| /* |
| * Tiny Vector Matrix Library |
| * Dense Vector Matrix Libary of Tiny size using Expression Templates |
| * |
| * Copyright (C) 2001 - 2003 Olaf Petzold <opetzold@users.sourceforge.net> |
| * |
| * This library is free software; you can redistribute it and/or |
| * modify it under the terms of the GNU lesser General Public |
| * License as published by the Free Software Foundation; either |
| * version 2.1 of the License, or (at your option) any later version. |
| * |
| * This library is distributed in the hope that it will be useful, |
| * but WITHOUT ANY WARRANTY; without even the implied warranty of |
| * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
| * lesser General Public License for more details. |
| * |
| * You should have received a copy of the GNU lesser General Public |
| * License along with this library; if not, write to the Free Software |
| * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA |
| * |
| * $Id: MatrixFunctions.h,v 1.39 2004/07/06 05:49:22 opetzold Exp $ |
| */ |
| |
| #ifndef TVMET_XPR_MATRIX_FUNCTIONS_H |
| #define TVMET_XPR_MATRIX_FUNCTIONS_H |
| |
| namespace tvmet { |
| |
| |
| /* forwards */ |
| template<class T, std::size_t Rows, std::size_t Cols> class Matrix; |
| template<class T, std::size_t Sz> class Vector; |
| template<class E, std::size_t Sz> class XprVector; |
| template<class E> class XprMatrixTranspose; |
| template<class E, std::size_t Sz> class XprMatrixDiag; |
| template<class E, std::size_t Rows, std::size_t Cols> class XprMatrixRow; |
| template<class E, std::size_t Rows, std::size_t Cols> class XprMatrixCol; |
| |
| |
| /********************************************************* |
| * PART I: DECLARATION |
| *********************************************************/ |
| |
| |
| /*++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| * Matrix arithmetic functions add, sub, mul and div |
| *+++++++++++++++++++++++++++++++++++++++++++++++++++++++*/ |
| |
| |
| /* |
| * function(XprMatrix<E1, Rows, Cols>, XprMatrix<E2, Rows, Cols>) |
| */ |
| #define TVMET_DECLARE_MACRO(NAME) \ |
| template<class E1, class E2, std::size_t Rows, std::size_t Cols> \ |
| XprMatrix< \ |
| XprBinOp< \ |
| Fcnl_##NAME<typename E1::value_type, typename E2::value_type>, \ |
| XprMatrix<E1, Rows, Cols>, \ |
| XprMatrix<E2, Rows, Cols> \ |
| >, \ |
| Rows, Cols \ |
| > \ |
| NAME (const XprMatrix<E1, Rows, Cols>& lhs, \ |
| const XprMatrix<E2, Rows, Cols>& rhs) TVMET_CXX_ALWAYS_INLINE; |
| |
| TVMET_DECLARE_MACRO(add) // per se element wise |
| TVMET_DECLARE_MACRO(sub) // per se element wise |
| namespace element_wise { |
| TVMET_DECLARE_MACRO(mul) // not defined for matrizes |
| TVMET_DECLARE_MACRO(div) // not defined for matrizes |
| } |
| |
| #undef TVMET_DECLARE_MACRO |
| |
| |
| /* |
| * function(XprMatrix<E, Rows, Cols>, POD) |
| * function(POD, XprMatrix<E, Rows, Cols>) |
| * Note: - operations +,-,*,/ are per se element wise |
| */ |
| #define TVMET_DECLARE_MACRO(NAME, POD) \ |
| template<class E, std::size_t Rows, std::size_t Cols> \ |
| XprMatrix< \ |
| XprBinOp< \ |
| Fcnl_##NAME<typename E::value_type, POD >, \ |
| XprMatrix<E, Rows, Cols>, \ |
| XprLiteral< POD > \ |
| >, \ |
| Rows, Cols \ |
| > \ |
| NAME (const XprMatrix<E, Rows, Cols>& lhs, \ |
| POD rhs) TVMET_CXX_ALWAYS_INLINE; \ |
| \ |
| template<class E, std::size_t Rows, std::size_t Cols> \ |
| XprMatrix< \ |
| XprBinOp< \ |
| Fcnl_##NAME< POD, typename E::value_type>, \ |
| XprLiteral< POD >, \ |
| XprMatrix<E, Rows, Cols> \ |
| >, \ |
| Rows, Cols \ |
| > \ |
| NAME (POD lhs, \ |
| const XprMatrix<E, Rows, Cols>& rhs) TVMET_CXX_ALWAYS_INLINE; |
| |
| TVMET_DECLARE_MACRO(add, int) |
| TVMET_DECLARE_MACRO(sub, int) |
| TVMET_DECLARE_MACRO(mul, int) |
| TVMET_DECLARE_MACRO(div, int) |
| |
| #if defined(TVMET_HAVE_LONG_LONG) |
| TVMET_DECLARE_MACRO(add, long long int) |
| TVMET_DECLARE_MACRO(sub, long long int) |
| TVMET_DECLARE_MACRO(mul, long long int) |
| TVMET_DECLARE_MACRO(div, long long int) |
| #endif |
| |
| TVMET_DECLARE_MACRO(add, float) |
| TVMET_DECLARE_MACRO(sub, float) |
| TVMET_DECLARE_MACRO(mul, float) |
| TVMET_DECLARE_MACRO(div, float) |
| |
| TVMET_DECLARE_MACRO(add, double) |
| TVMET_DECLARE_MACRO(sub, double) |
| TVMET_DECLARE_MACRO(mul, double) |
| TVMET_DECLARE_MACRO(div, double) |
| |
| #if defined(TVMET_HAVE_LONG_DOUBLE) |
| TVMET_DECLARE_MACRO(add, long double) |
| TVMET_DECLARE_MACRO(sub, long double) |
| TVMET_DECLARE_MACRO(mul, long double) |
| TVMET_DECLARE_MACRO(div, long double) |
| #endif |
| |
| #undef TVMET_DECLARE_MACRO |
| |
| |
| #if defined(TVMET_HAVE_COMPLEX) |
| /* |
| * function(XprMatrix<E, Rows, Cols>, complex<T>) |
| * function(complex<T>, XprMatrix<E, Rows, Cols>) |
| * Note: - operations +,-,*,/ are per se element wise |
| * \todo type promotion |
| */ |
| #define TVMET_DECLARE_MACRO(NAME) \ |
| template<class E, class T, std::size_t Rows, std::size_t Cols> \ |
| XprMatrix< \ |
| XprBinOp< \ |
| Fcnl_##NAME<typename E::value_type, std::complex<T> >, \ |
| XprMatrix<E, Rows, Cols>, \ |
| XprLiteral< std::complex<T> > \ |
| >, \ |
| Rows, Cols \ |
| > \ |
| NAME (const XprMatrix<E, Rows, Cols>& lhs, \ |
| const std::complex<T>& rhs) TVMET_CXX_ALWAYS_INLINE; \ |
| \ |
| template<class T, class E, std::size_t Rows, std::size_t Cols> \ |
| XprMatrix< \ |
| XprBinOp< \ |
| Fcnl_##NAME< std::complex<T>, typename E::value_type>, \ |
| XprLiteral< std::complex<T> >, \ |
| XprMatrix<E, Rows, Cols> \ |
| >, \ |
| Rows, Cols \ |
| > \ |
| NAME (const std::complex<T>& lhs, \ |
| const XprMatrix<E, Rows, Cols>& rhs) TVMET_CXX_ALWAYS_INLINE; |
| |
| TVMET_DECLARE_MACRO(add) |
| TVMET_DECLARE_MACRO(sub) |
| TVMET_DECLARE_MACRO(mul) |
| TVMET_DECLARE_MACRO(div) |
| |
| #undef TVMET_DECLARE_MACRO |
| |
| #endif // defined(TVMET_HAVE_COMPLEX) |
| |
| |
| /*++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| * matrix prod( ... ) functions |
| *+++++++++++++++++++++++++++++++++++++++++++++++++++++++*/ |
| |
| |
| template<class E1, std::size_t Rows1, std::size_t Cols1, |
| class E2, std::size_t Cols2> |
| XprMatrix< |
| XprMMProduct< |
| XprMatrix<E1, Rows1, Cols1>, Rows1, Cols1, // M1(Rows1, Cols1) |
| XprMatrix<E2, Cols1, Cols2>, Cols2 |
| >, |
| Rows1, Cols2 // return Dim |
| > |
| prod(const XprMatrix<E1, Rows1, Cols1>& lhs, |
| const XprMatrix<E2, Cols1, Cols2>& rhs) TVMET_CXX_ALWAYS_INLINE; |
| |
| |
| template<class E1, std::size_t Rows1, std::size_t Cols1, |
| class E2, std::size_t Cols2> |
| XprMatrix< |
| XprMMProductTransposed< |
| XprMatrix<E1, Rows1, Cols1>, Rows1, Cols1, // M1(Rows1, Cols1) |
| XprMatrix<E2, Cols1, Cols2>, Cols2 // M2(Cols1, Cols2) |
| >, |
| Cols2, Rows1 // return Dim |
| > |
| trans_prod(const XprMatrix<E1, Rows1, Cols1>& lhs, |
| const XprMatrix<E2, Cols1, Cols2>& rhs) TVMET_CXX_ALWAYS_INLINE; |
| |
| |
| template<class E1, std::size_t Rows1, std::size_t Cols1, |
| class E2, std::size_t Cols2> // Rows2 = Rows1 |
| XprMatrix< |
| XprMtMProduct< |
| XprMatrix<E1, Rows1, Cols1>, Rows1, Cols1, // M1(Rows1, Cols1) |
| XprMatrix<E2, Rows1, Cols2>, Cols2 // M2(Rows1, Cols2) |
| >, |
| Cols1, Cols2 // return Dim |
| > |
| MtM_prod(const XprMatrix<E1, Rows1, Cols1>& lhs, |
| const XprMatrix<E2, Rows1, Cols2>& rhs) TVMET_CXX_ALWAYS_INLINE; |
| |
| |
| template<class E1, std::size_t Rows1, std::size_t Cols1, |
| class E2, std::size_t Rows2> // Cols2 = Cols1 |
| XprMatrix< |
| XprMMtProduct< |
| XprMatrix<E1, Rows1, Cols1>, Rows1, Cols1, // M1(Rows1, Cols1) |
| XprMatrix<E2, Rows2, Cols1>, Cols1 // M2(Rows2, Cols1) |
| >, |
| Rows1, Rows2 // return Dim |
| > |
| MMt_prod(const XprMatrix<E1, Rows1, Cols1>& lhs, |
| const XprMatrix<E2, Rows2, Cols1>& rhs) TVMET_CXX_ALWAYS_INLINE; |
| |
| |
| /*++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| * matrix-vector specific prod( ... ) functions |
| *+++++++++++++++++++++++++++++++++++++++++++++++++++++++*/ |
| |
| |
| template<class E1, std::size_t Rows, std::size_t Cols, |
| class E2> |
| XprVector< |
| XprMVProduct< |
| XprMatrix<E1, Rows, Cols>, Rows, Cols, |
| XprVector<E2, Cols> |
| >, |
| Rows |
| > |
| prod(const XprMatrix<E1, Rows, Cols>& lhs, |
| const XprVector<E2, Cols>& rhs) TVMET_CXX_ALWAYS_INLINE; |
| |
| |
| /*++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| * matrix specific functions |
| *+++++++++++++++++++++++++++++++++++++++++++++++++++++++*/ |
| |
| |
| template<class E, std::size_t Rows, std::size_t Cols> |
| XprMatrix< |
| XprMatrixTranspose< |
| XprMatrix<E, Rows, Cols> |
| >, |
| Cols, Rows |
| > |
| trans(const XprMatrix<E, Rows, Cols>& rhs) TVMET_CXX_ALWAYS_INLINE; |
| |
| |
| #if 0 // XXX needs declaration of meta::Matrix<Sz, Sz, 0, 0>::trace |
| template<class E, std::size_t Sz> |
| typename NumericTraits<typename E::value_type>::sum_type |
| trace(const XprMatrix<E, Sz, Sz>& m)TVMET_CXX_ALWAYS_INLINE; |
| #endif |
| |
| |
| template<class E, std::size_t Rows, std::size_t Cols> |
| XprVector< |
| XprMatrixRow< |
| XprMatrix<E, Rows, Cols>, |
| Rows, Cols |
| >, |
| Cols |
| > |
| row(const XprMatrix<E, Rows, Cols>& m, |
| std::size_t no) TVMET_CXX_ALWAYS_INLINE; |
| |
| |
| template<class E, std::size_t Rows, std::size_t Cols> |
| XprVector< |
| XprMatrixCol< |
| XprMatrix<E, Rows, Cols>, |
| Rows, Cols |
| >, |
| Rows |
| > |
| col(const XprMatrix<E, Rows, Cols>& m, std::size_t no) TVMET_CXX_ALWAYS_INLINE; |
| |
| |
| template<class E, std::size_t Sz> |
| XprVector< |
| XprMatrixDiag< |
| XprMatrix<E, Sz, Sz>, |
| Sz |
| >, |
| Sz |
| > |
| diag(const XprMatrix<E, Sz, Sz>& m) TVMET_CXX_ALWAYS_INLINE; |
| |
| |
| /********************************************************* |
| * PART II: IMPLEMENTATION |
| *********************************************************/ |
| |
| |
| /*++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| * Matrix arithmetic functions add, sub, mul and div |
| *+++++++++++++++++++++++++++++++++++++++++++++++++++++++*/ |
| |
| |
| /* |
| * function(XprMatrix<E1, Rows, Cols>, XprMatrix<E2, Rows, Cols>) |
| */ |
| #define TVMET_IMPLEMENT_MACRO(NAME) \ |
| template<class E1, class E2, std::size_t Rows, std::size_t Cols> \ |
| inline \ |
| XprMatrix< \ |
| XprBinOp< \ |
| Fcnl_##NAME<typename E1::value_type, typename E2::value_type>, \ |
| XprMatrix<E1, Rows, Cols>, \ |
| XprMatrix<E2, Rows, Cols> \ |
| >, \ |
| Rows, Cols \ |
| > \ |
| NAME (const XprMatrix<E1, Rows, Cols>& lhs, \ |
| const XprMatrix<E2, Rows, Cols>& rhs) { \ |
| typedef XprBinOp< \ |
| Fcnl_##NAME<typename E1::value_type, typename E2::value_type>, \ |
| XprMatrix<E1, Rows, Cols>, \ |
| XprMatrix<E2, Rows, Cols> \ |
| > expr_type; \ |
| return XprMatrix<expr_type, Rows, Cols>(expr_type(lhs, rhs)); \ |
| } |
| |
| TVMET_IMPLEMENT_MACRO(add) // per se element wise |
| TVMET_IMPLEMENT_MACRO(sub) // per se element wise |
| namespace element_wise { |
| TVMET_IMPLEMENT_MACRO(mul) // not defined for matrizes |
| TVMET_IMPLEMENT_MACRO(div) // not defined for matrizes |
| } |
| |
| #undef TVMET_IMPLEMENT_MACRO |
| |
| |
| /* |
| * function(XprMatrix<E, Rows, Cols>, POD) |
| * function(POD, XprMatrix<E, Rows, Cols>) |
| * Note: - operations +,-,*,/ are per se element wise |
| */ |
| #define TVMET_IMPLEMENT_MACRO(NAME, POD) \ |
| template<class E, std::size_t Rows, std::size_t Cols> \ |
| inline \ |
| XprMatrix< \ |
| XprBinOp< \ |
| Fcnl_##NAME<typename E::value_type, POD >, \ |
| XprMatrix<E, Rows, Cols>, \ |
| XprLiteral< POD > \ |
| >, \ |
| Rows, Cols \ |
| > \ |
| NAME (const XprMatrix<E, Rows, Cols>& lhs, POD rhs) { \ |
| typedef XprBinOp< \ |
| Fcnl_##NAME<typename E::value_type, POD >, \ |
| XprMatrix<E, Rows, Cols>, \ |
| XprLiteral< POD > \ |
| > expr_type; \ |
| return XprMatrix<expr_type, Rows, Cols>( \ |
| expr_type(lhs, XprLiteral< POD >(rhs))); \ |
| } \ |
| \ |
| template<class E, std::size_t Rows, std::size_t Cols> \ |
| inline \ |
| XprMatrix< \ |
| XprBinOp< \ |
| Fcnl_##NAME< POD, typename E::value_type>, \ |
| XprLiteral< POD >, \ |
| XprMatrix<E, Rows, Cols> \ |
| >, \ |
| Rows, Cols \ |
| > \ |
| NAME (POD lhs, const XprMatrix<E, Rows, Cols>& rhs) { \ |
| typedef XprBinOp< \ |
| Fcnl_##NAME< POD, typename E::value_type>, \ |
| XprLiteral< POD >, \ |
| XprMatrix<E, Rows, Cols> \ |
| > expr_type; \ |
| return XprMatrix<expr_type, Rows, Cols>( \ |
| expr_type(XprLiteral< POD >(lhs), rhs)); \ |
| } |
| |
| TVMET_IMPLEMENT_MACRO(add, int) |
| TVMET_IMPLEMENT_MACRO(sub, int) |
| TVMET_IMPLEMENT_MACRO(mul, int) |
| TVMET_IMPLEMENT_MACRO(div, int) |
| |
| #if defined(TVMET_HAVE_LONG_LONG) |
| TVMET_IMPLEMENT_MACRO(add, long long int) |
| TVMET_IMPLEMENT_MACRO(sub, long long int) |
| TVMET_IMPLEMENT_MACRO(mul, long long int) |
| TVMET_IMPLEMENT_MACRO(div, long long int) |
| #endif |
| |
| TVMET_IMPLEMENT_MACRO(add, float) |
| TVMET_IMPLEMENT_MACRO(sub, float) |
| TVMET_IMPLEMENT_MACRO(mul, float) |
| TVMET_IMPLEMENT_MACRO(div, float) |
| |
| TVMET_IMPLEMENT_MACRO(add, double) |
| TVMET_IMPLEMENT_MACRO(sub, double) |
| TVMET_IMPLEMENT_MACRO(mul, double) |
| TVMET_IMPLEMENT_MACRO(div, double) |
| |
| #if defined(TVMET_HAVE_LONG_DOUBLE) |
| TVMET_IMPLEMENT_MACRO(add, long double) |
| TVMET_IMPLEMENT_MACRO(sub, long double) |
| TVMET_IMPLEMENT_MACRO(mul, long double) |
| TVMET_IMPLEMENT_MACRO(div, long double) |
| #endif |
| |
| #undef TVMET_IMPLEMENT_MACRO |
| |
| |
| #if defined(TVMET_HAVE_COMPLEX) |
| /* |
| * function(XprMatrix<E, Rows, Cols>, complex<T>) |
| * function(complex<T>, XprMatrix<E, Rows, Cols>) |
| * Note: - operations +,-,*,/ are per se element wise |
| * \todo type promotion |
| */ |
| #define TVMET_IMPLEMENT_MACRO(NAME) \ |
| template<class E, class T, std::size_t Rows, std::size_t Cols> \ |
| inline \ |
| XprMatrix< \ |
| XprBinOp< \ |
| Fcnl_##NAME<typename E::value_type, std::complex<T> >, \ |
| XprMatrix<E, Rows, Cols>, \ |
| XprLiteral< std::complex<T> > \ |
| >, \ |
| Rows, Cols \ |
| > \ |
| NAME (const XprMatrix<E, Rows, Cols>& lhs, \ |
| const std::complex<T>& rhs) { \ |
| typedef XprBinOp< \ |
| Fcnl_##NAME<typename E::value_type, std::complex<T> >, \ |
| XprMatrix<E, Rows, Cols>, \ |
| XprLiteral< std::complex<T> > \ |
| > expr_type; \ |
| return XprMatrix<expr_type, Rows, Cols>( \ |
| expr_type(lhs, XprLiteral< std::complex<T> >(rhs))); \ |
| } \ |
| \ |
| template<class T, class E, std::size_t Rows, std::size_t Cols> \ |
| inline \ |
| XprMatrix< \ |
| XprBinOp< \ |
| Fcnl_##NAME< std::complex<T>, typename E::value_type>, \ |
| XprLiteral< std::complex<T> >, \ |
| XprMatrix<E, Rows, Cols> \ |
| >, \ |
| Rows, Cols \ |
| > \ |
| NAME (const std::complex<T>& lhs, \ |
| const XprMatrix<E, Rows, Cols>& rhs) { \ |
| typedef XprBinOp< \ |
| Fcnl_##NAME< std::complex<T>, typename E::value_type>, \ |
| XprLiteral< std::complex<T> >, \ |
| XprMatrix<E, Rows, Cols> \ |
| > expr_type; \ |
| return XprMatrix<expr_type, Rows, Cols>( \ |
| expr_type(XprLiteral< std::complex<T> >(lhs), rhs)); \ |
| } |
| |
| TVMET_IMPLEMENT_MACRO(add) |
| TVMET_IMPLEMENT_MACRO(sub) |
| TVMET_IMPLEMENT_MACRO(mul) |
| TVMET_IMPLEMENT_MACRO(div) |
| |
| #undef TVMET_IMPLEMENT_MACRO |
| |
| #endif // defined(TVMET_HAVE_COMPLEX) |
| |
| |
| /*++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| * matrix prod( ... ) functions |
| *+++++++++++++++++++++++++++++++++++++++++++++++++++++++*/ |
| |
| |
| /** |
| * \fn prod(const XprMatrix<E1, Rows1, Cols1>& lhs, const XprMatrix<E2, Cols1, Cols2>& rhs) |
| * \brief Evaluate the product of two XprMatrix. |
| * Perform on given Matrix M1 and M2: |
| * \f[ |
| * M_1\,M_2 |
| * \f] |
| * \note The numer of Rows2 has to be equal to Cols1. |
| * \ingroup _binary_function |
| */ |
| template<class E1, std::size_t Rows1, std::size_t Cols1, |
| class E2, std::size_t Cols2> |
| inline |
| XprMatrix< |
| XprMMProduct< |
| XprMatrix<E1, Rows1, Cols1>, Rows1, Cols1, // M1(Rows1, Cols1) |
| XprMatrix<E2, Cols1, Cols2>, Cols2 |
| >, |
| Rows1, Cols2 // return Dim |
| > |
| prod(const XprMatrix<E1, Rows1, Cols1>& lhs, const XprMatrix<E2, Cols1, Cols2>& rhs) { |
| typedef XprMMProduct< |
| XprMatrix<E1, Rows1, Cols1>, Rows1, Cols1, |
| XprMatrix<E2, Cols1, Cols2>, Cols2 |
| > expr_type; |
| return XprMatrix<expr_type, Rows1, Cols2>(expr_type(lhs, rhs)); |
| } |
| |
| |
| /** |
| * \fn trans_prod(const XprMatrix<E1, Rows1, Cols1>& lhs, const XprMatrix<E2, Cols1, Cols2>& rhs) |
| * \brief Function for the trans(matrix-matrix-product) |
| * Perform on given Matrix M1 and M2: |
| * \f[ |
| * (M_1\,M_2)^T |
| * \f] |
| * \note The numer of Rows2 has to be equal to Cols1. |
| * \ingroup _binary_function |
| */ |
| template<class E1, std::size_t Rows1, std::size_t Cols1, |
| class E2, std::size_t Cols2> |
| inline |
| XprMatrix< |
| XprMMProductTransposed< |
| XprMatrix<E1, Rows1, Cols1>, Rows1, Cols1, // M1(Rows1, Cols1) |
| XprMatrix<E2, Cols1, Cols2>, Cols2 // M2(Cols1, Cols2) |
| >, |
| Cols2, Rows1 // return Dim |
| > |
| trans_prod(const XprMatrix<E1, Rows1, Cols1>& lhs, const XprMatrix<E2, Cols1, Cols2>& rhs) { |
| typedef XprMMProductTransposed< |
| XprMatrix<E1, Rows1, Cols1>, Rows1, Cols1, |
| XprMatrix<E2, Cols1, Cols2>, Cols2 |
| > expr_type; |
| return XprMatrix<expr_type, Cols2, Rows1>(expr_type(lhs, rhs)); |
| } |
| |
| |
| /** |
| * \fn MtM_prod(const XprMatrix<E1, Rows1, Cols1>& lhs, const XprMatrix<E2, Rows1, Cols2>& rhs) |
| * \brief Function for the trans(matrix)-matrix-product. |
| * using formula |
| * \f[ |
| * M_1^{T}\,M_2 |
| * \f] |
| * \note The number of cols of matrix 2 have to be equal to number of rows of |
| * matrix 1, since matrix 1 is trans - the result is a (Cols1 x Cols2) |
| * matrix. |
| * \ingroup _binary_function |
| */ |
| template<class E1, std::size_t Rows1, std::size_t Cols1, |
| class E2, std::size_t Cols2> // Rows2 = Rows1 |
| inline |
| XprMatrix< |
| XprMtMProduct< |
| XprMatrix<E1, Rows1, Cols1>, Rows1, Cols1, // M1(Rows1, Cols1) |
| XprMatrix<E2, Rows1, Cols2>, Cols2 // M2(Rows1, Cols2) |
| >, |
| Cols1, Cols2 // return Dim |
| > |
| MtM_prod(const XprMatrix<E1, Rows1, Cols1>& lhs, const XprMatrix<E2, Rows1, Cols2>& rhs) { |
| typedef XprMtMProduct< |
| XprMatrix<E1, Rows1, Cols1>, Rows1, Cols1, |
| XprMatrix<E2, Rows1, Cols2>, Cols2 |
| > expr_type; |
| return XprMatrix<expr_type, Cols1, Cols2>(expr_type(lhs, rhs)); |
| } |
| |
| |
| /** |
| * \fn MMt_prod(const XprMatrix<E1, Rows1, Cols1>& lhs, const XprMatrix<E2, Rows2, Cols1>& rhs) |
| * \brief Function for the matrix-trans(matrix)-product. |
| * \ingroup _binary_function |
| * \note The cols2 has to be equal to cols1. |
| */ |
| template<class E1, std::size_t Rows1, std::size_t Cols1, |
| class E2, std::size_t Rows2> // Cols2 = Cols1 |
| inline |
| XprMatrix< |
| XprMMtProduct< |
| XprMatrix<E1, Rows1, Cols1>, Rows1, Cols1, // M1(Rows1, Cols1) |
| XprMatrix<E2, Rows2, Cols1>, Cols1 // M2(Rows2, Cols1) |
| >, |
| Rows1, Rows2 // return Dim |
| > |
| MMt_prod(const XprMatrix<E1, Rows1, Cols1>& lhs, const XprMatrix<E2, Rows2, Cols1>& rhs) { |
| typedef XprMMtProduct< |
| XprMatrix<E1, Rows1, Cols1>, Rows1, Cols1, |
| XprMatrix<E2, Rows2, Cols1>, Cols1 |
| > expr_type; |
| return XprMatrix<expr_type, Rows1, Rows2>(expr_type(lhs, rhs)); |
| } |
| |
| |
| /*++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| * matrix-vector specific prod( ... ) functions |
| *+++++++++++++++++++++++++++++++++++++++++++++++++++++++*/ |
| |
| |
| /** |
| * \fn prod(const XprMatrix<E1, Rows, Cols>& lhs, const XprVector<E2, Cols>& rhs) |
| * \brief Evaluate the product of XprMatrix and XprVector. |
| * \ingroup _binary_function |
| */ |
| template<class E1, std::size_t Rows, std::size_t Cols, |
| class E2> |
| inline |
| XprVector< |
| XprMVProduct< |
| XprMatrix<E1, Rows, Cols>, Rows, Cols, |
| XprVector<E2, Cols> |
| >, |
| Rows |
| > |
| prod(const XprMatrix<E1, Rows, Cols>& lhs, const XprVector<E2, Cols>& rhs) { |
| typedef XprMVProduct< |
| XprMatrix<E1, Rows, Cols>, Rows, Cols, |
| XprVector<E2, Cols> |
| > expr_type; |
| return XprVector<expr_type, Rows>(expr_type(lhs, rhs)); |
| } |
| |
| |
| /*++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| * matrix specific functions |
| *+++++++++++++++++++++++++++++++++++++++++++++++++++++++*/ |
| |
| |
| /** |
| * \fn trans(const XprMatrix<E, Rows, Cols>& rhs) |
| * \brief Transpose an expression matrix. |
| * \ingroup _unary_function |
| */ |
| template<class E, std::size_t Rows, std::size_t Cols> |
| inline |
| XprMatrix< |
| XprMatrixTranspose< |
| XprMatrix<E, Rows, Cols> |
| >, |
| Cols, Rows |
| > |
| trans(const XprMatrix<E, Rows, Cols>& rhs) { |
| typedef XprMatrixTranspose< |
| XprMatrix<E, Rows, Cols> |
| > expr_type; |
| return XprMatrix<expr_type, Cols, Rows>(expr_type(rhs)); |
| } |
| |
| |
| #if 0 // XXX needs declaration of meta::Matrix<Sz, Sz, 0, 0>::trace |
| /* |
| * \fn trace(const XprMatrix<E, Sz, Sz>& m) |
| * \brief Compute the trace of a square matrix. |
| * \ingroup _unary_function |
| * |
| * Simply compute the trace of the given matrix as: |
| * \f[ |
| * \sum_{k = 0}^{Sz-1} m(k, k) |
| * \f] |
| */ |
| template<class E, std::size_t Sz> |
| inline |
| typename NumericTraits<typename E::value_type>::sum_type |
| trace(const XprMatrix<E, Sz, Sz>& m) { |
| return meta::Matrix<Sz, Sz, 0, 0>::trace(m); |
| } |
| #endif |
| |
| |
| /** |
| * \fn row(const XprMatrix<E, Rows, Cols>& m, std::size_t no) |
| * \brief Returns a row vector of the given matrix. |
| * \ingroup _binary_function |
| */ |
| template<class E, std::size_t Rows, std::size_t Cols> |
| inline |
| XprVector< |
| XprMatrixRow< |
| XprMatrix<E, Rows, Cols>, |
| Rows, Cols |
| >, |
| Cols |
| > |
| row(const XprMatrix<E, Rows, Cols>& m, std::size_t no) { |
| typedef XprMatrixRow< |
| XprMatrix<E, Rows, Cols>, |
| Rows, Cols |
| > expr_type; |
| |
| return XprVector<expr_type, Cols>(expr_type(m, no)); |
| } |
| |
| |
| /** |
| * \fn col(const XprMatrix<E, Rows, Cols>& m, std::size_t no) |
| * \brief Returns a column vector of the given matrix. |
| * \ingroup _binary_function |
| */ |
| template<class E, std::size_t Rows, std::size_t Cols> |
| inline |
| XprVector< |
| XprMatrixCol< |
| XprMatrix<E, Rows, Cols>, |
| Rows, Cols |
| >, |
| Rows |
| > |
| col(const XprMatrix<E, Rows, Cols>& m, std::size_t no) { |
| typedef XprMatrixCol< |
| XprMatrix<E, Rows, Cols>, |
| Rows, Cols |
| > expr_type; |
| |
| return XprVector<expr_type, Cols>(expr_type(m, no)); |
| } |
| |
| |
| /** |
| * \fn diag(const XprMatrix<E, Sz, Sz>& m) |
| * \brief Returns the diagonal vector of the given square matrix. |
| * \ingroup _unary_function |
| */ |
| template<class E, std::size_t Sz> |
| inline |
| XprVector< |
| XprMatrixDiag< |
| XprMatrix<E, Sz, Sz>, |
| Sz |
| >, |
| Sz |
| > |
| diag(const XprMatrix<E, Sz, Sz>& m) { |
| typedef XprMatrixDiag< |
| XprMatrix<E, Sz, Sz>, |
| Sz> expr_type; |
| |
| return XprVector<expr_type, Sz>(expr_type(m)); |
| } |
| |
| |
| } // namespace tvmet |
| |
| #endif // TVMET_XPR_MATRIX_FUNCTIONS_H |
| |
| // Local Variables: |
| // mode:C++ |
| // End: |
