Mercurial > hg > octave-lyh
annotate liboctave/dMatrix.cc @ 7801:776791438957
map symmetric cases to xHERK, xSYRK
| author | Jaroslav Hajek <highegg@gmail.com> |
|---|---|
| date | Thu, 08 May 2008 13:46:33 +0200 |
| parents | 5861b95e9879 |
| children | 9bcb31cc56be |
| rev | line source |
|---|---|
| 1993 | 1 // Matrix manipulations. |
| 458 | 2 /* |
| 3 | |
| 7017 | 4 Copyright (C) 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, |
| 5 2003, 2004, 2005, 2006, 2007 John W. Eaton | |
| 458 | 6 |
| 7 This file is part of Octave. | |
| 8 | |
| 9 Octave is free software; you can redistribute it and/or modify it | |
| 10 under the terms of the GNU General Public License as published by the | |
| 7016 | 11 Free Software Foundation; either version 3 of the License, or (at your |
| 12 option) any later version. | |
| 458 | 13 |
| 14 Octave is distributed in the hope that it will be useful, but WITHOUT | |
| 15 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
| 16 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
| 17 for more details. | |
| 18 | |
| 19 You should have received a copy of the GNU General Public License | |
| 7016 | 20 along with Octave; see the file COPYING. If not, see |
| 21 <http://www.gnu.org/licenses/>. | |
| 458 | 22 |
| 23 */ | |
| 24 | |
| 25 #ifdef HAVE_CONFIG_H | |
| 1192 | 26 #include <config.h> |
| 458 | 27 #endif |
| 28 | |
| 1367 | 29 #include <cfloat> |
| 30 | |
| 3503 | 31 #include <iostream> |
| 6209 | 32 #include <vector> |
| 1367 | 33 |
| 4669 | 34 #include "Array-util.h" |
| 2317 | 35 #include "byte-swap.h" |
| 2828 | 36 #include "dMatrix.h" |
| 1819 | 37 #include "dbleAEPBAL.h" |
| 458 | 38 #include "dbleDET.h" |
| 1819 | 39 #include "dbleSCHUR.h" |
| 740 | 40 #include "dbleSVD.h" |
| 6207 | 41 #include "dbleCHOL.h" |
| 1847 | 42 #include "f77-fcn.h" |
|
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43 #include "functor.h" |
| 458 | 44 #include "lo-error.h" |
| 2354 | 45 #include "lo-ieee.h" |
| 46 #include "lo-mappers.h" | |
| 1968 | 47 #include "lo-utils.h" |
| 1367 | 48 #include "mx-base.h" |
| 2828 | 49 #include "mx-m-dm.h" |
| 3176 | 50 #include "mx-dm-m.h" |
| 1367 | 51 #include "mx-inlines.cc" |
| 1650 | 52 #include "oct-cmplx.h" |
| 4153 | 53 #include "quit.h" |
| 458 | 54 |
| 4773 | 55 #if defined (HAVE_FFTW3) |
| 3827 | 56 #include "oct-fftw.h" |
| 57 #endif | |
| 58 | |
| 458 | 59 // Fortran functions we call. |
| 60 | |
| 61 extern "C" | |
| 62 { | |
| 7478 | 63 F77_RET_T |
| 7477 | 64 F77_FUNC (xilaenv, XILAENV) (const octave_idx_type&, F77_CONST_CHAR_ARG_DECL, |
| 65 F77_CONST_CHAR_ARG_DECL, | |
| 66 const octave_idx_type&, const octave_idx_type&, | |
| 7478 | 67 const octave_idx_type&, const octave_idx_type&, |
| 68 octave_idx_type& | |
| 69 F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); | |
| 7476 | 70 |
| 4552 | 71 F77_RET_T |
| 72 F77_FUNC (dgebal, DGEBAL) (F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 73 const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type&, |
| 74 octave_idx_type&, double*, octave_idx_type& | |
| 4552 | 75 F77_CHAR_ARG_LEN_DECL); |
| 76 | |
| 77 F77_RET_T | |
| 78 F77_FUNC (dgebak, DGEBAK) (F77_CONST_CHAR_ARG_DECL, | |
| 79 F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 80 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, double*, |
| 81 const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type& | |
| 4552 | 82 F77_CHAR_ARG_LEN_DECL |
| 83 F77_CHAR_ARG_LEN_DECL); | |
| 84 | |
| 85 | |
| 86 F77_RET_T | |
| 87 F77_FUNC (dgemm, DGEMM) (F77_CONST_CHAR_ARG_DECL, | |
| 88 F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 89 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
| 90 const double&, const double*, const octave_idx_type&, | |
| 91 const double*, const octave_idx_type&, const double&, | |
| 92 double*, const octave_idx_type& | |
| 4552 | 93 F77_CHAR_ARG_LEN_DECL |
| 94 F77_CHAR_ARG_LEN_DECL); | |
| 95 | |
| 96 F77_RET_T | |
| 5983 | 97 F77_FUNC (dgemv, DGEMV) (F77_CONST_CHAR_ARG_DECL, |
| 98 const octave_idx_type&, const octave_idx_type&, const double&, | |
| 99 const double*, const octave_idx_type&, const double*, | |
| 100 const octave_idx_type&, const double&, double*, | |
| 101 const octave_idx_type& | |
| 102 F77_CHAR_ARG_LEN_DECL); | |
| 103 | |
| 104 F77_RET_T | |
| 105 F77_FUNC (xddot, XDDOT) (const octave_idx_type&, const double*, const octave_idx_type&, | |
| 106 const double*, const octave_idx_type&, double&); | |
| 107 | |
| 108 F77_RET_T | |
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109 F77_FUNC (dsyrk, DSYRK) (F77_CONST_CHAR_ARG_DECL, |
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110 F77_CONST_CHAR_ARG_DECL, |
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111 const octave_idx_type&, const octave_idx_type&, |
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112 const double&, const double*, const octave_idx_type&, |
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113 const double&, double*, const octave_idx_type& |
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114 F77_CHAR_ARG_LEN_DECL |
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115 F77_CHAR_ARG_LEN_DECL); |
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116 |
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117 F77_RET_T |
| 5275 | 118 F77_FUNC (dgetrf, DGETRF) (const octave_idx_type&, const octave_idx_type&, double*, const octave_idx_type&, |
| 119 octave_idx_type*, octave_idx_type&); | |
| 4329 | 120 |
| 4552 | 121 F77_RET_T |
| 5275 | 122 F77_FUNC (dgetrs, DGETRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, |
| 123 const double*, const octave_idx_type&, | |
| 124 const octave_idx_type*, double*, const octave_idx_type&, octave_idx_type& | |
| 4552 | 125 F77_CHAR_ARG_LEN_DECL); |
| 126 | |
| 127 F77_RET_T | |
| 5275 | 128 F77_FUNC (dgetri, DGETRI) (const octave_idx_type&, double*, const octave_idx_type&, const octave_idx_type*, |
| 129 double*, const octave_idx_type&, octave_idx_type&); | |
| 4552 | 130 |
| 131 F77_RET_T | |
| 5275 | 132 F77_FUNC (dgecon, DGECON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, double*, |
| 133 const octave_idx_type&, const double&, double&, | |
| 134 double*, octave_idx_type*, octave_idx_type& | |
| 4552 | 135 F77_CHAR_ARG_LEN_DECL); |
| 136 | |
| 137 F77_RET_T | |
| 7072 | 138 F77_FUNC (dgelsy, DGELSY) (const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
| 139 double*, const octave_idx_type&, double*, | |
| 140 const octave_idx_type&, octave_idx_type*, double&, octave_idx_type&, | |
| 141 double*, const octave_idx_type&, octave_idx_type&); | |
| 142 | |
| 143 F77_RET_T | |
| 144 F77_FUNC (dgelsd, DGELSD) (const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, | |
| 5275 | 145 double*, const octave_idx_type&, double*, |
| 7071 | 146 const octave_idx_type&, double*, double&, octave_idx_type&, |
| 7072 | 147 double*, const octave_idx_type&, octave_idx_type*, |
| 148 octave_idx_type&); | |
| 458 | 149 |
| 5785 | 150 F77_RET_T |
| 151 F77_FUNC (dpotrf, DPOTRF) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 152 double *, const octave_idx_type&, | |
| 153 octave_idx_type& F77_CHAR_ARG_LEN_DECL); | |
| 154 | |
| 155 F77_RET_T | |
| 156 F77_FUNC (dpocon, DPOCON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 157 double*, const octave_idx_type&, const double&, | |
| 158 double&, double*, octave_idx_type*, | |
| 159 octave_idx_type& F77_CHAR_ARG_LEN_DECL); | |
| 160 F77_RET_T | |
| 161 F77_FUNC (dpotrs, DPOTRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 162 const octave_idx_type&, const double*, | |
| 163 const octave_idx_type&, double*, | |
| 164 const octave_idx_type&, octave_idx_type& | |
| 165 F77_CHAR_ARG_LEN_DECL); | |
| 166 | |
| 167 F77_RET_T | |
| 6207 | 168 F77_FUNC (dtrtri, DTRTRI) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, |
| 169 const octave_idx_type&, const double*, | |
| 170 const octave_idx_type&, octave_idx_type& | |
| 171 F77_CHAR_ARG_LEN_DECL | |
| 172 F77_CHAR_ARG_LEN_DECL); | |
| 173 F77_RET_T | |
| 5785 | 174 F77_FUNC (dtrcon, DTRCON) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, |
| 175 F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 176 const double*, const octave_idx_type&, double&, | |
| 177 double*, octave_idx_type*, octave_idx_type& | |
| 178 F77_CHAR_ARG_LEN_DECL | |
| 179 F77_CHAR_ARG_LEN_DECL | |
| 180 F77_CHAR_ARG_LEN_DECL); | |
| 181 F77_RET_T | |
| 182 F77_FUNC (dtrtrs, DTRTRS) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, | |
| 183 F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 184 const octave_idx_type&, const double*, | |
| 185 const octave_idx_type&, double*, | |
| 186 const octave_idx_type&, octave_idx_type& | |
| 187 F77_CHAR_ARG_LEN_DECL | |
| 188 F77_CHAR_ARG_LEN_DECL | |
| 189 F77_CHAR_ARG_LEN_DECL); | |
| 190 | |
| 1360 | 191 // Note that the original complex fft routines were not written for |
| 192 // double complex arguments. They have been modified by adding an | |
| 193 // implicit double precision (a-h,o-z) statement at the beginning of | |
| 194 // each subroutine. | |
| 458 | 195 |
| 4552 | 196 F77_RET_T |
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197 F77_FUNC (zffti, ZFFTI) (const octave_idx_type&, Complex*); |
| 4552 | 198 |
| 199 F77_RET_T | |
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200 F77_FUNC (zfftf, ZFFTF) (const octave_idx_type&, Complex*, Complex*); |
| 4552 | 201 |
| 202 F77_RET_T | |
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203 F77_FUNC (zfftb, ZFFTB) (const octave_idx_type&, Complex*, Complex*); |
| 4552 | 204 |
| 205 F77_RET_T | |
| 206 F77_FUNC (dlartg, DLARTG) (const double&, const double&, double&, | |
| 207 double&, double&); | |
| 208 | |
| 209 F77_RET_T | |
| 210 F77_FUNC (dtrsyl, DTRSYL) (F77_CONST_CHAR_ARG_DECL, | |
| 211 F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 212 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
| 213 const double*, const octave_idx_type&, const double*, | |
| 214 const octave_idx_type&, const double*, const octave_idx_type&, | |
| 215 double&, octave_idx_type& | |
| 4552 | 216 F77_CHAR_ARG_LEN_DECL |
| 217 F77_CHAR_ARG_LEN_DECL); | |
| 218 | |
| 219 F77_RET_T | |
| 5275 | 220 F77_FUNC (xdlange, XDLANGE) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, |
| 221 const octave_idx_type&, const double*, | |
| 222 const octave_idx_type&, double*, double& | |
| 4552 | 223 F77_CHAR_ARG_LEN_DECL); |
| 458 | 224 } |
| 225 | |
| 1360 | 226 // Matrix class. |
| 458 | 227 |
| 2349 | 228 Matrix::Matrix (const RowVector& rv) |
| 229 : MArray2<double> (1, rv.length (), 0.0) | |
| 230 { | |
| 5275 | 231 for (octave_idx_type i = 0; i < rv.length (); i++) |
| 2349 | 232 elem (0, i) = rv.elem (i); |
| 233 } | |
| 234 | |
| 235 Matrix::Matrix (const ColumnVector& cv) | |
| 236 : MArray2<double> (cv.length (), 1, 0.0) | |
| 237 { | |
| 5275 | 238 for (octave_idx_type i = 0; i < cv.length (); i++) |
| 2349 | 239 elem (i, 0) = cv.elem (i); |
| 240 } | |
| 241 | |
| 458 | 242 Matrix::Matrix (const DiagMatrix& a) |
| 1214 | 243 : MArray2<double> (a.rows (), a.cols (), 0.0) |
| 458 | 244 { |
| 5275 | 245 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 246 elem (i, i) = a.elem (i, i); |
| 247 } | |
| 248 | |
| 5775 | 249 // FIXME -- could we use a templated mixed-type copy function |
| 1574 | 250 // here? |
| 251 | |
| 2828 | 252 Matrix::Matrix (const boolMatrix& a) |
| 253 : MArray2<double> (a.rows (), a.cols ()) | |
| 254 { | |
| 5275 | 255 for (octave_idx_type i = 0; i < a.rows (); i++) |
| 256 for (octave_idx_type j = 0; j < a.cols (); j++) | |
| 2828 | 257 elem (i, j) = a.elem (i, j); |
| 258 } | |
| 259 | |
| 1574 | 260 Matrix::Matrix (const charMatrix& a) |
| 261 : MArray2<double> (a.rows (), a.cols ()) | |
| 262 { | |
| 5275 | 263 for (octave_idx_type i = 0; i < a.rows (); i++) |
| 264 for (octave_idx_type j = 0; j < a.cols (); j++) | |
| 1574 | 265 elem (i, j) = a.elem (i, j); |
| 266 } | |
| 267 | |
| 2385 | 268 bool |
| 458 | 269 Matrix::operator == (const Matrix& a) const |
| 270 { | |
| 271 if (rows () != a.rows () || cols () != a.cols ()) | |
| 2385 | 272 return false; |
| 458 | 273 |
| 3769 | 274 return mx_inline_equal (data (), a.data (), length ()); |
| 458 | 275 } |
| 276 | |
| 2385 | 277 bool |
| 458 | 278 Matrix::operator != (const Matrix& a) const |
| 279 { | |
| 280 return !(*this == a); | |
| 281 } | |
| 282 | |
| 3354 | 283 bool |
| 284 Matrix::is_symmetric (void) const | |
| 285 { | |
| 286 if (is_square () && rows () > 0) | |
| 287 { | |
| 5275 | 288 for (octave_idx_type i = 0; i < rows (); i++) |
| 289 for (octave_idx_type j = i+1; j < cols (); j++) | |
| 3354 | 290 if (elem (i, j) != elem (j, i)) |
| 291 return false; | |
| 292 | |
| 293 return true; | |
| 294 } | |
| 295 | |
| 296 return false; | |
| 297 } | |
| 298 | |
| 458 | 299 Matrix& |
| 5275 | 300 Matrix::insert (const Matrix& a, octave_idx_type r, octave_idx_type c) |
| 458 | 301 { |
| 1561 | 302 Array2<double>::insert (a, r, c); |
| 458 | 303 return *this; |
| 304 } | |
| 305 | |
| 306 Matrix& | |
| 5275 | 307 Matrix::insert (const RowVector& a, octave_idx_type r, octave_idx_type c) |
| 458 | 308 { |
| 5275 | 309 octave_idx_type a_len = a.length (); |
| 4316 | 310 |
| 1698 | 311 if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ()) |
| 458 | 312 { |
| 313 (*current_liboctave_error_handler) ("range error for insert"); | |
| 314 return *this; | |
| 315 } | |
| 316 | |
| 4316 | 317 if (a_len > 0) |
| 318 { | |
| 319 make_unique (); | |
| 320 | |
| 5275 | 321 for (octave_idx_type i = 0; i < a_len; i++) |
| 4316 | 322 xelem (r, c+i) = a.elem (i); |
| 323 } | |
| 458 | 324 |
| 325 return *this; | |
| 326 } | |
| 327 | |
| 328 Matrix& | |
| 5275 | 329 Matrix::insert (const ColumnVector& a, octave_idx_type r, octave_idx_type c) |
| 458 | 330 { |
| 5275 | 331 octave_idx_type a_len = a.length (); |
| 4316 | 332 |
| 1698 | 333 if (r < 0 || r + a_len > rows () || c < 0 || c >= cols ()) |
| 458 | 334 { |
| 335 (*current_liboctave_error_handler) ("range error for insert"); | |
| 336 return *this; | |
| 337 } | |
| 338 | |
| 4316 | 339 if (a_len > 0) |
| 340 { | |
| 341 make_unique (); | |
| 342 | |
| 5275 | 343 for (octave_idx_type i = 0; i < a_len; i++) |
| 4316 | 344 xelem (r+i, c) = a.elem (i); |
| 345 } | |
| 458 | 346 |
| 347 return *this; | |
| 348 } | |
| 349 | |
| 350 Matrix& | |
| 5275 | 351 Matrix::insert (const DiagMatrix& a, octave_idx_type r, octave_idx_type c) |
| 458 | 352 { |
| 5275 | 353 octave_idx_type a_nr = a.rows (); |
| 354 octave_idx_type a_nc = a.cols (); | |
| 1697 | 355 |
| 1698 | 356 if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) |
| 458 | 357 { |
| 358 (*current_liboctave_error_handler) ("range error for insert"); | |
| 359 return *this; | |
| 360 } | |
| 361 | |
| 1697 | 362 fill (0.0, r, c, r + a_nr - 1, c + a_nc - 1); |
| 363 | |
| 5275 | 364 octave_idx_type a_len = a.length (); |
| 4316 | 365 |
| 366 if (a_len > 0) | |
| 367 { | |
| 368 make_unique (); | |
| 369 | |
| 5275 | 370 for (octave_idx_type i = 0; i < a_len; i++) |
| 4316 | 371 xelem (r+i, c+i) = a.elem (i, i); |
| 372 } | |
| 458 | 373 |
| 374 return *this; | |
| 375 } | |
| 376 | |
| 377 Matrix& | |
| 378 Matrix::fill (double val) | |
| 379 { | |
| 5275 | 380 octave_idx_type nr = rows (); |
| 381 octave_idx_type nc = cols (); | |
| 4316 | 382 |
| 458 | 383 if (nr > 0 && nc > 0) |
| 4316 | 384 { |
| 385 make_unique (); | |
| 386 | |
| 5275 | 387 for (octave_idx_type j = 0; j < nc; j++) |
| 388 for (octave_idx_type i = 0; i < nr; i++) | |
| 4316 | 389 xelem (i, j) = val; |
| 390 } | |
| 458 | 391 |
| 392 return *this; | |
| 393 } | |
| 394 | |
| 395 Matrix& | |
| 5275 | 396 Matrix::fill (double val, octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) |
| 458 | 397 { |
| 5275 | 398 octave_idx_type nr = rows (); |
| 399 octave_idx_type nc = cols (); | |
| 4316 | 400 |
| 458 | 401 if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0 |
| 402 || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc) | |
| 403 { | |
| 404 (*current_liboctave_error_handler) ("range error for fill"); | |
| 405 return *this; | |
| 406 } | |
| 407 | |
| 5275 | 408 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } |
| 409 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } | |
| 458 | 410 |
| 4316 | 411 if (r2 >= r1 && c2 >= c1) |
| 412 { | |
| 413 make_unique (); | |
| 414 | |
| 5275 | 415 for (octave_idx_type j = c1; j <= c2; j++) |
| 416 for (octave_idx_type i = r1; i <= r2; i++) | |
| 4316 | 417 xelem (i, j) = val; |
| 418 } | |
| 458 | 419 |
| 420 return *this; | |
| 421 } | |
| 422 | |
| 423 Matrix | |
| 424 Matrix::append (const Matrix& a) const | |
| 425 { | |
| 5275 | 426 octave_idx_type nr = rows (); |
| 427 octave_idx_type nc = cols (); | |
| 458 | 428 if (nr != a.rows ()) |
| 429 { | |
| 430 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 431 return Matrix (); | |
| 432 } | |
| 433 | |
| 5275 | 434 octave_idx_type nc_insert = nc; |
| 458 | 435 Matrix retval (nr, nc + a.cols ()); |
| 436 retval.insert (*this, 0, 0); | |
| 437 retval.insert (a, 0, nc_insert); | |
| 438 return retval; | |
| 439 } | |
| 440 | |
| 441 Matrix | |
| 442 Matrix::append (const RowVector& a) const | |
| 443 { | |
| 5275 | 444 octave_idx_type nr = rows (); |
| 445 octave_idx_type nc = cols (); | |
| 458 | 446 if (nr != 1) |
| 447 { | |
| 448 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 449 return Matrix (); | |
| 450 } | |
| 451 | |
| 5275 | 452 octave_idx_type nc_insert = nc; |
| 458 | 453 Matrix retval (nr, nc + a.length ()); |
| 454 retval.insert (*this, 0, 0); | |
| 455 retval.insert (a, 0, nc_insert); | |
| 456 return retval; | |
| 457 } | |
| 458 | |
| 459 Matrix | |
| 460 Matrix::append (const ColumnVector& a) const | |
| 461 { | |
| 5275 | 462 octave_idx_type nr = rows (); |
| 463 octave_idx_type nc = cols (); | |
| 458 | 464 if (nr != a.length ()) |
| 465 { | |
| 466 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 467 return Matrix (); | |
| 468 } | |
| 469 | |
| 5275 | 470 octave_idx_type nc_insert = nc; |
| 458 | 471 Matrix retval (nr, nc + 1); |
| 472 retval.insert (*this, 0, 0); | |
| 473 retval.insert (a, 0, nc_insert); | |
| 474 return retval; | |
| 475 } | |
| 476 | |
| 477 Matrix | |
| 478 Matrix::append (const DiagMatrix& a) const | |
| 479 { | |
| 5275 | 480 octave_idx_type nr = rows (); |
| 481 octave_idx_type nc = cols (); | |
| 458 | 482 if (nr != a.rows ()) |
| 483 { | |
| 484 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 485 return *this; | |
| 486 } | |
| 487 | |
| 5275 | 488 octave_idx_type nc_insert = nc; |
| 458 | 489 Matrix retval (nr, nc + a.cols ()); |
| 490 retval.insert (*this, 0, 0); | |
| 491 retval.insert (a, 0, nc_insert); | |
| 492 return retval; | |
| 493 } | |
| 494 | |
| 495 Matrix | |
| 496 Matrix::stack (const Matrix& a) const | |
| 497 { | |
| 5275 | 498 octave_idx_type nr = rows (); |
| 499 octave_idx_type nc = cols (); | |
| 458 | 500 if (nc != a.cols ()) |
| 501 { | |
| 502 (*current_liboctave_error_handler) | |
| 503 ("column dimension mismatch for stack"); | |
| 504 return Matrix (); | |
| 505 } | |
| 506 | |
| 5275 | 507 octave_idx_type nr_insert = nr; |
| 458 | 508 Matrix retval (nr + a.rows (), nc); |
| 509 retval.insert (*this, 0, 0); | |
| 510 retval.insert (a, nr_insert, 0); | |
| 511 return retval; | |
| 512 } | |
| 513 | |
| 514 Matrix | |
| 515 Matrix::stack (const RowVector& a) const | |
| 516 { | |
| 5275 | 517 octave_idx_type nr = rows (); |
| 518 octave_idx_type nc = cols (); | |
| 458 | 519 if (nc != a.length ()) |
| 520 { | |
| 521 (*current_liboctave_error_handler) | |
| 522 ("column dimension mismatch for stack"); | |
| 523 return Matrix (); | |
| 524 } | |
| 525 | |
| 5275 | 526 octave_idx_type nr_insert = nr; |
| 458 | 527 Matrix retval (nr + 1, nc); |
| 528 retval.insert (*this, 0, 0); | |
| 529 retval.insert (a, nr_insert, 0); | |
| 530 return retval; | |
| 531 } | |
| 532 | |
| 533 Matrix | |
| 534 Matrix::stack (const ColumnVector& a) const | |
| 535 { | |
| 5275 | 536 octave_idx_type nr = rows (); |
| 537 octave_idx_type nc = cols (); | |
| 458 | 538 if (nc != 1) |
| 539 { | |
| 540 (*current_liboctave_error_handler) | |
| 541 ("column dimension mismatch for stack"); | |
| 542 return Matrix (); | |
| 543 } | |
| 544 | |
| 5275 | 545 octave_idx_type nr_insert = nr; |
| 458 | 546 Matrix retval (nr + a.length (), nc); |
| 547 retval.insert (*this, 0, 0); | |
| 548 retval.insert (a, nr_insert, 0); | |
| 549 return retval; | |
| 550 } | |
| 551 | |
| 552 Matrix | |
| 553 Matrix::stack (const DiagMatrix& a) const | |
| 554 { | |
| 5275 | 555 octave_idx_type nr = rows (); |
| 556 octave_idx_type nc = cols (); | |
| 458 | 557 if (nc != a.cols ()) |
| 558 { | |
| 559 (*current_liboctave_error_handler) | |
| 560 ("column dimension mismatch for stack"); | |
| 561 return Matrix (); | |
| 562 } | |
| 563 | |
| 5275 | 564 octave_idx_type nr_insert = nr; |
| 458 | 565 Matrix retval (nr + a.rows (), nc); |
| 566 retval.insert (*this, 0, 0); | |
| 567 retval.insert (a, nr_insert, 0); | |
| 568 return retval; | |
| 569 } | |
| 570 | |
| 571 Matrix | |
| 1205 | 572 real (const ComplexMatrix& a) |
| 573 { | |
| 5275 | 574 octave_idx_type a_len = a.length (); |
| 1205 | 575 Matrix retval; |
| 576 if (a_len > 0) | |
| 3769 | 577 retval = Matrix (mx_inline_real_dup (a.data (), a_len), |
| 578 a.rows (), a.cols ()); | |
| 1205 | 579 return retval; |
| 580 } | |
| 581 | |
| 582 Matrix | |
| 583 imag (const ComplexMatrix& a) | |
| 584 { | |
| 5275 | 585 octave_idx_type a_len = a.length (); |
| 1205 | 586 Matrix retval; |
| 587 if (a_len > 0) | |
| 3769 | 588 retval = Matrix (mx_inline_imag_dup (a.data (), a_len), |
| 589 a.rows (), a.cols ()); | |
| 1205 | 590 return retval; |
| 591 } | |
| 592 | |
| 593 Matrix | |
| 5275 | 594 Matrix::extract (octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) const |
| 458 | 595 { |
| 5275 | 596 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } |
| 597 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } | |
| 598 | |
| 599 octave_idx_type new_r = r2 - r1 + 1; | |
| 600 octave_idx_type new_c = c2 - c1 + 1; | |
| 458 | 601 |
| 602 Matrix result (new_r, new_c); | |
| 603 | |
| 5275 | 604 for (octave_idx_type j = 0; j < new_c; j++) |
| 605 for (octave_idx_type i = 0; i < new_r; i++) | |
| 4316 | 606 result.xelem (i, j) = elem (r1+i, c1+j); |
| 607 | |
| 608 return result; | |
| 609 } | |
| 610 | |
| 611 Matrix | |
| 5275 | 612 Matrix::extract_n (octave_idx_type r1, octave_idx_type c1, octave_idx_type nr, octave_idx_type nc) const |
| 4316 | 613 { |
| 614 Matrix result (nr, nc); | |
| 615 | |
| 5275 | 616 for (octave_idx_type j = 0; j < nc; j++) |
| 617 for (octave_idx_type i = 0; i < nr; i++) | |
| 4316 | 618 result.xelem (i, j) = elem (r1+i, c1+j); |
| 458 | 619 |
| 620 return result; | |
| 621 } | |
| 622 | |
| 623 // extract row or column i. | |
| 624 | |
| 625 RowVector | |
| 5275 | 626 Matrix::row (octave_idx_type i) const |
| 458 | 627 { |
| 5275 | 628 octave_idx_type nc = cols (); |
| 458 | 629 if (i < 0 || i >= rows ()) |
| 630 { | |
| 631 (*current_liboctave_error_handler) ("invalid row selection"); | |
| 632 return RowVector (); | |
| 633 } | |
| 634 | |
| 635 RowVector retval (nc); | |
| 5275 | 636 for (octave_idx_type j = 0; j < nc; j++) |
| 4316 | 637 retval.xelem (j) = elem (i, j); |
| 458 | 638 |
| 639 return retval; | |
| 640 } | |
| 641 | |
| 642 ColumnVector | |
| 5275 | 643 Matrix::column (octave_idx_type i) const |
| 458 | 644 { |
| 5275 | 645 octave_idx_type nr = rows (); |
| 458 | 646 if (i < 0 || i >= cols ()) |
| 647 { | |
| 648 (*current_liboctave_error_handler) ("invalid column selection"); | |
| 649 return ColumnVector (); | |
| 650 } | |
| 651 | |
| 652 ColumnVector retval (nr); | |
| 5275 | 653 for (octave_idx_type j = 0; j < nr; j++) |
| 4316 | 654 retval.xelem (j) = elem (j, i); |
| 458 | 655 |
| 656 return retval; | |
| 657 } | |
| 658 | |
| 659 Matrix | |
| 660 Matrix::inverse (void) const | |
| 661 { | |
| 5275 | 662 octave_idx_type info; |
| 7788 | 663 double rcon; |
| 6207 | 664 MatrixType mattype (*this); |
| 7788 | 665 return inverse (mattype, info, rcon, 0, 0); |
| 6207 | 666 } |
| 667 | |
| 668 Matrix | |
| 6479 | 669 Matrix::inverse (octave_idx_type& info) const |
| 670 { | |
| 7788 | 671 double rcon; |
| 6479 | 672 MatrixType mattype (*this); |
| 7788 | 673 return inverse (mattype, info, rcon, 0, 0); |
| 6479 | 674 } |
| 675 | |
| 676 Matrix | |
| 7788 | 677 Matrix::inverse (octave_idx_type& info, double& rcon, int force, |
| 6479 | 678 int calc_cond) const |
| 679 { | |
| 680 MatrixType mattype (*this); | |
| 7788 | 681 return inverse (mattype, info, rcon, force, calc_cond); |
| 6479 | 682 } |
| 683 | |
| 684 Matrix | |
| 6207 | 685 Matrix::inverse (MatrixType& mattype) const |
| 686 { | |
| 687 octave_idx_type info; | |
| 7788 | 688 double rcon; |
| 689 return inverse (mattype, info, rcon, 0, 0); | |
| 6207 | 690 } |
| 691 | |
| 692 Matrix | |
| 693 Matrix::inverse (MatrixType &mattype, octave_idx_type& info) const | |
| 694 { | |
| 7788 | 695 double rcon; |
| 696 return inverse (mattype, info, rcon, 0, 0); | |
| 458 | 697 } |
| 698 | |
| 699 Matrix | |
| 7788 | 700 Matrix::tinverse (MatrixType &mattype, octave_idx_type& info, double& rcon, |
| 6207 | 701 int force, int calc_cond) const |
| 458 | 702 { |
| 6207 | 703 Matrix retval; |
| 704 | |
| 705 octave_idx_type nr = rows (); | |
| 706 octave_idx_type nc = cols (); | |
| 707 | |
| 708 if (nr != nc || nr == 0 || nc == 0) | |
| 709 (*current_liboctave_error_handler) ("inverse requires square matrix"); | |
| 710 else | |
| 711 { | |
| 712 int typ = mattype.type (); | |
| 713 char uplo = (typ == MatrixType::Lower ? 'L' : 'U'); | |
| 714 char udiag = 'N'; | |
| 715 retval = *this; | |
| 716 double *tmp_data = retval.fortran_vec (); | |
| 717 | |
| 718 F77_XFCN (dtrtri, DTRTRI, (F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 719 F77_CONST_CHAR_ARG2 (&udiag, 1), | |
| 720 nr, tmp_data, nr, info | |
| 721 F77_CHAR_ARG_LEN (1) | |
| 722 F77_CHAR_ARG_LEN (1))); | |
| 723 | |
|
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724 // Throw-away extra info LAPACK gives so as to not change output. |
| 7788 | 725 rcon = 0.0; |
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726 if (info != 0) |
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727 info = -1; |
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728 else if (calc_cond) |
| 6207 | 729 { |
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730 octave_idx_type dtrcon_info = 0; |
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731 char job = '1'; |
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732 |
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733 OCTAVE_LOCAL_BUFFER (double, work, 3 * nr); |
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734 OCTAVE_LOCAL_BUFFER (octave_idx_type, iwork, nr); |
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735 |
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736 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&job, 1), |
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737 F77_CONST_CHAR_ARG2 (&uplo, 1), |
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738 F77_CONST_CHAR_ARG2 (&udiag, 1), |
| 7788 | 739 nr, tmp_data, nr, rcon, |
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740 work, iwork, dtrcon_info |
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741 F77_CHAR_ARG_LEN (1) |
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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 |
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745 if (dtrcon_info != 0) |
| 6207 | 746 info = -1; |
| 747 } | |
| 748 | |
| 749 if (info == -1 && ! force) | |
| 750 retval = *this; // Restore matrix contents. | |
| 751 } | |
| 752 | |
| 753 return retval; | |
| 458 | 754 } |
| 755 | |
| 6207 | 756 |
| 458 | 757 Matrix |
| 7788 | 758 Matrix::finverse (MatrixType &mattype, octave_idx_type& info, double& rcon, |
| 6207 | 759 int force, int calc_cond) const |
| 458 | 760 { |
| 1948 | 761 Matrix retval; |
| 762 | |
| 5275 | 763 octave_idx_type nr = rows (); |
| 764 octave_idx_type nc = cols (); | |
| 1948 | 765 |
| 458 | 766 if (nr != nc || nr == 0 || nc == 0) |
| 1948 | 767 (*current_liboctave_error_handler) ("inverse requires square matrix"); |
| 458 | 768 else |
| 769 { | |
| 5275 | 770 Array<octave_idx_type> ipvt (nr); |
| 771 octave_idx_type *pipvt = ipvt.fortran_vec (); | |
| 1948 | 772 |
| 773 retval = *this; | |
| 774 double *tmp_data = retval.fortran_vec (); | |
| 775 | |
| 4329 | 776 Array<double> z(1); |
| 5275 | 777 octave_idx_type lwork = -1; |
| 4329 | 778 |
| 4330 | 779 // Query the optimum work array size. |
| 4329 | 780 F77_XFCN (dgetri, DGETRI, (nc, tmp_data, nr, pipvt, |
| 781 z.fortran_vec (), lwork, info)); | |
| 782 | |
| 5275 | 783 lwork = static_cast<octave_idx_type> (z(0)); |
| 4329 | 784 lwork = (lwork < 2 *nc ? 2*nc : lwork); |
| 785 z.resize (lwork); | |
| 786 double *pz = z.fortran_vec (); | |
| 787 | |
| 788 info = 0; | |
| 789 | |
| 4330 | 790 // Calculate the norm of the matrix, for later use. |
| 4329 | 791 double anorm = 0; |
| 792 if (calc_cond) | |
| 5275 | 793 anorm = retval.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
| 4329 | 794 |
| 795 F77_XFCN (dgetrf, DGETRF, (nc, nc, tmp_data, nr, pipvt, info)); | |
| 1948 | 796 |
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797 // Throw-away extra info LAPACK gives so as to not change output. |
| 7788 | 798 rcon = 0.0; |
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799 if (info != 0) |
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800 info = -1; |
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801 else if (calc_cond) |
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802 { |
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803 octave_idx_type dgecon_info = 0; |
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804 |
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805 // Now calculate the condition number for non-singular matrix. |
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806 char job = '1'; |
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807 Array<octave_idx_type> iz (nc); |
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808 octave_idx_type *piz = iz.fortran_vec (); |
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809 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
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810 nc, tmp_data, nr, anorm, |
| 7788 | 811 rcon, pz, piz, dgecon_info |
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812 F77_CHAR_ARG_LEN (1))); |
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813 |
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814 if (dgecon_info != 0) |
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815 info = -1; |
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816 } |
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817 |
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818 if (info == -1 && ! force) |
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819 retval = *this; // Restore matrix contents. |
| 1948 | 820 else |
| 821 { | |
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822 octave_idx_type dgetri_info = 0; |
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823 |
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824 F77_XFCN (dgetri, DGETRI, (nc, tmp_data, nr, pipvt, |
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825 pz, lwork, dgetri_info)); |
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826 |
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827 if (dgetri_info != 0) |
| 1948 | 828 info = -1; |
| 829 } | |
| 6207 | 830 |
| 831 if (info != 0) | |
| 832 mattype.mark_as_rectangular(); | |
| 458 | 833 } |
| 834 | |
| 1948 | 835 return retval; |
| 458 | 836 } |
| 837 | |
| 740 | 838 Matrix |
| 7788 | 839 Matrix::inverse (MatrixType &mattype, octave_idx_type& info, double& rcon, |
| 6207 | 840 int force, int calc_cond) const |
| 841 { | |
| 842 int typ = mattype.type (false); | |
| 843 Matrix ret; | |
| 844 | |
| 845 if (typ == MatrixType::Unknown) | |
| 846 typ = mattype.type (*this); | |
| 847 | |
| 848 if (typ == MatrixType::Upper || typ == MatrixType::Lower) | |
| 7788 | 849 ret = tinverse (mattype, info, rcon, force, calc_cond); |
| 6840 | 850 else |
| 6207 | 851 { |
| 852 if (mattype.is_hermitian ()) | |
| 853 { | |
| 6486 | 854 CHOL chol (*this, info, calc_cond); |
| 6207 | 855 if (info == 0) |
| 6486 | 856 { |
| 857 if (calc_cond) | |
| 7788 | 858 rcon = chol.rcond (); |
| 6486 | 859 else |
| 7788 | 860 rcon = 1.0; |
| 6486 | 861 ret = chol.inverse (); |
| 862 } | |
| 6207 | 863 else |
| 864 mattype.mark_as_unsymmetric (); | |
| 865 } | |
| 866 | |
| 867 if (!mattype.is_hermitian ()) | |
| 7788 | 868 ret = finverse(mattype, info, rcon, force, calc_cond); |
| 869 | |
| 870 if ((mattype.is_hermitian () || calc_cond) && rcon == 0.) | |
| 6840 | 871 ret = Matrix (rows (), columns (), octave_Inf); |
| 6207 | 872 } |
| 873 | |
| 874 return ret; | |
| 875 } | |
| 876 | |
| 877 Matrix | |
| 4384 | 878 Matrix::pseudo_inverse (double tol) const |
| 740 | 879 { |
| 3480 | 880 SVD result (*this, SVD::economy); |
| 740 | 881 |
| 882 DiagMatrix S = result.singular_values (); | |
| 883 Matrix U = result.left_singular_matrix (); | |
| 884 Matrix V = result.right_singular_matrix (); | |
| 885 | |
| 886 ColumnVector sigma = S.diag (); | |
| 887 | |
| 5275 | 888 octave_idx_type r = sigma.length () - 1; |
| 889 octave_idx_type nr = rows (); | |
| 890 octave_idx_type nc = cols (); | |
| 740 | 891 |
| 892 if (tol <= 0.0) | |
| 893 { | |
| 894 if (nr > nc) | |
| 895 tol = nr * sigma.elem (0) * DBL_EPSILON; | |
| 896 else | |
| 897 tol = nc * sigma.elem (0) * DBL_EPSILON; | |
| 898 } | |
| 899 | |
| 900 while (r >= 0 && sigma.elem (r) < tol) | |
| 901 r--; | |
| 902 | |
| 903 if (r < 0) | |
| 904 return Matrix (nc, nr, 0.0); | |
| 905 else | |
| 906 { | |
| 907 Matrix Ur = U.extract (0, 0, nr-1, r); | |
| 908 DiagMatrix D = DiagMatrix (sigma.extract (0, r)) . inverse (); | |
| 909 Matrix Vr = V.extract (0, 0, nc-1, r); | |
| 910 return Vr * D * Ur.transpose (); | |
| 911 } | |
| 912 } | |
| 913 | |
| 4773 | 914 #if defined (HAVE_FFTW3) |
| 3827 | 915 |
| 916 ComplexMatrix | |
| 917 Matrix::fourier (void) const | |
| 918 { | |
| 919 size_t nr = rows (); | |
| 920 size_t nc = cols (); | |
| 921 | |
| 922 ComplexMatrix retval (nr, nc); | |
| 923 | |
| 924 size_t npts, nsamples; | |
| 925 | |
| 926 if (nr == 1 || nc == 1) | |
| 927 { | |
| 928 npts = nr > nc ? nr : nc; | |
| 929 nsamples = 1; | |
| 930 } | |
| 931 else | |
| 932 { | |
| 933 npts = nr; | |
| 934 nsamples = nc; | |
| 935 } | |
| 936 | |
| 4773 | 937 const double *in (fortran_vec ()); |
| 3827 | 938 Complex *out (retval.fortran_vec ()); |
| 939 | |
| 4773 | 940 octave_fftw::fft (in, out, npts, nsamples); |
| 3827 | 941 |
| 942 return retval; | |
| 943 } | |
| 944 | |
| 945 ComplexMatrix | |
| 946 Matrix::ifourier (void) const | |
| 947 { | |
| 948 size_t nr = rows (); | |
| 949 size_t nc = cols (); | |
| 950 | |
| 951 ComplexMatrix retval (nr, nc); | |
| 952 | |
| 953 size_t npts, nsamples; | |
| 954 | |
| 955 if (nr == 1 || nc == 1) | |
| 956 { | |
| 957 npts = nr > nc ? nr : nc; | |
| 958 nsamples = 1; | |
| 959 } | |
| 960 else | |
| 961 { | |
| 962 npts = nr; | |
| 963 nsamples = nc; | |
| 964 } | |
| 965 | |
| 966 ComplexMatrix tmp (*this); | |
| 967 Complex *in (tmp.fortran_vec ()); | |
| 968 Complex *out (retval.fortran_vec ()); | |
| 969 | |
| 4773 | 970 octave_fftw::ifft (in, out, npts, nsamples); |
| 3827 | 971 |
| 972 return retval; | |
| 973 } | |
| 974 | |
| 975 ComplexMatrix | |
| 976 Matrix::fourier2d (void) const | |
| 977 { | |
| 4773 | 978 dim_vector dv(rows (), cols ()); |
| 979 | |
| 980 const double *in = fortran_vec (); | |
| 981 ComplexMatrix retval (rows (), cols ()); | |
| 982 octave_fftw::fftNd (in, retval.fortran_vec (), 2, dv); | |
| 3827 | 983 |
| 984 return retval; | |
| 985 } | |
| 986 | |
| 987 ComplexMatrix | |
| 988 Matrix::ifourier2d (void) const | |
| 989 { | |
| 4773 | 990 dim_vector dv(rows (), cols ()); |
| 3827 | 991 |
| 992 ComplexMatrix retval (*this); | |
| 4773 | 993 Complex *out (retval.fortran_vec ()); |
| 994 | |
| 995 octave_fftw::ifftNd (out, out, 2, dv); | |
| 3827 | 996 |
| 997 return retval; | |
| 998 } | |
| 999 | |
| 1000 #else | |
| 1001 | |
| 458 | 1002 ComplexMatrix |
| 1003 Matrix::fourier (void) const | |
| 1004 { | |
| 1948 | 1005 ComplexMatrix retval; |
| 1006 | |
| 5275 | 1007 octave_idx_type nr = rows (); |
| 1008 octave_idx_type nc = cols (); | |
| 1009 | |
| 1010 octave_idx_type npts, nsamples; | |
| 1948 | 1011 |
| 458 | 1012 if (nr == 1 || nc == 1) |
| 1013 { | |
| 1014 npts = nr > nc ? nr : nc; | |
| 1015 nsamples = 1; | |
| 1016 } | |
| 1017 else | |
| 1018 { | |
| 1019 npts = nr; | |
| 1020 nsamples = nc; | |
| 1021 } | |
| 1022 | |
| 5275 | 1023 octave_idx_type nn = 4*npts+15; |
| 1948 | 1024 |
| 1025 Array<Complex> wsave (nn); | |
| 1026 Complex *pwsave = wsave.fortran_vec (); | |
| 1027 | |
| 3585 | 1028 retval = ComplexMatrix (*this); |
| 1948 | 1029 Complex *tmp_data = retval.fortran_vec (); |
| 1030 | |
|
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1031 F77_FUNC (zffti, ZFFTI) (npts, pwsave); |
| 458 | 1032 |
| 5275 | 1033 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1034 { |
| 1035 OCTAVE_QUIT; | |
| 1036 | |
|
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1037 F77_FUNC (zfftf, ZFFTF) (npts, &tmp_data[npts*j], pwsave); |
| 4153 | 1038 } |
| 1948 | 1039 |
| 1040 return retval; | |
| 458 | 1041 } |
| 1042 | |
| 1043 ComplexMatrix | |
| 1044 Matrix::ifourier (void) const | |
| 1045 { | |
| 1948 | 1046 ComplexMatrix retval; |
| 1047 | |
| 5275 | 1048 octave_idx_type nr = rows (); |
| 1049 octave_idx_type nc = cols (); | |
| 1050 | |
| 1051 octave_idx_type npts, nsamples; | |
| 1948 | 1052 |
| 458 | 1053 if (nr == 1 || nc == 1) |
| 1054 { | |
| 1055 npts = nr > nc ? nr : nc; | |
| 1056 nsamples = 1; | |
| 1057 } | |
| 1058 else | |
| 1059 { | |
| 1060 npts = nr; | |
| 1061 nsamples = nc; | |
| 1062 } | |
| 1063 | |
| 5275 | 1064 octave_idx_type nn = 4*npts+15; |
| 1948 | 1065 |
| 1066 Array<Complex> wsave (nn); | |
| 1067 Complex *pwsave = wsave.fortran_vec (); | |
| 1068 | |
| 3585 | 1069 retval = ComplexMatrix (*this); |
| 1948 | 1070 Complex *tmp_data = retval.fortran_vec (); |
| 1071 | |
|
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1072 F77_FUNC (zffti, ZFFTI) (npts, pwsave); |
| 458 | 1073 |
| 5275 | 1074 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1075 { |
| 1076 OCTAVE_QUIT; | |
| 1077 | |
|
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1078 F77_FUNC (zfftb, ZFFTB) (npts, &tmp_data[npts*j], pwsave); |
| 4153 | 1079 } |
| 458 | 1080 |
| 5275 | 1081 for (octave_idx_type j = 0; j < npts*nsamples; j++) |
| 3572 | 1082 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
| 458 | 1083 |
| 1948 | 1084 return retval; |
| 458 | 1085 } |
| 1086 | |
| 677 | 1087 ComplexMatrix |
| 1088 Matrix::fourier2d (void) const | |
| 1089 { | |
| 1948 | 1090 ComplexMatrix retval; |
| 1091 | |
| 5275 | 1092 octave_idx_type nr = rows (); |
| 1093 octave_idx_type nc = cols (); | |
| 1094 | |
| 1095 octave_idx_type npts, nsamples; | |
| 1948 | 1096 |
| 677 | 1097 if (nr == 1 || nc == 1) |
| 1098 { | |
| 1099 npts = nr > nc ? nr : nc; | |
| 1100 nsamples = 1; | |
| 1101 } | |
| 1102 else | |
| 1103 { | |
| 1104 npts = nr; | |
| 1105 nsamples = nc; | |
| 1106 } | |
| 1107 | |
| 5275 | 1108 octave_idx_type nn = 4*npts+15; |
| 1948 | 1109 |
| 1110 Array<Complex> wsave (nn); | |
| 1111 Complex *pwsave = wsave.fortran_vec (); | |
| 1112 | |
| 3585 | 1113 retval = ComplexMatrix (*this); |
| 1948 | 1114 Complex *tmp_data = retval.fortran_vec (); |
| 1115 | |
|
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|
1116 F77_FUNC (zffti, ZFFTI) (npts, pwsave); |
| 677 | 1117 |
| 5275 | 1118 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1119 { |
| 1120 OCTAVE_QUIT; | |
| 1121 | |
|
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1122 F77_FUNC (zfftf, ZFFTF) (npts, &tmp_data[npts*j], pwsave); |
| 4153 | 1123 } |
| 677 | 1124 |
| 1125 npts = nc; | |
| 1126 nsamples = nr; | |
| 1127 nn = 4*npts+15; | |
| 1948 | 1128 |
| 1129 wsave.resize (nn); | |
| 1130 pwsave = wsave.fortran_vec (); | |
| 1131 | |
| 4773 | 1132 Array<Complex> tmp (npts); |
| 1133 Complex *prow = tmp.fortran_vec (); | |
| 1948 | 1134 |
|
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1135 F77_FUNC (zffti, ZFFTI) (npts, pwsave); |
| 677 | 1136 |
| 5275 | 1137 for (octave_idx_type j = 0; j < nsamples; j++) |
| 677 | 1138 { |
| 4153 | 1139 OCTAVE_QUIT; |
| 1140 | |
| 5275 | 1141 for (octave_idx_type i = 0; i < npts; i++) |
| 1948 | 1142 prow[i] = tmp_data[i*nr + j]; |
| 1143 | |
|
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|
1144 F77_FUNC (zfftf, ZFFTF) (npts, prow, pwsave); |
| 677 | 1145 |
| 5275 | 1146 for (octave_idx_type i = 0; i < npts; i++) |
| 1948 | 1147 tmp_data[i*nr + j] = prow[i]; |
| 677 | 1148 } |
| 1149 | |
| 1948 | 1150 return retval; |
| 677 | 1151 } |
| 1152 | |
| 1153 ComplexMatrix | |
| 1154 Matrix::ifourier2d (void) const | |
| 1155 { | |
| 1948 | 1156 ComplexMatrix retval; |
| 1157 | |
| 5275 | 1158 octave_idx_type nr = rows (); |
| 1159 octave_idx_type nc = cols (); | |
| 1160 | |
| 1161 octave_idx_type npts, nsamples; | |
| 1948 | 1162 |
| 677 | 1163 if (nr == 1 || nc == 1) |
| 1164 { | |
| 1165 npts = nr > nc ? nr : nc; | |
| 1166 nsamples = 1; | |
| 1167 } | |
| 1168 else | |
| 1169 { | |
| 1170 npts = nr; | |
| 1171 nsamples = nc; | |
| 1172 } | |
| 1173 | |
| 5275 | 1174 octave_idx_type nn = 4*npts+15; |
| 1948 | 1175 |
| 1176 Array<Complex> wsave (nn); | |
| 1177 Complex *pwsave = wsave.fortran_vec (); | |
| 1178 | |
| 3585 | 1179 retval = ComplexMatrix (*this); |
| 1948 | 1180 Complex *tmp_data = retval.fortran_vec (); |
| 1181 | |
|
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|
1182 F77_FUNC (zffti, ZFFTI) (npts, pwsave); |
| 677 | 1183 |
| 5275 | 1184 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1185 { |
| 1186 OCTAVE_QUIT; | |
| 1187 | |
|
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|
1188 F77_FUNC (zfftb, ZFFTB) (npts, &tmp_data[npts*j], pwsave); |
| 4153 | 1189 } |
| 677 | 1190 |
| 5275 | 1191 for (octave_idx_type j = 0; j < npts*nsamples; j++) |
| 3572 | 1192 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
| 677 | 1193 |
| 1194 npts = nc; | |
| 1195 nsamples = nr; | |
| 1196 nn = 4*npts+15; | |
| 1948 | 1197 |
| 1198 wsave.resize (nn); | |
| 1199 pwsave = wsave.fortran_vec (); | |
| 1200 | |
| 4773 | 1201 Array<Complex> tmp (npts); |
| 1202 Complex *prow = tmp.fortran_vec (); | |
| 1948 | 1203 |
|
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1204 F77_FUNC (zffti, ZFFTI) (npts, pwsave); |
| 677 | 1205 |
| 5275 | 1206 for (octave_idx_type j = 0; j < nsamples; j++) |
| 677 | 1207 { |
| 4153 | 1208 OCTAVE_QUIT; |
| 1209 | |
| 5275 | 1210 for (octave_idx_type i = 0; i < npts; i++) |
| 1948 | 1211 prow[i] = tmp_data[i*nr + j]; |
| 1212 | |
|
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|
1213 F77_FUNC (zfftb, ZFFTB) (npts, prow, pwsave); |
| 677 | 1214 |
| 5275 | 1215 for (octave_idx_type i = 0; i < npts; i++) |
| 3572 | 1216 tmp_data[i*nr + j] = prow[i] / static_cast<double> (npts); |
| 677 | 1217 } |
| 1218 | |
| 1948 | 1219 return retval; |
| 677 | 1220 } |
| 1221 | |
| 3827 | 1222 #endif |
| 1223 | |
| 458 | 1224 DET |
| 1225 Matrix::determinant (void) const | |
| 1226 { | |
| 5275 | 1227 octave_idx_type info; |
| 7788 | 1228 double rcon; |
| 1229 return determinant (info, rcon, 0); | |
| 458 | 1230 } |
| 1231 | |
| 1232 DET | |
| 5275 | 1233 Matrix::determinant (octave_idx_type& info) const |
| 458 | 1234 { |
| 7788 | 1235 double rcon; |
| 1236 return determinant (info, rcon, 0); | |
| 458 | 1237 } |
| 1238 | |
| 1239 DET | |
| 7788 | 1240 Matrix::determinant (octave_idx_type& info, double& rcon, int calc_cond) const |
| 458 | 1241 { |
| 1242 DET retval; | |
| 1243 | |
| 5275 | 1244 octave_idx_type nr = rows (); |
| 1245 octave_idx_type nc = cols (); | |
| 458 | 1246 |
| 1247 if (nr == 0 || nc == 0) | |
| 1248 { | |
| 5634 | 1249 retval = DET (1.0, 0); |
| 458 | 1250 } |
| 1251 else | |
| 1252 { | |
| 5275 | 1253 Array<octave_idx_type> ipvt (nr); |
| 1254 octave_idx_type *pipvt = ipvt.fortran_vec (); | |
| 1948 | 1255 |
| 1256 Matrix atmp = *this; | |
| 1257 double *tmp_data = atmp.fortran_vec (); | |
| 1258 | |
| 4329 | 1259 info = 0; |
| 1260 | |
| 4330 | 1261 // Calculate the norm of the matrix, for later use. |
| 4329 | 1262 double anorm = 0; |
| 1263 if (calc_cond) | |
| 5275 | 1264 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
| 4329 | 1265 |
| 1266 F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); | |
| 1948 | 1267 |
|
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|
1268 // Throw-away extra info LAPACK gives so as to not change output. |
| 7788 | 1269 rcon = 0.0; |
|
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|
1270 if (info != 0) |
|
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|
1271 { |
|
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1272 info = -1; |
|
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1273 retval = DET (); |
|
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|
1274 } |
|
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|
1275 else |
| 458 | 1276 { |
|
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1277 if (calc_cond) |
|
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|
1278 { |
|
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1279 // Now calc the condition number for non-singular matrix. |
|
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1280 char job = '1'; |
|
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1281 Array<double> z (4 * nc); |
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1282 double *pz = z.fortran_vec (); |
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1283 Array<octave_idx_type> iz (nc); |
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1284 octave_idx_type *piz = iz.fortran_vec (); |
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1285 |
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1286 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
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1287 nc, tmp_data, nr, anorm, |
| 7788 | 1288 rcon, pz, piz, info |
|
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1289 F77_CHAR_ARG_LEN (1))); |
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1290 } |
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1291 |
| 4509 | 1292 if (info != 0) |
| 1948 | 1293 { |
| 4509 | 1294 info = -1; |
| 1295 retval = DET (); | |
| 4329 | 1296 } |
| 1297 else | |
| 1948 | 1298 { |
|
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1299 double c = 1.0; |
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1300 int e = 0; |
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1301 |
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1302 for (octave_idx_type i = 0; i < nc; i++) |
| 4329 | 1303 { |
|
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1304 if (ipvt(i) != (i+1)) |
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1305 c = -c; |
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1306 |
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1307 c *= atmp(i,i); |
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1308 |
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1309 if (c == 0.0) |
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1310 break; |
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1311 |
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1312 while (fabs (c) < 0.5) |
| 4329 | 1313 { |
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1314 c *= 2.0; |
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1315 e--; |
| 4329 | 1316 } |
| 5634 | 1317 |
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1318 while (fabs (c) >= 2.0) |
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1319 { |
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1320 c /= 2.0; |
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1321 e++; |
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1322 } |
| 4329 | 1323 } |
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1324 |
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|
1325 retval = DET (c, e); |
| 1948 | 1326 } |
| 458 | 1327 } |
| 1328 } | |
| 1329 | |
| 1330 return retval; | |
| 1331 } | |
| 1332 | |
| 7788 | 1333 double |
| 1334 Matrix::rcond (void) const | |
| 1335 { | |
| 1336 MatrixType mattype (*this); | |
| 1337 return rcond (mattype); | |
| 1338 } | |
| 1339 | |
| 1340 double | |
| 1341 Matrix::rcond (MatrixType &mattype) const | |
| 1342 { | |
| 1343 double rcon; | |
| 1344 octave_idx_type nr = rows (); | |
| 1345 octave_idx_type nc = cols (); | |
| 1346 | |
| 1347 if (nr != nc) | |
| 1348 (*current_liboctave_error_handler) ("matrix must be square"); | |
| 1349 else if (nr == 0 || nc == 0) | |
| 1350 rcon = octave_Inf; | |
| 1351 else | |
| 1352 { | |
| 1353 int typ = mattype.type (); | |
| 1354 | |
| 1355 if (typ == MatrixType::Unknown) | |
| 1356 typ = mattype.type (*this); | |
| 1357 | |
| 1358 // Only calculate the condition number for LU/Cholesky | |
| 1359 if (typ == MatrixType::Upper) | |
| 1360 { | |
| 1361 const double *tmp_data = fortran_vec (); | |
| 1362 octave_idx_type info = 0; | |
| 1363 char norm = '1'; | |
| 1364 char uplo = 'U'; | |
| 1365 char dia = 'N'; | |
| 1366 | |
| 1367 Array<double> z (3 * nc); | |
| 1368 double *pz = z.fortran_vec (); | |
| 1369 Array<octave_idx_type> iz (nc); | |
| 1370 octave_idx_type *piz = iz.fortran_vec (); | |
| 1371 | |
| 1372 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1373 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1374 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1375 nr, tmp_data, nr, rcon, | |
| 1376 pz, piz, info | |
| 1377 F77_CHAR_ARG_LEN (1) | |
| 1378 F77_CHAR_ARG_LEN (1) | |
| 1379 F77_CHAR_ARG_LEN (1))); | |
| 1380 | |
| 1381 if (info != 0) | |
| 1382 rcon = 0.0; | |
| 1383 } | |
| 1384 else if (typ == MatrixType::Permuted_Upper) | |
| 1385 (*current_liboctave_error_handler) | |
| 1386 ("permuted triangular matrix not implemented"); | |
| 1387 else if (typ == MatrixType::Lower) | |
| 1388 { | |
| 1389 const double *tmp_data = fortran_vec (); | |
| 1390 octave_idx_type info = 0; | |
| 1391 char norm = '1'; | |
| 1392 char uplo = 'L'; | |
| 1393 char dia = 'N'; | |
| 1394 | |
| 1395 Array<double> z (3 * nc); | |
| 1396 double *pz = z.fortran_vec (); | |
| 1397 Array<octave_idx_type> iz (nc); | |
| 1398 octave_idx_type *piz = iz.fortran_vec (); | |
| 1399 | |
| 1400 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1401 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1402 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1403 nr, tmp_data, nr, rcon, | |
| 1404 pz, piz, info | |
| 1405 F77_CHAR_ARG_LEN (1) | |
| 1406 F77_CHAR_ARG_LEN (1) | |
| 1407 F77_CHAR_ARG_LEN (1))); | |
| 1408 | |
| 1409 if (info != 0) | |
| 1410 rcon = 0.0; | |
| 1411 } | |
| 1412 else if (typ == MatrixType::Permuted_Lower) | |
| 1413 (*current_liboctave_error_handler) | |
| 1414 ("permuted triangular matrix not implemented"); | |
| 1415 else if (typ == MatrixType::Full || typ == MatrixType::Hermitian) | |
| 1416 { | |
| 1417 double anorm = -1.0; | |
| 1418 Matrix atmp = *this; | |
| 1419 double *tmp_data = atmp.fortran_vec (); | |
| 1420 | |
| 1421 if (typ == MatrixType::Hermitian) | |
| 1422 { | |
| 1423 octave_idx_type info = 0; | |
| 1424 char job = 'L'; | |
| 1425 anorm = atmp.abs().sum(). | |
| 1426 row(static_cast<octave_idx_type>(0)).max(); | |
| 1427 | |
| 1428 F77_XFCN (dpotrf, DPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, | |
| 1429 tmp_data, nr, info | |
| 1430 F77_CHAR_ARG_LEN (1))); | |
| 1431 | |
| 1432 if (info != 0) | |
| 1433 { | |
| 1434 rcon = 0.0; | |
| 1435 mattype.mark_as_unsymmetric (); | |
| 1436 typ = MatrixType::Full; | |
| 1437 } | |
| 1438 else | |
| 1439 { | |
| 1440 Array<double> z (3 * nc); | |
| 1441 double *pz = z.fortran_vec (); | |
| 1442 Array<octave_idx_type> iz (nc); | |
| 1443 octave_idx_type *piz = iz.fortran_vec (); | |
| 1444 | |
| 1445 F77_XFCN (dpocon, DPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), | |
| 1446 nr, tmp_data, nr, anorm, | |
| 1447 rcon, pz, piz, info | |
| 1448 F77_CHAR_ARG_LEN (1))); | |
| 1449 | |
| 1450 if (info != 0) | |
| 1451 rcon = 0.0; | |
| 1452 } | |
| 1453 } | |
| 1454 | |
| 1455 if (typ == MatrixType::Full) | |
| 1456 { | |
| 1457 octave_idx_type info = 0; | |
| 1458 | |
| 1459 Array<octave_idx_type> ipvt (nr); | |
| 1460 octave_idx_type *pipvt = ipvt.fortran_vec (); | |
| 1461 | |
| 1462 if(anorm < 0.) | |
| 1463 anorm = atmp.abs().sum(). | |
| 1464 row(static_cast<octave_idx_type>(0)).max(); | |
| 1465 | |
| 1466 Array<double> z (4 * nc); | |
| 1467 double *pz = z.fortran_vec (); | |
| 1468 Array<octave_idx_type> iz (nc); | |
| 1469 octave_idx_type *piz = iz.fortran_vec (); | |
| 1470 | |
| 1471 F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); | |
| 1472 | |
| 1473 if (info != 0) | |
| 1474 { | |
| 1475 rcon = 0.0; | |
| 1476 mattype.mark_as_rectangular (); | |
| 1477 } | |
| 1478 else | |
| 1479 { | |
| 1480 char job = '1'; | |
| 1481 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), | |
| 1482 nc, tmp_data, nr, anorm, | |
| 1483 rcon, pz, piz, info | |
| 1484 F77_CHAR_ARG_LEN (1))); | |
| 1485 | |
| 1486 if (info != 0) | |
| 1487 rcon = 0.0; | |
| 1488 } | |
| 1489 } | |
| 1490 } | |
| 1491 else | |
| 1492 rcon = 0.0; | |
| 1493 } | |
| 1494 | |
| 1495 return rcon; | |
| 1496 } | |
| 1497 | |
| 458 | 1498 Matrix |
| 5785 | 1499 Matrix::utsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, |
| 7788 | 1500 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 1501 bool calc_cond) const |
| 1502 { | |
| 1503 Matrix retval; | |
| 1504 | |
| 1505 octave_idx_type nr = rows (); | |
| 1506 octave_idx_type nc = cols (); | |
| 1507 | |
| 6924 | 1508 if (nr != b.rows ()) |
| 5785 | 1509 (*current_liboctave_error_handler) |
| 1510 ("matrix dimension mismatch solution of linear equations"); | |
| 6924 | 1511 else if (nr == 0 || nc == 0 || b.cols () == 0) |
| 1512 retval = Matrix (nc, b.cols (), 0.0); | |
| 5785 | 1513 else |
| 1514 { | |
| 1515 volatile int typ = mattype.type (); | |
| 1516 | |
| 1517 if (typ == MatrixType::Permuted_Upper || | |
| 1518 typ == MatrixType::Upper) | |
| 1519 { | |
| 1520 octave_idx_type b_nc = b.cols (); | |
| 7788 | 1521 rcon = 1.; |
| 5785 | 1522 info = 0; |
| 1523 | |
| 1524 if (typ == MatrixType::Permuted_Upper) | |
| 1525 { | |
| 1526 (*current_liboctave_error_handler) | |
| 6390 | 1527 ("permuted triangular matrix not implemented"); |
| 5785 | 1528 } |
| 1529 else | |
| 1530 { | |
| 1531 const double *tmp_data = fortran_vec (); | |
| 1532 | |
| 1533 if (calc_cond) | |
| 1534 { | |
| 1535 char norm = '1'; | |
| 1536 char uplo = 'U'; | |
| 1537 char dia = 'N'; | |
| 1538 | |
| 1539 Array<double> z (3 * nc); | |
| 1540 double *pz = z.fortran_vec (); | |
| 1541 Array<octave_idx_type> iz (nc); | |
| 1542 octave_idx_type *piz = iz.fortran_vec (); | |
| 1543 | |
| 1544 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1545 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1546 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 7788 | 1547 nr, tmp_data, nr, rcon, |
| 5785 | 1548 pz, piz, info |
| 1549 F77_CHAR_ARG_LEN (1) | |
| 1550 F77_CHAR_ARG_LEN (1) | |
| 1551 F77_CHAR_ARG_LEN (1))); | |
| 1552 | |
| 1553 if (info != 0) | |
| 1554 info = -2; | |
| 1555 | |
| 7788 | 1556 volatile double rcond_plus_one = rcon + 1.0; |
| 1557 | |
| 1558 if (rcond_plus_one == 1.0 || xisnan (rcon)) | |
| 5785 | 1559 { |
| 1560 info = -2; | |
| 1561 | |
| 1562 if (sing_handler) | |
| 7788 | 1563 sing_handler (rcon); |
| 5785 | 1564 else |
| 1565 (*current_liboctave_error_handler) | |
| 1566 ("matrix singular to machine precision, rcond = %g", | |
| 7788 | 1567 rcon); |
| 5785 | 1568 } |
| 1569 } | |
| 1570 | |
| 1571 if (info == 0) | |
| 1572 { | |
| 1573 retval = b; | |
| 1574 double *result = retval.fortran_vec (); | |
| 1575 | |
| 1576 char uplo = 'U'; | |
| 1577 char trans = 'N'; | |
| 1578 char dia = 'N'; | |
| 1579 | |
| 1580 F77_XFCN (dtrtrs, DTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1581 F77_CONST_CHAR_ARG2 (&trans, 1), | |
| 1582 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1583 nr, b_nc, tmp_data, nr, | |
| 1584 result, nr, info | |
| 1585 F77_CHAR_ARG_LEN (1) | |
| 1586 F77_CHAR_ARG_LEN (1) | |
| 1587 F77_CHAR_ARG_LEN (1))); | |
| 1588 } | |
| 1589 } | |
| 1590 } | |
| 1591 else | |
| 1592 (*current_liboctave_error_handler) ("incorrect matrix type"); | |
| 1593 } | |
| 1594 | |
| 1595 return retval; | |
| 1596 } | |
| 1597 | |
| 1598 Matrix | |
| 1599 Matrix::ltsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, | |
| 7788 | 1600 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 1601 bool calc_cond) const |
| 1602 { | |
| 1603 Matrix retval; | |
| 1604 | |
| 1605 octave_idx_type nr = rows (); | |
| 1606 octave_idx_type nc = cols (); | |
| 1607 | |
| 6924 | 1608 if (nr != b.rows ()) |
| 5785 | 1609 (*current_liboctave_error_handler) |
| 1610 ("matrix dimension mismatch solution of linear equations"); | |
| 6924 | 1611 else if (nr == 0 || nc == 0 || b.cols () == 0) |
| 1612 retval = Matrix (nc, b.cols (), 0.0); | |
| 5785 | 1613 else |
| 1614 { | |
| 1615 volatile int typ = mattype.type (); | |
| 1616 | |
| 1617 if (typ == MatrixType::Permuted_Lower || | |
| 1618 typ == MatrixType::Lower) | |
| 1619 { | |
| 1620 octave_idx_type b_nc = b.cols (); | |
| 7788 | 1621 rcon = 1.; |
| 5785 | 1622 info = 0; |
| 1623 | |
| 1624 if (typ == MatrixType::Permuted_Lower) | |
| 1625 { | |
| 1626 (*current_liboctave_error_handler) | |
| 6390 | 1627 ("permuted triangular matrix not implemented"); |
| 5785 | 1628 } |
| 1629 else | |
| 1630 { | |
| 1631 const double *tmp_data = fortran_vec (); | |
| 1632 | |
| 1633 if (calc_cond) | |
| 1634 { | |
| 1635 char norm = '1'; | |
| 1636 char uplo = 'L'; | |
| 1637 char dia = 'N'; | |
| 1638 | |
| 1639 Array<double> z (3 * nc); | |
| 1640 double *pz = z.fortran_vec (); | |
| 1641 Array<octave_idx_type> iz (nc); | |
| 1642 octave_idx_type *piz = iz.fortran_vec (); | |
| 1643 | |
| 1644 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1645 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1646 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 7788 | 1647 nr, tmp_data, nr, rcon, |
| 5785 | 1648 pz, piz, info |
| 1649 F77_CHAR_ARG_LEN (1) | |
| 1650 F77_CHAR_ARG_LEN (1) | |
| 1651 F77_CHAR_ARG_LEN (1))); | |
| 1652 | |
| 1653 if (info != 0) | |
| 1654 info = -2; | |
| 1655 | |
| 7788 | 1656 volatile double rcond_plus_one = rcon + 1.0; |
| 1657 | |
| 1658 if (rcond_plus_one == 1.0 || xisnan (rcon)) | |
| 5785 | 1659 { |
| 1660 info = -2; | |
| 1661 | |
| 1662 if (sing_handler) | |
| 7788 | 1663 sing_handler (rcon); |
| 5785 | 1664 else |
| 1665 (*current_liboctave_error_handler) | |
| 1666 ("matrix singular to machine precision, rcond = %g", | |
| 7788 | 1667 rcon); |
| 5785 | 1668 } |
| 1669 } | |
| 1670 | |
| 1671 if (info == 0) | |
| 1672 { | |
| 1673 retval = b; | |
| 1674 double *result = retval.fortran_vec (); | |
| 1675 | |
| 1676 char uplo = 'L'; | |
| 1677 char trans = 'N'; | |
| 1678 char dia = 'N'; | |
| 1679 | |
| 1680 F77_XFCN (dtrtrs, DTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1681 F77_CONST_CHAR_ARG2 (&trans, 1), | |
| 1682 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1683 nr, b_nc, tmp_data, nr, | |
| 1684 result, nr, info | |
| 1685 F77_CHAR_ARG_LEN (1) | |
| 1686 F77_CHAR_ARG_LEN (1) | |
| 1687 F77_CHAR_ARG_LEN (1))); | |
| 1688 } | |
| 1689 } | |
| 1690 } | |
| 1691 else | |
| 1692 (*current_liboctave_error_handler) ("incorrect matrix type"); | |
| 1693 } | |
| 1694 | |
| 1695 return retval; | |
| 1696 } | |
| 1697 | |
| 1698 Matrix | |
| 1699 Matrix::fsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, | |
| 7788 | 1700 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 1701 bool calc_cond) const |
| 1702 { | |
| 1703 Matrix retval; | |
| 1704 | |
| 1705 octave_idx_type nr = rows (); | |
| 1706 octave_idx_type nc = cols (); | |
| 1707 | |
| 6924 | 1708 if (nr != nc || nr != b.rows ()) |
| 5785 | 1709 (*current_liboctave_error_handler) |
| 1710 ("matrix dimension mismatch solution of linear equations"); | |
| 6924 | 1711 else if (nr == 0 || b.cols () == 0) |
| 1712 retval = Matrix (nc, b.cols (), 0.0); | |
| 5785 | 1713 else |
| 1714 { | |
| 1715 volatile int typ = mattype.type (); | |
| 1716 | |
| 1717 // Calculate the norm of the matrix, for later use. | |
| 1718 double anorm = -1.; | |
| 1719 | |
| 1720 if (typ == MatrixType::Hermitian) | |
| 1721 { | |
| 1722 info = 0; | |
| 1723 char job = 'L'; | |
| 1724 Matrix atmp = *this; | |
| 1725 double *tmp_data = atmp.fortran_vec (); | |
| 1726 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); | |
| 1727 | |
| 1728 F77_XFCN (dpotrf, DPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, | |
| 1729 tmp_data, nr, info | |
| 1730 F77_CHAR_ARG_LEN (1))); | |
| 1731 | |
|
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|
1732 // Throw-away extra info LAPACK gives so as to not change output. |
| 7788 | 1733 rcon = 0.0; |
|
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1734 if (info != 0) |
|
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1735 { |
|
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1736 info = -2; |
|
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|
1737 |
|
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1738 mattype.mark_as_unsymmetric (); |
|
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1739 typ = MatrixType::Full; |
|
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don't check f77_exception_encountered
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diff
changeset
|
1740 } |
|
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don't check f77_exception_encountered
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diff
changeset
|
1741 else |
| 5785 | 1742 { |
|
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29980c6b8604
don't check f77_exception_encountered
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diff
changeset
|
1743 if (calc_cond) |
| 5785 | 1744 { |
|
7482
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
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diff
changeset
|
1745 Array<double> z (3 * nc); |
|
29980c6b8604
don't check f77_exception_encountered
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diff
changeset
|
1746 double *pz = z.fortran_vec (); |
|
29980c6b8604
don't check f77_exception_encountered
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diff
changeset
|
1747 Array<octave_idx_type> iz (nc); |
|
29980c6b8604
don't check f77_exception_encountered
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diff
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|
1748 octave_idx_type *piz = iz.fortran_vec (); |
|
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don't check f77_exception_encountered
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diff
changeset
|
1749 |
|
29980c6b8604
don't check f77_exception_encountered
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diff
changeset
|
1750 F77_XFCN (dpocon, DPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
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diff
changeset
|
1751 nr, tmp_data, nr, anorm, |
| 7788 | 1752 rcon, pz, piz, info |
|
7482
29980c6b8604
don't check f77_exception_encountered
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diff
changeset
|
1753 F77_CHAR_ARG_LEN (1))); |
|
29980c6b8604
don't check f77_exception_encountered
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diff
changeset
|
1754 |
|
29980c6b8604
don't check f77_exception_encountered
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diff
changeset
|
1755 if (info != 0) |
|
29980c6b8604
don't check f77_exception_encountered
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parents:
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diff
changeset
|
1756 info = -2; |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
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diff
changeset
|
1757 |
| 7788 | 1758 volatile double rcond_plus_one = rcon + 1.0; |
| 1759 | |
| 1760 if (rcond_plus_one == 1.0 || xisnan (rcon)) | |
|
7482
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
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diff
changeset
|
1761 { |
|
29980c6b8604
don't check f77_exception_encountered
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parents:
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diff
changeset
|
1762 info = -2; |
|
29980c6b8604
don't check f77_exception_encountered
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diff
changeset
|
1763 |
|
29980c6b8604
don't check f77_exception_encountered
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diff
changeset
|
1764 if (sing_handler) |
| 7788 | 1765 sing_handler (rcon); |
|
7482
29980c6b8604
don't check f77_exception_encountered
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diff
changeset
|
1766 else |
|
29980c6b8604
don't check f77_exception_encountered
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parents:
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diff
changeset
|
1767 (*current_liboctave_error_handler) |
|
29980c6b8604
don't check f77_exception_encountered
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diff
changeset
|
1768 ("matrix singular to machine precision, rcond = %g", |
| 7788 | 1769 rcon); |
|
7482
29980c6b8604
don't check f77_exception_encountered
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diff
changeset
|
1770 } |
|
29980c6b8604
don't check f77_exception_encountered
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diff
changeset
|
1771 } |
|
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diff
changeset
|
1772 |
|
29980c6b8604
don't check f77_exception_encountered
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diff
changeset
|
1773 if (info == 0) |
|
29980c6b8604
don't check f77_exception_encountered
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diff
changeset
|
1774 { |
|
29980c6b8604
don't check f77_exception_encountered
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diff
changeset
|
1775 retval = b; |
|
29980c6b8604
don't check f77_exception_encountered
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diff
changeset
|
1776 double *result = retval.fortran_vec (); |
|
29980c6b8604
don't check f77_exception_encountered
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diff
changeset
|
1777 |
|
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diff
changeset
|
1778 octave_idx_type b_nc = b.cols (); |
|
29980c6b8604
don't check f77_exception_encountered
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diff
changeset
|
1779 |
|
29980c6b8604
don't check f77_exception_encountered
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diff
changeset
|
1780 F77_XFCN (dpotrs, DPOTRS, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
29980c6b8604
don't check f77_exception_encountered
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diff
changeset
|
1781 nr, b_nc, tmp_data, nr, |
|
29980c6b8604
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diff
changeset
|
1782 result, b.rows(), info |
|
29980c6b8604
don't check f77_exception_encountered
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diff
changeset
|
1783 F77_CHAR_ARG_LEN (1))); |
|
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diff
changeset
|
1784 } |
|
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diff
changeset
|
1785 else |
|
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diff
changeset
|
1786 { |
| 5785 | 1787 mattype.mark_as_unsymmetric (); |
| 1788 typ = MatrixType::Full; | |
|
7482
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changeset
|
1789 } |
| 5785 | 1790 } |
| 1791 } | |
| 1792 | |
| 1793 if (typ == MatrixType::Full) | |
| 1794 { | |
| 1795 info = 0; | |
| 1796 | |
| 1797 Array<octave_idx_type> ipvt (nr); | |
| 1798 octave_idx_type *pipvt = ipvt.fortran_vec (); | |
| 1799 | |
| 1800 Matrix atmp = *this; | |
| 1801 double *tmp_data = atmp.fortran_vec (); | |
| 1802 if(anorm < 0.) | |
| 1803 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); | |
| 1804 | |
| 1805 Array<double> z (4 * nc); | |
| 1806 double *pz = z.fortran_vec (); | |
| 1807 Array<octave_idx_type> iz (nc); | |
| 1808 octave_idx_type *piz = iz.fortran_vec (); | |
| 1809 | |
| 1810 F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); | |
| 1811 | |
|
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changeset
|
1812 // Throw-away extra info LAPACK gives so as to not change output. |
| 7788 | 1813 rcon = 0.0; |
|
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|
1814 if (info != 0) |
| 5785 | 1815 { |
|
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diff
changeset
|
1816 info = -2; |
|
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diff
changeset
|
1817 |
|
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diff
changeset
|
1818 if (sing_handler) |
| 7788 | 1819 sing_handler (rcon); |
|
7482
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diff
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|
1820 else |
|
29980c6b8604
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diff
changeset
|
1821 (*current_liboctave_error_handler) |
|
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diff
changeset
|
1822 ("matrix singular to machine precision"); |
|
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diff
changeset
|
1823 |
|
29980c6b8604
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diff
changeset
|
1824 mattype.mark_as_rectangular (); |
|
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diff
changeset
|
1825 } |
|
29980c6b8604
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diff
changeset
|
1826 else |
|
29980c6b8604
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diff
changeset
|
1827 { |
|
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diff
changeset
|
1828 if (calc_cond) |
| 5785 | 1829 { |
|
7482
29980c6b8604
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diff
changeset
|
1830 // Now calculate the condition number for |
|
29980c6b8604
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diff
changeset
|
1831 // non-singular matrix. |
|
29980c6b8604
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diff
changeset
|
1832 char job = '1'; |
|
29980c6b8604
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diff
changeset
|
1833 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
29980c6b8604
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diff
changeset
|
1834 nc, tmp_data, nr, anorm, |
| 7788 | 1835 rcon, pz, piz, info |
|
7482
29980c6b8604
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diff
changeset
|
1836 F77_CHAR_ARG_LEN (1))); |
|
29980c6b8604
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diff
changeset
|
1837 |
|
29980c6b8604
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7478
diff
changeset
|
1838 if (info != 0) |
|
29980c6b8604
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diff
changeset
|
1839 info = -2; |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
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7478
diff
changeset
|
1840 |
| 7788 | 1841 volatile double rcond_plus_one = rcon + 1.0; |
| 1842 | |
| 1843 if (rcond_plus_one == 1.0 || xisnan (rcon)) | |
| 5785 | 1844 { |
|
7482
29980c6b8604
don't check f77_exception_encountered
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7478
diff
changeset
|
1845 info = -2; |
|
29980c6b8604
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diff
changeset
|
1846 |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
1847 if (sing_handler) |
| 7788 | 1848 sing_handler (rcon); |
|
7482
29980c6b8604
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diff
changeset
|
1849 else |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
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diff
changeset
|
1850 (*current_liboctave_error_handler) |
|
29980c6b8604
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John W. Eaton <jwe@octave.org>
parents:
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diff
changeset
|
1851 ("matrix singular to machine precision, rcond = %g", |
| 7788 | 1852 rcon); |
| 5785 | 1853 } |
| 1854 } | |
|
7482
29980c6b8604
don't check f77_exception_encountered
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diff
changeset
|
1855 |
|
29980c6b8604
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John W. Eaton <jwe@octave.org>
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diff
changeset
|
1856 if (info == 0) |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
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diff
changeset
|
1857 { |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
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diff
changeset
|
1858 retval = b; |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
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diff
changeset
|
1859 double *result = retval.fortran_vec (); |
|
29980c6b8604
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diff
changeset
|
1860 |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
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diff
changeset
|
1861 octave_idx_type b_nc = b.cols (); |
|
29980c6b8604
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7478
diff
changeset
|
1862 |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
1863 char job = 'N'; |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
1864 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
|
1865 nr, b_nc, tmp_data, nr, |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
1866 pipvt, result, b.rows(), info |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
1867 F77_CHAR_ARG_LEN (1))); |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
1868 } |
|
29980c6b8604
don't check f77_exception_encountered
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parents:
7478
diff
changeset
|
1869 else |
|
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
1870 mattype.mark_as_rectangular (); |
| 5785 | 1871 } |
| 1872 } | |
| 1873 else if (typ != MatrixType::Hermitian) | |
| 1874 (*current_liboctave_error_handler) ("incorrect matrix type"); | |
| 1875 } | |
| 1876 | |
| 1877 return retval; | |
| 1878 } | |
| 1879 | |
| 1880 Matrix | |
| 1881 Matrix::solve (MatrixType &typ, const Matrix& b) const | |
| 1882 { | |
| 1883 octave_idx_type info; | |
| 7788 | 1884 double rcon; |
| 1885 return solve (typ, b, info, rcon, 0); | |
| 5785 | 1886 } |
| 1887 | |
| 1888 Matrix | |
| 1889 Matrix::solve (MatrixType &typ, const Matrix& b, octave_idx_type& info, | |
| 7788 | 1890 double& rcon) const |
| 5785 | 1891 { |
| 7788 | 1892 return solve (typ, b, info, rcon, 0); |
| 5785 | 1893 } |
| 1894 | |
| 1895 Matrix | |
| 1896 Matrix::solve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, | |
| 7788 | 1897 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 1898 bool singular_fallback) const |
| 1899 { | |
| 1900 Matrix retval; | |
| 1901 int typ = mattype.type (); | |
| 1902 | |
| 1903 if (typ == MatrixType::Unknown) | |
| 1904 typ = mattype.type (*this); | |
| 1905 | |
| 1906 // Only calculate the condition number for LU/Cholesky | |
| 1907 if (typ == MatrixType::Upper || typ == MatrixType::Permuted_Upper) | |
| 7788 | 1908 retval = utsolve (mattype, b, info, rcon, sing_handler, false); |
| 5785 | 1909 else if (typ == MatrixType::Lower || typ == MatrixType::Permuted_Lower) |
| 7788 | 1910 retval = ltsolve (mattype, b, info, rcon, sing_handler, false); |
| 5785 | 1911 else if (typ == MatrixType::Full || typ == MatrixType::Hermitian) |
| 7788 | 1912 retval = fsolve (mattype, b, info, rcon, sing_handler, true); |
| 5785 | 1913 else if (typ != MatrixType::Rectangular) |
| 1914 { | |
| 1915 (*current_liboctave_error_handler) ("unknown matrix type"); | |
| 1916 return Matrix (); | |
| 1917 } | |
| 1918 | |
| 1919 // Rectangular or one of the above solvers flags a singular matrix | |
| 1920 if (singular_fallback && mattype.type () == MatrixType::Rectangular) | |
| 1921 { | |
| 1922 octave_idx_type rank; | |
| 7788 | 1923 retval = lssolve (b, info, rank, rcon); |
| 5785 | 1924 } |
| 1925 | |
| 1926 return retval; | |
| 1927 } | |
| 1928 | |
| 1929 ComplexMatrix | |
| 1930 Matrix::solve (MatrixType &typ, const ComplexMatrix& b) const | |
| 1931 { | |
| 1932 ComplexMatrix tmp (*this); | |
| 1933 return tmp.solve (typ, b); | |
| 1934 } | |
| 1935 | |
| 1936 ComplexMatrix | |
| 1937 Matrix::solve (MatrixType &typ, const ComplexMatrix& b, | |
| 1938 octave_idx_type& info) const | |
| 1939 { | |
| 1940 ComplexMatrix tmp (*this); | |
| 1941 return tmp.solve (typ, b, info); | |
| 1942 } | |
| 1943 | |
| 1944 ComplexMatrix | |
| 1945 Matrix::solve (MatrixType &typ, const ComplexMatrix& b, octave_idx_type& info, | |
| 7788 | 1946 double& rcon) const |
| 5785 | 1947 { |
| 1948 ComplexMatrix tmp (*this); | |
| 7788 | 1949 return tmp.solve (typ, b, info, rcon); |
| 5785 | 1950 } |
| 1951 | |
| 1952 ComplexMatrix | |
| 1953 Matrix::solve (MatrixType &typ, const ComplexMatrix& b, octave_idx_type& info, | |
| 7788 | 1954 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 1955 bool singular_fallback) const |
| 1956 { | |
| 1957 ComplexMatrix tmp (*this); | |
| 7788 | 1958 return tmp.solve (typ, b, info, rcon, sing_handler, singular_fallback); |
| 5785 | 1959 } |
| 1960 | |
| 1961 ColumnVector | |
| 1962 Matrix::solve (MatrixType &typ, const ColumnVector& b) const | |
| 1963 { | |
| 7788 | 1964 octave_idx_type info; double rcon; |
| 1965 return solve (typ, b, info, rcon); | |
| 5785 | 1966 } |
| 1967 | |
| 1968 ColumnVector | |
| 1969 Matrix::solve (MatrixType &typ, const ColumnVector& b, | |
| 1970 octave_idx_type& info) const | |
| 1971 { | |
| 7788 | 1972 double rcon; |
| 1973 return solve (typ, b, info, rcon); | |
| 5785 | 1974 } |
| 1975 | |
| 1976 ColumnVector | |
| 1977 Matrix::solve (MatrixType &typ, const ColumnVector& b, octave_idx_type& info, | |
| 7788 | 1978 double& rcon) const |
| 5785 | 1979 { |
| 7788 | 1980 return solve (typ, b, info, rcon, 0); |
| 5785 | 1981 } |
| 1982 | |
| 1983 ColumnVector | |
| 1984 Matrix::solve (MatrixType &typ, const ColumnVector& b, octave_idx_type& info, | |
| 7788 | 1985 double& rcon, solve_singularity_handler sing_handler) const |
| 5785 | 1986 { |
| 1987 Matrix tmp (b); | |
| 7788 | 1988 return solve (typ, tmp, info, rcon, sing_handler).column(static_cast<octave_idx_type> (0)); |
| 5785 | 1989 } |
| 1990 | |
| 1991 ComplexColumnVector | |
| 1992 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b) const | |
| 1993 { | |
| 1994 ComplexMatrix tmp (*this); | |
| 1995 return tmp.solve (typ, b); | |
| 1996 } | |
| 1997 | |
| 1998 ComplexColumnVector | |
| 1999 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, | |
| 2000 octave_idx_type& info) const | |
| 2001 { | |
| 2002 ComplexMatrix tmp (*this); | |
| 2003 return tmp.solve (typ, b, info); | |
| 2004 } | |
| 2005 | |
| 2006 ComplexColumnVector | |
| 2007 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, | |
| 7788 | 2008 octave_idx_type& info, double& rcon) const |
| 5785 | 2009 { |
| 2010 ComplexMatrix tmp (*this); | |
| 7788 | 2011 return tmp.solve (typ, b, info, rcon); |
| 5785 | 2012 } |
| 2013 | |
| 2014 ComplexColumnVector | |
| 2015 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, | |
| 7788 | 2016 octave_idx_type& info, double& rcon, |
| 5785 | 2017 solve_singularity_handler sing_handler) const |
| 2018 { | |
| 2019 ComplexMatrix tmp (*this); | |
| 7788 | 2020 return tmp.solve(typ, b, info, rcon, sing_handler); |
| 5785 | 2021 } |
| 2022 | |
| 2023 Matrix | |
| 458 | 2024 Matrix::solve (const Matrix& b) const |
| 2025 { | |
| 5275 | 2026 octave_idx_type info; |
| 7788 | 2027 double rcon; |
| 2028 return solve (b, info, rcon, 0); | |
| 458 | 2029 } |
| 2030 | |
| 2031 Matrix | |
| 5275 | 2032 Matrix::solve (const Matrix& b, octave_idx_type& info) const |
| 458 | 2033 { |
| 7788 | 2034 double rcon; |
| 2035 return solve (b, info, rcon, 0); | |
| 458 | 2036 } |
| 2037 | |
| 2038 Matrix | |
| 7788 | 2039 Matrix::solve (const Matrix& b, octave_idx_type& info, double& rcon) const |
| 458 | 2040 { |
| 7788 | 2041 return solve (b, info, rcon, 0); |
| 3480 | 2042 } |
| 2043 | |
| 2044 Matrix | |
| 5785 | 2045 Matrix::solve (const Matrix& b, octave_idx_type& info, |
| 7788 | 2046 double& rcon, solve_singularity_handler sing_handler) const |
| 3480 | 2047 { |
| 5785 | 2048 MatrixType mattype (*this); |
| 7788 | 2049 return solve (mattype, b, info, rcon, sing_handler); |
| 458 | 2050 } |
| 2051 | |
| 2052 ComplexMatrix | |
| 2053 Matrix::solve (const ComplexMatrix& b) const | |
| 2054 { | |
| 2055 ComplexMatrix tmp (*this); | |
| 2056 return tmp.solve (b); | |
| 2057 } | |
| 2058 | |
| 2059 ComplexMatrix | |
| 5275 | 2060 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info) const |
| 458 | 2061 { |
| 2062 ComplexMatrix tmp (*this); | |
| 2063 return tmp.solve (b, info); | |
| 2064 } | |
| 2065 | |
| 2066 ComplexMatrix | |
| 7788 | 2067 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcon) const |
| 458 | 2068 { |
| 2069 ComplexMatrix tmp (*this); | |
| 7788 | 2070 return tmp.solve (b, info, rcon); |
| 458 | 2071 } |
| 2072 | |
| 3480 | 2073 ComplexMatrix |
| 7788 | 2074 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcon, |
| 3480 | 2075 solve_singularity_handler sing_handler) const |
| 2076 { | |
| 2077 ComplexMatrix tmp (*this); | |
| 7788 | 2078 return tmp.solve (b, info, rcon, sing_handler); |
| 3480 | 2079 } |
| 2080 | |
| 458 | 2081 ColumnVector |
| 2082 Matrix::solve (const ColumnVector& b) const | |
| 2083 { | |
| 7788 | 2084 octave_idx_type info; double rcon; |
| 2085 return solve (b, info, rcon); | |
| 458 | 2086 } |
| 2087 | |
| 2088 ColumnVector | |
| 5275 | 2089 Matrix::solve (const ColumnVector& b, octave_idx_type& info) const |
| 458 | 2090 { |
| 7788 | 2091 double rcon; |
| 2092 return solve (b, info, rcon); | |
| 458 | 2093 } |
| 2094 | |
| 2095 ColumnVector | |
| 7788 | 2096 Matrix::solve (const ColumnVector& b, octave_idx_type& info, double& rcon) const |
| 458 | 2097 { |
| 7788 | 2098 return solve (b, info, rcon, 0); |
| 3480 | 2099 } |
| 2100 | |
| 2101 ColumnVector | |
| 7788 | 2102 Matrix::solve (const ColumnVector& b, octave_idx_type& info, double& rcon, |
| 3480 | 2103 solve_singularity_handler sing_handler) const |
| 2104 { | |
| 5785 | 2105 MatrixType mattype (*this); |
| 7788 | 2106 return solve (mattype, b, info, rcon, sing_handler); |
| 458 | 2107 } |
| 2108 | |
| 2109 ComplexColumnVector | |
| 2110 Matrix::solve (const ComplexColumnVector& b) const | |
| 2111 { | |
| 2112 ComplexMatrix tmp (*this); | |
| 2113 return tmp.solve (b); | |
| 2114 } | |
| 2115 | |
| 2116 ComplexColumnVector | |
| 5275 | 2117 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info) const |
| 458 | 2118 { |
| 2119 ComplexMatrix tmp (*this); | |
| 2120 return tmp.solve (b, info); | |
| 2121 } | |
| 2122 | |
| 2123 ComplexColumnVector | |
| 7788 | 2124 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info, double& rcon) const |
| 458 | 2125 { |
| 2126 ComplexMatrix tmp (*this); | |
| 7788 | 2127 return tmp.solve (b, info, rcon); |
| 458 | 2128 } |
| 2129 | |
| 3480 | 2130 ComplexColumnVector |
| 7788 | 2131 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info, double& rcon, |
| 3480 | 2132 solve_singularity_handler sing_handler) const |
| 2133 { | |
| 2134 ComplexMatrix tmp (*this); | |
| 7788 | 2135 return tmp.solve (b, info, rcon, sing_handler); |
| 3480 | 2136 } |
| 2137 | |
| 458 | 2138 Matrix |
| 2139 Matrix::lssolve (const Matrix& b) const | |
| 2140 { | |
| 5275 | 2141 octave_idx_type info; |
| 2142 octave_idx_type rank; | |
| 7788 | 2143 double rcon; |
| 2144 return lssolve (b, info, rank, rcon); | |
| 458 | 2145 } |
| 2146 | |
| 2147 Matrix | |
| 5275 | 2148 Matrix::lssolve (const Matrix& b, octave_idx_type& info) const |
| 458 | 2149 { |
| 5275 | 2150 octave_idx_type rank; |
| 7788 | 2151 double rcon; |
| 2152 return lssolve (b, info, rank, rcon); | |
| 458 | 2153 } |
| 2154 | |
| 2155 Matrix | |
| 7072 | 2156 Matrix::lssolve (const Matrix& b, octave_idx_type& info, |
| 2157 octave_idx_type& rank) const | |
| 458 | 2158 { |
| 7788 | 2159 double rcon; |
| 2160 return lssolve (b, info, rank, rcon); | |
| 7076 | 2161 } |
| 2162 | |
| 2163 Matrix | |
| 2164 Matrix::lssolve (const Matrix& b, octave_idx_type& info, | |
| 7788 | 2165 octave_idx_type& rank, double &rcon) const |
| 7076 | 2166 { |
| 1948 | 2167 Matrix retval; |
| 2168 | |
| 5275 | 2169 octave_idx_type nrhs = b.cols (); |
| 2170 | |
| 2171 octave_idx_type m = rows (); | |
| 2172 octave_idx_type n = cols (); | |
| 458 | 2173 |
| 6924 | 2174 if (m != b.rows ()) |
| 1948 | 2175 (*current_liboctave_error_handler) |
| 6924 | 2176 ("matrix dimension mismatch solution of linear equations"); |
| 2177 else if (m == 0 || n == 0 || b.cols () == 0) | |
| 2178 retval = Matrix (n, b.cols (), 0.0); | |
| 1948 | 2179 else |
| 458 | 2180 { |
| 7072 | 2181 volatile octave_idx_type minmn = (m < n ? m : n); |
| 2182 octave_idx_type maxmn = m > n ? m : n; | |
| 7788 | 2183 rcon = -1.0; |
| 7072 | 2184 if (m != n) |
| 2185 { | |
| 2186 retval = Matrix (maxmn, nrhs, 0.0); | |
| 2187 | |
| 2188 for (octave_idx_type j = 0; j < nrhs; j++) | |
| 2189 for (octave_idx_type i = 0; i < m; i++) | |
| 2190 retval.elem (i, j) = b.elem (i, j); | |
| 2191 } | |
| 2192 else | |
| 2193 retval = b; | |
| 2194 | |
| 1948 | 2195 Matrix atmp = *this; |
| 2196 double *tmp_data = atmp.fortran_vec (); | |
| 2197 | |
| 7072 | 2198 double *pretval = retval.fortran_vec (); |
| 2199 Array<double> s (minmn); | |
| 7071 | 2200 double *ps = s.fortran_vec (); |
| 1948 | 2201 |
| 7072 | 2202 // Ask DGELSD what the dimension of WORK should be. |
| 5275 | 2203 octave_idx_type lwork = -1; |
| 3752 | 2204 |
| 2205 Array<double> work (1); | |
| 1948 | 2206 |
| 7477 | 2207 octave_idx_type smlsiz; |
| 2208 F77_FUNC (xilaenv, XILAENV) (9, F77_CONST_CHAR_ARG2 ("DGELSD", 6), | |
| 2209 F77_CONST_CHAR_ARG2 (" ", 1), | |
| 7478 | 2210 0, 0, 0, 0, smlsiz |
| 7477 | 2211 F77_CHAR_ARG_LEN (6) |
| 7478 | 2212 F77_CHAR_ARG_LEN (1)); |
| 7079 | 2213 |
|
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2214 octave_idx_type mnthr; |
|
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2215 F77_FUNC (xilaenv, XILAENV) (6, F77_CONST_CHAR_ARG2 ("DGELSD", 6), |
|
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|
2216 F77_CONST_CHAR_ARG2 (" ", 1), |
|
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|
2217 m, n, nrhs, -1, mnthr |
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|
2218 F77_CHAR_ARG_LEN (6) |
|
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|
2219 F77_CHAR_ARG_LEN (1)); |
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|
2220 |
| 7079 | 2221 // We compute the size of iwork because DGELSD in older versions |
| 2222 // of LAPACK does not return it on a query call. | |
| 7124 | 2223 double dminmn = static_cast<double> (minmn); |
| 2224 double dsmlsizp1 = static_cast<double> (smlsiz+1); | |
| 7079 | 2225 #if defined (HAVE_LOG2) |
| 7367 | 2226 double tmp = log2 (dminmn / dsmlsizp1); |
| 7079 | 2227 #else |
| 7367 | 2228 double tmp = log (dminmn / dsmlsizp1) / log (2.0); |
| 7079 | 2229 #endif |
|
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|
2230 octave_idx_type nlvl = static_cast<octave_idx_type> (tmp) + 1; |
| 7079 | 2231 if (nlvl < 0) |
| 2232 nlvl = 0; | |
| 2233 | |
| 2234 octave_idx_type liwork = 3 * minmn * nlvl + 11 * minmn; | |
| 2235 if (liwork < 1) | |
| 2236 liwork = 1; | |
| 7072 | 2237 Array<octave_idx_type> iwork (liwork); |
| 2238 octave_idx_type* piwork = iwork.fortran_vec (); | |
| 2239 | |
| 2240 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, | |
| 7788 | 2241 ps, rcon, rank, work.fortran_vec (), |
| 7072 | 2242 lwork, piwork, info)); |
| 1948 | 2243 |
| 7476 | 2244 // The workspace query is broken in at least LAPACK 3.0.0 |
|
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2245 // through 3.1.1 when n >= mnthr. The obtuse formula below |
| 7476 | 2246 // should provide sufficient workspace for DGELSD to operate |
| 2247 // efficiently. | |
|
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|
2248 if (n >= mnthr) |
| 7476 | 2249 { |
| 2250 const octave_idx_type wlalsd | |
| 2251 = 9*m + 2*m*smlsiz + 8*m*nlvl + m*nrhs + (smlsiz+1)*(smlsiz+1); | |
| 2252 | |
| 2253 octave_idx_type addend = m; | |
| 2254 | |
| 2255 if (2*m-4 > addend) | |
| 2256 addend = 2*m-4; | |
| 2257 | |
| 2258 if (nrhs > addend) | |
| 2259 addend = nrhs; | |
| 2260 | |
| 2261 if (n-3*m > addend) | |
| 2262 addend = n-3*m; | |
| 2263 | |
| 2264 if (wlalsd > addend) | |
| 2265 addend = wlalsd; | |
| 2266 | |
| 2267 const octave_idx_type lworkaround = 4*m + m*m + addend; | |
| 2268 | |
| 2269 if (work(0) < lworkaround) | |
| 2270 work(0) = lworkaround; | |
| 2271 } | |
|
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2272 else if (m >= n) |
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|
2273 { |
|
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|
2274 octave_idx_type lworkaround |
|
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|
2275 = 12*n + 2*n*smlsiz + 8*n*nlvl + n*nrhs + (smlsiz+1)*(smlsiz+1); |
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|
2276 |
|
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|
2277 if (work(0) < lworkaround) |
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|
2278 work(0) = lworkaround; |
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|
2279 } |
| 7476 | 2280 |
|
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|
2281 lwork = static_cast<octave_idx_type> (work(0)); |
|
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|
2282 work.resize (lwork); |
|
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|
2283 |
|
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|
2284 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, |
| 7788 | 2285 maxmn, ps, rcon, rank, |
|
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|
2286 work.fortran_vec (), lwork, |
|
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|
2287 piwork, info)); |
|
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|
2288 |
|
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|
2289 if (rank < minmn) |
|
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|
2290 (*current_liboctave_warning_handler) |
|
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|
2291 ("dgelsd: rank deficient %dx%d matrix, rank = %d", m, n, rank); |
|
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|
2292 if (s.elem (0) == 0.0) |
| 7788 | 2293 rcon = 0.0; |
| 1948 | 2294 else |
| 7788 | 2295 rcon = s.elem (minmn - 1) / s.elem (0); |
|
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|
2296 |
|
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|
2297 retval.resize (n, nrhs); |
| 458 | 2298 } |
| 2299 | |
| 2300 return retval; | |
| 2301 } | |
| 2302 | |
| 2303 ComplexMatrix | |
| 2304 Matrix::lssolve (const ComplexMatrix& b) const | |
| 2305 { | |
| 2306 ComplexMatrix tmp (*this); | |
| 5275 | 2307 octave_idx_type info; |
| 2308 octave_idx_type rank; | |
| 7788 | 2309 double rcon; |
| 2310 return tmp.lssolve (b, info, rank, rcon); | |
| 458 | 2311 } |
| 2312 | |
| 2313 ComplexMatrix | |
| 5275 | 2314 Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info) const |
| 458 | 2315 { |
| 2316 ComplexMatrix tmp (*this); | |
| 5275 | 2317 octave_idx_type rank; |
| 7788 | 2318 double rcon; |
| 2319 return tmp.lssolve (b, info, rank, rcon); | |
| 458 | 2320 } |
| 2321 | |
| 2322 ComplexMatrix | |
| 7076 | 2323 Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info, |
| 2324 octave_idx_type& rank) const | |
| 458 | 2325 { |
| 2326 ComplexMatrix tmp (*this); | |
| 7788 | 2327 double rcon; |
| 2328 return tmp.lssolve (b, info, rank, rcon); | |
| 7076 | 2329 } |
| 2330 | |
| 2331 ComplexMatrix | |
| 2332 Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info, | |
| 7788 | 2333 octave_idx_type& rank, double& rcon) const |
| 7076 | 2334 { |
| 2335 ComplexMatrix tmp (*this); | |
| 7788 | 2336 return tmp.lssolve (b, info, rank, rcon); |
| 458 | 2337 } |
| 2338 | |
| 2339 ColumnVector | |
| 2340 Matrix::lssolve (const ColumnVector& b) const | |
| 2341 { | |
| 5275 | 2342 octave_idx_type info; |
| 2343 octave_idx_type rank; | |
| 7788 | 2344 double rcon; |
| 2345 return lssolve (b, info, rank, rcon); | |
| 458 | 2346 } |
| 2347 | |
| 2348 ColumnVector | |
| 5275 | 2349 Matrix::lssolve (const ColumnVector& b, octave_idx_type& info) const |
| 458 | 2350 { |
| 5275 | 2351 octave_idx_type rank; |
| 7788 | 2352 double rcon; |
| 2353 return lssolve (b, info, rank, rcon); | |
| 458 | 2354 } |
| 2355 | |
| 2356 ColumnVector | |
| 7072 | 2357 Matrix::lssolve (const ColumnVector& b, octave_idx_type& info, |
| 2358 octave_idx_type& rank) const | |
| 458 | 2359 { |
| 7788 | 2360 double rcon; |
| 2361 return lssolve (b, info, rank, rcon); | |
| 7076 | 2362 } |
| 2363 | |
| 2364 ColumnVector | |
| 2365 Matrix::lssolve (const ColumnVector& b, octave_idx_type& info, | |
| 7788 | 2366 octave_idx_type& rank, double &rcon) const |
| 7076 | 2367 { |
| 1948 | 2368 ColumnVector retval; |
| 2369 | |
| 5275 | 2370 octave_idx_type nrhs = 1; |
| 2371 | |
| 2372 octave_idx_type m = rows (); | |
| 2373 octave_idx_type n = cols (); | |
| 458 | 2374 |
| 6924 | 2375 if (m != b.length ()) |
| 1948 | 2376 (*current_liboctave_error_handler) |
| 6924 | 2377 ("matrix dimension mismatch solution of linear equations"); |
| 2378 else if (m == 0 || n == 0) | |
| 2379 retval = ColumnVector (n, 0.0); | |
| 1948 | 2380 else |
| 458 | 2381 { |
| 7072 | 2382 volatile octave_idx_type minmn = (m < n ? m : n); |
| 2383 octave_idx_type maxmn = m > n ? m : n; | |
| 7788 | 2384 rcon = -1.0; |
| 7072 | 2385 |
| 2386 if (m != n) | |
| 2387 { | |
| 2388 retval = ColumnVector (maxmn, 0.0); | |
| 2389 | |
| 2390 for (octave_idx_type i = 0; i < m; i++) | |
| 2391 retval.elem (i) = b.elem (i); | |
| 2392 } | |
| 2393 else | |
| 2394 retval = b; | |
| 2395 | |
| 1948 | 2396 Matrix atmp = *this; |
| 2397 double *tmp_data = atmp.fortran_vec (); | |
| 2398 | |
| 7072 | 2399 double *pretval = retval.fortran_vec (); |
| 2400 Array<double> s (minmn); | |
| 7071 | 2401 double *ps = s.fortran_vec (); |
| 1948 | 2402 |
| 7072 | 2403 // Ask DGELSD what the dimension of WORK should be. |
| 5275 | 2404 octave_idx_type lwork = -1; |
| 3752 | 2405 |
| 2406 Array<double> work (1); | |
| 2407 | |
|
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2408 octave_idx_type smlsiz; |
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2409 F77_FUNC (xilaenv, XILAENV) (9, F77_CONST_CHAR_ARG2 ("DGELSD", 6), |
|
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2410 F77_CONST_CHAR_ARG2 (" ", 1), |
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2411 0, 0, 0, 0, smlsiz |
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2412 F77_CHAR_ARG_LEN (6) |
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|
2413 F77_CHAR_ARG_LEN (1)); |
| 7079 | 2414 |
| 2415 // We compute the size of iwork because DGELSD in older versions | |
| 2416 // of LAPACK does not return it on a query call. | |
| 7124 | 2417 double dminmn = static_cast<double> (minmn); |
| 2418 double dsmlsizp1 = static_cast<double> (smlsiz+1); | |
| 7079 | 2419 #if defined (HAVE_LOG2) |
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2420 double tmp = log2 (dminmn / dsmlsizp1); |
| 7079 | 2421 #else |
|
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2422 double tmp = log (dminmn / dsmlsizp1) / log (2.0); |
| 7079 | 2423 #endif |
|
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2424 octave_idx_type nlvl = static_cast<octave_idx_type> (tmp) + 1; |
| 7079 | 2425 if (nlvl < 0) |
| 2426 nlvl = 0; | |
| 2427 | |
| 2428 octave_idx_type liwork = 3 * minmn * nlvl + 11 * minmn; | |
| 2429 if (liwork < 1) | |
| 2430 liwork = 1; | |
| 7072 | 2431 Array<octave_idx_type> iwork (liwork); |
| 2432 octave_idx_type* piwork = iwork.fortran_vec (); | |
| 2433 | |
| 2434 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, | |
| 7788 | 2435 ps, rcon, rank, work.fortran_vec (), |
| 7072 | 2436 lwork, piwork, info)); |
| 1948 | 2437 |
|
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2438 lwork = static_cast<octave_idx_type> (work(0)); |
|
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2439 work.resize (lwork); |
|
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|
2440 |
|
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|
2441 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, |
| 7788 | 2442 maxmn, ps, rcon, rank, |
|
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2443 work.fortran_vec (), lwork, |
|
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2444 piwork, info)); |
|
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|
2445 |
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|
2446 if (rank < minmn) |
| 1948 | 2447 { |
|
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|
2448 if (rank < minmn) |
|
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|
2449 (*current_liboctave_warning_handler) |
|
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|
2450 ("dgelsd: rank deficient %dx%d matrix, rank = %d", m, n, rank); |
|
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|
2451 if (s.elem (0) == 0.0) |
| 7788 | 2452 rcon = 0.0; |
|
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|
2453 else |
| 7788 | 2454 rcon = s.elem (minmn - 1) / s.elem (0); |
| 1948 | 2455 } |
|
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|
2456 |
|
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|
2457 retval.resize (n, nrhs); |
| 458 | 2458 } |
| 2459 | |
| 2460 return retval; | |
| 2461 } | |
| 2462 | |
| 2463 ComplexColumnVector | |
| 2464 Matrix::lssolve (const ComplexColumnVector& b) const | |
| 2465 { | |
| 2466 ComplexMatrix tmp (*this); | |
| 7076 | 2467 octave_idx_type info; |
| 2468 octave_idx_type rank; | |
| 7788 | 2469 double rcon; |
| 2470 return tmp.lssolve (b, info, rank, rcon); | |
| 458 | 2471 } |
| 2472 | |
| 2473 ComplexColumnVector | |
| 5275 | 2474 Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info) const |
| 458 | 2475 { |
| 2476 ComplexMatrix tmp (*this); | |
| 7076 | 2477 octave_idx_type rank; |
| 7788 | 2478 double rcon; |
| 2479 return tmp.lssolve (b, info, rank, rcon); | |
| 458 | 2480 } |
| 2481 | |
| 2482 ComplexColumnVector | |
| 7076 | 2483 Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, |
| 2484 octave_idx_type& rank) const | |
| 458 | 2485 { |
| 2486 ComplexMatrix tmp (*this); | |
| 7788 | 2487 double rcon; |
| 2488 return tmp.lssolve (b, info, rank, rcon); | |
| 7076 | 2489 } |
| 2490 | |
| 2491 ComplexColumnVector | |
| 2492 Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, | |
| 7788 | 2493 octave_idx_type& rank, double &rcon) const |
| 7076 | 2494 { |
| 2495 ComplexMatrix tmp (*this); | |
| 7788 | 2496 return tmp.lssolve (b, info, rank, rcon); |
| 458 | 2497 } |
| 2498 | |
| 1819 | 2499 // Constants for matrix exponential calculation. |
| 2500 | |
| 2501 static double padec [] = | |
| 2502 { | |
| 2503 5.0000000000000000e-1, | |
| 2504 1.1666666666666667e-1, | |
| 2505 1.6666666666666667e-2, | |
| 2506 1.6025641025641026e-3, | |
| 2507 1.0683760683760684e-4, | |
| 2508 4.8562548562548563e-6, | |
| 2509 1.3875013875013875e-7, | |
| 2510 1.9270852604185938e-9, | |
| 2511 }; | |
| 2512 | |
| 7400 | 2513 static void |
| 7788 | 2514 solve_singularity_warning (double rcon) |
| 7400 | 2515 { |
| 2516 (*current_liboctave_warning_handler) | |
| 2517 ("singular matrix encountered in expm calculation, rcond = %g", | |
| 7788 | 2518 rcon); |
| 7400 | 2519 } |
| 2520 | |
| 1819 | 2521 Matrix |
| 2522 Matrix::expm (void) const | |
| 2523 { | |
| 2524 Matrix retval; | |
| 2525 | |
| 2526 Matrix m = *this; | |
| 2527 | |
| 6699 | 2528 if (numel () == 1) |
| 2529 return Matrix (1, 1, exp (m(0))); | |
| 2530 | |
| 5275 | 2531 octave_idx_type nc = columns (); |
| 1819 | 2532 |
| 3130 | 2533 // Preconditioning step 1: trace normalization to reduce dynamic |
| 2534 // range of poles, but avoid making stable eigenvalues unstable. | |
| 2535 | |
| 1819 | 2536 // trace shift value |
| 3331 | 2537 volatile double trshift = 0.0; |
| 1819 | 2538 |
| 5275 | 2539 for (octave_idx_type i = 0; i < nc; i++) |
| 1819 | 2540 trshift += m.elem (i, i); |
| 2541 | |
| 2542 trshift /= nc; | |
| 2543 | |
| 3130 | 2544 if (trshift > 0.0) |
| 2545 { | |
| 5275 | 2546 for (octave_idx_type i = 0; i < nc; i++) |
| 3130 | 2547 m.elem (i, i) -= trshift; |
| 2548 } | |
| 1819 | 2549 |
| 3331 | 2550 // Preconditioning step 2: balancing; code follows development |
| 2551 // in AEPBAL | |
| 2552 | |
| 2553 double *p_m = m.fortran_vec (); | |
| 2554 | |
| 5275 | 2555 octave_idx_type info, ilo, ihi, ilos, ihis; |
| 3468 | 2556 Array<double> dpermute (nc); |
| 2557 Array<double> dscale (nc); | |
| 3466 | 2558 |
| 3468 | 2559 // permutation first |
| 2560 char job = 'P'; | |
| 4552 | 2561 F77_XFCN (dgebal, DGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
| 2562 nc, p_m, nc, ilo, ihi, | |
| 2563 dpermute.fortran_vec (), info | |
| 2564 F77_CHAR_ARG_LEN (1))); | |
| 3466 | 2565 |
| 3468 | 2566 // then scaling |
| 2567 job = 'S'; | |
| 4552 | 2568 F77_XFCN (dgebal, DGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
| 2569 nc, p_m, nc, ilos, ihis, | |
| 2570 dscale.fortran_vec (), info | |
| 2571 F77_CHAR_ARG_LEN (1))); | |
| 3331 | 2572 |
| 1819 | 2573 // Preconditioning step 3: scaling. |
| 3331 | 2574 |
| 1819 | 2575 ColumnVector work(nc); |
| 3130 | 2576 double inf_norm; |
| 3331 | 2577 |
| 4552 | 2578 F77_XFCN (xdlange, XDLANGE, (F77_CONST_CHAR_ARG2 ("I", 1), |
| 2579 nc, nc, m.fortran_vec (), nc, | |
| 2580 work.fortran_vec (), inf_norm | |
| 2581 F77_CHAR_ARG_LEN (1))); | |
| 3331 | 2582 |
| 5275 | 2583 octave_idx_type sqpow = static_cast<octave_idx_type> (inf_norm > 0.0 |
| 1819 | 2584 ? (1.0 + log (inf_norm) / log (2.0)) |
| 2585 : 0.0); | |
| 3331 | 2586 |
| 1819 | 2587 // Check whether we need to square at all. |
| 3331 | 2588 |
| 1819 | 2589 if (sqpow < 0) |
| 2590 sqpow = 0; | |
| 3331 | 2591 |
| 1819 | 2592 if (sqpow > 0) |
| 2593 { | |
| 7400 | 2594 if (sqpow > 1023) |
| 2595 sqpow = 1023; | |
| 2596 | |
| 1819 | 2597 double scale_factor = 1.0; |
| 5275 | 2598 for (octave_idx_type i = 0; i < sqpow; i++) |
| 1819 | 2599 scale_factor *= 2.0; |
| 7400 | 2600 |
| 1819 | 2601 m = m / scale_factor; |
| 2602 } | |
| 3331 | 2603 |
| 1819 | 2604 // npp, dpp: pade' approx polynomial matrices. |
| 3331 | 2605 |
| 1819 | 2606 Matrix npp (nc, nc, 0.0); |
| 7265 | 2607 double *pnpp = npp.fortran_vec (); |
| 1819 | 2608 Matrix dpp = npp; |
| 7265 | 2609 double *pdpp = dpp.fortran_vec (); |
| 3331 | 2610 |
| 1819 | 2611 // Now powers a^8 ... a^1. |
| 3331 | 2612 |
| 5275 | 2613 octave_idx_type minus_one_j = -1; |
| 2614 for (octave_idx_type j = 7; j >= 0; j--) | |
| 1819 | 2615 { |
| 7265 | 2616 for (octave_idx_type i = 0; i < nc; i++) |
| 2617 { | |
| 2618 octave_idx_type k = i * nc + i; | |
| 2619 pnpp[k] += padec[j]; | |
| 2620 pdpp[k] += minus_one_j * padec[j]; | |
| 2621 } | |
| 2622 | |
| 2623 npp = m * npp; | |
| 2624 pnpp = npp.fortran_vec (); | |
| 2625 | |
| 2626 dpp = m * dpp; | |
| 2627 pdpp = dpp.fortran_vec (); | |
| 2628 | |
| 1819 | 2629 minus_one_j *= -1; |
| 2630 } | |
| 3331 | 2631 |
| 1819 | 2632 // Zero power. |
| 3331 | 2633 |
| 1819 | 2634 dpp = -dpp; |
| 5275 | 2635 for (octave_idx_type j = 0; j < nc; j++) |
| 1819 | 2636 { |
| 2637 npp.elem (j, j) += 1.0; | |
| 2638 dpp.elem (j, j) += 1.0; | |
| 2639 } | |
| 3331 | 2640 |
| 1819 | 2641 // Compute pade approximation = inverse (dpp) * npp. |
| 2642 | |
| 7788 | 2643 double rcon; |
| 2644 retval = dpp.solve (npp, info, rcon, solve_singularity_warning); | |
| 7400 | 2645 |
| 2646 if (info < 0) | |
| 2647 return retval; | |
| 2648 | |
| 1819 | 2649 // Reverse preconditioning step 3: repeated squaring. |
| 3331 | 2650 |
| 1819 | 2651 while (sqpow) |
| 2652 { | |
| 2653 retval = retval * retval; | |
| 2654 sqpow--; | |
| 2655 } | |
| 3331 | 2656 |
| 1819 | 2657 // Reverse preconditioning step 2: inverse balancing. |
| 3466 | 2658 // apply inverse scaling to computed exponential |
| 5275 | 2659 for (octave_idx_type i = 0; i < nc; i++) |
| 2660 for (octave_idx_type j = 0; j < nc; j++) | |
| 3468 | 2661 retval(i,j) *= dscale(i) / dscale(j); |
| 3466 | 2662 |
| 4153 | 2663 OCTAVE_QUIT; |
| 2664 | |
| 3466 | 2665 // construct balancing permutation vector |
| 5275 | 2666 Array<octave_idx_type> iperm (nc); |
| 2667 for (octave_idx_type i = 0; i < nc; i++) | |
| 4593 | 2668 iperm(i) = i; // identity permutation |
| 3466 | 2669 |
| 2670 // leading permutations in forward order | |
| 5275 | 2671 for (octave_idx_type i = 0; i < (ilo-1); i++) |
| 3468 | 2672 { |
| 5275 | 2673 octave_idx_type swapidx = static_cast<octave_idx_type> (dpermute(i)) - 1; |
| 2674 octave_idx_type tmp = iperm(i); | |
| 4593 | 2675 iperm(i) = iperm (swapidx); |
| 2676 iperm(swapidx) = tmp; | |
| 3468 | 2677 } |
| 3466 | 2678 |
| 7416 | 2679 // construct inverse balancing permutation vector |
| 2680 Array<octave_idx_type> invpvec (nc); | |
| 2681 for (octave_idx_type i = 0; i < nc; i++) | |
| 2682 invpvec(iperm(i)) = i; // Thanks to R. A. Lippert for this method | |
| 2683 | |
| 2684 OCTAVE_QUIT; | |
| 2685 | |
| 2686 Matrix tmpMat = retval; | |
| 2687 for (octave_idx_type i = 0; i < nc; i++) | |
| 2688 for (octave_idx_type j = 0; j < nc; j++) | |
| 2689 retval(i,j) = tmpMat(invpvec(i),invpvec(j)); | |
| 2690 | |
| 2691 OCTAVE_QUIT; | |
| 2692 | |
| 2693 for (octave_idx_type i = 0; i < nc; i++) | |
| 2694 iperm(i) = i; // identity permutation | |
| 2695 | |
| 3466 | 2696 // trailing permutations must be done in reverse order |
| 5275 | 2697 for (octave_idx_type i = nc - 1; i >= ihi; i--) |
| 3468 | 2698 { |
| 5275 | 2699 octave_idx_type swapidx = static_cast<octave_idx_type> (dpermute(i)) - 1; |
| 2700 octave_idx_type tmp = iperm(i); | |
| 4593 | 2701 iperm(i) = iperm(swapidx); |
| 2702 iperm(swapidx) = tmp; | |
| 3468 | 2703 } |
| 3466 | 2704 |
| 2705 // construct inverse balancing permutation vector | |
| 5275 | 2706 for (octave_idx_type i = 0; i < nc; i++) |
| 4593 | 2707 invpvec(iperm(i)) = i; // Thanks to R. A. Lippert for this method |
| 4153 | 2708 |
| 2709 OCTAVE_QUIT; | |
| 3466 | 2710 |
| 7416 | 2711 tmpMat = retval; |
| 5275 | 2712 for (octave_idx_type i = 0; i < nc; i++) |
| 2713 for (octave_idx_type j = 0; j < nc; j++) | |
| 3468 | 2714 retval(i,j) = tmpMat(invpvec(i),invpvec(j)); |
| 3466 | 2715 |
| 1819 | 2716 // Reverse preconditioning step 1: fix trace normalization. |
| 3331 | 2717 |
| 3130 | 2718 if (trshift > 0.0) |
| 2719 retval = exp (trshift) * retval; | |
| 2720 | |
| 2721 return retval; | |
| 1819 | 2722 } |
| 2723 | |
| 458 | 2724 Matrix& |
| 2725 Matrix::operator += (const DiagMatrix& a) | |
| 2726 { | |
| 5275 | 2727 octave_idx_type nr = rows (); |
| 2728 octave_idx_type nc = cols (); | |
| 2729 | |
| 2730 octave_idx_type a_nr = a.rows (); | |
| 2731 octave_idx_type a_nc = a.cols (); | |
| 2385 | 2732 |
| 2733 if (nr != a_nr || nc != a_nc) | |
| 458 | 2734 { |
| 2385 | 2735 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
| 458 | 2736 return *this; |
| 2737 } | |
| 2738 | |
| 5275 | 2739 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 2740 elem (i, i) += a.elem (i, i); |
| 2741 | |
| 2742 return *this; | |
| 2743 } | |
| 2744 | |
| 2745 Matrix& | |
| 2746 Matrix::operator -= (const DiagMatrix& a) | |
| 2747 { | |
| 5275 | 2748 octave_idx_type nr = rows (); |
| 2749 octave_idx_type nc = cols (); | |
| 2750 | |
| 2751 octave_idx_type a_nr = a.rows (); | |
| 2752 octave_idx_type a_nc = a.cols (); | |
| 2385 | 2753 |
| 2754 if (nr != a_nr || nc != a_nc) | |
| 458 | 2755 { |
| 2385 | 2756 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
| 458 | 2757 return *this; |
| 2758 } | |
| 2759 | |
| 5275 | 2760 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 2761 elem (i, i) -= a.elem (i, i); |
| 2762 | |
| 2763 return *this; | |
| 2764 } | |
| 2765 | |
| 2766 // unary operations | |
| 2767 | |
| 2964 | 2768 boolMatrix |
| 458 | 2769 Matrix::operator ! (void) const |
| 2770 { | |
| 5275 | 2771 octave_idx_type nr = rows (); |
| 2772 octave_idx_type nc = cols (); | |
| 458 | 2773 |
| 2964 | 2774 boolMatrix b (nr, nc); |
| 458 | 2775 |
| 5275 | 2776 for (octave_idx_type j = 0; j < nc; j++) |
| 2777 for (octave_idx_type i = 0; i < nr; i++) | |
| 458 | 2778 b.elem (i, j) = ! elem (i, j); |
| 2779 | |
| 2780 return b; | |
| 2781 } | |
| 2782 | |
| 1205 | 2783 // column vector by row vector -> matrix operations |
| 458 | 2784 |
| 1205 | 2785 Matrix |
| 2786 operator * (const ColumnVector& v, const RowVector& a) | |
| 458 | 2787 { |
| 1948 | 2788 Matrix retval; |
| 2789 | |
| 5275 | 2790 octave_idx_type len = v.length (); |
| 3233 | 2791 |
| 2792 if (len != 0) | |
| 1205 | 2793 { |
| 5275 | 2794 octave_idx_type a_len = a.length (); |
| 3233 | 2795 |
| 2796 retval.resize (len, a_len); | |
| 2797 double *c = retval.fortran_vec (); | |
| 2798 | |
| 4552 | 2799 F77_XFCN (dgemm, DGEMM, (F77_CONST_CHAR_ARG2 ("N", 1), |
| 2800 F77_CONST_CHAR_ARG2 ("N", 1), | |
| 2801 len, a_len, 1, 1.0, v.data (), len, | |
| 2802 a.data (), 1, 0.0, c, len | |
| 2803 F77_CHAR_ARG_LEN (1) | |
| 2804 F77_CHAR_ARG_LEN (1))); | |
| 1205 | 2805 } |
| 458 | 2806 |
| 1948 | 2807 return retval; |
| 458 | 2808 } |
| 2809 | |
| 2810 // other operations. | |
| 2811 | |
| 2812 Matrix | |
|
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2813 Matrix::map (dmapper fcn) const |
| 1205 | 2814 { |
|
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changeset
|
2815 return MArray2<double>::map<double> (func_ptr (fcn)); |
|
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changeset
|
2816 } |
|
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changeset
|
2817 |
|
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diff
changeset
|
2818 ComplexMatrix |
|
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diff
changeset
|
2819 Matrix::map (cmapper fcn) const |
|
8c32f95c2639
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7488
diff
changeset
|
2820 { |
|
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diff
changeset
|
2821 return MArray2<double>::map<Complex> (func_ptr (fcn)); |
| 1205 | 2822 } |
| 2823 | |
| 3248 | 2824 boolMatrix |
|
7503
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diff
changeset
|
2825 Matrix::map (bmapper fcn) const |
| 3248 | 2826 { |
|
7503
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|
2827 return MArray2<double>::map<bool> (func_ptr (fcn)); |
| 458 | 2828 } |
| 2829 | |
| 2385 | 2830 bool |
| 4431 | 2831 Matrix::any_element_is_negative (bool neg_zero) const |
| 2385 | 2832 { |
| 5275 | 2833 octave_idx_type nel = nelem (); |
| 2385 | 2834 |
| 4431 | 2835 if (neg_zero) |
| 2836 { | |
| 5275 | 2837 for (octave_idx_type i = 0; i < nel; i++) |
| 4634 | 2838 if (lo_ieee_signbit (elem (i))) |
| 2839 return true; | |
| 4431 | 2840 } |
| 2841 else | |
| 2842 { | |
| 5275 | 2843 for (octave_idx_type i = 0; i < nel; i++) |
| 4634 | 2844 if (elem (i) < 0) |
| 2845 return true; | |
| 4431 | 2846 } |
| 2385 | 2847 |
| 2848 return false; | |
| 2849 } | |
| 2850 | |
| 2851 | |
| 2852 bool | |
| 2853 Matrix::any_element_is_inf_or_nan (void) const | |
| 2854 { | |
| 5275 | 2855 octave_idx_type nel = nelem (); |
| 2856 | |
| 2857 for (octave_idx_type i = 0; i < nel; i++) | |
| 4634 | 2858 { |
| 2859 double val = elem (i); | |
| 2860 if (xisinf (val) || xisnan (val)) | |
| 2861 return true; | |
| 2862 } | |
| 2863 | |
| 2864 return false; | |
| 2385 | 2865 } |
| 2866 | |
| 2867 bool | |
| 5943 | 2868 Matrix::any_element_not_one_or_zero (void) const |
| 2869 { | |
| 2870 octave_idx_type nel = nelem (); | |
| 2871 | |
| 2872 for (octave_idx_type i = 0; i < nel; i++) | |
| 2873 { | |
| 2874 double val = elem (i); | |
| 2875 if (val != 0 && val != 1) | |
| 2876 return true; | |
| 2877 } | |
| 2878 | |
| 2879 return false; | |
| 2880 } | |
| 2881 | |
| 2882 bool | |
| 2385 | 2883 Matrix::all_elements_are_int_or_inf_or_nan (void) const |
| 2884 { | |
| 5275 | 2885 octave_idx_type nel = nelem (); |
| 2886 | |
| 2887 for (octave_idx_type i = 0; i < nel; i++) | |
| 4634 | 2888 { |
| 2889 double val = elem (i); | |
| 2890 if (xisnan (val) || D_NINT (val) == val) | |
| 2891 continue; | |
| 2892 else | |
| 2893 return false; | |
| 2894 } | |
| 2385 | 2895 |
| 2896 return true; | |
| 2897 } | |
| 2898 | |
| 1968 | 2899 // Return nonzero if any element of M is not an integer. Also extract |
| 2900 // the largest and smallest values and return them in MAX_VAL and MIN_VAL. | |
| 2901 | |
| 2385 | 2902 bool |
| 1968 | 2903 Matrix::all_integers (double& max_val, double& min_val) const |
| 2904 { | |
| 5275 | 2905 octave_idx_type nel = nelem (); |
| 4634 | 2906 |
| 2907 if (nel > 0) | |
| 1968 | 2908 { |
| 4634 | 2909 max_val = elem (0); |
| 2910 min_val = elem (0); | |
| 1968 | 2911 } |
| 2912 else | |
| 2385 | 2913 return false; |
| 1968 | 2914 |
| 5275 | 2915 for (octave_idx_type i = 0; i < nel; i++) |
| 4634 | 2916 { |
| 2917 double val = elem (i); | |
| 2918 | |
| 2919 if (val > max_val) | |
| 2920 max_val = val; | |
| 2921 | |
| 2922 if (val < min_val) | |
| 2923 min_val = val; | |
| 2924 | |
| 2925 if (D_NINT (val) != val) | |
| 2926 return false; | |
| 2927 } | |
| 2385 | 2928 |
| 2929 return true; | |
| 1968 | 2930 } |
| 2931 | |
| 2385 | 2932 bool |
| 1968 | 2933 Matrix::too_large_for_float (void) const |
| 2934 { | |
| 5275 | 2935 octave_idx_type nel = nelem (); |
| 2936 | |
| 2937 for (octave_idx_type i = 0; i < nel; i++) | |
| 4634 | 2938 { |
| 2939 double val = elem (i); | |
| 2940 | |
| 5389 | 2941 if (! (xisnan (val) || xisinf (val)) |
| 5387 | 2942 && fabs (val) > FLT_MAX) |
| 4634 | 2943 return true; |
| 2944 } | |
| 1968 | 2945 |
| 2385 | 2946 return false; |
| 1968 | 2947 } |
| 2948 | |
| 5775 | 2949 // FIXME Do these really belong here? Maybe they should be |
| 4015 | 2950 // in a base class? |
| 458 | 2951 |
| 2832 | 2952 boolMatrix |
| 4015 | 2953 Matrix::all (int dim) const |
| 458 | 2954 { |
| 4015 | 2955 MX_ALL_OP (dim); |
| 458 | 2956 } |
| 2957 | |
| 2832 | 2958 boolMatrix |
| 4015 | 2959 Matrix::any (int dim) const |
| 458 | 2960 { |
| 4015 | 2961 MX_ANY_OP (dim); |
| 458 | 2962 } |
| 2963 | |
| 2964 Matrix | |
| 3723 | 2965 Matrix::cumprod (int dim) const |
| 458 | 2966 { |
| 4015 | 2967 MX_CUMULATIVE_OP (Matrix, double, *=); |
| 458 | 2968 } |
| 2969 | |
| 2970 Matrix | |
| 3723 | 2971 Matrix::cumsum (int dim) const |
| 458 | 2972 { |
| 4015 | 2973 MX_CUMULATIVE_OP (Matrix, double, +=); |
| 458 | 2974 } |
| 2975 | |
| 2976 Matrix | |
| 3723 | 2977 Matrix::prod (int dim) const |
| 458 | 2978 { |
| 3864 | 2979 MX_REDUCTION_OP (Matrix, *=, 1.0, 1.0); |
| 458 | 2980 } |
| 2981 | |
| 2982 Matrix | |
| 3723 | 2983 Matrix::sum (int dim) const |
| 458 | 2984 { |
| 3864 | 2985 MX_REDUCTION_OP (Matrix, +=, 0.0, 0.0); |
| 458 | 2986 } |
| 2987 | |
| 2988 Matrix | |
| 3723 | 2989 Matrix::sumsq (int dim) const |
| 458 | 2990 { |
| 3864 | 2991 #define ROW_EXPR \ |
| 2992 double d = elem (i, j); \ | |
| 2993 retval.elem (i, 0) += d * d | |
| 2994 | |
| 2995 #define COL_EXPR \ | |
| 2996 double d = elem (i, j); \ | |
| 2997 retval.elem (0, j) += d * d | |
| 2998 | |
| 2999 MX_BASE_REDUCTION_OP (Matrix, ROW_EXPR, COL_EXPR, 0.0, 0.0); | |
| 3000 | |
| 3001 #undef ROW_EXPR | |
| 3002 #undef COL_EXPR | |
| 458 | 3003 } |
| 3004 | |
| 2385 | 3005 Matrix |
| 3006 Matrix::abs (void) const | |
| 3007 { | |
| 5275 | 3008 octave_idx_type nr = rows (); |
| 3009 octave_idx_type nc = cols (); | |
| 2385 | 3010 |
| 3011 Matrix retval (nr, nc); | |
| 3012 | |
| 5275 | 3013 for (octave_idx_type j = 0; j < nc; j++) |
| 3014 for (octave_idx_type i = 0; i < nr; i++) | |
| 2385 | 3015 retval (i, j) = fabs (elem (i, j)); |
| 3016 | |
| 3017 return retval; | |
| 3018 } | |
| 3019 | |
|
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parents:
7544
diff
changeset
|
3020 Matrix |
| 5275 | 3021 Matrix::diag (octave_idx_type k) const |
| 458 | 3022 { |
|
7620
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David Bateman <dbateman@free.fr>
parents:
7544
diff
changeset
|
3023 return MArray2<double>::diag (k); |
| 458 | 3024 } |
| 3025 | |
| 3026 ColumnVector | |
| 3027 Matrix::row_min (void) const | |
| 3028 { | |
| 5275 | 3029 Array<octave_idx_type> dummy_idx; |
| 4587 | 3030 return row_min (dummy_idx); |
| 458 | 3031 } |
| 3032 | |
| 3033 ColumnVector | |
| 5275 | 3034 Matrix::row_min (Array<octave_idx_type>& idx_arg) const |
| 458 | 3035 { |
| 3036 ColumnVector result; | |
| 3037 | |
| 5275 | 3038 octave_idx_type nr = rows (); |
| 3039 octave_idx_type nc = cols (); | |
| 458 | 3040 |
| 3041 if (nr > 0 && nc > 0) | |
| 3042 { | |
| 3043 result.resize (nr); | |
| 4587 | 3044 idx_arg.resize (nr); |
| 458 | 3045 |
| 5275 | 3046 for (octave_idx_type i = 0; i < nr; i++) |
| 458 | 3047 { |
| 5275 | 3048 octave_idx_type idx_j; |
| 4469 | 3049 |
| 3050 double tmp_min = octave_NaN; | |
| 3051 | |
| 3052 for (idx_j = 0; idx_j < nc; idx_j++) | |
| 2354 | 3053 { |
| 4469 | 3054 tmp_min = elem (i, idx_j); |
| 3055 | |
| 5389 | 3056 if (! xisnan (tmp_min)) |
| 4469 | 3057 break; |
| 3058 } | |
| 3059 | |
| 5275 | 3060 for (octave_idx_type j = idx_j+1; j < nc; j++) |
| 4469 | 3061 { |
| 3062 double tmp = elem (i, j); | |
| 3063 | |
| 5389 | 3064 if (xisnan (tmp)) |
| 4469 | 3065 continue; |
| 3066 else if (tmp < tmp_min) | |
| 2354 | 3067 { |
| 4469 | 3068 idx_j = j; |
| 3069 tmp_min = tmp; | |
| 2354 | 3070 } |
| 3071 } | |
| 3072 | |
| 4469 | 3073 result.elem (i) = tmp_min; |
| 5389 | 3074 idx_arg.elem (i) = xisnan (tmp_min) ? 0 : idx_j; |
| 458 | 3075 } |
| 3076 } | |
| 3077 | |
| 3078 return result; | |
| 3079 } | |
| 3080 | |
| 3081 ColumnVector | |
| 3082 Matrix::row_max (void) const | |
| 3083 { | |
| 5275 | 3084 Array<octave_idx_type> dummy_idx; |
| 4587 | 3085 return row_max (dummy_idx); |
| 458 | 3086 } |
| 3087 | |
| 3088 ColumnVector | |
| 5275 | 3089 Matrix::row_max (Array<octave_idx_type>& idx_arg) const |
| 458 | 3090 { |
| 3091 ColumnVector result; | |
| 3092 | |
| 5275 | 3093 octave_idx_type nr = rows (); |
| 3094 octave_idx_type nc = cols (); | |
| 458 | 3095 |
| 3096 if (nr > 0 && nc > 0) | |
| 3097 { | |
| 3098 result.resize (nr); | |
| 4587 | 3099 idx_arg.resize (nr); |
| 458 | 3100 |
| 5275 | 3101 for (octave_idx_type i = 0; i < nr; i++) |
| 458 | 3102 { |
| 5275 | 3103 octave_idx_type idx_j; |
| 4469 | 3104 |
| 3105 double tmp_max = octave_NaN; | |
| 3106 | |
| 3107 for (idx_j = 0; idx_j < nc; idx_j++) | |
| 2354 | 3108 { |
| 4469 | 3109 tmp_max = elem (i, idx_j); |
| 3110 | |
| 5389 | 3111 if (! xisnan (tmp_max)) |
| 4469 | 3112 break; |
| 3113 } | |
| 3114 | |
| 5275 | 3115 for (octave_idx_type j = idx_j+1; j < nc; j++) |
| 4469 | 3116 { |
| 3117 double tmp = elem (i, j); | |
| 3118 | |
| 5389 | 3119 if (xisnan (tmp)) |
| 4469 | 3120 continue; |
| 3121 else if (tmp > tmp_max) | |
| 2354 | 3122 { |
| 4469 | 3123 idx_j = j; |
| 3124 tmp_max = tmp; | |
| 2354 | 3125 } |
| 3126 } | |
| 3127 | |
| 4469 | 3128 result.elem (i) = tmp_max; |
| 5389 | 3129 idx_arg.elem (i) = xisnan (tmp_max) ? 0 : idx_j; |
| 458 | 3130 } |
| 3131 } | |
| 3132 | |
| 3133 return result; | |
| 3134 } | |
| 3135 | |
| 3136 RowVector | |
| 3137 Matrix::column_min (void) const | |
| 3138 { | |
| 5275 | 3139 Array<octave_idx_type> dummy_idx; |
| 4587 | 3140 return column_min (dummy_idx); |
| 458 | 3141 } |
| 2354 | 3142 |
| 458 | 3143 RowVector |
| 5275 | 3144 Matrix::column_min (Array<octave_idx_type>& idx_arg) const |
| 458 | 3145 { |
| 3146 RowVector result; | |
| 3147 | |
| 5275 | 3148 octave_idx_type nr = rows (); |
| 3149 octave_idx_type nc = cols (); | |
| 458 | 3150 |
| 3151 if (nr > 0 && nc > 0) | |
| 3152 { | |
| 3153 result.resize (nc); | |
| 4587 | 3154 idx_arg.resize (nc); |
| 458 | 3155 |
| 5275 | 3156 for (octave_idx_type j = 0; j < nc; j++) |
| 458 | 3157 { |
| 5275 | 3158 octave_idx_type idx_i; |
| 4469 | 3159 |
| 3160 double tmp_min = octave_NaN; | |
| 3161 | |
| 3162 for (idx_i = 0; idx_i < nr; idx_i++) | |
| 2354 | 3163 { |
| 4469 | 3164 tmp_min = elem (idx_i, j); |
| 3165 | |
| 5389 | 3166 if (! xisnan (tmp_min)) |
| 4469 | 3167 break; |
| 3168 } | |
| 3169 | |
| 5275 | 3170 for (octave_idx_type i = idx_i+1; i < nr; i++) |
| 4469 | 3171 { |
| 3172 double tmp = elem (i, j); | |
| 3173 | |
| 5389 | 3174 if (xisnan (tmp)) |
| 4469 | 3175 continue; |
| 3176 else if (tmp < tmp_min) | |
| 2354 | 3177 { |
| 4469 | 3178 idx_i = i; |
| 3179 tmp_min = tmp; | |
| 2354 | 3180 } |
| 3181 } | |
| 3182 | |
| 4469 | 3183 result.elem (j) = tmp_min; |
| 5389 | 3184 idx_arg.elem (j) = xisnan (tmp_min) ? 0 : idx_i; |
| 458 | 3185 } |
| 3186 } | |
| 3187 | |
| 3188 return result; | |
| 3189 } | |
| 3190 | |
| 2354 | 3191 RowVector |
| 3192 Matrix::column_max (void) const | |
| 3193 { | |
| 5275 | 3194 Array<octave_idx_type> dummy_idx; |
| 4587 | 3195 return column_max (dummy_idx); |
| 2354 | 3196 } |
| 458 | 3197 |
| 3198 RowVector | |
| 5275 | 3199 Matrix::column_max (Array<octave_idx_type>& idx_arg) const |
| 458 | 3200 { |
| 3201 RowVector result; | |
| 3202 | |
| 5275 | 3203 octave_idx_type nr = rows (); |
| 3204 octave_idx_type nc = cols (); | |
| 458 | 3205 |
| 3206 if (nr > 0 && nc > 0) | |
| 3207 { | |
| 3208 result.resize (nc); | |
| 4587 | 3209 idx_arg.resize (nc); |
| 458 | 3210 |
| 5275 | 3211 for (octave_idx_type j = 0; j < nc; j++) |
| 458 | 3212 { |
| 5275 | 3213 octave_idx_type idx_i; |
| 4469 | 3214 |
| 3215 double tmp_max = octave_NaN; | |
| 3216 | |
| 3217 for (idx_i = 0; idx_i < nr; idx_i++) | |
| 2354 | 3218 { |
| 4469 | 3219 tmp_max = elem (idx_i, j); |
| 3220 | |
| 5389 | 3221 if (! xisnan (tmp_max)) |
| 4469 | 3222 break; |
| 3223 } | |
| 3224 | |
| 5275 | 3225 for (octave_idx_type i = idx_i+1; i < nr; i++) |
| 4469 | 3226 { |
| 3227 double tmp = elem (i, j); | |
| 3228 | |
| 5389 | 3229 if (xisnan (tmp)) |
| 4469 | 3230 continue; |
| 3231 else if (tmp > tmp_max) | |
| 2354 | 3232 { |
| 4469 | 3233 idx_i = i; |
| 3234 tmp_max = tmp; | |
| 2354 | 3235 } |
| 3236 } | |
| 3237 | |
| 4469 | 3238 result.elem (j) = tmp_max; |
| 5389 | 3239 idx_arg.elem (j) = xisnan (tmp_max) ? 0 : idx_i; |
| 458 | 3240 } |
| 3241 } | |
| 3242 | |
| 3243 return result; | |
| 3244 } | |
| 3245 | |
| 3504 | 3246 std::ostream& |
| 3247 operator << (std::ostream& os, const Matrix& a) | |
| 458 | 3248 { |
| 5275 | 3249 for (octave_idx_type i = 0; i < a.rows (); i++) |
| 458 | 3250 { |
| 5275 | 3251 for (octave_idx_type j = 0; j < a.cols (); j++) |
| 4130 | 3252 { |
| 3253 os << " "; | |
| 3254 octave_write_double (os, a.elem (i, j)); | |
| 3255 } | |
| 458 | 3256 os << "\n"; |
| 3257 } | |
| 3258 return os; | |
| 3259 } | |
| 3260 | |
| 3504 | 3261 std::istream& |
| 3262 operator >> (std::istream& is, Matrix& a) | |
| 458 | 3263 { |
| 5275 | 3264 octave_idx_type nr = a.rows (); |
| 3265 octave_idx_type nc = a.cols (); | |
| 458 | 3266 |
| 3267 if (nr < 1 || nc < 1) | |
| 3504 | 3268 is.clear (std::ios::badbit); |
| 458 | 3269 else |
| 3270 { | |
| 3271 double tmp; | |
| 5275 | 3272 for (octave_idx_type i = 0; i < nr; i++) |
| 3273 for (octave_idx_type j = 0; j < nc; j++) | |
| 458 | 3274 { |
| 4130 | 3275 tmp = octave_read_double (is); |
| 458 | 3276 if (is) |
| 3277 a.elem (i, j) = tmp; | |
| 3278 else | |
| 2795 | 3279 goto done; |
| 458 | 3280 } |
| 3281 } | |
| 3282 | |
| 2795 | 3283 done: |
| 3284 | |
| 458 | 3285 return is; |
| 3286 } | |
| 3287 | |
| 1819 | 3288 Matrix |
| 3289 Givens (double x, double y) | |
| 3290 { | |
| 3291 double cc, s, temp_r; | |
| 3292 | |
| 3887 | 3293 F77_FUNC (dlartg, DLARTG) (x, y, cc, s, temp_r); |
| 1819 | 3294 |
| 3295 Matrix g (2, 2); | |
| 3296 | |
| 3297 g.elem (0, 0) = cc; | |
| 3298 g.elem (1, 1) = cc; | |
| 3299 g.elem (0, 1) = s; | |
| 3300 g.elem (1, 0) = -s; | |
| 3301 | |
| 3302 return g; | |
| 3303 } | |
| 3304 | |
| 3305 Matrix | |
| 3306 Sylvester (const Matrix& a, const Matrix& b, const Matrix& c) | |
| 3307 { | |
| 3308 Matrix retval; | |
| 3309 | |
| 5775 | 3310 // FIXME -- need to check that a, b, and c are all the same |
| 1819 | 3311 // size. |
| 3312 | |
| 3313 // Compute Schur decompositions. | |
| 3314 | |
| 3315 SCHUR as (a, "U"); | |
| 3316 SCHUR bs (b, "U"); | |
| 3317 | |
| 3318 // Transform c to new coordinates. | |
| 3319 | |
| 3320 Matrix ua = as.unitary_matrix (); | |
| 3321 Matrix sch_a = as.schur_matrix (); | |
| 3322 | |
| 3323 Matrix ub = bs.unitary_matrix (); | |
| 3324 Matrix sch_b = bs.schur_matrix (); | |
| 3325 | |
| 3326 Matrix cx = ua.transpose () * c * ub; | |
| 3327 | |
| 3328 // Solve the sylvester equation, back-transform, and return the | |
| 3329 // solution. | |
| 3330 | |
| 5275 | 3331 octave_idx_type a_nr = a.rows (); |
| 3332 octave_idx_type b_nr = b.rows (); | |
| 1819 | 3333 |
| 3334 double scale; | |
| 5275 | 3335 octave_idx_type info; |
| 1819 | 3336 |
| 1950 | 3337 double *pa = sch_a.fortran_vec (); |
| 3338 double *pb = sch_b.fortran_vec (); | |
| 3339 double *px = cx.fortran_vec (); | |
| 3340 | |
| 4552 | 3341 F77_XFCN (dtrsyl, DTRSYL, (F77_CONST_CHAR_ARG2 ("N", 1), |
| 3342 F77_CONST_CHAR_ARG2 ("N", 1), | |
| 3343 1, a_nr, b_nr, pa, a_nr, pb, | |
| 3344 b_nr, px, a_nr, scale, info | |
| 3345 F77_CHAR_ARG_LEN (1) | |
| 3346 F77_CHAR_ARG_LEN (1))); | |
| 1950 | 3347 |
| 3348 | |
|
7482
29980c6b8604
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John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
3349 // FIXME -- check info? |
| 1819 | 3350 |
|
7482
29980c6b8604
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John W. Eaton <jwe@octave.org>
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7478
diff
changeset
|
3351 retval = -ua*cx*ub.transpose (); |
| 1819 | 3352 |
| 3353 return retval; | |
| 3354 } | |
| 3355 | |
| 2828 | 3356 // matrix by matrix -> matrix operations |
| 3357 | |
| 6162 | 3358 /* Simple Dot Product, Matrix-Vector and Matrix-Matrix Unit tests |
| 3359 %!assert([1 2 3] * [ 4 ; 5 ; 6], 32, 1e-14) | |
| 3360 %!assert([1 2 ; 3 4 ] * [5 ; 6], [17 ; 39 ], 1e-14) | |
| 3361 %!assert([1 2 ; 3 4 ] * [5 6 ; 7 8], [19 22; 43 50], 1e-14) | |
| 3362 */ | |
| 3363 | |
| 3364 /* Test some simple identities | |
| 3365 %!shared M, cv, rv | |
| 3366 %! M = randn(10,10); | |
| 3367 %! cv = randn(10,1); | |
| 3368 %! rv = randn(1,10); | |
| 3369 %!assert([M*cv,M*cv],M*[cv,cv],1e-14) | |
| 3370 %!assert([rv*M;rv*M],[rv;rv]*M,1e-14) | |
| 3371 %!assert(2*rv*cv,[rv,rv]*[cv;cv],1e-14) | |
| 3372 */ | |
| 3373 | |
|
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
|
3374 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
|
3375 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
|
3376 { |
|
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 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
|
3378 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
|
3379 } |
|
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 // 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
|
3382 |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3383 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
|
3384 xgemm (bool transa, const Matrix& a, bool transb, const Matrix& b) |
| 2828 | 3385 { |
| 3386 Matrix retval; | |
| 3387 | |
|
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
|
3388 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
|
3389 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
|
3390 |
|
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 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
|
3392 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
|
3393 |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3394 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
|
3395 gripe_nonconformant ("operator *", a_nr, a_nc, b_nr, b_nc); |
| 2828 | 3396 else |
| 3397 { | |
|
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
|
3398 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
|
3399 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
|
3400 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
|
3401 { |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3402 octave_idx_type lda = a.rows (); |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3403 |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3404 retval.resize (a_nr, b_nc); |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3405 double *c = retval.fortran_vec (); |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3406 |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3407 const char *ctransa = get_blas_trans_arg (transa); |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3408 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
|
3409 F77_CONST_CHAR_ARG2 (ctransa, 1), |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3410 a_nr, a_nc, 1.0, |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3411 a.data (), lda, 0.0, c, a_nr |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3412 F77_CHAR_ARG_LEN (1) |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3413 F77_CHAR_ARG_LEN (1))); |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3414 for (int j = 0; j < a_nr; j++) |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3415 for (int i = 0; i < j; i++) |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3416 retval.xelem (j,i) = retval.xelem (i,j); |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3417 |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3418 } |
| 2828 | 3419 else |
| 3420 { | |
|
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
|
3421 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
|
3422 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
|
3423 |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3424 retval.resize (a_nr, b_nc); |
| 2828 | 3425 double *c = retval.fortran_vec (); |
| 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 (b_nc == 1) |
| 5983 | 3428 { |
|
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
|
3429 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
|
3430 F77_FUNC (xddot, XDDOT) (a_nc, a.data (), 1, b.data (), 1, *c); |
| 5983 | 3431 else |
| 6390 | 3432 { |
|
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
|
3433 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
|
3434 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
|
3435 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
|
3436 b.data (), 1, 0.0, c, 1 |
| 6390 | 3437 F77_CHAR_ARG_LEN (1))); |
| 3438 } | |
| 5983 | 3439 } |
|
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
|
3440 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
|
3441 { |
|
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 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
|
3443 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
|
3444 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
|
3445 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
|
3446 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
|
3447 } |
| 5983 | 3448 else |
| 6390 | 3449 { |
|
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
|
3450 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
|
3451 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
|
3452 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
|
3453 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
|
3454 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
|
3455 lda, b.data (), ldb, 0.0, c, a_nr |
| 6390 | 3456 F77_CHAR_ARG_LEN (1) |
| 3457 F77_CHAR_ARG_LEN (1))); | |
| 3458 } | |
| 2828 | 3459 } |
| 3460 } | |
| 3461 | |
| 3462 return retval; | |
| 3463 } | |
| 3464 | |
|
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
|
3465 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
|
3466 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
|
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 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
|
3469 } |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3470 |
| 5775 | 3471 // FIXME -- it would be nice to share code among the min/max |
| 4309 | 3472 // functions below. |
| 3473 | |
| 3474 #define EMPTY_RETURN_CHECK(T) \ | |
| 3475 if (nr == 0 || nc == 0) \ | |
| 3476 return T (nr, nc); | |
| 3477 | |
| 3478 Matrix | |
| 3479 min (double d, const Matrix& m) | |
| 3480 { | |
| 5275 | 3481 octave_idx_type nr = m.rows (); |
| 3482 octave_idx_type nc = m.columns (); | |
| 4309 | 3483 |
| 3484 EMPTY_RETURN_CHECK (Matrix); | |
| 3485 | |
| 3486 Matrix result (nr, nc); | |
| 3487 | |
| 5275 | 3488 for (octave_idx_type j = 0; j < nc; j++) |
| 3489 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3490 { |
| 3491 OCTAVE_QUIT; | |
| 3492 result (i, j) = xmin (d, m (i, j)); | |
| 3493 } | |
| 3494 | |
| 3495 return result; | |
| 3496 } | |
| 3497 | |
| 3498 Matrix | |
| 3499 min (const Matrix& m, double d) | |
| 3500 { | |
| 5275 | 3501 octave_idx_type nr = m.rows (); |
| 3502 octave_idx_type nc = m.columns (); | |
| 4309 | 3503 |
| 3504 EMPTY_RETURN_CHECK (Matrix); | |
| 3505 | |
| 3506 Matrix result (nr, nc); | |
| 3507 | |
| 5275 | 3508 for (octave_idx_type j = 0; j < nc; j++) |
| 3509 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3510 { |
| 3511 OCTAVE_QUIT; | |
| 3512 result (i, j) = xmin (m (i, j), d); | |
| 3513 } | |
| 3514 | |
| 3515 return result; | |
| 3516 } | |
| 3517 | |
| 3518 Matrix | |
| 3519 min (const Matrix& a, const Matrix& b) | |
| 3520 { | |
| 5275 | 3521 octave_idx_type nr = a.rows (); |
| 3522 octave_idx_type nc = a.columns (); | |
| 4309 | 3523 |
| 3524 if (nr != b.rows () || nc != b.columns ()) | |
| 3525 { | |
| 3526 (*current_liboctave_error_handler) | |
| 3527 ("two-arg min expecting args of same size"); | |
| 3528 return Matrix (); | |
| 3529 } | |
| 3530 | |
| 3531 EMPTY_RETURN_CHECK (Matrix); | |
| 3532 | |
| 3533 Matrix result (nr, nc); | |
| 3534 | |
| 5275 | 3535 for (octave_idx_type j = 0; j < nc; j++) |
| 3536 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3537 { |
| 3538 OCTAVE_QUIT; | |
| 3539 result (i, j) = xmin (a (i, j), b (i, j)); | |
| 3540 } | |
| 3541 | |
| 3542 return result; | |
| 3543 } | |
| 3544 | |
| 3545 Matrix | |
| 3546 max (double d, const Matrix& m) | |
| 3547 { | |
| 5275 | 3548 octave_idx_type nr = m.rows (); |
| 3549 octave_idx_type nc = m.columns (); | |
| 4309 | 3550 |
| 3551 EMPTY_RETURN_CHECK (Matrix); | |
| 3552 | |
| 3553 Matrix result (nr, nc); | |
| 3554 | |
| 5275 | 3555 for (octave_idx_type j = 0; j < nc; j++) |
| 3556 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3557 { |
| 3558 OCTAVE_QUIT; | |
| 3559 result (i, j) = xmax (d, m (i, j)); | |
| 3560 } | |
| 3561 | |
| 3562 return result; | |
| 3563 } | |
| 3564 | |
| 3565 Matrix | |
| 3566 max (const Matrix& m, double d) | |
| 3567 { | |
| 5275 | 3568 octave_idx_type nr = m.rows (); |
| 3569 octave_idx_type nc = m.columns (); | |
| 4309 | 3570 |
| 3571 EMPTY_RETURN_CHECK (Matrix); | |
| 3572 | |
| 3573 Matrix result (nr, nc); | |
| 3574 | |
| 5275 | 3575 for (octave_idx_type j = 0; j < nc; j++) |
| 3576 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3577 { |
| 3578 OCTAVE_QUIT; | |
| 3579 result (i, j) = xmax (m (i, j), d); | |
| 3580 } | |
| 3581 | |
| 3582 return result; | |
| 3583 } | |
| 3584 | |
| 3585 Matrix | |
| 3586 max (const Matrix& a, const Matrix& b) | |
| 3587 { | |
| 5275 | 3588 octave_idx_type nr = a.rows (); |
| 3589 octave_idx_type nc = a.columns (); | |
| 4309 | 3590 |
| 3591 if (nr != b.rows () || nc != b.columns ()) | |
| 3592 { | |
| 3593 (*current_liboctave_error_handler) | |
| 3594 ("two-arg max expecting args of same size"); | |
| 3595 return Matrix (); | |
| 3596 } | |
| 3597 | |
| 3598 EMPTY_RETURN_CHECK (Matrix); | |
| 3599 | |
| 3600 Matrix result (nr, nc); | |
| 3601 | |
| 5275 | 3602 for (octave_idx_type j = 0; j < nc; j++) |
| 3603 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3604 { |
| 3605 OCTAVE_QUIT; | |
| 3606 result (i, j) = xmax (a (i, j), b (i, j)); | |
| 3607 } | |
| 3608 | |
| 3609 return result; | |
| 3610 } | |
| 3611 | |
| 2870 | 3612 MS_CMP_OPS(Matrix, , double, ) |
| 3504 | 3613 MS_BOOL_OPS(Matrix, double, 0.0) |
| 2870 | 3614 |
| 3615 SM_CMP_OPS(double, , Matrix, ) | |
| 3504 | 3616 SM_BOOL_OPS(double, Matrix, 0.0) |
| 2870 | 3617 |
| 3618 MM_CMP_OPS(Matrix, , Matrix, ) | |
| 3504 | 3619 MM_BOOL_OPS(Matrix, Matrix, 0.0) |
| 2870 | 3620 |
| 458 | 3621 /* |
| 3622 ;;; Local Variables: *** | |
| 3623 ;;; mode: C++ *** | |
| 3624 ;;; End: *** | |
| 3625 */ |