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5683
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1 /* |
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2 |
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3 Copyright (C) 2006 David Bateman |
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4 |
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5 Octave is free software; you can redistribute it and/or modify it |
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6 under the terms of the GNU General Public License as published by the |
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7 Free Software Foundation; either version 2, or (at your option) any |
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8 later version. |
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9 |
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10 Octave is distributed in the hope that it will be useful, but WITHOUT |
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11 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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12 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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13 for more details. |
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14 |
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15 You should have received a copy of the GNU General Public License |
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16 along with this program; see the file COPYING. If not, write to the |
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17 Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, |
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18 Boston, MA 02110-1301, USA. |
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19 |
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20 */ |
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21 |
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22 #ifdef HAVE_CONFIG_H |
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23 #include <config.h> |
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24 #endif |
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25 |
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26 #include <vector> |
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27 |
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28 #include "MArray2.h" |
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29 #include "MSparse.h" |
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30 #include "SparseQR.h" |
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31 #include "SparseCmplxQR.h" |
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32 #include "MatrixType.h" |
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33 #include "oct-sort.h" |
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34 |
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35 template <class T> |
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36 static MSparse<T> |
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37 dmsolve_extract (const MSparse<T> &A, const octave_idx_type *Pinv, |
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38 const octave_idx_type *Q, octave_idx_type rst, |
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39 octave_idx_type rend, octave_idx_type cst, |
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40 octave_idx_type cend, octave_idx_type maxnz = -1, |
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41 bool lazy = false) |
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42 { |
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43 octave_idx_type nz = (rend - rst) * (cend - cst); |
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44 maxnz = (maxnz < 0 ? A.nnz () : maxnz); |
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45 MSparse<T> B (rend - rst, cend - cst, (nz < maxnz ? nz : maxnz)); |
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46 // Some sparse functions can support lazy indexing (where elements |
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47 // in the row are in no particular order), even though octave in |
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48 // general can't. For those functions that can using it is a big |
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49 // win here in terms of speed. |
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50 if (lazy) |
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51 { |
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52 nz = 0; |
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53 for (octave_idx_type j = cst ; j < cend ; j++) |
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54 { |
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55 octave_idx_type qq = (Q ? Q [j] : j); |
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56 B.xcidx (j - cst) = nz; |
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57 for (octave_idx_type p = A.cidx(qq) ; p < A.cidx (qq+1) ; p++) |
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58 { |
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59 OCTAVE_QUIT; |
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60 octave_idx_type r = (Pinv ? Pinv [A.ridx (p)] : A.ridx (p)); |
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61 if (r >= rst && r < rend) |
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62 { |
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63 B.xdata (nz) = A.data (p); |
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64 B.xridx (nz++) = r - rst ; |
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65 } |
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66 } |
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67 } |
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68 B.xcidx (cend - cst) = nz ; |
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69 } |
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70 else |
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71 { |
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72 OCTAVE_LOCAL_BUFFER (T, X, rend - rst); |
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73 octave_sort<octave_idx_type> sort; |
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74 octave_idx_type *ri = B.xridx(); |
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75 nz = 0; |
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76 for (octave_idx_type j = cst ; j < cend ; j++) |
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77 { |
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78 octave_idx_type qq = (Q ? Q [j] : j); |
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79 B.xcidx (j - cst) = nz; |
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80 for (octave_idx_type p = A.cidx(qq) ; p < A.cidx (qq+1) ; p++) |
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81 { |
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82 OCTAVE_QUIT; |
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83 octave_idx_type r = (Pinv ? Pinv [A.ridx (p)] : A.ridx (p)); |
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84 if (r >= rst && r < rend) |
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85 { |
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86 X [r-rst] = A.data (p); |
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87 B.xridx (nz++) = r - rst ; |
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88 } |
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89 } |
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90 sort.sort (ri + B.xcidx (j - cst), nz - B.xcidx (j - cst)); |
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91 for (octave_idx_type p = B.cidx (j - cst); p < nz; p++) |
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92 B.xdata (p) = X [B.xridx (p)]; |
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93 } |
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94 B.xcidx (cend - cst) = nz ; |
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95 } |
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96 |
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97 return B; |
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98 } |
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99 |
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100 #if !defined (CXX_NEW_FRIEND_TEMPLATE_DECL) |
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101 static MSparse<double> |
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102 dmsolve_extract (const MSparse<double> &A, const octave_idx_type *Pinv, |
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103 const octave_idx_type *Q, octave_idx_type rst, |
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104 octave_idx_type rend, octave_idx_type cst, |
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105 octave_idx_type cend, octave_idx_type maxnz, |
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106 bool lazy); |
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107 |
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108 static MSparse<Complex> |
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109 dmsolve_extract (const MSparse<Complex> &A, const octave_idx_type *Pinv, |
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110 const octave_idx_type *Q, octave_idx_type rst, |
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111 octave_idx_type rend, octave_idx_type cst, |
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112 octave_idx_type cend, octave_idx_type maxnz, |
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113 bool lazy); |
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114 #endif |
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115 |
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116 template <class T> |
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117 static MArray2<T> |
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118 dmsolve_extract (const MArray2<T> &m, const octave_idx_type *, |
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119 const octave_idx_type *, octave_idx_type r1, |
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120 octave_idx_type r2, octave_idx_type c1, |
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121 octave_idx_type c2) |
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122 { |
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123 r2 -= 1; |
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124 c2 -= 1; |
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125 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } |
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126 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } |
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127 |
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128 octave_idx_type new_r = r2 - r1 + 1; |
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129 octave_idx_type new_c = c2 - c1 + 1; |
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130 |
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131 MArray2<T> result (new_r, new_c); |
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132 |
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133 for (octave_idx_type j = 0; j < new_c; j++) |
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134 for (octave_idx_type i = 0; i < new_r; i++) |
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135 result.xelem (i, j) = m.elem (r1+i, c1+j); |
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136 |
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137 return result; |
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138 } |
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139 |
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140 #if !defined (CXX_NEW_FRIEND_TEMPLATE_DECL) |
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141 static MArray2<double> |
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142 dmsolve_extract (const MArray2<double> &m, const octave_idx_type *, |
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143 const octave_idx_type *, octave_idx_type r1, |
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144 octave_idx_type r2, octave_idx_type c1, |
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145 octave_idx_type c2) |
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146 |
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147 static MArray2<Complex> |
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148 dmsolve_extract (const MArray2<Complex> &m, const octave_idx_type *, |
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149 const octave_idx_type *, octave_idx_type r1, |
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150 octave_idx_type r2, octave_idx_type c1, |
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151 octave_idx_type c2) |
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152 #endif |
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153 |
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154 template <class T> |
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155 static void |
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156 dmsolve_insert (MArray2<T> &a, const MArray2<T> &b, const octave_idx_type *Q, |
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157 octave_idx_type r, octave_idx_type c) |
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158 { |
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159 T *ax = a.fortran_vec(); |
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160 const T *bx = b.fortran_vec(); |
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161 octave_idx_type anr = a.rows(); |
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162 octave_idx_type nr = b.rows(); |
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163 octave_idx_type nc = b.cols(); |
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164 for (octave_idx_type j = 0; j < nc; j++) |
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165 { |
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166 octave_idx_type aoff = (c + j) * anr; |
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167 octave_idx_type boff = j * nr; |
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168 for (octave_idx_type i = 0; i < nr; i++) |
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169 { |
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170 OCTAVE_QUIT; |
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171 ax [Q [r + i] + aoff] = bx [i + boff]; |
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172 } |
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173 } |
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174 } |
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175 |
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176 #if !defined (CXX_NEW_FRIEND_TEMPLATE_DECL) |
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177 static void |
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178 dmsolve_insert (MArray2<double> &a, const MArray2<double> &b, |
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179 const octave_idx_type *Q, octave_idx_type r, octave_idx_type c); |
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180 |
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181 static void |
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182 dmsolve_insert (MArray2<Complex> &a, const MArray2<Complex> &b, |
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183 const octave_idx_type *Q, octave_idx_type r, octave_idx_type c); |
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184 #endif |
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185 |
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186 template <class T> |
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187 static void |
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188 dmsolve_insert (MSparse<T> &a, const MSparse<T> &b, const octave_idx_type *Q, |
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189 octave_idx_type r, octave_idx_type c) |
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190 { |
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191 octave_idx_type b_rows = b.rows (); |
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192 octave_idx_type b_cols = b.cols (); |
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193 octave_idx_type nr = a.rows (); |
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194 octave_idx_type nc = a.cols (); |
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195 |
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196 OCTAVE_LOCAL_BUFFER (octave_idx_type, Qinv, nr); |
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197 for (octave_idx_type i = 0; i < nr; i++) |
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198 Qinv [Q [i]] = i; |
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199 |
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200 // First count the number of elements in the final array |
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201 octave_idx_type nel = a.xcidx(c) + b.nnz (); |
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202 |
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203 if (c + b_cols < nc) |
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204 nel += a.xcidx(nc) - a.xcidx(c + b_cols); |
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205 |
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206 for (octave_idx_type i = c; i < c + b_cols; i++) |
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207 for (octave_idx_type j = a.xcidx(i); j < a.xcidx(i+1); j++) |
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208 if (Qinv [a.xridx(j)] < r || Qinv [a.xridx(j)] >= r + b_rows) |
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209 nel++; |
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210 |
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211 OCTAVE_LOCAL_BUFFER (T, X, nr); |
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212 octave_sort<octave_idx_type> sort; |
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213 MSparse<T> tmp (a); |
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214 a = MSparse<T> (nr, nc, nel); |
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215 octave_idx_type *ri = a.xridx(); |
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216 |
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217 for (octave_idx_type i = 0; i < tmp.cidx(c); i++) |
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218 { |
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219 a.xdata(i) = tmp.xdata(i); |
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220 a.xridx(i) = tmp.xridx(i); |
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221 } |
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222 for (octave_idx_type i = 0; i < c + 1; i++) |
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223 a.xcidx(i) = tmp.xcidx(i); |
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224 |
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225 octave_idx_type ii = a.xcidx(c); |
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226 |
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227 for (octave_idx_type i = c; i < c + b_cols; i++) |
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228 { |
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229 OCTAVE_QUIT; |
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230 |
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231 for (octave_idx_type j = tmp.xcidx(i); j < tmp.xcidx(i+1); j++) |
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232 if (Qinv [tmp.xridx(j)] < r || Qinv [tmp.xridx(j)] >= r + b_rows) |
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233 { |
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234 X [tmp.xridx(j)] = tmp.xdata(j); |
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235 a.xridx(ii++) = tmp.xridx(j); |
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236 } |
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237 |
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238 OCTAVE_QUIT; |
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239 |
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240 for (octave_idx_type j = b.cidx(i-c); j < b.cidx(i-c+1); j++) |
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241 { |
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242 X [Q [r + b.ridx(j)]] = b.data(j); |
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243 a.xridx(ii++) = Q [r + b.ridx(j)]; |
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244 } |
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245 |
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246 sort.sort (ri + a.xcidx (i), ii - a.xcidx (i)); |
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247 for (octave_idx_type p = a.xcidx (i); p < ii; p++) |
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248 a.xdata (p) = X [a.xridx (p)]; |
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249 a.xcidx(i+1) = ii; |
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250 } |
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251 |
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252 for (octave_idx_type i = c + b_cols; i < nc; i++) |
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253 { |
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254 for (octave_idx_type j = tmp.xcidx(i); j < tmp.cidx(i+1); j++) |
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255 { |
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256 a.xdata(ii) = tmp.xdata(j); |
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257 a.xridx(ii++) = tmp.xridx(j); |
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258 } |
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259 a.xcidx(i+1) = ii; |
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260 } |
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261 } |
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262 |
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263 #if !defined (CXX_NEW_FRIEND_TEMPLATE_DECL) |
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264 static void |
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265 dmsolve_insert (MSparse<double> &a, const SparseMatrix &b, |
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266 const octave_idx_type *Q, octave_idx_type r, octave_idx_type c); |
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267 |
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268 static void |
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269 dmsolve_insert (MSparse<Complex> &a, const MSparse<Complex> &b, |
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270 const octave_idx_type *Q, octave_idx_type r, octave_idx_type c); |
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271 #endif |
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272 |
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273 template <class T, class RT> |
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274 static void |
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275 dmsolve_permute (MArray2<RT> &a, const MArray2<T>& b, const octave_idx_type *p) |
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276 { |
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277 octave_idx_type b_nr = b.rows (); |
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278 octave_idx_type b_nc = b.cols (); |
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279 const T *Bx = b.fortran_vec(); |
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280 a.resize(b_nr, b_nc); |
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281 RT *Btx = a.fortran_vec(); |
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282 for (octave_idx_type j = 0; j < b_nc; j++) |
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283 { |
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284 octave_idx_type off = j * b_nr; |
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285 for (octave_idx_type i = 0; i < b_nr; i++) |
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286 { |
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287 OCTAVE_QUIT; |
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288 Btx [p [i] + off] = Bx [ i + off]; |
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289 } |
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290 } |
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291 } |
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292 |
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293 #if !defined (CXX_NEW_FRIEND_TEMPLATE_DECL) |
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294 static void |
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295 dmsolve_permute (MArray2<double> &a, const MArray2<double>& b, |
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296 const octave_idx_type *p); |
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297 |
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298 static void |
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299 dmsolve_permute (MArray2<Complex> &a, const MArray2<double>& b, |
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300 const octave_idx_type *p); |
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301 |
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302 static void |
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303 dmsolve_permute (MArray2<Complex> &a, const MArray2<Complex>& b, |
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304 const octave_idx_type *p); |
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305 #endif |
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306 |
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307 template <class T, class RT> |
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308 static void |
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309 dmsolve_permute (MSparse<RT> &a, const MSparse<T>& b, const octave_idx_type *p) |
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310 { |
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311 octave_idx_type b_nr = b.rows (); |
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312 octave_idx_type b_nc = b.cols (); |
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313 octave_idx_type b_nz = b.nnz (); |
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314 octave_idx_type nz = 0; |
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315 a = MSparse<RT> (b_nr, b_nc, b_nz); |
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316 octave_sort<octave_idx_type> sort; |
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317 octave_idx_type *ri = a.xridx(); |
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318 OCTAVE_LOCAL_BUFFER (RT, X, b_nr); |
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319 a.xcidx(0) = 0; |
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320 for (octave_idx_type j = 0; j < b_nc; j++) |
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321 { |
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322 for (octave_idx_type i = b.cidx(j); i < b.cidx(j+1); i++) |
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323 { |
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324 OCTAVE_QUIT; |
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325 octave_idx_type r = p [b.ridx (i)]; |
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326 X [r] = b.data (i); |
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327 a.xridx(nz++) = p [b.ridx (i)]; |
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328 } |
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329 sort.sort (ri + a.xcidx (j), nz - a.xcidx (j)); |
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330 for (octave_idx_type i = a.cidx (j); i < nz; i++) |
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331 { |
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332 OCTAVE_QUIT; |
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333 a.xdata (i) = X [a.xridx (i)]; |
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334 } |
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335 a.xcidx(j+1) = nz; |
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336 } |
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337 } |
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338 |
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339 #if !defined (CXX_NEW_FRIEND_TEMPLATE_DECL) |
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340 static void |
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341 dmsolve_permute (MSparse<double> &a, const MSparse<double>& b, |
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342 const octave_idx_type *p); |
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343 |
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344 static void |
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345 dmsolve_permute (MSparse<Complex> &a, const MSparse<double>& b, |
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346 const octave_idx_type *p); |
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347 |
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348 static void |
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349 dmsolve_permute (MSparse<Complex> &a, const MSparse<Complex>& b, |
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350 const octave_idx_type *p); |
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351 #endif |
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352 |
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353 static void |
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354 solve_singularity_warning (double) |
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355 { |
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356 // Dummy singularity handler so that LU solver doesn't flag |
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357 // an error for numerically rank defficient matrices |
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358 } |
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359 |
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360 template <class RT, class ST, class T> |
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361 RT |
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362 dmsolve (const ST &a, const T &b, octave_idx_type &info) |
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363 { |
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5684
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364 #ifdef HAVE_CXSPARSE |
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365 octave_idx_type nr = a.rows (); |
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366 octave_idx_type nc = a.cols (); |
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367 octave_idx_type b_nr = b.rows (); |
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368 octave_idx_type b_nc = b.cols (); |
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369 RT retval; |
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370 |
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371 if (nr < 1 || nc < 1 || nr != b_nr) |
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372 (*current_liboctave_error_handler) |
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373 ("matrix dimension mismatch in solution of minimum norm problem"); |
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374 else |
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375 { |
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376 octave_idx_type nnz_remaining = a.nnz (); |
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377 CXSPARSE_DNAME () csm; |
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378 csm.m = nr; |
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379 csm.n = nc; |
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380 csm.x = NULL; |
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381 csm.nz = -1; |
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382 csm.nzmax = a.nnz (); |
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383 // Cast away const on A, with full knowledge that CSparse won't touch it. |
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384 // Prevents the methods below making a copy of the data. |
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385 csm.p = const_cast<octave_idx_type *>(a.cidx ()); |
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386 csm.i = const_cast<octave_idx_type *>(a.ridx ()); |
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387 |
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5792
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388 #if defined(CS_VER) && (CS_VER >= 2) |
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389 CXSPARSE_DNAME (d) *dm = CXSPARSE_DNAME(_dmperm) (&csm, 0); |
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390 octave_idx_type *p = dm->p; |
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391 octave_idx_type *q = dm->q; |
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392 #else |
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5683
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393 CXSPARSE_DNAME (d) *dm = CXSPARSE_DNAME(_dmperm) (&csm); |
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394 octave_idx_type *p = dm->P; |
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395 octave_idx_type *q = dm->Q; |
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5792
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396 #endif |
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5683
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397 OCTAVE_LOCAL_BUFFER (octave_idx_type, pinv, nr); |
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398 for (octave_idx_type i = 0; i < nr; i++) |
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399 pinv [p [i]] = i; |
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400 RT btmp; |
|
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401 dmsolve_permute (btmp, b, pinv); |
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402 info = 0; |
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403 retval.resize (nc, b_nc); |
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404 |
|
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405 // Leading over-determined block |
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406 if (dm->rr [2] < nr && dm->cc [3] < nc) |
|
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407 { |
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408 ST m = dmsolve_extract (a, pinv, q, dm->rr [2], nr, dm->cc [3], nc, |
|
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409 nnz_remaining, true); |
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410 nnz_remaining -= m.nnz(); |
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411 RT mtmp = |
|
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412 qrsolve (m, dmsolve_extract (btmp, NULL, NULL, dm->rr[2], b_nr, 0, |
|
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413 b_nc), info); |
|
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414 dmsolve_insert (retval, mtmp, q, dm->cc [3], 0); |
|
5797
|
415 if (dm->rr [2] > 0 && !info) |
|
5683
|
416 { |
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417 m = dmsolve_extract (a, pinv, q, 0, dm->rr [2], |
|
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418 dm->cc [3], nc, nnz_remaining, true); |
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419 nnz_remaining -= m.nnz(); |
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420 RT ctmp = dmsolve_extract (btmp, NULL, NULL, 0, |
|
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421 dm->rr[2], 0, b_nc); |
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422 btmp.insert (ctmp - m * mtmp, 0, 0); |
|
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423 } |
|
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424 } |
|
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425 |
|
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426 // Structurally non-singular blocks |
|
5775
|
427 // FIXME Should use fine Dulmange-Mendelsohn decomposition here. |
|
5797
|
428 if (dm->rr [1] < dm->rr [2] && dm->cc [2] < dm->cc [3] && !info) |
|
5683
|
429 { |
|
|
430 ST m = dmsolve_extract (a, pinv, q, dm->rr [1], dm->rr [2], |
|
|
431 dm->cc [2], dm->cc [3], nnz_remaining, false); |
|
|
432 nnz_remaining -= m.nnz(); |
|
|
433 RT btmp2 = dmsolve_extract (btmp, NULL, NULL, dm->rr [1], dm->rr [2], |
|
|
434 0, b_nc); |
|
|
435 double rcond = 0.0; |
|
5785
|
436 MatrixType mtyp (MatrixType::Full); |
|
5683
|
437 RT mtmp = m.solve (mtyp, btmp2, info, rcond, |
|
5697
|
438 solve_singularity_warning, false); |
|
5683
|
439 if (info != 0) |
|
|
440 { |
|
|
441 info = 0; |
|
|
442 mtmp = qrsolve (m, btmp2, info); |
|
|
443 } |
|
|
444 |
|
|
445 dmsolve_insert (retval, mtmp, q, dm->cc [2], 0); |
|
5797
|
446 if (dm->rr [1] > 0 && !info) |
|
5683
|
447 { |
|
|
448 m = dmsolve_extract (a, pinv, q, 0, dm->rr [1], dm->cc [2], |
|
|
449 dm->cc [3], nnz_remaining, true); |
|
|
450 nnz_remaining -= m.nnz(); |
|
|
451 RT ctmp = dmsolve_extract (btmp, NULL, NULL, 0, |
|
|
452 dm->rr[1], 0, b_nc); |
|
|
453 btmp.insert (ctmp - m * mtmp, 0, 0); |
|
|
454 } |
|
|
455 } |
|
|
456 |
|
|
457 // Trailing under-determined block |
|
5797
|
458 if (dm->rr [1] > 0 && dm->cc [2] > 0 && !info) |
|
5683
|
459 { |
|
|
460 ST m = dmsolve_extract (a, pinv, q, 0, dm->rr [1], 0, |
|
|
461 dm->cc [2], nnz_remaining, true); |
|
|
462 RT mtmp = |
|
|
463 qrsolve (m, dmsolve_extract(btmp, NULL, NULL, 0, dm->rr [1] , 0, |
|
|
464 b_nc), info); |
|
|
465 dmsolve_insert (retval, mtmp, q, 0, 0); |
|
|
466 } |
|
|
467 |
|
|
468 CXSPARSE_DNAME (_dfree) (dm); |
|
|
469 } |
|
|
470 return retval; |
|
5684
|
471 #else |
|
|
472 return RT (); |
|
|
473 #endif |
|
5683
|
474 } |
|
|
475 |
|
|
476 #if !defined (CXX_NEW_FRIEND_TEMPLATE_DECL) |
|
|
477 extern Matrix |
|
|
478 dmsolve (const SparseMatrix &a, const Matrix &b, |
|
|
479 octave_idx_type &info); |
|
|
480 |
|
|
481 extern ComplexMatrix |
|
|
482 dmsolve (const SparseMatrix &a, const ComplexMatrix &b, |
|
|
483 octave_idx_type &info); |
|
|
484 |
|
|
485 extern ComplexMatrix |
|
|
486 dmsolve (const SparseComplexMatrix &a, const Matrix &b, |
|
|
487 octave_idx_type &info); |
|
|
488 |
|
|
489 extern ComplexMatrix |
|
|
490 dmsolve (const SparseComplexMatrix &a, const ComplexMatrix &b, |
|
|
491 octave_idx_type &info); |
|
|
492 |
|
|
493 extern SparseMatrix |
|
|
494 dmsolve (const SparseMatrix &a, const SparseMatrix &b, |
|
|
495 octave_idx_type &info); |
|
|
496 |
|
|
497 extern SparseComplexMatrix |
|
|
498 dmsolve (const SparseMatrix &a, const SparseComplexMatrix &b, |
|
|
499 octave_idx_type &info); |
|
|
500 |
|
|
501 extern SparseComplexMatrix |
|
|
502 dmsolve (const SparseComplexMatrix &a, const SparseMatrix &b, |
|
|
503 octave_idx_type &info); |
|
|
504 |
|
|
505 extern SparseComplexMatrix |
|
|
506 dmsolve (const SparseComplexMatrix &a, const SparseComplexMatrix &b, |
|
|
507 octave_idx_type &info); |
|
|
508 #endif |
|
|
509 |
|
|
510 /* |
|
|
511 ;;; Local Variables: *** |
|
|
512 ;;; mode: C++ *** |
|
|
513 ;;; End: *** |
|
|
514 */ |
