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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 |
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18 Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, |
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19 Boston, MA 02110-1301, USA. |
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20 |
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21 */ |
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22 |
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23 // This is the octave interface to colamd, which bore the copyright given |
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24 // in the help of the functions. |
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25 |
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26 #ifdef HAVE_CONFIG_H |
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27 #include <config.h> |
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28 #endif |
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29 |
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30 #include <cstdlib> |
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31 |
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32 #include <string> |
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33 #include <vector> |
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34 |
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35 #include "ov.h" |
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36 #include "defun-dld.h" |
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37 #include "pager.h" |
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38 #include "ov-re-mat.h" |
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39 |
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40 #include "ov-re-sparse.h" |
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41 #include "ov-cx-sparse.h" |
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42 |
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43 #if SIZEOF_INT == SIZEOF_OCTAVE_IDX_TYPE |
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44 |
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45 // External COLAMD functions in C |
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46 extern "C" { |
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47 #include "COLAMD/colamd.h" |
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48 } |
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49 |
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50 // The symmetric column elimination tree code take from the Davis LDL code. |
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51 // Copyright given elsewhere in this file. |
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52 static |
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53 void symetree (const int *ridx, const int *cidx, int *Parent, int *P, int n) |
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54 { |
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55 OCTAVE_LOCAL_BUFFER (int, Flag, n); |
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56 OCTAVE_LOCAL_BUFFER (int, Pinv, (P ? n : 0)); |
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57 if (P) |
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58 // If P is present then compute Pinv, the inverse of P |
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59 for (int k = 0 ; k < n ; k++) |
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60 Pinv [P [k]] = k ; |
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61 |
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62 for (int k = 0 ; k < n ; k++) |
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63 { |
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64 // L(k,:) pattern: all nodes reachable in etree from nz in A(0:k-1,k) |
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65 Parent [k] = n ; // parent of k is not yet known |
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66 Flag [k] = k ; // mark node k as visited |
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67 int kk = (P) ? (P [k]) : (k) ; // kth original, or permuted, column |
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68 int p2 = cidx [kk+1] ; |
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69 for (int p = cidx [kk] ; p < p2 ; p++) |
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70 { |
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71 // A (i,k) is nonzero (original or permuted A) |
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72 int i = (Pinv) ? (Pinv [ridx [p]]) : (ridx [p]) ; |
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73 if (i < k) |
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74 { |
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75 // follow path from i to root of etree, stop at flagged node |
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76 for ( ; Flag [i] != k ; i = Parent [i]) |
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77 { |
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78 // find parent of i if not yet determined |
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79 if (Parent [i] == n) |
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80 Parent [i] = k ; |
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81 Flag [i] = k ; // mark i as visited |
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82 } |
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83 } |
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84 } |
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85 } |
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86 } |
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87 |
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88 // The elimination tree post-ordering code below is taken from SuperLU |
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89 static inline |
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90 int make_set (int i, int *pp) |
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91 { |
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92 pp[i] = i; |
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93 return i; |
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94 } |
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95 |
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96 static inline |
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97 int link (int s, int t, int *pp) |
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98 { |
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99 pp[s] = t; |
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100 return t; |
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101 } |
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102 |
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103 static inline |
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104 int find (int i, int *pp) |
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105 { |
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106 register int p, gp; |
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107 |
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108 p = pp[i]; |
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109 gp = pp[p]; |
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110 while (gp != p) { |
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111 pp[i] = gp; |
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112 i = gp; |
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113 p = pp[i]; |
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114 gp = pp[p]; |
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115 } |
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116 return (p); |
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117 } |
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118 |
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119 static |
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120 int etdfs (int v, int *first_kid, int *next_kid, int *post, int postnum) |
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121 { |
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122 for (int w = first_kid[v]; w != -1; w = next_kid[w]) { |
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123 postnum = etdfs (w, first_kid, next_kid, post, postnum); |
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124 } |
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125 post[postnum++] = v; |
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126 |
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127 return postnum; |
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128 } |
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129 |
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130 static |
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131 void TreePostorder(int n, int *parent, int *post) |
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132 { |
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133 // Allocate storage for working arrays and results |
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134 OCTAVE_LOCAL_BUFFER (int, first_kid, n+1); |
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135 OCTAVE_LOCAL_BUFFER (int, next_kid, n+1); |
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136 |
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137 // Set up structure describing children |
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138 for (int v = 0; v <= n; first_kid[v++] = -1); |
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139 for (int v = n-1; v >= 0; v--) |
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140 { |
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141 int dad = parent[v]; |
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142 next_kid[v] = first_kid[dad]; |
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143 first_kid[dad] = v; |
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144 } |
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145 |
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146 // Depth-first search from dummy root vertex #n |
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147 etdfs (n, first_kid, next_kid, post, 0); |
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148 } |
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149 |
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150 static |
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151 void coletree (const int *ridx, const int *colbeg, int *colend, |
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152 int *parent, int nr, int nc) |
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153 { |
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154 OCTAVE_LOCAL_BUFFER (int, root, nc); |
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155 OCTAVE_LOCAL_BUFFER (int, pp, nc); |
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156 OCTAVE_LOCAL_BUFFER (int, firstcol, nr); |
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157 |
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158 // Compute firstcol[row] = first nonzero column in row |
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159 for (int row = 0; row < nr; firstcol[row++] = nc); |
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160 for (int col = 0; col < nc; col++) |
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161 for (int p = colbeg[col]; p < colend[col]; p++) |
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162 { |
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163 int row = ridx[p]; |
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164 if (firstcol[row] > col) |
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165 firstcol[row] = col; |
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166 } |
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167 |
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168 // Compute etree by Liu's algorithm for symmetric matrices, |
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169 // except use (firstcol[r],c) in place of an edge (r,c) of A. |
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170 // Thus each row clique in A'*A is replaced by a star |
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171 // centered at its first vertex, which has the same fill. |
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172 for (int col = 0; col < nc; col++) |
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173 { |
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174 int cset = make_set (col, pp); |
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175 root[cset] = col; |
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176 parent[col] = nc; |
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177 for (int p = colbeg[col]; p < colend[col]; p++) |
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178 { |
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179 int row = firstcol[ridx[p]]; |
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180 if (row >= col) |
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181 continue; |
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182 int rset = find (row, pp); |
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183 int rroot = root[rset]; |
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184 if (rroot != col) |
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185 { |
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186 parent[rroot] = col; |
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187 cset = link (cset, rset, pp); |
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188 root[cset] = col; |
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189 } |
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190 } |
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191 } |
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192 } |
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193 |
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194 #endif |
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195 |
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196 DEFUN_DLD (colamd, args, nargout, |
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197 "-*- texinfo -*-\n\ |
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198 @deftypefn {Loadable Function} {@var{p} =} colamd (@var{s})\n\ |
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199 @deftypefnx {Loadable Function} {@var{p} =} colamd (@var{s}, @var{knobs})\n\ |
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200 @deftypefnx {Loadable Function} {[@var{p}, @var{stats}] =} colamd (@var{s})\n\ |
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201 @deftypefnx {Loadable Function} {[@var{p}, @var{stats}] =} colamd (@var{s}, @var{knobs})\n\ |
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202 \n\ |
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203 Column approximate minimum degree permutation. @code{@var{p} = colamd\n\ |
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204 (@var{s})} returns the column approximate minimum degree permutation\n\ |
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205 vector for the sparse matrix @var{s}. For a non-symmetric matrix @var{s},\n\ |
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206 @code{@var{s} (:,@var{p})} tends to have sparser LU factors than @var{s}.\n\ |
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207 The Cholesky factorization of @code{@var{s} (:,@var{p})' * @var{s}\n\ |
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208 (:,@var{p})} also tends to be sparser than that of @code{@var{s}' *\n\ |
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209 @var{s}}.\n\ |
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210 \n\ |
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211 @var{knobs} is an optional two-element input vector. If @var{s} is\n\ |
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212 m-by-n, then rows with more than @code{(@var{knobs} (1)) * @var{n}}\n\ |
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213 entries are ignored. Columns with more than @code{(@var{knobs} (2)) *\n\ |
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214 @var{m}} entries are removed prior to ordering, and ordered last in the\n\ |
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215 output permutation @var{p}. If the knobs parameter is not present, then\n\ |
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216 0.5 is used instead, for both @code{@var{knobs} (1)} and\n\ |
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217 @code{@var{knobs} (2)}. @code{@var{knobs} (3)} controls the printing of\n\ |
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218 statistics and error messages.\n\ |
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219 \n\ |
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220 @var{stats} is an optional 20-element output vector that provides data\n\ |
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221 about the ordering and the validity of the input matrix @var{s}. Ordering\n\ |
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222 statistics are in @code{@var{stats} (1:3)}. @code{@var{stats} (1)} and\n\ |
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223 @code{@var{stats} (2)} are the number of dense or empty rows and columns\n\ |
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224 ignored by COLAMD and @code{@var{stats} (3)} is the number of garbage\n\ |
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225 collections performed on the internal data structure used by COLAMD\n\ |
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226 (roughly of size @code{2.2 * nnz(@var{s}) + 4 * @var{m} + 7 * @var{n}}\n\ |
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227 integers).\n\ |
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228 \n\ |
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229 Octave built-in functions are intended to generate valid sparse matrices,\n\ |
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230 with no duplicate entries, with ascending row indices of the nonzeros\n\ |
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231 in each column, with a non-negative number of entries in each column (!)\n\ |
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232 and so on. If a matrix is invalid, then COLAMD may or may not be able\n\ |
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233 to continue. If there are duplicate entries (a row index appears two or\n\ |
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234 more times in the same column) or if the row indices in a column are out\n\ |
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235 of order, then COLAMD can correct these errors by ignoring the duplicate\n\ |
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236 entries and sorting each column of its internal copy of the matrix\n\ |
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237 @var{s} (the input matrix @var{s} is not repaired, however). If a matrix\n\ |
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238 is invalid in other ways then COLAMD cannot continue, an error message is\n\ |
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239 printed, and no output arguments (@var{p} or @var{stats}) are returned.\n\ |
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240 COLAMD is thus a simple way to check a sparse matrix to see if it's\n\ |
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241 valid.\n\ |
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242 \n\ |
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243 @code{@var{stats} (4:7)} provide information if COLAMD was able to\n\ |
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244 continue. The matrix is OK if @code{@var{stats} (4)} is zero, or 1 if\n\ |
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245 invalid. @code{@var{stats} (5)} is the rightmost column index that is\n\ |
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246 unsorted or contains duplicate entries, or zero if no such column exists.\n\ |
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247 @code{@var{stats} (6)} is the last seen duplicate or out-of-order row\n\ |
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248 index in the column index given by @code{@var{stats} (5)}, or zero if no\n\ |
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249 such row index exists. @code{@var{stats} (7)} is the number of duplicate\n\ |
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250 or out-of-order row indices. @code{@var{stats} (8:20)} is always zero in\n\ |
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251 the current version of COLAMD (reserved for future use).\n\ |
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252 \n\ |
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253 The ordering is followed by a column elimination tree post-ordering.\n\ |
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254 \n\ |
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255 The authors of the code itself are Stefan I. Larimore and Timothy A.\n\ |
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256 Davis (davis@@cise.ufl.edu), University of Florida. The algorithm was\n\ |
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257 developed in collaboration with John Gilbert, Xerox PARC, and Esmond\n\ |
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258 Ng, Oak Ridge National Laboratory. (see\n\ |
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259 @url{http://www.cise.ufl.edu/research/sparse/colamd})\n\ |
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260 @end deftypefn\n\ |
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261 @seealso{colperm, symamd}") |
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262 { |
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263 octave_value_list retval; |
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264 |
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265 #if SIZEOF_INT == SIZEOF_OCTAVE_IDX_TYPE |
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266 |
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267 int nargin = args.length (); |
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268 int spumoni = 0; |
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269 |
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270 if (nargout < 0 || nargout > 2 || nargin < 0 || nargin > 2) |
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271 usage ("colamd: incorrect number of input and/or output arguments"); |
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272 else |
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273 { |
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274 // Get knobs |
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275 OCTAVE_LOCAL_BUFFER (double, knobs, COLAMD_KNOBS); |
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276 colamd_set_defaults (knobs); |
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277 |
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278 // Check for user-passed knobs |
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279 if (nargin == 2) |
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280 { |
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281 NDArray User_knobs = args(1).array_value (); |
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282 int nel_User_knobs = User_knobs.length (); |
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283 |
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284 if (nel_User_knobs > 0) |
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285 knobs [COLAMD_DENSE_ROW] = User_knobs (COLAMD_DENSE_ROW); |
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286 if (nel_User_knobs > 1) |
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287 knobs [COLAMD_DENSE_COL] = User_knobs (COLAMD_DENSE_COL) ; |
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288 if (nel_User_knobs > 2) |
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289 spumoni = (int) User_knobs (2); |
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290 } |
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291 |
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292 // print knob settings if spumoni is set |
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293 if (spumoni > 0) |
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294 { |
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295 octave_stdout << "colamd: dense row fraction: " |
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296 << knobs [COLAMD_DENSE_ROW] << std::endl; |
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297 octave_stdout << "colamd: dense col fraction: " |
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298 << knobs [COLAMD_DENSE_COL] << std::endl; |
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299 } |
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300 |
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301 int n_row, n_col, nnz; |
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302 int *ridx, *cidx; |
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303 SparseComplexMatrix scm; |
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304 SparseMatrix sm; |
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305 |
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306 if (args(0).class_name () == "sparse") |
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307 { |
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308 if (args(0).is_complex_type ()) |
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309 { |
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310 scm = args(0). sparse_complex_matrix_value (); |
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311 n_row = scm.rows (); |
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312 n_col = scm.cols (); |
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313 nnz = scm.nnz (); |
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314 ridx = scm.xridx (); |
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315 cidx = scm.xcidx (); |
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316 } |
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317 else |
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318 { |
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319 sm = args(0).sparse_matrix_value (); |
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320 |
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321 n_row = sm.rows (); |
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322 n_col = sm.cols (); |
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323 nnz = sm.nnz (); |
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324 ridx = sm.xridx (); |
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325 cidx = sm.xcidx (); |
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326 } |
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327 } |
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328 else |
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329 { |
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330 if (args(0).is_complex_type ()) |
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331 sm = SparseMatrix (real (args(0).complex_matrix_value ())); |
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332 else |
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333 sm = SparseMatrix (args(0).matrix_value ()); |
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334 |
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335 n_row = sm.rows (); |
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336 n_col = sm.cols (); |
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337 nnz = sm.nnz (); |
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338 ridx = sm.xridx (); |
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339 cidx = sm.xcidx (); |
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340 } |
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341 |
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342 // Allocate workspace for colamd |
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343 OCTAVE_LOCAL_BUFFER (int, p, n_col+1); |
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344 for (int i = 0; i < n_col+1; i++) |
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345 p[i] = cidx [i]; |
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346 |
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347 int Alen = colamd_recommended (nnz, n_row, n_col); |
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348 OCTAVE_LOCAL_BUFFER (int, A, Alen); |
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349 for (int i = 0; i < nnz; i++) |
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350 A[i] = ridx [i]; |
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351 |
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352 // Order the columns (destroys A) |
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353 OCTAVE_LOCAL_BUFFER (int, stats, COLAMD_STATS); |
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354 if (!colamd (n_row, n_col, Alen, A, p, knobs, stats)) |
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355 { |
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356 colamd_report (stats) ; |
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357 error ("colamd: internal error!"); |
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358 return retval; |
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359 } |
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360 |
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361 // column elimination tree post-ordering (reuse variables) |
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362 OCTAVE_LOCAL_BUFFER (int, colbeg, n_col + 1); |
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363 OCTAVE_LOCAL_BUFFER (int, colend, n_col + 1); |
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364 OCTAVE_LOCAL_BUFFER (int, etree, n_col + 1); |
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365 |
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366 for (int i = 0; i < n_col; i++) |
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367 { |
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368 colbeg[i] = cidx[p[i]]; |
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369 colend[i] = cidx[p[i]+1]; |
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370 } |
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371 |
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372 coletree (ridx, colbeg, colend, etree, n_row, n_col); |
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373 |
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374 // Calculate the tree post-ordering |
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375 TreePostorder (n_col, etree, colbeg); |
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376 |
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377 // return the permutation vector |
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378 NDArray out_perm (dim_vector (1, n_col)); |
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379 for (int i = 0; i < n_col; i++) |
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380 out_perm(i) = p [colbeg [i]] + 1; |
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381 |
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382 retval (0) = out_perm; |
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383 |
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384 // print stats if spumoni > 0 |
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385 if (spumoni > 0) |
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386 colamd_report (stats) ; |
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387 |
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388 // Return the stats vector |
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389 if (nargout == 2) |
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390 { |
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391 NDArray out_stats (dim_vector (1, COLAMD_STATS)); |
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392 for (int i = 0 ; i < COLAMD_STATS ; i++) |
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393 out_stats (i) = stats [i] ; |
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394 retval(1) = out_stats; |
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395 |
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396 // fix stats (5) and (6), for 1-based information on |
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397 // jumbled matrix. note that this correction doesn't |
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398 // occur if symamd returns FALSE |
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399 out_stats (COLAMD_INFO1) ++ ; |
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400 out_stats (COLAMD_INFO2) ++ ; |
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401 } |
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402 } |
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403 |
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5297
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404 #else |
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405 |
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406 error ("colamd: not available in this version of Octave"); |
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407 |
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408 #endif |
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409 |
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410 return retval; |
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411 } |
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412 |
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413 DEFUN_DLD (symamd, args, nargout, |
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414 "-*- texinfo -*-\n\ |
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415 @deftypefn {Loadable Function} {@var{p} =} symamd (@var{s})\n\ |
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416 @deftypefnx {Loadable Function} {@var{p} =} symamd (@var{s}, @var{knobs})\n\ |
|
|
417 @deftypefnx {Loadable Function} {[@var{p}, @var{stats}] =} symamd (@var{s})\n\ |
|
|
418 @deftypefnx {Loadable Function} {[@var{p}, @var{stats}] =} symamd (@var{s}, @var{knobs})\n\ |
|
|
419 \n\ |
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|
420 For a symmetric positive definite matrix @var{s}, returns the permutation\n\ |
|
|
421 vector p such that @code{@var{s} (@var{p}, @var{p})} tends to have a\n\ |
|
|
422 sparser Cholesky factor than @var{s}. Sometimes SYMAMD works well for\n\ |
|
|
423 symmetric indefinite matrices too. The matrix @var{s} is assumed to be\n\ |
|
|
424 symmetric; only the strictly lower triangular part is referenced. @var{s}\n\ |
|
|
425 must be square.\n\ |
|
|
426 \n\ |
|
|
427 @var{knobs} is an optional input argument. If @var{s} is n-by-n, then\n\ |
|
|
428 rows and columns with more than @code{@var{knobs} (1) * @var{n}} entries\n\ |
|
|
429 are removed prior to ordering, and ordered last in the output permutation\n\ |
|
|
430 @var{p}. If the @var{knobs} parameter is not present, then the default of\n\ |
|
|
431 0.5 is used instead. @code{@var{knobs} (2)} controls the printing of\n\ |
|
|
432 statistics and error messages.\n\ |
|
|
433 \n\ |
|
|
434 @var{stats} is an optional 20-element output vector that provides data\n\ |
|
|
435 about the ordering and the validity of the input matrix @var{s}. Ordering\n\ |
|
|
436 statistics are in @code{@var{stats} (1:3)}. @code{@var{stats} (1) =\n\ |
|
|
437 @var{stats} (2)} is the number of dense or empty rows and columns\n\ |
|
|
438 ignored by SYMAMD and @code{@var{stats} (3)} is the number of garbage\n\ |
|
|
439 collections performed on the internal data structure used by SYMAMD\n\ |
|
|
440 (roughly of size @code{8.4 * nnz (tril (@var{s}, -1)) + 9 * @var{n}}\n\ |
|
|
441 integers).\n\ |
|
|
442 \n\ |
|
|
443 Octave built-in functions are intended to generate valid sparse matrices,\n\ |
|
|
444 with no duplicate entries, with ascending row indices of the nonzeros\n\ |
|
|
445 in each column, with a non-negative number of entries in each column (!)\n\ |
|
|
446 and so on. If a matrix is invalid, then SYMAMD may or may not be able\n\ |
|
|
447 to continue. If there are duplicate entries (a row index appears two or\n\ |
|
|
448 more times in the same column) or if the row indices in a column are out\n\ |
|
|
449 of order, then SYMAMD can correct these errors by ignoring the duplicate\n\ |
|
|
450 entries and sorting each column of its internal copy of the matrix S (the\n\ |
|
|
451 input matrix S is not repaired, however). If a matrix is invalid in\n\ |
|
|
452 other ways then SYMAMD cannot continue, an error message is printed, and\n\ |
|
|
453 no output arguments (@var{p} or @var{stats}) are returned. SYMAMD is\n\ |
|
|
454 thus a simple way to check a sparse matrix to see if it's valid.\n\ |
|
|
455 \n\ |
|
|
456 @code{@var{stats} (4:7)} provide information if SYMAMD was able to\n\ |
|
|
457 continue. The matrix is OK if @code{@var{stats} (4)} is zero, or 1\n\ |
|
|
458 if invalid. @code{@var{stats} (5)} is the rightmost column index that\n\ |
|
|
459 is unsorted or contains duplicate entries, or zero if no such column\n\ |
|
|
460 exists. @code{@var{stats} (6)} is the last seen duplicate or out-of-order\n\ |
|
|
461 row index in the column index given by @code{@var{stats} (5)}, or zero\n\ |
|
|
462 if no such row index exists. @code{@var{stats} (7)} is the number of\n\ |
|
|
463 duplicate or out-of-order row indices. @code{@var{stats} (8:20)} is\n\ |
|
|
464 always zero in the current version of SYMAMD (reserved for future use).\n\ |
|
|
465 \n\ |
|
|
466 The ordering is followed by a column elimination tree post-ordering.\n\ |
|
|
467 \n\ |
|
|
468 \n\ |
|
|
469 The authors of the code itself are Stefan I. Larimore and Timothy A.\n\ |
|
|
470 Davis (davis@@cise.ufl.edu), University of Florida. The algorithm was\n\ |
|
|
471 developed in collaboration with John Gilbert, Xerox PARC, and Esmond\n\ |
|
|
472 Ng, Oak Ridge National Laboratory. (see\n\ |
|
|
473 @url{http://www.cise.ufl.edu/research/sparse/colamd})\n\ |
|
|
474 @end deftypefn\n\ |
|
|
475 @seealso{colperm, colamd}") |
|
|
476 { |
|
|
477 octave_value_list retval; |
|
5297
|
478 |
|
|
479 #if SIZEOF_INT == SIZEOF_OCTAVE_IDX_TYPE |
|
|
480 |
|
5164
|
481 int nargin = args.length (); |
|
|
482 int spumoni = 0; |
|
|
483 |
|
|
484 if (nargout < 0 || nargout > 2 || nargin < 0 || nargin > 2) |
|
|
485 usage ("symamd: incorrect number of input and/or output arguments"); |
|
|
486 else |
|
|
487 { |
|
|
488 // Get knobs |
|
|
489 OCTAVE_LOCAL_BUFFER (double, knobs, COLAMD_KNOBS); |
|
|
490 colamd_set_defaults (knobs); |
|
|
491 |
|
|
492 // Check for user-passed knobs |
|
|
493 if (nargin == 2) |
|
|
494 { |
|
|
495 NDArray User_knobs = args(1).array_value (); |
|
|
496 int nel_User_knobs = User_knobs.length (); |
|
|
497 |
|
|
498 if (nel_User_knobs > 0) |
|
|
499 knobs [COLAMD_DENSE_ROW] = User_knobs (COLAMD_DENSE_ROW); |
|
|
500 if (nel_User_knobs > 1) |
|
|
501 spumoni = (int) User_knobs (1); |
|
|
502 } |
|
|
503 |
|
|
504 // print knob settings if spumoni is set |
|
|
505 if (spumoni > 0) |
|
|
506 octave_stdout << "symamd: dense row/col fraction: " |
|
|
507 << knobs [COLAMD_DENSE_ROW] << std::endl; |
|
|
508 |
|
|
509 int n_row, n_col, nnz; |
|
|
510 int *ridx, *cidx; |
|
|
511 SparseMatrix sm; |
|
|
512 SparseComplexMatrix scm; |
|
|
513 |
|
|
514 if (args(0).class_name () == "sparse") |
|
|
515 { |
|
|
516 if (args(0).is_complex_type ()) |
|
|
517 { |
|
|
518 scm = args(0).sparse_complex_matrix_value (); |
|
|
519 n_row = scm.rows (); |
|
|
520 n_col = scm.cols (); |
|
|
521 nnz = scm.nnz (); |
|
|
522 ridx = scm.xridx (); |
|
|
523 cidx = scm.xcidx (); |
|
|
524 } |
|
|
525 else |
|
|
526 { |
|
|
527 sm = args(0).sparse_matrix_value (); |
|
|
528 n_row = sm.rows (); |
|
|
529 n_col = sm.cols (); |
|
|
530 nnz = sm.nnz (); |
|
|
531 ridx = sm.xridx (); |
|
|
532 cidx = sm.xcidx (); |
|
|
533 } |
|
|
534 } |
|
|
535 else |
|
|
536 { |
|
|
537 if (args(0).is_complex_type ()) |
|
|
538 sm = SparseMatrix (real (args(0).complex_matrix_value ())); |
|
|
539 else |
|
|
540 sm = SparseMatrix (args(0).matrix_value ()); |
|
|
541 |
|
|
542 n_row = sm.rows (); |
|
|
543 n_col = sm.cols (); |
|
|
544 nnz = sm.nnz (); |
|
|
545 ridx = sm.xridx (); |
|
|
546 cidx = sm.xcidx (); |
|
|
547 } |
|
|
548 |
|
|
549 if (n_row != n_col) |
|
|
550 { |
|
|
551 error ("symamd: matrix must be square"); |
|
|
552 return retval; |
|
|
553 } |
|
|
554 |
|
|
555 // Allocate workspace for symamd |
|
|
556 OCTAVE_LOCAL_BUFFER (int, perm, n_col+1); |
|
|
557 OCTAVE_LOCAL_BUFFER (int, stats, COLAMD_STATS); |
|
|
558 if (!symamd (n_col, ridx, cidx, perm, knobs, stats, &calloc, &free)) |
|
|
559 { |
|
|
560 symamd_report (stats) ; |
|
|
561 error ("symamd: internal error!") ; |
|
|
562 return retval; |
|
|
563 } |
|
|
564 |
|
|
565 // column elimination tree post-ordering |
|
|
566 OCTAVE_LOCAL_BUFFER (int, etree, n_col + 1); |
|
|
567 symetree (ridx, cidx, etree, perm, n_col); |
|
|
568 |
|
|
569 // Calculate the tree post-ordering |
|
|
570 OCTAVE_LOCAL_BUFFER (int, post, n_col + 1); |
|
|
571 TreePostorder (n_col, etree, post); |
|
|
572 |
|
|
573 // return the permutation vector |
|
|
574 NDArray out_perm (dim_vector (1, n_col)); |
|
|
575 for (int i = 0; i < n_col; i++) |
|
|
576 out_perm(i) = perm [post [i]] + 1; |
|
|
577 |
|
|
578 retval (0) = out_perm; |
|
|
579 |
|
|
580 // print stats if spumoni > 0 |
|
|
581 if (spumoni > 0) |
|
|
582 symamd_report (stats) ; |
|
|
583 |
|
|
584 // Return the stats vector |
|
|
585 if (nargout == 2) |
|
|
586 { |
|
|
587 NDArray out_stats (dim_vector (1, COLAMD_STATS)); |
|
|
588 for (int i = 0 ; i < COLAMD_STATS ; i++) |
|
|
589 out_stats (i) = stats [i] ; |
|
|
590 retval(1) = out_stats; |
|
|
591 |
|
|
592 // fix stats (5) and (6), for 1-based information on |
|
|
593 // jumbled matrix. note that this correction doesn't |
|
|
594 // occur if symamd returns FALSE |
|
|
595 out_stats (COLAMD_INFO1) ++ ; |
|
|
596 out_stats (COLAMD_INFO2) ++ ; |
|
|
597 } |
|
|
598 } |
|
|
599 |
|
5297
|
600 #else |
|
|
601 |
|
|
602 error ("symamd: not available in this version of Octave"); |
|
|
603 |
|
|
604 #endif |
|
|
605 |
|
5164
|
606 return retval; |
|
|
607 } |
|
|
608 |
|
|
609 DEFUN_DLD (etree, args, nargout, |
|
|
610 "-*- texinfo -*-\n\ |
|
|
611 @deftypefn {Loadable Function} {@var{p} =} etree (@var{s})\n\ |
|
|
612 @deftypefnx {Loadable Function} {@var{p} =} etree (@var{s}, @var{typ})\n\ |
|
|
613 @deftypefnx {Loadable Function} {[@var{p}, @var{q}] =} etree (@var{s}, @var{typ})\n\ |
|
|
614 \n\ |
|
|
615 Returns the elimination tree for the matrix @var{s}. By default @var{s}\n\ |
|
|
616 is assumed to be symmetric and the symmetric elimination tree is\n\ |
|
|
617 returned. The argument @var{typ} controls whether a symmetric or\n\ |
|
|
618 column elimination tree is returned. Valid values of @var{typ} are\n\ |
|
|
619 'sym' or 'col', for symmetric or column elimination tree respectively\n\ |
|
|
620 \n\ |
|
|
621 Called with a second argument, @dfn{etree} also returns the postorder\n\ |
|
|
622 permutations on the tree.\n\ |
|
|
623 @end deftypefn") |
|
|
624 { |
|
|
625 octave_value_list retval; |
|
5297
|
626 |
|
|
627 #if SIZEOF_INT == SIZEOF_OCTAVE_IDX_TYPE |
|
|
628 |
|
5164
|
629 int nargin = args.length (); |
|
|
630 |
|
|
631 if (nargout < 0 || nargout > 2 || nargin < 0 || nargin > 2) |
|
|
632 usage ("etree: incorrect number of input and/or output arguments"); |
|
|
633 else |
|
|
634 { |
|
|
635 int n_row, n_col, nnz; |
|
|
636 int *ridx, *cidx; |
|
|
637 bool is_sym = true; |
|
|
638 SparseMatrix sm; |
|
|
639 SparseComplexMatrix scm; |
|
|
640 |
|
|
641 if (args(0).class_name () == "sparse") |
|
|
642 { |
|
|
643 if (args(0).is_complex_type ()) |
|
|
644 { |
|
|
645 scm = args(0).sparse_complex_matrix_value (); |
|
|
646 n_row = scm.rows (); |
|
|
647 n_col = scm.cols (); |
|
|
648 nnz = scm.nnz (); |
|
|
649 ridx = scm.xridx (); |
|
|
650 cidx = scm.xcidx (); |
|
|
651 } |
|
|
652 else |
|
|
653 { |
|
|
654 sm = args(0).sparse_matrix_value (); |
|
|
655 n_row = sm.rows (); |
|
|
656 n_col = sm.cols (); |
|
|
657 nnz = sm.nnz (); |
|
|
658 ridx = sm.xridx (); |
|
|
659 cidx = sm.xcidx (); |
|
|
660 } |
|
|
661 |
|
|
662 } |
|
|
663 else |
|
|
664 { |
|
|
665 error ("etree: must be called with a sparse matrix"); |
|
|
666 return retval; |
|
|
667 } |
|
|
668 |
|
|
669 if (nargin == 2) |
|
|
670 if (args(1).is_string ()) |
|
|
671 { |
|
|
672 std::string str = args(1).string_value (); |
|
|
673 if (str.find("C") == 0 || str.find("c") == 0) |
|
|
674 is_sym = false; |
|
|
675 } |
|
|
676 else |
|
|
677 { |
|
|
678 error ("etree: second argument must be a string"); |
|
|
679 return retval; |
|
|
680 } |
|
|
681 |
|
|
682 // column elimination tree post-ordering (reuse variables) |
|
|
683 OCTAVE_LOCAL_BUFFER (int, etree, n_col + 1); |
|
|
684 |
|
|
685 |
|
|
686 if (is_sym) |
|
|
687 { |
|
|
688 if (n_row != n_col) |
|
|
689 { |
|
|
690 error ("etree: matrix is marked as symmetric, but not square"); |
|
|
691 return retval; |
|
|
692 } |
|
|
693 symetree (ridx, cidx, etree, NULL, n_col); |
|
|
694 } |
|
|
695 else |
|
|
696 { |
|
|
697 OCTAVE_LOCAL_BUFFER (int, colbeg, n_col); |
|
|
698 OCTAVE_LOCAL_BUFFER (int, colend, n_col); |
|
|
699 |
|
|
700 for (int i = 0; i < n_col; i++) |
|
|
701 { |
|
|
702 colbeg[i] = cidx[i]; |
|
|
703 colend[i] = cidx[i+1]; |
|
|
704 } |
|
|
705 |
|
|
706 coletree (ridx, colbeg, colend, etree, n_row, n_col); |
|
|
707 } |
|
|
708 |
|
|
709 NDArray tree (dim_vector (1, n_col)); |
|
|
710 for (int i = 0; i < n_col; i++) |
|
|
711 // We flag a root with n_col while Matlab does it with zero |
|
|
712 // Convert for matlab compatiable output |
|
|
713 if (etree[i] == n_col) |
|
|
714 tree (i) = 0; |
|
|
715 else |
|
|
716 tree (i) = etree[i] + 1; |
|
|
717 |
|
|
718 retval (0) = tree; |
|
|
719 |
|
|
720 if (nargout == 2) |
|
|
721 { |
|
|
722 // Calculate the tree post-ordering |
|
|
723 OCTAVE_LOCAL_BUFFER (int, post, n_col + 1); |
|
|
724 TreePostorder (n_col, etree, post); |
|
|
725 |
|
|
726 NDArray postorder (dim_vector (1, n_col)); |
|
|
727 for (int i = 0; i < n_col; i++) |
|
|
728 postorder (i) = post[i] + 1; |
|
|
729 |
|
|
730 retval (1) = postorder; |
|
|
731 } |
|
|
732 } |
|
|
733 |
|
5297
|
734 #else |
|
|
735 |
|
|
736 error ("etree: not available in this version of Octave"); |
|
|
737 |
|
|
738 #endif |
|
|
739 |
|
5164
|
740 return retval; |
|
|
741 } |
|
|
742 |
|
|
743 DEFUN_DLD (symbfact, args, nargout, |
|
|
744 "-*- texinfo -*-\n\ |
|
|
745 @deftypefn {Loadable Function} {[@var{count}, @var{h}, @var{parent}, @var{post}, @var{r}]} = symbfact (@var{s}, @var{typ})\n\ |
|
|
746 \n\ |
|
|
747 Performs a symbolic factorization analysis on the sparse matrix @var{s}.\n\ |
|
|
748 @end deftypefn") |
|
|
749 { |
|
|
750 error ("symbfact: not implemented yet"); |
|
|
751 return octave_value (); |
|
|
752 } |
|
|
753 |
|
|
754 /* |
|
|
755 ;;; Local Variables: *** |
|
|
756 ;;; mode: C++ *** |
|
|
757 ;;; End: *** |
|
|
758 */ |
