Mercurial > octave-nkf
annotate src/DLD-FUNCTIONS/chol.cc @ 7700:efccca5f2ad7
more QR & Cholesky updating functions
author | Jaroslav Hajek <highegg@gmail.com> |
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date | Mon, 07 Apr 2008 11:43:19 -0400 |
parents | eb7bdde776f2 |
children | 82be108cc558 |
rev | line source |
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2928 | 1 /* |
2 | |
7017 | 3 Copyright (C) 1996, 1997, 1999, 2000, 2002, 2005, 2006, 2007 |
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 | |
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24 // The cholupdate, cholinsert, choldelete and cholshift functions were |
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25 // written by Jaroslav Hajek <highegg@gmail.com>, Copyright (C) 2008 |
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26 // VZLU Prague, a.s., Czech Republic. |
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27 |
2928 | 28 #ifdef HAVE_CONFIG_H |
29 #include <config.h> | |
30 #endif | |
31 | |
32 #include "CmplxCHOL.h" | |
33 #include "dbleCHOL.h" | |
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34 #include "SparseCmplxCHOL.h" |
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35 #include "SparsedbleCHOL.h" |
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36 #include "oct-spparms.h" |
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37 #include "sparse-util.h" |
2928 | 38 |
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39 #include "ov-re-sparse.h" |
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40 #include "ov-cx-sparse.h" |
2928 | 41 #include "defun-dld.h" |
42 #include "error.h" | |
43 #include "gripes.h" | |
44 #include "oct-obj.h" | |
45 #include "utils.h" | |
46 | |
47 DEFUN_DLD (chol, args, nargout, | |
3548 | 48 "-*- texinfo -*-\n\ |
7650 | 49 @deftypefn {Loadable Function} {@var{r} =} chol (@var{a})\n\ |
50 @deftypefnx {Loadable Function} {[@var{r}, @var{p}] =} chol (@var{a})\n\ | |
51 @deftypefnx {Loadable Function} {[@var{r}, @var{p}, @var{q}] =} chol (@var{s})\n\ | |
52 @deftypefnx {Loadable Function} {[@var{r}, @var{p}, @var{q}] =} chol (@var{s}, 'vector')\n\ | |
53 @deftypefnx {Loadable Function} {[@var{l}, @dots{}] =} chol (@dots{}, 'lower')\n\ | |
3372 | 54 @cindex Cholesky factorization\n\ |
55 Compute the Cholesky factor, @var{r}, of the symmetric positive definite\n\ | |
56 matrix @var{a}, where\n\ | |
57 @iftex\n\ | |
58 @tex\n\ | |
59 $ R^T R = A $.\n\ | |
60 @end tex\n\ | |
61 @end iftex\n\ | |
62 @ifinfo\n\ | |
63 \n\ | |
64 @example\n\ | |
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65 @var{r}' * @var{r} = @var{a}.\n\ |
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66 @end example\n\ |
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67 @end ifinfo\n\ |
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68 \n\ |
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69 Called with one output argument @code{chol} fails if @var{a} or @var{s} is\n\ |
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70 not positive definite. With two or more output arguments @var{p} flags\n\ |
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71 whether the matrix was positive definite and @code{chol} does not fail. A\n\ |
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72 zero value indicated that the matrix was positive definite and the @var{r}\n\ |
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73 gives the factorization, annd @var{p} will have a positive value otherwise.\n\ |
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74 \n\ |
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75 If called with 3 outputs then a sparsity preserving row/column permutation\n\ |
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76 is applied to @var{a} prior to the factorization. That is @var{r}\n\ |
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77 is the factorization of @code{@var{a}(@var{q},@var{q})} such that\n\ |
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78 @iftex\n\ |
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79 @tex\n\ |
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80 $ R^T R = Q^T A Q$.\n\ |
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81 @end tex\n\ |
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82 @end iftex\n\ |
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83 @ifinfo\n\ |
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84 \n\ |
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85 @example\n\ |
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86 @var{r}' * @var{r} = @var{q}' * @var{a} * @var{q}.\n\ |
3372 | 87 @end example\n\ |
88 @end ifinfo\n\ | |
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89 \n\ |
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90 The sparsity preserving permutation is generally returned as a matrix.\n\ |
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91 However, given the flag 'vector', @var{q} will be returned as a vector\n\ |
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92 such that\n\ |
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93 @iftex\n\ |
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94 @tex\n\ |
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95 $ R^T R = A (Q, Q)$.\n\ |
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96 @end tex\n\ |
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97 @end iftex\n\ |
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98 @ifinfo\n\ |
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99 \n\ |
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100 @example\n\ |
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101 @var{r}' * @var{r} = a (@var{q}, @var{q}).\n\ |
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102 @end example\n\ |
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103 @end ifinfo\n\ |
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104 \n\ |
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105 Called with either a sparse or full matrix and uing the 'lower' flag,\n\ |
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106 @code{chol} returns the lower triangular factorization such that\n\ |
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107 @iftex\n\ |
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108 @tex\n\ |
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109 $ L L^T = A $.\n\ |
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110 @end tex\n\ |
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111 @end iftex\n\ |
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112 @ifinfo\n\ |
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113 \n\ |
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114 @example\n\ |
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115 @var{l} * @var{l}' = @var{a}.\n\ |
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116 @end example\n\ |
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117 @end ifinfo\n\ |
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118 \n\ |
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119 In general the lower trinagular factorization is significantly faster for\n\ |
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120 sparse matrices.\n\ |
5340 | 121 @seealso{cholinv, chol2inv}\n\ |
3372 | 122 @end deftypefn") |
2928 | 123 { |
124 octave_value_list retval; | |
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125 int nargin = args.length (); |
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126 bool LLt = false; |
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127 bool vecout = false; |
2928 | 128 |
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129 if (nargin < 1 || nargin > 3 || nargout > 3 |
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130 || (! args(0).is_sparse_type () && nargout > 2)) |
2928 | 131 { |
5823 | 132 print_usage (); |
2928 | 133 return retval; |
134 } | |
135 | |
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136 int n = 1; |
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137 while (n < nargin && ! error_state) |
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138 { |
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139 std::string tmp = args(n++).string_value (); |
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140 |
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141 if (! error_state ) |
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142 { |
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143 if (tmp.compare ("vector") == 0) |
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144 vecout = true; |
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145 else if (tmp.compare ("lower") == 0) |
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146 LLt = true; |
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147 else if (tmp.compare ("upper") == 0) |
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148 LLt = false; |
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149 else |
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150 error ("chol: unexpected second or third input"); |
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151 } |
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152 else |
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153 error ("chol: expecting trailing string arguments"); |
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154 } |
2928 | 155 |
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156 if (! error_state) |
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157 { |
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158 octave_value arg = args(0); |
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159 |
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160 octave_idx_type nr = arg.rows (); |
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161 octave_idx_type nc = arg.columns (); |
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162 bool natural = (nargout != 3); |
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163 |
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164 int arg_is_empty = empty_arg ("chol", nr, nc); |
2928 | 165 |
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166 if (arg_is_empty < 0) |
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167 return retval; |
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168 if (arg_is_empty > 0) |
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169 return octave_value (Matrix ()); |
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170 |
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171 if (arg.is_sparse_type ()) |
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172 { |
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173 if (arg.is_real_type ()) |
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174 { |
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175 SparseMatrix m = arg.sparse_matrix_value (); |
2928 | 176 |
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177 if (! error_state) |
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178 { |
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179 octave_idx_type info; |
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180 SparseCHOL fact (m, info, natural); |
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181 if (nargout == 3) |
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182 if (vecout) |
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183 retval(2) = fact.perm (); |
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184 else |
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185 retval(2) = fact.Q(); |
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187 if (nargout > 1 || info == 0) |
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188 { |
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189 retval(1) = fact.P(); |
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190 if (LLt) |
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191 retval(0) = fact.L(); |
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192 else |
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193 retval(0) = fact.R(); |
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194 } |
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195 else |
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196 error ("chol: matrix not positive definite"); |
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197 } |
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198 } |
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199 else if (arg.is_complex_type ()) |
3243 | 200 { |
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201 SparseComplexMatrix m = arg.sparse_complex_matrix_value (); |
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202 |
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203 if (! error_state) |
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204 { |
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205 octave_idx_type info; |
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206 SparseComplexCHOL fact (m, info, natural); |
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207 |
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208 if (nargout == 3) |
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209 if (vecout) |
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210 retval(2) = fact.perm (); |
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211 else |
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212 retval(2) = fact.Q(); |
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213 |
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214 if (nargout > 1 || info == 0) |
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215 { |
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216 retval(1) = fact.P(); |
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217 if (LLt) |
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218 retval(0) = fact.L(); |
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219 else |
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220 retval(0) = fact.R(); |
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221 } |
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222 else |
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223 error ("chol: matrix not positive definite"); |
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224 } |
3243 | 225 } |
3244 | 226 else |
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227 gripe_wrong_type_arg ("chol", arg); |
2928 | 228 } |
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229 else |
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230 { |
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231 if (arg.is_real_type ()) |
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232 { |
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233 Matrix m = arg.matrix_value (); |
2928 | 234 |
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235 if (! error_state) |
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236 { |
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237 octave_idx_type info; |
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238 CHOL fact (m, info); |
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239 if (nargout == 2 || info == 0) |
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240 { |
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241 retval(1) = static_cast<double> (info); |
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242 if (LLt) |
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243 retval(0) = fact.chol_matrix ().transpose (); |
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244 else |
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245 retval(0) = fact.chol_matrix (); |
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246 } |
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247 else |
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248 error ("chol: matrix not positive definite"); |
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249 } |
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250 } |
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251 else if (arg.is_complex_type ()) |
3243 | 252 { |
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253 ComplexMatrix m = arg.complex_matrix_value (); |
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254 |
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255 if (! error_state) |
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256 { |
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257 octave_idx_type info; |
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258 ComplexCHOL fact (m, info); |
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259 if (nargout == 2 || info == 0) |
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260 { |
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261 retval(1) = static_cast<double> (info); |
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262 if (LLt) |
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263 retval(0) = fact.chol_matrix ().hermitian (); |
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264 else |
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265 retval(0) = fact.chol_matrix (); |
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266 } |
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267 else |
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268 error ("chol: matrix not positive definite"); |
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269 } |
3243 | 270 } |
3244 | 271 else |
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272 gripe_wrong_type_arg ("chol", arg); |
2928 | 273 } |
274 } | |
275 | |
276 return retval; | |
277 } | |
278 | |
5760 | 279 DEFUN_DLD (cholinv, args, , |
5340 | 280 "-*- texinfo -*-\n\ |
281 @deftypefn {Loadable Function} {} cholinv (@var{a})\n\ | |
5448 | 282 Use the Cholesky factorization to compute the inverse of the\n\ |
5340 | 283 symmetric positive definite matrix @var{a}.\n\ |
284 @seealso{chol, chol2inv}\n\ | |
285 @end deftypefn") | |
286 { | |
287 octave_value retval; | |
288 | |
289 int nargin = args.length (); | |
290 | |
291 if (nargin == 1) | |
292 { | |
293 octave_value arg = args(0); | |
294 | |
295 octave_idx_type nr = arg.rows (); | |
296 octave_idx_type nc = arg.columns (); | |
297 | |
298 if (nr == 0 || nc == 0) | |
299 retval = Matrix (); | |
300 else | |
301 { | |
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302 if (arg.is_sparse_type ()) |
5340 | 303 { |
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304 if (arg.is_real_type ()) |
5340 | 305 { |
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306 SparseMatrix m = arg.sparse_matrix_value (); |
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307 |
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308 if (! error_state) |
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309 { |
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310 octave_idx_type info; |
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311 SparseCHOL chol (m, info); |
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312 if (info == 0) |
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313 retval = chol.inverse (); |
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314 else |
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315 error ("cholinv: matrix not positive definite"); |
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316 } |
5340 | 317 } |
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318 else if (arg.is_complex_type ()) |
5340 | 319 { |
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320 SparseComplexMatrix m = arg.sparse_complex_matrix_value (); |
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321 |
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322 if (! error_state) |
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323 { |
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324 octave_idx_type info; |
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325 SparseComplexCHOL chol (m, info); |
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326 if (info == 0) |
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327 retval = chol.inverse (); |
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328 else |
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329 error ("cholinv: matrix not positive definite"); |
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330 } |
5340 | 331 } |
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332 else |
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|
333 gripe_wrong_type_arg ("cholinv", arg); |
5340 | 334 } |
335 else | |
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336 { |
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337 if (arg.is_real_type ()) |
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|
338 { |
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339 Matrix m = arg.matrix_value (); |
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340 |
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341 if (! error_state) |
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342 { |
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343 octave_idx_type info; |
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344 CHOL chol (m, info); |
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345 if (info == 0) |
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346 retval = chol.inverse (); |
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347 else |
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348 error ("cholinv: matrix not positive definite"); |
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349 } |
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350 } |
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351 else if (arg.is_complex_type ()) |
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352 { |
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353 ComplexMatrix m = arg.complex_matrix_value (); |
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354 |
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355 if (! error_state) |
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356 { |
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357 octave_idx_type info; |
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358 ComplexCHOL chol (m, info); |
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359 if (info == 0) |
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360 retval = chol.inverse (); |
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361 else |
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362 error ("cholinv: matrix not positive definite"); |
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363 } |
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364 } |
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365 else |
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366 gripe_wrong_type_arg ("chol", arg); |
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367 } |
5340 | 368 } |
369 } | |
370 else | |
5823 | 371 print_usage (); |
5340 | 372 |
373 return retval; | |
374 } | |
375 | |
5760 | 376 DEFUN_DLD (chol2inv, args, , |
5340 | 377 "-*- texinfo -*-\n\ |
5343 | 378 @deftypefn {Loadable Function} {} chol2inv (@var{u})\n\ |
5340 | 379 Invert a symmetric, positive definite square matrix from its Cholesky\n\ |
5343 | 380 decomposition, @var{u}. Note that @var{u} should be an upper-triangular\n\ |
381 matrix with positive diagonal elements. @code{chol2inv (@var{u})}\n\ | |
382 provides @code{inv (@var{u}'*@var{u})} but it is much faster than\n\ | |
383 using @code{inv}.\n\ | |
5340 | 384 @seealso{chol, cholinv}\n\ |
385 @end deftypefn") | |
386 { | |
387 octave_value retval; | |
388 | |
389 int nargin = args.length (); | |
390 | |
391 if (nargin == 1) | |
392 { | |
393 octave_value arg = args(0); | |
394 | |
395 octave_idx_type nr = arg.rows (); | |
396 octave_idx_type nc = arg.columns (); | |
397 | |
398 if (nr == 0 || nc == 0) | |
399 retval = Matrix (); | |
400 else | |
401 { | |
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402 if (arg.is_sparse_type ()) |
5340 | 403 { |
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404 if (arg.is_real_type ()) |
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405 { |
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406 SparseMatrix r = arg.sparse_matrix_value (); |
5340 | 407 |
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408 if (! error_state) |
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409 retval = chol2inv (r); |
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410 } |
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411 else if (arg.is_complex_type ()) |
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412 { |
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413 SparseComplexMatrix r = arg.sparse_complex_matrix_value (); |
5340 | 414 |
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415 if (! error_state) |
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416 retval = chol2inv (r); |
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417 } |
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418 else |
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419 gripe_wrong_type_arg ("chol2inv", arg); |
5340 | 420 } |
421 else | |
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422 { |
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423 if (arg.is_real_type ()) |
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424 { |
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425 Matrix r = arg.matrix_value (); |
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426 |
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427 if (! error_state) |
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428 retval = chol2inv (r); |
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429 } |
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430 else if (arg.is_complex_type ()) |
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431 { |
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432 ComplexMatrix r = arg.complex_matrix_value (); |
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433 |
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434 if (! error_state) |
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435 retval = chol2inv (r); |
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436 } |
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437 else |
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438 gripe_wrong_type_arg ("chol2inv", arg); |
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439 } |
5340 | 440 } |
441 } | |
442 else | |
5823 | 443 print_usage (); |
5340 | 444 |
445 return retval; | |
446 } | |
447 | |
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448 DEFUN_DLD (cholupdate, args, nargout, |
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449 "-*- texinfo -*-\n\ |
7650 | 450 @deftypefn {Loadable Function} {[@var{R1}, @var{info}] =} cholupdate (@var{R}, @var{u}, @var{op})\n\ |
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451 Update or downdate a Cholesky factorization. Given an upper triangular\n\ |
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452 matrix @var{R} and a column vector @var{u}, attempt to determine another\n\ |
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453 upper triangular matrix @var{R1} such that\n\ |
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454 @itemize @bullet\n\ |
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455 @item\n\ |
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456 @var{R1}'*@var{R1} = @var{R}'*@var{R} + @var{u}*@var{u}'\n\ |
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457 if @var{op} is \"+\"\n\ |
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458 @item\n\ |
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459 @var{R1}'*@var{R1} = @var{R}'*@var{R} - @var{u}*@var{u}'\n\ |
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460 if @var{op} is \"-\"\n\ |
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461 @end itemize\n\ |
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462 \n\ |
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463 If @var{op} is \"-\", @var{info} is set to\n\ |
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464 @itemize\n\ |
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465 @item 0 if the downdate was successful,\n\ |
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466 @item 1 if @var{R}'*@var{R} - @var{u}*@var{u}' is not positive definite,\n\ |
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467 @item 2 if @var{R} is singular.\n\ |
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468 @end itemize\n\ |
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469 \n\ |
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470 If @var{info} is not present, an error message is printed in cases 1 and 2.\n\ |
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471 @seealso{chol, qrupdate}\n\ |
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472 @end deftypefn") |
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473 { |
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474 octave_idx_type nargin = args.length (); |
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475 |
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476 octave_value_list retval; |
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477 |
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478 if (nargin > 3 || nargin < 2) |
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479 { |
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480 print_usage (); |
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481 return retval; |
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482 } |
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483 |
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484 octave_value argr = args(0); |
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485 octave_value argu = args(1); |
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486 |
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487 if (argr.is_matrix_type () && argu.is_matrix_type () |
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488 && (nargin < 3 || args(2).is_string ())) |
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489 { |
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490 octave_idx_type n = argr.rows (); |
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491 |
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492 std::string op = (nargin < 3) ? "+" : args(2).string_value (); |
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493 |
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494 bool down = op == "-"; |
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495 |
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496 if (down || op == "+") |
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497 if (argr.columns () == n && argu.rows () == n && argu.columns () == 1) |
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498 { |
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499 if (argr.is_real_matrix () && argu.is_real_matrix ()) |
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500 { |
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501 // real case |
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502 Matrix R = argr.matrix_value (); |
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503 Matrix u = argu.matrix_value (); |
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504 |
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505 CHOL fact; |
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506 fact.set (R); |
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507 int err = 0; |
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508 |
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509 if (down) |
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510 err = fact.downdate (u); |
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511 else |
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512 fact.update (u); |
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513 |
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514 if (nargout > 1) |
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515 retval(1) = err; |
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516 else if (err) |
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517 error ("cholupdate: downdate violates positiveness"); |
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518 |
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519 retval(0) = fact.chol_matrix (); |
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520 } |
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521 else |
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522 { |
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523 // complex case |
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524 ComplexMatrix R = argr.complex_matrix_value (); |
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525 ComplexMatrix u = argu.complex_matrix_value (); |
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526 |
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527 ComplexCHOL fact; |
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528 fact.set (R); |
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529 int err = 0; |
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530 |
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531 if (down) |
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532 err = fact.downdate (u); |
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533 else |
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534 fact.update (u); |
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535 |
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536 if (nargout > 1) |
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537 retval(1) = err; |
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538 else if (err) |
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539 error ("cholupdate: downdate violates positiveness"); |
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540 |
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541 retval(0) = fact.chol_matrix (); |
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542 } |
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543 } |
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544 else |
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545 error ("cholupdate: dimension mismatch"); |
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546 else |
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547 error ("cholupdate: op must be \"+\" or \"-\""); |
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548 } |
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549 else |
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550 print_usage (); |
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551 |
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552 return retval; |
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553 } |
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554 |
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555 /* |
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556 %!test |
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557 %! A = [ 0.436997 -0.131721 0.124120 -0.061673 ; |
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558 %! -0.131721 0.738529 0.019851 -0.140295 ; |
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559 %! 0.124120 0.019851 0.354879 -0.059472 ; |
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560 %! -0.061673 -0.140295 -0.059472 0.600939 ]; |
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561 %! |
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562 %! u = [ 0.98950 ; |
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563 %! 0.39844 ; |
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564 %! 0.63484 ; |
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565 %! 0.13351 ]; |
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566 %! |
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567 %! R = chol(A); |
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568 %! |
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569 %! R1 = cholupdate(R,u); |
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570 %! |
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571 %! assert(norm(triu(R1)-R1,Inf) == 0) |
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572 %! assert(norm(R1'*R1 - R'*R - u*u',Inf) < 1e1*eps) |
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573 %! |
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574 %! R1 = cholupdate(R1,u,"-"); |
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575 %! |
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576 %! assert(norm(triu(R1)-R1,Inf) == 0) |
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577 %! assert(norm(R1 - R,Inf) < 1e1*eps) |
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578 %! |
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579 %!test |
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580 %! A = [ 0.5585528 + 0.0000000i -0.1662088 - 0.0315341i 0.0107873 + 0.0236411i -0.0276775 - 0.0186073i ; |
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581 %! -0.1662088 + 0.0315341i 0.6760061 + 0.0000000i 0.0011452 - 0.0475528i 0.0145967 + 0.0247641i ; |
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582 %! 0.0107873 - 0.0236411i 0.0011452 + 0.0475528i 0.6263149 - 0.0000000i -0.1585837 - 0.0719763i ; |
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583 %! -0.0276775 + 0.0186073i 0.0145967 - 0.0247641i -0.1585837 + 0.0719763i 0.6034234 - 0.0000000i ]; |
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584 %! |
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585 %! u = [ 0.54267 + 0.91519i ; |
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586 %! 0.99647 + 0.43141i ; |
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587 %! 0.83760 + 0.68977i ; |
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588 %! 0.39160 + 0.90378i ]; |
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589 %! |
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590 %! R = chol(A); |
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591 %! |
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592 %! R1 = cholupdate(R,u); |
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593 %! |
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594 %! assert(norm(triu(R1)-R1,Inf) == 0) |
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595 %! assert(norm(R1'*R1 - R'*R - u*u',Inf) < 1e1*eps) |
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596 %! |
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597 %! R1 = cholupdate(R1,u,"-"); |
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|
598 %! |
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599 %! assert(norm(triu(R1)-R1,Inf) == 0) |
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600 %! assert(norm(R1 - R,Inf) < 1e1*eps) |
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|
601 */ |
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|
602 |
7700
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603 DEFUN_DLD (cholinsert, args, nargout, |
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604 "-*- texinfo -*-\n\ |
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605 @deftypefn {Loadable Function} {[@var{R1}, @var{info}] =} cholinsert (@var{R}, @var{j}, @var{u})\n\ |
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606 Given a Cholesky@tie{}factorization of a real symmetric or complex hermitian\n\ |
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607 positive definite matrix @w{@var{A} = @var{R}'*@var{R}}, @var{R}@tie{}upper triangular,\n\ |
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608 return the QR@tie{}factorization of\n\ |
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609 @var{A1}, where @w{A1(p,p) = A}, @w{A1(:,j) = A1(j,:)' = u} and\n\ |
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610 @w{p = [1:j-1,j+1:n+1]}. @w{u(j)} should be positive.\n\ |
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611 On return, @var{info} is set to\n\ |
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612 @itemize\n\ |
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613 @item 0 if the insertion was successful,\n\ |
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614 @item 1 if @var{A1} is not positive definite,\n\ |
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615 @item 2 if @var{R} is singular.\n\ |
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616 @end itemize\n\ |
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617 \n\ |
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618 If @var{info} is not present, an error message is printed in cases 1 and 2.\n\ |
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619 @seealso{chol, cholupdate, choldelete}\n\ |
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620 @end deftypefn") |
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621 { |
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622 octave_idx_type nargin = args.length (); |
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623 |
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624 octave_value_list retval; |
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parents:
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|
625 |
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626 if (nargin != 3) |
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|
627 { |
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|
628 print_usage (); |
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|
629 return retval; |
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|
630 } |
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|
631 |
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632 octave_value argr = args(0); |
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633 octave_value argj = args(1); |
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634 octave_value argu = args(2); |
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|
635 |
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636 if (argr.is_matrix_type () && argu.is_matrix_type () |
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637 && argj.is_real_scalar ()) |
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638 { |
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639 octave_idx_type n = argr.rows (); |
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640 octave_idx_type j = argj.scalar_value (); |
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641 |
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642 if (argr.columns () == n && argu.rows () == n+1 && argu.columns () == 1) |
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643 { |
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644 if (j > 0 && j <= n+1) |
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645 { |
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646 if (argr.is_real_matrix () && argu.is_real_matrix ()) |
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647 { |
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648 // real case |
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649 Matrix R = argr.matrix_value (); |
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650 Matrix u = argu.matrix_value (); |
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651 |
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652 CHOL fact; |
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653 fact.set (R); |
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654 int err = fact.insert_sym (u, j-1); |
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655 |
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656 if (nargout > 1) |
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657 retval(1) = err; |
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658 else if (err) |
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659 error ("cholinsert: insertion violates positiveness"); |
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660 |
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661 retval(0) = fact.chol_matrix (); |
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662 } |
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663 else |
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|
664 { |
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665 // complex case |
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666 ComplexMatrix R = argr.complex_matrix_value (); |
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667 ComplexMatrix u = argu.complex_matrix_value (); |
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668 |
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669 ComplexCHOL fact; |
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670 fact.set (R); |
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671 int err = fact.insert_sym (u, j-1); |
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|
672 |
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673 if (nargout > 1) |
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674 retval(1) = err; |
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675 else if (err) |
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676 error ("cholinsert: insertion violates positiveness"); |
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|
677 |
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678 retval(0) = fact.chol_matrix (); |
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679 } |
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|
680 } |
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681 else |
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682 error ("cholinsert: index out of range"); |
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|
683 } |
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684 else |
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|
685 error ("cholinsert: dimension mismatch"); |
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parents:
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|
686 } |
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|
687 else |
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|
688 print_usage (); |
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|
689 |
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|
690 return retval; |
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|
691 } |
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|
692 |
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|
693 /* |
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|
694 %!test |
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|
695 %! A = [ 0.436997 -0.131721 0.124120 -0.061673 ; |
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696 %! -0.131721 0.738529 0.019851 -0.140295 ; |
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parents:
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|
697 %! 0.124120 0.019851 0.354879 -0.059472 ; |
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|
698 %! -0.061673 -0.140295 -0.059472 0.600939 ]; |
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|
699 %! |
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diff
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|
700 %! u = [ 0.35080 ; |
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parents:
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|
701 %! 0.63930 ; |
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parents:
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|
702 %! 3.31057 ; |
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parents:
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|
703 %! -0.13825 ; |
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parents:
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|
704 %! 0.45266 ]; |
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parents:
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|
705 %! |
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parents:
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|
706 %! R = chol(A); |
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parents:
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|
707 %! |
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parents:
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|
708 %! j = 3; p = [1:j-1, j+1:5]; |
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parents:
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|
709 %! R1 = cholinsert(R,j,u); A1 = R1'*R1; |
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parents:
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|
710 %! |
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|
711 %! assert(norm(triu(R1)-R1,Inf) == 0) |
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|
712 %! assert(norm(A1(p,p) - A,Inf) < 1e1*eps) |
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|
713 %! |
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|
714 %!test |
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|
715 %! A = [ 0.5585528 + 0.0000000i -0.1662088 - 0.0315341i 0.0107873 + 0.0236411i -0.0276775 - 0.0186073i ; |
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more QR & Cholesky updating functions
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parents:
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|
716 %! -0.1662088 + 0.0315341i 0.6760061 + 0.0000000i 0.0011452 - 0.0475528i 0.0145967 + 0.0247641i ; |
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Jaroslav Hajek <highegg@gmail.com>
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|
717 %! 0.0107873 - 0.0236411i 0.0011452 + 0.0475528i 0.6263149 - 0.0000000i -0.1585837 - 0.0719763i ; |
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Jaroslav Hajek <highegg@gmail.com>
parents:
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diff
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|
718 %! -0.0276775 + 0.0186073i 0.0145967 - 0.0247641i -0.1585837 + 0.0719763i 0.6034234 - 0.0000000i ]; |
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|
719 %! |
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changeset
|
720 %! u = [ 0.35080 + 0.04298i; |
efccca5f2ad7
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parents:
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diff
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|
721 %! 0.63930 + 0.23778i; |
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|
722 %! 3.31057 + 0.00000i; |
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Jaroslav Hajek <highegg@gmail.com>
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diff
changeset
|
723 %! -0.13825 + 0.19879i; |
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|
724 %! 0.45266 + 0.50020i]; |
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parents:
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changeset
|
725 %! |
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parents:
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|
726 %! R = chol(A); |
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parents:
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changeset
|
727 %! |
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728 %! j = 3; p = [1:j-1, j+1:5]; |
efccca5f2ad7
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parents:
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|
729 %! R1 = cholinsert(R,j,u); A1 = R1'*R1; |
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|
730 %! |
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731 %! assert(norm(triu(R1)-R1,Inf) == 0) |
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|
732 %! assert(norm(A1(p,p) - A,Inf) < 1e1*eps) |
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changeset
|
733 %! |
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changeset
|
734 */ |
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changeset
|
735 |
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changeset
|
736 DEFUN_DLD (choldelete, args, nargout, |
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changeset
|
737 "-*- texinfo -*-\n\ |
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|
738 @deftypefn {Loadable Function} {@var{R1} =} choldelete (@var{R}, @var{j})\n\ |
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|
739 Given a Cholesky@tie{}factorization of a real symmetric or complex hermitian\n\ |
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changeset
|
740 positive definite matrix @w{@var{A} = @var{R}'*@var{R}}, @var{R}@tie{}upper triangular,\n\ |
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|
741 return the QR@tie{}factorization of @w{A(p,p)}, where @w{p = [1:j-1,j+1:n+1]}.\n\ |
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diff
changeset
|
742 @seealso{chol, cholupdate, cholinsert}\n\ |
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Jaroslav Hajek <highegg@gmail.com>
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|
743 @end deftypefn") |
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parents:
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|
744 { |
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parents:
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|
745 octave_idx_type nargin = args.length (); |
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parents:
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|
746 |
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|
747 octave_value_list retval; |
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Jaroslav Hajek <highegg@gmail.com>
parents:
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|
748 |
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parents:
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749 if (nargin != 2) |
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parents:
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|
750 { |
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parents:
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changeset
|
751 print_usage (); |
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Jaroslav Hajek <highegg@gmail.com>
parents:
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|
752 return retval; |
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Jaroslav Hajek <highegg@gmail.com>
parents:
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|
753 } |
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Jaroslav Hajek <highegg@gmail.com>
parents:
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|
754 |
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|
755 octave_value argr = args(0); |
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|
756 octave_value argj = args(1); |
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parents:
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|
757 |
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|
758 if (argr.is_matrix_type () && argj.is_real_scalar ()) |
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parents:
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|
759 { |
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760 octave_idx_type n = argr.rows (); |
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761 octave_idx_type j = argj.scalar_value (); |
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|
762 |
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763 if (argr.columns () == n) |
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parents:
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|
764 { |
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parents:
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|
765 if (j > 0 && j <= n) |
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parents:
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|
766 { |
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parents:
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|
767 if (argr.is_real_matrix ()) |
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parents:
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|
768 { |
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parents:
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|
769 // real case |
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|
770 Matrix R = argr.matrix_value (); |
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parents:
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|
771 |
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|
772 CHOL fact; |
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|
773 fact.set (R); |
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parents:
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774 fact.delete_sym (j-1); |
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parents:
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|
775 |
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|
776 retval(0) = fact.chol_matrix (); |
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parents:
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|
777 } |
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|
778 else |
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parents:
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changeset
|
779 { |
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changeset
|
780 // complex case |
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|
781 ComplexMatrix R = argr.complex_matrix_value (); |
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parents:
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|
782 |
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|
783 ComplexCHOL fact; |
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|
784 fact.set (R); |
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785 fact.delete_sym (j-1); |
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parents:
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|
786 |
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|
787 retval(0) = fact.chol_matrix (); |
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parents:
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|
788 } |
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parents:
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|
789 } |
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parents:
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changeset
|
790 else |
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parents:
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|
791 error ("choldelete: index out of range"); |
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parents:
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diff
changeset
|
792 } |
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parents:
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diff
changeset
|
793 else |
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parents:
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diff
changeset
|
794 error ("choldelete: dimension mismatch"); |
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parents:
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changeset
|
795 } |
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parents:
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diff
changeset
|
796 else |
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parents:
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diff
changeset
|
797 print_usage (); |
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parents:
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diff
changeset
|
798 |
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parents:
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|
799 return retval; |
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parents:
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changeset
|
800 } |
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parents:
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changeset
|
801 |
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parents:
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diff
changeset
|
802 /* |
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parents:
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|
803 %!test |
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parents:
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|
804 %! A = [ 0.436997 -0.131721 0.124120 -0.061673 ; |
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parents:
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|
805 %! -0.131721 0.738529 0.019851 -0.140295 ; |
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parents:
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|
806 %! 0.124120 0.019851 0.354879 -0.059472 ; |
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parents:
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diff
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|
807 %! -0.061673 -0.140295 -0.059472 0.600939 ]; |
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parents:
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|
808 %! |
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parents:
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|
809 %! R = chol(A); |
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Jaroslav Hajek <highegg@gmail.com>
parents:
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changeset
|
810 %! |
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parents:
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|
811 %! j = 3; p = [1:j-1,j+1:4]; |
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parents:
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changeset
|
812 %! R1 = choldelete(R,j); |
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parents:
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|
813 %! |
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parents:
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|
814 %! assert(norm(triu(R1)-R1,Inf) == 0) |
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parents:
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815 %! assert(norm(R1'*R1 - A(p,p),Inf) < 1e1*eps) |
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|
816 %! |
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parents:
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changeset
|
817 %!test |
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parents:
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|
818 %! A = [ 0.5585528 + 0.0000000i -0.1662088 - 0.0315341i 0.0107873 + 0.0236411i -0.0276775 - 0.0186073i ; |
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|
819 %! -0.1662088 + 0.0315341i 0.6760061 + 0.0000000i 0.0011452 - 0.0475528i 0.0145967 + 0.0247641i ; |
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parents:
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|
820 %! 0.0107873 - 0.0236411i 0.0011452 + 0.0475528i 0.6263149 - 0.0000000i -0.1585837 - 0.0719763i ; |
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diff
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|
821 %! -0.0276775 + 0.0186073i 0.0145967 - 0.0247641i -0.1585837 + 0.0719763i 0.6034234 - 0.0000000i ]; |
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parents:
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|
822 %! |
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|
823 %! R = chol(A); |
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parents:
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diff
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|
824 %! |
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parents:
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|
825 %! j = 3; p = [1:j-1,j+1:4]; |
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|
826 %! R1 = choldelete(R,j); |
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|
827 %! |
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|
828 %! assert(norm(triu(R1)-R1,Inf) == 0) |
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829 %! assert(norm(R1'*R1 - A(p,p),Inf) < 1e1*eps) |
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|
830 */ |
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changeset
|
831 |
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changeset
|
832 DEFUN_DLD (cholshift, args, nargout, |
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changeset
|
833 "-*- texinfo -*-\n\ |
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|
834 @deftypefn {Loadable Function} {@var{R1} =} cholshift (@var{R}, @var{i}, @var{j})\n\ |
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parents:
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|
835 Given a Cholesky@tie{}factorization of a real symmetric or complex hermitian\n\ |
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|
836 positive definite matrix @w{@var{A} = @var{R}'*@var{R}}, @var{R}@tie{}upper triangular,\n\ |
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|
837 return the QR@tie{}factorization of\n\ |
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|
838 @w{@var{A}(p,p)}, where @w{p} is the permutation @*\n\ |
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|
839 @code{p = [1:i-1, shift(i:j, 1), j+1:n]} if @w{@var{i} < @var{j}} @*\n\ |
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|
840 or @*\n\ |
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|
841 @code{p = [1:j-1, shift(j:i,-1), i+1:n]} if @w{@var{j} < @var{i}}. @*\n\ |
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|
842 \n\ |
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changeset
|
843 @seealso{chol, cholinsert, choldelete}\n\ |
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changeset
|
844 @end deftypefn") |
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parents:
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|
845 { |
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changeset
|
846 octave_idx_type nargin = args.length (); |
efccca5f2ad7
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|
847 |
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|
848 octave_value_list retval; |
efccca5f2ad7
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changeset
|
849 |
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|
850 if (nargin != 3) |
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changeset
|
851 { |
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changeset
|
852 print_usage (); |
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|
853 return retval; |
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parents:
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changeset
|
854 } |
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changeset
|
855 |
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changeset
|
856 octave_value argr = args(0); |
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|
857 octave_value argi = args(1); |
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|
858 octave_value argj = args(2); |
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changeset
|
859 |
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changeset
|
860 if (argr.is_matrix_type () && argi.is_real_scalar () && argj.is_real_scalar ()) |
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parents:
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861 { |
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862 octave_idx_type n = argr.rows (); |
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parents:
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863 octave_idx_type i = argi.scalar_value (); |
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864 octave_idx_type j = argj.scalar_value (); |
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|
865 |
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866 if (argr.columns () == n) |
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parents:
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|
867 { |
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868 if (j > 0 && j <= n+1 && i > 0 && i <= n+1) |
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869 { |
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870 if (argr.is_real_matrix ()) |
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871 { |
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872 // real case |
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873 Matrix R = argr.matrix_value (); |
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874 |
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875 CHOL fact; |
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876 fact.set (R); |
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|
877 fact.shift_sym (i-1, j-1); |
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parents:
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|
878 |
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879 retval(0) = fact.chol_matrix (); |
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880 } |
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881 else |
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|
882 { |
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883 // complex case |
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884 ComplexMatrix R = argr.complex_matrix_value (); |
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|
885 |
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886 ComplexCHOL fact; |
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|
887 fact.set (R); |
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888 fact.shift_sym (i-1, j-1); |
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parents:
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|
889 |
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890 retval(0) = fact.chol_matrix (); |
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parents:
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|
891 } |
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diff
changeset
|
892 } |
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diff
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|
893 else |
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894 error ("cholshift: index out of range"); |
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parents:
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|
895 } |
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896 else |
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parents:
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diff
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897 error ("cholshift: dimension mismatch"); |
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parents:
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|
898 } |
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parents:
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899 else |
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|
900 print_usage (); |
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|
901 |
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parents:
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|
902 return retval; |
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parents:
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diff
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|
903 } |
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parents:
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changeset
|
904 |
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|
905 /* |
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|
906 %!test |
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parents:
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diff
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|
907 %! A = [ 0.436997 -0.131721 0.124120 -0.061673 ; |
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parents:
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|
908 %! -0.131721 0.738529 0.019851 -0.140295 ; |
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parents:
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|
909 %! 0.124120 0.019851 0.354879 -0.059472 ; |
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parents:
7650
diff
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|
910 %! -0.061673 -0.140295 -0.059472 0.600939 ]; |
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parents:
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|
911 %! |
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parents:
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|
912 %! R = chol(A); |
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parents:
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diff
changeset
|
913 %! |
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parents:
7650
diff
changeset
|
914 %! i = 1; j = 3; p = [1:i-1, shift(i:j,-1), j+1:4]; |
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parents:
7650
diff
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|
915 %! R1 = cholshift(R,i,j); |
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parents:
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diff
changeset
|
916 %! |
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parents:
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|
917 %! assert(norm(triu(R1)-R1,Inf) == 0) |
efccca5f2ad7
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parents:
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diff
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|
918 %! assert(norm(R1'*R1 - A(p,p),Inf) < 1e1*eps) |
efccca5f2ad7
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parents:
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diff
changeset
|
919 %! |
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parents:
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changeset
|
920 %! j = 1; i = 3; p = [1:j-1, shift(j:i,+1), i+1:4]; |
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parents:
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diff
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|
921 %! R1 = cholshift(R,i,j); |
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parents:
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diff
changeset
|
922 %! |
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parents:
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changeset
|
923 %! assert(norm(triu(R1)-R1,Inf) == 0) |
efccca5f2ad7
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Jaroslav Hajek <highegg@gmail.com>
parents:
7650
diff
changeset
|
924 %! assert(norm(R1'*R1 - A(p,p),Inf) < 1e1*eps) |
efccca5f2ad7
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parents:
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diff
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|
925 %! |
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parents:
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diff
changeset
|
926 %!test |
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parents:
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changeset
|
927 %! A = [ 0.5585528 + 0.0000000i -0.1662088 - 0.0315341i 0.0107873 + 0.0236411i -0.0276775 - 0.0186073i ; |
efccca5f2ad7
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Jaroslav Hajek <highegg@gmail.com>
parents:
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diff
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|
928 %! -0.1662088 + 0.0315341i 0.6760061 + 0.0000000i 0.0011452 - 0.0475528i 0.0145967 + 0.0247641i ; |
efccca5f2ad7
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Jaroslav Hajek <highegg@gmail.com>
parents:
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diff
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|
929 %! 0.0107873 - 0.0236411i 0.0011452 + 0.0475528i 0.6263149 - 0.0000000i -0.1585837 - 0.0719763i ; |
efccca5f2ad7
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Jaroslav Hajek <highegg@gmail.com>
parents:
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diff
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|
930 %! -0.0276775 + 0.0186073i 0.0145967 - 0.0247641i -0.1585837 + 0.0719763i 0.6034234 - 0.0000000i ]; |
efccca5f2ad7
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parents:
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diff
changeset
|
931 %! |
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Jaroslav Hajek <highegg@gmail.com>
parents:
7650
diff
changeset
|
932 %! R = chol(A); |
efccca5f2ad7
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Jaroslav Hajek <highegg@gmail.com>
parents:
7650
diff
changeset
|
933 %! |
efccca5f2ad7
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parents:
7650
diff
changeset
|
934 %! i = 1; j = 3; p = [1:i-1, shift(i:j,-1), j+1:4]; |
efccca5f2ad7
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Jaroslav Hajek <highegg@gmail.com>
parents:
7650
diff
changeset
|
935 %! R1 = cholshift(R,i,j); |
efccca5f2ad7
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Jaroslav Hajek <highegg@gmail.com>
parents:
7650
diff
changeset
|
936 %! |
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Jaroslav Hajek <highegg@gmail.com>
parents:
7650
diff
changeset
|
937 %! assert(norm(triu(R1)-R1,Inf) == 0) |
efccca5f2ad7
more QR & Cholesky updating functions
Jaroslav Hajek <highegg@gmail.com>
parents:
7650
diff
changeset
|
938 %! assert(norm(R1'*R1 - A(p,p),Inf) < 1e1*eps) |
efccca5f2ad7
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Jaroslav Hajek <highegg@gmail.com>
parents:
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diff
changeset
|
939 %! |
efccca5f2ad7
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Jaroslav Hajek <highegg@gmail.com>
parents:
7650
diff
changeset
|
940 %! j = 1; i = 3; p = [1:j-1, shift(j:i,+1), i+1:4]; |
efccca5f2ad7
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Jaroslav Hajek <highegg@gmail.com>
parents:
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diff
changeset
|
941 %! R1 = cholshift(R,i,j); |
efccca5f2ad7
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Jaroslav Hajek <highegg@gmail.com>
parents:
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diff
changeset
|
942 %! |
efccca5f2ad7
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Jaroslav Hajek <highegg@gmail.com>
parents:
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diff
changeset
|
943 %! assert(norm(triu(R1)-R1,Inf) == 0) |
efccca5f2ad7
more QR & Cholesky updating functions
Jaroslav Hajek <highegg@gmail.com>
parents:
7650
diff
changeset
|
944 %! assert(norm(R1'*R1 - A(p,p),Inf) < 1e1*eps) |
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Jaroslav Hajek <highegg@gmail.com>
parents:
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diff
changeset
|
945 */ |
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changeset
|
946 |
2928 | 947 /* |
948 ;;; Local Variables: *** | |
949 ;;; mode: C++ *** | |
950 ;;; End: *** | |
951 */ | |
952 |