Mercurial > hg > octave-nkf
annotate liboctave/dMatrix.cc @ 7486:6a6d2abe51ff
more xGELSD workspace fixes
| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Fri, 15 Feb 2008 18:55:11 -0500 |
| parents | 29980c6b8604 |
| children | 6470f946a425 |
| 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 |
| 4669 | 34 #include "Array-util.h" |
| 2317 | 35 #include "byte-swap.h" |
| 2828 | 36 #include "dMatrix.h" |
| 1819 | 37 #include "dbleAEPBAL.h" |
| 458 | 38 #include "dbleDET.h" |
| 1819 | 39 #include "dbleSCHUR.h" |
| 740 | 40 #include "dbleSVD.h" |
| 6207 | 41 #include "dbleCHOL.h" |
| 1847 | 42 #include "f77-fcn.h" |
| 458 | 43 #include "lo-error.h" |
| 2354 | 44 #include "lo-ieee.h" |
| 45 #include "lo-mappers.h" | |
| 1968 | 46 #include "lo-utils.h" |
| 1367 | 47 #include "mx-base.h" |
| 2828 | 48 #include "mx-m-dm.h" |
| 3176 | 49 #include "mx-dm-m.h" |
| 1367 | 50 #include "mx-inlines.cc" |
| 1650 | 51 #include "oct-cmplx.h" |
| 4153 | 52 #include "quit.h" |
| 458 | 53 |
| 4773 | 54 #if defined (HAVE_FFTW3) |
| 3827 | 55 #include "oct-fftw.h" |
| 56 #endif | |
| 57 | |
| 458 | 58 // Fortran functions we call. |
| 59 | |
| 60 extern "C" | |
| 61 { | |
| 7478 | 62 F77_RET_T |
| 7477 | 63 F77_FUNC (xilaenv, XILAENV) (const octave_idx_type&, F77_CONST_CHAR_ARG_DECL, |
| 64 F77_CONST_CHAR_ARG_DECL, | |
| 65 const octave_idx_type&, const octave_idx_type&, | |
| 7478 | 66 const octave_idx_type&, const octave_idx_type&, |
| 67 octave_idx_type& | |
| 68 F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); | |
| 7476 | 69 |
| 4552 | 70 F77_RET_T |
| 71 F77_FUNC (dgebal, DGEBAL) (F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 72 const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type&, |
| 73 octave_idx_type&, double*, octave_idx_type& | |
| 4552 | 74 F77_CHAR_ARG_LEN_DECL); |
| 75 | |
| 76 F77_RET_T | |
| 77 F77_FUNC (dgebak, DGEBAK) (F77_CONST_CHAR_ARG_DECL, | |
| 78 F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 79 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, double*, |
| 80 const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type& | |
| 4552 | 81 F77_CHAR_ARG_LEN_DECL |
| 82 F77_CHAR_ARG_LEN_DECL); | |
| 83 | |
| 84 | |
| 85 F77_RET_T | |
| 86 F77_FUNC (dgemm, DGEMM) (F77_CONST_CHAR_ARG_DECL, | |
| 87 F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 88 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
| 89 const double&, const double*, const octave_idx_type&, | |
| 90 const double*, const octave_idx_type&, const double&, | |
| 91 double*, const octave_idx_type& | |
| 4552 | 92 F77_CHAR_ARG_LEN_DECL |
| 93 F77_CHAR_ARG_LEN_DECL); | |
| 94 | |
| 95 F77_RET_T | |
| 5983 | 96 F77_FUNC (dgemv, DGEMV) (F77_CONST_CHAR_ARG_DECL, |
| 97 const octave_idx_type&, const octave_idx_type&, const double&, | |
| 98 const double*, const octave_idx_type&, const double*, | |
| 99 const octave_idx_type&, const double&, double*, | |
| 100 const octave_idx_type& | |
| 101 F77_CHAR_ARG_LEN_DECL); | |
| 102 | |
| 103 F77_RET_T | |
| 104 F77_FUNC (xddot, XDDOT) (const octave_idx_type&, const double*, const octave_idx_type&, | |
| 105 const double*, const octave_idx_type&, double&); | |
| 106 | |
| 107 F77_RET_T | |
| 5275 | 108 F77_FUNC (dgetrf, DGETRF) (const octave_idx_type&, const octave_idx_type&, double*, const octave_idx_type&, |
| 109 octave_idx_type*, octave_idx_type&); | |
| 4329 | 110 |
| 4552 | 111 F77_RET_T |
| 5275 | 112 F77_FUNC (dgetrs, DGETRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, |
| 113 const double*, const octave_idx_type&, | |
| 114 const octave_idx_type*, double*, const octave_idx_type&, octave_idx_type& | |
| 4552 | 115 F77_CHAR_ARG_LEN_DECL); |
| 116 | |
| 117 F77_RET_T | |
| 5275 | 118 F77_FUNC (dgetri, DGETRI) (const octave_idx_type&, double*, const octave_idx_type&, const octave_idx_type*, |
| 119 double*, const octave_idx_type&, octave_idx_type&); | |
| 4552 | 120 |
| 121 F77_RET_T | |
| 5275 | 122 F77_FUNC (dgecon, DGECON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, double*, |
| 123 const octave_idx_type&, const double&, double&, | |
| 124 double*, octave_idx_type*, octave_idx_type& | |
| 4552 | 125 F77_CHAR_ARG_LEN_DECL); |
| 126 | |
| 127 F77_RET_T | |
| 7072 | 128 F77_FUNC (dgelsy, DGELSY) (const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
| 129 double*, const octave_idx_type&, double*, | |
| 130 const octave_idx_type&, octave_idx_type*, double&, octave_idx_type&, | |
| 131 double*, const octave_idx_type&, octave_idx_type&); | |
| 132 | |
| 133 F77_RET_T | |
| 134 F77_FUNC (dgelsd, DGELSD) (const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, | |
| 5275 | 135 double*, const octave_idx_type&, double*, |
| 7071 | 136 const octave_idx_type&, double*, double&, octave_idx_type&, |
| 7072 | 137 double*, const octave_idx_type&, octave_idx_type*, |
| 138 octave_idx_type&); | |
| 458 | 139 |
| 5785 | 140 F77_RET_T |
| 141 F77_FUNC (dpotrf, DPOTRF) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 142 double *, const octave_idx_type&, | |
| 143 octave_idx_type& F77_CHAR_ARG_LEN_DECL); | |
| 144 | |
| 145 F77_RET_T | |
| 146 F77_FUNC (dpocon, DPOCON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 147 double*, const octave_idx_type&, const double&, | |
| 148 double&, double*, octave_idx_type*, | |
| 149 octave_idx_type& F77_CHAR_ARG_LEN_DECL); | |
| 150 F77_RET_T | |
| 151 F77_FUNC (dpotrs, DPOTRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 152 const octave_idx_type&, const double*, | |
| 153 const octave_idx_type&, double*, | |
| 154 const octave_idx_type&, octave_idx_type& | |
| 155 F77_CHAR_ARG_LEN_DECL); | |
| 156 | |
| 157 F77_RET_T | |
| 6207 | 158 F77_FUNC (dtrtri, DTRTRI) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, |
| 159 const octave_idx_type&, const double*, | |
| 160 const octave_idx_type&, octave_idx_type& | |
| 161 F77_CHAR_ARG_LEN_DECL | |
| 162 F77_CHAR_ARG_LEN_DECL); | |
| 163 F77_RET_T | |
| 5785 | 164 F77_FUNC (dtrcon, DTRCON) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, |
| 165 F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 166 const double*, const octave_idx_type&, double&, | |
| 167 double*, octave_idx_type*, octave_idx_type& | |
| 168 F77_CHAR_ARG_LEN_DECL | |
| 169 F77_CHAR_ARG_LEN_DECL | |
| 170 F77_CHAR_ARG_LEN_DECL); | |
| 171 F77_RET_T | |
| 172 F77_FUNC (dtrtrs, DTRTRS) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, | |
| 173 F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 174 const octave_idx_type&, const double*, | |
| 175 const octave_idx_type&, double*, | |
| 176 const octave_idx_type&, octave_idx_type& | |
| 177 F77_CHAR_ARG_LEN_DECL | |
| 178 F77_CHAR_ARG_LEN_DECL | |
| 179 F77_CHAR_ARG_LEN_DECL); | |
| 180 | |
| 1360 | 181 // Note that the original complex fft routines were not written for |
| 182 // double complex arguments. They have been modified by adding an | |
| 183 // implicit double precision (a-h,o-z) statement at the beginning of | |
| 184 // each subroutine. | |
| 458 | 185 |
| 4552 | 186 F77_RET_T |
| 5275 | 187 F77_FUNC (cffti, CFFTI) (const octave_idx_type&, Complex*); |
| 4552 | 188 |
| 189 F77_RET_T | |
| 5275 | 190 F77_FUNC (cfftf, CFFTF) (const octave_idx_type&, Complex*, Complex*); |
| 4552 | 191 |
| 192 F77_RET_T | |
| 5275 | 193 F77_FUNC (cfftb, CFFTB) (const octave_idx_type&, Complex*, Complex*); |
| 4552 | 194 |
| 195 F77_RET_T | |
| 196 F77_FUNC (dlartg, DLARTG) (const double&, const double&, double&, | |
| 197 double&, double&); | |
| 198 | |
| 199 F77_RET_T | |
| 200 F77_FUNC (dtrsyl, DTRSYL) (F77_CONST_CHAR_ARG_DECL, | |
| 201 F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 202 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
| 203 const double*, const octave_idx_type&, const double*, | |
| 204 const octave_idx_type&, const double*, const octave_idx_type&, | |
| 205 double&, octave_idx_type& | |
| 4552 | 206 F77_CHAR_ARG_LEN_DECL |
| 207 F77_CHAR_ARG_LEN_DECL); | |
| 208 | |
| 209 F77_RET_T | |
| 5275 | 210 F77_FUNC (xdlange, XDLANGE) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, |
| 211 const octave_idx_type&, const double*, | |
| 212 const octave_idx_type&, double*, double& | |
| 4552 | 213 F77_CHAR_ARG_LEN_DECL); |
| 458 | 214 } |
| 215 | |
| 1360 | 216 // Matrix class. |
| 458 | 217 |
| 2349 | 218 Matrix::Matrix (const RowVector& rv) |
| 219 : MArray2<double> (1, rv.length (), 0.0) | |
| 220 { | |
| 5275 | 221 for (octave_idx_type i = 0; i < rv.length (); i++) |
| 2349 | 222 elem (0, i) = rv.elem (i); |
| 223 } | |
| 224 | |
| 225 Matrix::Matrix (const ColumnVector& cv) | |
| 226 : MArray2<double> (cv.length (), 1, 0.0) | |
| 227 { | |
| 5275 | 228 for (octave_idx_type i = 0; i < cv.length (); i++) |
| 2349 | 229 elem (i, 0) = cv.elem (i); |
| 230 } | |
| 231 | |
| 458 | 232 Matrix::Matrix (const DiagMatrix& a) |
| 1214 | 233 : MArray2<double> (a.rows (), a.cols (), 0.0) |
| 458 | 234 { |
| 5275 | 235 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 236 elem (i, i) = a.elem (i, i); |
| 237 } | |
| 238 | |
| 5775 | 239 // FIXME -- could we use a templated mixed-type copy function |
| 1574 | 240 // here? |
| 241 | |
| 2828 | 242 Matrix::Matrix (const boolMatrix& a) |
| 243 : MArray2<double> (a.rows (), a.cols ()) | |
| 244 { | |
| 5275 | 245 for (octave_idx_type i = 0; i < a.rows (); i++) |
| 246 for (octave_idx_type j = 0; j < a.cols (); j++) | |
| 2828 | 247 elem (i, j) = a.elem (i, j); |
| 248 } | |
| 249 | |
| 1574 | 250 Matrix::Matrix (const charMatrix& a) |
| 251 : MArray2<double> (a.rows (), a.cols ()) | |
| 252 { | |
| 5275 | 253 for (octave_idx_type i = 0; i < a.rows (); i++) |
| 254 for (octave_idx_type j = 0; j < a.cols (); j++) | |
| 1574 | 255 elem (i, j) = a.elem (i, j); |
| 256 } | |
| 257 | |
| 2385 | 258 bool |
| 458 | 259 Matrix::operator == (const Matrix& a) const |
| 260 { | |
| 261 if (rows () != a.rows () || cols () != a.cols ()) | |
| 2385 | 262 return false; |
| 458 | 263 |
| 3769 | 264 return mx_inline_equal (data (), a.data (), length ()); |
| 458 | 265 } |
| 266 | |
| 2385 | 267 bool |
| 458 | 268 Matrix::operator != (const Matrix& a) const |
| 269 { | |
| 270 return !(*this == a); | |
| 271 } | |
| 272 | |
| 3354 | 273 bool |
| 274 Matrix::is_symmetric (void) const | |
| 275 { | |
| 276 if (is_square () && rows () > 0) | |
| 277 { | |
| 5275 | 278 for (octave_idx_type i = 0; i < rows (); i++) |
| 279 for (octave_idx_type j = i+1; j < cols (); j++) | |
| 3354 | 280 if (elem (i, j) != elem (j, i)) |
| 281 return false; | |
| 282 | |
| 283 return true; | |
| 284 } | |
| 285 | |
| 286 return false; | |
| 287 } | |
| 288 | |
| 458 | 289 Matrix& |
| 5275 | 290 Matrix::insert (const Matrix& a, octave_idx_type r, octave_idx_type c) |
| 458 | 291 { |
| 1561 | 292 Array2<double>::insert (a, r, c); |
| 458 | 293 return *this; |
| 294 } | |
| 295 | |
| 296 Matrix& | |
| 5275 | 297 Matrix::insert (const RowVector& a, octave_idx_type r, octave_idx_type c) |
| 458 | 298 { |
| 5275 | 299 octave_idx_type a_len = a.length (); |
| 4316 | 300 |
| 1698 | 301 if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ()) |
| 458 | 302 { |
| 303 (*current_liboctave_error_handler) ("range error for insert"); | |
| 304 return *this; | |
| 305 } | |
| 306 | |
| 4316 | 307 if (a_len > 0) |
| 308 { | |
| 309 make_unique (); | |
| 310 | |
| 5275 | 311 for (octave_idx_type i = 0; i < a_len; i++) |
| 4316 | 312 xelem (r, c+i) = a.elem (i); |
| 313 } | |
| 458 | 314 |
| 315 return *this; | |
| 316 } | |
| 317 | |
| 318 Matrix& | |
| 5275 | 319 Matrix::insert (const ColumnVector& a, octave_idx_type r, octave_idx_type c) |
| 458 | 320 { |
| 5275 | 321 octave_idx_type a_len = a.length (); |
| 4316 | 322 |
| 1698 | 323 if (r < 0 || r + a_len > rows () || c < 0 || c >= cols ()) |
| 458 | 324 { |
| 325 (*current_liboctave_error_handler) ("range error for insert"); | |
| 326 return *this; | |
| 327 } | |
| 328 | |
| 4316 | 329 if (a_len > 0) |
| 330 { | |
| 331 make_unique (); | |
| 332 | |
| 5275 | 333 for (octave_idx_type i = 0; i < a_len; i++) |
| 4316 | 334 xelem (r+i, c) = a.elem (i); |
| 335 } | |
| 458 | 336 |
| 337 return *this; | |
| 338 } | |
| 339 | |
| 340 Matrix& | |
| 5275 | 341 Matrix::insert (const DiagMatrix& a, octave_idx_type r, octave_idx_type c) |
| 458 | 342 { |
| 5275 | 343 octave_idx_type a_nr = a.rows (); |
| 344 octave_idx_type a_nc = a.cols (); | |
| 1697 | 345 |
| 1698 | 346 if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) |
| 458 | 347 { |
| 348 (*current_liboctave_error_handler) ("range error for insert"); | |
| 349 return *this; | |
| 350 } | |
| 351 | |
| 1697 | 352 fill (0.0, r, c, r + a_nr - 1, c + a_nc - 1); |
| 353 | |
| 5275 | 354 octave_idx_type a_len = a.length (); |
| 4316 | 355 |
| 356 if (a_len > 0) | |
| 357 { | |
| 358 make_unique (); | |
| 359 | |
| 5275 | 360 for (octave_idx_type i = 0; i < a_len; i++) |
| 4316 | 361 xelem (r+i, c+i) = a.elem (i, i); |
| 362 } | |
| 458 | 363 |
| 364 return *this; | |
| 365 } | |
| 366 | |
| 367 Matrix& | |
| 368 Matrix::fill (double val) | |
| 369 { | |
| 5275 | 370 octave_idx_type nr = rows (); |
| 371 octave_idx_type nc = cols (); | |
| 4316 | 372 |
| 458 | 373 if (nr > 0 && nc > 0) |
| 4316 | 374 { |
| 375 make_unique (); | |
| 376 | |
| 5275 | 377 for (octave_idx_type j = 0; j < nc; j++) |
| 378 for (octave_idx_type i = 0; i < nr; i++) | |
| 4316 | 379 xelem (i, j) = val; |
| 380 } | |
| 458 | 381 |
| 382 return *this; | |
| 383 } | |
| 384 | |
| 385 Matrix& | |
| 5275 | 386 Matrix::fill (double val, octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) |
| 458 | 387 { |
| 5275 | 388 octave_idx_type nr = rows (); |
| 389 octave_idx_type nc = cols (); | |
| 4316 | 390 |
| 458 | 391 if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0 |
| 392 || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc) | |
| 393 { | |
| 394 (*current_liboctave_error_handler) ("range error for fill"); | |
| 395 return *this; | |
| 396 } | |
| 397 | |
| 5275 | 398 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } |
| 399 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } | |
| 458 | 400 |
| 4316 | 401 if (r2 >= r1 && c2 >= c1) |
| 402 { | |
| 403 make_unique (); | |
| 404 | |
| 5275 | 405 for (octave_idx_type j = c1; j <= c2; j++) |
| 406 for (octave_idx_type i = r1; i <= r2; i++) | |
| 4316 | 407 xelem (i, j) = val; |
| 408 } | |
| 458 | 409 |
| 410 return *this; | |
| 411 } | |
| 412 | |
| 413 Matrix | |
| 414 Matrix::append (const Matrix& a) const | |
| 415 { | |
| 5275 | 416 octave_idx_type nr = rows (); |
| 417 octave_idx_type nc = cols (); | |
| 458 | 418 if (nr != a.rows ()) |
| 419 { | |
| 420 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 421 return Matrix (); | |
| 422 } | |
| 423 | |
| 5275 | 424 octave_idx_type nc_insert = nc; |
| 458 | 425 Matrix retval (nr, nc + a.cols ()); |
| 426 retval.insert (*this, 0, 0); | |
| 427 retval.insert (a, 0, nc_insert); | |
| 428 return retval; | |
| 429 } | |
| 430 | |
| 431 Matrix | |
| 432 Matrix::append (const RowVector& a) const | |
| 433 { | |
| 5275 | 434 octave_idx_type nr = rows (); |
| 435 octave_idx_type nc = cols (); | |
| 458 | 436 if (nr != 1) |
| 437 { | |
| 438 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 439 return Matrix (); | |
| 440 } | |
| 441 | |
| 5275 | 442 octave_idx_type nc_insert = nc; |
| 458 | 443 Matrix retval (nr, nc + a.length ()); |
| 444 retval.insert (*this, 0, 0); | |
| 445 retval.insert (a, 0, nc_insert); | |
| 446 return retval; | |
| 447 } | |
| 448 | |
| 449 Matrix | |
| 450 Matrix::append (const ColumnVector& a) const | |
| 451 { | |
| 5275 | 452 octave_idx_type nr = rows (); |
| 453 octave_idx_type nc = cols (); | |
| 458 | 454 if (nr != a.length ()) |
| 455 { | |
| 456 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 457 return Matrix (); | |
| 458 } | |
| 459 | |
| 5275 | 460 octave_idx_type nc_insert = nc; |
| 458 | 461 Matrix retval (nr, nc + 1); |
| 462 retval.insert (*this, 0, 0); | |
| 463 retval.insert (a, 0, nc_insert); | |
| 464 return retval; | |
| 465 } | |
| 466 | |
| 467 Matrix | |
| 468 Matrix::append (const DiagMatrix& a) const | |
| 469 { | |
| 5275 | 470 octave_idx_type nr = rows (); |
| 471 octave_idx_type nc = cols (); | |
| 458 | 472 if (nr != a.rows ()) |
| 473 { | |
| 474 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 475 return *this; | |
| 476 } | |
| 477 | |
| 5275 | 478 octave_idx_type nc_insert = nc; |
| 458 | 479 Matrix retval (nr, nc + a.cols ()); |
| 480 retval.insert (*this, 0, 0); | |
| 481 retval.insert (a, 0, nc_insert); | |
| 482 return retval; | |
| 483 } | |
| 484 | |
| 485 Matrix | |
| 486 Matrix::stack (const Matrix& a) const | |
| 487 { | |
| 5275 | 488 octave_idx_type nr = rows (); |
| 489 octave_idx_type nc = cols (); | |
| 458 | 490 if (nc != a.cols ()) |
| 491 { | |
| 492 (*current_liboctave_error_handler) | |
| 493 ("column dimension mismatch for stack"); | |
| 494 return Matrix (); | |
| 495 } | |
| 496 | |
| 5275 | 497 octave_idx_type nr_insert = nr; |
| 458 | 498 Matrix retval (nr + a.rows (), nc); |
| 499 retval.insert (*this, 0, 0); | |
| 500 retval.insert (a, nr_insert, 0); | |
| 501 return retval; | |
| 502 } | |
| 503 | |
| 504 Matrix | |
| 505 Matrix::stack (const RowVector& a) const | |
| 506 { | |
| 5275 | 507 octave_idx_type nr = rows (); |
| 508 octave_idx_type nc = cols (); | |
| 458 | 509 if (nc != a.length ()) |
| 510 { | |
| 511 (*current_liboctave_error_handler) | |
| 512 ("column dimension mismatch for stack"); | |
| 513 return Matrix (); | |
| 514 } | |
| 515 | |
| 5275 | 516 octave_idx_type nr_insert = nr; |
| 458 | 517 Matrix retval (nr + 1, nc); |
| 518 retval.insert (*this, 0, 0); | |
| 519 retval.insert (a, nr_insert, 0); | |
| 520 return retval; | |
| 521 } | |
| 522 | |
| 523 Matrix | |
| 524 Matrix::stack (const ColumnVector& a) const | |
| 525 { | |
| 5275 | 526 octave_idx_type nr = rows (); |
| 527 octave_idx_type nc = cols (); | |
| 458 | 528 if (nc != 1) |
| 529 { | |
| 530 (*current_liboctave_error_handler) | |
| 531 ("column dimension mismatch for stack"); | |
| 532 return Matrix (); | |
| 533 } | |
| 534 | |
| 5275 | 535 octave_idx_type nr_insert = nr; |
| 458 | 536 Matrix retval (nr + a.length (), nc); |
| 537 retval.insert (*this, 0, 0); | |
| 538 retval.insert (a, nr_insert, 0); | |
| 539 return retval; | |
| 540 } | |
| 541 | |
| 542 Matrix | |
| 543 Matrix::stack (const DiagMatrix& a) const | |
| 544 { | |
| 5275 | 545 octave_idx_type nr = rows (); |
| 546 octave_idx_type nc = cols (); | |
| 458 | 547 if (nc != a.cols ()) |
| 548 { | |
| 549 (*current_liboctave_error_handler) | |
| 550 ("column dimension mismatch for stack"); | |
| 551 return Matrix (); | |
| 552 } | |
| 553 | |
| 5275 | 554 octave_idx_type nr_insert = nr; |
| 458 | 555 Matrix retval (nr + a.rows (), nc); |
| 556 retval.insert (*this, 0, 0); | |
| 557 retval.insert (a, nr_insert, 0); | |
| 558 return retval; | |
| 559 } | |
| 560 | |
| 561 Matrix | |
| 1205 | 562 real (const ComplexMatrix& a) |
| 563 { | |
| 5275 | 564 octave_idx_type a_len = a.length (); |
| 1205 | 565 Matrix retval; |
| 566 if (a_len > 0) | |
| 3769 | 567 retval = Matrix (mx_inline_real_dup (a.data (), a_len), |
| 568 a.rows (), a.cols ()); | |
| 1205 | 569 return retval; |
| 570 } | |
| 571 | |
| 572 Matrix | |
| 573 imag (const ComplexMatrix& a) | |
| 574 { | |
| 5275 | 575 octave_idx_type a_len = a.length (); |
| 1205 | 576 Matrix retval; |
| 577 if (a_len > 0) | |
| 3769 | 578 retval = Matrix (mx_inline_imag_dup (a.data (), a_len), |
| 579 a.rows (), a.cols ()); | |
| 1205 | 580 return retval; |
| 581 } | |
| 582 | |
| 583 Matrix | |
| 5275 | 584 Matrix::extract (octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) const |
| 458 | 585 { |
| 5275 | 586 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } |
| 587 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } | |
| 588 | |
| 589 octave_idx_type new_r = r2 - r1 + 1; | |
| 590 octave_idx_type new_c = c2 - c1 + 1; | |
| 458 | 591 |
| 592 Matrix result (new_r, new_c); | |
| 593 | |
| 5275 | 594 for (octave_idx_type j = 0; j < new_c; j++) |
| 595 for (octave_idx_type i = 0; i < new_r; i++) | |
| 4316 | 596 result.xelem (i, j) = elem (r1+i, c1+j); |
| 597 | |
| 598 return result; | |
| 599 } | |
| 600 | |
| 601 Matrix | |
| 5275 | 602 Matrix::extract_n (octave_idx_type r1, octave_idx_type c1, octave_idx_type nr, octave_idx_type nc) const |
| 4316 | 603 { |
| 604 Matrix result (nr, nc); | |
| 605 | |
| 5275 | 606 for (octave_idx_type j = 0; j < nc; j++) |
| 607 for (octave_idx_type i = 0; i < nr; i++) | |
| 4316 | 608 result.xelem (i, j) = elem (r1+i, c1+j); |
| 458 | 609 |
| 610 return result; | |
| 611 } | |
| 612 | |
| 613 // extract row or column i. | |
| 614 | |
| 615 RowVector | |
| 5275 | 616 Matrix::row (octave_idx_type i) const |
| 458 | 617 { |
| 5275 | 618 octave_idx_type nc = cols (); |
| 458 | 619 if (i < 0 || i >= rows ()) |
| 620 { | |
| 621 (*current_liboctave_error_handler) ("invalid row selection"); | |
| 622 return RowVector (); | |
| 623 } | |
| 624 | |
| 625 RowVector retval (nc); | |
| 5275 | 626 for (octave_idx_type j = 0; j < nc; j++) |
| 4316 | 627 retval.xelem (j) = elem (i, j); |
| 458 | 628 |
| 629 return retval; | |
| 630 } | |
| 631 | |
| 632 ColumnVector | |
| 5275 | 633 Matrix::column (octave_idx_type i) const |
| 458 | 634 { |
| 5275 | 635 octave_idx_type nr = rows (); |
| 458 | 636 if (i < 0 || i >= cols ()) |
| 637 { | |
| 638 (*current_liboctave_error_handler) ("invalid column selection"); | |
| 639 return ColumnVector (); | |
| 640 } | |
| 641 | |
| 642 ColumnVector retval (nr); | |
| 5275 | 643 for (octave_idx_type j = 0; j < nr; j++) |
| 4316 | 644 retval.xelem (j) = elem (j, i); |
| 458 | 645 |
| 646 return retval; | |
| 647 } | |
| 648 | |
| 649 Matrix | |
| 650 Matrix::inverse (void) const | |
| 651 { | |
| 5275 | 652 octave_idx_type info; |
| 458 | 653 double rcond; |
| 6207 | 654 MatrixType mattype (*this); |
| 655 return inverse (mattype, info, rcond, 0, 0); | |
| 656 } | |
| 657 | |
| 658 Matrix | |
| 6479 | 659 Matrix::inverse (octave_idx_type& info) const |
| 660 { | |
| 661 double rcond; | |
| 662 MatrixType mattype (*this); | |
| 663 return inverse (mattype, info, rcond, 0, 0); | |
| 664 } | |
| 665 | |
| 666 Matrix | |
| 667 Matrix::inverse (octave_idx_type& info, double& rcond, int force, | |
| 668 int calc_cond) const | |
| 669 { | |
| 670 MatrixType mattype (*this); | |
| 671 return inverse (mattype, info, rcond, force, calc_cond); | |
| 672 } | |
| 673 | |
| 674 Matrix | |
| 6207 | 675 Matrix::inverse (MatrixType& mattype) const |
| 676 { | |
| 677 octave_idx_type info; | |
| 678 double rcond; | |
| 679 return inverse (mattype, info, rcond, 0, 0); | |
| 680 } | |
| 681 | |
| 682 Matrix | |
| 683 Matrix::inverse (MatrixType &mattype, octave_idx_type& info) const | |
| 684 { | |
| 685 double rcond; | |
| 686 return inverse (mattype, info, rcond, 0, 0); | |
| 458 | 687 } |
| 688 | |
| 689 Matrix | |
| 6207 | 690 Matrix::tinverse (MatrixType &mattype, octave_idx_type& info, double& rcond, |
| 691 int force, int calc_cond) const | |
| 458 | 692 { |
| 6207 | 693 Matrix retval; |
| 694 | |
| 695 octave_idx_type nr = rows (); | |
| 696 octave_idx_type nc = cols (); | |
| 697 | |
| 698 if (nr != nc || nr == 0 || nc == 0) | |
| 699 (*current_liboctave_error_handler) ("inverse requires square matrix"); | |
| 700 else | |
| 701 { | |
| 702 int typ = mattype.type (); | |
| 703 char uplo = (typ == MatrixType::Lower ? 'L' : 'U'); | |
| 704 char udiag = 'N'; | |
| 705 retval = *this; | |
| 706 double *tmp_data = retval.fortran_vec (); | |
| 707 | |
| 708 F77_XFCN (dtrtri, DTRTRI, (F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 709 F77_CONST_CHAR_ARG2 (&udiag, 1), | |
| 710 nr, tmp_data, nr, info | |
| 711 F77_CHAR_ARG_LEN (1) | |
| 712 F77_CHAR_ARG_LEN (1))); | |
| 713 | |
|
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714 // Throw-away extra info LAPACK gives so as to not change output. |
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715 rcond = 0.0; |
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716 if (info != 0) |
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717 info = -1; |
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718 else if (calc_cond) |
| 6207 | 719 { |
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720 octave_idx_type dtrcon_info = 0; |
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721 char job = '1'; |
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722 |
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723 OCTAVE_LOCAL_BUFFER (double, work, 3 * nr); |
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724 OCTAVE_LOCAL_BUFFER (octave_idx_type, iwork, nr); |
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725 |
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726 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&job, 1), |
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727 F77_CONST_CHAR_ARG2 (&uplo, 1), |
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728 F77_CONST_CHAR_ARG2 (&udiag, 1), |
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729 nr, tmp_data, nr, rcond, |
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730 work, iwork, dtrcon_info |
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731 F77_CHAR_ARG_LEN (1) |
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732 F77_CHAR_ARG_LEN (1) |
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733 F77_CHAR_ARG_LEN (1))); |
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734 |
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735 if (dtrcon_info != 0) |
| 6207 | 736 info = -1; |
| 737 } | |
| 738 | |
| 739 if (info == -1 && ! force) | |
| 740 retval = *this; // Restore matrix contents. | |
| 741 } | |
| 742 | |
| 743 return retval; | |
| 458 | 744 } |
| 745 | |
| 6207 | 746 |
| 458 | 747 Matrix |
| 6207 | 748 Matrix::finverse (MatrixType &mattype, octave_idx_type& info, double& rcond, |
| 749 int force, int calc_cond) const | |
| 458 | 750 { |
| 1948 | 751 Matrix retval; |
| 752 | |
| 5275 | 753 octave_idx_type nr = rows (); |
| 754 octave_idx_type nc = cols (); | |
| 1948 | 755 |
| 458 | 756 if (nr != nc || nr == 0 || nc == 0) |
| 1948 | 757 (*current_liboctave_error_handler) ("inverse requires square matrix"); |
| 458 | 758 else |
| 759 { | |
| 5275 | 760 Array<octave_idx_type> ipvt (nr); |
| 761 octave_idx_type *pipvt = ipvt.fortran_vec (); | |
| 1948 | 762 |
| 763 retval = *this; | |
| 764 double *tmp_data = retval.fortran_vec (); | |
| 765 | |
| 4329 | 766 Array<double> z(1); |
| 5275 | 767 octave_idx_type lwork = -1; |
| 4329 | 768 |
| 4330 | 769 // Query the optimum work array size. |
| 4329 | 770 F77_XFCN (dgetri, DGETRI, (nc, tmp_data, nr, pipvt, |
| 771 z.fortran_vec (), lwork, info)); | |
| 772 | |
| 5275 | 773 lwork = static_cast<octave_idx_type> (z(0)); |
| 4329 | 774 lwork = (lwork < 2 *nc ? 2*nc : lwork); |
| 775 z.resize (lwork); | |
| 776 double *pz = z.fortran_vec (); | |
| 777 | |
| 778 info = 0; | |
| 779 | |
| 4330 | 780 // Calculate the norm of the matrix, for later use. |
| 4329 | 781 double anorm = 0; |
| 782 if (calc_cond) | |
| 5275 | 783 anorm = retval.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
| 4329 | 784 |
| 785 F77_XFCN (dgetrf, DGETRF, (nc, nc, tmp_data, nr, pipvt, info)); | |
| 1948 | 786 |
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787 // Throw-away extra info LAPACK gives so as to not change output. |
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788 rcond = 0.0; |
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789 if (info != 0) |
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790 info = -1; |
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791 else if (calc_cond) |
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792 { |
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793 octave_idx_type dgecon_info = 0; |
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794 |
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795 // Now calculate the condition number for non-singular matrix. |
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796 char job = '1'; |
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797 Array<octave_idx_type> iz (nc); |
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798 octave_idx_type *piz = iz.fortran_vec (); |
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799 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
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800 nc, tmp_data, nr, anorm, |
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801 rcond, pz, piz, dgecon_info |
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802 F77_CHAR_ARG_LEN (1))); |
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803 |
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804 if (dgecon_info != 0) |
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805 info = -1; |
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806 } |
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807 |
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808 if (info == -1 && ! force) |
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809 retval = *this; // Restore matrix contents. |
| 1948 | 810 else |
| 811 { | |
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812 octave_idx_type dgetri_info = 0; |
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813 |
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814 F77_XFCN (dgetri, DGETRI, (nc, tmp_data, nr, pipvt, |
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815 pz, lwork, dgetri_info)); |
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816 |
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817 if (dgetri_info != 0) |
| 1948 | 818 info = -1; |
| 819 } | |
| 6207 | 820 |
| 821 if (info != 0) | |
| 822 mattype.mark_as_rectangular(); | |
| 458 | 823 } |
| 824 | |
| 1948 | 825 return retval; |
| 458 | 826 } |
| 827 | |
| 740 | 828 Matrix |
| 6207 | 829 Matrix::inverse (MatrixType &mattype, octave_idx_type& info, double& rcond, |
| 830 int force, int calc_cond) const | |
| 831 { | |
| 832 int typ = mattype.type (false); | |
| 833 Matrix ret; | |
| 834 | |
| 835 if (typ == MatrixType::Unknown) | |
| 836 typ = mattype.type (*this); | |
| 837 | |
| 838 if (typ == MatrixType::Upper || typ == MatrixType::Lower) | |
| 839 ret = tinverse (mattype, info, rcond, force, calc_cond); | |
| 6840 | 840 else |
| 6207 | 841 { |
| 842 if (mattype.is_hermitian ()) | |
| 843 { | |
| 6486 | 844 CHOL chol (*this, info, calc_cond); |
| 6207 | 845 if (info == 0) |
| 6486 | 846 { |
| 847 if (calc_cond) | |
| 848 rcond = chol.rcond (); | |
| 849 else | |
| 850 rcond = 1.0; | |
| 851 ret = chol.inverse (); | |
| 852 } | |
| 6207 | 853 else |
| 854 mattype.mark_as_unsymmetric (); | |
| 855 } | |
| 856 | |
| 857 if (!mattype.is_hermitian ()) | |
| 858 ret = finverse(mattype, info, rcond, force, calc_cond); | |
| 6840 | 859 |
| 7033 | 860 if ((mattype.is_hermitian () || calc_cond) && rcond == 0.) |
| 6840 | 861 ret = Matrix (rows (), columns (), octave_Inf); |
| 6207 | 862 } |
| 863 | |
| 864 return ret; | |
| 865 } | |
| 866 | |
| 867 Matrix | |
| 4384 | 868 Matrix::pseudo_inverse (double tol) const |
| 740 | 869 { |
| 3480 | 870 SVD result (*this, SVD::economy); |
| 740 | 871 |
| 872 DiagMatrix S = result.singular_values (); | |
| 873 Matrix U = result.left_singular_matrix (); | |
| 874 Matrix V = result.right_singular_matrix (); | |
| 875 | |
| 876 ColumnVector sigma = S.diag (); | |
| 877 | |
| 5275 | 878 octave_idx_type r = sigma.length () - 1; |
| 879 octave_idx_type nr = rows (); | |
| 880 octave_idx_type nc = cols (); | |
| 740 | 881 |
| 882 if (tol <= 0.0) | |
| 883 { | |
| 884 if (nr > nc) | |
| 885 tol = nr * sigma.elem (0) * DBL_EPSILON; | |
| 886 else | |
| 887 tol = nc * sigma.elem (0) * DBL_EPSILON; | |
| 888 } | |
| 889 | |
| 890 while (r >= 0 && sigma.elem (r) < tol) | |
| 891 r--; | |
| 892 | |
| 893 if (r < 0) | |
| 894 return Matrix (nc, nr, 0.0); | |
| 895 else | |
| 896 { | |
| 897 Matrix Ur = U.extract (0, 0, nr-1, r); | |
| 898 DiagMatrix D = DiagMatrix (sigma.extract (0, r)) . inverse (); | |
| 899 Matrix Vr = V.extract (0, 0, nc-1, r); | |
| 900 return Vr * D * Ur.transpose (); | |
| 901 } | |
| 902 } | |
| 903 | |
| 4773 | 904 #if defined (HAVE_FFTW3) |
| 3827 | 905 |
| 906 ComplexMatrix | |
| 907 Matrix::fourier (void) const | |
| 908 { | |
| 909 size_t nr = rows (); | |
| 910 size_t nc = cols (); | |
| 911 | |
| 912 ComplexMatrix retval (nr, nc); | |
| 913 | |
| 914 size_t npts, nsamples; | |
| 915 | |
| 916 if (nr == 1 || nc == 1) | |
| 917 { | |
| 918 npts = nr > nc ? nr : nc; | |
| 919 nsamples = 1; | |
| 920 } | |
| 921 else | |
| 922 { | |
| 923 npts = nr; | |
| 924 nsamples = nc; | |
| 925 } | |
| 926 | |
| 4773 | 927 const double *in (fortran_vec ()); |
| 3827 | 928 Complex *out (retval.fortran_vec ()); |
| 929 | |
| 4773 | 930 octave_fftw::fft (in, out, npts, nsamples); |
| 3827 | 931 |
| 932 return retval; | |
| 933 } | |
| 934 | |
| 935 ComplexMatrix | |
| 936 Matrix::ifourier (void) const | |
| 937 { | |
| 938 size_t nr = rows (); | |
| 939 size_t nc = cols (); | |
| 940 | |
| 941 ComplexMatrix retval (nr, nc); | |
| 942 | |
| 943 size_t npts, nsamples; | |
| 944 | |
| 945 if (nr == 1 || nc == 1) | |
| 946 { | |
| 947 npts = nr > nc ? nr : nc; | |
| 948 nsamples = 1; | |
| 949 } | |
| 950 else | |
| 951 { | |
| 952 npts = nr; | |
| 953 nsamples = nc; | |
| 954 } | |
| 955 | |
| 956 ComplexMatrix tmp (*this); | |
| 957 Complex *in (tmp.fortran_vec ()); | |
| 958 Complex *out (retval.fortran_vec ()); | |
| 959 | |
| 4773 | 960 octave_fftw::ifft (in, out, npts, nsamples); |
| 3827 | 961 |
| 962 return retval; | |
| 963 } | |
| 964 | |
| 965 ComplexMatrix | |
| 966 Matrix::fourier2d (void) const | |
| 967 { | |
| 4773 | 968 dim_vector dv(rows (), cols ()); |
| 969 | |
| 970 const double *in = fortran_vec (); | |
| 971 ComplexMatrix retval (rows (), cols ()); | |
| 972 octave_fftw::fftNd (in, retval.fortran_vec (), 2, dv); | |
| 3827 | 973 |
| 974 return retval; | |
| 975 } | |
| 976 | |
| 977 ComplexMatrix | |
| 978 Matrix::ifourier2d (void) const | |
| 979 { | |
| 4773 | 980 dim_vector dv(rows (), cols ()); |
| 3827 | 981 |
| 982 ComplexMatrix retval (*this); | |
| 4773 | 983 Complex *out (retval.fortran_vec ()); |
| 984 | |
| 985 octave_fftw::ifftNd (out, out, 2, dv); | |
| 3827 | 986 |
| 987 return retval; | |
| 988 } | |
| 989 | |
| 990 #else | |
| 991 | |
| 458 | 992 ComplexMatrix |
| 993 Matrix::fourier (void) const | |
| 994 { | |
| 1948 | 995 ComplexMatrix retval; |
| 996 | |
| 5275 | 997 octave_idx_type nr = rows (); |
| 998 octave_idx_type nc = cols (); | |
| 999 | |
| 1000 octave_idx_type npts, nsamples; | |
| 1948 | 1001 |
| 458 | 1002 if (nr == 1 || nc == 1) |
| 1003 { | |
| 1004 npts = nr > nc ? nr : nc; | |
| 1005 nsamples = 1; | |
| 1006 } | |
| 1007 else | |
| 1008 { | |
| 1009 npts = nr; | |
| 1010 nsamples = nc; | |
| 1011 } | |
| 1012 | |
| 5275 | 1013 octave_idx_type nn = 4*npts+15; |
| 1948 | 1014 |
| 1015 Array<Complex> wsave (nn); | |
| 1016 Complex *pwsave = wsave.fortran_vec (); | |
| 1017 | |
| 3585 | 1018 retval = ComplexMatrix (*this); |
| 1948 | 1019 Complex *tmp_data = retval.fortran_vec (); |
| 1020 | |
| 3887 | 1021 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
| 458 | 1022 |
| 5275 | 1023 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1024 { |
| 1025 OCTAVE_QUIT; | |
| 1026 | |
| 1027 F77_FUNC (cfftf, CFFTF) (npts, &tmp_data[npts*j], pwsave); | |
| 1028 } | |
| 1948 | 1029 |
| 1030 return retval; | |
| 458 | 1031 } |
| 1032 | |
| 1033 ComplexMatrix | |
| 1034 Matrix::ifourier (void) const | |
| 1035 { | |
| 1948 | 1036 ComplexMatrix retval; |
| 1037 | |
| 5275 | 1038 octave_idx_type nr = rows (); |
| 1039 octave_idx_type nc = cols (); | |
| 1040 | |
| 1041 octave_idx_type npts, nsamples; | |
| 1948 | 1042 |
| 458 | 1043 if (nr == 1 || nc == 1) |
| 1044 { | |
| 1045 npts = nr > nc ? nr : nc; | |
| 1046 nsamples = 1; | |
| 1047 } | |
| 1048 else | |
| 1049 { | |
| 1050 npts = nr; | |
| 1051 nsamples = nc; | |
| 1052 } | |
| 1053 | |
| 5275 | 1054 octave_idx_type nn = 4*npts+15; |
| 1948 | 1055 |
| 1056 Array<Complex> wsave (nn); | |
| 1057 Complex *pwsave = wsave.fortran_vec (); | |
| 1058 | |
| 3585 | 1059 retval = ComplexMatrix (*this); |
| 1948 | 1060 Complex *tmp_data = retval.fortran_vec (); |
| 1061 | |
| 3887 | 1062 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
| 458 | 1063 |
| 5275 | 1064 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1065 { |
| 1066 OCTAVE_QUIT; | |
| 1067 | |
| 1068 F77_FUNC (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave); | |
| 1069 } | |
| 458 | 1070 |
| 5275 | 1071 for (octave_idx_type j = 0; j < npts*nsamples; j++) |
| 3572 | 1072 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
| 458 | 1073 |
| 1948 | 1074 return retval; |
| 458 | 1075 } |
| 1076 | |
| 677 | 1077 ComplexMatrix |
| 1078 Matrix::fourier2d (void) const | |
| 1079 { | |
| 1948 | 1080 ComplexMatrix retval; |
| 1081 | |
| 5275 | 1082 octave_idx_type nr = rows (); |
| 1083 octave_idx_type nc = cols (); | |
| 1084 | |
| 1085 octave_idx_type npts, nsamples; | |
| 1948 | 1086 |
| 677 | 1087 if (nr == 1 || nc == 1) |
| 1088 { | |
| 1089 npts = nr > nc ? nr : nc; | |
| 1090 nsamples = 1; | |
| 1091 } | |
| 1092 else | |
| 1093 { | |
| 1094 npts = nr; | |
| 1095 nsamples = nc; | |
| 1096 } | |
| 1097 | |
| 5275 | 1098 octave_idx_type nn = 4*npts+15; |
| 1948 | 1099 |
| 1100 Array<Complex> wsave (nn); | |
| 1101 Complex *pwsave = wsave.fortran_vec (); | |
| 1102 | |
| 3585 | 1103 retval = ComplexMatrix (*this); |
| 1948 | 1104 Complex *tmp_data = retval.fortran_vec (); |
| 1105 | |
| 3887 | 1106 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
| 677 | 1107 |
| 5275 | 1108 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1109 { |
| 1110 OCTAVE_QUIT; | |
| 1111 | |
| 1112 F77_FUNC (cfftf, CFFTF) (npts, &tmp_data[npts*j], pwsave); | |
| 1113 } | |
| 677 | 1114 |
| 1115 npts = nc; | |
| 1116 nsamples = nr; | |
| 1117 nn = 4*npts+15; | |
| 1948 | 1118 |
| 1119 wsave.resize (nn); | |
| 1120 pwsave = wsave.fortran_vec (); | |
| 1121 | |
| 4773 | 1122 Array<Complex> tmp (npts); |
| 1123 Complex *prow = tmp.fortran_vec (); | |
| 1948 | 1124 |
| 3887 | 1125 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
| 677 | 1126 |
| 5275 | 1127 for (octave_idx_type j = 0; j < nsamples; j++) |
| 677 | 1128 { |
| 4153 | 1129 OCTAVE_QUIT; |
| 1130 | |
| 5275 | 1131 for (octave_idx_type i = 0; i < npts; i++) |
| 1948 | 1132 prow[i] = tmp_data[i*nr + j]; |
| 1133 | |
| 3887 | 1134 F77_FUNC (cfftf, CFFTF) (npts, prow, pwsave); |
| 677 | 1135 |
| 5275 | 1136 for (octave_idx_type i = 0; i < npts; i++) |
| 1948 | 1137 tmp_data[i*nr + j] = prow[i]; |
| 677 | 1138 } |
| 1139 | |
| 1948 | 1140 return retval; |
| 677 | 1141 } |
| 1142 | |
| 1143 ComplexMatrix | |
| 1144 Matrix::ifourier2d (void) const | |
| 1145 { | |
| 1948 | 1146 ComplexMatrix retval; |
| 1147 | |
| 5275 | 1148 octave_idx_type nr = rows (); |
| 1149 octave_idx_type nc = cols (); | |
| 1150 | |
| 1151 octave_idx_type npts, nsamples; | |
| 1948 | 1152 |
| 677 | 1153 if (nr == 1 || nc == 1) |
| 1154 { | |
| 1155 npts = nr > nc ? nr : nc; | |
| 1156 nsamples = 1; | |
| 1157 } | |
| 1158 else | |
| 1159 { | |
| 1160 npts = nr; | |
| 1161 nsamples = nc; | |
| 1162 } | |
| 1163 | |
| 5275 | 1164 octave_idx_type nn = 4*npts+15; |
| 1948 | 1165 |
| 1166 Array<Complex> wsave (nn); | |
| 1167 Complex *pwsave = wsave.fortran_vec (); | |
| 1168 | |
| 3585 | 1169 retval = ComplexMatrix (*this); |
| 1948 | 1170 Complex *tmp_data = retval.fortran_vec (); |
| 1171 | |
| 3887 | 1172 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
| 677 | 1173 |
| 5275 | 1174 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1175 { |
| 1176 OCTAVE_QUIT; | |
| 1177 | |
| 1178 F77_FUNC (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave); | |
| 1179 } | |
| 677 | 1180 |
| 5275 | 1181 for (octave_idx_type j = 0; j < npts*nsamples; j++) |
| 3572 | 1182 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
| 677 | 1183 |
| 1184 npts = nc; | |
| 1185 nsamples = nr; | |
| 1186 nn = 4*npts+15; | |
| 1948 | 1187 |
| 1188 wsave.resize (nn); | |
| 1189 pwsave = wsave.fortran_vec (); | |
| 1190 | |
| 4773 | 1191 Array<Complex> tmp (npts); |
| 1192 Complex *prow = tmp.fortran_vec (); | |
| 1948 | 1193 |
| 3887 | 1194 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
| 677 | 1195 |
| 5275 | 1196 for (octave_idx_type j = 0; j < nsamples; j++) |
| 677 | 1197 { |
| 4153 | 1198 OCTAVE_QUIT; |
| 1199 | |
| 5275 | 1200 for (octave_idx_type i = 0; i < npts; i++) |
| 1948 | 1201 prow[i] = tmp_data[i*nr + j]; |
| 1202 | |
| 3887 | 1203 F77_FUNC (cfftb, CFFTB) (npts, prow, pwsave); |
| 677 | 1204 |
| 5275 | 1205 for (octave_idx_type i = 0; i < npts; i++) |
| 3572 | 1206 tmp_data[i*nr + j] = prow[i] / static_cast<double> (npts); |
| 677 | 1207 } |
| 1208 | |
| 1948 | 1209 return retval; |
| 677 | 1210 } |
| 1211 | |
| 3827 | 1212 #endif |
| 1213 | |
| 458 | 1214 DET |
| 1215 Matrix::determinant (void) const | |
| 1216 { | |
| 5275 | 1217 octave_idx_type info; |
| 458 | 1218 double rcond; |
| 4329 | 1219 return determinant (info, rcond, 0); |
| 458 | 1220 } |
| 1221 | |
| 1222 DET | |
| 5275 | 1223 Matrix::determinant (octave_idx_type& info) const |
| 458 | 1224 { |
| 1225 double rcond; | |
| 4329 | 1226 return determinant (info, rcond, 0); |
| 458 | 1227 } |
| 1228 | |
| 1229 DET | |
| 5275 | 1230 Matrix::determinant (octave_idx_type& info, double& rcond, int calc_cond) const |
| 458 | 1231 { |
| 1232 DET retval; | |
| 1233 | |
| 5275 | 1234 octave_idx_type nr = rows (); |
| 1235 octave_idx_type nc = cols (); | |
| 458 | 1236 |
| 1237 if (nr == 0 || nc == 0) | |
| 1238 { | |
| 5634 | 1239 retval = DET (1.0, 0); |
| 458 | 1240 } |
| 1241 else | |
| 1242 { | |
| 5275 | 1243 Array<octave_idx_type> ipvt (nr); |
| 1244 octave_idx_type *pipvt = ipvt.fortran_vec (); | |
| 1948 | 1245 |
| 1246 Matrix atmp = *this; | |
| 1247 double *tmp_data = atmp.fortran_vec (); | |
| 1248 | |
| 4329 | 1249 info = 0; |
| 1250 | |
| 4330 | 1251 // Calculate the norm of the matrix, for later use. |
| 4329 | 1252 double anorm = 0; |
| 1253 if (calc_cond) | |
| 5275 | 1254 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
| 4329 | 1255 |
| 1256 F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); | |
| 1948 | 1257 |
|
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1258 // Throw-away extra info LAPACK gives so as to not change output. |
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1259 rcond = 0.0; |
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1260 if (info != 0) |
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1261 { |
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1262 info = -1; |
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1263 retval = DET (); |
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1264 } |
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1265 else |
| 458 | 1266 { |
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1267 if (calc_cond) |
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1268 { |
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1269 // Now calc the condition number for non-singular matrix. |
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1270 char job = '1'; |
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1271 Array<double> z (4 * nc); |
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1272 double *pz = z.fortran_vec (); |
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1273 Array<octave_idx_type> iz (nc); |
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1274 octave_idx_type *piz = iz.fortran_vec (); |
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1275 |
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1276 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
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1277 nc, tmp_data, nr, anorm, |
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1278 rcond, pz, piz, info |
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1279 F77_CHAR_ARG_LEN (1))); |
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1280 } |
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1281 |
| 4509 | 1282 if (info != 0) |
| 1948 | 1283 { |
| 4509 | 1284 info = -1; |
| 1285 retval = DET (); | |
| 4329 | 1286 } |
| 1287 else | |
| 1948 | 1288 { |
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1289 double c = 1.0; |
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1290 int e = 0; |
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1291 |
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1292 for (octave_idx_type i = 0; i < nc; i++) |
| 4329 | 1293 { |
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1294 if (ipvt(i) != (i+1)) |
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1295 c = -c; |
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1296 |
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1297 c *= atmp(i,i); |
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1298 |
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1299 if (c == 0.0) |
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1300 break; |
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1301 |
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1302 while (fabs (c) < 0.5) |
| 4329 | 1303 { |
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1304 c *= 2.0; |
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1305 e--; |
| 4329 | 1306 } |
| 5634 | 1307 |
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|
1308 while (fabs (c) >= 2.0) |
|
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|
1309 { |
|
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1310 c /= 2.0; |
|
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1311 e++; |
|
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|
1312 } |
| 4329 | 1313 } |
|
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|
1314 |
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|
1315 retval = DET (c, e); |
| 1948 | 1316 } |
| 458 | 1317 } |
| 1318 } | |
| 1319 | |
| 1320 return retval; | |
| 1321 } | |
| 1322 | |
| 1323 Matrix | |
| 5785 | 1324 Matrix::utsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, |
| 1325 double& rcond, solve_singularity_handler sing_handler, | |
| 1326 bool calc_cond) const | |
| 1327 { | |
| 1328 Matrix retval; | |
| 1329 | |
| 1330 octave_idx_type nr = rows (); | |
| 1331 octave_idx_type nc = cols (); | |
| 1332 | |
| 6924 | 1333 if (nr != b.rows ()) |
| 5785 | 1334 (*current_liboctave_error_handler) |
| 1335 ("matrix dimension mismatch solution of linear equations"); | |
| 6924 | 1336 else if (nr == 0 || nc == 0 || b.cols () == 0) |
| 1337 retval = Matrix (nc, b.cols (), 0.0); | |
| 5785 | 1338 else |
| 1339 { | |
| 1340 volatile int typ = mattype.type (); | |
| 1341 | |
| 1342 if (typ == MatrixType::Permuted_Upper || | |
| 1343 typ == MatrixType::Upper) | |
| 1344 { | |
| 1345 octave_idx_type b_nc = b.cols (); | |
| 1346 rcond = 1.; | |
| 1347 info = 0; | |
| 1348 | |
| 1349 if (typ == MatrixType::Permuted_Upper) | |
| 1350 { | |
| 1351 (*current_liboctave_error_handler) | |
| 6390 | 1352 ("permuted triangular matrix not implemented"); |
| 5785 | 1353 } |
| 1354 else | |
| 1355 { | |
| 1356 const double *tmp_data = fortran_vec (); | |
| 1357 | |
| 1358 if (calc_cond) | |
| 1359 { | |
| 1360 char norm = '1'; | |
| 1361 char uplo = 'U'; | |
| 1362 char dia = 'N'; | |
| 1363 | |
| 1364 Array<double> z (3 * nc); | |
| 1365 double *pz = z.fortran_vec (); | |
| 1366 Array<octave_idx_type> iz (nc); | |
| 1367 octave_idx_type *piz = iz.fortran_vec (); | |
| 1368 | |
| 1369 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1370 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1371 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1372 nr, tmp_data, nr, rcond, | |
| 1373 pz, piz, info | |
| 1374 F77_CHAR_ARG_LEN (1) | |
| 1375 F77_CHAR_ARG_LEN (1) | |
| 1376 F77_CHAR_ARG_LEN (1))); | |
| 1377 | |
| 1378 if (info != 0) | |
| 1379 info = -2; | |
| 1380 | |
| 1381 volatile double rcond_plus_one = rcond + 1.0; | |
| 1382 | |
| 1383 if (rcond_plus_one == 1.0 || xisnan (rcond)) | |
| 1384 { | |
| 1385 info = -2; | |
| 1386 | |
| 1387 if (sing_handler) | |
| 1388 sing_handler (rcond); | |
| 1389 else | |
| 1390 (*current_liboctave_error_handler) | |
| 1391 ("matrix singular to machine precision, rcond = %g", | |
| 1392 rcond); | |
| 1393 } | |
| 1394 } | |
| 1395 | |
| 1396 if (info == 0) | |
| 1397 { | |
| 1398 retval = b; | |
| 1399 double *result = retval.fortran_vec (); | |
| 1400 | |
| 1401 char uplo = 'U'; | |
| 1402 char trans = 'N'; | |
| 1403 char dia = 'N'; | |
| 1404 | |
| 1405 F77_XFCN (dtrtrs, DTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1406 F77_CONST_CHAR_ARG2 (&trans, 1), | |
| 1407 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1408 nr, b_nc, tmp_data, nr, | |
| 1409 result, nr, info | |
| 1410 F77_CHAR_ARG_LEN (1) | |
| 1411 F77_CHAR_ARG_LEN (1) | |
| 1412 F77_CHAR_ARG_LEN (1))); | |
| 1413 } | |
| 1414 } | |
| 1415 } | |
| 1416 else | |
| 1417 (*current_liboctave_error_handler) ("incorrect matrix type"); | |
| 1418 } | |
| 1419 | |
| 1420 return retval; | |
| 1421 } | |
| 1422 | |
| 1423 Matrix | |
| 1424 Matrix::ltsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, | |
| 1425 double& rcond, solve_singularity_handler sing_handler, | |
| 1426 bool calc_cond) const | |
| 1427 { | |
| 1428 Matrix retval; | |
| 1429 | |
| 1430 octave_idx_type nr = rows (); | |
| 1431 octave_idx_type nc = cols (); | |
| 1432 | |
| 6924 | 1433 if (nr != b.rows ()) |
| 5785 | 1434 (*current_liboctave_error_handler) |
| 1435 ("matrix dimension mismatch solution of linear equations"); | |
| 6924 | 1436 else if (nr == 0 || nc == 0 || b.cols () == 0) |
| 1437 retval = Matrix (nc, b.cols (), 0.0); | |
| 5785 | 1438 else |
| 1439 { | |
| 1440 volatile int typ = mattype.type (); | |
| 1441 | |
| 1442 if (typ == MatrixType::Permuted_Lower || | |
| 1443 typ == MatrixType::Lower) | |
| 1444 { | |
| 1445 octave_idx_type b_nc = b.cols (); | |
| 1446 rcond = 1.; | |
| 1447 info = 0; | |
| 1448 | |
| 1449 if (typ == MatrixType::Permuted_Lower) | |
| 1450 { | |
| 1451 (*current_liboctave_error_handler) | |
| 6390 | 1452 ("permuted triangular matrix not implemented"); |
| 5785 | 1453 } |
| 1454 else | |
| 1455 { | |
| 1456 const double *tmp_data = fortran_vec (); | |
| 1457 | |
| 1458 if (calc_cond) | |
| 1459 { | |
| 1460 char norm = '1'; | |
| 1461 char uplo = 'L'; | |
| 1462 char dia = 'N'; | |
| 1463 | |
| 1464 Array<double> z (3 * nc); | |
| 1465 double *pz = z.fortran_vec (); | |
| 1466 Array<octave_idx_type> iz (nc); | |
| 1467 octave_idx_type *piz = iz.fortran_vec (); | |
| 1468 | |
| 1469 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1470 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1471 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1472 nr, tmp_data, nr, rcond, | |
| 1473 pz, piz, info | |
| 1474 F77_CHAR_ARG_LEN (1) | |
| 1475 F77_CHAR_ARG_LEN (1) | |
| 1476 F77_CHAR_ARG_LEN (1))); | |
| 1477 | |
| 1478 if (info != 0) | |
| 1479 info = -2; | |
| 1480 | |
| 1481 volatile double rcond_plus_one = rcond + 1.0; | |
| 1482 | |
| 1483 if (rcond_plus_one == 1.0 || xisnan (rcond)) | |
| 1484 { | |
| 1485 info = -2; | |
| 1486 | |
| 1487 if (sing_handler) | |
| 1488 sing_handler (rcond); | |
| 1489 else | |
| 1490 (*current_liboctave_error_handler) | |
| 1491 ("matrix singular to machine precision, rcond = %g", | |
| 1492 rcond); | |
| 1493 } | |
| 1494 } | |
| 1495 | |
| 1496 if (info == 0) | |
| 1497 { | |
| 1498 retval = b; | |
| 1499 double *result = retval.fortran_vec (); | |
| 1500 | |
| 1501 char uplo = 'L'; | |
| 1502 char trans = 'N'; | |
| 1503 char dia = 'N'; | |
| 1504 | |
| 1505 F77_XFCN (dtrtrs, DTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1506 F77_CONST_CHAR_ARG2 (&trans, 1), | |
| 1507 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1508 nr, b_nc, tmp_data, nr, | |
| 1509 result, nr, info | |
| 1510 F77_CHAR_ARG_LEN (1) | |
| 1511 F77_CHAR_ARG_LEN (1) | |
| 1512 F77_CHAR_ARG_LEN (1))); | |
| 1513 } | |
| 1514 } | |
| 1515 } | |
| 1516 else | |
| 1517 (*current_liboctave_error_handler) ("incorrect matrix type"); | |
| 1518 } | |
| 1519 | |
| 1520 return retval; | |
| 1521 } | |
| 1522 | |
| 1523 Matrix | |
| 1524 Matrix::fsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, | |
| 1525 double& rcond, solve_singularity_handler sing_handler, | |
| 1526 bool calc_cond) const | |
| 1527 { | |
| 1528 Matrix retval; | |
| 1529 | |
| 1530 octave_idx_type nr = rows (); | |
| 1531 octave_idx_type nc = cols (); | |
| 1532 | |
| 6924 | 1533 if (nr != nc || nr != b.rows ()) |
| 5785 | 1534 (*current_liboctave_error_handler) |
| 1535 ("matrix dimension mismatch solution of linear equations"); | |
| 6924 | 1536 else if (nr == 0 || b.cols () == 0) |
| 1537 retval = Matrix (nc, b.cols (), 0.0); | |
| 5785 | 1538 else |
| 1539 { | |
| 1540 volatile int typ = mattype.type (); | |
| 1541 | |
| 1542 // Calculate the norm of the matrix, for later use. | |
| 1543 double anorm = -1.; | |
| 1544 | |
| 1545 if (typ == MatrixType::Hermitian) | |
| 1546 { | |
| 1547 info = 0; | |
| 1548 char job = 'L'; | |
| 1549 Matrix atmp = *this; | |
| 1550 double *tmp_data = atmp.fortran_vec (); | |
| 1551 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); | |
| 1552 | |
| 1553 F77_XFCN (dpotrf, DPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, | |
| 1554 tmp_data, nr, info | |
| 1555 F77_CHAR_ARG_LEN (1))); | |
| 1556 | |
|
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|
1557 // Throw-away extra info LAPACK gives so as to not change output. |
|
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1558 rcond = 0.0; |
|
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1559 if (info != 0) |
|
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|
1560 { |
|
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|
1561 info = -2; |
|
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|
1562 |
|
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|
1563 mattype.mark_as_unsymmetric (); |
|
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1564 typ = MatrixType::Full; |
|
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|
1565 } |
|
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|
1566 else |
| 5785 | 1567 { |
|
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|
1568 if (calc_cond) |
| 5785 | 1569 { |
|
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|
1570 Array<double> z (3 * nc); |
|
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|
1571 double *pz = z.fortran_vec (); |
|
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1572 Array<octave_idx_type> iz (nc); |
|
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1573 octave_idx_type *piz = iz.fortran_vec (); |
|
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|
1574 |
|
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changeset
|
1575 F77_XFCN (dpocon, DPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
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1576 nr, tmp_data, nr, anorm, |
|
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|
1577 rcond, pz, piz, info |
|
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|
1578 F77_CHAR_ARG_LEN (1))); |
|
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|
1579 |
|
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|
1580 if (info != 0) |
|
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|
1581 info = -2; |
|
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|
1582 |
|
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|
1583 volatile double rcond_plus_one = rcond + 1.0; |
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|
1584 |
|
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|
1585 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
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|
1586 { |
|
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|
1587 info = -2; |
|
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|
1588 |
|
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|
1589 if (sing_handler) |
|
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1590 sing_handler (rcond); |
|
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1591 else |
|
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|
1592 (*current_liboctave_error_handler) |
|
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|
1593 ("matrix singular to machine precision, rcond = %g", |
|
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|
1594 rcond); |
|
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|
1595 } |
|
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|
1596 } |
|
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|
1597 |
|
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|
1598 if (info == 0) |
|
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|
1599 { |
|
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1600 retval = b; |
|
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|
1601 double *result = retval.fortran_vec (); |
|
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|
1602 |
|
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|
1603 octave_idx_type b_nc = b.cols (); |
|
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|
1604 |
|
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|
1605 F77_XFCN (dpotrs, DPOTRS, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
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|
1606 nr, b_nc, tmp_data, nr, |
|
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|
1607 result, b.rows(), info |
|
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|
1608 F77_CHAR_ARG_LEN (1))); |
|
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1609 } |
|
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|
1610 else |
|
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|
1611 { |
| 5785 | 1612 mattype.mark_as_unsymmetric (); |
| 1613 typ = MatrixType::Full; | |
|
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|
1614 } |
| 5785 | 1615 } |
| 1616 } | |
| 1617 | |
| 1618 if (typ == MatrixType::Full) | |
| 1619 { | |
| 1620 info = 0; | |
| 1621 | |
| 1622 Array<octave_idx_type> ipvt (nr); | |
| 1623 octave_idx_type *pipvt = ipvt.fortran_vec (); | |
| 1624 | |
| 1625 Matrix atmp = *this; | |
| 1626 double *tmp_data = atmp.fortran_vec (); | |
| 1627 if(anorm < 0.) | |
| 1628 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); | |
| 1629 | |
| 1630 Array<double> z (4 * nc); | |
| 1631 double *pz = z.fortran_vec (); | |
| 1632 Array<octave_idx_type> iz (nc); | |
| 1633 octave_idx_type *piz = iz.fortran_vec (); | |
| 1634 | |
| 1635 F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); | |
| 1636 | |
|
7482
29980c6b8604
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changeset
|
1637 // Throw-away extra info LAPACK gives so as to not change output. |
|
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|
1638 rcond = 0.0; |
|
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|
1639 if (info != 0) |
| 5785 | 1640 { |
|
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changeset
|
1641 info = -2; |
|
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diff
changeset
|
1642 |
|
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changeset
|
1643 if (sing_handler) |
|
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diff
changeset
|
1644 sing_handler (rcond); |
|
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don't check f77_exception_encountered
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diff
changeset
|
1645 else |
|
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diff
changeset
|
1646 (*current_liboctave_error_handler) |
|
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|
1647 ("matrix singular to machine precision"); |
|
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diff
changeset
|
1648 |
|
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diff
changeset
|
1649 mattype.mark_as_rectangular (); |
|
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|
1650 } |
|
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diff
changeset
|
1651 else |
|
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changeset
|
1652 { |
|
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changeset
|
1653 if (calc_cond) |
| 5785 | 1654 { |
|
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|
1655 // Now calculate the condition number for |
|
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|
1656 // non-singular matrix. |
|
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|
1657 char job = '1'; |
|
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changeset
|
1658 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
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|
1659 nc, tmp_data, nr, anorm, |
|
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|
1660 rcond, pz, piz, info |
|
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|
1661 F77_CHAR_ARG_LEN (1))); |
|
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changeset
|
1662 |
|
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|
1663 if (info != 0) |
|
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|
1664 info = -2; |
|
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changeset
|
1665 |
|
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|
1666 volatile double rcond_plus_one = rcond + 1.0; |
|
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|
1667 |
|
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changeset
|
1668 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
| 5785 | 1669 { |
|
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|
1670 info = -2; |
|
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changeset
|
1671 |
|
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changeset
|
1672 if (sing_handler) |
|
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changeset
|
1673 sing_handler (rcond); |
|
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changeset
|
1674 else |
|
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|
1675 (*current_liboctave_error_handler) |
|
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|
1676 ("matrix singular to machine precision, rcond = %g", |
|
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changeset
|
1677 rcond); |
| 5785 | 1678 } |
| 1679 } | |
|
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changeset
|
1680 |
|
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changeset
|
1681 if (info == 0) |
|
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changeset
|
1682 { |
|
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|
1683 retval = b; |
|
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|
1684 double *result = retval.fortran_vec (); |
|
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changeset
|
1685 |
|
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changeset
|
1686 octave_idx_type b_nc = b.cols (); |
|
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changeset
|
1687 |
|
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changeset
|
1688 char job = 'N'; |
|
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diff
changeset
|
1689 F77_XFCN (dgetrs, DGETRS, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
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changeset
|
1690 nr, b_nc, tmp_data, nr, |
|
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diff
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|
1691 pipvt, result, b.rows(), info |
|
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changeset
|
1692 F77_CHAR_ARG_LEN (1))); |
|
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changeset
|
1693 } |
|
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diff
changeset
|
1694 else |
|
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changeset
|
1695 mattype.mark_as_rectangular (); |
| 5785 | 1696 } |
| 1697 } | |
| 1698 else if (typ != MatrixType::Hermitian) | |
| 1699 (*current_liboctave_error_handler) ("incorrect matrix type"); | |
| 1700 } | |
| 1701 | |
| 1702 return retval; | |
| 1703 } | |
| 1704 | |
| 1705 Matrix | |
| 1706 Matrix::solve (MatrixType &typ, const Matrix& b) const | |
| 1707 { | |
| 1708 octave_idx_type info; | |
| 1709 double rcond; | |
| 1710 return solve (typ, b, info, rcond, 0); | |
| 1711 } | |
| 1712 | |
| 1713 Matrix | |
| 1714 Matrix::solve (MatrixType &typ, const Matrix& b, octave_idx_type& info, | |
| 1715 double& rcond) const | |
| 1716 { | |
| 1717 return solve (typ, b, info, rcond, 0); | |
| 1718 } | |
| 1719 | |
| 1720 Matrix | |
| 1721 Matrix::solve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, | |
| 1722 double& rcond, solve_singularity_handler sing_handler, | |
| 1723 bool singular_fallback) const | |
| 1724 { | |
| 1725 Matrix retval; | |
| 1726 int typ = mattype.type (); | |
| 1727 | |
| 1728 if (typ == MatrixType::Unknown) | |
| 1729 typ = mattype.type (*this); | |
| 1730 | |
| 1731 // Only calculate the condition number for LU/Cholesky | |
| 1732 if (typ == MatrixType::Upper || typ == MatrixType::Permuted_Upper) | |
| 1733 retval = utsolve (mattype, b, info, rcond, sing_handler, false); | |
| 1734 else if (typ == MatrixType::Lower || typ == MatrixType::Permuted_Lower) | |
| 1735 retval = ltsolve (mattype, b, info, rcond, sing_handler, false); | |
| 1736 else if (typ == MatrixType::Full || typ == MatrixType::Hermitian) | |
| 1737 retval = fsolve (mattype, b, info, rcond, sing_handler, true); | |
| 1738 else if (typ != MatrixType::Rectangular) | |
| 1739 { | |
| 1740 (*current_liboctave_error_handler) ("unknown matrix type"); | |
| 1741 return Matrix (); | |
| 1742 } | |
| 1743 | |
| 1744 // Rectangular or one of the above solvers flags a singular matrix | |
| 1745 if (singular_fallback && mattype.type () == MatrixType::Rectangular) | |
| 1746 { | |
| 1747 octave_idx_type rank; | |
| 7076 | 1748 retval = lssolve (b, info, rank, rcond); |
| 5785 | 1749 } |
| 1750 | |
| 1751 return retval; | |
| 1752 } | |
| 1753 | |
| 1754 ComplexMatrix | |
| 1755 Matrix::solve (MatrixType &typ, const ComplexMatrix& b) const | |
| 1756 { | |
| 1757 ComplexMatrix tmp (*this); | |
| 1758 return tmp.solve (typ, b); | |
| 1759 } | |
| 1760 | |
| 1761 ComplexMatrix | |
| 1762 Matrix::solve (MatrixType &typ, const ComplexMatrix& b, | |
| 1763 octave_idx_type& info) const | |
| 1764 { | |
| 1765 ComplexMatrix tmp (*this); | |
| 1766 return tmp.solve (typ, b, info); | |
| 1767 } | |
| 1768 | |
| 1769 ComplexMatrix | |
| 1770 Matrix::solve (MatrixType &typ, const ComplexMatrix& b, octave_idx_type& info, | |
| 1771 double& rcond) const | |
| 1772 { | |
| 1773 ComplexMatrix tmp (*this); | |
| 1774 return tmp.solve (typ, b, info, rcond); | |
| 1775 } | |
| 1776 | |
| 1777 ComplexMatrix | |
| 1778 Matrix::solve (MatrixType &typ, const ComplexMatrix& b, octave_idx_type& info, | |
| 1779 double& rcond, solve_singularity_handler sing_handler, | |
| 1780 bool singular_fallback) const | |
| 1781 { | |
| 1782 ComplexMatrix tmp (*this); | |
| 1783 return tmp.solve (typ, b, info, rcond, sing_handler, singular_fallback); | |
| 1784 } | |
| 1785 | |
| 1786 ColumnVector | |
| 1787 Matrix::solve (MatrixType &typ, const ColumnVector& b) const | |
| 1788 { | |
| 1789 octave_idx_type info; double rcond; | |
| 1790 return solve (typ, b, info, rcond); | |
| 1791 } | |
| 1792 | |
| 1793 ColumnVector | |
| 1794 Matrix::solve (MatrixType &typ, const ColumnVector& b, | |
| 1795 octave_idx_type& info) const | |
| 1796 { | |
| 1797 double rcond; | |
| 1798 return solve (typ, b, info, rcond); | |
| 1799 } | |
| 1800 | |
| 1801 ColumnVector | |
| 1802 Matrix::solve (MatrixType &typ, const ColumnVector& b, octave_idx_type& info, | |
| 1803 double& rcond) const | |
| 1804 { | |
| 1805 return solve (typ, b, info, rcond, 0); | |
| 1806 } | |
| 1807 | |
| 1808 ColumnVector | |
| 1809 Matrix::solve (MatrixType &typ, const ColumnVector& b, octave_idx_type& info, | |
| 1810 double& rcond, solve_singularity_handler sing_handler) const | |
| 1811 { | |
| 1812 Matrix tmp (b); | |
| 1813 return solve (typ, tmp, info, rcond, sing_handler).column(static_cast<octave_idx_type> (0)); | |
| 1814 } | |
| 1815 | |
| 1816 ComplexColumnVector | |
| 1817 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b) const | |
| 1818 { | |
| 1819 ComplexMatrix tmp (*this); | |
| 1820 return tmp.solve (typ, b); | |
| 1821 } | |
| 1822 | |
| 1823 ComplexColumnVector | |
| 1824 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, | |
| 1825 octave_idx_type& info) const | |
| 1826 { | |
| 1827 ComplexMatrix tmp (*this); | |
| 1828 return tmp.solve (typ, b, info); | |
| 1829 } | |
| 1830 | |
| 1831 ComplexColumnVector | |
| 1832 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, | |
| 1833 octave_idx_type& info, double& rcond) const | |
| 1834 { | |
| 1835 ComplexMatrix tmp (*this); | |
| 1836 return tmp.solve (typ, b, info, rcond); | |
| 1837 } | |
| 1838 | |
| 1839 ComplexColumnVector | |
| 1840 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, | |
| 1841 octave_idx_type& info, double& rcond, | |
| 1842 solve_singularity_handler sing_handler) const | |
| 1843 { | |
| 1844 ComplexMatrix tmp (*this); | |
| 1845 return tmp.solve(typ, b, info, rcond, sing_handler); | |
| 1846 } | |
| 1847 | |
| 1848 Matrix | |
| 458 | 1849 Matrix::solve (const Matrix& b) const |
| 1850 { | |
| 5275 | 1851 octave_idx_type info; |
| 458 | 1852 double rcond; |
| 4329 | 1853 return solve (b, info, rcond, 0); |
| 458 | 1854 } |
| 1855 | |
| 1856 Matrix | |
| 5275 | 1857 Matrix::solve (const Matrix& b, octave_idx_type& info) const |
| 458 | 1858 { |
| 1859 double rcond; | |
| 4329 | 1860 return solve (b, info, rcond, 0); |
| 458 | 1861 } |
| 1862 | |
| 1863 Matrix | |
| 5275 | 1864 Matrix::solve (const Matrix& b, octave_idx_type& info, double& rcond) const |
| 458 | 1865 { |
| 3480 | 1866 return solve (b, info, rcond, 0); |
| 1867 } | |
| 1868 | |
| 1869 Matrix | |
| 5785 | 1870 Matrix::solve (const Matrix& b, octave_idx_type& info, |
| 1871 double& rcond, solve_singularity_handler sing_handler) const | |
| 3480 | 1872 { |
| 5785 | 1873 MatrixType mattype (*this); |
| 1874 return solve (mattype, b, info, rcond, sing_handler); | |
| 458 | 1875 } |
| 1876 | |
| 1877 ComplexMatrix | |
| 1878 Matrix::solve (const ComplexMatrix& b) const | |
| 1879 { | |
| 1880 ComplexMatrix tmp (*this); | |
| 1881 return tmp.solve (b); | |
| 1882 } | |
| 1883 | |
| 1884 ComplexMatrix | |
| 5275 | 1885 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info) const |
| 458 | 1886 { |
| 1887 ComplexMatrix tmp (*this); | |
| 1888 return tmp.solve (b, info); | |
| 1889 } | |
| 1890 | |
| 1891 ComplexMatrix | |
| 5275 | 1892 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcond) const |
| 458 | 1893 { |
| 1894 ComplexMatrix tmp (*this); | |
| 1895 return tmp.solve (b, info, rcond); | |
| 1896 } | |
| 1897 | |
| 3480 | 1898 ComplexMatrix |
| 5275 | 1899 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcond, |
| 3480 | 1900 solve_singularity_handler sing_handler) const |
| 1901 { | |
| 1902 ComplexMatrix tmp (*this); | |
| 1903 return tmp.solve (b, info, rcond, sing_handler); | |
| 1904 } | |
| 1905 | |
| 458 | 1906 ColumnVector |
| 1907 Matrix::solve (const ColumnVector& b) const | |
| 1908 { | |
| 5275 | 1909 octave_idx_type info; double rcond; |
| 458 | 1910 return solve (b, info, rcond); |
| 1911 } | |
| 1912 | |
| 1913 ColumnVector | |
| 5275 | 1914 Matrix::solve (const ColumnVector& b, octave_idx_type& info) const |
| 458 | 1915 { |
| 1916 double rcond; | |
| 1917 return solve (b, info, rcond); | |
| 1918 } | |
| 1919 | |
| 1920 ColumnVector | |
| 5275 | 1921 Matrix::solve (const ColumnVector& b, octave_idx_type& info, double& rcond) const |
| 458 | 1922 { |
| 3480 | 1923 return solve (b, info, rcond, 0); |
| 1924 } | |
| 1925 | |
| 1926 ColumnVector | |
| 5275 | 1927 Matrix::solve (const ColumnVector& b, octave_idx_type& info, double& rcond, |
| 3480 | 1928 solve_singularity_handler sing_handler) const |
| 1929 { | |
| 5785 | 1930 MatrixType mattype (*this); |
| 1931 return solve (mattype, b, info, rcond, sing_handler); | |
| 458 | 1932 } |
| 1933 | |
| 1934 ComplexColumnVector | |
| 1935 Matrix::solve (const ComplexColumnVector& b) const | |
| 1936 { | |
| 1937 ComplexMatrix tmp (*this); | |
| 1938 return tmp.solve (b); | |
| 1939 } | |
| 1940 | |
| 1941 ComplexColumnVector | |
| 5275 | 1942 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info) const |
| 458 | 1943 { |
| 1944 ComplexMatrix tmp (*this); | |
| 1945 return tmp.solve (b, info); | |
| 1946 } | |
| 1947 | |
| 1948 ComplexColumnVector | |
| 5275 | 1949 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info, double& rcond) const |
| 458 | 1950 { |
| 1951 ComplexMatrix tmp (*this); | |
| 1952 return tmp.solve (b, info, rcond); | |
| 1953 } | |
| 1954 | |
| 3480 | 1955 ComplexColumnVector |
| 5275 | 1956 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info, double& rcond, |
| 3480 | 1957 solve_singularity_handler sing_handler) const |
| 1958 { | |
| 1959 ComplexMatrix tmp (*this); | |
| 1960 return tmp.solve (b, info, rcond, sing_handler); | |
| 1961 } | |
| 1962 | |
| 458 | 1963 Matrix |
| 1964 Matrix::lssolve (const Matrix& b) const | |
| 1965 { | |
| 5275 | 1966 octave_idx_type info; |
| 1967 octave_idx_type rank; | |
| 7076 | 1968 double rcond; |
| 1969 return lssolve (b, info, rank, rcond); | |
| 458 | 1970 } |
| 1971 | |
| 1972 Matrix | |
| 5275 | 1973 Matrix::lssolve (const Matrix& b, octave_idx_type& info) const |
| 458 | 1974 { |
| 5275 | 1975 octave_idx_type rank; |
| 7076 | 1976 double rcond; |
| 1977 return lssolve (b, info, rank, rcond); | |
| 458 | 1978 } |
| 1979 | |
| 1980 Matrix | |
| 7072 | 1981 Matrix::lssolve (const Matrix& b, octave_idx_type& info, |
| 1982 octave_idx_type& rank) const | |
| 458 | 1983 { |
| 7076 | 1984 double rcond; |
| 1985 return lssolve (b, info, rank, rcond); | |
| 1986 } | |
| 1987 | |
| 1988 Matrix | |
| 1989 Matrix::lssolve (const Matrix& b, octave_idx_type& info, | |
| 1990 octave_idx_type& rank, double &rcond) const | |
| 1991 { | |
| 1948 | 1992 Matrix retval; |
| 1993 | |
| 5275 | 1994 octave_idx_type nrhs = b.cols (); |
| 1995 | |
| 1996 octave_idx_type m = rows (); | |
| 1997 octave_idx_type n = cols (); | |
| 458 | 1998 |
| 6924 | 1999 if (m != b.rows ()) |
| 1948 | 2000 (*current_liboctave_error_handler) |
| 6924 | 2001 ("matrix dimension mismatch solution of linear equations"); |
| 2002 else if (m == 0 || n == 0 || b.cols () == 0) | |
| 2003 retval = Matrix (n, b.cols (), 0.0); | |
| 1948 | 2004 else |
| 458 | 2005 { |
| 7072 | 2006 volatile octave_idx_type minmn = (m < n ? m : n); |
| 2007 octave_idx_type maxmn = m > n ? m : n; | |
| 7076 | 2008 rcond = -1.0; |
| 7072 | 2009 if (m != n) |
| 2010 { | |
| 2011 retval = Matrix (maxmn, nrhs, 0.0); | |
| 2012 | |
| 2013 for (octave_idx_type j = 0; j < nrhs; j++) | |
| 2014 for (octave_idx_type i = 0; i < m; i++) | |
| 2015 retval.elem (i, j) = b.elem (i, j); | |
| 2016 } | |
| 2017 else | |
| 2018 retval = b; | |
| 2019 | |
| 1948 | 2020 Matrix atmp = *this; |
| 2021 double *tmp_data = atmp.fortran_vec (); | |
| 2022 | |
| 7072 | 2023 double *pretval = retval.fortran_vec (); |
| 2024 Array<double> s (minmn); | |
| 7071 | 2025 double *ps = s.fortran_vec (); |
| 1948 | 2026 |
| 7072 | 2027 // Ask DGELSD what the dimension of WORK should be. |
| 5275 | 2028 octave_idx_type lwork = -1; |
| 3752 | 2029 |
| 2030 Array<double> work (1); | |
| 1948 | 2031 |
| 7477 | 2032 octave_idx_type smlsiz; |
| 2033 F77_FUNC (xilaenv, XILAENV) (9, F77_CONST_CHAR_ARG2 ("DGELSD", 6), | |
| 2034 F77_CONST_CHAR_ARG2 (" ", 1), | |
| 7478 | 2035 0, 0, 0, 0, smlsiz |
| 7477 | 2036 F77_CHAR_ARG_LEN (6) |
| 7478 | 2037 F77_CHAR_ARG_LEN (1)); |
| 7079 | 2038 |
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2039 octave_idx_type mnthr; |
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2040 F77_FUNC (xilaenv, XILAENV) (6, F77_CONST_CHAR_ARG2 ("DGELSD", 6), |
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2041 F77_CONST_CHAR_ARG2 (" ", 1), |
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2042 m, n, nrhs, -1, mnthr |
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2043 F77_CHAR_ARG_LEN (6) |
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2044 F77_CHAR_ARG_LEN (1)); |
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2045 |
| 7079 | 2046 // We compute the size of iwork because DGELSD in older versions |
| 2047 // of LAPACK does not return it on a query call. | |
| 7124 | 2048 double dminmn = static_cast<double> (minmn); |
| 2049 double dsmlsizp1 = static_cast<double> (smlsiz+1); | |
| 7079 | 2050 #if defined (HAVE_LOG2) |
| 7367 | 2051 double tmp = log2 (dminmn / dsmlsizp1); |
| 7079 | 2052 #else |
| 7367 | 2053 double tmp = log (dminmn / dsmlsizp1) / log (2.0); |
| 7079 | 2054 #endif |
| 7367 | 2055 octave_idx_type nlvl = static_cast<int> (tmp) + 1; |
| 7079 | 2056 if (nlvl < 0) |
| 2057 nlvl = 0; | |
| 2058 | |
| 2059 octave_idx_type liwork = 3 * minmn * nlvl + 11 * minmn; | |
| 2060 if (liwork < 1) | |
| 2061 liwork = 1; | |
| 7072 | 2062 Array<octave_idx_type> iwork (liwork); |
| 2063 octave_idx_type* piwork = iwork.fortran_vec (); | |
| 2064 | |
| 2065 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, | |
| 2066 ps, rcond, rank, work.fortran_vec (), | |
| 2067 lwork, piwork, info)); | |
| 1948 | 2068 |
| 7476 | 2069 // The workspace query is broken in at least LAPACK 3.0.0 |
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2070 // through 3.1.1 when n > mnthr. The obtuse formula below |
| 7476 | 2071 // should provide sufficient workspace for DGELSD to operate |
| 2072 // efficiently. | |
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2073 if (n > mnthr) |
| 7476 | 2074 { |
| 2075 const octave_idx_type wlalsd | |
| 2076 = 9*m + 2*m*smlsiz + 8*m*nlvl + m*nrhs + (smlsiz+1)*(smlsiz+1); | |
| 2077 | |
| 2078 octave_idx_type addend = m; | |
| 2079 | |
| 2080 if (2*m-4 > addend) | |
| 2081 addend = 2*m-4; | |
| 2082 | |
| 2083 if (nrhs > addend) | |
| 2084 addend = nrhs; | |
| 2085 | |
| 2086 if (n-3*m > addend) | |
| 2087 addend = n-3*m; | |
| 2088 | |
| 2089 if (wlalsd > addend) | |
| 2090 addend = wlalsd; | |
| 2091 | |
| 2092 const octave_idx_type lworkaround = 4*m + m*m + addend; | |
| 2093 | |
| 2094 if (work(0) < lworkaround) | |
| 2095 work(0) = lworkaround; | |
| 2096 } | |
| 2097 | |
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2098 lwork = static_cast<octave_idx_type> (work(0)); |
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2099 work.resize (lwork); |
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2100 |
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2101 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, |
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2102 maxmn, ps, rcond, rank, |
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2103 work.fortran_vec (), lwork, |
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2104 piwork, info)); |
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2105 |
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2106 if (rank < minmn) |
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2107 (*current_liboctave_warning_handler) |
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2108 ("dgelsd: rank deficient %dx%d matrix, rank = %d", m, n, rank); |
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2109 if (s.elem (0) == 0.0) |
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2110 rcond = 0.0; |
| 1948 | 2111 else |
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2112 rcond = s.elem (minmn - 1) / s.elem (0); |
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2113 |
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|
2114 retval.resize (n, nrhs); |
| 458 | 2115 } |
| 2116 | |
| 2117 return retval; | |
| 2118 } | |
| 2119 | |
| 2120 ComplexMatrix | |
| 2121 Matrix::lssolve (const ComplexMatrix& b) const | |
| 2122 { | |
| 2123 ComplexMatrix tmp (*this); | |
| 5275 | 2124 octave_idx_type info; |
| 2125 octave_idx_type rank; | |
| 7076 | 2126 double rcond; |
| 2127 return tmp.lssolve (b, info, rank, rcond); | |
| 458 | 2128 } |
| 2129 | |
| 2130 ComplexMatrix | |
| 5275 | 2131 Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info) const |
| 458 | 2132 { |
| 2133 ComplexMatrix tmp (*this); | |
| 5275 | 2134 octave_idx_type rank; |
| 7076 | 2135 double rcond; |
| 2136 return tmp.lssolve (b, info, rank, rcond); | |
| 458 | 2137 } |
| 2138 | |
| 2139 ComplexMatrix | |
| 7076 | 2140 Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info, |
| 2141 octave_idx_type& rank) const | |
| 458 | 2142 { |
| 2143 ComplexMatrix tmp (*this); | |
| 7076 | 2144 double rcond; |
| 2145 return tmp.lssolve (b, info, rank, rcond); | |
| 2146 } | |
| 2147 | |
| 2148 ComplexMatrix | |
| 2149 Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info, | |
| 2150 octave_idx_type& rank, double& rcond) const | |
| 2151 { | |
| 2152 ComplexMatrix tmp (*this); | |
| 2153 return tmp.lssolve (b, info, rank, rcond); | |
| 458 | 2154 } |
| 2155 | |
| 2156 ColumnVector | |
| 2157 Matrix::lssolve (const ColumnVector& b) const | |
| 2158 { | |
| 5275 | 2159 octave_idx_type info; |
| 2160 octave_idx_type rank; | |
| 7076 | 2161 double rcond; |
| 2162 return lssolve (b, info, rank, rcond); | |
| 458 | 2163 } |
| 2164 | |
| 2165 ColumnVector | |
| 5275 | 2166 Matrix::lssolve (const ColumnVector& b, octave_idx_type& info) const |
| 458 | 2167 { |
| 5275 | 2168 octave_idx_type rank; |
| 7076 | 2169 double rcond; |
| 2170 return lssolve (b, info, rank, rcond); | |
| 458 | 2171 } |
| 2172 | |
| 2173 ColumnVector | |
| 7072 | 2174 Matrix::lssolve (const ColumnVector& b, octave_idx_type& info, |
| 2175 octave_idx_type& rank) const | |
| 458 | 2176 { |
| 7076 | 2177 double rcond; |
| 2178 return lssolve (b, info, rank, rcond); | |
| 2179 } | |
| 2180 | |
| 2181 ColumnVector | |
| 2182 Matrix::lssolve (const ColumnVector& b, octave_idx_type& info, | |
| 2183 octave_idx_type& rank, double &rcond) const | |
| 2184 { | |
| 1948 | 2185 ColumnVector retval; |
| 2186 | |
| 5275 | 2187 octave_idx_type nrhs = 1; |
| 2188 | |
| 2189 octave_idx_type m = rows (); | |
| 2190 octave_idx_type n = cols (); | |
| 458 | 2191 |
| 6924 | 2192 if (m != b.length ()) |
| 1948 | 2193 (*current_liboctave_error_handler) |
| 6924 | 2194 ("matrix dimension mismatch solution of linear equations"); |
| 2195 else if (m == 0 || n == 0) | |
| 2196 retval = ColumnVector (n, 0.0); | |
| 1948 | 2197 else |
| 458 | 2198 { |
| 7072 | 2199 volatile octave_idx_type minmn = (m < n ? m : n); |
| 2200 octave_idx_type maxmn = m > n ? m : n; | |
| 7076 | 2201 rcond = -1.0; |
| 7072 | 2202 |
| 2203 if (m != n) | |
| 2204 { | |
| 2205 retval = ColumnVector (maxmn, 0.0); | |
| 2206 | |
| 2207 for (octave_idx_type i = 0; i < m; i++) | |
| 2208 retval.elem (i) = b.elem (i); | |
| 2209 } | |
| 2210 else | |
| 2211 retval = b; | |
| 2212 | |
| 1948 | 2213 Matrix atmp = *this; |
| 2214 double *tmp_data = atmp.fortran_vec (); | |
| 2215 | |
| 7072 | 2216 double *pretval = retval.fortran_vec (); |
| 2217 Array<double> s (minmn); | |
| 7071 | 2218 double *ps = s.fortran_vec (); |
| 1948 | 2219 |
| 7072 | 2220 // Ask DGELSD what the dimension of WORK should be. |
| 5275 | 2221 octave_idx_type lwork = -1; |
| 3752 | 2222 |
| 2223 Array<double> work (1); | |
| 2224 | |
| 7072 | 2225 // FIXME: Can SMLSIZ be other than 25? |
| 7079 | 2226 octave_idx_type smlsiz = 25; |
| 2227 | |
| 2228 // We compute the size of iwork because DGELSD in older versions | |
| 2229 // of LAPACK does not return it on a query call. | |
| 7124 | 2230 double dminmn = static_cast<double> (minmn); |
| 2231 double dsmlsizp1 = static_cast<double> (smlsiz+1); | |
| 7079 | 2232 #if defined (HAVE_LOG2) |
| 7124 | 2233 double tmp = log2 (dminmn) / dsmlsizp1 + 1; |
| 7079 | 2234 #else |
| 7124 | 2235 double tmp = log (dminmn) / dsmlsizp1 / log (2.0) + 1; |
| 7079 | 2236 #endif |
| 2237 octave_idx_type nlvl = static_cast<int> (tmp); | |
| 2238 if (nlvl < 0) | |
| 2239 nlvl = 0; | |
| 2240 | |
| 2241 octave_idx_type liwork = 3 * minmn * nlvl + 11 * minmn; | |
| 2242 if (liwork < 1) | |
| 2243 liwork = 1; | |
| 7072 | 2244 Array<octave_idx_type> iwork (liwork); |
| 2245 octave_idx_type* piwork = iwork.fortran_vec (); | |
| 2246 | |
| 2247 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, | |
| 2248 ps, rcond, rank, work.fortran_vec (), | |
| 2249 lwork, piwork, info)); | |
| 1948 | 2250 |
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2251 lwork = static_cast<octave_idx_type> (work(0)); |
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2252 work.resize (lwork); |
|
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2253 |
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|
2254 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, |
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2255 maxmn, ps, rcond, rank, |
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2256 work.fortran_vec (), lwork, |
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|
2257 piwork, info)); |
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2258 |
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2259 if (rank < minmn) |
| 1948 | 2260 { |
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2261 if (rank < minmn) |
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2262 (*current_liboctave_warning_handler) |
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2263 ("dgelsd: rank deficient %dx%d matrix, rank = %d", m, n, rank); |
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2264 if (s.elem (0) == 0.0) |
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2265 rcond = 0.0; |
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2266 else |
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2267 rcond = s.elem (minmn - 1) / s.elem (0); |
| 1948 | 2268 } |
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2269 |
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|
2270 retval.resize (n, nrhs); |
| 458 | 2271 } |
| 2272 | |
| 2273 return retval; | |
| 2274 } | |
| 2275 | |
| 2276 ComplexColumnVector | |
| 2277 Matrix::lssolve (const ComplexColumnVector& b) const | |
| 2278 { | |
| 2279 ComplexMatrix tmp (*this); | |
| 7076 | 2280 octave_idx_type info; |
| 2281 octave_idx_type rank; | |
| 2282 double rcond; | |
| 2283 return tmp.lssolve (b, info, rank, rcond); | |
| 458 | 2284 } |
| 2285 | |
| 2286 ComplexColumnVector | |
| 5275 | 2287 Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info) const |
| 458 | 2288 { |
| 2289 ComplexMatrix tmp (*this); | |
| 7076 | 2290 octave_idx_type rank; |
| 2291 double rcond; | |
| 2292 return tmp.lssolve (b, info, rank, rcond); | |
| 458 | 2293 } |
| 2294 | |
| 2295 ComplexColumnVector | |
| 7076 | 2296 Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, |
| 2297 octave_idx_type& rank) const | |
| 458 | 2298 { |
| 2299 ComplexMatrix tmp (*this); | |
| 7076 | 2300 double rcond; |
| 2301 return tmp.lssolve (b, info, rank, rcond); | |
| 2302 } | |
| 2303 | |
| 2304 ComplexColumnVector | |
| 2305 Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, | |
| 2306 octave_idx_type& rank, double &rcond) const | |
| 2307 { | |
| 2308 ComplexMatrix tmp (*this); | |
| 2309 return tmp.lssolve (b, info, rank, rcond); | |
| 458 | 2310 } |
| 2311 | |
| 1819 | 2312 // Constants for matrix exponential calculation. |
| 2313 | |
| 2314 static double padec [] = | |
| 2315 { | |
| 2316 5.0000000000000000e-1, | |
| 2317 1.1666666666666667e-1, | |
| 2318 1.6666666666666667e-2, | |
| 2319 1.6025641025641026e-3, | |
| 2320 1.0683760683760684e-4, | |
| 2321 4.8562548562548563e-6, | |
| 2322 1.3875013875013875e-7, | |
| 2323 1.9270852604185938e-9, | |
| 2324 }; | |
| 2325 | |
| 7400 | 2326 static void |
| 2327 solve_singularity_warning (double rcond) | |
| 2328 { | |
| 2329 (*current_liboctave_warning_handler) | |
| 2330 ("singular matrix encountered in expm calculation, rcond = %g", | |
| 2331 rcond); | |
| 2332 } | |
| 2333 | |
| 1819 | 2334 Matrix |
| 2335 Matrix::expm (void) const | |
| 2336 { | |
| 2337 Matrix retval; | |
| 2338 | |
| 2339 Matrix m = *this; | |
| 2340 | |
| 6699 | 2341 if (numel () == 1) |
| 2342 return Matrix (1, 1, exp (m(0))); | |
| 2343 | |
| 5275 | 2344 octave_idx_type nc = columns (); |
| 1819 | 2345 |
| 3130 | 2346 // Preconditioning step 1: trace normalization to reduce dynamic |
| 2347 // range of poles, but avoid making stable eigenvalues unstable. | |
| 2348 | |
| 1819 | 2349 // trace shift value |
| 3331 | 2350 volatile double trshift = 0.0; |
| 1819 | 2351 |
| 5275 | 2352 for (octave_idx_type i = 0; i < nc; i++) |
| 1819 | 2353 trshift += m.elem (i, i); |
| 2354 | |
| 2355 trshift /= nc; | |
| 2356 | |
| 3130 | 2357 if (trshift > 0.0) |
| 2358 { | |
| 5275 | 2359 for (octave_idx_type i = 0; i < nc; i++) |
| 3130 | 2360 m.elem (i, i) -= trshift; |
| 2361 } | |
| 1819 | 2362 |
| 3331 | 2363 // Preconditioning step 2: balancing; code follows development |
| 2364 // in AEPBAL | |
| 2365 | |
| 2366 double *p_m = m.fortran_vec (); | |
| 2367 | |
| 5275 | 2368 octave_idx_type info, ilo, ihi, ilos, ihis; |
| 3468 | 2369 Array<double> dpermute (nc); |
| 2370 Array<double> dscale (nc); | |
| 3466 | 2371 |
| 3468 | 2372 // permutation first |
| 2373 char job = 'P'; | |
| 4552 | 2374 F77_XFCN (dgebal, DGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
| 2375 nc, p_m, nc, ilo, ihi, | |
| 2376 dpermute.fortran_vec (), info | |
| 2377 F77_CHAR_ARG_LEN (1))); | |
| 3466 | 2378 |
| 3468 | 2379 // then scaling |
| 2380 job = 'S'; | |
| 4552 | 2381 F77_XFCN (dgebal, DGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
| 2382 nc, p_m, nc, ilos, ihis, | |
| 2383 dscale.fortran_vec (), info | |
| 2384 F77_CHAR_ARG_LEN (1))); | |
| 3331 | 2385 |
| 1819 | 2386 // Preconditioning step 3: scaling. |
| 3331 | 2387 |
| 1819 | 2388 ColumnVector work(nc); |
| 3130 | 2389 double inf_norm; |
| 3331 | 2390 |
| 4552 | 2391 F77_XFCN (xdlange, XDLANGE, (F77_CONST_CHAR_ARG2 ("I", 1), |
| 2392 nc, nc, m.fortran_vec (), nc, | |
| 2393 work.fortran_vec (), inf_norm | |
| 2394 F77_CHAR_ARG_LEN (1))); | |
| 3331 | 2395 |
| 5275 | 2396 octave_idx_type sqpow = static_cast<octave_idx_type> (inf_norm > 0.0 |
| 1819 | 2397 ? (1.0 + log (inf_norm) / log (2.0)) |
| 2398 : 0.0); | |
| 3331 | 2399 |
| 1819 | 2400 // Check whether we need to square at all. |
| 3331 | 2401 |
| 1819 | 2402 if (sqpow < 0) |
| 2403 sqpow = 0; | |
| 3331 | 2404 |
| 1819 | 2405 if (sqpow > 0) |
| 2406 { | |
| 7400 | 2407 if (sqpow > 1023) |
| 2408 sqpow = 1023; | |
| 2409 | |
| 1819 | 2410 double scale_factor = 1.0; |
| 5275 | 2411 for (octave_idx_type i = 0; i < sqpow; i++) |
| 1819 | 2412 scale_factor *= 2.0; |
| 7400 | 2413 |
| 1819 | 2414 m = m / scale_factor; |
| 2415 } | |
| 3331 | 2416 |
| 1819 | 2417 // npp, dpp: pade' approx polynomial matrices. |
| 3331 | 2418 |
| 1819 | 2419 Matrix npp (nc, nc, 0.0); |
| 7265 | 2420 double *pnpp = npp.fortran_vec (); |
| 1819 | 2421 Matrix dpp = npp; |
| 7265 | 2422 double *pdpp = dpp.fortran_vec (); |
| 3331 | 2423 |
| 1819 | 2424 // Now powers a^8 ... a^1. |
| 3331 | 2425 |
| 5275 | 2426 octave_idx_type minus_one_j = -1; |
| 2427 for (octave_idx_type j = 7; j >= 0; j--) | |
| 1819 | 2428 { |
| 7265 | 2429 for (octave_idx_type i = 0; i < nc; i++) |
| 2430 { | |
| 2431 octave_idx_type k = i * nc + i; | |
| 2432 pnpp[k] += padec[j]; | |
| 2433 pdpp[k] += minus_one_j * padec[j]; | |
| 2434 } | |
| 2435 | |
| 2436 npp = m * npp; | |
| 2437 pnpp = npp.fortran_vec (); | |
| 2438 | |
| 2439 dpp = m * dpp; | |
| 2440 pdpp = dpp.fortran_vec (); | |
| 2441 | |
| 1819 | 2442 minus_one_j *= -1; |
| 2443 } | |
| 3331 | 2444 |
| 1819 | 2445 // Zero power. |
| 3331 | 2446 |
| 1819 | 2447 dpp = -dpp; |
| 5275 | 2448 for (octave_idx_type j = 0; j < nc; j++) |
| 1819 | 2449 { |
| 2450 npp.elem (j, j) += 1.0; | |
| 2451 dpp.elem (j, j) += 1.0; | |
| 2452 } | |
| 3331 | 2453 |
| 1819 | 2454 // Compute pade approximation = inverse (dpp) * npp. |
| 2455 | |
| 7400 | 2456 double rcond; |
| 2457 retval = dpp.solve (npp, info, rcond, solve_singularity_warning); | |
| 2458 | |
| 2459 if (info < 0) | |
| 2460 return retval; | |
| 2461 | |
| 1819 | 2462 // Reverse preconditioning step 3: repeated squaring. |
| 3331 | 2463 |
| 1819 | 2464 while (sqpow) |
| 2465 { | |
| 2466 retval = retval * retval; | |
| 2467 sqpow--; | |
| 2468 } | |
| 3331 | 2469 |
| 1819 | 2470 // Reverse preconditioning step 2: inverse balancing. |
| 3466 | 2471 // apply inverse scaling to computed exponential |
| 5275 | 2472 for (octave_idx_type i = 0; i < nc; i++) |
| 2473 for (octave_idx_type j = 0; j < nc; j++) | |
| 3468 | 2474 retval(i,j) *= dscale(i) / dscale(j); |
| 3466 | 2475 |
| 4153 | 2476 OCTAVE_QUIT; |
| 2477 | |
| 3466 | 2478 // construct balancing permutation vector |
| 5275 | 2479 Array<octave_idx_type> iperm (nc); |
| 2480 for (octave_idx_type i = 0; i < nc; i++) | |
| 4593 | 2481 iperm(i) = i; // identity permutation |
| 3466 | 2482 |
| 2483 // leading permutations in forward order | |
| 5275 | 2484 for (octave_idx_type i = 0; i < (ilo-1); i++) |
| 3468 | 2485 { |
| 5275 | 2486 octave_idx_type swapidx = static_cast<octave_idx_type> (dpermute(i)) - 1; |
| 2487 octave_idx_type tmp = iperm(i); | |
| 4593 | 2488 iperm(i) = iperm (swapidx); |
| 2489 iperm(swapidx) = tmp; | |
| 3468 | 2490 } |
| 3466 | 2491 |
| 7416 | 2492 // construct inverse balancing permutation vector |
| 2493 Array<octave_idx_type> invpvec (nc); | |
| 2494 for (octave_idx_type i = 0; i < nc; i++) | |
| 2495 invpvec(iperm(i)) = i; // Thanks to R. A. Lippert for this method | |
| 2496 | |
| 2497 OCTAVE_QUIT; | |
| 2498 | |
| 2499 Matrix tmpMat = retval; | |
| 2500 for (octave_idx_type i = 0; i < nc; i++) | |
| 2501 for (octave_idx_type j = 0; j < nc; j++) | |
| 2502 retval(i,j) = tmpMat(invpvec(i),invpvec(j)); | |
| 2503 | |
| 2504 OCTAVE_QUIT; | |
| 2505 | |
| 2506 for (octave_idx_type i = 0; i < nc; i++) | |
| 2507 iperm(i) = i; // identity permutation | |
| 2508 | |
| 3466 | 2509 // trailing permutations must be done in reverse order |
| 5275 | 2510 for (octave_idx_type i = nc - 1; i >= ihi; i--) |
| 3468 | 2511 { |
| 5275 | 2512 octave_idx_type swapidx = static_cast<octave_idx_type> (dpermute(i)) - 1; |
| 2513 octave_idx_type tmp = iperm(i); | |
| 4593 | 2514 iperm(i) = iperm(swapidx); |
| 2515 iperm(swapidx) = tmp; | |
| 3468 | 2516 } |
| 3466 | 2517 |
| 2518 // construct inverse balancing permutation vector | |
| 5275 | 2519 for (octave_idx_type i = 0; i < nc; i++) |
| 4593 | 2520 invpvec(iperm(i)) = i; // Thanks to R. A. Lippert for this method |
| 4153 | 2521 |
| 2522 OCTAVE_QUIT; | |
| 3466 | 2523 |
| 7416 | 2524 tmpMat = retval; |
| 5275 | 2525 for (octave_idx_type i = 0; i < nc; i++) |
| 2526 for (octave_idx_type j = 0; j < nc; j++) | |
| 3468 | 2527 retval(i,j) = tmpMat(invpvec(i),invpvec(j)); |
| 3466 | 2528 |
| 1819 | 2529 // Reverse preconditioning step 1: fix trace normalization. |
| 3331 | 2530 |
| 3130 | 2531 if (trshift > 0.0) |
| 2532 retval = exp (trshift) * retval; | |
| 2533 | |
| 2534 return retval; | |
| 1819 | 2535 } |
| 2536 | |
| 458 | 2537 Matrix& |
| 2538 Matrix::operator += (const DiagMatrix& a) | |
| 2539 { | |
| 5275 | 2540 octave_idx_type nr = rows (); |
| 2541 octave_idx_type nc = cols (); | |
| 2542 | |
| 2543 octave_idx_type a_nr = a.rows (); | |
| 2544 octave_idx_type a_nc = a.cols (); | |
| 2385 | 2545 |
| 2546 if (nr != a_nr || nc != a_nc) | |
| 458 | 2547 { |
| 2385 | 2548 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
| 458 | 2549 return *this; |
| 2550 } | |
| 2551 | |
| 5275 | 2552 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 2553 elem (i, i) += a.elem (i, i); |
| 2554 | |
| 2555 return *this; | |
| 2556 } | |
| 2557 | |
| 2558 Matrix& | |
| 2559 Matrix::operator -= (const DiagMatrix& a) | |
| 2560 { | |
| 5275 | 2561 octave_idx_type nr = rows (); |
| 2562 octave_idx_type nc = cols (); | |
| 2563 | |
| 2564 octave_idx_type a_nr = a.rows (); | |
| 2565 octave_idx_type a_nc = a.cols (); | |
| 2385 | 2566 |
| 2567 if (nr != a_nr || nc != a_nc) | |
| 458 | 2568 { |
| 2385 | 2569 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
| 458 | 2570 return *this; |
| 2571 } | |
| 2572 | |
| 5275 | 2573 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 2574 elem (i, i) -= a.elem (i, i); |
| 2575 | |
| 2576 return *this; | |
| 2577 } | |
| 2578 | |
| 2579 // unary operations | |
| 2580 | |
| 2964 | 2581 boolMatrix |
| 458 | 2582 Matrix::operator ! (void) const |
| 2583 { | |
| 5275 | 2584 octave_idx_type nr = rows (); |
| 2585 octave_idx_type nc = cols (); | |
| 458 | 2586 |
| 2964 | 2587 boolMatrix b (nr, nc); |
| 458 | 2588 |
| 5275 | 2589 for (octave_idx_type j = 0; j < nc; j++) |
| 2590 for (octave_idx_type i = 0; i < nr; i++) | |
| 458 | 2591 b.elem (i, j) = ! elem (i, j); |
| 2592 | |
| 2593 return b; | |
| 2594 } | |
| 2595 | |
| 1205 | 2596 // column vector by row vector -> matrix operations |
| 458 | 2597 |
| 1205 | 2598 Matrix |
| 2599 operator * (const ColumnVector& v, const RowVector& a) | |
| 458 | 2600 { |
| 1948 | 2601 Matrix retval; |
| 2602 | |
| 5275 | 2603 octave_idx_type len = v.length (); |
| 3233 | 2604 |
| 2605 if (len != 0) | |
| 1205 | 2606 { |
| 5275 | 2607 octave_idx_type a_len = a.length (); |
| 3233 | 2608 |
| 2609 retval.resize (len, a_len); | |
| 2610 double *c = retval.fortran_vec (); | |
| 2611 | |
| 4552 | 2612 F77_XFCN (dgemm, DGEMM, (F77_CONST_CHAR_ARG2 ("N", 1), |
| 2613 F77_CONST_CHAR_ARG2 ("N", 1), | |
| 2614 len, a_len, 1, 1.0, v.data (), len, | |
| 2615 a.data (), 1, 0.0, c, len | |
| 2616 F77_CHAR_ARG_LEN (1) | |
| 2617 F77_CHAR_ARG_LEN (1))); | |
| 1205 | 2618 } |
| 458 | 2619 |
| 1948 | 2620 return retval; |
| 458 | 2621 } |
| 2622 | |
| 2623 // other operations. | |
| 2624 | |
| 2625 Matrix | |
| 2676 | 2626 Matrix::map (d_d_Mapper f) const |
| 1205 | 2627 { |
| 2676 | 2628 Matrix b (*this); |
| 2629 return b.apply (f); | |
| 1205 | 2630 } |
| 2631 | |
| 3248 | 2632 boolMatrix |
| 2633 Matrix::map (b_d_Mapper f) const | |
| 2634 { | |
| 5275 | 2635 octave_idx_type nr = rows (); |
| 2636 octave_idx_type nc = cols (); | |
| 3248 | 2637 |
| 2638 boolMatrix retval (nr, nc); | |
| 2639 | |
| 5275 | 2640 for (octave_idx_type j = 0; j < nc; j++) |
| 2641 for (octave_idx_type i = 0; i < nr; i++) | |
| 3248 | 2642 retval(i,j) = f (elem(i,j)); |
| 2643 | |
| 2644 return retval; | |
| 2645 } | |
| 2646 | |
| 2676 | 2647 Matrix& |
| 2648 Matrix::apply (d_d_Mapper f) | |
| 458 | 2649 { |
| 2650 double *d = fortran_vec (); // Ensures only one reference to my privates! | |
| 2651 | |
| 5275 | 2652 for (octave_idx_type i = 0; i < length (); i++) |
| 458 | 2653 d[i] = f (d[i]); |
| 2676 | 2654 |
| 2655 return *this; | |
| 458 | 2656 } |
| 2657 | |
| 2385 | 2658 bool |
| 4431 | 2659 Matrix::any_element_is_negative (bool neg_zero) const |
| 2385 | 2660 { |
| 5275 | 2661 octave_idx_type nel = nelem (); |
| 2385 | 2662 |
| 4431 | 2663 if (neg_zero) |
| 2664 { | |
| 5275 | 2665 for (octave_idx_type i = 0; i < nel; i++) |
| 4634 | 2666 if (lo_ieee_signbit (elem (i))) |
| 2667 return true; | |
| 4431 | 2668 } |
| 2669 else | |
| 2670 { | |
| 5275 | 2671 for (octave_idx_type i = 0; i < nel; i++) |
| 4634 | 2672 if (elem (i) < 0) |
| 2673 return true; | |
| 4431 | 2674 } |
| 2385 | 2675 |
| 2676 return false; | |
| 2677 } | |
| 2678 | |
| 2679 | |
| 2680 bool | |
| 2681 Matrix::any_element_is_inf_or_nan (void) const | |
| 2682 { | |
| 5275 | 2683 octave_idx_type nel = nelem (); |
| 2684 | |
| 2685 for (octave_idx_type i = 0; i < nel; i++) | |
| 4634 | 2686 { |
| 2687 double val = elem (i); | |
| 2688 if (xisinf (val) || xisnan (val)) | |
| 2689 return true; | |
| 2690 } | |
| 2691 | |
| 2692 return false; | |
| 2385 | 2693 } |
| 2694 | |
| 2695 bool | |
| 5943 | 2696 Matrix::any_element_not_one_or_zero (void) const |
| 2697 { | |
| 2698 octave_idx_type nel = nelem (); | |
| 2699 | |
| 2700 for (octave_idx_type i = 0; i < nel; i++) | |
| 2701 { | |
| 2702 double val = elem (i); | |
| 2703 if (val != 0 && val != 1) | |
| 2704 return true; | |
| 2705 } | |
| 2706 | |
| 2707 return false; | |
| 2708 } | |
| 2709 | |
| 2710 bool | |
| 2385 | 2711 Matrix::all_elements_are_int_or_inf_or_nan (void) const |
| 2712 { | |
| 5275 | 2713 octave_idx_type nel = nelem (); |
| 2714 | |
| 2715 for (octave_idx_type i = 0; i < nel; i++) | |
| 4634 | 2716 { |
| 2717 double val = elem (i); | |
| 2718 if (xisnan (val) || D_NINT (val) == val) | |
| 2719 continue; | |
| 2720 else | |
| 2721 return false; | |
| 2722 } | |
| 2385 | 2723 |
| 2724 return true; | |
| 2725 } | |
| 2726 | |
| 1968 | 2727 // Return nonzero if any element of M is not an integer. Also extract |
| 2728 // the largest and smallest values and return them in MAX_VAL and MIN_VAL. | |
| 2729 | |
| 2385 | 2730 bool |
| 1968 | 2731 Matrix::all_integers (double& max_val, double& min_val) const |
| 2732 { | |
| 5275 | 2733 octave_idx_type nel = nelem (); |
| 4634 | 2734 |
| 2735 if (nel > 0) | |
| 1968 | 2736 { |
| 4634 | 2737 max_val = elem (0); |
| 2738 min_val = elem (0); | |
| 1968 | 2739 } |
| 2740 else | |
| 2385 | 2741 return false; |
| 1968 | 2742 |
| 5275 | 2743 for (octave_idx_type i = 0; i < nel; i++) |
| 4634 | 2744 { |
| 2745 double val = elem (i); | |
| 2746 | |
| 2747 if (val > max_val) | |
| 2748 max_val = val; | |
| 2749 | |
| 2750 if (val < min_val) | |
| 2751 min_val = val; | |
| 2752 | |
| 2753 if (D_NINT (val) != val) | |
| 2754 return false; | |
| 2755 } | |
| 2385 | 2756 |
| 2757 return true; | |
| 1968 | 2758 } |
| 2759 | |
| 2385 | 2760 bool |
| 1968 | 2761 Matrix::too_large_for_float (void) const |
| 2762 { | |
| 5275 | 2763 octave_idx_type nel = nelem (); |
| 2764 | |
| 2765 for (octave_idx_type i = 0; i < nel; i++) | |
| 4634 | 2766 { |
| 2767 double val = elem (i); | |
| 2768 | |
| 5389 | 2769 if (! (xisnan (val) || xisinf (val)) |
| 5387 | 2770 && fabs (val) > FLT_MAX) |
| 4634 | 2771 return true; |
| 2772 } | |
| 1968 | 2773 |
| 2385 | 2774 return false; |
| 1968 | 2775 } |
| 2776 | |
| 5775 | 2777 // FIXME Do these really belong here? Maybe they should be |
| 4015 | 2778 // in a base class? |
| 458 | 2779 |
| 2832 | 2780 boolMatrix |
| 4015 | 2781 Matrix::all (int dim) const |
| 458 | 2782 { |
| 4015 | 2783 MX_ALL_OP (dim); |
| 458 | 2784 } |
| 2785 | |
| 2832 | 2786 boolMatrix |
| 4015 | 2787 Matrix::any (int dim) const |
| 458 | 2788 { |
| 4015 | 2789 MX_ANY_OP (dim); |
| 458 | 2790 } |
| 2791 | |
| 2792 Matrix | |
| 3723 | 2793 Matrix::cumprod (int dim) const |
| 458 | 2794 { |
| 4015 | 2795 MX_CUMULATIVE_OP (Matrix, double, *=); |
| 458 | 2796 } |
| 2797 | |
| 2798 Matrix | |
| 3723 | 2799 Matrix::cumsum (int dim) const |
| 458 | 2800 { |
| 4015 | 2801 MX_CUMULATIVE_OP (Matrix, double, +=); |
| 458 | 2802 } |
| 2803 | |
| 2804 Matrix | |
| 3723 | 2805 Matrix::prod (int dim) const |
| 458 | 2806 { |
| 3864 | 2807 MX_REDUCTION_OP (Matrix, *=, 1.0, 1.0); |
| 458 | 2808 } |
| 2809 | |
| 2810 Matrix | |
| 3723 | 2811 Matrix::sum (int dim) const |
| 458 | 2812 { |
| 3864 | 2813 MX_REDUCTION_OP (Matrix, +=, 0.0, 0.0); |
| 458 | 2814 } |
| 2815 | |
| 2816 Matrix | |
| 3723 | 2817 Matrix::sumsq (int dim) const |
| 458 | 2818 { |
| 3864 | 2819 #define ROW_EXPR \ |
| 2820 double d = elem (i, j); \ | |
| 2821 retval.elem (i, 0) += d * d | |
| 2822 | |
| 2823 #define COL_EXPR \ | |
| 2824 double d = elem (i, j); \ | |
| 2825 retval.elem (0, j) += d * d | |
| 2826 | |
| 2827 MX_BASE_REDUCTION_OP (Matrix, ROW_EXPR, COL_EXPR, 0.0, 0.0); | |
| 2828 | |
| 2829 #undef ROW_EXPR | |
| 2830 #undef COL_EXPR | |
| 458 | 2831 } |
| 2832 | |
| 2385 | 2833 Matrix |
| 2834 Matrix::abs (void) const | |
| 2835 { | |
| 5275 | 2836 octave_idx_type nr = rows (); |
| 2837 octave_idx_type nc = cols (); | |
| 2385 | 2838 |
| 2839 Matrix retval (nr, nc); | |
| 2840 | |
| 5275 | 2841 for (octave_idx_type j = 0; j < nc; j++) |
| 2842 for (octave_idx_type i = 0; i < nr; i++) | |
| 2385 | 2843 retval (i, j) = fabs (elem (i, j)); |
| 2844 | |
| 2845 return retval; | |
| 2846 } | |
| 2847 | |
| 458 | 2848 ColumnVector |
| 2849 Matrix::diag (void) const | |
| 2850 { | |
| 2851 return diag (0); | |
| 2852 } | |
| 2853 | |
| 2854 ColumnVector | |
| 5275 | 2855 Matrix::diag (octave_idx_type k) const |
| 458 | 2856 { |
| 5275 | 2857 octave_idx_type nnr = rows (); |
| 2858 octave_idx_type nnc = cols (); | |
| 458 | 2859 if (k > 0) |
| 2860 nnc -= k; | |
| 2861 else if (k < 0) | |
| 2862 nnr += k; | |
| 2863 | |
| 2864 ColumnVector d; | |
| 2865 | |
| 2866 if (nnr > 0 && nnc > 0) | |
| 2867 { | |
| 5275 | 2868 octave_idx_type ndiag = (nnr < nnc) ? nnr : nnc; |
| 458 | 2869 |
| 2870 d.resize (ndiag); | |
| 2871 | |
| 2872 if (k > 0) | |
| 2873 { | |
| 5275 | 2874 for (octave_idx_type i = 0; i < ndiag; i++) |
| 458 | 2875 d.elem (i) = elem (i, i+k); |
| 2876 } | |
| 4509 | 2877 else if (k < 0) |
| 458 | 2878 { |
| 5275 | 2879 for (octave_idx_type i = 0; i < ndiag; i++) |
| 458 | 2880 d.elem (i) = elem (i-k, i); |
| 2881 } | |
| 2882 else | |
| 2883 { | |
| 5275 | 2884 for (octave_idx_type i = 0; i < ndiag; i++) |
| 458 | 2885 d.elem (i) = elem (i, i); |
| 2886 } | |
| 2887 } | |
| 2888 else | |
| 4513 | 2889 (*current_liboctave_error_handler) |
| 2890 ("diag: requested diagonal out of range"); | |
| 458 | 2891 |
| 2892 return d; | |
| 2893 } | |
| 2894 | |
| 2895 ColumnVector | |
| 2896 Matrix::row_min (void) const | |
| 2897 { | |
| 5275 | 2898 Array<octave_idx_type> dummy_idx; |
| 4587 | 2899 return row_min (dummy_idx); |
| 458 | 2900 } |
| 2901 | |
| 2902 ColumnVector | |
| 5275 | 2903 Matrix::row_min (Array<octave_idx_type>& idx_arg) const |
| 458 | 2904 { |
| 2905 ColumnVector result; | |
| 2906 | |
| 5275 | 2907 octave_idx_type nr = rows (); |
| 2908 octave_idx_type nc = cols (); | |
| 458 | 2909 |
| 2910 if (nr > 0 && nc > 0) | |
| 2911 { | |
| 2912 result.resize (nr); | |
| 4587 | 2913 idx_arg.resize (nr); |
| 458 | 2914 |
| 5275 | 2915 for (octave_idx_type i = 0; i < nr; i++) |
| 458 | 2916 { |
| 5275 | 2917 octave_idx_type idx_j; |
| 4469 | 2918 |
| 2919 double tmp_min = octave_NaN; | |
| 2920 | |
| 2921 for (idx_j = 0; idx_j < nc; idx_j++) | |
| 2354 | 2922 { |
| 4469 | 2923 tmp_min = elem (i, idx_j); |
| 2924 | |
| 5389 | 2925 if (! xisnan (tmp_min)) |
| 4469 | 2926 break; |
| 2927 } | |
| 2928 | |
| 5275 | 2929 for (octave_idx_type j = idx_j+1; j < nc; j++) |
| 4469 | 2930 { |
| 2931 double tmp = elem (i, j); | |
| 2932 | |
| 5389 | 2933 if (xisnan (tmp)) |
| 4469 | 2934 continue; |
| 2935 else if (tmp < tmp_min) | |
| 2354 | 2936 { |
| 4469 | 2937 idx_j = j; |
| 2938 tmp_min = tmp; | |
| 2354 | 2939 } |
| 2940 } | |
| 2941 | |
| 4469 | 2942 result.elem (i) = tmp_min; |
| 5389 | 2943 idx_arg.elem (i) = xisnan (tmp_min) ? 0 : idx_j; |
| 458 | 2944 } |
| 2945 } | |
| 2946 | |
| 2947 return result; | |
| 2948 } | |
| 2949 | |
| 2950 ColumnVector | |
| 2951 Matrix::row_max (void) const | |
| 2952 { | |
| 5275 | 2953 Array<octave_idx_type> dummy_idx; |
| 4587 | 2954 return row_max (dummy_idx); |
| 458 | 2955 } |
| 2956 | |
| 2957 ColumnVector | |
| 5275 | 2958 Matrix::row_max (Array<octave_idx_type>& idx_arg) const |
| 458 | 2959 { |
| 2960 ColumnVector result; | |
| 2961 | |
| 5275 | 2962 octave_idx_type nr = rows (); |
| 2963 octave_idx_type nc = cols (); | |
| 458 | 2964 |
| 2965 if (nr > 0 && nc > 0) | |
| 2966 { | |
| 2967 result.resize (nr); | |
| 4587 | 2968 idx_arg.resize (nr); |
| 458 | 2969 |
| 5275 | 2970 for (octave_idx_type i = 0; i < nr; i++) |
| 458 | 2971 { |
| 5275 | 2972 octave_idx_type idx_j; |
| 4469 | 2973 |
| 2974 double tmp_max = octave_NaN; | |
| 2975 | |
| 2976 for (idx_j = 0; idx_j < nc; idx_j++) | |
| 2354 | 2977 { |
| 4469 | 2978 tmp_max = elem (i, idx_j); |
| 2979 | |
| 5389 | 2980 if (! xisnan (tmp_max)) |
| 4469 | 2981 break; |
| 2982 } | |
| 2983 | |
| 5275 | 2984 for (octave_idx_type j = idx_j+1; j < nc; j++) |
| 4469 | 2985 { |
| 2986 double tmp = elem (i, j); | |
| 2987 | |
| 5389 | 2988 if (xisnan (tmp)) |
| 4469 | 2989 continue; |
| 2990 else if (tmp > tmp_max) | |
| 2354 | 2991 { |
| 4469 | 2992 idx_j = j; |
| 2993 tmp_max = tmp; | |
| 2354 | 2994 } |
| 2995 } | |
| 2996 | |
| 4469 | 2997 result.elem (i) = tmp_max; |
| 5389 | 2998 idx_arg.elem (i) = xisnan (tmp_max) ? 0 : idx_j; |
| 458 | 2999 } |
| 3000 } | |
| 3001 | |
| 3002 return result; | |
| 3003 } | |
| 3004 | |
| 3005 RowVector | |
| 3006 Matrix::column_min (void) const | |
| 3007 { | |
| 5275 | 3008 Array<octave_idx_type> dummy_idx; |
| 4587 | 3009 return column_min (dummy_idx); |
| 458 | 3010 } |
| 2354 | 3011 |
| 458 | 3012 RowVector |
| 5275 | 3013 Matrix::column_min (Array<octave_idx_type>& idx_arg) const |
| 458 | 3014 { |
| 3015 RowVector result; | |
| 3016 | |
| 5275 | 3017 octave_idx_type nr = rows (); |
| 3018 octave_idx_type nc = cols (); | |
| 458 | 3019 |
| 3020 if (nr > 0 && nc > 0) | |
| 3021 { | |
| 3022 result.resize (nc); | |
| 4587 | 3023 idx_arg.resize (nc); |
| 458 | 3024 |
| 5275 | 3025 for (octave_idx_type j = 0; j < nc; j++) |
| 458 | 3026 { |
| 5275 | 3027 octave_idx_type idx_i; |
| 4469 | 3028 |
| 3029 double tmp_min = octave_NaN; | |
| 3030 | |
| 3031 for (idx_i = 0; idx_i < nr; idx_i++) | |
| 2354 | 3032 { |
| 4469 | 3033 tmp_min = elem (idx_i, j); |
| 3034 | |
| 5389 | 3035 if (! xisnan (tmp_min)) |
| 4469 | 3036 break; |
| 3037 } | |
| 3038 | |
| 5275 | 3039 for (octave_idx_type i = idx_i+1; i < nr; i++) |
| 4469 | 3040 { |
| 3041 double tmp = elem (i, j); | |
| 3042 | |
| 5389 | 3043 if (xisnan (tmp)) |
| 4469 | 3044 continue; |
| 3045 else if (tmp < tmp_min) | |
| 2354 | 3046 { |
| 4469 | 3047 idx_i = i; |
| 3048 tmp_min = tmp; | |
| 2354 | 3049 } |
| 3050 } | |
| 3051 | |
| 4469 | 3052 result.elem (j) = tmp_min; |
| 5389 | 3053 idx_arg.elem (j) = xisnan (tmp_min) ? 0 : idx_i; |
| 458 | 3054 } |
| 3055 } | |
| 3056 | |
| 3057 return result; | |
| 3058 } | |
| 3059 | |
| 2354 | 3060 RowVector |
| 3061 Matrix::column_max (void) const | |
| 3062 { | |
| 5275 | 3063 Array<octave_idx_type> dummy_idx; |
| 4587 | 3064 return column_max (dummy_idx); |
| 2354 | 3065 } |
| 458 | 3066 |
| 3067 RowVector | |
| 5275 | 3068 Matrix::column_max (Array<octave_idx_type>& idx_arg) const |
| 458 | 3069 { |
| 3070 RowVector result; | |
| 3071 | |
| 5275 | 3072 octave_idx_type nr = rows (); |
| 3073 octave_idx_type nc = cols (); | |
| 458 | 3074 |
| 3075 if (nr > 0 && nc > 0) | |
| 3076 { | |
| 3077 result.resize (nc); | |
| 4587 | 3078 idx_arg.resize (nc); |
| 458 | 3079 |
| 5275 | 3080 for (octave_idx_type j = 0; j < nc; j++) |
| 458 | 3081 { |
| 5275 | 3082 octave_idx_type idx_i; |
| 4469 | 3083 |
| 3084 double tmp_max = octave_NaN; | |
| 3085 | |
| 3086 for (idx_i = 0; idx_i < nr; idx_i++) | |
| 2354 | 3087 { |
| 4469 | 3088 tmp_max = elem (idx_i, j); |
| 3089 | |
| 5389 | 3090 if (! xisnan (tmp_max)) |
| 4469 | 3091 break; |
| 3092 } | |
| 3093 | |
| 5275 | 3094 for (octave_idx_type i = idx_i+1; i < nr; i++) |
| 4469 | 3095 { |
| 3096 double tmp = elem (i, j); | |
| 3097 | |
| 5389 | 3098 if (xisnan (tmp)) |
| 4469 | 3099 continue; |
| 3100 else if (tmp > tmp_max) | |
| 2354 | 3101 { |
| 4469 | 3102 idx_i = i; |
| 3103 tmp_max = tmp; | |
| 2354 | 3104 } |
| 3105 } | |
| 3106 | |
| 4469 | 3107 result.elem (j) = tmp_max; |
| 5389 | 3108 idx_arg.elem (j) = xisnan (tmp_max) ? 0 : idx_i; |
| 458 | 3109 } |
| 3110 } | |
| 3111 | |
| 3112 return result; | |
| 3113 } | |
| 3114 | |
| 3504 | 3115 std::ostream& |
| 3116 operator << (std::ostream& os, const Matrix& a) | |
| 458 | 3117 { |
| 5275 | 3118 for (octave_idx_type i = 0; i < a.rows (); i++) |
| 458 | 3119 { |
| 5275 | 3120 for (octave_idx_type j = 0; j < a.cols (); j++) |
| 4130 | 3121 { |
| 3122 os << " "; | |
| 3123 octave_write_double (os, a.elem (i, j)); | |
| 3124 } | |
| 458 | 3125 os << "\n"; |
| 3126 } | |
| 3127 return os; | |
| 3128 } | |
| 3129 | |
| 3504 | 3130 std::istream& |
| 3131 operator >> (std::istream& is, Matrix& a) | |
| 458 | 3132 { |
| 5275 | 3133 octave_idx_type nr = a.rows (); |
| 3134 octave_idx_type nc = a.cols (); | |
| 458 | 3135 |
| 3136 if (nr < 1 || nc < 1) | |
| 3504 | 3137 is.clear (std::ios::badbit); |
| 458 | 3138 else |
| 3139 { | |
| 3140 double tmp; | |
| 5275 | 3141 for (octave_idx_type i = 0; i < nr; i++) |
| 3142 for (octave_idx_type j = 0; j < nc; j++) | |
| 458 | 3143 { |
| 4130 | 3144 tmp = octave_read_double (is); |
| 458 | 3145 if (is) |
| 3146 a.elem (i, j) = tmp; | |
| 3147 else | |
| 2795 | 3148 goto done; |
| 458 | 3149 } |
| 3150 } | |
| 3151 | |
| 2795 | 3152 done: |
| 3153 | |
| 458 | 3154 return is; |
| 3155 } | |
| 3156 | |
| 1819 | 3157 Matrix |
| 3158 Givens (double x, double y) | |
| 3159 { | |
| 3160 double cc, s, temp_r; | |
| 3161 | |
| 3887 | 3162 F77_FUNC (dlartg, DLARTG) (x, y, cc, s, temp_r); |
| 1819 | 3163 |
| 3164 Matrix g (2, 2); | |
| 3165 | |
| 3166 g.elem (0, 0) = cc; | |
| 3167 g.elem (1, 1) = cc; | |
| 3168 g.elem (0, 1) = s; | |
| 3169 g.elem (1, 0) = -s; | |
| 3170 | |
| 3171 return g; | |
| 3172 } | |
| 3173 | |
| 3174 Matrix | |
| 3175 Sylvester (const Matrix& a, const Matrix& b, const Matrix& c) | |
| 3176 { | |
| 3177 Matrix retval; | |
| 3178 | |
| 5775 | 3179 // FIXME -- need to check that a, b, and c are all the same |
| 1819 | 3180 // size. |
| 3181 | |
| 3182 // Compute Schur decompositions. | |
| 3183 | |
| 3184 SCHUR as (a, "U"); | |
| 3185 SCHUR bs (b, "U"); | |
| 3186 | |
| 3187 // Transform c to new coordinates. | |
| 3188 | |
| 3189 Matrix ua = as.unitary_matrix (); | |
| 3190 Matrix sch_a = as.schur_matrix (); | |
| 3191 | |
| 3192 Matrix ub = bs.unitary_matrix (); | |
| 3193 Matrix sch_b = bs.schur_matrix (); | |
| 3194 | |
| 3195 Matrix cx = ua.transpose () * c * ub; | |
| 3196 | |
| 3197 // Solve the sylvester equation, back-transform, and return the | |
| 3198 // solution. | |
| 3199 | |
| 5275 | 3200 octave_idx_type a_nr = a.rows (); |
| 3201 octave_idx_type b_nr = b.rows (); | |
| 1819 | 3202 |
| 3203 double scale; | |
| 5275 | 3204 octave_idx_type info; |
| 1819 | 3205 |
| 1950 | 3206 double *pa = sch_a.fortran_vec (); |
| 3207 double *pb = sch_b.fortran_vec (); | |
| 3208 double *px = cx.fortran_vec (); | |
| 3209 | |
| 4552 | 3210 F77_XFCN (dtrsyl, DTRSYL, (F77_CONST_CHAR_ARG2 ("N", 1), |
| 3211 F77_CONST_CHAR_ARG2 ("N", 1), | |
| 3212 1, a_nr, b_nr, pa, a_nr, pb, | |
| 3213 b_nr, px, a_nr, scale, info | |
| 3214 F77_CHAR_ARG_LEN (1) | |
| 3215 F77_CHAR_ARG_LEN (1))); | |
| 1950 | 3216 |
| 3217 | |
|
7482
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
3218 // FIXME -- check info? |
| 1819 | 3219 |
|
7482
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
3220 retval = -ua*cx*ub.transpose (); |
| 1819 | 3221 |
| 3222 return retval; | |
| 3223 } | |
| 3224 | |
| 2828 | 3225 // matrix by matrix -> matrix operations |
| 3226 | |
| 6162 | 3227 /* Simple Dot Product, Matrix-Vector and Matrix-Matrix Unit tests |
| 3228 %!assert([1 2 3] * [ 4 ; 5 ; 6], 32, 1e-14) | |
| 3229 %!assert([1 2 ; 3 4 ] * [5 ; 6], [17 ; 39 ], 1e-14) | |
| 3230 %!assert([1 2 ; 3 4 ] * [5 6 ; 7 8], [19 22; 43 50], 1e-14) | |
| 3231 */ | |
| 3232 | |
| 3233 /* Test some simple identities | |
| 3234 %!shared M, cv, rv | |
| 3235 %! M = randn(10,10); | |
| 3236 %! cv = randn(10,1); | |
| 3237 %! rv = randn(1,10); | |
| 3238 %!assert([M*cv,M*cv],M*[cv,cv],1e-14) | |
| 3239 %!assert([rv*M;rv*M],[rv;rv]*M,1e-14) | |
| 3240 %!assert(2*rv*cv,[rv,rv]*[cv;cv],1e-14) | |
| 3241 */ | |
| 3242 | |
| 3243 | |
| 2828 | 3244 Matrix |
| 3245 operator * (const Matrix& m, const Matrix& a) | |
| 3246 { | |
| 3247 Matrix retval; | |
| 3248 | |
| 5275 | 3249 octave_idx_type nr = m.rows (); |
| 3250 octave_idx_type nc = m.cols (); | |
| 3251 | |
| 3252 octave_idx_type a_nr = a.rows (); | |
| 3253 octave_idx_type a_nc = a.cols (); | |
| 2828 | 3254 |
| 3255 if (nc != a_nr) | |
| 3256 gripe_nonconformant ("operator *", nr, nc, a_nr, a_nc); | |
| 3257 else | |
| 3258 { | |
| 3259 if (nr == 0 || nc == 0 || a_nc == 0) | |
| 3260 retval.resize (nr, a_nc, 0.0); | |
| 3261 else | |
| 3262 { | |
| 5275 | 3263 octave_idx_type ld = nr; |
| 3264 octave_idx_type lda = a_nr; | |
| 2828 | 3265 |
| 3266 retval.resize (nr, a_nc); | |
| 3267 double *c = retval.fortran_vec (); | |
| 3268 | |
| 5983 | 3269 if (a_nc == 1) |
| 3270 { | |
| 3271 if (nr == 1) | |
| 3272 F77_FUNC (xddot, XDDOT) (nc, m.data (), 1, a.data (), 1, *c); | |
| 3273 else | |
| 6390 | 3274 { |
| 3275 F77_XFCN (dgemv, DGEMV, (F77_CONST_CHAR_ARG2 ("N", 1), | |
| 3276 nr, nc, 1.0, m.data (), ld, | |
| 3277 a.data (), 1, 0.0, c, 1 | |
| 3278 F77_CHAR_ARG_LEN (1))); | |
| 3279 } | |
| 5983 | 3280 } |
| 3281 else | |
| 6390 | 3282 { |
| 3283 F77_XFCN (dgemm, DGEMM, (F77_CONST_CHAR_ARG2 ("N", 1), | |
| 3284 F77_CONST_CHAR_ARG2 ("N", 1), | |
| 3285 nr, a_nc, nc, 1.0, m.data (), | |
| 3286 ld, a.data (), lda, 0.0, c, nr | |
| 3287 F77_CHAR_ARG_LEN (1) | |
| 3288 F77_CHAR_ARG_LEN (1))); | |
| 3289 } | |
| 2828 | 3290 } |
| 3291 } | |
| 3292 | |
| 3293 return retval; | |
| 3294 } | |
| 3295 | |
| 5775 | 3296 // FIXME -- it would be nice to share code among the min/max |
| 4309 | 3297 // functions below. |
| 3298 | |
| 3299 #define EMPTY_RETURN_CHECK(T) \ | |
| 3300 if (nr == 0 || nc == 0) \ | |
| 3301 return T (nr, nc); | |
| 3302 | |
| 3303 Matrix | |
| 3304 min (double d, const Matrix& m) | |
| 3305 { | |
| 5275 | 3306 octave_idx_type nr = m.rows (); |
| 3307 octave_idx_type nc = m.columns (); | |
| 4309 | 3308 |
| 3309 EMPTY_RETURN_CHECK (Matrix); | |
| 3310 | |
| 3311 Matrix result (nr, nc); | |
| 3312 | |
| 5275 | 3313 for (octave_idx_type j = 0; j < nc; j++) |
| 3314 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3315 { |
| 3316 OCTAVE_QUIT; | |
| 3317 result (i, j) = xmin (d, m (i, j)); | |
| 3318 } | |
| 3319 | |
| 3320 return result; | |
| 3321 } | |
| 3322 | |
| 3323 Matrix | |
| 3324 min (const Matrix& m, double d) | |
| 3325 { | |
| 5275 | 3326 octave_idx_type nr = m.rows (); |
| 3327 octave_idx_type nc = m.columns (); | |
| 4309 | 3328 |
| 3329 EMPTY_RETURN_CHECK (Matrix); | |
| 3330 | |
| 3331 Matrix result (nr, nc); | |
| 3332 | |
| 5275 | 3333 for (octave_idx_type j = 0; j < nc; j++) |
| 3334 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3335 { |
| 3336 OCTAVE_QUIT; | |
| 3337 result (i, j) = xmin (m (i, j), d); | |
| 3338 } | |
| 3339 | |
| 3340 return result; | |
| 3341 } | |
| 3342 | |
| 3343 Matrix | |
| 3344 min (const Matrix& a, const Matrix& b) | |
| 3345 { | |
| 5275 | 3346 octave_idx_type nr = a.rows (); |
| 3347 octave_idx_type nc = a.columns (); | |
| 4309 | 3348 |
| 3349 if (nr != b.rows () || nc != b.columns ()) | |
| 3350 { | |
| 3351 (*current_liboctave_error_handler) | |
| 3352 ("two-arg min expecting args of same size"); | |
| 3353 return Matrix (); | |
| 3354 } | |
| 3355 | |
| 3356 EMPTY_RETURN_CHECK (Matrix); | |
| 3357 | |
| 3358 Matrix result (nr, nc); | |
| 3359 | |
| 5275 | 3360 for (octave_idx_type j = 0; j < nc; j++) |
| 3361 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3362 { |
| 3363 OCTAVE_QUIT; | |
| 3364 result (i, j) = xmin (a (i, j), b (i, j)); | |
| 3365 } | |
| 3366 | |
| 3367 return result; | |
| 3368 } | |
| 3369 | |
| 3370 Matrix | |
| 3371 max (double d, const Matrix& m) | |
| 3372 { | |
| 5275 | 3373 octave_idx_type nr = m.rows (); |
| 3374 octave_idx_type nc = m.columns (); | |
| 4309 | 3375 |
| 3376 EMPTY_RETURN_CHECK (Matrix); | |
| 3377 | |
| 3378 Matrix result (nr, nc); | |
| 3379 | |
| 5275 | 3380 for (octave_idx_type j = 0; j < nc; j++) |
| 3381 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3382 { |
| 3383 OCTAVE_QUIT; | |
| 3384 result (i, j) = xmax (d, m (i, j)); | |
| 3385 } | |
| 3386 | |
| 3387 return result; | |
| 3388 } | |
| 3389 | |
| 3390 Matrix | |
| 3391 max (const Matrix& m, double d) | |
| 3392 { | |
| 5275 | 3393 octave_idx_type nr = m.rows (); |
| 3394 octave_idx_type nc = m.columns (); | |
| 4309 | 3395 |
| 3396 EMPTY_RETURN_CHECK (Matrix); | |
| 3397 | |
| 3398 Matrix result (nr, nc); | |
| 3399 | |
| 5275 | 3400 for (octave_idx_type j = 0; j < nc; j++) |
| 3401 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3402 { |
| 3403 OCTAVE_QUIT; | |
| 3404 result (i, j) = xmax (m (i, j), d); | |
| 3405 } | |
| 3406 | |
| 3407 return result; | |
| 3408 } | |
| 3409 | |
| 3410 Matrix | |
| 3411 max (const Matrix& a, const Matrix& b) | |
| 3412 { | |
| 5275 | 3413 octave_idx_type nr = a.rows (); |
| 3414 octave_idx_type nc = a.columns (); | |
| 4309 | 3415 |
| 3416 if (nr != b.rows () || nc != b.columns ()) | |
| 3417 { | |
| 3418 (*current_liboctave_error_handler) | |
| 3419 ("two-arg max expecting args of same size"); | |
| 3420 return Matrix (); | |
| 3421 } | |
| 3422 | |
| 3423 EMPTY_RETURN_CHECK (Matrix); | |
| 3424 | |
| 3425 Matrix result (nr, nc); | |
| 3426 | |
| 5275 | 3427 for (octave_idx_type j = 0; j < nc; j++) |
| 3428 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3429 { |
| 3430 OCTAVE_QUIT; | |
| 3431 result (i, j) = xmax (a (i, j), b (i, j)); | |
| 3432 } | |
| 3433 | |
| 3434 return result; | |
| 3435 } | |
| 3436 | |
| 2870 | 3437 MS_CMP_OPS(Matrix, , double, ) |
| 3504 | 3438 MS_BOOL_OPS(Matrix, double, 0.0) |
| 2870 | 3439 |
| 3440 SM_CMP_OPS(double, , Matrix, ) | |
| 3504 | 3441 SM_BOOL_OPS(double, Matrix, 0.0) |
| 2870 | 3442 |
| 3443 MM_CMP_OPS(Matrix, , Matrix, ) | |
| 3504 | 3444 MM_BOOL_OPS(Matrix, Matrix, 0.0) |
| 2870 | 3445 |
| 458 | 3446 /* |
| 3447 ;;; Local Variables: *** | |
| 3448 ;;; mode: C++ *** | |
| 3449 ;;; End: *** | |
| 3450 */ |