Mercurial > octave-dspies
annotate libinterp/corefcn/lu.cc @ 18678:6113e0c6920b
maint: Clean up extra spaces before/after parentheses.
author | Rik <rik@octave.org> |
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date | Fri, 25 Apr 2014 13:25:25 -0700 |
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rev | line source |
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2928 | 1 /* |
2 | |
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3 Copyright (C) 1996-2013 John W. Eaton |
2928 | 4 |
5 This file is part of Octave. | |
6 | |
7 Octave is free software; you can redistribute it and/or modify it | |
8 under the terms of the GNU General Public License as published by the | |
7016 | 9 Free Software Foundation; either version 3 of the License, or (at your |
10 option) any later version. | |
2928 | 11 |
12 Octave is distributed in the hope that it will be useful, but WITHOUT | |
13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
15 for more details. | |
16 | |
17 You should have received a copy of the GNU General Public License | |
7016 | 18 along with Octave; see the file COPYING. If not, see |
19 <http://www.gnu.org/licenses/>. | |
2928 | 20 |
21 */ | |
22 | |
23 #ifdef HAVE_CONFIG_H | |
24 #include <config.h> | |
25 #endif | |
26 | |
27 #include "CmplxLU.h" | |
28 #include "dbleLU.h" | |
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29 #include "fCmplxLU.h" |
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30 #include "floatLU.h" |
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31 #include "SparseCmplxLU.h" |
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32 #include "SparsedbleLU.h" |
2928 | 33 |
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34 #include "defun.h" |
2928 | 35 #include "error.h" |
36 #include "gripes.h" | |
37 #include "oct-obj.h" | |
38 #include "utils.h" | |
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39 #include "ov-re-sparse.h" |
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40 #include "ov-cx-sparse.h" |
2928 | 41 |
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42 template <class MT> |
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43 static octave_value |
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44 get_lu_l (const base_lu<MT>& fact) |
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45 { |
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46 MT L = fact.L (); |
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47 if (L.is_square ()) |
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48 return octave_value (L, MatrixType (MatrixType::Lower)); |
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49 else |
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50 return L; |
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51 } |
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52 |
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53 template <class MT> |
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54 static octave_value |
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55 get_lu_u (const base_lu<MT>& fact) |
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56 { |
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57 MT U = fact.U (); |
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58 if (U.is_square () && fact.regular ()) |
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59 return octave_value (U, MatrixType (MatrixType::Upper)); |
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60 else |
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61 return U; |
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62 } |
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63 |
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64 DEFUN (lu, args, nargout, |
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65 "-*- texinfo -*-\n\ |
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66 @deftypefn {Built-in Function} {[@var{L}, @var{U}] =} lu (@var{A})\n\ |
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67 @deftypefnx {Built-in Function} {[@var{L}, @var{U}, @var{P}] =} lu (@var{A})\n\ |
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68 @deftypefnx {Built-in Function} {[@var{L}, @var{U}, @var{P}, @var{Q}] =} lu (@var{S})\n\ |
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69 @deftypefnx {Built-in Function} {[@var{L}, @var{U}, @var{P}, @var{Q}, @var{R}] =} lu (@var{S})\n\ |
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70 @deftypefnx {Built-in Function} {[@dots{}] =} lu (@var{S}, @var{thres})\n\ |
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71 @deftypefnx {Built-in Function} {@var{y} =} lu (@dots{})\n\ |
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72 @deftypefnx {Built-in Function} {[@dots{}] =} lu (@dots{}, \"vector\")\n\ |
3372 | 73 @cindex LU decomposition\n\ |
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74 Compute the LU@tie{}decomposition of @var{A}. If @var{A} is full\n\ |
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75 subroutines from\n\ |
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76 @sc{lapack} are used and if @var{A} is sparse then @sc{umfpack} is used. The\n\ |
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77 result is returned in a permuted form, according to the optional return\n\ |
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78 value @var{P}. For example, given the matrix @code{a = [1, 2; 3, 4]},\n\ |
3372 | 79 \n\ |
80 @example\n\ | |
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81 [l, u, p] = lu (@var{a})\n\ |
3372 | 82 @end example\n\ |
83 \n\ | |
84 @noindent\n\ | |
85 returns\n\ | |
86 \n\ | |
87 @example\n\ | |
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88 @group\n\ |
3372 | 89 l =\n\ |
90 \n\ | |
91 1.00000 0.00000\n\ | |
92 0.33333 1.00000\n\ | |
93 \n\ | |
94 u =\n\ | |
95 \n\ | |
96 3.00000 4.00000\n\ | |
97 0.00000 0.66667\n\ | |
98 \n\ | |
99 p =\n\ | |
100 \n\ | |
101 0 1\n\ | |
102 1 0\n\ | |
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103 @end group\n\ |
3372 | 104 @end example\n\ |
4329 | 105 \n\ |
5457 | 106 The matrix is not required to be square.\n\ |
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107 \n\ |
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108 When called with two or three output arguments and a spare input matrix,\n\ |
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109 @code{lu} does not attempt to perform sparsity preserving column\n\ |
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110 permutations. Called with a fourth output argument, the sparsity\n\ |
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111 preserving column transformation @var{Q} is returned, such that\n\ |
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112 @code{@var{P} * @var{A} * @var{Q} = @var{L} * @var{U}}.\n\ |
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113 \n\ |
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114 Called with a fifth output argument and a sparse input matrix,\n\ |
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115 @code{lu} attempts to use a scaling factor @var{R} on the input matrix\n\ |
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116 such that\n\ |
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117 @code{@var{P} * (@var{R} \\ @var{A}) * @var{Q} = @var{L} * @var{U}}.\n\ |
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118 This typically leads to a sparser and more stable factorization.\n\ |
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119 \n\ |
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120 An additional input argument @var{thres}, that defines the pivoting\n\ |
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121 threshold can be given. @var{thres} can be a scalar, in which case\n\ |
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122 it defines the @sc{umfpack} pivoting tolerance for both symmetric and\n\ |
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123 unsymmetric cases. If @var{thres} is a 2-element vector, then the first\n\ |
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124 element defines the pivoting tolerance for the unsymmetric @sc{umfpack}\n\ |
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125 pivoting strategy and the second for the symmetric strategy. By default,\n\ |
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126 the values defined by @code{spparms} are used ([0.1, 0.001]).\n\ |
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127 \n\ |
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128 Given the string argument @qcode{\"vector\"}, @code{lu} returns the values\n\ |
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129 of @var{P} and @var{Q} as vector values, such that for full matrix,\n\ |
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130 @code{@var{A} (@var{P},:) = @var{L} * @var{U}}, and @code{@var{R}(@var{P},:)\n\ |
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131 * @var{A} (:, @var{Q}) = @var{L} * @var{U}}.\n\ |
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132 \n\ |
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133 With two output arguments, returns the permuted forms of the upper and\n\ |
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134 lower triangular matrices, such that @code{@var{A} = @var{L} * @var{U}}.\n\ |
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135 With one output argument @var{y}, then the matrix returned by the @sc{lapack}\n\ |
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136 routines is returned. If the input matrix is sparse then the matrix @var{L}\n\ |
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137 is embedded into @var{U} to give a return value similar to the full case.\n\ |
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138 For both full and sparse matrices, @code{lu} loses the permutation\n\ |
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139 information.\n\ |
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140 @seealso{luupdate, chol, hess, qr, qz, schur, svd}\n\ |
3372 | 141 @end deftypefn") |
2928 | 142 { |
143 octave_value_list retval; | |
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144 int nargin = args.length (); |
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145 bool issparse = (nargin > 0 && args(0).is_sparse_type ()); |
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146 bool scale = (nargout == 5); |
2928 | 147 |
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148 if (nargin < 1 || (issparse && (nargin > 3 || nargout > 5)) |
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149 || (!issparse && (nargin > 2 || nargout > 3))) |
2928 | 150 { |
5823 | 151 print_usage (); |
2928 | 152 return retval; |
153 } | |
154 | |
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155 bool vecout = false; |
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156 Matrix thres; |
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157 |
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158 int n = 1; |
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159 while (n < nargin && ! error_state) |
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160 { |
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161 if (args(n).is_string ()) |
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162 { |
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163 std::string tmp = args(n++).string_value (); |
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164 |
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165 if (! error_state) |
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166 { |
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167 if (tmp.compare ("vector") == 0) |
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168 vecout = true; |
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169 else |
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170 error ("lu: unrecognized string argument"); |
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171 } |
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172 } |
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173 else |
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174 { |
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175 Matrix tmp = args(n++).matrix_value (); |
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176 |
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177 if (! error_state) |
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178 { |
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179 if (!issparse) |
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180 error ("lu: can not define pivoting threshold THRES for full matrices"); |
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181 else if (tmp.nelem () == 1) |
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182 { |
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183 thres.resize (1,2); |
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184 thres(0) = tmp(0); |
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185 thres(1) = tmp(0); |
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186 } |
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187 else if (tmp.nelem () == 2) |
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188 thres = tmp; |
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189 else |
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190 error ("lu: expecting 2-element vector for THRES"); |
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191 } |
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192 } |
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193 } |
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194 |
2928 | 195 octave_value arg = args(0); |
196 | |
5275 | 197 octave_idx_type nr = arg.rows (); |
198 octave_idx_type nc = arg.columns (); | |
2928 | 199 |
200 int arg_is_empty = empty_arg ("lu", nr, nc); | |
201 | |
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202 if (issparse) |
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203 { |
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204 if (arg_is_empty < 0) |
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205 return retval; |
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206 else if (arg_is_empty > 0) |
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207 return octave_value_list (5, SparseMatrix ()); |
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208 |
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209 if (arg.is_real_type ()) |
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210 { |
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211 |
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212 SparseMatrix m = arg.sparse_matrix_value (); |
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213 |
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214 if (nargout < 4) |
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215 { |
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216 |
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217 ColumnVector Qinit; |
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218 Qinit.resize (nc); |
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219 for (octave_idx_type i = 0; i < nc; i++) |
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220 Qinit (i) = i; |
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221 SparseLU fact (m, Qinit, thres, false, true); |
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222 |
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223 if (nargout < 2) |
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224 retval(0) = fact.Y (); |
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225 else |
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226 { |
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227 |
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228 retval(1) |
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229 = octave_value ( |
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230 fact.U () * fact.Pc_mat ().transpose (), |
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231 MatrixType (MatrixType::Permuted_Upper, |
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232 nc, fact.col_perm ())); |
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233 |
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234 PermMatrix P = fact.Pr_mat (); |
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235 SparseMatrix L = fact.L (); |
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236 if (nargout < 3) |
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237 retval(0) |
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238 = octave_value (P.transpose () * L, |
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239 MatrixType (MatrixType::Permuted_Lower, |
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240 nr, fact.row_perm ())); |
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241 else |
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242 { |
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243 retval(0) = L; |
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244 if (vecout) |
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245 retval(2) = fact.Pr_vec(); |
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246 else |
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247 retval(2) = P; |
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248 } |
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249 |
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250 } |
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251 |
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252 } |
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253 else |
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254 { |
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255 |
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256 SparseLU fact (m, thres, scale); |
2928 | 257 |
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258 if (scale) |
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259 retval(4) = fact.R (); |
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260 |
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261 if (vecout) |
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262 { |
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263 retval(3) = fact.Pc_vec (); |
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264 retval(2) = fact.Pr_vec (); |
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265 } |
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266 else |
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267 { |
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268 retval(3) = fact.Pc_mat (); |
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269 retval(2) = fact.Pr_mat (); |
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270 } |
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271 retval(1) = octave_value (fact.U (), |
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272 MatrixType (MatrixType::Upper)); |
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273 retval(0) = octave_value (fact.L (), |
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274 MatrixType (MatrixType::Lower)); |
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275 } |
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276 |
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277 } |
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278 else if (arg.is_complex_type ()) |
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279 { |
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280 SparseComplexMatrix m = arg.sparse_complex_matrix_value (); |
2928 | 281 |
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282 if (nargout < 4) |
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283 { |
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284 |
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285 ColumnVector Qinit; |
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286 Qinit.resize (nc); |
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287 for (octave_idx_type i = 0; i < nc; i++) |
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288 Qinit (i) = i; |
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289 SparseComplexLU fact (m, Qinit, thres, false, true); |
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290 |
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291 if (nargout < 2) |
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292 |
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293 retval(0) = fact.Y (); |
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294 |
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295 else |
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296 { |
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297 |
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298 retval(1) |
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299 = octave_value ( |
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300 fact.U () * fact.Pc_mat ().transpose (), |
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301 MatrixType (MatrixType::Permuted_Upper, |
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302 nc, fact.col_perm ())); |
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303 |
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304 PermMatrix P = fact.Pr_mat (); |
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305 SparseComplexMatrix L = fact.L (); |
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306 if (nargout < 3) |
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307 retval(0) |
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308 = octave_value (P.transpose () * L, |
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309 MatrixType (MatrixType::Permuted_Lower, |
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310 nr, fact.row_perm ())); |
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311 else |
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312 { |
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313 retval(0) = L; |
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314 if (vecout) |
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315 retval(2) = fact.Pr_vec(); |
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316 else |
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317 retval(2) = P; |
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318 } |
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319 |
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320 } |
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321 |
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322 } |
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323 else |
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324 { |
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325 |
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326 SparseComplexLU fact (m, thres, scale); |
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327 |
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328 if (scale) |
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329 retval(4) = fact.R (); |
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330 |
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331 if (vecout) |
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332 { |
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333 retval(3) = fact.Pc_vec (); |
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334 retval(2) = fact.Pr_vec (); |
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335 } |
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336 else |
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337 { |
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338 retval(3) = fact.Pc_mat (); |
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339 retval(2) = fact.Pr_mat (); |
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340 } |
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341 retval(1) = octave_value (fact.U (), |
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342 MatrixType (MatrixType::Upper)); |
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343 retval(0) = octave_value (fact.L (), |
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344 MatrixType (MatrixType::Lower)); |
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345 } |
18427
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346 |
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347 } |
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348 else |
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349 gripe_wrong_type_arg ("lu", arg); |
2928 | 350 } |
351 else | |
352 { | |
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353 if (arg_is_empty < 0) |
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354 return retval; |
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355 else if (arg_is_empty > 0) |
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356 return octave_value_list (3, Matrix ()); |
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357 |
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358 if (arg.is_real_type ()) |
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359 { |
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360 if (arg.is_single_type ()) |
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361 { |
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362 FloatMatrix m = arg.float_matrix_value (); |
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363 |
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364 if (! error_state) |
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365 { |
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366 FloatLU fact (m); |
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367 |
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368 switch (nargout) |
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369 { |
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370 case 0: |
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371 case 1: |
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372 retval(0) = fact.Y (); |
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373 break; |
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374 |
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375 case 2: |
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376 { |
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377 PermMatrix P = fact.P (); |
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378 FloatMatrix L = P.transpose () * fact.L (); |
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379 retval(1) = get_lu_u (fact); |
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380 retval(0) = L; |
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381 } |
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382 break; |
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383 |
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384 case 3: |
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385 default: |
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386 { |
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387 if (vecout) |
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388 retval(2) = fact.P_vec (); |
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389 else |
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390 retval(2) = fact.P (); |
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391 retval(1) = get_lu_u (fact); |
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392 retval(0) = get_lu_l (fact); |
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393 } |
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394 break; |
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395 } |
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396 } |
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397 } |
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398 else |
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399 { |
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400 Matrix m = arg.matrix_value (); |
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401 |
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402 if (! error_state) |
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403 { |
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404 LU fact (m); |
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405 |
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406 switch (nargout) |
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407 { |
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408 case 0: |
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409 case 1: |
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410 retval(0) = fact.Y (); |
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411 break; |
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412 |
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413 case 2: |
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414 { |
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415 PermMatrix P = fact.P (); |
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416 Matrix L = P.transpose () * fact.L (); |
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417 retval(1) = get_lu_u (fact); |
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418 retval(0) = L; |
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419 } |
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420 break; |
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421 |
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422 case 3: |
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423 default: |
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424 { |
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425 if (vecout) |
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426 retval(2) = fact.P_vec (); |
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427 else |
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428 retval(2) = fact.P (); |
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429 retval(1) = get_lu_u (fact); |
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430 retval(0) = get_lu_l (fact); |
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431 } |
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432 break; |
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433 } |
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434 } |
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435 } |
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436 } |
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437 else if (arg.is_complex_type ()) |
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438 { |
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439 if (arg.is_single_type ()) |
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440 { |
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441 FloatComplexMatrix m = arg.float_complex_matrix_value (); |
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442 |
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443 if (! error_state) |
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444 { |
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445 FloatComplexLU fact (m); |
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446 |
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447 switch (nargout) |
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448 { |
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449 case 0: |
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450 case 1: |
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451 retval(0) = fact.Y (); |
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452 break; |
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453 |
10154
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454 case 2: |
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455 { |
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456 PermMatrix P = fact.P (); |
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457 FloatComplexMatrix L = P.transpose () * fact.L (); |
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458 retval(1) = get_lu_u (fact); |
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459 retval(0) = L; |
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460 } |
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461 break; |
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|
462 |
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463 case 3: |
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464 default: |
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465 { |
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466 if (vecout) |
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467 retval(2) = fact.P_vec (); |
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468 else |
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469 retval(2) = fact.P (); |
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470 retval(1) = get_lu_u (fact); |
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471 retval(0) = get_lu_l (fact); |
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472 } |
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|
473 break; |
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|
474 } |
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|
475 } |
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|
476 } |
40dfc0c99116
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|
477 else |
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|
478 { |
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|
479 ComplexMatrix m = arg.complex_matrix_value (); |
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|
480 |
10154
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|
481 if (! error_state) |
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|
482 { |
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|
483 ComplexLU fact (m); |
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Eliminate the rest of the dispatched sparse functions
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changeset
|
484 |
10154
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|
485 switch (nargout) |
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|
486 { |
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|
487 case 0: |
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|
488 case 1: |
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489 retval(0) = fact.Y (); |
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|
490 break; |
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|
491 |
10154
40dfc0c99116
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|
492 case 2: |
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|
493 { |
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|
494 PermMatrix P = fact.P (); |
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|
495 ComplexMatrix L = P.transpose () * fact.L (); |
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496 retval(1) = get_lu_u (fact); |
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497 retval(0) = L; |
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|
498 } |
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|
499 break; |
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First attempt at single precision tyeps
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|
500 |
10154
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|
501 case 3: |
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|
502 default: |
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|
503 { |
40dfc0c99116
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|
504 if (vecout) |
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|
505 retval(2) = fact.P_vec (); |
40dfc0c99116
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changeset
|
506 else |
40dfc0c99116
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|
507 retval(2) = fact.P (); |
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508 retval(1) = get_lu_u (fact); |
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|
509 retval(0) = get_lu_l (fact); |
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changeset
|
510 } |
40dfc0c99116
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changeset
|
511 break; |
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|
512 } |
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|
513 } |
40dfc0c99116
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|
514 } |
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515 } |
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Eliminate the rest of the dispatched sparse functions
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|
516 else |
10154
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|
517 gripe_wrong_type_arg ("lu", arg); |
2928 | 518 } |
519 | |
520 return retval; | |
521 } | |
522 | |
523 /* | |
7814
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Second set of single precision test code and fix of resulting bugs
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524 %!assert(lu ([1, 2; 3, 4]), [3, 4; 1/3, 2/3], eps); |
87865ed7405f
Second set of single precision test code and fix of resulting bugs
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|
525 |
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changeset
|
526 %!test |
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|
527 %! [l, u] = lu ([1, 2; 3, 4]); |
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|
528 %! assert (l, [1/3, 1; 1, 0], sqrt (eps)); |
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|
529 %! assert (u, [3, 4; 0, 2/3], sqrt (eps)); |
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|
530 |
87865ed7405f
Second set of single precision test code and fix of resulting bugs
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changeset
|
531 %!test |
87865ed7405f
Second set of single precision test code and fix of resulting bugs
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|
532 %! [l, u, p] = lu ([1, 2; 3, 4]); |
14501
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|
533 %! assert (l, [1, 0; 1/3, 1], sqrt (eps)); |
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|
534 %! assert (u, [3, 4; 0, 2/3], sqrt (eps)); |
60e5cf354d80
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|
535 %! assert (p(:,:), [0, 1; 1, 0], sqrt (eps)); |
7814
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|
536 |
87865ed7405f
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changeset
|
537 %!test |
14501
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changeset
|
538 %! [l, u, p] = lu ([1, 2; 3, 4], "vector"); |
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539 %! assert (l, [1, 0; 1/3, 1], sqrt (eps)); |
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540 %! assert (u, [3, 4; 0, 2/3], sqrt (eps)); |
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541 %! assert (p, [2;1], sqrt (eps)); |
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542 |
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543 %!test |
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544 %! [l, u, p] = lu ([1, 2; 3, 4; 5, 6]); |
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545 %! assert (l, [1, 0; 1/5, 1; 3/5, 1/2], sqrt (eps)); |
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546 %! assert (u, [5, 6; 0, 4/5], sqrt (eps)); |
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547 %! assert (p(:,:), [0, 0, 1; 1, 0, 0; 0 1 0], sqrt (eps)); |
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548 |
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549 %!assert (lu (single ([1, 2; 3, 4])), single ([3, 4; 1/3, 2/3]), eps ("single")) |
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550 |
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551 %!test |
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552 %! [l, u] = lu (single ([1, 2; 3, 4])); |
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553 %! assert (l, single ([1/3, 1; 1, 0]), sqrt (eps ("single"))); |
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554 %! assert (u, single ([3, 4; 0, 2/3]), sqrt (eps ("single"))); |
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555 |
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556 %!test |
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557 %! [l, u, p] = lu (single ([1, 2; 3, 4])); |
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558 %! assert (l, single ([1, 0; 1/3, 1]), sqrt (eps ("single"))); |
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559 %! assert (u, single ([3, 4; 0, 2/3]), sqrt (eps ("single"))); |
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560 %! assert (p(:,:), single ([0, 1; 1, 0]), sqrt (eps ("single"))); |
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561 |
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562 %!test |
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563 %! [l, u, p] = lu (single ([1, 2; 3, 4]), "vector"); |
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564 %! assert (l, single ([1, 0; 1/3, 1]), sqrt (eps ("single"))); |
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565 %! assert (u, single ([3, 4; 0, 2/3]), sqrt (eps ("single"))); |
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566 %! assert (p, single ([2;1]), sqrt (eps ("single"))); |
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567 |
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568 %!test |
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569 %! [l u p] = lu (single ([1, 2; 3, 4; 5, 6])); |
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570 %! assert (l, single ([1, 0; 1/5, 1; 3/5, 1/2]), sqrt (eps ("single"))); |
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571 %! assert (u, single ([5, 6; 0, 4/5]), sqrt (eps ("single"))); |
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572 %! assert (p(:,:), single ([0, 0, 1; 1, 0, 0; 0 1 0]), sqrt (eps ("single"))); |
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573 |
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574 %!error lu () |
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575 %!error <can not define pivoting threshold> lu ([1, 2; 3, 4], 2) |
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576 |
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577 %!testif HAVE_UMFPACK |
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578 %! Bi = [1 2 3 4 5 2 3 6 7 8 4 5 7 8 9]; |
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579 %! Bj = [1 3 4 5 6 7 8 9 11 12 13 14 15 16 17]; |
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580 %! Bv = [1 1 1 1 1 1 -1 1 1 1 1 -1 1 -1 1]; |
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581 %! B = sparse (Bi, Bj, Bv); |
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582 %! [L, U] = lu (B); |
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583 %! assert (L*U, B); |
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584 %! [L, U, P] = lu(B); |
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585 %! assert (P'*L*U, B); |
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586 %! [L, U, P, Q] = lu (B); |
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587 %! assert (P'*L*U*Q', B); |
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588 |
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589 */ |
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590 |
9708 | 591 static |
592 bool check_lu_dims (const octave_value& l, const octave_value& u, | |
593 const octave_value& p) | |
594 { | |
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595 octave_idx_type m = l.rows (); |
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596 octave_idx_type k = u.rows (); |
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597 octave_idx_type n = u.columns (); |
9708 | 598 return ((l.ndims () == 2 && u.ndims () == 2 && k == l.columns ()) |
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599 && k == std::min (m, n) && |
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600 (p.is_undefined () || p.rows () == m)); |
9708 | 601 } |
602 | |
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603 DEFUN (luupdate, args, , |
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604 "-*- texinfo -*-\n\ |
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605 @deftypefn {Built-in Function} {[@var{L}, @var{U}] =} luupdate (@var{L}, @var{U}, @var{x}, @var{y})\n\ |
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606 @deftypefnx {Built-in Function} {[@var{L}, @var{U}, @var{P}] =} luupdate (@var{L}, @var{U}, @var{P}, @var{x}, @var{y})\n\ |
9709 | 607 Given an LU@tie{}factorization of a real or complex matrix\n\ |
608 @w{@var{A} = @var{L}*@var{U}}, @var{L}@tie{}lower unit trapezoidal and\n\ | |
609 @var{U}@tie{}upper trapezoidal, return the LU@tie{}factorization\n\ | |
610 of @w{@var{A} + @var{x}*@var{y}.'}, where @var{x} and @var{y} are\n\ | |
611 column vectors (rank-1 update) or matrices with equal number of columns\n\ | |
612 (rank-k update).\n\ | |
613 Optionally, row-pivoted updating can be used by supplying\n\ | |
614 a row permutation (pivoting) matrix @var{P};\n\ | |
615 in that case, an updated permutation matrix is returned.\n\ | |
616 Note that if @var{L}, @var{U}, @var{P} is a pivoted LU@tie{}factorization\n\ | |
617 as obtained by @code{lu}:\n\ | |
618 \n\ | |
619 @example\n\ | |
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620 [@var{L}, @var{U}, @var{P}] = lu (@var{A});\n\ |
9709 | 621 @end example\n\ |
622 \n\ | |
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623 @noindent\n\ |
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624 then a factorization of @tcode{@var{A}+@var{x}*@var{y}.'} can be obtained\n\ |
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625 either as\n\ |
9709 | 626 \n\ |
627 @example\n\ | |
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628 [@var{L1}, @var{U1}] = lu (@var{L}, @var{U}, @var{P}*@var{x}, @var{y})\n\ |
9709 | 629 @end example\n\ |
630 \n\ | |
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631 @noindent\n\ |
9709 | 632 or\n\ |
633 \n\ | |
634 @example\n\ | |
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635 [@var{L1}, @var{U1}, @var{P1}] = lu (@var{L}, @var{U}, @var{P}, @var{x}, @var{y})\n\ |
9709 | 636 @end example\n\ |
637 \n\ | |
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638 The first form uses the unpivoted algorithm, which is faster, but less\n\ |
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639 stable. The second form uses a slower pivoted algorithm, which is more\n\ |
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640 stable.\n\ |
9709 | 641 \n\ |
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642 The matrix case is done as a sequence of rank-1 updates;\n\ |
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643 thus, for large enough k, it will be both faster and more accurate to\n\ |
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644 recompute the factorization from scratch.\n\ |
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645 @seealso{lu, cholupdate, qrupdate}\n\ |
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646 @end deftypefn") |
9708 | 647 { |
648 octave_idx_type nargin = args.length (); | |
649 octave_value_list retval; | |
650 | |
651 bool pivoted = nargin == 5; | |
652 | |
653 if (nargin != 4 && nargin != 5) | |
654 { | |
655 print_usage (); | |
656 return retval; | |
657 } | |
658 | |
659 octave_value argl = args(0); | |
660 octave_value argu = args(1); | |
661 octave_value argp = pivoted ? args(2) : octave_value (); | |
662 octave_value argx = args(2 + pivoted); | |
663 octave_value argy = args(3 + pivoted); | |
664 | |
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665 if (argl.is_numeric_type () && argu.is_numeric_type () |
9708 | 666 && argx.is_numeric_type () && argy.is_numeric_type () |
667 && (! pivoted || argp.is_perm_matrix ())) | |
668 { | |
669 if (check_lu_dims (argl, argu, argp)) | |
670 { | |
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671 PermMatrix P = (pivoted |
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672 ? argp.perm_matrix_value () |
9708 | 673 : PermMatrix::eye (argl.rows ())); |
674 | |
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675 if (argl.is_real_type () |
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676 && argu.is_real_type () |
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677 && argx.is_real_type () |
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678 && argy.is_real_type ()) |
9708 | 679 { |
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680 // all real case |
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681 if (argl.is_single_type () |
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682 || argu.is_single_type () |
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683 || argx.is_single_type () |
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684 || argy.is_single_type ()) |
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685 { |
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686 FloatMatrix L = argl.float_matrix_value (); |
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687 FloatMatrix U = argu.float_matrix_value (); |
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688 FloatMatrix x = argx.float_matrix_value (); |
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689 FloatMatrix y = argy.float_matrix_value (); |
9708 | 690 |
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691 FloatLU fact (L, U, P); |
9708 | 692 if (pivoted) |
693 fact.update_piv (x, y); | |
694 else | |
695 fact.update (x, y); | |
696 | |
697 if (pivoted) | |
698 retval(2) = fact.P (); | |
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699 retval(1) = get_lu_u (fact); |
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700 retval(0) = get_lu_l (fact); |
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701 } |
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702 else |
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703 { |
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704 Matrix L = argl.matrix_value (); |
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705 Matrix U = argu.matrix_value (); |
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706 Matrix x = argx.matrix_value (); |
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707 Matrix y = argy.matrix_value (); |
9708 | 708 |
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709 LU fact (L, U, P); |
9708 | 710 if (pivoted) |
711 fact.update_piv (x, y); | |
712 else | |
713 fact.update (x, y); | |
714 | |
715 if (pivoted) | |
716 retval(2) = fact.P (); | |
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717 retval(1) = get_lu_u (fact); |
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718 retval(0) = get_lu_l (fact); |
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719 } |
9708 | 720 } |
721 else | |
722 { | |
723 // complex case | |
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724 if (argl.is_single_type () |
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725 || argu.is_single_type () |
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726 || argx.is_single_type () |
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727 || argy.is_single_type ()) |
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728 { |
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729 FloatComplexMatrix L = argl.float_complex_matrix_value (); |
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730 FloatComplexMatrix U = argu.float_complex_matrix_value (); |
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731 FloatComplexMatrix x = argx.float_complex_matrix_value (); |
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732 FloatComplexMatrix y = argy.float_complex_matrix_value (); |
9708 | 733 |
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734 FloatComplexLU fact (L, U, P); |
9708 | 735 if (pivoted) |
736 fact.update_piv (x, y); | |
737 else | |
738 fact.update (x, y); | |
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739 |
9708 | 740 if (pivoted) |
741 retval(2) = fact.P (); | |
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742 retval(1) = get_lu_u (fact); |
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743 retval(0) = get_lu_l (fact); |
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744 } |
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745 else |
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746 { |
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747 ComplexMatrix L = argl.complex_matrix_value (); |
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748 ComplexMatrix U = argu.complex_matrix_value (); |
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749 ComplexMatrix x = argx.complex_matrix_value (); |
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750 ComplexMatrix y = argy.complex_matrix_value (); |
9708 | 751 |
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752 ComplexLU fact (L, U, P); |
9708 | 753 if (pivoted) |
754 fact.update_piv (x, y); | |
755 else | |
756 fact.update (x, y); | |
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757 |
9708 | 758 if (pivoted) |
759 retval(2) = fact.P (); | |
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760 retval(1) = get_lu_u (fact); |
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761 retval(0) = get_lu_l (fact); |
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762 } |
9708 | 763 } |
764 } | |
765 else | |
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|
766 error ("luupdate: dimension mismatch"); |
9708 | 767 } |
768 else | |
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|
769 error ("luupdate: L, U, X, and Y must be numeric"); |
9708 | 770 |
771 return retval; | |
772 } | |
773 | |
7814
87865ed7405f
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|
774 /* |
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775 %!shared A, u, v, Ac, uc, vc |
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776 %! A = [0.091364 0.613038 0.999083; |
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777 %! 0.594638 0.425302 0.603537; |
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778 %! 0.383594 0.291238 0.085574; |
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779 %! 0.265712 0.268003 0.238409; |
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780 %! 0.669966 0.743851 0.445057 ]; |
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781 %! |
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782 %! u = [0.85082; |
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783 %! 0.76426; |
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|
784 %! 0.42883; |
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785 %! 0.53010; |
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786 %! 0.80683 ]; |
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787 %! |
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788 %! v = [0.98810; |
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789 %! 0.24295; |
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790 %! 0.43167 ]; |
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791 %! |
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792 %! Ac = [0.620405 + 0.956953i 0.480013 + 0.048806i 0.402627 + 0.338171i; |
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793 %! 0.589077 + 0.658457i 0.013205 + 0.279323i 0.229284 + 0.721929i; |
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|
794 %! 0.092758 + 0.345687i 0.928679 + 0.241052i 0.764536 + 0.832406i; |
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795 %! 0.912098 + 0.721024i 0.049018 + 0.269452i 0.730029 + 0.796517i; |
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796 %! 0.112849 + 0.603871i 0.486352 + 0.142337i 0.355646 + 0.151496i ]; |
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797 %! |
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|
798 %! uc = [0.20351 + 0.05401i; |
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799 %! 0.13141 + 0.43708i; |
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800 %! 0.29808 + 0.08789i; |
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801 %! 0.69821 + 0.38844i; |
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802 %! 0.74871 + 0.25821i ]; |
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803 %! |
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804 %! vc = [0.85839 + 0.29468i; |
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805 %! 0.20820 + 0.93090i; |
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806 %! 0.86184 + 0.34689i ]; |
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807 %! |
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|
808 |
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809 %!testif HAVE_QRUPDATE_LUU |
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810 %! [L,U,P] = lu (A); |
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811 %! [L,U] = luupdate (L,U,P*u,v); |
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812 %! assert (norm (vec (tril (L)-L), Inf) == 0); |
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813 %! assert (norm (vec (triu (U)-U), Inf) == 0); |
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814 %! assert (norm (vec (P'*L*U - A - u*v.'), Inf) < norm (A)*1e1*eps); |
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815 %! |
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816 %!testif HAVE_QRUPDATE_LUU |
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817 %! [L,U,P] = lu (Ac); |
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818 %! [L,U] = luupdate (L,U,P*uc,vc); |
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819 %! assert (norm (vec (tril (L)-L), Inf) == 0); |
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820 %! assert (norm (vec (triu (U)-U), Inf) == 0); |
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821 %! assert (norm (vec (P'*L*U - Ac - uc*vc.'), Inf) < norm (Ac)*1e1*eps); |
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822 |
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823 %!testif HAVE_QRUPDATE_LUU |
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824 %! [L,U,P] = lu (single (A)); |
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825 %! [L,U] = luupdate (L,U,P*single (u), single (v)); |
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826 %! assert (norm (vec (tril (L)-L), Inf) == 0); |
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827 %! assert (norm (vec (triu (U)-U), Inf) == 0); |
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828 %! assert (norm (vec (P'*L*U - single (A) - single (u)*single (v).'), Inf) < norm (single (A))*1e1*eps ("single")); |
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829 %! |
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830 %!testif HAVE_QRUPDATE_LUU |
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831 %! [L,U,P] = lu (single (Ac)); |
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832 %! [L,U] = luupdate (L,U,P*single (uc),single (vc)); |
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833 %! assert (norm (vec (tril (L)-L), Inf) == 0); |
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834 %! assert (norm (vec (triu (U)-U), Inf) == 0); |
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835 %! assert (norm (vec (P'*L*U - single (Ac) - single (uc)*single (vc).'), Inf) < norm (single (Ac))*1e1*eps ("single")); |
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836 |
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837 %!testif HAVE_QRUPDATE_LUU |
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838 %! [L,U,P] = lu (A); |
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839 %! [L,U,P] = luupdate (L,U,P,u,v); |
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840 %! assert (norm (vec (tril (L)-L), Inf) == 0); |
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841 %! assert (norm (vec (triu (U)-U), Inf) == 0); |
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842 %! assert (norm (vec (P'*L*U - A - u*v.'), Inf) < norm (A)*1e1*eps); |
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843 %! |
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844 %!testif HAVE_QRUPDATE_LUU |
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845 %! [L,U,P] = lu (Ac); |
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846 %! [L,U,P] = luupdate (L,U,P,uc,vc); |
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847 %! assert (norm (vec (tril (L)-L), Inf) == 0); |
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848 %! assert (norm (vec (triu (U)-U), Inf) == 0); |
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849 %! assert (norm (vec (P'*L*U - Ac - uc*vc.'), Inf) < norm (Ac)*1e1*eps); |
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850 |
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851 %!testif HAVE_QRUPDATE_LUU |
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852 %! [L,U,P] = lu (single (A)); |
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853 %! [L,U,P] = luupdate (L,U,P,single (u),single (v)); |
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854 %! assert (norm (vec (tril (L)-L), Inf) == 0); |
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855 %! assert (norm (vec (triu (U)-U), Inf) == 0); |
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856 %! assert (norm (vec (P'*L*U - single (A) - single (u)*single (v).'), Inf) < norm (single (A))*1e1*eps ("single")); |
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857 %! |
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858 %!testif HAVE_QRUPDATE_LUU |
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859 %! [L,U,P] = lu (single (Ac)); |
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860 %! [L,U,P] = luupdate (L,U,P,single (uc),single (vc)); |
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861 %! assert (norm (vec (tril (L)-L), Inf) == 0); |
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862 %! assert (norm (vec (triu (U)-U), Inf) == 0); |
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863 %! assert (norm (vec (P'*L*U - single (Ac) - single (uc)*single (vc).'), Inf) < norm (single (Ac))*1e1*eps ("single")); |
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864 */ |