Mercurial > hg > octave-nkf
annotate liboctave/dMatrix.cc @ 8337:e02242c54c49
reuse matrix type detected in det
| author | Jaroslav Hajek <highegg@gmail.com> |
|---|---|
| date | Wed, 19 Nov 2008 16:55:47 +0100 |
| parents | 9813c07ca946 |
| children | 445d27d79f4e |
| 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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changeset
|
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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changeset
|
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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|
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, |
|
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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::Unknown) |
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1264 typ = mattype.type (*this); |
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1265 |
|
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1266 if (typ == MatrixType::Lower || typ == MatrixType::Upper) |
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|
1267 { |
|
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1268 for (octave_idx_type i = 0; i < nc; i++) |
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1269 retval *= elem (i,i); |
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1270 } |
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1271 else if (typ == MatrixType::Hermitian) |
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|
1272 { |
|
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1273 Matrix atmp = *this; |
|
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|
1274 double *tmp_data = atmp.fortran_vec (); |
|
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1275 |
|
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1276 info = 0; |
|
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1277 double anorm = 0; |
|
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1278 if (calc_cond) anorm = xnorm (*this, 1); |
|
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|
1279 |
|
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|
1280 |
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1281 char job = 'L'; |
|
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1282 F77_XFCN (dpotrf, DPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, |
|
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1283 tmp_data, nr, info |
|
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1284 F77_CHAR_ARG_LEN (1))); |
|
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|
1285 |
|
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1286 if (info != 0) |
|
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1287 { |
|
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1288 rcon = 0.0; |
|
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1289 mattype.mark_as_unsymmetric (); |
|
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1290 typ = MatrixType::Full; |
|
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1291 } |
|
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|
1292 else |
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|
1293 { |
|
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|
1294 Array<double> z (3 * nc); |
|
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1295 double *pz = z.fortran_vec (); |
|
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1296 Array<octave_idx_type> iz (nc); |
|
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1297 octave_idx_type *piz = iz.fortran_vec (); |
|
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1298 |
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1299 F77_XFCN (dpocon, DPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
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1300 nr, tmp_data, nr, anorm, |
|
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1301 rcon, pz, piz, info |
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1302 F77_CHAR_ARG_LEN (1))); |
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1303 |
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1304 if (info != 0) |
|
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1305 rcon = 0.0; |
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|
1306 |
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1307 for (octave_idx_type i = 0; i < nc; i++) |
|
8337
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1308 retval *= atmp (i,i); |
|
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1309 |
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1310 retval = retval.square (); |
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1311 } |
|
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|
1312 } |
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1313 else if (typ != MatrixType::Full) |
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1314 (*current_liboctave_error_handler) ("det: invalid dense matrix type"); |
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|
1315 |
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1316 if (typ == MatrixType::Full) |
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1317 { |
|
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1318 Array<octave_idx_type> ipvt (nr); |
|
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1319 octave_idx_type *pipvt = ipvt.fortran_vec (); |
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1320 |
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1321 Matrix atmp = *this; |
|
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1322 double *tmp_data = atmp.fortran_vec (); |
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1323 |
|
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1324 info = 0; |
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1325 |
|
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1326 // Calculate the norm of the matrix, for later use. |
|
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1327 double anorm = 0; |
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1328 if (calc_cond) anorm = xnorm (*this, 1); |
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1329 |
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1330 F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); |
|
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1331 |
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1332 // Throw-away extra info LAPACK gives so as to not change output. |
|
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1333 rcon = 0.0; |
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1334 if (info != 0) |
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1335 { |
|
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1336 info = -1; |
|
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1337 retval = DET (); |
|
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1338 } |
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|
1339 else |
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|
1340 { |
|
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1341 if (calc_cond) |
|
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1342 { |
|
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1343 // Now calc the condition number for non-singular matrix. |
|
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1344 char job = '1'; |
|
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1345 Array<double> z (4 * nc); |
|
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1346 double *pz = z.fortran_vec (); |
|
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1347 Array<octave_idx_type> iz (nc); |
|
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1348 octave_idx_type *piz = iz.fortran_vec (); |
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1349 |
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1350 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
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1351 nc, tmp_data, nr, anorm, |
|
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1352 rcon, pz, piz, info |
|
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|
1353 F77_CHAR_ARG_LEN (1))); |
| 8335 | 1354 } |
|
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1355 |
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1356 if (info != 0) |
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|
1357 { |
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1358 info = -1; |
|
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1359 retval = DET (); |
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1360 } |
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1361 else |
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|
1362 { |
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1363 for (octave_idx_type i = 0; i < nc; i++) |
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1364 { |
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1365 double c = atmp(i,i); |
|
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1366 retval *= (ipvt(i) != (i+1)) ? -c : c; |
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1367 } |
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|
1368 } |
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|
1369 } |
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|
1370 } |
| 458 | 1371 } |
| 1372 | |
| 1373 return retval; | |
| 1374 } | |
| 1375 | |
| 7788 | 1376 double |
| 1377 Matrix::rcond (void) const | |
| 1378 { | |
| 1379 MatrixType mattype (*this); | |
| 1380 return rcond (mattype); | |
| 1381 } | |
| 1382 | |
| 1383 double | |
| 1384 Matrix::rcond (MatrixType &mattype) const | |
| 1385 { | |
| 1386 double rcon; | |
| 1387 octave_idx_type nr = rows (); | |
| 1388 octave_idx_type nc = cols (); | |
| 1389 | |
| 1390 if (nr != nc) | |
| 1391 (*current_liboctave_error_handler) ("matrix must be square"); | |
| 1392 else if (nr == 0 || nc == 0) | |
| 1393 rcon = octave_Inf; | |
| 1394 else | |
| 1395 { | |
| 1396 int typ = mattype.type (); | |
| 1397 | |
| 1398 if (typ == MatrixType::Unknown) | |
| 1399 typ = mattype.type (*this); | |
| 1400 | |
| 1401 // Only calculate the condition number for LU/Cholesky | |
| 1402 if (typ == MatrixType::Upper) | |
| 1403 { | |
| 1404 const double *tmp_data = fortran_vec (); | |
| 1405 octave_idx_type info = 0; | |
| 1406 char norm = '1'; | |
| 1407 char uplo = 'U'; | |
| 1408 char dia = 'N'; | |
| 1409 | |
| 1410 Array<double> z (3 * nc); | |
| 1411 double *pz = z.fortran_vec (); | |
| 1412 Array<octave_idx_type> iz (nc); | |
| 1413 octave_idx_type *piz = iz.fortran_vec (); | |
| 1414 | |
| 1415 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1416 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1417 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1418 nr, tmp_data, nr, rcon, | |
| 1419 pz, piz, info | |
| 1420 F77_CHAR_ARG_LEN (1) | |
| 1421 F77_CHAR_ARG_LEN (1) | |
| 1422 F77_CHAR_ARG_LEN (1))); | |
| 1423 | |
| 1424 if (info != 0) | |
| 1425 rcon = 0.0; | |
| 1426 } | |
| 1427 else if (typ == MatrixType::Permuted_Upper) | |
| 1428 (*current_liboctave_error_handler) | |
| 1429 ("permuted triangular matrix not implemented"); | |
| 1430 else if (typ == MatrixType::Lower) | |
| 1431 { | |
| 1432 const double *tmp_data = fortran_vec (); | |
| 1433 octave_idx_type info = 0; | |
| 1434 char norm = '1'; | |
| 1435 char uplo = 'L'; | |
| 1436 char dia = 'N'; | |
| 1437 | |
| 1438 Array<double> z (3 * nc); | |
| 1439 double *pz = z.fortran_vec (); | |
| 1440 Array<octave_idx_type> iz (nc); | |
| 1441 octave_idx_type *piz = iz.fortran_vec (); | |
| 1442 | |
| 1443 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1444 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1445 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1446 nr, tmp_data, nr, rcon, | |
| 1447 pz, piz, info | |
| 1448 F77_CHAR_ARG_LEN (1) | |
| 1449 F77_CHAR_ARG_LEN (1) | |
| 1450 F77_CHAR_ARG_LEN (1))); | |
| 1451 | |
| 1452 if (info != 0) | |
| 1453 rcon = 0.0; | |
| 1454 } | |
| 1455 else if (typ == MatrixType::Permuted_Lower) | |
| 1456 (*current_liboctave_error_handler) | |
| 1457 ("permuted triangular matrix not implemented"); | |
| 1458 else if (typ == MatrixType::Full || typ == MatrixType::Hermitian) | |
| 1459 { | |
| 1460 double anorm = -1.0; | |
| 1461 Matrix atmp = *this; | |
| 1462 double *tmp_data = atmp.fortran_vec (); | |
| 1463 | |
| 1464 if (typ == MatrixType::Hermitian) | |
| 1465 { | |
| 1466 octave_idx_type info = 0; | |
| 1467 char job = 'L'; | |
| 1468 anorm = atmp.abs().sum(). | |
| 1469 row(static_cast<octave_idx_type>(0)).max(); | |
| 1470 | |
| 1471 F77_XFCN (dpotrf, DPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, | |
| 1472 tmp_data, nr, info | |
| 1473 F77_CHAR_ARG_LEN (1))); | |
| 1474 | |
| 1475 if (info != 0) | |
| 1476 { | |
| 1477 rcon = 0.0; | |
| 1478 mattype.mark_as_unsymmetric (); | |
| 1479 typ = MatrixType::Full; | |
| 1480 } | |
| 1481 else | |
| 1482 { | |
| 1483 Array<double> z (3 * nc); | |
| 1484 double *pz = z.fortran_vec (); | |
| 1485 Array<octave_idx_type> iz (nc); | |
| 1486 octave_idx_type *piz = iz.fortran_vec (); | |
| 1487 | |
| 1488 F77_XFCN (dpocon, DPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), | |
| 1489 nr, tmp_data, nr, anorm, | |
| 1490 rcon, pz, piz, info | |
| 1491 F77_CHAR_ARG_LEN (1))); | |
| 1492 | |
| 1493 if (info != 0) | |
| 1494 rcon = 0.0; | |
| 1495 } | |
| 1496 } | |
| 1497 | |
| 1498 if (typ == MatrixType::Full) | |
| 1499 { | |
| 1500 octave_idx_type info = 0; | |
| 1501 | |
| 1502 Array<octave_idx_type> ipvt (nr); | |
| 1503 octave_idx_type *pipvt = ipvt.fortran_vec (); | |
| 1504 | |
| 1505 if(anorm < 0.) | |
| 1506 anorm = atmp.abs().sum(). | |
| 1507 row(static_cast<octave_idx_type>(0)).max(); | |
| 1508 | |
| 1509 Array<double> z (4 * nc); | |
| 1510 double *pz = z.fortran_vec (); | |
| 1511 Array<octave_idx_type> iz (nc); | |
| 1512 octave_idx_type *piz = iz.fortran_vec (); | |
| 1513 | |
| 1514 F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); | |
| 1515 | |
| 1516 if (info != 0) | |
| 1517 { | |
| 1518 rcon = 0.0; | |
| 1519 mattype.mark_as_rectangular (); | |
| 1520 } | |
| 1521 else | |
| 1522 { | |
| 1523 char job = '1'; | |
| 1524 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), | |
| 1525 nc, tmp_data, nr, anorm, | |
| 1526 rcon, pz, piz, info | |
| 1527 F77_CHAR_ARG_LEN (1))); | |
| 1528 | |
| 1529 if (info != 0) | |
| 1530 rcon = 0.0; | |
| 1531 } | |
| 1532 } | |
| 1533 } | |
| 1534 else | |
| 1535 rcon = 0.0; | |
| 1536 } | |
| 1537 | |
| 1538 return rcon; | |
| 1539 } | |
| 1540 | |
| 458 | 1541 Matrix |
| 5785 | 1542 Matrix::utsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, |
| 7788 | 1543 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 1544 bool calc_cond) const |
| 1545 { | |
| 1546 Matrix retval; | |
| 1547 | |
| 1548 octave_idx_type nr = rows (); | |
| 1549 octave_idx_type nc = cols (); | |
| 1550 | |
| 6924 | 1551 if (nr != b.rows ()) |
| 5785 | 1552 (*current_liboctave_error_handler) |
| 1553 ("matrix dimension mismatch solution of linear equations"); | |
| 6924 | 1554 else if (nr == 0 || nc == 0 || b.cols () == 0) |
| 1555 retval = Matrix (nc, b.cols (), 0.0); | |
| 5785 | 1556 else |
| 1557 { | |
| 1558 volatile int typ = mattype.type (); | |
| 1559 | |
| 1560 if (typ == MatrixType::Permuted_Upper || | |
| 1561 typ == MatrixType::Upper) | |
| 1562 { | |
| 1563 octave_idx_type b_nc = b.cols (); | |
| 7788 | 1564 rcon = 1.; |
| 5785 | 1565 info = 0; |
| 1566 | |
| 1567 if (typ == MatrixType::Permuted_Upper) | |
| 1568 { | |
| 1569 (*current_liboctave_error_handler) | |
| 6390 | 1570 ("permuted triangular matrix not implemented"); |
| 5785 | 1571 } |
| 1572 else | |
| 1573 { | |
| 1574 const double *tmp_data = fortran_vec (); | |
| 1575 | |
| 1576 if (calc_cond) | |
| 1577 { | |
| 1578 char norm = '1'; | |
| 1579 char uplo = 'U'; | |
| 1580 char dia = 'N'; | |
| 1581 | |
| 1582 Array<double> z (3 * nc); | |
| 1583 double *pz = z.fortran_vec (); | |
| 1584 Array<octave_idx_type> iz (nc); | |
| 1585 octave_idx_type *piz = iz.fortran_vec (); | |
| 1586 | |
| 1587 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1588 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1589 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 7788 | 1590 nr, tmp_data, nr, rcon, |
| 5785 | 1591 pz, piz, info |
| 1592 F77_CHAR_ARG_LEN (1) | |
| 1593 F77_CHAR_ARG_LEN (1) | |
| 1594 F77_CHAR_ARG_LEN (1))); | |
| 1595 | |
| 1596 if (info != 0) | |
| 1597 info = -2; | |
| 1598 | |
| 7788 | 1599 volatile double rcond_plus_one = rcon + 1.0; |
| 1600 | |
| 1601 if (rcond_plus_one == 1.0 || xisnan (rcon)) | |
| 5785 | 1602 { |
| 1603 info = -2; | |
| 1604 | |
| 1605 if (sing_handler) | |
| 7788 | 1606 sing_handler (rcon); |
| 5785 | 1607 else |
| 1608 (*current_liboctave_error_handler) | |
| 1609 ("matrix singular to machine precision, rcond = %g", | |
| 7788 | 1610 rcon); |
| 5785 | 1611 } |
| 1612 } | |
| 1613 | |
| 1614 if (info == 0) | |
| 1615 { | |
| 1616 retval = b; | |
| 1617 double *result = retval.fortran_vec (); | |
| 1618 | |
| 1619 char uplo = 'U'; | |
| 1620 char trans = 'N'; | |
| 1621 char dia = 'N'; | |
| 1622 | |
| 1623 F77_XFCN (dtrtrs, DTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1624 F77_CONST_CHAR_ARG2 (&trans, 1), | |
| 1625 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1626 nr, b_nc, tmp_data, nr, | |
| 1627 result, nr, info | |
| 1628 F77_CHAR_ARG_LEN (1) | |
| 1629 F77_CHAR_ARG_LEN (1) | |
| 1630 F77_CHAR_ARG_LEN (1))); | |
| 1631 } | |
| 1632 } | |
| 1633 } | |
| 1634 else | |
| 1635 (*current_liboctave_error_handler) ("incorrect matrix type"); | |
| 1636 } | |
| 1637 | |
| 1638 return retval; | |
| 1639 } | |
| 1640 | |
| 1641 Matrix | |
| 1642 Matrix::ltsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, | |
| 7788 | 1643 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 1644 bool calc_cond) const |
| 1645 { | |
| 1646 Matrix retval; | |
| 1647 | |
| 1648 octave_idx_type nr = rows (); | |
| 1649 octave_idx_type nc = cols (); | |
| 1650 | |
| 6924 | 1651 if (nr != b.rows ()) |
| 5785 | 1652 (*current_liboctave_error_handler) |
| 1653 ("matrix dimension mismatch solution of linear equations"); | |
| 6924 | 1654 else if (nr == 0 || nc == 0 || b.cols () == 0) |
| 1655 retval = Matrix (nc, b.cols (), 0.0); | |
| 5785 | 1656 else |
| 1657 { | |
| 1658 volatile int typ = mattype.type (); | |
| 1659 | |
| 1660 if (typ == MatrixType::Permuted_Lower || | |
| 1661 typ == MatrixType::Lower) | |
| 1662 { | |
| 1663 octave_idx_type b_nc = b.cols (); | |
| 7788 | 1664 rcon = 1.; |
| 5785 | 1665 info = 0; |
| 1666 | |
| 1667 if (typ == MatrixType::Permuted_Lower) | |
| 1668 { | |
| 1669 (*current_liboctave_error_handler) | |
| 6390 | 1670 ("permuted triangular matrix not implemented"); |
| 5785 | 1671 } |
| 1672 else | |
| 1673 { | |
| 1674 const double *tmp_data = fortran_vec (); | |
| 1675 | |
| 1676 if (calc_cond) | |
| 1677 { | |
| 1678 char norm = '1'; | |
| 1679 char uplo = 'L'; | |
| 1680 char dia = 'N'; | |
| 1681 | |
| 1682 Array<double> z (3 * nc); | |
| 1683 double *pz = z.fortran_vec (); | |
| 1684 Array<octave_idx_type> iz (nc); | |
| 1685 octave_idx_type *piz = iz.fortran_vec (); | |
| 1686 | |
| 1687 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1688 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1689 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 7788 | 1690 nr, tmp_data, nr, rcon, |
| 5785 | 1691 pz, piz, info |
| 1692 F77_CHAR_ARG_LEN (1) | |
| 1693 F77_CHAR_ARG_LEN (1) | |
| 1694 F77_CHAR_ARG_LEN (1))); | |
| 1695 | |
| 1696 if (info != 0) | |
| 1697 info = -2; | |
| 1698 | |
| 7788 | 1699 volatile double rcond_plus_one = rcon + 1.0; |
| 1700 | |
| 1701 if (rcond_plus_one == 1.0 || xisnan (rcon)) | |
| 5785 | 1702 { |
| 1703 info = -2; | |
| 1704 | |
| 1705 if (sing_handler) | |
| 7788 | 1706 sing_handler (rcon); |
| 5785 | 1707 else |
| 1708 (*current_liboctave_error_handler) | |
| 1709 ("matrix singular to machine precision, rcond = %g", | |
| 7788 | 1710 rcon); |
| 5785 | 1711 } |
| 1712 } | |
| 1713 | |
| 1714 if (info == 0) | |
| 1715 { | |
| 1716 retval = b; | |
| 1717 double *result = retval.fortran_vec (); | |
| 1718 | |
| 1719 char uplo = 'L'; | |
| 1720 char trans = 'N'; | |
| 1721 char dia = 'N'; | |
| 1722 | |
| 1723 F77_XFCN (dtrtrs, DTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1724 F77_CONST_CHAR_ARG2 (&trans, 1), | |
| 1725 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1726 nr, b_nc, tmp_data, nr, | |
| 1727 result, nr, info | |
| 1728 F77_CHAR_ARG_LEN (1) | |
| 1729 F77_CHAR_ARG_LEN (1) | |
| 1730 F77_CHAR_ARG_LEN (1))); | |
| 1731 } | |
| 1732 } | |
| 1733 } | |
| 1734 else | |
| 1735 (*current_liboctave_error_handler) ("incorrect matrix type"); | |
| 1736 } | |
| 1737 | |
| 1738 return retval; | |
| 1739 } | |
| 1740 | |
| 1741 Matrix | |
| 1742 Matrix::fsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, | |
| 7788 | 1743 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 1744 bool calc_cond) const |
| 1745 { | |
| 1746 Matrix retval; | |
| 1747 | |
| 1748 octave_idx_type nr = rows (); | |
| 1749 octave_idx_type nc = cols (); | |
| 1750 | |
| 6924 | 1751 if (nr != nc || nr != b.rows ()) |
| 5785 | 1752 (*current_liboctave_error_handler) |
| 1753 ("matrix dimension mismatch solution of linear equations"); | |
| 6924 | 1754 else if (nr == 0 || b.cols () == 0) |
| 1755 retval = Matrix (nc, b.cols (), 0.0); | |
| 5785 | 1756 else |
| 1757 { | |
| 1758 volatile int typ = mattype.type (); | |
| 1759 | |
| 1760 // Calculate the norm of the matrix, for later use. | |
| 1761 double anorm = -1.; | |
| 1762 | |
| 1763 if (typ == MatrixType::Hermitian) | |
| 1764 { | |
| 1765 info = 0; | |
| 1766 char job = 'L'; | |
| 1767 Matrix atmp = *this; | |
| 1768 double *tmp_data = atmp.fortran_vec (); | |
| 1769 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); | |
| 1770 | |
| 1771 F77_XFCN (dpotrf, DPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, | |
| 1772 tmp_data, nr, info | |
| 1773 F77_CHAR_ARG_LEN (1))); | |
| 1774 | |
|
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|
1775 // Throw-away extra info LAPACK gives so as to not change output. |
| 7788 | 1776 rcon = 0.0; |
|
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1777 if (info != 0) |
|
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|
1778 { |
|
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|
1779 info = -2; |
|
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|
1780 |
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|
1781 mattype.mark_as_unsymmetric (); |
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1782 typ = MatrixType::Full; |
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1783 } |
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|
1784 else |
| 5785 | 1785 { |
|
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|
1786 if (calc_cond) |
| 5785 | 1787 { |
|
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|
1788 Array<double> z (3 * nc); |
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|
1789 double *pz = z.fortran_vec (); |
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1790 Array<octave_idx_type> iz (nc); |
|
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1791 octave_idx_type *piz = iz.fortran_vec (); |
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|
1792 |
|
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1793 F77_XFCN (dpocon, DPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
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|
1794 nr, tmp_data, nr, anorm, |
| 7788 | 1795 rcon, pz, piz, info |
|
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1796 F77_CHAR_ARG_LEN (1))); |
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|
1797 |
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1798 if (info != 0) |
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1799 info = -2; |
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|
1800 |
| 7788 | 1801 volatile double rcond_plus_one = rcon + 1.0; |
| 1802 | |
| 1803 if (rcond_plus_one == 1.0 || xisnan (rcon)) | |
|
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1804 { |
|
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1805 info = -2; |
|
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|
1806 |
|
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|
1807 if (sing_handler) |
| 7788 | 1808 sing_handler (rcon); |
|
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1809 else |
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1810 (*current_liboctave_error_handler) |
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1811 ("matrix singular to machine precision, rcond = %g", |
| 7788 | 1812 rcon); |
|
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1813 } |
|
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1814 } |
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1815 |
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1816 if (info == 0) |
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1817 { |
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1818 retval = b; |
|
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1819 double *result = retval.fortran_vec (); |
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1820 |
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1821 octave_idx_type b_nc = b.cols (); |
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1822 |
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1823 F77_XFCN (dpotrs, DPOTRS, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
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1824 nr, b_nc, tmp_data, nr, |
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1825 result, b.rows(), info |
|
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1826 F77_CHAR_ARG_LEN (1))); |
|
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1827 } |
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1828 else |
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|
1829 { |
| 5785 | 1830 mattype.mark_as_unsymmetric (); |
| 1831 typ = MatrixType::Full; | |
|
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|
1832 } |
| 5785 | 1833 } |
| 1834 } | |
| 1835 | |
| 1836 if (typ == MatrixType::Full) | |
| 1837 { | |
| 1838 info = 0; | |
| 1839 | |
| 1840 Array<octave_idx_type> ipvt (nr); | |
| 1841 octave_idx_type *pipvt = ipvt.fortran_vec (); | |
| 1842 | |
| 1843 Matrix atmp = *this; | |
| 1844 double *tmp_data = atmp.fortran_vec (); | |
| 1845 if(anorm < 0.) | |
| 1846 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); | |
| 1847 | |
| 1848 Array<double> z (4 * nc); | |
| 1849 double *pz = z.fortran_vec (); | |
| 1850 Array<octave_idx_type> iz (nc); | |
| 1851 octave_idx_type *piz = iz.fortran_vec (); | |
| 1852 | |
| 1853 F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); | |
| 1854 | |
|
7482
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1855 // Throw-away extra info LAPACK gives so as to not change output. |
| 7788 | 1856 rcon = 0.0; |
|
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1857 if (info != 0) |
| 5785 | 1858 { |
|
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1859 info = -2; |
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1860 |
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1861 if (sing_handler) |
| 7788 | 1862 sing_handler (rcon); |
|
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1863 else |
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1864 (*current_liboctave_error_handler) |
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1865 ("matrix singular to machine precision"); |
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1866 |
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1867 mattype.mark_as_rectangular (); |
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1868 } |
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1869 else |
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1870 { |
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1871 if (calc_cond) |
| 5785 | 1872 { |
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1873 // Now calculate the condition number for |
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1874 // non-singular matrix. |
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1875 char job = '1'; |
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1876 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
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1877 nc, tmp_data, nr, anorm, |
| 7788 | 1878 rcon, pz, piz, info |
|
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1879 F77_CHAR_ARG_LEN (1))); |
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1880 |
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1881 if (info != 0) |
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1882 info = -2; |
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1883 |
| 7788 | 1884 volatile double rcond_plus_one = rcon + 1.0; |
| 1885 | |
| 1886 if (rcond_plus_one == 1.0 || xisnan (rcon)) | |
| 5785 | 1887 { |
|
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1888 info = -2; |
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1889 |
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1890 if (sing_handler) |
| 7788 | 1891 sing_handler (rcon); |
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1892 else |
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1893 (*current_liboctave_error_handler) |
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1894 ("matrix singular to machine precision, rcond = %g", |
| 7788 | 1895 rcon); |
| 5785 | 1896 } |
| 1897 } | |
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1898 |
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1899 if (info == 0) |
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1900 { |
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1901 retval = b; |
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1902 double *result = retval.fortran_vec (); |
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1903 |
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1904 octave_idx_type b_nc = b.cols (); |
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1905 |
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1906 char job = 'N'; |
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1907 F77_XFCN (dgetrs, DGETRS, (F77_CONST_CHAR_ARG2 (&job, 1), |
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1908 nr, b_nc, tmp_data, nr, |
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1909 pipvt, result, b.rows(), info |
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1910 F77_CHAR_ARG_LEN (1))); |
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1911 } |
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1912 else |
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1913 mattype.mark_as_rectangular (); |
| 5785 | 1914 } |
| 1915 } | |
| 1916 else if (typ != MatrixType::Hermitian) | |
| 1917 (*current_liboctave_error_handler) ("incorrect matrix type"); | |
| 1918 } | |
| 1919 | |
| 1920 return retval; | |
| 1921 } | |
| 1922 | |
| 1923 Matrix | |
| 1924 Matrix::solve (MatrixType &typ, const Matrix& b) const | |
| 1925 { | |
| 1926 octave_idx_type info; | |
| 7788 | 1927 double rcon; |
| 1928 return solve (typ, b, info, rcon, 0); | |
| 5785 | 1929 } |
| 1930 | |
| 1931 Matrix | |
| 1932 Matrix::solve (MatrixType &typ, const Matrix& b, octave_idx_type& info, | |
| 7788 | 1933 double& rcon) const |
| 5785 | 1934 { |
| 7788 | 1935 return solve (typ, b, info, rcon, 0); |
| 5785 | 1936 } |
| 1937 | |
| 1938 Matrix | |
| 1939 Matrix::solve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, | |
| 7788 | 1940 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 1941 bool singular_fallback) const |
| 1942 { | |
| 1943 Matrix retval; | |
| 1944 int typ = mattype.type (); | |
| 1945 | |
| 1946 if (typ == MatrixType::Unknown) | |
| 1947 typ = mattype.type (*this); | |
| 1948 | |
| 1949 // Only calculate the condition number for LU/Cholesky | |
| 1950 if (typ == MatrixType::Upper || typ == MatrixType::Permuted_Upper) | |
| 7788 | 1951 retval = utsolve (mattype, b, info, rcon, sing_handler, false); |
| 5785 | 1952 else if (typ == MatrixType::Lower || typ == MatrixType::Permuted_Lower) |
| 7788 | 1953 retval = ltsolve (mattype, b, info, rcon, sing_handler, false); |
| 5785 | 1954 else if (typ == MatrixType::Full || typ == MatrixType::Hermitian) |
| 7788 | 1955 retval = fsolve (mattype, b, info, rcon, sing_handler, true); |
| 5785 | 1956 else if (typ != MatrixType::Rectangular) |
| 1957 { | |
| 1958 (*current_liboctave_error_handler) ("unknown matrix type"); | |
| 1959 return Matrix (); | |
| 1960 } | |
| 1961 | |
| 1962 // Rectangular or one of the above solvers flags a singular matrix | |
| 1963 if (singular_fallback && mattype.type () == MatrixType::Rectangular) | |
| 1964 { | |
| 1965 octave_idx_type rank; | |
| 7788 | 1966 retval = lssolve (b, info, rank, rcon); |
| 5785 | 1967 } |
| 1968 | |
| 1969 return retval; | |
| 1970 } | |
| 1971 | |
| 1972 ComplexMatrix | |
| 1973 Matrix::solve (MatrixType &typ, const ComplexMatrix& b) const | |
| 1974 { | |
| 1975 ComplexMatrix tmp (*this); | |
| 1976 return tmp.solve (typ, b); | |
| 1977 } | |
| 1978 | |
| 1979 ComplexMatrix | |
| 1980 Matrix::solve (MatrixType &typ, const ComplexMatrix& b, | |
| 1981 octave_idx_type& info) const | |
| 1982 { | |
| 1983 ComplexMatrix tmp (*this); | |
| 1984 return tmp.solve (typ, b, info); | |
| 1985 } | |
| 1986 | |
| 1987 ComplexMatrix | |
| 1988 Matrix::solve (MatrixType &typ, const ComplexMatrix& b, octave_idx_type& info, | |
| 7788 | 1989 double& rcon) const |
| 5785 | 1990 { |
| 1991 ComplexMatrix tmp (*this); | |
| 7788 | 1992 return tmp.solve (typ, b, info, rcon); |
| 5785 | 1993 } |
| 1994 | |
| 1995 ComplexMatrix | |
| 1996 Matrix::solve (MatrixType &typ, const ComplexMatrix& b, octave_idx_type& info, | |
| 7788 | 1997 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 1998 bool singular_fallback) const |
| 1999 { | |
| 2000 ComplexMatrix tmp (*this); | |
| 7788 | 2001 return tmp.solve (typ, b, info, rcon, sing_handler, singular_fallback); |
| 5785 | 2002 } |
| 2003 | |
| 2004 ColumnVector | |
| 2005 Matrix::solve (MatrixType &typ, const ColumnVector& b) const | |
| 2006 { | |
| 7788 | 2007 octave_idx_type info; double rcon; |
| 2008 return solve (typ, b, info, rcon); | |
| 5785 | 2009 } |
| 2010 | |
| 2011 ColumnVector | |
| 2012 Matrix::solve (MatrixType &typ, const ColumnVector& b, | |
| 2013 octave_idx_type& info) const | |
| 2014 { | |
| 7788 | 2015 double rcon; |
| 2016 return solve (typ, b, info, rcon); | |
| 5785 | 2017 } |
| 2018 | |
| 2019 ColumnVector | |
| 2020 Matrix::solve (MatrixType &typ, const ColumnVector& b, octave_idx_type& info, | |
| 7788 | 2021 double& rcon) const |
| 5785 | 2022 { |
| 7788 | 2023 return solve (typ, b, info, rcon, 0); |
| 5785 | 2024 } |
| 2025 | |
| 2026 ColumnVector | |
| 2027 Matrix::solve (MatrixType &typ, const ColumnVector& b, octave_idx_type& info, | |
| 7788 | 2028 double& rcon, solve_singularity_handler sing_handler) const |
| 5785 | 2029 { |
| 2030 Matrix tmp (b); | |
| 7788 | 2031 return solve (typ, tmp, info, rcon, sing_handler).column(static_cast<octave_idx_type> (0)); |
| 5785 | 2032 } |
| 2033 | |
| 2034 ComplexColumnVector | |
| 2035 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b) const | |
| 2036 { | |
| 2037 ComplexMatrix tmp (*this); | |
| 2038 return tmp.solve (typ, b); | |
| 2039 } | |
| 2040 | |
| 2041 ComplexColumnVector | |
| 2042 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, | |
| 2043 octave_idx_type& info) const | |
| 2044 { | |
| 2045 ComplexMatrix tmp (*this); | |
| 2046 return tmp.solve (typ, b, info); | |
| 2047 } | |
| 2048 | |
| 2049 ComplexColumnVector | |
| 2050 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, | |
| 7788 | 2051 octave_idx_type& info, double& rcon) const |
| 5785 | 2052 { |
| 2053 ComplexMatrix tmp (*this); | |
| 7788 | 2054 return tmp.solve (typ, b, info, rcon); |
| 5785 | 2055 } |
| 2056 | |
| 2057 ComplexColumnVector | |
| 2058 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, | |
| 7788 | 2059 octave_idx_type& info, double& rcon, |
| 5785 | 2060 solve_singularity_handler sing_handler) const |
| 2061 { | |
| 2062 ComplexMatrix tmp (*this); | |
| 7788 | 2063 return tmp.solve(typ, b, info, rcon, sing_handler); |
| 5785 | 2064 } |
| 2065 | |
| 2066 Matrix | |
| 458 | 2067 Matrix::solve (const Matrix& b) const |
| 2068 { | |
| 5275 | 2069 octave_idx_type info; |
| 7788 | 2070 double rcon; |
| 2071 return solve (b, info, rcon, 0); | |
| 458 | 2072 } |
| 2073 | |
| 2074 Matrix | |
| 5275 | 2075 Matrix::solve (const Matrix& b, octave_idx_type& info) const |
| 458 | 2076 { |
| 7788 | 2077 double rcon; |
| 2078 return solve (b, info, rcon, 0); | |
| 458 | 2079 } |
| 2080 | |
| 2081 Matrix | |
| 7788 | 2082 Matrix::solve (const Matrix& b, octave_idx_type& info, double& rcon) const |
| 458 | 2083 { |
| 7788 | 2084 return solve (b, info, rcon, 0); |
| 3480 | 2085 } |
| 2086 | |
| 2087 Matrix | |
| 5785 | 2088 Matrix::solve (const Matrix& b, octave_idx_type& info, |
| 7788 | 2089 double& rcon, solve_singularity_handler sing_handler) const |
| 3480 | 2090 { |
| 5785 | 2091 MatrixType mattype (*this); |
| 7788 | 2092 return solve (mattype, b, info, rcon, sing_handler); |
| 458 | 2093 } |
| 2094 | |
| 2095 ComplexMatrix | |
| 2096 Matrix::solve (const ComplexMatrix& b) const | |
| 2097 { | |
| 2098 ComplexMatrix tmp (*this); | |
| 2099 return tmp.solve (b); | |
| 2100 } | |
| 2101 | |
| 2102 ComplexMatrix | |
| 5275 | 2103 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info) const |
| 458 | 2104 { |
| 2105 ComplexMatrix tmp (*this); | |
| 2106 return tmp.solve (b, info); | |
| 2107 } | |
| 2108 | |
| 2109 ComplexMatrix | |
| 7788 | 2110 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcon) const |
| 458 | 2111 { |
| 2112 ComplexMatrix tmp (*this); | |
| 7788 | 2113 return tmp.solve (b, info, rcon); |
| 458 | 2114 } |
| 2115 | |
| 3480 | 2116 ComplexMatrix |
| 7788 | 2117 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcon, |
| 3480 | 2118 solve_singularity_handler sing_handler) const |
| 2119 { | |
| 2120 ComplexMatrix tmp (*this); | |
| 7788 | 2121 return tmp.solve (b, info, rcon, sing_handler); |
| 3480 | 2122 } |
| 2123 | |
| 458 | 2124 ColumnVector |
| 2125 Matrix::solve (const ColumnVector& b) const | |
| 2126 { | |
| 7788 | 2127 octave_idx_type info; double rcon; |
| 2128 return solve (b, info, rcon); | |
| 458 | 2129 } |
| 2130 | |
| 2131 ColumnVector | |
| 5275 | 2132 Matrix::solve (const ColumnVector& b, octave_idx_type& info) const |
| 458 | 2133 { |
| 7788 | 2134 double rcon; |
| 2135 return solve (b, info, rcon); | |
| 458 | 2136 } |
| 2137 | |
| 2138 ColumnVector | |
| 7788 | 2139 Matrix::solve (const ColumnVector& b, octave_idx_type& info, double& rcon) const |
| 458 | 2140 { |
| 7788 | 2141 return solve (b, info, rcon, 0); |
| 3480 | 2142 } |
| 2143 | |
| 2144 ColumnVector | |
| 7788 | 2145 Matrix::solve (const ColumnVector& b, octave_idx_type& info, double& rcon, |
| 3480 | 2146 solve_singularity_handler sing_handler) const |
| 2147 { | |
| 5785 | 2148 MatrixType mattype (*this); |
| 7788 | 2149 return solve (mattype, b, info, rcon, sing_handler); |
| 458 | 2150 } |
| 2151 | |
| 2152 ComplexColumnVector | |
| 2153 Matrix::solve (const ComplexColumnVector& b) const | |
| 2154 { | |
| 2155 ComplexMatrix tmp (*this); | |
| 2156 return tmp.solve (b); | |
| 2157 } | |
| 2158 | |
| 2159 ComplexColumnVector | |
| 5275 | 2160 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info) const |
| 458 | 2161 { |
| 2162 ComplexMatrix tmp (*this); | |
| 2163 return tmp.solve (b, info); | |
| 2164 } | |
| 2165 | |
| 2166 ComplexColumnVector | |
| 7788 | 2167 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info, double& rcon) const |
| 458 | 2168 { |
| 2169 ComplexMatrix tmp (*this); | |
| 7788 | 2170 return tmp.solve (b, info, rcon); |
| 458 | 2171 } |
| 2172 | |
| 3480 | 2173 ComplexColumnVector |
| 7788 | 2174 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info, double& rcon, |
| 3480 | 2175 solve_singularity_handler sing_handler) const |
| 2176 { | |
| 2177 ComplexMatrix tmp (*this); | |
| 7788 | 2178 return tmp.solve (b, info, rcon, sing_handler); |
| 3480 | 2179 } |
| 2180 | |
| 458 | 2181 Matrix |
| 2182 Matrix::lssolve (const Matrix& b) const | |
| 2183 { | |
| 5275 | 2184 octave_idx_type info; |
| 2185 octave_idx_type rank; | |
| 7788 | 2186 double rcon; |
| 2187 return lssolve (b, info, rank, rcon); | |
| 458 | 2188 } |
| 2189 | |
| 2190 Matrix | |
| 5275 | 2191 Matrix::lssolve (const Matrix& b, octave_idx_type& info) const |
| 458 | 2192 { |
| 5275 | 2193 octave_idx_type rank; |
| 7788 | 2194 double rcon; |
| 2195 return lssolve (b, info, rank, rcon); | |
| 458 | 2196 } |
| 2197 | |
| 2198 Matrix | |
| 7072 | 2199 Matrix::lssolve (const Matrix& b, octave_idx_type& info, |
| 2200 octave_idx_type& rank) const | |
| 458 | 2201 { |
| 7788 | 2202 double rcon; |
| 2203 return lssolve (b, info, rank, rcon); | |
| 7076 | 2204 } |
| 2205 | |
| 2206 Matrix | |
| 2207 Matrix::lssolve (const Matrix& b, octave_idx_type& info, | |
| 7788 | 2208 octave_idx_type& rank, double &rcon) const |
| 7076 | 2209 { |
| 1948 | 2210 Matrix retval; |
| 2211 | |
| 5275 | 2212 octave_idx_type nrhs = b.cols (); |
| 2213 | |
| 2214 octave_idx_type m = rows (); | |
| 2215 octave_idx_type n = cols (); | |
| 458 | 2216 |
| 6924 | 2217 if (m != b.rows ()) |
| 1948 | 2218 (*current_liboctave_error_handler) |
| 6924 | 2219 ("matrix dimension mismatch solution of linear equations"); |
| 2220 else if (m == 0 || n == 0 || b.cols () == 0) | |
| 2221 retval = Matrix (n, b.cols (), 0.0); | |
| 1948 | 2222 else |
| 458 | 2223 { |
| 7072 | 2224 volatile octave_idx_type minmn = (m < n ? m : n); |
| 2225 octave_idx_type maxmn = m > n ? m : n; | |
| 7788 | 2226 rcon = -1.0; |
| 7072 | 2227 if (m != n) |
| 2228 { | |
| 2229 retval = Matrix (maxmn, nrhs, 0.0); | |
| 2230 | |
| 2231 for (octave_idx_type j = 0; j < nrhs; j++) | |
| 2232 for (octave_idx_type i = 0; i < m; i++) | |
| 2233 retval.elem (i, j) = b.elem (i, j); | |
| 2234 } | |
| 2235 else | |
| 2236 retval = b; | |
| 2237 | |
| 1948 | 2238 Matrix atmp = *this; |
| 2239 double *tmp_data = atmp.fortran_vec (); | |
| 2240 | |
| 7072 | 2241 double *pretval = retval.fortran_vec (); |
| 2242 Array<double> s (minmn); | |
| 7071 | 2243 double *ps = s.fortran_vec (); |
| 1948 | 2244 |
| 7072 | 2245 // Ask DGELSD what the dimension of WORK should be. |
| 5275 | 2246 octave_idx_type lwork = -1; |
| 3752 | 2247 |
| 2248 Array<double> work (1); | |
| 1948 | 2249 |
| 7477 | 2250 octave_idx_type smlsiz; |
| 2251 F77_FUNC (xilaenv, XILAENV) (9, F77_CONST_CHAR_ARG2 ("DGELSD", 6), | |
| 2252 F77_CONST_CHAR_ARG2 (" ", 1), | |
| 7478 | 2253 0, 0, 0, 0, smlsiz |
| 7477 | 2254 F77_CHAR_ARG_LEN (6) |
| 7478 | 2255 F77_CHAR_ARG_LEN (1)); |
| 7079 | 2256 |
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2257 octave_idx_type mnthr; |
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2258 F77_FUNC (xilaenv, XILAENV) (6, F77_CONST_CHAR_ARG2 ("DGELSD", 6), |
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2259 F77_CONST_CHAR_ARG2 (" ", 1), |
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2260 m, n, nrhs, -1, mnthr |
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2261 F77_CHAR_ARG_LEN (6) |
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2262 F77_CHAR_ARG_LEN (1)); |
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2263 |
| 7079 | 2264 // We compute the size of iwork because DGELSD in older versions |
| 2265 // of LAPACK does not return it on a query call. | |
| 7124 | 2266 double dminmn = static_cast<double> (minmn); |
| 2267 double dsmlsizp1 = static_cast<double> (smlsiz+1); | |
| 7079 | 2268 #if defined (HAVE_LOG2) |
| 7367 | 2269 double tmp = log2 (dminmn / dsmlsizp1); |
| 7079 | 2270 #else |
| 7367 | 2271 double tmp = log (dminmn / dsmlsizp1) / log (2.0); |
| 7079 | 2272 #endif |
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2273 octave_idx_type nlvl = static_cast<octave_idx_type> (tmp) + 1; |
| 7079 | 2274 if (nlvl < 0) |
| 2275 nlvl = 0; | |
| 2276 | |
| 2277 octave_idx_type liwork = 3 * minmn * nlvl + 11 * minmn; | |
| 2278 if (liwork < 1) | |
| 2279 liwork = 1; | |
| 7072 | 2280 Array<octave_idx_type> iwork (liwork); |
| 2281 octave_idx_type* piwork = iwork.fortran_vec (); | |
| 2282 | |
| 2283 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, | |
| 7788 | 2284 ps, rcon, rank, work.fortran_vec (), |
| 7072 | 2285 lwork, piwork, info)); |
| 1948 | 2286 |
| 7476 | 2287 // The workspace query is broken in at least LAPACK 3.0.0 |
|
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2288 // through 3.1.1 when n >= mnthr. The obtuse formula below |
| 7476 | 2289 // should provide sufficient workspace for DGELSD to operate |
| 2290 // efficiently. | |
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2291 if (n >= mnthr) |
| 7476 | 2292 { |
| 2293 const octave_idx_type wlalsd | |
| 2294 = 9*m + 2*m*smlsiz + 8*m*nlvl + m*nrhs + (smlsiz+1)*(smlsiz+1); | |
| 2295 | |
| 2296 octave_idx_type addend = m; | |
| 2297 | |
| 2298 if (2*m-4 > addend) | |
| 2299 addend = 2*m-4; | |
| 2300 | |
| 2301 if (nrhs > addend) | |
| 2302 addend = nrhs; | |
| 2303 | |
| 2304 if (n-3*m > addend) | |
| 2305 addend = n-3*m; | |
| 2306 | |
| 2307 if (wlalsd > addend) | |
| 2308 addend = wlalsd; | |
| 2309 | |
| 2310 const octave_idx_type lworkaround = 4*m + m*m + addend; | |
| 2311 | |
| 2312 if (work(0) < lworkaround) | |
| 2313 work(0) = lworkaround; | |
| 2314 } | |
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2315 else if (m >= n) |
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2316 { |
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2317 octave_idx_type lworkaround |
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2318 = 12*n + 2*n*smlsiz + 8*n*nlvl + n*nrhs + (smlsiz+1)*(smlsiz+1); |
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2319 |
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2320 if (work(0) < lworkaround) |
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2321 work(0) = lworkaround; |
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2322 } |
| 7476 | 2323 |
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2324 lwork = static_cast<octave_idx_type> (work(0)); |
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2325 work.resize (lwork); |
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2326 |
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2327 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, |
| 7788 | 2328 maxmn, ps, rcon, rank, |
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2329 work.fortran_vec (), lwork, |
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2330 piwork, info)); |
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2331 |
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2332 if (rank < minmn) |
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2333 (*current_liboctave_warning_handler) |
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2334 ("dgelsd: rank deficient %dx%d matrix, rank = %d", m, n, rank); |
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2335 if (s.elem (0) == 0.0) |
| 7788 | 2336 rcon = 0.0; |
| 1948 | 2337 else |
| 7788 | 2338 rcon = s.elem (minmn - 1) / s.elem (0); |
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2339 |
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|
2340 retval.resize (n, nrhs); |
| 458 | 2341 } |
| 2342 | |
| 2343 return retval; | |
| 2344 } | |
| 2345 | |
| 2346 ComplexMatrix | |
| 2347 Matrix::lssolve (const ComplexMatrix& b) const | |
| 2348 { | |
| 2349 ComplexMatrix tmp (*this); | |
| 5275 | 2350 octave_idx_type info; |
| 2351 octave_idx_type rank; | |
| 7788 | 2352 double rcon; |
| 2353 return tmp.lssolve (b, info, rank, rcon); | |
| 458 | 2354 } |
| 2355 | |
| 2356 ComplexMatrix | |
| 5275 | 2357 Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info) const |
| 458 | 2358 { |
| 2359 ComplexMatrix tmp (*this); | |
| 5275 | 2360 octave_idx_type rank; |
| 7788 | 2361 double rcon; |
| 2362 return tmp.lssolve (b, info, rank, rcon); | |
| 458 | 2363 } |
| 2364 | |
| 2365 ComplexMatrix | |
| 7076 | 2366 Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info, |
| 2367 octave_idx_type& rank) const | |
| 458 | 2368 { |
| 2369 ComplexMatrix tmp (*this); | |
| 7788 | 2370 double rcon; |
| 2371 return tmp.lssolve (b, info, rank, rcon); | |
| 7076 | 2372 } |
| 2373 | |
| 2374 ComplexMatrix | |
| 2375 Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info, | |
| 7788 | 2376 octave_idx_type& rank, double& rcon) const |
| 7076 | 2377 { |
| 2378 ComplexMatrix tmp (*this); | |
| 7788 | 2379 return tmp.lssolve (b, info, rank, rcon); |
| 458 | 2380 } |
| 2381 | |
| 2382 ColumnVector | |
| 2383 Matrix::lssolve (const ColumnVector& b) const | |
| 2384 { | |
| 5275 | 2385 octave_idx_type info; |
| 2386 octave_idx_type rank; | |
| 7788 | 2387 double rcon; |
| 2388 return lssolve (b, info, rank, rcon); | |
| 458 | 2389 } |
| 2390 | |
| 2391 ColumnVector | |
| 5275 | 2392 Matrix::lssolve (const ColumnVector& b, octave_idx_type& info) const |
| 458 | 2393 { |
| 5275 | 2394 octave_idx_type rank; |
| 7788 | 2395 double rcon; |
| 2396 return lssolve (b, info, rank, rcon); | |
| 458 | 2397 } |
| 2398 | |
| 2399 ColumnVector | |
| 7072 | 2400 Matrix::lssolve (const ColumnVector& b, octave_idx_type& info, |
| 2401 octave_idx_type& rank) const | |
| 458 | 2402 { |
| 7788 | 2403 double rcon; |
| 2404 return lssolve (b, info, rank, rcon); | |
| 7076 | 2405 } |
| 2406 | |
| 2407 ColumnVector | |
| 2408 Matrix::lssolve (const ColumnVector& b, octave_idx_type& info, | |
| 7788 | 2409 octave_idx_type& rank, double &rcon) const |
| 7076 | 2410 { |
| 1948 | 2411 ColumnVector retval; |
| 2412 | |
| 5275 | 2413 octave_idx_type nrhs = 1; |
| 2414 | |
| 2415 octave_idx_type m = rows (); | |
| 2416 octave_idx_type n = cols (); | |
| 458 | 2417 |
| 6924 | 2418 if (m != b.length ()) |
| 1948 | 2419 (*current_liboctave_error_handler) |
| 6924 | 2420 ("matrix dimension mismatch solution of linear equations"); |
| 2421 else if (m == 0 || n == 0) | |
| 2422 retval = ColumnVector (n, 0.0); | |
| 1948 | 2423 else |
| 458 | 2424 { |
| 7072 | 2425 volatile octave_idx_type minmn = (m < n ? m : n); |
| 2426 octave_idx_type maxmn = m > n ? m : n; | |
| 7788 | 2427 rcon = -1.0; |
| 7072 | 2428 |
| 2429 if (m != n) | |
| 2430 { | |
| 2431 retval = ColumnVector (maxmn, 0.0); | |
| 2432 | |
| 2433 for (octave_idx_type i = 0; i < m; i++) | |
| 2434 retval.elem (i) = b.elem (i); | |
| 2435 } | |
| 2436 else | |
| 2437 retval = b; | |
| 2438 | |
| 1948 | 2439 Matrix atmp = *this; |
| 2440 double *tmp_data = atmp.fortran_vec (); | |
| 2441 | |
| 7072 | 2442 double *pretval = retval.fortran_vec (); |
| 2443 Array<double> s (minmn); | |
| 7071 | 2444 double *ps = s.fortran_vec (); |
| 1948 | 2445 |
| 7072 | 2446 // Ask DGELSD what the dimension of WORK should be. |
| 5275 | 2447 octave_idx_type lwork = -1; |
| 3752 | 2448 |
| 2449 Array<double> work (1); | |
| 2450 | |
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2451 octave_idx_type smlsiz; |
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2452 F77_FUNC (xilaenv, XILAENV) (9, F77_CONST_CHAR_ARG2 ("DGELSD", 6), |
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2453 F77_CONST_CHAR_ARG2 (" ", 1), |
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2454 0, 0, 0, 0, smlsiz |
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2455 F77_CHAR_ARG_LEN (6) |
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2456 F77_CHAR_ARG_LEN (1)); |
| 7079 | 2457 |
| 2458 // We compute the size of iwork because DGELSD in older versions | |
| 2459 // of LAPACK does not return it on a query call. | |
| 7124 | 2460 double dminmn = static_cast<double> (minmn); |
| 2461 double dsmlsizp1 = static_cast<double> (smlsiz+1); | |
| 7079 | 2462 #if defined (HAVE_LOG2) |
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2463 double tmp = log2 (dminmn / dsmlsizp1); |
| 7079 | 2464 #else |
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2465 double tmp = log (dminmn / dsmlsizp1) / log (2.0); |
| 7079 | 2466 #endif |
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2467 octave_idx_type nlvl = static_cast<octave_idx_type> (tmp) + 1; |
| 7079 | 2468 if (nlvl < 0) |
| 2469 nlvl = 0; | |
| 2470 | |
| 2471 octave_idx_type liwork = 3 * minmn * nlvl + 11 * minmn; | |
| 2472 if (liwork < 1) | |
| 2473 liwork = 1; | |
| 7072 | 2474 Array<octave_idx_type> iwork (liwork); |
| 2475 octave_idx_type* piwork = iwork.fortran_vec (); | |
| 2476 | |
| 2477 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, | |
| 7788 | 2478 ps, rcon, rank, work.fortran_vec (), |
| 7072 | 2479 lwork, piwork, info)); |
| 1948 | 2480 |
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2481 lwork = static_cast<octave_idx_type> (work(0)); |
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2482 work.resize (lwork); |
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2483 |
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2484 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, |
| 7788 | 2485 maxmn, ps, rcon, rank, |
|
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2486 work.fortran_vec (), lwork, |
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2487 piwork, info)); |
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2488 |
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2489 if (rank < minmn) |
| 1948 | 2490 { |
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2491 if (rank < minmn) |
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2492 (*current_liboctave_warning_handler) |
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2493 ("dgelsd: rank deficient %dx%d matrix, rank = %d", m, n, rank); |
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2494 if (s.elem (0) == 0.0) |
| 7788 | 2495 rcon = 0.0; |
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2496 else |
| 7788 | 2497 rcon = s.elem (minmn - 1) / s.elem (0); |
| 1948 | 2498 } |
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2499 |
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|
2500 retval.resize (n, nrhs); |
| 458 | 2501 } |
| 2502 | |
| 2503 return retval; | |
| 2504 } | |
| 2505 | |
| 2506 ComplexColumnVector | |
| 2507 Matrix::lssolve (const ComplexColumnVector& b) const | |
| 2508 { | |
| 2509 ComplexMatrix tmp (*this); | |
| 7076 | 2510 octave_idx_type info; |
| 2511 octave_idx_type rank; | |
| 7788 | 2512 double rcon; |
| 2513 return tmp.lssolve (b, info, rank, rcon); | |
| 458 | 2514 } |
| 2515 | |
| 2516 ComplexColumnVector | |
| 5275 | 2517 Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info) const |
| 458 | 2518 { |
| 2519 ComplexMatrix tmp (*this); | |
| 7076 | 2520 octave_idx_type rank; |
| 7788 | 2521 double rcon; |
| 2522 return tmp.lssolve (b, info, rank, rcon); | |
| 458 | 2523 } |
| 2524 | |
| 2525 ComplexColumnVector | |
| 7076 | 2526 Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, |
| 2527 octave_idx_type& rank) const | |
| 458 | 2528 { |
| 2529 ComplexMatrix tmp (*this); | |
| 7788 | 2530 double rcon; |
| 2531 return tmp.lssolve (b, info, rank, rcon); | |
| 7076 | 2532 } |
| 2533 | |
| 2534 ComplexColumnVector | |
| 2535 Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, | |
| 7788 | 2536 octave_idx_type& rank, double &rcon) const |
| 7076 | 2537 { |
| 2538 ComplexMatrix tmp (*this); | |
| 7788 | 2539 return tmp.lssolve (b, info, rank, rcon); |
| 458 | 2540 } |
| 2541 | |
| 1819 | 2542 // Constants for matrix exponential calculation. |
| 2543 | |
| 2544 static double padec [] = | |
| 2545 { | |
| 2546 5.0000000000000000e-1, | |
| 2547 1.1666666666666667e-1, | |
| 2548 1.6666666666666667e-2, | |
| 2549 1.6025641025641026e-3, | |
| 2550 1.0683760683760684e-4, | |
| 2551 4.8562548562548563e-6, | |
| 2552 1.3875013875013875e-7, | |
| 2553 1.9270852604185938e-9, | |
| 2554 }; | |
| 2555 | |
| 7400 | 2556 static void |
| 7788 | 2557 solve_singularity_warning (double rcon) |
| 7400 | 2558 { |
| 2559 (*current_liboctave_warning_handler) | |
| 2560 ("singular matrix encountered in expm calculation, rcond = %g", | |
| 7788 | 2561 rcon); |
| 7400 | 2562 } |
| 2563 | |
| 1819 | 2564 Matrix |
| 2565 Matrix::expm (void) const | |
| 2566 { | |
| 2567 Matrix retval; | |
| 2568 | |
| 2569 Matrix m = *this; | |
| 2570 | |
| 6699 | 2571 if (numel () == 1) |
| 2572 return Matrix (1, 1, exp (m(0))); | |
| 2573 | |
| 5275 | 2574 octave_idx_type nc = columns (); |
| 1819 | 2575 |
| 3130 | 2576 // Preconditioning step 1: trace normalization to reduce dynamic |
| 2577 // range of poles, but avoid making stable eigenvalues unstable. | |
| 2578 | |
| 1819 | 2579 // trace shift value |
| 3331 | 2580 volatile double trshift = 0.0; |
| 1819 | 2581 |
| 5275 | 2582 for (octave_idx_type i = 0; i < nc; i++) |
| 1819 | 2583 trshift += m.elem (i, i); |
| 2584 | |
| 2585 trshift /= nc; | |
| 2586 | |
| 3130 | 2587 if (trshift > 0.0) |
| 2588 { | |
| 5275 | 2589 for (octave_idx_type i = 0; i < nc; i++) |
| 3130 | 2590 m.elem (i, i) -= trshift; |
| 2591 } | |
| 1819 | 2592 |
| 3331 | 2593 // Preconditioning step 2: balancing; code follows development |
| 2594 // in AEPBAL | |
| 2595 | |
| 2596 double *p_m = m.fortran_vec (); | |
| 2597 | |
| 5275 | 2598 octave_idx_type info, ilo, ihi, ilos, ihis; |
| 3468 | 2599 Array<double> dpermute (nc); |
| 2600 Array<double> dscale (nc); | |
| 3466 | 2601 |
| 3468 | 2602 // permutation first |
| 2603 char job = 'P'; | |
| 4552 | 2604 F77_XFCN (dgebal, DGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
| 2605 nc, p_m, nc, ilo, ihi, | |
| 2606 dpermute.fortran_vec (), info | |
| 2607 F77_CHAR_ARG_LEN (1))); | |
| 3466 | 2608 |
| 3468 | 2609 // then scaling |
| 2610 job = 'S'; | |
| 4552 | 2611 F77_XFCN (dgebal, DGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
| 2612 nc, p_m, nc, ilos, ihis, | |
| 2613 dscale.fortran_vec (), info | |
| 2614 F77_CHAR_ARG_LEN (1))); | |
| 3331 | 2615 |
| 1819 | 2616 // Preconditioning step 3: scaling. |
| 3331 | 2617 |
| 1819 | 2618 ColumnVector work(nc); |
| 3130 | 2619 double inf_norm; |
| 3331 | 2620 |
| 4552 | 2621 F77_XFCN (xdlange, XDLANGE, (F77_CONST_CHAR_ARG2 ("I", 1), |
| 2622 nc, nc, m.fortran_vec (), nc, | |
| 2623 work.fortran_vec (), inf_norm | |
| 2624 F77_CHAR_ARG_LEN (1))); | |
| 3331 | 2625 |
| 5275 | 2626 octave_idx_type sqpow = static_cast<octave_idx_type> (inf_norm > 0.0 |
| 1819 | 2627 ? (1.0 + log (inf_norm) / log (2.0)) |
| 2628 : 0.0); | |
| 3331 | 2629 |
| 1819 | 2630 // Check whether we need to square at all. |
| 3331 | 2631 |
| 1819 | 2632 if (sqpow < 0) |
| 2633 sqpow = 0; | |
| 3331 | 2634 |
| 1819 | 2635 if (sqpow > 0) |
| 2636 { | |
| 7400 | 2637 if (sqpow > 1023) |
| 2638 sqpow = 1023; | |
| 2639 | |
| 1819 | 2640 double scale_factor = 1.0; |
| 5275 | 2641 for (octave_idx_type i = 0; i < sqpow; i++) |
| 1819 | 2642 scale_factor *= 2.0; |
| 7400 | 2643 |
| 1819 | 2644 m = m / scale_factor; |
| 2645 } | |
| 3331 | 2646 |
| 1819 | 2647 // npp, dpp: pade' approx polynomial matrices. |
| 3331 | 2648 |
| 1819 | 2649 Matrix npp (nc, nc, 0.0); |
| 7265 | 2650 double *pnpp = npp.fortran_vec (); |
| 1819 | 2651 Matrix dpp = npp; |
| 7265 | 2652 double *pdpp = dpp.fortran_vec (); |
| 3331 | 2653 |
| 1819 | 2654 // Now powers a^8 ... a^1. |
| 3331 | 2655 |
| 5275 | 2656 octave_idx_type minus_one_j = -1; |
| 2657 for (octave_idx_type j = 7; j >= 0; j--) | |
| 1819 | 2658 { |
| 7265 | 2659 for (octave_idx_type i = 0; i < nc; i++) |
| 2660 { | |
| 2661 octave_idx_type k = i * nc + i; | |
| 2662 pnpp[k] += padec[j]; | |
| 2663 pdpp[k] += minus_one_j * padec[j]; | |
| 2664 } | |
| 2665 | |
| 2666 npp = m * npp; | |
| 2667 pnpp = npp.fortran_vec (); | |
| 2668 | |
| 2669 dpp = m * dpp; | |
| 2670 pdpp = dpp.fortran_vec (); | |
| 2671 | |
| 1819 | 2672 minus_one_j *= -1; |
| 2673 } | |
| 3331 | 2674 |
| 1819 | 2675 // Zero power. |
| 3331 | 2676 |
| 1819 | 2677 dpp = -dpp; |
| 5275 | 2678 for (octave_idx_type j = 0; j < nc; j++) |
| 1819 | 2679 { |
| 2680 npp.elem (j, j) += 1.0; | |
| 2681 dpp.elem (j, j) += 1.0; | |
| 2682 } | |
| 3331 | 2683 |
| 1819 | 2684 // Compute pade approximation = inverse (dpp) * npp. |
| 2685 | |
| 7788 | 2686 double rcon; |
| 2687 retval = dpp.solve (npp, info, rcon, solve_singularity_warning); | |
| 7400 | 2688 |
| 2689 if (info < 0) | |
| 2690 return retval; | |
| 2691 | |
| 1819 | 2692 // Reverse preconditioning step 3: repeated squaring. |
| 3331 | 2693 |
| 1819 | 2694 while (sqpow) |
| 2695 { | |
| 2696 retval = retval * retval; | |
| 2697 sqpow--; | |
| 2698 } | |
| 3331 | 2699 |
| 1819 | 2700 // Reverse preconditioning step 2: inverse balancing. |
| 3466 | 2701 // apply inverse scaling to computed exponential |
| 5275 | 2702 for (octave_idx_type i = 0; i < nc; i++) |
| 2703 for (octave_idx_type j = 0; j < nc; j++) | |
|
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|
2704 retval(i,j) *= dscale(i) / dscale(j); |
| 3466 | 2705 |
| 4153 | 2706 OCTAVE_QUIT; |
| 2707 | |
| 3466 | 2708 // construct balancing permutation vector |
| 5275 | 2709 Array<octave_idx_type> iperm (nc); |
| 2710 for (octave_idx_type i = 0; i < nc; i++) | |
| 4593 | 2711 iperm(i) = i; // identity permutation |
| 3466 | 2712 |
|
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diff
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|
2713 // trailing permutations must be done in reverse order |
|
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diff
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|
2714 for (octave_idx_type i = nc - 1; i >= ihi; i--) |
|
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diff
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|
2715 { |
|
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diff
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|
2716 octave_idx_type swapidx = static_cast<octave_idx_type> (dpermute(i)) - 1; |
|
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diff
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|
2717 octave_idx_type tmp = iperm(i); |
|
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diff
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|
2718 iperm(i) = iperm(swapidx); |
|
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|
2719 iperm(swapidx) = tmp; |
|
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|
2720 } |
|
851803f7bb4d
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|
2721 |
| 3466 | 2722 // leading permutations in forward order |
| 5275 | 2723 for (octave_idx_type i = 0; i < (ilo-1); i++) |
| 3468 | 2724 { |
| 5275 | 2725 octave_idx_type swapidx = static_cast<octave_idx_type> (dpermute(i)) - 1; |
| 2726 octave_idx_type tmp = iperm(i); | |
| 4593 | 2727 iperm(i) = iperm (swapidx); |
| 2728 iperm(swapidx) = tmp; | |
| 3468 | 2729 } |
| 3466 | 2730 |
| 7416 | 2731 // construct inverse balancing permutation vector |
| 2732 Array<octave_idx_type> invpvec (nc); | |
| 2733 for (octave_idx_type i = 0; i < nc; i++) | |
| 2734 invpvec(iperm(i)) = i; // Thanks to R. A. Lippert for this method | |
| 2735 | |
| 2736 OCTAVE_QUIT; | |
|
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|
2737 |
| 7416 | 2738 Matrix tmpMat = retval; |
| 2739 for (octave_idx_type i = 0; i < nc; i++) | |
| 2740 for (octave_idx_type j = 0; j < nc; j++) | |
| 2741 retval(i,j) = tmpMat(invpvec(i),invpvec(j)); | |
| 2742 | |
|
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diff
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|
2743 // Reverse preconditioning step 1: fix trace normalization. |
| 3130 | 2744 if (trshift > 0.0) |
| 2745 retval = exp (trshift) * retval; | |
| 2746 | |
| 2747 return retval; | |
| 1819 | 2748 } |
| 2749 | |
| 458 | 2750 Matrix& |
| 2751 Matrix::operator += (const DiagMatrix& a) | |
| 2752 { | |
| 5275 | 2753 octave_idx_type nr = rows (); |
| 2754 octave_idx_type nc = cols (); | |
| 2755 | |
| 2756 octave_idx_type a_nr = a.rows (); | |
| 2757 octave_idx_type a_nc = a.cols (); | |
| 2385 | 2758 |
| 2759 if (nr != a_nr || nc != a_nc) | |
| 458 | 2760 { |
| 2385 | 2761 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
| 458 | 2762 return *this; |
| 2763 } | |
| 2764 | |
| 5275 | 2765 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 2766 elem (i, i) += a.elem (i, i); |
| 2767 | |
| 2768 return *this; | |
| 2769 } | |
| 2770 | |
| 2771 Matrix& | |
| 2772 Matrix::operator -= (const DiagMatrix& a) | |
| 2773 { | |
| 5275 | 2774 octave_idx_type nr = rows (); |
| 2775 octave_idx_type nc = cols (); | |
| 2776 | |
| 2777 octave_idx_type a_nr = a.rows (); | |
| 2778 octave_idx_type a_nc = a.cols (); | |
| 2385 | 2779 |
| 2780 if (nr != a_nr || nc != a_nc) | |
| 458 | 2781 { |
| 2385 | 2782 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
| 458 | 2783 return *this; |
| 2784 } | |
| 2785 | |
| 5275 | 2786 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 2787 elem (i, i) -= a.elem (i, i); |
| 2788 | |
| 2789 return *this; | |
| 2790 } | |
| 2791 | |
| 2792 // unary operations | |
| 2793 | |
| 2964 | 2794 boolMatrix |
| 458 | 2795 Matrix::operator ! (void) const |
| 2796 { | |
| 5275 | 2797 octave_idx_type nr = rows (); |
| 2798 octave_idx_type nc = cols (); | |
| 458 | 2799 |
| 2964 | 2800 boolMatrix b (nr, nc); |
| 458 | 2801 |
| 5275 | 2802 for (octave_idx_type j = 0; j < nc; j++) |
| 2803 for (octave_idx_type i = 0; i < nr; i++) | |
| 458 | 2804 b.elem (i, j) = ! elem (i, j); |
| 2805 | |
| 2806 return b; | |
| 2807 } | |
| 2808 | |
| 1205 | 2809 // column vector by row vector -> matrix operations |
| 458 | 2810 |
| 1205 | 2811 Matrix |
| 2812 operator * (const ColumnVector& v, const RowVector& a) | |
| 458 | 2813 { |
| 1948 | 2814 Matrix retval; |
| 2815 | |
| 5275 | 2816 octave_idx_type len = v.length (); |
| 3233 | 2817 |
| 2818 if (len != 0) | |
| 1205 | 2819 { |
| 5275 | 2820 octave_idx_type a_len = a.length (); |
| 3233 | 2821 |
| 2822 retval.resize (len, a_len); | |
| 2823 double *c = retval.fortran_vec (); | |
| 2824 | |
| 4552 | 2825 F77_XFCN (dgemm, DGEMM, (F77_CONST_CHAR_ARG2 ("N", 1), |
| 2826 F77_CONST_CHAR_ARG2 ("N", 1), | |
| 2827 len, a_len, 1, 1.0, v.data (), len, | |
| 2828 a.data (), 1, 0.0, c, len | |
| 2829 F77_CHAR_ARG_LEN (1) | |
| 2830 F77_CHAR_ARG_LEN (1))); | |
| 1205 | 2831 } |
| 458 | 2832 |
| 1948 | 2833 return retval; |
| 458 | 2834 } |
| 2835 | |
| 2836 // other operations. | |
| 2837 | |
| 2838 Matrix | |
|
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David Bateman <dbateman@free.fr>
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diff
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|
2839 Matrix::map (dmapper fcn) const |
| 1205 | 2840 { |
|
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diff
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|
2841 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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|
2842 } |
|
8c32f95c2639
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parents:
7488
diff
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|
2843 |
|
8c32f95c2639
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diff
changeset
|
2844 ComplexMatrix |
|
8c32f95c2639
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diff
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|
2845 Matrix::map (cmapper fcn) const |
|
8c32f95c2639
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diff
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|
2846 { |
|
8c32f95c2639
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David Bateman <dbateman@free.fr>
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7488
diff
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|
2847 return MArray2<double>::map<Complex> (func_ptr (fcn)); |
| 1205 | 2848 } |
| 2849 | |
| 3248 | 2850 boolMatrix |
|
7503
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David Bateman <dbateman@free.fr>
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diff
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|
2851 Matrix::map (bmapper fcn) const |
| 3248 | 2852 { |
|
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diff
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|
2853 return MArray2<double>::map<bool> (func_ptr (fcn)); |
| 458 | 2854 } |
| 2855 | |
| 2385 | 2856 bool |
| 4431 | 2857 Matrix::any_element_is_negative (bool neg_zero) const |
| 2385 | 2858 { |
| 5275 | 2859 octave_idx_type nel = nelem (); |
| 2385 | 2860 |
| 4431 | 2861 if (neg_zero) |
| 2862 { | |
| 5275 | 2863 for (octave_idx_type i = 0; i < nel; i++) |
| 4634 | 2864 if (lo_ieee_signbit (elem (i))) |
| 2865 return true; | |
| 4431 | 2866 } |
| 2867 else | |
| 2868 { | |
| 5275 | 2869 for (octave_idx_type i = 0; i < nel; i++) |
| 4634 | 2870 if (elem (i) < 0) |
| 2871 return true; | |
| 4431 | 2872 } |
| 2385 | 2873 |
| 2874 return false; | |
| 2875 } | |
| 2876 | |
|
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|
2877 bool |
|
935be827eaf8
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7803
diff
changeset
|
2878 Matrix::any_element_is_nan (void) const |
|
935be827eaf8
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parents:
7803
diff
changeset
|
2879 { |
|
935be827eaf8
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diff
changeset
|
2880 octave_idx_type nel = nelem (); |
|
935be827eaf8
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parents:
7803
diff
changeset
|
2881 |
|
935be827eaf8
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7803
diff
changeset
|
2882 for (octave_idx_type i = 0; i < nel; i++) |
|
935be827eaf8
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7803
diff
changeset
|
2883 { |
|
935be827eaf8
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7803
diff
changeset
|
2884 double val = elem (i); |
|
935be827eaf8
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parents:
7803
diff
changeset
|
2885 if (xisnan (val)) |
|
935be827eaf8
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7803
diff
changeset
|
2886 return true; |
|
935be827eaf8
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parents:
7803
diff
changeset
|
2887 } |
|
935be827eaf8
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7803
diff
changeset
|
2888 |
|
935be827eaf8
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diff
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|
2889 return false; |
|
935be827eaf8
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diff
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|
2890 } |
| 2385 | 2891 |
| 2892 bool | |
| 2893 Matrix::any_element_is_inf_or_nan (void) const | |
| 2894 { | |
| 5275 | 2895 octave_idx_type nel = nelem (); |
| 2896 | |
| 2897 for (octave_idx_type i = 0; i < nel; i++) | |
| 4634 | 2898 { |
| 2899 double val = elem (i); | |
| 2900 if (xisinf (val) || xisnan (val)) | |
| 2901 return true; | |
| 2902 } | |
| 2903 | |
| 2904 return false; | |
| 2385 | 2905 } |
| 2906 | |
| 2907 bool | |
| 5943 | 2908 Matrix::any_element_not_one_or_zero (void) const |
| 2909 { | |
| 2910 octave_idx_type nel = nelem (); | |
| 2911 | |
| 2912 for (octave_idx_type i = 0; i < nel; i++) | |
| 2913 { | |
| 2914 double val = elem (i); | |
| 2915 if (val != 0 && val != 1) | |
| 2916 return true; | |
| 2917 } | |
| 2918 | |
| 2919 return false; | |
| 2920 } | |
| 2921 | |
| 2922 bool | |
| 2385 | 2923 Matrix::all_elements_are_int_or_inf_or_nan (void) const |
| 2924 { | |
| 5275 | 2925 octave_idx_type nel = nelem (); |
| 2926 | |
| 2927 for (octave_idx_type i = 0; i < nel; i++) | |
| 4634 | 2928 { |
| 2929 double val = elem (i); | |
| 2930 if (xisnan (val) || D_NINT (val) == val) | |
| 2931 continue; | |
| 2932 else | |
| 2933 return false; | |
| 2934 } | |
| 2385 | 2935 |
| 2936 return true; | |
| 2937 } | |
| 2938 | |
| 1968 | 2939 // Return nonzero if any element of M is not an integer. Also extract |
| 2940 // the largest and smallest values and return them in MAX_VAL and MIN_VAL. | |
| 2941 | |
| 2385 | 2942 bool |
| 1968 | 2943 Matrix::all_integers (double& max_val, double& min_val) const |
| 2944 { | |
| 5275 | 2945 octave_idx_type nel = nelem (); |
| 4634 | 2946 |
| 2947 if (nel > 0) | |
| 1968 | 2948 { |
| 4634 | 2949 max_val = elem (0); |
| 2950 min_val = elem (0); | |
| 1968 | 2951 } |
| 2952 else | |
| 2385 | 2953 return false; |
| 1968 | 2954 |
| 5275 | 2955 for (octave_idx_type i = 0; i < nel; i++) |
| 4634 | 2956 { |
| 2957 double val = elem (i); | |
| 2958 | |
| 2959 if (val > max_val) | |
| 2960 max_val = val; | |
| 2961 | |
| 2962 if (val < min_val) | |
| 2963 min_val = val; | |
| 2964 | |
| 2965 if (D_NINT (val) != val) | |
| 2966 return false; | |
| 2967 } | |
| 2385 | 2968 |
| 2969 return true; | |
| 1968 | 2970 } |
| 2971 | |
| 2385 | 2972 bool |
| 1968 | 2973 Matrix::too_large_for_float (void) const |
| 2974 { | |
| 5275 | 2975 octave_idx_type nel = nelem (); |
| 2976 | |
| 2977 for (octave_idx_type i = 0; i < nel; i++) | |
| 4634 | 2978 { |
| 2979 double val = elem (i); | |
| 2980 | |
| 5389 | 2981 if (! (xisnan (val) || xisinf (val)) |
| 5387 | 2982 && fabs (val) > FLT_MAX) |
| 4634 | 2983 return true; |
| 2984 } | |
| 1968 | 2985 |
| 2385 | 2986 return false; |
| 1968 | 2987 } |
| 2988 | |
| 5775 | 2989 // FIXME Do these really belong here? Maybe they should be |
| 4015 | 2990 // in a base class? |
| 458 | 2991 |
| 2832 | 2992 boolMatrix |
| 4015 | 2993 Matrix::all (int dim) const |
| 458 | 2994 { |
| 4015 | 2995 MX_ALL_OP (dim); |
| 458 | 2996 } |
| 2997 | |
| 2832 | 2998 boolMatrix |
| 4015 | 2999 Matrix::any (int dim) const |
| 458 | 3000 { |
| 4015 | 3001 MX_ANY_OP (dim); |
| 458 | 3002 } |
| 3003 | |
| 3004 Matrix | |
| 3723 | 3005 Matrix::cumprod (int dim) const |
| 458 | 3006 { |
| 4015 | 3007 MX_CUMULATIVE_OP (Matrix, double, *=); |
| 458 | 3008 } |
| 3009 | |
| 3010 Matrix | |
| 3723 | 3011 Matrix::cumsum (int dim) const |
| 458 | 3012 { |
| 4015 | 3013 MX_CUMULATIVE_OP (Matrix, double, +=); |
| 458 | 3014 } |
| 3015 | |
| 3016 Matrix | |
| 3723 | 3017 Matrix::prod (int dim) const |
| 458 | 3018 { |
| 3864 | 3019 MX_REDUCTION_OP (Matrix, *=, 1.0, 1.0); |
| 458 | 3020 } |
| 3021 | |
| 3022 Matrix | |
| 3723 | 3023 Matrix::sum (int dim) const |
| 458 | 3024 { |
| 3864 | 3025 MX_REDUCTION_OP (Matrix, +=, 0.0, 0.0); |
| 458 | 3026 } |
| 3027 | |
| 3028 Matrix | |
| 3723 | 3029 Matrix::sumsq (int dim) const |
| 458 | 3030 { |
| 3864 | 3031 #define ROW_EXPR \ |
| 3032 double d = elem (i, j); \ | |
| 3033 retval.elem (i, 0) += d * d | |
| 3034 | |
| 3035 #define COL_EXPR \ | |
| 3036 double d = elem (i, j); \ | |
| 3037 retval.elem (0, j) += d * d | |
| 3038 | |
| 3039 MX_BASE_REDUCTION_OP (Matrix, ROW_EXPR, COL_EXPR, 0.0, 0.0); | |
| 3040 | |
| 3041 #undef ROW_EXPR | |
| 3042 #undef COL_EXPR | |
| 458 | 3043 } |
| 3044 | |
| 2385 | 3045 Matrix |
| 3046 Matrix::abs (void) const | |
| 3047 { | |
| 5275 | 3048 octave_idx_type nr = rows (); |
| 3049 octave_idx_type nc = cols (); | |
| 2385 | 3050 |
| 3051 Matrix retval (nr, nc); | |
| 3052 | |
| 5275 | 3053 for (octave_idx_type j = 0; j < nc; j++) |
| 3054 for (octave_idx_type i = 0; i < nr; i++) | |
| 2385 | 3055 retval (i, j) = fabs (elem (i, j)); |
| 3056 | |
| 3057 return retval; | |
| 3058 } | |
| 3059 | |
|
7620
36594d5bbe13
Move diag function into the octave_value class
David Bateman <dbateman@free.fr>
parents:
7544
diff
changeset
|
3060 Matrix |
| 5275 | 3061 Matrix::diag (octave_idx_type k) const |
| 458 | 3062 { |
|
7620
36594d5bbe13
Move diag function into the octave_value class
David Bateman <dbateman@free.fr>
parents:
7544
diff
changeset
|
3063 return MArray2<double>::diag (k); |
| 458 | 3064 } |
| 3065 | |
| 3066 ColumnVector | |
| 3067 Matrix::row_min (void) const | |
| 3068 { | |
| 5275 | 3069 Array<octave_idx_type> dummy_idx; |
| 4587 | 3070 return row_min (dummy_idx); |
| 458 | 3071 } |
| 3072 | |
| 3073 ColumnVector | |
| 5275 | 3074 Matrix::row_min (Array<octave_idx_type>& idx_arg) const |
| 458 | 3075 { |
| 3076 ColumnVector result; | |
| 3077 | |
| 5275 | 3078 octave_idx_type nr = rows (); |
| 3079 octave_idx_type nc = cols (); | |
| 458 | 3080 |
| 3081 if (nr > 0 && nc > 0) | |
| 3082 { | |
| 3083 result.resize (nr); | |
| 4587 | 3084 idx_arg.resize (nr); |
| 458 | 3085 |
| 5275 | 3086 for (octave_idx_type i = 0; i < nr; i++) |
| 458 | 3087 { |
| 5275 | 3088 octave_idx_type idx_j; |
| 4469 | 3089 |
| 3090 double tmp_min = octave_NaN; | |
| 3091 | |
| 3092 for (idx_j = 0; idx_j < nc; idx_j++) | |
| 2354 | 3093 { |
| 4469 | 3094 tmp_min = elem (i, idx_j); |
| 3095 | |
| 5389 | 3096 if (! xisnan (tmp_min)) |
| 4469 | 3097 break; |
| 3098 } | |
| 3099 | |
| 5275 | 3100 for (octave_idx_type j = idx_j+1; j < nc; j++) |
| 4469 | 3101 { |
| 3102 double tmp = elem (i, j); | |
| 3103 | |
| 5389 | 3104 if (xisnan (tmp)) |
| 4469 | 3105 continue; |
| 3106 else if (tmp < tmp_min) | |
| 2354 | 3107 { |
| 4469 | 3108 idx_j = j; |
| 3109 tmp_min = tmp; | |
| 2354 | 3110 } |
| 3111 } | |
| 3112 | |
| 4469 | 3113 result.elem (i) = tmp_min; |
| 5389 | 3114 idx_arg.elem (i) = xisnan (tmp_min) ? 0 : idx_j; |
| 458 | 3115 } |
| 3116 } | |
| 3117 | |
| 3118 return result; | |
| 3119 } | |
| 3120 | |
| 3121 ColumnVector | |
| 3122 Matrix::row_max (void) const | |
| 3123 { | |
| 5275 | 3124 Array<octave_idx_type> dummy_idx; |
| 4587 | 3125 return row_max (dummy_idx); |
| 458 | 3126 } |
| 3127 | |
| 3128 ColumnVector | |
| 5275 | 3129 Matrix::row_max (Array<octave_idx_type>& idx_arg) const |
| 458 | 3130 { |
| 3131 ColumnVector result; | |
| 3132 | |
| 5275 | 3133 octave_idx_type nr = rows (); |
| 3134 octave_idx_type nc = cols (); | |
| 458 | 3135 |
| 3136 if (nr > 0 && nc > 0) | |
| 3137 { | |
| 3138 result.resize (nr); | |
| 4587 | 3139 idx_arg.resize (nr); |
| 458 | 3140 |
| 5275 | 3141 for (octave_idx_type i = 0; i < nr; i++) |
| 458 | 3142 { |
| 5275 | 3143 octave_idx_type idx_j; |
| 4469 | 3144 |
| 3145 double tmp_max = octave_NaN; | |
| 3146 | |
| 3147 for (idx_j = 0; idx_j < nc; idx_j++) | |
| 2354 | 3148 { |
| 4469 | 3149 tmp_max = elem (i, idx_j); |
| 3150 | |
| 5389 | 3151 if (! xisnan (tmp_max)) |
| 4469 | 3152 break; |
| 3153 } | |
| 3154 | |
| 5275 | 3155 for (octave_idx_type j = idx_j+1; j < nc; j++) |
| 4469 | 3156 { |
| 3157 double tmp = elem (i, j); | |
| 3158 | |
| 5389 | 3159 if (xisnan (tmp)) |
| 4469 | 3160 continue; |
| 3161 else if (tmp > tmp_max) | |
| 2354 | 3162 { |
| 4469 | 3163 idx_j = j; |
| 3164 tmp_max = tmp; | |
| 2354 | 3165 } |
| 3166 } | |
| 3167 | |
| 4469 | 3168 result.elem (i) = tmp_max; |
| 5389 | 3169 idx_arg.elem (i) = xisnan (tmp_max) ? 0 : idx_j; |
| 458 | 3170 } |
| 3171 } | |
| 3172 | |
| 3173 return result; | |
| 3174 } | |
| 3175 | |
| 3176 RowVector | |
| 3177 Matrix::column_min (void) const | |
| 3178 { | |
| 5275 | 3179 Array<octave_idx_type> dummy_idx; |
| 4587 | 3180 return column_min (dummy_idx); |
| 458 | 3181 } |
| 2354 | 3182 |
| 458 | 3183 RowVector |
| 5275 | 3184 Matrix::column_min (Array<octave_idx_type>& idx_arg) const |
| 458 | 3185 { |
| 3186 RowVector result; | |
| 3187 | |
| 5275 | 3188 octave_idx_type nr = rows (); |
| 3189 octave_idx_type nc = cols (); | |
| 458 | 3190 |
| 3191 if (nr > 0 && nc > 0) | |
| 3192 { | |
| 3193 result.resize (nc); | |
| 4587 | 3194 idx_arg.resize (nc); |
| 458 | 3195 |
| 5275 | 3196 for (octave_idx_type j = 0; j < nc; j++) |
| 458 | 3197 { |
| 5275 | 3198 octave_idx_type idx_i; |
| 4469 | 3199 |
| 3200 double tmp_min = octave_NaN; | |
| 3201 | |
| 3202 for (idx_i = 0; idx_i < nr; idx_i++) | |
| 2354 | 3203 { |
| 4469 | 3204 tmp_min = elem (idx_i, j); |
| 3205 | |
| 5389 | 3206 if (! xisnan (tmp_min)) |
| 4469 | 3207 break; |
| 3208 } | |
| 3209 | |
| 5275 | 3210 for (octave_idx_type i = idx_i+1; i < nr; i++) |
| 4469 | 3211 { |
| 3212 double tmp = elem (i, j); | |
| 3213 | |
| 5389 | 3214 if (xisnan (tmp)) |
| 4469 | 3215 continue; |
| 3216 else if (tmp < tmp_min) | |
| 2354 | 3217 { |
| 4469 | 3218 idx_i = i; |
| 3219 tmp_min = tmp; | |
| 2354 | 3220 } |
| 3221 } | |
| 3222 | |
| 4469 | 3223 result.elem (j) = tmp_min; |
| 5389 | 3224 idx_arg.elem (j) = xisnan (tmp_min) ? 0 : idx_i; |
| 458 | 3225 } |
| 3226 } | |
| 3227 | |
| 3228 return result; | |
| 3229 } | |
| 3230 | |
| 2354 | 3231 RowVector |
| 3232 Matrix::column_max (void) const | |
| 3233 { | |
| 5275 | 3234 Array<octave_idx_type> dummy_idx; |
| 4587 | 3235 return column_max (dummy_idx); |
| 2354 | 3236 } |
| 458 | 3237 |
| 3238 RowVector | |
| 5275 | 3239 Matrix::column_max (Array<octave_idx_type>& idx_arg) const |
| 458 | 3240 { |
| 3241 RowVector result; | |
| 3242 | |
| 5275 | 3243 octave_idx_type nr = rows (); |
| 3244 octave_idx_type nc = cols (); | |
| 458 | 3245 |
| 3246 if (nr > 0 && nc > 0) | |
| 3247 { | |
| 3248 result.resize (nc); | |
| 4587 | 3249 idx_arg.resize (nc); |
| 458 | 3250 |
| 5275 | 3251 for (octave_idx_type j = 0; j < nc; j++) |
| 458 | 3252 { |
| 5275 | 3253 octave_idx_type idx_i; |
| 4469 | 3254 |
| 3255 double tmp_max = octave_NaN; | |
| 3256 | |
| 3257 for (idx_i = 0; idx_i < nr; idx_i++) | |
| 2354 | 3258 { |
| 4469 | 3259 tmp_max = elem (idx_i, j); |
| 3260 | |
| 5389 | 3261 if (! xisnan (tmp_max)) |
| 4469 | 3262 break; |
| 3263 } | |
| 3264 | |
| 5275 | 3265 for (octave_idx_type i = idx_i+1; i < nr; i++) |
| 4469 | 3266 { |
| 3267 double tmp = elem (i, j); | |
| 3268 | |
| 5389 | 3269 if (xisnan (tmp)) |
| 4469 | 3270 continue; |
| 3271 else if (tmp > tmp_max) | |
| 2354 | 3272 { |
| 4469 | 3273 idx_i = i; |
| 3274 tmp_max = tmp; | |
| 2354 | 3275 } |
| 3276 } | |
| 3277 | |
| 4469 | 3278 result.elem (j) = tmp_max; |
| 5389 | 3279 idx_arg.elem (j) = xisnan (tmp_max) ? 0 : idx_i; |
| 458 | 3280 } |
| 3281 } | |
| 3282 | |
| 3283 return result; | |
| 3284 } | |
| 3285 | |
| 3504 | 3286 std::ostream& |
| 3287 operator << (std::ostream& os, const Matrix& a) | |
| 458 | 3288 { |
| 5275 | 3289 for (octave_idx_type i = 0; i < a.rows (); i++) |
| 458 | 3290 { |
| 5275 | 3291 for (octave_idx_type j = 0; j < a.cols (); j++) |
| 4130 | 3292 { |
| 3293 os << " "; | |
| 3294 octave_write_double (os, a.elem (i, j)); | |
| 3295 } | |
| 458 | 3296 os << "\n"; |
| 3297 } | |
| 3298 return os; | |
| 3299 } | |
| 3300 | |
| 3504 | 3301 std::istream& |
| 3302 operator >> (std::istream& is, Matrix& a) | |
| 458 | 3303 { |
| 5275 | 3304 octave_idx_type nr = a.rows (); |
| 3305 octave_idx_type nc = a.cols (); | |
| 458 | 3306 |
| 3307 if (nr < 1 || nc < 1) | |
| 3504 | 3308 is.clear (std::ios::badbit); |
| 458 | 3309 else |
| 3310 { | |
| 3311 double tmp; | |
| 5275 | 3312 for (octave_idx_type i = 0; i < nr; i++) |
| 3313 for (octave_idx_type j = 0; j < nc; j++) | |
| 458 | 3314 { |
| 4130 | 3315 tmp = octave_read_double (is); |
| 458 | 3316 if (is) |
| 3317 a.elem (i, j) = tmp; | |
| 3318 else | |
| 2795 | 3319 goto done; |
| 458 | 3320 } |
| 3321 } | |
| 3322 | |
| 2795 | 3323 done: |
| 3324 | |
| 458 | 3325 return is; |
| 3326 } | |
| 3327 | |
| 1819 | 3328 Matrix |
| 3329 Givens (double x, double y) | |
| 3330 { | |
| 3331 double cc, s, temp_r; | |
| 3332 | |
| 3887 | 3333 F77_FUNC (dlartg, DLARTG) (x, y, cc, s, temp_r); |
| 1819 | 3334 |
| 3335 Matrix g (2, 2); | |
| 3336 | |
| 3337 g.elem (0, 0) = cc; | |
| 3338 g.elem (1, 1) = cc; | |
| 3339 g.elem (0, 1) = s; | |
| 3340 g.elem (1, 0) = -s; | |
| 3341 | |
| 3342 return g; | |
| 3343 } | |
| 3344 | |
| 3345 Matrix | |
| 3346 Sylvester (const Matrix& a, const Matrix& b, const Matrix& c) | |
| 3347 { | |
| 3348 Matrix retval; | |
| 3349 | |
| 5775 | 3350 // FIXME -- need to check that a, b, and c are all the same |
| 1819 | 3351 // size. |
| 3352 | |
| 3353 // Compute Schur decompositions. | |
| 3354 | |
| 3355 SCHUR as (a, "U"); | |
| 3356 SCHUR bs (b, "U"); | |
| 3357 | |
| 3358 // Transform c to new coordinates. | |
| 3359 | |
| 3360 Matrix ua = as.unitary_matrix (); | |
| 3361 Matrix sch_a = as.schur_matrix (); | |
| 3362 | |
| 3363 Matrix ub = bs.unitary_matrix (); | |
| 3364 Matrix sch_b = bs.schur_matrix (); | |
| 3365 | |
| 3366 Matrix cx = ua.transpose () * c * ub; | |
| 3367 | |
| 3368 // Solve the sylvester equation, back-transform, and return the | |
| 3369 // solution. | |
| 3370 | |
| 5275 | 3371 octave_idx_type a_nr = a.rows (); |
| 3372 octave_idx_type b_nr = b.rows (); | |
| 1819 | 3373 |
| 3374 double scale; | |
| 5275 | 3375 octave_idx_type info; |
| 1819 | 3376 |
| 1950 | 3377 double *pa = sch_a.fortran_vec (); |
| 3378 double *pb = sch_b.fortran_vec (); | |
| 3379 double *px = cx.fortran_vec (); | |
| 3380 | |
| 4552 | 3381 F77_XFCN (dtrsyl, DTRSYL, (F77_CONST_CHAR_ARG2 ("N", 1), |
| 3382 F77_CONST_CHAR_ARG2 ("N", 1), | |
| 3383 1, a_nr, b_nr, pa, a_nr, pb, | |
| 3384 b_nr, px, a_nr, scale, info | |
| 3385 F77_CHAR_ARG_LEN (1) | |
| 3386 F77_CHAR_ARG_LEN (1))); | |
| 1950 | 3387 |
| 3388 | |
|
7482
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
3389 // FIXME -- check info? |
| 1819 | 3390 |
|
7482
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
3391 retval = -ua*cx*ub.transpose (); |
| 1819 | 3392 |
| 3393 return retval; | |
| 3394 } | |
| 3395 | |
| 2828 | 3396 // matrix by matrix -> matrix operations |
| 3397 | |
| 6162 | 3398 /* Simple Dot Product, Matrix-Vector and Matrix-Matrix Unit tests |
| 3399 %!assert([1 2 3] * [ 4 ; 5 ; 6], 32, 1e-14) | |
| 3400 %!assert([1 2 ; 3 4 ] * [5 ; 6], [17 ; 39 ], 1e-14) | |
| 3401 %!assert([1 2 ; 3 4 ] * [5 6 ; 7 8], [19 22; 43 50], 1e-14) | |
| 3402 */ | |
| 3403 | |
| 3404 /* Test some simple identities | |
| 3405 %!shared M, cv, rv | |
| 3406 %! M = randn(10,10); | |
| 3407 %! cv = randn(10,1); | |
| 3408 %! rv = randn(1,10); | |
| 3409 %!assert([M*cv,M*cv],M*[cv,cv],1e-14) | |
| 3410 %!assert([rv*M;rv*M],[rv;rv]*M,1e-14) | |
| 3411 %!assert(2*rv*cv,[rv,rv]*[cv;cv],1e-14) | |
| 3412 */ | |
| 3413 | |
|
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
|
3414 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
|
3415 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
|
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 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
|
3418 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
|
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 |
|
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 // 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
|
3422 |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3423 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
|
3424 xgemm (bool transa, const Matrix& a, bool transb, const Matrix& b) |
| 2828 | 3425 { |
| 3426 Matrix retval; | |
| 3427 | |
|
7800
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3428 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
|
3429 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
|
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 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
|
3432 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
|
3433 |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3434 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
|
3435 gripe_nonconformant ("operator *", a_nr, a_nc, b_nr, b_nc); |
| 2828 | 3436 else |
| 3437 { | |
|
7800
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3438 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
|
3439 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
|
3440 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
|
3441 { |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3442 octave_idx_type lda = a.rows (); |
|
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 retval.resize (a_nr, b_nc); |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3445 double *c = retval.fortran_vec (); |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3446 |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3447 const char *ctransa = get_blas_trans_arg (transa); |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3448 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
|
3449 F77_CONST_CHAR_ARG2 (ctransa, 1), |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3450 a_nr, a_nc, 1.0, |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3451 a.data (), lda, 0.0, c, a_nr |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3452 F77_CHAR_ARG_LEN (1) |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3453 F77_CHAR_ARG_LEN (1))); |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3454 for (int j = 0; j < a_nr; j++) |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3455 for (int i = 0; i < j; i++) |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3456 retval.xelem (j,i) = retval.xelem (i,j); |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3457 |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3458 } |
| 2828 | 3459 else |
| 3460 { | |
|
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
|
3461 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
|
3462 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
|
3463 |
|
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 retval.resize (a_nr, b_nc); |
| 2828 | 3465 double *c = retval.fortran_vec (); |
| 3466 | |
|
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
|
3467 if (b_nc == 1) |
| 5983 | 3468 { |
|
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
|
3469 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
|
3470 F77_FUNC (xddot, XDDOT) (a_nc, a.data (), 1, b.data (), 1, *c); |
| 5983 | 3471 else |
| 6390 | 3472 { |
|
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
|
3473 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
|
3474 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
|
3475 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
|
3476 b.data (), 1, 0.0, c, 1 |
| 6390 | 3477 F77_CHAR_ARG_LEN (1))); |
| 3478 } | |
| 5983 | 3479 } |
|
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
|
3480 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
|
3481 { |
|
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 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
|
3483 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
|
3484 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
|
3485 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
|
3486 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
|
3487 } |
| 5983 | 3488 else |
| 6390 | 3489 { |
|
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
|
3490 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
|
3491 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
|
3492 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
|
3493 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
|
3494 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
|
3495 lda, b.data (), ldb, 0.0, c, a_nr |
| 6390 | 3496 F77_CHAR_ARG_LEN (1) |
| 3497 F77_CHAR_ARG_LEN (1))); | |
| 3498 } | |
| 2828 | 3499 } |
| 3500 } | |
| 3501 | |
| 3502 return retval; | |
| 3503 } | |
| 3504 | |
|
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
|
3505 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
|
3506 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
|
3507 { |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3508 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
|
3509 } |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3510 |
| 5775 | 3511 // FIXME -- it would be nice to share code among the min/max |
| 4309 | 3512 // functions below. |
| 3513 | |
| 3514 #define EMPTY_RETURN_CHECK(T) \ | |
| 3515 if (nr == 0 || nc == 0) \ | |
| 3516 return T (nr, nc); | |
| 3517 | |
| 3518 Matrix | |
| 3519 min (double d, const Matrix& m) | |
| 3520 { | |
| 5275 | 3521 octave_idx_type nr = m.rows (); |
| 3522 octave_idx_type nc = m.columns (); | |
| 4309 | 3523 |
| 3524 EMPTY_RETURN_CHECK (Matrix); | |
| 3525 | |
| 3526 Matrix result (nr, nc); | |
| 3527 | |
| 5275 | 3528 for (octave_idx_type j = 0; j < nc; j++) |
| 3529 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3530 { |
| 3531 OCTAVE_QUIT; | |
| 3532 result (i, j) = xmin (d, m (i, j)); | |
| 3533 } | |
| 3534 | |
| 3535 return result; | |
| 3536 } | |
| 3537 | |
| 3538 Matrix | |
| 3539 min (const Matrix& m, double d) | |
| 3540 { | |
| 5275 | 3541 octave_idx_type nr = m.rows (); |
| 3542 octave_idx_type nc = m.columns (); | |
| 4309 | 3543 |
| 3544 EMPTY_RETURN_CHECK (Matrix); | |
| 3545 | |
| 3546 Matrix result (nr, nc); | |
| 3547 | |
| 5275 | 3548 for (octave_idx_type j = 0; j < nc; j++) |
| 3549 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3550 { |
| 3551 OCTAVE_QUIT; | |
| 3552 result (i, j) = xmin (m (i, j), d); | |
| 3553 } | |
| 3554 | |
| 3555 return result; | |
| 3556 } | |
| 3557 | |
| 3558 Matrix | |
| 3559 min (const Matrix& a, const Matrix& b) | |
| 3560 { | |
| 5275 | 3561 octave_idx_type nr = a.rows (); |
| 3562 octave_idx_type nc = a.columns (); | |
| 4309 | 3563 |
| 3564 if (nr != b.rows () || nc != b.columns ()) | |
| 3565 { | |
| 3566 (*current_liboctave_error_handler) | |
| 3567 ("two-arg min expecting args of same size"); | |
| 3568 return Matrix (); | |
| 3569 } | |
| 3570 | |
| 3571 EMPTY_RETURN_CHECK (Matrix); | |
| 3572 | |
| 3573 Matrix result (nr, nc); | |
| 3574 | |
| 5275 | 3575 for (octave_idx_type j = 0; j < nc; j++) |
| 3576 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3577 { |
| 3578 OCTAVE_QUIT; | |
| 3579 result (i, j) = xmin (a (i, j), b (i, j)); | |
| 3580 } | |
| 3581 | |
| 3582 return result; | |
| 3583 } | |
| 3584 | |
| 3585 Matrix | |
| 3586 max (double d, const Matrix& m) | |
| 3587 { | |
| 5275 | 3588 octave_idx_type nr = m.rows (); |
| 3589 octave_idx_type nc = m.columns (); | |
| 4309 | 3590 |
| 3591 EMPTY_RETURN_CHECK (Matrix); | |
| 3592 | |
| 3593 Matrix result (nr, nc); | |
| 3594 | |
| 5275 | 3595 for (octave_idx_type j = 0; j < nc; j++) |
| 3596 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3597 { |
| 3598 OCTAVE_QUIT; | |
| 3599 result (i, j) = xmax (d, m (i, j)); | |
| 3600 } | |
| 3601 | |
| 3602 return result; | |
| 3603 } | |
| 3604 | |
| 3605 Matrix | |
| 3606 max (const Matrix& m, double d) | |
| 3607 { | |
| 5275 | 3608 octave_idx_type nr = m.rows (); |
| 3609 octave_idx_type nc = m.columns (); | |
| 4309 | 3610 |
| 3611 EMPTY_RETURN_CHECK (Matrix); | |
| 3612 | |
| 3613 Matrix result (nr, nc); | |
| 3614 | |
| 5275 | 3615 for (octave_idx_type j = 0; j < nc; j++) |
| 3616 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3617 { |
| 3618 OCTAVE_QUIT; | |
| 3619 result (i, j) = xmax (m (i, j), d); | |
| 3620 } | |
| 3621 | |
| 3622 return result; | |
| 3623 } | |
| 3624 | |
| 3625 Matrix | |
| 3626 max (const Matrix& a, const Matrix& b) | |
| 3627 { | |
| 5275 | 3628 octave_idx_type nr = a.rows (); |
| 3629 octave_idx_type nc = a.columns (); | |
| 4309 | 3630 |
| 3631 if (nr != b.rows () || nc != b.columns ()) | |
| 3632 { | |
| 3633 (*current_liboctave_error_handler) | |
| 3634 ("two-arg max expecting args of same size"); | |
| 3635 return Matrix (); | |
| 3636 } | |
| 3637 | |
| 3638 EMPTY_RETURN_CHECK (Matrix); | |
| 3639 | |
| 3640 Matrix result (nr, nc); | |
| 3641 | |
| 5275 | 3642 for (octave_idx_type j = 0; j < nc; j++) |
| 3643 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3644 { |
| 3645 OCTAVE_QUIT; | |
| 3646 result (i, j) = xmax (a (i, j), b (i, j)); | |
| 3647 } | |
| 3648 | |
| 3649 return result; | |
| 3650 } | |
| 3651 | |
| 2870 | 3652 MS_CMP_OPS(Matrix, , double, ) |
| 3504 | 3653 MS_BOOL_OPS(Matrix, double, 0.0) |
| 2870 | 3654 |
| 3655 SM_CMP_OPS(double, , Matrix, ) | |
| 3504 | 3656 SM_BOOL_OPS(double, Matrix, 0.0) |
| 2870 | 3657 |
| 3658 MM_CMP_OPS(Matrix, , Matrix, ) | |
| 3504 | 3659 MM_BOOL_OPS(Matrix, Matrix, 0.0) |
| 2870 | 3660 |
| 458 | 3661 /* |
| 3662 ;;; Local Variables: *** | |
| 3663 ;;; mode: C++ *** | |
| 3664 ;;; End: *** | |
| 3665 */ |