Shuto Naruse
Eurobot2012_Secondary
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Eurobot_2012_Secondary
by 
Shuto Naruse
Diff: tvmet/xpr/MatrixFunctions.h
- Revision:
- 1:cc2a9eb0bd55
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/tvmet/xpr/MatrixFunctions.h Wed Oct 17 22:25:31 2012 +0000
@@ -0,0 +1,761 @@
+/*
+ * 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: