Mercurial > hg > octave-lyh
annotate liboctave/dMatrix.cc @ 8211:851803f7bb4d
improve inverse preconditioning according to Marco Caliari
| author | Jaroslav Hajek <highegg@gmail.com> |
|---|---|
| date | Sun, 12 Oct 2008 08:44:55 +0200 |
| parents | 935be827eaf8 |
| children | 64cf956a109c |
| 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 | |
| 7803 | 6 Copyright (C) 2008 Jaroslav Hajek |
| 458 | 7 |
| 8 This file is part of Octave. | |
| 9 | |
| 10 Octave is free software; you can redistribute it and/or modify it | |
| 11 under the terms of the GNU General Public License as published by the | |
| 7016 | 12 Free Software Foundation; either version 3 of the License, or (at your |
| 13 option) any later version. | |
| 458 | 14 |
| 15 Octave is distributed in the hope that it will be useful, but WITHOUT | |
| 16 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
| 17 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
| 18 for more details. | |
| 19 | |
| 20 You should have received a copy of the GNU General Public License | |
| 7016 | 21 along with Octave; see the file COPYING. If not, see |
| 22 <http://www.gnu.org/licenses/>. | |
| 458 | 23 |
| 24 */ | |
| 25 | |
| 26 #ifdef HAVE_CONFIG_H | |
| 1192 | 27 #include <config.h> |
| 458 | 28 #endif |
| 29 | |
| 1367 | 30 #include <cfloat> |
| 31 | |
| 3503 | 32 #include <iostream> |
| 6209 | 33 #include <vector> |
| 1367 | 34 |
| 4669 | 35 #include "Array-util.h" |
| 2317 | 36 #include "byte-swap.h" |
| 2828 | 37 #include "dMatrix.h" |
| 1819 | 38 #include "dbleAEPBAL.h" |
| 458 | 39 #include "dbleDET.h" |
| 1819 | 40 #include "dbleSCHUR.h" |
| 740 | 41 #include "dbleSVD.h" |
| 6207 | 42 #include "dbleCHOL.h" |
| 1847 | 43 #include "f77-fcn.h" |
|
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44 #include "functor.h" |
| 458 | 45 #include "lo-error.h" |
| 2354 | 46 #include "lo-ieee.h" |
| 47 #include "lo-mappers.h" | |
| 1968 | 48 #include "lo-utils.h" |
| 1367 | 49 #include "mx-base.h" |
| 2828 | 50 #include "mx-m-dm.h" |
| 3176 | 51 #include "mx-dm-m.h" |
| 1367 | 52 #include "mx-inlines.cc" |
| 1650 | 53 #include "oct-cmplx.h" |
| 4153 | 54 #include "quit.h" |
| 458 | 55 |
| 4773 | 56 #if defined (HAVE_FFTW3) |
| 3827 | 57 #include "oct-fftw.h" |
| 58 #endif | |
| 59 | |
| 458 | 60 // Fortran functions we call. |
| 61 | |
| 62 extern "C" | |
| 63 { | |
| 7478 | 64 F77_RET_T |
| 7477 | 65 F77_FUNC (xilaenv, XILAENV) (const octave_idx_type&, F77_CONST_CHAR_ARG_DECL, |
| 66 F77_CONST_CHAR_ARG_DECL, | |
| 67 const octave_idx_type&, const octave_idx_type&, | |
| 7478 | 68 const octave_idx_type&, const octave_idx_type&, |
| 69 octave_idx_type& | |
| 70 F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); | |
| 7476 | 71 |
| 4552 | 72 F77_RET_T |
| 73 F77_FUNC (dgebal, DGEBAL) (F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 74 const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type&, |
| 75 octave_idx_type&, double*, octave_idx_type& | |
| 4552 | 76 F77_CHAR_ARG_LEN_DECL); |
| 77 | |
| 78 F77_RET_T | |
| 79 F77_FUNC (dgebak, DGEBAK) (F77_CONST_CHAR_ARG_DECL, | |
| 80 F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 81 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, double*, |
| 82 const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type& | |
| 4552 | 83 F77_CHAR_ARG_LEN_DECL |
| 84 F77_CHAR_ARG_LEN_DECL); | |
| 85 | |
| 86 | |
| 87 F77_RET_T | |
| 88 F77_FUNC (dgemm, DGEMM) (F77_CONST_CHAR_ARG_DECL, | |
| 89 F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 90 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
| 91 const double&, const double*, const octave_idx_type&, | |
| 92 const double*, const octave_idx_type&, const double&, | |
| 93 double*, const octave_idx_type& | |
| 4552 | 94 F77_CHAR_ARG_LEN_DECL |
| 95 F77_CHAR_ARG_LEN_DECL); | |
| 96 | |
| 97 F77_RET_T | |
| 5983 | 98 F77_FUNC (dgemv, DGEMV) (F77_CONST_CHAR_ARG_DECL, |
| 99 const octave_idx_type&, const octave_idx_type&, const double&, | |
| 100 const double*, const octave_idx_type&, const double*, | |
| 101 const octave_idx_type&, const double&, double*, | |
| 102 const octave_idx_type& | |
| 103 F77_CHAR_ARG_LEN_DECL); | |
| 104 | |
| 105 F77_RET_T | |
| 106 F77_FUNC (xddot, XDDOT) (const octave_idx_type&, const double*, const octave_idx_type&, | |
| 107 const double*, const octave_idx_type&, double&); | |
| 108 | |
| 109 F77_RET_T | |
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110 F77_FUNC (dsyrk, DSYRK) (F77_CONST_CHAR_ARG_DECL, |
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111 F77_CONST_CHAR_ARG_DECL, |
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112 const octave_idx_type&, const octave_idx_type&, |
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113 const double&, const double*, const octave_idx_type&, |
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114 const double&, double*, const octave_idx_type& |
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115 F77_CHAR_ARG_LEN_DECL |
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116 F77_CHAR_ARG_LEN_DECL); |
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117 |
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118 F77_RET_T |
| 5275 | 119 F77_FUNC (dgetrf, DGETRF) (const octave_idx_type&, const octave_idx_type&, double*, const octave_idx_type&, |
| 120 octave_idx_type*, octave_idx_type&); | |
| 4329 | 121 |
| 4552 | 122 F77_RET_T |
| 5275 | 123 F77_FUNC (dgetrs, DGETRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, |
| 124 const double*, const octave_idx_type&, | |
| 125 const octave_idx_type*, double*, const octave_idx_type&, octave_idx_type& | |
| 4552 | 126 F77_CHAR_ARG_LEN_DECL); |
| 127 | |
| 128 F77_RET_T | |
| 5275 | 129 F77_FUNC (dgetri, DGETRI) (const octave_idx_type&, double*, const octave_idx_type&, const octave_idx_type*, |
| 130 double*, const octave_idx_type&, octave_idx_type&); | |
| 4552 | 131 |
| 132 F77_RET_T | |
| 5275 | 133 F77_FUNC (dgecon, DGECON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, double*, |
| 134 const octave_idx_type&, const double&, double&, | |
| 135 double*, octave_idx_type*, octave_idx_type& | |
| 4552 | 136 F77_CHAR_ARG_LEN_DECL); |
| 137 | |
| 138 F77_RET_T | |
| 7072 | 139 F77_FUNC (dgelsy, DGELSY) (const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
| 140 double*, const octave_idx_type&, double*, | |
| 141 const octave_idx_type&, octave_idx_type*, double&, octave_idx_type&, | |
| 142 double*, const octave_idx_type&, octave_idx_type&); | |
| 143 | |
| 144 F77_RET_T | |
| 145 F77_FUNC (dgelsd, DGELSD) (const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, | |
| 5275 | 146 double*, const octave_idx_type&, double*, |
| 7071 | 147 const octave_idx_type&, double*, double&, octave_idx_type&, |
| 7072 | 148 double*, const octave_idx_type&, octave_idx_type*, |
| 149 octave_idx_type&); | |
| 458 | 150 |
| 5785 | 151 F77_RET_T |
| 152 F77_FUNC (dpotrf, DPOTRF) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 153 double *, const octave_idx_type&, | |
| 154 octave_idx_type& F77_CHAR_ARG_LEN_DECL); | |
| 155 | |
| 156 F77_RET_T | |
| 157 F77_FUNC (dpocon, DPOCON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 158 double*, const octave_idx_type&, const double&, | |
| 159 double&, double*, octave_idx_type*, | |
| 160 octave_idx_type& F77_CHAR_ARG_LEN_DECL); | |
| 161 F77_RET_T | |
| 162 F77_FUNC (dpotrs, DPOTRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 163 const octave_idx_type&, const double*, | |
| 164 const octave_idx_type&, double*, | |
| 165 const octave_idx_type&, octave_idx_type& | |
| 166 F77_CHAR_ARG_LEN_DECL); | |
| 167 | |
| 168 F77_RET_T | |
| 6207 | 169 F77_FUNC (dtrtri, DTRTRI) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, |
| 170 const octave_idx_type&, const double*, | |
| 171 const octave_idx_type&, octave_idx_type& | |
| 172 F77_CHAR_ARG_LEN_DECL | |
| 173 F77_CHAR_ARG_LEN_DECL); | |
| 174 F77_RET_T | |
| 5785 | 175 F77_FUNC (dtrcon, DTRCON) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, |
| 176 F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 177 const double*, const octave_idx_type&, double&, | |
| 178 double*, octave_idx_type*, octave_idx_type& | |
| 179 F77_CHAR_ARG_LEN_DECL | |
| 180 F77_CHAR_ARG_LEN_DECL | |
| 181 F77_CHAR_ARG_LEN_DECL); | |
| 182 F77_RET_T | |
| 183 F77_FUNC (dtrtrs, DTRTRS) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, | |
| 184 F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 185 const octave_idx_type&, const double*, | |
| 186 const octave_idx_type&, double*, | |
| 187 const octave_idx_type&, octave_idx_type& | |
| 188 F77_CHAR_ARG_LEN_DECL | |
| 189 F77_CHAR_ARG_LEN_DECL | |
| 190 F77_CHAR_ARG_LEN_DECL); | |
| 191 | |
| 1360 | 192 // Note that the original complex fft routines were not written for |
| 193 // double complex arguments. They have been modified by adding an | |
| 194 // implicit double precision (a-h,o-z) statement at the beginning of | |
| 195 // each subroutine. | |
| 458 | 196 |
| 4552 | 197 F77_RET_T |
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198 F77_FUNC (zffti, ZFFTI) (const octave_idx_type&, Complex*); |
| 4552 | 199 |
| 200 F77_RET_T | |
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201 F77_FUNC (zfftf, ZFFTF) (const octave_idx_type&, Complex*, Complex*); |
| 4552 | 202 |
| 203 F77_RET_T | |
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204 F77_FUNC (zfftb, ZFFTB) (const octave_idx_type&, Complex*, Complex*); |
| 4552 | 205 |
| 206 F77_RET_T | |
| 207 F77_FUNC (dlartg, DLARTG) (const double&, const double&, double&, | |
| 208 double&, double&); | |
| 209 | |
| 210 F77_RET_T | |
| 211 F77_FUNC (dtrsyl, DTRSYL) (F77_CONST_CHAR_ARG_DECL, | |
| 212 F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 213 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
| 214 const double*, const octave_idx_type&, const double*, | |
| 215 const octave_idx_type&, const double*, const octave_idx_type&, | |
| 216 double&, octave_idx_type& | |
| 4552 | 217 F77_CHAR_ARG_LEN_DECL |
| 218 F77_CHAR_ARG_LEN_DECL); | |
| 219 | |
| 220 F77_RET_T | |
| 5275 | 221 F77_FUNC (xdlange, XDLANGE) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, |
| 222 const octave_idx_type&, const double*, | |
| 223 const octave_idx_type&, double*, double& | |
| 4552 | 224 F77_CHAR_ARG_LEN_DECL); |
| 458 | 225 } |
| 226 | |
| 1360 | 227 // Matrix class. |
| 458 | 228 |
| 2349 | 229 Matrix::Matrix (const RowVector& rv) |
| 230 : MArray2<double> (1, rv.length (), 0.0) | |
| 231 { | |
| 5275 | 232 for (octave_idx_type i = 0; i < rv.length (); i++) |
| 2349 | 233 elem (0, i) = rv.elem (i); |
| 234 } | |
| 235 | |
| 236 Matrix::Matrix (const ColumnVector& cv) | |
| 237 : MArray2<double> (cv.length (), 1, 0.0) | |
| 238 { | |
| 5275 | 239 for (octave_idx_type i = 0; i < cv.length (); i++) |
| 2349 | 240 elem (i, 0) = cv.elem (i); |
| 241 } | |
| 242 | |
| 458 | 243 Matrix::Matrix (const DiagMatrix& a) |
| 1214 | 244 : MArray2<double> (a.rows (), a.cols (), 0.0) |
| 458 | 245 { |
| 5275 | 246 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 247 elem (i, i) = a.elem (i, i); |
| 248 } | |
| 249 | |
| 5775 | 250 // FIXME -- could we use a templated mixed-type copy function |
| 1574 | 251 // here? |
| 252 | |
| 2828 | 253 Matrix::Matrix (const boolMatrix& a) |
| 254 : MArray2<double> (a.rows (), a.cols ()) | |
| 255 { | |
| 5275 | 256 for (octave_idx_type i = 0; i < a.rows (); i++) |
| 257 for (octave_idx_type j = 0; j < a.cols (); j++) | |
| 2828 | 258 elem (i, j) = a.elem (i, j); |
| 259 } | |
| 260 | |
| 1574 | 261 Matrix::Matrix (const charMatrix& a) |
| 262 : MArray2<double> (a.rows (), a.cols ()) | |
| 263 { | |
| 5275 | 264 for (octave_idx_type i = 0; i < a.rows (); i++) |
| 265 for (octave_idx_type j = 0; j < a.cols (); j++) | |
| 1574 | 266 elem (i, j) = a.elem (i, j); |
| 267 } | |
| 268 | |
| 2385 | 269 bool |
| 458 | 270 Matrix::operator == (const Matrix& a) const |
| 271 { | |
| 272 if (rows () != a.rows () || cols () != a.cols ()) | |
| 2385 | 273 return false; |
| 458 | 274 |
| 3769 | 275 return mx_inline_equal (data (), a.data (), length ()); |
| 458 | 276 } |
| 277 | |
| 2385 | 278 bool |
| 458 | 279 Matrix::operator != (const Matrix& a) const |
| 280 { | |
| 281 return !(*this == a); | |
| 282 } | |
| 283 | |
| 3354 | 284 bool |
| 285 Matrix::is_symmetric (void) const | |
| 286 { | |
| 287 if (is_square () && rows () > 0) | |
| 288 { | |
| 5275 | 289 for (octave_idx_type i = 0; i < rows (); i++) |
| 290 for (octave_idx_type j = i+1; j < cols (); j++) | |
| 3354 | 291 if (elem (i, j) != elem (j, i)) |
| 292 return false; | |
| 293 | |
| 294 return true; | |
| 295 } | |
| 296 | |
| 297 return false; | |
| 298 } | |
| 299 | |
| 458 | 300 Matrix& |
| 5275 | 301 Matrix::insert (const Matrix& a, octave_idx_type r, octave_idx_type c) |
| 458 | 302 { |
| 1561 | 303 Array2<double>::insert (a, r, c); |
| 458 | 304 return *this; |
| 305 } | |
| 306 | |
| 307 Matrix& | |
| 5275 | 308 Matrix::insert (const RowVector& a, octave_idx_type r, octave_idx_type c) |
| 458 | 309 { |
| 5275 | 310 octave_idx_type a_len = a.length (); |
| 4316 | 311 |
| 1698 | 312 if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ()) |
| 458 | 313 { |
| 314 (*current_liboctave_error_handler) ("range error for insert"); | |
| 315 return *this; | |
| 316 } | |
| 317 | |
| 4316 | 318 if (a_len > 0) |
| 319 { | |
| 320 make_unique (); | |
| 321 | |
| 5275 | 322 for (octave_idx_type i = 0; i < a_len; i++) |
| 4316 | 323 xelem (r, c+i) = a.elem (i); |
| 324 } | |
| 458 | 325 |
| 326 return *this; | |
| 327 } | |
| 328 | |
| 329 Matrix& | |
| 5275 | 330 Matrix::insert (const ColumnVector& a, octave_idx_type r, octave_idx_type c) |
| 458 | 331 { |
| 5275 | 332 octave_idx_type a_len = a.length (); |
| 4316 | 333 |
| 1698 | 334 if (r < 0 || r + a_len > rows () || c < 0 || c >= cols ()) |
| 458 | 335 { |
| 336 (*current_liboctave_error_handler) ("range error for insert"); | |
| 337 return *this; | |
| 338 } | |
| 339 | |
| 4316 | 340 if (a_len > 0) |
| 341 { | |
| 342 make_unique (); | |
| 343 | |
| 5275 | 344 for (octave_idx_type i = 0; i < a_len; i++) |
| 4316 | 345 xelem (r+i, c) = a.elem (i); |
| 346 } | |
| 458 | 347 |
| 348 return *this; | |
| 349 } | |
| 350 | |
| 351 Matrix& | |
| 5275 | 352 Matrix::insert (const DiagMatrix& a, octave_idx_type r, octave_idx_type c) |
| 458 | 353 { |
| 5275 | 354 octave_idx_type a_nr = a.rows (); |
| 355 octave_idx_type a_nc = a.cols (); | |
| 1697 | 356 |
| 1698 | 357 if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) |
| 458 | 358 { |
| 359 (*current_liboctave_error_handler) ("range error for insert"); | |
| 360 return *this; | |
| 361 } | |
| 362 | |
| 1697 | 363 fill (0.0, r, c, r + a_nr - 1, c + a_nc - 1); |
| 364 | |
| 5275 | 365 octave_idx_type a_len = a.length (); |
| 4316 | 366 |
| 367 if (a_len > 0) | |
| 368 { | |
| 369 make_unique (); | |
| 370 | |
| 5275 | 371 for (octave_idx_type i = 0; i < a_len; i++) |
| 4316 | 372 xelem (r+i, c+i) = a.elem (i, i); |
| 373 } | |
| 458 | 374 |
| 375 return *this; | |
| 376 } | |
| 377 | |
| 378 Matrix& | |
| 379 Matrix::fill (double val) | |
| 380 { | |
| 5275 | 381 octave_idx_type nr = rows (); |
| 382 octave_idx_type nc = cols (); | |
| 4316 | 383 |
| 458 | 384 if (nr > 0 && nc > 0) |
| 4316 | 385 { |
| 386 make_unique (); | |
| 387 | |
| 5275 | 388 for (octave_idx_type j = 0; j < nc; j++) |
| 389 for (octave_idx_type i = 0; i < nr; i++) | |
| 4316 | 390 xelem (i, j) = val; |
| 391 } | |
| 458 | 392 |
| 393 return *this; | |
| 394 } | |
| 395 | |
| 396 Matrix& | |
| 5275 | 397 Matrix::fill (double val, octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) |
| 458 | 398 { |
| 5275 | 399 octave_idx_type nr = rows (); |
| 400 octave_idx_type nc = cols (); | |
| 4316 | 401 |
| 458 | 402 if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0 |
| 403 || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc) | |
| 404 { | |
| 405 (*current_liboctave_error_handler) ("range error for fill"); | |
| 406 return *this; | |
| 407 } | |
| 408 | |
| 5275 | 409 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } |
| 410 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } | |
| 458 | 411 |
| 4316 | 412 if (r2 >= r1 && c2 >= c1) |
| 413 { | |
| 414 make_unique (); | |
| 415 | |
| 5275 | 416 for (octave_idx_type j = c1; j <= c2; j++) |
| 417 for (octave_idx_type i = r1; i <= r2; i++) | |
| 4316 | 418 xelem (i, j) = val; |
| 419 } | |
| 458 | 420 |
| 421 return *this; | |
| 422 } | |
| 423 | |
| 424 Matrix | |
| 425 Matrix::append (const Matrix& a) const | |
| 426 { | |
| 5275 | 427 octave_idx_type nr = rows (); |
| 428 octave_idx_type nc = cols (); | |
| 458 | 429 if (nr != a.rows ()) |
| 430 { | |
| 431 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 432 return Matrix (); | |
| 433 } | |
| 434 | |
| 5275 | 435 octave_idx_type nc_insert = nc; |
| 458 | 436 Matrix retval (nr, nc + a.cols ()); |
| 437 retval.insert (*this, 0, 0); | |
| 438 retval.insert (a, 0, nc_insert); | |
| 439 return retval; | |
| 440 } | |
| 441 | |
| 442 Matrix | |
| 443 Matrix::append (const RowVector& a) const | |
| 444 { | |
| 5275 | 445 octave_idx_type nr = rows (); |
| 446 octave_idx_type nc = cols (); | |
| 458 | 447 if (nr != 1) |
| 448 { | |
| 449 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 450 return Matrix (); | |
| 451 } | |
| 452 | |
| 5275 | 453 octave_idx_type nc_insert = nc; |
| 458 | 454 Matrix retval (nr, nc + a.length ()); |
| 455 retval.insert (*this, 0, 0); | |
| 456 retval.insert (a, 0, nc_insert); | |
| 457 return retval; | |
| 458 } | |
| 459 | |
| 460 Matrix | |
| 461 Matrix::append (const ColumnVector& a) const | |
| 462 { | |
| 5275 | 463 octave_idx_type nr = rows (); |
| 464 octave_idx_type nc = cols (); | |
| 458 | 465 if (nr != a.length ()) |
| 466 { | |
| 467 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 468 return Matrix (); | |
| 469 } | |
| 470 | |
| 5275 | 471 octave_idx_type nc_insert = nc; |
| 458 | 472 Matrix retval (nr, nc + 1); |
| 473 retval.insert (*this, 0, 0); | |
| 474 retval.insert (a, 0, nc_insert); | |
| 475 return retval; | |
| 476 } | |
| 477 | |
| 478 Matrix | |
| 479 Matrix::append (const DiagMatrix& a) const | |
| 480 { | |
| 5275 | 481 octave_idx_type nr = rows (); |
| 482 octave_idx_type nc = cols (); | |
| 458 | 483 if (nr != a.rows ()) |
| 484 { | |
| 485 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 486 return *this; | |
| 487 } | |
| 488 | |
| 5275 | 489 octave_idx_type nc_insert = nc; |
| 458 | 490 Matrix retval (nr, nc + a.cols ()); |
| 491 retval.insert (*this, 0, 0); | |
| 492 retval.insert (a, 0, nc_insert); | |
| 493 return retval; | |
| 494 } | |
| 495 | |
| 496 Matrix | |
| 497 Matrix::stack (const Matrix& a) const | |
| 498 { | |
| 5275 | 499 octave_idx_type nr = rows (); |
| 500 octave_idx_type nc = cols (); | |
| 458 | 501 if (nc != a.cols ()) |
| 502 { | |
| 503 (*current_liboctave_error_handler) | |
| 504 ("column dimension mismatch for stack"); | |
| 505 return Matrix (); | |
| 506 } | |
| 507 | |
| 5275 | 508 octave_idx_type nr_insert = nr; |
| 458 | 509 Matrix retval (nr + a.rows (), nc); |
| 510 retval.insert (*this, 0, 0); | |
| 511 retval.insert (a, nr_insert, 0); | |
| 512 return retval; | |
| 513 } | |
| 514 | |
| 515 Matrix | |
| 516 Matrix::stack (const RowVector& a) const | |
| 517 { | |
| 5275 | 518 octave_idx_type nr = rows (); |
| 519 octave_idx_type nc = cols (); | |
| 458 | 520 if (nc != a.length ()) |
| 521 { | |
| 522 (*current_liboctave_error_handler) | |
| 523 ("column dimension mismatch for stack"); | |
| 524 return Matrix (); | |
| 525 } | |
| 526 | |
| 5275 | 527 octave_idx_type nr_insert = nr; |
| 458 | 528 Matrix retval (nr + 1, nc); |
| 529 retval.insert (*this, 0, 0); | |
| 530 retval.insert (a, nr_insert, 0); | |
| 531 return retval; | |
| 532 } | |
| 533 | |
| 534 Matrix | |
| 535 Matrix::stack (const ColumnVector& a) const | |
| 536 { | |
| 5275 | 537 octave_idx_type nr = rows (); |
| 538 octave_idx_type nc = cols (); | |
| 458 | 539 if (nc != 1) |
| 540 { | |
| 541 (*current_liboctave_error_handler) | |
| 542 ("column dimension mismatch for stack"); | |
| 543 return Matrix (); | |
| 544 } | |
| 545 | |
| 5275 | 546 octave_idx_type nr_insert = nr; |
| 458 | 547 Matrix retval (nr + a.length (), nc); |
| 548 retval.insert (*this, 0, 0); | |
| 549 retval.insert (a, nr_insert, 0); | |
| 550 return retval; | |
| 551 } | |
| 552 | |
| 553 Matrix | |
| 554 Matrix::stack (const DiagMatrix& a) const | |
| 555 { | |
| 5275 | 556 octave_idx_type nr = rows (); |
| 557 octave_idx_type nc = cols (); | |
| 458 | 558 if (nc != a.cols ()) |
| 559 { | |
| 560 (*current_liboctave_error_handler) | |
| 561 ("column dimension mismatch for stack"); | |
| 562 return Matrix (); | |
| 563 } | |
| 564 | |
| 5275 | 565 octave_idx_type nr_insert = nr; |
| 458 | 566 Matrix retval (nr + a.rows (), nc); |
| 567 retval.insert (*this, 0, 0); | |
| 568 retval.insert (a, nr_insert, 0); | |
| 569 return retval; | |
| 570 } | |
| 571 | |
| 572 Matrix | |
| 1205 | 573 real (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_real_dup (a.data (), a_len), |
| 579 a.rows (), a.cols ()); | |
| 1205 | 580 return retval; |
| 581 } | |
| 582 | |
| 583 Matrix | |
| 584 imag (const ComplexMatrix& a) | |
| 585 { | |
| 5275 | 586 octave_idx_type a_len = a.length (); |
| 1205 | 587 Matrix retval; |
| 588 if (a_len > 0) | |
| 3769 | 589 retval = Matrix (mx_inline_imag_dup (a.data (), a_len), |
| 590 a.rows (), a.cols ()); | |
| 1205 | 591 return retval; |
| 592 } | |
| 593 | |
| 594 Matrix | |
| 5275 | 595 Matrix::extract (octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) const |
| 458 | 596 { |
| 5275 | 597 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } |
| 598 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } | |
| 599 | |
| 600 octave_idx_type new_r = r2 - r1 + 1; | |
| 601 octave_idx_type new_c = c2 - c1 + 1; | |
| 458 | 602 |
| 603 Matrix result (new_r, new_c); | |
| 604 | |
| 5275 | 605 for (octave_idx_type j = 0; j < new_c; j++) |
| 606 for (octave_idx_type i = 0; i < new_r; i++) | |
| 4316 | 607 result.xelem (i, j) = elem (r1+i, c1+j); |
| 608 | |
| 609 return result; | |
| 610 } | |
| 611 | |
| 612 Matrix | |
| 5275 | 613 Matrix::extract_n (octave_idx_type r1, octave_idx_type c1, octave_idx_type nr, octave_idx_type nc) const |
| 4316 | 614 { |
| 615 Matrix result (nr, nc); | |
| 616 | |
| 5275 | 617 for (octave_idx_type j = 0; j < nc; j++) |
| 618 for (octave_idx_type i = 0; i < nr; i++) | |
| 4316 | 619 result.xelem (i, j) = elem (r1+i, c1+j); |
| 458 | 620 |
| 621 return result; | |
| 622 } | |
| 623 | |
| 624 // extract row or column i. | |
| 625 | |
| 626 RowVector | |
| 5275 | 627 Matrix::row (octave_idx_type i) const |
| 458 | 628 { |
| 5275 | 629 octave_idx_type nc = cols (); |
| 458 | 630 if (i < 0 || i >= rows ()) |
| 631 { | |
| 632 (*current_liboctave_error_handler) ("invalid row selection"); | |
| 633 return RowVector (); | |
| 634 } | |
| 635 | |
| 636 RowVector retval (nc); | |
| 5275 | 637 for (octave_idx_type j = 0; j < nc; j++) |
| 4316 | 638 retval.xelem (j) = elem (i, j); |
| 458 | 639 |
| 640 return retval; | |
| 641 } | |
| 642 | |
| 643 ColumnVector | |
| 5275 | 644 Matrix::column (octave_idx_type i) const |
| 458 | 645 { |
| 5275 | 646 octave_idx_type nr = rows (); |
| 458 | 647 if (i < 0 || i >= cols ()) |
| 648 { | |
| 649 (*current_liboctave_error_handler) ("invalid column selection"); | |
| 650 return ColumnVector (); | |
| 651 } | |
| 652 | |
| 653 ColumnVector retval (nr); | |
| 5275 | 654 for (octave_idx_type j = 0; j < nr; j++) |
| 4316 | 655 retval.xelem (j) = elem (j, i); |
| 458 | 656 |
| 657 return retval; | |
| 658 } | |
| 659 | |
| 660 Matrix | |
| 661 Matrix::inverse (void) const | |
| 662 { | |
| 5275 | 663 octave_idx_type info; |
| 7788 | 664 double rcon; |
| 6207 | 665 MatrixType mattype (*this); |
| 7788 | 666 return inverse (mattype, info, rcon, 0, 0); |
| 6207 | 667 } |
| 668 | |
| 669 Matrix | |
| 6479 | 670 Matrix::inverse (octave_idx_type& info) const |
| 671 { | |
| 7788 | 672 double rcon; |
| 6479 | 673 MatrixType mattype (*this); |
| 7788 | 674 return inverse (mattype, info, rcon, 0, 0); |
| 6479 | 675 } |
| 676 | |
| 677 Matrix | |
| 7788 | 678 Matrix::inverse (octave_idx_type& info, double& rcon, int force, |
| 6479 | 679 int calc_cond) const |
| 680 { | |
| 681 MatrixType mattype (*this); | |
| 7788 | 682 return inverse (mattype, info, rcon, force, calc_cond); |
| 6479 | 683 } |
| 684 | |
| 685 Matrix | |
| 6207 | 686 Matrix::inverse (MatrixType& mattype) const |
| 687 { | |
| 688 octave_idx_type info; | |
| 7788 | 689 double rcon; |
| 690 return inverse (mattype, info, rcon, 0, 0); | |
| 6207 | 691 } |
| 692 | |
| 693 Matrix | |
| 694 Matrix::inverse (MatrixType &mattype, octave_idx_type& info) const | |
| 695 { | |
| 7788 | 696 double rcon; |
| 697 return inverse (mattype, info, rcon, 0, 0); | |
| 458 | 698 } |
| 699 | |
| 700 Matrix | |
| 7788 | 701 Matrix::tinverse (MatrixType &mattype, octave_idx_type& info, double& rcon, |
| 6207 | 702 int force, int calc_cond) const |
| 458 | 703 { |
| 6207 | 704 Matrix retval; |
| 705 | |
| 706 octave_idx_type nr = rows (); | |
| 707 octave_idx_type nc = cols (); | |
| 708 | |
| 709 if (nr != nc || nr == 0 || nc == 0) | |
| 710 (*current_liboctave_error_handler) ("inverse requires square matrix"); | |
| 711 else | |
| 712 { | |
| 713 int typ = mattype.type (); | |
| 714 char uplo = (typ == MatrixType::Lower ? 'L' : 'U'); | |
| 715 char udiag = 'N'; | |
| 716 retval = *this; | |
| 717 double *tmp_data = retval.fortran_vec (); | |
| 718 | |
| 719 F77_XFCN (dtrtri, DTRTRI, (F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 720 F77_CONST_CHAR_ARG2 (&udiag, 1), | |
| 721 nr, tmp_data, nr, info | |
| 722 F77_CHAR_ARG_LEN (1) | |
| 723 F77_CHAR_ARG_LEN (1))); | |
| 724 | |
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725 // Throw-away extra info LAPACK gives so as to not change output. |
| 7788 | 726 rcon = 0.0; |
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727 if (info != 0) |
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728 info = -1; |
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729 else if (calc_cond) |
| 6207 | 730 { |
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731 octave_idx_type dtrcon_info = 0; |
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732 char job = '1'; |
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733 |
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734 OCTAVE_LOCAL_BUFFER (double, work, 3 * nr); |
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735 OCTAVE_LOCAL_BUFFER (octave_idx_type, iwork, nr); |
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736 |
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737 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&job, 1), |
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738 F77_CONST_CHAR_ARG2 (&uplo, 1), |
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739 F77_CONST_CHAR_ARG2 (&udiag, 1), |
| 7788 | 740 nr, tmp_data, nr, rcon, |
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741 work, iwork, dtrcon_info |
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742 F77_CHAR_ARG_LEN (1) |
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743 F77_CHAR_ARG_LEN (1) |
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744 F77_CHAR_ARG_LEN (1))); |
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745 |
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746 if (dtrcon_info != 0) |
| 6207 | 747 info = -1; |
| 748 } | |
| 749 | |
| 750 if (info == -1 && ! force) | |
| 751 retval = *this; // Restore matrix contents. | |
| 752 } | |
| 753 | |
| 754 return retval; | |
| 458 | 755 } |
| 756 | |
| 6207 | 757 |
| 458 | 758 Matrix |
| 7788 | 759 Matrix::finverse (MatrixType &mattype, octave_idx_type& info, double& rcon, |
| 6207 | 760 int force, int calc_cond) const |
| 458 | 761 { |
| 1948 | 762 Matrix retval; |
| 763 | |
| 5275 | 764 octave_idx_type nr = rows (); |
| 765 octave_idx_type nc = cols (); | |
| 1948 | 766 |
| 458 | 767 if (nr != nc || nr == 0 || nc == 0) |
| 1948 | 768 (*current_liboctave_error_handler) ("inverse requires square matrix"); |
| 458 | 769 else |
| 770 { | |
| 5275 | 771 Array<octave_idx_type> ipvt (nr); |
| 772 octave_idx_type *pipvt = ipvt.fortran_vec (); | |
| 1948 | 773 |
| 774 retval = *this; | |
| 775 double *tmp_data = retval.fortran_vec (); | |
| 776 | |
| 4329 | 777 Array<double> z(1); |
| 5275 | 778 octave_idx_type lwork = -1; |
| 4329 | 779 |
| 4330 | 780 // Query the optimum work array size. |
| 4329 | 781 F77_XFCN (dgetri, DGETRI, (nc, tmp_data, nr, pipvt, |
| 782 z.fortran_vec (), lwork, info)); | |
| 783 | |
| 5275 | 784 lwork = static_cast<octave_idx_type> (z(0)); |
| 4329 | 785 lwork = (lwork < 2 *nc ? 2*nc : lwork); |
| 786 z.resize (lwork); | |
| 787 double *pz = z.fortran_vec (); | |
| 788 | |
| 789 info = 0; | |
| 790 | |
| 4330 | 791 // Calculate the norm of the matrix, for later use. |
| 4329 | 792 double anorm = 0; |
| 793 if (calc_cond) | |
| 5275 | 794 anorm = retval.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
| 4329 | 795 |
| 796 F77_XFCN (dgetrf, DGETRF, (nc, nc, tmp_data, nr, pipvt, info)); | |
| 1948 | 797 |
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798 // Throw-away extra info LAPACK gives so as to not change output. |
| 7788 | 799 rcon = 0.0; |
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800 if (info != 0) |
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801 info = -1; |
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802 else if (calc_cond) |
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803 { |
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804 octave_idx_type dgecon_info = 0; |
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805 |
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806 // Now calculate the condition number for non-singular matrix. |
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807 char job = '1'; |
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808 Array<octave_idx_type> iz (nc); |
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809 octave_idx_type *piz = iz.fortran_vec (); |
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810 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
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811 nc, tmp_data, nr, anorm, |
| 7788 | 812 rcon, pz, piz, dgecon_info |
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813 F77_CHAR_ARG_LEN (1))); |
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814 |
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815 if (dgecon_info != 0) |
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816 info = -1; |
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817 } |
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818 |
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819 if (info == -1 && ! force) |
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820 retval = *this; // Restore matrix contents. |
| 1948 | 821 else |
| 822 { | |
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823 octave_idx_type dgetri_info = 0; |
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824 |
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825 F77_XFCN (dgetri, DGETRI, (nc, tmp_data, nr, pipvt, |
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826 pz, lwork, dgetri_info)); |
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827 |
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828 if (dgetri_info != 0) |
| 1948 | 829 info = -1; |
| 830 } | |
| 6207 | 831 |
| 832 if (info != 0) | |
| 833 mattype.mark_as_rectangular(); | |
| 458 | 834 } |
| 835 | |
| 1948 | 836 return retval; |
| 458 | 837 } |
| 838 | |
| 740 | 839 Matrix |
| 7788 | 840 Matrix::inverse (MatrixType &mattype, octave_idx_type& info, double& rcon, |
| 6207 | 841 int force, int calc_cond) const |
| 842 { | |
| 843 int typ = mattype.type (false); | |
| 844 Matrix ret; | |
| 845 | |
| 846 if (typ == MatrixType::Unknown) | |
| 847 typ = mattype.type (*this); | |
| 848 | |
| 849 if (typ == MatrixType::Upper || typ == MatrixType::Lower) | |
| 7788 | 850 ret = tinverse (mattype, info, rcon, force, calc_cond); |
| 6840 | 851 else |
| 6207 | 852 { |
| 853 if (mattype.is_hermitian ()) | |
| 854 { | |
| 6486 | 855 CHOL chol (*this, info, calc_cond); |
| 6207 | 856 if (info == 0) |
| 6486 | 857 { |
| 858 if (calc_cond) | |
| 7788 | 859 rcon = chol.rcond (); |
| 6486 | 860 else |
| 7788 | 861 rcon = 1.0; |
| 6486 | 862 ret = chol.inverse (); |
| 863 } | |
| 6207 | 864 else |
| 865 mattype.mark_as_unsymmetric (); | |
| 866 } | |
| 867 | |
| 868 if (!mattype.is_hermitian ()) | |
| 7788 | 869 ret = finverse(mattype, info, rcon, force, calc_cond); |
| 870 | |
| 871 if ((mattype.is_hermitian () || calc_cond) && rcon == 0.) | |
| 6840 | 872 ret = Matrix (rows (), columns (), octave_Inf); |
| 6207 | 873 } |
| 874 | |
| 875 return ret; | |
| 876 } | |
| 877 | |
| 878 Matrix | |
| 4384 | 879 Matrix::pseudo_inverse (double tol) const |
| 740 | 880 { |
| 3480 | 881 SVD result (*this, SVD::economy); |
| 740 | 882 |
| 883 DiagMatrix S = result.singular_values (); | |
| 884 Matrix U = result.left_singular_matrix (); | |
| 885 Matrix V = result.right_singular_matrix (); | |
| 886 | |
| 887 ColumnVector sigma = S.diag (); | |
| 888 | |
| 5275 | 889 octave_idx_type r = sigma.length () - 1; |
| 890 octave_idx_type nr = rows (); | |
| 891 octave_idx_type nc = cols (); | |
| 740 | 892 |
| 893 if (tol <= 0.0) | |
| 894 { | |
| 895 if (nr > nc) | |
| 896 tol = nr * sigma.elem (0) * DBL_EPSILON; | |
| 897 else | |
| 898 tol = nc * sigma.elem (0) * DBL_EPSILON; | |
| 899 } | |
| 900 | |
| 901 while (r >= 0 && sigma.elem (r) < tol) | |
| 902 r--; | |
| 903 | |
| 904 if (r < 0) | |
| 905 return Matrix (nc, nr, 0.0); | |
| 906 else | |
| 907 { | |
| 908 Matrix Ur = U.extract (0, 0, nr-1, r); | |
| 909 DiagMatrix D = DiagMatrix (sigma.extract (0, r)) . inverse (); | |
| 910 Matrix Vr = V.extract (0, 0, nc-1, r); | |
| 911 return Vr * D * Ur.transpose (); | |
| 912 } | |
| 913 } | |
| 914 | |
| 4773 | 915 #if defined (HAVE_FFTW3) |
| 3827 | 916 |
| 917 ComplexMatrix | |
| 918 Matrix::fourier (void) const | |
| 919 { | |
| 920 size_t nr = rows (); | |
| 921 size_t nc = cols (); | |
| 922 | |
| 923 ComplexMatrix retval (nr, nc); | |
| 924 | |
| 925 size_t npts, nsamples; | |
| 926 | |
| 927 if (nr == 1 || nc == 1) | |
| 928 { | |
| 929 npts = nr > nc ? nr : nc; | |
| 930 nsamples = 1; | |
| 931 } | |
| 932 else | |
| 933 { | |
| 934 npts = nr; | |
| 935 nsamples = nc; | |
| 936 } | |
| 937 | |
| 4773 | 938 const double *in (fortran_vec ()); |
| 3827 | 939 Complex *out (retval.fortran_vec ()); |
| 940 | |
| 4773 | 941 octave_fftw::fft (in, out, npts, nsamples); |
| 3827 | 942 |
| 943 return retval; | |
| 944 } | |
| 945 | |
| 946 ComplexMatrix | |
| 947 Matrix::ifourier (void) const | |
| 948 { | |
| 949 size_t nr = rows (); | |
| 950 size_t nc = cols (); | |
| 951 | |
| 952 ComplexMatrix retval (nr, nc); | |
| 953 | |
| 954 size_t npts, nsamples; | |
| 955 | |
| 956 if (nr == 1 || nc == 1) | |
| 957 { | |
| 958 npts = nr > nc ? nr : nc; | |
| 959 nsamples = 1; | |
| 960 } | |
| 961 else | |
| 962 { | |
| 963 npts = nr; | |
| 964 nsamples = nc; | |
| 965 } | |
| 966 | |
| 967 ComplexMatrix tmp (*this); | |
| 968 Complex *in (tmp.fortran_vec ()); | |
| 969 Complex *out (retval.fortran_vec ()); | |
| 970 | |
| 4773 | 971 octave_fftw::ifft (in, out, npts, nsamples); |
| 3827 | 972 |
| 973 return retval; | |
| 974 } | |
| 975 | |
| 976 ComplexMatrix | |
| 977 Matrix::fourier2d (void) const | |
| 978 { | |
| 4773 | 979 dim_vector dv(rows (), cols ()); |
| 980 | |
| 981 const double *in = fortran_vec (); | |
| 982 ComplexMatrix retval (rows (), cols ()); | |
| 983 octave_fftw::fftNd (in, retval.fortran_vec (), 2, dv); | |
| 3827 | 984 |
| 985 return retval; | |
| 986 } | |
| 987 | |
| 988 ComplexMatrix | |
| 989 Matrix::ifourier2d (void) const | |
| 990 { | |
| 4773 | 991 dim_vector dv(rows (), cols ()); |
| 3827 | 992 |
| 993 ComplexMatrix retval (*this); | |
| 4773 | 994 Complex *out (retval.fortran_vec ()); |
| 995 | |
| 996 octave_fftw::ifftNd (out, out, 2, dv); | |
| 3827 | 997 |
| 998 return retval; | |
| 999 } | |
| 1000 | |
| 1001 #else | |
| 1002 | |
| 458 | 1003 ComplexMatrix |
| 1004 Matrix::fourier (void) const | |
| 1005 { | |
| 1948 | 1006 ComplexMatrix retval; |
| 1007 | |
| 5275 | 1008 octave_idx_type nr = rows (); |
| 1009 octave_idx_type nc = cols (); | |
| 1010 | |
| 1011 octave_idx_type npts, nsamples; | |
| 1948 | 1012 |
| 458 | 1013 if (nr == 1 || nc == 1) |
| 1014 { | |
| 1015 npts = nr > nc ? nr : nc; | |
| 1016 nsamples = 1; | |
| 1017 } | |
| 1018 else | |
| 1019 { | |
| 1020 npts = nr; | |
| 1021 nsamples = nc; | |
| 1022 } | |
| 1023 | |
| 5275 | 1024 octave_idx_type nn = 4*npts+15; |
| 1948 | 1025 |
| 1026 Array<Complex> wsave (nn); | |
| 1027 Complex *pwsave = wsave.fortran_vec (); | |
| 1028 | |
| 3585 | 1029 retval = ComplexMatrix (*this); |
| 1948 | 1030 Complex *tmp_data = retval.fortran_vec (); |
| 1031 | |
|
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1032 F77_FUNC (zffti, ZFFTI) (npts, pwsave); |
| 458 | 1033 |
| 5275 | 1034 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1035 { |
| 1036 OCTAVE_QUIT; | |
| 1037 | |
|
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1038 F77_FUNC (zfftf, ZFFTF) (npts, &tmp_data[npts*j], pwsave); |
| 4153 | 1039 } |
| 1948 | 1040 |
| 1041 return retval; | |
| 458 | 1042 } |
| 1043 | |
| 1044 ComplexMatrix | |
| 1045 Matrix::ifourier (void) const | |
| 1046 { | |
| 1948 | 1047 ComplexMatrix retval; |
| 1048 | |
| 5275 | 1049 octave_idx_type nr = rows (); |
| 1050 octave_idx_type nc = cols (); | |
| 1051 | |
| 1052 octave_idx_type npts, nsamples; | |
| 1948 | 1053 |
| 458 | 1054 if (nr == 1 || nc == 1) |
| 1055 { | |
| 1056 npts = nr > nc ? nr : nc; | |
| 1057 nsamples = 1; | |
| 1058 } | |
| 1059 else | |
| 1060 { | |
| 1061 npts = nr; | |
| 1062 nsamples = nc; | |
| 1063 } | |
| 1064 | |
| 5275 | 1065 octave_idx_type nn = 4*npts+15; |
| 1948 | 1066 |
| 1067 Array<Complex> wsave (nn); | |
| 1068 Complex *pwsave = wsave.fortran_vec (); | |
| 1069 | |
| 3585 | 1070 retval = ComplexMatrix (*this); |
| 1948 | 1071 Complex *tmp_data = retval.fortran_vec (); |
| 1072 | |
|
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1073 F77_FUNC (zffti, ZFFTI) (npts, pwsave); |
| 458 | 1074 |
| 5275 | 1075 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1076 { |
| 1077 OCTAVE_QUIT; | |
| 1078 | |
|
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1079 F77_FUNC (zfftb, ZFFTB) (npts, &tmp_data[npts*j], pwsave); |
| 4153 | 1080 } |
| 458 | 1081 |
| 5275 | 1082 for (octave_idx_type j = 0; j < npts*nsamples; j++) |
| 3572 | 1083 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
| 458 | 1084 |
| 1948 | 1085 return retval; |
| 458 | 1086 } |
| 1087 | |
| 677 | 1088 ComplexMatrix |
| 1089 Matrix::fourier2d (void) const | |
| 1090 { | |
| 1948 | 1091 ComplexMatrix retval; |
| 1092 | |
| 5275 | 1093 octave_idx_type nr = rows (); |
| 1094 octave_idx_type nc = cols (); | |
| 1095 | |
| 1096 octave_idx_type npts, nsamples; | |
| 1948 | 1097 |
| 677 | 1098 if (nr == 1 || nc == 1) |
| 1099 { | |
| 1100 npts = nr > nc ? nr : nc; | |
| 1101 nsamples = 1; | |
| 1102 } | |
| 1103 else | |
| 1104 { | |
| 1105 npts = nr; | |
| 1106 nsamples = nc; | |
| 1107 } | |
| 1108 | |
| 5275 | 1109 octave_idx_type nn = 4*npts+15; |
| 1948 | 1110 |
| 1111 Array<Complex> wsave (nn); | |
| 1112 Complex *pwsave = wsave.fortran_vec (); | |
| 1113 | |
| 3585 | 1114 retval = ComplexMatrix (*this); |
| 1948 | 1115 Complex *tmp_data = retval.fortran_vec (); |
| 1116 | |
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1117 F77_FUNC (zffti, ZFFTI) (npts, pwsave); |
| 677 | 1118 |
| 5275 | 1119 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1120 { |
| 1121 OCTAVE_QUIT; | |
| 1122 | |
|
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1123 F77_FUNC (zfftf, ZFFTF) (npts, &tmp_data[npts*j], pwsave); |
| 4153 | 1124 } |
| 677 | 1125 |
| 1126 npts = nc; | |
| 1127 nsamples = nr; | |
| 1128 nn = 4*npts+15; | |
| 1948 | 1129 |
| 1130 wsave.resize (nn); | |
| 1131 pwsave = wsave.fortran_vec (); | |
| 1132 | |
| 4773 | 1133 Array<Complex> tmp (npts); |
| 1134 Complex *prow = tmp.fortran_vec (); | |
| 1948 | 1135 |
|
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1136 F77_FUNC (zffti, ZFFTI) (npts, pwsave); |
| 677 | 1137 |
| 5275 | 1138 for (octave_idx_type j = 0; j < nsamples; j++) |
| 677 | 1139 { |
| 4153 | 1140 OCTAVE_QUIT; |
| 1141 | |
| 5275 | 1142 for (octave_idx_type i = 0; i < npts; i++) |
| 1948 | 1143 prow[i] = tmp_data[i*nr + j]; |
| 1144 | |
|
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|
1145 F77_FUNC (zfftf, ZFFTF) (npts, prow, pwsave); |
| 677 | 1146 |
| 5275 | 1147 for (octave_idx_type i = 0; i < npts; i++) |
| 1948 | 1148 tmp_data[i*nr + j] = prow[i]; |
| 677 | 1149 } |
| 1150 | |
| 1948 | 1151 return retval; |
| 677 | 1152 } |
| 1153 | |
| 1154 ComplexMatrix | |
| 1155 Matrix::ifourier2d (void) const | |
| 1156 { | |
| 1948 | 1157 ComplexMatrix retval; |
| 1158 | |
| 5275 | 1159 octave_idx_type nr = rows (); |
| 1160 octave_idx_type nc = cols (); | |
| 1161 | |
| 1162 octave_idx_type npts, nsamples; | |
| 1948 | 1163 |
| 677 | 1164 if (nr == 1 || nc == 1) |
| 1165 { | |
| 1166 npts = nr > nc ? nr : nc; | |
| 1167 nsamples = 1; | |
| 1168 } | |
| 1169 else | |
| 1170 { | |
| 1171 npts = nr; | |
| 1172 nsamples = nc; | |
| 1173 } | |
| 1174 | |
| 5275 | 1175 octave_idx_type nn = 4*npts+15; |
| 1948 | 1176 |
| 1177 Array<Complex> wsave (nn); | |
| 1178 Complex *pwsave = wsave.fortran_vec (); | |
| 1179 | |
| 3585 | 1180 retval = ComplexMatrix (*this); |
| 1948 | 1181 Complex *tmp_data = retval.fortran_vec (); |
| 1182 | |
|
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|
1183 F77_FUNC (zffti, ZFFTI) (npts, pwsave); |
| 677 | 1184 |
| 5275 | 1185 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1186 { |
| 1187 OCTAVE_QUIT; | |
| 1188 | |
|
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|
1189 F77_FUNC (zfftb, ZFFTB) (npts, &tmp_data[npts*j], pwsave); |
| 4153 | 1190 } |
| 677 | 1191 |
| 5275 | 1192 for (octave_idx_type j = 0; j < npts*nsamples; j++) |
| 3572 | 1193 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
| 677 | 1194 |
| 1195 npts = nc; | |
| 1196 nsamples = nr; | |
| 1197 nn = 4*npts+15; | |
| 1948 | 1198 |
| 1199 wsave.resize (nn); | |
| 1200 pwsave = wsave.fortran_vec (); | |
| 1201 | |
| 4773 | 1202 Array<Complex> tmp (npts); |
| 1203 Complex *prow = tmp.fortran_vec (); | |
| 1948 | 1204 |
|
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1205 F77_FUNC (zffti, ZFFTI) (npts, pwsave); |
| 677 | 1206 |
| 5275 | 1207 for (octave_idx_type j = 0; j < nsamples; j++) |
| 677 | 1208 { |
| 4153 | 1209 OCTAVE_QUIT; |
| 1210 | |
| 5275 | 1211 for (octave_idx_type i = 0; i < npts; i++) |
| 1948 | 1212 prow[i] = tmp_data[i*nr + j]; |
| 1213 | |
|
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|
1214 F77_FUNC (zfftb, ZFFTB) (npts, prow, pwsave); |
| 677 | 1215 |
| 5275 | 1216 for (octave_idx_type i = 0; i < npts; i++) |
| 3572 | 1217 tmp_data[i*nr + j] = prow[i] / static_cast<double> (npts); |
| 677 | 1218 } |
| 1219 | |
| 1948 | 1220 return retval; |
| 677 | 1221 } |
| 1222 | |
| 3827 | 1223 #endif |
| 1224 | |
| 458 | 1225 DET |
| 1226 Matrix::determinant (void) const | |
| 1227 { | |
| 5275 | 1228 octave_idx_type info; |
| 7788 | 1229 double rcon; |
| 1230 return determinant (info, rcon, 0); | |
| 458 | 1231 } |
| 1232 | |
| 1233 DET | |
| 5275 | 1234 Matrix::determinant (octave_idx_type& info) const |
| 458 | 1235 { |
| 7788 | 1236 double rcon; |
| 1237 return determinant (info, rcon, 0); | |
| 458 | 1238 } |
| 1239 | |
| 1240 DET | |
| 7788 | 1241 Matrix::determinant (octave_idx_type& info, double& rcon, int calc_cond) const |
| 458 | 1242 { |
| 1243 DET retval; | |
| 1244 | |
| 5275 | 1245 octave_idx_type nr = rows (); |
| 1246 octave_idx_type nc = cols (); | |
| 458 | 1247 |
| 1248 if (nr == 0 || nc == 0) | |
| 1249 { | |
| 5634 | 1250 retval = DET (1.0, 0); |
| 458 | 1251 } |
| 1252 else | |
| 1253 { | |
| 5275 | 1254 Array<octave_idx_type> ipvt (nr); |
| 1255 octave_idx_type *pipvt = ipvt.fortran_vec (); | |
| 1948 | 1256 |
| 1257 Matrix atmp = *this; | |
| 1258 double *tmp_data = atmp.fortran_vec (); | |
| 1259 | |
| 4329 | 1260 info = 0; |
| 1261 | |
| 4330 | 1262 // Calculate the norm of the matrix, for later use. |
| 4329 | 1263 double anorm = 0; |
| 1264 if (calc_cond) | |
| 5275 | 1265 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
| 4329 | 1266 |
| 1267 F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); | |
| 1948 | 1268 |
|
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|
1269 // Throw-away extra info LAPACK gives so as to not change output. |
| 7788 | 1270 rcon = 0.0; |
|
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|
1271 if (info != 0) |
|
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|
1272 { |
|
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|
1273 info = -1; |
|
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1274 retval = DET (); |
|
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|
1275 } |
|
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|
1276 else |
| 458 | 1277 { |
|
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|
1278 if (calc_cond) |
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|
1279 { |
|
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1280 // Now calc the condition number for non-singular matrix. |
|
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1281 char job = '1'; |
|
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1282 Array<double> z (4 * nc); |
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1283 double *pz = z.fortran_vec (); |
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1284 Array<octave_idx_type> iz (nc); |
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1285 octave_idx_type *piz = iz.fortran_vec (); |
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|
1286 |
|
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1287 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
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1288 nc, tmp_data, nr, anorm, |
| 7788 | 1289 rcon, pz, piz, info |
|
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1290 F77_CHAR_ARG_LEN (1))); |
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1291 } |
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1292 |
| 4509 | 1293 if (info != 0) |
| 1948 | 1294 { |
| 4509 | 1295 info = -1; |
| 1296 retval = DET (); | |
| 4329 | 1297 } |
| 1298 else | |
| 1948 | 1299 { |
|
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1300 double c = 1.0; |
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1301 int e = 0; |
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1302 |
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1303 for (octave_idx_type i = 0; i < nc; i++) |
| 4329 | 1304 { |
|
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1305 if (ipvt(i) != (i+1)) |
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1306 c = -c; |
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1307 |
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1308 c *= atmp(i,i); |
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1309 |
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1310 if (c == 0.0) |
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1311 break; |
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1312 |
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1313 while (fabs (c) < 0.5) |
| 4329 | 1314 { |
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1315 c *= 2.0; |
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1316 e--; |
| 4329 | 1317 } |
| 5634 | 1318 |
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1319 while (fabs (c) >= 2.0) |
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1320 { |
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1321 c /= 2.0; |
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1322 e++; |
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1323 } |
| 4329 | 1324 } |
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1325 |
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1326 retval = DET (c, e); |
| 1948 | 1327 } |
| 458 | 1328 } |
| 1329 } | |
| 1330 | |
| 1331 return retval; | |
| 1332 } | |
| 1333 | |
| 7788 | 1334 double |
| 1335 Matrix::rcond (void) const | |
| 1336 { | |
| 1337 MatrixType mattype (*this); | |
| 1338 return rcond (mattype); | |
| 1339 } | |
| 1340 | |
| 1341 double | |
| 1342 Matrix::rcond (MatrixType &mattype) const | |
| 1343 { | |
| 1344 double rcon; | |
| 1345 octave_idx_type nr = rows (); | |
| 1346 octave_idx_type nc = cols (); | |
| 1347 | |
| 1348 if (nr != nc) | |
| 1349 (*current_liboctave_error_handler) ("matrix must be square"); | |
| 1350 else if (nr == 0 || nc == 0) | |
| 1351 rcon = octave_Inf; | |
| 1352 else | |
| 1353 { | |
| 1354 int typ = mattype.type (); | |
| 1355 | |
| 1356 if (typ == MatrixType::Unknown) | |
| 1357 typ = mattype.type (*this); | |
| 1358 | |
| 1359 // Only calculate the condition number for LU/Cholesky | |
| 1360 if (typ == MatrixType::Upper) | |
| 1361 { | |
| 1362 const double *tmp_data = fortran_vec (); | |
| 1363 octave_idx_type info = 0; | |
| 1364 char norm = '1'; | |
| 1365 char uplo = 'U'; | |
| 1366 char dia = 'N'; | |
| 1367 | |
| 1368 Array<double> z (3 * nc); | |
| 1369 double *pz = z.fortran_vec (); | |
| 1370 Array<octave_idx_type> iz (nc); | |
| 1371 octave_idx_type *piz = iz.fortran_vec (); | |
| 1372 | |
| 1373 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1374 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1375 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1376 nr, tmp_data, nr, rcon, | |
| 1377 pz, piz, info | |
| 1378 F77_CHAR_ARG_LEN (1) | |
| 1379 F77_CHAR_ARG_LEN (1) | |
| 1380 F77_CHAR_ARG_LEN (1))); | |
| 1381 | |
| 1382 if (info != 0) | |
| 1383 rcon = 0.0; | |
| 1384 } | |
| 1385 else if (typ == MatrixType::Permuted_Upper) | |
| 1386 (*current_liboctave_error_handler) | |
| 1387 ("permuted triangular matrix not implemented"); | |
| 1388 else if (typ == MatrixType::Lower) | |
| 1389 { | |
| 1390 const double *tmp_data = fortran_vec (); | |
| 1391 octave_idx_type info = 0; | |
| 1392 char norm = '1'; | |
| 1393 char uplo = 'L'; | |
| 1394 char dia = 'N'; | |
| 1395 | |
| 1396 Array<double> z (3 * nc); | |
| 1397 double *pz = z.fortran_vec (); | |
| 1398 Array<octave_idx_type> iz (nc); | |
| 1399 octave_idx_type *piz = iz.fortran_vec (); | |
| 1400 | |
| 1401 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1402 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1403 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1404 nr, tmp_data, nr, rcon, | |
| 1405 pz, piz, info | |
| 1406 F77_CHAR_ARG_LEN (1) | |
| 1407 F77_CHAR_ARG_LEN (1) | |
| 1408 F77_CHAR_ARG_LEN (1))); | |
| 1409 | |
| 1410 if (info != 0) | |
| 1411 rcon = 0.0; | |
| 1412 } | |
| 1413 else if (typ == MatrixType::Permuted_Lower) | |
| 1414 (*current_liboctave_error_handler) | |
| 1415 ("permuted triangular matrix not implemented"); | |
| 1416 else if (typ == MatrixType::Full || typ == MatrixType::Hermitian) | |
| 1417 { | |
| 1418 double anorm = -1.0; | |
| 1419 Matrix atmp = *this; | |
| 1420 double *tmp_data = atmp.fortran_vec (); | |
| 1421 | |
| 1422 if (typ == MatrixType::Hermitian) | |
| 1423 { | |
| 1424 octave_idx_type info = 0; | |
| 1425 char job = 'L'; | |
| 1426 anorm = atmp.abs().sum(). | |
| 1427 row(static_cast<octave_idx_type>(0)).max(); | |
| 1428 | |
| 1429 F77_XFCN (dpotrf, DPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, | |
| 1430 tmp_data, nr, info | |
| 1431 F77_CHAR_ARG_LEN (1))); | |
| 1432 | |
| 1433 if (info != 0) | |
| 1434 { | |
| 1435 rcon = 0.0; | |
| 1436 mattype.mark_as_unsymmetric (); | |
| 1437 typ = MatrixType::Full; | |
| 1438 } | |
| 1439 else | |
| 1440 { | |
| 1441 Array<double> z (3 * nc); | |
| 1442 double *pz = z.fortran_vec (); | |
| 1443 Array<octave_idx_type> iz (nc); | |
| 1444 octave_idx_type *piz = iz.fortran_vec (); | |
| 1445 | |
| 1446 F77_XFCN (dpocon, DPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), | |
| 1447 nr, tmp_data, nr, anorm, | |
| 1448 rcon, pz, piz, info | |
| 1449 F77_CHAR_ARG_LEN (1))); | |
| 1450 | |
| 1451 if (info != 0) | |
| 1452 rcon = 0.0; | |
| 1453 } | |
| 1454 } | |
| 1455 | |
| 1456 if (typ == MatrixType::Full) | |
| 1457 { | |
| 1458 octave_idx_type info = 0; | |
| 1459 | |
| 1460 Array<octave_idx_type> ipvt (nr); | |
| 1461 octave_idx_type *pipvt = ipvt.fortran_vec (); | |
| 1462 | |
| 1463 if(anorm < 0.) | |
| 1464 anorm = atmp.abs().sum(). | |
| 1465 row(static_cast<octave_idx_type>(0)).max(); | |
| 1466 | |
| 1467 Array<double> z (4 * nc); | |
| 1468 double *pz = z.fortran_vec (); | |
| 1469 Array<octave_idx_type> iz (nc); | |
| 1470 octave_idx_type *piz = iz.fortran_vec (); | |
| 1471 | |
| 1472 F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); | |
| 1473 | |
| 1474 if (info != 0) | |
| 1475 { | |
| 1476 rcon = 0.0; | |
| 1477 mattype.mark_as_rectangular (); | |
| 1478 } | |
| 1479 else | |
| 1480 { | |
| 1481 char job = '1'; | |
| 1482 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), | |
| 1483 nc, tmp_data, nr, anorm, | |
| 1484 rcon, pz, piz, info | |
| 1485 F77_CHAR_ARG_LEN (1))); | |
| 1486 | |
| 1487 if (info != 0) | |
| 1488 rcon = 0.0; | |
| 1489 } | |
| 1490 } | |
| 1491 } | |
| 1492 else | |
| 1493 rcon = 0.0; | |
| 1494 } | |
| 1495 | |
| 1496 return rcon; | |
| 1497 } | |
| 1498 | |
| 458 | 1499 Matrix |
| 5785 | 1500 Matrix::utsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, |
| 7788 | 1501 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 1502 bool calc_cond) const |
| 1503 { | |
| 1504 Matrix retval; | |
| 1505 | |
| 1506 octave_idx_type nr = rows (); | |
| 1507 octave_idx_type nc = cols (); | |
| 1508 | |
| 6924 | 1509 if (nr != b.rows ()) |
| 5785 | 1510 (*current_liboctave_error_handler) |
| 1511 ("matrix dimension mismatch solution of linear equations"); | |
| 6924 | 1512 else if (nr == 0 || nc == 0 || b.cols () == 0) |
| 1513 retval = Matrix (nc, b.cols (), 0.0); | |
| 5785 | 1514 else |
| 1515 { | |
| 1516 volatile int typ = mattype.type (); | |
| 1517 | |
| 1518 if (typ == MatrixType::Permuted_Upper || | |
| 1519 typ == MatrixType::Upper) | |
| 1520 { | |
| 1521 octave_idx_type b_nc = b.cols (); | |
| 7788 | 1522 rcon = 1.; |
| 5785 | 1523 info = 0; |
| 1524 | |
| 1525 if (typ == MatrixType::Permuted_Upper) | |
| 1526 { | |
| 1527 (*current_liboctave_error_handler) | |
| 6390 | 1528 ("permuted triangular matrix not implemented"); |
| 5785 | 1529 } |
| 1530 else | |
| 1531 { | |
| 1532 const double *tmp_data = fortran_vec (); | |
| 1533 | |
| 1534 if (calc_cond) | |
| 1535 { | |
| 1536 char norm = '1'; | |
| 1537 char uplo = 'U'; | |
| 1538 char dia = 'N'; | |
| 1539 | |
| 1540 Array<double> z (3 * nc); | |
| 1541 double *pz = z.fortran_vec (); | |
| 1542 Array<octave_idx_type> iz (nc); | |
| 1543 octave_idx_type *piz = iz.fortran_vec (); | |
| 1544 | |
| 1545 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1546 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1547 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 7788 | 1548 nr, tmp_data, nr, rcon, |
| 5785 | 1549 pz, piz, info |
| 1550 F77_CHAR_ARG_LEN (1) | |
| 1551 F77_CHAR_ARG_LEN (1) | |
| 1552 F77_CHAR_ARG_LEN (1))); | |
| 1553 | |
| 1554 if (info != 0) | |
| 1555 info = -2; | |
| 1556 | |
| 7788 | 1557 volatile double rcond_plus_one = rcon + 1.0; |
| 1558 | |
| 1559 if (rcond_plus_one == 1.0 || xisnan (rcon)) | |
| 5785 | 1560 { |
| 1561 info = -2; | |
| 1562 | |
| 1563 if (sing_handler) | |
| 7788 | 1564 sing_handler (rcon); |
| 5785 | 1565 else |
| 1566 (*current_liboctave_error_handler) | |
| 1567 ("matrix singular to machine precision, rcond = %g", | |
| 7788 | 1568 rcon); |
| 5785 | 1569 } |
| 1570 } | |
| 1571 | |
| 1572 if (info == 0) | |
| 1573 { | |
| 1574 retval = b; | |
| 1575 double *result = retval.fortran_vec (); | |
| 1576 | |
| 1577 char uplo = 'U'; | |
| 1578 char trans = 'N'; | |
| 1579 char dia = 'N'; | |
| 1580 | |
| 1581 F77_XFCN (dtrtrs, DTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1582 F77_CONST_CHAR_ARG2 (&trans, 1), | |
| 1583 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1584 nr, b_nc, tmp_data, nr, | |
| 1585 result, nr, info | |
| 1586 F77_CHAR_ARG_LEN (1) | |
| 1587 F77_CHAR_ARG_LEN (1) | |
| 1588 F77_CHAR_ARG_LEN (1))); | |
| 1589 } | |
| 1590 } | |
| 1591 } | |
| 1592 else | |
| 1593 (*current_liboctave_error_handler) ("incorrect matrix type"); | |
| 1594 } | |
| 1595 | |
| 1596 return retval; | |
| 1597 } | |
| 1598 | |
| 1599 Matrix | |
| 1600 Matrix::ltsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, | |
| 7788 | 1601 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 1602 bool calc_cond) const |
| 1603 { | |
| 1604 Matrix retval; | |
| 1605 | |
| 1606 octave_idx_type nr = rows (); | |
| 1607 octave_idx_type nc = cols (); | |
| 1608 | |
| 6924 | 1609 if (nr != b.rows ()) |
| 5785 | 1610 (*current_liboctave_error_handler) |
| 1611 ("matrix dimension mismatch solution of linear equations"); | |
| 6924 | 1612 else if (nr == 0 || nc == 0 || b.cols () == 0) |
| 1613 retval = Matrix (nc, b.cols (), 0.0); | |
| 5785 | 1614 else |
| 1615 { | |
| 1616 volatile int typ = mattype.type (); | |
| 1617 | |
| 1618 if (typ == MatrixType::Permuted_Lower || | |
| 1619 typ == MatrixType::Lower) | |
| 1620 { | |
| 1621 octave_idx_type b_nc = b.cols (); | |
| 7788 | 1622 rcon = 1.; |
| 5785 | 1623 info = 0; |
| 1624 | |
| 1625 if (typ == MatrixType::Permuted_Lower) | |
| 1626 { | |
| 1627 (*current_liboctave_error_handler) | |
| 6390 | 1628 ("permuted triangular matrix not implemented"); |
| 5785 | 1629 } |
| 1630 else | |
| 1631 { | |
| 1632 const double *tmp_data = fortran_vec (); | |
| 1633 | |
| 1634 if (calc_cond) | |
| 1635 { | |
| 1636 char norm = '1'; | |
| 1637 char uplo = 'L'; | |
| 1638 char dia = 'N'; | |
| 1639 | |
| 1640 Array<double> z (3 * nc); | |
| 1641 double *pz = z.fortran_vec (); | |
| 1642 Array<octave_idx_type> iz (nc); | |
| 1643 octave_idx_type *piz = iz.fortran_vec (); | |
| 1644 | |
| 1645 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1646 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1647 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 7788 | 1648 nr, tmp_data, nr, rcon, |
| 5785 | 1649 pz, piz, info |
| 1650 F77_CHAR_ARG_LEN (1) | |
| 1651 F77_CHAR_ARG_LEN (1) | |
| 1652 F77_CHAR_ARG_LEN (1))); | |
| 1653 | |
| 1654 if (info != 0) | |
| 1655 info = -2; | |
| 1656 | |
| 7788 | 1657 volatile double rcond_plus_one = rcon + 1.0; |
| 1658 | |
| 1659 if (rcond_plus_one == 1.0 || xisnan (rcon)) | |
| 5785 | 1660 { |
| 1661 info = -2; | |
| 1662 | |
| 1663 if (sing_handler) | |
| 7788 | 1664 sing_handler (rcon); |
| 5785 | 1665 else |
| 1666 (*current_liboctave_error_handler) | |
| 1667 ("matrix singular to machine precision, rcond = %g", | |
| 7788 | 1668 rcon); |
| 5785 | 1669 } |
| 1670 } | |
| 1671 | |
| 1672 if (info == 0) | |
| 1673 { | |
| 1674 retval = b; | |
| 1675 double *result = retval.fortran_vec (); | |
| 1676 | |
| 1677 char uplo = 'L'; | |
| 1678 char trans = 'N'; | |
| 1679 char dia = 'N'; | |
| 1680 | |
| 1681 F77_XFCN (dtrtrs, DTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1682 F77_CONST_CHAR_ARG2 (&trans, 1), | |
| 1683 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1684 nr, b_nc, tmp_data, nr, | |
| 1685 result, nr, info | |
| 1686 F77_CHAR_ARG_LEN (1) | |
| 1687 F77_CHAR_ARG_LEN (1) | |
| 1688 F77_CHAR_ARG_LEN (1))); | |
| 1689 } | |
| 1690 } | |
| 1691 } | |
| 1692 else | |
| 1693 (*current_liboctave_error_handler) ("incorrect matrix type"); | |
| 1694 } | |
| 1695 | |
| 1696 return retval; | |
| 1697 } | |
| 1698 | |
| 1699 Matrix | |
| 1700 Matrix::fsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, | |
| 7788 | 1701 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 1702 bool calc_cond) const |
| 1703 { | |
| 1704 Matrix retval; | |
| 1705 | |
| 1706 octave_idx_type nr = rows (); | |
| 1707 octave_idx_type nc = cols (); | |
| 1708 | |
| 6924 | 1709 if (nr != nc || nr != b.rows ()) |
| 5785 | 1710 (*current_liboctave_error_handler) |
| 1711 ("matrix dimension mismatch solution of linear equations"); | |
| 6924 | 1712 else if (nr == 0 || b.cols () == 0) |
| 1713 retval = Matrix (nc, b.cols (), 0.0); | |
| 5785 | 1714 else |
| 1715 { | |
| 1716 volatile int typ = mattype.type (); | |
| 1717 | |
| 1718 // Calculate the norm of the matrix, for later use. | |
| 1719 double anorm = -1.; | |
| 1720 | |
| 1721 if (typ == MatrixType::Hermitian) | |
| 1722 { | |
| 1723 info = 0; | |
| 1724 char job = 'L'; | |
| 1725 Matrix atmp = *this; | |
| 1726 double *tmp_data = atmp.fortran_vec (); | |
| 1727 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); | |
| 1728 | |
| 1729 F77_XFCN (dpotrf, DPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, | |
| 1730 tmp_data, nr, info | |
| 1731 F77_CHAR_ARG_LEN (1))); | |
| 1732 | |
|
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changeset
|
1733 // Throw-away extra info LAPACK gives so as to not change output. |
| 7788 | 1734 rcon = 0.0; |
|
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1735 if (info != 0) |
|
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1736 { |
|
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1737 info = -2; |
|
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1738 |
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1739 mattype.mark_as_unsymmetric (); |
|
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don't check f77_exception_encountered
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diff
changeset
|
1740 typ = MatrixType::Full; |
|
29980c6b8604
don't check f77_exception_encountered
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diff
changeset
|
1741 } |
|
29980c6b8604
don't check f77_exception_encountered
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parents:
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diff
changeset
|
1742 else |
| 5785 | 1743 { |
|
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29980c6b8604
don't check f77_exception_encountered
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diff
changeset
|
1744 if (calc_cond) |
| 5785 | 1745 { |
|
7482
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
1746 Array<double> z (3 * nc); |
|
29980c6b8604
don't check f77_exception_encountered
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parents:
7478
diff
changeset
|
1747 double *pz = z.fortran_vec (); |
|
29980c6b8604
don't check f77_exception_encountered
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diff
changeset
|
1748 Array<octave_idx_type> iz (nc); |
|
29980c6b8604
don't check f77_exception_encountered
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diff
changeset
|
1749 octave_idx_type *piz = iz.fortran_vec (); |
|
29980c6b8604
don't check f77_exception_encountered
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diff
changeset
|
1750 |
|
29980c6b8604
don't check f77_exception_encountered
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parents:
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diff
changeset
|
1751 F77_XFCN (dpocon, DPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
1752 nr, tmp_data, nr, anorm, |
| 7788 | 1753 rcon, pz, piz, info |
|
7482
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
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7478
diff
changeset
|
1754 F77_CHAR_ARG_LEN (1))); |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
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7478
diff
changeset
|
1755 |
|
29980c6b8604
don't check f77_exception_encountered
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diff
changeset
|
1756 if (info != 0) |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
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diff
changeset
|
1757 info = -2; |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
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diff
changeset
|
1758 |
| 7788 | 1759 volatile double rcond_plus_one = rcon + 1.0; |
| 1760 | |
| 1761 if (rcond_plus_one == 1.0 || xisnan (rcon)) | |
|
7482
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
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diff
changeset
|
1762 { |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
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diff
changeset
|
1763 info = -2; |
|
29980c6b8604
don't check f77_exception_encountered
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diff
changeset
|
1764 |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
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diff
changeset
|
1765 if (sing_handler) |
| 7788 | 1766 sing_handler (rcon); |
|
7482
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
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diff
changeset
|
1767 else |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
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diff
changeset
|
1768 (*current_liboctave_error_handler) |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
1769 ("matrix singular to machine precision, rcond = %g", |
| 7788 | 1770 rcon); |
|
7482
29980c6b8604
don't check f77_exception_encountered
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parents:
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diff
changeset
|
1771 } |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
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diff
changeset
|
1772 } |
|
29980c6b8604
don't check f77_exception_encountered
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diff
changeset
|
1773 |
|
29980c6b8604
don't check f77_exception_encountered
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parents:
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diff
changeset
|
1774 if (info == 0) |
|
29980c6b8604
don't check f77_exception_encountered
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diff
changeset
|
1775 { |
|
29980c6b8604
don't check f77_exception_encountered
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diff
changeset
|
1776 retval = b; |
|
29980c6b8604
don't check f77_exception_encountered
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parents:
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diff
changeset
|
1777 double *result = retval.fortran_vec (); |
|
29980c6b8604
don't check f77_exception_encountered
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diff
changeset
|
1778 |
|
29980c6b8604
don't check f77_exception_encountered
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diff
changeset
|
1779 octave_idx_type b_nc = b.cols (); |
|
29980c6b8604
don't check f77_exception_encountered
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diff
changeset
|
1780 |
|
29980c6b8604
don't check f77_exception_encountered
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diff
changeset
|
1781 F77_XFCN (dpotrs, DPOTRS, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
29980c6b8604
don't check f77_exception_encountered
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parents:
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diff
changeset
|
1782 nr, b_nc, tmp_data, nr, |
|
29980c6b8604
don't check f77_exception_encountered
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diff
changeset
|
1783 result, b.rows(), info |
|
29980c6b8604
don't check f77_exception_encountered
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diff
changeset
|
1784 F77_CHAR_ARG_LEN (1))); |
|
29980c6b8604
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diff
changeset
|
1785 } |
|
29980c6b8604
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diff
changeset
|
1786 else |
|
29980c6b8604
don't check f77_exception_encountered
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diff
changeset
|
1787 { |
| 5785 | 1788 mattype.mark_as_unsymmetric (); |
| 1789 typ = MatrixType::Full; | |
|
7482
29980c6b8604
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diff
changeset
|
1790 } |
| 5785 | 1791 } |
| 1792 } | |
| 1793 | |
| 1794 if (typ == MatrixType::Full) | |
| 1795 { | |
| 1796 info = 0; | |
| 1797 | |
| 1798 Array<octave_idx_type> ipvt (nr); | |
| 1799 octave_idx_type *pipvt = ipvt.fortran_vec (); | |
| 1800 | |
| 1801 Matrix atmp = *this; | |
| 1802 double *tmp_data = atmp.fortran_vec (); | |
| 1803 if(anorm < 0.) | |
| 1804 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); | |
| 1805 | |
| 1806 Array<double> z (4 * nc); | |
| 1807 double *pz = z.fortran_vec (); | |
| 1808 Array<octave_idx_type> iz (nc); | |
| 1809 octave_idx_type *piz = iz.fortran_vec (); | |
| 1810 | |
| 1811 F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); | |
| 1812 | |
|
7482
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diff
changeset
|
1813 // Throw-away extra info LAPACK gives so as to not change output. |
| 7788 | 1814 rcon = 0.0; |
|
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diff
changeset
|
1815 if (info != 0) |
| 5785 | 1816 { |
|
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diff
changeset
|
1817 info = -2; |
|
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diff
changeset
|
1818 |
|
29980c6b8604
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diff
changeset
|
1819 if (sing_handler) |
| 7788 | 1820 sing_handler (rcon); |
|
7482
29980c6b8604
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diff
changeset
|
1821 else |
|
29980c6b8604
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diff
changeset
|
1822 (*current_liboctave_error_handler) |
|
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diff
changeset
|
1823 ("matrix singular to machine precision"); |
|
29980c6b8604
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diff
changeset
|
1824 |
|
29980c6b8604
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diff
changeset
|
1825 mattype.mark_as_rectangular (); |
|
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diff
changeset
|
1826 } |
|
29980c6b8604
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diff
changeset
|
1827 else |
|
29980c6b8604
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parents:
7478
diff
changeset
|
1828 { |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
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diff
changeset
|
1829 if (calc_cond) |
| 5785 | 1830 { |
|
7482
29980c6b8604
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diff
changeset
|
1831 // Now calculate the condition number for |
|
29980c6b8604
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parents:
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diff
changeset
|
1832 // non-singular matrix. |
|
29980c6b8604
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diff
changeset
|
1833 char job = '1'; |
|
29980c6b8604
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diff
changeset
|
1834 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
29980c6b8604
don't check f77_exception_encountered
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parents:
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diff
changeset
|
1835 nc, tmp_data, nr, anorm, |
| 7788 | 1836 rcon, pz, piz, info |
|
7482
29980c6b8604
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diff
changeset
|
1837 F77_CHAR_ARG_LEN (1))); |
|
29980c6b8604
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diff
changeset
|
1838 |
|
29980c6b8604
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7478
diff
changeset
|
1839 if (info != 0) |
|
29980c6b8604
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John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
1840 info = -2; |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
1841 |
| 7788 | 1842 volatile double rcond_plus_one = rcon + 1.0; |
| 1843 | |
| 1844 if (rcond_plus_one == 1.0 || xisnan (rcon)) | |
| 5785 | 1845 { |
|
7482
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
1846 info = -2; |
|
29980c6b8604
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parents:
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diff
changeset
|
1847 |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
1848 if (sing_handler) |
| 7788 | 1849 sing_handler (rcon); |
|
7482
29980c6b8604
don't check f77_exception_encountered
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diff
changeset
|
1850 else |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
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diff
changeset
|
1851 (*current_liboctave_error_handler) |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
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diff
changeset
|
1852 ("matrix singular to machine precision, rcond = %g", |
| 7788 | 1853 rcon); |
| 5785 | 1854 } |
| 1855 } | |
|
7482
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
1856 |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
1857 if (info == 0) |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
1858 { |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
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diff
changeset
|
1859 retval = b; |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
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diff
changeset
|
1860 double *result = retval.fortran_vec (); |
|
29980c6b8604
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John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
1861 |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
1862 octave_idx_type b_nc = b.cols (); |
|
29980c6b8604
don't check f77_exception_encountered
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parents:
7478
diff
changeset
|
1863 |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
1864 char job = 'N'; |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
1865 F77_XFCN (dgetrs, DGETRS, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
1866 nr, b_nc, tmp_data, nr, |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
1867 pipvt, result, b.rows(), info |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
1868 F77_CHAR_ARG_LEN (1))); |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
1869 } |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
1870 else |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
1871 mattype.mark_as_rectangular (); |
| 5785 | 1872 } |
| 1873 } | |
| 1874 else if (typ != MatrixType::Hermitian) | |
| 1875 (*current_liboctave_error_handler) ("incorrect matrix type"); | |
| 1876 } | |
| 1877 | |
| 1878 return retval; | |
| 1879 } | |
| 1880 | |
| 1881 Matrix | |
| 1882 Matrix::solve (MatrixType &typ, const Matrix& b) const | |
| 1883 { | |
| 1884 octave_idx_type info; | |
| 7788 | 1885 double rcon; |
| 1886 return solve (typ, b, info, rcon, 0); | |
| 5785 | 1887 } |
| 1888 | |
| 1889 Matrix | |
| 1890 Matrix::solve (MatrixType &typ, const Matrix& b, octave_idx_type& info, | |
| 7788 | 1891 double& rcon) const |
| 5785 | 1892 { |
| 7788 | 1893 return solve (typ, b, info, rcon, 0); |
| 5785 | 1894 } |
| 1895 | |
| 1896 Matrix | |
| 1897 Matrix::solve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, | |
| 7788 | 1898 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 1899 bool singular_fallback) const |
| 1900 { | |
| 1901 Matrix retval; | |
| 1902 int typ = mattype.type (); | |
| 1903 | |
| 1904 if (typ == MatrixType::Unknown) | |
| 1905 typ = mattype.type (*this); | |
| 1906 | |
| 1907 // Only calculate the condition number for LU/Cholesky | |
| 1908 if (typ == MatrixType::Upper || typ == MatrixType::Permuted_Upper) | |
| 7788 | 1909 retval = utsolve (mattype, b, info, rcon, sing_handler, false); |
| 5785 | 1910 else if (typ == MatrixType::Lower || typ == MatrixType::Permuted_Lower) |
| 7788 | 1911 retval = ltsolve (mattype, b, info, rcon, sing_handler, false); |
| 5785 | 1912 else if (typ == MatrixType::Full || typ == MatrixType::Hermitian) |
| 7788 | 1913 retval = fsolve (mattype, b, info, rcon, sing_handler, true); |
| 5785 | 1914 else if (typ != MatrixType::Rectangular) |
| 1915 { | |
| 1916 (*current_liboctave_error_handler) ("unknown matrix type"); | |
| 1917 return Matrix (); | |
| 1918 } | |
| 1919 | |
| 1920 // Rectangular or one of the above solvers flags a singular matrix | |
| 1921 if (singular_fallback && mattype.type () == MatrixType::Rectangular) | |
| 1922 { | |
| 1923 octave_idx_type rank; | |
| 7788 | 1924 retval = lssolve (b, info, rank, rcon); |
| 5785 | 1925 } |
| 1926 | |
| 1927 return retval; | |
| 1928 } | |
| 1929 | |
| 1930 ComplexMatrix | |
| 1931 Matrix::solve (MatrixType &typ, const ComplexMatrix& b) const | |
| 1932 { | |
| 1933 ComplexMatrix tmp (*this); | |
| 1934 return tmp.solve (typ, b); | |
| 1935 } | |
| 1936 | |
| 1937 ComplexMatrix | |
| 1938 Matrix::solve (MatrixType &typ, const ComplexMatrix& b, | |
| 1939 octave_idx_type& info) const | |
| 1940 { | |
| 1941 ComplexMatrix tmp (*this); | |
| 1942 return tmp.solve (typ, b, info); | |
| 1943 } | |
| 1944 | |
| 1945 ComplexMatrix | |
| 1946 Matrix::solve (MatrixType &typ, const ComplexMatrix& b, octave_idx_type& info, | |
| 7788 | 1947 double& rcon) const |
| 5785 | 1948 { |
| 1949 ComplexMatrix tmp (*this); | |
| 7788 | 1950 return tmp.solve (typ, b, info, rcon); |
| 5785 | 1951 } |
| 1952 | |
| 1953 ComplexMatrix | |
| 1954 Matrix::solve (MatrixType &typ, const ComplexMatrix& b, octave_idx_type& info, | |
| 7788 | 1955 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 1956 bool singular_fallback) const |
| 1957 { | |
| 1958 ComplexMatrix tmp (*this); | |
| 7788 | 1959 return tmp.solve (typ, b, info, rcon, sing_handler, singular_fallback); |
| 5785 | 1960 } |
| 1961 | |
| 1962 ColumnVector | |
| 1963 Matrix::solve (MatrixType &typ, const ColumnVector& b) const | |
| 1964 { | |
| 7788 | 1965 octave_idx_type info; double rcon; |
| 1966 return solve (typ, b, info, rcon); | |
| 5785 | 1967 } |
| 1968 | |
| 1969 ColumnVector | |
| 1970 Matrix::solve (MatrixType &typ, const ColumnVector& b, | |
| 1971 octave_idx_type& info) const | |
| 1972 { | |
| 7788 | 1973 double rcon; |
| 1974 return solve (typ, b, info, rcon); | |
| 5785 | 1975 } |
| 1976 | |
| 1977 ColumnVector | |
| 1978 Matrix::solve (MatrixType &typ, const ColumnVector& b, octave_idx_type& info, | |
| 7788 | 1979 double& rcon) const |
| 5785 | 1980 { |
| 7788 | 1981 return solve (typ, b, info, rcon, 0); |
| 5785 | 1982 } |
| 1983 | |
| 1984 ColumnVector | |
| 1985 Matrix::solve (MatrixType &typ, const ColumnVector& b, octave_idx_type& info, | |
| 7788 | 1986 double& rcon, solve_singularity_handler sing_handler) const |
| 5785 | 1987 { |
| 1988 Matrix tmp (b); | |
| 7788 | 1989 return solve (typ, tmp, info, rcon, sing_handler).column(static_cast<octave_idx_type> (0)); |
| 5785 | 1990 } |
| 1991 | |
| 1992 ComplexColumnVector | |
| 1993 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b) const | |
| 1994 { | |
| 1995 ComplexMatrix tmp (*this); | |
| 1996 return tmp.solve (typ, b); | |
| 1997 } | |
| 1998 | |
| 1999 ComplexColumnVector | |
| 2000 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, | |
| 2001 octave_idx_type& info) const | |
| 2002 { | |
| 2003 ComplexMatrix tmp (*this); | |
| 2004 return tmp.solve (typ, b, info); | |
| 2005 } | |
| 2006 | |
| 2007 ComplexColumnVector | |
| 2008 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, | |
| 7788 | 2009 octave_idx_type& info, double& rcon) const |
| 5785 | 2010 { |
| 2011 ComplexMatrix tmp (*this); | |
| 7788 | 2012 return tmp.solve (typ, b, info, rcon); |
| 5785 | 2013 } |
| 2014 | |
| 2015 ComplexColumnVector | |
| 2016 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, | |
| 7788 | 2017 octave_idx_type& info, double& rcon, |
| 5785 | 2018 solve_singularity_handler sing_handler) const |
| 2019 { | |
| 2020 ComplexMatrix tmp (*this); | |
| 7788 | 2021 return tmp.solve(typ, b, info, rcon, sing_handler); |
| 5785 | 2022 } |
| 2023 | |
| 2024 Matrix | |
| 458 | 2025 Matrix::solve (const Matrix& b) const |
| 2026 { | |
| 5275 | 2027 octave_idx_type info; |
| 7788 | 2028 double rcon; |
| 2029 return solve (b, info, rcon, 0); | |
| 458 | 2030 } |
| 2031 | |
| 2032 Matrix | |
| 5275 | 2033 Matrix::solve (const Matrix& b, octave_idx_type& info) const |
| 458 | 2034 { |
| 7788 | 2035 double rcon; |
| 2036 return solve (b, info, rcon, 0); | |
| 458 | 2037 } |
| 2038 | |
| 2039 Matrix | |
| 7788 | 2040 Matrix::solve (const Matrix& b, octave_idx_type& info, double& rcon) const |
| 458 | 2041 { |
| 7788 | 2042 return solve (b, info, rcon, 0); |
| 3480 | 2043 } |
| 2044 | |
| 2045 Matrix | |
| 5785 | 2046 Matrix::solve (const Matrix& b, octave_idx_type& info, |
| 7788 | 2047 double& rcon, solve_singularity_handler sing_handler) const |
| 3480 | 2048 { |
| 5785 | 2049 MatrixType mattype (*this); |
| 7788 | 2050 return solve (mattype, b, info, rcon, sing_handler); |
| 458 | 2051 } |
| 2052 | |
| 2053 ComplexMatrix | |
| 2054 Matrix::solve (const ComplexMatrix& b) const | |
| 2055 { | |
| 2056 ComplexMatrix tmp (*this); | |
| 2057 return tmp.solve (b); | |
| 2058 } | |
| 2059 | |
| 2060 ComplexMatrix | |
| 5275 | 2061 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info) const |
| 458 | 2062 { |
| 2063 ComplexMatrix tmp (*this); | |
| 2064 return tmp.solve (b, info); | |
| 2065 } | |
| 2066 | |
| 2067 ComplexMatrix | |
| 7788 | 2068 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcon) const |
| 458 | 2069 { |
| 2070 ComplexMatrix tmp (*this); | |
| 7788 | 2071 return tmp.solve (b, info, rcon); |
| 458 | 2072 } |
| 2073 | |
| 3480 | 2074 ComplexMatrix |
| 7788 | 2075 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcon, |
| 3480 | 2076 solve_singularity_handler sing_handler) const |
| 2077 { | |
| 2078 ComplexMatrix tmp (*this); | |
| 7788 | 2079 return tmp.solve (b, info, rcon, sing_handler); |
| 3480 | 2080 } |
| 2081 | |
| 458 | 2082 ColumnVector |
| 2083 Matrix::solve (const ColumnVector& b) const | |
| 2084 { | |
| 7788 | 2085 octave_idx_type info; double rcon; |
| 2086 return solve (b, info, rcon); | |
| 458 | 2087 } |
| 2088 | |
| 2089 ColumnVector | |
| 5275 | 2090 Matrix::solve (const ColumnVector& b, octave_idx_type& info) const |
| 458 | 2091 { |
| 7788 | 2092 double rcon; |
| 2093 return solve (b, info, rcon); | |
| 458 | 2094 } |
| 2095 | |
| 2096 ColumnVector | |
| 7788 | 2097 Matrix::solve (const ColumnVector& b, octave_idx_type& info, double& rcon) const |
| 458 | 2098 { |
| 7788 | 2099 return solve (b, info, rcon, 0); |
| 3480 | 2100 } |
| 2101 | |
| 2102 ColumnVector | |
| 7788 | 2103 Matrix::solve (const ColumnVector& b, octave_idx_type& info, double& rcon, |
| 3480 | 2104 solve_singularity_handler sing_handler) const |
| 2105 { | |
| 5785 | 2106 MatrixType mattype (*this); |
| 7788 | 2107 return solve (mattype, b, info, rcon, sing_handler); |
| 458 | 2108 } |
| 2109 | |
| 2110 ComplexColumnVector | |
| 2111 Matrix::solve (const ComplexColumnVector& b) const | |
| 2112 { | |
| 2113 ComplexMatrix tmp (*this); | |
| 2114 return tmp.solve (b); | |
| 2115 } | |
| 2116 | |
| 2117 ComplexColumnVector | |
| 5275 | 2118 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info) const |
| 458 | 2119 { |
| 2120 ComplexMatrix tmp (*this); | |
| 2121 return tmp.solve (b, info); | |
| 2122 } | |
| 2123 | |
| 2124 ComplexColumnVector | |
| 7788 | 2125 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info, double& rcon) const |
| 458 | 2126 { |
| 2127 ComplexMatrix tmp (*this); | |
| 7788 | 2128 return tmp.solve (b, info, rcon); |
| 458 | 2129 } |
| 2130 | |
| 3480 | 2131 ComplexColumnVector |
| 7788 | 2132 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info, double& rcon, |
| 3480 | 2133 solve_singularity_handler sing_handler) const |
| 2134 { | |
| 2135 ComplexMatrix tmp (*this); | |
| 7788 | 2136 return tmp.solve (b, info, rcon, sing_handler); |
| 3480 | 2137 } |
| 2138 | |
| 458 | 2139 Matrix |
| 2140 Matrix::lssolve (const Matrix& b) const | |
| 2141 { | |
| 5275 | 2142 octave_idx_type info; |
| 2143 octave_idx_type rank; | |
| 7788 | 2144 double rcon; |
| 2145 return lssolve (b, info, rank, rcon); | |
| 458 | 2146 } |
| 2147 | |
| 2148 Matrix | |
| 5275 | 2149 Matrix::lssolve (const Matrix& b, octave_idx_type& info) const |
| 458 | 2150 { |
| 5275 | 2151 octave_idx_type rank; |
| 7788 | 2152 double rcon; |
| 2153 return lssolve (b, info, rank, rcon); | |
| 458 | 2154 } |
| 2155 | |
| 2156 Matrix | |
| 7072 | 2157 Matrix::lssolve (const Matrix& b, octave_idx_type& info, |
| 2158 octave_idx_type& rank) const | |
| 458 | 2159 { |
| 7788 | 2160 double rcon; |
| 2161 return lssolve (b, info, rank, rcon); | |
| 7076 | 2162 } |
| 2163 | |
| 2164 Matrix | |
| 2165 Matrix::lssolve (const Matrix& b, octave_idx_type& info, | |
| 7788 | 2166 octave_idx_type& rank, double &rcon) const |
| 7076 | 2167 { |
| 1948 | 2168 Matrix retval; |
| 2169 | |
| 5275 | 2170 octave_idx_type nrhs = b.cols (); |
| 2171 | |
| 2172 octave_idx_type m = rows (); | |
| 2173 octave_idx_type n = cols (); | |
| 458 | 2174 |
| 6924 | 2175 if (m != b.rows ()) |
| 1948 | 2176 (*current_liboctave_error_handler) |
| 6924 | 2177 ("matrix dimension mismatch solution of linear equations"); |
| 2178 else if (m == 0 || n == 0 || b.cols () == 0) | |
| 2179 retval = Matrix (n, b.cols (), 0.0); | |
| 1948 | 2180 else |
| 458 | 2181 { |
| 7072 | 2182 volatile octave_idx_type minmn = (m < n ? m : n); |
| 2183 octave_idx_type maxmn = m > n ? m : n; | |
| 7788 | 2184 rcon = -1.0; |
| 7072 | 2185 if (m != n) |
| 2186 { | |
| 2187 retval = Matrix (maxmn, nrhs, 0.0); | |
| 2188 | |
| 2189 for (octave_idx_type j = 0; j < nrhs; j++) | |
| 2190 for (octave_idx_type i = 0; i < m; i++) | |
| 2191 retval.elem (i, j) = b.elem (i, j); | |
| 2192 } | |
| 2193 else | |
| 2194 retval = b; | |
| 2195 | |
| 1948 | 2196 Matrix atmp = *this; |
| 2197 double *tmp_data = atmp.fortran_vec (); | |
| 2198 | |
| 7072 | 2199 double *pretval = retval.fortran_vec (); |
| 2200 Array<double> s (minmn); | |
| 7071 | 2201 double *ps = s.fortran_vec (); |
| 1948 | 2202 |
| 7072 | 2203 // Ask DGELSD what the dimension of WORK should be. |
| 5275 | 2204 octave_idx_type lwork = -1; |
| 3752 | 2205 |
| 2206 Array<double> work (1); | |
| 1948 | 2207 |
| 7477 | 2208 octave_idx_type smlsiz; |
| 2209 F77_FUNC (xilaenv, XILAENV) (9, F77_CONST_CHAR_ARG2 ("DGELSD", 6), | |
| 2210 F77_CONST_CHAR_ARG2 (" ", 1), | |
| 7478 | 2211 0, 0, 0, 0, smlsiz |
| 7477 | 2212 F77_CHAR_ARG_LEN (6) |
| 7478 | 2213 F77_CHAR_ARG_LEN (1)); |
| 7079 | 2214 |
|
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|
2215 octave_idx_type mnthr; |
|
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|
2216 F77_FUNC (xilaenv, XILAENV) (6, F77_CONST_CHAR_ARG2 ("DGELSD", 6), |
|
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|
2217 F77_CONST_CHAR_ARG2 (" ", 1), |
|
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|
2218 m, n, nrhs, -1, mnthr |
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|
2219 F77_CHAR_ARG_LEN (6) |
|
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|
2220 F77_CHAR_ARG_LEN (1)); |
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|
2221 |
| 7079 | 2222 // We compute the size of iwork because DGELSD in older versions |
| 2223 // of LAPACK does not return it on a query call. | |
| 7124 | 2224 double dminmn = static_cast<double> (minmn); |
| 2225 double dsmlsizp1 = static_cast<double> (smlsiz+1); | |
| 7079 | 2226 #if defined (HAVE_LOG2) |
| 7367 | 2227 double tmp = log2 (dminmn / dsmlsizp1); |
| 7079 | 2228 #else |
| 7367 | 2229 double tmp = log (dminmn / dsmlsizp1) / log (2.0); |
| 7079 | 2230 #endif |
|
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|
2231 octave_idx_type nlvl = static_cast<octave_idx_type> (tmp) + 1; |
| 7079 | 2232 if (nlvl < 0) |
| 2233 nlvl = 0; | |
| 2234 | |
| 2235 octave_idx_type liwork = 3 * minmn * nlvl + 11 * minmn; | |
| 2236 if (liwork < 1) | |
| 2237 liwork = 1; | |
| 7072 | 2238 Array<octave_idx_type> iwork (liwork); |
| 2239 octave_idx_type* piwork = iwork.fortran_vec (); | |
| 2240 | |
| 2241 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, | |
| 7788 | 2242 ps, rcon, rank, work.fortran_vec (), |
| 7072 | 2243 lwork, piwork, info)); |
| 1948 | 2244 |
| 7476 | 2245 // The workspace query is broken in at least LAPACK 3.0.0 |
|
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|
2246 // through 3.1.1 when n >= mnthr. The obtuse formula below |
| 7476 | 2247 // should provide sufficient workspace for DGELSD to operate |
| 2248 // efficiently. | |
|
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|
2249 if (n >= mnthr) |
| 7476 | 2250 { |
| 2251 const octave_idx_type wlalsd | |
| 2252 = 9*m + 2*m*smlsiz + 8*m*nlvl + m*nrhs + (smlsiz+1)*(smlsiz+1); | |
| 2253 | |
| 2254 octave_idx_type addend = m; | |
| 2255 | |
| 2256 if (2*m-4 > addend) | |
| 2257 addend = 2*m-4; | |
| 2258 | |
| 2259 if (nrhs > addend) | |
| 2260 addend = nrhs; | |
| 2261 | |
| 2262 if (n-3*m > addend) | |
| 2263 addend = n-3*m; | |
| 2264 | |
| 2265 if (wlalsd > addend) | |
| 2266 addend = wlalsd; | |
| 2267 | |
| 2268 const octave_idx_type lworkaround = 4*m + m*m + addend; | |
| 2269 | |
| 2270 if (work(0) < lworkaround) | |
| 2271 work(0) = lworkaround; | |
| 2272 } | |
|
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2273 else if (m >= n) |
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|
2274 { |
|
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|
2275 octave_idx_type lworkaround |
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|
2276 = 12*n + 2*n*smlsiz + 8*n*nlvl + n*nrhs + (smlsiz+1)*(smlsiz+1); |
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|
2277 |
|
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|
2278 if (work(0) < lworkaround) |
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|
2279 work(0) = lworkaround; |
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|
2280 } |
| 7476 | 2281 |
|
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|
2282 lwork = static_cast<octave_idx_type> (work(0)); |
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|
2283 work.resize (lwork); |
|
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|
2284 |
|
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|
2285 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, |
| 7788 | 2286 maxmn, ps, rcon, rank, |
|
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|
2287 work.fortran_vec (), lwork, |
|
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|
2288 piwork, info)); |
|
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|
2289 |
|
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|
2290 if (rank < minmn) |
|
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|
2291 (*current_liboctave_warning_handler) |
|
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|
2292 ("dgelsd: rank deficient %dx%d matrix, rank = %d", m, n, rank); |
|
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|
2293 if (s.elem (0) == 0.0) |
| 7788 | 2294 rcon = 0.0; |
| 1948 | 2295 else |
| 7788 | 2296 rcon = s.elem (minmn - 1) / s.elem (0); |
|
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|
2297 |
|
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|
2298 retval.resize (n, nrhs); |
| 458 | 2299 } |
| 2300 | |
| 2301 return retval; | |
| 2302 } | |
| 2303 | |
| 2304 ComplexMatrix | |
| 2305 Matrix::lssolve (const ComplexMatrix& b) const | |
| 2306 { | |
| 2307 ComplexMatrix tmp (*this); | |
| 5275 | 2308 octave_idx_type info; |
| 2309 octave_idx_type rank; | |
| 7788 | 2310 double rcon; |
| 2311 return tmp.lssolve (b, info, rank, rcon); | |
| 458 | 2312 } |
| 2313 | |
| 2314 ComplexMatrix | |
| 5275 | 2315 Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info) const |
| 458 | 2316 { |
| 2317 ComplexMatrix tmp (*this); | |
| 5275 | 2318 octave_idx_type rank; |
| 7788 | 2319 double rcon; |
| 2320 return tmp.lssolve (b, info, rank, rcon); | |
| 458 | 2321 } |
| 2322 | |
| 2323 ComplexMatrix | |
| 7076 | 2324 Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info, |
| 2325 octave_idx_type& rank) const | |
| 458 | 2326 { |
| 2327 ComplexMatrix tmp (*this); | |
| 7788 | 2328 double rcon; |
| 2329 return tmp.lssolve (b, info, rank, rcon); | |
| 7076 | 2330 } |
| 2331 | |
| 2332 ComplexMatrix | |
| 2333 Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info, | |
| 7788 | 2334 octave_idx_type& rank, double& rcon) const |
| 7076 | 2335 { |
| 2336 ComplexMatrix tmp (*this); | |
| 7788 | 2337 return tmp.lssolve (b, info, rank, rcon); |
| 458 | 2338 } |
| 2339 | |
| 2340 ColumnVector | |
| 2341 Matrix::lssolve (const ColumnVector& b) const | |
| 2342 { | |
| 5275 | 2343 octave_idx_type info; |
| 2344 octave_idx_type rank; | |
| 7788 | 2345 double rcon; |
| 2346 return lssolve (b, info, rank, rcon); | |
| 458 | 2347 } |
| 2348 | |
| 2349 ColumnVector | |
| 5275 | 2350 Matrix::lssolve (const ColumnVector& b, octave_idx_type& info) const |
| 458 | 2351 { |
| 5275 | 2352 octave_idx_type rank; |
| 7788 | 2353 double rcon; |
| 2354 return lssolve (b, info, rank, rcon); | |
| 458 | 2355 } |
| 2356 | |
| 2357 ColumnVector | |
| 7072 | 2358 Matrix::lssolve (const ColumnVector& b, octave_idx_type& info, |
| 2359 octave_idx_type& rank) const | |
| 458 | 2360 { |
| 7788 | 2361 double rcon; |
| 2362 return lssolve (b, info, rank, rcon); | |
| 7076 | 2363 } |
| 2364 | |
| 2365 ColumnVector | |
| 2366 Matrix::lssolve (const ColumnVector& b, octave_idx_type& info, | |
| 7788 | 2367 octave_idx_type& rank, double &rcon) const |
| 7076 | 2368 { |
| 1948 | 2369 ColumnVector retval; |
| 2370 | |
| 5275 | 2371 octave_idx_type nrhs = 1; |
| 2372 | |
| 2373 octave_idx_type m = rows (); | |
| 2374 octave_idx_type n = cols (); | |
| 458 | 2375 |
| 6924 | 2376 if (m != b.length ()) |
| 1948 | 2377 (*current_liboctave_error_handler) |
| 6924 | 2378 ("matrix dimension mismatch solution of linear equations"); |
| 2379 else if (m == 0 || n == 0) | |
| 2380 retval = ColumnVector (n, 0.0); | |
| 1948 | 2381 else |
| 458 | 2382 { |
| 7072 | 2383 volatile octave_idx_type minmn = (m < n ? m : n); |
| 2384 octave_idx_type maxmn = m > n ? m : n; | |
| 7788 | 2385 rcon = -1.0; |
| 7072 | 2386 |
| 2387 if (m != n) | |
| 2388 { | |
| 2389 retval = ColumnVector (maxmn, 0.0); | |
| 2390 | |
| 2391 for (octave_idx_type i = 0; i < m; i++) | |
| 2392 retval.elem (i) = b.elem (i); | |
| 2393 } | |
| 2394 else | |
| 2395 retval = b; | |
| 2396 | |
| 1948 | 2397 Matrix atmp = *this; |
| 2398 double *tmp_data = atmp.fortran_vec (); | |
| 2399 | |
| 7072 | 2400 double *pretval = retval.fortran_vec (); |
| 2401 Array<double> s (minmn); | |
| 7071 | 2402 double *ps = s.fortran_vec (); |
| 1948 | 2403 |
| 7072 | 2404 // Ask DGELSD what the dimension of WORK should be. |
| 5275 | 2405 octave_idx_type lwork = -1; |
| 3752 | 2406 |
| 2407 Array<double> work (1); | |
| 2408 | |
|
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2409 octave_idx_type smlsiz; |
|
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|
2410 F77_FUNC (xilaenv, XILAENV) (9, F77_CONST_CHAR_ARG2 ("DGELSD", 6), |
|
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|
2411 F77_CONST_CHAR_ARG2 (" ", 1), |
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|
2412 0, 0, 0, 0, smlsiz |
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|
2413 F77_CHAR_ARG_LEN (6) |
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|
2414 F77_CHAR_ARG_LEN (1)); |
| 7079 | 2415 |
| 2416 // We compute the size of iwork because DGELSD in older versions | |
| 2417 // of LAPACK does not return it on a query call. | |
| 7124 | 2418 double dminmn = static_cast<double> (minmn); |
| 2419 double dsmlsizp1 = static_cast<double> (smlsiz+1); | |
| 7079 | 2420 #if defined (HAVE_LOG2) |
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2421 double tmp = log2 (dminmn / dsmlsizp1); |
| 7079 | 2422 #else |
|
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|
2423 double tmp = log (dminmn / dsmlsizp1) / log (2.0); |
| 7079 | 2424 #endif |
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|
2425 octave_idx_type nlvl = static_cast<octave_idx_type> (tmp) + 1; |
| 7079 | 2426 if (nlvl < 0) |
| 2427 nlvl = 0; | |
| 2428 | |
| 2429 octave_idx_type liwork = 3 * minmn * nlvl + 11 * minmn; | |
| 2430 if (liwork < 1) | |
| 2431 liwork = 1; | |
| 7072 | 2432 Array<octave_idx_type> iwork (liwork); |
| 2433 octave_idx_type* piwork = iwork.fortran_vec (); | |
| 2434 | |
| 2435 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, | |
| 7788 | 2436 ps, rcon, rank, work.fortran_vec (), |
| 7072 | 2437 lwork, piwork, info)); |
| 1948 | 2438 |
|
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|
2439 lwork = static_cast<octave_idx_type> (work(0)); |
|
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2440 work.resize (lwork); |
|
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|
2441 |
|
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|
2442 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, |
| 7788 | 2443 maxmn, ps, rcon, rank, |
|
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|
2444 work.fortran_vec (), lwork, |
|
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|
2445 piwork, info)); |
|
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|
2446 |
|
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|
2447 if (rank < minmn) |
| 1948 | 2448 { |
|
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|
2449 if (rank < minmn) |
|
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|
2450 (*current_liboctave_warning_handler) |
|
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|
2451 ("dgelsd: rank deficient %dx%d matrix, rank = %d", m, n, rank); |
|
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|
2452 if (s.elem (0) == 0.0) |
| 7788 | 2453 rcon = 0.0; |
|
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|
2454 else |
| 7788 | 2455 rcon = s.elem (minmn - 1) / s.elem (0); |
| 1948 | 2456 } |
|
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|
2457 |
|
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|
2458 retval.resize (n, nrhs); |
| 458 | 2459 } |
| 2460 | |
| 2461 return retval; | |
| 2462 } | |
| 2463 | |
| 2464 ComplexColumnVector | |
| 2465 Matrix::lssolve (const ComplexColumnVector& b) const | |
| 2466 { | |
| 2467 ComplexMatrix tmp (*this); | |
| 7076 | 2468 octave_idx_type info; |
| 2469 octave_idx_type rank; | |
| 7788 | 2470 double rcon; |
| 2471 return tmp.lssolve (b, info, rank, rcon); | |
| 458 | 2472 } |
| 2473 | |
| 2474 ComplexColumnVector | |
| 5275 | 2475 Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info) const |
| 458 | 2476 { |
| 2477 ComplexMatrix tmp (*this); | |
| 7076 | 2478 octave_idx_type rank; |
| 7788 | 2479 double rcon; |
| 2480 return tmp.lssolve (b, info, rank, rcon); | |
| 458 | 2481 } |
| 2482 | |
| 2483 ComplexColumnVector | |
| 7076 | 2484 Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, |
| 2485 octave_idx_type& rank) const | |
| 458 | 2486 { |
| 2487 ComplexMatrix tmp (*this); | |
| 7788 | 2488 double rcon; |
| 2489 return tmp.lssolve (b, info, rank, rcon); | |
| 7076 | 2490 } |
| 2491 | |
| 2492 ComplexColumnVector | |
| 2493 Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, | |
| 7788 | 2494 octave_idx_type& rank, double &rcon) const |
| 7076 | 2495 { |
| 2496 ComplexMatrix tmp (*this); | |
| 7788 | 2497 return tmp.lssolve (b, info, rank, rcon); |
| 458 | 2498 } |
| 2499 | |
| 1819 | 2500 // Constants for matrix exponential calculation. |
| 2501 | |
| 2502 static double padec [] = | |
| 2503 { | |
| 2504 5.0000000000000000e-1, | |
| 2505 1.1666666666666667e-1, | |
| 2506 1.6666666666666667e-2, | |
| 2507 1.6025641025641026e-3, | |
| 2508 1.0683760683760684e-4, | |
| 2509 4.8562548562548563e-6, | |
| 2510 1.3875013875013875e-7, | |
| 2511 1.9270852604185938e-9, | |
| 2512 }; | |
| 2513 | |
| 7400 | 2514 static void |
| 7788 | 2515 solve_singularity_warning (double rcon) |
| 7400 | 2516 { |
| 2517 (*current_liboctave_warning_handler) | |
| 2518 ("singular matrix encountered in expm calculation, rcond = %g", | |
| 7788 | 2519 rcon); |
| 7400 | 2520 } |
| 2521 | |
| 1819 | 2522 Matrix |
| 2523 Matrix::expm (void) const | |
| 2524 { | |
| 2525 Matrix retval; | |
| 2526 | |
| 2527 Matrix m = *this; | |
| 2528 | |
| 6699 | 2529 if (numel () == 1) |
| 2530 return Matrix (1, 1, exp (m(0))); | |
| 2531 | |
| 5275 | 2532 octave_idx_type nc = columns (); |
| 1819 | 2533 |
| 3130 | 2534 // Preconditioning step 1: trace normalization to reduce dynamic |
| 2535 // range of poles, but avoid making stable eigenvalues unstable. | |
| 2536 | |
| 1819 | 2537 // trace shift value |
| 3331 | 2538 volatile double trshift = 0.0; |
| 1819 | 2539 |
| 5275 | 2540 for (octave_idx_type i = 0; i < nc; i++) |
| 1819 | 2541 trshift += m.elem (i, i); |
| 2542 | |
| 2543 trshift /= nc; | |
| 2544 | |
| 3130 | 2545 if (trshift > 0.0) |
| 2546 { | |
| 5275 | 2547 for (octave_idx_type i = 0; i < nc; i++) |
| 3130 | 2548 m.elem (i, i) -= trshift; |
| 2549 } | |
| 1819 | 2550 |
| 3331 | 2551 // Preconditioning step 2: balancing; code follows development |
| 2552 // in AEPBAL | |
| 2553 | |
| 2554 double *p_m = m.fortran_vec (); | |
| 2555 | |
| 5275 | 2556 octave_idx_type info, ilo, ihi, ilos, ihis; |
| 3468 | 2557 Array<double> dpermute (nc); |
| 2558 Array<double> dscale (nc); | |
| 3466 | 2559 |
| 3468 | 2560 // permutation first |
| 2561 char job = 'P'; | |
| 4552 | 2562 F77_XFCN (dgebal, DGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
| 2563 nc, p_m, nc, ilo, ihi, | |
| 2564 dpermute.fortran_vec (), info | |
| 2565 F77_CHAR_ARG_LEN (1))); | |
| 3466 | 2566 |
| 3468 | 2567 // then scaling |
| 2568 job = 'S'; | |
| 4552 | 2569 F77_XFCN (dgebal, DGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
| 2570 nc, p_m, nc, ilos, ihis, | |
| 2571 dscale.fortran_vec (), info | |
| 2572 F77_CHAR_ARG_LEN (1))); | |
| 3331 | 2573 |
| 1819 | 2574 // Preconditioning step 3: scaling. |
| 3331 | 2575 |
| 1819 | 2576 ColumnVector work(nc); |
| 3130 | 2577 double inf_norm; |
| 3331 | 2578 |
| 4552 | 2579 F77_XFCN (xdlange, XDLANGE, (F77_CONST_CHAR_ARG2 ("I", 1), |
| 2580 nc, nc, m.fortran_vec (), nc, | |
| 2581 work.fortran_vec (), inf_norm | |
| 2582 F77_CHAR_ARG_LEN (1))); | |
| 3331 | 2583 |
| 5275 | 2584 octave_idx_type sqpow = static_cast<octave_idx_type> (inf_norm > 0.0 |
| 1819 | 2585 ? (1.0 + log (inf_norm) / log (2.0)) |
| 2586 : 0.0); | |
| 3331 | 2587 |
| 1819 | 2588 // Check whether we need to square at all. |
| 3331 | 2589 |
| 1819 | 2590 if (sqpow < 0) |
| 2591 sqpow = 0; | |
| 3331 | 2592 |
| 1819 | 2593 if (sqpow > 0) |
| 2594 { | |
| 7400 | 2595 if (sqpow > 1023) |
| 2596 sqpow = 1023; | |
| 2597 | |
| 1819 | 2598 double scale_factor = 1.0; |
| 5275 | 2599 for (octave_idx_type i = 0; i < sqpow; i++) |
| 1819 | 2600 scale_factor *= 2.0; |
| 7400 | 2601 |
| 1819 | 2602 m = m / scale_factor; |
| 2603 } | |
| 3331 | 2604 |
| 1819 | 2605 // npp, dpp: pade' approx polynomial matrices. |
| 3331 | 2606 |
| 1819 | 2607 Matrix npp (nc, nc, 0.0); |
| 7265 | 2608 double *pnpp = npp.fortran_vec (); |
| 1819 | 2609 Matrix dpp = npp; |
| 7265 | 2610 double *pdpp = dpp.fortran_vec (); |
| 3331 | 2611 |
| 1819 | 2612 // Now powers a^8 ... a^1. |
| 3331 | 2613 |
| 5275 | 2614 octave_idx_type minus_one_j = -1; |
| 2615 for (octave_idx_type j = 7; j >= 0; j--) | |
| 1819 | 2616 { |
| 7265 | 2617 for (octave_idx_type i = 0; i < nc; i++) |
| 2618 { | |
| 2619 octave_idx_type k = i * nc + i; | |
| 2620 pnpp[k] += padec[j]; | |
| 2621 pdpp[k] += minus_one_j * padec[j]; | |
| 2622 } | |
| 2623 | |
| 2624 npp = m * npp; | |
| 2625 pnpp = npp.fortran_vec (); | |
| 2626 | |
| 2627 dpp = m * dpp; | |
| 2628 pdpp = dpp.fortran_vec (); | |
| 2629 | |
| 1819 | 2630 minus_one_j *= -1; |
| 2631 } | |
| 3331 | 2632 |
| 1819 | 2633 // Zero power. |
| 3331 | 2634 |
| 1819 | 2635 dpp = -dpp; |
| 5275 | 2636 for (octave_idx_type j = 0; j < nc; j++) |
| 1819 | 2637 { |
| 2638 npp.elem (j, j) += 1.0; | |
| 2639 dpp.elem (j, j) += 1.0; | |
| 2640 } | |
| 3331 | 2641 |
| 1819 | 2642 // Compute pade approximation = inverse (dpp) * npp. |
| 2643 | |
| 7788 | 2644 double rcon; |
| 2645 retval = dpp.solve (npp, info, rcon, solve_singularity_warning); | |
| 7400 | 2646 |
| 2647 if (info < 0) | |
| 2648 return retval; | |
| 2649 | |
| 1819 | 2650 // Reverse preconditioning step 3: repeated squaring. |
| 3331 | 2651 |
| 1819 | 2652 while (sqpow) |
| 2653 { | |
| 2654 retval = retval * retval; | |
| 2655 sqpow--; | |
| 2656 } | |
| 3331 | 2657 |
| 1819 | 2658 // Reverse preconditioning step 2: inverse balancing. |
| 3466 | 2659 // apply inverse scaling to computed exponential |
| 5275 | 2660 for (octave_idx_type i = 0; i < nc; i++) |
| 2661 for (octave_idx_type j = 0; j < nc; j++) | |
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|
2662 retval(i,j) *= dscale(i) / dscale(j); |
| 3466 | 2663 |
| 4153 | 2664 OCTAVE_QUIT; |
| 2665 | |
| 3466 | 2666 // construct balancing permutation vector |
| 5275 | 2667 Array<octave_idx_type> iperm (nc); |
| 2668 for (octave_idx_type i = 0; i < nc; i++) | |
| 4593 | 2669 iperm(i) = i; // identity permutation |
| 3466 | 2670 |
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|
2671 // trailing permutations must be done in reverse order |
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|
2672 for (octave_idx_type i = nc - 1; i >= ihi; i--) |
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2673 { |
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|
2674 octave_idx_type swapidx = static_cast<octave_idx_type> (dpermute(i)) - 1; |
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|
2675 octave_idx_type tmp = iperm(i); |
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|
2676 iperm(i) = iperm(swapidx); |
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|
2677 iperm(swapidx) = tmp; |
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|
2678 } |
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|
2679 |
| 3466 | 2680 // leading permutations in forward order |
| 5275 | 2681 for (octave_idx_type i = 0; i < (ilo-1); i++) |
| 3468 | 2682 { |
| 5275 | 2683 octave_idx_type swapidx = static_cast<octave_idx_type> (dpermute(i)) - 1; |
| 2684 octave_idx_type tmp = iperm(i); | |
| 4593 | 2685 iperm(i) = iperm (swapidx); |
| 2686 iperm(swapidx) = tmp; | |
| 3468 | 2687 } |
| 3466 | 2688 |
| 7416 | 2689 // construct inverse balancing permutation vector |
| 2690 Array<octave_idx_type> invpvec (nc); | |
| 2691 for (octave_idx_type i = 0; i < nc; i++) | |
| 2692 invpvec(iperm(i)) = i; // Thanks to R. A. Lippert for this method | |
| 2693 | |
| 2694 OCTAVE_QUIT; | |
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2695 |
| 7416 | 2696 Matrix tmpMat = retval; |
| 2697 for (octave_idx_type i = 0; i < nc; i++) | |
| 2698 for (octave_idx_type j = 0; j < nc; j++) | |
| 2699 retval(i,j) = tmpMat(invpvec(i),invpvec(j)); | |
| 2700 | |
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|
2701 // Reverse preconditioning step 1: fix trace normalization. |
| 3130 | 2702 if (trshift > 0.0) |
| 2703 retval = exp (trshift) * retval; | |
| 2704 | |
| 2705 return retval; | |
| 1819 | 2706 } |
| 2707 | |
| 458 | 2708 Matrix& |
| 2709 Matrix::operator += (const DiagMatrix& a) | |
| 2710 { | |
| 5275 | 2711 octave_idx_type nr = rows (); |
| 2712 octave_idx_type nc = cols (); | |
| 2713 | |
| 2714 octave_idx_type a_nr = a.rows (); | |
| 2715 octave_idx_type a_nc = a.cols (); | |
| 2385 | 2716 |
| 2717 if (nr != a_nr || nc != a_nc) | |
| 458 | 2718 { |
| 2385 | 2719 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
| 458 | 2720 return *this; |
| 2721 } | |
| 2722 | |
| 5275 | 2723 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 2724 elem (i, i) += a.elem (i, i); |
| 2725 | |
| 2726 return *this; | |
| 2727 } | |
| 2728 | |
| 2729 Matrix& | |
| 2730 Matrix::operator -= (const DiagMatrix& a) | |
| 2731 { | |
| 5275 | 2732 octave_idx_type nr = rows (); |
| 2733 octave_idx_type nc = cols (); | |
| 2734 | |
| 2735 octave_idx_type a_nr = a.rows (); | |
| 2736 octave_idx_type a_nc = a.cols (); | |
| 2385 | 2737 |
| 2738 if (nr != a_nr || nc != a_nc) | |
| 458 | 2739 { |
| 2385 | 2740 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
| 458 | 2741 return *this; |
| 2742 } | |
| 2743 | |
| 5275 | 2744 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 2745 elem (i, i) -= a.elem (i, i); |
| 2746 | |
| 2747 return *this; | |
| 2748 } | |
| 2749 | |
| 2750 // unary operations | |
| 2751 | |
| 2964 | 2752 boolMatrix |
| 458 | 2753 Matrix::operator ! (void) const |
| 2754 { | |
| 5275 | 2755 octave_idx_type nr = rows (); |
| 2756 octave_idx_type nc = cols (); | |
| 458 | 2757 |
| 2964 | 2758 boolMatrix b (nr, nc); |
| 458 | 2759 |
| 5275 | 2760 for (octave_idx_type j = 0; j < nc; j++) |
| 2761 for (octave_idx_type i = 0; i < nr; i++) | |
| 458 | 2762 b.elem (i, j) = ! elem (i, j); |
| 2763 | |
| 2764 return b; | |
| 2765 } | |
| 2766 | |
| 1205 | 2767 // column vector by row vector -> matrix operations |
| 458 | 2768 |
| 1205 | 2769 Matrix |
| 2770 operator * (const ColumnVector& v, const RowVector& a) | |
| 458 | 2771 { |
| 1948 | 2772 Matrix retval; |
| 2773 | |
| 5275 | 2774 octave_idx_type len = v.length (); |
| 3233 | 2775 |
| 2776 if (len != 0) | |
| 1205 | 2777 { |
| 5275 | 2778 octave_idx_type a_len = a.length (); |
| 3233 | 2779 |
| 2780 retval.resize (len, a_len); | |
| 2781 double *c = retval.fortran_vec (); | |
| 2782 | |
| 4552 | 2783 F77_XFCN (dgemm, DGEMM, (F77_CONST_CHAR_ARG2 ("N", 1), |
| 2784 F77_CONST_CHAR_ARG2 ("N", 1), | |
| 2785 len, a_len, 1, 1.0, v.data (), len, | |
| 2786 a.data (), 1, 0.0, c, len | |
| 2787 F77_CHAR_ARG_LEN (1) | |
| 2788 F77_CHAR_ARG_LEN (1))); | |
| 1205 | 2789 } |
| 458 | 2790 |
| 1948 | 2791 return retval; |
| 458 | 2792 } |
| 2793 | |
| 2794 // other operations. | |
| 2795 | |
| 2796 Matrix | |
|
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diff
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|
2797 Matrix::map (dmapper fcn) const |
| 1205 | 2798 { |
|
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diff
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|
2799 return MArray2<double>::map<double> (func_ptr (fcn)); |
|
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parents:
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diff
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|
2800 } |
|
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parents:
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diff
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|
2801 |
|
8c32f95c2639
convert mapper functions to new format
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parents:
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diff
changeset
|
2802 ComplexMatrix |
|
8c32f95c2639
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parents:
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diff
changeset
|
2803 Matrix::map (cmapper fcn) const |
|
8c32f95c2639
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parents:
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diff
changeset
|
2804 { |
|
8c32f95c2639
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diff
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|
2805 return MArray2<double>::map<Complex> (func_ptr (fcn)); |
| 1205 | 2806 } |
| 2807 | |
| 3248 | 2808 boolMatrix |
|
7503
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diff
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|
2809 Matrix::map (bmapper fcn) const |
| 3248 | 2810 { |
|
7503
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diff
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|
2811 return MArray2<double>::map<bool> (func_ptr (fcn)); |
| 458 | 2812 } |
| 2813 | |
| 2385 | 2814 bool |
| 4431 | 2815 Matrix::any_element_is_negative (bool neg_zero) const |
| 2385 | 2816 { |
| 5275 | 2817 octave_idx_type nel = nelem (); |
| 2385 | 2818 |
| 4431 | 2819 if (neg_zero) |
| 2820 { | |
| 5275 | 2821 for (octave_idx_type i = 0; i < nel; i++) |
| 4634 | 2822 if (lo_ieee_signbit (elem (i))) |
| 2823 return true; | |
| 4431 | 2824 } |
| 2825 else | |
| 2826 { | |
| 5275 | 2827 for (octave_idx_type i = 0; i < nel; i++) |
| 4634 | 2828 if (elem (i) < 0) |
| 2829 return true; | |
| 4431 | 2830 } |
| 2385 | 2831 |
| 2832 return false; | |
| 2833 } | |
| 2834 | |
|
7922
935be827eaf8
error for NaN values in & and | expressions
John W. Eaton <jwe@octave.org>
parents:
7803
diff
changeset
|
2835 bool |
|
935be827eaf8
error for NaN values in & and | expressions
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parents:
7803
diff
changeset
|
2836 Matrix::any_element_is_nan (void) const |
|
935be827eaf8
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parents:
7803
diff
changeset
|
2837 { |
|
935be827eaf8
error for NaN values in & and | expressions
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parents:
7803
diff
changeset
|
2838 octave_idx_type nel = nelem (); |
|
935be827eaf8
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John W. Eaton <jwe@octave.org>
parents:
7803
diff
changeset
|
2839 |
|
935be827eaf8
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John W. Eaton <jwe@octave.org>
parents:
7803
diff
changeset
|
2840 for (octave_idx_type i = 0; i < nel; i++) |
|
935be827eaf8
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John W. Eaton <jwe@octave.org>
parents:
7803
diff
changeset
|
2841 { |
|
935be827eaf8
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parents:
7803
diff
changeset
|
2842 double val = elem (i); |
|
935be827eaf8
error for NaN values in & and | expressions
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parents:
7803
diff
changeset
|
2843 if (xisnan (val)) |
|
935be827eaf8
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John W. Eaton <jwe@octave.org>
parents:
7803
diff
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|
2844 return true; |
|
935be827eaf8
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John W. Eaton <jwe@octave.org>
parents:
7803
diff
changeset
|
2845 } |
|
935be827eaf8
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John W. Eaton <jwe@octave.org>
parents:
7803
diff
changeset
|
2846 |
|
935be827eaf8
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John W. Eaton <jwe@octave.org>
parents:
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diff
changeset
|
2847 return false; |
|
935be827eaf8
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John W. Eaton <jwe@octave.org>
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diff
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|
2848 } |
| 2385 | 2849 |
| 2850 bool | |
| 2851 Matrix::any_element_is_inf_or_nan (void) const | |
| 2852 { | |
| 5275 | 2853 octave_idx_type nel = nelem (); |
| 2854 | |
| 2855 for (octave_idx_type i = 0; i < nel; i++) | |
| 4634 | 2856 { |
| 2857 double val = elem (i); | |
| 2858 if (xisinf (val) || xisnan (val)) | |
| 2859 return true; | |
| 2860 } | |
| 2861 | |
| 2862 return false; | |
| 2385 | 2863 } |
| 2864 | |
| 2865 bool | |
| 5943 | 2866 Matrix::any_element_not_one_or_zero (void) const |
| 2867 { | |
| 2868 octave_idx_type nel = nelem (); | |
| 2869 | |
| 2870 for (octave_idx_type i = 0; i < nel; i++) | |
| 2871 { | |
| 2872 double val = elem (i); | |
| 2873 if (val != 0 && val != 1) | |
| 2874 return true; | |
| 2875 } | |
| 2876 | |
| 2877 return false; | |
| 2878 } | |
| 2879 | |
| 2880 bool | |
| 2385 | 2881 Matrix::all_elements_are_int_or_inf_or_nan (void) const |
| 2882 { | |
| 5275 | 2883 octave_idx_type nel = nelem (); |
| 2884 | |
| 2885 for (octave_idx_type i = 0; i < nel; i++) | |
| 4634 | 2886 { |
| 2887 double val = elem (i); | |
| 2888 if (xisnan (val) || D_NINT (val) == val) | |
| 2889 continue; | |
| 2890 else | |
| 2891 return false; | |
| 2892 } | |
| 2385 | 2893 |
| 2894 return true; | |
| 2895 } | |
| 2896 | |
| 1968 | 2897 // Return nonzero if any element of M is not an integer. Also extract |
| 2898 // the largest and smallest values and return them in MAX_VAL and MIN_VAL. | |
| 2899 | |
| 2385 | 2900 bool |
| 1968 | 2901 Matrix::all_integers (double& max_val, double& min_val) const |
| 2902 { | |
| 5275 | 2903 octave_idx_type nel = nelem (); |
| 4634 | 2904 |
| 2905 if (nel > 0) | |
| 1968 | 2906 { |
| 4634 | 2907 max_val = elem (0); |
| 2908 min_val = elem (0); | |
| 1968 | 2909 } |
| 2910 else | |
| 2385 | 2911 return false; |
| 1968 | 2912 |
| 5275 | 2913 for (octave_idx_type i = 0; i < nel; i++) |
| 4634 | 2914 { |
| 2915 double val = elem (i); | |
| 2916 | |
| 2917 if (val > max_val) | |
| 2918 max_val = val; | |
| 2919 | |
| 2920 if (val < min_val) | |
| 2921 min_val = val; | |
| 2922 | |
| 2923 if (D_NINT (val) != val) | |
| 2924 return false; | |
| 2925 } | |
| 2385 | 2926 |
| 2927 return true; | |
| 1968 | 2928 } |
| 2929 | |
| 2385 | 2930 bool |
| 1968 | 2931 Matrix::too_large_for_float (void) const |
| 2932 { | |
| 5275 | 2933 octave_idx_type nel = nelem (); |
| 2934 | |
| 2935 for (octave_idx_type i = 0; i < nel; i++) | |
| 4634 | 2936 { |
| 2937 double val = elem (i); | |
| 2938 | |
| 5389 | 2939 if (! (xisnan (val) || xisinf (val)) |
| 5387 | 2940 && fabs (val) > FLT_MAX) |
| 4634 | 2941 return true; |
| 2942 } | |
| 1968 | 2943 |
| 2385 | 2944 return false; |
| 1968 | 2945 } |
| 2946 | |
| 5775 | 2947 // FIXME Do these really belong here? Maybe they should be |
| 4015 | 2948 // in a base class? |
| 458 | 2949 |
| 2832 | 2950 boolMatrix |
| 4015 | 2951 Matrix::all (int dim) const |
| 458 | 2952 { |
| 4015 | 2953 MX_ALL_OP (dim); |
| 458 | 2954 } |
| 2955 | |
| 2832 | 2956 boolMatrix |
| 4015 | 2957 Matrix::any (int dim) const |
| 458 | 2958 { |
| 4015 | 2959 MX_ANY_OP (dim); |
| 458 | 2960 } |
| 2961 | |
| 2962 Matrix | |
| 3723 | 2963 Matrix::cumprod (int dim) const |
| 458 | 2964 { |
| 4015 | 2965 MX_CUMULATIVE_OP (Matrix, double, *=); |
| 458 | 2966 } |
| 2967 | |
| 2968 Matrix | |
| 3723 | 2969 Matrix::cumsum (int dim) const |
| 458 | 2970 { |
| 4015 | 2971 MX_CUMULATIVE_OP (Matrix, double, +=); |
| 458 | 2972 } |
| 2973 | |
| 2974 Matrix | |
| 3723 | 2975 Matrix::prod (int dim) const |
| 458 | 2976 { |
| 3864 | 2977 MX_REDUCTION_OP (Matrix, *=, 1.0, 1.0); |
| 458 | 2978 } |
| 2979 | |
| 2980 Matrix | |
| 3723 | 2981 Matrix::sum (int dim) const |
| 458 | 2982 { |
| 3864 | 2983 MX_REDUCTION_OP (Matrix, +=, 0.0, 0.0); |
| 458 | 2984 } |
| 2985 | |
| 2986 Matrix | |
| 3723 | 2987 Matrix::sumsq (int dim) const |
| 458 | 2988 { |
| 3864 | 2989 #define ROW_EXPR \ |
| 2990 double d = elem (i, j); \ | |
| 2991 retval.elem (i, 0) += d * d | |
| 2992 | |
| 2993 #define COL_EXPR \ | |
| 2994 double d = elem (i, j); \ | |
| 2995 retval.elem (0, j) += d * d | |
| 2996 | |
| 2997 MX_BASE_REDUCTION_OP (Matrix, ROW_EXPR, COL_EXPR, 0.0, 0.0); | |
| 2998 | |
| 2999 #undef ROW_EXPR | |
| 3000 #undef COL_EXPR | |
| 458 | 3001 } |
| 3002 | |
| 2385 | 3003 Matrix |
| 3004 Matrix::abs (void) const | |
| 3005 { | |
| 5275 | 3006 octave_idx_type nr = rows (); |
| 3007 octave_idx_type nc = cols (); | |
| 2385 | 3008 |
| 3009 Matrix retval (nr, nc); | |
| 3010 | |
| 5275 | 3011 for (octave_idx_type j = 0; j < nc; j++) |
| 3012 for (octave_idx_type i = 0; i < nr; i++) | |
| 2385 | 3013 retval (i, j) = fabs (elem (i, j)); |
| 3014 | |
| 3015 return retval; | |
| 3016 } | |
| 3017 | |
|
7620
36594d5bbe13
Move diag function into the octave_value class
David Bateman <dbateman@free.fr>
parents:
7544
diff
changeset
|
3018 Matrix |
| 5275 | 3019 Matrix::diag (octave_idx_type k) const |
| 458 | 3020 { |
|
7620
36594d5bbe13
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David Bateman <dbateman@free.fr>
parents:
7544
diff
changeset
|
3021 return MArray2<double>::diag (k); |
| 458 | 3022 } |
| 3023 | |
| 3024 ColumnVector | |
| 3025 Matrix::row_min (void) const | |
| 3026 { | |
| 5275 | 3027 Array<octave_idx_type> dummy_idx; |
| 4587 | 3028 return row_min (dummy_idx); |
| 458 | 3029 } |
| 3030 | |
| 3031 ColumnVector | |
| 5275 | 3032 Matrix::row_min (Array<octave_idx_type>& idx_arg) const |
| 458 | 3033 { |
| 3034 ColumnVector result; | |
| 3035 | |
| 5275 | 3036 octave_idx_type nr = rows (); |
| 3037 octave_idx_type nc = cols (); | |
| 458 | 3038 |
| 3039 if (nr > 0 && nc > 0) | |
| 3040 { | |
| 3041 result.resize (nr); | |
| 4587 | 3042 idx_arg.resize (nr); |
| 458 | 3043 |
| 5275 | 3044 for (octave_idx_type i = 0; i < nr; i++) |
| 458 | 3045 { |
| 5275 | 3046 octave_idx_type idx_j; |
| 4469 | 3047 |
| 3048 double tmp_min = octave_NaN; | |
| 3049 | |
| 3050 for (idx_j = 0; idx_j < nc; idx_j++) | |
| 2354 | 3051 { |
| 4469 | 3052 tmp_min = elem (i, idx_j); |
| 3053 | |
| 5389 | 3054 if (! xisnan (tmp_min)) |
| 4469 | 3055 break; |
| 3056 } | |
| 3057 | |
| 5275 | 3058 for (octave_idx_type j = idx_j+1; j < nc; j++) |
| 4469 | 3059 { |
| 3060 double tmp = elem (i, j); | |
| 3061 | |
| 5389 | 3062 if (xisnan (tmp)) |
| 4469 | 3063 continue; |
| 3064 else if (tmp < tmp_min) | |
| 2354 | 3065 { |
| 4469 | 3066 idx_j = j; |
| 3067 tmp_min = tmp; | |
| 2354 | 3068 } |
| 3069 } | |
| 3070 | |
| 4469 | 3071 result.elem (i) = tmp_min; |
| 5389 | 3072 idx_arg.elem (i) = xisnan (tmp_min) ? 0 : idx_j; |
| 458 | 3073 } |
| 3074 } | |
| 3075 | |
| 3076 return result; | |
| 3077 } | |
| 3078 | |
| 3079 ColumnVector | |
| 3080 Matrix::row_max (void) const | |
| 3081 { | |
| 5275 | 3082 Array<octave_idx_type> dummy_idx; |
| 4587 | 3083 return row_max (dummy_idx); |
| 458 | 3084 } |
| 3085 | |
| 3086 ColumnVector | |
| 5275 | 3087 Matrix::row_max (Array<octave_idx_type>& idx_arg) const |
| 458 | 3088 { |
| 3089 ColumnVector result; | |
| 3090 | |
| 5275 | 3091 octave_idx_type nr = rows (); |
| 3092 octave_idx_type nc = cols (); | |
| 458 | 3093 |
| 3094 if (nr > 0 && nc > 0) | |
| 3095 { | |
| 3096 result.resize (nr); | |
| 4587 | 3097 idx_arg.resize (nr); |
| 458 | 3098 |
| 5275 | 3099 for (octave_idx_type i = 0; i < nr; i++) |
| 458 | 3100 { |
| 5275 | 3101 octave_idx_type idx_j; |
| 4469 | 3102 |
| 3103 double tmp_max = octave_NaN; | |
| 3104 | |
| 3105 for (idx_j = 0; idx_j < nc; idx_j++) | |
| 2354 | 3106 { |
| 4469 | 3107 tmp_max = elem (i, idx_j); |
| 3108 | |
| 5389 | 3109 if (! xisnan (tmp_max)) |
| 4469 | 3110 break; |
| 3111 } | |
| 3112 | |
| 5275 | 3113 for (octave_idx_type j = idx_j+1; j < nc; j++) |
| 4469 | 3114 { |
| 3115 double tmp = elem (i, j); | |
| 3116 | |
| 5389 | 3117 if (xisnan (tmp)) |
| 4469 | 3118 continue; |
| 3119 else if (tmp > tmp_max) | |
| 2354 | 3120 { |
| 4469 | 3121 idx_j = j; |
| 3122 tmp_max = tmp; | |
| 2354 | 3123 } |
| 3124 } | |
| 3125 | |
| 4469 | 3126 result.elem (i) = tmp_max; |
| 5389 | 3127 idx_arg.elem (i) = xisnan (tmp_max) ? 0 : idx_j; |
| 458 | 3128 } |
| 3129 } | |
| 3130 | |
| 3131 return result; | |
| 3132 } | |
| 3133 | |
| 3134 RowVector | |
| 3135 Matrix::column_min (void) const | |
| 3136 { | |
| 5275 | 3137 Array<octave_idx_type> dummy_idx; |
| 4587 | 3138 return column_min (dummy_idx); |
| 458 | 3139 } |
| 2354 | 3140 |
| 458 | 3141 RowVector |
| 5275 | 3142 Matrix::column_min (Array<octave_idx_type>& idx_arg) const |
| 458 | 3143 { |
| 3144 RowVector result; | |
| 3145 | |
| 5275 | 3146 octave_idx_type nr = rows (); |
| 3147 octave_idx_type nc = cols (); | |
| 458 | 3148 |
| 3149 if (nr > 0 && nc > 0) | |
| 3150 { | |
| 3151 result.resize (nc); | |
| 4587 | 3152 idx_arg.resize (nc); |
| 458 | 3153 |
| 5275 | 3154 for (octave_idx_type j = 0; j < nc; j++) |
| 458 | 3155 { |
| 5275 | 3156 octave_idx_type idx_i; |
| 4469 | 3157 |
| 3158 double tmp_min = octave_NaN; | |
| 3159 | |
| 3160 for (idx_i = 0; idx_i < nr; idx_i++) | |
| 2354 | 3161 { |
| 4469 | 3162 tmp_min = elem (idx_i, j); |
| 3163 | |
| 5389 | 3164 if (! xisnan (tmp_min)) |
| 4469 | 3165 break; |
| 3166 } | |
| 3167 | |
| 5275 | 3168 for (octave_idx_type i = idx_i+1; i < nr; i++) |
| 4469 | 3169 { |
| 3170 double tmp = elem (i, j); | |
| 3171 | |
| 5389 | 3172 if (xisnan (tmp)) |
| 4469 | 3173 continue; |
| 3174 else if (tmp < tmp_min) | |
| 2354 | 3175 { |
| 4469 | 3176 idx_i = i; |
| 3177 tmp_min = tmp; | |
| 2354 | 3178 } |
| 3179 } | |
| 3180 | |
| 4469 | 3181 result.elem (j) = tmp_min; |
| 5389 | 3182 idx_arg.elem (j) = xisnan (tmp_min) ? 0 : idx_i; |
| 458 | 3183 } |
| 3184 } | |
| 3185 | |
| 3186 return result; | |
| 3187 } | |
| 3188 | |
| 2354 | 3189 RowVector |
| 3190 Matrix::column_max (void) const | |
| 3191 { | |
| 5275 | 3192 Array<octave_idx_type> dummy_idx; |
| 4587 | 3193 return column_max (dummy_idx); |
| 2354 | 3194 } |
| 458 | 3195 |
| 3196 RowVector | |
| 5275 | 3197 Matrix::column_max (Array<octave_idx_type>& idx_arg) const |
| 458 | 3198 { |
| 3199 RowVector result; | |
| 3200 | |
| 5275 | 3201 octave_idx_type nr = rows (); |
| 3202 octave_idx_type nc = cols (); | |
| 458 | 3203 |
| 3204 if (nr > 0 && nc > 0) | |
| 3205 { | |
| 3206 result.resize (nc); | |
| 4587 | 3207 idx_arg.resize (nc); |
| 458 | 3208 |
| 5275 | 3209 for (octave_idx_type j = 0; j < nc; j++) |
| 458 | 3210 { |
| 5275 | 3211 octave_idx_type idx_i; |
| 4469 | 3212 |
| 3213 double tmp_max = octave_NaN; | |
| 3214 | |
| 3215 for (idx_i = 0; idx_i < nr; idx_i++) | |
| 2354 | 3216 { |
| 4469 | 3217 tmp_max = elem (idx_i, j); |
| 3218 | |
| 5389 | 3219 if (! xisnan (tmp_max)) |
| 4469 | 3220 break; |
| 3221 } | |
| 3222 | |
| 5275 | 3223 for (octave_idx_type i = idx_i+1; i < nr; i++) |
| 4469 | 3224 { |
| 3225 double tmp = elem (i, j); | |
| 3226 | |
| 5389 | 3227 if (xisnan (tmp)) |
| 4469 | 3228 continue; |
| 3229 else if (tmp > tmp_max) | |
| 2354 | 3230 { |
| 4469 | 3231 idx_i = i; |
| 3232 tmp_max = tmp; | |
| 2354 | 3233 } |
| 3234 } | |
| 3235 | |
| 4469 | 3236 result.elem (j) = tmp_max; |
| 5389 | 3237 idx_arg.elem (j) = xisnan (tmp_max) ? 0 : idx_i; |
| 458 | 3238 } |
| 3239 } | |
| 3240 | |
| 3241 return result; | |
| 3242 } | |
| 3243 | |
| 3504 | 3244 std::ostream& |
| 3245 operator << (std::ostream& os, const Matrix& a) | |
| 458 | 3246 { |
| 5275 | 3247 for (octave_idx_type i = 0; i < a.rows (); i++) |
| 458 | 3248 { |
| 5275 | 3249 for (octave_idx_type j = 0; j < a.cols (); j++) |
| 4130 | 3250 { |
| 3251 os << " "; | |
| 3252 octave_write_double (os, a.elem (i, j)); | |
| 3253 } | |
| 458 | 3254 os << "\n"; |
| 3255 } | |
| 3256 return os; | |
| 3257 } | |
| 3258 | |
| 3504 | 3259 std::istream& |
| 3260 operator >> (std::istream& is, Matrix& a) | |
| 458 | 3261 { |
| 5275 | 3262 octave_idx_type nr = a.rows (); |
| 3263 octave_idx_type nc = a.cols (); | |
| 458 | 3264 |
| 3265 if (nr < 1 || nc < 1) | |
| 3504 | 3266 is.clear (std::ios::badbit); |
| 458 | 3267 else |
| 3268 { | |
| 3269 double tmp; | |
| 5275 | 3270 for (octave_idx_type i = 0; i < nr; i++) |
| 3271 for (octave_idx_type j = 0; j < nc; j++) | |
| 458 | 3272 { |
| 4130 | 3273 tmp = octave_read_double (is); |
| 458 | 3274 if (is) |
| 3275 a.elem (i, j) = tmp; | |
| 3276 else | |
| 2795 | 3277 goto done; |
| 458 | 3278 } |
| 3279 } | |
| 3280 | |
| 2795 | 3281 done: |
| 3282 | |
| 458 | 3283 return is; |
| 3284 } | |
| 3285 | |
| 1819 | 3286 Matrix |
| 3287 Givens (double x, double y) | |
| 3288 { | |
| 3289 double cc, s, temp_r; | |
| 3290 | |
| 3887 | 3291 F77_FUNC (dlartg, DLARTG) (x, y, cc, s, temp_r); |
| 1819 | 3292 |
| 3293 Matrix g (2, 2); | |
| 3294 | |
| 3295 g.elem (0, 0) = cc; | |
| 3296 g.elem (1, 1) = cc; | |
| 3297 g.elem (0, 1) = s; | |
| 3298 g.elem (1, 0) = -s; | |
| 3299 | |
| 3300 return g; | |
| 3301 } | |
| 3302 | |
| 3303 Matrix | |
| 3304 Sylvester (const Matrix& a, const Matrix& b, const Matrix& c) | |
| 3305 { | |
| 3306 Matrix retval; | |
| 3307 | |
| 5775 | 3308 // FIXME -- need to check that a, b, and c are all the same |
| 1819 | 3309 // size. |
| 3310 | |
| 3311 // Compute Schur decompositions. | |
| 3312 | |
| 3313 SCHUR as (a, "U"); | |
| 3314 SCHUR bs (b, "U"); | |
| 3315 | |
| 3316 // Transform c to new coordinates. | |
| 3317 | |
| 3318 Matrix ua = as.unitary_matrix (); | |
| 3319 Matrix sch_a = as.schur_matrix (); | |
| 3320 | |
| 3321 Matrix ub = bs.unitary_matrix (); | |
| 3322 Matrix sch_b = bs.schur_matrix (); | |
| 3323 | |
| 3324 Matrix cx = ua.transpose () * c * ub; | |
| 3325 | |
| 3326 // Solve the sylvester equation, back-transform, and return the | |
| 3327 // solution. | |
| 3328 | |
| 5275 | 3329 octave_idx_type a_nr = a.rows (); |
| 3330 octave_idx_type b_nr = b.rows (); | |
| 1819 | 3331 |
| 3332 double scale; | |
| 5275 | 3333 octave_idx_type info; |
| 1819 | 3334 |
| 1950 | 3335 double *pa = sch_a.fortran_vec (); |
| 3336 double *pb = sch_b.fortran_vec (); | |
| 3337 double *px = cx.fortran_vec (); | |
| 3338 | |
| 4552 | 3339 F77_XFCN (dtrsyl, DTRSYL, (F77_CONST_CHAR_ARG2 ("N", 1), |
| 3340 F77_CONST_CHAR_ARG2 ("N", 1), | |
| 3341 1, a_nr, b_nr, pa, a_nr, pb, | |
| 3342 b_nr, px, a_nr, scale, info | |
| 3343 F77_CHAR_ARG_LEN (1) | |
| 3344 F77_CHAR_ARG_LEN (1))); | |
| 1950 | 3345 |
| 3346 | |
|
7482
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
3347 // FIXME -- check info? |
| 1819 | 3348 |
|
7482
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
3349 retval = -ua*cx*ub.transpose (); |
| 1819 | 3350 |
| 3351 return retval; | |
| 3352 } | |
| 3353 | |
| 2828 | 3354 // matrix by matrix -> matrix operations |
| 3355 | |
| 6162 | 3356 /* Simple Dot Product, Matrix-Vector and Matrix-Matrix Unit tests |
| 3357 %!assert([1 2 3] * [ 4 ; 5 ; 6], 32, 1e-14) | |
| 3358 %!assert([1 2 ; 3 4 ] * [5 ; 6], [17 ; 39 ], 1e-14) | |
| 3359 %!assert([1 2 ; 3 4 ] * [5 6 ; 7 8], [19 22; 43 50], 1e-14) | |
| 3360 */ | |
| 3361 | |
| 3362 /* Test some simple identities | |
| 3363 %!shared M, cv, rv | |
| 3364 %! M = randn(10,10); | |
| 3365 %! cv = randn(10,1); | |
| 3366 %! rv = randn(1,10); | |
| 3367 %!assert([M*cv,M*cv],M*[cv,cv],1e-14) | |
| 3368 %!assert([rv*M;rv*M],[rv;rv]*M,1e-14) | |
| 3369 %!assert(2*rv*cv,[rv,rv]*[cv;cv],1e-14) | |
| 3370 */ | |
| 3371 | |
|
7800
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3372 static const char * |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3373 get_blas_trans_arg (bool trans) |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3374 { |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3375 static char blas_notrans = 'N', blas_trans = 'T'; |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3376 return (trans) ? &blas_trans : &blas_notrans; |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3377 } |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3378 |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3379 // the general GEMM operation |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3380 |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3381 Matrix |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3382 xgemm (bool transa, const Matrix& a, bool transb, const Matrix& b) |
| 2828 | 3383 { |
| 3384 Matrix retval; | |
| 3385 | |
|
7800
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3386 octave_idx_type a_nr = transa ? a.cols () : a.rows (); |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3387 octave_idx_type a_nc = transa ? a.rows () : a.cols (); |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3388 |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3389 octave_idx_type b_nr = transb ? b.cols () : b.rows (); |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3390 octave_idx_type b_nc = transb ? b.rows () : b.cols (); |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3391 |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3392 if (a_nc != b_nr) |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3393 gripe_nonconformant ("operator *", a_nr, a_nc, b_nr, b_nc); |
| 2828 | 3394 else |
| 3395 { | |
|
7800
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3396 if (a_nr == 0 || a_nc == 0 || b_nc == 0) |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3397 retval.resize (a_nr, b_nc, 0.0); |
|
7801
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3398 else if (a.data () == b.data () && a_nr == b_nc && transa != transb) |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3399 { |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3400 octave_idx_type lda = a.rows (); |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3401 |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3402 retval.resize (a_nr, b_nc); |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3403 double *c = retval.fortran_vec (); |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3404 |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3405 const char *ctransa = get_blas_trans_arg (transa); |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3406 F77_XFCN (dsyrk, DSYRK, (F77_CONST_CHAR_ARG2 ("U", 1), |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3407 F77_CONST_CHAR_ARG2 (ctransa, 1), |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3408 a_nr, a_nc, 1.0, |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3409 a.data (), lda, 0.0, c, a_nr |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3410 F77_CHAR_ARG_LEN (1) |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3411 F77_CHAR_ARG_LEN (1))); |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3412 for (int j = 0; j < a_nr; j++) |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3413 for (int i = 0; i < j; i++) |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3414 retval.xelem (j,i) = retval.xelem (i,j); |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3415 |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3416 } |
| 2828 | 3417 else |
| 3418 { | |
|
7800
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3419 octave_idx_type lda = a.rows (), tda = a.cols (); |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3420 octave_idx_type ldb = b.rows (), tdb = b.cols (); |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3421 |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3422 retval.resize (a_nr, b_nc); |
| 2828 | 3423 double *c = retval.fortran_vec (); |
| 3424 | |
|
7800
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3425 if (b_nc == 1) |
| 5983 | 3426 { |
|
7800
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3427 if (a_nr == 1) |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3428 F77_FUNC (xddot, XDDOT) (a_nc, a.data (), 1, b.data (), 1, *c); |
| 5983 | 3429 else |
| 6390 | 3430 { |
|
7800
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3431 const char *ctransa = get_blas_trans_arg (transa); |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3432 F77_XFCN (dgemv, DGEMV, (F77_CONST_CHAR_ARG2 (ctransa, 1), |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3433 lda, tda, 1.0, a.data (), lda, |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3434 b.data (), 1, 0.0, c, 1 |
| 6390 | 3435 F77_CHAR_ARG_LEN (1))); |
| 3436 } | |
| 5983 | 3437 } |
|
7800
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3438 else if (a_nr == 1) |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3439 { |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3440 const char *crevtransb = get_blas_trans_arg (! transb); |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3441 F77_XFCN (dgemv, DGEMV, (F77_CONST_CHAR_ARG2 (crevtransb, 1), |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3442 ldb, tdb, 1.0, b.data (), ldb, |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3443 a.data (), 1, 0.0, c, 1 |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3444 F77_CHAR_ARG_LEN (1))); |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3445 } |
| 5983 | 3446 else |
| 6390 | 3447 { |
|
7800
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3448 const char *ctransa = get_blas_trans_arg (transa); |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3449 const char *ctransb = get_blas_trans_arg (transb); |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3450 F77_XFCN (dgemm, DGEMM, (F77_CONST_CHAR_ARG2 (ctransa, 1), |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3451 F77_CONST_CHAR_ARG2 (ctransb, 1), |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3452 a_nr, b_nc, a_nc, 1.0, a.data (), |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3453 lda, b.data (), ldb, 0.0, c, a_nr |
| 6390 | 3454 F77_CHAR_ARG_LEN (1) |
| 3455 F77_CHAR_ARG_LEN (1))); | |
| 3456 } | |
| 2828 | 3457 } |
| 3458 } | |
| 3459 | |
| 3460 return retval; | |
| 3461 } | |
| 3462 | |
|
7800
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3463 Matrix |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3464 operator * (const Matrix& a, const Matrix& b) |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3465 { |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3466 return xgemm (false, a, false, b); |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3467 } |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3468 |
| 5775 | 3469 // FIXME -- it would be nice to share code among the min/max |
| 4309 | 3470 // functions below. |
| 3471 | |
| 3472 #define EMPTY_RETURN_CHECK(T) \ | |
| 3473 if (nr == 0 || nc == 0) \ | |
| 3474 return T (nr, nc); | |
| 3475 | |
| 3476 Matrix | |
| 3477 min (double d, const Matrix& m) | |
| 3478 { | |
| 5275 | 3479 octave_idx_type nr = m.rows (); |
| 3480 octave_idx_type nc = m.columns (); | |
| 4309 | 3481 |
| 3482 EMPTY_RETURN_CHECK (Matrix); | |
| 3483 | |
| 3484 Matrix result (nr, nc); | |
| 3485 | |
| 5275 | 3486 for (octave_idx_type j = 0; j < nc; j++) |
| 3487 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3488 { |
| 3489 OCTAVE_QUIT; | |
| 3490 result (i, j) = xmin (d, m (i, j)); | |
| 3491 } | |
| 3492 | |
| 3493 return result; | |
| 3494 } | |
| 3495 | |
| 3496 Matrix | |
| 3497 min (const Matrix& m, double d) | |
| 3498 { | |
| 5275 | 3499 octave_idx_type nr = m.rows (); |
| 3500 octave_idx_type nc = m.columns (); | |
| 4309 | 3501 |
| 3502 EMPTY_RETURN_CHECK (Matrix); | |
| 3503 | |
| 3504 Matrix result (nr, nc); | |
| 3505 | |
| 5275 | 3506 for (octave_idx_type j = 0; j < nc; j++) |
| 3507 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3508 { |
| 3509 OCTAVE_QUIT; | |
| 3510 result (i, j) = xmin (m (i, j), d); | |
| 3511 } | |
| 3512 | |
| 3513 return result; | |
| 3514 } | |
| 3515 | |
| 3516 Matrix | |
| 3517 min (const Matrix& a, const Matrix& b) | |
| 3518 { | |
| 5275 | 3519 octave_idx_type nr = a.rows (); |
| 3520 octave_idx_type nc = a.columns (); | |
| 4309 | 3521 |
| 3522 if (nr != b.rows () || nc != b.columns ()) | |
| 3523 { | |
| 3524 (*current_liboctave_error_handler) | |
| 3525 ("two-arg min expecting args of same size"); | |
| 3526 return Matrix (); | |
| 3527 } | |
| 3528 | |
| 3529 EMPTY_RETURN_CHECK (Matrix); | |
| 3530 | |
| 3531 Matrix result (nr, nc); | |
| 3532 | |
| 5275 | 3533 for (octave_idx_type j = 0; j < nc; j++) |
| 3534 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3535 { |
| 3536 OCTAVE_QUIT; | |
| 3537 result (i, j) = xmin (a (i, j), b (i, j)); | |
| 3538 } | |
| 3539 | |
| 3540 return result; | |
| 3541 } | |
| 3542 | |
| 3543 Matrix | |
| 3544 max (double d, const Matrix& m) | |
| 3545 { | |
| 5275 | 3546 octave_idx_type nr = m.rows (); |
| 3547 octave_idx_type nc = m.columns (); | |
| 4309 | 3548 |
| 3549 EMPTY_RETURN_CHECK (Matrix); | |
| 3550 | |
| 3551 Matrix result (nr, nc); | |
| 3552 | |
| 5275 | 3553 for (octave_idx_type j = 0; j < nc; j++) |
| 3554 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3555 { |
| 3556 OCTAVE_QUIT; | |
| 3557 result (i, j) = xmax (d, m (i, j)); | |
| 3558 } | |
| 3559 | |
| 3560 return result; | |
| 3561 } | |
| 3562 | |
| 3563 Matrix | |
| 3564 max (const Matrix& m, double d) | |
| 3565 { | |
| 5275 | 3566 octave_idx_type nr = m.rows (); |
| 3567 octave_idx_type nc = m.columns (); | |
| 4309 | 3568 |
| 3569 EMPTY_RETURN_CHECK (Matrix); | |
| 3570 | |
| 3571 Matrix result (nr, nc); | |
| 3572 | |
| 5275 | 3573 for (octave_idx_type j = 0; j < nc; j++) |
| 3574 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3575 { |
| 3576 OCTAVE_QUIT; | |
| 3577 result (i, j) = xmax (m (i, j), d); | |
| 3578 } | |
| 3579 | |
| 3580 return result; | |
| 3581 } | |
| 3582 | |
| 3583 Matrix | |
| 3584 max (const Matrix& a, const Matrix& b) | |
| 3585 { | |
| 5275 | 3586 octave_idx_type nr = a.rows (); |
| 3587 octave_idx_type nc = a.columns (); | |
| 4309 | 3588 |
| 3589 if (nr != b.rows () || nc != b.columns ()) | |
| 3590 { | |
| 3591 (*current_liboctave_error_handler) | |
| 3592 ("two-arg max expecting args of same size"); | |
| 3593 return Matrix (); | |
| 3594 } | |
| 3595 | |
| 3596 EMPTY_RETURN_CHECK (Matrix); | |
| 3597 | |
| 3598 Matrix result (nr, nc); | |
| 3599 | |
| 5275 | 3600 for (octave_idx_type j = 0; j < nc; j++) |
| 3601 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3602 { |
| 3603 OCTAVE_QUIT; | |
| 3604 result (i, j) = xmax (a (i, j), b (i, j)); | |
| 3605 } | |
| 3606 | |
| 3607 return result; | |
| 3608 } | |
| 3609 | |
| 2870 | 3610 MS_CMP_OPS(Matrix, , double, ) |
| 3504 | 3611 MS_BOOL_OPS(Matrix, double, 0.0) |
| 2870 | 3612 |
| 3613 SM_CMP_OPS(double, , Matrix, ) | |
| 3504 | 3614 SM_BOOL_OPS(double, Matrix, 0.0) |
| 2870 | 3615 |
| 3616 MM_CMP_OPS(Matrix, , Matrix, ) | |
| 3504 | 3617 MM_BOOL_OPS(Matrix, Matrix, 0.0) |
| 2870 | 3618 |
| 458 | 3619 /* |
| 3620 ;;; Local Variables: *** | |
| 3621 ;;; mode: C++ *** | |
| 3622 ;;; End: *** | |
| 3623 */ |