Tiny Vector Matrix library using Expression Templates

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---

include/tvmet/MatrixFunctions.h

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/*
 * 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 1.65 2007-06-23 15:58:58 opetzold Exp $
 */

#ifndef TVMET_MATRIX_FUNCTIONS_H
#define TVMET_MATRIX_FUNCTIONS_H

#include <tvmet/Extremum.h>

namespace tvmet {

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


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


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


/*
 * function(Matrix<T1, Rows, Cols>, Matrix<T2, Rows, Cols>)
 * function(XprMatrix<E, Rows, Cols>, Matrix<T, Rows, Cols>)
 * function(Matrix<T, Rows, Cols>, XprMatrix<E, Rows, Cols>)
 */
#define TVMET_DECLARE_MACRO(NAME)         \
template<class T1, class T2, std::size_t Rows, std::size_t Cols>  \
XprMatrix<                \
  XprBinOp<               \
    Fcnl_##NAME<T1, T2>,            \
    MatrixConstReference<T1, Rows, Cols>,       \
    MatrixConstReference<T2, Rows, Cols>        \
  >,                  \
  Rows, Cols                \
>                 \
NAME (const Matrix<T1, Rows, Cols>& lhs,        \
      const Matrix<T2, Rows, Cols>& rhs) TVMET_CXX_ALWAYS_INLINE; \
                  \
template<class E, class T, std::size_t Rows, std::size_t Cols>    \
XprMatrix<                \
  XprBinOp<               \
    Fcnl_##NAME<typename E::value_type, T>,       \
    XprMatrix<E, Rows, Cols>,           \
    MatrixConstReference<T, Rows, Cols>         \
  >,                  \
  Rows, Cols                \
>                 \
NAME (const XprMatrix<E, Rows, Cols>& lhs,        \
      const Matrix<T, Rows, Cols>& rhs) TVMET_CXX_ALWAYS_INLINE;  \
                  \
template<class T, class E, std::size_t Rows, std::size_t Cols>    \
XprMatrix<                \
  XprBinOp<               \
    Fcnl_##NAME<typename E::value_type, T>,       \
    MatrixConstReference<T, Rows, Cols>,        \
    XprMatrix<E, Rows, Cols>            \
  >,                  \
  Rows, Cols                \
>                 \
NAME (const Matrix<T, Rows, Cols>& lhs,         \
      const XprMatrix<E, 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(Matrix<T, Rows, Cols>, POD)
 * function(POD, Matrix<T, Rows, Cols>)
 * Note: - operations +,-,*,/ are per se element wise
 */
#define TVMET_DECLARE_MACRO(NAME, POD)          \
template<class T, std::size_t Rows, std::size_t Cols>     \
XprMatrix<                \
  XprBinOp<               \
    Fcnl_##NAME<T, POD >,           \
    MatrixConstReference<T, Rows, Cols>,        \
    XprLiteral<POD >              \
  >,                  \
  Rows, Cols                \
>                 \
NAME (const Matrix<T, Rows, Cols>& lhs,         \
      POD rhs) TVMET_CXX_ALWAYS_INLINE;         \
                  \
template<class T, std::size_t Rows, std::size_t Cols>     \
XprMatrix<                \
  XprBinOp<               \
    Fcnl_##NAME< POD, T>,           \
    XprLiteral< POD >,              \
    MatrixConstReference<T, Rows, Cols>         \
  >,                  \
  Rows, Cols                \
>                 \
NAME (POD lhs,                \
      const Matrix<T, 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(Matrix<T, Rows, Cols>, complex<T>)
 * function(complex<T>, Matrix<T, Rows, Cols>)
 * Note: - operations +,-,*,/ are per se element wise
 * \todo type promotion
 */
#define TVMET_DECLARE_MACRO(NAME)           \
template<class T, std::size_t Rows, std::size_t Cols>       \
XprMatrix<                  \
  XprBinOp<                 \
    Fcnl_##NAME< std::complex<T>, std::complex<T> >,        \
    MatrixConstReference< std::complex<T>, Rows, Cols>,       \
    XprLiteral<std::complex<T> >            \
  >,                    \
  Rows, Cols                  \
>                   \
NAME (const Matrix< std::complex<T>, Rows, Cols>& lhs,        \
      const std::complex<T>& rhs) TVMET_CXX_ALWAYS_INLINE;      \
                    \
template<class T, std::size_t Rows, std::size_t Cols>       \
XprMatrix<                  \
  XprBinOp<                 \
    Fcnl_##NAME< std::complex<T>, std::complex<T> >,        \
    XprLiteral< std::complex<T> >,            \
    MatrixConstReference< std::complex<T>, Rows, Cols>        \
  >,                    \
  Rows, Cols                  \
>                   \
NAME (const std::complex<T>& lhs,           \
      const Matrix< std::complex<T>, 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 specific prod( ... ) functions
 *+++++++++++++++++++++++++++++++++++++++++++++++++++++++*/


template<class T1, std::size_t Rows1, std::size_t Cols1,
   class T2, std::size_t Cols2>
XprMatrix<
  XprMMProduct<
    MatrixConstReference<T1, Rows1, Cols1>, Rows1, Cols1, // M1(Rows1, Cols1)
    MatrixConstReference<T2, Cols1, Cols2>, Cols2     // M2(Cols1, Cols2)
  >,
  Rows1, Cols2              // return Dim
>
prod(const Matrix<T1, Rows1, Cols1>& lhs,
     const Matrix<T2, Cols1, Cols2>& rhs) TVMET_CXX_ALWAYS_INLINE;


template<class E1, std::size_t Rows1, std::size_t Cols1,
   class T2, std::size_t Cols2>
XprMatrix<
  XprMMProduct<
    XprMatrix<E1, Rows1, Cols1>, Rows1, Cols1,      // M1(Rows1, Cols1)
    MatrixConstReference<T2, Cols1, Cols2>, Cols2   // M2(Cols1, Cols2)
  >,
  Rows1, Cols2              // return Dim
>
prod(const XprMatrix<E1, Rows1, Cols1>& lhs,
     const Matrix<T2, Cols1, Cols2>& rhs) TVMET_CXX_ALWAYS_INLINE;


template<class T1, std::size_t Rows1, std::size_t Cols1,
   class E2, std::size_t Cols2>
XprMatrix<
  XprMMProduct<
    MatrixConstReference<T1, Rows1, Cols1>, Rows1, Cols1, // M1(Rows1, Cols1)
    XprMatrix<E2, Cols1, Cols2>, Cols2        // M2(Cols1, Cols2)
  >,
  Rows1, Cols2              // return Dim
>
prod(const Matrix<T1, Rows1, Cols1>& lhs,
     const XprMatrix<E2, Cols1, Cols2>& rhs) TVMET_CXX_ALWAYS_INLINE;


template<class T1, std::size_t Rows1, std::size_t Cols1,
   class T2, std::size_t Cols2>
XprMatrix<
  XprMMProductTransposed<
    MatrixConstReference<T1, Rows1, Cols1>, Rows1, Cols1, // M1(Rows1, Cols1)
    MatrixConstReference<T2, Cols1, Cols2>, Cols2   // M2(Cols1, Cols2)
  >,
  Cols2, Rows1              // return Dim
>
trans_prod(const Matrix<T1, Rows1, Cols1>& lhs,
     const Matrix<T2, Cols1, Cols2>& rhs) TVMET_CXX_ALWAYS_INLINE;


template<class T1, std::size_t Rows1, std::size_t Cols1,
   class T2, std::size_t Cols2> // Rows2 = Rows1
XprMatrix<
  XprMtMProduct<
    MatrixConstReference<T1, Rows1, Cols1>, Rows1, Cols1, // M1(Rows1, Cols1)
    MatrixConstReference<T2, Rows1, Cols2>, Cols2   // M2(Rows1, Cols2)
  >,
  Cols1, Cols2              // return Dim
>
MtM_prod(const Matrix<T1, Rows1, Cols1>& lhs,
   const Matrix<T2, Rows1, Cols2>& rhs) TVMET_CXX_ALWAYS_INLINE;


template<class T1, std::size_t Rows1, std::size_t Cols1,
   class T2, std::size_t Rows2>
XprMatrix<
  XprMMtProduct<
    MatrixConstReference<T1, Rows1, Cols1>, Rows1, Cols1, // M1(Rows1, Cols1)
    MatrixConstReference<T2, Rows2, Cols1>, Cols1     // M2(Rows2, Cols1)
  >,
  Rows1, Rows2              // return Dim
>
MMt_prod(const Matrix<T1, Rows1, Cols1>& lhs,
   const Matrix<T2, Rows2, Cols1>& rhs) TVMET_CXX_ALWAYS_INLINE;


/*++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 * matrix-vector specific prod( ... ) functions
 *+++++++++++++++++++++++++++++++++++++++++++++++++++++++*/


template<class T1, class T2, std::size_t Rows, std::size_t Cols>
XprVector<
  XprMVProduct<
    MatrixConstReference<T1, Rows, Cols>, Rows, Cols, // M(Rows, Cols)
    VectorConstReference<T2, Cols>      // V
  >,
  Rows
>
prod(const Matrix<T1, Rows, Cols>& lhs,
     const Vector<T2, Cols>& rhs) TVMET_CXX_ALWAYS_INLINE;


template<class T1, class E2, std::size_t Rows, std::size_t Cols>
XprVector<
  XprMVProduct<
    MatrixConstReference<T1, Rows, Cols>, Rows, Cols,
    XprVector<E2, Cols>
  >,
  Rows
>
prod(const Matrix<T1, Rows, Cols>& lhs,
     const XprVector<E2, Cols>& rhs) TVMET_CXX_ALWAYS_INLINE;


template<class E1, class T2, std::size_t Rows, std::size_t Cols>
XprVector<
  XprMVProduct<
    XprMatrix<E1, Rows, Cols>, Rows, Cols,    // M(Rows, Cols)
    VectorConstReference<T2, Cols>      // V
  >,
  Rows
>
prod(const XprMatrix<E1, Rows, Cols>& lhs,
     const Vector<T2, Cols>& rhs) TVMET_CXX_ALWAYS_INLINE;


template<class T1, class T2, std::size_t Rows, std::size_t Cols>
XprVector<
  XprMtVProduct<
    MatrixConstReference<T1, Rows, Cols>, Rows, Cols,   // M(Rows, Cols)
    VectorConstReference<T2, Rows>      // V
  >,
  Cols
>
Mtx_prod(const Matrix<T1, Rows, Cols>& lhs,
   const Vector<T2, Rows>& rhs) TVMET_CXX_ALWAYS_INLINE;


/*++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 * matrix specific functions
 *+++++++++++++++++++++++++++++++++++++++++++++++++++++++*/


template<class T, std::size_t Rows, std::size_t Cols>
XprMatrix<
  XprMatrixTranspose<
    MatrixConstReference<T, Rows, Cols>
  >,
  Cols, Rows
>
trans(const Matrix<T, Rows, Cols>& rhs) TVMET_CXX_ALWAYS_INLINE;


template<class T, std::size_t Sz>
typename NumericTraits<T>::sum_type
trace(const Matrix<T, Sz, Sz>& m) TVMET_CXX_ALWAYS_INLINE;


template<class T, std::size_t Rows, std::size_t Cols>
XprVector<
  XprMatrixRow<
    MatrixConstReference<T, Rows, Cols>,
    Rows, Cols
  >,
  Cols
>
row(const Matrix<T, Rows, Cols>& m,
    std::size_t no) TVMET_CXX_ALWAYS_INLINE;


template<class T, std::size_t Rows, std::size_t Cols>
XprVector<
  XprMatrixCol<
    MatrixConstReference<T, Rows, Cols>,
    Rows, Cols
  >,
  Rows
>
col(const Matrix<T, Rows, Cols>& m,
    std::size_t no) TVMET_CXX_ALWAYS_INLINE;


template<class T, std::size_t Sz>
XprVector<
  XprMatrixDiag<
    MatrixConstReference<T, Sz, Sz>,
    Sz
  >,
  Sz
>
diag(const Matrix<T, Sz, Sz>& m) TVMET_CXX_ALWAYS_INLINE;


/*++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 * min/max unary functions
 *+++++++++++++++++++++++++++++++++++++++++++++++++++++++*/


template<class E, std::size_t Rows, std::size_t Cols>
Extremum<typename E::value_type, std::size_t, matrix_tag>
maximum(const XprMatrix<E, Rows, Cols>& e); // NOT TVMET_CXX_ALWAYS_INLINE;


template<class T, std::size_t Rows, std::size_t Cols>
Extremum<T, std::size_t, matrix_tag>
maximum(const Matrix<T, Rows, Cols>& m) TVMET_CXX_ALWAYS_INLINE;


template<class E, std::size_t Rows, std::size_t Cols>
Extremum<typename E::value_type, std::size_t, matrix_tag>
minimum(const XprMatrix<E, Rows, Cols>& e); // NOT TVMET_CXX_ALWAYS_INLINE;


template<class T, std::size_t Rows, std::size_t Cols>
Extremum<T, std::size_t, matrix_tag>
minimum(const Matrix<T, Rows, Cols>& m) TVMET_CXX_ALWAYS_INLINE;


template<class E, std::size_t Rows, std::size_t Cols>
typename E::value_type
max(const XprMatrix<E, Rows, Cols>& e); // NOT TVMET_CXX_ALWAYS_INLINE;


template<class T, std::size_t Rows, std::size_t Cols>
T max(const Matrix<T, Rows, Cols>& m) TVMET_CXX_ALWAYS_INLINE;


template<class E, std::size_t Rows, std::size_t Cols>
typename E::value_type
min(const XprMatrix<E, Rows, Cols>& e); // NOT TVMET_CXX_ALWAYS_INLINE;


template<class T, std::size_t Rows, std::size_t Cols>
T min(const Matrix<T, Rows, Cols>& m) TVMET_CXX_ALWAYS_INLINE;


/*++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 * other unary functions
 *+++++++++++++++++++++++++++++++++++++++++++++++++++++++*/


template<class T, std::size_t Rows, std::size_t Cols>
XprMatrix<
  XprIdentity<T, Rows, Cols>,
  Rows, Cols
>
identity() TVMET_CXX_ALWAYS_INLINE;


template<class M>
XprMatrix<
  XprIdentity<
    typename M::value_type,
    M::Rows, M::Cols>,
  M::Rows, M::Cols
>
identity() TVMET_CXX_ALWAYS_INLINE;


template<class T, std::size_t Rows, std::size_t Cols>
XprMatrix<
  MatrixConstReference<T, Rows, Cols>,
  Rows, Cols
>
cmatrix_ref(const T* mem) TVMET_CXX_ALWAYS_INLINE;


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


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


/*
 * function(Matrix<T1, Rows, Cols>, Matrix<T2, Rows, Cols>)
 * function(XprMatrix<E, Rows, Cols>, Matrix<T, Rows, Cols>)
 * function(Matrix<T, Rows, Cols>, XprMatrix<E, Rows, Cols>)
 */
#define TVMET_IMPLEMENT_MACRO(NAME)           \
template<class T1, class T2, std::size_t Rows, std::size_t Cols>    \
inline                    \
XprMatrix<                  \
  XprBinOp<                 \
    Fcnl_##NAME<T1, T2>,              \
    MatrixConstReference<T1, Rows, Cols>,         \
    MatrixConstReference<T2, Rows, Cols>          \
  >,                    \
  Rows, Cols                  \
>                   \
NAME (const Matrix<T1, Rows, Cols>& lhs, const Matrix<T2, Rows, Cols>& rhs) { \
  typedef XprBinOp <                \
    Fcnl_##NAME<T1, T2>,              \
    MatrixConstReference<T1, Rows, Cols>,         \
    MatrixConstReference<T2, Rows, Cols>          \
  >             expr_type;    \
  return XprMatrix<expr_type, Rows, Cols>(          \
    expr_type(lhs.const_ref(), rhs.const_ref()));       \
}                   \
                    \
template<class E, class T, std::size_t Rows, std::size_t Cols>      \
inline                    \
XprMatrix<                  \
  XprBinOp<                 \
    Fcnl_##NAME<typename E::value_type, T>,         \
    XprMatrix<E, Rows, Cols>,             \
    MatrixConstReference<T, Rows, Cols>           \
  >,                    \
  Rows, Cols                  \
>                   \
NAME (const XprMatrix<E, Rows, Cols>& lhs, const Matrix<T, Rows, Cols>& rhs) {  \
  typedef XprBinOp<               \
    Fcnl_##NAME<typename E::value_type, T>,         \
    XprMatrix<E, Rows, Cols>,             \
    MatrixConstReference<T, Rows, Cols>           \
  >                expr_type;   \
  return XprMatrix<expr_type, Rows, Cols>(          \
    expr_type(lhs, rhs.const_ref()));           \
}                   \
                    \
template<class T, class E, std::size_t Rows, std::size_t Cols>      \
inline                    \
XprMatrix<                  \
  XprBinOp<                 \
    Fcnl_##NAME<typename E::value_type, T>,         \
    MatrixConstReference<T, Rows, Cols>,          \
    XprMatrix<E, Rows, Cols>              \
  >,                    \
  Rows, Cols                  \
>                   \
NAME (const Matrix<T, Rows, Cols>& lhs, const XprMatrix<E, Rows, Cols>& rhs) {  \
  typedef XprBinOp<               \
    Fcnl_##NAME<T, typename E::value_type>,         \
    MatrixConstReference<T, Rows, Cols>,          \
    XprMatrix<E, Rows, Cols>              \
  >              expr_type;   \
  return XprMatrix<expr_type, Rows, Cols>(          \
    expr_type(lhs.const_ref(), 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(Matrix<T, Rows, Cols>, POD)
 * function(POD, Matrix<T, Rows, Cols>)
 * Note: - operations +,-,*,/ are per se element wise
 */
#define TVMET_IMPLEMENT_MACRO(NAME, POD)        \
template<class T, std::size_t Rows, std::size_t Cols>     \
inline                  \
XprMatrix<                \
  XprBinOp<               \
    Fcnl_##NAME<T, POD >,           \
    MatrixConstReference<T, Rows, Cols>,        \
    XprLiteral<POD >              \
  >,                  \
  Rows, Cols                \
>                 \
NAME (const Matrix<T, Rows, Cols>& lhs, POD rhs) {      \
  typedef XprBinOp<             \
    Fcnl_##NAME<T, POD >,           \
    MatrixConstReference<T, Rows, Cols>,        \
    XprLiteral< POD >             \
  >             expr_type;  \
  return XprMatrix<expr_type, Rows, Cols>(        \
    expr_type(lhs.const_ref(), XprLiteral< POD >(rhs)));    \
}                 \
                  \
template<class T, std::size_t Rows, std::size_t Cols>     \
inline                  \
XprMatrix<                \
  XprBinOp<               \
    Fcnl_##NAME< POD, T>,           \
    XprLiteral< POD >,              \
    MatrixConstReference<T, Rows, Cols>         \
  >,                  \
  Rows, Cols                \
>                 \
NAME (POD lhs, const Matrix<T, Rows, Cols>& rhs) {      \
  typedef XprBinOp<             \
    Fcnl_##NAME< POD, T>,           \
    XprLiteral< POD >,              \
    MatrixConstReference<T, Rows, Cols>         \
  >             expr_type;  \
  return XprMatrix<expr_type, Rows, Cols>(        \
    expr_type(XprLiteral< POD >(lhs), rhs.const_ref()));    \
}

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(Matrix<T, Rows, Cols>, complex<T>)
 * function(complex<T>, Matrix<T, Rows, Cols>)
 * Note: - operations +,-,*,/ are per se element wise
 * \todo type promotion
 */
#define TVMET_IMPLEMENT_MACRO(NAME)         \
template<class T, std::size_t Rows, std::size_t Cols>     \
inline                  \
XprMatrix<                \
  XprBinOp<               \
    Fcnl_##NAME< std::complex<T>, std::complex<T> >,      \
    MatrixConstReference< std::complex<T>, Rows, Cols>,     \
    XprLiteral<std::complex<T> >          \
  >,                  \
  Rows, Cols                \
>                 \
NAME (const Matrix< std::complex<T>, Rows, Cols>& lhs,      \
      const std::complex<T>& rhs) {         \
  typedef XprBinOp<             \
    Fcnl_##NAME< std::complex<T>, std::complex<T> >,      \
    MatrixConstReference< std::complex<T>, Rows, Cols>,     \
    XprLiteral< std::complex<T> >         \
  >             expr_type;  \
  return XprMatrix<expr_type, Rows, Cols>(        \
    expr_type(lhs.const_ref(), XprLiteral< std::complex<T> >(rhs)));  \
}                 \
                  \
template<class T, std::size_t Rows, std::size_t Cols>     \
inline                  \
XprMatrix<                \
  XprBinOp<               \
    Fcnl_##NAME< std::complex<T>, std::complex<T> >,      \
    XprLiteral< std::complex<T> >,          \
    MatrixConstReference< std::complex<T>, Rows, Cols>      \
  >,                  \
  Rows, Cols                \
>                 \
NAME (const std::complex<T>& lhs,         \
      const Matrix< std::complex<T>, Rows, Cols>& rhs) {    \
  typedef XprBinOp<             \
    Fcnl_##NAME< std::complex<T>, std::complex<T> >,      \
    XprLiteral< std::complex<T> >,          \
    MatrixConstReference<std::complex<T>, Rows, Cols>     \
  >             expr_type;  \
  return XprMatrix<expr_type, Rows, Cols>(        \
    expr_type(XprLiteral< std::complex<T> >(lhs), rhs.const_ref()));  \
}

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 specific prod( ... ) functions
 *+++++++++++++++++++++++++++++++++++++++++++++++++++++++*/


template<class T1, std::size_t Rows1, std::size_t Cols1,
   class T2, std::size_t Cols2>
inline
XprMatrix<
  XprMMProduct<
    MatrixConstReference<T1, Rows1, Cols1>, Rows1, Cols1, // M1(Rows1, Cols1)
    MatrixConstReference<T2, Cols1, Cols2>, Cols2     // M2(Cols1, Cols2)
  >,
  Rows1, Cols2              // return Dim
>
prod(const Matrix<T1, Rows1, Cols1>& lhs, const Matrix<T2, Cols1, Cols2>& rhs) {
  typedef XprMMProduct<
    MatrixConstReference<T1, Rows1, Cols1>, Rows1, Cols1,
    MatrixConstReference<T2, Cols1, Cols2>, Cols2
  >             expr_type;
  return XprMatrix<expr_type, Rows1, Cols2>(
    expr_type(lhs.const_ref(), rhs.const_ref()));
}


template<class E1, std::size_t Rows1, std::size_t Cols1,
   class T2, std::size_t Cols2>
inline
XprMatrix<
  XprMMProduct<
    XprMatrix<E1, Rows1, Cols1>, Rows1, Cols1,      // M1(Rows1, Cols1)
    MatrixConstReference<T2, Cols1, Cols2>, Cols2   // M2(Cols1, Cols2)
  >,
  Rows1, Cols2              // return Dim
>
prod(const XprMatrix<E1, Rows1, Cols1>& lhs, const Matrix<T2, Cols1, Cols2>& rhs) {
  typedef XprMMProduct<
    XprMatrix<E1, Rows1, Cols1>, Rows1, Cols1,
    MatrixConstReference<T2, Cols1, Cols2>, Cols2
  >             expr_type;
  return XprMatrix<expr_type, Rows1, Cols2>(
    expr_type(lhs, rhs.const_ref()));
}


template<class T1, std::size_t Rows1, std::size_t Cols1,
   class E2, std::size_t Cols2>
inline
XprMatrix<
  XprMMProduct<
    MatrixConstReference<T1, Rows1, Cols1>, Rows1, Cols1, // M1(Rows1, Cols1)
    XprMatrix<E2, Cols1, Cols2>, Cols2        // M2(Cols1, Cols2)
  >,
  Rows1, Cols2              // return Dim
>
prod(const Matrix<T1, Rows1, Cols1>& lhs, const XprMatrix<E2, Cols1, Cols2>& rhs) {
  typedef XprMMProduct<
    MatrixConstReference<T1, Rows1, Cols1>, Rows1, Cols1,
    XprMatrix<E2, Cols1, Cols2>, Cols2
  >             expr_type;
  return XprMatrix<expr_type, Rows1, Cols2>(
    expr_type(lhs.const_ref(), rhs));
}


template<class T1, std::size_t Rows1, std::size_t Cols1,
   class T2, std::size_t Cols2>
inline
XprMatrix<
  XprMMProductTransposed<
    MatrixConstReference<T1, Rows1, Cols1>, Rows1, Cols1, // M1(Rows1, Cols1)
    MatrixConstReference<T2, Cols1, Cols2>, Cols2   // M2(Cols1, Cols2)
  >,
  Cols2, Rows1              // return Dim
>
trans_prod(const Matrix<T1, Rows1, Cols1>& lhs, const Matrix<T2, Cols1, Cols2>& rhs) {
  typedef XprMMProductTransposed<
    MatrixConstReference<T1, Rows1, Cols1>, Rows1, Cols1,
    MatrixConstReference<T2, Cols1, Cols2>, Cols2
  >             expr_type;
  return XprMatrix<expr_type, Cols2, Rows1>(
    expr_type(lhs.const_ref(), rhs.const_ref()));
}


template<class T1, std::size_t Rows1, std::size_t Cols1,
   class T2, std::size_t Cols2> // Rows2 = Rows1
inline
XprMatrix<
  XprMtMProduct<
    MatrixConstReference<T1, Rows1, Cols1>, Rows1, Cols1, // M1(Rows1, Cols1)
    MatrixConstReference<T2, Rows1, Cols2>, Cols2   // M2(Rows1, Cols2)
  >,
  Cols1, Cols2              // return Dim
>
MtM_prod(const Matrix<T1, Rows1, Cols1>& lhs, const Matrix<T2, Rows1, Cols2>& rhs) {
  typedef XprMtMProduct<
    MatrixConstReference<T1, Rows1, Cols1>, Rows1, Cols1,
    MatrixConstReference<T2, Rows1, Cols2>, Cols2
  >             expr_type;
  return XprMatrix<expr_type, Cols1, Cols2>(
    expr_type(lhs.const_ref(), rhs.const_ref()));
}


template<class T1, std::size_t Rows1, std::size_t Cols1,
   class T2, std::size_t Rows2>
inline
XprMatrix<
  XprMMtProduct<
    MatrixConstReference<T1, Rows1, Cols1>, Rows1, Cols1, // M1(Rows1, Cols1)
    MatrixConstReference<T2, Rows2, Cols1>, Cols1     // M2(Rows2, Cols1)
  >,
  Rows1, Rows2              // return Dim
>
MMt_prod(const Matrix<T1, Rows1, Cols1>& lhs, const Matrix<T2, Rows2, Cols1>& rhs) {
  typedef XprMMtProduct<
    MatrixConstReference<T1, Rows1, Cols1>, Rows1, Cols1,
    MatrixConstReference<T2, Rows2, Cols1>, Cols1
  >             expr_type;
  return XprMatrix<expr_type, Rows1, Rows2>(
    expr_type(lhs.const_ref(), rhs.const_ref()));
}


/*++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 * matrix-vector specific prod( ... ) functions
 *+++++++++++++++++++++++++++++++++++++++++++++++++++++++*/


template<class T1, class T2, std::size_t Rows, std::size_t Cols>
inline
XprVector<
  XprMVProduct<
    MatrixConstReference<T1, Rows, Cols>, Rows, Cols, // M(Rows, Cols)
    VectorConstReference<T2, Cols>      // V
  >,
  Rows
>
prod(const Matrix<T1, Rows, Cols>& lhs, const Vector<T2, Cols>& rhs) {
  typedef XprMVProduct<
    MatrixConstReference<T1, Rows, Cols>, Rows, Cols,
    VectorConstReference<T2, Cols>
  >               expr_type;
  return XprVector<expr_type, Rows>(
    expr_type(lhs.const_ref(), rhs.const_ref()));
}


template<class T1, class E2, std::size_t Rows, std::size_t Cols>
inline
XprVector<
  XprMVProduct<
    MatrixConstReference<T1, Rows, Cols>, Rows, Cols,
    XprVector<E2, Cols>
  >,
  Rows
>
prod(const Matrix<T1, Rows, Cols>& lhs, const XprVector<E2, Cols>& rhs) {
  typedef XprMVProduct<
    MatrixConstReference<T1, Rows, Cols>, Rows, Cols,
    XprVector<E2, Cols>
  >               expr_type;
  return XprVector<expr_type, Rows>(
    expr_type(lhs.const_ref(), rhs));
}


/*
 * \fn prod(const XprMatrix<E, Rows, Cols>& lhs, const Vector<T, Cols>& rhs)
 * \brief Compute the product of an XprMatrix with a Vector.
 * \ingroup _binary_function
 */
template<class E1, class T2, std::size_t Rows, std::size_t Cols>
inline
XprVector<
  XprMVProduct<
    XprMatrix<E1, Rows, Cols>, Rows, Cols,    // M(Rows, Cols)
    VectorConstReference<T2, Cols>      // V
  >,
  Rows
>
prod(const XprMatrix<E1, Rows, Cols>& lhs, const Vector<T2, Cols>& rhs) {
  typedef XprMVProduct<
    XprMatrix<E1, Rows, Cols>, Rows, Cols,
    VectorConstReference<T2, Cols>
  >               expr_type;
  return XprVector<expr_type, Rows>(
    expr_type(lhs, rhs.const_ref()));
}


template<class T1, class T2, std::size_t Rows, std::size_t Cols>
inline
XprVector<
  XprMtVProduct<
    MatrixConstReference<T1, Rows, Cols>, Rows, Cols,   // M(Rows, Cols)
    VectorConstReference<T2, Rows>      // V
  >,
  Cols
>
Mtx_prod(const Matrix<T1, Rows, Cols>& lhs, const Vector<T2, Rows>& rhs) {
  typedef XprMtVProduct<
    MatrixConstReference<T1, Rows, Cols>, Rows, Cols,
    VectorConstReference<T2, Rows>
  >               expr_type;
  return XprVector<expr_type, Cols>(
    expr_type(lhs.const_ref(), rhs.const_ref()));
}


/*++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 * matrix specific functions
 *+++++++++++++++++++++++++++++++++++++++++++++++++++++++*/


template<class T, std::size_t Rows, std::size_t Cols>
inline
XprMatrix<
  XprMatrixTranspose<
    MatrixConstReference<T, Rows, Cols>
  >,
  Cols, Rows
>
trans(const Matrix<T, Rows, Cols>& rhs) {
  typedef XprMatrixTranspose<
    MatrixConstReference<T, Rows, Cols>
  >             expr_type;
  return XprMatrix<expr_type, Cols, Rows>(
    expr_type(rhs.const_ref()));
}


/*
 * \fn trace(const Matrix<T, Sz, Sz>& m)
 * \brief Compute the trace of a square matrix.
 * \ingroup _unary_function
 *
 * Simply compute the trace of the given matrix as:
 * \f[
 *  \sum_{k = 0}^{Sz-1} m(k, k)
 * \f]
 */
template<class T, std::size_t Sz>
inline
typename NumericTraits<T>::sum_type
trace(const Matrix<T, Sz, Sz>& m) {
  return meta::Matrix<Sz, Sz, 0, 0>::trace(m);
}


template<class T, std::size_t Rows, std::size_t Cols>
inline
XprVector<
  XprMatrixRow<
    MatrixConstReference<T, Rows, Cols>,
    Rows, Cols
  >,
  Cols
>
row(const Matrix<T, Rows, Cols>& m, std::size_t no) {
  typedef XprMatrixRow<
    MatrixConstReference<T, Rows, Cols>,
    Rows, Cols
  >             expr_type;
  return XprVector<expr_type, Cols>(expr_type(m.const_ref(), no));
}


template<class T, std::size_t Rows, std::size_t Cols>
inline
XprVector<
  XprMatrixCol<
    MatrixConstReference<T, Rows, Cols>,
    Rows, Cols
  >,
  Rows
>
col(const Matrix<T, Rows, Cols>& m, std::size_t no) {
  typedef XprMatrixCol<
    MatrixConstReference<T, Rows, Cols>,
    Rows, Cols
  >             expr_type;
  return XprVector<expr_type, Rows>(expr_type(m.const_ref(), no));
}


template<class T, std::size_t Sz>
inline
XprVector<
  XprMatrixDiag<
    MatrixConstReference<T, Sz, Sz>,
    Sz
  >,
  Sz
>
diag(const Matrix<T, Sz, Sz>& m) {
  typedef XprMatrixDiag<
    MatrixConstReference<T, Sz, Sz>,
    Sz
  >             expr_type;
  return XprVector<expr_type, Sz>(expr_type(m.const_ref()));
}


/*++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 * min/max unary functions
 *+++++++++++++++++++++++++++++++++++++++++++++++++++++++*/


template<class E, std::size_t Rows, std::size_t Cols>
inline
Extremum<typename E::value_type, std::size_t, matrix_tag>
maximum(const XprMatrix<E, Rows, Cols>& e) {
  typedef typename E::value_type      value_type;

  value_type            temp(e(0, 0));
  std::size_t             row_no(0), col_no(0);

  for(std::size_t i = 0; i != Rows; ++i) {
    for(std::size_t j = 0; j != Cols; ++j) {
      if(e(i, j) > temp) {
  temp = e(i, j);
  row_no = i;
  col_no = j;
      }
    }
  }

  return Extremum<value_type, std::size_t, matrix_tag>(temp, row_no, col_no);
}


template<class T, std::size_t Rows, std::size_t Cols>
inline
Extremum<T, std::size_t, matrix_tag>
maximum(const Matrix<T, Rows, Cols>& m) { return maximum(m.as_expr()); }


template<class E, std::size_t Rows, std::size_t Cols>
inline
Extremum<typename E::value_type, std::size_t, matrix_tag>
minimum(const XprMatrix<E, Rows, Cols>& e) {
  typedef typename E::value_type      value_type;

  value_type            temp(e(0, 0));
  std::size_t             row_no(0), col_no(0);

  for(std::size_t i = 0; i != Rows; ++i) {
    for(std::size_t j = 0; j != Cols; ++j) {
      if(e(i, j) < temp) {
  temp = e(i, j);
  row_no = i;
  col_no = j;
      }
    }
  }

  return Extremum<value_type, std::size_t, matrix_tag>(temp, row_no, col_no);
}


template<class T, std::size_t Rows, std::size_t Cols>
inline
Extremum<T, std::size_t, matrix_tag>
minimum(const Matrix<T, Rows, Cols>& m) { return minimum(m.as_expr()); }


template<class E, std::size_t Rows, std::size_t Cols>
inline
typename E::value_type
max(const XprMatrix<E, Rows, Cols>& e) {
  typedef typename E::value_type      value_type;

  value_type            temp(e(0, 0));

  for(std::size_t i = 0; i != Rows; ++i)
    for(std::size_t j = 0; j != Cols; ++j)
      if(e(i, j) > temp)
  temp = e(i, j);

  return temp;
}


template<class T, std::size_t Rows, std::size_t Cols>
inline
T max(const Matrix<T, Rows, Cols>& m) {
  typedef T           value_type;
  typedef typename Matrix<
   T, Rows, Cols
  >::const_iterator         const_iterator;

  const_iterator          iter(m.begin());
  const_iterator          last(m.end());
  value_type            temp(*iter);

  for( ; iter != last; ++iter)
    if(*iter > temp)
      temp = *iter;

  return temp;
}


template<class E, std::size_t Rows, std::size_t Cols>
inline
typename E::value_type
min(const XprMatrix<E, Rows, Cols>& e) {
  typedef typename E::value_type      value_type;

  value_type            temp(e(0, 0));

  for(std::size_t i = 0; i != Rows; ++i)
    for(std::size_t j = 0; j != Cols; ++j)
      if(e(i, j) < temp)
  temp = e(i, j);

  return temp;
}


template<class T, std::size_t Rows, std::size_t Cols>
inline
T min(const Matrix<T, Rows, Cols>& m) {
  typedef T           value_type;
  typedef typename Matrix<
   T, Rows, Cols
  >::const_iterator         const_iterator;

  const_iterator          iter(m.begin());
  const_iterator          last(m.end());
  value_type            temp(*iter);

  for( ; iter != last; ++iter)
    if(*iter < temp)
      temp = *iter;

  return temp;
}


/*++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 * other unary functions
 *+++++++++++++++++++++++++++++++++++++++++++++++++++++++*/


template<class T, std::size_t Rows, std::size_t Cols>
inline
XprMatrix<
  XprIdentity<T, Rows, Cols>,
  Rows, Cols
>
identity() {
  typedef XprIdentity<T, Rows, Cols>    expr_type;

  return XprMatrix<expr_type, Rows, Cols>(expr_type());
}

template<class M>
inline
XprMatrix<
  XprIdentity<
    typename M::value_type,
    M::Rows, M::Cols>,
  M::Rows, M::Cols
>
identity() {
  return identity<typename M::value_type, M::Rows, M::Cols>();
}


template<class T, std::size_t Rows, std::size_t Cols>
inline
XprMatrix<
  MatrixConstReference<T, Rows, Cols>,
  Rows, Cols
>
cmatrix_ref(const T* mem) {
  typedef MatrixConstReference<T, Rows, Cols> expr_type;

  return XprMatrix<expr_type, Rows, Cols>(expr_type(mem));
}


} // namespace tvmet

#endif // TVMET_MATRIX_FUNCTIONS_H

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