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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 |
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18 Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, |
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19 Boston, MA 02110-1301, USA. |
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20 |
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21 */ |
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22 |
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23 #ifdef HAVE_CONFIG_H |
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24 #include <config.h> |
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25 #endif |
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26 |
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27 #include "defun-dld.h" |
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28 #include "error.h" |
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29 #include "gripes.h" |
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30 #include "oct-obj.h" |
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31 #include "utils.h" |
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32 |
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33 #include "SparseCmplxLU.h" |
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34 #include "SparsedbleLU.h" |
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35 #include "ov-re-sparse.h" |
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36 #include "ov-cx-sparse.h" |
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37 |
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38 // PKG_ADD: dispatch ("lu", "splu", "sparse matrix"); |
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39 // PKG_ADD: dispatch ("lu", "splu", "sparse complex matrix"); |
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40 // PKG_ADD: dispatch ("lu", "splu", "sparse bool matrix"); |
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41 DEFUN_DLD (splu, args, nargout, |
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42 "-*- texinfo -*-\n\ |
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43 @deftypefn {Loadable Function} {[@var{l}, @var{u}] =} splu (@var{a})\n\ |
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44 @deftypefnx {Loadable Function} {[@var{l}, @var{u}, @var{P}] =} splu (@var{a})\n\ |
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45 @deftypefnx {Loadable Function} {[@var{l}, @var{u}, @var{P}, @var{Q}] =} splu (@var{a})\n\ |
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46 @deftypefnx {Loadable Function} {[@var{l}, @var{u}, @var{P}, @var{Q}] =} splu (@dots{}, @var{thres})\n\ |
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47 @deftypefnx {Loadable Function} {[@var{l}, @var{u}, @var{P}] =} splu (@dots{}, @var{Q})\n\ |
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48 @cindex LU decomposition\n\ |
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49 Compute the LU decomposition of the sparse matrix @var{a}, using\n\ |
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50 subroutines from UMFPACK. The result is returned in a permuted\n\ |
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51 form, according to the optional return values @var{P} and @var{Q}.\n\ |
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52 \n\ |
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53 Called with two or three output arguments and a single input argument,\n\ |
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54 @dfn{splu} is a replacement for @dfn{lu}, and therefore the sparsity\n\ |
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55 preserving column permutations @var{Q} are not performed. Called with\n\ |
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56 a fourth output argument, the sparsity preserving column transformation\n\ |
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57 @var{Q} is returned, such that @code{@var{P} * @var{a} * @var{Q} =\n\ |
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58 @var{l} * @var{u}}.\n\ |
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59 \n\ |
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60 An additional input argument @var{thres}, that defines the pivoting\n\ |
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61 threshold can be given. Alternatively, the desired sparsity preserving\n\ |
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62 column permutations @var{Q} can be passed. Note that @var{Q} is assumed\n\ |
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63 to be fixed if three are fewer than four output arguments. Otherwise,\n\ |
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64 the updated column permutations are returned as the fourth argument.\n\ |
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65 \n\ |
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66 With two output arguments, returns the permuted forms of the upper and\n\ |
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67 lower triangular matrices, such that @code{@var{a} = @var{l} * @var{u}}.\n\ |
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68 With two or three output arguments, if a user-defined @var{Q} is given,\n\ |
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69 then @code{@var{u} * @var{Q}'} is returned. The matrix is not required to\n\ |
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70 be square.\n\ |
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71 @end deftypefn\n\ |
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72 @seealso{sparse, spinv, colamd, symamd}") |
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73 { |
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74 octave_value_list retval; |
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75 |
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76 int nargin = args.length (); |
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77 |
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78 if (nargin < 1 || nargin > 3 || nargout > 4) |
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79 { |
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80 print_usage ("splu"); |
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81 return retval; |
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82 } |
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83 |
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84 octave_value arg = args(0); |
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85 |
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86 octave_idx_type nr = arg.rows (); |
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87 octave_idx_type nc = arg.columns (); |
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88 |
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89 int arg_is_empty = empty_arg ("splu", nr, nc); |
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90 |
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91 if (arg_is_empty < 0) |
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92 return retval; |
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93 else if (arg_is_empty > 0) |
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94 return octave_value_list (3, SparseMatrix ()); |
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95 |
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96 ColumnVector Qinit; |
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97 bool have_Qinit = false; |
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98 double thres = -1.; |
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99 |
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100 for (int k = 1; k < nargin; k++) |
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101 { |
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102 if (args(k).is_sparse_type ()) |
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103 { |
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104 SparseMatrix tmp = args (k).sparse_matrix_value (); |
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105 |
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106 if (error_state) |
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107 { |
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108 error ("splu: Not a valid permutation/threshold"); |
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109 return retval; |
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110 } |
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111 |
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112 dim_vector dv = tmp.dims (); |
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113 |
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114 if (dv(0) == 1 && dv(1) == 1) |
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115 thres = tmp (0); |
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116 else if (dv(0) == 1 || dv(1) == 1) |
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117 { |
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118 octave_idx_type nel = tmp.numel (); |
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119 Qinit.resize (nel); |
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120 for (octave_idx_type i = 0; i < nel; i++) |
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121 Qinit (i) = tmp (i) - 1; |
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122 have_Qinit = true; |
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123 } |
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124 else |
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125 { |
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126 octave_idx_type t_nc = tmp.cols (); |
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127 |
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128 if (tmp.nzmax () != t_nc) |
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129 error ("splu: Not a valid permutation matrix"); |
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130 else |
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131 { |
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132 for (octave_idx_type i = 0; i < t_nc + 1; i++) |
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133 if (tmp.cidx(i) != i) |
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134 { |
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135 error ("splu: Not a valid permutation matrix"); |
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136 break; |
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137 } |
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138 } |
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139 |
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140 if (!error_state) |
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141 { |
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142 for (octave_idx_type i = 0; i < t_nc; i++) |
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143 if (tmp.data (i) != 1.) |
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144 { |
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145 error ("splu: Not a valid permutation matrix"); |
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146 break; |
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147 } |
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148 else |
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149 Qinit (i) = tmp.ridx (i) - 1; |
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150 } |
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151 |
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152 if (! error_state) |
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153 have_Qinit = true; |
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154 } |
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155 } |
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156 else |
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157 { |
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158 NDArray tmp = args(k).array_value (); |
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159 |
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160 if (error_state) |
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161 return retval; |
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162 |
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163 dim_vector dv = tmp.dims (); |
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164 if (dv.length () > 2) |
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165 { |
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166 error ("splu: second argument must be a vector/matrix or a scalar"); |
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167 } |
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168 else if (dv(0) == 1 && dv(1) == 1) |
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169 thres = tmp (0); |
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170 else if (dv(0) == 1 || dv(1) == 1) |
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171 { |
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172 octave_idx_type nel = tmp.numel (); |
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173 Qinit.resize (nel); |
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174 for (octave_idx_type i = 0; i < nel; i++) |
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175 Qinit (i) = tmp (i) - 1; |
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176 have_Qinit = true; |
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177 } |
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178 else |
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179 { |
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180 SparseMatrix tmp2 (tmp); |
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181 |
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182 octave_idx_type t_nc = tmp2.cols (); |
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183 |
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184 if (tmp2.nzmax () != t_nc) |
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185 error ("splu: Not a valid permutation matrix"); |
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186 else |
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187 { |
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188 for (octave_idx_type i = 0; i < t_nc + 1; i++) |
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189 if (tmp2.cidx(i) != i) |
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190 { |
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191 error ("splu: Not a valid permutation matrix"); |
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192 break; |
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193 } |
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194 } |
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195 |
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196 if (!error_state) |
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197 { |
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198 for (octave_idx_type i = 0; i < t_nc; i++) |
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199 if (tmp2.data (i) != 1.) |
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200 { |
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201 error ("splu: Not a valid permutation matrix"); |
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202 break; |
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203 } |
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204 else |
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205 Qinit (i) = tmp2.ridx (i) - 1; |
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206 } |
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207 |
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208 if (! error_state) |
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209 have_Qinit = true; |
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210 } |
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211 } |
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212 } |
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213 |
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214 if (error_state) |
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215 return retval; |
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216 |
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217 if (arg.is_real_type ()) |
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218 { |
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219 SparseMatrix m = arg.sparse_matrix_value (); |
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220 |
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221 if (nargout < 4 && ! have_Qinit) |
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222 { |
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223 octave_idx_type m_nc = m.cols (); |
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224 Qinit.resize (m_nc); |
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225 for (octave_idx_type i = 0; i < m_nc; i++) |
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226 Qinit (i) = i; |
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227 } |
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228 |
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229 if (! error_state) |
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230 { |
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231 switch (nargout) |
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232 { |
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233 case 0: |
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234 case 1: |
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235 case 2: |
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236 { |
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237 SparseLU fact (m, Qinit, thres, true); |
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238 |
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239 SparseMatrix P = fact.Pr (); |
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240 SparseMatrix L = P.transpose () * fact.L (); |
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241 if (have_Qinit) |
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242 retval(1) = octave_value (fact.U () * fact.Pc ().transpose (), |
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243 SparseType (SparseType::Permuted_Upper, nc, fact.col_perm ())); |
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244 else |
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245 retval(1) = octave_value (fact.U (), |
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246 SparseType (SparseType::Upper)); |
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247 |
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248 retval(0) = octave_value (L, |
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249 SparseType (SparseType::Permuted_Lower, nr, fact.row_perm ())); |
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250 } |
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251 break; |
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252 |
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253 case 3: |
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254 { |
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255 SparseLU fact (m, Qinit, thres, true); |
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256 |
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257 retval(2) = fact.Pr (); |
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258 if (have_Qinit) |
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259 retval(1) = octave_value (fact.U () * fact.Pc ().transpose (), |
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260 SparseType (SparseType::Permuted_Upper, nc, fact.col_perm ())); |
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261 else |
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262 retval(1) = octave_value (fact.U (), |
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263 SparseType (SparseType::Upper)); |
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264 |
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265 retval(0) = octave_value (fact.L (), |
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266 SparseType (SparseType::Lower)); |
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267 } |
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268 break; |
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269 |
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270 case 4: |
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271 default: |
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272 { |
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273 if (have_Qinit) |
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274 { |
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275 SparseLU fact (m, Qinit, thres, false); |
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276 |
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277 retval(3) = fact.Pc (); |
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278 retval(2) = fact.Pr (); |
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279 retval(1) = octave_value (fact.U (), |
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280 SparseType (SparseType::Upper)); |
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281 retval(0) = octave_value (fact.L (), |
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282 SparseType (SparseType::Lower)); |
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283 } |
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284 else |
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285 { |
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286 SparseLU fact (m, thres); |
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287 |
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288 retval(3) = fact.Pc (); |
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289 retval(2) = fact.Pr (); |
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290 retval(1) = octave_value (fact.U (), |
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291 SparseType (SparseType::Upper)); |
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292 retval(0) = octave_value (fact.L (), |
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293 SparseType (SparseType::Lower)); |
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294 } |
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295 } |
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296 break; |
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297 } |
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298 } |
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299 } |
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300 else if (arg.is_complex_type ()) |
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301 { |
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302 SparseComplexMatrix m = arg.sparse_complex_matrix_value (); |
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303 |
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304 if (nargout < 4 && ! have_Qinit) |
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305 { |
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306 octave_idx_type m_nc = m.cols (); |
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307 Qinit.resize (m_nc); |
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308 for (octave_idx_type i = 0; i < m_nc; i++) |
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309 Qinit (i) = i; |
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310 } |
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311 |
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312 if (! error_state) |
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313 { |
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314 switch (nargout) |
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315 { |
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316 case 0: |
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317 case 1: |
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318 case 2: |
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319 { |
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320 SparseComplexLU fact (m, Qinit, thres, true); |
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321 |
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322 SparseMatrix P = fact.Pr (); |
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323 SparseComplexMatrix L = P.transpose () * fact.L (); |
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324 |
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325 if (have_Qinit) |
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326 retval(1) = octave_value (fact.U () * fact.Pc ().transpose (), |
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327 SparseType (SparseType::Permuted_Upper, nc, fact.col_perm ())); |
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328 else |
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329 retval(1) = octave_value (fact.U (), |
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330 SparseType (SparseType::Upper)); |
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331 |
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332 retval(0) = octave_value (L, |
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333 SparseType (SparseType::Permuted_Lower, nr, fact.row_perm ())); |
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334 } |
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335 break; |
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336 |
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337 case 3: |
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338 { |
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339 SparseComplexLU fact (m, Qinit, thres, true); |
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340 |
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341 retval(2) = fact.Pr (); |
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342 if (have_Qinit) |
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343 retval(1) = octave_value (fact.U () * fact.Pc ().transpose (), |
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344 SparseType (SparseType::Permuted_Upper, nc, fact.col_perm ())); |
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345 else |
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346 retval(1) = octave_value (fact.U (), |
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347 SparseType (SparseType::Upper)); |
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348 |
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349 retval(0) = octave_value (fact.L (), |
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350 SparseType (SparseType::Lower)); |
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351 } |
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352 break; |
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353 |
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354 case 4: |
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355 default: |
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356 { |
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357 if (have_Qinit) |
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358 { |
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359 SparseComplexLU fact (m, Qinit, thres, false); |
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360 |
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361 retval(3) = fact.Pc (); |
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362 retval(2) = fact.Pr (); |
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363 retval(1) = octave_value (fact.U (), |
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364 SparseType (SparseType::Upper)); |
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365 retval(0) = octave_value (fact.L (), |
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366 SparseType (SparseType::Lower)); |
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367 } |
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368 else |
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369 { |
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370 SparseComplexLU fact (m, thres); |
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371 |
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372 retval(3) = fact.Pc (); |
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373 retval(2) = fact.Pr (); |
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374 retval(1) = octave_value (fact.U (), |
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375 SparseType (SparseType::Upper)); |
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376 retval(0) = octave_value (fact.L (), |
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377 SparseType (SparseType::Lower)); |
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378 } |
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379 } |
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380 break; |
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381 } |
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382 } |
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383 } |
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384 else |
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385 { |
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386 gripe_wrong_type_arg ("splu", arg); |
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387 } |
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388 |
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389 return retval; |
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390 } |
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391 |
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392 // PKG_ADD: dispatch ("inv", "spinv", "sparse matrix"); |
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393 // PKG_ADD: dispatch ("inv", "spinv", "sparse complex matrix"); |
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394 // PKG_ADD: dispatch ("inv", "spinv", "sparse bool matrix"); |
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395 // PKG_ADD: dispatch ("inverse", "spinv", "sparse matrix"); |
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396 // PKG_ADD: dispatch ("inverse", "spinv", "sparse complex matrix"); |
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397 // PKG_ADD: dispatch ("inverse", "spinv", "sparse bool matrix"); |
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398 DEFUN_DLD (spinv, args, nargout, |
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399 "-*- texinfo -*-\n\ |
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400 @deftypefn {Loadable Function} {[@var{x}, @var{rcond}] = } spinv (@var{a}, @var{Q})\n\ |
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401 Compute the inverse of the sparse square matrix @var{a}. Return an estimate\n\ |
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402 of the reciprocal condition number if requested, otherwise warn of an\n\ |
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403 ill-conditioned matrix if the reciprocal condition number is small.\n\ |
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404 This function takes advantage of the sparsity of the matrix to accelerate\n\ |
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405 the calculation of the inverse.\n\ |
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406 \n\ |
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407 In general @var{x} will be a full matrix, and so if possible forming the\n\ |
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408 inverse of a sparse matrix should be avoided. It is significantly more\n\ |
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409 accurate and faster to do @code{@var{y} = @var{a} \\ @var{b}}, rather\n\ |
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410 than @code{@var{y} = spinv (@var{a}) * @var{b}}.\n\ |
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411 @end deftypefn") |
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412 { |
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413 octave_value_list retval; |
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414 |
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415 int nargin = args.length (); |
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416 |
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417 if (nargin != 1) |
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418 { |
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419 print_usage ("inv"); |
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420 return retval; |
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421 } |
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422 |
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423 octave_value arg = args(0); |
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424 const octave_value& rep = arg.get_rep (); |
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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 |
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436 if (nr != nc) |
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437 { |
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438 gripe_square_matrix_required ("spinverse"); |
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439 return retval; |
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440 } |
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441 |
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442 if (arg.is_real_type ()) |
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443 { |
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444 |
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445 SparseMatrix m = arg.sparse_matrix_value (); |
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446 |
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447 if (! error_state) |
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448 { |
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449 octave_idx_type info; |
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450 double rcond = 0.0; |
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451 SparseType mattyp = ((octave_sparse_matrix &)rep).sparse_type (); |
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452 SparseMatrix result = m.inverse (mattyp, info, rcond, 1); |
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453 ((octave_sparse_matrix &)(arg.get_rep())).sparse_type (mattyp); |
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454 |
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455 if (nargout > 1) |
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456 retval(1) = rcond; |
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457 |
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458 retval(0) = result; |
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459 |
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460 volatile double xrcond = rcond; |
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461 xrcond += 1.0; |
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462 if (nargout < 2 && (info == -1 || xrcond == 1.0)) |
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463 warning ("spinverse: matrix singular to machine precision,\ |
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464 rcond = %g", rcond); |
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465 } |
|
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466 } |
|
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467 else if (arg.is_complex_type ()) |
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|
468 { |
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469 SparseComplexMatrix m = arg.sparse_complex_matrix_value (); |
|
|
470 |
|
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471 if (! error_state) |
|
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472 { |
|
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473 octave_idx_type info; |
|
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474 double rcond = 0.0; |
|
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475 |
|
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476 SparseType mattyp = |
|
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477 ((octave_sparse_complex_matrix &)rep).sparse_type (); |
|
|
478 SparseComplexMatrix result = m.inverse (mattyp, info, rcond, 1); |
|
|
479 ((octave_sparse_matrix &)rep).sparse_type (mattyp); |
|
|
480 |
|
|
481 if (nargout > 1) |
|
|
482 retval(1) = rcond; |
|
|
483 |
|
|
484 retval(0) = result; |
|
|
485 |
|
|
486 volatile double xrcond = rcond; |
|
|
487 xrcond += 1.0; |
|
|
488 if (nargout < 2 && (info == -1 || xrcond == 1.0)) |
|
|
489 warning ("spinverse: matrix singular to machine precision,\ |
|
|
490 rcond = %g", rcond); |
|
|
491 } |
|
|
492 } |
|
|
493 else |
|
|
494 gripe_wrong_type_arg ("spinverse", arg); |
|
|
495 |
|
|
496 return retval; |
|
5164
|
497 } |
|
|
498 |
|
|
499 /* |
|
|
500 ;;; Local Variables: *** |
|
|
501 ;;; mode: C++ *** |
|
|
502 ;;; End: *** |
|
|
503 */ |
