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1 /* |
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2 |
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3 Copyright (C) 2005, 2006, 2007 David Bateman |
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4 Copyright (C) 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005 Andy Adler |
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5 |
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6 This file is part of Octave. |
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7 |
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8 Octave is free software; you can redistribute it and/or modify it |
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9 under the terms of the GNU General Public License as published by the |
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10 Free Software Foundation; either version 3 of the License, or (at your |
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11 option) any later version. |
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12 |
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13 Octave is distributed in the hope that it will be useful, but WITHOUT |
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14 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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15 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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16 for more details. |
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17 |
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18 You should have received a copy of the GNU General Public License |
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19 along with Octave; see the file COPYING. If not, see |
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20 <http://www.gnu.org/licenses/>. |
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21 |
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22 */ |
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23 |
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24 #ifdef HAVE_CONFIG_H |
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25 #include <config.h> |
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26 #endif |
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27 |
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28 #include "defun-dld.h" |
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29 #include "error.h" |
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30 #include "gripes.h" |
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31 #include "oct-obj.h" |
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32 #include "utils.h" |
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33 |
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34 #include "SparseCmplxCHOL.h" |
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35 #include "SparsedbleCHOL.h" |
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36 #include "ov-re-sparse.h" |
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37 #include "ov-cx-sparse.h" |
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38 #include "oct-spparms.h" |
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39 #include "sparse-util.h" |
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40 |
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41 static octave_value_list |
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42 sparse_chol (const octave_value_list& args, const int nargout, |
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43 const std::string& name, const bool LLt) |
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44 { |
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45 octave_value_list retval; |
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46 int nargin = args.length (); |
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47 |
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48 if (nargin != 1 || nargout > 3) |
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49 { |
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50 print_usage (); |
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51 return retval; |
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52 } |
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53 |
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54 octave_value arg = args(0); |
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55 |
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56 octave_idx_type nr = arg.rows (); |
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57 octave_idx_type nc = arg.columns (); |
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58 bool natural = (nargout != 3); |
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59 |
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60 int arg_is_empty = empty_arg (name.c_str(), nr, nc); |
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61 |
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62 if (arg_is_empty < 0) |
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63 return retval; |
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64 if (arg_is_empty > 0) |
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65 return octave_value (Matrix ()); |
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66 |
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67 if (arg.is_real_type ()) |
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68 { |
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69 SparseMatrix m = arg.sparse_matrix_value (); |
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70 |
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71 if (! error_state) |
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72 { |
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73 octave_idx_type info; |
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74 SparseCHOL fact (m, info, natural); |
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75 if (nargout == 3) |
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76 retval(2) = fact.Q(); |
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77 |
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78 if (nargout > 1 || info == 0) |
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79 { |
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80 retval(1) = fact.P(); |
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81 if (LLt) |
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82 retval(0) = fact.L(); |
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83 else |
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84 retval(0) = fact.R(); |
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85 } |
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86 else |
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87 error ("%s: matrix not positive definite", name.c_str()); |
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88 } |
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89 } |
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90 else if (arg.is_complex_type ()) |
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91 { |
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92 SparseComplexMatrix m = arg.sparse_complex_matrix_value (); |
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93 |
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94 if (! error_state) |
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95 { |
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96 octave_idx_type info; |
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97 SparseComplexCHOL fact (m, info, natural); |
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98 |
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99 if (nargout == 3) |
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100 retval(2) = fact.Q(); |
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101 |
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102 if (nargout > 1 || info == 0) |
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103 { |
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104 retval(1) = fact.P(); |
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105 if (LLt) |
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106 retval(0) = fact.L(); |
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107 else |
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108 retval(0) = fact.R(); |
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109 } |
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110 else |
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111 error ("%s: matrix not positive definite", name.c_str()); |
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112 } |
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113 } |
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114 else |
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115 gripe_wrong_type_arg (name.c_str(), arg); |
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116 |
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117 return retval; |
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118 } |
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119 |
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120 // PKG_ADD: dispatch ("chol", "spchol", "sparse matrix"); |
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121 // PKG_ADD: dispatch ("chol", "spchol", "sparse complex matrix"); |
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122 // PKG_ADD: dispatch ("chol", "spchol", "sparse bool matrix"); |
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123 DEFUN_DLD (spchol, args, nargout, |
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124 "-*- texinfo -*-\n\ |
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125 @deftypefn {Loadable Function} {@var{r} =} spchol (@var{a})\n\ |
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126 @deftypefnx {Loadable Function} {[@var{r}, @var{p}] =} spchol (@var{a})\n\ |
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127 @deftypefnx {Loadable Function} {[@var{r}, @var{p}, @var{q}] =} spchol (@var{a})\n\ |
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128 @cindex Cholesky factorization\n\ |
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129 Compute the Cholesky factor, @var{r}, of the symmetric positive definite\n\ |
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130 sparse matrix @var{a}, where\n\ |
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131 @iftex\n\ |
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132 @tex\n\ |
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133 $ R^T R = A $.\n\ |
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134 @end tex\n\ |
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135 @end iftex\n\ |
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136 @ifinfo\n\ |
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137 \n\ |
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138 @example\n\ |
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139 r' * r = a.\n\ |
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140 @end example\n\ |
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141 @end ifinfo\n\ |
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142 \n\ |
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143 If called with 2 or more outputs @var{p} is the 0 when @var{r} is positive\n\ |
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144 definite and @var{p} is a positive integer otherwise.\n\ |
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145 \n\ |
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146 If called with 3 outputs then a sparsity preserving row/column permutation\n\ |
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147 is applied to @var{a} prior to the factorization. That is @var{r}\n\ |
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148 is the factorization of @code{@var{a}(@var{q},@var{q})} such that\n\ |
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149 @iftex\n\ |
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150 @tex\n\ |
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151 $ R^T R = Q A Q^T$.\n\ |
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152 @end tex\n\ |
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153 @end iftex\n\ |
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154 @ifinfo\n\ |
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155 \n\ |
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156 @example\n\ |
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157 r' * r = q * a * q'.\n\ |
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158 @end example\n\ |
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159 @end ifinfo\n\ |
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160 \n\ |
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161 Note that @code{splchol} factorization is faster and uses less memory.\n\ |
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162 @seealso{spcholinv, spchol2inv, splchol}\n\ |
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163 @end deftypefn") |
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164 { |
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165 return sparse_chol (args, nargout, "spchol", false); |
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166 } |
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167 |
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168 // PKG_ADD: dispatch ("lchol", "splchol", "sparse matrix"); |
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169 // PKG_ADD: dispatch ("lchol", "splchol", "sparse complex matrix"); |
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170 // PKG_ADD: dispatch ("lchol", "splchol", "sparse bool matrix"); |
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171 DEFUN_DLD (splchol, args, nargout, |
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172 "-*- texinfo -*-\n\ |
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173 @deftypefn {Loadable Function} {@var{l} =} splchol (@var{a})\n\ |
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174 @deftypefnx {Loadable Function} {[@var{l}, @var{p}] =} splchol (@var{a})\n\ |
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175 @deftypefnx {Loadable Function} {[@var{l}, @var{p}, @var{q}] =} splchol (@var{a})\n\ |
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176 @cindex Cholesky factorization\n\ |
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177 Compute the Cholesky factor, @var{l}, of the symmetric positive definite\n\ |
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178 sparse matrix @var{a}, where\n\ |
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179 @iftex\n\ |
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180 @tex\n\ |
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181 $ L L^T = A $.\n\ |
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182 @end tex\n\ |
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183 @end iftex\n\ |
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184 @ifinfo\n\ |
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185 \n\ |
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186 @example\n\ |
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187 l * l' = a.\n\ |
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188 @end example\n\ |
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189 @end ifinfo\n\ |
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190 \n\ |
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191 If called with 2 or more outputs @var{p} is the 0 when @var{l} is positive\n\ |
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192 definite and @var{l} is a positive integer otherwise.\n\ |
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193 \n\ |
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194 If called with 3 outputs that a sparsity preserving row/column permutation\n\ |
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195 is applied to @var{a} prior to the factorization. That is @var{l}\n\ |
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196 is the factorization of @code{@var{a}(@var{q},@var{q})} such that\n\ |
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197 @iftex\n\ |
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198 @tex\n\ |
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199 $ L R^T = A (Q, Q)$.\n\ |
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200 @end tex\n\ |
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201 @end iftex\n\ |
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202 @ifinfo\n\ |
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203 \n\ |
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204 @example\n\ |
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205 r * r' = a (q, q).\n\ |
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206 @end example\n\ |
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207 @end ifinfo\n\ |
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208 \n\ |
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209 Note that @code{splchol} factorization is faster and uses less memory\n\ |
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210 than @code{spchol}. @code{splchol(@var{a})} is equivalent to\n\ |
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211 @code{spchol(@var{a})'}.\n\ |
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212 @seealso{spcholinv, spchol2inv, splchol}\n\ |
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213 @end deftypefn") |
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214 { |
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215 return sparse_chol (args, nargout, "splchol", true); |
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216 } |
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217 |
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218 // PKG_ADD: dispatch ("cholinv", "spcholinv", "sparse matrix"); |
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219 // PKG_ADD: dispatch ("cholinv", "spcholinv", "sparse complex matrix"); |
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220 // PKG_ADD: dispatch ("cholinv", "spcholinv", "sparse bool matrix"); |
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221 DEFUN_DLD (spcholinv, args, , |
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222 "-*- texinfo -*-\n\ |
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223 @deftypefn {Loadable Function} {} spcholinv (@var{a})\n\ |
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224 Use the Cholesky factorization to compute the inverse of the\n\ |
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225 sparse symmetric positive definite matrix @var{a}.\n\ |
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226 @seealso{spchol, spchol2inv}\n\ |
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227 @end deftypefn") |
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228 { |
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229 octave_value retval; |
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230 |
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231 int nargin = args.length (); |
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232 |
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233 if (nargin == 1) |
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234 { |
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235 octave_value arg = args(0); |
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236 |
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237 octave_idx_type nr = arg.rows (); |
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238 octave_idx_type nc = arg.columns (); |
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239 |
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240 if (nr == 0 || nc == 0) |
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241 retval = Matrix (); |
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242 else |
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243 { |
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244 if (arg.is_real_type ()) |
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245 { |
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246 SparseMatrix m = arg.sparse_matrix_value (); |
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247 |
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248 if (! error_state) |
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249 { |
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250 octave_idx_type info; |
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251 SparseCHOL chol (m, info); |
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252 if (info == 0) |
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253 retval = chol.inverse (); |
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254 else |
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255 error ("spcholinv: matrix not positive definite"); |
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256 } |
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257 } |
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258 else if (arg.is_complex_type ()) |
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259 { |
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260 SparseComplexMatrix m = arg.sparse_complex_matrix_value (); |
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261 |
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262 if (! error_state) |
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263 { |
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264 octave_idx_type info; |
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265 SparseComplexCHOL chol (m, info); |
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266 if (info == 0) |
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267 retval = chol.inverse (); |
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268 else |
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269 error ("spcholinv: matrix not positive definite"); |
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270 } |
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271 } |
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272 else |
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273 gripe_wrong_type_arg ("spcholinv", arg); |
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274 } |
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275 } |
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276 else |
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277 print_usage (); |
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278 |
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279 return retval; |
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280 } |
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281 |
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282 // PKG_ADD: dispatch ("chol2inv", "spchol2inv", "sparse matrix"); |
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283 // PKG_ADD: dispatch ("chol2inv", "spchol2inv", "sparse complex matrix"); |
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284 // PKG_ADD: dispatch ("chol2inv", "spchol2inv", "sparse bool matrix"); |
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285 DEFUN_DLD (spchol2inv, args, , |
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286 "-*- texinfo -*-\n\ |
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287 @deftypefn {Loadable Function} {} spchol2inv (@var{u})\n\ |
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288 Invert a sparse symmetric, positive definite square matrix from its\n\ |
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289 Cholesky decomposition, @var{u}. Note that @var{u} should be an\n\ |
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290 upper-triangular matrix with positive diagonal elements.\n\ |
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291 @code{chol2inv (@var{u})} provides @code{inv (@var{u}'*@var{u})} but\n\ |
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292 it is much faster than using @code{inv}.\n\ |
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293 @seealso{spchol, spcholinv}\n\ |
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294 @end deftypefn") |
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295 { |
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296 octave_value retval; |
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297 |
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298 int nargin = args.length (); |
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299 |
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300 if (nargin == 1) |
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301 { |
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302 octave_value arg = args(0); |
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303 |
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304 octave_idx_type nr = arg.rows (); |
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305 octave_idx_type nc = arg.columns (); |
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306 |
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307 if (nr == 0 || nc == 0) |
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308 retval = Matrix (); |
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309 else |
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310 { |
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311 if (arg.is_real_type ()) |
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312 { |
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313 SparseMatrix r = arg.sparse_matrix_value (); |
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314 |
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315 if (! error_state) |
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316 retval = chol2inv (r); |
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317 } |
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318 else if (arg.is_complex_type ()) |
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319 { |
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320 SparseComplexMatrix r = arg.sparse_complex_matrix_value (); |
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321 |
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322 if (! error_state) |
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323 retval = chol2inv (r); |
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324 } |
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325 else |
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326 gripe_wrong_type_arg ("spchol2inv", arg); |
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327 } |
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328 } |
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329 else |
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330 print_usage (); |
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331 |
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332 return retval; |
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333 } |
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334 |
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335 DEFUN_DLD (symbfact, args, nargout, |
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336 "-*- texinfo -*-\n\ |
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337 @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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338 \n\ |
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339 Performs a symbolic factorization analysis on the sparse matrix @var{s}.\n\ |
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340 Where\n\ |
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341 \n\ |
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342 @table @asis\n\ |
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343 @item @var{s}\n\ |
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344 @var{s} is a complex or real sparse matrix.\n\ |
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345 \n\ |
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346 @item @var{typ}\n\ |
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347 Is the type of the factorization and can be one of\n\ |
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348 \n\ |
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349 @table @code\n\ |
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350 @item sym\n\ |
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351 Factorize @var{s}. This is the default.\n\ |
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352 \n\ |
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353 @item col\n\ |
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354 Factorize @code{@var{s}' * @var{s}}.\n\ |
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355 @item row\n\ |
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356 Factorize @code{@var{s} * @var{s}'}.\n\ |
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357 @item lo\n\ |
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358 Factorize @code{@var{s}'}\n\ |
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359 @end table\n\ |
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360 \n\ |
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361 @item @var{mode}\n\ |
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362 The default is to return the Cholesky factorization for @var{r}, and if\n\ |
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363 @var{mode} is 'L', the conjugate transpose of the Cholesky factorization\n\ |
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364 is returned. The conjugate transpose version is faster and uses less\n\ |
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365 memory, but returns the same values for @var{count}, @var{h}, @var{parent}\n\ |
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366 and @var{post} outputs.\n\ |
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367 @end table\n\ |
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368 \n\ |
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369 The output variables are\n\ |
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370 \n\ |
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371 @table @asis\n\ |
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372 @item @var{count}\n\ |
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373 The row counts of the Cholesky factorization as determined by @var{typ}.\n\ |
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374 \n\ |
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375 @item @var{h}\n\ |
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376 The height of the elimination tree.\n\ |
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377 \n\ |
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378 @item @var{parent}\n\ |
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379 The elimination tree itself.\n\ |
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380 \n\ |
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381 @item @var{post}\n\ |
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382 A sparse boolean matrix whose structure is that of the Cholesky\n\ |
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383 factorization as determined by @var{typ}.\n\ |
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384 @end table\n\ |
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385 @end deftypefn") |
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386 { |
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387 octave_value_list retval; |
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388 int nargin = args.length (); |
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389 |
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390 if (nargin < 1 || nargin > 3 || nargout > 5) |
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391 { |
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392 print_usage (); |
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393 return retval; |
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394 } |
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395 |
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396 #ifdef HAVE_CHOLMOD |
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397 |
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398 cholmod_common Common; |
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399 cholmod_common *cm = &Common; |
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400 CHOLMOD_NAME(start) (cm); |
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401 |
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402 double spu = octave_sparse_params::get_key ("spumoni"); |
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403 if (spu == 0.) |
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404 { |
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405 cm->print = -1; |
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406 cm->print_function = NULL; |
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407 } |
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408 else |
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409 { |
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410 cm->print = static_cast<int> (spu) + 2; |
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411 cm->print_function =&SparseCholPrint; |
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412 } |
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413 |
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414 cm->error_handler = &SparseCholError; |
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415 cm->complex_divide = CHOLMOD_NAME(divcomplex); |
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416 cm->hypotenuse = CHOLMOD_NAME(hypot); |
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417 |
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418 double dummy; |
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419 cholmod_sparse Astore; |
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420 cholmod_sparse *A = &Astore; |
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421 A->packed = true; |
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422 A->sorted = true; |
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423 A->nz = NULL; |
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424 #ifdef IDX_TYPE_LONG |
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425 A->itype = CHOLMOD_LONG; |
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426 #else |
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427 A->itype = CHOLMOD_INT; |
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428 #endif |
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429 A->dtype = CHOLMOD_DOUBLE; |
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430 A->stype = 1; |
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431 A->x = &dummy; |
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432 |
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433 if (args(0).is_real_type ()) |
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434 { |
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435 const SparseMatrix a = args(0).sparse_matrix_value(); |
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436 A->nrow = a.rows(); |
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437 A->ncol = a.cols(); |
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|
438 A->p = a.cidx(); |
|
|
439 A->i = a.ridx(); |
|
5604
|
440 A->nzmax = a.nnz(); |
|
5506
|
441 A->xtype = CHOLMOD_REAL; |
|
|
442 |
|
|
443 if (a.rows() > 0 && a.cols() > 0) |
|
|
444 A->x = a.data(); |
|
|
445 } |
|
|
446 else if (args(0).is_complex_type ()) |
|
|
447 { |
|
|
448 const SparseComplexMatrix a = args(0).sparse_complex_matrix_value(); |
|
|
449 A->nrow = a.rows(); |
|
|
450 A->ncol = a.cols(); |
|
|
451 A->p = a.cidx(); |
|
|
452 A->i = a.ridx(); |
|
5604
|
453 A->nzmax = a.nnz(); |
|
5506
|
454 A->xtype = CHOLMOD_COMPLEX; |
|
|
455 |
|
|
456 if (a.rows() > 0 && a.cols() > 0) |
|
|
457 A->x = a.data(); |
|
|
458 } |
|
|
459 else |
|
|
460 gripe_wrong_type_arg ("symbfact", arg(0)); |
|
|
461 |
|
5527
|
462 octave_idx_type coletree = false; |
|
5506
|
463 octave_idx_type n = A->nrow; |
|
|
464 |
|
|
465 if (nargin > 1) |
|
|
466 { |
|
|
467 char ch; |
|
|
468 std::string str = args(1).string_value(); |
|
|
469 ch = tolower (str.c_str()[0]); |
|
|
470 if (ch == 'r') |
|
|
471 A->stype = 0; |
|
|
472 else if (ch == 'c') |
|
|
473 { |
|
|
474 n = A->ncol; |
|
5527
|
475 coletree = true; |
|
5506
|
476 A->stype = 0; |
|
|
477 } |
|
|
478 else if (ch == 's') |
|
|
479 A->stype = 1; |
|
|
480 else if (ch == 's') |
|
|
481 A->stype = -1; |
|
|
482 else |
|
|
483 error ("Unrecognized typ in symbolic factorization"); |
|
|
484 } |
|
|
485 |
|
|
486 if (A->stype && A->nrow != A->ncol) |
|
|
487 error ("Matrix must be square"); |
|
|
488 |
|
|
489 if (!error_state) |
|
|
490 { |
|
|
491 OCTAVE_LOCAL_BUFFER (octave_idx_type, Parent, n); |
|
|
492 OCTAVE_LOCAL_BUFFER (octave_idx_type, Post, n); |
|
|
493 OCTAVE_LOCAL_BUFFER (octave_idx_type, ColCount, n); |
|
|
494 OCTAVE_LOCAL_BUFFER (octave_idx_type, First, n); |
|
|
495 OCTAVE_LOCAL_BUFFER (octave_idx_type, Level, n); |
|
|
496 |
|
|
497 cholmod_sparse *F = CHOLMOD_NAME(transpose) (A, 0, cm); |
|
|
498 cholmod_sparse *Aup, *Alo; |
|
|
499 |
|
|
500 if (A->stype == 1 || coletree) |
|
|
501 { |
|
|
502 Aup = A ; |
|
|
503 Alo = F ; |
|
|
504 } |
|
|
505 else |
|
|
506 { |
|
|
507 Aup = F ; |
|
|
508 Alo = A ; |
|
|
509 } |
|
|
510 |
|
|
511 CHOLMOD_NAME(etree) (Aup, Parent, cm); |
|
|
512 |
|
|
513 if (cm->status < CHOLMOD_OK) |
|
|
514 { |
|
|
515 error("matrix corrupted"); |
|
|
516 goto symbfact_error; |
|
|
517 } |
|
|
518 |
|
|
519 if (CHOLMOD_NAME(postorder) (Parent, n, NULL, Post, cm) != n) |
|
|
520 { |
|
|
521 error("postorder failed"); |
|
|
522 goto symbfact_error; |
|
|
523 } |
|
|
524 |
|
|
525 CHOLMOD_NAME(rowcolcounts) (Alo, NULL, 0, Parent, Post, NULL, |
|
|
526 ColCount, First, Level, cm); |
|
|
527 |
|
|
528 if (cm->status < CHOLMOD_OK) |
|
|
529 { |
|
|
530 error("matrix corrupted"); |
|
|
531 goto symbfact_error; |
|
|
532 } |
|
|
533 |
|
|
534 if (nargout > 4) |
|
|
535 { |
|
|
536 cholmod_sparse *A1, *A2; |
|
|
537 |
|
|
538 if (A->stype == 1) |
|
|
539 { |
|
|
540 A1 = A; |
|
|
541 A2 = NULL; |
|
|
542 } |
|
|
543 else if (A->stype == -1) |
|
|
544 { |
|
|
545 A1 = F; |
|
|
546 A2 = NULL; |
|
|
547 } |
|
|
548 else if (coletree) |
|
|
549 { |
|
|
550 A1 = F; |
|
|
551 A2 = A; |
|
|
552 } |
|
|
553 else |
|
|
554 { |
|
|
555 A1 = A; |
|
|
556 A2 = F; |
|
|
557 } |
|
|
558 |
|
|
559 // count the total number of entries in L |
|
|
560 octave_idx_type lnz = 0 ; |
|
|
561 for (octave_idx_type j = 0 ; j < n ; j++) |
|
|
562 lnz += ColCount [j] ; |
|
|
563 |
|
|
564 |
|
|
565 // allocate the output matrix L (pattern-only) |
|
|
566 SparseBoolMatrix L (n, n, lnz); |
|
|
567 |
|
|
568 // initialize column pointers |
|
|
569 lnz = 0; |
|
|
570 for (octave_idx_type j = 0 ; j < n ; j++) |
|
|
571 { |
|
|
572 L.xcidx(j) = lnz; |
|
|
573 lnz += ColCount [j]; |
|
|
574 } |
|
|
575 L.xcidx(n) = lnz; |
|
|
576 |
|
|
577 |
|
|
578 /* create a copy of the column pointers */ |
|
|
579 octave_idx_type *W = First; |
|
|
580 for (octave_idx_type j = 0 ; j < n ; j++) |
|
|
581 W [j] = L.xcidx(j); |
|
|
582 |
|
|
583 // get workspace for computing one row of L |
|
5527
|
584 cholmod_sparse *R = cholmod_allocate_sparse (n, 1, n, false, true, |
|
5506
|
585 0, CHOLMOD_PATTERN, cm); |
|
|
586 octave_idx_type *Rp = static_cast<octave_idx_type *>(R->p); |
|
|
587 octave_idx_type *Ri = static_cast<octave_idx_type *>(R->i); |
|
|
588 |
|
|
589 // compute L one row at a time |
|
|
590 for (octave_idx_type k = 0 ; k < n ; k++) |
|
|
591 { |
|
|
592 // get the kth row of L and store in the columns of L |
|
5717
|
593 CHOLMOD_NAME (row_subtree) (A1, A2, k, Parent, R, cm) ; |
|
5506
|
594 for (octave_idx_type p = 0 ; p < Rp [1] ; p++) |
|
|
595 L.xridx (W [Ri [p]]++) = k ; |
|
|
596 |
|
|
597 // add the diagonal entry |
|
|
598 L.xridx (W [k]++) = k ; |
|
|
599 } |
|
|
600 |
|
|
601 // free workspace |
|
|
602 cholmod_free_sparse (&R, cm) ; |
|
|
603 |
|
|
604 |
|
|
605 // transpose L to get R, or leave as is |
|
|
606 if (nargin < 3) |
|
|
607 L = L.transpose (); |
|
|
608 |
|
|
609 // fill numerical values of L with one's |
|
|
610 for (octave_idx_type p = 0 ; p < lnz ; p++) |
|
|
611 L.xdata(p) = true; |
|
|
612 |
|
|
613 retval(4) = L; |
|
|
614 } |
|
|
615 |
|
|
616 ColumnVector tmp (n); |
|
|
617 if (nargout > 3) |
|
|
618 { |
|
|
619 for (octave_idx_type i = 0; i < n; i++) |
|
|
620 tmp(i) = Post[i] + 1; |
|
|
621 retval(3) = tmp; |
|
|
622 } |
|
|
623 |
|
|
624 if (nargout > 2) |
|
|
625 { |
|
|
626 for (octave_idx_type i = 0; i < n; i++) |
|
|
627 tmp(i) = Parent[i] + 1; |
|
|
628 retval(2) = tmp; |
|
|
629 } |
|
|
630 |
|
|
631 if (nargout > 1) |
|
|
632 { |
|
|
633 /* compute the elimination tree height */ |
|
|
634 octave_idx_type height = 0 ; |
|
|
635 for (int i = 0 ; i < n ; i++) |
|
|
636 height = (height > Level[i] ? height : Level[i]); |
|
|
637 height++ ; |
|
5760
|
638 retval(1) = static_cast<double> (height); |
|
5506
|
639 } |
|
|
640 |
|
|
641 for (octave_idx_type i = 0; i < n; i++) |
|
|
642 tmp(i) = ColCount[i]; |
|
|
643 retval(0) = tmp; |
|
|
644 } |
|
|
645 |
|
5512
|
646 symbfact_error: |
|
|
647 #else |
|
|
648 error ("symbfact: not available in this version of Octave"); |
|
|
649 #endif |
|
|
650 |
|
5506
|
651 return retval; |
|
|
652 } |
|
|
653 |
|
|
654 /* |
|
|
655 ;;; Local Variables: *** |
|
|
656 ;;; mode: C++ *** |
|
|
657 ;;; End: *** |
|
|
658 */ |
|
|
659 |
