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1 /* |
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2 |
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3 Copyright (C) 2004, 2005, 2006, 2007 David Bateman |
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4 Copyright (C) 1998, 1999, 2000, 2001, 2002, 2003, 2004 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 "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 // PKG_ADD: dispatch ("lu", "splu", "sparse matrix"); |
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40 // PKG_ADD: dispatch ("lu", "splu", "sparse complex matrix"); |
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41 // PKG_ADD: dispatch ("lu", "splu", "sparse bool matrix"); |
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42 DEFUN_DLD (splu, args, nargout, |
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43 "-*- texinfo -*-\n\ |
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44 @deftypefn {Loadable Function} {[@var{l}, @var{u}] =} splu (@var{a})\n\ |
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45 @deftypefnx {Loadable Function} {[@var{l}, @var{u}, @var{P}] =} splu (@var{a})\n\ |
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46 @deftypefnx {Loadable Function} {[@var{l}, @var{u}, @var{P}, @var{Q}] =} splu (@var{a})\n\ |
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47 @deftypefnx {Loadable Function} {[@var{l}, @var{u}, @var{P}, @var{Q}] =} splu (@dots{}, @var{thres})\n\ |
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48 @deftypefnx {Loadable Function} {[@var{l}, @var{u}, @var{P}] =} splu (@dots{}, @var{Q})\n\ |
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49 @cindex LU decomposition\n\ |
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50 Compute the LU decomposition of the sparse matrix @var{a}, using\n\ |
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51 subroutines from UMFPACK. The result is returned in a permuted\n\ |
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52 form, according to the optional return values @var{P} and @var{Q}.\n\ |
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53 \n\ |
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54 Called with two or three output arguments and a single input argument,\n\ |
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55 @dfn{splu} is a replacement for @dfn{lu}, and therefore the sparsity\n\ |
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56 preserving column permutations @var{Q} are not performed. Called with\n\ |
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57 a fourth output argument, the sparsity preserving column transformation\n\ |
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58 @var{Q} is returned, such that @code{@var{P} * @var{a} * @var{Q} =\n\ |
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59 @var{l} * @var{u}}.\n\ |
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60 \n\ |
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61 An additional input argument @var{thres}, that defines the pivoting\n\ |
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62 threshold can be given. Alternatively, the desired sparsity preserving\n\ |
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63 column permutations @var{Q} can be passed. Note that @var{Q} is assumed\n\ |
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64 to be fixed if there are fewer than four output arguments. Otherwise,\n\ |
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65 the updated column permutations are returned as the fourth argument.\n\ |
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66 \n\ |
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67 With two output arguments, returns the permuted forms of the upper and\n\ |
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68 lower triangular matrices, such that @code{@var{a} = @var{l} * @var{u}}.\n\ |
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69 With two or three output arguments, if a user-defined @var{Q} is given,\n\ |
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70 then @code{@var{u} * @var{Q}'} is returned. The matrix is not required to\n\ |
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71 be square.\n\ |
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72 @seealso{sparse, spinv, colamd, symamd}\n\ |
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73 @end deftypefn") |
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74 { |
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75 octave_value_list retval; |
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76 |
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77 int nargin = args.length (); |
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78 |
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79 if (nargin < 1 || nargin > 3 || nargout > 4) |
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80 { |
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81 print_usage (); |
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82 return retval; |
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83 } |
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84 |
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85 octave_value arg = args(0); |
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86 |
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87 octave_idx_type nr = arg.rows (); |
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88 octave_idx_type nc = arg.columns (); |
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89 |
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90 int arg_is_empty = empty_arg ("splu", nr, nc); |
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91 |
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92 if (arg_is_empty < 0) |
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93 return retval; |
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94 else if (arg_is_empty > 0) |
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95 return octave_value_list (3, SparseMatrix ()); |
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96 |
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97 ColumnVector Qinit; |
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98 bool have_Qinit = false; |
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99 double thres = -1.; |
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100 |
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101 for (int k = 1; k < nargin; k++) |
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102 { |
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103 if (args(k).is_sparse_type ()) |
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104 { |
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105 SparseMatrix tmp = args (k).sparse_matrix_value (); |
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106 |
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107 if (error_state) |
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108 { |
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109 error ("splu: Not a valid permutation/threshold"); |
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110 return retval; |
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111 } |
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112 |
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113 dim_vector dv = tmp.dims (); |
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114 |
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115 if (dv(0) == 1 && dv(1) == 1) |
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116 thres = tmp (0); |
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117 else if (dv(0) == 1 || dv(1) == 1) |
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118 { |
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119 octave_idx_type nel = tmp.numel (); |
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120 Qinit.resize (nel); |
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121 for (octave_idx_type i = 0; i < nel; i++) |
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122 Qinit (i) = tmp (i) - 1; |
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123 have_Qinit = true; |
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124 } |
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125 else |
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126 { |
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127 octave_idx_type t_nc = tmp.cols (); |
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128 |
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129 if (tmp.nzmax () != t_nc) |
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130 error ("splu: Not a valid permutation matrix"); |
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131 else |
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132 { |
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133 for (octave_idx_type i = 0; i < t_nc + 1; i++) |
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134 if (tmp.cidx(i) != i) |
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135 { |
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136 error ("splu: Not a valid permutation matrix"); |
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137 break; |
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138 } |
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139 } |
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140 |
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141 if (!error_state) |
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142 { |
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143 for (octave_idx_type i = 0; i < t_nc; i++) |
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144 if (tmp.data (i) != 1.) |
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145 { |
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146 error ("splu: Not a valid permutation matrix"); |
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147 break; |
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148 } |
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149 else |
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150 Qinit (i) = tmp.ridx (i) - 1; |
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151 } |
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152 |
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153 if (! error_state) |
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154 have_Qinit = true; |
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155 } |
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156 } |
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157 else |
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158 { |
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159 NDArray tmp = args(k).array_value (); |
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160 |
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161 if (error_state) |
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162 return retval; |
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163 |
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164 dim_vector dv = tmp.dims (); |
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165 if (dv.length () > 2) |
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166 { |
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167 error ("splu: second argument must be a vector/matrix or a scalar"); |
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168 } |
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169 else if (dv(0) == 1 && dv(1) == 1) |
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170 thres = tmp (0); |
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171 else if (dv(0) == 1 || dv(1) == 1) |
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172 { |
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173 octave_idx_type nel = tmp.numel (); |
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174 Qinit.resize (nel); |
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175 for (octave_idx_type i = 0; i < nel; i++) |
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176 Qinit (i) = tmp (i) - 1; |
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177 have_Qinit = true; |
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178 } |
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179 else |
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180 { |
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181 SparseMatrix tmp2 (tmp); |
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182 |
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183 octave_idx_type t_nc = tmp2.cols (); |
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184 |
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185 if (tmp2.nzmax () != t_nc) |
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186 error ("splu: Not a valid permutation matrix"); |
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187 else |
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188 { |
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189 for (octave_idx_type i = 0; i < t_nc + 1; i++) |
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190 if (tmp2.cidx(i) != i) |
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191 { |
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192 error ("splu: Not a valid permutation matrix"); |
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193 break; |
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194 } |
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195 } |
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196 |
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197 if (!error_state) |
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198 { |
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199 for (octave_idx_type i = 0; i < t_nc; i++) |
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200 if (tmp2.data (i) != 1.) |
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201 { |
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202 error ("splu: Not a valid permutation matrix"); |
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203 break; |
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204 } |
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205 else |
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206 Qinit (i) = tmp2.ridx (i) - 1; |
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207 } |
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208 |
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209 if (! error_state) |
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210 have_Qinit = true; |
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211 } |
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212 } |
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213 } |
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214 |
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215 if (error_state) |
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216 return retval; |
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217 |
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218 if (arg.is_real_type ()) |
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219 { |
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220 SparseMatrix m = arg.sparse_matrix_value (); |
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221 |
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222 if (nargout < 4 && ! have_Qinit) |
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223 { |
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224 octave_idx_type m_nc = m.cols (); |
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225 Qinit.resize (m_nc); |
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226 for (octave_idx_type i = 0; i < m_nc; i++) |
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227 Qinit (i) = i; |
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228 } |
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229 |
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230 if (! error_state) |
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231 { |
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232 switch (nargout) |
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233 { |
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234 case 0: |
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235 case 1: |
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236 case 2: |
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237 { |
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238 SparseLU fact (m, Qinit, thres, true); |
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239 |
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240 SparseMatrix P = fact.Pr (); |
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241 SparseMatrix L = P.transpose () * fact.L (); |
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242 if (have_Qinit) |
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243 retval(1) = octave_value (fact.U () * fact.Pc ().transpose (), |
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244 MatrixType (MatrixType::Permuted_Upper, nc, fact.col_perm ())); |
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245 else |
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246 retval(1) = octave_value (fact.U (), |
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247 MatrixType (MatrixType::Upper)); |
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248 |
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249 retval(0) = octave_value (L, |
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250 MatrixType (MatrixType::Permuted_Lower, nr, fact.row_perm ())); |
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251 } |
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252 break; |
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253 |
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254 case 3: |
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255 { |
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256 SparseLU fact (m, Qinit, thres, true); |
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257 |
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258 retval(2) = fact.Pr (); |
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259 if (have_Qinit) |
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260 retval(1) = octave_value (fact.U () * fact.Pc ().transpose (), |
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261 MatrixType (MatrixType::Permuted_Upper, nc, fact.col_perm ())); |
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262 else |
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263 retval(1) = octave_value (fact.U (), |
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264 MatrixType (MatrixType::Upper)); |
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265 |
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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 case 4: |
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272 default: |
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273 { |
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274 if (have_Qinit) |
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275 { |
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276 SparseLU fact (m, Qinit, thres, false); |
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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) = octave_value (fact.U (), |
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281 MatrixType (MatrixType::Upper)); |
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282 retval(0) = octave_value (fact.L (), |
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283 MatrixType (MatrixType::Lower)); |
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284 } |
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285 else |
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286 { |
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287 SparseLU fact (m, thres); |
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288 |
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289 retval(3) = fact.Pc (); |
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290 retval(2) = fact.Pr (); |
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291 retval(1) = octave_value (fact.U (), |
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292 MatrixType (MatrixType::Upper)); |
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293 retval(0) = octave_value (fact.L (), |
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294 MatrixType (MatrixType::Lower)); |
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295 } |
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296 } |
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297 break; |
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298 } |
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299 } |
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300 } |
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301 else if (arg.is_complex_type ()) |
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302 { |
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303 SparseComplexMatrix m = arg.sparse_complex_matrix_value (); |
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304 |
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305 if (nargout < 4 && ! have_Qinit) |
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306 { |
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307 octave_idx_type m_nc = m.cols (); |
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308 Qinit.resize (m_nc); |
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309 for (octave_idx_type i = 0; i < m_nc; i++) |
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310 Qinit (i) = i; |
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311 } |
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312 |
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313 if (! error_state) |
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314 { |
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315 switch (nargout) |
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316 { |
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317 case 0: |
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318 case 1: |
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319 case 2: |
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320 { |
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321 SparseComplexLU fact (m, Qinit, thres, true); |
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322 |
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323 SparseMatrix P = fact.Pr (); |
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324 SparseComplexMatrix L = P.transpose () * fact.L (); |
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325 |
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326 if (have_Qinit) |
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327 retval(1) = octave_value (fact.U () * fact.Pc ().transpose (), |
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328 MatrixType (MatrixType::Permuted_Upper, nc, fact.col_perm ())); |
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329 else |
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330 retval(1) = octave_value (fact.U (), |
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331 MatrixType (MatrixType::Upper)); |
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332 |
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333 retval(0) = octave_value (L, |
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334 MatrixType (MatrixType::Permuted_Lower, nr, fact.row_perm ())); |
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335 } |
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336 break; |
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337 |
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338 case 3: |
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339 { |
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340 SparseComplexLU fact (m, Qinit, thres, true); |
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341 |
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342 retval(2) = fact.Pr (); |
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343 if (have_Qinit) |
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344 retval(1) = octave_value (fact.U () * fact.Pc ().transpose (), |
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345 MatrixType (MatrixType::Permuted_Upper, nc, fact.col_perm ())); |
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346 else |
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347 retval(1) = octave_value (fact.U (), |
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348 MatrixType (MatrixType::Upper)); |
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349 |
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350 retval(0) = octave_value (fact.L (), |
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351 MatrixType (MatrixType::Lower)); |
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352 } |
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353 break; |
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354 |
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355 case 4: |
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356 default: |
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357 { |
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358 if (have_Qinit) |
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359 { |
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360 SparseComplexLU fact (m, Qinit, thres, false); |
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361 |
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362 retval(3) = fact.Pc (); |
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363 retval(2) = fact.Pr (); |
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364 retval(1) = octave_value (fact.U (), |
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365 MatrixType (MatrixType::Upper)); |
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366 retval(0) = octave_value (fact.L (), |
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367 MatrixType (MatrixType::Lower)); |
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368 } |
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369 else |
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370 { |
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371 SparseComplexLU fact (m, thres); |
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372 |
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373 retval(3) = fact.Pc (); |
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374 retval(2) = fact.Pr (); |
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375 retval(1) = octave_value (fact.U (), |
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376 MatrixType (MatrixType::Upper)); |
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377 retval(0) = octave_value (fact.L (), |
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378 MatrixType (MatrixType::Lower)); |
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379 } |
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380 } |
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381 break; |
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382 } |
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383 } |
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384 } |
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385 else |
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386 { |
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387 gripe_wrong_type_arg ("splu", arg); |
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388 } |
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389 |
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390 return retval; |
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391 } |
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392 |
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393 // PKG_ADD: dispatch ("inv", "spinv", "sparse matrix"); |
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394 // PKG_ADD: dispatch ("inv", "spinv", "sparse complex matrix"); |
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395 // PKG_ADD: dispatch ("inv", "spinv", "sparse bool matrix"); |
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396 // PKG_ADD: dispatch ("inverse", "spinv", "sparse matrix"); |
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397 // PKG_ADD: dispatch ("inverse", "spinv", "sparse complex matrix"); |
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398 // PKG_ADD: dispatch ("inverse", "spinv", "sparse bool matrix"); |
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399 DEFUN_DLD (spinv, args, nargout, |
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400 "-*- texinfo -*-\n\ |
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401 @deftypefn {Loadable Function} {[@var{x}, @var{rcond}] = } spinv (@var{a}, @var{Q})\n\ |
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402 Compute the inverse of the sparse square matrix @var{a}. Return an estimate\n\ |
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403 of the reciprocal condition number if requested, otherwise warn of an\n\ |
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404 ill-conditioned matrix if the reciprocal condition number is small.\n\ |
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405 This function takes advantage of the sparsity of the matrix to accelerate\n\ |
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406 the calculation of the inverse.\n\ |
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407 \n\ |
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408 In general @var{x} will be a full matrix, and so if possible forming the\n\ |
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409 inverse of a sparse matrix should be avoided. It is significantly more\n\ |
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410 accurate and faster to do @code{@var{y} = @var{a} \\ @var{b}}, rather\n\ |
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411 than @code{@var{y} = spinv (@var{a}) * @var{b}}.\n\ |
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412 @end deftypefn") |
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413 { |
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414 octave_value_list retval; |
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415 |
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416 int nargin = args.length (); |
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417 |
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418 if (nargin != 1) |
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419 { |
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5823
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420 print_usage (); |
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421 return retval; |
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422 } |
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423 |
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424 octave_value arg = args(0); |
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425 |
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426 octave_idx_type nr = arg.rows (); |
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427 octave_idx_type nc = arg.columns (); |
|
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428 |
|
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429 int arg_is_empty = empty_arg ("spinverse", nr, nc); |
|
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430 |
|
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431 if (arg_is_empty < 0) |
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432 return retval; |
|
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433 else if (arg_is_empty > 0) |
|
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434 return octave_value (Matrix ()); |
|
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435 |
|
|
436 if (nr != nc) |
|
|
437 { |
|
|
438 gripe_square_matrix_required ("spinverse"); |
|
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439 return retval; |
|
|
440 } |
|
|
441 |
|
|
442 if (arg.is_real_type ()) |
|
|
443 { |
|
|
444 |
|
|
445 SparseMatrix m = arg.sparse_matrix_value (); |
|
|
446 |
|
|
447 if (! error_state) |
|
|
448 { |
|
5785
|
449 MatrixType mattyp = args(0).matrix_type (); |
|
5760
|
450 |
|
5506
|
451 octave_idx_type info; |
|
|
452 double rcond = 0.0; |
|
|
453 SparseMatrix result = m.inverse (mattyp, info, rcond, 1); |
|
5760
|
454 |
|
5785
|
455 args(0).matrix_type (mattyp); |
|
5506
|
456 |
|
|
457 if (nargout > 1) |
|
|
458 retval(1) = rcond; |
|
|
459 |
|
|
460 retval(0) = result; |
|
|
461 |
|
|
462 volatile double xrcond = rcond; |
|
|
463 xrcond += 1.0; |
|
|
464 if (nargout < 2 && (info == -1 || xrcond == 1.0)) |
|
|
465 warning ("spinverse: matrix singular to machine precision,\ |
|
|
466 rcond = %g", rcond); |
|
|
467 } |
|
|
468 } |
|
|
469 else if (arg.is_complex_type ()) |
|
|
470 { |
|
|
471 SparseComplexMatrix m = arg.sparse_complex_matrix_value (); |
|
|
472 |
|
|
473 if (! error_state) |
|
|
474 { |
|
5785
|
475 MatrixType mattyp = args(0).matrix_type (); |
|
5760
|
476 |
|
5506
|
477 octave_idx_type info; |
|
|
478 double rcond = 0.0; |
|
|
479 |
|
|
480 SparseComplexMatrix result = m.inverse (mattyp, info, rcond, 1); |
|
5760
|
481 |
|
5785
|
482 args(0).matrix_type (mattyp); |
|
5506
|
483 |
|
|
484 if (nargout > 1) |
|
|
485 retval(1) = rcond; |
|
|
486 |
|
|
487 retval(0) = result; |
|
|
488 |
|
|
489 volatile double xrcond = rcond; |
|
|
490 xrcond += 1.0; |
|
|
491 if (nargout < 2 && (info == -1 || xrcond == 1.0)) |
|
|
492 warning ("spinverse: matrix singular to machine precision,\ |
|
|
493 rcond = %g", rcond); |
|
|
494 } |
|
|
495 } |
|
|
496 else |
|
|
497 gripe_wrong_type_arg ("spinverse", arg); |
|
|
498 |
|
|
499 return retval; |
|
5164
|
500 } |
|
|
501 |
|
|
502 /* |
|
|
503 ;;; Local Variables: *** |
|
|
504 ;;; mode: C++ *** |
|
|
505 ;;; End: *** |
|
|
506 */ |
