const FloatComplex& a = reinterpret_cast<const FloatComplex&> (a_arg); |
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97 return (abs (a) < 1.0); |
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98 } |
457 | 99 |
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100 template <> |
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101 OCTAVE_API F77_INT |
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102 schur<Matrix>::init (const Matrix& a, const std::string& ord, bool calc_unitary) |
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103 { |
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104 F77_INT a_nr = to_f77_int (a.rows ()); |
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105 F77_INT a_nc = to_f77_int (a.cols ()); |
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106 |
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107 if (a_nr != a_nc) |
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108 (*current_liboctave_error_handler) ("schur: requires square matrix"); |
3334 | 109 |
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110 if (a_nr == 0) |
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111 { |
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112 schur_mat.clear (); |
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113 unitary_mat.clear (); |
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114 return 0; |
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115 } |
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116 |
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117 // Workspace requirements may need to be fixed if any of the |
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118 // following change. |
457 | 119 |
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120 char jobvs; |
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121 char sense = 'N'; |
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122 char sort = 'N'; |
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123 |
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124 if (calc_unitary) |
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125 jobvs = 'V'; |
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126 else |
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127 jobvs = 'N'; |
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129 char ord_char = (ord.empty () ? 'U' : ord[0]); |
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130 |
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131 if (ord_char == 'A' || ord_char == 'D' || ord_char == 'a' || ord_char == 'd') |
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132 sort = 'S'; |
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134 volatile double_selector selector = nullptr; |
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135 if (ord_char == 'A' || ord_char == 'a') |
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136 selector = select_ana; |
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137 else if (ord_char == 'D' || ord_char == 'd') |
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138 selector = select_dig; |
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140 F77_INT n = a_nc; |
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141 F77_INT lwork = 8 * n; |
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142 F77_INT liwork = 1; |
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143 F77_INT info; |
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144 F77_INT sdim; |
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145 double rconde; |
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146 double rcondv; |
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147 |
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148 schur_mat = a; |
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149 |
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150 if (calc_unitary) |
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151 unitary_mat.clear (n, n); |
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152 |
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153 double *s = schur_mat.fortran_vec (); |
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154 double *q = unitary_mat.fortran_vec (); |
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155 |
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156 Array<double> wr (dim_vector (n, 1)); |
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157 double *pwr = wr.fortran_vec (); |
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158 |
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159 Array<double> wi (dim_vector (n, 1)); |
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160 double *pwi = wi.fortran_vec (); |
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162 Array<double> work (dim_vector (lwork, 1)); |
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163 double *pwork = work.fortran_vec (); |
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164 |
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165 // BWORK is not referenced for the non-ordered Schur routine. |
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166 F77_INT ntmp = (ord_char == 'N' || ord_char == 'n') ? 0 : n; |
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167 Array<F77_INT> bwork (dim_vector (ntmp, 1)); |
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168 F77_INT *pbwork = bwork.fortran_vec (); |
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169 |
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170 Array<F77_INT> iwork (dim_vector (liwork, 1)); |
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171 F77_INT *piwork = iwork.fortran_vec (); |
457 | 172 |
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173 F77_XFCN (dgeesx, DGEESX, (F77_CONST_CHAR_ARG2 (&jobvs, 1), |
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174 F77_CONST_CHAR_ARG2 (&sort, 1), |
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175 selector, |
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176 F77_CONST_CHAR_ARG2 (&sense, 1), |
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177 n, s, n, sdim, pwr, pwi, q, n, rconde, rcondv, |
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178 pwork, lwork, piwork, liwork, pbwork, info |
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179 F77_CHAR_ARG_LEN (1) |
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180 F77_CHAR_ARG_LEN (1) |
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181 F77_CHAR_ARG_LEN (1))); |
1929 | 182 |
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183 return info; |
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184 } |
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186 template <> |
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187 OCTAVE_API F77_INT |
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188 schur<FloatMatrix>::init (const FloatMatrix& a, const std::string& ord, |
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189 bool calc_unitary) |
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190 { |
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191 F77_INT a_nr = to_f77_int (a.rows ()); |
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192 F77_INT a_nc = to_f77_int (a.cols ()); |
1929 | 193 |
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194 if (a_nr != a_nc) |
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195 (*current_liboctave_error_handler) ("SCHUR requires square matrix"); |
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196 |
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197 if (a_nr == 0) |
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198 { |
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199 schur_mat.clear (); |
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200 unitary_mat.clear (); |
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201 return 0; |
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202 } |
457 | 203 |
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204 // Workspace requirements may need to be fixed if any of the |
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205 // following change. |
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206 |
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207 char jobvs; |
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208 char sense = 'N'; |
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209 char sort = 'N'; |
1929 | 210 |
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211 if (calc_unitary) |
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212 jobvs = 'V'; |
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213 else |
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214 jobvs = 'N'; |
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215 |
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216 char ord_char = (ord.empty () ? 'U' : ord[0]); |
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217 |
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218 if (ord_char == 'A' || ord_char == 'D' || ord_char == 'a' || ord_char == 'd') |
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219 sort = 'S'; |
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220 |
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221 volatile float_selector selector = nullptr; |
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222 if (ord_char == 'A' || ord_char == 'a') |
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223 selector = select_ana; |
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224 else if (ord_char == 'D' || ord_char == 'd') |
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225 selector = select_dig; |
1929 | 226 |
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227 F77_INT n = a_nc; |
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228 F77_INT lwork = 8 * n; |
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229 F77_INT liwork = 1; |
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230 F77_INT info; |
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231 F77_INT sdim; |
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232 float rconde; |
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233 float rcondv; |
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234 |
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235 schur_mat = a; |
457 | 236 |
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237 if (calc_unitary) |
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238 unitary_mat.clear (n, n); |
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239 |
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240 float *s = schur_mat.fortran_vec (); |
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241 float *q = unitary_mat.fortran_vec (); |
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242 |
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243 Array<float> wr (dim_vector (n, 1)); |
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244 float *pwr = wr.fortran_vec (); |
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245 |
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246 Array<float> wi (dim_vector (n, 1)); |
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247 float *pwi = wi.fortran_vec (); |
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249 Array<float> work (dim_vector (lwork, 1)); |
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250 float *pwork = work.fortran_vec (); |
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251 |
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252 // BWORK is not referenced for the non-ordered Schur routine. |
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253 F77_INT ntmp = (ord_char == 'N' || ord_char == 'n') ? 0 : n; |
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254 Array<F77_INT> bwork (dim_vector (ntmp, 1)); |
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255 F77_INT *pbwork = bwork.fortran_vec (); |
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256 |
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257 Array<F77_INT> iwork (dim_vector (liwork, 1)); |
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258 F77_INT *piwork = iwork.fortran_vec (); |
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259 |
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260 F77_XFCN (sgeesx, SGEESX, (F77_CONST_CHAR_ARG2 (&jobvs, 1), |
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261 F77_CONST_CHAR_ARG2 (&sort, 1), |
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262 selector, |
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263 F77_CONST_CHAR_ARG2 (&sense, 1), |
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264 n, s, n, sdim, pwr, pwi, q, n, rconde, rcondv, |
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265 pwork, lwork, piwork, liwork, pbwork, info |
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266 F77_CHAR_ARG_LEN (1) |
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267 F77_CHAR_ARG_LEN (1) |
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268 F77_CHAR_ARG_LEN (1))); |
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269 |
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270 return info; |
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271 } |
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272 |
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273 template <> |
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274 OCTAVE_API F77_INT |
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275 schur<ComplexMatrix>::init (const ComplexMatrix& a, const std::string& ord, |
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276 bool calc_unitary) |
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277 { |
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278 F77_INT a_nr = to_f77_int (a.rows ()); |
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279 F77_INT a_nc = to_f77_int (a.cols ()); |
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280 |
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281 if (a_nr != a_nc) |
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282 (*current_liboctave_error_handler) ("SCHUR requires square matrix"); |
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283 |
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284 if (a_nr == 0) |
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285 { |
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286 schur_mat.clear (); |
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287 unitary_mat.clear (); |
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288 return 0; |
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289 } |
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290 |
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291 // Workspace requirements may need to be fixed if any of the |
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292 // following change. |
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293 |
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294 char jobvs; |
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295 char sense = 'N'; |
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296 char sort = 'N'; |
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297 |
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298 if (calc_unitary) |
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299 jobvs = 'V'; |
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300 else |
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301 jobvs = 'N'; |
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302 |
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303 char ord_char = (ord.empty () ? 'U' : ord[0]); |
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304 |
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305 if (ord_char == 'A' || ord_char == 'D' || ord_char == 'a' || ord_char == 'd') |
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306 sort = 'S'; |
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307 |
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308 volatile complex_selector selector = nullptr; |
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309 if (ord_char == 'A' || ord_char == 'a') |
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310 selector = select_ana; |
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311 else if (ord_char == 'D' || ord_char == 'd') |
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312 selector = select_dig; |
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313 |
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314 F77_INT n = a_nc; |
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315 F77_INT lwork = 8 * n; |
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316 F77_INT info; |
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317 F77_INT sdim; |
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318 double rconde; |
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319 double rcondv; |
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320 |
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321 schur_mat = a; |
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322 if (calc_unitary) |
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323 unitary_mat.clear (n, n); |
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324 |
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325 Complex *s = schur_mat.fortran_vec (); |
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326 Complex *q = unitary_mat.fortran_vec (); |
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327 |
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328 Array<double> rwork (dim_vector (n, 1)); |
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329 double *prwork = rwork.fortran_vec (); |
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330 |
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331 Array<Complex> w (dim_vector (n, 1)); |
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332 Complex *pw = w.fortran_vec (); |
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333 |
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334 Array<Complex> work (dim_vector (lwork, 1)); |
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335 Complex *pwork = work.fortran_vec (); |
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336 |
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337 // BWORK is not referenced for non-ordered Schur. |
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338 F77_INT ntmp = (ord_char == 'N' || ord_char == 'n') ? 0 : n; |
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339 Array<F77_INT> bwork (dim_vector (ntmp, 1)); |
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340 F77_INT *pbwork = bwork.fortran_vec (); |
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341 |
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342 F77_XFCN (zgeesx, ZGEESX, (F77_CONST_CHAR_ARG2 (&jobvs, 1), |
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343 F77_CONST_CHAR_ARG2 (&sort, 1), |
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344 selector, |
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345 F77_CONST_CHAR_ARG2 (&sense, 1), |
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346 n, F77_DBLE_CMPLX_ARG (s), n, sdim, F77_DBLE_CMPLX_ARG (pw), |
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347 F77_DBLE_CMPLX_ARG (q), n, rconde, rcondv, |
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348 F77_DBLE_CMPLX_ARG (pwork), lwork, prwork, pbwork, info |
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349 F77_CHAR_ARG_LEN (1) |
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350 F77_CHAR_ARG_LEN (1) |
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351 F77_CHAR_ARG_LEN (1))); |
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352 |
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353 return info; |
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354 } |
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355 |
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356 template <> |
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357 OCTAVE_API schur<ComplexMatrix> |
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358 rsf2csf<ComplexMatrix, Matrix> (const Matrix& s_arg, const Matrix& u_arg) |
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359 { |
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360 ComplexMatrix s (s_arg); |
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361 ComplexMatrix u (u_arg); |
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362 |
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363 F77_INT n = to_f77_int (s.rows ()); |
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364 |
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365 if (s.columns () != n || u.rows () != n || u.columns () != n) |
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366 (*current_liboctave_error_handler) |
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367 ("rsf2csf: inconsistent matrix dimensions"); |
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368 |
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369 if (n > 0) |
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370 { |
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371 OCTAVE_LOCAL_BUFFER (double, c, n-1); |
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372 OCTAVE_LOCAL_BUFFER (double, sx, n-1); |
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373 |
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374 F77_XFCN (zrsf2csf, ZRSF2CSF, (n, F77_DBLE_CMPLX_ARG (s.fortran_vec ()), |
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375 F77_DBLE_CMPLX_ARG (u.fortran_vec ()), c, sx)); |
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376 } |
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377 |
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378 return schur<ComplexMatrix> (s, u); |
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379 } |
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380 |
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381 template <> |
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382 OCTAVE_API F77_INT |
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383 schur<FloatComplexMatrix>::init (const FloatComplexMatrix& a, |
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384 const std::string& ord, bool calc_unitary) |
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385 { |
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386 F77_INT a_nr = to_f77_int (a.rows ()); |
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387 F77_INT a_nc = to_f77_int (a.cols ()); |
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388 |
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389 if (a_nr != a_nc) |
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390 (*current_liboctave_error_handler) ("SCHUR requires square matrix"); |
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391 |
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392 if (a_nr == 0) |
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393 { |
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394 schur_mat.clear (); |
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395 unitary_mat.clear (); |
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396 return 0; |
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397 } |
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398 |
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399 // Workspace requirements may need to be fixed if any of the |
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400 // following change. |
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401 |
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402 char jobvs; |
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403 char sense = 'N'; |
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404 char sort = 'N'; |
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405 |
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406 if (calc_unitary) |
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407 jobvs = 'V'; |
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408 else |
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409 jobvs = 'N'; |
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410 |
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411 char ord_char = (ord.empty () ? 'U' : ord[0]); |
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412 |
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413 if (ord_char == 'A' || ord_char == 'D' || ord_char == 'a' || ord_char == 'd') |
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414 sort = 'S'; |
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415 |
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416 volatile float_complex_selector selector = nullptr; |
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417 if (ord_char == 'A' || ord_char == 'a') |
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418 selector = select_ana; |
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419 else if (ord_char == 'D' || ord_char == 'd') |
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420 selector = select_dig; |
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421 |
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422 F77_INT n = a_nc; |
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423 F77_INT lwork = 8 * n; |
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424 F77_INT info; |
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425 F77_INT sdim; |
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426 float rconde; |
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427 float rcondv; |
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428 |
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429 schur_mat = a; |
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430 if (calc_unitary) |
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431 unitary_mat.clear (n, n); |
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432 |
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433 FloatComplex *s = schur_mat.fortran_vec (); |
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434 FloatComplex *q = unitary_mat.fortran_vec (); |
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435 |
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436 Array<float> rwork (dim_vector (n, 1)); |
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437 float *prwork = rwork.fortran_vec (); |
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438 |
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439 Array<FloatComplex> w (dim_vector (n, 1)); |
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440 FloatComplex *pw = w.fortran_vec (); |
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441 |
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442 Array<FloatComplex> work (dim_vector (lwork, 1)); |
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443 FloatComplex *pwork = work.fortran_vec (); |
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444 |
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445 // BWORK is not referenced for non-ordered Schur. |
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446 F77_INT ntmp = (ord_char == 'N' || ord_char == 'n') ? 0 : n; |
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447 Array<F77_INT> bwork (dim_vector (ntmp, 1)); |
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448 F77_INT *pbwork = bwork.fortran_vec (); |
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449 |
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450 F77_XFCN (cgeesx, CGEESX, (F77_CONST_CHAR_ARG2 (&jobvs, 1), |
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451 F77_CONST_CHAR_ARG2 (&sort, 1), |
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452 selector, |
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453 F77_CONST_CHAR_ARG2 (&sense, 1), |
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454 n, F77_CMPLX_ARG (s), n, sdim, F77_CMPLX_ARG (pw), F77_CMPLX_ARG (q), n, rconde, |
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455 rcondv, |
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456 F77_CMPLX_ARG (pwork), lwork, prwork, pbwork, info |
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457 F77_CHAR_ARG_LEN (1) |
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458 F77_CHAR_ARG_LEN (1) |
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459 F77_CHAR_ARG_LEN (1))); |
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460 |
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461 return info; |
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462 } |
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463 |
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464 template <> |
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465 OCTAVE_API schur<FloatComplexMatrix> |
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466 rsf2csf<FloatComplexMatrix, FloatMatrix> (const FloatMatrix& s_arg, |
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467 const FloatMatrix& u_arg) |
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468 { |
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469 FloatComplexMatrix s (s_arg); |
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470 FloatComplexMatrix u (u_arg); |
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471 |
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472 F77_INT n = to_f77_int (s.rows ()); |
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473 |
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474 if (s.columns () != n || u.rows () != n || u.columns () != n) |
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475 (*current_liboctave_error_handler) |
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476 ("rsf2csf: inconsistent matrix dimensions"); |
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477 |
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478 if (n > 0) |
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479 { |
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480 OCTAVE_LOCAL_BUFFER (float, c, n-1); |
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481 OCTAVE_LOCAL_BUFFER (float, sx, n-1); |
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482 |
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483 F77_XFCN (crsf2csf, CRSF2CSF, (n, F77_CMPLX_ARG (s.fortran_vec ()), |
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484 F77_CMPLX_ARG (u.fortran_vec ()), c, sx)); |
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485 } |
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486 |
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487 return schur<FloatComplexMatrix> (s, u); |
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488 } |
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489 |
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490 // Instantiations we need. |
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491 |
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492 template class schur<ComplexMatrix>; |
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493 |
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494 template class schur<FloatComplexMatrix>; |
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495 |
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496 template class schur<FloatMatrix>; |
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497 |
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498 template class schur<Matrix>; |
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499 } |
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500 } |