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1 /* |
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2 |
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3 Copyright (C) 2005 David Bateman |
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4 Copyright (C) 1998-2005 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 #ifdef HAVE_CONFIG_H |
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24 #include <config.h> |
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25 #endif |
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26 |
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27 #include "defun-dld.h" |
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28 #include "error.h" |
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29 #include "gripes.h" |
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30 #include "oct-obj.h" |
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31 #include "utils.h" |
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32 |
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33 #include "SparseCmplxCHOL.h" |
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34 #include "SparsedbleCHOL.h" |
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35 #include "ov-re-sparse.h" |
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36 #include "ov-cx-sparse.h" |
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37 #include "oct-spparms.h" |
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38 #include "sparse-util.h" |
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39 |
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40 static octave_value_list |
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41 sparse_chol (const octave_value_list& args, const int nargout, |
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42 const std::string& name, const bool LLt) |
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43 { |
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44 octave_value_list retval; |
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45 int nargin = args.length (); |
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46 |
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47 if (nargin != 1 || nargout > 3) |
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48 { |
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49 print_usage (name); |
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50 return retval; |
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51 } |
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52 |
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53 octave_value arg = args(0); |
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54 |
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55 octave_idx_type nr = arg.rows (); |
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56 octave_idx_type nc = arg.columns (); |
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57 bool natural = (nargout != 3); |
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58 |
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59 int arg_is_empty = empty_arg (name.c_str(), nr, nc); |
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60 |
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61 if (arg_is_empty < 0) |
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62 return retval; |
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63 if (arg_is_empty > 0) |
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64 return octave_value (Matrix ()); |
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65 |
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66 if (arg.is_real_type ()) |
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67 { |
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68 SparseMatrix m = arg.sparse_matrix_value (); |
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69 |
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70 if (! error_state) |
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71 { |
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72 octave_idx_type info; |
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73 SparseCHOL fact (m, info, natural); |
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74 if (nargout == 3) |
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75 retval(2) = fact.Q(); |
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76 |
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77 if (nargout > 1 || info == 0) |
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78 { |
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79 retval(1) = fact.P(); |
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80 if (LLt) |
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81 retval(0) = fact.L(); |
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82 else |
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83 retval(0) = fact.R(); |
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84 } |
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85 else |
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86 error ("%s: matrix not positive definite", name.c_str()); |
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87 } |
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88 } |
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89 else if (arg.is_complex_type ()) |
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90 { |
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91 SparseComplexMatrix m = arg.sparse_complex_matrix_value (); |
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92 |
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93 if (! error_state) |
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94 { |
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95 octave_idx_type info; |
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96 SparseComplexCHOL fact (m, info, natural); |
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97 |
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98 if (nargout == 3) |
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99 retval(2) = fact.Q(); |
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100 |
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101 if (nargout > 1 || info == 0) |
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102 { |
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103 retval(1) = fact.P(); |
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104 if (LLt) |
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105 retval(0) = fact.L(); |
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106 else |
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107 retval(0) = fact.R(); |
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108 } |
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109 else |
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110 error ("%s: matrix not positive definite", name.c_str()); |
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111 } |
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112 } |
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113 else |
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114 gripe_wrong_type_arg (name.c_str(), arg); |
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115 |
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116 return retval; |
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117 } |
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118 |
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119 // PKG_ADD: dispatch ("chol", "spchol", "sparse matrix"); |
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120 // PKG_ADD: dispatch ("chol", "spchol", "sparse complex matrix"); |
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121 // PKG_ADD: dispatch ("chol", "spchol", "sparse bool matrix"); |
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122 DEFUN_DLD (spchol, args, nargout, |
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123 "-*- texinfo -*-\n\ |
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124 @deftypefn {Loadable Function} {@var{r} =} spchol (@var{a})\n\ |
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125 @deftypefnx {Loadable Function} {[@var{r}, @var{p}] =} spchol (@var{a})\n\ |
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126 @deftypefnx {Loadable Function} {[@var{r}, @var{p}, @var{q}] =} spchol (@var{a})\n\ |
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127 @cindex Cholesky factorization\n\ |
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128 Compute the Cholesky factor, @var{r}, of the symmetric positive definite\n\ |
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129 sparse matrix @var{a}, where\n\ |
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130 @iftex\n\ |
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131 @tex\n\ |
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132 $ R^T R = A $.\n\ |
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133 @end tex\n\ |
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134 @end iftex\n\ |
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135 @ifinfo\n\ |
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136 \n\ |
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137 @example\n\ |
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138 r' * r = a.\n\ |
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139 @end example\n\ |
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140 @end ifinfo\n\ |
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141 \n\ |
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142 If called with 2 or more outputs @var{p} is the 0 when @var{r} is positive\n\ |
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143 definite and @var{p} is a positive integer otherwise.\n\ |
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144 \n\ |
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145 If called with 3 outputs then a sparsity preserving row/column permutation\n\ |
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146 is applied to @var{a} prior to the factorization. That is @var{r}\n\ |
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147 is the factorization of @code{@var{a}(@var{q},@var{q})} such that\n\ |
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148 @iftex\n\ |
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149 @tex\n\ |
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150 $ R^T R = Q A Q^T$.\n\ |
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151 @end tex\n\ |
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152 @end iftex\n\ |
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153 @ifinfo\n\ |
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154 \n\ |
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155 @example\n\ |
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156 r' * r = q * a * q'.\n\ |
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157 @end example\n\ |
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158 @end ifinfo\n\ |
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159 \n\ |
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160 Note that @code{splchol} factorizations is faster and use less memory.\n\ |
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161 @end deftypefn\n\ |
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162 @seealso{spcholinv, spchol2inv, splchol}") |
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163 { |
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164 return sparse_chol (args, nargout, "spchol", false); |
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165 } |
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166 |
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167 // PKG_ADD: dispatch ("lchol", "splchol", "sparse matrix"); |
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168 // PKG_ADD: dispatch ("lchol", "splchol", "sparse complex matrix"); |
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169 // PKG_ADD: dispatch ("lchol", "splchol", "sparse bool matrix"); |
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170 DEFUN_DLD (splchol, args, nargout, |
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171 "-*- texinfo -*-\n\ |
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172 @deftypefn {Loadable Function} {@var{l} =} splchol (@var{a})\n\ |
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173 @deftypefnx {Loadable Function} {[@var{l}, @var{p}] =} splchol (@var{a})\n\ |
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174 @deftypefnx {Loadable Function} {[@var{l}, @var{p}, @var{q}] =} splchol (@var{a})\n\ |
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175 @cindex Cholesky factorization\n\ |
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176 Compute the Cholesky factor, @var{l}, of the symmetric positive definite\n\ |
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177 sparse matrix @var{a}, where\n\ |
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178 @iftex\n\ |
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179 @tex\n\ |
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180 $ L L^T = A $.\n\ |
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181 @end tex\n\ |
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182 @end iftex\n\ |
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183 @ifinfo\n\ |
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184 \n\ |
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185 @example\n\ |
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186 l * l' = a.\n\ |
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187 @end example\n\ |
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188 @end ifinfo\n\ |
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189 \n\ |
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190 If called with 2 or more outputs @var{p} is the 0 when @var{l} is positive\n\ |
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191 definite and @var{l} is a positive integer otherwise.\n\ |
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192 \n\ |
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193 If called with 3 outputs that a sparsity preserving row/column permutation\n\ |
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194 is applied to @var{a} prior to the factorization. That is @var{l}\n\ |
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195 is the factorization of @code{@var{a}(@var{q},@var{q})} such that\n\ |
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196 @iftex\n\ |
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197 @tex\n\ |
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198 $ L R^T = A (Q, Q)$.\n\ |
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199 @end tex\n\ |
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200 @end iftex\n\ |
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201 @ifinfo\n\ |
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202 \n\ |
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203 @example\n\ |
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204 r * r' = a (q, q).\n\ |
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205 @end example\n\ |
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206 @end ifinfo\n\ |
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207 \n\ |
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208 Note that @code{splchol} factorizations is faster and use less memory\n\ |
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209 than @code{spchol}. @code{splchol(@var{a})} is equivalent to\n\ |
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210 @code{spchol(@var{a})'}.\n\ |
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211 @end deftypefn\n\ |
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212 @seealso{spcholinv, spchol2inv, splchol}") |
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213 { |
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214 return sparse_chol (args, nargout, "splchol", true); |
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215 } |
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216 |
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217 // PKG_ADD: dispatch ("cholinv", "spcholinv", "sparse matrix"); |
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218 // PKG_ADD: dispatch ("cholinv", "spcholinv", "sparse complex matrix"); |
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219 // PKG_ADD: dispatch ("cholinv", "spcholinv", "sparse bool matrix"); |
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220 DEFUN_DLD (spcholinv, args, , |
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221 "-*- texinfo -*-\n\ |
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222 @deftypefn {Loadable Function} {} spcholinv (@var{a})\n\ |
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223 Use the Cholesky factorization to compute the inverse of the\n\ |
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224 sparse symmetric positive definite matrix @var{a}.\n\ |
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225 @seealso{spchol, spchol2inv}\n\ |
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226 @end deftypefn") |
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227 { |
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228 octave_value retval; |
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229 |
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230 int nargin = args.length (); |
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231 |
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232 if (nargin == 1) |
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233 { |
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234 octave_value arg = args(0); |
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235 |
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236 octave_idx_type nr = arg.rows (); |
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237 octave_idx_type nc = arg.columns (); |
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238 |
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239 if (nr == 0 || nc == 0) |
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240 retval = Matrix (); |
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241 else |
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242 { |
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243 if (arg.is_real_type ()) |
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244 { |
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245 SparseMatrix m = arg.sparse_matrix_value (); |
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246 |
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247 if (! error_state) |
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248 { |
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249 octave_idx_type info; |
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250 SparseCHOL chol (m, info); |
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251 if (info == 0) |
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252 retval = chol.inverse (); |
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253 else |
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254 error ("spcholinv: matrix not positive definite"); |
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255 } |
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256 } |
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257 else if (arg.is_complex_type ()) |
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258 { |
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259 SparseComplexMatrix m = arg.sparse_complex_matrix_value (); |
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260 |
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261 if (! error_state) |
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262 { |
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263 octave_idx_type info; |
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264 SparseComplexCHOL chol (m, info); |
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265 if (info == 0) |
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266 retval = chol.inverse (); |
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267 else |
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268 error ("spcholinv: matrix not positive definite"); |
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269 } |
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270 } |
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271 else |
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272 gripe_wrong_type_arg ("spcholinv", arg); |
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273 } |
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274 } |
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275 else |
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276 print_usage ("spcholinv"); |
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277 |
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278 return retval; |
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279 } |
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280 |
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281 // PKG_ADD: dispatch ("chol2inv", "spchol2inv", "sparse matrix"); |
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282 // PKG_ADD: dispatch ("chol2inv", "spchol2inv", "sparse complex matrix"); |
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283 // PKG_ADD: dispatch ("chol2inv", "spchol2inv", "sparse bool matrix"); |
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284 DEFUN_DLD (spchol2inv, args, , |
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285 "-*- texinfo -*-\n\ |
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286 @deftypefn {Loadable Function} {} spchol2inv (@var{u})\n\ |
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287 Invert a sparse symmetric, positive definite square matrix from its\n\ |
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288 Cholesky decomposition, @var{u}. Note that @var{u} should be an\n\ |
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289 upper-triangular matrix with positive diagonal elements.\n\ |
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290 @code{chol2inv (@var{u})} provides @code{inv (@var{u}'*@var{u})} but\n\ |
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291 it is much faster than using @code{inv}.\n\ |
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292 @seealso{spchol, spcholinv}\n\ |
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293 @end deftypefn") |
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294 { |
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295 octave_value retval; |
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296 |
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297 int nargin = args.length (); |
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298 |
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299 if (nargin == 1) |
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300 { |
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301 octave_value arg = args(0); |
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302 |
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303 octave_idx_type nr = arg.rows (); |
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304 octave_idx_type nc = arg.columns (); |
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305 |
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306 if (nr == 0 || nc == 0) |
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307 retval = Matrix (); |
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308 else |
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309 { |
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310 if (arg.is_real_type ()) |
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311 { |
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312 SparseMatrix r = arg.sparse_matrix_value (); |
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313 |
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314 if (! error_state) |
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315 retval = chol2inv (r); |
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316 } |
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317 else if (arg.is_complex_type ()) |
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318 { |
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319 SparseComplexMatrix r = arg.sparse_complex_matrix_value (); |
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320 |
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321 if (! error_state) |
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322 retval = chol2inv (r); |
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323 } |
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324 else |
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325 gripe_wrong_type_arg ("spchol2inv", arg); |
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326 } |
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327 } |
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328 else |
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329 print_usage ("spchol2inv"); |
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330 |
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331 return retval; |
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332 } |
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333 |
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334 DEFUN_DLD (symbfact, args, nargout, |
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335 "-*- texinfo -*-\n\ |
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336 @deftypefn {Loadable Function} {[@var{count}, @var{h}, @var{parent}, @var{post}, @var{r}]} = symbfact (@var{s}, @var{typ}, @var{mode})\n\ |
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337 \n\ |
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338 Performs a symbolic factorization analysis on the sparse matrix @var{s}.\n\ |
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339 Where\n\ |
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340 \n\ |
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341 @table @asis\n\ |
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342 @item @var{s}\n\ |
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343 @var{s} is a complex or real sparse matrix.\n\ |
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344 \n\ |
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345 @item @var{typ}\n\ |
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346 Is the type of the factorization and can be one of\n\ |
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347 \n\ |
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348 @table @code\n\ |
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349 @item sym\n\ |
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350 Factorize @var{s}. This is the default.\n\ |
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351 \n\ |
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352 @item col\n\ |
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353 Factorize @code{@var{s}' * @var{s}}.\n\ |
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354 @item row\n\ |
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355 Factorize @code{@var{s} * @var{s}'}.\n\ |
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356 @item lo\n\ |
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357 Factorize @code{@var{s}'}\n\ |
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358 @end table\n\ |
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359 \n\ |
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360 @item @var{mode}\n\ |
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361 The default is to return the Cholesky factorization for @var{r}, and if\n\ |
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362 @var{mode} is 'L', the conjugate transpose of the Choleksy factorization\n\ |
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363 is returned. The conjugate transpose version is faster and uses less\n\ |
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364 memory, but returns the same values for @var{count}, @var{h}, @var{parent}\n\ |
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365 and @var{post} outputs.\n\ |
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366 @end table\n\ |
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367 \n\ |
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368 The output variables are\n\ |
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369 \n\ |
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370 @table @asis\n\ |
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371 @item @var{count}\n\ |
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372 The row counts of the Cholesky factorization as determined by @var{typ}.\n\ |
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373 \n\ |
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374 @item @var{h}\n\ |
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375 The height of the elimination tree.\n\ |
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376 \n\ |
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377 @item @var{parent}\n\ |
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378 The elimination tree itself.\n\ |
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379 \n\ |
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380 @item @var{post}\n\ |
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381 A sparse boolean matrix whose structure is that of the Cholesky\n\ |
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382 factorization as determined by @var{typ}.\n\ |
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383 @end table\n\ |
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384 @end deftypefn") |
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385 { |
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386 octave_value_list retval; |
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387 int nargin = args.length (); |
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388 |
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389 if (nargin < 1 || nargin > 3 || nargout > 5) |
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390 { |
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391 print_usage ("symbfact"); |
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392 return retval; |
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393 } |
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394 |
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5512
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395 #ifdef HAVE_CHOLMOD |
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396 |
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5506
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397 cholmod_common Common; |
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398 cholmod_common *cm = &Common; |
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399 CHOLMOD_NAME(start) (cm); |
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400 |
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401 double spu = Voctave_sparse_controls.get_key ("spumoni"); |
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402 if (spu == 0.) |
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403 { |
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404 cm->print = -1; |
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405 cm->print_function = NULL; |
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406 } |
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407 else |
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408 { |
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409 cm->print = (int)spu + 2; |
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410 cm->print_function =&SparseCholPrint; |
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411 } |
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412 |
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413 cm->error_handler = &SparseCholError; |
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414 cm->complex_divide = CHOLMOD_NAME(divcomplex); |
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415 cm->hypotenuse = CHOLMOD_NAME(hypot); |
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416 |
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417 #ifdef HAVE_METIS |
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418 // METIS 4.0.1 uses malloc and free, and will terminate MATLAB if it runs |
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419 // out of memory. Use CHOLMOD's memory guard for METIS, which mxMalloc's |
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420 // a huge block of memory (and then immediately mxFree's it) before calling |
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421 // METIS |
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422 cm->metis_memory = 2.0; |
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423 |
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424 #if defined(METIS_VERSION) |
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425 #if (METIS_VERSION >= METIS_VER(4,0,2)) |
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426 // METIS 4.0.2 uses function pointers for malloc and free |
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427 METIS_malloc = cm->malloc_memory; |
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428 METIS_free = cm->free_memory; |
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429 // Turn off METIS memory guard. It is not needed, because mxMalloc will |
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430 // safely terminate the mexFunction and free any workspace without killing |
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431 // all of MATLAB. |
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432 cm->metis_memory = 0.0; |
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433 #endif |
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434 #endif |
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435 #endif |
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436 |
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437 double dummy; |
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438 cholmod_sparse Astore; |
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439 cholmod_sparse *A = &Astore; |
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440 A->packed = true; |
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441 A->sorted = true; |
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5506
|
442 A->nz = NULL; |
|
|
443 #ifdef IDX_TYPE_LONG |
|
|
444 A->itype = CHOLMOD_LONG; |
|
|
445 #else |
|
|
446 A->itype = CHOLMOD_INT; |
|
|
447 #endif |
|
|
448 A->dtype = CHOLMOD_DOUBLE; |
|
|
449 A->stype = 1; |
|
|
450 A->x = &dummy; |
|
|
451 |
|
|
452 if (args(0).is_real_type ()) |
|
|
453 { |
|
|
454 const SparseMatrix a = args(0).sparse_matrix_value(); |
|
|
455 A->nrow = a.rows(); |
|
|
456 A->ncol = a.cols(); |
|
|
457 A->p = a.cidx(); |
|
|
458 A->i = a.ridx(); |
|
|
459 A->nzmax = a.nonzero(); |
|
|
460 A->xtype = CHOLMOD_REAL; |
|
|
461 |
|
|
462 if (a.rows() > 0 && a.cols() > 0) |
|
|
463 A->x = a.data(); |
|
|
464 } |
|
|
465 else if (args(0).is_complex_type ()) |
|
|
466 { |
|
|
467 const SparseComplexMatrix a = args(0).sparse_complex_matrix_value(); |
|
|
468 A->nrow = a.rows(); |
|
|
469 A->ncol = a.cols(); |
|
|
470 A->p = a.cidx(); |
|
|
471 A->i = a.ridx(); |
|
|
472 A->nzmax = a.nonzero(); |
|
|
473 A->xtype = CHOLMOD_COMPLEX; |
|
|
474 |
|
|
475 if (a.rows() > 0 && a.cols() > 0) |
|
|
476 A->x = a.data(); |
|
|
477 } |
|
|
478 else |
|
|
479 gripe_wrong_type_arg ("symbfact", arg(0)); |
|
|
480 |
|
5527
|
481 octave_idx_type coletree = false; |
|
5506
|
482 octave_idx_type n = A->nrow; |
|
|
483 |
|
|
484 if (nargin > 1) |
|
|
485 { |
|
|
486 char ch; |
|
|
487 std::string str = args(1).string_value(); |
|
|
488 ch = tolower (str.c_str()[0]); |
|
|
489 if (ch == 'r') |
|
|
490 A->stype = 0; |
|
|
491 else if (ch == 'c') |
|
|
492 { |
|
|
493 n = A->ncol; |
|
5527
|
494 coletree = true; |
|
5506
|
495 A->stype = 0; |
|
|
496 } |
|
|
497 else if (ch == 's') |
|
|
498 A->stype = 1; |
|
|
499 else if (ch == 's') |
|
|
500 A->stype = -1; |
|
|
501 else |
|
|
502 error ("Unrecognized typ in symbolic factorization"); |
|
|
503 } |
|
|
504 |
|
|
505 if (A->stype && A->nrow != A->ncol) |
|
|
506 error ("Matrix must be square"); |
|
|
507 |
|
|
508 if (!error_state) |
|
|
509 { |
|
|
510 OCTAVE_LOCAL_BUFFER (octave_idx_type, Parent, n); |
|
|
511 OCTAVE_LOCAL_BUFFER (octave_idx_type, Post, n); |
|
|
512 OCTAVE_LOCAL_BUFFER (octave_idx_type, ColCount, n); |
|
|
513 OCTAVE_LOCAL_BUFFER (octave_idx_type, First, n); |
|
|
514 OCTAVE_LOCAL_BUFFER (octave_idx_type, Level, n); |
|
|
515 |
|
|
516 cholmod_sparse *F = CHOLMOD_NAME(transpose) (A, 0, cm); |
|
|
517 cholmod_sparse *Aup, *Alo; |
|
|
518 |
|
|
519 if (A->stype == 1 || coletree) |
|
|
520 { |
|
|
521 Aup = A ; |
|
|
522 Alo = F ; |
|
|
523 } |
|
|
524 else |
|
|
525 { |
|
|
526 Aup = F ; |
|
|
527 Alo = A ; |
|
|
528 } |
|
|
529 |
|
|
530 CHOLMOD_NAME(etree) (Aup, Parent, cm); |
|
|
531 |
|
|
532 if (cm->status < CHOLMOD_OK) |
|
|
533 { |
|
|
534 error("matrix corrupted"); |
|
|
535 goto symbfact_error; |
|
|
536 } |
|
|
537 |
|
|
538 if (CHOLMOD_NAME(postorder) (Parent, n, NULL, Post, cm) != n) |
|
|
539 { |
|
|
540 error("postorder failed"); |
|
|
541 goto symbfact_error; |
|
|
542 } |
|
|
543 |
|
|
544 CHOLMOD_NAME(rowcolcounts) (Alo, NULL, 0, Parent, Post, NULL, |
|
|
545 ColCount, First, Level, cm); |
|
|
546 |
|
|
547 if (cm->status < CHOLMOD_OK) |
|
|
548 { |
|
|
549 error("matrix corrupted"); |
|
|
550 goto symbfact_error; |
|
|
551 } |
|
|
552 |
|
|
553 if (nargout > 4) |
|
|
554 { |
|
|
555 cholmod_sparse *A1, *A2; |
|
|
556 |
|
|
557 if (A->stype == 1) |
|
|
558 { |
|
|
559 A1 = A; |
|
|
560 A2 = NULL; |
|
|
561 } |
|
|
562 else if (A->stype == -1) |
|
|
563 { |
|
|
564 A1 = F; |
|
|
565 A2 = NULL; |
|
|
566 } |
|
|
567 else if (coletree) |
|
|
568 { |
|
|
569 A1 = F; |
|
|
570 A2 = A; |
|
|
571 } |
|
|
572 else |
|
|
573 { |
|
|
574 A1 = A; |
|
|
575 A2 = F; |
|
|
576 } |
|
|
577 |
|
|
578 // count the total number of entries in L |
|
|
579 octave_idx_type lnz = 0 ; |
|
|
580 for (octave_idx_type j = 0 ; j < n ; j++) |
|
|
581 lnz += ColCount [j] ; |
|
|
582 |
|
|
583 |
|
|
584 // allocate the output matrix L (pattern-only) |
|
|
585 SparseBoolMatrix L (n, n, lnz); |
|
|
586 |
|
|
587 // initialize column pointers |
|
|
588 lnz = 0; |
|
|
589 for (octave_idx_type j = 0 ; j < n ; j++) |
|
|
590 { |
|
|
591 L.xcidx(j) = lnz; |
|
|
592 lnz += ColCount [j]; |
|
|
593 } |
|
|
594 L.xcidx(n) = lnz; |
|
|
595 |
|
|
596 |
|
|
597 /* create a copy of the column pointers */ |
|
|
598 octave_idx_type *W = First; |
|
|
599 for (octave_idx_type j = 0 ; j < n ; j++) |
|
|
600 W [j] = L.xcidx(j); |
|
|
601 |
|
|
602 // get workspace for computing one row of L |
|
5527
|
603 cholmod_sparse *R = cholmod_allocate_sparse (n, 1, n, false, true, |
|
5506
|
604 0, CHOLMOD_PATTERN, cm); |
|
|
605 octave_idx_type *Rp = static_cast<octave_idx_type *>(R->p); |
|
|
606 octave_idx_type *Ri = static_cast<octave_idx_type *>(R->i); |
|
|
607 |
|
|
608 // compute L one row at a time |
|
|
609 for (octave_idx_type k = 0 ; k < n ; k++) |
|
|
610 { |
|
|
611 // get the kth row of L and store in the columns of L |
|
|
612 cholmod_row_subtree (A1, A2, k, Parent, R, cm) ; |
|
|
613 for (octave_idx_type p = 0 ; p < Rp [1] ; p++) |
|
|
614 L.xridx (W [Ri [p]]++) = k ; |
|
|
615 |
|
|
616 // add the diagonal entry |
|
|
617 L.xridx (W [k]++) = k ; |
|
|
618 } |
|
|
619 |
|
|
620 // free workspace |
|
|
621 cholmod_free_sparse (&R, cm) ; |
|
|
622 |
|
|
623 |
|
|
624 // transpose L to get R, or leave as is |
|
|
625 if (nargin < 3) |
|
|
626 L = L.transpose (); |
|
|
627 |
|
|
628 // fill numerical values of L with one's |
|
|
629 for (octave_idx_type p = 0 ; p < lnz ; p++) |
|
|
630 L.xdata(p) = true; |
|
|
631 |
|
|
632 retval(4) = L; |
|
|
633 } |
|
|
634 |
|
|
635 ColumnVector tmp (n); |
|
|
636 if (nargout > 3) |
|
|
637 { |
|
|
638 for (octave_idx_type i = 0; i < n; i++) |
|
|
639 tmp(i) = Post[i] + 1; |
|
|
640 retval(3) = tmp; |
|
|
641 } |
|
|
642 |
|
|
643 if (nargout > 2) |
|
|
644 { |
|
|
645 for (octave_idx_type i = 0; i < n; i++) |
|
|
646 tmp(i) = Parent[i] + 1; |
|
|
647 retval(2) = tmp; |
|
|
648 } |
|
|
649 |
|
|
650 if (nargout > 1) |
|
|
651 { |
|
|
652 /* compute the elimination tree height */ |
|
|
653 octave_idx_type height = 0 ; |
|
|
654 for (int i = 0 ; i < n ; i++) |
|
|
655 height = (height > Level[i] ? height : Level[i]); |
|
|
656 height++ ; |
|
|
657 retval(1) = (double)height; |
|
|
658 } |
|
|
659 |
|
|
660 for (octave_idx_type i = 0; i < n; i++) |
|
|
661 tmp(i) = ColCount[i]; |
|
|
662 retval(0) = tmp; |
|
|
663 } |
|
|
664 |
|
5512
|
665 symbfact_error: |
|
|
666 #else |
|
|
667 error ("symbfact: not available in this version of Octave"); |
|
|
668 #endif |
|
|
669 |
|
5506
|
670 return retval; |
|
|
671 } |
|
|
672 |
|
|
673 /* |
|
|
674 ;;; Local Variables: *** |
|
|
675 ;;; mode: C++ *** |
|
|
676 ;;; End: *** |
|
|
677 */ |
|
|
678 |
