Mercurial > octave-libgccjit
annotate liboctave/dMatrix.cc @ 8377:25bc2d31e1bf
improve OCTAVE_LOCAL_BUFFER
| author | Jaroslav Hajek <highegg@gmail.com> |
|---|---|
| date | Wed, 29 Oct 2008 16:52:10 +0100 |
| parents | e3c9102431a9 |
| children | c187f0e3a7ee |
| 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" |
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46 #include "oct-locbuf.h" |
| 2354 | 47 #include "lo-ieee.h" |
| 48 #include "lo-mappers.h" | |
| 1968 | 49 #include "lo-utils.h" |
| 1367 | 50 #include "mx-base.h" |
| 2828 | 51 #include "mx-m-dm.h" |
| 3176 | 52 #include "mx-dm-m.h" |
| 1367 | 53 #include "mx-inlines.cc" |
| 1650 | 54 #include "oct-cmplx.h" |
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55 #include "oct-norm.h" |
| 4153 | 56 #include "quit.h" |
| 458 | 57 |
| 4773 | 58 #if defined (HAVE_FFTW3) |
| 3827 | 59 #include "oct-fftw.h" |
| 60 #endif | |
| 61 | |
| 458 | 62 // Fortran functions we call. |
| 63 | |
| 64 extern "C" | |
| 65 { | |
| 7478 | 66 F77_RET_T |
| 7477 | 67 F77_FUNC (xilaenv, XILAENV) (const octave_idx_type&, F77_CONST_CHAR_ARG_DECL, |
| 68 F77_CONST_CHAR_ARG_DECL, | |
| 69 const octave_idx_type&, const octave_idx_type&, | |
| 7478 | 70 const octave_idx_type&, const octave_idx_type&, |
| 71 octave_idx_type& | |
| 72 F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); | |
| 7476 | 73 |
| 4552 | 74 F77_RET_T |
| 75 F77_FUNC (dgebal, DGEBAL) (F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 76 const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type&, |
| 77 octave_idx_type&, double*, octave_idx_type& | |
| 4552 | 78 F77_CHAR_ARG_LEN_DECL); |
| 79 | |
| 80 F77_RET_T | |
| 81 F77_FUNC (dgebak, DGEBAK) (F77_CONST_CHAR_ARG_DECL, | |
| 82 F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 83 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, double*, |
| 84 const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type& | |
| 4552 | 85 F77_CHAR_ARG_LEN_DECL |
| 86 F77_CHAR_ARG_LEN_DECL); | |
| 87 | |
| 88 | |
| 89 F77_RET_T | |
| 90 F77_FUNC (dgemm, DGEMM) (F77_CONST_CHAR_ARG_DECL, | |
| 91 F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 92 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
| 93 const double&, const double*, const octave_idx_type&, | |
| 94 const double*, const octave_idx_type&, const double&, | |
| 95 double*, const octave_idx_type& | |
| 4552 | 96 F77_CHAR_ARG_LEN_DECL |
| 97 F77_CHAR_ARG_LEN_DECL); | |
| 98 | |
| 99 F77_RET_T | |
| 5983 | 100 F77_FUNC (dgemv, DGEMV) (F77_CONST_CHAR_ARG_DECL, |
| 101 const octave_idx_type&, const octave_idx_type&, const double&, | |
| 102 const double*, const octave_idx_type&, const double*, | |
| 103 const octave_idx_type&, const double&, double*, | |
| 104 const octave_idx_type& | |
| 105 F77_CHAR_ARG_LEN_DECL); | |
| 106 | |
| 107 F77_RET_T | |
| 108 F77_FUNC (xddot, XDDOT) (const octave_idx_type&, const double*, const octave_idx_type&, | |
| 109 const double*, const octave_idx_type&, double&); | |
| 110 | |
| 111 F77_RET_T | |
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112 F77_FUNC (dsyrk, DSYRK) (F77_CONST_CHAR_ARG_DECL, |
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113 F77_CONST_CHAR_ARG_DECL, |
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114 const octave_idx_type&, const octave_idx_type&, |
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115 const double&, const double*, const octave_idx_type&, |
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116 const double&, double*, const octave_idx_type& |
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117 F77_CHAR_ARG_LEN_DECL |
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118 F77_CHAR_ARG_LEN_DECL); |
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119 |
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120 F77_RET_T |
| 5275 | 121 F77_FUNC (dgetrf, DGETRF) (const octave_idx_type&, const octave_idx_type&, double*, const octave_idx_type&, |
| 122 octave_idx_type*, octave_idx_type&); | |
| 4329 | 123 |
| 4552 | 124 F77_RET_T |
| 5275 | 125 F77_FUNC (dgetrs, DGETRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, |
| 126 const double*, const octave_idx_type&, | |
| 127 const octave_idx_type*, double*, const octave_idx_type&, octave_idx_type& | |
| 4552 | 128 F77_CHAR_ARG_LEN_DECL); |
| 129 | |
| 130 F77_RET_T | |
| 5275 | 131 F77_FUNC (dgetri, DGETRI) (const octave_idx_type&, double*, const octave_idx_type&, const octave_idx_type*, |
| 132 double*, const octave_idx_type&, octave_idx_type&); | |
| 4552 | 133 |
| 134 F77_RET_T | |
| 5275 | 135 F77_FUNC (dgecon, DGECON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, double*, |
| 136 const octave_idx_type&, const double&, double&, | |
| 137 double*, octave_idx_type*, octave_idx_type& | |
| 4552 | 138 F77_CHAR_ARG_LEN_DECL); |
| 139 | |
| 140 F77_RET_T | |
| 7072 | 141 F77_FUNC (dgelsy, DGELSY) (const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
| 142 double*, const octave_idx_type&, double*, | |
| 143 const octave_idx_type&, octave_idx_type*, double&, octave_idx_type&, | |
| 144 double*, const octave_idx_type&, octave_idx_type&); | |
| 145 | |
| 146 F77_RET_T | |
| 147 F77_FUNC (dgelsd, DGELSD) (const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, | |
| 5275 | 148 double*, const octave_idx_type&, double*, |
| 7071 | 149 const octave_idx_type&, double*, double&, octave_idx_type&, |
| 7072 | 150 double*, const octave_idx_type&, octave_idx_type*, |
| 151 octave_idx_type&); | |
| 458 | 152 |
| 5785 | 153 F77_RET_T |
| 154 F77_FUNC (dpotrf, DPOTRF) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 155 double *, const octave_idx_type&, | |
| 156 octave_idx_type& F77_CHAR_ARG_LEN_DECL); | |
| 157 | |
| 158 F77_RET_T | |
| 159 F77_FUNC (dpocon, DPOCON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 160 double*, const octave_idx_type&, const double&, | |
| 161 double&, double*, octave_idx_type*, | |
| 162 octave_idx_type& F77_CHAR_ARG_LEN_DECL); | |
| 163 F77_RET_T | |
| 164 F77_FUNC (dpotrs, DPOTRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 165 const octave_idx_type&, const double*, | |
| 166 const octave_idx_type&, double*, | |
| 167 const octave_idx_type&, octave_idx_type& | |
| 168 F77_CHAR_ARG_LEN_DECL); | |
| 169 | |
| 170 F77_RET_T | |
| 6207 | 171 F77_FUNC (dtrtri, DTRTRI) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, |
| 172 const octave_idx_type&, const double*, | |
| 173 const octave_idx_type&, octave_idx_type& | |
| 174 F77_CHAR_ARG_LEN_DECL | |
| 175 F77_CHAR_ARG_LEN_DECL); | |
| 176 F77_RET_T | |
| 5785 | 177 F77_FUNC (dtrcon, DTRCON) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, |
| 178 F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 179 const double*, const octave_idx_type&, double&, | |
| 180 double*, octave_idx_type*, octave_idx_type& | |
| 181 F77_CHAR_ARG_LEN_DECL | |
| 182 F77_CHAR_ARG_LEN_DECL | |
| 183 F77_CHAR_ARG_LEN_DECL); | |
| 184 F77_RET_T | |
| 185 F77_FUNC (dtrtrs, DTRTRS) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, | |
| 186 F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 187 const octave_idx_type&, const double*, | |
| 188 const octave_idx_type&, double*, | |
| 189 const octave_idx_type&, octave_idx_type& | |
| 190 F77_CHAR_ARG_LEN_DECL | |
| 191 F77_CHAR_ARG_LEN_DECL | |
| 192 F77_CHAR_ARG_LEN_DECL); | |
| 193 | |
| 1360 | 194 // Note that the original complex fft routines were not written for |
| 195 // double complex arguments. They have been modified by adding an | |
| 196 // implicit double precision (a-h,o-z) statement at the beginning of | |
| 197 // each subroutine. | |
| 458 | 198 |
| 4552 | 199 F77_RET_T |
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200 F77_FUNC (zffti, ZFFTI) (const octave_idx_type&, Complex*); |
| 4552 | 201 |
| 202 F77_RET_T | |
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203 F77_FUNC (zfftf, ZFFTF) (const octave_idx_type&, Complex*, Complex*); |
| 4552 | 204 |
| 205 F77_RET_T | |
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206 F77_FUNC (zfftb, ZFFTB) (const octave_idx_type&, Complex*, Complex*); |
| 4552 | 207 |
| 208 F77_RET_T | |
| 209 F77_FUNC (dlartg, DLARTG) (const double&, const double&, double&, | |
| 210 double&, double&); | |
| 211 | |
| 212 F77_RET_T | |
| 213 F77_FUNC (dtrsyl, DTRSYL) (F77_CONST_CHAR_ARG_DECL, | |
| 214 F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 215 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
| 216 const double*, const octave_idx_type&, const double*, | |
| 217 const octave_idx_type&, const double*, const octave_idx_type&, | |
| 218 double&, octave_idx_type& | |
| 4552 | 219 F77_CHAR_ARG_LEN_DECL |
| 220 F77_CHAR_ARG_LEN_DECL); | |
| 221 | |
| 222 F77_RET_T | |
| 5275 | 223 F77_FUNC (xdlange, XDLANGE) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, |
| 224 const octave_idx_type&, const double*, | |
| 225 const octave_idx_type&, double*, double& | |
| 4552 | 226 F77_CHAR_ARG_LEN_DECL); |
| 458 | 227 } |
| 228 | |
| 1360 | 229 // Matrix class. |
| 458 | 230 |
| 2349 | 231 Matrix::Matrix (const RowVector& rv) |
| 232 : MArray2<double> (1, rv.length (), 0.0) | |
| 233 { | |
| 5275 | 234 for (octave_idx_type i = 0; i < rv.length (); i++) |
| 2349 | 235 elem (0, i) = rv.elem (i); |
| 236 } | |
| 237 | |
| 238 Matrix::Matrix (const ColumnVector& cv) | |
| 239 : MArray2<double> (cv.length (), 1, 0.0) | |
| 240 { | |
| 5275 | 241 for (octave_idx_type i = 0; i < cv.length (); i++) |
| 2349 | 242 elem (i, 0) = cv.elem (i); |
| 243 } | |
| 244 | |
| 458 | 245 Matrix::Matrix (const DiagMatrix& a) |
| 1214 | 246 : MArray2<double> (a.rows (), a.cols (), 0.0) |
| 458 | 247 { |
| 5275 | 248 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 249 elem (i, i) = a.elem (i, i); |
| 250 } | |
| 251 | |
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252 Matrix::Matrix (const PermMatrix& a) |
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253 : MArray2<double> (a.rows (), a.cols (), 0.0) |
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254 { |
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255 const Array<octave_idx_type> ia (a.pvec ()); |
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256 octave_idx_type len = a.rows (); |
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257 if (a.is_col_perm ()) |
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258 for (octave_idx_type i = 0; i < len; i++) |
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259 elem (ia(i), i) = 1.0; |
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260 else |
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261 for (octave_idx_type i = 0; i < len; i++) |
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262 elem (i, ia(i)) = 1.0; |
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263 } |
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264 |
| 5775 | 265 // FIXME -- could we use a templated mixed-type copy function |
| 1574 | 266 // here? |
| 267 | |
| 2828 | 268 Matrix::Matrix (const boolMatrix& a) |
| 269 : MArray2<double> (a.rows (), a.cols ()) | |
| 270 { | |
| 5275 | 271 for (octave_idx_type i = 0; i < a.rows (); i++) |
| 272 for (octave_idx_type j = 0; j < a.cols (); j++) | |
| 2828 | 273 elem (i, j) = a.elem (i, j); |
| 274 } | |
| 275 | |
| 1574 | 276 Matrix::Matrix (const charMatrix& a) |
| 277 : MArray2<double> (a.rows (), a.cols ()) | |
| 278 { | |
| 5275 | 279 for (octave_idx_type i = 0; i < a.rows (); i++) |
| 280 for (octave_idx_type j = 0; j < a.cols (); j++) | |
| 1574 | 281 elem (i, j) = a.elem (i, j); |
| 282 } | |
| 283 | |
| 2385 | 284 bool |
| 458 | 285 Matrix::operator == (const Matrix& a) const |
| 286 { | |
| 287 if (rows () != a.rows () || cols () != a.cols ()) | |
| 2385 | 288 return false; |
| 458 | 289 |
| 3769 | 290 return mx_inline_equal (data (), a.data (), length ()); |
| 458 | 291 } |
| 292 | |
| 2385 | 293 bool |
| 458 | 294 Matrix::operator != (const Matrix& a) const |
| 295 { | |
| 296 return !(*this == a); | |
| 297 } | |
| 298 | |
| 3354 | 299 bool |
| 300 Matrix::is_symmetric (void) const | |
| 301 { | |
| 302 if (is_square () && rows () > 0) | |
| 303 { | |
| 5275 | 304 for (octave_idx_type i = 0; i < rows (); i++) |
| 305 for (octave_idx_type j = i+1; j < cols (); j++) | |
| 3354 | 306 if (elem (i, j) != elem (j, i)) |
| 307 return false; | |
| 308 | |
| 309 return true; | |
| 310 } | |
| 311 | |
| 312 return false; | |
| 313 } | |
| 314 | |
| 458 | 315 Matrix& |
| 5275 | 316 Matrix::insert (const Matrix& a, octave_idx_type r, octave_idx_type c) |
| 458 | 317 { |
| 1561 | 318 Array2<double>::insert (a, r, c); |
| 458 | 319 return *this; |
| 320 } | |
| 321 | |
| 322 Matrix& | |
| 5275 | 323 Matrix::insert (const RowVector& a, octave_idx_type r, octave_idx_type c) |
| 458 | 324 { |
| 5275 | 325 octave_idx_type a_len = a.length (); |
| 4316 | 326 |
| 1698 | 327 if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ()) |
| 458 | 328 { |
| 329 (*current_liboctave_error_handler) ("range error for insert"); | |
| 330 return *this; | |
| 331 } | |
| 332 | |
| 4316 | 333 if (a_len > 0) |
| 334 { | |
| 335 make_unique (); | |
| 336 | |
| 5275 | 337 for (octave_idx_type i = 0; i < a_len; i++) |
| 4316 | 338 xelem (r, c+i) = a.elem (i); |
| 339 } | |
| 458 | 340 |
| 341 return *this; | |
| 342 } | |
| 343 | |
| 344 Matrix& | |
| 5275 | 345 Matrix::insert (const ColumnVector& a, octave_idx_type r, octave_idx_type c) |
| 458 | 346 { |
| 5275 | 347 octave_idx_type a_len = a.length (); |
| 4316 | 348 |
| 1698 | 349 if (r < 0 || r + a_len > rows () || c < 0 || c >= cols ()) |
| 458 | 350 { |
| 351 (*current_liboctave_error_handler) ("range error for insert"); | |
| 352 return *this; | |
| 353 } | |
| 354 | |
| 4316 | 355 if (a_len > 0) |
| 356 { | |
| 357 make_unique (); | |
| 358 | |
| 5275 | 359 for (octave_idx_type i = 0; i < a_len; i++) |
| 4316 | 360 xelem (r+i, c) = a.elem (i); |
| 361 } | |
| 458 | 362 |
| 363 return *this; | |
| 364 } | |
| 365 | |
| 366 Matrix& | |
| 5275 | 367 Matrix::insert (const DiagMatrix& a, octave_idx_type r, octave_idx_type c) |
| 458 | 368 { |
| 5275 | 369 octave_idx_type a_nr = a.rows (); |
| 370 octave_idx_type a_nc = a.cols (); | |
| 1697 | 371 |
| 1698 | 372 if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) |
| 458 | 373 { |
| 374 (*current_liboctave_error_handler) ("range error for insert"); | |
| 375 return *this; | |
| 376 } | |
| 377 | |
| 1697 | 378 fill (0.0, r, c, r + a_nr - 1, c + a_nc - 1); |
| 379 | |
| 5275 | 380 octave_idx_type a_len = a.length (); |
| 4316 | 381 |
| 382 if (a_len > 0) | |
| 383 { | |
| 384 make_unique (); | |
| 385 | |
| 5275 | 386 for (octave_idx_type i = 0; i < a_len; i++) |
| 4316 | 387 xelem (r+i, c+i) = a.elem (i, i); |
| 388 } | |
| 458 | 389 |
| 390 return *this; | |
| 391 } | |
| 392 | |
| 393 Matrix& | |
| 394 Matrix::fill (double val) | |
| 395 { | |
| 5275 | 396 octave_idx_type nr = rows (); |
| 397 octave_idx_type nc = cols (); | |
| 4316 | 398 |
| 458 | 399 if (nr > 0 && nc > 0) |
| 4316 | 400 { |
| 401 make_unique (); | |
| 402 | |
| 5275 | 403 for (octave_idx_type j = 0; j < nc; j++) |
| 404 for (octave_idx_type i = 0; i < nr; i++) | |
| 4316 | 405 xelem (i, j) = val; |
| 406 } | |
| 458 | 407 |
| 408 return *this; | |
| 409 } | |
| 410 | |
| 411 Matrix& | |
| 5275 | 412 Matrix::fill (double val, octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) |
| 458 | 413 { |
| 5275 | 414 octave_idx_type nr = rows (); |
| 415 octave_idx_type nc = cols (); | |
| 4316 | 416 |
| 458 | 417 if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0 |
| 418 || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc) | |
| 419 { | |
| 420 (*current_liboctave_error_handler) ("range error for fill"); | |
| 421 return *this; | |
| 422 } | |
| 423 | |
| 5275 | 424 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } |
| 425 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } | |
| 458 | 426 |
| 4316 | 427 if (r2 >= r1 && c2 >= c1) |
| 428 { | |
| 429 make_unique (); | |
| 430 | |
| 5275 | 431 for (octave_idx_type j = c1; j <= c2; j++) |
| 432 for (octave_idx_type i = r1; i <= r2; i++) | |
| 4316 | 433 xelem (i, j) = val; |
| 434 } | |
| 458 | 435 |
| 436 return *this; | |
| 437 } | |
| 438 | |
| 439 Matrix | |
| 440 Matrix::append (const Matrix& a) const | |
| 441 { | |
| 5275 | 442 octave_idx_type nr = rows (); |
| 443 octave_idx_type nc = cols (); | |
| 458 | 444 if (nr != a.rows ()) |
| 445 { | |
| 446 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 447 return Matrix (); | |
| 448 } | |
| 449 | |
| 5275 | 450 octave_idx_type nc_insert = nc; |
| 458 | 451 Matrix retval (nr, nc + a.cols ()); |
| 452 retval.insert (*this, 0, 0); | |
| 453 retval.insert (a, 0, nc_insert); | |
| 454 return retval; | |
| 455 } | |
| 456 | |
| 457 Matrix | |
| 458 Matrix::append (const RowVector& a) const | |
| 459 { | |
| 5275 | 460 octave_idx_type nr = rows (); |
| 461 octave_idx_type nc = cols (); | |
| 458 | 462 if (nr != 1) |
| 463 { | |
| 464 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 465 return Matrix (); | |
| 466 } | |
| 467 | |
| 5275 | 468 octave_idx_type nc_insert = nc; |
| 458 | 469 Matrix retval (nr, nc + a.length ()); |
| 470 retval.insert (*this, 0, 0); | |
| 471 retval.insert (a, 0, nc_insert); | |
| 472 return retval; | |
| 473 } | |
| 474 | |
| 475 Matrix | |
| 476 Matrix::append (const ColumnVector& a) const | |
| 477 { | |
| 5275 | 478 octave_idx_type nr = rows (); |
| 479 octave_idx_type nc = cols (); | |
| 458 | 480 if (nr != a.length ()) |
| 481 { | |
| 482 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 483 return Matrix (); | |
| 484 } | |
| 485 | |
| 5275 | 486 octave_idx_type nc_insert = nc; |
| 458 | 487 Matrix retval (nr, nc + 1); |
| 488 retval.insert (*this, 0, 0); | |
| 489 retval.insert (a, 0, nc_insert); | |
| 490 return retval; | |
| 491 } | |
| 492 | |
| 493 Matrix | |
| 494 Matrix::append (const DiagMatrix& a) const | |
| 495 { | |
| 5275 | 496 octave_idx_type nr = rows (); |
| 497 octave_idx_type nc = cols (); | |
| 458 | 498 if (nr != a.rows ()) |
| 499 { | |
| 500 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 501 return *this; | |
| 502 } | |
| 503 | |
| 5275 | 504 octave_idx_type nc_insert = nc; |
| 458 | 505 Matrix retval (nr, nc + a.cols ()); |
| 506 retval.insert (*this, 0, 0); | |
| 507 retval.insert (a, 0, nc_insert); | |
| 508 return retval; | |
| 509 } | |
| 510 | |
| 511 Matrix | |
| 512 Matrix::stack (const Matrix& a) const | |
| 513 { | |
| 5275 | 514 octave_idx_type nr = rows (); |
| 515 octave_idx_type nc = cols (); | |
| 458 | 516 if (nc != a.cols ()) |
| 517 { | |
| 518 (*current_liboctave_error_handler) | |
| 519 ("column dimension mismatch for stack"); | |
| 520 return Matrix (); | |
| 521 } | |
| 522 | |
| 5275 | 523 octave_idx_type nr_insert = nr; |
| 458 | 524 Matrix retval (nr + a.rows (), nc); |
| 525 retval.insert (*this, 0, 0); | |
| 526 retval.insert (a, nr_insert, 0); | |
| 527 return retval; | |
| 528 } | |
| 529 | |
| 530 Matrix | |
| 531 Matrix::stack (const RowVector& a) const | |
| 532 { | |
| 5275 | 533 octave_idx_type nr = rows (); |
| 534 octave_idx_type nc = cols (); | |
| 458 | 535 if (nc != a.length ()) |
| 536 { | |
| 537 (*current_liboctave_error_handler) | |
| 538 ("column dimension mismatch for stack"); | |
| 539 return Matrix (); | |
| 540 } | |
| 541 | |
| 5275 | 542 octave_idx_type nr_insert = nr; |
| 458 | 543 Matrix retval (nr + 1, nc); |
| 544 retval.insert (*this, 0, 0); | |
| 545 retval.insert (a, nr_insert, 0); | |
| 546 return retval; | |
| 547 } | |
| 548 | |
| 549 Matrix | |
| 550 Matrix::stack (const ColumnVector& a) const | |
| 551 { | |
| 5275 | 552 octave_idx_type nr = rows (); |
| 553 octave_idx_type nc = cols (); | |
| 458 | 554 if (nc != 1) |
| 555 { | |
| 556 (*current_liboctave_error_handler) | |
| 557 ("column dimension mismatch for stack"); | |
| 558 return Matrix (); | |
| 559 } | |
| 560 | |
| 5275 | 561 octave_idx_type nr_insert = nr; |
| 458 | 562 Matrix retval (nr + a.length (), nc); |
| 563 retval.insert (*this, 0, 0); | |
| 564 retval.insert (a, nr_insert, 0); | |
| 565 return retval; | |
| 566 } | |
| 567 | |
| 568 Matrix | |
| 569 Matrix::stack (const DiagMatrix& a) const | |
| 570 { | |
| 5275 | 571 octave_idx_type nr = rows (); |
| 572 octave_idx_type nc = cols (); | |
| 458 | 573 if (nc != a.cols ()) |
| 574 { | |
| 575 (*current_liboctave_error_handler) | |
| 576 ("column dimension mismatch for stack"); | |
| 577 return Matrix (); | |
| 578 } | |
| 579 | |
| 5275 | 580 octave_idx_type nr_insert = nr; |
| 458 | 581 Matrix retval (nr + a.rows (), nc); |
| 582 retval.insert (*this, 0, 0); | |
| 583 retval.insert (a, nr_insert, 0); | |
| 584 return retval; | |
| 585 } | |
| 586 | |
| 587 Matrix | |
| 1205 | 588 real (const ComplexMatrix& a) |
| 589 { | |
| 5275 | 590 octave_idx_type a_len = a.length (); |
| 1205 | 591 Matrix retval; |
| 592 if (a_len > 0) | |
| 3769 | 593 retval = Matrix (mx_inline_real_dup (a.data (), a_len), |
| 594 a.rows (), a.cols ()); | |
| 1205 | 595 return retval; |
| 596 } | |
| 597 | |
| 598 Matrix | |
| 599 imag (const ComplexMatrix& a) | |
| 600 { | |
| 5275 | 601 octave_idx_type a_len = a.length (); |
| 1205 | 602 Matrix retval; |
| 603 if (a_len > 0) | |
| 3769 | 604 retval = Matrix (mx_inline_imag_dup (a.data (), a_len), |
| 605 a.rows (), a.cols ()); | |
| 1205 | 606 return retval; |
| 607 } | |
| 608 | |
| 609 Matrix | |
| 5275 | 610 Matrix::extract (octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) const |
| 458 | 611 { |
| 5275 | 612 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } |
| 613 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } | |
| 614 | |
| 615 octave_idx_type new_r = r2 - r1 + 1; | |
| 616 octave_idx_type new_c = c2 - c1 + 1; | |
| 458 | 617 |
| 618 Matrix result (new_r, new_c); | |
| 619 | |
| 5275 | 620 for (octave_idx_type j = 0; j < new_c; j++) |
| 621 for (octave_idx_type i = 0; i < new_r; i++) | |
| 4316 | 622 result.xelem (i, j) = elem (r1+i, c1+j); |
| 623 | |
| 624 return result; | |
| 625 } | |
| 626 | |
| 627 Matrix | |
| 5275 | 628 Matrix::extract_n (octave_idx_type r1, octave_idx_type c1, octave_idx_type nr, octave_idx_type nc) const |
| 4316 | 629 { |
| 630 Matrix result (nr, nc); | |
| 631 | |
| 5275 | 632 for (octave_idx_type j = 0; j < nc; j++) |
| 633 for (octave_idx_type i = 0; i < nr; i++) | |
| 4316 | 634 result.xelem (i, j) = elem (r1+i, c1+j); |
| 458 | 635 |
| 636 return result; | |
| 637 } | |
| 638 | |
| 639 // extract row or column i. | |
| 640 | |
| 641 RowVector | |
| 5275 | 642 Matrix::row (octave_idx_type i) const |
| 458 | 643 { |
| 5275 | 644 octave_idx_type nc = cols (); |
| 458 | 645 if (i < 0 || i >= rows ()) |
| 646 { | |
| 647 (*current_liboctave_error_handler) ("invalid row selection"); | |
| 648 return RowVector (); | |
| 649 } | |
| 650 | |
| 651 RowVector retval (nc); | |
| 5275 | 652 for (octave_idx_type j = 0; j < nc; j++) |
| 4316 | 653 retval.xelem (j) = elem (i, j); |
| 458 | 654 |
| 655 return retval; | |
| 656 } | |
| 657 | |
| 658 ColumnVector | |
| 5275 | 659 Matrix::column (octave_idx_type i) const |
| 458 | 660 { |
| 5275 | 661 octave_idx_type nr = rows (); |
| 458 | 662 if (i < 0 || i >= cols ()) |
| 663 { | |
| 664 (*current_liboctave_error_handler) ("invalid column selection"); | |
| 665 return ColumnVector (); | |
| 666 } | |
| 667 | |
| 668 ColumnVector retval (nr); | |
| 5275 | 669 for (octave_idx_type j = 0; j < nr; j++) |
| 4316 | 670 retval.xelem (j) = elem (j, i); |
| 458 | 671 |
| 672 return retval; | |
| 673 } | |
| 674 | |
| 675 Matrix | |
| 676 Matrix::inverse (void) const | |
| 677 { | |
| 5275 | 678 octave_idx_type info; |
| 7788 | 679 double rcon; |
| 6207 | 680 MatrixType mattype (*this); |
| 7788 | 681 return inverse (mattype, info, rcon, 0, 0); |
| 6207 | 682 } |
| 683 | |
| 684 Matrix | |
| 6479 | 685 Matrix::inverse (octave_idx_type& info) const |
| 686 { | |
| 7788 | 687 double rcon; |
| 6479 | 688 MatrixType mattype (*this); |
| 7788 | 689 return inverse (mattype, info, rcon, 0, 0); |
| 6479 | 690 } |
| 691 | |
| 692 Matrix | |
| 7788 | 693 Matrix::inverse (octave_idx_type& info, double& rcon, int force, |
| 6479 | 694 int calc_cond) const |
| 695 { | |
| 696 MatrixType mattype (*this); | |
| 7788 | 697 return inverse (mattype, info, rcon, force, calc_cond); |
| 6479 | 698 } |
| 699 | |
| 700 Matrix | |
| 6207 | 701 Matrix::inverse (MatrixType& mattype) const |
| 702 { | |
| 703 octave_idx_type info; | |
| 7788 | 704 double rcon; |
| 705 return inverse (mattype, info, rcon, 0, 0); | |
| 6207 | 706 } |
| 707 | |
| 708 Matrix | |
| 709 Matrix::inverse (MatrixType &mattype, octave_idx_type& info) const | |
| 710 { | |
| 7788 | 711 double rcon; |
| 712 return inverse (mattype, info, rcon, 0, 0); | |
| 458 | 713 } |
| 714 | |
| 715 Matrix | |
| 7788 | 716 Matrix::tinverse (MatrixType &mattype, octave_idx_type& info, double& rcon, |
| 6207 | 717 int force, int calc_cond) const |
| 458 | 718 { |
| 6207 | 719 Matrix retval; |
| 720 | |
| 721 octave_idx_type nr = rows (); | |
| 722 octave_idx_type nc = cols (); | |
| 723 | |
| 724 if (nr != nc || nr == 0 || nc == 0) | |
| 725 (*current_liboctave_error_handler) ("inverse requires square matrix"); | |
| 726 else | |
| 727 { | |
| 728 int typ = mattype.type (); | |
| 729 char uplo = (typ == MatrixType::Lower ? 'L' : 'U'); | |
| 730 char udiag = 'N'; | |
| 731 retval = *this; | |
| 732 double *tmp_data = retval.fortran_vec (); | |
| 733 | |
| 734 F77_XFCN (dtrtri, DTRTRI, (F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 735 F77_CONST_CHAR_ARG2 (&udiag, 1), | |
| 736 nr, tmp_data, nr, info | |
| 737 F77_CHAR_ARG_LEN (1) | |
| 738 F77_CHAR_ARG_LEN (1))); | |
| 739 | |
|
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740 // Throw-away extra info LAPACK gives so as to not change output. |
| 7788 | 741 rcon = 0.0; |
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742 if (info != 0) |
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743 info = -1; |
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744 else if (calc_cond) |
| 6207 | 745 { |
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746 octave_idx_type dtrcon_info = 0; |
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747 char job = '1'; |
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748 |
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749 OCTAVE_LOCAL_BUFFER (double, work, 3 * nr); |
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750 OCTAVE_LOCAL_BUFFER (octave_idx_type, iwork, nr); |
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751 |
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752 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&job, 1), |
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753 F77_CONST_CHAR_ARG2 (&uplo, 1), |
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754 F77_CONST_CHAR_ARG2 (&udiag, 1), |
| 7788 | 755 nr, tmp_data, nr, rcon, |
|
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756 work, iwork, dtrcon_info |
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757 F77_CHAR_ARG_LEN (1) |
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758 F77_CHAR_ARG_LEN (1) |
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759 F77_CHAR_ARG_LEN (1))); |
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760 |
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761 if (dtrcon_info != 0) |
| 6207 | 762 info = -1; |
| 763 } | |
| 764 | |
| 765 if (info == -1 && ! force) | |
| 766 retval = *this; // Restore matrix contents. | |
| 767 } | |
| 768 | |
| 769 return retval; | |
| 458 | 770 } |
| 771 | |
| 6207 | 772 |
| 458 | 773 Matrix |
| 7788 | 774 Matrix::finverse (MatrixType &mattype, octave_idx_type& info, double& rcon, |
| 6207 | 775 int force, int calc_cond) const |
| 458 | 776 { |
| 1948 | 777 Matrix retval; |
| 778 | |
| 5275 | 779 octave_idx_type nr = rows (); |
| 780 octave_idx_type nc = cols (); | |
| 1948 | 781 |
| 458 | 782 if (nr != nc || nr == 0 || nc == 0) |
| 1948 | 783 (*current_liboctave_error_handler) ("inverse requires square matrix"); |
| 458 | 784 else |
| 785 { | |
| 5275 | 786 Array<octave_idx_type> ipvt (nr); |
| 787 octave_idx_type *pipvt = ipvt.fortran_vec (); | |
| 1948 | 788 |
| 789 retval = *this; | |
| 790 double *tmp_data = retval.fortran_vec (); | |
| 791 | |
| 4329 | 792 Array<double> z(1); |
| 5275 | 793 octave_idx_type lwork = -1; |
| 4329 | 794 |
| 4330 | 795 // Query the optimum work array size. |
| 4329 | 796 F77_XFCN (dgetri, DGETRI, (nc, tmp_data, nr, pipvt, |
| 797 z.fortran_vec (), lwork, info)); | |
| 798 | |
| 5275 | 799 lwork = static_cast<octave_idx_type> (z(0)); |
| 4329 | 800 lwork = (lwork < 2 *nc ? 2*nc : lwork); |
| 801 z.resize (lwork); | |
| 802 double *pz = z.fortran_vec (); | |
| 803 | |
| 804 info = 0; | |
| 805 | |
| 4330 | 806 // Calculate the norm of the matrix, for later use. |
| 4329 | 807 double anorm = 0; |
| 808 if (calc_cond) | |
| 5275 | 809 anorm = retval.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
| 4329 | 810 |
| 811 F77_XFCN (dgetrf, DGETRF, (nc, nc, tmp_data, nr, pipvt, info)); | |
| 1948 | 812 |
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813 // Throw-away extra info LAPACK gives so as to not change output. |
| 7788 | 814 rcon = 0.0; |
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815 if (info != 0) |
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816 info = -1; |
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817 else if (calc_cond) |
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818 { |
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819 octave_idx_type dgecon_info = 0; |
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820 |
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821 // Now calculate the condition number for non-singular matrix. |
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822 char job = '1'; |
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823 Array<octave_idx_type> iz (nc); |
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824 octave_idx_type *piz = iz.fortran_vec (); |
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825 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
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|
826 nc, tmp_data, nr, anorm, |
| 7788 | 827 rcon, pz, piz, dgecon_info |
|
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828 F77_CHAR_ARG_LEN (1))); |
|
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|
829 |
|
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|
830 if (dgecon_info != 0) |
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831 info = -1; |
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|
832 } |
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|
833 |
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|
834 if (info == -1 && ! force) |
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835 retval = *this; // Restore matrix contents. |
| 1948 | 836 else |
| 837 { | |
|
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838 octave_idx_type dgetri_info = 0; |
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|
839 |
|
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840 F77_XFCN (dgetri, DGETRI, (nc, tmp_data, nr, pipvt, |
|
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841 pz, lwork, dgetri_info)); |
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|
842 |
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|
843 if (dgetri_info != 0) |
| 1948 | 844 info = -1; |
| 845 } | |
| 6207 | 846 |
| 847 if (info != 0) | |
| 848 mattype.mark_as_rectangular(); | |
| 458 | 849 } |
| 850 | |
| 1948 | 851 return retval; |
| 458 | 852 } |
| 853 | |
| 740 | 854 Matrix |
| 7788 | 855 Matrix::inverse (MatrixType &mattype, octave_idx_type& info, double& rcon, |
| 6207 | 856 int force, int calc_cond) const |
| 857 { | |
| 858 int typ = mattype.type (false); | |
| 859 Matrix ret; | |
| 860 | |
| 861 if (typ == MatrixType::Unknown) | |
| 862 typ = mattype.type (*this); | |
| 863 | |
| 864 if (typ == MatrixType::Upper || typ == MatrixType::Lower) | |
| 7788 | 865 ret = tinverse (mattype, info, rcon, force, calc_cond); |
| 6840 | 866 else |
| 6207 | 867 { |
| 868 if (mattype.is_hermitian ()) | |
| 869 { | |
| 6486 | 870 CHOL chol (*this, info, calc_cond); |
| 6207 | 871 if (info == 0) |
| 6486 | 872 { |
| 873 if (calc_cond) | |
| 7788 | 874 rcon = chol.rcond (); |
| 6486 | 875 else |
| 7788 | 876 rcon = 1.0; |
| 6486 | 877 ret = chol.inverse (); |
| 878 } | |
| 6207 | 879 else |
| 880 mattype.mark_as_unsymmetric (); | |
| 881 } | |
| 882 | |
| 883 if (!mattype.is_hermitian ()) | |
| 7788 | 884 ret = finverse(mattype, info, rcon, force, calc_cond); |
| 885 | |
| 886 if ((mattype.is_hermitian () || calc_cond) && rcon == 0.) | |
| 6840 | 887 ret = Matrix (rows (), columns (), octave_Inf); |
| 6207 | 888 } |
| 889 | |
| 890 return ret; | |
| 891 } | |
| 892 | |
| 893 Matrix | |
| 4384 | 894 Matrix::pseudo_inverse (double tol) const |
| 740 | 895 { |
| 3480 | 896 SVD result (*this, SVD::economy); |
| 740 | 897 |
| 898 DiagMatrix S = result.singular_values (); | |
| 899 Matrix U = result.left_singular_matrix (); | |
| 900 Matrix V = result.right_singular_matrix (); | |
| 901 | |
| 902 ColumnVector sigma = S.diag (); | |
| 903 | |
| 5275 | 904 octave_idx_type r = sigma.length () - 1; |
| 905 octave_idx_type nr = rows (); | |
| 906 octave_idx_type nc = cols (); | |
| 740 | 907 |
| 908 if (tol <= 0.0) | |
| 909 { | |
| 910 if (nr > nc) | |
| 911 tol = nr * sigma.elem (0) * DBL_EPSILON; | |
| 912 else | |
| 913 tol = nc * sigma.elem (0) * DBL_EPSILON; | |
| 914 } | |
| 915 | |
| 916 while (r >= 0 && sigma.elem (r) < tol) | |
| 917 r--; | |
| 918 | |
| 919 if (r < 0) | |
| 920 return Matrix (nc, nr, 0.0); | |
| 921 else | |
| 922 { | |
| 923 Matrix Ur = U.extract (0, 0, nr-1, r); | |
| 924 DiagMatrix D = DiagMatrix (sigma.extract (0, r)) . inverse (); | |
| 925 Matrix Vr = V.extract (0, 0, nc-1, r); | |
| 926 return Vr * D * Ur.transpose (); | |
| 927 } | |
| 928 } | |
| 929 | |
| 4773 | 930 #if defined (HAVE_FFTW3) |
| 3827 | 931 |
| 932 ComplexMatrix | |
| 933 Matrix::fourier (void) const | |
| 934 { | |
| 935 size_t nr = rows (); | |
| 936 size_t nc = cols (); | |
| 937 | |
| 938 ComplexMatrix retval (nr, nc); | |
| 939 | |
| 940 size_t npts, nsamples; | |
| 941 | |
| 942 if (nr == 1 || nc == 1) | |
| 943 { | |
| 944 npts = nr > nc ? nr : nc; | |
| 945 nsamples = 1; | |
| 946 } | |
| 947 else | |
| 948 { | |
| 949 npts = nr; | |
| 950 nsamples = nc; | |
| 951 } | |
| 952 | |
| 4773 | 953 const double *in (fortran_vec ()); |
| 3827 | 954 Complex *out (retval.fortran_vec ()); |
| 955 | |
| 4773 | 956 octave_fftw::fft (in, out, npts, nsamples); |
| 3827 | 957 |
| 958 return retval; | |
| 959 } | |
| 960 | |
| 961 ComplexMatrix | |
| 962 Matrix::ifourier (void) const | |
| 963 { | |
| 964 size_t nr = rows (); | |
| 965 size_t nc = cols (); | |
| 966 | |
| 967 ComplexMatrix retval (nr, nc); | |
| 968 | |
| 969 size_t npts, nsamples; | |
| 970 | |
| 971 if (nr == 1 || nc == 1) | |
| 972 { | |
| 973 npts = nr > nc ? nr : nc; | |
| 974 nsamples = 1; | |
| 975 } | |
| 976 else | |
| 977 { | |
| 978 npts = nr; | |
| 979 nsamples = nc; | |
| 980 } | |
| 981 | |
| 982 ComplexMatrix tmp (*this); | |
| 983 Complex *in (tmp.fortran_vec ()); | |
| 984 Complex *out (retval.fortran_vec ()); | |
| 985 | |
| 4773 | 986 octave_fftw::ifft (in, out, npts, nsamples); |
| 3827 | 987 |
| 988 return retval; | |
| 989 } | |
| 990 | |
| 991 ComplexMatrix | |
| 992 Matrix::fourier2d (void) const | |
| 993 { | |
| 4773 | 994 dim_vector dv(rows (), cols ()); |
| 995 | |
| 996 const double *in = fortran_vec (); | |
| 997 ComplexMatrix retval (rows (), cols ()); | |
| 998 octave_fftw::fftNd (in, retval.fortran_vec (), 2, dv); | |
| 3827 | 999 |
| 1000 return retval; | |
| 1001 } | |
| 1002 | |
| 1003 ComplexMatrix | |
| 1004 Matrix::ifourier2d (void) const | |
| 1005 { | |
| 4773 | 1006 dim_vector dv(rows (), cols ()); |
| 3827 | 1007 |
| 1008 ComplexMatrix retval (*this); | |
| 4773 | 1009 Complex *out (retval.fortran_vec ()); |
| 1010 | |
| 1011 octave_fftw::ifftNd (out, out, 2, dv); | |
| 3827 | 1012 |
| 1013 return retval; | |
| 1014 } | |
| 1015 | |
| 1016 #else | |
| 1017 | |
| 458 | 1018 ComplexMatrix |
| 1019 Matrix::fourier (void) const | |
| 1020 { | |
| 1948 | 1021 ComplexMatrix retval; |
| 1022 | |
| 5275 | 1023 octave_idx_type nr = rows (); |
| 1024 octave_idx_type nc = cols (); | |
| 1025 | |
| 1026 octave_idx_type npts, nsamples; | |
| 1948 | 1027 |
| 458 | 1028 if (nr == 1 || nc == 1) |
| 1029 { | |
| 1030 npts = nr > nc ? nr : nc; | |
| 1031 nsamples = 1; | |
| 1032 } | |
| 1033 else | |
| 1034 { | |
| 1035 npts = nr; | |
| 1036 nsamples = nc; | |
| 1037 } | |
| 1038 | |
| 5275 | 1039 octave_idx_type nn = 4*npts+15; |
| 1948 | 1040 |
| 1041 Array<Complex> wsave (nn); | |
| 1042 Complex *pwsave = wsave.fortran_vec (); | |
| 1043 | |
| 3585 | 1044 retval = ComplexMatrix (*this); |
| 1948 | 1045 Complex *tmp_data = retval.fortran_vec (); |
| 1046 | |
|
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1047 F77_FUNC (zffti, ZFFTI) (npts, pwsave); |
| 458 | 1048 |
| 5275 | 1049 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1050 { |
| 1051 OCTAVE_QUIT; | |
| 1052 | |
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|
1053 F77_FUNC (zfftf, ZFFTF) (npts, &tmp_data[npts*j], pwsave); |
| 4153 | 1054 } |
| 1948 | 1055 |
| 1056 return retval; | |
| 458 | 1057 } |
| 1058 | |
| 1059 ComplexMatrix | |
| 1060 Matrix::ifourier (void) const | |
| 1061 { | |
| 1948 | 1062 ComplexMatrix retval; |
| 1063 | |
| 5275 | 1064 octave_idx_type nr = rows (); |
| 1065 octave_idx_type nc = cols (); | |
| 1066 | |
| 1067 octave_idx_type npts, nsamples; | |
| 1948 | 1068 |
| 458 | 1069 if (nr == 1 || nc == 1) |
| 1070 { | |
| 1071 npts = nr > nc ? nr : nc; | |
| 1072 nsamples = 1; | |
| 1073 } | |
| 1074 else | |
| 1075 { | |
| 1076 npts = nr; | |
| 1077 nsamples = nc; | |
| 1078 } | |
| 1079 | |
| 5275 | 1080 octave_idx_type nn = 4*npts+15; |
| 1948 | 1081 |
| 1082 Array<Complex> wsave (nn); | |
| 1083 Complex *pwsave = wsave.fortran_vec (); | |
| 1084 | |
| 3585 | 1085 retval = ComplexMatrix (*this); |
| 1948 | 1086 Complex *tmp_data = retval.fortran_vec (); |
| 1087 | |
|
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changeset
|
1088 F77_FUNC (zffti, ZFFTI) (npts, pwsave); |
| 458 | 1089 |
| 5275 | 1090 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1091 { |
| 1092 OCTAVE_QUIT; | |
| 1093 | |
|
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changeset
|
1094 F77_FUNC (zfftb, ZFFTB) (npts, &tmp_data[npts*j], pwsave); |
| 4153 | 1095 } |
| 458 | 1096 |
| 5275 | 1097 for (octave_idx_type j = 0; j < npts*nsamples; j++) |
| 3572 | 1098 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
| 458 | 1099 |
| 1948 | 1100 return retval; |
| 458 | 1101 } |
| 1102 | |
| 677 | 1103 ComplexMatrix |
| 1104 Matrix::fourier2d (void) const | |
| 1105 { | |
| 1948 | 1106 ComplexMatrix retval; |
| 1107 | |
| 5275 | 1108 octave_idx_type nr = rows (); |
| 1109 octave_idx_type nc = cols (); | |
| 1110 | |
| 1111 octave_idx_type npts, nsamples; | |
| 1948 | 1112 |
| 677 | 1113 if (nr == 1 || nc == 1) |
| 1114 { | |
| 1115 npts = nr > nc ? nr : nc; | |
| 1116 nsamples = 1; | |
| 1117 } | |
| 1118 else | |
| 1119 { | |
| 1120 npts = nr; | |
| 1121 nsamples = nc; | |
| 1122 } | |
| 1123 | |
| 5275 | 1124 octave_idx_type nn = 4*npts+15; |
| 1948 | 1125 |
| 1126 Array<Complex> wsave (nn); | |
| 1127 Complex *pwsave = wsave.fortran_vec (); | |
| 1128 | |
| 3585 | 1129 retval = ComplexMatrix (*this); |
| 1948 | 1130 Complex *tmp_data = retval.fortran_vec (); |
| 1131 | |
|
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changeset
|
1132 F77_FUNC (zffti, ZFFTI) (npts, pwsave); |
| 677 | 1133 |
| 5275 | 1134 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1135 { |
| 1136 OCTAVE_QUIT; | |
| 1137 | |
|
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|
1138 F77_FUNC (zfftf, ZFFTF) (npts, &tmp_data[npts*j], pwsave); |
| 4153 | 1139 } |
| 677 | 1140 |
| 1141 npts = nc; | |
| 1142 nsamples = nr; | |
| 1143 nn = 4*npts+15; | |
| 1948 | 1144 |
| 1145 wsave.resize (nn); | |
| 1146 pwsave = wsave.fortran_vec (); | |
| 1147 | |
| 4773 | 1148 Array<Complex> tmp (npts); |
| 1149 Complex *prow = tmp.fortran_vec (); | |
| 1948 | 1150 |
|
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|
1151 F77_FUNC (zffti, ZFFTI) (npts, pwsave); |
| 677 | 1152 |
| 5275 | 1153 for (octave_idx_type j = 0; j < nsamples; j++) |
| 677 | 1154 { |
| 4153 | 1155 OCTAVE_QUIT; |
| 1156 | |
| 5275 | 1157 for (octave_idx_type i = 0; i < npts; i++) |
| 1948 | 1158 prow[i] = tmp_data[i*nr + j]; |
| 1159 | |
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|
1160 F77_FUNC (zfftf, ZFFTF) (npts, prow, pwsave); |
| 677 | 1161 |
| 5275 | 1162 for (octave_idx_type i = 0; i < npts; i++) |
| 1948 | 1163 tmp_data[i*nr + j] = prow[i]; |
| 677 | 1164 } |
| 1165 | |
| 1948 | 1166 return retval; |
| 677 | 1167 } |
| 1168 | |
| 1169 ComplexMatrix | |
| 1170 Matrix::ifourier2d (void) const | |
| 1171 { | |
| 1948 | 1172 ComplexMatrix retval; |
| 1173 | |
| 5275 | 1174 octave_idx_type nr = rows (); |
| 1175 octave_idx_type nc = cols (); | |
| 1176 | |
| 1177 octave_idx_type npts, nsamples; | |
| 1948 | 1178 |
| 677 | 1179 if (nr == 1 || nc == 1) |
| 1180 { | |
| 1181 npts = nr > nc ? nr : nc; | |
| 1182 nsamples = 1; | |
| 1183 } | |
| 1184 else | |
| 1185 { | |
| 1186 npts = nr; | |
| 1187 nsamples = nc; | |
| 1188 } | |
| 1189 | |
| 5275 | 1190 octave_idx_type nn = 4*npts+15; |
| 1948 | 1191 |
| 1192 Array<Complex> wsave (nn); | |
| 1193 Complex *pwsave = wsave.fortran_vec (); | |
| 1194 | |
| 3585 | 1195 retval = ComplexMatrix (*this); |
| 1948 | 1196 Complex *tmp_data = retval.fortran_vec (); |
| 1197 | |
|
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|
1198 F77_FUNC (zffti, ZFFTI) (npts, pwsave); |
| 677 | 1199 |
| 5275 | 1200 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1201 { |
| 1202 OCTAVE_QUIT; | |
| 1203 | |
|
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|
1204 F77_FUNC (zfftb, ZFFTB) (npts, &tmp_data[npts*j], pwsave); |
| 4153 | 1205 } |
| 677 | 1206 |
| 5275 | 1207 for (octave_idx_type j = 0; j < npts*nsamples; j++) |
| 3572 | 1208 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
| 677 | 1209 |
| 1210 npts = nc; | |
| 1211 nsamples = nr; | |
| 1212 nn = 4*npts+15; | |
| 1948 | 1213 |
| 1214 wsave.resize (nn); | |
| 1215 pwsave = wsave.fortran_vec (); | |
| 1216 | |
| 4773 | 1217 Array<Complex> tmp (npts); |
| 1218 Complex *prow = tmp.fortran_vec (); | |
| 1948 | 1219 |
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1220 F77_FUNC (zffti, ZFFTI) (npts, pwsave); |
| 677 | 1221 |
| 5275 | 1222 for (octave_idx_type j = 0; j < nsamples; j++) |
| 677 | 1223 { |
| 4153 | 1224 OCTAVE_QUIT; |
| 1225 | |
| 5275 | 1226 for (octave_idx_type i = 0; i < npts; i++) |
| 1948 | 1227 prow[i] = tmp_data[i*nr + j]; |
| 1228 | |
|
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|
1229 F77_FUNC (zfftb, ZFFTB) (npts, prow, pwsave); |
| 677 | 1230 |
| 5275 | 1231 for (octave_idx_type i = 0; i < npts; i++) |
| 3572 | 1232 tmp_data[i*nr + j] = prow[i] / static_cast<double> (npts); |
| 677 | 1233 } |
| 1234 | |
| 1948 | 1235 return retval; |
| 677 | 1236 } |
| 1237 | |
| 3827 | 1238 #endif |
| 1239 | |
| 458 | 1240 DET |
| 1241 Matrix::determinant (void) const | |
| 1242 { | |
| 5275 | 1243 octave_idx_type info; |
| 7788 | 1244 double rcon; |
| 1245 return determinant (info, rcon, 0); | |
| 458 | 1246 } |
| 1247 | |
| 1248 DET | |
| 5275 | 1249 Matrix::determinant (octave_idx_type& info) const |
| 458 | 1250 { |
| 7788 | 1251 double rcon; |
| 1252 return determinant (info, rcon, 0); | |
| 458 | 1253 } |
| 1254 | |
| 1255 DET | |
| 7788 | 1256 Matrix::determinant (octave_idx_type& info, double& rcon, int calc_cond) const |
| 458 | 1257 { |
|
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1258 MatrixType mattype (*this); |
|
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1259 return determinant (mattype, info, rcon, calc_cond); |
|
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1260 } |
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1261 |
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1262 DET |
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1263 Matrix::determinant (MatrixType& mattype, |
|
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1264 octave_idx_type& info, double& rcon, int calc_cond) const |
|
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1265 { |
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1266 DET retval (1.0); |
| 458 | 1267 |
| 5275 | 1268 octave_idx_type nr = rows (); |
| 1269 octave_idx_type nc = cols (); | |
| 458 | 1270 |
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1271 if (nr != nc) |
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|
1272 (*current_liboctave_error_handler) ("matrix must be square"); |
| 458 | 1273 else |
| 1274 { | |
|
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1275 int typ = mattype.type (); |
|
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|
1276 |
|
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|
1277 if (typ == MatrixType::Unknown) |
|
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|
1278 typ = mattype.type (*this); |
|
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|
1279 |
|
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1280 if (typ == MatrixType::Lower || typ == MatrixType::Upper) |
|
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|
1281 { |
|
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|
1282 for (octave_idx_type i = 0; i < nc; i++) |
|
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1283 retval *= elem (i,i); |
|
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1284 } |
|
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|
1285 else if (typ == MatrixType::Hermitian) |
|
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|
1286 { |
|
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|
1287 Matrix atmp = *this; |
|
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1288 double *tmp_data = atmp.fortran_vec (); |
|
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|
1289 |
|
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|
1290 info = 0; |
|
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1291 double anorm = 0; |
|
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1292 if (calc_cond) anorm = xnorm (*this, 1); |
|
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|
1293 |
|
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|
1294 |
|
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|
1295 char job = 'L'; |
|
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1296 F77_XFCN (dpotrf, DPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, |
|
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1297 tmp_data, nr, info |
|
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1298 F77_CHAR_ARG_LEN (1))); |
|
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1299 |
|
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1300 if (info != 0) |
|
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|
1301 { |
|
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|
1302 rcon = 0.0; |
|
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1303 mattype.mark_as_unsymmetric (); |
|
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1304 typ = MatrixType::Full; |
|
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1305 } |
|
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|
1306 else |
|
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|
1307 { |
|
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|
1308 Array<double> z (3 * nc); |
|
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1309 double *pz = z.fortran_vec (); |
|
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|
1310 Array<octave_idx_type> iz (nc); |
|
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1311 octave_idx_type *piz = iz.fortran_vec (); |
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1312 |
|
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|
1313 F77_XFCN (dpocon, DPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
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1314 nr, tmp_data, nr, anorm, |
|
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1315 rcon, pz, piz, info |
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1316 F77_CHAR_ARG_LEN (1))); |
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|
1317 |
|
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|
1318 if (info != 0) |
|
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1319 rcon = 0.0; |
|
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|
1320 |
|
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|
1321 for (octave_idx_type i = 0; i < nc; i++) |
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1322 retval *= atmp (i,i); |
|
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1323 |
|
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1324 retval = retval.square (); |
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1325 } |
|
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|
1326 } |
|
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1327 else if (typ != MatrixType::Full) |
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1328 (*current_liboctave_error_handler) ("det: invalid dense matrix type"); |
|
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1329 |
|
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1330 if (typ == MatrixType::Full) |
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1331 { |
|
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|
1332 Array<octave_idx_type> ipvt (nr); |
|
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1333 octave_idx_type *pipvt = ipvt.fortran_vec (); |
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1334 |
|
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1335 Matrix atmp = *this; |
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1336 double *tmp_data = atmp.fortran_vec (); |
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1337 |
|
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1338 info = 0; |
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1339 |
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1340 // Calculate the norm of the matrix, for later use. |
|
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1341 double anorm = 0; |
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1342 if (calc_cond) anorm = xnorm (*this, 1); |
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1343 |
|
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1344 F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); |
|
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1345 |
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1346 // Throw-away extra info LAPACK gives so as to not change output. |
|
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1347 rcon = 0.0; |
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1348 if (info != 0) |
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|
1349 { |
|
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1350 info = -1; |
|
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1351 retval = DET (); |
|
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1352 } |
|
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|
1353 else |
|
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|
1354 { |
|
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|
1355 if (calc_cond) |
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|
1356 { |
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1357 // Now calc the condition number for non-singular matrix. |
|
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1358 char job = '1'; |
|
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1359 Array<double> z (4 * nc); |
|
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1360 double *pz = z.fortran_vec (); |
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1361 Array<octave_idx_type> iz (nc); |
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1362 octave_idx_type *piz = iz.fortran_vec (); |
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1363 |
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1364 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
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1365 nc, tmp_data, nr, anorm, |
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1366 rcon, pz, piz, info |
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|
1367 F77_CHAR_ARG_LEN (1))); |
| 8335 | 1368 } |
|
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1369 |
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1370 if (info != 0) |
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|
1371 { |
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1372 info = -1; |
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1373 retval = DET (); |
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1374 } |
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|
1375 else |
|
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|
1376 { |
|
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|
1377 for (octave_idx_type i = 0; i < nc; i++) |
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|
1378 { |
|
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|
1379 double c = atmp(i,i); |
|
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1380 retval *= (ipvt(i) != (i+1)) ? -c : c; |
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|
1381 } |
|
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|
1382 } |
|
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|
1383 } |
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|
1384 } |
| 458 | 1385 } |
| 1386 | |
| 1387 return retval; | |
| 1388 } | |
| 1389 | |
| 7788 | 1390 double |
| 1391 Matrix::rcond (void) const | |
| 1392 { | |
| 1393 MatrixType mattype (*this); | |
| 1394 return rcond (mattype); | |
| 1395 } | |
| 1396 | |
| 1397 double | |
| 1398 Matrix::rcond (MatrixType &mattype) const | |
| 1399 { | |
| 1400 double rcon; | |
| 1401 octave_idx_type nr = rows (); | |
| 1402 octave_idx_type nc = cols (); | |
| 1403 | |
| 1404 if (nr != nc) | |
| 1405 (*current_liboctave_error_handler) ("matrix must be square"); | |
| 1406 else if (nr == 0 || nc == 0) | |
| 1407 rcon = octave_Inf; | |
| 1408 else | |
| 1409 { | |
| 1410 int typ = mattype.type (); | |
| 1411 | |
| 1412 if (typ == MatrixType::Unknown) | |
| 1413 typ = mattype.type (*this); | |
| 1414 | |
| 1415 // Only calculate the condition number for LU/Cholesky | |
| 1416 if (typ == MatrixType::Upper) | |
| 1417 { | |
| 1418 const double *tmp_data = fortran_vec (); | |
| 1419 octave_idx_type info = 0; | |
| 1420 char norm = '1'; | |
| 1421 char uplo = 'U'; | |
| 1422 char dia = 'N'; | |
| 1423 | |
| 1424 Array<double> z (3 * nc); | |
| 1425 double *pz = z.fortran_vec (); | |
| 1426 Array<octave_idx_type> iz (nc); | |
| 1427 octave_idx_type *piz = iz.fortran_vec (); | |
| 1428 | |
| 1429 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1430 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1431 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1432 nr, tmp_data, nr, rcon, | |
| 1433 pz, piz, info | |
| 1434 F77_CHAR_ARG_LEN (1) | |
| 1435 F77_CHAR_ARG_LEN (1) | |
| 1436 F77_CHAR_ARG_LEN (1))); | |
| 1437 | |
| 1438 if (info != 0) | |
| 1439 rcon = 0.0; | |
| 1440 } | |
| 1441 else if (typ == MatrixType::Permuted_Upper) | |
| 1442 (*current_liboctave_error_handler) | |
| 1443 ("permuted triangular matrix not implemented"); | |
| 1444 else if (typ == MatrixType::Lower) | |
| 1445 { | |
| 1446 const double *tmp_data = fortran_vec (); | |
| 1447 octave_idx_type info = 0; | |
| 1448 char norm = '1'; | |
| 1449 char uplo = 'L'; | |
| 1450 char dia = 'N'; | |
| 1451 | |
| 1452 Array<double> z (3 * nc); | |
| 1453 double *pz = z.fortran_vec (); | |
| 1454 Array<octave_idx_type> iz (nc); | |
| 1455 octave_idx_type *piz = iz.fortran_vec (); | |
| 1456 | |
| 1457 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1458 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1459 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1460 nr, tmp_data, nr, rcon, | |
| 1461 pz, piz, info | |
| 1462 F77_CHAR_ARG_LEN (1) | |
| 1463 F77_CHAR_ARG_LEN (1) | |
| 1464 F77_CHAR_ARG_LEN (1))); | |
| 1465 | |
| 1466 if (info != 0) | |
| 1467 rcon = 0.0; | |
| 1468 } | |
| 1469 else if (typ == MatrixType::Permuted_Lower) | |
| 1470 (*current_liboctave_error_handler) | |
| 1471 ("permuted triangular matrix not implemented"); | |
| 1472 else if (typ == MatrixType::Full || typ == MatrixType::Hermitian) | |
| 1473 { | |
| 1474 double anorm = -1.0; | |
| 1475 Matrix atmp = *this; | |
| 1476 double *tmp_data = atmp.fortran_vec (); | |
| 1477 | |
| 1478 if (typ == MatrixType::Hermitian) | |
| 1479 { | |
| 1480 octave_idx_type info = 0; | |
| 1481 char job = 'L'; | |
| 1482 anorm = atmp.abs().sum(). | |
| 1483 row(static_cast<octave_idx_type>(0)).max(); | |
| 1484 | |
| 1485 F77_XFCN (dpotrf, DPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, | |
| 1486 tmp_data, nr, info | |
| 1487 F77_CHAR_ARG_LEN (1))); | |
| 1488 | |
| 1489 if (info != 0) | |
| 1490 { | |
| 1491 rcon = 0.0; | |
| 1492 mattype.mark_as_unsymmetric (); | |
| 1493 typ = MatrixType::Full; | |
| 1494 } | |
| 1495 else | |
| 1496 { | |
| 1497 Array<double> z (3 * nc); | |
| 1498 double *pz = z.fortran_vec (); | |
| 1499 Array<octave_idx_type> iz (nc); | |
| 1500 octave_idx_type *piz = iz.fortran_vec (); | |
| 1501 | |
| 1502 F77_XFCN (dpocon, DPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), | |
| 1503 nr, tmp_data, nr, anorm, | |
| 1504 rcon, pz, piz, info | |
| 1505 F77_CHAR_ARG_LEN (1))); | |
| 1506 | |
| 1507 if (info != 0) | |
| 1508 rcon = 0.0; | |
| 1509 } | |
| 1510 } | |
| 1511 | |
| 1512 if (typ == MatrixType::Full) | |
| 1513 { | |
| 1514 octave_idx_type info = 0; | |
| 1515 | |
| 1516 Array<octave_idx_type> ipvt (nr); | |
| 1517 octave_idx_type *pipvt = ipvt.fortran_vec (); | |
| 1518 | |
| 1519 if(anorm < 0.) | |
| 1520 anorm = atmp.abs().sum(). | |
| 1521 row(static_cast<octave_idx_type>(0)).max(); | |
| 1522 | |
| 1523 Array<double> z (4 * nc); | |
| 1524 double *pz = z.fortran_vec (); | |
| 1525 Array<octave_idx_type> iz (nc); | |
| 1526 octave_idx_type *piz = iz.fortran_vec (); | |
| 1527 | |
| 1528 F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); | |
| 1529 | |
| 1530 if (info != 0) | |
| 1531 { | |
| 1532 rcon = 0.0; | |
| 1533 mattype.mark_as_rectangular (); | |
| 1534 } | |
| 1535 else | |
| 1536 { | |
| 1537 char job = '1'; | |
| 1538 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), | |
| 1539 nc, tmp_data, nr, anorm, | |
| 1540 rcon, pz, piz, info | |
| 1541 F77_CHAR_ARG_LEN (1))); | |
| 1542 | |
| 1543 if (info != 0) | |
| 1544 rcon = 0.0; | |
| 1545 } | |
| 1546 } | |
| 1547 } | |
| 1548 else | |
| 1549 rcon = 0.0; | |
| 1550 } | |
| 1551 | |
| 1552 return rcon; | |
| 1553 } | |
| 1554 | |
| 458 | 1555 Matrix |
| 5785 | 1556 Matrix::utsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, |
| 7788 | 1557 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 1558 bool calc_cond) const |
| 1559 { | |
| 1560 Matrix retval; | |
| 1561 | |
| 1562 octave_idx_type nr = rows (); | |
| 1563 octave_idx_type nc = cols (); | |
| 1564 | |
| 6924 | 1565 if (nr != b.rows ()) |
| 5785 | 1566 (*current_liboctave_error_handler) |
| 1567 ("matrix dimension mismatch solution of linear equations"); | |
| 6924 | 1568 else if (nr == 0 || nc == 0 || b.cols () == 0) |
| 1569 retval = Matrix (nc, b.cols (), 0.0); | |
| 5785 | 1570 else |
| 1571 { | |
| 1572 volatile int typ = mattype.type (); | |
| 1573 | |
| 1574 if (typ == MatrixType::Permuted_Upper || | |
| 1575 typ == MatrixType::Upper) | |
| 1576 { | |
| 1577 octave_idx_type b_nc = b.cols (); | |
| 7788 | 1578 rcon = 1.; |
| 5785 | 1579 info = 0; |
| 1580 | |
| 1581 if (typ == MatrixType::Permuted_Upper) | |
| 1582 { | |
| 1583 (*current_liboctave_error_handler) | |
| 6390 | 1584 ("permuted triangular matrix not implemented"); |
| 5785 | 1585 } |
| 1586 else | |
| 1587 { | |
| 1588 const double *tmp_data = fortran_vec (); | |
| 1589 | |
| 1590 if (calc_cond) | |
| 1591 { | |
| 1592 char norm = '1'; | |
| 1593 char uplo = 'U'; | |
| 1594 char dia = 'N'; | |
| 1595 | |
| 1596 Array<double> z (3 * nc); | |
| 1597 double *pz = z.fortran_vec (); | |
| 1598 Array<octave_idx_type> iz (nc); | |
| 1599 octave_idx_type *piz = iz.fortran_vec (); | |
| 1600 | |
| 1601 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1602 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1603 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 7788 | 1604 nr, tmp_data, nr, rcon, |
| 5785 | 1605 pz, piz, info |
| 1606 F77_CHAR_ARG_LEN (1) | |
| 1607 F77_CHAR_ARG_LEN (1) | |
| 1608 F77_CHAR_ARG_LEN (1))); | |
| 1609 | |
| 1610 if (info != 0) | |
| 1611 info = -2; | |
| 1612 | |
| 7788 | 1613 volatile double rcond_plus_one = rcon + 1.0; |
| 1614 | |
| 1615 if (rcond_plus_one == 1.0 || xisnan (rcon)) | |
| 5785 | 1616 { |
| 1617 info = -2; | |
| 1618 | |
| 1619 if (sing_handler) | |
| 7788 | 1620 sing_handler (rcon); |
| 5785 | 1621 else |
| 1622 (*current_liboctave_error_handler) | |
| 1623 ("matrix singular to machine precision, rcond = %g", | |
| 7788 | 1624 rcon); |
| 5785 | 1625 } |
| 1626 } | |
| 1627 | |
| 1628 if (info == 0) | |
| 1629 { | |
| 1630 retval = b; | |
| 1631 double *result = retval.fortran_vec (); | |
| 1632 | |
| 1633 char uplo = 'U'; | |
| 1634 char trans = 'N'; | |
| 1635 char dia = 'N'; | |
| 1636 | |
| 1637 F77_XFCN (dtrtrs, DTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1638 F77_CONST_CHAR_ARG2 (&trans, 1), | |
| 1639 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1640 nr, b_nc, tmp_data, nr, | |
| 1641 result, nr, info | |
| 1642 F77_CHAR_ARG_LEN (1) | |
| 1643 F77_CHAR_ARG_LEN (1) | |
| 1644 F77_CHAR_ARG_LEN (1))); | |
| 1645 } | |
| 1646 } | |
| 1647 } | |
| 1648 else | |
| 1649 (*current_liboctave_error_handler) ("incorrect matrix type"); | |
| 1650 } | |
| 1651 | |
| 1652 return retval; | |
| 1653 } | |
| 1654 | |
| 1655 Matrix | |
| 1656 Matrix::ltsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, | |
| 7788 | 1657 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 1658 bool calc_cond) const |
| 1659 { | |
| 1660 Matrix retval; | |
| 1661 | |
| 1662 octave_idx_type nr = rows (); | |
| 1663 octave_idx_type nc = cols (); | |
| 1664 | |
| 6924 | 1665 if (nr != b.rows ()) |
| 5785 | 1666 (*current_liboctave_error_handler) |
| 1667 ("matrix dimension mismatch solution of linear equations"); | |
| 6924 | 1668 else if (nr == 0 || nc == 0 || b.cols () == 0) |
| 1669 retval = Matrix (nc, b.cols (), 0.0); | |
| 5785 | 1670 else |
| 1671 { | |
| 1672 volatile int typ = mattype.type (); | |
| 1673 | |
| 1674 if (typ == MatrixType::Permuted_Lower || | |
| 1675 typ == MatrixType::Lower) | |
| 1676 { | |
| 1677 octave_idx_type b_nc = b.cols (); | |
| 7788 | 1678 rcon = 1.; |
| 5785 | 1679 info = 0; |
| 1680 | |
| 1681 if (typ == MatrixType::Permuted_Lower) | |
| 1682 { | |
| 1683 (*current_liboctave_error_handler) | |
| 6390 | 1684 ("permuted triangular matrix not implemented"); |
| 5785 | 1685 } |
| 1686 else | |
| 1687 { | |
| 1688 const double *tmp_data = fortran_vec (); | |
| 1689 | |
| 1690 if (calc_cond) | |
| 1691 { | |
| 1692 char norm = '1'; | |
| 1693 char uplo = 'L'; | |
| 1694 char dia = 'N'; | |
| 1695 | |
| 1696 Array<double> z (3 * nc); | |
| 1697 double *pz = z.fortran_vec (); | |
| 1698 Array<octave_idx_type> iz (nc); | |
| 1699 octave_idx_type *piz = iz.fortran_vec (); | |
| 1700 | |
| 1701 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1702 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1703 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 7788 | 1704 nr, tmp_data, nr, rcon, |
| 5785 | 1705 pz, piz, info |
| 1706 F77_CHAR_ARG_LEN (1) | |
| 1707 F77_CHAR_ARG_LEN (1) | |
| 1708 F77_CHAR_ARG_LEN (1))); | |
| 1709 | |
| 1710 if (info != 0) | |
| 1711 info = -2; | |
| 1712 | |
| 7788 | 1713 volatile double rcond_plus_one = rcon + 1.0; |
| 1714 | |
| 1715 if (rcond_plus_one == 1.0 || xisnan (rcon)) | |
| 5785 | 1716 { |
| 1717 info = -2; | |
| 1718 | |
| 1719 if (sing_handler) | |
| 7788 | 1720 sing_handler (rcon); |
| 5785 | 1721 else |
| 1722 (*current_liboctave_error_handler) | |
| 1723 ("matrix singular to machine precision, rcond = %g", | |
| 7788 | 1724 rcon); |
| 5785 | 1725 } |
| 1726 } | |
| 1727 | |
| 1728 if (info == 0) | |
| 1729 { | |
| 1730 retval = b; | |
| 1731 double *result = retval.fortran_vec (); | |
| 1732 | |
| 1733 char uplo = 'L'; | |
| 1734 char trans = 'N'; | |
| 1735 char dia = 'N'; | |
| 1736 | |
| 1737 F77_XFCN (dtrtrs, DTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1738 F77_CONST_CHAR_ARG2 (&trans, 1), | |
| 1739 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1740 nr, b_nc, tmp_data, nr, | |
| 1741 result, nr, info | |
| 1742 F77_CHAR_ARG_LEN (1) | |
| 1743 F77_CHAR_ARG_LEN (1) | |
| 1744 F77_CHAR_ARG_LEN (1))); | |
| 1745 } | |
| 1746 } | |
| 1747 } | |
| 1748 else | |
| 1749 (*current_liboctave_error_handler) ("incorrect matrix type"); | |
| 1750 } | |
| 1751 | |
| 1752 return retval; | |
| 1753 } | |
| 1754 | |
| 1755 Matrix | |
| 1756 Matrix::fsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, | |
| 7788 | 1757 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 1758 bool calc_cond) const |
| 1759 { | |
| 1760 Matrix retval; | |
| 1761 | |
| 1762 octave_idx_type nr = rows (); | |
| 1763 octave_idx_type nc = cols (); | |
| 1764 | |
| 6924 | 1765 if (nr != nc || nr != b.rows ()) |
| 5785 | 1766 (*current_liboctave_error_handler) |
| 1767 ("matrix dimension mismatch solution of linear equations"); | |
| 6924 | 1768 else if (nr == 0 || b.cols () == 0) |
| 1769 retval = Matrix (nc, b.cols (), 0.0); | |
| 5785 | 1770 else |
| 1771 { | |
| 1772 volatile int typ = mattype.type (); | |
| 1773 | |
| 1774 // Calculate the norm of the matrix, for later use. | |
| 1775 double anorm = -1.; | |
| 1776 | |
| 1777 if (typ == MatrixType::Hermitian) | |
| 1778 { | |
| 1779 info = 0; | |
| 1780 char job = 'L'; | |
| 1781 Matrix atmp = *this; | |
| 1782 double *tmp_data = atmp.fortran_vec (); | |
| 1783 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); | |
| 1784 | |
| 1785 F77_XFCN (dpotrf, DPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, | |
| 1786 tmp_data, nr, info | |
| 1787 F77_CHAR_ARG_LEN (1))); | |
| 1788 | |
|
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1789 // Throw-away extra info LAPACK gives so as to not change output. |
| 7788 | 1790 rcon = 0.0; |
|
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1791 if (info != 0) |
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1792 { |
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1793 info = -2; |
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1794 |
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1795 mattype.mark_as_unsymmetric (); |
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1796 typ = MatrixType::Full; |
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1797 } |
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1798 else |
| 5785 | 1799 { |
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1800 if (calc_cond) |
| 5785 | 1801 { |
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1802 Array<double> z (3 * nc); |
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1803 double *pz = z.fortran_vec (); |
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1804 Array<octave_idx_type> iz (nc); |
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1805 octave_idx_type *piz = iz.fortran_vec (); |
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1806 |
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1807 F77_XFCN (dpocon, DPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), |
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1808 nr, tmp_data, nr, anorm, |
| 7788 | 1809 rcon, pz, piz, info |
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1810 F77_CHAR_ARG_LEN (1))); |
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1811 |
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1812 if (info != 0) |
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1813 info = -2; |
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1814 |
| 7788 | 1815 volatile double rcond_plus_one = rcon + 1.0; |
| 1816 | |
| 1817 if (rcond_plus_one == 1.0 || xisnan (rcon)) | |
|
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1818 { |
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1819 info = -2; |
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1820 |
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1821 if (sing_handler) |
| 7788 | 1822 sing_handler (rcon); |
|
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1823 else |
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1824 (*current_liboctave_error_handler) |
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1825 ("matrix singular to machine precision, rcond = %g", |
| 7788 | 1826 rcon); |
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1827 } |
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1828 } |
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1829 |
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1830 if (info == 0) |
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1831 { |
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1832 retval = b; |
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1833 double *result = retval.fortran_vec (); |
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1834 |
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1835 octave_idx_type b_nc = b.cols (); |
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1836 |
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1837 F77_XFCN (dpotrs, DPOTRS, (F77_CONST_CHAR_ARG2 (&job, 1), |
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1838 nr, b_nc, tmp_data, nr, |
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1839 result, b.rows(), info |
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1840 F77_CHAR_ARG_LEN (1))); |
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1841 } |
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1842 else |
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|
1843 { |
| 5785 | 1844 mattype.mark_as_unsymmetric (); |
| 1845 typ = MatrixType::Full; | |
|
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1846 } |
| 5785 | 1847 } |
| 1848 } | |
| 1849 | |
| 1850 if (typ == MatrixType::Full) | |
| 1851 { | |
| 1852 info = 0; | |
| 1853 | |
| 1854 Array<octave_idx_type> ipvt (nr); | |
| 1855 octave_idx_type *pipvt = ipvt.fortran_vec (); | |
| 1856 | |
| 1857 Matrix atmp = *this; | |
| 1858 double *tmp_data = atmp.fortran_vec (); | |
| 1859 if(anorm < 0.) | |
| 1860 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); | |
| 1861 | |
| 1862 Array<double> z (4 * nc); | |
| 1863 double *pz = z.fortran_vec (); | |
| 1864 Array<octave_idx_type> iz (nc); | |
| 1865 octave_idx_type *piz = iz.fortran_vec (); | |
| 1866 | |
| 1867 F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); | |
| 1868 | |
|
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1869 // Throw-away extra info LAPACK gives so as to not change output. |
| 7788 | 1870 rcon = 0.0; |
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1871 if (info != 0) |
| 5785 | 1872 { |
|
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1873 info = -2; |
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1874 |
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1875 if (sing_handler) |
| 7788 | 1876 sing_handler (rcon); |
|
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1877 else |
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1878 (*current_liboctave_error_handler) |
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1879 ("matrix singular to machine precision"); |
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1880 |
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1881 mattype.mark_as_rectangular (); |
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1882 } |
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1883 else |
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1884 { |
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1885 if (calc_cond) |
| 5785 | 1886 { |
|
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1887 // Now calculate the condition number for |
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1888 // non-singular matrix. |
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1889 char job = '1'; |
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1890 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
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1891 nc, tmp_data, nr, anorm, |
| 7788 | 1892 rcon, pz, piz, info |
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1893 F77_CHAR_ARG_LEN (1))); |
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1894 |
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1895 if (info != 0) |
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1896 info = -2; |
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1897 |
| 7788 | 1898 volatile double rcond_plus_one = rcon + 1.0; |
| 1899 | |
| 1900 if (rcond_plus_one == 1.0 || xisnan (rcon)) | |
| 5785 | 1901 { |
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1902 info = -2; |
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1903 |
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1904 if (sing_handler) |
| 7788 | 1905 sing_handler (rcon); |
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1906 else |
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1907 (*current_liboctave_error_handler) |
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1908 ("matrix singular to machine precision, rcond = %g", |
| 7788 | 1909 rcon); |
| 5785 | 1910 } |
| 1911 } | |
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1912 |
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1913 if (info == 0) |
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1914 { |
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1915 retval = b; |
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1916 double *result = retval.fortran_vec (); |
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1917 |
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1918 octave_idx_type b_nc = b.cols (); |
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|
1919 |
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1920 char job = 'N'; |
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1921 F77_XFCN (dgetrs, DGETRS, (F77_CONST_CHAR_ARG2 (&job, 1), |
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|
1922 nr, b_nc, tmp_data, nr, |
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1923 pipvt, result, b.rows(), info |
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|
1924 F77_CHAR_ARG_LEN (1))); |
|
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|
1925 } |
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|
1926 else |
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|
1927 mattype.mark_as_rectangular (); |
| 5785 | 1928 } |
| 1929 } | |
| 1930 else if (typ != MatrixType::Hermitian) | |
| 1931 (*current_liboctave_error_handler) ("incorrect matrix type"); | |
| 1932 } | |
| 1933 | |
| 1934 return retval; | |
| 1935 } | |
| 1936 | |
| 1937 Matrix | |
| 1938 Matrix::solve (MatrixType &typ, const Matrix& b) const | |
| 1939 { | |
| 1940 octave_idx_type info; | |
| 7788 | 1941 double rcon; |
| 1942 return solve (typ, b, info, rcon, 0); | |
| 5785 | 1943 } |
| 1944 | |
| 1945 Matrix | |
| 1946 Matrix::solve (MatrixType &typ, const Matrix& b, octave_idx_type& info, | |
| 7788 | 1947 double& rcon) const |
| 5785 | 1948 { |
| 7788 | 1949 return solve (typ, b, info, rcon, 0); |
| 5785 | 1950 } |
| 1951 | |
| 1952 Matrix | |
| 1953 Matrix::solve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, | |
| 7788 | 1954 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 1955 bool singular_fallback) const |
| 1956 { | |
| 1957 Matrix retval; | |
| 1958 int typ = mattype.type (); | |
| 1959 | |
| 1960 if (typ == MatrixType::Unknown) | |
| 1961 typ = mattype.type (*this); | |
| 1962 | |
| 1963 // Only calculate the condition number for LU/Cholesky | |
| 1964 if (typ == MatrixType::Upper || typ == MatrixType::Permuted_Upper) | |
| 7788 | 1965 retval = utsolve (mattype, b, info, rcon, sing_handler, false); |
| 5785 | 1966 else if (typ == MatrixType::Lower || typ == MatrixType::Permuted_Lower) |
| 7788 | 1967 retval = ltsolve (mattype, b, info, rcon, sing_handler, false); |
| 5785 | 1968 else if (typ == MatrixType::Full || typ == MatrixType::Hermitian) |
| 7788 | 1969 retval = fsolve (mattype, b, info, rcon, sing_handler, true); |
| 5785 | 1970 else if (typ != MatrixType::Rectangular) |
| 1971 { | |
| 1972 (*current_liboctave_error_handler) ("unknown matrix type"); | |
| 1973 return Matrix (); | |
| 1974 } | |
| 1975 | |
| 1976 // Rectangular or one of the above solvers flags a singular matrix | |
| 1977 if (singular_fallback && mattype.type () == MatrixType::Rectangular) | |
| 1978 { | |
| 1979 octave_idx_type rank; | |
| 7788 | 1980 retval = lssolve (b, info, rank, rcon); |
| 5785 | 1981 } |
| 1982 | |
| 1983 return retval; | |
| 1984 } | |
| 1985 | |
| 1986 ComplexMatrix | |
| 1987 Matrix::solve (MatrixType &typ, const ComplexMatrix& b) const | |
| 1988 { | |
| 1989 ComplexMatrix tmp (*this); | |
| 1990 return tmp.solve (typ, b); | |
| 1991 } | |
| 1992 | |
| 1993 ComplexMatrix | |
| 1994 Matrix::solve (MatrixType &typ, const ComplexMatrix& b, | |
| 1995 octave_idx_type& info) const | |
| 1996 { | |
| 1997 ComplexMatrix tmp (*this); | |
| 1998 return tmp.solve (typ, b, info); | |
| 1999 } | |
| 2000 | |
| 2001 ComplexMatrix | |
| 2002 Matrix::solve (MatrixType &typ, const ComplexMatrix& b, octave_idx_type& info, | |
| 7788 | 2003 double& rcon) const |
| 5785 | 2004 { |
| 2005 ComplexMatrix tmp (*this); | |
| 7788 | 2006 return tmp.solve (typ, b, info, rcon); |
| 5785 | 2007 } |
| 2008 | |
| 2009 ComplexMatrix | |
| 2010 Matrix::solve (MatrixType &typ, const ComplexMatrix& b, octave_idx_type& info, | |
| 7788 | 2011 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 2012 bool singular_fallback) const |
| 2013 { | |
| 2014 ComplexMatrix tmp (*this); | |
| 7788 | 2015 return tmp.solve (typ, b, info, rcon, sing_handler, singular_fallback); |
| 5785 | 2016 } |
| 2017 | |
| 2018 ColumnVector | |
| 2019 Matrix::solve (MatrixType &typ, const ColumnVector& b) const | |
| 2020 { | |
| 7788 | 2021 octave_idx_type info; double rcon; |
| 2022 return solve (typ, b, info, rcon); | |
| 5785 | 2023 } |
| 2024 | |
| 2025 ColumnVector | |
| 2026 Matrix::solve (MatrixType &typ, const ColumnVector& b, | |
| 2027 octave_idx_type& info) const | |
| 2028 { | |
| 7788 | 2029 double rcon; |
| 2030 return solve (typ, b, info, rcon); | |
| 5785 | 2031 } |
| 2032 | |
| 2033 ColumnVector | |
| 2034 Matrix::solve (MatrixType &typ, const ColumnVector& b, octave_idx_type& info, | |
| 7788 | 2035 double& rcon) const |
| 5785 | 2036 { |
| 7788 | 2037 return solve (typ, b, info, rcon, 0); |
| 5785 | 2038 } |
| 2039 | |
| 2040 ColumnVector | |
| 2041 Matrix::solve (MatrixType &typ, const ColumnVector& b, octave_idx_type& info, | |
| 7788 | 2042 double& rcon, solve_singularity_handler sing_handler) const |
| 5785 | 2043 { |
| 2044 Matrix tmp (b); | |
| 7788 | 2045 return solve (typ, tmp, info, rcon, sing_handler).column(static_cast<octave_idx_type> (0)); |
| 5785 | 2046 } |
| 2047 | |
| 2048 ComplexColumnVector | |
| 2049 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b) const | |
| 2050 { | |
| 2051 ComplexMatrix tmp (*this); | |
| 2052 return tmp.solve (typ, b); | |
| 2053 } | |
| 2054 | |
| 2055 ComplexColumnVector | |
| 2056 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, | |
| 2057 octave_idx_type& info) const | |
| 2058 { | |
| 2059 ComplexMatrix tmp (*this); | |
| 2060 return tmp.solve (typ, b, info); | |
| 2061 } | |
| 2062 | |
| 2063 ComplexColumnVector | |
| 2064 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, | |
| 7788 | 2065 octave_idx_type& info, double& rcon) const |
| 5785 | 2066 { |
| 2067 ComplexMatrix tmp (*this); | |
| 7788 | 2068 return tmp.solve (typ, b, info, rcon); |
| 5785 | 2069 } |
| 2070 | |
| 2071 ComplexColumnVector | |
| 2072 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, | |
| 7788 | 2073 octave_idx_type& info, double& rcon, |
| 5785 | 2074 solve_singularity_handler sing_handler) const |
| 2075 { | |
| 2076 ComplexMatrix tmp (*this); | |
| 7788 | 2077 return tmp.solve(typ, b, info, rcon, sing_handler); |
| 5785 | 2078 } |
| 2079 | |
| 2080 Matrix | |
| 458 | 2081 Matrix::solve (const Matrix& b) const |
| 2082 { | |
| 5275 | 2083 octave_idx_type info; |
| 7788 | 2084 double rcon; |
| 2085 return solve (b, info, rcon, 0); | |
| 458 | 2086 } |
| 2087 | |
| 2088 Matrix | |
| 5275 | 2089 Matrix::solve (const Matrix& b, octave_idx_type& info) const |
| 458 | 2090 { |
| 7788 | 2091 double rcon; |
| 2092 return solve (b, info, rcon, 0); | |
| 458 | 2093 } |
| 2094 | |
| 2095 Matrix | |
| 7788 | 2096 Matrix::solve (const Matrix& b, octave_idx_type& info, double& rcon) const |
| 458 | 2097 { |
| 7788 | 2098 return solve (b, info, rcon, 0); |
| 3480 | 2099 } |
| 2100 | |
| 2101 Matrix | |
| 5785 | 2102 Matrix::solve (const Matrix& b, octave_idx_type& info, |
| 7788 | 2103 double& rcon, solve_singularity_handler sing_handler) const |
| 3480 | 2104 { |
| 5785 | 2105 MatrixType mattype (*this); |
| 7788 | 2106 return solve (mattype, b, info, rcon, sing_handler); |
| 458 | 2107 } |
| 2108 | |
| 2109 ComplexMatrix | |
| 2110 Matrix::solve (const ComplexMatrix& b) const | |
| 2111 { | |
| 2112 ComplexMatrix tmp (*this); | |
| 2113 return tmp.solve (b); | |
| 2114 } | |
| 2115 | |
| 2116 ComplexMatrix | |
| 5275 | 2117 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info) const |
| 458 | 2118 { |
| 2119 ComplexMatrix tmp (*this); | |
| 2120 return tmp.solve (b, info); | |
| 2121 } | |
| 2122 | |
| 2123 ComplexMatrix | |
| 7788 | 2124 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcon) const |
| 458 | 2125 { |
| 2126 ComplexMatrix tmp (*this); | |
| 7788 | 2127 return tmp.solve (b, info, rcon); |
| 458 | 2128 } |
| 2129 | |
| 3480 | 2130 ComplexMatrix |
| 7788 | 2131 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcon, |
| 3480 | 2132 solve_singularity_handler sing_handler) const |
| 2133 { | |
| 2134 ComplexMatrix tmp (*this); | |
| 7788 | 2135 return tmp.solve (b, info, rcon, sing_handler); |
| 3480 | 2136 } |
| 2137 | |
| 458 | 2138 ColumnVector |
| 2139 Matrix::solve (const ColumnVector& b) const | |
| 2140 { | |
| 7788 | 2141 octave_idx_type info; double rcon; |
| 2142 return solve (b, info, rcon); | |
| 458 | 2143 } |
| 2144 | |
| 2145 ColumnVector | |
| 5275 | 2146 Matrix::solve (const ColumnVector& b, octave_idx_type& info) const |
| 458 | 2147 { |
| 7788 | 2148 double rcon; |
| 2149 return solve (b, info, rcon); | |
| 458 | 2150 } |
| 2151 | |
| 2152 ColumnVector | |
| 7788 | 2153 Matrix::solve (const ColumnVector& b, octave_idx_type& info, double& rcon) const |
| 458 | 2154 { |
| 7788 | 2155 return solve (b, info, rcon, 0); |
| 3480 | 2156 } |
| 2157 | |
| 2158 ColumnVector | |
| 7788 | 2159 Matrix::solve (const ColumnVector& b, octave_idx_type& info, double& rcon, |
| 3480 | 2160 solve_singularity_handler sing_handler) const |
| 2161 { | |
| 5785 | 2162 MatrixType mattype (*this); |
| 7788 | 2163 return solve (mattype, b, info, rcon, sing_handler); |
| 458 | 2164 } |
| 2165 | |
| 2166 ComplexColumnVector | |
| 2167 Matrix::solve (const ComplexColumnVector& b) const | |
| 2168 { | |
| 2169 ComplexMatrix tmp (*this); | |
| 2170 return tmp.solve (b); | |
| 2171 } | |
| 2172 | |
| 2173 ComplexColumnVector | |
| 5275 | 2174 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info) const |
| 458 | 2175 { |
| 2176 ComplexMatrix tmp (*this); | |
| 2177 return tmp.solve (b, info); | |
| 2178 } | |
| 2179 | |
| 2180 ComplexColumnVector | |
| 7788 | 2181 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info, double& rcon) const |
| 458 | 2182 { |
| 2183 ComplexMatrix tmp (*this); | |
| 7788 | 2184 return tmp.solve (b, info, rcon); |
| 458 | 2185 } |
| 2186 | |
| 3480 | 2187 ComplexColumnVector |
| 7788 | 2188 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info, double& rcon, |
| 3480 | 2189 solve_singularity_handler sing_handler) const |
| 2190 { | |
| 2191 ComplexMatrix tmp (*this); | |
| 7788 | 2192 return tmp.solve (b, info, rcon, sing_handler); |
| 3480 | 2193 } |
| 2194 | |
| 458 | 2195 Matrix |
| 2196 Matrix::lssolve (const Matrix& b) const | |
| 2197 { | |
| 5275 | 2198 octave_idx_type info; |
| 2199 octave_idx_type rank; | |
| 7788 | 2200 double rcon; |
| 2201 return lssolve (b, info, rank, rcon); | |
| 458 | 2202 } |
| 2203 | |
| 2204 Matrix | |
| 5275 | 2205 Matrix::lssolve (const Matrix& b, octave_idx_type& info) const |
| 458 | 2206 { |
| 5275 | 2207 octave_idx_type rank; |
| 7788 | 2208 double rcon; |
| 2209 return lssolve (b, info, rank, rcon); | |
| 458 | 2210 } |
| 2211 | |
| 2212 Matrix | |
| 7072 | 2213 Matrix::lssolve (const Matrix& b, octave_idx_type& info, |
| 2214 octave_idx_type& rank) const | |
| 458 | 2215 { |
| 7788 | 2216 double rcon; |
| 2217 return lssolve (b, info, rank, rcon); | |
| 7076 | 2218 } |
| 2219 | |
| 2220 Matrix | |
| 2221 Matrix::lssolve (const Matrix& b, octave_idx_type& info, | |
| 7788 | 2222 octave_idx_type& rank, double &rcon) const |
| 7076 | 2223 { |
| 1948 | 2224 Matrix retval; |
| 2225 | |
| 5275 | 2226 octave_idx_type nrhs = b.cols (); |
| 2227 | |
| 2228 octave_idx_type m = rows (); | |
| 2229 octave_idx_type n = cols (); | |
| 458 | 2230 |
| 6924 | 2231 if (m != b.rows ()) |
| 1948 | 2232 (*current_liboctave_error_handler) |
| 6924 | 2233 ("matrix dimension mismatch solution of linear equations"); |
| 2234 else if (m == 0 || n == 0 || b.cols () == 0) | |
| 2235 retval = Matrix (n, b.cols (), 0.0); | |
| 1948 | 2236 else |
| 458 | 2237 { |
| 7072 | 2238 volatile octave_idx_type minmn = (m < n ? m : n); |
| 2239 octave_idx_type maxmn = m > n ? m : n; | |
| 7788 | 2240 rcon = -1.0; |
| 7072 | 2241 if (m != n) |
| 2242 { | |
| 2243 retval = Matrix (maxmn, nrhs, 0.0); | |
| 2244 | |
| 2245 for (octave_idx_type j = 0; j < nrhs; j++) | |
| 2246 for (octave_idx_type i = 0; i < m; i++) | |
| 2247 retval.elem (i, j) = b.elem (i, j); | |
| 2248 } | |
| 2249 else | |
| 2250 retval = b; | |
| 2251 | |
| 1948 | 2252 Matrix atmp = *this; |
| 2253 double *tmp_data = atmp.fortran_vec (); | |
| 2254 | |
| 7072 | 2255 double *pretval = retval.fortran_vec (); |
| 2256 Array<double> s (minmn); | |
| 7071 | 2257 double *ps = s.fortran_vec (); |
| 1948 | 2258 |
| 7072 | 2259 // Ask DGELSD what the dimension of WORK should be. |
| 5275 | 2260 octave_idx_type lwork = -1; |
| 3752 | 2261 |
| 2262 Array<double> work (1); | |
| 1948 | 2263 |
| 7477 | 2264 octave_idx_type smlsiz; |
| 2265 F77_FUNC (xilaenv, XILAENV) (9, F77_CONST_CHAR_ARG2 ("DGELSD", 6), | |
| 2266 F77_CONST_CHAR_ARG2 (" ", 1), | |
| 7478 | 2267 0, 0, 0, 0, smlsiz |
| 7477 | 2268 F77_CHAR_ARG_LEN (6) |
| 7478 | 2269 F77_CHAR_ARG_LEN (1)); |
| 7079 | 2270 |
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2271 octave_idx_type mnthr; |
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2272 F77_FUNC (xilaenv, XILAENV) (6, F77_CONST_CHAR_ARG2 ("DGELSD", 6), |
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2273 F77_CONST_CHAR_ARG2 (" ", 1), |
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2274 m, n, nrhs, -1, mnthr |
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2275 F77_CHAR_ARG_LEN (6) |
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2276 F77_CHAR_ARG_LEN (1)); |
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2277 |
| 7079 | 2278 // We compute the size of iwork because DGELSD in older versions |
| 2279 // of LAPACK does not return it on a query call. | |
| 7124 | 2280 double dminmn = static_cast<double> (minmn); |
| 2281 double dsmlsizp1 = static_cast<double> (smlsiz+1); | |
| 7079 | 2282 #if defined (HAVE_LOG2) |
| 7367 | 2283 double tmp = log2 (dminmn / dsmlsizp1); |
| 7079 | 2284 #else |
| 7367 | 2285 double tmp = log (dminmn / dsmlsizp1) / log (2.0); |
| 7079 | 2286 #endif |
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2287 octave_idx_type nlvl = static_cast<octave_idx_type> (tmp) + 1; |
| 7079 | 2288 if (nlvl < 0) |
| 2289 nlvl = 0; | |
| 2290 | |
| 2291 octave_idx_type liwork = 3 * minmn * nlvl + 11 * minmn; | |
| 2292 if (liwork < 1) | |
| 2293 liwork = 1; | |
| 7072 | 2294 Array<octave_idx_type> iwork (liwork); |
| 2295 octave_idx_type* piwork = iwork.fortran_vec (); | |
| 2296 | |
| 2297 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, | |
| 7788 | 2298 ps, rcon, rank, work.fortran_vec (), |
| 7072 | 2299 lwork, piwork, info)); |
| 1948 | 2300 |
| 7476 | 2301 // The workspace query is broken in at least LAPACK 3.0.0 |
|
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2302 // through 3.1.1 when n >= mnthr. The obtuse formula below |
| 7476 | 2303 // should provide sufficient workspace for DGELSD to operate |
| 2304 // efficiently. | |
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2305 if (n >= mnthr) |
| 7476 | 2306 { |
| 2307 const octave_idx_type wlalsd | |
| 2308 = 9*m + 2*m*smlsiz + 8*m*nlvl + m*nrhs + (smlsiz+1)*(smlsiz+1); | |
| 2309 | |
| 2310 octave_idx_type addend = m; | |
| 2311 | |
| 2312 if (2*m-4 > addend) | |
| 2313 addend = 2*m-4; | |
| 2314 | |
| 2315 if (nrhs > addend) | |
| 2316 addend = nrhs; | |
| 2317 | |
| 2318 if (n-3*m > addend) | |
| 2319 addend = n-3*m; | |
| 2320 | |
| 2321 if (wlalsd > addend) | |
| 2322 addend = wlalsd; | |
| 2323 | |
| 2324 const octave_idx_type lworkaround = 4*m + m*m + addend; | |
| 2325 | |
| 2326 if (work(0) < lworkaround) | |
| 2327 work(0) = lworkaround; | |
| 2328 } | |
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2329 else if (m >= n) |
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2330 { |
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2331 octave_idx_type lworkaround |
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2332 = 12*n + 2*n*smlsiz + 8*n*nlvl + n*nrhs + (smlsiz+1)*(smlsiz+1); |
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2333 |
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2334 if (work(0) < lworkaround) |
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2335 work(0) = lworkaround; |
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2336 } |
| 7476 | 2337 |
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2338 lwork = static_cast<octave_idx_type> (work(0)); |
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2339 work.resize (lwork); |
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2340 |
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2341 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, |
| 7788 | 2342 maxmn, ps, rcon, rank, |
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2343 work.fortran_vec (), lwork, |
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2344 piwork, info)); |
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2345 |
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2346 if (rank < minmn) |
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2347 (*current_liboctave_warning_handler) |
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2348 ("dgelsd: rank deficient %dx%d matrix, rank = %d", m, n, rank); |
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|
2349 if (s.elem (0) == 0.0) |
| 7788 | 2350 rcon = 0.0; |
| 1948 | 2351 else |
| 7788 | 2352 rcon = s.elem (minmn - 1) / s.elem (0); |
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2353 |
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|
2354 retval.resize (n, nrhs); |
| 458 | 2355 } |
| 2356 | |
| 2357 return retval; | |
| 2358 } | |
| 2359 | |
| 2360 ComplexMatrix | |
| 2361 Matrix::lssolve (const ComplexMatrix& b) const | |
| 2362 { | |
| 2363 ComplexMatrix tmp (*this); | |
| 5275 | 2364 octave_idx_type info; |
| 2365 octave_idx_type rank; | |
| 7788 | 2366 double rcon; |
| 2367 return tmp.lssolve (b, info, rank, rcon); | |
| 458 | 2368 } |
| 2369 | |
| 2370 ComplexMatrix | |
| 5275 | 2371 Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info) const |
| 458 | 2372 { |
| 2373 ComplexMatrix tmp (*this); | |
| 5275 | 2374 octave_idx_type rank; |
| 7788 | 2375 double rcon; |
| 2376 return tmp.lssolve (b, info, rank, rcon); | |
| 458 | 2377 } |
| 2378 | |
| 2379 ComplexMatrix | |
| 7076 | 2380 Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info, |
| 2381 octave_idx_type& rank) const | |
| 458 | 2382 { |
| 2383 ComplexMatrix tmp (*this); | |
| 7788 | 2384 double rcon; |
| 2385 return tmp.lssolve (b, info, rank, rcon); | |
| 7076 | 2386 } |
| 2387 | |
| 2388 ComplexMatrix | |
| 2389 Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info, | |
| 7788 | 2390 octave_idx_type& rank, double& rcon) const |
| 7076 | 2391 { |
| 2392 ComplexMatrix tmp (*this); | |
| 7788 | 2393 return tmp.lssolve (b, info, rank, rcon); |
| 458 | 2394 } |
| 2395 | |
| 2396 ColumnVector | |
| 2397 Matrix::lssolve (const ColumnVector& b) const | |
| 2398 { | |
| 5275 | 2399 octave_idx_type info; |
| 2400 octave_idx_type rank; | |
| 7788 | 2401 double rcon; |
| 2402 return lssolve (b, info, rank, rcon); | |
| 458 | 2403 } |
| 2404 | |
| 2405 ColumnVector | |
| 5275 | 2406 Matrix::lssolve (const ColumnVector& b, octave_idx_type& info) const |
| 458 | 2407 { |
| 5275 | 2408 octave_idx_type rank; |
| 7788 | 2409 double rcon; |
| 2410 return lssolve (b, info, rank, rcon); | |
| 458 | 2411 } |
| 2412 | |
| 2413 ColumnVector | |
| 7072 | 2414 Matrix::lssolve (const ColumnVector& b, octave_idx_type& info, |
| 2415 octave_idx_type& rank) const | |
| 458 | 2416 { |
| 7788 | 2417 double rcon; |
| 2418 return lssolve (b, info, rank, rcon); | |
| 7076 | 2419 } |
| 2420 | |
| 2421 ColumnVector | |
| 2422 Matrix::lssolve (const ColumnVector& b, octave_idx_type& info, | |
| 7788 | 2423 octave_idx_type& rank, double &rcon) const |
| 7076 | 2424 { |
| 1948 | 2425 ColumnVector retval; |
| 2426 | |
| 5275 | 2427 octave_idx_type nrhs = 1; |
| 2428 | |
| 2429 octave_idx_type m = rows (); | |
| 2430 octave_idx_type n = cols (); | |
| 458 | 2431 |
| 6924 | 2432 if (m != b.length ()) |
| 1948 | 2433 (*current_liboctave_error_handler) |
| 6924 | 2434 ("matrix dimension mismatch solution of linear equations"); |
| 2435 else if (m == 0 || n == 0) | |
| 2436 retval = ColumnVector (n, 0.0); | |
| 1948 | 2437 else |
| 458 | 2438 { |
| 7072 | 2439 volatile octave_idx_type minmn = (m < n ? m : n); |
| 2440 octave_idx_type maxmn = m > n ? m : n; | |
| 7788 | 2441 rcon = -1.0; |
| 7072 | 2442 |
| 2443 if (m != n) | |
| 2444 { | |
| 2445 retval = ColumnVector (maxmn, 0.0); | |
| 2446 | |
| 2447 for (octave_idx_type i = 0; i < m; i++) | |
| 2448 retval.elem (i) = b.elem (i); | |
| 2449 } | |
| 2450 else | |
| 2451 retval = b; | |
| 2452 | |
| 1948 | 2453 Matrix atmp = *this; |
| 2454 double *tmp_data = atmp.fortran_vec (); | |
| 2455 | |
| 7072 | 2456 double *pretval = retval.fortran_vec (); |
| 2457 Array<double> s (minmn); | |
| 7071 | 2458 double *ps = s.fortran_vec (); |
| 1948 | 2459 |
| 7072 | 2460 // Ask DGELSD what the dimension of WORK should be. |
| 5275 | 2461 octave_idx_type lwork = -1; |
| 3752 | 2462 |
| 2463 Array<double> work (1); | |
| 2464 | |
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2465 octave_idx_type smlsiz; |
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2466 F77_FUNC (xilaenv, XILAENV) (9, F77_CONST_CHAR_ARG2 ("DGELSD", 6), |
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2467 F77_CONST_CHAR_ARG2 (" ", 1), |
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2468 0, 0, 0, 0, smlsiz |
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2469 F77_CHAR_ARG_LEN (6) |
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2470 F77_CHAR_ARG_LEN (1)); |
| 7079 | 2471 |
| 2472 // We compute the size of iwork because DGELSD in older versions | |
| 2473 // of LAPACK does not return it on a query call. | |
| 7124 | 2474 double dminmn = static_cast<double> (minmn); |
| 2475 double dsmlsizp1 = static_cast<double> (smlsiz+1); | |
| 7079 | 2476 #if defined (HAVE_LOG2) |
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2477 double tmp = log2 (dminmn / dsmlsizp1); |
| 7079 | 2478 #else |
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2479 double tmp = log (dminmn / dsmlsizp1) / log (2.0); |
| 7079 | 2480 #endif |
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2481 octave_idx_type nlvl = static_cast<octave_idx_type> (tmp) + 1; |
| 7079 | 2482 if (nlvl < 0) |
| 2483 nlvl = 0; | |
| 2484 | |
| 2485 octave_idx_type liwork = 3 * minmn * nlvl + 11 * minmn; | |
| 2486 if (liwork < 1) | |
| 2487 liwork = 1; | |
| 7072 | 2488 Array<octave_idx_type> iwork (liwork); |
| 2489 octave_idx_type* piwork = iwork.fortran_vec (); | |
| 2490 | |
| 2491 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, | |
| 7788 | 2492 ps, rcon, rank, work.fortran_vec (), |
| 7072 | 2493 lwork, piwork, info)); |
| 1948 | 2494 |
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2495 lwork = static_cast<octave_idx_type> (work(0)); |
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2496 work.resize (lwork); |
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2497 |
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2498 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, |
| 7788 | 2499 maxmn, ps, rcon, rank, |
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2500 work.fortran_vec (), lwork, |
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2501 piwork, info)); |
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2502 |
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2503 if (rank < minmn) |
| 1948 | 2504 { |
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2505 if (rank < minmn) |
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2506 (*current_liboctave_warning_handler) |
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2507 ("dgelsd: rank deficient %dx%d matrix, rank = %d", m, n, rank); |
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changeset
|
2508 if (s.elem (0) == 0.0) |
| 7788 | 2509 rcon = 0.0; |
|
7482
29980c6b8604
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parents:
7478
diff
changeset
|
2510 else |
| 7788 | 2511 rcon = s.elem (minmn - 1) / s.elem (0); |
| 1948 | 2512 } |
|
7482
29980c6b8604
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John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
2513 |
|
29980c6b8604
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7478
diff
changeset
|
2514 retval.resize (n, nrhs); |
| 458 | 2515 } |
| 2516 | |
| 2517 return retval; | |
| 2518 } | |
| 2519 | |
| 2520 ComplexColumnVector | |
| 2521 Matrix::lssolve (const ComplexColumnVector& b) const | |
| 2522 { | |
| 2523 ComplexMatrix tmp (*this); | |
| 7076 | 2524 octave_idx_type info; |
| 2525 octave_idx_type rank; | |
| 7788 | 2526 double rcon; |
| 2527 return tmp.lssolve (b, info, rank, rcon); | |
| 458 | 2528 } |
| 2529 | |
| 2530 ComplexColumnVector | |
| 5275 | 2531 Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info) const |
| 458 | 2532 { |
| 2533 ComplexMatrix tmp (*this); | |
| 7076 | 2534 octave_idx_type rank; |
| 7788 | 2535 double rcon; |
| 2536 return tmp.lssolve (b, info, rank, rcon); | |
| 458 | 2537 } |
| 2538 | |
| 2539 ComplexColumnVector | |
| 7076 | 2540 Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, |
| 2541 octave_idx_type& rank) const | |
| 458 | 2542 { |
| 2543 ComplexMatrix tmp (*this); | |
| 7788 | 2544 double rcon; |
| 2545 return tmp.lssolve (b, info, rank, rcon); | |
| 7076 | 2546 } |
| 2547 | |
| 2548 ComplexColumnVector | |
| 2549 Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, | |
| 7788 | 2550 octave_idx_type& rank, double &rcon) const |
| 7076 | 2551 { |
| 2552 ComplexMatrix tmp (*this); | |
| 7788 | 2553 return tmp.lssolve (b, info, rank, rcon); |
| 458 | 2554 } |
| 2555 | |
| 1819 | 2556 // Constants for matrix exponential calculation. |
| 2557 | |
| 2558 static double padec [] = | |
| 2559 { | |
| 2560 5.0000000000000000e-1, | |
| 2561 1.1666666666666667e-1, | |
| 2562 1.6666666666666667e-2, | |
| 2563 1.6025641025641026e-3, | |
| 2564 1.0683760683760684e-4, | |
| 2565 4.8562548562548563e-6, | |
| 2566 1.3875013875013875e-7, | |
| 2567 1.9270852604185938e-9, | |
| 2568 }; | |
| 2569 | |
| 7400 | 2570 static void |
| 7788 | 2571 solve_singularity_warning (double rcon) |
| 7400 | 2572 { |
| 2573 (*current_liboctave_warning_handler) | |
| 2574 ("singular matrix encountered in expm calculation, rcond = %g", | |
| 7788 | 2575 rcon); |
| 7400 | 2576 } |
| 2577 | |
| 1819 | 2578 Matrix |
| 2579 Matrix::expm (void) const | |
| 2580 { | |
| 2581 Matrix retval; | |
| 2582 | |
| 2583 Matrix m = *this; | |
| 2584 | |
| 6699 | 2585 if (numel () == 1) |
| 2586 return Matrix (1, 1, exp (m(0))); | |
| 2587 | |
| 5275 | 2588 octave_idx_type nc = columns (); |
| 1819 | 2589 |
| 3130 | 2590 // Preconditioning step 1: trace normalization to reduce dynamic |
| 2591 // range of poles, but avoid making stable eigenvalues unstable. | |
| 2592 | |
| 1819 | 2593 // trace shift value |
| 3331 | 2594 volatile double trshift = 0.0; |
| 1819 | 2595 |
| 5275 | 2596 for (octave_idx_type i = 0; i < nc; i++) |
| 1819 | 2597 trshift += m.elem (i, i); |
| 2598 | |
| 2599 trshift /= nc; | |
| 2600 | |
| 3130 | 2601 if (trshift > 0.0) |
| 2602 { | |
| 5275 | 2603 for (octave_idx_type i = 0; i < nc; i++) |
| 3130 | 2604 m.elem (i, i) -= trshift; |
| 2605 } | |
| 1819 | 2606 |
| 3331 | 2607 // Preconditioning step 2: balancing; code follows development |
| 2608 // in AEPBAL | |
| 2609 | |
| 2610 double *p_m = m.fortran_vec (); | |
| 2611 | |
| 5275 | 2612 octave_idx_type info, ilo, ihi, ilos, ihis; |
| 3468 | 2613 Array<double> dpermute (nc); |
| 2614 Array<double> dscale (nc); | |
| 3466 | 2615 |
| 3468 | 2616 // permutation first |
| 2617 char job = 'P'; | |
| 4552 | 2618 F77_XFCN (dgebal, DGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
| 2619 nc, p_m, nc, ilo, ihi, | |
| 2620 dpermute.fortran_vec (), info | |
| 2621 F77_CHAR_ARG_LEN (1))); | |
| 3466 | 2622 |
| 3468 | 2623 // then scaling |
| 2624 job = 'S'; | |
| 4552 | 2625 F77_XFCN (dgebal, DGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
| 2626 nc, p_m, nc, ilos, ihis, | |
| 2627 dscale.fortran_vec (), info | |
| 2628 F77_CHAR_ARG_LEN (1))); | |
| 3331 | 2629 |
| 1819 | 2630 // Preconditioning step 3: scaling. |
| 3331 | 2631 |
| 1819 | 2632 ColumnVector work(nc); |
| 3130 | 2633 double inf_norm; |
| 3331 | 2634 |
| 4552 | 2635 F77_XFCN (xdlange, XDLANGE, (F77_CONST_CHAR_ARG2 ("I", 1), |
| 2636 nc, nc, m.fortran_vec (), nc, | |
| 2637 work.fortran_vec (), inf_norm | |
| 2638 F77_CHAR_ARG_LEN (1))); | |
| 3331 | 2639 |
| 5275 | 2640 octave_idx_type sqpow = static_cast<octave_idx_type> (inf_norm > 0.0 |
| 1819 | 2641 ? (1.0 + log (inf_norm) / log (2.0)) |
| 2642 : 0.0); | |
| 3331 | 2643 |
| 1819 | 2644 // Check whether we need to square at all. |
| 3331 | 2645 |
| 1819 | 2646 if (sqpow < 0) |
| 2647 sqpow = 0; | |
| 3331 | 2648 |
| 1819 | 2649 if (sqpow > 0) |
| 2650 { | |
| 7400 | 2651 if (sqpow > 1023) |
| 2652 sqpow = 1023; | |
| 2653 | |
| 1819 | 2654 double scale_factor = 1.0; |
| 5275 | 2655 for (octave_idx_type i = 0; i < sqpow; i++) |
| 1819 | 2656 scale_factor *= 2.0; |
| 7400 | 2657 |
| 1819 | 2658 m = m / scale_factor; |
| 2659 } | |
| 3331 | 2660 |
| 1819 | 2661 // npp, dpp: pade' approx polynomial matrices. |
| 3331 | 2662 |
| 1819 | 2663 Matrix npp (nc, nc, 0.0); |
| 7265 | 2664 double *pnpp = npp.fortran_vec (); |
| 1819 | 2665 Matrix dpp = npp; |
| 7265 | 2666 double *pdpp = dpp.fortran_vec (); |
| 3331 | 2667 |
| 1819 | 2668 // Now powers a^8 ... a^1. |
| 3331 | 2669 |
| 5275 | 2670 octave_idx_type minus_one_j = -1; |
| 2671 for (octave_idx_type j = 7; j >= 0; j--) | |
| 1819 | 2672 { |
| 7265 | 2673 for (octave_idx_type i = 0; i < nc; i++) |
| 2674 { | |
| 2675 octave_idx_type k = i * nc + i; | |
| 2676 pnpp[k] += padec[j]; | |
| 2677 pdpp[k] += minus_one_j * padec[j]; | |
| 2678 } | |
| 2679 | |
| 2680 npp = m * npp; | |
| 2681 pnpp = npp.fortran_vec (); | |
| 2682 | |
| 2683 dpp = m * dpp; | |
| 2684 pdpp = dpp.fortran_vec (); | |
| 2685 | |
| 1819 | 2686 minus_one_j *= -1; |
| 2687 } | |
| 3331 | 2688 |
| 1819 | 2689 // Zero power. |
| 3331 | 2690 |
| 1819 | 2691 dpp = -dpp; |
| 5275 | 2692 for (octave_idx_type j = 0; j < nc; j++) |
| 1819 | 2693 { |
| 2694 npp.elem (j, j) += 1.0; | |
| 2695 dpp.elem (j, j) += 1.0; | |
| 2696 } | |
| 3331 | 2697 |
| 1819 | 2698 // Compute pade approximation = inverse (dpp) * npp. |
| 2699 | |
| 7788 | 2700 double rcon; |
| 2701 retval = dpp.solve (npp, info, rcon, solve_singularity_warning); | |
| 7400 | 2702 |
| 2703 if (info < 0) | |
| 2704 return retval; | |
| 2705 | |
| 1819 | 2706 // Reverse preconditioning step 3: repeated squaring. |
| 3331 | 2707 |
| 1819 | 2708 while (sqpow) |
| 2709 { | |
| 2710 retval = retval * retval; | |
| 2711 sqpow--; | |
| 2712 } | |
| 3331 | 2713 |
| 1819 | 2714 // Reverse preconditioning step 2: inverse balancing. |
| 3466 | 2715 // apply inverse scaling to computed exponential |
| 5275 | 2716 for (octave_idx_type i = 0; i < nc; i++) |
| 2717 for (octave_idx_type j = 0; j < nc; j++) | |
|
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7922
diff
changeset
|
2718 retval(i,j) *= dscale(i) / dscale(j); |
| 3466 | 2719 |
| 4153 | 2720 OCTAVE_QUIT; |
| 2721 | |
| 3466 | 2722 // construct balancing permutation vector |
| 5275 | 2723 Array<octave_idx_type> iperm (nc); |
| 2724 for (octave_idx_type i = 0; i < nc; i++) | |
| 4593 | 2725 iperm(i) = i; // identity permutation |
| 3466 | 2726 |
|
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improve inverse preconditioning according to Marco Caliari
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parents:
7922
diff
changeset
|
2727 // trailing permutations must be done in reverse order |
|
851803f7bb4d
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parents:
7922
diff
changeset
|
2728 for (octave_idx_type i = nc - 1; i >= ihi; i--) |
|
851803f7bb4d
improve inverse preconditioning according to Marco Caliari
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parents:
7922
diff
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|
2729 { |
|
851803f7bb4d
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parents:
7922
diff
changeset
|
2730 octave_idx_type swapidx = static_cast<octave_idx_type> (dpermute(i)) - 1; |
|
851803f7bb4d
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parents:
7922
diff
changeset
|
2731 octave_idx_type tmp = iperm(i); |
|
851803f7bb4d
improve inverse preconditioning according to Marco Caliari
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parents:
7922
diff
changeset
|
2732 iperm(i) = iperm(swapidx); |
|
851803f7bb4d
improve inverse preconditioning according to Marco Caliari
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parents:
7922
diff
changeset
|
2733 iperm(swapidx) = tmp; |
|
851803f7bb4d
improve inverse preconditioning according to Marco Caliari
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parents:
7922
diff
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|
2734 } |
|
851803f7bb4d
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7922
diff
changeset
|
2735 |
| 3466 | 2736 // leading permutations in forward order |
| 5275 | 2737 for (octave_idx_type i = 0; i < (ilo-1); i++) |
| 3468 | 2738 { |
| 5275 | 2739 octave_idx_type swapidx = static_cast<octave_idx_type> (dpermute(i)) - 1; |
| 2740 octave_idx_type tmp = iperm(i); | |
| 4593 | 2741 iperm(i) = iperm (swapidx); |
| 2742 iperm(swapidx) = tmp; | |
| 3468 | 2743 } |
| 3466 | 2744 |
| 7416 | 2745 // construct inverse balancing permutation vector |
| 2746 Array<octave_idx_type> invpvec (nc); | |
| 2747 for (octave_idx_type i = 0; i < nc; i++) | |
| 2748 invpvec(iperm(i)) = i; // Thanks to R. A. Lippert for this method | |
| 2749 | |
| 2750 OCTAVE_QUIT; | |
|
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improve inverse preconditioning according to Marco Caliari
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7922
diff
changeset
|
2751 |
| 7416 | 2752 Matrix tmpMat = retval; |
| 2753 for (octave_idx_type i = 0; i < nc; i++) | |
| 2754 for (octave_idx_type j = 0; j < nc; j++) | |
| 2755 retval(i,j) = tmpMat(invpvec(i),invpvec(j)); | |
| 2756 | |
|
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7922
diff
changeset
|
2757 // Reverse preconditioning step 1: fix trace normalization. |
| 3130 | 2758 if (trshift > 0.0) |
| 2759 retval = exp (trshift) * retval; | |
| 2760 | |
| 2761 return retval; | |
| 1819 | 2762 } |
| 2763 | |
| 458 | 2764 Matrix& |
| 2765 Matrix::operator += (const DiagMatrix& a) | |
| 2766 { | |
| 5275 | 2767 octave_idx_type nr = rows (); |
| 2768 octave_idx_type nc = cols (); | |
| 2769 | |
| 2770 octave_idx_type a_nr = a.rows (); | |
| 2771 octave_idx_type a_nc = a.cols (); | |
| 2385 | 2772 |
| 2773 if (nr != a_nr || nc != a_nc) | |
| 458 | 2774 { |
| 2385 | 2775 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
| 458 | 2776 return *this; |
| 2777 } | |
| 2778 | |
| 5275 | 2779 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 2780 elem (i, i) += a.elem (i, i); |
| 2781 | |
| 2782 return *this; | |
| 2783 } | |
| 2784 | |
| 2785 Matrix& | |
| 2786 Matrix::operator -= (const DiagMatrix& a) | |
| 2787 { | |
| 5275 | 2788 octave_idx_type nr = rows (); |
| 2789 octave_idx_type nc = cols (); | |
| 2790 | |
| 2791 octave_idx_type a_nr = a.rows (); | |
| 2792 octave_idx_type a_nc = a.cols (); | |
| 2385 | 2793 |
| 2794 if (nr != a_nr || nc != a_nc) | |
| 458 | 2795 { |
| 2385 | 2796 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
| 458 | 2797 return *this; |
| 2798 } | |
| 2799 | |
| 5275 | 2800 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 2801 elem (i, i) -= a.elem (i, i); |
| 2802 | |
| 2803 return *this; | |
| 2804 } | |
| 2805 | |
| 2806 // unary operations | |
| 2807 | |
| 2964 | 2808 boolMatrix |
| 458 | 2809 Matrix::operator ! (void) const |
| 2810 { | |
| 5275 | 2811 octave_idx_type nr = rows (); |
| 2812 octave_idx_type nc = cols (); | |
| 458 | 2813 |
| 2964 | 2814 boolMatrix b (nr, nc); |
| 458 | 2815 |
| 5275 | 2816 for (octave_idx_type j = 0; j < nc; j++) |
| 2817 for (octave_idx_type i = 0; i < nr; i++) | |
| 458 | 2818 b.elem (i, j) = ! elem (i, j); |
| 2819 | |
| 2820 return b; | |
| 2821 } | |
| 2822 | |
| 1205 | 2823 // column vector by row vector -> matrix operations |
| 458 | 2824 |
| 1205 | 2825 Matrix |
| 2826 operator * (const ColumnVector& v, const RowVector& a) | |
| 458 | 2827 { |
| 1948 | 2828 Matrix retval; |
| 2829 | |
| 5275 | 2830 octave_idx_type len = v.length (); |
| 3233 | 2831 |
| 2832 if (len != 0) | |
| 1205 | 2833 { |
| 5275 | 2834 octave_idx_type a_len = a.length (); |
| 3233 | 2835 |
| 2836 retval.resize (len, a_len); | |
| 2837 double *c = retval.fortran_vec (); | |
| 2838 | |
| 4552 | 2839 F77_XFCN (dgemm, DGEMM, (F77_CONST_CHAR_ARG2 ("N", 1), |
| 2840 F77_CONST_CHAR_ARG2 ("N", 1), | |
| 2841 len, a_len, 1, 1.0, v.data (), len, | |
| 2842 a.data (), 1, 0.0, c, len | |
| 2843 F77_CHAR_ARG_LEN (1) | |
| 2844 F77_CHAR_ARG_LEN (1))); | |
| 1205 | 2845 } |
| 458 | 2846 |
| 1948 | 2847 return retval; |
| 458 | 2848 } |
| 2849 | |
| 2850 // other operations. | |
| 2851 | |
| 2852 Matrix | |
|
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convert mapper functions to new format
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diff
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|
2853 Matrix::map (dmapper fcn) const |
| 1205 | 2854 { |
|
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diff
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|
2855 return MArray2<double>::map<double> (func_ptr (fcn)); |
|
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diff
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|
2856 } |
|
8c32f95c2639
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diff
changeset
|
2857 |
|
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diff
changeset
|
2858 ComplexMatrix |
|
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diff
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|
2859 Matrix::map (cmapper fcn) const |
|
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diff
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|
2860 { |
|
8c32f95c2639
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diff
changeset
|
2861 return MArray2<double>::map<Complex> (func_ptr (fcn)); |
| 1205 | 2862 } |
| 2863 | |
| 3248 | 2864 boolMatrix |
|
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diff
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|
2865 Matrix::map (bmapper fcn) const |
| 3248 | 2866 { |
|
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|
2867 return MArray2<double>::map<bool> (func_ptr (fcn)); |
| 458 | 2868 } |
| 2869 | |
| 2385 | 2870 bool |
| 4431 | 2871 Matrix::any_element_is_negative (bool neg_zero) const |
| 2385 | 2872 { |
| 5275 | 2873 octave_idx_type nel = nelem (); |
| 2385 | 2874 |
| 4431 | 2875 if (neg_zero) |
| 2876 { | |
| 5275 | 2877 for (octave_idx_type i = 0; i < nel; i++) |
| 4634 | 2878 if (lo_ieee_signbit (elem (i))) |
| 2879 return true; | |
| 4431 | 2880 } |
| 2881 else | |
| 2882 { | |
| 5275 | 2883 for (octave_idx_type i = 0; i < nel; i++) |
| 4634 | 2884 if (elem (i) < 0) |
| 2885 return true; | |
| 4431 | 2886 } |
| 2385 | 2887 |
| 2888 return false; | |
| 2889 } | |
| 2890 | |
|
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|
2891 bool |
|
935be827eaf8
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changeset
|
2892 Matrix::any_element_is_nan (void) const |
|
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diff
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|
2893 { |
|
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changeset
|
2894 octave_idx_type nel = nelem (); |
|
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diff
changeset
|
2895 |
|
935be827eaf8
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|
2896 for (octave_idx_type i = 0; i < nel; i++) |
|
935be827eaf8
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7803
diff
changeset
|
2897 { |
|
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diff
changeset
|
2898 double val = elem (i); |
|
935be827eaf8
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7803
diff
changeset
|
2899 if (xisnan (val)) |
|
935be827eaf8
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7803
diff
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|
2900 return true; |
|
935be827eaf8
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diff
changeset
|
2901 } |
|
935be827eaf8
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diff
changeset
|
2902 |
|
935be827eaf8
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diff
changeset
|
2903 return false; |
|
935be827eaf8
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diff
changeset
|
2904 } |
| 2385 | 2905 |
| 2906 bool | |
| 2907 Matrix::any_element_is_inf_or_nan (void) const | |
| 2908 { | |
| 5275 | 2909 octave_idx_type nel = nelem (); |
| 2910 | |
| 2911 for (octave_idx_type i = 0; i < nel; i++) | |
| 4634 | 2912 { |
| 2913 double val = elem (i); | |
| 2914 if (xisinf (val) || xisnan (val)) | |
| 2915 return true; | |
| 2916 } | |
| 2917 | |
| 2918 return false; | |
| 2385 | 2919 } |
| 2920 | |
| 2921 bool | |
| 5943 | 2922 Matrix::any_element_not_one_or_zero (void) const |
| 2923 { | |
| 2924 octave_idx_type nel = nelem (); | |
| 2925 | |
| 2926 for (octave_idx_type i = 0; i < nel; i++) | |
| 2927 { | |
| 2928 double val = elem (i); | |
| 2929 if (val != 0 && val != 1) | |
| 2930 return true; | |
| 2931 } | |
| 2932 | |
| 2933 return false; | |
| 2934 } | |
| 2935 | |
| 2936 bool | |
| 2385 | 2937 Matrix::all_elements_are_int_or_inf_or_nan (void) const |
| 2938 { | |
| 5275 | 2939 octave_idx_type nel = nelem (); |
| 2940 | |
| 2941 for (octave_idx_type i = 0; i < nel; i++) | |
| 4634 | 2942 { |
| 2943 double val = elem (i); | |
| 2944 if (xisnan (val) || D_NINT (val) == val) | |
| 2945 continue; | |
| 2946 else | |
| 2947 return false; | |
| 2948 } | |
| 2385 | 2949 |
| 2950 return true; | |
| 2951 } | |
| 2952 | |
| 1968 | 2953 // Return nonzero if any element of M is not an integer. Also extract |
| 2954 // the largest and smallest values and return them in MAX_VAL and MIN_VAL. | |
| 2955 | |
| 2385 | 2956 bool |
| 1968 | 2957 Matrix::all_integers (double& max_val, double& min_val) const |
| 2958 { | |
| 5275 | 2959 octave_idx_type nel = nelem (); |
| 4634 | 2960 |
| 2961 if (nel > 0) | |
| 1968 | 2962 { |
| 4634 | 2963 max_val = elem (0); |
| 2964 min_val = elem (0); | |
| 1968 | 2965 } |
| 2966 else | |
| 2385 | 2967 return false; |
| 1968 | 2968 |
| 5275 | 2969 for (octave_idx_type i = 0; i < nel; i++) |
| 4634 | 2970 { |
| 2971 double val = elem (i); | |
| 2972 | |
| 2973 if (val > max_val) | |
| 2974 max_val = val; | |
| 2975 | |
| 2976 if (val < min_val) | |
| 2977 min_val = val; | |
| 2978 | |
| 2979 if (D_NINT (val) != val) | |
| 2980 return false; | |
| 2981 } | |
| 2385 | 2982 |
| 2983 return true; | |
| 1968 | 2984 } |
| 2985 | |
| 2385 | 2986 bool |
| 1968 | 2987 Matrix::too_large_for_float (void) const |
| 2988 { | |
| 5275 | 2989 octave_idx_type nel = nelem (); |
| 2990 | |
| 2991 for (octave_idx_type i = 0; i < nel; i++) | |
| 4634 | 2992 { |
| 2993 double val = elem (i); | |
| 2994 | |
| 5389 | 2995 if (! (xisnan (val) || xisinf (val)) |
| 5387 | 2996 && fabs (val) > FLT_MAX) |
| 4634 | 2997 return true; |
| 2998 } | |
| 1968 | 2999 |
| 2385 | 3000 return false; |
| 1968 | 3001 } |
| 3002 | |
| 5775 | 3003 // FIXME Do these really belong here? Maybe they should be |
| 4015 | 3004 // in a base class? |
| 458 | 3005 |
| 2832 | 3006 boolMatrix |
| 4015 | 3007 Matrix::all (int dim) const |
| 458 | 3008 { |
| 4015 | 3009 MX_ALL_OP (dim); |
| 458 | 3010 } |
| 3011 | |
| 2832 | 3012 boolMatrix |
| 4015 | 3013 Matrix::any (int dim) const |
| 458 | 3014 { |
| 4015 | 3015 MX_ANY_OP (dim); |
| 458 | 3016 } |
| 3017 | |
| 3018 Matrix | |
| 3723 | 3019 Matrix::cumprod (int dim) const |
| 458 | 3020 { |
| 4015 | 3021 MX_CUMULATIVE_OP (Matrix, double, *=); |
| 458 | 3022 } |
| 3023 | |
| 3024 Matrix | |
| 3723 | 3025 Matrix::cumsum (int dim) const |
| 458 | 3026 { |
| 4015 | 3027 MX_CUMULATIVE_OP (Matrix, double, +=); |
| 458 | 3028 } |
| 3029 | |
| 3030 Matrix | |
| 3723 | 3031 Matrix::prod (int dim) const |
| 458 | 3032 { |
| 3864 | 3033 MX_REDUCTION_OP (Matrix, *=, 1.0, 1.0); |
| 458 | 3034 } |
| 3035 | |
| 3036 Matrix | |
| 3723 | 3037 Matrix::sum (int dim) const |
| 458 | 3038 { |
| 3864 | 3039 MX_REDUCTION_OP (Matrix, +=, 0.0, 0.0); |
| 458 | 3040 } |
| 3041 | |
| 3042 Matrix | |
| 3723 | 3043 Matrix::sumsq (int dim) const |
| 458 | 3044 { |
| 3864 | 3045 #define ROW_EXPR \ |
| 3046 double d = elem (i, j); \ | |
| 3047 retval.elem (i, 0) += d * d | |
| 3048 | |
| 3049 #define COL_EXPR \ | |
| 3050 double d = elem (i, j); \ | |
| 3051 retval.elem (0, j) += d * d | |
| 3052 | |
| 3053 MX_BASE_REDUCTION_OP (Matrix, ROW_EXPR, COL_EXPR, 0.0, 0.0); | |
| 3054 | |
| 3055 #undef ROW_EXPR | |
| 3056 #undef COL_EXPR | |
| 458 | 3057 } |
| 3058 | |
| 2385 | 3059 Matrix |
| 3060 Matrix::abs (void) const | |
| 3061 { | |
| 5275 | 3062 octave_idx_type nr = rows (); |
| 3063 octave_idx_type nc = cols (); | |
| 2385 | 3064 |
| 3065 Matrix retval (nr, nc); | |
| 3066 | |
| 5275 | 3067 for (octave_idx_type j = 0; j < nc; j++) |
| 3068 for (octave_idx_type i = 0; i < nr; i++) | |
| 2385 | 3069 retval (i, j) = fabs (elem (i, j)); |
| 3070 | |
| 3071 return retval; | |
| 3072 } | |
| 3073 | |
|
7620
36594d5bbe13
Move diag function into the octave_value class
David Bateman <dbateman@free.fr>
parents:
7544
diff
changeset
|
3074 Matrix |
| 5275 | 3075 Matrix::diag (octave_idx_type k) const |
| 458 | 3076 { |
|
7620
36594d5bbe13
Move diag function into the octave_value class
David Bateman <dbateman@free.fr>
parents:
7544
diff
changeset
|
3077 return MArray2<double>::diag (k); |
| 458 | 3078 } |
| 3079 | |
| 3080 ColumnVector | |
| 3081 Matrix::row_min (void) const | |
| 3082 { | |
| 5275 | 3083 Array<octave_idx_type> dummy_idx; |
| 4587 | 3084 return row_min (dummy_idx); |
| 458 | 3085 } |
| 3086 | |
| 3087 ColumnVector | |
| 5275 | 3088 Matrix::row_min (Array<octave_idx_type>& idx_arg) const |
| 458 | 3089 { |
| 3090 ColumnVector result; | |
| 3091 | |
| 5275 | 3092 octave_idx_type nr = rows (); |
| 3093 octave_idx_type nc = cols (); | |
| 458 | 3094 |
| 3095 if (nr > 0 && nc > 0) | |
| 3096 { | |
| 3097 result.resize (nr); | |
| 4587 | 3098 idx_arg.resize (nr); |
| 458 | 3099 |
| 5275 | 3100 for (octave_idx_type i = 0; i < nr; i++) |
| 458 | 3101 { |
| 5275 | 3102 octave_idx_type idx_j; |
| 4469 | 3103 |
| 3104 double tmp_min = octave_NaN; | |
| 3105 | |
| 3106 for (idx_j = 0; idx_j < nc; idx_j++) | |
| 2354 | 3107 { |
| 4469 | 3108 tmp_min = elem (i, idx_j); |
| 3109 | |
| 5389 | 3110 if (! xisnan (tmp_min)) |
| 4469 | 3111 break; |
| 3112 } | |
| 3113 | |
| 5275 | 3114 for (octave_idx_type j = idx_j+1; j < nc; j++) |
| 4469 | 3115 { |
| 3116 double tmp = elem (i, j); | |
| 3117 | |
| 5389 | 3118 if (xisnan (tmp)) |
| 4469 | 3119 continue; |
| 3120 else if (tmp < tmp_min) | |
| 2354 | 3121 { |
| 4469 | 3122 idx_j = j; |
| 3123 tmp_min = tmp; | |
| 2354 | 3124 } |
| 3125 } | |
| 3126 | |
| 4469 | 3127 result.elem (i) = tmp_min; |
| 5389 | 3128 idx_arg.elem (i) = xisnan (tmp_min) ? 0 : idx_j; |
| 458 | 3129 } |
| 3130 } | |
| 3131 | |
| 3132 return result; | |
| 3133 } | |
| 3134 | |
| 3135 ColumnVector | |
| 3136 Matrix::row_max (void) const | |
| 3137 { | |
| 5275 | 3138 Array<octave_idx_type> dummy_idx; |
| 4587 | 3139 return row_max (dummy_idx); |
| 458 | 3140 } |
| 3141 | |
| 3142 ColumnVector | |
| 5275 | 3143 Matrix::row_max (Array<octave_idx_type>& idx_arg) const |
| 458 | 3144 { |
| 3145 ColumnVector result; | |
| 3146 | |
| 5275 | 3147 octave_idx_type nr = rows (); |
| 3148 octave_idx_type nc = cols (); | |
| 458 | 3149 |
| 3150 if (nr > 0 && nc > 0) | |
| 3151 { | |
| 3152 result.resize (nr); | |
| 4587 | 3153 idx_arg.resize (nr); |
| 458 | 3154 |
| 5275 | 3155 for (octave_idx_type i = 0; i < nr; i++) |
| 458 | 3156 { |
| 5275 | 3157 octave_idx_type idx_j; |
| 4469 | 3158 |
| 3159 double tmp_max = octave_NaN; | |
| 3160 | |
| 3161 for (idx_j = 0; idx_j < nc; idx_j++) | |
| 2354 | 3162 { |
| 4469 | 3163 tmp_max = elem (i, idx_j); |
| 3164 | |
| 5389 | 3165 if (! xisnan (tmp_max)) |
| 4469 | 3166 break; |
| 3167 } | |
| 3168 | |
| 5275 | 3169 for (octave_idx_type j = idx_j+1; j < nc; j++) |
| 4469 | 3170 { |
| 3171 double tmp = elem (i, j); | |
| 3172 | |
| 5389 | 3173 if (xisnan (tmp)) |
| 4469 | 3174 continue; |
| 3175 else if (tmp > tmp_max) | |
| 2354 | 3176 { |
| 4469 | 3177 idx_j = j; |
| 3178 tmp_max = tmp; | |
| 2354 | 3179 } |
| 3180 } | |
| 3181 | |
| 4469 | 3182 result.elem (i) = tmp_max; |
| 5389 | 3183 idx_arg.elem (i) = xisnan (tmp_max) ? 0 : idx_j; |
| 458 | 3184 } |
| 3185 } | |
| 3186 | |
| 3187 return result; | |
| 3188 } | |
| 3189 | |
| 3190 RowVector | |
| 3191 Matrix::column_min (void) const | |
| 3192 { | |
| 5275 | 3193 Array<octave_idx_type> dummy_idx; |
| 4587 | 3194 return column_min (dummy_idx); |
| 458 | 3195 } |
| 2354 | 3196 |
| 458 | 3197 RowVector |
| 5275 | 3198 Matrix::column_min (Array<octave_idx_type>& idx_arg) const |
| 458 | 3199 { |
| 3200 RowVector result; | |
| 3201 | |
| 5275 | 3202 octave_idx_type nr = rows (); |
| 3203 octave_idx_type nc = cols (); | |
| 458 | 3204 |
| 3205 if (nr > 0 && nc > 0) | |
| 3206 { | |
| 3207 result.resize (nc); | |
| 4587 | 3208 idx_arg.resize (nc); |
| 458 | 3209 |
| 5275 | 3210 for (octave_idx_type j = 0; j < nc; j++) |
| 458 | 3211 { |
| 5275 | 3212 octave_idx_type idx_i; |
| 4469 | 3213 |
| 3214 double tmp_min = octave_NaN; | |
| 3215 | |
| 3216 for (idx_i = 0; idx_i < nr; idx_i++) | |
| 2354 | 3217 { |
| 4469 | 3218 tmp_min = elem (idx_i, j); |
| 3219 | |
| 5389 | 3220 if (! xisnan (tmp_min)) |
| 4469 | 3221 break; |
| 3222 } | |
| 3223 | |
| 5275 | 3224 for (octave_idx_type i = idx_i+1; i < nr; i++) |
| 4469 | 3225 { |
| 3226 double tmp = elem (i, j); | |
| 3227 | |
| 5389 | 3228 if (xisnan (tmp)) |
| 4469 | 3229 continue; |
| 3230 else if (tmp < tmp_min) | |
| 2354 | 3231 { |
| 4469 | 3232 idx_i = i; |
| 3233 tmp_min = tmp; | |
| 2354 | 3234 } |
| 3235 } | |
| 3236 | |
| 4469 | 3237 result.elem (j) = tmp_min; |
| 5389 | 3238 idx_arg.elem (j) = xisnan (tmp_min) ? 0 : idx_i; |
| 458 | 3239 } |
| 3240 } | |
| 3241 | |
| 3242 return result; | |
| 3243 } | |
| 3244 | |
| 2354 | 3245 RowVector |
| 3246 Matrix::column_max (void) const | |
| 3247 { | |
| 5275 | 3248 Array<octave_idx_type> dummy_idx; |
| 4587 | 3249 return column_max (dummy_idx); |
| 2354 | 3250 } |
| 458 | 3251 |
| 3252 RowVector | |
| 5275 | 3253 Matrix::column_max (Array<octave_idx_type>& idx_arg) const |
| 458 | 3254 { |
| 3255 RowVector result; | |
| 3256 | |
| 5275 | 3257 octave_idx_type nr = rows (); |
| 3258 octave_idx_type nc = cols (); | |
| 458 | 3259 |
| 3260 if (nr > 0 && nc > 0) | |
| 3261 { | |
| 3262 result.resize (nc); | |
| 4587 | 3263 idx_arg.resize (nc); |
| 458 | 3264 |
| 5275 | 3265 for (octave_idx_type j = 0; j < nc; j++) |
| 458 | 3266 { |
| 5275 | 3267 octave_idx_type idx_i; |
| 4469 | 3268 |
| 3269 double tmp_max = octave_NaN; | |
| 3270 | |
| 3271 for (idx_i = 0; idx_i < nr; idx_i++) | |
| 2354 | 3272 { |
| 4469 | 3273 tmp_max = elem (idx_i, j); |
| 3274 | |
| 5389 | 3275 if (! xisnan (tmp_max)) |
| 4469 | 3276 break; |
| 3277 } | |
| 3278 | |
| 5275 | 3279 for (octave_idx_type i = idx_i+1; i < nr; i++) |
| 4469 | 3280 { |
| 3281 double tmp = elem (i, j); | |
| 3282 | |
| 5389 | 3283 if (xisnan (tmp)) |
| 4469 | 3284 continue; |
| 3285 else if (tmp > tmp_max) | |
| 2354 | 3286 { |
| 4469 | 3287 idx_i = i; |
| 3288 tmp_max = tmp; | |
| 2354 | 3289 } |
| 3290 } | |
| 3291 | |
| 4469 | 3292 result.elem (j) = tmp_max; |
| 5389 | 3293 idx_arg.elem (j) = xisnan (tmp_max) ? 0 : idx_i; |
| 458 | 3294 } |
| 3295 } | |
| 3296 | |
| 3297 return result; | |
| 3298 } | |
| 3299 | |
| 3504 | 3300 std::ostream& |
| 3301 operator << (std::ostream& os, const Matrix& a) | |
| 458 | 3302 { |
| 5275 | 3303 for (octave_idx_type i = 0; i < a.rows (); i++) |
| 458 | 3304 { |
| 5275 | 3305 for (octave_idx_type j = 0; j < a.cols (); j++) |
| 4130 | 3306 { |
| 3307 os << " "; | |
| 3308 octave_write_double (os, a.elem (i, j)); | |
| 3309 } | |
| 458 | 3310 os << "\n"; |
| 3311 } | |
| 3312 return os; | |
| 3313 } | |
| 3314 | |
| 3504 | 3315 std::istream& |
| 3316 operator >> (std::istream& is, Matrix& a) | |
| 458 | 3317 { |
| 5275 | 3318 octave_idx_type nr = a.rows (); |
| 3319 octave_idx_type nc = a.cols (); | |
| 458 | 3320 |
| 3321 if (nr < 1 || nc < 1) | |
| 3504 | 3322 is.clear (std::ios::badbit); |
| 458 | 3323 else |
| 3324 { | |
| 3325 double tmp; | |
| 5275 | 3326 for (octave_idx_type i = 0; i < nr; i++) |
| 3327 for (octave_idx_type j = 0; j < nc; j++) | |
| 458 | 3328 { |
| 4130 | 3329 tmp = octave_read_double (is); |
| 458 | 3330 if (is) |
| 3331 a.elem (i, j) = tmp; | |
| 3332 else | |
| 2795 | 3333 goto done; |
| 458 | 3334 } |
| 3335 } | |
| 3336 | |
| 2795 | 3337 done: |
| 3338 | |
| 458 | 3339 return is; |
| 3340 } | |
| 3341 | |
| 1819 | 3342 Matrix |
| 3343 Givens (double x, double y) | |
| 3344 { | |
| 3345 double cc, s, temp_r; | |
| 3346 | |
| 3887 | 3347 F77_FUNC (dlartg, DLARTG) (x, y, cc, s, temp_r); |
| 1819 | 3348 |
| 3349 Matrix g (2, 2); | |
| 3350 | |
| 3351 g.elem (0, 0) = cc; | |
| 3352 g.elem (1, 1) = cc; | |
| 3353 g.elem (0, 1) = s; | |
| 3354 g.elem (1, 0) = -s; | |
| 3355 | |
| 3356 return g; | |
| 3357 } | |
| 3358 | |
| 3359 Matrix | |
| 3360 Sylvester (const Matrix& a, const Matrix& b, const Matrix& c) | |
| 3361 { | |
| 3362 Matrix retval; | |
| 3363 | |
| 5775 | 3364 // FIXME -- need to check that a, b, and c are all the same |
| 1819 | 3365 // size. |
| 3366 | |
| 3367 // Compute Schur decompositions. | |
| 3368 | |
| 3369 SCHUR as (a, "U"); | |
| 3370 SCHUR bs (b, "U"); | |
| 3371 | |
| 3372 // Transform c to new coordinates. | |
| 3373 | |
| 3374 Matrix ua = as.unitary_matrix (); | |
| 3375 Matrix sch_a = as.schur_matrix (); | |
| 3376 | |
| 3377 Matrix ub = bs.unitary_matrix (); | |
| 3378 Matrix sch_b = bs.schur_matrix (); | |
| 3379 | |
| 3380 Matrix cx = ua.transpose () * c * ub; | |
| 3381 | |
| 3382 // Solve the sylvester equation, back-transform, and return the | |
| 3383 // solution. | |
| 3384 | |
| 5275 | 3385 octave_idx_type a_nr = a.rows (); |
| 3386 octave_idx_type b_nr = b.rows (); | |
| 1819 | 3387 |
| 3388 double scale; | |
| 5275 | 3389 octave_idx_type info; |
| 1819 | 3390 |
| 1950 | 3391 double *pa = sch_a.fortran_vec (); |
| 3392 double *pb = sch_b.fortran_vec (); | |
| 3393 double *px = cx.fortran_vec (); | |
| 3394 | |
| 4552 | 3395 F77_XFCN (dtrsyl, DTRSYL, (F77_CONST_CHAR_ARG2 ("N", 1), |
| 3396 F77_CONST_CHAR_ARG2 ("N", 1), | |
| 3397 1, a_nr, b_nr, pa, a_nr, pb, | |
| 3398 b_nr, px, a_nr, scale, info | |
| 3399 F77_CHAR_ARG_LEN (1) | |
| 3400 F77_CHAR_ARG_LEN (1))); | |
| 1950 | 3401 |
| 3402 | |
|
7482
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
3403 // FIXME -- check info? |
| 1819 | 3404 |
|
7482
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
3405 retval = -ua*cx*ub.transpose (); |
| 1819 | 3406 |
| 3407 return retval; | |
| 3408 } | |
| 3409 | |
| 2828 | 3410 // matrix by matrix -> matrix operations |
| 3411 | |
| 6162 | 3412 /* Simple Dot Product, Matrix-Vector and Matrix-Matrix Unit tests |
| 3413 %!assert([1 2 3] * [ 4 ; 5 ; 6], 32, 1e-14) | |
| 3414 %!assert([1 2 ; 3 4 ] * [5 ; 6], [17 ; 39 ], 1e-14) | |
| 3415 %!assert([1 2 ; 3 4 ] * [5 6 ; 7 8], [19 22; 43 50], 1e-14) | |
| 3416 */ | |
| 3417 | |
| 3418 /* Test some simple identities | |
| 3419 %!shared M, cv, rv | |
| 3420 %! M = randn(10,10); | |
| 3421 %! cv = randn(10,1); | |
| 3422 %! rv = randn(1,10); | |
| 3423 %!assert([M*cv,M*cv],M*[cv,cv],1e-14) | |
| 3424 %!assert([rv*M;rv*M],[rv;rv]*M,1e-14) | |
| 3425 %!assert(2*rv*cv,[rv,rv]*[cv;cv],1e-14) | |
| 3426 */ | |
| 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 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
|
3429 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
|
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 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
|
3432 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
|
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 |
|
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 // 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
|
3436 |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3437 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
|
3438 xgemm (bool transa, const Matrix& a, bool transb, const Matrix& b) |
| 2828 | 3439 { |
| 3440 Matrix retval; | |
| 3441 | |
|
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
|
3442 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
|
3443 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
|
3444 |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3445 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
|
3446 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
|
3447 |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3448 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
|
3449 gripe_nonconformant ("operator *", a_nr, a_nc, b_nr, b_nc); |
| 2828 | 3450 else |
| 3451 { | |
|
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
|
3452 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
|
3453 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
|
3454 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
|
3455 { |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3456 octave_idx_type lda = a.rows (); |
|
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 retval.resize (a_nr, b_nc); |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3459 double *c = retval.fortran_vec (); |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3460 |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3461 const char *ctransa = get_blas_trans_arg (transa); |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3462 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
|
3463 F77_CONST_CHAR_ARG2 (ctransa, 1), |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3464 a_nr, a_nc, 1.0, |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3465 a.data (), lda, 0.0, c, a_nr |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3466 F77_CHAR_ARG_LEN (1) |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3467 F77_CHAR_ARG_LEN (1))); |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3468 for (int j = 0; j < a_nr; j++) |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3469 for (int i = 0; i < j; i++) |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3470 retval.xelem (j,i) = retval.xelem (i,j); |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3471 |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3472 } |
| 2828 | 3473 else |
| 3474 { | |
|
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
|
3475 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
|
3476 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
|
3477 |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3478 retval.resize (a_nr, b_nc); |
| 2828 | 3479 double *c = retval.fortran_vec (); |
| 3480 | |
|
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
|
3481 if (b_nc == 1) |
| 5983 | 3482 { |
|
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
|
3483 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
|
3484 F77_FUNC (xddot, XDDOT) (a_nc, a.data (), 1, b.data (), 1, *c); |
| 5983 | 3485 else |
| 6390 | 3486 { |
|
7800
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3487 const char *ctransa = get_blas_trans_arg (transa); |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3488 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
|
3489 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
|
3490 b.data (), 1, 0.0, c, 1 |
| 6390 | 3491 F77_CHAR_ARG_LEN (1))); |
| 3492 } | |
| 5983 | 3493 } |
|
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
|
3494 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
|
3495 { |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3496 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
|
3497 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
|
3498 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
|
3499 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
|
3500 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
|
3501 } |
| 5983 | 3502 else |
| 6390 | 3503 { |
|
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
|
3504 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
|
3505 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
|
3506 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
|
3507 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
|
3508 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
|
3509 lda, b.data (), ldb, 0.0, c, a_nr |
| 6390 | 3510 F77_CHAR_ARG_LEN (1) |
| 3511 F77_CHAR_ARG_LEN (1))); | |
| 3512 } | |
| 2828 | 3513 } |
| 3514 } | |
| 3515 | |
| 3516 return retval; | |
| 3517 } | |
| 3518 | |
|
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
|
3519 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
|
3520 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
|
3521 { |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3522 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
|
3523 } |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3524 |
| 5775 | 3525 // FIXME -- it would be nice to share code among the min/max |
| 4309 | 3526 // functions below. |
| 3527 | |
| 3528 #define EMPTY_RETURN_CHECK(T) \ | |
| 3529 if (nr == 0 || nc == 0) \ | |
| 3530 return T (nr, nc); | |
| 3531 | |
| 3532 Matrix | |
| 3533 min (double d, const Matrix& m) | |
| 3534 { | |
| 5275 | 3535 octave_idx_type nr = m.rows (); |
| 3536 octave_idx_type nc = m.columns (); | |
| 4309 | 3537 |
| 3538 EMPTY_RETURN_CHECK (Matrix); | |
| 3539 | |
| 3540 Matrix result (nr, nc); | |
| 3541 | |
| 5275 | 3542 for (octave_idx_type j = 0; j < nc; j++) |
| 3543 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3544 { |
| 3545 OCTAVE_QUIT; | |
| 3546 result (i, j) = xmin (d, m (i, j)); | |
| 3547 } | |
| 3548 | |
| 3549 return result; | |
| 3550 } | |
| 3551 | |
| 3552 Matrix | |
| 3553 min (const Matrix& m, double d) | |
| 3554 { | |
| 5275 | 3555 octave_idx_type nr = m.rows (); |
| 3556 octave_idx_type nc = m.columns (); | |
| 4309 | 3557 |
| 3558 EMPTY_RETURN_CHECK (Matrix); | |
| 3559 | |
| 3560 Matrix result (nr, nc); | |
| 3561 | |
| 5275 | 3562 for (octave_idx_type j = 0; j < nc; j++) |
| 3563 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3564 { |
| 3565 OCTAVE_QUIT; | |
| 3566 result (i, j) = xmin (m (i, j), d); | |
| 3567 } | |
| 3568 | |
| 3569 return result; | |
| 3570 } | |
| 3571 | |
| 3572 Matrix | |
| 3573 min (const Matrix& a, const Matrix& b) | |
| 3574 { | |
| 5275 | 3575 octave_idx_type nr = a.rows (); |
| 3576 octave_idx_type nc = a.columns (); | |
| 4309 | 3577 |
| 3578 if (nr != b.rows () || nc != b.columns ()) | |
| 3579 { | |
| 3580 (*current_liboctave_error_handler) | |
| 3581 ("two-arg min expecting args of same size"); | |
| 3582 return Matrix (); | |
| 3583 } | |
| 3584 | |
| 3585 EMPTY_RETURN_CHECK (Matrix); | |
| 3586 | |
| 3587 Matrix result (nr, nc); | |
| 3588 | |
| 5275 | 3589 for (octave_idx_type j = 0; j < nc; j++) |
| 3590 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3591 { |
| 3592 OCTAVE_QUIT; | |
| 3593 result (i, j) = xmin (a (i, j), b (i, j)); | |
| 3594 } | |
| 3595 | |
| 3596 return result; | |
| 3597 } | |
| 3598 | |
| 3599 Matrix | |
| 3600 max (double d, const Matrix& m) | |
| 3601 { | |
| 5275 | 3602 octave_idx_type nr = m.rows (); |
| 3603 octave_idx_type nc = m.columns (); | |
| 4309 | 3604 |
| 3605 EMPTY_RETURN_CHECK (Matrix); | |
| 3606 | |
| 3607 Matrix result (nr, nc); | |
| 3608 | |
| 5275 | 3609 for (octave_idx_type j = 0; j < nc; j++) |
| 3610 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3611 { |
| 3612 OCTAVE_QUIT; | |
| 3613 result (i, j) = xmax (d, m (i, j)); | |
| 3614 } | |
| 3615 | |
| 3616 return result; | |
| 3617 } | |
| 3618 | |
| 3619 Matrix | |
| 3620 max (const Matrix& m, double d) | |
| 3621 { | |
| 5275 | 3622 octave_idx_type nr = m.rows (); |
| 3623 octave_idx_type nc = m.columns (); | |
| 4309 | 3624 |
| 3625 EMPTY_RETURN_CHECK (Matrix); | |
| 3626 | |
| 3627 Matrix result (nr, nc); | |
| 3628 | |
| 5275 | 3629 for (octave_idx_type j = 0; j < nc; j++) |
| 3630 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3631 { |
| 3632 OCTAVE_QUIT; | |
| 3633 result (i, j) = xmax (m (i, j), d); | |
| 3634 } | |
| 3635 | |
| 3636 return result; | |
| 3637 } | |
| 3638 | |
| 3639 Matrix | |
| 3640 max (const Matrix& a, const Matrix& b) | |
| 3641 { | |
| 5275 | 3642 octave_idx_type nr = a.rows (); |
| 3643 octave_idx_type nc = a.columns (); | |
| 4309 | 3644 |
| 3645 if (nr != b.rows () || nc != b.columns ()) | |
| 3646 { | |
| 3647 (*current_liboctave_error_handler) | |
| 3648 ("two-arg max expecting args of same size"); | |
| 3649 return Matrix (); | |
| 3650 } | |
| 3651 | |
| 3652 EMPTY_RETURN_CHECK (Matrix); | |
| 3653 | |
| 3654 Matrix result (nr, nc); | |
| 3655 | |
| 5275 | 3656 for (octave_idx_type j = 0; j < nc; j++) |
| 3657 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3658 { |
| 3659 OCTAVE_QUIT; | |
| 3660 result (i, j) = xmax (a (i, j), b (i, j)); | |
| 3661 } | |
| 3662 | |
| 3663 return result; | |
| 3664 } | |
| 3665 | |
| 2870 | 3666 MS_CMP_OPS(Matrix, , double, ) |
| 3504 | 3667 MS_BOOL_OPS(Matrix, double, 0.0) |
| 2870 | 3668 |
| 3669 SM_CMP_OPS(double, , Matrix, ) | |
| 3504 | 3670 SM_BOOL_OPS(double, Matrix, 0.0) |
| 2870 | 3671 |
| 3672 MM_CMP_OPS(Matrix, , Matrix, ) | |
| 3504 | 3673 MM_BOOL_OPS(Matrix, Matrix, 0.0) |
| 2870 | 3674 |
| 458 | 3675 /* |
| 3676 ;;; Local Variables: *** | |
| 3677 ;;; mode: C++ *** | |
| 3678 ;;; End: *** | |
| 3679 */ |