Mercurial > hg > octave-lyh
annotate src/DLD-FUNCTIONS/svd.cc @ 13951:79aa00a94e9e
doc: Document "local" option for configuration variables.
* svd.cc, defaults.cc, dirfns.cc, error.cc, help.cc, input.cc, load-save.cc,
ls-oct-ascii.cc, oct-hist.cc, ov-base.cc, ov-range.cc, ov-struct.cc,
ov-usr-fcn.cc, pager.cc, pr-output.cc, pt-binop.cc, pt-eval.cc, pt-mat.cc,
sighandlers.cc, variables.cc: Document "local" option for configuration
variables.
author | Rik <octave@nomad.inbox5.com> |
---|---|
date | Sun, 27 Nov 2011 16:07:13 -0800 |
parents | 5fa482628bf6 |
children | 72c96de7a403 |
rev | line source |
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2928 | 1 /* |
2 | |
11523 | 3 Copyright (C) 1996-2011 John W. Eaton |
2928 | 4 |
5 This file is part of Octave. | |
6 | |
7 Octave is free software; you can redistribute it and/or modify it | |
8 under the terms of the GNU General Public License as published by the | |
7016 | 9 Free Software Foundation; either version 3 of the License, or (at your |
10 option) any later version. | |
2928 | 11 |
12 Octave is distributed in the hope that it will be useful, but WITHOUT | |
13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
15 for more details. | |
16 | |
17 You should have received a copy of the GNU General Public License | |
7016 | 18 along with Octave; see the file COPYING. If not, see |
19 <http://www.gnu.org/licenses/>. | |
2928 | 20 |
21 */ | |
22 | |
23 #ifdef HAVE_CONFIG_H | |
24 #include <config.h> | |
25 #endif | |
26 | |
27 #include "CmplxSVD.h" | |
28 #include "dbleSVD.h" | |
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29 #include "fCmplxSVD.h" |
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30 #include "floatSVD.h" |
2928 | 31 |
32 #include "defun-dld.h" | |
33 #include "error.h" | |
34 #include "gripes.h" | |
35 #include "oct-obj.h" | |
36 #include "pr-output.h" | |
37 #include "utils.h" | |
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38 #include "variables.h" |
2928 | 39 |
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40 static int Vsvd_driver = SVD::GESVD; |
10601 | 41 |
2928 | 42 DEFUN_DLD (svd, args, nargout, |
3548 | 43 "-*- texinfo -*-\n\ |
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44 @deftypefn {Loadable Function} {@var{s} =} svd (@var{A})\n\ |
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45 @deftypefnx {Loadable Function} {[@var{U}, @var{S}, @var{V}] =} svd (@var{A})\n\ |
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46 @deftypefnx {Loadable Function} {[@var{U}, @var{S}, @var{V}] =} svd (@var{A}, @var{econ})\n\ |
3372 | 47 @cindex singular value decomposition\n\ |
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48 Compute the singular value decomposition of @var{A}\n\ |
3372 | 49 @tex\n\ |
50 $$\n\ | |
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51 A = U S V^{\\dagger}\n\ |
3372 | 52 $$\n\ |
53 @end tex\n\ | |
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54 @ifnottex\n\ |
3372 | 55 \n\ |
56 @example\n\ | |
6620 | 57 A = U*S*V'\n\ |
3372 | 58 @end example\n\ |
10840 | 59 \n\ |
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60 @end ifnottex\n\ |
3372 | 61 \n\ |
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62 The function @code{svd} normally returns only the vector of singular values.\n\ |
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63 When called with three return values, it computes\n\ |
3372 | 64 @tex\n\ |
65 $U$, $S$, and $V$.\n\ | |
66 @end tex\n\ | |
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67 @ifnottex\n\ |
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68 @var{U}, @var{S}, and @var{V}.\n\ |
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69 @end ifnottex\n\ |
3372 | 70 For example,\n\ |
71 \n\ | |
72 @example\n\ | |
73 svd (hilb (3))\n\ | |
74 @end example\n\ | |
75 \n\ | |
76 @noindent\n\ | |
77 returns\n\ | |
2928 | 78 \n\ |
3372 | 79 @example\n\ |
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80 @group\n\ |
3372 | 81 ans =\n\ |
82 \n\ | |
83 1.4083189\n\ | |
84 0.1223271\n\ | |
85 0.0026873\n\ | |
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86 @end group\n\ |
3372 | 87 @end example\n\ |
88 \n\ | |
89 @noindent\n\ | |
90 and\n\ | |
91 \n\ | |
92 @example\n\ | |
93 [u, s, v] = svd (hilb (3))\n\ | |
94 @end example\n\ | |
95 \n\ | |
96 @noindent\n\ | |
97 returns\n\ | |
98 \n\ | |
99 @example\n\ | |
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100 @group\n\ |
3372 | 101 u =\n\ |
2928 | 102 \n\ |
3372 | 103 -0.82704 0.54745 0.12766\n\ |
104 -0.45986 -0.52829 -0.71375\n\ | |
105 -0.32330 -0.64901 0.68867\n\ | |
106 \n\ | |
107 s =\n\ | |
108 \n\ | |
109 1.40832 0.00000 0.00000\n\ | |
110 0.00000 0.12233 0.00000\n\ | |
111 0.00000 0.00000 0.00269\n\ | |
112 \n\ | |
113 v =\n\ | |
114 \n\ | |
115 -0.82704 0.54745 0.12766\n\ | |
116 -0.45986 -0.52829 -0.71375\n\ | |
117 -0.32330 -0.64901 0.68867\n\ | |
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118 @end group\n\ |
3372 | 119 @end example\n\ |
120 \n\ | |
121 If given a second argument, @code{svd} returns an economy-sized\n\ | |
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122 decomposition, eliminating the unnecessary rows or columns of @var{U} or\n\ |
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123 @var{V}.\n\ |
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124 @seealso{svd_driver, svds, eig}\n\ |
3372 | 125 @end deftypefn") |
2928 | 126 { |
127 octave_value_list retval; | |
128 | |
129 int nargin = args.length (); | |
130 | |
131 if (nargin < 1 || nargin > 2 || nargout == 2 || nargout > 3) | |
132 { | |
5823 | 133 print_usage (); |
2928 | 134 return retval; |
135 } | |
136 | |
137 octave_value arg = args(0); | |
138 | |
5275 | 139 octave_idx_type nr = arg.rows (); |
140 octave_idx_type nc = arg.columns (); | |
2928 | 141 |
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142 if (arg.ndims () != 2) |
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143 { |
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144 error ("svd: A must be a 2-D matrix"); |
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145 return retval; |
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146 } |
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147 |
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148 bool isfloat = arg.is_single_type (); |
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149 |
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150 SVD::type type = ((nargout == 0 || nargout == 1) |
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151 ? SVD::sigma_only |
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152 : (nargin == 2) ? SVD::economy : SVD::std); |
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153 |
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154 SVD::driver driver = static_cast<SVD::driver> (Vsvd_driver); |
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155 |
4478 | 156 if (nr == 0 || nc == 0) |
2928 | 157 { |
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158 if (isfloat) |
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159 { |
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160 switch (type) |
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161 { |
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162 case SVD::std: |
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163 retval(2) = FloatDiagMatrix (nc, nc, 1.0f); |
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164 retval(1) = FloatMatrix (nr, nc); |
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165 retval(0) = FloatDiagMatrix (nr, nr, 1.0f); |
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166 break; |
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167 case SVD::economy: |
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168 retval(2) = FloatDiagMatrix (0, nc, 1.0f); |
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169 retval(1) = FloatMatrix (0, 0); |
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170 retval(0) = FloatDiagMatrix (nr, 0, 1.0f); |
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171 break; |
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172 case SVD::sigma_only: default: |
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173 retval(0) = FloatMatrix (0, 1); |
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174 break; |
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175 } |
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176 } |
4478 | 177 else |
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178 { |
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179 switch (type) |
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180 { |
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181 case SVD::std: |
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182 retval(2) = DiagMatrix (nc, nc, 1.0); |
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183 retval(1) = Matrix (nr, nc); |
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184 retval(0) = DiagMatrix (nr, nr, 1.0); |
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185 break; |
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186 case SVD::economy: |
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187 retval(2) = DiagMatrix (0, nc, 1.0); |
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188 retval(1) = Matrix (0, 0); |
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189 retval(0) = DiagMatrix (nr, 0, 1.0); |
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190 break; |
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191 case SVD::sigma_only: default: |
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192 retval(0) = Matrix (0, 1); |
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193 break; |
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194 } |
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195 } |
2928 | 196 } |
197 else | |
198 { | |
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199 if (isfloat) |
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200 { |
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201 if (arg.is_real_type ()) |
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202 { |
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203 FloatMatrix tmp = arg.float_matrix_value (); |
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204 |
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205 if (! error_state) |
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206 { |
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207 if (tmp.any_element_is_inf_or_nan ()) |
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208 { |
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209 error ("svd: cannot take SVD of matrix containing Inf or NaN values"); |
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210 return retval; |
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211 } |
4478 | 212 |
10601 | 213 FloatSVD result (tmp, type, driver); |
4478 | 214 |
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215 FloatDiagMatrix sigma = result.singular_values (); |
4478 | 216 |
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217 if (nargout == 0 || nargout == 1) |
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218 { |
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219 retval(0) = sigma.diag (); |
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220 } |
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221 else |
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222 { |
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223 retval(2) = result.right_singular_matrix (); |
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224 retval(1) = sigma; |
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225 retval(0) = result.left_singular_matrix (); |
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226 } |
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227 } |
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228 } |
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229 else if (arg.is_complex_type ()) |
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230 { |
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231 FloatComplexMatrix ctmp = arg.float_complex_matrix_value (); |
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233 if (! error_state) |
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234 { |
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235 if (ctmp.any_element_is_inf_or_nan ()) |
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236 { |
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237 error ("svd: cannot take SVD of matrix containing Inf or NaN values"); |
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238 return retval; |
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239 } |
4478 | 240 |
10601 | 241 FloatComplexSVD result (ctmp, type, driver); |
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243 FloatDiagMatrix sigma = result.singular_values (); |
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245 if (nargout == 0 || nargout == 1) |
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246 { |
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247 retval(0) = sigma.diag (); |
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248 } |
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249 else |
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250 { |
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251 retval(2) = result.right_singular_matrix (); |
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252 retval(1) = sigma; |
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253 retval(0) = result.left_singular_matrix (); |
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254 } |
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255 } |
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256 } |
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257 } |
4478 | 258 else |
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259 { |
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260 if (arg.is_real_type ()) |
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261 { |
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262 Matrix tmp = arg.matrix_value (); |
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263 |
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264 if (! error_state) |
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265 { |
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266 if (tmp.any_element_is_inf_or_nan ()) |
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267 { |
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268 error ("svd: cannot take SVD of matrix containing Inf or NaN values"); |
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269 return retval; |
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270 } |
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271 |
10601 | 272 SVD result (tmp, type, driver); |
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273 |
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274 DiagMatrix sigma = result.singular_values (); |
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275 |
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276 if (nargout == 0 || nargout == 1) |
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277 { |
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278 retval(0) = sigma.diag (); |
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279 } |
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280 else |
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281 { |
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282 retval(2) = result.right_singular_matrix (); |
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283 retval(1) = sigma; |
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284 retval(0) = result.left_singular_matrix (); |
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285 } |
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286 } |
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287 } |
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288 else if (arg.is_complex_type ()) |
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289 { |
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290 ComplexMatrix ctmp = arg.complex_matrix_value (); |
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291 |
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292 if (! error_state) |
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293 { |
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294 if (ctmp.any_element_is_inf_or_nan ()) |
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295 { |
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296 error ("svd: cannot take SVD of matrix containing Inf or NaN values"); |
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297 return retval; |
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298 } |
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299 |
10601 | 300 ComplexSVD result (ctmp, type, driver); |
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301 |
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302 DiagMatrix sigma = result.singular_values (); |
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303 |
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304 if (nargout == 0 || nargout == 1) |
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305 { |
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306 retval(0) = sigma.diag (); |
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307 } |
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308 else |
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309 { |
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310 retval(2) = result.right_singular_matrix (); |
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311 retval(1) = sigma; |
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312 retval(0) = result.left_singular_matrix (); |
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313 } |
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314 } |
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315 } |
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316 else |
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317 { |
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318 gripe_wrong_type_arg ("svd", arg); |
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319 return retval; |
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320 } |
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321 } |
2928 | 322 } |
323 | |
324 return retval; | |
325 } | |
326 | |
327 /* | |
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328 |
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329 %!assert(svd ([1, 2; 2, 1]), [3; 1], sqrt (eps)); |
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330 |
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331 %!test |
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332 %! [u, s, v] = svd ([1, 2; 2, 1]); |
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333 %! x = 1 / sqrt (2); |
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334 %! assert (u, [-x, -x; -x, x], sqrt (eps)); |
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335 %! assert (s, [3, 0; 0, 1], sqrt (eps)); |
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336 %! assert (v, [-x, x; -x, -x], sqrt (eps)); |
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337 |
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338 %!test |
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339 %! a = [1, 2, 3; 4, 5, 6]; |
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340 %! [u, s, v] = svd (a); |
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341 %! assert (u * s * v', a, sqrt (eps)); |
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342 |
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343 %!test |
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344 %! a = [1, 2; 3, 4; 5, 6]; |
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345 %! [u, s, v] = svd (a); |
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346 %! assert (u * s * v', a, sqrt (eps)); |
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347 |
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348 %!test |
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349 %! a = [1, 2, 3; 4, 5, 6]; |
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350 %! [u, s, v] = svd (a, 1); |
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351 %! assert (u * s * v', a, sqrt (eps)); |
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352 |
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353 %!test |
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354 %! a = [1, 2; 3, 4; 5, 6]; |
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355 %! [u, s, v] = svd (a, 1); |
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356 %! assert (u * s * v', a, sqrt (eps)); |
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357 |
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358 %!assert(svd (single([1, 2; 2, 1])), single([3; 1]), sqrt (eps('single'))); |
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359 |
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360 %!test |
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361 %! [u, s, v] = svd (single([1, 2; 2, 1])); |
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362 %! x = single (1 / sqrt (2)); |
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363 %! assert (u, [-x, -x; -x, x], sqrt (eps('single'))); |
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364 %! assert (s, single([3, 0; 0, 1]), sqrt (eps('single'))); |
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365 %! assert (v, [-x, x; -x, -x], sqrt (eps('single'))); |
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366 |
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367 %!test |
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368 %! a = single([1, 2, 3; 4, 5, 6]); |
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369 %! [u, s, v] = svd (a); |
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370 %! assert (u * s * v', a, sqrt (eps('single'))); |
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371 |
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372 %!test |
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373 %! a = single([1, 2; 3, 4; 5, 6]); |
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374 %! [u, s, v] = svd (a); |
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375 %! assert (u * s * v', a, sqrt (eps('single'))); |
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376 |
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377 %!test |
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378 %! a = single([1, 2, 3; 4, 5, 6]); |
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379 %! [u, s, v] = svd (a, 1); |
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380 %! assert (u * s * v', a, sqrt (eps('single'))); |
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381 |
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382 %!test |
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383 %! a = single([1, 2; 3, 4; 5, 6]); |
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384 %! [u, s, v] = svd (a, 1); |
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385 %! assert (u * s * v', a, sqrt (eps('single'))); |
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386 |
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387 %!test |
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388 %! a = zeros (0, 5); |
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389 %! [u, s, v] = svd (a); |
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390 %! assert (size (u), [0, 0]); |
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391 %! assert (size (s), [0, 5]); |
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392 %! assert (size (v), [5, 5]); |
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393 |
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394 %!test |
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395 %! a = zeros (5, 0); |
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396 %! [u, s, v] = svd (a, 1); |
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397 %! assert (size (u), [5, 0]); |
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398 %! assert (size (s), [0, 0]); |
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399 %! assert (size (v), [0, 0]); |
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400 |
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401 %!error <Invalid call to svd> svd (); |
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402 %!error <Invalid call to svd> svd ([1, 2; 4, 5], 2, 3); |
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403 %!error <Invalid call to svd> [u, v] = svd ([1, 2; 3, 4]); |
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404 |
2928 | 405 */ |
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407 DEFUN_DLD (svd_driver, args, nargout, |
10601 | 408 "-*- texinfo -*-\n\ |
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409 @deftypefn {Loadable Function} {@var{val} =} svd_driver ()\n\ |
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410 @deftypefnx {Loadable Function} {@var{old_val} =} svd_driver (@var{new_val})\n\ |
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411 @deftypefnx {Loadable Function} {} svd_driver (@var{new_val}, \"local\")\n\ |
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412 Query or set the underlying @sc{lapack} driver used by @code{svd}.\n\ |
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413 Currently recognized values are \"gesvd\" and \"gesdd\". The default\n\ |
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414 is \"gesvd\".\n\ |
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415 \n\ |
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416 When called from inside a function with the \"local\" option, the variable is\n\ |
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417 changed locally for the function and any subroutines it calls. The original\n\ |
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418 variable value is restored when exiting the function.\n\ |
10601 | 419 @seealso{svd}\n\ |
420 @end deftypefn") | |
421 { | |
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422 static const char *driver_names[] = { "gesvd", "gesdd", 0 }; |
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424 return SET_INTERNAL_VARIABLE_CHOICES (svd_driver, driver_names); |
10601 | 425 } |