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