Mercurial > hg > octave-nkf
annotate liboctave/CMatrix.cc @ 7544:f9983d2761df
more xGELSD workspace fixes
| author | Jaroslav Hajek <highegg@gmail.com> |
|---|---|
| date | Mon, 03 Mar 2008 02:18:12 -0500 |
| parents | 493bb0de3199 |
| children | 36594d5bbe13 |
| rev | line source |
|---|---|
| 1993 | 1 // Matrix manipulations. |
| 458 | 2 /* |
| 3 | |
| 7017 | 4 Copyright (C) 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, |
| 5 2003, 2004, 2005, 2006, 2007 John W. Eaton | |
| 458 | 6 |
| 7 This file is part of Octave. | |
| 8 | |
| 9 Octave is free software; you can redistribute it and/or modify it | |
| 10 under the terms of the GNU General Public License as published by the | |
| 7016 | 11 Free Software Foundation; either version 3 of the License, or (at your |
| 12 option) any later version. | |
| 458 | 13 |
| 14 Octave is distributed in the hope that it will be useful, but WITHOUT | |
| 15 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
| 16 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
| 17 for more details. | |
| 18 | |
| 19 You should have received a copy of the GNU General Public License | |
| 7016 | 20 along with Octave; see the file COPYING. If not, see |
| 21 <http://www.gnu.org/licenses/>. | |
| 458 | 22 |
| 23 */ | |
| 24 | |
| 25 #ifdef HAVE_CONFIG_H | |
| 1192 | 26 #include <config.h> |
| 458 | 27 #endif |
| 28 | |
| 1367 | 29 #include <cfloat> |
| 30 | |
| 3503 | 31 #include <iostream> |
| 6209 | 32 #include <vector> |
| 1367 | 33 |
| 5775 | 34 // FIXME |
| 2443 | 35 #ifdef HAVE_SYS_TYPES_H |
| 36 #include <sys/types.h> | |
| 37 #endif | |
| 458 | 38 |
| 4669 | 39 #include "Array-util.h" |
| 2828 | 40 #include "CMatrix.h" |
| 1819 | 41 #include "CmplxAEPBAL.h" |
| 458 | 42 #include "CmplxDET.h" |
| 1819 | 43 #include "CmplxSCHUR.h" |
| 740 | 44 #include "CmplxSVD.h" |
| 6207 | 45 #include "CmplxCHOL.h" |
| 1847 | 46 #include "f77-fcn.h" |
|
7503
8c32f95c2639
convert mapper functions to new format
David Bateman <dbateman@free.fr>
parents:
7488
diff
changeset
|
47 #include "functor.h" |
| 458 | 48 #include "lo-error.h" |
| 2354 | 49 #include "lo-ieee.h" |
| 50 #include "lo-mappers.h" | |
| 1968 | 51 #include "lo-utils.h" |
| 1367 | 52 #include "mx-base.h" |
| 2828 | 53 #include "mx-cm-dm.h" |
| 3176 | 54 #include "mx-dm-cm.h" |
| 2828 | 55 #include "mx-cm-s.h" |
| 1367 | 56 #include "mx-inlines.cc" |
| 1650 | 57 #include "oct-cmplx.h" |
| 458 | 58 |
| 4773 | 59 #if defined (HAVE_FFTW3) |
| 3827 | 60 #include "oct-fftw.h" |
| 61 #endif | |
| 62 | |
| 458 | 63 // Fortran functions we call. |
| 64 | |
| 65 extern "C" | |
| 66 { | |
| 7477 | 67 F77_RET_T |
| 68 F77_FUNC (xilaenv, XILAENV) (const octave_idx_type&, F77_CONST_CHAR_ARG_DECL, | |
| 69 F77_CONST_CHAR_ARG_DECL, | |
| 70 const octave_idx_type&, const octave_idx_type&, | |
| 7478 | 71 const octave_idx_type&, const octave_idx_type&, |
| 72 octave_idx_type& | |
| 73 F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); | |
| 7476 | 74 |
| 4552 | 75 F77_RET_T |
| 76 F77_FUNC (zgebal, ZGEBAL) (F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 77 const octave_idx_type&, Complex*, const octave_idx_type&, octave_idx_type&, |
| 78 octave_idx_type&, double*, octave_idx_type& | |
| 4552 | 79 F77_CHAR_ARG_LEN_DECL); |
| 80 | |
| 81 F77_RET_T | |
| 82 F77_FUNC (dgebak, DGEBAK) (F77_CONST_CHAR_ARG_DECL, | |
| 83 F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 84 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, double*, |
| 85 const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type& | |
| 4552 | 86 F77_CHAR_ARG_LEN_DECL |
| 87 F77_CHAR_ARG_LEN_DECL); | |
| 88 | |
| 89 F77_RET_T | |
| 90 F77_FUNC (zgemm, ZGEMM) (F77_CONST_CHAR_ARG_DECL, | |
| 91 F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 92 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
| 93 const Complex&, const Complex*, const octave_idx_type&, | |
| 94 const Complex*, const octave_idx_type&, const Complex&, | |
| 95 Complex*, const octave_idx_type& | |
| 4552 | 96 F77_CHAR_ARG_LEN_DECL |
| 97 F77_CHAR_ARG_LEN_DECL); | |
| 98 | |
| 99 F77_RET_T | |
| 5983 | 100 F77_FUNC (zgemv, ZGEMV) (F77_CONST_CHAR_ARG_DECL, |
| 101 const octave_idx_type&, const octave_idx_type&, const Complex&, | |
| 102 const Complex*, const octave_idx_type&, const Complex*, | |
| 103 const octave_idx_type&, const Complex&, Complex*, const octave_idx_type& | |
| 104 F77_CHAR_ARG_LEN_DECL); | |
| 105 | |
| 106 F77_RET_T | |
| 107 F77_FUNC (xzdotu, XZDOTU) (const octave_idx_type&, const Complex*, const octave_idx_type&, | |
| 108 const Complex*, const octave_idx_type&, Complex&); | |
| 109 | |
| 110 F77_RET_T | |
| 5275 | 111 F77_FUNC (zgetrf, ZGETRF) (const octave_idx_type&, const octave_idx_type&, Complex*, const octave_idx_type&, |
| 112 octave_idx_type*, octave_idx_type&); | |
| 4552 | 113 |
| 114 F77_RET_T | |
| 115 F77_FUNC (zgetrs, ZGETRS) (F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 116 const octave_idx_type&, const octave_idx_type&, Complex*, const octave_idx_type&, |
| 117 const octave_idx_type*, Complex*, const octave_idx_type&, octave_idx_type& | |
| 4552 | 118 F77_CHAR_ARG_LEN_DECL); |
| 119 | |
| 120 F77_RET_T | |
| 5275 | 121 F77_FUNC (zgetri, ZGETRI) (const octave_idx_type&, Complex*, const octave_idx_type&, const octave_idx_type*, |
| 122 Complex*, const octave_idx_type&, octave_idx_type&); | |
| 4552 | 123 |
| 124 F77_RET_T | |
| 125 F77_FUNC (zgecon, ZGECON) (F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 126 const octave_idx_type&, Complex*, |
| 127 const octave_idx_type&, const double&, double&, | |
| 128 Complex*, double*, octave_idx_type& | |
| 4552 | 129 F77_CHAR_ARG_LEN_DECL); |
| 130 | |
| 131 F77_RET_T | |
| 7072 | 132 F77_FUNC (zgelsy, ZGELSY) (const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
| 133 Complex*, const octave_idx_type&, Complex*, | |
| 134 const octave_idx_type&, octave_idx_type*, double&, octave_idx_type&, | |
| 135 Complex*, const octave_idx_type&, double*, octave_idx_type&); | |
| 136 | |
| 137 F77_RET_T | |
| 138 F77_FUNC (zgelsd, ZGELSD) (const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, | |
| 5275 | 139 Complex*, const octave_idx_type&, Complex*, |
| 7071 | 140 const octave_idx_type&, double*, double&, octave_idx_type&, |
| 7072 | 141 Complex*, const octave_idx_type&, double*, |
| 142 octave_idx_type*, octave_idx_type&); | |
| 458 | 143 |
| 5785 | 144 F77_RET_T |
| 145 F77_FUNC (zpotrf, ZPOTRF) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 146 Complex*, const octave_idx_type&, | |
| 147 octave_idx_type& F77_CHAR_ARG_LEN_DECL); | |
| 148 | |
| 149 F77_RET_T | |
| 150 F77_FUNC (zpocon, ZPOCON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 151 Complex*, const octave_idx_type&, const double&, | |
| 152 double&, Complex*, double*, | |
| 153 octave_idx_type& F77_CHAR_ARG_LEN_DECL); | |
| 154 | |
| 155 F77_RET_T | |
| 156 F77_FUNC (zpotrs, ZPOTRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 157 const octave_idx_type&, const Complex*, | |
| 158 const octave_idx_type&, Complex*, | |
| 159 const octave_idx_type&, octave_idx_type& | |
| 160 F77_CHAR_ARG_LEN_DECL); | |
| 161 | |
| 162 F77_RET_T | |
| 6207 | 163 F77_FUNC (ztrtri, ZTRTRI) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, |
| 164 const octave_idx_type&, const Complex*, | |
| 165 const octave_idx_type&, octave_idx_type& | |
| 166 F77_CHAR_ARG_LEN_DECL | |
| 167 F77_CHAR_ARG_LEN_DECL); | |
| 168 | |
| 169 F77_RET_T | |
| 5785 | 170 F77_FUNC (ztrcon, ZTRCON) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, |
| 171 F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 172 const Complex*, const octave_idx_type&, double&, | |
| 173 Complex*, double*, octave_idx_type& | |
| 174 F77_CHAR_ARG_LEN_DECL | |
| 175 F77_CHAR_ARG_LEN_DECL | |
| 176 F77_CHAR_ARG_LEN_DECL); | |
| 177 | |
| 178 F77_RET_T | |
| 179 F77_FUNC (ztrtrs, ZTRTRS) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, | |
| 180 F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 181 const octave_idx_type&, const Complex*, | |
| 182 const octave_idx_type&, Complex*, | |
| 183 const octave_idx_type&, octave_idx_type& | |
| 184 F77_CHAR_ARG_LEN_DECL | |
| 185 F77_CHAR_ARG_LEN_DECL | |
| 186 F77_CHAR_ARG_LEN_DECL); | |
| 187 | |
| 1360 | 188 // Note that the original complex fft routines were not written for |
| 189 // double complex arguments. They have been modified by adding an | |
| 190 // implicit double precision (a-h,o-z) statement at the beginning of | |
| 191 // each subroutine. | |
| 458 | 192 |
| 4552 | 193 F77_RET_T |
| 5275 | 194 F77_FUNC (cffti, CFFTI) (const octave_idx_type&, Complex*); |
| 4552 | 195 |
| 196 F77_RET_T | |
| 5275 | 197 F77_FUNC (cfftf, CFFTF) (const octave_idx_type&, Complex*, Complex*); |
| 4552 | 198 |
| 199 F77_RET_T | |
| 5275 | 200 F77_FUNC (cfftb, CFFTB) (const octave_idx_type&, Complex*, Complex*); |
| 4552 | 201 |
| 202 F77_RET_T | |
| 203 F77_FUNC (zlartg, ZLARTG) (const Complex&, const Complex&, | |
| 204 double&, Complex&, Complex&); | |
| 205 | |
| 206 F77_RET_T | |
| 207 F77_FUNC (ztrsyl, ZTRSYL) (F77_CONST_CHAR_ARG_DECL, | |
| 208 F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 209 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
| 210 const Complex*, const octave_idx_type&, | |
| 211 const Complex*, const octave_idx_type&, | |
| 212 const Complex*, const octave_idx_type&, double&, octave_idx_type& | |
| 4552 | 213 F77_CHAR_ARG_LEN_DECL |
| 214 F77_CHAR_ARG_LEN_DECL); | |
| 215 | |
| 216 F77_RET_T | |
| 217 F77_FUNC (xzlange, XZLANGE) (F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 218 const octave_idx_type&, const octave_idx_type&, const Complex*, |
| 219 const octave_idx_type&, double*, double& | |
| 4552 | 220 F77_CHAR_ARG_LEN_DECL); |
| 458 | 221 } |
| 222 | |
| 2354 | 223 static const Complex Complex_NaN_result (octave_NaN, octave_NaN); |
| 224 | |
| 1360 | 225 // Complex Matrix class |
| 458 | 226 |
| 227 ComplexMatrix::ComplexMatrix (const Matrix& a) | |
| 1214 | 228 : MArray2<Complex> (a.rows (), a.cols ()) |
| 458 | 229 { |
| 5275 | 230 for (octave_idx_type j = 0; j < cols (); j++) |
| 231 for (octave_idx_type i = 0; i < rows (); i++) | |
| 458 | 232 elem (i, j) = a.elem (i, j); |
| 233 } | |
| 234 | |
| 2349 | 235 ComplexMatrix::ComplexMatrix (const RowVector& rv) |
| 236 : MArray2<Complex> (1, rv.length (), 0.0) | |
| 237 { | |
| 5275 | 238 for (octave_idx_type i = 0; i < rv.length (); i++) |
| 2349 | 239 elem (0, i) = rv.elem (i); |
| 240 } | |
| 241 | |
| 242 ComplexMatrix::ComplexMatrix (const ColumnVector& cv) | |
| 243 : MArray2<Complex> (cv.length (), 1, 0.0) | |
| 244 { | |
| 5275 | 245 for (octave_idx_type i = 0; i < cv.length (); i++) |
| 2349 | 246 elem (i, 0) = cv.elem (i); |
| 247 } | |
| 248 | |
| 458 | 249 ComplexMatrix::ComplexMatrix (const DiagMatrix& a) |
| 1214 | 250 : MArray2<Complex> (a.rows (), a.cols (), 0.0) |
| 458 | 251 { |
| 5275 | 252 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 253 elem (i, i) = a.elem (i, i); |
| 254 } | |
| 255 | |
| 2349 | 256 ComplexMatrix::ComplexMatrix (const ComplexRowVector& rv) |
| 257 : MArray2<Complex> (1, rv.length (), 0.0) | |
| 258 { | |
| 5275 | 259 for (octave_idx_type i = 0; i < rv.length (); i++) |
| 2349 | 260 elem (0, i) = rv.elem (i); |
| 261 } | |
| 262 | |
| 263 ComplexMatrix::ComplexMatrix (const ComplexColumnVector& cv) | |
| 264 : MArray2<Complex> (cv.length (), 1, 0.0) | |
| 265 { | |
| 5275 | 266 for (octave_idx_type i = 0; i < cv.length (); i++) |
| 2349 | 267 elem (i, 0) = cv.elem (i); |
| 268 } | |
| 269 | |
| 458 | 270 ComplexMatrix::ComplexMatrix (const ComplexDiagMatrix& a) |
| 1214 | 271 : MArray2<Complex> (a.rows (), a.cols (), 0.0) |
| 458 | 272 { |
| 5275 | 273 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 274 elem (i, i) = a.elem (i, i); |
| 275 } | |
| 276 | |
| 5775 | 277 // FIXME -- could we use a templated mixed-type copy function |
| 1574 | 278 // here? |
| 279 | |
| 2828 | 280 ComplexMatrix::ComplexMatrix (const boolMatrix& a) |
| 3180 | 281 : MArray2<Complex> (a.rows (), a.cols (), 0.0) |
| 2828 | 282 { |
| 5275 | 283 for (octave_idx_type i = 0; i < a.rows (); i++) |
| 284 for (octave_idx_type j = 0; j < a.cols (); j++) | |
| 2828 | 285 elem (i, j) = a.elem (i, j); |
| 286 } | |
| 287 | |
| 1574 | 288 ComplexMatrix::ComplexMatrix (const charMatrix& a) |
| 3180 | 289 : MArray2<Complex> (a.rows (), a.cols (), 0.0) |
| 1574 | 290 { |
| 5275 | 291 for (octave_idx_type i = 0; i < a.rows (); i++) |
| 292 for (octave_idx_type j = 0; j < a.cols (); j++) | |
| 1574 | 293 elem (i, j) = a.elem (i, j); |
| 294 } | |
| 295 | |
| 2384 | 296 bool |
| 458 | 297 ComplexMatrix::operator == (const ComplexMatrix& a) const |
| 298 { | |
| 299 if (rows () != a.rows () || cols () != a.cols ()) | |
| 2384 | 300 return false; |
| 458 | 301 |
| 3769 | 302 return mx_inline_equal (data (), a.data (), length ()); |
| 458 | 303 } |
| 304 | |
| 2384 | 305 bool |
| 458 | 306 ComplexMatrix::operator != (const ComplexMatrix& a) const |
| 307 { | |
| 308 return !(*this == a); | |
| 309 } | |
| 310 | |
| 2815 | 311 bool |
| 312 ComplexMatrix::is_hermitian (void) const | |
| 313 { | |
| 5275 | 314 octave_idx_type nr = rows (); |
| 315 octave_idx_type nc = cols (); | |
| 2815 | 316 |
| 317 if (is_square () && nr > 0) | |
| 318 { | |
| 5275 | 319 for (octave_idx_type i = 0; i < nr; i++) |
| 320 for (octave_idx_type j = i; j < nc; j++) | |
| 2815 | 321 if (elem (i, j) != conj (elem (j, i))) |
| 322 return false; | |
| 323 | |
| 324 return true; | |
| 325 } | |
| 326 | |
| 327 return false; | |
| 328 } | |
| 329 | |
| 458 | 330 // destructive insert/delete/reorder operations |
| 331 | |
| 332 ComplexMatrix& | |
| 5275 | 333 ComplexMatrix::insert (const Matrix& a, octave_idx_type r, octave_idx_type c) |
| 458 | 334 { |
| 5275 | 335 octave_idx_type a_nr = a.rows (); |
| 336 octave_idx_type a_nc = a.cols (); | |
| 1699 | 337 |
| 338 if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) | |
| 458 | 339 { |
| 340 (*current_liboctave_error_handler) ("range error for insert"); | |
| 341 return *this; | |
| 342 } | |
| 343 | |
| 4316 | 344 if (a_nr >0 && a_nc > 0) |
| 345 { | |
| 346 make_unique (); | |
| 347 | |
| 5275 | 348 for (octave_idx_type j = 0; j < a_nc; j++) |
| 349 for (octave_idx_type i = 0; i < a_nr; i++) | |
| 4316 | 350 xelem (r+i, c+j) = a.elem (i, j); |
| 351 } | |
| 458 | 352 |
| 353 return *this; | |
| 354 } | |
| 355 | |
| 356 ComplexMatrix& | |
| 5275 | 357 ComplexMatrix::insert (const RowVector& a, octave_idx_type r, octave_idx_type c) |
| 458 | 358 { |
| 5275 | 359 octave_idx_type a_len = a.length (); |
| 4316 | 360 |
| 1699 | 361 if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ()) |
| 458 | 362 { |
| 363 (*current_liboctave_error_handler) ("range error for insert"); | |
| 364 return *this; | |
| 365 } | |
| 366 | |
| 4316 | 367 if (a_len > 0) |
| 368 { | |
| 369 make_unique (); | |
| 370 | |
| 5275 | 371 for (octave_idx_type i = 0; i < a_len; i++) |
| 4316 | 372 xelem (r, c+i) = a.elem (i); |
| 373 } | |
| 458 | 374 |
| 375 return *this; | |
| 376 } | |
| 377 | |
| 378 ComplexMatrix& | |
| 5275 | 379 ComplexMatrix::insert (const ColumnVector& a, octave_idx_type r, octave_idx_type c) |
| 458 | 380 { |
| 5275 | 381 octave_idx_type a_len = a.length (); |
| 4316 | 382 |
| 1699 | 383 if (r < 0 || r + a_len > rows () || c < 0 || c >= cols ()) |
| 458 | 384 { |
| 385 (*current_liboctave_error_handler) ("range error for insert"); | |
| 386 return *this; | |
| 387 } | |
| 388 | |
| 4316 | 389 if (a_len > 0) |
| 390 { | |
| 391 make_unique (); | |
| 392 | |
| 5275 | 393 for (octave_idx_type i = 0; i < a_len; i++) |
| 4316 | 394 xelem (r+i, c) = a.elem (i); |
| 395 } | |
| 458 | 396 |
| 397 return *this; | |
| 398 } | |
| 399 | |
| 400 ComplexMatrix& | |
| 5275 | 401 ComplexMatrix::insert (const DiagMatrix& a, octave_idx_type r, octave_idx_type c) |
| 458 | 402 { |
| 5275 | 403 octave_idx_type a_nr = a.rows (); |
| 404 octave_idx_type a_nc = a.cols (); | |
| 1699 | 405 |
| 406 if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) | |
| 458 | 407 { |
| 408 (*current_liboctave_error_handler) ("range error for insert"); | |
| 409 return *this; | |
| 410 } | |
| 411 | |
| 1699 | 412 fill (0.0, r, c, r + a_nr - 1, c + a_nc - 1); |
| 413 | |
| 5275 | 414 octave_idx_type a_len = a.length (); |
| 4316 | 415 |
| 416 if (a_len > 0) | |
| 417 { | |
| 418 make_unique (); | |
| 419 | |
| 5275 | 420 for (octave_idx_type i = 0; i < a_len; i++) |
| 4316 | 421 xelem (r+i, c+i) = a.elem (i, i); |
| 422 } | |
| 458 | 423 |
| 424 return *this; | |
| 425 } | |
| 426 | |
| 427 ComplexMatrix& | |
| 5275 | 428 ComplexMatrix::insert (const ComplexMatrix& a, octave_idx_type r, octave_idx_type c) |
| 458 | 429 { |
| 1561 | 430 Array2<Complex>::insert (a, r, c); |
| 458 | 431 return *this; |
| 432 } | |
| 433 | |
| 434 ComplexMatrix& | |
| 5275 | 435 ComplexMatrix::insert (const ComplexRowVector& a, octave_idx_type r, octave_idx_type c) |
| 458 | 436 { |
| 5275 | 437 octave_idx_type a_len = a.length (); |
| 1699 | 438 if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ()) |
| 458 | 439 { |
| 440 (*current_liboctave_error_handler) ("range error for insert"); | |
| 441 return *this; | |
| 442 } | |
| 443 | |
| 5275 | 444 for (octave_idx_type i = 0; i < a_len; i++) |
| 458 | 445 elem (r, c+i) = a.elem (i); |
| 446 | |
| 447 return *this; | |
| 448 } | |
| 449 | |
| 450 ComplexMatrix& | |
| 5275 | 451 ComplexMatrix::insert (const ComplexColumnVector& a, octave_idx_type r, octave_idx_type c) |
| 458 | 452 { |
| 5275 | 453 octave_idx_type a_len = a.length (); |
| 4316 | 454 |
| 1699 | 455 if (r < 0 || r + a_len > rows () || c < 0 || c >= cols ()) |
| 458 | 456 { |
| 457 (*current_liboctave_error_handler) ("range error for insert"); | |
| 458 return *this; | |
| 459 } | |
| 460 | |
| 4316 | 461 if (a_len > 0) |
| 462 { | |
| 463 make_unique (); | |
| 464 | |
| 5275 | 465 for (octave_idx_type i = 0; i < a_len; i++) |
| 4316 | 466 xelem (r+i, c) = a.elem (i); |
| 467 } | |
| 458 | 468 |
| 469 return *this; | |
| 470 } | |
| 471 | |
| 472 ComplexMatrix& | |
| 5275 | 473 ComplexMatrix::insert (const ComplexDiagMatrix& a, octave_idx_type r, octave_idx_type c) |
| 458 | 474 { |
| 5275 | 475 octave_idx_type a_nr = a.rows (); |
| 476 octave_idx_type a_nc = a.cols (); | |
| 1699 | 477 |
| 478 if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) | |
| 458 | 479 { |
| 480 (*current_liboctave_error_handler) ("range error for insert"); | |
| 481 return *this; | |
| 482 } | |
| 483 | |
| 1699 | 484 fill (0.0, r, c, r + a_nr - 1, c + a_nc - 1); |
| 485 | |
| 5275 | 486 octave_idx_type a_len = a.length (); |
| 4316 | 487 |
| 488 if (a_len > 0) | |
| 489 { | |
| 490 make_unique (); | |
| 491 | |
| 5275 | 492 for (octave_idx_type i = 0; i < a_len; i++) |
| 4316 | 493 xelem (r+i, c+i) = a.elem (i, i); |
| 494 } | |
| 458 | 495 |
| 496 return *this; | |
| 497 } | |
| 498 | |
| 499 ComplexMatrix& | |
| 500 ComplexMatrix::fill (double val) | |
| 501 { | |
| 5275 | 502 octave_idx_type nr = rows (); |
| 503 octave_idx_type nc = cols (); | |
| 4316 | 504 |
| 458 | 505 if (nr > 0 && nc > 0) |
| 4316 | 506 { |
| 507 make_unique (); | |
| 508 | |
| 5275 | 509 for (octave_idx_type j = 0; j < nc; j++) |
| 510 for (octave_idx_type i = 0; i < nr; i++) | |
| 4316 | 511 xelem (i, j) = val; |
| 512 } | |
| 458 | 513 |
| 514 return *this; | |
| 515 } | |
| 516 | |
| 517 ComplexMatrix& | |
| 518 ComplexMatrix::fill (const Complex& val) | |
| 519 { | |
| 5275 | 520 octave_idx_type nr = rows (); |
| 521 octave_idx_type nc = cols (); | |
| 4316 | 522 |
| 458 | 523 if (nr > 0 && nc > 0) |
| 4316 | 524 { |
| 525 make_unique (); | |
| 526 | |
| 5275 | 527 for (octave_idx_type j = 0; j < nc; j++) |
| 528 for (octave_idx_type i = 0; i < nr; i++) | |
| 4316 | 529 xelem (i, j) = val; |
| 530 } | |
| 458 | 531 |
| 532 return *this; | |
| 533 } | |
| 534 | |
| 535 ComplexMatrix& | |
| 5275 | 536 ComplexMatrix::fill (double val, octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) |
| 458 | 537 { |
| 5275 | 538 octave_idx_type nr = rows (); |
| 539 octave_idx_type nc = cols (); | |
| 4316 | 540 |
| 458 | 541 if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0 |
| 542 || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc) | |
| 543 { | |
| 544 (*current_liboctave_error_handler) ("range error for fill"); | |
| 545 return *this; | |
| 546 } | |
| 547 | |
| 5275 | 548 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } |
| 549 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } | |
| 458 | 550 |
| 4316 | 551 if (r2 >= r1 && c2 >= c1) |
| 552 { | |
| 553 make_unique (); | |
| 554 | |
| 5275 | 555 for (octave_idx_type j = c1; j <= c2; j++) |
| 556 for (octave_idx_type i = r1; i <= r2; i++) | |
| 4316 | 557 xelem (i, j) = val; |
| 558 } | |
| 458 | 559 |
| 560 return *this; | |
| 561 } | |
| 562 | |
| 563 ComplexMatrix& | |
| 5275 | 564 ComplexMatrix::fill (const Complex& val, octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) |
| 458 | 565 { |
| 5275 | 566 octave_idx_type nr = rows (); |
| 567 octave_idx_type nc = cols (); | |
| 4316 | 568 |
| 458 | 569 if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0 |
| 570 || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc) | |
| 571 { | |
| 572 (*current_liboctave_error_handler) ("range error for fill"); | |
| 573 return *this; | |
| 574 } | |
| 575 | |
| 5275 | 576 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } |
| 577 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } | |
| 458 | 578 |
| 4316 | 579 if (r2 >= r1 && c2 >=c1) |
| 580 { | |
| 581 make_unique (); | |
| 582 | |
| 5275 | 583 for (octave_idx_type j = c1; j <= c2; j++) |
| 584 for (octave_idx_type i = r1; i <= r2; i++) | |
| 4316 | 585 xelem (i, j) = val; |
| 586 } | |
| 458 | 587 |
| 588 return *this; | |
| 589 } | |
| 590 | |
| 591 ComplexMatrix | |
| 592 ComplexMatrix::append (const Matrix& a) const | |
| 593 { | |
| 5275 | 594 octave_idx_type nr = rows (); |
| 595 octave_idx_type nc = cols (); | |
| 458 | 596 if (nr != a.rows ()) |
| 597 { | |
| 598 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 599 return *this; | |
| 600 } | |
| 601 | |
| 5275 | 602 octave_idx_type nc_insert = nc; |
| 458 | 603 ComplexMatrix retval (nr, nc + a.cols ()); |
| 604 retval.insert (*this, 0, 0); | |
| 605 retval.insert (a, 0, nc_insert); | |
| 606 return retval; | |
| 607 } | |
| 608 | |
| 609 ComplexMatrix | |
| 610 ComplexMatrix::append (const RowVector& a) const | |
| 611 { | |
| 5275 | 612 octave_idx_type nr = rows (); |
| 613 octave_idx_type nc = cols (); | |
| 458 | 614 if (nr != 1) |
| 615 { | |
| 616 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 617 return *this; | |
| 618 } | |
| 619 | |
| 5275 | 620 octave_idx_type nc_insert = nc; |
| 458 | 621 ComplexMatrix retval (nr, nc + a.length ()); |
| 622 retval.insert (*this, 0, 0); | |
| 623 retval.insert (a, 0, nc_insert); | |
| 624 return retval; | |
| 625 } | |
| 626 | |
| 627 ComplexMatrix | |
| 628 ComplexMatrix::append (const ColumnVector& a) const | |
| 629 { | |
| 5275 | 630 octave_idx_type nr = rows (); |
| 631 octave_idx_type nc = cols (); | |
| 458 | 632 if (nr != a.length ()) |
| 633 { | |
| 634 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 635 return *this; | |
| 636 } | |
| 637 | |
| 5275 | 638 octave_idx_type nc_insert = nc; |
| 458 | 639 ComplexMatrix retval (nr, nc + 1); |
| 640 retval.insert (*this, 0, 0); | |
| 641 retval.insert (a, 0, nc_insert); | |
| 642 return retval; | |
| 643 } | |
| 644 | |
| 645 ComplexMatrix | |
| 646 ComplexMatrix::append (const DiagMatrix& a) const | |
| 647 { | |
| 5275 | 648 octave_idx_type nr = rows (); |
| 649 octave_idx_type nc = cols (); | |
| 458 | 650 if (nr != a.rows ()) |
| 651 { | |
| 652 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 653 return *this; | |
| 654 } | |
| 655 | |
| 5275 | 656 octave_idx_type nc_insert = nc; |
| 458 | 657 ComplexMatrix retval (nr, nc + a.cols ()); |
| 658 retval.insert (*this, 0, 0); | |
| 659 retval.insert (a, 0, nc_insert); | |
| 660 return retval; | |
| 661 } | |
| 662 | |
| 663 ComplexMatrix | |
| 664 ComplexMatrix::append (const ComplexMatrix& a) const | |
| 665 { | |
| 5275 | 666 octave_idx_type nr = rows (); |
| 667 octave_idx_type nc = cols (); | |
| 458 | 668 if (nr != a.rows ()) |
| 669 { | |
| 670 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 671 return *this; | |
| 672 } | |
| 673 | |
| 5275 | 674 octave_idx_type nc_insert = nc; |
| 458 | 675 ComplexMatrix retval (nr, nc + a.cols ()); |
| 676 retval.insert (*this, 0, 0); | |
| 677 retval.insert (a, 0, nc_insert); | |
| 678 return retval; | |
| 679 } | |
| 680 | |
| 681 ComplexMatrix | |
| 682 ComplexMatrix::append (const ComplexRowVector& a) const | |
| 683 { | |
| 5275 | 684 octave_idx_type nr = rows (); |
| 685 octave_idx_type nc = cols (); | |
| 458 | 686 if (nr != 1) |
| 687 { | |
| 688 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 689 return *this; | |
| 690 } | |
| 691 | |
| 5275 | 692 octave_idx_type nc_insert = nc; |
| 458 | 693 ComplexMatrix retval (nr, nc + a.length ()); |
| 694 retval.insert (*this, 0, 0); | |
| 695 retval.insert (a, 0, nc_insert); | |
| 696 return retval; | |
| 697 } | |
| 698 | |
| 699 ComplexMatrix | |
| 700 ComplexMatrix::append (const ComplexColumnVector& a) const | |
| 701 { | |
| 5275 | 702 octave_idx_type nr = rows (); |
| 703 octave_idx_type nc = cols (); | |
| 458 | 704 if (nr != a.length ()) |
| 705 { | |
| 706 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 707 return *this; | |
| 708 } | |
| 709 | |
| 5275 | 710 octave_idx_type nc_insert = nc; |
| 458 | 711 ComplexMatrix retval (nr, nc + 1); |
| 712 retval.insert (*this, 0, 0); | |
| 713 retval.insert (a, 0, nc_insert); | |
| 714 return retval; | |
| 715 } | |
| 716 | |
| 717 ComplexMatrix | |
| 718 ComplexMatrix::append (const ComplexDiagMatrix& a) const | |
| 719 { | |
| 5275 | 720 octave_idx_type nr = rows (); |
| 721 octave_idx_type nc = cols (); | |
| 458 | 722 if (nr != a.rows ()) |
| 723 { | |
| 724 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 725 return *this; | |
| 726 } | |
| 727 | |
| 5275 | 728 octave_idx_type nc_insert = nc; |
| 458 | 729 ComplexMatrix retval (nr, nc + a.cols ()); |
| 730 retval.insert (*this, 0, 0); | |
| 731 retval.insert (a, 0, nc_insert); | |
| 732 return retval; | |
| 733 } | |
| 734 | |
| 735 ComplexMatrix | |
| 736 ComplexMatrix::stack (const Matrix& a) const | |
| 737 { | |
| 5275 | 738 octave_idx_type nr = rows (); |
| 739 octave_idx_type nc = cols (); | |
| 458 | 740 if (nc != a.cols ()) |
| 741 { | |
| 742 (*current_liboctave_error_handler) | |
| 743 ("column dimension mismatch for stack"); | |
| 744 return *this; | |
| 745 } | |
| 746 | |
| 5275 | 747 octave_idx_type nr_insert = nr; |
| 458 | 748 ComplexMatrix retval (nr + a.rows (), nc); |
| 749 retval.insert (*this, 0, 0); | |
| 750 retval.insert (a, nr_insert, 0); | |
| 751 return retval; | |
| 752 } | |
| 753 | |
| 754 ComplexMatrix | |
| 755 ComplexMatrix::stack (const RowVector& a) const | |
| 756 { | |
| 5275 | 757 octave_idx_type nr = rows (); |
| 758 octave_idx_type nc = cols (); | |
| 458 | 759 if (nc != a.length ()) |
| 760 { | |
| 761 (*current_liboctave_error_handler) | |
| 762 ("column dimension mismatch for stack"); | |
| 763 return *this; | |
| 764 } | |
| 765 | |
| 5275 | 766 octave_idx_type nr_insert = nr; |
| 458 | 767 ComplexMatrix retval (nr + 1, nc); |
| 768 retval.insert (*this, 0, 0); | |
| 769 retval.insert (a, nr_insert, 0); | |
| 770 return retval; | |
| 771 } | |
| 772 | |
| 773 ComplexMatrix | |
| 774 ComplexMatrix::stack (const ColumnVector& a) const | |
| 775 { | |
| 5275 | 776 octave_idx_type nr = rows (); |
| 777 octave_idx_type nc = cols (); | |
| 458 | 778 if (nc != 1) |
| 779 { | |
| 780 (*current_liboctave_error_handler) | |
| 781 ("column dimension mismatch for stack"); | |
| 782 return *this; | |
| 783 } | |
| 784 | |
| 5275 | 785 octave_idx_type nr_insert = nr; |
| 458 | 786 ComplexMatrix retval (nr + a.length (), nc); |
| 787 retval.insert (*this, 0, 0); | |
| 788 retval.insert (a, nr_insert, 0); | |
| 789 return retval; | |
| 790 } | |
| 791 | |
| 792 ComplexMatrix | |
| 793 ComplexMatrix::stack (const DiagMatrix& a) const | |
| 794 { | |
| 5275 | 795 octave_idx_type nr = rows (); |
| 796 octave_idx_type nc = cols (); | |
| 458 | 797 if (nc != a.cols ()) |
| 798 { | |
| 799 (*current_liboctave_error_handler) | |
| 800 ("column dimension mismatch for stack"); | |
| 801 return *this; | |
| 802 } | |
| 803 | |
| 5275 | 804 octave_idx_type nr_insert = nr; |
| 458 | 805 ComplexMatrix retval (nr + a.rows (), nc); |
| 806 retval.insert (*this, 0, 0); | |
| 807 retval.insert (a, nr_insert, 0); | |
| 808 return retval; | |
| 809 } | |
| 810 | |
| 811 ComplexMatrix | |
| 812 ComplexMatrix::stack (const ComplexMatrix& a) const | |
| 813 { | |
| 5275 | 814 octave_idx_type nr = rows (); |
| 815 octave_idx_type nc = cols (); | |
| 458 | 816 if (nc != a.cols ()) |
| 817 { | |
| 818 (*current_liboctave_error_handler) | |
| 819 ("column dimension mismatch for stack"); | |
| 820 return *this; | |
| 821 } | |
| 822 | |
| 5275 | 823 octave_idx_type nr_insert = nr; |
| 458 | 824 ComplexMatrix retval (nr + a.rows (), nc); |
| 825 retval.insert (*this, 0, 0); | |
| 826 retval.insert (a, nr_insert, 0); | |
| 827 return retval; | |
| 828 } | |
| 829 | |
| 830 ComplexMatrix | |
| 831 ComplexMatrix::stack (const ComplexRowVector& a) const | |
| 832 { | |
| 5275 | 833 octave_idx_type nr = rows (); |
| 834 octave_idx_type nc = cols (); | |
| 458 | 835 if (nc != a.length ()) |
| 836 { | |
| 837 (*current_liboctave_error_handler) | |
| 838 ("column dimension mismatch for stack"); | |
| 839 return *this; | |
| 840 } | |
| 841 | |
| 5275 | 842 octave_idx_type nr_insert = nr; |
| 458 | 843 ComplexMatrix retval (nr + 1, nc); |
| 844 retval.insert (*this, 0, 0); | |
| 845 retval.insert (a, nr_insert, 0); | |
| 846 return retval; | |
| 847 } | |
| 848 | |
| 849 ComplexMatrix | |
| 850 ComplexMatrix::stack (const ComplexColumnVector& a) const | |
| 851 { | |
| 5275 | 852 octave_idx_type nr = rows (); |
| 853 octave_idx_type nc = cols (); | |
| 458 | 854 if (nc != 1) |
| 855 { | |
| 856 (*current_liboctave_error_handler) | |
| 857 ("column dimension mismatch for stack"); | |
| 858 return *this; | |
| 859 } | |
| 860 | |
| 5275 | 861 octave_idx_type nr_insert = nr; |
| 458 | 862 ComplexMatrix retval (nr + a.length (), nc); |
| 863 retval.insert (*this, 0, 0); | |
| 864 retval.insert (a, nr_insert, 0); | |
| 865 return retval; | |
| 866 } | |
| 867 | |
| 868 ComplexMatrix | |
| 869 ComplexMatrix::stack (const ComplexDiagMatrix& a) const | |
| 870 { | |
| 5275 | 871 octave_idx_type nr = rows (); |
| 872 octave_idx_type nc = cols (); | |
| 458 | 873 if (nc != a.cols ()) |
| 874 { | |
| 875 (*current_liboctave_error_handler) | |
| 876 ("column dimension mismatch for stack"); | |
| 877 return *this; | |
| 878 } | |
| 879 | |
| 5275 | 880 octave_idx_type nr_insert = nr; |
| 458 | 881 ComplexMatrix retval (nr + a.rows (), nc); |
| 882 retval.insert (*this, 0, 0); | |
| 883 retval.insert (a, nr_insert, 0); | |
| 884 return retval; | |
| 885 } | |
| 886 | |
| 887 ComplexMatrix | |
| 888 ComplexMatrix::hermitian (void) const | |
| 889 { | |
| 5275 | 890 octave_idx_type nr = rows (); |
| 891 octave_idx_type nc = cols (); | |
| 458 | 892 ComplexMatrix result; |
| 893 if (length () > 0) | |
| 894 { | |
| 895 result.resize (nc, nr); | |
| 5275 | 896 for (octave_idx_type j = 0; j < nc; j++) |
| 897 for (octave_idx_type i = 0; i < nr; i++) | |
| 458 | 898 result.elem (j, i) = conj (elem (i, j)); |
| 899 } | |
| 900 return result; | |
| 901 } | |
| 902 | |
| 903 ComplexMatrix | |
| 904 conj (const ComplexMatrix& a) | |
| 905 { | |
| 5275 | 906 octave_idx_type a_len = a.length (); |
| 458 | 907 ComplexMatrix retval; |
| 908 if (a_len > 0) | |
| 3769 | 909 retval = ComplexMatrix (mx_inline_conj_dup (a.data (), a_len), |
| 910 a.rows (), a.cols ()); | |
| 458 | 911 return retval; |
| 912 } | |
| 913 | |
| 914 // resize is the destructive equivalent for this one | |
| 915 | |
| 916 ComplexMatrix | |
| 5275 | 917 ComplexMatrix::extract (octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) const |
| 458 | 918 { |
| 5275 | 919 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } |
| 920 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } | |
| 921 | |
| 922 octave_idx_type new_r = r2 - r1 + 1; | |
| 923 octave_idx_type new_c = c2 - c1 + 1; | |
| 458 | 924 |
| 925 ComplexMatrix result (new_r, new_c); | |
| 926 | |
| 5275 | 927 for (octave_idx_type j = 0; j < new_c; j++) |
| 928 for (octave_idx_type i = 0; i < new_r; i++) | |
| 4316 | 929 result.xelem (i, j) = elem (r1+i, c1+j); |
| 930 | |
| 931 return result; | |
| 932 } | |
| 933 | |
| 934 ComplexMatrix | |
| 5275 | 935 ComplexMatrix::extract_n (octave_idx_type r1, octave_idx_type c1, octave_idx_type nr, octave_idx_type nc) const |
| 4316 | 936 { |
| 937 ComplexMatrix result (nr, nc); | |
| 938 | |
| 5275 | 939 for (octave_idx_type j = 0; j < nc; j++) |
| 940 for (octave_idx_type i = 0; i < nr; i++) | |
| 4316 | 941 result.xelem (i, j) = elem (r1+i, c1+j); |
| 458 | 942 |
| 943 return result; | |
| 944 } | |
| 945 | |
| 946 // extract row or column i. | |
| 947 | |
| 948 ComplexRowVector | |
| 5275 | 949 ComplexMatrix::row (octave_idx_type i) const |
| 458 | 950 { |
| 5275 | 951 octave_idx_type nc = cols (); |
| 458 | 952 if (i < 0 || i >= rows ()) |
| 953 { | |
| 954 (*current_liboctave_error_handler) ("invalid row selection"); | |
| 955 return ComplexRowVector (); | |
| 956 } | |
| 957 | |
| 958 ComplexRowVector retval (nc); | |
| 5275 | 959 for (octave_idx_type j = 0; j < cols (); j++) |
| 4316 | 960 retval.xelem (j) = elem (i, j); |
| 458 | 961 |
| 962 return retval; | |
| 963 } | |
| 964 | |
| 965 ComplexColumnVector | |
| 5275 | 966 ComplexMatrix::column (octave_idx_type i) const |
| 458 | 967 { |
| 5275 | 968 octave_idx_type nr = rows (); |
| 458 | 969 if (i < 0 || i >= cols ()) |
| 970 { | |
| 971 (*current_liboctave_error_handler) ("invalid column selection"); | |
| 972 return ComplexColumnVector (); | |
| 973 } | |
| 974 | |
| 975 ComplexColumnVector retval (nr); | |
| 5275 | 976 for (octave_idx_type j = 0; j < nr; j++) |
| 4316 | 977 retval.xelem (j) = elem (j, i); |
| 458 | 978 |
| 979 return retval; | |
| 980 } | |
| 981 | |
| 982 ComplexMatrix | |
| 983 ComplexMatrix::inverse (void) const | |
| 984 { | |
| 5275 | 985 octave_idx_type info; |
| 479 | 986 double rcond; |
| 6207 | 987 MatrixType mattype (*this); |
| 988 return inverse (mattype, info, rcond, 0, 0); | |
| 989 } | |
| 990 | |
| 991 ComplexMatrix | |
| 6479 | 992 ComplexMatrix::inverse (octave_idx_type& info) const |
| 993 { | |
| 994 double rcond; | |
| 995 MatrixType mattype (*this); | |
| 996 return inverse (mattype, info, rcond, 0, 0); | |
| 997 } | |
| 998 | |
| 999 ComplexMatrix | |
| 1000 ComplexMatrix::inverse (octave_idx_type& info, double& rcond, int force, | |
| 1001 int calc_cond) const | |
| 1002 { | |
| 1003 MatrixType mattype (*this); | |
| 6482 | 1004 return inverse (mattype, info, rcond, force, calc_cond); |
| 6479 | 1005 } |
| 1006 | |
| 1007 ComplexMatrix | |
| 6207 | 1008 ComplexMatrix::inverse (MatrixType &mattype) const |
| 1009 { | |
| 1010 octave_idx_type info; | |
| 1011 double rcond; | |
| 1012 return inverse (mattype, info, rcond, 0, 0); | |
| 1013 } | |
| 1014 | |
| 1015 ComplexMatrix | |
| 1016 ComplexMatrix::inverse (MatrixType &mattype, octave_idx_type& info) const | |
| 1017 { | |
| 1018 double rcond; | |
| 1019 return inverse (mattype, info, rcond, 0, 0); | |
| 458 | 1020 } |
| 1021 | |
| 1022 ComplexMatrix | |
| 6207 | 1023 ComplexMatrix::tinverse (MatrixType &mattype, octave_idx_type& info, |
| 1024 double& rcond, int force, int calc_cond) const | |
| 458 | 1025 { |
| 6207 | 1026 ComplexMatrix retval; |
| 1027 | |
| 1028 octave_idx_type nr = rows (); | |
| 1029 octave_idx_type nc = cols (); | |
| 1030 | |
| 1031 if (nr != nc || nr == 0 || nc == 0) | |
| 1032 (*current_liboctave_error_handler) ("inverse requires square matrix"); | |
| 1033 else | |
| 1034 { | |
| 1035 int typ = mattype.type (); | |
| 1036 char uplo = (typ == MatrixType::Lower ? 'L' : 'U'); | |
| 1037 char udiag = 'N'; | |
| 1038 retval = *this; | |
| 1039 Complex *tmp_data = retval.fortran_vec (); | |
| 1040 | |
| 1041 F77_XFCN (ztrtri, ZTRTRI, (F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1042 F77_CONST_CHAR_ARG2 (&udiag, 1), | |
| 1043 nr, tmp_data, nr, info | |
| 1044 F77_CHAR_ARG_LEN (1) | |
| 1045 F77_CHAR_ARG_LEN (1))); | |
| 1046 | |
|
7482
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
1047 // Throw-away extra info LAPACK gives so as to not change output. |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
1048 rcond = 0.0; |
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1049 if (info != 0) |
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1050 info = -1; |
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1051 else if (calc_cond) |
| 6207 | 1052 { |
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1053 octave_idx_type ztrcon_info = 0; |
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1054 char job = '1'; |
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1055 |
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1056 OCTAVE_LOCAL_BUFFER (Complex, cwork, 2*nr); |
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1057 OCTAVE_LOCAL_BUFFER (double, rwork, nr); |
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1058 |
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1059 F77_XFCN (ztrcon, ZTRCON, (F77_CONST_CHAR_ARG2 (&job, 1), |
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1060 F77_CONST_CHAR_ARG2 (&uplo, 1), |
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1061 F77_CONST_CHAR_ARG2 (&udiag, 1), |
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1062 nr, tmp_data, nr, rcond, |
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1063 cwork, rwork, ztrcon_info |
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1064 F77_CHAR_ARG_LEN (1) |
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1065 F77_CHAR_ARG_LEN (1) |
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1066 F77_CHAR_ARG_LEN (1))); |
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1067 |
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1068 if (ztrcon_info != 0) |
| 6207 | 1069 info = -1; |
| 1070 } | |
| 1071 | |
| 1072 if (info == -1 && ! force) | |
| 1073 retval = *this; // Restore matrix contents. | |
| 1074 } | |
| 1075 | |
| 1076 return retval; | |
| 458 | 1077 } |
| 1078 | |
| 1079 ComplexMatrix | |
| 6207 | 1080 ComplexMatrix::finverse (MatrixType &mattype, octave_idx_type& info, |
| 1081 double& rcond, int force, int calc_cond) const | |
| 458 | 1082 { |
| 1948 | 1083 ComplexMatrix retval; |
| 1084 | |
| 5275 | 1085 octave_idx_type nr = rows (); |
| 1086 octave_idx_type nc = cols (); | |
| 1948 | 1087 |
| 458 | 1088 if (nr != nc) |
| 1948 | 1089 (*current_liboctave_error_handler) ("inverse requires square matrix"); |
| 458 | 1090 else |
| 1091 { | |
| 5275 | 1092 Array<octave_idx_type> ipvt (nr); |
| 1093 octave_idx_type *pipvt = ipvt.fortran_vec (); | |
| 1948 | 1094 |
| 1095 retval = *this; | |
| 1096 Complex *tmp_data = retval.fortran_vec (); | |
| 1097 | |
| 4329 | 1098 Array<Complex> z(1); |
| 5275 | 1099 octave_idx_type lwork = -1; |
| 4330 | 1100 |
| 1101 // Query the optimum work array size. | |
| 4329 | 1102 |
| 1103 F77_XFCN (zgetri, ZGETRI, (nc, tmp_data, nr, pipvt, | |
| 1104 z.fortran_vec (), lwork, info)); | |
| 1105 | |
| 5315 | 1106 lwork = static_cast<octave_idx_type> (std::real(z(0))); |
| 4329 | 1107 lwork = (lwork < 2 *nc ? 2*nc : lwork); |
| 1108 z.resize (lwork); | |
| 1109 Complex *pz = z.fortran_vec (); | |
| 1110 | |
| 1111 info = 0; | |
| 1112 | |
| 4330 | 1113 // Calculate the norm of the matrix, for later use. |
| 4329 | 1114 double anorm; |
| 1115 if (calc_cond) | |
| 5275 | 1116 anorm = retval.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
| 4329 | 1117 |
| 1118 F77_XFCN (zgetrf, ZGETRF, (nc, nc, tmp_data, nr, pipvt, info)); | |
| 1948 | 1119 |
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1120 // Throw-away extra info LAPACK gives so as to not change output. |
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1121 rcond = 0.0; |
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1122 if (info != 0) |
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1123 info = -1; |
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1124 else if (calc_cond) |
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1125 { |
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1126 // Now calculate the condition number for non-singular matrix. |
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1127 octave_idx_type zgecon_info = 0; |
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1128 char job = '1'; |
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1129 Array<double> rz (2 * nc); |
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1130 double *prz = rz.fortran_vec (); |
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1131 F77_XFCN (zgecon, ZGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
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1132 nc, tmp_data, nr, anorm, |
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1133 rcond, pz, prz, zgecon_info |
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1134 F77_CHAR_ARG_LEN (1))); |
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1135 |
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1136 if (zgecon_info != 0) |
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1137 info = -1; |
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1138 } |
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1139 |
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1140 if (info == -1 && ! force) |
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1141 retval = *this; // Restore contents. |
| 1948 | 1142 else |
| 1143 { | |
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1144 octave_idx_type zgetri_info = 0; |
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1145 |
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1146 F77_XFCN (zgetri, ZGETRI, (nc, tmp_data, nr, pipvt, |
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1147 pz, lwork, zgetri_info)); |
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1148 |
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1149 if (zgetri_info != 0) |
| 1948 | 1150 info = -1; |
| 1151 } | |
| 6207 | 1152 |
| 1153 if (info != 0) | |
| 1154 mattype.mark_as_rectangular(); | |
| 458 | 1155 } |
| 4329 | 1156 |
| 1948 | 1157 return retval; |
| 458 | 1158 } |
| 1159 | |
| 1160 ComplexMatrix | |
| 6207 | 1161 ComplexMatrix::inverse (MatrixType &mattype, octave_idx_type& info, |
| 1162 double& rcond, int force, int calc_cond) const | |
| 1163 { | |
| 1164 int typ = mattype.type (false); | |
| 1165 ComplexMatrix ret; | |
| 1166 | |
| 1167 if (typ == MatrixType::Unknown) | |
| 1168 typ = mattype.type (*this); | |
| 1169 | |
| 1170 if (typ == MatrixType::Upper || typ == MatrixType::Lower) | |
| 1171 ret = tinverse (mattype, info, rcond, force, calc_cond); | |
| 6840 | 1172 else |
| 6207 | 1173 { |
| 1174 if (mattype.is_hermitian ()) | |
| 1175 { | |
| 6486 | 1176 ComplexCHOL chol (*this, info, calc_cond); |
| 6207 | 1177 if (info == 0) |
| 6486 | 1178 { |
| 1179 if (calc_cond) | |
| 1180 rcond = chol.rcond(); | |
| 1181 else | |
| 1182 rcond = 1.0; | |
| 1183 ret = chol.inverse (); | |
| 1184 } | |
| 6207 | 1185 else |
| 1186 mattype.mark_as_unsymmetric (); | |
| 1187 } | |
| 1188 | |
| 1189 if (!mattype.is_hermitian ()) | |
| 1190 ret = finverse(mattype, info, rcond, force, calc_cond); | |
| 6840 | 1191 |
| 7033 | 1192 if ((mattype.is_hermitian () || calc_cond) && rcond == 0.) |
| 6840 | 1193 ret = ComplexMatrix (rows (), columns (), Complex (octave_Inf, 0.)); |
| 6207 | 1194 } |
| 1195 | |
| 1196 return ret; | |
| 1197 } | |
| 1198 | |
| 1199 ComplexMatrix | |
| 4384 | 1200 ComplexMatrix::pseudo_inverse (double tol) const |
| 740 | 1201 { |
| 1549 | 1202 ComplexMatrix retval; |
| 1203 | |
| 3480 | 1204 ComplexSVD result (*this, SVD::economy); |
| 740 | 1205 |
| 1206 DiagMatrix S = result.singular_values (); | |
| 1207 ComplexMatrix U = result.left_singular_matrix (); | |
| 1208 ComplexMatrix V = result.right_singular_matrix (); | |
| 1209 | |
| 1210 ColumnVector sigma = S.diag (); | |
| 1211 | |
| 5275 | 1212 octave_idx_type r = sigma.length () - 1; |
| 1213 octave_idx_type nr = rows (); | |
| 1214 octave_idx_type nc = cols (); | |
| 740 | 1215 |
| 1216 if (tol <= 0.0) | |
| 1217 { | |
| 1218 if (nr > nc) | |
| 1219 tol = nr * sigma.elem (0) * DBL_EPSILON; | |
| 1220 else | |
| 1221 tol = nc * sigma.elem (0) * DBL_EPSILON; | |
| 1222 } | |
| 1223 | |
| 1224 while (r >= 0 && sigma.elem (r) < tol) | |
| 1225 r--; | |
| 1226 | |
| 1227 if (r < 0) | |
| 1549 | 1228 retval = ComplexMatrix (nc, nr, 0.0); |
| 740 | 1229 else |
| 1230 { | |
| 1231 ComplexMatrix Ur = U.extract (0, 0, nr-1, r); | |
| 1232 DiagMatrix D = DiagMatrix (sigma.extract (0, r)) . inverse (); | |
| 1233 ComplexMatrix Vr = V.extract (0, 0, nc-1, r); | |
| 1549 | 1234 retval = Vr * D * Ur.hermitian (); |
| 740 | 1235 } |
| 1549 | 1236 |
| 1237 return retval; | |
| 740 | 1238 } |
| 1239 | |
| 4773 | 1240 #if defined (HAVE_FFTW3) |
| 3827 | 1241 |
| 1242 ComplexMatrix | |
| 1243 ComplexMatrix::fourier (void) const | |
| 1244 { | |
| 1245 size_t nr = rows (); | |
| 1246 size_t nc = cols (); | |
| 1247 | |
| 1248 ComplexMatrix retval (nr, nc); | |
| 1249 | |
| 1250 size_t npts, nsamples; | |
| 1251 | |
| 1252 if (nr == 1 || nc == 1) | |
| 1253 { | |
| 1254 npts = nr > nc ? nr : nc; | |
| 1255 nsamples = 1; | |
| 1256 } | |
| 1257 else | |
| 1258 { | |
| 1259 npts = nr; | |
| 1260 nsamples = nc; | |
| 1261 } | |
| 1262 | |
| 1263 const Complex *in (data ()); | |
| 1264 Complex *out (retval.fortran_vec ()); | |
| 1265 | |
| 4773 | 1266 octave_fftw::fft (in, out, npts, nsamples); |
| 3827 | 1267 |
| 1268 return retval; | |
| 1269 } | |
| 1270 | |
| 1271 ComplexMatrix | |
| 1272 ComplexMatrix::ifourier (void) const | |
| 1273 { | |
| 1274 size_t nr = rows (); | |
| 1275 size_t nc = cols (); | |
| 1276 | |
| 1277 ComplexMatrix retval (nr, nc); | |
| 1278 | |
| 1279 size_t npts, nsamples; | |
| 1280 | |
| 1281 if (nr == 1 || nc == 1) | |
| 1282 { | |
| 1283 npts = nr > nc ? nr : nc; | |
| 1284 nsamples = 1; | |
| 1285 } | |
| 1286 else | |
| 1287 { | |
| 1288 npts = nr; | |
| 1289 nsamples = nc; | |
| 1290 } | |
| 1291 | |
| 1292 const Complex *in (data ()); | |
| 1293 Complex *out (retval.fortran_vec ()); | |
| 1294 | |
| 4773 | 1295 octave_fftw::ifft (in, out, npts, nsamples); |
| 3827 | 1296 |
| 1297 return retval; | |
| 1298 } | |
| 1299 | |
| 1300 ComplexMatrix | |
| 1301 ComplexMatrix::fourier2d (void) const | |
| 1302 { | |
| 4773 | 1303 dim_vector dv(rows (), cols ()); |
| 1304 | |
| 1305 ComplexMatrix retval (rows (), cols ()); | |
| 1306 const Complex *in (data ()); | |
| 1307 Complex *out (retval.fortran_vec ()); | |
| 1308 | |
| 1309 octave_fftw::fftNd (in, out, 2, dv); | |
| 3827 | 1310 |
| 1311 return retval; | |
| 1312 } | |
| 1313 | |
| 1314 ComplexMatrix | |
| 1315 ComplexMatrix::ifourier2d (void) const | |
| 1316 { | |
| 4773 | 1317 dim_vector dv(rows (), cols ()); |
| 1318 | |
| 1319 ComplexMatrix retval (rows (), cols ()); | |
| 1320 const Complex *in (data ()); | |
| 1321 Complex *out (retval.fortran_vec ()); | |
| 1322 | |
| 1323 octave_fftw::ifftNd (in, out, 2, dv); | |
| 3827 | 1324 |
| 1325 return retval; | |
| 1326 } | |
| 1327 | |
| 1328 #else | |
| 1329 | |
| 740 | 1330 ComplexMatrix |
| 458 | 1331 ComplexMatrix::fourier (void) const |
| 1332 { | |
| 1948 | 1333 ComplexMatrix retval; |
| 1334 | |
| 5275 | 1335 octave_idx_type nr = rows (); |
| 1336 octave_idx_type nc = cols (); | |
| 1337 | |
| 1338 octave_idx_type npts, nsamples; | |
| 1948 | 1339 |
| 458 | 1340 if (nr == 1 || nc == 1) |
| 1341 { | |
| 1342 npts = nr > nc ? nr : nc; | |
| 1343 nsamples = 1; | |
| 1344 } | |
| 1345 else | |
| 1346 { | |
| 1347 npts = nr; | |
| 1348 nsamples = nc; | |
| 1349 } | |
| 1350 | |
| 5275 | 1351 octave_idx_type nn = 4*npts+15; |
| 1948 | 1352 |
| 1353 Array<Complex> wsave (nn); | |
| 1354 Complex *pwsave = wsave.fortran_vec (); | |
| 1355 | |
| 1356 retval = *this; | |
| 1357 Complex *tmp_data = retval.fortran_vec (); | |
| 1358 | |
| 3887 | 1359 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
| 458 | 1360 |
| 5275 | 1361 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1362 { |
| 1363 OCTAVE_QUIT; | |
| 1364 | |
| 1365 F77_FUNC (cfftf, CFFTF) (npts, &tmp_data[npts*j], pwsave); | |
| 1366 } | |
| 1948 | 1367 |
| 1368 return retval; | |
| 458 | 1369 } |
| 1370 | |
| 1371 ComplexMatrix | |
| 1372 ComplexMatrix::ifourier (void) const | |
| 1373 { | |
| 1948 | 1374 ComplexMatrix retval; |
| 1375 | |
| 5275 | 1376 octave_idx_type nr = rows (); |
| 1377 octave_idx_type nc = cols (); | |
| 1378 | |
| 1379 octave_idx_type npts, nsamples; | |
| 1948 | 1380 |
| 458 | 1381 if (nr == 1 || nc == 1) |
| 1382 { | |
| 1383 npts = nr > nc ? nr : nc; | |
| 1384 nsamples = 1; | |
| 1385 } | |
| 1386 else | |
| 1387 { | |
| 1388 npts = nr; | |
| 1389 nsamples = nc; | |
| 1390 } | |
| 1391 | |
| 5275 | 1392 octave_idx_type nn = 4*npts+15; |
| 1948 | 1393 |
| 1394 Array<Complex> wsave (nn); | |
| 1395 Complex *pwsave = wsave.fortran_vec (); | |
| 1396 | |
| 1397 retval = *this; | |
| 1398 Complex *tmp_data = retval.fortran_vec (); | |
| 1399 | |
| 3887 | 1400 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
| 458 | 1401 |
| 5275 | 1402 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1403 { |
| 1404 OCTAVE_QUIT; | |
| 1405 | |
| 1406 F77_FUNC (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave); | |
| 1407 } | |
| 458 | 1408 |
| 5275 | 1409 for (octave_idx_type j = 0; j < npts*nsamples; j++) |
| 3572 | 1410 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
| 458 | 1411 |
| 1948 | 1412 return retval; |
| 458 | 1413 } |
| 1414 | |
| 677 | 1415 ComplexMatrix |
| 1416 ComplexMatrix::fourier2d (void) const | |
| 1417 { | |
| 1948 | 1418 ComplexMatrix retval; |
| 1419 | |
| 5275 | 1420 octave_idx_type nr = rows (); |
| 1421 octave_idx_type nc = cols (); | |
| 1422 | |
| 1423 octave_idx_type npts, nsamples; | |
| 1948 | 1424 |
| 677 | 1425 if (nr == 1 || nc == 1) |
| 1426 { | |
| 1427 npts = nr > nc ? nr : nc; | |
| 1428 nsamples = 1; | |
| 1429 } | |
| 1430 else | |
| 1431 { | |
| 1432 npts = nr; | |
| 1433 nsamples = nc; | |
| 1434 } | |
| 1435 | |
| 5275 | 1436 octave_idx_type nn = 4*npts+15; |
| 1948 | 1437 |
| 1438 Array<Complex> wsave (nn); | |
| 1439 Complex *pwsave = wsave.fortran_vec (); | |
| 1440 | |
| 1441 retval = *this; | |
| 1442 Complex *tmp_data = retval.fortran_vec (); | |
| 1443 | |
| 3887 | 1444 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
| 677 | 1445 |
| 5275 | 1446 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1447 { |
| 1448 OCTAVE_QUIT; | |
| 1449 | |
| 1450 F77_FUNC (cfftf, CFFTF) (npts, &tmp_data[npts*j], pwsave); | |
| 1451 } | |
| 677 | 1452 |
| 1453 npts = nc; | |
| 1454 nsamples = nr; | |
| 1455 nn = 4*npts+15; | |
| 1948 | 1456 |
| 1457 wsave.resize (nn); | |
| 1458 pwsave = wsave.fortran_vec (); | |
| 1459 | |
| 4773 | 1460 Array<Complex> tmp (npts); |
| 1461 Complex *prow = tmp.fortran_vec (); | |
| 1948 | 1462 |
| 3887 | 1463 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
| 677 | 1464 |
| 5275 | 1465 for (octave_idx_type j = 0; j < nsamples; j++) |
| 677 | 1466 { |
| 4153 | 1467 OCTAVE_QUIT; |
| 1468 | |
| 5275 | 1469 for (octave_idx_type i = 0; i < npts; i++) |
| 1948 | 1470 prow[i] = tmp_data[i*nr + j]; |
| 1471 | |
| 3887 | 1472 F77_FUNC (cfftf, CFFTF) (npts, prow, pwsave); |
| 677 | 1473 |
| 5275 | 1474 for (octave_idx_type i = 0; i < npts; i++) |
| 1948 | 1475 tmp_data[i*nr + j] = prow[i]; |
| 677 | 1476 } |
| 1477 | |
| 1948 | 1478 return retval; |
| 677 | 1479 } |
| 1480 | |
| 1481 ComplexMatrix | |
| 1482 ComplexMatrix::ifourier2d (void) const | |
| 1483 { | |
| 1948 | 1484 ComplexMatrix retval; |
| 1485 | |
| 5275 | 1486 octave_idx_type nr = rows (); |
| 1487 octave_idx_type nc = cols (); | |
| 1488 | |
| 1489 octave_idx_type npts, nsamples; | |
| 1948 | 1490 |
| 677 | 1491 if (nr == 1 || nc == 1) |
| 1492 { | |
| 1493 npts = nr > nc ? nr : nc; | |
| 1494 nsamples = 1; | |
| 1495 } | |
| 1496 else | |
| 1497 { | |
| 1498 npts = nr; | |
| 1499 nsamples = nc; | |
| 1500 } | |
| 1501 | |
| 5275 | 1502 octave_idx_type nn = 4*npts+15; |
| 1948 | 1503 |
| 1504 Array<Complex> wsave (nn); | |
| 1505 Complex *pwsave = wsave.fortran_vec (); | |
| 1506 | |
| 1507 retval = *this; | |
| 1508 Complex *tmp_data = retval.fortran_vec (); | |
| 1509 | |
| 3887 | 1510 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
| 677 | 1511 |
| 5275 | 1512 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1513 { |
| 1514 OCTAVE_QUIT; | |
| 1515 | |
| 1516 F77_FUNC (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave); | |
| 1517 } | |
| 677 | 1518 |
| 5275 | 1519 for (octave_idx_type j = 0; j < npts*nsamples; j++) |
| 3572 | 1520 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
| 677 | 1521 |
| 1522 npts = nc; | |
| 1523 nsamples = nr; | |
| 1524 nn = 4*npts+15; | |
| 1948 | 1525 |
| 1526 wsave.resize (nn); | |
| 1527 pwsave = wsave.fortran_vec (); | |
| 1528 | |
| 4773 | 1529 Array<Complex> tmp (npts); |
| 1530 Complex *prow = tmp.fortran_vec (); | |
| 1948 | 1531 |
| 3887 | 1532 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
| 677 | 1533 |
| 5275 | 1534 for (octave_idx_type j = 0; j < nsamples; j++) |
| 677 | 1535 { |
| 4153 | 1536 OCTAVE_QUIT; |
| 1537 | |
| 5275 | 1538 for (octave_idx_type i = 0; i < npts; i++) |
| 1948 | 1539 prow[i] = tmp_data[i*nr + j]; |
| 1540 | |
| 3887 | 1541 F77_FUNC (cfftb, CFFTB) (npts, prow, pwsave); |
| 677 | 1542 |
| 5275 | 1543 for (octave_idx_type i = 0; i < npts; i++) |
| 3572 | 1544 tmp_data[i*nr + j] = prow[i] / static_cast<double> (npts); |
| 677 | 1545 } |
| 1546 | |
| 1948 | 1547 return retval; |
| 677 | 1548 } |
| 1549 | |
| 3827 | 1550 #endif |
| 1551 | |
| 458 | 1552 ComplexDET |
| 1553 ComplexMatrix::determinant (void) const | |
| 1554 { | |
| 5275 | 1555 octave_idx_type info; |
| 458 | 1556 double rcond; |
| 4329 | 1557 return determinant (info, rcond, 0); |
| 458 | 1558 } |
| 1559 | |
| 1560 ComplexDET | |
| 5275 | 1561 ComplexMatrix::determinant (octave_idx_type& info) const |
| 458 | 1562 { |
| 1563 double rcond; | |
| 4329 | 1564 return determinant (info, rcond, 0); |
| 458 | 1565 } |
| 1566 | |
| 1567 ComplexDET | |
| 5275 | 1568 ComplexMatrix::determinant (octave_idx_type& info, double& rcond, int calc_cond) const |
| 458 | 1569 { |
| 1570 ComplexDET retval; | |
| 1571 | |
| 5275 | 1572 octave_idx_type nr = rows (); |
| 1573 octave_idx_type nc = cols (); | |
| 458 | 1574 |
| 1575 if (nr == 0 || nc == 0) | |
| 1576 { | |
| 5634 | 1577 retval = ComplexDET (1.0, 0); |
| 458 | 1578 } |
| 1579 else | |
| 1580 { | |
| 5275 | 1581 Array<octave_idx_type> ipvt (nr); |
| 1582 octave_idx_type *pipvt = ipvt.fortran_vec (); | |
| 1948 | 1583 |
| 1584 ComplexMatrix atmp = *this; | |
| 1585 Complex *tmp_data = atmp.fortran_vec (); | |
| 1586 | |
| 4329 | 1587 info = 0; |
| 1588 | |
| 4330 | 1589 // Calculate the norm of the matrix, for later use. |
| 4329 | 1590 double anorm = 0; |
| 1591 if (calc_cond) | |
| 5275 | 1592 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
| 4329 | 1593 |
| 1594 F77_XFCN (zgetrf, ZGETRF, (nr, nc, tmp_data, nr, pipvt, info)); | |
| 1948 | 1595 |
|
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|
1596 // Throw-away extra info LAPACK gives so as to not change output. |
|
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1597 rcond = 0.0; |
|
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1598 if (info != 0) |
|
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|
1599 { |
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1600 info = -1; |
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1601 retval = ComplexDET (); |
|
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1602 } |
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1603 else |
| 458 | 1604 { |
|
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1605 if (calc_cond) |
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1606 { |
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1607 // Now calc the condition number for non-singular matrix. |
|
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1608 char job = '1'; |
|
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1609 Array<Complex> z (2*nr); |
|
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1610 Complex *pz = z.fortran_vec (); |
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1611 Array<double> rz (2*nr); |
|
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1612 double *prz = rz.fortran_vec (); |
|
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|
1613 |
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|
1614 F77_XFCN (zgecon, ZGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
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1615 nc, tmp_data, nr, anorm, |
|
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1616 rcond, pz, prz, info |
|
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|
1617 F77_CHAR_ARG_LEN (1))); |
|
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|
1618 } |
|
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|
1619 |
| 4509 | 1620 if (info != 0) |
| 1948 | 1621 { |
| 1622 info = -1; | |
| 1623 retval = ComplexDET (); | |
| 4329 | 1624 } |
| 1625 else | |
| 1948 | 1626 { |
|
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|
1627 Complex c = 1.0; |
|
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1628 int e = 0; |
|
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|
1629 |
|
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|
1630 for (octave_idx_type i = 0; i < nc; i++) |
| 4329 | 1631 { |
|
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1632 if (ipvt(i) != (i+1)) |
|
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1633 c = -c; |
|
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|
1634 |
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|
1635 c *= atmp(i,i); |
|
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|
1636 |
|
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|
1637 if (c == 0.0) |
|
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|
1638 break; |
|
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|
1639 |
|
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|
1640 while (std::abs(c) < 0.5) |
| 4329 | 1641 { |
|
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|
1642 c *= 2.0; |
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|
1643 e--; |
| 4329 | 1644 } |
| 5634 | 1645 |
|
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|
1646 while (std::abs(c) >= 2.0) |
|
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|
1647 { |
|
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1648 c /= 2.0; |
|
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1649 e++; |
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|
1650 } |
| 4329 | 1651 } |
|
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|
1652 |
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|
1653 retval = ComplexDET (c, e); |
| 1948 | 1654 } |
| 458 | 1655 } |
| 1656 } | |
| 4329 | 1657 |
| 458 | 1658 return retval; |
| 1659 } | |
| 1660 | |
| 1661 ComplexMatrix | |
| 5785 | 1662 ComplexMatrix::utsolve (MatrixType &mattype, const ComplexMatrix& b, |
| 1663 octave_idx_type& info, double& rcond, | |
| 1664 solve_singularity_handler sing_handler, | |
| 1665 bool calc_cond) const | |
| 1666 { | |
| 1667 ComplexMatrix retval; | |
| 1668 | |
| 1669 octave_idx_type nr = rows (); | |
| 1670 octave_idx_type nc = cols (); | |
| 1671 | |
| 6924 | 1672 if (nr != b.rows ()) |
| 5785 | 1673 (*current_liboctave_error_handler) |
| 1674 ("matrix dimension mismatch solution of linear equations"); | |
| 6924 | 1675 else if (nr == 0 || nc == 0 || b.cols () == 0) |
| 1676 retval = ComplexMatrix (nc, b.cols (), Complex (0.0, 0.0)); | |
| 5785 | 1677 else |
| 1678 { | |
| 1679 volatile int typ = mattype.type (); | |
| 1680 | |
| 1681 if (typ == MatrixType::Permuted_Upper || | |
| 1682 typ == MatrixType::Upper) | |
| 1683 { | |
| 1684 octave_idx_type b_nc = b.cols (); | |
| 1685 rcond = 1.; | |
| 1686 info = 0; | |
| 1687 | |
| 1688 if (typ == MatrixType::Permuted_Upper) | |
| 1689 { | |
| 1690 (*current_liboctave_error_handler) | |
| 6390 | 1691 ("permuted triangular matrix not implemented"); |
| 5785 | 1692 } |
| 1693 else | |
| 1694 { | |
| 1695 const Complex *tmp_data = fortran_vec (); | |
| 1696 | |
| 1697 if (calc_cond) | |
| 1698 { | |
| 1699 char norm = '1'; | |
| 1700 char uplo = 'U'; | |
| 1701 char dia = 'N'; | |
| 1702 | |
| 1703 Array<Complex> z (2 * nc); | |
| 1704 Complex *pz = z.fortran_vec (); | |
| 1705 Array<double> rz (nc); | |
| 1706 double *prz = rz.fortran_vec (); | |
| 1707 | |
| 1708 F77_XFCN (ztrcon, ZTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1709 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1710 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1711 nr, tmp_data, nr, rcond, | |
| 1712 pz, prz, info | |
| 1713 F77_CHAR_ARG_LEN (1) | |
| 1714 F77_CHAR_ARG_LEN (1) | |
| 1715 F77_CHAR_ARG_LEN (1))); | |
| 1716 | |
| 1717 if (info != 0) | |
| 1718 info = -2; | |
| 1719 | |
| 1720 volatile double rcond_plus_one = rcond + 1.0; | |
| 1721 | |
| 1722 if (rcond_plus_one == 1.0 || xisnan (rcond)) | |
| 1723 { | |
| 1724 info = -2; | |
| 1725 | |
| 1726 if (sing_handler) | |
| 1727 sing_handler (rcond); | |
| 1728 else | |
| 1729 (*current_liboctave_error_handler) | |
| 1730 ("matrix singular to machine precision, rcond = %g", | |
| 1731 rcond); | |
| 1732 } | |
| 1733 } | |
| 1734 | |
| 1735 if (info == 0) | |
| 1736 { | |
| 1737 retval = b; | |
| 1738 Complex *result = retval.fortran_vec (); | |
| 1739 | |
| 1740 char uplo = 'U'; | |
| 1741 char trans = 'N'; | |
| 1742 char dia = 'N'; | |
| 1743 | |
| 1744 F77_XFCN (ztrtrs, ZTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1745 F77_CONST_CHAR_ARG2 (&trans, 1), | |
| 1746 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1747 nr, b_nc, tmp_data, nr, | |
| 1748 result, nr, info | |
| 1749 F77_CHAR_ARG_LEN (1) | |
| 1750 F77_CHAR_ARG_LEN (1) | |
| 1751 F77_CHAR_ARG_LEN (1))); | |
| 1752 } | |
| 1753 } | |
| 1754 } | |
| 1755 else | |
| 1756 (*current_liboctave_error_handler) ("incorrect matrix type"); | |
| 1757 } | |
| 1758 | |
| 1759 return retval; | |
| 1760 } | |
| 1761 | |
| 1762 ComplexMatrix | |
| 1763 ComplexMatrix::ltsolve (MatrixType &mattype, const ComplexMatrix& b, | |
| 1764 octave_idx_type& info, double& rcond, | |
| 1765 solve_singularity_handler sing_handler, | |
| 1766 bool calc_cond) const | |
| 1767 { | |
| 1768 ComplexMatrix retval; | |
| 1769 | |
| 1770 octave_idx_type nr = rows (); | |
| 1771 octave_idx_type nc = cols (); | |
| 1772 | |
| 6924 | 1773 if (nr != b.rows ()) |
| 5785 | 1774 (*current_liboctave_error_handler) |
| 1775 ("matrix dimension mismatch solution of linear equations"); | |
| 6924 | 1776 else if (nr == 0 || nc == 0 || b.cols () == 0) |
| 1777 retval = ComplexMatrix (nc, b.cols (), Complex (0.0, 0.0)); | |
| 5785 | 1778 else |
| 1779 { | |
| 1780 volatile int typ = mattype.type (); | |
| 1781 | |
| 1782 if (typ == MatrixType::Permuted_Lower || | |
| 1783 typ == MatrixType::Lower) | |
| 1784 { | |
| 1785 octave_idx_type b_nc = b.cols (); | |
| 1786 rcond = 1.; | |
| 1787 info = 0; | |
| 1788 | |
| 1789 if (typ == MatrixType::Permuted_Lower) | |
| 1790 { | |
| 1791 (*current_liboctave_error_handler) | |
| 6390 | 1792 ("permuted triangular matrix not implemented"); |
| 5785 | 1793 } |
| 1794 else | |
| 1795 { | |
| 1796 const Complex *tmp_data = fortran_vec (); | |
| 1797 | |
| 1798 if (calc_cond) | |
| 1799 { | |
| 1800 char norm = '1'; | |
| 1801 char uplo = 'L'; | |
| 1802 char dia = 'N'; | |
| 1803 | |
| 1804 Array<Complex> z (2 * nc); | |
| 1805 Complex *pz = z.fortran_vec (); | |
| 1806 Array<double> rz (nc); | |
| 1807 double *prz = rz.fortran_vec (); | |
| 1808 | |
| 1809 F77_XFCN (ztrcon, ZTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1810 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1811 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1812 nr, tmp_data, nr, rcond, | |
| 1813 pz, prz, info | |
| 1814 F77_CHAR_ARG_LEN (1) | |
| 1815 F77_CHAR_ARG_LEN (1) | |
| 1816 F77_CHAR_ARG_LEN (1))); | |
| 1817 | |
| 1818 if (info != 0) | |
| 1819 info = -2; | |
| 1820 | |
| 1821 volatile double rcond_plus_one = rcond + 1.0; | |
| 1822 | |
| 1823 if (rcond_plus_one == 1.0 || xisnan (rcond)) | |
| 1824 { | |
| 1825 info = -2; | |
| 1826 | |
| 1827 if (sing_handler) | |
| 1828 sing_handler (rcond); | |
| 1829 else | |
| 1830 (*current_liboctave_error_handler) | |
| 1831 ("matrix singular to machine precision, rcond = %g", | |
| 1832 rcond); | |
| 1833 } | |
| 1834 } | |
| 1835 | |
| 1836 if (info == 0) | |
| 1837 { | |
| 1838 retval = b; | |
| 1839 Complex *result = retval.fortran_vec (); | |
| 1840 | |
| 1841 char uplo = 'L'; | |
| 1842 char trans = 'N'; | |
| 1843 char dia = 'N'; | |
| 1844 | |
| 1845 F77_XFCN (ztrtrs, ZTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1846 F77_CONST_CHAR_ARG2 (&trans, 1), | |
| 1847 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1848 nr, b_nc, tmp_data, nr, | |
| 1849 result, nr, info | |
| 1850 F77_CHAR_ARG_LEN (1) | |
| 1851 F77_CHAR_ARG_LEN (1) | |
| 1852 F77_CHAR_ARG_LEN (1))); | |
| 1853 } | |
| 1854 } | |
| 1855 } | |
| 1856 else | |
| 1857 (*current_liboctave_error_handler) ("incorrect matrix type"); | |
| 1858 } | |
| 1859 | |
| 1860 return retval; | |
| 1861 } | |
| 1862 | |
| 1863 ComplexMatrix | |
| 1864 ComplexMatrix::fsolve (MatrixType &mattype, const ComplexMatrix& b, | |
| 1865 octave_idx_type& info, double& rcond, | |
| 1866 solve_singularity_handler sing_handler, | |
| 1867 bool calc_cond) const | |
| 1868 { | |
| 1869 ComplexMatrix retval; | |
| 1870 | |
| 1871 octave_idx_type nr = rows (); | |
| 1872 octave_idx_type nc = cols (); | |
| 1873 | |
| 6924 | 1874 |
| 1875 if (nr != nc || nr != b.rows ()) | |
| 5785 | 1876 (*current_liboctave_error_handler) |
| 6924 | 1877 ("matrix dimension mismatch solution of linear equations"); |
| 1878 else if (nr == 0 || b.cols () == 0) | |
| 1879 retval = ComplexMatrix (nc, b.cols (), Complex (0.0, 0.0)); | |
| 5785 | 1880 else |
| 1881 { | |
| 1882 volatile int typ = mattype.type (); | |
| 1883 | |
| 1884 // Calculate the norm of the matrix, for later use. | |
| 1885 double anorm = -1.; | |
| 1886 | |
| 1887 if (typ == MatrixType::Hermitian) | |
| 1888 { | |
| 1889 info = 0; | |
| 1890 char job = 'L'; | |
| 1891 ComplexMatrix atmp = *this; | |
| 1892 Complex *tmp_data = atmp.fortran_vec (); | |
| 1893 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); | |
| 1894 | |
| 1895 F77_XFCN (zpotrf, ZPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, | |
| 1896 tmp_data, nr, info | |
| 1897 F77_CHAR_ARG_LEN (1))); | |
| 1898 | |
|
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|
1899 // Throw-away extra info LAPACK gives so as to not change output. |
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1900 rcond = 0.0; |
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|
1901 if (info != 0) |
|
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|
1902 { |
|
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|
1903 info = -2; |
|
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|
1904 |
|
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|
1905 mattype.mark_as_unsymmetric (); |
|
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|
1906 typ = MatrixType::Full; |
|
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|
1907 } |
|
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|
1908 else |
| 5785 | 1909 { |
|
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|
1910 if (calc_cond) |
| 5785 | 1911 { |
|
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|
1912 Array<Complex> z (2 * nc); |
|
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1913 Complex *pz = z.fortran_vec (); |
|
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1914 Array<double> rz (nc); |
|
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|
1915 double *prz = rz.fortran_vec (); |
|
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|
1916 |
|
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|
1917 F77_XFCN (zpocon, ZPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
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1918 nr, tmp_data, nr, anorm, |
|
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|
1919 rcond, pz, prz, info |
|
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|
1920 F77_CHAR_ARG_LEN (1))); |
|
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|
1921 |
|
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|
1922 if (info != 0) |
|
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|
1923 info = -2; |
|
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|
1924 |
|
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|
1925 volatile double rcond_plus_one = rcond + 1.0; |
|
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|
1926 |
|
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|
1927 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
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|
1928 { |
|
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|
1929 info = -2; |
|
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|
1930 |
|
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|
1931 if (sing_handler) |
|
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1932 sing_handler (rcond); |
|
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|
1933 else |
|
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changeset
|
1934 (*current_liboctave_error_handler) |
|
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|
1935 ("matrix singular to machine precision, rcond = %g", |
|
29980c6b8604
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|
1936 rcond); |
|
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|
1937 } |
|
29980c6b8604
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changeset
|
1938 } |
|
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changeset
|
1939 |
|
29980c6b8604
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changeset
|
1940 if (info == 0) |
|
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changeset
|
1941 { |
|
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changeset
|
1942 retval = b; |
|
29980c6b8604
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|
1943 Complex *result = retval.fortran_vec (); |
|
29980c6b8604
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|
1944 |
|
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|
1945 octave_idx_type b_nc = b.cols (); |
|
29980c6b8604
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changeset
|
1946 |
|
29980c6b8604
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changeset
|
1947 F77_XFCN (zpotrs, ZPOTRS, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
29980c6b8604
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|
1948 nr, b_nc, tmp_data, nr, |
|
29980c6b8604
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diff
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|
1949 result, b.rows(), info |
|
29980c6b8604
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changeset
|
1950 F77_CHAR_ARG_LEN (1))); |
|
29980c6b8604
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changeset
|
1951 } |
|
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diff
changeset
|
1952 else |
|
29980c6b8604
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diff
changeset
|
1953 { |
| 5785 | 1954 mattype.mark_as_unsymmetric (); |
| 1955 typ = MatrixType::Full; | |
| 1956 } | |
| 1957 } | |
| 1958 } | |
| 1959 | |
| 1960 if (typ == MatrixType::Full) | |
| 1961 { | |
| 1962 info = 0; | |
| 1963 | |
| 1964 Array<octave_idx_type> ipvt (nr); | |
| 1965 octave_idx_type *pipvt = ipvt.fortran_vec (); | |
| 1966 | |
| 1967 ComplexMatrix atmp = *this; | |
| 1968 Complex *tmp_data = atmp.fortran_vec (); | |
| 1969 | |
| 1970 Array<Complex> z (2 * nc); | |
| 1971 Complex *pz = z.fortran_vec (); | |
| 1972 Array<double> rz (2 * nc); | |
| 1973 double *prz = rz.fortran_vec (); | |
| 1974 | |
| 1975 // Calculate the norm of the matrix, for later use. | |
| 1976 if (anorm < 0.) | |
| 1977 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); | |
| 1978 | |
| 1979 F77_XFCN (zgetrf, ZGETRF, (nr, nr, tmp_data, nr, pipvt, info)); | |
| 1980 | |
|
7482
29980c6b8604
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changeset
|
1981 // Throw-away extra info LAPACK gives so as to not change output. |
|
29980c6b8604
don't check f77_exception_encountered
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parents:
7478
diff
changeset
|
1982 rcond = 0.0; |
|
29980c6b8604
don't check f77_exception_encountered
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parents:
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diff
changeset
|
1983 if (info != 0) |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
1984 { |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
1985 info = -2; |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
1986 |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
1987 if (sing_handler) |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
1988 sing_handler (rcond); |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
1989 else |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
1990 (*current_liboctave_error_handler) |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
1991 ("matrix singular to machine precision"); |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
1992 |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
1993 mattype.mark_as_rectangular (); |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
1994 } |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
1995 else |
| 5785 | 1996 { |
|
7482
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
1997 if (calc_cond) |
| 5785 | 1998 { |
|
7482
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
1999 // Now calculate the condition number for |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
2000 // non-singular matrix. |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
2001 char job = '1'; |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
2002 F77_XFCN (zgecon, ZGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
2003 nc, tmp_data, nr, anorm, |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
2004 rcond, pz, prz, info |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
2005 F77_CHAR_ARG_LEN (1))); |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
2006 |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
2007 if (info != 0) |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
2008 info = -2; |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
2009 |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
2010 volatile double rcond_plus_one = rcond + 1.0; |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
2011 |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
2012 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
| 5785 | 2013 { |
|
7482
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
2014 info = -2; |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
2015 |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
2016 if (sing_handler) |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
2017 sing_handler (rcond); |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
2018 else |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
2019 (*current_liboctave_error_handler) |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
2020 ("matrix singular to machine precision, rcond = %g", |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
2021 rcond); |
| 5785 | 2022 } |
| 2023 } | |
|
7482
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
2024 |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
2025 if (info == 0) |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
2026 { |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
2027 retval = b; |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
2028 Complex *result = retval.fortran_vec (); |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
2029 |
|
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|
2030 octave_idx_type b_nc = b.cols (); |
|
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7478
diff
changeset
|
2031 |
|
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changeset
|
2032 char job = 'N'; |
|
29980c6b8604
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7478
diff
changeset
|
2033 F77_XFCN (zgetrs, ZGETRS, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
29980c6b8604
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changeset
|
2034 nr, b_nc, tmp_data, nr, |
|
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parents:
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diff
changeset
|
2035 pipvt, result, b.rows(), info |
|
29980c6b8604
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diff
changeset
|
2036 F77_CHAR_ARG_LEN (1))); |
|
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|
2037 } |
|
29980c6b8604
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|
2038 else |
|
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changeset
|
2039 mattype.mark_as_rectangular (); |
| 5785 | 2040 } |
| 2041 } | |
| 2042 } | |
| 2043 | |
| 2044 return retval; | |
| 2045 } | |
| 2046 | |
| 2047 ComplexMatrix | |
| 2048 ComplexMatrix::solve (MatrixType &typ, const Matrix& b) const | |
| 2049 { | |
| 2050 octave_idx_type info; | |
| 2051 double rcond; | |
| 2052 return solve (typ, b, info, rcond, 0); | |
| 2053 } | |
| 2054 | |
| 2055 ComplexMatrix | |
| 2056 ComplexMatrix::solve (MatrixType &typ, const Matrix& b, | |
| 2057 octave_idx_type& info) const | |
| 2058 { | |
| 2059 double rcond; | |
| 2060 return solve (typ, b, info, rcond, 0); | |
| 2061 } | |
| 2062 | |
| 2063 ComplexMatrix | |
| 2064 ComplexMatrix::solve (MatrixType &typ, const Matrix& b, octave_idx_type& info, | |
| 2065 double& rcond) const | |
| 2066 { | |
| 2067 return solve (typ, b, info, rcond, 0); | |
| 2068 } | |
| 2069 | |
| 2070 ComplexMatrix | |
| 2071 ComplexMatrix::solve (MatrixType &typ, const Matrix& b, octave_idx_type& info, | |
| 2072 double& rcond, solve_singularity_handler sing_handler, | |
| 2073 bool singular_fallback) const | |
| 2074 { | |
| 2075 ComplexMatrix tmp (b); | |
| 2076 return solve (typ, tmp, info, rcond, sing_handler, singular_fallback); | |
| 2077 } | |
| 2078 | |
| 2079 ComplexMatrix | |
| 2080 ComplexMatrix::solve (MatrixType &typ, const ComplexMatrix& b) const | |
| 2081 { | |
| 2082 octave_idx_type info; | |
| 2083 double rcond; | |
| 2084 return solve (typ, b, info, rcond, 0); | |
| 2085 } | |
| 2086 | |
| 2087 ComplexMatrix | |
| 2088 ComplexMatrix::solve (MatrixType &typ, const ComplexMatrix& b, | |
| 2089 octave_idx_type& info) const | |
| 2090 { | |
| 2091 double rcond; | |
| 2092 return solve (typ, b, info, rcond, 0); | |
| 2093 } | |
| 2094 | |
| 2095 ComplexMatrix | |
| 2096 ComplexMatrix::solve (MatrixType &typ, const ComplexMatrix& b, | |
| 2097 octave_idx_type& info, double& rcond) const | |
| 2098 { | |
| 2099 return solve (typ, b, info, rcond, 0); | |
| 2100 } | |
| 2101 | |
| 2102 ComplexMatrix | |
| 2103 ComplexMatrix::solve (MatrixType &mattype, const ComplexMatrix& b, | |
| 2104 octave_idx_type& info, double& rcond, | |
| 2105 solve_singularity_handler sing_handler, | |
| 2106 bool singular_fallback) const | |
| 2107 { | |
| 2108 ComplexMatrix retval; | |
| 2109 int typ = mattype.type (); | |
| 2110 | |
| 2111 if (typ == MatrixType::Unknown) | |
| 2112 typ = mattype.type (*this); | |
| 2113 | |
| 2114 // Only calculate the condition number for LU/Cholesky | |
| 2115 if (typ == MatrixType::Upper || typ == MatrixType::Permuted_Upper) | |
| 2116 retval = utsolve (mattype, b, info, rcond, sing_handler, false); | |
| 2117 else if (typ == MatrixType::Lower || typ == MatrixType::Permuted_Lower) | |
| 2118 retval = ltsolve (mattype, b, info, rcond, sing_handler, false); | |
| 2119 else if (typ == MatrixType::Full || typ == MatrixType::Hermitian) | |
| 2120 retval = fsolve (mattype, b, info, rcond, sing_handler, true); | |
| 2121 else if (typ != MatrixType::Rectangular) | |
| 2122 { | |
| 2123 (*current_liboctave_error_handler) ("unknown matrix type"); | |
| 2124 return ComplexMatrix (); | |
| 2125 } | |
| 2126 | |
| 2127 // Rectangular or one of the above solvers flags a singular matrix | |
| 2128 if (singular_fallback && mattype.type () == MatrixType::Rectangular) | |
| 2129 { | |
| 2130 octave_idx_type rank; | |
| 7076 | 2131 retval = lssolve (b, info, rank, rcond); |
| 5785 | 2132 } |
| 2133 | |
| 2134 return retval; | |
| 2135 } | |
| 2136 | |
| 2137 ComplexColumnVector | |
| 2138 ComplexMatrix::solve (MatrixType &typ, const ColumnVector& b) const | |
| 2139 { | |
| 2140 octave_idx_type info; | |
| 2141 double rcond; | |
| 2142 return solve (typ, ComplexColumnVector (b), info, rcond, 0); | |
| 2143 } | |
| 2144 | |
| 2145 ComplexColumnVector | |
| 2146 ComplexMatrix::solve (MatrixType &typ, const ColumnVector& b, | |
| 2147 octave_idx_type& info) const | |
| 2148 { | |
| 2149 double rcond; | |
| 2150 return solve (typ, ComplexColumnVector (b), info, rcond, 0); | |
| 2151 } | |
| 2152 | |
| 2153 ComplexColumnVector | |
| 2154 ComplexMatrix::solve (MatrixType &typ, const ColumnVector& b, | |
| 2155 octave_idx_type& info, double& rcond) const | |
| 2156 { | |
| 2157 return solve (typ, ComplexColumnVector (b), info, rcond, 0); | |
| 2158 } | |
| 2159 | |
| 2160 ComplexColumnVector | |
| 2161 ComplexMatrix::solve (MatrixType &typ, const ColumnVector& b, | |
| 2162 octave_idx_type& info, double& rcond, | |
| 2163 solve_singularity_handler sing_handler) const | |
| 2164 { | |
| 2165 return solve (typ, ComplexColumnVector (b), info, rcond, sing_handler); | |
| 2166 } | |
| 2167 | |
| 2168 ComplexColumnVector | |
| 2169 ComplexMatrix::solve (MatrixType &typ, const ComplexColumnVector& b) const | |
| 2170 { | |
| 2171 octave_idx_type info; | |
| 2172 double rcond; | |
| 2173 return solve (typ, b, info, rcond, 0); | |
| 2174 } | |
| 2175 | |
| 2176 ComplexColumnVector | |
| 2177 ComplexMatrix::solve (MatrixType &typ, const ComplexColumnVector& b, | |
| 2178 octave_idx_type& info) const | |
| 2179 { | |
| 2180 double rcond; | |
| 2181 return solve (typ, b, info, rcond, 0); | |
| 2182 } | |
| 2183 | |
| 2184 ComplexColumnVector | |
| 2185 ComplexMatrix::solve (MatrixType &typ, const ComplexColumnVector& b, | |
| 2186 octave_idx_type& info, double& rcond) const | |
| 2187 { | |
| 2188 return solve (typ, b, info, rcond, 0); | |
| 2189 } | |
| 2190 | |
| 2191 ComplexColumnVector | |
| 2192 ComplexMatrix::solve (MatrixType &typ, const ComplexColumnVector& b, | |
| 2193 octave_idx_type& info, double& rcond, | |
| 2194 solve_singularity_handler sing_handler) const | |
| 2195 { | |
| 2196 | |
| 2197 ComplexMatrix tmp (b); | |
| 2198 return solve (typ, tmp, info, rcond, sing_handler).column(static_cast<octave_idx_type> (0)); | |
| 2199 } | |
| 2200 | |
| 2201 ComplexMatrix | |
| 458 | 2202 ComplexMatrix::solve (const Matrix& b) const |
| 2203 { | |
| 5275 | 2204 octave_idx_type info; |
| 458 | 2205 double rcond; |
| 3480 | 2206 return solve (b, info, rcond, 0); |
| 458 | 2207 } |
| 2208 | |
| 2209 ComplexMatrix | |
| 5275 | 2210 ComplexMatrix::solve (const Matrix& b, octave_idx_type& info) const |
| 458 | 2211 { |
| 2212 double rcond; | |
| 3480 | 2213 return solve (b, info, rcond, 0); |
| 458 | 2214 } |
| 2215 | |
| 2216 ComplexMatrix | |
| 5275 | 2217 ComplexMatrix::solve (const Matrix& b, octave_idx_type& info, double& rcond) const |
| 458 | 2218 { |
| 3480 | 2219 return solve (b, info, rcond, 0); |
| 2220 } | |
| 2221 | |
| 2222 ComplexMatrix | |
| 5275 | 2223 ComplexMatrix::solve (const Matrix& b, octave_idx_type& info, double& rcond, |
| 3480 | 2224 solve_singularity_handler sing_handler) const |
| 2225 { | |
| 458 | 2226 ComplexMatrix tmp (b); |
| 3480 | 2227 return solve (tmp, info, rcond, sing_handler); |
| 458 | 2228 } |
| 2229 | |
| 2230 ComplexMatrix | |
| 2231 ComplexMatrix::solve (const ComplexMatrix& b) const | |
| 2232 { | |
| 5275 | 2233 octave_idx_type info; |
| 458 | 2234 double rcond; |
| 3480 | 2235 return solve (b, info, rcond, 0); |
| 458 | 2236 } |
| 2237 | |
| 2238 ComplexMatrix | |
| 5275 | 2239 ComplexMatrix::solve (const ComplexMatrix& b, octave_idx_type& info) const |
| 458 | 2240 { |
| 2241 double rcond; | |
| 3480 | 2242 return solve (b, info, rcond, 0); |
| 458 | 2243 } |
| 3480 | 2244 |
| 458 | 2245 ComplexMatrix |
| 5275 | 2246 ComplexMatrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcond) const |
| 458 | 2247 { |
| 3480 | 2248 return solve (b, info, rcond, 0); |
| 2249 } | |
| 2250 | |
| 2251 ComplexMatrix | |
| 5275 | 2252 ComplexMatrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcond, |
| 3480 | 2253 solve_singularity_handler sing_handler) const |
| 2254 { | |
| 5785 | 2255 MatrixType mattype (*this); |
| 6060 | 2256 return solve (mattype, b, info, rcond, sing_handler); |
| 458 | 2257 } |
| 2258 | |
| 2259 ComplexColumnVector | |
| 3585 | 2260 ComplexMatrix::solve (const ColumnVector& b) const |
| 2261 { | |
| 5275 | 2262 octave_idx_type info; |
| 3585 | 2263 double rcond; |
| 2264 return solve (ComplexColumnVector (b), info, rcond, 0); | |
| 2265 } | |
| 2266 | |
| 2267 ComplexColumnVector | |
| 5275 | 2268 ComplexMatrix::solve (const ColumnVector& b, octave_idx_type& info) const |
| 3585 | 2269 { |
| 2270 double rcond; | |
| 2271 return solve (ComplexColumnVector (b), info, rcond, 0); | |
| 2272 } | |
| 2273 | |
| 2274 ComplexColumnVector | |
| 5785 | 2275 ComplexMatrix::solve (const ColumnVector& b, octave_idx_type& info, |
| 2276 double& rcond) const | |
| 3585 | 2277 { |
| 2278 return solve (ComplexColumnVector (b), info, rcond, 0); | |
| 2279 } | |
| 2280 | |
| 2281 ComplexColumnVector | |
| 5785 | 2282 ComplexMatrix::solve (const ColumnVector& b, octave_idx_type& info, |
| 2283 double& rcond, | |
| 3585 | 2284 solve_singularity_handler sing_handler) const |
| 2285 { | |
| 2286 return solve (ComplexColumnVector (b), info, rcond, sing_handler); | |
| 2287 } | |
| 2288 | |
| 2289 ComplexColumnVector | |
| 458 | 2290 ComplexMatrix::solve (const ComplexColumnVector& b) const |
| 2291 { | |
| 5275 | 2292 octave_idx_type info; |
| 458 | 2293 double rcond; |
| 3480 | 2294 return solve (b, info, rcond, 0); |
| 458 | 2295 } |
| 2296 | |
| 2297 ComplexColumnVector | |
| 5275 | 2298 ComplexMatrix::solve (const ComplexColumnVector& b, octave_idx_type& info) const |
| 458 | 2299 { |
| 2300 double rcond; | |
| 3480 | 2301 return solve (b, info, rcond, 0); |
| 458 | 2302 } |
| 2303 | |
| 2304 ComplexColumnVector | |
| 5275 | 2305 ComplexMatrix::solve (const ComplexColumnVector& b, octave_idx_type& info, |
| 532 | 2306 double& rcond) const |
| 458 | 2307 { |
| 3480 | 2308 return solve (b, info, rcond, 0); |
| 2309 } | |
| 2310 | |
| 2311 ComplexColumnVector | |
| 5275 | 2312 ComplexMatrix::solve (const ComplexColumnVector& b, octave_idx_type& info, |
| 3480 | 2313 double& rcond, |
| 2314 solve_singularity_handler sing_handler) const | |
| 2315 { | |
| 5785 | 2316 MatrixType mattype (*this); |
| 2317 return solve (mattype, b, info, rcond, sing_handler); | |
| 458 | 2318 } |
| 2319 | |
| 2320 ComplexMatrix | |
| 3585 | 2321 ComplexMatrix::lssolve (const Matrix& b) const |
| 2322 { | |
| 5275 | 2323 octave_idx_type info; |
| 2324 octave_idx_type rank; | |
| 7076 | 2325 double rcond; |
| 2326 return lssolve (ComplexMatrix (b), info, rank, rcond); | |
| 3585 | 2327 } |
| 2328 | |
| 2329 ComplexMatrix | |
| 5275 | 2330 ComplexMatrix::lssolve (const Matrix& b, octave_idx_type& info) const |
| 3585 | 2331 { |
| 5275 | 2332 octave_idx_type rank; |
| 7076 | 2333 double rcond; |
| 2334 return lssolve (ComplexMatrix (b), info, rank, rcond); | |
| 3585 | 2335 } |
| 2336 | |
| 2337 ComplexMatrix | |
| 7076 | 2338 ComplexMatrix::lssolve (const Matrix& b, octave_idx_type& info, |
| 2339 octave_idx_type& rank) const | |
| 3585 | 2340 { |
| 7076 | 2341 double rcond; |
| 2342 return lssolve (ComplexMatrix (b), info, rank, rcond); | |
| 2343 } | |
| 2344 | |
| 2345 ComplexMatrix | |
| 2346 ComplexMatrix::lssolve (const Matrix& b, octave_idx_type& info, | |
| 2347 octave_idx_type& rank, double& rcond) const | |
| 2348 { | |
| 2349 return lssolve (ComplexMatrix (b), info, rank, rcond); | |
| 3585 | 2350 } |
| 2351 | |
| 2352 ComplexMatrix | |
| 458 | 2353 ComplexMatrix::lssolve (const ComplexMatrix& b) const |
| 2354 { | |
| 5275 | 2355 octave_idx_type info; |
| 2356 octave_idx_type rank; | |
| 7076 | 2357 double rcond; |
| 2358 return lssolve (b, info, rank, rcond); | |
| 458 | 2359 } |
| 2360 | |
| 2361 ComplexMatrix | |
| 5275 | 2362 ComplexMatrix::lssolve (const ComplexMatrix& b, octave_idx_type& info) const |
| 458 | 2363 { |
| 5275 | 2364 octave_idx_type rank; |
| 7076 | 2365 double rcond; |
| 2366 return lssolve (b, info, rank, rcond); | |
| 458 | 2367 } |
| 2368 | |
| 2369 ComplexMatrix | |
| 7076 | 2370 ComplexMatrix::lssolve (const ComplexMatrix& b, octave_idx_type& info, |
| 2371 octave_idx_type& rank) const | |
| 2372 { | |
| 2373 double rcond; | |
| 2374 return lssolve (b, info, rank, rcond); | |
| 2375 } | |
| 2376 | |
| 2377 ComplexMatrix | |
| 2378 ComplexMatrix::lssolve (const ComplexMatrix& b, octave_idx_type& info, | |
| 2379 octave_idx_type& rank, double& rcond) const | |
| 458 | 2380 { |
| 1948 | 2381 ComplexMatrix retval; |
| 2382 | |
| 5275 | 2383 octave_idx_type nrhs = b.cols (); |
| 2384 | |
| 2385 octave_idx_type m = rows (); | |
| 2386 octave_idx_type n = cols (); | |
| 458 | 2387 |
| 6924 | 2388 if (m != b.rows ()) |
| 1948 | 2389 (*current_liboctave_error_handler) |
| 2390 ("matrix dimension mismatch solution of linear equations"); | |
| 6924 | 2391 else if (m== 0 || n == 0 || b.cols () == 0) |
| 2392 retval = ComplexMatrix (n, b.cols (), Complex (0.0, 0.0)); | |
| 1948 | 2393 else |
| 458 | 2394 { |
| 7072 | 2395 volatile octave_idx_type minmn = (m < n ? m : n); |
| 2396 octave_idx_type maxmn = m > n ? m : n; | |
| 7076 | 2397 rcond = -1.0; |
| 7072 | 2398 |
| 2399 if (m != n) | |
| 2400 { | |
| 2401 retval = ComplexMatrix (maxmn, nrhs); | |
| 2402 | |
| 2403 for (octave_idx_type j = 0; j < nrhs; j++) | |
| 2404 for (octave_idx_type i = 0; i < m; i++) | |
| 2405 retval.elem (i, j) = b.elem (i, j); | |
| 2406 } | |
| 2407 else | |
| 2408 retval = b; | |
| 2409 | |
| 1948 | 2410 ComplexMatrix atmp = *this; |
| 2411 Complex *tmp_data = atmp.fortran_vec (); | |
| 2412 | |
| 7072 | 2413 Complex *pretval = retval.fortran_vec (); |
| 2414 Array<double> s (minmn); | |
| 7071 | 2415 double *ps = s.fortran_vec (); |
| 2563 | 2416 |
| 7072 | 2417 // Ask ZGELSD what the dimension of WORK should be. |
| 5275 | 2418 octave_idx_type lwork = -1; |
| 3752 | 2419 |
| 2420 Array<Complex> work (1); | |
| 7079 | 2421 |
| 7477 | 2422 octave_idx_type smlsiz; |
| 2423 F77_FUNC (xilaenv, XILAENV) (9, F77_CONST_CHAR_ARG2 ("ZGELSD", 6), | |
| 2424 F77_CONST_CHAR_ARG2 (" ", 1), | |
| 7478 | 2425 0, 0, 0, 0, smlsiz |
| 7477 | 2426 F77_CHAR_ARG_LEN (6) |
| 7478 | 2427 F77_CHAR_ARG_LEN (1)); |
| 7079 | 2428 |
|
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2429 octave_idx_type mnthr; |
|
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|
2430 F77_FUNC (xilaenv, XILAENV) (6, F77_CONST_CHAR_ARG2 ("ZGELSD", 6), |
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2431 F77_CONST_CHAR_ARG2 (" ", 1), |
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2432 m, n, nrhs, -1, mnthr |
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2433 F77_CHAR_ARG_LEN (6) |
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2434 F77_CHAR_ARG_LEN (1)); |
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|
2435 |
| 7079 | 2436 // We compute the size of rwork and iwork because ZGELSD in |
| 2437 // older versions of LAPACK does not return them on a query | |
| 2438 // call. | |
| 7124 | 2439 double dminmn = static_cast<double> (minmn); |
| 2440 double dsmlsizp1 = static_cast<double> (smlsiz+1); | |
| 7079 | 2441 #if defined (HAVE_LOG2) |
|
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2442 double tmp = log2 (dminmn / dsmlsizp1); |
| 7079 | 2443 #else |
|
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2444 double tmp = log (dminmn / dsmlsizp1) / log (2.0); |
| 7079 | 2445 #endif |
|
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|
2446 octave_idx_type nlvl = static_cast<octave_idx_type> (tmp) + 1; |
| 7079 | 2447 if (nlvl < 0) |
| 2448 nlvl = 0; | |
| 2449 | |
| 2450 octave_idx_type lrwork = minmn*(10 + 2*smlsiz + 8*nlvl) | |
| 2451 + 3*smlsiz*nrhs + (smlsiz+1)*(smlsiz+1); | |
| 2452 if (lrwork < 1) | |
| 2453 lrwork = 1; | |
| 2454 Array<double> rwork (lrwork); | |
| 2455 double *prwork = rwork.fortran_vec (); | |
| 2456 | |
| 2457 octave_idx_type liwork = 3 * minmn * nlvl + 11 * minmn; | |
| 2458 if (liwork < 1) | |
| 2459 liwork = 1; | |
| 2460 Array<octave_idx_type> iwork (liwork); | |
| 2461 octave_idx_type* piwork = iwork.fortran_vec (); | |
| 7072 | 2462 |
| 2463 F77_XFCN (zgelsd, ZGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, | |
| 2464 ps, rcond, rank, work.fortran_vec (), | |
| 7079 | 2465 lwork, prwork, piwork, info)); |
| 1948 | 2466 |
| 7476 | 2467 // The workspace query is broken in at least LAPACK 3.0.0 |
|
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2468 // through 3.1.1 when n >= mnthr. The obtuse formula below |
|
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2469 // should provide sufficient workspace for ZGELSD to operate |
| 7476 | 2470 // efficiently. |
|
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|
2471 if (n >= mnthr) |
| 7476 | 2472 { |
| 2473 octave_idx_type addend = m; | |
| 2474 | |
| 2475 if (2*m-4 > addend) | |
| 2476 addend = 2*m-4; | |
| 2477 | |
| 2478 if (nrhs > addend) | |
| 2479 addend = nrhs; | |
| 2480 | |
| 2481 if (n-3*m > addend) | |
| 2482 addend = n-3*m; | |
| 2483 | |
| 2484 const octave_idx_type lworkaround = 4*m + m*m + addend; | |
| 2485 | |
| 2486 if (std::real (work(0)) < lworkaround) | |
| 2487 work(0) = lworkaround; | |
| 2488 } | |
|
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2489 else if (m >= n) |
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|
2490 { |
|
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|
2491 octave_idx_type lworkaround = 2*m + m*nrhs; |
|
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|
2492 |
|
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|
2493 if (std::real (work(0)) < lworkaround) |
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|
2494 work(0) = lworkaround; |
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|
2495 } |
| 7476 | 2496 |
|
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2497 lwork = static_cast<octave_idx_type> (std::real (work(0))); |
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2498 work.resize (lwork); |
|
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|
2499 |
|
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2500 F77_XFCN (zgelsd, ZGELSD, (m, n, nrhs, tmp_data, m, pretval, |
|
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|
2501 maxmn, ps, rcond, rank, |
|
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|
2502 work.fortran_vec (), lwork, |
|
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2503 prwork, piwork, info)); |
|
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|
2504 |
|
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|
2505 if (rank < minmn) |
|
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|
2506 (*current_liboctave_warning_handler) |
|
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|
2507 ("zgelsd: rank deficient %dx%d matrix, rank = %d, tol = %e", |
|
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|
2508 m, n, rank, rcond); |
|
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|
2509 |
|
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|
2510 if (s.elem (0) == 0.0) |
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|
2511 rcond = 0.0; |
| 1948 | 2512 else |
|
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|
2513 rcond = s.elem (minmn - 1) / s.elem (0); |
|
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|
2514 |
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|
2515 retval.resize (n, nrhs); |
| 458 | 2516 } |
| 2517 | |
| 2518 return retval; | |
| 2519 } | |
| 2520 | |
| 2521 ComplexColumnVector | |
| 3585 | 2522 ComplexMatrix::lssolve (const ColumnVector& b) const |
| 2523 { | |
| 5275 | 2524 octave_idx_type info; |
| 2525 octave_idx_type rank; | |
| 7076 | 2526 double rcond; |
| 2527 return lssolve (ComplexColumnVector (b), info, rank, rcond); | |
| 3585 | 2528 } |
| 2529 | |
| 2530 ComplexColumnVector | |
| 5275 | 2531 ComplexMatrix::lssolve (const ColumnVector& b, octave_idx_type& info) const |
| 3585 | 2532 { |
| 5275 | 2533 octave_idx_type rank; |
| 7076 | 2534 double rcond; |
| 2535 return lssolve (ComplexColumnVector (b), info, rank, rcond); | |
| 3585 | 2536 } |
| 2537 | |
| 2538 ComplexColumnVector | |
| 7076 | 2539 ComplexMatrix::lssolve (const ColumnVector& b, octave_idx_type& info, |
| 2540 octave_idx_type& rank) const | |
| 3585 | 2541 { |
| 7076 | 2542 double rcond; |
| 2543 return lssolve (ComplexColumnVector (b), info, rank, rcond); | |
| 2544 } | |
| 2545 | |
| 2546 ComplexColumnVector | |
| 2547 ComplexMatrix::lssolve (const ColumnVector& b, octave_idx_type& info, | |
| 2548 octave_idx_type& rank, double& rcond) const | |
| 2549 { | |
| 2550 return lssolve (ComplexColumnVector (b), info, rank, rcond); | |
| 3585 | 2551 } |
| 2552 | |
| 2553 ComplexColumnVector | |
| 458 | 2554 ComplexMatrix::lssolve (const ComplexColumnVector& b) const |
| 2555 { | |
| 5275 | 2556 octave_idx_type info; |
| 2557 octave_idx_type rank; | |
| 7076 | 2558 double rcond; |
| 2559 return lssolve (b, info, rank, rcond); | |
| 458 | 2560 } |
| 2561 | |
| 2562 ComplexColumnVector | |
| 5275 | 2563 ComplexMatrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info) const |
| 458 | 2564 { |
| 5275 | 2565 octave_idx_type rank; |
| 7076 | 2566 double rcond; |
| 2567 return lssolve (b, info, rank, rcond); | |
| 458 | 2568 } |
| 2569 | |
| 2570 ComplexColumnVector | |
| 5275 | 2571 ComplexMatrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, |
| 2572 octave_idx_type& rank) const | |
| 458 | 2573 { |
| 7076 | 2574 double rcond; |
| 2575 return lssolve (b, info, rank, rcond); | |
| 2576 | |
| 2577 } | |
| 2578 | |
| 2579 ComplexColumnVector | |
| 2580 ComplexMatrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, | |
| 2581 octave_idx_type& rank, double& rcond) const | |
| 2582 { | |
| 1948 | 2583 ComplexColumnVector retval; |
| 2584 | |
| 5275 | 2585 octave_idx_type nrhs = 1; |
| 2586 | |
| 2587 octave_idx_type m = rows (); | |
| 2588 octave_idx_type n = cols (); | |
| 458 | 2589 |
| 6924 | 2590 if (m != b.length ()) |
| 1948 | 2591 (*current_liboctave_error_handler) |
| 6924 | 2592 ("matrix dimension mismatch solution of linear equations"); |
| 2593 else if (m == 0 || n == 0 || b.cols () == 0) | |
| 2594 retval = ComplexColumnVector (n, Complex (0.0, 0.0)); | |
| 1948 | 2595 else |
| 458 | 2596 { |
| 7072 | 2597 volatile octave_idx_type minmn = (m < n ? m : n); |
| 2598 octave_idx_type maxmn = m > n ? m : n; | |
| 7076 | 2599 rcond = -1.0; |
| 7072 | 2600 |
| 2601 if (m != n) | |
| 2602 { | |
| 2603 retval = ComplexColumnVector (maxmn); | |
| 2604 | |
| 2605 for (octave_idx_type i = 0; i < m; i++) | |
| 2606 retval.elem (i) = b.elem (i); | |
| 2607 } | |
| 2608 else | |
| 2609 retval = b; | |
| 2610 | |
| 1948 | 2611 ComplexMatrix atmp = *this; |
| 2612 Complex *tmp_data = atmp.fortran_vec (); | |
| 2613 | |
| 7072 | 2614 Complex *pretval = retval.fortran_vec (); |
| 2615 Array<double> s (minmn); | |
| 7071 | 2616 double *ps = s.fortran_vec (); |
| 1948 | 2617 |
| 7072 | 2618 // Ask ZGELSD what the dimension of WORK should be. |
| 5275 | 2619 octave_idx_type lwork = -1; |
| 3752 | 2620 |
| 2621 Array<Complex> work (1); | |
| 7079 | 2622 |
|
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2623 octave_idx_type smlsiz; |
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2624 F77_FUNC (xilaenv, XILAENV) (9, F77_CONST_CHAR_ARG2 ("ZGELSD", 6), |
|
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|
2625 F77_CONST_CHAR_ARG2 (" ", 1), |
|
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|
2626 0, 0, 0, 0, smlsiz |
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|
2627 F77_CHAR_ARG_LEN (6) |
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|
2628 F77_CHAR_ARG_LEN (1)); |
| 7079 | 2629 |
| 2630 // We compute the size of rwork and iwork because ZGELSD in | |
| 2631 // older versions of LAPACK does not return them on a query | |
| 2632 // call. | |
| 7124 | 2633 double dminmn = static_cast<double> (minmn); |
| 2634 double dsmlsizp1 = static_cast<double> (smlsiz+1); | |
| 7079 | 2635 #if defined (HAVE_LOG2) |
|
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|
2636 double tmp = log2 (dminmn / dsmlsizp1); |
| 7079 | 2637 #else |
|
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|
2638 double tmp = log (dminmn / dsmlsizp1) / log (2.0); |
| 7079 | 2639 #endif |
|
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|
2640 octave_idx_type nlvl = static_cast<octave_idx_type> (tmp) + 1; |
| 7079 | 2641 if (nlvl < 0) |
| 2642 nlvl = 0; | |
| 2643 | |
| 2644 octave_idx_type lrwork = minmn*(10 + 2*smlsiz + 8*nlvl) | |
| 2645 + 3*smlsiz*nrhs + (smlsiz+1)*(smlsiz+1); | |
| 2646 if (lrwork < 1) | |
| 2647 lrwork = 1; | |
| 2648 Array<double> rwork (lrwork); | |
| 2649 double *prwork = rwork.fortran_vec (); | |
| 2650 | |
| 2651 octave_idx_type liwork = 3 * minmn * nlvl + 11 * minmn; | |
| 2652 if (liwork < 1) | |
| 2653 liwork = 1; | |
| 2654 Array<octave_idx_type> iwork (liwork); | |
| 2655 octave_idx_type* piwork = iwork.fortran_vec (); | |
| 7072 | 2656 |
| 2657 F77_XFCN (zgelsd, ZGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, | |
| 2658 ps, rcond, rank, work.fortran_vec (), | |
| 7079 | 2659 lwork, prwork, piwork, info)); |
| 1948 | 2660 |
|
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|
2661 lwork = static_cast<octave_idx_type> (std::real (work(0))); |
|
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|
2662 work.resize (lwork); |
|
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diff
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|
2663 rwork.resize (static_cast<octave_idx_type> (rwork(0))); |
|
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|
2664 iwork.resize (iwork(0)); |
|
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diff
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|
2665 |
|
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changeset
|
2666 F77_XFCN (zgelsd, ZGELSD, (m, n, nrhs, tmp_data, m, pretval, |
|
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|
2667 maxmn, ps, rcond, rank, |
|
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|
2668 work.fortran_vec (), lwork, |
|
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|
2669 prwork, piwork, info)); |
|
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diff
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|
2670 |
|
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changeset
|
2671 if (rank < minmn) |
| 1948 | 2672 { |
|
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|
2673 if (rank < minmn) |
|
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|
2674 (*current_liboctave_warning_handler) |
|
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|
2675 ("zgelsd: rank deficient %dx%d matrix, rank = %d, tol = %e", |
|
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changeset
|
2676 m, n, rank, rcond); |
|
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|
2677 |
|
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|
2678 if (s.elem (0) == 0.0) |
|
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|
2679 rcond = 0.0; |
|
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|
2680 else |
|
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|
2681 rcond = s.elem (minmn - 1) / s.elem (0); |
|
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|
2682 |
|
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|
2683 retval.resize (n, nrhs); |
| 1948 | 2684 } |
| 458 | 2685 } |
| 2686 | |
| 2687 return retval; | |
| 2688 } | |
| 2689 | |
| 1819 | 2690 // Constants for matrix exponential calculation. |
| 2691 | |
| 2692 static double padec [] = | |
| 2693 { | |
| 2694 5.0000000000000000e-1, | |
| 2695 1.1666666666666667e-1, | |
| 2696 1.6666666666666667e-2, | |
| 2697 1.6025641025641026e-3, | |
| 2698 1.0683760683760684e-4, | |
| 2699 4.8562548562548563e-6, | |
| 2700 1.3875013875013875e-7, | |
| 2701 1.9270852604185938e-9, | |
| 2702 }; | |
| 2703 | |
| 7400 | 2704 static void |
| 2705 solve_singularity_warning (double rcond) | |
| 2706 { | |
| 2707 (*current_liboctave_warning_handler) | |
| 2708 ("singular matrix encountered in expm calculation, rcond = %g", | |
| 2709 rcond); | |
| 2710 } | |
| 2711 | |
| 1819 | 2712 ComplexMatrix |
| 2713 ComplexMatrix::expm (void) const | |
| 2714 { | |
| 2715 ComplexMatrix retval; | |
| 2716 | |
| 2717 ComplexMatrix m = *this; | |
| 2718 | |
| 5275 | 2719 octave_idx_type nc = columns (); |
| 1819 | 2720 |
| 3130 | 2721 // Preconditioning step 1: trace normalization to reduce dynamic |
| 2722 // range of poles, but avoid making stable eigenvalues unstable. | |
| 2723 | |
| 1819 | 2724 // trace shift value |
| 2725 Complex trshift = 0.0; | |
| 2726 | |
| 5275 | 2727 for (octave_idx_type i = 0; i < nc; i++) |
| 1819 | 2728 trshift += m.elem (i, i); |
| 2729 | |
| 2730 trshift /= nc; | |
| 2731 | |
| 3130 | 2732 if (trshift.real () < 0.0) |
| 6958 | 2733 { |
| 2734 trshift = trshift.imag (); | |
| 2735 if (trshift.real () > 709.0) | |
| 2736 trshift = 709.0; | |
| 2737 } | |
| 3130 | 2738 |
| 5275 | 2739 for (octave_idx_type i = 0; i < nc; i++) |
| 1819 | 2740 m.elem (i, i) -= trshift; |
| 2741 | |
| 2742 // Preconditioning step 2: eigenvalue balancing. | |
| 3331 | 2743 // code follows development in AEPBAL |
| 2744 | |
| 2745 Complex *mp = m.fortran_vec (); | |
| 3467 | 2746 |
| 5275 | 2747 octave_idx_type info, ilo, ihi,ilos,ihis; |
| 3468 | 2748 Array<double> dpermute (nc); |
| 2749 Array<double> dscale (nc); | |
| 2750 | |
| 5775 | 2751 // FIXME -- should pass job as a parameter in expm |
| 3468 | 2752 |
| 2753 // Permute first | |
| 2754 char job = 'P'; | |
| 4552 | 2755 F77_XFCN (zgebal, ZGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
| 2756 nc, mp, nc, ilo, ihi, | |
| 2757 dpermute.fortran_vec (), info | |
| 2758 F77_CHAR_ARG_LEN (1))); | |
| 3331 | 2759 |
| 3468 | 2760 // then scale |
| 2761 job = 'S'; | |
| 4552 | 2762 F77_XFCN (zgebal, ZGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
| 2763 nc, mp, nc, ilos, ihis, | |
| 2764 dscale.fortran_vec (), info | |
| 2765 F77_CHAR_ARG_LEN (1))); | |
| 3331 | 2766 |
| 1819 | 2767 // Preconditioning step 3: scaling. |
| 2768 | |
| 2769 ColumnVector work (nc); | |
| 3130 | 2770 double inf_norm; |
| 2771 | |
| 4552 | 2772 F77_XFCN (xzlange, XZLANGE, (F77_CONST_CHAR_ARG2 ("I", 1), |
| 2773 nc, nc, m.fortran_vec (), nc, | |
| 2774 work.fortran_vec (), inf_norm | |
| 2775 F77_CHAR_ARG_LEN (1))); | |
| 3331 | 2776 |
| 2800 | 2777 int sqpow = (inf_norm > 0.0 |
| 2778 ? static_cast<int> (1.0 + log (inf_norm) / log (2.0)) : 0); | |
| 1819 | 2779 |
| 2780 // Check whether we need to square at all. | |
| 2781 | |
| 2782 if (sqpow < 0) | |
| 2783 sqpow = 0; | |
| 2784 | |
| 2785 if (sqpow > 0) | |
| 2786 { | |
| 7400 | 2787 if (sqpow > 1023) |
| 2788 sqpow = 1023; | |
| 2789 | |
| 1819 | 2790 double scale_factor = 1.0; |
| 5275 | 2791 for (octave_idx_type i = 0; i < sqpow; i++) |
| 1819 | 2792 scale_factor *= 2.0; |
| 2793 | |
| 2794 m = m / scale_factor; | |
| 2795 } | |
| 2796 | |
| 2797 // npp, dpp: pade' approx polynomial matrices. | |
| 2798 | |
| 2799 ComplexMatrix npp (nc, nc, 0.0); | |
| 6958 | 2800 Complex *pnpp = npp.fortran_vec (); |
| 1819 | 2801 ComplexMatrix dpp = npp; |
| 6958 | 2802 Complex *pdpp = dpp.fortran_vec (); |
| 1819 | 2803 |
| 2804 // Now powers a^8 ... a^1. | |
| 2805 | |
| 2806 int minus_one_j = -1; | |
| 5275 | 2807 for (octave_idx_type j = 7; j >= 0; j--) |
| 1819 | 2808 { |
| 6958 | 2809 for (octave_idx_type i = 0; i < nc; i++) |
| 2810 { | |
| 2811 octave_idx_type k = i * nc + i; | |
| 7265 | 2812 pnpp[k] += padec[j]; |
| 2813 pdpp[k] += minus_one_j * padec[j]; | |
| 6958 | 2814 } |
| 7265 | 2815 |
| 6958 | 2816 npp = m * npp; |
| 7265 | 2817 pnpp = npp.fortran_vec (); |
| 2818 | |
| 6958 | 2819 dpp = m * dpp; |
| 7265 | 2820 pdpp = dpp.fortran_vec (); |
| 2821 | |
| 1819 | 2822 minus_one_j *= -1; |
| 2823 } | |
| 2824 | |
| 2825 // Zero power. | |
| 2826 | |
| 2827 dpp = -dpp; | |
| 5275 | 2828 for (octave_idx_type j = 0; j < nc; j++) |
| 1819 | 2829 { |
| 2830 npp.elem (j, j) += 1.0; | |
| 2831 dpp.elem (j, j) += 1.0; | |
| 2832 } | |
| 2833 | |
| 2834 // Compute pade approximation = inverse (dpp) * npp. | |
| 2835 | |
| 7400 | 2836 double rcond; |
| 2837 retval = dpp.solve (npp, info, rcond, solve_singularity_warning); | |
| 2838 | |
| 2839 if (info < 0) | |
| 2840 return retval; | |
| 2841 | |
| 1819 | 2842 // Reverse preconditioning step 3: repeated squaring. |
| 2843 | |
| 2844 while (sqpow) | |
| 2845 { | |
| 2846 retval = retval * retval; | |
| 2847 sqpow--; | |
| 2848 } | |
| 2849 | |
| 2850 // Reverse preconditioning step 2: inverse balancing. | |
| 3467 | 2851 // Done in two steps: inverse scaling, then inverse permutation |
| 2852 | |
| 2853 // inverse scaling (diagonal transformation) | |
| 5275 | 2854 for (octave_idx_type i = 0; i < nc; i++) |
| 2855 for (octave_idx_type j = 0; j < nc; j++) | |
| 3468 | 2856 retval(i,j) *= dscale(i) / dscale(j); |
| 3467 | 2857 |
| 4153 | 2858 OCTAVE_QUIT; |
| 2859 | |
| 3467 | 2860 // construct balancing permutation vector |
| 6867 | 2861 Array<octave_idx_type> iperm (nc); |
| 5275 | 2862 for (octave_idx_type i = 0; i < nc; i++) |
| 4593 | 2863 iperm(i) = i; // initialize to identity permutation |
| 3467 | 2864 |
| 2865 // leading permutations in forward order | |
| 5275 | 2866 for (octave_idx_type i = 0; i < (ilo-1); i++) |
| 3468 | 2867 { |
| 6867 | 2868 octave_idx_type swapidx = static_cast<octave_idx_type> (dpermute(i)) - 1; |
| 5275 | 2869 octave_idx_type tmp = iperm(i); |
| 4593 | 2870 iperm(i) = iperm(swapidx); |
| 2871 iperm(swapidx) = tmp; | |
| 3468 | 2872 } |
| 3467 | 2873 |
| 7416 | 2874 // construct inverse balancing permutation vector |
| 2875 Array<octave_idx_type> invpvec (nc); | |
| 2876 for (octave_idx_type i = 0; i < nc; i++) | |
| 2877 invpvec(iperm(i)) = i; // Thanks to R. A. Lippert for this method | |
| 2878 | |
| 2879 OCTAVE_QUIT; | |
| 2880 | |
| 2881 ComplexMatrix tmpMat = retval; | |
| 2882 for (octave_idx_type i = 0; i < nc; i++) | |
| 2883 for (octave_idx_type j = 0; j < nc; j++) | |
| 2884 retval(i,j) = tmpMat(invpvec(i),invpvec(j)); | |
| 2885 | |
| 2886 OCTAVE_QUIT; | |
| 2887 | |
| 2888 for (octave_idx_type i = 0; i < nc; i++) | |
| 2889 iperm(i) = i; // initialize to identity permutation | |
| 2890 | |
| 3467 | 2891 // trailing permutations must be done in reverse order |
| 5275 | 2892 for (octave_idx_type i = nc - 1; i >= ihi; i--) |
| 3468 | 2893 { |
| 6867 | 2894 octave_idx_type swapidx = static_cast<octave_idx_type> (dpermute(i)) - 1; |
| 5275 | 2895 octave_idx_type tmp = iperm(i); |
| 4593 | 2896 iperm(i) = iperm(swapidx); |
| 2897 iperm(swapidx) = tmp; | |
| 3468 | 2898 } |
| 3467 | 2899 |
| 2900 // construct inverse balancing permutation vector | |
| 5275 | 2901 for (octave_idx_type i = 0; i < nc; i++) |
| 4593 | 2902 invpvec(iperm(i)) = i; // Thanks to R. A. Lippert for this method |
| 3467 | 2903 |
| 4153 | 2904 OCTAVE_QUIT; |
| 2905 | |
| 7416 | 2906 tmpMat = retval; |
| 5275 | 2907 for (octave_idx_type i = 0; i < nc; i++) |
| 2908 for (octave_idx_type j = 0; j < nc; j++) | |
| 3468 | 2909 retval(i,j) = tmpMat(invpvec(i),invpvec(j)); |
| 1819 | 2910 |
| 2911 // Reverse preconditioning step 1: fix trace normalization. | |
| 2912 | |
| 3130 | 2913 return exp (trshift) * retval; |
| 1819 | 2914 } |
| 2915 | |
| 1205 | 2916 // column vector by row vector -> matrix operations |
| 2917 | |
| 2918 ComplexMatrix | |
| 2919 operator * (const ColumnVector& v, const ComplexRowVector& a) | |
| 2920 { | |
| 2921 ComplexColumnVector tmp (v); | |
| 2922 return tmp * a; | |
| 2923 } | |
| 2924 | |
| 2925 ComplexMatrix | |
| 2926 operator * (const ComplexColumnVector& a, const RowVector& b) | |
| 2927 { | |
| 2928 ComplexRowVector tmp (b); | |
| 2929 return a * tmp; | |
| 2930 } | |
| 2931 | |
| 2932 ComplexMatrix | |
| 2933 operator * (const ComplexColumnVector& v, const ComplexRowVector& a) | |
| 2934 { | |
| 1948 | 2935 ComplexMatrix retval; |
| 2936 | |
| 5275 | 2937 octave_idx_type len = v.length (); |
| 3233 | 2938 |
| 2939 if (len != 0) | |
| 1205 | 2940 { |
| 5275 | 2941 octave_idx_type a_len = a.length (); |
| 3233 | 2942 |
| 2943 retval.resize (len, a_len); | |
| 2944 Complex *c = retval.fortran_vec (); | |
| 2945 | |
| 4552 | 2946 F77_XFCN (zgemm, ZGEMM, (F77_CONST_CHAR_ARG2 ("N", 1), |
| 2947 F77_CONST_CHAR_ARG2 ("N", 1), | |
| 2948 len, a_len, 1, 1.0, v.data (), len, | |
| 2949 a.data (), 1, 0.0, c, len | |
| 2950 F77_CHAR_ARG_LEN (1) | |
| 2951 F77_CHAR_ARG_LEN (1))); | |
| 1205 | 2952 } |
| 2953 | |
| 1948 | 2954 return retval; |
| 1205 | 2955 } |
| 2956 | |
| 458 | 2957 // matrix by diagonal matrix -> matrix operations |
| 2958 | |
| 2959 ComplexMatrix& | |
| 2960 ComplexMatrix::operator += (const DiagMatrix& a) | |
| 2961 { | |
| 5275 | 2962 octave_idx_type nr = rows (); |
| 2963 octave_idx_type nc = cols (); | |
| 2964 | |
| 2965 octave_idx_type a_nr = rows (); | |
| 2966 octave_idx_type a_nc = cols (); | |
| 2384 | 2967 |
| 2968 if (nr != a_nr || nc != a_nc) | |
| 458 | 2969 { |
| 2384 | 2970 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
| 889 | 2971 return *this; |
| 458 | 2972 } |
| 2973 | |
| 5275 | 2974 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 2975 elem (i, i) += a.elem (i, i); |
| 2976 | |
| 2977 return *this; | |
| 2978 } | |
| 2979 | |
| 2980 ComplexMatrix& | |
| 2981 ComplexMatrix::operator -= (const DiagMatrix& a) | |
| 2982 { | |
| 5275 | 2983 octave_idx_type nr = rows (); |
| 2984 octave_idx_type nc = cols (); | |
| 2985 | |
| 2986 octave_idx_type a_nr = rows (); | |
| 2987 octave_idx_type a_nc = cols (); | |
| 2384 | 2988 |
| 2989 if (nr != a_nr || nc != a_nc) | |
| 458 | 2990 { |
| 2384 | 2991 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
| 889 | 2992 return *this; |
| 458 | 2993 } |
| 2994 | |
| 5275 | 2995 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 2996 elem (i, i) -= a.elem (i, i); |
| 2997 | |
| 2998 return *this; | |
| 2999 } | |
| 3000 | |
| 3001 ComplexMatrix& | |
| 3002 ComplexMatrix::operator += (const ComplexDiagMatrix& a) | |
| 3003 { | |
| 5275 | 3004 octave_idx_type nr = rows (); |
| 3005 octave_idx_type nc = cols (); | |
| 3006 | |
| 3007 octave_idx_type a_nr = rows (); | |
| 3008 octave_idx_type a_nc = cols (); | |
| 2384 | 3009 |
| 3010 if (nr != a_nr || nc != a_nc) | |
| 458 | 3011 { |
| 2384 | 3012 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
| 889 | 3013 return *this; |
| 458 | 3014 } |
| 3015 | |
| 5275 | 3016 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 3017 elem (i, i) += a.elem (i, i); |
| 3018 | |
| 3019 return *this; | |
| 3020 } | |
| 3021 | |
| 3022 ComplexMatrix& | |
| 3023 ComplexMatrix::operator -= (const ComplexDiagMatrix& a) | |
| 3024 { | |
| 5275 | 3025 octave_idx_type nr = rows (); |
| 3026 octave_idx_type nc = cols (); | |
| 3027 | |
| 3028 octave_idx_type a_nr = rows (); | |
| 3029 octave_idx_type a_nc = cols (); | |
| 2384 | 3030 |
| 3031 if (nr != a_nr || nc != a_nc) | |
| 458 | 3032 { |
| 2384 | 3033 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
| 889 | 3034 return *this; |
| 458 | 3035 } |
| 3036 | |
| 5275 | 3037 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 3038 elem (i, i) -= a.elem (i, i); |
| 3039 | |
| 3040 return *this; | |
| 3041 } | |
| 3042 | |
| 3043 // matrix by matrix -> matrix operations | |
| 3044 | |
| 3045 ComplexMatrix& | |
| 3046 ComplexMatrix::operator += (const Matrix& a) | |
| 3047 { | |
| 5275 | 3048 octave_idx_type nr = rows (); |
| 3049 octave_idx_type nc = cols (); | |
| 3050 | |
| 3051 octave_idx_type a_nr = a.rows (); | |
| 3052 octave_idx_type a_nc = a.cols (); | |
| 2384 | 3053 |
| 3054 if (nr != a_nr || nc != a_nc) | |
| 458 | 3055 { |
| 2384 | 3056 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
| 458 | 3057 return *this; |
| 3058 } | |
| 3059 | |
| 3060 if (nr == 0 || nc == 0) | |
| 3061 return *this; | |
| 3062 | |
| 3063 Complex *d = fortran_vec (); // Ensures only one reference to my privates! | |
| 3064 | |
| 3769 | 3065 mx_inline_add2 (d, a.data (), length ()); |
| 458 | 3066 return *this; |
| 3067 } | |
| 3068 | |
| 3069 ComplexMatrix& | |
| 3070 ComplexMatrix::operator -= (const Matrix& a) | |
| 3071 { | |
| 5275 | 3072 octave_idx_type nr = rows (); |
| 3073 octave_idx_type nc = cols (); | |
| 3074 | |
| 3075 octave_idx_type a_nr = a.rows (); | |
| 3076 octave_idx_type a_nc = a.cols (); | |
| 2384 | 3077 |
| 3078 if (nr != a_nr || nc != a_nc) | |
| 458 | 3079 { |
| 2384 | 3080 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
| 458 | 3081 return *this; |
| 3082 } | |
| 3083 | |
| 3084 if (nr == 0 || nc == 0) | |
| 3085 return *this; | |
| 3086 | |
| 3087 Complex *d = fortran_vec (); // Ensures only one reference to my privates! | |
| 3088 | |
| 3769 | 3089 mx_inline_subtract2 (d, a.data (), length ()); |
| 458 | 3090 return *this; |
| 3091 } | |
| 3092 | |
| 3093 // unary operations | |
| 3094 | |
| 2964 | 3095 boolMatrix |
| 458 | 3096 ComplexMatrix::operator ! (void) const |
| 3097 { | |
| 5275 | 3098 octave_idx_type nr = rows (); |
| 3099 octave_idx_type nc = cols (); | |
| 2964 | 3100 |
| 3101 boolMatrix b (nr, nc); | |
| 3102 | |
| 5275 | 3103 for (octave_idx_type j = 0; j < nc; j++) |
| 3104 for (octave_idx_type i = 0; i < nr; i++) | |
| 5139 | 3105 b.elem (i, j) = elem (i, j) == 0.0; |
| 2964 | 3106 |
| 3107 return b; | |
| 458 | 3108 } |
| 3109 | |
| 3110 // other operations | |
| 3111 | |
| 2676 | 3112 Matrix |
|
7503
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David Bateman <dbateman@free.fr>
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|
3113 ComplexMatrix::map (dmapper fcn) const |
| 458 | 3114 { |
|
7503
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|
3115 return MArray2<Complex>::map<double> (func_ptr (fcn)); |
|
8c32f95c2639
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parents:
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diff
changeset
|
3116 } |
|
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David Bateman <dbateman@free.fr>
parents:
7488
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|
3117 |
|
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parents:
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|
3118 ComplexMatrix |
|
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parents:
7488
diff
changeset
|
3119 ComplexMatrix::map (cmapper fcn) const |
|
8c32f95c2639
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David Bateman <dbateman@free.fr>
parents:
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|
3120 { |
|
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David Bateman <dbateman@free.fr>
parents:
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|
3121 return MArray2<Complex>::map<Complex> (func_ptr (fcn)); |
| 3248 | 3122 } |
| 3123 | |
| 3124 boolMatrix | |
|
7503
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|
3125 ComplexMatrix::map (bmapper fcn) const |
| 3248 | 3126 { |
|
7503
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|
3127 return MArray2<Complex>::map<bool> (func_ptr (fcn)); |
| 458 | 3128 } |
| 3129 | |
| 2384 | 3130 bool |
| 3131 ComplexMatrix::any_element_is_inf_or_nan (void) const | |
| 3132 { | |
| 5275 | 3133 octave_idx_type nr = rows (); |
| 3134 octave_idx_type nc = cols (); | |
| 3135 | |
| 3136 for (octave_idx_type j = 0; j < nc; j++) | |
| 3137 for (octave_idx_type i = 0; i < nr; i++) | |
| 2384 | 3138 { |
| 3139 Complex val = elem (i, j); | |
| 3140 if (xisinf (val) || xisnan (val)) | |
| 3141 return true; | |
| 3142 } | |
| 3143 | |
| 3144 return false; | |
| 3145 } | |
| 3146 | |
| 2408 | 3147 // Return true if no elements have imaginary components. |
| 3148 | |
| 3149 bool | |
| 3150 ComplexMatrix::all_elements_are_real (void) const | |
| 3151 { | |
| 5275 | 3152 octave_idx_type nr = rows (); |
| 3153 octave_idx_type nc = cols (); | |
| 3154 | |
| 3155 for (octave_idx_type j = 0; j < nc; j++) | |
| 4349 | 3156 { |
| 5275 | 3157 for (octave_idx_type i = 0; i < nr; i++) |
| 4349 | 3158 { |
| 5315 | 3159 double ip = std::imag (elem (i, j)); |
| 4349 | 3160 |
| 3161 if (ip != 0.0 || lo_ieee_signbit (ip)) | |
| 3162 return false; | |
| 3163 } | |
| 3164 } | |
| 2408 | 3165 |
| 3166 return true; | |
| 3167 } | |
| 3168 | |
| 1968 | 3169 // Return nonzero if any element of CM has a non-integer real or |
| 3170 // imaginary part. Also extract the largest and smallest (real or | |
| 3171 // imaginary) values and return them in MAX_VAL and MIN_VAL. | |
| 3172 | |
| 2384 | 3173 bool |
| 1968 | 3174 ComplexMatrix::all_integers (double& max_val, double& min_val) const |
| 3175 { | |
| 5275 | 3176 octave_idx_type nr = rows (); |
| 3177 octave_idx_type nc = cols (); | |
| 1968 | 3178 |
| 3179 if (nr > 0 && nc > 0) | |
| 3180 { | |
| 3181 Complex val = elem (0, 0); | |
| 3182 | |
| 5315 | 3183 double r_val = std::real (val); |
| 3184 double i_val = std::imag (val); | |
| 1968 | 3185 |
| 3186 max_val = r_val; | |
| 3187 min_val = r_val; | |
| 3188 | |
| 3189 if (i_val > max_val) | |
| 3190 max_val = i_val; | |
| 3191 | |
| 3192 if (i_val < max_val) | |
| 3193 min_val = i_val; | |
| 3194 } | |
| 3195 else | |
| 2384 | 3196 return false; |
| 1968 | 3197 |
| 5275 | 3198 for (octave_idx_type j = 0; j < nc; j++) |
| 3199 for (octave_idx_type i = 0; i < nr; i++) | |
| 1968 | 3200 { |
| 3201 Complex val = elem (i, j); | |
| 3202 | |
| 5315 | 3203 double r_val = std::real (val); |
| 3204 double i_val = std::imag (val); | |
| 1968 | 3205 |
| 3206 if (r_val > max_val) | |
| 3207 max_val = r_val; | |
| 3208 | |
| 3209 if (i_val > max_val) | |
| 3210 max_val = i_val; | |
| 3211 | |
| 3212 if (r_val < min_val) | |
| 3213 min_val = r_val; | |
| 3214 | |
| 3215 if (i_val < min_val) | |
| 3216 min_val = i_val; | |
| 3217 | |
| 3218 if (D_NINT (r_val) != r_val || D_NINT (i_val) != i_val) | |
| 2384 | 3219 return false; |
| 1968 | 3220 } |
| 2384 | 3221 |
| 3222 return true; | |
| 1968 | 3223 } |
| 3224 | |
| 2384 | 3225 bool |
| 1968 | 3226 ComplexMatrix::too_large_for_float (void) const |
| 3227 { | |
| 5275 | 3228 octave_idx_type nr = rows (); |
| 3229 octave_idx_type nc = cols (); | |
| 3230 | |
| 3231 for (octave_idx_type j = 0; j < nc; j++) | |
| 3232 for (octave_idx_type i = 0; i < nr; i++) | |
| 1968 | 3233 { |
| 3234 Complex val = elem (i, j); | |
| 3235 | |
| 5315 | 3236 double r_val = std::real (val); |
| 3237 double i_val = std::imag (val); | |
| 1968 | 3238 |
| 5389 | 3239 if ((! (xisnan (r_val) || xisinf (r_val)) |
| 5387 | 3240 && fabs (r_val) > FLT_MAX) |
| 5389 | 3241 || (! (xisnan (i_val) || xisinf (i_val)) |
| 5387 | 3242 && fabs (i_val) > FLT_MAX)) |
| 2384 | 3243 return true; |
| 1968 | 3244 } |
| 3245 | |
| 2384 | 3246 return false; |
| 1968 | 3247 } |
| 3248 | |
| 5775 | 3249 // FIXME Do these really belong here? Maybe they should be |
| 4015 | 3250 // in a base class? |
| 3251 | |
| 2832 | 3252 boolMatrix |
| 4015 | 3253 ComplexMatrix::all (int dim) const |
| 458 | 3254 { |
| 4015 | 3255 MX_ALL_OP (dim); |
| 458 | 3256 } |
| 3257 | |
| 2832 | 3258 boolMatrix |
| 4015 | 3259 ComplexMatrix::any (int dim) const |
| 458 | 3260 { |
| 4015 | 3261 MX_ANY_OP (dim); |
| 458 | 3262 } |
| 3263 | |
| 3264 ComplexMatrix | |
| 3723 | 3265 ComplexMatrix::cumprod (int dim) const |
| 458 | 3266 { |
| 4015 | 3267 MX_CUMULATIVE_OP (ComplexMatrix, Complex, *=); |
| 458 | 3268 } |
| 3269 | |
| 3270 ComplexMatrix | |
| 3723 | 3271 ComplexMatrix::cumsum (int dim) const |
| 458 | 3272 { |
| 4015 | 3273 MX_CUMULATIVE_OP (ComplexMatrix, Complex, +=); |
| 458 | 3274 } |
| 3275 | |
| 3276 ComplexMatrix | |
| 3723 | 3277 ComplexMatrix::prod (int dim) const |
| 458 | 3278 { |
| 3864 | 3279 MX_REDUCTION_OP (ComplexMatrix, *=, 1.0, 1.0); |
| 458 | 3280 } |
| 3281 | |
| 3282 ComplexMatrix | |
| 3723 | 3283 ComplexMatrix::sum (int dim) const |
| 458 | 3284 { |
| 3864 | 3285 MX_REDUCTION_OP (ComplexMatrix, +=, 0.0, 0.0); |
| 458 | 3286 } |
| 3287 | |
| 3288 ComplexMatrix | |
| 3723 | 3289 ComplexMatrix::sumsq (int dim) const |
| 458 | 3290 { |
| 3864 | 3291 #define ROW_EXPR \ |
| 3292 Complex d = elem (i, j); \ | |
| 3293 retval.elem (i, 0) += d * conj (d) | |
| 3294 | |
| 3295 #define COL_EXPR \ | |
| 3296 Complex d = elem (i, j); \ | |
| 3297 retval.elem (0, j) += d * conj (d) | |
| 3298 | |
| 3299 MX_BASE_REDUCTION_OP (ComplexMatrix, ROW_EXPR, COL_EXPR, 0.0, 0.0); | |
| 3300 | |
| 3301 #undef ROW_EXPR | |
| 3302 #undef COL_EXPR | |
| 458 | 3303 } |
| 3304 | |
| 4329 | 3305 Matrix ComplexMatrix::abs (void) const |
| 3306 { | |
| 5275 | 3307 octave_idx_type nr = rows (); |
| 3308 octave_idx_type nc = cols (); | |
| 4329 | 3309 |
| 3310 Matrix retval (nr, nc); | |
| 3311 | |
| 5275 | 3312 for (octave_idx_type j = 0; j < nc; j++) |
| 3313 for (octave_idx_type i = 0; i < nr; i++) | |
| 5315 | 3314 retval (i, j) = std::abs (elem (i, j)); |
| 4329 | 3315 |
| 3316 return retval; | |
| 3317 } | |
| 3318 | |
| 458 | 3319 ComplexColumnVector |
| 3320 ComplexMatrix::diag (void) const | |
| 3321 { | |
| 3322 return diag (0); | |
| 3323 } | |
| 3324 | |
| 3325 ComplexColumnVector | |
| 5275 | 3326 ComplexMatrix::diag (octave_idx_type k) const |
| 458 | 3327 { |
| 5275 | 3328 octave_idx_type nnr = rows (); |
| 3329 octave_idx_type nnc = cols (); | |
| 458 | 3330 if (k > 0) |
| 3331 nnc -= k; | |
| 3332 else if (k < 0) | |
| 3333 nnr += k; | |
| 3334 | |
| 3335 ComplexColumnVector d; | |
| 3336 | |
| 3337 if (nnr > 0 && nnc > 0) | |
| 3338 { | |
| 5275 | 3339 octave_idx_type ndiag = (nnr < nnc) ? nnr : nnc; |
| 458 | 3340 |
| 3341 d.resize (ndiag); | |
| 3342 | |
| 3343 if (k > 0) | |
| 3344 { | |
| 5275 | 3345 for (octave_idx_type i = 0; i < ndiag; i++) |
| 458 | 3346 d.elem (i) = elem (i, i+k); |
| 3347 } | |
| 4509 | 3348 else if (k < 0) |
| 458 | 3349 { |
| 5275 | 3350 for (octave_idx_type i = 0; i < ndiag; i++) |
| 458 | 3351 d.elem (i) = elem (i-k, i); |
| 3352 } | |
| 3353 else | |
| 3354 { | |
| 5275 | 3355 for (octave_idx_type i = 0; i < ndiag; i++) |
| 458 | 3356 d.elem (i) = elem (i, i); |
| 3357 } | |
| 3358 } | |
| 3359 else | |
| 4513 | 3360 (*current_liboctave_error_handler) |
| 3361 ("diag: requested diagonal out of range"); | |
| 458 | 3362 |
| 3363 return d; | |
| 3364 } | |
| 3365 | |
| 2354 | 3366 bool |
| 5275 | 3367 ComplexMatrix::row_is_real_only (octave_idx_type i) const |
| 2354 | 3368 { |
| 3369 bool retval = true; | |
| 3370 | |
| 5275 | 3371 octave_idx_type nc = columns (); |
| 3372 | |
| 3373 for (octave_idx_type j = 0; j < nc; j++) | |
| 2354 | 3374 { |
| 5315 | 3375 if (std::imag (elem (i, j)) != 0.0) |
| 2354 | 3376 { |
| 3377 retval = false; | |
| 3378 break; | |
| 3379 } | |
| 3380 } | |
| 3381 | |
| 3382 return retval; | |
| 3383 } | |
| 3384 | |
| 3385 bool | |
| 5275 | 3386 ComplexMatrix::column_is_real_only (octave_idx_type j) const |
| 2354 | 3387 { |
| 3388 bool retval = true; | |
| 3389 | |
| 5275 | 3390 octave_idx_type nr = rows (); |
| 3391 | |
| 3392 for (octave_idx_type i = 0; i < nr; i++) | |
| 2354 | 3393 { |
| 5315 | 3394 if (std::imag (elem (i, j)) != 0.0) |
| 2354 | 3395 { |
| 3396 retval = false; | |
| 3397 break; | |
| 3398 } | |
| 3399 } | |
| 3400 | |
| 3401 return retval; | |
| 3402 } | |
| 891 | 3403 |
| 458 | 3404 ComplexColumnVector |
| 3405 ComplexMatrix::row_min (void) const | |
| 3406 { | |
| 5275 | 3407 Array<octave_idx_type> dummy_idx; |
| 4587 | 3408 return row_min (dummy_idx); |
| 458 | 3409 } |
| 3410 | |
| 3411 ComplexColumnVector | |
| 5275 | 3412 ComplexMatrix::row_min (Array<octave_idx_type>& idx_arg) const |
| 458 | 3413 { |
| 3414 ComplexColumnVector result; | |
| 3415 | |
| 5275 | 3416 octave_idx_type nr = rows (); |
| 3417 octave_idx_type nc = cols (); | |
| 458 | 3418 |
| 3419 if (nr > 0 && nc > 0) | |
| 3420 { | |
| 3421 result.resize (nr); | |
| 4587 | 3422 idx_arg.resize (nr); |
| 458 | 3423 |
| 5275 | 3424 for (octave_idx_type i = 0; i < nr; i++) |
| 458 | 3425 { |
| 2354 | 3426 bool real_only = row_is_real_only (i); |
| 3427 | |
| 5275 | 3428 octave_idx_type idx_j; |
| 4469 | 3429 |
| 3430 Complex tmp_min; | |
| 3431 | |
| 3432 double abs_min = octave_NaN; | |
| 3433 | |
| 3434 for (idx_j = 0; idx_j < nc; idx_j++) | |
| 3435 { | |
| 3436 tmp_min = elem (i, idx_j); | |
| 3437 | |
| 5389 | 3438 if (! xisnan (tmp_min)) |
| 4469 | 3439 { |
| 5315 | 3440 abs_min = real_only ? std::real (tmp_min) : std::abs (tmp_min); |
| 4469 | 3441 break; |
| 3442 } | |
| 3443 } | |
| 3444 | |
| 5275 | 3445 for (octave_idx_type j = idx_j+1; j < nc; j++) |
| 4469 | 3446 { |
| 3447 Complex tmp = elem (i, j); | |
| 3448 | |
| 5389 | 3449 if (xisnan (tmp)) |
| 4469 | 3450 continue; |
| 3451 | |
| 5315 | 3452 double abs_tmp = real_only ? std::real (tmp) : std::abs (tmp); |
| 4469 | 3453 |
| 3454 if (abs_tmp < abs_min) | |
| 3455 { | |
| 3456 idx_j = j; | |
| 3457 tmp_min = tmp; | |
| 3458 abs_min = abs_tmp; | |
| 3459 } | |
| 3460 } | |
| 3461 | |
| 5389 | 3462 if (xisnan (tmp_min)) |
| 4469 | 3463 { |
| 3464 result.elem (i) = Complex_NaN_result; | |
| 4587 | 3465 idx_arg.elem (i) = 0; |
| 4469 | 3466 } |
| 891 | 3467 else |
| 3468 { | |
| 4469 | 3469 result.elem (i) = tmp_min; |
| 4587 | 3470 idx_arg.elem (i) = idx_j; |
| 891 | 3471 } |
| 458 | 3472 } |
| 3473 } | |
| 3474 | |
| 3475 return result; | |
| 3476 } | |
| 3477 | |
| 3478 ComplexColumnVector | |
| 3479 ComplexMatrix::row_max (void) const | |
| 3480 { | |
| 5275 | 3481 Array<octave_idx_type> dummy_idx; |
| 4587 | 3482 return row_max (dummy_idx); |
| 458 | 3483 } |
| 3484 | |
| 3485 ComplexColumnVector | |
| 5275 | 3486 ComplexMatrix::row_max (Array<octave_idx_type>& idx_arg) const |
| 458 | 3487 { |
| 3488 ComplexColumnVector result; | |
| 3489 | |
| 5275 | 3490 octave_idx_type nr = rows (); |
| 3491 octave_idx_type nc = cols (); | |
| 458 | 3492 |
| 3493 if (nr > 0 && nc > 0) | |
| 3494 { | |
| 3495 result.resize (nr); | |
| 4587 | 3496 idx_arg.resize (nr); |
| 458 | 3497 |
| 5275 | 3498 for (octave_idx_type i = 0; i < nr; i++) |
| 458 | 3499 { |
| 2354 | 3500 bool real_only = row_is_real_only (i); |
| 3501 | |
| 5275 | 3502 octave_idx_type idx_j; |
| 4469 | 3503 |
| 3504 Complex tmp_max; | |
| 3505 | |
| 3506 double abs_max = octave_NaN; | |
| 3507 | |
| 3508 for (idx_j = 0; idx_j < nc; idx_j++) | |
| 3509 { | |
| 3510 tmp_max = elem (i, idx_j); | |
| 3511 | |
| 5389 | 3512 if (! xisnan (tmp_max)) |
| 4469 | 3513 { |
| 5315 | 3514 abs_max = real_only ? std::real (tmp_max) : std::abs (tmp_max); |
| 4469 | 3515 break; |
| 3516 } | |
| 3517 } | |
| 3518 | |
| 5275 | 3519 for (octave_idx_type j = idx_j+1; j < nc; j++) |
| 4469 | 3520 { |
| 3521 Complex tmp = elem (i, j); | |
| 3522 | |
| 5389 | 3523 if (xisnan (tmp)) |
| 4469 | 3524 continue; |
| 3525 | |
| 5315 | 3526 double abs_tmp = real_only ? std::real (tmp) : std::abs (tmp); |
| 4469 | 3527 |
| 3528 if (abs_tmp > abs_max) | |
| 3529 { | |
| 3530 idx_j = j; | |
| 3531 tmp_max = tmp; | |
| 3532 abs_max = abs_tmp; | |
| 3533 } | |
| 3534 } | |
| 3535 | |
| 5389 | 3536 if (xisnan (tmp_max)) |
| 4469 | 3537 { |
| 3538 result.elem (i) = Complex_NaN_result; | |
| 4587 | 3539 idx_arg.elem (i) = 0; |
| 4469 | 3540 } |
| 891 | 3541 else |
| 3542 { | |
| 4469 | 3543 result.elem (i) = tmp_max; |
| 4587 | 3544 idx_arg.elem (i) = idx_j; |
| 891 | 3545 } |
| 458 | 3546 } |
| 3547 } | |
| 3548 | |
| 3549 return result; | |
| 3550 } | |
| 3551 | |
| 3552 ComplexRowVector | |
| 3553 ComplexMatrix::column_min (void) const | |
| 3554 { | |
| 5275 | 3555 Array<octave_idx_type> dummy_idx; |
| 4587 | 3556 return column_min (dummy_idx); |
| 458 | 3557 } |
| 3558 | |
| 3559 ComplexRowVector | |
| 5275 | 3560 ComplexMatrix::column_min (Array<octave_idx_type>& idx_arg) const |
| 458 | 3561 { |
| 3562 ComplexRowVector result; | |
| 3563 | |
| 5275 | 3564 octave_idx_type nr = rows (); |
| 3565 octave_idx_type nc = cols (); | |
| 458 | 3566 |
| 3567 if (nr > 0 && nc > 0) | |
| 3568 { | |
| 3569 result.resize (nc); | |
| 4587 | 3570 idx_arg.resize (nc); |
| 458 | 3571 |
| 5275 | 3572 for (octave_idx_type j = 0; j < nc; j++) |
| 458 | 3573 { |
| 2354 | 3574 bool real_only = column_is_real_only (j); |
| 3575 | |
| 5275 | 3576 octave_idx_type idx_i; |
| 4469 | 3577 |
| 3578 Complex tmp_min; | |
| 3579 | |
| 3580 double abs_min = octave_NaN; | |
| 3581 | |
| 3582 for (idx_i = 0; idx_i < nr; idx_i++) | |
| 3583 { | |
| 3584 tmp_min = elem (idx_i, j); | |
| 3585 | |
| 5389 | 3586 if (! xisnan (tmp_min)) |
| 4469 | 3587 { |
| 5315 | 3588 abs_min = real_only ? std::real (tmp_min) : std::abs (tmp_min); |
| 4469 | 3589 break; |
| 3590 } | |
| 3591 } | |
| 3592 | |
| 5275 | 3593 for (octave_idx_type i = idx_i+1; i < nr; i++) |
| 4469 | 3594 { |
| 3595 Complex tmp = elem (i, j); | |
| 3596 | |
| 5389 | 3597 if (xisnan (tmp)) |
| 4469 | 3598 continue; |
| 3599 | |
| 5315 | 3600 double abs_tmp = real_only ? std::real (tmp) : std::abs (tmp); |
| 4469 | 3601 |
| 3602 if (abs_tmp < abs_min) | |
| 3603 { | |
| 3604 idx_i = i; | |
| 3605 tmp_min = tmp; | |
| 3606 abs_min = abs_tmp; | |
| 3607 } | |
| 3608 } | |
| 3609 | |
| 5389 | 3610 if (xisnan (tmp_min)) |
| 4469 | 3611 { |
| 3612 result.elem (j) = Complex_NaN_result; | |
| 4587 | 3613 idx_arg.elem (j) = 0; |
| 4469 | 3614 } |
| 891 | 3615 else |
| 3616 { | |
| 4469 | 3617 result.elem (j) = tmp_min; |
| 4587 | 3618 idx_arg.elem (j) = idx_i; |
| 891 | 3619 } |
| 458 | 3620 } |
| 3621 } | |
| 3622 | |
| 3623 return result; | |
| 3624 } | |
| 3625 | |
| 3626 ComplexRowVector | |
| 3627 ComplexMatrix::column_max (void) const | |
| 3628 { | |
| 5275 | 3629 Array<octave_idx_type> dummy_idx; |
| 4587 | 3630 return column_max (dummy_idx); |
| 458 | 3631 } |
| 3632 | |
| 3633 ComplexRowVector | |
| 5275 | 3634 ComplexMatrix::column_max (Array<octave_idx_type>& idx_arg) const |
| 458 | 3635 { |
| 3636 ComplexRowVector result; | |
| 3637 | |
| 5275 | 3638 octave_idx_type nr = rows (); |
| 3639 octave_idx_type nc = cols (); | |
| 458 | 3640 |
| 3641 if (nr > 0 && nc > 0) | |
| 3642 { | |
| 3643 result.resize (nc); | |
| 4587 | 3644 idx_arg.resize (nc); |
| 458 | 3645 |
| 5275 | 3646 for (octave_idx_type j = 0; j < nc; j++) |
| 458 | 3647 { |
| 2354 | 3648 bool real_only = column_is_real_only (j); |
| 3649 | |
| 5275 | 3650 octave_idx_type idx_i; |
| 4469 | 3651 |
| 3652 Complex tmp_max; | |
| 3653 | |
| 3654 double abs_max = octave_NaN; | |
| 3655 | |
| 3656 for (idx_i = 0; idx_i < nr; idx_i++) | |
| 3657 { | |
| 3658 tmp_max = elem (idx_i, j); | |
| 3659 | |
| 5389 | 3660 if (! xisnan (tmp_max)) |
| 4469 | 3661 { |
| 5315 | 3662 abs_max = real_only ? std::real (tmp_max) : std::abs (tmp_max); |
| 4469 | 3663 break; |
| 3664 } | |
| 3665 } | |
| 3666 | |
| 5275 | 3667 for (octave_idx_type i = idx_i+1; i < nr; i++) |
| 4469 | 3668 { |
| 3669 Complex tmp = elem (i, j); | |
| 3670 | |
| 5389 | 3671 if (xisnan (tmp)) |
| 4469 | 3672 continue; |
| 3673 | |
| 5315 | 3674 double abs_tmp = real_only ? std::real (tmp) : std::abs (tmp); |
| 4469 | 3675 |
| 3676 if (abs_tmp > abs_max) | |
| 3677 { | |
| 3678 idx_i = i; | |
| 3679 tmp_max = tmp; | |
| 3680 abs_max = abs_tmp; | |
| 3681 } | |
| 3682 } | |
| 3683 | |
| 5389 | 3684 if (xisnan (tmp_max)) |
| 4469 | 3685 { |
| 3686 result.elem (j) = Complex_NaN_result; | |
| 4587 | 3687 idx_arg.elem (j) = 0; |
| 4469 | 3688 } |
| 891 | 3689 else |
| 3690 { | |
| 4469 | 3691 result.elem (j) = tmp_max; |
| 4587 | 3692 idx_arg.elem (j) = idx_i; |
| 891 | 3693 } |
| 458 | 3694 } |
| 3695 } | |
| 3696 | |
| 3697 return result; | |
| 3698 } | |
| 3699 | |
| 3700 // i/o | |
| 3701 | |
| 3504 | 3702 std::ostream& |
| 3703 operator << (std::ostream& os, const ComplexMatrix& a) | |
| 458 | 3704 { |
| 5275 | 3705 for (octave_idx_type i = 0; i < a.rows (); i++) |
| 458 | 3706 { |
| 5275 | 3707 for (octave_idx_type j = 0; j < a.cols (); j++) |
| 4130 | 3708 { |
| 3709 os << " "; | |
| 3710 octave_write_complex (os, a.elem (i, j)); | |
| 3711 } | |
| 458 | 3712 os << "\n"; |
| 3713 } | |
| 3714 return os; | |
| 3715 } | |
| 3716 | |
| 3504 | 3717 std::istream& |
| 3718 operator >> (std::istream& is, ComplexMatrix& a) | |
| 458 | 3719 { |
| 5275 | 3720 octave_idx_type nr = a.rows (); |
| 3721 octave_idx_type nc = a.cols (); | |
| 458 | 3722 |
| 3723 if (nr < 1 || nc < 1) | |
| 3504 | 3724 is.clear (std::ios::badbit); |
| 458 | 3725 else |
| 3726 { | |
| 3727 Complex tmp; | |
| 5275 | 3728 for (octave_idx_type i = 0; i < nr; i++) |
| 3729 for (octave_idx_type j = 0; j < nc; j++) | |
| 458 | 3730 { |
| 4130 | 3731 tmp = octave_read_complex (is); |
| 458 | 3732 if (is) |
| 3733 a.elem (i, j) = tmp; | |
| 3734 else | |
| 2993 | 3735 goto done; |
| 458 | 3736 } |
| 3737 } | |
| 3738 | |
| 2993 | 3739 done: |
| 3740 | |
| 458 | 3741 return is; |
| 3742 } | |
| 3743 | |
| 1819 | 3744 ComplexMatrix |
| 3745 Givens (const Complex& x, const Complex& y) | |
| 3746 { | |
| 3747 double cc; | |
| 3748 Complex cs, temp_r; | |
| 3749 | |
| 3887 | 3750 F77_FUNC (zlartg, ZLARTG) (x, y, cc, cs, temp_r); |
| 1819 | 3751 |
| 3752 ComplexMatrix g (2, 2); | |
| 3753 | |
| 3754 g.elem (0, 0) = cc; | |
| 3755 g.elem (1, 1) = cc; | |
| 3756 g.elem (0, 1) = cs; | |
| 3757 g.elem (1, 0) = -conj (cs); | |
| 3758 | |
| 3759 return g; | |
| 3760 } | |
| 3761 | |
| 3762 ComplexMatrix | |
| 3763 Sylvester (const ComplexMatrix& a, const ComplexMatrix& b, | |
| 3764 const ComplexMatrix& c) | |
| 3765 { | |
| 3766 ComplexMatrix retval; | |
| 3767 | |
| 5775 | 3768 // FIXME -- need to check that a, b, and c are all the same |
| 1819 | 3769 // size. |
| 3770 | |
| 3771 // Compute Schur decompositions | |
| 3772 | |
| 3773 ComplexSCHUR as (a, "U"); | |
| 3774 ComplexSCHUR bs (b, "U"); | |
| 3775 | |
| 3776 // Transform c to new coordinates. | |
| 3777 | |
| 3778 ComplexMatrix ua = as.unitary_matrix (); | |
| 3779 ComplexMatrix sch_a = as.schur_matrix (); | |
| 3780 | |
| 3781 ComplexMatrix ub = bs.unitary_matrix (); | |
| 3782 ComplexMatrix sch_b = bs.schur_matrix (); | |
| 3783 | |
| 3784 ComplexMatrix cx = ua.hermitian () * c * ub; | |
| 3785 | |
| 3786 // Solve the sylvester equation, back-transform, and return the | |
| 3787 // solution. | |
| 3788 | |
| 5275 | 3789 octave_idx_type a_nr = a.rows (); |
| 3790 octave_idx_type b_nr = b.rows (); | |
| 1819 | 3791 |
| 3792 double scale; | |
| 5275 | 3793 octave_idx_type info; |
| 1950 | 3794 |
| 3795 Complex *pa = sch_a.fortran_vec (); | |
| 3796 Complex *pb = sch_b.fortran_vec (); | |
| 3797 Complex *px = cx.fortran_vec (); | |
| 1819 | 3798 |
| 4552 | 3799 F77_XFCN (ztrsyl, ZTRSYL, (F77_CONST_CHAR_ARG2 ("N", 1), |
| 3800 F77_CONST_CHAR_ARG2 ("N", 1), | |
| 3801 1, a_nr, b_nr, pa, a_nr, pb, | |
| 3802 b_nr, px, a_nr, scale, info | |
| 3803 F77_CHAR_ARG_LEN (1) | |
| 3804 F77_CHAR_ARG_LEN (1))); | |
| 1950 | 3805 |
|
7482
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
3806 // FIXME -- check info? |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
3807 |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
3808 retval = -ua * cx * ub.hermitian (); |
| 1819 | 3809 |
| 3810 return retval; | |
| 3811 } | |
| 3812 | |
| 2828 | 3813 ComplexMatrix |
| 3814 operator * (const ComplexMatrix& m, const Matrix& a) | |
| 3815 { | |
| 3816 ComplexMatrix tmp (a); | |
| 3817 return m * tmp; | |
| 3818 } | |
| 3819 | |
| 3820 ComplexMatrix | |
| 3821 operator * (const Matrix& m, const ComplexMatrix& a) | |
| 3822 { | |
| 3823 ComplexMatrix tmp (m); | |
| 3824 return tmp * a; | |
| 3825 } | |
| 3826 | |
| 6162 | 3827 /* Simple Dot Product, Matrix-Vector and Matrix-Matrix Unit tests |
| 3828 %!assert([1+i 2+i 3+i] * [ 4+i ; 5+i ; 6+i], 29+21i, 1e-14) | |
| 3829 %!assert([1+i 2+i ; 3+i 4+i ] * [5+i ; 6+i], [15 + 14i ; 37 + 18i], 1e-14) | |
| 3830 %!assert([1+i 2+i ; 3+i 4+i ] * [5+i 6+i ; 7+i 8+i], [17 + 15i 20 + 17i; 41 + 19i 48 + 21i], 1e-14) | |
| 3831 */ | |
| 3832 | |
| 3833 /* Test some simple identities | |
| 3834 %!shared M, cv, rv | |
| 3835 %! M = randn(10,10)+i*rand(10,10); | |
| 3836 %! cv = randn(10,1)+i*rand(10,1); | |
| 3837 %! rv = randn(1,10)+i*rand(1,10); | |
| 3838 %!assert([M*cv,M*cv],M*[cv,cv],1e-14) | |
| 3839 %!assert([rv*M;rv*M],[rv;rv]*M,1e-14) | |
| 3840 %!assert(2*rv*cv,[rv,rv]*[cv;cv],1e-14) | |
| 3841 */ | |
| 3842 | |
| 2828 | 3843 ComplexMatrix |
| 3844 operator * (const ComplexMatrix& m, const ComplexMatrix& a) | |
| 3845 { | |
| 3846 ComplexMatrix retval; | |
| 3847 | |
| 5275 | 3848 octave_idx_type nr = m.rows (); |
| 3849 octave_idx_type nc = m.cols (); | |
| 3850 | |
| 3851 octave_idx_type a_nr = a.rows (); | |
| 3852 octave_idx_type a_nc = a.cols (); | |
| 2828 | 3853 |
| 3854 if (nc != a_nr) | |
| 3855 gripe_nonconformant ("operator *", nr, nc, a_nr, a_nc); | |
| 3856 else | |
| 3857 { | |
| 3858 if (nr == 0 || nc == 0 || a_nc == 0) | |
| 3760 | 3859 retval.resize (nr, a_nc, 0.0); |
| 2828 | 3860 else |
| 3861 { | |
| 5275 | 3862 octave_idx_type ld = nr; |
| 3863 octave_idx_type lda = a.rows (); | |
| 2828 | 3864 |
| 3865 retval.resize (nr, a_nc); | |
| 3866 Complex *c = retval.fortran_vec (); | |
| 3867 | |
| 5983 | 3868 if (a_nc == 1) |
| 3869 { | |
| 3870 if (nr == 1) | |
| 3871 F77_FUNC (xzdotu, XZDOTU) (nc, m.data (), 1, a.data (), 1, *c); | |
| 3872 else | |
| 6390 | 3873 { |
| 3874 F77_XFCN (zgemv, ZGEMV, (F77_CONST_CHAR_ARG2 ("N", 1), | |
| 3875 nr, nc, 1.0, m.data (), ld, | |
| 3876 a.data (), 1, 0.0, c, 1 | |
| 3877 F77_CHAR_ARG_LEN (1))); | |
| 3878 } | |
| 5983 | 3879 } |
| 3880 else | |
| 6390 | 3881 { |
| 3882 F77_XFCN (zgemm, ZGEMM, (F77_CONST_CHAR_ARG2 ("N", 1), | |
| 3883 F77_CONST_CHAR_ARG2 ("N", 1), | |
| 3884 nr, a_nc, nc, 1.0, m.data (), | |
| 3885 ld, a.data (), lda, 0.0, c, nr | |
| 3886 F77_CHAR_ARG_LEN (1) | |
| 3887 F77_CHAR_ARG_LEN (1))); | |
| 3888 } | |
| 2828 | 3889 } |
| 3890 } | |
| 3891 | |
| 3892 return retval; | |
| 3893 } | |
| 3894 | |
| 5775 | 3895 // FIXME -- it would be nice to share code among the min/max |
| 4309 | 3896 // functions below. |
| 3897 | |
| 3898 #define EMPTY_RETURN_CHECK(T) \ | |
| 3899 if (nr == 0 || nc == 0) \ | |
| 3900 return T (nr, nc); | |
| 3901 | |
| 3902 ComplexMatrix | |
| 3903 min (const Complex& c, const ComplexMatrix& m) | |
| 3904 { | |
| 5275 | 3905 octave_idx_type nr = m.rows (); |
| 3906 octave_idx_type nc = m.columns (); | |
| 4309 | 3907 |
| 3908 EMPTY_RETURN_CHECK (ComplexMatrix); | |
| 3909 | |
| 3910 ComplexMatrix result (nr, nc); | |
| 3911 | |
| 5275 | 3912 for (octave_idx_type j = 0; j < nc; j++) |
| 3913 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3914 { |
| 3915 OCTAVE_QUIT; | |
| 3916 result (i, j) = xmin (c, m (i, j)); | |
| 3917 } | |
| 3918 | |
| 3919 return result; | |
| 3920 } | |
| 3921 | |
| 3922 ComplexMatrix | |
| 3923 min (const ComplexMatrix& m, const Complex& c) | |
| 3924 { | |
| 5275 | 3925 octave_idx_type nr = m.rows (); |
| 3926 octave_idx_type nc = m.columns (); | |
| 4309 | 3927 |
| 3928 EMPTY_RETURN_CHECK (ComplexMatrix); | |
| 3929 | |
| 3930 ComplexMatrix result (nr, nc); | |
| 3931 | |
| 5275 | 3932 for (octave_idx_type j = 0; j < nc; j++) |
| 3933 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3934 { |
| 3935 OCTAVE_QUIT; | |
| 3936 result (i, j) = xmin (m (i, j), c); | |
| 3937 } | |
| 3938 | |
| 3939 return result; | |
| 3940 } | |
| 3941 | |
| 3942 ComplexMatrix | |
| 3943 min (const ComplexMatrix& a, const ComplexMatrix& b) | |
| 3944 { | |
| 5275 | 3945 octave_idx_type nr = a.rows (); |
| 3946 octave_idx_type nc = a.columns (); | |
| 4309 | 3947 |
| 3948 if (nr != b.rows () || nc != b.columns ()) | |
| 3949 { | |
| 3950 (*current_liboctave_error_handler) | |
| 3951 ("two-arg min expecting args of same size"); | |
| 3952 return ComplexMatrix (); | |
| 3953 } | |
| 3954 | |
| 3955 EMPTY_RETURN_CHECK (ComplexMatrix); | |
| 3956 | |
| 3957 ComplexMatrix result (nr, nc); | |
| 3958 | |
| 5275 | 3959 for (octave_idx_type j = 0; j < nc; j++) |
| 4309 | 3960 { |
| 3961 int columns_are_real_only = 1; | |
| 5275 | 3962 for (octave_idx_type i = 0; i < nr; i++) |
| 4309 | 3963 { |
| 3964 OCTAVE_QUIT; | |
| 5315 | 3965 if (std::imag (a (i, j)) != 0.0 || std::imag (b (i, j)) != 0.0) |
| 4309 | 3966 { |
| 3967 columns_are_real_only = 0; | |
| 3968 break; | |
| 3969 } | |
| 3970 } | |
| 3971 | |
| 3972 if (columns_are_real_only) | |
| 3973 { | |
| 5275 | 3974 for (octave_idx_type i = 0; i < nr; i++) |
| 5315 | 3975 result (i, j) = xmin (std::real (a (i, j)), std::real (b (i, j))); |
| 4309 | 3976 } |
| 3977 else | |
| 3978 { | |
| 5275 | 3979 for (octave_idx_type i = 0; i < nr; i++) |
| 4309 | 3980 { |
| 3981 OCTAVE_QUIT; | |
| 3982 result (i, j) = xmin (a (i, j), b (i, j)); | |
| 3983 } | |
| 3984 } | |
| 3985 } | |
| 3986 | |
| 3987 return result; | |
| 3988 } | |
| 3989 | |
| 3990 ComplexMatrix | |
| 3991 max (const Complex& c, const ComplexMatrix& m) | |
| 3992 { | |
| 5275 | 3993 octave_idx_type nr = m.rows (); |
| 3994 octave_idx_type nc = m.columns (); | |
| 4309 | 3995 |
| 3996 EMPTY_RETURN_CHECK (ComplexMatrix); | |
| 3997 | |
| 3998 ComplexMatrix result (nr, nc); | |
| 3999 | |
| 5275 | 4000 for (octave_idx_type j = 0; j < nc; j++) |
| 4001 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 4002 { |
| 4003 OCTAVE_QUIT; | |
| 4004 result (i, j) = xmax (c, m (i, j)); | |
| 4005 } | |
| 4006 | |
| 4007 return result; | |
| 4008 } | |
| 4009 | |
| 4010 ComplexMatrix | |
| 4011 max (const ComplexMatrix& m, const Complex& c) | |
| 4012 { | |
| 5275 | 4013 octave_idx_type nr = m.rows (); |
| 4014 octave_idx_type nc = m.columns (); | |
| 4309 | 4015 |
| 4016 EMPTY_RETURN_CHECK (ComplexMatrix); | |
| 4017 | |
| 4018 ComplexMatrix result (nr, nc); | |
| 4019 | |
| 5275 | 4020 for (octave_idx_type j = 0; j < nc; j++) |
| 4021 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 4022 { |
| 4023 OCTAVE_QUIT; | |
| 4024 result (i, j) = xmax (m (i, j), c); | |
| 4025 } | |
| 4026 | |
| 4027 return result; | |
| 4028 } | |
| 4029 | |
| 4030 ComplexMatrix | |
| 4031 max (const ComplexMatrix& a, const ComplexMatrix& b) | |
| 4032 { | |
| 5275 | 4033 octave_idx_type nr = a.rows (); |
| 4034 octave_idx_type nc = a.columns (); | |
| 4309 | 4035 |
| 4036 if (nr != b.rows () || nc != b.columns ()) | |
| 4037 { | |
| 4038 (*current_liboctave_error_handler) | |
| 4039 ("two-arg max expecting args of same size"); | |
| 4040 return ComplexMatrix (); | |
| 4041 } | |
| 4042 | |
| 4043 EMPTY_RETURN_CHECK (ComplexMatrix); | |
| 4044 | |
| 4045 ComplexMatrix result (nr, nc); | |
| 4046 | |
| 5275 | 4047 for (octave_idx_type j = 0; j < nc; j++) |
| 4309 | 4048 { |
| 4049 int columns_are_real_only = 1; | |
| 5275 | 4050 for (octave_idx_type i = 0; i < nr; i++) |
| 4309 | 4051 { |
| 4052 OCTAVE_QUIT; | |
| 5315 | 4053 if (std::imag (a (i, j)) != 0.0 || std::imag (b (i, j)) != 0.0) |
| 4309 | 4054 { |
| 4055 columns_are_real_only = 0; | |
| 4056 break; | |
| 4057 } | |
| 4058 } | |
| 4059 | |
| 4060 if (columns_are_real_only) | |
| 4061 { | |
| 5275 | 4062 for (octave_idx_type i = 0; i < nr; i++) |
| 4309 | 4063 { |
| 4064 OCTAVE_QUIT; | |
| 5315 | 4065 result (i, j) = xmax (std::real (a (i, j)), std::real (b (i, j))); |
| 4309 | 4066 } |
| 4067 } | |
| 4068 else | |
| 4069 { | |
| 5275 | 4070 for (octave_idx_type i = 0; i < nr; i++) |
| 4309 | 4071 { |
| 4072 OCTAVE_QUIT; | |
| 4073 result (i, j) = xmax (a (i, j), b (i, j)); | |
| 4074 } | |
| 4075 } | |
| 4076 } | |
| 4077 | |
| 4078 return result; | |
| 4079 } | |
| 4080 | |
| 5315 | 4081 MS_CMP_OPS(ComplexMatrix, std::real, Complex, std::real) |
| 3504 | 4082 MS_BOOL_OPS(ComplexMatrix, Complex, 0.0) |
| 2870 | 4083 |
| 5315 | 4084 SM_CMP_OPS(Complex, std::real, ComplexMatrix, std::real) |
| 3504 | 4085 SM_BOOL_OPS(Complex, ComplexMatrix, 0.0) |
| 2870 | 4086 |
| 5315 | 4087 MM_CMP_OPS(ComplexMatrix, std::real, ComplexMatrix, std::real) |
| 3504 | 4088 MM_BOOL_OPS(ComplexMatrix, ComplexMatrix, 0.0) |
| 2870 | 4089 |
| 458 | 4090 /* |
| 4091 ;;; Local Variables: *** | |
| 4092 ;;; mode: C++ *** | |
| 4093 ;;; End: *** | |
| 4094 */ |