/*
 * 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: VectorFunctions.h,v 1.21 2007-06-23 15:59:00 opetzold Exp $
 */

#ifndef TVMET_XPR_VECTOR_FUNCTIONS_H
#define TVMET_XPR_VECTOR_FUNCTIONS_H

namespace tvmet {


/* forwards */
template<class T, std::size_t Sz> class Vector;


/*********************************************************
 * PART I: DECLARATION
 *********************************************************/


/*++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 * Vector arithmetic functions add, sub, mul and div
 *+++++++++++++++++++++++++++++++++++++++++++++++++++++++*/


/*
 * function(XprVector<E1, Sz>, XprVector<E2, Sz>)
 */
#define TVMET_DECLARE_MACRO(NAME)                    \
template<class E1, class E2, std::size_t Sz>                \
XprVector<                                \
  XprBinOp<                                \
    Fcnl_##NAME<typename E1::value_type, typename E2::value_type>,    \
    XprVector<E1, Sz>,                            \
    XprVector<E2, Sz>                            \
  >,                                    \
  Sz                                    \
>                                    \
NAME (const XprVector<E1, Sz>& lhs,                    \
      const XprVector<E2, Sz>& rhs) TVMET_CXX_ALWAYS_INLINE;

TVMET_DECLARE_MACRO(add)        // per se element wise
TVMET_DECLARE_MACRO(sub)        // per se element wise
TVMET_DECLARE_MACRO(mul)        // per se element wise
namespace element_wise {
  TVMET_DECLARE_MACRO(div)        // not defined for vectors
}

#undef TVMET_DECLARE_MACRO


/*
 * function(XprVector<E, Sz>, POD)
 * function(POD, XprVector<E, Sz>)
 * Note: - operations +,-,*,/ are per se element wise
 */
#define TVMET_DECLARE_MACRO(NAME, POD)                \
template<class E, std::size_t Sz>                \
XprVector<                            \
  XprBinOp<                            \
    Fcnl_##NAME< typename E::value_type, POD >,            \
    XprVector<E, Sz>,                        \
    XprLiteral< POD >                        \
  >,                                \
  Sz                                \
>                                \
NAME (const XprVector<E, Sz>& lhs,                 \
      POD rhs) TVMET_CXX_ALWAYS_INLINE;                \
                                \
template<class E, std::size_t Sz>                \
XprVector<                            \
  XprBinOp<                            \
    Fcnl_##NAME< POD, typename E::value_type>,            \
    XprLiteral< POD >,                        \
    XprVector<E, Sz>                        \
  >,                                \
  Sz                                \
>                                \
NAME (POD lhs,                             \
      const XprVector<E, Sz>& 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, std::size_t Sz, class T>            \
XprVector<                            \
  XprBinOp<                            \
    Fcnl_##NAME< typename E::value_type, std::complex<T> >,    \
    XprVector<E, Sz>,                        \
    XprLiteral< std::complex<T> >                \
  >,                                \
  Sz                                \
>                                \
NAME (const XprVector<E, Sz>& lhs,                \
      const std::complex<T>& rhs) TVMET_CXX_ALWAYS_INLINE;    \
                                \
template<class E, std::size_t Sz, class T>            \
XprVector<                            \
  XprBinOp<                            \
    Fcnl_##NAME< std::complex<T>, typename E::value_type>,    \
    XprLiteral< std::complex<T> >,                \
    XprVector<E, Sz>                        \
  >,                                \
  Sz                                \
>                                \
NAME (const std::complex<T>& lhs,                 \
      const XprVector<E, Sz>& 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)


/*++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 * vector specific functions
 *+++++++++++++++++++++++++++++++++++++++++++++++++++++++*/


template<class E, std::size_t Sz>
typename NumericTraits<typename E::value_type>::sum_type
sum(const XprVector<E, Sz>& v) TVMET_CXX_ALWAYS_INLINE;


template<class E, std::size_t Sz>
typename NumericTraits<typename E::value_type>::sum_type
product(const XprVector<E, Sz>& v) TVMET_CXX_ALWAYS_INLINE;


template<class E1, class E2, std::size_t Sz>
typename PromoteTraits<
  typename E1::value_type,
  typename E2::value_type
>::value_type
dot(const XprVector<E1, Sz>& lhs,
    const XprVector<E2, Sz>& rhs) TVMET_CXX_ALWAYS_INLINE;


template<class T, class E, std::size_t Sz>
typename PromoteTraits<T, typename E::value_type>::value_type
dot(const Vector<T, Sz>& lhs,
    const XprVector<E, Sz>& rhs) TVMET_CXX_ALWAYS_INLINE;


template<class E, class T, std::size_t Sz>
typename PromoteTraits<T, typename E::value_type>::value_type
dot(const XprVector<E, Sz>& lhs,
    const Vector<T, Sz>& rhs) TVMET_CXX_ALWAYS_INLINE;


template<class E1, class E2>
Vector<
  typename PromoteTraits<
    typename E1::value_type,
    typename E2::value_type
  >::value_type,
  3
>
cross(const XprVector<E1, 3>& lhs,
      const XprVector<E2, 3>& rhs) TVMET_CXX_ALWAYS_INLINE;


template<class T, class E>
Vector<
  typename PromoteTraits<T, typename E::value_type>::value_type, 3>
cross(const Vector<T, 3>& lhs,
      const XprVector<E, 3>& rhs) TVMET_CXX_ALWAYS_INLINE;


template<class E, class T>
Vector<
  typename PromoteTraits<T, typename E::value_type>::value_type, 3>
cross(const XprVector<E, 3>& lhs,
      const Vector<T, 3>& rhs) TVMET_CXX_ALWAYS_INLINE;


template<class E, std::size_t Sz>
typename NumericTraits<typename E::value_type>::sum_type
norm1(const XprVector<E, Sz>& v) TVMET_CXX_ALWAYS_INLINE;


template<class E, std::size_t Sz>
typename NumericTraits<typename E::value_type>::sum_type
norm2(const XprVector<E, Sz>& v) TVMET_CXX_ALWAYS_INLINE;


template<class E, std::size_t Sz>
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) TVMET_CXX_ALWAYS_INLINE;


/*********************************************************
 * PART II: IMPLEMENTATION
 *********************************************************/


/*
 * function(XprVector<E1, Sz>, XprVector<E2, Sz>)
 */
#define TVMET_IMPLEMENT_MACRO(NAME)                    \
template<class E1, class E2, std::size_t Sz>                \
inline                                    \
XprVector<                                \
  XprBinOp<                                \
    Fcnl_##NAME<typename E1::value_type, typename E2::value_type>,    \
    XprVector<E1, Sz>,                            \
    XprVector<E2, Sz>                            \
  >,                                    \
  Sz                                    \
>                                    \
NAME (const XprVector<E1, Sz>& lhs, const XprVector<E2, Sz>& rhs) {    \
  typedef XprBinOp<                            \
    Fcnl_##NAME<typename E1::value_type, typename E2::value_type>,    \
    XprVector<E1, Sz>,                            \
    XprVector<E2, Sz>                            \
  >                              expr_type;    \
  return XprVector<expr_type, Sz>(expr_type(lhs, rhs));            \
}

TVMET_IMPLEMENT_MACRO(add)        // per se element wise
TVMET_IMPLEMENT_MACRO(sub)        // per se element wise
TVMET_IMPLEMENT_MACRO(mul)        // per se element wise
namespace element_wise {
  TVMET_IMPLEMENT_MACRO(div)        // not defined for vectors
}

#undef TVMET_IMPLEMENT_MACRO


/*
 * function(XprVector<E, Sz>, POD)
 * function(POD, XprVector<E, Sz>)
 * Note: - operations +,-,*,/ are per se element wise
 */
#define TVMET_IMPLEMENT_MACRO(NAME, POD)                \
template<class E, std::size_t Sz>                    \
inline                                    \
XprVector<                                \
  XprBinOp<                                \
    Fcnl_##NAME< typename E::value_type, POD >,                \
    XprVector<E, Sz>,                            \
    XprLiteral< POD >                            \
  >,                                    \
  Sz                                    \
>                                    \
NAME (const XprVector<E, Sz>& lhs, POD rhs) {                \
  typedef XprBinOp<                            \
    Fcnl_##NAME< typename E::value_type, POD >,                \
    XprVector<E, Sz>,                            \
    XprLiteral< POD >                            \
  >                            expr_type;    \
  return XprVector<expr_type, Sz>(                    \
    expr_type(lhs, XprLiteral< POD >(rhs)));                \
}                                    \
                                    \
template<class E, std::size_t Sz>                    \
inline                                    \
XprVector<                                \
  XprBinOp<                                \
    Fcnl_##NAME< POD, typename E::value_type>,                \
    XprLiteral< POD >,                            \
    XprVector<E, Sz>                            \
  >,                                    \
  Sz                                    \
>                                    \
NAME (POD lhs, const XprVector<E, Sz>& rhs) {                \
  typedef XprBinOp<                            \
    Fcnl_##NAME< POD, typename E::value_type>,                \
    XprLiteral< POD >,                            \
    XprVector<E, Sz>                            \
  >                            expr_type;    \
  return XprVector<expr_type, Sz>(                    \
    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, std::size_t Sz, class T>                \
inline                                    \
XprVector<                                \
  XprBinOp<                                \
    Fcnl_##NAME< typename E::value_type, std::complex<T> >,        \
    XprVector<E, Sz>,                            \
    XprLiteral< std::complex<T> >                    \
  >,                                    \
  Sz                                    \
>                                    \
NAME (const XprVector<E, Sz>& lhs, const std::complex<T>& rhs) {    \
  typedef XprBinOp<                            \
    Fcnl_##NAME< typename E::value_type, std::complex<T> >,        \
    XprVector<E, Sz>,                            \
    XprLiteral< std::complex<T> >                    \
  >                            expr_type;    \
  return XprVector<expr_type, Sz>(                    \
    expr_type(lhs, XprLiteral< std::complex<T> >(rhs)));        \
}                                    \
                                    \
template<class E, std::size_t Sz, class T>                \
inline                                    \
XprVector<                                \
  XprBinOp<                                \
    Fcnl_##NAME< std::complex<T>, typename E::value_type>,        \
    XprLiteral< std::complex<T> >,                    \
    XprVector<E, Sz>                            \
  >,                                    \
  Sz                                    \
>                                    \
NAME (const std::complex<T>& lhs, const XprVector<E, Sz>& rhs) {    \
  typedef XprBinOp<                            \
    Fcnl_##NAME< std::complex<T>, typename E::value_type>,        \
    XprLiteral< std::complex<T> >,                    \
    XprVector<E, Sz>                            \
  >                            expr_type;    \
  return XprVector<expr_type, Sz>(                    \
    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)


/*++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 * vector specific functions
 *+++++++++++++++++++++++++++++++++++++++++++++++++++++++*/


/**
 * \fn sum(const XprVector<E, Sz>& v)
 * \brief Compute the sum of the vector expression.
 * \ingroup _unary_function
 *
 * Simply compute the sum of the given vector as:
 * \f[
 * \sum_{i = 0}^{Sz-1} v[i]
 * \f]
 */
template<class E, std::size_t Sz>
inline
typename NumericTraits<typename E::value_type>::sum_type
sum(const XprVector<E, Sz>& v) {
  return meta::Vector<Sz>::sum(v);
}


/**
 * \fn product(const XprVector<E, Sz>& v)
 * \brief Compute the product of the vector elements.
 * \ingroup _unary_function
 *
 * Simply computer the product of the given vector expression as:
 * \f[
 * \prod_{i = 0}^{Sz - 1} v[i]
 * \f]
 */
template<class E, std::size_t Sz>
inline
typename NumericTraits<typename E::value_type>::sum_type
product(const XprVector<E, Sz>& v) {
  return meta::Vector<Sz>::product(v);
}


/**
 * \fn dot(const XprVector<E1, Sz>& lhs, const XprVector<E2, Sz>& rhs)
 * \brief Compute the dot/inner product
 * \ingroup _binary_function
 *
 * Compute the dot product as:
 * \f[
 * \sum_{i = 0}^{Sz - 1} ( lhs[i] * rhs[i] )
 * \f]
 * where lhs is a column vector and rhs is a row vector, both vectors
 * have the same dimension.
 */
template<class E1, class E2, std::size_t Sz>
inline
typename PromoteTraits<
  typename E1::value_type,
  typename E2::value_type
>::value_type
dot(const XprVector<E1, Sz>& lhs, const XprVector<E2, Sz>& rhs) {
  return meta::Vector<Sz>::dot(lhs, rhs);
}


/**
 * \fn dot(const Vector<T, Sz>& lhs, const XprVector<E, Sz>& rhs)
 * \brief Compute the dot/inner product
 * \ingroup _binary_function
 *
 * Compute the dot product as:
 * \f[
 * \sum_{i = 0}^{Sz - 1} ( lhs[i] * rhs[i] )
 * \f]
 * where lhs is a column vector and rhs is a row vector, both vectors
 * have the same dimension.
 */
template<class T, class E, std::size_t Sz>
inline
typename PromoteTraits<T, typename E::value_type>::value_type
dot(const Vector<T, Sz>& lhs, const XprVector<E, Sz>& rhs) {
  return meta::Vector<Sz>::dot(lhs, rhs);
}


/**
 * \fn dot(const XprVector<E, Sz>& lhs, const Vector<T, Sz>& rhs)
 * \brief Compute the dot/inner product
 * \ingroup _binary_function
 *
 * Compute the dot product as:
 * \f[
 * \sum_{i = 0}^{Sz - 1} ( lhs[i] * rhs[i] )
 * \f]
 * where lhs is a column vector and rhs is a row vector, both vectors
 * have the same dimension.
 */
template<class E, class T, std::size_t Sz>
inline
typename PromoteTraits<T, typename E::value_type>::value_type
dot(const XprVector<E, Sz>& lhs, const Vector<T, Sz>& rhs) {
  return meta::Vector<Sz>::dot(lhs, rhs);
}


/**
 * \fn cross(const XprVector<E1, 3>& lhs, const XprVector<E2, 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 E1, class E2>
inline
Vector<
  typename PromoteTraits<
    typename E1::value_type,
    typename E2::value_type
  >::value_type,
  3
>
cross(const XprVector<E1, 3>& lhs, const XprVector<E2, 3>& rhs) {
  typedef typename PromoteTraits<
    typename E1::value_type,
    typename E2::value_type
  >::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 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, std::size_t Sz>
inline
typename NumericTraits<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, std::size_t Sz>
inline
typename NumericTraits<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, std::size_t 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++
// tab-width:8
// End:
