Mercurial > hg > octave-nkf
annotate src/DLD-FUNCTIONS/lu.cc @ 10840:89f4d7e294cc
Grammarcheck .cc files
author | Rik <octave@nomad.inbox5.com> |
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date | Sat, 31 Jul 2010 11:18:11 -0700 |
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2928 | 1 /* |
2 | |
8920 | 3 Copyright (C) 1996, 1997, 1999, 2000, 2003, 2005, 2006, 2007, 2008, 2009 |
7017 | 4 John W. Eaton |
2928 | 5 |
6 This file is part of Octave. | |
7 | |
8 Octave is free software; you can redistribute it and/or modify it | |
9 under the terms of the GNU General Public License as published by the | |
7016 | 10 Free Software Foundation; either version 3 of the License, or (at your |
11 option) any later version. | |
2928 | 12 |
13 Octave is distributed in the hope that it will be useful, but WITHOUT | |
14 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
15 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
16 for more details. | |
17 | |
18 You should have received a copy of the GNU General Public License | |
7016 | 19 along with Octave; see the file COPYING. If not, see |
20 <http://www.gnu.org/licenses/>. | |
2928 | 21 |
22 */ | |
23 | |
24 #ifdef HAVE_CONFIG_H | |
25 #include <config.h> | |
26 #endif | |
27 | |
28 #include "CmplxLU.h" | |
29 #include "dbleLU.h" | |
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30 #include "fCmplxLU.h" |
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31 #include "floatLU.h" |
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32 #include "SparseCmplxLU.h" |
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33 #include "SparsedbleLU.h" |
2928 | 34 |
35 #include "defun-dld.h" | |
36 #include "error.h" | |
37 #include "gripes.h" | |
38 #include "oct-obj.h" | |
39 #include "utils.h" | |
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40 #include "ov-re-sparse.h" |
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41 #include "ov-cx-sparse.h" |
2928 | 42 |
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43 template <class MT> |
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44 static octave_value |
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45 get_lu_l (const base_lu<MT>& fact) |
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46 { |
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47 MT L = fact.L (); |
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48 if (L.is_square ()) |
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49 return octave_value (L, MatrixType (MatrixType::Lower)); |
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50 else |
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51 return L; |
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52 } |
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53 |
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54 template <class MT> |
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55 static octave_value |
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56 get_lu_u (const base_lu<MT>& fact) |
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57 { |
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58 MT U = fact.U (); |
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59 if (U.is_square () && fact.regular ()) |
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60 return octave_value (U, MatrixType (MatrixType::Upper)); |
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61 else |
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62 return U; |
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63 } |
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64 |
2928 | 65 DEFUN_DLD (lu, args, nargout, |
3548 | 66 "-*- texinfo -*-\n\ |
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67 @deftypefn {Loadable Function} {[@var{l}, @var{u}] =} lu (@var{a})\n\ |
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68 @deftypefnx {Loadable Function} {[@var{l}, @var{u}, @var{p}] =} lu (@var{a})\n\ |
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69 @deftypefnx {Loadable Function} {[@var{l}, @var{u}, @var{p}, @var{q}] =} lu (@var{s})\n\ |
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70 @deftypefnx {Loadable Function} {[@var{l}, @var{u}, @var{p}, @var{q}, @var{r}] =} lu (@var{s})\n\ |
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71 @deftypefnx {Loadable Function} {[@dots{}] =} lu (@var{s}, @var{thres})\n\ |
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72 @deftypefnx {Loadable Function} {@var{y} =} lu (@dots{})\n\ |
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73 @deftypefnx {Loadable Function} {[@dots{}] =} lu (@dots{}, 'vector')\n\ |
3372 | 74 @cindex LU decomposition\n\ |
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75 Compute the LU decomposition of @var{a}. If @var{a} is full 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\ | |
81 [l, u, p] = lu (a)\n\ | |
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 Called with two or three output arguments and a spare input matrix,\n\ |
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109 then @dfn{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, then\n\ |
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115 @dfn{lu} attempts to use a scaling factor @var{r} on the input matrix\n\ |
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116 such that @code{@var{p} * (@var{r} \\ @var{a}) * @var{q} = @var{l} * @var{u}}.\n\ |
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117 This typically leads to a sparser and more stable factorization.\n\ |
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118 \n\ |
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119 An additional input argument @var{thres}, that defines the pivoting\n\ |
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120 threshold can be given. @var{thres} can be a scalar, in which case\n\ |
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121 it defines @sc{umfpack} pivoting tolerance for both symmetric and unsymmetric\n\ |
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122 cases. If @var{thres} is a two element vector, then the first element\n\ |
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123 defines the pivoting tolerance for the unsymmetric @sc{umfpack} pivoting\n\ |
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124 strategy and the second the symmetric strategy. By default, the values\n\ |
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125 defined by @code{spparms} are used and are by default @code{[0.1, 0.001]}.\n\ |
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126 \n\ |
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127 Given the string argument 'vector', @dfn{lu} returns the values of @var{p}\n\ |
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128 @var{q} as vector values, such that for full matrix, @code{@var{a}\n\ |
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129 (@var{p},:) = @var{l} * @var{u}}, and @code{@var{r}(@var{p},:) * @var{a}\n\ |
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130 (:, @var{q}) = @var{l} * @var{u}}.\n\ |
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131 \n\ |
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132 With two output arguments, returns the permuted forms of the upper and\n\ |
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133 lower triangular matrices, such that @code{@var{a} = @var{l} * @var{u}}.\n\ |
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134 With one output argument @var{y}, then the matrix returned by the @sc{lapack}\n\ |
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135 routines is returned. If the input matrix is sparse then the matrix @var{l}\n\ |
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136 is embedded into @var{u} to give a return value similar to the full case.\n\ |
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137 For both full and sparse matrices, @dfn{lu} loses the permutation\n\ |
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138 information.\n\ |
3372 | 139 @end deftypefn") |
2928 | 140 { |
141 octave_value_list retval; | |
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142 int nargin = args.length (); |
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143 bool issparse = (nargin > 0 && args(0).is_sparse_type ()); |
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144 bool scale = (nargout == 5); |
2928 | 145 |
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146 if (nargin < 1 || (issparse && (nargin > 3 || nargout > 5)) |
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147 || (!issparse && (nargin > 2 || nargout > 3))) |
2928 | 148 { |
5823 | 149 print_usage (); |
2928 | 150 return retval; |
151 } | |
152 | |
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153 bool vecout = false; |
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154 Matrix thres; |
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155 |
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156 int n = 1; |
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157 while (n < nargin && ! error_state) |
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158 { |
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159 if (args (n).is_string ()) |
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160 { |
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161 std::string tmp = args(n++).string_value (); |
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162 |
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163 if (! error_state ) |
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164 { |
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165 if (tmp.compare ("vector") == 0) |
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166 vecout = true; |
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167 else |
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168 error ("lu: unrecognized string argument"); |
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169 } |
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170 } |
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171 else |
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172 { |
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173 Matrix tmp = args(n++).matrix_value (); |
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174 |
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175 if (! error_state ) |
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176 { |
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177 if (!issparse) |
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178 error ("lu: can not define pivoting threshold for full matrices"); |
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179 else if (tmp.nelem () == 1) |
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180 { |
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181 thres.resize(1,2); |
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182 thres(0) = tmp(0); |
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183 thres(1) = tmp(0); |
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184 } |
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185 else if (tmp.nelem () == 2) |
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186 thres = tmp; |
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187 else |
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188 error ("lu: expecting 2 element vector for thres"); |
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189 } |
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190 } |
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191 } |
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192 |
2928 | 193 octave_value arg = args(0); |
194 | |
5275 | 195 octave_idx_type nr = arg.rows (); |
196 octave_idx_type nc = arg.columns (); | |
2928 | 197 |
198 int arg_is_empty = empty_arg ("lu", nr, nc); | |
199 | |
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200 if (issparse) |
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201 { |
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202 if (arg_is_empty < 0) |
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203 return retval; |
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204 else if (arg_is_empty > 0) |
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205 return octave_value_list (5, SparseMatrix ()); |
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206 |
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207 ColumnVector Qinit; |
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208 if (nargout < 4) |
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209 { |
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210 Qinit.resize (nc); |
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211 for (octave_idx_type i = 0; i < nc; i++) |
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212 Qinit (i) = i; |
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213 } |
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214 |
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215 if (arg.is_real_type ()) |
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216 { |
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217 SparseMatrix m = arg.sparse_matrix_value (); |
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218 |
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219 switch (nargout) |
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220 { |
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221 case 0: |
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222 case 1: |
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223 case 2: |
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224 { |
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225 SparseLU fact (m, Qinit, thres, false, true); |
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226 |
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227 if (nargout < 2) |
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228 retval (0) = fact.Y (); |
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229 else |
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230 { |
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231 PermMatrix P = fact.Pr_mat (); |
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232 SparseMatrix L = P.transpose () * fact.L (); |
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233 retval(1) = octave_value (fact.U (), |
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234 MatrixType (MatrixType::Upper)); |
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235 |
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236 retval(0) = octave_value (L, |
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237 MatrixType (MatrixType::Permuted_Lower, |
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238 nr, fact.row_perm ())); |
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239 } |
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240 } |
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241 break; |
2928 | 242 |
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243 case 3: |
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244 { |
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245 SparseLU fact (m, Qinit, thres, false, true); |
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246 |
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247 if (vecout) |
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248 retval (2) = fact.Pr_vec (); |
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249 else |
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250 retval(2) = fact.Pr_mat (); |
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251 |
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252 retval(1) = octave_value (fact.U (), |
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253 MatrixType (MatrixType::Upper)); |
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254 retval(0) = octave_value (fact.L (), |
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255 MatrixType (MatrixType::Lower)); |
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256 } |
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257 break; |
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258 |
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259 case 4: |
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260 default: |
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261 { |
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262 SparseLU fact (m, thres, scale); |
2928 | 263 |
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264 if (scale) |
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265 retval(4) = fact.R (); |
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266 |
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267 if (vecout) |
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268 { |
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269 retval(3) = fact.Pc_vec (); |
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270 retval(2) = fact.Pr_vec (); |
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271 } |
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272 else |
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273 { |
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274 retval(3) = fact.Pc_mat (); |
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275 retval(2) = fact.Pr_mat (); |
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276 } |
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277 retval(1) = octave_value (fact.U (), |
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278 MatrixType (MatrixType::Upper)); |
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279 retval(0) = octave_value (fact.L (), |
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280 MatrixType (MatrixType::Lower)); |
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281 } |
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282 break; |
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283 } |
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284 } |
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285 else if (arg.is_complex_type ()) |
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286 { |
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287 SparseComplexMatrix m = arg.sparse_complex_matrix_value (); |
2928 | 288 |
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289 switch (nargout) |
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290 { |
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291 case 0: |
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292 case 1: |
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293 case 2: |
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294 { |
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295 SparseComplexLU fact (m, Qinit, thres, false, true); |
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296 |
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297 if (nargout < 2) |
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298 retval (0) = fact.Y (); |
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299 else |
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300 { |
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301 PermMatrix P = fact.Pr_mat (); |
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302 SparseComplexMatrix L = P.transpose () * fact.L (); |
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303 retval(1) = octave_value (fact.U (), |
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304 MatrixType (MatrixType::Upper)); |
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305 |
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306 retval(0) = octave_value (L, |
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307 MatrixType (MatrixType::Permuted_Lower, |
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308 nr, fact.row_perm ())); |
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309 } |
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310 } |
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311 break; |
2928 | 312 |
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313 case 3: |
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314 { |
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315 SparseComplexLU fact (m, Qinit, thres, false, true); |
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316 |
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317 if (vecout) |
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318 retval (2) = fact.Pr_vec (); |
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319 else |
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320 retval(2) = fact.Pr_mat (); |
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321 |
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322 retval(1) = octave_value (fact.U (), |
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323 MatrixType (MatrixType::Upper)); |
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324 retval(0) = octave_value (fact.L (), |
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325 MatrixType (MatrixType::Lower)); |
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326 } |
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327 break; |
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328 |
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329 case 4: |
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330 default: |
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331 { |
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332 SparseComplexLU fact (m, thres, scale); |
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333 |
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334 if (scale) |
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335 retval(4) = fact.R (); |
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336 |
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337 if (vecout) |
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338 { |
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339 retval(3) = fact.Pc_vec (); |
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340 retval(2) = fact.Pr_vec (); |
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341 } |
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342 else |
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343 { |
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344 retval(3) = fact.Pc_mat (); |
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345 retval(2) = fact.Pr_mat (); |
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346 } |
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347 retval(1) = octave_value (fact.U (), |
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348 MatrixType (MatrixType::Upper)); |
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349 retval(0) = octave_value (fact.L (), |
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350 MatrixType (MatrixType::Lower)); |
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351 } |
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352 break; |
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353 } |
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354 } |
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355 else |
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356 gripe_wrong_type_arg ("lu", arg); |
2928 | 357 } |
358 else | |
359 { | |
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360 if (arg_is_empty < 0) |
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361 return retval; |
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362 else if (arg_is_empty > 0) |
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363 return octave_value_list (3, Matrix ()); |
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364 |
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365 if (arg.is_real_type ()) |
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366 { |
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367 if (arg.is_single_type ()) |
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368 { |
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369 FloatMatrix m = arg.float_matrix_value (); |
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370 |
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371 if (! error_state) |
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372 { |
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373 FloatLU fact (m); |
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374 |
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375 switch (nargout) |
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376 { |
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377 case 0: |
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378 case 1: |
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379 retval(0) = fact.Y (); |
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380 break; |
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381 |
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382 case 2: |
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383 { |
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384 PermMatrix P = fact.P (); |
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385 FloatMatrix L = P.transpose () * fact.L (); |
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386 retval(1) = get_lu_u (fact); |
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387 retval(0) = L; |
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388 } |
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389 break; |
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|
390 |
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391 case 3: |
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|
392 default: |
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393 { |
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394 if (vecout) |
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395 retval(2) = fact.P_vec (); |
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396 else |
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397 retval(2) = fact.P (); |
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398 retval(1) = get_lu_u (fact); |
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399 retval(0) = get_lu_l (fact); |
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400 } |
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|
401 break; |
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|
402 } |
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|
403 } |
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|
404 } |
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|
405 else |
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|
406 { |
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|
407 Matrix m = arg.matrix_value (); |
7789
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408 |
10154
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409 if (! error_state) |
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|
410 { |
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|
411 LU fact (m); |
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|
412 |
10154
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413 switch (nargout) |
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414 { |
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|
415 case 0: |
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|
416 case 1: |
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417 retval(0) = fact.Y (); |
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418 break; |
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419 |
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420 case 2: |
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421 { |
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422 PermMatrix P = fact.P (); |
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423 Matrix L = P.transpose () * fact.L (); |
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424 retval(1) = get_lu_u (fact); |
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425 retval(0) = L; |
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426 } |
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427 break; |
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428 |
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429 case 3: |
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430 default: |
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431 { |
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432 if (vecout) |
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433 retval(2) = fact.P_vec (); |
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434 else |
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435 retval(2) = fact.P (); |
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436 retval(1) = get_lu_u (fact); |
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437 retval(0) = get_lu_l (fact); |
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438 } |
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439 break; |
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440 } |
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441 } |
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442 } |
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443 } |
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444 else if (arg.is_complex_type ()) |
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445 { |
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446 if (arg.is_single_type ()) |
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447 { |
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448 FloatComplexMatrix m = arg.float_complex_matrix_value (); |
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449 |
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450 if (! error_state) |
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451 { |
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452 FloatComplexLU fact (m); |
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453 |
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454 switch (nargout) |
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455 { |
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456 case 0: |
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457 case 1: |
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458 retval(0) = fact.Y (); |
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459 break; |
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460 |
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461 case 2: |
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462 { |
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463 PermMatrix P = fact.P (); |
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464 FloatComplexMatrix L = P.transpose () * fact.L (); |
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465 retval(1) = get_lu_u (fact); |
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466 retval(0) = L; |
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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) |
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474 retval(2) = fact.P_vec (); |
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475 else |
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476 retval(2) = fact.P (); |
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477 retval(1) = get_lu_u (fact); |
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478 retval(0) = get_lu_l (fact); |
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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 |
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485 { |
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|
486 ComplexMatrix m = arg.complex_matrix_value (); |
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487 |
10154
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|
488 if (! error_state) |
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|
489 { |
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|
490 ComplexLU fact (m); |
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changeset
|
491 |
10154
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492 switch (nargout) |
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493 { |
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|
494 case 0: |
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|
495 case 1: |
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496 retval(0) = fact.Y (); |
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|
497 break; |
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|
498 |
10154
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|
499 case 2: |
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|
500 { |
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|
501 PermMatrix P = fact.P (); |
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|
502 ComplexMatrix L = P.transpose () * fact.L (); |
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503 retval(1) = get_lu_u (fact); |
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504 retval(0) = L; |
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|
505 } |
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diff
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|
506 break; |
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|
507 |
10154
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|
508 case 3: |
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|
509 default: |
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|
510 { |
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|
511 if (vecout) |
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|
512 retval(2) = fact.P_vec (); |
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diff
changeset
|
513 else |
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514 retval(2) = fact.P (); |
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515 retval(1) = get_lu_u (fact); |
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|
516 retval(0) = get_lu_l (fact); |
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|
517 } |
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|
518 break; |
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diff
changeset
|
519 } |
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|
520 } |
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changeset
|
521 } |
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|
522 } |
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Eliminate the rest of the dispatched sparse functions
David Bateman <dbateman@free.fr>
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diff
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|
523 else |
10154
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|
524 gripe_wrong_type_arg ("lu", arg); |
2928 | 525 } |
526 | |
527 return retval; | |
528 } | |
529 | |
530 /* | |
7814
87865ed7405f
Second set of single precision test code and fix of resulting bugs
David Bateman <dbateman@free.fr>
parents:
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diff
changeset
|
531 |
87865ed7405f
Second set of single precision test code and fix of resulting bugs
David Bateman <dbateman@free.fr>
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|
532 %!assert(lu ([1, 2; 3, 4]), [3, 4; 1/3, 2/3], eps); |
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Second set of single precision test code and fix of resulting bugs
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|
533 |
87865ed7405f
Second set of single precision test code and fix of resulting bugs
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changeset
|
534 %!test |
87865ed7405f
Second set of single precision test code and fix of resulting bugs
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changeset
|
535 %! [l, u] = lu ([1, 2; 3, 4]); |
87865ed7405f
Second set of single precision test code and fix of resulting bugs
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|
536 %! assert(l, [1/3, 1; 1, 0], sqrt (eps)); |
87865ed7405f
Second set of single precision test code and fix of resulting bugs
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|
537 %! assert(u, [3, 4; 0, 2/3], sqrt (eps)); |
87865ed7405f
Second set of single precision test code and fix of resulting bugs
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changeset
|
538 |
87865ed7405f
Second set of single precision test code and fix of resulting bugs
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diff
changeset
|
539 %!test |
87865ed7405f
Second set of single precision test code and fix of resulting bugs
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changeset
|
540 %! [l, u, p] = lu ([1, 2; 3, 4]); |
87865ed7405f
Second set of single precision test code and fix of resulting bugs
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diff
changeset
|
541 %! assert(l, [1, 0; 1/3, 1], sqrt (eps)); |
87865ed7405f
Second set of single precision test code and fix of resulting bugs
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diff
changeset
|
542 %! assert(u, [3, 4; 0, 2/3], sqrt (eps)); |
8367
445d27d79f4e
support permutation matrix objects
Jaroslav Hajek <highegg@gmail.com>
parents:
7814
diff
changeset
|
543 %! assert(p(:,:), [0, 1; 1, 0], sqrt (eps)); |
7814
87865ed7405f
Second set of single precision test code and fix of resulting bugs
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|
544 |
87865ed7405f
Second set of single precision test code and fix of resulting bugs
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changeset
|
545 %!test |
87865ed7405f
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diff
changeset
|
546 %! [l, u, p] = lu ([1, 2; 3, 4],'vector'); |
87865ed7405f
Second set of single precision test code and fix of resulting bugs
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changeset
|
547 %! assert(l, [1, 0; 1/3, 1], sqrt (eps)); |
87865ed7405f
Second set of single precision test code and fix of resulting bugs
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diff
changeset
|
548 %! assert(u, [3, 4; 0, 2/3], sqrt (eps)); |
87865ed7405f
Second set of single precision test code and fix of resulting bugs
David Bateman <dbateman@free.fr>
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diff
changeset
|
549 %! assert(p, [2;1], sqrt (eps)); |
87865ed7405f
Second set of single precision test code and fix of resulting bugs
David Bateman <dbateman@free.fr>
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changeset
|
550 |
87865ed7405f
Second set of single precision test code and fix of resulting bugs
David Bateman <dbateman@free.fr>
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changeset
|
551 %!test |
87865ed7405f
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changeset
|
552 %! [l u p] = lu ([1, 2; 3, 4; 5, 6]); |
87865ed7405f
Second set of single precision test code and fix of resulting bugs
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553 %! assert(l, [1, 0; 1/5, 1; 3/5, 1/2], sqrt (eps)); |
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554 %! assert(u, [5, 6; 0, 4/5], sqrt (eps)); |
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555 %! assert(p(:,:), [0, 0, 1; 1, 0, 0; 0 1 0], sqrt (eps)); |
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556 |
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557 %!assert(lu (single([1, 2; 3, 4])), single([3, 4; 1/3, 2/3]), eps('single')); |
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558 |
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559 %!test |
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560 %! [l, u] = lu (single([1, 2; 3, 4])); |
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561 %! assert(l, single([1/3, 1; 1, 0]), sqrt (eps('single'))); |
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562 %! assert(u, single([3, 4; 0, 2/3]), sqrt (eps('single'))); |
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563 |
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564 %!test |
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565 %! [l, u, p] = lu (single([1, 2; 3, 4])); |
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566 %! assert(l, single([1, 0; 1/3, 1]), sqrt (eps('single'))); |
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567 %! assert(u, single([3, 4; 0, 2/3]), sqrt (eps('single'))); |
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568 %! assert(p(:,:), single([0, 1; 1, 0]), sqrt (eps('single'))); |
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569 |
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570 %!test |
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571 %! [l, u, p] = lu (single([1, 2; 3, 4]),'vector'); |
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572 %! assert(l, single([1, 0; 1/3, 1]), sqrt (eps('single'))); |
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573 %! assert(u, single([3, 4; 0, 2/3]), sqrt (eps('single'))); |
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574 %! assert(p, single([2;1]), sqrt (eps('single'))); |
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575 |
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576 %!test |
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577 %! [l u p] = lu (single([1, 2; 3, 4; 5, 6])); |
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578 %! assert(l, single([1, 0; 1/5, 1; 3/5, 1/2]), sqrt (eps('single'))); |
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579 %! assert(u, single([5, 6; 0, 4/5]), sqrt (eps('single'))); |
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580 %! assert(p(:,:), single([0, 0, 1; 1, 0, 0; 0 1 0]), sqrt (eps('single'))); |
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581 |
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582 %!error <Invalid call to lu.*> lu (); |
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583 %!error lu ([1, 2; 3, 4], 2); |
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584 |
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585 */ |
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586 |
9708 | 587 static |
588 bool check_lu_dims (const octave_value& l, const octave_value& u, | |
589 const octave_value& p) | |
590 { | |
591 octave_idx_type m = l.rows (), k = u.rows (), n = u.columns (); | |
592 return ((l.ndims () == 2 && u.ndims () == 2 && k == l.columns ()) | |
593 && k == std::min (m, n) && | |
594 (p.is_undefined () || p.rows () == m)); | |
595 } | |
596 | |
9709 | 597 DEFUN_DLD (luupdate, args, , |
9708 | 598 "-*- texinfo -*-\n\ |
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599 @deftypefn {Loadable Function} {[@var{L}, @var{U}] =} luupdate (@var{l}, @var{u}, @var{x}, @var{y})\n\ |
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600 @deftypefnx {Loadable Function} {[@var{L}, @var{U}, @var{P}] =} luupdate (@var{L}, @var{U}, @var{P}, @var{x}, @var{y})\n\ |
9709 | 601 Given an LU@tie{}factorization of a real or complex matrix\n\ |
602 @w{@var{A} = @var{L}*@var{U}}, @var{L}@tie{}lower unit trapezoidal and\n\ | |
603 @var{U}@tie{}upper trapezoidal, return the LU@tie{}factorization\n\ | |
604 of @w{@var{A} + @var{x}*@var{y}.'}, where @var{x} and @var{y} are\n\ | |
605 column vectors (rank-1 update) or matrices with equal number of columns\n\ | |
606 (rank-k update).\n\ | |
607 Optionally, row-pivoted updating can be used by supplying\n\ | |
608 a row permutation (pivoting) matrix @var{P};\n\ | |
609 in that case, an updated permutation matrix is returned.\n\ | |
610 Note that if @var{L}, @var{U}, @var{P} is a pivoted LU@tie{}factorization\n\ | |
611 as obtained by @code{lu}:\n\ | |
612 \n\ | |
613 @example\n\ | |
614 [@var{L}, @var{U}, @var{P}] = lu (@var{A});\n\ | |
615 @end example\n\ | |
616 \n\ | |
10840 | 617 then a factorization of @code{@var{a}+@var{x}*@var{y}.'} can be obtained either\n\ |
618 as\n\ | |
9709 | 619 \n\ |
620 @example\n\ | |
621 [@var{L1}, @var{U1}] = lu (@var{L}, @var{U}, @var{P}*@var{x}, @var{y})\n\ | |
622 @end example\n\ | |
623 \n\ | |
624 or\n\ | |
625 \n\ | |
626 @example\n\ | |
627 [@var{L1}, @var{U1}, @var{P1}] = lu (@var{L}, @var{U}, @var{P}, @var{x}, @var{y})\n\ | |
628 @end example\n\ | |
629 \n\ | |
630 The first form uses the unpivoted algorithm, which is faster, but less stable.\n\ | |
631 The second form uses a slower pivoted algorithm, which is more stable.\n\ | |
632 \n\ | |
633 Note that the matrix case is done as a sequence of rank-1 updates;\n\ | |
634 thus, for k large enough, it will be both faster and more accurate to recompute\n\ | |
635 the factorization from scratch.\n\ | |
636 @seealso{lu,qrupdate,cholupdate}\n\ | |
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637 @end deftypefn") |
9708 | 638 { |
639 octave_idx_type nargin = args.length (); | |
640 octave_value_list retval; | |
641 | |
642 bool pivoted = nargin == 5; | |
643 | |
644 if (nargin != 4 && nargin != 5) | |
645 { | |
646 print_usage (); | |
647 return retval; | |
648 } | |
649 | |
650 octave_value argl = args(0); | |
651 octave_value argu = args(1); | |
652 octave_value argp = pivoted ? args(2) : octave_value (); | |
653 octave_value argx = args(2 + pivoted); | |
654 octave_value argy = args(3 + pivoted); | |
655 | |
656 if (argl.is_numeric_type () && argu.is_numeric_type () | |
657 && argx.is_numeric_type () && argy.is_numeric_type () | |
658 && (! pivoted || argp.is_perm_matrix ())) | |
659 { | |
660 if (check_lu_dims (argl, argu, argp)) | |
661 { | |
662 PermMatrix P = (pivoted | |
663 ? argp.perm_matrix_value () | |
664 : PermMatrix::eye (argl.rows ())); | |
665 | |
666 if (argl.is_real_type () | |
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667 && argu.is_real_type () |
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668 && argx.is_real_type () |
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669 && argy.is_real_type ()) |
9708 | 670 { |
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671 // all real case |
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672 if (argl.is_single_type () |
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673 || argu.is_single_type () |
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674 || argx.is_single_type () |
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675 || argy.is_single_type ()) |
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676 { |
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677 FloatMatrix L = argl.float_matrix_value (); |
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678 FloatMatrix U = argu.float_matrix_value (); |
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679 FloatMatrix x = argx.float_matrix_value (); |
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680 FloatMatrix y = argy.float_matrix_value (); |
9708 | 681 |
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682 FloatLU fact (L, U, P); |
9708 | 683 if (pivoted) |
684 fact.update_piv (x, y); | |
685 else | |
686 fact.update (x, y); | |
687 | |
688 if (pivoted) | |
689 retval(2) = fact.P (); | |
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690 retval(1) = get_lu_u (fact); |
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691 retval(0) = get_lu_l (fact); |
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692 } |
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693 else |
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694 { |
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695 Matrix L = argl.matrix_value (); |
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696 Matrix U = argu.matrix_value (); |
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697 Matrix x = argx.matrix_value (); |
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698 Matrix y = argy.matrix_value (); |
9708 | 699 |
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700 LU fact (L, U, P); |
9708 | 701 if (pivoted) |
702 fact.update_piv (x, y); | |
703 else | |
704 fact.update (x, y); | |
705 | |
706 if (pivoted) | |
707 retval(2) = fact.P (); | |
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708 retval(1) = get_lu_u (fact); |
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709 retval(0) = get_lu_l (fact); |
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710 } |
9708 | 711 } |
712 else | |
713 { | |
714 // complex case | |
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715 if (argl.is_single_type () |
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716 || argu.is_single_type () |
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717 || argx.is_single_type () |
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718 || argy.is_single_type ()) |
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719 { |
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720 FloatComplexMatrix L = argl.float_complex_matrix_value (); |
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721 FloatComplexMatrix U = argu.float_complex_matrix_value (); |
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722 FloatComplexMatrix x = argx.float_complex_matrix_value (); |
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723 FloatComplexMatrix y = argy.float_complex_matrix_value (); |
9708 | 724 |
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725 FloatComplexLU fact (L, U, P); |
9708 | 726 if (pivoted) |
727 fact.update_piv (x, y); | |
728 else | |
729 fact.update (x, y); | |
730 | |
731 if (pivoted) | |
732 retval(2) = fact.P (); | |
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733 retval(1) = get_lu_u (fact); |
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734 retval(0) = get_lu_l (fact); |
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735 } |
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736 else |
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737 { |
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738 ComplexMatrix L = argl.complex_matrix_value (); |
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739 ComplexMatrix U = argu.complex_matrix_value (); |
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740 ComplexMatrix x = argx.complex_matrix_value (); |
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741 ComplexMatrix y = argy.complex_matrix_value (); |
9708 | 742 |
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743 ComplexLU fact (L, U, P); |
9708 | 744 if (pivoted) |
745 fact.update_piv (x, y); | |
746 else | |
747 fact.update (x, y); | |
748 | |
749 if (pivoted) | |
750 retval(2) = fact.P (); | |
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751 retval(1) = get_lu_u (fact); |
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752 retval(0) = get_lu_l (fact); |
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753 } |
9708 | 754 } |
755 } | |
756 else | |
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757 error ("luupdate: dimensions mismatch"); |
9708 | 758 } |
759 else | |
760 error ("luupdate: expecting numeric arguments"); | |
761 | |
762 return retval; | |
763 } | |
764 | |
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765 /* |
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766 %!shared A, u, v, Ac, uc, vc |
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767 %! A = [0.091364 0.613038 0.999083; |
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768 %! 0.594638 0.425302 0.603537; |
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769 %! 0.383594 0.291238 0.085574; |
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770 %! 0.265712 0.268003 0.238409; |
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771 %! 0.669966 0.743851 0.445057 ]; |
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772 %! |
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773 %! u = [0.85082; |
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774 %! 0.76426; |
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775 %! 0.42883; |
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776 %! 0.53010; |
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777 %! 0.80683 ]; |
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778 %! |
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779 %! v = [0.98810; |
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780 %! 0.24295; |
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781 %! 0.43167 ]; |
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782 %! |
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783 %! Ac = [0.620405 + 0.956953i 0.480013 + 0.048806i 0.402627 + 0.338171i; |
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784 %! 0.589077 + 0.658457i 0.013205 + 0.279323i 0.229284 + 0.721929i; |
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785 %! 0.092758 + 0.345687i 0.928679 + 0.241052i 0.764536 + 0.832406i; |
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786 %! 0.912098 + 0.721024i 0.049018 + 0.269452i 0.730029 + 0.796517i; |
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787 %! 0.112849 + 0.603871i 0.486352 + 0.142337i 0.355646 + 0.151496i ]; |
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788 %! |
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789 %! uc = [0.20351 + 0.05401i; |
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790 %! 0.13141 + 0.43708i; |
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791 %! 0.29808 + 0.08789i; |
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792 %! 0.69821 + 0.38844i; |
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793 %! 0.74871 + 0.25821i ]; |
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794 %! |
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795 %! vc = [0.85839 + 0.29468i; |
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796 %! 0.20820 + 0.93090i; |
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797 %! 0.86184 + 0.34689i ]; |
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798 %! |
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799 |
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John W. Eaton <jwe@octave.org>
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800 %!testif HAVE_QRUPDATE_LUU |
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801 %! [L,U,P] = lu(A); |
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802 %! [L,U] = luupdate(L,U,P*u,v); |
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803 %! assert(norm(vec(tril(L)-L),Inf) == 0) |
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804 %! assert(norm(vec(triu(U)-U),Inf) == 0) |
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parents:
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805 %! assert(norm(vec(P'*L*U - A - u*v.'),Inf) < norm(A)*1e1*eps) |
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806 %! |
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parents:
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807 %!testif HAVE_QRUPDATE_LUU |
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808 %! [L,U,P] = lu(Ac); |
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809 %! [L,U] = luupdate(L,U,P*uc,vc); |
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810 %! assert(norm(vec(tril(L)-L),Inf) == 0) |
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811 %! assert(norm(vec(triu(U)-U),Inf) == 0) |
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812 %! assert(norm(vec(P'*L*U - Ac - uc*vc.'),Inf) < norm(Ac)*1e1*eps) |
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813 |
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John W. Eaton <jwe@octave.org>
parents:
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814 %!testif HAVE_QRUPDATE_LUU |
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815 %! [L,U,P] = lu(single(A)); |
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parents:
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816 %! [L,U] = luupdate(L,U,P*single(u),single(v)); |
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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 - single(A) - single(u)*single(v).'),Inf) < norm(single(A))*1e1*eps('single')) |
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parents:
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820 %! |
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parents:
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821 %!testif HAVE_QRUPDATE_LUU |
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parents:
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822 %! [L,U,P] = lu(single(Ac)); |
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parents:
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823 %! [L,U] = luupdate(L,U,P*single(uc),single(vc)); |
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824 %! assert(norm(vec(tril(L)-L),Inf) == 0) |
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parents:
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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(Ac) - single(uc)*single(vc).'),Inf) < norm(single(Ac))*1e1*eps('single')) |
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827 |
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parents:
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828 %!testif HAVE_QRUPDATE_LUU |
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829 %! [L,U,P] = lu(A); |
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Jaroslav Hajek <highegg@gmail.com>
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830 %! [L,U,P] = luupdate(L,U,P,u,v); |
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Jaroslav Hajek <highegg@gmail.com>
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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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parents:
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833 %! assert(norm(vec(P'*L*U - A - u*v.'),Inf) < norm(A)*1e1*eps) |
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834 %! |
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parents:
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835 %!testif HAVE_QRUPDATE_LUU |
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836 %! [L,U,P] = lu(Ac); |
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Jaroslav Hajek <highegg@gmail.com>
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837 %! [L,U,P] = luupdate(L,U,P,uc,vc); |
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838 %! assert(norm(vec(tril(L)-L),Inf) == 0) |
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839 %! assert(norm(vec(triu(U)-U),Inf) == 0) |
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parents:
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840 %! assert(norm(vec(P'*L*U - Ac - uc*vc.'),Inf) < norm(Ac)*1e1*eps) |
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841 |
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842 %!testif HAVE_QRUPDATE_LUU |
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843 %! [L,U,P] = lu(single(A)); |
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844 %! [L,U,P] = luupdate(L,U,P,single(u),single(v)); |
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845 %! assert(norm(vec(tril(L)-L),Inf) == 0) |
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846 %! assert(norm(vec(triu(U)-U),Inf) == 0) |
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Jaroslav Hajek <highegg@gmail.com>
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847 %! assert(norm(vec(P'*L*U - single(A) - single(u)*single(v).'),Inf) < norm(single(A))*1e1*eps('single')) |
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848 %! |
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849 %!testif HAVE_QRUPDATE_LUU |
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850 %! [L,U,P] = lu(single(Ac)); |
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Jaroslav Hajek <highegg@gmail.com>
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851 %! [L,U,P] = luupdate(L,U,P,single(uc),single(vc)); |
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852 %! assert(norm(vec(tril(L)-L),Inf) == 0) |
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853 %! assert(norm(vec(triu(U)-U),Inf) == 0) |
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854 %! assert(norm(vec(P'*L*U - single(Ac) - single(uc)*single(vc).'),Inf) < norm(single(Ac))*1e1*eps('single')) |
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855 */ |