Mercurial > hg > octave-nkf
annotate liboctave/dMatrix.cc @ 11729:de826649dfa2 release-3-0-x
fix to enable compiling with Intel C++
| author | Jaroslav Hajek <highegg@gmail.com> |
|---|---|
| date | Thu, 03 Apr 2008 10:24:18 -0400 |
| parents | c6ce7274fb14 |
| children | 72830070a17b |
| rev | line source |
|---|---|
| 1993 | 1 // Matrix manipulations. |
| 458 | 2 /* |
| 3 | |
| 7017 | 4 Copyright (C) 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, |
| 5 2003, 2004, 2005, 2006, 2007 John W. Eaton | |
| 458 | 6 |
| 7 This file is part of Octave. | |
| 8 | |
| 9 Octave is free software; you can redistribute it and/or modify it | |
| 10 under the terms of the GNU General Public License as published by the | |
| 7016 | 11 Free Software Foundation; either version 3 of the License, or (at your |
| 12 option) any later version. | |
| 458 | 13 |
| 14 Octave is distributed in the hope that it will be useful, but WITHOUT | |
| 15 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
| 16 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
| 17 for more details. | |
| 18 | |
| 19 You should have received a copy of the GNU General Public License | |
| 7016 | 20 along with Octave; see the file COPYING. If not, see |
| 21 <http://www.gnu.org/licenses/>. | |
| 458 | 22 |
| 23 */ | |
| 24 | |
| 25 #ifdef HAVE_CONFIG_H | |
| 1192 | 26 #include <config.h> |
| 458 | 27 #endif |
| 28 | |
| 1367 | 29 #include <cfloat> |
| 30 | |
| 3503 | 31 #include <iostream> |
| 6209 | 32 #include <vector> |
| 1367 | 33 |
| 4669 | 34 #include "Array-util.h" |
| 2317 | 35 #include "byte-swap.h" |
| 2828 | 36 #include "dMatrix.h" |
| 1819 | 37 #include "dbleAEPBAL.h" |
| 458 | 38 #include "dbleDET.h" |
| 1819 | 39 #include "dbleSCHUR.h" |
| 740 | 40 #include "dbleSVD.h" |
| 6207 | 41 #include "dbleCHOL.h" |
| 1847 | 42 #include "f77-fcn.h" |
| 458 | 43 #include "lo-error.h" |
| 2354 | 44 #include "lo-ieee.h" |
| 45 #include "lo-mappers.h" | |
| 1968 | 46 #include "lo-utils.h" |
| 1367 | 47 #include "mx-base.h" |
| 2828 | 48 #include "mx-m-dm.h" |
| 3176 | 49 #include "mx-dm-m.h" |
| 1367 | 50 #include "mx-inlines.cc" |
| 1650 | 51 #include "oct-cmplx.h" |
| 4153 | 52 #include "quit.h" |
| 458 | 53 |
| 4773 | 54 #if defined (HAVE_FFTW3) |
| 3827 | 55 #include "oct-fftw.h" |
| 56 #endif | |
| 57 | |
| 458 | 58 // Fortran functions we call. |
| 59 | |
| 60 extern "C" | |
| 61 { | |
| 11646 | 62 F77_RET_T |
| 63 F77_FUNC (xilaenv, XILAENV) (const octave_idx_type&, F77_CONST_CHAR_ARG_DECL, | |
| 64 F77_CONST_CHAR_ARG_DECL, | |
| 65 const octave_idx_type&, const octave_idx_type&, | |
| 66 const octave_idx_type&, const octave_idx_type&, | |
| 67 octave_idx_type& | |
| 68 F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); | |
| 11640 | 69 |
| 4552 | 70 F77_RET_T |
| 71 F77_FUNC (dgebal, DGEBAL) (F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 72 const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type&, |
| 73 octave_idx_type&, double*, octave_idx_type& | |
| 4552 | 74 F77_CHAR_ARG_LEN_DECL); |
| 75 | |
| 76 F77_RET_T | |
| 77 F77_FUNC (dgebak, DGEBAK) (F77_CONST_CHAR_ARG_DECL, | |
| 78 F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 79 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, double*, |
| 80 const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type& | |
| 4552 | 81 F77_CHAR_ARG_LEN_DECL |
| 82 F77_CHAR_ARG_LEN_DECL); | |
| 83 | |
| 84 | |
| 85 F77_RET_T | |
| 86 F77_FUNC (dgemm, DGEMM) (F77_CONST_CHAR_ARG_DECL, | |
| 87 F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 88 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
| 89 const double&, const double*, const octave_idx_type&, | |
| 90 const double*, const octave_idx_type&, const double&, | |
| 91 double*, const octave_idx_type& | |
| 4552 | 92 F77_CHAR_ARG_LEN_DECL |
| 93 F77_CHAR_ARG_LEN_DECL); | |
| 94 | |
| 95 F77_RET_T | |
| 5983 | 96 F77_FUNC (dgemv, DGEMV) (F77_CONST_CHAR_ARG_DECL, |
| 97 const octave_idx_type&, const octave_idx_type&, const double&, | |
| 98 const double*, const octave_idx_type&, const double*, | |
| 99 const octave_idx_type&, const double&, double*, | |
| 100 const octave_idx_type& | |
| 101 F77_CHAR_ARG_LEN_DECL); | |
| 102 | |
| 103 F77_RET_T | |
| 104 F77_FUNC (xddot, XDDOT) (const octave_idx_type&, const double*, const octave_idx_type&, | |
| 105 const double*, const octave_idx_type&, double&); | |
| 106 | |
| 107 F77_RET_T | |
| 5275 | 108 F77_FUNC (dgetrf, DGETRF) (const octave_idx_type&, const octave_idx_type&, double*, const octave_idx_type&, |
| 109 octave_idx_type*, octave_idx_type&); | |
| 4329 | 110 |
| 4552 | 111 F77_RET_T |
| 5275 | 112 F77_FUNC (dgetrs, DGETRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, |
| 113 const double*, const octave_idx_type&, | |
| 114 const octave_idx_type*, double*, const octave_idx_type&, octave_idx_type& | |
| 4552 | 115 F77_CHAR_ARG_LEN_DECL); |
| 116 | |
| 117 F77_RET_T | |
| 5275 | 118 F77_FUNC (dgetri, DGETRI) (const octave_idx_type&, double*, const octave_idx_type&, const octave_idx_type*, |
| 119 double*, const octave_idx_type&, octave_idx_type&); | |
| 4552 | 120 |
| 121 F77_RET_T | |
| 5275 | 122 F77_FUNC (dgecon, DGECON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, double*, |
| 123 const octave_idx_type&, const double&, double&, | |
| 124 double*, octave_idx_type*, octave_idx_type& | |
| 4552 | 125 F77_CHAR_ARG_LEN_DECL); |
| 126 | |
| 127 F77_RET_T | |
| 7072 | 128 F77_FUNC (dgelsy, DGELSY) (const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
| 129 double*, const octave_idx_type&, double*, | |
| 130 const octave_idx_type&, octave_idx_type*, double&, octave_idx_type&, | |
| 131 double*, const octave_idx_type&, octave_idx_type&); | |
| 132 | |
| 133 F77_RET_T | |
| 134 F77_FUNC (dgelsd, DGELSD) (const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, | |
| 5275 | 135 double*, const octave_idx_type&, double*, |
| 7071 | 136 const octave_idx_type&, double*, double&, octave_idx_type&, |
| 7072 | 137 double*, const octave_idx_type&, octave_idx_type*, |
| 138 octave_idx_type&); | |
| 458 | 139 |
| 5785 | 140 F77_RET_T |
| 141 F77_FUNC (dpotrf, DPOTRF) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 142 double *, const octave_idx_type&, | |
| 143 octave_idx_type& F77_CHAR_ARG_LEN_DECL); | |
| 144 | |
| 145 F77_RET_T | |
| 146 F77_FUNC (dpocon, DPOCON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 147 double*, const octave_idx_type&, const double&, | |
| 148 double&, double*, octave_idx_type*, | |
| 149 octave_idx_type& F77_CHAR_ARG_LEN_DECL); | |
| 150 F77_RET_T | |
| 151 F77_FUNC (dpotrs, DPOTRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 152 const octave_idx_type&, const double*, | |
| 153 const octave_idx_type&, double*, | |
| 154 const octave_idx_type&, octave_idx_type& | |
| 155 F77_CHAR_ARG_LEN_DECL); | |
| 156 | |
| 157 F77_RET_T | |
| 6207 | 158 F77_FUNC (dtrtri, DTRTRI) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, |
| 159 const octave_idx_type&, const double*, | |
| 160 const octave_idx_type&, octave_idx_type& | |
| 161 F77_CHAR_ARG_LEN_DECL | |
| 162 F77_CHAR_ARG_LEN_DECL); | |
| 163 F77_RET_T | |
| 5785 | 164 F77_FUNC (dtrcon, DTRCON) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, |
| 165 F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 166 const double*, const octave_idx_type&, double&, | |
| 167 double*, octave_idx_type*, octave_idx_type& | |
| 168 F77_CHAR_ARG_LEN_DECL | |
| 169 F77_CHAR_ARG_LEN_DECL | |
| 170 F77_CHAR_ARG_LEN_DECL); | |
| 171 F77_RET_T | |
| 172 F77_FUNC (dtrtrs, DTRTRS) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, | |
| 173 F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 174 const octave_idx_type&, const double*, | |
| 175 const octave_idx_type&, double*, | |
| 176 const octave_idx_type&, octave_idx_type& | |
| 177 F77_CHAR_ARG_LEN_DECL | |
| 178 F77_CHAR_ARG_LEN_DECL | |
| 179 F77_CHAR_ARG_LEN_DECL); | |
| 180 | |
| 1360 | 181 // Note that the original complex fft routines were not written for |
| 182 // double complex arguments. They have been modified by adding an | |
| 183 // implicit double precision (a-h,o-z) statement at the beginning of | |
| 184 // each subroutine. | |
| 458 | 185 |
| 4552 | 186 F77_RET_T |
| 5275 | 187 F77_FUNC (cffti, CFFTI) (const octave_idx_type&, Complex*); |
| 4552 | 188 |
| 189 F77_RET_T | |
| 5275 | 190 F77_FUNC (cfftf, CFFTF) (const octave_idx_type&, Complex*, Complex*); |
| 4552 | 191 |
| 192 F77_RET_T | |
| 5275 | 193 F77_FUNC (cfftb, CFFTB) (const octave_idx_type&, Complex*, Complex*); |
| 4552 | 194 |
| 195 F77_RET_T | |
| 196 F77_FUNC (dlartg, DLARTG) (const double&, const double&, double&, | |
| 197 double&, double&); | |
| 198 | |
| 199 F77_RET_T | |
| 200 F77_FUNC (dtrsyl, DTRSYL) (F77_CONST_CHAR_ARG_DECL, | |
| 201 F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 202 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
| 203 const double*, const octave_idx_type&, const double*, | |
| 204 const octave_idx_type&, const double*, const octave_idx_type&, | |
| 205 double&, octave_idx_type& | |
| 4552 | 206 F77_CHAR_ARG_LEN_DECL |
| 207 F77_CHAR_ARG_LEN_DECL); | |
| 208 | |
| 209 F77_RET_T | |
| 5275 | 210 F77_FUNC (xdlange, XDLANGE) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, |
| 211 const octave_idx_type&, const double*, | |
| 212 const octave_idx_type&, double*, double& | |
| 4552 | 213 F77_CHAR_ARG_LEN_DECL); |
| 458 | 214 } |
| 215 | |
| 1360 | 216 // Matrix class. |
| 458 | 217 |
| 2349 | 218 Matrix::Matrix (const RowVector& rv) |
| 219 : MArray2<double> (1, rv.length (), 0.0) | |
| 220 { | |
| 5275 | 221 for (octave_idx_type i = 0; i < rv.length (); i++) |
| 2349 | 222 elem (0, i) = rv.elem (i); |
| 223 } | |
| 224 | |
| 225 Matrix::Matrix (const ColumnVector& cv) | |
| 226 : MArray2<double> (cv.length (), 1, 0.0) | |
| 227 { | |
| 5275 | 228 for (octave_idx_type i = 0; i < cv.length (); i++) |
| 2349 | 229 elem (i, 0) = cv.elem (i); |
| 230 } | |
| 231 | |
| 458 | 232 Matrix::Matrix (const DiagMatrix& a) |
| 1214 | 233 : MArray2<double> (a.rows (), a.cols (), 0.0) |
| 458 | 234 { |
| 5275 | 235 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 236 elem (i, i) = a.elem (i, i); |
| 237 } | |
| 238 | |
| 5775 | 239 // FIXME -- could we use a templated mixed-type copy function |
| 1574 | 240 // here? |
| 241 | |
| 2828 | 242 Matrix::Matrix (const boolMatrix& a) |
| 243 : MArray2<double> (a.rows (), a.cols ()) | |
| 244 { | |
| 5275 | 245 for (octave_idx_type i = 0; i < a.rows (); i++) |
| 246 for (octave_idx_type j = 0; j < a.cols (); j++) | |
| 2828 | 247 elem (i, j) = a.elem (i, j); |
| 248 } | |
| 249 | |
| 1574 | 250 Matrix::Matrix (const charMatrix& a) |
| 251 : MArray2<double> (a.rows (), a.cols ()) | |
| 252 { | |
| 5275 | 253 for (octave_idx_type i = 0; i < a.rows (); i++) |
| 254 for (octave_idx_type j = 0; j < a.cols (); j++) | |
| 1574 | 255 elem (i, j) = a.elem (i, j); |
| 256 } | |
| 257 | |
| 2385 | 258 bool |
| 458 | 259 Matrix::operator == (const Matrix& a) const |
| 260 { | |
| 261 if (rows () != a.rows () || cols () != a.cols ()) | |
| 2385 | 262 return false; |
| 458 | 263 |
| 3769 | 264 return mx_inline_equal (data (), a.data (), length ()); |
| 458 | 265 } |
| 266 | |
| 2385 | 267 bool |
| 458 | 268 Matrix::operator != (const Matrix& a) const |
| 269 { | |
| 270 return !(*this == a); | |
| 271 } | |
| 272 | |
| 3354 | 273 bool |
| 274 Matrix::is_symmetric (void) const | |
| 275 { | |
| 276 if (is_square () && rows () > 0) | |
| 277 { | |
| 5275 | 278 for (octave_idx_type i = 0; i < rows (); i++) |
| 279 for (octave_idx_type j = i+1; j < cols (); j++) | |
| 3354 | 280 if (elem (i, j) != elem (j, i)) |
| 281 return false; | |
| 282 | |
| 283 return true; | |
| 284 } | |
| 285 | |
| 286 return false; | |
| 287 } | |
| 288 | |
| 458 | 289 Matrix& |
| 5275 | 290 Matrix::insert (const Matrix& a, octave_idx_type r, octave_idx_type c) |
| 458 | 291 { |
| 1561 | 292 Array2<double>::insert (a, r, c); |
| 458 | 293 return *this; |
| 294 } | |
| 295 | |
| 296 Matrix& | |
| 5275 | 297 Matrix::insert (const RowVector& a, octave_idx_type r, octave_idx_type c) |
| 458 | 298 { |
| 5275 | 299 octave_idx_type a_len = a.length (); |
| 4316 | 300 |
| 1698 | 301 if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ()) |
| 458 | 302 { |
| 303 (*current_liboctave_error_handler) ("range error for insert"); | |
| 304 return *this; | |
| 305 } | |
| 306 | |
| 4316 | 307 if (a_len > 0) |
| 308 { | |
| 309 make_unique (); | |
| 310 | |
| 5275 | 311 for (octave_idx_type i = 0; i < a_len; i++) |
| 4316 | 312 xelem (r, c+i) = a.elem (i); |
| 313 } | |
| 458 | 314 |
| 315 return *this; | |
| 316 } | |
| 317 | |
| 318 Matrix& | |
| 5275 | 319 Matrix::insert (const ColumnVector& a, octave_idx_type r, octave_idx_type c) |
| 458 | 320 { |
| 5275 | 321 octave_idx_type a_len = a.length (); |
| 4316 | 322 |
| 1698 | 323 if (r < 0 || r + a_len > rows () || c < 0 || c >= cols ()) |
| 458 | 324 { |
| 325 (*current_liboctave_error_handler) ("range error for insert"); | |
| 326 return *this; | |
| 327 } | |
| 328 | |
| 4316 | 329 if (a_len > 0) |
| 330 { | |
| 331 make_unique (); | |
| 332 | |
| 5275 | 333 for (octave_idx_type i = 0; i < a_len; i++) |
| 4316 | 334 xelem (r+i, c) = a.elem (i); |
| 335 } | |
| 458 | 336 |
| 337 return *this; | |
| 338 } | |
| 339 | |
| 340 Matrix& | |
| 5275 | 341 Matrix::insert (const DiagMatrix& a, octave_idx_type r, octave_idx_type c) |
| 458 | 342 { |
| 5275 | 343 octave_idx_type a_nr = a.rows (); |
| 344 octave_idx_type a_nc = a.cols (); | |
| 1697 | 345 |
| 1698 | 346 if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) |
| 458 | 347 { |
| 348 (*current_liboctave_error_handler) ("range error for insert"); | |
| 349 return *this; | |
| 350 } | |
| 351 | |
| 1697 | 352 fill (0.0, r, c, r + a_nr - 1, c + a_nc - 1); |
| 353 | |
| 5275 | 354 octave_idx_type a_len = a.length (); |
| 4316 | 355 |
| 356 if (a_len > 0) | |
| 357 { | |
| 358 make_unique (); | |
| 359 | |
| 5275 | 360 for (octave_idx_type i = 0; i < a_len; i++) |
| 4316 | 361 xelem (r+i, c+i) = a.elem (i, i); |
| 362 } | |
| 458 | 363 |
| 364 return *this; | |
| 365 } | |
| 366 | |
| 367 Matrix& | |
| 368 Matrix::fill (double val) | |
| 369 { | |
| 5275 | 370 octave_idx_type nr = rows (); |
| 371 octave_idx_type nc = cols (); | |
| 4316 | 372 |
| 458 | 373 if (nr > 0 && nc > 0) |
| 4316 | 374 { |
| 375 make_unique (); | |
| 376 | |
| 5275 | 377 for (octave_idx_type j = 0; j < nc; j++) |
| 378 for (octave_idx_type i = 0; i < nr; i++) | |
| 4316 | 379 xelem (i, j) = val; |
| 380 } | |
| 458 | 381 |
| 382 return *this; | |
| 383 } | |
| 384 | |
| 385 Matrix& | |
| 5275 | 386 Matrix::fill (double val, octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) |
| 458 | 387 { |
| 5275 | 388 octave_idx_type nr = rows (); |
| 389 octave_idx_type nc = cols (); | |
| 4316 | 390 |
| 458 | 391 if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0 |
| 392 || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc) | |
| 393 { | |
| 394 (*current_liboctave_error_handler) ("range error for fill"); | |
| 395 return *this; | |
| 396 } | |
| 397 | |
| 5275 | 398 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } |
| 399 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } | |
| 458 | 400 |
| 4316 | 401 if (r2 >= r1 && c2 >= c1) |
| 402 { | |
| 403 make_unique (); | |
| 404 | |
| 5275 | 405 for (octave_idx_type j = c1; j <= c2; j++) |
| 406 for (octave_idx_type i = r1; i <= r2; i++) | |
| 4316 | 407 xelem (i, j) = val; |
| 408 } | |
| 458 | 409 |
| 410 return *this; | |
| 411 } | |
| 412 | |
| 413 Matrix | |
| 414 Matrix::append (const Matrix& a) const | |
| 415 { | |
| 5275 | 416 octave_idx_type nr = rows (); |
| 417 octave_idx_type nc = cols (); | |
| 458 | 418 if (nr != a.rows ()) |
| 419 { | |
| 420 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 421 return Matrix (); | |
| 422 } | |
| 423 | |
| 5275 | 424 octave_idx_type nc_insert = nc; |
| 458 | 425 Matrix retval (nr, nc + a.cols ()); |
| 426 retval.insert (*this, 0, 0); | |
| 427 retval.insert (a, 0, nc_insert); | |
| 428 return retval; | |
| 429 } | |
| 430 | |
| 431 Matrix | |
| 432 Matrix::append (const RowVector& a) const | |
| 433 { | |
| 5275 | 434 octave_idx_type nr = rows (); |
| 435 octave_idx_type nc = cols (); | |
| 458 | 436 if (nr != 1) |
| 437 { | |
| 438 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 439 return Matrix (); | |
| 440 } | |
| 441 | |
| 5275 | 442 octave_idx_type nc_insert = nc; |
| 458 | 443 Matrix retval (nr, nc + a.length ()); |
| 444 retval.insert (*this, 0, 0); | |
| 445 retval.insert (a, 0, nc_insert); | |
| 446 return retval; | |
| 447 } | |
| 448 | |
| 449 Matrix | |
| 450 Matrix::append (const ColumnVector& a) const | |
| 451 { | |
| 5275 | 452 octave_idx_type nr = rows (); |
| 453 octave_idx_type nc = cols (); | |
| 458 | 454 if (nr != a.length ()) |
| 455 { | |
| 456 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 457 return Matrix (); | |
| 458 } | |
| 459 | |
| 5275 | 460 octave_idx_type nc_insert = nc; |
| 458 | 461 Matrix retval (nr, nc + 1); |
| 462 retval.insert (*this, 0, 0); | |
| 463 retval.insert (a, 0, nc_insert); | |
| 464 return retval; | |
| 465 } | |
| 466 | |
| 467 Matrix | |
| 468 Matrix::append (const DiagMatrix& a) const | |
| 469 { | |
| 5275 | 470 octave_idx_type nr = rows (); |
| 471 octave_idx_type nc = cols (); | |
| 458 | 472 if (nr != a.rows ()) |
| 473 { | |
| 474 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 475 return *this; | |
| 476 } | |
| 477 | |
| 5275 | 478 octave_idx_type nc_insert = nc; |
| 458 | 479 Matrix retval (nr, nc + a.cols ()); |
| 480 retval.insert (*this, 0, 0); | |
| 481 retval.insert (a, 0, nc_insert); | |
| 482 return retval; | |
| 483 } | |
| 484 | |
| 485 Matrix | |
| 486 Matrix::stack (const Matrix& a) const | |
| 487 { | |
| 5275 | 488 octave_idx_type nr = rows (); |
| 489 octave_idx_type nc = cols (); | |
| 458 | 490 if (nc != a.cols ()) |
| 491 { | |
| 492 (*current_liboctave_error_handler) | |
| 493 ("column dimension mismatch for stack"); | |
| 494 return Matrix (); | |
| 495 } | |
| 496 | |
| 5275 | 497 octave_idx_type nr_insert = nr; |
| 458 | 498 Matrix retval (nr + a.rows (), nc); |
| 499 retval.insert (*this, 0, 0); | |
| 500 retval.insert (a, nr_insert, 0); | |
| 501 return retval; | |
| 502 } | |
| 503 | |
| 504 Matrix | |
| 505 Matrix::stack (const RowVector& a) const | |
| 506 { | |
| 5275 | 507 octave_idx_type nr = rows (); |
| 508 octave_idx_type nc = cols (); | |
| 458 | 509 if (nc != a.length ()) |
| 510 { | |
| 511 (*current_liboctave_error_handler) | |
| 512 ("column dimension mismatch for stack"); | |
| 513 return Matrix (); | |
| 514 } | |
| 515 | |
| 5275 | 516 octave_idx_type nr_insert = nr; |
| 458 | 517 Matrix retval (nr + 1, nc); |
| 518 retval.insert (*this, 0, 0); | |
| 519 retval.insert (a, nr_insert, 0); | |
| 520 return retval; | |
| 521 } | |
| 522 | |
| 523 Matrix | |
| 524 Matrix::stack (const ColumnVector& a) const | |
| 525 { | |
| 5275 | 526 octave_idx_type nr = rows (); |
| 527 octave_idx_type nc = cols (); | |
| 458 | 528 if (nc != 1) |
| 529 { | |
| 530 (*current_liboctave_error_handler) | |
| 531 ("column dimension mismatch for stack"); | |
| 532 return Matrix (); | |
| 533 } | |
| 534 | |
| 5275 | 535 octave_idx_type nr_insert = nr; |
| 458 | 536 Matrix retval (nr + a.length (), nc); |
| 537 retval.insert (*this, 0, 0); | |
| 538 retval.insert (a, nr_insert, 0); | |
| 539 return retval; | |
| 540 } | |
| 541 | |
| 542 Matrix | |
| 543 Matrix::stack (const DiagMatrix& a) const | |
| 544 { | |
| 5275 | 545 octave_idx_type nr = rows (); |
| 546 octave_idx_type nc = cols (); | |
| 458 | 547 if (nc != a.cols ()) |
| 548 { | |
| 549 (*current_liboctave_error_handler) | |
| 550 ("column dimension mismatch for stack"); | |
| 551 return Matrix (); | |
| 552 } | |
| 553 | |
| 5275 | 554 octave_idx_type nr_insert = nr; |
| 458 | 555 Matrix retval (nr + a.rows (), nc); |
| 556 retval.insert (*this, 0, 0); | |
| 557 retval.insert (a, nr_insert, 0); | |
| 558 return retval; | |
| 559 } | |
| 560 | |
| 561 Matrix | |
| 1205 | 562 real (const ComplexMatrix& a) |
| 563 { | |
| 5275 | 564 octave_idx_type a_len = a.length (); |
| 1205 | 565 Matrix retval; |
| 566 if (a_len > 0) | |
| 3769 | 567 retval = Matrix (mx_inline_real_dup (a.data (), a_len), |
| 568 a.rows (), a.cols ()); | |
| 1205 | 569 return retval; |
| 570 } | |
| 571 | |
| 572 Matrix | |
| 573 imag (const ComplexMatrix& a) | |
| 574 { | |
| 5275 | 575 octave_idx_type a_len = a.length (); |
| 1205 | 576 Matrix retval; |
| 577 if (a_len > 0) | |
| 3769 | 578 retval = Matrix (mx_inline_imag_dup (a.data (), a_len), |
| 579 a.rows (), a.cols ()); | |
| 1205 | 580 return retval; |
| 581 } | |
| 582 | |
| 583 Matrix | |
| 5275 | 584 Matrix::extract (octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) const |
| 458 | 585 { |
| 5275 | 586 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } |
| 587 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } | |
| 588 | |
| 589 octave_idx_type new_r = r2 - r1 + 1; | |
| 590 octave_idx_type new_c = c2 - c1 + 1; | |
| 458 | 591 |
| 592 Matrix result (new_r, new_c); | |
| 593 | |
| 5275 | 594 for (octave_idx_type j = 0; j < new_c; j++) |
| 595 for (octave_idx_type i = 0; i < new_r; i++) | |
| 4316 | 596 result.xelem (i, j) = elem (r1+i, c1+j); |
| 597 | |
| 598 return result; | |
| 599 } | |
| 600 | |
| 601 Matrix | |
| 5275 | 602 Matrix::extract_n (octave_idx_type r1, octave_idx_type c1, octave_idx_type nr, octave_idx_type nc) const |
| 4316 | 603 { |
| 604 Matrix result (nr, nc); | |
| 605 | |
| 5275 | 606 for (octave_idx_type j = 0; j < nc; j++) |
| 607 for (octave_idx_type i = 0; i < nr; i++) | |
| 4316 | 608 result.xelem (i, j) = elem (r1+i, c1+j); |
| 458 | 609 |
| 610 return result; | |
| 611 } | |
| 612 | |
| 613 // extract row or column i. | |
| 614 | |
| 615 RowVector | |
| 5275 | 616 Matrix::row (octave_idx_type i) const |
| 458 | 617 { |
| 5275 | 618 octave_idx_type nc = cols (); |
| 458 | 619 if (i < 0 || i >= rows ()) |
| 620 { | |
| 621 (*current_liboctave_error_handler) ("invalid row selection"); | |
| 622 return RowVector (); | |
| 623 } | |
| 624 | |
| 625 RowVector retval (nc); | |
| 5275 | 626 for (octave_idx_type j = 0; j < nc; j++) |
| 4316 | 627 retval.xelem (j) = elem (i, j); |
| 458 | 628 |
| 629 return retval; | |
| 630 } | |
| 631 | |
| 632 ColumnVector | |
| 5275 | 633 Matrix::column (octave_idx_type i) const |
| 458 | 634 { |
| 5275 | 635 octave_idx_type nr = rows (); |
| 458 | 636 if (i < 0 || i >= cols ()) |
| 637 { | |
| 638 (*current_liboctave_error_handler) ("invalid column selection"); | |
| 639 return ColumnVector (); | |
| 640 } | |
| 641 | |
| 642 ColumnVector retval (nr); | |
| 5275 | 643 for (octave_idx_type j = 0; j < nr; j++) |
| 4316 | 644 retval.xelem (j) = elem (j, i); |
| 458 | 645 |
| 646 return retval; | |
| 647 } | |
| 648 | |
| 649 Matrix | |
| 650 Matrix::inverse (void) const | |
| 651 { | |
| 5275 | 652 octave_idx_type info; |
| 458 | 653 double rcond; |
| 6207 | 654 MatrixType mattype (*this); |
| 655 return inverse (mattype, info, rcond, 0, 0); | |
| 656 } | |
| 657 | |
| 658 Matrix | |
| 6479 | 659 Matrix::inverse (octave_idx_type& info) const |
| 660 { | |
| 661 double rcond; | |
| 662 MatrixType mattype (*this); | |
| 663 return inverse (mattype, info, rcond, 0, 0); | |
| 664 } | |
| 665 | |
| 666 Matrix | |
| 667 Matrix::inverse (octave_idx_type& info, double& rcond, int force, | |
| 668 int calc_cond) const | |
| 669 { | |
| 670 MatrixType mattype (*this); | |
| 671 return inverse (mattype, info, rcond, force, calc_cond); | |
| 672 } | |
| 673 | |
| 674 Matrix | |
| 6207 | 675 Matrix::inverse (MatrixType& mattype) const |
| 676 { | |
| 677 octave_idx_type info; | |
| 678 double rcond; | |
| 679 return inverse (mattype, info, rcond, 0, 0); | |
| 680 } | |
| 681 | |
| 682 Matrix | |
| 683 Matrix::inverse (MatrixType &mattype, octave_idx_type& info) const | |
| 684 { | |
| 685 double rcond; | |
| 686 return inverse (mattype, info, rcond, 0, 0); | |
| 458 | 687 } |
| 688 | |
| 689 Matrix | |
| 6207 | 690 Matrix::tinverse (MatrixType &mattype, octave_idx_type& info, double& rcond, |
| 691 int force, int calc_cond) const | |
| 458 | 692 { |
| 6207 | 693 Matrix retval; |
| 694 | |
| 695 octave_idx_type nr = rows (); | |
| 696 octave_idx_type nc = cols (); | |
| 697 | |
| 698 if (nr != nc || nr == 0 || nc == 0) | |
| 699 (*current_liboctave_error_handler) ("inverse requires square matrix"); | |
| 700 else | |
| 701 { | |
| 702 int typ = mattype.type (); | |
| 703 char uplo = (typ == MatrixType::Lower ? 'L' : 'U'); | |
| 704 char udiag = 'N'; | |
| 705 retval = *this; | |
| 706 double *tmp_data = retval.fortran_vec (); | |
| 707 | |
| 708 F77_XFCN (dtrtri, DTRTRI, (F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 709 F77_CONST_CHAR_ARG2 (&udiag, 1), | |
| 710 nr, tmp_data, nr, info | |
| 711 F77_CHAR_ARG_LEN (1) | |
| 712 F77_CHAR_ARG_LEN (1))); | |
| 713 | |
| 714 if (f77_exception_encountered) | |
| 715 (*current_liboctave_error_handler) ("unrecoverable error in dtrtri"); | |
| 716 else | |
| 717 { | |
| 718 // Throw-away extra info LAPACK gives so as to not change output. | |
| 719 rcond = 0.0; | |
| 720 if (info != 0) | |
| 721 info = -1; | |
| 722 else if (calc_cond) | |
| 723 { | |
| 724 octave_idx_type dtrcon_info = 0; | |
| 725 char job = '1'; | |
| 726 | |
| 727 OCTAVE_LOCAL_BUFFER (double, work, 3 * nr); | |
| 728 OCTAVE_LOCAL_BUFFER (octave_idx_type, iwork, nr); | |
| 729 | |
| 730 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&job, 1), | |
| 731 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 732 F77_CONST_CHAR_ARG2 (&udiag, 1), | |
| 733 nr, tmp_data, nr, rcond, | |
| 734 work, iwork, dtrcon_info | |
| 735 F77_CHAR_ARG_LEN (1) | |
| 736 F77_CHAR_ARG_LEN (1) | |
| 737 F77_CHAR_ARG_LEN (1))); | |
| 738 | |
| 739 if (f77_exception_encountered) | |
| 740 (*current_liboctave_error_handler) | |
| 741 ("unrecoverable error in dtrcon"); | |
| 742 | |
| 743 if (dtrcon_info != 0) | |
| 744 info = -1; | |
| 745 } | |
| 746 } | |
| 747 | |
| 748 if (info == -1 && ! force) | |
| 749 retval = *this; // Restore matrix contents. | |
| 750 } | |
| 751 | |
| 752 return retval; | |
| 458 | 753 } |
| 754 | |
| 6207 | 755 |
| 458 | 756 Matrix |
| 6207 | 757 Matrix::finverse (MatrixType &mattype, octave_idx_type& info, double& rcond, |
| 758 int force, int calc_cond) const | |
| 458 | 759 { |
| 1948 | 760 Matrix retval; |
| 761 | |
| 5275 | 762 octave_idx_type nr = rows (); |
| 763 octave_idx_type nc = cols (); | |
| 1948 | 764 |
| 458 | 765 if (nr != nc || nr == 0 || nc == 0) |
| 1948 | 766 (*current_liboctave_error_handler) ("inverse requires square matrix"); |
| 458 | 767 else |
| 768 { | |
| 5275 | 769 Array<octave_idx_type> ipvt (nr); |
| 770 octave_idx_type *pipvt = ipvt.fortran_vec (); | |
| 1948 | 771 |
| 772 retval = *this; | |
| 773 double *tmp_data = retval.fortran_vec (); | |
| 774 | |
| 4329 | 775 Array<double> z(1); |
| 5275 | 776 octave_idx_type lwork = -1; |
| 4329 | 777 |
| 4330 | 778 // Query the optimum work array size. |
| 4329 | 779 F77_XFCN (dgetri, DGETRI, (nc, tmp_data, nr, pipvt, |
| 780 z.fortran_vec (), lwork, info)); | |
| 781 | |
| 782 if (f77_exception_encountered) | |
| 783 { | |
| 784 (*current_liboctave_error_handler) | |
| 785 ("unrecoverable error in dgetri"); | |
| 786 return retval; | |
| 787 } | |
| 788 | |
| 5275 | 789 lwork = static_cast<octave_idx_type> (z(0)); |
| 4329 | 790 lwork = (lwork < 2 *nc ? 2*nc : lwork); |
| 791 z.resize (lwork); | |
| 792 double *pz = z.fortran_vec (); | |
| 793 | |
| 794 info = 0; | |
| 795 | |
| 4330 | 796 // Calculate the norm of the matrix, for later use. |
| 4329 | 797 double anorm = 0; |
| 798 if (calc_cond) | |
| 5275 | 799 anorm = retval.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
| 4329 | 800 |
| 801 F77_XFCN (dgetrf, DGETRF, (nc, nc, tmp_data, nr, pipvt, info)); | |
| 1948 | 802 |
| 803 if (f77_exception_encountered) | |
| 4329 | 804 (*current_liboctave_error_handler) ("unrecoverable error in dgetrf"); |
| 1948 | 805 else |
| 806 { | |
| 4330 | 807 // Throw-away extra info LAPACK gives so as to not change output. |
| 4509 | 808 rcond = 0.0; |
| 809 if (info != 0) | |
| 1948 | 810 info = -1; |
| 4329 | 811 else if (calc_cond) |
| 812 { | |
| 5275 | 813 octave_idx_type dgecon_info = 0; |
| 5061 | 814 |
| 4330 | 815 // Now calculate the condition number for non-singular matrix. |
| 4329 | 816 char job = '1'; |
| 5275 | 817 Array<octave_idx_type> iz (nc); |
| 818 octave_idx_type *piz = iz.fortran_vec (); | |
| 4552 | 819 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
| 820 nc, tmp_data, nr, anorm, | |
| 5061 | 821 rcond, pz, piz, dgecon_info |
| 4552 | 822 F77_CHAR_ARG_LEN (1))); |
| 4329 | 823 |
| 824 if (f77_exception_encountered) | |
| 825 (*current_liboctave_error_handler) | |
| 826 ("unrecoverable error in dgecon"); | |
| 827 | |
| 5061 | 828 if (dgecon_info != 0) |
| 4329 | 829 info = -1; |
| 830 } | |
| 1948 | 831 |
| 832 if (info == -1 && ! force) | |
| 833 retval = *this; // Restore matrix contents. | |
| 834 else | |
| 835 { | |
| 5275 | 836 octave_idx_type dgetri_info = 0; |
| 5061 | 837 |
| 4329 | 838 F77_XFCN (dgetri, DGETRI, (nc, tmp_data, nr, pipvt, |
| 5061 | 839 pz, lwork, dgetri_info)); |
| 1948 | 840 |
| 841 if (f77_exception_encountered) | |
| 842 (*current_liboctave_error_handler) | |
| 4329 | 843 ("unrecoverable error in dgetri"); |
| 844 | |
| 5061 | 845 if (dgetri_info != 0) |
| 4329 | 846 info = -1; |
| 1948 | 847 } |
| 848 } | |
| 6207 | 849 |
| 850 if (info != 0) | |
| 851 mattype.mark_as_rectangular(); | |
| 458 | 852 } |
| 853 | |
| 1948 | 854 return retval; |
| 458 | 855 } |
| 856 | |
| 740 | 857 Matrix |
| 6207 | 858 Matrix::inverse (MatrixType &mattype, octave_idx_type& info, double& rcond, |
| 859 int force, int calc_cond) const | |
| 860 { | |
| 861 int typ = mattype.type (false); | |
| 862 Matrix ret; | |
| 863 | |
| 864 if (typ == MatrixType::Unknown) | |
| 865 typ = mattype.type (*this); | |
| 866 | |
| 867 if (typ == MatrixType::Upper || typ == MatrixType::Lower) | |
| 868 ret = tinverse (mattype, info, rcond, force, calc_cond); | |
| 6840 | 869 else |
| 6207 | 870 { |
| 871 if (mattype.is_hermitian ()) | |
| 872 { | |
| 6486 | 873 CHOL chol (*this, info, calc_cond); |
| 6207 | 874 if (info == 0) |
| 6486 | 875 { |
| 876 if (calc_cond) | |
| 877 rcond = chol.rcond (); | |
| 878 else | |
| 879 rcond = 1.0; | |
| 880 ret = chol.inverse (); | |
| 881 } | |
| 6207 | 882 else |
| 883 mattype.mark_as_unsymmetric (); | |
| 884 } | |
| 885 | |
| 886 if (!mattype.is_hermitian ()) | |
| 887 ret = finverse(mattype, info, rcond, force, calc_cond); | |
| 6840 | 888 |
| 7033 | 889 if ((mattype.is_hermitian () || calc_cond) && rcond == 0.) |
| 6840 | 890 ret = Matrix (rows (), columns (), octave_Inf); |
| 6207 | 891 } |
| 892 | |
| 893 return ret; | |
| 894 } | |
| 895 | |
| 896 Matrix | |
| 4384 | 897 Matrix::pseudo_inverse (double tol) const |
| 740 | 898 { |
| 3480 | 899 SVD result (*this, SVD::economy); |
| 740 | 900 |
| 901 DiagMatrix S = result.singular_values (); | |
| 902 Matrix U = result.left_singular_matrix (); | |
| 903 Matrix V = result.right_singular_matrix (); | |
| 904 | |
| 905 ColumnVector sigma = S.diag (); | |
| 906 | |
| 5275 | 907 octave_idx_type r = sigma.length () - 1; |
| 908 octave_idx_type nr = rows (); | |
| 909 octave_idx_type nc = cols (); | |
| 740 | 910 |
| 911 if (tol <= 0.0) | |
| 912 { | |
| 913 if (nr > nc) | |
| 914 tol = nr * sigma.elem (0) * DBL_EPSILON; | |
| 915 else | |
| 916 tol = nc * sigma.elem (0) * DBL_EPSILON; | |
| 917 } | |
| 918 | |
| 919 while (r >= 0 && sigma.elem (r) < tol) | |
| 920 r--; | |
| 921 | |
| 922 if (r < 0) | |
| 923 return Matrix (nc, nr, 0.0); | |
| 924 else | |
| 925 { | |
| 926 Matrix Ur = U.extract (0, 0, nr-1, r); | |
| 927 DiagMatrix D = DiagMatrix (sigma.extract (0, r)) . inverse (); | |
| 928 Matrix Vr = V.extract (0, 0, nc-1, r); | |
| 929 return Vr * D * Ur.transpose (); | |
| 930 } | |
| 931 } | |
| 932 | |
| 4773 | 933 #if defined (HAVE_FFTW3) |
| 3827 | 934 |
| 935 ComplexMatrix | |
| 936 Matrix::fourier (void) const | |
| 937 { | |
| 938 size_t nr = rows (); | |
| 939 size_t nc = cols (); | |
| 940 | |
| 941 ComplexMatrix retval (nr, nc); | |
| 942 | |
| 943 size_t npts, nsamples; | |
| 944 | |
| 945 if (nr == 1 || nc == 1) | |
| 946 { | |
| 947 npts = nr > nc ? nr : nc; | |
| 948 nsamples = 1; | |
| 949 } | |
| 950 else | |
| 951 { | |
| 952 npts = nr; | |
| 953 nsamples = nc; | |
| 954 } | |
| 955 | |
| 4773 | 956 const double *in (fortran_vec ()); |
| 3827 | 957 Complex *out (retval.fortran_vec ()); |
| 958 | |
| 4773 | 959 octave_fftw::fft (in, out, npts, nsamples); |
| 3827 | 960 |
| 961 return retval; | |
| 962 } | |
| 963 | |
| 964 ComplexMatrix | |
| 965 Matrix::ifourier (void) const | |
| 966 { | |
| 967 size_t nr = rows (); | |
| 968 size_t nc = cols (); | |
| 969 | |
| 970 ComplexMatrix retval (nr, nc); | |
| 971 | |
| 972 size_t npts, nsamples; | |
| 973 | |
| 974 if (nr == 1 || nc == 1) | |
| 975 { | |
| 976 npts = nr > nc ? nr : nc; | |
| 977 nsamples = 1; | |
| 978 } | |
| 979 else | |
| 980 { | |
| 981 npts = nr; | |
| 982 nsamples = nc; | |
| 983 } | |
| 984 | |
| 985 ComplexMatrix tmp (*this); | |
| 986 Complex *in (tmp.fortran_vec ()); | |
| 987 Complex *out (retval.fortran_vec ()); | |
| 988 | |
| 4773 | 989 octave_fftw::ifft (in, out, npts, nsamples); |
| 3827 | 990 |
| 991 return retval; | |
| 992 } | |
| 993 | |
| 994 ComplexMatrix | |
| 995 Matrix::fourier2d (void) const | |
| 996 { | |
| 4773 | 997 dim_vector dv(rows (), cols ()); |
| 998 | |
| 999 const double *in = fortran_vec (); | |
| 1000 ComplexMatrix retval (rows (), cols ()); | |
| 1001 octave_fftw::fftNd (in, retval.fortran_vec (), 2, dv); | |
| 3827 | 1002 |
| 1003 return retval; | |
| 1004 } | |
| 1005 | |
| 1006 ComplexMatrix | |
| 1007 Matrix::ifourier2d (void) const | |
| 1008 { | |
| 4773 | 1009 dim_vector dv(rows (), cols ()); |
| 3827 | 1010 |
| 1011 ComplexMatrix retval (*this); | |
| 4773 | 1012 Complex *out (retval.fortran_vec ()); |
| 1013 | |
| 1014 octave_fftw::ifftNd (out, out, 2, dv); | |
| 3827 | 1015 |
| 1016 return retval; | |
| 1017 } | |
| 1018 | |
| 1019 #else | |
| 1020 | |
| 458 | 1021 ComplexMatrix |
| 1022 Matrix::fourier (void) const | |
| 1023 { | |
| 1948 | 1024 ComplexMatrix retval; |
| 1025 | |
| 5275 | 1026 octave_idx_type nr = rows (); |
| 1027 octave_idx_type nc = cols (); | |
| 1028 | |
| 1029 octave_idx_type npts, nsamples; | |
| 1948 | 1030 |
| 458 | 1031 if (nr == 1 || nc == 1) |
| 1032 { | |
| 1033 npts = nr > nc ? nr : nc; | |
| 1034 nsamples = 1; | |
| 1035 } | |
| 1036 else | |
| 1037 { | |
| 1038 npts = nr; | |
| 1039 nsamples = nc; | |
| 1040 } | |
| 1041 | |
| 5275 | 1042 octave_idx_type nn = 4*npts+15; |
| 1948 | 1043 |
| 1044 Array<Complex> wsave (nn); | |
| 1045 Complex *pwsave = wsave.fortran_vec (); | |
| 1046 | |
| 3585 | 1047 retval = ComplexMatrix (*this); |
| 1948 | 1048 Complex *tmp_data = retval.fortran_vec (); |
| 1049 | |
| 3887 | 1050 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
| 458 | 1051 |
| 5275 | 1052 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1053 { |
| 1054 OCTAVE_QUIT; | |
| 1055 | |
| 1056 F77_FUNC (cfftf, CFFTF) (npts, &tmp_data[npts*j], pwsave); | |
| 1057 } | |
| 1948 | 1058 |
| 1059 return retval; | |
| 458 | 1060 } |
| 1061 | |
| 1062 ComplexMatrix | |
| 1063 Matrix::ifourier (void) const | |
| 1064 { | |
| 1948 | 1065 ComplexMatrix retval; |
| 1066 | |
| 5275 | 1067 octave_idx_type nr = rows (); |
| 1068 octave_idx_type nc = cols (); | |
| 1069 | |
| 1070 octave_idx_type npts, nsamples; | |
| 1948 | 1071 |
| 458 | 1072 if (nr == 1 || nc == 1) |
| 1073 { | |
| 1074 npts = nr > nc ? nr : nc; | |
| 1075 nsamples = 1; | |
| 1076 } | |
| 1077 else | |
| 1078 { | |
| 1079 npts = nr; | |
| 1080 nsamples = nc; | |
| 1081 } | |
| 1082 | |
| 5275 | 1083 octave_idx_type nn = 4*npts+15; |
| 1948 | 1084 |
| 1085 Array<Complex> wsave (nn); | |
| 1086 Complex *pwsave = wsave.fortran_vec (); | |
| 1087 | |
| 3585 | 1088 retval = ComplexMatrix (*this); |
| 1948 | 1089 Complex *tmp_data = retval.fortran_vec (); |
| 1090 | |
| 3887 | 1091 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
| 458 | 1092 |
| 5275 | 1093 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1094 { |
| 1095 OCTAVE_QUIT; | |
| 1096 | |
| 1097 F77_FUNC (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave); | |
| 1098 } | |
| 458 | 1099 |
| 5275 | 1100 for (octave_idx_type j = 0; j < npts*nsamples; j++) |
| 3572 | 1101 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
| 458 | 1102 |
| 1948 | 1103 return retval; |
| 458 | 1104 } |
| 1105 | |
| 677 | 1106 ComplexMatrix |
| 1107 Matrix::fourier2d (void) const | |
| 1108 { | |
| 1948 | 1109 ComplexMatrix retval; |
| 1110 | |
| 5275 | 1111 octave_idx_type nr = rows (); |
| 1112 octave_idx_type nc = cols (); | |
| 1113 | |
| 1114 octave_idx_type npts, nsamples; | |
| 1948 | 1115 |
| 677 | 1116 if (nr == 1 || nc == 1) |
| 1117 { | |
| 1118 npts = nr > nc ? nr : nc; | |
| 1119 nsamples = 1; | |
| 1120 } | |
| 1121 else | |
| 1122 { | |
| 1123 npts = nr; | |
| 1124 nsamples = nc; | |
| 1125 } | |
| 1126 | |
| 5275 | 1127 octave_idx_type nn = 4*npts+15; |
| 1948 | 1128 |
| 1129 Array<Complex> wsave (nn); | |
| 1130 Complex *pwsave = wsave.fortran_vec (); | |
| 1131 | |
| 3585 | 1132 retval = ComplexMatrix (*this); |
| 1948 | 1133 Complex *tmp_data = retval.fortran_vec (); |
| 1134 | |
| 3887 | 1135 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
| 677 | 1136 |
| 5275 | 1137 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1138 { |
| 1139 OCTAVE_QUIT; | |
| 1140 | |
| 1141 F77_FUNC (cfftf, CFFTF) (npts, &tmp_data[npts*j], pwsave); | |
| 1142 } | |
| 677 | 1143 |
| 1144 npts = nc; | |
| 1145 nsamples = nr; | |
| 1146 nn = 4*npts+15; | |
| 1948 | 1147 |
| 1148 wsave.resize (nn); | |
| 1149 pwsave = wsave.fortran_vec (); | |
| 1150 | |
| 4773 | 1151 Array<Complex> tmp (npts); |
| 1152 Complex *prow = tmp.fortran_vec (); | |
| 1948 | 1153 |
| 3887 | 1154 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
| 677 | 1155 |
| 5275 | 1156 for (octave_idx_type j = 0; j < nsamples; j++) |
| 677 | 1157 { |
| 4153 | 1158 OCTAVE_QUIT; |
| 1159 | |
| 5275 | 1160 for (octave_idx_type i = 0; i < npts; i++) |
| 1948 | 1161 prow[i] = tmp_data[i*nr + j]; |
| 1162 | |
| 3887 | 1163 F77_FUNC (cfftf, CFFTF) (npts, prow, pwsave); |
| 677 | 1164 |
| 5275 | 1165 for (octave_idx_type i = 0; i < npts; i++) |
| 1948 | 1166 tmp_data[i*nr + j] = prow[i]; |
| 677 | 1167 } |
| 1168 | |
| 1948 | 1169 return retval; |
| 677 | 1170 } |
| 1171 | |
| 1172 ComplexMatrix | |
| 1173 Matrix::ifourier2d (void) const | |
| 1174 { | |
| 1948 | 1175 ComplexMatrix retval; |
| 1176 | |
| 5275 | 1177 octave_idx_type nr = rows (); |
| 1178 octave_idx_type nc = cols (); | |
| 1179 | |
| 1180 octave_idx_type npts, nsamples; | |
| 1948 | 1181 |
| 677 | 1182 if (nr == 1 || nc == 1) |
| 1183 { | |
| 1184 npts = nr > nc ? nr : nc; | |
| 1185 nsamples = 1; | |
| 1186 } | |
| 1187 else | |
| 1188 { | |
| 1189 npts = nr; | |
| 1190 nsamples = nc; | |
| 1191 } | |
| 1192 | |
| 5275 | 1193 octave_idx_type nn = 4*npts+15; |
| 1948 | 1194 |
| 1195 Array<Complex> wsave (nn); | |
| 1196 Complex *pwsave = wsave.fortran_vec (); | |
| 1197 | |
| 3585 | 1198 retval = ComplexMatrix (*this); |
| 1948 | 1199 Complex *tmp_data = retval.fortran_vec (); |
| 1200 | |
| 3887 | 1201 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
| 677 | 1202 |
| 5275 | 1203 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1204 { |
| 1205 OCTAVE_QUIT; | |
| 1206 | |
| 1207 F77_FUNC (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave); | |
| 1208 } | |
| 677 | 1209 |
| 5275 | 1210 for (octave_idx_type j = 0; j < npts*nsamples; j++) |
| 3572 | 1211 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
| 677 | 1212 |
| 1213 npts = nc; | |
| 1214 nsamples = nr; | |
| 1215 nn = 4*npts+15; | |
| 1948 | 1216 |
| 1217 wsave.resize (nn); | |
| 1218 pwsave = wsave.fortran_vec (); | |
| 1219 | |
| 4773 | 1220 Array<Complex> tmp (npts); |
| 1221 Complex *prow = tmp.fortran_vec (); | |
| 1948 | 1222 |
| 3887 | 1223 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
| 677 | 1224 |
| 5275 | 1225 for (octave_idx_type j = 0; j < nsamples; j++) |
| 677 | 1226 { |
| 4153 | 1227 OCTAVE_QUIT; |
| 1228 | |
| 5275 | 1229 for (octave_idx_type i = 0; i < npts; i++) |
| 1948 | 1230 prow[i] = tmp_data[i*nr + j]; |
| 1231 | |
| 3887 | 1232 F77_FUNC (cfftb, CFFTB) (npts, prow, pwsave); |
| 677 | 1233 |
| 5275 | 1234 for (octave_idx_type i = 0; i < npts; i++) |
| 3572 | 1235 tmp_data[i*nr + j] = prow[i] / static_cast<double> (npts); |
| 677 | 1236 } |
| 1237 | |
| 1948 | 1238 return retval; |
| 677 | 1239 } |
| 1240 | |
| 3827 | 1241 #endif |
| 1242 | |
| 458 | 1243 DET |
| 1244 Matrix::determinant (void) const | |
| 1245 { | |
| 5275 | 1246 octave_idx_type info; |
| 458 | 1247 double rcond; |
| 4329 | 1248 return determinant (info, rcond, 0); |
| 458 | 1249 } |
| 1250 | |
| 1251 DET | |
| 5275 | 1252 Matrix::determinant (octave_idx_type& info) const |
| 458 | 1253 { |
| 1254 double rcond; | |
| 4329 | 1255 return determinant (info, rcond, 0); |
| 458 | 1256 } |
| 1257 | |
| 1258 DET | |
| 5275 | 1259 Matrix::determinant (octave_idx_type& info, double& rcond, int calc_cond) const |
| 458 | 1260 { |
| 1261 DET retval; | |
| 1262 | |
| 5275 | 1263 octave_idx_type nr = rows (); |
| 1264 octave_idx_type nc = cols (); | |
| 458 | 1265 |
| 1266 if (nr == 0 || nc == 0) | |
| 1267 { | |
| 5634 | 1268 retval = DET (1.0, 0); |
| 458 | 1269 } |
| 1270 else | |
| 1271 { | |
| 5275 | 1272 Array<octave_idx_type> ipvt (nr); |
| 1273 octave_idx_type *pipvt = ipvt.fortran_vec (); | |
| 1948 | 1274 |
| 1275 Matrix atmp = *this; | |
| 1276 double *tmp_data = atmp.fortran_vec (); | |
| 1277 | |
| 4329 | 1278 info = 0; |
| 1279 | |
| 4330 | 1280 // Calculate the norm of the matrix, for later use. |
| 4329 | 1281 double anorm = 0; |
| 1282 if (calc_cond) | |
| 5275 | 1283 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
| 4329 | 1284 |
| 1285 F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); | |
| 1948 | 1286 |
| 1287 if (f77_exception_encountered) | |
| 4329 | 1288 (*current_liboctave_error_handler) ("unrecoverable error in dgetrf"); |
| 458 | 1289 else |
| 1290 { | |
| 4330 | 1291 // Throw-away extra info LAPACK gives so as to not change output. |
| 4509 | 1292 rcond = 0.0; |
| 1293 if (info != 0) | |
| 1948 | 1294 { |
| 4509 | 1295 info = -1; |
| 1296 retval = DET (); | |
| 4329 | 1297 } |
| 1298 else | |
| 1948 | 1299 { |
| 4329 | 1300 if (calc_cond) |
| 1301 { | |
| 4330 | 1302 // Now calc the condition number for non-singular matrix. |
| 4329 | 1303 char job = '1'; |
| 1304 Array<double> z (4 * nc); | |
| 1305 double *pz = z.fortran_vec (); | |
| 5275 | 1306 Array<octave_idx_type> iz (nc); |
| 1307 octave_idx_type *piz = iz.fortran_vec (); | |
| 4329 | 1308 |
| 4552 | 1309 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
| 1310 nc, tmp_data, nr, anorm, | |
| 1311 rcond, pz, piz, info | |
| 1312 F77_CHAR_ARG_LEN (1))); | |
| 4329 | 1313 |
| 1314 if (f77_exception_encountered) | |
| 1315 (*current_liboctave_error_handler) | |
| 1316 ("unrecoverable error in dgecon"); | |
| 1317 } | |
| 1318 | |
| 4509 | 1319 if (info != 0) |
| 4329 | 1320 { |
| 1321 info = -1; | |
| 1322 retval = DET (); | |
| 1323 } | |
| 1324 else | |
| 1325 { | |
| 5634 | 1326 double c = 1.0; |
| 1327 int e = 0; | |
| 1328 | |
| 1329 for (octave_idx_type i = 0; i < nc; i++) | |
| 4329 | 1330 { |
| 5634 | 1331 if (ipvt(i) != (i+1)) |
| 1332 c = -c; | |
| 1333 | |
| 1334 c *= atmp(i,i); | |
| 1335 | |
| 1336 if (c == 0.0) | |
| 1337 break; | |
| 1338 | |
| 1339 while (fabs (c) < 0.5) | |
| 4329 | 1340 { |
| 5634 | 1341 c *= 2.0; |
| 1342 e--; | |
| 4329 | 1343 } |
| 5634 | 1344 |
| 1345 while (fabs (c) >= 2.0) | |
| 4329 | 1346 { |
| 5634 | 1347 c /= 2.0; |
| 1348 e++; | |
| 4329 | 1349 } |
| 1350 } | |
| 5634 | 1351 |
| 1352 retval = DET (c, e); | |
| 4329 | 1353 } |
| 1948 | 1354 } |
| 458 | 1355 } |
| 1356 } | |
| 1357 | |
| 1358 return retval; | |
| 1359 } | |
| 1360 | |
| 1361 Matrix | |
| 5785 | 1362 Matrix::utsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, |
| 1363 double& rcond, solve_singularity_handler sing_handler, | |
| 1364 bool calc_cond) const | |
| 1365 { | |
| 1366 Matrix retval; | |
| 1367 | |
| 1368 octave_idx_type nr = rows (); | |
| 1369 octave_idx_type nc = cols (); | |
| 1370 | |
| 6924 | 1371 if (nr != b.rows ()) |
| 5785 | 1372 (*current_liboctave_error_handler) |
| 1373 ("matrix dimension mismatch solution of linear equations"); | |
| 6924 | 1374 else if (nr == 0 || nc == 0 || b.cols () == 0) |
| 1375 retval = Matrix (nc, b.cols (), 0.0); | |
| 5785 | 1376 else |
| 1377 { | |
| 1378 volatile int typ = mattype.type (); | |
| 1379 | |
| 1380 if (typ == MatrixType::Permuted_Upper || | |
| 1381 typ == MatrixType::Upper) | |
| 1382 { | |
| 1383 octave_idx_type b_nc = b.cols (); | |
| 1384 rcond = 1.; | |
| 1385 info = 0; | |
| 1386 | |
| 1387 if (typ == MatrixType::Permuted_Upper) | |
| 1388 { | |
| 1389 (*current_liboctave_error_handler) | |
| 6390 | 1390 ("permuted triangular matrix not implemented"); |
| 5785 | 1391 } |
| 1392 else | |
| 1393 { | |
| 1394 const double *tmp_data = fortran_vec (); | |
| 1395 | |
| 1396 if (calc_cond) | |
| 1397 { | |
| 1398 char norm = '1'; | |
| 1399 char uplo = 'U'; | |
| 1400 char dia = 'N'; | |
| 1401 | |
| 1402 Array<double> z (3 * nc); | |
| 1403 double *pz = z.fortran_vec (); | |
| 1404 Array<octave_idx_type> iz (nc); | |
| 1405 octave_idx_type *piz = iz.fortran_vec (); | |
| 1406 | |
| 1407 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1408 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1409 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1410 nr, tmp_data, nr, rcond, | |
| 1411 pz, piz, info | |
| 1412 F77_CHAR_ARG_LEN (1) | |
| 1413 F77_CHAR_ARG_LEN (1) | |
| 1414 F77_CHAR_ARG_LEN (1))); | |
| 1415 | |
| 1416 if (f77_exception_encountered) | |
| 1417 (*current_liboctave_error_handler) | |
| 1418 ("unrecoverable error in dtrcon"); | |
| 1419 | |
| 1420 if (info != 0) | |
| 1421 info = -2; | |
| 1422 | |
| 1423 volatile double rcond_plus_one = rcond + 1.0; | |
| 1424 | |
| 1425 if (rcond_plus_one == 1.0 || xisnan (rcond)) | |
| 1426 { | |
| 1427 info = -2; | |
| 1428 | |
| 1429 if (sing_handler) | |
| 1430 sing_handler (rcond); | |
| 1431 else | |
| 1432 (*current_liboctave_error_handler) | |
| 1433 ("matrix singular to machine precision, rcond = %g", | |
| 1434 rcond); | |
| 1435 } | |
| 1436 } | |
| 1437 | |
| 1438 if (info == 0) | |
| 1439 { | |
| 1440 retval = b; | |
| 1441 double *result = retval.fortran_vec (); | |
| 1442 | |
| 1443 char uplo = 'U'; | |
| 1444 char trans = 'N'; | |
| 1445 char dia = 'N'; | |
| 1446 | |
| 1447 F77_XFCN (dtrtrs, DTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1448 F77_CONST_CHAR_ARG2 (&trans, 1), | |
| 1449 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1450 nr, b_nc, tmp_data, nr, | |
| 1451 result, nr, info | |
| 1452 F77_CHAR_ARG_LEN (1) | |
| 1453 F77_CHAR_ARG_LEN (1) | |
| 1454 F77_CHAR_ARG_LEN (1))); | |
| 1455 | |
| 1456 if (f77_exception_encountered) | |
| 1457 (*current_liboctave_error_handler) | |
| 1458 ("unrecoverable error in dtrtrs"); | |
| 1459 } | |
| 1460 } | |
| 1461 } | |
| 1462 else | |
| 1463 (*current_liboctave_error_handler) ("incorrect matrix type"); | |
| 1464 } | |
| 1465 | |
| 1466 return retval; | |
| 1467 } | |
| 1468 | |
| 1469 Matrix | |
| 1470 Matrix::ltsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, | |
| 1471 double& rcond, solve_singularity_handler sing_handler, | |
| 1472 bool calc_cond) const | |
| 1473 { | |
| 1474 Matrix retval; | |
| 1475 | |
| 1476 octave_idx_type nr = rows (); | |
| 1477 octave_idx_type nc = cols (); | |
| 1478 | |
| 6924 | 1479 if (nr != b.rows ()) |
| 5785 | 1480 (*current_liboctave_error_handler) |
| 1481 ("matrix dimension mismatch solution of linear equations"); | |
| 6924 | 1482 else if (nr == 0 || nc == 0 || b.cols () == 0) |
| 1483 retval = Matrix (nc, b.cols (), 0.0); | |
| 5785 | 1484 else |
| 1485 { | |
| 1486 volatile int typ = mattype.type (); | |
| 1487 | |
| 1488 if (typ == MatrixType::Permuted_Lower || | |
| 1489 typ == MatrixType::Lower) | |
| 1490 { | |
| 1491 octave_idx_type b_nc = b.cols (); | |
| 1492 rcond = 1.; | |
| 1493 info = 0; | |
| 1494 | |
| 1495 if (typ == MatrixType::Permuted_Lower) | |
| 1496 { | |
| 1497 (*current_liboctave_error_handler) | |
| 6390 | 1498 ("permuted triangular matrix not implemented"); |
| 5785 | 1499 } |
| 1500 else | |
| 1501 { | |
| 1502 const double *tmp_data = fortran_vec (); | |
| 1503 | |
| 1504 if (calc_cond) | |
| 1505 { | |
| 1506 char norm = '1'; | |
| 1507 char uplo = 'L'; | |
| 1508 char dia = 'N'; | |
| 1509 | |
| 1510 Array<double> z (3 * nc); | |
| 1511 double *pz = z.fortran_vec (); | |
| 1512 Array<octave_idx_type> iz (nc); | |
| 1513 octave_idx_type *piz = iz.fortran_vec (); | |
| 1514 | |
| 1515 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1516 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1517 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1518 nr, tmp_data, nr, rcond, | |
| 1519 pz, piz, info | |
| 1520 F77_CHAR_ARG_LEN (1) | |
| 1521 F77_CHAR_ARG_LEN (1) | |
| 1522 F77_CHAR_ARG_LEN (1))); | |
| 1523 | |
| 1524 if (f77_exception_encountered) | |
| 1525 (*current_liboctave_error_handler) | |
| 1526 ("unrecoverable error in dtrcon"); | |
| 1527 | |
| 1528 if (info != 0) | |
| 1529 info = -2; | |
| 1530 | |
| 1531 volatile double rcond_plus_one = rcond + 1.0; | |
| 1532 | |
| 1533 if (rcond_plus_one == 1.0 || xisnan (rcond)) | |
| 1534 { | |
| 1535 info = -2; | |
| 1536 | |
| 1537 if (sing_handler) | |
| 1538 sing_handler (rcond); | |
| 1539 else | |
| 1540 (*current_liboctave_error_handler) | |
| 1541 ("matrix singular to machine precision, rcond = %g", | |
| 1542 rcond); | |
| 1543 } | |
| 1544 } | |
| 1545 | |
| 1546 if (info == 0) | |
| 1547 { | |
| 1548 retval = b; | |
| 1549 double *result = retval.fortran_vec (); | |
| 1550 | |
| 1551 char uplo = 'L'; | |
| 1552 char trans = 'N'; | |
| 1553 char dia = 'N'; | |
| 1554 | |
| 1555 F77_XFCN (dtrtrs, DTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1556 F77_CONST_CHAR_ARG2 (&trans, 1), | |
| 1557 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1558 nr, b_nc, tmp_data, nr, | |
| 1559 result, nr, info | |
| 1560 F77_CHAR_ARG_LEN (1) | |
| 1561 F77_CHAR_ARG_LEN (1) | |
| 1562 F77_CHAR_ARG_LEN (1))); | |
| 1563 | |
| 1564 if (f77_exception_encountered) | |
| 1565 (*current_liboctave_error_handler) | |
| 1566 ("unrecoverable error in dtrtrs"); | |
| 1567 } | |
| 1568 } | |
| 1569 } | |
| 1570 else | |
| 1571 (*current_liboctave_error_handler) ("incorrect matrix type"); | |
| 1572 } | |
| 1573 | |
| 1574 return retval; | |
| 1575 } | |
| 1576 | |
| 1577 Matrix | |
| 1578 Matrix::fsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, | |
| 1579 double& rcond, solve_singularity_handler sing_handler, | |
| 1580 bool calc_cond) const | |
| 1581 { | |
| 1582 Matrix retval; | |
| 1583 | |
| 1584 octave_idx_type nr = rows (); | |
| 1585 octave_idx_type nc = cols (); | |
| 1586 | |
| 6924 | 1587 if (nr != nc || nr != b.rows ()) |
| 5785 | 1588 (*current_liboctave_error_handler) |
| 1589 ("matrix dimension mismatch solution of linear equations"); | |
| 6924 | 1590 else if (nr == 0 || b.cols () == 0) |
| 1591 retval = Matrix (nc, b.cols (), 0.0); | |
| 5785 | 1592 else |
| 1593 { | |
| 1594 volatile int typ = mattype.type (); | |
| 1595 | |
| 1596 // Calculate the norm of the matrix, for later use. | |
| 1597 double anorm = -1.; | |
| 1598 | |
| 1599 if (typ == MatrixType::Hermitian) | |
| 1600 { | |
| 1601 info = 0; | |
| 1602 char job = 'L'; | |
| 1603 Matrix atmp = *this; | |
| 1604 double *tmp_data = atmp.fortran_vec (); | |
| 1605 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); | |
| 1606 | |
| 1607 F77_XFCN (dpotrf, DPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, | |
| 1608 tmp_data, nr, info | |
| 1609 F77_CHAR_ARG_LEN (1))); | |
| 1610 | |
| 1611 if (f77_exception_encountered) | |
| 1612 (*current_liboctave_error_handler) | |
| 1613 ("unrecoverable error in dpotrf"); | |
| 1614 else | |
| 1615 { | |
| 1616 // Throw-away extra info LAPACK gives so as to not change output. | |
| 1617 rcond = 0.0; | |
| 1618 if (info != 0) | |
| 1619 { | |
| 1620 info = -2; | |
| 1621 | |
| 1622 mattype.mark_as_unsymmetric (); | |
| 1623 typ = MatrixType::Full; | |
| 1624 } | |
| 1625 else | |
| 1626 { | |
| 1627 if (calc_cond) | |
| 1628 { | |
| 1629 Array<double> z (3 * nc); | |
| 1630 double *pz = z.fortran_vec (); | |
| 1631 Array<octave_idx_type> iz (nc); | |
| 1632 octave_idx_type *piz = iz.fortran_vec (); | |
| 1633 | |
| 1634 F77_XFCN (dpocon, DPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), | |
| 1635 nr, tmp_data, nr, anorm, | |
| 1636 rcond, pz, piz, info | |
| 1637 F77_CHAR_ARG_LEN (1))); | |
| 1638 | |
| 1639 if (f77_exception_encountered) | |
| 1640 (*current_liboctave_error_handler) | |
| 1641 ("unrecoverable error in dpocon"); | |
| 1642 | |
| 1643 if (info != 0) | |
| 1644 info = -2; | |
| 1645 | |
| 1646 volatile double rcond_plus_one = rcond + 1.0; | |
| 1647 | |
| 1648 if (rcond_plus_one == 1.0 || xisnan (rcond)) | |
| 1649 { | |
| 1650 info = -2; | |
| 1651 | |
| 1652 if (sing_handler) | |
| 1653 sing_handler (rcond); | |
| 1654 else | |
| 1655 (*current_liboctave_error_handler) | |
| 1656 ("matrix singular to machine precision, rcond = %g", | |
| 1657 rcond); | |
| 1658 } | |
| 1659 } | |
| 1660 | |
| 1661 if (info == 0) | |
| 1662 { | |
| 1663 retval = b; | |
| 1664 double *result = retval.fortran_vec (); | |
| 1665 | |
| 1666 octave_idx_type b_nc = b.cols (); | |
| 1667 | |
| 1668 F77_XFCN (dpotrs, DPOTRS, (F77_CONST_CHAR_ARG2 (&job, 1), | |
| 1669 nr, b_nc, tmp_data, nr, | |
| 1670 result, b.rows(), info | |
| 1671 F77_CHAR_ARG_LEN (1))); | |
| 1672 | |
| 1673 if (f77_exception_encountered) | |
| 1674 (*current_liboctave_error_handler) | |
| 1675 ("unrecoverable error in dpotrs"); | |
| 1676 } | |
| 1677 else | |
| 1678 { | |
| 1679 mattype.mark_as_unsymmetric (); | |
| 1680 typ = MatrixType::Full; | |
| 1681 } | |
| 1682 } | |
| 1683 } | |
| 1684 } | |
| 1685 | |
| 1686 if (typ == MatrixType::Full) | |
| 1687 { | |
| 1688 info = 0; | |
| 1689 | |
| 1690 Array<octave_idx_type> ipvt (nr); | |
| 1691 octave_idx_type *pipvt = ipvt.fortran_vec (); | |
| 1692 | |
| 1693 Matrix atmp = *this; | |
| 1694 double *tmp_data = atmp.fortran_vec (); | |
| 1695 if(anorm < 0.) | |
| 1696 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); | |
| 1697 | |
| 1698 Array<double> z (4 * nc); | |
| 1699 double *pz = z.fortran_vec (); | |
| 1700 Array<octave_idx_type> iz (nc); | |
| 1701 octave_idx_type *piz = iz.fortran_vec (); | |
| 1702 | |
| 1703 F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); | |
| 1704 | |
| 1705 if (f77_exception_encountered) | |
| 1706 (*current_liboctave_error_handler) | |
| 1707 ("unrecoverable error in dgetrf"); | |
| 1708 else | |
| 1709 { | |
| 1710 // Throw-away extra info LAPACK gives so as to not change output. | |
| 1711 rcond = 0.0; | |
| 1712 if (info != 0) | |
| 1713 { | |
| 1714 info = -2; | |
| 1715 | |
| 1716 if (sing_handler) | |
| 1717 sing_handler (rcond); | |
| 1718 else | |
| 1719 (*current_liboctave_error_handler) | |
| 1720 ("matrix singular to machine precision"); | |
| 1721 | |
| 1722 mattype.mark_as_rectangular (); | |
| 1723 } | |
| 1724 else | |
| 1725 { | |
| 1726 if (calc_cond) | |
| 1727 { | |
| 1728 // Now calculate the condition number for | |
| 1729 // non-singular matrix. | |
| 1730 char job = '1'; | |
| 1731 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), | |
| 1732 nc, tmp_data, nr, anorm, | |
| 1733 rcond, pz, piz, info | |
| 1734 F77_CHAR_ARG_LEN (1))); | |
| 1735 | |
| 1736 if (f77_exception_encountered) | |
| 1737 (*current_liboctave_error_handler) | |
| 1738 ("unrecoverable error in dgecon"); | |
| 1739 | |
| 1740 if (info != 0) | |
| 1741 info = -2; | |
| 1742 | |
| 1743 volatile double rcond_plus_one = rcond + 1.0; | |
| 1744 | |
| 1745 if (rcond_plus_one == 1.0 || xisnan (rcond)) | |
| 1746 { | |
| 1747 info = -2; | |
| 1748 | |
| 1749 if (sing_handler) | |
| 1750 sing_handler (rcond); | |
| 1751 else | |
| 1752 (*current_liboctave_error_handler) | |
| 1753 ("matrix singular to machine precision, rcond = %g", | |
| 1754 rcond); | |
| 1755 } | |
| 1756 } | |
| 1757 | |
| 1758 if (info == 0) | |
| 1759 { | |
| 1760 retval = b; | |
| 1761 double *result = retval.fortran_vec (); | |
| 1762 | |
| 1763 octave_idx_type b_nc = b.cols (); | |
| 1764 | |
| 1765 char job = 'N'; | |
| 1766 F77_XFCN (dgetrs, DGETRS, (F77_CONST_CHAR_ARG2 (&job, 1), | |
| 1767 nr, b_nc, tmp_data, nr, | |
| 1768 pipvt, result, b.rows(), info | |
| 1769 F77_CHAR_ARG_LEN (1))); | |
| 1770 | |
| 1771 if (f77_exception_encountered) | |
| 1772 (*current_liboctave_error_handler) | |
| 1773 ("unrecoverable error in dgetrs"); | |
| 1774 } | |
| 1775 else | |
| 1776 mattype.mark_as_rectangular (); | |
| 1777 } | |
| 1778 } | |
| 1779 } | |
| 1780 else if (typ != MatrixType::Hermitian) | |
| 1781 (*current_liboctave_error_handler) ("incorrect matrix type"); | |
| 1782 } | |
| 1783 | |
| 1784 return retval; | |
| 1785 } | |
| 1786 | |
| 1787 Matrix | |
| 1788 Matrix::solve (MatrixType &typ, const Matrix& b) const | |
| 1789 { | |
| 1790 octave_idx_type info; | |
| 1791 double rcond; | |
| 1792 return solve (typ, b, info, rcond, 0); | |
| 1793 } | |
| 1794 | |
| 1795 Matrix | |
| 1796 Matrix::solve (MatrixType &typ, const Matrix& b, octave_idx_type& info, | |
| 1797 double& rcond) const | |
| 1798 { | |
| 1799 return solve (typ, b, info, rcond, 0); | |
| 1800 } | |
| 1801 | |
| 1802 Matrix | |
| 1803 Matrix::solve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, | |
| 1804 double& rcond, solve_singularity_handler sing_handler, | |
| 1805 bool singular_fallback) const | |
| 1806 { | |
| 1807 Matrix retval; | |
| 1808 int typ = mattype.type (); | |
| 1809 | |
| 1810 if (typ == MatrixType::Unknown) | |
| 1811 typ = mattype.type (*this); | |
| 1812 | |
| 1813 // Only calculate the condition number for LU/Cholesky | |
| 1814 if (typ == MatrixType::Upper || typ == MatrixType::Permuted_Upper) | |
| 1815 retval = utsolve (mattype, b, info, rcond, sing_handler, false); | |
| 1816 else if (typ == MatrixType::Lower || typ == MatrixType::Permuted_Lower) | |
| 1817 retval = ltsolve (mattype, b, info, rcond, sing_handler, false); | |
| 1818 else if (typ == MatrixType::Full || typ == MatrixType::Hermitian) | |
| 1819 retval = fsolve (mattype, b, info, rcond, sing_handler, true); | |
| 1820 else if (typ != MatrixType::Rectangular) | |
| 1821 { | |
| 1822 (*current_liboctave_error_handler) ("unknown matrix type"); | |
| 1823 return Matrix (); | |
| 1824 } | |
| 1825 | |
| 1826 // Rectangular or one of the above solvers flags a singular matrix | |
| 1827 if (singular_fallback && mattype.type () == MatrixType::Rectangular) | |
| 1828 { | |
| 1829 octave_idx_type rank; | |
| 7076 | 1830 retval = lssolve (b, info, rank, rcond); |
| 5785 | 1831 } |
| 1832 | |
| 1833 return retval; | |
| 1834 } | |
| 1835 | |
| 1836 ComplexMatrix | |
| 1837 Matrix::solve (MatrixType &typ, const ComplexMatrix& b) const | |
| 1838 { | |
| 1839 ComplexMatrix tmp (*this); | |
| 1840 return tmp.solve (typ, b); | |
| 1841 } | |
| 1842 | |
| 1843 ComplexMatrix | |
| 1844 Matrix::solve (MatrixType &typ, const ComplexMatrix& b, | |
| 1845 octave_idx_type& info) const | |
| 1846 { | |
| 1847 ComplexMatrix tmp (*this); | |
| 1848 return tmp.solve (typ, b, info); | |
| 1849 } | |
| 1850 | |
| 1851 ComplexMatrix | |
| 1852 Matrix::solve (MatrixType &typ, const ComplexMatrix& b, octave_idx_type& info, | |
| 1853 double& rcond) const | |
| 1854 { | |
| 1855 ComplexMatrix tmp (*this); | |
| 1856 return tmp.solve (typ, b, info, rcond); | |
| 1857 } | |
| 1858 | |
| 1859 ComplexMatrix | |
| 1860 Matrix::solve (MatrixType &typ, const ComplexMatrix& b, octave_idx_type& info, | |
| 1861 double& rcond, solve_singularity_handler sing_handler, | |
| 1862 bool singular_fallback) const | |
| 1863 { | |
| 1864 ComplexMatrix tmp (*this); | |
| 1865 return tmp.solve (typ, b, info, rcond, sing_handler, singular_fallback); | |
| 1866 } | |
| 1867 | |
| 1868 ColumnVector | |
| 1869 Matrix::solve (MatrixType &typ, const ColumnVector& b) const | |
| 1870 { | |
| 1871 octave_idx_type info; double rcond; | |
| 1872 return solve (typ, b, info, rcond); | |
| 1873 } | |
| 1874 | |
| 1875 ColumnVector | |
| 1876 Matrix::solve (MatrixType &typ, const ColumnVector& b, | |
| 1877 octave_idx_type& info) const | |
| 1878 { | |
| 1879 double rcond; | |
| 1880 return solve (typ, b, info, rcond); | |
| 1881 } | |
| 1882 | |
| 1883 ColumnVector | |
| 1884 Matrix::solve (MatrixType &typ, const ColumnVector& b, octave_idx_type& info, | |
| 1885 double& rcond) const | |
| 1886 { | |
| 1887 return solve (typ, b, info, rcond, 0); | |
| 1888 } | |
| 1889 | |
| 1890 ColumnVector | |
| 1891 Matrix::solve (MatrixType &typ, const ColumnVector& b, octave_idx_type& info, | |
| 1892 double& rcond, solve_singularity_handler sing_handler) const | |
| 1893 { | |
| 1894 Matrix tmp (b); | |
| 1895 return solve (typ, tmp, info, rcond, sing_handler).column(static_cast<octave_idx_type> (0)); | |
| 1896 } | |
| 1897 | |
| 1898 ComplexColumnVector | |
| 1899 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b) const | |
| 1900 { | |
| 1901 ComplexMatrix tmp (*this); | |
| 1902 return tmp.solve (typ, b); | |
| 1903 } | |
| 1904 | |
| 1905 ComplexColumnVector | |
| 1906 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, | |
| 1907 octave_idx_type& info) const | |
| 1908 { | |
| 1909 ComplexMatrix tmp (*this); | |
| 1910 return tmp.solve (typ, b, info); | |
| 1911 } | |
| 1912 | |
| 1913 ComplexColumnVector | |
| 1914 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, | |
| 1915 octave_idx_type& info, double& rcond) const | |
| 1916 { | |
| 1917 ComplexMatrix tmp (*this); | |
| 1918 return tmp.solve (typ, b, info, rcond); | |
| 1919 } | |
| 1920 | |
| 1921 ComplexColumnVector | |
| 1922 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, | |
| 1923 octave_idx_type& info, double& rcond, | |
| 1924 solve_singularity_handler sing_handler) const | |
| 1925 { | |
| 1926 ComplexMatrix tmp (*this); | |
| 1927 return tmp.solve(typ, b, info, rcond, sing_handler); | |
| 1928 } | |
| 1929 | |
| 1930 Matrix | |
| 458 | 1931 Matrix::solve (const Matrix& b) const |
| 1932 { | |
| 5275 | 1933 octave_idx_type info; |
| 458 | 1934 double rcond; |
| 4329 | 1935 return solve (b, info, rcond, 0); |
| 458 | 1936 } |
| 1937 | |
| 1938 Matrix | |
| 5275 | 1939 Matrix::solve (const Matrix& b, octave_idx_type& info) const |
| 458 | 1940 { |
| 1941 double rcond; | |
| 4329 | 1942 return solve (b, info, rcond, 0); |
| 458 | 1943 } |
| 1944 | |
| 1945 Matrix | |
| 5275 | 1946 Matrix::solve (const Matrix& b, octave_idx_type& info, double& rcond) const |
| 458 | 1947 { |
| 3480 | 1948 return solve (b, info, rcond, 0); |
| 1949 } | |
| 1950 | |
| 1951 Matrix | |
| 5785 | 1952 Matrix::solve (const Matrix& b, octave_idx_type& info, |
| 1953 double& rcond, solve_singularity_handler sing_handler) const | |
| 3480 | 1954 { |
| 5785 | 1955 MatrixType mattype (*this); |
| 1956 return solve (mattype, b, info, rcond, sing_handler); | |
| 458 | 1957 } |
| 1958 | |
| 1959 ComplexMatrix | |
| 1960 Matrix::solve (const ComplexMatrix& b) const | |
| 1961 { | |
| 1962 ComplexMatrix tmp (*this); | |
| 1963 return tmp.solve (b); | |
| 1964 } | |
| 1965 | |
| 1966 ComplexMatrix | |
| 5275 | 1967 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info) const |
| 458 | 1968 { |
| 1969 ComplexMatrix tmp (*this); | |
| 1970 return tmp.solve (b, info); | |
| 1971 } | |
| 1972 | |
| 1973 ComplexMatrix | |
| 5275 | 1974 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcond) const |
| 458 | 1975 { |
| 1976 ComplexMatrix tmp (*this); | |
| 1977 return tmp.solve (b, info, rcond); | |
| 1978 } | |
| 1979 | |
| 3480 | 1980 ComplexMatrix |
| 5275 | 1981 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcond, |
| 3480 | 1982 solve_singularity_handler sing_handler) const |
| 1983 { | |
| 1984 ComplexMatrix tmp (*this); | |
| 1985 return tmp.solve (b, info, rcond, sing_handler); | |
| 1986 } | |
| 1987 | |
| 458 | 1988 ColumnVector |
| 1989 Matrix::solve (const ColumnVector& b) const | |
| 1990 { | |
| 5275 | 1991 octave_idx_type info; double rcond; |
| 458 | 1992 return solve (b, info, rcond); |
| 1993 } | |
| 1994 | |
| 1995 ColumnVector | |
| 5275 | 1996 Matrix::solve (const ColumnVector& b, octave_idx_type& info) const |
| 458 | 1997 { |
| 1998 double rcond; | |
| 1999 return solve (b, info, rcond); | |
| 2000 } | |
| 2001 | |
| 2002 ColumnVector | |
| 5275 | 2003 Matrix::solve (const ColumnVector& b, octave_idx_type& info, double& rcond) const |
| 458 | 2004 { |
| 3480 | 2005 return solve (b, info, rcond, 0); |
| 2006 } | |
| 2007 | |
| 2008 ColumnVector | |
| 5275 | 2009 Matrix::solve (const ColumnVector& b, octave_idx_type& info, double& rcond, |
| 3480 | 2010 solve_singularity_handler sing_handler) const |
| 2011 { | |
| 5785 | 2012 MatrixType mattype (*this); |
| 2013 return solve (mattype, b, info, rcond, sing_handler); | |
| 458 | 2014 } |
| 2015 | |
| 2016 ComplexColumnVector | |
| 2017 Matrix::solve (const ComplexColumnVector& b) const | |
| 2018 { | |
| 2019 ComplexMatrix tmp (*this); | |
| 2020 return tmp.solve (b); | |
| 2021 } | |
| 2022 | |
| 2023 ComplexColumnVector | |
| 5275 | 2024 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info) const |
| 458 | 2025 { |
| 2026 ComplexMatrix tmp (*this); | |
| 2027 return tmp.solve (b, info); | |
| 2028 } | |
| 2029 | |
| 2030 ComplexColumnVector | |
| 5275 | 2031 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info, double& rcond) const |
| 458 | 2032 { |
| 2033 ComplexMatrix tmp (*this); | |
| 2034 return tmp.solve (b, info, rcond); | |
| 2035 } | |
| 2036 | |
| 3480 | 2037 ComplexColumnVector |
| 5275 | 2038 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info, double& rcond, |
| 3480 | 2039 solve_singularity_handler sing_handler) const |
| 2040 { | |
| 2041 ComplexMatrix tmp (*this); | |
| 2042 return tmp.solve (b, info, rcond, sing_handler); | |
| 2043 } | |
| 2044 | |
| 458 | 2045 Matrix |
| 2046 Matrix::lssolve (const Matrix& b) const | |
| 2047 { | |
| 5275 | 2048 octave_idx_type info; |
| 2049 octave_idx_type rank; | |
| 7076 | 2050 double rcond; |
| 2051 return lssolve (b, info, rank, rcond); | |
| 458 | 2052 } |
| 2053 | |
| 2054 Matrix | |
| 5275 | 2055 Matrix::lssolve (const Matrix& b, octave_idx_type& info) const |
| 458 | 2056 { |
| 5275 | 2057 octave_idx_type rank; |
| 7076 | 2058 double rcond; |
| 2059 return lssolve (b, info, rank, rcond); | |
| 458 | 2060 } |
| 2061 | |
| 2062 Matrix | |
| 7072 | 2063 Matrix::lssolve (const Matrix& b, octave_idx_type& info, |
| 2064 octave_idx_type& rank) const | |
| 458 | 2065 { |
| 7076 | 2066 double rcond; |
| 2067 return lssolve (b, info, rank, rcond); | |
| 2068 } | |
| 2069 | |
| 2070 Matrix | |
| 2071 Matrix::lssolve (const Matrix& b, octave_idx_type& info, | |
| 2072 octave_idx_type& rank, double &rcond) const | |
| 2073 { | |
| 1948 | 2074 Matrix retval; |
| 2075 | |
| 5275 | 2076 octave_idx_type nrhs = b.cols (); |
| 2077 | |
| 2078 octave_idx_type m = rows (); | |
| 2079 octave_idx_type n = cols (); | |
| 458 | 2080 |
| 6924 | 2081 if (m != b.rows ()) |
| 1948 | 2082 (*current_liboctave_error_handler) |
| 6924 | 2083 ("matrix dimension mismatch solution of linear equations"); |
| 2084 else if (m == 0 || n == 0 || b.cols () == 0) | |
| 2085 retval = Matrix (n, b.cols (), 0.0); | |
| 1948 | 2086 else |
| 458 | 2087 { |
| 7072 | 2088 volatile octave_idx_type minmn = (m < n ? m : n); |
| 2089 octave_idx_type maxmn = m > n ? m : n; | |
| 7076 | 2090 rcond = -1.0; |
| 7072 | 2091 if (m != n) |
| 2092 { | |
| 2093 retval = Matrix (maxmn, nrhs, 0.0); | |
| 2094 | |
| 2095 for (octave_idx_type j = 0; j < nrhs; j++) | |
| 2096 for (octave_idx_type i = 0; i < m; i++) | |
| 2097 retval.elem (i, j) = b.elem (i, j); | |
| 2098 } | |
| 2099 else | |
| 2100 retval = b; | |
| 2101 | |
| 1948 | 2102 Matrix atmp = *this; |
| 2103 double *tmp_data = atmp.fortran_vec (); | |
| 2104 | |
| 7072 | 2105 double *pretval = retval.fortran_vec (); |
| 2106 Array<double> s (minmn); | |
| 7071 | 2107 double *ps = s.fortran_vec (); |
| 1948 | 2108 |
| 7072 | 2109 // Ask DGELSD what the dimension of WORK should be. |
| 5275 | 2110 octave_idx_type lwork = -1; |
| 3752 | 2111 |
| 2112 Array<double> work (1); | |
| 1948 | 2113 |
| 11646 | 2114 octave_idx_type smlsiz; |
| 2115 F77_FUNC (xilaenv, XILAENV) (9, F77_CONST_CHAR_ARG2 ("DGELSD", 6), | |
| 2116 F77_CONST_CHAR_ARG2 (" ", 1), | |
| 2117 0, 0, 0, 0, smlsiz | |
| 2118 F77_CHAR_ARG_LEN (6) | |
| 2119 F77_CHAR_ARG_LEN (1)); | |
| 7079 | 2120 |
|
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|
2121 octave_idx_type mnthr; |
|
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parents:
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|
2122 F77_FUNC (xilaenv, XILAENV) (6, F77_CONST_CHAR_ARG2 ("DGELSD", 6), |
|
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parents:
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changeset
|
2123 F77_CONST_CHAR_ARG2 (" ", 1), |
|
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changeset
|
2124 m, n, nrhs, -1, mnthr |
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parents:
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|
2125 F77_CHAR_ARG_LEN (6) |
|
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parents:
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changeset
|
2126 F77_CHAR_ARG_LEN (1)); |
|
74de76325d12
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parents:
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changeset
|
2127 |
| 7079 | 2128 // We compute the size of iwork because DGELSD in older versions |
| 2129 // of LAPACK does not return it on a query call. | |
| 7124 | 2130 double dminmn = static_cast<double> (minmn); |
| 2131 double dsmlsizp1 = static_cast<double> (smlsiz+1); | |
| 7079 | 2132 #if defined (HAVE_LOG2) |
|
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2133 double tmp = log2 (dminmn / dsmlsizp1); |
| 7079 | 2134 #else |
|
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|
2135 double tmp = log (dminmn / dsmlsizp1) / log (2.0); |
| 7079 | 2136 #endif |
|
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2137 octave_idx_type nlvl = static_cast<octave_idx_type> (tmp) + 1; |
| 7079 | 2138 if (nlvl < 0) |
| 2139 nlvl = 0; | |
| 2140 | |
| 2141 octave_idx_type liwork = 3 * minmn * nlvl + 11 * minmn; | |
| 2142 if (liwork < 1) | |
| 2143 liwork = 1; | |
| 7072 | 2144 Array<octave_idx_type> iwork (liwork); |
| 2145 octave_idx_type* piwork = iwork.fortran_vec (); | |
| 2146 | |
| 2147 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, | |
| 2148 ps, rcond, rank, work.fortran_vec (), | |
| 2149 lwork, piwork, info)); | |
| 1948 | 2150 |
| 11640 | 2151 // The workspace query is broken in at least LAPACK 3.0.0 |
|
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|
2152 // through 3.1.1 when n >= mnthr. The obtuse formula below |
| 11640 | 2153 // should provide sufficient workspace for DGELSD to operate |
| 2154 // efficiently. | |
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|
2155 if (n >= mnthr) |
| 11640 | 2156 { |
| 2157 const octave_idx_type wlalsd | |
| 2158 = 9*m + 2*m*smlsiz + 8*m*nlvl + m*nrhs + (smlsiz+1)*(smlsiz+1); | |
| 2159 | |
| 2160 octave_idx_type addend = m; | |
| 2161 | |
| 2162 if (2*m-4 > addend) | |
| 2163 addend = 2*m-4; | |
| 2164 | |
| 2165 if (nrhs > addend) | |
| 2166 addend = nrhs; | |
| 2167 | |
| 2168 if (n-3*m > addend) | |
| 2169 addend = n-3*m; | |
| 2170 | |
| 2171 if (wlalsd > addend) | |
| 2172 addend = wlalsd; | |
| 2173 | |
| 2174 const octave_idx_type lworkaround = 4*m + m*m + addend; | |
| 2175 | |
| 2176 if (work(0) < lworkaround) | |
| 2177 work(0) = lworkaround; | |
| 2178 } | |
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2179 else if (m >= n) |
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2180 { |
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2181 octave_idx_type lworkaround |
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2182 = 12*n + 2*n*smlsiz + 8*n*nlvl + n*nrhs + (smlsiz+1)*(smlsiz+1); |
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2183 |
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2184 if (work(0) < lworkaround) |
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2185 work(0) = lworkaround; |
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2186 } |
| 11640 | 2187 |
| 1948 | 2188 if (f77_exception_encountered) |
| 7072 | 2189 (*current_liboctave_error_handler) |
| 2190 ("unrecoverable error in dgelsd"); | |
| 1948 | 2191 else |
| 2192 { | |
| 5275 | 2193 lwork = static_cast<octave_idx_type> (work(0)); |
| 3752 | 2194 work.resize (lwork); |
| 2195 | |
| 7072 | 2196 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, |
| 2197 maxmn, ps, rcond, rank, | |
| 2198 work.fortran_vec (), lwork, | |
| 2199 piwork, info)); | |
| 3752 | 2200 |
| 2201 if (f77_exception_encountered) | |
| 7072 | 2202 (*current_liboctave_error_handler) |
| 2203 ("unrecoverable error in dgelsd"); | |
| 7076 | 2204 else |
| 2205 { | |
| 2206 if (rank < minmn) | |
| 2207 (*current_liboctave_warning_handler) | |
| 2208 ("dgelsd: rank deficient %dx%d matrix, rank = %d", m, n, rank); | |
| 2209 if (s.elem (0) == 0.0) | |
| 2210 rcond = 0.0; | |
| 2211 else | |
| 2212 rcond = s.elem (minmn - 1) / s.elem (0); | |
| 7079 | 2213 |
| 2214 retval.resize (n, nrhs); | |
| 7076 | 2215 } |
| 1948 | 2216 } |
| 458 | 2217 } |
| 2218 | |
| 2219 return retval; | |
| 2220 } | |
| 2221 | |
| 2222 ComplexMatrix | |
| 2223 Matrix::lssolve (const ComplexMatrix& b) const | |
| 2224 { | |
| 2225 ComplexMatrix tmp (*this); | |
| 5275 | 2226 octave_idx_type info; |
| 2227 octave_idx_type rank; | |
| 7076 | 2228 double rcond; |
| 2229 return tmp.lssolve (b, info, rank, rcond); | |
| 458 | 2230 } |
| 2231 | |
| 2232 ComplexMatrix | |
| 5275 | 2233 Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info) const |
| 458 | 2234 { |
| 2235 ComplexMatrix tmp (*this); | |
| 5275 | 2236 octave_idx_type rank; |
| 7076 | 2237 double rcond; |
| 2238 return tmp.lssolve (b, info, rank, rcond); | |
| 458 | 2239 } |
| 2240 | |
| 2241 ComplexMatrix | |
| 7076 | 2242 Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info, |
| 2243 octave_idx_type& rank) const | |
| 458 | 2244 { |
| 2245 ComplexMatrix tmp (*this); | |
| 7076 | 2246 double rcond; |
| 2247 return tmp.lssolve (b, info, rank, rcond); | |
| 2248 } | |
| 2249 | |
| 2250 ComplexMatrix | |
| 2251 Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info, | |
| 2252 octave_idx_type& rank, double& rcond) const | |
| 2253 { | |
| 2254 ComplexMatrix tmp (*this); | |
| 2255 return tmp.lssolve (b, info, rank, rcond); | |
| 458 | 2256 } |
| 2257 | |
| 2258 ColumnVector | |
| 2259 Matrix::lssolve (const ColumnVector& b) const | |
| 2260 { | |
| 5275 | 2261 octave_idx_type info; |
| 2262 octave_idx_type rank; | |
| 7076 | 2263 double rcond; |
| 2264 return lssolve (b, info, rank, rcond); | |
| 458 | 2265 } |
| 2266 | |
| 2267 ColumnVector | |
| 5275 | 2268 Matrix::lssolve (const ColumnVector& b, octave_idx_type& info) const |
| 458 | 2269 { |
| 5275 | 2270 octave_idx_type rank; |
| 7076 | 2271 double rcond; |
| 2272 return lssolve (b, info, rank, rcond); | |
| 458 | 2273 } |
| 2274 | |
| 2275 ColumnVector | |
| 7072 | 2276 Matrix::lssolve (const ColumnVector& b, octave_idx_type& info, |
| 2277 octave_idx_type& rank) const | |
| 458 | 2278 { |
| 7076 | 2279 double rcond; |
| 2280 return lssolve (b, info, rank, rcond); | |
| 2281 } | |
| 2282 | |
| 2283 ColumnVector | |
| 2284 Matrix::lssolve (const ColumnVector& b, octave_idx_type& info, | |
| 2285 octave_idx_type& rank, double &rcond) const | |
| 2286 { | |
| 1948 | 2287 ColumnVector retval; |
| 2288 | |
| 5275 | 2289 octave_idx_type nrhs = 1; |
| 2290 | |
| 2291 octave_idx_type m = rows (); | |
| 2292 octave_idx_type n = cols (); | |
| 458 | 2293 |
| 6924 | 2294 if (m != b.length ()) |
| 1948 | 2295 (*current_liboctave_error_handler) |
| 6924 | 2296 ("matrix dimension mismatch solution of linear equations"); |
| 2297 else if (m == 0 || n == 0) | |
| 2298 retval = ColumnVector (n, 0.0); | |
| 1948 | 2299 else |
| 458 | 2300 { |
| 7072 | 2301 volatile octave_idx_type minmn = (m < n ? m : n); |
| 2302 octave_idx_type maxmn = m > n ? m : n; | |
| 7076 | 2303 rcond = -1.0; |
| 7072 | 2304 |
| 2305 if (m != n) | |
| 2306 { | |
| 2307 retval = ColumnVector (maxmn, 0.0); | |
| 2308 | |
| 2309 for (octave_idx_type i = 0; i < m; i++) | |
| 2310 retval.elem (i) = b.elem (i); | |
| 2311 } | |
| 2312 else | |
| 2313 retval = b; | |
| 2314 | |
| 1948 | 2315 Matrix atmp = *this; |
| 2316 double *tmp_data = atmp.fortran_vec (); | |
| 2317 | |
| 7072 | 2318 double *pretval = retval.fortran_vec (); |
| 2319 Array<double> s (minmn); | |
| 7071 | 2320 double *ps = s.fortran_vec (); |
| 1948 | 2321 |
| 7072 | 2322 // Ask DGELSD what the dimension of WORK should be. |
| 5275 | 2323 octave_idx_type lwork = -1; |
| 3752 | 2324 |
| 2325 Array<double> work (1); | |
| 2326 | |
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2327 octave_idx_type smlsiz; |
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2328 F77_FUNC (xilaenv, XILAENV) (9, F77_CONST_CHAR_ARG2 ("DGELSD", 6), |
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2329 F77_CONST_CHAR_ARG2 (" ", 1), |
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2330 0, 0, 0, 0, smlsiz |
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2331 F77_CHAR_ARG_LEN (6) |
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2332 F77_CHAR_ARG_LEN (1)); |
| 7079 | 2333 |
| 2334 // We compute the size of iwork because DGELSD in older versions | |
| 2335 // of LAPACK does not return it on a query call. | |
| 7124 | 2336 double dminmn = static_cast<double> (minmn); |
| 2337 double dsmlsizp1 = static_cast<double> (smlsiz+1); | |
| 7079 | 2338 #if defined (HAVE_LOG2) |
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2339 double tmp = log2 (dminmn / dsmlsizp1); |
| 7079 | 2340 #else |
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2341 double tmp = log (dminmn / dsmlsizp1) / log (2.0); |
| 7079 | 2342 #endif |
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2343 octave_idx_type nlvl = static_cast<octave_idx_type> (tmp) + 1; |
| 7079 | 2344 if (nlvl < 0) |
| 2345 nlvl = 0; | |
| 2346 | |
| 2347 octave_idx_type liwork = 3 * minmn * nlvl + 11 * minmn; | |
| 2348 if (liwork < 1) | |
| 2349 liwork = 1; | |
| 7072 | 2350 Array<octave_idx_type> iwork (liwork); |
| 2351 octave_idx_type* piwork = iwork.fortran_vec (); | |
| 2352 | |
| 2353 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, | |
| 2354 ps, rcond, rank, work.fortran_vec (), | |
| 2355 lwork, piwork, info)); | |
| 1948 | 2356 |
| 2357 if (f77_exception_encountered) | |
| 7072 | 2358 (*current_liboctave_error_handler) |
| 2359 ("unrecoverable error in dgelsd"); | |
| 1948 | 2360 else |
| 2361 { | |
| 5275 | 2362 lwork = static_cast<octave_idx_type> (work(0)); |
| 3752 | 2363 work.resize (lwork); |
| 2364 | |
| 7072 | 2365 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, |
| 2366 maxmn, ps, rcond, rank, | |
| 2367 work.fortran_vec (), lwork, | |
| 2368 piwork, info)); | |
| 3752 | 2369 |
| 2370 if (f77_exception_encountered) | |
| 7072 | 2371 (*current_liboctave_error_handler) |
| 2372 ("unrecoverable error in dgelsd"); | |
| 2373 else if (rank < minmn) | |
| 7076 | 2374 { |
| 2375 if (rank < minmn) | |
| 2376 (*current_liboctave_warning_handler) | |
| 2377 ("dgelsd: rank deficient %dx%d matrix, rank = %d", m, n, rank); | |
| 2378 if (s.elem (0) == 0.0) | |
| 2379 rcond = 0.0; | |
| 2380 else | |
| 2381 rcond = s.elem (minmn - 1) / s.elem (0); | |
| 2382 } | |
| 7079 | 2383 |
| 2384 retval.resize (n, nrhs); | |
| 1948 | 2385 } |
| 458 | 2386 } |
| 2387 | |
| 2388 return retval; | |
| 2389 } | |
| 2390 | |
| 2391 ComplexColumnVector | |
| 2392 Matrix::lssolve (const ComplexColumnVector& b) const | |
| 2393 { | |
| 2394 ComplexMatrix tmp (*this); | |
| 7076 | 2395 octave_idx_type info; |
| 2396 octave_idx_type rank; | |
| 2397 double rcond; | |
| 2398 return tmp.lssolve (b, info, rank, rcond); | |
| 458 | 2399 } |
| 2400 | |
| 2401 ComplexColumnVector | |
| 5275 | 2402 Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info) const |
| 458 | 2403 { |
| 2404 ComplexMatrix tmp (*this); | |
| 7076 | 2405 octave_idx_type rank; |
| 2406 double rcond; | |
| 2407 return tmp.lssolve (b, info, rank, rcond); | |
| 458 | 2408 } |
| 2409 | |
| 2410 ComplexColumnVector | |
| 7076 | 2411 Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, |
| 2412 octave_idx_type& rank) const | |
| 458 | 2413 { |
| 2414 ComplexMatrix tmp (*this); | |
| 7076 | 2415 double rcond; |
| 2416 return tmp.lssolve (b, info, rank, rcond); | |
| 2417 } | |
| 2418 | |
| 2419 ComplexColumnVector | |
| 2420 Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, | |
| 2421 octave_idx_type& rank, double &rcond) const | |
| 2422 { | |
| 2423 ComplexMatrix tmp (*this); | |
| 2424 return tmp.lssolve (b, info, rank, rcond); | |
| 458 | 2425 } |
| 2426 | |
| 1819 | 2427 // Constants for matrix exponential calculation. |
| 2428 | |
| 2429 static double padec [] = | |
| 2430 { | |
| 2431 5.0000000000000000e-1, | |
| 2432 1.1666666666666667e-1, | |
| 2433 1.6666666666666667e-2, | |
| 2434 1.6025641025641026e-3, | |
| 2435 1.0683760683760684e-4, | |
| 2436 4.8562548562548563e-6, | |
| 2437 1.3875013875013875e-7, | |
| 2438 1.9270852604185938e-9, | |
| 2439 }; | |
| 2440 | |
| 2441 Matrix | |
| 2442 Matrix::expm (void) const | |
| 2443 { | |
| 2444 Matrix retval; | |
| 2445 | |
| 2446 Matrix m = *this; | |
| 2447 | |
| 6699 | 2448 if (numel () == 1) |
| 2449 return Matrix (1, 1, exp (m(0))); | |
| 2450 | |
| 5275 | 2451 octave_idx_type nc = columns (); |
| 1819 | 2452 |
| 3130 | 2453 // Preconditioning step 1: trace normalization to reduce dynamic |
| 2454 // range of poles, but avoid making stable eigenvalues unstable. | |
| 2455 | |
| 1819 | 2456 // trace shift value |
| 3331 | 2457 volatile double trshift = 0.0; |
| 1819 | 2458 |
| 5275 | 2459 for (octave_idx_type i = 0; i < nc; i++) |
| 1819 | 2460 trshift += m.elem (i, i); |
| 2461 | |
| 2462 trshift /= nc; | |
| 2463 | |
| 3130 | 2464 if (trshift > 0.0) |
| 2465 { | |
| 5275 | 2466 for (octave_idx_type i = 0; i < nc; i++) |
| 3130 | 2467 m.elem (i, i) -= trshift; |
| 2468 } | |
| 1819 | 2469 |
| 3331 | 2470 // Preconditioning step 2: balancing; code follows development |
| 2471 // in AEPBAL | |
| 2472 | |
| 2473 double *p_m = m.fortran_vec (); | |
| 2474 | |
| 5275 | 2475 octave_idx_type info, ilo, ihi, ilos, ihis; |
| 3468 | 2476 Array<double> dpermute (nc); |
| 2477 Array<double> dscale (nc); | |
| 3466 | 2478 |
| 3468 | 2479 // permutation first |
| 2480 char job = 'P'; | |
| 4552 | 2481 F77_XFCN (dgebal, DGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
| 2482 nc, p_m, nc, ilo, ihi, | |
| 2483 dpermute.fortran_vec (), info | |
| 2484 F77_CHAR_ARG_LEN (1))); | |
| 3466 | 2485 |
| 3468 | 2486 // then scaling |
| 2487 job = 'S'; | |
| 4552 | 2488 F77_XFCN (dgebal, DGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
| 2489 nc, p_m, nc, ilos, ihis, | |
| 2490 dscale.fortran_vec (), info | |
| 2491 F77_CHAR_ARG_LEN (1))); | |
| 3331 | 2492 |
| 2493 if (f77_exception_encountered) | |
| 2494 { | |
| 2495 (*current_liboctave_error_handler) ("unrecoverable error in dgebal"); | |
| 2496 return retval; | |
| 2497 } | |
| 2498 | |
| 1819 | 2499 // Preconditioning step 3: scaling. |
| 3331 | 2500 |
| 1819 | 2501 ColumnVector work(nc); |
| 3130 | 2502 double inf_norm; |
| 3331 | 2503 |
| 4552 | 2504 F77_XFCN (xdlange, XDLANGE, (F77_CONST_CHAR_ARG2 ("I", 1), |
| 2505 nc, nc, m.fortran_vec (), nc, | |
| 2506 work.fortran_vec (), inf_norm | |
| 2507 F77_CHAR_ARG_LEN (1))); | |
| 3331 | 2508 |
| 2509 if (f77_exception_encountered) | |
| 2510 { | |
| 2511 (*current_liboctave_error_handler) ("unrecoverable error in dlange"); | |
| 2512 return retval; | |
| 2513 } | |
| 1819 | 2514 |
| 5275 | 2515 octave_idx_type sqpow = static_cast<octave_idx_type> (inf_norm > 0.0 |
| 1819 | 2516 ? (1.0 + log (inf_norm) / log (2.0)) |
| 2517 : 0.0); | |
| 3331 | 2518 |
| 1819 | 2519 // Check whether we need to square at all. |
| 3331 | 2520 |
| 1819 | 2521 if (sqpow < 0) |
| 2522 sqpow = 0; | |
| 3331 | 2523 |
| 1819 | 2524 if (sqpow > 0) |
| 2525 { | |
| 2526 double scale_factor = 1.0; | |
| 5275 | 2527 for (octave_idx_type i = 0; i < sqpow; i++) |
| 1819 | 2528 scale_factor *= 2.0; |
| 3331 | 2529 |
| 1819 | 2530 m = m / scale_factor; |
| 2531 } | |
| 3331 | 2532 |
| 1819 | 2533 // npp, dpp: pade' approx polynomial matrices. |
| 3331 | 2534 |
| 1819 | 2535 Matrix npp (nc, nc, 0.0); |
| 7265 | 2536 double *pnpp = npp.fortran_vec (); |
| 1819 | 2537 Matrix dpp = npp; |
| 7265 | 2538 double *pdpp = dpp.fortran_vec (); |
| 3331 | 2539 |
| 1819 | 2540 // Now powers a^8 ... a^1. |
| 3331 | 2541 |
| 5275 | 2542 octave_idx_type minus_one_j = -1; |
| 2543 for (octave_idx_type j = 7; j >= 0; j--) | |
| 1819 | 2544 { |
| 7265 | 2545 for (octave_idx_type i = 0; i < nc; i++) |
| 2546 { | |
| 2547 octave_idx_type k = i * nc + i; | |
| 2548 pnpp[k] += padec[j]; | |
| 2549 pdpp[k] += minus_one_j * padec[j]; | |
| 2550 } | |
| 2551 | |
| 2552 npp = m * npp; | |
| 2553 pnpp = npp.fortran_vec (); | |
| 2554 | |
| 2555 dpp = m * dpp; | |
| 2556 pdpp = dpp.fortran_vec (); | |
| 2557 | |
| 1819 | 2558 minus_one_j *= -1; |
| 2559 } | |
| 3331 | 2560 |
| 1819 | 2561 // Zero power. |
| 3331 | 2562 |
| 1819 | 2563 dpp = -dpp; |
| 5275 | 2564 for (octave_idx_type j = 0; j < nc; j++) |
| 1819 | 2565 { |
| 2566 npp.elem (j, j) += 1.0; | |
| 2567 dpp.elem (j, j) += 1.0; | |
| 2568 } | |
| 3331 | 2569 |
| 1819 | 2570 // Compute pade approximation = inverse (dpp) * npp. |
| 2571 | |
| 3331 | 2572 retval = dpp.solve (npp, info); |
| 2573 | |
| 1819 | 2574 // Reverse preconditioning step 3: repeated squaring. |
| 3331 | 2575 |
| 1819 | 2576 while (sqpow) |
| 2577 { | |
| 2578 retval = retval * retval; | |
| 2579 sqpow--; | |
| 2580 } | |
| 3331 | 2581 |
| 1819 | 2582 // Reverse preconditioning step 2: inverse balancing. |
| 3466 | 2583 // apply inverse scaling to computed exponential |
| 5275 | 2584 for (octave_idx_type i = 0; i < nc; i++) |
| 2585 for (octave_idx_type j = 0; j < nc; j++) | |
| 3468 | 2586 retval(i,j) *= dscale(i) / dscale(j); |
| 3466 | 2587 |
| 4153 | 2588 OCTAVE_QUIT; |
| 2589 | |
| 3466 | 2590 // construct balancing permutation vector |
| 5275 | 2591 Array<octave_idx_type> iperm (nc); |
| 2592 for (octave_idx_type i = 0; i < nc; i++) | |
| 4593 | 2593 iperm(i) = i; // identity permutation |
| 3466 | 2594 |
| 2595 // leading permutations in forward order | |
| 5275 | 2596 for (octave_idx_type i = 0; i < (ilo-1); i++) |
| 3468 | 2597 { |
| 5275 | 2598 octave_idx_type swapidx = static_cast<octave_idx_type> (dpermute(i)) - 1; |
| 2599 octave_idx_type tmp = iperm(i); | |
| 4593 | 2600 iperm(i) = iperm (swapidx); |
| 2601 iperm(swapidx) = tmp; | |
| 3468 | 2602 } |
| 3466 | 2603 |
| 2604 // trailing permutations must be done in reverse order | |
| 5275 | 2605 for (octave_idx_type i = nc - 1; i >= ihi; i--) |
| 3468 | 2606 { |
| 5275 | 2607 octave_idx_type swapidx = static_cast<octave_idx_type> (dpermute(i)) - 1; |
| 2608 octave_idx_type tmp = iperm(i); | |
| 4593 | 2609 iperm(i) = iperm(swapidx); |
| 2610 iperm(swapidx) = tmp; | |
| 3468 | 2611 } |
| 3466 | 2612 |
| 2613 // construct inverse balancing permutation vector | |
| 5275 | 2614 Array<octave_idx_type> invpvec (nc); |
| 2615 for (octave_idx_type i = 0; i < nc; i++) | |
| 4593 | 2616 invpvec(iperm(i)) = i; // Thanks to R. A. Lippert for this method |
| 4153 | 2617 |
| 2618 OCTAVE_QUIT; | |
| 3466 | 2619 |
| 2620 Matrix tmpMat = retval; | |
| 5275 | 2621 for (octave_idx_type i = 0; i < nc; i++) |
| 2622 for (octave_idx_type j = 0; j < nc; j++) | |
| 3468 | 2623 retval(i,j) = tmpMat(invpvec(i),invpvec(j)); |
| 3466 | 2624 |
| 1819 | 2625 // Reverse preconditioning step 1: fix trace normalization. |
| 3331 | 2626 |
| 3130 | 2627 if (trshift > 0.0) |
| 2628 retval = exp (trshift) * retval; | |
| 2629 | |
| 2630 return retval; | |
| 1819 | 2631 } |
| 2632 | |
| 458 | 2633 Matrix& |
| 2634 Matrix::operator += (const DiagMatrix& a) | |
| 2635 { | |
| 5275 | 2636 octave_idx_type nr = rows (); |
| 2637 octave_idx_type nc = cols (); | |
| 2638 | |
| 2639 octave_idx_type a_nr = a.rows (); | |
| 2640 octave_idx_type a_nc = a.cols (); | |
| 2385 | 2641 |
| 2642 if (nr != a_nr || nc != a_nc) | |
| 458 | 2643 { |
| 2385 | 2644 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
| 458 | 2645 return *this; |
| 2646 } | |
| 2647 | |
| 5275 | 2648 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 2649 elem (i, i) += a.elem (i, i); |
| 2650 | |
| 2651 return *this; | |
| 2652 } | |
| 2653 | |
| 2654 Matrix& | |
| 2655 Matrix::operator -= (const DiagMatrix& a) | |
| 2656 { | |
| 5275 | 2657 octave_idx_type nr = rows (); |
| 2658 octave_idx_type nc = cols (); | |
| 2659 | |
| 2660 octave_idx_type a_nr = a.rows (); | |
| 2661 octave_idx_type a_nc = a.cols (); | |
| 2385 | 2662 |
| 2663 if (nr != a_nr || nc != a_nc) | |
| 458 | 2664 { |
| 2385 | 2665 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
| 458 | 2666 return *this; |
| 2667 } | |
| 2668 | |
| 5275 | 2669 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 2670 elem (i, i) -= a.elem (i, i); |
| 2671 | |
| 2672 return *this; | |
| 2673 } | |
| 2674 | |
| 2675 // unary operations | |
| 2676 | |
| 2964 | 2677 boolMatrix |
| 458 | 2678 Matrix::operator ! (void) const |
| 2679 { | |
| 5275 | 2680 octave_idx_type nr = rows (); |
| 2681 octave_idx_type nc = cols (); | |
| 458 | 2682 |
| 2964 | 2683 boolMatrix b (nr, nc); |
| 458 | 2684 |
| 5275 | 2685 for (octave_idx_type j = 0; j < nc; j++) |
| 2686 for (octave_idx_type i = 0; i < nr; i++) | |
| 458 | 2687 b.elem (i, j) = ! elem (i, j); |
| 2688 | |
| 2689 return b; | |
| 2690 } | |
| 2691 | |
| 1205 | 2692 // column vector by row vector -> matrix operations |
| 458 | 2693 |
| 1205 | 2694 Matrix |
| 2695 operator * (const ColumnVector& v, const RowVector& a) | |
| 458 | 2696 { |
| 1948 | 2697 Matrix retval; |
| 2698 | |
| 5275 | 2699 octave_idx_type len = v.length (); |
| 3233 | 2700 |
| 2701 if (len != 0) | |
| 1205 | 2702 { |
| 5275 | 2703 octave_idx_type a_len = a.length (); |
| 3233 | 2704 |
| 2705 retval.resize (len, a_len); | |
| 2706 double *c = retval.fortran_vec (); | |
| 2707 | |
| 4552 | 2708 F77_XFCN (dgemm, DGEMM, (F77_CONST_CHAR_ARG2 ("N", 1), |
| 2709 F77_CONST_CHAR_ARG2 ("N", 1), | |
| 2710 len, a_len, 1, 1.0, v.data (), len, | |
| 2711 a.data (), 1, 0.0, c, len | |
| 2712 F77_CHAR_ARG_LEN (1) | |
| 2713 F77_CHAR_ARG_LEN (1))); | |
| 3233 | 2714 |
| 2715 if (f77_exception_encountered) | |
| 2716 (*current_liboctave_error_handler) | |
| 2717 ("unrecoverable error in dgemm"); | |
| 1205 | 2718 } |
| 458 | 2719 |
| 1948 | 2720 return retval; |
| 458 | 2721 } |
| 2722 | |
| 2723 // other operations. | |
| 2724 | |
| 2725 Matrix | |
| 2676 | 2726 Matrix::map (d_d_Mapper f) const |
| 1205 | 2727 { |
| 2676 | 2728 Matrix b (*this); |
| 2729 return b.apply (f); | |
| 1205 | 2730 } |
| 2731 | |
| 3248 | 2732 boolMatrix |
| 2733 Matrix::map (b_d_Mapper f) const | |
| 2734 { | |
| 5275 | 2735 octave_idx_type nr = rows (); |
| 2736 octave_idx_type nc = cols (); | |
| 3248 | 2737 |
| 2738 boolMatrix retval (nr, nc); | |
| 2739 | |
| 5275 | 2740 for (octave_idx_type j = 0; j < nc; j++) |
| 2741 for (octave_idx_type i = 0; i < nr; i++) | |
| 3248 | 2742 retval(i,j) = f (elem(i,j)); |
| 2743 | |
| 2744 return retval; | |
| 2745 } | |
| 2746 | |
| 2676 | 2747 Matrix& |
| 2748 Matrix::apply (d_d_Mapper f) | |
| 458 | 2749 { |
| 2750 double *d = fortran_vec (); // Ensures only one reference to my privates! | |
| 2751 | |
| 5275 | 2752 for (octave_idx_type i = 0; i < length (); i++) |
| 458 | 2753 d[i] = f (d[i]); |
| 2676 | 2754 |
| 2755 return *this; | |
| 458 | 2756 } |
| 2757 | |
| 2385 | 2758 bool |
| 4431 | 2759 Matrix::any_element_is_negative (bool neg_zero) const |
| 2385 | 2760 { |
| 5275 | 2761 octave_idx_type nel = nelem (); |
| 2385 | 2762 |
| 4431 | 2763 if (neg_zero) |
| 2764 { | |
| 5275 | 2765 for (octave_idx_type i = 0; i < nel; i++) |
| 4634 | 2766 if (lo_ieee_signbit (elem (i))) |
| 2767 return true; | |
| 4431 | 2768 } |
| 2769 else | |
| 2770 { | |
| 5275 | 2771 for (octave_idx_type i = 0; i < nel; i++) |
| 4634 | 2772 if (elem (i) < 0) |
| 2773 return true; | |
| 4431 | 2774 } |
| 2385 | 2775 |
| 2776 return false; | |
| 2777 } | |
| 2778 | |
| 2779 | |
| 2780 bool | |
| 2781 Matrix::any_element_is_inf_or_nan (void) const | |
| 2782 { | |
| 5275 | 2783 octave_idx_type nel = nelem (); |
| 2784 | |
| 2785 for (octave_idx_type i = 0; i < nel; i++) | |
| 4634 | 2786 { |
| 2787 double val = elem (i); | |
| 2788 if (xisinf (val) || xisnan (val)) | |
| 2789 return true; | |
| 2790 } | |
| 2791 | |
| 2792 return false; | |
| 2385 | 2793 } |
| 2794 | |
| 2795 bool | |
| 5943 | 2796 Matrix::any_element_not_one_or_zero (void) const |
| 2797 { | |
| 2798 octave_idx_type nel = nelem (); | |
| 2799 | |
| 2800 for (octave_idx_type i = 0; i < nel; i++) | |
| 2801 { | |
| 2802 double val = elem (i); | |
| 2803 if (val != 0 && val != 1) | |
| 2804 return true; | |
| 2805 } | |
| 2806 | |
| 2807 return false; | |
| 2808 } | |
| 2809 | |
| 2810 bool | |
| 2385 | 2811 Matrix::all_elements_are_int_or_inf_or_nan (void) const |
| 2812 { | |
| 5275 | 2813 octave_idx_type nel = nelem (); |
| 2814 | |
| 2815 for (octave_idx_type i = 0; i < nel; i++) | |
| 4634 | 2816 { |
| 2817 double val = elem (i); | |
| 2818 if (xisnan (val) || D_NINT (val) == val) | |
| 2819 continue; | |
| 2820 else | |
| 2821 return false; | |
| 2822 } | |
| 2385 | 2823 |
| 2824 return true; | |
| 2825 } | |
| 2826 | |
| 1968 | 2827 // Return nonzero if any element of M is not an integer. Also extract |
| 2828 // the largest and smallest values and return them in MAX_VAL and MIN_VAL. | |
| 2829 | |
| 2385 | 2830 bool |
| 1968 | 2831 Matrix::all_integers (double& max_val, double& min_val) const |
| 2832 { | |
| 5275 | 2833 octave_idx_type nel = nelem (); |
| 4634 | 2834 |
| 2835 if (nel > 0) | |
| 1968 | 2836 { |
| 4634 | 2837 max_val = elem (0); |
| 2838 min_val = elem (0); | |
| 1968 | 2839 } |
| 2840 else | |
| 2385 | 2841 return false; |
| 1968 | 2842 |
| 5275 | 2843 for (octave_idx_type i = 0; i < nel; i++) |
| 4634 | 2844 { |
| 2845 double val = elem (i); | |
| 2846 | |
| 2847 if (val > max_val) | |
| 2848 max_val = val; | |
| 2849 | |
| 2850 if (val < min_val) | |
| 2851 min_val = val; | |
| 2852 | |
| 2853 if (D_NINT (val) != val) | |
| 2854 return false; | |
| 2855 } | |
| 2385 | 2856 |
| 2857 return true; | |
| 1968 | 2858 } |
| 2859 | |
| 2385 | 2860 bool |
| 1968 | 2861 Matrix::too_large_for_float (void) const |
| 2862 { | |
| 5275 | 2863 octave_idx_type nel = nelem (); |
| 2864 | |
| 2865 for (octave_idx_type i = 0; i < nel; i++) | |
| 4634 | 2866 { |
| 2867 double val = elem (i); | |
| 2868 | |
| 5389 | 2869 if (! (xisnan (val) || xisinf (val)) |
| 5387 | 2870 && fabs (val) > FLT_MAX) |
| 4634 | 2871 return true; |
| 2872 } | |
| 1968 | 2873 |
| 2385 | 2874 return false; |
| 1968 | 2875 } |
| 2876 | |
| 5775 | 2877 // FIXME Do these really belong here? Maybe they should be |
| 4015 | 2878 // in a base class? |
| 458 | 2879 |
| 2832 | 2880 boolMatrix |
| 4015 | 2881 Matrix::all (int dim) const |
| 458 | 2882 { |
| 4015 | 2883 MX_ALL_OP (dim); |
| 458 | 2884 } |
| 2885 | |
| 2832 | 2886 boolMatrix |
| 4015 | 2887 Matrix::any (int dim) const |
| 458 | 2888 { |
| 4015 | 2889 MX_ANY_OP (dim); |
| 458 | 2890 } |
| 2891 | |
| 2892 Matrix | |
| 3723 | 2893 Matrix::cumprod (int dim) const |
| 458 | 2894 { |
| 4015 | 2895 MX_CUMULATIVE_OP (Matrix, double, *=); |
| 458 | 2896 } |
| 2897 | |
| 2898 Matrix | |
| 3723 | 2899 Matrix::cumsum (int dim) const |
| 458 | 2900 { |
| 4015 | 2901 MX_CUMULATIVE_OP (Matrix, double, +=); |
| 458 | 2902 } |
| 2903 | |
| 2904 Matrix | |
| 3723 | 2905 Matrix::prod (int dim) const |
| 458 | 2906 { |
| 3864 | 2907 MX_REDUCTION_OP (Matrix, *=, 1.0, 1.0); |
| 458 | 2908 } |
| 2909 | |
| 2910 Matrix | |
| 3723 | 2911 Matrix::sum (int dim) const |
| 458 | 2912 { |
| 3864 | 2913 MX_REDUCTION_OP (Matrix, +=, 0.0, 0.0); |
| 458 | 2914 } |
| 2915 | |
| 2916 Matrix | |
| 3723 | 2917 Matrix::sumsq (int dim) const |
| 458 | 2918 { |
| 3864 | 2919 #define ROW_EXPR \ |
| 2920 double d = elem (i, j); \ | |
| 2921 retval.elem (i, 0) += d * d | |
| 2922 | |
| 2923 #define COL_EXPR \ | |
| 2924 double d = elem (i, j); \ | |
| 2925 retval.elem (0, j) += d * d | |
| 2926 | |
| 2927 MX_BASE_REDUCTION_OP (Matrix, ROW_EXPR, COL_EXPR, 0.0, 0.0); | |
| 2928 | |
| 2929 #undef ROW_EXPR | |
| 2930 #undef COL_EXPR | |
| 458 | 2931 } |
| 2932 | |
| 2385 | 2933 Matrix |
| 2934 Matrix::abs (void) const | |
| 2935 { | |
| 5275 | 2936 octave_idx_type nr = rows (); |
| 2937 octave_idx_type nc = cols (); | |
| 2385 | 2938 |
| 2939 Matrix retval (nr, nc); | |
| 2940 | |
| 5275 | 2941 for (octave_idx_type j = 0; j < nc; j++) |
| 2942 for (octave_idx_type i = 0; i < nr; i++) | |
| 2385 | 2943 retval (i, j) = fabs (elem (i, j)); |
| 2944 | |
| 2945 return retval; | |
| 2946 } | |
| 2947 | |
| 458 | 2948 ColumnVector |
| 2949 Matrix::diag (void) const | |
| 2950 { | |
| 2951 return diag (0); | |
| 2952 } | |
| 2953 | |
| 2954 ColumnVector | |
| 5275 | 2955 Matrix::diag (octave_idx_type k) const |
| 458 | 2956 { |
| 5275 | 2957 octave_idx_type nnr = rows (); |
| 2958 octave_idx_type nnc = cols (); | |
| 458 | 2959 if (k > 0) |
| 2960 nnc -= k; | |
| 2961 else if (k < 0) | |
| 2962 nnr += k; | |
| 2963 | |
| 2964 ColumnVector d; | |
| 2965 | |
| 2966 if (nnr > 0 && nnc > 0) | |
| 2967 { | |
| 5275 | 2968 octave_idx_type ndiag = (nnr < nnc) ? nnr : nnc; |
| 458 | 2969 |
| 2970 d.resize (ndiag); | |
| 2971 | |
| 2972 if (k > 0) | |
| 2973 { | |
| 5275 | 2974 for (octave_idx_type i = 0; i < ndiag; i++) |
| 458 | 2975 d.elem (i) = elem (i, i+k); |
| 2976 } | |
| 4509 | 2977 else if (k < 0) |
| 458 | 2978 { |
| 5275 | 2979 for (octave_idx_type i = 0; i < ndiag; i++) |
| 458 | 2980 d.elem (i) = elem (i-k, i); |
| 2981 } | |
| 2982 else | |
| 2983 { | |
| 5275 | 2984 for (octave_idx_type i = 0; i < ndiag; i++) |
| 458 | 2985 d.elem (i) = elem (i, i); |
| 2986 } | |
| 2987 } | |
| 2988 else | |
| 4513 | 2989 (*current_liboctave_error_handler) |
| 2990 ("diag: requested diagonal out of range"); | |
| 458 | 2991 |
| 2992 return d; | |
| 2993 } | |
| 2994 | |
| 2995 ColumnVector | |
| 2996 Matrix::row_min (void) const | |
| 2997 { | |
| 5275 | 2998 Array<octave_idx_type> dummy_idx; |
| 4587 | 2999 return row_min (dummy_idx); |
| 458 | 3000 } |
| 3001 | |
| 3002 ColumnVector | |
| 5275 | 3003 Matrix::row_min (Array<octave_idx_type>& idx_arg) const |
| 458 | 3004 { |
| 3005 ColumnVector result; | |
| 3006 | |
| 5275 | 3007 octave_idx_type nr = rows (); |
| 3008 octave_idx_type nc = cols (); | |
| 458 | 3009 |
| 3010 if (nr > 0 && nc > 0) | |
| 3011 { | |
| 3012 result.resize (nr); | |
| 4587 | 3013 idx_arg.resize (nr); |
| 458 | 3014 |
| 5275 | 3015 for (octave_idx_type i = 0; i < nr; i++) |
| 458 | 3016 { |
| 5275 | 3017 octave_idx_type idx_j; |
| 4469 | 3018 |
| 3019 double tmp_min = octave_NaN; | |
| 3020 | |
| 3021 for (idx_j = 0; idx_j < nc; idx_j++) | |
| 2354 | 3022 { |
| 4469 | 3023 tmp_min = elem (i, idx_j); |
| 3024 | |
| 5389 | 3025 if (! xisnan (tmp_min)) |
| 4469 | 3026 break; |
| 3027 } | |
| 3028 | |
| 5275 | 3029 for (octave_idx_type j = idx_j+1; j < nc; j++) |
| 4469 | 3030 { |
| 3031 double tmp = elem (i, j); | |
| 3032 | |
| 5389 | 3033 if (xisnan (tmp)) |
| 4469 | 3034 continue; |
| 3035 else if (tmp < tmp_min) | |
| 2354 | 3036 { |
| 4469 | 3037 idx_j = j; |
| 3038 tmp_min = tmp; | |
| 2354 | 3039 } |
| 3040 } | |
| 3041 | |
| 4469 | 3042 result.elem (i) = tmp_min; |
| 5389 | 3043 idx_arg.elem (i) = xisnan (tmp_min) ? 0 : idx_j; |
| 458 | 3044 } |
| 3045 } | |
| 3046 | |
| 3047 return result; | |
| 3048 } | |
| 3049 | |
| 3050 ColumnVector | |
| 3051 Matrix::row_max (void) const | |
| 3052 { | |
| 5275 | 3053 Array<octave_idx_type> dummy_idx; |
| 4587 | 3054 return row_max (dummy_idx); |
| 458 | 3055 } |
| 3056 | |
| 3057 ColumnVector | |
| 5275 | 3058 Matrix::row_max (Array<octave_idx_type>& idx_arg) const |
| 458 | 3059 { |
| 3060 ColumnVector result; | |
| 3061 | |
| 5275 | 3062 octave_idx_type nr = rows (); |
| 3063 octave_idx_type nc = cols (); | |
| 458 | 3064 |
| 3065 if (nr > 0 && nc > 0) | |
| 3066 { | |
| 3067 result.resize (nr); | |
| 4587 | 3068 idx_arg.resize (nr); |
| 458 | 3069 |
| 5275 | 3070 for (octave_idx_type i = 0; i < nr; i++) |
| 458 | 3071 { |
| 5275 | 3072 octave_idx_type idx_j; |
| 4469 | 3073 |
| 3074 double tmp_max = octave_NaN; | |
| 3075 | |
| 3076 for (idx_j = 0; idx_j < nc; idx_j++) | |
| 2354 | 3077 { |
| 4469 | 3078 tmp_max = elem (i, idx_j); |
| 3079 | |
| 5389 | 3080 if (! xisnan (tmp_max)) |
| 4469 | 3081 break; |
| 3082 } | |
| 3083 | |
| 5275 | 3084 for (octave_idx_type j = idx_j+1; j < nc; j++) |
| 4469 | 3085 { |
| 3086 double tmp = elem (i, j); | |
| 3087 | |
| 5389 | 3088 if (xisnan (tmp)) |
| 4469 | 3089 continue; |
| 3090 else if (tmp > tmp_max) | |
| 2354 | 3091 { |
| 4469 | 3092 idx_j = j; |
| 3093 tmp_max = tmp; | |
| 2354 | 3094 } |
| 3095 } | |
| 3096 | |
| 4469 | 3097 result.elem (i) = tmp_max; |
| 5389 | 3098 idx_arg.elem (i) = xisnan (tmp_max) ? 0 : idx_j; |
| 458 | 3099 } |
| 3100 } | |
| 3101 | |
| 3102 return result; | |
| 3103 } | |
| 3104 | |
| 3105 RowVector | |
| 3106 Matrix::column_min (void) const | |
| 3107 { | |
| 5275 | 3108 Array<octave_idx_type> dummy_idx; |
| 4587 | 3109 return column_min (dummy_idx); |
| 458 | 3110 } |
| 2354 | 3111 |
| 458 | 3112 RowVector |
| 5275 | 3113 Matrix::column_min (Array<octave_idx_type>& idx_arg) const |
| 458 | 3114 { |
| 3115 RowVector result; | |
| 3116 | |
| 5275 | 3117 octave_idx_type nr = rows (); |
| 3118 octave_idx_type nc = cols (); | |
| 458 | 3119 |
| 3120 if (nr > 0 && nc > 0) | |
| 3121 { | |
| 3122 result.resize (nc); | |
| 4587 | 3123 idx_arg.resize (nc); |
| 458 | 3124 |
| 5275 | 3125 for (octave_idx_type j = 0; j < nc; j++) |
| 458 | 3126 { |
| 5275 | 3127 octave_idx_type idx_i; |
| 4469 | 3128 |
| 3129 double tmp_min = octave_NaN; | |
| 3130 | |
| 3131 for (idx_i = 0; idx_i < nr; idx_i++) | |
| 2354 | 3132 { |
| 4469 | 3133 tmp_min = elem (idx_i, j); |
| 3134 | |
| 5389 | 3135 if (! xisnan (tmp_min)) |
| 4469 | 3136 break; |
| 3137 } | |
| 3138 | |
| 5275 | 3139 for (octave_idx_type i = idx_i+1; i < nr; i++) |
| 4469 | 3140 { |
| 3141 double tmp = elem (i, j); | |
| 3142 | |
| 5389 | 3143 if (xisnan (tmp)) |
| 4469 | 3144 continue; |
| 3145 else if (tmp < tmp_min) | |
| 2354 | 3146 { |
| 4469 | 3147 idx_i = i; |
| 3148 tmp_min = tmp; | |
| 2354 | 3149 } |
| 3150 } | |
| 3151 | |
| 4469 | 3152 result.elem (j) = tmp_min; |
| 5389 | 3153 idx_arg.elem (j) = xisnan (tmp_min) ? 0 : idx_i; |
| 458 | 3154 } |
| 3155 } | |
| 3156 | |
| 3157 return result; | |
| 3158 } | |
| 3159 | |
| 2354 | 3160 RowVector |
| 3161 Matrix::column_max (void) const | |
| 3162 { | |
| 5275 | 3163 Array<octave_idx_type> dummy_idx; |
| 4587 | 3164 return column_max (dummy_idx); |
| 2354 | 3165 } |
| 458 | 3166 |
| 3167 RowVector | |
| 5275 | 3168 Matrix::column_max (Array<octave_idx_type>& idx_arg) const |
| 458 | 3169 { |
| 3170 RowVector result; | |
| 3171 | |
| 5275 | 3172 octave_idx_type nr = rows (); |
| 3173 octave_idx_type nc = cols (); | |
| 458 | 3174 |
| 3175 if (nr > 0 && nc > 0) | |
| 3176 { | |
| 3177 result.resize (nc); | |
| 4587 | 3178 idx_arg.resize (nc); |
| 458 | 3179 |
| 5275 | 3180 for (octave_idx_type j = 0; j < nc; j++) |
| 458 | 3181 { |
| 5275 | 3182 octave_idx_type idx_i; |
| 4469 | 3183 |
| 3184 double tmp_max = octave_NaN; | |
| 3185 | |
| 3186 for (idx_i = 0; idx_i < nr; idx_i++) | |
| 2354 | 3187 { |
| 4469 | 3188 tmp_max = elem (idx_i, j); |
| 3189 | |
| 5389 | 3190 if (! xisnan (tmp_max)) |
| 4469 | 3191 break; |
| 3192 } | |
| 3193 | |
| 5275 | 3194 for (octave_idx_type i = idx_i+1; i < nr; i++) |
| 4469 | 3195 { |
| 3196 double tmp = elem (i, j); | |
| 3197 | |
| 5389 | 3198 if (xisnan (tmp)) |
| 4469 | 3199 continue; |
| 3200 else if (tmp > tmp_max) | |
| 2354 | 3201 { |
| 4469 | 3202 idx_i = i; |
| 3203 tmp_max = tmp; | |
| 2354 | 3204 } |
| 3205 } | |
| 3206 | |
| 4469 | 3207 result.elem (j) = tmp_max; |
| 5389 | 3208 idx_arg.elem (j) = xisnan (tmp_max) ? 0 : idx_i; |
| 458 | 3209 } |
| 3210 } | |
| 3211 | |
| 3212 return result; | |
| 3213 } | |
| 3214 | |
| 3504 | 3215 std::ostream& |
| 3216 operator << (std::ostream& os, const Matrix& a) | |
| 458 | 3217 { |
| 5275 | 3218 for (octave_idx_type i = 0; i < a.rows (); i++) |
| 458 | 3219 { |
| 5275 | 3220 for (octave_idx_type j = 0; j < a.cols (); j++) |
| 4130 | 3221 { |
| 3222 os << " "; | |
| 3223 octave_write_double (os, a.elem (i, j)); | |
| 3224 } | |
| 458 | 3225 os << "\n"; |
| 3226 } | |
| 3227 return os; | |
| 3228 } | |
| 3229 | |
| 3504 | 3230 std::istream& |
| 3231 operator >> (std::istream& is, Matrix& a) | |
| 458 | 3232 { |
| 5275 | 3233 octave_idx_type nr = a.rows (); |
| 3234 octave_idx_type nc = a.cols (); | |
| 458 | 3235 |
| 3236 if (nr < 1 || nc < 1) | |
| 3504 | 3237 is.clear (std::ios::badbit); |
| 458 | 3238 else |
| 3239 { | |
| 3240 double tmp; | |
| 5275 | 3241 for (octave_idx_type i = 0; i < nr; i++) |
| 3242 for (octave_idx_type j = 0; j < nc; j++) | |
| 458 | 3243 { |
| 4130 | 3244 tmp = octave_read_double (is); |
| 458 | 3245 if (is) |
| 3246 a.elem (i, j) = tmp; | |
| 3247 else | |
| 2795 | 3248 goto done; |
| 458 | 3249 } |
| 3250 } | |
| 3251 | |
| 2795 | 3252 done: |
| 3253 | |
| 458 | 3254 return is; |
| 3255 } | |
| 3256 | |
| 1819 | 3257 Matrix |
| 3258 Givens (double x, double y) | |
| 3259 { | |
| 3260 double cc, s, temp_r; | |
| 3261 | |
| 3887 | 3262 F77_FUNC (dlartg, DLARTG) (x, y, cc, s, temp_r); |
| 1819 | 3263 |
| 3264 Matrix g (2, 2); | |
| 3265 | |
| 3266 g.elem (0, 0) = cc; | |
| 3267 g.elem (1, 1) = cc; | |
| 3268 g.elem (0, 1) = s; | |
| 3269 g.elem (1, 0) = -s; | |
| 3270 | |
| 3271 return g; | |
| 3272 } | |
| 3273 | |
| 3274 Matrix | |
| 3275 Sylvester (const Matrix& a, const Matrix& b, const Matrix& c) | |
| 3276 { | |
| 3277 Matrix retval; | |
| 3278 | |
| 5775 | 3279 // FIXME -- need to check that a, b, and c are all the same |
| 1819 | 3280 // size. |
| 3281 | |
| 3282 // Compute Schur decompositions. | |
| 3283 | |
| 3284 SCHUR as (a, "U"); | |
| 3285 SCHUR bs (b, "U"); | |
| 3286 | |
| 3287 // Transform c to new coordinates. | |
| 3288 | |
| 3289 Matrix ua = as.unitary_matrix (); | |
| 3290 Matrix sch_a = as.schur_matrix (); | |
| 3291 | |
| 3292 Matrix ub = bs.unitary_matrix (); | |
| 3293 Matrix sch_b = bs.schur_matrix (); | |
| 3294 | |
| 3295 Matrix cx = ua.transpose () * c * ub; | |
| 3296 | |
| 3297 // Solve the sylvester equation, back-transform, and return the | |
| 3298 // solution. | |
| 3299 | |
| 5275 | 3300 octave_idx_type a_nr = a.rows (); |
| 3301 octave_idx_type b_nr = b.rows (); | |
| 1819 | 3302 |
| 3303 double scale; | |
| 5275 | 3304 octave_idx_type info; |
| 1819 | 3305 |
| 1950 | 3306 double *pa = sch_a.fortran_vec (); |
| 3307 double *pb = sch_b.fortran_vec (); | |
| 3308 double *px = cx.fortran_vec (); | |
| 3309 | |
| 4552 | 3310 F77_XFCN (dtrsyl, DTRSYL, (F77_CONST_CHAR_ARG2 ("N", 1), |
| 3311 F77_CONST_CHAR_ARG2 ("N", 1), | |
| 3312 1, a_nr, b_nr, pa, a_nr, pb, | |
| 3313 b_nr, px, a_nr, scale, info | |
| 3314 F77_CHAR_ARG_LEN (1) | |
| 3315 F77_CHAR_ARG_LEN (1))); | |
| 1950 | 3316 |
| 3317 | |
| 3318 if (f77_exception_encountered) | |
| 3319 (*current_liboctave_error_handler) ("unrecoverable error in dtrsyl"); | |
| 3320 else | |
| 3321 { | |
| 5775 | 3322 // FIXME -- check info? |
| 1819 | 3323 |
| 1950 | 3324 retval = -ua*cx*ub.transpose (); |
| 3325 } | |
| 1819 | 3326 |
| 3327 return retval; | |
| 3328 } | |
| 3329 | |
| 2828 | 3330 // matrix by matrix -> matrix operations |
| 3331 | |
| 6162 | 3332 /* Simple Dot Product, Matrix-Vector and Matrix-Matrix Unit tests |
| 3333 %!assert([1 2 3] * [ 4 ; 5 ; 6], 32, 1e-14) | |
| 3334 %!assert([1 2 ; 3 4 ] * [5 ; 6], [17 ; 39 ], 1e-14) | |
| 3335 %!assert([1 2 ; 3 4 ] * [5 6 ; 7 8], [19 22; 43 50], 1e-14) | |
| 3336 */ | |
| 3337 | |
| 3338 /* Test some simple identities | |
| 3339 %!shared M, cv, rv | |
| 3340 %! M = randn(10,10); | |
| 3341 %! cv = randn(10,1); | |
| 3342 %! rv = randn(1,10); | |
| 3343 %!assert([M*cv,M*cv],M*[cv,cv],1e-14) | |
| 3344 %!assert([rv*M;rv*M],[rv;rv]*M,1e-14) | |
| 3345 %!assert(2*rv*cv,[rv,rv]*[cv;cv],1e-14) | |
| 3346 */ | |
| 3347 | |
| 3348 | |
| 2828 | 3349 Matrix |
| 3350 operator * (const Matrix& m, const Matrix& a) | |
| 3351 { | |
| 3352 Matrix retval; | |
| 3353 | |
| 5275 | 3354 octave_idx_type nr = m.rows (); |
| 3355 octave_idx_type nc = m.cols (); | |
| 3356 | |
| 3357 octave_idx_type a_nr = a.rows (); | |
| 3358 octave_idx_type a_nc = a.cols (); | |
| 2828 | 3359 |
| 3360 if (nc != a_nr) | |
| 3361 gripe_nonconformant ("operator *", nr, nc, a_nr, a_nc); | |
| 3362 else | |
| 3363 { | |
| 3364 if (nr == 0 || nc == 0 || a_nc == 0) | |
| 3365 retval.resize (nr, a_nc, 0.0); | |
| 3366 else | |
| 3367 { | |
| 5275 | 3368 octave_idx_type ld = nr; |
| 3369 octave_idx_type lda = a_nr; | |
| 2828 | 3370 |
| 3371 retval.resize (nr, a_nc); | |
| 3372 double *c = retval.fortran_vec (); | |
| 3373 | |
| 5983 | 3374 if (a_nc == 1) |
| 3375 { | |
| 3376 if (nr == 1) | |
| 3377 F77_FUNC (xddot, XDDOT) (nc, m.data (), 1, a.data (), 1, *c); | |
| 3378 else | |
| 6390 | 3379 { |
| 3380 F77_XFCN (dgemv, DGEMV, (F77_CONST_CHAR_ARG2 ("N", 1), | |
| 3381 nr, nc, 1.0, m.data (), ld, | |
| 3382 a.data (), 1, 0.0, c, 1 | |
| 3383 F77_CHAR_ARG_LEN (1))); | |
| 3384 | |
| 3385 if (f77_exception_encountered) | |
| 3386 (*current_liboctave_error_handler) | |
| 3387 ("unrecoverable error in dgemv"); | |
| 3388 } | |
| 5983 | 3389 } |
| 3390 else | |
| 6390 | 3391 { |
| 3392 F77_XFCN (dgemm, DGEMM, (F77_CONST_CHAR_ARG2 ("N", 1), | |
| 3393 F77_CONST_CHAR_ARG2 ("N", 1), | |
| 3394 nr, a_nc, nc, 1.0, m.data (), | |
| 3395 ld, a.data (), lda, 0.0, c, nr | |
| 3396 F77_CHAR_ARG_LEN (1) | |
| 3397 F77_CHAR_ARG_LEN (1))); | |
| 3398 | |
| 3399 if (f77_exception_encountered) | |
| 3400 (*current_liboctave_error_handler) | |
| 3401 ("unrecoverable error in dgemm"); | |
| 3402 } | |
| 2828 | 3403 } |
| 3404 } | |
| 3405 | |
| 3406 return retval; | |
| 3407 } | |
| 3408 | |
| 5775 | 3409 // FIXME -- it would be nice to share code among the min/max |
| 4309 | 3410 // functions below. |
| 3411 | |
| 3412 #define EMPTY_RETURN_CHECK(T) \ | |
| 3413 if (nr == 0 || nc == 0) \ | |
| 3414 return T (nr, nc); | |
| 3415 | |
| 3416 Matrix | |
| 3417 min (double d, const Matrix& m) | |
| 3418 { | |
| 5275 | 3419 octave_idx_type nr = m.rows (); |
| 3420 octave_idx_type nc = m.columns (); | |
| 4309 | 3421 |
| 3422 EMPTY_RETURN_CHECK (Matrix); | |
| 3423 | |
| 3424 Matrix result (nr, nc); | |
| 3425 | |
| 5275 | 3426 for (octave_idx_type j = 0; j < nc; j++) |
| 3427 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3428 { |
| 3429 OCTAVE_QUIT; | |
| 3430 result (i, j) = xmin (d, m (i, j)); | |
| 3431 } | |
| 3432 | |
| 3433 return result; | |
| 3434 } | |
| 3435 | |
| 3436 Matrix | |
| 3437 min (const Matrix& m, double d) | |
| 3438 { | |
| 5275 | 3439 octave_idx_type nr = m.rows (); |
| 3440 octave_idx_type nc = m.columns (); | |
| 4309 | 3441 |
| 3442 EMPTY_RETURN_CHECK (Matrix); | |
| 3443 | |
| 3444 Matrix result (nr, nc); | |
| 3445 | |
| 5275 | 3446 for (octave_idx_type j = 0; j < nc; j++) |
| 3447 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3448 { |
| 3449 OCTAVE_QUIT; | |
| 3450 result (i, j) = xmin (m (i, j), d); | |
| 3451 } | |
| 3452 | |
| 3453 return result; | |
| 3454 } | |
| 3455 | |
| 3456 Matrix | |
| 3457 min (const Matrix& a, const Matrix& b) | |
| 3458 { | |
| 5275 | 3459 octave_idx_type nr = a.rows (); |
| 3460 octave_idx_type nc = a.columns (); | |
| 4309 | 3461 |
| 3462 if (nr != b.rows () || nc != b.columns ()) | |
| 3463 { | |
| 3464 (*current_liboctave_error_handler) | |
| 3465 ("two-arg min expecting args of same size"); | |
| 3466 return Matrix (); | |
| 3467 } | |
| 3468 | |
| 3469 EMPTY_RETURN_CHECK (Matrix); | |
| 3470 | |
| 3471 Matrix result (nr, nc); | |
| 3472 | |
| 5275 | 3473 for (octave_idx_type j = 0; j < nc; j++) |
| 3474 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3475 { |
| 3476 OCTAVE_QUIT; | |
| 3477 result (i, j) = xmin (a (i, j), b (i, j)); | |
| 3478 } | |
| 3479 | |
| 3480 return result; | |
| 3481 } | |
| 3482 | |
| 3483 Matrix | |
| 3484 max (double d, const Matrix& m) | |
| 3485 { | |
| 5275 | 3486 octave_idx_type nr = m.rows (); |
| 3487 octave_idx_type nc = m.columns (); | |
| 4309 | 3488 |
| 3489 EMPTY_RETURN_CHECK (Matrix); | |
| 3490 | |
| 3491 Matrix result (nr, nc); | |
| 3492 | |
| 5275 | 3493 for (octave_idx_type j = 0; j < nc; j++) |
| 3494 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3495 { |
| 3496 OCTAVE_QUIT; | |
| 3497 result (i, j) = xmax (d, m (i, j)); | |
| 3498 } | |
| 3499 | |
| 3500 return result; | |
| 3501 } | |
| 3502 | |
| 3503 Matrix | |
| 3504 max (const Matrix& m, double d) | |
| 3505 { | |
| 5275 | 3506 octave_idx_type nr = m.rows (); |
| 3507 octave_idx_type nc = m.columns (); | |
| 4309 | 3508 |
| 3509 EMPTY_RETURN_CHECK (Matrix); | |
| 3510 | |
| 3511 Matrix result (nr, nc); | |
| 3512 | |
| 5275 | 3513 for (octave_idx_type j = 0; j < nc; j++) |
| 3514 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3515 { |
| 3516 OCTAVE_QUIT; | |
| 3517 result (i, j) = xmax (m (i, j), d); | |
| 3518 } | |
| 3519 | |
| 3520 return result; | |
| 3521 } | |
| 3522 | |
| 3523 Matrix | |
| 3524 max (const Matrix& a, const Matrix& b) | |
| 3525 { | |
| 5275 | 3526 octave_idx_type nr = a.rows (); |
| 3527 octave_idx_type nc = a.columns (); | |
| 4309 | 3528 |
| 3529 if (nr != b.rows () || nc != b.columns ()) | |
| 3530 { | |
| 3531 (*current_liboctave_error_handler) | |
| 3532 ("two-arg max expecting args of same size"); | |
| 3533 return Matrix (); | |
| 3534 } | |
| 3535 | |
| 3536 EMPTY_RETURN_CHECK (Matrix); | |
| 3537 | |
| 3538 Matrix result (nr, nc); | |
| 3539 | |
| 5275 | 3540 for (octave_idx_type j = 0; j < nc; j++) |
| 3541 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3542 { |
| 3543 OCTAVE_QUIT; | |
| 3544 result (i, j) = xmax (a (i, j), b (i, j)); | |
| 3545 } | |
| 3546 | |
| 3547 return result; | |
| 3548 } | |
| 3549 | |
| 2870 | 3550 MS_CMP_OPS(Matrix, , double, ) |
| 3504 | 3551 MS_BOOL_OPS(Matrix, double, 0.0) |
| 2870 | 3552 |
| 3553 SM_CMP_OPS(double, , Matrix, ) | |
| 3504 | 3554 SM_BOOL_OPS(double, Matrix, 0.0) |
| 2870 | 3555 |
| 3556 MM_CMP_OPS(Matrix, , Matrix, ) | |
| 3504 | 3557 MM_BOOL_OPS(Matrix, Matrix, 0.0) |
| 2870 | 3558 |
| 458 | 3559 /* |
| 3560 ;;; Local Variables: *** | |
| 3561 ;;; mode: C++ *** | |
| 3562 ;;; End: *** | |
| 3563 */ |