Mercurial > octave
annotate liboctave/numeric/schur.cc @ 33634:4a70f390c85e default tip @
maint: Merge stable to default.
author | Markus Mützel <markus.muetzel@gmx.de> |
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date | Tue, 28 May 2024 15:25:54 +0200 |
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1 //////////////////////////////////////////////////////////////////////// |
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2 // |
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3 // Copyright (C) 1994-2024 The Octave Project Developers |
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4 // |
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5 // See the file COPYRIGHT.md in the top-level directory of this |
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6 // distribution or <https://octave.org/copyright/>. |
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7 // |
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8 // This file is part of Octave. |
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9 // |
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10 // Octave is free software: you can redistribute it and/or modify it |
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11 // under the terms of the GNU General Public License as published by |
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12 // the Free Software Foundation, either version 3 of the License, or |
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13 // (at your option) any later version. |
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14 // |
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15 // Octave is distributed in the hope that it will be useful, but |
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16 // WITHOUT ANY WARRANTY; without even the implied warranty of |
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17 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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18 // GNU General Public License for more details. |
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19 // |
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20 // You should have received a copy of the GNU General Public License |
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21 // along with Octave; see the file COPYING. If not, see |
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22 // <https://www.gnu.org/licenses/>. |
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23 // |
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24 //////////////////////////////////////////////////////////////////////// |
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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 OCTAVE_BEGIN_NAMESPACE(octave) |
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41 |
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42 OCTAVE_BEGIN_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 } |
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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 } |
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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, |
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103 bool calc_unitary) |
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104 { |
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105 F77_INT a_nr = to_f77_int (a.rows ()); |
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106 F77_INT a_nc = to_f77_int (a.cols ()); |
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107 |
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108 if (a_nr != a_nc) |
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109 (*current_liboctave_error_handler) ("schur: requires square matrix"); |
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110 |
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111 if (a_nr == 0) |
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112 { |
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113 m_schur_mat.clear (); |
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114 m_unitary_schur_mat.clear (); |
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115 return 0; |
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116 } |
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118 // Workspace requirements may need to be fixed if any of the |
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119 // following change. |
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120 |
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121 char jobvs; |
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122 char sense = 'N'; |
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123 char sort = 'N'; |
457 | 124 |
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125 if (calc_unitary) |
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126 jobvs = 'V'; |
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127 else |
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128 jobvs = 'N'; |
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130 char ord_char = (ord.empty () ? 'U' : ord[0]); |
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132 if (ord_char == 'A' || ord_char == 'D' |
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133 || ord_char == 'a' || ord_char == 'd') |
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134 sort = 'S'; |
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136 double_selector selector = nullptr; |
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137 if (ord_char == 'A' || ord_char == 'a') |
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138 selector = select_ana; |
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139 else if (ord_char == 'D' || ord_char == 'd') |
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140 selector = select_dig; |
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141 |
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142 F77_INT n = a_nc; |
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143 F77_INT lwork = 8 * n; |
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144 F77_INT liwork = 1; |
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145 F77_INT info; |
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146 F77_INT sdim; |
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147 double rconde; |
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148 double rcondv; |
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149 |
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150 m_schur_mat = a; |
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151 |
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152 if (calc_unitary) |
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153 m_unitary_schur_mat.clear (n, n); |
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155 double *s = m_schur_mat.rwdata (); |
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156 double *q = m_unitary_schur_mat.rwdata (); |
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157 |
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158 Array<double> wr (dim_vector (n, 1)); |
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159 double *pwr = wr.rwdata (); |
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161 Array<double> wi (dim_vector (n, 1)); |
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162 double *pwi = wi.rwdata (); |
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164 Array<double> work (dim_vector (lwork, 1)); |
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165 double *pwork = work.rwdata (); |
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167 // BWORK is not referenced for the non-ordered Schur routine. |
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168 F77_INT ntmp = (ord_char == 'N' || ord_char == 'n') ? 0 : n; |
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169 Array<F77_INT> bwork (dim_vector (ntmp, 1)); |
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170 F77_INT *pbwork = bwork.rwdata (); |
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171 |
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172 Array<F77_INT> iwork (dim_vector (liwork, 1)); |
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173 F77_INT *piwork = iwork.rwdata (); |
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175 F77_XFCN (dgeesx, DGEESX, (F77_CONST_CHAR_ARG2 (&jobvs, 1), |
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176 F77_CONST_CHAR_ARG2 (&sort, 1), |
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177 selector, |
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178 F77_CONST_CHAR_ARG2 (&sense, 1), |
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179 n, s, n, sdim, pwr, pwi, q, n, rconde, rcondv, |
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180 pwork, lwork, piwork, liwork, pbwork, info |
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181 F77_CHAR_ARG_LEN (1) |
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182 F77_CHAR_ARG_LEN (1) |
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183 F77_CHAR_ARG_LEN (1))); |
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185 return info; |
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186 } |
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188 template <> |
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189 OCTAVE_API F77_INT |
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190 schur<FloatMatrix>::init (const FloatMatrix& a, const std::string& ord, |
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191 bool calc_unitary) |
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192 { |
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193 F77_INT a_nr = to_f77_int (a.rows ()); |
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194 F77_INT a_nc = to_f77_int (a.cols ()); |
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195 |
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196 if (a_nr != a_nc) |
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197 (*current_liboctave_error_handler) ("SCHUR requires square matrix"); |
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198 |
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199 if (a_nr == 0) |
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200 { |
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201 m_schur_mat.clear (); |
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202 m_unitary_schur_mat.clear (); |
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203 return 0; |
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204 } |
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205 |
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206 // Workspace requirements may need to be fixed if any of the |
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207 // following change. |
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208 |
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209 char jobvs; |
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210 char sense = 'N'; |
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211 char sort = 'N'; |
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212 |
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213 if (calc_unitary) |
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214 jobvs = 'V'; |
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215 else |
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216 jobvs = 'N'; |
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217 |
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218 char ord_char = (ord.empty () ? 'U' : ord[0]); |
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219 |
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220 if (ord_char == 'A' || ord_char == 'D' |
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221 || ord_char == 'a' || ord_char == 'd') |
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222 sort = 'S'; |
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223 |
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224 float_selector selector = nullptr; |
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225 if (ord_char == 'A' || ord_char == 'a') |
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226 selector = select_ana; |
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227 else if (ord_char == 'D' || ord_char == 'd') |
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228 selector = select_dig; |
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229 |
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230 F77_INT n = a_nc; |
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231 F77_INT lwork = 8 * n; |
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232 F77_INT liwork = 1; |
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233 F77_INT info; |
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234 F77_INT sdim; |
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235 float rconde; |
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236 float rcondv; |
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237 |
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238 m_schur_mat = a; |
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239 |
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240 if (calc_unitary) |
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241 m_unitary_schur_mat.clear (n, n); |
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242 |
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243 float *s = m_schur_mat.rwdata (); |
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244 float *q = m_unitary_schur_mat.rwdata (); |
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245 |
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246 Array<float> wr (dim_vector (n, 1)); |
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247 float *pwr = wr.rwdata (); |
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248 |
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249 Array<float> wi (dim_vector (n, 1)); |
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250 float *pwi = wi.rwdata (); |
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251 |
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252 Array<float> work (dim_vector (lwork, 1)); |
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253 float *pwork = work.rwdata (); |
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254 |
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255 // BWORK is not referenced for the non-ordered Schur routine. |
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256 F77_INT ntmp = (ord_char == 'N' || ord_char == 'n') ? 0 : n; |
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257 Array<F77_INT> bwork (dim_vector (ntmp, 1)); |
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258 F77_INT *pbwork = bwork.rwdata (); |
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259 |
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260 Array<F77_INT> iwork (dim_vector (liwork, 1)); |
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261 F77_INT *piwork = iwork.rwdata (); |
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262 |
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263 F77_XFCN (sgeesx, SGEESX, (F77_CONST_CHAR_ARG2 (&jobvs, 1), |
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264 F77_CONST_CHAR_ARG2 (&sort, 1), |
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265 selector, |
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266 F77_CONST_CHAR_ARG2 (&sense, 1), |
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267 n, s, n, sdim, pwr, pwi, q, n, rconde, rcondv, |
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268 pwork, lwork, piwork, liwork, pbwork, info |
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269 F77_CHAR_ARG_LEN (1) |
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270 F77_CHAR_ARG_LEN (1) |
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271 F77_CHAR_ARG_LEN (1))); |
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272 |
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273 return info; |
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274 } |
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275 |
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276 template <> |
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277 OCTAVE_API F77_INT |
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278 schur<ComplexMatrix>::init (const ComplexMatrix& a, const std::string& ord, |
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279 bool calc_unitary) |
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280 { |
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281 F77_INT a_nr = to_f77_int (a.rows ()); |
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282 F77_INT a_nc = to_f77_int (a.cols ()); |
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283 |
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284 if (a_nr != a_nc) |
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285 (*current_liboctave_error_handler) ("SCHUR requires square matrix"); |
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286 |
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287 if (a_nr == 0) |
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288 { |
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289 m_schur_mat.clear (); |
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290 m_unitary_schur_mat.clear (); |
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291 return 0; |
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292 } |
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293 |
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294 // Workspace requirements may need to be fixed if any of the |
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295 // following change. |
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296 |
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297 char jobvs; |
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298 char sense = 'N'; |
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299 char sort = 'N'; |
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300 |
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301 if (calc_unitary) |
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302 jobvs = 'V'; |
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303 else |
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304 jobvs = 'N'; |
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305 |
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306 char ord_char = (ord.empty () ? 'U' : ord[0]); |
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307 |
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308 if (ord_char == 'A' || ord_char == 'D' |
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309 || ord_char == 'a' || ord_char == 'd') |
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310 sort = 'S'; |
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311 |
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312 complex_selector selector = nullptr; |
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313 if (ord_char == 'A' || ord_char == 'a') |
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314 selector = select_ana; |
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315 else if (ord_char == 'D' || ord_char == 'd') |
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316 selector = select_dig; |
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317 |
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318 F77_INT n = a_nc; |
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319 F77_INT lwork = 8 * n; |
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320 F77_INT info; |
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321 F77_INT sdim; |
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322 double rconde; |
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323 double rcondv; |
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324 |
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325 m_schur_mat = a; |
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326 if (calc_unitary) |
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327 m_unitary_schur_mat.clear (n, n); |
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328 |
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329 Complex *s = m_schur_mat.rwdata (); |
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330 Complex *q = m_unitary_schur_mat.rwdata (); |
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331 |
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332 Array<double> rwork (dim_vector (n, 1)); |
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333 double *prwork = rwork.rwdata (); |
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334 |
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335 Array<Complex> w (dim_vector (n, 1)); |
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336 Complex *pw = w.rwdata (); |
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337 |
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338 Array<Complex> work (dim_vector (lwork, 1)); |
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339 Complex *pwork = work.rwdata (); |
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340 |
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341 // BWORK is not referenced for non-ordered Schur. |
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342 F77_INT ntmp = (ord_char == 'N' || ord_char == 'n') ? 0 : n; |
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343 Array<F77_INT> bwork (dim_vector (ntmp, 1)); |
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344 F77_INT *pbwork = bwork.rwdata (); |
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345 |
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346 F77_XFCN (zgeesx, ZGEESX, |
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347 (F77_CONST_CHAR_ARG2 (&jobvs, 1), |
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348 F77_CONST_CHAR_ARG2 (&sort, 1), |
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349 selector, |
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350 F77_CONST_CHAR_ARG2 (&sense, 1), |
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351 n, F77_DBLE_CMPLX_ARG (s), n, sdim, F77_DBLE_CMPLX_ARG (pw), |
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352 F77_DBLE_CMPLX_ARG (q), n, rconde, rcondv, |
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353 F77_DBLE_CMPLX_ARG (pwork), lwork, prwork, pbwork, info |
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354 F77_CHAR_ARG_LEN (1) |
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355 F77_CHAR_ARG_LEN (1) |
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356 F77_CHAR_ARG_LEN (1))); |
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357 |
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358 return info; |
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359 } |
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360 |
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361 template <> |
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362 OCTAVE_API schur<ComplexMatrix> |
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363 rsf2csf<ComplexMatrix, Matrix> (const Matrix& s_arg, const Matrix& u_arg) |
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364 { |
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365 ComplexMatrix s (s_arg); |
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366 ComplexMatrix u (u_arg); |
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367 |
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368 F77_INT n = to_f77_int (s.rows ()); |
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369 |
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370 if (s.columns () != n || u.rows () != n || u.columns () != n) |
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371 (*current_liboctave_error_handler) |
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372 ("rsf2csf: inconsistent matrix dimensions"); |
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373 |
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374 if (n > 0) |
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375 { |
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376 OCTAVE_LOCAL_BUFFER (double, c, n-1); |
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377 OCTAVE_LOCAL_BUFFER (double, sx, n-1); |
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378 |
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379 F77_XFCN (zrsf2csf, ZRSF2CSF, |
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380 (n, F77_DBLE_CMPLX_ARG (s.rwdata ()), |
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381 F77_DBLE_CMPLX_ARG (u.rwdata ()), c, sx)); |
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382 } |
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383 |
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384 return schur<ComplexMatrix> (s, u); |
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385 } |
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386 |
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387 template <> |
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388 OCTAVE_API F77_INT |
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389 schur<FloatComplexMatrix>::init (const FloatComplexMatrix& a, |
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390 const std::string& ord, bool calc_unitary) |
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391 { |
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392 F77_INT a_nr = to_f77_int (a.rows ()); |
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393 F77_INT a_nc = to_f77_int (a.cols ()); |
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394 |
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395 if (a_nr != a_nc) |
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396 (*current_liboctave_error_handler) ("SCHUR requires square matrix"); |
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397 |
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398 if (a_nr == 0) |
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399 { |
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400 m_schur_mat.clear (); |
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401 m_unitary_schur_mat.clear (); |
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402 return 0; |
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403 } |
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404 |
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405 // Workspace requirements may need to be fixed if any of the |
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406 // following change. |
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407 |
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408 char jobvs; |
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409 char sense = 'N'; |
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410 char sort = 'N'; |
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411 |
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412 if (calc_unitary) |
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413 jobvs = 'V'; |
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414 else |
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415 jobvs = 'N'; |
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416 |
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417 char ord_char = (ord.empty () ? 'U' : ord[0]); |
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418 |
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419 if (ord_char == 'A' || ord_char == 'D' |
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420 || ord_char == 'a' || ord_char == 'd') |
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421 sort = 'S'; |
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422 |
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423 float_complex_selector selector = nullptr; |
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424 if (ord_char == 'A' || ord_char == 'a') |
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425 selector = select_ana; |
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426 else if (ord_char == 'D' || ord_char == 'd') |
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427 selector = select_dig; |
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428 |
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429 F77_INT n = a_nc; |
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430 F77_INT lwork = 8 * n; |
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431 F77_INT info; |
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432 F77_INT sdim; |
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433 float rconde; |
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434 float rcondv; |
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435 |
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436 m_schur_mat = a; |
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437 if (calc_unitary) |
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438 m_unitary_schur_mat.clear (n, n); |
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439 |
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440 FloatComplex *s = m_schur_mat.rwdata (); |
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441 FloatComplex *q = m_unitary_schur_mat.rwdata (); |
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442 |
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443 Array<float> rwork (dim_vector (n, 1)); |
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444 float *prwork = rwork.rwdata (); |
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445 |
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446 Array<FloatComplex> w (dim_vector (n, 1)); |
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447 FloatComplex *pw = w.rwdata (); |
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448 |
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449 Array<FloatComplex> work (dim_vector (lwork, 1)); |
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450 FloatComplex *pwork = work.rwdata (); |
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451 |
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452 // BWORK is not referenced for non-ordered Schur. |
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453 F77_INT ntmp = (ord_char == 'N' || ord_char == 'n') ? 0 : n; |
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454 Array<F77_INT> bwork (dim_vector (ntmp, 1)); |
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455 F77_INT *pbwork = bwork.rwdata (); |
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456 |
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457 F77_XFCN (cgeesx, CGEESX, |
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458 (F77_CONST_CHAR_ARG2 (&jobvs, 1), |
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459 F77_CONST_CHAR_ARG2 (&sort, 1), |
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460 selector, |
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461 F77_CONST_CHAR_ARG2 (&sense, 1), |
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462 n, F77_CMPLX_ARG (s), n, sdim, F77_CMPLX_ARG (pw), |
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463 F77_CMPLX_ARG (q), n, |
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464 rconde, rcondv, |
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465 F77_CMPLX_ARG (pwork), lwork, prwork, pbwork, info |
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466 F77_CHAR_ARG_LEN (1) |
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467 F77_CHAR_ARG_LEN (1) |
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468 F77_CHAR_ARG_LEN (1))); |
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469 |
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470 return info; |
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471 } |
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472 |
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473 template <> |
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474 OCTAVE_API schur<FloatComplexMatrix> |
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475 rsf2csf<FloatComplexMatrix, FloatMatrix> (const FloatMatrix& s_arg, |
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476 const FloatMatrix& u_arg) |
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477 { |
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478 FloatComplexMatrix s (s_arg); |
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479 FloatComplexMatrix u (u_arg); |
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480 |
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481 F77_INT n = to_f77_int (s.rows ()); |
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482 |
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483 if (s.columns () != n || u.rows () != n || u.columns () != n) |
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484 (*current_liboctave_error_handler) |
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485 ("rsf2csf: inconsistent matrix dimensions"); |
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486 |
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487 if (n > 0) |
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488 { |
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489 OCTAVE_LOCAL_BUFFER (float, c, n-1); |
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490 OCTAVE_LOCAL_BUFFER (float, sx, n-1); |
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491 |
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492 F77_XFCN (crsf2csf, CRSF2CSF, |
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493 (n, F77_CMPLX_ARG (s.rwdata ()), |
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494 F77_CMPLX_ARG (u.rwdata ()), c, sx)); |
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495 } |
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496 |
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497 return schur<FloatComplexMatrix> (s, u); |
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498 } |
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499 |
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500 // Instantiations we need. |
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501 |
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502 template class schur<ComplexMatrix>; |
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503 |
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504 template class schur<FloatComplexMatrix>; |
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505 |
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506 template class schur<FloatMatrix>; |
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507 |
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508 template class schur<Matrix>; |
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509 |
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510 OCTAVE_END_NAMESPACE(math) |
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511 OCTAVE_END_NAMESPACE(octave) |