Mercurial > hg > octave-nkf
annotate liboctave/dMatrix.cc @ 7544:f9983d2761df
more xGELSD workspace fixes
| author | Jaroslav Hajek <highegg@gmail.com> |
|---|---|
| date | Mon, 03 Mar 2008 02:18:12 -0500 |
| parents | 493bb0de3199 |
| children | 36594d5bbe13 |
| rev | line source |
|---|---|
| 1993 | 1 // Matrix manipulations. |
| 458 | 2 /* |
| 3 | |
| 7017 | 4 Copyright (C) 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, |
| 5 2003, 2004, 2005, 2006, 2007 John W. Eaton | |
| 458 | 6 |
| 7 This file is part of Octave. | |
| 8 | |
| 9 Octave is free software; you can redistribute it and/or modify it | |
| 10 under the terms of the GNU General Public License as published by the | |
| 7016 | 11 Free Software Foundation; either version 3 of the License, or (at your |
| 12 option) any later version. | |
| 458 | 13 |
| 14 Octave is distributed in the hope that it will be useful, but WITHOUT | |
| 15 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
| 16 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
| 17 for more details. | |
| 18 | |
| 19 You should have received a copy of the GNU General Public License | |
| 7016 | 20 along with Octave; see the file COPYING. If not, see |
| 21 <http://www.gnu.org/licenses/>. | |
| 458 | 22 |
| 23 */ | |
| 24 | |
| 25 #ifdef HAVE_CONFIG_H | |
| 1192 | 26 #include <config.h> |
| 458 | 27 #endif |
| 28 | |
| 1367 | 29 #include <cfloat> |
| 30 | |
| 3503 | 31 #include <iostream> |
| 6209 | 32 #include <vector> |
| 1367 | 33 |
| 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" |
|
7503
8c32f95c2639
convert mapper functions to new format
David Bateman <dbateman@free.fr>
parents:
7488
diff
changeset
|
43 #include "functor.h" |
| 458 | 44 #include "lo-error.h" |
| 2354 | 45 #include "lo-ieee.h" |
| 46 #include "lo-mappers.h" | |
| 1968 | 47 #include "lo-utils.h" |
| 1367 | 48 #include "mx-base.h" |
| 2828 | 49 #include "mx-m-dm.h" |
| 3176 | 50 #include "mx-dm-m.h" |
| 1367 | 51 #include "mx-inlines.cc" |
| 1650 | 52 #include "oct-cmplx.h" |
| 4153 | 53 #include "quit.h" |
| 458 | 54 |
| 4773 | 55 #if defined (HAVE_FFTW3) |
| 3827 | 56 #include "oct-fftw.h" |
| 57 #endif | |
| 58 | |
| 458 | 59 // Fortran functions we call. |
| 60 | |
| 61 extern "C" | |
| 62 { | |
| 7478 | 63 F77_RET_T |
| 7477 | 64 F77_FUNC (xilaenv, XILAENV) (const octave_idx_type&, F77_CONST_CHAR_ARG_DECL, |
| 65 F77_CONST_CHAR_ARG_DECL, | |
| 66 const octave_idx_type&, const octave_idx_type&, | |
| 7478 | 67 const octave_idx_type&, const octave_idx_type&, |
| 68 octave_idx_type& | |
| 69 F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); | |
| 7476 | 70 |
| 4552 | 71 F77_RET_T |
| 72 F77_FUNC (dgebal, DGEBAL) (F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 73 const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type&, |
| 74 octave_idx_type&, double*, octave_idx_type& | |
| 4552 | 75 F77_CHAR_ARG_LEN_DECL); |
| 76 | |
| 77 F77_RET_T | |
| 78 F77_FUNC (dgebak, DGEBAK) (F77_CONST_CHAR_ARG_DECL, | |
| 79 F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 80 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, double*, |
| 81 const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type& | |
| 4552 | 82 F77_CHAR_ARG_LEN_DECL |
| 83 F77_CHAR_ARG_LEN_DECL); | |
| 84 | |
| 85 | |
| 86 F77_RET_T | |
| 87 F77_FUNC (dgemm, DGEMM) (F77_CONST_CHAR_ARG_DECL, | |
| 88 F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 89 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
| 90 const double&, const double*, const octave_idx_type&, | |
| 91 const double*, const octave_idx_type&, const double&, | |
| 92 double*, const octave_idx_type& | |
| 4552 | 93 F77_CHAR_ARG_LEN_DECL |
| 94 F77_CHAR_ARG_LEN_DECL); | |
| 95 | |
| 96 F77_RET_T | |
| 5983 | 97 F77_FUNC (dgemv, DGEMV) (F77_CONST_CHAR_ARG_DECL, |
| 98 const octave_idx_type&, const octave_idx_type&, const double&, | |
| 99 const double*, const octave_idx_type&, const double*, | |
| 100 const octave_idx_type&, const double&, double*, | |
| 101 const octave_idx_type& | |
| 102 F77_CHAR_ARG_LEN_DECL); | |
| 103 | |
| 104 F77_RET_T | |
| 105 F77_FUNC (xddot, XDDOT) (const octave_idx_type&, const double*, const octave_idx_type&, | |
| 106 const double*, const octave_idx_type&, double&); | |
| 107 | |
| 108 F77_RET_T | |
| 5275 | 109 F77_FUNC (dgetrf, DGETRF) (const octave_idx_type&, const octave_idx_type&, double*, const octave_idx_type&, |
| 110 octave_idx_type*, octave_idx_type&); | |
| 4329 | 111 |
| 4552 | 112 F77_RET_T |
| 5275 | 113 F77_FUNC (dgetrs, DGETRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, |
| 114 const double*, const octave_idx_type&, | |
| 115 const octave_idx_type*, double*, const octave_idx_type&, octave_idx_type& | |
| 4552 | 116 F77_CHAR_ARG_LEN_DECL); |
| 117 | |
| 118 F77_RET_T | |
| 5275 | 119 F77_FUNC (dgetri, DGETRI) (const octave_idx_type&, double*, const octave_idx_type&, const octave_idx_type*, |
| 120 double*, const octave_idx_type&, octave_idx_type&); | |
| 4552 | 121 |
| 122 F77_RET_T | |
| 5275 | 123 F77_FUNC (dgecon, DGECON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, double*, |
| 124 const octave_idx_type&, const double&, double&, | |
| 125 double*, octave_idx_type*, octave_idx_type& | |
| 4552 | 126 F77_CHAR_ARG_LEN_DECL); |
| 127 | |
| 128 F77_RET_T | |
| 7072 | 129 F77_FUNC (dgelsy, DGELSY) (const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
| 130 double*, const octave_idx_type&, double*, | |
| 131 const octave_idx_type&, octave_idx_type*, double&, octave_idx_type&, | |
| 132 double*, const octave_idx_type&, octave_idx_type&); | |
| 133 | |
| 134 F77_RET_T | |
| 135 F77_FUNC (dgelsd, DGELSD) (const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, | |
| 5275 | 136 double*, const octave_idx_type&, double*, |
| 7071 | 137 const octave_idx_type&, double*, double&, octave_idx_type&, |
| 7072 | 138 double*, const octave_idx_type&, octave_idx_type*, |
| 139 octave_idx_type&); | |
| 458 | 140 |
| 5785 | 141 F77_RET_T |
| 142 F77_FUNC (dpotrf, DPOTRF) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 143 double *, const octave_idx_type&, | |
| 144 octave_idx_type& F77_CHAR_ARG_LEN_DECL); | |
| 145 | |
| 146 F77_RET_T | |
| 147 F77_FUNC (dpocon, DPOCON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 148 double*, const octave_idx_type&, const double&, | |
| 149 double&, double*, octave_idx_type*, | |
| 150 octave_idx_type& F77_CHAR_ARG_LEN_DECL); | |
| 151 F77_RET_T | |
| 152 F77_FUNC (dpotrs, DPOTRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 153 const octave_idx_type&, const double*, | |
| 154 const octave_idx_type&, double*, | |
| 155 const octave_idx_type&, octave_idx_type& | |
| 156 F77_CHAR_ARG_LEN_DECL); | |
| 157 | |
| 158 F77_RET_T | |
| 6207 | 159 F77_FUNC (dtrtri, DTRTRI) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, |
| 160 const octave_idx_type&, const double*, | |
| 161 const octave_idx_type&, octave_idx_type& | |
| 162 F77_CHAR_ARG_LEN_DECL | |
| 163 F77_CHAR_ARG_LEN_DECL); | |
| 164 F77_RET_T | |
| 5785 | 165 F77_FUNC (dtrcon, DTRCON) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, |
| 166 F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 167 const double*, const octave_idx_type&, double&, | |
| 168 double*, octave_idx_type*, octave_idx_type& | |
| 169 F77_CHAR_ARG_LEN_DECL | |
| 170 F77_CHAR_ARG_LEN_DECL | |
| 171 F77_CHAR_ARG_LEN_DECL); | |
| 172 F77_RET_T | |
| 173 F77_FUNC (dtrtrs, DTRTRS) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, | |
| 174 F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 175 const octave_idx_type&, const double*, | |
| 176 const octave_idx_type&, double*, | |
| 177 const octave_idx_type&, octave_idx_type& | |
| 178 F77_CHAR_ARG_LEN_DECL | |
| 179 F77_CHAR_ARG_LEN_DECL | |
| 180 F77_CHAR_ARG_LEN_DECL); | |
| 181 | |
| 1360 | 182 // Note that the original complex fft routines were not written for |
| 183 // double complex arguments. They have been modified by adding an | |
| 184 // implicit double precision (a-h,o-z) statement at the beginning of | |
| 185 // each subroutine. | |
| 458 | 186 |
| 4552 | 187 F77_RET_T |
| 5275 | 188 F77_FUNC (cffti, CFFTI) (const octave_idx_type&, Complex*); |
| 4552 | 189 |
| 190 F77_RET_T | |
| 5275 | 191 F77_FUNC (cfftf, CFFTF) (const octave_idx_type&, Complex*, Complex*); |
| 4552 | 192 |
| 193 F77_RET_T | |
| 5275 | 194 F77_FUNC (cfftb, CFFTB) (const octave_idx_type&, Complex*, Complex*); |
| 4552 | 195 |
| 196 F77_RET_T | |
| 197 F77_FUNC (dlartg, DLARTG) (const double&, const double&, double&, | |
| 198 double&, double&); | |
| 199 | |
| 200 F77_RET_T | |
| 201 F77_FUNC (dtrsyl, DTRSYL) (F77_CONST_CHAR_ARG_DECL, | |
| 202 F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 203 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
| 204 const double*, const octave_idx_type&, const double*, | |
| 205 const octave_idx_type&, const double*, const octave_idx_type&, | |
| 206 double&, octave_idx_type& | |
| 4552 | 207 F77_CHAR_ARG_LEN_DECL |
| 208 F77_CHAR_ARG_LEN_DECL); | |
| 209 | |
| 210 F77_RET_T | |
| 5275 | 211 F77_FUNC (xdlange, XDLANGE) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, |
| 212 const octave_idx_type&, const double*, | |
| 213 const octave_idx_type&, double*, double& | |
| 4552 | 214 F77_CHAR_ARG_LEN_DECL); |
| 458 | 215 } |
| 216 | |
| 1360 | 217 // Matrix class. |
| 458 | 218 |
| 2349 | 219 Matrix::Matrix (const RowVector& rv) |
| 220 : MArray2<double> (1, rv.length (), 0.0) | |
| 221 { | |
| 5275 | 222 for (octave_idx_type i = 0; i < rv.length (); i++) |
| 2349 | 223 elem (0, i) = rv.elem (i); |
| 224 } | |
| 225 | |
| 226 Matrix::Matrix (const ColumnVector& cv) | |
| 227 : MArray2<double> (cv.length (), 1, 0.0) | |
| 228 { | |
| 5275 | 229 for (octave_idx_type i = 0; i < cv.length (); i++) |
| 2349 | 230 elem (i, 0) = cv.elem (i); |
| 231 } | |
| 232 | |
| 458 | 233 Matrix::Matrix (const DiagMatrix& a) |
| 1214 | 234 : MArray2<double> (a.rows (), a.cols (), 0.0) |
| 458 | 235 { |
| 5275 | 236 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 237 elem (i, i) = a.elem (i, i); |
| 238 } | |
| 239 | |
| 5775 | 240 // FIXME -- could we use a templated mixed-type copy function |
| 1574 | 241 // here? |
| 242 | |
| 2828 | 243 Matrix::Matrix (const boolMatrix& a) |
| 244 : MArray2<double> (a.rows (), a.cols ()) | |
| 245 { | |
| 5275 | 246 for (octave_idx_type i = 0; i < a.rows (); i++) |
| 247 for (octave_idx_type j = 0; j < a.cols (); j++) | |
| 2828 | 248 elem (i, j) = a.elem (i, j); |
| 249 } | |
| 250 | |
| 1574 | 251 Matrix::Matrix (const charMatrix& a) |
| 252 : MArray2<double> (a.rows (), a.cols ()) | |
| 253 { | |
| 5275 | 254 for (octave_idx_type i = 0; i < a.rows (); i++) |
| 255 for (octave_idx_type j = 0; j < a.cols (); j++) | |
| 1574 | 256 elem (i, j) = a.elem (i, j); |
| 257 } | |
| 258 | |
| 2385 | 259 bool |
| 458 | 260 Matrix::operator == (const Matrix& a) const |
| 261 { | |
| 262 if (rows () != a.rows () || cols () != a.cols ()) | |
| 2385 | 263 return false; |
| 458 | 264 |
| 3769 | 265 return mx_inline_equal (data (), a.data (), length ()); |
| 458 | 266 } |
| 267 | |
| 2385 | 268 bool |
| 458 | 269 Matrix::operator != (const Matrix& a) const |
| 270 { | |
| 271 return !(*this == a); | |
| 272 } | |
| 273 | |
| 3354 | 274 bool |
| 275 Matrix::is_symmetric (void) const | |
| 276 { | |
| 277 if (is_square () && rows () > 0) | |
| 278 { | |
| 5275 | 279 for (octave_idx_type i = 0; i < rows (); i++) |
| 280 for (octave_idx_type j = i+1; j < cols (); j++) | |
| 3354 | 281 if (elem (i, j) != elem (j, i)) |
| 282 return false; | |
| 283 | |
| 284 return true; | |
| 285 } | |
| 286 | |
| 287 return false; | |
| 288 } | |
| 289 | |
| 458 | 290 Matrix& |
| 5275 | 291 Matrix::insert (const Matrix& a, octave_idx_type r, octave_idx_type c) |
| 458 | 292 { |
| 1561 | 293 Array2<double>::insert (a, r, c); |
| 458 | 294 return *this; |
| 295 } | |
| 296 | |
| 297 Matrix& | |
| 5275 | 298 Matrix::insert (const RowVector& a, octave_idx_type r, octave_idx_type c) |
| 458 | 299 { |
| 5275 | 300 octave_idx_type a_len = a.length (); |
| 4316 | 301 |
| 1698 | 302 if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ()) |
| 458 | 303 { |
| 304 (*current_liboctave_error_handler) ("range error for insert"); | |
| 305 return *this; | |
| 306 } | |
| 307 | |
| 4316 | 308 if (a_len > 0) |
| 309 { | |
| 310 make_unique (); | |
| 311 | |
| 5275 | 312 for (octave_idx_type i = 0; i < a_len; i++) |
| 4316 | 313 xelem (r, c+i) = a.elem (i); |
| 314 } | |
| 458 | 315 |
| 316 return *this; | |
| 317 } | |
| 318 | |
| 319 Matrix& | |
| 5275 | 320 Matrix::insert (const ColumnVector& a, octave_idx_type r, octave_idx_type c) |
| 458 | 321 { |
| 5275 | 322 octave_idx_type a_len = a.length (); |
| 4316 | 323 |
| 1698 | 324 if (r < 0 || r + a_len > rows () || c < 0 || c >= cols ()) |
| 458 | 325 { |
| 326 (*current_liboctave_error_handler) ("range error for insert"); | |
| 327 return *this; | |
| 328 } | |
| 329 | |
| 4316 | 330 if (a_len > 0) |
| 331 { | |
| 332 make_unique (); | |
| 333 | |
| 5275 | 334 for (octave_idx_type i = 0; i < a_len; i++) |
| 4316 | 335 xelem (r+i, c) = a.elem (i); |
| 336 } | |
| 458 | 337 |
| 338 return *this; | |
| 339 } | |
| 340 | |
| 341 Matrix& | |
| 5275 | 342 Matrix::insert (const DiagMatrix& a, octave_idx_type r, octave_idx_type c) |
| 458 | 343 { |
| 5275 | 344 octave_idx_type a_nr = a.rows (); |
| 345 octave_idx_type a_nc = a.cols (); | |
| 1697 | 346 |
| 1698 | 347 if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) |
| 458 | 348 { |
| 349 (*current_liboctave_error_handler) ("range error for insert"); | |
| 350 return *this; | |
| 351 } | |
| 352 | |
| 1697 | 353 fill (0.0, r, c, r + a_nr - 1, c + a_nc - 1); |
| 354 | |
| 5275 | 355 octave_idx_type a_len = a.length (); |
| 4316 | 356 |
| 357 if (a_len > 0) | |
| 358 { | |
| 359 make_unique (); | |
| 360 | |
| 5275 | 361 for (octave_idx_type i = 0; i < a_len; i++) |
| 4316 | 362 xelem (r+i, c+i) = a.elem (i, i); |
| 363 } | |
| 458 | 364 |
| 365 return *this; | |
| 366 } | |
| 367 | |
| 368 Matrix& | |
| 369 Matrix::fill (double val) | |
| 370 { | |
| 5275 | 371 octave_idx_type nr = rows (); |
| 372 octave_idx_type nc = cols (); | |
| 4316 | 373 |
| 458 | 374 if (nr > 0 && nc > 0) |
| 4316 | 375 { |
| 376 make_unique (); | |
| 377 | |
| 5275 | 378 for (octave_idx_type j = 0; j < nc; j++) |
| 379 for (octave_idx_type i = 0; i < nr; i++) | |
| 4316 | 380 xelem (i, j) = val; |
| 381 } | |
| 458 | 382 |
| 383 return *this; | |
| 384 } | |
| 385 | |
| 386 Matrix& | |
| 5275 | 387 Matrix::fill (double val, octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) |
| 458 | 388 { |
| 5275 | 389 octave_idx_type nr = rows (); |
| 390 octave_idx_type nc = cols (); | |
| 4316 | 391 |
| 458 | 392 if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0 |
| 393 || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc) | |
| 394 { | |
| 395 (*current_liboctave_error_handler) ("range error for fill"); | |
| 396 return *this; | |
| 397 } | |
| 398 | |
| 5275 | 399 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } |
| 400 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } | |
| 458 | 401 |
| 4316 | 402 if (r2 >= r1 && c2 >= c1) |
| 403 { | |
| 404 make_unique (); | |
| 405 | |
| 5275 | 406 for (octave_idx_type j = c1; j <= c2; j++) |
| 407 for (octave_idx_type i = r1; i <= r2; i++) | |
| 4316 | 408 xelem (i, j) = val; |
| 409 } | |
| 458 | 410 |
| 411 return *this; | |
| 412 } | |
| 413 | |
| 414 Matrix | |
| 415 Matrix::append (const Matrix& a) const | |
| 416 { | |
| 5275 | 417 octave_idx_type nr = rows (); |
| 418 octave_idx_type nc = cols (); | |
| 458 | 419 if (nr != a.rows ()) |
| 420 { | |
| 421 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 422 return Matrix (); | |
| 423 } | |
| 424 | |
| 5275 | 425 octave_idx_type nc_insert = nc; |
| 458 | 426 Matrix retval (nr, nc + a.cols ()); |
| 427 retval.insert (*this, 0, 0); | |
| 428 retval.insert (a, 0, nc_insert); | |
| 429 return retval; | |
| 430 } | |
| 431 | |
| 432 Matrix | |
| 433 Matrix::append (const RowVector& a) const | |
| 434 { | |
| 5275 | 435 octave_idx_type nr = rows (); |
| 436 octave_idx_type nc = cols (); | |
| 458 | 437 if (nr != 1) |
| 438 { | |
| 439 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 440 return Matrix (); | |
| 441 } | |
| 442 | |
| 5275 | 443 octave_idx_type nc_insert = nc; |
| 458 | 444 Matrix retval (nr, nc + a.length ()); |
| 445 retval.insert (*this, 0, 0); | |
| 446 retval.insert (a, 0, nc_insert); | |
| 447 return retval; | |
| 448 } | |
| 449 | |
| 450 Matrix | |
| 451 Matrix::append (const ColumnVector& a) const | |
| 452 { | |
| 5275 | 453 octave_idx_type nr = rows (); |
| 454 octave_idx_type nc = cols (); | |
| 458 | 455 if (nr != a.length ()) |
| 456 { | |
| 457 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 458 return Matrix (); | |
| 459 } | |
| 460 | |
| 5275 | 461 octave_idx_type nc_insert = nc; |
| 458 | 462 Matrix retval (nr, nc + 1); |
| 463 retval.insert (*this, 0, 0); | |
| 464 retval.insert (a, 0, nc_insert); | |
| 465 return retval; | |
| 466 } | |
| 467 | |
| 468 Matrix | |
| 469 Matrix::append (const DiagMatrix& a) const | |
| 470 { | |
| 5275 | 471 octave_idx_type nr = rows (); |
| 472 octave_idx_type nc = cols (); | |
| 458 | 473 if (nr != a.rows ()) |
| 474 { | |
| 475 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 476 return *this; | |
| 477 } | |
| 478 | |
| 5275 | 479 octave_idx_type nc_insert = nc; |
| 458 | 480 Matrix retval (nr, nc + a.cols ()); |
| 481 retval.insert (*this, 0, 0); | |
| 482 retval.insert (a, 0, nc_insert); | |
| 483 return retval; | |
| 484 } | |
| 485 | |
| 486 Matrix | |
| 487 Matrix::stack (const Matrix& a) const | |
| 488 { | |
| 5275 | 489 octave_idx_type nr = rows (); |
| 490 octave_idx_type nc = cols (); | |
| 458 | 491 if (nc != a.cols ()) |
| 492 { | |
| 493 (*current_liboctave_error_handler) | |
| 494 ("column dimension mismatch for stack"); | |
| 495 return Matrix (); | |
| 496 } | |
| 497 | |
| 5275 | 498 octave_idx_type nr_insert = nr; |
| 458 | 499 Matrix retval (nr + a.rows (), nc); |
| 500 retval.insert (*this, 0, 0); | |
| 501 retval.insert (a, nr_insert, 0); | |
| 502 return retval; | |
| 503 } | |
| 504 | |
| 505 Matrix | |
| 506 Matrix::stack (const RowVector& a) const | |
| 507 { | |
| 5275 | 508 octave_idx_type nr = rows (); |
| 509 octave_idx_type nc = cols (); | |
| 458 | 510 if (nc != a.length ()) |
| 511 { | |
| 512 (*current_liboctave_error_handler) | |
| 513 ("column dimension mismatch for stack"); | |
| 514 return Matrix (); | |
| 515 } | |
| 516 | |
| 5275 | 517 octave_idx_type nr_insert = nr; |
| 458 | 518 Matrix retval (nr + 1, nc); |
| 519 retval.insert (*this, 0, 0); | |
| 520 retval.insert (a, nr_insert, 0); | |
| 521 return retval; | |
| 522 } | |
| 523 | |
| 524 Matrix | |
| 525 Matrix::stack (const ColumnVector& a) const | |
| 526 { | |
| 5275 | 527 octave_idx_type nr = rows (); |
| 528 octave_idx_type nc = cols (); | |
| 458 | 529 if (nc != 1) |
| 530 { | |
| 531 (*current_liboctave_error_handler) | |
| 532 ("column dimension mismatch for stack"); | |
| 533 return Matrix (); | |
| 534 } | |
| 535 | |
| 5275 | 536 octave_idx_type nr_insert = nr; |
| 458 | 537 Matrix retval (nr + a.length (), nc); |
| 538 retval.insert (*this, 0, 0); | |
| 539 retval.insert (a, nr_insert, 0); | |
| 540 return retval; | |
| 541 } | |
| 542 | |
| 543 Matrix | |
| 544 Matrix::stack (const DiagMatrix& a) const | |
| 545 { | |
| 5275 | 546 octave_idx_type nr = rows (); |
| 547 octave_idx_type nc = cols (); | |
| 458 | 548 if (nc != a.cols ()) |
| 549 { | |
| 550 (*current_liboctave_error_handler) | |
| 551 ("column dimension mismatch for stack"); | |
| 552 return Matrix (); | |
| 553 } | |
| 554 | |
| 5275 | 555 octave_idx_type nr_insert = nr; |
| 458 | 556 Matrix retval (nr + a.rows (), nc); |
| 557 retval.insert (*this, 0, 0); | |
| 558 retval.insert (a, nr_insert, 0); | |
| 559 return retval; | |
| 560 } | |
| 561 | |
| 562 Matrix | |
| 1205 | 563 real (const ComplexMatrix& a) |
| 564 { | |
| 5275 | 565 octave_idx_type a_len = a.length (); |
| 1205 | 566 Matrix retval; |
| 567 if (a_len > 0) | |
| 3769 | 568 retval = Matrix (mx_inline_real_dup (a.data (), a_len), |
| 569 a.rows (), a.cols ()); | |
| 1205 | 570 return retval; |
| 571 } | |
| 572 | |
| 573 Matrix | |
| 574 imag (const ComplexMatrix& a) | |
| 575 { | |
| 5275 | 576 octave_idx_type a_len = a.length (); |
| 1205 | 577 Matrix retval; |
| 578 if (a_len > 0) | |
| 3769 | 579 retval = Matrix (mx_inline_imag_dup (a.data (), a_len), |
| 580 a.rows (), a.cols ()); | |
| 1205 | 581 return retval; |
| 582 } | |
| 583 | |
| 584 Matrix | |
| 5275 | 585 Matrix::extract (octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) const |
| 458 | 586 { |
| 5275 | 587 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } |
| 588 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } | |
| 589 | |
| 590 octave_idx_type new_r = r2 - r1 + 1; | |
| 591 octave_idx_type new_c = c2 - c1 + 1; | |
| 458 | 592 |
| 593 Matrix result (new_r, new_c); | |
| 594 | |
| 5275 | 595 for (octave_idx_type j = 0; j < new_c; j++) |
| 596 for (octave_idx_type i = 0; i < new_r; i++) | |
| 4316 | 597 result.xelem (i, j) = elem (r1+i, c1+j); |
| 598 | |
| 599 return result; | |
| 600 } | |
| 601 | |
| 602 Matrix | |
| 5275 | 603 Matrix::extract_n (octave_idx_type r1, octave_idx_type c1, octave_idx_type nr, octave_idx_type nc) const |
| 4316 | 604 { |
| 605 Matrix result (nr, nc); | |
| 606 | |
| 5275 | 607 for (octave_idx_type j = 0; j < nc; j++) |
| 608 for (octave_idx_type i = 0; i < nr; i++) | |
| 4316 | 609 result.xelem (i, j) = elem (r1+i, c1+j); |
| 458 | 610 |
| 611 return result; | |
| 612 } | |
| 613 | |
| 614 // extract row or column i. | |
| 615 | |
| 616 RowVector | |
| 5275 | 617 Matrix::row (octave_idx_type i) const |
| 458 | 618 { |
| 5275 | 619 octave_idx_type nc = cols (); |
| 458 | 620 if (i < 0 || i >= rows ()) |
| 621 { | |
| 622 (*current_liboctave_error_handler) ("invalid row selection"); | |
| 623 return RowVector (); | |
| 624 } | |
| 625 | |
| 626 RowVector retval (nc); | |
| 5275 | 627 for (octave_idx_type j = 0; j < nc; j++) |
| 4316 | 628 retval.xelem (j) = elem (i, j); |
| 458 | 629 |
| 630 return retval; | |
| 631 } | |
| 632 | |
| 633 ColumnVector | |
| 5275 | 634 Matrix::column (octave_idx_type i) const |
| 458 | 635 { |
| 5275 | 636 octave_idx_type nr = rows (); |
| 458 | 637 if (i < 0 || i >= cols ()) |
| 638 { | |
| 639 (*current_liboctave_error_handler) ("invalid column selection"); | |
| 640 return ColumnVector (); | |
| 641 } | |
| 642 | |
| 643 ColumnVector retval (nr); | |
| 5275 | 644 for (octave_idx_type j = 0; j < nr; j++) |
| 4316 | 645 retval.xelem (j) = elem (j, i); |
| 458 | 646 |
| 647 return retval; | |
| 648 } | |
| 649 | |
| 650 Matrix | |
| 651 Matrix::inverse (void) const | |
| 652 { | |
| 5275 | 653 octave_idx_type info; |
| 458 | 654 double rcond; |
| 6207 | 655 MatrixType mattype (*this); |
| 656 return inverse (mattype, info, rcond, 0, 0); | |
| 657 } | |
| 658 | |
| 659 Matrix | |
| 6479 | 660 Matrix::inverse (octave_idx_type& info) const |
| 661 { | |
| 662 double rcond; | |
| 663 MatrixType mattype (*this); | |
| 664 return inverse (mattype, info, rcond, 0, 0); | |
| 665 } | |
| 666 | |
| 667 Matrix | |
| 668 Matrix::inverse (octave_idx_type& info, double& rcond, int force, | |
| 669 int calc_cond) const | |
| 670 { | |
| 671 MatrixType mattype (*this); | |
| 672 return inverse (mattype, info, rcond, force, calc_cond); | |
| 673 } | |
| 674 | |
| 675 Matrix | |
| 6207 | 676 Matrix::inverse (MatrixType& mattype) const |
| 677 { | |
| 678 octave_idx_type info; | |
| 679 double rcond; | |
| 680 return inverse (mattype, info, rcond, 0, 0); | |
| 681 } | |
| 682 | |
| 683 Matrix | |
| 684 Matrix::inverse (MatrixType &mattype, octave_idx_type& info) const | |
| 685 { | |
| 686 double rcond; | |
| 687 return inverse (mattype, info, rcond, 0, 0); | |
| 458 | 688 } |
| 689 | |
| 690 Matrix | |
| 6207 | 691 Matrix::tinverse (MatrixType &mattype, octave_idx_type& info, double& rcond, |
| 692 int force, int calc_cond) const | |
| 458 | 693 { |
| 6207 | 694 Matrix retval; |
| 695 | |
| 696 octave_idx_type nr = rows (); | |
| 697 octave_idx_type nc = cols (); | |
| 698 | |
| 699 if (nr != nc || nr == 0 || nc == 0) | |
| 700 (*current_liboctave_error_handler) ("inverse requires square matrix"); | |
| 701 else | |
| 702 { | |
| 703 int typ = mattype.type (); | |
| 704 char uplo = (typ == MatrixType::Lower ? 'L' : 'U'); | |
| 705 char udiag = 'N'; | |
| 706 retval = *this; | |
| 707 double *tmp_data = retval.fortran_vec (); | |
| 708 | |
| 709 F77_XFCN (dtrtri, DTRTRI, (F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 710 F77_CONST_CHAR_ARG2 (&udiag, 1), | |
| 711 nr, tmp_data, nr, info | |
| 712 F77_CHAR_ARG_LEN (1) | |
| 713 F77_CHAR_ARG_LEN (1))); | |
| 714 | |
|
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715 // Throw-away extra info LAPACK gives so as to not change output. |
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716 rcond = 0.0; |
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717 if (info != 0) |
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718 info = -1; |
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719 else if (calc_cond) |
| 6207 | 720 { |
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721 octave_idx_type dtrcon_info = 0; |
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722 char job = '1'; |
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723 |
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724 OCTAVE_LOCAL_BUFFER (double, work, 3 * nr); |
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725 OCTAVE_LOCAL_BUFFER (octave_idx_type, iwork, nr); |
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726 |
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727 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&job, 1), |
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728 F77_CONST_CHAR_ARG2 (&uplo, 1), |
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729 F77_CONST_CHAR_ARG2 (&udiag, 1), |
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730 nr, tmp_data, nr, rcond, |
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731 work, iwork, dtrcon_info |
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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 F77_CHAR_ARG_LEN (1))); |
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735 |
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736 if (dtrcon_info != 0) |
| 6207 | 737 info = -1; |
| 738 } | |
| 739 | |
| 740 if (info == -1 && ! force) | |
| 741 retval = *this; // Restore matrix contents. | |
| 742 } | |
| 743 | |
| 744 return retval; | |
| 458 | 745 } |
| 746 | |
| 6207 | 747 |
| 458 | 748 Matrix |
| 6207 | 749 Matrix::finverse (MatrixType &mattype, octave_idx_type& info, double& rcond, |
| 750 int force, int calc_cond) const | |
| 458 | 751 { |
| 1948 | 752 Matrix retval; |
| 753 | |
| 5275 | 754 octave_idx_type nr = rows (); |
| 755 octave_idx_type nc = cols (); | |
| 1948 | 756 |
| 458 | 757 if (nr != nc || nr == 0 || nc == 0) |
| 1948 | 758 (*current_liboctave_error_handler) ("inverse requires square matrix"); |
| 458 | 759 else |
| 760 { | |
| 5275 | 761 Array<octave_idx_type> ipvt (nr); |
| 762 octave_idx_type *pipvt = ipvt.fortran_vec (); | |
| 1948 | 763 |
| 764 retval = *this; | |
| 765 double *tmp_data = retval.fortran_vec (); | |
| 766 | |
| 4329 | 767 Array<double> z(1); |
| 5275 | 768 octave_idx_type lwork = -1; |
| 4329 | 769 |
| 4330 | 770 // Query the optimum work array size. |
| 4329 | 771 F77_XFCN (dgetri, DGETRI, (nc, tmp_data, nr, pipvt, |
| 772 z.fortran_vec (), lwork, info)); | |
| 773 | |
| 5275 | 774 lwork = static_cast<octave_idx_type> (z(0)); |
| 4329 | 775 lwork = (lwork < 2 *nc ? 2*nc : lwork); |
| 776 z.resize (lwork); | |
| 777 double *pz = z.fortran_vec (); | |
| 778 | |
| 779 info = 0; | |
| 780 | |
| 4330 | 781 // Calculate the norm of the matrix, for later use. |
| 4329 | 782 double anorm = 0; |
| 783 if (calc_cond) | |
| 5275 | 784 anorm = retval.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
| 4329 | 785 |
| 786 F77_XFCN (dgetrf, DGETRF, (nc, nc, tmp_data, nr, pipvt, info)); | |
| 1948 | 787 |
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788 // Throw-away extra info LAPACK gives so as to not change output. |
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789 rcond = 0.0; |
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790 if (info != 0) |
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791 info = -1; |
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792 else if (calc_cond) |
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793 { |
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794 octave_idx_type dgecon_info = 0; |
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795 |
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796 // Now calculate the condition number for non-singular matrix. |
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797 char job = '1'; |
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798 Array<octave_idx_type> iz (nc); |
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799 octave_idx_type *piz = iz.fortran_vec (); |
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800 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
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801 nc, tmp_data, nr, anorm, |
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802 rcond, pz, piz, dgecon_info |
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803 F77_CHAR_ARG_LEN (1))); |
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804 |
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805 if (dgecon_info != 0) |
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806 info = -1; |
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807 } |
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808 |
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809 if (info == -1 && ! force) |
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810 retval = *this; // Restore matrix contents. |
| 1948 | 811 else |
| 812 { | |
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813 octave_idx_type dgetri_info = 0; |
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814 |
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815 F77_XFCN (dgetri, DGETRI, (nc, tmp_data, nr, pipvt, |
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816 pz, lwork, dgetri_info)); |
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817 |
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818 if (dgetri_info != 0) |
| 1948 | 819 info = -1; |
| 820 } | |
| 6207 | 821 |
| 822 if (info != 0) | |
| 823 mattype.mark_as_rectangular(); | |
| 458 | 824 } |
| 825 | |
| 1948 | 826 return retval; |
| 458 | 827 } |
| 828 | |
| 740 | 829 Matrix |
| 6207 | 830 Matrix::inverse (MatrixType &mattype, octave_idx_type& info, double& rcond, |
| 831 int force, int calc_cond) const | |
| 832 { | |
| 833 int typ = mattype.type (false); | |
| 834 Matrix ret; | |
| 835 | |
| 836 if (typ == MatrixType::Unknown) | |
| 837 typ = mattype.type (*this); | |
| 838 | |
| 839 if (typ == MatrixType::Upper || typ == MatrixType::Lower) | |
| 840 ret = tinverse (mattype, info, rcond, force, calc_cond); | |
| 6840 | 841 else |
| 6207 | 842 { |
| 843 if (mattype.is_hermitian ()) | |
| 844 { | |
| 6486 | 845 CHOL chol (*this, info, calc_cond); |
| 6207 | 846 if (info == 0) |
| 6486 | 847 { |
| 848 if (calc_cond) | |
| 849 rcond = chol.rcond (); | |
| 850 else | |
| 851 rcond = 1.0; | |
| 852 ret = chol.inverse (); | |
| 853 } | |
| 6207 | 854 else |
| 855 mattype.mark_as_unsymmetric (); | |
| 856 } | |
| 857 | |
| 858 if (!mattype.is_hermitian ()) | |
| 859 ret = finverse(mattype, info, rcond, force, calc_cond); | |
| 6840 | 860 |
| 7033 | 861 if ((mattype.is_hermitian () || calc_cond) && rcond == 0.) |
| 6840 | 862 ret = Matrix (rows (), columns (), octave_Inf); |
| 6207 | 863 } |
| 864 | |
| 865 return ret; | |
| 866 } | |
| 867 | |
| 868 Matrix | |
| 4384 | 869 Matrix::pseudo_inverse (double tol) const |
| 740 | 870 { |
| 3480 | 871 SVD result (*this, SVD::economy); |
| 740 | 872 |
| 873 DiagMatrix S = result.singular_values (); | |
| 874 Matrix U = result.left_singular_matrix (); | |
| 875 Matrix V = result.right_singular_matrix (); | |
| 876 | |
| 877 ColumnVector sigma = S.diag (); | |
| 878 | |
| 5275 | 879 octave_idx_type r = sigma.length () - 1; |
| 880 octave_idx_type nr = rows (); | |
| 881 octave_idx_type nc = cols (); | |
| 740 | 882 |
| 883 if (tol <= 0.0) | |
| 884 { | |
| 885 if (nr > nc) | |
| 886 tol = nr * sigma.elem (0) * DBL_EPSILON; | |
| 887 else | |
| 888 tol = nc * sigma.elem (0) * DBL_EPSILON; | |
| 889 } | |
| 890 | |
| 891 while (r >= 0 && sigma.elem (r) < tol) | |
| 892 r--; | |
| 893 | |
| 894 if (r < 0) | |
| 895 return Matrix (nc, nr, 0.0); | |
| 896 else | |
| 897 { | |
| 898 Matrix Ur = U.extract (0, 0, nr-1, r); | |
| 899 DiagMatrix D = DiagMatrix (sigma.extract (0, r)) . inverse (); | |
| 900 Matrix Vr = V.extract (0, 0, nc-1, r); | |
| 901 return Vr * D * Ur.transpose (); | |
| 902 } | |
| 903 } | |
| 904 | |
| 4773 | 905 #if defined (HAVE_FFTW3) |
| 3827 | 906 |
| 907 ComplexMatrix | |
| 908 Matrix::fourier (void) const | |
| 909 { | |
| 910 size_t nr = rows (); | |
| 911 size_t nc = cols (); | |
| 912 | |
| 913 ComplexMatrix retval (nr, nc); | |
| 914 | |
| 915 size_t npts, nsamples; | |
| 916 | |
| 917 if (nr == 1 || nc == 1) | |
| 918 { | |
| 919 npts = nr > nc ? nr : nc; | |
| 920 nsamples = 1; | |
| 921 } | |
| 922 else | |
| 923 { | |
| 924 npts = nr; | |
| 925 nsamples = nc; | |
| 926 } | |
| 927 | |
| 4773 | 928 const double *in (fortran_vec ()); |
| 3827 | 929 Complex *out (retval.fortran_vec ()); |
| 930 | |
| 4773 | 931 octave_fftw::fft (in, out, npts, nsamples); |
| 3827 | 932 |
| 933 return retval; | |
| 934 } | |
| 935 | |
| 936 ComplexMatrix | |
| 937 Matrix::ifourier (void) const | |
| 938 { | |
| 939 size_t nr = rows (); | |
| 940 size_t nc = cols (); | |
| 941 | |
| 942 ComplexMatrix retval (nr, nc); | |
| 943 | |
| 944 size_t npts, nsamples; | |
| 945 | |
| 946 if (nr == 1 || nc == 1) | |
| 947 { | |
| 948 npts = nr > nc ? nr : nc; | |
| 949 nsamples = 1; | |
| 950 } | |
| 951 else | |
| 952 { | |
| 953 npts = nr; | |
| 954 nsamples = nc; | |
| 955 } | |
| 956 | |
| 957 ComplexMatrix tmp (*this); | |
| 958 Complex *in (tmp.fortran_vec ()); | |
| 959 Complex *out (retval.fortran_vec ()); | |
| 960 | |
| 4773 | 961 octave_fftw::ifft (in, out, npts, nsamples); |
| 3827 | 962 |
| 963 return retval; | |
| 964 } | |
| 965 | |
| 966 ComplexMatrix | |
| 967 Matrix::fourier2d (void) const | |
| 968 { | |
| 4773 | 969 dim_vector dv(rows (), cols ()); |
| 970 | |
| 971 const double *in = fortran_vec (); | |
| 972 ComplexMatrix retval (rows (), cols ()); | |
| 973 octave_fftw::fftNd (in, retval.fortran_vec (), 2, dv); | |
| 3827 | 974 |
| 975 return retval; | |
| 976 } | |
| 977 | |
| 978 ComplexMatrix | |
| 979 Matrix::ifourier2d (void) const | |
| 980 { | |
| 4773 | 981 dim_vector dv(rows (), cols ()); |
| 3827 | 982 |
| 983 ComplexMatrix retval (*this); | |
| 4773 | 984 Complex *out (retval.fortran_vec ()); |
| 985 | |
| 986 octave_fftw::ifftNd (out, out, 2, dv); | |
| 3827 | 987 |
| 988 return retval; | |
| 989 } | |
| 990 | |
| 991 #else | |
| 992 | |
| 458 | 993 ComplexMatrix |
| 994 Matrix::fourier (void) const | |
| 995 { | |
| 1948 | 996 ComplexMatrix retval; |
| 997 | |
| 5275 | 998 octave_idx_type nr = rows (); |
| 999 octave_idx_type nc = cols (); | |
| 1000 | |
| 1001 octave_idx_type npts, nsamples; | |
| 1948 | 1002 |
| 458 | 1003 if (nr == 1 || nc == 1) |
| 1004 { | |
| 1005 npts = nr > nc ? nr : nc; | |
| 1006 nsamples = 1; | |
| 1007 } | |
| 1008 else | |
| 1009 { | |
| 1010 npts = nr; | |
| 1011 nsamples = nc; | |
| 1012 } | |
| 1013 | |
| 5275 | 1014 octave_idx_type nn = 4*npts+15; |
| 1948 | 1015 |
| 1016 Array<Complex> wsave (nn); | |
| 1017 Complex *pwsave = wsave.fortran_vec (); | |
| 1018 | |
| 3585 | 1019 retval = ComplexMatrix (*this); |
| 1948 | 1020 Complex *tmp_data = retval.fortran_vec (); |
| 1021 | |
| 3887 | 1022 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
| 458 | 1023 |
| 5275 | 1024 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1025 { |
| 1026 OCTAVE_QUIT; | |
| 1027 | |
| 1028 F77_FUNC (cfftf, CFFTF) (npts, &tmp_data[npts*j], pwsave); | |
| 1029 } | |
| 1948 | 1030 |
| 1031 return retval; | |
| 458 | 1032 } |
| 1033 | |
| 1034 ComplexMatrix | |
| 1035 Matrix::ifourier (void) const | |
| 1036 { | |
| 1948 | 1037 ComplexMatrix retval; |
| 1038 | |
| 5275 | 1039 octave_idx_type nr = rows (); |
| 1040 octave_idx_type nc = cols (); | |
| 1041 | |
| 1042 octave_idx_type npts, nsamples; | |
| 1948 | 1043 |
| 458 | 1044 if (nr == 1 || nc == 1) |
| 1045 { | |
| 1046 npts = nr > nc ? nr : nc; | |
| 1047 nsamples = 1; | |
| 1048 } | |
| 1049 else | |
| 1050 { | |
| 1051 npts = nr; | |
| 1052 nsamples = nc; | |
| 1053 } | |
| 1054 | |
| 5275 | 1055 octave_idx_type nn = 4*npts+15; |
| 1948 | 1056 |
| 1057 Array<Complex> wsave (nn); | |
| 1058 Complex *pwsave = wsave.fortran_vec (); | |
| 1059 | |
| 3585 | 1060 retval = ComplexMatrix (*this); |
| 1948 | 1061 Complex *tmp_data = retval.fortran_vec (); |
| 1062 | |
| 3887 | 1063 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
| 458 | 1064 |
| 5275 | 1065 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1066 { |
| 1067 OCTAVE_QUIT; | |
| 1068 | |
| 1069 F77_FUNC (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave); | |
| 1070 } | |
| 458 | 1071 |
| 5275 | 1072 for (octave_idx_type j = 0; j < npts*nsamples; j++) |
| 3572 | 1073 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
| 458 | 1074 |
| 1948 | 1075 return retval; |
| 458 | 1076 } |
| 1077 | |
| 677 | 1078 ComplexMatrix |
| 1079 Matrix::fourier2d (void) const | |
| 1080 { | |
| 1948 | 1081 ComplexMatrix retval; |
| 1082 | |
| 5275 | 1083 octave_idx_type nr = rows (); |
| 1084 octave_idx_type nc = cols (); | |
| 1085 | |
| 1086 octave_idx_type npts, nsamples; | |
| 1948 | 1087 |
| 677 | 1088 if (nr == 1 || nc == 1) |
| 1089 { | |
| 1090 npts = nr > nc ? nr : nc; | |
| 1091 nsamples = 1; | |
| 1092 } | |
| 1093 else | |
| 1094 { | |
| 1095 npts = nr; | |
| 1096 nsamples = nc; | |
| 1097 } | |
| 1098 | |
| 5275 | 1099 octave_idx_type nn = 4*npts+15; |
| 1948 | 1100 |
| 1101 Array<Complex> wsave (nn); | |
| 1102 Complex *pwsave = wsave.fortran_vec (); | |
| 1103 | |
| 3585 | 1104 retval = ComplexMatrix (*this); |
| 1948 | 1105 Complex *tmp_data = retval.fortran_vec (); |
| 1106 | |
| 3887 | 1107 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
| 677 | 1108 |
| 5275 | 1109 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1110 { |
| 1111 OCTAVE_QUIT; | |
| 1112 | |
| 1113 F77_FUNC (cfftf, CFFTF) (npts, &tmp_data[npts*j], pwsave); | |
| 1114 } | |
| 677 | 1115 |
| 1116 npts = nc; | |
| 1117 nsamples = nr; | |
| 1118 nn = 4*npts+15; | |
| 1948 | 1119 |
| 1120 wsave.resize (nn); | |
| 1121 pwsave = wsave.fortran_vec (); | |
| 1122 | |
| 4773 | 1123 Array<Complex> tmp (npts); |
| 1124 Complex *prow = tmp.fortran_vec (); | |
| 1948 | 1125 |
| 3887 | 1126 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
| 677 | 1127 |
| 5275 | 1128 for (octave_idx_type j = 0; j < nsamples; j++) |
| 677 | 1129 { |
| 4153 | 1130 OCTAVE_QUIT; |
| 1131 | |
| 5275 | 1132 for (octave_idx_type i = 0; i < npts; i++) |
| 1948 | 1133 prow[i] = tmp_data[i*nr + j]; |
| 1134 | |
| 3887 | 1135 F77_FUNC (cfftf, CFFTF) (npts, prow, pwsave); |
| 677 | 1136 |
| 5275 | 1137 for (octave_idx_type i = 0; i < npts; i++) |
| 1948 | 1138 tmp_data[i*nr + j] = prow[i]; |
| 677 | 1139 } |
| 1140 | |
| 1948 | 1141 return retval; |
| 677 | 1142 } |
| 1143 | |
| 1144 ComplexMatrix | |
| 1145 Matrix::ifourier2d (void) const | |
| 1146 { | |
| 1948 | 1147 ComplexMatrix retval; |
| 1148 | |
| 5275 | 1149 octave_idx_type nr = rows (); |
| 1150 octave_idx_type nc = cols (); | |
| 1151 | |
| 1152 octave_idx_type npts, nsamples; | |
| 1948 | 1153 |
| 677 | 1154 if (nr == 1 || nc == 1) |
| 1155 { | |
| 1156 npts = nr > nc ? nr : nc; | |
| 1157 nsamples = 1; | |
| 1158 } | |
| 1159 else | |
| 1160 { | |
| 1161 npts = nr; | |
| 1162 nsamples = nc; | |
| 1163 } | |
| 1164 | |
| 5275 | 1165 octave_idx_type nn = 4*npts+15; |
| 1948 | 1166 |
| 1167 Array<Complex> wsave (nn); | |
| 1168 Complex *pwsave = wsave.fortran_vec (); | |
| 1169 | |
| 3585 | 1170 retval = ComplexMatrix (*this); |
| 1948 | 1171 Complex *tmp_data = retval.fortran_vec (); |
| 1172 | |
| 3887 | 1173 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
| 677 | 1174 |
| 5275 | 1175 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1176 { |
| 1177 OCTAVE_QUIT; | |
| 1178 | |
| 1179 F77_FUNC (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave); | |
| 1180 } | |
| 677 | 1181 |
| 5275 | 1182 for (octave_idx_type j = 0; j < npts*nsamples; j++) |
| 3572 | 1183 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
| 677 | 1184 |
| 1185 npts = nc; | |
| 1186 nsamples = nr; | |
| 1187 nn = 4*npts+15; | |
| 1948 | 1188 |
| 1189 wsave.resize (nn); | |
| 1190 pwsave = wsave.fortran_vec (); | |
| 1191 | |
| 4773 | 1192 Array<Complex> tmp (npts); |
| 1193 Complex *prow = tmp.fortran_vec (); | |
| 1948 | 1194 |
| 3887 | 1195 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
| 677 | 1196 |
| 5275 | 1197 for (octave_idx_type j = 0; j < nsamples; j++) |
| 677 | 1198 { |
| 4153 | 1199 OCTAVE_QUIT; |
| 1200 | |
| 5275 | 1201 for (octave_idx_type i = 0; i < npts; i++) |
| 1948 | 1202 prow[i] = tmp_data[i*nr + j]; |
| 1203 | |
| 3887 | 1204 F77_FUNC (cfftb, CFFTB) (npts, prow, pwsave); |
| 677 | 1205 |
| 5275 | 1206 for (octave_idx_type i = 0; i < npts; i++) |
| 3572 | 1207 tmp_data[i*nr + j] = prow[i] / static_cast<double> (npts); |
| 677 | 1208 } |
| 1209 | |
| 1948 | 1210 return retval; |
| 677 | 1211 } |
| 1212 | |
| 3827 | 1213 #endif |
| 1214 | |
| 458 | 1215 DET |
| 1216 Matrix::determinant (void) const | |
| 1217 { | |
| 5275 | 1218 octave_idx_type info; |
| 458 | 1219 double rcond; |
| 4329 | 1220 return determinant (info, rcond, 0); |
| 458 | 1221 } |
| 1222 | |
| 1223 DET | |
| 5275 | 1224 Matrix::determinant (octave_idx_type& info) const |
| 458 | 1225 { |
| 1226 double rcond; | |
| 4329 | 1227 return determinant (info, rcond, 0); |
| 458 | 1228 } |
| 1229 | |
| 1230 DET | |
| 5275 | 1231 Matrix::determinant (octave_idx_type& info, double& rcond, int calc_cond) const |
| 458 | 1232 { |
| 1233 DET retval; | |
| 1234 | |
| 5275 | 1235 octave_idx_type nr = rows (); |
| 1236 octave_idx_type nc = cols (); | |
| 458 | 1237 |
| 1238 if (nr == 0 || nc == 0) | |
| 1239 { | |
| 5634 | 1240 retval = DET (1.0, 0); |
| 458 | 1241 } |
| 1242 else | |
| 1243 { | |
| 5275 | 1244 Array<octave_idx_type> ipvt (nr); |
| 1245 octave_idx_type *pipvt = ipvt.fortran_vec (); | |
| 1948 | 1246 |
| 1247 Matrix atmp = *this; | |
| 1248 double *tmp_data = atmp.fortran_vec (); | |
| 1249 | |
| 4329 | 1250 info = 0; |
| 1251 | |
| 4330 | 1252 // Calculate the norm of the matrix, for later use. |
| 4329 | 1253 double anorm = 0; |
| 1254 if (calc_cond) | |
| 5275 | 1255 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
| 4329 | 1256 |
| 1257 F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); | |
| 1948 | 1258 |
|
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1259 // Throw-away extra info LAPACK gives so as to not change output. |
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1260 rcond = 0.0; |
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1261 if (info != 0) |
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1262 { |
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1263 info = -1; |
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1264 retval = DET (); |
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1265 } |
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1266 else |
| 458 | 1267 { |
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1268 if (calc_cond) |
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1269 { |
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1270 // Now calc the condition number for non-singular matrix. |
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1271 char job = '1'; |
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1272 Array<double> z (4 * nc); |
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1273 double *pz = z.fortran_vec (); |
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1274 Array<octave_idx_type> iz (nc); |
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1275 octave_idx_type *piz = iz.fortran_vec (); |
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1276 |
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1277 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
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1278 nc, tmp_data, nr, anorm, |
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1279 rcond, pz, piz, info |
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1280 F77_CHAR_ARG_LEN (1))); |
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1281 } |
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1282 |
| 4509 | 1283 if (info != 0) |
| 1948 | 1284 { |
| 4509 | 1285 info = -1; |
| 1286 retval = DET (); | |
| 4329 | 1287 } |
| 1288 else | |
| 1948 | 1289 { |
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1290 double c = 1.0; |
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1291 int e = 0; |
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1292 |
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1293 for (octave_idx_type i = 0; i < nc; i++) |
| 4329 | 1294 { |
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1295 if (ipvt(i) != (i+1)) |
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1296 c = -c; |
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1297 |
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1298 c *= atmp(i,i); |
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1299 |
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1300 if (c == 0.0) |
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1301 break; |
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1302 |
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1303 while (fabs (c) < 0.5) |
| 4329 | 1304 { |
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1305 c *= 2.0; |
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|
1306 e--; |
| 4329 | 1307 } |
| 5634 | 1308 |
|
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|
1309 while (fabs (c) >= 2.0) |
|
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|
1310 { |
|
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|
1311 c /= 2.0; |
|
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|
1312 e++; |
|
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|
1313 } |
| 4329 | 1314 } |
|
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|
1315 |
|
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|
1316 retval = DET (c, e); |
| 1948 | 1317 } |
| 458 | 1318 } |
| 1319 } | |
| 1320 | |
| 1321 return retval; | |
| 1322 } | |
| 1323 | |
| 1324 Matrix | |
| 5785 | 1325 Matrix::utsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, |
| 1326 double& rcond, solve_singularity_handler sing_handler, | |
| 1327 bool calc_cond) const | |
| 1328 { | |
| 1329 Matrix retval; | |
| 1330 | |
| 1331 octave_idx_type nr = rows (); | |
| 1332 octave_idx_type nc = cols (); | |
| 1333 | |
| 6924 | 1334 if (nr != b.rows ()) |
| 5785 | 1335 (*current_liboctave_error_handler) |
| 1336 ("matrix dimension mismatch solution of linear equations"); | |
| 6924 | 1337 else if (nr == 0 || nc == 0 || b.cols () == 0) |
| 1338 retval = Matrix (nc, b.cols (), 0.0); | |
| 5785 | 1339 else |
| 1340 { | |
| 1341 volatile int typ = mattype.type (); | |
| 1342 | |
| 1343 if (typ == MatrixType::Permuted_Upper || | |
| 1344 typ == MatrixType::Upper) | |
| 1345 { | |
| 1346 octave_idx_type b_nc = b.cols (); | |
| 1347 rcond = 1.; | |
| 1348 info = 0; | |
| 1349 | |
| 1350 if (typ == MatrixType::Permuted_Upper) | |
| 1351 { | |
| 1352 (*current_liboctave_error_handler) | |
| 6390 | 1353 ("permuted triangular matrix not implemented"); |
| 5785 | 1354 } |
| 1355 else | |
| 1356 { | |
| 1357 const double *tmp_data = fortran_vec (); | |
| 1358 | |
| 1359 if (calc_cond) | |
| 1360 { | |
| 1361 char norm = '1'; | |
| 1362 char uplo = 'U'; | |
| 1363 char dia = 'N'; | |
| 1364 | |
| 1365 Array<double> z (3 * nc); | |
| 1366 double *pz = z.fortran_vec (); | |
| 1367 Array<octave_idx_type> iz (nc); | |
| 1368 octave_idx_type *piz = iz.fortran_vec (); | |
| 1369 | |
| 1370 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1371 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1372 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1373 nr, tmp_data, nr, rcond, | |
| 1374 pz, piz, info | |
| 1375 F77_CHAR_ARG_LEN (1) | |
| 1376 F77_CHAR_ARG_LEN (1) | |
| 1377 F77_CHAR_ARG_LEN (1))); | |
| 1378 | |
| 1379 if (info != 0) | |
| 1380 info = -2; | |
| 1381 | |
| 1382 volatile double rcond_plus_one = rcond + 1.0; | |
| 1383 | |
| 1384 if (rcond_plus_one == 1.0 || xisnan (rcond)) | |
| 1385 { | |
| 1386 info = -2; | |
| 1387 | |
| 1388 if (sing_handler) | |
| 1389 sing_handler (rcond); | |
| 1390 else | |
| 1391 (*current_liboctave_error_handler) | |
| 1392 ("matrix singular to machine precision, rcond = %g", | |
| 1393 rcond); | |
| 1394 } | |
| 1395 } | |
| 1396 | |
| 1397 if (info == 0) | |
| 1398 { | |
| 1399 retval = b; | |
| 1400 double *result = retval.fortran_vec (); | |
| 1401 | |
| 1402 char uplo = 'U'; | |
| 1403 char trans = 'N'; | |
| 1404 char dia = 'N'; | |
| 1405 | |
| 1406 F77_XFCN (dtrtrs, DTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1407 F77_CONST_CHAR_ARG2 (&trans, 1), | |
| 1408 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1409 nr, b_nc, tmp_data, nr, | |
| 1410 result, nr, info | |
| 1411 F77_CHAR_ARG_LEN (1) | |
| 1412 F77_CHAR_ARG_LEN (1) | |
| 1413 F77_CHAR_ARG_LEN (1))); | |
| 1414 } | |
| 1415 } | |
| 1416 } | |
| 1417 else | |
| 1418 (*current_liboctave_error_handler) ("incorrect matrix type"); | |
| 1419 } | |
| 1420 | |
| 1421 return retval; | |
| 1422 } | |
| 1423 | |
| 1424 Matrix | |
| 1425 Matrix::ltsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, | |
| 1426 double& rcond, solve_singularity_handler sing_handler, | |
| 1427 bool calc_cond) const | |
| 1428 { | |
| 1429 Matrix retval; | |
| 1430 | |
| 1431 octave_idx_type nr = rows (); | |
| 1432 octave_idx_type nc = cols (); | |
| 1433 | |
| 6924 | 1434 if (nr != b.rows ()) |
| 5785 | 1435 (*current_liboctave_error_handler) |
| 1436 ("matrix dimension mismatch solution of linear equations"); | |
| 6924 | 1437 else if (nr == 0 || nc == 0 || b.cols () == 0) |
| 1438 retval = Matrix (nc, b.cols (), 0.0); | |
| 5785 | 1439 else |
| 1440 { | |
| 1441 volatile int typ = mattype.type (); | |
| 1442 | |
| 1443 if (typ == MatrixType::Permuted_Lower || | |
| 1444 typ == MatrixType::Lower) | |
| 1445 { | |
| 1446 octave_idx_type b_nc = b.cols (); | |
| 1447 rcond = 1.; | |
| 1448 info = 0; | |
| 1449 | |
| 1450 if (typ == MatrixType::Permuted_Lower) | |
| 1451 { | |
| 1452 (*current_liboctave_error_handler) | |
| 6390 | 1453 ("permuted triangular matrix not implemented"); |
| 5785 | 1454 } |
| 1455 else | |
| 1456 { | |
| 1457 const double *tmp_data = fortran_vec (); | |
| 1458 | |
| 1459 if (calc_cond) | |
| 1460 { | |
| 1461 char norm = '1'; | |
| 1462 char uplo = 'L'; | |
| 1463 char dia = 'N'; | |
| 1464 | |
| 1465 Array<double> z (3 * nc); | |
| 1466 double *pz = z.fortran_vec (); | |
| 1467 Array<octave_idx_type> iz (nc); | |
| 1468 octave_idx_type *piz = iz.fortran_vec (); | |
| 1469 | |
| 1470 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1471 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1472 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1473 nr, tmp_data, nr, rcond, | |
| 1474 pz, piz, info | |
| 1475 F77_CHAR_ARG_LEN (1) | |
| 1476 F77_CHAR_ARG_LEN (1) | |
| 1477 F77_CHAR_ARG_LEN (1))); | |
| 1478 | |
| 1479 if (info != 0) | |
| 1480 info = -2; | |
| 1481 | |
| 1482 volatile double rcond_plus_one = rcond + 1.0; | |
| 1483 | |
| 1484 if (rcond_plus_one == 1.0 || xisnan (rcond)) | |
| 1485 { | |
| 1486 info = -2; | |
| 1487 | |
| 1488 if (sing_handler) | |
| 1489 sing_handler (rcond); | |
| 1490 else | |
| 1491 (*current_liboctave_error_handler) | |
| 1492 ("matrix singular to machine precision, rcond = %g", | |
| 1493 rcond); | |
| 1494 } | |
| 1495 } | |
| 1496 | |
| 1497 if (info == 0) | |
| 1498 { | |
| 1499 retval = b; | |
| 1500 double *result = retval.fortran_vec (); | |
| 1501 | |
| 1502 char uplo = 'L'; | |
| 1503 char trans = 'N'; | |
| 1504 char dia = 'N'; | |
| 1505 | |
| 1506 F77_XFCN (dtrtrs, DTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1507 F77_CONST_CHAR_ARG2 (&trans, 1), | |
| 1508 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1509 nr, b_nc, tmp_data, nr, | |
| 1510 result, nr, info | |
| 1511 F77_CHAR_ARG_LEN (1) | |
| 1512 F77_CHAR_ARG_LEN (1) | |
| 1513 F77_CHAR_ARG_LEN (1))); | |
| 1514 } | |
| 1515 } | |
| 1516 } | |
| 1517 else | |
| 1518 (*current_liboctave_error_handler) ("incorrect matrix type"); | |
| 1519 } | |
| 1520 | |
| 1521 return retval; | |
| 1522 } | |
| 1523 | |
| 1524 Matrix | |
| 1525 Matrix::fsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, | |
| 1526 double& rcond, solve_singularity_handler sing_handler, | |
| 1527 bool calc_cond) const | |
| 1528 { | |
| 1529 Matrix retval; | |
| 1530 | |
| 1531 octave_idx_type nr = rows (); | |
| 1532 octave_idx_type nc = cols (); | |
| 1533 | |
| 6924 | 1534 if (nr != nc || nr != b.rows ()) |
| 5785 | 1535 (*current_liboctave_error_handler) |
| 1536 ("matrix dimension mismatch solution of linear equations"); | |
| 6924 | 1537 else if (nr == 0 || b.cols () == 0) |
| 1538 retval = Matrix (nc, b.cols (), 0.0); | |
| 5785 | 1539 else |
| 1540 { | |
| 1541 volatile int typ = mattype.type (); | |
| 1542 | |
| 1543 // Calculate the norm of the matrix, for later use. | |
| 1544 double anorm = -1.; | |
| 1545 | |
| 1546 if (typ == MatrixType::Hermitian) | |
| 1547 { | |
| 1548 info = 0; | |
| 1549 char job = 'L'; | |
| 1550 Matrix atmp = *this; | |
| 1551 double *tmp_data = atmp.fortran_vec (); | |
| 1552 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); | |
| 1553 | |
| 1554 F77_XFCN (dpotrf, DPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, | |
| 1555 tmp_data, nr, info | |
| 1556 F77_CHAR_ARG_LEN (1))); | |
| 1557 | |
|
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|
1558 // Throw-away extra info LAPACK gives so as to not change output. |
|
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|
1559 rcond = 0.0; |
|
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|
1560 if (info != 0) |
|
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diff
changeset
|
1561 { |
|
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|
1562 info = -2; |
|
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changeset
|
1563 |
|
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|
1564 mattype.mark_as_unsymmetric (); |
|
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|
1565 typ = MatrixType::Full; |
|
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|
1566 } |
|
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|
1567 else |
| 5785 | 1568 { |
|
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changeset
|
1569 if (calc_cond) |
| 5785 | 1570 { |
|
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|
1571 Array<double> z (3 * nc); |
|
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changeset
|
1572 double *pz = z.fortran_vec (); |
|
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changeset
|
1573 Array<octave_idx_type> iz (nc); |
|
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changeset
|
1574 octave_idx_type *piz = iz.fortran_vec (); |
|
29980c6b8604
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changeset
|
1575 |
|
29980c6b8604
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diff
changeset
|
1576 F77_XFCN (dpocon, DPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
29980c6b8604
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|
1577 nr, tmp_data, nr, anorm, |
|
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|
1578 rcond, pz, piz, info |
|
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diff
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|
1579 F77_CHAR_ARG_LEN (1))); |
|
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changeset
|
1580 |
|
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changeset
|
1581 if (info != 0) |
|
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|
1582 info = -2; |
|
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changeset
|
1583 |
|
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changeset
|
1584 volatile double rcond_plus_one = rcond + 1.0; |
|
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changeset
|
1585 |
|
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changeset
|
1586 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
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changeset
|
1587 { |
|
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changeset
|
1588 info = -2; |
|
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changeset
|
1589 |
|
29980c6b8604
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changeset
|
1590 if (sing_handler) |
|
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|
1591 sing_handler (rcond); |
|
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|
1592 else |
|
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|
1593 (*current_liboctave_error_handler) |
|
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|
1594 ("matrix singular to machine precision, rcond = %g", |
|
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changeset
|
1595 rcond); |
|
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|
1596 } |
|
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|
1597 } |
|
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|
1598 |
|
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changeset
|
1599 if (info == 0) |
|
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changeset
|
1600 { |
|
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|
1601 retval = b; |
|
29980c6b8604
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|
1602 double *result = retval.fortran_vec (); |
|
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changeset
|
1603 |
|
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changeset
|
1604 octave_idx_type b_nc = b.cols (); |
|
29980c6b8604
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|
1605 |
|
29980c6b8604
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diff
changeset
|
1606 F77_XFCN (dpotrs, DPOTRS, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
29980c6b8604
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|
1607 nr, b_nc, tmp_data, nr, |
|
29980c6b8604
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changeset
|
1608 result, b.rows(), info |
|
29980c6b8604
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changeset
|
1609 F77_CHAR_ARG_LEN (1))); |
|
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diff
changeset
|
1610 } |
|
29980c6b8604
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diff
changeset
|
1611 else |
|
29980c6b8604
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changeset
|
1612 { |
| 5785 | 1613 mattype.mark_as_unsymmetric (); |
| 1614 typ = MatrixType::Full; | |
|
7482
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|
1615 } |
| 5785 | 1616 } |
| 1617 } | |
| 1618 | |
| 1619 if (typ == MatrixType::Full) | |
| 1620 { | |
| 1621 info = 0; | |
| 1622 | |
| 1623 Array<octave_idx_type> ipvt (nr); | |
| 1624 octave_idx_type *pipvt = ipvt.fortran_vec (); | |
| 1625 | |
| 1626 Matrix atmp = *this; | |
| 1627 double *tmp_data = atmp.fortran_vec (); | |
| 1628 if(anorm < 0.) | |
| 1629 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); | |
| 1630 | |
| 1631 Array<double> z (4 * nc); | |
| 1632 double *pz = z.fortran_vec (); | |
| 1633 Array<octave_idx_type> iz (nc); | |
| 1634 octave_idx_type *piz = iz.fortran_vec (); | |
| 1635 | |
| 1636 F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); | |
| 1637 | |
|
7482
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|
1638 // Throw-away extra info LAPACK gives so as to not change output. |
|
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|
1639 rcond = 0.0; |
|
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diff
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|
1640 if (info != 0) |
| 5785 | 1641 { |
|
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changeset
|
1642 info = -2; |
|
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diff
changeset
|
1643 |
|
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diff
changeset
|
1644 if (sing_handler) |
|
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diff
changeset
|
1645 sing_handler (rcond); |
|
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don't check f77_exception_encountered
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diff
changeset
|
1646 else |
|
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diff
changeset
|
1647 (*current_liboctave_error_handler) |
|
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|
1648 ("matrix singular to machine precision"); |
|
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diff
changeset
|
1649 |
|
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diff
changeset
|
1650 mattype.mark_as_rectangular (); |
|
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|
1651 } |
|
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diff
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|
1652 else |
|
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changeset
|
1653 { |
|
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|
1654 if (calc_cond) |
| 5785 | 1655 { |
|
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|
1656 // Now calculate the condition number for |
|
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|
1657 // non-singular matrix. |
|
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|
1658 char job = '1'; |
|
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|
1659 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
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|
1660 nc, tmp_data, nr, anorm, |
|
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|
1661 rcond, pz, piz, info |
|
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|
1662 F77_CHAR_ARG_LEN (1))); |
|
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|
1663 |
|
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|
1664 if (info != 0) |
|
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|
1665 info = -2; |
|
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changeset
|
1666 |
|
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|
1667 volatile double rcond_plus_one = rcond + 1.0; |
|
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|
1668 |
|
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|
1669 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
| 5785 | 1670 { |
|
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|
1671 info = -2; |
|
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changeset
|
1672 |
|
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changeset
|
1673 if (sing_handler) |
|
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|
1674 sing_handler (rcond); |
|
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changeset
|
1675 else |
|
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|
1676 (*current_liboctave_error_handler) |
|
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|
1677 ("matrix singular to machine precision, rcond = %g", |
|
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|
1678 rcond); |
| 5785 | 1679 } |
| 1680 } | |
|
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|
1681 |
|
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changeset
|
1682 if (info == 0) |
|
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changeset
|
1683 { |
|
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|
1684 retval = b; |
|
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|
1685 double *result = retval.fortran_vec (); |
|
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changeset
|
1686 |
|
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changeset
|
1687 octave_idx_type b_nc = b.cols (); |
|
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changeset
|
1688 |
|
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changeset
|
1689 char job = 'N'; |
|
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diff
changeset
|
1690 F77_XFCN (dgetrs, DGETRS, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
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|
1691 nr, b_nc, tmp_data, nr, |
|
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diff
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|
1692 pipvt, result, b.rows(), info |
|
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|
1693 F77_CHAR_ARG_LEN (1))); |
|
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changeset
|
1694 } |
|
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|
1695 else |
|
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changeset
|
1696 mattype.mark_as_rectangular (); |
| 5785 | 1697 } |
| 1698 } | |
| 1699 else if (typ != MatrixType::Hermitian) | |
| 1700 (*current_liboctave_error_handler) ("incorrect matrix type"); | |
| 1701 } | |
| 1702 | |
| 1703 return retval; | |
| 1704 } | |
| 1705 | |
| 1706 Matrix | |
| 1707 Matrix::solve (MatrixType &typ, const Matrix& b) const | |
| 1708 { | |
| 1709 octave_idx_type info; | |
| 1710 double rcond; | |
| 1711 return solve (typ, b, info, rcond, 0); | |
| 1712 } | |
| 1713 | |
| 1714 Matrix | |
| 1715 Matrix::solve (MatrixType &typ, const Matrix& b, octave_idx_type& info, | |
| 1716 double& rcond) const | |
| 1717 { | |
| 1718 return solve (typ, b, info, rcond, 0); | |
| 1719 } | |
| 1720 | |
| 1721 Matrix | |
| 1722 Matrix::solve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, | |
| 1723 double& rcond, solve_singularity_handler sing_handler, | |
| 1724 bool singular_fallback) const | |
| 1725 { | |
| 1726 Matrix retval; | |
| 1727 int typ = mattype.type (); | |
| 1728 | |
| 1729 if (typ == MatrixType::Unknown) | |
| 1730 typ = mattype.type (*this); | |
| 1731 | |
| 1732 // Only calculate the condition number for LU/Cholesky | |
| 1733 if (typ == MatrixType::Upper || typ == MatrixType::Permuted_Upper) | |
| 1734 retval = utsolve (mattype, b, info, rcond, sing_handler, false); | |
| 1735 else if (typ == MatrixType::Lower || typ == MatrixType::Permuted_Lower) | |
| 1736 retval = ltsolve (mattype, b, info, rcond, sing_handler, false); | |
| 1737 else if (typ == MatrixType::Full || typ == MatrixType::Hermitian) | |
| 1738 retval = fsolve (mattype, b, info, rcond, sing_handler, true); | |
| 1739 else if (typ != MatrixType::Rectangular) | |
| 1740 { | |
| 1741 (*current_liboctave_error_handler) ("unknown matrix type"); | |
| 1742 return Matrix (); | |
| 1743 } | |
| 1744 | |
| 1745 // Rectangular or one of the above solvers flags a singular matrix | |
| 1746 if (singular_fallback && mattype.type () == MatrixType::Rectangular) | |
| 1747 { | |
| 1748 octave_idx_type rank; | |
| 7076 | 1749 retval = lssolve (b, info, rank, rcond); |
| 5785 | 1750 } |
| 1751 | |
| 1752 return retval; | |
| 1753 } | |
| 1754 | |
| 1755 ComplexMatrix | |
| 1756 Matrix::solve (MatrixType &typ, const ComplexMatrix& b) const | |
| 1757 { | |
| 1758 ComplexMatrix tmp (*this); | |
| 1759 return tmp.solve (typ, b); | |
| 1760 } | |
| 1761 | |
| 1762 ComplexMatrix | |
| 1763 Matrix::solve (MatrixType &typ, const ComplexMatrix& b, | |
| 1764 octave_idx_type& info) const | |
| 1765 { | |
| 1766 ComplexMatrix tmp (*this); | |
| 1767 return tmp.solve (typ, b, info); | |
| 1768 } | |
| 1769 | |
| 1770 ComplexMatrix | |
| 1771 Matrix::solve (MatrixType &typ, const ComplexMatrix& b, octave_idx_type& info, | |
| 1772 double& rcond) const | |
| 1773 { | |
| 1774 ComplexMatrix tmp (*this); | |
| 1775 return tmp.solve (typ, b, info, rcond); | |
| 1776 } | |
| 1777 | |
| 1778 ComplexMatrix | |
| 1779 Matrix::solve (MatrixType &typ, const ComplexMatrix& b, octave_idx_type& info, | |
| 1780 double& rcond, solve_singularity_handler sing_handler, | |
| 1781 bool singular_fallback) const | |
| 1782 { | |
| 1783 ComplexMatrix tmp (*this); | |
| 1784 return tmp.solve (typ, b, info, rcond, sing_handler, singular_fallback); | |
| 1785 } | |
| 1786 | |
| 1787 ColumnVector | |
| 1788 Matrix::solve (MatrixType &typ, const ColumnVector& b) const | |
| 1789 { | |
| 1790 octave_idx_type info; double rcond; | |
| 1791 return solve (typ, b, info, rcond); | |
| 1792 } | |
| 1793 | |
| 1794 ColumnVector | |
| 1795 Matrix::solve (MatrixType &typ, const ColumnVector& b, | |
| 1796 octave_idx_type& info) const | |
| 1797 { | |
| 1798 double rcond; | |
| 1799 return solve (typ, b, info, rcond); | |
| 1800 } | |
| 1801 | |
| 1802 ColumnVector | |
| 1803 Matrix::solve (MatrixType &typ, const ColumnVector& b, octave_idx_type& info, | |
| 1804 double& rcond) const | |
| 1805 { | |
| 1806 return solve (typ, b, info, rcond, 0); | |
| 1807 } | |
| 1808 | |
| 1809 ColumnVector | |
| 1810 Matrix::solve (MatrixType &typ, const ColumnVector& b, octave_idx_type& info, | |
| 1811 double& rcond, solve_singularity_handler sing_handler) const | |
| 1812 { | |
| 1813 Matrix tmp (b); | |
| 1814 return solve (typ, tmp, info, rcond, sing_handler).column(static_cast<octave_idx_type> (0)); | |
| 1815 } | |
| 1816 | |
| 1817 ComplexColumnVector | |
| 1818 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b) const | |
| 1819 { | |
| 1820 ComplexMatrix tmp (*this); | |
| 1821 return tmp.solve (typ, b); | |
| 1822 } | |
| 1823 | |
| 1824 ComplexColumnVector | |
| 1825 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, | |
| 1826 octave_idx_type& info) const | |
| 1827 { | |
| 1828 ComplexMatrix tmp (*this); | |
| 1829 return tmp.solve (typ, b, info); | |
| 1830 } | |
| 1831 | |
| 1832 ComplexColumnVector | |
| 1833 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, | |
| 1834 octave_idx_type& info, double& rcond) const | |
| 1835 { | |
| 1836 ComplexMatrix tmp (*this); | |
| 1837 return tmp.solve (typ, b, info, rcond); | |
| 1838 } | |
| 1839 | |
| 1840 ComplexColumnVector | |
| 1841 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, | |
| 1842 octave_idx_type& info, double& rcond, | |
| 1843 solve_singularity_handler sing_handler) const | |
| 1844 { | |
| 1845 ComplexMatrix tmp (*this); | |
| 1846 return tmp.solve(typ, b, info, rcond, sing_handler); | |
| 1847 } | |
| 1848 | |
| 1849 Matrix | |
| 458 | 1850 Matrix::solve (const Matrix& b) const |
| 1851 { | |
| 5275 | 1852 octave_idx_type info; |
| 458 | 1853 double rcond; |
| 4329 | 1854 return solve (b, info, rcond, 0); |
| 458 | 1855 } |
| 1856 | |
| 1857 Matrix | |
| 5275 | 1858 Matrix::solve (const Matrix& b, octave_idx_type& info) const |
| 458 | 1859 { |
| 1860 double rcond; | |
| 4329 | 1861 return solve (b, info, rcond, 0); |
| 458 | 1862 } |
| 1863 | |
| 1864 Matrix | |
| 5275 | 1865 Matrix::solve (const Matrix& b, octave_idx_type& info, double& rcond) const |
| 458 | 1866 { |
| 3480 | 1867 return solve (b, info, rcond, 0); |
| 1868 } | |
| 1869 | |
| 1870 Matrix | |
| 5785 | 1871 Matrix::solve (const Matrix& b, octave_idx_type& info, |
| 1872 double& rcond, solve_singularity_handler sing_handler) const | |
| 3480 | 1873 { |
| 5785 | 1874 MatrixType mattype (*this); |
| 1875 return solve (mattype, b, info, rcond, sing_handler); | |
| 458 | 1876 } |
| 1877 | |
| 1878 ComplexMatrix | |
| 1879 Matrix::solve (const ComplexMatrix& b) const | |
| 1880 { | |
| 1881 ComplexMatrix tmp (*this); | |
| 1882 return tmp.solve (b); | |
| 1883 } | |
| 1884 | |
| 1885 ComplexMatrix | |
| 5275 | 1886 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info) const |
| 458 | 1887 { |
| 1888 ComplexMatrix tmp (*this); | |
| 1889 return tmp.solve (b, info); | |
| 1890 } | |
| 1891 | |
| 1892 ComplexMatrix | |
| 5275 | 1893 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcond) const |
| 458 | 1894 { |
| 1895 ComplexMatrix tmp (*this); | |
| 1896 return tmp.solve (b, info, rcond); | |
| 1897 } | |
| 1898 | |
| 3480 | 1899 ComplexMatrix |
| 5275 | 1900 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcond, |
| 3480 | 1901 solve_singularity_handler sing_handler) const |
| 1902 { | |
| 1903 ComplexMatrix tmp (*this); | |
| 1904 return tmp.solve (b, info, rcond, sing_handler); | |
| 1905 } | |
| 1906 | |
| 458 | 1907 ColumnVector |
| 1908 Matrix::solve (const ColumnVector& b) const | |
| 1909 { | |
| 5275 | 1910 octave_idx_type info; double rcond; |
| 458 | 1911 return solve (b, info, rcond); |
| 1912 } | |
| 1913 | |
| 1914 ColumnVector | |
| 5275 | 1915 Matrix::solve (const ColumnVector& b, octave_idx_type& info) const |
| 458 | 1916 { |
| 1917 double rcond; | |
| 1918 return solve (b, info, rcond); | |
| 1919 } | |
| 1920 | |
| 1921 ColumnVector | |
| 5275 | 1922 Matrix::solve (const ColumnVector& b, octave_idx_type& info, double& rcond) const |
| 458 | 1923 { |
| 3480 | 1924 return solve (b, info, rcond, 0); |
| 1925 } | |
| 1926 | |
| 1927 ColumnVector | |
| 5275 | 1928 Matrix::solve (const ColumnVector& b, octave_idx_type& info, double& rcond, |
| 3480 | 1929 solve_singularity_handler sing_handler) const |
| 1930 { | |
| 5785 | 1931 MatrixType mattype (*this); |
| 1932 return solve (mattype, b, info, rcond, sing_handler); | |
| 458 | 1933 } |
| 1934 | |
| 1935 ComplexColumnVector | |
| 1936 Matrix::solve (const ComplexColumnVector& b) const | |
| 1937 { | |
| 1938 ComplexMatrix tmp (*this); | |
| 1939 return tmp.solve (b); | |
| 1940 } | |
| 1941 | |
| 1942 ComplexColumnVector | |
| 5275 | 1943 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info) const |
| 458 | 1944 { |
| 1945 ComplexMatrix tmp (*this); | |
| 1946 return tmp.solve (b, info); | |
| 1947 } | |
| 1948 | |
| 1949 ComplexColumnVector | |
| 5275 | 1950 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info, double& rcond) const |
| 458 | 1951 { |
| 1952 ComplexMatrix tmp (*this); | |
| 1953 return tmp.solve (b, info, rcond); | |
| 1954 } | |
| 1955 | |
| 3480 | 1956 ComplexColumnVector |
| 5275 | 1957 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info, double& rcond, |
| 3480 | 1958 solve_singularity_handler sing_handler) const |
| 1959 { | |
| 1960 ComplexMatrix tmp (*this); | |
| 1961 return tmp.solve (b, info, rcond, sing_handler); | |
| 1962 } | |
| 1963 | |
| 458 | 1964 Matrix |
| 1965 Matrix::lssolve (const Matrix& b) const | |
| 1966 { | |
| 5275 | 1967 octave_idx_type info; |
| 1968 octave_idx_type rank; | |
| 7076 | 1969 double rcond; |
| 1970 return lssolve (b, info, rank, rcond); | |
| 458 | 1971 } |
| 1972 | |
| 1973 Matrix | |
| 5275 | 1974 Matrix::lssolve (const Matrix& b, octave_idx_type& info) const |
| 458 | 1975 { |
| 5275 | 1976 octave_idx_type rank; |
| 7076 | 1977 double rcond; |
| 1978 return lssolve (b, info, rank, rcond); | |
| 458 | 1979 } |
| 1980 | |
| 1981 Matrix | |
| 7072 | 1982 Matrix::lssolve (const Matrix& b, octave_idx_type& info, |
| 1983 octave_idx_type& rank) const | |
| 458 | 1984 { |
| 7076 | 1985 double rcond; |
| 1986 return lssolve (b, info, rank, rcond); | |
| 1987 } | |
| 1988 | |
| 1989 Matrix | |
| 1990 Matrix::lssolve (const Matrix& b, octave_idx_type& info, | |
| 1991 octave_idx_type& rank, double &rcond) const | |
| 1992 { | |
| 1948 | 1993 Matrix retval; |
| 1994 | |
| 5275 | 1995 octave_idx_type nrhs = b.cols (); |
| 1996 | |
| 1997 octave_idx_type m = rows (); | |
| 1998 octave_idx_type n = cols (); | |
| 458 | 1999 |
| 6924 | 2000 if (m != b.rows ()) |
| 1948 | 2001 (*current_liboctave_error_handler) |
| 6924 | 2002 ("matrix dimension mismatch solution of linear equations"); |
| 2003 else if (m == 0 || n == 0 || b.cols () == 0) | |
| 2004 retval = Matrix (n, b.cols (), 0.0); | |
| 1948 | 2005 else |
| 458 | 2006 { |
| 7072 | 2007 volatile octave_idx_type minmn = (m < n ? m : n); |
| 2008 octave_idx_type maxmn = m > n ? m : n; | |
| 7076 | 2009 rcond = -1.0; |
| 7072 | 2010 if (m != n) |
| 2011 { | |
| 2012 retval = Matrix (maxmn, nrhs, 0.0); | |
| 2013 | |
| 2014 for (octave_idx_type j = 0; j < nrhs; j++) | |
| 2015 for (octave_idx_type i = 0; i < m; i++) | |
| 2016 retval.elem (i, j) = b.elem (i, j); | |
| 2017 } | |
| 2018 else | |
| 2019 retval = b; | |
| 2020 | |
| 1948 | 2021 Matrix atmp = *this; |
| 2022 double *tmp_data = atmp.fortran_vec (); | |
| 2023 | |
| 7072 | 2024 double *pretval = retval.fortran_vec (); |
| 2025 Array<double> s (minmn); | |
| 7071 | 2026 double *ps = s.fortran_vec (); |
| 1948 | 2027 |
| 7072 | 2028 // Ask DGELSD what the dimension of WORK should be. |
| 5275 | 2029 octave_idx_type lwork = -1; |
| 3752 | 2030 |
| 2031 Array<double> work (1); | |
| 1948 | 2032 |
| 7477 | 2033 octave_idx_type smlsiz; |
| 2034 F77_FUNC (xilaenv, XILAENV) (9, F77_CONST_CHAR_ARG2 ("DGELSD", 6), | |
| 2035 F77_CONST_CHAR_ARG2 (" ", 1), | |
| 7478 | 2036 0, 0, 0, 0, smlsiz |
| 7477 | 2037 F77_CHAR_ARG_LEN (6) |
| 7478 | 2038 F77_CHAR_ARG_LEN (1)); |
| 7079 | 2039 |
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2040 octave_idx_type mnthr; |
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2041 F77_FUNC (xilaenv, XILAENV) (6, F77_CONST_CHAR_ARG2 ("DGELSD", 6), |
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2042 F77_CONST_CHAR_ARG2 (" ", 1), |
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2043 m, n, nrhs, -1, mnthr |
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2044 F77_CHAR_ARG_LEN (6) |
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2045 F77_CHAR_ARG_LEN (1)); |
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2046 |
| 7079 | 2047 // We compute the size of iwork because DGELSD in older versions |
| 2048 // of LAPACK does not return it on a query call. | |
| 7124 | 2049 double dminmn = static_cast<double> (minmn); |
| 2050 double dsmlsizp1 = static_cast<double> (smlsiz+1); | |
| 7079 | 2051 #if defined (HAVE_LOG2) |
| 7367 | 2052 double tmp = log2 (dminmn / dsmlsizp1); |
| 7079 | 2053 #else |
| 7367 | 2054 double tmp = log (dminmn / dsmlsizp1) / log (2.0); |
| 7079 | 2055 #endif |
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2056 octave_idx_type nlvl = static_cast<octave_idx_type> (tmp) + 1; |
| 7079 | 2057 if (nlvl < 0) |
| 2058 nlvl = 0; | |
| 2059 | |
| 2060 octave_idx_type liwork = 3 * minmn * nlvl + 11 * minmn; | |
| 2061 if (liwork < 1) | |
| 2062 liwork = 1; | |
| 7072 | 2063 Array<octave_idx_type> iwork (liwork); |
| 2064 octave_idx_type* piwork = iwork.fortran_vec (); | |
| 2065 | |
| 2066 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, | |
| 2067 ps, rcond, rank, work.fortran_vec (), | |
| 2068 lwork, piwork, info)); | |
| 1948 | 2069 |
| 7476 | 2070 // The workspace query is broken in at least LAPACK 3.0.0 |
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2071 // through 3.1.1 when n >= mnthr. The obtuse formula below |
| 7476 | 2072 // should provide sufficient workspace for DGELSD to operate |
| 2073 // efficiently. | |
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2074 if (n >= mnthr) |
| 7476 | 2075 { |
| 2076 const octave_idx_type wlalsd | |
| 2077 = 9*m + 2*m*smlsiz + 8*m*nlvl + m*nrhs + (smlsiz+1)*(smlsiz+1); | |
| 2078 | |
| 2079 octave_idx_type addend = m; | |
| 2080 | |
| 2081 if (2*m-4 > addend) | |
| 2082 addend = 2*m-4; | |
| 2083 | |
| 2084 if (nrhs > addend) | |
| 2085 addend = nrhs; | |
| 2086 | |
| 2087 if (n-3*m > addend) | |
| 2088 addend = n-3*m; | |
| 2089 | |
| 2090 if (wlalsd > addend) | |
| 2091 addend = wlalsd; | |
| 2092 | |
| 2093 const octave_idx_type lworkaround = 4*m + m*m + addend; | |
| 2094 | |
| 2095 if (work(0) < lworkaround) | |
| 2096 work(0) = lworkaround; | |
| 2097 } | |
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2098 else if (m >= n) |
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2099 { |
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2100 octave_idx_type lworkaround |
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2101 = 12*n + 2*n*smlsiz + 8*n*nlvl + n*nrhs + (smlsiz+1)*(smlsiz+1); |
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2102 |
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2103 if (work(0) < lworkaround) |
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2104 work(0) = lworkaround; |
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2105 } |
| 7476 | 2106 |
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2107 lwork = static_cast<octave_idx_type> (work(0)); |
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2108 work.resize (lwork); |
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2109 |
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2110 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, |
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2111 maxmn, ps, rcond, rank, |
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2112 work.fortran_vec (), lwork, |
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2113 piwork, info)); |
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2114 |
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2115 if (rank < minmn) |
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2116 (*current_liboctave_warning_handler) |
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2117 ("dgelsd: rank deficient %dx%d matrix, rank = %d", m, n, rank); |
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2118 if (s.elem (0) == 0.0) |
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2119 rcond = 0.0; |
| 1948 | 2120 else |
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2121 rcond = s.elem (minmn - 1) / s.elem (0); |
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2122 |
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|
2123 retval.resize (n, nrhs); |
| 458 | 2124 } |
| 2125 | |
| 2126 return retval; | |
| 2127 } | |
| 2128 | |
| 2129 ComplexMatrix | |
| 2130 Matrix::lssolve (const ComplexMatrix& b) const | |
| 2131 { | |
| 2132 ComplexMatrix tmp (*this); | |
| 5275 | 2133 octave_idx_type info; |
| 2134 octave_idx_type rank; | |
| 7076 | 2135 double rcond; |
| 2136 return tmp.lssolve (b, info, rank, rcond); | |
| 458 | 2137 } |
| 2138 | |
| 2139 ComplexMatrix | |
| 5275 | 2140 Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info) const |
| 458 | 2141 { |
| 2142 ComplexMatrix tmp (*this); | |
| 5275 | 2143 octave_idx_type rank; |
| 7076 | 2144 double rcond; |
| 2145 return tmp.lssolve (b, info, rank, rcond); | |
| 458 | 2146 } |
| 2147 | |
| 2148 ComplexMatrix | |
| 7076 | 2149 Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info, |
| 2150 octave_idx_type& rank) const | |
| 458 | 2151 { |
| 2152 ComplexMatrix tmp (*this); | |
| 7076 | 2153 double rcond; |
| 2154 return tmp.lssolve (b, info, rank, rcond); | |
| 2155 } | |
| 2156 | |
| 2157 ComplexMatrix | |
| 2158 Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info, | |
| 2159 octave_idx_type& rank, double& rcond) const | |
| 2160 { | |
| 2161 ComplexMatrix tmp (*this); | |
| 2162 return tmp.lssolve (b, info, rank, rcond); | |
| 458 | 2163 } |
| 2164 | |
| 2165 ColumnVector | |
| 2166 Matrix::lssolve (const ColumnVector& b) const | |
| 2167 { | |
| 5275 | 2168 octave_idx_type info; |
| 2169 octave_idx_type rank; | |
| 7076 | 2170 double rcond; |
| 2171 return lssolve (b, info, rank, rcond); | |
| 458 | 2172 } |
| 2173 | |
| 2174 ColumnVector | |
| 5275 | 2175 Matrix::lssolve (const ColumnVector& b, octave_idx_type& info) const |
| 458 | 2176 { |
| 5275 | 2177 octave_idx_type rank; |
| 7076 | 2178 double rcond; |
| 2179 return lssolve (b, info, rank, rcond); | |
| 458 | 2180 } |
| 2181 | |
| 2182 ColumnVector | |
| 7072 | 2183 Matrix::lssolve (const ColumnVector& b, octave_idx_type& info, |
| 2184 octave_idx_type& rank) const | |
| 458 | 2185 { |
| 7076 | 2186 double rcond; |
| 2187 return lssolve (b, info, rank, rcond); | |
| 2188 } | |
| 2189 | |
| 2190 ColumnVector | |
| 2191 Matrix::lssolve (const ColumnVector& b, octave_idx_type& info, | |
| 2192 octave_idx_type& rank, double &rcond) const | |
| 2193 { | |
| 1948 | 2194 ColumnVector retval; |
| 2195 | |
| 5275 | 2196 octave_idx_type nrhs = 1; |
| 2197 | |
| 2198 octave_idx_type m = rows (); | |
| 2199 octave_idx_type n = cols (); | |
| 458 | 2200 |
| 6924 | 2201 if (m != b.length ()) |
| 1948 | 2202 (*current_liboctave_error_handler) |
| 6924 | 2203 ("matrix dimension mismatch solution of linear equations"); |
| 2204 else if (m == 0 || n == 0) | |
| 2205 retval = ColumnVector (n, 0.0); | |
| 1948 | 2206 else |
| 458 | 2207 { |
| 7072 | 2208 volatile octave_idx_type minmn = (m < n ? m : n); |
| 2209 octave_idx_type maxmn = m > n ? m : n; | |
| 7076 | 2210 rcond = -1.0; |
| 7072 | 2211 |
| 2212 if (m != n) | |
| 2213 { | |
| 2214 retval = ColumnVector (maxmn, 0.0); | |
| 2215 | |
| 2216 for (octave_idx_type i = 0; i < m; i++) | |
| 2217 retval.elem (i) = b.elem (i); | |
| 2218 } | |
| 2219 else | |
| 2220 retval = b; | |
| 2221 | |
| 1948 | 2222 Matrix atmp = *this; |
| 2223 double *tmp_data = atmp.fortran_vec (); | |
| 2224 | |
| 7072 | 2225 double *pretval = retval.fortran_vec (); |
| 2226 Array<double> s (minmn); | |
| 7071 | 2227 double *ps = s.fortran_vec (); |
| 1948 | 2228 |
| 7072 | 2229 // Ask DGELSD what the dimension of WORK should be. |
| 5275 | 2230 octave_idx_type lwork = -1; |
| 3752 | 2231 |
| 2232 Array<double> work (1); | |
| 2233 | |
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2234 octave_idx_type smlsiz; |
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2235 F77_FUNC (xilaenv, XILAENV) (9, F77_CONST_CHAR_ARG2 ("DGELSD", 6), |
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2236 F77_CONST_CHAR_ARG2 (" ", 1), |
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2237 0, 0, 0, 0, smlsiz |
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2238 F77_CHAR_ARG_LEN (6) |
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2239 F77_CHAR_ARG_LEN (1)); |
| 7079 | 2240 |
| 2241 // We compute the size of iwork because DGELSD in older versions | |
| 2242 // of LAPACK does not return it on a query call. | |
| 7124 | 2243 double dminmn = static_cast<double> (minmn); |
| 2244 double dsmlsizp1 = static_cast<double> (smlsiz+1); | |
| 7079 | 2245 #if defined (HAVE_LOG2) |
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2246 double tmp = log2 (dminmn / dsmlsizp1); |
| 7079 | 2247 #else |
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2248 double tmp = log (dminmn / dsmlsizp1) / log (2.0); |
| 7079 | 2249 #endif |
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2250 octave_idx_type nlvl = static_cast<octave_idx_type> (tmp) + 1; |
| 7079 | 2251 if (nlvl < 0) |
| 2252 nlvl = 0; | |
| 2253 | |
| 2254 octave_idx_type liwork = 3 * minmn * nlvl + 11 * minmn; | |
| 2255 if (liwork < 1) | |
| 2256 liwork = 1; | |
| 7072 | 2257 Array<octave_idx_type> iwork (liwork); |
| 2258 octave_idx_type* piwork = iwork.fortran_vec (); | |
| 2259 | |
| 2260 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, | |
| 2261 ps, rcond, rank, work.fortran_vec (), | |
| 2262 lwork, piwork, info)); | |
| 1948 | 2263 |
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2264 lwork = static_cast<octave_idx_type> (work(0)); |
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2265 work.resize (lwork); |
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2266 |
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2267 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, |
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2268 maxmn, ps, rcond, rank, |
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2269 work.fortran_vec (), lwork, |
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2270 piwork, info)); |
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2271 |
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2272 if (rank < minmn) |
| 1948 | 2273 { |
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2274 if (rank < minmn) |
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2275 (*current_liboctave_warning_handler) |
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2276 ("dgelsd: rank deficient %dx%d matrix, rank = %d", m, n, rank); |
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2277 if (s.elem (0) == 0.0) |
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2278 rcond = 0.0; |
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2279 else |
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2280 rcond = s.elem (minmn - 1) / s.elem (0); |
| 1948 | 2281 } |
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2282 |
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2283 retval.resize (n, nrhs); |
| 458 | 2284 } |
| 2285 | |
| 2286 return retval; | |
| 2287 } | |
| 2288 | |
| 2289 ComplexColumnVector | |
| 2290 Matrix::lssolve (const ComplexColumnVector& b) const | |
| 2291 { | |
| 2292 ComplexMatrix tmp (*this); | |
| 7076 | 2293 octave_idx_type info; |
| 2294 octave_idx_type rank; | |
| 2295 double rcond; | |
| 2296 return tmp.lssolve (b, info, rank, rcond); | |
| 458 | 2297 } |
| 2298 | |
| 2299 ComplexColumnVector | |
| 5275 | 2300 Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info) const |
| 458 | 2301 { |
| 2302 ComplexMatrix tmp (*this); | |
| 7076 | 2303 octave_idx_type rank; |
| 2304 double rcond; | |
| 2305 return tmp.lssolve (b, info, rank, rcond); | |
| 458 | 2306 } |
| 2307 | |
| 2308 ComplexColumnVector | |
| 7076 | 2309 Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, |
| 2310 octave_idx_type& rank) const | |
| 458 | 2311 { |
| 2312 ComplexMatrix tmp (*this); | |
| 7076 | 2313 double rcond; |
| 2314 return tmp.lssolve (b, info, rank, rcond); | |
| 2315 } | |
| 2316 | |
| 2317 ComplexColumnVector | |
| 2318 Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, | |
| 2319 octave_idx_type& rank, double &rcond) const | |
| 2320 { | |
| 2321 ComplexMatrix tmp (*this); | |
| 2322 return tmp.lssolve (b, info, rank, rcond); | |
| 458 | 2323 } |
| 2324 | |
| 1819 | 2325 // Constants for matrix exponential calculation. |
| 2326 | |
| 2327 static double padec [] = | |
| 2328 { | |
| 2329 5.0000000000000000e-1, | |
| 2330 1.1666666666666667e-1, | |
| 2331 1.6666666666666667e-2, | |
| 2332 1.6025641025641026e-3, | |
| 2333 1.0683760683760684e-4, | |
| 2334 4.8562548562548563e-6, | |
| 2335 1.3875013875013875e-7, | |
| 2336 1.9270852604185938e-9, | |
| 2337 }; | |
| 2338 | |
| 7400 | 2339 static void |
| 2340 solve_singularity_warning (double rcond) | |
| 2341 { | |
| 2342 (*current_liboctave_warning_handler) | |
| 2343 ("singular matrix encountered in expm calculation, rcond = %g", | |
| 2344 rcond); | |
| 2345 } | |
| 2346 | |
| 1819 | 2347 Matrix |
| 2348 Matrix::expm (void) const | |
| 2349 { | |
| 2350 Matrix retval; | |
| 2351 | |
| 2352 Matrix m = *this; | |
| 2353 | |
| 6699 | 2354 if (numel () == 1) |
| 2355 return Matrix (1, 1, exp (m(0))); | |
| 2356 | |
| 5275 | 2357 octave_idx_type nc = columns (); |
| 1819 | 2358 |
| 3130 | 2359 // Preconditioning step 1: trace normalization to reduce dynamic |
| 2360 // range of poles, but avoid making stable eigenvalues unstable. | |
| 2361 | |
| 1819 | 2362 // trace shift value |
| 3331 | 2363 volatile double trshift = 0.0; |
| 1819 | 2364 |
| 5275 | 2365 for (octave_idx_type i = 0; i < nc; i++) |
| 1819 | 2366 trshift += m.elem (i, i); |
| 2367 | |
| 2368 trshift /= nc; | |
| 2369 | |
| 3130 | 2370 if (trshift > 0.0) |
| 2371 { | |
| 5275 | 2372 for (octave_idx_type i = 0; i < nc; i++) |
| 3130 | 2373 m.elem (i, i) -= trshift; |
| 2374 } | |
| 1819 | 2375 |
| 3331 | 2376 // Preconditioning step 2: balancing; code follows development |
| 2377 // in AEPBAL | |
| 2378 | |
| 2379 double *p_m = m.fortran_vec (); | |
| 2380 | |
| 5275 | 2381 octave_idx_type info, ilo, ihi, ilos, ihis; |
| 3468 | 2382 Array<double> dpermute (nc); |
| 2383 Array<double> dscale (nc); | |
| 3466 | 2384 |
| 3468 | 2385 // permutation first |
| 2386 char job = 'P'; | |
| 4552 | 2387 F77_XFCN (dgebal, DGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
| 2388 nc, p_m, nc, ilo, ihi, | |
| 2389 dpermute.fortran_vec (), info | |
| 2390 F77_CHAR_ARG_LEN (1))); | |
| 3466 | 2391 |
| 3468 | 2392 // then scaling |
| 2393 job = 'S'; | |
| 4552 | 2394 F77_XFCN (dgebal, DGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
| 2395 nc, p_m, nc, ilos, ihis, | |
| 2396 dscale.fortran_vec (), info | |
| 2397 F77_CHAR_ARG_LEN (1))); | |
| 3331 | 2398 |
| 1819 | 2399 // Preconditioning step 3: scaling. |
| 3331 | 2400 |
| 1819 | 2401 ColumnVector work(nc); |
| 3130 | 2402 double inf_norm; |
| 3331 | 2403 |
| 4552 | 2404 F77_XFCN (xdlange, XDLANGE, (F77_CONST_CHAR_ARG2 ("I", 1), |
| 2405 nc, nc, m.fortran_vec (), nc, | |
| 2406 work.fortran_vec (), inf_norm | |
| 2407 F77_CHAR_ARG_LEN (1))); | |
| 3331 | 2408 |
| 5275 | 2409 octave_idx_type sqpow = static_cast<octave_idx_type> (inf_norm > 0.0 |
| 1819 | 2410 ? (1.0 + log (inf_norm) / log (2.0)) |
| 2411 : 0.0); | |
| 3331 | 2412 |
| 1819 | 2413 // Check whether we need to square at all. |
| 3331 | 2414 |
| 1819 | 2415 if (sqpow < 0) |
| 2416 sqpow = 0; | |
| 3331 | 2417 |
| 1819 | 2418 if (sqpow > 0) |
| 2419 { | |
| 7400 | 2420 if (sqpow > 1023) |
| 2421 sqpow = 1023; | |
| 2422 | |
| 1819 | 2423 double scale_factor = 1.0; |
| 5275 | 2424 for (octave_idx_type i = 0; i < sqpow; i++) |
| 1819 | 2425 scale_factor *= 2.0; |
| 7400 | 2426 |
| 1819 | 2427 m = m / scale_factor; |
| 2428 } | |
| 3331 | 2429 |
| 1819 | 2430 // npp, dpp: pade' approx polynomial matrices. |
| 3331 | 2431 |
| 1819 | 2432 Matrix npp (nc, nc, 0.0); |
| 7265 | 2433 double *pnpp = npp.fortran_vec (); |
| 1819 | 2434 Matrix dpp = npp; |
| 7265 | 2435 double *pdpp = dpp.fortran_vec (); |
| 3331 | 2436 |
| 1819 | 2437 // Now powers a^8 ... a^1. |
| 3331 | 2438 |
| 5275 | 2439 octave_idx_type minus_one_j = -1; |
| 2440 for (octave_idx_type j = 7; j >= 0; j--) | |
| 1819 | 2441 { |
| 7265 | 2442 for (octave_idx_type i = 0; i < nc; i++) |
| 2443 { | |
| 2444 octave_idx_type k = i * nc + i; | |
| 2445 pnpp[k] += padec[j]; | |
| 2446 pdpp[k] += minus_one_j * padec[j]; | |
| 2447 } | |
| 2448 | |
| 2449 npp = m * npp; | |
| 2450 pnpp = npp.fortran_vec (); | |
| 2451 | |
| 2452 dpp = m * dpp; | |
| 2453 pdpp = dpp.fortran_vec (); | |
| 2454 | |
| 1819 | 2455 minus_one_j *= -1; |
| 2456 } | |
| 3331 | 2457 |
| 1819 | 2458 // Zero power. |
| 3331 | 2459 |
| 1819 | 2460 dpp = -dpp; |
| 5275 | 2461 for (octave_idx_type j = 0; j < nc; j++) |
| 1819 | 2462 { |
| 2463 npp.elem (j, j) += 1.0; | |
| 2464 dpp.elem (j, j) += 1.0; | |
| 2465 } | |
| 3331 | 2466 |
| 1819 | 2467 // Compute pade approximation = inverse (dpp) * npp. |
| 2468 | |
| 7400 | 2469 double rcond; |
| 2470 retval = dpp.solve (npp, info, rcond, solve_singularity_warning); | |
| 2471 | |
| 2472 if (info < 0) | |
| 2473 return retval; | |
| 2474 | |
| 1819 | 2475 // Reverse preconditioning step 3: repeated squaring. |
| 3331 | 2476 |
| 1819 | 2477 while (sqpow) |
| 2478 { | |
| 2479 retval = retval * retval; | |
| 2480 sqpow--; | |
| 2481 } | |
| 3331 | 2482 |
| 1819 | 2483 // Reverse preconditioning step 2: inverse balancing. |
| 3466 | 2484 // apply inverse scaling to computed exponential |
| 5275 | 2485 for (octave_idx_type i = 0; i < nc; i++) |
| 2486 for (octave_idx_type j = 0; j < nc; j++) | |
| 3468 | 2487 retval(i,j) *= dscale(i) / dscale(j); |
| 3466 | 2488 |
| 4153 | 2489 OCTAVE_QUIT; |
| 2490 | |
| 3466 | 2491 // construct balancing permutation vector |
| 5275 | 2492 Array<octave_idx_type> iperm (nc); |
| 2493 for (octave_idx_type i = 0; i < nc; i++) | |
| 4593 | 2494 iperm(i) = i; // identity permutation |
| 3466 | 2495 |
| 2496 // leading permutations in forward order | |
| 5275 | 2497 for (octave_idx_type i = 0; i < (ilo-1); i++) |
| 3468 | 2498 { |
| 5275 | 2499 octave_idx_type swapidx = static_cast<octave_idx_type> (dpermute(i)) - 1; |
| 2500 octave_idx_type tmp = iperm(i); | |
| 4593 | 2501 iperm(i) = iperm (swapidx); |
| 2502 iperm(swapidx) = tmp; | |
| 3468 | 2503 } |
| 3466 | 2504 |
| 7416 | 2505 // construct inverse balancing permutation vector |
| 2506 Array<octave_idx_type> invpvec (nc); | |
| 2507 for (octave_idx_type i = 0; i < nc; i++) | |
| 2508 invpvec(iperm(i)) = i; // Thanks to R. A. Lippert for this method | |
| 2509 | |
| 2510 OCTAVE_QUIT; | |
| 2511 | |
| 2512 Matrix tmpMat = retval; | |
| 2513 for (octave_idx_type i = 0; i < nc; i++) | |
| 2514 for (octave_idx_type j = 0; j < nc; j++) | |
| 2515 retval(i,j) = tmpMat(invpvec(i),invpvec(j)); | |
| 2516 | |
| 2517 OCTAVE_QUIT; | |
| 2518 | |
| 2519 for (octave_idx_type i = 0; i < nc; i++) | |
| 2520 iperm(i) = i; // identity permutation | |
| 2521 | |
| 3466 | 2522 // trailing permutations must be done in reverse order |
| 5275 | 2523 for (octave_idx_type i = nc - 1; i >= ihi; i--) |
| 3468 | 2524 { |
| 5275 | 2525 octave_idx_type swapidx = static_cast<octave_idx_type> (dpermute(i)) - 1; |
| 2526 octave_idx_type tmp = iperm(i); | |
| 4593 | 2527 iperm(i) = iperm(swapidx); |
| 2528 iperm(swapidx) = tmp; | |
| 3468 | 2529 } |
| 3466 | 2530 |
| 2531 // construct inverse balancing permutation vector | |
| 5275 | 2532 for (octave_idx_type i = 0; i < nc; i++) |
| 4593 | 2533 invpvec(iperm(i)) = i; // Thanks to R. A. Lippert for this method |
| 4153 | 2534 |
| 2535 OCTAVE_QUIT; | |
| 3466 | 2536 |
| 7416 | 2537 tmpMat = retval; |
| 5275 | 2538 for (octave_idx_type i = 0; i < nc; i++) |
| 2539 for (octave_idx_type j = 0; j < nc; j++) | |
| 3468 | 2540 retval(i,j) = tmpMat(invpvec(i),invpvec(j)); |
| 3466 | 2541 |
| 1819 | 2542 // Reverse preconditioning step 1: fix trace normalization. |
| 3331 | 2543 |
| 3130 | 2544 if (trshift > 0.0) |
| 2545 retval = exp (trshift) * retval; | |
| 2546 | |
| 2547 return retval; | |
| 1819 | 2548 } |
| 2549 | |
| 458 | 2550 Matrix& |
| 2551 Matrix::operator += (const DiagMatrix& a) | |
| 2552 { | |
| 5275 | 2553 octave_idx_type nr = rows (); |
| 2554 octave_idx_type nc = cols (); | |
| 2555 | |
| 2556 octave_idx_type a_nr = a.rows (); | |
| 2557 octave_idx_type a_nc = a.cols (); | |
| 2385 | 2558 |
| 2559 if (nr != a_nr || nc != a_nc) | |
| 458 | 2560 { |
| 2385 | 2561 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
| 458 | 2562 return *this; |
| 2563 } | |
| 2564 | |
| 5275 | 2565 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 2566 elem (i, i) += a.elem (i, i); |
| 2567 | |
| 2568 return *this; | |
| 2569 } | |
| 2570 | |
| 2571 Matrix& | |
| 2572 Matrix::operator -= (const DiagMatrix& a) | |
| 2573 { | |
| 5275 | 2574 octave_idx_type nr = rows (); |
| 2575 octave_idx_type nc = cols (); | |
| 2576 | |
| 2577 octave_idx_type a_nr = a.rows (); | |
| 2578 octave_idx_type a_nc = a.cols (); | |
| 2385 | 2579 |
| 2580 if (nr != a_nr || nc != a_nc) | |
| 458 | 2581 { |
| 2385 | 2582 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
| 458 | 2583 return *this; |
| 2584 } | |
| 2585 | |
| 5275 | 2586 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 2587 elem (i, i) -= a.elem (i, i); |
| 2588 | |
| 2589 return *this; | |
| 2590 } | |
| 2591 | |
| 2592 // unary operations | |
| 2593 | |
| 2964 | 2594 boolMatrix |
| 458 | 2595 Matrix::operator ! (void) const |
| 2596 { | |
| 5275 | 2597 octave_idx_type nr = rows (); |
| 2598 octave_idx_type nc = cols (); | |
| 458 | 2599 |
| 2964 | 2600 boolMatrix b (nr, nc); |
| 458 | 2601 |
| 5275 | 2602 for (octave_idx_type j = 0; j < nc; j++) |
| 2603 for (octave_idx_type i = 0; i < nr; i++) | |
| 458 | 2604 b.elem (i, j) = ! elem (i, j); |
| 2605 | |
| 2606 return b; | |
| 2607 } | |
| 2608 | |
| 1205 | 2609 // column vector by row vector -> matrix operations |
| 458 | 2610 |
| 1205 | 2611 Matrix |
| 2612 operator * (const ColumnVector& v, const RowVector& a) | |
| 458 | 2613 { |
| 1948 | 2614 Matrix retval; |
| 2615 | |
| 5275 | 2616 octave_idx_type len = v.length (); |
| 3233 | 2617 |
| 2618 if (len != 0) | |
| 1205 | 2619 { |
| 5275 | 2620 octave_idx_type a_len = a.length (); |
| 3233 | 2621 |
| 2622 retval.resize (len, a_len); | |
| 2623 double *c = retval.fortran_vec (); | |
| 2624 | |
| 4552 | 2625 F77_XFCN (dgemm, DGEMM, (F77_CONST_CHAR_ARG2 ("N", 1), |
| 2626 F77_CONST_CHAR_ARG2 ("N", 1), | |
| 2627 len, a_len, 1, 1.0, v.data (), len, | |
| 2628 a.data (), 1, 0.0, c, len | |
| 2629 F77_CHAR_ARG_LEN (1) | |
| 2630 F77_CHAR_ARG_LEN (1))); | |
| 1205 | 2631 } |
| 458 | 2632 |
| 1948 | 2633 return retval; |
| 458 | 2634 } |
| 2635 | |
| 2636 // other operations. | |
| 2637 | |
| 2638 Matrix | |
|
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2639 Matrix::map (dmapper fcn) const |
| 1205 | 2640 { |
|
7503
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2641 return MArray2<double>::map<double> (func_ptr (fcn)); |
|
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|
2642 } |
|
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|
2643 |
|
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|
2644 ComplexMatrix |
|
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|
2645 Matrix::map (cmapper fcn) const |
|
8c32f95c2639
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2646 { |
|
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2647 return MArray2<double>::map<Complex> (func_ptr (fcn)); |
| 1205 | 2648 } |
| 2649 | |
| 3248 | 2650 boolMatrix |
|
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2651 Matrix::map (bmapper fcn) const |
| 3248 | 2652 { |
|
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2653 return MArray2<double>::map<bool> (func_ptr (fcn)); |
| 458 | 2654 } |
| 2655 | |
| 2385 | 2656 bool |
| 4431 | 2657 Matrix::any_element_is_negative (bool neg_zero) const |
| 2385 | 2658 { |
| 5275 | 2659 octave_idx_type nel = nelem (); |
| 2385 | 2660 |
| 4431 | 2661 if (neg_zero) |
| 2662 { | |
| 5275 | 2663 for (octave_idx_type i = 0; i < nel; i++) |
| 4634 | 2664 if (lo_ieee_signbit (elem (i))) |
| 2665 return true; | |
| 4431 | 2666 } |
| 2667 else | |
| 2668 { | |
| 5275 | 2669 for (octave_idx_type i = 0; i < nel; i++) |
| 4634 | 2670 if (elem (i) < 0) |
| 2671 return true; | |
| 4431 | 2672 } |
| 2385 | 2673 |
| 2674 return false; | |
| 2675 } | |
| 2676 | |
| 2677 | |
| 2678 bool | |
| 2679 Matrix::any_element_is_inf_or_nan (void) const | |
| 2680 { | |
| 5275 | 2681 octave_idx_type nel = nelem (); |
| 2682 | |
| 2683 for (octave_idx_type i = 0; i < nel; i++) | |
| 4634 | 2684 { |
| 2685 double val = elem (i); | |
| 2686 if (xisinf (val) || xisnan (val)) | |
| 2687 return true; | |
| 2688 } | |
| 2689 | |
| 2690 return false; | |
| 2385 | 2691 } |
| 2692 | |
| 2693 bool | |
| 5943 | 2694 Matrix::any_element_not_one_or_zero (void) const |
| 2695 { | |
| 2696 octave_idx_type nel = nelem (); | |
| 2697 | |
| 2698 for (octave_idx_type i = 0; i < nel; i++) | |
| 2699 { | |
| 2700 double val = elem (i); | |
| 2701 if (val != 0 && val != 1) | |
| 2702 return true; | |
| 2703 } | |
| 2704 | |
| 2705 return false; | |
| 2706 } | |
| 2707 | |
| 2708 bool | |
| 2385 | 2709 Matrix::all_elements_are_int_or_inf_or_nan (void) const |
| 2710 { | |
| 5275 | 2711 octave_idx_type nel = nelem (); |
| 2712 | |
| 2713 for (octave_idx_type i = 0; i < nel; i++) | |
| 4634 | 2714 { |
| 2715 double val = elem (i); | |
| 2716 if (xisnan (val) || D_NINT (val) == val) | |
| 2717 continue; | |
| 2718 else | |
| 2719 return false; | |
| 2720 } | |
| 2385 | 2721 |
| 2722 return true; | |
| 2723 } | |
| 2724 | |
| 1968 | 2725 // Return nonzero if any element of M is not an integer. Also extract |
| 2726 // the largest and smallest values and return them in MAX_VAL and MIN_VAL. | |
| 2727 | |
| 2385 | 2728 bool |
| 1968 | 2729 Matrix::all_integers (double& max_val, double& min_val) const |
| 2730 { | |
| 5275 | 2731 octave_idx_type nel = nelem (); |
| 4634 | 2732 |
| 2733 if (nel > 0) | |
| 1968 | 2734 { |
| 4634 | 2735 max_val = elem (0); |
| 2736 min_val = elem (0); | |
| 1968 | 2737 } |
| 2738 else | |
| 2385 | 2739 return false; |
| 1968 | 2740 |
| 5275 | 2741 for (octave_idx_type i = 0; i < nel; i++) |
| 4634 | 2742 { |
| 2743 double val = elem (i); | |
| 2744 | |
| 2745 if (val > max_val) | |
| 2746 max_val = val; | |
| 2747 | |
| 2748 if (val < min_val) | |
| 2749 min_val = val; | |
| 2750 | |
| 2751 if (D_NINT (val) != val) | |
| 2752 return false; | |
| 2753 } | |
| 2385 | 2754 |
| 2755 return true; | |
| 1968 | 2756 } |
| 2757 | |
| 2385 | 2758 bool |
| 1968 | 2759 Matrix::too_large_for_float (void) const |
| 2760 { | |
| 5275 | 2761 octave_idx_type nel = nelem (); |
| 2762 | |
| 2763 for (octave_idx_type i = 0; i < nel; i++) | |
| 4634 | 2764 { |
| 2765 double val = elem (i); | |
| 2766 | |
| 5389 | 2767 if (! (xisnan (val) || xisinf (val)) |
| 5387 | 2768 && fabs (val) > FLT_MAX) |
| 4634 | 2769 return true; |
| 2770 } | |
| 1968 | 2771 |
| 2385 | 2772 return false; |
| 1968 | 2773 } |
| 2774 | |
| 5775 | 2775 // FIXME Do these really belong here? Maybe they should be |
| 4015 | 2776 // in a base class? |
| 458 | 2777 |
| 2832 | 2778 boolMatrix |
| 4015 | 2779 Matrix::all (int dim) const |
| 458 | 2780 { |
| 4015 | 2781 MX_ALL_OP (dim); |
| 458 | 2782 } |
| 2783 | |
| 2832 | 2784 boolMatrix |
| 4015 | 2785 Matrix::any (int dim) const |
| 458 | 2786 { |
| 4015 | 2787 MX_ANY_OP (dim); |
| 458 | 2788 } |
| 2789 | |
| 2790 Matrix | |
| 3723 | 2791 Matrix::cumprod (int dim) const |
| 458 | 2792 { |
| 4015 | 2793 MX_CUMULATIVE_OP (Matrix, double, *=); |
| 458 | 2794 } |
| 2795 | |
| 2796 Matrix | |
| 3723 | 2797 Matrix::cumsum (int dim) const |
| 458 | 2798 { |
| 4015 | 2799 MX_CUMULATIVE_OP (Matrix, double, +=); |
| 458 | 2800 } |
| 2801 | |
| 2802 Matrix | |
| 3723 | 2803 Matrix::prod (int dim) const |
| 458 | 2804 { |
| 3864 | 2805 MX_REDUCTION_OP (Matrix, *=, 1.0, 1.0); |
| 458 | 2806 } |
| 2807 | |
| 2808 Matrix | |
| 3723 | 2809 Matrix::sum (int dim) const |
| 458 | 2810 { |
| 3864 | 2811 MX_REDUCTION_OP (Matrix, +=, 0.0, 0.0); |
| 458 | 2812 } |
| 2813 | |
| 2814 Matrix | |
| 3723 | 2815 Matrix::sumsq (int dim) const |
| 458 | 2816 { |
| 3864 | 2817 #define ROW_EXPR \ |
| 2818 double d = elem (i, j); \ | |
| 2819 retval.elem (i, 0) += d * d | |
| 2820 | |
| 2821 #define COL_EXPR \ | |
| 2822 double d = elem (i, j); \ | |
| 2823 retval.elem (0, j) += d * d | |
| 2824 | |
| 2825 MX_BASE_REDUCTION_OP (Matrix, ROW_EXPR, COL_EXPR, 0.0, 0.0); | |
| 2826 | |
| 2827 #undef ROW_EXPR | |
| 2828 #undef COL_EXPR | |
| 458 | 2829 } |
| 2830 | |
| 2385 | 2831 Matrix |
| 2832 Matrix::abs (void) const | |
| 2833 { | |
| 5275 | 2834 octave_idx_type nr = rows (); |
| 2835 octave_idx_type nc = cols (); | |
| 2385 | 2836 |
| 2837 Matrix retval (nr, nc); | |
| 2838 | |
| 5275 | 2839 for (octave_idx_type j = 0; j < nc; j++) |
| 2840 for (octave_idx_type i = 0; i < nr; i++) | |
| 2385 | 2841 retval (i, j) = fabs (elem (i, j)); |
| 2842 | |
| 2843 return retval; | |
| 2844 } | |
| 2845 | |
| 458 | 2846 ColumnVector |
| 2847 Matrix::diag (void) const | |
| 2848 { | |
| 2849 return diag (0); | |
| 2850 } | |
| 2851 | |
| 2852 ColumnVector | |
| 5275 | 2853 Matrix::diag (octave_idx_type k) const |
| 458 | 2854 { |
| 5275 | 2855 octave_idx_type nnr = rows (); |
| 2856 octave_idx_type nnc = cols (); | |
| 458 | 2857 if (k > 0) |
| 2858 nnc -= k; | |
| 2859 else if (k < 0) | |
| 2860 nnr += k; | |
| 2861 | |
| 2862 ColumnVector d; | |
| 2863 | |
| 2864 if (nnr > 0 && nnc > 0) | |
| 2865 { | |
| 5275 | 2866 octave_idx_type ndiag = (nnr < nnc) ? nnr : nnc; |
| 458 | 2867 |
| 2868 d.resize (ndiag); | |
| 2869 | |
| 2870 if (k > 0) | |
| 2871 { | |
| 5275 | 2872 for (octave_idx_type i = 0; i < ndiag; i++) |
| 458 | 2873 d.elem (i) = elem (i, i+k); |
| 2874 } | |
| 4509 | 2875 else if (k < 0) |
| 458 | 2876 { |
| 5275 | 2877 for (octave_idx_type i = 0; i < ndiag; i++) |
| 458 | 2878 d.elem (i) = elem (i-k, i); |
| 2879 } | |
| 2880 else | |
| 2881 { | |
| 5275 | 2882 for (octave_idx_type i = 0; i < ndiag; i++) |
| 458 | 2883 d.elem (i) = elem (i, i); |
| 2884 } | |
| 2885 } | |
| 2886 else | |
| 4513 | 2887 (*current_liboctave_error_handler) |
| 2888 ("diag: requested diagonal out of range"); | |
| 458 | 2889 |
| 2890 return d; | |
| 2891 } | |
| 2892 | |
| 2893 ColumnVector | |
| 2894 Matrix::row_min (void) const | |
| 2895 { | |
| 5275 | 2896 Array<octave_idx_type> dummy_idx; |
| 4587 | 2897 return row_min (dummy_idx); |
| 458 | 2898 } |
| 2899 | |
| 2900 ColumnVector | |
| 5275 | 2901 Matrix::row_min (Array<octave_idx_type>& idx_arg) const |
| 458 | 2902 { |
| 2903 ColumnVector result; | |
| 2904 | |
| 5275 | 2905 octave_idx_type nr = rows (); |
| 2906 octave_idx_type nc = cols (); | |
| 458 | 2907 |
| 2908 if (nr > 0 && nc > 0) | |
| 2909 { | |
| 2910 result.resize (nr); | |
| 4587 | 2911 idx_arg.resize (nr); |
| 458 | 2912 |
| 5275 | 2913 for (octave_idx_type i = 0; i < nr; i++) |
| 458 | 2914 { |
| 5275 | 2915 octave_idx_type idx_j; |
| 4469 | 2916 |
| 2917 double tmp_min = octave_NaN; | |
| 2918 | |
| 2919 for (idx_j = 0; idx_j < nc; idx_j++) | |
| 2354 | 2920 { |
| 4469 | 2921 tmp_min = elem (i, idx_j); |
| 2922 | |
| 5389 | 2923 if (! xisnan (tmp_min)) |
| 4469 | 2924 break; |
| 2925 } | |
| 2926 | |
| 5275 | 2927 for (octave_idx_type j = idx_j+1; j < nc; j++) |
| 4469 | 2928 { |
| 2929 double tmp = elem (i, j); | |
| 2930 | |
| 5389 | 2931 if (xisnan (tmp)) |
| 4469 | 2932 continue; |
| 2933 else if (tmp < tmp_min) | |
| 2354 | 2934 { |
| 4469 | 2935 idx_j = j; |
| 2936 tmp_min = tmp; | |
| 2354 | 2937 } |
| 2938 } | |
| 2939 | |
| 4469 | 2940 result.elem (i) = tmp_min; |
| 5389 | 2941 idx_arg.elem (i) = xisnan (tmp_min) ? 0 : idx_j; |
| 458 | 2942 } |
| 2943 } | |
| 2944 | |
| 2945 return result; | |
| 2946 } | |
| 2947 | |
| 2948 ColumnVector | |
| 2949 Matrix::row_max (void) const | |
| 2950 { | |
| 5275 | 2951 Array<octave_idx_type> dummy_idx; |
| 4587 | 2952 return row_max (dummy_idx); |
| 458 | 2953 } |
| 2954 | |
| 2955 ColumnVector | |
| 5275 | 2956 Matrix::row_max (Array<octave_idx_type>& idx_arg) const |
| 458 | 2957 { |
| 2958 ColumnVector result; | |
| 2959 | |
| 5275 | 2960 octave_idx_type nr = rows (); |
| 2961 octave_idx_type nc = cols (); | |
| 458 | 2962 |
| 2963 if (nr > 0 && nc > 0) | |
| 2964 { | |
| 2965 result.resize (nr); | |
| 4587 | 2966 idx_arg.resize (nr); |
| 458 | 2967 |
| 5275 | 2968 for (octave_idx_type i = 0; i < nr; i++) |
| 458 | 2969 { |
| 5275 | 2970 octave_idx_type idx_j; |
| 4469 | 2971 |
| 2972 double tmp_max = octave_NaN; | |
| 2973 | |
| 2974 for (idx_j = 0; idx_j < nc; idx_j++) | |
| 2354 | 2975 { |
| 4469 | 2976 tmp_max = elem (i, idx_j); |
| 2977 | |
| 5389 | 2978 if (! xisnan (tmp_max)) |
| 4469 | 2979 break; |
| 2980 } | |
| 2981 | |
| 5275 | 2982 for (octave_idx_type j = idx_j+1; j < nc; j++) |
| 4469 | 2983 { |
| 2984 double tmp = elem (i, j); | |
| 2985 | |
| 5389 | 2986 if (xisnan (tmp)) |
| 4469 | 2987 continue; |
| 2988 else if (tmp > tmp_max) | |
| 2354 | 2989 { |
| 4469 | 2990 idx_j = j; |
| 2991 tmp_max = tmp; | |
| 2354 | 2992 } |
| 2993 } | |
| 2994 | |
| 4469 | 2995 result.elem (i) = tmp_max; |
| 5389 | 2996 idx_arg.elem (i) = xisnan (tmp_max) ? 0 : idx_j; |
| 458 | 2997 } |
| 2998 } | |
| 2999 | |
| 3000 return result; | |
| 3001 } | |
| 3002 | |
| 3003 RowVector | |
| 3004 Matrix::column_min (void) const | |
| 3005 { | |
| 5275 | 3006 Array<octave_idx_type> dummy_idx; |
| 4587 | 3007 return column_min (dummy_idx); |
| 458 | 3008 } |
| 2354 | 3009 |
| 458 | 3010 RowVector |
| 5275 | 3011 Matrix::column_min (Array<octave_idx_type>& idx_arg) const |
| 458 | 3012 { |
| 3013 RowVector result; | |
| 3014 | |
| 5275 | 3015 octave_idx_type nr = rows (); |
| 3016 octave_idx_type nc = cols (); | |
| 458 | 3017 |
| 3018 if (nr > 0 && nc > 0) | |
| 3019 { | |
| 3020 result.resize (nc); | |
| 4587 | 3021 idx_arg.resize (nc); |
| 458 | 3022 |
| 5275 | 3023 for (octave_idx_type j = 0; j < nc; j++) |
| 458 | 3024 { |
| 5275 | 3025 octave_idx_type idx_i; |
| 4469 | 3026 |
| 3027 double tmp_min = octave_NaN; | |
| 3028 | |
| 3029 for (idx_i = 0; idx_i < nr; idx_i++) | |
| 2354 | 3030 { |
| 4469 | 3031 tmp_min = elem (idx_i, j); |
| 3032 | |
| 5389 | 3033 if (! xisnan (tmp_min)) |
| 4469 | 3034 break; |
| 3035 } | |
| 3036 | |
| 5275 | 3037 for (octave_idx_type i = idx_i+1; i < nr; i++) |
| 4469 | 3038 { |
| 3039 double tmp = elem (i, j); | |
| 3040 | |
| 5389 | 3041 if (xisnan (tmp)) |
| 4469 | 3042 continue; |
| 3043 else if (tmp < tmp_min) | |
| 2354 | 3044 { |
| 4469 | 3045 idx_i = i; |
| 3046 tmp_min = tmp; | |
| 2354 | 3047 } |
| 3048 } | |
| 3049 | |
| 4469 | 3050 result.elem (j) = tmp_min; |
| 5389 | 3051 idx_arg.elem (j) = xisnan (tmp_min) ? 0 : idx_i; |
| 458 | 3052 } |
| 3053 } | |
| 3054 | |
| 3055 return result; | |
| 3056 } | |
| 3057 | |
| 2354 | 3058 RowVector |
| 3059 Matrix::column_max (void) const | |
| 3060 { | |
| 5275 | 3061 Array<octave_idx_type> dummy_idx; |
| 4587 | 3062 return column_max (dummy_idx); |
| 2354 | 3063 } |
| 458 | 3064 |
| 3065 RowVector | |
| 5275 | 3066 Matrix::column_max (Array<octave_idx_type>& idx_arg) const |
| 458 | 3067 { |
| 3068 RowVector result; | |
| 3069 | |
| 5275 | 3070 octave_idx_type nr = rows (); |
| 3071 octave_idx_type nc = cols (); | |
| 458 | 3072 |
| 3073 if (nr > 0 && nc > 0) | |
| 3074 { | |
| 3075 result.resize (nc); | |
| 4587 | 3076 idx_arg.resize (nc); |
| 458 | 3077 |
| 5275 | 3078 for (octave_idx_type j = 0; j < nc; j++) |
| 458 | 3079 { |
| 5275 | 3080 octave_idx_type idx_i; |
| 4469 | 3081 |
| 3082 double tmp_max = octave_NaN; | |
| 3083 | |
| 3084 for (idx_i = 0; idx_i < nr; idx_i++) | |
| 2354 | 3085 { |
| 4469 | 3086 tmp_max = elem (idx_i, j); |
| 3087 | |
| 5389 | 3088 if (! xisnan (tmp_max)) |
| 4469 | 3089 break; |
| 3090 } | |
| 3091 | |
| 5275 | 3092 for (octave_idx_type i = idx_i+1; i < nr; i++) |
| 4469 | 3093 { |
| 3094 double tmp = elem (i, j); | |
| 3095 | |
| 5389 | 3096 if (xisnan (tmp)) |
| 4469 | 3097 continue; |
| 3098 else if (tmp > tmp_max) | |
| 2354 | 3099 { |
| 4469 | 3100 idx_i = i; |
| 3101 tmp_max = tmp; | |
| 2354 | 3102 } |
| 3103 } | |
| 3104 | |
| 4469 | 3105 result.elem (j) = tmp_max; |
| 5389 | 3106 idx_arg.elem (j) = xisnan (tmp_max) ? 0 : idx_i; |
| 458 | 3107 } |
| 3108 } | |
| 3109 | |
| 3110 return result; | |
| 3111 } | |
| 3112 | |
| 3504 | 3113 std::ostream& |
| 3114 operator << (std::ostream& os, const Matrix& a) | |
| 458 | 3115 { |
| 5275 | 3116 for (octave_idx_type i = 0; i < a.rows (); i++) |
| 458 | 3117 { |
| 5275 | 3118 for (octave_idx_type j = 0; j < a.cols (); j++) |
| 4130 | 3119 { |
| 3120 os << " "; | |
| 3121 octave_write_double (os, a.elem (i, j)); | |
| 3122 } | |
| 458 | 3123 os << "\n"; |
| 3124 } | |
| 3125 return os; | |
| 3126 } | |
| 3127 | |
| 3504 | 3128 std::istream& |
| 3129 operator >> (std::istream& is, Matrix& a) | |
| 458 | 3130 { |
| 5275 | 3131 octave_idx_type nr = a.rows (); |
| 3132 octave_idx_type nc = a.cols (); | |
| 458 | 3133 |
| 3134 if (nr < 1 || nc < 1) | |
| 3504 | 3135 is.clear (std::ios::badbit); |
| 458 | 3136 else |
| 3137 { | |
| 3138 double tmp; | |
| 5275 | 3139 for (octave_idx_type i = 0; i < nr; i++) |
| 3140 for (octave_idx_type j = 0; j < nc; j++) | |
| 458 | 3141 { |
| 4130 | 3142 tmp = octave_read_double (is); |
| 458 | 3143 if (is) |
| 3144 a.elem (i, j) = tmp; | |
| 3145 else | |
| 2795 | 3146 goto done; |
| 458 | 3147 } |
| 3148 } | |
| 3149 | |
| 2795 | 3150 done: |
| 3151 | |
| 458 | 3152 return is; |
| 3153 } | |
| 3154 | |
| 1819 | 3155 Matrix |
| 3156 Givens (double x, double y) | |
| 3157 { | |
| 3158 double cc, s, temp_r; | |
| 3159 | |
| 3887 | 3160 F77_FUNC (dlartg, DLARTG) (x, y, cc, s, temp_r); |
| 1819 | 3161 |
| 3162 Matrix g (2, 2); | |
| 3163 | |
| 3164 g.elem (0, 0) = cc; | |
| 3165 g.elem (1, 1) = cc; | |
| 3166 g.elem (0, 1) = s; | |
| 3167 g.elem (1, 0) = -s; | |
| 3168 | |
| 3169 return g; | |
| 3170 } | |
| 3171 | |
| 3172 Matrix | |
| 3173 Sylvester (const Matrix& a, const Matrix& b, const Matrix& c) | |
| 3174 { | |
| 3175 Matrix retval; | |
| 3176 | |
| 5775 | 3177 // FIXME -- need to check that a, b, and c are all the same |
| 1819 | 3178 // size. |
| 3179 | |
| 3180 // Compute Schur decompositions. | |
| 3181 | |
| 3182 SCHUR as (a, "U"); | |
| 3183 SCHUR bs (b, "U"); | |
| 3184 | |
| 3185 // Transform c to new coordinates. | |
| 3186 | |
| 3187 Matrix ua = as.unitary_matrix (); | |
| 3188 Matrix sch_a = as.schur_matrix (); | |
| 3189 | |
| 3190 Matrix ub = bs.unitary_matrix (); | |
| 3191 Matrix sch_b = bs.schur_matrix (); | |
| 3192 | |
| 3193 Matrix cx = ua.transpose () * c * ub; | |
| 3194 | |
| 3195 // Solve the sylvester equation, back-transform, and return the | |
| 3196 // solution. | |
| 3197 | |
| 5275 | 3198 octave_idx_type a_nr = a.rows (); |
| 3199 octave_idx_type b_nr = b.rows (); | |
| 1819 | 3200 |
| 3201 double scale; | |
| 5275 | 3202 octave_idx_type info; |
| 1819 | 3203 |
| 1950 | 3204 double *pa = sch_a.fortran_vec (); |
| 3205 double *pb = sch_b.fortran_vec (); | |
| 3206 double *px = cx.fortran_vec (); | |
| 3207 | |
| 4552 | 3208 F77_XFCN (dtrsyl, DTRSYL, (F77_CONST_CHAR_ARG2 ("N", 1), |
| 3209 F77_CONST_CHAR_ARG2 ("N", 1), | |
| 3210 1, a_nr, b_nr, pa, a_nr, pb, | |
| 3211 b_nr, px, a_nr, scale, info | |
| 3212 F77_CHAR_ARG_LEN (1) | |
| 3213 F77_CHAR_ARG_LEN (1))); | |
| 1950 | 3214 |
| 3215 | |
|
7482
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
3216 // FIXME -- check info? |
| 1819 | 3217 |
|
7482
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
3218 retval = -ua*cx*ub.transpose (); |
| 1819 | 3219 |
| 3220 return retval; | |
| 3221 } | |
| 3222 | |
| 2828 | 3223 // matrix by matrix -> matrix operations |
| 3224 | |
| 6162 | 3225 /* Simple Dot Product, Matrix-Vector and Matrix-Matrix Unit tests |
| 3226 %!assert([1 2 3] * [ 4 ; 5 ; 6], 32, 1e-14) | |
| 3227 %!assert([1 2 ; 3 4 ] * [5 ; 6], [17 ; 39 ], 1e-14) | |
| 3228 %!assert([1 2 ; 3 4 ] * [5 6 ; 7 8], [19 22; 43 50], 1e-14) | |
| 3229 */ | |
| 3230 | |
| 3231 /* Test some simple identities | |
| 3232 %!shared M, cv, rv | |
| 3233 %! M = randn(10,10); | |
| 3234 %! cv = randn(10,1); | |
| 3235 %! rv = randn(1,10); | |
| 3236 %!assert([M*cv,M*cv],M*[cv,cv],1e-14) | |
| 3237 %!assert([rv*M;rv*M],[rv;rv]*M,1e-14) | |
| 3238 %!assert(2*rv*cv,[rv,rv]*[cv;cv],1e-14) | |
| 3239 */ | |
| 3240 | |
| 3241 | |
| 2828 | 3242 Matrix |
| 3243 operator * (const Matrix& m, const Matrix& a) | |
| 3244 { | |
| 3245 Matrix retval; | |
| 3246 | |
| 5275 | 3247 octave_idx_type nr = m.rows (); |
| 3248 octave_idx_type nc = m.cols (); | |
| 3249 | |
| 3250 octave_idx_type a_nr = a.rows (); | |
| 3251 octave_idx_type a_nc = a.cols (); | |
| 2828 | 3252 |
| 3253 if (nc != a_nr) | |
| 3254 gripe_nonconformant ("operator *", nr, nc, a_nr, a_nc); | |
| 3255 else | |
| 3256 { | |
| 3257 if (nr == 0 || nc == 0 || a_nc == 0) | |
| 3258 retval.resize (nr, a_nc, 0.0); | |
| 3259 else | |
| 3260 { | |
| 5275 | 3261 octave_idx_type ld = nr; |
| 3262 octave_idx_type lda = a_nr; | |
| 2828 | 3263 |
| 3264 retval.resize (nr, a_nc); | |
| 3265 double *c = retval.fortran_vec (); | |
| 3266 | |
| 5983 | 3267 if (a_nc == 1) |
| 3268 { | |
| 3269 if (nr == 1) | |
| 3270 F77_FUNC (xddot, XDDOT) (nc, m.data (), 1, a.data (), 1, *c); | |
| 3271 else | |
| 6390 | 3272 { |
| 3273 F77_XFCN (dgemv, DGEMV, (F77_CONST_CHAR_ARG2 ("N", 1), | |
| 3274 nr, nc, 1.0, m.data (), ld, | |
| 3275 a.data (), 1, 0.0, c, 1 | |
| 3276 F77_CHAR_ARG_LEN (1))); | |
| 3277 } | |
| 5983 | 3278 } |
| 3279 else | |
| 6390 | 3280 { |
| 3281 F77_XFCN (dgemm, DGEMM, (F77_CONST_CHAR_ARG2 ("N", 1), | |
| 3282 F77_CONST_CHAR_ARG2 ("N", 1), | |
| 3283 nr, a_nc, nc, 1.0, m.data (), | |
| 3284 ld, a.data (), lda, 0.0, c, nr | |
| 3285 F77_CHAR_ARG_LEN (1) | |
| 3286 F77_CHAR_ARG_LEN (1))); | |
| 3287 } | |
| 2828 | 3288 } |
| 3289 } | |
| 3290 | |
| 3291 return retval; | |
| 3292 } | |
| 3293 | |
| 5775 | 3294 // FIXME -- it would be nice to share code among the min/max |
| 4309 | 3295 // functions below. |
| 3296 | |
| 3297 #define EMPTY_RETURN_CHECK(T) \ | |
| 3298 if (nr == 0 || nc == 0) \ | |
| 3299 return T (nr, nc); | |
| 3300 | |
| 3301 Matrix | |
| 3302 min (double d, const Matrix& m) | |
| 3303 { | |
| 5275 | 3304 octave_idx_type nr = m.rows (); |
| 3305 octave_idx_type nc = m.columns (); | |
| 4309 | 3306 |
| 3307 EMPTY_RETURN_CHECK (Matrix); | |
| 3308 | |
| 3309 Matrix result (nr, nc); | |
| 3310 | |
| 5275 | 3311 for (octave_idx_type j = 0; j < nc; j++) |
| 3312 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3313 { |
| 3314 OCTAVE_QUIT; | |
| 3315 result (i, j) = xmin (d, m (i, j)); | |
| 3316 } | |
| 3317 | |
| 3318 return result; | |
| 3319 } | |
| 3320 | |
| 3321 Matrix | |
| 3322 min (const Matrix& m, double d) | |
| 3323 { | |
| 5275 | 3324 octave_idx_type nr = m.rows (); |
| 3325 octave_idx_type nc = m.columns (); | |
| 4309 | 3326 |
| 3327 EMPTY_RETURN_CHECK (Matrix); | |
| 3328 | |
| 3329 Matrix result (nr, nc); | |
| 3330 | |
| 5275 | 3331 for (octave_idx_type j = 0; j < nc; j++) |
| 3332 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3333 { |
| 3334 OCTAVE_QUIT; | |
| 3335 result (i, j) = xmin (m (i, j), d); | |
| 3336 } | |
| 3337 | |
| 3338 return result; | |
| 3339 } | |
| 3340 | |
| 3341 Matrix | |
| 3342 min (const Matrix& a, const Matrix& b) | |
| 3343 { | |
| 5275 | 3344 octave_idx_type nr = a.rows (); |
| 3345 octave_idx_type nc = a.columns (); | |
| 4309 | 3346 |
| 3347 if (nr != b.rows () || nc != b.columns ()) | |
| 3348 { | |
| 3349 (*current_liboctave_error_handler) | |
| 3350 ("two-arg min expecting args of same size"); | |
| 3351 return Matrix (); | |
| 3352 } | |
| 3353 | |
| 3354 EMPTY_RETURN_CHECK (Matrix); | |
| 3355 | |
| 3356 Matrix result (nr, nc); | |
| 3357 | |
| 5275 | 3358 for (octave_idx_type j = 0; j < nc; j++) |
| 3359 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3360 { |
| 3361 OCTAVE_QUIT; | |
| 3362 result (i, j) = xmin (a (i, j), b (i, j)); | |
| 3363 } | |
| 3364 | |
| 3365 return result; | |
| 3366 } | |
| 3367 | |
| 3368 Matrix | |
| 3369 max (double d, const Matrix& m) | |
| 3370 { | |
| 5275 | 3371 octave_idx_type nr = m.rows (); |
| 3372 octave_idx_type nc = m.columns (); | |
| 4309 | 3373 |
| 3374 EMPTY_RETURN_CHECK (Matrix); | |
| 3375 | |
| 3376 Matrix result (nr, nc); | |
| 3377 | |
| 5275 | 3378 for (octave_idx_type j = 0; j < nc; j++) |
| 3379 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3380 { |
| 3381 OCTAVE_QUIT; | |
| 3382 result (i, j) = xmax (d, m (i, j)); | |
| 3383 } | |
| 3384 | |
| 3385 return result; | |
| 3386 } | |
| 3387 | |
| 3388 Matrix | |
| 3389 max (const Matrix& m, double d) | |
| 3390 { | |
| 5275 | 3391 octave_idx_type nr = m.rows (); |
| 3392 octave_idx_type nc = m.columns (); | |
| 4309 | 3393 |
| 3394 EMPTY_RETURN_CHECK (Matrix); | |
| 3395 | |
| 3396 Matrix result (nr, nc); | |
| 3397 | |
| 5275 | 3398 for (octave_idx_type j = 0; j < nc; j++) |
| 3399 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3400 { |
| 3401 OCTAVE_QUIT; | |
| 3402 result (i, j) = xmax (m (i, j), d); | |
| 3403 } | |
| 3404 | |
| 3405 return result; | |
| 3406 } | |
| 3407 | |
| 3408 Matrix | |
| 3409 max (const Matrix& a, const Matrix& b) | |
| 3410 { | |
| 5275 | 3411 octave_idx_type nr = a.rows (); |
| 3412 octave_idx_type nc = a.columns (); | |
| 4309 | 3413 |
| 3414 if (nr != b.rows () || nc != b.columns ()) | |
| 3415 { | |
| 3416 (*current_liboctave_error_handler) | |
| 3417 ("two-arg max expecting args of same size"); | |
| 3418 return Matrix (); | |
| 3419 } | |
| 3420 | |
| 3421 EMPTY_RETURN_CHECK (Matrix); | |
| 3422 | |
| 3423 Matrix result (nr, nc); | |
| 3424 | |
| 5275 | 3425 for (octave_idx_type j = 0; j < nc; j++) |
| 3426 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3427 { |
| 3428 OCTAVE_QUIT; | |
| 3429 result (i, j) = xmax (a (i, j), b (i, j)); | |
| 3430 } | |
| 3431 | |
| 3432 return result; | |
| 3433 } | |
| 3434 | |
| 2870 | 3435 MS_CMP_OPS(Matrix, , double, ) |
| 3504 | 3436 MS_BOOL_OPS(Matrix, double, 0.0) |
| 2870 | 3437 |
| 3438 SM_CMP_OPS(double, , Matrix, ) | |
| 3504 | 3439 SM_BOOL_OPS(double, Matrix, 0.0) |
| 2870 | 3440 |
| 3441 MM_CMP_OPS(Matrix, , Matrix, ) | |
| 3504 | 3442 MM_BOOL_OPS(Matrix, Matrix, 0.0) |
| 2870 | 3443 |
| 458 | 3444 /* |
| 3445 ;;; Local Variables: *** | |
| 3446 ;;; mode: C++ *** | |
| 3447 ;;; End: *** | |
| 3448 */ |