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tvmet/xpr/MatrixFunctions.h
- Committer:
- madcowswe
- Date:
- 2013-04-17
- Revision:
- 90:e4164bb8c60e
- Parent:
- 15:9c5aaeda36dc
File content as of revision 90:e4164bb8c60e:
/* * Tiny Vector Matrix Library * Dense Vector Matrix Libary of Tiny size using Expression Templates * * Copyright (C) 2001 - 2007 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 1.44 2007-06-23 15:59:00 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; 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; 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)); } /* * \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 expression 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); } /** * \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++ // tab-width:8 // End: