annotate liboctave/sparse-dmsolve.cc @ 16088:b29b10fbb744 stable release-3-6-4

Version 3.6.4 released. * configure.ac (AC_INIT): Version is now 3.6.4. (OCTAVE_RELEASE_DATE): Now 2013-02-21.
author John W. Eaton <jwe@octave.org>
date Thu, 21 Feb 2013 15:17:54 -0500
parents 1316bfc6e260
children 4328e28414aa
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1 /*
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2
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3 Copyright (C) 2006-2012 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
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe]
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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 "MArray.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 #include "oct-locbuf.h"
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36 #include "oct-inttypes.h"
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37
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38 template <class T>
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39 static MSparse<T>
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40 dmsolve_extract (const MSparse<T> &A, const octave_idx_type *Pinv,
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41 const octave_idx_type *Q, octave_idx_type rst,
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42 octave_idx_type rend, octave_idx_type cst,
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43 octave_idx_type cend, octave_idx_type maxnz = -1,
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44 bool lazy = false)
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45 {
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46 octave_idx_type nr = rend - rst, nc = cend - cst;
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47 maxnz = (maxnz < 0 ? A.nnz () : maxnz);
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48 octave_idx_type nz;
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49
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50 // Cast to uint64 to handle overflow in this multiplication
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51 if (octave_uint64 (nr)*octave_uint64 (nc) < octave_uint64 (maxnz))
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52 nz = nr*nc;
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53 else
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54 nz = maxnz;
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55
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56 MSparse<T> B (nr, nc, (nz < maxnz ? nz : maxnz));
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57 // Some sparse functions can support lazy indexing (where elements
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58 // in the row are in no particular order), even though octave in
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59 // general can't. For those functions that can using it is a big
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60 // win here in terms of speed.
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61 if (lazy)
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62 {
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63 nz = 0;
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64 for (octave_idx_type j = cst ; j < cend ; j++)
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65 {
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66 octave_idx_type qq = (Q ? Q [j] : j);
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67 B.xcidx (j - cst) = nz;
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68 for (octave_idx_type p = A.cidx(qq) ; p < A.cidx (qq+1) ; p++)
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69 {
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70 octave_quit ();
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71 octave_idx_type r = (Pinv ? Pinv [A.ridx (p)] : A.ridx (p));
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72 if (r >= rst && r < rend)
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73 {
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74 B.xdata (nz) = A.data (p);
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75 B.xridx (nz++) = r - rst ;
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76 }
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77 }
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78 }
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79 B.xcidx (cend - cst) = nz ;
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80 }
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81 else
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82 {
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83 OCTAVE_LOCAL_BUFFER (T, X, rend - rst);
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84 octave_sort<octave_idx_type> sort;
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85 octave_idx_type *ri = B.xridx();
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86 nz = 0;
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87 for (octave_idx_type j = cst ; j < cend ; j++)
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88 {
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89 octave_idx_type qq = (Q ? Q [j] : j);
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90 B.xcidx (j - cst) = nz;
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91 for (octave_idx_type p = A.cidx(qq) ; p < A.cidx (qq+1) ; p++)
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92 {
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93 octave_quit ();
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94 octave_idx_type r = (Pinv ? Pinv [A.ridx (p)] : A.ridx (p));
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95 if (r >= rst && r < rend)
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96 {
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97 X [r-rst] = A.data (p);
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98 B.xridx (nz++) = r - rst ;
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99 }
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100 }
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101 sort.sort (ri + B.xcidx (j - cst), nz - B.xcidx (j - cst));
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102 for (octave_idx_type p = B.cidx (j - cst); p < nz; p++)
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103 B.xdata (p) = X [B.xridx (p)];
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104 }
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105 B.xcidx (cend - cst) = nz ;
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106 }
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107
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108 return B;
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109 }
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110
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111 #if !defined (CXX_NEW_FRIEND_TEMPLATE_DECL)
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112 static MSparse<double>
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113 dmsolve_extract (const MSparse<double> &A, const octave_idx_type *Pinv,
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114 const octave_idx_type *Q, octave_idx_type rst,
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115 octave_idx_type rend, octave_idx_type cst,
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116 octave_idx_type cend, octave_idx_type maxnz,
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117 bool lazy);
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118
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119 static MSparse<Complex>
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120 dmsolve_extract (const MSparse<Complex> &A, const octave_idx_type *Pinv,
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121 const octave_idx_type *Q, octave_idx_type rst,
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122 octave_idx_type rend, octave_idx_type cst,
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123 octave_idx_type cend, octave_idx_type maxnz,
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124 bool lazy);
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125 #endif
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126
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127 template <class T>
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128 static MArray<T>
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129 dmsolve_extract (const MArray<T> &m, const octave_idx_type *,
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130 const octave_idx_type *, octave_idx_type r1,
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131 octave_idx_type r2, octave_idx_type c1,
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132 octave_idx_type c2)
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133 {
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134 r2 -= 1;
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135 c2 -= 1;
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136 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; }
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137 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; }
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138
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139 octave_idx_type new_r = r2 - r1 + 1;
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140 octave_idx_type new_c = c2 - c1 + 1;
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141
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142 MArray<T> result (dim_vector (new_r, new_c));
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143
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144 for (octave_idx_type j = 0; j < new_c; j++)
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145 for (octave_idx_type i = 0; i < new_r; i++)
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146 result.xelem (i, j) = m.elem (r1+i, c1+j);
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147
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148 return result;
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149 }
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150
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151 #if !defined (CXX_NEW_FRIEND_TEMPLATE_DECL)
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152 static MArray<double>
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153 dmsolve_extract (const MArray<double> &m, const octave_idx_type *,
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154 const octave_idx_type *, octave_idx_type r1,
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155 octave_idx_type r2, octave_idx_type c1,
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156 octave_idx_type c2)
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157
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158 static MArray<Complex>
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159 dmsolve_extract (const MArray<Complex> &m, const octave_idx_type *,
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160 const octave_idx_type *, octave_idx_type r1,
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161 octave_idx_type r2, octave_idx_type c1,
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162 octave_idx_type c2)
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163 #endif
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164
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165 template <class T>
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166 static void
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167 dmsolve_insert (MArray<T> &a, const MArray<T> &b, const octave_idx_type *Q,
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168 octave_idx_type r, octave_idx_type c)
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169 {
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170 T *ax = a.fortran_vec();
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171 const T *bx = b.fortran_vec();
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172 octave_idx_type anr = a.rows();
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173 octave_idx_type nr = b.rows();
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174 octave_idx_type nc = b.cols();
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175 for (octave_idx_type j = 0; j < nc; j++)
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176 {
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177 octave_idx_type aoff = (c + j) * anr;
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178 octave_idx_type boff = j * nr;
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179 for (octave_idx_type i = 0; i < nr; i++)
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180 {
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181 octave_quit ();
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182 ax [Q [r + i] + aoff] = bx [i + boff];
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183 }
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184 }
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185 }
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186
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187 #if !defined (CXX_NEW_FRIEND_TEMPLATE_DECL)
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188 static void
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189 dmsolve_insert (MArray<double> &a, const MArray<double> &b,
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190 const octave_idx_type *Q, octave_idx_type r, octave_idx_type c);
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191
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192 static void
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193 dmsolve_insert (MArray<Complex> &a, const MArray<Complex> &b,
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194 const octave_idx_type *Q, octave_idx_type r, octave_idx_type c);
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195 #endif
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196
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197 template <class T>
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198 static void
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199 dmsolve_insert (MSparse<T> &a, const MSparse<T> &b, const octave_idx_type *Q,
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200 octave_idx_type r, octave_idx_type c)
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201 {
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202 octave_idx_type b_rows = b.rows ();
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203 octave_idx_type b_cols = b.cols ();
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204 octave_idx_type nr = a.rows ();
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205 octave_idx_type nc = a.cols ();
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206
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207 OCTAVE_LOCAL_BUFFER (octave_idx_type, Qinv, nr);
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208 for (octave_idx_type i = 0; i < nr; i++)
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209 Qinv [Q [i]] = i;
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210
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211 // First count the number of elements in the final array
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212 octave_idx_type nel = a.xcidx(c) + b.nnz ();
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213
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214 if (c + b_cols < nc)
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215 nel += a.xcidx(nc) - a.xcidx(c + b_cols);
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216
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217 for (octave_idx_type i = c; i < c + b_cols; i++)
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218 for (octave_idx_type j = a.xcidx(i); j < a.xcidx(i+1); j++)
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219 if (Qinv [a.xridx(j)] < r || Qinv [a.xridx(j)] >= r + b_rows)
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220 nel++;
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221
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222 OCTAVE_LOCAL_BUFFER (T, X, nr);
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223 octave_sort<octave_idx_type> sort;
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224 MSparse<T> tmp (a);
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225 a = MSparse<T> (nr, nc, nel);
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226 octave_idx_type *ri = a.xridx();
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227
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228 for (octave_idx_type i = 0; i < tmp.cidx(c); i++)
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229 {
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230 a.xdata(i) = tmp.xdata(i);
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231 a.xridx(i) = tmp.xridx(i);
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232 }
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233 for (octave_idx_type i = 0; i < c + 1; i++)
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234 a.xcidx(i) = tmp.xcidx(i);
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235
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236 octave_idx_type ii = a.xcidx(c);
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237
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238 for (octave_idx_type i = c; i < c + b_cols; i++)
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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 = tmp.xcidx(i); j < tmp.xcidx(i+1); j++)
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243 if (Qinv [tmp.xridx(j)] < r || Qinv [tmp.xridx(j)] >= r + b_rows)
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244 {
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245 X [tmp.xridx(j)] = tmp.xdata(j);
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246 a.xridx(ii++) = tmp.xridx(j);
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247 }
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248
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249 octave_quit ();
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250
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251 for (octave_idx_type j = b.cidx(i-c); j < b.cidx(i-c+1); j++)
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252 {
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253 X [Q [r + b.ridx(j)]] = b.data(j);
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254 a.xridx(ii++) = Q [r + b.ridx(j)];
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255 }
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256
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257 sort.sort (ri + a.xcidx (i), ii - a.xcidx (i));
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258 for (octave_idx_type p = a.xcidx (i); p < ii; p++)
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259 a.xdata (p) = X [a.xridx (p)];
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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 for (octave_idx_type i = c + b_cols; i < nc; i++)
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264 {
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265 for (octave_idx_type j = tmp.xcidx(i); j < tmp.cidx(i+1); j++)
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266 {
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267 a.xdata(ii) = tmp.xdata(j);
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268 a.xridx(ii++) = tmp.xridx(j);
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269 }
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270 a.xcidx(i+1) = ii;
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271 }
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272 }
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273
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274 #if !defined (CXX_NEW_FRIEND_TEMPLATE_DECL)
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275 static void
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276 dmsolve_insert (MSparse<double> &a, const SparseMatrix &b,
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277 const octave_idx_type *Q, octave_idx_type r, octave_idx_type c);
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278
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279 static void
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280 dmsolve_insert (MSparse<Complex> &a, const MSparse<Complex> &b,
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281 const octave_idx_type *Q, octave_idx_type r, octave_idx_type c);
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282 #endif
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283
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284 template <class T, class RT>
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285 static void
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286 dmsolve_permute (MArray<RT> &a, const MArray<T>& b, const octave_idx_type *p)
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287 {
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288 octave_idx_type b_nr = b.rows ();
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289 octave_idx_type b_nc = b.cols ();
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290 const T *Bx = b.fortran_vec();
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291 a.resize (dim_vector (b_nr, b_nc));
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292 RT *Btx = a.fortran_vec();
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293 for (octave_idx_type j = 0; j < b_nc; j++)
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294 {
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295 octave_idx_type off = j * b_nr;
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296 for (octave_idx_type i = 0; i < b_nr; i++)
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297 {
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298 octave_quit ();
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299 Btx [p [i] + off] = Bx [ i + off];
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300 }
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301 }
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302 }
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303
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304 #if !defined (CXX_NEW_FRIEND_TEMPLATE_DECL)
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305 static void
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306 dmsolve_permute (MArray<double> &a, const MArray<double>& b,
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307 const octave_idx_type *p);
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308
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309 static void
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310 dmsolve_permute (MArray<Complex> &a, const MArray<double>& b,
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311 const octave_idx_type *p);
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312
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313 static void
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314 dmsolve_permute (MArray<Complex> &a, const MArray<Complex>& b,
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315 const octave_idx_type *p);
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316 #endif
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317
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318 template <class T, class RT>
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319 static void
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320 dmsolve_permute (MSparse<RT> &a, const MSparse<T>& b, const octave_idx_type *p)
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321 {
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322 octave_idx_type b_nr = b.rows ();
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323 octave_idx_type b_nc = b.cols ();
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324 octave_idx_type b_nz = b.nnz ();
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325 octave_idx_type nz = 0;
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326 a = MSparse<RT> (b_nr, b_nc, b_nz);
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327 octave_sort<octave_idx_type> sort;
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328 octave_idx_type *ri = a.xridx();
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329 OCTAVE_LOCAL_BUFFER (RT, X, b_nr);
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330 a.xcidx(0) = 0;
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331 for (octave_idx_type j = 0; j < b_nc; j++)
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332 {
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333 for (octave_idx_type i = b.cidx(j); i < b.cidx(j+1); i++)
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334 {
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335 octave_quit ();
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336 octave_idx_type r = p [b.ridx (i)];
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337 X [r] = b.data (i);
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338 a.xridx(nz++) = p [b.ridx (i)];
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339 }
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340 sort.sort (ri + a.xcidx (j), nz - a.xcidx (j));
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341 for (octave_idx_type i = a.cidx (j); i < nz; i++)
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342 {
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343 octave_quit ();
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344 a.xdata (i) = X [a.xridx (i)];
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345 }
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346 a.xcidx(j+1) = nz;
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347 }
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348 }
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349
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350 #if !defined (CXX_NEW_FRIEND_TEMPLATE_DECL)
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351 static void
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352 dmsolve_permute (MSparse<double> &a, const MSparse<double>& b,
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353 const octave_idx_type *p);
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354
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355 static void
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356 dmsolve_permute (MSparse<Complex> &a, const MSparse<double>& b,
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357 const octave_idx_type *p);
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358
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359 static void
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360 dmsolve_permute (MSparse<Complex> &a, const MSparse<Complex>& b,
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361 const octave_idx_type *p);
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362 #endif
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363
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364 static void
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365 solve_singularity_warning (double)
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366 {
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367 // Dummy singularity handler so that LU solver doesn't flag
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368 // an error for numerically rank defficient matrices
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369 }
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370
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371 template <class RT, class ST, class T>
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372 RT
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373 dmsolve (const ST &a, const T &b, octave_idx_type &info)
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374 {
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375 #ifdef HAVE_CXSPARSE
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376 octave_idx_type nr = a.rows ();
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377 octave_idx_type nc = a.cols ();
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378 octave_idx_type b_nr = b.rows ();
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379 octave_idx_type b_nc = b.cols ();
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diff changeset
380 RT retval;
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381
6924
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382 if (nr < 0 || nc < 0 || nr != b_nr)
5683
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383 (*current_liboctave_error_handler)
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384 ("matrix dimension mismatch in solution of minimum norm problem");
6924
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385 else if (nr == 0 || nc == 0 || b_nc == 0)
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386 retval = RT (nc, b_nc, 0.0);
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387 else
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388 {
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389 octave_idx_type nnz_remaining = a.nnz ();
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390 CXSPARSE_DNAME () csm;
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391 csm.m = nr;
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392 csm.n = nc;
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diff changeset
393 csm.x = 0;
5683
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394 csm.nz = -1;
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395 csm.nzmax = a.nnz ();
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396 // Cast away const on A, with full knowledge that CSparse won't touch it.
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397 // Prevents the methods below making a copy of the data.
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398 csm.p = const_cast<octave_idx_type *>(a.cidx ());
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399 csm.i = const_cast<octave_idx_type *>(a.ridx ());
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400
5792
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diff changeset
401 #if defined(CS_VER) && (CS_VER >= 2)
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402 CXSPARSE_DNAME (d) *dm = CXSPARSE_DNAME(_dmperm) (&csm, 0);
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diff changeset
403 octave_idx_type *p = dm->p;
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diff changeset
404 octave_idx_type *q = dm->q;
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diff changeset
405 #else
5683
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406 CXSPARSE_DNAME (d) *dm = CXSPARSE_DNAME(_dmperm) (&csm);
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diff changeset
407 octave_idx_type *p = dm->P;
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diff changeset
408 octave_idx_type *q = dm->Q;
5792
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diff changeset
409 #endif
5683
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diff changeset
410 OCTAVE_LOCAL_BUFFER (octave_idx_type, pinv, nr);
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diff changeset
411 for (octave_idx_type i = 0; i < nr; i++)
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diff changeset
412 pinv [p [i]] = i;
5683
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diff changeset
413 RT btmp;
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diff changeset
414 dmsolve_permute (btmp, b, pinv);
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diff changeset
415 info = 0;
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diff changeset
416 retval.resize (nc, b_nc);
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417
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418 // Leading over-determined block
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419 if (dm->rr [2] < nr && dm->cc [3] < nc)
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420 {
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421 ST m = dmsolve_extract (a, pinv, q, dm->rr [2], nr, dm->cc [3], nc,
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422 nnz_remaining, true);
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423 nnz_remaining -= m.nnz();
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424 RT mtmp =
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425 qrsolve (m, dmsolve_extract (btmp, 0, 0, dm->rr[2], b_nr, 0,
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426 b_nc), info);
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427 dmsolve_insert (retval, mtmp, q, dm->cc [3], 0);
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428 if (dm->rr [2] > 0 && !info)
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429 {
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430 m = dmsolve_extract (a, pinv, q, 0, dm->rr [2],
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431 dm->cc [3], nc, nnz_remaining, true);
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432 nnz_remaining -= m.nnz();
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433 RT ctmp = dmsolve_extract (btmp, 0, 0, 0,
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434 dm->rr[2], 0, b_nc);
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435 btmp.insert (ctmp - m * mtmp, 0, 0);
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436 }
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437 }
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438
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439 // Structurally non-singular blocks
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440 // FIXME Should use fine Dulmange-Mendelsohn decomposition here.
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441 if (dm->rr [1] < dm->rr [2] && dm->cc [2] < dm->cc [3] && !info)
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442 {
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443 ST m = dmsolve_extract (a, pinv, q, dm->rr [1], dm->rr [2],
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444 dm->cc [2], dm->cc [3], nnz_remaining, false);
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445 nnz_remaining -= m.nnz();
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446 RT btmp2 = dmsolve_extract (btmp, 0, 0, dm->rr [1], dm->rr [2],
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447 0, b_nc);
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448 double rcond = 0.0;
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449 MatrixType mtyp (MatrixType::Full);
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450 RT mtmp = m.solve (mtyp, btmp2, info, rcond,
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451 solve_singularity_warning, false);
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452 if (info != 0)
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453 {
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454 info = 0;
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455 mtmp = qrsolve (m, btmp2, info);
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456 }
5683
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457
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458 dmsolve_insert (retval, mtmp, q, dm->cc [2], 0);
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459 if (dm->rr [1] > 0 && !info)
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diff changeset
460 {
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461 m = dmsolve_extract (a, pinv, q, 0, dm->rr [1], dm->cc [2],
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462 dm->cc [3], nnz_remaining, true);
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463 nnz_remaining -= m.nnz();
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464 RT ctmp = dmsolve_extract (btmp, 0, 0, 0,
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465 dm->rr[1], 0, b_nc);
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466 btmp.insert (ctmp - m * mtmp, 0, 0);
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467 }
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468 }
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469
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470 // Trailing under-determined block
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471 if (dm->rr [1] > 0 && dm->cc [2] > 0 && !info)
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diff changeset
472 {
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473 ST m = dmsolve_extract (a, pinv, q, 0, dm->rr [1], 0,
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474 dm->cc [2], nnz_remaining, true);
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475 RT mtmp =
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476 qrsolve (m, dmsolve_extract(btmp, 0, 0, 0, dm->rr [1] , 0,
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477 b_nc), info);
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478 dmsolve_insert (retval, mtmp, q, 0, 0);
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479 }
5683
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480
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481 CXSPARSE_DNAME (_dfree) (dm);
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482 }
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483 return retval;
5684
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diff changeset
484 #else
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485 return RT ();
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diff changeset
486 #endif
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487 }
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488
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diff changeset
489 #if !defined (CXX_NEW_FRIEND_TEMPLATE_DECL)
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490 extern Matrix
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491 dmsolve (const SparseMatrix &a, const Matrix &b,
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492 octave_idx_type &info);
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493
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494 extern ComplexMatrix
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495 dmsolve (const SparseMatrix &a, const ComplexMatrix &b,
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496 octave_idx_type &info);
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497
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498 extern ComplexMatrix
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499 dmsolve (const SparseComplexMatrix &a, const Matrix &b,
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diff changeset
500 octave_idx_type &info);
5683
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diff changeset
501
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502 extern ComplexMatrix
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503 dmsolve (const SparseComplexMatrix &a, const ComplexMatrix &b,
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504 octave_idx_type &info);
5683
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diff changeset
505
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506 extern SparseMatrix
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507 dmsolve (const SparseMatrix &a, const SparseMatrix &b,
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diff changeset
508 octave_idx_type &info);
5683
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diff changeset
509
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510 extern SparseComplexMatrix
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511 dmsolve (const SparseMatrix &a, const SparseComplexMatrix &b,
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512 octave_idx_type &info);
5683
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513
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diff changeset
514 extern SparseComplexMatrix
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515 dmsolve (const SparseComplexMatrix &a, const SparseMatrix &b,
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diff changeset
516 octave_idx_type &info);
5683
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517
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diff changeset
518 extern SparseComplexMatrix
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519 dmsolve (const SparseComplexMatrix &a, const SparseComplexMatrix &b,
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520 octave_idx_type &info);
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521 #endif