librheolef-dev 6.6-1build2 / usr / include / rheolef / jacobi_roots.icc

/// 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/tqli.h"
#include "rheolef/sqr.h"
#include <vector>
#include <cmath>
#include <algorithm>
template <class Size, class T, class OutputIterator>
void jacobi_roots (Size R, T alpha, T beta, OutputIterator zeta) {
	if (R == 0) { return; }
	if (R == 1) { zeta [0] = (beta-alpha)/(alpha+beta+2); return; }
	OutputIterator a = zeta;
	a[0] = (beta-alpha)/(alpha+beta+2);
	for (size_t r = 1; r < R; r++)
	    a[r] = (sqr(beta) - sqr(alpha))/((alpha+beta+T(2.*r))*(alpha+beta+T(2.*r+2)));
	std::vector<T> b(R);
	b[0] = 0.;
	b[1] = 2/(alpha+beta+2)*sqrt((alpha+1)*(beta+1)/(alpha+beta+3));
	for (size_t r = 2; r < R; r++)
	    b[r] = 2/(alpha+beta+T(2.*r))
	          *sqrt(T(1.*r)*(alpha+T(1.*r))*(beta+T(1.*r))*(alpha+beta+T(1.*r))/((alpha+beta+T(2.*r-1))*(alpha+beta+T(2.*r+1))));
        tqli (zeta-1, b.begin()-1, R);
        sort (zeta, zeta+R);
	if (alpha == beta && R % 2 == 1) zeta[R/2] = 0.;
}