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1 /* |
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2 |
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3 Copyright (C) 2006, 2007 David Bateman |
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4 |
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5 This file is part of Octave. |
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6 |
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7 Octave is free software; you can redistribute it and/or modify it |
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8 under the terms of the GNU General Public License as published by the |
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9 Free Software Foundation; either version 3 of the License, or (at your |
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10 option) any later version. |
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11 |
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12 Octave is distributed in the hope that it will be useful, but WITHOUT |
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13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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15 for more details. |
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16 |
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17 You should have received a copy of the GNU General Public License |
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18 along with Octave; see the file COPYING. If not, see |
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19 <http://www.gnu.org/licenses/>. |
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20 |
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21 */ |
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22 |
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23 #ifdef HAVE_CONFIG_H |
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24 #include <config.h> |
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25 #endif |
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26 |
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27 #include <vector> |
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28 |
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29 #include "MArray2.h" |
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30 #include "MSparse.h" |
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31 #include "SparseQR.h" |
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32 #include "SparseCmplxQR.h" |
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33 #include "MatrixType.h" |
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34 #include "oct-sort.h" |
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35 |
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36 template <class T> |
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37 static MSparse<T> |
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38 dmsolve_extract (const MSparse<T> &A, const octave_idx_type *Pinv, |
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39 const octave_idx_type *Q, octave_idx_type rst, |
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40 octave_idx_type rend, octave_idx_type cst, |
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41 octave_idx_type cend, octave_idx_type maxnz = -1, |
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42 bool lazy = false) |
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43 { |
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44 octave_idx_type nz = (rend - rst) * (cend - cst); |
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45 maxnz = (maxnz < 0 ? A.nnz () : maxnz); |
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46 MSparse<T> B (rend - rst, cend - cst, (nz < maxnz ? nz : maxnz)); |
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47 // Some sparse functions can support lazy indexing (where elements |
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48 // in the row are in no particular order), even though octave in |
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49 // general can't. For those functions that can using it is a big |
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50 // win here in terms of speed. |
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51 if (lazy) |
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52 { |
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53 nz = 0; |
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54 for (octave_idx_type j = cst ; j < cend ; j++) |
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55 { |
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56 octave_idx_type qq = (Q ? Q [j] : j); |
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57 B.xcidx (j - cst) = nz; |
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58 for (octave_idx_type p = A.cidx(qq) ; p < A.cidx (qq+1) ; p++) |
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59 { |
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60 OCTAVE_QUIT; |
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61 octave_idx_type r = (Pinv ? Pinv [A.ridx (p)] : A.ridx (p)); |
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62 if (r >= rst && r < rend) |
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63 { |
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64 B.xdata (nz) = A.data (p); |
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65 B.xridx (nz++) = r - rst ; |
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66 } |
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67 } |
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68 } |
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69 B.xcidx (cend - cst) = nz ; |
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70 } |
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71 else |
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72 { |
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73 OCTAVE_LOCAL_BUFFER (T, X, rend - rst); |
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74 octave_sort<octave_idx_type> sort; |
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75 octave_idx_type *ri = B.xridx(); |
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76 nz = 0; |
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77 for (octave_idx_type j = cst ; j < cend ; j++) |
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78 { |
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79 octave_idx_type qq = (Q ? Q [j] : j); |
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80 B.xcidx (j - cst) = nz; |
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81 for (octave_idx_type p = A.cidx(qq) ; p < A.cidx (qq+1) ; p++) |
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82 { |
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83 OCTAVE_QUIT; |
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84 octave_idx_type r = (Pinv ? Pinv [A.ridx (p)] : A.ridx (p)); |
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85 if (r >= rst && r < rend) |
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86 { |
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87 X [r-rst] = A.data (p); |
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88 B.xridx (nz++) = r - rst ; |
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89 } |
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90 } |
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91 sort.sort (ri + B.xcidx (j - cst), nz - B.xcidx (j - cst)); |
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92 for (octave_idx_type p = B.cidx (j - cst); p < nz; p++) |
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93 B.xdata (p) = X [B.xridx (p)]; |
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94 } |
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95 B.xcidx (cend - cst) = nz ; |
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96 } |
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97 |
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98 return B; |
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99 } |
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100 |
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101 #if !defined (CXX_NEW_FRIEND_TEMPLATE_DECL) |
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102 static MSparse<double> |
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103 dmsolve_extract (const MSparse<double> &A, const octave_idx_type *Pinv, |
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104 const octave_idx_type *Q, octave_idx_type rst, |
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105 octave_idx_type rend, octave_idx_type cst, |
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106 octave_idx_type cend, octave_idx_type maxnz, |
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107 bool lazy); |
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108 |
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109 static MSparse<Complex> |
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110 dmsolve_extract (const MSparse<Complex> &A, const octave_idx_type *Pinv, |
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111 const octave_idx_type *Q, octave_idx_type rst, |
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112 octave_idx_type rend, octave_idx_type cst, |
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113 octave_idx_type cend, octave_idx_type maxnz, |
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114 bool lazy); |
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115 #endif |
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116 |
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117 template <class T> |
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118 static MArray2<T> |
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119 dmsolve_extract (const MArray2<T> &m, const octave_idx_type *, |
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120 const octave_idx_type *, octave_idx_type r1, |
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121 octave_idx_type r2, octave_idx_type c1, |
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122 octave_idx_type c2) |
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123 { |
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124 r2 -= 1; |
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125 c2 -= 1; |
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126 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } |
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127 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } |
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128 |
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129 octave_idx_type new_r = r2 - r1 + 1; |
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130 octave_idx_type new_c = c2 - c1 + 1; |
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131 |
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132 MArray2<T> result (new_r, new_c); |
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133 |
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134 for (octave_idx_type j = 0; j < new_c; j++) |
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135 for (octave_idx_type i = 0; i < new_r; i++) |
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136 result.xelem (i, j) = m.elem (r1+i, c1+j); |
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137 |
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138 return result; |
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139 } |
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140 |
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141 #if !defined (CXX_NEW_FRIEND_TEMPLATE_DECL) |
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142 static MArray2<double> |
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143 dmsolve_extract (const MArray2<double> &m, const octave_idx_type *, |
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144 const octave_idx_type *, octave_idx_type r1, |
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145 octave_idx_type r2, octave_idx_type c1, |
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146 octave_idx_type c2) |
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147 |
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148 static MArray2<Complex> |
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149 dmsolve_extract (const MArray2<Complex> &m, const octave_idx_type *, |
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150 const octave_idx_type *, octave_idx_type r1, |
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151 octave_idx_type r2, octave_idx_type c1, |
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152 octave_idx_type c2) |
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153 #endif |
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154 |
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155 template <class T> |
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156 static void |
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157 dmsolve_insert (MArray2<T> &a, const MArray2<T> &b, const octave_idx_type *Q, |
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158 octave_idx_type r, octave_idx_type c) |
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159 { |
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160 T *ax = a.fortran_vec(); |
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161 const T *bx = b.fortran_vec(); |
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162 octave_idx_type anr = a.rows(); |
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163 octave_idx_type nr = b.rows(); |
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164 octave_idx_type nc = b.cols(); |
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165 for (octave_idx_type j = 0; j < nc; j++) |
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166 { |
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167 octave_idx_type aoff = (c + j) * anr; |
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168 octave_idx_type boff = j * nr; |
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169 for (octave_idx_type i = 0; i < nr; i++) |
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170 { |
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171 OCTAVE_QUIT; |
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172 ax [Q [r + i] + aoff] = bx [i + boff]; |
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173 } |
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174 } |
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175 } |
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176 |
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177 #if !defined (CXX_NEW_FRIEND_TEMPLATE_DECL) |
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178 static void |
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179 dmsolve_insert (MArray2<double> &a, const MArray2<double> &b, |
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180 const octave_idx_type *Q, octave_idx_type r, octave_idx_type c); |
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181 |
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182 static void |
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183 dmsolve_insert (MArray2<Complex> &a, const MArray2<Complex> &b, |
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184 const octave_idx_type *Q, octave_idx_type r, octave_idx_type c); |
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185 #endif |
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186 |
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187 template <class T> |
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188 static void |
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189 dmsolve_insert (MSparse<T> &a, const MSparse<T> &b, const octave_idx_type *Q, |
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190 octave_idx_type r, octave_idx_type c) |
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191 { |
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192 octave_idx_type b_rows = b.rows (); |
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193 octave_idx_type b_cols = b.cols (); |
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194 octave_idx_type nr = a.rows (); |
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195 octave_idx_type nc = a.cols (); |
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196 |
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197 OCTAVE_LOCAL_BUFFER (octave_idx_type, Qinv, nr); |
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198 for (octave_idx_type i = 0; i < nr; i++) |
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199 Qinv [Q [i]] = i; |
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200 |
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201 // First count the number of elements in the final array |
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202 octave_idx_type nel = a.xcidx(c) + b.nnz (); |
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203 |
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204 if (c + b_cols < nc) |
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205 nel += a.xcidx(nc) - a.xcidx(c + b_cols); |
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206 |
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207 for (octave_idx_type i = c; i < c + b_cols; i++) |
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208 for (octave_idx_type j = a.xcidx(i); j < a.xcidx(i+1); j++) |
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209 if (Qinv [a.xridx(j)] < r || Qinv [a.xridx(j)] >= r + b_rows) |
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210 nel++; |
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211 |
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212 OCTAVE_LOCAL_BUFFER (T, X, nr); |
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213 octave_sort<octave_idx_type> sort; |
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214 MSparse<T> tmp (a); |
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215 a = MSparse<T> (nr, nc, nel); |
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216 octave_idx_type *ri = a.xridx(); |
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217 |
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218 for (octave_idx_type i = 0; i < tmp.cidx(c); i++) |
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219 { |
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220 a.xdata(i) = tmp.xdata(i); |
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221 a.xridx(i) = tmp.xridx(i); |
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222 } |
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223 for (octave_idx_type i = 0; i < c + 1; i++) |
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224 a.xcidx(i) = tmp.xcidx(i); |
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225 |
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226 octave_idx_type ii = a.xcidx(c); |
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227 |
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228 for (octave_idx_type i = c; i < c + b_cols; i++) |
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229 { |
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230 OCTAVE_QUIT; |
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231 |
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232 for (octave_idx_type j = tmp.xcidx(i); j < tmp.xcidx(i+1); j++) |
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233 if (Qinv [tmp.xridx(j)] < r || Qinv [tmp.xridx(j)] >= r + b_rows) |
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234 { |
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235 X [tmp.xridx(j)] = tmp.xdata(j); |
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236 a.xridx(ii++) = tmp.xridx(j); |
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237 } |
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238 |
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239 OCTAVE_QUIT; |
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240 |
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241 for (octave_idx_type j = b.cidx(i-c); j < b.cidx(i-c+1); j++) |
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242 { |
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243 X [Q [r + b.ridx(j)]] = b.data(j); |
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244 a.xridx(ii++) = Q [r + b.ridx(j)]; |
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245 } |
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246 |
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247 sort.sort (ri + a.xcidx (i), ii - a.xcidx (i)); |
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248 for (octave_idx_type p = a.xcidx (i); p < ii; p++) |
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249 a.xdata (p) = X [a.xridx (p)]; |
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250 a.xcidx(i+1) = ii; |
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251 } |
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252 |
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253 for (octave_idx_type i = c + b_cols; i < nc; i++) |
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254 { |
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255 for (octave_idx_type j = tmp.xcidx(i); j < tmp.cidx(i+1); j++) |
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256 { |
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257 a.xdata(ii) = tmp.xdata(j); |
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258 a.xridx(ii++) = tmp.xridx(j); |
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259 } |
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260 a.xcidx(i+1) = ii; |
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261 } |
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262 } |
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263 |
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264 #if !defined (CXX_NEW_FRIEND_TEMPLATE_DECL) |
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265 static void |
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266 dmsolve_insert (MSparse<double> &a, const SparseMatrix &b, |
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267 const octave_idx_type *Q, octave_idx_type r, octave_idx_type c); |
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268 |
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269 static void |
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270 dmsolve_insert (MSparse<Complex> &a, const MSparse<Complex> &b, |
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271 const octave_idx_type *Q, octave_idx_type r, octave_idx_type c); |
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272 #endif |
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273 |
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274 template <class T, class RT> |
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275 static void |
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276 dmsolve_permute (MArray2<RT> &a, const MArray2<T>& b, const octave_idx_type *p) |
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277 { |
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278 octave_idx_type b_nr = b.rows (); |
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279 octave_idx_type b_nc = b.cols (); |
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280 const T *Bx = b.fortran_vec(); |
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281 a.resize(b_nr, b_nc); |
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282 RT *Btx = a.fortran_vec(); |
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283 for (octave_idx_type j = 0; j < b_nc; j++) |
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284 { |
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285 octave_idx_type off = j * b_nr; |
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286 for (octave_idx_type i = 0; i < b_nr; i++) |
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287 { |
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288 OCTAVE_QUIT; |
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289 Btx [p [i] + off] = Bx [ i + off]; |
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290 } |
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291 } |
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292 } |
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293 |
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294 #if !defined (CXX_NEW_FRIEND_TEMPLATE_DECL) |
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295 static void |
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296 dmsolve_permute (MArray2<double> &a, const MArray2<double>& b, |
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297 const octave_idx_type *p); |
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298 |
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299 static void |
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300 dmsolve_permute (MArray2<Complex> &a, const MArray2<double>& b, |
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301 const octave_idx_type *p); |
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302 |
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303 static void |
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304 dmsolve_permute (MArray2<Complex> &a, const MArray2<Complex>& b, |
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305 const octave_idx_type *p); |
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306 #endif |
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307 |
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308 template <class T, class RT> |
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309 static void |
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310 dmsolve_permute (MSparse<RT> &a, const MSparse<T>& b, const octave_idx_type *p) |
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311 { |
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312 octave_idx_type b_nr = b.rows (); |
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313 octave_idx_type b_nc = b.cols (); |
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314 octave_idx_type b_nz = b.nnz (); |
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315 octave_idx_type nz = 0; |
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316 a = MSparse<RT> (b_nr, b_nc, b_nz); |
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317 octave_sort<octave_idx_type> sort; |
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318 octave_idx_type *ri = a.xridx(); |
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319 OCTAVE_LOCAL_BUFFER (RT, X, b_nr); |
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320 a.xcidx(0) = 0; |
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321 for (octave_idx_type j = 0; j < b_nc; j++) |
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322 { |
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323 for (octave_idx_type i = b.cidx(j); i < b.cidx(j+1); i++) |
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324 { |
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325 OCTAVE_QUIT; |
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326 octave_idx_type r = p [b.ridx (i)]; |
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327 X [r] = b.data (i); |
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328 a.xridx(nz++) = p [b.ridx (i)]; |
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329 } |
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330 sort.sort (ri + a.xcidx (j), nz - a.xcidx (j)); |
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331 for (octave_idx_type i = a.cidx (j); i < nz; i++) |
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332 { |
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333 OCTAVE_QUIT; |
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334 a.xdata (i) = X [a.xridx (i)]; |
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335 } |
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336 a.xcidx(j+1) = nz; |
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337 } |
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338 } |
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339 |
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340 #if !defined (CXX_NEW_FRIEND_TEMPLATE_DECL) |
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341 static void |
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342 dmsolve_permute (MSparse<double> &a, const MSparse<double>& b, |
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343 const octave_idx_type *p); |
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344 |
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345 static void |
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346 dmsolve_permute (MSparse<Complex> &a, const MSparse<double>& b, |
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347 const octave_idx_type *p); |
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348 |
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349 static void |
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350 dmsolve_permute (MSparse<Complex> &a, const MSparse<Complex>& b, |
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351 const octave_idx_type *p); |
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352 #endif |
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353 |
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354 static void |
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355 solve_singularity_warning (double) |
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356 { |
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357 // Dummy singularity handler so that LU solver doesn't flag |
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358 // an error for numerically rank defficient matrices |
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359 } |
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360 |
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361 template <class RT, class ST, class T> |
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362 RT |
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363 dmsolve (const ST &a, const T &b, octave_idx_type &info) |
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364 { |
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5684
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365 #ifdef HAVE_CXSPARSE |
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366 octave_idx_type nr = a.rows (); |
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367 octave_idx_type nc = a.cols (); |
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368 octave_idx_type b_nr = b.rows (); |
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369 octave_idx_type b_nc = b.cols (); |
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370 RT retval; |
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371 |
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372 if (nr < 0 || nc < 0 || nr != b_nr) |
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373 (*current_liboctave_error_handler) |
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374 ("matrix dimension mismatch in solution of minimum norm problem"); |
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375 else if (nr == 0 || nc == 0 || b_nc == 0) |
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376 retval = RT (nc, b_nc, 0.0); |
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377 else |
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378 { |
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379 octave_idx_type nnz_remaining = a.nnz (); |
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380 CXSPARSE_DNAME () csm; |
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381 csm.m = nr; |
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382 csm.n = nc; |
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383 csm.x = 0; |
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384 csm.nz = -1; |
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385 csm.nzmax = a.nnz (); |
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386 // Cast away const on A, with full knowledge that CSparse won't touch it. |
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387 // Prevents the methods below making a copy of the data. |
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388 csm.p = const_cast<octave_idx_type *>(a.cidx ()); |
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389 csm.i = const_cast<octave_idx_type *>(a.ridx ()); |
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390 |
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5792
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391 #if defined(CS_VER) && (CS_VER >= 2) |
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392 CXSPARSE_DNAME (d) *dm = CXSPARSE_DNAME(_dmperm) (&csm, 0); |
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393 octave_idx_type *p = dm->p; |
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394 octave_idx_type *q = dm->q; |
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395 #else |
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5683
|
396 CXSPARSE_DNAME (d) *dm = CXSPARSE_DNAME(_dmperm) (&csm); |
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397 octave_idx_type *p = dm->P; |
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398 octave_idx_type *q = dm->Q; |
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5792
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399 #endif |
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5683
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400 OCTAVE_LOCAL_BUFFER (octave_idx_type, pinv, nr); |
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401 for (octave_idx_type i = 0; i < nr; i++) |
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402 pinv [p [i]] = i; |
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403 RT btmp; |
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404 dmsolve_permute (btmp, b, pinv); |
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405 info = 0; |
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406 retval.resize (nc, b_nc); |
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407 |
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408 // Leading over-determined block |
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409 if (dm->rr [2] < nr && dm->cc [3] < nc) |
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410 { |
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411 ST m = dmsolve_extract (a, pinv, q, dm->rr [2], nr, dm->cc [3], nc, |
|
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412 nnz_remaining, true); |
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413 nnz_remaining -= m.nnz(); |
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414 RT mtmp = |
|
7520
|
415 qrsolve (m, dmsolve_extract (btmp, 0, 0, dm->rr[2], b_nr, 0, |
|
5683
|
416 b_nc), info); |
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417 dmsolve_insert (retval, mtmp, q, dm->cc [3], 0); |
|
5797
|
418 if (dm->rr [2] > 0 && !info) |
|
5683
|
419 { |
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420 m = dmsolve_extract (a, pinv, q, 0, dm->rr [2], |
|
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421 dm->cc [3], nc, nnz_remaining, true); |
|
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422 nnz_remaining -= m.nnz(); |
|
7520
|
423 RT ctmp = dmsolve_extract (btmp, 0, 0, 0, |
|
5683
|
424 dm->rr[2], 0, b_nc); |
|
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425 btmp.insert (ctmp - m * mtmp, 0, 0); |
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426 } |
|
|
427 } |
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|
428 |
|
|
429 // Structurally non-singular blocks |
|
5775
|
430 // FIXME Should use fine Dulmange-Mendelsohn decomposition here. |
|
5797
|
431 if (dm->rr [1] < dm->rr [2] && dm->cc [2] < dm->cc [3] && !info) |
|
5683
|
432 { |
|
|
433 ST m = dmsolve_extract (a, pinv, q, dm->rr [1], dm->rr [2], |
|
|
434 dm->cc [2], dm->cc [3], nnz_remaining, false); |
|
|
435 nnz_remaining -= m.nnz(); |
|
7520
|
436 RT btmp2 = dmsolve_extract (btmp, 0, 0, dm->rr [1], dm->rr [2], |
|
5683
|
437 0, b_nc); |
|
|
438 double rcond = 0.0; |
|
5785
|
439 MatrixType mtyp (MatrixType::Full); |
|
5683
|
440 RT mtmp = m.solve (mtyp, btmp2, info, rcond, |
|
5697
|
441 solve_singularity_warning, false); |
|
5683
|
442 if (info != 0) |
|
|
443 { |
|
|
444 info = 0; |
|
|
445 mtmp = qrsolve (m, btmp2, info); |
|
|
446 } |
|
|
447 |
|
|
448 dmsolve_insert (retval, mtmp, q, dm->cc [2], 0); |
|
5797
|
449 if (dm->rr [1] > 0 && !info) |
|
5683
|
450 { |
|
|
451 m = dmsolve_extract (a, pinv, q, 0, dm->rr [1], dm->cc [2], |
|
|
452 dm->cc [3], nnz_remaining, true); |
|
|
453 nnz_remaining -= m.nnz(); |
|
7520
|
454 RT ctmp = dmsolve_extract (btmp, 0, 0, 0, |
|
5683
|
455 dm->rr[1], 0, b_nc); |
|
|
456 btmp.insert (ctmp - m * mtmp, 0, 0); |
|
|
457 } |
|
|
458 } |
|
|
459 |
|
|
460 // Trailing under-determined block |
|
5797
|
461 if (dm->rr [1] > 0 && dm->cc [2] > 0 && !info) |
|
5683
|
462 { |
|
|
463 ST m = dmsolve_extract (a, pinv, q, 0, dm->rr [1], 0, |
|
|
464 dm->cc [2], nnz_remaining, true); |
|
|
465 RT mtmp = |
|
7520
|
466 qrsolve (m, dmsolve_extract(btmp, 0, 0, 0, dm->rr [1] , 0, |
|
5683
|
467 b_nc), info); |
|
|
468 dmsolve_insert (retval, mtmp, q, 0, 0); |
|
|
469 } |
|
|
470 |
|
|
471 CXSPARSE_DNAME (_dfree) (dm); |
|
|
472 } |
|
|
473 return retval; |
|
5684
|
474 #else |
|
|
475 return RT (); |
|
|
476 #endif |
|
5683
|
477 } |
|
|
478 |
|
|
479 #if !defined (CXX_NEW_FRIEND_TEMPLATE_DECL) |
|
|
480 extern Matrix |
|
|
481 dmsolve (const SparseMatrix &a, const Matrix &b, |
|
|
482 octave_idx_type &info); |
|
|
483 |
|
|
484 extern ComplexMatrix |
|
|
485 dmsolve (const SparseMatrix &a, const ComplexMatrix &b, |
|
|
486 octave_idx_type &info); |
|
|
487 |
|
|
488 extern ComplexMatrix |
|
|
489 dmsolve (const SparseComplexMatrix &a, const Matrix &b, |
|
|
490 octave_idx_type &info); |
|
|
491 |
|
|
492 extern ComplexMatrix |
|
|
493 dmsolve (const SparseComplexMatrix &a, const ComplexMatrix &b, |
|
|
494 octave_idx_type &info); |
|
|
495 |
|
|
496 extern SparseMatrix |
|
|
497 dmsolve (const SparseMatrix &a, const SparseMatrix &b, |
|
|
498 octave_idx_type &info); |
|
|
499 |
|
|
500 extern SparseComplexMatrix |
|
|
501 dmsolve (const SparseMatrix &a, const SparseComplexMatrix &b, |
|
|
502 octave_idx_type &info); |
|
|
503 |
|
|
504 extern SparseComplexMatrix |
|
|
505 dmsolve (const SparseComplexMatrix &a, const SparseMatrix &b, |
|
|
506 octave_idx_type &info); |
|
|
507 |
|
|
508 extern SparseComplexMatrix |
|
|
509 dmsolve (const SparseComplexMatrix &a, const SparseComplexMatrix &b, |
|
|
510 octave_idx_type &info); |
|
|
511 #endif |
|
|
512 |
|
|
513 /* |
|
|
514 ;;; Local Variables: *** |
|
|
515 ;;; mode: C++ *** |
|
|
516 ;;; End: *** |
|
|
517 */ |
