Mercurial > octave-libgccjit
annotate liboctave/dMatrix.cc @ 7788:45f5faba05a2
Add the rcond function
| author | David Bateman <dbateman@free.fr> |
|---|---|
| date | Wed, 14 May 2008 18:09:56 +0200 |
| parents | 36594d5bbe13 |
| children | 82be108cc558 |
| rev | line source |
|---|---|
| 1993 | 1 // Matrix manipulations. |
| 458 | 2 /* |
| 3 | |
| 7017 | 4 Copyright (C) 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, |
| 5 2003, 2004, 2005, 2006, 2007 John W. Eaton | |
| 458 | 6 |
| 7 This file is part of Octave. | |
| 8 | |
| 9 Octave is free software; you can redistribute it and/or modify it | |
| 10 under the terms of the GNU General Public License as published by the | |
| 7016 | 11 Free Software Foundation; either version 3 of the License, or (at your |
| 12 option) any later version. | |
| 458 | 13 |
| 14 Octave is distributed in the hope that it will be useful, but WITHOUT | |
| 15 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
| 16 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
| 17 for more details. | |
| 18 | |
| 19 You should have received a copy of the GNU General Public License | |
| 7016 | 20 along with Octave; see the file COPYING. If not, see |
| 21 <http://www.gnu.org/licenses/>. | |
| 458 | 22 |
| 23 */ | |
| 24 | |
| 25 #ifdef HAVE_CONFIG_H | |
| 1192 | 26 #include <config.h> |
| 458 | 27 #endif |
| 28 | |
| 1367 | 29 #include <cfloat> |
| 30 | |
| 3503 | 31 #include <iostream> |
| 6209 | 32 #include <vector> |
| 1367 | 33 |
| 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; |
| 7788 | 654 double rcon; |
| 6207 | 655 MatrixType mattype (*this); |
| 7788 | 656 return inverse (mattype, info, rcon, 0, 0); |
| 6207 | 657 } |
| 658 | |
| 659 Matrix | |
| 6479 | 660 Matrix::inverse (octave_idx_type& info) const |
| 661 { | |
| 7788 | 662 double rcon; |
| 6479 | 663 MatrixType mattype (*this); |
| 7788 | 664 return inverse (mattype, info, rcon, 0, 0); |
| 6479 | 665 } |
| 666 | |
| 667 Matrix | |
| 7788 | 668 Matrix::inverse (octave_idx_type& info, double& rcon, int force, |
| 6479 | 669 int calc_cond) const |
| 670 { | |
| 671 MatrixType mattype (*this); | |
| 7788 | 672 return inverse (mattype, info, rcon, force, calc_cond); |
| 6479 | 673 } |
| 674 | |
| 675 Matrix | |
| 6207 | 676 Matrix::inverse (MatrixType& mattype) const |
| 677 { | |
| 678 octave_idx_type info; | |
| 7788 | 679 double rcon; |
| 680 return inverse (mattype, info, rcon, 0, 0); | |
| 6207 | 681 } |
| 682 | |
| 683 Matrix | |
| 684 Matrix::inverse (MatrixType &mattype, octave_idx_type& info) const | |
| 685 { | |
| 7788 | 686 double rcon; |
| 687 return inverse (mattype, info, rcon, 0, 0); | |
| 458 | 688 } |
| 689 | |
| 690 Matrix | |
| 7788 | 691 Matrix::tinverse (MatrixType &mattype, octave_idx_type& info, double& rcon, |
| 6207 | 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. |
| 7788 | 716 rcon = 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), |
| 7788 | 730 nr, tmp_data, nr, rcon, |
|
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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 |
| 7788 | 749 Matrix::finverse (MatrixType &mattype, octave_idx_type& info, double& rcon, |
| 6207 | 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. |
| 7788 | 789 rcon = 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, |
| 7788 | 802 rcon, 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 |
| 7788 | 830 Matrix::inverse (MatrixType &mattype, octave_idx_type& info, double& rcon, |
| 6207 | 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) | |
| 7788 | 840 ret = tinverse (mattype, info, rcon, 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) | |
| 7788 | 849 rcon = chol.rcond (); |
| 6486 | 850 else |
| 7788 | 851 rcon = 1.0; |
| 6486 | 852 ret = chol.inverse (); |
| 853 } | |
| 6207 | 854 else |
| 855 mattype.mark_as_unsymmetric (); | |
| 856 } | |
| 857 | |
| 858 if (!mattype.is_hermitian ()) | |
| 7788 | 859 ret = finverse(mattype, info, rcon, force, calc_cond); |
| 860 | |
| 861 if ((mattype.is_hermitian () || calc_cond) && rcon == 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; |
| 7788 | 1219 double rcon; |
| 1220 return determinant (info, rcon, 0); | |
| 458 | 1221 } |
| 1222 | |
| 1223 DET | |
| 5275 | 1224 Matrix::determinant (octave_idx_type& info) const |
| 458 | 1225 { |
| 7788 | 1226 double rcon; |
| 1227 return determinant (info, rcon, 0); | |
| 458 | 1228 } |
| 1229 | |
| 1230 DET | |
| 7788 | 1231 Matrix::determinant (octave_idx_type& info, double& rcon, 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. |
| 7788 | 1260 rcon = 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, |
| 7788 | 1279 rcon, 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 | |
| 7788 | 1324 double |
| 1325 Matrix::rcond (void) const | |
| 1326 { | |
| 1327 MatrixType mattype (*this); | |
| 1328 return rcond (mattype); | |
| 1329 } | |
| 1330 | |
| 1331 double | |
| 1332 Matrix::rcond (MatrixType &mattype) const | |
| 1333 { | |
| 1334 double rcon; | |
| 1335 octave_idx_type nr = rows (); | |
| 1336 octave_idx_type nc = cols (); | |
| 1337 | |
| 1338 if (nr != nc) | |
| 1339 (*current_liboctave_error_handler) ("matrix must be square"); | |
| 1340 else if (nr == 0 || nc == 0) | |
| 1341 rcon = octave_Inf; | |
| 1342 else | |
| 1343 { | |
| 1344 int typ = mattype.type (); | |
| 1345 | |
| 1346 if (typ == MatrixType::Unknown) | |
| 1347 typ = mattype.type (*this); | |
| 1348 | |
| 1349 // Only calculate the condition number for LU/Cholesky | |
| 1350 if (typ == MatrixType::Upper) | |
| 1351 { | |
| 1352 const double *tmp_data = fortran_vec (); | |
| 1353 octave_idx_type info = 0; | |
| 1354 char norm = '1'; | |
| 1355 char uplo = 'U'; | |
| 1356 char dia = 'N'; | |
| 1357 | |
| 1358 Array<double> z (3 * nc); | |
| 1359 double *pz = z.fortran_vec (); | |
| 1360 Array<octave_idx_type> iz (nc); | |
| 1361 octave_idx_type *piz = iz.fortran_vec (); | |
| 1362 | |
| 1363 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1364 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1365 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1366 nr, tmp_data, nr, rcon, | |
| 1367 pz, piz, info | |
| 1368 F77_CHAR_ARG_LEN (1) | |
| 1369 F77_CHAR_ARG_LEN (1) | |
| 1370 F77_CHAR_ARG_LEN (1))); | |
| 1371 | |
| 1372 if (info != 0) | |
| 1373 rcon = 0.0; | |
| 1374 } | |
| 1375 else if (typ == MatrixType::Permuted_Upper) | |
| 1376 (*current_liboctave_error_handler) | |
| 1377 ("permuted triangular matrix not implemented"); | |
| 1378 else if (typ == MatrixType::Lower) | |
| 1379 { | |
| 1380 const double *tmp_data = fortran_vec (); | |
| 1381 octave_idx_type info = 0; | |
| 1382 char norm = '1'; | |
| 1383 char uplo = 'L'; | |
| 1384 char dia = 'N'; | |
| 1385 | |
| 1386 Array<double> z (3 * nc); | |
| 1387 double *pz = z.fortran_vec (); | |
| 1388 Array<octave_idx_type> iz (nc); | |
| 1389 octave_idx_type *piz = iz.fortran_vec (); | |
| 1390 | |
| 1391 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1392 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1393 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1394 nr, tmp_data, nr, rcon, | |
| 1395 pz, piz, info | |
| 1396 F77_CHAR_ARG_LEN (1) | |
| 1397 F77_CHAR_ARG_LEN (1) | |
| 1398 F77_CHAR_ARG_LEN (1))); | |
| 1399 | |
| 1400 if (info != 0) | |
| 1401 rcon = 0.0; | |
| 1402 } | |
| 1403 else if (typ == MatrixType::Permuted_Lower) | |
| 1404 (*current_liboctave_error_handler) | |
| 1405 ("permuted triangular matrix not implemented"); | |
| 1406 else if (typ == MatrixType::Full || typ == MatrixType::Hermitian) | |
| 1407 { | |
| 1408 double anorm = -1.0; | |
| 1409 Matrix atmp = *this; | |
| 1410 double *tmp_data = atmp.fortran_vec (); | |
| 1411 | |
| 1412 if (typ == MatrixType::Hermitian) | |
| 1413 { | |
| 1414 octave_idx_type info = 0; | |
| 1415 char job = 'L'; | |
| 1416 anorm = atmp.abs().sum(). | |
| 1417 row(static_cast<octave_idx_type>(0)).max(); | |
| 1418 | |
| 1419 F77_XFCN (dpotrf, DPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, | |
| 1420 tmp_data, nr, info | |
| 1421 F77_CHAR_ARG_LEN (1))); | |
| 1422 | |
| 1423 if (info != 0) | |
| 1424 { | |
| 1425 rcon = 0.0; | |
| 1426 mattype.mark_as_unsymmetric (); | |
| 1427 typ = MatrixType::Full; | |
| 1428 } | |
| 1429 else | |
| 1430 { | |
| 1431 Array<double> z (3 * nc); | |
| 1432 double *pz = z.fortran_vec (); | |
| 1433 Array<octave_idx_type> iz (nc); | |
| 1434 octave_idx_type *piz = iz.fortran_vec (); | |
| 1435 | |
| 1436 F77_XFCN (dpocon, DPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), | |
| 1437 nr, tmp_data, nr, anorm, | |
| 1438 rcon, pz, piz, info | |
| 1439 F77_CHAR_ARG_LEN (1))); | |
| 1440 | |
| 1441 if (info != 0) | |
| 1442 rcon = 0.0; | |
| 1443 } | |
| 1444 } | |
| 1445 | |
| 1446 if (typ == MatrixType::Full) | |
| 1447 { | |
| 1448 octave_idx_type info = 0; | |
| 1449 | |
| 1450 Array<octave_idx_type> ipvt (nr); | |
| 1451 octave_idx_type *pipvt = ipvt.fortran_vec (); | |
| 1452 | |
| 1453 if(anorm < 0.) | |
| 1454 anorm = atmp.abs().sum(). | |
| 1455 row(static_cast<octave_idx_type>(0)).max(); | |
| 1456 | |
| 1457 Array<double> z (4 * nc); | |
| 1458 double *pz = z.fortran_vec (); | |
| 1459 Array<octave_idx_type> iz (nc); | |
| 1460 octave_idx_type *piz = iz.fortran_vec (); | |
| 1461 | |
| 1462 F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); | |
| 1463 | |
| 1464 if (info != 0) | |
| 1465 { | |
| 1466 rcon = 0.0; | |
| 1467 mattype.mark_as_rectangular (); | |
| 1468 } | |
| 1469 else | |
| 1470 { | |
| 1471 char job = '1'; | |
| 1472 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), | |
| 1473 nc, tmp_data, nr, anorm, | |
| 1474 rcon, pz, piz, info | |
| 1475 F77_CHAR_ARG_LEN (1))); | |
| 1476 | |
| 1477 if (info != 0) | |
| 1478 rcon = 0.0; | |
| 1479 } | |
| 1480 } | |
| 1481 } | |
| 1482 else | |
| 1483 rcon = 0.0; | |
| 1484 } | |
| 1485 | |
| 1486 return rcon; | |
| 1487 } | |
| 1488 | |
| 458 | 1489 Matrix |
| 5785 | 1490 Matrix::utsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, |
| 7788 | 1491 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 1492 bool calc_cond) const |
| 1493 { | |
| 1494 Matrix retval; | |
| 1495 | |
| 1496 octave_idx_type nr = rows (); | |
| 1497 octave_idx_type nc = cols (); | |
| 1498 | |
| 6924 | 1499 if (nr != b.rows ()) |
| 5785 | 1500 (*current_liboctave_error_handler) |
| 1501 ("matrix dimension mismatch solution of linear equations"); | |
| 6924 | 1502 else if (nr == 0 || nc == 0 || b.cols () == 0) |
| 1503 retval = Matrix (nc, b.cols (), 0.0); | |
| 5785 | 1504 else |
| 1505 { | |
| 1506 volatile int typ = mattype.type (); | |
| 1507 | |
| 1508 if (typ == MatrixType::Permuted_Upper || | |
| 1509 typ == MatrixType::Upper) | |
| 1510 { | |
| 1511 octave_idx_type b_nc = b.cols (); | |
| 7788 | 1512 rcon = 1.; |
| 5785 | 1513 info = 0; |
| 1514 | |
| 1515 if (typ == MatrixType::Permuted_Upper) | |
| 1516 { | |
| 1517 (*current_liboctave_error_handler) | |
| 6390 | 1518 ("permuted triangular matrix not implemented"); |
| 5785 | 1519 } |
| 1520 else | |
| 1521 { | |
| 1522 const double *tmp_data = fortran_vec (); | |
| 1523 | |
| 1524 if (calc_cond) | |
| 1525 { | |
| 1526 char norm = '1'; | |
| 1527 char uplo = 'U'; | |
| 1528 char dia = 'N'; | |
| 1529 | |
| 1530 Array<double> z (3 * nc); | |
| 1531 double *pz = z.fortran_vec (); | |
| 1532 Array<octave_idx_type> iz (nc); | |
| 1533 octave_idx_type *piz = iz.fortran_vec (); | |
| 1534 | |
| 1535 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1536 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1537 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 7788 | 1538 nr, tmp_data, nr, rcon, |
| 5785 | 1539 pz, piz, info |
| 1540 F77_CHAR_ARG_LEN (1) | |
| 1541 F77_CHAR_ARG_LEN (1) | |
| 1542 F77_CHAR_ARG_LEN (1))); | |
| 1543 | |
| 1544 if (info != 0) | |
| 1545 info = -2; | |
| 1546 | |
| 7788 | 1547 volatile double rcond_plus_one = rcon + 1.0; |
| 1548 | |
| 1549 if (rcond_plus_one == 1.0 || xisnan (rcon)) | |
| 5785 | 1550 { |
| 1551 info = -2; | |
| 1552 | |
| 1553 if (sing_handler) | |
| 7788 | 1554 sing_handler (rcon); |
| 5785 | 1555 else |
| 1556 (*current_liboctave_error_handler) | |
| 1557 ("matrix singular to machine precision, rcond = %g", | |
| 7788 | 1558 rcon); |
| 5785 | 1559 } |
| 1560 } | |
| 1561 | |
| 1562 if (info == 0) | |
| 1563 { | |
| 1564 retval = b; | |
| 1565 double *result = retval.fortran_vec (); | |
| 1566 | |
| 1567 char uplo = 'U'; | |
| 1568 char trans = 'N'; | |
| 1569 char dia = 'N'; | |
| 1570 | |
| 1571 F77_XFCN (dtrtrs, DTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1572 F77_CONST_CHAR_ARG2 (&trans, 1), | |
| 1573 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1574 nr, b_nc, tmp_data, nr, | |
| 1575 result, nr, info | |
| 1576 F77_CHAR_ARG_LEN (1) | |
| 1577 F77_CHAR_ARG_LEN (1) | |
| 1578 F77_CHAR_ARG_LEN (1))); | |
| 1579 } | |
| 1580 } | |
| 1581 } | |
| 1582 else | |
| 1583 (*current_liboctave_error_handler) ("incorrect matrix type"); | |
| 1584 } | |
| 1585 | |
| 1586 return retval; | |
| 1587 } | |
| 1588 | |
| 1589 Matrix | |
| 1590 Matrix::ltsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, | |
| 7788 | 1591 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 1592 bool calc_cond) const |
| 1593 { | |
| 1594 Matrix retval; | |
| 1595 | |
| 1596 octave_idx_type nr = rows (); | |
| 1597 octave_idx_type nc = cols (); | |
| 1598 | |
| 6924 | 1599 if (nr != b.rows ()) |
| 5785 | 1600 (*current_liboctave_error_handler) |
| 1601 ("matrix dimension mismatch solution of linear equations"); | |
| 6924 | 1602 else if (nr == 0 || nc == 0 || b.cols () == 0) |
| 1603 retval = Matrix (nc, b.cols (), 0.0); | |
| 5785 | 1604 else |
| 1605 { | |
| 1606 volatile int typ = mattype.type (); | |
| 1607 | |
| 1608 if (typ == MatrixType::Permuted_Lower || | |
| 1609 typ == MatrixType::Lower) | |
| 1610 { | |
| 1611 octave_idx_type b_nc = b.cols (); | |
| 7788 | 1612 rcon = 1.; |
| 5785 | 1613 info = 0; |
| 1614 | |
| 1615 if (typ == MatrixType::Permuted_Lower) | |
| 1616 { | |
| 1617 (*current_liboctave_error_handler) | |
| 6390 | 1618 ("permuted triangular matrix not implemented"); |
| 5785 | 1619 } |
| 1620 else | |
| 1621 { | |
| 1622 const double *tmp_data = fortran_vec (); | |
| 1623 | |
| 1624 if (calc_cond) | |
| 1625 { | |
| 1626 char norm = '1'; | |
| 1627 char uplo = 'L'; | |
| 1628 char dia = 'N'; | |
| 1629 | |
| 1630 Array<double> z (3 * nc); | |
| 1631 double *pz = z.fortran_vec (); | |
| 1632 Array<octave_idx_type> iz (nc); | |
| 1633 octave_idx_type *piz = iz.fortran_vec (); | |
| 1634 | |
| 1635 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1636 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1637 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 7788 | 1638 nr, tmp_data, nr, rcon, |
| 5785 | 1639 pz, piz, info |
| 1640 F77_CHAR_ARG_LEN (1) | |
| 1641 F77_CHAR_ARG_LEN (1) | |
| 1642 F77_CHAR_ARG_LEN (1))); | |
| 1643 | |
| 1644 if (info != 0) | |
| 1645 info = -2; | |
| 1646 | |
| 7788 | 1647 volatile double rcond_plus_one = rcon + 1.0; |
| 1648 | |
| 1649 if (rcond_plus_one == 1.0 || xisnan (rcon)) | |
| 5785 | 1650 { |
| 1651 info = -2; | |
| 1652 | |
| 1653 if (sing_handler) | |
| 7788 | 1654 sing_handler (rcon); |
| 5785 | 1655 else |
| 1656 (*current_liboctave_error_handler) | |
| 1657 ("matrix singular to machine precision, rcond = %g", | |
| 7788 | 1658 rcon); |
| 5785 | 1659 } |
| 1660 } | |
| 1661 | |
| 1662 if (info == 0) | |
| 1663 { | |
| 1664 retval = b; | |
| 1665 double *result = retval.fortran_vec (); | |
| 1666 | |
| 1667 char uplo = 'L'; | |
| 1668 char trans = 'N'; | |
| 1669 char dia = 'N'; | |
| 1670 | |
| 1671 F77_XFCN (dtrtrs, DTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1672 F77_CONST_CHAR_ARG2 (&trans, 1), | |
| 1673 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1674 nr, b_nc, tmp_data, nr, | |
| 1675 result, nr, info | |
| 1676 F77_CHAR_ARG_LEN (1) | |
| 1677 F77_CHAR_ARG_LEN (1) | |
| 1678 F77_CHAR_ARG_LEN (1))); | |
| 1679 } | |
| 1680 } | |
| 1681 } | |
| 1682 else | |
| 1683 (*current_liboctave_error_handler) ("incorrect matrix type"); | |
| 1684 } | |
| 1685 | |
| 1686 return retval; | |
| 1687 } | |
| 1688 | |
| 1689 Matrix | |
| 1690 Matrix::fsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, | |
| 7788 | 1691 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 1692 bool calc_cond) const |
| 1693 { | |
| 1694 Matrix retval; | |
| 1695 | |
| 1696 octave_idx_type nr = rows (); | |
| 1697 octave_idx_type nc = cols (); | |
| 1698 | |
| 6924 | 1699 if (nr != nc || nr != b.rows ()) |
| 5785 | 1700 (*current_liboctave_error_handler) |
| 1701 ("matrix dimension mismatch solution of linear equations"); | |
| 6924 | 1702 else if (nr == 0 || b.cols () == 0) |
| 1703 retval = Matrix (nc, b.cols (), 0.0); | |
| 5785 | 1704 else |
| 1705 { | |
| 1706 volatile int typ = mattype.type (); | |
| 1707 | |
| 1708 // Calculate the norm of the matrix, for later use. | |
| 1709 double anorm = -1.; | |
| 1710 | |
| 1711 if (typ == MatrixType::Hermitian) | |
| 1712 { | |
| 1713 info = 0; | |
| 1714 char job = 'L'; | |
| 1715 Matrix atmp = *this; | |
| 1716 double *tmp_data = atmp.fortran_vec (); | |
| 1717 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); | |
| 1718 | |
| 1719 F77_XFCN (dpotrf, DPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, | |
| 1720 tmp_data, nr, info | |
| 1721 F77_CHAR_ARG_LEN (1))); | |
| 1722 | |
|
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1723 // Throw-away extra info LAPACK gives so as to not change output. |
| 7788 | 1724 rcon = 0.0; |
|
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1725 if (info != 0) |
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1726 { |
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1727 info = -2; |
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1728 |
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1729 mattype.mark_as_unsymmetric (); |
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1730 typ = MatrixType::Full; |
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1731 } |
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1732 else |
| 5785 | 1733 { |
|
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1734 if (calc_cond) |
| 5785 | 1735 { |
|
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1736 Array<double> z (3 * nc); |
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1737 double *pz = z.fortran_vec (); |
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1738 Array<octave_idx_type> iz (nc); |
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1739 octave_idx_type *piz = iz.fortran_vec (); |
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1740 |
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1741 F77_XFCN (dpocon, DPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), |
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1742 nr, tmp_data, nr, anorm, |
| 7788 | 1743 rcon, pz, piz, info |
|
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1744 F77_CHAR_ARG_LEN (1))); |
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1745 |
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1746 if (info != 0) |
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1747 info = -2; |
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1748 |
| 7788 | 1749 volatile double rcond_plus_one = rcon + 1.0; |
| 1750 | |
| 1751 if (rcond_plus_one == 1.0 || xisnan (rcon)) | |
|
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1752 { |
|
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1753 info = -2; |
|
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1754 |
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1755 if (sing_handler) |
| 7788 | 1756 sing_handler (rcon); |
|
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diff
changeset
|
1757 else |
|
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|
1758 (*current_liboctave_error_handler) |
|
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diff
changeset
|
1759 ("matrix singular to machine precision, rcond = %g", |
| 7788 | 1760 rcon); |
|
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29980c6b8604
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diff
changeset
|
1761 } |
|
29980c6b8604
don't check f77_exception_encountered
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diff
changeset
|
1762 } |
|
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don't check f77_exception_encountered
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diff
changeset
|
1763 |
|
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diff
changeset
|
1764 if (info == 0) |
|
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|
1765 { |
|
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|
1766 retval = b; |
|
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don't check f77_exception_encountered
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|
1767 double *result = retval.fortran_vec (); |
|
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changeset
|
1768 |
|
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diff
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|
1769 octave_idx_type b_nc = b.cols (); |
|
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diff
changeset
|
1770 |
|
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diff
changeset
|
1771 F77_XFCN (dpotrs, DPOTRS, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
29980c6b8604
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diff
changeset
|
1772 nr, b_nc, tmp_data, nr, |
|
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|
1773 result, b.rows(), info |
|
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|
1774 F77_CHAR_ARG_LEN (1))); |
|
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|
1775 } |
|
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diff
changeset
|
1776 else |
|
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|
1777 { |
| 5785 | 1778 mattype.mark_as_unsymmetric (); |
| 1779 typ = MatrixType::Full; | |
|
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|
1780 } |
| 5785 | 1781 } |
| 1782 } | |
| 1783 | |
| 1784 if (typ == MatrixType::Full) | |
| 1785 { | |
| 1786 info = 0; | |
| 1787 | |
| 1788 Array<octave_idx_type> ipvt (nr); | |
| 1789 octave_idx_type *pipvt = ipvt.fortran_vec (); | |
| 1790 | |
| 1791 Matrix atmp = *this; | |
| 1792 double *tmp_data = atmp.fortran_vec (); | |
| 1793 if(anorm < 0.) | |
| 1794 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); | |
| 1795 | |
| 1796 Array<double> z (4 * nc); | |
| 1797 double *pz = z.fortran_vec (); | |
| 1798 Array<octave_idx_type> iz (nc); | |
| 1799 octave_idx_type *piz = iz.fortran_vec (); | |
| 1800 | |
| 1801 F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); | |
| 1802 | |
|
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|
1803 // Throw-away extra info LAPACK gives so as to not change output. |
| 7788 | 1804 rcon = 0.0; |
|
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|
1805 if (info != 0) |
| 5785 | 1806 { |
|
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|
1807 info = -2; |
|
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|
1808 |
|
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diff
changeset
|
1809 if (sing_handler) |
| 7788 | 1810 sing_handler (rcon); |
|
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|
1811 else |
|
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|
1812 (*current_liboctave_error_handler) |
|
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|
1813 ("matrix singular to machine precision"); |
|
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|
1814 |
|
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|
1815 mattype.mark_as_rectangular (); |
|
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|
1816 } |
|
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|
1817 else |
|
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|
1818 { |
|
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|
1819 if (calc_cond) |
| 5785 | 1820 { |
|
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|
1821 // Now calculate the condition number for |
|
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1822 // non-singular matrix. |
|
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|
1823 char job = '1'; |
|
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|
1824 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
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changeset
|
1825 nc, tmp_data, nr, anorm, |
| 7788 | 1826 rcon, pz, piz, info |
|
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|
1827 F77_CHAR_ARG_LEN (1))); |
|
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changeset
|
1828 |
|
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|
1829 if (info != 0) |
|
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|
1830 info = -2; |
|
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|
1831 |
| 7788 | 1832 volatile double rcond_plus_one = rcon + 1.0; |
| 1833 | |
| 1834 if (rcond_plus_one == 1.0 || xisnan (rcon)) | |
| 5785 | 1835 { |
|
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|
1836 info = -2; |
|
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changeset
|
1837 |
|
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changeset
|
1838 if (sing_handler) |
| 7788 | 1839 sing_handler (rcon); |
|
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|
1840 else |
|
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|
1841 (*current_liboctave_error_handler) |
|
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diff
changeset
|
1842 ("matrix singular to machine precision, rcond = %g", |
| 7788 | 1843 rcon); |
| 5785 | 1844 } |
| 1845 } | |
|
7482
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diff
changeset
|
1846 |
|
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changeset
|
1847 if (info == 0) |
|
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diff
changeset
|
1848 { |
|
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diff
changeset
|
1849 retval = b; |
|
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changeset
|
1850 double *result = retval.fortran_vec (); |
|
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changeset
|
1851 |
|
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diff
changeset
|
1852 octave_idx_type b_nc = b.cols (); |
|
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diff
changeset
|
1853 |
|
29980c6b8604
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diff
changeset
|
1854 char job = 'N'; |
|
29980c6b8604
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diff
changeset
|
1855 F77_XFCN (dgetrs, DGETRS, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
29980c6b8604
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diff
changeset
|
1856 nr, b_nc, tmp_data, nr, |
|
29980c6b8604
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diff
changeset
|
1857 pipvt, result, b.rows(), info |
|
29980c6b8604
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diff
changeset
|
1858 F77_CHAR_ARG_LEN (1))); |
|
29980c6b8604
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diff
changeset
|
1859 } |
|
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diff
changeset
|
1860 else |
|
29980c6b8604
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diff
changeset
|
1861 mattype.mark_as_rectangular (); |
| 5785 | 1862 } |
| 1863 } | |
| 1864 else if (typ != MatrixType::Hermitian) | |
| 1865 (*current_liboctave_error_handler) ("incorrect matrix type"); | |
| 1866 } | |
| 1867 | |
| 1868 return retval; | |
| 1869 } | |
| 1870 | |
| 1871 Matrix | |
| 1872 Matrix::solve (MatrixType &typ, const Matrix& b) const | |
| 1873 { | |
| 1874 octave_idx_type info; | |
| 7788 | 1875 double rcon; |
| 1876 return solve (typ, b, info, rcon, 0); | |
| 5785 | 1877 } |
| 1878 | |
| 1879 Matrix | |
| 1880 Matrix::solve (MatrixType &typ, const Matrix& b, octave_idx_type& info, | |
| 7788 | 1881 double& rcon) const |
| 5785 | 1882 { |
| 7788 | 1883 return solve (typ, b, info, rcon, 0); |
| 5785 | 1884 } |
| 1885 | |
| 1886 Matrix | |
| 1887 Matrix::solve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, | |
| 7788 | 1888 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 1889 bool singular_fallback) const |
| 1890 { | |
| 1891 Matrix retval; | |
| 1892 int typ = mattype.type (); | |
| 1893 | |
| 1894 if (typ == MatrixType::Unknown) | |
| 1895 typ = mattype.type (*this); | |
| 1896 | |
| 1897 // Only calculate the condition number for LU/Cholesky | |
| 1898 if (typ == MatrixType::Upper || typ == MatrixType::Permuted_Upper) | |
| 7788 | 1899 retval = utsolve (mattype, b, info, rcon, sing_handler, false); |
| 5785 | 1900 else if (typ == MatrixType::Lower || typ == MatrixType::Permuted_Lower) |
| 7788 | 1901 retval = ltsolve (mattype, b, info, rcon, sing_handler, false); |
| 5785 | 1902 else if (typ == MatrixType::Full || typ == MatrixType::Hermitian) |
| 7788 | 1903 retval = fsolve (mattype, b, info, rcon, sing_handler, true); |
| 5785 | 1904 else if (typ != MatrixType::Rectangular) |
| 1905 { | |
| 1906 (*current_liboctave_error_handler) ("unknown matrix type"); | |
| 1907 return Matrix (); | |
| 1908 } | |
| 1909 | |
| 1910 // Rectangular or one of the above solvers flags a singular matrix | |
| 1911 if (singular_fallback && mattype.type () == MatrixType::Rectangular) | |
| 1912 { | |
| 1913 octave_idx_type rank; | |
| 7788 | 1914 retval = lssolve (b, info, rank, rcon); |
| 5785 | 1915 } |
| 1916 | |
| 1917 return retval; | |
| 1918 } | |
| 1919 | |
| 1920 ComplexMatrix | |
| 1921 Matrix::solve (MatrixType &typ, const ComplexMatrix& b) const | |
| 1922 { | |
| 1923 ComplexMatrix tmp (*this); | |
| 1924 return tmp.solve (typ, b); | |
| 1925 } | |
| 1926 | |
| 1927 ComplexMatrix | |
| 1928 Matrix::solve (MatrixType &typ, const ComplexMatrix& b, | |
| 1929 octave_idx_type& info) const | |
| 1930 { | |
| 1931 ComplexMatrix tmp (*this); | |
| 1932 return tmp.solve (typ, b, info); | |
| 1933 } | |
| 1934 | |
| 1935 ComplexMatrix | |
| 1936 Matrix::solve (MatrixType &typ, const ComplexMatrix& b, octave_idx_type& info, | |
| 7788 | 1937 double& rcon) const |
| 5785 | 1938 { |
| 1939 ComplexMatrix tmp (*this); | |
| 7788 | 1940 return tmp.solve (typ, b, info, rcon); |
| 5785 | 1941 } |
| 1942 | |
| 1943 ComplexMatrix | |
| 1944 Matrix::solve (MatrixType &typ, const ComplexMatrix& b, octave_idx_type& info, | |
| 7788 | 1945 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 1946 bool singular_fallback) const |
| 1947 { | |
| 1948 ComplexMatrix tmp (*this); | |
| 7788 | 1949 return tmp.solve (typ, b, info, rcon, sing_handler, singular_fallback); |
| 5785 | 1950 } |
| 1951 | |
| 1952 ColumnVector | |
| 1953 Matrix::solve (MatrixType &typ, const ColumnVector& b) const | |
| 1954 { | |
| 7788 | 1955 octave_idx_type info; double rcon; |
| 1956 return solve (typ, b, info, rcon); | |
| 5785 | 1957 } |
| 1958 | |
| 1959 ColumnVector | |
| 1960 Matrix::solve (MatrixType &typ, const ColumnVector& b, | |
| 1961 octave_idx_type& info) const | |
| 1962 { | |
| 7788 | 1963 double rcon; |
| 1964 return solve (typ, b, info, rcon); | |
| 5785 | 1965 } |
| 1966 | |
| 1967 ColumnVector | |
| 1968 Matrix::solve (MatrixType &typ, const ColumnVector& b, octave_idx_type& info, | |
| 7788 | 1969 double& rcon) const |
| 5785 | 1970 { |
| 7788 | 1971 return solve (typ, b, info, rcon, 0); |
| 5785 | 1972 } |
| 1973 | |
| 1974 ColumnVector | |
| 1975 Matrix::solve (MatrixType &typ, const ColumnVector& b, octave_idx_type& info, | |
| 7788 | 1976 double& rcon, solve_singularity_handler sing_handler) const |
| 5785 | 1977 { |
| 1978 Matrix tmp (b); | |
| 7788 | 1979 return solve (typ, tmp, info, rcon, sing_handler).column(static_cast<octave_idx_type> (0)); |
| 5785 | 1980 } |
| 1981 | |
| 1982 ComplexColumnVector | |
| 1983 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b) const | |
| 1984 { | |
| 1985 ComplexMatrix tmp (*this); | |
| 1986 return tmp.solve (typ, b); | |
| 1987 } | |
| 1988 | |
| 1989 ComplexColumnVector | |
| 1990 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, | |
| 1991 octave_idx_type& info) const | |
| 1992 { | |
| 1993 ComplexMatrix tmp (*this); | |
| 1994 return tmp.solve (typ, b, info); | |
| 1995 } | |
| 1996 | |
| 1997 ComplexColumnVector | |
| 1998 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, | |
| 7788 | 1999 octave_idx_type& info, double& rcon) const |
| 5785 | 2000 { |
| 2001 ComplexMatrix tmp (*this); | |
| 7788 | 2002 return tmp.solve (typ, b, info, rcon); |
| 5785 | 2003 } |
| 2004 | |
| 2005 ComplexColumnVector | |
| 2006 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, | |
| 7788 | 2007 octave_idx_type& info, double& rcon, |
| 5785 | 2008 solve_singularity_handler sing_handler) const |
| 2009 { | |
| 2010 ComplexMatrix tmp (*this); | |
| 7788 | 2011 return tmp.solve(typ, b, info, rcon, sing_handler); |
| 5785 | 2012 } |
| 2013 | |
| 2014 Matrix | |
| 458 | 2015 Matrix::solve (const Matrix& b) const |
| 2016 { | |
| 5275 | 2017 octave_idx_type info; |
| 7788 | 2018 double rcon; |
| 2019 return solve (b, info, rcon, 0); | |
| 458 | 2020 } |
| 2021 | |
| 2022 Matrix | |
| 5275 | 2023 Matrix::solve (const Matrix& b, octave_idx_type& info) const |
| 458 | 2024 { |
| 7788 | 2025 double rcon; |
| 2026 return solve (b, info, rcon, 0); | |
| 458 | 2027 } |
| 2028 | |
| 2029 Matrix | |
| 7788 | 2030 Matrix::solve (const Matrix& b, octave_idx_type& info, double& rcon) const |
| 458 | 2031 { |
| 7788 | 2032 return solve (b, info, rcon, 0); |
| 3480 | 2033 } |
| 2034 | |
| 2035 Matrix | |
| 5785 | 2036 Matrix::solve (const Matrix& b, octave_idx_type& info, |
| 7788 | 2037 double& rcon, solve_singularity_handler sing_handler) const |
| 3480 | 2038 { |
| 5785 | 2039 MatrixType mattype (*this); |
| 7788 | 2040 return solve (mattype, b, info, rcon, sing_handler); |
| 458 | 2041 } |
| 2042 | |
| 2043 ComplexMatrix | |
| 2044 Matrix::solve (const ComplexMatrix& b) const | |
| 2045 { | |
| 2046 ComplexMatrix tmp (*this); | |
| 2047 return tmp.solve (b); | |
| 2048 } | |
| 2049 | |
| 2050 ComplexMatrix | |
| 5275 | 2051 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info) const |
| 458 | 2052 { |
| 2053 ComplexMatrix tmp (*this); | |
| 2054 return tmp.solve (b, info); | |
| 2055 } | |
| 2056 | |
| 2057 ComplexMatrix | |
| 7788 | 2058 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcon) const |
| 458 | 2059 { |
| 2060 ComplexMatrix tmp (*this); | |
| 7788 | 2061 return tmp.solve (b, info, rcon); |
| 458 | 2062 } |
| 2063 | |
| 3480 | 2064 ComplexMatrix |
| 7788 | 2065 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcon, |
| 3480 | 2066 solve_singularity_handler sing_handler) const |
| 2067 { | |
| 2068 ComplexMatrix tmp (*this); | |
| 7788 | 2069 return tmp.solve (b, info, rcon, sing_handler); |
| 3480 | 2070 } |
| 2071 | |
| 458 | 2072 ColumnVector |
| 2073 Matrix::solve (const ColumnVector& b) const | |
| 2074 { | |
| 7788 | 2075 octave_idx_type info; double rcon; |
| 2076 return solve (b, info, rcon); | |
| 458 | 2077 } |
| 2078 | |
| 2079 ColumnVector | |
| 5275 | 2080 Matrix::solve (const ColumnVector& b, octave_idx_type& info) const |
| 458 | 2081 { |
| 7788 | 2082 double rcon; |
| 2083 return solve (b, info, rcon); | |
| 458 | 2084 } |
| 2085 | |
| 2086 ColumnVector | |
| 7788 | 2087 Matrix::solve (const ColumnVector& b, octave_idx_type& info, double& rcon) const |
| 458 | 2088 { |
| 7788 | 2089 return solve (b, info, rcon, 0); |
| 3480 | 2090 } |
| 2091 | |
| 2092 ColumnVector | |
| 7788 | 2093 Matrix::solve (const ColumnVector& b, octave_idx_type& info, double& rcon, |
| 3480 | 2094 solve_singularity_handler sing_handler) const |
| 2095 { | |
| 5785 | 2096 MatrixType mattype (*this); |
| 7788 | 2097 return solve (mattype, b, info, rcon, sing_handler); |
| 458 | 2098 } |
| 2099 | |
| 2100 ComplexColumnVector | |
| 2101 Matrix::solve (const ComplexColumnVector& b) const | |
| 2102 { | |
| 2103 ComplexMatrix tmp (*this); | |
| 2104 return tmp.solve (b); | |
| 2105 } | |
| 2106 | |
| 2107 ComplexColumnVector | |
| 5275 | 2108 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info) const |
| 458 | 2109 { |
| 2110 ComplexMatrix tmp (*this); | |
| 2111 return tmp.solve (b, info); | |
| 2112 } | |
| 2113 | |
| 2114 ComplexColumnVector | |
| 7788 | 2115 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info, double& rcon) const |
| 458 | 2116 { |
| 2117 ComplexMatrix tmp (*this); | |
| 7788 | 2118 return tmp.solve (b, info, rcon); |
| 458 | 2119 } |
| 2120 | |
| 3480 | 2121 ComplexColumnVector |
| 7788 | 2122 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info, double& rcon, |
| 3480 | 2123 solve_singularity_handler sing_handler) const |
| 2124 { | |
| 2125 ComplexMatrix tmp (*this); | |
| 7788 | 2126 return tmp.solve (b, info, rcon, sing_handler); |
| 3480 | 2127 } |
| 2128 | |
| 458 | 2129 Matrix |
| 2130 Matrix::lssolve (const Matrix& b) const | |
| 2131 { | |
| 5275 | 2132 octave_idx_type info; |
| 2133 octave_idx_type rank; | |
| 7788 | 2134 double rcon; |
| 2135 return lssolve (b, info, rank, rcon); | |
| 458 | 2136 } |
| 2137 | |
| 2138 Matrix | |
| 5275 | 2139 Matrix::lssolve (const Matrix& b, octave_idx_type& info) const |
| 458 | 2140 { |
| 5275 | 2141 octave_idx_type rank; |
| 7788 | 2142 double rcon; |
| 2143 return lssolve (b, info, rank, rcon); | |
| 458 | 2144 } |
| 2145 | |
| 2146 Matrix | |
| 7072 | 2147 Matrix::lssolve (const Matrix& b, octave_idx_type& info, |
| 2148 octave_idx_type& rank) const | |
| 458 | 2149 { |
| 7788 | 2150 double rcon; |
| 2151 return lssolve (b, info, rank, rcon); | |
| 7076 | 2152 } |
| 2153 | |
| 2154 Matrix | |
| 2155 Matrix::lssolve (const Matrix& b, octave_idx_type& info, | |
| 7788 | 2156 octave_idx_type& rank, double &rcon) const |
| 7076 | 2157 { |
| 1948 | 2158 Matrix retval; |
| 2159 | |
| 5275 | 2160 octave_idx_type nrhs = b.cols (); |
| 2161 | |
| 2162 octave_idx_type m = rows (); | |
| 2163 octave_idx_type n = cols (); | |
| 458 | 2164 |
| 6924 | 2165 if (m != b.rows ()) |
| 1948 | 2166 (*current_liboctave_error_handler) |
| 6924 | 2167 ("matrix dimension mismatch solution of linear equations"); |
| 2168 else if (m == 0 || n == 0 || b.cols () == 0) | |
| 2169 retval = Matrix (n, b.cols (), 0.0); | |
| 1948 | 2170 else |
| 458 | 2171 { |
| 7072 | 2172 volatile octave_idx_type minmn = (m < n ? m : n); |
| 2173 octave_idx_type maxmn = m > n ? m : n; | |
| 7788 | 2174 rcon = -1.0; |
| 7072 | 2175 if (m != n) |
| 2176 { | |
| 2177 retval = Matrix (maxmn, nrhs, 0.0); | |
| 2178 | |
| 2179 for (octave_idx_type j = 0; j < nrhs; j++) | |
| 2180 for (octave_idx_type i = 0; i < m; i++) | |
| 2181 retval.elem (i, j) = b.elem (i, j); | |
| 2182 } | |
| 2183 else | |
| 2184 retval = b; | |
| 2185 | |
| 1948 | 2186 Matrix atmp = *this; |
| 2187 double *tmp_data = atmp.fortran_vec (); | |
| 2188 | |
| 7072 | 2189 double *pretval = retval.fortran_vec (); |
| 2190 Array<double> s (minmn); | |
| 7071 | 2191 double *ps = s.fortran_vec (); |
| 1948 | 2192 |
| 7072 | 2193 // Ask DGELSD what the dimension of WORK should be. |
| 5275 | 2194 octave_idx_type lwork = -1; |
| 3752 | 2195 |
| 2196 Array<double> work (1); | |
| 1948 | 2197 |
| 7477 | 2198 octave_idx_type smlsiz; |
| 2199 F77_FUNC (xilaenv, XILAENV) (9, F77_CONST_CHAR_ARG2 ("DGELSD", 6), | |
| 2200 F77_CONST_CHAR_ARG2 (" ", 1), | |
| 7478 | 2201 0, 0, 0, 0, smlsiz |
| 7477 | 2202 F77_CHAR_ARG_LEN (6) |
| 7478 | 2203 F77_CHAR_ARG_LEN (1)); |
| 7079 | 2204 |
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2205 octave_idx_type mnthr; |
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2206 F77_FUNC (xilaenv, XILAENV) (6, F77_CONST_CHAR_ARG2 ("DGELSD", 6), |
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2207 F77_CONST_CHAR_ARG2 (" ", 1), |
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2208 m, n, nrhs, -1, mnthr |
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2209 F77_CHAR_ARG_LEN (6) |
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2210 F77_CHAR_ARG_LEN (1)); |
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2211 |
| 7079 | 2212 // We compute the size of iwork because DGELSD in older versions |
| 2213 // of LAPACK does not return it on a query call. | |
| 7124 | 2214 double dminmn = static_cast<double> (minmn); |
| 2215 double dsmlsizp1 = static_cast<double> (smlsiz+1); | |
| 7079 | 2216 #if defined (HAVE_LOG2) |
| 7367 | 2217 double tmp = log2 (dminmn / dsmlsizp1); |
| 7079 | 2218 #else |
| 7367 | 2219 double tmp = log (dminmn / dsmlsizp1) / log (2.0); |
| 7079 | 2220 #endif |
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2221 octave_idx_type nlvl = static_cast<octave_idx_type> (tmp) + 1; |
| 7079 | 2222 if (nlvl < 0) |
| 2223 nlvl = 0; | |
| 2224 | |
| 2225 octave_idx_type liwork = 3 * minmn * nlvl + 11 * minmn; | |
| 2226 if (liwork < 1) | |
| 2227 liwork = 1; | |
| 7072 | 2228 Array<octave_idx_type> iwork (liwork); |
| 2229 octave_idx_type* piwork = iwork.fortran_vec (); | |
| 2230 | |
| 2231 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, | |
| 7788 | 2232 ps, rcon, rank, work.fortran_vec (), |
| 7072 | 2233 lwork, piwork, info)); |
| 1948 | 2234 |
| 7476 | 2235 // The workspace query is broken in at least LAPACK 3.0.0 |
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2236 // through 3.1.1 when n >= mnthr. The obtuse formula below |
| 7476 | 2237 // should provide sufficient workspace for DGELSD to operate |
| 2238 // efficiently. | |
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2239 if (n >= mnthr) |
| 7476 | 2240 { |
| 2241 const octave_idx_type wlalsd | |
| 2242 = 9*m + 2*m*smlsiz + 8*m*nlvl + m*nrhs + (smlsiz+1)*(smlsiz+1); | |
| 2243 | |
| 2244 octave_idx_type addend = m; | |
| 2245 | |
| 2246 if (2*m-4 > addend) | |
| 2247 addend = 2*m-4; | |
| 2248 | |
| 2249 if (nrhs > addend) | |
| 2250 addend = nrhs; | |
| 2251 | |
| 2252 if (n-3*m > addend) | |
| 2253 addend = n-3*m; | |
| 2254 | |
| 2255 if (wlalsd > addend) | |
| 2256 addend = wlalsd; | |
| 2257 | |
| 2258 const octave_idx_type lworkaround = 4*m + m*m + addend; | |
| 2259 | |
| 2260 if (work(0) < lworkaround) | |
| 2261 work(0) = lworkaround; | |
| 2262 } | |
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2263 else if (m >= n) |
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2264 { |
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2265 octave_idx_type lworkaround |
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2266 = 12*n + 2*n*smlsiz + 8*n*nlvl + n*nrhs + (smlsiz+1)*(smlsiz+1); |
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2267 |
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2268 if (work(0) < lworkaround) |
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2269 work(0) = lworkaround; |
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2270 } |
| 7476 | 2271 |
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2272 lwork = static_cast<octave_idx_type> (work(0)); |
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2273 work.resize (lwork); |
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2274 |
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2275 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, |
| 7788 | 2276 maxmn, ps, rcon, rank, |
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2277 work.fortran_vec (), lwork, |
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2278 piwork, info)); |
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2279 |
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2280 if (rank < minmn) |
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2281 (*current_liboctave_warning_handler) |
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2282 ("dgelsd: rank deficient %dx%d matrix, rank = %d", m, n, rank); |
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2283 if (s.elem (0) == 0.0) |
| 7788 | 2284 rcon = 0.0; |
| 1948 | 2285 else |
| 7788 | 2286 rcon = s.elem (minmn - 1) / s.elem (0); |
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2287 |
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2288 retval.resize (n, nrhs); |
| 458 | 2289 } |
| 2290 | |
| 2291 return retval; | |
| 2292 } | |
| 2293 | |
| 2294 ComplexMatrix | |
| 2295 Matrix::lssolve (const ComplexMatrix& b) const | |
| 2296 { | |
| 2297 ComplexMatrix tmp (*this); | |
| 5275 | 2298 octave_idx_type info; |
| 2299 octave_idx_type rank; | |
| 7788 | 2300 double rcon; |
| 2301 return tmp.lssolve (b, info, rank, rcon); | |
| 458 | 2302 } |
| 2303 | |
| 2304 ComplexMatrix | |
| 5275 | 2305 Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info) const |
| 458 | 2306 { |
| 2307 ComplexMatrix tmp (*this); | |
| 5275 | 2308 octave_idx_type rank; |
| 7788 | 2309 double rcon; |
| 2310 return tmp.lssolve (b, info, rank, rcon); | |
| 458 | 2311 } |
| 2312 | |
| 2313 ComplexMatrix | |
| 7076 | 2314 Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info, |
| 2315 octave_idx_type& rank) const | |
| 458 | 2316 { |
| 2317 ComplexMatrix tmp (*this); | |
| 7788 | 2318 double rcon; |
| 2319 return tmp.lssolve (b, info, rank, rcon); | |
| 7076 | 2320 } |
| 2321 | |
| 2322 ComplexMatrix | |
| 2323 Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info, | |
| 7788 | 2324 octave_idx_type& rank, double& rcon) const |
| 7076 | 2325 { |
| 2326 ComplexMatrix tmp (*this); | |
| 7788 | 2327 return tmp.lssolve (b, info, rank, rcon); |
| 458 | 2328 } |
| 2329 | |
| 2330 ColumnVector | |
| 2331 Matrix::lssolve (const ColumnVector& b) const | |
| 2332 { | |
| 5275 | 2333 octave_idx_type info; |
| 2334 octave_idx_type rank; | |
| 7788 | 2335 double rcon; |
| 2336 return lssolve (b, info, rank, rcon); | |
| 458 | 2337 } |
| 2338 | |
| 2339 ColumnVector | |
| 5275 | 2340 Matrix::lssolve (const ColumnVector& b, octave_idx_type& info) const |
| 458 | 2341 { |
| 5275 | 2342 octave_idx_type rank; |
| 7788 | 2343 double rcon; |
| 2344 return lssolve (b, info, rank, rcon); | |
| 458 | 2345 } |
| 2346 | |
| 2347 ColumnVector | |
| 7072 | 2348 Matrix::lssolve (const ColumnVector& b, octave_idx_type& info, |
| 2349 octave_idx_type& rank) const | |
| 458 | 2350 { |
| 7788 | 2351 double rcon; |
| 2352 return lssolve (b, info, rank, rcon); | |
| 7076 | 2353 } |
| 2354 | |
| 2355 ColumnVector | |
| 2356 Matrix::lssolve (const ColumnVector& b, octave_idx_type& info, | |
| 7788 | 2357 octave_idx_type& rank, double &rcon) const |
| 7076 | 2358 { |
| 1948 | 2359 ColumnVector retval; |
| 2360 | |
| 5275 | 2361 octave_idx_type nrhs = 1; |
| 2362 | |
| 2363 octave_idx_type m = rows (); | |
| 2364 octave_idx_type n = cols (); | |
| 458 | 2365 |
| 6924 | 2366 if (m != b.length ()) |
| 1948 | 2367 (*current_liboctave_error_handler) |
| 6924 | 2368 ("matrix dimension mismatch solution of linear equations"); |
| 2369 else if (m == 0 || n == 0) | |
| 2370 retval = ColumnVector (n, 0.0); | |
| 1948 | 2371 else |
| 458 | 2372 { |
| 7072 | 2373 volatile octave_idx_type minmn = (m < n ? m : n); |
| 2374 octave_idx_type maxmn = m > n ? m : n; | |
| 7788 | 2375 rcon = -1.0; |
| 7072 | 2376 |
| 2377 if (m != n) | |
| 2378 { | |
| 2379 retval = ColumnVector (maxmn, 0.0); | |
| 2380 | |
| 2381 for (octave_idx_type i = 0; i < m; i++) | |
| 2382 retval.elem (i) = b.elem (i); | |
| 2383 } | |
| 2384 else | |
| 2385 retval = b; | |
| 2386 | |
| 1948 | 2387 Matrix atmp = *this; |
| 2388 double *tmp_data = atmp.fortran_vec (); | |
| 2389 | |
| 7072 | 2390 double *pretval = retval.fortran_vec (); |
| 2391 Array<double> s (minmn); | |
| 7071 | 2392 double *ps = s.fortran_vec (); |
| 1948 | 2393 |
| 7072 | 2394 // Ask DGELSD what the dimension of WORK should be. |
| 5275 | 2395 octave_idx_type lwork = -1; |
| 3752 | 2396 |
| 2397 Array<double> work (1); | |
| 2398 | |
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2399 octave_idx_type smlsiz; |
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2400 F77_FUNC (xilaenv, XILAENV) (9, F77_CONST_CHAR_ARG2 ("DGELSD", 6), |
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2401 F77_CONST_CHAR_ARG2 (" ", 1), |
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2402 0, 0, 0, 0, smlsiz |
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2403 F77_CHAR_ARG_LEN (6) |
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2404 F77_CHAR_ARG_LEN (1)); |
| 7079 | 2405 |
| 2406 // We compute the size of iwork because DGELSD in older versions | |
| 2407 // of LAPACK does not return it on a query call. | |
| 7124 | 2408 double dminmn = static_cast<double> (minmn); |
| 2409 double dsmlsizp1 = static_cast<double> (smlsiz+1); | |
| 7079 | 2410 #if defined (HAVE_LOG2) |
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2411 double tmp = log2 (dminmn / dsmlsizp1); |
| 7079 | 2412 #else |
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2413 double tmp = log (dminmn / dsmlsizp1) / log (2.0); |
| 7079 | 2414 #endif |
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2415 octave_idx_type nlvl = static_cast<octave_idx_type> (tmp) + 1; |
| 7079 | 2416 if (nlvl < 0) |
| 2417 nlvl = 0; | |
| 2418 | |
| 2419 octave_idx_type liwork = 3 * minmn * nlvl + 11 * minmn; | |
| 2420 if (liwork < 1) | |
| 2421 liwork = 1; | |
| 7072 | 2422 Array<octave_idx_type> iwork (liwork); |
| 2423 octave_idx_type* piwork = iwork.fortran_vec (); | |
| 2424 | |
| 2425 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, | |
| 7788 | 2426 ps, rcon, rank, work.fortran_vec (), |
| 7072 | 2427 lwork, piwork, info)); |
| 1948 | 2428 |
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2429 lwork = static_cast<octave_idx_type> (work(0)); |
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|
2430 work.resize (lwork); |
|
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|
2431 |
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|
2432 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, |
| 7788 | 2433 maxmn, ps, rcon, rank, |
|
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2434 work.fortran_vec (), lwork, |
|
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|
2435 piwork, info)); |
|
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|
2436 |
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|
2437 if (rank < minmn) |
| 1948 | 2438 { |
|
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|
2439 if (rank < minmn) |
|
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|
2440 (*current_liboctave_warning_handler) |
|
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|
2441 ("dgelsd: rank deficient %dx%d matrix, rank = %d", m, n, rank); |
|
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|
2442 if (s.elem (0) == 0.0) |
| 7788 | 2443 rcon = 0.0; |
|
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|
2444 else |
| 7788 | 2445 rcon = s.elem (minmn - 1) / s.elem (0); |
| 1948 | 2446 } |
|
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|
2447 |
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|
2448 retval.resize (n, nrhs); |
| 458 | 2449 } |
| 2450 | |
| 2451 return retval; | |
| 2452 } | |
| 2453 | |
| 2454 ComplexColumnVector | |
| 2455 Matrix::lssolve (const ComplexColumnVector& b) const | |
| 2456 { | |
| 2457 ComplexMatrix tmp (*this); | |
| 7076 | 2458 octave_idx_type info; |
| 2459 octave_idx_type rank; | |
| 7788 | 2460 double rcon; |
| 2461 return tmp.lssolve (b, info, rank, rcon); | |
| 458 | 2462 } |
| 2463 | |
| 2464 ComplexColumnVector | |
| 5275 | 2465 Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info) const |
| 458 | 2466 { |
| 2467 ComplexMatrix tmp (*this); | |
| 7076 | 2468 octave_idx_type rank; |
| 7788 | 2469 double rcon; |
| 2470 return tmp.lssolve (b, info, rank, rcon); | |
| 458 | 2471 } |
| 2472 | |
| 2473 ComplexColumnVector | |
| 7076 | 2474 Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, |
| 2475 octave_idx_type& rank) const | |
| 458 | 2476 { |
| 2477 ComplexMatrix tmp (*this); | |
| 7788 | 2478 double rcon; |
| 2479 return tmp.lssolve (b, info, rank, rcon); | |
| 7076 | 2480 } |
| 2481 | |
| 2482 ComplexColumnVector | |
| 2483 Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, | |
| 7788 | 2484 octave_idx_type& rank, double &rcon) const |
| 7076 | 2485 { |
| 2486 ComplexMatrix tmp (*this); | |
| 7788 | 2487 return tmp.lssolve (b, info, rank, rcon); |
| 458 | 2488 } |
| 2489 | |
| 1819 | 2490 // Constants for matrix exponential calculation. |
| 2491 | |
| 2492 static double padec [] = | |
| 2493 { | |
| 2494 5.0000000000000000e-1, | |
| 2495 1.1666666666666667e-1, | |
| 2496 1.6666666666666667e-2, | |
| 2497 1.6025641025641026e-3, | |
| 2498 1.0683760683760684e-4, | |
| 2499 4.8562548562548563e-6, | |
| 2500 1.3875013875013875e-7, | |
| 2501 1.9270852604185938e-9, | |
| 2502 }; | |
| 2503 | |
| 7400 | 2504 static void |
| 7788 | 2505 solve_singularity_warning (double rcon) |
| 7400 | 2506 { |
| 2507 (*current_liboctave_warning_handler) | |
| 2508 ("singular matrix encountered in expm calculation, rcond = %g", | |
| 7788 | 2509 rcon); |
| 7400 | 2510 } |
| 2511 | |
| 1819 | 2512 Matrix |
| 2513 Matrix::expm (void) const | |
| 2514 { | |
| 2515 Matrix retval; | |
| 2516 | |
| 2517 Matrix m = *this; | |
| 2518 | |
| 6699 | 2519 if (numel () == 1) |
| 2520 return Matrix (1, 1, exp (m(0))); | |
| 2521 | |
| 5275 | 2522 octave_idx_type nc = columns (); |
| 1819 | 2523 |
| 3130 | 2524 // Preconditioning step 1: trace normalization to reduce dynamic |
| 2525 // range of poles, but avoid making stable eigenvalues unstable. | |
| 2526 | |
| 1819 | 2527 // trace shift value |
| 3331 | 2528 volatile double trshift = 0.0; |
| 1819 | 2529 |
| 5275 | 2530 for (octave_idx_type i = 0; i < nc; i++) |
| 1819 | 2531 trshift += m.elem (i, i); |
| 2532 | |
| 2533 trshift /= nc; | |
| 2534 | |
| 3130 | 2535 if (trshift > 0.0) |
| 2536 { | |
| 5275 | 2537 for (octave_idx_type i = 0; i < nc; i++) |
| 3130 | 2538 m.elem (i, i) -= trshift; |
| 2539 } | |
| 1819 | 2540 |
| 3331 | 2541 // Preconditioning step 2: balancing; code follows development |
| 2542 // in AEPBAL | |
| 2543 | |
| 2544 double *p_m = m.fortran_vec (); | |
| 2545 | |
| 5275 | 2546 octave_idx_type info, ilo, ihi, ilos, ihis; |
| 3468 | 2547 Array<double> dpermute (nc); |
| 2548 Array<double> dscale (nc); | |
| 3466 | 2549 |
| 3468 | 2550 // permutation first |
| 2551 char job = 'P'; | |
| 4552 | 2552 F77_XFCN (dgebal, DGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
| 2553 nc, p_m, nc, ilo, ihi, | |
| 2554 dpermute.fortran_vec (), info | |
| 2555 F77_CHAR_ARG_LEN (1))); | |
| 3466 | 2556 |
| 3468 | 2557 // then scaling |
| 2558 job = 'S'; | |
| 4552 | 2559 F77_XFCN (dgebal, DGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
| 2560 nc, p_m, nc, ilos, ihis, | |
| 2561 dscale.fortran_vec (), info | |
| 2562 F77_CHAR_ARG_LEN (1))); | |
| 3331 | 2563 |
| 1819 | 2564 // Preconditioning step 3: scaling. |
| 3331 | 2565 |
| 1819 | 2566 ColumnVector work(nc); |
| 3130 | 2567 double inf_norm; |
| 3331 | 2568 |
| 4552 | 2569 F77_XFCN (xdlange, XDLANGE, (F77_CONST_CHAR_ARG2 ("I", 1), |
| 2570 nc, nc, m.fortran_vec (), nc, | |
| 2571 work.fortran_vec (), inf_norm | |
| 2572 F77_CHAR_ARG_LEN (1))); | |
| 3331 | 2573 |
| 5275 | 2574 octave_idx_type sqpow = static_cast<octave_idx_type> (inf_norm > 0.0 |
| 1819 | 2575 ? (1.0 + log (inf_norm) / log (2.0)) |
| 2576 : 0.0); | |
| 3331 | 2577 |
| 1819 | 2578 // Check whether we need to square at all. |
| 3331 | 2579 |
| 1819 | 2580 if (sqpow < 0) |
| 2581 sqpow = 0; | |
| 3331 | 2582 |
| 1819 | 2583 if (sqpow > 0) |
| 2584 { | |
| 7400 | 2585 if (sqpow > 1023) |
| 2586 sqpow = 1023; | |
| 2587 | |
| 1819 | 2588 double scale_factor = 1.0; |
| 5275 | 2589 for (octave_idx_type i = 0; i < sqpow; i++) |
| 1819 | 2590 scale_factor *= 2.0; |
| 7400 | 2591 |
| 1819 | 2592 m = m / scale_factor; |
| 2593 } | |
| 3331 | 2594 |
| 1819 | 2595 // npp, dpp: pade' approx polynomial matrices. |
| 3331 | 2596 |
| 1819 | 2597 Matrix npp (nc, nc, 0.0); |
| 7265 | 2598 double *pnpp = npp.fortran_vec (); |
| 1819 | 2599 Matrix dpp = npp; |
| 7265 | 2600 double *pdpp = dpp.fortran_vec (); |
| 3331 | 2601 |
| 1819 | 2602 // Now powers a^8 ... a^1. |
| 3331 | 2603 |
| 5275 | 2604 octave_idx_type minus_one_j = -1; |
| 2605 for (octave_idx_type j = 7; j >= 0; j--) | |
| 1819 | 2606 { |
| 7265 | 2607 for (octave_idx_type i = 0; i < nc; i++) |
| 2608 { | |
| 2609 octave_idx_type k = i * nc + i; | |
| 2610 pnpp[k] += padec[j]; | |
| 2611 pdpp[k] += minus_one_j * padec[j]; | |
| 2612 } | |
| 2613 | |
| 2614 npp = m * npp; | |
| 2615 pnpp = npp.fortran_vec (); | |
| 2616 | |
| 2617 dpp = m * dpp; | |
| 2618 pdpp = dpp.fortran_vec (); | |
| 2619 | |
| 1819 | 2620 minus_one_j *= -1; |
| 2621 } | |
| 3331 | 2622 |
| 1819 | 2623 // Zero power. |
| 3331 | 2624 |
| 1819 | 2625 dpp = -dpp; |
| 5275 | 2626 for (octave_idx_type j = 0; j < nc; j++) |
| 1819 | 2627 { |
| 2628 npp.elem (j, j) += 1.0; | |
| 2629 dpp.elem (j, j) += 1.0; | |
| 2630 } | |
| 3331 | 2631 |
| 1819 | 2632 // Compute pade approximation = inverse (dpp) * npp. |
| 2633 | |
| 7788 | 2634 double rcon; |
| 2635 retval = dpp.solve (npp, info, rcon, solve_singularity_warning); | |
| 7400 | 2636 |
| 2637 if (info < 0) | |
| 2638 return retval; | |
| 2639 | |
| 1819 | 2640 // Reverse preconditioning step 3: repeated squaring. |
| 3331 | 2641 |
| 1819 | 2642 while (sqpow) |
| 2643 { | |
| 2644 retval = retval * retval; | |
| 2645 sqpow--; | |
| 2646 } | |
| 3331 | 2647 |
| 1819 | 2648 // Reverse preconditioning step 2: inverse balancing. |
| 3466 | 2649 // apply inverse scaling to computed exponential |
| 5275 | 2650 for (octave_idx_type i = 0; i < nc; i++) |
| 2651 for (octave_idx_type j = 0; j < nc; j++) | |
| 3468 | 2652 retval(i,j) *= dscale(i) / dscale(j); |
| 3466 | 2653 |
| 4153 | 2654 OCTAVE_QUIT; |
| 2655 | |
| 3466 | 2656 // construct balancing permutation vector |
| 5275 | 2657 Array<octave_idx_type> iperm (nc); |
| 2658 for (octave_idx_type i = 0; i < nc; i++) | |
| 4593 | 2659 iperm(i) = i; // identity permutation |
| 3466 | 2660 |
| 2661 // leading permutations in forward order | |
| 5275 | 2662 for (octave_idx_type i = 0; i < (ilo-1); i++) |
| 3468 | 2663 { |
| 5275 | 2664 octave_idx_type swapidx = static_cast<octave_idx_type> (dpermute(i)) - 1; |
| 2665 octave_idx_type tmp = iperm(i); | |
| 4593 | 2666 iperm(i) = iperm (swapidx); |
| 2667 iperm(swapidx) = tmp; | |
| 3468 | 2668 } |
| 3466 | 2669 |
| 7416 | 2670 // construct inverse balancing permutation vector |
| 2671 Array<octave_idx_type> invpvec (nc); | |
| 2672 for (octave_idx_type i = 0; i < nc; i++) | |
| 2673 invpvec(iperm(i)) = i; // Thanks to R. A. Lippert for this method | |
| 2674 | |
| 2675 OCTAVE_QUIT; | |
| 2676 | |
| 2677 Matrix tmpMat = retval; | |
| 2678 for (octave_idx_type i = 0; i < nc; i++) | |
| 2679 for (octave_idx_type j = 0; j < nc; j++) | |
| 2680 retval(i,j) = tmpMat(invpvec(i),invpvec(j)); | |
| 2681 | |
| 2682 OCTAVE_QUIT; | |
| 2683 | |
| 2684 for (octave_idx_type i = 0; i < nc; i++) | |
| 2685 iperm(i) = i; // identity permutation | |
| 2686 | |
| 3466 | 2687 // trailing permutations must be done in reverse order |
| 5275 | 2688 for (octave_idx_type i = nc - 1; i >= ihi; i--) |
| 3468 | 2689 { |
| 5275 | 2690 octave_idx_type swapidx = static_cast<octave_idx_type> (dpermute(i)) - 1; |
| 2691 octave_idx_type tmp = iperm(i); | |
| 4593 | 2692 iperm(i) = iperm(swapidx); |
| 2693 iperm(swapidx) = tmp; | |
| 3468 | 2694 } |
| 3466 | 2695 |
| 2696 // construct inverse balancing permutation vector | |
| 5275 | 2697 for (octave_idx_type i = 0; i < nc; i++) |
| 4593 | 2698 invpvec(iperm(i)) = i; // Thanks to R. A. Lippert for this method |
| 4153 | 2699 |
| 2700 OCTAVE_QUIT; | |
| 3466 | 2701 |
| 7416 | 2702 tmpMat = retval; |
| 5275 | 2703 for (octave_idx_type i = 0; i < nc; i++) |
| 2704 for (octave_idx_type j = 0; j < nc; j++) | |
| 3468 | 2705 retval(i,j) = tmpMat(invpvec(i),invpvec(j)); |
| 3466 | 2706 |
| 1819 | 2707 // Reverse preconditioning step 1: fix trace normalization. |
| 3331 | 2708 |
| 3130 | 2709 if (trshift > 0.0) |
| 2710 retval = exp (trshift) * retval; | |
| 2711 | |
| 2712 return retval; | |
| 1819 | 2713 } |
| 2714 | |
| 458 | 2715 Matrix& |
| 2716 Matrix::operator += (const DiagMatrix& a) | |
| 2717 { | |
| 5275 | 2718 octave_idx_type nr = rows (); |
| 2719 octave_idx_type nc = cols (); | |
| 2720 | |
| 2721 octave_idx_type a_nr = a.rows (); | |
| 2722 octave_idx_type a_nc = a.cols (); | |
| 2385 | 2723 |
| 2724 if (nr != a_nr || nc != a_nc) | |
| 458 | 2725 { |
| 2385 | 2726 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
| 458 | 2727 return *this; |
| 2728 } | |
| 2729 | |
| 5275 | 2730 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 2731 elem (i, i) += a.elem (i, i); |
| 2732 | |
| 2733 return *this; | |
| 2734 } | |
| 2735 | |
| 2736 Matrix& | |
| 2737 Matrix::operator -= (const DiagMatrix& a) | |
| 2738 { | |
| 5275 | 2739 octave_idx_type nr = rows (); |
| 2740 octave_idx_type nc = cols (); | |
| 2741 | |
| 2742 octave_idx_type a_nr = a.rows (); | |
| 2743 octave_idx_type a_nc = a.cols (); | |
| 2385 | 2744 |
| 2745 if (nr != a_nr || nc != a_nc) | |
| 458 | 2746 { |
| 2385 | 2747 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
| 458 | 2748 return *this; |
| 2749 } | |
| 2750 | |
| 5275 | 2751 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 2752 elem (i, i) -= a.elem (i, i); |
| 2753 | |
| 2754 return *this; | |
| 2755 } | |
| 2756 | |
| 2757 // unary operations | |
| 2758 | |
| 2964 | 2759 boolMatrix |
| 458 | 2760 Matrix::operator ! (void) const |
| 2761 { | |
| 5275 | 2762 octave_idx_type nr = rows (); |
| 2763 octave_idx_type nc = cols (); | |
| 458 | 2764 |
| 2964 | 2765 boolMatrix b (nr, nc); |
| 458 | 2766 |
| 5275 | 2767 for (octave_idx_type j = 0; j < nc; j++) |
| 2768 for (octave_idx_type i = 0; i < nr; i++) | |
| 458 | 2769 b.elem (i, j) = ! elem (i, j); |
| 2770 | |
| 2771 return b; | |
| 2772 } | |
| 2773 | |
| 1205 | 2774 // column vector by row vector -> matrix operations |
| 458 | 2775 |
| 1205 | 2776 Matrix |
| 2777 operator * (const ColumnVector& v, const RowVector& a) | |
| 458 | 2778 { |
| 1948 | 2779 Matrix retval; |
| 2780 | |
| 5275 | 2781 octave_idx_type len = v.length (); |
| 3233 | 2782 |
| 2783 if (len != 0) | |
| 1205 | 2784 { |
| 5275 | 2785 octave_idx_type a_len = a.length (); |
| 3233 | 2786 |
| 2787 retval.resize (len, a_len); | |
| 2788 double *c = retval.fortran_vec (); | |
| 2789 | |
| 4552 | 2790 F77_XFCN (dgemm, DGEMM, (F77_CONST_CHAR_ARG2 ("N", 1), |
| 2791 F77_CONST_CHAR_ARG2 ("N", 1), | |
| 2792 len, a_len, 1, 1.0, v.data (), len, | |
| 2793 a.data (), 1, 0.0, c, len | |
| 2794 F77_CHAR_ARG_LEN (1) | |
| 2795 F77_CHAR_ARG_LEN (1))); | |
| 1205 | 2796 } |
| 458 | 2797 |
| 1948 | 2798 return retval; |
| 458 | 2799 } |
| 2800 | |
| 2801 // other operations. | |
| 2802 | |
| 2803 Matrix | |
|
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2804 Matrix::map (dmapper fcn) const |
| 1205 | 2805 { |
|
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2806 return MArray2<double>::map<double> (func_ptr (fcn)); |
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2807 } |
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2808 |
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2809 ComplexMatrix |
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2810 Matrix::map (cmapper fcn) const |
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2811 { |
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2812 return MArray2<double>::map<Complex> (func_ptr (fcn)); |
| 1205 | 2813 } |
| 2814 | |
| 3248 | 2815 boolMatrix |
|
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2816 Matrix::map (bmapper fcn) const |
| 3248 | 2817 { |
|
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2818 return MArray2<double>::map<bool> (func_ptr (fcn)); |
| 458 | 2819 } |
| 2820 | |
| 2385 | 2821 bool |
| 4431 | 2822 Matrix::any_element_is_negative (bool neg_zero) const |
| 2385 | 2823 { |
| 5275 | 2824 octave_idx_type nel = nelem (); |
| 2385 | 2825 |
| 4431 | 2826 if (neg_zero) |
| 2827 { | |
| 5275 | 2828 for (octave_idx_type i = 0; i < nel; i++) |
| 4634 | 2829 if (lo_ieee_signbit (elem (i))) |
| 2830 return true; | |
| 4431 | 2831 } |
| 2832 else | |
| 2833 { | |
| 5275 | 2834 for (octave_idx_type i = 0; i < nel; i++) |
| 4634 | 2835 if (elem (i) < 0) |
| 2836 return true; | |
| 4431 | 2837 } |
| 2385 | 2838 |
| 2839 return false; | |
| 2840 } | |
| 2841 | |
| 2842 | |
| 2843 bool | |
| 2844 Matrix::any_element_is_inf_or_nan (void) const | |
| 2845 { | |
| 5275 | 2846 octave_idx_type nel = nelem (); |
| 2847 | |
| 2848 for (octave_idx_type i = 0; i < nel; i++) | |
| 4634 | 2849 { |
| 2850 double val = elem (i); | |
| 2851 if (xisinf (val) || xisnan (val)) | |
| 2852 return true; | |
| 2853 } | |
| 2854 | |
| 2855 return false; | |
| 2385 | 2856 } |
| 2857 | |
| 2858 bool | |
| 5943 | 2859 Matrix::any_element_not_one_or_zero (void) const |
| 2860 { | |
| 2861 octave_idx_type nel = nelem (); | |
| 2862 | |
| 2863 for (octave_idx_type i = 0; i < nel; i++) | |
| 2864 { | |
| 2865 double val = elem (i); | |
| 2866 if (val != 0 && val != 1) | |
| 2867 return true; | |
| 2868 } | |
| 2869 | |
| 2870 return false; | |
| 2871 } | |
| 2872 | |
| 2873 bool | |
| 2385 | 2874 Matrix::all_elements_are_int_or_inf_or_nan (void) const |
| 2875 { | |
| 5275 | 2876 octave_idx_type nel = nelem (); |
| 2877 | |
| 2878 for (octave_idx_type i = 0; i < nel; i++) | |
| 4634 | 2879 { |
| 2880 double val = elem (i); | |
| 2881 if (xisnan (val) || D_NINT (val) == val) | |
| 2882 continue; | |
| 2883 else | |
| 2884 return false; | |
| 2885 } | |
| 2385 | 2886 |
| 2887 return true; | |
| 2888 } | |
| 2889 | |
| 1968 | 2890 // Return nonzero if any element of M is not an integer. Also extract |
| 2891 // the largest and smallest values and return them in MAX_VAL and MIN_VAL. | |
| 2892 | |
| 2385 | 2893 bool |
| 1968 | 2894 Matrix::all_integers (double& max_val, double& min_val) const |
| 2895 { | |
| 5275 | 2896 octave_idx_type nel = nelem (); |
| 4634 | 2897 |
| 2898 if (nel > 0) | |
| 1968 | 2899 { |
| 4634 | 2900 max_val = elem (0); |
| 2901 min_val = elem (0); | |
| 1968 | 2902 } |
| 2903 else | |
| 2385 | 2904 return false; |
| 1968 | 2905 |
| 5275 | 2906 for (octave_idx_type i = 0; i < nel; i++) |
| 4634 | 2907 { |
| 2908 double val = elem (i); | |
| 2909 | |
| 2910 if (val > max_val) | |
| 2911 max_val = val; | |
| 2912 | |
| 2913 if (val < min_val) | |
| 2914 min_val = val; | |
| 2915 | |
| 2916 if (D_NINT (val) != val) | |
| 2917 return false; | |
| 2918 } | |
| 2385 | 2919 |
| 2920 return true; | |
| 1968 | 2921 } |
| 2922 | |
| 2385 | 2923 bool |
| 1968 | 2924 Matrix::too_large_for_float (void) const |
| 2925 { | |
| 5275 | 2926 octave_idx_type nel = nelem (); |
| 2927 | |
| 2928 for (octave_idx_type i = 0; i < nel; i++) | |
| 4634 | 2929 { |
| 2930 double val = elem (i); | |
| 2931 | |
| 5389 | 2932 if (! (xisnan (val) || xisinf (val)) |
| 5387 | 2933 && fabs (val) > FLT_MAX) |
| 4634 | 2934 return true; |
| 2935 } | |
| 1968 | 2936 |
| 2385 | 2937 return false; |
| 1968 | 2938 } |
| 2939 | |
| 5775 | 2940 // FIXME Do these really belong here? Maybe they should be |
| 4015 | 2941 // in a base class? |
| 458 | 2942 |
| 2832 | 2943 boolMatrix |
| 4015 | 2944 Matrix::all (int dim) const |
| 458 | 2945 { |
| 4015 | 2946 MX_ALL_OP (dim); |
| 458 | 2947 } |
| 2948 | |
| 2832 | 2949 boolMatrix |
| 4015 | 2950 Matrix::any (int dim) const |
| 458 | 2951 { |
| 4015 | 2952 MX_ANY_OP (dim); |
| 458 | 2953 } |
| 2954 | |
| 2955 Matrix | |
| 3723 | 2956 Matrix::cumprod (int dim) const |
| 458 | 2957 { |
| 4015 | 2958 MX_CUMULATIVE_OP (Matrix, double, *=); |
| 458 | 2959 } |
| 2960 | |
| 2961 Matrix | |
| 3723 | 2962 Matrix::cumsum (int dim) const |
| 458 | 2963 { |
| 4015 | 2964 MX_CUMULATIVE_OP (Matrix, double, +=); |
| 458 | 2965 } |
| 2966 | |
| 2967 Matrix | |
| 3723 | 2968 Matrix::prod (int dim) const |
| 458 | 2969 { |
| 3864 | 2970 MX_REDUCTION_OP (Matrix, *=, 1.0, 1.0); |
| 458 | 2971 } |
| 2972 | |
| 2973 Matrix | |
| 3723 | 2974 Matrix::sum (int dim) const |
| 458 | 2975 { |
| 3864 | 2976 MX_REDUCTION_OP (Matrix, +=, 0.0, 0.0); |
| 458 | 2977 } |
| 2978 | |
| 2979 Matrix | |
| 3723 | 2980 Matrix::sumsq (int dim) const |
| 458 | 2981 { |
| 3864 | 2982 #define ROW_EXPR \ |
| 2983 double d = elem (i, j); \ | |
| 2984 retval.elem (i, 0) += d * d | |
| 2985 | |
| 2986 #define COL_EXPR \ | |
| 2987 double d = elem (i, j); \ | |
| 2988 retval.elem (0, j) += d * d | |
| 2989 | |
| 2990 MX_BASE_REDUCTION_OP (Matrix, ROW_EXPR, COL_EXPR, 0.0, 0.0); | |
| 2991 | |
| 2992 #undef ROW_EXPR | |
| 2993 #undef COL_EXPR | |
| 458 | 2994 } |
| 2995 | |
| 2385 | 2996 Matrix |
| 2997 Matrix::abs (void) const | |
| 2998 { | |
| 5275 | 2999 octave_idx_type nr = rows (); |
| 3000 octave_idx_type nc = cols (); | |
| 2385 | 3001 |
| 3002 Matrix retval (nr, nc); | |
| 3003 | |
| 5275 | 3004 for (octave_idx_type j = 0; j < nc; j++) |
| 3005 for (octave_idx_type i = 0; i < nr; i++) | |
| 2385 | 3006 retval (i, j) = fabs (elem (i, j)); |
| 3007 | |
| 3008 return retval; | |
| 3009 } | |
| 3010 | |
|
7620
36594d5bbe13
Move diag function into the octave_value class
David Bateman <dbateman@free.fr>
parents:
7544
diff
changeset
|
3011 Matrix |
| 5275 | 3012 Matrix::diag (octave_idx_type k) const |
| 458 | 3013 { |
|
7620
36594d5bbe13
Move diag function into the octave_value class
David Bateman <dbateman@free.fr>
parents:
7544
diff
changeset
|
3014 return MArray2<double>::diag (k); |
| 458 | 3015 } |
| 3016 | |
| 3017 ColumnVector | |
| 3018 Matrix::row_min (void) const | |
| 3019 { | |
| 5275 | 3020 Array<octave_idx_type> dummy_idx; |
| 4587 | 3021 return row_min (dummy_idx); |
| 458 | 3022 } |
| 3023 | |
| 3024 ColumnVector | |
| 5275 | 3025 Matrix::row_min (Array<octave_idx_type>& idx_arg) const |
| 458 | 3026 { |
| 3027 ColumnVector result; | |
| 3028 | |
| 5275 | 3029 octave_idx_type nr = rows (); |
| 3030 octave_idx_type nc = cols (); | |
| 458 | 3031 |
| 3032 if (nr > 0 && nc > 0) | |
| 3033 { | |
| 3034 result.resize (nr); | |
| 4587 | 3035 idx_arg.resize (nr); |
| 458 | 3036 |
| 5275 | 3037 for (octave_idx_type i = 0; i < nr; i++) |
| 458 | 3038 { |
| 5275 | 3039 octave_idx_type idx_j; |
| 4469 | 3040 |
| 3041 double tmp_min = octave_NaN; | |
| 3042 | |
| 3043 for (idx_j = 0; idx_j < nc; idx_j++) | |
| 2354 | 3044 { |
| 4469 | 3045 tmp_min = elem (i, idx_j); |
| 3046 | |
| 5389 | 3047 if (! xisnan (tmp_min)) |
| 4469 | 3048 break; |
| 3049 } | |
| 3050 | |
| 5275 | 3051 for (octave_idx_type j = idx_j+1; j < nc; j++) |
| 4469 | 3052 { |
| 3053 double tmp = elem (i, j); | |
| 3054 | |
| 5389 | 3055 if (xisnan (tmp)) |
| 4469 | 3056 continue; |
| 3057 else if (tmp < tmp_min) | |
| 2354 | 3058 { |
| 4469 | 3059 idx_j = j; |
| 3060 tmp_min = tmp; | |
| 2354 | 3061 } |
| 3062 } | |
| 3063 | |
| 4469 | 3064 result.elem (i) = tmp_min; |
| 5389 | 3065 idx_arg.elem (i) = xisnan (tmp_min) ? 0 : idx_j; |
| 458 | 3066 } |
| 3067 } | |
| 3068 | |
| 3069 return result; | |
| 3070 } | |
| 3071 | |
| 3072 ColumnVector | |
| 3073 Matrix::row_max (void) const | |
| 3074 { | |
| 5275 | 3075 Array<octave_idx_type> dummy_idx; |
| 4587 | 3076 return row_max (dummy_idx); |
| 458 | 3077 } |
| 3078 | |
| 3079 ColumnVector | |
| 5275 | 3080 Matrix::row_max (Array<octave_idx_type>& idx_arg) const |
| 458 | 3081 { |
| 3082 ColumnVector result; | |
| 3083 | |
| 5275 | 3084 octave_idx_type nr = rows (); |
| 3085 octave_idx_type nc = cols (); | |
| 458 | 3086 |
| 3087 if (nr > 0 && nc > 0) | |
| 3088 { | |
| 3089 result.resize (nr); | |
| 4587 | 3090 idx_arg.resize (nr); |
| 458 | 3091 |
| 5275 | 3092 for (octave_idx_type i = 0; i < nr; i++) |
| 458 | 3093 { |
| 5275 | 3094 octave_idx_type idx_j; |
| 4469 | 3095 |
| 3096 double tmp_max = octave_NaN; | |
| 3097 | |
| 3098 for (idx_j = 0; idx_j < nc; idx_j++) | |
| 2354 | 3099 { |
| 4469 | 3100 tmp_max = elem (i, idx_j); |
| 3101 | |
| 5389 | 3102 if (! xisnan (tmp_max)) |
| 4469 | 3103 break; |
| 3104 } | |
| 3105 | |
| 5275 | 3106 for (octave_idx_type j = idx_j+1; j < nc; j++) |
| 4469 | 3107 { |
| 3108 double tmp = elem (i, j); | |
| 3109 | |
| 5389 | 3110 if (xisnan (tmp)) |
| 4469 | 3111 continue; |
| 3112 else if (tmp > tmp_max) | |
| 2354 | 3113 { |
| 4469 | 3114 idx_j = j; |
| 3115 tmp_max = tmp; | |
| 2354 | 3116 } |
| 3117 } | |
| 3118 | |
| 4469 | 3119 result.elem (i) = tmp_max; |
| 5389 | 3120 idx_arg.elem (i) = xisnan (tmp_max) ? 0 : idx_j; |
| 458 | 3121 } |
| 3122 } | |
| 3123 | |
| 3124 return result; | |
| 3125 } | |
| 3126 | |
| 3127 RowVector | |
| 3128 Matrix::column_min (void) const | |
| 3129 { | |
| 5275 | 3130 Array<octave_idx_type> dummy_idx; |
| 4587 | 3131 return column_min (dummy_idx); |
| 458 | 3132 } |
| 2354 | 3133 |
| 458 | 3134 RowVector |
| 5275 | 3135 Matrix::column_min (Array<octave_idx_type>& idx_arg) const |
| 458 | 3136 { |
| 3137 RowVector result; | |
| 3138 | |
| 5275 | 3139 octave_idx_type nr = rows (); |
| 3140 octave_idx_type nc = cols (); | |
| 458 | 3141 |
| 3142 if (nr > 0 && nc > 0) | |
| 3143 { | |
| 3144 result.resize (nc); | |
| 4587 | 3145 idx_arg.resize (nc); |
| 458 | 3146 |
| 5275 | 3147 for (octave_idx_type j = 0; j < nc; j++) |
| 458 | 3148 { |
| 5275 | 3149 octave_idx_type idx_i; |
| 4469 | 3150 |
| 3151 double tmp_min = octave_NaN; | |
| 3152 | |
| 3153 for (idx_i = 0; idx_i < nr; idx_i++) | |
| 2354 | 3154 { |
| 4469 | 3155 tmp_min = elem (idx_i, j); |
| 3156 | |
| 5389 | 3157 if (! xisnan (tmp_min)) |
| 4469 | 3158 break; |
| 3159 } | |
| 3160 | |
| 5275 | 3161 for (octave_idx_type i = idx_i+1; i < nr; i++) |
| 4469 | 3162 { |
| 3163 double tmp = elem (i, j); | |
| 3164 | |
| 5389 | 3165 if (xisnan (tmp)) |
| 4469 | 3166 continue; |
| 3167 else if (tmp < tmp_min) | |
| 2354 | 3168 { |
| 4469 | 3169 idx_i = i; |
| 3170 tmp_min = tmp; | |
| 2354 | 3171 } |
| 3172 } | |
| 3173 | |
| 4469 | 3174 result.elem (j) = tmp_min; |
| 5389 | 3175 idx_arg.elem (j) = xisnan (tmp_min) ? 0 : idx_i; |
| 458 | 3176 } |
| 3177 } | |
| 3178 | |
| 3179 return result; | |
| 3180 } | |
| 3181 | |
| 2354 | 3182 RowVector |
| 3183 Matrix::column_max (void) const | |
| 3184 { | |
| 5275 | 3185 Array<octave_idx_type> dummy_idx; |
| 4587 | 3186 return column_max (dummy_idx); |
| 2354 | 3187 } |
| 458 | 3188 |
| 3189 RowVector | |
| 5275 | 3190 Matrix::column_max (Array<octave_idx_type>& idx_arg) const |
| 458 | 3191 { |
| 3192 RowVector result; | |
| 3193 | |
| 5275 | 3194 octave_idx_type nr = rows (); |
| 3195 octave_idx_type nc = cols (); | |
| 458 | 3196 |
| 3197 if (nr > 0 && nc > 0) | |
| 3198 { | |
| 3199 result.resize (nc); | |
| 4587 | 3200 idx_arg.resize (nc); |
| 458 | 3201 |
| 5275 | 3202 for (octave_idx_type j = 0; j < nc; j++) |
| 458 | 3203 { |
| 5275 | 3204 octave_idx_type idx_i; |
| 4469 | 3205 |
| 3206 double tmp_max = octave_NaN; | |
| 3207 | |
| 3208 for (idx_i = 0; idx_i < nr; idx_i++) | |
| 2354 | 3209 { |
| 4469 | 3210 tmp_max = elem (idx_i, j); |
| 3211 | |
| 5389 | 3212 if (! xisnan (tmp_max)) |
| 4469 | 3213 break; |
| 3214 } | |
| 3215 | |
| 5275 | 3216 for (octave_idx_type i = idx_i+1; i < nr; i++) |
| 4469 | 3217 { |
| 3218 double tmp = elem (i, j); | |
| 3219 | |
| 5389 | 3220 if (xisnan (tmp)) |
| 4469 | 3221 continue; |
| 3222 else if (tmp > tmp_max) | |
| 2354 | 3223 { |
| 4469 | 3224 idx_i = i; |
| 3225 tmp_max = tmp; | |
| 2354 | 3226 } |
| 3227 } | |
| 3228 | |
| 4469 | 3229 result.elem (j) = tmp_max; |
| 5389 | 3230 idx_arg.elem (j) = xisnan (tmp_max) ? 0 : idx_i; |
| 458 | 3231 } |
| 3232 } | |
| 3233 | |
| 3234 return result; | |
| 3235 } | |
| 3236 | |
| 3504 | 3237 std::ostream& |
| 3238 operator << (std::ostream& os, const Matrix& a) | |
| 458 | 3239 { |
| 5275 | 3240 for (octave_idx_type i = 0; i < a.rows (); i++) |
| 458 | 3241 { |
| 5275 | 3242 for (octave_idx_type j = 0; j < a.cols (); j++) |
| 4130 | 3243 { |
| 3244 os << " "; | |
| 3245 octave_write_double (os, a.elem (i, j)); | |
| 3246 } | |
| 458 | 3247 os << "\n"; |
| 3248 } | |
| 3249 return os; | |
| 3250 } | |
| 3251 | |
| 3504 | 3252 std::istream& |
| 3253 operator >> (std::istream& is, Matrix& a) | |
| 458 | 3254 { |
| 5275 | 3255 octave_idx_type nr = a.rows (); |
| 3256 octave_idx_type nc = a.cols (); | |
| 458 | 3257 |
| 3258 if (nr < 1 || nc < 1) | |
| 3504 | 3259 is.clear (std::ios::badbit); |
| 458 | 3260 else |
| 3261 { | |
| 3262 double tmp; | |
| 5275 | 3263 for (octave_idx_type i = 0; i < nr; i++) |
| 3264 for (octave_idx_type j = 0; j < nc; j++) | |
| 458 | 3265 { |
| 4130 | 3266 tmp = octave_read_double (is); |
| 458 | 3267 if (is) |
| 3268 a.elem (i, j) = tmp; | |
| 3269 else | |
| 2795 | 3270 goto done; |
| 458 | 3271 } |
| 3272 } | |
| 3273 | |
| 2795 | 3274 done: |
| 3275 | |
| 458 | 3276 return is; |
| 3277 } | |
| 3278 | |
| 1819 | 3279 Matrix |
| 3280 Givens (double x, double y) | |
| 3281 { | |
| 3282 double cc, s, temp_r; | |
| 3283 | |
| 3887 | 3284 F77_FUNC (dlartg, DLARTG) (x, y, cc, s, temp_r); |
| 1819 | 3285 |
| 3286 Matrix g (2, 2); | |
| 3287 | |
| 3288 g.elem (0, 0) = cc; | |
| 3289 g.elem (1, 1) = cc; | |
| 3290 g.elem (0, 1) = s; | |
| 3291 g.elem (1, 0) = -s; | |
| 3292 | |
| 3293 return g; | |
| 3294 } | |
| 3295 | |
| 3296 Matrix | |
| 3297 Sylvester (const Matrix& a, const Matrix& b, const Matrix& c) | |
| 3298 { | |
| 3299 Matrix retval; | |
| 3300 | |
| 5775 | 3301 // FIXME -- need to check that a, b, and c are all the same |
| 1819 | 3302 // size. |
| 3303 | |
| 3304 // Compute Schur decompositions. | |
| 3305 | |
| 3306 SCHUR as (a, "U"); | |
| 3307 SCHUR bs (b, "U"); | |
| 3308 | |
| 3309 // Transform c to new coordinates. | |
| 3310 | |
| 3311 Matrix ua = as.unitary_matrix (); | |
| 3312 Matrix sch_a = as.schur_matrix (); | |
| 3313 | |
| 3314 Matrix ub = bs.unitary_matrix (); | |
| 3315 Matrix sch_b = bs.schur_matrix (); | |
| 3316 | |
| 3317 Matrix cx = ua.transpose () * c * ub; | |
| 3318 | |
| 3319 // Solve the sylvester equation, back-transform, and return the | |
| 3320 // solution. | |
| 3321 | |
| 5275 | 3322 octave_idx_type a_nr = a.rows (); |
| 3323 octave_idx_type b_nr = b.rows (); | |
| 1819 | 3324 |
| 3325 double scale; | |
| 5275 | 3326 octave_idx_type info; |
| 1819 | 3327 |
| 1950 | 3328 double *pa = sch_a.fortran_vec (); |
| 3329 double *pb = sch_b.fortran_vec (); | |
| 3330 double *px = cx.fortran_vec (); | |
| 3331 | |
| 4552 | 3332 F77_XFCN (dtrsyl, DTRSYL, (F77_CONST_CHAR_ARG2 ("N", 1), |
| 3333 F77_CONST_CHAR_ARG2 ("N", 1), | |
| 3334 1, a_nr, b_nr, pa, a_nr, pb, | |
| 3335 b_nr, px, a_nr, scale, info | |
| 3336 F77_CHAR_ARG_LEN (1) | |
| 3337 F77_CHAR_ARG_LEN (1))); | |
| 1950 | 3338 |
| 3339 | |
|
7482
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
3340 // FIXME -- check info? |
| 1819 | 3341 |
|
7482
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
3342 retval = -ua*cx*ub.transpose (); |
| 1819 | 3343 |
| 3344 return retval; | |
| 3345 } | |
| 3346 | |
| 2828 | 3347 // matrix by matrix -> matrix operations |
| 3348 | |
| 6162 | 3349 /* Simple Dot Product, Matrix-Vector and Matrix-Matrix Unit tests |
| 3350 %!assert([1 2 3] * [ 4 ; 5 ; 6], 32, 1e-14) | |
| 3351 %!assert([1 2 ; 3 4 ] * [5 ; 6], [17 ; 39 ], 1e-14) | |
| 3352 %!assert([1 2 ; 3 4 ] * [5 6 ; 7 8], [19 22; 43 50], 1e-14) | |
| 3353 */ | |
| 3354 | |
| 3355 /* Test some simple identities | |
| 3356 %!shared M, cv, rv | |
| 3357 %! M = randn(10,10); | |
| 3358 %! cv = randn(10,1); | |
| 3359 %! rv = randn(1,10); | |
| 3360 %!assert([M*cv,M*cv],M*[cv,cv],1e-14) | |
| 3361 %!assert([rv*M;rv*M],[rv;rv]*M,1e-14) | |
| 3362 %!assert(2*rv*cv,[rv,rv]*[cv;cv],1e-14) | |
| 3363 */ | |
| 3364 | |
| 3365 | |
| 2828 | 3366 Matrix |
| 3367 operator * (const Matrix& m, const Matrix& a) | |
| 3368 { | |
| 3369 Matrix retval; | |
| 3370 | |
| 5275 | 3371 octave_idx_type nr = m.rows (); |
| 3372 octave_idx_type nc = m.cols (); | |
| 3373 | |
| 3374 octave_idx_type a_nr = a.rows (); | |
| 3375 octave_idx_type a_nc = a.cols (); | |
| 2828 | 3376 |
| 3377 if (nc != a_nr) | |
| 3378 gripe_nonconformant ("operator *", nr, nc, a_nr, a_nc); | |
| 3379 else | |
| 3380 { | |
| 3381 if (nr == 0 || nc == 0 || a_nc == 0) | |
| 3382 retval.resize (nr, a_nc, 0.0); | |
| 3383 else | |
| 3384 { | |
| 5275 | 3385 octave_idx_type ld = nr; |
| 3386 octave_idx_type lda = a_nr; | |
| 2828 | 3387 |
| 3388 retval.resize (nr, a_nc); | |
| 3389 double *c = retval.fortran_vec (); | |
| 3390 | |
| 5983 | 3391 if (a_nc == 1) |
| 3392 { | |
| 3393 if (nr == 1) | |
| 3394 F77_FUNC (xddot, XDDOT) (nc, m.data (), 1, a.data (), 1, *c); | |
| 3395 else | |
| 6390 | 3396 { |
| 3397 F77_XFCN (dgemv, DGEMV, (F77_CONST_CHAR_ARG2 ("N", 1), | |
| 3398 nr, nc, 1.0, m.data (), ld, | |
| 3399 a.data (), 1, 0.0, c, 1 | |
| 3400 F77_CHAR_ARG_LEN (1))); | |
| 3401 } | |
| 5983 | 3402 } |
| 3403 else | |
| 6390 | 3404 { |
| 3405 F77_XFCN (dgemm, DGEMM, (F77_CONST_CHAR_ARG2 ("N", 1), | |
| 3406 F77_CONST_CHAR_ARG2 ("N", 1), | |
| 3407 nr, a_nc, nc, 1.0, m.data (), | |
| 3408 ld, a.data (), lda, 0.0, c, nr | |
| 3409 F77_CHAR_ARG_LEN (1) | |
| 3410 F77_CHAR_ARG_LEN (1))); | |
| 3411 } | |
| 2828 | 3412 } |
| 3413 } | |
| 3414 | |
| 3415 return retval; | |
| 3416 } | |
| 3417 | |
| 5775 | 3418 // FIXME -- it would be nice to share code among the min/max |
| 4309 | 3419 // functions below. |
| 3420 | |
| 3421 #define EMPTY_RETURN_CHECK(T) \ | |
| 3422 if (nr == 0 || nc == 0) \ | |
| 3423 return T (nr, nc); | |
| 3424 | |
| 3425 Matrix | |
| 3426 min (double d, const Matrix& m) | |
| 3427 { | |
| 5275 | 3428 octave_idx_type nr = m.rows (); |
| 3429 octave_idx_type nc = m.columns (); | |
| 4309 | 3430 |
| 3431 EMPTY_RETURN_CHECK (Matrix); | |
| 3432 | |
| 3433 Matrix result (nr, nc); | |
| 3434 | |
| 5275 | 3435 for (octave_idx_type j = 0; j < nc; j++) |
| 3436 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3437 { |
| 3438 OCTAVE_QUIT; | |
| 3439 result (i, j) = xmin (d, m (i, j)); | |
| 3440 } | |
| 3441 | |
| 3442 return result; | |
| 3443 } | |
| 3444 | |
| 3445 Matrix | |
| 3446 min (const Matrix& m, double d) | |
| 3447 { | |
| 5275 | 3448 octave_idx_type nr = m.rows (); |
| 3449 octave_idx_type nc = m.columns (); | |
| 4309 | 3450 |
| 3451 EMPTY_RETURN_CHECK (Matrix); | |
| 3452 | |
| 3453 Matrix result (nr, nc); | |
| 3454 | |
| 5275 | 3455 for (octave_idx_type j = 0; j < nc; j++) |
| 3456 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3457 { |
| 3458 OCTAVE_QUIT; | |
| 3459 result (i, j) = xmin (m (i, j), d); | |
| 3460 } | |
| 3461 | |
| 3462 return result; | |
| 3463 } | |
| 3464 | |
| 3465 Matrix | |
| 3466 min (const Matrix& a, const Matrix& b) | |
| 3467 { | |
| 5275 | 3468 octave_idx_type nr = a.rows (); |
| 3469 octave_idx_type nc = a.columns (); | |
| 4309 | 3470 |
| 3471 if (nr != b.rows () || nc != b.columns ()) | |
| 3472 { | |
| 3473 (*current_liboctave_error_handler) | |
| 3474 ("two-arg min expecting args of same size"); | |
| 3475 return Matrix (); | |
| 3476 } | |
| 3477 | |
| 3478 EMPTY_RETURN_CHECK (Matrix); | |
| 3479 | |
| 3480 Matrix result (nr, nc); | |
| 3481 | |
| 5275 | 3482 for (octave_idx_type j = 0; j < nc; j++) |
| 3483 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3484 { |
| 3485 OCTAVE_QUIT; | |
| 3486 result (i, j) = xmin (a (i, j), b (i, j)); | |
| 3487 } | |
| 3488 | |
| 3489 return result; | |
| 3490 } | |
| 3491 | |
| 3492 Matrix | |
| 3493 max (double d, const Matrix& m) | |
| 3494 { | |
| 5275 | 3495 octave_idx_type nr = m.rows (); |
| 3496 octave_idx_type nc = m.columns (); | |
| 4309 | 3497 |
| 3498 EMPTY_RETURN_CHECK (Matrix); | |
| 3499 | |
| 3500 Matrix result (nr, nc); | |
| 3501 | |
| 5275 | 3502 for (octave_idx_type j = 0; j < nc; j++) |
| 3503 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3504 { |
| 3505 OCTAVE_QUIT; | |
| 3506 result (i, j) = xmax (d, m (i, j)); | |
| 3507 } | |
| 3508 | |
| 3509 return result; | |
| 3510 } | |
| 3511 | |
| 3512 Matrix | |
| 3513 max (const Matrix& m, double d) | |
| 3514 { | |
| 5275 | 3515 octave_idx_type nr = m.rows (); |
| 3516 octave_idx_type nc = m.columns (); | |
| 4309 | 3517 |
| 3518 EMPTY_RETURN_CHECK (Matrix); | |
| 3519 | |
| 3520 Matrix result (nr, nc); | |
| 3521 | |
| 5275 | 3522 for (octave_idx_type j = 0; j < nc; j++) |
| 3523 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3524 { |
| 3525 OCTAVE_QUIT; | |
| 3526 result (i, j) = xmax (m (i, j), d); | |
| 3527 } | |
| 3528 | |
| 3529 return result; | |
| 3530 } | |
| 3531 | |
| 3532 Matrix | |
| 3533 max (const Matrix& a, const Matrix& b) | |
| 3534 { | |
| 5275 | 3535 octave_idx_type nr = a.rows (); |
| 3536 octave_idx_type nc = a.columns (); | |
| 4309 | 3537 |
| 3538 if (nr != b.rows () || nc != b.columns ()) | |
| 3539 { | |
| 3540 (*current_liboctave_error_handler) | |
| 3541 ("two-arg max expecting args of same size"); | |
| 3542 return Matrix (); | |
| 3543 } | |
| 3544 | |
| 3545 EMPTY_RETURN_CHECK (Matrix); | |
| 3546 | |
| 3547 Matrix result (nr, nc); | |
| 3548 | |
| 5275 | 3549 for (octave_idx_type j = 0; j < nc; j++) |
| 3550 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3551 { |
| 3552 OCTAVE_QUIT; | |
| 3553 result (i, j) = xmax (a (i, j), b (i, j)); | |
| 3554 } | |
| 3555 | |
| 3556 return result; | |
| 3557 } | |
| 3558 | |
| 2870 | 3559 MS_CMP_OPS(Matrix, , double, ) |
| 3504 | 3560 MS_BOOL_OPS(Matrix, double, 0.0) |
| 2870 | 3561 |
| 3562 SM_CMP_OPS(double, , Matrix, ) | |
| 3504 | 3563 SM_BOOL_OPS(double, Matrix, 0.0) |
| 2870 | 3564 |
| 3565 MM_CMP_OPS(Matrix, , Matrix, ) | |
| 3504 | 3566 MM_BOOL_OPS(Matrix, Matrix, 0.0) |
| 2870 | 3567 |
| 458 | 3568 /* |
| 3569 ;;; Local Variables: *** | |
| 3570 ;;; mode: C++ *** | |
| 3571 ;;; End: *** | |
| 3572 */ |