Mercurial > octave-nkf
annotate liboctave/dMatrix.cc @ 8336:9813c07ca946
make det take advantage of matrix type
| author | Jaroslav Hajek <highegg@gmail.com> |
|---|---|
| date | Wed, 19 Nov 2008 15:26:39 +0100 |
| parents | 64cf956a109c |
| children | e02242c54c49 |
| 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" |
|
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54 #include "oct-norm.h" |
| 4153 | 55 #include "quit.h" |
| 458 | 56 |
| 4773 | 57 #if defined (HAVE_FFTW3) |
| 3827 | 58 #include "oct-fftw.h" |
| 59 #endif | |
| 60 | |
| 458 | 61 // Fortran functions we call. |
| 62 | |
| 63 extern "C" | |
| 64 { | |
| 7478 | 65 F77_RET_T |
| 7477 | 66 F77_FUNC (xilaenv, XILAENV) (const octave_idx_type&, F77_CONST_CHAR_ARG_DECL, |
| 67 F77_CONST_CHAR_ARG_DECL, | |
| 68 const octave_idx_type&, const octave_idx_type&, | |
| 7478 | 69 const octave_idx_type&, const octave_idx_type&, |
| 70 octave_idx_type& | |
| 71 F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); | |
| 7476 | 72 |
| 4552 | 73 F77_RET_T |
| 74 F77_FUNC (dgebal, DGEBAL) (F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 75 const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type&, |
| 76 octave_idx_type&, double*, octave_idx_type& | |
| 4552 | 77 F77_CHAR_ARG_LEN_DECL); |
| 78 | |
| 79 F77_RET_T | |
| 80 F77_FUNC (dgebak, DGEBAK) (F77_CONST_CHAR_ARG_DECL, | |
| 81 F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 82 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, double*, |
| 83 const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type& | |
| 4552 | 84 F77_CHAR_ARG_LEN_DECL |
| 85 F77_CHAR_ARG_LEN_DECL); | |
| 86 | |
| 87 | |
| 88 F77_RET_T | |
| 89 F77_FUNC (dgemm, DGEMM) (F77_CONST_CHAR_ARG_DECL, | |
| 90 F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 91 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
| 92 const double&, const double*, const octave_idx_type&, | |
| 93 const double*, const octave_idx_type&, const double&, | |
| 94 double*, const octave_idx_type& | |
| 4552 | 95 F77_CHAR_ARG_LEN_DECL |
| 96 F77_CHAR_ARG_LEN_DECL); | |
| 97 | |
| 98 F77_RET_T | |
| 5983 | 99 F77_FUNC (dgemv, DGEMV) (F77_CONST_CHAR_ARG_DECL, |
| 100 const octave_idx_type&, const octave_idx_type&, const double&, | |
| 101 const double*, const octave_idx_type&, const double*, | |
| 102 const octave_idx_type&, const double&, double*, | |
| 103 const octave_idx_type& | |
| 104 F77_CHAR_ARG_LEN_DECL); | |
| 105 | |
| 106 F77_RET_T | |
| 107 F77_FUNC (xddot, XDDOT) (const octave_idx_type&, const double*, const octave_idx_type&, | |
| 108 const double*, const octave_idx_type&, double&); | |
| 109 | |
| 110 F77_RET_T | |
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111 F77_FUNC (dsyrk, DSYRK) (F77_CONST_CHAR_ARG_DECL, |
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112 F77_CONST_CHAR_ARG_DECL, |
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113 const octave_idx_type&, const octave_idx_type&, |
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114 const double&, const double*, const octave_idx_type&, |
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115 const double&, double*, const octave_idx_type& |
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116 F77_CHAR_ARG_LEN_DECL |
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117 F77_CHAR_ARG_LEN_DECL); |
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118 |
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119 F77_RET_T |
| 5275 | 120 F77_FUNC (dgetrf, DGETRF) (const octave_idx_type&, const octave_idx_type&, double*, const octave_idx_type&, |
| 121 octave_idx_type*, octave_idx_type&); | |
| 4329 | 122 |
| 4552 | 123 F77_RET_T |
| 5275 | 124 F77_FUNC (dgetrs, DGETRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, |
| 125 const double*, const octave_idx_type&, | |
| 126 const octave_idx_type*, double*, const octave_idx_type&, octave_idx_type& | |
| 4552 | 127 F77_CHAR_ARG_LEN_DECL); |
| 128 | |
| 129 F77_RET_T | |
| 5275 | 130 F77_FUNC (dgetri, DGETRI) (const octave_idx_type&, double*, const octave_idx_type&, const octave_idx_type*, |
| 131 double*, const octave_idx_type&, octave_idx_type&); | |
| 4552 | 132 |
| 133 F77_RET_T | |
| 5275 | 134 F77_FUNC (dgecon, DGECON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, double*, |
| 135 const octave_idx_type&, const double&, double&, | |
| 136 double*, octave_idx_type*, octave_idx_type& | |
| 4552 | 137 F77_CHAR_ARG_LEN_DECL); |
| 138 | |
| 139 F77_RET_T | |
| 7072 | 140 F77_FUNC (dgelsy, DGELSY) (const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
| 141 double*, const octave_idx_type&, double*, | |
| 142 const octave_idx_type&, octave_idx_type*, double&, octave_idx_type&, | |
| 143 double*, const octave_idx_type&, octave_idx_type&); | |
| 144 | |
| 145 F77_RET_T | |
| 146 F77_FUNC (dgelsd, DGELSD) (const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, | |
| 5275 | 147 double*, const octave_idx_type&, double*, |
| 7071 | 148 const octave_idx_type&, double*, double&, octave_idx_type&, |
| 7072 | 149 double*, const octave_idx_type&, octave_idx_type*, |
| 150 octave_idx_type&); | |
| 458 | 151 |
| 5785 | 152 F77_RET_T |
| 153 F77_FUNC (dpotrf, DPOTRF) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 154 double *, const octave_idx_type&, | |
| 155 octave_idx_type& F77_CHAR_ARG_LEN_DECL); | |
| 156 | |
| 157 F77_RET_T | |
| 158 F77_FUNC (dpocon, DPOCON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 159 double*, const octave_idx_type&, const double&, | |
| 160 double&, double*, octave_idx_type*, | |
| 161 octave_idx_type& F77_CHAR_ARG_LEN_DECL); | |
| 162 F77_RET_T | |
| 163 F77_FUNC (dpotrs, DPOTRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 164 const octave_idx_type&, const double*, | |
| 165 const octave_idx_type&, double*, | |
| 166 const octave_idx_type&, octave_idx_type& | |
| 167 F77_CHAR_ARG_LEN_DECL); | |
| 168 | |
| 169 F77_RET_T | |
| 6207 | 170 F77_FUNC (dtrtri, DTRTRI) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, |
| 171 const octave_idx_type&, const double*, | |
| 172 const octave_idx_type&, octave_idx_type& | |
| 173 F77_CHAR_ARG_LEN_DECL | |
| 174 F77_CHAR_ARG_LEN_DECL); | |
| 175 F77_RET_T | |
| 5785 | 176 F77_FUNC (dtrcon, DTRCON) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, |
| 177 F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 178 const double*, const octave_idx_type&, double&, | |
| 179 double*, octave_idx_type*, octave_idx_type& | |
| 180 F77_CHAR_ARG_LEN_DECL | |
| 181 F77_CHAR_ARG_LEN_DECL | |
| 182 F77_CHAR_ARG_LEN_DECL); | |
| 183 F77_RET_T | |
| 184 F77_FUNC (dtrtrs, DTRTRS) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, | |
| 185 F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 186 const octave_idx_type&, const double*, | |
| 187 const octave_idx_type&, double*, | |
| 188 const octave_idx_type&, octave_idx_type& | |
| 189 F77_CHAR_ARG_LEN_DECL | |
| 190 F77_CHAR_ARG_LEN_DECL | |
| 191 F77_CHAR_ARG_LEN_DECL); | |
| 192 | |
| 1360 | 193 // Note that the original complex fft routines were not written for |
| 194 // double complex arguments. They have been modified by adding an | |
| 195 // implicit double precision (a-h,o-z) statement at the beginning of | |
| 196 // each subroutine. | |
| 458 | 197 |
| 4552 | 198 F77_RET_T |
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199 F77_FUNC (zffti, ZFFTI) (const octave_idx_type&, Complex*); |
| 4552 | 200 |
| 201 F77_RET_T | |
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202 F77_FUNC (zfftf, ZFFTF) (const octave_idx_type&, Complex*, Complex*); |
| 4552 | 203 |
| 204 F77_RET_T | |
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205 F77_FUNC (zfftb, ZFFTB) (const octave_idx_type&, Complex*, Complex*); |
| 4552 | 206 |
| 207 F77_RET_T | |
| 208 F77_FUNC (dlartg, DLARTG) (const double&, const double&, double&, | |
| 209 double&, double&); | |
| 210 | |
| 211 F77_RET_T | |
| 212 F77_FUNC (dtrsyl, DTRSYL) (F77_CONST_CHAR_ARG_DECL, | |
| 213 F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 214 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
| 215 const double*, const octave_idx_type&, const double*, | |
| 216 const octave_idx_type&, const double*, const octave_idx_type&, | |
| 217 double&, octave_idx_type& | |
| 4552 | 218 F77_CHAR_ARG_LEN_DECL |
| 219 F77_CHAR_ARG_LEN_DECL); | |
| 220 | |
| 221 F77_RET_T | |
| 5275 | 222 F77_FUNC (xdlange, XDLANGE) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, |
| 223 const octave_idx_type&, const double*, | |
| 224 const octave_idx_type&, double*, double& | |
| 4552 | 225 F77_CHAR_ARG_LEN_DECL); |
| 458 | 226 } |
| 227 | |
| 1360 | 228 // Matrix class. |
| 458 | 229 |
| 2349 | 230 Matrix::Matrix (const RowVector& rv) |
| 231 : MArray2<double> (1, rv.length (), 0.0) | |
| 232 { | |
| 5275 | 233 for (octave_idx_type i = 0; i < rv.length (); i++) |
| 2349 | 234 elem (0, i) = rv.elem (i); |
| 235 } | |
| 236 | |
| 237 Matrix::Matrix (const ColumnVector& cv) | |
| 238 : MArray2<double> (cv.length (), 1, 0.0) | |
| 239 { | |
| 5275 | 240 for (octave_idx_type i = 0; i < cv.length (); i++) |
| 2349 | 241 elem (i, 0) = cv.elem (i); |
| 242 } | |
| 243 | |
| 458 | 244 Matrix::Matrix (const DiagMatrix& a) |
| 1214 | 245 : MArray2<double> (a.rows (), a.cols (), 0.0) |
| 458 | 246 { |
| 5275 | 247 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 248 elem (i, i) = a.elem (i, i); |
| 249 } | |
| 250 | |
| 5775 | 251 // FIXME -- could we use a templated mixed-type copy function |
| 1574 | 252 // here? |
| 253 | |
| 2828 | 254 Matrix::Matrix (const boolMatrix& a) |
| 255 : MArray2<double> (a.rows (), a.cols ()) | |
| 256 { | |
| 5275 | 257 for (octave_idx_type i = 0; i < a.rows (); i++) |
| 258 for (octave_idx_type j = 0; j < a.cols (); j++) | |
| 2828 | 259 elem (i, j) = a.elem (i, j); |
| 260 } | |
| 261 | |
| 1574 | 262 Matrix::Matrix (const charMatrix& a) |
| 263 : MArray2<double> (a.rows (), a.cols ()) | |
| 264 { | |
| 5275 | 265 for (octave_idx_type i = 0; i < a.rows (); i++) |
| 266 for (octave_idx_type j = 0; j < a.cols (); j++) | |
| 1574 | 267 elem (i, j) = a.elem (i, j); |
| 268 } | |
| 269 | |
| 2385 | 270 bool |
| 458 | 271 Matrix::operator == (const Matrix& a) const |
| 272 { | |
| 273 if (rows () != a.rows () || cols () != a.cols ()) | |
| 2385 | 274 return false; |
| 458 | 275 |
| 3769 | 276 return mx_inline_equal (data (), a.data (), length ()); |
| 458 | 277 } |
| 278 | |
| 2385 | 279 bool |
| 458 | 280 Matrix::operator != (const Matrix& a) const |
| 281 { | |
| 282 return !(*this == a); | |
| 283 } | |
| 284 | |
| 3354 | 285 bool |
| 286 Matrix::is_symmetric (void) const | |
| 287 { | |
| 288 if (is_square () && rows () > 0) | |
| 289 { | |
| 5275 | 290 for (octave_idx_type i = 0; i < rows (); i++) |
| 291 for (octave_idx_type j = i+1; j < cols (); j++) | |
| 3354 | 292 if (elem (i, j) != elem (j, i)) |
| 293 return false; | |
| 294 | |
| 295 return true; | |
| 296 } | |
| 297 | |
| 298 return false; | |
| 299 } | |
| 300 | |
| 458 | 301 Matrix& |
| 5275 | 302 Matrix::insert (const Matrix& a, octave_idx_type r, octave_idx_type c) |
| 458 | 303 { |
| 1561 | 304 Array2<double>::insert (a, r, c); |
| 458 | 305 return *this; |
| 306 } | |
| 307 | |
| 308 Matrix& | |
| 5275 | 309 Matrix::insert (const RowVector& a, octave_idx_type r, octave_idx_type c) |
| 458 | 310 { |
| 5275 | 311 octave_idx_type a_len = a.length (); |
| 4316 | 312 |
| 1698 | 313 if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ()) |
| 458 | 314 { |
| 315 (*current_liboctave_error_handler) ("range error for insert"); | |
| 316 return *this; | |
| 317 } | |
| 318 | |
| 4316 | 319 if (a_len > 0) |
| 320 { | |
| 321 make_unique (); | |
| 322 | |
| 5275 | 323 for (octave_idx_type i = 0; i < a_len; i++) |
| 4316 | 324 xelem (r, c+i) = a.elem (i); |
| 325 } | |
| 458 | 326 |
| 327 return *this; | |
| 328 } | |
| 329 | |
| 330 Matrix& | |
| 5275 | 331 Matrix::insert (const ColumnVector& a, octave_idx_type r, octave_idx_type c) |
| 458 | 332 { |
| 5275 | 333 octave_idx_type a_len = a.length (); |
| 4316 | 334 |
| 1698 | 335 if (r < 0 || r + a_len > rows () || c < 0 || c >= cols ()) |
| 458 | 336 { |
| 337 (*current_liboctave_error_handler) ("range error for insert"); | |
| 338 return *this; | |
| 339 } | |
| 340 | |
| 4316 | 341 if (a_len > 0) |
| 342 { | |
| 343 make_unique (); | |
| 344 | |
| 5275 | 345 for (octave_idx_type i = 0; i < a_len; i++) |
| 4316 | 346 xelem (r+i, c) = a.elem (i); |
| 347 } | |
| 458 | 348 |
| 349 return *this; | |
| 350 } | |
| 351 | |
| 352 Matrix& | |
| 5275 | 353 Matrix::insert (const DiagMatrix& a, octave_idx_type r, octave_idx_type c) |
| 458 | 354 { |
| 5275 | 355 octave_idx_type a_nr = a.rows (); |
| 356 octave_idx_type a_nc = a.cols (); | |
| 1697 | 357 |
| 1698 | 358 if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) |
| 458 | 359 { |
| 360 (*current_liboctave_error_handler) ("range error for insert"); | |
| 361 return *this; | |
| 362 } | |
| 363 | |
| 1697 | 364 fill (0.0, r, c, r + a_nr - 1, c + a_nc - 1); |
| 365 | |
| 5275 | 366 octave_idx_type a_len = a.length (); |
| 4316 | 367 |
| 368 if (a_len > 0) | |
| 369 { | |
| 370 make_unique (); | |
| 371 | |
| 5275 | 372 for (octave_idx_type i = 0; i < a_len; i++) |
| 4316 | 373 xelem (r+i, c+i) = a.elem (i, i); |
| 374 } | |
| 458 | 375 |
| 376 return *this; | |
| 377 } | |
| 378 | |
| 379 Matrix& | |
| 380 Matrix::fill (double val) | |
| 381 { | |
| 5275 | 382 octave_idx_type nr = rows (); |
| 383 octave_idx_type nc = cols (); | |
| 4316 | 384 |
| 458 | 385 if (nr > 0 && nc > 0) |
| 4316 | 386 { |
| 387 make_unique (); | |
| 388 | |
| 5275 | 389 for (octave_idx_type j = 0; j < nc; j++) |
| 390 for (octave_idx_type i = 0; i < nr; i++) | |
| 4316 | 391 xelem (i, j) = val; |
| 392 } | |
| 458 | 393 |
| 394 return *this; | |
| 395 } | |
| 396 | |
| 397 Matrix& | |
| 5275 | 398 Matrix::fill (double val, octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) |
| 458 | 399 { |
| 5275 | 400 octave_idx_type nr = rows (); |
| 401 octave_idx_type nc = cols (); | |
| 4316 | 402 |
| 458 | 403 if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0 |
| 404 || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc) | |
| 405 { | |
| 406 (*current_liboctave_error_handler) ("range error for fill"); | |
| 407 return *this; | |
| 408 } | |
| 409 | |
| 5275 | 410 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } |
| 411 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } | |
| 458 | 412 |
| 4316 | 413 if (r2 >= r1 && c2 >= c1) |
| 414 { | |
| 415 make_unique (); | |
| 416 | |
| 5275 | 417 for (octave_idx_type j = c1; j <= c2; j++) |
| 418 for (octave_idx_type i = r1; i <= r2; i++) | |
| 4316 | 419 xelem (i, j) = val; |
| 420 } | |
| 458 | 421 |
| 422 return *this; | |
| 423 } | |
| 424 | |
| 425 Matrix | |
| 426 Matrix::append (const Matrix& a) const | |
| 427 { | |
| 5275 | 428 octave_idx_type nr = rows (); |
| 429 octave_idx_type nc = cols (); | |
| 458 | 430 if (nr != a.rows ()) |
| 431 { | |
| 432 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 433 return Matrix (); | |
| 434 } | |
| 435 | |
| 5275 | 436 octave_idx_type nc_insert = nc; |
| 458 | 437 Matrix retval (nr, nc + a.cols ()); |
| 438 retval.insert (*this, 0, 0); | |
| 439 retval.insert (a, 0, nc_insert); | |
| 440 return retval; | |
| 441 } | |
| 442 | |
| 443 Matrix | |
| 444 Matrix::append (const RowVector& a) const | |
| 445 { | |
| 5275 | 446 octave_idx_type nr = rows (); |
| 447 octave_idx_type nc = cols (); | |
| 458 | 448 if (nr != 1) |
| 449 { | |
| 450 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 451 return Matrix (); | |
| 452 } | |
| 453 | |
| 5275 | 454 octave_idx_type nc_insert = nc; |
| 458 | 455 Matrix retval (nr, nc + a.length ()); |
| 456 retval.insert (*this, 0, 0); | |
| 457 retval.insert (a, 0, nc_insert); | |
| 458 return retval; | |
| 459 } | |
| 460 | |
| 461 Matrix | |
| 462 Matrix::append (const ColumnVector& a) const | |
| 463 { | |
| 5275 | 464 octave_idx_type nr = rows (); |
| 465 octave_idx_type nc = cols (); | |
| 458 | 466 if (nr != a.length ()) |
| 467 { | |
| 468 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 469 return Matrix (); | |
| 470 } | |
| 471 | |
| 5275 | 472 octave_idx_type nc_insert = nc; |
| 458 | 473 Matrix retval (nr, nc + 1); |
| 474 retval.insert (*this, 0, 0); | |
| 475 retval.insert (a, 0, nc_insert); | |
| 476 return retval; | |
| 477 } | |
| 478 | |
| 479 Matrix | |
| 480 Matrix::append (const DiagMatrix& a) const | |
| 481 { | |
| 5275 | 482 octave_idx_type nr = rows (); |
| 483 octave_idx_type nc = cols (); | |
| 458 | 484 if (nr != a.rows ()) |
| 485 { | |
| 486 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 487 return *this; | |
| 488 } | |
| 489 | |
| 5275 | 490 octave_idx_type nc_insert = nc; |
| 458 | 491 Matrix retval (nr, nc + a.cols ()); |
| 492 retval.insert (*this, 0, 0); | |
| 493 retval.insert (a, 0, nc_insert); | |
| 494 return retval; | |
| 495 } | |
| 496 | |
| 497 Matrix | |
| 498 Matrix::stack (const Matrix& a) const | |
| 499 { | |
| 5275 | 500 octave_idx_type nr = rows (); |
| 501 octave_idx_type nc = cols (); | |
| 458 | 502 if (nc != a.cols ()) |
| 503 { | |
| 504 (*current_liboctave_error_handler) | |
| 505 ("column dimension mismatch for stack"); | |
| 506 return Matrix (); | |
| 507 } | |
| 508 | |
| 5275 | 509 octave_idx_type nr_insert = nr; |
| 458 | 510 Matrix retval (nr + a.rows (), nc); |
| 511 retval.insert (*this, 0, 0); | |
| 512 retval.insert (a, nr_insert, 0); | |
| 513 return retval; | |
| 514 } | |
| 515 | |
| 516 Matrix | |
| 517 Matrix::stack (const RowVector& a) const | |
| 518 { | |
| 5275 | 519 octave_idx_type nr = rows (); |
| 520 octave_idx_type nc = cols (); | |
| 458 | 521 if (nc != a.length ()) |
| 522 { | |
| 523 (*current_liboctave_error_handler) | |
| 524 ("column dimension mismatch for stack"); | |
| 525 return Matrix (); | |
| 526 } | |
| 527 | |
| 5275 | 528 octave_idx_type nr_insert = nr; |
| 458 | 529 Matrix retval (nr + 1, nc); |
| 530 retval.insert (*this, 0, 0); | |
| 531 retval.insert (a, nr_insert, 0); | |
| 532 return retval; | |
| 533 } | |
| 534 | |
| 535 Matrix | |
| 536 Matrix::stack (const ColumnVector& a) const | |
| 537 { | |
| 5275 | 538 octave_idx_type nr = rows (); |
| 539 octave_idx_type nc = cols (); | |
| 458 | 540 if (nc != 1) |
| 541 { | |
| 542 (*current_liboctave_error_handler) | |
| 543 ("column dimension mismatch for stack"); | |
| 544 return Matrix (); | |
| 545 } | |
| 546 | |
| 5275 | 547 octave_idx_type nr_insert = nr; |
| 458 | 548 Matrix retval (nr + a.length (), nc); |
| 549 retval.insert (*this, 0, 0); | |
| 550 retval.insert (a, nr_insert, 0); | |
| 551 return retval; | |
| 552 } | |
| 553 | |
| 554 Matrix | |
| 555 Matrix::stack (const DiagMatrix& a) const | |
| 556 { | |
| 5275 | 557 octave_idx_type nr = rows (); |
| 558 octave_idx_type nc = cols (); | |
| 458 | 559 if (nc != a.cols ()) |
| 560 { | |
| 561 (*current_liboctave_error_handler) | |
| 562 ("column dimension mismatch for stack"); | |
| 563 return Matrix (); | |
| 564 } | |
| 565 | |
| 5275 | 566 octave_idx_type nr_insert = nr; |
| 458 | 567 Matrix retval (nr + a.rows (), nc); |
| 568 retval.insert (*this, 0, 0); | |
| 569 retval.insert (a, nr_insert, 0); | |
| 570 return retval; | |
| 571 } | |
| 572 | |
| 573 Matrix | |
| 1205 | 574 real (const ComplexMatrix& a) |
| 575 { | |
| 5275 | 576 octave_idx_type a_len = a.length (); |
| 1205 | 577 Matrix retval; |
| 578 if (a_len > 0) | |
| 3769 | 579 retval = Matrix (mx_inline_real_dup (a.data (), a_len), |
| 580 a.rows (), a.cols ()); | |
| 1205 | 581 return retval; |
| 582 } | |
| 583 | |
| 584 Matrix | |
| 585 imag (const ComplexMatrix& a) | |
| 586 { | |
| 5275 | 587 octave_idx_type a_len = a.length (); |
| 1205 | 588 Matrix retval; |
| 589 if (a_len > 0) | |
| 3769 | 590 retval = Matrix (mx_inline_imag_dup (a.data (), a_len), |
| 591 a.rows (), a.cols ()); | |
| 1205 | 592 return retval; |
| 593 } | |
| 594 | |
| 595 Matrix | |
| 5275 | 596 Matrix::extract (octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) const |
| 458 | 597 { |
| 5275 | 598 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } |
| 599 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } | |
| 600 | |
| 601 octave_idx_type new_r = r2 - r1 + 1; | |
| 602 octave_idx_type new_c = c2 - c1 + 1; | |
| 458 | 603 |
| 604 Matrix result (new_r, new_c); | |
| 605 | |
| 5275 | 606 for (octave_idx_type j = 0; j < new_c; j++) |
| 607 for (octave_idx_type i = 0; i < new_r; i++) | |
| 4316 | 608 result.xelem (i, j) = elem (r1+i, c1+j); |
| 609 | |
| 610 return result; | |
| 611 } | |
| 612 | |
| 613 Matrix | |
| 5275 | 614 Matrix::extract_n (octave_idx_type r1, octave_idx_type c1, octave_idx_type nr, octave_idx_type nc) const |
| 4316 | 615 { |
| 616 Matrix result (nr, nc); | |
| 617 | |
| 5275 | 618 for (octave_idx_type j = 0; j < nc; j++) |
| 619 for (octave_idx_type i = 0; i < nr; i++) | |
| 4316 | 620 result.xelem (i, j) = elem (r1+i, c1+j); |
| 458 | 621 |
| 622 return result; | |
| 623 } | |
| 624 | |
| 625 // extract row or column i. | |
| 626 | |
| 627 RowVector | |
| 5275 | 628 Matrix::row (octave_idx_type i) const |
| 458 | 629 { |
| 5275 | 630 octave_idx_type nc = cols (); |
| 458 | 631 if (i < 0 || i >= rows ()) |
| 632 { | |
| 633 (*current_liboctave_error_handler) ("invalid row selection"); | |
| 634 return RowVector (); | |
| 635 } | |
| 636 | |
| 637 RowVector retval (nc); | |
| 5275 | 638 for (octave_idx_type j = 0; j < nc; j++) |
| 4316 | 639 retval.xelem (j) = elem (i, j); |
| 458 | 640 |
| 641 return retval; | |
| 642 } | |
| 643 | |
| 644 ColumnVector | |
| 5275 | 645 Matrix::column (octave_idx_type i) const |
| 458 | 646 { |
| 5275 | 647 octave_idx_type nr = rows (); |
| 458 | 648 if (i < 0 || i >= cols ()) |
| 649 { | |
| 650 (*current_liboctave_error_handler) ("invalid column selection"); | |
| 651 return ColumnVector (); | |
| 652 } | |
| 653 | |
| 654 ColumnVector retval (nr); | |
| 5275 | 655 for (octave_idx_type j = 0; j < nr; j++) |
| 4316 | 656 retval.xelem (j) = elem (j, i); |
| 458 | 657 |
| 658 return retval; | |
| 659 } | |
| 660 | |
| 661 Matrix | |
| 662 Matrix::inverse (void) const | |
| 663 { | |
| 5275 | 664 octave_idx_type info; |
| 7788 | 665 double rcon; |
| 6207 | 666 MatrixType mattype (*this); |
| 7788 | 667 return inverse (mattype, info, rcon, 0, 0); |
| 6207 | 668 } |
| 669 | |
| 670 Matrix | |
| 6479 | 671 Matrix::inverse (octave_idx_type& info) const |
| 672 { | |
| 7788 | 673 double rcon; |
| 6479 | 674 MatrixType mattype (*this); |
| 7788 | 675 return inverse (mattype, info, rcon, 0, 0); |
| 6479 | 676 } |
| 677 | |
| 678 Matrix | |
| 7788 | 679 Matrix::inverse (octave_idx_type& info, double& rcon, int force, |
| 6479 | 680 int calc_cond) const |
| 681 { | |
| 682 MatrixType mattype (*this); | |
| 7788 | 683 return inverse (mattype, info, rcon, force, calc_cond); |
| 6479 | 684 } |
| 685 | |
| 686 Matrix | |
| 6207 | 687 Matrix::inverse (MatrixType& mattype) const |
| 688 { | |
| 689 octave_idx_type info; | |
| 7788 | 690 double rcon; |
| 691 return inverse (mattype, info, rcon, 0, 0); | |
| 6207 | 692 } |
| 693 | |
| 694 Matrix | |
| 695 Matrix::inverse (MatrixType &mattype, octave_idx_type& info) const | |
| 696 { | |
| 7788 | 697 double rcon; |
| 698 return inverse (mattype, info, rcon, 0, 0); | |
| 458 | 699 } |
| 700 | |
| 701 Matrix | |
| 7788 | 702 Matrix::tinverse (MatrixType &mattype, octave_idx_type& info, double& rcon, |
| 6207 | 703 int force, int calc_cond) const |
| 458 | 704 { |
| 6207 | 705 Matrix retval; |
| 706 | |
| 707 octave_idx_type nr = rows (); | |
| 708 octave_idx_type nc = cols (); | |
| 709 | |
| 710 if (nr != nc || nr == 0 || nc == 0) | |
| 711 (*current_liboctave_error_handler) ("inverse requires square matrix"); | |
| 712 else | |
| 713 { | |
| 714 int typ = mattype.type (); | |
| 715 char uplo = (typ == MatrixType::Lower ? 'L' : 'U'); | |
| 716 char udiag = 'N'; | |
| 717 retval = *this; | |
| 718 double *tmp_data = retval.fortran_vec (); | |
| 719 | |
| 720 F77_XFCN (dtrtri, DTRTRI, (F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 721 F77_CONST_CHAR_ARG2 (&udiag, 1), | |
| 722 nr, tmp_data, nr, info | |
| 723 F77_CHAR_ARG_LEN (1) | |
| 724 F77_CHAR_ARG_LEN (1))); | |
| 725 | |
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726 // Throw-away extra info LAPACK gives so as to not change output. |
| 7788 | 727 rcon = 0.0; |
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728 if (info != 0) |
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729 info = -1; |
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730 else if (calc_cond) |
| 6207 | 731 { |
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732 octave_idx_type dtrcon_info = 0; |
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733 char job = '1'; |
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734 |
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735 OCTAVE_LOCAL_BUFFER (double, work, 3 * nr); |
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736 OCTAVE_LOCAL_BUFFER (octave_idx_type, iwork, nr); |
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737 |
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738 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&job, 1), |
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739 F77_CONST_CHAR_ARG2 (&uplo, 1), |
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740 F77_CONST_CHAR_ARG2 (&udiag, 1), |
| 7788 | 741 nr, tmp_data, nr, rcon, |
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742 work, iwork, dtrcon_info |
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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 F77_CHAR_ARG_LEN (1))); |
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746 |
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747 if (dtrcon_info != 0) |
| 6207 | 748 info = -1; |
| 749 } | |
| 750 | |
| 751 if (info == -1 && ! force) | |
| 752 retval = *this; // Restore matrix contents. | |
| 753 } | |
| 754 | |
| 755 return retval; | |
| 458 | 756 } |
| 757 | |
| 6207 | 758 |
| 458 | 759 Matrix |
| 7788 | 760 Matrix::finverse (MatrixType &mattype, octave_idx_type& info, double& rcon, |
| 6207 | 761 int force, int calc_cond) const |
| 458 | 762 { |
| 1948 | 763 Matrix retval; |
| 764 | |
| 5275 | 765 octave_idx_type nr = rows (); |
| 766 octave_idx_type nc = cols (); | |
| 1948 | 767 |
| 458 | 768 if (nr != nc || nr == 0 || nc == 0) |
| 1948 | 769 (*current_liboctave_error_handler) ("inverse requires square matrix"); |
| 458 | 770 else |
| 771 { | |
| 5275 | 772 Array<octave_idx_type> ipvt (nr); |
| 773 octave_idx_type *pipvt = ipvt.fortran_vec (); | |
| 1948 | 774 |
| 775 retval = *this; | |
| 776 double *tmp_data = retval.fortran_vec (); | |
| 777 | |
| 4329 | 778 Array<double> z(1); |
| 5275 | 779 octave_idx_type lwork = -1; |
| 4329 | 780 |
| 4330 | 781 // Query the optimum work array size. |
| 4329 | 782 F77_XFCN (dgetri, DGETRI, (nc, tmp_data, nr, pipvt, |
| 783 z.fortran_vec (), lwork, info)); | |
| 784 | |
| 5275 | 785 lwork = static_cast<octave_idx_type> (z(0)); |
| 4329 | 786 lwork = (lwork < 2 *nc ? 2*nc : lwork); |
| 787 z.resize (lwork); | |
| 788 double *pz = z.fortran_vec (); | |
| 789 | |
| 790 info = 0; | |
| 791 | |
| 4330 | 792 // Calculate the norm of the matrix, for later use. |
| 4329 | 793 double anorm = 0; |
| 794 if (calc_cond) | |
| 5275 | 795 anorm = retval.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
| 4329 | 796 |
| 797 F77_XFCN (dgetrf, DGETRF, (nc, nc, tmp_data, nr, pipvt, info)); | |
| 1948 | 798 |
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799 // Throw-away extra info LAPACK gives so as to not change output. |
| 7788 | 800 rcon = 0.0; |
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801 if (info != 0) |
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802 info = -1; |
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803 else if (calc_cond) |
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804 { |
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805 octave_idx_type dgecon_info = 0; |
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806 |
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807 // Now calculate the condition number for non-singular matrix. |
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808 char job = '1'; |
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809 Array<octave_idx_type> iz (nc); |
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810 octave_idx_type *piz = iz.fortran_vec (); |
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811 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
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812 nc, tmp_data, nr, anorm, |
| 7788 | 813 rcon, pz, piz, dgecon_info |
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814 F77_CHAR_ARG_LEN (1))); |
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815 |
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816 if (dgecon_info != 0) |
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817 info = -1; |
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818 } |
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819 |
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820 if (info == -1 && ! force) |
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821 retval = *this; // Restore matrix contents. |
| 1948 | 822 else |
| 823 { | |
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824 octave_idx_type dgetri_info = 0; |
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825 |
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826 F77_XFCN (dgetri, DGETRI, (nc, tmp_data, nr, pipvt, |
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827 pz, lwork, dgetri_info)); |
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828 |
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|
829 if (dgetri_info != 0) |
| 1948 | 830 info = -1; |
| 831 } | |
| 6207 | 832 |
| 833 if (info != 0) | |
| 834 mattype.mark_as_rectangular(); | |
| 458 | 835 } |
| 836 | |
| 1948 | 837 return retval; |
| 458 | 838 } |
| 839 | |
| 740 | 840 Matrix |
| 7788 | 841 Matrix::inverse (MatrixType &mattype, octave_idx_type& info, double& rcon, |
| 6207 | 842 int force, int calc_cond) const |
| 843 { | |
| 844 int typ = mattype.type (false); | |
| 845 Matrix ret; | |
| 846 | |
| 847 if (typ == MatrixType::Unknown) | |
| 848 typ = mattype.type (*this); | |
| 849 | |
| 850 if (typ == MatrixType::Upper || typ == MatrixType::Lower) | |
| 7788 | 851 ret = tinverse (mattype, info, rcon, force, calc_cond); |
| 6840 | 852 else |
| 6207 | 853 { |
| 854 if (mattype.is_hermitian ()) | |
| 855 { | |
| 6486 | 856 CHOL chol (*this, info, calc_cond); |
| 6207 | 857 if (info == 0) |
| 6486 | 858 { |
| 859 if (calc_cond) | |
| 7788 | 860 rcon = chol.rcond (); |
| 6486 | 861 else |
| 7788 | 862 rcon = 1.0; |
| 6486 | 863 ret = chol.inverse (); |
| 864 } | |
| 6207 | 865 else |
| 866 mattype.mark_as_unsymmetric (); | |
| 867 } | |
| 868 | |
| 869 if (!mattype.is_hermitian ()) | |
| 7788 | 870 ret = finverse(mattype, info, rcon, force, calc_cond); |
| 871 | |
| 872 if ((mattype.is_hermitian () || calc_cond) && rcon == 0.) | |
| 6840 | 873 ret = Matrix (rows (), columns (), octave_Inf); |
| 6207 | 874 } |
| 875 | |
| 876 return ret; | |
| 877 } | |
| 878 | |
| 879 Matrix | |
| 4384 | 880 Matrix::pseudo_inverse (double tol) const |
| 740 | 881 { |
| 3480 | 882 SVD result (*this, SVD::economy); |
| 740 | 883 |
| 884 DiagMatrix S = result.singular_values (); | |
| 885 Matrix U = result.left_singular_matrix (); | |
| 886 Matrix V = result.right_singular_matrix (); | |
| 887 | |
| 888 ColumnVector sigma = S.diag (); | |
| 889 | |
| 5275 | 890 octave_idx_type r = sigma.length () - 1; |
| 891 octave_idx_type nr = rows (); | |
| 892 octave_idx_type nc = cols (); | |
| 740 | 893 |
| 894 if (tol <= 0.0) | |
| 895 { | |
| 896 if (nr > nc) | |
| 897 tol = nr * sigma.elem (0) * DBL_EPSILON; | |
| 898 else | |
| 899 tol = nc * sigma.elem (0) * DBL_EPSILON; | |
| 900 } | |
| 901 | |
| 902 while (r >= 0 && sigma.elem (r) < tol) | |
| 903 r--; | |
| 904 | |
| 905 if (r < 0) | |
| 906 return Matrix (nc, nr, 0.0); | |
| 907 else | |
| 908 { | |
| 909 Matrix Ur = U.extract (0, 0, nr-1, r); | |
| 910 DiagMatrix D = DiagMatrix (sigma.extract (0, r)) . inverse (); | |
| 911 Matrix Vr = V.extract (0, 0, nc-1, r); | |
| 912 return Vr * D * Ur.transpose (); | |
| 913 } | |
| 914 } | |
| 915 | |
| 4773 | 916 #if defined (HAVE_FFTW3) |
| 3827 | 917 |
| 918 ComplexMatrix | |
| 919 Matrix::fourier (void) const | |
| 920 { | |
| 921 size_t nr = rows (); | |
| 922 size_t nc = cols (); | |
| 923 | |
| 924 ComplexMatrix retval (nr, nc); | |
| 925 | |
| 926 size_t npts, nsamples; | |
| 927 | |
| 928 if (nr == 1 || nc == 1) | |
| 929 { | |
| 930 npts = nr > nc ? nr : nc; | |
| 931 nsamples = 1; | |
| 932 } | |
| 933 else | |
| 934 { | |
| 935 npts = nr; | |
| 936 nsamples = nc; | |
| 937 } | |
| 938 | |
| 4773 | 939 const double *in (fortran_vec ()); |
| 3827 | 940 Complex *out (retval.fortran_vec ()); |
| 941 | |
| 4773 | 942 octave_fftw::fft (in, out, npts, nsamples); |
| 3827 | 943 |
| 944 return retval; | |
| 945 } | |
| 946 | |
| 947 ComplexMatrix | |
| 948 Matrix::ifourier (void) const | |
| 949 { | |
| 950 size_t nr = rows (); | |
| 951 size_t nc = cols (); | |
| 952 | |
| 953 ComplexMatrix retval (nr, nc); | |
| 954 | |
| 955 size_t npts, nsamples; | |
| 956 | |
| 957 if (nr == 1 || nc == 1) | |
| 958 { | |
| 959 npts = nr > nc ? nr : nc; | |
| 960 nsamples = 1; | |
| 961 } | |
| 962 else | |
| 963 { | |
| 964 npts = nr; | |
| 965 nsamples = nc; | |
| 966 } | |
| 967 | |
| 968 ComplexMatrix tmp (*this); | |
| 969 Complex *in (tmp.fortran_vec ()); | |
| 970 Complex *out (retval.fortran_vec ()); | |
| 971 | |
| 4773 | 972 octave_fftw::ifft (in, out, npts, nsamples); |
| 3827 | 973 |
| 974 return retval; | |
| 975 } | |
| 976 | |
| 977 ComplexMatrix | |
| 978 Matrix::fourier2d (void) const | |
| 979 { | |
| 4773 | 980 dim_vector dv(rows (), cols ()); |
| 981 | |
| 982 const double *in = fortran_vec (); | |
| 983 ComplexMatrix retval (rows (), cols ()); | |
| 984 octave_fftw::fftNd (in, retval.fortran_vec (), 2, dv); | |
| 3827 | 985 |
| 986 return retval; | |
| 987 } | |
| 988 | |
| 989 ComplexMatrix | |
| 990 Matrix::ifourier2d (void) const | |
| 991 { | |
| 4773 | 992 dim_vector dv(rows (), cols ()); |
| 3827 | 993 |
| 994 ComplexMatrix retval (*this); | |
| 4773 | 995 Complex *out (retval.fortran_vec ()); |
| 996 | |
| 997 octave_fftw::ifftNd (out, out, 2, dv); | |
| 3827 | 998 |
| 999 return retval; | |
| 1000 } | |
| 1001 | |
| 1002 #else | |
| 1003 | |
| 458 | 1004 ComplexMatrix |
| 1005 Matrix::fourier (void) const | |
| 1006 { | |
| 1948 | 1007 ComplexMatrix retval; |
| 1008 | |
| 5275 | 1009 octave_idx_type nr = rows (); |
| 1010 octave_idx_type nc = cols (); | |
| 1011 | |
| 1012 octave_idx_type npts, nsamples; | |
| 1948 | 1013 |
| 458 | 1014 if (nr == 1 || nc == 1) |
| 1015 { | |
| 1016 npts = nr > nc ? nr : nc; | |
| 1017 nsamples = 1; | |
| 1018 } | |
| 1019 else | |
| 1020 { | |
| 1021 npts = nr; | |
| 1022 nsamples = nc; | |
| 1023 } | |
| 1024 | |
| 5275 | 1025 octave_idx_type nn = 4*npts+15; |
| 1948 | 1026 |
| 1027 Array<Complex> wsave (nn); | |
| 1028 Complex *pwsave = wsave.fortran_vec (); | |
| 1029 | |
| 3585 | 1030 retval = ComplexMatrix (*this); |
| 1948 | 1031 Complex *tmp_data = retval.fortran_vec (); |
| 1032 | |
|
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|
1033 F77_FUNC (zffti, ZFFTI) (npts, pwsave); |
| 458 | 1034 |
| 5275 | 1035 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1036 { |
| 1037 OCTAVE_QUIT; | |
| 1038 | |
|
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|
1039 F77_FUNC (zfftf, ZFFTF) (npts, &tmp_data[npts*j], pwsave); |
| 4153 | 1040 } |
| 1948 | 1041 |
| 1042 return retval; | |
| 458 | 1043 } |
| 1044 | |
| 1045 ComplexMatrix | |
| 1046 Matrix::ifourier (void) const | |
| 1047 { | |
| 1948 | 1048 ComplexMatrix retval; |
| 1049 | |
| 5275 | 1050 octave_idx_type nr = rows (); |
| 1051 octave_idx_type nc = cols (); | |
| 1052 | |
| 1053 octave_idx_type npts, nsamples; | |
| 1948 | 1054 |
| 458 | 1055 if (nr == 1 || nc == 1) |
| 1056 { | |
| 1057 npts = nr > nc ? nr : nc; | |
| 1058 nsamples = 1; | |
| 1059 } | |
| 1060 else | |
| 1061 { | |
| 1062 npts = nr; | |
| 1063 nsamples = nc; | |
| 1064 } | |
| 1065 | |
| 5275 | 1066 octave_idx_type nn = 4*npts+15; |
| 1948 | 1067 |
| 1068 Array<Complex> wsave (nn); | |
| 1069 Complex *pwsave = wsave.fortran_vec (); | |
| 1070 | |
| 3585 | 1071 retval = ComplexMatrix (*this); |
| 1948 | 1072 Complex *tmp_data = retval.fortran_vec (); |
| 1073 | |
|
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|
1074 F77_FUNC (zffti, ZFFTI) (npts, pwsave); |
| 458 | 1075 |
| 5275 | 1076 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1077 { |
| 1078 OCTAVE_QUIT; | |
| 1079 | |
|
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|
1080 F77_FUNC (zfftb, ZFFTB) (npts, &tmp_data[npts*j], pwsave); |
| 4153 | 1081 } |
| 458 | 1082 |
| 5275 | 1083 for (octave_idx_type j = 0; j < npts*nsamples; j++) |
| 3572 | 1084 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
| 458 | 1085 |
| 1948 | 1086 return retval; |
| 458 | 1087 } |
| 1088 | |
| 677 | 1089 ComplexMatrix |
| 1090 Matrix::fourier2d (void) const | |
| 1091 { | |
| 1948 | 1092 ComplexMatrix retval; |
| 1093 | |
| 5275 | 1094 octave_idx_type nr = rows (); |
| 1095 octave_idx_type nc = cols (); | |
| 1096 | |
| 1097 octave_idx_type npts, nsamples; | |
| 1948 | 1098 |
| 677 | 1099 if (nr == 1 || nc == 1) |
| 1100 { | |
| 1101 npts = nr > nc ? nr : nc; | |
| 1102 nsamples = 1; | |
| 1103 } | |
| 1104 else | |
| 1105 { | |
| 1106 npts = nr; | |
| 1107 nsamples = nc; | |
| 1108 } | |
| 1109 | |
| 5275 | 1110 octave_idx_type nn = 4*npts+15; |
| 1948 | 1111 |
| 1112 Array<Complex> wsave (nn); | |
| 1113 Complex *pwsave = wsave.fortran_vec (); | |
| 1114 | |
| 3585 | 1115 retval = ComplexMatrix (*this); |
| 1948 | 1116 Complex *tmp_data = retval.fortran_vec (); |
| 1117 | |
|
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|
1118 F77_FUNC (zffti, ZFFTI) (npts, pwsave); |
| 677 | 1119 |
| 5275 | 1120 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1121 { |
| 1122 OCTAVE_QUIT; | |
| 1123 | |
|
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diff
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|
1124 F77_FUNC (zfftf, ZFFTF) (npts, &tmp_data[npts*j], pwsave); |
| 4153 | 1125 } |
| 677 | 1126 |
| 1127 npts = nc; | |
| 1128 nsamples = nr; | |
| 1129 nn = 4*npts+15; | |
| 1948 | 1130 |
| 1131 wsave.resize (nn); | |
| 1132 pwsave = wsave.fortran_vec (); | |
| 1133 | |
| 4773 | 1134 Array<Complex> tmp (npts); |
| 1135 Complex *prow = tmp.fortran_vec (); | |
| 1948 | 1136 |
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|
1137 F77_FUNC (zffti, ZFFTI) (npts, pwsave); |
| 677 | 1138 |
| 5275 | 1139 for (octave_idx_type j = 0; j < nsamples; j++) |
| 677 | 1140 { |
| 4153 | 1141 OCTAVE_QUIT; |
| 1142 | |
| 5275 | 1143 for (octave_idx_type i = 0; i < npts; i++) |
| 1948 | 1144 prow[i] = tmp_data[i*nr + j]; |
| 1145 | |
|
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|
1146 F77_FUNC (zfftf, ZFFTF) (npts, prow, pwsave); |
| 677 | 1147 |
| 5275 | 1148 for (octave_idx_type i = 0; i < npts; i++) |
| 1948 | 1149 tmp_data[i*nr + j] = prow[i]; |
| 677 | 1150 } |
| 1151 | |
| 1948 | 1152 return retval; |
| 677 | 1153 } |
| 1154 | |
| 1155 ComplexMatrix | |
| 1156 Matrix::ifourier2d (void) const | |
| 1157 { | |
| 1948 | 1158 ComplexMatrix retval; |
| 1159 | |
| 5275 | 1160 octave_idx_type nr = rows (); |
| 1161 octave_idx_type nc = cols (); | |
| 1162 | |
| 1163 octave_idx_type npts, nsamples; | |
| 1948 | 1164 |
| 677 | 1165 if (nr == 1 || nc == 1) |
| 1166 { | |
| 1167 npts = nr > nc ? nr : nc; | |
| 1168 nsamples = 1; | |
| 1169 } | |
| 1170 else | |
| 1171 { | |
| 1172 npts = nr; | |
| 1173 nsamples = nc; | |
| 1174 } | |
| 1175 | |
| 5275 | 1176 octave_idx_type nn = 4*npts+15; |
| 1948 | 1177 |
| 1178 Array<Complex> wsave (nn); | |
| 1179 Complex *pwsave = wsave.fortran_vec (); | |
| 1180 | |
| 3585 | 1181 retval = ComplexMatrix (*this); |
| 1948 | 1182 Complex *tmp_data = retval.fortran_vec (); |
| 1183 | |
|
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|
1184 F77_FUNC (zffti, ZFFTI) (npts, pwsave); |
| 677 | 1185 |
| 5275 | 1186 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1187 { |
| 1188 OCTAVE_QUIT; | |
| 1189 | |
|
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|
1190 F77_FUNC (zfftb, ZFFTB) (npts, &tmp_data[npts*j], pwsave); |
| 4153 | 1191 } |
| 677 | 1192 |
| 5275 | 1193 for (octave_idx_type j = 0; j < npts*nsamples; j++) |
| 3572 | 1194 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
| 677 | 1195 |
| 1196 npts = nc; | |
| 1197 nsamples = nr; | |
| 1198 nn = 4*npts+15; | |
| 1948 | 1199 |
| 1200 wsave.resize (nn); | |
| 1201 pwsave = wsave.fortran_vec (); | |
| 1202 | |
| 4773 | 1203 Array<Complex> tmp (npts); |
| 1204 Complex *prow = tmp.fortran_vec (); | |
| 1948 | 1205 |
|
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|
1206 F77_FUNC (zffti, ZFFTI) (npts, pwsave); |
| 677 | 1207 |
| 5275 | 1208 for (octave_idx_type j = 0; j < nsamples; j++) |
| 677 | 1209 { |
| 4153 | 1210 OCTAVE_QUIT; |
| 1211 | |
| 5275 | 1212 for (octave_idx_type i = 0; i < npts; i++) |
| 1948 | 1213 prow[i] = tmp_data[i*nr + j]; |
| 1214 | |
|
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|
1215 F77_FUNC (zfftb, ZFFTB) (npts, prow, pwsave); |
| 677 | 1216 |
| 5275 | 1217 for (octave_idx_type i = 0; i < npts; i++) |
| 3572 | 1218 tmp_data[i*nr + j] = prow[i] / static_cast<double> (npts); |
| 677 | 1219 } |
| 1220 | |
| 1948 | 1221 return retval; |
| 677 | 1222 } |
| 1223 | |
| 3827 | 1224 #endif |
| 1225 | |
| 458 | 1226 DET |
| 1227 Matrix::determinant (void) const | |
| 1228 { | |
| 5275 | 1229 octave_idx_type info; |
| 7788 | 1230 double rcon; |
| 1231 return determinant (info, rcon, 0); | |
| 458 | 1232 } |
| 1233 | |
| 1234 DET | |
| 5275 | 1235 Matrix::determinant (octave_idx_type& info) const |
| 458 | 1236 { |
| 7788 | 1237 double rcon; |
| 1238 return determinant (info, rcon, 0); | |
| 458 | 1239 } |
| 1240 | |
| 1241 DET | |
| 7788 | 1242 Matrix::determinant (octave_idx_type& info, double& rcon, int calc_cond) const |
| 458 | 1243 { |
|
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|
1244 MatrixType mattype (*this); |
|
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|
1245 return determinant (mattype, info, rcon, calc_cond); |
|
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1246 } |
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|
1247 |
|
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|
1248 DET |
|
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|
1249 Matrix::determinant (MatrixType& mattype, |
|
9813c07ca946
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|
1250 octave_idx_type& info, double& rcon, int calc_cond) const |
|
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|
1251 { |
|
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|
1252 DET retval (1.0); |
| 458 | 1253 |
| 5275 | 1254 octave_idx_type nr = rows (); |
| 1255 octave_idx_type nc = cols (); | |
| 458 | 1256 |
|
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1257 if (nr != nc) |
|
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1258 (*current_liboctave_error_handler) ("matrix must be square"); |
| 458 | 1259 else |
| 1260 { | |
|
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1261 int typ = mattype.type (); |
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1262 |
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1263 if (typ == MatrixType::Lower || typ == MatrixType::Upper) |
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1264 { |
|
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1265 for (octave_idx_type i = 0; i < nc; i++) |
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1266 retval *= elem (i,i); |
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1267 } |
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1268 else if (typ == MatrixType::Hermitian) |
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1269 { |
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1270 Matrix atmp = *this; |
|
9813c07ca946
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1271 double *tmp_data = atmp.fortran_vec (); |
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1272 |
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1273 info = 0; |
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1274 double anorm = 0; |
|
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|
1275 if (calc_cond) anorm = xnorm (*this, 1); |
|
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|
1276 |
|
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|
1277 |
|
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|
1278 char job = 'L'; |
|
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1279 F77_XFCN (dpotrf, DPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, |
|
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1280 tmp_data, nr, info |
|
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|
1281 F77_CHAR_ARG_LEN (1))); |
|
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|
1282 |
|
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1283 if (info != 0) |
|
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1284 { |
|
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|
1285 rcon = 0.0; |
|
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1286 mattype.mark_as_unsymmetric (); |
|
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1287 typ = MatrixType::Full; |
|
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1288 } |
|
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1289 else |
|
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|
1290 { |
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1291 Array<double> z (3 * nc); |
|
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1292 double *pz = z.fortran_vec (); |
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1293 Array<octave_idx_type> iz (nc); |
|
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1294 octave_idx_type *piz = iz.fortran_vec (); |
|
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1295 |
|
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|
1296 F77_XFCN (dpocon, DPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
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1297 nr, tmp_data, nr, anorm, |
|
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1298 rcon, pz, piz, info |
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1299 F77_CHAR_ARG_LEN (1))); |
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|
1300 |
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1301 if (info != 0) |
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1302 rcon = 0.0; |
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|
1303 |
|
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1304 for (octave_idx_type i = 0; i < nc; i++) |
|
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1305 retval *= elem (i,i); |
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1306 |
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1307 retval = retval.square (); |
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1308 } |
|
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|
1309 } |
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1310 else if (typ != MatrixType::Full) |
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1311 (*current_liboctave_error_handler) ("det: invalid dense matrix type"); |
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|
1312 |
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1313 if (typ == MatrixType::Full) |
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1314 { |
|
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1315 Array<octave_idx_type> ipvt (nr); |
|
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1316 octave_idx_type *pipvt = ipvt.fortran_vec (); |
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1317 |
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1318 Matrix atmp = *this; |
|
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1319 double *tmp_data = atmp.fortran_vec (); |
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|
1320 |
|
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1321 info = 0; |
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1322 |
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1323 // Calculate the norm of the matrix, for later use. |
|
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1324 double anorm = 0; |
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1325 if (calc_cond) anorm = xnorm (*this, 1); |
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1326 |
|
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1327 F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); |
|
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1328 |
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1329 // Throw-away extra info LAPACK gives so as to not change output. |
|
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1330 rcon = 0.0; |
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1331 if (info != 0) |
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1332 { |
|
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1333 info = -1; |
|
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1334 retval = DET (); |
|
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1335 } |
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|
1336 else |
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|
1337 { |
|
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1338 if (calc_cond) |
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1339 { |
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1340 // Now calc the condition number for non-singular matrix. |
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1341 char job = '1'; |
|
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1342 Array<double> z (4 * nc); |
|
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1343 double *pz = z.fortran_vec (); |
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1344 Array<octave_idx_type> iz (nc); |
|
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1345 octave_idx_type *piz = iz.fortran_vec (); |
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1346 |
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1347 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
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1348 nc, tmp_data, nr, anorm, |
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1349 rcon, pz, piz, info |
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|
1350 F77_CHAR_ARG_LEN (1))); |
| 8335 | 1351 } |
|
8336
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1352 |
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1353 if (info != 0) |
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1354 { |
|
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1355 info = -1; |
|
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1356 retval = DET (); |
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1357 } |
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1358 else |
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|
1359 { |
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1360 for (octave_idx_type i = 0; i < nc; i++) |
|
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1361 { |
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1362 double c = atmp(i,i); |
|
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1363 retval *= (ipvt(i) != (i+1)) ? -c : c; |
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1364 } |
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|
1365 } |
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|
1366 } |
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|
1367 } |
| 458 | 1368 } |
| 1369 | |
| 1370 return retval; | |
| 1371 } | |
| 1372 | |
| 7788 | 1373 double |
| 1374 Matrix::rcond (void) const | |
| 1375 { | |
| 1376 MatrixType mattype (*this); | |
| 1377 return rcond (mattype); | |
| 1378 } | |
| 1379 | |
| 1380 double | |
| 1381 Matrix::rcond (MatrixType &mattype) const | |
| 1382 { | |
| 1383 double rcon; | |
| 1384 octave_idx_type nr = rows (); | |
| 1385 octave_idx_type nc = cols (); | |
| 1386 | |
| 1387 if (nr != nc) | |
| 1388 (*current_liboctave_error_handler) ("matrix must be square"); | |
| 1389 else if (nr == 0 || nc == 0) | |
| 1390 rcon = octave_Inf; | |
| 1391 else | |
| 1392 { | |
| 1393 int typ = mattype.type (); | |
| 1394 | |
| 1395 if (typ == MatrixType::Unknown) | |
| 1396 typ = mattype.type (*this); | |
| 1397 | |
| 1398 // Only calculate the condition number for LU/Cholesky | |
| 1399 if (typ == MatrixType::Upper) | |
| 1400 { | |
| 1401 const double *tmp_data = fortran_vec (); | |
| 1402 octave_idx_type info = 0; | |
| 1403 char norm = '1'; | |
| 1404 char uplo = 'U'; | |
| 1405 char dia = 'N'; | |
| 1406 | |
| 1407 Array<double> z (3 * nc); | |
| 1408 double *pz = z.fortran_vec (); | |
| 1409 Array<octave_idx_type> iz (nc); | |
| 1410 octave_idx_type *piz = iz.fortran_vec (); | |
| 1411 | |
| 1412 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1413 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1414 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1415 nr, tmp_data, nr, rcon, | |
| 1416 pz, piz, info | |
| 1417 F77_CHAR_ARG_LEN (1) | |
| 1418 F77_CHAR_ARG_LEN (1) | |
| 1419 F77_CHAR_ARG_LEN (1))); | |
| 1420 | |
| 1421 if (info != 0) | |
| 1422 rcon = 0.0; | |
| 1423 } | |
| 1424 else if (typ == MatrixType::Permuted_Upper) | |
| 1425 (*current_liboctave_error_handler) | |
| 1426 ("permuted triangular matrix not implemented"); | |
| 1427 else if (typ == MatrixType::Lower) | |
| 1428 { | |
| 1429 const double *tmp_data = fortran_vec (); | |
| 1430 octave_idx_type info = 0; | |
| 1431 char norm = '1'; | |
| 1432 char uplo = 'L'; | |
| 1433 char dia = 'N'; | |
| 1434 | |
| 1435 Array<double> z (3 * nc); | |
| 1436 double *pz = z.fortran_vec (); | |
| 1437 Array<octave_idx_type> iz (nc); | |
| 1438 octave_idx_type *piz = iz.fortran_vec (); | |
| 1439 | |
| 1440 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1441 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1442 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1443 nr, tmp_data, nr, rcon, | |
| 1444 pz, piz, info | |
| 1445 F77_CHAR_ARG_LEN (1) | |
| 1446 F77_CHAR_ARG_LEN (1) | |
| 1447 F77_CHAR_ARG_LEN (1))); | |
| 1448 | |
| 1449 if (info != 0) | |
| 1450 rcon = 0.0; | |
| 1451 } | |
| 1452 else if (typ == MatrixType::Permuted_Lower) | |
| 1453 (*current_liboctave_error_handler) | |
| 1454 ("permuted triangular matrix not implemented"); | |
| 1455 else if (typ == MatrixType::Full || typ == MatrixType::Hermitian) | |
| 1456 { | |
| 1457 double anorm = -1.0; | |
| 1458 Matrix atmp = *this; | |
| 1459 double *tmp_data = atmp.fortran_vec (); | |
| 1460 | |
| 1461 if (typ == MatrixType::Hermitian) | |
| 1462 { | |
| 1463 octave_idx_type info = 0; | |
| 1464 char job = 'L'; | |
| 1465 anorm = atmp.abs().sum(). | |
| 1466 row(static_cast<octave_idx_type>(0)).max(); | |
| 1467 | |
| 1468 F77_XFCN (dpotrf, DPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, | |
| 1469 tmp_data, nr, info | |
| 1470 F77_CHAR_ARG_LEN (1))); | |
| 1471 | |
| 1472 if (info != 0) | |
| 1473 { | |
| 1474 rcon = 0.0; | |
| 1475 mattype.mark_as_unsymmetric (); | |
| 1476 typ = MatrixType::Full; | |
| 1477 } | |
| 1478 else | |
| 1479 { | |
| 1480 Array<double> z (3 * nc); | |
| 1481 double *pz = z.fortran_vec (); | |
| 1482 Array<octave_idx_type> iz (nc); | |
| 1483 octave_idx_type *piz = iz.fortran_vec (); | |
| 1484 | |
| 1485 F77_XFCN (dpocon, DPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), | |
| 1486 nr, tmp_data, nr, anorm, | |
| 1487 rcon, pz, piz, info | |
| 1488 F77_CHAR_ARG_LEN (1))); | |
| 1489 | |
| 1490 if (info != 0) | |
| 1491 rcon = 0.0; | |
| 1492 } | |
| 1493 } | |
| 1494 | |
| 1495 if (typ == MatrixType::Full) | |
| 1496 { | |
| 1497 octave_idx_type info = 0; | |
| 1498 | |
| 1499 Array<octave_idx_type> ipvt (nr); | |
| 1500 octave_idx_type *pipvt = ipvt.fortran_vec (); | |
| 1501 | |
| 1502 if(anorm < 0.) | |
| 1503 anorm = atmp.abs().sum(). | |
| 1504 row(static_cast<octave_idx_type>(0)).max(); | |
| 1505 | |
| 1506 Array<double> z (4 * nc); | |
| 1507 double *pz = z.fortran_vec (); | |
| 1508 Array<octave_idx_type> iz (nc); | |
| 1509 octave_idx_type *piz = iz.fortran_vec (); | |
| 1510 | |
| 1511 F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); | |
| 1512 | |
| 1513 if (info != 0) | |
| 1514 { | |
| 1515 rcon = 0.0; | |
| 1516 mattype.mark_as_rectangular (); | |
| 1517 } | |
| 1518 else | |
| 1519 { | |
| 1520 char job = '1'; | |
| 1521 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), | |
| 1522 nc, tmp_data, nr, anorm, | |
| 1523 rcon, pz, piz, info | |
| 1524 F77_CHAR_ARG_LEN (1))); | |
| 1525 | |
| 1526 if (info != 0) | |
| 1527 rcon = 0.0; | |
| 1528 } | |
| 1529 } | |
| 1530 } | |
| 1531 else | |
| 1532 rcon = 0.0; | |
| 1533 } | |
| 1534 | |
| 1535 return rcon; | |
| 1536 } | |
| 1537 | |
| 458 | 1538 Matrix |
| 5785 | 1539 Matrix::utsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, |
| 7788 | 1540 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 1541 bool calc_cond) const |
| 1542 { | |
| 1543 Matrix retval; | |
| 1544 | |
| 1545 octave_idx_type nr = rows (); | |
| 1546 octave_idx_type nc = cols (); | |
| 1547 | |
| 6924 | 1548 if (nr != b.rows ()) |
| 5785 | 1549 (*current_liboctave_error_handler) |
| 1550 ("matrix dimension mismatch solution of linear equations"); | |
| 6924 | 1551 else if (nr == 0 || nc == 0 || b.cols () == 0) |
| 1552 retval = Matrix (nc, b.cols (), 0.0); | |
| 5785 | 1553 else |
| 1554 { | |
| 1555 volatile int typ = mattype.type (); | |
| 1556 | |
| 1557 if (typ == MatrixType::Permuted_Upper || | |
| 1558 typ == MatrixType::Upper) | |
| 1559 { | |
| 1560 octave_idx_type b_nc = b.cols (); | |
| 7788 | 1561 rcon = 1.; |
| 5785 | 1562 info = 0; |
| 1563 | |
| 1564 if (typ == MatrixType::Permuted_Upper) | |
| 1565 { | |
| 1566 (*current_liboctave_error_handler) | |
| 6390 | 1567 ("permuted triangular matrix not implemented"); |
| 5785 | 1568 } |
| 1569 else | |
| 1570 { | |
| 1571 const double *tmp_data = fortran_vec (); | |
| 1572 | |
| 1573 if (calc_cond) | |
| 1574 { | |
| 1575 char norm = '1'; | |
| 1576 char uplo = 'U'; | |
| 1577 char dia = 'N'; | |
| 1578 | |
| 1579 Array<double> z (3 * nc); | |
| 1580 double *pz = z.fortran_vec (); | |
| 1581 Array<octave_idx_type> iz (nc); | |
| 1582 octave_idx_type *piz = iz.fortran_vec (); | |
| 1583 | |
| 1584 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1585 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1586 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 7788 | 1587 nr, tmp_data, nr, rcon, |
| 5785 | 1588 pz, piz, info |
| 1589 F77_CHAR_ARG_LEN (1) | |
| 1590 F77_CHAR_ARG_LEN (1) | |
| 1591 F77_CHAR_ARG_LEN (1))); | |
| 1592 | |
| 1593 if (info != 0) | |
| 1594 info = -2; | |
| 1595 | |
| 7788 | 1596 volatile double rcond_plus_one = rcon + 1.0; |
| 1597 | |
| 1598 if (rcond_plus_one == 1.0 || xisnan (rcon)) | |
| 5785 | 1599 { |
| 1600 info = -2; | |
| 1601 | |
| 1602 if (sing_handler) | |
| 7788 | 1603 sing_handler (rcon); |
| 5785 | 1604 else |
| 1605 (*current_liboctave_error_handler) | |
| 1606 ("matrix singular to machine precision, rcond = %g", | |
| 7788 | 1607 rcon); |
| 5785 | 1608 } |
| 1609 } | |
| 1610 | |
| 1611 if (info == 0) | |
| 1612 { | |
| 1613 retval = b; | |
| 1614 double *result = retval.fortran_vec (); | |
| 1615 | |
| 1616 char uplo = 'U'; | |
| 1617 char trans = 'N'; | |
| 1618 char dia = 'N'; | |
| 1619 | |
| 1620 F77_XFCN (dtrtrs, DTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1621 F77_CONST_CHAR_ARG2 (&trans, 1), | |
| 1622 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1623 nr, b_nc, tmp_data, nr, | |
| 1624 result, nr, info | |
| 1625 F77_CHAR_ARG_LEN (1) | |
| 1626 F77_CHAR_ARG_LEN (1) | |
| 1627 F77_CHAR_ARG_LEN (1))); | |
| 1628 } | |
| 1629 } | |
| 1630 } | |
| 1631 else | |
| 1632 (*current_liboctave_error_handler) ("incorrect matrix type"); | |
| 1633 } | |
| 1634 | |
| 1635 return retval; | |
| 1636 } | |
| 1637 | |
| 1638 Matrix | |
| 1639 Matrix::ltsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, | |
| 7788 | 1640 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 1641 bool calc_cond) const |
| 1642 { | |
| 1643 Matrix retval; | |
| 1644 | |
| 1645 octave_idx_type nr = rows (); | |
| 1646 octave_idx_type nc = cols (); | |
| 1647 | |
| 6924 | 1648 if (nr != b.rows ()) |
| 5785 | 1649 (*current_liboctave_error_handler) |
| 1650 ("matrix dimension mismatch solution of linear equations"); | |
| 6924 | 1651 else if (nr == 0 || nc == 0 || b.cols () == 0) |
| 1652 retval = Matrix (nc, b.cols (), 0.0); | |
| 5785 | 1653 else |
| 1654 { | |
| 1655 volatile int typ = mattype.type (); | |
| 1656 | |
| 1657 if (typ == MatrixType::Permuted_Lower || | |
| 1658 typ == MatrixType::Lower) | |
| 1659 { | |
| 1660 octave_idx_type b_nc = b.cols (); | |
| 7788 | 1661 rcon = 1.; |
| 5785 | 1662 info = 0; |
| 1663 | |
| 1664 if (typ == MatrixType::Permuted_Lower) | |
| 1665 { | |
| 1666 (*current_liboctave_error_handler) | |
| 6390 | 1667 ("permuted triangular matrix not implemented"); |
| 5785 | 1668 } |
| 1669 else | |
| 1670 { | |
| 1671 const double *tmp_data = fortran_vec (); | |
| 1672 | |
| 1673 if (calc_cond) | |
| 1674 { | |
| 1675 char norm = '1'; | |
| 1676 char uplo = 'L'; | |
| 1677 char dia = 'N'; | |
| 1678 | |
| 1679 Array<double> z (3 * nc); | |
| 1680 double *pz = z.fortran_vec (); | |
| 1681 Array<octave_idx_type> iz (nc); | |
| 1682 octave_idx_type *piz = iz.fortran_vec (); | |
| 1683 | |
| 1684 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1685 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1686 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 7788 | 1687 nr, tmp_data, nr, rcon, |
| 5785 | 1688 pz, piz, info |
| 1689 F77_CHAR_ARG_LEN (1) | |
| 1690 F77_CHAR_ARG_LEN (1) | |
| 1691 F77_CHAR_ARG_LEN (1))); | |
| 1692 | |
| 1693 if (info != 0) | |
| 1694 info = -2; | |
| 1695 | |
| 7788 | 1696 volatile double rcond_plus_one = rcon + 1.0; |
| 1697 | |
| 1698 if (rcond_plus_one == 1.0 || xisnan (rcon)) | |
| 5785 | 1699 { |
| 1700 info = -2; | |
| 1701 | |
| 1702 if (sing_handler) | |
| 7788 | 1703 sing_handler (rcon); |
| 5785 | 1704 else |
| 1705 (*current_liboctave_error_handler) | |
| 1706 ("matrix singular to machine precision, rcond = %g", | |
| 7788 | 1707 rcon); |
| 5785 | 1708 } |
| 1709 } | |
| 1710 | |
| 1711 if (info == 0) | |
| 1712 { | |
| 1713 retval = b; | |
| 1714 double *result = retval.fortran_vec (); | |
| 1715 | |
| 1716 char uplo = 'L'; | |
| 1717 char trans = 'N'; | |
| 1718 char dia = 'N'; | |
| 1719 | |
| 1720 F77_XFCN (dtrtrs, DTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1721 F77_CONST_CHAR_ARG2 (&trans, 1), | |
| 1722 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1723 nr, b_nc, tmp_data, nr, | |
| 1724 result, nr, info | |
| 1725 F77_CHAR_ARG_LEN (1) | |
| 1726 F77_CHAR_ARG_LEN (1) | |
| 1727 F77_CHAR_ARG_LEN (1))); | |
| 1728 } | |
| 1729 } | |
| 1730 } | |
| 1731 else | |
| 1732 (*current_liboctave_error_handler) ("incorrect matrix type"); | |
| 1733 } | |
| 1734 | |
| 1735 return retval; | |
| 1736 } | |
| 1737 | |
| 1738 Matrix | |
| 1739 Matrix::fsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, | |
| 7788 | 1740 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 1741 bool calc_cond) const |
| 1742 { | |
| 1743 Matrix retval; | |
| 1744 | |
| 1745 octave_idx_type nr = rows (); | |
| 1746 octave_idx_type nc = cols (); | |
| 1747 | |
| 6924 | 1748 if (nr != nc || nr != b.rows ()) |
| 5785 | 1749 (*current_liboctave_error_handler) |
| 1750 ("matrix dimension mismatch solution of linear equations"); | |
| 6924 | 1751 else if (nr == 0 || b.cols () == 0) |
| 1752 retval = Matrix (nc, b.cols (), 0.0); | |
| 5785 | 1753 else |
| 1754 { | |
| 1755 volatile int typ = mattype.type (); | |
| 1756 | |
| 1757 // Calculate the norm of the matrix, for later use. | |
| 1758 double anorm = -1.; | |
| 1759 | |
| 1760 if (typ == MatrixType::Hermitian) | |
| 1761 { | |
| 1762 info = 0; | |
| 1763 char job = 'L'; | |
| 1764 Matrix atmp = *this; | |
| 1765 double *tmp_data = atmp.fortran_vec (); | |
| 1766 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); | |
| 1767 | |
| 1768 F77_XFCN (dpotrf, DPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, | |
| 1769 tmp_data, nr, info | |
| 1770 F77_CHAR_ARG_LEN (1))); | |
| 1771 | |
|
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1772 // Throw-away extra info LAPACK gives so as to not change output. |
| 7788 | 1773 rcon = 0.0; |
|
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|
1774 if (info != 0) |
|
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|
1775 { |
|
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|
1776 info = -2; |
|
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|
1777 |
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|
1778 mattype.mark_as_unsymmetric (); |
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1779 typ = MatrixType::Full; |
|
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1780 } |
|
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1781 else |
| 5785 | 1782 { |
|
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|
1783 if (calc_cond) |
| 5785 | 1784 { |
|
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|
1785 Array<double> z (3 * nc); |
|
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|
1786 double *pz = z.fortran_vec (); |
|
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|
1787 Array<octave_idx_type> iz (nc); |
|
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|
1788 octave_idx_type *piz = iz.fortran_vec (); |
|
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|
1789 |
|
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|
1790 F77_XFCN (dpocon, DPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
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|
1791 nr, tmp_data, nr, anorm, |
| 7788 | 1792 rcon, pz, piz, info |
|
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1793 F77_CHAR_ARG_LEN (1))); |
|
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|
1794 |
|
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|
1795 if (info != 0) |
|
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|
1796 info = -2; |
|
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|
1797 |
| 7788 | 1798 volatile double rcond_plus_one = rcon + 1.0; |
| 1799 | |
| 1800 if (rcond_plus_one == 1.0 || xisnan (rcon)) | |
|
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|
1801 { |
|
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|
1802 info = -2; |
|
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|
1803 |
|
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|
1804 if (sing_handler) |
| 7788 | 1805 sing_handler (rcon); |
|
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|
1806 else |
|
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1807 (*current_liboctave_error_handler) |
|
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|
1808 ("matrix singular to machine precision, rcond = %g", |
| 7788 | 1809 rcon); |
|
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|
1810 } |
|
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1811 } |
|
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|
1812 |
|
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1813 if (info == 0) |
|
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1814 { |
|
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1815 retval = b; |
|
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1816 double *result = retval.fortran_vec (); |
|
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1817 |
|
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1818 octave_idx_type b_nc = b.cols (); |
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1819 |
|
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1820 F77_XFCN (dpotrs, DPOTRS, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
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1821 nr, b_nc, tmp_data, nr, |
|
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1822 result, b.rows(), info |
|
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1823 F77_CHAR_ARG_LEN (1))); |
|
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1824 } |
|
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1825 else |
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|
1826 { |
| 5785 | 1827 mattype.mark_as_unsymmetric (); |
| 1828 typ = MatrixType::Full; | |
|
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|
1829 } |
| 5785 | 1830 } |
| 1831 } | |
| 1832 | |
| 1833 if (typ == MatrixType::Full) | |
| 1834 { | |
| 1835 info = 0; | |
| 1836 | |
| 1837 Array<octave_idx_type> ipvt (nr); | |
| 1838 octave_idx_type *pipvt = ipvt.fortran_vec (); | |
| 1839 | |
| 1840 Matrix atmp = *this; | |
| 1841 double *tmp_data = atmp.fortran_vec (); | |
| 1842 if(anorm < 0.) | |
| 1843 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); | |
| 1844 | |
| 1845 Array<double> z (4 * nc); | |
| 1846 double *pz = z.fortran_vec (); | |
| 1847 Array<octave_idx_type> iz (nc); | |
| 1848 octave_idx_type *piz = iz.fortran_vec (); | |
| 1849 | |
| 1850 F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); | |
| 1851 | |
|
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|
1852 // Throw-away extra info LAPACK gives so as to not change output. |
| 7788 | 1853 rcon = 0.0; |
|
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|
1854 if (info != 0) |
| 5785 | 1855 { |
|
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|
1856 info = -2; |
|
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1857 |
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1858 if (sing_handler) |
| 7788 | 1859 sing_handler (rcon); |
|
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1860 else |
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1861 (*current_liboctave_error_handler) |
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1862 ("matrix singular to machine precision"); |
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1863 |
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1864 mattype.mark_as_rectangular (); |
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1865 } |
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1866 else |
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1867 { |
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1868 if (calc_cond) |
| 5785 | 1869 { |
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1870 // Now calculate the condition number for |
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1871 // non-singular matrix. |
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1872 char job = '1'; |
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1873 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
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1874 nc, tmp_data, nr, anorm, |
| 7788 | 1875 rcon, pz, piz, info |
|
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1876 F77_CHAR_ARG_LEN (1))); |
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1877 |
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1878 if (info != 0) |
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1879 info = -2; |
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1880 |
| 7788 | 1881 volatile double rcond_plus_one = rcon + 1.0; |
| 1882 | |
| 1883 if (rcond_plus_one == 1.0 || xisnan (rcon)) | |
| 5785 | 1884 { |
|
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1885 info = -2; |
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1886 |
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1887 if (sing_handler) |
| 7788 | 1888 sing_handler (rcon); |
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1889 else |
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1890 (*current_liboctave_error_handler) |
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1891 ("matrix singular to machine precision, rcond = %g", |
| 7788 | 1892 rcon); |
| 5785 | 1893 } |
| 1894 } | |
|
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1895 |
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1896 if (info == 0) |
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1897 { |
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1898 retval = b; |
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1899 double *result = retval.fortran_vec (); |
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1900 |
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1901 octave_idx_type b_nc = b.cols (); |
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1902 |
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1903 char job = 'N'; |
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1904 F77_XFCN (dgetrs, DGETRS, (F77_CONST_CHAR_ARG2 (&job, 1), |
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1905 nr, b_nc, tmp_data, nr, |
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1906 pipvt, result, b.rows(), info |
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1907 F77_CHAR_ARG_LEN (1))); |
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1908 } |
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1909 else |
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|
1910 mattype.mark_as_rectangular (); |
| 5785 | 1911 } |
| 1912 } | |
| 1913 else if (typ != MatrixType::Hermitian) | |
| 1914 (*current_liboctave_error_handler) ("incorrect matrix type"); | |
| 1915 } | |
| 1916 | |
| 1917 return retval; | |
| 1918 } | |
| 1919 | |
| 1920 Matrix | |
| 1921 Matrix::solve (MatrixType &typ, const Matrix& b) const | |
| 1922 { | |
| 1923 octave_idx_type info; | |
| 7788 | 1924 double rcon; |
| 1925 return solve (typ, b, info, rcon, 0); | |
| 5785 | 1926 } |
| 1927 | |
| 1928 Matrix | |
| 1929 Matrix::solve (MatrixType &typ, const Matrix& b, octave_idx_type& info, | |
| 7788 | 1930 double& rcon) const |
| 5785 | 1931 { |
| 7788 | 1932 return solve (typ, b, info, rcon, 0); |
| 5785 | 1933 } |
| 1934 | |
| 1935 Matrix | |
| 1936 Matrix::solve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, | |
| 7788 | 1937 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 1938 bool singular_fallback) const |
| 1939 { | |
| 1940 Matrix retval; | |
| 1941 int typ = mattype.type (); | |
| 1942 | |
| 1943 if (typ == MatrixType::Unknown) | |
| 1944 typ = mattype.type (*this); | |
| 1945 | |
| 1946 // Only calculate the condition number for LU/Cholesky | |
| 1947 if (typ == MatrixType::Upper || typ == MatrixType::Permuted_Upper) | |
| 7788 | 1948 retval = utsolve (mattype, b, info, rcon, sing_handler, false); |
| 5785 | 1949 else if (typ == MatrixType::Lower || typ == MatrixType::Permuted_Lower) |
| 7788 | 1950 retval = ltsolve (mattype, b, info, rcon, sing_handler, false); |
| 5785 | 1951 else if (typ == MatrixType::Full || typ == MatrixType::Hermitian) |
| 7788 | 1952 retval = fsolve (mattype, b, info, rcon, sing_handler, true); |
| 5785 | 1953 else if (typ != MatrixType::Rectangular) |
| 1954 { | |
| 1955 (*current_liboctave_error_handler) ("unknown matrix type"); | |
| 1956 return Matrix (); | |
| 1957 } | |
| 1958 | |
| 1959 // Rectangular or one of the above solvers flags a singular matrix | |
| 1960 if (singular_fallback && mattype.type () == MatrixType::Rectangular) | |
| 1961 { | |
| 1962 octave_idx_type rank; | |
| 7788 | 1963 retval = lssolve (b, info, rank, rcon); |
| 5785 | 1964 } |
| 1965 | |
| 1966 return retval; | |
| 1967 } | |
| 1968 | |
| 1969 ComplexMatrix | |
| 1970 Matrix::solve (MatrixType &typ, const ComplexMatrix& b) const | |
| 1971 { | |
| 1972 ComplexMatrix tmp (*this); | |
| 1973 return tmp.solve (typ, b); | |
| 1974 } | |
| 1975 | |
| 1976 ComplexMatrix | |
| 1977 Matrix::solve (MatrixType &typ, const ComplexMatrix& b, | |
| 1978 octave_idx_type& info) const | |
| 1979 { | |
| 1980 ComplexMatrix tmp (*this); | |
| 1981 return tmp.solve (typ, b, info); | |
| 1982 } | |
| 1983 | |
| 1984 ComplexMatrix | |
| 1985 Matrix::solve (MatrixType &typ, const ComplexMatrix& b, octave_idx_type& info, | |
| 7788 | 1986 double& rcon) const |
| 5785 | 1987 { |
| 1988 ComplexMatrix tmp (*this); | |
| 7788 | 1989 return tmp.solve (typ, b, info, rcon); |
| 5785 | 1990 } |
| 1991 | |
| 1992 ComplexMatrix | |
| 1993 Matrix::solve (MatrixType &typ, const ComplexMatrix& b, octave_idx_type& info, | |
| 7788 | 1994 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 1995 bool singular_fallback) const |
| 1996 { | |
| 1997 ComplexMatrix tmp (*this); | |
| 7788 | 1998 return tmp.solve (typ, b, info, rcon, sing_handler, singular_fallback); |
| 5785 | 1999 } |
| 2000 | |
| 2001 ColumnVector | |
| 2002 Matrix::solve (MatrixType &typ, const ColumnVector& b) const | |
| 2003 { | |
| 7788 | 2004 octave_idx_type info; double rcon; |
| 2005 return solve (typ, b, info, rcon); | |
| 5785 | 2006 } |
| 2007 | |
| 2008 ColumnVector | |
| 2009 Matrix::solve (MatrixType &typ, const ColumnVector& b, | |
| 2010 octave_idx_type& info) const | |
| 2011 { | |
| 7788 | 2012 double rcon; |
| 2013 return solve (typ, b, info, rcon); | |
| 5785 | 2014 } |
| 2015 | |
| 2016 ColumnVector | |
| 2017 Matrix::solve (MatrixType &typ, const ColumnVector& b, octave_idx_type& info, | |
| 7788 | 2018 double& rcon) const |
| 5785 | 2019 { |
| 7788 | 2020 return solve (typ, b, info, rcon, 0); |
| 5785 | 2021 } |
| 2022 | |
| 2023 ColumnVector | |
| 2024 Matrix::solve (MatrixType &typ, const ColumnVector& b, octave_idx_type& info, | |
| 7788 | 2025 double& rcon, solve_singularity_handler sing_handler) const |
| 5785 | 2026 { |
| 2027 Matrix tmp (b); | |
| 7788 | 2028 return solve (typ, tmp, info, rcon, sing_handler).column(static_cast<octave_idx_type> (0)); |
| 5785 | 2029 } |
| 2030 | |
| 2031 ComplexColumnVector | |
| 2032 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b) const | |
| 2033 { | |
| 2034 ComplexMatrix tmp (*this); | |
| 2035 return tmp.solve (typ, b); | |
| 2036 } | |
| 2037 | |
| 2038 ComplexColumnVector | |
| 2039 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, | |
| 2040 octave_idx_type& info) const | |
| 2041 { | |
| 2042 ComplexMatrix tmp (*this); | |
| 2043 return tmp.solve (typ, b, info); | |
| 2044 } | |
| 2045 | |
| 2046 ComplexColumnVector | |
| 2047 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, | |
| 7788 | 2048 octave_idx_type& info, double& rcon) const |
| 5785 | 2049 { |
| 2050 ComplexMatrix tmp (*this); | |
| 7788 | 2051 return tmp.solve (typ, b, info, rcon); |
| 5785 | 2052 } |
| 2053 | |
| 2054 ComplexColumnVector | |
| 2055 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, | |
| 7788 | 2056 octave_idx_type& info, double& rcon, |
| 5785 | 2057 solve_singularity_handler sing_handler) const |
| 2058 { | |
| 2059 ComplexMatrix tmp (*this); | |
| 7788 | 2060 return tmp.solve(typ, b, info, rcon, sing_handler); |
| 5785 | 2061 } |
| 2062 | |
| 2063 Matrix | |
| 458 | 2064 Matrix::solve (const Matrix& b) const |
| 2065 { | |
| 5275 | 2066 octave_idx_type info; |
| 7788 | 2067 double rcon; |
| 2068 return solve (b, info, rcon, 0); | |
| 458 | 2069 } |
| 2070 | |
| 2071 Matrix | |
| 5275 | 2072 Matrix::solve (const Matrix& b, octave_idx_type& info) const |
| 458 | 2073 { |
| 7788 | 2074 double rcon; |
| 2075 return solve (b, info, rcon, 0); | |
| 458 | 2076 } |
| 2077 | |
| 2078 Matrix | |
| 7788 | 2079 Matrix::solve (const Matrix& b, octave_idx_type& info, double& rcon) const |
| 458 | 2080 { |
| 7788 | 2081 return solve (b, info, rcon, 0); |
| 3480 | 2082 } |
| 2083 | |
| 2084 Matrix | |
| 5785 | 2085 Matrix::solve (const Matrix& b, octave_idx_type& info, |
| 7788 | 2086 double& rcon, solve_singularity_handler sing_handler) const |
| 3480 | 2087 { |
| 5785 | 2088 MatrixType mattype (*this); |
| 7788 | 2089 return solve (mattype, b, info, rcon, sing_handler); |
| 458 | 2090 } |
| 2091 | |
| 2092 ComplexMatrix | |
| 2093 Matrix::solve (const ComplexMatrix& b) const | |
| 2094 { | |
| 2095 ComplexMatrix tmp (*this); | |
| 2096 return tmp.solve (b); | |
| 2097 } | |
| 2098 | |
| 2099 ComplexMatrix | |
| 5275 | 2100 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info) const |
| 458 | 2101 { |
| 2102 ComplexMatrix tmp (*this); | |
| 2103 return tmp.solve (b, info); | |
| 2104 } | |
| 2105 | |
| 2106 ComplexMatrix | |
| 7788 | 2107 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcon) const |
| 458 | 2108 { |
| 2109 ComplexMatrix tmp (*this); | |
| 7788 | 2110 return tmp.solve (b, info, rcon); |
| 458 | 2111 } |
| 2112 | |
| 3480 | 2113 ComplexMatrix |
| 7788 | 2114 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcon, |
| 3480 | 2115 solve_singularity_handler sing_handler) const |
| 2116 { | |
| 2117 ComplexMatrix tmp (*this); | |
| 7788 | 2118 return tmp.solve (b, info, rcon, sing_handler); |
| 3480 | 2119 } |
| 2120 | |
| 458 | 2121 ColumnVector |
| 2122 Matrix::solve (const ColumnVector& b) const | |
| 2123 { | |
| 7788 | 2124 octave_idx_type info; double rcon; |
| 2125 return solve (b, info, rcon); | |
| 458 | 2126 } |
| 2127 | |
| 2128 ColumnVector | |
| 5275 | 2129 Matrix::solve (const ColumnVector& b, octave_idx_type& info) const |
| 458 | 2130 { |
| 7788 | 2131 double rcon; |
| 2132 return solve (b, info, rcon); | |
| 458 | 2133 } |
| 2134 | |
| 2135 ColumnVector | |
| 7788 | 2136 Matrix::solve (const ColumnVector& b, octave_idx_type& info, double& rcon) const |
| 458 | 2137 { |
| 7788 | 2138 return solve (b, info, rcon, 0); |
| 3480 | 2139 } |
| 2140 | |
| 2141 ColumnVector | |
| 7788 | 2142 Matrix::solve (const ColumnVector& b, octave_idx_type& info, double& rcon, |
| 3480 | 2143 solve_singularity_handler sing_handler) const |
| 2144 { | |
| 5785 | 2145 MatrixType mattype (*this); |
| 7788 | 2146 return solve (mattype, b, info, rcon, sing_handler); |
| 458 | 2147 } |
| 2148 | |
| 2149 ComplexColumnVector | |
| 2150 Matrix::solve (const ComplexColumnVector& b) const | |
| 2151 { | |
| 2152 ComplexMatrix tmp (*this); | |
| 2153 return tmp.solve (b); | |
| 2154 } | |
| 2155 | |
| 2156 ComplexColumnVector | |
| 5275 | 2157 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info) const |
| 458 | 2158 { |
| 2159 ComplexMatrix tmp (*this); | |
| 2160 return tmp.solve (b, info); | |
| 2161 } | |
| 2162 | |
| 2163 ComplexColumnVector | |
| 7788 | 2164 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info, double& rcon) const |
| 458 | 2165 { |
| 2166 ComplexMatrix tmp (*this); | |
| 7788 | 2167 return tmp.solve (b, info, rcon); |
| 458 | 2168 } |
| 2169 | |
| 3480 | 2170 ComplexColumnVector |
| 7788 | 2171 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info, double& rcon, |
| 3480 | 2172 solve_singularity_handler sing_handler) const |
| 2173 { | |
| 2174 ComplexMatrix tmp (*this); | |
| 7788 | 2175 return tmp.solve (b, info, rcon, sing_handler); |
| 3480 | 2176 } |
| 2177 | |
| 458 | 2178 Matrix |
| 2179 Matrix::lssolve (const Matrix& b) const | |
| 2180 { | |
| 5275 | 2181 octave_idx_type info; |
| 2182 octave_idx_type rank; | |
| 7788 | 2183 double rcon; |
| 2184 return lssolve (b, info, rank, rcon); | |
| 458 | 2185 } |
| 2186 | |
| 2187 Matrix | |
| 5275 | 2188 Matrix::lssolve (const Matrix& b, octave_idx_type& info) const |
| 458 | 2189 { |
| 5275 | 2190 octave_idx_type rank; |
| 7788 | 2191 double rcon; |
| 2192 return lssolve (b, info, rank, rcon); | |
| 458 | 2193 } |
| 2194 | |
| 2195 Matrix | |
| 7072 | 2196 Matrix::lssolve (const Matrix& b, octave_idx_type& info, |
| 2197 octave_idx_type& rank) const | |
| 458 | 2198 { |
| 7788 | 2199 double rcon; |
| 2200 return lssolve (b, info, rank, rcon); | |
| 7076 | 2201 } |
| 2202 | |
| 2203 Matrix | |
| 2204 Matrix::lssolve (const Matrix& b, octave_idx_type& info, | |
| 7788 | 2205 octave_idx_type& rank, double &rcon) const |
| 7076 | 2206 { |
| 1948 | 2207 Matrix retval; |
| 2208 | |
| 5275 | 2209 octave_idx_type nrhs = b.cols (); |
| 2210 | |
| 2211 octave_idx_type m = rows (); | |
| 2212 octave_idx_type n = cols (); | |
| 458 | 2213 |
| 6924 | 2214 if (m != b.rows ()) |
| 1948 | 2215 (*current_liboctave_error_handler) |
| 6924 | 2216 ("matrix dimension mismatch solution of linear equations"); |
| 2217 else if (m == 0 || n == 0 || b.cols () == 0) | |
| 2218 retval = Matrix (n, b.cols (), 0.0); | |
| 1948 | 2219 else |
| 458 | 2220 { |
| 7072 | 2221 volatile octave_idx_type minmn = (m < n ? m : n); |
| 2222 octave_idx_type maxmn = m > n ? m : n; | |
| 7788 | 2223 rcon = -1.0; |
| 7072 | 2224 if (m != n) |
| 2225 { | |
| 2226 retval = Matrix (maxmn, nrhs, 0.0); | |
| 2227 | |
| 2228 for (octave_idx_type j = 0; j < nrhs; j++) | |
| 2229 for (octave_idx_type i = 0; i < m; i++) | |
| 2230 retval.elem (i, j) = b.elem (i, j); | |
| 2231 } | |
| 2232 else | |
| 2233 retval = b; | |
| 2234 | |
| 1948 | 2235 Matrix atmp = *this; |
| 2236 double *tmp_data = atmp.fortran_vec (); | |
| 2237 | |
| 7072 | 2238 double *pretval = retval.fortran_vec (); |
| 2239 Array<double> s (minmn); | |
| 7071 | 2240 double *ps = s.fortran_vec (); |
| 1948 | 2241 |
| 7072 | 2242 // Ask DGELSD what the dimension of WORK should be. |
| 5275 | 2243 octave_idx_type lwork = -1; |
| 3752 | 2244 |
| 2245 Array<double> work (1); | |
| 1948 | 2246 |
| 7477 | 2247 octave_idx_type smlsiz; |
| 2248 F77_FUNC (xilaenv, XILAENV) (9, F77_CONST_CHAR_ARG2 ("DGELSD", 6), | |
| 2249 F77_CONST_CHAR_ARG2 (" ", 1), | |
| 7478 | 2250 0, 0, 0, 0, smlsiz |
| 7477 | 2251 F77_CHAR_ARG_LEN (6) |
| 7478 | 2252 F77_CHAR_ARG_LEN (1)); |
| 7079 | 2253 |
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2254 octave_idx_type mnthr; |
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2255 F77_FUNC (xilaenv, XILAENV) (6, F77_CONST_CHAR_ARG2 ("DGELSD", 6), |
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2256 F77_CONST_CHAR_ARG2 (" ", 1), |
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2257 m, n, nrhs, -1, mnthr |
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2258 F77_CHAR_ARG_LEN (6) |
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2259 F77_CHAR_ARG_LEN (1)); |
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2260 |
| 7079 | 2261 // We compute the size of iwork because DGELSD in older versions |
| 2262 // of LAPACK does not return it on a query call. | |
| 7124 | 2263 double dminmn = static_cast<double> (minmn); |
| 2264 double dsmlsizp1 = static_cast<double> (smlsiz+1); | |
| 7079 | 2265 #if defined (HAVE_LOG2) |
| 7367 | 2266 double tmp = log2 (dminmn / dsmlsizp1); |
| 7079 | 2267 #else |
| 7367 | 2268 double tmp = log (dminmn / dsmlsizp1) / log (2.0); |
| 7079 | 2269 #endif |
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2270 octave_idx_type nlvl = static_cast<octave_idx_type> (tmp) + 1; |
| 7079 | 2271 if (nlvl < 0) |
| 2272 nlvl = 0; | |
| 2273 | |
| 2274 octave_idx_type liwork = 3 * minmn * nlvl + 11 * minmn; | |
| 2275 if (liwork < 1) | |
| 2276 liwork = 1; | |
| 7072 | 2277 Array<octave_idx_type> iwork (liwork); |
| 2278 octave_idx_type* piwork = iwork.fortran_vec (); | |
| 2279 | |
| 2280 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, | |
| 7788 | 2281 ps, rcon, rank, work.fortran_vec (), |
| 7072 | 2282 lwork, piwork, info)); |
| 1948 | 2283 |
| 7476 | 2284 // The workspace query is broken in at least LAPACK 3.0.0 |
|
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2285 // through 3.1.1 when n >= mnthr. The obtuse formula below |
| 7476 | 2286 // should provide sufficient workspace for DGELSD to operate |
| 2287 // efficiently. | |
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2288 if (n >= mnthr) |
| 7476 | 2289 { |
| 2290 const octave_idx_type wlalsd | |
| 2291 = 9*m + 2*m*smlsiz + 8*m*nlvl + m*nrhs + (smlsiz+1)*(smlsiz+1); | |
| 2292 | |
| 2293 octave_idx_type addend = m; | |
| 2294 | |
| 2295 if (2*m-4 > addend) | |
| 2296 addend = 2*m-4; | |
| 2297 | |
| 2298 if (nrhs > addend) | |
| 2299 addend = nrhs; | |
| 2300 | |
| 2301 if (n-3*m > addend) | |
| 2302 addend = n-3*m; | |
| 2303 | |
| 2304 if (wlalsd > addend) | |
| 2305 addend = wlalsd; | |
| 2306 | |
| 2307 const octave_idx_type lworkaround = 4*m + m*m + addend; | |
| 2308 | |
| 2309 if (work(0) < lworkaround) | |
| 2310 work(0) = lworkaround; | |
| 2311 } | |
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2312 else if (m >= n) |
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2313 { |
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2314 octave_idx_type lworkaround |
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2315 = 12*n + 2*n*smlsiz + 8*n*nlvl + n*nrhs + (smlsiz+1)*(smlsiz+1); |
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2316 |
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2317 if (work(0) < lworkaround) |
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2318 work(0) = lworkaround; |
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2319 } |
| 7476 | 2320 |
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2321 lwork = static_cast<octave_idx_type> (work(0)); |
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2322 work.resize (lwork); |
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2323 |
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2324 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, |
| 7788 | 2325 maxmn, ps, rcon, rank, |
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2326 work.fortran_vec (), lwork, |
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2327 piwork, info)); |
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2328 |
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2329 if (rank < minmn) |
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2330 (*current_liboctave_warning_handler) |
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2331 ("dgelsd: rank deficient %dx%d matrix, rank = %d", m, n, rank); |
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|
2332 if (s.elem (0) == 0.0) |
| 7788 | 2333 rcon = 0.0; |
| 1948 | 2334 else |
| 7788 | 2335 rcon = s.elem (minmn - 1) / s.elem (0); |
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2336 |
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|
2337 retval.resize (n, nrhs); |
| 458 | 2338 } |
| 2339 | |
| 2340 return retval; | |
| 2341 } | |
| 2342 | |
| 2343 ComplexMatrix | |
| 2344 Matrix::lssolve (const ComplexMatrix& b) const | |
| 2345 { | |
| 2346 ComplexMatrix tmp (*this); | |
| 5275 | 2347 octave_idx_type info; |
| 2348 octave_idx_type rank; | |
| 7788 | 2349 double rcon; |
| 2350 return tmp.lssolve (b, info, rank, rcon); | |
| 458 | 2351 } |
| 2352 | |
| 2353 ComplexMatrix | |
| 5275 | 2354 Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info) const |
| 458 | 2355 { |
| 2356 ComplexMatrix tmp (*this); | |
| 5275 | 2357 octave_idx_type rank; |
| 7788 | 2358 double rcon; |
| 2359 return tmp.lssolve (b, info, rank, rcon); | |
| 458 | 2360 } |
| 2361 | |
| 2362 ComplexMatrix | |
| 7076 | 2363 Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info, |
| 2364 octave_idx_type& rank) const | |
| 458 | 2365 { |
| 2366 ComplexMatrix tmp (*this); | |
| 7788 | 2367 double rcon; |
| 2368 return tmp.lssolve (b, info, rank, rcon); | |
| 7076 | 2369 } |
| 2370 | |
| 2371 ComplexMatrix | |
| 2372 Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info, | |
| 7788 | 2373 octave_idx_type& rank, double& rcon) const |
| 7076 | 2374 { |
| 2375 ComplexMatrix tmp (*this); | |
| 7788 | 2376 return tmp.lssolve (b, info, rank, rcon); |
| 458 | 2377 } |
| 2378 | |
| 2379 ColumnVector | |
| 2380 Matrix::lssolve (const ColumnVector& b) const | |
| 2381 { | |
| 5275 | 2382 octave_idx_type info; |
| 2383 octave_idx_type rank; | |
| 7788 | 2384 double rcon; |
| 2385 return lssolve (b, info, rank, rcon); | |
| 458 | 2386 } |
| 2387 | |
| 2388 ColumnVector | |
| 5275 | 2389 Matrix::lssolve (const ColumnVector& b, octave_idx_type& info) const |
| 458 | 2390 { |
| 5275 | 2391 octave_idx_type rank; |
| 7788 | 2392 double rcon; |
| 2393 return lssolve (b, info, rank, rcon); | |
| 458 | 2394 } |
| 2395 | |
| 2396 ColumnVector | |
| 7072 | 2397 Matrix::lssolve (const ColumnVector& b, octave_idx_type& info, |
| 2398 octave_idx_type& rank) const | |
| 458 | 2399 { |
| 7788 | 2400 double rcon; |
| 2401 return lssolve (b, info, rank, rcon); | |
| 7076 | 2402 } |
| 2403 | |
| 2404 ColumnVector | |
| 2405 Matrix::lssolve (const ColumnVector& b, octave_idx_type& info, | |
| 7788 | 2406 octave_idx_type& rank, double &rcon) const |
| 7076 | 2407 { |
| 1948 | 2408 ColumnVector retval; |
| 2409 | |
| 5275 | 2410 octave_idx_type nrhs = 1; |
| 2411 | |
| 2412 octave_idx_type m = rows (); | |
| 2413 octave_idx_type n = cols (); | |
| 458 | 2414 |
| 6924 | 2415 if (m != b.length ()) |
| 1948 | 2416 (*current_liboctave_error_handler) |
| 6924 | 2417 ("matrix dimension mismatch solution of linear equations"); |
| 2418 else if (m == 0 || n == 0) | |
| 2419 retval = ColumnVector (n, 0.0); | |
| 1948 | 2420 else |
| 458 | 2421 { |
| 7072 | 2422 volatile octave_idx_type minmn = (m < n ? m : n); |
| 2423 octave_idx_type maxmn = m > n ? m : n; | |
| 7788 | 2424 rcon = -1.0; |
| 7072 | 2425 |
| 2426 if (m != n) | |
| 2427 { | |
| 2428 retval = ColumnVector (maxmn, 0.0); | |
| 2429 | |
| 2430 for (octave_idx_type i = 0; i < m; i++) | |
| 2431 retval.elem (i) = b.elem (i); | |
| 2432 } | |
| 2433 else | |
| 2434 retval = b; | |
| 2435 | |
| 1948 | 2436 Matrix atmp = *this; |
| 2437 double *tmp_data = atmp.fortran_vec (); | |
| 2438 | |
| 7072 | 2439 double *pretval = retval.fortran_vec (); |
| 2440 Array<double> s (minmn); | |
| 7071 | 2441 double *ps = s.fortran_vec (); |
| 1948 | 2442 |
| 7072 | 2443 // Ask DGELSD what the dimension of WORK should be. |
| 5275 | 2444 octave_idx_type lwork = -1; |
| 3752 | 2445 |
| 2446 Array<double> work (1); | |
| 2447 | |
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2448 octave_idx_type smlsiz; |
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2449 F77_FUNC (xilaenv, XILAENV) (9, F77_CONST_CHAR_ARG2 ("DGELSD", 6), |
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2450 F77_CONST_CHAR_ARG2 (" ", 1), |
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2451 0, 0, 0, 0, smlsiz |
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2452 F77_CHAR_ARG_LEN (6) |
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2453 F77_CHAR_ARG_LEN (1)); |
| 7079 | 2454 |
| 2455 // We compute the size of iwork because DGELSD in older versions | |
| 2456 // of LAPACK does not return it on a query call. | |
| 7124 | 2457 double dminmn = static_cast<double> (minmn); |
| 2458 double dsmlsizp1 = static_cast<double> (smlsiz+1); | |
| 7079 | 2459 #if defined (HAVE_LOG2) |
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2460 double tmp = log2 (dminmn / dsmlsizp1); |
| 7079 | 2461 #else |
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2462 double tmp = log (dminmn / dsmlsizp1) / log (2.0); |
| 7079 | 2463 #endif |
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2464 octave_idx_type nlvl = static_cast<octave_idx_type> (tmp) + 1; |
| 7079 | 2465 if (nlvl < 0) |
| 2466 nlvl = 0; | |
| 2467 | |
| 2468 octave_idx_type liwork = 3 * minmn * nlvl + 11 * minmn; | |
| 2469 if (liwork < 1) | |
| 2470 liwork = 1; | |
| 7072 | 2471 Array<octave_idx_type> iwork (liwork); |
| 2472 octave_idx_type* piwork = iwork.fortran_vec (); | |
| 2473 | |
| 2474 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, | |
| 7788 | 2475 ps, rcon, rank, work.fortran_vec (), |
| 7072 | 2476 lwork, piwork, info)); |
| 1948 | 2477 |
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2478 lwork = static_cast<octave_idx_type> (work(0)); |
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2479 work.resize (lwork); |
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2480 |
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2481 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, |
| 7788 | 2482 maxmn, ps, rcon, rank, |
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2483 work.fortran_vec (), lwork, |
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2484 piwork, info)); |
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2485 |
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2486 if (rank < minmn) |
| 1948 | 2487 { |
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2488 if (rank < minmn) |
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2489 (*current_liboctave_warning_handler) |
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2490 ("dgelsd: rank deficient %dx%d matrix, rank = %d", m, n, rank); |
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2491 if (s.elem (0) == 0.0) |
| 7788 | 2492 rcon = 0.0; |
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2493 else |
| 7788 | 2494 rcon = s.elem (minmn - 1) / s.elem (0); |
| 1948 | 2495 } |
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2496 |
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|
2497 retval.resize (n, nrhs); |
| 458 | 2498 } |
| 2499 | |
| 2500 return retval; | |
| 2501 } | |
| 2502 | |
| 2503 ComplexColumnVector | |
| 2504 Matrix::lssolve (const ComplexColumnVector& b) const | |
| 2505 { | |
| 2506 ComplexMatrix tmp (*this); | |
| 7076 | 2507 octave_idx_type info; |
| 2508 octave_idx_type rank; | |
| 7788 | 2509 double rcon; |
| 2510 return tmp.lssolve (b, info, rank, rcon); | |
| 458 | 2511 } |
| 2512 | |
| 2513 ComplexColumnVector | |
| 5275 | 2514 Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info) const |
| 458 | 2515 { |
| 2516 ComplexMatrix tmp (*this); | |
| 7076 | 2517 octave_idx_type rank; |
| 7788 | 2518 double rcon; |
| 2519 return tmp.lssolve (b, info, rank, rcon); | |
| 458 | 2520 } |
| 2521 | |
| 2522 ComplexColumnVector | |
| 7076 | 2523 Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, |
| 2524 octave_idx_type& rank) const | |
| 458 | 2525 { |
| 2526 ComplexMatrix tmp (*this); | |
| 7788 | 2527 double rcon; |
| 2528 return tmp.lssolve (b, info, rank, rcon); | |
| 7076 | 2529 } |
| 2530 | |
| 2531 ComplexColumnVector | |
| 2532 Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, | |
| 7788 | 2533 octave_idx_type& rank, double &rcon) const |
| 7076 | 2534 { |
| 2535 ComplexMatrix tmp (*this); | |
| 7788 | 2536 return tmp.lssolve (b, info, rank, rcon); |
| 458 | 2537 } |
| 2538 | |
| 1819 | 2539 // Constants for matrix exponential calculation. |
| 2540 | |
| 2541 static double padec [] = | |
| 2542 { | |
| 2543 5.0000000000000000e-1, | |
| 2544 1.1666666666666667e-1, | |
| 2545 1.6666666666666667e-2, | |
| 2546 1.6025641025641026e-3, | |
| 2547 1.0683760683760684e-4, | |
| 2548 4.8562548562548563e-6, | |
| 2549 1.3875013875013875e-7, | |
| 2550 1.9270852604185938e-9, | |
| 2551 }; | |
| 2552 | |
| 7400 | 2553 static void |
| 7788 | 2554 solve_singularity_warning (double rcon) |
| 7400 | 2555 { |
| 2556 (*current_liboctave_warning_handler) | |
| 2557 ("singular matrix encountered in expm calculation, rcond = %g", | |
| 7788 | 2558 rcon); |
| 7400 | 2559 } |
| 2560 | |
| 1819 | 2561 Matrix |
| 2562 Matrix::expm (void) const | |
| 2563 { | |
| 2564 Matrix retval; | |
| 2565 | |
| 2566 Matrix m = *this; | |
| 2567 | |
| 6699 | 2568 if (numel () == 1) |
| 2569 return Matrix (1, 1, exp (m(0))); | |
| 2570 | |
| 5275 | 2571 octave_idx_type nc = columns (); |
| 1819 | 2572 |
| 3130 | 2573 // Preconditioning step 1: trace normalization to reduce dynamic |
| 2574 // range of poles, but avoid making stable eigenvalues unstable. | |
| 2575 | |
| 1819 | 2576 // trace shift value |
| 3331 | 2577 volatile double trshift = 0.0; |
| 1819 | 2578 |
| 5275 | 2579 for (octave_idx_type i = 0; i < nc; i++) |
| 1819 | 2580 trshift += m.elem (i, i); |
| 2581 | |
| 2582 trshift /= nc; | |
| 2583 | |
| 3130 | 2584 if (trshift > 0.0) |
| 2585 { | |
| 5275 | 2586 for (octave_idx_type i = 0; i < nc; i++) |
| 3130 | 2587 m.elem (i, i) -= trshift; |
| 2588 } | |
| 1819 | 2589 |
| 3331 | 2590 // Preconditioning step 2: balancing; code follows development |
| 2591 // in AEPBAL | |
| 2592 | |
| 2593 double *p_m = m.fortran_vec (); | |
| 2594 | |
| 5275 | 2595 octave_idx_type info, ilo, ihi, ilos, ihis; |
| 3468 | 2596 Array<double> dpermute (nc); |
| 2597 Array<double> dscale (nc); | |
| 3466 | 2598 |
| 3468 | 2599 // permutation first |
| 2600 char job = 'P'; | |
| 4552 | 2601 F77_XFCN (dgebal, DGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
| 2602 nc, p_m, nc, ilo, ihi, | |
| 2603 dpermute.fortran_vec (), info | |
| 2604 F77_CHAR_ARG_LEN (1))); | |
| 3466 | 2605 |
| 3468 | 2606 // then scaling |
| 2607 job = 'S'; | |
| 4552 | 2608 F77_XFCN (dgebal, DGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
| 2609 nc, p_m, nc, ilos, ihis, | |
| 2610 dscale.fortran_vec (), info | |
| 2611 F77_CHAR_ARG_LEN (1))); | |
| 3331 | 2612 |
| 1819 | 2613 // Preconditioning step 3: scaling. |
| 3331 | 2614 |
| 1819 | 2615 ColumnVector work(nc); |
| 3130 | 2616 double inf_norm; |
| 3331 | 2617 |
| 4552 | 2618 F77_XFCN (xdlange, XDLANGE, (F77_CONST_CHAR_ARG2 ("I", 1), |
| 2619 nc, nc, m.fortran_vec (), nc, | |
| 2620 work.fortran_vec (), inf_norm | |
| 2621 F77_CHAR_ARG_LEN (1))); | |
| 3331 | 2622 |
| 5275 | 2623 octave_idx_type sqpow = static_cast<octave_idx_type> (inf_norm > 0.0 |
| 1819 | 2624 ? (1.0 + log (inf_norm) / log (2.0)) |
| 2625 : 0.0); | |
| 3331 | 2626 |
| 1819 | 2627 // Check whether we need to square at all. |
| 3331 | 2628 |
| 1819 | 2629 if (sqpow < 0) |
| 2630 sqpow = 0; | |
| 3331 | 2631 |
| 1819 | 2632 if (sqpow > 0) |
| 2633 { | |
| 7400 | 2634 if (sqpow > 1023) |
| 2635 sqpow = 1023; | |
| 2636 | |
| 1819 | 2637 double scale_factor = 1.0; |
| 5275 | 2638 for (octave_idx_type i = 0; i < sqpow; i++) |
| 1819 | 2639 scale_factor *= 2.0; |
| 7400 | 2640 |
| 1819 | 2641 m = m / scale_factor; |
| 2642 } | |
| 3331 | 2643 |
| 1819 | 2644 // npp, dpp: pade' approx polynomial matrices. |
| 3331 | 2645 |
| 1819 | 2646 Matrix npp (nc, nc, 0.0); |
| 7265 | 2647 double *pnpp = npp.fortran_vec (); |
| 1819 | 2648 Matrix dpp = npp; |
| 7265 | 2649 double *pdpp = dpp.fortran_vec (); |
| 3331 | 2650 |
| 1819 | 2651 // Now powers a^8 ... a^1. |
| 3331 | 2652 |
| 5275 | 2653 octave_idx_type minus_one_j = -1; |
| 2654 for (octave_idx_type j = 7; j >= 0; j--) | |
| 1819 | 2655 { |
| 7265 | 2656 for (octave_idx_type i = 0; i < nc; i++) |
| 2657 { | |
| 2658 octave_idx_type k = i * nc + i; | |
| 2659 pnpp[k] += padec[j]; | |
| 2660 pdpp[k] += minus_one_j * padec[j]; | |
| 2661 } | |
| 2662 | |
| 2663 npp = m * npp; | |
| 2664 pnpp = npp.fortran_vec (); | |
| 2665 | |
| 2666 dpp = m * dpp; | |
| 2667 pdpp = dpp.fortran_vec (); | |
| 2668 | |
| 1819 | 2669 minus_one_j *= -1; |
| 2670 } | |
| 3331 | 2671 |
| 1819 | 2672 // Zero power. |
| 3331 | 2673 |
| 1819 | 2674 dpp = -dpp; |
| 5275 | 2675 for (octave_idx_type j = 0; j < nc; j++) |
| 1819 | 2676 { |
| 2677 npp.elem (j, j) += 1.0; | |
| 2678 dpp.elem (j, j) += 1.0; | |
| 2679 } | |
| 3331 | 2680 |
| 1819 | 2681 // Compute pade approximation = inverse (dpp) * npp. |
| 2682 | |
| 7788 | 2683 double rcon; |
| 2684 retval = dpp.solve (npp, info, rcon, solve_singularity_warning); | |
| 7400 | 2685 |
| 2686 if (info < 0) | |
| 2687 return retval; | |
| 2688 | |
| 1819 | 2689 // Reverse preconditioning step 3: repeated squaring. |
| 3331 | 2690 |
| 1819 | 2691 while (sqpow) |
| 2692 { | |
| 2693 retval = retval * retval; | |
| 2694 sqpow--; | |
| 2695 } | |
| 3331 | 2696 |
| 1819 | 2697 // Reverse preconditioning step 2: inverse balancing. |
| 3466 | 2698 // apply inverse scaling to computed exponential |
| 5275 | 2699 for (octave_idx_type i = 0; i < nc; i++) |
| 2700 for (octave_idx_type j = 0; j < nc; j++) | |
|
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|
2701 retval(i,j) *= dscale(i) / dscale(j); |
| 3466 | 2702 |
| 4153 | 2703 OCTAVE_QUIT; |
| 2704 | |
| 3466 | 2705 // construct balancing permutation vector |
| 5275 | 2706 Array<octave_idx_type> iperm (nc); |
| 2707 for (octave_idx_type i = 0; i < nc; i++) | |
| 4593 | 2708 iperm(i) = i; // identity permutation |
| 3466 | 2709 |
|
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diff
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|
2710 // trailing permutations must be done in reverse order |
|
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diff
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|
2711 for (octave_idx_type i = nc - 1; i >= ihi; i--) |
|
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diff
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|
2712 { |
|
851803f7bb4d
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diff
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|
2713 octave_idx_type swapidx = static_cast<octave_idx_type> (dpermute(i)) - 1; |
|
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diff
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|
2714 octave_idx_type tmp = iperm(i); |
|
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diff
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|
2715 iperm(i) = iperm(swapidx); |
|
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parents:
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diff
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|
2716 iperm(swapidx) = tmp; |
|
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|
2717 } |
|
851803f7bb4d
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|
2718 |
| 3466 | 2719 // leading permutations in forward order |
| 5275 | 2720 for (octave_idx_type i = 0; i < (ilo-1); i++) |
| 3468 | 2721 { |
| 5275 | 2722 octave_idx_type swapidx = static_cast<octave_idx_type> (dpermute(i)) - 1; |
| 2723 octave_idx_type tmp = iperm(i); | |
| 4593 | 2724 iperm(i) = iperm (swapidx); |
| 2725 iperm(swapidx) = tmp; | |
| 3468 | 2726 } |
| 3466 | 2727 |
| 7416 | 2728 // construct inverse balancing permutation vector |
| 2729 Array<octave_idx_type> invpvec (nc); | |
| 2730 for (octave_idx_type i = 0; i < nc; i++) | |
| 2731 invpvec(iperm(i)) = i; // Thanks to R. A. Lippert for this method | |
| 2732 | |
| 2733 OCTAVE_QUIT; | |
|
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|
2734 |
| 7416 | 2735 Matrix tmpMat = retval; |
| 2736 for (octave_idx_type i = 0; i < nc; i++) | |
| 2737 for (octave_idx_type j = 0; j < nc; j++) | |
| 2738 retval(i,j) = tmpMat(invpvec(i),invpvec(j)); | |
| 2739 | |
|
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diff
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|
2740 // Reverse preconditioning step 1: fix trace normalization. |
| 3130 | 2741 if (trshift > 0.0) |
| 2742 retval = exp (trshift) * retval; | |
| 2743 | |
| 2744 return retval; | |
| 1819 | 2745 } |
| 2746 | |
| 458 | 2747 Matrix& |
| 2748 Matrix::operator += (const DiagMatrix& a) | |
| 2749 { | |
| 5275 | 2750 octave_idx_type nr = rows (); |
| 2751 octave_idx_type nc = cols (); | |
| 2752 | |
| 2753 octave_idx_type a_nr = a.rows (); | |
| 2754 octave_idx_type a_nc = a.cols (); | |
| 2385 | 2755 |
| 2756 if (nr != a_nr || nc != a_nc) | |
| 458 | 2757 { |
| 2385 | 2758 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
| 458 | 2759 return *this; |
| 2760 } | |
| 2761 | |
| 5275 | 2762 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 2763 elem (i, i) += a.elem (i, i); |
| 2764 | |
| 2765 return *this; | |
| 2766 } | |
| 2767 | |
| 2768 Matrix& | |
| 2769 Matrix::operator -= (const DiagMatrix& a) | |
| 2770 { | |
| 5275 | 2771 octave_idx_type nr = rows (); |
| 2772 octave_idx_type nc = cols (); | |
| 2773 | |
| 2774 octave_idx_type a_nr = a.rows (); | |
| 2775 octave_idx_type a_nc = a.cols (); | |
| 2385 | 2776 |
| 2777 if (nr != a_nr || nc != a_nc) | |
| 458 | 2778 { |
| 2385 | 2779 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
| 458 | 2780 return *this; |
| 2781 } | |
| 2782 | |
| 5275 | 2783 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 2784 elem (i, i) -= a.elem (i, i); |
| 2785 | |
| 2786 return *this; | |
| 2787 } | |
| 2788 | |
| 2789 // unary operations | |
| 2790 | |
| 2964 | 2791 boolMatrix |
| 458 | 2792 Matrix::operator ! (void) const |
| 2793 { | |
| 5275 | 2794 octave_idx_type nr = rows (); |
| 2795 octave_idx_type nc = cols (); | |
| 458 | 2796 |
| 2964 | 2797 boolMatrix b (nr, nc); |
| 458 | 2798 |
| 5275 | 2799 for (octave_idx_type j = 0; j < nc; j++) |
| 2800 for (octave_idx_type i = 0; i < nr; i++) | |
| 458 | 2801 b.elem (i, j) = ! elem (i, j); |
| 2802 | |
| 2803 return b; | |
| 2804 } | |
| 2805 | |
| 1205 | 2806 // column vector by row vector -> matrix operations |
| 458 | 2807 |
| 1205 | 2808 Matrix |
| 2809 operator * (const ColumnVector& v, const RowVector& a) | |
| 458 | 2810 { |
| 1948 | 2811 Matrix retval; |
| 2812 | |
| 5275 | 2813 octave_idx_type len = v.length (); |
| 3233 | 2814 |
| 2815 if (len != 0) | |
| 1205 | 2816 { |
| 5275 | 2817 octave_idx_type a_len = a.length (); |
| 3233 | 2818 |
| 2819 retval.resize (len, a_len); | |
| 2820 double *c = retval.fortran_vec (); | |
| 2821 | |
| 4552 | 2822 F77_XFCN (dgemm, DGEMM, (F77_CONST_CHAR_ARG2 ("N", 1), |
| 2823 F77_CONST_CHAR_ARG2 ("N", 1), | |
| 2824 len, a_len, 1, 1.0, v.data (), len, | |
| 2825 a.data (), 1, 0.0, c, len | |
| 2826 F77_CHAR_ARG_LEN (1) | |
| 2827 F77_CHAR_ARG_LEN (1))); | |
| 1205 | 2828 } |
| 458 | 2829 |
| 1948 | 2830 return retval; |
| 458 | 2831 } |
| 2832 | |
| 2833 // other operations. | |
| 2834 | |
| 2835 Matrix | |
|
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David Bateman <dbateman@free.fr>
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diff
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|
2836 Matrix::map (dmapper fcn) const |
| 1205 | 2837 { |
|
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diff
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|
2838 return MArray2<double>::map<double> (func_ptr (fcn)); |
|
8c32f95c2639
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David Bateman <dbateman@free.fr>
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diff
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|
2839 } |
|
8c32f95c2639
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parents:
7488
diff
changeset
|
2840 |
|
8c32f95c2639
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David Bateman <dbateman@free.fr>
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7488
diff
changeset
|
2841 ComplexMatrix |
|
8c32f95c2639
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diff
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|
2842 Matrix::map (cmapper fcn) const |
|
8c32f95c2639
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diff
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|
2843 { |
|
8c32f95c2639
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diff
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|
2844 return MArray2<double>::map<Complex> (func_ptr (fcn)); |
| 1205 | 2845 } |
| 2846 | |
| 3248 | 2847 boolMatrix |
|
7503
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David Bateman <dbateman@free.fr>
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diff
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|
2848 Matrix::map (bmapper fcn) const |
| 3248 | 2849 { |
|
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diff
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|
2850 return MArray2<double>::map<bool> (func_ptr (fcn)); |
| 458 | 2851 } |
| 2852 | |
| 2385 | 2853 bool |
| 4431 | 2854 Matrix::any_element_is_negative (bool neg_zero) const |
| 2385 | 2855 { |
| 5275 | 2856 octave_idx_type nel = nelem (); |
| 2385 | 2857 |
| 4431 | 2858 if (neg_zero) |
| 2859 { | |
| 5275 | 2860 for (octave_idx_type i = 0; i < nel; i++) |
| 4634 | 2861 if (lo_ieee_signbit (elem (i))) |
| 2862 return true; | |
| 4431 | 2863 } |
| 2864 else | |
| 2865 { | |
| 5275 | 2866 for (octave_idx_type i = 0; i < nel; i++) |
| 4634 | 2867 if (elem (i) < 0) |
| 2868 return true; | |
| 4431 | 2869 } |
| 2385 | 2870 |
| 2871 return false; | |
| 2872 } | |
| 2873 | |
|
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|
2874 bool |
|
935be827eaf8
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diff
changeset
|
2875 Matrix::any_element_is_nan (void) const |
|
935be827eaf8
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parents:
7803
diff
changeset
|
2876 { |
|
935be827eaf8
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diff
changeset
|
2877 octave_idx_type nel = nelem (); |
|
935be827eaf8
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7803
diff
changeset
|
2878 |
|
935be827eaf8
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7803
diff
changeset
|
2879 for (octave_idx_type i = 0; i < nel; i++) |
|
935be827eaf8
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7803
diff
changeset
|
2880 { |
|
935be827eaf8
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7803
diff
changeset
|
2881 double val = elem (i); |
|
935be827eaf8
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parents:
7803
diff
changeset
|
2882 if (xisnan (val)) |
|
935be827eaf8
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7803
diff
changeset
|
2883 return true; |
|
935be827eaf8
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diff
changeset
|
2884 } |
|
935be827eaf8
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7803
diff
changeset
|
2885 |
|
935be827eaf8
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diff
changeset
|
2886 return false; |
|
935be827eaf8
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diff
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|
2887 } |
| 2385 | 2888 |
| 2889 bool | |
| 2890 Matrix::any_element_is_inf_or_nan (void) const | |
| 2891 { | |
| 5275 | 2892 octave_idx_type nel = nelem (); |
| 2893 | |
| 2894 for (octave_idx_type i = 0; i < nel; i++) | |
| 4634 | 2895 { |
| 2896 double val = elem (i); | |
| 2897 if (xisinf (val) || xisnan (val)) | |
| 2898 return true; | |
| 2899 } | |
| 2900 | |
| 2901 return false; | |
| 2385 | 2902 } |
| 2903 | |
| 2904 bool | |
| 5943 | 2905 Matrix::any_element_not_one_or_zero (void) const |
| 2906 { | |
| 2907 octave_idx_type nel = nelem (); | |
| 2908 | |
| 2909 for (octave_idx_type i = 0; i < nel; i++) | |
| 2910 { | |
| 2911 double val = elem (i); | |
| 2912 if (val != 0 && val != 1) | |
| 2913 return true; | |
| 2914 } | |
| 2915 | |
| 2916 return false; | |
| 2917 } | |
| 2918 | |
| 2919 bool | |
| 2385 | 2920 Matrix::all_elements_are_int_or_inf_or_nan (void) const |
| 2921 { | |
| 5275 | 2922 octave_idx_type nel = nelem (); |
| 2923 | |
| 2924 for (octave_idx_type i = 0; i < nel; i++) | |
| 4634 | 2925 { |
| 2926 double val = elem (i); | |
| 2927 if (xisnan (val) || D_NINT (val) == val) | |
| 2928 continue; | |
| 2929 else | |
| 2930 return false; | |
| 2931 } | |
| 2385 | 2932 |
| 2933 return true; | |
| 2934 } | |
| 2935 | |
| 1968 | 2936 // Return nonzero if any element of M is not an integer. Also extract |
| 2937 // the largest and smallest values and return them in MAX_VAL and MIN_VAL. | |
| 2938 | |
| 2385 | 2939 bool |
| 1968 | 2940 Matrix::all_integers (double& max_val, double& min_val) const |
| 2941 { | |
| 5275 | 2942 octave_idx_type nel = nelem (); |
| 4634 | 2943 |
| 2944 if (nel > 0) | |
| 1968 | 2945 { |
| 4634 | 2946 max_val = elem (0); |
| 2947 min_val = elem (0); | |
| 1968 | 2948 } |
| 2949 else | |
| 2385 | 2950 return false; |
| 1968 | 2951 |
| 5275 | 2952 for (octave_idx_type i = 0; i < nel; i++) |
| 4634 | 2953 { |
| 2954 double val = elem (i); | |
| 2955 | |
| 2956 if (val > max_val) | |
| 2957 max_val = val; | |
| 2958 | |
| 2959 if (val < min_val) | |
| 2960 min_val = val; | |
| 2961 | |
| 2962 if (D_NINT (val) != val) | |
| 2963 return false; | |
| 2964 } | |
| 2385 | 2965 |
| 2966 return true; | |
| 1968 | 2967 } |
| 2968 | |
| 2385 | 2969 bool |
| 1968 | 2970 Matrix::too_large_for_float (void) const |
| 2971 { | |
| 5275 | 2972 octave_idx_type nel = nelem (); |
| 2973 | |
| 2974 for (octave_idx_type i = 0; i < nel; i++) | |
| 4634 | 2975 { |
| 2976 double val = elem (i); | |
| 2977 | |
| 5389 | 2978 if (! (xisnan (val) || xisinf (val)) |
| 5387 | 2979 && fabs (val) > FLT_MAX) |
| 4634 | 2980 return true; |
| 2981 } | |
| 1968 | 2982 |
| 2385 | 2983 return false; |
| 1968 | 2984 } |
| 2985 | |
| 5775 | 2986 // FIXME Do these really belong here? Maybe they should be |
| 4015 | 2987 // in a base class? |
| 458 | 2988 |
| 2832 | 2989 boolMatrix |
| 4015 | 2990 Matrix::all (int dim) const |
| 458 | 2991 { |
| 4015 | 2992 MX_ALL_OP (dim); |
| 458 | 2993 } |
| 2994 | |
| 2832 | 2995 boolMatrix |
| 4015 | 2996 Matrix::any (int dim) const |
| 458 | 2997 { |
| 4015 | 2998 MX_ANY_OP (dim); |
| 458 | 2999 } |
| 3000 | |
| 3001 Matrix | |
| 3723 | 3002 Matrix::cumprod (int dim) const |
| 458 | 3003 { |
| 4015 | 3004 MX_CUMULATIVE_OP (Matrix, double, *=); |
| 458 | 3005 } |
| 3006 | |
| 3007 Matrix | |
| 3723 | 3008 Matrix::cumsum (int dim) const |
| 458 | 3009 { |
| 4015 | 3010 MX_CUMULATIVE_OP (Matrix, double, +=); |
| 458 | 3011 } |
| 3012 | |
| 3013 Matrix | |
| 3723 | 3014 Matrix::prod (int dim) const |
| 458 | 3015 { |
| 3864 | 3016 MX_REDUCTION_OP (Matrix, *=, 1.0, 1.0); |
| 458 | 3017 } |
| 3018 | |
| 3019 Matrix | |
| 3723 | 3020 Matrix::sum (int dim) const |
| 458 | 3021 { |
| 3864 | 3022 MX_REDUCTION_OP (Matrix, +=, 0.0, 0.0); |
| 458 | 3023 } |
| 3024 | |
| 3025 Matrix | |
| 3723 | 3026 Matrix::sumsq (int dim) const |
| 458 | 3027 { |
| 3864 | 3028 #define ROW_EXPR \ |
| 3029 double d = elem (i, j); \ | |
| 3030 retval.elem (i, 0) += d * d | |
| 3031 | |
| 3032 #define COL_EXPR \ | |
| 3033 double d = elem (i, j); \ | |
| 3034 retval.elem (0, j) += d * d | |
| 3035 | |
| 3036 MX_BASE_REDUCTION_OP (Matrix, ROW_EXPR, COL_EXPR, 0.0, 0.0); | |
| 3037 | |
| 3038 #undef ROW_EXPR | |
| 3039 #undef COL_EXPR | |
| 458 | 3040 } |
| 3041 | |
| 2385 | 3042 Matrix |
| 3043 Matrix::abs (void) const | |
| 3044 { | |
| 5275 | 3045 octave_idx_type nr = rows (); |
| 3046 octave_idx_type nc = cols (); | |
| 2385 | 3047 |
| 3048 Matrix retval (nr, nc); | |
| 3049 | |
| 5275 | 3050 for (octave_idx_type j = 0; j < nc; j++) |
| 3051 for (octave_idx_type i = 0; i < nr; i++) | |
| 2385 | 3052 retval (i, j) = fabs (elem (i, j)); |
| 3053 | |
| 3054 return retval; | |
| 3055 } | |
| 3056 | |
|
7620
36594d5bbe13
Move diag function into the octave_value class
David Bateman <dbateman@free.fr>
parents:
7544
diff
changeset
|
3057 Matrix |
| 5275 | 3058 Matrix::diag (octave_idx_type k) const |
| 458 | 3059 { |
|
7620
36594d5bbe13
Move diag function into the octave_value class
David Bateman <dbateman@free.fr>
parents:
7544
diff
changeset
|
3060 return MArray2<double>::diag (k); |
| 458 | 3061 } |
| 3062 | |
| 3063 ColumnVector | |
| 3064 Matrix::row_min (void) const | |
| 3065 { | |
| 5275 | 3066 Array<octave_idx_type> dummy_idx; |
| 4587 | 3067 return row_min (dummy_idx); |
| 458 | 3068 } |
| 3069 | |
| 3070 ColumnVector | |
| 5275 | 3071 Matrix::row_min (Array<octave_idx_type>& idx_arg) const |
| 458 | 3072 { |
| 3073 ColumnVector result; | |
| 3074 | |
| 5275 | 3075 octave_idx_type nr = rows (); |
| 3076 octave_idx_type nc = cols (); | |
| 458 | 3077 |
| 3078 if (nr > 0 && nc > 0) | |
| 3079 { | |
| 3080 result.resize (nr); | |
| 4587 | 3081 idx_arg.resize (nr); |
| 458 | 3082 |
| 5275 | 3083 for (octave_idx_type i = 0; i < nr; i++) |
| 458 | 3084 { |
| 5275 | 3085 octave_idx_type idx_j; |
| 4469 | 3086 |
| 3087 double tmp_min = octave_NaN; | |
| 3088 | |
| 3089 for (idx_j = 0; idx_j < nc; idx_j++) | |
| 2354 | 3090 { |
| 4469 | 3091 tmp_min = elem (i, idx_j); |
| 3092 | |
| 5389 | 3093 if (! xisnan (tmp_min)) |
| 4469 | 3094 break; |
| 3095 } | |
| 3096 | |
| 5275 | 3097 for (octave_idx_type j = idx_j+1; j < nc; j++) |
| 4469 | 3098 { |
| 3099 double tmp = elem (i, j); | |
| 3100 | |
| 5389 | 3101 if (xisnan (tmp)) |
| 4469 | 3102 continue; |
| 3103 else if (tmp < tmp_min) | |
| 2354 | 3104 { |
| 4469 | 3105 idx_j = j; |
| 3106 tmp_min = tmp; | |
| 2354 | 3107 } |
| 3108 } | |
| 3109 | |
| 4469 | 3110 result.elem (i) = tmp_min; |
| 5389 | 3111 idx_arg.elem (i) = xisnan (tmp_min) ? 0 : idx_j; |
| 458 | 3112 } |
| 3113 } | |
| 3114 | |
| 3115 return result; | |
| 3116 } | |
| 3117 | |
| 3118 ColumnVector | |
| 3119 Matrix::row_max (void) const | |
| 3120 { | |
| 5275 | 3121 Array<octave_idx_type> dummy_idx; |
| 4587 | 3122 return row_max (dummy_idx); |
| 458 | 3123 } |
| 3124 | |
| 3125 ColumnVector | |
| 5275 | 3126 Matrix::row_max (Array<octave_idx_type>& idx_arg) const |
| 458 | 3127 { |
| 3128 ColumnVector result; | |
| 3129 | |
| 5275 | 3130 octave_idx_type nr = rows (); |
| 3131 octave_idx_type nc = cols (); | |
| 458 | 3132 |
| 3133 if (nr > 0 && nc > 0) | |
| 3134 { | |
| 3135 result.resize (nr); | |
| 4587 | 3136 idx_arg.resize (nr); |
| 458 | 3137 |
| 5275 | 3138 for (octave_idx_type i = 0; i < nr; i++) |
| 458 | 3139 { |
| 5275 | 3140 octave_idx_type idx_j; |
| 4469 | 3141 |
| 3142 double tmp_max = octave_NaN; | |
| 3143 | |
| 3144 for (idx_j = 0; idx_j < nc; idx_j++) | |
| 2354 | 3145 { |
| 4469 | 3146 tmp_max = elem (i, idx_j); |
| 3147 | |
| 5389 | 3148 if (! xisnan (tmp_max)) |
| 4469 | 3149 break; |
| 3150 } | |
| 3151 | |
| 5275 | 3152 for (octave_idx_type j = idx_j+1; j < nc; j++) |
| 4469 | 3153 { |
| 3154 double tmp = elem (i, j); | |
| 3155 | |
| 5389 | 3156 if (xisnan (tmp)) |
| 4469 | 3157 continue; |
| 3158 else if (tmp > tmp_max) | |
| 2354 | 3159 { |
| 4469 | 3160 idx_j = j; |
| 3161 tmp_max = tmp; | |
| 2354 | 3162 } |
| 3163 } | |
| 3164 | |
| 4469 | 3165 result.elem (i) = tmp_max; |
| 5389 | 3166 idx_arg.elem (i) = xisnan (tmp_max) ? 0 : idx_j; |
| 458 | 3167 } |
| 3168 } | |
| 3169 | |
| 3170 return result; | |
| 3171 } | |
| 3172 | |
| 3173 RowVector | |
| 3174 Matrix::column_min (void) const | |
| 3175 { | |
| 5275 | 3176 Array<octave_idx_type> dummy_idx; |
| 4587 | 3177 return column_min (dummy_idx); |
| 458 | 3178 } |
| 2354 | 3179 |
| 458 | 3180 RowVector |
| 5275 | 3181 Matrix::column_min (Array<octave_idx_type>& idx_arg) const |
| 458 | 3182 { |
| 3183 RowVector result; | |
| 3184 | |
| 5275 | 3185 octave_idx_type nr = rows (); |
| 3186 octave_idx_type nc = cols (); | |
| 458 | 3187 |
| 3188 if (nr > 0 && nc > 0) | |
| 3189 { | |
| 3190 result.resize (nc); | |
| 4587 | 3191 idx_arg.resize (nc); |
| 458 | 3192 |
| 5275 | 3193 for (octave_idx_type j = 0; j < nc; j++) |
| 458 | 3194 { |
| 5275 | 3195 octave_idx_type idx_i; |
| 4469 | 3196 |
| 3197 double tmp_min = octave_NaN; | |
| 3198 | |
| 3199 for (idx_i = 0; idx_i < nr; idx_i++) | |
| 2354 | 3200 { |
| 4469 | 3201 tmp_min = elem (idx_i, j); |
| 3202 | |
| 5389 | 3203 if (! xisnan (tmp_min)) |
| 4469 | 3204 break; |
| 3205 } | |
| 3206 | |
| 5275 | 3207 for (octave_idx_type i = idx_i+1; i < nr; i++) |
| 4469 | 3208 { |
| 3209 double tmp = elem (i, j); | |
| 3210 | |
| 5389 | 3211 if (xisnan (tmp)) |
| 4469 | 3212 continue; |
| 3213 else if (tmp < tmp_min) | |
| 2354 | 3214 { |
| 4469 | 3215 idx_i = i; |
| 3216 tmp_min = tmp; | |
| 2354 | 3217 } |
| 3218 } | |
| 3219 | |
| 4469 | 3220 result.elem (j) = tmp_min; |
| 5389 | 3221 idx_arg.elem (j) = xisnan (tmp_min) ? 0 : idx_i; |
| 458 | 3222 } |
| 3223 } | |
| 3224 | |
| 3225 return result; | |
| 3226 } | |
| 3227 | |
| 2354 | 3228 RowVector |
| 3229 Matrix::column_max (void) const | |
| 3230 { | |
| 5275 | 3231 Array<octave_idx_type> dummy_idx; |
| 4587 | 3232 return column_max (dummy_idx); |
| 2354 | 3233 } |
| 458 | 3234 |
| 3235 RowVector | |
| 5275 | 3236 Matrix::column_max (Array<octave_idx_type>& idx_arg) const |
| 458 | 3237 { |
| 3238 RowVector result; | |
| 3239 | |
| 5275 | 3240 octave_idx_type nr = rows (); |
| 3241 octave_idx_type nc = cols (); | |
| 458 | 3242 |
| 3243 if (nr > 0 && nc > 0) | |
| 3244 { | |
| 3245 result.resize (nc); | |
| 4587 | 3246 idx_arg.resize (nc); |
| 458 | 3247 |
| 5275 | 3248 for (octave_idx_type j = 0; j < nc; j++) |
| 458 | 3249 { |
| 5275 | 3250 octave_idx_type idx_i; |
| 4469 | 3251 |
| 3252 double tmp_max = octave_NaN; | |
| 3253 | |
| 3254 for (idx_i = 0; idx_i < nr; idx_i++) | |
| 2354 | 3255 { |
| 4469 | 3256 tmp_max = elem (idx_i, j); |
| 3257 | |
| 5389 | 3258 if (! xisnan (tmp_max)) |
| 4469 | 3259 break; |
| 3260 } | |
| 3261 | |
| 5275 | 3262 for (octave_idx_type i = idx_i+1; i < nr; i++) |
| 4469 | 3263 { |
| 3264 double tmp = elem (i, j); | |
| 3265 | |
| 5389 | 3266 if (xisnan (tmp)) |
| 4469 | 3267 continue; |
| 3268 else if (tmp > tmp_max) | |
| 2354 | 3269 { |
| 4469 | 3270 idx_i = i; |
| 3271 tmp_max = tmp; | |
| 2354 | 3272 } |
| 3273 } | |
| 3274 | |
| 4469 | 3275 result.elem (j) = tmp_max; |
| 5389 | 3276 idx_arg.elem (j) = xisnan (tmp_max) ? 0 : idx_i; |
| 458 | 3277 } |
| 3278 } | |
| 3279 | |
| 3280 return result; | |
| 3281 } | |
| 3282 | |
| 3504 | 3283 std::ostream& |
| 3284 operator << (std::ostream& os, const Matrix& a) | |
| 458 | 3285 { |
| 5275 | 3286 for (octave_idx_type i = 0; i < a.rows (); i++) |
| 458 | 3287 { |
| 5275 | 3288 for (octave_idx_type j = 0; j < a.cols (); j++) |
| 4130 | 3289 { |
| 3290 os << " "; | |
| 3291 octave_write_double (os, a.elem (i, j)); | |
| 3292 } | |
| 458 | 3293 os << "\n"; |
| 3294 } | |
| 3295 return os; | |
| 3296 } | |
| 3297 | |
| 3504 | 3298 std::istream& |
| 3299 operator >> (std::istream& is, Matrix& a) | |
| 458 | 3300 { |
| 5275 | 3301 octave_idx_type nr = a.rows (); |
| 3302 octave_idx_type nc = a.cols (); | |
| 458 | 3303 |
| 3304 if (nr < 1 || nc < 1) | |
| 3504 | 3305 is.clear (std::ios::badbit); |
| 458 | 3306 else |
| 3307 { | |
| 3308 double tmp; | |
| 5275 | 3309 for (octave_idx_type i = 0; i < nr; i++) |
| 3310 for (octave_idx_type j = 0; j < nc; j++) | |
| 458 | 3311 { |
| 4130 | 3312 tmp = octave_read_double (is); |
| 458 | 3313 if (is) |
| 3314 a.elem (i, j) = tmp; | |
| 3315 else | |
| 2795 | 3316 goto done; |
| 458 | 3317 } |
| 3318 } | |
| 3319 | |
| 2795 | 3320 done: |
| 3321 | |
| 458 | 3322 return is; |
| 3323 } | |
| 3324 | |
| 1819 | 3325 Matrix |
| 3326 Givens (double x, double y) | |
| 3327 { | |
| 3328 double cc, s, temp_r; | |
| 3329 | |
| 3887 | 3330 F77_FUNC (dlartg, DLARTG) (x, y, cc, s, temp_r); |
| 1819 | 3331 |
| 3332 Matrix g (2, 2); | |
| 3333 | |
| 3334 g.elem (0, 0) = cc; | |
| 3335 g.elem (1, 1) = cc; | |
| 3336 g.elem (0, 1) = s; | |
| 3337 g.elem (1, 0) = -s; | |
| 3338 | |
| 3339 return g; | |
| 3340 } | |
| 3341 | |
| 3342 Matrix | |
| 3343 Sylvester (const Matrix& a, const Matrix& b, const Matrix& c) | |
| 3344 { | |
| 3345 Matrix retval; | |
| 3346 | |
| 5775 | 3347 // FIXME -- need to check that a, b, and c are all the same |
| 1819 | 3348 // size. |
| 3349 | |
| 3350 // Compute Schur decompositions. | |
| 3351 | |
| 3352 SCHUR as (a, "U"); | |
| 3353 SCHUR bs (b, "U"); | |
| 3354 | |
| 3355 // Transform c to new coordinates. | |
| 3356 | |
| 3357 Matrix ua = as.unitary_matrix (); | |
| 3358 Matrix sch_a = as.schur_matrix (); | |
| 3359 | |
| 3360 Matrix ub = bs.unitary_matrix (); | |
| 3361 Matrix sch_b = bs.schur_matrix (); | |
| 3362 | |
| 3363 Matrix cx = ua.transpose () * c * ub; | |
| 3364 | |
| 3365 // Solve the sylvester equation, back-transform, and return the | |
| 3366 // solution. | |
| 3367 | |
| 5275 | 3368 octave_idx_type a_nr = a.rows (); |
| 3369 octave_idx_type b_nr = b.rows (); | |
| 1819 | 3370 |
| 3371 double scale; | |
| 5275 | 3372 octave_idx_type info; |
| 1819 | 3373 |
| 1950 | 3374 double *pa = sch_a.fortran_vec (); |
| 3375 double *pb = sch_b.fortran_vec (); | |
| 3376 double *px = cx.fortran_vec (); | |
| 3377 | |
| 4552 | 3378 F77_XFCN (dtrsyl, DTRSYL, (F77_CONST_CHAR_ARG2 ("N", 1), |
| 3379 F77_CONST_CHAR_ARG2 ("N", 1), | |
| 3380 1, a_nr, b_nr, pa, a_nr, pb, | |
| 3381 b_nr, px, a_nr, scale, info | |
| 3382 F77_CHAR_ARG_LEN (1) | |
| 3383 F77_CHAR_ARG_LEN (1))); | |
| 1950 | 3384 |
| 3385 | |
|
7482
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
3386 // FIXME -- check info? |
| 1819 | 3387 |
|
7482
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
3388 retval = -ua*cx*ub.transpose (); |
| 1819 | 3389 |
| 3390 return retval; | |
| 3391 } | |
| 3392 | |
| 2828 | 3393 // matrix by matrix -> matrix operations |
| 3394 | |
| 6162 | 3395 /* Simple Dot Product, Matrix-Vector and Matrix-Matrix Unit tests |
| 3396 %!assert([1 2 3] * [ 4 ; 5 ; 6], 32, 1e-14) | |
| 3397 %!assert([1 2 ; 3 4 ] * [5 ; 6], [17 ; 39 ], 1e-14) | |
| 3398 %!assert([1 2 ; 3 4 ] * [5 6 ; 7 8], [19 22; 43 50], 1e-14) | |
| 3399 */ | |
| 3400 | |
| 3401 /* Test some simple identities | |
| 3402 %!shared M, cv, rv | |
| 3403 %! M = randn(10,10); | |
| 3404 %! cv = randn(10,1); | |
| 3405 %! rv = randn(1,10); | |
| 3406 %!assert([M*cv,M*cv],M*[cv,cv],1e-14) | |
| 3407 %!assert([rv*M;rv*M],[rv;rv]*M,1e-14) | |
| 3408 %!assert(2*rv*cv,[rv,rv]*[cv;cv],1e-14) | |
| 3409 */ | |
| 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 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
|
3412 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
|
3413 { |
|
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 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
|
3415 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
|
3416 } |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3417 |
|
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 // 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
|
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 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
|
3421 xgemm (bool transa, const Matrix& a, bool transb, const Matrix& b) |
| 2828 | 3422 { |
| 3423 Matrix retval; | |
| 3424 | |
|
7800
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3425 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
|
3426 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
|
3427 |
|
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 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
|
3429 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
|
3430 |
|
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 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
|
3432 gripe_nonconformant ("operator *", a_nr, a_nc, b_nr, b_nc); |
| 2828 | 3433 else |
| 3434 { | |
|
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
|
3435 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
|
3436 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
|
3437 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
|
3438 { |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3439 octave_idx_type lda = a.rows (); |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3440 |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3441 retval.resize (a_nr, b_nc); |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3442 double *c = retval.fortran_vec (); |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3443 |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3444 const char *ctransa = get_blas_trans_arg (transa); |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3445 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
|
3446 F77_CONST_CHAR_ARG2 (ctransa, 1), |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3447 a_nr, a_nc, 1.0, |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3448 a.data (), lda, 0.0, c, a_nr |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3449 F77_CHAR_ARG_LEN (1) |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3450 F77_CHAR_ARG_LEN (1))); |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3451 for (int j = 0; j < a_nr; j++) |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3452 for (int i = 0; i < j; i++) |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3453 retval.xelem (j,i) = retval.xelem (i,j); |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3454 |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3455 } |
| 2828 | 3456 else |
| 3457 { | |
|
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
|
3458 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
|
3459 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
|
3460 |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3461 retval.resize (a_nr, b_nc); |
| 2828 | 3462 double *c = retval.fortran_vec (); |
| 3463 | |
|
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
|
3464 if (b_nc == 1) |
| 5983 | 3465 { |
|
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
|
3466 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
|
3467 F77_FUNC (xddot, XDDOT) (a_nc, a.data (), 1, b.data (), 1, *c); |
| 5983 | 3468 else |
| 6390 | 3469 { |
|
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
|
3470 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
|
3471 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
|
3472 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
|
3473 b.data (), 1, 0.0, c, 1 |
| 6390 | 3474 F77_CHAR_ARG_LEN (1))); |
| 3475 } | |
| 5983 | 3476 } |
|
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
|
3477 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
|
3478 { |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3479 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
|
3480 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
|
3481 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
|
3482 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
|
3483 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
|
3484 } |
| 5983 | 3485 else |
| 6390 | 3486 { |
|
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
|
3487 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
|
3488 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
|
3489 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
|
3490 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
|
3491 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
|
3492 lda, b.data (), ldb, 0.0, c, a_nr |
| 6390 | 3493 F77_CHAR_ARG_LEN (1) |
| 3494 F77_CHAR_ARG_LEN (1))); | |
| 3495 } | |
| 2828 | 3496 } |
| 3497 } | |
| 3498 | |
| 3499 return retval; | |
| 3500 } | |
| 3501 | |
|
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
|
3502 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
|
3503 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
|
3504 { |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3505 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
|
3506 } |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3507 |
| 5775 | 3508 // FIXME -- it would be nice to share code among the min/max |
| 4309 | 3509 // functions below. |
| 3510 | |
| 3511 #define EMPTY_RETURN_CHECK(T) \ | |
| 3512 if (nr == 0 || nc == 0) \ | |
| 3513 return T (nr, nc); | |
| 3514 | |
| 3515 Matrix | |
| 3516 min (double d, const Matrix& m) | |
| 3517 { | |
| 5275 | 3518 octave_idx_type nr = m.rows (); |
| 3519 octave_idx_type nc = m.columns (); | |
| 4309 | 3520 |
| 3521 EMPTY_RETURN_CHECK (Matrix); | |
| 3522 | |
| 3523 Matrix result (nr, nc); | |
| 3524 | |
| 5275 | 3525 for (octave_idx_type j = 0; j < nc; j++) |
| 3526 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3527 { |
| 3528 OCTAVE_QUIT; | |
| 3529 result (i, j) = xmin (d, m (i, j)); | |
| 3530 } | |
| 3531 | |
| 3532 return result; | |
| 3533 } | |
| 3534 | |
| 3535 Matrix | |
| 3536 min (const Matrix& m, double d) | |
| 3537 { | |
| 5275 | 3538 octave_idx_type nr = m.rows (); |
| 3539 octave_idx_type nc = m.columns (); | |
| 4309 | 3540 |
| 3541 EMPTY_RETURN_CHECK (Matrix); | |
| 3542 | |
| 3543 Matrix result (nr, nc); | |
| 3544 | |
| 5275 | 3545 for (octave_idx_type j = 0; j < nc; j++) |
| 3546 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3547 { |
| 3548 OCTAVE_QUIT; | |
| 3549 result (i, j) = xmin (m (i, j), d); | |
| 3550 } | |
| 3551 | |
| 3552 return result; | |
| 3553 } | |
| 3554 | |
| 3555 Matrix | |
| 3556 min (const Matrix& a, const Matrix& b) | |
| 3557 { | |
| 5275 | 3558 octave_idx_type nr = a.rows (); |
| 3559 octave_idx_type nc = a.columns (); | |
| 4309 | 3560 |
| 3561 if (nr != b.rows () || nc != b.columns ()) | |
| 3562 { | |
| 3563 (*current_liboctave_error_handler) | |
| 3564 ("two-arg min expecting args of same size"); | |
| 3565 return Matrix (); | |
| 3566 } | |
| 3567 | |
| 3568 EMPTY_RETURN_CHECK (Matrix); | |
| 3569 | |
| 3570 Matrix result (nr, nc); | |
| 3571 | |
| 5275 | 3572 for (octave_idx_type j = 0; j < nc; j++) |
| 3573 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3574 { |
| 3575 OCTAVE_QUIT; | |
| 3576 result (i, j) = xmin (a (i, j), b (i, j)); | |
| 3577 } | |
| 3578 | |
| 3579 return result; | |
| 3580 } | |
| 3581 | |
| 3582 Matrix | |
| 3583 max (double d, const Matrix& m) | |
| 3584 { | |
| 5275 | 3585 octave_idx_type nr = m.rows (); |
| 3586 octave_idx_type nc = m.columns (); | |
| 4309 | 3587 |
| 3588 EMPTY_RETURN_CHECK (Matrix); | |
| 3589 | |
| 3590 Matrix result (nr, nc); | |
| 3591 | |
| 5275 | 3592 for (octave_idx_type j = 0; j < nc; j++) |
| 3593 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3594 { |
| 3595 OCTAVE_QUIT; | |
| 3596 result (i, j) = xmax (d, m (i, j)); | |
| 3597 } | |
| 3598 | |
| 3599 return result; | |
| 3600 } | |
| 3601 | |
| 3602 Matrix | |
| 3603 max (const Matrix& m, double d) | |
| 3604 { | |
| 5275 | 3605 octave_idx_type nr = m.rows (); |
| 3606 octave_idx_type nc = m.columns (); | |
| 4309 | 3607 |
| 3608 EMPTY_RETURN_CHECK (Matrix); | |
| 3609 | |
| 3610 Matrix result (nr, nc); | |
| 3611 | |
| 5275 | 3612 for (octave_idx_type j = 0; j < nc; j++) |
| 3613 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3614 { |
| 3615 OCTAVE_QUIT; | |
| 3616 result (i, j) = xmax (m (i, j), d); | |
| 3617 } | |
| 3618 | |
| 3619 return result; | |
| 3620 } | |
| 3621 | |
| 3622 Matrix | |
| 3623 max (const Matrix& a, const Matrix& b) | |
| 3624 { | |
| 5275 | 3625 octave_idx_type nr = a.rows (); |
| 3626 octave_idx_type nc = a.columns (); | |
| 4309 | 3627 |
| 3628 if (nr != b.rows () || nc != b.columns ()) | |
| 3629 { | |
| 3630 (*current_liboctave_error_handler) | |
| 3631 ("two-arg max expecting args of same size"); | |
| 3632 return Matrix (); | |
| 3633 } | |
| 3634 | |
| 3635 EMPTY_RETURN_CHECK (Matrix); | |
| 3636 | |
| 3637 Matrix result (nr, nc); | |
| 3638 | |
| 5275 | 3639 for (octave_idx_type j = 0; j < nc; j++) |
| 3640 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3641 { |
| 3642 OCTAVE_QUIT; | |
| 3643 result (i, j) = xmax (a (i, j), b (i, j)); | |
| 3644 } | |
| 3645 | |
| 3646 return result; | |
| 3647 } | |
| 3648 | |
| 2870 | 3649 MS_CMP_OPS(Matrix, , double, ) |
| 3504 | 3650 MS_BOOL_OPS(Matrix, double, 0.0) |
| 2870 | 3651 |
| 3652 SM_CMP_OPS(double, , Matrix, ) | |
| 3504 | 3653 SM_BOOL_OPS(double, Matrix, 0.0) |
| 2870 | 3654 |
| 3655 MM_CMP_OPS(Matrix, , Matrix, ) | |
| 3504 | 3656 MM_BOOL_OPS(Matrix, Matrix, 0.0) |
| 2870 | 3657 |
| 458 | 3658 /* |
| 3659 ;;; Local Variables: *** | |
| 3660 ;;; mode: C++ *** | |
| 3661 ;;; End: *** | |
| 3662 */ |