Mercurial > octave-nkf
annotate src/corefcn/sqrtm.cc @ 15039:e753177cde93
maint: Move non-dynamically linked functions from DLD-FUNCTIONS/ to corefcn/ directory
* __contourc__.cc, __dispatch__.cc, __lin_interpn__.cc, __pchip_deriv__.cc,
__qp__.cc, balance.cc, besselj.cc, betainc.cc, bsxfun.cc, cellfun.cc,
colloc.cc, conv2.cc, daspk.cc, dasrt.cc, dassl.cc, det.cc, dlmread.cc, dot.cc,
eig.cc, fft.cc, fft2.cc, fftn.cc, filter.cc, find.cc, gammainc.cc, gcd.cc,
getgrent.cc, getpwent.cc, getrusage.cc, givens.cc, hess.cc, hex2num.cc, inv.cc,
kron.cc, lookup.cc, lsode.cc, lu.cc, luinc.cc, matrix_type.cc, max.cc,
md5sum.cc, mgorth.cc, nproc.cc, pinv.cc, quad.cc, quadcc.cc, qz.cc,
rand.cc, rcond.cc, regexp.cc, schur.cc, spparms.cc, sqrtm.cc, str2double.cc,
strfind.cc, sub2ind.cc, svd.cc, syl.cc, time.cc, tril.cc, typecast.cc:
Move functions from DLD-FUNCTIONS/ to corefcn/ directory. Include "defun.h",
not "defun-dld.h". Change docstring to refer to these as "Built-in Functions".
* build-aux/mk-opts.pl: Generate options code with '#include "defun.h"'. Change
option docstrings to refer to these as "Built-in Functions".
* corefcn/module.mk: List of functions to build in corefcn/ dir.
* DLD-FUNCTIONS/config-module.awk: Update to new build system.
* DLD-FUNCTIONS/module-files: Remove functions which are now in corefcn/ directory.
* src/Makefile.am: Update to build "convenience library" in corefcn/. Octave
program now links against all other libraries + corefcn libary.
* src/find-defun-files.sh: Strip $srcdir from filename.
* src/link-deps.mk: Add REGEX and FFTW link dependencies for liboctinterp.
* type.m, which.m: Change failing tests to use 'amd', still a dynamic function,
rather than 'dot', which isn't.
author | Rik <rik@octave.org> |
---|---|
date | Fri, 27 Jul 2012 15:35:00 -0700 |
parents | src/DLD-FUNCTIONS/sqrtm.cc@60e5cf354d80 |
children |
rev | line source |
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4331 | 1 /* |
2 | |
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3 Copyright (C) 2001-2012 Ross Lippert and Paul Kienzle |
10608 | 4 Copyright (C) 2010 VZLU Prague |
4331 | 5 |
7016 | 6 This file is part of Octave. |
4331 | 7 |
7016 | 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 | |
10 Free Software Foundation; either version 3 of the License, or (at your | |
11 option) any later version. | |
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. | |
4331 | 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/>. | |
4331 | 21 |
22 */ | |
23 | |
24 #ifdef HAVE_CONFIG_H | |
25 #include <config.h> | |
26 #endif | |
27 | |
28 #include <float.h> | |
29 | |
30 #include "CmplxSCHUR.h" | |
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31 #include "fCmplxSCHUR.h" |
4331 | 32 #include "lo-ieee.h" |
33 #include "lo-mappers.h" | |
10608 | 34 #include "oct-norm.h" |
4331 | 35 |
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36 #include "defun.h" |
4331 | 37 #include "error.h" |
38 #include "gripes.h" | |
39 #include "utils.h" | |
10608 | 40 #include "xnorm.h" |
4331 | 41 |
10608 | 42 template <class Matrix> |
43 static void | |
44 sqrtm_utri_inplace (Matrix& T) | |
4331 | 45 { |
10608 | 46 typedef typename Matrix::element_type element_type; |
4331 | 47 |
10608 | 48 const element_type zero = element_type (); |
4331 | 49 |
10608 | 50 bool singular = false; |
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51 |
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52 // The following code is equivalent to this triple loop: |
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53 // |
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54 // n = rows (T); |
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55 // for j = 1:n |
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56 // T(j,j) = sqrt (T(j,j)); |
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57 // for i = j-1:-1:1 |
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58 // T(i,j) /= (T(i,i) + T(j,j)); |
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59 // k = 1:i-1; |
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60 // T(k,j) -= T(k,i) * T(i,j); |
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61 // endfor |
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62 // endfor |
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63 // |
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64 // this is an in-place, cache-aligned variant of the code |
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65 // given in Higham's paper. |
4331 | 66 |
10608 | 67 const octave_idx_type n = T.rows (); |
68 element_type *Tp = T.fortran_vec (); | |
5275 | 69 for (octave_idx_type j = 0; j < n; j++) |
4331 | 70 { |
10608 | 71 element_type *colj = Tp + n*j; |
72 if (colj[j] != zero) | |
73 colj[j] = sqrt (colj[j]); | |
74 else | |
75 singular = true; | |
4331 | 76 |
10608 | 77 for (octave_idx_type i = j-1; i >= 0; i--) |
78 { | |
79 const element_type *coli = Tp + n*i; | |
80 const element_type colji = colj[i] /= (coli[i] + colj[j]); | |
81 for (octave_idx_type k = 0; k < i; k++) | |
82 colj[k] -= coli[k] * colji; | |
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83 } |
4331 | 84 } |
85 | |
10608 | 86 if (singular) |
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87 warning_with_id ("Octave:sqrtm:SingularMatrix", |
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88 "sqrtm: matrix is singular, may not have a square root"); |
4331 | 89 } |
90 | |
10608 | 91 template <class Matrix, class ComplexMatrix, class ComplexSCHUR> |
92 static octave_value | |
93 do_sqrtm (const octave_value& arg) | |
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94 { |
10608 | 95 |
96 octave_value retval; | |
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97 |
10608 | 98 MatrixType mt = arg.matrix_type (); |
99 | |
100 bool iscomplex = arg.is_complex_type (); | |
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101 |
10608 | 102 typedef typename Matrix::element_type real_type; |
103 | |
104 real_type cutoff = 0, one = 1; | |
105 real_type eps = std::numeric_limits<real_type>::epsilon (); | |
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106 |
10608 | 107 if (! iscomplex) |
108 { | |
109 Matrix x = octave_value_extract<Matrix> (arg); | |
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110 |
10608 | 111 if (mt.is_unknown ()) // if type is not known, compute it now. |
112 arg.matrix_type (mt = MatrixType (x)); | |
113 | |
114 switch (mt.type ()) | |
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115 { |
10608 | 116 case MatrixType::Upper: |
117 case MatrixType::Diagonal: | |
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118 if (! x.diag ().any_element_is_negative ()) |
10608 | 119 { |
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120 // Do it in real arithmetic. |
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121 sqrtm_utri_inplace (x); |
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122 retval = x; |
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123 retval.matrix_type (mt); |
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124 } |
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125 else |
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126 iscomplex = true; |
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127 break; |
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128 |
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129 case MatrixType::Lower: |
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130 if (! x.diag ().any_element_is_negative ()) |
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131 { |
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132 x = x.transpose (); |
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133 sqrtm_utri_inplace (x); |
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134 retval = x.transpose (); |
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135 retval.matrix_type (mt); |
10608 | 136 } |
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137 else |
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138 iscomplex = true; |
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139 break; |
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140 |
10608 | 141 default: |
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142 iscomplex = true; |
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143 break; |
10608 | 144 } |
145 | |
146 if (iscomplex) | |
147 cutoff = 10 * x.rows () * eps * xnorm (x, one); | |
148 } | |
149 | |
150 if (iscomplex) | |
151 { | |
152 ComplexMatrix x = octave_value_extract<ComplexMatrix> (arg); | |
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153 |
10608 | 154 if (mt.is_unknown ()) // if type is not known, compute it now. |
155 arg.matrix_type (mt = MatrixType (x)); | |
156 | |
157 switch (mt.type ()) | |
158 { | |
159 case MatrixType::Upper: | |
160 case MatrixType::Diagonal: | |
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161 sqrtm_utri_inplace (x); |
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162 retval = x; |
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163 retval.matrix_type (mt); |
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164 break; |
10608 | 165 |
166 case MatrixType::Lower: | |
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167 x = x.transpose (); |
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168 sqrtm_utri_inplace (x); |
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169 retval = x.transpose (); |
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170 retval.matrix_type (mt); |
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171 break; |
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172 |
10608 | 173 default: |
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174 { |
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175 ComplexMatrix u; |
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176 |
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177 do |
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178 { |
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179 ComplexSCHUR schur (x, std::string (), true); |
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180 x = schur.schur_matrix (); |
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181 u = schur.unitary_matrix (); |
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182 } |
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183 while (0); // schur no longer needed. |
10608 | 184 |
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185 sqrtm_utri_inplace (x); |
10608 | 186 |
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187 x = u * x; // original x no longer needed. |
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188 ComplexMatrix res = xgemm (x, u, blas_no_trans, blas_conj_trans); |
10608 | 189 |
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190 if (cutoff > 0 && xnorm (imag (res), one) <= cutoff) |
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191 retval = real (res); |
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192 else |
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193 retval = res; |
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194 } |
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195 break; |
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196 } |
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197 } |
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198 |
10608 | 199 return retval; |
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200 } |
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201 |
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202 DEFUN (sqrtm, args, nargout, |
4331 | 203 "-*- texinfo -*-\n\ |
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204 @deftypefn {Built-in Function} {@var{s} =} sqrtm (@var{A})\n\ |
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205 @deftypefnx {Built-in Function} {[@var{s}, @var{error_estimate}] =} sqrtm (@var{A})\n\ |
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206 Compute the matrix square root of the square matrix @var{A}.\n\ |
4331 | 207 \n\ |
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208 Ref: N.J. Higham. @cite{A New sqrtm for @sc{matlab}}. Numerical\n\ |
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209 Analysis Report No. 336, Manchester @nospell{Centre} for Computational\n\ |
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210 Mathematics, Manchester, England, January 1999.\n\ |
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211 @seealso{expm, logm}\n\ |
5642 | 212 @end deftypefn") |
4331 | 213 { |
214 octave_value_list retval; | |
215 | |
216 int nargin = args.length (); | |
217 | |
218 if (nargin != 1) | |
219 { | |
5823 | 220 print_usage (); |
4331 | 221 return retval; |
222 } | |
223 | |
224 octave_value arg = args(0); | |
225 | |
5275 | 226 octave_idx_type n = arg.rows (); |
227 octave_idx_type nc = arg.columns (); | |
4331 | 228 |
10608 | 229 if (n != nc || arg.ndims () > 2) |
4331 | 230 { |
231 gripe_square_matrix_required ("sqrtm"); | |
232 return retval; | |
233 } | |
234 | |
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235 if (nargout > 1) |
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236 { |
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237 retval.resize (1, 2); |
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238 retval(2) = -1.0; |
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239 } |
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240 |
10608 | 241 if (arg.is_diag_matrix ()) |
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242 // sqrtm of a diagonal matrix is just sqrt. |
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243 retval(0) = arg.sqrt (); |
10608 | 244 else if (arg.is_single_type ()) |
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245 retval(0) = do_sqrtm<FloatMatrix, FloatComplexMatrix, FloatComplexSCHUR> (arg); |
10608 | 246 else if (arg.is_numeric_type ()) |
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247 retval(0) = do_sqrtm<Matrix, ComplexMatrix, ComplexSCHUR> (arg); |
4331 | 248 |
10608 | 249 if (nargout > 1 && ! error_state) |
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250 { |
10608 | 251 // This corresponds to generic code |
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252 // |
10608 | 253 // norm (s*s - x, "fro") / norm (x, "fro"); |
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254 |
10608 | 255 octave_value s = retval(0); |
256 retval(1) = xfrobnorm (s*s - arg) / xfrobnorm (arg); | |
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257 } |
4331 | 258 |
259 return retval; | |
260 } | |
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261 |
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262 /* |
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263 %!assert (sqrtm (2*ones (2)), ones (2), 3*eps) |
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264 |
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265 ## The following two tests are from the reference in the docstring above. |
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266 %!test |
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267 %! x = [0 1; 0 0]; |
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268 %! assert (any (isnan (sqrtm (x))(:))); |
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269 |
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270 %!test |
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271 %! x = eye (4); x(2,2) = x(3,3) = 2^-26; x(1,4) = 1; |
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272 %! z = eye (4); z(2,2) = z(3,3) = 2^-13; z(1,4) = 0.5; |
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273 %! [y, err] = sqrtm (x); |
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274 %! assert (y, z); |
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275 %! assert (err, 0); ## Yes, this one has to hold exactly |
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276 */ |