656 lines
18 KiB
C++
656 lines
18 KiB
C++
/*
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* Tiny Vector Matrix Library
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* Dense Vector Matrix Libary of Tiny size using Expression Templates
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*
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* Copyright (C) 2001 - 2003 Olaf Petzold <opetzold@users.sourceforge.net>
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*
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* This library is free software; you can redistribute it and/or
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* modify it under the terms of the GNU Lesser General Public
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* License as published by the Free Software Foundation; either
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* version 2.1 of the License, or (at your option) any later version.
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*
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* This library is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* Lesser General Public License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public
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* License along with this library; if not, write to the Free Software
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* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
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*
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* $Id: VectorFunctions.h,v 1.17 2005/03/25 07:11:29 opetzold Exp $
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*/
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#ifndef TVMET_XPR_VECTOR_FUNCTIONS_H
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#define TVMET_XPR_VECTOR_FUNCTIONS_H
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namespace tvmet {
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/* forwards */
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template<class T, int Sz> class Vector;
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/*********************************************************
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* PART I: DECLARATION
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*********************************************************/
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/*++++++++++++++++++++++++++++++++++++++++++++++++++++++++
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* Vector arithmetic functions add, sub, mul and div
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*+++++++++++++++++++++++++++++++++++++++++++++++++++++++*/
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/*
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* function(XprVector<E1, Sz>, XprVector<E2, Sz>)
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*/
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#define TVMET_DECLARE_MACRO(NAME) \
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template<class E1, class E2, int Sz> \
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XprVector< \
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XprBinOp< \
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Fcnl_##NAME<typename E1::value_type, typename E2::value_type>, \
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XprVector<E1, Sz>, \
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XprVector<E2, Sz> \
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>, \
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Sz \
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> \
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NAME (const XprVector<E1, Sz>& lhs, \
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const XprVector<E2, Sz>& rhs) _tvmet_always_inline;
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TVMET_DECLARE_MACRO(add) // per se element wise
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TVMET_DECLARE_MACRO(sub) // per se element wise
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TVMET_DECLARE_MACRO(mul) // per se element wise
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namespace element_wise {
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TVMET_DECLARE_MACRO(div) // not defined for vectors
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}
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#undef TVMET_DECLARE_MACRO
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/*
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* function(XprVector<E, Sz>, POD)
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* function(POD, XprVector<E, Sz>)
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* Note: - operations +,-,*,/ are per se element wise
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*/
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#define TVMET_DECLARE_MACRO(NAME, POD) \
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template<class E, int Sz> \
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XprVector< \
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XprBinOp< \
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Fcnl_##NAME< typename E::value_type, POD >, \
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XprVector<E, Sz>, \
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XprLiteral< POD > \
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>, \
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Sz \
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> \
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NAME (const XprVector<E, Sz>& lhs, \
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POD rhs) _tvmet_always_inline; \
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\
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template<class E, int Sz> \
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XprVector< \
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XprBinOp< \
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Fcnl_##NAME< POD, typename E::value_type>, \
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XprLiteral< POD >, \
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XprVector<E, Sz> \
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>, \
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Sz \
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> \
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NAME (POD lhs, \
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const XprVector<E, Sz>& rhs) _tvmet_always_inline;
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TVMET_DECLARE_MACRO(add, int)
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TVMET_DECLARE_MACRO(sub, int)
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TVMET_DECLARE_MACRO(mul, int)
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TVMET_DECLARE_MACRO(div, int)
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TVMET_DECLARE_MACRO(add, float)
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TVMET_DECLARE_MACRO(sub, float)
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TVMET_DECLARE_MACRO(mul, float)
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TVMET_DECLARE_MACRO(div, float)
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TVMET_DECLARE_MACRO(add, double)
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TVMET_DECLARE_MACRO(sub, double)
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TVMET_DECLARE_MACRO(mul, double)
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TVMET_DECLARE_MACRO(div, double)
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#undef TVMET_DECLARE_MACRO
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#if defined(EIGEN_USE_COMPLEX)
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/*
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* function(XprMatrix<E, Rows, Cols>, complex<T>)
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* function(complex<T>, XprMatrix<E, Rows, Cols>)
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* Note: - operations +,-,*,/ are per se element wise
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* \todo type promotion
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*/
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#define TVMET_DECLARE_MACRO(NAME) \
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template<class E, int Sz, class T> \
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XprVector< \
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XprBinOp< \
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Fcnl_##NAME< typename E::value_type, std::complex<T> >, \
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XprVector<E, Sz>, \
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XprLiteral< std::complex<T> > \
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>, \
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Sz \
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> \
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NAME (const XprVector<E, Sz>& lhs, \
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const std::complex<T>& rhs) _tvmet_always_inline; \
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\
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template<class E, int Sz, class T> \
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XprVector< \
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XprBinOp< \
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Fcnl_##NAME< std::complex<T>, typename E::value_type>, \
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XprLiteral< std::complex<T> >, \
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XprVector<E, Sz> \
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>, \
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Sz \
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> \
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NAME (const std::complex<T>& lhs, \
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const XprVector<E, Sz>& rhs) _tvmet_always_inline;
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TVMET_DECLARE_MACRO(add)
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TVMET_DECLARE_MACRO(sub)
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TVMET_DECLARE_MACRO(mul)
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TVMET_DECLARE_MACRO(div)
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#undef TVMET_DECLARE_MACRO
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#endif // defined(EIGEN_USE_COMPLEX)
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/*++++++++++++++++++++++++++++++++++++++++++++++++++++++++
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* vector specific functions
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*+++++++++++++++++++++++++++++++++++++++++++++++++++++++*/
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template<class E, int Sz>
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typename Traits<typename E::value_type>::sum_type
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sum(const XprVector<E, Sz>& v) _tvmet_always_inline;
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template<class E, int Sz>
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typename Traits<typename E::value_type>::sum_type
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product(const XprVector<E, Sz>& v) _tvmet_always_inline;
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template<class E1, class E2, int Sz>
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typename PromoteTraits<
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typename E1::value_type,
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typename E2::value_type
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>::value_type
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dot(const XprVector<E1, Sz>& lhs,
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const XprVector<E2, Sz>& rhs) _tvmet_always_inline;
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template<class T, class E, int Sz>
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typename PromoteTraits<T, typename E::value_type>::value_type
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dot(const Vector<T, Sz>& lhs,
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const XprVector<E, Sz>& rhs) _tvmet_always_inline;
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template<class E, class T, int Sz>
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typename PromoteTraits<T, typename E::value_type>::value_type
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dot(const XprVector<E, Sz>& lhs,
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const Vector<T, Sz>& rhs) _tvmet_always_inline;
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template<class E1, class E2>
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Vector<
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typename PromoteTraits<
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typename E1::value_type,
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typename E2::value_type
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>::value_type,
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3
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>
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cross(const XprVector<E1, 3>& lhs,
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const XprVector<E2, 3>& rhs) _tvmet_always_inline;
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template<class T, class E>
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Vector<
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typename PromoteTraits<T, typename E::value_type>::value_type, 3>
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cross(const Vector<T, 3>& lhs,
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const XprVector<E, 3>& rhs) _tvmet_always_inline;
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template<class E, class T>
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Vector<
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typename PromoteTraits<T, typename E::value_type>::value_type, 3>
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cross(const XprVector<E, 3>& lhs,
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const Vector<T, 3>& rhs) _tvmet_always_inline;
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template<class E, int Sz>
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typename Traits<typename E::value_type>::sum_type
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norm1(const XprVector<E, Sz>& v) _tvmet_always_inline;
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template<class E, int Sz>
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typename Traits<typename E::value_type>::sum_type
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norm2(const XprVector<E, Sz>& v) _tvmet_always_inline;
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template<class E, int Sz>
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XprVector<
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XprBinOp<
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Fcnl_div<typename E::value_type, typename E::value_type>,
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XprVector<E, Sz>,
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XprLiteral<typename E::value_type>
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>,
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Sz
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>
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normalize(const XprVector<E, Sz>& v) _tvmet_always_inline;
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/*********************************************************
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* PART II: IMPLEMENTATION
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*********************************************************/
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/*
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* function(XprVector<E1, Sz>, XprVector<E2, Sz>)
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*/
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#define TVMET_IMPLEMENT_MACRO(NAME) \
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template<class E1, class E2, int Sz> \
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inline \
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XprVector< \
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XprBinOp< \
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Fcnl_##NAME<typename E1::value_type, typename E2::value_type>, \
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XprVector<E1, Sz>, \
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XprVector<E2, Sz> \
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>, \
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Sz \
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> \
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NAME (const XprVector<E1, Sz>& lhs, const XprVector<E2, Sz>& rhs) { \
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typedef XprBinOp< \
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Fcnl_##NAME<typename E1::value_type, typename E2::value_type>, \
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XprVector<E1, Sz>, \
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XprVector<E2, Sz> \
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> expr_type; \
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return XprVector<expr_type, Sz>(expr_type(lhs, rhs)); \
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}
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TVMET_IMPLEMENT_MACRO(add) // per se element wise
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TVMET_IMPLEMENT_MACRO(sub) // per se element wise
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TVMET_IMPLEMENT_MACRO(mul) // per se element wise
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namespace element_wise {
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TVMET_IMPLEMENT_MACRO(div) // not defined for vectors
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}
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#undef TVMET_IMPLEMENT_MACRO
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/*
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* function(XprVector<E, Sz>, POD)
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* function(POD, XprVector<E, Sz>)
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* Note: - operations +,-,*,/ are per se element wise
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*/
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#define TVMET_IMPLEMENT_MACRO(NAME, POD) \
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template<class E, int Sz> \
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inline \
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XprVector< \
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XprBinOp< \
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Fcnl_##NAME< typename E::value_type, POD >, \
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XprVector<E, Sz>, \
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XprLiteral< POD > \
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>, \
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Sz \
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> \
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NAME (const XprVector<E, Sz>& lhs, POD rhs) { \
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typedef XprBinOp< \
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Fcnl_##NAME< typename E::value_type, POD >, \
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XprVector<E, Sz>, \
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XprLiteral< POD > \
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> expr_type; \
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return XprVector<expr_type, Sz>( \
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expr_type(lhs, XprLiteral< POD >(rhs))); \
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} \
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\
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template<class E, int Sz> \
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inline \
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XprVector< \
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XprBinOp< \
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Fcnl_##NAME< POD, typename E::value_type>, \
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XprLiteral< POD >, \
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XprVector<E, Sz> \
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>, \
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Sz \
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> \
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NAME (POD lhs, const XprVector<E, Sz>& rhs) { \
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typedef XprBinOp< \
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Fcnl_##NAME< POD, typename E::value_type>, \
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XprLiteral< POD >, \
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XprVector<E, Sz> \
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> expr_type; \
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return XprVector<expr_type, Sz>( \
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expr_type(XprLiteral< POD >(lhs), rhs)); \
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}
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TVMET_IMPLEMENT_MACRO(add, int)
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TVMET_IMPLEMENT_MACRO(sub, int)
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TVMET_IMPLEMENT_MACRO(mul, int)
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TVMET_IMPLEMENT_MACRO(div, int)
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TVMET_IMPLEMENT_MACRO(add, float)
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TVMET_IMPLEMENT_MACRO(sub, float)
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TVMET_IMPLEMENT_MACRO(mul, float)
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TVMET_IMPLEMENT_MACRO(div, float)
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TVMET_IMPLEMENT_MACRO(add, double)
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TVMET_IMPLEMENT_MACRO(sub, double)
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TVMET_IMPLEMENT_MACRO(mul, double)
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TVMET_IMPLEMENT_MACRO(div, double)
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#undef TVMET_IMPLEMENT_MACRO
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#if defined(EIGEN_USE_COMPLEX)
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/*
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* function(XprMatrix<E, Rows, Cols>, complex<T>)
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* function(complex<T>, XprMatrix<E, Rows, Cols>)
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* Note: - operations +,-,*,/ are per se element wise
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* \todo type promotion
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*/
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#define TVMET_IMPLEMENT_MACRO(NAME) \
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template<class E, int Sz, class T> \
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inline \
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XprVector< \
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XprBinOp< \
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Fcnl_##NAME< typename E::value_type, std::complex<T> >, \
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XprVector<E, Sz>, \
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XprLiteral< std::complex<T> > \
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>, \
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Sz \
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> \
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NAME (const XprVector<E, Sz>& lhs, const std::complex<T>& rhs) { \
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typedef XprBinOp< \
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Fcnl_##NAME< typename E::value_type, std::complex<T> >, \
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XprVector<E, Sz>, \
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XprLiteral< std::complex<T> > \
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> expr_type; \
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return XprVector<expr_type, Sz>( \
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expr_type(lhs, XprLiteral< std::complex<T> >(rhs))); \
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} \
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\
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template<class E, int Sz, class T> \
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inline \
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XprVector< \
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XprBinOp< \
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Fcnl_##NAME< std::complex<T>, typename E::value_type>, \
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XprLiteral< std::complex<T> >, \
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XprVector<E, Sz> \
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>, \
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Sz \
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> \
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NAME (const std::complex<T>& lhs, const XprVector<E, Sz>& rhs) { \
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typedef XprBinOp< \
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Fcnl_##NAME< std::complex<T>, typename E::value_type>, \
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XprLiteral< std::complex<T> >, \
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XprVector<E, Sz> \
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> expr_type; \
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return XprVector<expr_type, Sz>( \
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expr_type(XprLiteral< std::complex<T> >(lhs), rhs)); \
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}
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TVMET_IMPLEMENT_MACRO(add)
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TVMET_IMPLEMENT_MACRO(sub)
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TVMET_IMPLEMENT_MACRO(mul)
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TVMET_IMPLEMENT_MACRO(div)
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#undef TVMET_IMPLEMENT_MACRO
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#endif // defined(EIGEN_USE_COMPLEX)
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/*++++++++++++++++++++++++++++++++++++++++++++++++++++++++
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* vector specific functions
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*+++++++++++++++++++++++++++++++++++++++++++++++++++++++*/
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/**
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* \fn sum(const XprVector<E, Sz>& v)
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* \brief Compute the sum of the vector expression.
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* \ingroup _unary_function
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*
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* Simply compute the sum of the given vector as:
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* \f[
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* \sum_{i = 0}^{Sz-1} v[i]
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* \f]
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*/
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template<class E, int Sz>
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inline
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typename Traits<typename E::value_type>::sum_type
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sum(const XprVector<E, Sz>& v) {
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return meta::Vector<Sz>::sum(v);
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}
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/**
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* \fn product(const XprVector<E, Sz>& v)
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* \brief Compute the product of the vector elements.
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* \ingroup _unary_function
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*
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* Simply computer the product of the given vector expression as:
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* \f[
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* \prod_{i = 0}^{Sz - 1} v[i]
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* \f]
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*/
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template<class E, int Sz>
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inline
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typename Traits<typename E::value_type>::sum_type
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product(const XprVector<E, Sz>& v) {
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return meta::Vector<Sz>::product(v);
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}
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/**
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* \fn dot(const XprVector<E1, Sz>& lhs, const XprVector<E2, Sz>& rhs)
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* \brief Compute the dot/inner product
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* \ingroup _binary_function
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*
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* Compute the dot product as:
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* \f[
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* \sum_{i = 0}^{Sz - 1} ( lhs[i] * rhs[i] )
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* \f]
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* where lhs is a column vector and rhs is a row vector, both vectors
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* have the same dimension.
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*/
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template<class E1, class E2, int Sz>
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inline
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typename PromoteTraits<
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typename E1::value_type,
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typename E2::value_type
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>::value_type
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dot(const XprVector<E1, Sz>& lhs, const XprVector<E2, Sz>& rhs) {
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return meta::Vector<Sz>::dot(lhs, rhs);
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}
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/**
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* \fn dot(const Vector<T, Sz>& lhs, const XprVector<E, Sz>& rhs)
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* \brief Compute the dot/inner product
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* \ingroup _binary_function
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*
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* Compute the dot product as:
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* \f[
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* \sum_{i = 0}^{Sz - 1} ( lhs[i] * rhs[i] )
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* \f]
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* where lhs is a column vector and rhs is a row vector, both vectors
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* have the same dimension.
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*/
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template<class T, class E, int Sz>
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inline
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typename PromoteTraits<T, typename E::value_type>::value_type
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dot(const Vector<T, Sz>& lhs, const XprVector<E, Sz>& rhs) {
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return meta::Vector<Sz>::dot(lhs, rhs);
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}
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/**
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* \fn dot(const XprVector<E, Sz>& lhs, const Vector<T, Sz>& rhs)
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* \brief Compute the dot/inner product
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* \ingroup _binary_function
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*
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* Compute the dot product as:
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* \f[
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* \sum_{i = 0}^{Sz - 1} ( lhs[i] * rhs[i] )
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* \f]
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* where lhs is a column vector and rhs is a row vector, both vectors
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* have the same dimension.
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*/
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template<class E, class T, int Sz>
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inline
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typename PromoteTraits<T, typename E::value_type>::value_type
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dot(const XprVector<E, Sz>& lhs, const Vector<T, Sz>& rhs) {
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return meta::Vector<Sz>::dot(lhs, rhs);
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}
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/**
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* \fn cross(const XprVector<E1, 3>& lhs, const XprVector<E2, 3>& rhs)
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* \brief Compute the cross/outer product
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* \ingroup _binary_function
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* \note working only for vectors of size = 3
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* \todo Implement vector outer product as ET and MT, returning a XprVector
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|
*/
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|
template<class E1, class E2>
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|
inline
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|
Vector<
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|
typename PromoteTraits<
|
|
typename E1::value_type,
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|
typename E2::value_type
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|
>::value_type,
|
|
3
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|
>
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|
cross(const XprVector<E1, 3>& lhs, const XprVector<E2, 3>& rhs) {
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|
typedef typename PromoteTraits<
|
|
typename E1::value_type,
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|
typename E2::value_type
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>::value_type value_type;
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|
return Vector<value_type, 3>(lhs(1)*rhs(2) - rhs(1)*lhs(2),
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|
rhs(0)*lhs(2) - lhs(0)*rhs(2),
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lhs(0)*rhs(1) - rhs(0)*lhs(1));
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|
}
|
|
|
|
|
|
/**
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|
* \fn cross(const XprVector<E, 3>& lhs, const Vector<T, 3>& rhs)
|
|
* \brief Compute the cross/outer product
|
|
* \ingroup _binary_function
|
|
* \note working only for vectors of size = 3
|
|
* \todo Implement vector outer product as ET and MT, returning a XprVector
|
|
*/
|
|
template<class E, class T>
|
|
inline
|
|
Vector<
|
|
typename PromoteTraits<T, typename E::value_type>::value_type, 3>
|
|
cross(const XprVector<E, 3>& lhs, const Vector<T, 3>& rhs) {
|
|
typedef typename PromoteTraits<
|
|
typename E::value_type, T>::value_type value_type;
|
|
return Vector<value_type, 3>(lhs(1)*rhs(2) - rhs(1)*lhs(2),
|
|
rhs(0)*lhs(2) - lhs(0)*rhs(2),
|
|
lhs(0)*rhs(1) - rhs(0)*lhs(1));
|
|
}
|
|
|
|
|
|
/**
|
|
* \fn cross(const Vector<T, 3>& lhs, const XprVector<E, 3>& rhs)
|
|
* \brief Compute the cross/outer product
|
|
* \ingroup _binary_function
|
|
* \note working only for vectors of size = 3
|
|
* \todo Implement vector outer product as ET and MT, returning a XprVector
|
|
*/
|
|
template<class T1, class E2>
|
|
inline
|
|
Vector<
|
|
typename PromoteTraits<T1, typename E2::value_type>::value_type, 3>
|
|
cross(const Vector<T1, 3>& lhs, const XprVector<E2, 3>& rhs) {
|
|
typedef typename PromoteTraits<
|
|
typename E2::value_type, T1>::value_type value_type;
|
|
return Vector<value_type, 3>(lhs(1)*rhs(2) - rhs(1)*lhs(2),
|
|
rhs(0)*lhs(2) - lhs(0)*rhs(2),
|
|
lhs(0)*rhs(1) - rhs(0)*lhs(1));
|
|
}
|
|
|
|
|
|
/**
|
|
* \fn norm1(const XprVector<E, Sz>& v)
|
|
* \brief The \f$l_1\f$ norm of a vector expression.
|
|
* \ingroup _unary_function
|
|
* The norm of any vector is just the square root of the dot product of
|
|
* a vector with itself, or
|
|
*
|
|
* \f[
|
|
* |Vector<T, Sz> v| = |v| = \sum_{i=0}^{Sz-1}\,|v[i]|
|
|
* \f]
|
|
*/
|
|
template<class E, int Sz>
|
|
inline
|
|
typename Traits<typename E::value_type>::sum_type
|
|
norm1(const XprVector<E, Sz>& v) {
|
|
return sum(abs(v));
|
|
}
|
|
|
|
|
|
/**
|
|
* \fn norm2(const XprVector<E, Sz>& v)
|
|
* \brief The euklidian norm (or \f$l_2\f$ norm) of a vector expression.
|
|
* \ingroup _unary_function
|
|
* The norm of any vector is just the square root of the dot product of
|
|
* a vector with itself, or
|
|
*
|
|
* \f[
|
|
* |Vector<T, Sz> v| = |v| = \sqrt{ \sum_{i=0}^{Sz-1}\,v[i]^2 }
|
|
* \f]
|
|
*
|
|
* \note The internal cast for Vector<int> avoids warnings on sqrt.
|
|
*/
|
|
template<class E, int Sz>
|
|
inline
|
|
typename Traits<typename E::value_type>::sum_type
|
|
norm2(const XprVector<E, Sz>& v) {
|
|
typedef typename E::value_type value_type;
|
|
return static_cast<value_type>( std::sqrt(static_cast<value_type>(dot(v, v))) );
|
|
}
|
|
|
|
|
|
/**
|
|
* \fn normalize(const XprVector<E, Sz>& v)
|
|
* \brief Normalize the given vector expression.
|
|
* \ingroup _unary_function
|
|
* \sa norm2
|
|
*
|
|
* using the equation:
|
|
* \f[
|
|
* \frac{Vector<T, Sz> v}{\sqrt{ \sum_{i=0}^{Sz-1}\,v[i]^2 }}
|
|
* \f]
|
|
*/
|
|
template<class E, int Sz>
|
|
inline
|
|
XprVector<
|
|
XprBinOp<
|
|
Fcnl_div<typename E::value_type, typename E::value_type>,
|
|
XprVector<E, Sz>,
|
|
XprLiteral<typename E::value_type>
|
|
>,
|
|
Sz
|
|
>
|
|
normalize(const XprVector<E, Sz>& v) {
|
|
typedef typename E::value_type value_type;
|
|
typedef XprBinOp<
|
|
Fcnl_div<value_type, value_type>,
|
|
XprVector<E, Sz>,
|
|
XprLiteral<value_type>
|
|
> expr_type;
|
|
return XprVector<expr_type, Sz>(
|
|
expr_type(v, XprLiteral< value_type >(norm2(v))));
|
|
}
|
|
|
|
|
|
} // namespace tvmet
|
|
|
|
#endif // TVMET_XPR_VECTOR_FUNCTIONS_H
|
|
|
|
// Local Variables:
|
|
// mode:C++
|
|
// End:
|