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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 <cstdlib>
template <class T>
class jacobi {
    public:
	jacobi (size_t R1, T alpha1, T beta1)
 	: R(R1), alpha(alpha1), beta(beta1) {}
 	T operator() (T x) const {
	    if (R == 0) return 1;
  	    T P_prev  = 1;
  	    T P       = ((alpha+beta+2)*x + alpha - beta)/2;
  	    for (size_t r = 1; r < R; r++) {
    		T P_save = P;
    		T a = (beta*beta - alpha*alpha)/((alpha+beta+T(2*r))*(alpha+beta+T(2*r+2)));
    		T b = 2*(alpha+T(r))*(beta+T(r))/((alpha+beta+T(2*r))*(alpha+beta+T(2*r+1)));
    		T c = 2*T(r+1)*(alpha+beta+T(r+1))/((alpha+beta+T(2*r+1))*(alpha+beta+T(2*r+2)));
    		P  = ((x-a)*P - b*P_prev)/c;
    		P_prev = P_save;
  	    }
  	    return P;
 	}
    protected:
 	size_t R;
 	T      alpha, beta;
};