Mercurial > octave-nkf
annotate liboctave/CMatrix.cc @ 7788:45f5faba05a2
Add the rcond function
| author | David Bateman <dbateman@free.fr> |
|---|---|
| date | Wed, 14 May 2008 18:09:56 +0200 |
| parents | 36594d5bbe13 |
| children | 82be108cc558 |
| 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; |
| 7788 | 986 double rcon; |
| 6207 | 987 MatrixType mattype (*this); |
| 7788 | 988 return inverse (mattype, info, rcon, 0, 0); |
| 6207 | 989 } |
| 990 | |
| 991 ComplexMatrix | |
| 6479 | 992 ComplexMatrix::inverse (octave_idx_type& info) const |
| 993 { | |
| 7788 | 994 double rcon; |
| 6479 | 995 MatrixType mattype (*this); |
| 7788 | 996 return inverse (mattype, info, rcon, 0, 0); |
| 6479 | 997 } |
| 998 | |
| 999 ComplexMatrix | |
| 7788 | 1000 ComplexMatrix::inverse (octave_idx_type& info, double& rcon, int force, |
| 6479 | 1001 int calc_cond) const |
| 1002 { | |
| 1003 MatrixType mattype (*this); | |
| 7788 | 1004 return inverse (mattype, info, rcon, force, calc_cond); |
| 6479 | 1005 } |
| 1006 | |
| 1007 ComplexMatrix | |
| 6207 | 1008 ComplexMatrix::inverse (MatrixType &mattype) const |
| 1009 { | |
| 1010 octave_idx_type info; | |
| 7788 | 1011 double rcon; |
| 1012 return inverse (mattype, info, rcon, 0, 0); | |
| 6207 | 1013 } |
| 1014 | |
| 1015 ComplexMatrix | |
| 1016 ComplexMatrix::inverse (MatrixType &mattype, octave_idx_type& info) const | |
| 1017 { | |
| 7788 | 1018 double rcon; |
| 1019 return inverse (mattype, info, rcon, 0, 0); | |
| 458 | 1020 } |
| 1021 | |
| 1022 ComplexMatrix | |
| 6207 | 1023 ComplexMatrix::tinverse (MatrixType &mattype, octave_idx_type& info, |
| 7788 | 1024 double& rcon, 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
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John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
1047 // Throw-away extra info LAPACK gives so as to not change output. |
| 7788 | 1048 rcon = 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), |
| 7788 | 1062 nr, tmp_data, nr, rcon, |
|
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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, |
| 7788 | 1081 double& rcon, 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. |
| 7788 | 1121 rcon = 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, |
| 7788 | 1133 rcon, 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, |
| 7788 | 1162 double& rcon, int force, int calc_cond) const |
| 6207 | 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) | |
| 7788 | 1171 ret = tinverse (mattype, info, rcon, 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) | |
| 7788 | 1180 rcon = chol.rcond(); |
| 6486 | 1181 else |
| 7788 | 1182 rcon = 1.0; |
| 6486 | 1183 ret = chol.inverse (); |
| 1184 } | |
| 6207 | 1185 else |
| 1186 mattype.mark_as_unsymmetric (); | |
| 1187 } | |
| 1188 | |
| 1189 if (!mattype.is_hermitian ()) | |
| 7788 | 1190 ret = finverse(mattype, info, rcon, force, calc_cond); |
| 1191 | |
| 1192 if ((mattype.is_hermitian () || calc_cond) && rcon == 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; |
| 7788 | 1556 double rcon; |
| 1557 return determinant (info, rcon, 0); | |
| 458 | 1558 } |
| 1559 | |
| 1560 ComplexDET | |
| 5275 | 1561 ComplexMatrix::determinant (octave_idx_type& info) const |
| 458 | 1562 { |
| 7788 | 1563 double rcon; |
| 1564 return determinant (info, rcon, 0); | |
| 458 | 1565 } |
| 1566 | |
| 1567 ComplexDET | |
| 7788 | 1568 ComplexMatrix::determinant (octave_idx_type& info, double& rcon, 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. |
| 7788 | 1597 rcon = 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, |
| 7788 | 1616 rcon, 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 | |
| 7788 | 1661 double |
| 1662 ComplexMatrix::rcond (void) const | |
| 1663 { | |
| 1664 MatrixType mattype (*this); | |
| 1665 return rcond (mattype); | |
| 1666 } | |
| 1667 | |
| 1668 double | |
| 1669 ComplexMatrix::rcond (MatrixType &mattype) const | |
| 1670 { | |
| 1671 double rcon; | |
| 1672 octave_idx_type nr = rows (); | |
| 1673 octave_idx_type nc = cols (); | |
| 1674 | |
| 1675 if (nr != nc) | |
| 1676 (*current_liboctave_error_handler) ("matrix must be square"); | |
| 1677 else if (nr == 0 || nc == 0) | |
| 1678 rcon = octave_Inf; | |
| 1679 else | |
| 1680 { | |
| 1681 int typ = mattype.type (); | |
| 1682 | |
| 1683 if (typ == MatrixType::Unknown) | |
| 1684 typ = mattype.type (*this); | |
| 1685 | |
| 1686 // Only calculate the condition number for LU/Cholesky | |
| 1687 if (typ == MatrixType::Upper) | |
| 1688 { | |
| 1689 const Complex *tmp_data = fortran_vec (); | |
| 1690 octave_idx_type info = 0; | |
| 1691 char norm = '1'; | |
| 1692 char uplo = 'U'; | |
| 1693 char dia = 'N'; | |
| 1694 | |
| 1695 Array<Complex> z (2 * nc); | |
| 1696 Complex *pz = z.fortran_vec (); | |
| 1697 Array<double> rz (nc); | |
| 1698 double *prz = rz.fortran_vec (); | |
| 1699 | |
| 1700 F77_XFCN (ztrcon, ZTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1701 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1702 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1703 nr, tmp_data, nr, rcon, | |
| 1704 pz, prz, info | |
| 1705 F77_CHAR_ARG_LEN (1) | |
| 1706 F77_CHAR_ARG_LEN (1) | |
| 1707 F77_CHAR_ARG_LEN (1))); | |
| 1708 | |
| 1709 if (info != 0) | |
| 1710 rcon = 0; | |
| 1711 } | |
| 1712 else if (typ == MatrixType::Permuted_Upper) | |
| 1713 (*current_liboctave_error_handler) | |
| 1714 ("permuted triangular matrix not implemented"); | |
| 1715 else if (typ == MatrixType::Lower) | |
| 1716 { | |
| 1717 const Complex *tmp_data = fortran_vec (); | |
| 1718 octave_idx_type info = 0; | |
| 1719 char norm = '1'; | |
| 1720 char uplo = 'L'; | |
| 1721 char dia = 'N'; | |
| 1722 | |
| 1723 Array<Complex> z (2 * nc); | |
| 1724 Complex *pz = z.fortran_vec (); | |
| 1725 Array<double> rz (nc); | |
| 1726 double *prz = rz.fortran_vec (); | |
| 1727 | |
| 1728 F77_XFCN (ztrcon, ZTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1729 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1730 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1731 nr, tmp_data, nr, rcon, | |
| 1732 pz, prz, info | |
| 1733 F77_CHAR_ARG_LEN (1) | |
| 1734 F77_CHAR_ARG_LEN (1) | |
| 1735 F77_CHAR_ARG_LEN (1))); | |
| 1736 | |
| 1737 if (info != 0) | |
| 1738 rcon = 0.0; | |
| 1739 } | |
| 1740 else if (typ == MatrixType::Permuted_Lower) | |
| 1741 (*current_liboctave_error_handler) | |
| 1742 ("permuted triangular matrix not implemented"); | |
| 1743 else if (typ == MatrixType::Full || typ == MatrixType::Hermitian) | |
| 1744 { | |
| 1745 double anorm = -1.0; | |
| 1746 ComplexMatrix atmp = *this; | |
| 1747 Complex *tmp_data = atmp.fortran_vec (); | |
| 1748 | |
| 1749 if (typ == MatrixType::Hermitian) | |
| 1750 { | |
| 1751 octave_idx_type info = 0; | |
| 1752 char job = 'L'; | |
| 1753 anorm = atmp.abs().sum(). | |
| 1754 row(static_cast<octave_idx_type>(0)).max(); | |
| 1755 | |
| 1756 F77_XFCN (zpotrf, ZPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, | |
| 1757 tmp_data, nr, info | |
| 1758 F77_CHAR_ARG_LEN (1))); | |
| 1759 | |
| 1760 if (info != 0) | |
| 1761 { | |
| 1762 rcon = 0.0; | |
| 1763 | |
| 1764 mattype.mark_as_unsymmetric (); | |
| 1765 typ = MatrixType::Full; | |
| 1766 } | |
| 1767 else | |
| 1768 { | |
| 1769 Array<Complex> z (2 * nc); | |
| 1770 Complex *pz = z.fortran_vec (); | |
| 1771 Array<double> rz (nc); | |
| 1772 double *prz = rz.fortran_vec (); | |
| 1773 | |
| 1774 F77_XFCN (zpocon, ZPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), | |
| 1775 nr, tmp_data, nr, anorm, | |
| 1776 rcon, pz, prz, info | |
| 1777 F77_CHAR_ARG_LEN (1))); | |
| 1778 | |
| 1779 if (info != 0) | |
| 1780 rcon = 0.0; | |
| 1781 } | |
| 1782 } | |
| 1783 | |
| 1784 | |
| 1785 if (typ == MatrixType::Full) | |
| 1786 { | |
| 1787 octave_idx_type info = 0; | |
| 1788 | |
| 1789 Array<octave_idx_type> ipvt (nr); | |
| 1790 octave_idx_type *pipvt = ipvt.fortran_vec (); | |
| 1791 | |
| 1792 if(anorm < 0.) | |
| 1793 anorm = atmp.abs().sum(). | |
| 1794 row(static_cast<octave_idx_type>(0)).max(); | |
| 1795 | |
| 1796 Array<Complex> z (2 * nc); | |
| 1797 Complex *pz = z.fortran_vec (); | |
| 1798 Array<double> rz (2 * nc); | |
| 1799 double *prz = rz.fortran_vec (); | |
| 1800 | |
| 1801 F77_XFCN (zgetrf, ZGETRF, (nr, nr, tmp_data, nr, pipvt, info)); | |
| 1802 | |
| 1803 if (info != 0) | |
| 1804 { | |
| 1805 rcon = 0.0; | |
| 1806 mattype.mark_as_rectangular (); | |
| 1807 } | |
| 1808 else | |
| 1809 { | |
| 1810 char job = '1'; | |
| 1811 F77_XFCN (zgecon, ZGECON, (F77_CONST_CHAR_ARG2 (&job, 1), | |
| 1812 nc, tmp_data, nr, anorm, | |
| 1813 rcon, pz, prz, info | |
| 1814 F77_CHAR_ARG_LEN (1))); | |
| 1815 | |
| 1816 if (info != 0) | |
| 1817 rcon = 0.0; | |
| 1818 } | |
| 1819 } | |
| 1820 } | |
| 1821 else | |
| 1822 rcon = 0.0; | |
| 1823 } | |
| 1824 | |
| 1825 return rcon; | |
| 1826 } | |
| 1827 | |
| 458 | 1828 ComplexMatrix |
| 5785 | 1829 ComplexMatrix::utsolve (MatrixType &mattype, const ComplexMatrix& b, |
| 7788 | 1830 octave_idx_type& info, double& rcon, |
| 5785 | 1831 solve_singularity_handler sing_handler, |
| 1832 bool calc_cond) const | |
| 1833 { | |
| 1834 ComplexMatrix retval; | |
| 1835 | |
| 1836 octave_idx_type nr = rows (); | |
| 1837 octave_idx_type nc = cols (); | |
| 1838 | |
| 6924 | 1839 if (nr != b.rows ()) |
| 5785 | 1840 (*current_liboctave_error_handler) |
| 1841 ("matrix dimension mismatch solution of linear equations"); | |
| 6924 | 1842 else if (nr == 0 || nc == 0 || b.cols () == 0) |
| 1843 retval = ComplexMatrix (nc, b.cols (), Complex (0.0, 0.0)); | |
| 5785 | 1844 else |
| 1845 { | |
| 1846 volatile int typ = mattype.type (); | |
| 1847 | |
| 1848 if (typ == MatrixType::Permuted_Upper || | |
| 1849 typ == MatrixType::Upper) | |
| 1850 { | |
| 1851 octave_idx_type b_nc = b.cols (); | |
| 7788 | 1852 rcon = 1.; |
| 5785 | 1853 info = 0; |
| 1854 | |
| 1855 if (typ == MatrixType::Permuted_Upper) | |
| 1856 { | |
| 1857 (*current_liboctave_error_handler) | |
| 6390 | 1858 ("permuted triangular matrix not implemented"); |
| 5785 | 1859 } |
| 1860 else | |
| 1861 { | |
| 1862 const Complex *tmp_data = fortran_vec (); | |
| 1863 | |
| 1864 if (calc_cond) | |
| 1865 { | |
| 1866 char norm = '1'; | |
| 1867 char uplo = 'U'; | |
| 1868 char dia = 'N'; | |
| 1869 | |
| 1870 Array<Complex> z (2 * nc); | |
| 1871 Complex *pz = z.fortran_vec (); | |
| 1872 Array<double> rz (nc); | |
| 1873 double *prz = rz.fortran_vec (); | |
| 1874 | |
| 1875 F77_XFCN (ztrcon, ZTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1876 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1877 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 7788 | 1878 nr, tmp_data, nr, rcon, |
| 5785 | 1879 pz, prz, info |
| 1880 F77_CHAR_ARG_LEN (1) | |
| 1881 F77_CHAR_ARG_LEN (1) | |
| 1882 F77_CHAR_ARG_LEN (1))); | |
| 1883 | |
| 1884 if (info != 0) | |
| 1885 info = -2; | |
| 1886 | |
| 7788 | 1887 volatile double rcond_plus_one = rcon + 1.0; |
| 1888 | |
| 1889 if (rcond_plus_one == 1.0 || xisnan (rcon)) | |
| 5785 | 1890 { |
| 1891 info = -2; | |
| 1892 | |
| 1893 if (sing_handler) | |
| 7788 | 1894 sing_handler (rcon); |
| 5785 | 1895 else |
| 1896 (*current_liboctave_error_handler) | |
| 1897 ("matrix singular to machine precision, rcond = %g", | |
| 7788 | 1898 rcon); |
| 5785 | 1899 } |
| 1900 } | |
| 1901 | |
| 1902 if (info == 0) | |
| 1903 { | |
| 1904 retval = b; | |
| 1905 Complex *result = retval.fortran_vec (); | |
| 1906 | |
| 1907 char uplo = 'U'; | |
| 1908 char trans = 'N'; | |
| 1909 char dia = 'N'; | |
| 1910 | |
| 1911 F77_XFCN (ztrtrs, ZTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1912 F77_CONST_CHAR_ARG2 (&trans, 1), | |
| 1913 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1914 nr, b_nc, tmp_data, nr, | |
| 1915 result, nr, info | |
| 1916 F77_CHAR_ARG_LEN (1) | |
| 1917 F77_CHAR_ARG_LEN (1) | |
| 1918 F77_CHAR_ARG_LEN (1))); | |
| 1919 } | |
| 1920 } | |
| 1921 } | |
| 1922 else | |
| 1923 (*current_liboctave_error_handler) ("incorrect matrix type"); | |
| 1924 } | |
| 1925 | |
| 1926 return retval; | |
| 1927 } | |
| 1928 | |
| 1929 ComplexMatrix | |
| 1930 ComplexMatrix::ltsolve (MatrixType &mattype, const ComplexMatrix& b, | |
| 7788 | 1931 octave_idx_type& info, double& rcon, |
| 5785 | 1932 solve_singularity_handler sing_handler, |
| 1933 bool calc_cond) const | |
| 1934 { | |
| 1935 ComplexMatrix retval; | |
| 1936 | |
| 1937 octave_idx_type nr = rows (); | |
| 1938 octave_idx_type nc = cols (); | |
| 1939 | |
| 6924 | 1940 if (nr != b.rows ()) |
| 5785 | 1941 (*current_liboctave_error_handler) |
| 1942 ("matrix dimension mismatch solution of linear equations"); | |
| 6924 | 1943 else if (nr == 0 || nc == 0 || b.cols () == 0) |
| 1944 retval = ComplexMatrix (nc, b.cols (), Complex (0.0, 0.0)); | |
| 5785 | 1945 else |
| 1946 { | |
| 1947 volatile int typ = mattype.type (); | |
| 1948 | |
| 1949 if (typ == MatrixType::Permuted_Lower || | |
| 1950 typ == MatrixType::Lower) | |
| 1951 { | |
| 1952 octave_idx_type b_nc = b.cols (); | |
| 7788 | 1953 rcon = 1.; |
| 5785 | 1954 info = 0; |
| 1955 | |
| 1956 if (typ == MatrixType::Permuted_Lower) | |
| 1957 { | |
| 1958 (*current_liboctave_error_handler) | |
| 6390 | 1959 ("permuted triangular matrix not implemented"); |
| 5785 | 1960 } |
| 1961 else | |
| 1962 { | |
| 1963 const Complex *tmp_data = fortran_vec (); | |
| 1964 | |
| 1965 if (calc_cond) | |
| 1966 { | |
| 1967 char norm = '1'; | |
| 1968 char uplo = 'L'; | |
| 1969 char dia = 'N'; | |
| 1970 | |
| 1971 Array<Complex> z (2 * nc); | |
| 1972 Complex *pz = z.fortran_vec (); | |
| 1973 Array<double> rz (nc); | |
| 1974 double *prz = rz.fortran_vec (); | |
| 1975 | |
| 1976 F77_XFCN (ztrcon, ZTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1977 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1978 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 7788 | 1979 nr, tmp_data, nr, rcon, |
| 5785 | 1980 pz, prz, info |
| 1981 F77_CHAR_ARG_LEN (1) | |
| 1982 F77_CHAR_ARG_LEN (1) | |
| 1983 F77_CHAR_ARG_LEN (1))); | |
| 1984 | |
| 1985 if (info != 0) | |
| 1986 info = -2; | |
| 1987 | |
| 7788 | 1988 volatile double rcond_plus_one = rcon + 1.0; |
| 1989 | |
| 1990 if (rcond_plus_one == 1.0 || xisnan (rcon)) | |
| 5785 | 1991 { |
| 1992 info = -2; | |
| 1993 | |
| 1994 if (sing_handler) | |
| 7788 | 1995 sing_handler (rcon); |
| 5785 | 1996 else |
| 1997 (*current_liboctave_error_handler) | |
| 1998 ("matrix singular to machine precision, rcond = %g", | |
| 7788 | 1999 rcon); |
| 5785 | 2000 } |
| 2001 } | |
| 2002 | |
| 2003 if (info == 0) | |
| 2004 { | |
| 2005 retval = b; | |
| 2006 Complex *result = retval.fortran_vec (); | |
| 2007 | |
| 2008 char uplo = 'L'; | |
| 2009 char trans = 'N'; | |
| 2010 char dia = 'N'; | |
| 2011 | |
| 2012 F77_XFCN (ztrtrs, ZTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 2013 F77_CONST_CHAR_ARG2 (&trans, 1), | |
| 2014 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 2015 nr, b_nc, tmp_data, nr, | |
| 2016 result, nr, info | |
| 2017 F77_CHAR_ARG_LEN (1) | |
| 2018 F77_CHAR_ARG_LEN (1) | |
| 2019 F77_CHAR_ARG_LEN (1))); | |
| 2020 } | |
| 2021 } | |
| 2022 } | |
| 2023 else | |
| 2024 (*current_liboctave_error_handler) ("incorrect matrix type"); | |
| 2025 } | |
| 2026 | |
| 2027 return retval; | |
| 2028 } | |
| 2029 | |
| 2030 ComplexMatrix | |
| 2031 ComplexMatrix::fsolve (MatrixType &mattype, const ComplexMatrix& b, | |
| 7788 | 2032 octave_idx_type& info, double& rcon, |
| 5785 | 2033 solve_singularity_handler sing_handler, |
| 2034 bool calc_cond) const | |
| 2035 { | |
| 2036 ComplexMatrix retval; | |
| 2037 | |
| 2038 octave_idx_type nr = rows (); | |
| 2039 octave_idx_type nc = cols (); | |
| 2040 | |
| 6924 | 2041 |
| 2042 if (nr != nc || nr != b.rows ()) | |
| 5785 | 2043 (*current_liboctave_error_handler) |
| 6924 | 2044 ("matrix dimension mismatch solution of linear equations"); |
| 2045 else if (nr == 0 || b.cols () == 0) | |
| 2046 retval = ComplexMatrix (nc, b.cols (), Complex (0.0, 0.0)); | |
| 5785 | 2047 else |
| 2048 { | |
| 2049 volatile int typ = mattype.type (); | |
| 2050 | |
| 2051 // Calculate the norm of the matrix, for later use. | |
| 2052 double anorm = -1.; | |
| 2053 | |
| 2054 if (typ == MatrixType::Hermitian) | |
| 2055 { | |
| 2056 info = 0; | |
| 2057 char job = 'L'; | |
| 2058 ComplexMatrix atmp = *this; | |
| 2059 Complex *tmp_data = atmp.fortran_vec (); | |
| 2060 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); | |
| 2061 | |
| 2062 F77_XFCN (zpotrf, ZPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, | |
| 2063 tmp_data, nr, info | |
| 2064 F77_CHAR_ARG_LEN (1))); | |
| 2065 | |
|
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|
2066 // Throw-away extra info LAPACK gives so as to not change output. |
| 7788 | 2067 rcon = 0.0; |
|
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|
2068 if (info != 0) |
|
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|
2069 { |
|
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|
2070 info = -2; |
|
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|
2071 |
|
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|
2072 mattype.mark_as_unsymmetric (); |
|
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2073 typ = MatrixType::Full; |
|
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|
2074 } |
|
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|
2075 else |
| 5785 | 2076 { |
|
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|
2077 if (calc_cond) |
| 5785 | 2078 { |
|
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|
2079 Array<Complex> z (2 * nc); |
|
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2080 Complex *pz = z.fortran_vec (); |
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2081 Array<double> rz (nc); |
|
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|
2082 double *prz = rz.fortran_vec (); |
|
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|
2083 |
|
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|
2084 F77_XFCN (zpocon, ZPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
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|
2085 nr, tmp_data, nr, anorm, |
| 7788 | 2086 rcon, pz, prz, info |
|
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|
2087 F77_CHAR_ARG_LEN (1))); |
|
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|
2088 |
|
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|
2089 if (info != 0) |
|
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|
2090 info = -2; |
|
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|
2091 |
| 7788 | 2092 volatile double rcond_plus_one = rcon + 1.0; |
| 2093 | |
| 2094 if (rcond_plus_one == 1.0 || xisnan (rcon)) | |
|
7482
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|
2095 { |
|
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|
2096 info = -2; |
|
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|
2097 |
|
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|
2098 if (sing_handler) |
| 7788 | 2099 sing_handler (rcon); |
|
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|
2100 else |
|
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|
2101 (*current_liboctave_error_handler) |
|
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|
2102 ("matrix singular to machine precision, rcond = %g", |
| 7788 | 2103 rcon); |
|
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|
2104 } |
|
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|
2105 } |
|
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|
2106 |
|
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|
2107 if (info == 0) |
|
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|
2108 { |
|
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|
2109 retval = b; |
|
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|
2110 Complex *result = retval.fortran_vec (); |
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|
2111 |
|
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|
2112 octave_idx_type b_nc = b.cols (); |
|
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|
2113 |
|
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|
2114 F77_XFCN (zpotrs, ZPOTRS, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
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|
2115 nr, b_nc, tmp_data, nr, |
|
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|
2116 result, b.rows(), info |
|
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|
2117 F77_CHAR_ARG_LEN (1))); |
|
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|
2118 } |
|
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|
2119 else |
|
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|
2120 { |
| 5785 | 2121 mattype.mark_as_unsymmetric (); |
| 2122 typ = MatrixType::Full; | |
| 2123 } | |
| 2124 } | |
| 2125 } | |
| 2126 | |
| 2127 if (typ == MatrixType::Full) | |
| 2128 { | |
| 2129 info = 0; | |
| 2130 | |
| 2131 Array<octave_idx_type> ipvt (nr); | |
| 2132 octave_idx_type *pipvt = ipvt.fortran_vec (); | |
| 2133 | |
| 2134 ComplexMatrix atmp = *this; | |
| 2135 Complex *tmp_data = atmp.fortran_vec (); | |
| 2136 | |
| 2137 Array<Complex> z (2 * nc); | |
| 2138 Complex *pz = z.fortran_vec (); | |
| 2139 Array<double> rz (2 * nc); | |
| 2140 double *prz = rz.fortran_vec (); | |
| 2141 | |
| 2142 // Calculate the norm of the matrix, for later use. | |
| 2143 if (anorm < 0.) | |
| 2144 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); | |
| 2145 | |
| 2146 F77_XFCN (zgetrf, ZGETRF, (nr, nr, tmp_data, nr, pipvt, info)); | |
| 2147 | |
|
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|
2148 // Throw-away extra info LAPACK gives so as to not change output. |
| 7788 | 2149 rcon = 0.0; |
|
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|
2150 if (info != 0) |
|
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|
2151 { |
|
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|
2152 info = -2; |
|
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|
2153 |
|
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changeset
|
2154 if (sing_handler) |
| 7788 | 2155 sing_handler (rcon); |
|
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|
2156 else |
|
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|
2157 (*current_liboctave_error_handler) |
|
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changeset
|
2158 ("matrix singular to machine precision"); |
|
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diff
changeset
|
2159 |
|
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changeset
|
2160 mattype.mark_as_rectangular (); |
|
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|
2161 } |
|
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changeset
|
2162 else |
| 5785 | 2163 { |
|
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changeset
|
2164 if (calc_cond) |
| 5785 | 2165 { |
|
7482
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diff
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|
2166 // Now calculate the condition number for |
|
29980c6b8604
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|
2167 // non-singular matrix. |
|
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|
2168 char job = '1'; |
|
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changeset
|
2169 F77_XFCN (zgecon, ZGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
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diff
changeset
|
2170 nc, tmp_data, nr, anorm, |
| 7788 | 2171 rcon, pz, prz, info |
|
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|
2172 F77_CHAR_ARG_LEN (1))); |
|
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diff
changeset
|
2173 |
|
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changeset
|
2174 if (info != 0) |
|
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diff
changeset
|
2175 info = -2; |
|
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|
2176 |
| 7788 | 2177 volatile double rcond_plus_one = rcon + 1.0; |
| 2178 | |
| 2179 if (rcond_plus_one == 1.0 || xisnan (rcon)) | |
| 5785 | 2180 { |
|
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diff
changeset
|
2181 info = -2; |
|
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changeset
|
2182 |
|
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changeset
|
2183 if (sing_handler) |
| 7788 | 2184 sing_handler (rcon); |
|
7482
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|
2185 else |
|
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parents:
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diff
changeset
|
2186 (*current_liboctave_error_handler) |
|
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diff
changeset
|
2187 ("matrix singular to machine precision, rcond = %g", |
| 7788 | 2188 rcon); |
| 5785 | 2189 } |
| 2190 } | |
|
7482
29980c6b8604
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diff
changeset
|
2191 |
|
29980c6b8604
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parents:
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diff
changeset
|
2192 if (info == 0) |
|
29980c6b8604
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diff
changeset
|
2193 { |
|
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diff
changeset
|
2194 retval = b; |
|
29980c6b8604
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diff
changeset
|
2195 Complex *result = retval.fortran_vec (); |
|
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diff
changeset
|
2196 |
|
29980c6b8604
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diff
changeset
|
2197 octave_idx_type b_nc = b.cols (); |
|
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diff
changeset
|
2198 |
|
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changeset
|
2199 char job = 'N'; |
|
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diff
changeset
|
2200 F77_XFCN (zgetrs, ZGETRS, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
29980c6b8604
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parents:
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diff
changeset
|
2201 nr, b_nc, tmp_data, nr, |
|
29980c6b8604
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parents:
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diff
changeset
|
2202 pipvt, result, b.rows(), info |
|
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parents:
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diff
changeset
|
2203 F77_CHAR_ARG_LEN (1))); |
|
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parents:
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diff
changeset
|
2204 } |
|
29980c6b8604
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parents:
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diff
changeset
|
2205 else |
|
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parents:
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diff
changeset
|
2206 mattype.mark_as_rectangular (); |
| 5785 | 2207 } |
| 2208 } | |
| 2209 } | |
| 2210 | |
| 2211 return retval; | |
| 2212 } | |
| 2213 | |
| 2214 ComplexMatrix | |
| 2215 ComplexMatrix::solve (MatrixType &typ, const Matrix& b) const | |
| 2216 { | |
| 2217 octave_idx_type info; | |
| 7788 | 2218 double rcon; |
| 2219 return solve (typ, b, info, rcon, 0); | |
| 5785 | 2220 } |
| 2221 | |
| 2222 ComplexMatrix | |
| 2223 ComplexMatrix::solve (MatrixType &typ, const Matrix& b, | |
| 2224 octave_idx_type& info) const | |
| 2225 { | |
| 7788 | 2226 double rcon; |
| 2227 return solve (typ, b, info, rcon, 0); | |
| 5785 | 2228 } |
| 2229 | |
| 2230 ComplexMatrix | |
| 2231 ComplexMatrix::solve (MatrixType &typ, const Matrix& b, octave_idx_type& info, | |
| 7788 | 2232 double& rcon) const |
| 5785 | 2233 { |
| 7788 | 2234 return solve (typ, b, info, rcon, 0); |
| 5785 | 2235 } |
| 2236 | |
| 2237 ComplexMatrix | |
| 2238 ComplexMatrix::solve (MatrixType &typ, const Matrix& b, octave_idx_type& info, | |
| 7788 | 2239 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 2240 bool singular_fallback) const |
| 2241 { | |
| 2242 ComplexMatrix tmp (b); | |
| 7788 | 2243 return solve (typ, tmp, info, rcon, sing_handler, singular_fallback); |
| 5785 | 2244 } |
| 2245 | |
| 2246 ComplexMatrix | |
| 2247 ComplexMatrix::solve (MatrixType &typ, const ComplexMatrix& b) const | |
| 2248 { | |
| 2249 octave_idx_type info; | |
| 7788 | 2250 double rcon; |
| 2251 return solve (typ, b, info, rcon, 0); | |
| 5785 | 2252 } |
| 2253 | |
| 2254 ComplexMatrix | |
| 2255 ComplexMatrix::solve (MatrixType &typ, const ComplexMatrix& b, | |
| 2256 octave_idx_type& info) const | |
| 2257 { | |
| 7788 | 2258 double rcon; |
| 2259 return solve (typ, b, info, rcon, 0); | |
| 5785 | 2260 } |
| 2261 | |
| 2262 ComplexMatrix | |
| 2263 ComplexMatrix::solve (MatrixType &typ, const ComplexMatrix& b, | |
| 7788 | 2264 octave_idx_type& info, double& rcon) const |
| 5785 | 2265 { |
| 7788 | 2266 return solve (typ, b, info, rcon, 0); |
| 5785 | 2267 } |
| 2268 | |
| 2269 ComplexMatrix | |
| 2270 ComplexMatrix::solve (MatrixType &mattype, const ComplexMatrix& b, | |
| 7788 | 2271 octave_idx_type& info, double& rcon, |
| 5785 | 2272 solve_singularity_handler sing_handler, |
| 2273 bool singular_fallback) const | |
| 2274 { | |
| 2275 ComplexMatrix retval; | |
| 2276 int typ = mattype.type (); | |
| 2277 | |
| 2278 if (typ == MatrixType::Unknown) | |
| 2279 typ = mattype.type (*this); | |
| 2280 | |
| 2281 // Only calculate the condition number for LU/Cholesky | |
| 2282 if (typ == MatrixType::Upper || typ == MatrixType::Permuted_Upper) | |
| 7788 | 2283 retval = utsolve (mattype, b, info, rcon, sing_handler, false); |
| 5785 | 2284 else if (typ == MatrixType::Lower || typ == MatrixType::Permuted_Lower) |
| 7788 | 2285 retval = ltsolve (mattype, b, info, rcon, sing_handler, false); |
| 5785 | 2286 else if (typ == MatrixType::Full || typ == MatrixType::Hermitian) |
| 7788 | 2287 retval = fsolve (mattype, b, info, rcon, sing_handler, true); |
| 5785 | 2288 else if (typ != MatrixType::Rectangular) |
| 2289 { | |
| 2290 (*current_liboctave_error_handler) ("unknown matrix type"); | |
| 2291 return ComplexMatrix (); | |
| 2292 } | |
| 2293 | |
| 2294 // Rectangular or one of the above solvers flags a singular matrix | |
| 2295 if (singular_fallback && mattype.type () == MatrixType::Rectangular) | |
| 2296 { | |
| 2297 octave_idx_type rank; | |
| 7788 | 2298 retval = lssolve (b, info, rank, rcon); |
| 5785 | 2299 } |
| 2300 | |
| 2301 return retval; | |
| 2302 } | |
| 2303 | |
| 2304 ComplexColumnVector | |
| 2305 ComplexMatrix::solve (MatrixType &typ, const ColumnVector& b) const | |
| 2306 { | |
| 2307 octave_idx_type info; | |
| 7788 | 2308 double rcon; |
| 2309 return solve (typ, ComplexColumnVector (b), info, rcon, 0); | |
| 5785 | 2310 } |
| 2311 | |
| 2312 ComplexColumnVector | |
| 2313 ComplexMatrix::solve (MatrixType &typ, const ColumnVector& b, | |
| 2314 octave_idx_type& info) const | |
| 2315 { | |
| 7788 | 2316 double rcon; |
| 2317 return solve (typ, ComplexColumnVector (b), info, rcon, 0); | |
| 5785 | 2318 } |
| 2319 | |
| 2320 ComplexColumnVector | |
| 2321 ComplexMatrix::solve (MatrixType &typ, const ColumnVector& b, | |
| 7788 | 2322 octave_idx_type& info, double& rcon) const |
| 5785 | 2323 { |
| 7788 | 2324 return solve (typ, ComplexColumnVector (b), info, rcon, 0); |
| 5785 | 2325 } |
| 2326 | |
| 2327 ComplexColumnVector | |
| 2328 ComplexMatrix::solve (MatrixType &typ, const ColumnVector& b, | |
| 7788 | 2329 octave_idx_type& info, double& rcon, |
| 5785 | 2330 solve_singularity_handler sing_handler) const |
| 2331 { | |
| 7788 | 2332 return solve (typ, ComplexColumnVector (b), info, rcon, sing_handler); |
| 5785 | 2333 } |
| 2334 | |
| 2335 ComplexColumnVector | |
| 2336 ComplexMatrix::solve (MatrixType &typ, const ComplexColumnVector& b) const | |
| 2337 { | |
| 2338 octave_idx_type info; | |
| 7788 | 2339 double rcon; |
| 2340 return solve (typ, b, info, rcon, 0); | |
| 5785 | 2341 } |
| 2342 | |
| 2343 ComplexColumnVector | |
| 2344 ComplexMatrix::solve (MatrixType &typ, const ComplexColumnVector& b, | |
| 2345 octave_idx_type& info) const | |
| 2346 { | |
| 7788 | 2347 double rcon; |
| 2348 return solve (typ, b, info, rcon, 0); | |
| 5785 | 2349 } |
| 2350 | |
| 2351 ComplexColumnVector | |
| 2352 ComplexMatrix::solve (MatrixType &typ, const ComplexColumnVector& b, | |
| 7788 | 2353 octave_idx_type& info, double& rcon) const |
| 5785 | 2354 { |
| 7788 | 2355 return solve (typ, b, info, rcon, 0); |
| 5785 | 2356 } |
| 2357 | |
| 2358 ComplexColumnVector | |
| 2359 ComplexMatrix::solve (MatrixType &typ, const ComplexColumnVector& b, | |
| 7788 | 2360 octave_idx_type& info, double& rcon, |
| 5785 | 2361 solve_singularity_handler sing_handler) const |
| 2362 { | |
| 2363 | |
| 2364 ComplexMatrix tmp (b); | |
| 7788 | 2365 return solve (typ, tmp, info, rcon, sing_handler).column(static_cast<octave_idx_type> (0)); |
| 5785 | 2366 } |
| 2367 | |
| 2368 ComplexMatrix | |
| 458 | 2369 ComplexMatrix::solve (const Matrix& b) const |
| 2370 { | |
| 5275 | 2371 octave_idx_type info; |
| 7788 | 2372 double rcon; |
| 2373 return solve (b, info, rcon, 0); | |
| 458 | 2374 } |
| 2375 | |
| 2376 ComplexMatrix | |
| 5275 | 2377 ComplexMatrix::solve (const Matrix& b, octave_idx_type& info) const |
| 458 | 2378 { |
| 7788 | 2379 double rcon; |
| 2380 return solve (b, info, rcon, 0); | |
| 458 | 2381 } |
| 2382 | |
| 2383 ComplexMatrix | |
| 7788 | 2384 ComplexMatrix::solve (const Matrix& b, octave_idx_type& info, double& rcon) const |
| 458 | 2385 { |
| 7788 | 2386 return solve (b, info, rcon, 0); |
| 3480 | 2387 } |
| 2388 | |
| 2389 ComplexMatrix | |
| 7788 | 2390 ComplexMatrix::solve (const Matrix& b, octave_idx_type& info, double& rcon, |
| 3480 | 2391 solve_singularity_handler sing_handler) const |
| 2392 { | |
| 458 | 2393 ComplexMatrix tmp (b); |
| 7788 | 2394 return solve (tmp, info, rcon, sing_handler); |
| 458 | 2395 } |
| 2396 | |
| 2397 ComplexMatrix | |
| 2398 ComplexMatrix::solve (const ComplexMatrix& b) const | |
| 2399 { | |
| 5275 | 2400 octave_idx_type info; |
| 7788 | 2401 double rcon; |
| 2402 return solve (b, info, rcon, 0); | |
| 458 | 2403 } |
| 2404 | |
| 2405 ComplexMatrix | |
| 5275 | 2406 ComplexMatrix::solve (const ComplexMatrix& b, octave_idx_type& info) const |
| 458 | 2407 { |
| 7788 | 2408 double rcon; |
| 2409 return solve (b, info, rcon, 0); | |
| 458 | 2410 } |
| 3480 | 2411 |
| 458 | 2412 ComplexMatrix |
| 7788 | 2413 ComplexMatrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcon) const |
| 458 | 2414 { |
| 7788 | 2415 return solve (b, info, rcon, 0); |
| 3480 | 2416 } |
| 2417 | |
| 2418 ComplexMatrix | |
| 7788 | 2419 ComplexMatrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcon, |
| 3480 | 2420 solve_singularity_handler sing_handler) const |
| 2421 { | |
| 5785 | 2422 MatrixType mattype (*this); |
| 7788 | 2423 return solve (mattype, b, info, rcon, sing_handler); |
| 458 | 2424 } |
| 2425 | |
| 2426 ComplexColumnVector | |
| 3585 | 2427 ComplexMatrix::solve (const ColumnVector& b) const |
| 2428 { | |
| 5275 | 2429 octave_idx_type info; |
| 7788 | 2430 double rcon; |
| 2431 return solve (ComplexColumnVector (b), info, rcon, 0); | |
| 3585 | 2432 } |
| 2433 | |
| 2434 ComplexColumnVector | |
| 5275 | 2435 ComplexMatrix::solve (const ColumnVector& b, octave_idx_type& info) const |
| 3585 | 2436 { |
| 7788 | 2437 double rcon; |
| 2438 return solve (ComplexColumnVector (b), info, rcon, 0); | |
| 3585 | 2439 } |
| 2440 | |
| 2441 ComplexColumnVector | |
| 5785 | 2442 ComplexMatrix::solve (const ColumnVector& b, octave_idx_type& info, |
| 7788 | 2443 double& rcon) const |
| 3585 | 2444 { |
| 7788 | 2445 return solve (ComplexColumnVector (b), info, rcon, 0); |
| 3585 | 2446 } |
| 2447 | |
| 2448 ComplexColumnVector | |
| 5785 | 2449 ComplexMatrix::solve (const ColumnVector& b, octave_idx_type& info, |
| 7788 | 2450 double& rcon, |
| 3585 | 2451 solve_singularity_handler sing_handler) const |
| 2452 { | |
| 7788 | 2453 return solve (ComplexColumnVector (b), info, rcon, sing_handler); |
| 3585 | 2454 } |
| 2455 | |
| 2456 ComplexColumnVector | |
| 458 | 2457 ComplexMatrix::solve (const ComplexColumnVector& b) const |
| 2458 { | |
| 5275 | 2459 octave_idx_type info; |
| 7788 | 2460 double rcon; |
| 2461 return solve (b, info, rcon, 0); | |
| 458 | 2462 } |
| 2463 | |
| 2464 ComplexColumnVector | |
| 5275 | 2465 ComplexMatrix::solve (const ComplexColumnVector& b, octave_idx_type& info) const |
| 458 | 2466 { |
| 7788 | 2467 double rcon; |
| 2468 return solve (b, info, rcon, 0); | |
| 458 | 2469 } |
| 2470 | |
| 2471 ComplexColumnVector | |
| 5275 | 2472 ComplexMatrix::solve (const ComplexColumnVector& b, octave_idx_type& info, |
| 7788 | 2473 double& rcon) const |
| 458 | 2474 { |
| 7788 | 2475 return solve (b, info, rcon, 0); |
| 3480 | 2476 } |
| 2477 | |
| 2478 ComplexColumnVector | |
| 5275 | 2479 ComplexMatrix::solve (const ComplexColumnVector& b, octave_idx_type& info, |
| 7788 | 2480 double& rcon, |
| 3480 | 2481 solve_singularity_handler sing_handler) const |
| 2482 { | |
| 5785 | 2483 MatrixType mattype (*this); |
| 7788 | 2484 return solve (mattype, b, info, rcon, sing_handler); |
| 458 | 2485 } |
| 2486 | |
| 2487 ComplexMatrix | |
| 3585 | 2488 ComplexMatrix::lssolve (const Matrix& b) const |
| 2489 { | |
| 5275 | 2490 octave_idx_type info; |
| 2491 octave_idx_type rank; | |
| 7788 | 2492 double rcon; |
| 2493 return lssolve (ComplexMatrix (b), info, rank, rcon); | |
| 3585 | 2494 } |
| 2495 | |
| 2496 ComplexMatrix | |
| 5275 | 2497 ComplexMatrix::lssolve (const Matrix& b, octave_idx_type& info) const |
| 3585 | 2498 { |
| 5275 | 2499 octave_idx_type rank; |
| 7788 | 2500 double rcon; |
| 2501 return lssolve (ComplexMatrix (b), info, rank, rcon); | |
| 3585 | 2502 } |
| 2503 | |
| 2504 ComplexMatrix | |
| 7076 | 2505 ComplexMatrix::lssolve (const Matrix& b, octave_idx_type& info, |
| 2506 octave_idx_type& rank) const | |
| 3585 | 2507 { |
| 7788 | 2508 double rcon; |
| 2509 return lssolve (ComplexMatrix (b), info, rank, rcon); | |
| 7076 | 2510 } |
| 2511 | |
| 2512 ComplexMatrix | |
| 2513 ComplexMatrix::lssolve (const Matrix& b, octave_idx_type& info, | |
| 7788 | 2514 octave_idx_type& rank, double& rcon) const |
| 7076 | 2515 { |
| 7788 | 2516 return lssolve (ComplexMatrix (b), info, rank, rcon); |
| 3585 | 2517 } |
| 2518 | |
| 2519 ComplexMatrix | |
| 458 | 2520 ComplexMatrix::lssolve (const ComplexMatrix& b) const |
| 2521 { | |
| 5275 | 2522 octave_idx_type info; |
| 2523 octave_idx_type rank; | |
| 7788 | 2524 double rcon; |
| 2525 return lssolve (b, info, rank, rcon); | |
| 458 | 2526 } |
| 2527 | |
| 2528 ComplexMatrix | |
| 5275 | 2529 ComplexMatrix::lssolve (const ComplexMatrix& b, octave_idx_type& info) const |
| 458 | 2530 { |
| 5275 | 2531 octave_idx_type rank; |
| 7788 | 2532 double rcon; |
| 2533 return lssolve (b, info, rank, rcon); | |
| 458 | 2534 } |
| 2535 | |
| 2536 ComplexMatrix | |
| 7076 | 2537 ComplexMatrix::lssolve (const ComplexMatrix& b, octave_idx_type& info, |
| 2538 octave_idx_type& rank) const | |
| 2539 { | |
| 7788 | 2540 double rcon; |
| 2541 return lssolve (b, info, rank, rcon); | |
| 7076 | 2542 } |
| 2543 | |
| 2544 ComplexMatrix | |
| 2545 ComplexMatrix::lssolve (const ComplexMatrix& b, octave_idx_type& info, | |
| 7788 | 2546 octave_idx_type& rank, double& rcon) const |
| 458 | 2547 { |
| 1948 | 2548 ComplexMatrix retval; |
| 2549 | |
| 5275 | 2550 octave_idx_type nrhs = b.cols (); |
| 2551 | |
| 2552 octave_idx_type m = rows (); | |
| 2553 octave_idx_type n = cols (); | |
| 458 | 2554 |
| 6924 | 2555 if (m != b.rows ()) |
| 1948 | 2556 (*current_liboctave_error_handler) |
| 2557 ("matrix dimension mismatch solution of linear equations"); | |
| 6924 | 2558 else if (m== 0 || n == 0 || b.cols () == 0) |
| 2559 retval = ComplexMatrix (n, b.cols (), Complex (0.0, 0.0)); | |
| 1948 | 2560 else |
| 458 | 2561 { |
| 7072 | 2562 volatile octave_idx_type minmn = (m < n ? m : n); |
| 2563 octave_idx_type maxmn = m > n ? m : n; | |
| 7788 | 2564 rcon = -1.0; |
| 7072 | 2565 |
| 2566 if (m != n) | |
| 2567 { | |
| 2568 retval = ComplexMatrix (maxmn, nrhs); | |
| 2569 | |
| 2570 for (octave_idx_type j = 0; j < nrhs; j++) | |
| 2571 for (octave_idx_type i = 0; i < m; i++) | |
| 2572 retval.elem (i, j) = b.elem (i, j); | |
| 2573 } | |
| 2574 else | |
| 2575 retval = b; | |
| 2576 | |
| 1948 | 2577 ComplexMatrix atmp = *this; |
| 2578 Complex *tmp_data = atmp.fortran_vec (); | |
| 2579 | |
| 7072 | 2580 Complex *pretval = retval.fortran_vec (); |
| 2581 Array<double> s (minmn); | |
| 7071 | 2582 double *ps = s.fortran_vec (); |
| 2563 | 2583 |
| 7072 | 2584 // Ask ZGELSD what the dimension of WORK should be. |
| 5275 | 2585 octave_idx_type lwork = -1; |
| 3752 | 2586 |
| 2587 Array<Complex> work (1); | |
| 7079 | 2588 |
| 7477 | 2589 octave_idx_type smlsiz; |
| 2590 F77_FUNC (xilaenv, XILAENV) (9, F77_CONST_CHAR_ARG2 ("ZGELSD", 6), | |
| 2591 F77_CONST_CHAR_ARG2 (" ", 1), | |
| 7478 | 2592 0, 0, 0, 0, smlsiz |
| 7477 | 2593 F77_CHAR_ARG_LEN (6) |
| 7478 | 2594 F77_CHAR_ARG_LEN (1)); |
| 7079 | 2595 |
|
7486
6a6d2abe51ff
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changeset
|
2596 octave_idx_type mnthr; |
|
6a6d2abe51ff
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diff
changeset
|
2597 F77_FUNC (xilaenv, XILAENV) (6, F77_CONST_CHAR_ARG2 ("ZGELSD", 6), |
|
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2598 F77_CONST_CHAR_ARG2 (" ", 1), |
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2599 m, n, nrhs, -1, mnthr |
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2600 F77_CHAR_ARG_LEN (6) |
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2601 F77_CHAR_ARG_LEN (1)); |
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2602 |
| 7079 | 2603 // We compute the size of rwork and iwork because ZGELSD in |
| 2604 // older versions of LAPACK does not return them on a query | |
| 2605 // call. | |
| 7124 | 2606 double dminmn = static_cast<double> (minmn); |
| 2607 double dsmlsizp1 = static_cast<double> (smlsiz+1); | |
| 7079 | 2608 #if defined (HAVE_LOG2) |
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2609 double tmp = log2 (dminmn / dsmlsizp1); |
| 7079 | 2610 #else |
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2611 double tmp = log (dminmn / dsmlsizp1) / log (2.0); |
| 7079 | 2612 #endif |
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2613 octave_idx_type nlvl = static_cast<octave_idx_type> (tmp) + 1; |
| 7079 | 2614 if (nlvl < 0) |
| 2615 nlvl = 0; | |
| 2616 | |
| 2617 octave_idx_type lrwork = minmn*(10 + 2*smlsiz + 8*nlvl) | |
| 2618 + 3*smlsiz*nrhs + (smlsiz+1)*(smlsiz+1); | |
| 2619 if (lrwork < 1) | |
| 2620 lrwork = 1; | |
| 2621 Array<double> rwork (lrwork); | |
| 2622 double *prwork = rwork.fortran_vec (); | |
| 2623 | |
| 2624 octave_idx_type liwork = 3 * minmn * nlvl + 11 * minmn; | |
| 2625 if (liwork < 1) | |
| 2626 liwork = 1; | |
| 2627 Array<octave_idx_type> iwork (liwork); | |
| 2628 octave_idx_type* piwork = iwork.fortran_vec (); | |
| 7072 | 2629 |
| 2630 F77_XFCN (zgelsd, ZGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, | |
| 7788 | 2631 ps, rcon, rank, work.fortran_vec (), |
| 7079 | 2632 lwork, prwork, piwork, info)); |
| 1948 | 2633 |
| 7476 | 2634 // The workspace query is broken in at least LAPACK 3.0.0 |
|
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2635 // through 3.1.1 when n >= mnthr. The obtuse formula below |
|
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2636 // should provide sufficient workspace for ZGELSD to operate |
| 7476 | 2637 // efficiently. |
|
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|
2638 if (n >= mnthr) |
| 7476 | 2639 { |
| 2640 octave_idx_type addend = m; | |
| 2641 | |
| 2642 if (2*m-4 > addend) | |
| 2643 addend = 2*m-4; | |
| 2644 | |
| 2645 if (nrhs > addend) | |
| 2646 addend = nrhs; | |
| 2647 | |
| 2648 if (n-3*m > addend) | |
| 2649 addend = n-3*m; | |
| 2650 | |
| 2651 const octave_idx_type lworkaround = 4*m + m*m + addend; | |
| 2652 | |
| 2653 if (std::real (work(0)) < lworkaround) | |
| 2654 work(0) = lworkaround; | |
| 2655 } | |
|
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2656 else if (m >= n) |
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|
2657 { |
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|
2658 octave_idx_type lworkaround = 2*m + m*nrhs; |
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|
2659 |
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|
2660 if (std::real (work(0)) < lworkaround) |
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2661 work(0) = lworkaround; |
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|
2662 } |
| 7476 | 2663 |
|
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2664 lwork = static_cast<octave_idx_type> (std::real (work(0))); |
|
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2665 work.resize (lwork); |
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|
2666 |
|
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|
2667 F77_XFCN (zgelsd, ZGELSD, (m, n, nrhs, tmp_data, m, pretval, |
| 7788 | 2668 maxmn, ps, rcon, rank, |
|
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|
2669 work.fortran_vec (), lwork, |
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|
2670 prwork, piwork, info)); |
|
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|
2671 |
|
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|
2672 if (rank < minmn) |
|
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|
2673 (*current_liboctave_warning_handler) |
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|
2674 ("zgelsd: rank deficient %dx%d matrix, rank = %d, tol = %e", |
| 7788 | 2675 m, n, rank, rcon); |
|
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|
2676 |
|
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|
2677 if (s.elem (0) == 0.0) |
| 7788 | 2678 rcon = 0.0; |
| 1948 | 2679 else |
| 7788 | 2680 rcon = s.elem (minmn - 1) / s.elem (0); |
|
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|
2681 |
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|
2682 retval.resize (n, nrhs); |
| 458 | 2683 } |
| 2684 | |
| 2685 return retval; | |
| 2686 } | |
| 2687 | |
| 2688 ComplexColumnVector | |
| 3585 | 2689 ComplexMatrix::lssolve (const ColumnVector& b) const |
| 2690 { | |
| 5275 | 2691 octave_idx_type info; |
| 2692 octave_idx_type rank; | |
| 7788 | 2693 double rcon; |
| 2694 return lssolve (ComplexColumnVector (b), info, rank, rcon); | |
| 3585 | 2695 } |
| 2696 | |
| 2697 ComplexColumnVector | |
| 5275 | 2698 ComplexMatrix::lssolve (const ColumnVector& b, octave_idx_type& info) const |
| 3585 | 2699 { |
| 5275 | 2700 octave_idx_type rank; |
| 7788 | 2701 double rcon; |
| 2702 return lssolve (ComplexColumnVector (b), info, rank, rcon); | |
| 3585 | 2703 } |
| 2704 | |
| 2705 ComplexColumnVector | |
| 7076 | 2706 ComplexMatrix::lssolve (const ColumnVector& b, octave_idx_type& info, |
| 2707 octave_idx_type& rank) const | |
| 3585 | 2708 { |
| 7788 | 2709 double rcon; |
| 2710 return lssolve (ComplexColumnVector (b), info, rank, rcon); | |
| 7076 | 2711 } |
| 2712 | |
| 2713 ComplexColumnVector | |
| 2714 ComplexMatrix::lssolve (const ColumnVector& b, octave_idx_type& info, | |
| 7788 | 2715 octave_idx_type& rank, double& rcon) const |
| 7076 | 2716 { |
| 7788 | 2717 return lssolve (ComplexColumnVector (b), info, rank, rcon); |
| 3585 | 2718 } |
| 2719 | |
| 2720 ComplexColumnVector | |
| 458 | 2721 ComplexMatrix::lssolve (const ComplexColumnVector& b) const |
| 2722 { | |
| 5275 | 2723 octave_idx_type info; |
| 2724 octave_idx_type rank; | |
| 7788 | 2725 double rcon; |
| 2726 return lssolve (b, info, rank, rcon); | |
| 458 | 2727 } |
| 2728 | |
| 2729 ComplexColumnVector | |
| 5275 | 2730 ComplexMatrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info) const |
| 458 | 2731 { |
| 5275 | 2732 octave_idx_type rank; |
| 7788 | 2733 double rcon; |
| 2734 return lssolve (b, info, rank, rcon); | |
| 458 | 2735 } |
| 2736 | |
| 2737 ComplexColumnVector | |
| 5275 | 2738 ComplexMatrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, |
| 2739 octave_idx_type& rank) const | |
| 458 | 2740 { |
| 7788 | 2741 double rcon; |
| 2742 return lssolve (b, info, rank, rcon); | |
| 7076 | 2743 |
| 2744 } | |
| 2745 | |
| 2746 ComplexColumnVector | |
| 2747 ComplexMatrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, | |
| 7788 | 2748 octave_idx_type& rank, double& rcon) const |
| 7076 | 2749 { |
| 1948 | 2750 ComplexColumnVector retval; |
| 2751 | |
| 5275 | 2752 octave_idx_type nrhs = 1; |
| 2753 | |
| 2754 octave_idx_type m = rows (); | |
| 2755 octave_idx_type n = cols (); | |
| 458 | 2756 |
| 6924 | 2757 if (m != b.length ()) |
| 1948 | 2758 (*current_liboctave_error_handler) |
| 6924 | 2759 ("matrix dimension mismatch solution of linear equations"); |
| 2760 else if (m == 0 || n == 0 || b.cols () == 0) | |
| 2761 retval = ComplexColumnVector (n, Complex (0.0, 0.0)); | |
| 1948 | 2762 else |
| 458 | 2763 { |
| 7072 | 2764 volatile octave_idx_type minmn = (m < n ? m : n); |
| 2765 octave_idx_type maxmn = m > n ? m : n; | |
| 7788 | 2766 rcon = -1.0; |
| 7072 | 2767 |
| 2768 if (m != n) | |
| 2769 { | |
| 2770 retval = ComplexColumnVector (maxmn); | |
| 2771 | |
| 2772 for (octave_idx_type i = 0; i < m; i++) | |
| 2773 retval.elem (i) = b.elem (i); | |
| 2774 } | |
| 2775 else | |
| 2776 retval = b; | |
| 2777 | |
| 1948 | 2778 ComplexMatrix atmp = *this; |
| 2779 Complex *tmp_data = atmp.fortran_vec (); | |
| 2780 | |
| 7072 | 2781 Complex *pretval = retval.fortran_vec (); |
| 2782 Array<double> s (minmn); | |
| 7071 | 2783 double *ps = s.fortran_vec (); |
| 1948 | 2784 |
| 7072 | 2785 // Ask ZGELSD what the dimension of WORK should be. |
| 5275 | 2786 octave_idx_type lwork = -1; |
| 3752 | 2787 |
| 2788 Array<Complex> work (1); | |
| 7079 | 2789 |
|
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2790 octave_idx_type smlsiz; |
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|
2791 F77_FUNC (xilaenv, XILAENV) (9, F77_CONST_CHAR_ARG2 ("ZGELSD", 6), |
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2792 F77_CONST_CHAR_ARG2 (" ", 1), |
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|
2793 0, 0, 0, 0, smlsiz |
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|
2794 F77_CHAR_ARG_LEN (6) |
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|
2795 F77_CHAR_ARG_LEN (1)); |
| 7079 | 2796 |
| 2797 // We compute the size of rwork and iwork because ZGELSD in | |
| 2798 // older versions of LAPACK does not return them on a query | |
| 2799 // call. | |
| 7124 | 2800 double dminmn = static_cast<double> (minmn); |
| 2801 double dsmlsizp1 = static_cast<double> (smlsiz+1); | |
| 7079 | 2802 #if defined (HAVE_LOG2) |
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2803 double tmp = log2 (dminmn / dsmlsizp1); |
| 7079 | 2804 #else |
|
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2805 double tmp = log (dminmn / dsmlsizp1) / log (2.0); |
| 7079 | 2806 #endif |
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2807 octave_idx_type nlvl = static_cast<octave_idx_type> (tmp) + 1; |
| 7079 | 2808 if (nlvl < 0) |
| 2809 nlvl = 0; | |
| 2810 | |
| 2811 octave_idx_type lrwork = minmn*(10 + 2*smlsiz + 8*nlvl) | |
| 2812 + 3*smlsiz*nrhs + (smlsiz+1)*(smlsiz+1); | |
| 2813 if (lrwork < 1) | |
| 2814 lrwork = 1; | |
| 2815 Array<double> rwork (lrwork); | |
| 2816 double *prwork = rwork.fortran_vec (); | |
| 2817 | |
| 2818 octave_idx_type liwork = 3 * minmn * nlvl + 11 * minmn; | |
| 2819 if (liwork < 1) | |
| 2820 liwork = 1; | |
| 2821 Array<octave_idx_type> iwork (liwork); | |
| 2822 octave_idx_type* piwork = iwork.fortran_vec (); | |
| 7072 | 2823 |
| 2824 F77_XFCN (zgelsd, ZGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, | |
| 7788 | 2825 ps, rcon, rank, work.fortran_vec (), |
| 7079 | 2826 lwork, prwork, piwork, info)); |
| 1948 | 2827 |
|
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2828 lwork = static_cast<octave_idx_type> (std::real (work(0))); |
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2829 work.resize (lwork); |
|
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2830 rwork.resize (static_cast<octave_idx_type> (rwork(0))); |
|
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2831 iwork.resize (iwork(0)); |
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|
2832 |
|
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|
2833 F77_XFCN (zgelsd, ZGELSD, (m, n, nrhs, tmp_data, m, pretval, |
| 7788 | 2834 maxmn, ps, rcon, rank, |
|
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2835 work.fortran_vec (), lwork, |
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|
2836 prwork, piwork, info)); |
|
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2837 |
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|
2838 if (rank < minmn) |
| 1948 | 2839 { |
|
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|
2840 if (rank < minmn) |
|
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|
2841 (*current_liboctave_warning_handler) |
|
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|
2842 ("zgelsd: rank deficient %dx%d matrix, rank = %d, tol = %e", |
| 7788 | 2843 m, n, rank, rcon); |
|
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|
2844 |
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|
2845 if (s.elem (0) == 0.0) |
| 7788 | 2846 rcon = 0.0; |
|
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|
2847 else |
| 7788 | 2848 rcon = s.elem (minmn - 1) / s.elem (0); |
|
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|
2849 |
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|
2850 retval.resize (n, nrhs); |
| 1948 | 2851 } |
| 458 | 2852 } |
| 2853 | |
| 2854 return retval; | |
| 2855 } | |
| 2856 | |
| 1819 | 2857 // Constants for matrix exponential calculation. |
| 2858 | |
| 2859 static double padec [] = | |
| 2860 { | |
| 2861 5.0000000000000000e-1, | |
| 2862 1.1666666666666667e-1, | |
| 2863 1.6666666666666667e-2, | |
| 2864 1.6025641025641026e-3, | |
| 2865 1.0683760683760684e-4, | |
| 2866 4.8562548562548563e-6, | |
| 2867 1.3875013875013875e-7, | |
| 2868 1.9270852604185938e-9, | |
| 2869 }; | |
| 2870 | |
| 7400 | 2871 static void |
| 7788 | 2872 solve_singularity_warning (double rcon) |
| 7400 | 2873 { |
| 2874 (*current_liboctave_warning_handler) | |
| 2875 ("singular matrix encountered in expm calculation, rcond = %g", | |
| 7788 | 2876 rcon); |
| 7400 | 2877 } |
| 2878 | |
| 1819 | 2879 ComplexMatrix |
| 2880 ComplexMatrix::expm (void) const | |
| 2881 { | |
| 2882 ComplexMatrix retval; | |
| 2883 | |
| 2884 ComplexMatrix m = *this; | |
| 2885 | |
| 5275 | 2886 octave_idx_type nc = columns (); |
| 1819 | 2887 |
| 3130 | 2888 // Preconditioning step 1: trace normalization to reduce dynamic |
| 2889 // range of poles, but avoid making stable eigenvalues unstable. | |
| 2890 | |
| 1819 | 2891 // trace shift value |
| 2892 Complex trshift = 0.0; | |
| 2893 | |
| 5275 | 2894 for (octave_idx_type i = 0; i < nc; i++) |
| 1819 | 2895 trshift += m.elem (i, i); |
| 2896 | |
| 2897 trshift /= nc; | |
| 2898 | |
| 3130 | 2899 if (trshift.real () < 0.0) |
| 6958 | 2900 { |
| 2901 trshift = trshift.imag (); | |
| 2902 if (trshift.real () > 709.0) | |
| 2903 trshift = 709.0; | |
| 2904 } | |
| 3130 | 2905 |
| 5275 | 2906 for (octave_idx_type i = 0; i < nc; i++) |
| 1819 | 2907 m.elem (i, i) -= trshift; |
| 2908 | |
| 2909 // Preconditioning step 2: eigenvalue balancing. | |
| 3331 | 2910 // code follows development in AEPBAL |
| 2911 | |
| 2912 Complex *mp = m.fortran_vec (); | |
| 3467 | 2913 |
| 5275 | 2914 octave_idx_type info, ilo, ihi,ilos,ihis; |
| 3468 | 2915 Array<double> dpermute (nc); |
| 2916 Array<double> dscale (nc); | |
| 2917 | |
| 5775 | 2918 // FIXME -- should pass job as a parameter in expm |
| 3468 | 2919 |
| 2920 // Permute first | |
| 2921 char job = 'P'; | |
| 4552 | 2922 F77_XFCN (zgebal, ZGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
| 2923 nc, mp, nc, ilo, ihi, | |
| 2924 dpermute.fortran_vec (), info | |
| 2925 F77_CHAR_ARG_LEN (1))); | |
| 3331 | 2926 |
| 3468 | 2927 // then scale |
| 2928 job = 'S'; | |
| 4552 | 2929 F77_XFCN (zgebal, ZGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
| 2930 nc, mp, nc, ilos, ihis, | |
| 2931 dscale.fortran_vec (), info | |
| 2932 F77_CHAR_ARG_LEN (1))); | |
| 3331 | 2933 |
| 1819 | 2934 // Preconditioning step 3: scaling. |
| 2935 | |
| 2936 ColumnVector work (nc); | |
| 3130 | 2937 double inf_norm; |
| 2938 | |
| 4552 | 2939 F77_XFCN (xzlange, XZLANGE, (F77_CONST_CHAR_ARG2 ("I", 1), |
| 2940 nc, nc, m.fortran_vec (), nc, | |
| 2941 work.fortran_vec (), inf_norm | |
| 2942 F77_CHAR_ARG_LEN (1))); | |
| 3331 | 2943 |
| 2800 | 2944 int sqpow = (inf_norm > 0.0 |
| 2945 ? static_cast<int> (1.0 + log (inf_norm) / log (2.0)) : 0); | |
| 1819 | 2946 |
| 2947 // Check whether we need to square at all. | |
| 2948 | |
| 2949 if (sqpow < 0) | |
| 2950 sqpow = 0; | |
| 2951 | |
| 2952 if (sqpow > 0) | |
| 2953 { | |
| 7400 | 2954 if (sqpow > 1023) |
| 2955 sqpow = 1023; | |
| 2956 | |
| 1819 | 2957 double scale_factor = 1.0; |
| 5275 | 2958 for (octave_idx_type i = 0; i < sqpow; i++) |
| 1819 | 2959 scale_factor *= 2.0; |
| 2960 | |
| 2961 m = m / scale_factor; | |
| 2962 } | |
| 2963 | |
| 2964 // npp, dpp: pade' approx polynomial matrices. | |
| 2965 | |
| 2966 ComplexMatrix npp (nc, nc, 0.0); | |
| 6958 | 2967 Complex *pnpp = npp.fortran_vec (); |
| 1819 | 2968 ComplexMatrix dpp = npp; |
| 6958 | 2969 Complex *pdpp = dpp.fortran_vec (); |
| 1819 | 2970 |
| 2971 // Now powers a^8 ... a^1. | |
| 2972 | |
| 2973 int minus_one_j = -1; | |
| 5275 | 2974 for (octave_idx_type j = 7; j >= 0; j--) |
| 1819 | 2975 { |
| 6958 | 2976 for (octave_idx_type i = 0; i < nc; i++) |
| 2977 { | |
| 2978 octave_idx_type k = i * nc + i; | |
| 7265 | 2979 pnpp[k] += padec[j]; |
| 2980 pdpp[k] += minus_one_j * padec[j]; | |
| 6958 | 2981 } |
| 7265 | 2982 |
| 6958 | 2983 npp = m * npp; |
| 7265 | 2984 pnpp = npp.fortran_vec (); |
| 2985 | |
| 6958 | 2986 dpp = m * dpp; |
| 7265 | 2987 pdpp = dpp.fortran_vec (); |
| 2988 | |
| 1819 | 2989 minus_one_j *= -1; |
| 2990 } | |
| 2991 | |
| 2992 // Zero power. | |
| 2993 | |
| 2994 dpp = -dpp; | |
| 5275 | 2995 for (octave_idx_type j = 0; j < nc; j++) |
| 1819 | 2996 { |
| 2997 npp.elem (j, j) += 1.0; | |
| 2998 dpp.elem (j, j) += 1.0; | |
| 2999 } | |
| 3000 | |
| 3001 // Compute pade approximation = inverse (dpp) * npp. | |
| 3002 | |
| 7788 | 3003 double rcon; |
| 3004 retval = dpp.solve (npp, info, rcon, solve_singularity_warning); | |
| 7400 | 3005 |
| 3006 if (info < 0) | |
| 3007 return retval; | |
| 3008 | |
| 1819 | 3009 // Reverse preconditioning step 3: repeated squaring. |
| 3010 | |
| 3011 while (sqpow) | |
| 3012 { | |
| 3013 retval = retval * retval; | |
| 3014 sqpow--; | |
| 3015 } | |
| 3016 | |
| 3017 // Reverse preconditioning step 2: inverse balancing. | |
| 3467 | 3018 // Done in two steps: inverse scaling, then inverse permutation |
| 3019 | |
| 3020 // inverse scaling (diagonal transformation) | |
| 5275 | 3021 for (octave_idx_type i = 0; i < nc; i++) |
| 3022 for (octave_idx_type j = 0; j < nc; j++) | |
| 3468 | 3023 retval(i,j) *= dscale(i) / dscale(j); |
| 3467 | 3024 |
| 4153 | 3025 OCTAVE_QUIT; |
| 3026 | |
| 3467 | 3027 // construct balancing permutation vector |
| 6867 | 3028 Array<octave_idx_type> iperm (nc); |
| 5275 | 3029 for (octave_idx_type i = 0; i < nc; i++) |
| 4593 | 3030 iperm(i) = i; // initialize to identity permutation |
| 3467 | 3031 |
| 3032 // leading permutations in forward order | |
| 5275 | 3033 for (octave_idx_type i = 0; i < (ilo-1); i++) |
| 3468 | 3034 { |
| 6867 | 3035 octave_idx_type swapidx = static_cast<octave_idx_type> (dpermute(i)) - 1; |
| 5275 | 3036 octave_idx_type tmp = iperm(i); |
| 4593 | 3037 iperm(i) = iperm(swapidx); |
| 3038 iperm(swapidx) = tmp; | |
| 3468 | 3039 } |
| 3467 | 3040 |
| 7416 | 3041 // construct inverse balancing permutation vector |
| 3042 Array<octave_idx_type> invpvec (nc); | |
| 3043 for (octave_idx_type i = 0; i < nc; i++) | |
| 3044 invpvec(iperm(i)) = i; // Thanks to R. A. Lippert for this method | |
| 3045 | |
| 3046 OCTAVE_QUIT; | |
| 3047 | |
| 3048 ComplexMatrix tmpMat = retval; | |
| 3049 for (octave_idx_type i = 0; i < nc; i++) | |
| 3050 for (octave_idx_type j = 0; j < nc; j++) | |
| 3051 retval(i,j) = tmpMat(invpvec(i),invpvec(j)); | |
| 3052 | |
| 3053 OCTAVE_QUIT; | |
| 3054 | |
| 3055 for (octave_idx_type i = 0; i < nc; i++) | |
| 3056 iperm(i) = i; // initialize to identity permutation | |
| 3057 | |
| 3467 | 3058 // trailing permutations must be done in reverse order |
| 5275 | 3059 for (octave_idx_type i = nc - 1; i >= ihi; i--) |
| 3468 | 3060 { |
| 6867 | 3061 octave_idx_type swapidx = static_cast<octave_idx_type> (dpermute(i)) - 1; |
| 5275 | 3062 octave_idx_type tmp = iperm(i); |
| 4593 | 3063 iperm(i) = iperm(swapidx); |
| 3064 iperm(swapidx) = tmp; | |
| 3468 | 3065 } |
| 3467 | 3066 |
| 3067 // construct inverse balancing permutation vector | |
| 5275 | 3068 for (octave_idx_type i = 0; i < nc; i++) |
| 4593 | 3069 invpvec(iperm(i)) = i; // Thanks to R. A. Lippert for this method |
| 3467 | 3070 |
| 4153 | 3071 OCTAVE_QUIT; |
| 3072 | |
| 7416 | 3073 tmpMat = retval; |
| 5275 | 3074 for (octave_idx_type i = 0; i < nc; i++) |
| 3075 for (octave_idx_type j = 0; j < nc; j++) | |
| 3468 | 3076 retval(i,j) = tmpMat(invpvec(i),invpvec(j)); |
| 1819 | 3077 |
| 3078 // Reverse preconditioning step 1: fix trace normalization. | |
| 3079 | |
| 3130 | 3080 return exp (trshift) * retval; |
| 1819 | 3081 } |
| 3082 | |
| 1205 | 3083 // column vector by row vector -> matrix operations |
| 3084 | |
| 3085 ComplexMatrix | |
| 3086 operator * (const ColumnVector& v, const ComplexRowVector& a) | |
| 3087 { | |
| 3088 ComplexColumnVector tmp (v); | |
| 3089 return tmp * a; | |
| 3090 } | |
| 3091 | |
| 3092 ComplexMatrix | |
| 3093 operator * (const ComplexColumnVector& a, const RowVector& b) | |
| 3094 { | |
| 3095 ComplexRowVector tmp (b); | |
| 3096 return a * tmp; | |
| 3097 } | |
| 3098 | |
| 3099 ComplexMatrix | |
| 3100 operator * (const ComplexColumnVector& v, const ComplexRowVector& a) | |
| 3101 { | |
| 1948 | 3102 ComplexMatrix retval; |
| 3103 | |
| 5275 | 3104 octave_idx_type len = v.length (); |
| 3233 | 3105 |
| 3106 if (len != 0) | |
| 1205 | 3107 { |
| 5275 | 3108 octave_idx_type a_len = a.length (); |
| 3233 | 3109 |
| 3110 retval.resize (len, a_len); | |
| 3111 Complex *c = retval.fortran_vec (); | |
| 3112 | |
| 4552 | 3113 F77_XFCN (zgemm, ZGEMM, (F77_CONST_CHAR_ARG2 ("N", 1), |
| 3114 F77_CONST_CHAR_ARG2 ("N", 1), | |
| 3115 len, a_len, 1, 1.0, v.data (), len, | |
| 3116 a.data (), 1, 0.0, c, len | |
| 3117 F77_CHAR_ARG_LEN (1) | |
| 3118 F77_CHAR_ARG_LEN (1))); | |
| 1205 | 3119 } |
| 3120 | |
| 1948 | 3121 return retval; |
| 1205 | 3122 } |
| 3123 | |
| 458 | 3124 // matrix by diagonal matrix -> matrix operations |
| 3125 | |
| 3126 ComplexMatrix& | |
| 3127 ComplexMatrix::operator += (const DiagMatrix& a) | |
| 3128 { | |
| 5275 | 3129 octave_idx_type nr = rows (); |
| 3130 octave_idx_type nc = cols (); | |
| 3131 | |
| 3132 octave_idx_type a_nr = rows (); | |
| 3133 octave_idx_type a_nc = cols (); | |
| 2384 | 3134 |
| 3135 if (nr != a_nr || nc != a_nc) | |
| 458 | 3136 { |
| 2384 | 3137 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
| 889 | 3138 return *this; |
| 458 | 3139 } |
| 3140 | |
| 5275 | 3141 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 3142 elem (i, i) += a.elem (i, i); |
| 3143 | |
| 3144 return *this; | |
| 3145 } | |
| 3146 | |
| 3147 ComplexMatrix& | |
| 3148 ComplexMatrix::operator -= (const DiagMatrix& a) | |
| 3149 { | |
| 5275 | 3150 octave_idx_type nr = rows (); |
| 3151 octave_idx_type nc = cols (); | |
| 3152 | |
| 3153 octave_idx_type a_nr = rows (); | |
| 3154 octave_idx_type a_nc = cols (); | |
| 2384 | 3155 |
| 3156 if (nr != a_nr || nc != a_nc) | |
| 458 | 3157 { |
| 2384 | 3158 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
| 889 | 3159 return *this; |
| 458 | 3160 } |
| 3161 | |
| 5275 | 3162 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 3163 elem (i, i) -= a.elem (i, i); |
| 3164 | |
| 3165 return *this; | |
| 3166 } | |
| 3167 | |
| 3168 ComplexMatrix& | |
| 3169 ComplexMatrix::operator += (const ComplexDiagMatrix& a) | |
| 3170 { | |
| 5275 | 3171 octave_idx_type nr = rows (); |
| 3172 octave_idx_type nc = cols (); | |
| 3173 | |
| 3174 octave_idx_type a_nr = rows (); | |
| 3175 octave_idx_type a_nc = cols (); | |
| 2384 | 3176 |
| 3177 if (nr != a_nr || nc != a_nc) | |
| 458 | 3178 { |
| 2384 | 3179 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
| 889 | 3180 return *this; |
| 458 | 3181 } |
| 3182 | |
| 5275 | 3183 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 3184 elem (i, i) += a.elem (i, i); |
| 3185 | |
| 3186 return *this; | |
| 3187 } | |
| 3188 | |
| 3189 ComplexMatrix& | |
| 3190 ComplexMatrix::operator -= (const ComplexDiagMatrix& a) | |
| 3191 { | |
| 5275 | 3192 octave_idx_type nr = rows (); |
| 3193 octave_idx_type nc = cols (); | |
| 3194 | |
| 3195 octave_idx_type a_nr = rows (); | |
| 3196 octave_idx_type a_nc = cols (); | |
| 2384 | 3197 |
| 3198 if (nr != a_nr || nc != a_nc) | |
| 458 | 3199 { |
| 2384 | 3200 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
| 889 | 3201 return *this; |
| 458 | 3202 } |
| 3203 | |
| 5275 | 3204 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 3205 elem (i, i) -= a.elem (i, i); |
| 3206 | |
| 3207 return *this; | |
| 3208 } | |
| 3209 | |
| 3210 // matrix by matrix -> matrix operations | |
| 3211 | |
| 3212 ComplexMatrix& | |
| 3213 ComplexMatrix::operator += (const Matrix& a) | |
| 3214 { | |
| 5275 | 3215 octave_idx_type nr = rows (); |
| 3216 octave_idx_type nc = cols (); | |
| 3217 | |
| 3218 octave_idx_type a_nr = a.rows (); | |
| 3219 octave_idx_type a_nc = a.cols (); | |
| 2384 | 3220 |
| 3221 if (nr != a_nr || nc != a_nc) | |
| 458 | 3222 { |
| 2384 | 3223 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
| 458 | 3224 return *this; |
| 3225 } | |
| 3226 | |
| 3227 if (nr == 0 || nc == 0) | |
| 3228 return *this; | |
| 3229 | |
| 3230 Complex *d = fortran_vec (); // Ensures only one reference to my privates! | |
| 3231 | |
| 3769 | 3232 mx_inline_add2 (d, a.data (), length ()); |
| 458 | 3233 return *this; |
| 3234 } | |
| 3235 | |
| 3236 ComplexMatrix& | |
| 3237 ComplexMatrix::operator -= (const Matrix& a) | |
| 3238 { | |
| 5275 | 3239 octave_idx_type nr = rows (); |
| 3240 octave_idx_type nc = cols (); | |
| 3241 | |
| 3242 octave_idx_type a_nr = a.rows (); | |
| 3243 octave_idx_type a_nc = a.cols (); | |
| 2384 | 3244 |
| 3245 if (nr != a_nr || nc != a_nc) | |
| 458 | 3246 { |
| 2384 | 3247 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
| 458 | 3248 return *this; |
| 3249 } | |
| 3250 | |
| 3251 if (nr == 0 || nc == 0) | |
| 3252 return *this; | |
| 3253 | |
| 3254 Complex *d = fortran_vec (); // Ensures only one reference to my privates! | |
| 3255 | |
| 3769 | 3256 mx_inline_subtract2 (d, a.data (), length ()); |
| 458 | 3257 return *this; |
| 3258 } | |
| 3259 | |
| 3260 // unary operations | |
| 3261 | |
| 2964 | 3262 boolMatrix |
| 458 | 3263 ComplexMatrix::operator ! (void) const |
| 3264 { | |
| 5275 | 3265 octave_idx_type nr = rows (); |
| 3266 octave_idx_type nc = cols (); | |
| 2964 | 3267 |
| 3268 boolMatrix b (nr, nc); | |
| 3269 | |
| 5275 | 3270 for (octave_idx_type j = 0; j < nc; j++) |
| 3271 for (octave_idx_type i = 0; i < nr; i++) | |
| 5139 | 3272 b.elem (i, j) = elem (i, j) == 0.0; |
| 2964 | 3273 |
| 3274 return b; | |
| 458 | 3275 } |
| 3276 | |
| 3277 // other operations | |
| 3278 | |
| 2676 | 3279 Matrix |
|
7503
8c32f95c2639
convert mapper functions to new format
David Bateman <dbateman@free.fr>
parents:
7488
diff
changeset
|
3280 ComplexMatrix::map (dmapper fcn) const |
| 458 | 3281 { |
|
7503
8c32f95c2639
convert mapper functions to new format
David Bateman <dbateman@free.fr>
parents:
7488
diff
changeset
|
3282 return MArray2<Complex>::map<double> (func_ptr (fcn)); |
|
8c32f95c2639
convert mapper functions to new format
David Bateman <dbateman@free.fr>
parents:
7488
diff
changeset
|
3283 } |
|
8c32f95c2639
convert mapper functions to new format
David Bateman <dbateman@free.fr>
parents:
7488
diff
changeset
|
3284 |
|
8c32f95c2639
convert mapper functions to new format
David Bateman <dbateman@free.fr>
parents:
7488
diff
changeset
|
3285 ComplexMatrix |
|
8c32f95c2639
convert mapper functions to new format
David Bateman <dbateman@free.fr>
parents:
7488
diff
changeset
|
3286 ComplexMatrix::map (cmapper fcn) const |
|
8c32f95c2639
convert mapper functions to new format
David Bateman <dbateman@free.fr>
parents:
7488
diff
changeset
|
3287 { |
|
8c32f95c2639
convert mapper functions to new format
David Bateman <dbateman@free.fr>
parents:
7488
diff
changeset
|
3288 return MArray2<Complex>::map<Complex> (func_ptr (fcn)); |
| 3248 | 3289 } |
| 3290 | |
| 3291 boolMatrix | |
|
7503
8c32f95c2639
convert mapper functions to new format
David Bateman <dbateman@free.fr>
parents:
7488
diff
changeset
|
3292 ComplexMatrix::map (bmapper fcn) const |
| 3248 | 3293 { |
|
7503
8c32f95c2639
convert mapper functions to new format
David Bateman <dbateman@free.fr>
parents:
7488
diff
changeset
|
3294 return MArray2<Complex>::map<bool> (func_ptr (fcn)); |
| 458 | 3295 } |
| 3296 | |
| 2384 | 3297 bool |
| 3298 ComplexMatrix::any_element_is_inf_or_nan (void) const | |
| 3299 { | |
| 5275 | 3300 octave_idx_type nr = rows (); |
| 3301 octave_idx_type nc = cols (); | |
| 3302 | |
| 3303 for (octave_idx_type j = 0; j < nc; j++) | |
| 3304 for (octave_idx_type i = 0; i < nr; i++) | |
| 2384 | 3305 { |
| 3306 Complex val = elem (i, j); | |
| 3307 if (xisinf (val) || xisnan (val)) | |
| 3308 return true; | |
| 3309 } | |
| 3310 | |
| 3311 return false; | |
| 3312 } | |
| 3313 | |
| 2408 | 3314 // Return true if no elements have imaginary components. |
| 3315 | |
| 3316 bool | |
| 3317 ComplexMatrix::all_elements_are_real (void) const | |
| 3318 { | |
| 5275 | 3319 octave_idx_type nr = rows (); |
| 3320 octave_idx_type nc = cols (); | |
| 3321 | |
| 3322 for (octave_idx_type j = 0; j < nc; j++) | |
| 4349 | 3323 { |
| 5275 | 3324 for (octave_idx_type i = 0; i < nr; i++) |
| 4349 | 3325 { |
| 5315 | 3326 double ip = std::imag (elem (i, j)); |
| 4349 | 3327 |
| 3328 if (ip != 0.0 || lo_ieee_signbit (ip)) | |
| 3329 return false; | |
| 3330 } | |
| 3331 } | |
| 2408 | 3332 |
| 3333 return true; | |
| 3334 } | |
| 3335 | |
| 1968 | 3336 // Return nonzero if any element of CM has a non-integer real or |
| 3337 // imaginary part. Also extract the largest and smallest (real or | |
| 3338 // imaginary) values and return them in MAX_VAL and MIN_VAL. | |
| 3339 | |
| 2384 | 3340 bool |
| 1968 | 3341 ComplexMatrix::all_integers (double& max_val, double& min_val) const |
| 3342 { | |
| 5275 | 3343 octave_idx_type nr = rows (); |
| 3344 octave_idx_type nc = cols (); | |
| 1968 | 3345 |
| 3346 if (nr > 0 && nc > 0) | |
| 3347 { | |
| 3348 Complex val = elem (0, 0); | |
| 3349 | |
| 5315 | 3350 double r_val = std::real (val); |
| 3351 double i_val = std::imag (val); | |
| 1968 | 3352 |
| 3353 max_val = r_val; | |
| 3354 min_val = r_val; | |
| 3355 | |
| 3356 if (i_val > max_val) | |
| 3357 max_val = i_val; | |
| 3358 | |
| 3359 if (i_val < max_val) | |
| 3360 min_val = i_val; | |
| 3361 } | |
| 3362 else | |
| 2384 | 3363 return false; |
| 1968 | 3364 |
| 5275 | 3365 for (octave_idx_type j = 0; j < nc; j++) |
| 3366 for (octave_idx_type i = 0; i < nr; i++) | |
| 1968 | 3367 { |
| 3368 Complex val = elem (i, j); | |
| 3369 | |
| 5315 | 3370 double r_val = std::real (val); |
| 3371 double i_val = std::imag (val); | |
| 1968 | 3372 |
| 3373 if (r_val > max_val) | |
| 3374 max_val = r_val; | |
| 3375 | |
| 3376 if (i_val > max_val) | |
| 3377 max_val = i_val; | |
| 3378 | |
| 3379 if (r_val < min_val) | |
| 3380 min_val = r_val; | |
| 3381 | |
| 3382 if (i_val < min_val) | |
| 3383 min_val = i_val; | |
| 3384 | |
| 3385 if (D_NINT (r_val) != r_val || D_NINT (i_val) != i_val) | |
| 2384 | 3386 return false; |
| 1968 | 3387 } |
| 2384 | 3388 |
| 3389 return true; | |
| 1968 | 3390 } |
| 3391 | |
| 2384 | 3392 bool |
| 1968 | 3393 ComplexMatrix::too_large_for_float (void) const |
| 3394 { | |
| 5275 | 3395 octave_idx_type nr = rows (); |
| 3396 octave_idx_type nc = cols (); | |
| 3397 | |
| 3398 for (octave_idx_type j = 0; j < nc; j++) | |
| 3399 for (octave_idx_type i = 0; i < nr; i++) | |
| 1968 | 3400 { |
| 3401 Complex val = elem (i, j); | |
| 3402 | |
| 5315 | 3403 double r_val = std::real (val); |
| 3404 double i_val = std::imag (val); | |
| 1968 | 3405 |
| 5389 | 3406 if ((! (xisnan (r_val) || xisinf (r_val)) |
| 5387 | 3407 && fabs (r_val) > FLT_MAX) |
| 5389 | 3408 || (! (xisnan (i_val) || xisinf (i_val)) |
| 5387 | 3409 && fabs (i_val) > FLT_MAX)) |
| 2384 | 3410 return true; |
| 1968 | 3411 } |
| 3412 | |
| 2384 | 3413 return false; |
| 1968 | 3414 } |
| 3415 | |
| 5775 | 3416 // FIXME Do these really belong here? Maybe they should be |
| 4015 | 3417 // in a base class? |
| 3418 | |
| 2832 | 3419 boolMatrix |
| 4015 | 3420 ComplexMatrix::all (int dim) const |
| 458 | 3421 { |
| 4015 | 3422 MX_ALL_OP (dim); |
| 458 | 3423 } |
| 3424 | |
| 2832 | 3425 boolMatrix |
| 4015 | 3426 ComplexMatrix::any (int dim) const |
| 458 | 3427 { |
| 4015 | 3428 MX_ANY_OP (dim); |
| 458 | 3429 } |
| 3430 | |
| 3431 ComplexMatrix | |
| 3723 | 3432 ComplexMatrix::cumprod (int dim) const |
| 458 | 3433 { |
| 4015 | 3434 MX_CUMULATIVE_OP (ComplexMatrix, Complex, *=); |
| 458 | 3435 } |
| 3436 | |
| 3437 ComplexMatrix | |
| 3723 | 3438 ComplexMatrix::cumsum (int dim) const |
| 458 | 3439 { |
| 4015 | 3440 MX_CUMULATIVE_OP (ComplexMatrix, Complex, +=); |
| 458 | 3441 } |
| 3442 | |
| 3443 ComplexMatrix | |
| 3723 | 3444 ComplexMatrix::prod (int dim) const |
| 458 | 3445 { |
| 3864 | 3446 MX_REDUCTION_OP (ComplexMatrix, *=, 1.0, 1.0); |
| 458 | 3447 } |
| 3448 | |
| 3449 ComplexMatrix | |
| 3723 | 3450 ComplexMatrix::sum (int dim) const |
| 458 | 3451 { |
| 3864 | 3452 MX_REDUCTION_OP (ComplexMatrix, +=, 0.0, 0.0); |
| 458 | 3453 } |
| 3454 | |
| 3455 ComplexMatrix | |
| 3723 | 3456 ComplexMatrix::sumsq (int dim) const |
| 458 | 3457 { |
| 3864 | 3458 #define ROW_EXPR \ |
| 3459 Complex d = elem (i, j); \ | |
| 3460 retval.elem (i, 0) += d * conj (d) | |
| 3461 | |
| 3462 #define COL_EXPR \ | |
| 3463 Complex d = elem (i, j); \ | |
| 3464 retval.elem (0, j) += d * conj (d) | |
| 3465 | |
| 3466 MX_BASE_REDUCTION_OP (ComplexMatrix, ROW_EXPR, COL_EXPR, 0.0, 0.0); | |
| 3467 | |
| 3468 #undef ROW_EXPR | |
| 3469 #undef COL_EXPR | |
| 458 | 3470 } |
| 3471 | |
| 4329 | 3472 Matrix ComplexMatrix::abs (void) const |
| 3473 { | |
| 5275 | 3474 octave_idx_type nr = rows (); |
| 3475 octave_idx_type nc = cols (); | |
| 4329 | 3476 |
| 3477 Matrix retval (nr, nc); | |
| 3478 | |
| 5275 | 3479 for (octave_idx_type j = 0; j < nc; j++) |
| 3480 for (octave_idx_type i = 0; i < nr; i++) | |
| 5315 | 3481 retval (i, j) = std::abs (elem (i, j)); |
| 4329 | 3482 |
| 3483 return retval; | |
| 3484 } | |
| 3485 | |
|
7620
36594d5bbe13
Move diag function into the octave_value class
David Bateman <dbateman@free.fr>
parents:
7544
diff
changeset
|
3486 ComplexMatrix |
| 5275 | 3487 ComplexMatrix::diag (octave_idx_type k) const |
| 458 | 3488 { |
|
7620
36594d5bbe13
Move diag function into the octave_value class
David Bateman <dbateman@free.fr>
parents:
7544
diff
changeset
|
3489 return MArray2<Complex>::diag (k); |
| 458 | 3490 } |
| 3491 | |
| 2354 | 3492 bool |
| 5275 | 3493 ComplexMatrix::row_is_real_only (octave_idx_type i) const |
| 2354 | 3494 { |
| 3495 bool retval = true; | |
| 3496 | |
| 5275 | 3497 octave_idx_type nc = columns (); |
| 3498 | |
| 3499 for (octave_idx_type j = 0; j < nc; j++) | |
| 2354 | 3500 { |
| 5315 | 3501 if (std::imag (elem (i, j)) != 0.0) |
| 2354 | 3502 { |
| 3503 retval = false; | |
| 3504 break; | |
| 3505 } | |
| 3506 } | |
| 3507 | |
| 3508 return retval; | |
| 3509 } | |
| 3510 | |
| 3511 bool | |
| 5275 | 3512 ComplexMatrix::column_is_real_only (octave_idx_type j) const |
| 2354 | 3513 { |
| 3514 bool retval = true; | |
| 3515 | |
| 5275 | 3516 octave_idx_type nr = rows (); |
| 3517 | |
| 3518 for (octave_idx_type i = 0; i < nr; i++) | |
| 2354 | 3519 { |
| 5315 | 3520 if (std::imag (elem (i, j)) != 0.0) |
| 2354 | 3521 { |
| 3522 retval = false; | |
| 3523 break; | |
| 3524 } | |
| 3525 } | |
| 3526 | |
| 3527 return retval; | |
| 3528 } | |
| 891 | 3529 |
| 458 | 3530 ComplexColumnVector |
| 3531 ComplexMatrix::row_min (void) const | |
| 3532 { | |
| 5275 | 3533 Array<octave_idx_type> dummy_idx; |
| 4587 | 3534 return row_min (dummy_idx); |
| 458 | 3535 } |
| 3536 | |
| 3537 ComplexColumnVector | |
| 5275 | 3538 ComplexMatrix::row_min (Array<octave_idx_type>& idx_arg) const |
| 458 | 3539 { |
| 3540 ComplexColumnVector result; | |
| 3541 | |
| 5275 | 3542 octave_idx_type nr = rows (); |
| 3543 octave_idx_type nc = cols (); | |
| 458 | 3544 |
| 3545 if (nr > 0 && nc > 0) | |
| 3546 { | |
| 3547 result.resize (nr); | |
| 4587 | 3548 idx_arg.resize (nr); |
| 458 | 3549 |
| 5275 | 3550 for (octave_idx_type i = 0; i < nr; i++) |
| 458 | 3551 { |
| 2354 | 3552 bool real_only = row_is_real_only (i); |
| 3553 | |
| 5275 | 3554 octave_idx_type idx_j; |
| 4469 | 3555 |
| 3556 Complex tmp_min; | |
| 3557 | |
| 3558 double abs_min = octave_NaN; | |
| 3559 | |
| 3560 for (idx_j = 0; idx_j < nc; idx_j++) | |
| 3561 { | |
| 3562 tmp_min = elem (i, idx_j); | |
| 3563 | |
| 5389 | 3564 if (! xisnan (tmp_min)) |
| 4469 | 3565 { |
| 5315 | 3566 abs_min = real_only ? std::real (tmp_min) : std::abs (tmp_min); |
| 4469 | 3567 break; |
| 3568 } | |
| 3569 } | |
| 3570 | |
| 5275 | 3571 for (octave_idx_type j = idx_j+1; j < nc; j++) |
| 4469 | 3572 { |
| 3573 Complex tmp = elem (i, j); | |
| 3574 | |
| 5389 | 3575 if (xisnan (tmp)) |
| 4469 | 3576 continue; |
| 3577 | |
| 5315 | 3578 double abs_tmp = real_only ? std::real (tmp) : std::abs (tmp); |
| 4469 | 3579 |
| 3580 if (abs_tmp < abs_min) | |
| 3581 { | |
| 3582 idx_j = j; | |
| 3583 tmp_min = tmp; | |
| 3584 abs_min = abs_tmp; | |
| 3585 } | |
| 3586 } | |
| 3587 | |
| 5389 | 3588 if (xisnan (tmp_min)) |
| 4469 | 3589 { |
| 3590 result.elem (i) = Complex_NaN_result; | |
| 4587 | 3591 idx_arg.elem (i) = 0; |
| 4469 | 3592 } |
| 891 | 3593 else |
| 3594 { | |
| 4469 | 3595 result.elem (i) = tmp_min; |
| 4587 | 3596 idx_arg.elem (i) = idx_j; |
| 891 | 3597 } |
| 458 | 3598 } |
| 3599 } | |
| 3600 | |
| 3601 return result; | |
| 3602 } | |
| 3603 | |
| 3604 ComplexColumnVector | |
| 3605 ComplexMatrix::row_max (void) const | |
| 3606 { | |
| 5275 | 3607 Array<octave_idx_type> dummy_idx; |
| 4587 | 3608 return row_max (dummy_idx); |
| 458 | 3609 } |
| 3610 | |
| 3611 ComplexColumnVector | |
| 5275 | 3612 ComplexMatrix::row_max (Array<octave_idx_type>& idx_arg) const |
| 458 | 3613 { |
| 3614 ComplexColumnVector result; | |
| 3615 | |
| 5275 | 3616 octave_idx_type nr = rows (); |
| 3617 octave_idx_type nc = cols (); | |
| 458 | 3618 |
| 3619 if (nr > 0 && nc > 0) | |
| 3620 { | |
| 3621 result.resize (nr); | |
| 4587 | 3622 idx_arg.resize (nr); |
| 458 | 3623 |
| 5275 | 3624 for (octave_idx_type i = 0; i < nr; i++) |
| 458 | 3625 { |
| 2354 | 3626 bool real_only = row_is_real_only (i); |
| 3627 | |
| 5275 | 3628 octave_idx_type idx_j; |
| 4469 | 3629 |
| 3630 Complex tmp_max; | |
| 3631 | |
| 3632 double abs_max = octave_NaN; | |
| 3633 | |
| 3634 for (idx_j = 0; idx_j < nc; idx_j++) | |
| 3635 { | |
| 3636 tmp_max = elem (i, idx_j); | |
| 3637 | |
| 5389 | 3638 if (! xisnan (tmp_max)) |
| 4469 | 3639 { |
| 5315 | 3640 abs_max = real_only ? std::real (tmp_max) : std::abs (tmp_max); |
| 4469 | 3641 break; |
| 3642 } | |
| 3643 } | |
| 3644 | |
| 5275 | 3645 for (octave_idx_type j = idx_j+1; j < nc; j++) |
| 4469 | 3646 { |
| 3647 Complex tmp = elem (i, j); | |
| 3648 | |
| 5389 | 3649 if (xisnan (tmp)) |
| 4469 | 3650 continue; |
| 3651 | |
| 5315 | 3652 double abs_tmp = real_only ? std::real (tmp) : std::abs (tmp); |
| 4469 | 3653 |
| 3654 if (abs_tmp > abs_max) | |
| 3655 { | |
| 3656 idx_j = j; | |
| 3657 tmp_max = tmp; | |
| 3658 abs_max = abs_tmp; | |
| 3659 } | |
| 3660 } | |
| 3661 | |
| 5389 | 3662 if (xisnan (tmp_max)) |
| 4469 | 3663 { |
| 3664 result.elem (i) = Complex_NaN_result; | |
| 4587 | 3665 idx_arg.elem (i) = 0; |
| 4469 | 3666 } |
| 891 | 3667 else |
| 3668 { | |
| 4469 | 3669 result.elem (i) = tmp_max; |
| 4587 | 3670 idx_arg.elem (i) = idx_j; |
| 891 | 3671 } |
| 458 | 3672 } |
| 3673 } | |
| 3674 | |
| 3675 return result; | |
| 3676 } | |
| 3677 | |
| 3678 ComplexRowVector | |
| 3679 ComplexMatrix::column_min (void) const | |
| 3680 { | |
| 5275 | 3681 Array<octave_idx_type> dummy_idx; |
| 4587 | 3682 return column_min (dummy_idx); |
| 458 | 3683 } |
| 3684 | |
| 3685 ComplexRowVector | |
| 5275 | 3686 ComplexMatrix::column_min (Array<octave_idx_type>& idx_arg) const |
| 458 | 3687 { |
| 3688 ComplexRowVector result; | |
| 3689 | |
| 5275 | 3690 octave_idx_type nr = rows (); |
| 3691 octave_idx_type nc = cols (); | |
| 458 | 3692 |
| 3693 if (nr > 0 && nc > 0) | |
| 3694 { | |
| 3695 result.resize (nc); | |
| 4587 | 3696 idx_arg.resize (nc); |
| 458 | 3697 |
| 5275 | 3698 for (octave_idx_type j = 0; j < nc; j++) |
| 458 | 3699 { |
| 2354 | 3700 bool real_only = column_is_real_only (j); |
| 3701 | |
| 5275 | 3702 octave_idx_type idx_i; |
| 4469 | 3703 |
| 3704 Complex tmp_min; | |
| 3705 | |
| 3706 double abs_min = octave_NaN; | |
| 3707 | |
| 3708 for (idx_i = 0; idx_i < nr; idx_i++) | |
| 3709 { | |
| 3710 tmp_min = elem (idx_i, j); | |
| 3711 | |
| 5389 | 3712 if (! xisnan (tmp_min)) |
| 4469 | 3713 { |
| 5315 | 3714 abs_min = real_only ? std::real (tmp_min) : std::abs (tmp_min); |
| 4469 | 3715 break; |
| 3716 } | |
| 3717 } | |
| 3718 | |
| 5275 | 3719 for (octave_idx_type i = idx_i+1; i < nr; i++) |
| 4469 | 3720 { |
| 3721 Complex tmp = elem (i, j); | |
| 3722 | |
| 5389 | 3723 if (xisnan (tmp)) |
| 4469 | 3724 continue; |
| 3725 | |
| 5315 | 3726 double abs_tmp = real_only ? std::real (tmp) : std::abs (tmp); |
| 4469 | 3727 |
| 3728 if (abs_tmp < abs_min) | |
| 3729 { | |
| 3730 idx_i = i; | |
| 3731 tmp_min = tmp; | |
| 3732 abs_min = abs_tmp; | |
| 3733 } | |
| 3734 } | |
| 3735 | |
| 5389 | 3736 if (xisnan (tmp_min)) |
| 4469 | 3737 { |
| 3738 result.elem (j) = Complex_NaN_result; | |
| 4587 | 3739 idx_arg.elem (j) = 0; |
| 4469 | 3740 } |
| 891 | 3741 else |
| 3742 { | |
| 4469 | 3743 result.elem (j) = tmp_min; |
| 4587 | 3744 idx_arg.elem (j) = idx_i; |
| 891 | 3745 } |
| 458 | 3746 } |
| 3747 } | |
| 3748 | |
| 3749 return result; | |
| 3750 } | |
| 3751 | |
| 3752 ComplexRowVector | |
| 3753 ComplexMatrix::column_max (void) const | |
| 3754 { | |
| 5275 | 3755 Array<octave_idx_type> dummy_idx; |
| 4587 | 3756 return column_max (dummy_idx); |
| 458 | 3757 } |
| 3758 | |
| 3759 ComplexRowVector | |
| 5275 | 3760 ComplexMatrix::column_max (Array<octave_idx_type>& idx_arg) const |
| 458 | 3761 { |
| 3762 ComplexRowVector result; | |
| 3763 | |
| 5275 | 3764 octave_idx_type nr = rows (); |
| 3765 octave_idx_type nc = cols (); | |
| 458 | 3766 |
| 3767 if (nr > 0 && nc > 0) | |
| 3768 { | |
| 3769 result.resize (nc); | |
| 4587 | 3770 idx_arg.resize (nc); |
| 458 | 3771 |
| 5275 | 3772 for (octave_idx_type j = 0; j < nc; j++) |
| 458 | 3773 { |
| 2354 | 3774 bool real_only = column_is_real_only (j); |
| 3775 | |
| 5275 | 3776 octave_idx_type idx_i; |
| 4469 | 3777 |
| 3778 Complex tmp_max; | |
| 3779 | |
| 3780 double abs_max = octave_NaN; | |
| 3781 | |
| 3782 for (idx_i = 0; idx_i < nr; idx_i++) | |
| 3783 { | |
| 3784 tmp_max = elem (idx_i, j); | |
| 3785 | |
| 5389 | 3786 if (! xisnan (tmp_max)) |
| 4469 | 3787 { |
| 5315 | 3788 abs_max = real_only ? std::real (tmp_max) : std::abs (tmp_max); |
| 4469 | 3789 break; |
| 3790 } | |
| 3791 } | |
| 3792 | |
| 5275 | 3793 for (octave_idx_type i = idx_i+1; i < nr; i++) |
| 4469 | 3794 { |
| 3795 Complex tmp = elem (i, j); | |
| 3796 | |
| 5389 | 3797 if (xisnan (tmp)) |
| 4469 | 3798 continue; |
| 3799 | |
| 5315 | 3800 double abs_tmp = real_only ? std::real (tmp) : std::abs (tmp); |
| 4469 | 3801 |
| 3802 if (abs_tmp > abs_max) | |
| 3803 { | |
| 3804 idx_i = i; | |
| 3805 tmp_max = tmp; | |
| 3806 abs_max = abs_tmp; | |
| 3807 } | |
| 3808 } | |
| 3809 | |
| 5389 | 3810 if (xisnan (tmp_max)) |
| 4469 | 3811 { |
| 3812 result.elem (j) = Complex_NaN_result; | |
| 4587 | 3813 idx_arg.elem (j) = 0; |
| 4469 | 3814 } |
| 891 | 3815 else |
| 3816 { | |
| 4469 | 3817 result.elem (j) = tmp_max; |
| 4587 | 3818 idx_arg.elem (j) = idx_i; |
| 891 | 3819 } |
| 458 | 3820 } |
| 3821 } | |
| 3822 | |
| 3823 return result; | |
| 3824 } | |
| 3825 | |
| 3826 // i/o | |
| 3827 | |
| 3504 | 3828 std::ostream& |
| 3829 operator << (std::ostream& os, const ComplexMatrix& a) | |
| 458 | 3830 { |
| 5275 | 3831 for (octave_idx_type i = 0; i < a.rows (); i++) |
| 458 | 3832 { |
| 5275 | 3833 for (octave_idx_type j = 0; j < a.cols (); j++) |
| 4130 | 3834 { |
| 3835 os << " "; | |
| 3836 octave_write_complex (os, a.elem (i, j)); | |
| 3837 } | |
| 458 | 3838 os << "\n"; |
| 3839 } | |
| 3840 return os; | |
| 3841 } | |
| 3842 | |
| 3504 | 3843 std::istream& |
| 3844 operator >> (std::istream& is, ComplexMatrix& a) | |
| 458 | 3845 { |
| 5275 | 3846 octave_idx_type nr = a.rows (); |
| 3847 octave_idx_type nc = a.cols (); | |
| 458 | 3848 |
| 3849 if (nr < 1 || nc < 1) | |
| 3504 | 3850 is.clear (std::ios::badbit); |
| 458 | 3851 else |
| 3852 { | |
| 3853 Complex tmp; | |
| 5275 | 3854 for (octave_idx_type i = 0; i < nr; i++) |
| 3855 for (octave_idx_type j = 0; j < nc; j++) | |
| 458 | 3856 { |
| 4130 | 3857 tmp = octave_read_complex (is); |
| 458 | 3858 if (is) |
| 3859 a.elem (i, j) = tmp; | |
| 3860 else | |
| 2993 | 3861 goto done; |
| 458 | 3862 } |
| 3863 } | |
| 3864 | |
| 2993 | 3865 done: |
| 3866 | |
| 458 | 3867 return is; |
| 3868 } | |
| 3869 | |
| 1819 | 3870 ComplexMatrix |
| 3871 Givens (const Complex& x, const Complex& y) | |
| 3872 { | |
| 3873 double cc; | |
| 3874 Complex cs, temp_r; | |
| 3875 | |
| 3887 | 3876 F77_FUNC (zlartg, ZLARTG) (x, y, cc, cs, temp_r); |
| 1819 | 3877 |
| 3878 ComplexMatrix g (2, 2); | |
| 3879 | |
| 3880 g.elem (0, 0) = cc; | |
| 3881 g.elem (1, 1) = cc; | |
| 3882 g.elem (0, 1) = cs; | |
| 3883 g.elem (1, 0) = -conj (cs); | |
| 3884 | |
| 3885 return g; | |
| 3886 } | |
| 3887 | |
| 3888 ComplexMatrix | |
| 3889 Sylvester (const ComplexMatrix& a, const ComplexMatrix& b, | |
| 3890 const ComplexMatrix& c) | |
| 3891 { | |
| 3892 ComplexMatrix retval; | |
| 3893 | |
| 5775 | 3894 // FIXME -- need to check that a, b, and c are all the same |
| 1819 | 3895 // size. |
| 3896 | |
| 3897 // Compute Schur decompositions | |
| 3898 | |
| 3899 ComplexSCHUR as (a, "U"); | |
| 3900 ComplexSCHUR bs (b, "U"); | |
| 3901 | |
| 3902 // Transform c to new coordinates. | |
| 3903 | |
| 3904 ComplexMatrix ua = as.unitary_matrix (); | |
| 3905 ComplexMatrix sch_a = as.schur_matrix (); | |
| 3906 | |
| 3907 ComplexMatrix ub = bs.unitary_matrix (); | |
| 3908 ComplexMatrix sch_b = bs.schur_matrix (); | |
| 3909 | |
| 3910 ComplexMatrix cx = ua.hermitian () * c * ub; | |
| 3911 | |
| 3912 // Solve the sylvester equation, back-transform, and return the | |
| 3913 // solution. | |
| 3914 | |
| 5275 | 3915 octave_idx_type a_nr = a.rows (); |
| 3916 octave_idx_type b_nr = b.rows (); | |
| 1819 | 3917 |
| 3918 double scale; | |
| 5275 | 3919 octave_idx_type info; |
| 1950 | 3920 |
| 3921 Complex *pa = sch_a.fortran_vec (); | |
| 3922 Complex *pb = sch_b.fortran_vec (); | |
| 3923 Complex *px = cx.fortran_vec (); | |
| 1819 | 3924 |
| 4552 | 3925 F77_XFCN (ztrsyl, ZTRSYL, (F77_CONST_CHAR_ARG2 ("N", 1), |
| 3926 F77_CONST_CHAR_ARG2 ("N", 1), | |
| 3927 1, a_nr, b_nr, pa, a_nr, pb, | |
| 3928 b_nr, px, a_nr, scale, info | |
| 3929 F77_CHAR_ARG_LEN (1) | |
| 3930 F77_CHAR_ARG_LEN (1))); | |
| 1950 | 3931 |
|
7482
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
3932 // FIXME -- check info? |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
3933 |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
3934 retval = -ua * cx * ub.hermitian (); |
| 1819 | 3935 |
| 3936 return retval; | |
| 3937 } | |
| 3938 | |
| 2828 | 3939 ComplexMatrix |
| 3940 operator * (const ComplexMatrix& m, const Matrix& a) | |
| 3941 { | |
| 3942 ComplexMatrix tmp (a); | |
| 3943 return m * tmp; | |
| 3944 } | |
| 3945 | |
| 3946 ComplexMatrix | |
| 3947 operator * (const Matrix& m, const ComplexMatrix& a) | |
| 3948 { | |
| 3949 ComplexMatrix tmp (m); | |
| 3950 return tmp * a; | |
| 3951 } | |
| 3952 | |
| 6162 | 3953 /* Simple Dot Product, Matrix-Vector and Matrix-Matrix Unit tests |
| 3954 %!assert([1+i 2+i 3+i] * [ 4+i ; 5+i ; 6+i], 29+21i, 1e-14) | |
| 3955 %!assert([1+i 2+i ; 3+i 4+i ] * [5+i ; 6+i], [15 + 14i ; 37 + 18i], 1e-14) | |
| 3956 %!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) | |
| 3957 */ | |
| 3958 | |
| 3959 /* Test some simple identities | |
| 3960 %!shared M, cv, rv | |
| 3961 %! M = randn(10,10)+i*rand(10,10); | |
| 3962 %! cv = randn(10,1)+i*rand(10,1); | |
| 3963 %! rv = randn(1,10)+i*rand(1,10); | |
| 3964 %!assert([M*cv,M*cv],M*[cv,cv],1e-14) | |
| 3965 %!assert([rv*M;rv*M],[rv;rv]*M,1e-14) | |
| 3966 %!assert(2*rv*cv,[rv,rv]*[cv;cv],1e-14) | |
| 3967 */ | |
| 3968 | |
| 2828 | 3969 ComplexMatrix |
| 3970 operator * (const ComplexMatrix& m, const ComplexMatrix& a) | |
| 3971 { | |
| 3972 ComplexMatrix retval; | |
| 3973 | |
| 5275 | 3974 octave_idx_type nr = m.rows (); |
| 3975 octave_idx_type nc = m.cols (); | |
| 3976 | |
| 3977 octave_idx_type a_nr = a.rows (); | |
| 3978 octave_idx_type a_nc = a.cols (); | |
| 2828 | 3979 |
| 3980 if (nc != a_nr) | |
| 3981 gripe_nonconformant ("operator *", nr, nc, a_nr, a_nc); | |
| 3982 else | |
| 3983 { | |
| 3984 if (nr == 0 || nc == 0 || a_nc == 0) | |
| 3760 | 3985 retval.resize (nr, a_nc, 0.0); |
| 2828 | 3986 else |
| 3987 { | |
| 5275 | 3988 octave_idx_type ld = nr; |
| 3989 octave_idx_type lda = a.rows (); | |
| 2828 | 3990 |
| 3991 retval.resize (nr, a_nc); | |
| 3992 Complex *c = retval.fortran_vec (); | |
| 3993 | |
| 5983 | 3994 if (a_nc == 1) |
| 3995 { | |
| 3996 if (nr == 1) | |
| 3997 F77_FUNC (xzdotu, XZDOTU) (nc, m.data (), 1, a.data (), 1, *c); | |
| 3998 else | |
| 6390 | 3999 { |
| 4000 F77_XFCN (zgemv, ZGEMV, (F77_CONST_CHAR_ARG2 ("N", 1), | |
| 4001 nr, nc, 1.0, m.data (), ld, | |
| 4002 a.data (), 1, 0.0, c, 1 | |
| 4003 F77_CHAR_ARG_LEN (1))); | |
| 4004 } | |
| 5983 | 4005 } |
| 4006 else | |
| 6390 | 4007 { |
| 4008 F77_XFCN (zgemm, ZGEMM, (F77_CONST_CHAR_ARG2 ("N", 1), | |
| 4009 F77_CONST_CHAR_ARG2 ("N", 1), | |
| 4010 nr, a_nc, nc, 1.0, m.data (), | |
| 4011 ld, a.data (), lda, 0.0, c, nr | |
| 4012 F77_CHAR_ARG_LEN (1) | |
| 4013 F77_CHAR_ARG_LEN (1))); | |
| 4014 } | |
| 2828 | 4015 } |
| 4016 } | |
| 4017 | |
| 4018 return retval; | |
| 4019 } | |
| 4020 | |
| 5775 | 4021 // FIXME -- it would be nice to share code among the min/max |
| 4309 | 4022 // functions below. |
| 4023 | |
| 4024 #define EMPTY_RETURN_CHECK(T) \ | |
| 4025 if (nr == 0 || nc == 0) \ | |
| 4026 return T (nr, nc); | |
| 4027 | |
| 4028 ComplexMatrix | |
| 4029 min (const Complex& c, const ComplexMatrix& m) | |
| 4030 { | |
| 5275 | 4031 octave_idx_type nr = m.rows (); |
| 4032 octave_idx_type nc = m.columns (); | |
| 4309 | 4033 |
| 4034 EMPTY_RETURN_CHECK (ComplexMatrix); | |
| 4035 | |
| 4036 ComplexMatrix result (nr, nc); | |
| 4037 | |
| 5275 | 4038 for (octave_idx_type j = 0; j < nc; j++) |
| 4039 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 4040 { |
| 4041 OCTAVE_QUIT; | |
| 4042 result (i, j) = xmin (c, m (i, j)); | |
| 4043 } | |
| 4044 | |
| 4045 return result; | |
| 4046 } | |
| 4047 | |
| 4048 ComplexMatrix | |
| 4049 min (const ComplexMatrix& m, const Complex& c) | |
| 4050 { | |
| 5275 | 4051 octave_idx_type nr = m.rows (); |
| 4052 octave_idx_type nc = m.columns (); | |
| 4309 | 4053 |
| 4054 EMPTY_RETURN_CHECK (ComplexMatrix); | |
| 4055 | |
| 4056 ComplexMatrix result (nr, nc); | |
| 4057 | |
| 5275 | 4058 for (octave_idx_type j = 0; j < nc; j++) |
| 4059 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 4060 { |
| 4061 OCTAVE_QUIT; | |
| 4062 result (i, j) = xmin (m (i, j), c); | |
| 4063 } | |
| 4064 | |
| 4065 return result; | |
| 4066 } | |
| 4067 | |
| 4068 ComplexMatrix | |
| 4069 min (const ComplexMatrix& a, const ComplexMatrix& b) | |
| 4070 { | |
| 5275 | 4071 octave_idx_type nr = a.rows (); |
| 4072 octave_idx_type nc = a.columns (); | |
| 4309 | 4073 |
| 4074 if (nr != b.rows () || nc != b.columns ()) | |
| 4075 { | |
| 4076 (*current_liboctave_error_handler) | |
| 4077 ("two-arg min expecting args of same size"); | |
| 4078 return ComplexMatrix (); | |
| 4079 } | |
| 4080 | |
| 4081 EMPTY_RETURN_CHECK (ComplexMatrix); | |
| 4082 | |
| 4083 ComplexMatrix result (nr, nc); | |
| 4084 | |
| 5275 | 4085 for (octave_idx_type j = 0; j < nc; j++) |
| 4309 | 4086 { |
| 4087 int columns_are_real_only = 1; | |
| 5275 | 4088 for (octave_idx_type i = 0; i < nr; i++) |
| 4309 | 4089 { |
| 4090 OCTAVE_QUIT; | |
| 5315 | 4091 if (std::imag (a (i, j)) != 0.0 || std::imag (b (i, j)) != 0.0) |
| 4309 | 4092 { |
| 4093 columns_are_real_only = 0; | |
| 4094 break; | |
| 4095 } | |
| 4096 } | |
| 4097 | |
| 4098 if (columns_are_real_only) | |
| 4099 { | |
| 5275 | 4100 for (octave_idx_type i = 0; i < nr; i++) |
| 5315 | 4101 result (i, j) = xmin (std::real (a (i, j)), std::real (b (i, j))); |
| 4309 | 4102 } |
| 4103 else | |
| 4104 { | |
| 5275 | 4105 for (octave_idx_type i = 0; i < nr; i++) |
| 4309 | 4106 { |
| 4107 OCTAVE_QUIT; | |
| 4108 result (i, j) = xmin (a (i, j), b (i, j)); | |
| 4109 } | |
| 4110 } | |
| 4111 } | |
| 4112 | |
| 4113 return result; | |
| 4114 } | |
| 4115 | |
| 4116 ComplexMatrix | |
| 4117 max (const Complex& c, const ComplexMatrix& m) | |
| 4118 { | |
| 5275 | 4119 octave_idx_type nr = m.rows (); |
| 4120 octave_idx_type nc = m.columns (); | |
| 4309 | 4121 |
| 4122 EMPTY_RETURN_CHECK (ComplexMatrix); | |
| 4123 | |
| 4124 ComplexMatrix result (nr, nc); | |
| 4125 | |
| 5275 | 4126 for (octave_idx_type j = 0; j < nc; j++) |
| 4127 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 4128 { |
| 4129 OCTAVE_QUIT; | |
| 4130 result (i, j) = xmax (c, m (i, j)); | |
| 4131 } | |
| 4132 | |
| 4133 return result; | |
| 4134 } | |
| 4135 | |
| 4136 ComplexMatrix | |
| 4137 max (const ComplexMatrix& m, const Complex& c) | |
| 4138 { | |
| 5275 | 4139 octave_idx_type nr = m.rows (); |
| 4140 octave_idx_type nc = m.columns (); | |
| 4309 | 4141 |
| 4142 EMPTY_RETURN_CHECK (ComplexMatrix); | |
| 4143 | |
| 4144 ComplexMatrix result (nr, nc); | |
| 4145 | |
| 5275 | 4146 for (octave_idx_type j = 0; j < nc; j++) |
| 4147 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 4148 { |
| 4149 OCTAVE_QUIT; | |
| 4150 result (i, j) = xmax (m (i, j), c); | |
| 4151 } | |
| 4152 | |
| 4153 return result; | |
| 4154 } | |
| 4155 | |
| 4156 ComplexMatrix | |
| 4157 max (const ComplexMatrix& a, const ComplexMatrix& b) | |
| 4158 { | |
| 5275 | 4159 octave_idx_type nr = a.rows (); |
| 4160 octave_idx_type nc = a.columns (); | |
| 4309 | 4161 |
| 4162 if (nr != b.rows () || nc != b.columns ()) | |
| 4163 { | |
| 4164 (*current_liboctave_error_handler) | |
| 4165 ("two-arg max expecting args of same size"); | |
| 4166 return ComplexMatrix (); | |
| 4167 } | |
| 4168 | |
| 4169 EMPTY_RETURN_CHECK (ComplexMatrix); | |
| 4170 | |
| 4171 ComplexMatrix result (nr, nc); | |
| 4172 | |
| 5275 | 4173 for (octave_idx_type j = 0; j < nc; j++) |
| 4309 | 4174 { |
| 4175 int columns_are_real_only = 1; | |
| 5275 | 4176 for (octave_idx_type i = 0; i < nr; i++) |
| 4309 | 4177 { |
| 4178 OCTAVE_QUIT; | |
| 5315 | 4179 if (std::imag (a (i, j)) != 0.0 || std::imag (b (i, j)) != 0.0) |
| 4309 | 4180 { |
| 4181 columns_are_real_only = 0; | |
| 4182 break; | |
| 4183 } | |
| 4184 } | |
| 4185 | |
| 4186 if (columns_are_real_only) | |
| 4187 { | |
| 5275 | 4188 for (octave_idx_type i = 0; i < nr; i++) |
| 4309 | 4189 { |
| 4190 OCTAVE_QUIT; | |
| 5315 | 4191 result (i, j) = xmax (std::real (a (i, j)), std::real (b (i, j))); |
| 4309 | 4192 } |
| 4193 } | |
| 4194 else | |
| 4195 { | |
| 5275 | 4196 for (octave_idx_type i = 0; i < nr; i++) |
| 4309 | 4197 { |
| 4198 OCTAVE_QUIT; | |
| 4199 result (i, j) = xmax (a (i, j), b (i, j)); | |
| 4200 } | |
| 4201 } | |
| 4202 } | |
| 4203 | |
| 4204 return result; | |
| 4205 } | |
| 4206 | |
| 5315 | 4207 MS_CMP_OPS(ComplexMatrix, std::real, Complex, std::real) |
| 3504 | 4208 MS_BOOL_OPS(ComplexMatrix, Complex, 0.0) |
| 2870 | 4209 |
| 5315 | 4210 SM_CMP_OPS(Complex, std::real, ComplexMatrix, std::real) |
| 3504 | 4211 SM_BOOL_OPS(Complex, ComplexMatrix, 0.0) |
| 2870 | 4212 |
| 5315 | 4213 MM_CMP_OPS(ComplexMatrix, std::real, ComplexMatrix, std::real) |
| 3504 | 4214 MM_BOOL_OPS(ComplexMatrix, ComplexMatrix, 0.0) |
| 2870 | 4215 |
| 458 | 4216 /* |
| 4217 ;;; Local Variables: *** | |
| 4218 ;;; mode: C++ *** | |
| 4219 ;;; End: *** | |
| 4220 */ |