Mercurial > hg > octave-nkf
annotate src/DLD-FUNCTIONS/svd.cc @ 10840:89f4d7e294cc
Grammarcheck .cc files
author | Rik <octave@nomad.inbox5.com> |
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date | Sat, 31 Jul 2010 11:18:11 -0700 |
parents | fbd7843974fa |
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rev | line source |
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2928 | 1 /* |
2 | |
8920 | 3 Copyright (C) 1996, 1997, 1999, 2000, 2003, 2005, 2006, 2007, 2008, 2009 |
7017 | 4 John W. Eaton |
2928 | 5 |
6 This file is part of Octave. | |
7 | |
8 Octave is free software; you can redistribute it and/or modify it | |
9 under the terms of the GNU General Public License as published by the | |
7016 | 10 Free Software Foundation; either version 3 of the License, or (at your |
11 option) any later version. | |
2928 | 12 |
13 Octave is distributed in the hope that it will be useful, but WITHOUT | |
14 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
15 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
16 for more details. | |
17 | |
18 You should have received a copy of the GNU General Public License | |
7016 | 19 along with Octave; see the file COPYING. If not, see |
20 <http://www.gnu.org/licenses/>. | |
2928 | 21 |
22 */ | |
23 | |
24 #ifdef HAVE_CONFIG_H | |
25 #include <config.h> | |
26 #endif | |
27 | |
28 #include "CmplxSVD.h" | |
29 #include "dbleSVD.h" | |
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30 #include "fCmplxSVD.h" |
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31 #include "floatSVD.h" |
2928 | 32 |
33 #include "defun-dld.h" | |
34 #include "error.h" | |
35 #include "gripes.h" | |
36 #include "oct-obj.h" | |
37 #include "pr-output.h" | |
38 #include "utils.h" | |
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39 #include "variables.h" |
2928 | 40 |
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41 static int Vsvd_driver = SVD::GESVD; |
10601 | 42 |
2928 | 43 DEFUN_DLD (svd, args, nargout, |
3548 | 44 "-*- texinfo -*-\n\ |
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45 @deftypefn {Loadable Function} {@var{s} =} svd (@var{a})\n\ |
3372 | 46 @deftypefnx {Loadable Function} {[@var{u}, @var{s}, @var{v}] =} svd (@var{a})\n\ |
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47 @deftypefnx {Loadable Function} {[@var{u}, @var{s}, @var{v}] =} svd (@var{a}, @var{econ})\n\ |
3372 | 48 @cindex singular value decomposition\n\ |
49 Compute the singular value decomposition of @var{a}\n\ | |
50 @tex\n\ | |
51 $$\n\ | |
6620 | 52 A = U S V^H\n\ |
3372 | 53 $$\n\ |
54 @end tex\n\ | |
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55 @ifnottex\n\ |
3372 | 56 \n\ |
57 @example\n\ | |
6620 | 58 A = U*S*V'\n\ |
3372 | 59 @end example\n\ |
10840 | 60 \n\ |
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61 @end ifnottex\n\ |
3372 | 62 \n\ |
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63 The function @code{svd} normally returns only the vector of singular values.\n\ |
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64 When called with three return values, it computes\n\ |
3372 | 65 @tex\n\ |
66 $U$, $S$, and $V$.\n\ | |
67 @end tex\n\ | |
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68 @ifnottex\n\ |
3372 | 69 U, S, and V.\n\ |
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70 @end ifnottex\n\ |
3372 | 71 For example,\n\ |
72 \n\ | |
73 @example\n\ | |
74 svd (hilb (3))\n\ | |
75 @end example\n\ | |
76 \n\ | |
77 @noindent\n\ | |
78 returns\n\ | |
2928 | 79 \n\ |
3372 | 80 @example\n\ |
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81 @group\n\ |
3372 | 82 ans =\n\ |
83 \n\ | |
84 1.4083189\n\ | |
85 0.1223271\n\ | |
86 0.0026873\n\ | |
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87 @end group\n\ |
3372 | 88 @end example\n\ |
89 \n\ | |
90 @noindent\n\ | |
91 and\n\ | |
92 \n\ | |
93 @example\n\ | |
94 [u, s, v] = svd (hilb (3))\n\ | |
95 @end example\n\ | |
96 \n\ | |
97 @noindent\n\ | |
98 returns\n\ | |
99 \n\ | |
100 @example\n\ | |
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101 @group\n\ |
3372 | 102 u =\n\ |
2928 | 103 \n\ |
3372 | 104 -0.82704 0.54745 0.12766\n\ |
105 -0.45986 -0.52829 -0.71375\n\ | |
106 -0.32330 -0.64901 0.68867\n\ | |
107 \n\ | |
108 s =\n\ | |
109 \n\ | |
110 1.40832 0.00000 0.00000\n\ | |
111 0.00000 0.12233 0.00000\n\ | |
112 0.00000 0.00000 0.00269\n\ | |
113 \n\ | |
114 v =\n\ | |
115 \n\ | |
116 -0.82704 0.54745 0.12766\n\ | |
117 -0.45986 -0.52829 -0.71375\n\ | |
118 -0.32330 -0.64901 0.68867\n\ | |
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119 @end group\n\ |
3372 | 120 @end example\n\ |
121 \n\ | |
122 If given a second argument, @code{svd} returns an economy-sized\n\ | |
123 decomposition, eliminating the unnecessary rows or columns of @var{u} or\n\ | |
124 @var{v}.\n\ | |
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: only valid for matrices"); |
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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 assert (driver == SVD::GESVD || driver == SVD::GESDD); |
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156 |
4478 | 157 if (nr == 0 || nc == 0) |
2928 | 158 { |
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159 if (isfloat) |
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160 { |
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161 switch (type) |
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162 { |
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163 case SVD::std: |
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164 retval(2) = FloatDiagMatrix (nc, nc, 1.0f); |
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165 retval(1) = FloatMatrix (nr, nc); |
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166 retval(0) = FloatDiagMatrix (nr, nr, 1.0f); |
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167 break; |
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168 case SVD::economy: |
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169 retval(2) = FloatDiagMatrix (0, nc, 1.0f); |
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170 retval(1) = FloatMatrix (0, 0); |
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171 retval(0) = FloatDiagMatrix (nr, 0, 1.0f); |
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172 break; |
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173 case SVD::sigma_only: default: |
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174 retval(0) = FloatMatrix (0, 1); |
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175 break; |
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176 } |
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177 } |
4478 | 178 else |
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179 { |
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180 switch (type) |
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181 { |
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182 case SVD::std: |
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183 retval(2) = DiagMatrix (nc, nc, 1.0); |
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184 retval(1) = Matrix (nr, nc); |
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185 retval(0) = DiagMatrix (nr, nr, 1.0); |
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186 break; |
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187 case SVD::economy: |
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188 retval(2) = DiagMatrix (0, nc, 1.0); |
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189 retval(1) = Matrix (0, 0); |
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190 retval(0) = DiagMatrix (nr, 0, 1.0); |
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191 break; |
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192 case SVD::sigma_only: default: |
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193 retval(0) = Matrix (0, 1); |
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194 break; |
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195 } |
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196 } |
2928 | 197 } |
198 else | |
199 { | |
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200 if (isfloat) |
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201 { |
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202 if (arg.is_real_type ()) |
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203 { |
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204 FloatMatrix tmp = arg.float_matrix_value (); |
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205 |
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206 if (! error_state) |
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207 { |
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208 if (tmp.any_element_is_inf_or_nan ()) |
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209 { |
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210 error ("svd: cannot take SVD of matrix containing Inf or NaN values"); |
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211 return retval; |
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212 } |
4478 | 213 |
10601 | 214 FloatSVD result (tmp, type, driver); |
4478 | 215 |
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216 FloatDiagMatrix sigma = result.singular_values (); |
4478 | 217 |
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218 if (nargout == 0 || nargout == 1) |
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219 { |
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220 retval(0) = sigma.diag (); |
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221 } |
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222 else |
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223 { |
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224 retval(2) = result.right_singular_matrix (); |
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225 retval(1) = sigma; |
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226 retval(0) = result.left_singular_matrix (); |
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227 } |
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228 } |
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229 } |
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230 else if (arg.is_complex_type ()) |
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231 { |
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232 FloatComplexMatrix ctmp = arg.float_complex_matrix_value (); |
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234 if (! error_state) |
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235 { |
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236 if (ctmp.any_element_is_inf_or_nan ()) |
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237 { |
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238 error ("svd: cannot take SVD of matrix containing Inf or NaN values"); |
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239 return retval; |
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240 } |
4478 | 241 |
10601 | 242 FloatComplexSVD result (ctmp, type, driver); |
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244 FloatDiagMatrix sigma = result.singular_values (); |
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246 if (nargout == 0 || nargout == 1) |
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247 { |
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248 retval(0) = sigma.diag (); |
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249 } |
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250 else |
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251 { |
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252 retval(2) = result.right_singular_matrix (); |
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253 retval(1) = sigma; |
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254 retval(0) = result.left_singular_matrix (); |
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255 } |
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256 } |
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257 } |
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258 } |
4478 | 259 else |
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260 { |
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261 if (arg.is_real_type ()) |
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262 { |
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263 Matrix tmp = arg.matrix_value (); |
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264 |
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265 if (! error_state) |
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266 { |
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267 if (tmp.any_element_is_inf_or_nan ()) |
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268 { |
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269 error ("svd: cannot take SVD of matrix containing Inf or NaN values"); |
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270 return retval; |
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271 } |
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272 |
10601 | 273 SVD result (tmp, type, driver); |
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274 |
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275 DiagMatrix sigma = result.singular_values (); |
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276 |
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277 if (nargout == 0 || nargout == 1) |
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278 { |
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279 retval(0) = sigma.diag (); |
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280 } |
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281 else |
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282 { |
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283 retval(2) = result.right_singular_matrix (); |
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284 retval(1) = sigma; |
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285 retval(0) = result.left_singular_matrix (); |
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286 } |
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287 } |
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288 } |
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289 else if (arg.is_complex_type ()) |
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290 { |
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291 ComplexMatrix ctmp = arg.complex_matrix_value (); |
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292 |
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293 if (! error_state) |
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294 { |
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295 if (ctmp.any_element_is_inf_or_nan ()) |
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296 { |
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297 error ("svd: cannot take SVD of matrix containing Inf or NaN values"); |
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298 return retval; |
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299 } |
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300 |
10601 | 301 ComplexSVD result (ctmp, type, driver); |
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302 |
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303 DiagMatrix sigma = result.singular_values (); |
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304 |
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305 if (nargout == 0 || nargout == 1) |
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306 { |
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307 retval(0) = sigma.diag (); |
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308 } |
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309 else |
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310 { |
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311 retval(2) = result.right_singular_matrix (); |
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312 retval(1) = sigma; |
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313 retval(0) = result.left_singular_matrix (); |
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314 } |
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315 } |
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316 } |
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317 else |
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318 { |
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319 gripe_wrong_type_arg ("svd", arg); |
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320 return retval; |
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321 } |
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322 } |
2928 | 323 } |
324 | |
325 return retval; | |
326 } | |
327 | |
328 /* | |
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329 |
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330 %!assert(svd ([1, 2; 2, 1]), [3; 1], sqrt (eps)); |
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331 |
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332 %!test |
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333 %! [u, s, v] = svd ([1, 2; 2, 1]); |
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334 %! x = 1 / sqrt (2); |
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335 %! assert (u, [-x, -x; -x, x], sqrt (eps)); |
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336 %! assert (s, [3, 0; 0, 1], sqrt (eps)); |
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337 %! assert (v, [-x, x; -x, -x], sqrt (eps)); |
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338 |
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339 %!test |
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340 %! a = [1, 2, 3; 4, 5, 6]; |
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341 %! [u, s, v] = svd (a); |
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342 %! assert (u * s * v', a, sqrt (eps)); |
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343 |
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344 %!test |
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345 %! a = [1, 2; 3, 4; 5, 6]; |
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346 %! [u, s, v] = svd (a); |
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347 %! assert (u * s * v', a, sqrt (eps)); |
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348 |
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349 %!test |
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350 %! a = [1, 2, 3; 4, 5, 6]; |
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351 %! [u, s, v] = svd (a, 1); |
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352 %! assert (u * s * v', a, sqrt (eps)); |
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353 |
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354 %!test |
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355 %! a = [1, 2; 3, 4; 5, 6]; |
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356 %! [u, s, v] = svd (a, 1); |
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357 %! assert (u * s * v', a, sqrt (eps)); |
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358 |
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359 %!assert(svd (single([1, 2; 2, 1])), single([3; 1]), sqrt (eps('single'))); |
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360 |
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361 %!test |
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362 %! [u, s, v] = svd (single([1, 2; 2, 1])); |
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363 %! x = single (1 / sqrt (2)); |
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364 %! assert (u, [-x, -x; -x, x], sqrt (eps('single'))); |
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365 %! assert (s, single([3, 0; 0, 1]), sqrt (eps('single'))); |
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366 %! assert (v, [-x, x; -x, -x], sqrt (eps('single'))); |
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367 |
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368 %!test |
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369 %! a = single([1, 2, 3; 4, 5, 6]); |
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370 %! [u, s, v] = svd (a); |
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371 %! assert (u * s * v', a, sqrt (eps('single'))); |
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372 |
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373 %!test |
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374 %! a = single([1, 2; 3, 4; 5, 6]); |
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375 %! [u, s, v] = svd (a); |
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376 %! assert (u * s * v', a, sqrt (eps('single'))); |
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377 |
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378 %!test |
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379 %! a = single([1, 2, 3; 4, 5, 6]); |
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380 %! [u, s, v] = svd (a, 1); |
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381 %! assert (u * s * v', a, sqrt (eps('single'))); |
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382 |
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383 %!test |
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384 %! a = single([1, 2; 3, 4; 5, 6]); |
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385 %! [u, s, v] = svd (a, 1); |
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386 %! assert (u * s * v', a, sqrt (eps('single'))); |
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387 |
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388 %!test |
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389 %! a = zeros (0, 5); |
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390 %! [u, s, v] = svd (a); |
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391 %! assert (size (u), [0, 0]); |
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392 %! assert (size (s), [0, 5]); |
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393 %! assert (size (v), [5, 5]); |
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394 |
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395 %!test |
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396 %! a = zeros (5, 0); |
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397 %! [u, s, v] = svd (a, 1); |
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398 %! assert (size (u), [5, 0]); |
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399 %! assert (size (s), [0, 0]); |
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400 %! assert (size (v), [0, 0]); |
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401 |
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402 %!error <Invalid call to svd.*> svd (); |
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403 %!error <Invalid call to svd.*> svd ([1, 2; 4, 5], 2, 3); |
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404 %!error <Invalid call to svd.*> [u, v] = svd ([1, 2; 3, 4]); |
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405 |
2928 | 406 */ |
10601 | 407 |
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408 DEFUN_DLD (svd_driver, args, nargout, |
10601 | 409 "-*- texinfo -*-\n\ |
410 @deftypefn {Loadable Function} {@var{old} =} svd_driver (@var{new})\n\ | |
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411 Sets or queries the underlying @sc{lapack} driver used by svd.\n\ |
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412 Currently recognized are \"gesvd\" and \"gesdd\". Default is \"gesvd\".\n\ |
10601 | 413 @seealso{svd}\n\ |
414 @end deftypefn") | |
415 { | |
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416 static const char *driver_names[] = { "gesvd", "gesdd", 0 }; |
10601 | 417 |
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418 return SET_INTERNAL_VARIABLE_CHOICES (svd_driver, driver_names); |
10601 | 419 } |