// ==========================================================================
// $Source: /var/lib/cvs/Givaro/src/library/poly1/givinterp.h,v $
// Copyright(c)'1994-2009 by The Givaro group
// This file is part of Givaro.
// Givaro is governed by the CeCILL-B license under French law
// and abiding by the rules of distribution of free software.
// see the COPYRIGHT file for more details.
// Authors: JG Dumas
// $Id: givinterp.h,v 1.3 2011-02-02 16:23:56 bboyer Exp $
// ==========================================================================

/** @file givinterp.h
 * @ingroup poly1
 * @brief NO DOC
 */

#ifndef __GIVARO_interpolation_H
#define __GIVARO_interpolation_H

#include "givaro/givconfig.h"
#include "givaro/giverror.h"
#include "givaro/givpoly1.h"

namespace Givaro {

	//! Interpolation
template<class Domain, bool REDUCE = true>
struct Interpolation : Poly1Dom<Domain,Dense>  {
    typedef std::vector< typename Domain::Element > Vect_t;
    typedef typename Poly1Dom<Domain, Dense>::Element Element;


    Interpolation (const Domain& d, const Indeter& X = Indeter() ) : Poly1Dom<Domain,Dense>(d,X), Pi(this->one) {}

    void operator() ( const typename Domain::Element& x, const typename Domain::Element& f) {
        DD.push_back(f);
        Element M;
        this->init(M);

        if (DD.size() > 1) {
                // Pi *= (X-x_{n});
            this->mul(M, Pi, Points.back());
            this->shiftin(Pi, 1); // Pi *= X;
            this->subin(Pi, M);

                // Update divided differences
            typename Domain::Element tmp;
            this->_domain.init(tmp);
                // Adds the last evaluation
            for( typename Vect_t::reverse_iterator prev = DD.rbegin(), next = DD.rbegin(), point = Points.rbegin(); ++next != DD.rend(); ++prev, ++point)
		// [x_i, ..., x_{n+1}] = ([x_i, ..., x_n] - [x_{i+1}, ..., x_{n+1}])
                //			 / ( x_i - x_{n+1} )
                this->_domain.divin(
                    this->_domain.subin(*next, *prev),
                    this->_domain.sub(tmp, *point, x)
                    );
        }
        Points.push_back(x);


            // inter += [x_0, ..., x_{n+1}] (X-x_0)...(X-x_n)
        this->mul(M, Pi, DD.front());
        this->addin(inter, M);

    }

    Element& interpolator() {
        return inter;
    }

private:

    Element inter;
    Element Pi;
    Vect_t Points, DD;
};

} // Givaro

#endif // __GIVARO_interpolation_H
