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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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232 * HESS stuff |
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233 */ |
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234 |
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235 int |
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236 HESS::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 jobbal = 'N'; |
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242 char side = 'R'; |
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243 |
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244 int n = a.nc; |
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245 int lwork = 32 * n; |
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246 int info; |
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247 int ilo; |
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248 int ihi; |
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249 |
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250 double *h = dup(a.data, a.len); |
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251 |
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252 double *tau = new double [n+1]; |
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253 double *scale = new double [n]; |
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254 double *z = new double [n*n]; |
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255 double *work = new double [lwork]; |
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256 |
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257 F77_FCN (dgebal) (&jobbal, &n, h, &n, &ilo, &ihi, scale, &info, |
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258 1L, 1L); |
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259 |
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260 F77_FCN (dgehrd) (&n, &ilo, &ihi, h, &n, tau, work, &lwork, &info, |
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261 1L, 1L); |
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262 |
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263 copy(z,h,n*n); |
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264 |
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265 F77_FCN (dorghr) (&n, &ilo, &ihi, z, &n, tau, work, &lwork, &info, |
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266 1L, 1L); |
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267 |
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268 F77_FCN (dgebak) (&jobbal, &side, &n, &ilo, &ihi, scale, &n, z, &n, |
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269 &info, 1L, 1L); |
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270 |
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271 // We need to clear out all of the area below the sub-diagonal which was used |
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272 // to store the unitary matrix. |
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273 |
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274 hess_mat = Matrix(h,n,n); |
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275 unitary_hess_mat = Matrix(z,n,n); |
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276 |
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277 // If someone thinks of a more graceful way of doing this (or faster for |
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278 // that matter :-)), please let me know! |
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279 |
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280 if (n > 2) |
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281 for (int j = 0; j < a.nc; j++) |
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282 for (int i = j+2; i < a.nr; i++) |
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283 hess_mat.elem(i,j) = 0; |
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284 |
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285 delete [] tau; |
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286 delete [] work; |
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287 delete [] scale; |
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288 |
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289 return info; |
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290 } |
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291 |
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292 |
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293 int |
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294 ComplexHESS::init (const ComplexMatrix& a) |
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295 { |
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296 if (a.nr != a.nc) |
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297 FAIL; |
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298 |
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299 char job = 'N'; |
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300 char side = 'R'; |
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301 |
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302 int n = a.nc; |
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303 int lwork = 32 * n; |
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304 int info; |
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305 int ilo; |
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306 int ihi; |
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307 |
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308 Complex *h = dup(a.data,a.len); |
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309 |
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310 double *scale = new double [n]; |
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311 Complex *tau = new Complex [n-1]; |
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312 Complex *work = new Complex [lwork]; |
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313 Complex *z = new Complex [n*n]; |
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314 |
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315 F77_FCN (zgebal) (&job, &n, h, &n, &ilo, &ihi, scale, &info, 1L, 1L); |
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316 |
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317 F77_FCN (zgehrd) (&n, &ilo, &ihi, h, &n, tau, work, &lwork, &info, 1L, |
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318 1L); |
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319 |
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320 copy(z,h,n*n); |
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321 |
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322 F77_FCN (zunghr) (&n, &ilo, &ihi, z, &n, tau, work, &lwork, &info, 1L, |
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323 1L); |
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324 |
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325 F77_FCN (zgebak) (&job, &side, &n, &ilo, &ihi, scale, &n, z, &n, &info, |
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326 1L, 1L); |
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327 |
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328 hess_mat = ComplexMatrix (h,n,n); |
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329 unitary_hess_mat = ComplexMatrix (z,n,n); |
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330 |
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331 // If someone thinks of a more graceful way of doing this (or faster for |
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332 // that matter :-)), please let me know! |
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333 |
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334 if (n > 2) |
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335 for (int j = 0; j < a.nc; j++) |
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336 for (int i = j+2; i < a.nr; i++) |
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337 hess_mat.elem(i,j) = 0; |
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338 |
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339 delete [] work; |
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340 delete [] tau; |
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341 delete [] scale; |
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342 |
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343 return info; |
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344 } |
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345 |
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346 /* |
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347 * SCHUR stuff |
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348 */ |
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349 |
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350 static int |
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351 select_ana (double *a, double *b) |
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352 { |
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353 return (*a < 0.0); |
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354 } |
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355 |
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356 static int |
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357 select_dig (double *a, double *b) |
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358 { |
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359 return (hypot (*a, *b) < 1.0); |
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360 } |
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361 |
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362 // GAG. |
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363 extern "C" { static int (*dummy_select)(); } |
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364 |
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365 int |
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366 SCHUR::init (const Matrix& a, const char *ord) |
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367 { |
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368 if (a.nr != a.nc) |
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369 FAIL; |
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370 |
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371 char jobvs = 'V'; |
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372 char sort; |
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373 |
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374 if (*ord == 'A' || *ord == 'D' || *ord == 'a' || *ord == 'd') |
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375 sort = 'S'; |
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376 else |
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377 sort = 'N'; |
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378 |
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379 char sense = 'N'; |
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380 |
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381 int n = a.nc; |
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382 int lwork = 8 * n; |
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383 int liwork = 1; |
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384 int info; |
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385 int sdim; |
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386 double rconde; |
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387 double rcondv; |
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388 |
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389 double *s = dup(a.data,a.len); |
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390 |
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391 double *wr = new double [n]; |
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392 double *wi = new double [n]; |
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393 double *q = new double [n*n]; |
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394 double *work = new double [lwork]; |
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395 |
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396 // These are not referenced for the non-ordered Schur routine. |
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397 |
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398 int *iwork = (int *) NULL; |
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399 int *bwork = (int *) NULL; |
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400 if (*ord == 'A' || *ord == 'D' || *ord == 'a' || *ord == 'd') |
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401 { |
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402 iwork = new int [liwork]; |
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403 bwork = new int [n]; |
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404 } |
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405 |
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406 if (*ord == 'A' || *ord == 'a') |
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407 { |
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408 F77_FCN (dgeesx) (&jobvs, &sort, select_ana, &sense, &n, s, &n, |
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409 &sdim, wr, wi, q, &n, &rconde, &rcondv, work, |
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410 &lwork, iwork, &liwork, bwork, &info, 1L, 1L); |
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411 } |
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412 else if (*ord == 'D' || *ord == 'd') |
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413 { |
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414 F77_FCN (dgeesx) (&jobvs, &sort, select_dig, &sense, &n, s, &n, |
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415 &sdim, wr, wi, q, &n, &rconde, &rcondv, work, |
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416 &lwork, iwork, &liwork, bwork, &info, 1L, 1L); |
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417 |
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418 } |
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419 else |
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420 { |
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421 F77_FCN (dgeesx) (&jobvs, &sort, dummy_select, &sense, &n, s, |
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422 &n, &sdim, wr, wi, q, &n, &rconde, &rcondv, |
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423 work, &lwork, iwork, &liwork, bwork, &info, |
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424 1L, 1L); |
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425 } |
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426 |
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427 |
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428 schur_mat = Matrix (s, n, n); |
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429 unitary_mat = Matrix (q, n, n); |
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430 |
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431 delete [] wr; |
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432 delete [] wi; |
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433 delete [] work; |
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434 delete [] iwork; |
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435 delete [] bwork; |
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436 |
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437 return info; |
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438 } |
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439 |
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440 static int |
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441 complex_select_ana (Complex *a) |
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442 { |
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443 return (real (*a) < 0.0); |
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444 } |
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445 |
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446 static int |
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447 complex_select_dig (Complex *a) |
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448 { |
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449 return (abs (*a) < 1.0); |
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450 } |
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451 |
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452 int |
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453 ComplexSCHUR::init (const ComplexMatrix& a, const char *ord) |
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454 { |
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455 if (a.nr != a.nc) |
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456 FAIL; |
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457 |
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458 char jobvs = 'V'; |
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459 char sort; |
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460 if (*ord == 'A' || *ord == 'D' || *ord == 'a' || *ord == 'd') |
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461 sort = 'S'; |
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462 else |
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463 sort = 'N'; |
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464 |
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465 char sense = 'N'; |
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466 |
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467 int n = a.nc; |
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468 int lwork = 8 * n; |
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469 int info; |
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470 int sdim; |
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471 double rconde; |
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472 double rcondv; |
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473 |
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474 double *rwork = new double [n]; |
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475 |
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476 // bwork is not referenced for non-ordered Schur. |
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477 |
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478 int *bwork = (int *) NULL; |
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479 if (*ord == 'A' || *ord == 'D' || *ord == 'a' || *ord == 'd') |
|
|
480 bwork = new int [n]; |
|
|
481 |
|
|
482 Complex *s = dup(a.data,a.len); |
|
|
483 |
|
|
484 Complex *work = new Complex [lwork]; |
|
|
485 Complex *q = new Complex [n*n]; |
|
|
486 Complex *w = new Complex [n]; |
|
|
487 |
|
|
488 if (*ord == 'A' || *ord == 'a') |
|
|
489 { |
|
|
490 F77_FCN (zgeesx) (&jobvs, &sort, complex_select_ana, &sense, |
|
|
491 &n, s, &n, &sdim, w, q, &n, &rconde, &rcondv, |
|
|
492 work, &lwork, rwork, bwork, &info, 1L, 1L); |
|
|
493 } |
|
|
494 else if (*ord == 'D' || *ord == 'd') |
|
|
495 { |
|
|
496 F77_FCN (zgeesx) (&jobvs, &sort, complex_select_dig, &sense, |
|
|
497 &n, s, &n, &sdim, w, q, &n, &rconde, &rcondv, |
|
|
498 work, &lwork, rwork, bwork, &info, 1L, 1L); |
|
|
499 } |
|
|
500 else |
|
|
501 { |
|
|
502 F77_FCN (zgeesx) (&jobvs, &sort, dummy_select, &sense, &n, s, |
|
|
503 &n, &sdim, w, q, &n, &rconde, &rcondv, work, |
|
|
504 &lwork, rwork, bwork, &info, 1L, 1L); |
|
|
505 } |
|
|
506 |
|
|
507 schur_mat = ComplexMatrix (s,n,n); |
|
|
508 unitary_mat = ComplexMatrix (q,n,n); |
|
|
509 |
|
|
510 delete [] w; |
|
|
511 delete [] work; |
|
|
512 delete [] rwork; |
|
|
513 delete [] bwork; |
|
|
514 |
|
|
515 return info; |
|
|
516 } |
|
|
517 |
|
|
518 ostream& |
|
|
519 operator << (ostream& os, const SCHUR& a) |
|
|
520 { |
|
|
521 os << a.schur_matrix () << "\n"; |
|
|
522 os << a.unitary_matrix () << "\n"; |
|
|
523 |
|
|
524 return os; |
|
|
525 } |
|
|
526 |
|
|
527 /* |
|
|
528 * SVD stuff |
|
|
529 */ |
|
|
530 |
|
|
531 int |
|
|
532 SVD::init (const Matrix& a) |
|
|
533 { |
|
|
534 int info; |
|
|
535 |
|
|
536 int m = a.nr; |
|
|
537 int n = a.nc; |
|
|
538 |
|
|
539 char jobu = 'A'; |
|
|
540 char jobv = 'A'; |
|
|
541 |
|
|
542 double *tmp_data = dup (a.data, a.len); |
|
|
543 |
|
|
544 int min_mn = m < n ? m : n; |
|
|
545 int max_mn = m > n ? m : n; |
|
|
546 |
|
|
547 double *u = new double[m*m]; |
|
|
548 double *s_vec = new double[min_mn]; |
|
|
549 double *vt = new double[n*n]; |
|
|
550 |
|
|
551 int tmp1 = 3*min_mn + max_mn; |
|
|
552 int tmp2 = 5*min_mn - 4; |
|
|
553 int lwork = tmp1 > tmp2 ? tmp1 : tmp2; |
|
|
554 double *work = new double[lwork]; |
|
|
555 |
|
|
556 F77_FCN (dgesvd) (&jobu, &jobv, &m, &n, tmp_data, &m, s_vec, u, &m, |
|
|
557 vt, &n, work, &lwork, &info, 1L, 1L); |
|
|
558 |
|
|
559 left_sm = Matrix (u, m, m); |
|
|
560 sigma = DiagMatrix (s_vec, m, n); |
|
|
561 Matrix vt_m (vt, n, n); |
|
|
562 right_sm = Matrix (vt_m.transpose ()); |
|
|
563 |
|
|
564 delete [] tmp_data; |
|
|
565 delete [] work; |
|
|
566 |
|
|
567 return info; |
|
|
568 } |
|
|
569 |
|
|
570 ostream& |
|
|
571 operator << (ostream& os, const SVD& a) |
|
|
572 { |
|
|
573 os << a.left_singular_matrix () << "\n"; |
|
|
574 os << a.singular_values () << "\n"; |
|
|
575 os << a.right_singular_matrix () << "\n"; |
|
|
576 |
|
|
577 return os; |
|
|
578 } |
|
|
579 |
|
|
580 int |
|
|
581 ComplexSVD::init (const ComplexMatrix& a) |
|
|
582 { |
|
|
583 int info; |
|
|
584 |
|
|
585 int m = a.nr; |
|
|
586 int n = a.nc; |
|
|
587 |
|
|
588 char jobu = 'A'; |
|
|
589 char jobv = 'A'; |
|
|
590 |
|
|
591 Complex *tmp_data = dup (a.data, a.len); |
|
|
592 |
|
|
593 int min_mn = m < n ? m : n; |
|
|
594 int max_mn = m > n ? m : n; |
|
|
595 |
|
|
596 Complex *u = new Complex[m*m]; |
|
|
597 double *s_vec = new double[min_mn]; |
|
|
598 Complex *vt = new Complex[n*n]; |
|
|
599 |
|
|
600 int lwork = 2*min_mn + max_mn; |
|
|
601 Complex *work = new Complex[lwork]; |
|
|
602 |
|
|
603 int lrwork = 5*max_mn; |
|
|
604 double *rwork = new double[lrwork]; |
|
|
605 |
|
|
606 F77_FCN (zgesvd) (&jobu, &jobv, &m, &n, tmp_data, &m, s_vec, u, &m, |
|
|
607 vt, &n, work, &lwork, rwork, &info, 1L, 1L); |
|
|
608 |
|
|
609 left_sm = ComplexMatrix (u, m, m); |
|
|
610 sigma = DiagMatrix (s_vec, m, n); |
|
|
611 ComplexMatrix vt_m (vt, n, n); |
|
|
612 right_sm = ComplexMatrix (vt_m.hermitian ()); |
|
|
613 |
|
|
614 delete [] tmp_data; |
|
|
615 delete [] work; |
|
|
616 |
|
|
617 return info; |
|
|
618 } |
|
|
619 |
|
|
620 /* |
|
|
621 * EIG stuff. |
|
|
622 */ |
|
|
623 |
|
|
624 int |
|
|
625 EIG::init (const Matrix& a) |
|
|
626 { |
|
|
627 if (a.nr != a.nc) |
|
|
628 FAIL; |
|
|
629 |
|
|
630 int n = a.nr; |
|
|
631 |
|
|
632 int info; |
|
|
633 |
|
|
634 char jobvl = 'N'; |
|
|
635 char jobvr = 'V'; |
|
|
636 |
|
|
637 double *tmp_data = dup (a.data, a.len); |
|
|
638 double *wr = new double[n]; |
|
|
639 double *wi = new double[n]; |
|
|
640 Matrix vr (n, n); |
|
|
641 double *pvr = vr.fortran_vec (); |
|
|
642 int lwork = 8*n; |
|
|
643 double *work = new double[lwork]; |
|
|
644 |
|
|
645 double dummy; |
|
|
646 int idummy = 1; |
|
|
647 |
|
|
648 F77_FCN (dgeev) (&jobvl, &jobvr, &n, tmp_data, &n, wr, wi, &dummy, |
|
|
649 &idummy, pvr, &n, work, &lwork, &info, 1L, 1L); |
|
|
650 |
|
|
651 lambda.resize (n); |
|
|
652 v.resize (n, n); |
|
|
653 |
|
|
654 for (int j = 0; j < n; j++) |
|
|
655 { |
|
|
656 if (wi[j] == 0.0) |
|
|
657 { |
|
|
658 lambda.elem (j) = Complex (wr[j]); |
|
|
659 for (int i = 0; i < n; i++) |
|
|
660 v.elem (i, j) = vr.elem (i, j); |
|
|
661 } |
|
|
662 else |
|
|
663 { |
|
|
664 if (j+1 >= n) |
|
|
665 FAIL; |
|
|
666 |
|
|
667 for (int i = 0; i < n; i++) |
|
|
668 { |
|
|
669 lambda.elem (j) = Complex (wr[j], wi[j]); |
|
|
670 lambda.elem (j+1) = Complex (wr[j+1], wi[j+1]); |
|
|
671 double real_part = vr.elem (i, j); |
|
|
672 double imag_part = vr.elem (i, j+1); |
|
|
673 v.elem (i, j) = Complex (real_part, imag_part); |
|
|
674 v.elem (i, j+1) = Complex (real_part, -imag_part); |
|
|
675 } |
|
|
676 j++; |
|
|
677 } |
|
|
678 } |
|
|
679 |
|
|
680 delete [] tmp_data; |
|
|
681 delete [] wr; |
|
|
682 delete [] wi; |
|
|
683 delete [] work; |
|
|
684 |
|
|
685 return info; |
|
|
686 } |
|
|
687 |
|
|
688 int |
|
|
689 EIG::init (const ComplexMatrix& a) |
|
|
690 { |
|
|
691 |
|
|
692 if (a.nr != a.nc) |
|
|
693 FAIL; |
|
|
694 |
|
|
695 int n = a.nr; |
|
|
696 |
|
|
697 int info; |
|
|
698 |
|
|
699 char jobvl = 'N'; |
|
|
700 char jobvr = 'V'; |
|
|
701 |
|
|
702 lambda.resize (n); |
|
|
703 v.resize (n, n); |
|
|
704 |
|
|
705 Complex *pw = lambda.fortran_vec (); |
|
|
706 Complex *pvr = v.fortran_vec (); |
|
|
707 |
|
|
708 Complex *tmp_data = dup (a.data, a.len); |
|
|
709 |
|
|
710 int lwork = 8*n; |
|
|
711 Complex *work = new Complex[lwork]; |
|
|
712 double *rwork = new double[4*n]; |
|
|
713 |
|
|
714 Complex dummy; |
|
|
715 int idummy = 1; |
|
|
716 |
|
|
717 F77_FCN (zgeev) (&jobvl, &jobvr, &n, tmp_data, &n, pw, &dummy, |
|
|
718 &idummy, pvr, &n, work, &lwork, rwork, &info, 1L, |
|
|
719 1L); |
|
|
720 |
|
|
721 delete [] tmp_data; |
|
|
722 delete [] work; |
|
|
723 delete [] rwork; |
|
|
724 |
|
|
725 return info; |
|
|
726 } |
|
|
727 |
|
|
728 /* |
|
|
729 * LU stuff. |
|
|
730 */ |
|
|
731 |
|
|
732 LU::LU (const Matrix& a) |
|
|
733 { |
|
|
734 if (a.nr == 0 || a.nc == 0 || a.nr != a.nc) |
|
|
735 FAIL; |
|
|
736 |
|
|
737 int n = a.nr; |
|
|
738 |
|
|
739 int *ipvt = new int [n]; |
|
|
740 int *pvt = new int [n]; |
|
|
741 double *tmp_data = dup (a.data, a.len); |
|
|
742 int info = 0; |
|
|
743 int zero = 0; |
|
|
744 double b; |
|
|
745 |
|
|
746 F77_FCN (dgesv) (&n, &zero, tmp_data, &n, ipvt, &b, &n, &info); |
|
|
747 |
|
|
748 Matrix A_fact (tmp_data, n, n); |
|
|
749 |
|
|
750 int i; |
|
|
751 |
|
|
752 for (i = 0; i < n; i++) |
|
|
753 { |
|
|
754 ipvt[i] -= 1; |
|
|
755 pvt[i] = i; |
|
|
756 } |
|
|
757 |
|
|
758 for (i = 0; i < n - 1; i++) |
|
|
759 { |
|
|
760 int k = ipvt[i]; |
|
|
761 if (k != i) |
|
|
762 { |
|
|
763 int tmp = pvt[k]; |
|
|
764 pvt[k] = pvt[i]; |
|
|
765 pvt[i] = tmp; |
|
|
766 } |
|
|
767 } |
|
|
768 |
|
|
769 l.resize (n, n, 0.0); |
|
|
770 u.resize (n, n, 0.0); |
|
|
771 p.resize (n, n, 0.0); |
|
|
772 |
|
|
773 for (i = 0; i < n; i++) |
|
|
774 { |
|
|
775 p.elem (i, pvt[i]) = 1.0; |
|
|
776 |
|
|
777 int j; |
|
|
778 |
|
|
779 l.elem (i, i) = 1.0; |
|
|
780 for (j = 0; j < i; j++) |
|
|
781 l.elem (i, j) = A_fact.elem (i, j); |
|
|
782 |
|
|
783 for (j = i; j < n; j++) |
|
|
784 u.elem (i, j) = A_fact.elem (i, j); |
|
|
785 } |
|
|
786 |
|
|
787 delete [] ipvt; |
|
|
788 delete [] pvt; |
|
|
789 } |
|
|
790 |
|
|
791 ComplexLU::ComplexLU (const ComplexMatrix& a) |
|
|
792 { |
|
|
793 if (a.nr == 0 || a.nc == 0 || a.nr != a.nc) |
|
|
794 FAIL; |
|
|
795 |
|
|
796 int n = a.nr; |
|
|
797 |
|
|
798 int *ipvt = new int [n]; |
|
|
799 int *pvt = new int [n]; |
|
|
800 Complex *tmp_data = dup (a.data, a.len); |
|
|
801 int info = 0; |
|
|
802 int zero = 0; |
|
|
803 Complex b; |
|
|
804 |
|
|
805 F77_FCN (zgesv) (&n, &zero, tmp_data, &n, ipvt, &b, &n, &info); |
|
|
806 |
|
|
807 ComplexMatrix A_fact (tmp_data, n, n); |
|
|
808 |
|
|
809 int i; |
|
|
810 |
|
|
811 for (i = 0; i < n; i++) |
|
|
812 { |
|
|
813 ipvt[i] -= 1; |
|
|
814 pvt[i] = i; |
|
|
815 } |
|
|
816 |
|
|
817 for (i = 0; i < n - 1; i++) |
|
|
818 { |
|
|
819 int k = ipvt[i]; |
|
|
820 if (k != i) |
|
|
821 { |
|
|
822 int tmp = pvt[k]; |
|
|
823 pvt[k] = pvt[i]; |
|
|
824 pvt[i] = tmp; |
|
|
825 } |
|
|
826 } |
|
|
827 |
|
|
828 l.resize (n, n, 0.0); |
|
|
829 u.resize (n, n, 0.0); |
|
|
830 p.resize (n, n, 0.0); |
|
|
831 |
|
|
832 for (i = 0; i < n; i++) |
|
|
833 { |
|
|
834 p.elem (i, pvt[i]) = 1.0; |
|
|
835 |
|
|
836 int j; |
|
|
837 |
|
|
838 l.elem (i, i) = 1.0; |
|
|
839 for (j = 0; j < i; j++) |
|
|
840 l.elem (i, j) = A_fact.elem (i, j); |
|
|
841 |
|
|
842 for (j = i; j < n; j++) |
|
|
843 u.elem (i, j) = A_fact.elem (i, j); |
|
|
844 } |
|
|
845 |
|
|
846 delete [] ipvt; |
|
|
847 delete [] pvt; |
|
|
848 } |
|
|
849 |
|
|
850 /* |
|
|
851 * QR stuff. |
|
|
852 */ |
|
|
853 |
|
|
854 QR::QR (const Matrix& a) |
|
|
855 { |
|
|
856 int m = a.nr; |
|
|
857 int n = a.nc; |
|
|
858 |
|
|
859 if (m == 0 || n == 0) |
|
|
860 FAIL; |
|
|
861 |
|
|
862 double *tmp_data; |
|
|
863 int min_mn = m < n ? m : n; |
|
|
864 double *tau = new double[min_mn]; |
|
|
865 int lwork = 32*n; |
|
|
866 double *work = new double[lwork]; |
|
|
867 int info = 0; |
|
|
868 |
|
|
869 if (m > n) |
|
|
870 { |
|
|
871 tmp_data = new double [m*m]; |
|
|
872 copy (tmp_data, a.data, a.len); |
|
|
873 } |
|
|
874 else |
|
|
875 tmp_data = dup (a.data, a.len); |
|
|
876 |
|
|
877 F77_FCN (dgeqrf) (&m, &n, tmp_data, &m, tau, work, &lwork, &info); |
|
|
878 |
|
|
879 delete [] work; |
|
|
880 |
|
|
881 r.resize (m, n, 0.0); |
|
|
882 for (int j = 0; j < n; j++) |
|
|
883 { |
|
|
884 int limit = j < min_mn-1 ? j : min_mn-1; |
|
|
885 for (int i = 0; i <= limit; i++) |
|
|
886 r.elem (i, j) = tmp_data[m*j+i]; |
|
|
887 } |
|
|
888 |
|
|
889 lwork = 32*m; |
|
|
890 work = new double[lwork]; |
|
|
891 |
|
|
892 F77_FCN (dorgqr) (&m, &m, &min_mn, tmp_data, &m, tau, work, &lwork, &info); |
|
|
893 |
|
|
894 q = Matrix (tmp_data, m, m); |
|
|
895 |
|
|
896 delete [] tau; |
|
|
897 delete [] work; |
|
|
898 } |
|
|
899 |
|
|
900 ComplexQR::ComplexQR (const ComplexMatrix& a) |
|
|
901 { |
|
|
902 int m = a.nr; |
|
|
903 int n = a.nc; |
|
|
904 |
|
|
905 if (m == 0 || n == 0) |
|
|
906 FAIL; |
|
|
907 |
|
|
908 Complex *tmp_data; |
|
|
909 int min_mn = m < n ? m : n; |
|
|
910 Complex *tau = new Complex[min_mn]; |
|
|
911 int lwork = 32*n; |
|
|
912 Complex *work = new Complex[lwork]; |
|
|
913 int info = 0; |
|
|
914 |
|
|
915 if (m > n) |
|
|
916 { |
|
|
917 tmp_data = new Complex [m*m]; |
|
|
918 copy (tmp_data, a.data, a.len); |
|
|
919 } |
|
|
920 else |
|
|
921 tmp_data = dup (a.data, a.len); |
|
|
922 |
|
|
923 F77_FCN (zgeqrf) (&m, &n, tmp_data, &m, tau, work, &lwork, &info); |
|
|
924 |
|
|
925 delete [] work; |
|
|
926 |
|
|
927 r.resize (m, n, 0.0); |
|
|
928 for (int j = 0; j < n; j++) |
|
|
929 { |
|
|
930 int limit = j < min_mn-1 ? j : min_mn-1; |
|
|
931 for (int i = 0; i <= limit; i++) |
|
|
932 r.elem (i, j) = tmp_data[m*j+i]; |
|
|
933 } |
|
|
934 |
|
|
935 lwork = 32*m; |
|
|
936 work = new Complex[lwork]; |
|
|
937 |
|
|
938 F77_FCN (zungqr) (&m, &m, &min_mn, tmp_data, &m, tau, work, &lwork, &info); |
|
|
939 |
|
|
940 q = ComplexMatrix (tmp_data, m, m); |
|
|
941 |
|
|
942 delete [] tau; |
|
|
943 delete [] work; |
|
|
944 } |
|
|
945 |
|
|
946 /* |
|
|
947 ;;; Local Variables: *** |
|
|
948 ;;; mode: C++ *** |
|
|
949 ;;; page-delimiter: "^/\\*" *** |
|
|
950 ;;; End: *** |
|
|
951 */ |
