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5164
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1 /* |
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2 |
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3 Copyright (C) 2004 David Bateman |
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4 Copyright (C) 1998-2004 Andy Adler |
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5 |
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6 Octave is free software; you can redistribute it and/or modify it |
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7 under the terms of the GNU General Public License as published by the |
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8 Free Software Foundation; either version 2, or (at your option) any |
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9 later version. |
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10 |
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11 Octave is distributed in the hope that it will be useful, but WITHOUT |
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12 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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13 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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14 for more details. |
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15 |
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16 You should have received a copy of the GNU General Public License |
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17 along with this program; see the file COPYING. If not, write to the Free |
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18 Software Foundation, 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
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19 |
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20 */ |
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21 |
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22 // This is the octave interface to colamd, which bore the copyright given |
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23 // in the help of the functions. |
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24 |
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25 #ifdef HAVE_CONFIG_H |
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26 #include <config.h> |
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27 #endif |
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28 |
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29 #include <cstdlib> |
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30 |
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31 #include <string> |
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32 #include <vector> |
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33 |
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34 #include "ov.h" |
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35 #include "defun-dld.h" |
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36 #include "pager.h" |
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37 #include "ov-re-mat.h" |
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38 |
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39 #include "ov-re-sparse.h" |
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40 #include "ov-cx-sparse.h" |
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41 |
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42 // External COLAMD functions in C |
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43 extern "C" { |
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44 #include "COLAMD/colamd.h" |
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45 } |
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46 |
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47 // The symmetric column elimination tree code take from the Davis LDL code. |
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48 // Copyright given elsewhere in this file. |
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49 static |
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50 void symetree (const int *ridx, const int *cidx, int *Parent, int *P, int n) |
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51 { |
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52 OCTAVE_LOCAL_BUFFER (int, Flag, n); |
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53 OCTAVE_LOCAL_BUFFER (int, Pinv, (P ? n : 0)); |
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54 if (P) |
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55 // If P is present then compute Pinv, the inverse of P |
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56 for (int k = 0 ; k < n ; k++) |
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57 Pinv [P [k]] = k ; |
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58 |
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59 for (int k = 0 ; k < n ; k++) |
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60 { |
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61 // L(k,:) pattern: all nodes reachable in etree from nz in A(0:k-1,k) |
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62 Parent [k] = n ; // parent of k is not yet known |
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63 Flag [k] = k ; // mark node k as visited |
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64 int kk = (P) ? (P [k]) : (k) ; // kth original, or permuted, column |
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65 int p2 = cidx [kk+1] ; |
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66 for (int p = cidx [kk] ; p < p2 ; p++) |
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67 { |
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68 // A (i,k) is nonzero (original or permuted A) |
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69 int i = (Pinv) ? (Pinv [ridx [p]]) : (ridx [p]) ; |
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70 if (i < k) |
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71 { |
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72 // follow path from i to root of etree, stop at flagged node |
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73 for ( ; Flag [i] != k ; i = Parent [i]) |
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74 { |
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75 // find parent of i if not yet determined |
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76 if (Parent [i] == n) |
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77 Parent [i] = k ; |
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78 Flag [i] = k ; // mark i as visited |
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79 } |
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80 } |
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81 } |
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82 } |
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83 } |
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84 |
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85 // The elimination tree post-ordering code below is taken from SuperLU |
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86 static inline |
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87 int make_set (int i, int *pp) |
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88 { |
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89 pp[i] = i; |
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90 return i; |
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91 } |
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92 |
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93 static inline |
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94 int link (int s, int t, int *pp) |
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95 { |
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96 pp[s] = t; |
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97 return t; |
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98 } |
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99 |
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100 static inline |
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101 int find (int i, int *pp) |
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102 { |
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103 register int p, gp; |
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104 |
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105 p = pp[i]; |
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106 gp = pp[p]; |
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107 while (gp != p) { |
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108 pp[i] = gp; |
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109 i = gp; |
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110 p = pp[i]; |
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111 gp = pp[p]; |
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112 } |
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113 return (p); |
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114 } |
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115 |
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116 static |
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117 int etdfs (int v, int *first_kid, int *next_kid, int *post, int postnum) |
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118 { |
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119 for (int w = first_kid[v]; w != -1; w = next_kid[w]) { |
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120 postnum = etdfs (w, first_kid, next_kid, post, postnum); |
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121 } |
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122 post[postnum++] = v; |
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123 |
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124 return postnum; |
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125 } |
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126 |
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127 static |
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128 void TreePostorder(int n, int *parent, int *post) |
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129 { |
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130 // Allocate storage for working arrays and results |
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131 OCTAVE_LOCAL_BUFFER (int, first_kid, n+1); |
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132 OCTAVE_LOCAL_BUFFER (int, next_kid, n+1); |
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133 |
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134 // Set up structure describing children |
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135 for (int v = 0; v <= n; first_kid[v++] = -1); |
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136 for (int v = n-1; v >= 0; v--) |
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137 { |
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138 int dad = parent[v]; |
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139 next_kid[v] = first_kid[dad]; |
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140 first_kid[dad] = v; |
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141 } |
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142 |
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143 // Depth-first search from dummy root vertex #n |
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144 etdfs (n, first_kid, next_kid, post, 0); |
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145 } |
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146 |
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147 static |
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148 void coletree (const int *ridx, const int *colbeg, int *colend, |
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149 int *parent, int nr, int nc) |
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150 { |
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151 OCTAVE_LOCAL_BUFFER (int, root, nc); |
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152 OCTAVE_LOCAL_BUFFER (int, pp, nc); |
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153 OCTAVE_LOCAL_BUFFER (int, firstcol, nr); |
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154 |
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155 // Compute firstcol[row] = first nonzero column in row |
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156 for (int row = 0; row < nr; firstcol[row++] = nc); |
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157 for (int col = 0; col < nc; col++) |
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158 for (int p = colbeg[col]; p < colend[col]; p++) |
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159 { |
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160 int row = ridx[p]; |
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161 if (firstcol[row] > col) |
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162 firstcol[row] = col; |
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163 } |
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164 |
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165 // Compute etree by Liu's algorithm for symmetric matrices, |
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166 // except use (firstcol[r],c) in place of an edge (r,c) of A. |
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167 // Thus each row clique in A'*A is replaced by a star |
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168 // centered at its first vertex, which has the same fill. |
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169 for (int col = 0; col < nc; col++) |
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170 { |
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171 int cset = make_set (col, pp); |
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172 root[cset] = col; |
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173 parent[col] = nc; |
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174 for (int p = colbeg[col]; p < colend[col]; p++) |
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175 { |
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176 int row = firstcol[ridx[p]]; |
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177 if (row >= col) |
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178 continue; |
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179 int rset = find (row, pp); |
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180 int rroot = root[rset]; |
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181 if (rroot != col) |
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182 { |
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183 parent[rroot] = col; |
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184 cset = link (cset, rset, pp); |
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185 root[cset] = col; |
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186 } |
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187 } |
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188 } |
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189 } |
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190 |
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191 DEFUN_DLD (colamd, args, nargout, |
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192 "-*- texinfo -*-\n\ |
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193 @deftypefn {Loadable Function} {@var{p} =} colamd (@var{s})\n\ |
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194 @deftypefnx {Loadable Function} {@var{p} =} colamd (@var{s}, @var{knobs})\n\ |
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195 @deftypefnx {Loadable Function} {[@var{p}, @var{stats}] =} colamd (@var{s})\n\ |
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196 @deftypefnx {Loadable Function} {[@var{p}, @var{stats}] =} colamd (@var{s}, @var{knobs})\n\ |
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197 \n\ |
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198 Column approximate minimum degree permutation. @code{@var{p} = colamd\n\ |
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199 (@var{s})} returns the column approximate minimum degree permutation\n\ |
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200 vector for the sparse matrix @var{s}. For a non-symmetric matrix @var{s},\n\ |
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201 @code{@var{s} (:,@var{p})} tends to have sparser LU factors than @var{s}.\n\ |
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202 The Cholesky factorization of @code{@var{s} (:,@var{p})' * @var{s}\n\ |
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203 (:,@var{p})} also tends to be sparser than that of @code{@var{s}' *\n\ |
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204 @var{s}}.\n\ |
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205 \n\ |
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206 @var{knobs} is an optional two-element input vector. If @var{s} is\n\ |
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207 m-by-n, then rows with more than @code{(@var{knobs} (1)) * @var{n}}\n\ |
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208 entries are ignored. Columns with more than @code{(@var{knobs} (2)) *\n\ |
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209 @var{m}} entries are removed prior to ordering, and ordered last in the\n\ |
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210 output permutation @var{p}. If the knobs parameter is not present, then\n\ |
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211 0.5 is used instead, for both @code{@var{knobs} (1)} and\n\ |
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212 @code{@var{knobs} (2)}. @code{@var{knobs} (3)} controls the printing of\n\ |
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213 statistics and error messages.\n\ |
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214 \n\ |
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215 @var{stats} is an optional 20-element output vector that provides data\n\ |
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216 about the ordering and the validity of the input matrix @var{s}. Ordering\n\ |
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217 statistics are in @code{@var{stats} (1:3)}. @code{@var{stats} (1)} and\n\ |
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218 @code{@var{stats} (2)} are the number of dense or empty rows and columns\n\ |
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219 ignored by COLAMD and @code{@var{stats} (3)} is the number of garbage\n\ |
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220 collections performed on the internal data structure used by COLAMD\n\ |
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221 (roughly of size @code{2.2 * nnz(@var{s}) + 4 * @var{m} + 7 * @var{n}}\n\ |
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222 integers).\n\ |
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223 \n\ |
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224 Octave built-in functions are intended to generate valid sparse matrices,\n\ |
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225 with no duplicate entries, with ascending row indices of the nonzeros\n\ |
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226 in each column, with a non-negative number of entries in each column (!)\n\ |
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227 and so on. If a matrix is invalid, then COLAMD may or may not be able\n\ |
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228 to continue. If there are duplicate entries (a row index appears two or\n\ |
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229 more times in the same column) or if the row indices in a column are out\n\ |
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230 of order, then COLAMD can correct these errors by ignoring the duplicate\n\ |
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231 entries and sorting each column of its internal copy of the matrix\n\ |
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232 @var{s} (the input matrix @var{s} is not repaired, however). If a matrix\n\ |
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233 is invalid in other ways then COLAMD cannot continue, an error message is\n\ |
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234 printed, and no output arguments (@var{p} or @var{stats}) are returned.\n\ |
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235 COLAMD is thus a simple way to check a sparse matrix to see if it's\n\ |
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236 valid.\n\ |
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237 \n\ |
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238 @code{@var{stats} (4:7)} provide information if COLAMD was able to\n\ |
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239 continue. The matrix is OK if @code{@var{stats} (4)} is zero, or 1 if\n\ |
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240 invalid. @code{@var{stats} (5)} is the rightmost column index that is\n\ |
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241 unsorted or contains duplicate entries, or zero if no such column exists.\n\ |
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242 @code{@var{stats} (6)} is the last seen duplicate or out-of-order row\n\ |
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243 index in the column index given by @code{@var{stats} (5)}, or zero if no\n\ |
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244 such row index exists. @code{@var{stats} (7)} is the number of duplicate\n\ |
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245 or out-of-order row indices. @code{@var{stats} (8:20)} is always zero in\n\ |
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246 the current version of COLAMD (reserved for future use).\n\ |
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247 \n\ |
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248 The ordering is followed by a column elimination tree post-ordering.\n\ |
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249 \n\ |
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250 The authors of the code itself are Stefan I. Larimore and Timothy A.\n\ |
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251 Davis (davis@@cise.ufl.edu), University of Florida. The algorithm was\n\ |
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252 developed in collaboration with John Gilbert, Xerox PARC, and Esmond\n\ |
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253 Ng, Oak Ridge National Laboratory. (see\n\ |
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254 @url{http://www.cise.ufl.edu/research/sparse/colamd})\n\ |
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255 @end deftypefn\n\ |
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256 @seealso{colperm, symamd}") |
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257 { |
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258 octave_value_list retval; |
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259 int nargin = args.length (); |
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260 int spumoni = 0; |
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261 |
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262 if (nargout < 0 || nargout > 2 || nargin < 0 || nargin > 2) |
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263 usage ("colamd: incorrect number of input and/or output arguments"); |
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264 else |
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265 { |
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266 // Get knobs |
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267 OCTAVE_LOCAL_BUFFER (double, knobs, COLAMD_KNOBS); |
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268 colamd_set_defaults (knobs); |
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269 |
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270 // Check for user-passed knobs |
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271 if (nargin == 2) |
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272 { |
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273 NDArray User_knobs = args(1).array_value (); |
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274 int nel_User_knobs = User_knobs.length (); |
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275 |
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276 if (nel_User_knobs > 0) |
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277 knobs [COLAMD_DENSE_ROW] = User_knobs (COLAMD_DENSE_ROW); |
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278 if (nel_User_knobs > 1) |
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279 knobs [COLAMD_DENSE_COL] = User_knobs (COLAMD_DENSE_COL) ; |
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280 if (nel_User_knobs > 2) |
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281 spumoni = (int) User_knobs (2); |
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282 } |
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283 |
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284 // print knob settings if spumoni is set |
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285 if (spumoni > 0) |
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286 { |
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287 octave_stdout << "colamd: dense row fraction: " |
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288 << knobs [COLAMD_DENSE_ROW] << std::endl; |
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289 octave_stdout << "colamd: dense col fraction: " |
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290 << knobs [COLAMD_DENSE_COL] << std::endl; |
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291 } |
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292 |
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293 int n_row, n_col, nnz; |
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294 int *ridx, *cidx; |
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295 SparseComplexMatrix scm; |
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296 SparseMatrix sm; |
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297 |
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298 if (args(0).class_name () == "sparse") |
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299 { |
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300 if (args(0).is_complex_type ()) |
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301 { |
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302 scm = args(0). sparse_complex_matrix_value (); |
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303 n_row = scm.rows (); |
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304 n_col = scm.cols (); |
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305 nnz = scm.nnz (); |
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306 ridx = scm.xridx (); |
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307 cidx = scm.xcidx (); |
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308 } |
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309 else |
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310 { |
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311 sm = args(0).sparse_matrix_value (); |
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312 |
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313 n_row = sm.rows (); |
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314 n_col = sm.cols (); |
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315 nnz = sm.nnz (); |
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316 ridx = sm.xridx (); |
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317 cidx = sm.xcidx (); |
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318 } |
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319 } |
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320 else |
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321 { |
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322 if (args(0).is_complex_type ()) |
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323 sm = SparseMatrix (real (args(0).complex_matrix_value ())); |
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324 else |
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325 sm = SparseMatrix (args(0).matrix_value ()); |
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326 |
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327 n_row = sm.rows (); |
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328 n_col = sm.cols (); |
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329 nnz = sm.nnz (); |
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330 ridx = sm.xridx (); |
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331 cidx = sm.xcidx (); |
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332 } |
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333 |
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334 // Allocate workspace for colamd |
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335 OCTAVE_LOCAL_BUFFER (int, p, n_col+1); |
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336 for (int i = 0; i < n_col+1; i++) |
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337 p[i] = cidx [i]; |
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338 |
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339 int Alen = colamd_recommended (nnz, n_row, n_col); |
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340 OCTAVE_LOCAL_BUFFER (int, A, Alen); |
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341 for (int i = 0; i < nnz; i++) |
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342 A[i] = ridx [i]; |
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343 |
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344 // Order the columns (destroys A) |
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345 OCTAVE_LOCAL_BUFFER (int, stats, COLAMD_STATS); |
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346 if (!colamd (n_row, n_col, Alen, A, p, knobs, stats)) |
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347 { |
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348 colamd_report (stats) ; |
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349 error ("colamd: internal error!"); |
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350 return retval; |
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351 } |
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352 |
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353 // column elimination tree post-ordering (reuse variables) |
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354 OCTAVE_LOCAL_BUFFER (int, colbeg, n_col + 1); |
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355 OCTAVE_LOCAL_BUFFER (int, colend, n_col + 1); |
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356 OCTAVE_LOCAL_BUFFER (int, etree, n_col + 1); |
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357 |
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358 for (int i = 0; i < n_col; i++) |
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359 { |
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360 colbeg[i] = cidx[p[i]]; |
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361 colend[i] = cidx[p[i]+1]; |
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362 } |
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363 |
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364 coletree (ridx, colbeg, colend, etree, n_row, n_col); |
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365 |
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366 // Calculate the tree post-ordering |
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367 TreePostorder (n_col, etree, colbeg); |
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368 |
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369 // return the permutation vector |
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370 NDArray out_perm (dim_vector (1, n_col)); |
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371 for (int i = 0; i < n_col; i++) |
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372 out_perm(i) = p [colbeg [i]] + 1; |
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373 |
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374 retval (0) = out_perm; |
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375 |
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376 // print stats if spumoni > 0 |
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377 if (spumoni > 0) |
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378 colamd_report (stats) ; |
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379 |
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380 // Return the stats vector |
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381 if (nargout == 2) |
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382 { |
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383 NDArray out_stats (dim_vector (1, COLAMD_STATS)); |
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384 for (int i = 0 ; i < COLAMD_STATS ; i++) |
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385 out_stats (i) = stats [i] ; |
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386 retval(1) = out_stats; |
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387 |
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388 // fix stats (5) and (6), for 1-based information on |
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389 // jumbled matrix. note that this correction doesn't |
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390 // occur if symamd returns FALSE |
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391 out_stats (COLAMD_INFO1) ++ ; |
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392 out_stats (COLAMD_INFO2) ++ ; |
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393 } |
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394 } |
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395 |
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396 return retval; |
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397 } |
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398 |
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399 DEFUN_DLD (symamd, args, nargout, |
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400 "-*- texinfo -*-\n\ |
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401 @deftypefn {Loadable Function} {@var{p} =} symamd (@var{s})\n\ |
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402 @deftypefnx {Loadable Function} {@var{p} =} symamd (@var{s}, @var{knobs})\n\ |
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403 @deftypefnx {Loadable Function} {[@var{p}, @var{stats}] =} symamd (@var{s})\n\ |
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404 @deftypefnx {Loadable Function} {[@var{p}, @var{stats}] =} symamd (@var{s}, @var{knobs})\n\ |
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405 \n\ |
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406 For a symmetric positive definite matrix @var{s}, returns the permutation\n\ |
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407 vector p such that @code{@var{s} (@var{p}, @var{p})} tends to have a\n\ |
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408 sparser Cholesky factor than @var{s}. Sometimes SYMAMD works well for\n\ |
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409 symmetric indefinite matrices too. The matrix @var{s} is assumed to be\n\ |
|
|
410 symmetric; only the strictly lower triangular part is referenced. @var{s}\n\ |
|
|
411 must be square.\n\ |
|
|
412 \n\ |
|
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413 @var{knobs} is an optional input argument. If @var{s} is n-by-n, then\n\ |
|
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414 rows and columns with more than @code{@var{knobs} (1) * @var{n}} entries\n\ |
|
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415 are removed prior to ordering, and ordered last in the output permutation\n\ |
|
|
416 @var{p}. If the @var{knobs} parameter is not present, then the default of\n\ |
|
|
417 0.5 is used instead. @code{@var{knobs} (2)} controls the printing of\n\ |
|
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418 statistics and error messages.\n\ |
|
|
419 \n\ |
|
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420 @var{stats} is an optional 20-element output vector that provides data\n\ |
|
|
421 about the ordering and the validity of the input matrix @var{s}. Ordering\n\ |
|
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422 statistics are in @code{@var{stats} (1:3)}. @code{@var{stats} (1) =\n\ |
|
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423 @var{stats} (2)} is the number of dense or empty rows and columns\n\ |
|
|
424 ignored by SYMAMD and @code{@var{stats} (3)} is the number of garbage\n\ |
|
|
425 collections performed on the internal data structure used by SYMAMD\n\ |
|
|
426 (roughly of size @code{8.4 * nnz (tril (@var{s}, -1)) + 9 * @var{n}}\n\ |
|
|
427 integers).\n\ |
|
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428 \n\ |
|
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429 Octave built-in functions are intended to generate valid sparse matrices,\n\ |
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430 with no duplicate entries, with ascending row indices of the nonzeros\n\ |
|
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431 in each column, with a non-negative number of entries in each column (!)\n\ |
|
|
432 and so on. If a matrix is invalid, then SYMAMD may or may not be able\n\ |
|
|
433 to continue. If there are duplicate entries (a row index appears two or\n\ |
|
|
434 more times in the same column) or if the row indices in a column are out\n\ |
|
|
435 of order, then SYMAMD can correct these errors by ignoring the duplicate\n\ |
|
|
436 entries and sorting each column of its internal copy of the matrix S (the\n\ |
|
|
437 input matrix S is not repaired, however). If a matrix is invalid in\n\ |
|
|
438 other ways then SYMAMD cannot continue, an error message is printed, and\n\ |
|
|
439 no output arguments (@var{p} or @var{stats}) are returned. SYMAMD is\n\ |
|
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440 thus a simple way to check a sparse matrix to see if it's valid.\n\ |
|
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441 \n\ |
|
|
442 @code{@var{stats} (4:7)} provide information if SYMAMD was able to\n\ |
|
|
443 continue. The matrix is OK if @code{@var{stats} (4)} is zero, or 1\n\ |
|
|
444 if invalid. @code{@var{stats} (5)} is the rightmost column index that\n\ |
|
|
445 is unsorted or contains duplicate entries, or zero if no such column\n\ |
|
|
446 exists. @code{@var{stats} (6)} is the last seen duplicate or out-of-order\n\ |
|
|
447 row index in the column index given by @code{@var{stats} (5)}, or zero\n\ |
|
|
448 if no such row index exists. @code{@var{stats} (7)} is the number of\n\ |
|
|
449 duplicate or out-of-order row indices. @code{@var{stats} (8:20)} is\n\ |
|
|
450 always zero in the current version of SYMAMD (reserved for future use).\n\ |
|
|
451 \n\ |
|
|
452 The ordering is followed by a column elimination tree post-ordering.\n\ |
|
|
453 \n\ |
|
|
454 \n\ |
|
|
455 The authors of the code itself are Stefan I. Larimore and Timothy A.\n\ |
|
|
456 Davis (davis@@cise.ufl.edu), University of Florida. The algorithm was\n\ |
|
|
457 developed in collaboration with John Gilbert, Xerox PARC, and Esmond\n\ |
|
|
458 Ng, Oak Ridge National Laboratory. (see\n\ |
|
|
459 @url{http://www.cise.ufl.edu/research/sparse/colamd})\n\ |
|
|
460 @end deftypefn\n\ |
|
|
461 @seealso{colperm, colamd}") |
|
|
462 { |
|
|
463 octave_value_list retval; |
|
|
464 int nargin = args.length (); |
|
|
465 int spumoni = 0; |
|
|
466 |
|
|
467 if (nargout < 0 || nargout > 2 || nargin < 0 || nargin > 2) |
|
|
468 usage ("symamd: incorrect number of input and/or output arguments"); |
|
|
469 else |
|
|
470 { |
|
|
471 // Get knobs |
|
|
472 OCTAVE_LOCAL_BUFFER (double, knobs, COLAMD_KNOBS); |
|
|
473 colamd_set_defaults (knobs); |
|
|
474 |
|
|
475 // Check for user-passed knobs |
|
|
476 if (nargin == 2) |
|
|
477 { |
|
|
478 NDArray User_knobs = args(1).array_value (); |
|
|
479 int nel_User_knobs = User_knobs.length (); |
|
|
480 |
|
|
481 if (nel_User_knobs > 0) |
|
|
482 knobs [COLAMD_DENSE_ROW] = User_knobs (COLAMD_DENSE_ROW); |
|
|
483 if (nel_User_knobs > 1) |
|
|
484 spumoni = (int) User_knobs (1); |
|
|
485 } |
|
|
486 |
|
|
487 // print knob settings if spumoni is set |
|
|
488 if (spumoni > 0) |
|
|
489 octave_stdout << "symamd: dense row/col fraction: " |
|
|
490 << knobs [COLAMD_DENSE_ROW] << std::endl; |
|
|
491 |
|
|
492 int n_row, n_col, nnz; |
|
|
493 int *ridx, *cidx; |
|
|
494 SparseMatrix sm; |
|
|
495 SparseComplexMatrix scm; |
|
|
496 |
|
|
497 if (args(0).class_name () == "sparse") |
|
|
498 { |
|
|
499 if (args(0).is_complex_type ()) |
|
|
500 { |
|
|
501 scm = args(0).sparse_complex_matrix_value (); |
|
|
502 n_row = scm.rows (); |
|
|
503 n_col = scm.cols (); |
|
|
504 nnz = scm.nnz (); |
|
|
505 ridx = scm.xridx (); |
|
|
506 cidx = scm.xcidx (); |
|
|
507 } |
|
|
508 else |
|
|
509 { |
|
|
510 sm = args(0).sparse_matrix_value (); |
|
|
511 n_row = sm.rows (); |
|
|
512 n_col = sm.cols (); |
|
|
513 nnz = sm.nnz (); |
|
|
514 ridx = sm.xridx (); |
|
|
515 cidx = sm.xcidx (); |
|
|
516 } |
|
|
517 } |
|
|
518 else |
|
|
519 { |
|
|
520 if (args(0).is_complex_type ()) |
|
|
521 sm = SparseMatrix (real (args(0).complex_matrix_value ())); |
|
|
522 else |
|
|
523 sm = SparseMatrix (args(0).matrix_value ()); |
|
|
524 |
|
|
525 n_row = sm.rows (); |
|
|
526 n_col = sm.cols (); |
|
|
527 nnz = sm.nnz (); |
|
|
528 ridx = sm.xridx (); |
|
|
529 cidx = sm.xcidx (); |
|
|
530 } |
|
|
531 |
|
|
532 if (n_row != n_col) |
|
|
533 { |
|
|
534 error ("symamd: matrix must be square"); |
|
|
535 return retval; |
|
|
536 } |
|
|
537 |
|
|
538 // Allocate workspace for symamd |
|
|
539 OCTAVE_LOCAL_BUFFER (int, perm, n_col+1); |
|
|
540 OCTAVE_LOCAL_BUFFER (int, stats, COLAMD_STATS); |
|
|
541 if (!symamd (n_col, ridx, cidx, perm, knobs, stats, &calloc, &free)) |
|
|
542 { |
|
|
543 symamd_report (stats) ; |
|
|
544 error ("symamd: internal error!") ; |
|
|
545 return retval; |
|
|
546 } |
|
|
547 |
|
|
548 // column elimination tree post-ordering |
|
|
549 OCTAVE_LOCAL_BUFFER (int, etree, n_col + 1); |
|
|
550 symetree (ridx, cidx, etree, perm, n_col); |
|
|
551 |
|
|
552 // Calculate the tree post-ordering |
|
|
553 OCTAVE_LOCAL_BUFFER (int, post, n_col + 1); |
|
|
554 TreePostorder (n_col, etree, post); |
|
|
555 |
|
|
556 // return the permutation vector |
|
|
557 NDArray out_perm (dim_vector (1, n_col)); |
|
|
558 for (int i = 0; i < n_col; i++) |
|
|
559 out_perm(i) = perm [post [i]] + 1; |
|
|
560 |
|
|
561 retval (0) = out_perm; |
|
|
562 |
|
|
563 // print stats if spumoni > 0 |
|
|
564 if (spumoni > 0) |
|
|
565 symamd_report (stats) ; |
|
|
566 |
|
|
567 // Return the stats vector |
|
|
568 if (nargout == 2) |
|
|
569 { |
|
|
570 NDArray out_stats (dim_vector (1, COLAMD_STATS)); |
|
|
571 for (int i = 0 ; i < COLAMD_STATS ; i++) |
|
|
572 out_stats (i) = stats [i] ; |
|
|
573 retval(1) = out_stats; |
|
|
574 |
|
|
575 // fix stats (5) and (6), for 1-based information on |
|
|
576 // jumbled matrix. note that this correction doesn't |
|
|
577 // occur if symamd returns FALSE |
|
|
578 out_stats (COLAMD_INFO1) ++ ; |
|
|
579 out_stats (COLAMD_INFO2) ++ ; |
|
|
580 } |
|
|
581 } |
|
|
582 |
|
|
583 return retval; |
|
|
584 } |
|
|
585 |
|
|
586 DEFUN_DLD (etree, args, nargout, |
|
|
587 "-*- texinfo -*-\n\ |
|
|
588 @deftypefn {Loadable Function} {@var{p} =} etree (@var{s})\n\ |
|
|
589 @deftypefnx {Loadable Function} {@var{p} =} etree (@var{s}, @var{typ})\n\ |
|
|
590 @deftypefnx {Loadable Function} {[@var{p}, @var{q}] =} etree (@var{s}, @var{typ})\n\ |
|
|
591 \n\ |
|
|
592 Returns the elimination tree for the matrix @var{s}. By default @var{s}\n\ |
|
|
593 is assumed to be symmetric and the symmetric elimination tree is\n\ |
|
|
594 returned. The argument @var{typ} controls whether a symmetric or\n\ |
|
|
595 column elimination tree is returned. Valid values of @var{typ} are\n\ |
|
|
596 'sym' or 'col', for symmetric or column elimination tree respectively\n\ |
|
|
597 \n\ |
|
|
598 Called with a second argument, @dfn{etree} also returns the postorder\n\ |
|
|
599 permutations on the tree.\n\ |
|
|
600 @end deftypefn") |
|
|
601 { |
|
|
602 octave_value_list retval; |
|
|
603 int nargin = args.length (); |
|
|
604 |
|
|
605 if (nargout < 0 || nargout > 2 || nargin < 0 || nargin > 2) |
|
|
606 usage ("etree: incorrect number of input and/or output arguments"); |
|
|
607 else |
|
|
608 { |
|
|
609 int n_row, n_col, nnz; |
|
|
610 int *ridx, *cidx; |
|
|
611 bool is_sym = true; |
|
|
612 SparseMatrix sm; |
|
|
613 SparseComplexMatrix scm; |
|
|
614 |
|
|
615 if (args(0).class_name () == "sparse") |
|
|
616 { |
|
|
617 if (args(0).is_complex_type ()) |
|
|
618 { |
|
|
619 scm = args(0).sparse_complex_matrix_value (); |
|
|
620 n_row = scm.rows (); |
|
|
621 n_col = scm.cols (); |
|
|
622 nnz = scm.nnz (); |
|
|
623 ridx = scm.xridx (); |
|
|
624 cidx = scm.xcidx (); |
|
|
625 } |
|
|
626 else |
|
|
627 { |
|
|
628 sm = args(0).sparse_matrix_value (); |
|
|
629 n_row = sm.rows (); |
|
|
630 n_col = sm.cols (); |
|
|
631 nnz = sm.nnz (); |
|
|
632 ridx = sm.xridx (); |
|
|
633 cidx = sm.xcidx (); |
|
|
634 } |
|
|
635 |
|
|
636 } |
|
|
637 else |
|
|
638 { |
|
|
639 error ("etree: must be called with a sparse matrix"); |
|
|
640 return retval; |
|
|
641 } |
|
|
642 |
|
|
643 if (nargin == 2) |
|
|
644 if (args(1).is_string ()) |
|
|
645 { |
|
|
646 std::string str = args(1).string_value (); |
|
|
647 if (str.find("C") == 0 || str.find("c") == 0) |
|
|
648 is_sym = false; |
|
|
649 } |
|
|
650 else |
|
|
651 { |
|
|
652 error ("etree: second argument must be a string"); |
|
|
653 return retval; |
|
|
654 } |
|
|
655 |
|
|
656 // column elimination tree post-ordering (reuse variables) |
|
|
657 OCTAVE_LOCAL_BUFFER (int, etree, n_col + 1); |
|
|
658 |
|
|
659 |
|
|
660 if (is_sym) |
|
|
661 { |
|
|
662 if (n_row != n_col) |
|
|
663 { |
|
|
664 error ("etree: matrix is marked as symmetric, but not square"); |
|
|
665 return retval; |
|
|
666 } |
|
|
667 symetree (ridx, cidx, etree, NULL, n_col); |
|
|
668 } |
|
|
669 else |
|
|
670 { |
|
|
671 OCTAVE_LOCAL_BUFFER (int, colbeg, n_col); |
|
|
672 OCTAVE_LOCAL_BUFFER (int, colend, n_col); |
|
|
673 |
|
|
674 for (int i = 0; i < n_col; i++) |
|
|
675 { |
|
|
676 colbeg[i] = cidx[i]; |
|
|
677 colend[i] = cidx[i+1]; |
|
|
678 } |
|
|
679 |
|
|
680 coletree (ridx, colbeg, colend, etree, n_row, n_col); |
|
|
681 } |
|
|
682 |
|
|
683 NDArray tree (dim_vector (1, n_col)); |
|
|
684 for (int i = 0; i < n_col; i++) |
|
|
685 // We flag a root with n_col while Matlab does it with zero |
|
|
686 // Convert for matlab compatiable output |
|
|
687 if (etree[i] == n_col) |
|
|
688 tree (i) = 0; |
|
|
689 else |
|
|
690 tree (i) = etree[i] + 1; |
|
|
691 |
|
|
692 retval (0) = tree; |
|
|
693 |
|
|
694 if (nargout == 2) |
|
|
695 { |
|
|
696 // Calculate the tree post-ordering |
|
|
697 OCTAVE_LOCAL_BUFFER (int, post, n_col + 1); |
|
|
698 TreePostorder (n_col, etree, post); |
|
|
699 |
|
|
700 NDArray postorder (dim_vector (1, n_col)); |
|
|
701 for (int i = 0; i < n_col; i++) |
|
|
702 postorder (i) = post[i] + 1; |
|
|
703 |
|
|
704 retval (1) = postorder; |
|
|
705 } |
|
|
706 } |
|
|
707 |
|
|
708 return retval; |
|
|
709 } |
|
|
710 |
|
|
711 DEFUN_DLD (symbfact, args, nargout, |
|
|
712 "-*- texinfo -*-\n\ |
|
|
713 @deftypefn {Loadable Function} {[@var{count}, @var{h}, @var{parent}, @var{post}, @var{r}]} = symbfact (@var{s}, @var{typ})\n\ |
|
|
714 \n\ |
|
|
715 Performs a symbolic factorization analysis on the sparse matrix @var{s}.\n\ |
|
|
716 @end deftypefn") |
|
|
717 { |
|
|
718 error ("symbfact: not implemented yet"); |
|
|
719 return octave_value (); |
|
|
720 } |
|
|
721 |
|
|
722 /* |
|
|
723 ;;; Local Variables: *** |
|
|
724 ;;; mode: C++ *** |
|
|
725 ;;; End: *** |
|
|
726 */ |
