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/// This file is part of Rheolef.
///
/// Copyright (C) 2000-2009 Pierre Saramito 
///
/// Rheolef is free software; you can redistribute it and/or modify
/// it under the terms of the GNU General Public License as published by
/// the Free Software Foundation; either version 2 of the License, or
/// (at your option) any later version.
///
/// Rheolef 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 General Public License for more details.
///
/// You should have received a copy of the GNU General Public License
/// along with Rheolef; if not, write to the Free Software
/// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
/// lexer for qmg mesh files
/// =========================================================================
#include "rheolef/gamma.h"
#include "rheolef/jacobi.h"
#include "rheolef/jacobi_roots.h"
#include <iterator>
template <class Size, class OutputIterator1, class OutputIterator2>
void 
gauss_jacobi (Size R, 
   	typename std::iterator_traits<OutputIterator1>::value_type alpha, 
   	typename std::iterator_traits<OutputIterator1>::value_type beta,
   	OutputIterator1 zeta, OutputIterator2 omega)
{ 
        typedef typename std::iterator_traits<OutputIterator1>::value_type T;
	T num = pow(T(2), alpha+beta+3)/sqr(alpha+beta+T(R)+1);
	if (alpha == T(int(alpha)) && beta == T(int(beta))) 
	  for (Size k = 1; k <= size_t(int(beta)); k++)
	    num *= (T(R)+T(k))/(alpha+T(R)+T(k));
        else
	    num *= (my_gamma(alpha+T(R)+1)/my_gamma(alpha+beta+T(R)+1))
	          *(my_gamma(beta+T(R)+1)/my_gamma(T(R)+1));
  	jacobi_roots (R, alpha, beta, zeta);
  	jacobi<T> P (R-1, alpha+1, beta+1);
  	for (Size r = 0; r < R; r++)
      	    omega[r] = num/((1-sqr(zeta[r]))*sqr(P(zeta[r])));
}