Thomas Branch
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MatrixFunctions.h
00001 /* 00002 * Tiny Vector Matrix Library 00003 * Dense Vector Matrix Libary of Tiny size using Expression Templates 00004 * 00005 * Copyright (C) 2001 - 2007 Olaf Petzold <opetzold@users.sourceforge.net> 00006 * 00007 * This library is free software; you can redistribute it and/or 00008 * modify it under the terms of the GNU lesser General Public 00009 * License as published by the Free Software Foundation; either 00010 * version 2.1 of the License, or (at your option) any later version. 00011 * 00012 * This library is distributed in the hope that it will be useful, 00013 * but WITHOUT ANY WARRANTY; without even the implied warranty of 00014 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 00015 * lesser General Public License for more details. 00016 * 00017 * You should have received a copy of the GNU lesser General Public 00018 * License along with this library; if not, write to the Free Software 00019 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA 00020 * 00021 * $Id: MatrixFunctions.h,v 1.44 2007-06-23 15:59:00 opetzold Exp $ 00022 */ 00023 00024 #ifndef TVMET_XPR_MATRIX_FUNCTIONS_H 00025 #define TVMET_XPR_MATRIX_FUNCTIONS_H 00026 00027 namespace tvmet { 00028 00029 00030 /* forwards */ 00031 template<class T, std::size_t Rows, std::size_t Cols> class Matrix; 00032 template<class T, std::size_t Sz> class Vector; 00033 template<class E, std::size_t Sz> class XprVector; 00034 template<class E> class XprMatrixTranspose; 00035 template<class E, std::size_t Sz> class XprMatrixDiag; 00036 template<class E, std::size_t Rows, std::size_t Cols> class XprMatrixRow; 00037 template<class E, std::size_t Rows, std::size_t Cols> class XprMatrixCol; 00038 00039 00040 /********************************************************* 00041 * PART I: DECLARATION 00042 *********************************************************/ 00043 00044 00045 /*++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 00046 * Matrix arithmetic functions add, sub, mul and div 00047 *+++++++++++++++++++++++++++++++++++++++++++++++++++++++*/ 00048 00049 00050 /* 00051 * function(XprMatrix<E1, Rows, Cols>, XprMatrix<E2, Rows, Cols>) 00052 */ 00053 #define TVMET_DECLARE_MACRO(NAME) \ 00054 template<class E1, class E2, std::size_t Rows, std::size_t Cols> \ 00055 XprMatrix< \ 00056 XprBinOp< \ 00057 Fcnl_##NAME<typename E1::value_type, typename E2::value_type>, \ 00058 XprMatrix<E1, Rows, Cols>, \ 00059 XprMatrix<E2, Rows, Cols> \ 00060 >, \ 00061 Rows, Cols \ 00062 > \ 00063 NAME (const XprMatrix<E1, Rows, Cols>& lhs, \ 00064 const XprMatrix<E2, Rows, Cols>& rhs) TVMET_CXX_ALWAYS_INLINE; 00065 00066 TVMET_DECLARE_MACRO(add) // per se element wise 00067 TVMET_DECLARE_MACRO(sub) // per se element wise 00068 namespace element_wise { 00069 TVMET_DECLARE_MACRO(mul) // not defined for matrizes 00070 TVMET_DECLARE_MACRO(div) // not defined for matrizes 00071 } 00072 00073 #undef TVMET_DECLARE_MACRO 00074 00075 00076 /* 00077 * function(XprMatrix<E, Rows, Cols>, POD) 00078 * function(POD, XprMatrix<E, Rows, Cols>) 00079 * Note: - operations +,-,*,/ are per se element wise 00080 */ 00081 #define TVMET_DECLARE_MACRO(NAME, POD) \ 00082 template<class E, std::size_t Rows, std::size_t Cols> \ 00083 XprMatrix< \ 00084 XprBinOp< \ 00085 Fcnl_##NAME<typename E::value_type, POD >, \ 00086 XprMatrix<E, Rows, Cols>, \ 00087 XprLiteral< POD > \ 00088 >, \ 00089 Rows, Cols \ 00090 > \ 00091 NAME (const XprMatrix<E, Rows, Cols>& lhs, \ 00092 POD rhs) TVMET_CXX_ALWAYS_INLINE; \ 00093 \ 00094 template<class E, std::size_t Rows, std::size_t Cols> \ 00095 XprMatrix< \ 00096 XprBinOp< \ 00097 Fcnl_##NAME< POD, typename E::value_type>, \ 00098 XprLiteral< POD >, \ 00099 XprMatrix<E, Rows, Cols> \ 00100 >, \ 00101 Rows, Cols \ 00102 > \ 00103 NAME (POD lhs, \ 00104 const XprMatrix<E, Rows, Cols>& rhs) TVMET_CXX_ALWAYS_INLINE; 00105 00106 TVMET_DECLARE_MACRO(add, int) 00107 TVMET_DECLARE_MACRO(sub, int) 00108 TVMET_DECLARE_MACRO(mul, int) 00109 TVMET_DECLARE_MACRO(div, int) 00110 00111 #if defined(TVMET_HAVE_LONG_LONG) 00112 TVMET_DECLARE_MACRO(add, long long int) 00113 TVMET_DECLARE_MACRO(sub, long long int) 00114 TVMET_DECLARE_MACRO(mul, long long int) 00115 TVMET_DECLARE_MACRO(div, long long int) 00116 #endif 00117 00118 TVMET_DECLARE_MACRO(add, float) 00119 TVMET_DECLARE_MACRO(sub, float) 00120 TVMET_DECLARE_MACRO(mul, float) 00121 TVMET_DECLARE_MACRO(div, float) 00122 00123 TVMET_DECLARE_MACRO(add, double) 00124 TVMET_DECLARE_MACRO(sub, double) 00125 TVMET_DECLARE_MACRO(mul, double) 00126 TVMET_DECLARE_MACRO(div, double) 00127 00128 #if defined(TVMET_HAVE_LONG_DOUBLE) 00129 TVMET_DECLARE_MACRO(add, long double) 00130 TVMET_DECLARE_MACRO(sub, long double) 00131 TVMET_DECLARE_MACRO(mul, long double) 00132 TVMET_DECLARE_MACRO(div, long double) 00133 #endif 00134 00135 #undef TVMET_DECLARE_MACRO 00136 00137 00138 #if defined(TVMET_HAVE_COMPLEX) 00139 /* 00140 * function(XprMatrix<E, Rows, Cols>, complex<T>) 00141 * function(complex<T>, XprMatrix<E, Rows, Cols>) 00142 * Note: - operations +,-,*,/ are per se element wise 00143 * \todo type promotion 00144 */ 00145 #define TVMET_DECLARE_MACRO(NAME) \ 00146 template<class E, class T, std::size_t Rows, std::size_t Cols> \ 00147 XprMatrix< \ 00148 XprBinOp< \ 00149 Fcnl_##NAME<typename E::value_type, std::complex<T> >, \ 00150 XprMatrix<E, Rows, Cols>, \ 00151 XprLiteral< std::complex<T> > \ 00152 >, \ 00153 Rows, Cols \ 00154 > \ 00155 NAME (const XprMatrix<E, Rows, Cols>& lhs, \ 00156 const std::complex<T>& rhs) TVMET_CXX_ALWAYS_INLINE; \ 00157 \ 00158 template<class T, class E, std::size_t Rows, std::size_t Cols> \ 00159 XprMatrix< \ 00160 XprBinOp< \ 00161 Fcnl_##NAME< std::complex<T>, typename E::value_type>, \ 00162 XprLiteral< std::complex<T> >, \ 00163 XprMatrix<E, Rows, Cols> \ 00164 >, \ 00165 Rows, Cols \ 00166 > \ 00167 NAME (const std::complex<T>& lhs, \ 00168 const XprMatrix<E, Rows, Cols>& rhs) TVMET_CXX_ALWAYS_INLINE; 00169 00170 TVMET_DECLARE_MACRO(add) 00171 TVMET_DECLARE_MACRO(sub) 00172 TVMET_DECLARE_MACRO(mul) 00173 TVMET_DECLARE_MACRO(div) 00174 00175 #undef TVMET_DECLARE_MACRO 00176 00177 #endif // defined(TVMET_HAVE_COMPLEX) 00178 00179 00180 /*++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 00181 * matrix prod( ... ) functions 00182 *+++++++++++++++++++++++++++++++++++++++++++++++++++++++*/ 00183 00184 00185 template<class E1, std::size_t Rows1, std::size_t Cols1, 00186 class E2, std::size_t Cols2> 00187 XprMatrix< 00188 XprMMProduct< 00189 XprMatrix<E1, Rows1, Cols1>, Rows1, Cols1, // M1(Rows1, Cols1) 00190 XprMatrix<E2, Cols1, Cols2>, Cols2 00191 >, 00192 Rows1, Cols2 // return Dim 00193 > 00194 prod(const XprMatrix<E1, Rows1, Cols1>& lhs, 00195 const XprMatrix<E2, Cols1, Cols2>& rhs) TVMET_CXX_ALWAYS_INLINE; 00196 00197 00198 template<class E1, std::size_t Rows1, std::size_t Cols1, 00199 class E2, std::size_t Cols2> 00200 XprMatrix< 00201 XprMMProductTransposed< 00202 XprMatrix<E1, Rows1, Cols1>, Rows1, Cols1, // M1(Rows1, Cols1) 00203 XprMatrix<E2, Cols1, Cols2>, Cols2 // M2(Cols1, Cols2) 00204 >, 00205 Cols2, Rows1 // return Dim 00206 > 00207 trans_prod(const XprMatrix<E1, Rows1, Cols1>& lhs, 00208 const XprMatrix<E2, Cols1, Cols2>& rhs) TVMET_CXX_ALWAYS_INLINE; 00209 00210 00211 template<class E1, std::size_t Rows1, std::size_t Cols1, 00212 class E2, std::size_t Cols2> // Rows2 = Rows1 00213 XprMatrix< 00214 XprMtMProduct< 00215 XprMatrix<E1, Rows1, Cols1>, Rows1, Cols1, // M1(Rows1, Cols1) 00216 XprMatrix<E2, Rows1, Cols2>, Cols2 // M2(Rows1, Cols2) 00217 >, 00218 Cols1, Cols2 // return Dim 00219 > 00220 MtM_prod(const XprMatrix<E1, Rows1, Cols1>& lhs, 00221 const XprMatrix<E2, Rows1, Cols2>& rhs) TVMET_CXX_ALWAYS_INLINE; 00222 00223 00224 template<class E1, std::size_t Rows1, std::size_t Cols1, 00225 class E2, std::size_t Rows2> // Cols2 = Cols1 00226 XprMatrix< 00227 XprMMtProduct< 00228 XprMatrix<E1, Rows1, Cols1>, Rows1, Cols1, // M1(Rows1, Cols1) 00229 XprMatrix<E2, Rows2, Cols1>, Cols1 // M2(Rows2, Cols1) 00230 >, 00231 Rows1, Rows2 // return Dim 00232 > 00233 MMt_prod(const XprMatrix<E1, Rows1, Cols1>& lhs, 00234 const XprMatrix<E2, Rows2, Cols1>& rhs) TVMET_CXX_ALWAYS_INLINE; 00235 00236 00237 /*++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 00238 * matrix-vector specific prod( ... ) functions 00239 *+++++++++++++++++++++++++++++++++++++++++++++++++++++++*/ 00240 00241 00242 template<class E1, std::size_t Rows, std::size_t Cols, 00243 class E2> 00244 XprVector< 00245 XprMVProduct< 00246 XprMatrix<E1, Rows, Cols>, Rows, Cols, 00247 XprVector<E2, Cols> 00248 >, 00249 Rows 00250 > 00251 prod(const XprMatrix<E1, Rows, Cols>& lhs, 00252 const XprVector<E2, Cols>& rhs) TVMET_CXX_ALWAYS_INLINE; 00253 00254 00255 /*++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 00256 * matrix specific functions 00257 *+++++++++++++++++++++++++++++++++++++++++++++++++++++++*/ 00258 00259 00260 template<class E, std::size_t Rows, std::size_t Cols> 00261 XprMatrix< 00262 XprMatrixTranspose< 00263 XprMatrix<E, Rows, Cols> 00264 >, 00265 Cols, Rows 00266 > 00267 trans(const XprMatrix<E, Rows, Cols>& rhs) TVMET_CXX_ALWAYS_INLINE; 00268 00269 00270 template<class E, std::size_t Sz> 00271 typename NumericTraits<typename E::value_type>::sum_type 00272 trace(const XprMatrix<E, Sz, Sz>& m) TVMET_CXX_ALWAYS_INLINE; 00273 00274 00275 template<class E, std::size_t Rows, std::size_t Cols> 00276 XprVector< 00277 XprMatrixRow< 00278 XprMatrix<E, Rows, Cols>, 00279 Rows, Cols 00280 >, 00281 Cols 00282 > 00283 row(const XprMatrix<E, Rows, Cols>& m, 00284 std::size_t no) TVMET_CXX_ALWAYS_INLINE; 00285 00286 00287 template<class E, std::size_t Rows, std::size_t Cols> 00288 XprVector< 00289 XprMatrixCol< 00290 XprMatrix<E, Rows, Cols>, 00291 Rows, Cols 00292 >, 00293 Rows 00294 > 00295 col(const XprMatrix<E, Rows, Cols>& m, std::size_t no) TVMET_CXX_ALWAYS_INLINE; 00296 00297 00298 template<class E, std::size_t Sz> 00299 XprVector< 00300 XprMatrixDiag< 00301 XprMatrix<E, Sz, Sz>, 00302 Sz 00303 >, 00304 Sz 00305 > 00306 diag(const XprMatrix<E, Sz, Sz>& m) TVMET_CXX_ALWAYS_INLINE; 00307 00308 00309 /********************************************************* 00310 * PART II: IMPLEMENTATION 00311 *********************************************************/ 00312 00313 00314 /*++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 00315 * Matrix arithmetic functions add, sub, mul and div 00316 *+++++++++++++++++++++++++++++++++++++++++++++++++++++++*/ 00317 00318 00319 /* 00320 * function(XprMatrix<E1, Rows, Cols>, XprMatrix<E2, Rows, Cols>) 00321 */ 00322 #define TVMET_IMPLEMENT_MACRO(NAME) \ 00323 template<class E1, class E2, std::size_t Rows, std::size_t Cols> \ 00324 inline \ 00325 XprMatrix< \ 00326 XprBinOp< \ 00327 Fcnl_##NAME<typename E1::value_type, typename E2::value_type>, \ 00328 XprMatrix<E1, Rows, Cols>, \ 00329 XprMatrix<E2, Rows, Cols> \ 00330 >, \ 00331 Rows, Cols \ 00332 > \ 00333 NAME (const XprMatrix<E1, Rows, Cols>& lhs, \ 00334 const XprMatrix<E2, Rows, Cols>& rhs) { \ 00335 typedef XprBinOp< \ 00336 Fcnl_##NAME<typename E1::value_type, typename E2::value_type>, \ 00337 XprMatrix<E1, Rows, Cols>, \ 00338 XprMatrix<E2, Rows, Cols> \ 00339 > expr_type; \ 00340 return XprMatrix<expr_type, Rows, Cols>(expr_type(lhs, rhs)); \ 00341 } 00342 00343 TVMET_IMPLEMENT_MACRO(add) // per se element wise 00344 TVMET_IMPLEMENT_MACRO(sub) // per se element wise 00345 namespace element_wise { 00346 TVMET_IMPLEMENT_MACRO(mul) // not defined for matrizes 00347 TVMET_IMPLEMENT_MACRO(div) // not defined for matrizes 00348 } 00349 00350 #undef TVMET_IMPLEMENT_MACRO 00351 00352 00353 /* 00354 * function(XprMatrix<E, Rows, Cols>, POD) 00355 * function(POD, XprMatrix<E, Rows, Cols>) 00356 * Note: - operations +,-,*,/ are per se element wise 00357 */ 00358 #define TVMET_IMPLEMENT_MACRO(NAME, POD) \ 00359 template<class E, std::size_t Rows, std::size_t Cols> \ 00360 inline \ 00361 XprMatrix< \ 00362 XprBinOp< \ 00363 Fcnl_##NAME<typename E::value_type, POD >, \ 00364 XprMatrix<E, Rows, Cols>, \ 00365 XprLiteral< POD > \ 00366 >, \ 00367 Rows, Cols \ 00368 > \ 00369 NAME (const XprMatrix<E, Rows, Cols>& lhs, POD rhs) { \ 00370 typedef XprBinOp< \ 00371 Fcnl_##NAME<typename E::value_type, POD >, \ 00372 XprMatrix<E, Rows, Cols>, \ 00373 XprLiteral< POD > \ 00374 > expr_type; \ 00375 return XprMatrix<expr_type, Rows, Cols>( \ 00376 expr_type(lhs, XprLiteral< POD >(rhs))); \ 00377 } \ 00378 \ 00379 template<class E, std::size_t Rows, std::size_t Cols> \ 00380 inline \ 00381 XprMatrix< \ 00382 XprBinOp< \ 00383 Fcnl_##NAME< POD, typename E::value_type>, \ 00384 XprLiteral< POD >, \ 00385 XprMatrix<E, Rows, Cols> \ 00386 >, \ 00387 Rows, Cols \ 00388 > \ 00389 NAME (POD lhs, const XprMatrix<E, Rows, Cols>& rhs) { \ 00390 typedef XprBinOp< \ 00391 Fcnl_##NAME< POD, typename E::value_type>, \ 00392 XprLiteral< POD >, \ 00393 XprMatrix<E, Rows, Cols> \ 00394 > expr_type; \ 00395 return XprMatrix<expr_type, Rows, Cols>( \ 00396 expr_type(XprLiteral< POD >(lhs), rhs)); \ 00397 } 00398 00399 TVMET_IMPLEMENT_MACRO(add, int) 00400 TVMET_IMPLEMENT_MACRO(sub, int) 00401 TVMET_IMPLEMENT_MACRO(mul, int) 00402 TVMET_IMPLEMENT_MACRO(div, int) 00403 00404 #if defined(TVMET_HAVE_LONG_LONG) 00405 TVMET_IMPLEMENT_MACRO(add, long long int) 00406 TVMET_IMPLEMENT_MACRO(sub, long long int) 00407 TVMET_IMPLEMENT_MACRO(mul, long long int) 00408 TVMET_IMPLEMENT_MACRO(div, long long int) 00409 #endif 00410 00411 TVMET_IMPLEMENT_MACRO(add, float) 00412 TVMET_IMPLEMENT_MACRO(sub, float) 00413 TVMET_IMPLEMENT_MACRO(mul, float) 00414 TVMET_IMPLEMENT_MACRO(div, float) 00415 00416 TVMET_IMPLEMENT_MACRO(add, double) 00417 TVMET_IMPLEMENT_MACRO(sub, double) 00418 TVMET_IMPLEMENT_MACRO(mul, double) 00419 TVMET_IMPLEMENT_MACRO(div, double) 00420 00421 #if defined(TVMET_HAVE_LONG_DOUBLE) 00422 TVMET_IMPLEMENT_MACRO(add, long double) 00423 TVMET_IMPLEMENT_MACRO(sub, long double) 00424 TVMET_IMPLEMENT_MACRO(mul, long double) 00425 TVMET_IMPLEMENT_MACRO(div, long double) 00426 #endif 00427 00428 #undef TVMET_IMPLEMENT_MACRO 00429 00430 00431 #if defined(TVMET_HAVE_COMPLEX) 00432 /* 00433 * function(XprMatrix<E, Rows, Cols>, complex<T>) 00434 * function(complex<T>, XprMatrix<E, Rows, Cols>) 00435 * Note: - operations +,-,*,/ are per se element wise 00436 * \todo type promotion 00437 */ 00438 #define TVMET_IMPLEMENT_MACRO(NAME) \ 00439 template<class E, class T, std::size_t Rows, std::size_t Cols> \ 00440 inline \ 00441 XprMatrix< \ 00442 XprBinOp< \ 00443 Fcnl_##NAME<typename E::value_type, std::complex<T> >, \ 00444 XprMatrix<E, Rows, Cols>, \ 00445 XprLiteral< std::complex<T> > \ 00446 >, \ 00447 Rows, Cols \ 00448 > \ 00449 NAME (const XprMatrix<E, Rows, Cols>& lhs, \ 00450 const std::complex<T>& rhs) { \ 00451 typedef XprBinOp< \ 00452 Fcnl_##NAME<typename E::value_type, std::complex<T> >, \ 00453 XprMatrix<E, Rows, Cols>, \ 00454 XprLiteral< std::complex<T> > \ 00455 > expr_type; \ 00456 return XprMatrix<expr_type, Rows, Cols>( \ 00457 expr_type(lhs, XprLiteral< std::complex<T> >(rhs))); \ 00458 } \ 00459 \ 00460 template<class T, class E, std::size_t Rows, std::size_t Cols> \ 00461 inline \ 00462 XprMatrix< \ 00463 XprBinOp< \ 00464 Fcnl_##NAME< std::complex<T>, typename E::value_type>, \ 00465 XprLiteral< std::complex<T> >, \ 00466 XprMatrix<E, Rows, Cols> \ 00467 >, \ 00468 Rows, Cols \ 00469 > \ 00470 NAME (const std::complex<T>& lhs, \ 00471 const XprMatrix<E, Rows, Cols>& rhs) { \ 00472 typedef XprBinOp< \ 00473 Fcnl_##NAME< std::complex<T>, typename E::value_type>, \ 00474 XprLiteral< std::complex<T> >, \ 00475 XprMatrix<E, Rows, Cols> \ 00476 > expr_type; \ 00477 return XprMatrix<expr_type, Rows, Cols>( \ 00478 expr_type(XprLiteral< std::complex<T> >(lhs), rhs)); \ 00479 } 00480 00481 TVMET_IMPLEMENT_MACRO(add) 00482 TVMET_IMPLEMENT_MACRO(sub) 00483 TVMET_IMPLEMENT_MACRO(mul) 00484 TVMET_IMPLEMENT_MACRO(div) 00485 00486 #undef TVMET_IMPLEMENT_MACRO 00487 00488 #endif // defined(TVMET_HAVE_COMPLEX) 00489 00490 00491 /*++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 00492 * matrix prod( ... ) functions 00493 *+++++++++++++++++++++++++++++++++++++++++++++++++++++++*/ 00494 00495 00496 /** 00497 * \fn prod(const XprMatrix<E1, Rows1, Cols1>& lhs, const XprMatrix<E2, Cols1, Cols2>& rhs) 00498 * \brief Evaluate the product of two XprMatrix. 00499 * Perform on given Matrix M1 and M2: 00500 * \f[ 00501 * M_1\,M_2 00502 * \f] 00503 * \note The numer of Rows2 has to be equal to Cols1. 00504 * \ingroup _binary_function 00505 */ 00506 template<class E1, std::size_t Rows1, std::size_t Cols1, 00507 class E2, std::size_t Cols2> 00508 inline 00509 XprMatrix< 00510 XprMMProduct< 00511 XprMatrix<E1, Rows1, Cols1>, Rows1, Cols1, // M1(Rows1, Cols1) 00512 XprMatrix<E2, Cols1, Cols2>, Cols2 00513 >, 00514 Rows1, Cols2 // return Dim 00515 > 00516 prod(const XprMatrix<E1, Rows1, Cols1>& lhs, const XprMatrix<E2, Cols1, Cols2>& rhs) { 00517 typedef XprMMProduct< 00518 XprMatrix<E1, Rows1, Cols1>, Rows1, Cols1, 00519 XprMatrix<E2, Cols1, Cols2>, Cols2 00520 > expr_type; 00521 return XprMatrix<expr_type, Rows1, Cols2>(expr_type(lhs, rhs)); 00522 } 00523 00524 00525 /** 00526 * \fn trans_prod(const XprMatrix<E1, Rows1, Cols1>& lhs, const XprMatrix<E2, Cols1, Cols2>& rhs) 00527 * \brief Function for the trans(matrix-matrix-product) 00528 * Perform on given Matrix M1 and M2: 00529 * \f[ 00530 * (M_1\,M_2)^T 00531 * \f] 00532 * \note The numer of Rows2 has to be equal to Cols1. 00533 * \ingroup _binary_function 00534 */ 00535 template<class E1, std::size_t Rows1, std::size_t Cols1, 00536 class E2, std::size_t Cols2> 00537 inline 00538 XprMatrix< 00539 XprMMProductTransposed< 00540 XprMatrix<E1, Rows1, Cols1>, Rows1, Cols1, // M1(Rows1, Cols1) 00541 XprMatrix<E2, Cols1, Cols2>, Cols2 // M2(Cols1, Cols2) 00542 >, 00543 Cols2, Rows1 // return Dim 00544 > 00545 trans_prod(const XprMatrix<E1, Rows1, Cols1>& lhs, const XprMatrix<E2, Cols1, Cols2>& rhs) { 00546 typedef XprMMProductTransposed< 00547 XprMatrix<E1, Rows1, Cols1>, Rows1, Cols1, 00548 XprMatrix<E2, Cols1, Cols2>, Cols2 00549 > expr_type; 00550 return XprMatrix<expr_type, Cols2, Rows1>(expr_type(lhs, rhs)); 00551 } 00552 00553 00554 /** 00555 * \fn MtM_prod(const XprMatrix<E1, Rows1, Cols1>& lhs, const XprMatrix<E2, Rows1, Cols2>& rhs) 00556 * \brief Function for the trans(matrix)-matrix-product. 00557 * using formula 00558 * \f[ 00559 * M_1^{T}\,M_2 00560 * \f] 00561 * \note The number of cols of matrix 2 have to be equal to number of rows of 00562 * matrix 1, since matrix 1 is trans - the result is a (Cols1 x Cols2) 00563 * matrix. 00564 * \ingroup _binary_function 00565 */ 00566 template<class E1, std::size_t Rows1, std::size_t Cols1, 00567 class E2, std::size_t Cols2> // Rows2 = Rows1 00568 inline 00569 XprMatrix< 00570 XprMtMProduct< 00571 XprMatrix<E1, Rows1, Cols1>, Rows1, Cols1, // M1(Rows1, Cols1) 00572 XprMatrix<E2, Rows1, Cols2>, Cols2 // M2(Rows1, Cols2) 00573 >, 00574 Cols1, Cols2 // return Dim 00575 > 00576 MtM_prod(const XprMatrix<E1, Rows1, Cols1>& lhs, const XprMatrix<E2, Rows1, Cols2>& rhs) { 00577 typedef XprMtMProduct< 00578 XprMatrix<E1, Rows1, Cols1>, Rows1, Cols1, 00579 XprMatrix<E2, Rows1, Cols2>, Cols2 00580 > expr_type; 00581 return XprMatrix<expr_type, Cols1, Cols2>(expr_type(lhs, rhs)); 00582 } 00583 00584 00585 /** 00586 * \fn MMt_prod(const XprMatrix<E1, Rows1, Cols1>& lhs, const XprMatrix<E2, Rows2, Cols1>& rhs) 00587 * \brief Function for the matrix-trans(matrix)-product. 00588 * \ingroup _binary_function 00589 * \note The cols2 has to be equal to cols1. 00590 */ 00591 template<class E1, std::size_t Rows1, std::size_t Cols1, 00592 class E2, std::size_t Rows2> // Cols2 = Cols1 00593 inline 00594 XprMatrix< 00595 XprMMtProduct< 00596 XprMatrix<E1, Rows1, Cols1>, Rows1, Cols1, // M1(Rows1, Cols1) 00597 XprMatrix<E2, Rows2, Cols1>, Cols1 // M2(Rows2, Cols1) 00598 >, 00599 Rows1, Rows2 // return Dim 00600 > 00601 MMt_prod(const XprMatrix<E1, Rows1, Cols1>& lhs, const XprMatrix<E2, Rows2, Cols1>& rhs) { 00602 typedef XprMMtProduct< 00603 XprMatrix<E1, Rows1, Cols1>, Rows1, Cols1, 00604 XprMatrix<E2, Rows2, Cols1>, Cols1 00605 > expr_type; 00606 return XprMatrix<expr_type, Rows1, Rows2>(expr_type(lhs, rhs)); 00607 } 00608 00609 00610 /*++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 00611 * matrix-vector specific prod( ... ) functions 00612 *+++++++++++++++++++++++++++++++++++++++++++++++++++++++*/ 00613 00614 00615 /** 00616 * \fn prod(const XprMatrix<E1, Rows, Cols>& lhs, const XprVector<E2, Cols>& rhs) 00617 * \brief Evaluate the product of XprMatrix and XprVector. 00618 * \ingroup _binary_function 00619 */ 00620 template<class E1, std::size_t Rows, std::size_t Cols, 00621 class E2> 00622 inline 00623 XprVector< 00624 XprMVProduct< 00625 XprMatrix<E1, Rows, Cols>, Rows, Cols, 00626 XprVector<E2, Cols> 00627 >, 00628 Rows 00629 > 00630 prod(const XprMatrix<E1, Rows, Cols>& lhs, const XprVector<E2, Cols>& rhs) { 00631 typedef XprMVProduct< 00632 XprMatrix<E1, Rows, Cols>, Rows, Cols, 00633 XprVector<E2, Cols> 00634 > expr_type; 00635 return XprVector<expr_type, Rows>(expr_type(lhs, rhs)); 00636 } 00637 00638 00639 /*++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 00640 * matrix specific functions 00641 *+++++++++++++++++++++++++++++++++++++++++++++++++++++++*/ 00642 00643 00644 /** 00645 * \fn trans(const XprMatrix<E, Rows, Cols>& rhs) 00646 * \brief Transpose an expression matrix. 00647 * \ingroup _unary_function 00648 */ 00649 template<class E, std::size_t Rows, std::size_t Cols> 00650 inline 00651 XprMatrix< 00652 XprMatrixTranspose< 00653 XprMatrix<E, Rows, Cols> 00654 >, 00655 Cols, Rows 00656 > 00657 trans(const XprMatrix<E, Rows, Cols>& rhs) { 00658 typedef XprMatrixTranspose< 00659 XprMatrix<E, Rows, Cols> 00660 > expr_type; 00661 return XprMatrix<expr_type, Cols, Rows>(expr_type(rhs)); 00662 } 00663 00664 00665 /* 00666 * \fn trace(const XprMatrix<E, Sz, Sz>& m) 00667 * \brief Compute the trace of a square matrix. 00668 * \ingroup _unary_function 00669 * 00670 * Simply compute the trace of the given matrix expression as: 00671 * \f[ 00672 * \sum_{k = 0}^{Sz-1} m(k, k) 00673 * \f] 00674 */ 00675 template<class E, std::size_t Sz> 00676 inline 00677 typename NumericTraits<typename E::value_type>::sum_type 00678 trace(const XprMatrix<E, Sz, Sz>& m) { 00679 return meta::Matrix<Sz, Sz, 0, 0>::trace(m); 00680 } 00681 00682 00683 /** 00684 * \fn row(const XprMatrix<E, Rows, Cols>& m, std::size_t no) 00685 * \brief Returns a row vector of the given matrix. 00686 * \ingroup _binary_function 00687 */ 00688 template<class E, std::size_t Rows, std::size_t Cols> 00689 inline 00690 XprVector< 00691 XprMatrixRow< 00692 XprMatrix<E, Rows, Cols>, 00693 Rows, Cols 00694 >, 00695 Cols 00696 > 00697 row(const XprMatrix<E, Rows, Cols>& m, std::size_t no) { 00698 typedef XprMatrixRow< 00699 XprMatrix<E, Rows, Cols>, 00700 Rows, Cols 00701 > expr_type; 00702 00703 return XprVector<expr_type, Cols>(expr_type(m, no)); 00704 } 00705 00706 00707 /** 00708 * \fn col(const XprMatrix<E, Rows, Cols>& m, std::size_t no) 00709 * \brief Returns a column vector of the given matrix. 00710 * \ingroup _binary_function 00711 */ 00712 template<class E, std::size_t Rows, std::size_t Cols> 00713 inline 00714 XprVector< 00715 XprMatrixCol< 00716 XprMatrix<E, Rows, Cols>, 00717 Rows, Cols 00718 >, 00719 Rows 00720 > 00721 col(const XprMatrix<E, Rows, Cols>& m, std::size_t no) { 00722 typedef XprMatrixCol< 00723 XprMatrix<E, Rows, Cols>, 00724 Rows, Cols 00725 > expr_type; 00726 00727 return XprVector<expr_type, Cols>(expr_type(m, no)); 00728 } 00729 00730 00731 /** 00732 * \fn diag(const XprMatrix<E, Sz, Sz>& m) 00733 * \brief Returns the diagonal vector of the given square matrix. 00734 * \ingroup _unary_function 00735 */ 00736 template<class E, std::size_t Sz> 00737 inline 00738 XprVector< 00739 XprMatrixDiag< 00740 XprMatrix<E, Sz, Sz>, 00741 Sz 00742 >, 00743 Sz 00744 > 00745 diag(const XprMatrix<E, Sz, Sz>& m) { 00746 typedef XprMatrixDiag< 00747 XprMatrix<E, Sz, Sz>, 00748 Sz> expr_type; 00749 00750 return XprVector<expr_type, Sz>(expr_type(m)); 00751 } 00752 00753 00754 } // namespace tvmet 00755 00756 #endif // TVMET_XPR_MATRIX_FUNCTIONS_H 00757 00758 // Local Variables: 00759 // mode:C++ 00760 // tab-width:8 00761 // End:
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