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///
/// This file is part of Rheolef.
///
/// Copyright (C) 2000-2009 Pierre Saramito <Pierre.Saramito@imag.fr>
///
/// 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
/// 
/// =========================================================================
#include "rheolef/compiler.h"
#include <iterator>
#include <iostream>
#include "rheolef/pythag.h"


template <class T>
inline T SIGN(T a, T b) { return b >= T(0) ? fabs(a) : -fabs(a); }

template <class Iterator1, class Iterator2, class Size>
void tqli (Iterator1 d, Iterator2 e, Size n)
{
	typedef typename std::iterator_traits<Iterator1>::value_type T;
	static const Size max_iter = 30;
        static const T eps = std::numeric_limits<T>::epsilon();
	Size m,l,iter,i;
	T s,r,p,g,f,dd,c,b;
	for (i=2;i<=n;i++) e[i-1]=e[i];
	e[n]=0.0;
#ifdef TO_CLEAN
	// dump:
	std::cout << std::setprecision(31);
	for (i=1; i <= n; i++) {
	  std::cout << "d("<<i<<") = " << d[i] << std::endl;
        }
	for (i=1; i <= n; i++) {
	  std::cout << "e("<<i<<") = " << e[i] << std::endl;
        }
#endif // TO_CLEAN
	for (l=1; l<=n; l++) {
	    iter=0;
	    do {
	      for (m = l; m <= n-1; m++) {
		dd = fabs(d[m]) + fabs(d[m+1]);
		if (fabs(e[m]) < dd && fabs(e[m])*dd < eps*dd) break; // i.e. e[m] << dd
	      }
	      if (m != l) {
		iter++;
		check_macro (iter < max_iter, "too many ("<<max_iter<<") iterations in tqli");
		g = (d[l+1]-d[l])/(2.0*e[l]);
		r = pythag (g, T(1));
		g = d[m] - d[l] + e[l]/(g+SIGN(r,g));
		s = c = 1.0;
		p = 0.0;
		for (i = m-1; i>=l; i--) {
			f = s*e[i];
			b = c*e[i];
			r=pythag(f,g);
			e[i+1] = r;
			if (r == T(0)) {
				d[i+1] -= p;
				e[m] = 0.0;
				break;
			}
			s = f/r;
			c = g/r;
			g = d[i+1] - p;
			r = (d[i] - g)*s + 2.0*c*b;
			p=s*r;
			d[i+1] = g + p;
			g = c*r - b;
		}
		if (r == T(0) && i >= l) continue;
		d[l] -= p;
		e[l] = g;
		e[m] = 0.0;
	      }
	    } while (m != l);
	}
}