Mercurial > hg > octave-nkf
annotate liboctave/CMatrix.cc @ 11652:ef95e842ba81 release-3-0-x
another small xGELSD workspace fix
| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Fri, 15 Feb 2008 19:54:25 -0500 |
| parents | 74de76325d12 |
| children | ef2b2df1ed9a |
| rev | line source |
|---|---|
| 1993 | 1 // Matrix manipulations. |
| 458 | 2 /* |
| 3 | |
| 7017 | 4 Copyright (C) 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, |
| 5 2003, 2004, 2005, 2006, 2007 John W. Eaton | |
| 458 | 6 |
| 7 This file is part of Octave. | |
| 8 | |
| 9 Octave is free software; you can redistribute it and/or modify it | |
| 10 under the terms of the GNU General Public License as published by the | |
| 7016 | 11 Free Software Foundation; either version 3 of the License, or (at your |
| 12 option) any later version. | |
| 458 | 13 |
| 14 Octave is distributed in the hope that it will be useful, but WITHOUT | |
| 15 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
| 16 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
| 17 for more details. | |
| 18 | |
| 19 You should have received a copy of the GNU General Public License | |
| 7016 | 20 along with Octave; see the file COPYING. If not, see |
| 21 <http://www.gnu.org/licenses/>. | |
| 458 | 22 |
| 23 */ | |
| 24 | |
| 25 #ifdef HAVE_CONFIG_H | |
| 1192 | 26 #include <config.h> |
| 458 | 27 #endif |
| 28 | |
| 1367 | 29 #include <cfloat> |
| 30 | |
| 3503 | 31 #include <iostream> |
| 6209 | 32 #include <vector> |
| 1367 | 33 |
| 5775 | 34 // FIXME |
| 2443 | 35 #ifdef HAVE_SYS_TYPES_H |
| 36 #include <sys/types.h> | |
| 37 #endif | |
| 458 | 38 |
| 4669 | 39 #include "Array-util.h" |
| 2828 | 40 #include "CMatrix.h" |
| 1819 | 41 #include "CmplxAEPBAL.h" |
| 458 | 42 #include "CmplxDET.h" |
| 1819 | 43 #include "CmplxSCHUR.h" |
| 740 | 44 #include "CmplxSVD.h" |
| 6207 | 45 #include "CmplxCHOL.h" |
| 1847 | 46 #include "f77-fcn.h" |
| 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 |
|
11651
74de76325d12
more xGELSD workspace fixes
John W. Eaton <jwe@octave.org>
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diff
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|
2510 octave_idx_type mnthr; |
|
74de76325d12
more xGELSD workspace fixes
John W. Eaton <jwe@octave.org>
parents:
11646
diff
changeset
|
2511 F77_FUNC (xilaenv, XILAENV) (6, F77_CONST_CHAR_ARG2 ("ZGELSD", 6), |
|
74de76325d12
more xGELSD workspace fixes
John W. Eaton <jwe@octave.org>
parents:
11646
diff
changeset
|
2512 F77_CONST_CHAR_ARG2 (" ", 1), |
|
74de76325d12
more xGELSD workspace fixes
John W. Eaton <jwe@octave.org>
parents:
11646
diff
changeset
|
2513 m, n, nrhs, -1, mnthr |
|
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more xGELSD workspace fixes
John W. Eaton <jwe@octave.org>
parents:
11646
diff
changeset
|
2514 F77_CHAR_ARG_LEN (6) |
|
74de76325d12
more xGELSD workspace fixes
John W. Eaton <jwe@octave.org>
parents:
11646
diff
changeset
|
2515 F77_CHAR_ARG_LEN (1)); |
|
74de76325d12
more xGELSD workspace fixes
John W. Eaton <jwe@octave.org>
parents:
11646
diff
changeset
|
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) |
| 7124 | 2523 double tmp = log2 (dminmn) / dsmlsizp1 + 1; |
| 7079 | 2524 #else |
| 7124 | 2525 double tmp = log (dminmn) / dsmlsizp1 / log (2.0) + 1; |
| 7079 | 2526 #endif |
| 2527 octave_idx_type nlvl = static_cast<int> (tmp); | |
| 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
ef95e842ba81
another small xGELSD workspace fix
John W. Eaton <jwe@octave.org>
parents:
11651
diff
changeset
|
2549 // through 3.1.1 when n >= mnthr. The obtuse formula below |
|
11651
74de76325d12
more xGELSD workspace fixes
John W. Eaton <jwe@octave.org>
parents:
11646
diff
changeset
|
2550 // should provide sufficient workspace for ZGELSD to operate |
| 11640 | 2551 // efficiently. |
|
11652
ef95e842ba81
another small xGELSD workspace fix
John W. Eaton <jwe@octave.org>
parents:
11651
diff
changeset
|
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 } | |
| 2570 | |
| 1948 | 2571 if (f77_exception_encountered) |
| 7072 | 2572 (*current_liboctave_error_handler) |
| 2573 ("unrecoverable error in zgelsd"); | |
| 1948 | 2574 else |
| 2575 { | |
| 5315 | 2576 lwork = static_cast<octave_idx_type> (std::real (work(0))); |
| 3752 | 2577 work.resize (lwork); |
| 7072 | 2578 |
| 2579 F77_XFCN (zgelsd, ZGELSD, (m, n, nrhs, tmp_data, m, pretval, | |
| 2580 maxmn, ps, rcond, rank, | |
| 2581 work.fortran_vec (), lwork, | |
| 7079 | 2582 prwork, piwork, info)); |
| 3752 | 2583 |
| 2584 if (f77_exception_encountered) | |
| 7072 | 2585 (*current_liboctave_error_handler) |
| 2586 ("unrecoverable error in zgelsd"); | |
| 7076 | 2587 else |
| 2588 { | |
| 2589 if (rank < minmn) | |
| 2590 (*current_liboctave_warning_handler) | |
| 2591 ("zgelsd: rank deficient %dx%d matrix, rank = %d, tol = %e", | |
| 2592 m, n, rank, rcond); | |
| 2593 | |
| 2594 if (s.elem (0) == 0.0) | |
| 2595 rcond = 0.0; | |
| 2596 else | |
| 2597 rcond = s.elem (minmn - 1) / s.elem (0); | |
| 7079 | 2598 |
| 2599 retval.resize (n, nrhs); | |
| 7076 | 2600 } |
| 1948 | 2601 } |
| 458 | 2602 } |
| 2603 | |
| 2604 return retval; | |
| 2605 } | |
| 2606 | |
| 2607 ComplexColumnVector | |
| 3585 | 2608 ComplexMatrix::lssolve (const ColumnVector& b) const |
| 2609 { | |
| 5275 | 2610 octave_idx_type info; |
| 2611 octave_idx_type rank; | |
| 7076 | 2612 double rcond; |
| 2613 return lssolve (ComplexColumnVector (b), info, rank, rcond); | |
| 3585 | 2614 } |
| 2615 | |
| 2616 ComplexColumnVector | |
| 5275 | 2617 ComplexMatrix::lssolve (const ColumnVector& b, octave_idx_type& info) const |
| 3585 | 2618 { |
| 5275 | 2619 octave_idx_type rank; |
| 7076 | 2620 double rcond; |
| 2621 return lssolve (ComplexColumnVector (b), info, rank, rcond); | |
| 3585 | 2622 } |
| 2623 | |
| 2624 ComplexColumnVector | |
| 7076 | 2625 ComplexMatrix::lssolve (const ColumnVector& b, octave_idx_type& info, |
| 2626 octave_idx_type& rank) const | |
| 3585 | 2627 { |
| 7076 | 2628 double rcond; |
| 2629 return lssolve (ComplexColumnVector (b), info, rank, rcond); | |
| 2630 } | |
| 2631 | |
| 2632 ComplexColumnVector | |
| 2633 ComplexMatrix::lssolve (const ColumnVector& b, octave_idx_type& info, | |
| 2634 octave_idx_type& rank, double& rcond) const | |
| 2635 { | |
| 2636 return lssolve (ComplexColumnVector (b), info, rank, rcond); | |
| 3585 | 2637 } |
| 2638 | |
| 2639 ComplexColumnVector | |
| 458 | 2640 ComplexMatrix::lssolve (const ComplexColumnVector& b) const |
| 2641 { | |
| 5275 | 2642 octave_idx_type info; |
| 2643 octave_idx_type rank; | |
| 7076 | 2644 double rcond; |
| 2645 return lssolve (b, info, rank, rcond); | |
| 458 | 2646 } |
| 2647 | |
| 2648 ComplexColumnVector | |
| 5275 | 2649 ComplexMatrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info) const |
| 458 | 2650 { |
| 5275 | 2651 octave_idx_type rank; |
| 7076 | 2652 double rcond; |
| 2653 return lssolve (b, info, rank, rcond); | |
| 458 | 2654 } |
| 2655 | |
| 2656 ComplexColumnVector | |
| 5275 | 2657 ComplexMatrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, |
| 2658 octave_idx_type& rank) const | |
| 458 | 2659 { |
| 7076 | 2660 double rcond; |
| 2661 return lssolve (b, info, rank, rcond); | |
| 2662 | |
| 2663 } | |
| 2664 | |
| 2665 ComplexColumnVector | |
| 2666 ComplexMatrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, | |
| 2667 octave_idx_type& rank, double& rcond) const | |
| 2668 { | |
| 1948 | 2669 ComplexColumnVector retval; |
| 2670 | |
| 5275 | 2671 octave_idx_type nrhs = 1; |
| 2672 | |
| 2673 octave_idx_type m = rows (); | |
| 2674 octave_idx_type n = cols (); | |
| 458 | 2675 |
| 6924 | 2676 if (m != b.length ()) |
| 1948 | 2677 (*current_liboctave_error_handler) |
| 6924 | 2678 ("matrix dimension mismatch solution of linear equations"); |
| 2679 else if (m == 0 || n == 0 || b.cols () == 0) | |
| 2680 retval = ComplexColumnVector (n, Complex (0.0, 0.0)); | |
| 1948 | 2681 else |
| 458 | 2682 { |
| 7072 | 2683 volatile octave_idx_type minmn = (m < n ? m : n); |
| 2684 octave_idx_type maxmn = m > n ? m : n; | |
| 7076 | 2685 rcond = -1.0; |
| 7072 | 2686 |
| 2687 if (m != n) | |
| 2688 { | |
| 2689 retval = ComplexColumnVector (maxmn); | |
| 2690 | |
| 2691 for (octave_idx_type i = 0; i < m; i++) | |
| 2692 retval.elem (i) = b.elem (i); | |
| 2693 } | |
| 2694 else | |
| 2695 retval = b; | |
| 2696 | |
| 1948 | 2697 ComplexMatrix atmp = *this; |
| 2698 Complex *tmp_data = atmp.fortran_vec (); | |
| 2699 | |
| 7072 | 2700 Complex *pretval = retval.fortran_vec (); |
| 2701 Array<double> s (minmn); | |
| 7071 | 2702 double *ps = s.fortran_vec (); |
| 1948 | 2703 |
| 7072 | 2704 // Ask ZGELSD what the dimension of WORK should be. |
| 5275 | 2705 octave_idx_type lwork = -1; |
| 3752 | 2706 |
| 2707 Array<Complex> work (1); | |
| 7079 | 2708 |
| 2709 // FIXME: Can SMLSIZ be other than 25? | |
| 2710 octave_idx_type smlsiz = 25; | |
| 2711 | |
| 2712 // We compute the size of rwork and iwork because ZGELSD in | |
| 2713 // older versions of LAPACK does not return them on a query | |
| 2714 // call. | |
| 7124 | 2715 double dminmn = static_cast<double> (minmn); |
| 2716 double dsmlsizp1 = static_cast<double> (smlsiz+1); | |
| 7079 | 2717 #if defined (HAVE_LOG2) |
| 7124 | 2718 double tmp = log2 (dminmn) / dsmlsizp1 + 1; |
| 7079 | 2719 #else |
| 7124 | 2720 double tmp = log (dminmn) / dsmlsizp1 / log (2.0) + 1; |
| 7079 | 2721 #endif |
| 2722 octave_idx_type nlvl = static_cast<int> (tmp); | |
| 2723 if (nlvl < 0) | |
| 2724 nlvl = 0; | |
| 2725 | |
| 2726 octave_idx_type lrwork = minmn*(10 + 2*smlsiz + 8*nlvl) | |
| 2727 + 3*smlsiz*nrhs + (smlsiz+1)*(smlsiz+1); | |
| 2728 if (lrwork < 1) | |
| 2729 lrwork = 1; | |
| 2730 Array<double> rwork (lrwork); | |
| 2731 double *prwork = rwork.fortran_vec (); | |
| 2732 | |
| 2733 octave_idx_type liwork = 3 * minmn * nlvl + 11 * minmn; | |
| 2734 if (liwork < 1) | |
| 2735 liwork = 1; | |
| 2736 Array<octave_idx_type> iwork (liwork); | |
| 2737 octave_idx_type* piwork = iwork.fortran_vec (); | |
| 7072 | 2738 |
| 2739 F77_XFCN (zgelsd, ZGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, | |
| 2740 ps, rcond, rank, work.fortran_vec (), | |
| 7079 | 2741 lwork, prwork, piwork, info)); |
| 1948 | 2742 |
| 2743 if (f77_exception_encountered) | |
| 7072 | 2744 (*current_liboctave_error_handler) |
| 2745 ("unrecoverable error in zgelsd"); | |
| 1948 | 2746 else |
| 2747 { | |
| 7072 | 2748 lwork = static_cast<octave_idx_type> (std::real (work(0))); |
| 3752 | 2749 work.resize (lwork); |
| 7072 | 2750 rwork.resize (static_cast<octave_idx_type> (rwork(0))); |
| 2751 iwork.resize (iwork(0)); | |
| 2752 | |
| 2753 F77_XFCN (zgelsd, ZGELSD, (m, n, nrhs, tmp_data, m, pretval, | |
| 2754 maxmn, ps, rcond, rank, | |
| 2755 work.fortran_vec (), lwork, | |
| 7079 | 2756 prwork, piwork, info)); |
| 3752 | 2757 |
| 2758 if (f77_exception_encountered) | |
| 7072 | 2759 (*current_liboctave_error_handler) |
| 2760 ("unrecoverable error in zgelsd"); | |
| 2761 else if (rank < minmn) | |
| 7076 | 2762 { |
| 2763 if (rank < minmn) | |
| 2764 (*current_liboctave_warning_handler) | |
| 2765 ("zgelsd: rank deficient %dx%d matrix, rank = %d, tol = %e", | |
| 2766 m, n, rank, rcond); | |
| 2767 | |
| 2768 if (s.elem (0) == 0.0) | |
| 2769 rcond = 0.0; | |
| 2770 else | |
| 2771 rcond = s.elem (minmn - 1) / s.elem (0); | |
| 7079 | 2772 |
| 2773 retval.resize (n, nrhs); | |
| 7076 | 2774 } |
| 1948 | 2775 } |
| 458 | 2776 } |
| 2777 | |
| 2778 return retval; | |
| 2779 } | |
| 2780 | |
| 1819 | 2781 // Constants for matrix exponential calculation. |
| 2782 | |
| 2783 static double padec [] = | |
| 2784 { | |
| 2785 5.0000000000000000e-1, | |
| 2786 1.1666666666666667e-1, | |
| 2787 1.6666666666666667e-2, | |
| 2788 1.6025641025641026e-3, | |
| 2789 1.0683760683760684e-4, | |
| 2790 4.8562548562548563e-6, | |
| 2791 1.3875013875013875e-7, | |
| 2792 1.9270852604185938e-9, | |
| 2793 }; | |
| 2794 | |
| 2795 ComplexMatrix | |
| 2796 ComplexMatrix::expm (void) const | |
| 2797 { | |
| 2798 ComplexMatrix retval; | |
| 2799 | |
| 2800 ComplexMatrix m = *this; | |
| 2801 | |
| 5275 | 2802 octave_idx_type nc = columns (); |
| 1819 | 2803 |
| 3130 | 2804 // Preconditioning step 1: trace normalization to reduce dynamic |
| 2805 // range of poles, but avoid making stable eigenvalues unstable. | |
| 2806 | |
| 1819 | 2807 // trace shift value |
| 2808 Complex trshift = 0.0; | |
| 2809 | |
| 5275 | 2810 for (octave_idx_type i = 0; i < nc; i++) |
| 1819 | 2811 trshift += m.elem (i, i); |
| 2812 | |
| 2813 trshift /= nc; | |
| 2814 | |
| 3130 | 2815 if (trshift.real () < 0.0) |
| 6958 | 2816 { |
| 2817 trshift = trshift.imag (); | |
| 2818 if (trshift.real () > 709.0) | |
| 2819 trshift = 709.0; | |
| 2820 } | |
| 3130 | 2821 |
| 5275 | 2822 for (octave_idx_type i = 0; i < nc; i++) |
| 1819 | 2823 m.elem (i, i) -= trshift; |
| 2824 | |
| 2825 // Preconditioning step 2: eigenvalue balancing. | |
| 3331 | 2826 // code follows development in AEPBAL |
| 2827 | |
| 2828 Complex *mp = m.fortran_vec (); | |
| 3467 | 2829 |
| 5275 | 2830 octave_idx_type info, ilo, ihi,ilos,ihis; |
| 3468 | 2831 Array<double> dpermute (nc); |
| 2832 Array<double> dscale (nc); | |
| 2833 | |
| 5775 | 2834 // FIXME -- should pass job as a parameter in expm |
| 3468 | 2835 |
| 2836 // Permute first | |
| 2837 char job = 'P'; | |
| 4552 | 2838 F77_XFCN (zgebal, ZGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
| 2839 nc, mp, nc, ilo, ihi, | |
| 2840 dpermute.fortran_vec (), info | |
| 2841 F77_CHAR_ARG_LEN (1))); | |
| 3331 | 2842 |
| 2843 if (f77_exception_encountered) | |
| 2844 { | |
| 2845 (*current_liboctave_error_handler) ("unrecoverable error in zgebal"); | |
| 2846 return retval; | |
| 2847 } | |
| 2848 | |
| 3468 | 2849 // then scale |
| 2850 job = 'S'; | |
| 4552 | 2851 F77_XFCN (zgebal, ZGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
| 2852 nc, mp, nc, ilos, ihis, | |
| 2853 dscale.fortran_vec (), info | |
| 2854 F77_CHAR_ARG_LEN (1))); | |
| 3331 | 2855 |
| 2856 if (f77_exception_encountered) | |
| 2857 { | |
| 3467 | 2858 (*current_liboctave_error_handler) ("unrecoverable error in zgebal"); |
| 3331 | 2859 return retval; |
| 2860 } | |
| 1819 | 2861 |
| 2862 // Preconditioning step 3: scaling. | |
| 2863 | |
| 2864 ColumnVector work (nc); | |
| 3130 | 2865 double inf_norm; |
| 2866 | |
| 4552 | 2867 F77_XFCN (xzlange, XZLANGE, (F77_CONST_CHAR_ARG2 ("I", 1), |
| 2868 nc, nc, m.fortran_vec (), nc, | |
| 2869 work.fortran_vec (), inf_norm | |
| 2870 F77_CHAR_ARG_LEN (1))); | |
| 3331 | 2871 |
| 2872 if (f77_exception_encountered) | |
| 2873 { | |
| 2874 (*current_liboctave_error_handler) ("unrecoverable error in zlange"); | |
| 2875 return retval; | |
| 2876 } | |
| 1819 | 2877 |
| 2800 | 2878 int sqpow = (inf_norm > 0.0 |
| 2879 ? static_cast<int> (1.0 + log (inf_norm) / log (2.0)) : 0); | |
| 1819 | 2880 |
| 2881 // Check whether we need to square at all. | |
| 2882 | |
| 2883 if (sqpow < 0) | |
| 2884 sqpow = 0; | |
| 2885 | |
| 2886 if (sqpow > 0) | |
| 2887 { | |
| 2888 double scale_factor = 1.0; | |
| 5275 | 2889 for (octave_idx_type i = 0; i < sqpow; i++) |
| 1819 | 2890 scale_factor *= 2.0; |
| 2891 | |
| 2892 m = m / scale_factor; | |
| 2893 } | |
| 2894 | |
| 2895 // npp, dpp: pade' approx polynomial matrices. | |
| 2896 | |
| 2897 ComplexMatrix npp (nc, nc, 0.0); | |
| 6958 | 2898 Complex *pnpp = npp.fortran_vec (); |
| 1819 | 2899 ComplexMatrix dpp = npp; |
| 6958 | 2900 Complex *pdpp = dpp.fortran_vec (); |
| 1819 | 2901 |
| 2902 // Now powers a^8 ... a^1. | |
| 2903 | |
| 2904 int minus_one_j = -1; | |
| 5275 | 2905 for (octave_idx_type j = 7; j >= 0; j--) |
| 1819 | 2906 { |
| 6958 | 2907 for (octave_idx_type i = 0; i < nc; i++) |
| 2908 { | |
| 2909 octave_idx_type k = i * nc + i; | |
| 7265 | 2910 pnpp[k] += padec[j]; |
| 2911 pdpp[k] += minus_one_j * padec[j]; | |
| 6958 | 2912 } |
| 7265 | 2913 |
| 6958 | 2914 npp = m * npp; |
| 7265 | 2915 pnpp = npp.fortran_vec (); |
| 2916 | |
| 6958 | 2917 dpp = m * dpp; |
| 7265 | 2918 pdpp = dpp.fortran_vec (); |
| 2919 | |
| 1819 | 2920 minus_one_j *= -1; |
| 2921 } | |
| 2922 | |
| 2923 // Zero power. | |
| 2924 | |
| 2925 dpp = -dpp; | |
| 5275 | 2926 for (octave_idx_type j = 0; j < nc; j++) |
| 1819 | 2927 { |
| 2928 npp.elem (j, j) += 1.0; | |
| 2929 dpp.elem (j, j) += 1.0; | |
| 2930 } | |
| 2931 | |
| 2932 // Compute pade approximation = inverse (dpp) * npp. | |
| 2933 | |
| 2934 retval = dpp.solve (npp); | |
| 2935 | |
| 2936 // Reverse preconditioning step 3: repeated squaring. | |
| 2937 | |
| 2938 while (sqpow) | |
| 2939 { | |
| 2940 retval = retval * retval; | |
| 2941 sqpow--; | |
| 2942 } | |
| 2943 | |
| 2944 // Reverse preconditioning step 2: inverse balancing. | |
| 3467 | 2945 // Done in two steps: inverse scaling, then inverse permutation |
| 2946 | |
| 2947 // inverse scaling (diagonal transformation) | |
| 5275 | 2948 for (octave_idx_type i = 0; i < nc; i++) |
| 2949 for (octave_idx_type j = 0; j < nc; j++) | |
| 3468 | 2950 retval(i,j) *= dscale(i) / dscale(j); |
| 3467 | 2951 |
| 4153 | 2952 OCTAVE_QUIT; |
| 2953 | |
| 3467 | 2954 // construct balancing permutation vector |
| 6867 | 2955 Array<octave_idx_type> iperm (nc); |
| 5275 | 2956 for (octave_idx_type i = 0; i < nc; i++) |
| 4593 | 2957 iperm(i) = i; // initialize to identity permutation |
| 3467 | 2958 |
| 2959 // leading permutations in forward order | |
| 5275 | 2960 for (octave_idx_type i = 0; i < (ilo-1); i++) |
| 3468 | 2961 { |
| 6867 | 2962 octave_idx_type swapidx = static_cast<octave_idx_type> (dpermute(i)) - 1; |
| 5275 | 2963 octave_idx_type tmp = iperm(i); |
| 4593 | 2964 iperm(i) = iperm(swapidx); |
| 2965 iperm(swapidx) = tmp; | |
| 3468 | 2966 } |
| 3467 | 2967 |
| 2968 // trailing permutations must be done in reverse order | |
| 5275 | 2969 for (octave_idx_type i = nc - 1; i >= ihi; i--) |
| 3468 | 2970 { |
| 6867 | 2971 octave_idx_type swapidx = static_cast<octave_idx_type> (dpermute(i)) - 1; |
| 5275 | 2972 octave_idx_type tmp = iperm(i); |
| 4593 | 2973 iperm(i) = iperm(swapidx); |
| 2974 iperm(swapidx) = tmp; | |
| 3468 | 2975 } |
| 3467 | 2976 |
| 2977 // construct inverse balancing permutation vector | |
| 6867 | 2978 Array<octave_idx_type> invpvec (nc); |
| 5275 | 2979 for (octave_idx_type i = 0; i < nc; i++) |
| 4593 | 2980 invpvec(iperm(i)) = i; // Thanks to R. A. Lippert for this method |
| 3467 | 2981 |
| 4153 | 2982 OCTAVE_QUIT; |
| 2983 | |
| 3467 | 2984 ComplexMatrix tmpMat = retval; |
| 5275 | 2985 for (octave_idx_type i = 0; i < nc; i++) |
| 2986 for (octave_idx_type j = 0; j < nc; j++) | |
| 3468 | 2987 retval(i,j) = tmpMat(invpvec(i),invpvec(j)); |
| 1819 | 2988 |
| 2989 // Reverse preconditioning step 1: fix trace normalization. | |
| 2990 | |
| 3130 | 2991 return exp (trshift) * retval; |
| 1819 | 2992 } |
| 2993 | |
| 1205 | 2994 // column vector by row vector -> matrix operations |
| 2995 | |
| 2996 ComplexMatrix | |
| 2997 operator * (const ColumnVector& v, const ComplexRowVector& a) | |
| 2998 { | |
| 2999 ComplexColumnVector tmp (v); | |
| 3000 return tmp * a; | |
| 3001 } | |
| 3002 | |
| 3003 ComplexMatrix | |
| 3004 operator * (const ComplexColumnVector& a, const RowVector& b) | |
| 3005 { | |
| 3006 ComplexRowVector tmp (b); | |
| 3007 return a * tmp; | |
| 3008 } | |
| 3009 | |
| 3010 ComplexMatrix | |
| 3011 operator * (const ComplexColumnVector& v, const ComplexRowVector& a) | |
| 3012 { | |
| 1948 | 3013 ComplexMatrix retval; |
| 3014 | |
| 5275 | 3015 octave_idx_type len = v.length (); |
| 3233 | 3016 |
| 3017 if (len != 0) | |
| 1205 | 3018 { |
| 5275 | 3019 octave_idx_type a_len = a.length (); |
| 3233 | 3020 |
| 3021 retval.resize (len, a_len); | |
| 3022 Complex *c = retval.fortran_vec (); | |
| 3023 | |
| 4552 | 3024 F77_XFCN (zgemm, ZGEMM, (F77_CONST_CHAR_ARG2 ("N", 1), |
| 3025 F77_CONST_CHAR_ARG2 ("N", 1), | |
| 3026 len, a_len, 1, 1.0, v.data (), len, | |
| 3027 a.data (), 1, 0.0, c, len | |
| 3028 F77_CHAR_ARG_LEN (1) | |
| 3029 F77_CHAR_ARG_LEN (1))); | |
| 3233 | 3030 |
| 3031 if (f77_exception_encountered) | |
| 3032 (*current_liboctave_error_handler) | |
| 3033 ("unrecoverable error in zgemm"); | |
| 1205 | 3034 } |
| 3035 | |
| 1948 | 3036 return retval; |
| 1205 | 3037 } |
| 3038 | |
| 458 | 3039 // matrix by diagonal matrix -> matrix operations |
| 3040 | |
| 3041 ComplexMatrix& | |
| 3042 ComplexMatrix::operator += (const DiagMatrix& a) | |
| 3043 { | |
| 5275 | 3044 octave_idx_type nr = rows (); |
| 3045 octave_idx_type nc = cols (); | |
| 3046 | |
| 3047 octave_idx_type a_nr = rows (); | |
| 3048 octave_idx_type a_nc = cols (); | |
| 2384 | 3049 |
| 3050 if (nr != a_nr || nc != a_nc) | |
| 458 | 3051 { |
| 2384 | 3052 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
| 889 | 3053 return *this; |
| 458 | 3054 } |
| 3055 | |
| 5275 | 3056 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 3057 elem (i, i) += a.elem (i, i); |
| 3058 | |
| 3059 return *this; | |
| 3060 } | |
| 3061 | |
| 3062 ComplexMatrix& | |
| 3063 ComplexMatrix::operator -= (const DiagMatrix& a) | |
| 3064 { | |
| 5275 | 3065 octave_idx_type nr = rows (); |
| 3066 octave_idx_type nc = cols (); | |
| 3067 | |
| 3068 octave_idx_type a_nr = rows (); | |
| 3069 octave_idx_type a_nc = cols (); | |
| 2384 | 3070 |
| 3071 if (nr != a_nr || nc != a_nc) | |
| 458 | 3072 { |
| 2384 | 3073 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
| 889 | 3074 return *this; |
| 458 | 3075 } |
| 3076 | |
| 5275 | 3077 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 3078 elem (i, i) -= a.elem (i, i); |
| 3079 | |
| 3080 return *this; | |
| 3081 } | |
| 3082 | |
| 3083 ComplexMatrix& | |
| 3084 ComplexMatrix::operator += (const ComplexDiagMatrix& a) | |
| 3085 { | |
| 5275 | 3086 octave_idx_type nr = rows (); |
| 3087 octave_idx_type nc = cols (); | |
| 3088 | |
| 3089 octave_idx_type a_nr = rows (); | |
| 3090 octave_idx_type a_nc = cols (); | |
| 2384 | 3091 |
| 3092 if (nr != a_nr || nc != a_nc) | |
| 458 | 3093 { |
| 2384 | 3094 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
| 889 | 3095 return *this; |
| 458 | 3096 } |
| 3097 | |
| 5275 | 3098 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 3099 elem (i, i) += a.elem (i, i); |
| 3100 | |
| 3101 return *this; | |
| 3102 } | |
| 3103 | |
| 3104 ComplexMatrix& | |
| 3105 ComplexMatrix::operator -= (const ComplexDiagMatrix& a) | |
| 3106 { | |
| 5275 | 3107 octave_idx_type nr = rows (); |
| 3108 octave_idx_type nc = cols (); | |
| 3109 | |
| 3110 octave_idx_type a_nr = rows (); | |
| 3111 octave_idx_type a_nc = cols (); | |
| 2384 | 3112 |
| 3113 if (nr != a_nr || nc != a_nc) | |
| 458 | 3114 { |
| 2384 | 3115 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
| 889 | 3116 return *this; |
| 458 | 3117 } |
| 3118 | |
| 5275 | 3119 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 3120 elem (i, i) -= a.elem (i, i); |
| 3121 | |
| 3122 return *this; | |
| 3123 } | |
| 3124 | |
| 3125 // matrix by matrix -> matrix operations | |
| 3126 | |
| 3127 ComplexMatrix& | |
| 3128 ComplexMatrix::operator += (const Matrix& a) | |
| 3129 { | |
| 5275 | 3130 octave_idx_type nr = rows (); |
| 3131 octave_idx_type nc = cols (); | |
| 3132 | |
| 3133 octave_idx_type a_nr = a.rows (); | |
| 3134 octave_idx_type a_nc = a.cols (); | |
| 2384 | 3135 |
| 3136 if (nr != a_nr || nc != a_nc) | |
| 458 | 3137 { |
| 2384 | 3138 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
| 458 | 3139 return *this; |
| 3140 } | |
| 3141 | |
| 3142 if (nr == 0 || nc == 0) | |
| 3143 return *this; | |
| 3144 | |
| 3145 Complex *d = fortran_vec (); // Ensures only one reference to my privates! | |
| 3146 | |
| 3769 | 3147 mx_inline_add2 (d, a.data (), length ()); |
| 458 | 3148 return *this; |
| 3149 } | |
| 3150 | |
| 3151 ComplexMatrix& | |
| 3152 ComplexMatrix::operator -= (const Matrix& a) | |
| 3153 { | |
| 5275 | 3154 octave_idx_type nr = rows (); |
| 3155 octave_idx_type nc = cols (); | |
| 3156 | |
| 3157 octave_idx_type a_nr = a.rows (); | |
| 3158 octave_idx_type a_nc = a.cols (); | |
| 2384 | 3159 |
| 3160 if (nr != a_nr || nc != a_nc) | |
| 458 | 3161 { |
| 2384 | 3162 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
| 458 | 3163 return *this; |
| 3164 } | |
| 3165 | |
| 3166 if (nr == 0 || nc == 0) | |
| 3167 return *this; | |
| 3168 | |
| 3169 Complex *d = fortran_vec (); // Ensures only one reference to my privates! | |
| 3170 | |
| 3769 | 3171 mx_inline_subtract2 (d, a.data (), length ()); |
| 458 | 3172 return *this; |
| 3173 } | |
| 3174 | |
| 3175 // unary operations | |
| 3176 | |
| 2964 | 3177 boolMatrix |
| 458 | 3178 ComplexMatrix::operator ! (void) const |
| 3179 { | |
| 5275 | 3180 octave_idx_type nr = rows (); |
| 3181 octave_idx_type nc = cols (); | |
| 2964 | 3182 |
| 3183 boolMatrix b (nr, nc); | |
| 3184 | |
| 5275 | 3185 for (octave_idx_type j = 0; j < nc; j++) |
| 3186 for (octave_idx_type i = 0; i < nr; i++) | |
| 5139 | 3187 b.elem (i, j) = elem (i, j) == 0.0; |
| 2964 | 3188 |
| 3189 return b; | |
| 458 | 3190 } |
| 3191 | |
| 3192 // other operations | |
| 3193 | |
| 3194 ComplexMatrix | |
| 2676 | 3195 ComplexMatrix::map (c_c_Mapper f) const |
| 458 | 3196 { |
| 2676 | 3197 ComplexMatrix b (*this); |
| 3198 return b.apply (f); | |
| 458 | 3199 } |
| 3200 | |
| 2676 | 3201 Matrix |
| 3202 ComplexMatrix::map (d_c_Mapper f) const | |
| 458 | 3203 { |
| 5275 | 3204 octave_idx_type nr = rows (); |
| 3205 octave_idx_type nc = cols (); | |
| 3248 | 3206 |
| 3207 Matrix retval (nr, nc); | |
| 3208 | |
| 5275 | 3209 for (octave_idx_type j = 0; j < nc; j++) |
| 3210 for (octave_idx_type i = 0; i < nr; i++) | |
| 3248 | 3211 retval(i,j) = f (elem(i,j)); |
| 3212 | |
| 3213 return retval; | |
| 3214 } | |
| 3215 | |
| 3216 boolMatrix | |
| 3217 ComplexMatrix::map (b_c_Mapper f) const | |
| 3218 { | |
| 5275 | 3219 octave_idx_type nr = rows (); |
| 3220 octave_idx_type nc = cols (); | |
| 3248 | 3221 |
| 3222 boolMatrix retval (nr, nc); | |
| 3223 | |
| 5275 | 3224 for (octave_idx_type j = 0; j < nc; j++) |
| 3225 for (octave_idx_type i = 0; i < nr; i++) | |
| 3248 | 3226 retval(i,j) = f (elem(i,j)); |
| 2676 | 3227 |
| 3228 return retval; | |
| 3229 } | |
| 3230 | |
| 3231 ComplexMatrix& | |
| 3232 ComplexMatrix::apply (c_c_Mapper f) | |
| 3233 { | |
| 3234 Complex *d = fortran_vec (); // Ensures only one reference to my privates! | |
| 3235 | |
| 5275 | 3236 for (octave_idx_type i = 0; i < length (); i++) |
| 2676 | 3237 d[i] = f (d[i]); |
| 3238 | |
| 3239 return *this; | |
| 458 | 3240 } |
| 3241 | |
| 2384 | 3242 bool |
| 3243 ComplexMatrix::any_element_is_inf_or_nan (void) const | |
| 3244 { | |
| 5275 | 3245 octave_idx_type nr = rows (); |
| 3246 octave_idx_type nc = cols (); | |
| 3247 | |
| 3248 for (octave_idx_type j = 0; j < nc; j++) | |
| 3249 for (octave_idx_type i = 0; i < nr; i++) | |
| 2384 | 3250 { |
| 3251 Complex val = elem (i, j); | |
| 3252 if (xisinf (val) || xisnan (val)) | |
| 3253 return true; | |
| 3254 } | |
| 3255 | |
| 3256 return false; | |
| 3257 } | |
| 3258 | |
| 2408 | 3259 // Return true if no elements have imaginary components. |
| 3260 | |
| 3261 bool | |
| 3262 ComplexMatrix::all_elements_are_real (void) const | |
| 3263 { | |
| 5275 | 3264 octave_idx_type nr = rows (); |
| 3265 octave_idx_type nc = cols (); | |
| 3266 | |
| 3267 for (octave_idx_type j = 0; j < nc; j++) | |
| 4349 | 3268 { |
| 5275 | 3269 for (octave_idx_type i = 0; i < nr; i++) |
| 4349 | 3270 { |
| 5315 | 3271 double ip = std::imag (elem (i, j)); |
| 4349 | 3272 |
| 3273 if (ip != 0.0 || lo_ieee_signbit (ip)) | |
| 3274 return false; | |
| 3275 } | |
| 3276 } | |
| 2408 | 3277 |
| 3278 return true; | |
| 3279 } | |
| 3280 | |
| 1968 | 3281 // Return nonzero if any element of CM has a non-integer real or |
| 3282 // imaginary part. Also extract the largest and smallest (real or | |
| 3283 // imaginary) values and return them in MAX_VAL and MIN_VAL. | |
| 3284 | |
| 2384 | 3285 bool |
| 1968 | 3286 ComplexMatrix::all_integers (double& max_val, double& min_val) const |
| 3287 { | |
| 5275 | 3288 octave_idx_type nr = rows (); |
| 3289 octave_idx_type nc = cols (); | |
| 1968 | 3290 |
| 3291 if (nr > 0 && nc > 0) | |
| 3292 { | |
| 3293 Complex val = elem (0, 0); | |
| 3294 | |
| 5315 | 3295 double r_val = std::real (val); |
| 3296 double i_val = std::imag (val); | |
| 1968 | 3297 |
| 3298 max_val = r_val; | |
| 3299 min_val = r_val; | |
| 3300 | |
| 3301 if (i_val > max_val) | |
| 3302 max_val = i_val; | |
| 3303 | |
| 3304 if (i_val < max_val) | |
| 3305 min_val = i_val; | |
| 3306 } | |
| 3307 else | |
| 2384 | 3308 return false; |
| 1968 | 3309 |
| 5275 | 3310 for (octave_idx_type j = 0; j < nc; j++) |
| 3311 for (octave_idx_type i = 0; i < nr; i++) | |
| 1968 | 3312 { |
| 3313 Complex val = elem (i, j); | |
| 3314 | |
| 5315 | 3315 double r_val = std::real (val); |
| 3316 double i_val = std::imag (val); | |
| 1968 | 3317 |
| 3318 if (r_val > max_val) | |
| 3319 max_val = r_val; | |
| 3320 | |
| 3321 if (i_val > max_val) | |
| 3322 max_val = i_val; | |
| 3323 | |
| 3324 if (r_val < min_val) | |
| 3325 min_val = r_val; | |
| 3326 | |
| 3327 if (i_val < min_val) | |
| 3328 min_val = i_val; | |
| 3329 | |
| 3330 if (D_NINT (r_val) != r_val || D_NINT (i_val) != i_val) | |
| 2384 | 3331 return false; |
| 1968 | 3332 } |
| 2384 | 3333 |
| 3334 return true; | |
| 1968 | 3335 } |
| 3336 | |
| 2384 | 3337 bool |
| 1968 | 3338 ComplexMatrix::too_large_for_float (void) const |
| 3339 { | |
| 5275 | 3340 octave_idx_type nr = rows (); |
| 3341 octave_idx_type nc = cols (); | |
| 3342 | |
| 3343 for (octave_idx_type j = 0; j < nc; j++) | |
| 3344 for (octave_idx_type i = 0; i < nr; i++) | |
| 1968 | 3345 { |
| 3346 Complex val = elem (i, j); | |
| 3347 | |
| 5315 | 3348 double r_val = std::real (val); |
| 3349 double i_val = std::imag (val); | |
| 1968 | 3350 |
| 5389 | 3351 if ((! (xisnan (r_val) || xisinf (r_val)) |
| 5387 | 3352 && fabs (r_val) > FLT_MAX) |
| 5389 | 3353 || (! (xisnan (i_val) || xisinf (i_val)) |
| 5387 | 3354 && fabs (i_val) > FLT_MAX)) |
| 2384 | 3355 return true; |
| 1968 | 3356 } |
| 3357 | |
| 2384 | 3358 return false; |
| 1968 | 3359 } |
| 3360 | |
| 5775 | 3361 // FIXME Do these really belong here? Maybe they should be |
| 4015 | 3362 // in a base class? |
| 3363 | |
| 2832 | 3364 boolMatrix |
| 4015 | 3365 ComplexMatrix::all (int dim) const |
| 458 | 3366 { |
| 4015 | 3367 MX_ALL_OP (dim); |
| 458 | 3368 } |
| 3369 | |
| 2832 | 3370 boolMatrix |
| 4015 | 3371 ComplexMatrix::any (int dim) const |
| 458 | 3372 { |
| 4015 | 3373 MX_ANY_OP (dim); |
| 458 | 3374 } |
| 3375 | |
| 3376 ComplexMatrix | |
| 3723 | 3377 ComplexMatrix::cumprod (int dim) const |
| 458 | 3378 { |
| 4015 | 3379 MX_CUMULATIVE_OP (ComplexMatrix, Complex, *=); |
| 458 | 3380 } |
| 3381 | |
| 3382 ComplexMatrix | |
| 3723 | 3383 ComplexMatrix::cumsum (int dim) const |
| 458 | 3384 { |
| 4015 | 3385 MX_CUMULATIVE_OP (ComplexMatrix, Complex, +=); |
| 458 | 3386 } |
| 3387 | |
| 3388 ComplexMatrix | |
| 3723 | 3389 ComplexMatrix::prod (int dim) const |
| 458 | 3390 { |
| 3864 | 3391 MX_REDUCTION_OP (ComplexMatrix, *=, 1.0, 1.0); |
| 458 | 3392 } |
| 3393 | |
| 3394 ComplexMatrix | |
| 3723 | 3395 ComplexMatrix::sum (int dim) const |
| 458 | 3396 { |
| 3864 | 3397 MX_REDUCTION_OP (ComplexMatrix, +=, 0.0, 0.0); |
| 458 | 3398 } |
| 3399 | |
| 3400 ComplexMatrix | |
| 3723 | 3401 ComplexMatrix::sumsq (int dim) const |
| 458 | 3402 { |
| 3864 | 3403 #define ROW_EXPR \ |
| 3404 Complex d = elem (i, j); \ | |
| 3405 retval.elem (i, 0) += d * conj (d) | |
| 3406 | |
| 3407 #define COL_EXPR \ | |
| 3408 Complex d = elem (i, j); \ | |
| 3409 retval.elem (0, j) += d * conj (d) | |
| 3410 | |
| 3411 MX_BASE_REDUCTION_OP (ComplexMatrix, ROW_EXPR, COL_EXPR, 0.0, 0.0); | |
| 3412 | |
| 3413 #undef ROW_EXPR | |
| 3414 #undef COL_EXPR | |
| 458 | 3415 } |
| 3416 | |
| 4329 | 3417 Matrix ComplexMatrix::abs (void) const |
| 3418 { | |
| 5275 | 3419 octave_idx_type nr = rows (); |
| 3420 octave_idx_type nc = cols (); | |
| 4329 | 3421 |
| 3422 Matrix retval (nr, nc); | |
| 3423 | |
| 5275 | 3424 for (octave_idx_type j = 0; j < nc; j++) |
| 3425 for (octave_idx_type i = 0; i < nr; i++) | |
| 5315 | 3426 retval (i, j) = std::abs (elem (i, j)); |
| 4329 | 3427 |
| 3428 return retval; | |
| 3429 } | |
| 3430 | |
| 458 | 3431 ComplexColumnVector |
| 3432 ComplexMatrix::diag (void) const | |
| 3433 { | |
| 3434 return diag (0); | |
| 3435 } | |
| 3436 | |
| 3437 ComplexColumnVector | |
| 5275 | 3438 ComplexMatrix::diag (octave_idx_type k) const |
| 458 | 3439 { |
| 5275 | 3440 octave_idx_type nnr = rows (); |
| 3441 octave_idx_type nnc = cols (); | |
| 458 | 3442 if (k > 0) |
| 3443 nnc -= k; | |
| 3444 else if (k < 0) | |
| 3445 nnr += k; | |
| 3446 | |
| 3447 ComplexColumnVector d; | |
| 3448 | |
| 3449 if (nnr > 0 && nnc > 0) | |
| 3450 { | |
| 5275 | 3451 octave_idx_type ndiag = (nnr < nnc) ? nnr : nnc; |
| 458 | 3452 |
| 3453 d.resize (ndiag); | |
| 3454 | |
| 3455 if (k > 0) | |
| 3456 { | |
| 5275 | 3457 for (octave_idx_type i = 0; i < ndiag; i++) |
| 458 | 3458 d.elem (i) = elem (i, i+k); |
| 3459 } | |
| 4509 | 3460 else if (k < 0) |
| 458 | 3461 { |
| 5275 | 3462 for (octave_idx_type i = 0; i < ndiag; i++) |
| 458 | 3463 d.elem (i) = elem (i-k, i); |
| 3464 } | |
| 3465 else | |
| 3466 { | |
| 5275 | 3467 for (octave_idx_type i = 0; i < ndiag; i++) |
| 458 | 3468 d.elem (i) = elem (i, i); |
| 3469 } | |
| 3470 } | |
| 3471 else | |
| 4513 | 3472 (*current_liboctave_error_handler) |
| 3473 ("diag: requested diagonal out of range"); | |
| 458 | 3474 |
| 3475 return d; | |
| 3476 } | |
| 3477 | |
| 2354 | 3478 bool |
| 5275 | 3479 ComplexMatrix::row_is_real_only (octave_idx_type i) const |
| 2354 | 3480 { |
| 3481 bool retval = true; | |
| 3482 | |
| 5275 | 3483 octave_idx_type nc = columns (); |
| 3484 | |
| 3485 for (octave_idx_type j = 0; j < nc; j++) | |
| 2354 | 3486 { |
| 5315 | 3487 if (std::imag (elem (i, j)) != 0.0) |
| 2354 | 3488 { |
| 3489 retval = false; | |
| 3490 break; | |
| 3491 } | |
| 3492 } | |
| 3493 | |
| 3494 return retval; | |
| 3495 } | |
| 3496 | |
| 3497 bool | |
| 5275 | 3498 ComplexMatrix::column_is_real_only (octave_idx_type j) const |
| 2354 | 3499 { |
| 3500 bool retval = true; | |
| 3501 | |
| 5275 | 3502 octave_idx_type nr = rows (); |
| 3503 | |
| 3504 for (octave_idx_type i = 0; i < nr; i++) | |
| 2354 | 3505 { |
| 5315 | 3506 if (std::imag (elem (i, j)) != 0.0) |
| 2354 | 3507 { |
| 3508 retval = false; | |
| 3509 break; | |
| 3510 } | |
| 3511 } | |
| 3512 | |
| 3513 return retval; | |
| 3514 } | |
| 891 | 3515 |
| 458 | 3516 ComplexColumnVector |
| 3517 ComplexMatrix::row_min (void) const | |
| 3518 { | |
| 5275 | 3519 Array<octave_idx_type> dummy_idx; |
| 4587 | 3520 return row_min (dummy_idx); |
| 458 | 3521 } |
| 3522 | |
| 3523 ComplexColumnVector | |
| 5275 | 3524 ComplexMatrix::row_min (Array<octave_idx_type>& idx_arg) const |
| 458 | 3525 { |
| 3526 ComplexColumnVector result; | |
| 3527 | |
| 5275 | 3528 octave_idx_type nr = rows (); |
| 3529 octave_idx_type nc = cols (); | |
| 458 | 3530 |
| 3531 if (nr > 0 && nc > 0) | |
| 3532 { | |
| 3533 result.resize (nr); | |
| 4587 | 3534 idx_arg.resize (nr); |
| 458 | 3535 |
| 5275 | 3536 for (octave_idx_type i = 0; i < nr; i++) |
| 458 | 3537 { |
| 2354 | 3538 bool real_only = row_is_real_only (i); |
| 3539 | |
| 5275 | 3540 octave_idx_type idx_j; |
| 4469 | 3541 |
| 3542 Complex tmp_min; | |
| 3543 | |
| 3544 double abs_min = octave_NaN; | |
| 3545 | |
| 3546 for (idx_j = 0; idx_j < nc; idx_j++) | |
| 3547 { | |
| 3548 tmp_min = elem (i, idx_j); | |
| 3549 | |
| 5389 | 3550 if (! xisnan (tmp_min)) |
| 4469 | 3551 { |
| 5315 | 3552 abs_min = real_only ? std::real (tmp_min) : std::abs (tmp_min); |
| 4469 | 3553 break; |
| 3554 } | |
| 3555 } | |
| 3556 | |
| 5275 | 3557 for (octave_idx_type j = idx_j+1; j < nc; j++) |
| 4469 | 3558 { |
| 3559 Complex tmp = elem (i, j); | |
| 3560 | |
| 5389 | 3561 if (xisnan (tmp)) |
| 4469 | 3562 continue; |
| 3563 | |
| 5315 | 3564 double abs_tmp = real_only ? std::real (tmp) : std::abs (tmp); |
| 4469 | 3565 |
| 3566 if (abs_tmp < abs_min) | |
| 3567 { | |
| 3568 idx_j = j; | |
| 3569 tmp_min = tmp; | |
| 3570 abs_min = abs_tmp; | |
| 3571 } | |
| 3572 } | |
| 3573 | |
| 5389 | 3574 if (xisnan (tmp_min)) |
| 4469 | 3575 { |
| 3576 result.elem (i) = Complex_NaN_result; | |
| 4587 | 3577 idx_arg.elem (i) = 0; |
| 4469 | 3578 } |
| 891 | 3579 else |
| 3580 { | |
| 4469 | 3581 result.elem (i) = tmp_min; |
| 4587 | 3582 idx_arg.elem (i) = idx_j; |
| 891 | 3583 } |
| 458 | 3584 } |
| 3585 } | |
| 3586 | |
| 3587 return result; | |
| 3588 } | |
| 3589 | |
| 3590 ComplexColumnVector | |
| 3591 ComplexMatrix::row_max (void) const | |
| 3592 { | |
| 5275 | 3593 Array<octave_idx_type> dummy_idx; |
| 4587 | 3594 return row_max (dummy_idx); |
| 458 | 3595 } |
| 3596 | |
| 3597 ComplexColumnVector | |
| 5275 | 3598 ComplexMatrix::row_max (Array<octave_idx_type>& idx_arg) const |
| 458 | 3599 { |
| 3600 ComplexColumnVector result; | |
| 3601 | |
| 5275 | 3602 octave_idx_type nr = rows (); |
| 3603 octave_idx_type nc = cols (); | |
| 458 | 3604 |
| 3605 if (nr > 0 && nc > 0) | |
| 3606 { | |
| 3607 result.resize (nr); | |
| 4587 | 3608 idx_arg.resize (nr); |
| 458 | 3609 |
| 5275 | 3610 for (octave_idx_type i = 0; i < nr; i++) |
| 458 | 3611 { |
| 2354 | 3612 bool real_only = row_is_real_only (i); |
| 3613 | |
| 5275 | 3614 octave_idx_type idx_j; |
| 4469 | 3615 |
| 3616 Complex tmp_max; | |
| 3617 | |
| 3618 double abs_max = octave_NaN; | |
| 3619 | |
| 3620 for (idx_j = 0; idx_j < nc; idx_j++) | |
| 3621 { | |
| 3622 tmp_max = elem (i, idx_j); | |
| 3623 | |
| 5389 | 3624 if (! xisnan (tmp_max)) |
| 4469 | 3625 { |
| 5315 | 3626 abs_max = real_only ? std::real (tmp_max) : std::abs (tmp_max); |
| 4469 | 3627 break; |
| 3628 } | |
| 3629 } | |
| 3630 | |
| 5275 | 3631 for (octave_idx_type j = idx_j+1; j < nc; j++) |
| 4469 | 3632 { |
| 3633 Complex tmp = elem (i, j); | |
| 3634 | |
| 5389 | 3635 if (xisnan (tmp)) |
| 4469 | 3636 continue; |
| 3637 | |
| 5315 | 3638 double abs_tmp = real_only ? std::real (tmp) : std::abs (tmp); |
| 4469 | 3639 |
| 3640 if (abs_tmp > abs_max) | |
| 3641 { | |
| 3642 idx_j = j; | |
| 3643 tmp_max = tmp; | |
| 3644 abs_max = abs_tmp; | |
| 3645 } | |
| 3646 } | |
| 3647 | |
| 5389 | 3648 if (xisnan (tmp_max)) |
| 4469 | 3649 { |
| 3650 result.elem (i) = Complex_NaN_result; | |
| 4587 | 3651 idx_arg.elem (i) = 0; |
| 4469 | 3652 } |
| 891 | 3653 else |
| 3654 { | |
| 4469 | 3655 result.elem (i) = tmp_max; |
| 4587 | 3656 idx_arg.elem (i) = idx_j; |
| 891 | 3657 } |
| 458 | 3658 } |
| 3659 } | |
| 3660 | |
| 3661 return result; | |
| 3662 } | |
| 3663 | |
| 3664 ComplexRowVector | |
| 3665 ComplexMatrix::column_min (void) const | |
| 3666 { | |
| 5275 | 3667 Array<octave_idx_type> dummy_idx; |
| 4587 | 3668 return column_min (dummy_idx); |
| 458 | 3669 } |
| 3670 | |
| 3671 ComplexRowVector | |
| 5275 | 3672 ComplexMatrix::column_min (Array<octave_idx_type>& idx_arg) const |
| 458 | 3673 { |
| 3674 ComplexRowVector result; | |
| 3675 | |
| 5275 | 3676 octave_idx_type nr = rows (); |
| 3677 octave_idx_type nc = cols (); | |
| 458 | 3678 |
| 3679 if (nr > 0 && nc > 0) | |
| 3680 { | |
| 3681 result.resize (nc); | |
| 4587 | 3682 idx_arg.resize (nc); |
| 458 | 3683 |
| 5275 | 3684 for (octave_idx_type j = 0; j < nc; j++) |
| 458 | 3685 { |
| 2354 | 3686 bool real_only = column_is_real_only (j); |
| 3687 | |
| 5275 | 3688 octave_idx_type idx_i; |
| 4469 | 3689 |
| 3690 Complex tmp_min; | |
| 3691 | |
| 3692 double abs_min = octave_NaN; | |
| 3693 | |
| 3694 for (idx_i = 0; idx_i < nr; idx_i++) | |
| 3695 { | |
| 3696 tmp_min = elem (idx_i, j); | |
| 3697 | |
| 5389 | 3698 if (! xisnan (tmp_min)) |
| 4469 | 3699 { |
| 5315 | 3700 abs_min = real_only ? std::real (tmp_min) : std::abs (tmp_min); |
| 4469 | 3701 break; |
| 3702 } | |
| 3703 } | |
| 3704 | |
| 5275 | 3705 for (octave_idx_type i = idx_i+1; i < nr; i++) |
| 4469 | 3706 { |
| 3707 Complex tmp = elem (i, j); | |
| 3708 | |
| 5389 | 3709 if (xisnan (tmp)) |
| 4469 | 3710 continue; |
| 3711 | |
| 5315 | 3712 double abs_tmp = real_only ? std::real (tmp) : std::abs (tmp); |
| 4469 | 3713 |
| 3714 if (abs_tmp < abs_min) | |
| 3715 { | |
| 3716 idx_i = i; | |
| 3717 tmp_min = tmp; | |
| 3718 abs_min = abs_tmp; | |
| 3719 } | |
| 3720 } | |
| 3721 | |
| 5389 | 3722 if (xisnan (tmp_min)) |
| 4469 | 3723 { |
| 3724 result.elem (j) = Complex_NaN_result; | |
| 4587 | 3725 idx_arg.elem (j) = 0; |
| 4469 | 3726 } |
| 891 | 3727 else |
| 3728 { | |
| 4469 | 3729 result.elem (j) = tmp_min; |
| 4587 | 3730 idx_arg.elem (j) = idx_i; |
| 891 | 3731 } |
| 458 | 3732 } |
| 3733 } | |
| 3734 | |
| 3735 return result; | |
| 3736 } | |
| 3737 | |
| 3738 ComplexRowVector | |
| 3739 ComplexMatrix::column_max (void) const | |
| 3740 { | |
| 5275 | 3741 Array<octave_idx_type> dummy_idx; |
| 4587 | 3742 return column_max (dummy_idx); |
| 458 | 3743 } |
| 3744 | |
| 3745 ComplexRowVector | |
| 5275 | 3746 ComplexMatrix::column_max (Array<octave_idx_type>& idx_arg) const |
| 458 | 3747 { |
| 3748 ComplexRowVector result; | |
| 3749 | |
| 5275 | 3750 octave_idx_type nr = rows (); |
| 3751 octave_idx_type nc = cols (); | |
| 458 | 3752 |
| 3753 if (nr > 0 && nc > 0) | |
| 3754 { | |
| 3755 result.resize (nc); | |
| 4587 | 3756 idx_arg.resize (nc); |
| 458 | 3757 |
| 5275 | 3758 for (octave_idx_type j = 0; j < nc; j++) |
| 458 | 3759 { |
| 2354 | 3760 bool real_only = column_is_real_only (j); |
| 3761 | |
| 5275 | 3762 octave_idx_type idx_i; |
| 4469 | 3763 |
| 3764 Complex tmp_max; | |
| 3765 | |
| 3766 double abs_max = octave_NaN; | |
| 3767 | |
| 3768 for (idx_i = 0; idx_i < nr; idx_i++) | |
| 3769 { | |
| 3770 tmp_max = elem (idx_i, j); | |
| 3771 | |
| 5389 | 3772 if (! xisnan (tmp_max)) |
| 4469 | 3773 { |
| 5315 | 3774 abs_max = real_only ? std::real (tmp_max) : std::abs (tmp_max); |
| 4469 | 3775 break; |
| 3776 } | |
| 3777 } | |
| 3778 | |
| 5275 | 3779 for (octave_idx_type i = idx_i+1; i < nr; i++) |
| 4469 | 3780 { |
| 3781 Complex tmp = elem (i, j); | |
| 3782 | |
| 5389 | 3783 if (xisnan (tmp)) |
| 4469 | 3784 continue; |
| 3785 | |
| 5315 | 3786 double abs_tmp = real_only ? std::real (tmp) : std::abs (tmp); |
| 4469 | 3787 |
| 3788 if (abs_tmp > abs_max) | |
| 3789 { | |
| 3790 idx_i = i; | |
| 3791 tmp_max = tmp; | |
| 3792 abs_max = abs_tmp; | |
| 3793 } | |
| 3794 } | |
| 3795 | |
| 5389 | 3796 if (xisnan (tmp_max)) |
| 4469 | 3797 { |
| 3798 result.elem (j) = Complex_NaN_result; | |
| 4587 | 3799 idx_arg.elem (j) = 0; |
| 4469 | 3800 } |
| 891 | 3801 else |
| 3802 { | |
| 4469 | 3803 result.elem (j) = tmp_max; |
| 4587 | 3804 idx_arg.elem (j) = idx_i; |
| 891 | 3805 } |
| 458 | 3806 } |
| 3807 } | |
| 3808 | |
| 3809 return result; | |
| 3810 } | |
| 3811 | |
| 3812 // i/o | |
| 3813 | |
| 3504 | 3814 std::ostream& |
| 3815 operator << (std::ostream& os, const ComplexMatrix& a) | |
| 458 | 3816 { |
| 5275 | 3817 for (octave_idx_type i = 0; i < a.rows (); i++) |
| 458 | 3818 { |
| 5275 | 3819 for (octave_idx_type j = 0; j < a.cols (); j++) |
| 4130 | 3820 { |
| 3821 os << " "; | |
| 3822 octave_write_complex (os, a.elem (i, j)); | |
| 3823 } | |
| 458 | 3824 os << "\n"; |
| 3825 } | |
| 3826 return os; | |
| 3827 } | |
| 3828 | |
| 3504 | 3829 std::istream& |
| 3830 operator >> (std::istream& is, ComplexMatrix& a) | |
| 458 | 3831 { |
| 5275 | 3832 octave_idx_type nr = a.rows (); |
| 3833 octave_idx_type nc = a.cols (); | |
| 458 | 3834 |
| 3835 if (nr < 1 || nc < 1) | |
| 3504 | 3836 is.clear (std::ios::badbit); |
| 458 | 3837 else |
| 3838 { | |
| 3839 Complex tmp; | |
| 5275 | 3840 for (octave_idx_type i = 0; i < nr; i++) |
| 3841 for (octave_idx_type j = 0; j < nc; j++) | |
| 458 | 3842 { |
| 4130 | 3843 tmp = octave_read_complex (is); |
| 458 | 3844 if (is) |
| 3845 a.elem (i, j) = tmp; | |
| 3846 else | |
| 2993 | 3847 goto done; |
| 458 | 3848 } |
| 3849 } | |
| 3850 | |
| 2993 | 3851 done: |
| 3852 | |
| 458 | 3853 return is; |
| 3854 } | |
| 3855 | |
| 1819 | 3856 ComplexMatrix |
| 3857 Givens (const Complex& x, const Complex& y) | |
| 3858 { | |
| 3859 double cc; | |
| 3860 Complex cs, temp_r; | |
| 3861 | |
| 3887 | 3862 F77_FUNC (zlartg, ZLARTG) (x, y, cc, cs, temp_r); |
| 1819 | 3863 |
| 3864 ComplexMatrix g (2, 2); | |
| 3865 | |
| 3866 g.elem (0, 0) = cc; | |
| 3867 g.elem (1, 1) = cc; | |
| 3868 g.elem (0, 1) = cs; | |
| 3869 g.elem (1, 0) = -conj (cs); | |
| 3870 | |
| 3871 return g; | |
| 3872 } | |
| 3873 | |
| 3874 ComplexMatrix | |
| 3875 Sylvester (const ComplexMatrix& a, const ComplexMatrix& b, | |
| 3876 const ComplexMatrix& c) | |
| 3877 { | |
| 3878 ComplexMatrix retval; | |
| 3879 | |
| 5775 | 3880 // FIXME -- need to check that a, b, and c are all the same |
| 1819 | 3881 // size. |
| 3882 | |
| 3883 // Compute Schur decompositions | |
| 3884 | |
| 3885 ComplexSCHUR as (a, "U"); | |
| 3886 ComplexSCHUR bs (b, "U"); | |
| 3887 | |
| 3888 // Transform c to new coordinates. | |
| 3889 | |
| 3890 ComplexMatrix ua = as.unitary_matrix (); | |
| 3891 ComplexMatrix sch_a = as.schur_matrix (); | |
| 3892 | |
| 3893 ComplexMatrix ub = bs.unitary_matrix (); | |
| 3894 ComplexMatrix sch_b = bs.schur_matrix (); | |
| 3895 | |
| 3896 ComplexMatrix cx = ua.hermitian () * c * ub; | |
| 3897 | |
| 3898 // Solve the sylvester equation, back-transform, and return the | |
| 3899 // solution. | |
| 3900 | |
| 5275 | 3901 octave_idx_type a_nr = a.rows (); |
| 3902 octave_idx_type b_nr = b.rows (); | |
| 1819 | 3903 |
| 3904 double scale; | |
| 5275 | 3905 octave_idx_type info; |
| 1950 | 3906 |
| 3907 Complex *pa = sch_a.fortran_vec (); | |
| 3908 Complex *pb = sch_b.fortran_vec (); | |
| 3909 Complex *px = cx.fortran_vec (); | |
| 1819 | 3910 |
| 4552 | 3911 F77_XFCN (ztrsyl, ZTRSYL, (F77_CONST_CHAR_ARG2 ("N", 1), |
| 3912 F77_CONST_CHAR_ARG2 ("N", 1), | |
| 3913 1, a_nr, b_nr, pa, a_nr, pb, | |
| 3914 b_nr, px, a_nr, scale, info | |
| 3915 F77_CHAR_ARG_LEN (1) | |
| 3916 F77_CHAR_ARG_LEN (1))); | |
| 1950 | 3917 |
| 3918 if (f77_exception_encountered) | |
| 3919 (*current_liboctave_error_handler) ("unrecoverable error in ztrsyl"); | |
| 3920 else | |
| 3921 { | |
| 5775 | 3922 // FIXME -- check info? |
| 1950 | 3923 |
| 3924 retval = -ua * cx * ub.hermitian (); | |
| 3925 } | |
| 1819 | 3926 |
| 3927 return retval; | |
| 3928 } | |
| 3929 | |
| 2828 | 3930 ComplexMatrix |
| 3931 operator * (const ComplexMatrix& m, const Matrix& a) | |
| 3932 { | |
| 3933 ComplexMatrix tmp (a); | |
| 3934 return m * tmp; | |
| 3935 } | |
| 3936 | |
| 3937 ComplexMatrix | |
| 3938 operator * (const Matrix& m, const ComplexMatrix& a) | |
| 3939 { | |
| 3940 ComplexMatrix tmp (m); | |
| 3941 return tmp * a; | |
| 3942 } | |
| 3943 | |
| 6162 | 3944 /* Simple Dot Product, Matrix-Vector and Matrix-Matrix Unit tests |
| 3945 %!assert([1+i 2+i 3+i] * [ 4+i ; 5+i ; 6+i], 29+21i, 1e-14) | |
| 3946 %!assert([1+i 2+i ; 3+i 4+i ] * [5+i ; 6+i], [15 + 14i ; 37 + 18i], 1e-14) | |
| 3947 %!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) | |
| 3948 */ | |
| 3949 | |
| 3950 /* Test some simple identities | |
| 3951 %!shared M, cv, rv | |
| 3952 %! M = randn(10,10)+i*rand(10,10); | |
| 3953 %! cv = randn(10,1)+i*rand(10,1); | |
| 3954 %! rv = randn(1,10)+i*rand(1,10); | |
| 3955 %!assert([M*cv,M*cv],M*[cv,cv],1e-14) | |
| 3956 %!assert([rv*M;rv*M],[rv;rv]*M,1e-14) | |
| 3957 %!assert(2*rv*cv,[rv,rv]*[cv;cv],1e-14) | |
| 3958 */ | |
| 3959 | |
| 2828 | 3960 ComplexMatrix |
| 3961 operator * (const ComplexMatrix& m, const ComplexMatrix& a) | |
| 3962 { | |
| 3963 ComplexMatrix retval; | |
| 3964 | |
| 5275 | 3965 octave_idx_type nr = m.rows (); |
| 3966 octave_idx_type nc = m.cols (); | |
| 3967 | |
| 3968 octave_idx_type a_nr = a.rows (); | |
| 3969 octave_idx_type a_nc = a.cols (); | |
| 2828 | 3970 |
| 3971 if (nc != a_nr) | |
| 3972 gripe_nonconformant ("operator *", nr, nc, a_nr, a_nc); | |
| 3973 else | |
| 3974 { | |
| 3975 if (nr == 0 || nc == 0 || a_nc == 0) | |
| 3760 | 3976 retval.resize (nr, a_nc, 0.0); |
| 2828 | 3977 else |
| 3978 { | |
| 5275 | 3979 octave_idx_type ld = nr; |
| 3980 octave_idx_type lda = a.rows (); | |
| 2828 | 3981 |
| 3982 retval.resize (nr, a_nc); | |
| 3983 Complex *c = retval.fortran_vec (); | |
| 3984 | |
| 5983 | 3985 if (a_nc == 1) |
| 3986 { | |
| 3987 if (nr == 1) | |
| 3988 F77_FUNC (xzdotu, XZDOTU) (nc, m.data (), 1, a.data (), 1, *c); | |
| 3989 else | |
| 6390 | 3990 { |
| 3991 F77_XFCN (zgemv, ZGEMV, (F77_CONST_CHAR_ARG2 ("N", 1), | |
| 3992 nr, nc, 1.0, m.data (), ld, | |
| 3993 a.data (), 1, 0.0, c, 1 | |
| 3994 F77_CHAR_ARG_LEN (1))); | |
| 3995 | |
| 3996 if (f77_exception_encountered) | |
| 3997 (*current_liboctave_error_handler) | |
| 3998 ("unrecoverable error in zgemv"); | |
| 3999 } | |
| 5983 | 4000 } |
| 4001 else | |
| 6390 | 4002 { |
| 4003 F77_XFCN (zgemm, ZGEMM, (F77_CONST_CHAR_ARG2 ("N", 1), | |
| 4004 F77_CONST_CHAR_ARG2 ("N", 1), | |
| 4005 nr, a_nc, nc, 1.0, m.data (), | |
| 4006 ld, a.data (), lda, 0.0, c, nr | |
| 4007 F77_CHAR_ARG_LEN (1) | |
| 4008 F77_CHAR_ARG_LEN (1))); | |
| 4009 | |
| 4010 if (f77_exception_encountered) | |
| 4011 (*current_liboctave_error_handler) | |
| 4012 ("unrecoverable error in zgemm"); | |
| 4013 } | |
| 2828 | 4014 } |
| 4015 } | |
| 4016 | |
| 4017 return retval; | |
| 4018 } | |
| 4019 | |
| 5775 | 4020 // FIXME -- it would be nice to share code among the min/max |
| 4309 | 4021 // functions below. |
| 4022 | |
| 4023 #define EMPTY_RETURN_CHECK(T) \ | |
| 4024 if (nr == 0 || nc == 0) \ | |
| 4025 return T (nr, nc); | |
| 4026 | |
| 4027 ComplexMatrix | |
| 4028 min (const Complex& c, const ComplexMatrix& m) | |
| 4029 { | |
| 5275 | 4030 octave_idx_type nr = m.rows (); |
| 4031 octave_idx_type nc = m.columns (); | |
| 4309 | 4032 |
| 4033 EMPTY_RETURN_CHECK (ComplexMatrix); | |
| 4034 | |
| 4035 ComplexMatrix result (nr, nc); | |
| 4036 | |
| 5275 | 4037 for (octave_idx_type j = 0; j < nc; j++) |
| 4038 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 4039 { |
| 4040 OCTAVE_QUIT; | |
| 4041 result (i, j) = xmin (c, m (i, j)); | |
| 4042 } | |
| 4043 | |
| 4044 return result; | |
| 4045 } | |
| 4046 | |
| 4047 ComplexMatrix | |
| 4048 min (const ComplexMatrix& m, const Complex& c) | |
| 4049 { | |
| 5275 | 4050 octave_idx_type nr = m.rows (); |
| 4051 octave_idx_type nc = m.columns (); | |
| 4309 | 4052 |
| 4053 EMPTY_RETURN_CHECK (ComplexMatrix); | |
| 4054 | |
| 4055 ComplexMatrix result (nr, nc); | |
| 4056 | |
| 5275 | 4057 for (octave_idx_type j = 0; j < nc; j++) |
| 4058 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 4059 { |
| 4060 OCTAVE_QUIT; | |
| 4061 result (i, j) = xmin (m (i, j), c); | |
| 4062 } | |
| 4063 | |
| 4064 return result; | |
| 4065 } | |
| 4066 | |
| 4067 ComplexMatrix | |
| 4068 min (const ComplexMatrix& a, const ComplexMatrix& b) | |
| 4069 { | |
| 5275 | 4070 octave_idx_type nr = a.rows (); |
| 4071 octave_idx_type nc = a.columns (); | |
| 4309 | 4072 |
| 4073 if (nr != b.rows () || nc != b.columns ()) | |
| 4074 { | |
| 4075 (*current_liboctave_error_handler) | |
| 4076 ("two-arg min expecting args of same size"); | |
| 4077 return ComplexMatrix (); | |
| 4078 } | |
| 4079 | |
| 4080 EMPTY_RETURN_CHECK (ComplexMatrix); | |
| 4081 | |
| 4082 ComplexMatrix result (nr, nc); | |
| 4083 | |
| 5275 | 4084 for (octave_idx_type j = 0; j < nc; j++) |
| 4309 | 4085 { |
| 4086 int columns_are_real_only = 1; | |
| 5275 | 4087 for (octave_idx_type i = 0; i < nr; i++) |
| 4309 | 4088 { |
| 4089 OCTAVE_QUIT; | |
| 5315 | 4090 if (std::imag (a (i, j)) != 0.0 || std::imag (b (i, j)) != 0.0) |
| 4309 | 4091 { |
| 4092 columns_are_real_only = 0; | |
| 4093 break; | |
| 4094 } | |
| 4095 } | |
| 4096 | |
| 4097 if (columns_are_real_only) | |
| 4098 { | |
| 5275 | 4099 for (octave_idx_type i = 0; i < nr; i++) |
| 5315 | 4100 result (i, j) = xmin (std::real (a (i, j)), std::real (b (i, j))); |
| 4309 | 4101 } |
| 4102 else | |
| 4103 { | |
| 5275 | 4104 for (octave_idx_type i = 0; i < nr; i++) |
| 4309 | 4105 { |
| 4106 OCTAVE_QUIT; | |
| 4107 result (i, j) = xmin (a (i, j), b (i, j)); | |
| 4108 } | |
| 4109 } | |
| 4110 } | |
| 4111 | |
| 4112 return result; | |
| 4113 } | |
| 4114 | |
| 4115 ComplexMatrix | |
| 4116 max (const Complex& c, const ComplexMatrix& m) | |
| 4117 { | |
| 5275 | 4118 octave_idx_type nr = m.rows (); |
| 4119 octave_idx_type nc = m.columns (); | |
| 4309 | 4120 |
| 4121 EMPTY_RETURN_CHECK (ComplexMatrix); | |
| 4122 | |
| 4123 ComplexMatrix result (nr, nc); | |
| 4124 | |
| 5275 | 4125 for (octave_idx_type j = 0; j < nc; j++) |
| 4126 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 4127 { |
| 4128 OCTAVE_QUIT; | |
| 4129 result (i, j) = xmax (c, m (i, j)); | |
| 4130 } | |
| 4131 | |
| 4132 return result; | |
| 4133 } | |
| 4134 | |
| 4135 ComplexMatrix | |
| 4136 max (const ComplexMatrix& m, const Complex& c) | |
| 4137 { | |
| 5275 | 4138 octave_idx_type nr = m.rows (); |
| 4139 octave_idx_type nc = m.columns (); | |
| 4309 | 4140 |
| 4141 EMPTY_RETURN_CHECK (ComplexMatrix); | |
| 4142 | |
| 4143 ComplexMatrix result (nr, nc); | |
| 4144 | |
| 5275 | 4145 for (octave_idx_type j = 0; j < nc; j++) |
| 4146 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 4147 { |
| 4148 OCTAVE_QUIT; | |
| 4149 result (i, j) = xmax (m (i, j), c); | |
| 4150 } | |
| 4151 | |
| 4152 return result; | |
| 4153 } | |
| 4154 | |
| 4155 ComplexMatrix | |
| 4156 max (const ComplexMatrix& a, const ComplexMatrix& b) | |
| 4157 { | |
| 5275 | 4158 octave_idx_type nr = a.rows (); |
| 4159 octave_idx_type nc = a.columns (); | |
| 4309 | 4160 |
| 4161 if (nr != b.rows () || nc != b.columns ()) | |
| 4162 { | |
| 4163 (*current_liboctave_error_handler) | |
| 4164 ("two-arg max expecting args of same size"); | |
| 4165 return ComplexMatrix (); | |
| 4166 } | |
| 4167 | |
| 4168 EMPTY_RETURN_CHECK (ComplexMatrix); | |
| 4169 | |
| 4170 ComplexMatrix result (nr, nc); | |
| 4171 | |
| 5275 | 4172 for (octave_idx_type j = 0; j < nc; j++) |
| 4309 | 4173 { |
| 4174 int columns_are_real_only = 1; | |
| 5275 | 4175 for (octave_idx_type i = 0; i < nr; i++) |
| 4309 | 4176 { |
| 4177 OCTAVE_QUIT; | |
| 5315 | 4178 if (std::imag (a (i, j)) != 0.0 || std::imag (b (i, j)) != 0.0) |
| 4309 | 4179 { |
| 4180 columns_are_real_only = 0; | |
| 4181 break; | |
| 4182 } | |
| 4183 } | |
| 4184 | |
| 4185 if (columns_are_real_only) | |
| 4186 { | |
| 5275 | 4187 for (octave_idx_type i = 0; i < nr; i++) |
| 4309 | 4188 { |
| 4189 OCTAVE_QUIT; | |
| 5315 | 4190 result (i, j) = xmax (std::real (a (i, j)), std::real (b (i, j))); |
| 4309 | 4191 } |
| 4192 } | |
| 4193 else | |
| 4194 { | |
| 5275 | 4195 for (octave_idx_type i = 0; i < nr; i++) |
| 4309 | 4196 { |
| 4197 OCTAVE_QUIT; | |
| 4198 result (i, j) = xmax (a (i, j), b (i, j)); | |
| 4199 } | |
| 4200 } | |
| 4201 } | |
| 4202 | |
| 4203 return result; | |
| 4204 } | |
| 4205 | |
| 5315 | 4206 MS_CMP_OPS(ComplexMatrix, std::real, Complex, std::real) |
| 3504 | 4207 MS_BOOL_OPS(ComplexMatrix, Complex, 0.0) |
| 2870 | 4208 |
| 5315 | 4209 SM_CMP_OPS(Complex, std::real, ComplexMatrix, std::real) |
| 3504 | 4210 SM_BOOL_OPS(Complex, ComplexMatrix, 0.0) |
| 2870 | 4211 |
| 5315 | 4212 MM_CMP_OPS(ComplexMatrix, std::real, ComplexMatrix, std::real) |
| 3504 | 4213 MM_BOOL_OPS(ComplexMatrix, ComplexMatrix, 0.0) |
| 2870 | 4214 |
| 458 | 4215 /* |
| 4216 ;;; Local Variables: *** | |
| 4217 ;;; mode: C++ *** | |
| 4218 ;;; End: *** | |
| 4219 */ |