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