Mercurial > octave
annotate libinterp/corefcn/lu.cc @ 28154:e7fe6703a81f stable
doc: Update documentation for lu().
* lu.cc (Flu): Rename input "thres" to "tresh" for clarity. Use uppercase
letters for L,U,P.
author | Rik <rik@octave.org> |
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date | Thu, 12 Mar 2020 16:56:18 -0700 |
parents | bd51beb6205e |
children | 09c071328135 0a5b15007766 |
rev | line source |
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1 //////////////////////////////////////////////////////////////////////// |
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2 // |
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3 // Copyright (C) 1996-2020 The Octave Project Developers |
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4 // |
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5 // See the file COPYRIGHT.md in the top-level directory of this |
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6 // distribution or <https://octave.org/copyright/>. |
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7 // |
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8 // This file is part of Octave. |
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9 // |
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10 // Octave is free software: you can redistribute it and/or modify it |
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11 // under the terms of the GNU General Public License as published by |
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12 // the Free Software Foundation, either version 3 of the License, or |
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13 // (at your option) any later version. |
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14 // |
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15 // Octave is distributed in the hope that it will be useful, but |
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16 // WITHOUT ANY WARRANTY; without even the implied warranty of |
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17 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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18 // GNU General Public License for more details. |
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19 // |
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20 // You should have received a copy of the GNU General Public License |
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21 // along with Octave; see the file COPYING. If not, see |
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22 // <https://www.gnu.org/licenses/>. |
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23 // |
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24 //////////////////////////////////////////////////////////////////////// |
2928 | 25 |
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26 #if defined (HAVE_CONFIG_H) |
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27 # include "config.h" |
2928 | 28 #endif |
29 | |
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30 #include "lu.h" |
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31 #include "sparse-lu.h" |
2928 | 32 |
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33 #include "defun.h" |
2928 | 34 #include "error.h" |
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35 #include "errwarn.h" |
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36 #include "ovl.h" |
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37 #include "ov-re-sparse.h" |
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38 #include "ov-cx-sparse.h" |
2928 | 39 |
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40 template <typename MT> |
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41 static octave_value |
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42 get_lu_l (const octave::math::lu<MT>& fact) |
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43 { |
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44 MT L = fact.L (); |
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45 if (L.issquare ()) |
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46 return octave_value (L, MatrixType (MatrixType::Lower)); |
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47 else |
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48 return L; |
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49 } |
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50 |
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51 template <typename MT> |
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52 static octave_value |
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53 get_lu_u (const octave::math::lu<MT>& fact) |
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54 { |
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55 MT U = fact.U (); |
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56 if (U.issquare () && fact.regular ()) |
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57 return octave_value (U, MatrixType (MatrixType::Upper)); |
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58 else |
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59 return U; |
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60 } |
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61 |
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62 DEFUN (lu, args, nargout, |
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63 doc: /* -*- texinfo -*- |
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64 @deftypefn {} {[@var{L}, @var{U}] =} lu (@var{A}) |
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65 @deftypefnx {} {[@var{L}, @var{U}, @var{P}] =} lu (@var{A}) |
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66 @deftypefnx {} {[@var{L}, @var{U}, @var{P}, @var{Q}] =} lu (@var{S}) |
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67 @deftypefnx {} {[@var{L}, @var{U}, @var{P}, @var{Q}, @var{R}] =} lu (@var{S}) |
28154 | 68 @deftypefnx {} {[@dots{}] =} lu (@var{S}, @var{thresh}) |
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69 @deftypefnx {} {@var{y} =} lu (@dots{}) |
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70 @deftypefnx {} {[@dots{}] =} lu (@dots{}, "vector") |
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71 @cindex LU decomposition |
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72 Compute the LU@tie{}decomposition of @var{A}. |
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73 |
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74 If @var{A} is full then subroutines from @sc{lapack} are used, and if |
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75 @var{A} is sparse then @sc{umfpack} is used. |
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76 |
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77 The result is returned in a permuted form, according to the optional return |
28154 | 78 value @var{P}. For example, given the matrix @code{@var{A} = [1, 2; 3, 4]}, |
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79 |
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80 @example |
28154 | 81 [@var{L}, @var{U}, @var{P}] = lu (@var{A}) |
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82 @end example |
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83 |
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84 @noindent |
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85 returns |
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86 |
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87 @example |
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88 @group |
28154 | 89 L = |
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90 |
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91 1.00000 0.00000 |
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92 0.33333 1.00000 |
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93 |
28154 | 94 U = |
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95 |
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96 3.00000 4.00000 |
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97 0.00000 0.66667 |
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98 |
28154 | 99 P = |
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100 |
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101 0 1 |
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102 1 0 |
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103 @end group |
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104 @end example |
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105 |
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106 The matrix is not required to be square. |
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107 |
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108 When called with two or three output arguments and a sparse input matrix, |
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109 @code{lu} does not attempt to perform sparsity preserving column permutations. |
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110 Called with a fourth output argument, the sparsity preserving column |
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111 transformation @var{Q} is returned, such that |
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112 @code{@var{P} * @var{A} * @var{Q} = @var{L} * @var{U}}. This is the |
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113 @strong{preferred} way to call @code{lu} with sparse input matrices. |
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114 |
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115 Called with a fifth output argument and a sparse input matrix, @code{lu} |
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116 attempts to use a scaling factor @var{R} on the input matrix such that |
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117 @code{@var{P} * (@var{R} \ @var{A}) * @var{Q} = @var{L} * @var{U}}. |
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118 This typically leads to a sparser and more stable factorization. |
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119 |
28154 | 120 An additional input argument @var{thresh} that defines the pivoting |
121 threshold can be given. @var{thresh} can be a scalar, in which case | |
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122 it defines the @sc{umfpack} pivoting tolerance for both symmetric and |
28154 | 123 unsymmetric cases. If @var{thresh} is a 2-element vector, then the first |
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124 element defines the pivoting tolerance for the unsymmetric @sc{umfpack} |
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125 pivoting strategy and the second for the symmetric strategy. By default, |
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126 the values defined by @code{spparms} are used ([0.1, 0.001]). |
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127 |
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128 Given the string argument @qcode{"vector"}, @code{lu} returns the values |
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129 of @var{P} and @var{Q} as vector values, such that for full matrix, |
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130 @code{@var{A}(@var{P},:) = @var{L} * @var{U}}, and @code{@var{R}(@var{P},:) |
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131 * @var{A}(:,@var{Q}) = @var{L} * @var{U}}. |
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132 |
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133 With two output arguments, returns the permuted forms of the upper and |
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134 lower triangular matrices, such that @code{@var{A} = @var{L} * @var{U}}. |
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135 With one output argument @var{y}, then the matrix returned by the |
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136 @sc{lapack} routines is returned. If the input matrix is sparse then the |
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137 matrix @var{L} is embedded into @var{U} to give a return value similar to |
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138 the full case. For both full and sparse matrices, @code{lu} loses the |
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139 permutation information. |
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140 @seealso{luupdate, ilu, chol, hess, qr, qz, schur, svd} |
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141 @end deftypefn */) |
2928 | 142 { |
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143 int nargin = args.length (); |
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144 bool issparse = (nargin > 0 && args(0).issparse ()); |
2928 | 145 |
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146 if (nargin < 1 || (issparse && nargin > 3) || (! issparse && nargin > 2)) |
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147 print_usage (); |
2928 | 148 |
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149 bool vecout = false; |
28154 | 150 Matrix thresh; |
20892 | 151 int n = 1; |
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152 |
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153 while (n < nargin) |
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154 { |
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155 if (args(n).is_string ()) |
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156 { |
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157 std::string tmp = args(n++).string_value (); |
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158 |
20892 | 159 if (tmp == "vector") |
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160 vecout = true; |
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161 else |
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162 error ("lu: unrecognized string argument"); |
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163 } |
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164 else |
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165 { |
20892 | 166 if (! issparse) |
28154 | 167 error ("lu: can not define pivoting threshold THRESH for full matrices"); |
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168 |
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169 Matrix tmp = args(n++).matrix_value (); |
20892 | 170 if (tmp.numel () == 1) |
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171 { |
28154 | 172 thresh.resize (1,2); |
173 thresh(0) = tmp(0); | |
174 thresh(1) = tmp(0); | |
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175 } |
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176 else if (tmp.numel () == 2) |
28154 | 177 thresh = tmp; |
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178 else |
28154 | 179 error ("lu: THRESH must be a 1- or 2-element vector"); |
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180 } |
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181 } |
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182 |
20892 | 183 octave_value_list retval; |
184 bool scale = (nargout == 5); | |
185 | |
2928 | 186 octave_value arg = args(0); |
187 | |
5275 | 188 octave_idx_type nr = arg.rows (); |
189 octave_idx_type nc = arg.columns (); | |
2928 | 190 |
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191 if (issparse) |
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192 { |
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193 if (arg.isempty ()) |
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194 return octave_value_list (5, SparseMatrix ()); |
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195 |
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196 if (arg.isreal ()) |
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197 { |
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198 SparseMatrix m = arg.sparse_matrix_value (); |
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199 |
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200 if (nargout < 4) |
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201 { |
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202 warning_with_id ("Octave:lu:sparse_input", |
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203 "lu: function may fail when called with less than 4 output arguments and a sparse input"); |
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204 |
20892 | 205 ColumnVector Qinit (nc); |
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206 for (octave_idx_type i = 0; i < nc; i++) |
20892 | 207 Qinit(i) = i; |
28154 | 208 octave::math::sparse_lu<SparseMatrix> fact (m, Qinit, thresh, |
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209 false, true); |
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210 |
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211 if (nargout < 2) |
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212 retval(0) = fact.Y (); |
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213 else |
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214 { |
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215 retval.resize (nargout == 3 ? 3 : 2); |
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216 retval(1) |
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217 = octave_value (fact.U () * fact.Pc_mat ().transpose (), |
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218 MatrixType (MatrixType::Permuted_Upper, |
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219 nc, fact.col_perm ())); |
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220 |
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221 PermMatrix P = fact.Pr_mat (); |
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222 SparseMatrix L = fact.L (); |
20892 | 223 |
224 if (nargout == 2) | |
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225 retval(0) |
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226 = octave_value (P.transpose () * L, |
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227 MatrixType (MatrixType::Permuted_Lower, |
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228 nr, fact.row_perm ())); |
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229 else |
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230 { |
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231 retval(0) = L; |
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232 if (vecout) |
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233 retval(2) = fact.Pr_vec(); |
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234 else |
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235 retval(2) = P; |
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236 } |
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237 } |
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238 } |
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239 else |
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240 { |
20892 | 241 retval.resize (scale ? 5 : 4); |
28154 | 242 octave::math::sparse_lu<SparseMatrix> fact (m, thresh, scale); |
2928 | 243 |
20892 | 244 retval(0) = octave_value (fact.L (), |
245 MatrixType (MatrixType::Lower)); | |
246 retval(1) = octave_value (fact.U (), | |
247 MatrixType (MatrixType::Upper)); | |
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248 |
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249 if (vecout) |
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250 { |
20892 | 251 retval(2) = fact.Pr_vec (); |
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252 retval(3) = fact.Pc_vec (); |
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253 } |
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254 else |
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255 { |
20892 | 256 retval(2) = fact.Pr_mat (); |
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257 retval(3) = fact.Pc_mat (); |
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258 } |
20892 | 259 |
260 if (scale) | |
261 retval(4) = fact.R (); | |
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262 } |
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263 } |
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264 else if (arg.iscomplex ()) |
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265 { |
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266 SparseComplexMatrix m = arg.sparse_complex_matrix_value (); |
2928 | 267 |
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268 if (nargout < 4) |
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269 { |
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270 warning_with_id ("Octave:lu:sparse_input", |
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271 "lu: function may fail when called with less than 4 output arguments and a sparse input"); |
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272 |
20892 | 273 ColumnVector Qinit (nc); |
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274 for (octave_idx_type i = 0; i < nc; i++) |
20892 | 275 Qinit(i) = i; |
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276 octave::math::sparse_lu<SparseComplexMatrix> fact (m, Qinit, |
28154 | 277 thresh, false, |
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278 true); |
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279 |
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280 if (nargout < 2) |
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281 retval(0) = fact.Y (); |
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282 else |
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283 { |
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284 retval.resize (nargout == 3 ? 3 : 2); |
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285 retval(1) |
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286 = octave_value (fact.U () * fact.Pc_mat ().transpose (), |
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287 MatrixType (MatrixType::Permuted_Upper, |
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288 nc, fact.col_perm ())); |
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289 |
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290 PermMatrix P = fact.Pr_mat (); |
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291 SparseComplexMatrix L = fact.L (); |
20892 | 292 if (nargout == 2) |
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293 retval(0) |
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294 = octave_value (P.transpose () * L, |
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295 MatrixType (MatrixType::Permuted_Lower, |
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296 nr, fact.row_perm ())); |
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297 else |
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298 { |
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299 retval(0) = L; |
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300 if (vecout) |
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301 retval(2) = fact.Pr_vec(); |
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302 else |
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303 retval(2) = P; |
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304 } |
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305 } |
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306 } |
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307 else |
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308 { |
20892 | 309 retval.resize (scale ? 5 : 4); |
28154 | 310 octave::math::sparse_lu<SparseComplexMatrix> fact (m, thresh, |
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311 scale); |
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312 |
20892 | 313 retval(0) = octave_value (fact.L (), |
314 MatrixType (MatrixType::Lower)); | |
315 retval(1) = octave_value (fact.U (), | |
316 MatrixType (MatrixType::Upper)); | |
317 | |
318 if (vecout) | |
319 { | |
320 retval(2) = fact.Pr_vec (); | |
321 retval(3) = fact.Pc_vec (); | |
322 } | |
323 else | |
324 { | |
325 retval(2) = fact.Pr_mat (); | |
326 retval(3) = fact.Pc_mat (); | |
327 } | |
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328 |
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329 if (scale) |
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330 retval(4) = fact.R (); |
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331 } |
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332 |
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333 } |
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334 else |
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335 err_wrong_type_arg ("lu", arg); |
2928 | 336 } |
337 else | |
338 { | |
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339 if (arg.isempty ()) |
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340 return octave_value_list (3, Matrix ()); |
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341 |
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342 if (arg.isreal ()) |
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343 { |
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344 if (arg.is_single_type ()) |
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345 { |
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346 FloatMatrix m = arg.float_matrix_value (); |
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347 |
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348 octave::math::lu<FloatMatrix> fact (m); |
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349 |
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350 switch (nargout) |
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351 { |
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352 case 0: |
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353 case 1: |
20892 | 354 retval = ovl (fact.Y ()); |
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355 break; |
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356 |
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357 case 2: |
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358 { |
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359 PermMatrix P = fact.P (); |
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360 FloatMatrix L = P.transpose () * fact.L (); |
20892 | 361 retval = ovl (L, get_lu_u (fact)); |
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362 } |
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363 break; |
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364 |
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365 case 3: |
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366 default: |
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367 { |
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368 if (vecout) |
20892 | 369 retval = ovl (get_lu_l (fact), get_lu_u (fact), |
370 fact.P_vec ()); | |
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371 else |
20892 | 372 retval = ovl (get_lu_l (fact), get_lu_u (fact), |
373 fact.P ()); | |
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374 } |
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375 break; |
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376 } |
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377 } |
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378 else |
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379 { |
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380 Matrix m = arg.matrix_value (); |
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381 |
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382 octave::math::lu<Matrix> fact (m); |
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383 |
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384 switch (nargout) |
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385 { |
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386 case 0: |
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387 case 1: |
20892 | 388 retval = ovl (fact.Y ()); |
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389 break; |
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390 |
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391 case 2: |
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392 { |
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393 PermMatrix P = fact.P (); |
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394 Matrix L = P.transpose () * fact.L (); |
20892 | 395 retval = ovl (L, get_lu_u (fact)); |
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396 } |
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397 break; |
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398 |
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399 case 3: |
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400 default: |
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401 { |
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402 if (vecout) |
20892 | 403 retval = ovl (get_lu_l (fact), get_lu_u (fact), |
404 fact.P_vec ()); | |
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405 else |
20892 | 406 retval = ovl (get_lu_l (fact), get_lu_u (fact), |
407 fact.P ()); | |
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408 } |
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409 break; |
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410 } |
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411 } |
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412 } |
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413 else if (arg.iscomplex ()) |
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414 { |
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415 if (arg.is_single_type ()) |
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416 { |
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417 FloatComplexMatrix m = arg.float_complex_matrix_value (); |
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418 |
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419 octave::math::lu<FloatComplexMatrix> fact (m); |
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420 |
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421 switch (nargout) |
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422 { |
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423 case 0: |
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424 case 1: |
20892 | 425 retval = ovl (fact.Y ()); |
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426 break; |
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427 |
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428 case 2: |
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429 { |
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430 PermMatrix P = fact.P (); |
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431 FloatComplexMatrix L = P.transpose () * fact.L (); |
20892 | 432 retval = ovl (L, get_lu_u (fact)); |
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433 } |
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434 break; |
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435 |
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436 case 3: |
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437 default: |
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438 { |
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439 if (vecout) |
20892 | 440 retval = ovl (get_lu_l (fact), get_lu_u (fact), |
441 fact.P_vec ()); | |
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442 else |
20892 | 443 retval = ovl (get_lu_l (fact), get_lu_u (fact), |
444 fact.P ()); | |
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445 } |
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446 break; |
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447 } |
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448 } |
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449 else |
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450 { |
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451 ComplexMatrix m = arg.complex_matrix_value (); |
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452 |
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453 octave::math::lu<ComplexMatrix> fact (m); |
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454 |
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455 switch (nargout) |
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456 { |
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457 case 0: |
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458 case 1: |
20892 | 459 retval = ovl (fact.Y ()); |
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460 break; |
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461 |
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462 case 2: |
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463 { |
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464 PermMatrix P = fact.P (); |
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465 ComplexMatrix L = P.transpose () * fact.L (); |
20892 | 466 retval = ovl (L, get_lu_u (fact)); |
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467 } |
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468 break; |
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469 |
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470 case 3: |
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471 default: |
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472 { |
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473 if (vecout) |
20892 | 474 retval = ovl (get_lu_l (fact), get_lu_u (fact), |
475 fact.P_vec ()); | |
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476 else |
20892 | 477 retval = ovl (get_lu_l (fact), get_lu_u (fact), |
478 fact.P ()); | |
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479 } |
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480 break; |
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481 } |
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482 } |
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483 } |
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484 else |
21100
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|
485 err_wrong_type_arg ("lu", arg); |
2928 | 486 } |
487 | |
488 return retval; | |
489 } | |
490 | |
491 /* | |
21317
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492 %!assert(lu ([1, 2; 3, 4]), [3, 4; 1/3, 2/3], eps) |
7814
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493 |
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494 %!test |
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495 %! [l, u] = lu ([1, 2; 3, 4]); |
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496 %! assert (l, [1/3, 1; 1, 0], sqrt (eps)); |
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497 %! assert (u, [3, 4; 0, 2/3], sqrt (eps)); |
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498 |
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499 %!test |
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500 %! [l, u, p] = lu ([1, 2; 3, 4]); |
14501
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501 %! assert (l, [1, 0; 1/3, 1], sqrt (eps)); |
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502 %! assert (u, [3, 4; 0, 2/3], sqrt (eps)); |
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503 %! assert (p(:,:), [0, 1; 1, 0], sqrt (eps)); |
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504 |
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505 %!test |
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506 %! [l, u, p] = lu ([1, 2; 3, 4], "vector"); |
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507 %! assert (l, [1, 0; 1/3, 1], sqrt (eps)); |
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508 %! assert (u, [3, 4; 0, 2/3], sqrt (eps)); |
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|
509 %! assert (p, [2;1], sqrt (eps)); |
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|
510 |
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|
511 %!test |
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512 %! [l, u, p] = lu ([1, 2; 3, 4; 5, 6]); |
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513 %! assert (l, [1, 0; 1/5, 1; 3/5, 1/2], sqrt (eps)); |
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514 %! assert (u, [5, 6; 0, 4/5], sqrt (eps)); |
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|
515 %! assert (p(:,:), [0, 0, 1; 1, 0, 0; 0 1 0], sqrt (eps)); |
7814
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|
516 |
14501
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|
517 %!assert (lu (single ([1, 2; 3, 4])), single ([3, 4; 1/3, 2/3]), eps ("single")) |
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518 |
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|
519 %!test |
14501
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520 %! [l, u] = lu (single ([1, 2; 3, 4])); |
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521 %! assert (l, single ([1/3, 1; 1, 0]), sqrt (eps ("single"))); |
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522 %! assert (u, single ([3, 4; 0, 2/3]), sqrt (eps ("single"))); |
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523 |
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|
524 %!test |
14501
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|
525 %! [l, u, p] = lu (single ([1, 2; 3, 4])); |
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526 %! assert (l, single ([1, 0; 1/3, 1]), sqrt (eps ("single"))); |
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527 %! assert (u, single ([3, 4; 0, 2/3]), sqrt (eps ("single"))); |
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528 %! assert (p(:,:), single ([0, 1; 1, 0]), sqrt (eps ("single"))); |
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529 |
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|
530 %!test |
14501
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|
531 %! [l, u, p] = lu (single ([1, 2; 3, 4]), "vector"); |
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532 %! assert (l, single ([1, 0; 1/3, 1]), sqrt (eps ("single"))); |
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|
533 %! assert (u, single ([3, 4; 0, 2/3]), sqrt (eps ("single"))); |
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|
534 %! assert (p, single ([2;1]), sqrt (eps ("single"))); |
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|
535 |
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|
536 %!test |
14501
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|
537 %! [l u p] = lu (single ([1, 2; 3, 4; 5, 6])); |
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|
538 %! assert (l, single ([1, 0; 1/5, 1; 3/5, 1/2]), sqrt (eps ("single"))); |
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|
539 %! assert (u, single ([5, 6; 0, 4/5]), sqrt (eps ("single"))); |
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|
540 %! assert (p(:,:), single ([0, 0, 1; 1, 0, 0; 0 1 0]), sqrt (eps ("single"))); |
7814
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|
541 |
18488
4c2465444a96
Use %!testif HAVE_UMFPACK for sparse lu test added in cset 2a45b6b87bee
Mike Miller <mtmiller@ieee.org>
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18427
diff
changeset
|
542 %!testif HAVE_UMFPACK |
18425
2a45b6b87bee
correct numerical errors in sparse LU factorization (bug #41116).
Michael C. Grant <mcg@cvxr.com>
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17787
diff
changeset
|
543 %! Bi = [1 2 3 4 5 2 3 6 7 8 4 5 7 8 9]; |
2a45b6b87bee
correct numerical errors in sparse LU factorization (bug #41116).
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changeset
|
544 %! Bj = [1 3 4 5 6 7 8 9 11 12 13 14 15 16 17]; |
2a45b6b87bee
correct numerical errors in sparse LU factorization (bug #41116).
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|
545 %! Bv = [1 1 1 1 1 1 -1 1 1 1 1 -1 1 -1 1]; |
18427
93c019f00e59
maint: whitespace fixes for libinterp/corefcn/lu.cc
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
18426
diff
changeset
|
546 %! B = sparse (Bi, Bj, Bv); |
25037
1c077d652c57
Add new warning ID and message when lu is called with sparse input incorrectly (bug #53390).
Rik <rik@octave.org>
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25036
diff
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547 %! warning ("off", "Octave:lu:sparse_input", "local"); |
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548 %! [L, U] = lu (B); |
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549 %! assert (L*U, B); |
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550 %! [L, U, P] = lu(B); |
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551 %! assert (P'*L*U, B); |
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552 %! [L, U, P, Q] = lu (B); |
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553 %! assert (P'*L*U*Q', B); |
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554 |
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555 %!error lu () |
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556 %!testif HAVE_UMFPACK |
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557 %! fail ("[l,u] = lu (sparse (magic (3)))", "warning", "function may fail"); |
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558 %!error <can not define pivoting threshold> lu ([1, 2; 3, 4], 2) |
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559 |
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560 */ |
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561 |
9708 | 562 static |
563 bool check_lu_dims (const octave_value& l, const octave_value& u, | |
564 const octave_value& p) | |
565 { | |
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566 octave_idx_type m = l.rows (); |
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567 octave_idx_type k = u.rows (); |
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568 octave_idx_type n = u.columns (); |
20892 | 569 |
9708 | 570 return ((l.ndims () == 2 && u.ndims () == 2 && k == l.columns ()) |
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571 && k == std::min (m, n) |
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572 && (p.is_undefined () || p.rows () == m)); |
9708 | 573 } |
574 | |
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575 DEFUN (luupdate, args, , |
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576 doc: /* -*- texinfo -*- |
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577 @deftypefn {} {[@var{L}, @var{U}] =} luupdate (@var{L}, @var{U}, @var{x}, @var{y}) |
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578 @deftypefnx {} {[@var{L}, @var{U}, @var{P}] =} luupdate (@var{L}, @var{U}, @var{P}, @var{x}, @var{y}) |
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579 Given an LU@tie{}factorization of a real or complex matrix |
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580 @w{@var{A} = @var{L}*@var{U}}, @var{L}@tie{}lower unit trapezoidal and |
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581 @var{U}@tie{}upper trapezoidal, return the LU@tie{}factorization |
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582 of @w{@var{A} + @var{x}*@var{y}.'}, where @var{x} and @var{y} are |
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583 column vectors (rank-1 update) or matrices with equal number of columns |
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584 (rank-k update). |
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585 |
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586 Optionally, row-pivoted updating can be used by supplying a row permutation |
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587 (pivoting) matrix @var{P}; in that case, an updated permutation matrix is |
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588 returned. Note that if @var{L}, @var{U}, @var{P} is a pivoted |
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589 LU@tie{}factorization as obtained by @code{lu}: |
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590 |
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591 @example |
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592 [@var{L}, @var{U}, @var{P}] = lu (@var{A}); |
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593 @end example |
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594 |
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595 @noindent |
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596 then a factorization of @tcode{@var{A}+@var{x}*@var{y}.'} can be obtained |
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597 either as |
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598 |
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599 @example |
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600 [@var{L1}, @var{U1}] = lu (@var{L}, @var{U}, @var{P}*@var{x}, @var{y}) |
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601 @end example |
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602 |
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603 @noindent |
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604 or |
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605 |
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606 @example |
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607 [@var{L1}, @var{U1}, @var{P1}] = lu (@var{L}, @var{U}, @var{P}, @var{x}, @var{y}) |
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608 @end example |
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609 |
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610 The first form uses the unpivoted algorithm, which is faster, but less |
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611 stable. The second form uses a slower pivoted algorithm, which is more |
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612 stable. |
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613 |
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614 The matrix case is done as a sequence of rank-1 updates; thus, for large |
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615 enough k, it will be both faster and more accurate to recompute the |
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616 factorization from scratch. |
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617 @seealso{lu, cholupdate, qrupdate} |
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618 @end deftypefn */) |
9708 | 619 { |
20816
b16bcd7a2a33
Use int rather than octave_idx_type for nargin data type.
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diff
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620 int nargin = args.length (); |
9708 | 621 |
622 if (nargin != 4 && nargin != 5) | |
20802
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eliminate return statements after calls to print_usage
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|
623 print_usage (); |
9708 | 624 |
20812
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maint: Clean-up more instances of print_usage().
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diff
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625 bool pivoted = (nargin == 5); |
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|
626 |
9708 | 627 octave_value argl = args(0); |
628 octave_value argu = args(1); | |
23450
855122b993da
maint: Wrap tertiary operator in parentheses "(COND ? x : y)".
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23220
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|
629 octave_value argp = (pivoted ? args(2) : octave_value ()); |
9708 | 630 octave_value argx = args(2 + pivoted); |
631 octave_value argy = args(3 + pivoted); | |
632 | |
23586
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|
633 if (! (argl.isnumeric () && argu.isnumeric () |
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634 && argx.isnumeric () && argy.isnumeric () |
20892 | 635 && (! pivoted || argp.is_perm_matrix ()))) |
636 error ("luupdate: L, U, X, and Y must be numeric"); | |
9708 | 637 |
20892 | 638 if (! check_lu_dims (argl, argu, argp)) |
639 error ("luupdate: dimension mismatch"); | |
9708 | 640 |
20892 | 641 PermMatrix P = (pivoted |
642 ? argp.perm_matrix_value () | |
643 : PermMatrix::eye (argl.rows ())); | |
9708 | 644 |
23582
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maint: Deprecate is_real_type and replace with isreal.
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645 if (argl.isreal () && argu.isreal () |
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646 && argx.isreal () && argy.isreal ()) |
20892 | 647 { |
648 // all real case | |
649 if (argl.is_single_type () || argu.is_single_type () | |
650 || argx.is_single_type () || argy.is_single_type ()) | |
651 { | |
652 FloatMatrix L = argl.float_matrix_value (); | |
653 FloatMatrix U = argu.float_matrix_value (); | |
654 FloatMatrix x = argx.float_matrix_value (); | |
655 FloatMatrix y = argy.float_matrix_value (); | |
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656 |
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657 octave::math::lu<FloatMatrix> fact (L, U, P); |
20892 | 658 if (pivoted) |
659 fact.update_piv (x, y); | |
660 else | |
661 fact.update (x, y); | |
9708 | 662 |
20892 | 663 if (pivoted) |
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664 return ovl (get_lu_l (fact), get_lu_u (fact), fact.P ()); |
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665 else |
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666 return ovl (get_lu_l (fact), get_lu_u (fact)); |
9708 | 667 } |
668 else | |
20892 | 669 { |
670 Matrix L = argl.matrix_value (); | |
671 Matrix U = argu.matrix_value (); | |
672 Matrix x = argx.matrix_value (); | |
673 Matrix y = argy.matrix_value (); | |
674 | |
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675 octave::math::lu<Matrix> fact (L, U, P); |
20892 | 676 if (pivoted) |
677 fact.update_piv (x, y); | |
678 else | |
679 fact.update (x, y); | |
680 | |
681 if (pivoted) | |
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682 return ovl (get_lu_l (fact), get_lu_u (fact), fact.P ()); |
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683 else |
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684 return ovl (get_lu_l (fact), get_lu_u (fact)); |
20892 | 685 } |
9708 | 686 } |
687 else | |
20892 | 688 { |
689 // complex case | |
690 if (argl.is_single_type () || argu.is_single_type () | |
691 || argx.is_single_type () || argy.is_single_type ()) | |
692 { | |
693 FloatComplexMatrix L = argl.float_complex_matrix_value (); | |
694 FloatComplexMatrix U = argu.float_complex_matrix_value (); | |
695 FloatComplexMatrix x = argx.float_complex_matrix_value (); | |
696 FloatComplexMatrix y = argy.float_complex_matrix_value (); | |
697 | |
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698 octave::math::lu<FloatComplexMatrix> fact (L, U, P); |
20892 | 699 if (pivoted) |
700 fact.update_piv (x, y); | |
701 else | |
702 fact.update (x, y); | |
703 | |
704 if (pivoted) | |
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705 return ovl (get_lu_l (fact), get_lu_u (fact), fact.P ()); |
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706 else |
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707 return ovl (get_lu_l (fact), get_lu_u (fact)); |
20892 | 708 } |
709 else | |
710 { | |
711 ComplexMatrix L = argl.complex_matrix_value (); | |
712 ComplexMatrix U = argu.complex_matrix_value (); | |
713 ComplexMatrix x = argx.complex_matrix_value (); | |
714 ComplexMatrix y = argy.complex_matrix_value (); | |
715 | |
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716 octave::math::lu<ComplexMatrix> fact (L, U, P); |
20892 | 717 if (pivoted) |
718 fact.update_piv (x, y); | |
719 else | |
720 fact.update (x, y); | |
721 | |
722 if (pivoted) | |
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723 return ovl (get_lu_l (fact), get_lu_u (fact), fact.P ()); |
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724 else |
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725 return ovl (get_lu_l (fact), get_lu_u (fact)); |
20892 | 726 } |
727 } | |
9708 | 728 } |
729 | |
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730 /* |
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731 %!shared A, u, v, Ac, uc, vc |
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|
732 %! A = [0.091364 0.613038 0.999083; |
cf70ee43077c
add tests for LU updating
Jaroslav Hajek <highegg@gmail.com>
parents:
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diff
changeset
|
733 %! 0.594638 0.425302 0.603537; |
cf70ee43077c
add tests for LU updating
Jaroslav Hajek <highegg@gmail.com>
parents:
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diff
changeset
|
734 %! 0.383594 0.291238 0.085574; |
cf70ee43077c
add tests for LU updating
Jaroslav Hajek <highegg@gmail.com>
parents:
9724
diff
changeset
|
735 %! 0.265712 0.268003 0.238409; |
cf70ee43077c
add tests for LU updating
Jaroslav Hajek <highegg@gmail.com>
parents:
9724
diff
changeset
|
736 %! 0.669966 0.743851 0.445057 ]; |
cf70ee43077c
add tests for LU updating
Jaroslav Hajek <highegg@gmail.com>
parents:
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diff
changeset
|
737 %! |
11586
12df7854fa7c
strip trailing whitespace from source files
John W. Eaton <jwe@octave.org>
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|
738 %! u = [0.85082; |
12df7854fa7c
strip trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents:
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diff
changeset
|
739 %! 0.76426; |
12df7854fa7c
strip trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents:
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diff
changeset
|
740 %! 0.42883; |
12df7854fa7c
strip trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents:
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diff
changeset
|
741 %! 0.53010; |
10080
cf70ee43077c
add tests for LU updating
Jaroslav Hajek <highegg@gmail.com>
parents:
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diff
changeset
|
742 %! 0.80683 ]; |
cf70ee43077c
add tests for LU updating
Jaroslav Hajek <highegg@gmail.com>
parents:
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diff
changeset
|
743 %! |
cf70ee43077c
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Jaroslav Hajek <highegg@gmail.com>
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diff
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|
744 %! v = [0.98810; |
cf70ee43077c
add tests for LU updating
Jaroslav Hajek <highegg@gmail.com>
parents:
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changeset
|
745 %! 0.24295; |
cf70ee43077c
add tests for LU updating
Jaroslav Hajek <highegg@gmail.com>
parents:
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diff
changeset
|
746 %! 0.43167 ]; |
cf70ee43077c
add tests for LU updating
Jaroslav Hajek <highegg@gmail.com>
parents:
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diff
changeset
|
747 %! |
cf70ee43077c
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Jaroslav Hajek <highegg@gmail.com>
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diff
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|
748 %! Ac = [0.620405 + 0.956953i 0.480013 + 0.048806i 0.402627 + 0.338171i; |
14501
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|
749 %! 0.589077 + 0.658457i 0.013205 + 0.279323i 0.229284 + 0.721929i; |
60e5cf354d80
Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents:
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|
750 %! 0.092758 + 0.345687i 0.928679 + 0.241052i 0.764536 + 0.832406i; |
60e5cf354d80
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Rik <octave@nomad.inbox5.com>
parents:
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|
751 %! 0.912098 + 0.721024i 0.049018 + 0.269452i 0.730029 + 0.796517i; |
60e5cf354d80
Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents:
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changeset
|
752 %! 0.112849 + 0.603871i 0.486352 + 0.142337i 0.355646 + 0.151496i ]; |
10080
cf70ee43077c
add tests for LU updating
Jaroslav Hajek <highegg@gmail.com>
parents:
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diff
changeset
|
753 %! |
cf70ee43077c
add tests for LU updating
Jaroslav Hajek <highegg@gmail.com>
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|
754 %! uc = [0.20351 + 0.05401i; |
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|
755 %! 0.13141 + 0.43708i; |
60e5cf354d80
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Rik <octave@nomad.inbox5.com>
parents:
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|
756 %! 0.29808 + 0.08789i; |
60e5cf354d80
Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents:
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|
757 %! 0.69821 + 0.38844i; |
60e5cf354d80
Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents:
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|
758 %! 0.74871 + 0.25821i ]; |
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cf70ee43077c
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Jaroslav Hajek <highegg@gmail.com>
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|
759 %! |
cf70ee43077c
add tests for LU updating
Jaroslav Hajek <highegg@gmail.com>
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|
760 %! vc = [0.85839 + 0.29468i; |
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Rik <octave@nomad.inbox5.com>
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|
761 %! 0.20820 + 0.93090i; |
60e5cf354d80
Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents:
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|
762 %! 0.86184 + 0.34689i ]; |
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cf70ee43077c
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Jaroslav Hajek <highegg@gmail.com>
parents:
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diff
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|
763 %! |
cf70ee43077c
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Jaroslav Hajek <highegg@gmail.com>
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|
764 |
10094
ab1101011a6d
lu.cc: avoid test failures if HAVE_QRUPDATE_LUU is not defined
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|
765 %!testif HAVE_QRUPDATE_LUU |
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|
766 %! [L,U,P] = lu (A); |
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767 %! [L,U] = luupdate (L,U,P*u,v); |
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|
768 %! assert (norm (vec (tril (L)-L), Inf) == 0); |
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|
769 %! assert (norm (vec (triu (U)-U), Inf) == 0); |
60e5cf354d80
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|
770 %! assert (norm (vec (P'*L*U - A - u*v.'), Inf) < norm (A)*1e1*eps); |
11586
12df7854fa7c
strip trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents:
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diff
changeset
|
771 %! |
10094
ab1101011a6d
lu.cc: avoid test failures if HAVE_QRUPDATE_LUU is not defined
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|
772 %!testif HAVE_QRUPDATE_LUU |
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|
773 %! [L,U,P] = lu (Ac); |
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774 %! [L,U] = luupdate (L,U,P*uc,vc); |
60e5cf354d80
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|
775 %! assert (norm (vec (tril (L)-L), Inf) == 0); |
60e5cf354d80
Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
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|
776 %! assert (norm (vec (triu (U)-U), Inf) == 0); |
60e5cf354d80
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|
777 %! assert (norm (vec (P'*L*U - Ac - uc*vc.'), Inf) < norm (Ac)*1e1*eps); |
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cf70ee43077c
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Jaroslav Hajek <highegg@gmail.com>
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|
778 |
10094
ab1101011a6d
lu.cc: avoid test failures if HAVE_QRUPDATE_LUU is not defined
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|
779 %!testif HAVE_QRUPDATE_LUU |
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|
780 %! [L,U,P] = lu (single (A)); |
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|
781 %! [L,U] = luupdate (L,U,P*single (u), single (v)); |
60e5cf354d80
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|
782 %! assert (norm (vec (tril (L)-L), Inf) == 0); |
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Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
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|
783 %! assert (norm (vec (triu (U)-U), Inf) == 0); |
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parents:
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|
784 %! assert (norm (vec (P'*L*U - single (A) - single (u)*single (v).'), Inf) < norm (single (A))*1e1*eps ("single")); |
11586
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|
785 %! |
10094
ab1101011a6d
lu.cc: avoid test failures if HAVE_QRUPDATE_LUU is not defined
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parents:
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|
786 %!testif HAVE_QRUPDATE_LUU |
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|
787 %! [L,U,P] = lu (single (Ac)); |
60e5cf354d80
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|
788 %! [L,U] = luupdate (L,U,P*single (uc),single (vc)); |
60e5cf354d80
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|
789 %! assert (norm (vec (tril (L)-L), Inf) == 0); |
60e5cf354d80
Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
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parents:
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|
790 %! assert (norm (vec (triu (U)-U), Inf) == 0); |
60e5cf354d80
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|
791 %! assert (norm (vec (P'*L*U - single (Ac) - single (uc)*single (vc).'), Inf) < norm (single (Ac))*1e1*eps ("single")); |
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Jaroslav Hajek <highegg@gmail.com>
parents:
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diff
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|
792 |
10094
ab1101011a6d
lu.cc: avoid test failures if HAVE_QRUPDATE_LUU is not defined
John W. Eaton <jwe@octave.org>
parents:
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diff
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|
793 %!testif HAVE_QRUPDATE_LUU |
14501
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|
794 %! [L,U,P] = lu (A); |
60e5cf354d80
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|
795 %! [L,U,P] = luupdate (L,U,P,u,v); |
60e5cf354d80
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|
796 %! assert (norm (vec (tril (L)-L), Inf) == 0); |
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|
797 %! assert (norm (vec (triu (U)-U), Inf) == 0); |
60e5cf354d80
Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
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|
798 %! assert (norm (vec (P'*L*U - A - u*v.'), Inf) < norm (A)*1e1*eps); |
11586
12df7854fa7c
strip trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents:
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diff
changeset
|
799 %! |
10094
ab1101011a6d
lu.cc: avoid test failures if HAVE_QRUPDATE_LUU is not defined
John W. Eaton <jwe@octave.org>
parents:
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diff
changeset
|
800 %!testif HAVE_QRUPDATE_LUU |
18849
aa9ca67f09fb
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David Spies <dnspies@gmail.com>
parents:
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diff
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|
801 %! [L,U,P] = lu (A); |
aa9ca67f09fb
make all permutation matrices column permutations (bug #42418)
David Spies <dnspies@gmail.com>
parents:
18678
diff
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|
802 %! [~,ordcols] = max (P,[],1); |
aa9ca67f09fb
make all permutation matrices column permutations (bug #42418)
David Spies <dnspies@gmail.com>
parents:
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diff
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|
803 %! [~,ordrows] = max (P,[],2); |
aa9ca67f09fb
make all permutation matrices column permutations (bug #42418)
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parents:
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diff
changeset
|
804 %! P1 = eye (size(P))(:,ordcols); |
aa9ca67f09fb
make all permutation matrices column permutations (bug #42418)
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parents:
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diff
changeset
|
805 %! P2 = eye (size(P))(ordrows,:); |
aa9ca67f09fb
make all permutation matrices column permutations (bug #42418)
David Spies <dnspies@gmail.com>
parents:
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diff
changeset
|
806 %! assert(P1 == P); |
aa9ca67f09fb
make all permutation matrices column permutations (bug #42418)
David Spies <dnspies@gmail.com>
parents:
18678
diff
changeset
|
807 %! assert(P2 == P); |
aa9ca67f09fb
make all permutation matrices column permutations (bug #42418)
David Spies <dnspies@gmail.com>
parents:
18678
diff
changeset
|
808 %! [L,U,P] = luupdate (L,U,P,u,v); |
aa9ca67f09fb
make all permutation matrices column permutations (bug #42418)
David Spies <dnspies@gmail.com>
parents:
18678
diff
changeset
|
809 %! [L,U,P1] = luupdate (L,U,P1,u,v); |
aa9ca67f09fb
make all permutation matrices column permutations (bug #42418)
David Spies <dnspies@gmail.com>
parents:
18678
diff
changeset
|
810 %! [L,U,P2] = luupdate (L,U,P2,u,v); |
aa9ca67f09fb
make all permutation matrices column permutations (bug #42418)
David Spies <dnspies@gmail.com>
parents:
18678
diff
changeset
|
811 %! assert(P1 == P); |
aa9ca67f09fb
make all permutation matrices column permutations (bug #42418)
David Spies <dnspies@gmail.com>
parents:
18678
diff
changeset
|
812 %! assert(P2 == P); |
aa9ca67f09fb
make all permutation matrices column permutations (bug #42418)
David Spies <dnspies@gmail.com>
parents:
18678
diff
changeset
|
813 %! |
aa9ca67f09fb
make all permutation matrices column permutations (bug #42418)
David Spies <dnspies@gmail.com>
parents:
18678
diff
changeset
|
814 %!testif HAVE_QRUPDATE_LUU |
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|
815 %! [L,U,P] = lu (Ac); |
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parents:
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|
816 %! [L,U,P] = luupdate (L,U,P,uc,vc); |
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|
817 %! assert (norm (vec (tril (L)-L), Inf) == 0); |
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|
818 %! assert (norm (vec (triu (U)-U), Inf) == 0); |
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|
819 %! assert (norm (vec (P'*L*U - Ac - uc*vc.'), Inf) < norm (Ac)*1e1*eps); |
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Jaroslav Hajek <highegg@gmail.com>
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|
820 |
10094
ab1101011a6d
lu.cc: avoid test failures if HAVE_QRUPDATE_LUU is not defined
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|
821 %!testif HAVE_QRUPDATE_LUU |
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|
822 %! [L,U,P] = lu (single (A)); |
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|
823 %! [L,U,P] = luupdate (L,U,P,single (u),single (v)); |
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|
824 %! assert (norm (vec (tril (L)-L), Inf) == 0); |
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|
825 %! assert (norm (vec (triu (U)-U), Inf) == 0); |
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|
826 %! assert (norm (vec (P'*L*U - single (A) - single (u)*single (v).'), Inf) < norm (single (A))*1e1*eps ("single")); |
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changeset
|
827 %! |
10094
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lu.cc: avoid test failures if HAVE_QRUPDATE_LUU is not defined
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|
828 %!testif HAVE_QRUPDATE_LUU |
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|
829 %! [L,U,P] = lu (single (Ac)); |
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|
830 %! [L,U,P] = luupdate (L,U,P,single (uc),single (vc)); |
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|
831 %! assert (norm (vec (tril (L)-L), Inf) == 0); |
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|
832 %! assert (norm (vec (triu (U)-U), Inf) == 0); |
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833 %! assert (norm (vec (P'*L*U - single (Ac) - single (uc)*single (vc).'), Inf) < norm (single (Ac))*1e1*eps ("single")); |
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cf70ee43077c
add tests for LU updating
Jaroslav Hajek <highegg@gmail.com>
parents:
9724
diff
changeset
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834 */ |