Mercurial > hg > octave-nkf
annotate liboctave/CMatrix.cc @ 11875:f53f57d2ee51 release-3-0-x
improve inverse preconditioning according to Marco Caliari
| author | Jaroslav Hajek <highegg@gmail.com> |
|---|---|
| date | Sun, 12 Oct 2008 10:31:14 +0200 |
| parents | 0b9c56b6bf0e |
| children |
| rev | line source |
|---|---|
| 1993 | 1 // Matrix manipulations. |
| 458 | 2 /* |
| 3 | |
| 7017 | 4 Copyright (C) 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, |
| 11740 | 5 2003, 2004, 2005, 2006, 2007, 2008 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" |
| 458 | 47 #include "lo-error.h" |
| 2354 | 48 #include "lo-ieee.h" |
| 49 #include "lo-mappers.h" | |
| 1968 | 50 #include "lo-utils.h" |
| 1367 | 51 #include "mx-base.h" |
| 2828 | 52 #include "mx-cm-dm.h" |
| 3176 | 53 #include "mx-dm-cm.h" |
| 2828 | 54 #include "mx-cm-s.h" |
| 1367 | 55 #include "mx-inlines.cc" |
| 1650 | 56 #include "oct-cmplx.h" |
| 458 | 57 |
| 4773 | 58 #if defined (HAVE_FFTW3) |
| 3827 | 59 #include "oct-fftw.h" |
| 60 #endif | |
| 61 | |
| 458 | 62 // Fortran functions we call. |
| 63 | |
| 64 extern "C" | |
| 65 { | |
| 11646 | 66 F77_RET_T |
| 67 F77_FUNC (xilaenv, XILAENV) (const octave_idx_type&, F77_CONST_CHAR_ARG_DECL, | |
| 68 F77_CONST_CHAR_ARG_DECL, | |
| 69 const octave_idx_type&, const octave_idx_type&, | |
| 70 const octave_idx_type&, const octave_idx_type&, | |
| 71 octave_idx_type& | |
| 72 F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); | |
| 11640 | 73 |
| 4552 | 74 F77_RET_T |
| 75 F77_FUNC (zgebal, ZGEBAL) (F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 76 const octave_idx_type&, Complex*, const octave_idx_type&, octave_idx_type&, |
| 77 octave_idx_type&, double*, octave_idx_type& | |
| 4552 | 78 F77_CHAR_ARG_LEN_DECL); |
| 79 | |
| 80 F77_RET_T | |
| 81 F77_FUNC (dgebak, DGEBAK) (F77_CONST_CHAR_ARG_DECL, | |
| 82 F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 83 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, double*, |
| 84 const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type& | |
| 4552 | 85 F77_CHAR_ARG_LEN_DECL |
| 86 F77_CHAR_ARG_LEN_DECL); | |
| 87 | |
| 88 F77_RET_T | |
| 89 F77_FUNC (zgemm, ZGEMM) (F77_CONST_CHAR_ARG_DECL, | |
| 90 F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 91 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
| 92 const Complex&, const Complex*, const octave_idx_type&, | |
| 93 const Complex*, const octave_idx_type&, const Complex&, | |
| 94 Complex*, const octave_idx_type& | |
| 4552 | 95 F77_CHAR_ARG_LEN_DECL |
| 96 F77_CHAR_ARG_LEN_DECL); | |
| 97 | |
| 98 F77_RET_T | |
| 5983 | 99 F77_FUNC (zgemv, ZGEMV) (F77_CONST_CHAR_ARG_DECL, |
| 100 const octave_idx_type&, const octave_idx_type&, const Complex&, | |
| 101 const Complex*, const octave_idx_type&, const Complex*, | |
| 102 const octave_idx_type&, const Complex&, Complex*, const octave_idx_type& | |
| 103 F77_CHAR_ARG_LEN_DECL); | |
| 104 | |
| 105 F77_RET_T | |
| 106 F77_FUNC (xzdotu, XZDOTU) (const octave_idx_type&, const Complex*, const octave_idx_type&, | |
| 107 const Complex*, const octave_idx_type&, Complex&); | |
| 108 | |
| 109 F77_RET_T | |
| 5275 | 110 F77_FUNC (zgetrf, ZGETRF) (const octave_idx_type&, const octave_idx_type&, Complex*, const octave_idx_type&, |
| 111 octave_idx_type*, octave_idx_type&); | |
| 4552 | 112 |
| 113 F77_RET_T | |
| 114 F77_FUNC (zgetrs, ZGETRS) (F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 115 const octave_idx_type&, const octave_idx_type&, Complex*, const octave_idx_type&, |
| 116 const octave_idx_type*, Complex*, const octave_idx_type&, octave_idx_type& | |
| 4552 | 117 F77_CHAR_ARG_LEN_DECL); |
| 118 | |
| 119 F77_RET_T | |
| 5275 | 120 F77_FUNC (zgetri, ZGETRI) (const octave_idx_type&, Complex*, const octave_idx_type&, const octave_idx_type*, |
| 121 Complex*, const octave_idx_type&, octave_idx_type&); | |
| 4552 | 122 |
| 123 F77_RET_T | |
| 124 F77_FUNC (zgecon, ZGECON) (F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 125 const octave_idx_type&, Complex*, |
| 126 const octave_idx_type&, const double&, double&, | |
| 127 Complex*, double*, octave_idx_type& | |
| 4552 | 128 F77_CHAR_ARG_LEN_DECL); |
| 129 | |
| 130 F77_RET_T | |
| 7072 | 131 F77_FUNC (zgelsy, ZGELSY) (const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
| 132 Complex*, const octave_idx_type&, Complex*, | |
| 133 const octave_idx_type&, octave_idx_type*, double&, octave_idx_type&, | |
| 134 Complex*, const octave_idx_type&, double*, octave_idx_type&); | |
| 135 | |
| 136 F77_RET_T | |
| 137 F77_FUNC (zgelsd, ZGELSD) (const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, | |
| 5275 | 138 Complex*, const octave_idx_type&, Complex*, |
| 7071 | 139 const octave_idx_type&, double*, double&, octave_idx_type&, |
| 7072 | 140 Complex*, const octave_idx_type&, double*, |
| 141 octave_idx_type*, octave_idx_type&); | |
| 458 | 142 |
| 5785 | 143 F77_RET_T |
| 144 F77_FUNC (zpotrf, ZPOTRF) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 145 Complex*, const octave_idx_type&, | |
| 146 octave_idx_type& F77_CHAR_ARG_LEN_DECL); | |
| 147 | |
| 148 F77_RET_T | |
| 149 F77_FUNC (zpocon, ZPOCON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 150 Complex*, const octave_idx_type&, const double&, | |
| 151 double&, Complex*, double*, | |
| 152 octave_idx_type& F77_CHAR_ARG_LEN_DECL); | |
| 153 | |
| 154 F77_RET_T | |
| 155 F77_FUNC (zpotrs, ZPOTRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 156 const octave_idx_type&, const Complex*, | |
| 157 const octave_idx_type&, Complex*, | |
| 158 const octave_idx_type&, octave_idx_type& | |
| 159 F77_CHAR_ARG_LEN_DECL); | |
| 160 | |
| 161 F77_RET_T | |
| 6207 | 162 F77_FUNC (ztrtri, ZTRTRI) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, |
| 163 const octave_idx_type&, const Complex*, | |
| 164 const octave_idx_type&, octave_idx_type& | |
| 165 F77_CHAR_ARG_LEN_DECL | |
| 166 F77_CHAR_ARG_LEN_DECL); | |
| 167 | |
| 168 F77_RET_T | |
| 5785 | 169 F77_FUNC (ztrcon, ZTRCON) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, |
| 170 F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 171 const Complex*, const octave_idx_type&, double&, | |
| 172 Complex*, double*, octave_idx_type& | |
| 173 F77_CHAR_ARG_LEN_DECL | |
| 174 F77_CHAR_ARG_LEN_DECL | |
| 175 F77_CHAR_ARG_LEN_DECL); | |
| 176 | |
| 177 F77_RET_T | |
| 178 F77_FUNC (ztrtrs, ZTRTRS) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, | |
| 179 F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 180 const octave_idx_type&, const Complex*, | |
| 181 const octave_idx_type&, Complex*, | |
| 182 const octave_idx_type&, octave_idx_type& | |
| 183 F77_CHAR_ARG_LEN_DECL | |
| 184 F77_CHAR_ARG_LEN_DECL | |
| 185 F77_CHAR_ARG_LEN_DECL); | |
| 186 | |
| 1360 | 187 // Note that the original complex fft routines were not written for |
| 188 // double complex arguments. They have been modified by adding an | |
| 189 // implicit double precision (a-h,o-z) statement at the beginning of | |
| 190 // each subroutine. | |
| 458 | 191 |
| 4552 | 192 F77_RET_T |
| 5275 | 193 F77_FUNC (cffti, CFFTI) (const octave_idx_type&, Complex*); |
| 4552 | 194 |
| 195 F77_RET_T | |
| 5275 | 196 F77_FUNC (cfftf, CFFTF) (const octave_idx_type&, Complex*, Complex*); |
| 4552 | 197 |
| 198 F77_RET_T | |
| 5275 | 199 F77_FUNC (cfftb, CFFTB) (const octave_idx_type&, Complex*, Complex*); |
| 4552 | 200 |
| 201 F77_RET_T | |
| 202 F77_FUNC (zlartg, ZLARTG) (const Complex&, const Complex&, | |
| 203 double&, Complex&, Complex&); | |
| 204 | |
| 205 F77_RET_T | |
| 206 F77_FUNC (ztrsyl, ZTRSYL) (F77_CONST_CHAR_ARG_DECL, | |
| 207 F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 208 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
| 209 const Complex*, const octave_idx_type&, | |
| 210 const Complex*, const octave_idx_type&, | |
| 211 const Complex*, const octave_idx_type&, double&, octave_idx_type& | |
| 4552 | 212 F77_CHAR_ARG_LEN_DECL |
| 213 F77_CHAR_ARG_LEN_DECL); | |
| 214 | |
| 215 F77_RET_T | |
| 216 F77_FUNC (xzlange, XZLANGE) (F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 217 const octave_idx_type&, const octave_idx_type&, const Complex*, |
| 218 const octave_idx_type&, double*, double& | |
| 4552 | 219 F77_CHAR_ARG_LEN_DECL); |
| 458 | 220 } |
| 221 | |
| 2354 | 222 static const Complex Complex_NaN_result (octave_NaN, octave_NaN); |
| 223 | |
| 1360 | 224 // Complex Matrix class |
| 458 | 225 |
| 226 ComplexMatrix::ComplexMatrix (const Matrix& a) | |
| 1214 | 227 : MArray2<Complex> (a.rows (), a.cols ()) |
| 458 | 228 { |
| 5275 | 229 for (octave_idx_type j = 0; j < cols (); j++) |
| 230 for (octave_idx_type i = 0; i < rows (); i++) | |
| 458 | 231 elem (i, j) = a.elem (i, j); |
| 232 } | |
| 233 | |
| 2349 | 234 ComplexMatrix::ComplexMatrix (const RowVector& rv) |
| 235 : MArray2<Complex> (1, rv.length (), 0.0) | |
| 236 { | |
| 5275 | 237 for (octave_idx_type i = 0; i < rv.length (); i++) |
| 2349 | 238 elem (0, i) = rv.elem (i); |
| 239 } | |
| 240 | |
| 241 ComplexMatrix::ComplexMatrix (const ColumnVector& cv) | |
| 242 : MArray2<Complex> (cv.length (), 1, 0.0) | |
| 243 { | |
| 5275 | 244 for (octave_idx_type i = 0; i < cv.length (); i++) |
| 2349 | 245 elem (i, 0) = cv.elem (i); |
| 246 } | |
| 247 | |
| 458 | 248 ComplexMatrix::ComplexMatrix (const DiagMatrix& a) |
| 1214 | 249 : MArray2<Complex> (a.rows (), a.cols (), 0.0) |
| 458 | 250 { |
| 5275 | 251 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 252 elem (i, i) = a.elem (i, i); |
| 253 } | |
| 254 | |
| 2349 | 255 ComplexMatrix::ComplexMatrix (const ComplexRowVector& rv) |
| 256 : MArray2<Complex> (1, rv.length (), 0.0) | |
| 257 { | |
| 5275 | 258 for (octave_idx_type i = 0; i < rv.length (); i++) |
| 2349 | 259 elem (0, i) = rv.elem (i); |
| 260 } | |
| 261 | |
| 262 ComplexMatrix::ComplexMatrix (const ComplexColumnVector& cv) | |
| 263 : MArray2<Complex> (cv.length (), 1, 0.0) | |
| 264 { | |
| 5275 | 265 for (octave_idx_type i = 0; i < cv.length (); i++) |
| 2349 | 266 elem (i, 0) = cv.elem (i); |
| 267 } | |
| 268 | |
| 458 | 269 ComplexMatrix::ComplexMatrix (const ComplexDiagMatrix& a) |
| 1214 | 270 : MArray2<Complex> (a.rows (), a.cols (), 0.0) |
| 458 | 271 { |
| 5275 | 272 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 273 elem (i, i) = a.elem (i, i); |
| 274 } | |
| 275 | |
| 5775 | 276 // FIXME -- could we use a templated mixed-type copy function |
| 1574 | 277 // here? |
| 278 | |
| 2828 | 279 ComplexMatrix::ComplexMatrix (const boolMatrix& a) |
| 3180 | 280 : MArray2<Complex> (a.rows (), a.cols (), 0.0) |
| 2828 | 281 { |
| 5275 | 282 for (octave_idx_type i = 0; i < a.rows (); i++) |
| 283 for (octave_idx_type j = 0; j < a.cols (); j++) | |
| 2828 | 284 elem (i, j) = a.elem (i, j); |
| 285 } | |
| 286 | |
| 1574 | 287 ComplexMatrix::ComplexMatrix (const charMatrix& a) |
| 3180 | 288 : MArray2<Complex> (a.rows (), a.cols (), 0.0) |
| 1574 | 289 { |
| 5275 | 290 for (octave_idx_type i = 0; i < a.rows (); i++) |
| 291 for (octave_idx_type j = 0; j < a.cols (); j++) | |
| 1574 | 292 elem (i, j) = a.elem (i, j); |
| 293 } | |
| 294 | |
| 2384 | 295 bool |
| 458 | 296 ComplexMatrix::operator == (const ComplexMatrix& a) const |
| 297 { | |
| 298 if (rows () != a.rows () || cols () != a.cols ()) | |
| 2384 | 299 return false; |
| 458 | 300 |
| 3769 | 301 return mx_inline_equal (data (), a.data (), length ()); |
| 458 | 302 } |
| 303 | |
| 2384 | 304 bool |
| 458 | 305 ComplexMatrix::operator != (const ComplexMatrix& a) const |
| 306 { | |
| 307 return !(*this == a); | |
| 308 } | |
| 309 | |
| 2815 | 310 bool |
| 311 ComplexMatrix::is_hermitian (void) const | |
| 312 { | |
| 5275 | 313 octave_idx_type nr = rows (); |
| 314 octave_idx_type nc = cols (); | |
| 2815 | 315 |
| 316 if (is_square () && nr > 0) | |
| 317 { | |
| 5275 | 318 for (octave_idx_type i = 0; i < nr; i++) |
| 319 for (octave_idx_type j = i; j < nc; j++) | |
| 2815 | 320 if (elem (i, j) != conj (elem (j, i))) |
| 321 return false; | |
| 322 | |
| 323 return true; | |
| 324 } | |
| 325 | |
| 326 return false; | |
| 327 } | |
| 328 | |
| 458 | 329 // destructive insert/delete/reorder operations |
| 330 | |
| 331 ComplexMatrix& | |
| 5275 | 332 ComplexMatrix::insert (const Matrix& a, octave_idx_type r, octave_idx_type c) |
| 458 | 333 { |
| 5275 | 334 octave_idx_type a_nr = a.rows (); |
| 335 octave_idx_type a_nc = a.cols (); | |
| 1699 | 336 |
| 337 if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) | |
| 458 | 338 { |
| 339 (*current_liboctave_error_handler) ("range error for insert"); | |
| 340 return *this; | |
| 341 } | |
| 342 | |
| 4316 | 343 if (a_nr >0 && a_nc > 0) |
| 344 { | |
| 345 make_unique (); | |
| 346 | |
| 5275 | 347 for (octave_idx_type j = 0; j < a_nc; j++) |
| 348 for (octave_idx_type i = 0; i < a_nr; i++) | |
| 4316 | 349 xelem (r+i, c+j) = a.elem (i, j); |
| 350 } | |
| 458 | 351 |
| 352 return *this; | |
| 353 } | |
| 354 | |
| 355 ComplexMatrix& | |
| 5275 | 356 ComplexMatrix::insert (const RowVector& a, octave_idx_type r, octave_idx_type c) |
| 458 | 357 { |
| 5275 | 358 octave_idx_type a_len = a.length (); |
| 4316 | 359 |
| 1699 | 360 if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ()) |
| 458 | 361 { |
| 362 (*current_liboctave_error_handler) ("range error for insert"); | |
| 363 return *this; | |
| 364 } | |
| 365 | |
| 4316 | 366 if (a_len > 0) |
| 367 { | |
| 368 make_unique (); | |
| 369 | |
| 5275 | 370 for (octave_idx_type i = 0; i < a_len; i++) |
| 4316 | 371 xelem (r, c+i) = a.elem (i); |
| 372 } | |
| 458 | 373 |
| 374 return *this; | |
| 375 } | |
| 376 | |
| 377 ComplexMatrix& | |
| 5275 | 378 ComplexMatrix::insert (const ColumnVector& a, octave_idx_type r, octave_idx_type c) |
| 458 | 379 { |
| 5275 | 380 octave_idx_type a_len = a.length (); |
| 4316 | 381 |
| 1699 | 382 if (r < 0 || r + a_len > rows () || c < 0 || c >= cols ()) |
| 458 | 383 { |
| 384 (*current_liboctave_error_handler) ("range error for insert"); | |
| 385 return *this; | |
| 386 } | |
| 387 | |
| 4316 | 388 if (a_len > 0) |
| 389 { | |
| 390 make_unique (); | |
| 391 | |
| 5275 | 392 for (octave_idx_type i = 0; i < a_len; i++) |
| 4316 | 393 xelem (r+i, c) = a.elem (i); |
| 394 } | |
| 458 | 395 |
| 396 return *this; | |
| 397 } | |
| 398 | |
| 399 ComplexMatrix& | |
| 5275 | 400 ComplexMatrix::insert (const DiagMatrix& a, octave_idx_type r, octave_idx_type c) |
| 458 | 401 { |
| 5275 | 402 octave_idx_type a_nr = a.rows (); |
| 403 octave_idx_type a_nc = a.cols (); | |
| 1699 | 404 |
| 405 if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) | |
| 458 | 406 { |
| 407 (*current_liboctave_error_handler) ("range error for insert"); | |
| 408 return *this; | |
| 409 } | |
| 410 | |
| 1699 | 411 fill (0.0, r, c, r + a_nr - 1, c + a_nc - 1); |
| 412 | |
| 5275 | 413 octave_idx_type a_len = a.length (); |
| 4316 | 414 |
| 415 if (a_len > 0) | |
| 416 { | |
| 417 make_unique (); | |
| 418 | |
| 5275 | 419 for (octave_idx_type i = 0; i < a_len; i++) |
| 4316 | 420 xelem (r+i, c+i) = a.elem (i, i); |
| 421 } | |
| 458 | 422 |
| 423 return *this; | |
| 424 } | |
| 425 | |
| 426 ComplexMatrix& | |
| 5275 | 427 ComplexMatrix::insert (const ComplexMatrix& a, octave_idx_type r, octave_idx_type c) |
| 458 | 428 { |
| 1561 | 429 Array2<Complex>::insert (a, r, c); |
| 458 | 430 return *this; |
| 431 } | |
| 432 | |
| 433 ComplexMatrix& | |
| 5275 | 434 ComplexMatrix::insert (const ComplexRowVector& a, octave_idx_type r, octave_idx_type c) |
| 458 | 435 { |
| 5275 | 436 octave_idx_type a_len = a.length (); |
| 1699 | 437 if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ()) |
| 458 | 438 { |
| 439 (*current_liboctave_error_handler) ("range error for insert"); | |
| 440 return *this; | |
| 441 } | |
| 442 | |
| 5275 | 443 for (octave_idx_type i = 0; i < a_len; i++) |
| 458 | 444 elem (r, c+i) = a.elem (i); |
| 445 | |
| 446 return *this; | |
| 447 } | |
| 448 | |
| 449 ComplexMatrix& | |
| 5275 | 450 ComplexMatrix::insert (const ComplexColumnVector& a, octave_idx_type r, octave_idx_type c) |
| 458 | 451 { |
| 5275 | 452 octave_idx_type a_len = a.length (); |
| 4316 | 453 |
| 1699 | 454 if (r < 0 || r + a_len > rows () || c < 0 || c >= cols ()) |
| 458 | 455 { |
| 456 (*current_liboctave_error_handler) ("range error for insert"); | |
| 457 return *this; | |
| 458 } | |
| 459 | |
| 4316 | 460 if (a_len > 0) |
| 461 { | |
| 462 make_unique (); | |
| 463 | |
| 5275 | 464 for (octave_idx_type i = 0; i < a_len; i++) |
| 4316 | 465 xelem (r+i, c) = a.elem (i); |
| 466 } | |
| 458 | 467 |
| 468 return *this; | |
| 469 } | |
| 470 | |
| 471 ComplexMatrix& | |
| 5275 | 472 ComplexMatrix::insert (const ComplexDiagMatrix& a, octave_idx_type r, octave_idx_type c) |
| 458 | 473 { |
| 5275 | 474 octave_idx_type a_nr = a.rows (); |
| 475 octave_idx_type a_nc = a.cols (); | |
| 1699 | 476 |
| 477 if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) | |
| 458 | 478 { |
| 479 (*current_liboctave_error_handler) ("range error for insert"); | |
| 480 return *this; | |
| 481 } | |
| 482 | |
| 1699 | 483 fill (0.0, r, c, r + a_nr - 1, c + a_nc - 1); |
| 484 | |
| 5275 | 485 octave_idx_type a_len = a.length (); |
| 4316 | 486 |
| 487 if (a_len > 0) | |
| 488 { | |
| 489 make_unique (); | |
| 490 | |
| 5275 | 491 for (octave_idx_type i = 0; i < a_len; i++) |
| 4316 | 492 xelem (r+i, c+i) = a.elem (i, i); |
| 493 } | |
| 458 | 494 |
| 495 return *this; | |
| 496 } | |
| 497 | |
| 498 ComplexMatrix& | |
| 499 ComplexMatrix::fill (double val) | |
| 500 { | |
| 5275 | 501 octave_idx_type nr = rows (); |
| 502 octave_idx_type nc = cols (); | |
| 4316 | 503 |
| 458 | 504 if (nr > 0 && nc > 0) |
| 4316 | 505 { |
| 506 make_unique (); | |
| 507 | |
| 5275 | 508 for (octave_idx_type j = 0; j < nc; j++) |
| 509 for (octave_idx_type i = 0; i < nr; i++) | |
| 4316 | 510 xelem (i, j) = val; |
| 511 } | |
| 458 | 512 |
| 513 return *this; | |
| 514 } | |
| 515 | |
| 516 ComplexMatrix& | |
| 517 ComplexMatrix::fill (const Complex& val) | |
| 518 { | |
| 5275 | 519 octave_idx_type nr = rows (); |
| 520 octave_idx_type nc = cols (); | |
| 4316 | 521 |
| 458 | 522 if (nr > 0 && nc > 0) |
| 4316 | 523 { |
| 524 make_unique (); | |
| 525 | |
| 5275 | 526 for (octave_idx_type j = 0; j < nc; j++) |
| 527 for (octave_idx_type i = 0; i < nr; i++) | |
| 4316 | 528 xelem (i, j) = val; |
| 529 } | |
| 458 | 530 |
| 531 return *this; | |
| 532 } | |
| 533 | |
| 534 ComplexMatrix& | |
| 5275 | 535 ComplexMatrix::fill (double val, octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) |
| 458 | 536 { |
| 5275 | 537 octave_idx_type nr = rows (); |
| 538 octave_idx_type nc = cols (); | |
| 4316 | 539 |
| 458 | 540 if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0 |
| 541 || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc) | |
| 542 { | |
| 543 (*current_liboctave_error_handler) ("range error for fill"); | |
| 544 return *this; | |
| 545 } | |
| 546 | |
| 5275 | 547 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } |
| 548 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } | |
| 458 | 549 |
| 4316 | 550 if (r2 >= r1 && c2 >= c1) |
| 551 { | |
| 552 make_unique (); | |
| 553 | |
| 5275 | 554 for (octave_idx_type j = c1; j <= c2; j++) |
| 555 for (octave_idx_type i = r1; i <= r2; i++) | |
| 4316 | 556 xelem (i, j) = val; |
| 557 } | |
| 458 | 558 |
| 559 return *this; | |
| 560 } | |
| 561 | |
| 562 ComplexMatrix& | |
| 5275 | 563 ComplexMatrix::fill (const Complex& val, octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) |
| 458 | 564 { |
| 5275 | 565 octave_idx_type nr = rows (); |
| 566 octave_idx_type nc = cols (); | |
| 4316 | 567 |
| 458 | 568 if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0 |
| 569 || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc) | |
| 570 { | |
| 571 (*current_liboctave_error_handler) ("range error for fill"); | |
| 572 return *this; | |
| 573 } | |
| 574 | |
| 5275 | 575 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } |
| 576 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } | |
| 458 | 577 |
| 4316 | 578 if (r2 >= r1 && c2 >=c1) |
| 579 { | |
| 580 make_unique (); | |
| 581 | |
| 5275 | 582 for (octave_idx_type j = c1; j <= c2; j++) |
| 583 for (octave_idx_type i = r1; i <= r2; i++) | |
| 4316 | 584 xelem (i, j) = val; |
| 585 } | |
| 458 | 586 |
| 587 return *this; | |
| 588 } | |
| 589 | |
| 590 ComplexMatrix | |
| 591 ComplexMatrix::append (const Matrix& a) const | |
| 592 { | |
| 5275 | 593 octave_idx_type nr = rows (); |
| 594 octave_idx_type nc = cols (); | |
| 458 | 595 if (nr != a.rows ()) |
| 596 { | |
| 597 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 598 return *this; | |
| 599 } | |
| 600 | |
| 5275 | 601 octave_idx_type nc_insert = nc; |
| 458 | 602 ComplexMatrix retval (nr, nc + a.cols ()); |
| 603 retval.insert (*this, 0, 0); | |
| 604 retval.insert (a, 0, nc_insert); | |
| 605 return retval; | |
| 606 } | |
| 607 | |
| 608 ComplexMatrix | |
| 609 ComplexMatrix::append (const RowVector& a) const | |
| 610 { | |
| 5275 | 611 octave_idx_type nr = rows (); |
| 612 octave_idx_type nc = cols (); | |
| 458 | 613 if (nr != 1) |
| 614 { | |
| 615 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 616 return *this; | |
| 617 } | |
| 618 | |
| 5275 | 619 octave_idx_type nc_insert = nc; |
| 458 | 620 ComplexMatrix retval (nr, nc + a.length ()); |
| 621 retval.insert (*this, 0, 0); | |
| 622 retval.insert (a, 0, nc_insert); | |
| 623 return retval; | |
| 624 } | |
| 625 | |
| 626 ComplexMatrix | |
| 627 ComplexMatrix::append (const ColumnVector& a) const | |
| 628 { | |
| 5275 | 629 octave_idx_type nr = rows (); |
| 630 octave_idx_type nc = cols (); | |
| 458 | 631 if (nr != a.length ()) |
| 632 { | |
| 633 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 634 return *this; | |
| 635 } | |
| 636 | |
| 5275 | 637 octave_idx_type nc_insert = nc; |
| 458 | 638 ComplexMatrix retval (nr, nc + 1); |
| 639 retval.insert (*this, 0, 0); | |
| 640 retval.insert (a, 0, nc_insert); | |
| 641 return retval; | |
| 642 } | |
| 643 | |
| 644 ComplexMatrix | |
| 645 ComplexMatrix::append (const DiagMatrix& a) const | |
| 646 { | |
| 5275 | 647 octave_idx_type nr = rows (); |
| 648 octave_idx_type nc = cols (); | |
| 458 | 649 if (nr != a.rows ()) |
| 650 { | |
| 651 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 652 return *this; | |
| 653 } | |
| 654 | |
| 5275 | 655 octave_idx_type nc_insert = nc; |
| 458 | 656 ComplexMatrix retval (nr, nc + a.cols ()); |
| 657 retval.insert (*this, 0, 0); | |
| 658 retval.insert (a, 0, nc_insert); | |
| 659 return retval; | |
| 660 } | |
| 661 | |
| 662 ComplexMatrix | |
| 663 ComplexMatrix::append (const ComplexMatrix& a) const | |
| 664 { | |
| 5275 | 665 octave_idx_type nr = rows (); |
| 666 octave_idx_type nc = cols (); | |
| 458 | 667 if (nr != a.rows ()) |
| 668 { | |
| 669 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 670 return *this; | |
| 671 } | |
| 672 | |
| 5275 | 673 octave_idx_type nc_insert = nc; |
| 458 | 674 ComplexMatrix retval (nr, nc + a.cols ()); |
| 675 retval.insert (*this, 0, 0); | |
| 676 retval.insert (a, 0, nc_insert); | |
| 677 return retval; | |
| 678 } | |
| 679 | |
| 680 ComplexMatrix | |
| 681 ComplexMatrix::append (const ComplexRowVector& a) const | |
| 682 { | |
| 5275 | 683 octave_idx_type nr = rows (); |
| 684 octave_idx_type nc = cols (); | |
| 458 | 685 if (nr != 1) |
| 686 { | |
| 687 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 688 return *this; | |
| 689 } | |
| 690 | |
| 5275 | 691 octave_idx_type nc_insert = nc; |
| 458 | 692 ComplexMatrix retval (nr, nc + a.length ()); |
| 693 retval.insert (*this, 0, 0); | |
| 694 retval.insert (a, 0, nc_insert); | |
| 695 return retval; | |
| 696 } | |
| 697 | |
| 698 ComplexMatrix | |
| 699 ComplexMatrix::append (const ComplexColumnVector& a) const | |
| 700 { | |
| 5275 | 701 octave_idx_type nr = rows (); |
| 702 octave_idx_type nc = cols (); | |
| 458 | 703 if (nr != a.length ()) |
| 704 { | |
| 705 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 706 return *this; | |
| 707 } | |
| 708 | |
| 5275 | 709 octave_idx_type nc_insert = nc; |
| 458 | 710 ComplexMatrix retval (nr, nc + 1); |
| 711 retval.insert (*this, 0, 0); | |
| 712 retval.insert (a, 0, nc_insert); | |
| 713 return retval; | |
| 714 } | |
| 715 | |
| 716 ComplexMatrix | |
| 717 ComplexMatrix::append (const ComplexDiagMatrix& a) const | |
| 718 { | |
| 5275 | 719 octave_idx_type nr = rows (); |
| 720 octave_idx_type nc = cols (); | |
| 458 | 721 if (nr != a.rows ()) |
| 722 { | |
| 723 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 724 return *this; | |
| 725 } | |
| 726 | |
| 5275 | 727 octave_idx_type nc_insert = nc; |
| 458 | 728 ComplexMatrix retval (nr, nc + a.cols ()); |
| 729 retval.insert (*this, 0, 0); | |
| 730 retval.insert (a, 0, nc_insert); | |
| 731 return retval; | |
| 732 } | |
| 733 | |
| 734 ComplexMatrix | |
| 735 ComplexMatrix::stack (const Matrix& a) const | |
| 736 { | |
| 5275 | 737 octave_idx_type nr = rows (); |
| 738 octave_idx_type nc = cols (); | |
| 458 | 739 if (nc != a.cols ()) |
| 740 { | |
| 741 (*current_liboctave_error_handler) | |
| 742 ("column dimension mismatch for stack"); | |
| 743 return *this; | |
| 744 } | |
| 745 | |
| 5275 | 746 octave_idx_type nr_insert = nr; |
| 458 | 747 ComplexMatrix retval (nr + a.rows (), nc); |
| 748 retval.insert (*this, 0, 0); | |
| 749 retval.insert (a, nr_insert, 0); | |
| 750 return retval; | |
| 751 } | |
| 752 | |
| 753 ComplexMatrix | |
| 754 ComplexMatrix::stack (const RowVector& a) const | |
| 755 { | |
| 5275 | 756 octave_idx_type nr = rows (); |
| 757 octave_idx_type nc = cols (); | |
| 458 | 758 if (nc != a.length ()) |
| 759 { | |
| 760 (*current_liboctave_error_handler) | |
| 761 ("column dimension mismatch for stack"); | |
| 762 return *this; | |
| 763 } | |
| 764 | |
| 5275 | 765 octave_idx_type nr_insert = nr; |
| 458 | 766 ComplexMatrix retval (nr + 1, nc); |
| 767 retval.insert (*this, 0, 0); | |
| 768 retval.insert (a, nr_insert, 0); | |
| 769 return retval; | |
| 770 } | |
| 771 | |
| 772 ComplexMatrix | |
| 773 ComplexMatrix::stack (const ColumnVector& a) const | |
| 774 { | |
| 5275 | 775 octave_idx_type nr = rows (); |
| 776 octave_idx_type nc = cols (); | |
| 458 | 777 if (nc != 1) |
| 778 { | |
| 779 (*current_liboctave_error_handler) | |
| 780 ("column dimension mismatch for stack"); | |
| 781 return *this; | |
| 782 } | |
| 783 | |
| 5275 | 784 octave_idx_type nr_insert = nr; |
| 458 | 785 ComplexMatrix retval (nr + a.length (), nc); |
| 786 retval.insert (*this, 0, 0); | |
| 787 retval.insert (a, nr_insert, 0); | |
| 788 return retval; | |
| 789 } | |
| 790 | |
| 791 ComplexMatrix | |
| 792 ComplexMatrix::stack (const DiagMatrix& a) const | |
| 793 { | |
| 5275 | 794 octave_idx_type nr = rows (); |
| 795 octave_idx_type nc = cols (); | |
| 458 | 796 if (nc != a.cols ()) |
| 797 { | |
| 798 (*current_liboctave_error_handler) | |
| 799 ("column dimension mismatch for stack"); | |
| 800 return *this; | |
| 801 } | |
| 802 | |
| 5275 | 803 octave_idx_type nr_insert = nr; |
| 458 | 804 ComplexMatrix retval (nr + a.rows (), nc); |
| 805 retval.insert (*this, 0, 0); | |
| 806 retval.insert (a, nr_insert, 0); | |
| 807 return retval; | |
| 808 } | |
| 809 | |
| 810 ComplexMatrix | |
| 811 ComplexMatrix::stack (const ComplexMatrix& a) const | |
| 812 { | |
| 5275 | 813 octave_idx_type nr = rows (); |
| 814 octave_idx_type nc = cols (); | |
| 458 | 815 if (nc != a.cols ()) |
| 816 { | |
| 817 (*current_liboctave_error_handler) | |
| 818 ("column dimension mismatch for stack"); | |
| 819 return *this; | |
| 820 } | |
| 821 | |
| 5275 | 822 octave_idx_type nr_insert = nr; |
| 458 | 823 ComplexMatrix retval (nr + a.rows (), nc); |
| 824 retval.insert (*this, 0, 0); | |
| 825 retval.insert (a, nr_insert, 0); | |
| 826 return retval; | |
| 827 } | |
| 828 | |
| 829 ComplexMatrix | |
| 830 ComplexMatrix::stack (const ComplexRowVector& a) const | |
| 831 { | |
| 5275 | 832 octave_idx_type nr = rows (); |
| 833 octave_idx_type nc = cols (); | |
| 458 | 834 if (nc != a.length ()) |
| 835 { | |
| 836 (*current_liboctave_error_handler) | |
| 837 ("column dimension mismatch for stack"); | |
| 838 return *this; | |
| 839 } | |
| 840 | |
| 5275 | 841 octave_idx_type nr_insert = nr; |
| 458 | 842 ComplexMatrix retval (nr + 1, nc); |
| 843 retval.insert (*this, 0, 0); | |
| 844 retval.insert (a, nr_insert, 0); | |
| 845 return retval; | |
| 846 } | |
| 847 | |
| 848 ComplexMatrix | |
| 849 ComplexMatrix::stack (const ComplexColumnVector& a) const | |
| 850 { | |
| 5275 | 851 octave_idx_type nr = rows (); |
| 852 octave_idx_type nc = cols (); | |
| 458 | 853 if (nc != 1) |
| 854 { | |
| 855 (*current_liboctave_error_handler) | |
| 856 ("column dimension mismatch for stack"); | |
| 857 return *this; | |
| 858 } | |
| 859 | |
| 5275 | 860 octave_idx_type nr_insert = nr; |
| 458 | 861 ComplexMatrix retval (nr + a.length (), nc); |
| 862 retval.insert (*this, 0, 0); | |
| 863 retval.insert (a, nr_insert, 0); | |
| 864 return retval; | |
| 865 } | |
| 866 | |
| 867 ComplexMatrix | |
| 868 ComplexMatrix::stack (const ComplexDiagMatrix& a) const | |
| 869 { | |
| 5275 | 870 octave_idx_type nr = rows (); |
| 871 octave_idx_type nc = cols (); | |
| 458 | 872 if (nc != a.cols ()) |
| 873 { | |
| 874 (*current_liboctave_error_handler) | |
| 875 ("column dimension mismatch for stack"); | |
| 876 return *this; | |
| 877 } | |
| 878 | |
| 5275 | 879 octave_idx_type nr_insert = nr; |
| 458 | 880 ComplexMatrix retval (nr + a.rows (), nc); |
| 881 retval.insert (*this, 0, 0); | |
| 882 retval.insert (a, nr_insert, 0); | |
| 883 return retval; | |
| 884 } | |
| 885 | |
| 886 ComplexMatrix | |
| 887 ComplexMatrix::hermitian (void) const | |
| 888 { | |
| 5275 | 889 octave_idx_type nr = rows (); |
| 890 octave_idx_type nc = cols (); | |
| 458 | 891 ComplexMatrix result; |
| 892 if (length () > 0) | |
| 893 { | |
| 894 result.resize (nc, nr); | |
| 5275 | 895 for (octave_idx_type j = 0; j < nc; j++) |
| 896 for (octave_idx_type i = 0; i < nr; i++) | |
| 458 | 897 result.elem (j, i) = conj (elem (i, j)); |
| 898 } | |
| 899 return result; | |
| 900 } | |
| 901 | |
| 902 ComplexMatrix | |
| 903 conj (const ComplexMatrix& a) | |
| 904 { | |
| 5275 | 905 octave_idx_type a_len = a.length (); |
| 458 | 906 ComplexMatrix retval; |
| 907 if (a_len > 0) | |
| 3769 | 908 retval = ComplexMatrix (mx_inline_conj_dup (a.data (), a_len), |
| 909 a.rows (), a.cols ()); | |
| 458 | 910 return retval; |
| 911 } | |
| 912 | |
| 913 // resize is the destructive equivalent for this one | |
| 914 | |
| 915 ComplexMatrix | |
| 5275 | 916 ComplexMatrix::extract (octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) const |
| 458 | 917 { |
| 5275 | 918 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } |
| 919 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } | |
| 920 | |
| 921 octave_idx_type new_r = r2 - r1 + 1; | |
| 922 octave_idx_type new_c = c2 - c1 + 1; | |
| 458 | 923 |
| 924 ComplexMatrix result (new_r, new_c); | |
| 925 | |
| 5275 | 926 for (octave_idx_type j = 0; j < new_c; j++) |
| 927 for (octave_idx_type i = 0; i < new_r; i++) | |
| 4316 | 928 result.xelem (i, j) = elem (r1+i, c1+j); |
| 929 | |
| 930 return result; | |
| 931 } | |
| 932 | |
| 933 ComplexMatrix | |
| 5275 | 934 ComplexMatrix::extract_n (octave_idx_type r1, octave_idx_type c1, octave_idx_type nr, octave_idx_type nc) const |
| 4316 | 935 { |
| 936 ComplexMatrix result (nr, nc); | |
| 937 | |
| 5275 | 938 for (octave_idx_type j = 0; j < nc; j++) |
| 939 for (octave_idx_type i = 0; i < nr; i++) | |
| 4316 | 940 result.xelem (i, j) = elem (r1+i, c1+j); |
| 458 | 941 |
| 942 return result; | |
| 943 } | |
| 944 | |
| 945 // extract row or column i. | |
| 946 | |
| 947 ComplexRowVector | |
| 5275 | 948 ComplexMatrix::row (octave_idx_type i) const |
| 458 | 949 { |
| 5275 | 950 octave_idx_type nc = cols (); |
| 458 | 951 if (i < 0 || i >= rows ()) |
| 952 { | |
| 953 (*current_liboctave_error_handler) ("invalid row selection"); | |
| 954 return ComplexRowVector (); | |
| 955 } | |
| 956 | |
| 957 ComplexRowVector retval (nc); | |
| 5275 | 958 for (octave_idx_type j = 0; j < cols (); j++) |
| 4316 | 959 retval.xelem (j) = elem (i, j); |
| 458 | 960 |
| 961 return retval; | |
| 962 } | |
| 963 | |
| 964 ComplexColumnVector | |
| 5275 | 965 ComplexMatrix::column (octave_idx_type i) const |
| 458 | 966 { |
| 5275 | 967 octave_idx_type nr = rows (); |
| 458 | 968 if (i < 0 || i >= cols ()) |
| 969 { | |
| 970 (*current_liboctave_error_handler) ("invalid column selection"); | |
| 971 return ComplexColumnVector (); | |
| 972 } | |
| 973 | |
| 974 ComplexColumnVector retval (nr); | |
| 5275 | 975 for (octave_idx_type j = 0; j < nr; j++) |
| 4316 | 976 retval.xelem (j) = elem (j, i); |
| 458 | 977 |
| 978 return retval; | |
| 979 } | |
| 980 | |
| 981 ComplexMatrix | |
| 982 ComplexMatrix::inverse (void) const | |
| 983 { | |
| 5275 | 984 octave_idx_type info; |
| 479 | 985 double rcond; |
| 6207 | 986 MatrixType mattype (*this); |
| 987 return inverse (mattype, info, rcond, 0, 0); | |
| 988 } | |
| 989 | |
| 990 ComplexMatrix | |
| 6479 | 991 ComplexMatrix::inverse (octave_idx_type& info) const |
| 992 { | |
| 993 double rcond; | |
| 994 MatrixType mattype (*this); | |
| 995 return inverse (mattype, info, rcond, 0, 0); | |
| 996 } | |
| 997 | |
| 998 ComplexMatrix | |
| 999 ComplexMatrix::inverse (octave_idx_type& info, double& rcond, int force, | |
| 1000 int calc_cond) const | |
| 1001 { | |
| 1002 MatrixType mattype (*this); | |
| 6482 | 1003 return inverse (mattype, info, rcond, force, calc_cond); |
| 6479 | 1004 } |
| 1005 | |
| 1006 ComplexMatrix | |
| 6207 | 1007 ComplexMatrix::inverse (MatrixType &mattype) const |
| 1008 { | |
| 1009 octave_idx_type info; | |
| 1010 double rcond; | |
| 1011 return inverse (mattype, info, rcond, 0, 0); | |
| 1012 } | |
| 1013 | |
| 1014 ComplexMatrix | |
| 1015 ComplexMatrix::inverse (MatrixType &mattype, octave_idx_type& info) const | |
| 1016 { | |
| 1017 double rcond; | |
| 1018 return inverse (mattype, info, rcond, 0, 0); | |
| 458 | 1019 } |
| 1020 | |
| 1021 ComplexMatrix | |
| 6207 | 1022 ComplexMatrix::tinverse (MatrixType &mattype, octave_idx_type& info, |
| 1023 double& rcond, int force, int calc_cond) const | |
| 458 | 1024 { |
| 6207 | 1025 ComplexMatrix retval; |
| 1026 | |
| 1027 octave_idx_type nr = rows (); | |
| 1028 octave_idx_type nc = cols (); | |
| 1029 | |
| 1030 if (nr != nc || nr == 0 || nc == 0) | |
| 1031 (*current_liboctave_error_handler) ("inverse requires square matrix"); | |
| 1032 else | |
| 1033 { | |
| 1034 int typ = mattype.type (); | |
| 1035 char uplo = (typ == MatrixType::Lower ? 'L' : 'U'); | |
| 1036 char udiag = 'N'; | |
| 1037 retval = *this; | |
| 1038 Complex *tmp_data = retval.fortran_vec (); | |
| 1039 | |
| 1040 F77_XFCN (ztrtri, ZTRTRI, (F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1041 F77_CONST_CHAR_ARG2 (&udiag, 1), | |
| 1042 nr, tmp_data, nr, info | |
| 1043 F77_CHAR_ARG_LEN (1) | |
| 1044 F77_CHAR_ARG_LEN (1))); | |
| 1045 | |
| 1046 if (f77_exception_encountered) | |
| 1047 (*current_liboctave_error_handler) ("unrecoverable error in ztrtri"); | |
| 1048 else | |
| 1049 { | |
| 1050 // Throw-away extra info LAPACK gives so as to not change output. | |
| 1051 rcond = 0.0; | |
| 1052 if (info != 0) | |
| 1053 info = -1; | |
| 1054 else if (calc_cond) | |
| 1055 { | |
| 1056 octave_idx_type ztrcon_info = 0; | |
| 1057 char job = '1'; | |
| 1058 | |
| 6482 | 1059 OCTAVE_LOCAL_BUFFER (Complex, cwork, 2*nr); |
| 6207 | 1060 OCTAVE_LOCAL_BUFFER (double, rwork, nr); |
| 1061 | |
| 1062 F77_XFCN (ztrcon, ZTRCON, (F77_CONST_CHAR_ARG2 (&job, 1), | |
| 1063 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1064 F77_CONST_CHAR_ARG2 (&udiag, 1), | |
| 1065 nr, tmp_data, nr, rcond, | |
| 1066 cwork, rwork, ztrcon_info | |
| 1067 F77_CHAR_ARG_LEN (1) | |
| 1068 F77_CHAR_ARG_LEN (1) | |
| 1069 F77_CHAR_ARG_LEN (1))); | |
| 1070 | |
| 1071 if (f77_exception_encountered) | |
| 1072 (*current_liboctave_error_handler) | |
| 1073 ("unrecoverable error in ztrcon"); | |
| 1074 | |
| 1075 if (ztrcon_info != 0) | |
| 1076 info = -1; | |
| 1077 } | |
| 1078 } | |
| 1079 | |
| 1080 if (info == -1 && ! force) | |
| 1081 retval = *this; // Restore matrix contents. | |
| 1082 } | |
| 1083 | |
| 1084 return retval; | |
| 458 | 1085 } |
| 1086 | |
| 1087 ComplexMatrix | |
| 6207 | 1088 ComplexMatrix::finverse (MatrixType &mattype, octave_idx_type& info, |
| 1089 double& rcond, int force, int calc_cond) const | |
| 458 | 1090 { |
| 1948 | 1091 ComplexMatrix retval; |
| 1092 | |
| 5275 | 1093 octave_idx_type nr = rows (); |
| 1094 octave_idx_type nc = cols (); | |
| 1948 | 1095 |
| 458 | 1096 if (nr != nc) |
| 1948 | 1097 (*current_liboctave_error_handler) ("inverse requires square matrix"); |
| 458 | 1098 else |
| 1099 { | |
| 5275 | 1100 Array<octave_idx_type> ipvt (nr); |
| 1101 octave_idx_type *pipvt = ipvt.fortran_vec (); | |
| 1948 | 1102 |
| 1103 retval = *this; | |
| 1104 Complex *tmp_data = retval.fortran_vec (); | |
| 1105 | |
| 4329 | 1106 Array<Complex> z(1); |
| 5275 | 1107 octave_idx_type lwork = -1; |
| 4330 | 1108 |
| 1109 // Query the optimum work array size. | |
| 4329 | 1110 |
| 1111 F77_XFCN (zgetri, ZGETRI, (nc, tmp_data, nr, pipvt, | |
| 1112 z.fortran_vec (), lwork, info)); | |
| 1113 | |
| 1114 if (f77_exception_encountered) | |
| 1115 { | |
| 1116 (*current_liboctave_error_handler) | |
| 1117 ("unrecoverable error in zgetri"); | |
| 1118 return retval; | |
| 1119 } | |
| 1120 | |
| 5315 | 1121 lwork = static_cast<octave_idx_type> (std::real(z(0))); |
| 4329 | 1122 lwork = (lwork < 2 *nc ? 2*nc : lwork); |
| 1123 z.resize (lwork); | |
| 1124 Complex *pz = z.fortran_vec (); | |
| 1125 | |
| 1126 info = 0; | |
| 1127 | |
| 4330 | 1128 // Calculate the norm of the matrix, for later use. |
| 4329 | 1129 double anorm; |
| 1130 if (calc_cond) | |
| 5275 | 1131 anorm = retval.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
| 4329 | 1132 |
| 1133 F77_XFCN (zgetrf, ZGETRF, (nc, nc, tmp_data, nr, pipvt, info)); | |
| 1948 | 1134 |
| 1135 if (f77_exception_encountered) | |
| 4329 | 1136 (*current_liboctave_error_handler) ("unrecoverable error in zgetrf"); |
| 1948 | 1137 else |
| 1138 { | |
| 4330 | 1139 // Throw-away extra info LAPACK gives so as to not change output. |
| 4509 | 1140 rcond = 0.0; |
| 1141 if (info != 0) | |
| 1948 | 1142 info = -1; |
| 4329 | 1143 else if (calc_cond) |
| 1144 { | |
| 4330 | 1145 // Now calculate the condition number for non-singular matrix. |
| 5275 | 1146 octave_idx_type zgecon_info = 0; |
| 4329 | 1147 char job = '1'; |
| 1148 Array<double> rz (2 * nc); | |
| 1149 double *prz = rz.fortran_vec (); | |
| 4552 | 1150 F77_XFCN (zgecon, ZGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
| 1151 nc, tmp_data, nr, anorm, | |
| 5061 | 1152 rcond, pz, prz, zgecon_info |
| 4552 | 1153 F77_CHAR_ARG_LEN (1))); |
| 4329 | 1154 |
| 1155 if (f77_exception_encountered) | |
| 1156 (*current_liboctave_error_handler) | |
| 1157 ("unrecoverable error in zgecon"); | |
| 1158 | |
| 5061 | 1159 if (zgecon_info != 0) |
| 4329 | 1160 info = -1; |
| 1161 } | |
| 1948 | 1162 |
| 1163 if (info == -1 && ! force) | |
| 1164 retval = *this; // Restore contents. | |
| 1165 else | |
| 1166 { | |
| 5275 | 1167 octave_idx_type zgetri_info = 0; |
| 5061 | 1168 |
| 4329 | 1169 F77_XFCN (zgetri, ZGETRI, (nc, tmp_data, nr, pipvt, |
| 5061 | 1170 pz, lwork, zgetri_info)); |
| 1948 | 1171 |
| 1172 if (f77_exception_encountered) | |
| 1173 (*current_liboctave_error_handler) | |
| 4329 | 1174 ("unrecoverable error in zgetri"); |
| 1175 | |
| 5061 | 1176 if (zgetri_info != 0) |
| 4329 | 1177 info = -1; |
| 1948 | 1178 } |
| 1179 } | |
| 6207 | 1180 |
| 1181 if (info != 0) | |
| 1182 mattype.mark_as_rectangular(); | |
| 458 | 1183 } |
| 4329 | 1184 |
| 1948 | 1185 return retval; |
| 458 | 1186 } |
| 1187 | |
| 1188 ComplexMatrix | |
| 6207 | 1189 ComplexMatrix::inverse (MatrixType &mattype, octave_idx_type& info, |
| 1190 double& rcond, int force, int calc_cond) const | |
| 1191 { | |
| 1192 int typ = mattype.type (false); | |
| 1193 ComplexMatrix ret; | |
| 1194 | |
| 1195 if (typ == MatrixType::Unknown) | |
| 1196 typ = mattype.type (*this); | |
| 1197 | |
| 1198 if (typ == MatrixType::Upper || typ == MatrixType::Lower) | |
| 1199 ret = tinverse (mattype, info, rcond, force, calc_cond); | |
| 6840 | 1200 else |
| 6207 | 1201 { |
| 1202 if (mattype.is_hermitian ()) | |
| 1203 { | |
| 6486 | 1204 ComplexCHOL chol (*this, info, calc_cond); |
| 6207 | 1205 if (info == 0) |
| 6486 | 1206 { |
| 1207 if (calc_cond) | |
| 1208 rcond = chol.rcond(); | |
| 1209 else | |
| 1210 rcond = 1.0; | |
| 1211 ret = chol.inverse (); | |
| 1212 } | |
| 6207 | 1213 else |
| 1214 mattype.mark_as_unsymmetric (); | |
| 1215 } | |
| 1216 | |
| 1217 if (!mattype.is_hermitian ()) | |
| 1218 ret = finverse(mattype, info, rcond, force, calc_cond); | |
| 6840 | 1219 |
| 7033 | 1220 if ((mattype.is_hermitian () || calc_cond) && rcond == 0.) |
| 6840 | 1221 ret = ComplexMatrix (rows (), columns (), Complex (octave_Inf, 0.)); |
| 6207 | 1222 } |
| 1223 | |
| 1224 return ret; | |
| 1225 } | |
| 1226 | |
| 1227 ComplexMatrix | |
| 4384 | 1228 ComplexMatrix::pseudo_inverse (double tol) const |
| 740 | 1229 { |
| 1549 | 1230 ComplexMatrix retval; |
| 1231 | |
| 3480 | 1232 ComplexSVD result (*this, SVD::economy); |
| 740 | 1233 |
| 1234 DiagMatrix S = result.singular_values (); | |
| 1235 ComplexMatrix U = result.left_singular_matrix (); | |
| 1236 ComplexMatrix V = result.right_singular_matrix (); | |
| 1237 | |
| 1238 ColumnVector sigma = S.diag (); | |
| 1239 | |
| 5275 | 1240 octave_idx_type r = sigma.length () - 1; |
| 1241 octave_idx_type nr = rows (); | |
| 1242 octave_idx_type nc = cols (); | |
| 740 | 1243 |
| 1244 if (tol <= 0.0) | |
| 1245 { | |
| 1246 if (nr > nc) | |
| 1247 tol = nr * sigma.elem (0) * DBL_EPSILON; | |
| 1248 else | |
| 1249 tol = nc * sigma.elem (0) * DBL_EPSILON; | |
| 1250 } | |
| 1251 | |
| 1252 while (r >= 0 && sigma.elem (r) < tol) | |
| 1253 r--; | |
| 1254 | |
| 1255 if (r < 0) | |
| 1549 | 1256 retval = ComplexMatrix (nc, nr, 0.0); |
| 740 | 1257 else |
| 1258 { | |
| 1259 ComplexMatrix Ur = U.extract (0, 0, nr-1, r); | |
| 1260 DiagMatrix D = DiagMatrix (sigma.extract (0, r)) . inverse (); | |
| 1261 ComplexMatrix Vr = V.extract (0, 0, nc-1, r); | |
| 1549 | 1262 retval = Vr * D * Ur.hermitian (); |
| 740 | 1263 } |
| 1549 | 1264 |
| 1265 return retval; | |
| 740 | 1266 } |
| 1267 | |
| 4773 | 1268 #if defined (HAVE_FFTW3) |
| 3827 | 1269 |
| 1270 ComplexMatrix | |
| 1271 ComplexMatrix::fourier (void) const | |
| 1272 { | |
| 1273 size_t nr = rows (); | |
| 1274 size_t nc = cols (); | |
| 1275 | |
| 1276 ComplexMatrix retval (nr, nc); | |
| 1277 | |
| 1278 size_t npts, nsamples; | |
| 1279 | |
| 1280 if (nr == 1 || nc == 1) | |
| 1281 { | |
| 1282 npts = nr > nc ? nr : nc; | |
| 1283 nsamples = 1; | |
| 1284 } | |
| 1285 else | |
| 1286 { | |
| 1287 npts = nr; | |
| 1288 nsamples = nc; | |
| 1289 } | |
| 1290 | |
| 1291 const Complex *in (data ()); | |
| 1292 Complex *out (retval.fortran_vec ()); | |
| 1293 | |
| 4773 | 1294 octave_fftw::fft (in, out, npts, nsamples); |
| 3827 | 1295 |
| 1296 return retval; | |
| 1297 } | |
| 1298 | |
| 1299 ComplexMatrix | |
| 1300 ComplexMatrix::ifourier (void) const | |
| 1301 { | |
| 1302 size_t nr = rows (); | |
| 1303 size_t nc = cols (); | |
| 1304 | |
| 1305 ComplexMatrix retval (nr, nc); | |
| 1306 | |
| 1307 size_t npts, nsamples; | |
| 1308 | |
| 1309 if (nr == 1 || nc == 1) | |
| 1310 { | |
| 1311 npts = nr > nc ? nr : nc; | |
| 1312 nsamples = 1; | |
| 1313 } | |
| 1314 else | |
| 1315 { | |
| 1316 npts = nr; | |
| 1317 nsamples = nc; | |
| 1318 } | |
| 1319 | |
| 1320 const Complex *in (data ()); | |
| 1321 Complex *out (retval.fortran_vec ()); | |
| 1322 | |
| 4773 | 1323 octave_fftw::ifft (in, out, npts, nsamples); |
| 3827 | 1324 |
| 1325 return retval; | |
| 1326 } | |
| 1327 | |
| 1328 ComplexMatrix | |
| 1329 ComplexMatrix::fourier2d (void) const | |
| 1330 { | |
| 4773 | 1331 dim_vector dv(rows (), cols ()); |
| 1332 | |
| 1333 ComplexMatrix retval (rows (), cols ()); | |
| 1334 const Complex *in (data ()); | |
| 1335 Complex *out (retval.fortran_vec ()); | |
| 1336 | |
| 1337 octave_fftw::fftNd (in, out, 2, dv); | |
| 3827 | 1338 |
| 1339 return retval; | |
| 1340 } | |
| 1341 | |
| 1342 ComplexMatrix | |
| 1343 ComplexMatrix::ifourier2d (void) const | |
| 1344 { | |
| 4773 | 1345 dim_vector dv(rows (), cols ()); |
| 1346 | |
| 1347 ComplexMatrix retval (rows (), cols ()); | |
| 1348 const Complex *in (data ()); | |
| 1349 Complex *out (retval.fortran_vec ()); | |
| 1350 | |
| 1351 octave_fftw::ifftNd (in, out, 2, dv); | |
| 3827 | 1352 |
| 1353 return retval; | |
| 1354 } | |
| 1355 | |
| 1356 #else | |
| 1357 | |
| 740 | 1358 ComplexMatrix |
| 458 | 1359 ComplexMatrix::fourier (void) const |
| 1360 { | |
| 1948 | 1361 ComplexMatrix retval; |
| 1362 | |
| 5275 | 1363 octave_idx_type nr = rows (); |
| 1364 octave_idx_type nc = cols (); | |
| 1365 | |
| 1366 octave_idx_type npts, nsamples; | |
| 1948 | 1367 |
| 458 | 1368 if (nr == 1 || nc == 1) |
| 1369 { | |
| 1370 npts = nr > nc ? nr : nc; | |
| 1371 nsamples = 1; | |
| 1372 } | |
| 1373 else | |
| 1374 { | |
| 1375 npts = nr; | |
| 1376 nsamples = nc; | |
| 1377 } | |
| 1378 | |
| 5275 | 1379 octave_idx_type nn = 4*npts+15; |
| 1948 | 1380 |
| 1381 Array<Complex> wsave (nn); | |
| 1382 Complex *pwsave = wsave.fortran_vec (); | |
| 1383 | |
| 1384 retval = *this; | |
| 1385 Complex *tmp_data = retval.fortran_vec (); | |
| 1386 | |
| 3887 | 1387 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
| 458 | 1388 |
| 5275 | 1389 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1390 { |
| 1391 OCTAVE_QUIT; | |
| 1392 | |
| 1393 F77_FUNC (cfftf, CFFTF) (npts, &tmp_data[npts*j], pwsave); | |
| 1394 } | |
| 1948 | 1395 |
| 1396 return retval; | |
| 458 | 1397 } |
| 1398 | |
| 1399 ComplexMatrix | |
| 1400 ComplexMatrix::ifourier (void) const | |
| 1401 { | |
| 1948 | 1402 ComplexMatrix retval; |
| 1403 | |
| 5275 | 1404 octave_idx_type nr = rows (); |
| 1405 octave_idx_type nc = cols (); | |
| 1406 | |
| 1407 octave_idx_type npts, nsamples; | |
| 1948 | 1408 |
| 458 | 1409 if (nr == 1 || nc == 1) |
| 1410 { | |
| 1411 npts = nr > nc ? nr : nc; | |
| 1412 nsamples = 1; | |
| 1413 } | |
| 1414 else | |
| 1415 { | |
| 1416 npts = nr; | |
| 1417 nsamples = nc; | |
| 1418 } | |
| 1419 | |
| 5275 | 1420 octave_idx_type nn = 4*npts+15; |
| 1948 | 1421 |
| 1422 Array<Complex> wsave (nn); | |
| 1423 Complex *pwsave = wsave.fortran_vec (); | |
| 1424 | |
| 1425 retval = *this; | |
| 1426 Complex *tmp_data = retval.fortran_vec (); | |
| 1427 | |
| 3887 | 1428 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
| 458 | 1429 |
| 5275 | 1430 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1431 { |
| 1432 OCTAVE_QUIT; | |
| 1433 | |
| 1434 F77_FUNC (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave); | |
| 1435 } | |
| 458 | 1436 |
| 5275 | 1437 for (octave_idx_type j = 0; j < npts*nsamples; j++) |
| 3572 | 1438 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
| 458 | 1439 |
| 1948 | 1440 return retval; |
| 458 | 1441 } |
| 1442 | |
| 677 | 1443 ComplexMatrix |
| 1444 ComplexMatrix::fourier2d (void) const | |
| 1445 { | |
| 1948 | 1446 ComplexMatrix retval; |
| 1447 | |
| 5275 | 1448 octave_idx_type nr = rows (); |
| 1449 octave_idx_type nc = cols (); | |
| 1450 | |
| 1451 octave_idx_type npts, nsamples; | |
| 1948 | 1452 |
| 677 | 1453 if (nr == 1 || nc == 1) |
| 1454 { | |
| 1455 npts = nr > nc ? nr : nc; | |
| 1456 nsamples = 1; | |
| 1457 } | |
| 1458 else | |
| 1459 { | |
| 1460 npts = nr; | |
| 1461 nsamples = nc; | |
| 1462 } | |
| 1463 | |
| 5275 | 1464 octave_idx_type nn = 4*npts+15; |
| 1948 | 1465 |
| 1466 Array<Complex> wsave (nn); | |
| 1467 Complex *pwsave = wsave.fortran_vec (); | |
| 1468 | |
| 1469 retval = *this; | |
| 1470 Complex *tmp_data = retval.fortran_vec (); | |
| 1471 | |
| 3887 | 1472 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
| 677 | 1473 |
| 5275 | 1474 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1475 { |
| 1476 OCTAVE_QUIT; | |
| 1477 | |
| 1478 F77_FUNC (cfftf, CFFTF) (npts, &tmp_data[npts*j], pwsave); | |
| 1479 } | |
| 677 | 1480 |
| 1481 npts = nc; | |
| 1482 nsamples = nr; | |
| 1483 nn = 4*npts+15; | |
| 1948 | 1484 |
| 1485 wsave.resize (nn); | |
| 1486 pwsave = wsave.fortran_vec (); | |
| 1487 | |
| 4773 | 1488 Array<Complex> tmp (npts); |
| 1489 Complex *prow = tmp.fortran_vec (); | |
| 1948 | 1490 |
| 3887 | 1491 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
| 677 | 1492 |
| 5275 | 1493 for (octave_idx_type j = 0; j < nsamples; j++) |
| 677 | 1494 { |
| 4153 | 1495 OCTAVE_QUIT; |
| 1496 | |
| 5275 | 1497 for (octave_idx_type i = 0; i < npts; i++) |
| 1948 | 1498 prow[i] = tmp_data[i*nr + j]; |
| 1499 | |
| 3887 | 1500 F77_FUNC (cfftf, CFFTF) (npts, prow, pwsave); |
| 677 | 1501 |
| 5275 | 1502 for (octave_idx_type i = 0; i < npts; i++) |
| 1948 | 1503 tmp_data[i*nr + j] = prow[i]; |
| 677 | 1504 } |
| 1505 | |
| 1948 | 1506 return retval; |
| 677 | 1507 } |
| 1508 | |
| 1509 ComplexMatrix | |
| 1510 ComplexMatrix::ifourier2d (void) const | |
| 1511 { | |
| 1948 | 1512 ComplexMatrix retval; |
| 1513 | |
| 5275 | 1514 octave_idx_type nr = rows (); |
| 1515 octave_idx_type nc = cols (); | |
| 1516 | |
| 1517 octave_idx_type npts, nsamples; | |
| 1948 | 1518 |
| 677 | 1519 if (nr == 1 || nc == 1) |
| 1520 { | |
| 1521 npts = nr > nc ? nr : nc; | |
| 1522 nsamples = 1; | |
| 1523 } | |
| 1524 else | |
| 1525 { | |
| 1526 npts = nr; | |
| 1527 nsamples = nc; | |
| 1528 } | |
| 1529 | |
| 5275 | 1530 octave_idx_type nn = 4*npts+15; |
| 1948 | 1531 |
| 1532 Array<Complex> wsave (nn); | |
| 1533 Complex *pwsave = wsave.fortran_vec (); | |
| 1534 | |
| 1535 retval = *this; | |
| 1536 Complex *tmp_data = retval.fortran_vec (); | |
| 1537 | |
| 3887 | 1538 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
| 677 | 1539 |
| 5275 | 1540 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1541 { |
| 1542 OCTAVE_QUIT; | |
| 1543 | |
| 1544 F77_FUNC (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave); | |
| 1545 } | |
| 677 | 1546 |
| 5275 | 1547 for (octave_idx_type j = 0; j < npts*nsamples; j++) |
| 3572 | 1548 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
| 677 | 1549 |
| 1550 npts = nc; | |
| 1551 nsamples = nr; | |
| 1552 nn = 4*npts+15; | |
| 1948 | 1553 |
| 1554 wsave.resize (nn); | |
| 1555 pwsave = wsave.fortran_vec (); | |
| 1556 | |
| 4773 | 1557 Array<Complex> tmp (npts); |
| 1558 Complex *prow = tmp.fortran_vec (); | |
| 1948 | 1559 |
| 3887 | 1560 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
| 677 | 1561 |
| 5275 | 1562 for (octave_idx_type j = 0; j < nsamples; j++) |
| 677 | 1563 { |
| 4153 | 1564 OCTAVE_QUIT; |
| 1565 | |
| 5275 | 1566 for (octave_idx_type i = 0; i < npts; i++) |
| 1948 | 1567 prow[i] = tmp_data[i*nr + j]; |
| 1568 | |
| 3887 | 1569 F77_FUNC (cfftb, CFFTB) (npts, prow, pwsave); |
| 677 | 1570 |
| 5275 | 1571 for (octave_idx_type i = 0; i < npts; i++) |
| 3572 | 1572 tmp_data[i*nr + j] = prow[i] / static_cast<double> (npts); |
| 677 | 1573 } |
| 1574 | |
| 1948 | 1575 return retval; |
| 677 | 1576 } |
| 1577 | |
| 3827 | 1578 #endif |
| 1579 | |
| 458 | 1580 ComplexDET |
| 1581 ComplexMatrix::determinant (void) const | |
| 1582 { | |
| 5275 | 1583 octave_idx_type info; |
| 458 | 1584 double rcond; |
| 4329 | 1585 return determinant (info, rcond, 0); |
| 458 | 1586 } |
| 1587 | |
| 1588 ComplexDET | |
| 5275 | 1589 ComplexMatrix::determinant (octave_idx_type& info) const |
| 458 | 1590 { |
| 1591 double rcond; | |
| 4329 | 1592 return determinant (info, rcond, 0); |
| 458 | 1593 } |
| 1594 | |
| 1595 ComplexDET | |
| 5275 | 1596 ComplexMatrix::determinant (octave_idx_type& info, double& rcond, int calc_cond) const |
| 458 | 1597 { |
| 1598 ComplexDET retval; | |
| 1599 | |
| 5275 | 1600 octave_idx_type nr = rows (); |
| 1601 octave_idx_type nc = cols (); | |
| 458 | 1602 |
| 1603 if (nr == 0 || nc == 0) | |
| 1604 { | |
| 5634 | 1605 retval = ComplexDET (1.0, 0); |
| 458 | 1606 } |
| 1607 else | |
| 1608 { | |
| 5275 | 1609 Array<octave_idx_type> ipvt (nr); |
| 1610 octave_idx_type *pipvt = ipvt.fortran_vec (); | |
| 1948 | 1611 |
| 1612 ComplexMatrix atmp = *this; | |
| 1613 Complex *tmp_data = atmp.fortran_vec (); | |
| 1614 | |
| 4329 | 1615 info = 0; |
| 1616 | |
| 4330 | 1617 // Calculate the norm of the matrix, for later use. |
| 4329 | 1618 double anorm = 0; |
| 1619 if (calc_cond) | |
| 5275 | 1620 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
| 4329 | 1621 |
| 1622 F77_XFCN (zgetrf, ZGETRF, (nr, nc, tmp_data, nr, pipvt, info)); | |
| 1948 | 1623 |
| 1624 if (f77_exception_encountered) | |
| 4329 | 1625 (*current_liboctave_error_handler) ("unrecoverable error in zgetrf"); |
| 458 | 1626 else |
| 1627 { | |
| 4330 | 1628 // Throw-away extra info LAPACK gives so as to not change output. |
| 4509 | 1629 rcond = 0.0; |
| 1630 if (info != 0) | |
| 1948 | 1631 { |
| 1632 info = -1; | |
| 1633 retval = ComplexDET (); | |
| 4329 | 1634 } |
| 1635 else | |
| 1948 | 1636 { |
| 4329 | 1637 if (calc_cond) |
| 1638 { | |
| 4330 | 1639 // Now calc the condition number for non-singular matrix. |
| 4329 | 1640 char job = '1'; |
| 1641 Array<Complex> z (2*nr); | |
| 1642 Complex *pz = z.fortran_vec (); | |
| 1643 Array<double> rz (2*nr); | |
| 1644 double *prz = rz.fortran_vec (); | |
| 1645 | |
| 4552 | 1646 F77_XFCN (zgecon, ZGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
| 1647 nc, tmp_data, nr, anorm, | |
| 1648 rcond, pz, prz, info | |
| 1649 F77_CHAR_ARG_LEN (1))); | |
| 4329 | 1650 |
| 1651 if (f77_exception_encountered) | |
| 1652 (*current_liboctave_error_handler) | |
| 1653 ("unrecoverable error in zgecon"); | |
| 1654 } | |
| 1655 | |
| 4509 | 1656 if (info != 0) |
| 4329 | 1657 { |
| 1658 info = -1; | |
| 1659 retval = ComplexDET (); | |
| 1660 } | |
| 1661 else | |
| 1662 { | |
| 5634 | 1663 Complex c = 1.0; |
| 1664 int e = 0; | |
| 1665 | |
| 1666 for (octave_idx_type i = 0; i < nc; i++) | |
| 4329 | 1667 { |
| 5634 | 1668 if (ipvt(i) != (i+1)) |
| 1669 c = -c; | |
| 1670 | |
| 1671 c *= atmp(i,i); | |
| 1672 | |
| 1673 if (c == 0.0) | |
| 1674 break; | |
| 1675 | |
| 1676 while (std::abs(c) < 0.5) | |
| 4329 | 1677 { |
| 5634 | 1678 c *= 2.0; |
| 1679 e--; | |
| 4329 | 1680 } |
| 5634 | 1681 |
| 1682 while (std::abs(c) >= 2.0) | |
| 4329 | 1683 { |
| 5634 | 1684 c /= 2.0; |
| 1685 e++; | |
| 4329 | 1686 } |
| 1687 } | |
| 5634 | 1688 |
| 1689 retval = ComplexDET (c, e); | |
| 4329 | 1690 } |
| 1948 | 1691 } |
| 458 | 1692 } |
| 1693 } | |
| 4329 | 1694 |
| 458 | 1695 return retval; |
| 1696 } | |
| 1697 | |
| 1698 ComplexMatrix | |
| 5785 | 1699 ComplexMatrix::utsolve (MatrixType &mattype, const ComplexMatrix& b, |
| 1700 octave_idx_type& info, double& rcond, | |
| 1701 solve_singularity_handler sing_handler, | |
| 1702 bool calc_cond) const | |
| 1703 { | |
| 1704 ComplexMatrix retval; | |
| 1705 | |
| 1706 octave_idx_type nr = rows (); | |
| 1707 octave_idx_type nc = cols (); | |
| 1708 | |
| 6924 | 1709 if (nr != b.rows ()) |
| 5785 | 1710 (*current_liboctave_error_handler) |
| 1711 ("matrix dimension mismatch solution of linear equations"); | |
| 6924 | 1712 else if (nr == 0 || nc == 0 || b.cols () == 0) |
| 1713 retval = ComplexMatrix (nc, b.cols (), Complex (0.0, 0.0)); | |
| 5785 | 1714 else |
| 1715 { | |
| 1716 volatile int typ = mattype.type (); | |
| 1717 | |
| 1718 if (typ == MatrixType::Permuted_Upper || | |
| 1719 typ == MatrixType::Upper) | |
| 1720 { | |
| 1721 octave_idx_type b_nc = b.cols (); | |
| 1722 rcond = 1.; | |
| 1723 info = 0; | |
| 1724 | |
| 1725 if (typ == MatrixType::Permuted_Upper) | |
| 1726 { | |
| 1727 (*current_liboctave_error_handler) | |
| 6390 | 1728 ("permuted triangular matrix not implemented"); |
| 5785 | 1729 } |
| 1730 else | |
| 1731 { | |
| 1732 const Complex *tmp_data = fortran_vec (); | |
| 1733 | |
| 1734 if (calc_cond) | |
| 1735 { | |
| 1736 char norm = '1'; | |
| 1737 char uplo = 'U'; | |
| 1738 char dia = 'N'; | |
| 1739 | |
| 1740 Array<Complex> z (2 * nc); | |
| 1741 Complex *pz = z.fortran_vec (); | |
| 1742 Array<double> rz (nc); | |
| 1743 double *prz = rz.fortran_vec (); | |
| 1744 | |
| 1745 F77_XFCN (ztrcon, ZTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1746 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1747 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1748 nr, tmp_data, nr, rcond, | |
| 1749 pz, prz, info | |
| 1750 F77_CHAR_ARG_LEN (1) | |
| 1751 F77_CHAR_ARG_LEN (1) | |
| 1752 F77_CHAR_ARG_LEN (1))); | |
| 1753 | |
| 1754 if (f77_exception_encountered) | |
| 1755 (*current_liboctave_error_handler) | |
| 1756 ("unrecoverable error in ztrcon"); | |
| 1757 | |
| 1758 if (info != 0) | |
| 1759 info = -2; | |
| 1760 | |
| 1761 volatile double rcond_plus_one = rcond + 1.0; | |
| 1762 | |
| 1763 if (rcond_plus_one == 1.0 || xisnan (rcond)) | |
| 1764 { | |
| 1765 info = -2; | |
| 1766 | |
| 1767 if (sing_handler) | |
| 1768 sing_handler (rcond); | |
| 1769 else | |
| 1770 (*current_liboctave_error_handler) | |
| 1771 ("matrix singular to machine precision, rcond = %g", | |
| 1772 rcond); | |
| 1773 } | |
| 1774 } | |
| 1775 | |
| 1776 if (info == 0) | |
| 1777 { | |
| 1778 retval = b; | |
| 1779 Complex *result = retval.fortran_vec (); | |
| 1780 | |
| 1781 char uplo = 'U'; | |
| 1782 char trans = 'N'; | |
| 1783 char dia = 'N'; | |
| 1784 | |
| 1785 F77_XFCN (ztrtrs, ZTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1786 F77_CONST_CHAR_ARG2 (&trans, 1), | |
| 1787 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1788 nr, b_nc, tmp_data, nr, | |
| 1789 result, nr, info | |
| 1790 F77_CHAR_ARG_LEN (1) | |
| 1791 F77_CHAR_ARG_LEN (1) | |
| 1792 F77_CHAR_ARG_LEN (1))); | |
| 1793 | |
| 1794 if (f77_exception_encountered) | |
| 1795 (*current_liboctave_error_handler) | |
| 1796 ("unrecoverable error in dtrtrs"); | |
| 1797 } | |
| 1798 } | |
| 1799 } | |
| 1800 else | |
| 1801 (*current_liboctave_error_handler) ("incorrect matrix type"); | |
| 1802 } | |
| 1803 | |
| 1804 return retval; | |
| 1805 } | |
| 1806 | |
| 1807 ComplexMatrix | |
| 1808 ComplexMatrix::ltsolve (MatrixType &mattype, const ComplexMatrix& b, | |
| 1809 octave_idx_type& info, double& rcond, | |
| 1810 solve_singularity_handler sing_handler, | |
| 1811 bool calc_cond) const | |
| 1812 { | |
| 1813 ComplexMatrix retval; | |
| 1814 | |
| 1815 octave_idx_type nr = rows (); | |
| 1816 octave_idx_type nc = cols (); | |
| 1817 | |
| 6924 | 1818 if (nr != b.rows ()) |
| 5785 | 1819 (*current_liboctave_error_handler) |
| 1820 ("matrix dimension mismatch solution of linear equations"); | |
| 6924 | 1821 else if (nr == 0 || nc == 0 || b.cols () == 0) |
| 1822 retval = ComplexMatrix (nc, b.cols (), Complex (0.0, 0.0)); | |
| 5785 | 1823 else |
| 1824 { | |
| 1825 volatile int typ = mattype.type (); | |
| 1826 | |
| 1827 if (typ == MatrixType::Permuted_Lower || | |
| 1828 typ == MatrixType::Lower) | |
| 1829 { | |
| 1830 octave_idx_type b_nc = b.cols (); | |
| 1831 rcond = 1.; | |
| 1832 info = 0; | |
| 1833 | |
| 1834 if (typ == MatrixType::Permuted_Lower) | |
| 1835 { | |
| 1836 (*current_liboctave_error_handler) | |
| 6390 | 1837 ("permuted triangular matrix not implemented"); |
| 5785 | 1838 } |
| 1839 else | |
| 1840 { | |
| 1841 const Complex *tmp_data = fortran_vec (); | |
| 1842 | |
| 1843 if (calc_cond) | |
| 1844 { | |
| 1845 char norm = '1'; | |
| 1846 char uplo = 'L'; | |
| 1847 char dia = 'N'; | |
| 1848 | |
| 1849 Array<Complex> z (2 * nc); | |
| 1850 Complex *pz = z.fortran_vec (); | |
| 1851 Array<double> rz (nc); | |
| 1852 double *prz = rz.fortran_vec (); | |
| 1853 | |
| 1854 F77_XFCN (ztrcon, ZTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1855 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1856 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1857 nr, tmp_data, nr, rcond, | |
| 1858 pz, prz, info | |
| 1859 F77_CHAR_ARG_LEN (1) | |
| 1860 F77_CHAR_ARG_LEN (1) | |
| 1861 F77_CHAR_ARG_LEN (1))); | |
| 1862 | |
| 1863 if (f77_exception_encountered) | |
| 1864 (*current_liboctave_error_handler) | |
| 1865 ("unrecoverable error in ztrcon"); | |
| 1866 | |
| 1867 if (info != 0) | |
| 1868 info = -2; | |
| 1869 | |
| 1870 volatile double rcond_plus_one = rcond + 1.0; | |
| 1871 | |
| 1872 if (rcond_plus_one == 1.0 || xisnan (rcond)) | |
| 1873 { | |
| 1874 info = -2; | |
| 1875 | |
| 1876 if (sing_handler) | |
| 1877 sing_handler (rcond); | |
| 1878 else | |
| 1879 (*current_liboctave_error_handler) | |
| 1880 ("matrix singular to machine precision, rcond = %g", | |
| 1881 rcond); | |
| 1882 } | |
| 1883 } | |
| 1884 | |
| 1885 if (info == 0) | |
| 1886 { | |
| 1887 retval = b; | |
| 1888 Complex *result = retval.fortran_vec (); | |
| 1889 | |
| 1890 char uplo = 'L'; | |
| 1891 char trans = 'N'; | |
| 1892 char dia = 'N'; | |
| 1893 | |
| 1894 F77_XFCN (ztrtrs, ZTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1895 F77_CONST_CHAR_ARG2 (&trans, 1), | |
| 1896 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1897 nr, b_nc, tmp_data, nr, | |
| 1898 result, nr, info | |
| 1899 F77_CHAR_ARG_LEN (1) | |
| 1900 F77_CHAR_ARG_LEN (1) | |
| 1901 F77_CHAR_ARG_LEN (1))); | |
| 1902 | |
| 1903 if (f77_exception_encountered) | |
| 1904 (*current_liboctave_error_handler) | |
| 1905 ("unrecoverable error in dtrtrs"); | |
| 1906 } | |
| 1907 } | |
| 1908 } | |
| 1909 else | |
| 1910 (*current_liboctave_error_handler) ("incorrect matrix type"); | |
| 1911 } | |
| 1912 | |
| 1913 return retval; | |
| 1914 } | |
| 1915 | |
| 1916 ComplexMatrix | |
| 1917 ComplexMatrix::fsolve (MatrixType &mattype, const ComplexMatrix& b, | |
| 1918 octave_idx_type& info, double& rcond, | |
| 1919 solve_singularity_handler sing_handler, | |
| 1920 bool calc_cond) const | |
| 1921 { | |
| 1922 ComplexMatrix retval; | |
| 1923 | |
| 1924 octave_idx_type nr = rows (); | |
| 1925 octave_idx_type nc = cols (); | |
| 1926 | |
| 6924 | 1927 |
| 1928 if (nr != nc || nr != b.rows ()) | |
| 5785 | 1929 (*current_liboctave_error_handler) |
| 6924 | 1930 ("matrix dimension mismatch solution of linear equations"); |
| 1931 else if (nr == 0 || b.cols () == 0) | |
| 1932 retval = ComplexMatrix (nc, b.cols (), Complex (0.0, 0.0)); | |
| 5785 | 1933 else |
| 1934 { | |
| 1935 volatile int typ = mattype.type (); | |
| 1936 | |
| 1937 // Calculate the norm of the matrix, for later use. | |
| 1938 double anorm = -1.; | |
| 1939 | |
| 1940 if (typ == MatrixType::Hermitian) | |
| 1941 { | |
| 1942 info = 0; | |
| 1943 char job = 'L'; | |
| 1944 ComplexMatrix atmp = *this; | |
| 1945 Complex *tmp_data = atmp.fortran_vec (); | |
| 1946 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); | |
| 1947 | |
| 1948 F77_XFCN (zpotrf, ZPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, | |
| 1949 tmp_data, nr, info | |
| 1950 F77_CHAR_ARG_LEN (1))); | |
| 1951 | |
| 1952 if (f77_exception_encountered) | |
| 1953 (*current_liboctave_error_handler) | |
| 1954 ("unrecoverable error in zpotrf"); | |
| 1955 else | |
| 1956 { | |
| 1957 // Throw-away extra info LAPACK gives so as to not change output. | |
| 1958 rcond = 0.0; | |
| 1959 if (info != 0) | |
| 1960 { | |
| 1961 info = -2; | |
| 1962 | |
| 1963 mattype.mark_as_unsymmetric (); | |
| 1964 typ = MatrixType::Full; | |
| 1965 } | |
| 1966 else | |
| 1967 { | |
| 1968 if (calc_cond) | |
| 1969 { | |
| 1970 Array<Complex> z (2 * nc); | |
| 1971 Complex *pz = z.fortran_vec (); | |
| 1972 Array<double> rz (nc); | |
| 1973 double *prz = rz.fortran_vec (); | |
| 1974 | |
| 1975 F77_XFCN (zpocon, ZPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), | |
| 1976 nr, tmp_data, nr, anorm, | |
| 1977 rcond, pz, prz, info | |
| 1978 F77_CHAR_ARG_LEN (1))); | |
| 1979 | |
| 1980 if (f77_exception_encountered) | |
| 1981 (*current_liboctave_error_handler) | |
| 1982 ("unrecoverable error in zpocon"); | |
| 1983 | |
| 1984 if (info != 0) | |
| 1985 info = -2; | |
| 1986 | |
| 1987 volatile double rcond_plus_one = rcond + 1.0; | |
| 1988 | |
| 1989 if (rcond_plus_one == 1.0 || xisnan (rcond)) | |
| 1990 { | |
| 1991 info = -2; | |
| 1992 | |
| 1993 if (sing_handler) | |
| 1994 sing_handler (rcond); | |
| 1995 else | |
| 1996 (*current_liboctave_error_handler) | |
| 1997 ("matrix singular to machine precision, rcond = %g", | |
| 1998 rcond); | |
| 1999 } | |
| 2000 } | |
| 2001 | |
| 2002 if (info == 0) | |
| 2003 { | |
| 2004 retval = b; | |
| 2005 Complex *result = retval.fortran_vec (); | |
| 2006 | |
| 2007 octave_idx_type b_nc = b.cols (); | |
| 2008 | |
| 2009 F77_XFCN (zpotrs, ZPOTRS, (F77_CONST_CHAR_ARG2 (&job, 1), | |
| 2010 nr, b_nc, tmp_data, nr, | |
| 2011 result, b.rows(), info | |
| 2012 F77_CHAR_ARG_LEN (1))); | |
| 2013 | |
| 2014 if (f77_exception_encountered) | |
| 2015 (*current_liboctave_error_handler) | |
| 2016 ("unrecoverable error in zpotrs"); | |
| 2017 } | |
| 2018 else | |
| 2019 { | |
| 2020 mattype.mark_as_unsymmetric (); | |
| 2021 typ = MatrixType::Full; | |
| 2022 } | |
| 2023 } | |
| 2024 } | |
| 2025 } | |
| 2026 | |
| 2027 if (typ == MatrixType::Full) | |
| 2028 { | |
| 2029 info = 0; | |
| 2030 | |
| 2031 Array<octave_idx_type> ipvt (nr); | |
| 2032 octave_idx_type *pipvt = ipvt.fortran_vec (); | |
| 2033 | |
| 2034 ComplexMatrix atmp = *this; | |
| 2035 Complex *tmp_data = atmp.fortran_vec (); | |
| 2036 | |
| 2037 Array<Complex> z (2 * nc); | |
| 2038 Complex *pz = z.fortran_vec (); | |
| 2039 Array<double> rz (2 * nc); | |
| 2040 double *prz = rz.fortran_vec (); | |
| 2041 | |
| 2042 // Calculate the norm of the matrix, for later use. | |
| 2043 if (anorm < 0.) | |
| 2044 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); | |
| 2045 | |
| 2046 F77_XFCN (zgetrf, ZGETRF, (nr, nr, tmp_data, nr, pipvt, info)); | |
| 2047 | |
| 2048 if (f77_exception_encountered) | |
| 2049 (*current_liboctave_error_handler) | |
| 2050 ("unrecoverable error in zgetrf"); | |
| 2051 else | |
| 2052 { | |
| 2053 // Throw-away extra info LAPACK gives so as to not change output. | |
| 2054 rcond = 0.0; | |
| 2055 if (info != 0) | |
| 2056 { | |
| 2057 info = -2; | |
| 2058 | |
| 2059 if (sing_handler) | |
| 2060 sing_handler (rcond); | |
| 2061 else | |
| 2062 (*current_liboctave_error_handler) | |
| 2063 ("matrix singular to machine precision"); | |
| 2064 | |
| 2065 mattype.mark_as_rectangular (); | |
| 2066 } | |
| 2067 else | |
| 2068 { | |
| 2069 if (calc_cond) | |
| 2070 { | |
| 2071 // Now calculate the condition number for | |
| 2072 // non-singular matrix. | |
| 2073 char job = '1'; | |
| 2074 F77_XFCN (zgecon, ZGECON, (F77_CONST_CHAR_ARG2 (&job, 1), | |
| 2075 nc, tmp_data, nr, anorm, | |
| 2076 rcond, pz, prz, info | |
| 2077 F77_CHAR_ARG_LEN (1))); | |
| 2078 | |
| 2079 if (f77_exception_encountered) | |
| 2080 (*current_liboctave_error_handler) | |
| 2081 ("unrecoverable error in zgecon"); | |
| 2082 | |
| 2083 if (info != 0) | |
| 2084 info = -2; | |
| 2085 | |
| 2086 volatile double rcond_plus_one = rcond + 1.0; | |
| 2087 | |
| 2088 if (rcond_plus_one == 1.0 || xisnan (rcond)) | |
| 2089 { | |
| 2090 info = -2; | |
| 2091 | |
| 2092 if (sing_handler) | |
| 2093 sing_handler (rcond); | |
| 2094 else | |
| 2095 (*current_liboctave_error_handler) | |
| 2096 ("matrix singular to machine precision, rcond = %g", | |
| 2097 rcond); | |
| 2098 } | |
| 2099 } | |
| 2100 | |
| 2101 if (info == 0) | |
| 2102 { | |
| 2103 retval = b; | |
| 2104 Complex *result = retval.fortran_vec (); | |
| 2105 | |
| 2106 octave_idx_type b_nc = b.cols (); | |
| 2107 | |
| 2108 char job = 'N'; | |
| 2109 F77_XFCN (zgetrs, ZGETRS, (F77_CONST_CHAR_ARG2 (&job, 1), | |
| 2110 nr, b_nc, tmp_data, nr, | |
| 2111 pipvt, result, b.rows(), info | |
| 2112 F77_CHAR_ARG_LEN (1))); | |
| 2113 | |
| 2114 if (f77_exception_encountered) | |
| 2115 (*current_liboctave_error_handler) | |
| 2116 ("unrecoverable error in zgetrs"); | |
| 2117 } | |
| 2118 else | |
| 2119 mattype.mark_as_rectangular (); | |
| 2120 } | |
| 2121 } | |
| 2122 } | |
| 2123 } | |
| 2124 | |
| 2125 return retval; | |
| 2126 } | |
| 2127 | |
| 2128 ComplexMatrix | |
| 2129 ComplexMatrix::solve (MatrixType &typ, const Matrix& b) const | |
| 2130 { | |
| 2131 octave_idx_type info; | |
| 2132 double rcond; | |
| 2133 return solve (typ, b, info, rcond, 0); | |
| 2134 } | |
| 2135 | |
| 2136 ComplexMatrix | |
| 2137 ComplexMatrix::solve (MatrixType &typ, const Matrix& b, | |
| 2138 octave_idx_type& info) const | |
| 2139 { | |
| 2140 double rcond; | |
| 2141 return solve (typ, b, info, rcond, 0); | |
| 2142 } | |
| 2143 | |
| 2144 ComplexMatrix | |
| 2145 ComplexMatrix::solve (MatrixType &typ, const Matrix& b, octave_idx_type& info, | |
| 2146 double& rcond) const | |
| 2147 { | |
| 2148 return solve (typ, b, info, rcond, 0); | |
| 2149 } | |
| 2150 | |
| 2151 ComplexMatrix | |
| 2152 ComplexMatrix::solve (MatrixType &typ, const Matrix& b, octave_idx_type& info, | |
| 2153 double& rcond, solve_singularity_handler sing_handler, | |
| 2154 bool singular_fallback) const | |
| 2155 { | |
| 2156 ComplexMatrix tmp (b); | |
| 2157 return solve (typ, tmp, info, rcond, sing_handler, singular_fallback); | |
| 2158 } | |
| 2159 | |
| 2160 ComplexMatrix | |
| 2161 ComplexMatrix::solve (MatrixType &typ, const ComplexMatrix& b) const | |
| 2162 { | |
| 2163 octave_idx_type info; | |
| 2164 double rcond; | |
| 2165 return solve (typ, b, info, rcond, 0); | |
| 2166 } | |
| 2167 | |
| 2168 ComplexMatrix | |
| 2169 ComplexMatrix::solve (MatrixType &typ, const ComplexMatrix& b, | |
| 2170 octave_idx_type& info) const | |
| 2171 { | |
| 2172 double rcond; | |
| 2173 return solve (typ, b, info, rcond, 0); | |
| 2174 } | |
| 2175 | |
| 2176 ComplexMatrix | |
| 2177 ComplexMatrix::solve (MatrixType &typ, const ComplexMatrix& b, | |
| 2178 octave_idx_type& info, double& rcond) const | |
| 2179 { | |
| 2180 return solve (typ, b, info, rcond, 0); | |
| 2181 } | |
| 2182 | |
| 2183 ComplexMatrix | |
| 2184 ComplexMatrix::solve (MatrixType &mattype, const ComplexMatrix& b, | |
| 2185 octave_idx_type& info, double& rcond, | |
| 2186 solve_singularity_handler sing_handler, | |
| 2187 bool singular_fallback) const | |
| 2188 { | |
| 2189 ComplexMatrix retval; | |
| 2190 int typ = mattype.type (); | |
| 2191 | |
| 2192 if (typ == MatrixType::Unknown) | |
| 2193 typ = mattype.type (*this); | |
| 2194 | |
| 2195 // Only calculate the condition number for LU/Cholesky | |
| 2196 if (typ == MatrixType::Upper || typ == MatrixType::Permuted_Upper) | |
| 2197 retval = utsolve (mattype, b, info, rcond, sing_handler, false); | |
| 2198 else if (typ == MatrixType::Lower || typ == MatrixType::Permuted_Lower) | |
| 2199 retval = ltsolve (mattype, b, info, rcond, sing_handler, false); | |
| 2200 else if (typ == MatrixType::Full || typ == MatrixType::Hermitian) | |
| 2201 retval = fsolve (mattype, b, info, rcond, sing_handler, true); | |
| 2202 else if (typ != MatrixType::Rectangular) | |
| 2203 { | |
| 2204 (*current_liboctave_error_handler) ("unknown matrix type"); | |
| 2205 return ComplexMatrix (); | |
| 2206 } | |
| 2207 | |
| 2208 // Rectangular or one of the above solvers flags a singular matrix | |
| 2209 if (singular_fallback && mattype.type () == MatrixType::Rectangular) | |
| 2210 { | |
| 2211 octave_idx_type rank; | |
| 7076 | 2212 retval = lssolve (b, info, rank, rcond); |
| 5785 | 2213 } |
| 2214 | |
| 2215 return retval; | |
| 2216 } | |
| 2217 | |
| 2218 ComplexColumnVector | |
| 2219 ComplexMatrix::solve (MatrixType &typ, const ColumnVector& b) const | |
| 2220 { | |
| 2221 octave_idx_type info; | |
| 2222 double rcond; | |
| 2223 return solve (typ, ComplexColumnVector (b), info, rcond, 0); | |
| 2224 } | |
| 2225 | |
| 2226 ComplexColumnVector | |
| 2227 ComplexMatrix::solve (MatrixType &typ, const ColumnVector& b, | |
| 2228 octave_idx_type& info) const | |
| 2229 { | |
| 2230 double rcond; | |
| 2231 return solve (typ, ComplexColumnVector (b), info, rcond, 0); | |
| 2232 } | |
| 2233 | |
| 2234 ComplexColumnVector | |
| 2235 ComplexMatrix::solve (MatrixType &typ, const ColumnVector& b, | |
| 2236 octave_idx_type& info, double& rcond) const | |
| 2237 { | |
| 2238 return solve (typ, ComplexColumnVector (b), info, rcond, 0); | |
| 2239 } | |
| 2240 | |
| 2241 ComplexColumnVector | |
| 2242 ComplexMatrix::solve (MatrixType &typ, const ColumnVector& b, | |
| 2243 octave_idx_type& info, double& rcond, | |
| 2244 solve_singularity_handler sing_handler) const | |
| 2245 { | |
| 2246 return solve (typ, ComplexColumnVector (b), info, rcond, sing_handler); | |
| 2247 } | |
| 2248 | |
| 2249 ComplexColumnVector | |
| 2250 ComplexMatrix::solve (MatrixType &typ, const ComplexColumnVector& b) const | |
| 2251 { | |
| 2252 octave_idx_type info; | |
| 2253 double rcond; | |
| 2254 return solve (typ, b, info, rcond, 0); | |
| 2255 } | |
| 2256 | |
| 2257 ComplexColumnVector | |
| 2258 ComplexMatrix::solve (MatrixType &typ, const ComplexColumnVector& b, | |
| 2259 octave_idx_type& info) const | |
| 2260 { | |
| 2261 double rcond; | |
| 2262 return solve (typ, b, info, rcond, 0); | |
| 2263 } | |
| 2264 | |
| 2265 ComplexColumnVector | |
| 2266 ComplexMatrix::solve (MatrixType &typ, const ComplexColumnVector& b, | |
| 2267 octave_idx_type& info, double& rcond) const | |
| 2268 { | |
| 2269 return solve (typ, b, info, rcond, 0); | |
| 2270 } | |
| 2271 | |
| 2272 ComplexColumnVector | |
| 2273 ComplexMatrix::solve (MatrixType &typ, const ComplexColumnVector& b, | |
| 2274 octave_idx_type& info, double& rcond, | |
| 2275 solve_singularity_handler sing_handler) const | |
| 2276 { | |
| 2277 | |
| 2278 ComplexMatrix tmp (b); | |
| 2279 return solve (typ, tmp, info, rcond, sing_handler).column(static_cast<octave_idx_type> (0)); | |
| 2280 } | |
| 2281 | |
| 2282 ComplexMatrix | |
| 458 | 2283 ComplexMatrix::solve (const Matrix& b) const |
| 2284 { | |
| 5275 | 2285 octave_idx_type info; |
| 458 | 2286 double rcond; |
| 3480 | 2287 return solve (b, info, rcond, 0); |
| 458 | 2288 } |
| 2289 | |
| 2290 ComplexMatrix | |
| 5275 | 2291 ComplexMatrix::solve (const Matrix& b, octave_idx_type& info) const |
| 458 | 2292 { |
| 2293 double rcond; | |
| 3480 | 2294 return solve (b, info, rcond, 0); |
| 458 | 2295 } |
| 2296 | |
| 2297 ComplexMatrix | |
| 5275 | 2298 ComplexMatrix::solve (const Matrix& b, octave_idx_type& info, double& rcond) const |
| 458 | 2299 { |
| 3480 | 2300 return solve (b, info, rcond, 0); |
| 2301 } | |
| 2302 | |
| 2303 ComplexMatrix | |
| 5275 | 2304 ComplexMatrix::solve (const Matrix& b, octave_idx_type& info, double& rcond, |
| 3480 | 2305 solve_singularity_handler sing_handler) const |
| 2306 { | |
| 458 | 2307 ComplexMatrix tmp (b); |
| 3480 | 2308 return solve (tmp, info, rcond, sing_handler); |
| 458 | 2309 } |
| 2310 | |
| 2311 ComplexMatrix | |
| 2312 ComplexMatrix::solve (const ComplexMatrix& b) const | |
| 2313 { | |
| 5275 | 2314 octave_idx_type info; |
| 458 | 2315 double rcond; |
| 3480 | 2316 return solve (b, info, rcond, 0); |
| 458 | 2317 } |
| 2318 | |
| 2319 ComplexMatrix | |
| 5275 | 2320 ComplexMatrix::solve (const ComplexMatrix& b, octave_idx_type& info) const |
| 458 | 2321 { |
| 2322 double rcond; | |
| 3480 | 2323 return solve (b, info, rcond, 0); |
| 458 | 2324 } |
| 3480 | 2325 |
| 458 | 2326 ComplexMatrix |
| 5275 | 2327 ComplexMatrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcond) const |
| 458 | 2328 { |
| 3480 | 2329 return solve (b, info, rcond, 0); |
| 2330 } | |
| 2331 | |
| 2332 ComplexMatrix | |
| 5275 | 2333 ComplexMatrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcond, |
| 3480 | 2334 solve_singularity_handler sing_handler) const |
| 2335 { | |
| 5785 | 2336 MatrixType mattype (*this); |
| 6060 | 2337 return solve (mattype, b, info, rcond, sing_handler); |
| 458 | 2338 } |
| 2339 | |
| 2340 ComplexColumnVector | |
| 3585 | 2341 ComplexMatrix::solve (const ColumnVector& b) const |
| 2342 { | |
| 5275 | 2343 octave_idx_type info; |
| 3585 | 2344 double rcond; |
| 2345 return solve (ComplexColumnVector (b), info, rcond, 0); | |
| 2346 } | |
| 2347 | |
| 2348 ComplexColumnVector | |
| 5275 | 2349 ComplexMatrix::solve (const ColumnVector& b, octave_idx_type& info) const |
| 3585 | 2350 { |
| 2351 double rcond; | |
| 2352 return solve (ComplexColumnVector (b), info, rcond, 0); | |
| 2353 } | |
| 2354 | |
| 2355 ComplexColumnVector | |
| 5785 | 2356 ComplexMatrix::solve (const ColumnVector& b, octave_idx_type& info, |
| 2357 double& rcond) const | |
| 3585 | 2358 { |
| 2359 return solve (ComplexColumnVector (b), info, rcond, 0); | |
| 2360 } | |
| 2361 | |
| 2362 ComplexColumnVector | |
| 5785 | 2363 ComplexMatrix::solve (const ColumnVector& b, octave_idx_type& info, |
| 2364 double& rcond, | |
| 3585 | 2365 solve_singularity_handler sing_handler) const |
| 2366 { | |
| 2367 return solve (ComplexColumnVector (b), info, rcond, sing_handler); | |
| 2368 } | |
| 2369 | |
| 2370 ComplexColumnVector | |
| 458 | 2371 ComplexMatrix::solve (const ComplexColumnVector& b) const |
| 2372 { | |
| 5275 | 2373 octave_idx_type info; |
| 458 | 2374 double rcond; |
| 3480 | 2375 return solve (b, info, rcond, 0); |
| 458 | 2376 } |
| 2377 | |
| 2378 ComplexColumnVector | |
| 5275 | 2379 ComplexMatrix::solve (const ComplexColumnVector& b, octave_idx_type& info) const |
| 458 | 2380 { |
| 2381 double rcond; | |
| 3480 | 2382 return solve (b, info, rcond, 0); |
| 458 | 2383 } |
| 2384 | |
| 2385 ComplexColumnVector | |
| 5275 | 2386 ComplexMatrix::solve (const ComplexColumnVector& b, octave_idx_type& info, |
| 532 | 2387 double& rcond) const |
| 458 | 2388 { |
| 3480 | 2389 return solve (b, info, rcond, 0); |
| 2390 } | |
| 2391 | |
| 2392 ComplexColumnVector | |
| 5275 | 2393 ComplexMatrix::solve (const ComplexColumnVector& b, octave_idx_type& info, |
| 3480 | 2394 double& rcond, |
| 2395 solve_singularity_handler sing_handler) const | |
| 2396 { | |
| 5785 | 2397 MatrixType mattype (*this); |
| 2398 return solve (mattype, b, info, rcond, sing_handler); | |
| 458 | 2399 } |
| 2400 | |
| 2401 ComplexMatrix | |
| 3585 | 2402 ComplexMatrix::lssolve (const Matrix& b) const |
| 2403 { | |
| 5275 | 2404 octave_idx_type info; |
| 2405 octave_idx_type rank; | |
| 7076 | 2406 double rcond; |
| 2407 return lssolve (ComplexMatrix (b), info, rank, rcond); | |
| 3585 | 2408 } |
| 2409 | |
| 2410 ComplexMatrix | |
| 5275 | 2411 ComplexMatrix::lssolve (const Matrix& b, octave_idx_type& info) const |
| 3585 | 2412 { |
| 5275 | 2413 octave_idx_type rank; |
| 7076 | 2414 double rcond; |
| 2415 return lssolve (ComplexMatrix (b), info, rank, rcond); | |
| 3585 | 2416 } |
| 2417 | |
| 2418 ComplexMatrix | |
| 7076 | 2419 ComplexMatrix::lssolve (const Matrix& b, octave_idx_type& info, |
| 2420 octave_idx_type& rank) const | |
| 3585 | 2421 { |
| 7076 | 2422 double rcond; |
| 2423 return lssolve (ComplexMatrix (b), info, rank, rcond); | |
| 2424 } | |
| 2425 | |
| 2426 ComplexMatrix | |
| 2427 ComplexMatrix::lssolve (const Matrix& b, octave_idx_type& info, | |
| 2428 octave_idx_type& rank, double& rcond) const | |
| 2429 { | |
| 2430 return lssolve (ComplexMatrix (b), info, rank, rcond); | |
| 3585 | 2431 } |
| 2432 | |
| 2433 ComplexMatrix | |
| 458 | 2434 ComplexMatrix::lssolve (const ComplexMatrix& b) const |
| 2435 { | |
| 5275 | 2436 octave_idx_type info; |
| 2437 octave_idx_type rank; | |
| 7076 | 2438 double rcond; |
| 2439 return lssolve (b, info, rank, rcond); | |
| 458 | 2440 } |
| 2441 | |
| 2442 ComplexMatrix | |
| 5275 | 2443 ComplexMatrix::lssolve (const ComplexMatrix& b, octave_idx_type& info) const |
| 458 | 2444 { |
| 5275 | 2445 octave_idx_type rank; |
| 7076 | 2446 double rcond; |
| 2447 return lssolve (b, info, rank, rcond); | |
| 458 | 2448 } |
| 2449 | |
| 2450 ComplexMatrix | |
| 7076 | 2451 ComplexMatrix::lssolve (const ComplexMatrix& b, octave_idx_type& info, |
| 2452 octave_idx_type& rank) const | |
| 2453 { | |
| 2454 double rcond; | |
| 2455 return lssolve (b, info, rank, rcond); | |
| 2456 } | |
| 2457 | |
| 2458 ComplexMatrix | |
| 2459 ComplexMatrix::lssolve (const ComplexMatrix& b, octave_idx_type& info, | |
| 2460 octave_idx_type& rank, double& rcond) const | |
| 458 | 2461 { |
| 1948 | 2462 ComplexMatrix retval; |
| 2463 | |
| 5275 | 2464 octave_idx_type nrhs = b.cols (); |
| 2465 | |
| 2466 octave_idx_type m = rows (); | |
| 2467 octave_idx_type n = cols (); | |
| 458 | 2468 |
| 6924 | 2469 if (m != b.rows ()) |
| 1948 | 2470 (*current_liboctave_error_handler) |
| 2471 ("matrix dimension mismatch solution of linear equations"); | |
| 6924 | 2472 else if (m== 0 || n == 0 || b.cols () == 0) |
| 2473 retval = ComplexMatrix (n, b.cols (), Complex (0.0, 0.0)); | |
| 1948 | 2474 else |
| 458 | 2475 { |
| 7072 | 2476 volatile octave_idx_type minmn = (m < n ? m : n); |
| 2477 octave_idx_type maxmn = m > n ? m : n; | |
| 7076 | 2478 rcond = -1.0; |
| 7072 | 2479 |
| 2480 if (m != n) | |
| 2481 { | |
| 2482 retval = ComplexMatrix (maxmn, nrhs); | |
| 2483 | |
| 2484 for (octave_idx_type j = 0; j < nrhs; j++) | |
| 2485 for (octave_idx_type i = 0; i < m; i++) | |
| 2486 retval.elem (i, j) = b.elem (i, j); | |
| 2487 } | |
| 2488 else | |
| 2489 retval = b; | |
| 2490 | |
| 1948 | 2491 ComplexMatrix atmp = *this; |
| 2492 Complex *tmp_data = atmp.fortran_vec (); | |
| 2493 | |
| 7072 | 2494 Complex *pretval = retval.fortran_vec (); |
| 2495 Array<double> s (minmn); | |
| 7071 | 2496 double *ps = s.fortran_vec (); |
| 2563 | 2497 |
| 7072 | 2498 // Ask ZGELSD what the dimension of WORK should be. |
| 5275 | 2499 octave_idx_type lwork = -1; |
| 3752 | 2500 |
| 2501 Array<Complex> work (1); | |
| 7079 | 2502 |
| 11646 | 2503 octave_idx_type smlsiz; |
| 2504 F77_FUNC (xilaenv, XILAENV) (9, F77_CONST_CHAR_ARG2 ("ZGELSD", 6), | |
| 2505 F77_CONST_CHAR_ARG2 (" ", 1), | |
| 2506 0, 0, 0, 0, smlsiz | |
| 2507 F77_CHAR_ARG_LEN (6) | |
| 2508 F77_CHAR_ARG_LEN (1)); | |
| 7079 | 2509 |
|
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diff
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|
2510 octave_idx_type mnthr; |
|
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more xGELSD workspace fixes
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parents:
11646
diff
changeset
|
2511 F77_FUNC (xilaenv, XILAENV) (6, F77_CONST_CHAR_ARG2 ("ZGELSD", 6), |
|
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more xGELSD workspace fixes
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parents:
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diff
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|
2512 F77_CONST_CHAR_ARG2 (" ", 1), |
|
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more xGELSD workspace fixes
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diff
changeset
|
2513 m, n, nrhs, -1, mnthr |
|
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more xGELSD workspace fixes
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diff
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|
2514 F77_CHAR_ARG_LEN (6) |
|
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diff
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|
2515 F77_CHAR_ARG_LEN (1)); |
|
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more xGELSD workspace fixes
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parents:
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diff
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|
2516 |
| 7079 | 2517 // We compute the size of rwork and iwork because ZGELSD in |
| 2518 // older versions of LAPACK does not return them on a query | |
| 2519 // call. | |
| 7124 | 2520 double dminmn = static_cast<double> (minmn); |
| 2521 double dsmlsizp1 = static_cast<double> (smlsiz+1); | |
| 7079 | 2522 #if defined (HAVE_LOG2) |
|
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|
2523 double tmp = log2 (dminmn / dsmlsizp1); |
| 7079 | 2524 #else |
|
11668
8ac2994e4596
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diff
changeset
|
2525 double tmp = log (dminmn / dsmlsizp1) / log (2.0); |
| 7079 | 2526 #endif |
|
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diff
changeset
|
2527 octave_idx_type nlvl = static_cast<octave_idx_type> (tmp) + 1; |
| 7079 | 2528 if (nlvl < 0) |
| 2529 nlvl = 0; | |
| 2530 | |
| 2531 octave_idx_type lrwork = minmn*(10 + 2*smlsiz + 8*nlvl) | |
| 2532 + 3*smlsiz*nrhs + (smlsiz+1)*(smlsiz+1); | |
| 2533 if (lrwork < 1) | |
| 2534 lrwork = 1; | |
| 2535 Array<double> rwork (lrwork); | |
| 2536 double *prwork = rwork.fortran_vec (); | |
| 2537 | |
| 2538 octave_idx_type liwork = 3 * minmn * nlvl + 11 * minmn; | |
| 2539 if (liwork < 1) | |
| 2540 liwork = 1; | |
| 2541 Array<octave_idx_type> iwork (liwork); | |
| 2542 octave_idx_type* piwork = iwork.fortran_vec (); | |
| 7072 | 2543 |
| 2544 F77_XFCN (zgelsd, ZGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, | |
| 2545 ps, rcond, rank, work.fortran_vec (), | |
| 7079 | 2546 lwork, prwork, piwork, info)); |
| 1948 | 2547 |
| 11640 | 2548 // The workspace query is broken in at least LAPACK 3.0.0 |
|
11652
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|
2549 // through 3.1.1 when n >= mnthr. The obtuse formula below |
|
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diff
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|
2550 // should provide sufficient workspace for ZGELSD to operate |
| 11640 | 2551 // efficiently. |
|
11652
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|
2552 if (n >= mnthr) |
| 11640 | 2553 { |
| 2554 octave_idx_type addend = m; | |
| 2555 | |
| 2556 if (2*m-4 > addend) | |
| 2557 addend = 2*m-4; | |
| 2558 | |
| 2559 if (nrhs > addend) | |
| 2560 addend = nrhs; | |
| 2561 | |
| 2562 if (n-3*m > addend) | |
| 2563 addend = n-3*m; | |
| 2564 | |
| 2565 const octave_idx_type lworkaround = 4*m + m*m + addend; | |
| 2566 | |
| 2567 if (std::real (work(0)) < lworkaround) | |
| 2568 work(0) = lworkaround; | |
| 2569 } | |
|
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|
2570 else if (m >= n) |
|
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11652
diff
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|
2571 { |
|
ef2b2df1ed9a
avoid another xGELSD workspace query bug
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parents:
11652
diff
changeset
|
2572 octave_idx_type lworkaround = 2*m + m*nrhs; |
|
ef2b2df1ed9a
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changeset
|
2573 |
|
ef2b2df1ed9a
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diff
changeset
|
2574 if (std::real (work(0)) < lworkaround) |
|
ef2b2df1ed9a
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diff
changeset
|
2575 work(0) = lworkaround; |
|
ef2b2df1ed9a
avoid another xGELSD workspace query bug
John W. Eaton <jwe@octave.org>
parents:
11652
diff
changeset
|
2576 } |
| 11640 | 2577 |
| 1948 | 2578 if (f77_exception_encountered) |
| 7072 | 2579 (*current_liboctave_error_handler) |
| 2580 ("unrecoverable error in zgelsd"); | |
| 1948 | 2581 else |
| 2582 { | |
| 5315 | 2583 lwork = static_cast<octave_idx_type> (std::real (work(0))); |
| 3752 | 2584 work.resize (lwork); |
| 7072 | 2585 |
| 2586 F77_XFCN (zgelsd, ZGELSD, (m, n, nrhs, tmp_data, m, pretval, | |
| 2587 maxmn, ps, rcond, rank, | |
| 2588 work.fortran_vec (), lwork, | |
| 7079 | 2589 prwork, piwork, info)); |
| 3752 | 2590 |
| 2591 if (f77_exception_encountered) | |
| 7072 | 2592 (*current_liboctave_error_handler) |
| 2593 ("unrecoverable error in zgelsd"); | |
| 7076 | 2594 else |
| 2595 { | |
| 2596 if (rank < minmn) | |
| 2597 (*current_liboctave_warning_handler) | |
| 2598 ("zgelsd: rank deficient %dx%d matrix, rank = %d, tol = %e", | |
| 2599 m, n, rank, rcond); | |
| 2600 | |
| 2601 if (s.elem (0) == 0.0) | |
| 2602 rcond = 0.0; | |
| 2603 else | |
| 2604 rcond = s.elem (minmn - 1) / s.elem (0); | |
| 7079 | 2605 |
| 2606 retval.resize (n, nrhs); | |
| 7076 | 2607 } |
| 1948 | 2608 } |
| 458 | 2609 } |
| 2610 | |
| 2611 return retval; | |
| 2612 } | |
| 2613 | |
| 2614 ComplexColumnVector | |
| 3585 | 2615 ComplexMatrix::lssolve (const ColumnVector& b) const |
| 2616 { | |
| 5275 | 2617 octave_idx_type info; |
| 2618 octave_idx_type rank; | |
| 7076 | 2619 double rcond; |
| 2620 return lssolve (ComplexColumnVector (b), info, rank, rcond); | |
| 3585 | 2621 } |
| 2622 | |
| 2623 ComplexColumnVector | |
| 5275 | 2624 ComplexMatrix::lssolve (const ColumnVector& b, octave_idx_type& info) const |
| 3585 | 2625 { |
| 5275 | 2626 octave_idx_type rank; |
| 7076 | 2627 double rcond; |
| 2628 return lssolve (ComplexColumnVector (b), info, rank, rcond); | |
| 3585 | 2629 } |
| 2630 | |
| 2631 ComplexColumnVector | |
| 7076 | 2632 ComplexMatrix::lssolve (const ColumnVector& b, octave_idx_type& info, |
| 2633 octave_idx_type& rank) const | |
| 3585 | 2634 { |
| 7076 | 2635 double rcond; |
| 2636 return lssolve (ComplexColumnVector (b), info, rank, rcond); | |
| 2637 } | |
| 2638 | |
| 2639 ComplexColumnVector | |
| 2640 ComplexMatrix::lssolve (const ColumnVector& b, octave_idx_type& info, | |
| 2641 octave_idx_type& rank, double& rcond) const | |
| 2642 { | |
| 2643 return lssolve (ComplexColumnVector (b), info, rank, rcond); | |
| 3585 | 2644 } |
| 2645 | |
| 2646 ComplexColumnVector | |
| 458 | 2647 ComplexMatrix::lssolve (const ComplexColumnVector& b) const |
| 2648 { | |
| 5275 | 2649 octave_idx_type info; |
| 2650 octave_idx_type rank; | |
| 7076 | 2651 double rcond; |
| 2652 return lssolve (b, info, rank, rcond); | |
| 458 | 2653 } |
| 2654 | |
| 2655 ComplexColumnVector | |
| 5275 | 2656 ComplexMatrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info) const |
| 458 | 2657 { |
| 5275 | 2658 octave_idx_type rank; |
| 7076 | 2659 double rcond; |
| 2660 return lssolve (b, info, rank, rcond); | |
| 458 | 2661 } |
| 2662 | |
| 2663 ComplexColumnVector | |
| 5275 | 2664 ComplexMatrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, |
| 2665 octave_idx_type& rank) const | |
| 458 | 2666 { |
| 7076 | 2667 double rcond; |
| 2668 return lssolve (b, info, rank, rcond); | |
| 2669 | |
| 2670 } | |
| 2671 | |
| 2672 ComplexColumnVector | |
| 2673 ComplexMatrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, | |
| 2674 octave_idx_type& rank, double& rcond) const | |
| 2675 { | |
| 1948 | 2676 ComplexColumnVector retval; |
| 2677 | |
| 5275 | 2678 octave_idx_type nrhs = 1; |
| 2679 | |
| 2680 octave_idx_type m = rows (); | |
| 2681 octave_idx_type n = cols (); | |
| 458 | 2682 |
| 6924 | 2683 if (m != b.length ()) |
| 1948 | 2684 (*current_liboctave_error_handler) |
| 6924 | 2685 ("matrix dimension mismatch solution of linear equations"); |
| 2686 else if (m == 0 || n == 0 || b.cols () == 0) | |
| 2687 retval = ComplexColumnVector (n, Complex (0.0, 0.0)); | |
| 1948 | 2688 else |
| 458 | 2689 { |
| 7072 | 2690 volatile octave_idx_type minmn = (m < n ? m : n); |
| 2691 octave_idx_type maxmn = m > n ? m : n; | |
| 7076 | 2692 rcond = -1.0; |
| 7072 | 2693 |
| 2694 if (m != n) | |
| 2695 { | |
| 2696 retval = ComplexColumnVector (maxmn); | |
| 2697 | |
| 2698 for (octave_idx_type i = 0; i < m; i++) | |
| 2699 retval.elem (i) = b.elem (i); | |
| 2700 } | |
| 2701 else | |
| 2702 retval = b; | |
| 2703 | |
| 1948 | 2704 ComplexMatrix atmp = *this; |
| 2705 Complex *tmp_data = atmp.fortran_vec (); | |
| 2706 | |
| 7072 | 2707 Complex *pretval = retval.fortran_vec (); |
| 2708 Array<double> s (minmn); | |
| 7071 | 2709 double *ps = s.fortran_vec (); |
| 1948 | 2710 |
| 7072 | 2711 // Ask ZGELSD what the dimension of WORK should be. |
| 5275 | 2712 octave_idx_type lwork = -1; |
| 3752 | 2713 |
| 2714 Array<Complex> work (1); | |
| 7079 | 2715 |
|
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2716 octave_idx_type smlsiz; |
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2717 F77_FUNC (xilaenv, XILAENV) (9, F77_CONST_CHAR_ARG2 ("ZGELSD", 6), |
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|
2718 F77_CONST_CHAR_ARG2 (" ", 1), |
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|
2719 0, 0, 0, 0, smlsiz |
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2720 F77_CHAR_ARG_LEN (6) |
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|
2721 F77_CHAR_ARG_LEN (1)); |
| 7079 | 2722 |
| 2723 // We compute the size of rwork and iwork because ZGELSD in | |
| 2724 // older versions of LAPACK does not return them on a query | |
| 2725 // call. | |
| 7124 | 2726 double dminmn = static_cast<double> (minmn); |
| 2727 double dsmlsizp1 = static_cast<double> (smlsiz+1); | |
| 7079 | 2728 #if defined (HAVE_LOG2) |
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|
2729 double tmp = log2 (dminmn / dsmlsizp1); |
| 7079 | 2730 #else |
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|
2731 double tmp = log (dminmn / dsmlsizp1) / log (2.0); |
| 7079 | 2732 #endif |
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|
2733 octave_idx_type nlvl = static_cast<octave_idx_type> (tmp) + 1; |
| 7079 | 2734 if (nlvl < 0) |
| 2735 nlvl = 0; | |
| 2736 | |
| 2737 octave_idx_type lrwork = minmn*(10 + 2*smlsiz + 8*nlvl) | |
| 2738 + 3*smlsiz*nrhs + (smlsiz+1)*(smlsiz+1); | |
| 2739 if (lrwork < 1) | |
| 2740 lrwork = 1; | |
| 2741 Array<double> rwork (lrwork); | |
| 2742 double *prwork = rwork.fortran_vec (); | |
| 2743 | |
| 2744 octave_idx_type liwork = 3 * minmn * nlvl + 11 * minmn; | |
| 2745 if (liwork < 1) | |
| 2746 liwork = 1; | |
| 2747 Array<octave_idx_type> iwork (liwork); | |
| 2748 octave_idx_type* piwork = iwork.fortran_vec (); | |
| 7072 | 2749 |
| 2750 F77_XFCN (zgelsd, ZGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, | |
| 2751 ps, rcond, rank, work.fortran_vec (), | |
| 7079 | 2752 lwork, prwork, piwork, info)); |
| 1948 | 2753 |
| 2754 if (f77_exception_encountered) | |
| 7072 | 2755 (*current_liboctave_error_handler) |
| 2756 ("unrecoverable error in zgelsd"); | |
| 1948 | 2757 else |
| 2758 { | |
| 7072 | 2759 lwork = static_cast<octave_idx_type> (std::real (work(0))); |
| 3752 | 2760 work.resize (lwork); |
| 7072 | 2761 rwork.resize (static_cast<octave_idx_type> (rwork(0))); |
| 2762 iwork.resize (iwork(0)); | |
| 2763 | |
| 2764 F77_XFCN (zgelsd, ZGELSD, (m, n, nrhs, tmp_data, m, pretval, | |
| 2765 maxmn, ps, rcond, rank, | |
| 2766 work.fortran_vec (), lwork, | |
| 7079 | 2767 prwork, piwork, info)); |
| 3752 | 2768 |
| 2769 if (f77_exception_encountered) | |
| 7072 | 2770 (*current_liboctave_error_handler) |
| 2771 ("unrecoverable error in zgelsd"); | |
| 2772 else if (rank < minmn) | |
| 7076 | 2773 { |
| 2774 if (rank < minmn) | |
| 2775 (*current_liboctave_warning_handler) | |
| 2776 ("zgelsd: rank deficient %dx%d matrix, rank = %d, tol = %e", | |
| 2777 m, n, rank, rcond); | |
| 2778 | |
| 2779 if (s.elem (0) == 0.0) | |
| 2780 rcond = 0.0; | |
| 2781 else | |
| 2782 rcond = s.elem (minmn - 1) / s.elem (0); | |
| 7079 | 2783 |
| 2784 retval.resize (n, nrhs); | |
| 7076 | 2785 } |
| 1948 | 2786 } |
| 458 | 2787 } |
| 2788 | |
| 2789 return retval; | |
| 2790 } | |
| 2791 | |
| 1819 | 2792 // Constants for matrix exponential calculation. |
| 2793 | |
| 2794 static double padec [] = | |
| 2795 { | |
| 2796 5.0000000000000000e-1, | |
| 2797 1.1666666666666667e-1, | |
| 2798 1.6666666666666667e-2, | |
| 2799 1.6025641025641026e-3, | |
| 2800 1.0683760683760684e-4, | |
| 2801 4.8562548562548563e-6, | |
| 2802 1.3875013875013875e-7, | |
| 2803 1.9270852604185938e-9, | |
| 2804 }; | |
| 2805 | |
| 2806 ComplexMatrix | |
| 2807 ComplexMatrix::expm (void) const | |
| 2808 { | |
| 2809 ComplexMatrix retval; | |
| 2810 | |
| 2811 ComplexMatrix m = *this; | |
| 2812 | |
| 5275 | 2813 octave_idx_type nc = columns (); |
| 1819 | 2814 |
| 3130 | 2815 // Preconditioning step 1: trace normalization to reduce dynamic |
| 2816 // range of poles, but avoid making stable eigenvalues unstable. | |
| 2817 | |
| 1819 | 2818 // trace shift value |
| 2819 Complex trshift = 0.0; | |
| 2820 | |
| 5275 | 2821 for (octave_idx_type i = 0; i < nc; i++) |
| 1819 | 2822 trshift += m.elem (i, i); |
| 2823 | |
| 2824 trshift /= nc; | |
| 2825 | |
| 3130 | 2826 if (trshift.real () < 0.0) |
| 6958 | 2827 { |
| 2828 trshift = trshift.imag (); | |
| 2829 if (trshift.real () > 709.0) | |
| 2830 trshift = 709.0; | |
| 2831 } | |
| 3130 | 2832 |
| 5275 | 2833 for (octave_idx_type i = 0; i < nc; i++) |
| 1819 | 2834 m.elem (i, i) -= trshift; |
| 2835 | |
| 2836 // Preconditioning step 2: eigenvalue balancing. | |
| 3331 | 2837 // code follows development in AEPBAL |
| 2838 | |
| 2839 Complex *mp = m.fortran_vec (); | |
| 3467 | 2840 |
| 5275 | 2841 octave_idx_type info, ilo, ihi,ilos,ihis; |
| 3468 | 2842 Array<double> dpermute (nc); |
| 2843 Array<double> dscale (nc); | |
| 2844 | |
| 5775 | 2845 // FIXME -- should pass job as a parameter in expm |
| 3468 | 2846 |
| 2847 // Permute first | |
| 2848 char job = 'P'; | |
| 4552 | 2849 F77_XFCN (zgebal, ZGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
| 2850 nc, mp, nc, ilo, ihi, | |
| 2851 dpermute.fortran_vec (), info | |
| 2852 F77_CHAR_ARG_LEN (1))); | |
| 3331 | 2853 |
| 2854 if (f77_exception_encountered) | |
| 2855 { | |
| 2856 (*current_liboctave_error_handler) ("unrecoverable error in zgebal"); | |
| 2857 return retval; | |
| 2858 } | |
| 2859 | |
| 3468 | 2860 // then scale |
| 2861 job = 'S'; | |
| 4552 | 2862 F77_XFCN (zgebal, ZGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
| 2863 nc, mp, nc, ilos, ihis, | |
| 2864 dscale.fortran_vec (), info | |
| 2865 F77_CHAR_ARG_LEN (1))); | |
| 3331 | 2866 |
| 2867 if (f77_exception_encountered) | |
| 2868 { | |
| 3467 | 2869 (*current_liboctave_error_handler) ("unrecoverable error in zgebal"); |
| 3331 | 2870 return retval; |
| 2871 } | |
| 1819 | 2872 |
| 2873 // Preconditioning step 3: scaling. | |
| 2874 | |
| 2875 ColumnVector work (nc); | |
| 3130 | 2876 double inf_norm; |
| 2877 | |
| 4552 | 2878 F77_XFCN (xzlange, XZLANGE, (F77_CONST_CHAR_ARG2 ("I", 1), |
| 2879 nc, nc, m.fortran_vec (), nc, | |
| 2880 work.fortran_vec (), inf_norm | |
| 2881 F77_CHAR_ARG_LEN (1))); | |
| 3331 | 2882 |
| 2883 if (f77_exception_encountered) | |
| 2884 { | |
| 2885 (*current_liboctave_error_handler) ("unrecoverable error in zlange"); | |
| 2886 return retval; | |
| 2887 } | |
| 1819 | 2888 |
| 2800 | 2889 int sqpow = (inf_norm > 0.0 |
| 2890 ? static_cast<int> (1.0 + log (inf_norm) / log (2.0)) : 0); | |
| 1819 | 2891 |
| 2892 // Check whether we need to square at all. | |
| 2893 | |
| 2894 if (sqpow < 0) | |
| 2895 sqpow = 0; | |
| 2896 | |
| 2897 if (sqpow > 0) | |
| 2898 { | |
|
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|
2899 if (sqpow > 1023) |
|
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|
2900 sqpow = 1023; |
|
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|
2901 |
| 1819 | 2902 double scale_factor = 1.0; |
| 5275 | 2903 for (octave_idx_type i = 0; i < sqpow; i++) |
| 1819 | 2904 scale_factor *= 2.0; |
| 2905 | |
| 2906 m = m / scale_factor; | |
| 2907 } | |
| 2908 | |
| 2909 // npp, dpp: pade' approx polynomial matrices. | |
| 2910 | |
| 2911 ComplexMatrix npp (nc, nc, 0.0); | |
| 6958 | 2912 Complex *pnpp = npp.fortran_vec (); |
| 1819 | 2913 ComplexMatrix dpp = npp; |
| 6958 | 2914 Complex *pdpp = dpp.fortran_vec (); |
| 1819 | 2915 |
| 2916 // Now powers a^8 ... a^1. | |
| 2917 | |
| 2918 int minus_one_j = -1; | |
| 5275 | 2919 for (octave_idx_type j = 7; j >= 0; j--) |
| 1819 | 2920 { |
| 6958 | 2921 for (octave_idx_type i = 0; i < nc; i++) |
| 2922 { | |
| 2923 octave_idx_type k = i * nc + i; | |
| 7265 | 2924 pnpp[k] += padec[j]; |
| 2925 pdpp[k] += minus_one_j * padec[j]; | |
| 6958 | 2926 } |
| 7265 | 2927 |
| 6958 | 2928 npp = m * npp; |
| 7265 | 2929 pnpp = npp.fortran_vec (); |
| 2930 | |
| 6958 | 2931 dpp = m * dpp; |
| 7265 | 2932 pdpp = dpp.fortran_vec (); |
| 2933 | |
| 1819 | 2934 minus_one_j *= -1; |
| 2935 } | |
| 2936 | |
| 2937 // Zero power. | |
| 2938 | |
| 2939 dpp = -dpp; | |
| 5275 | 2940 for (octave_idx_type j = 0; j < nc; j++) |
| 1819 | 2941 { |
| 2942 npp.elem (j, j) += 1.0; | |
| 2943 dpp.elem (j, j) += 1.0; | |
| 2944 } | |
| 2945 | |
| 2946 // Compute pade approximation = inverse (dpp) * npp. | |
| 2947 | |
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|
2948 retval = dpp.solve (npp, info); |
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|
2949 |
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|
2950 if (info < 0) |
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|
2951 return retval; |
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|
2952 |
| 1819 | 2953 // Reverse preconditioning step 3: repeated squaring. |
| 2954 | |
| 2955 while (sqpow) | |
| 2956 { | |
| 2957 retval = retval * retval; | |
| 2958 sqpow--; | |
| 2959 } | |
| 2960 | |
| 2961 // Reverse preconditioning step 2: inverse balancing. | |
| 3467 | 2962 // Done in two steps: inverse scaling, then inverse permutation |
| 2963 | |
| 2964 // inverse scaling (diagonal transformation) | |
| 5275 | 2965 for (octave_idx_type i = 0; i < nc; i++) |
| 2966 for (octave_idx_type j = 0; j < nc; j++) | |
|
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|
2967 retval(i,j) *= dscale(i) / dscale(j); |
| 3467 | 2968 |
| 4153 | 2969 OCTAVE_QUIT; |
| 2970 | |
| 3467 | 2971 // construct balancing permutation vector |
| 6867 | 2972 Array<octave_idx_type> iperm (nc); |
| 5275 | 2973 for (octave_idx_type i = 0; i < nc; i++) |
|
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2974 iperm(i) = i; // identity permutation |
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2975 |
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|
2976 // trailing permutations must be done in reverse order |
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|
2977 for (octave_idx_type i = nc - 1; i >= ihi; i--) |
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|
2978 { |
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|
2979 octave_idx_type swapidx = static_cast<octave_idx_type> (dpermute(i)) - 1; |
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|
2980 octave_idx_type tmp = iperm(i); |
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|
2981 iperm(i) = iperm(swapidx); |
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|
2982 iperm(swapidx) = tmp; |
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|
2983 } |
| 3467 | 2984 |
| 2985 // leading permutations in forward order | |
| 5275 | 2986 for (octave_idx_type i = 0; i < (ilo-1); i++) |
| 3468 | 2987 { |
| 6867 | 2988 octave_idx_type swapidx = static_cast<octave_idx_type> (dpermute(i)) - 1; |
| 5275 | 2989 octave_idx_type tmp = iperm(i); |
|
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|
2990 iperm(i) = iperm (swapidx); |
| 4593 | 2991 iperm(swapidx) = tmp; |
| 3468 | 2992 } |
| 3467 | 2993 |
| 11841 | 2994 // construct inverse balancing permutation vector |
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|
2995 Array<octave_idx_type> invpvec (nc); |
| 11841 | 2996 for (octave_idx_type i = 0; i < nc; i++) |
| 2997 invpvec(iperm(i)) = i; // Thanks to R. A. Lippert for this method | |
| 2998 | |
| 2999 OCTAVE_QUIT; | |
| 3000 | |
|
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|
3001 ComplexMatrix tmpMat = retval; |
| 11841 | 3002 for (octave_idx_type i = 0; i < nc; i++) |
| 3003 for (octave_idx_type j = 0; j < nc; j++) | |
| 3004 retval(i,j) = tmpMat(invpvec(i),invpvec(j)); | |
| 3005 | |
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|
3006 // Reverse preconditioning step 1: fix trace normalization. |
| 1819 | 3007 |
| 3130 | 3008 return exp (trshift) * retval; |
| 1819 | 3009 } |
| 3010 | |
| 1205 | 3011 // column vector by row vector -> matrix operations |
| 3012 | |
| 3013 ComplexMatrix | |
| 3014 operator * (const ColumnVector& v, const ComplexRowVector& a) | |
| 3015 { | |
| 3016 ComplexColumnVector tmp (v); | |
| 3017 return tmp * a; | |
| 3018 } | |
| 3019 | |
| 3020 ComplexMatrix | |
| 3021 operator * (const ComplexColumnVector& a, const RowVector& b) | |
| 3022 { | |
| 3023 ComplexRowVector tmp (b); | |
| 3024 return a * tmp; | |
| 3025 } | |
| 3026 | |
| 3027 ComplexMatrix | |
| 3028 operator * (const ComplexColumnVector& v, const ComplexRowVector& a) | |
| 3029 { | |
| 1948 | 3030 ComplexMatrix retval; |
| 3031 | |
| 5275 | 3032 octave_idx_type len = v.length (); |
| 3233 | 3033 |
| 3034 if (len != 0) | |
| 1205 | 3035 { |
| 5275 | 3036 octave_idx_type a_len = a.length (); |
| 3233 | 3037 |
| 3038 retval.resize (len, a_len); | |
| 3039 Complex *c = retval.fortran_vec (); | |
| 3040 | |
| 4552 | 3041 F77_XFCN (zgemm, ZGEMM, (F77_CONST_CHAR_ARG2 ("N", 1), |
| 3042 F77_CONST_CHAR_ARG2 ("N", 1), | |
| 3043 len, a_len, 1, 1.0, v.data (), len, | |
| 3044 a.data (), 1, 0.0, c, len | |
| 3045 F77_CHAR_ARG_LEN (1) | |
| 3046 F77_CHAR_ARG_LEN (1))); | |
| 3233 | 3047 |
| 3048 if (f77_exception_encountered) | |
| 3049 (*current_liboctave_error_handler) | |
| 3050 ("unrecoverable error in zgemm"); | |
| 1205 | 3051 } |
| 3052 | |
| 1948 | 3053 return retval; |
| 1205 | 3054 } |
| 3055 | |
| 458 | 3056 // matrix by diagonal matrix -> matrix operations |
| 3057 | |
| 3058 ComplexMatrix& | |
| 3059 ComplexMatrix::operator += (const DiagMatrix& a) | |
| 3060 { | |
| 5275 | 3061 octave_idx_type nr = rows (); |
| 3062 octave_idx_type nc = cols (); | |
| 3063 | |
| 3064 octave_idx_type a_nr = rows (); | |
| 3065 octave_idx_type a_nc = cols (); | |
| 2384 | 3066 |
| 3067 if (nr != a_nr || nc != a_nc) | |
| 458 | 3068 { |
| 2384 | 3069 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
| 889 | 3070 return *this; |
| 458 | 3071 } |
| 3072 | |
| 5275 | 3073 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 3074 elem (i, i) += a.elem (i, i); |
| 3075 | |
| 3076 return *this; | |
| 3077 } | |
| 3078 | |
| 3079 ComplexMatrix& | |
| 3080 ComplexMatrix::operator -= (const DiagMatrix& a) | |
| 3081 { | |
| 5275 | 3082 octave_idx_type nr = rows (); |
| 3083 octave_idx_type nc = cols (); | |
| 3084 | |
| 3085 octave_idx_type a_nr = rows (); | |
| 3086 octave_idx_type a_nc = cols (); | |
| 2384 | 3087 |
| 3088 if (nr != a_nr || nc != a_nc) | |
| 458 | 3089 { |
| 2384 | 3090 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
| 889 | 3091 return *this; |
| 458 | 3092 } |
| 3093 | |
| 5275 | 3094 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 3095 elem (i, i) -= a.elem (i, i); |
| 3096 | |
| 3097 return *this; | |
| 3098 } | |
| 3099 | |
| 3100 ComplexMatrix& | |
| 3101 ComplexMatrix::operator += (const ComplexDiagMatrix& a) | |
| 3102 { | |
| 5275 | 3103 octave_idx_type nr = rows (); |
| 3104 octave_idx_type nc = cols (); | |
| 3105 | |
| 3106 octave_idx_type a_nr = rows (); | |
| 3107 octave_idx_type a_nc = cols (); | |
| 2384 | 3108 |
| 3109 if (nr != a_nr || nc != a_nc) | |
| 458 | 3110 { |
| 2384 | 3111 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
| 889 | 3112 return *this; |
| 458 | 3113 } |
| 3114 | |
| 5275 | 3115 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 3116 elem (i, i) += a.elem (i, i); |
| 3117 | |
| 3118 return *this; | |
| 3119 } | |
| 3120 | |
| 3121 ComplexMatrix& | |
| 3122 ComplexMatrix::operator -= (const ComplexDiagMatrix& a) | |
| 3123 { | |
| 5275 | 3124 octave_idx_type nr = rows (); |
| 3125 octave_idx_type nc = cols (); | |
| 3126 | |
| 3127 octave_idx_type a_nr = rows (); | |
| 3128 octave_idx_type a_nc = cols (); | |
| 2384 | 3129 |
| 3130 if (nr != a_nr || nc != a_nc) | |
| 458 | 3131 { |
| 2384 | 3132 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
| 889 | 3133 return *this; |
| 458 | 3134 } |
| 3135 | |
| 5275 | 3136 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 3137 elem (i, i) -= a.elem (i, i); |
| 3138 | |
| 3139 return *this; | |
| 3140 } | |
| 3141 | |
| 3142 // matrix by matrix -> matrix operations | |
| 3143 | |
| 3144 ComplexMatrix& | |
| 3145 ComplexMatrix::operator += (const Matrix& a) | |
| 3146 { | |
| 5275 | 3147 octave_idx_type nr = rows (); |
| 3148 octave_idx_type nc = cols (); | |
| 3149 | |
| 3150 octave_idx_type a_nr = a.rows (); | |
| 3151 octave_idx_type a_nc = a.cols (); | |
| 2384 | 3152 |
| 3153 if (nr != a_nr || nc != a_nc) | |
| 458 | 3154 { |
| 2384 | 3155 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
| 458 | 3156 return *this; |
| 3157 } | |
| 3158 | |
| 3159 if (nr == 0 || nc == 0) | |
| 3160 return *this; | |
| 3161 | |
| 3162 Complex *d = fortran_vec (); // Ensures only one reference to my privates! | |
| 3163 | |
| 3769 | 3164 mx_inline_add2 (d, a.data (), length ()); |
| 458 | 3165 return *this; |
| 3166 } | |
| 3167 | |
| 3168 ComplexMatrix& | |
| 3169 ComplexMatrix::operator -= (const Matrix& a) | |
| 3170 { | |
| 5275 | 3171 octave_idx_type nr = rows (); |
| 3172 octave_idx_type nc = cols (); | |
| 3173 | |
| 3174 octave_idx_type a_nr = a.rows (); | |
| 3175 octave_idx_type a_nc = a.cols (); | |
| 2384 | 3176 |
| 3177 if (nr != a_nr || nc != a_nc) | |
| 458 | 3178 { |
| 2384 | 3179 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
| 458 | 3180 return *this; |
| 3181 } | |
| 3182 | |
| 3183 if (nr == 0 || nc == 0) | |
| 3184 return *this; | |
| 3185 | |
| 3186 Complex *d = fortran_vec (); // Ensures only one reference to my privates! | |
| 3187 | |
| 3769 | 3188 mx_inline_subtract2 (d, a.data (), length ()); |
| 458 | 3189 return *this; |
| 3190 } | |
| 3191 | |
| 3192 // unary operations | |
| 3193 | |
| 2964 | 3194 boolMatrix |
| 458 | 3195 ComplexMatrix::operator ! (void) const |
| 3196 { | |
| 5275 | 3197 octave_idx_type nr = rows (); |
| 3198 octave_idx_type nc = cols (); | |
| 2964 | 3199 |
| 3200 boolMatrix b (nr, nc); | |
| 3201 | |
| 5275 | 3202 for (octave_idx_type j = 0; j < nc; j++) |
| 3203 for (octave_idx_type i = 0; i < nr; i++) | |
| 5139 | 3204 b.elem (i, j) = elem (i, j) == 0.0; |
| 2964 | 3205 |
| 3206 return b; | |
| 458 | 3207 } |
| 3208 | |
| 3209 // other operations | |
| 3210 | |
| 3211 ComplexMatrix | |
| 2676 | 3212 ComplexMatrix::map (c_c_Mapper f) const |
| 458 | 3213 { |
| 2676 | 3214 ComplexMatrix b (*this); |
| 3215 return b.apply (f); | |
| 458 | 3216 } |
| 3217 | |
| 2676 | 3218 Matrix |
| 3219 ComplexMatrix::map (d_c_Mapper f) const | |
| 458 | 3220 { |
| 5275 | 3221 octave_idx_type nr = rows (); |
| 3222 octave_idx_type nc = cols (); | |
| 3248 | 3223 |
| 3224 Matrix retval (nr, nc); | |
| 3225 | |
| 5275 | 3226 for (octave_idx_type j = 0; j < nc; j++) |
| 3227 for (octave_idx_type i = 0; i < nr; i++) | |
| 3248 | 3228 retval(i,j) = f (elem(i,j)); |
| 3229 | |
| 3230 return retval; | |
| 3231 } | |
| 3232 | |
| 3233 boolMatrix | |
| 3234 ComplexMatrix::map (b_c_Mapper f) const | |
| 3235 { | |
| 5275 | 3236 octave_idx_type nr = rows (); |
| 3237 octave_idx_type nc = cols (); | |
| 3248 | 3238 |
| 3239 boolMatrix retval (nr, nc); | |
| 3240 | |
| 5275 | 3241 for (octave_idx_type j = 0; j < nc; j++) |
| 3242 for (octave_idx_type i = 0; i < nr; i++) | |
| 3248 | 3243 retval(i,j) = f (elem(i,j)); |
| 2676 | 3244 |
| 3245 return retval; | |
| 3246 } | |
| 3247 | |
| 3248 ComplexMatrix& | |
| 3249 ComplexMatrix::apply (c_c_Mapper f) | |
| 3250 { | |
| 3251 Complex *d = fortran_vec (); // Ensures only one reference to my privates! | |
| 3252 | |
| 5275 | 3253 for (octave_idx_type i = 0; i < length (); i++) |
| 2676 | 3254 d[i] = f (d[i]); |
| 3255 | |
| 3256 return *this; | |
| 458 | 3257 } |
| 3258 | |
| 2384 | 3259 bool |
| 3260 ComplexMatrix::any_element_is_inf_or_nan (void) const | |
| 3261 { | |
| 5275 | 3262 octave_idx_type nr = rows (); |
| 3263 octave_idx_type nc = cols (); | |
| 3264 | |
| 3265 for (octave_idx_type j = 0; j < nc; j++) | |
| 3266 for (octave_idx_type i = 0; i < nr; i++) | |
| 2384 | 3267 { |
| 3268 Complex val = elem (i, j); | |
| 3269 if (xisinf (val) || xisnan (val)) | |
| 3270 return true; | |
| 3271 } | |
| 3272 | |
| 3273 return false; | |
| 3274 } | |
| 3275 | |
| 2408 | 3276 // Return true if no elements have imaginary components. |
| 3277 | |
| 3278 bool | |
| 3279 ComplexMatrix::all_elements_are_real (void) const | |
| 3280 { | |
| 5275 | 3281 octave_idx_type nr = rows (); |
| 3282 octave_idx_type nc = cols (); | |
| 3283 | |
| 3284 for (octave_idx_type j = 0; j < nc; j++) | |
| 4349 | 3285 { |
| 5275 | 3286 for (octave_idx_type i = 0; i < nr; i++) |
| 4349 | 3287 { |
| 5315 | 3288 double ip = std::imag (elem (i, j)); |
| 4349 | 3289 |
| 3290 if (ip != 0.0 || lo_ieee_signbit (ip)) | |
| 3291 return false; | |
| 3292 } | |
| 3293 } | |
| 2408 | 3294 |
| 3295 return true; | |
| 3296 } | |
| 3297 | |
| 1968 | 3298 // Return nonzero if any element of CM has a non-integer real or |
| 3299 // imaginary part. Also extract the largest and smallest (real or | |
| 3300 // imaginary) values and return them in MAX_VAL and MIN_VAL. | |
| 3301 | |
| 2384 | 3302 bool |
| 1968 | 3303 ComplexMatrix::all_integers (double& max_val, double& min_val) const |
| 3304 { | |
| 5275 | 3305 octave_idx_type nr = rows (); |
| 3306 octave_idx_type nc = cols (); | |
| 1968 | 3307 |
| 3308 if (nr > 0 && nc > 0) | |
| 3309 { | |
| 3310 Complex val = elem (0, 0); | |
| 3311 | |
| 5315 | 3312 double r_val = std::real (val); |
| 3313 double i_val = std::imag (val); | |
| 1968 | 3314 |
| 3315 max_val = r_val; | |
| 3316 min_val = r_val; | |
| 3317 | |
| 3318 if (i_val > max_val) | |
| 3319 max_val = i_val; | |
| 3320 | |
| 3321 if (i_val < max_val) | |
| 3322 min_val = i_val; | |
| 3323 } | |
| 3324 else | |
| 2384 | 3325 return false; |
| 1968 | 3326 |
| 5275 | 3327 for (octave_idx_type j = 0; j < nc; j++) |
| 3328 for (octave_idx_type i = 0; i < nr; i++) | |
| 1968 | 3329 { |
| 3330 Complex val = elem (i, j); | |
| 3331 | |
| 5315 | 3332 double r_val = std::real (val); |
| 3333 double i_val = std::imag (val); | |
| 1968 | 3334 |
| 3335 if (r_val > max_val) | |
| 3336 max_val = r_val; | |
| 3337 | |
| 3338 if (i_val > max_val) | |
| 3339 max_val = i_val; | |
| 3340 | |
| 3341 if (r_val < min_val) | |
| 3342 min_val = r_val; | |
| 3343 | |
| 3344 if (i_val < min_val) | |
| 3345 min_val = i_val; | |
| 3346 | |
| 3347 if (D_NINT (r_val) != r_val || D_NINT (i_val) != i_val) | |
| 2384 | 3348 return false; |
| 1968 | 3349 } |
| 2384 | 3350 |
| 3351 return true; | |
| 1968 | 3352 } |
| 3353 | |
| 2384 | 3354 bool |
| 1968 | 3355 ComplexMatrix::too_large_for_float (void) const |
| 3356 { | |
| 5275 | 3357 octave_idx_type nr = rows (); |
| 3358 octave_idx_type nc = cols (); | |
| 3359 | |
| 3360 for (octave_idx_type j = 0; j < nc; j++) | |
| 3361 for (octave_idx_type i = 0; i < nr; i++) | |
| 1968 | 3362 { |
| 3363 Complex val = elem (i, j); | |
| 3364 | |
| 5315 | 3365 double r_val = std::real (val); |
| 3366 double i_val = std::imag (val); | |
| 1968 | 3367 |
| 5389 | 3368 if ((! (xisnan (r_val) || xisinf (r_val)) |
| 5387 | 3369 && fabs (r_val) > FLT_MAX) |
| 5389 | 3370 || (! (xisnan (i_val) || xisinf (i_val)) |
| 5387 | 3371 && fabs (i_val) > FLT_MAX)) |
| 2384 | 3372 return true; |
| 1968 | 3373 } |
| 3374 | |
| 2384 | 3375 return false; |
| 1968 | 3376 } |
| 3377 | |
| 5775 | 3378 // FIXME Do these really belong here? Maybe they should be |
| 4015 | 3379 // in a base class? |
| 3380 | |
| 2832 | 3381 boolMatrix |
| 4015 | 3382 ComplexMatrix::all (int dim) const |
| 458 | 3383 { |
| 4015 | 3384 MX_ALL_OP (dim); |
| 458 | 3385 } |
| 3386 | |
| 2832 | 3387 boolMatrix |
| 4015 | 3388 ComplexMatrix::any (int dim) const |
| 458 | 3389 { |
| 4015 | 3390 MX_ANY_OP (dim); |
| 458 | 3391 } |
| 3392 | |
| 3393 ComplexMatrix | |
| 3723 | 3394 ComplexMatrix::cumprod (int dim) const |
| 458 | 3395 { |
| 4015 | 3396 MX_CUMULATIVE_OP (ComplexMatrix, Complex, *=); |
| 458 | 3397 } |
| 3398 | |
| 3399 ComplexMatrix | |
| 3723 | 3400 ComplexMatrix::cumsum (int dim) const |
| 458 | 3401 { |
| 4015 | 3402 MX_CUMULATIVE_OP (ComplexMatrix, Complex, +=); |
| 458 | 3403 } |
| 3404 | |
| 3405 ComplexMatrix | |
| 3723 | 3406 ComplexMatrix::prod (int dim) const |
| 458 | 3407 { |
| 3864 | 3408 MX_REDUCTION_OP (ComplexMatrix, *=, 1.0, 1.0); |
| 458 | 3409 } |
| 3410 | |
| 3411 ComplexMatrix | |
| 3723 | 3412 ComplexMatrix::sum (int dim) const |
| 458 | 3413 { |
| 3864 | 3414 MX_REDUCTION_OP (ComplexMatrix, +=, 0.0, 0.0); |
| 458 | 3415 } |
| 3416 | |
| 3417 ComplexMatrix | |
| 3723 | 3418 ComplexMatrix::sumsq (int dim) const |
| 458 | 3419 { |
| 3864 | 3420 #define ROW_EXPR \ |
| 3421 Complex d = elem (i, j); \ | |
| 3422 retval.elem (i, 0) += d * conj (d) | |
| 3423 | |
| 3424 #define COL_EXPR \ | |
| 3425 Complex d = elem (i, j); \ | |
| 3426 retval.elem (0, j) += d * conj (d) | |
| 3427 | |
| 3428 MX_BASE_REDUCTION_OP (ComplexMatrix, ROW_EXPR, COL_EXPR, 0.0, 0.0); | |
| 3429 | |
| 3430 #undef ROW_EXPR | |
| 3431 #undef COL_EXPR | |
| 458 | 3432 } |
| 3433 | |
| 4329 | 3434 Matrix ComplexMatrix::abs (void) const |
| 3435 { | |
| 5275 | 3436 octave_idx_type nr = rows (); |
| 3437 octave_idx_type nc = cols (); | |
| 4329 | 3438 |
| 3439 Matrix retval (nr, nc); | |
| 3440 | |
| 5275 | 3441 for (octave_idx_type j = 0; j < nc; j++) |
| 3442 for (octave_idx_type i = 0; i < nr; i++) | |
| 5315 | 3443 retval (i, j) = std::abs (elem (i, j)); |
| 4329 | 3444 |
| 3445 return retval; | |
| 3446 } | |
| 3447 | |
| 458 | 3448 ComplexColumnVector |
| 3449 ComplexMatrix::diag (void) const | |
| 3450 { | |
| 3451 return diag (0); | |
| 3452 } | |
| 3453 | |
| 3454 ComplexColumnVector | |
| 5275 | 3455 ComplexMatrix::diag (octave_idx_type k) const |
| 458 | 3456 { |
| 5275 | 3457 octave_idx_type nnr = rows (); |
| 3458 octave_idx_type nnc = cols (); | |
| 458 | 3459 if (k > 0) |
| 3460 nnc -= k; | |
| 3461 else if (k < 0) | |
| 3462 nnr += k; | |
| 3463 | |
| 3464 ComplexColumnVector d; | |
| 3465 | |
| 3466 if (nnr > 0 && nnc > 0) | |
| 3467 { | |
| 5275 | 3468 octave_idx_type ndiag = (nnr < nnc) ? nnr : nnc; |
| 458 | 3469 |
| 3470 d.resize (ndiag); | |
| 3471 | |
| 3472 if (k > 0) | |
| 3473 { | |
| 5275 | 3474 for (octave_idx_type i = 0; i < ndiag; i++) |
| 458 | 3475 d.elem (i) = elem (i, i+k); |
| 3476 } | |
| 4509 | 3477 else if (k < 0) |
| 458 | 3478 { |
| 5275 | 3479 for (octave_idx_type i = 0; i < ndiag; i++) |
| 458 | 3480 d.elem (i) = elem (i-k, i); |
| 3481 } | |
| 3482 else | |
| 3483 { | |
| 5275 | 3484 for (octave_idx_type i = 0; i < ndiag; i++) |
| 458 | 3485 d.elem (i) = elem (i, i); |
| 3486 } | |
| 3487 } | |
| 3488 else | |
| 4513 | 3489 (*current_liboctave_error_handler) |
| 3490 ("diag: requested diagonal out of range"); | |
| 458 | 3491 |
| 3492 return d; | |
| 3493 } | |
| 3494 | |
| 2354 | 3495 bool |
| 5275 | 3496 ComplexMatrix::row_is_real_only (octave_idx_type i) const |
| 2354 | 3497 { |
| 3498 bool retval = true; | |
| 3499 | |
| 5275 | 3500 octave_idx_type nc = columns (); |
| 3501 | |
| 3502 for (octave_idx_type j = 0; j < nc; j++) | |
| 2354 | 3503 { |
| 5315 | 3504 if (std::imag (elem (i, j)) != 0.0) |
| 2354 | 3505 { |
| 3506 retval = false; | |
| 3507 break; | |
| 3508 } | |
| 3509 } | |
| 3510 | |
| 3511 return retval; | |
| 3512 } | |
| 3513 | |
| 3514 bool | |
| 5275 | 3515 ComplexMatrix::column_is_real_only (octave_idx_type j) const |
| 2354 | 3516 { |
| 3517 bool retval = true; | |
| 3518 | |
| 5275 | 3519 octave_idx_type nr = rows (); |
| 3520 | |
| 3521 for (octave_idx_type i = 0; i < nr; i++) | |
| 2354 | 3522 { |
| 5315 | 3523 if (std::imag (elem (i, j)) != 0.0) |
| 2354 | 3524 { |
| 3525 retval = false; | |
| 3526 break; | |
| 3527 } | |
| 3528 } | |
| 3529 | |
| 3530 return retval; | |
| 3531 } | |
| 891 | 3532 |
| 458 | 3533 ComplexColumnVector |
| 3534 ComplexMatrix::row_min (void) const | |
| 3535 { | |
| 5275 | 3536 Array<octave_idx_type> dummy_idx; |
| 4587 | 3537 return row_min (dummy_idx); |
| 458 | 3538 } |
| 3539 | |
| 3540 ComplexColumnVector | |
| 5275 | 3541 ComplexMatrix::row_min (Array<octave_idx_type>& idx_arg) const |
| 458 | 3542 { |
| 3543 ComplexColumnVector result; | |
| 3544 | |
| 5275 | 3545 octave_idx_type nr = rows (); |
| 3546 octave_idx_type nc = cols (); | |
| 458 | 3547 |
| 3548 if (nr > 0 && nc > 0) | |
| 3549 { | |
| 3550 result.resize (nr); | |
| 4587 | 3551 idx_arg.resize (nr); |
| 458 | 3552 |
| 5275 | 3553 for (octave_idx_type i = 0; i < nr; i++) |
| 458 | 3554 { |
| 2354 | 3555 bool real_only = row_is_real_only (i); |
| 3556 | |
| 5275 | 3557 octave_idx_type idx_j; |
| 4469 | 3558 |
| 3559 Complex tmp_min; | |
| 3560 | |
| 3561 double abs_min = octave_NaN; | |
| 3562 | |
| 3563 for (idx_j = 0; idx_j < nc; idx_j++) | |
| 3564 { | |
| 3565 tmp_min = elem (i, idx_j); | |
| 3566 | |
| 5389 | 3567 if (! xisnan (tmp_min)) |
| 4469 | 3568 { |
| 5315 | 3569 abs_min = real_only ? std::real (tmp_min) : std::abs (tmp_min); |
| 4469 | 3570 break; |
| 3571 } | |
| 3572 } | |
| 3573 | |
| 5275 | 3574 for (octave_idx_type j = idx_j+1; j < nc; j++) |
| 4469 | 3575 { |
| 3576 Complex tmp = elem (i, j); | |
| 3577 | |
| 5389 | 3578 if (xisnan (tmp)) |
| 4469 | 3579 continue; |
| 3580 | |
| 5315 | 3581 double abs_tmp = real_only ? std::real (tmp) : std::abs (tmp); |
| 4469 | 3582 |
| 3583 if (abs_tmp < abs_min) | |
| 3584 { | |
| 3585 idx_j = j; | |
| 3586 tmp_min = tmp; | |
| 3587 abs_min = abs_tmp; | |
| 3588 } | |
| 3589 } | |
| 3590 | |
| 5389 | 3591 if (xisnan (tmp_min)) |
| 4469 | 3592 { |
| 3593 result.elem (i) = Complex_NaN_result; | |
| 4587 | 3594 idx_arg.elem (i) = 0; |
| 4469 | 3595 } |
| 891 | 3596 else |
| 3597 { | |
| 4469 | 3598 result.elem (i) = tmp_min; |
| 4587 | 3599 idx_arg.elem (i) = idx_j; |
| 891 | 3600 } |
| 458 | 3601 } |
| 3602 } | |
| 3603 | |
| 3604 return result; | |
| 3605 } | |
| 3606 | |
| 3607 ComplexColumnVector | |
| 3608 ComplexMatrix::row_max (void) const | |
| 3609 { | |
| 5275 | 3610 Array<octave_idx_type> dummy_idx; |
| 4587 | 3611 return row_max (dummy_idx); |
| 458 | 3612 } |
| 3613 | |
| 3614 ComplexColumnVector | |
| 5275 | 3615 ComplexMatrix::row_max (Array<octave_idx_type>& idx_arg) const |
| 458 | 3616 { |
| 3617 ComplexColumnVector result; | |
| 3618 | |
| 5275 | 3619 octave_idx_type nr = rows (); |
| 3620 octave_idx_type nc = cols (); | |
| 458 | 3621 |
| 3622 if (nr > 0 && nc > 0) | |
| 3623 { | |
| 3624 result.resize (nr); | |
| 4587 | 3625 idx_arg.resize (nr); |
| 458 | 3626 |
| 5275 | 3627 for (octave_idx_type i = 0; i < nr; i++) |
| 458 | 3628 { |
| 2354 | 3629 bool real_only = row_is_real_only (i); |
| 3630 | |
| 5275 | 3631 octave_idx_type idx_j; |
| 4469 | 3632 |
| 3633 Complex tmp_max; | |
| 3634 | |
| 3635 double abs_max = octave_NaN; | |
| 3636 | |
| 3637 for (idx_j = 0; idx_j < nc; idx_j++) | |
| 3638 { | |
| 3639 tmp_max = elem (i, idx_j); | |
| 3640 | |
| 5389 | 3641 if (! xisnan (tmp_max)) |
| 4469 | 3642 { |
| 5315 | 3643 abs_max = real_only ? std::real (tmp_max) : std::abs (tmp_max); |
| 4469 | 3644 break; |
| 3645 } | |
| 3646 } | |
| 3647 | |
| 5275 | 3648 for (octave_idx_type j = idx_j+1; j < nc; j++) |
| 4469 | 3649 { |
| 3650 Complex tmp = elem (i, j); | |
| 3651 | |
| 5389 | 3652 if (xisnan (tmp)) |
| 4469 | 3653 continue; |
| 3654 | |
| 5315 | 3655 double abs_tmp = real_only ? std::real (tmp) : std::abs (tmp); |
| 4469 | 3656 |
| 3657 if (abs_tmp > abs_max) | |
| 3658 { | |
| 3659 idx_j = j; | |
| 3660 tmp_max = tmp; | |
| 3661 abs_max = abs_tmp; | |
| 3662 } | |
| 3663 } | |
| 3664 | |
| 5389 | 3665 if (xisnan (tmp_max)) |
| 4469 | 3666 { |
| 3667 result.elem (i) = Complex_NaN_result; | |
| 4587 | 3668 idx_arg.elem (i) = 0; |
| 4469 | 3669 } |
| 891 | 3670 else |
| 3671 { | |
| 4469 | 3672 result.elem (i) = tmp_max; |
| 4587 | 3673 idx_arg.elem (i) = idx_j; |
| 891 | 3674 } |
| 458 | 3675 } |
| 3676 } | |
| 3677 | |
| 3678 return result; | |
| 3679 } | |
| 3680 | |
| 3681 ComplexRowVector | |
| 3682 ComplexMatrix::column_min (void) const | |
| 3683 { | |
| 5275 | 3684 Array<octave_idx_type> dummy_idx; |
| 4587 | 3685 return column_min (dummy_idx); |
| 458 | 3686 } |
| 3687 | |
| 3688 ComplexRowVector | |
| 5275 | 3689 ComplexMatrix::column_min (Array<octave_idx_type>& idx_arg) const |
| 458 | 3690 { |
| 3691 ComplexRowVector result; | |
| 3692 | |
| 5275 | 3693 octave_idx_type nr = rows (); |
| 3694 octave_idx_type nc = cols (); | |
| 458 | 3695 |
| 3696 if (nr > 0 && nc > 0) | |
| 3697 { | |
| 3698 result.resize (nc); | |
| 4587 | 3699 idx_arg.resize (nc); |
| 458 | 3700 |
| 5275 | 3701 for (octave_idx_type j = 0; j < nc; j++) |
| 458 | 3702 { |
| 2354 | 3703 bool real_only = column_is_real_only (j); |
| 3704 | |
| 5275 | 3705 octave_idx_type idx_i; |
| 4469 | 3706 |
| 3707 Complex tmp_min; | |
| 3708 | |
| 3709 double abs_min = octave_NaN; | |
| 3710 | |
| 3711 for (idx_i = 0; idx_i < nr; idx_i++) | |
| 3712 { | |
| 3713 tmp_min = elem (idx_i, j); | |
| 3714 | |
| 5389 | 3715 if (! xisnan (tmp_min)) |
| 4469 | 3716 { |
| 5315 | 3717 abs_min = real_only ? std::real (tmp_min) : std::abs (tmp_min); |
| 4469 | 3718 break; |
| 3719 } | |
| 3720 } | |
| 3721 | |
| 5275 | 3722 for (octave_idx_type i = idx_i+1; i < nr; i++) |
| 4469 | 3723 { |
| 3724 Complex tmp = elem (i, j); | |
| 3725 | |
| 5389 | 3726 if (xisnan (tmp)) |
| 4469 | 3727 continue; |
| 3728 | |
| 5315 | 3729 double abs_tmp = real_only ? std::real (tmp) : std::abs (tmp); |
| 4469 | 3730 |
| 3731 if (abs_tmp < abs_min) | |
| 3732 { | |
| 3733 idx_i = i; | |
| 3734 tmp_min = tmp; | |
| 3735 abs_min = abs_tmp; | |
| 3736 } | |
| 3737 } | |
| 3738 | |
| 5389 | 3739 if (xisnan (tmp_min)) |
| 4469 | 3740 { |
| 3741 result.elem (j) = Complex_NaN_result; | |
| 4587 | 3742 idx_arg.elem (j) = 0; |
| 4469 | 3743 } |
| 891 | 3744 else |
| 3745 { | |
| 4469 | 3746 result.elem (j) = tmp_min; |
| 4587 | 3747 idx_arg.elem (j) = idx_i; |
| 891 | 3748 } |
| 458 | 3749 } |
| 3750 } | |
| 3751 | |
| 3752 return result; | |
| 3753 } | |
| 3754 | |
| 3755 ComplexRowVector | |
| 3756 ComplexMatrix::column_max (void) const | |
| 3757 { | |
| 5275 | 3758 Array<octave_idx_type> dummy_idx; |
| 4587 | 3759 return column_max (dummy_idx); |
| 458 | 3760 } |
| 3761 | |
| 3762 ComplexRowVector | |
| 5275 | 3763 ComplexMatrix::column_max (Array<octave_idx_type>& idx_arg) const |
| 458 | 3764 { |
| 3765 ComplexRowVector result; | |
| 3766 | |
| 5275 | 3767 octave_idx_type nr = rows (); |
| 3768 octave_idx_type nc = cols (); | |
| 458 | 3769 |
| 3770 if (nr > 0 && nc > 0) | |
| 3771 { | |
| 3772 result.resize (nc); | |
| 4587 | 3773 idx_arg.resize (nc); |
| 458 | 3774 |
| 5275 | 3775 for (octave_idx_type j = 0; j < nc; j++) |
| 458 | 3776 { |
| 2354 | 3777 bool real_only = column_is_real_only (j); |
| 3778 | |
| 5275 | 3779 octave_idx_type idx_i; |
| 4469 | 3780 |
| 3781 Complex tmp_max; | |
| 3782 | |
| 3783 double abs_max = octave_NaN; | |
| 3784 | |
| 3785 for (idx_i = 0; idx_i < nr; idx_i++) | |
| 3786 { | |
| 3787 tmp_max = elem (idx_i, j); | |
| 3788 | |
| 5389 | 3789 if (! xisnan (tmp_max)) |
| 4469 | 3790 { |
| 5315 | 3791 abs_max = real_only ? std::real (tmp_max) : std::abs (tmp_max); |
| 4469 | 3792 break; |
| 3793 } | |
| 3794 } | |
| 3795 | |
| 5275 | 3796 for (octave_idx_type i = idx_i+1; i < nr; i++) |
| 4469 | 3797 { |
| 3798 Complex tmp = elem (i, j); | |
| 3799 | |
| 5389 | 3800 if (xisnan (tmp)) |
| 4469 | 3801 continue; |
| 3802 | |
| 5315 | 3803 double abs_tmp = real_only ? std::real (tmp) : std::abs (tmp); |
| 4469 | 3804 |
| 3805 if (abs_tmp > abs_max) | |
| 3806 { | |
| 3807 idx_i = i; | |
| 3808 tmp_max = tmp; | |
| 3809 abs_max = abs_tmp; | |
| 3810 } | |
| 3811 } | |
| 3812 | |
| 5389 | 3813 if (xisnan (tmp_max)) |
| 4469 | 3814 { |
| 3815 result.elem (j) = Complex_NaN_result; | |
| 4587 | 3816 idx_arg.elem (j) = 0; |
| 4469 | 3817 } |
| 891 | 3818 else |
| 3819 { | |
| 4469 | 3820 result.elem (j) = tmp_max; |
| 4587 | 3821 idx_arg.elem (j) = idx_i; |
| 891 | 3822 } |
| 458 | 3823 } |
| 3824 } | |
| 3825 | |
| 3826 return result; | |
| 3827 } | |
| 3828 | |
| 3829 // i/o | |
| 3830 | |
| 3504 | 3831 std::ostream& |
| 3832 operator << (std::ostream& os, const ComplexMatrix& a) | |
| 458 | 3833 { |
| 5275 | 3834 for (octave_idx_type i = 0; i < a.rows (); i++) |
| 458 | 3835 { |
| 5275 | 3836 for (octave_idx_type j = 0; j < a.cols (); j++) |
| 4130 | 3837 { |
| 3838 os << " "; | |
| 3839 octave_write_complex (os, a.elem (i, j)); | |
| 3840 } | |
| 458 | 3841 os << "\n"; |
| 3842 } | |
| 3843 return os; | |
| 3844 } | |
| 3845 | |
| 3504 | 3846 std::istream& |
| 3847 operator >> (std::istream& is, ComplexMatrix& a) | |
| 458 | 3848 { |
| 5275 | 3849 octave_idx_type nr = a.rows (); |
| 3850 octave_idx_type nc = a.cols (); | |
| 458 | 3851 |
| 3852 if (nr < 1 || nc < 1) | |
| 3504 | 3853 is.clear (std::ios::badbit); |
| 458 | 3854 else |
| 3855 { | |
| 3856 Complex tmp; | |
| 5275 | 3857 for (octave_idx_type i = 0; i < nr; i++) |
| 3858 for (octave_idx_type j = 0; j < nc; j++) | |
| 458 | 3859 { |
| 4130 | 3860 tmp = octave_read_complex (is); |
| 458 | 3861 if (is) |
| 3862 a.elem (i, j) = tmp; | |
| 3863 else | |
| 2993 | 3864 goto done; |
| 458 | 3865 } |
| 3866 } | |
| 3867 | |
| 2993 | 3868 done: |
| 3869 | |
| 458 | 3870 return is; |
| 3871 } | |
| 3872 | |
| 1819 | 3873 ComplexMatrix |
| 3874 Givens (const Complex& x, const Complex& y) | |
| 3875 { | |
| 3876 double cc; | |
| 3877 Complex cs, temp_r; | |
| 3878 | |
| 3887 | 3879 F77_FUNC (zlartg, ZLARTG) (x, y, cc, cs, temp_r); |
| 1819 | 3880 |
| 3881 ComplexMatrix g (2, 2); | |
| 3882 | |
| 3883 g.elem (0, 0) = cc; | |
| 3884 g.elem (1, 1) = cc; | |
| 3885 g.elem (0, 1) = cs; | |
| 3886 g.elem (1, 0) = -conj (cs); | |
| 3887 | |
| 3888 return g; | |
| 3889 } | |
| 3890 | |
| 3891 ComplexMatrix | |
| 3892 Sylvester (const ComplexMatrix& a, const ComplexMatrix& b, | |
| 3893 const ComplexMatrix& c) | |
| 3894 { | |
| 3895 ComplexMatrix retval; | |
| 3896 | |
| 5775 | 3897 // FIXME -- need to check that a, b, and c are all the same |
| 1819 | 3898 // size. |
| 3899 | |
| 3900 // Compute Schur decompositions | |
| 3901 | |
| 3902 ComplexSCHUR as (a, "U"); | |
| 3903 ComplexSCHUR bs (b, "U"); | |
| 3904 | |
| 3905 // Transform c to new coordinates. | |
| 3906 | |
| 3907 ComplexMatrix ua = as.unitary_matrix (); | |
| 3908 ComplexMatrix sch_a = as.schur_matrix (); | |
| 3909 | |
| 3910 ComplexMatrix ub = bs.unitary_matrix (); | |
| 3911 ComplexMatrix sch_b = bs.schur_matrix (); | |
| 3912 | |
| 3913 ComplexMatrix cx = ua.hermitian () * c * ub; | |
| 3914 | |
| 3915 // Solve the sylvester equation, back-transform, and return the | |
| 3916 // solution. | |
| 3917 | |
| 5275 | 3918 octave_idx_type a_nr = a.rows (); |
| 3919 octave_idx_type b_nr = b.rows (); | |
| 1819 | 3920 |
| 3921 double scale; | |
| 5275 | 3922 octave_idx_type info; |
| 1950 | 3923 |
| 3924 Complex *pa = sch_a.fortran_vec (); | |
| 3925 Complex *pb = sch_b.fortran_vec (); | |
| 3926 Complex *px = cx.fortran_vec (); | |
| 1819 | 3927 |
| 4552 | 3928 F77_XFCN (ztrsyl, ZTRSYL, (F77_CONST_CHAR_ARG2 ("N", 1), |
| 3929 F77_CONST_CHAR_ARG2 ("N", 1), | |
| 3930 1, a_nr, b_nr, pa, a_nr, pb, | |
| 3931 b_nr, px, a_nr, scale, info | |
| 3932 F77_CHAR_ARG_LEN (1) | |
| 3933 F77_CHAR_ARG_LEN (1))); | |
| 1950 | 3934 |
| 3935 if (f77_exception_encountered) | |
| 3936 (*current_liboctave_error_handler) ("unrecoverable error in ztrsyl"); | |
| 3937 else | |
| 3938 { | |
| 5775 | 3939 // FIXME -- check info? |
| 1950 | 3940 |
| 3941 retval = -ua * cx * ub.hermitian (); | |
| 3942 } | |
| 1819 | 3943 |
| 3944 return retval; | |
| 3945 } | |
| 3946 | |
| 2828 | 3947 ComplexMatrix |
| 3948 operator * (const ComplexMatrix& m, const Matrix& a) | |
| 3949 { | |
| 3950 ComplexMatrix tmp (a); | |
| 3951 return m * tmp; | |
| 3952 } | |
| 3953 | |
| 3954 ComplexMatrix | |
| 3955 operator * (const Matrix& m, const ComplexMatrix& a) | |
| 3956 { | |
| 3957 ComplexMatrix tmp (m); | |
| 3958 return tmp * a; | |
| 3959 } | |
| 3960 | |
| 6162 | 3961 /* Simple Dot Product, Matrix-Vector and Matrix-Matrix Unit tests |
| 3962 %!assert([1+i 2+i 3+i] * [ 4+i ; 5+i ; 6+i], 29+21i, 1e-14) | |
| 3963 %!assert([1+i 2+i ; 3+i 4+i ] * [5+i ; 6+i], [15 + 14i ; 37 + 18i], 1e-14) | |
| 3964 %!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) | |
| 3965 */ | |
| 3966 | |
| 3967 /* Test some simple identities | |
| 3968 %!shared M, cv, rv | |
| 3969 %! M = randn(10,10)+i*rand(10,10); | |
| 3970 %! cv = randn(10,1)+i*rand(10,1); | |
| 3971 %! rv = randn(1,10)+i*rand(1,10); | |
| 3972 %!assert([M*cv,M*cv],M*[cv,cv],1e-14) | |
| 3973 %!assert([rv*M;rv*M],[rv;rv]*M,1e-14) | |
| 3974 %!assert(2*rv*cv,[rv,rv]*[cv;cv],1e-14) | |
| 3975 */ | |
| 3976 | |
| 2828 | 3977 ComplexMatrix |
| 3978 operator * (const ComplexMatrix& m, const ComplexMatrix& a) | |
| 3979 { | |
| 3980 ComplexMatrix retval; | |
| 3981 | |
| 5275 | 3982 octave_idx_type nr = m.rows (); |
| 3983 octave_idx_type nc = m.cols (); | |
| 3984 | |
| 3985 octave_idx_type a_nr = a.rows (); | |
| 3986 octave_idx_type a_nc = a.cols (); | |
| 2828 | 3987 |
| 3988 if (nc != a_nr) | |
| 3989 gripe_nonconformant ("operator *", nr, nc, a_nr, a_nc); | |
| 3990 else | |
| 3991 { | |
| 3992 if (nr == 0 || nc == 0 || a_nc == 0) | |
| 3760 | 3993 retval.resize (nr, a_nc, 0.0); |
| 2828 | 3994 else |
| 3995 { | |
| 5275 | 3996 octave_idx_type ld = nr; |
| 3997 octave_idx_type lda = a.rows (); | |
| 2828 | 3998 |
| 3999 retval.resize (nr, a_nc); | |
| 4000 Complex *c = retval.fortran_vec (); | |
| 4001 | |
| 5983 | 4002 if (a_nc == 1) |
| 4003 { | |
| 4004 if (nr == 1) | |
| 4005 F77_FUNC (xzdotu, XZDOTU) (nc, m.data (), 1, a.data (), 1, *c); | |
| 4006 else | |
| 6390 | 4007 { |
| 4008 F77_XFCN (zgemv, ZGEMV, (F77_CONST_CHAR_ARG2 ("N", 1), | |
| 4009 nr, nc, 1.0, m.data (), ld, | |
| 4010 a.data (), 1, 0.0, c, 1 | |
| 4011 F77_CHAR_ARG_LEN (1))); | |
| 4012 | |
| 4013 if (f77_exception_encountered) | |
| 4014 (*current_liboctave_error_handler) | |
| 4015 ("unrecoverable error in zgemv"); | |
| 4016 } | |
| 5983 | 4017 } |
| 4018 else | |
| 6390 | 4019 { |
| 4020 F77_XFCN (zgemm, ZGEMM, (F77_CONST_CHAR_ARG2 ("N", 1), | |
| 4021 F77_CONST_CHAR_ARG2 ("N", 1), | |
| 4022 nr, a_nc, nc, 1.0, m.data (), | |
| 4023 ld, a.data (), lda, 0.0, c, nr | |
| 4024 F77_CHAR_ARG_LEN (1) | |
| 4025 F77_CHAR_ARG_LEN (1))); | |
| 4026 | |
| 4027 if (f77_exception_encountered) | |
| 4028 (*current_liboctave_error_handler) | |
| 4029 ("unrecoverable error in zgemm"); | |
| 4030 } | |
| 2828 | 4031 } |
| 4032 } | |
| 4033 | |
| 4034 return retval; | |
| 4035 } | |
| 4036 | |
| 5775 | 4037 // FIXME -- it would be nice to share code among the min/max |
| 4309 | 4038 // functions below. |
| 4039 | |
| 4040 #define EMPTY_RETURN_CHECK(T) \ | |
| 4041 if (nr == 0 || nc == 0) \ | |
| 4042 return T (nr, nc); | |
| 4043 | |
| 4044 ComplexMatrix | |
| 4045 min (const Complex& c, const ComplexMatrix& m) | |
| 4046 { | |
| 5275 | 4047 octave_idx_type nr = m.rows (); |
| 4048 octave_idx_type nc = m.columns (); | |
| 4309 | 4049 |
| 4050 EMPTY_RETURN_CHECK (ComplexMatrix); | |
| 4051 | |
| 4052 ComplexMatrix result (nr, nc); | |
| 4053 | |
| 5275 | 4054 for (octave_idx_type j = 0; j < nc; j++) |
| 4055 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 4056 { |
| 4057 OCTAVE_QUIT; | |
| 4058 result (i, j) = xmin (c, m (i, j)); | |
| 4059 } | |
| 4060 | |
| 4061 return result; | |
| 4062 } | |
| 4063 | |
| 4064 ComplexMatrix | |
| 4065 min (const ComplexMatrix& m, const Complex& c) | |
| 4066 { | |
| 5275 | 4067 octave_idx_type nr = m.rows (); |
| 4068 octave_idx_type nc = m.columns (); | |
| 4309 | 4069 |
| 4070 EMPTY_RETURN_CHECK (ComplexMatrix); | |
| 4071 | |
| 4072 ComplexMatrix result (nr, nc); | |
| 4073 | |
| 5275 | 4074 for (octave_idx_type j = 0; j < nc; j++) |
| 4075 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 4076 { |
| 4077 OCTAVE_QUIT; | |
| 4078 result (i, j) = xmin (m (i, j), c); | |
| 4079 } | |
| 4080 | |
| 4081 return result; | |
| 4082 } | |
| 4083 | |
| 4084 ComplexMatrix | |
| 4085 min (const ComplexMatrix& a, const ComplexMatrix& b) | |
| 4086 { | |
| 5275 | 4087 octave_idx_type nr = a.rows (); |
| 4088 octave_idx_type nc = a.columns (); | |
| 4309 | 4089 |
| 4090 if (nr != b.rows () || nc != b.columns ()) | |
| 4091 { | |
| 4092 (*current_liboctave_error_handler) | |
| 4093 ("two-arg min expecting args of same size"); | |
| 4094 return ComplexMatrix (); | |
| 4095 } | |
| 4096 | |
| 4097 EMPTY_RETURN_CHECK (ComplexMatrix); | |
| 4098 | |
| 4099 ComplexMatrix result (nr, nc); | |
| 4100 | |
| 5275 | 4101 for (octave_idx_type j = 0; j < nc; j++) |
| 4309 | 4102 { |
| 4103 int columns_are_real_only = 1; | |
| 5275 | 4104 for (octave_idx_type i = 0; i < nr; i++) |
| 4309 | 4105 { |
| 4106 OCTAVE_QUIT; | |
| 5315 | 4107 if (std::imag (a (i, j)) != 0.0 || std::imag (b (i, j)) != 0.0) |
| 4309 | 4108 { |
| 4109 columns_are_real_only = 0; | |
| 4110 break; | |
| 4111 } | |
| 4112 } | |
| 4113 | |
| 4114 if (columns_are_real_only) | |
| 4115 { | |
| 5275 | 4116 for (octave_idx_type i = 0; i < nr; i++) |
| 5315 | 4117 result (i, j) = xmin (std::real (a (i, j)), std::real (b (i, j))); |
| 4309 | 4118 } |
| 4119 else | |
| 4120 { | |
| 5275 | 4121 for (octave_idx_type i = 0; i < nr; i++) |
| 4309 | 4122 { |
| 4123 OCTAVE_QUIT; | |
| 4124 result (i, j) = xmin (a (i, j), b (i, j)); | |
| 4125 } | |
| 4126 } | |
| 4127 } | |
| 4128 | |
| 4129 return result; | |
| 4130 } | |
| 4131 | |
| 4132 ComplexMatrix | |
| 4133 max (const Complex& c, const ComplexMatrix& m) | |
| 4134 { | |
| 5275 | 4135 octave_idx_type nr = m.rows (); |
| 4136 octave_idx_type nc = m.columns (); | |
| 4309 | 4137 |
| 4138 EMPTY_RETURN_CHECK (ComplexMatrix); | |
| 4139 | |
| 4140 ComplexMatrix result (nr, nc); | |
| 4141 | |
| 5275 | 4142 for (octave_idx_type j = 0; j < nc; j++) |
| 4143 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 4144 { |
| 4145 OCTAVE_QUIT; | |
| 4146 result (i, j) = xmax (c, m (i, j)); | |
| 4147 } | |
| 4148 | |
| 4149 return result; | |
| 4150 } | |
| 4151 | |
| 4152 ComplexMatrix | |
| 4153 max (const ComplexMatrix& m, const Complex& c) | |
| 4154 { | |
| 5275 | 4155 octave_idx_type nr = m.rows (); |
| 4156 octave_idx_type nc = m.columns (); | |
| 4309 | 4157 |
| 4158 EMPTY_RETURN_CHECK (ComplexMatrix); | |
| 4159 | |
| 4160 ComplexMatrix result (nr, nc); | |
| 4161 | |
| 5275 | 4162 for (octave_idx_type j = 0; j < nc; j++) |
| 4163 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 4164 { |
| 4165 OCTAVE_QUIT; | |
| 4166 result (i, j) = xmax (m (i, j), c); | |
| 4167 } | |
| 4168 | |
| 4169 return result; | |
| 4170 } | |
| 4171 | |
| 4172 ComplexMatrix | |
| 4173 max (const ComplexMatrix& a, const ComplexMatrix& b) | |
| 4174 { | |
| 5275 | 4175 octave_idx_type nr = a.rows (); |
| 4176 octave_idx_type nc = a.columns (); | |
| 4309 | 4177 |
| 4178 if (nr != b.rows () || nc != b.columns ()) | |
| 4179 { | |
| 4180 (*current_liboctave_error_handler) | |
| 4181 ("two-arg max expecting args of same size"); | |
| 4182 return ComplexMatrix (); | |
| 4183 } | |
| 4184 | |
| 4185 EMPTY_RETURN_CHECK (ComplexMatrix); | |
| 4186 | |
| 4187 ComplexMatrix result (nr, nc); | |
| 4188 | |
| 5275 | 4189 for (octave_idx_type j = 0; j < nc; j++) |
| 4309 | 4190 { |
| 4191 int columns_are_real_only = 1; | |
| 5275 | 4192 for (octave_idx_type i = 0; i < nr; i++) |
| 4309 | 4193 { |
| 4194 OCTAVE_QUIT; | |
| 5315 | 4195 if (std::imag (a (i, j)) != 0.0 || std::imag (b (i, j)) != 0.0) |
| 4309 | 4196 { |
| 4197 columns_are_real_only = 0; | |
| 4198 break; | |
| 4199 } | |
| 4200 } | |
| 4201 | |
| 4202 if (columns_are_real_only) | |
| 4203 { | |
| 5275 | 4204 for (octave_idx_type i = 0; i < nr; i++) |
| 4309 | 4205 { |
| 4206 OCTAVE_QUIT; | |
| 5315 | 4207 result (i, j) = xmax (std::real (a (i, j)), std::real (b (i, j))); |
| 4309 | 4208 } |
| 4209 } | |
| 4210 else | |
| 4211 { | |
| 5275 | 4212 for (octave_idx_type i = 0; i < nr; i++) |
| 4309 | 4213 { |
| 4214 OCTAVE_QUIT; | |
| 4215 result (i, j) = xmax (a (i, j), b (i, j)); | |
| 4216 } | |
| 4217 } | |
| 4218 } | |
| 4219 | |
| 4220 return result; | |
| 4221 } | |
| 4222 | |
| 5315 | 4223 MS_CMP_OPS(ComplexMatrix, std::real, Complex, std::real) |
| 3504 | 4224 MS_BOOL_OPS(ComplexMatrix, Complex, 0.0) |
| 2870 | 4225 |
| 5315 | 4226 SM_CMP_OPS(Complex, std::real, ComplexMatrix, std::real) |
| 3504 | 4227 SM_BOOL_OPS(Complex, ComplexMatrix, 0.0) |
| 2870 | 4228 |
| 5315 | 4229 MM_CMP_OPS(ComplexMatrix, std::real, ComplexMatrix, std::real) |
| 3504 | 4230 MM_BOOL_OPS(ComplexMatrix, ComplexMatrix, 0.0) |
| 2870 | 4231 |
| 458 | 4232 /* |
| 4233 ;;; Local Variables: *** | |
| 4234 ;;; mode: C++ *** | |
| 4235 ;;; End: *** | |
| 4236 */ |