Mercurial > octave-nkf
annotate liboctave/dMatrix.cc @ 8335:64cf956a109c
templatize & fix DET
| author | Jaroslav Hajek <highegg@gmail.com> |
|---|---|
| date | Wed, 19 Nov 2008 11:23:07 +0100 |
| parents | 851803f7bb4d |
| children | 9813c07ca946 |
| rev | line source |
|---|---|
| 1993 | 1 // Matrix manipulations. |
| 458 | 2 /* |
| 3 | |
| 7017 | 4 Copyright (C) 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, |
| 5 2003, 2004, 2005, 2006, 2007 John W. Eaton | |
| 7803 | 6 Copyright (C) 2008 Jaroslav Hajek |
| 458 | 7 |
| 8 This file is part of Octave. | |
| 9 | |
| 10 Octave is free software; you can redistribute it and/or modify it | |
| 11 under the terms of the GNU General Public License as published by the | |
| 7016 | 12 Free Software Foundation; either version 3 of the License, or (at your |
| 13 option) any later version. | |
| 458 | 14 |
| 15 Octave is distributed in the hope that it will be useful, but WITHOUT | |
| 16 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
| 17 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
| 18 for more details. | |
| 19 | |
| 20 You should have received a copy of the GNU General Public License | |
| 7016 | 21 along with Octave; see the file COPYING. If not, see |
| 22 <http://www.gnu.org/licenses/>. | |
| 458 | 23 |
| 24 */ | |
| 25 | |
| 26 #ifdef HAVE_CONFIG_H | |
| 1192 | 27 #include <config.h> |
| 458 | 28 #endif |
| 29 | |
| 1367 | 30 #include <cfloat> |
| 31 | |
| 3503 | 32 #include <iostream> |
| 6209 | 33 #include <vector> |
| 1367 | 34 |
| 4669 | 35 #include "Array-util.h" |
| 2317 | 36 #include "byte-swap.h" |
| 2828 | 37 #include "dMatrix.h" |
| 1819 | 38 #include "dbleAEPBAL.h" |
| 8335 | 39 #include "DET.h" |
| 1819 | 40 #include "dbleSCHUR.h" |
| 740 | 41 #include "dbleSVD.h" |
| 6207 | 42 #include "dbleCHOL.h" |
| 1847 | 43 #include "f77-fcn.h" |
|
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44 #include "functor.h" |
| 458 | 45 #include "lo-error.h" |
| 2354 | 46 #include "lo-ieee.h" |
| 47 #include "lo-mappers.h" | |
| 1968 | 48 #include "lo-utils.h" |
| 1367 | 49 #include "mx-base.h" |
| 2828 | 50 #include "mx-m-dm.h" |
| 3176 | 51 #include "mx-dm-m.h" |
| 1367 | 52 #include "mx-inlines.cc" |
| 1650 | 53 #include "oct-cmplx.h" |
| 4153 | 54 #include "quit.h" |
| 458 | 55 |
| 4773 | 56 #if defined (HAVE_FFTW3) |
| 3827 | 57 #include "oct-fftw.h" |
| 58 #endif | |
| 59 | |
| 458 | 60 // Fortran functions we call. |
| 61 | |
| 62 extern "C" | |
| 63 { | |
| 7478 | 64 F77_RET_T |
| 7477 | 65 F77_FUNC (xilaenv, XILAENV) (const octave_idx_type&, F77_CONST_CHAR_ARG_DECL, |
| 66 F77_CONST_CHAR_ARG_DECL, | |
| 67 const octave_idx_type&, const octave_idx_type&, | |
| 7478 | 68 const octave_idx_type&, const octave_idx_type&, |
| 69 octave_idx_type& | |
| 70 F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); | |
| 7476 | 71 |
| 4552 | 72 F77_RET_T |
| 73 F77_FUNC (dgebal, DGEBAL) (F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 74 const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type&, |
| 75 octave_idx_type&, double*, octave_idx_type& | |
| 4552 | 76 F77_CHAR_ARG_LEN_DECL); |
| 77 | |
| 78 F77_RET_T | |
| 79 F77_FUNC (dgebak, DGEBAK) (F77_CONST_CHAR_ARG_DECL, | |
| 80 F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 81 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, double*, |
| 82 const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type& | |
| 4552 | 83 F77_CHAR_ARG_LEN_DECL |
| 84 F77_CHAR_ARG_LEN_DECL); | |
| 85 | |
| 86 | |
| 87 F77_RET_T | |
| 88 F77_FUNC (dgemm, DGEMM) (F77_CONST_CHAR_ARG_DECL, | |
| 89 F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 90 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
| 91 const double&, const double*, const octave_idx_type&, | |
| 92 const double*, const octave_idx_type&, const double&, | |
| 93 double*, const octave_idx_type& | |
| 4552 | 94 F77_CHAR_ARG_LEN_DECL |
| 95 F77_CHAR_ARG_LEN_DECL); | |
| 96 | |
| 97 F77_RET_T | |
| 5983 | 98 F77_FUNC (dgemv, DGEMV) (F77_CONST_CHAR_ARG_DECL, |
| 99 const octave_idx_type&, const octave_idx_type&, const double&, | |
| 100 const double*, const octave_idx_type&, const double*, | |
| 101 const octave_idx_type&, const double&, double*, | |
| 102 const octave_idx_type& | |
| 103 F77_CHAR_ARG_LEN_DECL); | |
| 104 | |
| 105 F77_RET_T | |
| 106 F77_FUNC (xddot, XDDOT) (const octave_idx_type&, const double*, const octave_idx_type&, | |
| 107 const double*, const octave_idx_type&, double&); | |
| 108 | |
| 109 F77_RET_T | |
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110 F77_FUNC (dsyrk, DSYRK) (F77_CONST_CHAR_ARG_DECL, |
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111 F77_CONST_CHAR_ARG_DECL, |
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112 const octave_idx_type&, const octave_idx_type&, |
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113 const double&, const double*, const octave_idx_type&, |
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114 const double&, double*, const octave_idx_type& |
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115 F77_CHAR_ARG_LEN_DECL |
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116 F77_CHAR_ARG_LEN_DECL); |
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117 |
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118 F77_RET_T |
| 5275 | 119 F77_FUNC (dgetrf, DGETRF) (const octave_idx_type&, const octave_idx_type&, double*, const octave_idx_type&, |
| 120 octave_idx_type*, octave_idx_type&); | |
| 4329 | 121 |
| 4552 | 122 F77_RET_T |
| 5275 | 123 F77_FUNC (dgetrs, DGETRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, |
| 124 const double*, const octave_idx_type&, | |
| 125 const octave_idx_type*, double*, const octave_idx_type&, octave_idx_type& | |
| 4552 | 126 F77_CHAR_ARG_LEN_DECL); |
| 127 | |
| 128 F77_RET_T | |
| 5275 | 129 F77_FUNC (dgetri, DGETRI) (const octave_idx_type&, double*, const octave_idx_type&, const octave_idx_type*, |
| 130 double*, const octave_idx_type&, octave_idx_type&); | |
| 4552 | 131 |
| 132 F77_RET_T | |
| 5275 | 133 F77_FUNC (dgecon, DGECON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, double*, |
| 134 const octave_idx_type&, const double&, double&, | |
| 135 double*, octave_idx_type*, octave_idx_type& | |
| 4552 | 136 F77_CHAR_ARG_LEN_DECL); |
| 137 | |
| 138 F77_RET_T | |
| 7072 | 139 F77_FUNC (dgelsy, DGELSY) (const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
| 140 double*, const octave_idx_type&, double*, | |
| 141 const octave_idx_type&, octave_idx_type*, double&, octave_idx_type&, | |
| 142 double*, const octave_idx_type&, octave_idx_type&); | |
| 143 | |
| 144 F77_RET_T | |
| 145 F77_FUNC (dgelsd, DGELSD) (const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, | |
| 5275 | 146 double*, const octave_idx_type&, double*, |
| 7071 | 147 const octave_idx_type&, double*, double&, octave_idx_type&, |
| 7072 | 148 double*, const octave_idx_type&, octave_idx_type*, |
| 149 octave_idx_type&); | |
| 458 | 150 |
| 5785 | 151 F77_RET_T |
| 152 F77_FUNC (dpotrf, DPOTRF) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 153 double *, const octave_idx_type&, | |
| 154 octave_idx_type& F77_CHAR_ARG_LEN_DECL); | |
| 155 | |
| 156 F77_RET_T | |
| 157 F77_FUNC (dpocon, DPOCON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 158 double*, const octave_idx_type&, const double&, | |
| 159 double&, double*, octave_idx_type*, | |
| 160 octave_idx_type& F77_CHAR_ARG_LEN_DECL); | |
| 161 F77_RET_T | |
| 162 F77_FUNC (dpotrs, DPOTRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 163 const octave_idx_type&, const double*, | |
| 164 const octave_idx_type&, double*, | |
| 165 const octave_idx_type&, octave_idx_type& | |
| 166 F77_CHAR_ARG_LEN_DECL); | |
| 167 | |
| 168 F77_RET_T | |
| 6207 | 169 F77_FUNC (dtrtri, DTRTRI) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, |
| 170 const octave_idx_type&, const double*, | |
| 171 const octave_idx_type&, octave_idx_type& | |
| 172 F77_CHAR_ARG_LEN_DECL | |
| 173 F77_CHAR_ARG_LEN_DECL); | |
| 174 F77_RET_T | |
| 5785 | 175 F77_FUNC (dtrcon, DTRCON) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, |
| 176 F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 177 const double*, const octave_idx_type&, double&, | |
| 178 double*, octave_idx_type*, octave_idx_type& | |
| 179 F77_CHAR_ARG_LEN_DECL | |
| 180 F77_CHAR_ARG_LEN_DECL | |
| 181 F77_CHAR_ARG_LEN_DECL); | |
| 182 F77_RET_T | |
| 183 F77_FUNC (dtrtrs, DTRTRS) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, | |
| 184 F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 185 const octave_idx_type&, const double*, | |
| 186 const octave_idx_type&, double*, | |
| 187 const octave_idx_type&, octave_idx_type& | |
| 188 F77_CHAR_ARG_LEN_DECL | |
| 189 F77_CHAR_ARG_LEN_DECL | |
| 190 F77_CHAR_ARG_LEN_DECL); | |
| 191 | |
| 1360 | 192 // Note that the original complex fft routines were not written for |
| 193 // double complex arguments. They have been modified by adding an | |
| 194 // implicit double precision (a-h,o-z) statement at the beginning of | |
| 195 // each subroutine. | |
| 458 | 196 |
| 4552 | 197 F77_RET_T |
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198 F77_FUNC (zffti, ZFFTI) (const octave_idx_type&, Complex*); |
| 4552 | 199 |
| 200 F77_RET_T | |
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201 F77_FUNC (zfftf, ZFFTF) (const octave_idx_type&, Complex*, Complex*); |
| 4552 | 202 |
| 203 F77_RET_T | |
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204 F77_FUNC (zfftb, ZFFTB) (const octave_idx_type&, Complex*, Complex*); |
| 4552 | 205 |
| 206 F77_RET_T | |
| 207 F77_FUNC (dlartg, DLARTG) (const double&, const double&, double&, | |
| 208 double&, double&); | |
| 209 | |
| 210 F77_RET_T | |
| 211 F77_FUNC (dtrsyl, DTRSYL) (F77_CONST_CHAR_ARG_DECL, | |
| 212 F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 213 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
| 214 const double*, const octave_idx_type&, const double*, | |
| 215 const octave_idx_type&, const double*, const octave_idx_type&, | |
| 216 double&, octave_idx_type& | |
| 4552 | 217 F77_CHAR_ARG_LEN_DECL |
| 218 F77_CHAR_ARG_LEN_DECL); | |
| 219 | |
| 220 F77_RET_T | |
| 5275 | 221 F77_FUNC (xdlange, XDLANGE) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, |
| 222 const octave_idx_type&, const double*, | |
| 223 const octave_idx_type&, double*, double& | |
| 4552 | 224 F77_CHAR_ARG_LEN_DECL); |
| 458 | 225 } |
| 226 | |
| 1360 | 227 // Matrix class. |
| 458 | 228 |
| 2349 | 229 Matrix::Matrix (const RowVector& rv) |
| 230 : MArray2<double> (1, rv.length (), 0.0) | |
| 231 { | |
| 5275 | 232 for (octave_idx_type i = 0; i < rv.length (); i++) |
| 2349 | 233 elem (0, i) = rv.elem (i); |
| 234 } | |
| 235 | |
| 236 Matrix::Matrix (const ColumnVector& cv) | |
| 237 : MArray2<double> (cv.length (), 1, 0.0) | |
| 238 { | |
| 5275 | 239 for (octave_idx_type i = 0; i < cv.length (); i++) |
| 2349 | 240 elem (i, 0) = cv.elem (i); |
| 241 } | |
| 242 | |
| 458 | 243 Matrix::Matrix (const DiagMatrix& a) |
| 1214 | 244 : MArray2<double> (a.rows (), a.cols (), 0.0) |
| 458 | 245 { |
| 5275 | 246 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 247 elem (i, i) = a.elem (i, i); |
| 248 } | |
| 249 | |
| 5775 | 250 // FIXME -- could we use a templated mixed-type copy function |
| 1574 | 251 // here? |
| 252 | |
| 2828 | 253 Matrix::Matrix (const boolMatrix& a) |
| 254 : MArray2<double> (a.rows (), a.cols ()) | |
| 255 { | |
| 5275 | 256 for (octave_idx_type i = 0; i < a.rows (); i++) |
| 257 for (octave_idx_type j = 0; j < a.cols (); j++) | |
| 2828 | 258 elem (i, j) = a.elem (i, j); |
| 259 } | |
| 260 | |
| 1574 | 261 Matrix::Matrix (const charMatrix& a) |
| 262 : MArray2<double> (a.rows (), a.cols ()) | |
| 263 { | |
| 5275 | 264 for (octave_idx_type i = 0; i < a.rows (); i++) |
| 265 for (octave_idx_type j = 0; j < a.cols (); j++) | |
| 1574 | 266 elem (i, j) = a.elem (i, j); |
| 267 } | |
| 268 | |
| 2385 | 269 bool |
| 458 | 270 Matrix::operator == (const Matrix& a) const |
| 271 { | |
| 272 if (rows () != a.rows () || cols () != a.cols ()) | |
| 2385 | 273 return false; |
| 458 | 274 |
| 3769 | 275 return mx_inline_equal (data (), a.data (), length ()); |
| 458 | 276 } |
| 277 | |
| 2385 | 278 bool |
| 458 | 279 Matrix::operator != (const Matrix& a) const |
| 280 { | |
| 281 return !(*this == a); | |
| 282 } | |
| 283 | |
| 3354 | 284 bool |
| 285 Matrix::is_symmetric (void) const | |
| 286 { | |
| 287 if (is_square () && rows () > 0) | |
| 288 { | |
| 5275 | 289 for (octave_idx_type i = 0; i < rows (); i++) |
| 290 for (octave_idx_type j = i+1; j < cols (); j++) | |
| 3354 | 291 if (elem (i, j) != elem (j, i)) |
| 292 return false; | |
| 293 | |
| 294 return true; | |
| 295 } | |
| 296 | |
| 297 return false; | |
| 298 } | |
| 299 | |
| 458 | 300 Matrix& |
| 5275 | 301 Matrix::insert (const Matrix& a, octave_idx_type r, octave_idx_type c) |
| 458 | 302 { |
| 1561 | 303 Array2<double>::insert (a, r, c); |
| 458 | 304 return *this; |
| 305 } | |
| 306 | |
| 307 Matrix& | |
| 5275 | 308 Matrix::insert (const RowVector& a, octave_idx_type r, octave_idx_type c) |
| 458 | 309 { |
| 5275 | 310 octave_idx_type a_len = a.length (); |
| 4316 | 311 |
| 1698 | 312 if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ()) |
| 458 | 313 { |
| 314 (*current_liboctave_error_handler) ("range error for insert"); | |
| 315 return *this; | |
| 316 } | |
| 317 | |
| 4316 | 318 if (a_len > 0) |
| 319 { | |
| 320 make_unique (); | |
| 321 | |
| 5275 | 322 for (octave_idx_type i = 0; i < a_len; i++) |
| 4316 | 323 xelem (r, c+i) = a.elem (i); |
| 324 } | |
| 458 | 325 |
| 326 return *this; | |
| 327 } | |
| 328 | |
| 329 Matrix& | |
| 5275 | 330 Matrix::insert (const ColumnVector& a, octave_idx_type r, octave_idx_type c) |
| 458 | 331 { |
| 5275 | 332 octave_idx_type a_len = a.length (); |
| 4316 | 333 |
| 1698 | 334 if (r < 0 || r + a_len > rows () || c < 0 || c >= cols ()) |
| 458 | 335 { |
| 336 (*current_liboctave_error_handler) ("range error for insert"); | |
| 337 return *this; | |
| 338 } | |
| 339 | |
| 4316 | 340 if (a_len > 0) |
| 341 { | |
| 342 make_unique (); | |
| 343 | |
| 5275 | 344 for (octave_idx_type i = 0; i < a_len; i++) |
| 4316 | 345 xelem (r+i, c) = a.elem (i); |
| 346 } | |
| 458 | 347 |
| 348 return *this; | |
| 349 } | |
| 350 | |
| 351 Matrix& | |
| 5275 | 352 Matrix::insert (const DiagMatrix& a, octave_idx_type r, octave_idx_type c) |
| 458 | 353 { |
| 5275 | 354 octave_idx_type a_nr = a.rows (); |
| 355 octave_idx_type a_nc = a.cols (); | |
| 1697 | 356 |
| 1698 | 357 if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) |
| 458 | 358 { |
| 359 (*current_liboctave_error_handler) ("range error for insert"); | |
| 360 return *this; | |
| 361 } | |
| 362 | |
| 1697 | 363 fill (0.0, r, c, r + a_nr - 1, c + a_nc - 1); |
| 364 | |
| 5275 | 365 octave_idx_type a_len = a.length (); |
| 4316 | 366 |
| 367 if (a_len > 0) | |
| 368 { | |
| 369 make_unique (); | |
| 370 | |
| 5275 | 371 for (octave_idx_type i = 0; i < a_len; i++) |
| 4316 | 372 xelem (r+i, c+i) = a.elem (i, i); |
| 373 } | |
| 458 | 374 |
| 375 return *this; | |
| 376 } | |
| 377 | |
| 378 Matrix& | |
| 379 Matrix::fill (double val) | |
| 380 { | |
| 5275 | 381 octave_idx_type nr = rows (); |
| 382 octave_idx_type nc = cols (); | |
| 4316 | 383 |
| 458 | 384 if (nr > 0 && nc > 0) |
| 4316 | 385 { |
| 386 make_unique (); | |
| 387 | |
| 5275 | 388 for (octave_idx_type j = 0; j < nc; j++) |
| 389 for (octave_idx_type i = 0; i < nr; i++) | |
| 4316 | 390 xelem (i, j) = val; |
| 391 } | |
| 458 | 392 |
| 393 return *this; | |
| 394 } | |
| 395 | |
| 396 Matrix& | |
| 5275 | 397 Matrix::fill (double val, octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) |
| 458 | 398 { |
| 5275 | 399 octave_idx_type nr = rows (); |
| 400 octave_idx_type nc = cols (); | |
| 4316 | 401 |
| 458 | 402 if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0 |
| 403 || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc) | |
| 404 { | |
| 405 (*current_liboctave_error_handler) ("range error for fill"); | |
| 406 return *this; | |
| 407 } | |
| 408 | |
| 5275 | 409 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } |
| 410 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } | |
| 458 | 411 |
| 4316 | 412 if (r2 >= r1 && c2 >= c1) |
| 413 { | |
| 414 make_unique (); | |
| 415 | |
| 5275 | 416 for (octave_idx_type j = c1; j <= c2; j++) |
| 417 for (octave_idx_type i = r1; i <= r2; i++) | |
| 4316 | 418 xelem (i, j) = val; |
| 419 } | |
| 458 | 420 |
| 421 return *this; | |
| 422 } | |
| 423 | |
| 424 Matrix | |
| 425 Matrix::append (const Matrix& a) const | |
| 426 { | |
| 5275 | 427 octave_idx_type nr = rows (); |
| 428 octave_idx_type nc = cols (); | |
| 458 | 429 if (nr != a.rows ()) |
| 430 { | |
| 431 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 432 return Matrix (); | |
| 433 } | |
| 434 | |
| 5275 | 435 octave_idx_type nc_insert = nc; |
| 458 | 436 Matrix retval (nr, nc + a.cols ()); |
| 437 retval.insert (*this, 0, 0); | |
| 438 retval.insert (a, 0, nc_insert); | |
| 439 return retval; | |
| 440 } | |
| 441 | |
| 442 Matrix | |
| 443 Matrix::append (const RowVector& a) const | |
| 444 { | |
| 5275 | 445 octave_idx_type nr = rows (); |
| 446 octave_idx_type nc = cols (); | |
| 458 | 447 if (nr != 1) |
| 448 { | |
| 449 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 450 return Matrix (); | |
| 451 } | |
| 452 | |
| 5275 | 453 octave_idx_type nc_insert = nc; |
| 458 | 454 Matrix retval (nr, nc + a.length ()); |
| 455 retval.insert (*this, 0, 0); | |
| 456 retval.insert (a, 0, nc_insert); | |
| 457 return retval; | |
| 458 } | |
| 459 | |
| 460 Matrix | |
| 461 Matrix::append (const ColumnVector& a) const | |
| 462 { | |
| 5275 | 463 octave_idx_type nr = rows (); |
| 464 octave_idx_type nc = cols (); | |
| 458 | 465 if (nr != a.length ()) |
| 466 { | |
| 467 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 468 return Matrix (); | |
| 469 } | |
| 470 | |
| 5275 | 471 octave_idx_type nc_insert = nc; |
| 458 | 472 Matrix retval (nr, nc + 1); |
| 473 retval.insert (*this, 0, 0); | |
| 474 retval.insert (a, 0, nc_insert); | |
| 475 return retval; | |
| 476 } | |
| 477 | |
| 478 Matrix | |
| 479 Matrix::append (const DiagMatrix& a) const | |
| 480 { | |
| 5275 | 481 octave_idx_type nr = rows (); |
| 482 octave_idx_type nc = cols (); | |
| 458 | 483 if (nr != a.rows ()) |
| 484 { | |
| 485 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 486 return *this; | |
| 487 } | |
| 488 | |
| 5275 | 489 octave_idx_type nc_insert = nc; |
| 458 | 490 Matrix retval (nr, nc + a.cols ()); |
| 491 retval.insert (*this, 0, 0); | |
| 492 retval.insert (a, 0, nc_insert); | |
| 493 return retval; | |
| 494 } | |
| 495 | |
| 496 Matrix | |
| 497 Matrix::stack (const Matrix& a) const | |
| 498 { | |
| 5275 | 499 octave_idx_type nr = rows (); |
| 500 octave_idx_type nc = cols (); | |
| 458 | 501 if (nc != a.cols ()) |
| 502 { | |
| 503 (*current_liboctave_error_handler) | |
| 504 ("column dimension mismatch for stack"); | |
| 505 return Matrix (); | |
| 506 } | |
| 507 | |
| 5275 | 508 octave_idx_type nr_insert = nr; |
| 458 | 509 Matrix retval (nr + a.rows (), nc); |
| 510 retval.insert (*this, 0, 0); | |
| 511 retval.insert (a, nr_insert, 0); | |
| 512 return retval; | |
| 513 } | |
| 514 | |
| 515 Matrix | |
| 516 Matrix::stack (const RowVector& a) const | |
| 517 { | |
| 5275 | 518 octave_idx_type nr = rows (); |
| 519 octave_idx_type nc = cols (); | |
| 458 | 520 if (nc != a.length ()) |
| 521 { | |
| 522 (*current_liboctave_error_handler) | |
| 523 ("column dimension mismatch for stack"); | |
| 524 return Matrix (); | |
| 525 } | |
| 526 | |
| 5275 | 527 octave_idx_type nr_insert = nr; |
| 458 | 528 Matrix retval (nr + 1, nc); |
| 529 retval.insert (*this, 0, 0); | |
| 530 retval.insert (a, nr_insert, 0); | |
| 531 return retval; | |
| 532 } | |
| 533 | |
| 534 Matrix | |
| 535 Matrix::stack (const ColumnVector& a) const | |
| 536 { | |
| 5275 | 537 octave_idx_type nr = rows (); |
| 538 octave_idx_type nc = cols (); | |
| 458 | 539 if (nc != 1) |
| 540 { | |
| 541 (*current_liboctave_error_handler) | |
| 542 ("column dimension mismatch for stack"); | |
| 543 return Matrix (); | |
| 544 } | |
| 545 | |
| 5275 | 546 octave_idx_type nr_insert = nr; |
| 458 | 547 Matrix retval (nr + a.length (), nc); |
| 548 retval.insert (*this, 0, 0); | |
| 549 retval.insert (a, nr_insert, 0); | |
| 550 return retval; | |
| 551 } | |
| 552 | |
| 553 Matrix | |
| 554 Matrix::stack (const DiagMatrix& a) const | |
| 555 { | |
| 5275 | 556 octave_idx_type nr = rows (); |
| 557 octave_idx_type nc = cols (); | |
| 458 | 558 if (nc != a.cols ()) |
| 559 { | |
| 560 (*current_liboctave_error_handler) | |
| 561 ("column dimension mismatch for stack"); | |
| 562 return Matrix (); | |
| 563 } | |
| 564 | |
| 5275 | 565 octave_idx_type nr_insert = nr; |
| 458 | 566 Matrix retval (nr + a.rows (), nc); |
| 567 retval.insert (*this, 0, 0); | |
| 568 retval.insert (a, nr_insert, 0); | |
| 569 return retval; | |
| 570 } | |
| 571 | |
| 572 Matrix | |
| 1205 | 573 real (const ComplexMatrix& a) |
| 574 { | |
| 5275 | 575 octave_idx_type a_len = a.length (); |
| 1205 | 576 Matrix retval; |
| 577 if (a_len > 0) | |
| 3769 | 578 retval = Matrix (mx_inline_real_dup (a.data (), a_len), |
| 579 a.rows (), a.cols ()); | |
| 1205 | 580 return retval; |
| 581 } | |
| 582 | |
| 583 Matrix | |
| 584 imag (const ComplexMatrix& a) | |
| 585 { | |
| 5275 | 586 octave_idx_type a_len = a.length (); |
| 1205 | 587 Matrix retval; |
| 588 if (a_len > 0) | |
| 3769 | 589 retval = Matrix (mx_inline_imag_dup (a.data (), a_len), |
| 590 a.rows (), a.cols ()); | |
| 1205 | 591 return retval; |
| 592 } | |
| 593 | |
| 594 Matrix | |
| 5275 | 595 Matrix::extract (octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) const |
| 458 | 596 { |
| 5275 | 597 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } |
| 598 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } | |
| 599 | |
| 600 octave_idx_type new_r = r2 - r1 + 1; | |
| 601 octave_idx_type new_c = c2 - c1 + 1; | |
| 458 | 602 |
| 603 Matrix result (new_r, new_c); | |
| 604 | |
| 5275 | 605 for (octave_idx_type j = 0; j < new_c; j++) |
| 606 for (octave_idx_type i = 0; i < new_r; i++) | |
| 4316 | 607 result.xelem (i, j) = elem (r1+i, c1+j); |
| 608 | |
| 609 return result; | |
| 610 } | |
| 611 | |
| 612 Matrix | |
| 5275 | 613 Matrix::extract_n (octave_idx_type r1, octave_idx_type c1, octave_idx_type nr, octave_idx_type nc) const |
| 4316 | 614 { |
| 615 Matrix result (nr, nc); | |
| 616 | |
| 5275 | 617 for (octave_idx_type j = 0; j < nc; j++) |
| 618 for (octave_idx_type i = 0; i < nr; i++) | |
| 4316 | 619 result.xelem (i, j) = elem (r1+i, c1+j); |
| 458 | 620 |
| 621 return result; | |
| 622 } | |
| 623 | |
| 624 // extract row or column i. | |
| 625 | |
| 626 RowVector | |
| 5275 | 627 Matrix::row (octave_idx_type i) const |
| 458 | 628 { |
| 5275 | 629 octave_idx_type nc = cols (); |
| 458 | 630 if (i < 0 || i >= rows ()) |
| 631 { | |
| 632 (*current_liboctave_error_handler) ("invalid row selection"); | |
| 633 return RowVector (); | |
| 634 } | |
| 635 | |
| 636 RowVector retval (nc); | |
| 5275 | 637 for (octave_idx_type j = 0; j < nc; j++) |
| 4316 | 638 retval.xelem (j) = elem (i, j); |
| 458 | 639 |
| 640 return retval; | |
| 641 } | |
| 642 | |
| 643 ColumnVector | |
| 5275 | 644 Matrix::column (octave_idx_type i) const |
| 458 | 645 { |
| 5275 | 646 octave_idx_type nr = rows (); |
| 458 | 647 if (i < 0 || i >= cols ()) |
| 648 { | |
| 649 (*current_liboctave_error_handler) ("invalid column selection"); | |
| 650 return ColumnVector (); | |
| 651 } | |
| 652 | |
| 653 ColumnVector retval (nr); | |
| 5275 | 654 for (octave_idx_type j = 0; j < nr; j++) |
| 4316 | 655 retval.xelem (j) = elem (j, i); |
| 458 | 656 |
| 657 return retval; | |
| 658 } | |
| 659 | |
| 660 Matrix | |
| 661 Matrix::inverse (void) const | |
| 662 { | |
| 5275 | 663 octave_idx_type info; |
| 7788 | 664 double rcon; |
| 6207 | 665 MatrixType mattype (*this); |
| 7788 | 666 return inverse (mattype, info, rcon, 0, 0); |
| 6207 | 667 } |
| 668 | |
| 669 Matrix | |
| 6479 | 670 Matrix::inverse (octave_idx_type& info) const |
| 671 { | |
| 7788 | 672 double rcon; |
| 6479 | 673 MatrixType mattype (*this); |
| 7788 | 674 return inverse (mattype, info, rcon, 0, 0); |
| 6479 | 675 } |
| 676 | |
| 677 Matrix | |
| 7788 | 678 Matrix::inverse (octave_idx_type& info, double& rcon, int force, |
| 6479 | 679 int calc_cond) const |
| 680 { | |
| 681 MatrixType mattype (*this); | |
| 7788 | 682 return inverse (mattype, info, rcon, force, calc_cond); |
| 6479 | 683 } |
| 684 | |
| 685 Matrix | |
| 6207 | 686 Matrix::inverse (MatrixType& mattype) const |
| 687 { | |
| 688 octave_idx_type info; | |
| 7788 | 689 double rcon; |
| 690 return inverse (mattype, info, rcon, 0, 0); | |
| 6207 | 691 } |
| 692 | |
| 693 Matrix | |
| 694 Matrix::inverse (MatrixType &mattype, octave_idx_type& info) const | |
| 695 { | |
| 7788 | 696 double rcon; |
| 697 return inverse (mattype, info, rcon, 0, 0); | |
| 458 | 698 } |
| 699 | |
| 700 Matrix | |
| 7788 | 701 Matrix::tinverse (MatrixType &mattype, octave_idx_type& info, double& rcon, |
| 6207 | 702 int force, int calc_cond) const |
| 458 | 703 { |
| 6207 | 704 Matrix retval; |
| 705 | |
| 706 octave_idx_type nr = rows (); | |
| 707 octave_idx_type nc = cols (); | |
| 708 | |
| 709 if (nr != nc || nr == 0 || nc == 0) | |
| 710 (*current_liboctave_error_handler) ("inverse requires square matrix"); | |
| 711 else | |
| 712 { | |
| 713 int typ = mattype.type (); | |
| 714 char uplo = (typ == MatrixType::Lower ? 'L' : 'U'); | |
| 715 char udiag = 'N'; | |
| 716 retval = *this; | |
| 717 double *tmp_data = retval.fortran_vec (); | |
| 718 | |
| 719 F77_XFCN (dtrtri, DTRTRI, (F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 720 F77_CONST_CHAR_ARG2 (&udiag, 1), | |
| 721 nr, tmp_data, nr, info | |
| 722 F77_CHAR_ARG_LEN (1) | |
| 723 F77_CHAR_ARG_LEN (1))); | |
| 724 | |
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725 // Throw-away extra info LAPACK gives so as to not change output. |
| 7788 | 726 rcon = 0.0; |
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727 if (info != 0) |
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728 info = -1; |
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729 else if (calc_cond) |
| 6207 | 730 { |
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731 octave_idx_type dtrcon_info = 0; |
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732 char job = '1'; |
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733 |
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734 OCTAVE_LOCAL_BUFFER (double, work, 3 * nr); |
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735 OCTAVE_LOCAL_BUFFER (octave_idx_type, iwork, nr); |
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736 |
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737 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&job, 1), |
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738 F77_CONST_CHAR_ARG2 (&uplo, 1), |
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739 F77_CONST_CHAR_ARG2 (&udiag, 1), |
| 7788 | 740 nr, tmp_data, nr, rcon, |
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741 work, iwork, dtrcon_info |
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742 F77_CHAR_ARG_LEN (1) |
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743 F77_CHAR_ARG_LEN (1) |
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744 F77_CHAR_ARG_LEN (1))); |
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745 |
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746 if (dtrcon_info != 0) |
| 6207 | 747 info = -1; |
| 748 } | |
| 749 | |
| 750 if (info == -1 && ! force) | |
| 751 retval = *this; // Restore matrix contents. | |
| 752 } | |
| 753 | |
| 754 return retval; | |
| 458 | 755 } |
| 756 | |
| 6207 | 757 |
| 458 | 758 Matrix |
| 7788 | 759 Matrix::finverse (MatrixType &mattype, octave_idx_type& info, double& rcon, |
| 6207 | 760 int force, int calc_cond) const |
| 458 | 761 { |
| 1948 | 762 Matrix retval; |
| 763 | |
| 5275 | 764 octave_idx_type nr = rows (); |
| 765 octave_idx_type nc = cols (); | |
| 1948 | 766 |
| 458 | 767 if (nr != nc || nr == 0 || nc == 0) |
| 1948 | 768 (*current_liboctave_error_handler) ("inverse requires square matrix"); |
| 458 | 769 else |
| 770 { | |
| 5275 | 771 Array<octave_idx_type> ipvt (nr); |
| 772 octave_idx_type *pipvt = ipvt.fortran_vec (); | |
| 1948 | 773 |
| 774 retval = *this; | |
| 775 double *tmp_data = retval.fortran_vec (); | |
| 776 | |
| 4329 | 777 Array<double> z(1); |
| 5275 | 778 octave_idx_type lwork = -1; |
| 4329 | 779 |
| 4330 | 780 // Query the optimum work array size. |
| 4329 | 781 F77_XFCN (dgetri, DGETRI, (nc, tmp_data, nr, pipvt, |
| 782 z.fortran_vec (), lwork, info)); | |
| 783 | |
| 5275 | 784 lwork = static_cast<octave_idx_type> (z(0)); |
| 4329 | 785 lwork = (lwork < 2 *nc ? 2*nc : lwork); |
| 786 z.resize (lwork); | |
| 787 double *pz = z.fortran_vec (); | |
| 788 | |
| 789 info = 0; | |
| 790 | |
| 4330 | 791 // Calculate the norm of the matrix, for later use. |
| 4329 | 792 double anorm = 0; |
| 793 if (calc_cond) | |
| 5275 | 794 anorm = retval.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
| 4329 | 795 |
| 796 F77_XFCN (dgetrf, DGETRF, (nc, nc, tmp_data, nr, pipvt, info)); | |
| 1948 | 797 |
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798 // Throw-away extra info LAPACK gives so as to not change output. |
| 7788 | 799 rcon = 0.0; |
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800 if (info != 0) |
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801 info = -1; |
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802 else if (calc_cond) |
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803 { |
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804 octave_idx_type dgecon_info = 0; |
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805 |
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806 // Now calculate the condition number for non-singular matrix. |
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807 char job = '1'; |
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808 Array<octave_idx_type> iz (nc); |
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809 octave_idx_type *piz = iz.fortran_vec (); |
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810 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
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811 nc, tmp_data, nr, anorm, |
| 7788 | 812 rcon, pz, piz, dgecon_info |
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813 F77_CHAR_ARG_LEN (1))); |
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814 |
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815 if (dgecon_info != 0) |
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816 info = -1; |
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817 } |
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818 |
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819 if (info == -1 && ! force) |
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820 retval = *this; // Restore matrix contents. |
| 1948 | 821 else |
| 822 { | |
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823 octave_idx_type dgetri_info = 0; |
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824 |
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825 F77_XFCN (dgetri, DGETRI, (nc, tmp_data, nr, pipvt, |
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826 pz, lwork, dgetri_info)); |
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827 |
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828 if (dgetri_info != 0) |
| 1948 | 829 info = -1; |
| 830 } | |
| 6207 | 831 |
| 832 if (info != 0) | |
| 833 mattype.mark_as_rectangular(); | |
| 458 | 834 } |
| 835 | |
| 1948 | 836 return retval; |
| 458 | 837 } |
| 838 | |
| 740 | 839 Matrix |
| 7788 | 840 Matrix::inverse (MatrixType &mattype, octave_idx_type& info, double& rcon, |
| 6207 | 841 int force, int calc_cond) const |
| 842 { | |
| 843 int typ = mattype.type (false); | |
| 844 Matrix ret; | |
| 845 | |
| 846 if (typ == MatrixType::Unknown) | |
| 847 typ = mattype.type (*this); | |
| 848 | |
| 849 if (typ == MatrixType::Upper || typ == MatrixType::Lower) | |
| 7788 | 850 ret = tinverse (mattype, info, rcon, force, calc_cond); |
| 6840 | 851 else |
| 6207 | 852 { |
| 853 if (mattype.is_hermitian ()) | |
| 854 { | |
| 6486 | 855 CHOL chol (*this, info, calc_cond); |
| 6207 | 856 if (info == 0) |
| 6486 | 857 { |
| 858 if (calc_cond) | |
| 7788 | 859 rcon = chol.rcond (); |
| 6486 | 860 else |
| 7788 | 861 rcon = 1.0; |
| 6486 | 862 ret = chol.inverse (); |
| 863 } | |
| 6207 | 864 else |
| 865 mattype.mark_as_unsymmetric (); | |
| 866 } | |
| 867 | |
| 868 if (!mattype.is_hermitian ()) | |
| 7788 | 869 ret = finverse(mattype, info, rcon, force, calc_cond); |
| 870 | |
| 871 if ((mattype.is_hermitian () || calc_cond) && rcon == 0.) | |
| 6840 | 872 ret = Matrix (rows (), columns (), octave_Inf); |
| 6207 | 873 } |
| 874 | |
| 875 return ret; | |
| 876 } | |
| 877 | |
| 878 Matrix | |
| 4384 | 879 Matrix::pseudo_inverse (double tol) const |
| 740 | 880 { |
| 3480 | 881 SVD result (*this, SVD::economy); |
| 740 | 882 |
| 883 DiagMatrix S = result.singular_values (); | |
| 884 Matrix U = result.left_singular_matrix (); | |
| 885 Matrix V = result.right_singular_matrix (); | |
| 886 | |
| 887 ColumnVector sigma = S.diag (); | |
| 888 | |
| 5275 | 889 octave_idx_type r = sigma.length () - 1; |
| 890 octave_idx_type nr = rows (); | |
| 891 octave_idx_type nc = cols (); | |
| 740 | 892 |
| 893 if (tol <= 0.0) | |
| 894 { | |
| 895 if (nr > nc) | |
| 896 tol = nr * sigma.elem (0) * DBL_EPSILON; | |
| 897 else | |
| 898 tol = nc * sigma.elem (0) * DBL_EPSILON; | |
| 899 } | |
| 900 | |
| 901 while (r >= 0 && sigma.elem (r) < tol) | |
| 902 r--; | |
| 903 | |
| 904 if (r < 0) | |
| 905 return Matrix (nc, nr, 0.0); | |
| 906 else | |
| 907 { | |
| 908 Matrix Ur = U.extract (0, 0, nr-1, r); | |
| 909 DiagMatrix D = DiagMatrix (sigma.extract (0, r)) . inverse (); | |
| 910 Matrix Vr = V.extract (0, 0, nc-1, r); | |
| 911 return Vr * D * Ur.transpose (); | |
| 912 } | |
| 913 } | |
| 914 | |
| 4773 | 915 #if defined (HAVE_FFTW3) |
| 3827 | 916 |
| 917 ComplexMatrix | |
| 918 Matrix::fourier (void) const | |
| 919 { | |
| 920 size_t nr = rows (); | |
| 921 size_t nc = cols (); | |
| 922 | |
| 923 ComplexMatrix retval (nr, nc); | |
| 924 | |
| 925 size_t npts, nsamples; | |
| 926 | |
| 927 if (nr == 1 || nc == 1) | |
| 928 { | |
| 929 npts = nr > nc ? nr : nc; | |
| 930 nsamples = 1; | |
| 931 } | |
| 932 else | |
| 933 { | |
| 934 npts = nr; | |
| 935 nsamples = nc; | |
| 936 } | |
| 937 | |
| 4773 | 938 const double *in (fortran_vec ()); |
| 3827 | 939 Complex *out (retval.fortran_vec ()); |
| 940 | |
| 4773 | 941 octave_fftw::fft (in, out, npts, nsamples); |
| 3827 | 942 |
| 943 return retval; | |
| 944 } | |
| 945 | |
| 946 ComplexMatrix | |
| 947 Matrix::ifourier (void) const | |
| 948 { | |
| 949 size_t nr = rows (); | |
| 950 size_t nc = cols (); | |
| 951 | |
| 952 ComplexMatrix retval (nr, nc); | |
| 953 | |
| 954 size_t npts, nsamples; | |
| 955 | |
| 956 if (nr == 1 || nc == 1) | |
| 957 { | |
| 958 npts = nr > nc ? nr : nc; | |
| 959 nsamples = 1; | |
| 960 } | |
| 961 else | |
| 962 { | |
| 963 npts = nr; | |
| 964 nsamples = nc; | |
| 965 } | |
| 966 | |
| 967 ComplexMatrix tmp (*this); | |
| 968 Complex *in (tmp.fortran_vec ()); | |
| 969 Complex *out (retval.fortran_vec ()); | |
| 970 | |
| 4773 | 971 octave_fftw::ifft (in, out, npts, nsamples); |
| 3827 | 972 |
| 973 return retval; | |
| 974 } | |
| 975 | |
| 976 ComplexMatrix | |
| 977 Matrix::fourier2d (void) const | |
| 978 { | |
| 4773 | 979 dim_vector dv(rows (), cols ()); |
| 980 | |
| 981 const double *in = fortran_vec (); | |
| 982 ComplexMatrix retval (rows (), cols ()); | |
| 983 octave_fftw::fftNd (in, retval.fortran_vec (), 2, dv); | |
| 3827 | 984 |
| 985 return retval; | |
| 986 } | |
| 987 | |
| 988 ComplexMatrix | |
| 989 Matrix::ifourier2d (void) const | |
| 990 { | |
| 4773 | 991 dim_vector dv(rows (), cols ()); |
| 3827 | 992 |
| 993 ComplexMatrix retval (*this); | |
| 4773 | 994 Complex *out (retval.fortran_vec ()); |
| 995 | |
| 996 octave_fftw::ifftNd (out, out, 2, dv); | |
| 3827 | 997 |
| 998 return retval; | |
| 999 } | |
| 1000 | |
| 1001 #else | |
| 1002 | |
| 458 | 1003 ComplexMatrix |
| 1004 Matrix::fourier (void) const | |
| 1005 { | |
| 1948 | 1006 ComplexMatrix retval; |
| 1007 | |
| 5275 | 1008 octave_idx_type nr = rows (); |
| 1009 octave_idx_type nc = cols (); | |
| 1010 | |
| 1011 octave_idx_type npts, nsamples; | |
| 1948 | 1012 |
| 458 | 1013 if (nr == 1 || nc == 1) |
| 1014 { | |
| 1015 npts = nr > nc ? nr : nc; | |
| 1016 nsamples = 1; | |
| 1017 } | |
| 1018 else | |
| 1019 { | |
| 1020 npts = nr; | |
| 1021 nsamples = nc; | |
| 1022 } | |
| 1023 | |
| 5275 | 1024 octave_idx_type nn = 4*npts+15; |
| 1948 | 1025 |
| 1026 Array<Complex> wsave (nn); | |
| 1027 Complex *pwsave = wsave.fortran_vec (); | |
| 1028 | |
| 3585 | 1029 retval = ComplexMatrix (*this); |
| 1948 | 1030 Complex *tmp_data = retval.fortran_vec (); |
| 1031 | |
|
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1032 F77_FUNC (zffti, ZFFTI) (npts, pwsave); |
| 458 | 1033 |
| 5275 | 1034 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1035 { |
| 1036 OCTAVE_QUIT; | |
| 1037 | |
|
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1038 F77_FUNC (zfftf, ZFFTF) (npts, &tmp_data[npts*j], pwsave); |
| 4153 | 1039 } |
| 1948 | 1040 |
| 1041 return retval; | |
| 458 | 1042 } |
| 1043 | |
| 1044 ComplexMatrix | |
| 1045 Matrix::ifourier (void) const | |
| 1046 { | |
| 1948 | 1047 ComplexMatrix retval; |
| 1048 | |
| 5275 | 1049 octave_idx_type nr = rows (); |
| 1050 octave_idx_type nc = cols (); | |
| 1051 | |
| 1052 octave_idx_type npts, nsamples; | |
| 1948 | 1053 |
| 458 | 1054 if (nr == 1 || nc == 1) |
| 1055 { | |
| 1056 npts = nr > nc ? nr : nc; | |
| 1057 nsamples = 1; | |
| 1058 } | |
| 1059 else | |
| 1060 { | |
| 1061 npts = nr; | |
| 1062 nsamples = nc; | |
| 1063 } | |
| 1064 | |
| 5275 | 1065 octave_idx_type nn = 4*npts+15; |
| 1948 | 1066 |
| 1067 Array<Complex> wsave (nn); | |
| 1068 Complex *pwsave = wsave.fortran_vec (); | |
| 1069 | |
| 3585 | 1070 retval = ComplexMatrix (*this); |
| 1948 | 1071 Complex *tmp_data = retval.fortran_vec (); |
| 1072 | |
|
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1073 F77_FUNC (zffti, ZFFTI) (npts, pwsave); |
| 458 | 1074 |
| 5275 | 1075 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1076 { |
| 1077 OCTAVE_QUIT; | |
| 1078 | |
|
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|
1079 F77_FUNC (zfftb, ZFFTB) (npts, &tmp_data[npts*j], pwsave); |
| 4153 | 1080 } |
| 458 | 1081 |
| 5275 | 1082 for (octave_idx_type j = 0; j < npts*nsamples; j++) |
| 3572 | 1083 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
| 458 | 1084 |
| 1948 | 1085 return retval; |
| 458 | 1086 } |
| 1087 | |
| 677 | 1088 ComplexMatrix |
| 1089 Matrix::fourier2d (void) const | |
| 1090 { | |
| 1948 | 1091 ComplexMatrix retval; |
| 1092 | |
| 5275 | 1093 octave_idx_type nr = rows (); |
| 1094 octave_idx_type nc = cols (); | |
| 1095 | |
| 1096 octave_idx_type npts, nsamples; | |
| 1948 | 1097 |
| 677 | 1098 if (nr == 1 || nc == 1) |
| 1099 { | |
| 1100 npts = nr > nc ? nr : nc; | |
| 1101 nsamples = 1; | |
| 1102 } | |
| 1103 else | |
| 1104 { | |
| 1105 npts = nr; | |
| 1106 nsamples = nc; | |
| 1107 } | |
| 1108 | |
| 5275 | 1109 octave_idx_type nn = 4*npts+15; |
| 1948 | 1110 |
| 1111 Array<Complex> wsave (nn); | |
| 1112 Complex *pwsave = wsave.fortran_vec (); | |
| 1113 | |
| 3585 | 1114 retval = ComplexMatrix (*this); |
| 1948 | 1115 Complex *tmp_data = retval.fortran_vec (); |
| 1116 | |
|
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|
1117 F77_FUNC (zffti, ZFFTI) (npts, pwsave); |
| 677 | 1118 |
| 5275 | 1119 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1120 { |
| 1121 OCTAVE_QUIT; | |
| 1122 | |
|
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|
1123 F77_FUNC (zfftf, ZFFTF) (npts, &tmp_data[npts*j], pwsave); |
| 4153 | 1124 } |
| 677 | 1125 |
| 1126 npts = nc; | |
| 1127 nsamples = nr; | |
| 1128 nn = 4*npts+15; | |
| 1948 | 1129 |
| 1130 wsave.resize (nn); | |
| 1131 pwsave = wsave.fortran_vec (); | |
| 1132 | |
| 4773 | 1133 Array<Complex> tmp (npts); |
| 1134 Complex *prow = tmp.fortran_vec (); | |
| 1948 | 1135 |
|
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|
1136 F77_FUNC (zffti, ZFFTI) (npts, pwsave); |
| 677 | 1137 |
| 5275 | 1138 for (octave_idx_type j = 0; j < nsamples; j++) |
| 677 | 1139 { |
| 4153 | 1140 OCTAVE_QUIT; |
| 1141 | |
| 5275 | 1142 for (octave_idx_type i = 0; i < npts; i++) |
| 1948 | 1143 prow[i] = tmp_data[i*nr + j]; |
| 1144 | |
|
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|
1145 F77_FUNC (zfftf, ZFFTF) (npts, prow, pwsave); |
| 677 | 1146 |
| 5275 | 1147 for (octave_idx_type i = 0; i < npts; i++) |
| 1948 | 1148 tmp_data[i*nr + j] = prow[i]; |
| 677 | 1149 } |
| 1150 | |
| 1948 | 1151 return retval; |
| 677 | 1152 } |
| 1153 | |
| 1154 ComplexMatrix | |
| 1155 Matrix::ifourier2d (void) const | |
| 1156 { | |
| 1948 | 1157 ComplexMatrix retval; |
| 1158 | |
| 5275 | 1159 octave_idx_type nr = rows (); |
| 1160 octave_idx_type nc = cols (); | |
| 1161 | |
| 1162 octave_idx_type npts, nsamples; | |
| 1948 | 1163 |
| 677 | 1164 if (nr == 1 || nc == 1) |
| 1165 { | |
| 1166 npts = nr > nc ? nr : nc; | |
| 1167 nsamples = 1; | |
| 1168 } | |
| 1169 else | |
| 1170 { | |
| 1171 npts = nr; | |
| 1172 nsamples = nc; | |
| 1173 } | |
| 1174 | |
| 5275 | 1175 octave_idx_type nn = 4*npts+15; |
| 1948 | 1176 |
| 1177 Array<Complex> wsave (nn); | |
| 1178 Complex *pwsave = wsave.fortran_vec (); | |
| 1179 | |
| 3585 | 1180 retval = ComplexMatrix (*this); |
| 1948 | 1181 Complex *tmp_data = retval.fortran_vec (); |
| 1182 | |
|
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|
1183 F77_FUNC (zffti, ZFFTI) (npts, pwsave); |
| 677 | 1184 |
| 5275 | 1185 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1186 { |
| 1187 OCTAVE_QUIT; | |
| 1188 | |
|
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|
1189 F77_FUNC (zfftb, ZFFTB) (npts, &tmp_data[npts*j], pwsave); |
| 4153 | 1190 } |
| 677 | 1191 |
| 5275 | 1192 for (octave_idx_type j = 0; j < npts*nsamples; j++) |
| 3572 | 1193 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
| 677 | 1194 |
| 1195 npts = nc; | |
| 1196 nsamples = nr; | |
| 1197 nn = 4*npts+15; | |
| 1948 | 1198 |
| 1199 wsave.resize (nn); | |
| 1200 pwsave = wsave.fortran_vec (); | |
| 1201 | |
| 4773 | 1202 Array<Complex> tmp (npts); |
| 1203 Complex *prow = tmp.fortran_vec (); | |
| 1948 | 1204 |
|
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|
1205 F77_FUNC (zffti, ZFFTI) (npts, pwsave); |
| 677 | 1206 |
| 5275 | 1207 for (octave_idx_type j = 0; j < nsamples; j++) |
| 677 | 1208 { |
| 4153 | 1209 OCTAVE_QUIT; |
| 1210 | |
| 5275 | 1211 for (octave_idx_type i = 0; i < npts; i++) |
| 1948 | 1212 prow[i] = tmp_data[i*nr + j]; |
| 1213 | |
|
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|
1214 F77_FUNC (zfftb, ZFFTB) (npts, prow, pwsave); |
| 677 | 1215 |
| 5275 | 1216 for (octave_idx_type i = 0; i < npts; i++) |
| 3572 | 1217 tmp_data[i*nr + j] = prow[i] / static_cast<double> (npts); |
| 677 | 1218 } |
| 1219 | |
| 1948 | 1220 return retval; |
| 677 | 1221 } |
| 1222 | |
| 3827 | 1223 #endif |
| 1224 | |
| 458 | 1225 DET |
| 1226 Matrix::determinant (void) const | |
| 1227 { | |
| 5275 | 1228 octave_idx_type info; |
| 7788 | 1229 double rcon; |
| 1230 return determinant (info, rcon, 0); | |
| 458 | 1231 } |
| 1232 | |
| 1233 DET | |
| 5275 | 1234 Matrix::determinant (octave_idx_type& info) const |
| 458 | 1235 { |
| 7788 | 1236 double rcon; |
| 1237 return determinant (info, rcon, 0); | |
| 458 | 1238 } |
| 1239 | |
| 1240 DET | |
| 7788 | 1241 Matrix::determinant (octave_idx_type& info, double& rcon, int calc_cond) const |
| 458 | 1242 { |
| 1243 DET retval; | |
| 1244 | |
| 5275 | 1245 octave_idx_type nr = rows (); |
| 1246 octave_idx_type nc = cols (); | |
| 458 | 1247 |
| 1248 if (nr == 0 || nc == 0) | |
| 1249 { | |
| 5634 | 1250 retval = DET (1.0, 0); |
| 458 | 1251 } |
| 1252 else | |
| 1253 { | |
| 5275 | 1254 Array<octave_idx_type> ipvt (nr); |
| 1255 octave_idx_type *pipvt = ipvt.fortran_vec (); | |
| 1948 | 1256 |
| 1257 Matrix atmp = *this; | |
| 1258 double *tmp_data = atmp.fortran_vec (); | |
| 1259 | |
| 4329 | 1260 info = 0; |
| 1261 | |
| 4330 | 1262 // Calculate the norm of the matrix, for later use. |
| 4329 | 1263 double anorm = 0; |
| 1264 if (calc_cond) | |
| 5275 | 1265 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
| 4329 | 1266 |
| 1267 F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); | |
| 1948 | 1268 |
|
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|
1269 // Throw-away extra info LAPACK gives so as to not change output. |
| 7788 | 1270 rcon = 0.0; |
|
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|
1271 if (info != 0) |
|
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|
1272 { |
|
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|
1273 info = -1; |
|
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1274 retval = DET (); |
|
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|
1275 } |
|
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|
1276 else |
| 458 | 1277 { |
|
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|
1278 if (calc_cond) |
|
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|
1279 { |
|
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1280 // Now calc the condition number for non-singular matrix. |
|
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1281 char job = '1'; |
|
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1282 Array<double> z (4 * nc); |
|
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1283 double *pz = z.fortran_vec (); |
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|
1284 Array<octave_idx_type> iz (nc); |
|
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1285 octave_idx_type *piz = iz.fortran_vec (); |
|
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|
1286 |
|
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|
1287 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
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|
1288 nc, tmp_data, nr, anorm, |
| 7788 | 1289 rcon, pz, piz, info |
|
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1290 F77_CHAR_ARG_LEN (1))); |
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|
1291 } |
|
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|
1292 |
| 4509 | 1293 if (info != 0) |
| 1948 | 1294 { |
| 4509 | 1295 info = -1; |
| 1296 retval = DET (); | |
| 4329 | 1297 } |
| 1298 else | |
| 1948 | 1299 { |
| 8335 | 1300 retval = DET (1.0); |
| 1301 | |
|
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|
1302 for (octave_idx_type i = 0; i < nc; i++) |
| 4329 | 1303 { |
| 8335 | 1304 double c = atmp(i,i); |
| 1305 retval *= (ipvt(i) != (i+1)) ? -c : c; | |
| 1306 } | |
| 1948 | 1307 } |
| 458 | 1308 } |
| 1309 } | |
| 1310 | |
| 1311 return retval; | |
| 1312 } | |
| 1313 | |
| 7788 | 1314 double |
| 1315 Matrix::rcond (void) const | |
| 1316 { | |
| 1317 MatrixType mattype (*this); | |
| 1318 return rcond (mattype); | |
| 1319 } | |
| 1320 | |
| 1321 double | |
| 1322 Matrix::rcond (MatrixType &mattype) const | |
| 1323 { | |
| 1324 double rcon; | |
| 1325 octave_idx_type nr = rows (); | |
| 1326 octave_idx_type nc = cols (); | |
| 1327 | |
| 1328 if (nr != nc) | |
| 1329 (*current_liboctave_error_handler) ("matrix must be square"); | |
| 1330 else if (nr == 0 || nc == 0) | |
| 1331 rcon = octave_Inf; | |
| 1332 else | |
| 1333 { | |
| 1334 int typ = mattype.type (); | |
| 1335 | |
| 1336 if (typ == MatrixType::Unknown) | |
| 1337 typ = mattype.type (*this); | |
| 1338 | |
| 1339 // Only calculate the condition number for LU/Cholesky | |
| 1340 if (typ == MatrixType::Upper) | |
| 1341 { | |
| 1342 const double *tmp_data = fortran_vec (); | |
| 1343 octave_idx_type info = 0; | |
| 1344 char norm = '1'; | |
| 1345 char uplo = 'U'; | |
| 1346 char dia = 'N'; | |
| 1347 | |
| 1348 Array<double> z (3 * nc); | |
| 1349 double *pz = z.fortran_vec (); | |
| 1350 Array<octave_idx_type> iz (nc); | |
| 1351 octave_idx_type *piz = iz.fortran_vec (); | |
| 1352 | |
| 1353 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1354 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1355 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1356 nr, tmp_data, nr, rcon, | |
| 1357 pz, piz, info | |
| 1358 F77_CHAR_ARG_LEN (1) | |
| 1359 F77_CHAR_ARG_LEN (1) | |
| 1360 F77_CHAR_ARG_LEN (1))); | |
| 1361 | |
| 1362 if (info != 0) | |
| 1363 rcon = 0.0; | |
| 1364 } | |
| 1365 else if (typ == MatrixType::Permuted_Upper) | |
| 1366 (*current_liboctave_error_handler) | |
| 1367 ("permuted triangular matrix not implemented"); | |
| 1368 else if (typ == MatrixType::Lower) | |
| 1369 { | |
| 1370 const double *tmp_data = fortran_vec (); | |
| 1371 octave_idx_type info = 0; | |
| 1372 char norm = '1'; | |
| 1373 char uplo = 'L'; | |
| 1374 char dia = 'N'; | |
| 1375 | |
| 1376 Array<double> z (3 * nc); | |
| 1377 double *pz = z.fortran_vec (); | |
| 1378 Array<octave_idx_type> iz (nc); | |
| 1379 octave_idx_type *piz = iz.fortran_vec (); | |
| 1380 | |
| 1381 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1382 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1383 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1384 nr, tmp_data, nr, rcon, | |
| 1385 pz, piz, info | |
| 1386 F77_CHAR_ARG_LEN (1) | |
| 1387 F77_CHAR_ARG_LEN (1) | |
| 1388 F77_CHAR_ARG_LEN (1))); | |
| 1389 | |
| 1390 if (info != 0) | |
| 1391 rcon = 0.0; | |
| 1392 } | |
| 1393 else if (typ == MatrixType::Permuted_Lower) | |
| 1394 (*current_liboctave_error_handler) | |
| 1395 ("permuted triangular matrix not implemented"); | |
| 1396 else if (typ == MatrixType::Full || typ == MatrixType::Hermitian) | |
| 1397 { | |
| 1398 double anorm = -1.0; | |
| 1399 Matrix atmp = *this; | |
| 1400 double *tmp_data = atmp.fortran_vec (); | |
| 1401 | |
| 1402 if (typ == MatrixType::Hermitian) | |
| 1403 { | |
| 1404 octave_idx_type info = 0; | |
| 1405 char job = 'L'; | |
| 1406 anorm = atmp.abs().sum(). | |
| 1407 row(static_cast<octave_idx_type>(0)).max(); | |
| 1408 | |
| 1409 F77_XFCN (dpotrf, DPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, | |
| 1410 tmp_data, nr, info | |
| 1411 F77_CHAR_ARG_LEN (1))); | |
| 1412 | |
| 1413 if (info != 0) | |
| 1414 { | |
| 1415 rcon = 0.0; | |
| 1416 mattype.mark_as_unsymmetric (); | |
| 1417 typ = MatrixType::Full; | |
| 1418 } | |
| 1419 else | |
| 1420 { | |
| 1421 Array<double> z (3 * nc); | |
| 1422 double *pz = z.fortran_vec (); | |
| 1423 Array<octave_idx_type> iz (nc); | |
| 1424 octave_idx_type *piz = iz.fortran_vec (); | |
| 1425 | |
| 1426 F77_XFCN (dpocon, DPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), | |
| 1427 nr, tmp_data, nr, anorm, | |
| 1428 rcon, pz, piz, info | |
| 1429 F77_CHAR_ARG_LEN (1))); | |
| 1430 | |
| 1431 if (info != 0) | |
| 1432 rcon = 0.0; | |
| 1433 } | |
| 1434 } | |
| 1435 | |
| 1436 if (typ == MatrixType::Full) | |
| 1437 { | |
| 1438 octave_idx_type info = 0; | |
| 1439 | |
| 1440 Array<octave_idx_type> ipvt (nr); | |
| 1441 octave_idx_type *pipvt = ipvt.fortran_vec (); | |
| 1442 | |
| 1443 if(anorm < 0.) | |
| 1444 anorm = atmp.abs().sum(). | |
| 1445 row(static_cast<octave_idx_type>(0)).max(); | |
| 1446 | |
| 1447 Array<double> z (4 * nc); | |
| 1448 double *pz = z.fortran_vec (); | |
| 1449 Array<octave_idx_type> iz (nc); | |
| 1450 octave_idx_type *piz = iz.fortran_vec (); | |
| 1451 | |
| 1452 F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); | |
| 1453 | |
| 1454 if (info != 0) | |
| 1455 { | |
| 1456 rcon = 0.0; | |
| 1457 mattype.mark_as_rectangular (); | |
| 1458 } | |
| 1459 else | |
| 1460 { | |
| 1461 char job = '1'; | |
| 1462 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), | |
| 1463 nc, tmp_data, nr, anorm, | |
| 1464 rcon, pz, piz, info | |
| 1465 F77_CHAR_ARG_LEN (1))); | |
| 1466 | |
| 1467 if (info != 0) | |
| 1468 rcon = 0.0; | |
| 1469 } | |
| 1470 } | |
| 1471 } | |
| 1472 else | |
| 1473 rcon = 0.0; | |
| 1474 } | |
| 1475 | |
| 1476 return rcon; | |
| 1477 } | |
| 1478 | |
| 458 | 1479 Matrix |
| 5785 | 1480 Matrix::utsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, |
| 7788 | 1481 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 1482 bool calc_cond) const |
| 1483 { | |
| 1484 Matrix retval; | |
| 1485 | |
| 1486 octave_idx_type nr = rows (); | |
| 1487 octave_idx_type nc = cols (); | |
| 1488 | |
| 6924 | 1489 if (nr != b.rows ()) |
| 5785 | 1490 (*current_liboctave_error_handler) |
| 1491 ("matrix dimension mismatch solution of linear equations"); | |
| 6924 | 1492 else if (nr == 0 || nc == 0 || b.cols () == 0) |
| 1493 retval = Matrix (nc, b.cols (), 0.0); | |
| 5785 | 1494 else |
| 1495 { | |
| 1496 volatile int typ = mattype.type (); | |
| 1497 | |
| 1498 if (typ == MatrixType::Permuted_Upper || | |
| 1499 typ == MatrixType::Upper) | |
| 1500 { | |
| 1501 octave_idx_type b_nc = b.cols (); | |
| 7788 | 1502 rcon = 1.; |
| 5785 | 1503 info = 0; |
| 1504 | |
| 1505 if (typ == MatrixType::Permuted_Upper) | |
| 1506 { | |
| 1507 (*current_liboctave_error_handler) | |
| 6390 | 1508 ("permuted triangular matrix not implemented"); |
| 5785 | 1509 } |
| 1510 else | |
| 1511 { | |
| 1512 const double *tmp_data = fortran_vec (); | |
| 1513 | |
| 1514 if (calc_cond) | |
| 1515 { | |
| 1516 char norm = '1'; | |
| 1517 char uplo = 'U'; | |
| 1518 char dia = 'N'; | |
| 1519 | |
| 1520 Array<double> z (3 * nc); | |
| 1521 double *pz = z.fortran_vec (); | |
| 1522 Array<octave_idx_type> iz (nc); | |
| 1523 octave_idx_type *piz = iz.fortran_vec (); | |
| 1524 | |
| 1525 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1526 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1527 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 7788 | 1528 nr, tmp_data, nr, rcon, |
| 5785 | 1529 pz, piz, info |
| 1530 F77_CHAR_ARG_LEN (1) | |
| 1531 F77_CHAR_ARG_LEN (1) | |
| 1532 F77_CHAR_ARG_LEN (1))); | |
| 1533 | |
| 1534 if (info != 0) | |
| 1535 info = -2; | |
| 1536 | |
| 7788 | 1537 volatile double rcond_plus_one = rcon + 1.0; |
| 1538 | |
| 1539 if (rcond_plus_one == 1.0 || xisnan (rcon)) | |
| 5785 | 1540 { |
| 1541 info = -2; | |
| 1542 | |
| 1543 if (sing_handler) | |
| 7788 | 1544 sing_handler (rcon); |
| 5785 | 1545 else |
| 1546 (*current_liboctave_error_handler) | |
| 1547 ("matrix singular to machine precision, rcond = %g", | |
| 7788 | 1548 rcon); |
| 5785 | 1549 } |
| 1550 } | |
| 1551 | |
| 1552 if (info == 0) | |
| 1553 { | |
| 1554 retval = b; | |
| 1555 double *result = retval.fortran_vec (); | |
| 1556 | |
| 1557 char uplo = 'U'; | |
| 1558 char trans = 'N'; | |
| 1559 char dia = 'N'; | |
| 1560 | |
| 1561 F77_XFCN (dtrtrs, DTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1562 F77_CONST_CHAR_ARG2 (&trans, 1), | |
| 1563 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1564 nr, b_nc, tmp_data, nr, | |
| 1565 result, nr, info | |
| 1566 F77_CHAR_ARG_LEN (1) | |
| 1567 F77_CHAR_ARG_LEN (1) | |
| 1568 F77_CHAR_ARG_LEN (1))); | |
| 1569 } | |
| 1570 } | |
| 1571 } | |
| 1572 else | |
| 1573 (*current_liboctave_error_handler) ("incorrect matrix type"); | |
| 1574 } | |
| 1575 | |
| 1576 return retval; | |
| 1577 } | |
| 1578 | |
| 1579 Matrix | |
| 1580 Matrix::ltsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, | |
| 7788 | 1581 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 1582 bool calc_cond) const |
| 1583 { | |
| 1584 Matrix retval; | |
| 1585 | |
| 1586 octave_idx_type nr = rows (); | |
| 1587 octave_idx_type nc = cols (); | |
| 1588 | |
| 6924 | 1589 if (nr != b.rows ()) |
| 5785 | 1590 (*current_liboctave_error_handler) |
| 1591 ("matrix dimension mismatch solution of linear equations"); | |
| 6924 | 1592 else if (nr == 0 || nc == 0 || b.cols () == 0) |
| 1593 retval = Matrix (nc, b.cols (), 0.0); | |
| 5785 | 1594 else |
| 1595 { | |
| 1596 volatile int typ = mattype.type (); | |
| 1597 | |
| 1598 if (typ == MatrixType::Permuted_Lower || | |
| 1599 typ == MatrixType::Lower) | |
| 1600 { | |
| 1601 octave_idx_type b_nc = b.cols (); | |
| 7788 | 1602 rcon = 1.; |
| 5785 | 1603 info = 0; |
| 1604 | |
| 1605 if (typ == MatrixType::Permuted_Lower) | |
| 1606 { | |
| 1607 (*current_liboctave_error_handler) | |
| 6390 | 1608 ("permuted triangular matrix not implemented"); |
| 5785 | 1609 } |
| 1610 else | |
| 1611 { | |
| 1612 const double *tmp_data = fortran_vec (); | |
| 1613 | |
| 1614 if (calc_cond) | |
| 1615 { | |
| 1616 char norm = '1'; | |
| 1617 char uplo = 'L'; | |
| 1618 char dia = 'N'; | |
| 1619 | |
| 1620 Array<double> z (3 * nc); | |
| 1621 double *pz = z.fortran_vec (); | |
| 1622 Array<octave_idx_type> iz (nc); | |
| 1623 octave_idx_type *piz = iz.fortran_vec (); | |
| 1624 | |
| 1625 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1626 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1627 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 7788 | 1628 nr, tmp_data, nr, rcon, |
| 5785 | 1629 pz, piz, info |
| 1630 F77_CHAR_ARG_LEN (1) | |
| 1631 F77_CHAR_ARG_LEN (1) | |
| 1632 F77_CHAR_ARG_LEN (1))); | |
| 1633 | |
| 1634 if (info != 0) | |
| 1635 info = -2; | |
| 1636 | |
| 7788 | 1637 volatile double rcond_plus_one = rcon + 1.0; |
| 1638 | |
| 1639 if (rcond_plus_one == 1.0 || xisnan (rcon)) | |
| 5785 | 1640 { |
| 1641 info = -2; | |
| 1642 | |
| 1643 if (sing_handler) | |
| 7788 | 1644 sing_handler (rcon); |
| 5785 | 1645 else |
| 1646 (*current_liboctave_error_handler) | |
| 1647 ("matrix singular to machine precision, rcond = %g", | |
| 7788 | 1648 rcon); |
| 5785 | 1649 } |
| 1650 } | |
| 1651 | |
| 1652 if (info == 0) | |
| 1653 { | |
| 1654 retval = b; | |
| 1655 double *result = retval.fortran_vec (); | |
| 1656 | |
| 1657 char uplo = 'L'; | |
| 1658 char trans = 'N'; | |
| 1659 char dia = 'N'; | |
| 1660 | |
| 1661 F77_XFCN (dtrtrs, DTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1662 F77_CONST_CHAR_ARG2 (&trans, 1), | |
| 1663 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1664 nr, b_nc, tmp_data, nr, | |
| 1665 result, nr, info | |
| 1666 F77_CHAR_ARG_LEN (1) | |
| 1667 F77_CHAR_ARG_LEN (1) | |
| 1668 F77_CHAR_ARG_LEN (1))); | |
| 1669 } | |
| 1670 } | |
| 1671 } | |
| 1672 else | |
| 1673 (*current_liboctave_error_handler) ("incorrect matrix type"); | |
| 1674 } | |
| 1675 | |
| 1676 return retval; | |
| 1677 } | |
| 1678 | |
| 1679 Matrix | |
| 1680 Matrix::fsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, | |
| 7788 | 1681 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 1682 bool calc_cond) const |
| 1683 { | |
| 1684 Matrix retval; | |
| 1685 | |
| 1686 octave_idx_type nr = rows (); | |
| 1687 octave_idx_type nc = cols (); | |
| 1688 | |
| 6924 | 1689 if (nr != nc || nr != b.rows ()) |
| 5785 | 1690 (*current_liboctave_error_handler) |
| 1691 ("matrix dimension mismatch solution of linear equations"); | |
| 6924 | 1692 else if (nr == 0 || b.cols () == 0) |
| 1693 retval = Matrix (nc, b.cols (), 0.0); | |
| 5785 | 1694 else |
| 1695 { | |
| 1696 volatile int typ = mattype.type (); | |
| 1697 | |
| 1698 // Calculate the norm of the matrix, for later use. | |
| 1699 double anorm = -1.; | |
| 1700 | |
| 1701 if (typ == MatrixType::Hermitian) | |
| 1702 { | |
| 1703 info = 0; | |
| 1704 char job = 'L'; | |
| 1705 Matrix atmp = *this; | |
| 1706 double *tmp_data = atmp.fortran_vec (); | |
| 1707 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); | |
| 1708 | |
| 1709 F77_XFCN (dpotrf, DPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, | |
| 1710 tmp_data, nr, info | |
| 1711 F77_CHAR_ARG_LEN (1))); | |
| 1712 | |
|
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|
1713 // Throw-away extra info LAPACK gives so as to not change output. |
| 7788 | 1714 rcon = 0.0; |
|
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|
1715 if (info != 0) |
|
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1716 { |
|
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1717 info = -2; |
|
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1718 |
|
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|
1719 mattype.mark_as_unsymmetric (); |
|
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1720 typ = MatrixType::Full; |
|
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1721 } |
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1722 else |
| 5785 | 1723 { |
|
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1724 if (calc_cond) |
| 5785 | 1725 { |
|
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1726 Array<double> z (3 * nc); |
|
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1727 double *pz = z.fortran_vec (); |
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1728 Array<octave_idx_type> iz (nc); |
|
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1729 octave_idx_type *piz = iz.fortran_vec (); |
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1730 |
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1731 F77_XFCN (dpocon, DPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), |
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1732 nr, tmp_data, nr, anorm, |
| 7788 | 1733 rcon, pz, piz, info |
|
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1734 F77_CHAR_ARG_LEN (1))); |
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1735 |
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1736 if (info != 0) |
|
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1737 info = -2; |
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1738 |
| 7788 | 1739 volatile double rcond_plus_one = rcon + 1.0; |
| 1740 | |
| 1741 if (rcond_plus_one == 1.0 || xisnan (rcon)) | |
|
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1742 { |
|
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|
1743 info = -2; |
|
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1744 |
|
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diff
changeset
|
1745 if (sing_handler) |
| 7788 | 1746 sing_handler (rcon); |
|
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diff
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|
1747 else |
|
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|
1748 (*current_liboctave_error_handler) |
|
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changeset
|
1749 ("matrix singular to machine precision, rcond = %g", |
| 7788 | 1750 rcon); |
|
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diff
changeset
|
1751 } |
|
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diff
changeset
|
1752 } |
|
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diff
changeset
|
1753 |
|
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diff
changeset
|
1754 if (info == 0) |
|
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changeset
|
1755 { |
|
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|
1756 retval = b; |
|
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don't check f77_exception_encountered
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changeset
|
1757 double *result = retval.fortran_vec (); |
|
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diff
changeset
|
1758 |
|
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diff
changeset
|
1759 octave_idx_type b_nc = b.cols (); |
|
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diff
changeset
|
1760 |
|
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diff
changeset
|
1761 F77_XFCN (dpotrs, DPOTRS, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
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diff
changeset
|
1762 nr, b_nc, tmp_data, nr, |
|
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changeset
|
1763 result, b.rows(), info |
|
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changeset
|
1764 F77_CHAR_ARG_LEN (1))); |
|
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|
1765 } |
|
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diff
changeset
|
1766 else |
|
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changeset
|
1767 { |
| 5785 | 1768 mattype.mark_as_unsymmetric (); |
| 1769 typ = MatrixType::Full; | |
|
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|
1770 } |
| 5785 | 1771 } |
| 1772 } | |
| 1773 | |
| 1774 if (typ == MatrixType::Full) | |
| 1775 { | |
| 1776 info = 0; | |
| 1777 | |
| 1778 Array<octave_idx_type> ipvt (nr); | |
| 1779 octave_idx_type *pipvt = ipvt.fortran_vec (); | |
| 1780 | |
| 1781 Matrix atmp = *this; | |
| 1782 double *tmp_data = atmp.fortran_vec (); | |
| 1783 if(anorm < 0.) | |
| 1784 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); | |
| 1785 | |
| 1786 Array<double> z (4 * nc); | |
| 1787 double *pz = z.fortran_vec (); | |
| 1788 Array<octave_idx_type> iz (nc); | |
| 1789 octave_idx_type *piz = iz.fortran_vec (); | |
| 1790 | |
| 1791 F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); | |
| 1792 | |
|
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|
1793 // Throw-away extra info LAPACK gives so as to not change output. |
| 7788 | 1794 rcon = 0.0; |
|
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|
1795 if (info != 0) |
| 5785 | 1796 { |
|
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changeset
|
1797 info = -2; |
|
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changeset
|
1798 |
|
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changeset
|
1799 if (sing_handler) |
| 7788 | 1800 sing_handler (rcon); |
|
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|
1801 else |
|
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diff
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|
1802 (*current_liboctave_error_handler) |
|
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|
1803 ("matrix singular to machine precision"); |
|
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|
1804 |
|
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|
1805 mattype.mark_as_rectangular (); |
|
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|
1806 } |
|
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|
1807 else |
|
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|
1808 { |
|
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|
1809 if (calc_cond) |
| 5785 | 1810 { |
|
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|
1811 // Now calculate the condition number for |
|
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|
1812 // non-singular matrix. |
|
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|
1813 char job = '1'; |
|
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|
1814 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
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changeset
|
1815 nc, tmp_data, nr, anorm, |
| 7788 | 1816 rcon, pz, piz, info |
|
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|
1817 F77_CHAR_ARG_LEN (1))); |
|
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changeset
|
1818 |
|
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|
1819 if (info != 0) |
|
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|
1820 info = -2; |
|
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|
1821 |
| 7788 | 1822 volatile double rcond_plus_one = rcon + 1.0; |
| 1823 | |
| 1824 if (rcond_plus_one == 1.0 || xisnan (rcon)) | |
| 5785 | 1825 { |
|
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|
1826 info = -2; |
|
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changeset
|
1827 |
|
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changeset
|
1828 if (sing_handler) |
| 7788 | 1829 sing_handler (rcon); |
|
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|
1830 else |
|
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|
1831 (*current_liboctave_error_handler) |
|
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diff
changeset
|
1832 ("matrix singular to machine precision, rcond = %g", |
| 7788 | 1833 rcon); |
| 5785 | 1834 } |
| 1835 } | |
|
7482
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diff
changeset
|
1836 |
|
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changeset
|
1837 if (info == 0) |
|
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diff
changeset
|
1838 { |
|
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diff
changeset
|
1839 retval = b; |
|
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changeset
|
1840 double *result = retval.fortran_vec (); |
|
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diff
changeset
|
1841 |
|
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diff
changeset
|
1842 octave_idx_type b_nc = b.cols (); |
|
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diff
changeset
|
1843 |
|
29980c6b8604
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diff
changeset
|
1844 char job = 'N'; |
|
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diff
changeset
|
1845 F77_XFCN (dgetrs, DGETRS, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
29980c6b8604
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diff
changeset
|
1846 nr, b_nc, tmp_data, nr, |
|
29980c6b8604
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diff
changeset
|
1847 pipvt, result, b.rows(), info |
|
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diff
changeset
|
1848 F77_CHAR_ARG_LEN (1))); |
|
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diff
changeset
|
1849 } |
|
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diff
changeset
|
1850 else |
|
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diff
changeset
|
1851 mattype.mark_as_rectangular (); |
| 5785 | 1852 } |
| 1853 } | |
| 1854 else if (typ != MatrixType::Hermitian) | |
| 1855 (*current_liboctave_error_handler) ("incorrect matrix type"); | |
| 1856 } | |
| 1857 | |
| 1858 return retval; | |
| 1859 } | |
| 1860 | |
| 1861 Matrix | |
| 1862 Matrix::solve (MatrixType &typ, const Matrix& b) const | |
| 1863 { | |
| 1864 octave_idx_type info; | |
| 7788 | 1865 double rcon; |
| 1866 return solve (typ, b, info, rcon, 0); | |
| 5785 | 1867 } |
| 1868 | |
| 1869 Matrix | |
| 1870 Matrix::solve (MatrixType &typ, const Matrix& b, octave_idx_type& info, | |
| 7788 | 1871 double& rcon) const |
| 5785 | 1872 { |
| 7788 | 1873 return solve (typ, b, info, rcon, 0); |
| 5785 | 1874 } |
| 1875 | |
| 1876 Matrix | |
| 1877 Matrix::solve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, | |
| 7788 | 1878 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 1879 bool singular_fallback) const |
| 1880 { | |
| 1881 Matrix retval; | |
| 1882 int typ = mattype.type (); | |
| 1883 | |
| 1884 if (typ == MatrixType::Unknown) | |
| 1885 typ = mattype.type (*this); | |
| 1886 | |
| 1887 // Only calculate the condition number for LU/Cholesky | |
| 1888 if (typ == MatrixType::Upper || typ == MatrixType::Permuted_Upper) | |
| 7788 | 1889 retval = utsolve (mattype, b, info, rcon, sing_handler, false); |
| 5785 | 1890 else if (typ == MatrixType::Lower || typ == MatrixType::Permuted_Lower) |
| 7788 | 1891 retval = ltsolve (mattype, b, info, rcon, sing_handler, false); |
| 5785 | 1892 else if (typ == MatrixType::Full || typ == MatrixType::Hermitian) |
| 7788 | 1893 retval = fsolve (mattype, b, info, rcon, sing_handler, true); |
| 5785 | 1894 else if (typ != MatrixType::Rectangular) |
| 1895 { | |
| 1896 (*current_liboctave_error_handler) ("unknown matrix type"); | |
| 1897 return Matrix (); | |
| 1898 } | |
| 1899 | |
| 1900 // Rectangular or one of the above solvers flags a singular matrix | |
| 1901 if (singular_fallback && mattype.type () == MatrixType::Rectangular) | |
| 1902 { | |
| 1903 octave_idx_type rank; | |
| 7788 | 1904 retval = lssolve (b, info, rank, rcon); |
| 5785 | 1905 } |
| 1906 | |
| 1907 return retval; | |
| 1908 } | |
| 1909 | |
| 1910 ComplexMatrix | |
| 1911 Matrix::solve (MatrixType &typ, const ComplexMatrix& b) const | |
| 1912 { | |
| 1913 ComplexMatrix tmp (*this); | |
| 1914 return tmp.solve (typ, b); | |
| 1915 } | |
| 1916 | |
| 1917 ComplexMatrix | |
| 1918 Matrix::solve (MatrixType &typ, const ComplexMatrix& b, | |
| 1919 octave_idx_type& info) const | |
| 1920 { | |
| 1921 ComplexMatrix tmp (*this); | |
| 1922 return tmp.solve (typ, b, info); | |
| 1923 } | |
| 1924 | |
| 1925 ComplexMatrix | |
| 1926 Matrix::solve (MatrixType &typ, const ComplexMatrix& b, octave_idx_type& info, | |
| 7788 | 1927 double& rcon) const |
| 5785 | 1928 { |
| 1929 ComplexMatrix tmp (*this); | |
| 7788 | 1930 return tmp.solve (typ, b, info, rcon); |
| 5785 | 1931 } |
| 1932 | |
| 1933 ComplexMatrix | |
| 1934 Matrix::solve (MatrixType &typ, const ComplexMatrix& b, octave_idx_type& info, | |
| 7788 | 1935 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 1936 bool singular_fallback) const |
| 1937 { | |
| 1938 ComplexMatrix tmp (*this); | |
| 7788 | 1939 return tmp.solve (typ, b, info, rcon, sing_handler, singular_fallback); |
| 5785 | 1940 } |
| 1941 | |
| 1942 ColumnVector | |
| 1943 Matrix::solve (MatrixType &typ, const ColumnVector& b) const | |
| 1944 { | |
| 7788 | 1945 octave_idx_type info; double rcon; |
| 1946 return solve (typ, b, info, rcon); | |
| 5785 | 1947 } |
| 1948 | |
| 1949 ColumnVector | |
| 1950 Matrix::solve (MatrixType &typ, const ColumnVector& b, | |
| 1951 octave_idx_type& info) const | |
| 1952 { | |
| 7788 | 1953 double rcon; |
| 1954 return solve (typ, b, info, rcon); | |
| 5785 | 1955 } |
| 1956 | |
| 1957 ColumnVector | |
| 1958 Matrix::solve (MatrixType &typ, const ColumnVector& b, octave_idx_type& info, | |
| 7788 | 1959 double& rcon) const |
| 5785 | 1960 { |
| 7788 | 1961 return solve (typ, b, info, rcon, 0); |
| 5785 | 1962 } |
| 1963 | |
| 1964 ColumnVector | |
| 1965 Matrix::solve (MatrixType &typ, const ColumnVector& b, octave_idx_type& info, | |
| 7788 | 1966 double& rcon, solve_singularity_handler sing_handler) const |
| 5785 | 1967 { |
| 1968 Matrix tmp (b); | |
| 7788 | 1969 return solve (typ, tmp, info, rcon, sing_handler).column(static_cast<octave_idx_type> (0)); |
| 5785 | 1970 } |
| 1971 | |
| 1972 ComplexColumnVector | |
| 1973 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b) const | |
| 1974 { | |
| 1975 ComplexMatrix tmp (*this); | |
| 1976 return tmp.solve (typ, b); | |
| 1977 } | |
| 1978 | |
| 1979 ComplexColumnVector | |
| 1980 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, | |
| 1981 octave_idx_type& info) const | |
| 1982 { | |
| 1983 ComplexMatrix tmp (*this); | |
| 1984 return tmp.solve (typ, b, info); | |
| 1985 } | |
| 1986 | |
| 1987 ComplexColumnVector | |
| 1988 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, | |
| 7788 | 1989 octave_idx_type& info, double& rcon) const |
| 5785 | 1990 { |
| 1991 ComplexMatrix tmp (*this); | |
| 7788 | 1992 return tmp.solve (typ, b, info, rcon); |
| 5785 | 1993 } |
| 1994 | |
| 1995 ComplexColumnVector | |
| 1996 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, | |
| 7788 | 1997 octave_idx_type& info, double& rcon, |
| 5785 | 1998 solve_singularity_handler sing_handler) const |
| 1999 { | |
| 2000 ComplexMatrix tmp (*this); | |
| 7788 | 2001 return tmp.solve(typ, b, info, rcon, sing_handler); |
| 5785 | 2002 } |
| 2003 | |
| 2004 Matrix | |
| 458 | 2005 Matrix::solve (const Matrix& b) const |
| 2006 { | |
| 5275 | 2007 octave_idx_type info; |
| 7788 | 2008 double rcon; |
| 2009 return solve (b, info, rcon, 0); | |
| 458 | 2010 } |
| 2011 | |
| 2012 Matrix | |
| 5275 | 2013 Matrix::solve (const Matrix& b, octave_idx_type& info) const |
| 458 | 2014 { |
| 7788 | 2015 double rcon; |
| 2016 return solve (b, info, rcon, 0); | |
| 458 | 2017 } |
| 2018 | |
| 2019 Matrix | |
| 7788 | 2020 Matrix::solve (const Matrix& b, octave_idx_type& info, double& rcon) const |
| 458 | 2021 { |
| 7788 | 2022 return solve (b, info, rcon, 0); |
| 3480 | 2023 } |
| 2024 | |
| 2025 Matrix | |
| 5785 | 2026 Matrix::solve (const Matrix& b, octave_idx_type& info, |
| 7788 | 2027 double& rcon, solve_singularity_handler sing_handler) const |
| 3480 | 2028 { |
| 5785 | 2029 MatrixType mattype (*this); |
| 7788 | 2030 return solve (mattype, b, info, rcon, sing_handler); |
| 458 | 2031 } |
| 2032 | |
| 2033 ComplexMatrix | |
| 2034 Matrix::solve (const ComplexMatrix& b) const | |
| 2035 { | |
| 2036 ComplexMatrix tmp (*this); | |
| 2037 return tmp.solve (b); | |
| 2038 } | |
| 2039 | |
| 2040 ComplexMatrix | |
| 5275 | 2041 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info) const |
| 458 | 2042 { |
| 2043 ComplexMatrix tmp (*this); | |
| 2044 return tmp.solve (b, info); | |
| 2045 } | |
| 2046 | |
| 2047 ComplexMatrix | |
| 7788 | 2048 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcon) const |
| 458 | 2049 { |
| 2050 ComplexMatrix tmp (*this); | |
| 7788 | 2051 return tmp.solve (b, info, rcon); |
| 458 | 2052 } |
| 2053 | |
| 3480 | 2054 ComplexMatrix |
| 7788 | 2055 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcon, |
| 3480 | 2056 solve_singularity_handler sing_handler) const |
| 2057 { | |
| 2058 ComplexMatrix tmp (*this); | |
| 7788 | 2059 return tmp.solve (b, info, rcon, sing_handler); |
| 3480 | 2060 } |
| 2061 | |
| 458 | 2062 ColumnVector |
| 2063 Matrix::solve (const ColumnVector& b) const | |
| 2064 { | |
| 7788 | 2065 octave_idx_type info; double rcon; |
| 2066 return solve (b, info, rcon); | |
| 458 | 2067 } |
| 2068 | |
| 2069 ColumnVector | |
| 5275 | 2070 Matrix::solve (const ColumnVector& b, octave_idx_type& info) const |
| 458 | 2071 { |
| 7788 | 2072 double rcon; |
| 2073 return solve (b, info, rcon); | |
| 458 | 2074 } |
| 2075 | |
| 2076 ColumnVector | |
| 7788 | 2077 Matrix::solve (const ColumnVector& b, octave_idx_type& info, double& rcon) const |
| 458 | 2078 { |
| 7788 | 2079 return solve (b, info, rcon, 0); |
| 3480 | 2080 } |
| 2081 | |
| 2082 ColumnVector | |
| 7788 | 2083 Matrix::solve (const ColumnVector& b, octave_idx_type& info, double& rcon, |
| 3480 | 2084 solve_singularity_handler sing_handler) const |
| 2085 { | |
| 5785 | 2086 MatrixType mattype (*this); |
| 7788 | 2087 return solve (mattype, b, info, rcon, sing_handler); |
| 458 | 2088 } |
| 2089 | |
| 2090 ComplexColumnVector | |
| 2091 Matrix::solve (const ComplexColumnVector& b) const | |
| 2092 { | |
| 2093 ComplexMatrix tmp (*this); | |
| 2094 return tmp.solve (b); | |
| 2095 } | |
| 2096 | |
| 2097 ComplexColumnVector | |
| 5275 | 2098 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info) const |
| 458 | 2099 { |
| 2100 ComplexMatrix tmp (*this); | |
| 2101 return tmp.solve (b, info); | |
| 2102 } | |
| 2103 | |
| 2104 ComplexColumnVector | |
| 7788 | 2105 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info, double& rcon) const |
| 458 | 2106 { |
| 2107 ComplexMatrix tmp (*this); | |
| 7788 | 2108 return tmp.solve (b, info, rcon); |
| 458 | 2109 } |
| 2110 | |
| 3480 | 2111 ComplexColumnVector |
| 7788 | 2112 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info, double& rcon, |
| 3480 | 2113 solve_singularity_handler sing_handler) const |
| 2114 { | |
| 2115 ComplexMatrix tmp (*this); | |
| 7788 | 2116 return tmp.solve (b, info, rcon, sing_handler); |
| 3480 | 2117 } |
| 2118 | |
| 458 | 2119 Matrix |
| 2120 Matrix::lssolve (const Matrix& b) const | |
| 2121 { | |
| 5275 | 2122 octave_idx_type info; |
| 2123 octave_idx_type rank; | |
| 7788 | 2124 double rcon; |
| 2125 return lssolve (b, info, rank, rcon); | |
| 458 | 2126 } |
| 2127 | |
| 2128 Matrix | |
| 5275 | 2129 Matrix::lssolve (const Matrix& b, octave_idx_type& info) const |
| 458 | 2130 { |
| 5275 | 2131 octave_idx_type rank; |
| 7788 | 2132 double rcon; |
| 2133 return lssolve (b, info, rank, rcon); | |
| 458 | 2134 } |
| 2135 | |
| 2136 Matrix | |
| 7072 | 2137 Matrix::lssolve (const Matrix& b, octave_idx_type& info, |
| 2138 octave_idx_type& rank) const | |
| 458 | 2139 { |
| 7788 | 2140 double rcon; |
| 2141 return lssolve (b, info, rank, rcon); | |
| 7076 | 2142 } |
| 2143 | |
| 2144 Matrix | |
| 2145 Matrix::lssolve (const Matrix& b, octave_idx_type& info, | |
| 7788 | 2146 octave_idx_type& rank, double &rcon) const |
| 7076 | 2147 { |
| 1948 | 2148 Matrix retval; |
| 2149 | |
| 5275 | 2150 octave_idx_type nrhs = b.cols (); |
| 2151 | |
| 2152 octave_idx_type m = rows (); | |
| 2153 octave_idx_type n = cols (); | |
| 458 | 2154 |
| 6924 | 2155 if (m != b.rows ()) |
| 1948 | 2156 (*current_liboctave_error_handler) |
| 6924 | 2157 ("matrix dimension mismatch solution of linear equations"); |
| 2158 else if (m == 0 || n == 0 || b.cols () == 0) | |
| 2159 retval = Matrix (n, b.cols (), 0.0); | |
| 1948 | 2160 else |
| 458 | 2161 { |
| 7072 | 2162 volatile octave_idx_type minmn = (m < n ? m : n); |
| 2163 octave_idx_type maxmn = m > n ? m : n; | |
| 7788 | 2164 rcon = -1.0; |
| 7072 | 2165 if (m != n) |
| 2166 { | |
| 2167 retval = Matrix (maxmn, nrhs, 0.0); | |
| 2168 | |
| 2169 for (octave_idx_type j = 0; j < nrhs; j++) | |
| 2170 for (octave_idx_type i = 0; i < m; i++) | |
| 2171 retval.elem (i, j) = b.elem (i, j); | |
| 2172 } | |
| 2173 else | |
| 2174 retval = b; | |
| 2175 | |
| 1948 | 2176 Matrix atmp = *this; |
| 2177 double *tmp_data = atmp.fortran_vec (); | |
| 2178 | |
| 7072 | 2179 double *pretval = retval.fortran_vec (); |
| 2180 Array<double> s (minmn); | |
| 7071 | 2181 double *ps = s.fortran_vec (); |
| 1948 | 2182 |
| 7072 | 2183 // Ask DGELSD what the dimension of WORK should be. |
| 5275 | 2184 octave_idx_type lwork = -1; |
| 3752 | 2185 |
| 2186 Array<double> work (1); | |
| 1948 | 2187 |
| 7477 | 2188 octave_idx_type smlsiz; |
| 2189 F77_FUNC (xilaenv, XILAENV) (9, F77_CONST_CHAR_ARG2 ("DGELSD", 6), | |
| 2190 F77_CONST_CHAR_ARG2 (" ", 1), | |
| 7478 | 2191 0, 0, 0, 0, smlsiz |
| 7477 | 2192 F77_CHAR_ARG_LEN (6) |
| 7478 | 2193 F77_CHAR_ARG_LEN (1)); |
| 7079 | 2194 |
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2195 octave_idx_type mnthr; |
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2196 F77_FUNC (xilaenv, XILAENV) (6, F77_CONST_CHAR_ARG2 ("DGELSD", 6), |
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2197 F77_CONST_CHAR_ARG2 (" ", 1), |
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2198 m, n, nrhs, -1, mnthr |
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2199 F77_CHAR_ARG_LEN (6) |
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2200 F77_CHAR_ARG_LEN (1)); |
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2201 |
| 7079 | 2202 // We compute the size of iwork because DGELSD in older versions |
| 2203 // of LAPACK does not return it on a query call. | |
| 7124 | 2204 double dminmn = static_cast<double> (minmn); |
| 2205 double dsmlsizp1 = static_cast<double> (smlsiz+1); | |
| 7079 | 2206 #if defined (HAVE_LOG2) |
| 7367 | 2207 double tmp = log2 (dminmn / dsmlsizp1); |
| 7079 | 2208 #else |
| 7367 | 2209 double tmp = log (dminmn / dsmlsizp1) / log (2.0); |
| 7079 | 2210 #endif |
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2211 octave_idx_type nlvl = static_cast<octave_idx_type> (tmp) + 1; |
| 7079 | 2212 if (nlvl < 0) |
| 2213 nlvl = 0; | |
| 2214 | |
| 2215 octave_idx_type liwork = 3 * minmn * nlvl + 11 * minmn; | |
| 2216 if (liwork < 1) | |
| 2217 liwork = 1; | |
| 7072 | 2218 Array<octave_idx_type> iwork (liwork); |
| 2219 octave_idx_type* piwork = iwork.fortran_vec (); | |
| 2220 | |
| 2221 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, | |
| 7788 | 2222 ps, rcon, rank, work.fortran_vec (), |
| 7072 | 2223 lwork, piwork, info)); |
| 1948 | 2224 |
| 7476 | 2225 // The workspace query is broken in at least LAPACK 3.0.0 |
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2226 // through 3.1.1 when n >= mnthr. The obtuse formula below |
| 7476 | 2227 // should provide sufficient workspace for DGELSD to operate |
| 2228 // efficiently. | |
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2229 if (n >= mnthr) |
| 7476 | 2230 { |
| 2231 const octave_idx_type wlalsd | |
| 2232 = 9*m + 2*m*smlsiz + 8*m*nlvl + m*nrhs + (smlsiz+1)*(smlsiz+1); | |
| 2233 | |
| 2234 octave_idx_type addend = m; | |
| 2235 | |
| 2236 if (2*m-4 > addend) | |
| 2237 addend = 2*m-4; | |
| 2238 | |
| 2239 if (nrhs > addend) | |
| 2240 addend = nrhs; | |
| 2241 | |
| 2242 if (n-3*m > addend) | |
| 2243 addend = n-3*m; | |
| 2244 | |
| 2245 if (wlalsd > addend) | |
| 2246 addend = wlalsd; | |
| 2247 | |
| 2248 const octave_idx_type lworkaround = 4*m + m*m + addend; | |
| 2249 | |
| 2250 if (work(0) < lworkaround) | |
| 2251 work(0) = lworkaround; | |
| 2252 } | |
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2253 else if (m >= n) |
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2254 { |
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2255 octave_idx_type lworkaround |
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2256 = 12*n + 2*n*smlsiz + 8*n*nlvl + n*nrhs + (smlsiz+1)*(smlsiz+1); |
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2257 |
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2258 if (work(0) < lworkaround) |
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2259 work(0) = lworkaround; |
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2260 } |
| 7476 | 2261 |
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2262 lwork = static_cast<octave_idx_type> (work(0)); |
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2263 work.resize (lwork); |
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2264 |
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2265 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, |
| 7788 | 2266 maxmn, ps, rcon, rank, |
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2267 work.fortran_vec (), lwork, |
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2268 piwork, info)); |
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2269 |
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2270 if (rank < minmn) |
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2271 (*current_liboctave_warning_handler) |
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2272 ("dgelsd: rank deficient %dx%d matrix, rank = %d", m, n, rank); |
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2273 if (s.elem (0) == 0.0) |
| 7788 | 2274 rcon = 0.0; |
| 1948 | 2275 else |
| 7788 | 2276 rcon = s.elem (minmn - 1) / s.elem (0); |
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2277 |
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2278 retval.resize (n, nrhs); |
| 458 | 2279 } |
| 2280 | |
| 2281 return retval; | |
| 2282 } | |
| 2283 | |
| 2284 ComplexMatrix | |
| 2285 Matrix::lssolve (const ComplexMatrix& b) const | |
| 2286 { | |
| 2287 ComplexMatrix tmp (*this); | |
| 5275 | 2288 octave_idx_type info; |
| 2289 octave_idx_type rank; | |
| 7788 | 2290 double rcon; |
| 2291 return tmp.lssolve (b, info, rank, rcon); | |
| 458 | 2292 } |
| 2293 | |
| 2294 ComplexMatrix | |
| 5275 | 2295 Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info) const |
| 458 | 2296 { |
| 2297 ComplexMatrix tmp (*this); | |
| 5275 | 2298 octave_idx_type rank; |
| 7788 | 2299 double rcon; |
| 2300 return tmp.lssolve (b, info, rank, rcon); | |
| 458 | 2301 } |
| 2302 | |
| 2303 ComplexMatrix | |
| 7076 | 2304 Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info, |
| 2305 octave_idx_type& rank) const | |
| 458 | 2306 { |
| 2307 ComplexMatrix tmp (*this); | |
| 7788 | 2308 double rcon; |
| 2309 return tmp.lssolve (b, info, rank, rcon); | |
| 7076 | 2310 } |
| 2311 | |
| 2312 ComplexMatrix | |
| 2313 Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info, | |
| 7788 | 2314 octave_idx_type& rank, double& rcon) const |
| 7076 | 2315 { |
| 2316 ComplexMatrix tmp (*this); | |
| 7788 | 2317 return tmp.lssolve (b, info, rank, rcon); |
| 458 | 2318 } |
| 2319 | |
| 2320 ColumnVector | |
| 2321 Matrix::lssolve (const ColumnVector& b) const | |
| 2322 { | |
| 5275 | 2323 octave_idx_type info; |
| 2324 octave_idx_type rank; | |
| 7788 | 2325 double rcon; |
| 2326 return lssolve (b, info, rank, rcon); | |
| 458 | 2327 } |
| 2328 | |
| 2329 ColumnVector | |
| 5275 | 2330 Matrix::lssolve (const ColumnVector& b, octave_idx_type& info) const |
| 458 | 2331 { |
| 5275 | 2332 octave_idx_type rank; |
| 7788 | 2333 double rcon; |
| 2334 return lssolve (b, info, rank, rcon); | |
| 458 | 2335 } |
| 2336 | |
| 2337 ColumnVector | |
| 7072 | 2338 Matrix::lssolve (const ColumnVector& b, octave_idx_type& info, |
| 2339 octave_idx_type& rank) const | |
| 458 | 2340 { |
| 7788 | 2341 double rcon; |
| 2342 return lssolve (b, info, rank, rcon); | |
| 7076 | 2343 } |
| 2344 | |
| 2345 ColumnVector | |
| 2346 Matrix::lssolve (const ColumnVector& b, octave_idx_type& info, | |
| 7788 | 2347 octave_idx_type& rank, double &rcon) const |
| 7076 | 2348 { |
| 1948 | 2349 ColumnVector retval; |
| 2350 | |
| 5275 | 2351 octave_idx_type nrhs = 1; |
| 2352 | |
| 2353 octave_idx_type m = rows (); | |
| 2354 octave_idx_type n = cols (); | |
| 458 | 2355 |
| 6924 | 2356 if (m != b.length ()) |
| 1948 | 2357 (*current_liboctave_error_handler) |
| 6924 | 2358 ("matrix dimension mismatch solution of linear equations"); |
| 2359 else if (m == 0 || n == 0) | |
| 2360 retval = ColumnVector (n, 0.0); | |
| 1948 | 2361 else |
| 458 | 2362 { |
| 7072 | 2363 volatile octave_idx_type minmn = (m < n ? m : n); |
| 2364 octave_idx_type maxmn = m > n ? m : n; | |
| 7788 | 2365 rcon = -1.0; |
| 7072 | 2366 |
| 2367 if (m != n) | |
| 2368 { | |
| 2369 retval = ColumnVector (maxmn, 0.0); | |
| 2370 | |
| 2371 for (octave_idx_type i = 0; i < m; i++) | |
| 2372 retval.elem (i) = b.elem (i); | |
| 2373 } | |
| 2374 else | |
| 2375 retval = b; | |
| 2376 | |
| 1948 | 2377 Matrix atmp = *this; |
| 2378 double *tmp_data = atmp.fortran_vec (); | |
| 2379 | |
| 7072 | 2380 double *pretval = retval.fortran_vec (); |
| 2381 Array<double> s (minmn); | |
| 7071 | 2382 double *ps = s.fortran_vec (); |
| 1948 | 2383 |
| 7072 | 2384 // Ask DGELSD what the dimension of WORK should be. |
| 5275 | 2385 octave_idx_type lwork = -1; |
| 3752 | 2386 |
| 2387 Array<double> work (1); | |
| 2388 | |
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2389 octave_idx_type smlsiz; |
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2390 F77_FUNC (xilaenv, XILAENV) (9, F77_CONST_CHAR_ARG2 ("DGELSD", 6), |
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2391 F77_CONST_CHAR_ARG2 (" ", 1), |
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2392 0, 0, 0, 0, smlsiz |
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2393 F77_CHAR_ARG_LEN (6) |
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2394 F77_CHAR_ARG_LEN (1)); |
| 7079 | 2395 |
| 2396 // We compute the size of iwork because DGELSD in older versions | |
| 2397 // of LAPACK does not return it on a query call. | |
| 7124 | 2398 double dminmn = static_cast<double> (minmn); |
| 2399 double dsmlsizp1 = static_cast<double> (smlsiz+1); | |
| 7079 | 2400 #if defined (HAVE_LOG2) |
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2401 double tmp = log2 (dminmn / dsmlsizp1); |
| 7079 | 2402 #else |
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2403 double tmp = log (dminmn / dsmlsizp1) / log (2.0); |
| 7079 | 2404 #endif |
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2405 octave_idx_type nlvl = static_cast<octave_idx_type> (tmp) + 1; |
| 7079 | 2406 if (nlvl < 0) |
| 2407 nlvl = 0; | |
| 2408 | |
| 2409 octave_idx_type liwork = 3 * minmn * nlvl + 11 * minmn; | |
| 2410 if (liwork < 1) | |
| 2411 liwork = 1; | |
| 7072 | 2412 Array<octave_idx_type> iwork (liwork); |
| 2413 octave_idx_type* piwork = iwork.fortran_vec (); | |
| 2414 | |
| 2415 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, | |
| 7788 | 2416 ps, rcon, rank, work.fortran_vec (), |
| 7072 | 2417 lwork, piwork, info)); |
| 1948 | 2418 |
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2419 lwork = static_cast<octave_idx_type> (work(0)); |
|
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|
2420 work.resize (lwork); |
|
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|
2421 |
|
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diff
changeset
|
2422 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, |
| 7788 | 2423 maxmn, ps, rcon, rank, |
|
7482
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7478
diff
changeset
|
2424 work.fortran_vec (), lwork, |
|
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diff
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|
2425 piwork, info)); |
|
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changeset
|
2426 |
|
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|
2427 if (rank < minmn) |
| 1948 | 2428 { |
|
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diff
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|
2429 if (rank < minmn) |
|
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diff
changeset
|
2430 (*current_liboctave_warning_handler) |
|
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7478
diff
changeset
|
2431 ("dgelsd: rank deficient %dx%d matrix, rank = %d", m, n, rank); |
|
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7478
diff
changeset
|
2432 if (s.elem (0) == 0.0) |
| 7788 | 2433 rcon = 0.0; |
|
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diff
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|
2434 else |
| 7788 | 2435 rcon = s.elem (minmn - 1) / s.elem (0); |
| 1948 | 2436 } |
|
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diff
changeset
|
2437 |
|
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changeset
|
2438 retval.resize (n, nrhs); |
| 458 | 2439 } |
| 2440 | |
| 2441 return retval; | |
| 2442 } | |
| 2443 | |
| 2444 ComplexColumnVector | |
| 2445 Matrix::lssolve (const ComplexColumnVector& b) const | |
| 2446 { | |
| 2447 ComplexMatrix tmp (*this); | |
| 7076 | 2448 octave_idx_type info; |
| 2449 octave_idx_type rank; | |
| 7788 | 2450 double rcon; |
| 2451 return tmp.lssolve (b, info, rank, rcon); | |
| 458 | 2452 } |
| 2453 | |
| 2454 ComplexColumnVector | |
| 5275 | 2455 Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info) const |
| 458 | 2456 { |
| 2457 ComplexMatrix tmp (*this); | |
| 7076 | 2458 octave_idx_type rank; |
| 7788 | 2459 double rcon; |
| 2460 return tmp.lssolve (b, info, rank, rcon); | |
| 458 | 2461 } |
| 2462 | |
| 2463 ComplexColumnVector | |
| 7076 | 2464 Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, |
| 2465 octave_idx_type& rank) const | |
| 458 | 2466 { |
| 2467 ComplexMatrix tmp (*this); | |
| 7788 | 2468 double rcon; |
| 2469 return tmp.lssolve (b, info, rank, rcon); | |
| 7076 | 2470 } |
| 2471 | |
| 2472 ComplexColumnVector | |
| 2473 Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, | |
| 7788 | 2474 octave_idx_type& rank, double &rcon) const |
| 7076 | 2475 { |
| 2476 ComplexMatrix tmp (*this); | |
| 7788 | 2477 return tmp.lssolve (b, info, rank, rcon); |
| 458 | 2478 } |
| 2479 | |
| 1819 | 2480 // Constants for matrix exponential calculation. |
| 2481 | |
| 2482 static double padec [] = | |
| 2483 { | |
| 2484 5.0000000000000000e-1, | |
| 2485 1.1666666666666667e-1, | |
| 2486 1.6666666666666667e-2, | |
| 2487 1.6025641025641026e-3, | |
| 2488 1.0683760683760684e-4, | |
| 2489 4.8562548562548563e-6, | |
| 2490 1.3875013875013875e-7, | |
| 2491 1.9270852604185938e-9, | |
| 2492 }; | |
| 2493 | |
| 7400 | 2494 static void |
| 7788 | 2495 solve_singularity_warning (double rcon) |
| 7400 | 2496 { |
| 2497 (*current_liboctave_warning_handler) | |
| 2498 ("singular matrix encountered in expm calculation, rcond = %g", | |
| 7788 | 2499 rcon); |
| 7400 | 2500 } |
| 2501 | |
| 1819 | 2502 Matrix |
| 2503 Matrix::expm (void) const | |
| 2504 { | |
| 2505 Matrix retval; | |
| 2506 | |
| 2507 Matrix m = *this; | |
| 2508 | |
| 6699 | 2509 if (numel () == 1) |
| 2510 return Matrix (1, 1, exp (m(0))); | |
| 2511 | |
| 5275 | 2512 octave_idx_type nc = columns (); |
| 1819 | 2513 |
| 3130 | 2514 // Preconditioning step 1: trace normalization to reduce dynamic |
| 2515 // range of poles, but avoid making stable eigenvalues unstable. | |
| 2516 | |
| 1819 | 2517 // trace shift value |
| 3331 | 2518 volatile double trshift = 0.0; |
| 1819 | 2519 |
| 5275 | 2520 for (octave_idx_type i = 0; i < nc; i++) |
| 1819 | 2521 trshift += m.elem (i, i); |
| 2522 | |
| 2523 trshift /= nc; | |
| 2524 | |
| 3130 | 2525 if (trshift > 0.0) |
| 2526 { | |
| 5275 | 2527 for (octave_idx_type i = 0; i < nc; i++) |
| 3130 | 2528 m.elem (i, i) -= trshift; |
| 2529 } | |
| 1819 | 2530 |
| 3331 | 2531 // Preconditioning step 2: balancing; code follows development |
| 2532 // in AEPBAL | |
| 2533 | |
| 2534 double *p_m = m.fortran_vec (); | |
| 2535 | |
| 5275 | 2536 octave_idx_type info, ilo, ihi, ilos, ihis; |
| 3468 | 2537 Array<double> dpermute (nc); |
| 2538 Array<double> dscale (nc); | |
| 3466 | 2539 |
| 3468 | 2540 // permutation first |
| 2541 char job = 'P'; | |
| 4552 | 2542 F77_XFCN (dgebal, DGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
| 2543 nc, p_m, nc, ilo, ihi, | |
| 2544 dpermute.fortran_vec (), info | |
| 2545 F77_CHAR_ARG_LEN (1))); | |
| 3466 | 2546 |
| 3468 | 2547 // then scaling |
| 2548 job = 'S'; | |
| 4552 | 2549 F77_XFCN (dgebal, DGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
| 2550 nc, p_m, nc, ilos, ihis, | |
| 2551 dscale.fortran_vec (), info | |
| 2552 F77_CHAR_ARG_LEN (1))); | |
| 3331 | 2553 |
| 1819 | 2554 // Preconditioning step 3: scaling. |
| 3331 | 2555 |
| 1819 | 2556 ColumnVector work(nc); |
| 3130 | 2557 double inf_norm; |
| 3331 | 2558 |
| 4552 | 2559 F77_XFCN (xdlange, XDLANGE, (F77_CONST_CHAR_ARG2 ("I", 1), |
| 2560 nc, nc, m.fortran_vec (), nc, | |
| 2561 work.fortran_vec (), inf_norm | |
| 2562 F77_CHAR_ARG_LEN (1))); | |
| 3331 | 2563 |
| 5275 | 2564 octave_idx_type sqpow = static_cast<octave_idx_type> (inf_norm > 0.0 |
| 1819 | 2565 ? (1.0 + log (inf_norm) / log (2.0)) |
| 2566 : 0.0); | |
| 3331 | 2567 |
| 1819 | 2568 // Check whether we need to square at all. |
| 3331 | 2569 |
| 1819 | 2570 if (sqpow < 0) |
| 2571 sqpow = 0; | |
| 3331 | 2572 |
| 1819 | 2573 if (sqpow > 0) |
| 2574 { | |
| 7400 | 2575 if (sqpow > 1023) |
| 2576 sqpow = 1023; | |
| 2577 | |
| 1819 | 2578 double scale_factor = 1.0; |
| 5275 | 2579 for (octave_idx_type i = 0; i < sqpow; i++) |
| 1819 | 2580 scale_factor *= 2.0; |
| 7400 | 2581 |
| 1819 | 2582 m = m / scale_factor; |
| 2583 } | |
| 3331 | 2584 |
| 1819 | 2585 // npp, dpp: pade' approx polynomial matrices. |
| 3331 | 2586 |
| 1819 | 2587 Matrix npp (nc, nc, 0.0); |
| 7265 | 2588 double *pnpp = npp.fortran_vec (); |
| 1819 | 2589 Matrix dpp = npp; |
| 7265 | 2590 double *pdpp = dpp.fortran_vec (); |
| 3331 | 2591 |
| 1819 | 2592 // Now powers a^8 ... a^1. |
| 3331 | 2593 |
| 5275 | 2594 octave_idx_type minus_one_j = -1; |
| 2595 for (octave_idx_type j = 7; j >= 0; j--) | |
| 1819 | 2596 { |
| 7265 | 2597 for (octave_idx_type i = 0; i < nc; i++) |
| 2598 { | |
| 2599 octave_idx_type k = i * nc + i; | |
| 2600 pnpp[k] += padec[j]; | |
| 2601 pdpp[k] += minus_one_j * padec[j]; | |
| 2602 } | |
| 2603 | |
| 2604 npp = m * npp; | |
| 2605 pnpp = npp.fortran_vec (); | |
| 2606 | |
| 2607 dpp = m * dpp; | |
| 2608 pdpp = dpp.fortran_vec (); | |
| 2609 | |
| 1819 | 2610 minus_one_j *= -1; |
| 2611 } | |
| 3331 | 2612 |
| 1819 | 2613 // Zero power. |
| 3331 | 2614 |
| 1819 | 2615 dpp = -dpp; |
| 5275 | 2616 for (octave_idx_type j = 0; j < nc; j++) |
| 1819 | 2617 { |
| 2618 npp.elem (j, j) += 1.0; | |
| 2619 dpp.elem (j, j) += 1.0; | |
| 2620 } | |
| 3331 | 2621 |
| 1819 | 2622 // Compute pade approximation = inverse (dpp) * npp. |
| 2623 | |
| 7788 | 2624 double rcon; |
| 2625 retval = dpp.solve (npp, info, rcon, solve_singularity_warning); | |
| 7400 | 2626 |
| 2627 if (info < 0) | |
| 2628 return retval; | |
| 2629 | |
| 1819 | 2630 // Reverse preconditioning step 3: repeated squaring. |
| 3331 | 2631 |
| 1819 | 2632 while (sqpow) |
| 2633 { | |
| 2634 retval = retval * retval; | |
| 2635 sqpow--; | |
| 2636 } | |
| 3331 | 2637 |
| 1819 | 2638 // Reverse preconditioning step 2: inverse balancing. |
| 3466 | 2639 // apply inverse scaling to computed exponential |
| 5275 | 2640 for (octave_idx_type i = 0; i < nc; i++) |
| 2641 for (octave_idx_type j = 0; j < nc; j++) | |
|
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|
2642 retval(i,j) *= dscale(i) / dscale(j); |
| 3466 | 2643 |
| 4153 | 2644 OCTAVE_QUIT; |
| 2645 | |
| 3466 | 2646 // construct balancing permutation vector |
| 5275 | 2647 Array<octave_idx_type> iperm (nc); |
| 2648 for (octave_idx_type i = 0; i < nc; i++) | |
| 4593 | 2649 iperm(i) = i; // identity permutation |
| 3466 | 2650 |
|
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diff
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|
2651 // trailing permutations must be done in reverse order |
|
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diff
changeset
|
2652 for (octave_idx_type i = nc - 1; i >= ihi; i--) |
|
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diff
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|
2653 { |
|
851803f7bb4d
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diff
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|
2654 octave_idx_type swapidx = static_cast<octave_idx_type> (dpermute(i)) - 1; |
|
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diff
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|
2655 octave_idx_type tmp = iperm(i); |
|
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diff
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|
2656 iperm(i) = iperm(swapidx); |
|
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diff
changeset
|
2657 iperm(swapidx) = tmp; |
|
851803f7bb4d
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diff
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|
2658 } |
|
851803f7bb4d
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diff
changeset
|
2659 |
| 3466 | 2660 // leading permutations in forward order |
| 5275 | 2661 for (octave_idx_type i = 0; i < (ilo-1); i++) |
| 3468 | 2662 { |
| 5275 | 2663 octave_idx_type swapidx = static_cast<octave_idx_type> (dpermute(i)) - 1; |
| 2664 octave_idx_type tmp = iperm(i); | |
| 4593 | 2665 iperm(i) = iperm (swapidx); |
| 2666 iperm(swapidx) = tmp; | |
| 3468 | 2667 } |
| 3466 | 2668 |
| 7416 | 2669 // construct inverse balancing permutation vector |
| 2670 Array<octave_idx_type> invpvec (nc); | |
| 2671 for (octave_idx_type i = 0; i < nc; i++) | |
| 2672 invpvec(iperm(i)) = i; // Thanks to R. A. Lippert for this method | |
| 2673 | |
| 2674 OCTAVE_QUIT; | |
|
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diff
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|
2675 |
| 7416 | 2676 Matrix tmpMat = retval; |
| 2677 for (octave_idx_type i = 0; i < nc; i++) | |
| 2678 for (octave_idx_type j = 0; j < nc; j++) | |
| 2679 retval(i,j) = tmpMat(invpvec(i),invpvec(j)); | |
| 2680 | |
|
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diff
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|
2681 // Reverse preconditioning step 1: fix trace normalization. |
| 3130 | 2682 if (trshift > 0.0) |
| 2683 retval = exp (trshift) * retval; | |
| 2684 | |
| 2685 return retval; | |
| 1819 | 2686 } |
| 2687 | |
| 458 | 2688 Matrix& |
| 2689 Matrix::operator += (const DiagMatrix& a) | |
| 2690 { | |
| 5275 | 2691 octave_idx_type nr = rows (); |
| 2692 octave_idx_type nc = cols (); | |
| 2693 | |
| 2694 octave_idx_type a_nr = a.rows (); | |
| 2695 octave_idx_type a_nc = a.cols (); | |
| 2385 | 2696 |
| 2697 if (nr != a_nr || nc != a_nc) | |
| 458 | 2698 { |
| 2385 | 2699 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
| 458 | 2700 return *this; |
| 2701 } | |
| 2702 | |
| 5275 | 2703 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 2704 elem (i, i) += a.elem (i, i); |
| 2705 | |
| 2706 return *this; | |
| 2707 } | |
| 2708 | |
| 2709 Matrix& | |
| 2710 Matrix::operator -= (const DiagMatrix& a) | |
| 2711 { | |
| 5275 | 2712 octave_idx_type nr = rows (); |
| 2713 octave_idx_type nc = cols (); | |
| 2714 | |
| 2715 octave_idx_type a_nr = a.rows (); | |
| 2716 octave_idx_type a_nc = a.cols (); | |
| 2385 | 2717 |
| 2718 if (nr != a_nr || nc != a_nc) | |
| 458 | 2719 { |
| 2385 | 2720 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
| 458 | 2721 return *this; |
| 2722 } | |
| 2723 | |
| 5275 | 2724 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 2725 elem (i, i) -= a.elem (i, i); |
| 2726 | |
| 2727 return *this; | |
| 2728 } | |
| 2729 | |
| 2730 // unary operations | |
| 2731 | |
| 2964 | 2732 boolMatrix |
| 458 | 2733 Matrix::operator ! (void) const |
| 2734 { | |
| 5275 | 2735 octave_idx_type nr = rows (); |
| 2736 octave_idx_type nc = cols (); | |
| 458 | 2737 |
| 2964 | 2738 boolMatrix b (nr, nc); |
| 458 | 2739 |
| 5275 | 2740 for (octave_idx_type j = 0; j < nc; j++) |
| 2741 for (octave_idx_type i = 0; i < nr; i++) | |
| 458 | 2742 b.elem (i, j) = ! elem (i, j); |
| 2743 | |
| 2744 return b; | |
| 2745 } | |
| 2746 | |
| 1205 | 2747 // column vector by row vector -> matrix operations |
| 458 | 2748 |
| 1205 | 2749 Matrix |
| 2750 operator * (const ColumnVector& v, const RowVector& a) | |
| 458 | 2751 { |
| 1948 | 2752 Matrix retval; |
| 2753 | |
| 5275 | 2754 octave_idx_type len = v.length (); |
| 3233 | 2755 |
| 2756 if (len != 0) | |
| 1205 | 2757 { |
| 5275 | 2758 octave_idx_type a_len = a.length (); |
| 3233 | 2759 |
| 2760 retval.resize (len, a_len); | |
| 2761 double *c = retval.fortran_vec (); | |
| 2762 | |
| 4552 | 2763 F77_XFCN (dgemm, DGEMM, (F77_CONST_CHAR_ARG2 ("N", 1), |
| 2764 F77_CONST_CHAR_ARG2 ("N", 1), | |
| 2765 len, a_len, 1, 1.0, v.data (), len, | |
| 2766 a.data (), 1, 0.0, c, len | |
| 2767 F77_CHAR_ARG_LEN (1) | |
| 2768 F77_CHAR_ARG_LEN (1))); | |
| 1205 | 2769 } |
| 458 | 2770 |
| 1948 | 2771 return retval; |
| 458 | 2772 } |
| 2773 | |
| 2774 // other operations. | |
| 2775 | |
| 2776 Matrix | |
|
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|
2777 Matrix::map (dmapper fcn) const |
| 1205 | 2778 { |
|
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2779 return MArray2<double>::map<double> (func_ptr (fcn)); |
|
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|
2780 } |
|
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|
2781 |
|
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|
2782 ComplexMatrix |
|
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|
2783 Matrix::map (cmapper fcn) const |
|
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|
2784 { |
|
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|
2785 return MArray2<double>::map<Complex> (func_ptr (fcn)); |
| 1205 | 2786 } |
| 2787 | |
| 3248 | 2788 boolMatrix |
|
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|
2789 Matrix::map (bmapper fcn) const |
| 3248 | 2790 { |
|
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2791 return MArray2<double>::map<bool> (func_ptr (fcn)); |
| 458 | 2792 } |
| 2793 | |
| 2385 | 2794 bool |
| 4431 | 2795 Matrix::any_element_is_negative (bool neg_zero) const |
| 2385 | 2796 { |
| 5275 | 2797 octave_idx_type nel = nelem (); |
| 2385 | 2798 |
| 4431 | 2799 if (neg_zero) |
| 2800 { | |
| 5275 | 2801 for (octave_idx_type i = 0; i < nel; i++) |
| 4634 | 2802 if (lo_ieee_signbit (elem (i))) |
| 2803 return true; | |
| 4431 | 2804 } |
| 2805 else | |
| 2806 { | |
| 5275 | 2807 for (octave_idx_type i = 0; i < nel; i++) |
| 4634 | 2808 if (elem (i) < 0) |
| 2809 return true; | |
| 4431 | 2810 } |
| 2385 | 2811 |
| 2812 return false; | |
| 2813 } | |
| 2814 | |
|
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|
2815 bool |
|
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|
2816 Matrix::any_element_is_nan (void) const |
|
935be827eaf8
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John W. Eaton <jwe@octave.org>
parents:
7803
diff
changeset
|
2817 { |
|
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parents:
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diff
changeset
|
2818 octave_idx_type nel = nelem (); |
|
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John W. Eaton <jwe@octave.org>
parents:
7803
diff
changeset
|
2819 |
|
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John W. Eaton <jwe@octave.org>
parents:
7803
diff
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|
2820 for (octave_idx_type i = 0; i < nel; i++) |
|
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John W. Eaton <jwe@octave.org>
parents:
7803
diff
changeset
|
2821 { |
|
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John W. Eaton <jwe@octave.org>
parents:
7803
diff
changeset
|
2822 double val = elem (i); |
|
935be827eaf8
error for NaN values in & and | expressions
John W. Eaton <jwe@octave.org>
parents:
7803
diff
changeset
|
2823 if (xisnan (val)) |
|
935be827eaf8
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John W. Eaton <jwe@octave.org>
parents:
7803
diff
changeset
|
2824 return true; |
|
935be827eaf8
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John W. Eaton <jwe@octave.org>
parents:
7803
diff
changeset
|
2825 } |
|
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parents:
7803
diff
changeset
|
2826 |
|
935be827eaf8
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parents:
7803
diff
changeset
|
2827 return false; |
|
935be827eaf8
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John W. Eaton <jwe@octave.org>
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diff
changeset
|
2828 } |
| 2385 | 2829 |
| 2830 bool | |
| 2831 Matrix::any_element_is_inf_or_nan (void) const | |
| 2832 { | |
| 5275 | 2833 octave_idx_type nel = nelem (); |
| 2834 | |
| 2835 for (octave_idx_type i = 0; i < nel; i++) | |
| 4634 | 2836 { |
| 2837 double val = elem (i); | |
| 2838 if (xisinf (val) || xisnan (val)) | |
| 2839 return true; | |
| 2840 } | |
| 2841 | |
| 2842 return false; | |
| 2385 | 2843 } |
| 2844 | |
| 2845 bool | |
| 5943 | 2846 Matrix::any_element_not_one_or_zero (void) const |
| 2847 { | |
| 2848 octave_idx_type nel = nelem (); | |
| 2849 | |
| 2850 for (octave_idx_type i = 0; i < nel; i++) | |
| 2851 { | |
| 2852 double val = elem (i); | |
| 2853 if (val != 0 && val != 1) | |
| 2854 return true; | |
| 2855 } | |
| 2856 | |
| 2857 return false; | |
| 2858 } | |
| 2859 | |
| 2860 bool | |
| 2385 | 2861 Matrix::all_elements_are_int_or_inf_or_nan (void) const |
| 2862 { | |
| 5275 | 2863 octave_idx_type nel = nelem (); |
| 2864 | |
| 2865 for (octave_idx_type i = 0; i < nel; i++) | |
| 4634 | 2866 { |
| 2867 double val = elem (i); | |
| 2868 if (xisnan (val) || D_NINT (val) == val) | |
| 2869 continue; | |
| 2870 else | |
| 2871 return false; | |
| 2872 } | |
| 2385 | 2873 |
| 2874 return true; | |
| 2875 } | |
| 2876 | |
| 1968 | 2877 // Return nonzero if any element of M is not an integer. Also extract |
| 2878 // the largest and smallest values and return them in MAX_VAL and MIN_VAL. | |
| 2879 | |
| 2385 | 2880 bool |
| 1968 | 2881 Matrix::all_integers (double& max_val, double& min_val) const |
| 2882 { | |
| 5275 | 2883 octave_idx_type nel = nelem (); |
| 4634 | 2884 |
| 2885 if (nel > 0) | |
| 1968 | 2886 { |
| 4634 | 2887 max_val = elem (0); |
| 2888 min_val = elem (0); | |
| 1968 | 2889 } |
| 2890 else | |
| 2385 | 2891 return false; |
| 1968 | 2892 |
| 5275 | 2893 for (octave_idx_type i = 0; i < nel; i++) |
| 4634 | 2894 { |
| 2895 double val = elem (i); | |
| 2896 | |
| 2897 if (val > max_val) | |
| 2898 max_val = val; | |
| 2899 | |
| 2900 if (val < min_val) | |
| 2901 min_val = val; | |
| 2902 | |
| 2903 if (D_NINT (val) != val) | |
| 2904 return false; | |
| 2905 } | |
| 2385 | 2906 |
| 2907 return true; | |
| 1968 | 2908 } |
| 2909 | |
| 2385 | 2910 bool |
| 1968 | 2911 Matrix::too_large_for_float (void) const |
| 2912 { | |
| 5275 | 2913 octave_idx_type nel = nelem (); |
| 2914 | |
| 2915 for (octave_idx_type i = 0; i < nel; i++) | |
| 4634 | 2916 { |
| 2917 double val = elem (i); | |
| 2918 | |
| 5389 | 2919 if (! (xisnan (val) || xisinf (val)) |
| 5387 | 2920 && fabs (val) > FLT_MAX) |
| 4634 | 2921 return true; |
| 2922 } | |
| 1968 | 2923 |
| 2385 | 2924 return false; |
| 1968 | 2925 } |
| 2926 | |
| 5775 | 2927 // FIXME Do these really belong here? Maybe they should be |
| 4015 | 2928 // in a base class? |
| 458 | 2929 |
| 2832 | 2930 boolMatrix |
| 4015 | 2931 Matrix::all (int dim) const |
| 458 | 2932 { |
| 4015 | 2933 MX_ALL_OP (dim); |
| 458 | 2934 } |
| 2935 | |
| 2832 | 2936 boolMatrix |
| 4015 | 2937 Matrix::any (int dim) const |
| 458 | 2938 { |
| 4015 | 2939 MX_ANY_OP (dim); |
| 458 | 2940 } |
| 2941 | |
| 2942 Matrix | |
| 3723 | 2943 Matrix::cumprod (int dim) const |
| 458 | 2944 { |
| 4015 | 2945 MX_CUMULATIVE_OP (Matrix, double, *=); |
| 458 | 2946 } |
| 2947 | |
| 2948 Matrix | |
| 3723 | 2949 Matrix::cumsum (int dim) const |
| 458 | 2950 { |
| 4015 | 2951 MX_CUMULATIVE_OP (Matrix, double, +=); |
| 458 | 2952 } |
| 2953 | |
| 2954 Matrix | |
| 3723 | 2955 Matrix::prod (int dim) const |
| 458 | 2956 { |
| 3864 | 2957 MX_REDUCTION_OP (Matrix, *=, 1.0, 1.0); |
| 458 | 2958 } |
| 2959 | |
| 2960 Matrix | |
| 3723 | 2961 Matrix::sum (int dim) const |
| 458 | 2962 { |
| 3864 | 2963 MX_REDUCTION_OP (Matrix, +=, 0.0, 0.0); |
| 458 | 2964 } |
| 2965 | |
| 2966 Matrix | |
| 3723 | 2967 Matrix::sumsq (int dim) const |
| 458 | 2968 { |
| 3864 | 2969 #define ROW_EXPR \ |
| 2970 double d = elem (i, j); \ | |
| 2971 retval.elem (i, 0) += d * d | |
| 2972 | |
| 2973 #define COL_EXPR \ | |
| 2974 double d = elem (i, j); \ | |
| 2975 retval.elem (0, j) += d * d | |
| 2976 | |
| 2977 MX_BASE_REDUCTION_OP (Matrix, ROW_EXPR, COL_EXPR, 0.0, 0.0); | |
| 2978 | |
| 2979 #undef ROW_EXPR | |
| 2980 #undef COL_EXPR | |
| 458 | 2981 } |
| 2982 | |
| 2385 | 2983 Matrix |
| 2984 Matrix::abs (void) const | |
| 2985 { | |
| 5275 | 2986 octave_idx_type nr = rows (); |
| 2987 octave_idx_type nc = cols (); | |
| 2385 | 2988 |
| 2989 Matrix retval (nr, nc); | |
| 2990 | |
| 5275 | 2991 for (octave_idx_type j = 0; j < nc; j++) |
| 2992 for (octave_idx_type i = 0; i < nr; i++) | |
| 2385 | 2993 retval (i, j) = fabs (elem (i, j)); |
| 2994 | |
| 2995 return retval; | |
| 2996 } | |
| 2997 | |
|
7620
36594d5bbe13
Move diag function into the octave_value class
David Bateman <dbateman@free.fr>
parents:
7544
diff
changeset
|
2998 Matrix |
| 5275 | 2999 Matrix::diag (octave_idx_type k) const |
| 458 | 3000 { |
|
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parents:
7544
diff
changeset
|
3001 return MArray2<double>::diag (k); |
| 458 | 3002 } |
| 3003 | |
| 3004 ColumnVector | |
| 3005 Matrix::row_min (void) const | |
| 3006 { | |
| 5275 | 3007 Array<octave_idx_type> dummy_idx; |
| 4587 | 3008 return row_min (dummy_idx); |
| 458 | 3009 } |
| 3010 | |
| 3011 ColumnVector | |
| 5275 | 3012 Matrix::row_min (Array<octave_idx_type>& idx_arg) const |
| 458 | 3013 { |
| 3014 ColumnVector result; | |
| 3015 | |
| 5275 | 3016 octave_idx_type nr = rows (); |
| 3017 octave_idx_type nc = cols (); | |
| 458 | 3018 |
| 3019 if (nr > 0 && nc > 0) | |
| 3020 { | |
| 3021 result.resize (nr); | |
| 4587 | 3022 idx_arg.resize (nr); |
| 458 | 3023 |
| 5275 | 3024 for (octave_idx_type i = 0; i < nr; i++) |
| 458 | 3025 { |
| 5275 | 3026 octave_idx_type idx_j; |
| 4469 | 3027 |
| 3028 double tmp_min = octave_NaN; | |
| 3029 | |
| 3030 for (idx_j = 0; idx_j < nc; idx_j++) | |
| 2354 | 3031 { |
| 4469 | 3032 tmp_min = elem (i, idx_j); |
| 3033 | |
| 5389 | 3034 if (! xisnan (tmp_min)) |
| 4469 | 3035 break; |
| 3036 } | |
| 3037 | |
| 5275 | 3038 for (octave_idx_type j = idx_j+1; j < nc; j++) |
| 4469 | 3039 { |
| 3040 double tmp = elem (i, j); | |
| 3041 | |
| 5389 | 3042 if (xisnan (tmp)) |
| 4469 | 3043 continue; |
| 3044 else if (tmp < tmp_min) | |
| 2354 | 3045 { |
| 4469 | 3046 idx_j = j; |
| 3047 tmp_min = tmp; | |
| 2354 | 3048 } |
| 3049 } | |
| 3050 | |
| 4469 | 3051 result.elem (i) = tmp_min; |
| 5389 | 3052 idx_arg.elem (i) = xisnan (tmp_min) ? 0 : idx_j; |
| 458 | 3053 } |
| 3054 } | |
| 3055 | |
| 3056 return result; | |
| 3057 } | |
| 3058 | |
| 3059 ColumnVector | |
| 3060 Matrix::row_max (void) const | |
| 3061 { | |
| 5275 | 3062 Array<octave_idx_type> dummy_idx; |
| 4587 | 3063 return row_max (dummy_idx); |
| 458 | 3064 } |
| 3065 | |
| 3066 ColumnVector | |
| 5275 | 3067 Matrix::row_max (Array<octave_idx_type>& idx_arg) const |
| 458 | 3068 { |
| 3069 ColumnVector result; | |
| 3070 | |
| 5275 | 3071 octave_idx_type nr = rows (); |
| 3072 octave_idx_type nc = cols (); | |
| 458 | 3073 |
| 3074 if (nr > 0 && nc > 0) | |
| 3075 { | |
| 3076 result.resize (nr); | |
| 4587 | 3077 idx_arg.resize (nr); |
| 458 | 3078 |
| 5275 | 3079 for (octave_idx_type i = 0; i < nr; i++) |
| 458 | 3080 { |
| 5275 | 3081 octave_idx_type idx_j; |
| 4469 | 3082 |
| 3083 double tmp_max = octave_NaN; | |
| 3084 | |
| 3085 for (idx_j = 0; idx_j < nc; idx_j++) | |
| 2354 | 3086 { |
| 4469 | 3087 tmp_max = elem (i, idx_j); |
| 3088 | |
| 5389 | 3089 if (! xisnan (tmp_max)) |
| 4469 | 3090 break; |
| 3091 } | |
| 3092 | |
| 5275 | 3093 for (octave_idx_type j = idx_j+1; j < nc; j++) |
| 4469 | 3094 { |
| 3095 double tmp = elem (i, j); | |
| 3096 | |
| 5389 | 3097 if (xisnan (tmp)) |
| 4469 | 3098 continue; |
| 3099 else if (tmp > tmp_max) | |
| 2354 | 3100 { |
| 4469 | 3101 idx_j = j; |
| 3102 tmp_max = tmp; | |
| 2354 | 3103 } |
| 3104 } | |
| 3105 | |
| 4469 | 3106 result.elem (i) = tmp_max; |
| 5389 | 3107 idx_arg.elem (i) = xisnan (tmp_max) ? 0 : idx_j; |
| 458 | 3108 } |
| 3109 } | |
| 3110 | |
| 3111 return result; | |
| 3112 } | |
| 3113 | |
| 3114 RowVector | |
| 3115 Matrix::column_min (void) const | |
| 3116 { | |
| 5275 | 3117 Array<octave_idx_type> dummy_idx; |
| 4587 | 3118 return column_min (dummy_idx); |
| 458 | 3119 } |
| 2354 | 3120 |
| 458 | 3121 RowVector |
| 5275 | 3122 Matrix::column_min (Array<octave_idx_type>& idx_arg) const |
| 458 | 3123 { |
| 3124 RowVector result; | |
| 3125 | |
| 5275 | 3126 octave_idx_type nr = rows (); |
| 3127 octave_idx_type nc = cols (); | |
| 458 | 3128 |
| 3129 if (nr > 0 && nc > 0) | |
| 3130 { | |
| 3131 result.resize (nc); | |
| 4587 | 3132 idx_arg.resize (nc); |
| 458 | 3133 |
| 5275 | 3134 for (octave_idx_type j = 0; j < nc; j++) |
| 458 | 3135 { |
| 5275 | 3136 octave_idx_type idx_i; |
| 4469 | 3137 |
| 3138 double tmp_min = octave_NaN; | |
| 3139 | |
| 3140 for (idx_i = 0; idx_i < nr; idx_i++) | |
| 2354 | 3141 { |
| 4469 | 3142 tmp_min = elem (idx_i, j); |
| 3143 | |
| 5389 | 3144 if (! xisnan (tmp_min)) |
| 4469 | 3145 break; |
| 3146 } | |
| 3147 | |
| 5275 | 3148 for (octave_idx_type i = idx_i+1; i < nr; i++) |
| 4469 | 3149 { |
| 3150 double tmp = elem (i, j); | |
| 3151 | |
| 5389 | 3152 if (xisnan (tmp)) |
| 4469 | 3153 continue; |
| 3154 else if (tmp < tmp_min) | |
| 2354 | 3155 { |
| 4469 | 3156 idx_i = i; |
| 3157 tmp_min = tmp; | |
| 2354 | 3158 } |
| 3159 } | |
| 3160 | |
| 4469 | 3161 result.elem (j) = tmp_min; |
| 5389 | 3162 idx_arg.elem (j) = xisnan (tmp_min) ? 0 : idx_i; |
| 458 | 3163 } |
| 3164 } | |
| 3165 | |
| 3166 return result; | |
| 3167 } | |
| 3168 | |
| 2354 | 3169 RowVector |
| 3170 Matrix::column_max (void) const | |
| 3171 { | |
| 5275 | 3172 Array<octave_idx_type> dummy_idx; |
| 4587 | 3173 return column_max (dummy_idx); |
| 2354 | 3174 } |
| 458 | 3175 |
| 3176 RowVector | |
| 5275 | 3177 Matrix::column_max (Array<octave_idx_type>& idx_arg) const |
| 458 | 3178 { |
| 3179 RowVector result; | |
| 3180 | |
| 5275 | 3181 octave_idx_type nr = rows (); |
| 3182 octave_idx_type nc = cols (); | |
| 458 | 3183 |
| 3184 if (nr > 0 && nc > 0) | |
| 3185 { | |
| 3186 result.resize (nc); | |
| 4587 | 3187 idx_arg.resize (nc); |
| 458 | 3188 |
| 5275 | 3189 for (octave_idx_type j = 0; j < nc; j++) |
| 458 | 3190 { |
| 5275 | 3191 octave_idx_type idx_i; |
| 4469 | 3192 |
| 3193 double tmp_max = octave_NaN; | |
| 3194 | |
| 3195 for (idx_i = 0; idx_i < nr; idx_i++) | |
| 2354 | 3196 { |
| 4469 | 3197 tmp_max = elem (idx_i, j); |
| 3198 | |
| 5389 | 3199 if (! xisnan (tmp_max)) |
| 4469 | 3200 break; |
| 3201 } | |
| 3202 | |
| 5275 | 3203 for (octave_idx_type i = idx_i+1; i < nr; i++) |
| 4469 | 3204 { |
| 3205 double tmp = elem (i, j); | |
| 3206 | |
| 5389 | 3207 if (xisnan (tmp)) |
| 4469 | 3208 continue; |
| 3209 else if (tmp > tmp_max) | |
| 2354 | 3210 { |
| 4469 | 3211 idx_i = i; |
| 3212 tmp_max = tmp; | |
| 2354 | 3213 } |
| 3214 } | |
| 3215 | |
| 4469 | 3216 result.elem (j) = tmp_max; |
| 5389 | 3217 idx_arg.elem (j) = xisnan (tmp_max) ? 0 : idx_i; |
| 458 | 3218 } |
| 3219 } | |
| 3220 | |
| 3221 return result; | |
| 3222 } | |
| 3223 | |
| 3504 | 3224 std::ostream& |
| 3225 operator << (std::ostream& os, const Matrix& a) | |
| 458 | 3226 { |
| 5275 | 3227 for (octave_idx_type i = 0; i < a.rows (); i++) |
| 458 | 3228 { |
| 5275 | 3229 for (octave_idx_type j = 0; j < a.cols (); j++) |
| 4130 | 3230 { |
| 3231 os << " "; | |
| 3232 octave_write_double (os, a.elem (i, j)); | |
| 3233 } | |
| 458 | 3234 os << "\n"; |
| 3235 } | |
| 3236 return os; | |
| 3237 } | |
| 3238 | |
| 3504 | 3239 std::istream& |
| 3240 operator >> (std::istream& is, Matrix& a) | |
| 458 | 3241 { |
| 5275 | 3242 octave_idx_type nr = a.rows (); |
| 3243 octave_idx_type nc = a.cols (); | |
| 458 | 3244 |
| 3245 if (nr < 1 || nc < 1) | |
| 3504 | 3246 is.clear (std::ios::badbit); |
| 458 | 3247 else |
| 3248 { | |
| 3249 double tmp; | |
| 5275 | 3250 for (octave_idx_type i = 0; i < nr; i++) |
| 3251 for (octave_idx_type j = 0; j < nc; j++) | |
| 458 | 3252 { |
| 4130 | 3253 tmp = octave_read_double (is); |
| 458 | 3254 if (is) |
| 3255 a.elem (i, j) = tmp; | |
| 3256 else | |
| 2795 | 3257 goto done; |
| 458 | 3258 } |
| 3259 } | |
| 3260 | |
| 2795 | 3261 done: |
| 3262 | |
| 458 | 3263 return is; |
| 3264 } | |
| 3265 | |
| 1819 | 3266 Matrix |
| 3267 Givens (double x, double y) | |
| 3268 { | |
| 3269 double cc, s, temp_r; | |
| 3270 | |
| 3887 | 3271 F77_FUNC (dlartg, DLARTG) (x, y, cc, s, temp_r); |
| 1819 | 3272 |
| 3273 Matrix g (2, 2); | |
| 3274 | |
| 3275 g.elem (0, 0) = cc; | |
| 3276 g.elem (1, 1) = cc; | |
| 3277 g.elem (0, 1) = s; | |
| 3278 g.elem (1, 0) = -s; | |
| 3279 | |
| 3280 return g; | |
| 3281 } | |
| 3282 | |
| 3283 Matrix | |
| 3284 Sylvester (const Matrix& a, const Matrix& b, const Matrix& c) | |
| 3285 { | |
| 3286 Matrix retval; | |
| 3287 | |
| 5775 | 3288 // FIXME -- need to check that a, b, and c are all the same |
| 1819 | 3289 // size. |
| 3290 | |
| 3291 // Compute Schur decompositions. | |
| 3292 | |
| 3293 SCHUR as (a, "U"); | |
| 3294 SCHUR bs (b, "U"); | |
| 3295 | |
| 3296 // Transform c to new coordinates. | |
| 3297 | |
| 3298 Matrix ua = as.unitary_matrix (); | |
| 3299 Matrix sch_a = as.schur_matrix (); | |
| 3300 | |
| 3301 Matrix ub = bs.unitary_matrix (); | |
| 3302 Matrix sch_b = bs.schur_matrix (); | |
| 3303 | |
| 3304 Matrix cx = ua.transpose () * c * ub; | |
| 3305 | |
| 3306 // Solve the sylvester equation, back-transform, and return the | |
| 3307 // solution. | |
| 3308 | |
| 5275 | 3309 octave_idx_type a_nr = a.rows (); |
| 3310 octave_idx_type b_nr = b.rows (); | |
| 1819 | 3311 |
| 3312 double scale; | |
| 5275 | 3313 octave_idx_type info; |
| 1819 | 3314 |
| 1950 | 3315 double *pa = sch_a.fortran_vec (); |
| 3316 double *pb = sch_b.fortran_vec (); | |
| 3317 double *px = cx.fortran_vec (); | |
| 3318 | |
| 4552 | 3319 F77_XFCN (dtrsyl, DTRSYL, (F77_CONST_CHAR_ARG2 ("N", 1), |
| 3320 F77_CONST_CHAR_ARG2 ("N", 1), | |
| 3321 1, a_nr, b_nr, pa, a_nr, pb, | |
| 3322 b_nr, px, a_nr, scale, info | |
| 3323 F77_CHAR_ARG_LEN (1) | |
| 3324 F77_CHAR_ARG_LEN (1))); | |
| 1950 | 3325 |
| 3326 | |
|
7482
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
3327 // FIXME -- check info? |
| 1819 | 3328 |
|
7482
29980c6b8604
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John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
3329 retval = -ua*cx*ub.transpose (); |
| 1819 | 3330 |
| 3331 return retval; | |
| 3332 } | |
| 3333 | |
| 2828 | 3334 // matrix by matrix -> matrix operations |
| 3335 | |
| 6162 | 3336 /* Simple Dot Product, Matrix-Vector and Matrix-Matrix Unit tests |
| 3337 %!assert([1 2 3] * [ 4 ; 5 ; 6], 32, 1e-14) | |
| 3338 %!assert([1 2 ; 3 4 ] * [5 ; 6], [17 ; 39 ], 1e-14) | |
| 3339 %!assert([1 2 ; 3 4 ] * [5 6 ; 7 8], [19 22; 43 50], 1e-14) | |
| 3340 */ | |
| 3341 | |
| 3342 /* Test some simple identities | |
| 3343 %!shared M, cv, rv | |
| 3344 %! M = randn(10,10); | |
| 3345 %! cv = randn(10,1); | |
| 3346 %! rv = randn(1,10); | |
| 3347 %!assert([M*cv,M*cv],M*[cv,cv],1e-14) | |
| 3348 %!assert([rv*M;rv*M],[rv;rv]*M,1e-14) | |
| 3349 %!assert(2*rv*cv,[rv,rv]*[cv;cv],1e-14) | |
| 3350 */ | |
| 3351 | |
|
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
|
3352 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
|
3353 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
|
3354 { |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3355 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
|
3356 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
|
3357 } |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3358 |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3359 // 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
|
3360 |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3361 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
|
3362 xgemm (bool transa, const Matrix& a, bool transb, const Matrix& b) |
| 2828 | 3363 { |
| 3364 Matrix retval; | |
| 3365 | |
|
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
|
3366 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
|
3367 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
|
3368 |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3369 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
|
3370 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
|
3371 |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3372 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
|
3373 gripe_nonconformant ("operator *", a_nr, a_nc, b_nr, b_nc); |
| 2828 | 3374 else |
| 3375 { | |
|
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
|
3376 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
|
3377 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
|
3378 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
|
3379 { |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3380 octave_idx_type lda = a.rows (); |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3381 |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3382 retval.resize (a_nr, b_nc); |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3383 double *c = retval.fortran_vec (); |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3384 |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3385 const char *ctransa = get_blas_trans_arg (transa); |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3386 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
|
3387 F77_CONST_CHAR_ARG2 (ctransa, 1), |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3388 a_nr, a_nc, 1.0, |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3389 a.data (), lda, 0.0, c, a_nr |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3390 F77_CHAR_ARG_LEN (1) |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3391 F77_CHAR_ARG_LEN (1))); |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3392 for (int j = 0; j < a_nr; j++) |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3393 for (int i = 0; i < j; i++) |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3394 retval.xelem (j,i) = retval.xelem (i,j); |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3395 |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3396 } |
| 2828 | 3397 else |
| 3398 { | |
|
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
|
3399 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
|
3400 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
|
3401 |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3402 retval.resize (a_nr, b_nc); |
| 2828 | 3403 double *c = retval.fortran_vec (); |
| 3404 | |
|
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
|
3405 if (b_nc == 1) |
| 5983 | 3406 { |
|
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
|
3407 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
|
3408 F77_FUNC (xddot, XDDOT) (a_nc, a.data (), 1, b.data (), 1, *c); |
| 5983 | 3409 else |
| 6390 | 3410 { |
|
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
|
3411 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
|
3412 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
|
3413 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
|
3414 b.data (), 1, 0.0, c, 1 |
| 6390 | 3415 F77_CHAR_ARG_LEN (1))); |
| 3416 } | |
| 5983 | 3417 } |
|
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
|
3418 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
|
3419 { |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3420 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
|
3421 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
|
3422 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
|
3423 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
|
3424 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
|
3425 } |
| 5983 | 3426 else |
| 6390 | 3427 { |
|
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
|
3428 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
|
3429 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
|
3430 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
|
3431 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
|
3432 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
|
3433 lda, b.data (), ldb, 0.0, c, a_nr |
| 6390 | 3434 F77_CHAR_ARG_LEN (1) |
| 3435 F77_CHAR_ARG_LEN (1))); | |
| 3436 } | |
| 2828 | 3437 } |
| 3438 } | |
| 3439 | |
| 3440 return retval; | |
| 3441 } | |
| 3442 | |
|
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
|
3443 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
|
3444 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
|
3445 { |
|
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 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
|
3447 } |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3448 |
| 5775 | 3449 // FIXME -- it would be nice to share code among the min/max |
| 4309 | 3450 // functions below. |
| 3451 | |
| 3452 #define EMPTY_RETURN_CHECK(T) \ | |
| 3453 if (nr == 0 || nc == 0) \ | |
| 3454 return T (nr, nc); | |
| 3455 | |
| 3456 Matrix | |
| 3457 min (double d, const Matrix& m) | |
| 3458 { | |
| 5275 | 3459 octave_idx_type nr = m.rows (); |
| 3460 octave_idx_type nc = m.columns (); | |
| 4309 | 3461 |
| 3462 EMPTY_RETURN_CHECK (Matrix); | |
| 3463 | |
| 3464 Matrix result (nr, nc); | |
| 3465 | |
| 5275 | 3466 for (octave_idx_type j = 0; j < nc; j++) |
| 3467 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3468 { |
| 3469 OCTAVE_QUIT; | |
| 3470 result (i, j) = xmin (d, m (i, j)); | |
| 3471 } | |
| 3472 | |
| 3473 return result; | |
| 3474 } | |
| 3475 | |
| 3476 Matrix | |
| 3477 min (const Matrix& m, double d) | |
| 3478 { | |
| 5275 | 3479 octave_idx_type nr = m.rows (); |
| 3480 octave_idx_type nc = m.columns (); | |
| 4309 | 3481 |
| 3482 EMPTY_RETURN_CHECK (Matrix); | |
| 3483 | |
| 3484 Matrix result (nr, nc); | |
| 3485 | |
| 5275 | 3486 for (octave_idx_type j = 0; j < nc; j++) |
| 3487 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3488 { |
| 3489 OCTAVE_QUIT; | |
| 3490 result (i, j) = xmin (m (i, j), d); | |
| 3491 } | |
| 3492 | |
| 3493 return result; | |
| 3494 } | |
| 3495 | |
| 3496 Matrix | |
| 3497 min (const Matrix& a, const Matrix& b) | |
| 3498 { | |
| 5275 | 3499 octave_idx_type nr = a.rows (); |
| 3500 octave_idx_type nc = a.columns (); | |
| 4309 | 3501 |
| 3502 if (nr != b.rows () || nc != b.columns ()) | |
| 3503 { | |
| 3504 (*current_liboctave_error_handler) | |
| 3505 ("two-arg min expecting args of same size"); | |
| 3506 return Matrix (); | |
| 3507 } | |
| 3508 | |
| 3509 EMPTY_RETURN_CHECK (Matrix); | |
| 3510 | |
| 3511 Matrix result (nr, nc); | |
| 3512 | |
| 5275 | 3513 for (octave_idx_type j = 0; j < nc; j++) |
| 3514 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3515 { |
| 3516 OCTAVE_QUIT; | |
| 3517 result (i, j) = xmin (a (i, j), b (i, j)); | |
| 3518 } | |
| 3519 | |
| 3520 return result; | |
| 3521 } | |
| 3522 | |
| 3523 Matrix | |
| 3524 max (double d, const Matrix& m) | |
| 3525 { | |
| 5275 | 3526 octave_idx_type nr = m.rows (); |
| 3527 octave_idx_type nc = m.columns (); | |
| 4309 | 3528 |
| 3529 EMPTY_RETURN_CHECK (Matrix); | |
| 3530 | |
| 3531 Matrix result (nr, nc); | |
| 3532 | |
| 5275 | 3533 for (octave_idx_type j = 0; j < nc; j++) |
| 3534 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3535 { |
| 3536 OCTAVE_QUIT; | |
| 3537 result (i, j) = xmax (d, m (i, j)); | |
| 3538 } | |
| 3539 | |
| 3540 return result; | |
| 3541 } | |
| 3542 | |
| 3543 Matrix | |
| 3544 max (const Matrix& m, double d) | |
| 3545 { | |
| 5275 | 3546 octave_idx_type nr = m.rows (); |
| 3547 octave_idx_type nc = m.columns (); | |
| 4309 | 3548 |
| 3549 EMPTY_RETURN_CHECK (Matrix); | |
| 3550 | |
| 3551 Matrix result (nr, nc); | |
| 3552 | |
| 5275 | 3553 for (octave_idx_type j = 0; j < nc; j++) |
| 3554 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3555 { |
| 3556 OCTAVE_QUIT; | |
| 3557 result (i, j) = xmax (m (i, j), d); | |
| 3558 } | |
| 3559 | |
| 3560 return result; | |
| 3561 } | |
| 3562 | |
| 3563 Matrix | |
| 3564 max (const Matrix& a, const Matrix& b) | |
| 3565 { | |
| 5275 | 3566 octave_idx_type nr = a.rows (); |
| 3567 octave_idx_type nc = a.columns (); | |
| 4309 | 3568 |
| 3569 if (nr != b.rows () || nc != b.columns ()) | |
| 3570 { | |
| 3571 (*current_liboctave_error_handler) | |
| 3572 ("two-arg max expecting args of same size"); | |
| 3573 return Matrix (); | |
| 3574 } | |
| 3575 | |
| 3576 EMPTY_RETURN_CHECK (Matrix); | |
| 3577 | |
| 3578 Matrix result (nr, nc); | |
| 3579 | |
| 5275 | 3580 for (octave_idx_type j = 0; j < nc; j++) |
| 3581 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3582 { |
| 3583 OCTAVE_QUIT; | |
| 3584 result (i, j) = xmax (a (i, j), b (i, j)); | |
| 3585 } | |
| 3586 | |
| 3587 return result; | |
| 3588 } | |
| 3589 | |
| 2870 | 3590 MS_CMP_OPS(Matrix, , double, ) |
| 3504 | 3591 MS_BOOL_OPS(Matrix, double, 0.0) |
| 2870 | 3592 |
| 3593 SM_CMP_OPS(double, , Matrix, ) | |
| 3504 | 3594 SM_BOOL_OPS(double, Matrix, 0.0) |
| 2870 | 3595 |
| 3596 MM_CMP_OPS(Matrix, , Matrix, ) | |
| 3504 | 3597 MM_BOOL_OPS(Matrix, Matrix, 0.0) |
| 2870 | 3598 |
| 458 | 3599 /* |
| 3600 ;;; Local Variables: *** | |
| 3601 ;;; mode: C++ *** | |
| 3602 ;;; End: *** | |
| 3603 */ |