Mercurial > hg > octave-lyh
annotate liboctave/dMatrix.cc @ 8367:445d27d79f4e
support permutation matrix objects
| author | Jaroslav Hajek <highegg@gmail.com> |
|---|---|
| date | Thu, 04 Dec 2008 08:31:56 +0100 |
| parents | e02242c54c49 |
| children | e3c9102431a9 |
| rev | line source |
|---|---|
| 1993 | 1 // Matrix manipulations. |
| 458 | 2 /* |
| 3 | |
| 7017 | 4 Copyright (C) 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, |
| 5 2003, 2004, 2005, 2006, 2007 John W. Eaton | |
| 7803 | 6 Copyright (C) 2008 Jaroslav Hajek |
| 458 | 7 |
| 8 This file is part of Octave. | |
| 9 | |
| 10 Octave is free software; you can redistribute it and/or modify it | |
| 11 under the terms of the GNU General Public License as published by the | |
| 7016 | 12 Free Software Foundation; either version 3 of the License, or (at your |
| 13 option) any later version. | |
| 458 | 14 |
| 15 Octave is distributed in the hope that it will be useful, but WITHOUT | |
| 16 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
| 17 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
| 18 for more details. | |
| 19 | |
| 20 You should have received a copy of the GNU General Public License | |
| 7016 | 21 along with Octave; see the file COPYING. If not, see |
| 22 <http://www.gnu.org/licenses/>. | |
| 458 | 23 |
| 24 */ | |
| 25 | |
| 26 #ifdef HAVE_CONFIG_H | |
| 1192 | 27 #include <config.h> |
| 458 | 28 #endif |
| 29 | |
| 1367 | 30 #include <cfloat> |
| 31 | |
| 3503 | 32 #include <iostream> |
| 6209 | 33 #include <vector> |
| 1367 | 34 |
| 4669 | 35 #include "Array-util.h" |
| 2317 | 36 #include "byte-swap.h" |
| 2828 | 37 #include "dMatrix.h" |
| 1819 | 38 #include "dbleAEPBAL.h" |
| 8335 | 39 #include "DET.h" |
| 1819 | 40 #include "dbleSCHUR.h" |
| 740 | 41 #include "dbleSVD.h" |
| 6207 | 42 #include "dbleCHOL.h" |
| 1847 | 43 #include "f77-fcn.h" |
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44 #include "functor.h" |
| 458 | 45 #include "lo-error.h" |
| 2354 | 46 #include "lo-ieee.h" |
| 47 #include "lo-mappers.h" | |
| 1968 | 48 #include "lo-utils.h" |
| 1367 | 49 #include "mx-base.h" |
| 2828 | 50 #include "mx-m-dm.h" |
| 3176 | 51 #include "mx-dm-m.h" |
| 1367 | 52 #include "mx-inlines.cc" |
| 1650 | 53 #include "oct-cmplx.h" |
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54 #include "oct-norm.h" |
| 4153 | 55 #include "quit.h" |
| 458 | 56 |
| 4773 | 57 #if defined (HAVE_FFTW3) |
| 3827 | 58 #include "oct-fftw.h" |
| 59 #endif | |
| 60 | |
| 458 | 61 // Fortran functions we call. |
| 62 | |
| 63 extern "C" | |
| 64 { | |
| 7478 | 65 F77_RET_T |
| 7477 | 66 F77_FUNC (xilaenv, XILAENV) (const octave_idx_type&, F77_CONST_CHAR_ARG_DECL, |
| 67 F77_CONST_CHAR_ARG_DECL, | |
| 68 const octave_idx_type&, const octave_idx_type&, | |
| 7478 | 69 const octave_idx_type&, const octave_idx_type&, |
| 70 octave_idx_type& | |
| 71 F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); | |
| 7476 | 72 |
| 4552 | 73 F77_RET_T |
| 74 F77_FUNC (dgebal, DGEBAL) (F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 75 const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type&, |
| 76 octave_idx_type&, double*, octave_idx_type& | |
| 4552 | 77 F77_CHAR_ARG_LEN_DECL); |
| 78 | |
| 79 F77_RET_T | |
| 80 F77_FUNC (dgebak, DGEBAK) (F77_CONST_CHAR_ARG_DECL, | |
| 81 F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 82 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, double*, |
| 83 const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type& | |
| 4552 | 84 F77_CHAR_ARG_LEN_DECL |
| 85 F77_CHAR_ARG_LEN_DECL); | |
| 86 | |
| 87 | |
| 88 F77_RET_T | |
| 89 F77_FUNC (dgemm, DGEMM) (F77_CONST_CHAR_ARG_DECL, | |
| 90 F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 91 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
| 92 const double&, const double*, const octave_idx_type&, | |
| 93 const double*, const octave_idx_type&, const double&, | |
| 94 double*, const octave_idx_type& | |
| 4552 | 95 F77_CHAR_ARG_LEN_DECL |
| 96 F77_CHAR_ARG_LEN_DECL); | |
| 97 | |
| 98 F77_RET_T | |
| 5983 | 99 F77_FUNC (dgemv, DGEMV) (F77_CONST_CHAR_ARG_DECL, |
| 100 const octave_idx_type&, const octave_idx_type&, const double&, | |
| 101 const double*, const octave_idx_type&, const double*, | |
| 102 const octave_idx_type&, const double&, double*, | |
| 103 const octave_idx_type& | |
| 104 F77_CHAR_ARG_LEN_DECL); | |
| 105 | |
| 106 F77_RET_T | |
| 107 F77_FUNC (xddot, XDDOT) (const octave_idx_type&, const double*, const octave_idx_type&, | |
| 108 const double*, const octave_idx_type&, double&); | |
| 109 | |
| 110 F77_RET_T | |
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111 F77_FUNC (dsyrk, DSYRK) (F77_CONST_CHAR_ARG_DECL, |
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112 F77_CONST_CHAR_ARG_DECL, |
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113 const octave_idx_type&, const octave_idx_type&, |
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114 const double&, const double*, const octave_idx_type&, |
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115 const double&, double*, const octave_idx_type& |
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116 F77_CHAR_ARG_LEN_DECL |
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117 F77_CHAR_ARG_LEN_DECL); |
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118 |
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119 F77_RET_T |
| 5275 | 120 F77_FUNC (dgetrf, DGETRF) (const octave_idx_type&, const octave_idx_type&, double*, const octave_idx_type&, |
| 121 octave_idx_type*, octave_idx_type&); | |
| 4329 | 122 |
| 4552 | 123 F77_RET_T |
| 5275 | 124 F77_FUNC (dgetrs, DGETRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, |
| 125 const double*, const octave_idx_type&, | |
| 126 const octave_idx_type*, double*, const octave_idx_type&, octave_idx_type& | |
| 4552 | 127 F77_CHAR_ARG_LEN_DECL); |
| 128 | |
| 129 F77_RET_T | |
| 5275 | 130 F77_FUNC (dgetri, DGETRI) (const octave_idx_type&, double*, const octave_idx_type&, const octave_idx_type*, |
| 131 double*, const octave_idx_type&, octave_idx_type&); | |
| 4552 | 132 |
| 133 F77_RET_T | |
| 5275 | 134 F77_FUNC (dgecon, DGECON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, double*, |
| 135 const octave_idx_type&, const double&, double&, | |
| 136 double*, octave_idx_type*, octave_idx_type& | |
| 4552 | 137 F77_CHAR_ARG_LEN_DECL); |
| 138 | |
| 139 F77_RET_T | |
| 7072 | 140 F77_FUNC (dgelsy, DGELSY) (const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
| 141 double*, const octave_idx_type&, double*, | |
| 142 const octave_idx_type&, octave_idx_type*, double&, octave_idx_type&, | |
| 143 double*, const octave_idx_type&, octave_idx_type&); | |
| 144 | |
| 145 F77_RET_T | |
| 146 F77_FUNC (dgelsd, DGELSD) (const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, | |
| 5275 | 147 double*, const octave_idx_type&, double*, |
| 7071 | 148 const octave_idx_type&, double*, double&, octave_idx_type&, |
| 7072 | 149 double*, const octave_idx_type&, octave_idx_type*, |
| 150 octave_idx_type&); | |
| 458 | 151 |
| 5785 | 152 F77_RET_T |
| 153 F77_FUNC (dpotrf, DPOTRF) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 154 double *, const octave_idx_type&, | |
| 155 octave_idx_type& F77_CHAR_ARG_LEN_DECL); | |
| 156 | |
| 157 F77_RET_T | |
| 158 F77_FUNC (dpocon, DPOCON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 159 double*, const octave_idx_type&, const double&, | |
| 160 double&, double*, octave_idx_type*, | |
| 161 octave_idx_type& F77_CHAR_ARG_LEN_DECL); | |
| 162 F77_RET_T | |
| 163 F77_FUNC (dpotrs, DPOTRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 164 const octave_idx_type&, const double*, | |
| 165 const octave_idx_type&, double*, | |
| 166 const octave_idx_type&, octave_idx_type& | |
| 167 F77_CHAR_ARG_LEN_DECL); | |
| 168 | |
| 169 F77_RET_T | |
| 6207 | 170 F77_FUNC (dtrtri, DTRTRI) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, |
| 171 const octave_idx_type&, const double*, | |
| 172 const octave_idx_type&, octave_idx_type& | |
| 173 F77_CHAR_ARG_LEN_DECL | |
| 174 F77_CHAR_ARG_LEN_DECL); | |
| 175 F77_RET_T | |
| 5785 | 176 F77_FUNC (dtrcon, DTRCON) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, |
| 177 F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 178 const double*, const octave_idx_type&, double&, | |
| 179 double*, octave_idx_type*, octave_idx_type& | |
| 180 F77_CHAR_ARG_LEN_DECL | |
| 181 F77_CHAR_ARG_LEN_DECL | |
| 182 F77_CHAR_ARG_LEN_DECL); | |
| 183 F77_RET_T | |
| 184 F77_FUNC (dtrtrs, DTRTRS) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, | |
| 185 F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 186 const octave_idx_type&, const double*, | |
| 187 const octave_idx_type&, double*, | |
| 188 const octave_idx_type&, octave_idx_type& | |
| 189 F77_CHAR_ARG_LEN_DECL | |
| 190 F77_CHAR_ARG_LEN_DECL | |
| 191 F77_CHAR_ARG_LEN_DECL); | |
| 192 | |
| 1360 | 193 // Note that the original complex fft routines were not written for |
| 194 // double complex arguments. They have been modified by adding an | |
| 195 // implicit double precision (a-h,o-z) statement at the beginning of | |
| 196 // each subroutine. | |
| 458 | 197 |
| 4552 | 198 F77_RET_T |
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199 F77_FUNC (zffti, ZFFTI) (const octave_idx_type&, Complex*); |
| 4552 | 200 |
| 201 F77_RET_T | |
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202 F77_FUNC (zfftf, ZFFTF) (const octave_idx_type&, Complex*, Complex*); |
| 4552 | 203 |
| 204 F77_RET_T | |
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205 F77_FUNC (zfftb, ZFFTB) (const octave_idx_type&, Complex*, Complex*); |
| 4552 | 206 |
| 207 F77_RET_T | |
| 208 F77_FUNC (dlartg, DLARTG) (const double&, const double&, double&, | |
| 209 double&, double&); | |
| 210 | |
| 211 F77_RET_T | |
| 212 F77_FUNC (dtrsyl, DTRSYL) (F77_CONST_CHAR_ARG_DECL, | |
| 213 F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 214 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
| 215 const double*, const octave_idx_type&, const double*, | |
| 216 const octave_idx_type&, const double*, const octave_idx_type&, | |
| 217 double&, octave_idx_type& | |
| 4552 | 218 F77_CHAR_ARG_LEN_DECL |
| 219 F77_CHAR_ARG_LEN_DECL); | |
| 220 | |
| 221 F77_RET_T | |
| 5275 | 222 F77_FUNC (xdlange, XDLANGE) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, |
| 223 const octave_idx_type&, const double*, | |
| 224 const octave_idx_type&, double*, double& | |
| 4552 | 225 F77_CHAR_ARG_LEN_DECL); |
| 458 | 226 } |
| 227 | |
| 1360 | 228 // Matrix class. |
| 458 | 229 |
| 2349 | 230 Matrix::Matrix (const RowVector& rv) |
| 231 : MArray2<double> (1, rv.length (), 0.0) | |
| 232 { | |
| 5275 | 233 for (octave_idx_type i = 0; i < rv.length (); i++) |
| 2349 | 234 elem (0, i) = rv.elem (i); |
| 235 } | |
| 236 | |
| 237 Matrix::Matrix (const ColumnVector& cv) | |
| 238 : MArray2<double> (cv.length (), 1, 0.0) | |
| 239 { | |
| 5275 | 240 for (octave_idx_type i = 0; i < cv.length (); i++) |
| 2349 | 241 elem (i, 0) = cv.elem (i); |
| 242 } | |
| 243 | |
| 458 | 244 Matrix::Matrix (const DiagMatrix& a) |
| 1214 | 245 : MArray2<double> (a.rows (), a.cols (), 0.0) |
| 458 | 246 { |
| 5275 | 247 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 248 elem (i, i) = a.elem (i, i); |
| 249 } | |
| 250 | |
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251 Matrix::Matrix (const PermMatrix& a) |
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252 : MArray2<double> (a.rows (), a.cols (), 0.0) |
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253 { |
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254 const Array<octave_idx_type> ia (a); |
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255 octave_idx_type len = a.rows (); |
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256 if (a.is_col_perm ()) |
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257 for (octave_idx_type i = 0; i < len; i++) |
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258 elem (ia(i), i) = 1.0; |
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259 else |
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260 for (octave_idx_type i = 0; i < len; i++) |
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261 elem (i, ia(i)) = 1.0; |
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262 } |
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263 |
| 5775 | 264 // FIXME -- could we use a templated mixed-type copy function |
| 1574 | 265 // here? |
| 266 | |
| 2828 | 267 Matrix::Matrix (const boolMatrix& a) |
| 268 : MArray2<double> (a.rows (), a.cols ()) | |
| 269 { | |
| 5275 | 270 for (octave_idx_type i = 0; i < a.rows (); i++) |
| 271 for (octave_idx_type j = 0; j < a.cols (); j++) | |
| 2828 | 272 elem (i, j) = a.elem (i, j); |
| 273 } | |
| 274 | |
| 1574 | 275 Matrix::Matrix (const charMatrix& a) |
| 276 : MArray2<double> (a.rows (), a.cols ()) | |
| 277 { | |
| 5275 | 278 for (octave_idx_type i = 0; i < a.rows (); i++) |
| 279 for (octave_idx_type j = 0; j < a.cols (); j++) | |
| 1574 | 280 elem (i, j) = a.elem (i, j); |
| 281 } | |
| 282 | |
| 2385 | 283 bool |
| 458 | 284 Matrix::operator == (const Matrix& a) const |
| 285 { | |
| 286 if (rows () != a.rows () || cols () != a.cols ()) | |
| 2385 | 287 return false; |
| 458 | 288 |
| 3769 | 289 return mx_inline_equal (data (), a.data (), length ()); |
| 458 | 290 } |
| 291 | |
| 2385 | 292 bool |
| 458 | 293 Matrix::operator != (const Matrix& a) const |
| 294 { | |
| 295 return !(*this == a); | |
| 296 } | |
| 297 | |
| 3354 | 298 bool |
| 299 Matrix::is_symmetric (void) const | |
| 300 { | |
| 301 if (is_square () && rows () > 0) | |
| 302 { | |
| 5275 | 303 for (octave_idx_type i = 0; i < rows (); i++) |
| 304 for (octave_idx_type j = i+1; j < cols (); j++) | |
| 3354 | 305 if (elem (i, j) != elem (j, i)) |
| 306 return false; | |
| 307 | |
| 308 return true; | |
| 309 } | |
| 310 | |
| 311 return false; | |
| 312 } | |
| 313 | |
| 458 | 314 Matrix& |
| 5275 | 315 Matrix::insert (const Matrix& a, octave_idx_type r, octave_idx_type c) |
| 458 | 316 { |
| 1561 | 317 Array2<double>::insert (a, r, c); |
| 458 | 318 return *this; |
| 319 } | |
| 320 | |
| 321 Matrix& | |
| 5275 | 322 Matrix::insert (const RowVector& a, octave_idx_type r, octave_idx_type c) |
| 458 | 323 { |
| 5275 | 324 octave_idx_type a_len = a.length (); |
| 4316 | 325 |
| 1698 | 326 if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ()) |
| 458 | 327 { |
| 328 (*current_liboctave_error_handler) ("range error for insert"); | |
| 329 return *this; | |
| 330 } | |
| 331 | |
| 4316 | 332 if (a_len > 0) |
| 333 { | |
| 334 make_unique (); | |
| 335 | |
| 5275 | 336 for (octave_idx_type i = 0; i < a_len; i++) |
| 4316 | 337 xelem (r, c+i) = a.elem (i); |
| 338 } | |
| 458 | 339 |
| 340 return *this; | |
| 341 } | |
| 342 | |
| 343 Matrix& | |
| 5275 | 344 Matrix::insert (const ColumnVector& a, octave_idx_type r, octave_idx_type c) |
| 458 | 345 { |
| 5275 | 346 octave_idx_type a_len = a.length (); |
| 4316 | 347 |
| 1698 | 348 if (r < 0 || r + a_len > rows () || c < 0 || c >= cols ()) |
| 458 | 349 { |
| 350 (*current_liboctave_error_handler) ("range error for insert"); | |
| 351 return *this; | |
| 352 } | |
| 353 | |
| 4316 | 354 if (a_len > 0) |
| 355 { | |
| 356 make_unique (); | |
| 357 | |
| 5275 | 358 for (octave_idx_type i = 0; i < a_len; i++) |
| 4316 | 359 xelem (r+i, c) = a.elem (i); |
| 360 } | |
| 458 | 361 |
| 362 return *this; | |
| 363 } | |
| 364 | |
| 365 Matrix& | |
| 5275 | 366 Matrix::insert (const DiagMatrix& a, octave_idx_type r, octave_idx_type c) |
| 458 | 367 { |
| 5275 | 368 octave_idx_type a_nr = a.rows (); |
| 369 octave_idx_type a_nc = a.cols (); | |
| 1697 | 370 |
| 1698 | 371 if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) |
| 458 | 372 { |
| 373 (*current_liboctave_error_handler) ("range error for insert"); | |
| 374 return *this; | |
| 375 } | |
| 376 | |
| 1697 | 377 fill (0.0, r, c, r + a_nr - 1, c + a_nc - 1); |
| 378 | |
| 5275 | 379 octave_idx_type a_len = a.length (); |
| 4316 | 380 |
| 381 if (a_len > 0) | |
| 382 { | |
| 383 make_unique (); | |
| 384 | |
| 5275 | 385 for (octave_idx_type i = 0; i < a_len; i++) |
| 4316 | 386 xelem (r+i, c+i) = a.elem (i, i); |
| 387 } | |
| 458 | 388 |
| 389 return *this; | |
| 390 } | |
| 391 | |
| 392 Matrix& | |
| 393 Matrix::fill (double val) | |
| 394 { | |
| 5275 | 395 octave_idx_type nr = rows (); |
| 396 octave_idx_type nc = cols (); | |
| 4316 | 397 |
| 458 | 398 if (nr > 0 && nc > 0) |
| 4316 | 399 { |
| 400 make_unique (); | |
| 401 | |
| 5275 | 402 for (octave_idx_type j = 0; j < nc; j++) |
| 403 for (octave_idx_type i = 0; i < nr; i++) | |
| 4316 | 404 xelem (i, j) = val; |
| 405 } | |
| 458 | 406 |
| 407 return *this; | |
| 408 } | |
| 409 | |
| 410 Matrix& | |
| 5275 | 411 Matrix::fill (double val, octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) |
| 458 | 412 { |
| 5275 | 413 octave_idx_type nr = rows (); |
| 414 octave_idx_type nc = cols (); | |
| 4316 | 415 |
| 458 | 416 if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0 |
| 417 || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc) | |
| 418 { | |
| 419 (*current_liboctave_error_handler) ("range error for fill"); | |
| 420 return *this; | |
| 421 } | |
| 422 | |
| 5275 | 423 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } |
| 424 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } | |
| 458 | 425 |
| 4316 | 426 if (r2 >= r1 && c2 >= c1) |
| 427 { | |
| 428 make_unique (); | |
| 429 | |
| 5275 | 430 for (octave_idx_type j = c1; j <= c2; j++) |
| 431 for (octave_idx_type i = r1; i <= r2; i++) | |
| 4316 | 432 xelem (i, j) = val; |
| 433 } | |
| 458 | 434 |
| 435 return *this; | |
| 436 } | |
| 437 | |
| 438 Matrix | |
| 439 Matrix::append (const Matrix& a) const | |
| 440 { | |
| 5275 | 441 octave_idx_type nr = rows (); |
| 442 octave_idx_type nc = cols (); | |
| 458 | 443 if (nr != a.rows ()) |
| 444 { | |
| 445 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 446 return Matrix (); | |
| 447 } | |
| 448 | |
| 5275 | 449 octave_idx_type nc_insert = nc; |
| 458 | 450 Matrix retval (nr, nc + a.cols ()); |
| 451 retval.insert (*this, 0, 0); | |
| 452 retval.insert (a, 0, nc_insert); | |
| 453 return retval; | |
| 454 } | |
| 455 | |
| 456 Matrix | |
| 457 Matrix::append (const RowVector& a) const | |
| 458 { | |
| 5275 | 459 octave_idx_type nr = rows (); |
| 460 octave_idx_type nc = cols (); | |
| 458 | 461 if (nr != 1) |
| 462 { | |
| 463 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 464 return Matrix (); | |
| 465 } | |
| 466 | |
| 5275 | 467 octave_idx_type nc_insert = nc; |
| 458 | 468 Matrix retval (nr, nc + a.length ()); |
| 469 retval.insert (*this, 0, 0); | |
| 470 retval.insert (a, 0, nc_insert); | |
| 471 return retval; | |
| 472 } | |
| 473 | |
| 474 Matrix | |
| 475 Matrix::append (const ColumnVector& a) const | |
| 476 { | |
| 5275 | 477 octave_idx_type nr = rows (); |
| 478 octave_idx_type nc = cols (); | |
| 458 | 479 if (nr != a.length ()) |
| 480 { | |
| 481 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 482 return Matrix (); | |
| 483 } | |
| 484 | |
| 5275 | 485 octave_idx_type nc_insert = nc; |
| 458 | 486 Matrix retval (nr, nc + 1); |
| 487 retval.insert (*this, 0, 0); | |
| 488 retval.insert (a, 0, nc_insert); | |
| 489 return retval; | |
| 490 } | |
| 491 | |
| 492 Matrix | |
| 493 Matrix::append (const DiagMatrix& a) const | |
| 494 { | |
| 5275 | 495 octave_idx_type nr = rows (); |
| 496 octave_idx_type nc = cols (); | |
| 458 | 497 if (nr != a.rows ()) |
| 498 { | |
| 499 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 500 return *this; | |
| 501 } | |
| 502 | |
| 5275 | 503 octave_idx_type nc_insert = nc; |
| 458 | 504 Matrix retval (nr, nc + a.cols ()); |
| 505 retval.insert (*this, 0, 0); | |
| 506 retval.insert (a, 0, nc_insert); | |
| 507 return retval; | |
| 508 } | |
| 509 | |
| 510 Matrix | |
| 511 Matrix::stack (const Matrix& a) const | |
| 512 { | |
| 5275 | 513 octave_idx_type nr = rows (); |
| 514 octave_idx_type nc = cols (); | |
| 458 | 515 if (nc != a.cols ()) |
| 516 { | |
| 517 (*current_liboctave_error_handler) | |
| 518 ("column dimension mismatch for stack"); | |
| 519 return Matrix (); | |
| 520 } | |
| 521 | |
| 5275 | 522 octave_idx_type nr_insert = nr; |
| 458 | 523 Matrix retval (nr + a.rows (), nc); |
| 524 retval.insert (*this, 0, 0); | |
| 525 retval.insert (a, nr_insert, 0); | |
| 526 return retval; | |
| 527 } | |
| 528 | |
| 529 Matrix | |
| 530 Matrix::stack (const RowVector& a) const | |
| 531 { | |
| 5275 | 532 octave_idx_type nr = rows (); |
| 533 octave_idx_type nc = cols (); | |
| 458 | 534 if (nc != a.length ()) |
| 535 { | |
| 536 (*current_liboctave_error_handler) | |
| 537 ("column dimension mismatch for stack"); | |
| 538 return Matrix (); | |
| 539 } | |
| 540 | |
| 5275 | 541 octave_idx_type nr_insert = nr; |
| 458 | 542 Matrix retval (nr + 1, nc); |
| 543 retval.insert (*this, 0, 0); | |
| 544 retval.insert (a, nr_insert, 0); | |
| 545 return retval; | |
| 546 } | |
| 547 | |
| 548 Matrix | |
| 549 Matrix::stack (const ColumnVector& a) const | |
| 550 { | |
| 5275 | 551 octave_idx_type nr = rows (); |
| 552 octave_idx_type nc = cols (); | |
| 458 | 553 if (nc != 1) |
| 554 { | |
| 555 (*current_liboctave_error_handler) | |
| 556 ("column dimension mismatch for stack"); | |
| 557 return Matrix (); | |
| 558 } | |
| 559 | |
| 5275 | 560 octave_idx_type nr_insert = nr; |
| 458 | 561 Matrix retval (nr + a.length (), nc); |
| 562 retval.insert (*this, 0, 0); | |
| 563 retval.insert (a, nr_insert, 0); | |
| 564 return retval; | |
| 565 } | |
| 566 | |
| 567 Matrix | |
| 568 Matrix::stack (const DiagMatrix& a) const | |
| 569 { | |
| 5275 | 570 octave_idx_type nr = rows (); |
| 571 octave_idx_type nc = cols (); | |
| 458 | 572 if (nc != a.cols ()) |
| 573 { | |
| 574 (*current_liboctave_error_handler) | |
| 575 ("column dimension mismatch for stack"); | |
| 576 return Matrix (); | |
| 577 } | |
| 578 | |
| 5275 | 579 octave_idx_type nr_insert = nr; |
| 458 | 580 Matrix retval (nr + a.rows (), nc); |
| 581 retval.insert (*this, 0, 0); | |
| 582 retval.insert (a, nr_insert, 0); | |
| 583 return retval; | |
| 584 } | |
| 585 | |
| 586 Matrix | |
| 1205 | 587 real (const ComplexMatrix& a) |
| 588 { | |
| 5275 | 589 octave_idx_type a_len = a.length (); |
| 1205 | 590 Matrix retval; |
| 591 if (a_len > 0) | |
| 3769 | 592 retval = Matrix (mx_inline_real_dup (a.data (), a_len), |
| 593 a.rows (), a.cols ()); | |
| 1205 | 594 return retval; |
| 595 } | |
| 596 | |
| 597 Matrix | |
| 598 imag (const ComplexMatrix& a) | |
| 599 { | |
| 5275 | 600 octave_idx_type a_len = a.length (); |
| 1205 | 601 Matrix retval; |
| 602 if (a_len > 0) | |
| 3769 | 603 retval = Matrix (mx_inline_imag_dup (a.data (), a_len), |
| 604 a.rows (), a.cols ()); | |
| 1205 | 605 return retval; |
| 606 } | |
| 607 | |
| 608 Matrix | |
| 5275 | 609 Matrix::extract (octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) const |
| 458 | 610 { |
| 5275 | 611 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } |
| 612 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } | |
| 613 | |
| 614 octave_idx_type new_r = r2 - r1 + 1; | |
| 615 octave_idx_type new_c = c2 - c1 + 1; | |
| 458 | 616 |
| 617 Matrix result (new_r, new_c); | |
| 618 | |
| 5275 | 619 for (octave_idx_type j = 0; j < new_c; j++) |
| 620 for (octave_idx_type i = 0; i < new_r; i++) | |
| 4316 | 621 result.xelem (i, j) = elem (r1+i, c1+j); |
| 622 | |
| 623 return result; | |
| 624 } | |
| 625 | |
| 626 Matrix | |
| 5275 | 627 Matrix::extract_n (octave_idx_type r1, octave_idx_type c1, octave_idx_type nr, octave_idx_type nc) const |
| 4316 | 628 { |
| 629 Matrix result (nr, nc); | |
| 630 | |
| 5275 | 631 for (octave_idx_type j = 0; j < nc; j++) |
| 632 for (octave_idx_type i = 0; i < nr; i++) | |
| 4316 | 633 result.xelem (i, j) = elem (r1+i, c1+j); |
| 458 | 634 |
| 635 return result; | |
| 636 } | |
| 637 | |
| 638 // extract row or column i. | |
| 639 | |
| 640 RowVector | |
| 5275 | 641 Matrix::row (octave_idx_type i) const |
| 458 | 642 { |
| 5275 | 643 octave_idx_type nc = cols (); |
| 458 | 644 if (i < 0 || i >= rows ()) |
| 645 { | |
| 646 (*current_liboctave_error_handler) ("invalid row selection"); | |
| 647 return RowVector (); | |
| 648 } | |
| 649 | |
| 650 RowVector retval (nc); | |
| 5275 | 651 for (octave_idx_type j = 0; j < nc; j++) |
| 4316 | 652 retval.xelem (j) = elem (i, j); |
| 458 | 653 |
| 654 return retval; | |
| 655 } | |
| 656 | |
| 657 ColumnVector | |
| 5275 | 658 Matrix::column (octave_idx_type i) const |
| 458 | 659 { |
| 5275 | 660 octave_idx_type nr = rows (); |
| 458 | 661 if (i < 0 || i >= cols ()) |
| 662 { | |
| 663 (*current_liboctave_error_handler) ("invalid column selection"); | |
| 664 return ColumnVector (); | |
| 665 } | |
| 666 | |
| 667 ColumnVector retval (nr); | |
| 5275 | 668 for (octave_idx_type j = 0; j < nr; j++) |
| 4316 | 669 retval.xelem (j) = elem (j, i); |
| 458 | 670 |
| 671 return retval; | |
| 672 } | |
| 673 | |
| 674 Matrix | |
| 675 Matrix::inverse (void) const | |
| 676 { | |
| 5275 | 677 octave_idx_type info; |
| 7788 | 678 double rcon; |
| 6207 | 679 MatrixType mattype (*this); |
| 7788 | 680 return inverse (mattype, info, rcon, 0, 0); |
| 6207 | 681 } |
| 682 | |
| 683 Matrix | |
| 6479 | 684 Matrix::inverse (octave_idx_type& info) const |
| 685 { | |
| 7788 | 686 double rcon; |
| 6479 | 687 MatrixType mattype (*this); |
| 7788 | 688 return inverse (mattype, info, rcon, 0, 0); |
| 6479 | 689 } |
| 690 | |
| 691 Matrix | |
| 7788 | 692 Matrix::inverse (octave_idx_type& info, double& rcon, int force, |
| 6479 | 693 int calc_cond) const |
| 694 { | |
| 695 MatrixType mattype (*this); | |
| 7788 | 696 return inverse (mattype, info, rcon, force, calc_cond); |
| 6479 | 697 } |
| 698 | |
| 699 Matrix | |
| 6207 | 700 Matrix::inverse (MatrixType& mattype) const |
| 701 { | |
| 702 octave_idx_type info; | |
| 7788 | 703 double rcon; |
| 704 return inverse (mattype, info, rcon, 0, 0); | |
| 6207 | 705 } |
| 706 | |
| 707 Matrix | |
| 708 Matrix::inverse (MatrixType &mattype, octave_idx_type& info) const | |
| 709 { | |
| 7788 | 710 double rcon; |
| 711 return inverse (mattype, info, rcon, 0, 0); | |
| 458 | 712 } |
| 713 | |
| 714 Matrix | |
| 7788 | 715 Matrix::tinverse (MatrixType &mattype, octave_idx_type& info, double& rcon, |
| 6207 | 716 int force, int calc_cond) const |
| 458 | 717 { |
| 6207 | 718 Matrix retval; |
| 719 | |
| 720 octave_idx_type nr = rows (); | |
| 721 octave_idx_type nc = cols (); | |
| 722 | |
| 723 if (nr != nc || nr == 0 || nc == 0) | |
| 724 (*current_liboctave_error_handler) ("inverse requires square matrix"); | |
| 725 else | |
| 726 { | |
| 727 int typ = mattype.type (); | |
| 728 char uplo = (typ == MatrixType::Lower ? 'L' : 'U'); | |
| 729 char udiag = 'N'; | |
| 730 retval = *this; | |
| 731 double *tmp_data = retval.fortran_vec (); | |
| 732 | |
| 733 F77_XFCN (dtrtri, DTRTRI, (F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 734 F77_CONST_CHAR_ARG2 (&udiag, 1), | |
| 735 nr, tmp_data, nr, info | |
| 736 F77_CHAR_ARG_LEN (1) | |
| 737 F77_CHAR_ARG_LEN (1))); | |
| 738 | |
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739 // Throw-away extra info LAPACK gives so as to not change output. |
| 7788 | 740 rcon = 0.0; |
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741 if (info != 0) |
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742 info = -1; |
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743 else if (calc_cond) |
| 6207 | 744 { |
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745 octave_idx_type dtrcon_info = 0; |
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746 char job = '1'; |
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747 |
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748 OCTAVE_LOCAL_BUFFER (double, work, 3 * nr); |
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749 OCTAVE_LOCAL_BUFFER (octave_idx_type, iwork, nr); |
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750 |
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751 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&job, 1), |
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752 F77_CONST_CHAR_ARG2 (&uplo, 1), |
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753 F77_CONST_CHAR_ARG2 (&udiag, 1), |
| 7788 | 754 nr, tmp_data, nr, rcon, |
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755 work, iwork, dtrcon_info |
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756 F77_CHAR_ARG_LEN (1) |
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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 |
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760 if (dtrcon_info != 0) |
| 6207 | 761 info = -1; |
| 762 } | |
| 763 | |
| 764 if (info == -1 && ! force) | |
| 765 retval = *this; // Restore matrix contents. | |
| 766 } | |
| 767 | |
| 768 return retval; | |
| 458 | 769 } |
| 770 | |
| 6207 | 771 |
| 458 | 772 Matrix |
| 7788 | 773 Matrix::finverse (MatrixType &mattype, octave_idx_type& info, double& rcon, |
| 6207 | 774 int force, int calc_cond) const |
| 458 | 775 { |
| 1948 | 776 Matrix retval; |
| 777 | |
| 5275 | 778 octave_idx_type nr = rows (); |
| 779 octave_idx_type nc = cols (); | |
| 1948 | 780 |
| 458 | 781 if (nr != nc || nr == 0 || nc == 0) |
| 1948 | 782 (*current_liboctave_error_handler) ("inverse requires square matrix"); |
| 458 | 783 else |
| 784 { | |
| 5275 | 785 Array<octave_idx_type> ipvt (nr); |
| 786 octave_idx_type *pipvt = ipvt.fortran_vec (); | |
| 1948 | 787 |
| 788 retval = *this; | |
| 789 double *tmp_data = retval.fortran_vec (); | |
| 790 | |
| 4329 | 791 Array<double> z(1); |
| 5275 | 792 octave_idx_type lwork = -1; |
| 4329 | 793 |
| 4330 | 794 // Query the optimum work array size. |
| 4329 | 795 F77_XFCN (dgetri, DGETRI, (nc, tmp_data, nr, pipvt, |
| 796 z.fortran_vec (), lwork, info)); | |
| 797 | |
| 5275 | 798 lwork = static_cast<octave_idx_type> (z(0)); |
| 4329 | 799 lwork = (lwork < 2 *nc ? 2*nc : lwork); |
| 800 z.resize (lwork); | |
| 801 double *pz = z.fortran_vec (); | |
| 802 | |
| 803 info = 0; | |
| 804 | |
| 4330 | 805 // Calculate the norm of the matrix, for later use. |
| 4329 | 806 double anorm = 0; |
| 807 if (calc_cond) | |
| 5275 | 808 anorm = retval.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
| 4329 | 809 |
| 810 F77_XFCN (dgetrf, DGETRF, (nc, nc, tmp_data, nr, pipvt, info)); | |
| 1948 | 811 |
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812 // Throw-away extra info LAPACK gives so as to not change output. |
| 7788 | 813 rcon = 0.0; |
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814 if (info != 0) |
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815 info = -1; |
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816 else if (calc_cond) |
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817 { |
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818 octave_idx_type dgecon_info = 0; |
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819 |
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820 // Now calculate the condition number for non-singular matrix. |
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821 char job = '1'; |
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822 Array<octave_idx_type> iz (nc); |
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823 octave_idx_type *piz = iz.fortran_vec (); |
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824 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
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825 nc, tmp_data, nr, anorm, |
| 7788 | 826 rcon, pz, piz, dgecon_info |
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827 F77_CHAR_ARG_LEN (1))); |
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828 |
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829 if (dgecon_info != 0) |
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830 info = -1; |
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831 } |
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832 |
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833 if (info == -1 && ! force) |
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834 retval = *this; // Restore matrix contents. |
| 1948 | 835 else |
| 836 { | |
|
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837 octave_idx_type dgetri_info = 0; |
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838 |
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839 F77_XFCN (dgetri, DGETRI, (nc, tmp_data, nr, pipvt, |
|
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840 pz, lwork, dgetri_info)); |
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841 |
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|
842 if (dgetri_info != 0) |
| 1948 | 843 info = -1; |
| 844 } | |
| 6207 | 845 |
| 846 if (info != 0) | |
| 847 mattype.mark_as_rectangular(); | |
| 458 | 848 } |
| 849 | |
| 1948 | 850 return retval; |
| 458 | 851 } |
| 852 | |
| 740 | 853 Matrix |
| 7788 | 854 Matrix::inverse (MatrixType &mattype, octave_idx_type& info, double& rcon, |
| 6207 | 855 int force, int calc_cond) const |
| 856 { | |
| 857 int typ = mattype.type (false); | |
| 858 Matrix ret; | |
| 859 | |
| 860 if (typ == MatrixType::Unknown) | |
| 861 typ = mattype.type (*this); | |
| 862 | |
| 863 if (typ == MatrixType::Upper || typ == MatrixType::Lower) | |
| 7788 | 864 ret = tinverse (mattype, info, rcon, force, calc_cond); |
| 6840 | 865 else |
| 6207 | 866 { |
| 867 if (mattype.is_hermitian ()) | |
| 868 { | |
| 6486 | 869 CHOL chol (*this, info, calc_cond); |
| 6207 | 870 if (info == 0) |
| 6486 | 871 { |
| 872 if (calc_cond) | |
| 7788 | 873 rcon = chol.rcond (); |
| 6486 | 874 else |
| 7788 | 875 rcon = 1.0; |
| 6486 | 876 ret = chol.inverse (); |
| 877 } | |
| 6207 | 878 else |
| 879 mattype.mark_as_unsymmetric (); | |
| 880 } | |
| 881 | |
| 882 if (!mattype.is_hermitian ()) | |
| 7788 | 883 ret = finverse(mattype, info, rcon, force, calc_cond); |
| 884 | |
| 885 if ((mattype.is_hermitian () || calc_cond) && rcon == 0.) | |
| 6840 | 886 ret = Matrix (rows (), columns (), octave_Inf); |
| 6207 | 887 } |
| 888 | |
| 889 return ret; | |
| 890 } | |
| 891 | |
| 892 Matrix | |
| 4384 | 893 Matrix::pseudo_inverse (double tol) const |
| 740 | 894 { |
| 3480 | 895 SVD result (*this, SVD::economy); |
| 740 | 896 |
| 897 DiagMatrix S = result.singular_values (); | |
| 898 Matrix U = result.left_singular_matrix (); | |
| 899 Matrix V = result.right_singular_matrix (); | |
| 900 | |
| 901 ColumnVector sigma = S.diag (); | |
| 902 | |
| 5275 | 903 octave_idx_type r = sigma.length () - 1; |
| 904 octave_idx_type nr = rows (); | |
| 905 octave_idx_type nc = cols (); | |
| 740 | 906 |
| 907 if (tol <= 0.0) | |
| 908 { | |
| 909 if (nr > nc) | |
| 910 tol = nr * sigma.elem (0) * DBL_EPSILON; | |
| 911 else | |
| 912 tol = nc * sigma.elem (0) * DBL_EPSILON; | |
| 913 } | |
| 914 | |
| 915 while (r >= 0 && sigma.elem (r) < tol) | |
| 916 r--; | |
| 917 | |
| 918 if (r < 0) | |
| 919 return Matrix (nc, nr, 0.0); | |
| 920 else | |
| 921 { | |
| 922 Matrix Ur = U.extract (0, 0, nr-1, r); | |
| 923 DiagMatrix D = DiagMatrix (sigma.extract (0, r)) . inverse (); | |
| 924 Matrix Vr = V.extract (0, 0, nc-1, r); | |
| 925 return Vr * D * Ur.transpose (); | |
| 926 } | |
| 927 } | |
| 928 | |
| 4773 | 929 #if defined (HAVE_FFTW3) |
| 3827 | 930 |
| 931 ComplexMatrix | |
| 932 Matrix::fourier (void) const | |
| 933 { | |
| 934 size_t nr = rows (); | |
| 935 size_t nc = cols (); | |
| 936 | |
| 937 ComplexMatrix retval (nr, nc); | |
| 938 | |
| 939 size_t npts, nsamples; | |
| 940 | |
| 941 if (nr == 1 || nc == 1) | |
| 942 { | |
| 943 npts = nr > nc ? nr : nc; | |
| 944 nsamples = 1; | |
| 945 } | |
| 946 else | |
| 947 { | |
| 948 npts = nr; | |
| 949 nsamples = nc; | |
| 950 } | |
| 951 | |
| 4773 | 952 const double *in (fortran_vec ()); |
| 3827 | 953 Complex *out (retval.fortran_vec ()); |
| 954 | |
| 4773 | 955 octave_fftw::fft (in, out, npts, nsamples); |
| 3827 | 956 |
| 957 return retval; | |
| 958 } | |
| 959 | |
| 960 ComplexMatrix | |
| 961 Matrix::ifourier (void) const | |
| 962 { | |
| 963 size_t nr = rows (); | |
| 964 size_t nc = cols (); | |
| 965 | |
| 966 ComplexMatrix retval (nr, nc); | |
| 967 | |
| 968 size_t npts, nsamples; | |
| 969 | |
| 970 if (nr == 1 || nc == 1) | |
| 971 { | |
| 972 npts = nr > nc ? nr : nc; | |
| 973 nsamples = 1; | |
| 974 } | |
| 975 else | |
| 976 { | |
| 977 npts = nr; | |
| 978 nsamples = nc; | |
| 979 } | |
| 980 | |
| 981 ComplexMatrix tmp (*this); | |
| 982 Complex *in (tmp.fortran_vec ()); | |
| 983 Complex *out (retval.fortran_vec ()); | |
| 984 | |
| 4773 | 985 octave_fftw::ifft (in, out, npts, nsamples); |
| 3827 | 986 |
| 987 return retval; | |
| 988 } | |
| 989 | |
| 990 ComplexMatrix | |
| 991 Matrix::fourier2d (void) const | |
| 992 { | |
| 4773 | 993 dim_vector dv(rows (), cols ()); |
| 994 | |
| 995 const double *in = fortran_vec (); | |
| 996 ComplexMatrix retval (rows (), cols ()); | |
| 997 octave_fftw::fftNd (in, retval.fortran_vec (), 2, dv); | |
| 3827 | 998 |
| 999 return retval; | |
| 1000 } | |
| 1001 | |
| 1002 ComplexMatrix | |
| 1003 Matrix::ifourier2d (void) const | |
| 1004 { | |
| 4773 | 1005 dim_vector dv(rows (), cols ()); |
| 3827 | 1006 |
| 1007 ComplexMatrix retval (*this); | |
| 4773 | 1008 Complex *out (retval.fortran_vec ()); |
| 1009 | |
| 1010 octave_fftw::ifftNd (out, out, 2, dv); | |
| 3827 | 1011 |
| 1012 return retval; | |
| 1013 } | |
| 1014 | |
| 1015 #else | |
| 1016 | |
| 458 | 1017 ComplexMatrix |
| 1018 Matrix::fourier (void) const | |
| 1019 { | |
| 1948 | 1020 ComplexMatrix retval; |
| 1021 | |
| 5275 | 1022 octave_idx_type nr = rows (); |
| 1023 octave_idx_type nc = cols (); | |
| 1024 | |
| 1025 octave_idx_type npts, nsamples; | |
| 1948 | 1026 |
| 458 | 1027 if (nr == 1 || nc == 1) |
| 1028 { | |
| 1029 npts = nr > nc ? nr : nc; | |
| 1030 nsamples = 1; | |
| 1031 } | |
| 1032 else | |
| 1033 { | |
| 1034 npts = nr; | |
| 1035 nsamples = nc; | |
| 1036 } | |
| 1037 | |
| 5275 | 1038 octave_idx_type nn = 4*npts+15; |
| 1948 | 1039 |
| 1040 Array<Complex> wsave (nn); | |
| 1041 Complex *pwsave = wsave.fortran_vec (); | |
| 1042 | |
| 3585 | 1043 retval = ComplexMatrix (*this); |
| 1948 | 1044 Complex *tmp_data = retval.fortran_vec (); |
| 1045 | |
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1046 F77_FUNC (zffti, ZFFTI) (npts, pwsave); |
| 458 | 1047 |
| 5275 | 1048 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1049 { |
| 1050 OCTAVE_QUIT; | |
| 1051 | |
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1052 F77_FUNC (zfftf, ZFFTF) (npts, &tmp_data[npts*j], pwsave); |
| 4153 | 1053 } |
| 1948 | 1054 |
| 1055 return retval; | |
| 458 | 1056 } |
| 1057 | |
| 1058 ComplexMatrix | |
| 1059 Matrix::ifourier (void) const | |
| 1060 { | |
| 1948 | 1061 ComplexMatrix retval; |
| 1062 | |
| 5275 | 1063 octave_idx_type nr = rows (); |
| 1064 octave_idx_type nc = cols (); | |
| 1065 | |
| 1066 octave_idx_type npts, nsamples; | |
| 1948 | 1067 |
| 458 | 1068 if (nr == 1 || nc == 1) |
| 1069 { | |
| 1070 npts = nr > nc ? nr : nc; | |
| 1071 nsamples = 1; | |
| 1072 } | |
| 1073 else | |
| 1074 { | |
| 1075 npts = nr; | |
| 1076 nsamples = nc; | |
| 1077 } | |
| 1078 | |
| 5275 | 1079 octave_idx_type nn = 4*npts+15; |
| 1948 | 1080 |
| 1081 Array<Complex> wsave (nn); | |
| 1082 Complex *pwsave = wsave.fortran_vec (); | |
| 1083 | |
| 3585 | 1084 retval = ComplexMatrix (*this); |
| 1948 | 1085 Complex *tmp_data = retval.fortran_vec (); |
| 1086 | |
|
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changeset
|
1087 F77_FUNC (zffti, ZFFTI) (npts, pwsave); |
| 458 | 1088 |
| 5275 | 1089 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1090 { |
| 1091 OCTAVE_QUIT; | |
| 1092 | |
|
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|
1093 F77_FUNC (zfftb, ZFFTB) (npts, &tmp_data[npts*j], pwsave); |
| 4153 | 1094 } |
| 458 | 1095 |
| 5275 | 1096 for (octave_idx_type j = 0; j < npts*nsamples; j++) |
| 3572 | 1097 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
| 458 | 1098 |
| 1948 | 1099 return retval; |
| 458 | 1100 } |
| 1101 | |
| 677 | 1102 ComplexMatrix |
| 1103 Matrix::fourier2d (void) const | |
| 1104 { | |
| 1948 | 1105 ComplexMatrix retval; |
| 1106 | |
| 5275 | 1107 octave_idx_type nr = rows (); |
| 1108 octave_idx_type nc = cols (); | |
| 1109 | |
| 1110 octave_idx_type npts, nsamples; | |
| 1948 | 1111 |
| 677 | 1112 if (nr == 1 || nc == 1) |
| 1113 { | |
| 1114 npts = nr > nc ? nr : nc; | |
| 1115 nsamples = 1; | |
| 1116 } | |
| 1117 else | |
| 1118 { | |
| 1119 npts = nr; | |
| 1120 nsamples = nc; | |
| 1121 } | |
| 1122 | |
| 5275 | 1123 octave_idx_type nn = 4*npts+15; |
| 1948 | 1124 |
| 1125 Array<Complex> wsave (nn); | |
| 1126 Complex *pwsave = wsave.fortran_vec (); | |
| 1127 | |
| 3585 | 1128 retval = ComplexMatrix (*this); |
| 1948 | 1129 Complex *tmp_data = retval.fortran_vec (); |
| 1130 | |
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|
1131 F77_FUNC (zffti, ZFFTI) (npts, pwsave); |
| 677 | 1132 |
| 5275 | 1133 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1134 { |
| 1135 OCTAVE_QUIT; | |
| 1136 | |
|
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|
1137 F77_FUNC (zfftf, ZFFTF) (npts, &tmp_data[npts*j], pwsave); |
| 4153 | 1138 } |
| 677 | 1139 |
| 1140 npts = nc; | |
| 1141 nsamples = nr; | |
| 1142 nn = 4*npts+15; | |
| 1948 | 1143 |
| 1144 wsave.resize (nn); | |
| 1145 pwsave = wsave.fortran_vec (); | |
| 1146 | |
| 4773 | 1147 Array<Complex> tmp (npts); |
| 1148 Complex *prow = tmp.fortran_vec (); | |
| 1948 | 1149 |
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|
1150 F77_FUNC (zffti, ZFFTI) (npts, pwsave); |
| 677 | 1151 |
| 5275 | 1152 for (octave_idx_type j = 0; j < nsamples; j++) |
| 677 | 1153 { |
| 4153 | 1154 OCTAVE_QUIT; |
| 1155 | |
| 5275 | 1156 for (octave_idx_type i = 0; i < npts; i++) |
| 1948 | 1157 prow[i] = tmp_data[i*nr + j]; |
| 1158 | |
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|
1159 F77_FUNC (zfftf, ZFFTF) (npts, prow, pwsave); |
| 677 | 1160 |
| 5275 | 1161 for (octave_idx_type i = 0; i < npts; i++) |
| 1948 | 1162 tmp_data[i*nr + j] = prow[i]; |
| 677 | 1163 } |
| 1164 | |
| 1948 | 1165 return retval; |
| 677 | 1166 } |
| 1167 | |
| 1168 ComplexMatrix | |
| 1169 Matrix::ifourier2d (void) const | |
| 1170 { | |
| 1948 | 1171 ComplexMatrix retval; |
| 1172 | |
| 5275 | 1173 octave_idx_type nr = rows (); |
| 1174 octave_idx_type nc = cols (); | |
| 1175 | |
| 1176 octave_idx_type npts, nsamples; | |
| 1948 | 1177 |
| 677 | 1178 if (nr == 1 || nc == 1) |
| 1179 { | |
| 1180 npts = nr > nc ? nr : nc; | |
| 1181 nsamples = 1; | |
| 1182 } | |
| 1183 else | |
| 1184 { | |
| 1185 npts = nr; | |
| 1186 nsamples = nc; | |
| 1187 } | |
| 1188 | |
| 5275 | 1189 octave_idx_type nn = 4*npts+15; |
| 1948 | 1190 |
| 1191 Array<Complex> wsave (nn); | |
| 1192 Complex *pwsave = wsave.fortran_vec (); | |
| 1193 | |
| 3585 | 1194 retval = ComplexMatrix (*this); |
| 1948 | 1195 Complex *tmp_data = retval.fortran_vec (); |
| 1196 | |
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1197 F77_FUNC (zffti, ZFFTI) (npts, pwsave); |
| 677 | 1198 |
| 5275 | 1199 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1200 { |
| 1201 OCTAVE_QUIT; | |
| 1202 | |
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1203 F77_FUNC (zfftb, ZFFTB) (npts, &tmp_data[npts*j], pwsave); |
| 4153 | 1204 } |
| 677 | 1205 |
| 5275 | 1206 for (octave_idx_type j = 0; j < npts*nsamples; j++) |
| 3572 | 1207 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
| 677 | 1208 |
| 1209 npts = nc; | |
| 1210 nsamples = nr; | |
| 1211 nn = 4*npts+15; | |
| 1948 | 1212 |
| 1213 wsave.resize (nn); | |
| 1214 pwsave = wsave.fortran_vec (); | |
| 1215 | |
| 4773 | 1216 Array<Complex> tmp (npts); |
| 1217 Complex *prow = tmp.fortran_vec (); | |
| 1948 | 1218 |
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1219 F77_FUNC (zffti, ZFFTI) (npts, pwsave); |
| 677 | 1220 |
| 5275 | 1221 for (octave_idx_type j = 0; j < nsamples; j++) |
| 677 | 1222 { |
| 4153 | 1223 OCTAVE_QUIT; |
| 1224 | |
| 5275 | 1225 for (octave_idx_type i = 0; i < npts; i++) |
| 1948 | 1226 prow[i] = tmp_data[i*nr + j]; |
| 1227 | |
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1228 F77_FUNC (zfftb, ZFFTB) (npts, prow, pwsave); |
| 677 | 1229 |
| 5275 | 1230 for (octave_idx_type i = 0; i < npts; i++) |
| 3572 | 1231 tmp_data[i*nr + j] = prow[i] / static_cast<double> (npts); |
| 677 | 1232 } |
| 1233 | |
| 1948 | 1234 return retval; |
| 677 | 1235 } |
| 1236 | |
| 3827 | 1237 #endif |
| 1238 | |
| 458 | 1239 DET |
| 1240 Matrix::determinant (void) const | |
| 1241 { | |
| 5275 | 1242 octave_idx_type info; |
| 7788 | 1243 double rcon; |
| 1244 return determinant (info, rcon, 0); | |
| 458 | 1245 } |
| 1246 | |
| 1247 DET | |
| 5275 | 1248 Matrix::determinant (octave_idx_type& info) const |
| 458 | 1249 { |
| 7788 | 1250 double rcon; |
| 1251 return determinant (info, rcon, 0); | |
| 458 | 1252 } |
| 1253 | |
| 1254 DET | |
| 7788 | 1255 Matrix::determinant (octave_idx_type& info, double& rcon, int calc_cond) const |
| 458 | 1256 { |
|
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1257 MatrixType mattype (*this); |
|
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1258 return determinant (mattype, info, rcon, calc_cond); |
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1259 } |
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1260 |
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1261 DET |
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1262 Matrix::determinant (MatrixType& mattype, |
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1263 octave_idx_type& info, double& rcon, int calc_cond) const |
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1264 { |
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1265 DET retval (1.0); |
| 458 | 1266 |
| 5275 | 1267 octave_idx_type nr = rows (); |
| 1268 octave_idx_type nc = cols (); | |
| 458 | 1269 |
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1270 if (nr != nc) |
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1271 (*current_liboctave_error_handler) ("matrix must be square"); |
| 458 | 1272 else |
| 1273 { | |
|
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1274 int typ = mattype.type (); |
|
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1275 |
|
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|
1276 if (typ == MatrixType::Unknown) |
|
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|
1277 typ = mattype.type (*this); |
|
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|
1278 |
|
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1279 if (typ == MatrixType::Lower || typ == MatrixType::Upper) |
|
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|
1280 { |
|
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|
1281 for (octave_idx_type i = 0; i < nc; i++) |
|
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|
1282 retval *= elem (i,i); |
|
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1283 } |
|
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1284 else if (typ == MatrixType::Hermitian) |
|
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|
1285 { |
|
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|
1286 Matrix atmp = *this; |
|
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1287 double *tmp_data = atmp.fortran_vec (); |
|
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|
1288 |
|
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|
1289 info = 0; |
|
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1290 double anorm = 0; |
|
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1291 if (calc_cond) anorm = xnorm (*this, 1); |
|
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|
1292 |
|
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|
1293 |
|
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|
1294 char job = 'L'; |
|
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1295 F77_XFCN (dpotrf, DPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, |
|
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|
1296 tmp_data, nr, info |
|
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|
1297 F77_CHAR_ARG_LEN (1))); |
|
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|
1298 |
|
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1299 if (info != 0) |
|
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|
1300 { |
|
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|
1301 rcon = 0.0; |
|
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1302 mattype.mark_as_unsymmetric (); |
|
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1303 typ = MatrixType::Full; |
|
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1304 } |
|
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|
1305 else |
|
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|
1306 { |
|
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|
1307 Array<double> z (3 * nc); |
|
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1308 double *pz = z.fortran_vec (); |
|
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|
1309 Array<octave_idx_type> iz (nc); |
|
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1310 octave_idx_type *piz = iz.fortran_vec (); |
|
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|
1311 |
|
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|
1312 F77_XFCN (dpocon, DPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
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1313 nr, tmp_data, nr, anorm, |
|
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1314 rcon, pz, piz, info |
|
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|
1315 F77_CHAR_ARG_LEN (1))); |
|
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|
1316 |
|
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|
1317 if (info != 0) |
|
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1318 rcon = 0.0; |
|
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|
1319 |
|
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|
1320 for (octave_idx_type i = 0; i < nc; i++) |
|
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1321 retval *= atmp (i,i); |
|
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|
1322 |
|
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1323 retval = retval.square (); |
|
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1324 } |
|
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|
1325 } |
|
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1326 else if (typ != MatrixType::Full) |
|
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1327 (*current_liboctave_error_handler) ("det: invalid dense matrix type"); |
|
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1328 |
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1329 if (typ == MatrixType::Full) |
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|
1330 { |
|
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|
1331 Array<octave_idx_type> ipvt (nr); |
|
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1332 octave_idx_type *pipvt = ipvt.fortran_vec (); |
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1333 |
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1334 Matrix atmp = *this; |
|
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1335 double *tmp_data = atmp.fortran_vec (); |
|
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|
1336 |
|
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1337 info = 0; |
|
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|
1338 |
|
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1339 // Calculate the norm of the matrix, for later use. |
|
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1340 double anorm = 0; |
|
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1341 if (calc_cond) anorm = xnorm (*this, 1); |
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|
1342 |
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1343 F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); |
|
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|
1344 |
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1345 // Throw-away extra info LAPACK gives so as to not change output. |
|
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1346 rcon = 0.0; |
|
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1347 if (info != 0) |
|
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|
1348 { |
|
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1349 info = -1; |
|
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1350 retval = DET (); |
|
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|
1351 } |
|
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|
1352 else |
|
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|
1353 { |
|
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|
1354 if (calc_cond) |
|
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|
1355 { |
|
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1356 // Now calc the condition number for non-singular matrix. |
|
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1357 char job = '1'; |
|
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1358 Array<double> z (4 * nc); |
|
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1359 double *pz = z.fortran_vec (); |
|
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1360 Array<octave_idx_type> iz (nc); |
|
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1361 octave_idx_type *piz = iz.fortran_vec (); |
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|
1362 |
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1363 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
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1364 nc, tmp_data, nr, anorm, |
|
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1365 rcon, pz, piz, info |
|
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|
1366 F77_CHAR_ARG_LEN (1))); |
| 8335 | 1367 } |
|
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|
1368 |
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1369 if (info != 0) |
|
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|
1370 { |
|
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1371 info = -1; |
|
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1372 retval = DET (); |
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|
1373 } |
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|
1374 else |
|
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|
1375 { |
|
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|
1376 for (octave_idx_type i = 0; i < nc; i++) |
|
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|
1377 { |
|
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|
1378 double c = atmp(i,i); |
|
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1379 retval *= (ipvt(i) != (i+1)) ? -c : c; |
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|
1380 } |
|
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|
1381 } |
|
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|
1382 } |
|
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|
1383 } |
| 458 | 1384 } |
| 1385 | |
| 1386 return retval; | |
| 1387 } | |
| 1388 | |
| 7788 | 1389 double |
| 1390 Matrix::rcond (void) const | |
| 1391 { | |
| 1392 MatrixType mattype (*this); | |
| 1393 return rcond (mattype); | |
| 1394 } | |
| 1395 | |
| 1396 double | |
| 1397 Matrix::rcond (MatrixType &mattype) const | |
| 1398 { | |
| 1399 double rcon; | |
| 1400 octave_idx_type nr = rows (); | |
| 1401 octave_idx_type nc = cols (); | |
| 1402 | |
| 1403 if (nr != nc) | |
| 1404 (*current_liboctave_error_handler) ("matrix must be square"); | |
| 1405 else if (nr == 0 || nc == 0) | |
| 1406 rcon = octave_Inf; | |
| 1407 else | |
| 1408 { | |
| 1409 int typ = mattype.type (); | |
| 1410 | |
| 1411 if (typ == MatrixType::Unknown) | |
| 1412 typ = mattype.type (*this); | |
| 1413 | |
| 1414 // Only calculate the condition number for LU/Cholesky | |
| 1415 if (typ == MatrixType::Upper) | |
| 1416 { | |
| 1417 const double *tmp_data = fortran_vec (); | |
| 1418 octave_idx_type info = 0; | |
| 1419 char norm = '1'; | |
| 1420 char uplo = 'U'; | |
| 1421 char dia = 'N'; | |
| 1422 | |
| 1423 Array<double> z (3 * nc); | |
| 1424 double *pz = z.fortran_vec (); | |
| 1425 Array<octave_idx_type> iz (nc); | |
| 1426 octave_idx_type *piz = iz.fortran_vec (); | |
| 1427 | |
| 1428 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1429 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1430 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1431 nr, tmp_data, nr, rcon, | |
| 1432 pz, piz, info | |
| 1433 F77_CHAR_ARG_LEN (1) | |
| 1434 F77_CHAR_ARG_LEN (1) | |
| 1435 F77_CHAR_ARG_LEN (1))); | |
| 1436 | |
| 1437 if (info != 0) | |
| 1438 rcon = 0.0; | |
| 1439 } | |
| 1440 else if (typ == MatrixType::Permuted_Upper) | |
| 1441 (*current_liboctave_error_handler) | |
| 1442 ("permuted triangular matrix not implemented"); | |
| 1443 else if (typ == MatrixType::Lower) | |
| 1444 { | |
| 1445 const double *tmp_data = fortran_vec (); | |
| 1446 octave_idx_type info = 0; | |
| 1447 char norm = '1'; | |
| 1448 char uplo = 'L'; | |
| 1449 char dia = 'N'; | |
| 1450 | |
| 1451 Array<double> z (3 * nc); | |
| 1452 double *pz = z.fortran_vec (); | |
| 1453 Array<octave_idx_type> iz (nc); | |
| 1454 octave_idx_type *piz = iz.fortran_vec (); | |
| 1455 | |
| 1456 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1457 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1458 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1459 nr, tmp_data, nr, rcon, | |
| 1460 pz, piz, info | |
| 1461 F77_CHAR_ARG_LEN (1) | |
| 1462 F77_CHAR_ARG_LEN (1) | |
| 1463 F77_CHAR_ARG_LEN (1))); | |
| 1464 | |
| 1465 if (info != 0) | |
| 1466 rcon = 0.0; | |
| 1467 } | |
| 1468 else if (typ == MatrixType::Permuted_Lower) | |
| 1469 (*current_liboctave_error_handler) | |
| 1470 ("permuted triangular matrix not implemented"); | |
| 1471 else if (typ == MatrixType::Full || typ == MatrixType::Hermitian) | |
| 1472 { | |
| 1473 double anorm = -1.0; | |
| 1474 Matrix atmp = *this; | |
| 1475 double *tmp_data = atmp.fortran_vec (); | |
| 1476 | |
| 1477 if (typ == MatrixType::Hermitian) | |
| 1478 { | |
| 1479 octave_idx_type info = 0; | |
| 1480 char job = 'L'; | |
| 1481 anorm = atmp.abs().sum(). | |
| 1482 row(static_cast<octave_idx_type>(0)).max(); | |
| 1483 | |
| 1484 F77_XFCN (dpotrf, DPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, | |
| 1485 tmp_data, nr, info | |
| 1486 F77_CHAR_ARG_LEN (1))); | |
| 1487 | |
| 1488 if (info != 0) | |
| 1489 { | |
| 1490 rcon = 0.0; | |
| 1491 mattype.mark_as_unsymmetric (); | |
| 1492 typ = MatrixType::Full; | |
| 1493 } | |
| 1494 else | |
| 1495 { | |
| 1496 Array<double> z (3 * nc); | |
| 1497 double *pz = z.fortran_vec (); | |
| 1498 Array<octave_idx_type> iz (nc); | |
| 1499 octave_idx_type *piz = iz.fortran_vec (); | |
| 1500 | |
| 1501 F77_XFCN (dpocon, DPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), | |
| 1502 nr, tmp_data, nr, anorm, | |
| 1503 rcon, pz, piz, info | |
| 1504 F77_CHAR_ARG_LEN (1))); | |
| 1505 | |
| 1506 if (info != 0) | |
| 1507 rcon = 0.0; | |
| 1508 } | |
| 1509 } | |
| 1510 | |
| 1511 if (typ == MatrixType::Full) | |
| 1512 { | |
| 1513 octave_idx_type info = 0; | |
| 1514 | |
| 1515 Array<octave_idx_type> ipvt (nr); | |
| 1516 octave_idx_type *pipvt = ipvt.fortran_vec (); | |
| 1517 | |
| 1518 if(anorm < 0.) | |
| 1519 anorm = atmp.abs().sum(). | |
| 1520 row(static_cast<octave_idx_type>(0)).max(); | |
| 1521 | |
| 1522 Array<double> z (4 * nc); | |
| 1523 double *pz = z.fortran_vec (); | |
| 1524 Array<octave_idx_type> iz (nc); | |
| 1525 octave_idx_type *piz = iz.fortran_vec (); | |
| 1526 | |
| 1527 F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); | |
| 1528 | |
| 1529 if (info != 0) | |
| 1530 { | |
| 1531 rcon = 0.0; | |
| 1532 mattype.mark_as_rectangular (); | |
| 1533 } | |
| 1534 else | |
| 1535 { | |
| 1536 char job = '1'; | |
| 1537 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), | |
| 1538 nc, tmp_data, nr, anorm, | |
| 1539 rcon, pz, piz, info | |
| 1540 F77_CHAR_ARG_LEN (1))); | |
| 1541 | |
| 1542 if (info != 0) | |
| 1543 rcon = 0.0; | |
| 1544 } | |
| 1545 } | |
| 1546 } | |
| 1547 else | |
| 1548 rcon = 0.0; | |
| 1549 } | |
| 1550 | |
| 1551 return rcon; | |
| 1552 } | |
| 1553 | |
| 458 | 1554 Matrix |
| 5785 | 1555 Matrix::utsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, |
| 7788 | 1556 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 1557 bool calc_cond) const |
| 1558 { | |
| 1559 Matrix retval; | |
| 1560 | |
| 1561 octave_idx_type nr = rows (); | |
| 1562 octave_idx_type nc = cols (); | |
| 1563 | |
| 6924 | 1564 if (nr != b.rows ()) |
| 5785 | 1565 (*current_liboctave_error_handler) |
| 1566 ("matrix dimension mismatch solution of linear equations"); | |
| 6924 | 1567 else if (nr == 0 || nc == 0 || b.cols () == 0) |
| 1568 retval = Matrix (nc, b.cols (), 0.0); | |
| 5785 | 1569 else |
| 1570 { | |
| 1571 volatile int typ = mattype.type (); | |
| 1572 | |
| 1573 if (typ == MatrixType::Permuted_Upper || | |
| 1574 typ == MatrixType::Upper) | |
| 1575 { | |
| 1576 octave_idx_type b_nc = b.cols (); | |
| 7788 | 1577 rcon = 1.; |
| 5785 | 1578 info = 0; |
| 1579 | |
| 1580 if (typ == MatrixType::Permuted_Upper) | |
| 1581 { | |
| 1582 (*current_liboctave_error_handler) | |
| 6390 | 1583 ("permuted triangular matrix not implemented"); |
| 5785 | 1584 } |
| 1585 else | |
| 1586 { | |
| 1587 const double *tmp_data = fortran_vec (); | |
| 1588 | |
| 1589 if (calc_cond) | |
| 1590 { | |
| 1591 char norm = '1'; | |
| 1592 char uplo = 'U'; | |
| 1593 char dia = 'N'; | |
| 1594 | |
| 1595 Array<double> z (3 * nc); | |
| 1596 double *pz = z.fortran_vec (); | |
| 1597 Array<octave_idx_type> iz (nc); | |
| 1598 octave_idx_type *piz = iz.fortran_vec (); | |
| 1599 | |
| 1600 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1601 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1602 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 7788 | 1603 nr, tmp_data, nr, rcon, |
| 5785 | 1604 pz, piz, info |
| 1605 F77_CHAR_ARG_LEN (1) | |
| 1606 F77_CHAR_ARG_LEN (1) | |
| 1607 F77_CHAR_ARG_LEN (1))); | |
| 1608 | |
| 1609 if (info != 0) | |
| 1610 info = -2; | |
| 1611 | |
| 7788 | 1612 volatile double rcond_plus_one = rcon + 1.0; |
| 1613 | |
| 1614 if (rcond_plus_one == 1.0 || xisnan (rcon)) | |
| 5785 | 1615 { |
| 1616 info = -2; | |
| 1617 | |
| 1618 if (sing_handler) | |
| 7788 | 1619 sing_handler (rcon); |
| 5785 | 1620 else |
| 1621 (*current_liboctave_error_handler) | |
| 1622 ("matrix singular to machine precision, rcond = %g", | |
| 7788 | 1623 rcon); |
| 5785 | 1624 } |
| 1625 } | |
| 1626 | |
| 1627 if (info == 0) | |
| 1628 { | |
| 1629 retval = b; | |
| 1630 double *result = retval.fortran_vec (); | |
| 1631 | |
| 1632 char uplo = 'U'; | |
| 1633 char trans = 'N'; | |
| 1634 char dia = 'N'; | |
| 1635 | |
| 1636 F77_XFCN (dtrtrs, DTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1637 F77_CONST_CHAR_ARG2 (&trans, 1), | |
| 1638 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1639 nr, b_nc, tmp_data, nr, | |
| 1640 result, nr, info | |
| 1641 F77_CHAR_ARG_LEN (1) | |
| 1642 F77_CHAR_ARG_LEN (1) | |
| 1643 F77_CHAR_ARG_LEN (1))); | |
| 1644 } | |
| 1645 } | |
| 1646 } | |
| 1647 else | |
| 1648 (*current_liboctave_error_handler) ("incorrect matrix type"); | |
| 1649 } | |
| 1650 | |
| 1651 return retval; | |
| 1652 } | |
| 1653 | |
| 1654 Matrix | |
| 1655 Matrix::ltsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, | |
| 7788 | 1656 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 1657 bool calc_cond) const |
| 1658 { | |
| 1659 Matrix retval; | |
| 1660 | |
| 1661 octave_idx_type nr = rows (); | |
| 1662 octave_idx_type nc = cols (); | |
| 1663 | |
| 6924 | 1664 if (nr != b.rows ()) |
| 5785 | 1665 (*current_liboctave_error_handler) |
| 1666 ("matrix dimension mismatch solution of linear equations"); | |
| 6924 | 1667 else if (nr == 0 || nc == 0 || b.cols () == 0) |
| 1668 retval = Matrix (nc, b.cols (), 0.0); | |
| 5785 | 1669 else |
| 1670 { | |
| 1671 volatile int typ = mattype.type (); | |
| 1672 | |
| 1673 if (typ == MatrixType::Permuted_Lower || | |
| 1674 typ == MatrixType::Lower) | |
| 1675 { | |
| 1676 octave_idx_type b_nc = b.cols (); | |
| 7788 | 1677 rcon = 1.; |
| 5785 | 1678 info = 0; |
| 1679 | |
| 1680 if (typ == MatrixType::Permuted_Lower) | |
| 1681 { | |
| 1682 (*current_liboctave_error_handler) | |
| 6390 | 1683 ("permuted triangular matrix not implemented"); |
| 5785 | 1684 } |
| 1685 else | |
| 1686 { | |
| 1687 const double *tmp_data = fortran_vec (); | |
| 1688 | |
| 1689 if (calc_cond) | |
| 1690 { | |
| 1691 char norm = '1'; | |
| 1692 char uplo = 'L'; | |
| 1693 char dia = 'N'; | |
| 1694 | |
| 1695 Array<double> z (3 * nc); | |
| 1696 double *pz = z.fortran_vec (); | |
| 1697 Array<octave_idx_type> iz (nc); | |
| 1698 octave_idx_type *piz = iz.fortran_vec (); | |
| 1699 | |
| 1700 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1701 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1702 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 7788 | 1703 nr, tmp_data, nr, rcon, |
| 5785 | 1704 pz, piz, info |
| 1705 F77_CHAR_ARG_LEN (1) | |
| 1706 F77_CHAR_ARG_LEN (1) | |
| 1707 F77_CHAR_ARG_LEN (1))); | |
| 1708 | |
| 1709 if (info != 0) | |
| 1710 info = -2; | |
| 1711 | |
| 7788 | 1712 volatile double rcond_plus_one = rcon + 1.0; |
| 1713 | |
| 1714 if (rcond_plus_one == 1.0 || xisnan (rcon)) | |
| 5785 | 1715 { |
| 1716 info = -2; | |
| 1717 | |
| 1718 if (sing_handler) | |
| 7788 | 1719 sing_handler (rcon); |
| 5785 | 1720 else |
| 1721 (*current_liboctave_error_handler) | |
| 1722 ("matrix singular to machine precision, rcond = %g", | |
| 7788 | 1723 rcon); |
| 5785 | 1724 } |
| 1725 } | |
| 1726 | |
| 1727 if (info == 0) | |
| 1728 { | |
| 1729 retval = b; | |
| 1730 double *result = retval.fortran_vec (); | |
| 1731 | |
| 1732 char uplo = 'L'; | |
| 1733 char trans = 'N'; | |
| 1734 char dia = 'N'; | |
| 1735 | |
| 1736 F77_XFCN (dtrtrs, DTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1737 F77_CONST_CHAR_ARG2 (&trans, 1), | |
| 1738 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1739 nr, b_nc, tmp_data, nr, | |
| 1740 result, nr, info | |
| 1741 F77_CHAR_ARG_LEN (1) | |
| 1742 F77_CHAR_ARG_LEN (1) | |
| 1743 F77_CHAR_ARG_LEN (1))); | |
| 1744 } | |
| 1745 } | |
| 1746 } | |
| 1747 else | |
| 1748 (*current_liboctave_error_handler) ("incorrect matrix type"); | |
| 1749 } | |
| 1750 | |
| 1751 return retval; | |
| 1752 } | |
| 1753 | |
| 1754 Matrix | |
| 1755 Matrix::fsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, | |
| 7788 | 1756 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 1757 bool calc_cond) const |
| 1758 { | |
| 1759 Matrix retval; | |
| 1760 | |
| 1761 octave_idx_type nr = rows (); | |
| 1762 octave_idx_type nc = cols (); | |
| 1763 | |
| 6924 | 1764 if (nr != nc || nr != b.rows ()) |
| 5785 | 1765 (*current_liboctave_error_handler) |
| 1766 ("matrix dimension mismatch solution of linear equations"); | |
| 6924 | 1767 else if (nr == 0 || b.cols () == 0) |
| 1768 retval = Matrix (nc, b.cols (), 0.0); | |
| 5785 | 1769 else |
| 1770 { | |
| 1771 volatile int typ = mattype.type (); | |
| 1772 | |
| 1773 // Calculate the norm of the matrix, for later use. | |
| 1774 double anorm = -1.; | |
| 1775 | |
| 1776 if (typ == MatrixType::Hermitian) | |
| 1777 { | |
| 1778 info = 0; | |
| 1779 char job = 'L'; | |
| 1780 Matrix atmp = *this; | |
| 1781 double *tmp_data = atmp.fortran_vec (); | |
| 1782 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); | |
| 1783 | |
| 1784 F77_XFCN (dpotrf, DPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, | |
| 1785 tmp_data, nr, info | |
| 1786 F77_CHAR_ARG_LEN (1))); | |
| 1787 | |
|
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1788 // Throw-away extra info LAPACK gives so as to not change output. |
| 7788 | 1789 rcon = 0.0; |
|
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1790 if (info != 0) |
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1791 { |
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1792 info = -2; |
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1793 |
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1794 mattype.mark_as_unsymmetric (); |
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1795 typ = MatrixType::Full; |
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1796 } |
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1797 else |
| 5785 | 1798 { |
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1799 if (calc_cond) |
| 5785 | 1800 { |
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1801 Array<double> z (3 * nc); |
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1802 double *pz = z.fortran_vec (); |
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1803 Array<octave_idx_type> iz (nc); |
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1804 octave_idx_type *piz = iz.fortran_vec (); |
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1805 |
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1806 F77_XFCN (dpocon, DPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), |
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1807 nr, tmp_data, nr, anorm, |
| 7788 | 1808 rcon, pz, piz, info |
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1809 F77_CHAR_ARG_LEN (1))); |
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1810 |
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1811 if (info != 0) |
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1812 info = -2; |
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1813 |
| 7788 | 1814 volatile double rcond_plus_one = rcon + 1.0; |
| 1815 | |
| 1816 if (rcond_plus_one == 1.0 || xisnan (rcon)) | |
|
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1817 { |
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1818 info = -2; |
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1819 |
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1820 if (sing_handler) |
| 7788 | 1821 sing_handler (rcon); |
|
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1822 else |
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1823 (*current_liboctave_error_handler) |
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1824 ("matrix singular to machine precision, rcond = %g", |
| 7788 | 1825 rcon); |
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1826 } |
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1827 } |
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1828 |
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1829 if (info == 0) |
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1830 { |
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1831 retval = b; |
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1832 double *result = retval.fortran_vec (); |
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1833 |
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1834 octave_idx_type b_nc = b.cols (); |
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1835 |
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1836 F77_XFCN (dpotrs, DPOTRS, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
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1837 nr, b_nc, tmp_data, nr, |
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1838 result, b.rows(), info |
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1839 F77_CHAR_ARG_LEN (1))); |
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1840 } |
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1841 else |
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|
1842 { |
| 5785 | 1843 mattype.mark_as_unsymmetric (); |
| 1844 typ = MatrixType::Full; | |
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1845 } |
| 5785 | 1846 } |
| 1847 } | |
| 1848 | |
| 1849 if (typ == MatrixType::Full) | |
| 1850 { | |
| 1851 info = 0; | |
| 1852 | |
| 1853 Array<octave_idx_type> ipvt (nr); | |
| 1854 octave_idx_type *pipvt = ipvt.fortran_vec (); | |
| 1855 | |
| 1856 Matrix atmp = *this; | |
| 1857 double *tmp_data = atmp.fortran_vec (); | |
| 1858 if(anorm < 0.) | |
| 1859 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); | |
| 1860 | |
| 1861 Array<double> z (4 * nc); | |
| 1862 double *pz = z.fortran_vec (); | |
| 1863 Array<octave_idx_type> iz (nc); | |
| 1864 octave_idx_type *piz = iz.fortran_vec (); | |
| 1865 | |
| 1866 F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); | |
| 1867 | |
|
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1868 // Throw-away extra info LAPACK gives so as to not change output. |
| 7788 | 1869 rcon = 0.0; |
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1870 if (info != 0) |
| 5785 | 1871 { |
|
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1872 info = -2; |
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1873 |
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|
1874 if (sing_handler) |
| 7788 | 1875 sing_handler (rcon); |
|
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1876 else |
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1877 (*current_liboctave_error_handler) |
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1878 ("matrix singular to machine precision"); |
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1879 |
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|
1880 mattype.mark_as_rectangular (); |
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1881 } |
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1882 else |
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1883 { |
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1884 if (calc_cond) |
| 5785 | 1885 { |
|
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1886 // Now calculate the condition number for |
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1887 // non-singular matrix. |
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1888 char job = '1'; |
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1889 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
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1890 nc, tmp_data, nr, anorm, |
| 7788 | 1891 rcon, pz, piz, info |
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1892 F77_CHAR_ARG_LEN (1))); |
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1893 |
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1894 if (info != 0) |
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1895 info = -2; |
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1896 |
| 7788 | 1897 volatile double rcond_plus_one = rcon + 1.0; |
| 1898 | |
| 1899 if (rcond_plus_one == 1.0 || xisnan (rcon)) | |
| 5785 | 1900 { |
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1901 info = -2; |
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1902 |
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1903 if (sing_handler) |
| 7788 | 1904 sing_handler (rcon); |
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1905 else |
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1906 (*current_liboctave_error_handler) |
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1907 ("matrix singular to machine precision, rcond = %g", |
| 7788 | 1908 rcon); |
| 5785 | 1909 } |
| 1910 } | |
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1911 |
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1912 if (info == 0) |
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1913 { |
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1914 retval = b; |
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1915 double *result = retval.fortran_vec (); |
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|
1916 |
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|
1917 octave_idx_type b_nc = b.cols (); |
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|
1918 |
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|
1919 char job = 'N'; |
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1920 F77_XFCN (dgetrs, DGETRS, (F77_CONST_CHAR_ARG2 (&job, 1), |
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|
1921 nr, b_nc, tmp_data, nr, |
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|
1922 pipvt, result, b.rows(), info |
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|
1923 F77_CHAR_ARG_LEN (1))); |
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|
1924 } |
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|
1925 else |
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|
1926 mattype.mark_as_rectangular (); |
| 5785 | 1927 } |
| 1928 } | |
| 1929 else if (typ != MatrixType::Hermitian) | |
| 1930 (*current_liboctave_error_handler) ("incorrect matrix type"); | |
| 1931 } | |
| 1932 | |
| 1933 return retval; | |
| 1934 } | |
| 1935 | |
| 1936 Matrix | |
| 1937 Matrix::solve (MatrixType &typ, const Matrix& b) const | |
| 1938 { | |
| 1939 octave_idx_type info; | |
| 7788 | 1940 double rcon; |
| 1941 return solve (typ, b, info, rcon, 0); | |
| 5785 | 1942 } |
| 1943 | |
| 1944 Matrix | |
| 1945 Matrix::solve (MatrixType &typ, const Matrix& b, octave_idx_type& info, | |
| 7788 | 1946 double& rcon) const |
| 5785 | 1947 { |
| 7788 | 1948 return solve (typ, b, info, rcon, 0); |
| 5785 | 1949 } |
| 1950 | |
| 1951 Matrix | |
| 1952 Matrix::solve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, | |
| 7788 | 1953 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 1954 bool singular_fallback) const |
| 1955 { | |
| 1956 Matrix retval; | |
| 1957 int typ = mattype.type (); | |
| 1958 | |
| 1959 if (typ == MatrixType::Unknown) | |
| 1960 typ = mattype.type (*this); | |
| 1961 | |
| 1962 // Only calculate the condition number for LU/Cholesky | |
| 1963 if (typ == MatrixType::Upper || typ == MatrixType::Permuted_Upper) | |
| 7788 | 1964 retval = utsolve (mattype, b, info, rcon, sing_handler, false); |
| 5785 | 1965 else if (typ == MatrixType::Lower || typ == MatrixType::Permuted_Lower) |
| 7788 | 1966 retval = ltsolve (mattype, b, info, rcon, sing_handler, false); |
| 5785 | 1967 else if (typ == MatrixType::Full || typ == MatrixType::Hermitian) |
| 7788 | 1968 retval = fsolve (mattype, b, info, rcon, sing_handler, true); |
| 5785 | 1969 else if (typ != MatrixType::Rectangular) |
| 1970 { | |
| 1971 (*current_liboctave_error_handler) ("unknown matrix type"); | |
| 1972 return Matrix (); | |
| 1973 } | |
| 1974 | |
| 1975 // Rectangular or one of the above solvers flags a singular matrix | |
| 1976 if (singular_fallback && mattype.type () == MatrixType::Rectangular) | |
| 1977 { | |
| 1978 octave_idx_type rank; | |
| 7788 | 1979 retval = lssolve (b, info, rank, rcon); |
| 5785 | 1980 } |
| 1981 | |
| 1982 return retval; | |
| 1983 } | |
| 1984 | |
| 1985 ComplexMatrix | |
| 1986 Matrix::solve (MatrixType &typ, const ComplexMatrix& b) const | |
| 1987 { | |
| 1988 ComplexMatrix tmp (*this); | |
| 1989 return tmp.solve (typ, b); | |
| 1990 } | |
| 1991 | |
| 1992 ComplexMatrix | |
| 1993 Matrix::solve (MatrixType &typ, const ComplexMatrix& b, | |
| 1994 octave_idx_type& info) const | |
| 1995 { | |
| 1996 ComplexMatrix tmp (*this); | |
| 1997 return tmp.solve (typ, b, info); | |
| 1998 } | |
| 1999 | |
| 2000 ComplexMatrix | |
| 2001 Matrix::solve (MatrixType &typ, const ComplexMatrix& b, octave_idx_type& info, | |
| 7788 | 2002 double& rcon) const |
| 5785 | 2003 { |
| 2004 ComplexMatrix tmp (*this); | |
| 7788 | 2005 return tmp.solve (typ, b, info, rcon); |
| 5785 | 2006 } |
| 2007 | |
| 2008 ComplexMatrix | |
| 2009 Matrix::solve (MatrixType &typ, const ComplexMatrix& b, octave_idx_type& info, | |
| 7788 | 2010 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 2011 bool singular_fallback) const |
| 2012 { | |
| 2013 ComplexMatrix tmp (*this); | |
| 7788 | 2014 return tmp.solve (typ, b, info, rcon, sing_handler, singular_fallback); |
| 5785 | 2015 } |
| 2016 | |
| 2017 ColumnVector | |
| 2018 Matrix::solve (MatrixType &typ, const ColumnVector& b) const | |
| 2019 { | |
| 7788 | 2020 octave_idx_type info; double rcon; |
| 2021 return solve (typ, b, info, rcon); | |
| 5785 | 2022 } |
| 2023 | |
| 2024 ColumnVector | |
| 2025 Matrix::solve (MatrixType &typ, const ColumnVector& b, | |
| 2026 octave_idx_type& info) const | |
| 2027 { | |
| 7788 | 2028 double rcon; |
| 2029 return solve (typ, b, info, rcon); | |
| 5785 | 2030 } |
| 2031 | |
| 2032 ColumnVector | |
| 2033 Matrix::solve (MatrixType &typ, const ColumnVector& b, octave_idx_type& info, | |
| 7788 | 2034 double& rcon) const |
| 5785 | 2035 { |
| 7788 | 2036 return solve (typ, b, info, rcon, 0); |
| 5785 | 2037 } |
| 2038 | |
| 2039 ColumnVector | |
| 2040 Matrix::solve (MatrixType &typ, const ColumnVector& b, octave_idx_type& info, | |
| 7788 | 2041 double& rcon, solve_singularity_handler sing_handler) const |
| 5785 | 2042 { |
| 2043 Matrix tmp (b); | |
| 7788 | 2044 return solve (typ, tmp, info, rcon, sing_handler).column(static_cast<octave_idx_type> (0)); |
| 5785 | 2045 } |
| 2046 | |
| 2047 ComplexColumnVector | |
| 2048 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b) const | |
| 2049 { | |
| 2050 ComplexMatrix tmp (*this); | |
| 2051 return tmp.solve (typ, b); | |
| 2052 } | |
| 2053 | |
| 2054 ComplexColumnVector | |
| 2055 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, | |
| 2056 octave_idx_type& info) const | |
| 2057 { | |
| 2058 ComplexMatrix tmp (*this); | |
| 2059 return tmp.solve (typ, b, info); | |
| 2060 } | |
| 2061 | |
| 2062 ComplexColumnVector | |
| 2063 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, | |
| 7788 | 2064 octave_idx_type& info, double& rcon) const |
| 5785 | 2065 { |
| 2066 ComplexMatrix tmp (*this); | |
| 7788 | 2067 return tmp.solve (typ, b, info, rcon); |
| 5785 | 2068 } |
| 2069 | |
| 2070 ComplexColumnVector | |
| 2071 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, | |
| 7788 | 2072 octave_idx_type& info, double& rcon, |
| 5785 | 2073 solve_singularity_handler sing_handler) const |
| 2074 { | |
| 2075 ComplexMatrix tmp (*this); | |
| 7788 | 2076 return tmp.solve(typ, b, info, rcon, sing_handler); |
| 5785 | 2077 } |
| 2078 | |
| 2079 Matrix | |
| 458 | 2080 Matrix::solve (const Matrix& b) const |
| 2081 { | |
| 5275 | 2082 octave_idx_type info; |
| 7788 | 2083 double rcon; |
| 2084 return solve (b, info, rcon, 0); | |
| 458 | 2085 } |
| 2086 | |
| 2087 Matrix | |
| 5275 | 2088 Matrix::solve (const Matrix& b, octave_idx_type& info) const |
| 458 | 2089 { |
| 7788 | 2090 double rcon; |
| 2091 return solve (b, info, rcon, 0); | |
| 458 | 2092 } |
| 2093 | |
| 2094 Matrix | |
| 7788 | 2095 Matrix::solve (const Matrix& b, octave_idx_type& info, double& rcon) const |
| 458 | 2096 { |
| 7788 | 2097 return solve (b, info, rcon, 0); |
| 3480 | 2098 } |
| 2099 | |
| 2100 Matrix | |
| 5785 | 2101 Matrix::solve (const Matrix& b, octave_idx_type& info, |
| 7788 | 2102 double& rcon, solve_singularity_handler sing_handler) const |
| 3480 | 2103 { |
| 5785 | 2104 MatrixType mattype (*this); |
| 7788 | 2105 return solve (mattype, b, info, rcon, sing_handler); |
| 458 | 2106 } |
| 2107 | |
| 2108 ComplexMatrix | |
| 2109 Matrix::solve (const ComplexMatrix& b) const | |
| 2110 { | |
| 2111 ComplexMatrix tmp (*this); | |
| 2112 return tmp.solve (b); | |
| 2113 } | |
| 2114 | |
| 2115 ComplexMatrix | |
| 5275 | 2116 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info) const |
| 458 | 2117 { |
| 2118 ComplexMatrix tmp (*this); | |
| 2119 return tmp.solve (b, info); | |
| 2120 } | |
| 2121 | |
| 2122 ComplexMatrix | |
| 7788 | 2123 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcon) const |
| 458 | 2124 { |
| 2125 ComplexMatrix tmp (*this); | |
| 7788 | 2126 return tmp.solve (b, info, rcon); |
| 458 | 2127 } |
| 2128 | |
| 3480 | 2129 ComplexMatrix |
| 7788 | 2130 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcon, |
| 3480 | 2131 solve_singularity_handler sing_handler) const |
| 2132 { | |
| 2133 ComplexMatrix tmp (*this); | |
| 7788 | 2134 return tmp.solve (b, info, rcon, sing_handler); |
| 3480 | 2135 } |
| 2136 | |
| 458 | 2137 ColumnVector |
| 2138 Matrix::solve (const ColumnVector& b) const | |
| 2139 { | |
| 7788 | 2140 octave_idx_type info; double rcon; |
| 2141 return solve (b, info, rcon); | |
| 458 | 2142 } |
| 2143 | |
| 2144 ColumnVector | |
| 5275 | 2145 Matrix::solve (const ColumnVector& b, octave_idx_type& info) const |
| 458 | 2146 { |
| 7788 | 2147 double rcon; |
| 2148 return solve (b, info, rcon); | |
| 458 | 2149 } |
| 2150 | |
| 2151 ColumnVector | |
| 7788 | 2152 Matrix::solve (const ColumnVector& b, octave_idx_type& info, double& rcon) const |
| 458 | 2153 { |
| 7788 | 2154 return solve (b, info, rcon, 0); |
| 3480 | 2155 } |
| 2156 | |
| 2157 ColumnVector | |
| 7788 | 2158 Matrix::solve (const ColumnVector& b, octave_idx_type& info, double& rcon, |
| 3480 | 2159 solve_singularity_handler sing_handler) const |
| 2160 { | |
| 5785 | 2161 MatrixType mattype (*this); |
| 7788 | 2162 return solve (mattype, b, info, rcon, sing_handler); |
| 458 | 2163 } |
| 2164 | |
| 2165 ComplexColumnVector | |
| 2166 Matrix::solve (const ComplexColumnVector& b) const | |
| 2167 { | |
| 2168 ComplexMatrix tmp (*this); | |
| 2169 return tmp.solve (b); | |
| 2170 } | |
| 2171 | |
| 2172 ComplexColumnVector | |
| 5275 | 2173 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info) const |
| 458 | 2174 { |
| 2175 ComplexMatrix tmp (*this); | |
| 2176 return tmp.solve (b, info); | |
| 2177 } | |
| 2178 | |
| 2179 ComplexColumnVector | |
| 7788 | 2180 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info, double& rcon) const |
| 458 | 2181 { |
| 2182 ComplexMatrix tmp (*this); | |
| 7788 | 2183 return tmp.solve (b, info, rcon); |
| 458 | 2184 } |
| 2185 | |
| 3480 | 2186 ComplexColumnVector |
| 7788 | 2187 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info, double& rcon, |
| 3480 | 2188 solve_singularity_handler sing_handler) const |
| 2189 { | |
| 2190 ComplexMatrix tmp (*this); | |
| 7788 | 2191 return tmp.solve (b, info, rcon, sing_handler); |
| 3480 | 2192 } |
| 2193 | |
| 458 | 2194 Matrix |
| 2195 Matrix::lssolve (const Matrix& b) const | |
| 2196 { | |
| 5275 | 2197 octave_idx_type info; |
| 2198 octave_idx_type rank; | |
| 7788 | 2199 double rcon; |
| 2200 return lssolve (b, info, rank, rcon); | |
| 458 | 2201 } |
| 2202 | |
| 2203 Matrix | |
| 5275 | 2204 Matrix::lssolve (const Matrix& b, octave_idx_type& info) const |
| 458 | 2205 { |
| 5275 | 2206 octave_idx_type rank; |
| 7788 | 2207 double rcon; |
| 2208 return lssolve (b, info, rank, rcon); | |
| 458 | 2209 } |
| 2210 | |
| 2211 Matrix | |
| 7072 | 2212 Matrix::lssolve (const Matrix& b, octave_idx_type& info, |
| 2213 octave_idx_type& rank) const | |
| 458 | 2214 { |
| 7788 | 2215 double rcon; |
| 2216 return lssolve (b, info, rank, rcon); | |
| 7076 | 2217 } |
| 2218 | |
| 2219 Matrix | |
| 2220 Matrix::lssolve (const Matrix& b, octave_idx_type& info, | |
| 7788 | 2221 octave_idx_type& rank, double &rcon) const |
| 7076 | 2222 { |
| 1948 | 2223 Matrix retval; |
| 2224 | |
| 5275 | 2225 octave_idx_type nrhs = b.cols (); |
| 2226 | |
| 2227 octave_idx_type m = rows (); | |
| 2228 octave_idx_type n = cols (); | |
| 458 | 2229 |
| 6924 | 2230 if (m != b.rows ()) |
| 1948 | 2231 (*current_liboctave_error_handler) |
| 6924 | 2232 ("matrix dimension mismatch solution of linear equations"); |
| 2233 else if (m == 0 || n == 0 || b.cols () == 0) | |
| 2234 retval = Matrix (n, b.cols (), 0.0); | |
| 1948 | 2235 else |
| 458 | 2236 { |
| 7072 | 2237 volatile octave_idx_type minmn = (m < n ? m : n); |
| 2238 octave_idx_type maxmn = m > n ? m : n; | |
| 7788 | 2239 rcon = -1.0; |
| 7072 | 2240 if (m != n) |
| 2241 { | |
| 2242 retval = Matrix (maxmn, nrhs, 0.0); | |
| 2243 | |
| 2244 for (octave_idx_type j = 0; j < nrhs; j++) | |
| 2245 for (octave_idx_type i = 0; i < m; i++) | |
| 2246 retval.elem (i, j) = b.elem (i, j); | |
| 2247 } | |
| 2248 else | |
| 2249 retval = b; | |
| 2250 | |
| 1948 | 2251 Matrix atmp = *this; |
| 2252 double *tmp_data = atmp.fortran_vec (); | |
| 2253 | |
| 7072 | 2254 double *pretval = retval.fortran_vec (); |
| 2255 Array<double> s (minmn); | |
| 7071 | 2256 double *ps = s.fortran_vec (); |
| 1948 | 2257 |
| 7072 | 2258 // Ask DGELSD what the dimension of WORK should be. |
| 5275 | 2259 octave_idx_type lwork = -1; |
| 3752 | 2260 |
| 2261 Array<double> work (1); | |
| 1948 | 2262 |
| 7477 | 2263 octave_idx_type smlsiz; |
| 2264 F77_FUNC (xilaenv, XILAENV) (9, F77_CONST_CHAR_ARG2 ("DGELSD", 6), | |
| 2265 F77_CONST_CHAR_ARG2 (" ", 1), | |
| 7478 | 2266 0, 0, 0, 0, smlsiz |
| 7477 | 2267 F77_CHAR_ARG_LEN (6) |
| 7478 | 2268 F77_CHAR_ARG_LEN (1)); |
| 7079 | 2269 |
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2270 octave_idx_type mnthr; |
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2271 F77_FUNC (xilaenv, XILAENV) (6, F77_CONST_CHAR_ARG2 ("DGELSD", 6), |
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2272 F77_CONST_CHAR_ARG2 (" ", 1), |
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2273 m, n, nrhs, -1, mnthr |
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2274 F77_CHAR_ARG_LEN (6) |
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2275 F77_CHAR_ARG_LEN (1)); |
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2276 |
| 7079 | 2277 // We compute the size of iwork because DGELSD in older versions |
| 2278 // of LAPACK does not return it on a query call. | |
| 7124 | 2279 double dminmn = static_cast<double> (minmn); |
| 2280 double dsmlsizp1 = static_cast<double> (smlsiz+1); | |
| 7079 | 2281 #if defined (HAVE_LOG2) |
| 7367 | 2282 double tmp = log2 (dminmn / dsmlsizp1); |
| 7079 | 2283 #else |
| 7367 | 2284 double tmp = log (dminmn / dsmlsizp1) / log (2.0); |
| 7079 | 2285 #endif |
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2286 octave_idx_type nlvl = static_cast<octave_idx_type> (tmp) + 1; |
| 7079 | 2287 if (nlvl < 0) |
| 2288 nlvl = 0; | |
| 2289 | |
| 2290 octave_idx_type liwork = 3 * minmn * nlvl + 11 * minmn; | |
| 2291 if (liwork < 1) | |
| 2292 liwork = 1; | |
| 7072 | 2293 Array<octave_idx_type> iwork (liwork); |
| 2294 octave_idx_type* piwork = iwork.fortran_vec (); | |
| 2295 | |
| 2296 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, | |
| 7788 | 2297 ps, rcon, rank, work.fortran_vec (), |
| 7072 | 2298 lwork, piwork, info)); |
| 1948 | 2299 |
| 7476 | 2300 // The workspace query is broken in at least LAPACK 3.0.0 |
|
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2301 // through 3.1.1 when n >= mnthr. The obtuse formula below |
| 7476 | 2302 // should provide sufficient workspace for DGELSD to operate |
| 2303 // efficiently. | |
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2304 if (n >= mnthr) |
| 7476 | 2305 { |
| 2306 const octave_idx_type wlalsd | |
| 2307 = 9*m + 2*m*smlsiz + 8*m*nlvl + m*nrhs + (smlsiz+1)*(smlsiz+1); | |
| 2308 | |
| 2309 octave_idx_type addend = m; | |
| 2310 | |
| 2311 if (2*m-4 > addend) | |
| 2312 addend = 2*m-4; | |
| 2313 | |
| 2314 if (nrhs > addend) | |
| 2315 addend = nrhs; | |
| 2316 | |
| 2317 if (n-3*m > addend) | |
| 2318 addend = n-3*m; | |
| 2319 | |
| 2320 if (wlalsd > addend) | |
| 2321 addend = wlalsd; | |
| 2322 | |
| 2323 const octave_idx_type lworkaround = 4*m + m*m + addend; | |
| 2324 | |
| 2325 if (work(0) < lworkaround) | |
| 2326 work(0) = lworkaround; | |
| 2327 } | |
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2328 else if (m >= n) |
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2329 { |
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2330 octave_idx_type lworkaround |
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2331 = 12*n + 2*n*smlsiz + 8*n*nlvl + n*nrhs + (smlsiz+1)*(smlsiz+1); |
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2332 |
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|
2333 if (work(0) < lworkaround) |
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2334 work(0) = lworkaround; |
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2335 } |
| 7476 | 2336 |
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2337 lwork = static_cast<octave_idx_type> (work(0)); |
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2338 work.resize (lwork); |
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2339 |
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|
2340 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, |
| 7788 | 2341 maxmn, ps, rcon, rank, |
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2342 work.fortran_vec (), lwork, |
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|
2343 piwork, info)); |
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|
2344 |
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2345 if (rank < minmn) |
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2346 (*current_liboctave_warning_handler) |
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|
2347 ("dgelsd: rank deficient %dx%d matrix, rank = %d", m, n, rank); |
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|
2348 if (s.elem (0) == 0.0) |
| 7788 | 2349 rcon = 0.0; |
| 1948 | 2350 else |
| 7788 | 2351 rcon = s.elem (minmn - 1) / s.elem (0); |
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|
2352 |
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|
2353 retval.resize (n, nrhs); |
| 458 | 2354 } |
| 2355 | |
| 2356 return retval; | |
| 2357 } | |
| 2358 | |
| 2359 ComplexMatrix | |
| 2360 Matrix::lssolve (const ComplexMatrix& b) const | |
| 2361 { | |
| 2362 ComplexMatrix tmp (*this); | |
| 5275 | 2363 octave_idx_type info; |
| 2364 octave_idx_type rank; | |
| 7788 | 2365 double rcon; |
| 2366 return tmp.lssolve (b, info, rank, rcon); | |
| 458 | 2367 } |
| 2368 | |
| 2369 ComplexMatrix | |
| 5275 | 2370 Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info) const |
| 458 | 2371 { |
| 2372 ComplexMatrix tmp (*this); | |
| 5275 | 2373 octave_idx_type rank; |
| 7788 | 2374 double rcon; |
| 2375 return tmp.lssolve (b, info, rank, rcon); | |
| 458 | 2376 } |
| 2377 | |
| 2378 ComplexMatrix | |
| 7076 | 2379 Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info, |
| 2380 octave_idx_type& rank) const | |
| 458 | 2381 { |
| 2382 ComplexMatrix tmp (*this); | |
| 7788 | 2383 double rcon; |
| 2384 return tmp.lssolve (b, info, rank, rcon); | |
| 7076 | 2385 } |
| 2386 | |
| 2387 ComplexMatrix | |
| 2388 Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info, | |
| 7788 | 2389 octave_idx_type& rank, double& rcon) const |
| 7076 | 2390 { |
| 2391 ComplexMatrix tmp (*this); | |
| 7788 | 2392 return tmp.lssolve (b, info, rank, rcon); |
| 458 | 2393 } |
| 2394 | |
| 2395 ColumnVector | |
| 2396 Matrix::lssolve (const ColumnVector& b) const | |
| 2397 { | |
| 5275 | 2398 octave_idx_type info; |
| 2399 octave_idx_type rank; | |
| 7788 | 2400 double rcon; |
| 2401 return lssolve (b, info, rank, rcon); | |
| 458 | 2402 } |
| 2403 | |
| 2404 ColumnVector | |
| 5275 | 2405 Matrix::lssolve (const ColumnVector& b, octave_idx_type& info) const |
| 458 | 2406 { |
| 5275 | 2407 octave_idx_type rank; |
| 7788 | 2408 double rcon; |
| 2409 return lssolve (b, info, rank, rcon); | |
| 458 | 2410 } |
| 2411 | |
| 2412 ColumnVector | |
| 7072 | 2413 Matrix::lssolve (const ColumnVector& b, octave_idx_type& info, |
| 2414 octave_idx_type& rank) const | |
| 458 | 2415 { |
| 7788 | 2416 double rcon; |
| 2417 return lssolve (b, info, rank, rcon); | |
| 7076 | 2418 } |
| 2419 | |
| 2420 ColumnVector | |
| 2421 Matrix::lssolve (const ColumnVector& b, octave_idx_type& info, | |
| 7788 | 2422 octave_idx_type& rank, double &rcon) const |
| 7076 | 2423 { |
| 1948 | 2424 ColumnVector retval; |
| 2425 | |
| 5275 | 2426 octave_idx_type nrhs = 1; |
| 2427 | |
| 2428 octave_idx_type m = rows (); | |
| 2429 octave_idx_type n = cols (); | |
| 458 | 2430 |
| 6924 | 2431 if (m != b.length ()) |
| 1948 | 2432 (*current_liboctave_error_handler) |
| 6924 | 2433 ("matrix dimension mismatch solution of linear equations"); |
| 2434 else if (m == 0 || n == 0) | |
| 2435 retval = ColumnVector (n, 0.0); | |
| 1948 | 2436 else |
| 458 | 2437 { |
| 7072 | 2438 volatile octave_idx_type minmn = (m < n ? m : n); |
| 2439 octave_idx_type maxmn = m > n ? m : n; | |
| 7788 | 2440 rcon = -1.0; |
| 7072 | 2441 |
| 2442 if (m != n) | |
| 2443 { | |
| 2444 retval = ColumnVector (maxmn, 0.0); | |
| 2445 | |
| 2446 for (octave_idx_type i = 0; i < m; i++) | |
| 2447 retval.elem (i) = b.elem (i); | |
| 2448 } | |
| 2449 else | |
| 2450 retval = b; | |
| 2451 | |
| 1948 | 2452 Matrix atmp = *this; |
| 2453 double *tmp_data = atmp.fortran_vec (); | |
| 2454 | |
| 7072 | 2455 double *pretval = retval.fortran_vec (); |
| 2456 Array<double> s (minmn); | |
| 7071 | 2457 double *ps = s.fortran_vec (); |
| 1948 | 2458 |
| 7072 | 2459 // Ask DGELSD what the dimension of WORK should be. |
| 5275 | 2460 octave_idx_type lwork = -1; |
| 3752 | 2461 |
| 2462 Array<double> work (1); | |
| 2463 | |
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2464 octave_idx_type smlsiz; |
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2465 F77_FUNC (xilaenv, XILAENV) (9, F77_CONST_CHAR_ARG2 ("DGELSD", 6), |
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2466 F77_CONST_CHAR_ARG2 (" ", 1), |
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2467 0, 0, 0, 0, smlsiz |
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2468 F77_CHAR_ARG_LEN (6) |
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2469 F77_CHAR_ARG_LEN (1)); |
| 7079 | 2470 |
| 2471 // We compute the size of iwork because DGELSD in older versions | |
| 2472 // of LAPACK does not return it on a query call. | |
| 7124 | 2473 double dminmn = static_cast<double> (minmn); |
| 2474 double dsmlsizp1 = static_cast<double> (smlsiz+1); | |
| 7079 | 2475 #if defined (HAVE_LOG2) |
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2476 double tmp = log2 (dminmn / dsmlsizp1); |
| 7079 | 2477 #else |
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2478 double tmp = log (dminmn / dsmlsizp1) / log (2.0); |
| 7079 | 2479 #endif |
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2480 octave_idx_type nlvl = static_cast<octave_idx_type> (tmp) + 1; |
| 7079 | 2481 if (nlvl < 0) |
| 2482 nlvl = 0; | |
| 2483 | |
| 2484 octave_idx_type liwork = 3 * minmn * nlvl + 11 * minmn; | |
| 2485 if (liwork < 1) | |
| 2486 liwork = 1; | |
| 7072 | 2487 Array<octave_idx_type> iwork (liwork); |
| 2488 octave_idx_type* piwork = iwork.fortran_vec (); | |
| 2489 | |
| 2490 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, | |
| 7788 | 2491 ps, rcon, rank, work.fortran_vec (), |
| 7072 | 2492 lwork, piwork, info)); |
| 1948 | 2493 |
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2494 lwork = static_cast<octave_idx_type> (work(0)); |
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2495 work.resize (lwork); |
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2496 |
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2497 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, |
| 7788 | 2498 maxmn, ps, rcon, rank, |
|
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2499 work.fortran_vec (), lwork, |
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2500 piwork, info)); |
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2501 |
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2502 if (rank < minmn) |
| 1948 | 2503 { |
|
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2504 if (rank < minmn) |
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2505 (*current_liboctave_warning_handler) |
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2506 ("dgelsd: rank deficient %dx%d matrix, rank = %d", m, n, rank); |
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2507 if (s.elem (0) == 0.0) |
| 7788 | 2508 rcon = 0.0; |
|
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2509 else |
| 7788 | 2510 rcon = s.elem (minmn - 1) / s.elem (0); |
| 1948 | 2511 } |
|
7482
29980c6b8604
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John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
2512 |
|
29980c6b8604
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parents:
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diff
changeset
|
2513 retval.resize (n, nrhs); |
| 458 | 2514 } |
| 2515 | |
| 2516 return retval; | |
| 2517 } | |
| 2518 | |
| 2519 ComplexColumnVector | |
| 2520 Matrix::lssolve (const ComplexColumnVector& b) const | |
| 2521 { | |
| 2522 ComplexMatrix tmp (*this); | |
| 7076 | 2523 octave_idx_type info; |
| 2524 octave_idx_type rank; | |
| 7788 | 2525 double rcon; |
| 2526 return tmp.lssolve (b, info, rank, rcon); | |
| 458 | 2527 } |
| 2528 | |
| 2529 ComplexColumnVector | |
| 5275 | 2530 Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info) const |
| 458 | 2531 { |
| 2532 ComplexMatrix tmp (*this); | |
| 7076 | 2533 octave_idx_type rank; |
| 7788 | 2534 double rcon; |
| 2535 return tmp.lssolve (b, info, rank, rcon); | |
| 458 | 2536 } |
| 2537 | |
| 2538 ComplexColumnVector | |
| 7076 | 2539 Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, |
| 2540 octave_idx_type& rank) const | |
| 458 | 2541 { |
| 2542 ComplexMatrix tmp (*this); | |
| 7788 | 2543 double rcon; |
| 2544 return tmp.lssolve (b, info, rank, rcon); | |
| 7076 | 2545 } |
| 2546 | |
| 2547 ComplexColumnVector | |
| 2548 Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, | |
| 7788 | 2549 octave_idx_type& rank, double &rcon) const |
| 7076 | 2550 { |
| 2551 ComplexMatrix tmp (*this); | |
| 7788 | 2552 return tmp.lssolve (b, info, rank, rcon); |
| 458 | 2553 } |
| 2554 | |
| 1819 | 2555 // Constants for matrix exponential calculation. |
| 2556 | |
| 2557 static double padec [] = | |
| 2558 { | |
| 2559 5.0000000000000000e-1, | |
| 2560 1.1666666666666667e-1, | |
| 2561 1.6666666666666667e-2, | |
| 2562 1.6025641025641026e-3, | |
| 2563 1.0683760683760684e-4, | |
| 2564 4.8562548562548563e-6, | |
| 2565 1.3875013875013875e-7, | |
| 2566 1.9270852604185938e-9, | |
| 2567 }; | |
| 2568 | |
| 7400 | 2569 static void |
| 7788 | 2570 solve_singularity_warning (double rcon) |
| 7400 | 2571 { |
| 2572 (*current_liboctave_warning_handler) | |
| 2573 ("singular matrix encountered in expm calculation, rcond = %g", | |
| 7788 | 2574 rcon); |
| 7400 | 2575 } |
| 2576 | |
| 1819 | 2577 Matrix |
| 2578 Matrix::expm (void) const | |
| 2579 { | |
| 2580 Matrix retval; | |
| 2581 | |
| 2582 Matrix m = *this; | |
| 2583 | |
| 6699 | 2584 if (numel () == 1) |
| 2585 return Matrix (1, 1, exp (m(0))); | |
| 2586 | |
| 5275 | 2587 octave_idx_type nc = columns (); |
| 1819 | 2588 |
| 3130 | 2589 // Preconditioning step 1: trace normalization to reduce dynamic |
| 2590 // range of poles, but avoid making stable eigenvalues unstable. | |
| 2591 | |
| 1819 | 2592 // trace shift value |
| 3331 | 2593 volatile double trshift = 0.0; |
| 1819 | 2594 |
| 5275 | 2595 for (octave_idx_type i = 0; i < nc; i++) |
| 1819 | 2596 trshift += m.elem (i, i); |
| 2597 | |
| 2598 trshift /= nc; | |
| 2599 | |
| 3130 | 2600 if (trshift > 0.0) |
| 2601 { | |
| 5275 | 2602 for (octave_idx_type i = 0; i < nc; i++) |
| 3130 | 2603 m.elem (i, i) -= trshift; |
| 2604 } | |
| 1819 | 2605 |
| 3331 | 2606 // Preconditioning step 2: balancing; code follows development |
| 2607 // in AEPBAL | |
| 2608 | |
| 2609 double *p_m = m.fortran_vec (); | |
| 2610 | |
| 5275 | 2611 octave_idx_type info, ilo, ihi, ilos, ihis; |
| 3468 | 2612 Array<double> dpermute (nc); |
| 2613 Array<double> dscale (nc); | |
| 3466 | 2614 |
| 3468 | 2615 // permutation first |
| 2616 char job = 'P'; | |
| 4552 | 2617 F77_XFCN (dgebal, DGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
| 2618 nc, p_m, nc, ilo, ihi, | |
| 2619 dpermute.fortran_vec (), info | |
| 2620 F77_CHAR_ARG_LEN (1))); | |
| 3466 | 2621 |
| 3468 | 2622 // then scaling |
| 2623 job = 'S'; | |
| 4552 | 2624 F77_XFCN (dgebal, DGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), |
| 2625 nc, p_m, nc, ilos, ihis, | |
| 2626 dscale.fortran_vec (), info | |
| 2627 F77_CHAR_ARG_LEN (1))); | |
| 3331 | 2628 |
| 1819 | 2629 // Preconditioning step 3: scaling. |
| 3331 | 2630 |
| 1819 | 2631 ColumnVector work(nc); |
| 3130 | 2632 double inf_norm; |
| 3331 | 2633 |
| 4552 | 2634 F77_XFCN (xdlange, XDLANGE, (F77_CONST_CHAR_ARG2 ("I", 1), |
| 2635 nc, nc, m.fortran_vec (), nc, | |
| 2636 work.fortran_vec (), inf_norm | |
| 2637 F77_CHAR_ARG_LEN (1))); | |
| 3331 | 2638 |
| 5275 | 2639 octave_idx_type sqpow = static_cast<octave_idx_type> (inf_norm > 0.0 |
| 1819 | 2640 ? (1.0 + log (inf_norm) / log (2.0)) |
| 2641 : 0.0); | |
| 3331 | 2642 |
| 1819 | 2643 // Check whether we need to square at all. |
| 3331 | 2644 |
| 1819 | 2645 if (sqpow < 0) |
| 2646 sqpow = 0; | |
| 3331 | 2647 |
| 1819 | 2648 if (sqpow > 0) |
| 2649 { | |
| 7400 | 2650 if (sqpow > 1023) |
| 2651 sqpow = 1023; | |
| 2652 | |
| 1819 | 2653 double scale_factor = 1.0; |
| 5275 | 2654 for (octave_idx_type i = 0; i < sqpow; i++) |
| 1819 | 2655 scale_factor *= 2.0; |
| 7400 | 2656 |
| 1819 | 2657 m = m / scale_factor; |
| 2658 } | |
| 3331 | 2659 |
| 1819 | 2660 // npp, dpp: pade' approx polynomial matrices. |
| 3331 | 2661 |
| 1819 | 2662 Matrix npp (nc, nc, 0.0); |
| 7265 | 2663 double *pnpp = npp.fortran_vec (); |
| 1819 | 2664 Matrix dpp = npp; |
| 7265 | 2665 double *pdpp = dpp.fortran_vec (); |
| 3331 | 2666 |
| 1819 | 2667 // Now powers a^8 ... a^1. |
| 3331 | 2668 |
| 5275 | 2669 octave_idx_type minus_one_j = -1; |
| 2670 for (octave_idx_type j = 7; j >= 0; j--) | |
| 1819 | 2671 { |
| 7265 | 2672 for (octave_idx_type i = 0; i < nc; i++) |
| 2673 { | |
| 2674 octave_idx_type k = i * nc + i; | |
| 2675 pnpp[k] += padec[j]; | |
| 2676 pdpp[k] += minus_one_j * padec[j]; | |
| 2677 } | |
| 2678 | |
| 2679 npp = m * npp; | |
| 2680 pnpp = npp.fortran_vec (); | |
| 2681 | |
| 2682 dpp = m * dpp; | |
| 2683 pdpp = dpp.fortran_vec (); | |
| 2684 | |
| 1819 | 2685 minus_one_j *= -1; |
| 2686 } | |
| 3331 | 2687 |
| 1819 | 2688 // Zero power. |
| 3331 | 2689 |
| 1819 | 2690 dpp = -dpp; |
| 5275 | 2691 for (octave_idx_type j = 0; j < nc; j++) |
| 1819 | 2692 { |
| 2693 npp.elem (j, j) += 1.0; | |
| 2694 dpp.elem (j, j) += 1.0; | |
| 2695 } | |
| 3331 | 2696 |
| 1819 | 2697 // Compute pade approximation = inverse (dpp) * npp. |
| 2698 | |
| 7788 | 2699 double rcon; |
| 2700 retval = dpp.solve (npp, info, rcon, solve_singularity_warning); | |
| 7400 | 2701 |
| 2702 if (info < 0) | |
| 2703 return retval; | |
| 2704 | |
| 1819 | 2705 // Reverse preconditioning step 3: repeated squaring. |
| 3331 | 2706 |
| 1819 | 2707 while (sqpow) |
| 2708 { | |
| 2709 retval = retval * retval; | |
| 2710 sqpow--; | |
| 2711 } | |
| 3331 | 2712 |
| 1819 | 2713 // Reverse preconditioning step 2: inverse balancing. |
| 3466 | 2714 // apply inverse scaling to computed exponential |
| 5275 | 2715 for (octave_idx_type i = 0; i < nc; i++) |
| 2716 for (octave_idx_type j = 0; j < nc; j++) | |
|
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diff
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|
2717 retval(i,j) *= dscale(i) / dscale(j); |
| 3466 | 2718 |
| 4153 | 2719 OCTAVE_QUIT; |
| 2720 | |
| 3466 | 2721 // construct balancing permutation vector |
| 5275 | 2722 Array<octave_idx_type> iperm (nc); |
| 2723 for (octave_idx_type i = 0; i < nc; i++) | |
| 4593 | 2724 iperm(i) = i; // identity permutation |
| 3466 | 2725 |
|
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parents:
7922
diff
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|
2726 // trailing permutations must be done in reverse order |
|
851803f7bb4d
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parents:
7922
diff
changeset
|
2727 for (octave_idx_type i = nc - 1; i >= ihi; i--) |
|
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parents:
7922
diff
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|
2728 { |
|
851803f7bb4d
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parents:
7922
diff
changeset
|
2729 octave_idx_type swapidx = static_cast<octave_idx_type> (dpermute(i)) - 1; |
|
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parents:
7922
diff
changeset
|
2730 octave_idx_type tmp = iperm(i); |
|
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parents:
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diff
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|
2731 iperm(i) = iperm(swapidx); |
|
851803f7bb4d
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parents:
7922
diff
changeset
|
2732 iperm(swapidx) = tmp; |
|
851803f7bb4d
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parents:
7922
diff
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|
2733 } |
|
851803f7bb4d
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diff
changeset
|
2734 |
| 3466 | 2735 // leading permutations in forward order |
| 5275 | 2736 for (octave_idx_type i = 0; i < (ilo-1); i++) |
| 3468 | 2737 { |
| 5275 | 2738 octave_idx_type swapidx = static_cast<octave_idx_type> (dpermute(i)) - 1; |
| 2739 octave_idx_type tmp = iperm(i); | |
| 4593 | 2740 iperm(i) = iperm (swapidx); |
| 2741 iperm(swapidx) = tmp; | |
| 3468 | 2742 } |
| 3466 | 2743 |
| 7416 | 2744 // construct inverse balancing permutation vector |
| 2745 Array<octave_idx_type> invpvec (nc); | |
| 2746 for (octave_idx_type i = 0; i < nc; i++) | |
| 2747 invpvec(iperm(i)) = i; // Thanks to R. A. Lippert for this method | |
| 2748 | |
| 2749 OCTAVE_QUIT; | |
|
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improve inverse preconditioning according to Marco Caliari
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7922
diff
changeset
|
2750 |
| 7416 | 2751 Matrix tmpMat = retval; |
| 2752 for (octave_idx_type i = 0; i < nc; i++) | |
| 2753 for (octave_idx_type j = 0; j < nc; j++) | |
| 2754 retval(i,j) = tmpMat(invpvec(i),invpvec(j)); | |
| 2755 | |
|
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diff
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|
2756 // Reverse preconditioning step 1: fix trace normalization. |
| 3130 | 2757 if (trshift > 0.0) |
| 2758 retval = exp (trshift) * retval; | |
| 2759 | |
| 2760 return retval; | |
| 1819 | 2761 } |
| 2762 | |
| 458 | 2763 Matrix& |
| 2764 Matrix::operator += (const DiagMatrix& a) | |
| 2765 { | |
| 5275 | 2766 octave_idx_type nr = rows (); |
| 2767 octave_idx_type nc = cols (); | |
| 2768 | |
| 2769 octave_idx_type a_nr = a.rows (); | |
| 2770 octave_idx_type a_nc = a.cols (); | |
| 2385 | 2771 |
| 2772 if (nr != a_nr || nc != a_nc) | |
| 458 | 2773 { |
| 2385 | 2774 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
| 458 | 2775 return *this; |
| 2776 } | |
| 2777 | |
| 5275 | 2778 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 2779 elem (i, i) += a.elem (i, i); |
| 2780 | |
| 2781 return *this; | |
| 2782 } | |
| 2783 | |
| 2784 Matrix& | |
| 2785 Matrix::operator -= (const DiagMatrix& a) | |
| 2786 { | |
| 5275 | 2787 octave_idx_type nr = rows (); |
| 2788 octave_idx_type nc = cols (); | |
| 2789 | |
| 2790 octave_idx_type a_nr = a.rows (); | |
| 2791 octave_idx_type a_nc = a.cols (); | |
| 2385 | 2792 |
| 2793 if (nr != a_nr || nc != a_nc) | |
| 458 | 2794 { |
| 2385 | 2795 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
| 458 | 2796 return *this; |
| 2797 } | |
| 2798 | |
| 5275 | 2799 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 2800 elem (i, i) -= a.elem (i, i); |
| 2801 | |
| 2802 return *this; | |
| 2803 } | |
| 2804 | |
| 2805 // unary operations | |
| 2806 | |
| 2964 | 2807 boolMatrix |
| 458 | 2808 Matrix::operator ! (void) const |
| 2809 { | |
| 5275 | 2810 octave_idx_type nr = rows (); |
| 2811 octave_idx_type nc = cols (); | |
| 458 | 2812 |
| 2964 | 2813 boolMatrix b (nr, nc); |
| 458 | 2814 |
| 5275 | 2815 for (octave_idx_type j = 0; j < nc; j++) |
| 2816 for (octave_idx_type i = 0; i < nr; i++) | |
| 458 | 2817 b.elem (i, j) = ! elem (i, j); |
| 2818 | |
| 2819 return b; | |
| 2820 } | |
| 2821 | |
| 1205 | 2822 // column vector by row vector -> matrix operations |
| 458 | 2823 |
| 1205 | 2824 Matrix |
| 2825 operator * (const ColumnVector& v, const RowVector& a) | |
| 458 | 2826 { |
| 1948 | 2827 Matrix retval; |
| 2828 | |
| 5275 | 2829 octave_idx_type len = v.length (); |
| 3233 | 2830 |
| 2831 if (len != 0) | |
| 1205 | 2832 { |
| 5275 | 2833 octave_idx_type a_len = a.length (); |
| 3233 | 2834 |
| 2835 retval.resize (len, a_len); | |
| 2836 double *c = retval.fortran_vec (); | |
| 2837 | |
| 4552 | 2838 F77_XFCN (dgemm, DGEMM, (F77_CONST_CHAR_ARG2 ("N", 1), |
| 2839 F77_CONST_CHAR_ARG2 ("N", 1), | |
| 2840 len, a_len, 1, 1.0, v.data (), len, | |
| 2841 a.data (), 1, 0.0, c, len | |
| 2842 F77_CHAR_ARG_LEN (1) | |
| 2843 F77_CHAR_ARG_LEN (1))); | |
| 1205 | 2844 } |
| 458 | 2845 |
| 1948 | 2846 return retval; |
| 458 | 2847 } |
| 2848 | |
| 2849 // other operations. | |
| 2850 | |
| 2851 Matrix | |
|
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diff
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|
2852 Matrix::map (dmapper fcn) const |
| 1205 | 2853 { |
|
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diff
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|
2854 return MArray2<double>::map<double> (func_ptr (fcn)); |
|
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diff
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|
2855 } |
|
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diff
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|
2856 |
|
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diff
changeset
|
2857 ComplexMatrix |
|
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diff
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|
2858 Matrix::map (cmapper fcn) const |
|
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diff
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|
2859 { |
|
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diff
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|
2860 return MArray2<double>::map<Complex> (func_ptr (fcn)); |
| 1205 | 2861 } |
| 2862 | |
| 3248 | 2863 boolMatrix |
|
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|
2864 Matrix::map (bmapper fcn) const |
| 3248 | 2865 { |
|
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|
2866 return MArray2<double>::map<bool> (func_ptr (fcn)); |
| 458 | 2867 } |
| 2868 | |
| 2385 | 2869 bool |
| 4431 | 2870 Matrix::any_element_is_negative (bool neg_zero) const |
| 2385 | 2871 { |
| 5275 | 2872 octave_idx_type nel = nelem (); |
| 2385 | 2873 |
| 4431 | 2874 if (neg_zero) |
| 2875 { | |
| 5275 | 2876 for (octave_idx_type i = 0; i < nel; i++) |
| 4634 | 2877 if (lo_ieee_signbit (elem (i))) |
| 2878 return true; | |
| 4431 | 2879 } |
| 2880 else | |
| 2881 { | |
| 5275 | 2882 for (octave_idx_type i = 0; i < nel; i++) |
| 4634 | 2883 if (elem (i) < 0) |
| 2884 return true; | |
| 4431 | 2885 } |
| 2385 | 2886 |
| 2887 return false; | |
| 2888 } | |
| 2889 | |
|
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|
2890 bool |
|
935be827eaf8
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|
2891 Matrix::any_element_is_nan (void) const |
|
935be827eaf8
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parents:
7803
diff
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|
2892 { |
|
935be827eaf8
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|
2893 octave_idx_type nel = nelem (); |
|
935be827eaf8
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7803
diff
changeset
|
2894 |
|
935be827eaf8
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7803
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|
2895 for (octave_idx_type i = 0; i < nel; i++) |
|
935be827eaf8
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7803
diff
changeset
|
2896 { |
|
935be827eaf8
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7803
diff
changeset
|
2897 double val = elem (i); |
|
935be827eaf8
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parents:
7803
diff
changeset
|
2898 if (xisnan (val)) |
|
935be827eaf8
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7803
diff
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|
2899 return true; |
|
935be827eaf8
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diff
changeset
|
2900 } |
|
935be827eaf8
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diff
changeset
|
2901 |
|
935be827eaf8
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diff
changeset
|
2902 return false; |
|
935be827eaf8
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diff
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|
2903 } |
| 2385 | 2904 |
| 2905 bool | |
| 2906 Matrix::any_element_is_inf_or_nan (void) const | |
| 2907 { | |
| 5275 | 2908 octave_idx_type nel = nelem (); |
| 2909 | |
| 2910 for (octave_idx_type i = 0; i < nel; i++) | |
| 4634 | 2911 { |
| 2912 double val = elem (i); | |
| 2913 if (xisinf (val) || xisnan (val)) | |
| 2914 return true; | |
| 2915 } | |
| 2916 | |
| 2917 return false; | |
| 2385 | 2918 } |
| 2919 | |
| 2920 bool | |
| 5943 | 2921 Matrix::any_element_not_one_or_zero (void) const |
| 2922 { | |
| 2923 octave_idx_type nel = nelem (); | |
| 2924 | |
| 2925 for (octave_idx_type i = 0; i < nel; i++) | |
| 2926 { | |
| 2927 double val = elem (i); | |
| 2928 if (val != 0 && val != 1) | |
| 2929 return true; | |
| 2930 } | |
| 2931 | |
| 2932 return false; | |
| 2933 } | |
| 2934 | |
| 2935 bool | |
| 2385 | 2936 Matrix::all_elements_are_int_or_inf_or_nan (void) const |
| 2937 { | |
| 5275 | 2938 octave_idx_type nel = nelem (); |
| 2939 | |
| 2940 for (octave_idx_type i = 0; i < nel; i++) | |
| 4634 | 2941 { |
| 2942 double val = elem (i); | |
| 2943 if (xisnan (val) || D_NINT (val) == val) | |
| 2944 continue; | |
| 2945 else | |
| 2946 return false; | |
| 2947 } | |
| 2385 | 2948 |
| 2949 return true; | |
| 2950 } | |
| 2951 | |
| 1968 | 2952 // Return nonzero if any element of M is not an integer. Also extract |
| 2953 // the largest and smallest values and return them in MAX_VAL and MIN_VAL. | |
| 2954 | |
| 2385 | 2955 bool |
| 1968 | 2956 Matrix::all_integers (double& max_val, double& min_val) const |
| 2957 { | |
| 5275 | 2958 octave_idx_type nel = nelem (); |
| 4634 | 2959 |
| 2960 if (nel > 0) | |
| 1968 | 2961 { |
| 4634 | 2962 max_val = elem (0); |
| 2963 min_val = elem (0); | |
| 1968 | 2964 } |
| 2965 else | |
| 2385 | 2966 return false; |
| 1968 | 2967 |
| 5275 | 2968 for (octave_idx_type i = 0; i < nel; i++) |
| 4634 | 2969 { |
| 2970 double val = elem (i); | |
| 2971 | |
| 2972 if (val > max_val) | |
| 2973 max_val = val; | |
| 2974 | |
| 2975 if (val < min_val) | |
| 2976 min_val = val; | |
| 2977 | |
| 2978 if (D_NINT (val) != val) | |
| 2979 return false; | |
| 2980 } | |
| 2385 | 2981 |
| 2982 return true; | |
| 1968 | 2983 } |
| 2984 | |
| 2385 | 2985 bool |
| 1968 | 2986 Matrix::too_large_for_float (void) const |
| 2987 { | |
| 5275 | 2988 octave_idx_type nel = nelem (); |
| 2989 | |
| 2990 for (octave_idx_type i = 0; i < nel; i++) | |
| 4634 | 2991 { |
| 2992 double val = elem (i); | |
| 2993 | |
| 5389 | 2994 if (! (xisnan (val) || xisinf (val)) |
| 5387 | 2995 && fabs (val) > FLT_MAX) |
| 4634 | 2996 return true; |
| 2997 } | |
| 1968 | 2998 |
| 2385 | 2999 return false; |
| 1968 | 3000 } |
| 3001 | |
| 5775 | 3002 // FIXME Do these really belong here? Maybe they should be |
| 4015 | 3003 // in a base class? |
| 458 | 3004 |
| 2832 | 3005 boolMatrix |
| 4015 | 3006 Matrix::all (int dim) const |
| 458 | 3007 { |
| 4015 | 3008 MX_ALL_OP (dim); |
| 458 | 3009 } |
| 3010 | |
| 2832 | 3011 boolMatrix |
| 4015 | 3012 Matrix::any (int dim) const |
| 458 | 3013 { |
| 4015 | 3014 MX_ANY_OP (dim); |
| 458 | 3015 } |
| 3016 | |
| 3017 Matrix | |
| 3723 | 3018 Matrix::cumprod (int dim) const |
| 458 | 3019 { |
| 4015 | 3020 MX_CUMULATIVE_OP (Matrix, double, *=); |
| 458 | 3021 } |
| 3022 | |
| 3023 Matrix | |
| 3723 | 3024 Matrix::cumsum (int dim) const |
| 458 | 3025 { |
| 4015 | 3026 MX_CUMULATIVE_OP (Matrix, double, +=); |
| 458 | 3027 } |
| 3028 | |
| 3029 Matrix | |
| 3723 | 3030 Matrix::prod (int dim) const |
| 458 | 3031 { |
| 3864 | 3032 MX_REDUCTION_OP (Matrix, *=, 1.0, 1.0); |
| 458 | 3033 } |
| 3034 | |
| 3035 Matrix | |
| 3723 | 3036 Matrix::sum (int dim) const |
| 458 | 3037 { |
| 3864 | 3038 MX_REDUCTION_OP (Matrix, +=, 0.0, 0.0); |
| 458 | 3039 } |
| 3040 | |
| 3041 Matrix | |
| 3723 | 3042 Matrix::sumsq (int dim) const |
| 458 | 3043 { |
| 3864 | 3044 #define ROW_EXPR \ |
| 3045 double d = elem (i, j); \ | |
| 3046 retval.elem (i, 0) += d * d | |
| 3047 | |
| 3048 #define COL_EXPR \ | |
| 3049 double d = elem (i, j); \ | |
| 3050 retval.elem (0, j) += d * d | |
| 3051 | |
| 3052 MX_BASE_REDUCTION_OP (Matrix, ROW_EXPR, COL_EXPR, 0.0, 0.0); | |
| 3053 | |
| 3054 #undef ROW_EXPR | |
| 3055 #undef COL_EXPR | |
| 458 | 3056 } |
| 3057 | |
| 2385 | 3058 Matrix |
| 3059 Matrix::abs (void) const | |
| 3060 { | |
| 5275 | 3061 octave_idx_type nr = rows (); |
| 3062 octave_idx_type nc = cols (); | |
| 2385 | 3063 |
| 3064 Matrix retval (nr, nc); | |
| 3065 | |
| 5275 | 3066 for (octave_idx_type j = 0; j < nc; j++) |
| 3067 for (octave_idx_type i = 0; i < nr; i++) | |
| 2385 | 3068 retval (i, j) = fabs (elem (i, j)); |
| 3069 | |
| 3070 return retval; | |
| 3071 } | |
| 3072 | |
|
7620
36594d5bbe13
Move diag function into the octave_value class
David Bateman <dbateman@free.fr>
parents:
7544
diff
changeset
|
3073 Matrix |
| 5275 | 3074 Matrix::diag (octave_idx_type k) const |
| 458 | 3075 { |
|
7620
36594d5bbe13
Move diag function into the octave_value class
David Bateman <dbateman@free.fr>
parents:
7544
diff
changeset
|
3076 return MArray2<double>::diag (k); |
| 458 | 3077 } |
| 3078 | |
| 3079 ColumnVector | |
| 3080 Matrix::row_min (void) const | |
| 3081 { | |
| 5275 | 3082 Array<octave_idx_type> dummy_idx; |
| 4587 | 3083 return row_min (dummy_idx); |
| 458 | 3084 } |
| 3085 | |
| 3086 ColumnVector | |
| 5275 | 3087 Matrix::row_min (Array<octave_idx_type>& idx_arg) const |
| 458 | 3088 { |
| 3089 ColumnVector result; | |
| 3090 | |
| 5275 | 3091 octave_idx_type nr = rows (); |
| 3092 octave_idx_type nc = cols (); | |
| 458 | 3093 |
| 3094 if (nr > 0 && nc > 0) | |
| 3095 { | |
| 3096 result.resize (nr); | |
| 4587 | 3097 idx_arg.resize (nr); |
| 458 | 3098 |
| 5275 | 3099 for (octave_idx_type i = 0; i < nr; i++) |
| 458 | 3100 { |
| 5275 | 3101 octave_idx_type idx_j; |
| 4469 | 3102 |
| 3103 double tmp_min = octave_NaN; | |
| 3104 | |
| 3105 for (idx_j = 0; idx_j < nc; idx_j++) | |
| 2354 | 3106 { |
| 4469 | 3107 tmp_min = elem (i, idx_j); |
| 3108 | |
| 5389 | 3109 if (! xisnan (tmp_min)) |
| 4469 | 3110 break; |
| 3111 } | |
| 3112 | |
| 5275 | 3113 for (octave_idx_type j = idx_j+1; j < nc; j++) |
| 4469 | 3114 { |
| 3115 double tmp = elem (i, j); | |
| 3116 | |
| 5389 | 3117 if (xisnan (tmp)) |
| 4469 | 3118 continue; |
| 3119 else if (tmp < tmp_min) | |
| 2354 | 3120 { |
| 4469 | 3121 idx_j = j; |
| 3122 tmp_min = tmp; | |
| 2354 | 3123 } |
| 3124 } | |
| 3125 | |
| 4469 | 3126 result.elem (i) = tmp_min; |
| 5389 | 3127 idx_arg.elem (i) = xisnan (tmp_min) ? 0 : idx_j; |
| 458 | 3128 } |
| 3129 } | |
| 3130 | |
| 3131 return result; | |
| 3132 } | |
| 3133 | |
| 3134 ColumnVector | |
| 3135 Matrix::row_max (void) const | |
| 3136 { | |
| 5275 | 3137 Array<octave_idx_type> dummy_idx; |
| 4587 | 3138 return row_max (dummy_idx); |
| 458 | 3139 } |
| 3140 | |
| 3141 ColumnVector | |
| 5275 | 3142 Matrix::row_max (Array<octave_idx_type>& idx_arg) const |
| 458 | 3143 { |
| 3144 ColumnVector result; | |
| 3145 | |
| 5275 | 3146 octave_idx_type nr = rows (); |
| 3147 octave_idx_type nc = cols (); | |
| 458 | 3148 |
| 3149 if (nr > 0 && nc > 0) | |
| 3150 { | |
| 3151 result.resize (nr); | |
| 4587 | 3152 idx_arg.resize (nr); |
| 458 | 3153 |
| 5275 | 3154 for (octave_idx_type i = 0; i < nr; i++) |
| 458 | 3155 { |
| 5275 | 3156 octave_idx_type idx_j; |
| 4469 | 3157 |
| 3158 double tmp_max = octave_NaN; | |
| 3159 | |
| 3160 for (idx_j = 0; idx_j < nc; idx_j++) | |
| 2354 | 3161 { |
| 4469 | 3162 tmp_max = elem (i, idx_j); |
| 3163 | |
| 5389 | 3164 if (! xisnan (tmp_max)) |
| 4469 | 3165 break; |
| 3166 } | |
| 3167 | |
| 5275 | 3168 for (octave_idx_type j = idx_j+1; j < nc; j++) |
| 4469 | 3169 { |
| 3170 double tmp = elem (i, j); | |
| 3171 | |
| 5389 | 3172 if (xisnan (tmp)) |
| 4469 | 3173 continue; |
| 3174 else if (tmp > tmp_max) | |
| 2354 | 3175 { |
| 4469 | 3176 idx_j = j; |
| 3177 tmp_max = tmp; | |
| 2354 | 3178 } |
| 3179 } | |
| 3180 | |
| 4469 | 3181 result.elem (i) = tmp_max; |
| 5389 | 3182 idx_arg.elem (i) = xisnan (tmp_max) ? 0 : idx_j; |
| 458 | 3183 } |
| 3184 } | |
| 3185 | |
| 3186 return result; | |
| 3187 } | |
| 3188 | |
| 3189 RowVector | |
| 3190 Matrix::column_min (void) const | |
| 3191 { | |
| 5275 | 3192 Array<octave_idx_type> dummy_idx; |
| 4587 | 3193 return column_min (dummy_idx); |
| 458 | 3194 } |
| 2354 | 3195 |
| 458 | 3196 RowVector |
| 5275 | 3197 Matrix::column_min (Array<octave_idx_type>& idx_arg) const |
| 458 | 3198 { |
| 3199 RowVector result; | |
| 3200 | |
| 5275 | 3201 octave_idx_type nr = rows (); |
| 3202 octave_idx_type nc = cols (); | |
| 458 | 3203 |
| 3204 if (nr > 0 && nc > 0) | |
| 3205 { | |
| 3206 result.resize (nc); | |
| 4587 | 3207 idx_arg.resize (nc); |
| 458 | 3208 |
| 5275 | 3209 for (octave_idx_type j = 0; j < nc; j++) |
| 458 | 3210 { |
| 5275 | 3211 octave_idx_type idx_i; |
| 4469 | 3212 |
| 3213 double tmp_min = octave_NaN; | |
| 3214 | |
| 3215 for (idx_i = 0; idx_i < nr; idx_i++) | |
| 2354 | 3216 { |
| 4469 | 3217 tmp_min = elem (idx_i, j); |
| 3218 | |
| 5389 | 3219 if (! xisnan (tmp_min)) |
| 4469 | 3220 break; |
| 3221 } | |
| 3222 | |
| 5275 | 3223 for (octave_idx_type i = idx_i+1; i < nr; i++) |
| 4469 | 3224 { |
| 3225 double tmp = elem (i, j); | |
| 3226 | |
| 5389 | 3227 if (xisnan (tmp)) |
| 4469 | 3228 continue; |
| 3229 else if (tmp < tmp_min) | |
| 2354 | 3230 { |
| 4469 | 3231 idx_i = i; |
| 3232 tmp_min = tmp; | |
| 2354 | 3233 } |
| 3234 } | |
| 3235 | |
| 4469 | 3236 result.elem (j) = tmp_min; |
| 5389 | 3237 idx_arg.elem (j) = xisnan (tmp_min) ? 0 : idx_i; |
| 458 | 3238 } |
| 3239 } | |
| 3240 | |
| 3241 return result; | |
| 3242 } | |
| 3243 | |
| 2354 | 3244 RowVector |
| 3245 Matrix::column_max (void) const | |
| 3246 { | |
| 5275 | 3247 Array<octave_idx_type> dummy_idx; |
| 4587 | 3248 return column_max (dummy_idx); |
| 2354 | 3249 } |
| 458 | 3250 |
| 3251 RowVector | |
| 5275 | 3252 Matrix::column_max (Array<octave_idx_type>& idx_arg) const |
| 458 | 3253 { |
| 3254 RowVector result; | |
| 3255 | |
| 5275 | 3256 octave_idx_type nr = rows (); |
| 3257 octave_idx_type nc = cols (); | |
| 458 | 3258 |
| 3259 if (nr > 0 && nc > 0) | |
| 3260 { | |
| 3261 result.resize (nc); | |
| 4587 | 3262 idx_arg.resize (nc); |
| 458 | 3263 |
| 5275 | 3264 for (octave_idx_type j = 0; j < nc; j++) |
| 458 | 3265 { |
| 5275 | 3266 octave_idx_type idx_i; |
| 4469 | 3267 |
| 3268 double tmp_max = octave_NaN; | |
| 3269 | |
| 3270 for (idx_i = 0; idx_i < nr; idx_i++) | |
| 2354 | 3271 { |
| 4469 | 3272 tmp_max = elem (idx_i, j); |
| 3273 | |
| 5389 | 3274 if (! xisnan (tmp_max)) |
| 4469 | 3275 break; |
| 3276 } | |
| 3277 | |
| 5275 | 3278 for (octave_idx_type i = idx_i+1; i < nr; i++) |
| 4469 | 3279 { |
| 3280 double tmp = elem (i, j); | |
| 3281 | |
| 5389 | 3282 if (xisnan (tmp)) |
| 4469 | 3283 continue; |
| 3284 else if (tmp > tmp_max) | |
| 2354 | 3285 { |
| 4469 | 3286 idx_i = i; |
| 3287 tmp_max = tmp; | |
| 2354 | 3288 } |
| 3289 } | |
| 3290 | |
| 4469 | 3291 result.elem (j) = tmp_max; |
| 5389 | 3292 idx_arg.elem (j) = xisnan (tmp_max) ? 0 : idx_i; |
| 458 | 3293 } |
| 3294 } | |
| 3295 | |
| 3296 return result; | |
| 3297 } | |
| 3298 | |
| 3504 | 3299 std::ostream& |
| 3300 operator << (std::ostream& os, const Matrix& a) | |
| 458 | 3301 { |
| 5275 | 3302 for (octave_idx_type i = 0; i < a.rows (); i++) |
| 458 | 3303 { |
| 5275 | 3304 for (octave_idx_type j = 0; j < a.cols (); j++) |
| 4130 | 3305 { |
| 3306 os << " "; | |
| 3307 octave_write_double (os, a.elem (i, j)); | |
| 3308 } | |
| 458 | 3309 os << "\n"; |
| 3310 } | |
| 3311 return os; | |
| 3312 } | |
| 3313 | |
| 3504 | 3314 std::istream& |
| 3315 operator >> (std::istream& is, Matrix& a) | |
| 458 | 3316 { |
| 5275 | 3317 octave_idx_type nr = a.rows (); |
| 3318 octave_idx_type nc = a.cols (); | |
| 458 | 3319 |
| 3320 if (nr < 1 || nc < 1) | |
| 3504 | 3321 is.clear (std::ios::badbit); |
| 458 | 3322 else |
| 3323 { | |
| 3324 double tmp; | |
| 5275 | 3325 for (octave_idx_type i = 0; i < nr; i++) |
| 3326 for (octave_idx_type j = 0; j < nc; j++) | |
| 458 | 3327 { |
| 4130 | 3328 tmp = octave_read_double (is); |
| 458 | 3329 if (is) |
| 3330 a.elem (i, j) = tmp; | |
| 3331 else | |
| 2795 | 3332 goto done; |
| 458 | 3333 } |
| 3334 } | |
| 3335 | |
| 2795 | 3336 done: |
| 3337 | |
| 458 | 3338 return is; |
| 3339 } | |
| 3340 | |
| 1819 | 3341 Matrix |
| 3342 Givens (double x, double y) | |
| 3343 { | |
| 3344 double cc, s, temp_r; | |
| 3345 | |
| 3887 | 3346 F77_FUNC (dlartg, DLARTG) (x, y, cc, s, temp_r); |
| 1819 | 3347 |
| 3348 Matrix g (2, 2); | |
| 3349 | |
| 3350 g.elem (0, 0) = cc; | |
| 3351 g.elem (1, 1) = cc; | |
| 3352 g.elem (0, 1) = s; | |
| 3353 g.elem (1, 0) = -s; | |
| 3354 | |
| 3355 return g; | |
| 3356 } | |
| 3357 | |
| 3358 Matrix | |
| 3359 Sylvester (const Matrix& a, const Matrix& b, const Matrix& c) | |
| 3360 { | |
| 3361 Matrix retval; | |
| 3362 | |
| 5775 | 3363 // FIXME -- need to check that a, b, and c are all the same |
| 1819 | 3364 // size. |
| 3365 | |
| 3366 // Compute Schur decompositions. | |
| 3367 | |
| 3368 SCHUR as (a, "U"); | |
| 3369 SCHUR bs (b, "U"); | |
| 3370 | |
| 3371 // Transform c to new coordinates. | |
| 3372 | |
| 3373 Matrix ua = as.unitary_matrix (); | |
| 3374 Matrix sch_a = as.schur_matrix (); | |
| 3375 | |
| 3376 Matrix ub = bs.unitary_matrix (); | |
| 3377 Matrix sch_b = bs.schur_matrix (); | |
| 3378 | |
| 3379 Matrix cx = ua.transpose () * c * ub; | |
| 3380 | |
| 3381 // Solve the sylvester equation, back-transform, and return the | |
| 3382 // solution. | |
| 3383 | |
| 5275 | 3384 octave_idx_type a_nr = a.rows (); |
| 3385 octave_idx_type b_nr = b.rows (); | |
| 1819 | 3386 |
| 3387 double scale; | |
| 5275 | 3388 octave_idx_type info; |
| 1819 | 3389 |
| 1950 | 3390 double *pa = sch_a.fortran_vec (); |
| 3391 double *pb = sch_b.fortran_vec (); | |
| 3392 double *px = cx.fortran_vec (); | |
| 3393 | |
| 4552 | 3394 F77_XFCN (dtrsyl, DTRSYL, (F77_CONST_CHAR_ARG2 ("N", 1), |
| 3395 F77_CONST_CHAR_ARG2 ("N", 1), | |
| 3396 1, a_nr, b_nr, pa, a_nr, pb, | |
| 3397 b_nr, px, a_nr, scale, info | |
| 3398 F77_CHAR_ARG_LEN (1) | |
| 3399 F77_CHAR_ARG_LEN (1))); | |
| 1950 | 3400 |
| 3401 | |
|
7482
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
3402 // FIXME -- check info? |
| 1819 | 3403 |
|
7482
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
3404 retval = -ua*cx*ub.transpose (); |
| 1819 | 3405 |
| 3406 return retval; | |
| 3407 } | |
| 3408 | |
| 2828 | 3409 // matrix by matrix -> matrix operations |
| 3410 | |
| 6162 | 3411 /* Simple Dot Product, Matrix-Vector and Matrix-Matrix Unit tests |
| 3412 %!assert([1 2 3] * [ 4 ; 5 ; 6], 32, 1e-14) | |
| 3413 %!assert([1 2 ; 3 4 ] * [5 ; 6], [17 ; 39 ], 1e-14) | |
| 3414 %!assert([1 2 ; 3 4 ] * [5 6 ; 7 8], [19 22; 43 50], 1e-14) | |
| 3415 */ | |
| 3416 | |
| 3417 /* Test some simple identities | |
| 3418 %!shared M, cv, rv | |
| 3419 %! M = randn(10,10); | |
| 3420 %! cv = randn(10,1); | |
| 3421 %! rv = randn(1,10); | |
| 3422 %!assert([M*cv,M*cv],M*[cv,cv],1e-14) | |
| 3423 %!assert([rv*M;rv*M],[rv;rv]*M,1e-14) | |
| 3424 %!assert(2*rv*cv,[rv,rv]*[cv;cv],1e-14) | |
| 3425 */ | |
| 3426 | |
|
7800
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3427 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
|
3428 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
|
3429 { |
|
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 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
|
3431 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
|
3432 } |
|
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 // 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
|
3435 |
|
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 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
|
3437 xgemm (bool transa, const Matrix& a, bool transb, const Matrix& b) |
| 2828 | 3438 { |
| 3439 Matrix retval; | |
| 3440 | |
|
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
|
3441 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
|
3442 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
|
3443 |
|
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 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
|
3445 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
|
3446 |
|
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 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
|
3448 gripe_nonconformant ("operator *", a_nr, a_nc, b_nr, b_nc); |
| 2828 | 3449 else |
| 3450 { | |
|
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
|
3451 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
|
3452 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
|
3453 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
|
3454 { |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3455 octave_idx_type lda = a.rows (); |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3456 |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3457 retval.resize (a_nr, b_nc); |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3458 double *c = retval.fortran_vec (); |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3459 |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3460 const char *ctransa = get_blas_trans_arg (transa); |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3461 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
|
3462 F77_CONST_CHAR_ARG2 (ctransa, 1), |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3463 a_nr, a_nc, 1.0, |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3464 a.data (), lda, 0.0, c, a_nr |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3465 F77_CHAR_ARG_LEN (1) |
|
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 for (int j = 0; j < a_nr; j++) |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3468 for (int i = 0; i < j; i++) |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3469 retval.xelem (j,i) = retval.xelem (i,j); |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3470 |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3471 } |
| 2828 | 3472 else |
| 3473 { | |
|
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
|
3474 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
|
3475 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
|
3476 |
|
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 retval.resize (a_nr, b_nc); |
| 2828 | 3478 double *c = retval.fortran_vec (); |
| 3479 | |
|
7800
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3480 if (b_nc == 1) |
| 5983 | 3481 { |
|
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
|
3482 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
|
3483 F77_FUNC (xddot, XDDOT) (a_nc, a.data (), 1, b.data (), 1, *c); |
| 5983 | 3484 else |
| 6390 | 3485 { |
|
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
|
3486 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
|
3487 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
|
3488 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
|
3489 b.data (), 1, 0.0, c, 1 |
| 6390 | 3490 F77_CHAR_ARG_LEN (1))); |
| 3491 } | |
| 5983 | 3492 } |
|
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
|
3493 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
|
3494 { |
|
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 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
|
3496 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
|
3497 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
|
3498 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
|
3499 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
|
3500 } |
| 5983 | 3501 else |
| 6390 | 3502 { |
|
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
|
3503 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
|
3504 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
|
3505 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
|
3506 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
|
3507 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
|
3508 lda, b.data (), ldb, 0.0, c, a_nr |
| 6390 | 3509 F77_CHAR_ARG_LEN (1) |
| 3510 F77_CHAR_ARG_LEN (1))); | |
| 3511 } | |
| 2828 | 3512 } |
| 3513 } | |
| 3514 | |
| 3515 return retval; | |
| 3516 } | |
| 3517 | |
|
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
|
3518 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
|
3519 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
|
3520 { |
|
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 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
|
3522 } |
|
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 |
| 5775 | 3524 // FIXME -- it would be nice to share code among the min/max |
| 4309 | 3525 // functions below. |
| 3526 | |
| 3527 #define EMPTY_RETURN_CHECK(T) \ | |
| 3528 if (nr == 0 || nc == 0) \ | |
| 3529 return T (nr, nc); | |
| 3530 | |
| 3531 Matrix | |
| 3532 min (double d, const Matrix& m) | |
| 3533 { | |
| 5275 | 3534 octave_idx_type nr = m.rows (); |
| 3535 octave_idx_type nc = m.columns (); | |
| 4309 | 3536 |
| 3537 EMPTY_RETURN_CHECK (Matrix); | |
| 3538 | |
| 3539 Matrix result (nr, nc); | |
| 3540 | |
| 5275 | 3541 for (octave_idx_type j = 0; j < nc; j++) |
| 3542 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3543 { |
| 3544 OCTAVE_QUIT; | |
| 3545 result (i, j) = xmin (d, m (i, j)); | |
| 3546 } | |
| 3547 | |
| 3548 return result; | |
| 3549 } | |
| 3550 | |
| 3551 Matrix | |
| 3552 min (const Matrix& m, double d) | |
| 3553 { | |
| 5275 | 3554 octave_idx_type nr = m.rows (); |
| 3555 octave_idx_type nc = m.columns (); | |
| 4309 | 3556 |
| 3557 EMPTY_RETURN_CHECK (Matrix); | |
| 3558 | |
| 3559 Matrix result (nr, nc); | |
| 3560 | |
| 5275 | 3561 for (octave_idx_type j = 0; j < nc; j++) |
| 3562 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3563 { |
| 3564 OCTAVE_QUIT; | |
| 3565 result (i, j) = xmin (m (i, j), d); | |
| 3566 } | |
| 3567 | |
| 3568 return result; | |
| 3569 } | |
| 3570 | |
| 3571 Matrix | |
| 3572 min (const Matrix& a, const Matrix& b) | |
| 3573 { | |
| 5275 | 3574 octave_idx_type nr = a.rows (); |
| 3575 octave_idx_type nc = a.columns (); | |
| 4309 | 3576 |
| 3577 if (nr != b.rows () || nc != b.columns ()) | |
| 3578 { | |
| 3579 (*current_liboctave_error_handler) | |
| 3580 ("two-arg min expecting args of same size"); | |
| 3581 return Matrix (); | |
| 3582 } | |
| 3583 | |
| 3584 EMPTY_RETURN_CHECK (Matrix); | |
| 3585 | |
| 3586 Matrix result (nr, nc); | |
| 3587 | |
| 5275 | 3588 for (octave_idx_type j = 0; j < nc; j++) |
| 3589 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3590 { |
| 3591 OCTAVE_QUIT; | |
| 3592 result (i, j) = xmin (a (i, j), b (i, j)); | |
| 3593 } | |
| 3594 | |
| 3595 return result; | |
| 3596 } | |
| 3597 | |
| 3598 Matrix | |
| 3599 max (double d, const Matrix& m) | |
| 3600 { | |
| 5275 | 3601 octave_idx_type nr = m.rows (); |
| 3602 octave_idx_type nc = m.columns (); | |
| 4309 | 3603 |
| 3604 EMPTY_RETURN_CHECK (Matrix); | |
| 3605 | |
| 3606 Matrix result (nr, nc); | |
| 3607 | |
| 5275 | 3608 for (octave_idx_type j = 0; j < nc; j++) |
| 3609 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3610 { |
| 3611 OCTAVE_QUIT; | |
| 3612 result (i, j) = xmax (d, m (i, j)); | |
| 3613 } | |
| 3614 | |
| 3615 return result; | |
| 3616 } | |
| 3617 | |
| 3618 Matrix | |
| 3619 max (const Matrix& m, double d) | |
| 3620 { | |
| 5275 | 3621 octave_idx_type nr = m.rows (); |
| 3622 octave_idx_type nc = m.columns (); | |
| 4309 | 3623 |
| 3624 EMPTY_RETURN_CHECK (Matrix); | |
| 3625 | |
| 3626 Matrix result (nr, nc); | |
| 3627 | |
| 5275 | 3628 for (octave_idx_type j = 0; j < nc; j++) |
| 3629 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3630 { |
| 3631 OCTAVE_QUIT; | |
| 3632 result (i, j) = xmax (m (i, j), d); | |
| 3633 } | |
| 3634 | |
| 3635 return result; | |
| 3636 } | |
| 3637 | |
| 3638 Matrix | |
| 3639 max (const Matrix& a, const Matrix& b) | |
| 3640 { | |
| 5275 | 3641 octave_idx_type nr = a.rows (); |
| 3642 octave_idx_type nc = a.columns (); | |
| 4309 | 3643 |
| 3644 if (nr != b.rows () || nc != b.columns ()) | |
| 3645 { | |
| 3646 (*current_liboctave_error_handler) | |
| 3647 ("two-arg max expecting args of same size"); | |
| 3648 return Matrix (); | |
| 3649 } | |
| 3650 | |
| 3651 EMPTY_RETURN_CHECK (Matrix); | |
| 3652 | |
| 3653 Matrix result (nr, nc); | |
| 3654 | |
| 5275 | 3655 for (octave_idx_type j = 0; j < nc; j++) |
| 3656 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3657 { |
| 3658 OCTAVE_QUIT; | |
| 3659 result (i, j) = xmax (a (i, j), b (i, j)); | |
| 3660 } | |
| 3661 | |
| 3662 return result; | |
| 3663 } | |
| 3664 | |
| 2870 | 3665 MS_CMP_OPS(Matrix, , double, ) |
| 3504 | 3666 MS_BOOL_OPS(Matrix, double, 0.0) |
| 2870 | 3667 |
| 3668 SM_CMP_OPS(double, , Matrix, ) | |
| 3504 | 3669 SM_BOOL_OPS(double, Matrix, 0.0) |
| 2870 | 3670 |
| 3671 MM_CMP_OPS(Matrix, , Matrix, ) | |
| 3504 | 3672 MM_BOOL_OPS(Matrix, Matrix, 0.0) |
| 2870 | 3673 |
| 458 | 3674 /* |
| 3675 ;;; Local Variables: *** | |
| 3676 ;;; mode: C++ *** | |
| 3677 ;;; End: *** | |
| 3678 */ |