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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 |
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5 Octave is free software; you can redistribute it and/or modify it |
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6 under the terms of the GNU General Public License as published by the |
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7 Free Software Foundation; either version 2, or (at your option) any |
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8 later version. |
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9 |
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10 Octave is distributed in the hope that it will be useful, but WITHOUT |
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11 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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12 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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13 for more details. |
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14 |
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15 You should have received a copy of the GNU General Public License |
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16 along with this program; see the file COPYING. If not, write to the |
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17 Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, |
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18 Boston, MA 02110-1301, USA. |
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19 |
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20 */ |
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21 |
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22 #ifdef HAVE_CONFIG_H |
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23 #include <config.h> |
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24 #endif |
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25 |
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26 #include "defun-dld.h" |
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27 #include "error.h" |
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28 #include "gripes.h" |
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29 #include "oct-obj.h" |
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30 #include "utils.h" |
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31 #include "oct-map.h" |
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32 |
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33 #include "MatrixType.h" |
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34 #include "SparseCmplxLU.h" |
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35 #include "SparsedbleLU.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 |
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39 DEFUN_DLD (luinc, args, nargout, |
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40 "-*- texinfo -*-\n\ |
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41 @deftypefn {Loadable Function} {[@var{l}, @var{u}, @var{p}, @var{q}] =} luinc (@var{a}, '0')\n\ |
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42 @deftypefnx {Loadable Function} {[@var{l}, @var{u}, @var{p}, @var{q}] =} luinc (@var{a}, @var{droptol})\n\ |
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43 @deftypefnx {Loadable Function} {[@var{l}, @var{u}, @var{p}, @var{q}] =} luinc (@var{a}, @var{opts})\n\ |
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44 @cindex LU decomposition\n\ |
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45 Produce the incomplete LU factorization of the sparse matrix @var{a}.\n\ |
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46 Two types of incomplete factorization are possible, and the type\n\ |
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47 is determined by the second argument to @dfn{luinc}.\n\ |
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48 \n\ |
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49 Called with a second argument of '0', the zero-level incomplete\n\ |
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50 LU factorization is produced. This creates a factorization of @var{a}\n\ |
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51 where the position of the non-zero arguments correspond to the same\n\ |
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52 positions as in the matrix @var{a}.\n\ |
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53 \n\ |
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54 Alternatively, the fill-in of the incomplete LU factorization can\n\ |
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55 be controlled through the variable @var{droptol} or the structure\n\ |
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56 @var{opts}. The UMFPACK multifrontal factorization code by Tim A.\n\ |
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57 Davis is used for the incomplete LU factorication, (availability\n\ |
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58 @url{http://www.cise.ufl.edu/research/sparse/umfpack/})\n\ |
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59 \n\ |
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60 @var{droptol} determines the values below which the values in the LU\n\ |
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61 factorization are dropped and replaced by zero. It must be a positive\n\ |
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62 scalar, and any values in the factorization whose absolute value are\n\ |
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63 less than this value are dropped, expect if leaving them increase the\n\ |
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64 sparsity of the matrix. Setting @var{droptol} to zero results in a\n\ |
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65 complete LU factorization which is the default.\n\ |
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66 \n\ |
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67 @var{opts} is a structure containing one or more of the fields\n\ |
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68 \n\ |
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69 @table @code\n\ |
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70 @item droptol\n\ |
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71 The drop tolerance as above. If @var{opts} only contains @code{droptol}\n\ |
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72 then this is equivalent to using the variable @var{droptol}.\n\ |
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73 \n\ |
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74 @item milu\n\ |
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75 A logical variable flagging whether to use the modified incomplete LU\n\ |
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76 factorization. In the case that @code{milu} is true, the dropped values\n\ |
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77 are subtract from the diagonal of the matrix U of the factorization.\n\ |
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78 The default is @code{false}.\n\ |
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79 \n\ |
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80 @item udiag\n\ |
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81 A logical variable that flags whether zero elements on the diagonal of U\n\ |
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82 should be replaced with @var{droptol} to attempt to avoid singular\n\ |
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83 factors. The default is @code{false}.\n\ |
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84 \n\ |
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85 @item thresh\n\ |
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86 Defines the pivot threshold in the interval [0,1]. Values outside that\n\ |
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87 range are ignored.\n\ |
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88 @end table\n\ |
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89 \n\ |
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90 All other fields in @var{opts} are ignored. The outputs from @dfn{luinc}\n\ |
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91 are the same as for @dfn{lu}.\n\ |
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92 @seealso{sparse, lu, cholinc}\n\ |
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93 @end deftypefn") |
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94 { |
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95 int nargin = args.length (); |
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96 octave_value_list retval; |
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97 |
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98 if (nargin == 0) |
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99 print_usage (); |
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100 else if (nargin != 2) |
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101 error ("luinc: incorrect number of arguments"); |
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102 else |
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103 { |
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104 bool zero_level = false; |
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105 bool milu = false; |
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106 bool udiag = false; |
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107 bool thresh = -1; |
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108 double droptol = -1.; |
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109 |
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110 if (args(1).is_string ()) |
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111 { |
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112 if (args(1).string_value () == "0") |
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113 zero_level = true; |
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114 else |
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115 error ("luinc: unrecognized string argument"); |
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116 } |
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117 else if (args(1).is_map ()) |
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118 { |
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119 Octave_map map = args(1).map_value (); |
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120 |
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121 if (map.contains ("droptol")) |
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122 droptol = map.contents ("droptol")(0).double_value (); |
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123 |
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124 if (map.contains ("milu")) |
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125 { |
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126 double tmp = map.contents ("milu")(0).double_value (); |
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127 |
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128 milu = (tmp == 0. ? false : true); |
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129 } |
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130 |
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131 if (map.contains ("udiag")) |
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132 { |
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133 double tmp = map.contents ("udiag")(0).double_value (); |
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134 |
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135 udiag = (tmp == 0. ? false : true); |
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136 } |
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137 |
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138 if (map.contains ("thresh")) |
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139 thresh = map.contents ("thresh")(0).double_value (); |
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140 } |
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141 else |
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142 droptol = args(1).double_value (); |
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143 |
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144 // FIXME Add code for zero-level factorization |
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145 if (zero_level) |
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146 error ("luinc: zero-level factorization not implemented"); |
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147 |
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148 if (!error_state) |
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149 { |
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150 if (args(0).type_name () == "sparse matrix") |
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151 { |
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152 SparseMatrix sm = args(0).sparse_matrix_value (); |
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153 octave_idx_type sm_nr = sm.rows (); |
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154 octave_idx_type sm_nc = sm.cols (); |
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155 ColumnVector Qinit (sm_nc); |
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156 |
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157 for (octave_idx_type i = 0; i < sm_nc; i++) |
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158 Qinit (i) = i; |
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159 |
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160 if (! error_state) |
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161 { |
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162 switch (nargout) |
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163 { |
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164 case 0: |
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165 case 1: |
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166 case 2: |
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167 { |
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168 SparseLU fact (sm, Qinit, thresh, true, droptol, |
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169 milu, udiag); |
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170 |
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171 SparseMatrix P = fact.Pr (); |
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172 SparseMatrix L = P.transpose () * fact.L (); |
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173 retval(1) = octave_value (fact.U (), |
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174 MatrixType (MatrixType::Upper)); |
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175 retval(0) = octave_value (L, MatrixType |
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176 (MatrixType::Permuted_Lower, |
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177 sm_nr, fact.row_perm ())); |
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178 } |
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179 break; |
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180 |
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181 case 3: |
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182 { |
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183 SparseLU fact (sm, Qinit, thresh, true, droptol, |
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184 milu, udiag); |
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185 |
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186 retval(2) = fact.Pr (); |
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187 retval(1) = octave_value (fact.U (), |
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188 MatrixType (MatrixType::Upper)); |
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189 retval(0) = octave_value (fact.L (), |
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190 MatrixType (MatrixType::Lower)); |
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191 } |
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192 break; |
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193 |
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194 case 4: |
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195 default: |
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196 { |
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197 SparseLU fact (sm, Qinit, thresh, false, droptol, |
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198 milu, udiag); |
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199 |
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200 retval(3) = fact.Pc (); |
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201 retval(2) = fact.Pr (); |
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202 retval(1) = octave_value (fact.U (), |
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203 MatrixType (MatrixType::Upper)); |
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204 retval(0) = octave_value (fact.L (), |
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205 MatrixType (MatrixType::Lower)); |
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206 } |
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207 break; |
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208 } |
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209 } |
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210 } |
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211 else if (args(0).type_name () == "sparse complex matrix") |
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212 { |
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213 SparseComplexMatrix sm = |
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214 args(0).sparse_complex_matrix_value (); |
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215 octave_idx_type sm_nr = sm.rows (); |
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216 octave_idx_type sm_nc = sm.cols (); |
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217 ColumnVector Qinit (sm_nc); |
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218 |
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219 for (octave_idx_type i = 0; i < sm_nc; i++) |
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220 Qinit (i) = i; |
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221 |
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222 if (! error_state) |
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223 { |
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224 switch (nargout) |
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225 { |
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226 case 0: |
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227 case 1: |
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228 case 2: |
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229 { |
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230 SparseComplexLU fact (sm, Qinit, thresh, true, |
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231 droptol, milu, udiag); |
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232 |
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233 SparseMatrix P = fact.Pr (); |
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234 SparseComplexMatrix L = P.transpose () * fact.L (); |
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235 retval(1) = octave_value (fact.U (), |
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236 MatrixType (MatrixType::Upper)); |
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237 retval(0) = octave_value (L, MatrixType |
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238 (MatrixType::Permuted_Lower, |
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239 sm_nr, fact.row_perm ())); |
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240 } |
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241 break; |
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242 |
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243 case 3: |
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244 { |
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245 SparseComplexLU fact (sm, Qinit, thresh, true, |
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246 droptol, milu, udiag); |
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247 |
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248 retval(2) = fact.Pr (); |
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249 retval(1) = octave_value (fact.U (), |
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250 MatrixType (MatrixType::Upper)); |
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251 retval(0) = octave_value (fact.L (), |
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252 MatrixType (MatrixType::Lower)); |
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253 } |
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254 break; |
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255 |
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256 case 4: |
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257 default: |
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258 { |
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259 SparseComplexLU fact (sm, Qinit, thresh, false, |
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260 droptol, milu, udiag); |
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261 |
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262 retval(3) = fact.Pc (); |
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263 retval(2) = fact.Pr (); |
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264 retval(1) = octave_value (fact.U (), |
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265 MatrixType (MatrixType::Upper)); |
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266 retval(0) = octave_value (fact.L (), |
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267 MatrixType (MatrixType::Lower)); |
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268 } |
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269 break; |
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270 } |
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271 } |
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272 } |
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273 else |
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274 error ("luinc: first argument must be sparse"); |
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275 } |
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276 } |
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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 /* |
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282 |
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283 %!test |
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284 %! a=sparse([1,2,0,0;0,1,2,0;1e-14,0,3,0;0,0,0,1]); |
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285 %! [l,u]=luinc(a,1e-10); |
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286 %! assert(l*u, sparse([1,2,0,0;0,1,2,0;0,0,3,0;0,0,0,1]),1e-10); |
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287 %! opts.droptol=1e-10; |
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288 %! [l,u]=luinc(a,opts); |
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289 %! assert(l*u, sparse([1,2,0,0;0,1,2,0;0,0,3,0;0,0,0,1]),1e-10); |
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290 |
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291 %!test |
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292 %! a=sparse([1i,2,0,0;0,1,2,0;1e-14,0,3,0;0,0,0,1]); |
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293 %! [l,u]=luinc(a,1e-10); |
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294 %! assert(l*u, sparse([1i,2,0,0;0,1,2,0;0,0,3,0;0,0,0,1]),1e-10); |
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295 %! opts.droptol=1e-10; |
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296 %! [l,u]=luinc(a,opts); |
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297 %! assert(l*u, sparse([1i,2,0,0;0,1,2,0;0,0,3,0;0,0,0,1]),1e-10); |
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298 |
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299 */ |
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300 |
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301 /* |
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302 ;;; Local Variables: *** |
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303 ;;; mode: C++ *** |
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304 ;;; End: *** |
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305 */ |
