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3
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1 // Extra Matrix manipulations. -*- C++ -*- |
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2 /* |
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3 |
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4 Copyright (C) 1992 John W. Eaton |
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5 |
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6 This file is part of Octave. |
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7 |
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8 Octave is free software; you can redistribute it and/or modify it |
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9 under the terms of the GNU General Public License as published by the |
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10 Free Software Foundation; either version 2, or (at your option) any |
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11 later version. |
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12 |
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13 Octave is distributed in the hope that it will be useful, but WITHOUT |
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14 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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15 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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16 for more details. |
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17 |
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18 You should have received a copy of the GNU General Public License |
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19 along with Octave; see the file COPYING. If not, write to the Free |
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20 Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA. |
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21 |
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22 */ |
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23 |
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24 #ifdef __GNUG__ |
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25 #pragma implementation |
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26 #endif |
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27 |
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28 #include "Matrix.h" |
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29 #include "mx-inlines.cc" |
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227
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30 #include "lo-error.h" |
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31 |
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32 /* |
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22
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33 * AEPBALANCE operations |
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34 */ |
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35 |
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36 int |
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37 AEPBALANCE::init (const Matrix& a, const char *balance_job) |
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38 { |
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39 if (a.nr != a.nc) |
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227
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40 { |
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41 (*current_liboctave_error_handler) ("AEPBALANCE requires square matrix"); |
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42 return -1; |
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43 } |
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22
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44 |
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45 int n = a.nc; |
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46 |
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47 // Parameters for balance call. |
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48 |
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49 int info; |
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50 int ilo; |
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51 int ihi; |
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52 double *scale = new double [n]; |
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53 |
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54 // Copy matrix into local structure. |
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55 |
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56 balanced_mat = a; |
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57 |
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58 F77_FCN (dgebal) (balance_job, &n, balanced_mat.fortran_vec (), |
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59 &n, &ilo, &ihi, scale, &info, 1L, 1L); |
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60 |
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61 // Initialize balancing matrix to identity. |
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62 |
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63 balancing_mat = Matrix (n, n, 0.0); |
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64 for (int i = 0; i < n; i++) |
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65 balancing_mat.elem (i ,i) = 1.0; |
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66 |
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67 F77_FCN (dgebak) (balance_job, "R", &n, &ilo, &ihi, scale, &n, |
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68 balancing_mat.fortran_vec (), &n, &info, 1L, 1L); |
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69 |
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70 delete [] scale; |
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71 |
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72 return info; |
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73 } |
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74 |
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75 int |
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76 ComplexAEPBALANCE::init (const ComplexMatrix& a, const char *balance_job) |
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77 { |
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78 |
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79 int n = a.nc; |
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80 |
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81 // Parameters for balance call. |
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82 |
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83 int info; |
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84 int ilo; |
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85 int ihi; |
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86 double *scale = new double [n]; |
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87 |
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88 // Copy matrix into local structure. |
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89 |
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90 balanced_mat = a; |
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91 |
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92 F77_FCN (zgebal) (balance_job, &n, balanced_mat.fortran_vec (), |
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93 &n, &ilo, &ihi, scale, &info, 1L, 1L); |
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94 |
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95 // Initialize balancing matrix to identity. |
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96 |
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97 balancing_mat = Matrix (n, n, 0.0); |
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98 for (int i = 0; i < n; i++) |
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99 balancing_mat (i, i) = 1.0; |
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100 |
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101 F77_FCN (zgebak) (balance_job, "R", &n, &ilo, &ihi, scale, &n, |
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102 balancing_mat.fortran_vec(), &n, &info, 1L, 1L); |
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103 |
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104 delete [] scale; |
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105 |
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106 return info; |
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107 } |
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108 |
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109 /* |
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110 * GEPBALANCE operations |
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111 */ |
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112 |
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113 int |
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114 GEPBALANCE::init (const Matrix& a, const Matrix& b, const char *balance_job) |
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115 { |
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116 if (a.nr != a.nc || a.nr != b.nr || b.nr != b.nc) |
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227
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117 { |
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118 (*current_liboctave_error_handler) |
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119 ("GEPBALANCE requires square matrices of the same size"); |
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120 return -1; |
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121 } |
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122 |
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123 int n = a.nc; |
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124 |
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125 // Parameters for balance call. |
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126 |
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127 int info; |
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128 int ilo; |
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129 int ihi; |
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130 double *cscale = new double [n]; |
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131 double *cperm = new double [n]; |
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132 Matrix wk (n, 6, 0.0); |
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133 |
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134 // Back out the permutations: |
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135 // |
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136 // cscale contains the exponents of the column scaling factors in its |
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137 // ilo through ihi locations and the reducing column permutations in |
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138 // its first ilo-1 and its ihi+1 through n locations. |
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139 // |
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140 // cperm contains the column permutations applied in grading the a and b |
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141 // submatrices in its ilo through ihi locations. |
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142 // |
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143 // wk contains the exponents of the row scaling factors in its ilo |
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144 // through ihi locations, the reducing row permutations in its first |
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145 // ilo-1 and its ihi+1 through n locations, and the row permutations |
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146 // applied in grading the a and b submatrices in its n+ilo through |
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147 // n+ihi locations. |
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148 |
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149 // Copy matrices into local structure. |
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150 |
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151 balanced_a_mat = a; |
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152 balanced_b_mat = b; |
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153 |
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154 // Initialize balancing matrices to identity. |
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155 |
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156 left_balancing_mat = Matrix(n,n,0.0); |
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157 for (int i = 0; i < n; i++) |
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158 left_balancing_mat (i, i) = 1.0; |
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159 |
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160 right_balancing_mat = left_balancing_mat; |
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161 |
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162 // Check for permutation option. |
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163 |
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164 if (*balance_job == 'P' || *balance_job == 'B') |
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165 { |
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166 F77_FCN(reduce)(&n, &n, balanced_a_mat.fortran_vec (), |
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167 &n, balanced_b_mat.fortran_vec (), &ilo, &ihi, |
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168 cscale, wk.fortran_vec ()); |
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169 } |
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170 else |
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171 { |
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172 |
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173 // Set up for scaling later. |
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174 |
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175 ilo = 1; |
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176 ihi = n; |
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177 } |
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178 |
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179 // Check for scaling option. |
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180 |
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181 if ((*balance_job == 'S' || *balance_job == 'B') && ilo != ihi) |
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182 { |
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183 F77_FCN(scaleg)(&n, &n, balanced_a_mat.fortran_vec (), |
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184 &n, balanced_b_mat.fortran_vec (), &ilo, &ihi, |
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185 cscale, cperm, wk.fortran_vec ()); |
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186 } |
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187 else |
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188 { |
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189 |
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190 // Set scaling data to 0's. |
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191 |
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192 for (int tmp = ilo-1; tmp < ihi; tmp++) |
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193 { |
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194 cscale[tmp] = 0.0; |
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195 wk.elem(tmp,0) = 0.0; |
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196 } |
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197 } |
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198 |
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199 // Scaleg returns exponents, not values, so... |
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200 |
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201 for (int tmp = ilo-1; tmp < ihi; tmp++) |
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202 { |
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203 cscale[tmp] = pow(2.0,cscale[tmp]); |
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204 wk.elem(tmp,0) = pow(2.0,-wk.elem(tmp,0)); |
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205 } |
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206 |
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207 // Column permutations/scaling. |
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208 |
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209 F77_FCN (dgebak) (balance_job, "R", &n, &ilo, &ihi, cscale, &n, |
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210 right_balancing_mat.fortran_vec (), &n, &info, 1L, |
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211 1L); |
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212 |
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213 // Row permutations/scaling. |
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214 |
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215 F77_FCN (dgebak) (balance_job, "L", &n, &ilo, &ihi, &wk.elem (0, 0), &n, |
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216 left_balancing_mat.fortran_vec (), &n, &info, 1L, 1L); |
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217 |
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218 // XXX FIXME XXX --- these four lines need to be added and debugged. |
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219 // GEPBALANCE::init will work without them, though, so here they are. |
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220 |
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221 #if 0 |
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222 if ((*balance_job == 'P' || *balance_job == 'B') && ilo != ihi) |
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223 { |
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224 F77_FCN (gradeq) (&n, &n, balanced_a_mat.fortran_vec (), |
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225 &n, balanced_b_mat.fortran_vec (), &ilo, &ihi, |
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226 cperm, &wk.elem (0, 1)); |
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227 } |
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228 #endif |
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229 |
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230 // Transpose for aa = cc*a*dd convention... |
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231 left_balancing_mat = left_balancing_mat.transpose (); |
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232 |
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233 delete [] cscale; |
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234 delete [] cperm; |
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235 |
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236 return info; |
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237 } |
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238 |
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239 /* |
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182
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240 * CHOL stuff |
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241 */ |
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242 |
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243 int |
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244 CHOL::init (const Matrix& a) |
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245 { |
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246 if (a.nr != a.nc) |
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227
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247 { |
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248 (*current_liboctave_error_handler) ("CHOL requires square matrix"); |
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249 return -1; |
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250 } |
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182
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251 |
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252 char uplo = 'U'; |
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253 |
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254 int n = a.nc; |
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255 int info; |
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256 |
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257 double *h = dup (a.data, a.len); |
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258 |
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259 F77_FCN (dpotrf) (&uplo, &n, h, &n, &info, 1L); |
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260 |
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261 chol_mat = Matrix (h, n, n); |
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262 |
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263 // If someone thinks of a more graceful way of doing this (or faster for |
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264 // that matter :-)), please let me know! |
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265 |
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266 if (n > 1) |
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267 for (int j = 0; j < a.nc; j++) |
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268 for (int i = j+1; i < a.nr; i++) |
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269 chol_mat.elem (i, j) = 0.0; |
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270 |
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271 |
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272 return info; |
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273 } |
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274 |
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275 |
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276 int |
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277 ComplexCHOL::init (const ComplexMatrix& a) |
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278 { |
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279 if (a.nr != a.nc) |
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227
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280 { |
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281 (*current_liboctave_error_handler) |
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282 ("ComplexCHOL requires square matrix"); |
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283 return -1; |
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284 } |
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182
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285 |
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286 char uplo = 'U'; |
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287 |
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288 int n = a.nc; |
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289 int info; |
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290 |
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291 Complex *h = dup (a.data, a.len); |
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292 |
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293 F77_FCN (zpotrf) (&uplo, &n, h, &n, &info, 1L); |
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294 |
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295 chol_mat = ComplexMatrix (h, n, n); |
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296 |
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297 // If someone thinks of a more graceful way of doing this (or faster for |
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298 // that matter :-)), please let me know! |
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299 |
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300 if (n > 1) |
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301 for (int j = 0; j < a.nc; j++) |
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302 for (int i = j+1; i < a.nr; i++) |
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303 chol_mat.elem (i, j) = 0.0; |
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304 |
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305 return info; |
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306 } |
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307 |
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308 |
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309 /* |
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3
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310 * HESS stuff |
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311 */ |
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312 |
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313 int |
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314 HESS::init (const Matrix& a) |
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315 { |
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316 if (a.nr != a.nc) |
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227
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317 { |
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318 (*current_liboctave_error_handler) ("HESS requires square matrix"); |
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319 return -1; |
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320 } |
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321 |
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322 char jobbal = 'N'; |
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323 char side = 'R'; |
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324 |
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325 int n = a.nc; |
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326 int lwork = 32 * n; |
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327 int info; |
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328 int ilo; |
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329 int ihi; |
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330 |
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331 double *h = dup(a.data, a.len); |
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332 |
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333 double *tau = new double [n+1]; |
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334 double *scale = new double [n]; |
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335 double *z = new double [n*n]; |
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336 double *work = new double [lwork]; |
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337 |
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338 F77_FCN (dgebal) (&jobbal, &n, h, &n, &ilo, &ihi, scale, &info, |
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339 1L, 1L); |
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340 |
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341 F77_FCN (dgehrd) (&n, &ilo, &ihi, h, &n, tau, work, &lwork, &info, |
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342 1L, 1L); |
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343 |
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344 copy(z,h,n*n); |
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345 |
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346 F77_FCN (dorghr) (&n, &ilo, &ihi, z, &n, tau, work, &lwork, &info, |
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347 1L, 1L); |
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348 |
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349 F77_FCN (dgebak) (&jobbal, &side, &n, &ilo, &ihi, scale, &n, z, &n, |
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350 &info, 1L, 1L); |
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351 |
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352 // We need to clear out all of the area below the sub-diagonal which was used |
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353 // to store the unitary matrix. |
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354 |
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355 hess_mat = Matrix(h,n,n); |
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356 unitary_hess_mat = Matrix(z,n,n); |
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357 |
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358 // If someone thinks of a more graceful way of doing this (or faster for |
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359 // that matter :-)), please let me know! |
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360 |
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361 if (n > 2) |
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362 for (int j = 0; j < a.nc; j++) |
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363 for (int i = j+2; i < a.nr; i++) |
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364 hess_mat.elem(i,j) = 0; |
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365 |
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366 delete [] tau; |
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367 delete [] work; |
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368 delete [] scale; |
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369 |
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370 return info; |
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371 } |
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372 |
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373 |
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374 int |
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375 ComplexHESS::init (const ComplexMatrix& a) |
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376 { |
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377 if (a.nr != a.nc) |
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227
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378 { |
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379 (*current_liboctave_error_handler) |
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380 ("ComplexHESS requires square matrix"); |
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381 return -1; |
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382 } |
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383 |
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22
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384 char job = 'N'; |
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385 char side = 'R'; |
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386 |
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387 int n = a.nc; |
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388 int lwork = 32 * n; |
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389 int info; |
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390 int ilo; |
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391 int ihi; |
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392 |
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393 Complex *h = dup(a.data,a.len); |
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394 |
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395 double *scale = new double [n]; |
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396 Complex *tau = new Complex [n-1]; |
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397 Complex *work = new Complex [lwork]; |
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398 Complex *z = new Complex [n*n]; |
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399 |
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400 F77_FCN (zgebal) (&job, &n, h, &n, &ilo, &ihi, scale, &info, 1L, 1L); |
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401 |
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402 F77_FCN (zgehrd) (&n, &ilo, &ihi, h, &n, tau, work, &lwork, &info, 1L, |
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403 1L); |
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404 |
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405 copy(z,h,n*n); |
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406 |
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407 F77_FCN (zunghr) (&n, &ilo, &ihi, z, &n, tau, work, &lwork, &info, 1L, |
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408 1L); |
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409 |
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410 F77_FCN (zgebak) (&job, &side, &n, &ilo, &ihi, scale, &n, z, &n, &info, |
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411 1L, 1L); |
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412 |
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413 hess_mat = ComplexMatrix (h,n,n); |
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414 unitary_hess_mat = ComplexMatrix (z,n,n); |
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415 |
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416 // If someone thinks of a more graceful way of doing this (or faster for |
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417 // that matter :-)), please let me know! |
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418 |
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419 if (n > 2) |
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420 for (int j = 0; j < a.nc; j++) |
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421 for (int i = j+2; i < a.nr; i++) |
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422 hess_mat.elem(i,j) = 0; |
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423 |
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424 delete [] work; |
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425 delete [] tau; |
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426 delete [] scale; |
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427 |
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428 return info; |
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429 } |
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430 |
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431 /* |
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432 * SCHUR stuff |
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433 */ |
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434 |
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435 static int |
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436 select_ana (double *a, double *b) |
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437 { |
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438 return (*a < 0.0); |
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439 } |
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440 |
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441 static int |
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442 select_dig (double *a, double *b) |
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443 { |
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444 return (hypot (*a, *b) < 1.0); |
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445 } |
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446 |
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447 // GAG. |
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448 extern "C" { static int (*dummy_select)(); } |
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449 |
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450 int |
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451 SCHUR::init (const Matrix& a, const char *ord) |
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452 { |
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453 if (a.nr != a.nc) |
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227
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454 { |
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455 (*current_liboctave_error_handler) ("SCHUR requires square matrix"); |
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456 return -1; |
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457 } |
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3
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458 |
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459 char jobvs = 'V'; |
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460 char sort; |
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461 |
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462 if (*ord == 'A' || *ord == 'D' || *ord == 'a' || *ord == 'd') |
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463 sort = 'S'; |
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464 else |
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465 sort = 'N'; |
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466 |
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467 char sense = 'N'; |
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468 |
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469 int n = a.nc; |
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470 int lwork = 8 * n; |
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471 int liwork = 1; |
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472 int info; |
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473 int sdim; |
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474 double rconde; |
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475 double rcondv; |
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476 |
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477 double *s = dup(a.data,a.len); |
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478 |
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479 double *wr = new double [n]; |
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480 double *wi = new double [n]; |
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481 double *q = new double [n*n]; |
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482 double *work = new double [lwork]; |
|
|
483 |
|
|
484 // These are not referenced for the non-ordered Schur routine. |
|
|
485 |
|
|
486 int *iwork = (int *) NULL; |
|
|
487 int *bwork = (int *) NULL; |
|
|
488 if (*ord == 'A' || *ord == 'D' || *ord == 'a' || *ord == 'd') |
|
|
489 { |
|
|
490 iwork = new int [liwork]; |
|
|
491 bwork = new int [n]; |
|
|
492 } |
|
|
493 |
|
|
494 if (*ord == 'A' || *ord == 'a') |
|
|
495 { |
|
|
496 F77_FCN (dgeesx) (&jobvs, &sort, select_ana, &sense, &n, s, &n, |
|
|
497 &sdim, wr, wi, q, &n, &rconde, &rcondv, work, |
|
|
498 &lwork, iwork, &liwork, bwork, &info, 1L, 1L); |
|
|
499 } |
|
|
500 else if (*ord == 'D' || *ord == 'd') |
|
|
501 { |
|
|
502 F77_FCN (dgeesx) (&jobvs, &sort, select_dig, &sense, &n, s, &n, |
|
|
503 &sdim, wr, wi, q, &n, &rconde, &rcondv, work, |
|
|
504 &lwork, iwork, &liwork, bwork, &info, 1L, 1L); |
|
|
505 |
|
|
506 } |
|
|
507 else |
|
|
508 { |
|
|
509 F77_FCN (dgeesx) (&jobvs, &sort, dummy_select, &sense, &n, s, |
|
|
510 &n, &sdim, wr, wi, q, &n, &rconde, &rcondv, |
|
|
511 work, &lwork, iwork, &liwork, bwork, &info, |
|
|
512 1L, 1L); |
|
|
513 } |
|
|
514 |
|
|
515 |
|
|
516 schur_mat = Matrix (s, n, n); |
|
|
517 unitary_mat = Matrix (q, n, n); |
|
|
518 |
|
|
519 delete [] wr; |
|
|
520 delete [] wi; |
|
|
521 delete [] work; |
|
|
522 delete [] iwork; |
|
|
523 delete [] bwork; |
|
|
524 |
|
|
525 return info; |
|
|
526 } |
|
|
527 |
|
|
528 static int |
|
|
529 complex_select_ana (Complex *a) |
|
|
530 { |
|
|
531 return (real (*a) < 0.0); |
|
|
532 } |
|
|
533 |
|
|
534 static int |
|
|
535 complex_select_dig (Complex *a) |
|
|
536 { |
|
|
537 return (abs (*a) < 1.0); |
|
|
538 } |
|
|
539 |
|
|
540 int |
|
|
541 ComplexSCHUR::init (const ComplexMatrix& a, const char *ord) |
|
|
542 { |
|
|
543 if (a.nr != a.nc) |
|
227
|
544 { |
|
|
545 (*current_liboctave_error_handler) |
|
|
546 ("ComplexSCHUR requires square matrix"); |
|
|
547 return -1; |
|
|
548 } |
|
3
|
549 |
|
|
550 char jobvs = 'V'; |
|
|
551 char sort; |
|
|
552 if (*ord == 'A' || *ord == 'D' || *ord == 'a' || *ord == 'd') |
|
|
553 sort = 'S'; |
|
|
554 else |
|
|
555 sort = 'N'; |
|
|
556 |
|
|
557 char sense = 'N'; |
|
|
558 |
|
|
559 int n = a.nc; |
|
|
560 int lwork = 8 * n; |
|
|
561 int info; |
|
|
562 int sdim; |
|
|
563 double rconde; |
|
|
564 double rcondv; |
|
|
565 |
|
|
566 double *rwork = new double [n]; |
|
|
567 |
|
|
568 // bwork is not referenced for non-ordered Schur. |
|
|
569 |
|
|
570 int *bwork = (int *) NULL; |
|
|
571 if (*ord == 'A' || *ord == 'D' || *ord == 'a' || *ord == 'd') |
|
|
572 bwork = new int [n]; |
|
|
573 |
|
|
574 Complex *s = dup(a.data,a.len); |
|
|
575 |
|
|
576 Complex *work = new Complex [lwork]; |
|
|
577 Complex *q = new Complex [n*n]; |
|
|
578 Complex *w = new Complex [n]; |
|
|
579 |
|
|
580 if (*ord == 'A' || *ord == 'a') |
|
|
581 { |
|
|
582 F77_FCN (zgeesx) (&jobvs, &sort, complex_select_ana, &sense, |
|
|
583 &n, s, &n, &sdim, w, q, &n, &rconde, &rcondv, |
|
|
584 work, &lwork, rwork, bwork, &info, 1L, 1L); |
|
|
585 } |
|
|
586 else if (*ord == 'D' || *ord == 'd') |
|
|
587 { |
|
|
588 F77_FCN (zgeesx) (&jobvs, &sort, complex_select_dig, &sense, |
|
|
589 &n, s, &n, &sdim, w, q, &n, &rconde, &rcondv, |
|
|
590 work, &lwork, rwork, bwork, &info, 1L, 1L); |
|
|
591 } |
|
|
592 else |
|
|
593 { |
|
|
594 F77_FCN (zgeesx) (&jobvs, &sort, dummy_select, &sense, &n, s, |
|
|
595 &n, &sdim, w, q, &n, &rconde, &rcondv, work, |
|
|
596 &lwork, rwork, bwork, &info, 1L, 1L); |
|
|
597 } |
|
|
598 |
|
|
599 schur_mat = ComplexMatrix (s,n,n); |
|
|
600 unitary_mat = ComplexMatrix (q,n,n); |
|
|
601 |
|
|
602 delete [] w; |
|
|
603 delete [] work; |
|
|
604 delete [] rwork; |
|
|
605 delete [] bwork; |
|
|
606 |
|
|
607 return info; |
|
|
608 } |
|
|
609 |
|
|
610 ostream& |
|
|
611 operator << (ostream& os, const SCHUR& a) |
|
|
612 { |
|
|
613 os << a.schur_matrix () << "\n"; |
|
|
614 os << a.unitary_matrix () << "\n"; |
|
|
615 |
|
|
616 return os; |
|
|
617 } |
|
|
618 |
|
|
619 /* |
|
|
620 * SVD stuff |
|
|
621 */ |
|
|
622 |
|
|
623 int |
|
|
624 SVD::init (const Matrix& a) |
|
|
625 { |
|
|
626 int info; |
|
|
627 |
|
|
628 int m = a.nr; |
|
|
629 int n = a.nc; |
|
|
630 |
|
|
631 char jobu = 'A'; |
|
|
632 char jobv = 'A'; |
|
|
633 |
|
|
634 double *tmp_data = dup (a.data, a.len); |
|
|
635 |
|
|
636 int min_mn = m < n ? m : n; |
|
|
637 int max_mn = m > n ? m : n; |
|
|
638 |
|
|
639 double *u = new double[m*m]; |
|
|
640 double *s_vec = new double[min_mn]; |
|
|
641 double *vt = new double[n*n]; |
|
|
642 |
|
|
643 int tmp1 = 3*min_mn + max_mn; |
|
|
644 int tmp2 = 5*min_mn - 4; |
|
|
645 int lwork = tmp1 > tmp2 ? tmp1 : tmp2; |
|
|
646 double *work = new double[lwork]; |
|
|
647 |
|
|
648 F77_FCN (dgesvd) (&jobu, &jobv, &m, &n, tmp_data, &m, s_vec, u, &m, |
|
|
649 vt, &n, work, &lwork, &info, 1L, 1L); |
|
|
650 |
|
|
651 left_sm = Matrix (u, m, m); |
|
|
652 sigma = DiagMatrix (s_vec, m, n); |
|
|
653 Matrix vt_m (vt, n, n); |
|
|
654 right_sm = Matrix (vt_m.transpose ()); |
|
|
655 |
|
|
656 delete [] tmp_data; |
|
|
657 delete [] work; |
|
|
658 |
|
|
659 return info; |
|
|
660 } |
|
|
661 |
|
|
662 ostream& |
|
|
663 operator << (ostream& os, const SVD& a) |
|
|
664 { |
|
|
665 os << a.left_singular_matrix () << "\n"; |
|
|
666 os << a.singular_values () << "\n"; |
|
|
667 os << a.right_singular_matrix () << "\n"; |
|
|
668 |
|
|
669 return os; |
|
|
670 } |
|
|
671 |
|
|
672 int |
|
|
673 ComplexSVD::init (const ComplexMatrix& a) |
|
|
674 { |
|
|
675 int info; |
|
|
676 |
|
|
677 int m = a.nr; |
|
|
678 int n = a.nc; |
|
|
679 |
|
|
680 char jobu = 'A'; |
|
|
681 char jobv = 'A'; |
|
|
682 |
|
|
683 Complex *tmp_data = dup (a.data, a.len); |
|
|
684 |
|
|
685 int min_mn = m < n ? m : n; |
|
|
686 int max_mn = m > n ? m : n; |
|
|
687 |
|
|
688 Complex *u = new Complex[m*m]; |
|
|
689 double *s_vec = new double[min_mn]; |
|
|
690 Complex *vt = new Complex[n*n]; |
|
|
691 |
|
|
692 int lwork = 2*min_mn + max_mn; |
|
|
693 Complex *work = new Complex[lwork]; |
|
|
694 |
|
|
695 int lrwork = 5*max_mn; |
|
|
696 double *rwork = new double[lrwork]; |
|
|
697 |
|
|
698 F77_FCN (zgesvd) (&jobu, &jobv, &m, &n, tmp_data, &m, s_vec, u, &m, |
|
|
699 vt, &n, work, &lwork, rwork, &info, 1L, 1L); |
|
|
700 |
|
|
701 left_sm = ComplexMatrix (u, m, m); |
|
|
702 sigma = DiagMatrix (s_vec, m, n); |
|
|
703 ComplexMatrix vt_m (vt, n, n); |
|
|
704 right_sm = ComplexMatrix (vt_m.hermitian ()); |
|
|
705 |
|
|
706 delete [] tmp_data; |
|
|
707 delete [] work; |
|
|
708 |
|
|
709 return info; |
|
|
710 } |
|
|
711 |
|
|
712 /* |
|
|
713 * EIG stuff. |
|
|
714 */ |
|
|
715 |
|
|
716 int |
|
|
717 EIG::init (const Matrix& a) |
|
|
718 { |
|
|
719 if (a.nr != a.nc) |
|
227
|
720 { |
|
|
721 (*current_liboctave_error_handler) ("EIG requires square matrix"); |
|
|
722 return -1; |
|
|
723 } |
|
3
|
724 |
|
|
725 int n = a.nr; |
|
|
726 |
|
|
727 int info; |
|
|
728 |
|
|
729 char jobvl = 'N'; |
|
|
730 char jobvr = 'V'; |
|
|
731 |
|
|
732 double *tmp_data = dup (a.data, a.len); |
|
|
733 double *wr = new double[n]; |
|
|
734 double *wi = new double[n]; |
|
|
735 Matrix vr (n, n); |
|
|
736 double *pvr = vr.fortran_vec (); |
|
|
737 int lwork = 8*n; |
|
|
738 double *work = new double[lwork]; |
|
|
739 |
|
|
740 double dummy; |
|
|
741 int idummy = 1; |
|
|
742 |
|
|
743 F77_FCN (dgeev) (&jobvl, &jobvr, &n, tmp_data, &n, wr, wi, &dummy, |
|
|
744 &idummy, pvr, &n, work, &lwork, &info, 1L, 1L); |
|
|
745 |
|
|
746 lambda.resize (n); |
|
|
747 v.resize (n, n); |
|
|
748 |
|
|
749 for (int j = 0; j < n; j++) |
|
|
750 { |
|
|
751 if (wi[j] == 0.0) |
|
|
752 { |
|
|
753 lambda.elem (j) = Complex (wr[j]); |
|
|
754 for (int i = 0; i < n; i++) |
|
|
755 v.elem (i, j) = vr.elem (i, j); |
|
|
756 } |
|
|
757 else |
|
|
758 { |
|
|
759 if (j+1 >= n) |
|
227
|
760 { |
|
|
761 (*current_liboctave_error_handler) ("EIG: internal error"); |
|
|
762 return -1; |
|
|
763 } |
|
3
|
764 |
|
|
765 for (int i = 0; i < n; i++) |
|
|
766 { |
|
|
767 lambda.elem (j) = Complex (wr[j], wi[j]); |
|
|
768 lambda.elem (j+1) = Complex (wr[j+1], wi[j+1]); |
|
|
769 double real_part = vr.elem (i, j); |
|
|
770 double imag_part = vr.elem (i, j+1); |
|
|
771 v.elem (i, j) = Complex (real_part, imag_part); |
|
|
772 v.elem (i, j+1) = Complex (real_part, -imag_part); |
|
|
773 } |
|
|
774 j++; |
|
|
775 } |
|
|
776 } |
|
|
777 |
|
|
778 delete [] tmp_data; |
|
|
779 delete [] wr; |
|
|
780 delete [] wi; |
|
|
781 delete [] work; |
|
|
782 |
|
|
783 return info; |
|
|
784 } |
|
|
785 |
|
|
786 int |
|
|
787 EIG::init (const ComplexMatrix& a) |
|
|
788 { |
|
|
789 |
|
|
790 if (a.nr != a.nc) |
|
227
|
791 { |
|
|
792 (*current_liboctave_error_handler) ("EIG requires square matrix"); |
|
|
793 return -1; |
|
|
794 } |
|
3
|
795 |
|
|
796 int n = a.nr; |
|
|
797 |
|
|
798 int info; |
|
|
799 |
|
|
800 char jobvl = 'N'; |
|
|
801 char jobvr = 'V'; |
|
|
802 |
|
|
803 lambda.resize (n); |
|
|
804 v.resize (n, n); |
|
|
805 |
|
|
806 Complex *pw = lambda.fortran_vec (); |
|
|
807 Complex *pvr = v.fortran_vec (); |
|
|
808 |
|
|
809 Complex *tmp_data = dup (a.data, a.len); |
|
|
810 |
|
|
811 int lwork = 8*n; |
|
|
812 Complex *work = new Complex[lwork]; |
|
|
813 double *rwork = new double[4*n]; |
|
|
814 |
|
|
815 Complex dummy; |
|
|
816 int idummy = 1; |
|
|
817 |
|
|
818 F77_FCN (zgeev) (&jobvl, &jobvr, &n, tmp_data, &n, pw, &dummy, |
|
|
819 &idummy, pvr, &n, work, &lwork, rwork, &info, 1L, |
|
|
820 1L); |
|
|
821 |
|
|
822 delete [] tmp_data; |
|
|
823 delete [] work; |
|
|
824 delete [] rwork; |
|
|
825 |
|
|
826 return info; |
|
|
827 } |
|
|
828 |
|
|
829 /* |
|
|
830 * LU stuff. |
|
|
831 */ |
|
|
832 |
|
|
833 LU::LU (const Matrix& a) |
|
|
834 { |
|
|
835 if (a.nr == 0 || a.nc == 0 || a.nr != a.nc) |
|
227
|
836 { |
|
|
837 (*current_liboctave_error_handler) ("LU requires square matrix"); |
|
|
838 return; |
|
|
839 } |
|
3
|
840 |
|
|
841 int n = a.nr; |
|
|
842 |
|
|
843 int *ipvt = new int [n]; |
|
|
844 int *pvt = new int [n]; |
|
|
845 double *tmp_data = dup (a.data, a.len); |
|
|
846 int info = 0; |
|
|
847 int zero = 0; |
|
|
848 double b; |
|
|
849 |
|
|
850 F77_FCN (dgesv) (&n, &zero, tmp_data, &n, ipvt, &b, &n, &info); |
|
|
851 |
|
|
852 Matrix A_fact (tmp_data, n, n); |
|
|
853 |
|
|
854 int i; |
|
|
855 |
|
|
856 for (i = 0; i < n; i++) |
|
|
857 { |
|
|
858 ipvt[i] -= 1; |
|
|
859 pvt[i] = i; |
|
|
860 } |
|
|
861 |
|
|
862 for (i = 0; i < n - 1; i++) |
|
|
863 { |
|
|
864 int k = ipvt[i]; |
|
|
865 if (k != i) |
|
|
866 { |
|
|
867 int tmp = pvt[k]; |
|
|
868 pvt[k] = pvt[i]; |
|
|
869 pvt[i] = tmp; |
|
|
870 } |
|
|
871 } |
|
|
872 |
|
|
873 l.resize (n, n, 0.0); |
|
|
874 u.resize (n, n, 0.0); |
|
|
875 p.resize (n, n, 0.0); |
|
|
876 |
|
|
877 for (i = 0; i < n; i++) |
|
|
878 { |
|
|
879 p.elem (i, pvt[i]) = 1.0; |
|
|
880 |
|
|
881 int j; |
|
|
882 |
|
|
883 l.elem (i, i) = 1.0; |
|
|
884 for (j = 0; j < i; j++) |
|
|
885 l.elem (i, j) = A_fact.elem (i, j); |
|
|
886 |
|
|
887 for (j = i; j < n; j++) |
|
|
888 u.elem (i, j) = A_fact.elem (i, j); |
|
|
889 } |
|
|
890 |
|
|
891 delete [] ipvt; |
|
|
892 delete [] pvt; |
|
|
893 } |
|
|
894 |
|
|
895 ComplexLU::ComplexLU (const ComplexMatrix& a) |
|
|
896 { |
|
|
897 if (a.nr == 0 || a.nc == 0 || a.nr != a.nc) |
|
227
|
898 { |
|
|
899 (*current_liboctave_error_handler) ("ComplexLU requires square matrix"); |
|
|
900 return; |
|
|
901 } |
|
3
|
902 |
|
|
903 int n = a.nr; |
|
|
904 |
|
|
905 int *ipvt = new int [n]; |
|
|
906 int *pvt = new int [n]; |
|
|
907 Complex *tmp_data = dup (a.data, a.len); |
|
|
908 int info = 0; |
|
|
909 int zero = 0; |
|
|
910 Complex b; |
|
|
911 |
|
|
912 F77_FCN (zgesv) (&n, &zero, tmp_data, &n, ipvt, &b, &n, &info); |
|
|
913 |
|
|
914 ComplexMatrix A_fact (tmp_data, n, n); |
|
|
915 |
|
|
916 int i; |
|
|
917 |
|
|
918 for (i = 0; i < n; i++) |
|
|
919 { |
|
|
920 ipvt[i] -= 1; |
|
|
921 pvt[i] = i; |
|
|
922 } |
|
|
923 |
|
|
924 for (i = 0; i < n - 1; i++) |
|
|
925 { |
|
|
926 int k = ipvt[i]; |
|
|
927 if (k != i) |
|
|
928 { |
|
|
929 int tmp = pvt[k]; |
|
|
930 pvt[k] = pvt[i]; |
|
|
931 pvt[i] = tmp; |
|
|
932 } |
|
|
933 } |
|
|
934 |
|
|
935 l.resize (n, n, 0.0); |
|
|
936 u.resize (n, n, 0.0); |
|
|
937 p.resize (n, n, 0.0); |
|
|
938 |
|
|
939 for (i = 0; i < n; i++) |
|
|
940 { |
|
|
941 p.elem (i, pvt[i]) = 1.0; |
|
|
942 |
|
|
943 int j; |
|
|
944 |
|
|
945 l.elem (i, i) = 1.0; |
|
|
946 for (j = 0; j < i; j++) |
|
|
947 l.elem (i, j) = A_fact.elem (i, j); |
|
|
948 |
|
|
949 for (j = i; j < n; j++) |
|
|
950 u.elem (i, j) = A_fact.elem (i, j); |
|
|
951 } |
|
|
952 |
|
|
953 delete [] ipvt; |
|
|
954 delete [] pvt; |
|
|
955 } |
|
|
956 |
|
|
957 /* |
|
|
958 * QR stuff. |
|
|
959 */ |
|
|
960 |
|
|
961 QR::QR (const Matrix& a) |
|
|
962 { |
|
|
963 int m = a.nr; |
|
|
964 int n = a.nc; |
|
|
965 |
|
|
966 if (m == 0 || n == 0) |
|
227
|
967 { |
|
|
968 (*current_liboctave_error_handler) ("QR must have non-empty matrix"); |
|
|
969 return; |
|
|
970 } |
|
3
|
971 |
|
|
972 double *tmp_data; |
|
|
973 int min_mn = m < n ? m : n; |
|
|
974 double *tau = new double[min_mn]; |
|
|
975 int lwork = 32*n; |
|
|
976 double *work = new double[lwork]; |
|
|
977 int info = 0; |
|
|
978 |
|
|
979 if (m > n) |
|
|
980 { |
|
|
981 tmp_data = new double [m*m]; |
|
|
982 copy (tmp_data, a.data, a.len); |
|
|
983 } |
|
|
984 else |
|
|
985 tmp_data = dup (a.data, a.len); |
|
|
986 |
|
|
987 F77_FCN (dgeqrf) (&m, &n, tmp_data, &m, tau, work, &lwork, &info); |
|
|
988 |
|
|
989 delete [] work; |
|
|
990 |
|
|
991 r.resize (m, n, 0.0); |
|
|
992 for (int j = 0; j < n; j++) |
|
|
993 { |
|
|
994 int limit = j < min_mn-1 ? j : min_mn-1; |
|
|
995 for (int i = 0; i <= limit; i++) |
|
|
996 r.elem (i, j) = tmp_data[m*j+i]; |
|
|
997 } |
|
|
998 |
|
|
999 lwork = 32*m; |
|
|
1000 work = new double[lwork]; |
|
|
1001 |
|
|
1002 F77_FCN (dorgqr) (&m, &m, &min_mn, tmp_data, &m, tau, work, &lwork, &info); |
|
|
1003 |
|
|
1004 q = Matrix (tmp_data, m, m); |
|
|
1005 |
|
|
1006 delete [] tau; |
|
|
1007 delete [] work; |
|
|
1008 } |
|
|
1009 |
|
|
1010 ComplexQR::ComplexQR (const ComplexMatrix& a) |
|
|
1011 { |
|
|
1012 int m = a.nr; |
|
|
1013 int n = a.nc; |
|
|
1014 |
|
|
1015 if (m == 0 || n == 0) |
|
227
|
1016 { |
|
|
1017 (*current_liboctave_error_handler) |
|
|
1018 ("ComplexQR must have non-empty matrix"); |
|
|
1019 return; |
|
|
1020 } |
|
3
|
1021 |
|
|
1022 Complex *tmp_data; |
|
|
1023 int min_mn = m < n ? m : n; |
|
|
1024 Complex *tau = new Complex[min_mn]; |
|
|
1025 int lwork = 32*n; |
|
|
1026 Complex *work = new Complex[lwork]; |
|
|
1027 int info = 0; |
|
|
1028 |
|
|
1029 if (m > n) |
|
|
1030 { |
|
|
1031 tmp_data = new Complex [m*m]; |
|
|
1032 copy (tmp_data, a.data, a.len); |
|
|
1033 } |
|
|
1034 else |
|
|
1035 tmp_data = dup (a.data, a.len); |
|
|
1036 |
|
|
1037 F77_FCN (zgeqrf) (&m, &n, tmp_data, &m, tau, work, &lwork, &info); |
|
|
1038 |
|
|
1039 delete [] work; |
|
|
1040 |
|
|
1041 r.resize (m, n, 0.0); |
|
|
1042 for (int j = 0; j < n; j++) |
|
|
1043 { |
|
|
1044 int limit = j < min_mn-1 ? j : min_mn-1; |
|
|
1045 for (int i = 0; i <= limit; i++) |
|
|
1046 r.elem (i, j) = tmp_data[m*j+i]; |
|
|
1047 } |
|
|
1048 |
|
|
1049 lwork = 32*m; |
|
|
1050 work = new Complex[lwork]; |
|
|
1051 |
|
|
1052 F77_FCN (zungqr) (&m, &m, &min_mn, tmp_data, &m, tau, work, &lwork, &info); |
|
|
1053 |
|
|
1054 q = ComplexMatrix (tmp_data, m, m); |
|
|
1055 |
|
|
1056 delete [] tau; |
|
|
1057 delete [] work; |
|
|
1058 } |
|
|
1059 |
|
|
1060 /* |
|
|
1061 ;;; Local Variables: *** |
|
|
1062 ;;; mode: C++ *** |
|
|
1063 ;;; page-delimiter: "^/\\*" *** |
|
|
1064 ;;; End: *** |
|
|
1065 */ |
