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1 /* |
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2 |
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3 Copyright (C) 2004 David Bateman |
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4 Copyright (C) 1998-2004 Andy Adler |
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5 |
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6 Octave is free software; you can redistribute it and/or modify it |
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7 under the terms of the GNU General Public License as published by the |
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8 Free Software Foundation; either version 2, or (at your option) any |
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9 later version. |
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10 |
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11 Octave is distributed in the hope that it will be useful, but WITHOUT |
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12 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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13 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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14 for more details. |
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15 |
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16 You should have received a copy of the GNU General Public License |
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17 along with this program; see the file COPYING. If not, write to the Free |
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18 Software Foundation, 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
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19 |
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20 */ |
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21 |
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22 #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 |
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32 #include "SparseCmplxLU.h" |
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33 #include "SparsedbleLU.h" |
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34 #include "ov-re-sparse.h" |
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35 #include "ov-cx-sparse.h" |
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36 |
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37 // PKG_ADD: dispatch ("lu", "splu", "sparse matrix") |
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38 // PKG_ADD: dispatch ("lu", "splu", "sparse complex matrix") |
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39 // PKG_ADD: dispatch ("lu", "splu", "sparse bool matrix") |
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40 DEFUN_DLD (splu, args, nargout, |
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41 "-*- texinfo -*-\n\ |
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42 @deftypefn {Loadable Function} {[@var{l}, @var{u}] =} splu (@var{a})\n\ |
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43 @deftypefnx {Loadable Function} {[@var{l}, @var{u}, @var{P}] =} splu (@var{a})\n\ |
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44 @deftypefnx {Loadable Function} {[@var{l}, @var{u}, @var{P}, @var{Q}] =} splu (@var{a})\n\ |
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45 @deftypefnx {Loadable Function} {[@var{l}, @var{u}, @var{P}, @var{Q}] =} splu (@dots{}, @var{thres})\n\ |
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46 @deftypefnx {Loadable Function} {[@var{l}, @var{u}, @var{P}] =} splu (@dots{}, @var{Q})\n\ |
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47 @cindex LU decomposition\n\ |
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48 Compute the LU decomposition of the sparse matrix @var{a}, using\n\ |
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49 subroutines from UMFPACK. The result is returned in a permuted\n\ |
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50 form, according to the optional return values @var{P} and @var{Q}.\n\ |
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51 \n\ |
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52 Called with two or three output arguments and a single input argument,\n\ |
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53 @dfn{splu} is a replacement for @dfn{lu}, and therefore the sparsity\n\ |
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54 preserving column permutations @var{Q} are not performed. Called with\n\ |
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55 a fourth output argument, the sparsity preserving column transformation\n\ |
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56 @var{Q} is returned, such that @code{@var{P} * @var{a} * @var{Q} =\n\ |
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57 @var{l} * @var{u}}.\n\ |
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58 \n\ |
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59 An additional input argument @var{thres}, that defines the pivoting\n\ |
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60 threshold can be given. Alternatively, the desired sparsity preserving\n\ |
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61 column permutations @var{Q} can be passed. Note that @var{Q} is assumed\n\ |
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62 to be fixed if three are fewer than four output arguments. Otherwise,\n\ |
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63 the updated column permutations are returned as the fourth argument.\n\ |
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64 \n\ |
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65 With two output arguments, returns the permuted forms of the upper and\n\ |
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66 lower triangular matrices, such that @code{@var{a} = @var{l} * @var{u}}.\n\ |
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67 With two or three output arguments, if a user-defined @var{Q} is given,\n\ |
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68 then @code{@var{u} * @var{Q}'} is returned. The matrix is not required to\n\ |
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69 be square.\n\ |
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70 @end deftypefn\n\ |
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71 @seealso{sparse, spinv, colamd, symamd}") |
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72 { |
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73 octave_value_list retval; |
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74 |
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75 int nargin = args.length (); |
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76 |
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77 if (nargin < 1 || nargin > 3 || nargout > 4) |
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78 { |
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79 print_usage ("splu"); |
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80 return retval; |
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81 } |
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82 |
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83 octave_value arg = args(0); |
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84 |
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85 int nr = arg.rows (); |
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86 int nc = arg.columns (); |
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87 |
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88 int arg_is_empty = empty_arg ("splu", nr, nc); |
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89 |
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90 if (arg_is_empty < 0) |
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91 return retval; |
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92 else if (arg_is_empty > 0) |
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93 return octave_value_list (3, SparseMatrix ()); |
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94 |
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95 ColumnVector Qinit; |
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96 bool have_Qinit = false; |
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97 double thres = -1.; |
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98 |
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99 for (int k = 1; k < nargin; k++) |
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100 { |
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101 if (args(k).class_name () == "sparse") |
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102 { |
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103 SparseMatrix tmp = args (k).sparse_matrix_value (); |
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104 |
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105 if (error_state) |
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106 { |
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107 error ("splu: Not a valid permutation/threshold"); |
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108 return retval; |
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109 } |
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110 |
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111 dim_vector dv = tmp.dims (); |
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112 |
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113 if (dv(0) == 1 && dv(1) == 1) |
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114 thres = tmp (0); |
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115 else if (dv(0) == 1 || dv(1) == 1) |
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116 { |
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117 int nel = tmp.numel (); |
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118 Qinit.resize (nel); |
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119 for (int i = 0; i < nel; i++) |
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120 Qinit (i) = tmp (i) - 1; |
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121 have_Qinit = true; |
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122 } |
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123 else |
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124 { |
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125 int t_nc = tmp.cols (); |
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126 |
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127 if (tmp.nnz () != t_nc) |
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128 error ("splu: Not a valid permutation matrix"); |
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129 else |
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130 { |
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131 for (int i = 0; i < t_nc + 1; i++) |
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132 if (tmp.cidx(i) != i) |
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133 { |
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134 error ("splu: Not a valid permutation matrix"); |
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135 break; |
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136 } |
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137 } |
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138 |
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139 if (!error_state) |
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140 { |
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141 for (int i = 0; i < t_nc; i++) |
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142 if (tmp.data (i) != 1.) |
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143 { |
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144 error ("splu: Not a valid permutation matrix"); |
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145 break; |
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146 } |
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147 else |
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148 Qinit (i) = tmp.ridx (i) - 1; |
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149 } |
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150 |
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151 if (! error_state) |
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152 have_Qinit = true; |
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153 } |
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154 } |
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155 else |
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156 { |
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157 NDArray tmp = args(k).array_value (); |
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158 |
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159 if (error_state) |
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160 return retval; |
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161 |
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162 dim_vector dv = tmp.dims (); |
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163 if (dv.length () > 2) |
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164 { |
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165 error ("splu: second argument must be a vector/matrix or a scalar"); |
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166 } |
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167 else if (dv(0) == 1 && dv(1) == 1) |
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168 thres = tmp (0); |
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169 else if (dv(0) == 1 || dv(1) == 1) |
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170 { |
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171 int nel = tmp.numel (); |
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172 Qinit.resize (nel); |
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173 for (int i = 0; i < nel; i++) |
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174 Qinit (i) = tmp (i) - 1; |
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175 have_Qinit = true; |
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176 } |
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177 else |
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178 { |
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179 SparseMatrix tmp2 (tmp); |
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180 |
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181 int t_nc = tmp2.cols (); |
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182 |
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183 if (tmp2.nnz () != t_nc) |
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184 error ("splu: Not a valid permutation matrix"); |
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185 else |
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186 { |
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187 for (int i = 0; i < t_nc + 1; i++) |
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188 if (tmp2.cidx(i) != i) |
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189 { |
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190 error ("splu: Not a valid permutation matrix"); |
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191 break; |
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192 } |
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193 } |
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194 |
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195 if (!error_state) |
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196 { |
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197 for (int i = 0; i < t_nc; i++) |
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198 if (tmp2.data (i) != 1.) |
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199 { |
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200 error ("splu: Not a valid permutation matrix"); |
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201 break; |
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202 } |
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203 else |
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204 Qinit (i) = tmp2.ridx (i) - 1; |
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205 } |
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206 |
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207 if (! error_state) |
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208 have_Qinit = true; |
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209 } |
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210 } |
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211 } |
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212 |
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213 if (error_state) |
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214 return retval; |
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215 |
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216 if (arg.is_real_type ()) |
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217 { |
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218 SparseMatrix m = arg.sparse_matrix_value (); |
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219 |
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220 if (nargout < 4 && ! have_Qinit) |
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221 { |
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222 int m_nc = m.cols (); |
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223 Qinit.resize (m_nc); |
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224 for (int i = 0; i < m_nc; i++) |
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225 Qinit (i) = i; |
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226 } |
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227 |
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228 if (! error_state) |
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229 { |
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230 switch (nargout) |
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231 { |
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232 case 0: |
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233 case 1: |
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234 case 2: |
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235 { |
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236 SparseLU fact (m, Qinit, thres, true); |
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237 |
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238 SparseMatrix P = fact.Pr (); |
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239 SparseMatrix L = P.transpose () * fact.L (); |
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240 if (have_Qinit) |
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241 retval(1) = fact.U () * fact.Pc ().transpose (); |
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242 else |
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243 retval(1) = fact.U (); |
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244 |
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245 retval(0) = L; |
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246 } |
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247 break; |
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248 |
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249 case 3: |
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250 { |
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251 SparseLU fact (m, Qinit, thres, true); |
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252 |
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253 retval(2) = fact.Pr (); |
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254 if (have_Qinit) |
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255 retval(1) = fact.U () * fact.Pc ().transpose (); |
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256 else |
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257 retval(1) = fact.U (); |
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258 retval(0) = fact.L (); |
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259 } |
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260 break; |
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261 |
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262 case 4: |
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263 default: |
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264 { |
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265 if (have_Qinit) |
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266 { |
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267 SparseLU fact (m, Qinit, thres, false); |
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268 |
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269 retval(3) = fact.Pc (); |
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270 retval(2) = fact.Pr (); |
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271 retval(1) = fact.U (); |
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272 retval(0) = fact.L (); |
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273 } |
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274 else |
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275 { |
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276 SparseLU fact (m, thres); |
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277 |
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278 retval(3) = fact.Pc (); |
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279 retval(2) = fact.Pr (); |
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280 retval(1) = fact.U (); |
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281 retval(0) = fact.L (); |
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282 } |
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283 } |
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284 break; |
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285 } |
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286 } |
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287 } |
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288 else if (arg.is_complex_type ()) |
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289 { |
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290 SparseComplexMatrix m = arg.sparse_complex_matrix_value (); |
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291 |
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292 if (nargout < 4 && ! have_Qinit) |
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293 { |
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294 int m_nc = m.cols (); |
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295 Qinit.resize (m_nc); |
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296 for (int i = 0; i < m_nc; i++) |
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297 Qinit (i) = i; |
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298 } |
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299 |
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300 if (! error_state) |
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301 { |
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302 switch (nargout) |
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303 { |
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304 case 0: |
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305 case 1: |
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306 case 2: |
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307 { |
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308 SparseComplexLU fact (m, Qinit, thres, true); |
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309 |
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310 SparseMatrix P = fact.Pr (); |
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311 SparseComplexMatrix L = P.transpose () * fact.L (); |
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312 |
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313 if (have_Qinit) |
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314 retval(1) = fact.U () * fact.Pc ().transpose (); |
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315 else |
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316 retval(1) = fact.U (); |
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317 retval(0) = L; |
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318 } |
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319 break; |
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320 |
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321 case 3: |
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322 { |
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323 SparseComplexLU fact (m, Qinit, thres, true); |
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324 |
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325 retval(2) = fact.Pr (); |
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326 if (have_Qinit) |
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327 retval(1) = fact.U () * fact.Pc ().transpose (); |
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328 else |
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329 retval(1) = fact.U (); |
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330 retval(0) = fact.L (); |
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331 } |
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332 break; |
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333 |
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334 case 4: |
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335 default: |
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336 { |
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337 if (have_Qinit) |
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338 { |
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339 SparseComplexLU fact (m, Qinit, thres, false); |
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340 |
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341 retval(3) = fact.Pc (); |
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342 retval(2) = fact.Pr (); |
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343 retval(1) = fact.U (); |
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344 retval(0) = fact.L (); |
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345 } |
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346 else |
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347 { |
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348 SparseComplexLU fact (m, thres); |
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349 |
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350 retval(3) = fact.Pc (); |
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351 retval(2) = fact.Pr (); |
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352 retval(1) = fact.U (); |
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353 retval(0) = fact.L (); |
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354 } |
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355 } |
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356 break; |
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357 } |
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358 } |
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359 } |
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360 else |
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361 { |
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362 gripe_wrong_type_arg ("splu", arg); |
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363 } |
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364 |
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365 return retval; |
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366 } |
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367 |
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368 // PKG_ADD: dispatch ("inv", "spinv", "sparse matrix") |
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369 // PKG_ADD: dispatch ("inv", "spinv", "sparse complex matrix") |
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370 // PKG_ADD: dispatch ("inv", "spinv", "sparse bool matrix") |
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371 // PKG_ADD: dispatch ("inverse", "spinv", "sparse matrix") |
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372 // PKG_ADD: dispatch ("inverse", "spinv", "sparse complex matrix") |
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373 // PKG_ADD: dispatch ("inverse", "spinv", "sparse bool matrix") |
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374 DEFUN_DLD (spinv, args, nargout, |
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375 "-*- texinfo -*-\n\ |
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376 @deftypefn {Loadable Function} {[@var{x}, @var{rcond}] = } spinv (@var{a}, @var{Q})\n\ |
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377 @deftypefnx {Loadable Function} {[@var{x}, @var{rcond}, @var{Q}] = } spinv (@var{a}, @var{Q})\n\ |
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378 Compute the inverse of the square matrix @var{a}. Return an estimate\n\ |
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379 of the reciprocal condition number if requested, otherwise warn of an\n\ |
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380 ill-conditioned matrix if the reciprocal condition number is small.\n\ |
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381 \n\ |
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382 An optional second input argument @var{Q} is the optional pre-ordering of\n\ |
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383 the matrix, such that @code{@var{x} = inv (@var{a} (:, @var{Q}))}. @var{Q}\n\ |
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384 can equally be a matrix, in which case @code{@var{x} = inv (@var{a} *\n\ |
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385 @var{Q}))}.\n\ |
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386 \n\ |
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387 If a third output argument is given then the permuations to achieve a sparse\n\ |
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388 inverse are returned. It is not required that the return column permutations\n\ |
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389 @var{Q} and the same as the user supplied permutations\n\ |
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390 @end deftypefn") |
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391 { |
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392 error ("spinv: not implemented yet"); |
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393 return octave_value (); |
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394 } |
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395 |
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396 /* |
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397 ;;; Local Variables: *** |
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398 ;;; mode: C++ *** |
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399 ;;; End: *** |
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400 */ |
