Mercurial > octave-libgccjit
annotate liboctave/dMatrix.cc @ 8920:eb63fbe60fab
update copyright notices
| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Sat, 07 Mar 2009 10:41:27 -0500 |
| parents | c7864bb74914 |
| children | d91fa4b20bbb |
| rev | line source |
|---|---|
| 1993 | 1 // Matrix manipulations. |
| 458 | 2 /* |
| 3 | |
| 7017 | 4 Copyright (C) 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, |
| 8920 | 5 2003, 2004, 2005, 2006, 2007, 2009 John W. Eaton |
| 7803 | 6 Copyright (C) 2008 Jaroslav Hajek |
| 458 | 7 |
| 8 This file is part of Octave. | |
| 9 | |
| 10 Octave is free software; you can redistribute it and/or modify it | |
| 11 under the terms of the GNU General Public License as published by the | |
| 7016 | 12 Free Software Foundation; either version 3 of the License, or (at your |
| 13 option) any later version. | |
| 458 | 14 |
| 15 Octave is distributed in the hope that it will be useful, but WITHOUT | |
| 16 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
| 17 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
| 18 for more details. | |
| 19 | |
| 20 You should have received a copy of the GNU General Public License | |
| 7016 | 21 along with Octave; see the file COPYING. If not, see |
| 22 <http://www.gnu.org/licenses/>. | |
| 458 | 23 |
| 24 */ | |
| 25 | |
| 26 #ifdef HAVE_CONFIG_H | |
| 1192 | 27 #include <config.h> |
| 458 | 28 #endif |
| 29 | |
| 1367 | 30 #include <cfloat> |
| 31 | |
| 3503 | 32 #include <iostream> |
| 6209 | 33 #include <vector> |
| 1367 | 34 |
| 4669 | 35 #include "Array-util.h" |
| 2317 | 36 #include "byte-swap.h" |
| 2828 | 37 #include "dMatrix.h" |
| 1819 | 38 #include "dbleAEPBAL.h" |
| 8335 | 39 #include "DET.h" |
| 1819 | 40 #include "dbleSCHUR.h" |
| 740 | 41 #include "dbleSVD.h" |
| 6207 | 42 #include "dbleCHOL.h" |
| 1847 | 43 #include "f77-fcn.h" |
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44 #include "functor.h" |
| 458 | 45 #include "lo-error.h" |
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46 #include "oct-locbuf.h" |
| 2354 | 47 #include "lo-ieee.h" |
| 48 #include "lo-mappers.h" | |
| 1968 | 49 #include "lo-utils.h" |
| 1367 | 50 #include "mx-base.h" |
| 2828 | 51 #include "mx-m-dm.h" |
| 3176 | 52 #include "mx-dm-m.h" |
| 1367 | 53 #include "mx-inlines.cc" |
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54 #include "mx-op-defs.h" |
| 1650 | 55 #include "oct-cmplx.h" |
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56 #include "oct-norm.h" |
| 4153 | 57 #include "quit.h" |
| 458 | 58 |
| 4773 | 59 #if defined (HAVE_FFTW3) |
| 3827 | 60 #include "oct-fftw.h" |
| 61 #endif | |
| 62 | |
| 458 | 63 // Fortran functions we call. |
| 64 | |
| 65 extern "C" | |
| 66 { | |
| 7478 | 67 F77_RET_T |
| 7477 | 68 F77_FUNC (xilaenv, XILAENV) (const octave_idx_type&, F77_CONST_CHAR_ARG_DECL, |
| 69 F77_CONST_CHAR_ARG_DECL, | |
| 70 const octave_idx_type&, const octave_idx_type&, | |
| 7478 | 71 const octave_idx_type&, const octave_idx_type&, |
| 72 octave_idx_type& | |
| 73 F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); | |
| 7476 | 74 |
| 4552 | 75 F77_RET_T |
| 76 F77_FUNC (dgebal, DGEBAL) (F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 77 const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type&, |
| 78 octave_idx_type&, double*, octave_idx_type& | |
| 4552 | 79 F77_CHAR_ARG_LEN_DECL); |
| 80 | |
| 81 F77_RET_T | |
| 82 F77_FUNC (dgebak, DGEBAK) (F77_CONST_CHAR_ARG_DECL, | |
| 83 F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 84 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, double*, |
| 85 const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type& | |
| 4552 | 86 F77_CHAR_ARG_LEN_DECL |
| 87 F77_CHAR_ARG_LEN_DECL); | |
| 88 | |
| 89 | |
| 90 F77_RET_T | |
| 91 F77_FUNC (dgemm, DGEMM) (F77_CONST_CHAR_ARG_DECL, | |
| 92 F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 93 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
| 94 const double&, const double*, const octave_idx_type&, | |
| 95 const double*, const octave_idx_type&, const double&, | |
| 96 double*, const octave_idx_type& | |
| 4552 | 97 F77_CHAR_ARG_LEN_DECL |
| 98 F77_CHAR_ARG_LEN_DECL); | |
| 99 | |
| 100 F77_RET_T | |
| 5983 | 101 F77_FUNC (dgemv, DGEMV) (F77_CONST_CHAR_ARG_DECL, |
| 102 const octave_idx_type&, const octave_idx_type&, const double&, | |
| 103 const double*, const octave_idx_type&, const double*, | |
| 104 const octave_idx_type&, const double&, double*, | |
| 105 const octave_idx_type& | |
| 106 F77_CHAR_ARG_LEN_DECL); | |
| 107 | |
| 108 F77_RET_T | |
| 109 F77_FUNC (xddot, XDDOT) (const octave_idx_type&, const double*, const octave_idx_type&, | |
| 110 const double*, const octave_idx_type&, double&); | |
| 111 | |
| 112 F77_RET_T | |
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113 F77_FUNC (dsyrk, DSYRK) (F77_CONST_CHAR_ARG_DECL, |
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114 F77_CONST_CHAR_ARG_DECL, |
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115 const octave_idx_type&, const octave_idx_type&, |
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116 const double&, const double*, const octave_idx_type&, |
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117 const double&, double*, const octave_idx_type& |
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118 F77_CHAR_ARG_LEN_DECL |
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119 F77_CHAR_ARG_LEN_DECL); |
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120 |
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121 F77_RET_T |
| 5275 | 122 F77_FUNC (dgetrf, DGETRF) (const octave_idx_type&, const octave_idx_type&, double*, const octave_idx_type&, |
| 123 octave_idx_type*, octave_idx_type&); | |
| 4329 | 124 |
| 4552 | 125 F77_RET_T |
| 5275 | 126 F77_FUNC (dgetrs, DGETRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, |
| 127 const double*, const octave_idx_type&, | |
| 128 const octave_idx_type*, double*, const octave_idx_type&, octave_idx_type& | |
| 4552 | 129 F77_CHAR_ARG_LEN_DECL); |
| 130 | |
| 131 F77_RET_T | |
| 5275 | 132 F77_FUNC (dgetri, DGETRI) (const octave_idx_type&, double*, const octave_idx_type&, const octave_idx_type*, |
| 133 double*, const octave_idx_type&, octave_idx_type&); | |
| 4552 | 134 |
| 135 F77_RET_T | |
| 5275 | 136 F77_FUNC (dgecon, DGECON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, double*, |
| 137 const octave_idx_type&, const double&, double&, | |
| 138 double*, octave_idx_type*, octave_idx_type& | |
| 4552 | 139 F77_CHAR_ARG_LEN_DECL); |
| 140 | |
| 141 F77_RET_T | |
| 7072 | 142 F77_FUNC (dgelsy, DGELSY) (const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
| 143 double*, const octave_idx_type&, double*, | |
| 144 const octave_idx_type&, octave_idx_type*, double&, octave_idx_type&, | |
| 145 double*, const octave_idx_type&, octave_idx_type&); | |
| 146 | |
| 147 F77_RET_T | |
| 148 F77_FUNC (dgelsd, DGELSD) (const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, | |
| 5275 | 149 double*, const octave_idx_type&, double*, |
| 7071 | 150 const octave_idx_type&, double*, double&, octave_idx_type&, |
| 7072 | 151 double*, const octave_idx_type&, octave_idx_type*, |
| 152 octave_idx_type&); | |
| 458 | 153 |
| 5785 | 154 F77_RET_T |
| 155 F77_FUNC (dpotrf, DPOTRF) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 156 double *, const octave_idx_type&, | |
| 157 octave_idx_type& F77_CHAR_ARG_LEN_DECL); | |
| 158 | |
| 159 F77_RET_T | |
| 160 F77_FUNC (dpocon, DPOCON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 161 double*, const octave_idx_type&, const double&, | |
| 162 double&, double*, octave_idx_type*, | |
| 163 octave_idx_type& F77_CHAR_ARG_LEN_DECL); | |
| 164 F77_RET_T | |
| 165 F77_FUNC (dpotrs, DPOTRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 166 const octave_idx_type&, const double*, | |
| 167 const octave_idx_type&, double*, | |
| 168 const octave_idx_type&, octave_idx_type& | |
| 169 F77_CHAR_ARG_LEN_DECL); | |
| 170 | |
| 171 F77_RET_T | |
| 6207 | 172 F77_FUNC (dtrtri, DTRTRI) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, |
| 173 const octave_idx_type&, const double*, | |
| 174 const octave_idx_type&, octave_idx_type& | |
| 175 F77_CHAR_ARG_LEN_DECL | |
| 176 F77_CHAR_ARG_LEN_DECL); | |
| 177 F77_RET_T | |
| 5785 | 178 F77_FUNC (dtrcon, DTRCON) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, |
| 179 F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 180 const double*, const octave_idx_type&, double&, | |
| 181 double*, octave_idx_type*, octave_idx_type& | |
| 182 F77_CHAR_ARG_LEN_DECL | |
| 183 F77_CHAR_ARG_LEN_DECL | |
| 184 F77_CHAR_ARG_LEN_DECL); | |
| 185 F77_RET_T | |
| 186 F77_FUNC (dtrtrs, DTRTRS) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, | |
| 187 F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, | |
| 188 const octave_idx_type&, const double*, | |
| 189 const octave_idx_type&, double*, | |
| 190 const octave_idx_type&, octave_idx_type& | |
| 191 F77_CHAR_ARG_LEN_DECL | |
| 192 F77_CHAR_ARG_LEN_DECL | |
| 193 F77_CHAR_ARG_LEN_DECL); | |
| 194 | |
| 1360 | 195 // Note that the original complex fft routines were not written for |
| 196 // double complex arguments. They have been modified by adding an | |
| 197 // implicit double precision (a-h,o-z) statement at the beginning of | |
| 198 // each subroutine. | |
| 458 | 199 |
| 4552 | 200 F77_RET_T |
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201 F77_FUNC (zffti, ZFFTI) (const octave_idx_type&, Complex*); |
| 4552 | 202 |
| 203 F77_RET_T | |
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204 F77_FUNC (zfftf, ZFFTF) (const octave_idx_type&, Complex*, Complex*); |
| 4552 | 205 |
| 206 F77_RET_T | |
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207 F77_FUNC (zfftb, ZFFTB) (const octave_idx_type&, Complex*, Complex*); |
| 4552 | 208 |
| 209 F77_RET_T | |
| 210 F77_FUNC (dlartg, DLARTG) (const double&, const double&, double&, | |
| 211 double&, double&); | |
| 212 | |
| 213 F77_RET_T | |
| 214 F77_FUNC (dtrsyl, DTRSYL) (F77_CONST_CHAR_ARG_DECL, | |
| 215 F77_CONST_CHAR_ARG_DECL, | |
| 5275 | 216 const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, |
| 217 const double*, const octave_idx_type&, const double*, | |
| 218 const octave_idx_type&, const double*, const octave_idx_type&, | |
| 219 double&, octave_idx_type& | |
| 4552 | 220 F77_CHAR_ARG_LEN_DECL |
| 221 F77_CHAR_ARG_LEN_DECL); | |
| 222 | |
| 223 F77_RET_T | |
| 5275 | 224 F77_FUNC (xdlange, XDLANGE) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, |
| 225 const octave_idx_type&, const double*, | |
| 226 const octave_idx_type&, double*, double& | |
| 4552 | 227 F77_CHAR_ARG_LEN_DECL); |
| 458 | 228 } |
| 229 | |
| 1360 | 230 // Matrix class. |
| 458 | 231 |
| 2349 | 232 Matrix::Matrix (const RowVector& rv) |
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233 : MArray2<double> (Array2<double> (rv, 1, rv.length ())) |
| 2349 | 234 { |
| 235 } | |
| 236 | |
| 237 Matrix::Matrix (const ColumnVector& cv) | |
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238 : MArray2<double> (Array2<double> (cv, cv.length (), 1)) |
| 2349 | 239 { |
| 240 } | |
| 241 | |
| 458 | 242 Matrix::Matrix (const DiagMatrix& a) |
| 1214 | 243 : MArray2<double> (a.rows (), a.cols (), 0.0) |
| 458 | 244 { |
| 5275 | 245 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 246 elem (i, i) = a.elem (i, i); |
| 247 } | |
| 248 | |
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249 Matrix::Matrix (const PermMatrix& a) |
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250 : MArray2<double> (a.rows (), a.cols (), 0.0) |
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251 { |
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252 const Array<octave_idx_type> ia (a.pvec ()); |
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253 octave_idx_type len = a.rows (); |
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254 if (a.is_col_perm ()) |
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255 for (octave_idx_type i = 0; i < len; i++) |
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256 elem (ia(i), i) = 1.0; |
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257 else |
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258 for (octave_idx_type i = 0; i < len; i++) |
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259 elem (i, ia(i)) = 1.0; |
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260 } |
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261 |
| 5775 | 262 // FIXME -- could we use a templated mixed-type copy function |
| 1574 | 263 // here? |
| 264 | |
| 2828 | 265 Matrix::Matrix (const boolMatrix& a) |
| 266 : MArray2<double> (a.rows (), a.cols ()) | |
| 267 { | |
| 5275 | 268 for (octave_idx_type i = 0; i < a.rows (); i++) |
| 269 for (octave_idx_type j = 0; j < a.cols (); j++) | |
| 2828 | 270 elem (i, j) = a.elem (i, j); |
| 271 } | |
| 272 | |
| 1574 | 273 Matrix::Matrix (const charMatrix& a) |
| 274 : MArray2<double> (a.rows (), a.cols ()) | |
| 275 { | |
| 5275 | 276 for (octave_idx_type i = 0; i < a.rows (); i++) |
| 277 for (octave_idx_type j = 0; j < a.cols (); j++) | |
| 1574 | 278 elem (i, j) = a.elem (i, j); |
| 279 } | |
| 280 | |
| 2385 | 281 bool |
| 458 | 282 Matrix::operator == (const Matrix& a) const |
| 283 { | |
| 284 if (rows () != a.rows () || cols () != a.cols ()) | |
| 2385 | 285 return false; |
| 458 | 286 |
| 3769 | 287 return mx_inline_equal (data (), a.data (), length ()); |
| 458 | 288 } |
| 289 | |
| 2385 | 290 bool |
| 458 | 291 Matrix::operator != (const Matrix& a) const |
| 292 { | |
| 293 return !(*this == a); | |
| 294 } | |
| 295 | |
| 3354 | 296 bool |
| 297 Matrix::is_symmetric (void) const | |
| 298 { | |
| 299 if (is_square () && rows () > 0) | |
| 300 { | |
| 5275 | 301 for (octave_idx_type i = 0; i < rows (); i++) |
| 302 for (octave_idx_type j = i+1; j < cols (); j++) | |
| 3354 | 303 if (elem (i, j) != elem (j, i)) |
| 304 return false; | |
| 305 | |
| 306 return true; | |
| 307 } | |
| 308 | |
| 309 return false; | |
| 310 } | |
| 311 | |
| 458 | 312 Matrix& |
| 5275 | 313 Matrix::insert (const Matrix& a, octave_idx_type r, octave_idx_type c) |
| 458 | 314 { |
| 1561 | 315 Array2<double>::insert (a, r, c); |
| 458 | 316 return *this; |
| 317 } | |
| 318 | |
| 319 Matrix& | |
| 5275 | 320 Matrix::insert (const RowVector& a, octave_idx_type r, octave_idx_type c) |
| 458 | 321 { |
| 5275 | 322 octave_idx_type a_len = a.length (); |
| 4316 | 323 |
| 1698 | 324 if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ()) |
| 458 | 325 { |
| 326 (*current_liboctave_error_handler) ("range error for insert"); | |
| 327 return *this; | |
| 328 } | |
| 329 | |
| 4316 | 330 if (a_len > 0) |
| 331 { | |
| 332 make_unique (); | |
| 333 | |
| 5275 | 334 for (octave_idx_type i = 0; i < a_len; i++) |
| 4316 | 335 xelem (r, c+i) = a.elem (i); |
| 336 } | |
| 458 | 337 |
| 338 return *this; | |
| 339 } | |
| 340 | |
| 341 Matrix& | |
| 5275 | 342 Matrix::insert (const ColumnVector& a, octave_idx_type r, octave_idx_type c) |
| 458 | 343 { |
| 5275 | 344 octave_idx_type a_len = a.length (); |
| 4316 | 345 |
| 1698 | 346 if (r < 0 || r + a_len > rows () || c < 0 || c >= cols ()) |
| 458 | 347 { |
| 348 (*current_liboctave_error_handler) ("range error for insert"); | |
| 349 return *this; | |
| 350 } | |
| 351 | |
| 4316 | 352 if (a_len > 0) |
| 353 { | |
| 354 make_unique (); | |
| 355 | |
| 5275 | 356 for (octave_idx_type i = 0; i < a_len; i++) |
| 4316 | 357 xelem (r+i, c) = a.elem (i); |
| 358 } | |
| 458 | 359 |
| 360 return *this; | |
| 361 } | |
| 362 | |
| 363 Matrix& | |
| 5275 | 364 Matrix::insert (const DiagMatrix& a, octave_idx_type r, octave_idx_type c) |
| 458 | 365 { |
| 5275 | 366 octave_idx_type a_nr = a.rows (); |
| 367 octave_idx_type a_nc = a.cols (); | |
| 1697 | 368 |
| 1698 | 369 if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) |
| 458 | 370 { |
| 371 (*current_liboctave_error_handler) ("range error for insert"); | |
| 372 return *this; | |
| 373 } | |
| 374 | |
| 1697 | 375 fill (0.0, r, c, r + a_nr - 1, c + a_nc - 1); |
| 376 | |
| 5275 | 377 octave_idx_type a_len = a.length (); |
| 4316 | 378 |
| 379 if (a_len > 0) | |
| 380 { | |
| 381 make_unique (); | |
| 382 | |
| 5275 | 383 for (octave_idx_type i = 0; i < a_len; i++) |
| 4316 | 384 xelem (r+i, c+i) = a.elem (i, i); |
| 385 } | |
| 458 | 386 |
| 387 return *this; | |
| 388 } | |
| 389 | |
| 390 Matrix& | |
| 391 Matrix::fill (double val) | |
| 392 { | |
| 5275 | 393 octave_idx_type nr = rows (); |
| 394 octave_idx_type nc = cols (); | |
| 4316 | 395 |
| 458 | 396 if (nr > 0 && nc > 0) |
| 4316 | 397 { |
| 398 make_unique (); | |
| 399 | |
| 5275 | 400 for (octave_idx_type j = 0; j < nc; j++) |
| 401 for (octave_idx_type i = 0; i < nr; i++) | |
| 4316 | 402 xelem (i, j) = val; |
| 403 } | |
| 458 | 404 |
| 405 return *this; | |
| 406 } | |
| 407 | |
| 408 Matrix& | |
| 5275 | 409 Matrix::fill (double val, octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) |
| 458 | 410 { |
| 5275 | 411 octave_idx_type nr = rows (); |
| 412 octave_idx_type nc = cols (); | |
| 4316 | 413 |
| 458 | 414 if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0 |
| 415 || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc) | |
| 416 { | |
| 417 (*current_liboctave_error_handler) ("range error for fill"); | |
| 418 return *this; | |
| 419 } | |
| 420 | |
| 5275 | 421 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } |
| 422 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } | |
| 458 | 423 |
| 4316 | 424 if (r2 >= r1 && c2 >= c1) |
| 425 { | |
| 426 make_unique (); | |
| 427 | |
| 5275 | 428 for (octave_idx_type j = c1; j <= c2; j++) |
| 429 for (octave_idx_type i = r1; i <= r2; i++) | |
| 4316 | 430 xelem (i, j) = val; |
| 431 } | |
| 458 | 432 |
| 433 return *this; | |
| 434 } | |
| 435 | |
| 436 Matrix | |
| 437 Matrix::append (const Matrix& a) const | |
| 438 { | |
| 5275 | 439 octave_idx_type nr = rows (); |
| 440 octave_idx_type nc = cols (); | |
| 458 | 441 if (nr != a.rows ()) |
| 442 { | |
| 443 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 444 return Matrix (); | |
| 445 } | |
| 446 | |
| 5275 | 447 octave_idx_type nc_insert = nc; |
| 458 | 448 Matrix retval (nr, nc + a.cols ()); |
| 449 retval.insert (*this, 0, 0); | |
| 450 retval.insert (a, 0, nc_insert); | |
| 451 return retval; | |
| 452 } | |
| 453 | |
| 454 Matrix | |
| 455 Matrix::append (const RowVector& a) const | |
| 456 { | |
| 5275 | 457 octave_idx_type nr = rows (); |
| 458 octave_idx_type nc = cols (); | |
| 458 | 459 if (nr != 1) |
| 460 { | |
| 461 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 462 return Matrix (); | |
| 463 } | |
| 464 | |
| 5275 | 465 octave_idx_type nc_insert = nc; |
| 458 | 466 Matrix retval (nr, nc + a.length ()); |
| 467 retval.insert (*this, 0, 0); | |
| 468 retval.insert (a, 0, nc_insert); | |
| 469 return retval; | |
| 470 } | |
| 471 | |
| 472 Matrix | |
| 473 Matrix::append (const ColumnVector& a) const | |
| 474 { | |
| 5275 | 475 octave_idx_type nr = rows (); |
| 476 octave_idx_type nc = cols (); | |
| 458 | 477 if (nr != a.length ()) |
| 478 { | |
| 479 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 480 return Matrix (); | |
| 481 } | |
| 482 | |
| 5275 | 483 octave_idx_type nc_insert = nc; |
| 458 | 484 Matrix retval (nr, nc + 1); |
| 485 retval.insert (*this, 0, 0); | |
| 486 retval.insert (a, 0, nc_insert); | |
| 487 return retval; | |
| 488 } | |
| 489 | |
| 490 Matrix | |
| 491 Matrix::append (const DiagMatrix& a) const | |
| 492 { | |
| 5275 | 493 octave_idx_type nr = rows (); |
| 494 octave_idx_type nc = cols (); | |
| 458 | 495 if (nr != a.rows ()) |
| 496 { | |
| 497 (*current_liboctave_error_handler) ("row dimension mismatch for append"); | |
| 498 return *this; | |
| 499 } | |
| 500 | |
| 5275 | 501 octave_idx_type nc_insert = nc; |
| 458 | 502 Matrix retval (nr, nc + a.cols ()); |
| 503 retval.insert (*this, 0, 0); | |
| 504 retval.insert (a, 0, nc_insert); | |
| 505 return retval; | |
| 506 } | |
| 507 | |
| 508 Matrix | |
| 509 Matrix::stack (const Matrix& a) const | |
| 510 { | |
| 5275 | 511 octave_idx_type nr = rows (); |
| 512 octave_idx_type nc = cols (); | |
| 458 | 513 if (nc != a.cols ()) |
| 514 { | |
| 515 (*current_liboctave_error_handler) | |
| 516 ("column dimension mismatch for stack"); | |
| 517 return Matrix (); | |
| 518 } | |
| 519 | |
| 5275 | 520 octave_idx_type nr_insert = nr; |
| 458 | 521 Matrix retval (nr + a.rows (), nc); |
| 522 retval.insert (*this, 0, 0); | |
| 523 retval.insert (a, nr_insert, 0); | |
| 524 return retval; | |
| 525 } | |
| 526 | |
| 527 Matrix | |
| 528 Matrix::stack (const RowVector& a) const | |
| 529 { | |
| 5275 | 530 octave_idx_type nr = rows (); |
| 531 octave_idx_type nc = cols (); | |
| 458 | 532 if (nc != a.length ()) |
| 533 { | |
| 534 (*current_liboctave_error_handler) | |
| 535 ("column dimension mismatch for stack"); | |
| 536 return Matrix (); | |
| 537 } | |
| 538 | |
| 5275 | 539 octave_idx_type nr_insert = nr; |
| 458 | 540 Matrix retval (nr + 1, nc); |
| 541 retval.insert (*this, 0, 0); | |
| 542 retval.insert (a, nr_insert, 0); | |
| 543 return retval; | |
| 544 } | |
| 545 | |
| 546 Matrix | |
| 547 Matrix::stack (const ColumnVector& a) const | |
| 548 { | |
| 5275 | 549 octave_idx_type nr = rows (); |
| 550 octave_idx_type nc = cols (); | |
| 458 | 551 if (nc != 1) |
| 552 { | |
| 553 (*current_liboctave_error_handler) | |
| 554 ("column dimension mismatch for stack"); | |
| 555 return Matrix (); | |
| 556 } | |
| 557 | |
| 5275 | 558 octave_idx_type nr_insert = nr; |
| 458 | 559 Matrix retval (nr + a.length (), nc); |
| 560 retval.insert (*this, 0, 0); | |
| 561 retval.insert (a, nr_insert, 0); | |
| 562 return retval; | |
| 563 } | |
| 564 | |
| 565 Matrix | |
| 566 Matrix::stack (const DiagMatrix& a) const | |
| 567 { | |
| 5275 | 568 octave_idx_type nr = rows (); |
| 569 octave_idx_type nc = cols (); | |
| 458 | 570 if (nc != a.cols ()) |
| 571 { | |
| 572 (*current_liboctave_error_handler) | |
| 573 ("column dimension mismatch for stack"); | |
| 574 return Matrix (); | |
| 575 } | |
| 576 | |
| 5275 | 577 octave_idx_type nr_insert = nr; |
| 458 | 578 Matrix retval (nr + a.rows (), nc); |
| 579 retval.insert (*this, 0, 0); | |
| 580 retval.insert (a, nr_insert, 0); | |
| 581 return retval; | |
| 582 } | |
| 583 | |
| 584 Matrix | |
| 1205 | 585 real (const ComplexMatrix& a) |
| 586 { | |
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587 return Matrix (mx_inline_real_dup (a.data (), a.length ()), |
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588 a.rows (), a.cols ()); |
| 1205 | 589 } |
| 590 | |
| 591 Matrix | |
| 592 imag (const ComplexMatrix& a) | |
| 593 { | |
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594 return Matrix (mx_inline_imag_dup (a.data (), a.length ()), |
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595 a.rows (), a.cols ()); |
| 1205 | 596 } |
| 597 | |
| 598 Matrix | |
| 5275 | 599 Matrix::extract (octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) const |
| 458 | 600 { |
| 5275 | 601 if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } |
| 602 if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } | |
| 603 | |
| 604 octave_idx_type new_r = r2 - r1 + 1; | |
| 605 octave_idx_type new_c = c2 - c1 + 1; | |
| 458 | 606 |
| 607 Matrix result (new_r, new_c); | |
| 608 | |
| 5275 | 609 for (octave_idx_type j = 0; j < new_c; j++) |
| 610 for (octave_idx_type i = 0; i < new_r; i++) | |
| 4316 | 611 result.xelem (i, j) = elem (r1+i, c1+j); |
| 612 | |
| 613 return result; | |
| 614 } | |
| 615 | |
| 616 Matrix | |
| 5275 | 617 Matrix::extract_n (octave_idx_type r1, octave_idx_type c1, octave_idx_type nr, octave_idx_type nc) const |
| 4316 | 618 { |
| 619 Matrix result (nr, nc); | |
| 620 | |
| 5275 | 621 for (octave_idx_type j = 0; j < nc; j++) |
| 622 for (octave_idx_type i = 0; i < nr; i++) | |
| 4316 | 623 result.xelem (i, j) = elem (r1+i, c1+j); |
| 458 | 624 |
| 625 return result; | |
| 626 } | |
| 627 | |
| 628 // extract row or column i. | |
| 629 | |
| 630 RowVector | |
| 5275 | 631 Matrix::row (octave_idx_type i) const |
| 458 | 632 { |
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633 return MArray<double> (index (idx_vector (i), idx_vector::colon)); |
| 458 | 634 } |
| 635 | |
| 636 ColumnVector | |
| 5275 | 637 Matrix::column (octave_idx_type i) const |
| 458 | 638 { |
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639 return MArray<double> (index (idx_vector::colon, idx_vector (i))); |
| 458 | 640 } |
| 641 | |
| 642 Matrix | |
| 643 Matrix::inverse (void) const | |
| 644 { | |
| 5275 | 645 octave_idx_type info; |
| 7788 | 646 double rcon; |
| 6207 | 647 MatrixType mattype (*this); |
| 7788 | 648 return inverse (mattype, info, rcon, 0, 0); |
| 6207 | 649 } |
| 650 | |
| 651 Matrix | |
| 6479 | 652 Matrix::inverse (octave_idx_type& info) const |
| 653 { | |
| 7788 | 654 double rcon; |
| 6479 | 655 MatrixType mattype (*this); |
| 7788 | 656 return inverse (mattype, info, rcon, 0, 0); |
| 6479 | 657 } |
| 658 | |
| 659 Matrix | |
| 7788 | 660 Matrix::inverse (octave_idx_type& info, double& rcon, int force, |
| 6479 | 661 int calc_cond) const |
| 662 { | |
| 663 MatrixType mattype (*this); | |
| 7788 | 664 return inverse (mattype, info, rcon, force, calc_cond); |
| 6479 | 665 } |
| 666 | |
| 667 Matrix | |
| 6207 | 668 Matrix::inverse (MatrixType& mattype) const |
| 669 { | |
| 670 octave_idx_type info; | |
| 7788 | 671 double rcon; |
| 672 return inverse (mattype, info, rcon, 0, 0); | |
| 6207 | 673 } |
| 674 | |
| 675 Matrix | |
| 676 Matrix::inverse (MatrixType &mattype, octave_idx_type& info) const | |
| 677 { | |
| 7788 | 678 double rcon; |
| 679 return inverse (mattype, info, rcon, 0, 0); | |
| 458 | 680 } |
| 681 | |
| 682 Matrix | |
| 7788 | 683 Matrix::tinverse (MatrixType &mattype, octave_idx_type& info, double& rcon, |
| 6207 | 684 int force, int calc_cond) const |
| 458 | 685 { |
| 6207 | 686 Matrix retval; |
| 687 | |
| 688 octave_idx_type nr = rows (); | |
| 689 octave_idx_type nc = cols (); | |
| 690 | |
| 691 if (nr != nc || nr == 0 || nc == 0) | |
| 692 (*current_liboctave_error_handler) ("inverse requires square matrix"); | |
| 693 else | |
| 694 { | |
| 695 int typ = mattype.type (); | |
| 696 char uplo = (typ == MatrixType::Lower ? 'L' : 'U'); | |
| 697 char udiag = 'N'; | |
| 698 retval = *this; | |
| 699 double *tmp_data = retval.fortran_vec (); | |
| 700 | |
| 701 F77_XFCN (dtrtri, DTRTRI, (F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 702 F77_CONST_CHAR_ARG2 (&udiag, 1), | |
| 703 nr, tmp_data, nr, info | |
| 704 F77_CHAR_ARG_LEN (1) | |
| 705 F77_CHAR_ARG_LEN (1))); | |
| 706 | |
|
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707 // Throw-away extra info LAPACK gives so as to not change output. |
| 7788 | 708 rcon = 0.0; |
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709 if (info != 0) |
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710 info = -1; |
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711 else if (calc_cond) |
| 6207 | 712 { |
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713 octave_idx_type dtrcon_info = 0; |
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714 char job = '1'; |
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715 |
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716 OCTAVE_LOCAL_BUFFER (double, work, 3 * nr); |
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717 OCTAVE_LOCAL_BUFFER (octave_idx_type, iwork, nr); |
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718 |
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719 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&job, 1), |
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720 F77_CONST_CHAR_ARG2 (&uplo, 1), |
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721 F77_CONST_CHAR_ARG2 (&udiag, 1), |
| 7788 | 722 nr, tmp_data, nr, rcon, |
|
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723 work, iwork, dtrcon_info |
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724 F77_CHAR_ARG_LEN (1) |
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725 F77_CHAR_ARG_LEN (1) |
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726 F77_CHAR_ARG_LEN (1))); |
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727 |
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728 if (dtrcon_info != 0) |
| 6207 | 729 info = -1; |
| 730 } | |
| 731 | |
| 732 if (info == -1 && ! force) | |
| 733 retval = *this; // Restore matrix contents. | |
| 734 } | |
| 735 | |
| 736 return retval; | |
| 458 | 737 } |
| 738 | |
| 6207 | 739 |
| 458 | 740 Matrix |
| 7788 | 741 Matrix::finverse (MatrixType &mattype, octave_idx_type& info, double& rcon, |
| 6207 | 742 int force, int calc_cond) const |
| 458 | 743 { |
| 1948 | 744 Matrix retval; |
| 745 | |
| 5275 | 746 octave_idx_type nr = rows (); |
| 747 octave_idx_type nc = cols (); | |
| 1948 | 748 |
| 458 | 749 if (nr != nc || nr == 0 || nc == 0) |
| 1948 | 750 (*current_liboctave_error_handler) ("inverse requires square matrix"); |
| 458 | 751 else |
| 752 { | |
| 5275 | 753 Array<octave_idx_type> ipvt (nr); |
| 754 octave_idx_type *pipvt = ipvt.fortran_vec (); | |
| 1948 | 755 |
| 756 retval = *this; | |
| 757 double *tmp_data = retval.fortran_vec (); | |
| 758 | |
| 4329 | 759 Array<double> z(1); |
| 5275 | 760 octave_idx_type lwork = -1; |
| 4329 | 761 |
| 4330 | 762 // Query the optimum work array size. |
| 4329 | 763 F77_XFCN (dgetri, DGETRI, (nc, tmp_data, nr, pipvt, |
| 764 z.fortran_vec (), lwork, info)); | |
| 765 | |
| 5275 | 766 lwork = static_cast<octave_idx_type> (z(0)); |
| 4329 | 767 lwork = (lwork < 2 *nc ? 2*nc : lwork); |
| 768 z.resize (lwork); | |
| 769 double *pz = z.fortran_vec (); | |
| 770 | |
| 771 info = 0; | |
| 772 | |
| 4330 | 773 // Calculate the norm of the matrix, for later use. |
| 4329 | 774 double anorm = 0; |
| 775 if (calc_cond) | |
| 5275 | 776 anorm = retval.abs().sum().row(static_cast<octave_idx_type>(0)).max(); |
| 4329 | 777 |
| 778 F77_XFCN (dgetrf, DGETRF, (nc, nc, tmp_data, nr, pipvt, info)); | |
| 1948 | 779 |
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780 // Throw-away extra info LAPACK gives so as to not change output. |
| 7788 | 781 rcon = 0.0; |
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782 if (info != 0) |
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783 info = -1; |
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784 else if (calc_cond) |
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785 { |
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786 octave_idx_type dgecon_info = 0; |
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787 |
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788 // Now calculate the condition number for non-singular matrix. |
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789 char job = '1'; |
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790 Array<octave_idx_type> iz (nc); |
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791 octave_idx_type *piz = iz.fortran_vec (); |
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|
792 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
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793 nc, tmp_data, nr, anorm, |
| 7788 | 794 rcon, pz, piz, dgecon_info |
|
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795 F77_CHAR_ARG_LEN (1))); |
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|
796 |
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797 if (dgecon_info != 0) |
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798 info = -1; |
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799 } |
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|
800 |
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801 if (info == -1 && ! force) |
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802 retval = *this; // Restore matrix contents. |
| 1948 | 803 else |
| 804 { | |
|
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805 octave_idx_type dgetri_info = 0; |
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|
806 |
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807 F77_XFCN (dgetri, DGETRI, (nc, tmp_data, nr, pipvt, |
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808 pz, lwork, dgetri_info)); |
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809 |
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|
810 if (dgetri_info != 0) |
| 1948 | 811 info = -1; |
| 812 } | |
| 6207 | 813 |
| 814 if (info != 0) | |
| 815 mattype.mark_as_rectangular(); | |
| 458 | 816 } |
| 817 | |
| 1948 | 818 return retval; |
| 458 | 819 } |
| 820 | |
| 740 | 821 Matrix |
| 7788 | 822 Matrix::inverse (MatrixType &mattype, octave_idx_type& info, double& rcon, |
| 6207 | 823 int force, int calc_cond) const |
| 824 { | |
| 825 int typ = mattype.type (false); | |
| 826 Matrix ret; | |
| 827 | |
| 828 if (typ == MatrixType::Unknown) | |
| 829 typ = mattype.type (*this); | |
| 830 | |
| 831 if (typ == MatrixType::Upper || typ == MatrixType::Lower) | |
| 7788 | 832 ret = tinverse (mattype, info, rcon, force, calc_cond); |
| 6840 | 833 else |
| 6207 | 834 { |
| 835 if (mattype.is_hermitian ()) | |
| 836 { | |
| 6486 | 837 CHOL chol (*this, info, calc_cond); |
| 6207 | 838 if (info == 0) |
| 6486 | 839 { |
| 840 if (calc_cond) | |
| 7788 | 841 rcon = chol.rcond (); |
| 6486 | 842 else |
| 7788 | 843 rcon = 1.0; |
| 6486 | 844 ret = chol.inverse (); |
| 845 } | |
| 6207 | 846 else |
| 847 mattype.mark_as_unsymmetric (); | |
| 848 } | |
| 849 | |
| 850 if (!mattype.is_hermitian ()) | |
| 7788 | 851 ret = finverse(mattype, info, rcon, force, calc_cond); |
| 852 | |
| 853 if ((mattype.is_hermitian () || calc_cond) && rcon == 0.) | |
| 6840 | 854 ret = Matrix (rows (), columns (), octave_Inf); |
| 6207 | 855 } |
| 856 | |
| 857 return ret; | |
| 858 } | |
| 859 | |
| 860 Matrix | |
| 4384 | 861 Matrix::pseudo_inverse (double tol) const |
| 740 | 862 { |
| 3480 | 863 SVD result (*this, SVD::economy); |
| 740 | 864 |
| 865 DiagMatrix S = result.singular_values (); | |
| 866 Matrix U = result.left_singular_matrix (); | |
| 867 Matrix V = result.right_singular_matrix (); | |
| 868 | |
| 869 ColumnVector sigma = S.diag (); | |
| 870 | |
| 5275 | 871 octave_idx_type r = sigma.length () - 1; |
| 872 octave_idx_type nr = rows (); | |
| 873 octave_idx_type nc = cols (); | |
| 740 | 874 |
| 875 if (tol <= 0.0) | |
| 876 { | |
| 877 if (nr > nc) | |
| 878 tol = nr * sigma.elem (0) * DBL_EPSILON; | |
| 879 else | |
| 880 tol = nc * sigma.elem (0) * DBL_EPSILON; | |
| 881 } | |
| 882 | |
| 883 while (r >= 0 && sigma.elem (r) < tol) | |
| 884 r--; | |
| 885 | |
| 886 if (r < 0) | |
| 887 return Matrix (nc, nr, 0.0); | |
| 888 else | |
| 889 { | |
| 890 Matrix Ur = U.extract (0, 0, nr-1, r); | |
| 891 DiagMatrix D = DiagMatrix (sigma.extract (0, r)) . inverse (); | |
| 892 Matrix Vr = V.extract (0, 0, nc-1, r); | |
| 893 return Vr * D * Ur.transpose (); | |
| 894 } | |
| 895 } | |
| 896 | |
| 4773 | 897 #if defined (HAVE_FFTW3) |
| 3827 | 898 |
| 899 ComplexMatrix | |
| 900 Matrix::fourier (void) const | |
| 901 { | |
| 902 size_t nr = rows (); | |
| 903 size_t nc = cols (); | |
| 904 | |
| 905 ComplexMatrix retval (nr, nc); | |
| 906 | |
| 907 size_t npts, nsamples; | |
| 908 | |
| 909 if (nr == 1 || nc == 1) | |
| 910 { | |
| 911 npts = nr > nc ? nr : nc; | |
| 912 nsamples = 1; | |
| 913 } | |
| 914 else | |
| 915 { | |
| 916 npts = nr; | |
| 917 nsamples = nc; | |
| 918 } | |
| 919 | |
| 4773 | 920 const double *in (fortran_vec ()); |
| 3827 | 921 Complex *out (retval.fortran_vec ()); |
| 922 | |
| 4773 | 923 octave_fftw::fft (in, out, npts, nsamples); |
| 3827 | 924 |
| 925 return retval; | |
| 926 } | |
| 927 | |
| 928 ComplexMatrix | |
| 929 Matrix::ifourier (void) const | |
| 930 { | |
| 931 size_t nr = rows (); | |
| 932 size_t nc = cols (); | |
| 933 | |
| 934 ComplexMatrix retval (nr, nc); | |
| 935 | |
| 936 size_t npts, nsamples; | |
| 937 | |
| 938 if (nr == 1 || nc == 1) | |
| 939 { | |
| 940 npts = nr > nc ? nr : nc; | |
| 941 nsamples = 1; | |
| 942 } | |
| 943 else | |
| 944 { | |
| 945 npts = nr; | |
| 946 nsamples = nc; | |
| 947 } | |
| 948 | |
| 949 ComplexMatrix tmp (*this); | |
| 950 Complex *in (tmp.fortran_vec ()); | |
| 951 Complex *out (retval.fortran_vec ()); | |
| 952 | |
| 4773 | 953 octave_fftw::ifft (in, out, npts, nsamples); |
| 3827 | 954 |
| 955 return retval; | |
| 956 } | |
| 957 | |
| 958 ComplexMatrix | |
| 959 Matrix::fourier2d (void) const | |
| 960 { | |
| 4773 | 961 dim_vector dv(rows (), cols ()); |
| 962 | |
| 963 const double *in = fortran_vec (); | |
| 964 ComplexMatrix retval (rows (), cols ()); | |
| 965 octave_fftw::fftNd (in, retval.fortran_vec (), 2, dv); | |
| 3827 | 966 |
| 967 return retval; | |
| 968 } | |
| 969 | |
| 970 ComplexMatrix | |
| 971 Matrix::ifourier2d (void) const | |
| 972 { | |
| 4773 | 973 dim_vector dv(rows (), cols ()); |
| 3827 | 974 |
| 975 ComplexMatrix retval (*this); | |
| 4773 | 976 Complex *out (retval.fortran_vec ()); |
| 977 | |
| 978 octave_fftw::ifftNd (out, out, 2, dv); | |
| 3827 | 979 |
| 980 return retval; | |
| 981 } | |
| 982 | |
| 983 #else | |
| 984 | |
| 458 | 985 ComplexMatrix |
| 986 Matrix::fourier (void) const | |
| 987 { | |
| 1948 | 988 ComplexMatrix retval; |
| 989 | |
| 5275 | 990 octave_idx_type nr = rows (); |
| 991 octave_idx_type nc = cols (); | |
| 992 | |
| 993 octave_idx_type npts, nsamples; | |
| 1948 | 994 |
| 458 | 995 if (nr == 1 || nc == 1) |
| 996 { | |
| 997 npts = nr > nc ? nr : nc; | |
| 998 nsamples = 1; | |
| 999 } | |
| 1000 else | |
| 1001 { | |
| 1002 npts = nr; | |
| 1003 nsamples = nc; | |
| 1004 } | |
| 1005 | |
| 5275 | 1006 octave_idx_type nn = 4*npts+15; |
| 1948 | 1007 |
| 1008 Array<Complex> wsave (nn); | |
| 1009 Complex *pwsave = wsave.fortran_vec (); | |
| 1010 | |
| 3585 | 1011 retval = ComplexMatrix (*this); |
| 1948 | 1012 Complex *tmp_data = retval.fortran_vec (); |
| 1013 | |
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1014 F77_FUNC (zffti, ZFFTI) (npts, pwsave); |
| 458 | 1015 |
| 5275 | 1016 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1017 { |
| 1018 OCTAVE_QUIT; | |
| 1019 | |
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|
1020 F77_FUNC (zfftf, ZFFTF) (npts, &tmp_data[npts*j], pwsave); |
| 4153 | 1021 } |
| 1948 | 1022 |
| 1023 return retval; | |
| 458 | 1024 } |
| 1025 | |
| 1026 ComplexMatrix | |
| 1027 Matrix::ifourier (void) const | |
| 1028 { | |
| 1948 | 1029 ComplexMatrix retval; |
| 1030 | |
| 5275 | 1031 octave_idx_type nr = rows (); |
| 1032 octave_idx_type nc = cols (); | |
| 1033 | |
| 1034 octave_idx_type npts, nsamples; | |
| 1948 | 1035 |
| 458 | 1036 if (nr == 1 || nc == 1) |
| 1037 { | |
| 1038 npts = nr > nc ? nr : nc; | |
| 1039 nsamples = 1; | |
| 1040 } | |
| 1041 else | |
| 1042 { | |
| 1043 npts = nr; | |
| 1044 nsamples = nc; | |
| 1045 } | |
| 1046 | |
| 5275 | 1047 octave_idx_type nn = 4*npts+15; |
| 1948 | 1048 |
| 1049 Array<Complex> wsave (nn); | |
| 1050 Complex *pwsave = wsave.fortran_vec (); | |
| 1051 | |
| 3585 | 1052 retval = ComplexMatrix (*this); |
| 1948 | 1053 Complex *tmp_data = retval.fortran_vec (); |
| 1054 | |
|
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diff
changeset
|
1055 F77_FUNC (zffti, ZFFTI) (npts, pwsave); |
| 458 | 1056 |
| 5275 | 1057 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1058 { |
| 1059 OCTAVE_QUIT; | |
| 1060 | |
|
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changeset
|
1061 F77_FUNC (zfftb, ZFFTB) (npts, &tmp_data[npts*j], pwsave); |
| 4153 | 1062 } |
| 458 | 1063 |
| 5275 | 1064 for (octave_idx_type j = 0; j < npts*nsamples; j++) |
| 3572 | 1065 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
| 458 | 1066 |
| 1948 | 1067 return retval; |
| 458 | 1068 } |
| 1069 | |
| 677 | 1070 ComplexMatrix |
| 1071 Matrix::fourier2d (void) const | |
| 1072 { | |
| 1948 | 1073 ComplexMatrix retval; |
| 1074 | |
| 5275 | 1075 octave_idx_type nr = rows (); |
| 1076 octave_idx_type nc = cols (); | |
| 1077 | |
| 1078 octave_idx_type npts, nsamples; | |
| 1948 | 1079 |
| 677 | 1080 if (nr == 1 || nc == 1) |
| 1081 { | |
| 1082 npts = nr > nc ? nr : nc; | |
| 1083 nsamples = 1; | |
| 1084 } | |
| 1085 else | |
| 1086 { | |
| 1087 npts = nr; | |
| 1088 nsamples = nc; | |
| 1089 } | |
| 1090 | |
| 5275 | 1091 octave_idx_type nn = 4*npts+15; |
| 1948 | 1092 |
| 1093 Array<Complex> wsave (nn); | |
| 1094 Complex *pwsave = wsave.fortran_vec (); | |
| 1095 | |
| 3585 | 1096 retval = ComplexMatrix (*this); |
| 1948 | 1097 Complex *tmp_data = retval.fortran_vec (); |
| 1098 | |
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changeset
|
1099 F77_FUNC (zffti, ZFFTI) (npts, pwsave); |
| 677 | 1100 |
| 5275 | 1101 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1102 { |
| 1103 OCTAVE_QUIT; | |
| 1104 | |
|
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|
1105 F77_FUNC (zfftf, ZFFTF) (npts, &tmp_data[npts*j], pwsave); |
| 4153 | 1106 } |
| 677 | 1107 |
| 1108 npts = nc; | |
| 1109 nsamples = nr; | |
| 1110 nn = 4*npts+15; | |
| 1948 | 1111 |
| 1112 wsave.resize (nn); | |
| 1113 pwsave = wsave.fortran_vec (); | |
| 1114 | |
| 4773 | 1115 Array<Complex> tmp (npts); |
| 1116 Complex *prow = tmp.fortran_vec (); | |
| 1948 | 1117 |
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|
1118 F77_FUNC (zffti, ZFFTI) (npts, pwsave); |
| 677 | 1119 |
| 5275 | 1120 for (octave_idx_type j = 0; j < nsamples; j++) |
| 677 | 1121 { |
| 4153 | 1122 OCTAVE_QUIT; |
| 1123 | |
| 5275 | 1124 for (octave_idx_type i = 0; i < npts; i++) |
| 1948 | 1125 prow[i] = tmp_data[i*nr + j]; |
| 1126 | |
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changeset
|
1127 F77_FUNC (zfftf, ZFFTF) (npts, prow, pwsave); |
| 677 | 1128 |
| 5275 | 1129 for (octave_idx_type i = 0; i < npts; i++) |
| 1948 | 1130 tmp_data[i*nr + j] = prow[i]; |
| 677 | 1131 } |
| 1132 | |
| 1948 | 1133 return retval; |
| 677 | 1134 } |
| 1135 | |
| 1136 ComplexMatrix | |
| 1137 Matrix::ifourier2d (void) const | |
| 1138 { | |
| 1948 | 1139 ComplexMatrix retval; |
| 1140 | |
| 5275 | 1141 octave_idx_type nr = rows (); |
| 1142 octave_idx_type nc = cols (); | |
| 1143 | |
| 1144 octave_idx_type npts, nsamples; | |
| 1948 | 1145 |
| 677 | 1146 if (nr == 1 || nc == 1) |
| 1147 { | |
| 1148 npts = nr > nc ? nr : nc; | |
| 1149 nsamples = 1; | |
| 1150 } | |
| 1151 else | |
| 1152 { | |
| 1153 npts = nr; | |
| 1154 nsamples = nc; | |
| 1155 } | |
| 1156 | |
| 5275 | 1157 octave_idx_type nn = 4*npts+15; |
| 1948 | 1158 |
| 1159 Array<Complex> wsave (nn); | |
| 1160 Complex *pwsave = wsave.fortran_vec (); | |
| 1161 | |
| 3585 | 1162 retval = ComplexMatrix (*this); |
| 1948 | 1163 Complex *tmp_data = retval.fortran_vec (); |
| 1164 | |
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|
1165 F77_FUNC (zffti, ZFFTI) (npts, pwsave); |
| 677 | 1166 |
| 5275 | 1167 for (octave_idx_type j = 0; j < nsamples; j++) |
| 4153 | 1168 { |
| 1169 OCTAVE_QUIT; | |
| 1170 | |
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|
1171 F77_FUNC (zfftb, ZFFTB) (npts, &tmp_data[npts*j], pwsave); |
| 4153 | 1172 } |
| 677 | 1173 |
| 5275 | 1174 for (octave_idx_type j = 0; j < npts*nsamples; j++) |
| 3572 | 1175 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
| 677 | 1176 |
| 1177 npts = nc; | |
| 1178 nsamples = nr; | |
| 1179 nn = 4*npts+15; | |
| 1948 | 1180 |
| 1181 wsave.resize (nn); | |
| 1182 pwsave = wsave.fortran_vec (); | |
| 1183 | |
| 4773 | 1184 Array<Complex> tmp (npts); |
| 1185 Complex *prow = tmp.fortran_vec (); | |
| 1948 | 1186 |
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|
1187 F77_FUNC (zffti, ZFFTI) (npts, pwsave); |
| 677 | 1188 |
| 5275 | 1189 for (octave_idx_type j = 0; j < nsamples; j++) |
| 677 | 1190 { |
| 4153 | 1191 OCTAVE_QUIT; |
| 1192 | |
| 5275 | 1193 for (octave_idx_type i = 0; i < npts; i++) |
| 1948 | 1194 prow[i] = tmp_data[i*nr + j]; |
| 1195 | |
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1196 F77_FUNC (zfftb, ZFFTB) (npts, prow, pwsave); |
| 677 | 1197 |
| 5275 | 1198 for (octave_idx_type i = 0; i < npts; i++) |
| 3572 | 1199 tmp_data[i*nr + j] = prow[i] / static_cast<double> (npts); |
| 677 | 1200 } |
| 1201 | |
| 1948 | 1202 return retval; |
| 677 | 1203 } |
| 1204 | |
| 3827 | 1205 #endif |
| 1206 | |
| 458 | 1207 DET |
| 1208 Matrix::determinant (void) const | |
| 1209 { | |
| 5275 | 1210 octave_idx_type info; |
| 7788 | 1211 double rcon; |
| 1212 return determinant (info, rcon, 0); | |
| 458 | 1213 } |
| 1214 | |
| 1215 DET | |
| 5275 | 1216 Matrix::determinant (octave_idx_type& info) const |
| 458 | 1217 { |
| 7788 | 1218 double rcon; |
| 1219 return determinant (info, rcon, 0); | |
| 458 | 1220 } |
| 1221 | |
| 1222 DET | |
| 7788 | 1223 Matrix::determinant (octave_idx_type& info, double& rcon, int calc_cond) const |
| 458 | 1224 { |
|
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1225 MatrixType mattype (*this); |
|
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1226 return determinant (mattype, info, rcon, calc_cond); |
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1227 } |
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1228 |
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1229 DET |
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1230 Matrix::determinant (MatrixType& mattype, |
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1231 octave_idx_type& info, double& rcon, int calc_cond) const |
|
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1232 { |
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1233 DET retval (1.0); |
| 458 | 1234 |
| 5275 | 1235 octave_idx_type nr = rows (); |
| 1236 octave_idx_type nc = cols (); | |
| 458 | 1237 |
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diff
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|
1238 if (nr != nc) |
|
9813c07ca946
make det take advantage of matrix type
Jaroslav Hajek <highegg@gmail.com>
parents:
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|
1239 (*current_liboctave_error_handler) ("matrix must be square"); |
| 458 | 1240 else |
| 1241 { | |
| 8806 | 1242 volatile int typ = mattype.type (); |
|
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|
1243 |
|
8337
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parents:
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diff
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|
1244 if (typ == MatrixType::Unknown) |
|
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reuse matrix type detected in det
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parents:
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diff
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|
1245 typ = mattype.type (*this); |
|
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reuse matrix type detected in det
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parents:
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diff
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|
1246 |
|
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9813c07ca946
make det take advantage of matrix type
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parents:
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|
1247 if (typ == MatrixType::Lower || typ == MatrixType::Upper) |
|
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parents:
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diff
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|
1248 { |
|
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parents:
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diff
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|
1249 for (octave_idx_type i = 0; i < nc; i++) |
|
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make det take advantage of matrix type
Jaroslav Hajek <highegg@gmail.com>
parents:
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|
1250 retval *= elem (i,i); |
|
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make det take advantage of matrix type
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diff
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|
1251 } |
|
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diff
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|
1252 else if (typ == MatrixType::Hermitian) |
|
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Jaroslav Hajek <highegg@gmail.com>
parents:
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diff
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|
1253 { |
|
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parents:
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diff
changeset
|
1254 Matrix atmp = *this; |
|
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make det take advantage of matrix type
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|
1255 double *tmp_data = atmp.fortran_vec (); |
|
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|
1256 |
|
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|
1257 info = 0; |
|
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|
1258 double anorm = 0; |
|
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|
1259 if (calc_cond) anorm = xnorm (*this, 1); |
|
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|
1260 |
|
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|
1261 |
|
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|
1262 char job = 'L'; |
|
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|
1263 F77_XFCN (dpotrf, DPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, |
|
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Jaroslav Hajek <highegg@gmail.com>
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|
1264 tmp_data, nr, info |
|
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make det take advantage of matrix type
Jaroslav Hajek <highegg@gmail.com>
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|
1265 F77_CHAR_ARG_LEN (1))); |
|
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|
1266 |
|
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|
1267 if (info != 0) |
|
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Jaroslav Hajek <highegg@gmail.com>
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|
1268 { |
|
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|
1269 rcon = 0.0; |
|
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|
1270 mattype.mark_as_unsymmetric (); |
|
9813c07ca946
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|
1271 typ = MatrixType::Full; |
|
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|
1272 } |
|
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|
1273 else |
|
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|
1274 { |
|
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|
1275 Array<double> z (3 * nc); |
|
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|
1276 double *pz = z.fortran_vec (); |
|
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|
1277 Array<octave_idx_type> iz (nc); |
|
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|
1278 octave_idx_type *piz = iz.fortran_vec (); |
|
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|
1279 |
|
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|
1280 F77_XFCN (dpocon, DPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
9813c07ca946
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|
1281 nr, tmp_data, nr, anorm, |
|
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|
1282 rcon, pz, piz, info |
|
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|
1283 F77_CHAR_ARG_LEN (1))); |
|
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|
1284 |
|
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|
1285 if (info != 0) |
|
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|
1286 rcon = 0.0; |
|
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|
1287 |
|
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|
1288 for (octave_idx_type i = 0; i < nc; i++) |
|
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|
1289 retval *= atmp (i,i); |
|
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|
1290 |
|
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|
1291 retval = retval.square (); |
|
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|
1292 } |
|
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|
1293 } |
|
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|
1294 else if (typ != MatrixType::Full) |
|
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|
1295 (*current_liboctave_error_handler) ("det: invalid dense matrix type"); |
|
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|
1296 |
|
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|
1297 if (typ == MatrixType::Full) |
|
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|
1298 { |
|
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|
1299 Array<octave_idx_type> ipvt (nr); |
|
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1300 octave_idx_type *pipvt = ipvt.fortran_vec (); |
|
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|
1301 |
|
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|
1302 Matrix atmp = *this; |
|
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|
1303 double *tmp_data = atmp.fortran_vec (); |
|
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|
1304 |
|
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|
1305 info = 0; |
|
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|
1306 |
|
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|
1307 // Calculate the norm of the matrix, for later use. |
|
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1308 double anorm = 0; |
|
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1309 if (calc_cond) anorm = xnorm (*this, 1); |
|
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|
1310 |
|
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|
1311 F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); |
|
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|
1312 |
|
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|
1313 // Throw-away extra info LAPACK gives so as to not change output. |
|
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1314 rcon = 0.0; |
|
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1315 if (info != 0) |
|
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|
1316 { |
|
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|
1317 info = -1; |
|
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|
1318 retval = DET (); |
|
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|
1319 } |
|
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|
1320 else |
|
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|
1321 { |
|
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|
1322 if (calc_cond) |
|
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|
1323 { |
|
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1324 // Now calc the condition number for non-singular matrix. |
|
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1325 char job = '1'; |
|
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|
1326 Array<double> z (4 * nc); |
|
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1327 double *pz = z.fortran_vec (); |
|
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|
1328 Array<octave_idx_type> iz (nc); |
|
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1329 octave_idx_type *piz = iz.fortran_vec (); |
|
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1330 |
|
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|
1331 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
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1332 nc, tmp_data, nr, anorm, |
|
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1333 rcon, pz, piz, info |
|
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|
1334 F77_CHAR_ARG_LEN (1))); |
| 8335 | 1335 } |
|
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|
1336 |
|
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|
1337 if (info != 0) |
|
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|
1338 { |
|
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|
1339 info = -1; |
|
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|
1340 retval = DET (); |
|
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|
1341 } |
|
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|
1342 else |
|
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|
1343 { |
|
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|
1344 for (octave_idx_type i = 0; i < nc; i++) |
|
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|
1345 { |
|
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|
1346 double c = atmp(i,i); |
|
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|
1347 retval *= (ipvt(i) != (i+1)) ? -c : c; |
|
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|
1348 } |
|
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|
1349 } |
|
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|
1350 } |
|
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|
1351 } |
| 458 | 1352 } |
| 1353 | |
| 1354 return retval; | |
| 1355 } | |
| 1356 | |
| 7788 | 1357 double |
| 1358 Matrix::rcond (void) const | |
| 1359 { | |
| 1360 MatrixType mattype (*this); | |
| 1361 return rcond (mattype); | |
| 1362 } | |
| 1363 | |
| 1364 double | |
| 1365 Matrix::rcond (MatrixType &mattype) const | |
| 1366 { | |
| 1367 double rcon; | |
| 1368 octave_idx_type nr = rows (); | |
| 1369 octave_idx_type nc = cols (); | |
| 1370 | |
| 1371 if (nr != nc) | |
| 1372 (*current_liboctave_error_handler) ("matrix must be square"); | |
| 1373 else if (nr == 0 || nc == 0) | |
| 1374 rcon = octave_Inf; | |
| 1375 else | |
| 1376 { | |
| 1377 int typ = mattype.type (); | |
| 1378 | |
| 1379 if (typ == MatrixType::Unknown) | |
| 1380 typ = mattype.type (*this); | |
| 1381 | |
| 1382 // Only calculate the condition number for LU/Cholesky | |
| 1383 if (typ == MatrixType::Upper) | |
| 1384 { | |
| 1385 const double *tmp_data = fortran_vec (); | |
| 1386 octave_idx_type info = 0; | |
| 1387 char norm = '1'; | |
| 1388 char uplo = 'U'; | |
| 1389 char dia = 'N'; | |
| 1390 | |
| 1391 Array<double> z (3 * nc); | |
| 1392 double *pz = z.fortran_vec (); | |
| 1393 Array<octave_idx_type> iz (nc); | |
| 1394 octave_idx_type *piz = iz.fortran_vec (); | |
| 1395 | |
| 1396 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1397 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1398 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1399 nr, tmp_data, nr, rcon, | |
| 1400 pz, piz, info | |
| 1401 F77_CHAR_ARG_LEN (1) | |
| 1402 F77_CHAR_ARG_LEN (1) | |
| 1403 F77_CHAR_ARG_LEN (1))); | |
| 1404 | |
| 1405 if (info != 0) | |
| 1406 rcon = 0.0; | |
| 1407 } | |
| 1408 else if (typ == MatrixType::Permuted_Upper) | |
| 1409 (*current_liboctave_error_handler) | |
| 1410 ("permuted triangular matrix not implemented"); | |
| 1411 else if (typ == MatrixType::Lower) | |
| 1412 { | |
| 1413 const double *tmp_data = fortran_vec (); | |
| 1414 octave_idx_type info = 0; | |
| 1415 char norm = '1'; | |
| 1416 char uplo = 'L'; | |
| 1417 char dia = 'N'; | |
| 1418 | |
| 1419 Array<double> z (3 * nc); | |
| 1420 double *pz = z.fortran_vec (); | |
| 1421 Array<octave_idx_type> iz (nc); | |
| 1422 octave_idx_type *piz = iz.fortran_vec (); | |
| 1423 | |
| 1424 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1425 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1426 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1427 nr, tmp_data, nr, rcon, | |
| 1428 pz, piz, info | |
| 1429 F77_CHAR_ARG_LEN (1) | |
| 1430 F77_CHAR_ARG_LEN (1) | |
| 1431 F77_CHAR_ARG_LEN (1))); | |
| 1432 | |
| 1433 if (info != 0) | |
| 1434 rcon = 0.0; | |
| 1435 } | |
| 1436 else if (typ == MatrixType::Permuted_Lower) | |
| 1437 (*current_liboctave_error_handler) | |
| 1438 ("permuted triangular matrix not implemented"); | |
| 1439 else if (typ == MatrixType::Full || typ == MatrixType::Hermitian) | |
| 1440 { | |
| 1441 double anorm = -1.0; | |
| 1442 Matrix atmp = *this; | |
| 1443 double *tmp_data = atmp.fortran_vec (); | |
| 1444 | |
| 1445 if (typ == MatrixType::Hermitian) | |
| 1446 { | |
| 1447 octave_idx_type info = 0; | |
| 1448 char job = 'L'; | |
| 1449 anorm = atmp.abs().sum(). | |
| 1450 row(static_cast<octave_idx_type>(0)).max(); | |
| 1451 | |
| 1452 F77_XFCN (dpotrf, DPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, | |
| 1453 tmp_data, nr, info | |
| 1454 F77_CHAR_ARG_LEN (1))); | |
| 1455 | |
| 1456 if (info != 0) | |
| 1457 { | |
| 1458 rcon = 0.0; | |
| 1459 mattype.mark_as_unsymmetric (); | |
| 1460 typ = MatrixType::Full; | |
| 1461 } | |
| 1462 else | |
| 1463 { | |
| 1464 Array<double> z (3 * nc); | |
| 1465 double *pz = z.fortran_vec (); | |
| 1466 Array<octave_idx_type> iz (nc); | |
| 1467 octave_idx_type *piz = iz.fortran_vec (); | |
| 1468 | |
| 1469 F77_XFCN (dpocon, DPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), | |
| 1470 nr, tmp_data, nr, anorm, | |
| 1471 rcon, pz, piz, info | |
| 1472 F77_CHAR_ARG_LEN (1))); | |
| 1473 | |
| 1474 if (info != 0) | |
| 1475 rcon = 0.0; | |
| 1476 } | |
| 1477 } | |
| 1478 | |
| 1479 if (typ == MatrixType::Full) | |
| 1480 { | |
| 1481 octave_idx_type info = 0; | |
| 1482 | |
| 1483 Array<octave_idx_type> ipvt (nr); | |
| 1484 octave_idx_type *pipvt = ipvt.fortran_vec (); | |
| 1485 | |
| 1486 if(anorm < 0.) | |
| 1487 anorm = atmp.abs().sum(). | |
| 1488 row(static_cast<octave_idx_type>(0)).max(); | |
| 1489 | |
| 1490 Array<double> z (4 * nc); | |
| 1491 double *pz = z.fortran_vec (); | |
| 1492 Array<octave_idx_type> iz (nc); | |
| 1493 octave_idx_type *piz = iz.fortran_vec (); | |
| 1494 | |
| 1495 F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); | |
| 1496 | |
| 1497 if (info != 0) | |
| 1498 { | |
| 1499 rcon = 0.0; | |
| 1500 mattype.mark_as_rectangular (); | |
| 1501 } | |
| 1502 else | |
| 1503 { | |
| 1504 char job = '1'; | |
| 1505 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), | |
| 1506 nc, tmp_data, nr, anorm, | |
| 1507 rcon, pz, piz, info | |
| 1508 F77_CHAR_ARG_LEN (1))); | |
| 1509 | |
| 1510 if (info != 0) | |
| 1511 rcon = 0.0; | |
| 1512 } | |
| 1513 } | |
| 1514 } | |
| 1515 else | |
| 1516 rcon = 0.0; | |
| 1517 } | |
| 1518 | |
| 1519 return rcon; | |
| 1520 } | |
| 1521 | |
| 458 | 1522 Matrix |
| 5785 | 1523 Matrix::utsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, |
| 7788 | 1524 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 1525 bool calc_cond) const |
| 1526 { | |
| 1527 Matrix retval; | |
| 1528 | |
| 1529 octave_idx_type nr = rows (); | |
| 1530 octave_idx_type nc = cols (); | |
| 1531 | |
| 6924 | 1532 if (nr != b.rows ()) |
| 5785 | 1533 (*current_liboctave_error_handler) |
| 1534 ("matrix dimension mismatch solution of linear equations"); | |
| 6924 | 1535 else if (nr == 0 || nc == 0 || b.cols () == 0) |
| 1536 retval = Matrix (nc, b.cols (), 0.0); | |
| 5785 | 1537 else |
| 1538 { | |
| 1539 volatile int typ = mattype.type (); | |
| 1540 | |
| 1541 if (typ == MatrixType::Permuted_Upper || | |
| 1542 typ == MatrixType::Upper) | |
| 1543 { | |
| 1544 octave_idx_type b_nc = b.cols (); | |
| 7788 | 1545 rcon = 1.; |
| 5785 | 1546 info = 0; |
| 1547 | |
| 1548 if (typ == MatrixType::Permuted_Upper) | |
| 1549 { | |
| 1550 (*current_liboctave_error_handler) | |
| 6390 | 1551 ("permuted triangular matrix not implemented"); |
| 5785 | 1552 } |
| 1553 else | |
| 1554 { | |
| 1555 const double *tmp_data = fortran_vec (); | |
| 1556 | |
| 1557 if (calc_cond) | |
| 1558 { | |
| 1559 char norm = '1'; | |
| 1560 char uplo = 'U'; | |
| 1561 char dia = 'N'; | |
| 1562 | |
| 1563 Array<double> z (3 * nc); | |
| 1564 double *pz = z.fortran_vec (); | |
| 1565 Array<octave_idx_type> iz (nc); | |
| 1566 octave_idx_type *piz = iz.fortran_vec (); | |
| 1567 | |
| 1568 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1569 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1570 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 7788 | 1571 nr, tmp_data, nr, rcon, |
| 5785 | 1572 pz, piz, info |
| 1573 F77_CHAR_ARG_LEN (1) | |
| 1574 F77_CHAR_ARG_LEN (1) | |
| 1575 F77_CHAR_ARG_LEN (1))); | |
| 1576 | |
| 1577 if (info != 0) | |
| 1578 info = -2; | |
| 1579 | |
| 7788 | 1580 volatile double rcond_plus_one = rcon + 1.0; |
| 1581 | |
| 1582 if (rcond_plus_one == 1.0 || xisnan (rcon)) | |
| 5785 | 1583 { |
| 1584 info = -2; | |
| 1585 | |
| 1586 if (sing_handler) | |
| 7788 | 1587 sing_handler (rcon); |
| 5785 | 1588 else |
| 1589 (*current_liboctave_error_handler) | |
| 1590 ("matrix singular to machine precision, rcond = %g", | |
| 7788 | 1591 rcon); |
| 5785 | 1592 } |
| 1593 } | |
| 1594 | |
| 1595 if (info == 0) | |
| 1596 { | |
| 1597 retval = b; | |
| 1598 double *result = retval.fortran_vec (); | |
| 1599 | |
| 1600 char uplo = 'U'; | |
| 1601 char trans = 'N'; | |
| 1602 char dia = 'N'; | |
| 1603 | |
| 1604 F77_XFCN (dtrtrs, DTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1605 F77_CONST_CHAR_ARG2 (&trans, 1), | |
| 1606 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1607 nr, b_nc, tmp_data, nr, | |
| 1608 result, nr, info | |
| 1609 F77_CHAR_ARG_LEN (1) | |
| 1610 F77_CHAR_ARG_LEN (1) | |
| 1611 F77_CHAR_ARG_LEN (1))); | |
| 1612 } | |
| 1613 } | |
| 1614 } | |
| 1615 else | |
| 1616 (*current_liboctave_error_handler) ("incorrect matrix type"); | |
| 1617 } | |
| 1618 | |
| 1619 return retval; | |
| 1620 } | |
| 1621 | |
| 1622 Matrix | |
| 1623 Matrix::ltsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, | |
| 7788 | 1624 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 1625 bool calc_cond) const |
| 1626 { | |
| 1627 Matrix retval; | |
| 1628 | |
| 1629 octave_idx_type nr = rows (); | |
| 1630 octave_idx_type nc = cols (); | |
| 1631 | |
| 6924 | 1632 if (nr != b.rows ()) |
| 5785 | 1633 (*current_liboctave_error_handler) |
| 1634 ("matrix dimension mismatch solution of linear equations"); | |
| 6924 | 1635 else if (nr == 0 || nc == 0 || b.cols () == 0) |
| 1636 retval = Matrix (nc, b.cols (), 0.0); | |
| 5785 | 1637 else |
| 1638 { | |
| 1639 volatile int typ = mattype.type (); | |
| 1640 | |
| 1641 if (typ == MatrixType::Permuted_Lower || | |
| 1642 typ == MatrixType::Lower) | |
| 1643 { | |
| 1644 octave_idx_type b_nc = b.cols (); | |
| 7788 | 1645 rcon = 1.; |
| 5785 | 1646 info = 0; |
| 1647 | |
| 1648 if (typ == MatrixType::Permuted_Lower) | |
| 1649 { | |
| 1650 (*current_liboctave_error_handler) | |
| 6390 | 1651 ("permuted triangular matrix not implemented"); |
| 5785 | 1652 } |
| 1653 else | |
| 1654 { | |
| 1655 const double *tmp_data = fortran_vec (); | |
| 1656 | |
| 1657 if (calc_cond) | |
| 1658 { | |
| 1659 char norm = '1'; | |
| 1660 char uplo = 'L'; | |
| 1661 char dia = 'N'; | |
| 1662 | |
| 1663 Array<double> z (3 * nc); | |
| 1664 double *pz = z.fortran_vec (); | |
| 1665 Array<octave_idx_type> iz (nc); | |
| 1666 octave_idx_type *piz = iz.fortran_vec (); | |
| 1667 | |
| 1668 F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), | |
| 1669 F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1670 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 7788 | 1671 nr, tmp_data, nr, rcon, |
| 5785 | 1672 pz, piz, info |
| 1673 F77_CHAR_ARG_LEN (1) | |
| 1674 F77_CHAR_ARG_LEN (1) | |
| 1675 F77_CHAR_ARG_LEN (1))); | |
| 1676 | |
| 1677 if (info != 0) | |
| 1678 info = -2; | |
| 1679 | |
| 7788 | 1680 volatile double rcond_plus_one = rcon + 1.0; |
| 1681 | |
| 1682 if (rcond_plus_one == 1.0 || xisnan (rcon)) | |
| 5785 | 1683 { |
| 1684 info = -2; | |
| 1685 | |
| 1686 if (sing_handler) | |
| 7788 | 1687 sing_handler (rcon); |
| 5785 | 1688 else |
| 1689 (*current_liboctave_error_handler) | |
| 1690 ("matrix singular to machine precision, rcond = %g", | |
| 7788 | 1691 rcon); |
| 5785 | 1692 } |
| 1693 } | |
| 1694 | |
| 1695 if (info == 0) | |
| 1696 { | |
| 1697 retval = b; | |
| 1698 double *result = retval.fortran_vec (); | |
| 1699 | |
| 1700 char uplo = 'L'; | |
| 1701 char trans = 'N'; | |
| 1702 char dia = 'N'; | |
| 1703 | |
| 1704 F77_XFCN (dtrtrs, DTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), | |
| 1705 F77_CONST_CHAR_ARG2 (&trans, 1), | |
| 1706 F77_CONST_CHAR_ARG2 (&dia, 1), | |
| 1707 nr, b_nc, tmp_data, nr, | |
| 1708 result, nr, info | |
| 1709 F77_CHAR_ARG_LEN (1) | |
| 1710 F77_CHAR_ARG_LEN (1) | |
| 1711 F77_CHAR_ARG_LEN (1))); | |
| 1712 } | |
| 1713 } | |
| 1714 } | |
| 1715 else | |
| 1716 (*current_liboctave_error_handler) ("incorrect matrix type"); | |
| 1717 } | |
| 1718 | |
| 1719 return retval; | |
| 1720 } | |
| 1721 | |
| 1722 Matrix | |
| 1723 Matrix::fsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, | |
| 7788 | 1724 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 1725 bool calc_cond) const |
| 1726 { | |
| 1727 Matrix retval; | |
| 1728 | |
| 1729 octave_idx_type nr = rows (); | |
| 1730 octave_idx_type nc = cols (); | |
| 1731 | |
| 6924 | 1732 if (nr != nc || nr != b.rows ()) |
| 5785 | 1733 (*current_liboctave_error_handler) |
| 1734 ("matrix dimension mismatch solution of linear equations"); | |
| 6924 | 1735 else if (nr == 0 || b.cols () == 0) |
| 1736 retval = Matrix (nc, b.cols (), 0.0); | |
| 5785 | 1737 else |
| 1738 { | |
| 1739 volatile int typ = mattype.type (); | |
| 1740 | |
| 1741 // Calculate the norm of the matrix, for later use. | |
| 1742 double anorm = -1.; | |
| 1743 | |
| 1744 if (typ == MatrixType::Hermitian) | |
| 1745 { | |
| 1746 info = 0; | |
| 1747 char job = 'L'; | |
| 1748 Matrix atmp = *this; | |
| 1749 double *tmp_data = atmp.fortran_vec (); | |
| 1750 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); | |
| 1751 | |
| 1752 F77_XFCN (dpotrf, DPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, | |
| 1753 tmp_data, nr, info | |
| 1754 F77_CHAR_ARG_LEN (1))); | |
| 1755 | |
|
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|
1756 // Throw-away extra info LAPACK gives so as to not change output. |
| 7788 | 1757 rcon = 0.0; |
|
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|
1758 if (info != 0) |
|
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|
1759 { |
|
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|
1760 info = -2; |
|
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|
1761 |
|
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|
1762 mattype.mark_as_unsymmetric (); |
|
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1763 typ = MatrixType::Full; |
|
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|
1764 } |
|
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|
1765 else |
| 5785 | 1766 { |
|
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|
1767 if (calc_cond) |
| 5785 | 1768 { |
|
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|
1769 Array<double> z (3 * nc); |
|
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|
1770 double *pz = z.fortran_vec (); |
|
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|
1771 Array<octave_idx_type> iz (nc); |
|
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|
1772 octave_idx_type *piz = iz.fortran_vec (); |
|
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1773 |
|
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|
1774 F77_XFCN (dpocon, DPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
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|
1775 nr, tmp_data, nr, anorm, |
| 7788 | 1776 rcon, pz, piz, info |
|
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|
1777 F77_CHAR_ARG_LEN (1))); |
|
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1778 |
|
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|
1779 if (info != 0) |
|
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1780 info = -2; |
|
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|
1781 |
| 7788 | 1782 volatile double rcond_plus_one = rcon + 1.0; |
| 1783 | |
| 1784 if (rcond_plus_one == 1.0 || xisnan (rcon)) | |
|
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|
1785 { |
|
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1786 info = -2; |
|
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|
1787 |
|
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|
1788 if (sing_handler) |
| 7788 | 1789 sing_handler (rcon); |
|
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|
1790 else |
|
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|
1791 (*current_liboctave_error_handler) |
|
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|
1792 ("matrix singular to machine precision, rcond = %g", |
| 7788 | 1793 rcon); |
|
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|
1794 } |
|
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1795 } |
|
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|
1796 |
|
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|
1797 if (info == 0) |
|
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|
1798 { |
|
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|
1799 retval = b; |
|
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1800 double *result = retval.fortran_vec (); |
|
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1801 |
|
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|
1802 octave_idx_type b_nc = b.cols (); |
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1803 |
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1804 F77_XFCN (dpotrs, DPOTRS, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
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1805 nr, b_nc, tmp_data, nr, |
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1806 result, b.rows(), info |
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1807 F77_CHAR_ARG_LEN (1))); |
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1808 } |
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1809 else |
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|
1810 { |
| 5785 | 1811 mattype.mark_as_unsymmetric (); |
| 1812 typ = MatrixType::Full; | |
|
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1813 } |
| 5785 | 1814 } |
| 1815 } | |
| 1816 | |
| 1817 if (typ == MatrixType::Full) | |
| 1818 { | |
| 1819 info = 0; | |
| 1820 | |
| 1821 Array<octave_idx_type> ipvt (nr); | |
| 1822 octave_idx_type *pipvt = ipvt.fortran_vec (); | |
| 1823 | |
| 1824 Matrix atmp = *this; | |
| 1825 double *tmp_data = atmp.fortran_vec (); | |
| 1826 if(anorm < 0.) | |
| 1827 anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); | |
| 1828 | |
| 1829 Array<double> z (4 * nc); | |
| 1830 double *pz = z.fortran_vec (); | |
| 1831 Array<octave_idx_type> iz (nc); | |
| 1832 octave_idx_type *piz = iz.fortran_vec (); | |
| 1833 | |
| 1834 F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); | |
| 1835 | |
|
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1836 // Throw-away extra info LAPACK gives so as to not change output. |
| 7788 | 1837 rcon = 0.0; |
|
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1838 if (info != 0) |
| 5785 | 1839 { |
|
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1840 info = -2; |
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1841 |
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1842 if (sing_handler) |
| 7788 | 1843 sing_handler (rcon); |
|
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1844 else |
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1845 (*current_liboctave_error_handler) |
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1846 ("matrix singular to machine precision"); |
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1847 |
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1848 mattype.mark_as_rectangular (); |
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1849 } |
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1850 else |
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1851 { |
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1852 if (calc_cond) |
| 5785 | 1853 { |
|
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1854 // Now calculate the condition number for |
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1855 // non-singular matrix. |
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1856 char job = '1'; |
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1857 F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), |
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1858 nc, tmp_data, nr, anorm, |
| 7788 | 1859 rcon, pz, piz, info |
|
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1860 F77_CHAR_ARG_LEN (1))); |
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1861 |
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1862 if (info != 0) |
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1863 info = -2; |
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1864 |
| 7788 | 1865 volatile double rcond_plus_one = rcon + 1.0; |
| 1866 | |
| 1867 if (rcond_plus_one == 1.0 || xisnan (rcon)) | |
| 5785 | 1868 { |
|
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1869 info = -2; |
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1870 |
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1871 if (sing_handler) |
| 7788 | 1872 sing_handler (rcon); |
|
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1873 else |
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1874 (*current_liboctave_error_handler) |
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1875 ("matrix singular to machine precision, rcond = %g", |
| 7788 | 1876 rcon); |
| 5785 | 1877 } |
| 1878 } | |
|
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1879 |
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1880 if (info == 0) |
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1881 { |
|
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1882 retval = b; |
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1883 double *result = retval.fortran_vec (); |
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1884 |
|
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|
1885 octave_idx_type b_nc = b.cols (); |
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|
1886 |
|
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|
1887 char job = 'N'; |
|
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changeset
|
1888 F77_XFCN (dgetrs, DGETRS, (F77_CONST_CHAR_ARG2 (&job, 1), |
|
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|
1889 nr, b_nc, tmp_data, nr, |
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|
1890 pipvt, result, b.rows(), info |
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|
1891 F77_CHAR_ARG_LEN (1))); |
|
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|
1892 } |
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|
1893 else |
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|
1894 mattype.mark_as_rectangular (); |
| 5785 | 1895 } |
| 1896 } | |
| 1897 else if (typ != MatrixType::Hermitian) | |
| 1898 (*current_liboctave_error_handler) ("incorrect matrix type"); | |
| 1899 } | |
| 1900 | |
| 1901 return retval; | |
| 1902 } | |
| 1903 | |
| 1904 Matrix | |
| 1905 Matrix::solve (MatrixType &typ, const Matrix& b) const | |
| 1906 { | |
| 1907 octave_idx_type info; | |
| 7788 | 1908 double rcon; |
| 1909 return solve (typ, b, info, rcon, 0); | |
| 5785 | 1910 } |
| 1911 | |
| 1912 Matrix | |
| 1913 Matrix::solve (MatrixType &typ, const Matrix& b, octave_idx_type& info, | |
| 7788 | 1914 double& rcon) const |
| 5785 | 1915 { |
| 7788 | 1916 return solve (typ, b, info, rcon, 0); |
| 5785 | 1917 } |
| 1918 | |
| 1919 Matrix | |
| 1920 Matrix::solve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, | |
| 7788 | 1921 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 1922 bool singular_fallback) const |
| 1923 { | |
| 1924 Matrix retval; | |
| 1925 int typ = mattype.type (); | |
| 1926 | |
| 1927 if (typ == MatrixType::Unknown) | |
| 1928 typ = mattype.type (*this); | |
| 1929 | |
| 1930 // Only calculate the condition number for LU/Cholesky | |
| 1931 if (typ == MatrixType::Upper || typ == MatrixType::Permuted_Upper) | |
| 7788 | 1932 retval = utsolve (mattype, b, info, rcon, sing_handler, false); |
| 5785 | 1933 else if (typ == MatrixType::Lower || typ == MatrixType::Permuted_Lower) |
| 7788 | 1934 retval = ltsolve (mattype, b, info, rcon, sing_handler, false); |
| 5785 | 1935 else if (typ == MatrixType::Full || typ == MatrixType::Hermitian) |
| 7788 | 1936 retval = fsolve (mattype, b, info, rcon, sing_handler, true); |
| 5785 | 1937 else if (typ != MatrixType::Rectangular) |
| 1938 { | |
| 1939 (*current_liboctave_error_handler) ("unknown matrix type"); | |
| 1940 return Matrix (); | |
| 1941 } | |
| 1942 | |
| 1943 // Rectangular or one of the above solvers flags a singular matrix | |
| 1944 if (singular_fallback && mattype.type () == MatrixType::Rectangular) | |
| 1945 { | |
| 1946 octave_idx_type rank; | |
| 7788 | 1947 retval = lssolve (b, info, rank, rcon); |
| 5785 | 1948 } |
| 1949 | |
| 1950 return retval; | |
| 1951 } | |
| 1952 | |
| 1953 ComplexMatrix | |
| 1954 Matrix::solve (MatrixType &typ, const ComplexMatrix& b) const | |
| 1955 { | |
| 1956 ComplexMatrix tmp (*this); | |
| 1957 return tmp.solve (typ, b); | |
| 1958 } | |
| 1959 | |
| 1960 ComplexMatrix | |
| 1961 Matrix::solve (MatrixType &typ, const ComplexMatrix& b, | |
| 1962 octave_idx_type& info) const | |
| 1963 { | |
| 1964 ComplexMatrix tmp (*this); | |
| 1965 return tmp.solve (typ, b, info); | |
| 1966 } | |
| 1967 | |
| 1968 ComplexMatrix | |
| 1969 Matrix::solve (MatrixType &typ, const ComplexMatrix& b, octave_idx_type& info, | |
| 7788 | 1970 double& rcon) const |
| 5785 | 1971 { |
| 1972 ComplexMatrix tmp (*this); | |
| 7788 | 1973 return tmp.solve (typ, b, info, rcon); |
| 5785 | 1974 } |
| 1975 | |
| 1976 ComplexMatrix | |
| 1977 Matrix::solve (MatrixType &typ, const ComplexMatrix& b, octave_idx_type& info, | |
| 7788 | 1978 double& rcon, solve_singularity_handler sing_handler, |
| 5785 | 1979 bool singular_fallback) const |
| 1980 { | |
| 1981 ComplexMatrix tmp (*this); | |
| 7788 | 1982 return tmp.solve (typ, b, info, rcon, sing_handler, singular_fallback); |
| 5785 | 1983 } |
| 1984 | |
| 1985 ColumnVector | |
| 1986 Matrix::solve (MatrixType &typ, const ColumnVector& b) const | |
| 1987 { | |
| 7788 | 1988 octave_idx_type info; double rcon; |
| 1989 return solve (typ, b, info, rcon); | |
| 5785 | 1990 } |
| 1991 | |
| 1992 ColumnVector | |
| 1993 Matrix::solve (MatrixType &typ, const ColumnVector& b, | |
| 1994 octave_idx_type& info) const | |
| 1995 { | |
| 7788 | 1996 double rcon; |
| 1997 return solve (typ, b, info, rcon); | |
| 5785 | 1998 } |
| 1999 | |
| 2000 ColumnVector | |
| 2001 Matrix::solve (MatrixType &typ, const ColumnVector& b, octave_idx_type& info, | |
| 7788 | 2002 double& rcon) const |
| 5785 | 2003 { |
| 7788 | 2004 return solve (typ, b, info, rcon, 0); |
| 5785 | 2005 } |
| 2006 | |
| 2007 ColumnVector | |
| 2008 Matrix::solve (MatrixType &typ, const ColumnVector& b, octave_idx_type& info, | |
| 7788 | 2009 double& rcon, solve_singularity_handler sing_handler) const |
| 5785 | 2010 { |
| 2011 Matrix tmp (b); | |
| 7788 | 2012 return solve (typ, tmp, info, rcon, sing_handler).column(static_cast<octave_idx_type> (0)); |
| 5785 | 2013 } |
| 2014 | |
| 2015 ComplexColumnVector | |
| 2016 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b) const | |
| 2017 { | |
| 2018 ComplexMatrix tmp (*this); | |
| 2019 return tmp.solve (typ, b); | |
| 2020 } | |
| 2021 | |
| 2022 ComplexColumnVector | |
| 2023 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, | |
| 2024 octave_idx_type& info) const | |
| 2025 { | |
| 2026 ComplexMatrix tmp (*this); | |
| 2027 return tmp.solve (typ, b, info); | |
| 2028 } | |
| 2029 | |
| 2030 ComplexColumnVector | |
| 2031 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, | |
| 7788 | 2032 octave_idx_type& info, double& rcon) const |
| 5785 | 2033 { |
| 2034 ComplexMatrix tmp (*this); | |
| 7788 | 2035 return tmp.solve (typ, b, info, rcon); |
| 5785 | 2036 } |
| 2037 | |
| 2038 ComplexColumnVector | |
| 2039 Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, | |
| 7788 | 2040 octave_idx_type& info, double& rcon, |
| 5785 | 2041 solve_singularity_handler sing_handler) const |
| 2042 { | |
| 2043 ComplexMatrix tmp (*this); | |
| 7788 | 2044 return tmp.solve(typ, b, info, rcon, sing_handler); |
| 5785 | 2045 } |
| 2046 | |
| 2047 Matrix | |
| 458 | 2048 Matrix::solve (const Matrix& b) const |
| 2049 { | |
| 5275 | 2050 octave_idx_type info; |
| 7788 | 2051 double rcon; |
| 2052 return solve (b, info, rcon, 0); | |
| 458 | 2053 } |
| 2054 | |
| 2055 Matrix | |
| 5275 | 2056 Matrix::solve (const Matrix& b, octave_idx_type& info) const |
| 458 | 2057 { |
| 7788 | 2058 double rcon; |
| 2059 return solve (b, info, rcon, 0); | |
| 458 | 2060 } |
| 2061 | |
| 2062 Matrix | |
| 7788 | 2063 Matrix::solve (const Matrix& b, octave_idx_type& info, double& rcon) const |
| 458 | 2064 { |
| 7788 | 2065 return solve (b, info, rcon, 0); |
| 3480 | 2066 } |
| 2067 | |
| 2068 Matrix | |
| 5785 | 2069 Matrix::solve (const Matrix& b, octave_idx_type& info, |
| 7788 | 2070 double& rcon, solve_singularity_handler sing_handler) const |
| 3480 | 2071 { |
| 5785 | 2072 MatrixType mattype (*this); |
| 7788 | 2073 return solve (mattype, b, info, rcon, sing_handler); |
| 458 | 2074 } |
| 2075 | |
| 2076 ComplexMatrix | |
| 2077 Matrix::solve (const ComplexMatrix& b) const | |
| 2078 { | |
| 2079 ComplexMatrix tmp (*this); | |
| 2080 return tmp.solve (b); | |
| 2081 } | |
| 2082 | |
| 2083 ComplexMatrix | |
| 5275 | 2084 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info) const |
| 458 | 2085 { |
| 2086 ComplexMatrix tmp (*this); | |
| 2087 return tmp.solve (b, info); | |
| 2088 } | |
| 2089 | |
| 2090 ComplexMatrix | |
| 7788 | 2091 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcon) const |
| 458 | 2092 { |
| 2093 ComplexMatrix tmp (*this); | |
| 7788 | 2094 return tmp.solve (b, info, rcon); |
| 458 | 2095 } |
| 2096 | |
| 3480 | 2097 ComplexMatrix |
| 7788 | 2098 Matrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcon, |
| 3480 | 2099 solve_singularity_handler sing_handler) const |
| 2100 { | |
| 2101 ComplexMatrix tmp (*this); | |
| 7788 | 2102 return tmp.solve (b, info, rcon, sing_handler); |
| 3480 | 2103 } |
| 2104 | |
| 458 | 2105 ColumnVector |
| 2106 Matrix::solve (const ColumnVector& b) const | |
| 2107 { | |
| 7788 | 2108 octave_idx_type info; double rcon; |
| 2109 return solve (b, info, rcon); | |
| 458 | 2110 } |
| 2111 | |
| 2112 ColumnVector | |
| 5275 | 2113 Matrix::solve (const ColumnVector& b, octave_idx_type& info) const |
| 458 | 2114 { |
| 7788 | 2115 double rcon; |
| 2116 return solve (b, info, rcon); | |
| 458 | 2117 } |
| 2118 | |
| 2119 ColumnVector | |
| 7788 | 2120 Matrix::solve (const ColumnVector& b, octave_idx_type& info, double& rcon) const |
| 458 | 2121 { |
| 7788 | 2122 return solve (b, info, rcon, 0); |
| 3480 | 2123 } |
| 2124 | |
| 2125 ColumnVector | |
| 7788 | 2126 Matrix::solve (const ColumnVector& b, octave_idx_type& info, double& rcon, |
| 3480 | 2127 solve_singularity_handler sing_handler) const |
| 2128 { | |
| 5785 | 2129 MatrixType mattype (*this); |
| 7788 | 2130 return solve (mattype, b, info, rcon, sing_handler); |
| 458 | 2131 } |
| 2132 | |
| 2133 ComplexColumnVector | |
| 2134 Matrix::solve (const ComplexColumnVector& b) const | |
| 2135 { | |
| 2136 ComplexMatrix tmp (*this); | |
| 2137 return tmp.solve (b); | |
| 2138 } | |
| 2139 | |
| 2140 ComplexColumnVector | |
| 5275 | 2141 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info) const |
| 458 | 2142 { |
| 2143 ComplexMatrix tmp (*this); | |
| 2144 return tmp.solve (b, info); | |
| 2145 } | |
| 2146 | |
| 2147 ComplexColumnVector | |
| 7788 | 2148 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info, double& rcon) const |
| 458 | 2149 { |
| 2150 ComplexMatrix tmp (*this); | |
| 7788 | 2151 return tmp.solve (b, info, rcon); |
| 458 | 2152 } |
| 2153 | |
| 3480 | 2154 ComplexColumnVector |
| 7788 | 2155 Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info, double& rcon, |
| 3480 | 2156 solve_singularity_handler sing_handler) const |
| 2157 { | |
| 2158 ComplexMatrix tmp (*this); | |
| 7788 | 2159 return tmp.solve (b, info, rcon, sing_handler); |
| 3480 | 2160 } |
| 2161 | |
| 458 | 2162 Matrix |
| 2163 Matrix::lssolve (const Matrix& b) const | |
| 2164 { | |
| 5275 | 2165 octave_idx_type info; |
| 2166 octave_idx_type rank; | |
| 7788 | 2167 double rcon; |
| 2168 return lssolve (b, info, rank, rcon); | |
| 458 | 2169 } |
| 2170 | |
| 2171 Matrix | |
| 5275 | 2172 Matrix::lssolve (const Matrix& b, octave_idx_type& info) const |
| 458 | 2173 { |
| 5275 | 2174 octave_idx_type rank; |
| 7788 | 2175 double rcon; |
| 2176 return lssolve (b, info, rank, rcon); | |
| 458 | 2177 } |
| 2178 | |
| 2179 Matrix | |
| 7072 | 2180 Matrix::lssolve (const Matrix& b, octave_idx_type& info, |
| 2181 octave_idx_type& rank) const | |
| 458 | 2182 { |
| 7788 | 2183 double rcon; |
| 2184 return lssolve (b, info, rank, rcon); | |
| 7076 | 2185 } |
| 2186 | |
| 2187 Matrix | |
| 2188 Matrix::lssolve (const Matrix& b, octave_idx_type& info, | |
| 7788 | 2189 octave_idx_type& rank, double &rcon) const |
| 7076 | 2190 { |
| 1948 | 2191 Matrix retval; |
| 2192 | |
| 5275 | 2193 octave_idx_type nrhs = b.cols (); |
| 2194 | |
| 2195 octave_idx_type m = rows (); | |
| 2196 octave_idx_type n = cols (); | |
| 458 | 2197 |
| 6924 | 2198 if (m != b.rows ()) |
| 1948 | 2199 (*current_liboctave_error_handler) |
| 6924 | 2200 ("matrix dimension mismatch solution of linear equations"); |
| 2201 else if (m == 0 || n == 0 || b.cols () == 0) | |
| 2202 retval = Matrix (n, b.cols (), 0.0); | |
| 1948 | 2203 else |
| 458 | 2204 { |
| 7072 | 2205 volatile octave_idx_type minmn = (m < n ? m : n); |
| 2206 octave_idx_type maxmn = m > n ? m : n; | |
| 7788 | 2207 rcon = -1.0; |
| 7072 | 2208 if (m != n) |
| 2209 { | |
| 2210 retval = Matrix (maxmn, nrhs, 0.0); | |
| 2211 | |
| 2212 for (octave_idx_type j = 0; j < nrhs; j++) | |
| 2213 for (octave_idx_type i = 0; i < m; i++) | |
| 2214 retval.elem (i, j) = b.elem (i, j); | |
| 2215 } | |
| 2216 else | |
| 2217 retval = b; | |
| 2218 | |
| 1948 | 2219 Matrix atmp = *this; |
| 2220 double *tmp_data = atmp.fortran_vec (); | |
| 2221 | |
| 7072 | 2222 double *pretval = retval.fortran_vec (); |
| 2223 Array<double> s (minmn); | |
| 7071 | 2224 double *ps = s.fortran_vec (); |
| 1948 | 2225 |
| 7072 | 2226 // Ask DGELSD what the dimension of WORK should be. |
| 5275 | 2227 octave_idx_type lwork = -1; |
| 3752 | 2228 |
| 2229 Array<double> work (1); | |
| 1948 | 2230 |
| 7477 | 2231 octave_idx_type smlsiz; |
| 2232 F77_FUNC (xilaenv, XILAENV) (9, F77_CONST_CHAR_ARG2 ("DGELSD", 6), | |
| 2233 F77_CONST_CHAR_ARG2 (" ", 1), | |
| 7478 | 2234 0, 0, 0, 0, smlsiz |
| 7477 | 2235 F77_CHAR_ARG_LEN (6) |
| 7478 | 2236 F77_CHAR_ARG_LEN (1)); |
| 7079 | 2237 |
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2238 octave_idx_type mnthr; |
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2239 F77_FUNC (xilaenv, XILAENV) (6, F77_CONST_CHAR_ARG2 ("DGELSD", 6), |
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2240 F77_CONST_CHAR_ARG2 (" ", 1), |
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2241 m, n, nrhs, -1, mnthr |
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2242 F77_CHAR_ARG_LEN (6) |
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2243 F77_CHAR_ARG_LEN (1)); |
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2244 |
| 7079 | 2245 // We compute the size of iwork because DGELSD in older versions |
| 2246 // of LAPACK does not return it on a query call. | |
| 7124 | 2247 double dminmn = static_cast<double> (minmn); |
| 2248 double dsmlsizp1 = static_cast<double> (smlsiz+1); | |
| 7079 | 2249 #if defined (HAVE_LOG2) |
| 7367 | 2250 double tmp = log2 (dminmn / dsmlsizp1); |
| 7079 | 2251 #else |
| 7367 | 2252 double tmp = log (dminmn / dsmlsizp1) / log (2.0); |
| 7079 | 2253 #endif |
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2254 octave_idx_type nlvl = static_cast<octave_idx_type> (tmp) + 1; |
| 7079 | 2255 if (nlvl < 0) |
| 2256 nlvl = 0; | |
| 2257 | |
| 2258 octave_idx_type liwork = 3 * minmn * nlvl + 11 * minmn; | |
| 2259 if (liwork < 1) | |
| 2260 liwork = 1; | |
| 7072 | 2261 Array<octave_idx_type> iwork (liwork); |
| 2262 octave_idx_type* piwork = iwork.fortran_vec (); | |
| 2263 | |
| 2264 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, | |
| 7788 | 2265 ps, rcon, rank, work.fortran_vec (), |
| 7072 | 2266 lwork, piwork, info)); |
| 1948 | 2267 |
| 7476 | 2268 // The workspace query is broken in at least LAPACK 3.0.0 |
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2269 // through 3.1.1 when n >= mnthr. The obtuse formula below |
| 7476 | 2270 // should provide sufficient workspace for DGELSD to operate |
| 2271 // efficiently. | |
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2272 if (n >= mnthr) |
| 7476 | 2273 { |
| 2274 const octave_idx_type wlalsd | |
| 2275 = 9*m + 2*m*smlsiz + 8*m*nlvl + m*nrhs + (smlsiz+1)*(smlsiz+1); | |
| 2276 | |
| 2277 octave_idx_type addend = m; | |
| 2278 | |
| 2279 if (2*m-4 > addend) | |
| 2280 addend = 2*m-4; | |
| 2281 | |
| 2282 if (nrhs > addend) | |
| 2283 addend = nrhs; | |
| 2284 | |
| 2285 if (n-3*m > addend) | |
| 2286 addend = n-3*m; | |
| 2287 | |
| 2288 if (wlalsd > addend) | |
| 2289 addend = wlalsd; | |
| 2290 | |
| 2291 const octave_idx_type lworkaround = 4*m + m*m + addend; | |
| 2292 | |
| 2293 if (work(0) < lworkaround) | |
| 2294 work(0) = lworkaround; | |
| 2295 } | |
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2296 else if (m >= n) |
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2297 { |
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2298 octave_idx_type lworkaround |
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2299 = 12*n + 2*n*smlsiz + 8*n*nlvl + n*nrhs + (smlsiz+1)*(smlsiz+1); |
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2300 |
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2301 if (work(0) < lworkaround) |
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2302 work(0) = lworkaround; |
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2303 } |
| 7476 | 2304 |
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2305 lwork = static_cast<octave_idx_type> (work(0)); |
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2306 work.resize (lwork); |
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2307 |
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2308 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, |
| 7788 | 2309 maxmn, ps, rcon, rank, |
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2310 work.fortran_vec (), lwork, |
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2311 piwork, info)); |
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2312 |
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2313 if (rank < minmn) |
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2314 (*current_liboctave_warning_handler) |
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2315 ("dgelsd: rank deficient %dx%d matrix, rank = %d", m, n, rank); |
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|
2316 if (s.elem (0) == 0.0) |
| 7788 | 2317 rcon = 0.0; |
| 1948 | 2318 else |
| 7788 | 2319 rcon = s.elem (minmn - 1) / s.elem (0); |
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|
2320 |
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|
2321 retval.resize (n, nrhs); |
| 458 | 2322 } |
| 2323 | |
| 2324 return retval; | |
| 2325 } | |
| 2326 | |
| 2327 ComplexMatrix | |
| 2328 Matrix::lssolve (const ComplexMatrix& b) const | |
| 2329 { | |
| 2330 ComplexMatrix tmp (*this); | |
| 5275 | 2331 octave_idx_type info; |
| 2332 octave_idx_type rank; | |
| 7788 | 2333 double rcon; |
| 2334 return tmp.lssolve (b, info, rank, rcon); | |
| 458 | 2335 } |
| 2336 | |
| 2337 ComplexMatrix | |
| 5275 | 2338 Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info) const |
| 458 | 2339 { |
| 2340 ComplexMatrix tmp (*this); | |
| 5275 | 2341 octave_idx_type rank; |
| 7788 | 2342 double rcon; |
| 2343 return tmp.lssolve (b, info, rank, rcon); | |
| 458 | 2344 } |
| 2345 | |
| 2346 ComplexMatrix | |
| 7076 | 2347 Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info, |
| 2348 octave_idx_type& rank) const | |
| 458 | 2349 { |
| 2350 ComplexMatrix tmp (*this); | |
| 7788 | 2351 double rcon; |
| 2352 return tmp.lssolve (b, info, rank, rcon); | |
| 7076 | 2353 } |
| 2354 | |
| 2355 ComplexMatrix | |
| 2356 Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info, | |
| 7788 | 2357 octave_idx_type& rank, double& rcon) const |
| 7076 | 2358 { |
| 2359 ComplexMatrix tmp (*this); | |
| 7788 | 2360 return tmp.lssolve (b, info, rank, rcon); |
| 458 | 2361 } |
| 2362 | |
| 2363 ColumnVector | |
| 2364 Matrix::lssolve (const ColumnVector& b) const | |
| 2365 { | |
| 5275 | 2366 octave_idx_type info; |
| 2367 octave_idx_type rank; | |
| 7788 | 2368 double rcon; |
| 2369 return lssolve (b, info, rank, rcon); | |
| 458 | 2370 } |
| 2371 | |
| 2372 ColumnVector | |
| 5275 | 2373 Matrix::lssolve (const ColumnVector& b, octave_idx_type& info) const |
| 458 | 2374 { |
| 5275 | 2375 octave_idx_type rank; |
| 7788 | 2376 double rcon; |
| 2377 return lssolve (b, info, rank, rcon); | |
| 458 | 2378 } |
| 2379 | |
| 2380 ColumnVector | |
| 7072 | 2381 Matrix::lssolve (const ColumnVector& b, octave_idx_type& info, |
| 2382 octave_idx_type& rank) const | |
| 458 | 2383 { |
| 7788 | 2384 double rcon; |
| 2385 return lssolve (b, info, rank, rcon); | |
| 7076 | 2386 } |
| 2387 | |
| 2388 ColumnVector | |
| 2389 Matrix::lssolve (const ColumnVector& b, octave_idx_type& info, | |
| 7788 | 2390 octave_idx_type& rank, double &rcon) const |
| 7076 | 2391 { |
| 1948 | 2392 ColumnVector retval; |
| 2393 | |
| 5275 | 2394 octave_idx_type nrhs = 1; |
| 2395 | |
| 2396 octave_idx_type m = rows (); | |
| 2397 octave_idx_type n = cols (); | |
| 458 | 2398 |
| 6924 | 2399 if (m != b.length ()) |
| 1948 | 2400 (*current_liboctave_error_handler) |
| 6924 | 2401 ("matrix dimension mismatch solution of linear equations"); |
| 2402 else if (m == 0 || n == 0) | |
| 2403 retval = ColumnVector (n, 0.0); | |
| 1948 | 2404 else |
| 458 | 2405 { |
| 7072 | 2406 volatile octave_idx_type minmn = (m < n ? m : n); |
| 2407 octave_idx_type maxmn = m > n ? m : n; | |
| 7788 | 2408 rcon = -1.0; |
| 7072 | 2409 |
| 2410 if (m != n) | |
| 2411 { | |
| 2412 retval = ColumnVector (maxmn, 0.0); | |
| 2413 | |
| 2414 for (octave_idx_type i = 0; i < m; i++) | |
| 2415 retval.elem (i) = b.elem (i); | |
| 2416 } | |
| 2417 else | |
| 2418 retval = b; | |
| 2419 | |
| 1948 | 2420 Matrix atmp = *this; |
| 2421 double *tmp_data = atmp.fortran_vec (); | |
| 2422 | |
| 7072 | 2423 double *pretval = retval.fortran_vec (); |
| 2424 Array<double> s (minmn); | |
| 7071 | 2425 double *ps = s.fortran_vec (); |
| 1948 | 2426 |
| 7072 | 2427 // Ask DGELSD what the dimension of WORK should be. |
| 5275 | 2428 octave_idx_type lwork = -1; |
| 3752 | 2429 |
| 2430 Array<double> work (1); | |
| 2431 | |
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2432 octave_idx_type smlsiz; |
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2433 F77_FUNC (xilaenv, XILAENV) (9, F77_CONST_CHAR_ARG2 ("DGELSD", 6), |
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2434 F77_CONST_CHAR_ARG2 (" ", 1), |
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2435 0, 0, 0, 0, smlsiz |
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2436 F77_CHAR_ARG_LEN (6) |
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2437 F77_CHAR_ARG_LEN (1)); |
| 7079 | 2438 |
| 2439 // We compute the size of iwork because DGELSD in older versions | |
| 2440 // of LAPACK does not return it on a query call. | |
| 7124 | 2441 double dminmn = static_cast<double> (minmn); |
| 2442 double dsmlsizp1 = static_cast<double> (smlsiz+1); | |
| 7079 | 2443 #if defined (HAVE_LOG2) |
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2444 double tmp = log2 (dminmn / dsmlsizp1); |
| 7079 | 2445 #else |
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2446 double tmp = log (dminmn / dsmlsizp1) / log (2.0); |
| 7079 | 2447 #endif |
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2448 octave_idx_type nlvl = static_cast<octave_idx_type> (tmp) + 1; |
| 7079 | 2449 if (nlvl < 0) |
| 2450 nlvl = 0; | |
| 2451 | |
| 2452 octave_idx_type liwork = 3 * minmn * nlvl + 11 * minmn; | |
| 2453 if (liwork < 1) | |
| 2454 liwork = 1; | |
| 7072 | 2455 Array<octave_idx_type> iwork (liwork); |
| 2456 octave_idx_type* piwork = iwork.fortran_vec (); | |
| 2457 | |
| 2458 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, | |
| 7788 | 2459 ps, rcon, rank, work.fortran_vec (), |
| 7072 | 2460 lwork, piwork, info)); |
| 1948 | 2461 |
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2462 lwork = static_cast<octave_idx_type> (work(0)); |
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2463 work.resize (lwork); |
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2464 |
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2465 F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, |
| 7788 | 2466 maxmn, ps, rcon, rank, |
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2467 work.fortran_vec (), lwork, |
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2468 piwork, info)); |
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2469 |
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2470 if (rank < minmn) |
| 1948 | 2471 { |
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2472 if (rank < minmn) |
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2473 (*current_liboctave_warning_handler) |
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2474 ("dgelsd: rank deficient %dx%d matrix, rank = %d", m, n, rank); |
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|
2475 if (s.elem (0) == 0.0) |
| 7788 | 2476 rcon = 0.0; |
|
7482
29980c6b8604
don't check f77_exception_encountered
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parents:
7478
diff
changeset
|
2477 else |
| 7788 | 2478 rcon = s.elem (minmn - 1) / s.elem (0); |
| 1948 | 2479 } |
|
7482
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
2480 |
|
29980c6b8604
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diff
changeset
|
2481 retval.resize (n, nrhs); |
| 458 | 2482 } |
| 2483 | |
| 2484 return retval; | |
| 2485 } | |
| 2486 | |
| 2487 ComplexColumnVector | |
| 2488 Matrix::lssolve (const ComplexColumnVector& b) const | |
| 2489 { | |
| 2490 ComplexMatrix tmp (*this); | |
| 7076 | 2491 octave_idx_type info; |
| 2492 octave_idx_type rank; | |
| 7788 | 2493 double rcon; |
| 2494 return tmp.lssolve (b, info, rank, rcon); | |
| 458 | 2495 } |
| 2496 | |
| 2497 ComplexColumnVector | |
| 5275 | 2498 Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info) const |
| 458 | 2499 { |
| 2500 ComplexMatrix tmp (*this); | |
| 7076 | 2501 octave_idx_type rank; |
| 7788 | 2502 double rcon; |
| 2503 return tmp.lssolve (b, info, rank, rcon); | |
| 458 | 2504 } |
| 2505 | |
| 2506 ComplexColumnVector | |
| 7076 | 2507 Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, |
| 2508 octave_idx_type& rank) const | |
| 458 | 2509 { |
| 2510 ComplexMatrix tmp (*this); | |
| 7788 | 2511 double rcon; |
| 2512 return tmp.lssolve (b, info, rank, rcon); | |
| 7076 | 2513 } |
| 2514 | |
| 2515 ComplexColumnVector | |
| 2516 Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, | |
| 7788 | 2517 octave_idx_type& rank, double &rcon) const |
| 7076 | 2518 { |
| 2519 ComplexMatrix tmp (*this); | |
| 7788 | 2520 return tmp.lssolve (b, info, rank, rcon); |
| 458 | 2521 } |
| 2522 | |
| 2523 Matrix& | |
| 2524 Matrix::operator += (const DiagMatrix& a) | |
| 2525 { | |
| 5275 | 2526 octave_idx_type nr = rows (); |
| 2527 octave_idx_type nc = cols (); | |
| 2528 | |
| 2529 octave_idx_type a_nr = a.rows (); | |
| 2530 octave_idx_type a_nc = a.cols (); | |
| 2385 | 2531 |
| 2532 if (nr != a_nr || nc != a_nc) | |
| 458 | 2533 { |
| 2385 | 2534 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
| 458 | 2535 return *this; |
| 2536 } | |
| 2537 | |
| 5275 | 2538 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 2539 elem (i, i) += a.elem (i, i); |
| 2540 | |
| 2541 return *this; | |
| 2542 } | |
| 2543 | |
| 2544 Matrix& | |
| 2545 Matrix::operator -= (const DiagMatrix& a) | |
| 2546 { | |
| 5275 | 2547 octave_idx_type nr = rows (); |
| 2548 octave_idx_type nc = cols (); | |
| 2549 | |
| 2550 octave_idx_type a_nr = a.rows (); | |
| 2551 octave_idx_type a_nc = a.cols (); | |
| 2385 | 2552 |
| 2553 if (nr != a_nr || nc != a_nc) | |
| 458 | 2554 { |
| 2385 | 2555 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
| 458 | 2556 return *this; |
| 2557 } | |
| 2558 | |
| 5275 | 2559 for (octave_idx_type i = 0; i < a.length (); i++) |
| 458 | 2560 elem (i, i) -= a.elem (i, i); |
| 2561 | |
| 2562 return *this; | |
| 2563 } | |
| 2564 | |
| 2565 // unary operations | |
| 2566 | |
| 2964 | 2567 boolMatrix |
| 458 | 2568 Matrix::operator ! (void) const |
| 2569 { | |
| 5275 | 2570 octave_idx_type nr = rows (); |
| 2571 octave_idx_type nc = cols (); | |
| 458 | 2572 |
| 2964 | 2573 boolMatrix b (nr, nc); |
| 458 | 2574 |
| 5275 | 2575 for (octave_idx_type j = 0; j < nc; j++) |
| 2576 for (octave_idx_type i = 0; i < nr; i++) | |
| 458 | 2577 b.elem (i, j) = ! elem (i, j); |
| 2578 | |
| 2579 return b; | |
| 2580 } | |
| 2581 | |
| 1205 | 2582 // column vector by row vector -> matrix operations |
| 458 | 2583 |
| 1205 | 2584 Matrix |
| 2585 operator * (const ColumnVector& v, const RowVector& a) | |
| 458 | 2586 { |
| 1948 | 2587 Matrix retval; |
| 2588 | |
| 5275 | 2589 octave_idx_type len = v.length (); |
| 3233 | 2590 |
| 2591 if (len != 0) | |
| 1205 | 2592 { |
| 5275 | 2593 octave_idx_type a_len = a.length (); |
| 3233 | 2594 |
| 2595 retval.resize (len, a_len); | |
| 2596 double *c = retval.fortran_vec (); | |
| 2597 | |
| 4552 | 2598 F77_XFCN (dgemm, DGEMM, (F77_CONST_CHAR_ARG2 ("N", 1), |
| 2599 F77_CONST_CHAR_ARG2 ("N", 1), | |
| 2600 len, a_len, 1, 1.0, v.data (), len, | |
| 2601 a.data (), 1, 0.0, c, len | |
| 2602 F77_CHAR_ARG_LEN (1) | |
| 2603 F77_CHAR_ARG_LEN (1))); | |
| 1205 | 2604 } |
| 458 | 2605 |
| 1948 | 2606 return retval; |
| 458 | 2607 } |
| 2608 | |
| 2609 // other operations. | |
| 2610 | |
| 2611 Matrix | |
|
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diff
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|
2612 Matrix::map (dmapper fcn) const |
| 1205 | 2613 { |
|
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convert mapper functions to new format
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parents:
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diff
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|
2614 return MArray2<double>::map<double> (func_ptr (fcn)); |
|
8c32f95c2639
convert mapper functions to new format
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parents:
7488
diff
changeset
|
2615 } |
|
8c32f95c2639
convert mapper functions to new format
David Bateman <dbateman@free.fr>
parents:
7488
diff
changeset
|
2616 |
|
8c32f95c2639
convert mapper functions to new format
David Bateman <dbateman@free.fr>
parents:
7488
diff
changeset
|
2617 ComplexMatrix |
|
8c32f95c2639
convert mapper functions to new format
David Bateman <dbateman@free.fr>
parents:
7488
diff
changeset
|
2618 Matrix::map (cmapper fcn) const |
|
8c32f95c2639
convert mapper functions to new format
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parents:
7488
diff
changeset
|
2619 { |
|
8c32f95c2639
convert mapper functions to new format
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parents:
7488
diff
changeset
|
2620 return MArray2<double>::map<Complex> (func_ptr (fcn)); |
| 1205 | 2621 } |
| 2622 | |
| 3248 | 2623 boolMatrix |
|
7503
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parents:
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diff
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|
2624 Matrix::map (bmapper fcn) const |
| 3248 | 2625 { |
|
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diff
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|
2626 return MArray2<double>::map<bool> (func_ptr (fcn)); |
| 458 | 2627 } |
| 2628 | |
| 2385 | 2629 bool |
| 4431 | 2630 Matrix::any_element_is_negative (bool neg_zero) const |
| 2385 | 2631 { |
| 5275 | 2632 octave_idx_type nel = nelem (); |
| 2385 | 2633 |
| 4431 | 2634 if (neg_zero) |
| 2635 { | |
| 5275 | 2636 for (octave_idx_type i = 0; i < nel; i++) |
| 4634 | 2637 if (lo_ieee_signbit (elem (i))) |
| 2638 return true; | |
| 4431 | 2639 } |
| 2640 else | |
| 2641 { | |
| 5275 | 2642 for (octave_idx_type i = 0; i < nel; i++) |
| 4634 | 2643 if (elem (i) < 0) |
| 2644 return true; | |
| 4431 | 2645 } |
| 2385 | 2646 |
| 2647 return false; | |
| 2648 } | |
| 2649 | |
|
7922
935be827eaf8
error for NaN values in & and | expressions
John W. Eaton <jwe@octave.org>
parents:
7803
diff
changeset
|
2650 bool |
|
935be827eaf8
error for NaN values in & and | expressions
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parents:
7803
diff
changeset
|
2651 Matrix::any_element_is_nan (void) const |
|
935be827eaf8
error for NaN values in & and | expressions
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parents:
7803
diff
changeset
|
2652 { |
|
935be827eaf8
error for NaN values in & and | expressions
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parents:
7803
diff
changeset
|
2653 octave_idx_type nel = nelem (); |
|
935be827eaf8
error for NaN values in & and | expressions
John W. Eaton <jwe@octave.org>
parents:
7803
diff
changeset
|
2654 |
|
935be827eaf8
error for NaN values in & and | expressions
John W. Eaton <jwe@octave.org>
parents:
7803
diff
changeset
|
2655 for (octave_idx_type i = 0; i < nel; i++) |
|
935be827eaf8
error for NaN values in & and | expressions
John W. Eaton <jwe@octave.org>
parents:
7803
diff
changeset
|
2656 { |
|
935be827eaf8
error for NaN values in & and | expressions
John W. Eaton <jwe@octave.org>
parents:
7803
diff
changeset
|
2657 double val = elem (i); |
|
935be827eaf8
error for NaN values in & and | expressions
John W. Eaton <jwe@octave.org>
parents:
7803
diff
changeset
|
2658 if (xisnan (val)) |
|
935be827eaf8
error for NaN values in & and | expressions
John W. Eaton <jwe@octave.org>
parents:
7803
diff
changeset
|
2659 return true; |
|
935be827eaf8
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John W. Eaton <jwe@octave.org>
parents:
7803
diff
changeset
|
2660 } |
|
935be827eaf8
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John W. Eaton <jwe@octave.org>
parents:
7803
diff
changeset
|
2661 |
|
935be827eaf8
error for NaN values in & and | expressions
John W. Eaton <jwe@octave.org>
parents:
7803
diff
changeset
|
2662 return false; |
|
935be827eaf8
error for NaN values in & and | expressions
John W. Eaton <jwe@octave.org>
parents:
7803
diff
changeset
|
2663 } |
| 2385 | 2664 |
| 2665 bool | |
| 2666 Matrix::any_element_is_inf_or_nan (void) const | |
| 2667 { | |
| 5275 | 2668 octave_idx_type nel = nelem (); |
| 2669 | |
| 2670 for (octave_idx_type i = 0; i < nel; i++) | |
| 4634 | 2671 { |
| 2672 double val = elem (i); | |
| 2673 if (xisinf (val) || xisnan (val)) | |
| 2674 return true; | |
| 2675 } | |
| 2676 | |
| 2677 return false; | |
| 2385 | 2678 } |
| 2679 | |
| 2680 bool | |
| 5943 | 2681 Matrix::any_element_not_one_or_zero (void) const |
| 2682 { | |
| 2683 octave_idx_type nel = nelem (); | |
| 2684 | |
| 2685 for (octave_idx_type i = 0; i < nel; i++) | |
| 2686 { | |
| 2687 double val = elem (i); | |
| 2688 if (val != 0 && val != 1) | |
| 2689 return true; | |
| 2690 } | |
| 2691 | |
| 2692 return false; | |
| 2693 } | |
| 2694 | |
| 2695 bool | |
| 2385 | 2696 Matrix::all_elements_are_int_or_inf_or_nan (void) const |
| 2697 { | |
| 5275 | 2698 octave_idx_type nel = nelem (); |
| 2699 | |
| 2700 for (octave_idx_type i = 0; i < nel; i++) | |
| 4634 | 2701 { |
| 2702 double val = elem (i); | |
| 2703 if (xisnan (val) || D_NINT (val) == val) | |
| 2704 continue; | |
| 2705 else | |
| 2706 return false; | |
| 2707 } | |
| 2385 | 2708 |
| 2709 return true; | |
| 2710 } | |
| 2711 | |
| 1968 | 2712 // Return nonzero if any element of M is not an integer. Also extract |
| 2713 // the largest and smallest values and return them in MAX_VAL and MIN_VAL. | |
| 2714 | |
| 2385 | 2715 bool |
| 1968 | 2716 Matrix::all_integers (double& max_val, double& min_val) const |
| 2717 { | |
| 5275 | 2718 octave_idx_type nel = nelem (); |
| 4634 | 2719 |
| 2720 if (nel > 0) | |
| 1968 | 2721 { |
| 4634 | 2722 max_val = elem (0); |
| 2723 min_val = elem (0); | |
| 1968 | 2724 } |
| 2725 else | |
| 2385 | 2726 return false; |
| 1968 | 2727 |
| 5275 | 2728 for (octave_idx_type i = 0; i < nel; i++) |
| 4634 | 2729 { |
| 2730 double val = elem (i); | |
| 2731 | |
| 2732 if (val > max_val) | |
| 2733 max_val = val; | |
| 2734 | |
| 2735 if (val < min_val) | |
| 2736 min_val = val; | |
| 2737 | |
| 2738 if (D_NINT (val) != val) | |
| 2739 return false; | |
| 2740 } | |
| 2385 | 2741 |
| 2742 return true; | |
| 1968 | 2743 } |
| 2744 | |
| 2385 | 2745 bool |
| 1968 | 2746 Matrix::too_large_for_float (void) const |
| 2747 { | |
| 5275 | 2748 octave_idx_type nel = nelem (); |
| 2749 | |
| 2750 for (octave_idx_type i = 0; i < nel; i++) | |
| 4634 | 2751 { |
| 2752 double val = elem (i); | |
| 2753 | |
| 5389 | 2754 if (! (xisnan (val) || xisinf (val)) |
| 5387 | 2755 && fabs (val) > FLT_MAX) |
| 4634 | 2756 return true; |
| 2757 } | |
| 1968 | 2758 |
| 2385 | 2759 return false; |
| 1968 | 2760 } |
| 2761 | |
| 5775 | 2762 // FIXME Do these really belong here? Maybe they should be |
| 4015 | 2763 // in a base class? |
| 458 | 2764 |
| 2832 | 2765 boolMatrix |
| 4015 | 2766 Matrix::all (int dim) const |
| 458 | 2767 { |
|
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Jaroslav Hajek <highegg@gmail.com>
parents:
8736
diff
changeset
|
2768 return do_mx_red_op<boolMatrix> (*this, dim, mx_inline_all); |
| 458 | 2769 } |
| 2770 | |
| 2832 | 2771 boolMatrix |
| 4015 | 2772 Matrix::any (int dim) const |
| 458 | 2773 { |
|
8743
1bd918cfb6e2
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Jaroslav Hajek <highegg@gmail.com>
parents:
8736
diff
changeset
|
2774 return do_mx_red_op<boolMatrix> (*this, dim, mx_inline_any); |
| 458 | 2775 } |
| 2776 | |
| 2777 Matrix | |
| 3723 | 2778 Matrix::cumprod (int dim) const |
| 458 | 2779 { |
|
8736
53b4fdeacc2e
improve reduction functions
Jaroslav Hajek <highegg@gmail.com>
parents:
8650
diff
changeset
|
2780 return do_mx_cum_op<Matrix> (*this, dim, mx_inline_cumprod); |
| 458 | 2781 } |
| 2782 | |
| 2783 Matrix | |
| 3723 | 2784 Matrix::cumsum (int dim) const |
| 458 | 2785 { |
|
8736
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parents:
8650
diff
changeset
|
2786 return do_mx_cum_op<Matrix> (*this, dim, mx_inline_cumsum); |
| 458 | 2787 } |
| 2788 | |
| 2789 Matrix | |
| 3723 | 2790 Matrix::prod (int dim) const |
| 458 | 2791 { |
|
8736
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8650
diff
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|
2792 return do_mx_red_op<Matrix> (*this, dim, mx_inline_prod); |
| 458 | 2793 } |
| 2794 | |
| 2795 Matrix | |
| 3723 | 2796 Matrix::sum (int dim) const |
| 458 | 2797 { |
|
8736
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8650
diff
changeset
|
2798 return do_mx_red_op<Matrix> (*this, dim, mx_inline_sum); |
| 458 | 2799 } |
| 2800 | |
| 2801 Matrix | |
| 3723 | 2802 Matrix::sumsq (int dim) const |
| 458 | 2803 { |
|
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8650
diff
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|
2804 return do_mx_red_op<Matrix> (*this, dim, mx_inline_sumsq); |
| 458 | 2805 } |
| 2806 | |
| 2385 | 2807 Matrix |
| 2808 Matrix::abs (void) const | |
| 2809 { | |
|
8650
a1ae2aae903e
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8614
diff
changeset
|
2810 return Matrix (mx_inline_fabs_dup (data (), length ()), |
|
a1ae2aae903e
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diff
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|
2811 rows (), cols ()); |
| 2385 | 2812 } |
| 2813 | |
|
7620
36594d5bbe13
Move diag function into the octave_value class
David Bateman <dbateman@free.fr>
parents:
7544
diff
changeset
|
2814 Matrix |
| 5275 | 2815 Matrix::diag (octave_idx_type k) const |
| 458 | 2816 { |
|
7620
36594d5bbe13
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7544
diff
changeset
|
2817 return MArray2<double>::diag (k); |
| 458 | 2818 } |
| 2819 | |
| 2820 ColumnVector | |
| 2821 Matrix::row_min (void) const | |
| 2822 { | |
| 5275 | 2823 Array<octave_idx_type> dummy_idx; |
| 4587 | 2824 return row_min (dummy_idx); |
| 458 | 2825 } |
| 2826 | |
| 2827 ColumnVector | |
| 5275 | 2828 Matrix::row_min (Array<octave_idx_type>& idx_arg) const |
| 458 | 2829 { |
| 2830 ColumnVector result; | |
| 2831 | |
| 5275 | 2832 octave_idx_type nr = rows (); |
| 2833 octave_idx_type nc = cols (); | |
| 458 | 2834 |
| 2835 if (nr > 0 && nc > 0) | |
| 2836 { | |
| 2837 result.resize (nr); | |
| 4587 | 2838 idx_arg.resize (nr); |
| 458 | 2839 |
| 5275 | 2840 for (octave_idx_type i = 0; i < nr; i++) |
| 458 | 2841 { |
| 5275 | 2842 octave_idx_type idx_j; |
| 4469 | 2843 |
| 2844 double tmp_min = octave_NaN; | |
| 2845 | |
| 2846 for (idx_j = 0; idx_j < nc; idx_j++) | |
| 2354 | 2847 { |
| 4469 | 2848 tmp_min = elem (i, idx_j); |
| 2849 | |
| 5389 | 2850 if (! xisnan (tmp_min)) |
| 4469 | 2851 break; |
| 2852 } | |
| 2853 | |
| 5275 | 2854 for (octave_idx_type j = idx_j+1; j < nc; j++) |
| 4469 | 2855 { |
| 2856 double tmp = elem (i, j); | |
| 2857 | |
| 5389 | 2858 if (xisnan (tmp)) |
| 4469 | 2859 continue; |
| 2860 else if (tmp < tmp_min) | |
| 2354 | 2861 { |
| 4469 | 2862 idx_j = j; |
| 2863 tmp_min = tmp; | |
| 2354 | 2864 } |
| 2865 } | |
| 2866 | |
| 4469 | 2867 result.elem (i) = tmp_min; |
| 5389 | 2868 idx_arg.elem (i) = xisnan (tmp_min) ? 0 : idx_j; |
| 458 | 2869 } |
| 2870 } | |
| 2871 | |
| 2872 return result; | |
| 2873 } | |
| 2874 | |
| 2875 ColumnVector | |
| 2876 Matrix::row_max (void) const | |
| 2877 { | |
| 5275 | 2878 Array<octave_idx_type> dummy_idx; |
| 4587 | 2879 return row_max (dummy_idx); |
| 458 | 2880 } |
| 2881 | |
| 2882 ColumnVector | |
| 5275 | 2883 Matrix::row_max (Array<octave_idx_type>& idx_arg) const |
| 458 | 2884 { |
| 2885 ColumnVector result; | |
| 2886 | |
| 5275 | 2887 octave_idx_type nr = rows (); |
| 2888 octave_idx_type nc = cols (); | |
| 458 | 2889 |
| 2890 if (nr > 0 && nc > 0) | |
| 2891 { | |
| 2892 result.resize (nr); | |
| 4587 | 2893 idx_arg.resize (nr); |
| 458 | 2894 |
| 5275 | 2895 for (octave_idx_type i = 0; i < nr; i++) |
| 458 | 2896 { |
| 5275 | 2897 octave_idx_type idx_j; |
| 4469 | 2898 |
| 2899 double tmp_max = octave_NaN; | |
| 2900 | |
| 2901 for (idx_j = 0; idx_j < nc; idx_j++) | |
| 2354 | 2902 { |
| 4469 | 2903 tmp_max = elem (i, idx_j); |
| 2904 | |
| 5389 | 2905 if (! xisnan (tmp_max)) |
| 4469 | 2906 break; |
| 2907 } | |
| 2908 | |
| 5275 | 2909 for (octave_idx_type j = idx_j+1; j < nc; j++) |
| 4469 | 2910 { |
| 2911 double tmp = elem (i, j); | |
| 2912 | |
| 5389 | 2913 if (xisnan (tmp)) |
| 4469 | 2914 continue; |
| 2915 else if (tmp > tmp_max) | |
| 2354 | 2916 { |
| 4469 | 2917 idx_j = j; |
| 2918 tmp_max = tmp; | |
| 2354 | 2919 } |
| 2920 } | |
| 2921 | |
| 4469 | 2922 result.elem (i) = tmp_max; |
| 5389 | 2923 idx_arg.elem (i) = xisnan (tmp_max) ? 0 : idx_j; |
| 458 | 2924 } |
| 2925 } | |
| 2926 | |
| 2927 return result; | |
| 2928 } | |
| 2929 | |
| 2930 RowVector | |
| 2931 Matrix::column_min (void) const | |
| 2932 { | |
| 5275 | 2933 Array<octave_idx_type> dummy_idx; |
| 4587 | 2934 return column_min (dummy_idx); |
| 458 | 2935 } |
| 2354 | 2936 |
| 458 | 2937 RowVector |
| 5275 | 2938 Matrix::column_min (Array<octave_idx_type>& idx_arg) const |
| 458 | 2939 { |
| 2940 RowVector result; | |
| 2941 | |
| 5275 | 2942 octave_idx_type nr = rows (); |
| 2943 octave_idx_type nc = cols (); | |
| 458 | 2944 |
| 2945 if (nr > 0 && nc > 0) | |
| 2946 { | |
| 2947 result.resize (nc); | |
| 4587 | 2948 idx_arg.resize (nc); |
| 458 | 2949 |
| 5275 | 2950 for (octave_idx_type j = 0; j < nc; j++) |
| 458 | 2951 { |
| 5275 | 2952 octave_idx_type idx_i; |
| 4469 | 2953 |
| 2954 double tmp_min = octave_NaN; | |
| 2955 | |
| 2956 for (idx_i = 0; idx_i < nr; idx_i++) | |
| 2354 | 2957 { |
| 4469 | 2958 tmp_min = elem (idx_i, j); |
| 2959 | |
| 5389 | 2960 if (! xisnan (tmp_min)) |
| 4469 | 2961 break; |
| 2962 } | |
| 2963 | |
| 5275 | 2964 for (octave_idx_type i = idx_i+1; i < nr; i++) |
| 4469 | 2965 { |
| 2966 double tmp = elem (i, j); | |
| 2967 | |
| 5389 | 2968 if (xisnan (tmp)) |
| 4469 | 2969 continue; |
| 2970 else if (tmp < tmp_min) | |
| 2354 | 2971 { |
| 4469 | 2972 idx_i = i; |
| 2973 tmp_min = tmp; | |
| 2354 | 2974 } |
| 2975 } | |
| 2976 | |
| 4469 | 2977 result.elem (j) = tmp_min; |
| 5389 | 2978 idx_arg.elem (j) = xisnan (tmp_min) ? 0 : idx_i; |
| 458 | 2979 } |
| 2980 } | |
| 2981 | |
| 2982 return result; | |
| 2983 } | |
| 2984 | |
| 2354 | 2985 RowVector |
| 2986 Matrix::column_max (void) const | |
| 2987 { | |
| 5275 | 2988 Array<octave_idx_type> dummy_idx; |
| 4587 | 2989 return column_max (dummy_idx); |
| 2354 | 2990 } |
| 458 | 2991 |
| 2992 RowVector | |
| 5275 | 2993 Matrix::column_max (Array<octave_idx_type>& idx_arg) const |
| 458 | 2994 { |
| 2995 RowVector result; | |
| 2996 | |
| 5275 | 2997 octave_idx_type nr = rows (); |
| 2998 octave_idx_type nc = cols (); | |
| 458 | 2999 |
| 3000 if (nr > 0 && nc > 0) | |
| 3001 { | |
| 3002 result.resize (nc); | |
| 4587 | 3003 idx_arg.resize (nc); |
| 458 | 3004 |
| 5275 | 3005 for (octave_idx_type j = 0; j < nc; j++) |
| 458 | 3006 { |
| 5275 | 3007 octave_idx_type idx_i; |
| 4469 | 3008 |
| 3009 double tmp_max = octave_NaN; | |
| 3010 | |
| 3011 for (idx_i = 0; idx_i < nr; idx_i++) | |
| 2354 | 3012 { |
| 4469 | 3013 tmp_max = elem (idx_i, j); |
| 3014 | |
| 5389 | 3015 if (! xisnan (tmp_max)) |
| 4469 | 3016 break; |
| 3017 } | |
| 3018 | |
| 5275 | 3019 for (octave_idx_type i = idx_i+1; i < nr; i++) |
| 4469 | 3020 { |
| 3021 double tmp = elem (i, j); | |
| 3022 | |
| 5389 | 3023 if (xisnan (tmp)) |
| 4469 | 3024 continue; |
| 3025 else if (tmp > tmp_max) | |
| 2354 | 3026 { |
| 4469 | 3027 idx_i = i; |
| 3028 tmp_max = tmp; | |
| 2354 | 3029 } |
| 3030 } | |
| 3031 | |
| 4469 | 3032 result.elem (j) = tmp_max; |
| 5389 | 3033 idx_arg.elem (j) = xisnan (tmp_max) ? 0 : idx_i; |
| 458 | 3034 } |
| 3035 } | |
| 3036 | |
| 3037 return result; | |
| 3038 } | |
| 3039 | |
| 3504 | 3040 std::ostream& |
| 3041 operator << (std::ostream& os, const Matrix& a) | |
| 458 | 3042 { |
| 5275 | 3043 for (octave_idx_type i = 0; i < a.rows (); i++) |
| 458 | 3044 { |
| 5275 | 3045 for (octave_idx_type j = 0; j < a.cols (); j++) |
| 4130 | 3046 { |
| 3047 os << " "; | |
| 3048 octave_write_double (os, a.elem (i, j)); | |
| 3049 } | |
| 458 | 3050 os << "\n"; |
| 3051 } | |
| 3052 return os; | |
| 3053 } | |
| 3054 | |
| 3504 | 3055 std::istream& |
| 3056 operator >> (std::istream& is, Matrix& a) | |
| 458 | 3057 { |
| 5275 | 3058 octave_idx_type nr = a.rows (); |
| 3059 octave_idx_type nc = a.cols (); | |
| 458 | 3060 |
| 3061 if (nr < 1 || nc < 1) | |
| 3504 | 3062 is.clear (std::ios::badbit); |
| 458 | 3063 else |
| 3064 { | |
| 3065 double tmp; | |
| 5275 | 3066 for (octave_idx_type i = 0; i < nr; i++) |
| 3067 for (octave_idx_type j = 0; j < nc; j++) | |
| 458 | 3068 { |
| 4130 | 3069 tmp = octave_read_double (is); |
| 458 | 3070 if (is) |
| 3071 a.elem (i, j) = tmp; | |
| 3072 else | |
| 2795 | 3073 goto done; |
| 458 | 3074 } |
| 3075 } | |
| 3076 | |
| 2795 | 3077 done: |
| 3078 | |
| 458 | 3079 return is; |
| 3080 } | |
| 3081 | |
| 1819 | 3082 Matrix |
| 3083 Givens (double x, double y) | |
| 3084 { | |
| 3085 double cc, s, temp_r; | |
| 3086 | |
| 3887 | 3087 F77_FUNC (dlartg, DLARTG) (x, y, cc, s, temp_r); |
| 1819 | 3088 |
| 3089 Matrix g (2, 2); | |
| 3090 | |
| 3091 g.elem (0, 0) = cc; | |
| 3092 g.elem (1, 1) = cc; | |
| 3093 g.elem (0, 1) = s; | |
| 3094 g.elem (1, 0) = -s; | |
| 3095 | |
| 3096 return g; | |
| 3097 } | |
| 3098 | |
| 3099 Matrix | |
| 3100 Sylvester (const Matrix& a, const Matrix& b, const Matrix& c) | |
| 3101 { | |
| 3102 Matrix retval; | |
| 3103 | |
| 5775 | 3104 // FIXME -- need to check that a, b, and c are all the same |
| 1819 | 3105 // size. |
| 3106 | |
| 3107 // Compute Schur decompositions. | |
| 3108 | |
| 3109 SCHUR as (a, "U"); | |
| 3110 SCHUR bs (b, "U"); | |
| 3111 | |
| 3112 // Transform c to new coordinates. | |
| 3113 | |
| 3114 Matrix ua = as.unitary_matrix (); | |
| 3115 Matrix sch_a = as.schur_matrix (); | |
| 3116 | |
| 3117 Matrix ub = bs.unitary_matrix (); | |
| 3118 Matrix sch_b = bs.schur_matrix (); | |
| 3119 | |
| 3120 Matrix cx = ua.transpose () * c * ub; | |
| 3121 | |
| 3122 // Solve the sylvester equation, back-transform, and return the | |
| 3123 // solution. | |
| 3124 | |
| 5275 | 3125 octave_idx_type a_nr = a.rows (); |
| 3126 octave_idx_type b_nr = b.rows (); | |
| 1819 | 3127 |
| 3128 double scale; | |
| 5275 | 3129 octave_idx_type info; |
| 1819 | 3130 |
| 1950 | 3131 double *pa = sch_a.fortran_vec (); |
| 3132 double *pb = sch_b.fortran_vec (); | |
| 3133 double *px = cx.fortran_vec (); | |
| 3134 | |
| 4552 | 3135 F77_XFCN (dtrsyl, DTRSYL, (F77_CONST_CHAR_ARG2 ("N", 1), |
| 3136 F77_CONST_CHAR_ARG2 ("N", 1), | |
| 3137 1, a_nr, b_nr, pa, a_nr, pb, | |
| 3138 b_nr, px, a_nr, scale, info | |
| 3139 F77_CHAR_ARG_LEN (1) | |
| 3140 F77_CHAR_ARG_LEN (1))); | |
| 1950 | 3141 |
| 3142 | |
|
7482
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
3143 // FIXME -- check info? |
| 1819 | 3144 |
|
7482
29980c6b8604
don't check f77_exception_encountered
John W. Eaton <jwe@octave.org>
parents:
7478
diff
changeset
|
3145 retval = -ua*cx*ub.transpose (); |
| 1819 | 3146 |
| 3147 return retval; | |
| 3148 } | |
| 3149 | |
| 2828 | 3150 // matrix by matrix -> matrix operations |
| 3151 | |
| 6162 | 3152 /* Simple Dot Product, Matrix-Vector and Matrix-Matrix Unit tests |
| 3153 %!assert([1 2 3] * [ 4 ; 5 ; 6], 32, 1e-14) | |
| 3154 %!assert([1 2 ; 3 4 ] * [5 ; 6], [17 ; 39 ], 1e-14) | |
| 3155 %!assert([1 2 ; 3 4 ] * [5 6 ; 7 8], [19 22; 43 50], 1e-14) | |
| 3156 */ | |
| 3157 | |
| 3158 /* Test some simple identities | |
| 3159 %!shared M, cv, rv | |
| 3160 %! M = randn(10,10); | |
| 3161 %! cv = randn(10,1); | |
| 3162 %! rv = randn(1,10); | |
| 3163 %!assert([M*cv,M*cv],M*[cv,cv],1e-14) | |
| 3164 %!assert([rv*M;rv*M],[rv;rv]*M,1e-14) | |
| 3165 %!assert(2*rv*cv,[rv,rv]*[cv;cv],1e-14) | |
| 3166 */ | |
| 3167 | |
|
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
|
3168 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
|
3169 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
|
3170 { |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3171 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
|
3172 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
|
3173 } |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3174 |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3175 // 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
|
3176 |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3177 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
|
3178 xgemm (bool transa, const Matrix& a, bool transb, const Matrix& b) |
| 2828 | 3179 { |
| 3180 Matrix retval; | |
| 3181 | |
|
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
|
3182 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
|
3183 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
|
3184 |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3185 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
|
3186 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
|
3187 |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3188 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
|
3189 gripe_nonconformant ("operator *", a_nr, a_nc, b_nr, b_nc); |
| 2828 | 3190 else |
| 3191 { | |
|
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
|
3192 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
|
3193 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
|
3194 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
|
3195 { |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3196 octave_idx_type lda = a.rows (); |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3197 |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3198 retval.resize (a_nr, b_nc); |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3199 double *c = retval.fortran_vec (); |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3200 |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3201 const char *ctransa = get_blas_trans_arg (transa); |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3202 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
|
3203 F77_CONST_CHAR_ARG2 (ctransa, 1), |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3204 a_nr, a_nc, 1.0, |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3205 a.data (), lda, 0.0, c, a_nr |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3206 F77_CHAR_ARG_LEN (1) |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3207 F77_CHAR_ARG_LEN (1))); |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3208 for (int j = 0; j < a_nr; j++) |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3209 for (int i = 0; i < j; i++) |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3210 retval.xelem (j,i) = retval.xelem (i,j); |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3211 |
|
776791438957
map symmetric cases to xHERK, xSYRK
Jaroslav Hajek <highegg@gmail.com>
parents:
7800
diff
changeset
|
3212 } |
| 2828 | 3213 else |
| 3214 { | |
|
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
|
3215 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
|
3216 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
|
3217 |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3218 retval.resize (a_nr, b_nc); |
| 2828 | 3219 double *c = retval.fortran_vec (); |
| 3220 | |
|
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
|
3221 if (b_nc == 1) |
| 5983 | 3222 { |
|
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
|
3223 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
|
3224 F77_FUNC (xddot, XDDOT) (a_nc, a.data (), 1, b.data (), 1, *c); |
| 5983 | 3225 else |
| 6390 | 3226 { |
|
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
|
3227 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
|
3228 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
|
3229 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
|
3230 b.data (), 1, 0.0, c, 1 |
| 6390 | 3231 F77_CHAR_ARG_LEN (1))); |
| 3232 } | |
| 5983 | 3233 } |
|
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
|
3234 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
|
3235 { |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3236 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
|
3237 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
|
3238 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
|
3239 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
|
3240 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
|
3241 } |
| 5983 | 3242 else |
| 6390 | 3243 { |
|
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
|
3244 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
|
3245 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
|
3246 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
|
3247 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
|
3248 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
|
3249 lda, b.data (), ldb, 0.0, c, a_nr |
| 6390 | 3250 F77_CHAR_ARG_LEN (1) |
| 3251 F77_CHAR_ARG_LEN (1))); | |
| 3252 } | |
| 2828 | 3253 } |
| 3254 } | |
| 3255 | |
| 3256 return retval; | |
| 3257 } | |
| 3258 | |
|
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
|
3259 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
|
3260 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
|
3261 { |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3262 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
|
3263 } |
|
5861b95e9879
support for compound operators, implement trans_mul, mul_trans, herm_mul and mul_herm
Jaroslav Hajek <highegg@gmail.com>
parents:
7789
diff
changeset
|
3264 |
| 5775 | 3265 // FIXME -- it would be nice to share code among the min/max |
| 4309 | 3266 // functions below. |
| 3267 | |
| 3268 #define EMPTY_RETURN_CHECK(T) \ | |
| 3269 if (nr == 0 || nc == 0) \ | |
| 3270 return T (nr, nc); | |
| 3271 | |
| 3272 Matrix | |
| 3273 min (double d, const Matrix& m) | |
| 3274 { | |
| 5275 | 3275 octave_idx_type nr = m.rows (); |
| 3276 octave_idx_type nc = m.columns (); | |
| 4309 | 3277 |
| 3278 EMPTY_RETURN_CHECK (Matrix); | |
| 3279 | |
| 3280 Matrix result (nr, nc); | |
| 3281 | |
| 5275 | 3282 for (octave_idx_type j = 0; j < nc; j++) |
| 3283 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3284 { |
| 3285 OCTAVE_QUIT; | |
| 3286 result (i, j) = xmin (d, m (i, j)); | |
| 3287 } | |
| 3288 | |
| 3289 return result; | |
| 3290 } | |
| 3291 | |
| 3292 Matrix | |
| 3293 min (const Matrix& m, double d) | |
| 3294 { | |
| 5275 | 3295 octave_idx_type nr = m.rows (); |
| 3296 octave_idx_type nc = m.columns (); | |
| 4309 | 3297 |
| 3298 EMPTY_RETURN_CHECK (Matrix); | |
| 3299 | |
| 3300 Matrix result (nr, nc); | |
| 3301 | |
| 5275 | 3302 for (octave_idx_type j = 0; j < nc; j++) |
| 3303 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3304 { |
| 3305 OCTAVE_QUIT; | |
| 3306 result (i, j) = xmin (m (i, j), d); | |
| 3307 } | |
| 3308 | |
| 3309 return result; | |
| 3310 } | |
| 3311 | |
| 3312 Matrix | |
| 3313 min (const Matrix& a, const Matrix& b) | |
| 3314 { | |
| 5275 | 3315 octave_idx_type nr = a.rows (); |
| 3316 octave_idx_type nc = a.columns (); | |
| 4309 | 3317 |
| 3318 if (nr != b.rows () || nc != b.columns ()) | |
| 3319 { | |
| 3320 (*current_liboctave_error_handler) | |
| 3321 ("two-arg min expecting args of same size"); | |
| 3322 return Matrix (); | |
| 3323 } | |
| 3324 | |
| 3325 EMPTY_RETURN_CHECK (Matrix); | |
| 3326 | |
| 3327 Matrix result (nr, nc); | |
| 3328 | |
| 5275 | 3329 for (octave_idx_type j = 0; j < nc; j++) |
| 3330 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3331 { |
| 3332 OCTAVE_QUIT; | |
| 3333 result (i, j) = xmin (a (i, j), b (i, j)); | |
| 3334 } | |
| 3335 | |
| 3336 return result; | |
| 3337 } | |
| 3338 | |
| 3339 Matrix | |
| 3340 max (double d, const Matrix& m) | |
| 3341 { | |
| 5275 | 3342 octave_idx_type nr = m.rows (); |
| 3343 octave_idx_type nc = m.columns (); | |
| 4309 | 3344 |
| 3345 EMPTY_RETURN_CHECK (Matrix); | |
| 3346 | |
| 3347 Matrix result (nr, nc); | |
| 3348 | |
| 5275 | 3349 for (octave_idx_type j = 0; j < nc; j++) |
| 3350 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3351 { |
| 3352 OCTAVE_QUIT; | |
| 3353 result (i, j) = xmax (d, m (i, j)); | |
| 3354 } | |
| 3355 | |
| 3356 return result; | |
| 3357 } | |
| 3358 | |
| 3359 Matrix | |
| 3360 max (const Matrix& m, double d) | |
| 3361 { | |
| 5275 | 3362 octave_idx_type nr = m.rows (); |
| 3363 octave_idx_type nc = m.columns (); | |
| 4309 | 3364 |
| 3365 EMPTY_RETURN_CHECK (Matrix); | |
| 3366 | |
| 3367 Matrix result (nr, nc); | |
| 3368 | |
| 5275 | 3369 for (octave_idx_type j = 0; j < nc; j++) |
| 3370 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3371 { |
| 3372 OCTAVE_QUIT; | |
| 3373 result (i, j) = xmax (m (i, j), d); | |
| 3374 } | |
| 3375 | |
| 3376 return result; | |
| 3377 } | |
| 3378 | |
| 3379 Matrix | |
| 3380 max (const Matrix& a, const Matrix& b) | |
| 3381 { | |
| 5275 | 3382 octave_idx_type nr = a.rows (); |
| 3383 octave_idx_type nc = a.columns (); | |
| 4309 | 3384 |
| 3385 if (nr != b.rows () || nc != b.columns ()) | |
| 3386 { | |
| 3387 (*current_liboctave_error_handler) | |
| 3388 ("two-arg max expecting args of same size"); | |
| 3389 return Matrix (); | |
| 3390 } | |
| 3391 | |
| 3392 EMPTY_RETURN_CHECK (Matrix); | |
| 3393 | |
| 3394 Matrix result (nr, nc); | |
| 3395 | |
| 5275 | 3396 for (octave_idx_type j = 0; j < nc; j++) |
| 3397 for (octave_idx_type i = 0; i < nr; i++) | |
| 4309 | 3398 { |
| 3399 OCTAVE_QUIT; | |
| 3400 result (i, j) = xmax (a (i, j), b (i, j)); | |
| 3401 } | |
| 3402 | |
| 3403 return result; | |
| 3404 } | |
| 3405 | |
| 2870 | 3406 MS_CMP_OPS(Matrix, , double, ) |
| 3504 | 3407 MS_BOOL_OPS(Matrix, double, 0.0) |
| 2870 | 3408 |
| 3409 SM_CMP_OPS(double, , Matrix, ) | |
| 3504 | 3410 SM_BOOL_OPS(double, Matrix, 0.0) |
| 2870 | 3411 |
| 3412 MM_CMP_OPS(Matrix, , Matrix, ) | |
| 3504 | 3413 MM_BOOL_OPS(Matrix, Matrix, 0.0) |
| 2870 | 3414 |
| 458 | 3415 /* |
| 3416 ;;; Local Variables: *** | |
| 3417 ;;; mode: C++ *** | |
| 3418 ;;; End: *** | |
| 3419 */ |