Minkowski.h

//-*-C++-*-
/***************************************************************************
 *
 *   Copyright (C) 2014 by Willem van Straten
 *   Licensed under the Academic Free License version 2.1
 *
 ***************************************************************************/
 
// epsic/src/util/Minkowski.h
 
#ifndef __Minkowski_H
#define __Minkowski_H
 
#include "Matrix.h"
 
namespace Minkowski
{

  template<typename T, typename U> typename PromoteTraits<T,U>::promote_type
  inner (const Vector<4,T>& A, const Vector<4,U>& B)
  {
    typename PromoteTraits<T,U>::promote_type result = A[0] * B[0];
    for (unsigned i=1; i<4; i++)
      result -= A[i] * B[i];
    return result;
  }

  template<typename T, typename U> 
  Matrix<4,4,typename PromoteTraits<T,U>::promote_type>
  outer (const Vector<4,T>& A, const Vector<4,U>& B)
  {
    Matrix<4,4,typename PromoteTraits<T,U>::promote_type> result = ::outer(A,B);
    typename PromoteTraits<T,U>::promote_type inv = 0.5 * inner(A,B);
    result[0][0] -= inv;
    for (unsigned i=1; i<4; i++)
      result[i][i] += inv;
    return result;
  }
}
 
#endif