127 lines
3.3 KiB
C
127 lines
3.3 KiB
C
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// Copyright (c) 2008 Max-Planck-Institute Saarbruecken (Germany)
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//
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// This file is part of CGAL (www.cgal.org)
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//
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// $URL: https://github.com/CGAL/cgal/blob/v5.1/Polynomial/include/CGAL/Polynomial/Interpolator.h $
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// $Id: Interpolator.h 0779373 2020-03-26T13:31:46+01:00 Sébastien Loriot
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// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
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//
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//
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// Author(s) : Michael Hemmer <hemmer@informatik.uni-mainz.de>
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#ifndef CGAL_POLYNOMIAL_INTERPOLATE_H
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#define CGAL_POLYNOMIAL_INTERPOLATE_H
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namespace CGAL {
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namespace internal {
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// Class for interpolation of univariate or multivariate polynomials.
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// The template argument must be a model of concept Polynomial_d
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//
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//
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template <class Polynomial_d_>
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class Interpolator{
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typedef CGAL::Polynomial_traits_d<Polynomial_d_> PT;
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public:
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typedef typename PT::Polynomial_d Polynomial_d;
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typedef typename PT::Coefficient_type Coeff;
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typedef typename PT::Innermost_coefficient_type IC;
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private:
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typedef typename CGAL::Coercion_traits<Coeff,IC>::Cast IC2Coeff;
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typedef typename PT::Construct_polynomial Construct;
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std::vector<IC> xvals;
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std::vector<Coeff> yvals;
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std::vector<Coeff> b;
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bool valid;
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Polynomial_d interpolant;
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Coeff eval_newton(int n, IC z)
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{
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Coeff p(b[n]);
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for (int i = n-1; i >=0; i--){
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Coeff tmp(IC2Coeff()((z - xvals[i])));
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p = p * tmp + b[i];
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}
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return p;
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}
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Polynomial_d eval_newton_poly(int n)
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{
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CGAL_precondition(n >=0);
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Polynomial_d p(Construct()(b[n]));
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for (int i = n-1; i >=0; i--) {
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Polynomial_d tmp = Construct()(IC2Coeff()(-xvals[i]),Coeff(1));
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p = (p * tmp) + b[i];
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}
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return p;
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}
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public:
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Interpolator(){};
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// constructor from an InputIterator range with value type std::pair<IC,Coeff>
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template<class InputIterator>
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Interpolator(InputIterator begin, InputIterator end){
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for(InputIterator it = begin; it != end; it++){
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add_interpolation_point(*it);
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}
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}
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/*
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Interpolator(std::vector<IC> xvals_, std::vector<Coeff> yvals_)
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: valid(false) {
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CGAL_precondition(xvals_.size() != 0);
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CGAL_precondition(xvals_.size() == yvals_.size());
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for(unsigned i = 0; i < xvals_.size(); i++){
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add_interpolation_point(xvals_[i],yvals_[i]);
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}
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}
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*/
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// void add_interpolation_point(std::pair<IC,Coeff> point){
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// add_interpolation_point(point.first, point.second);
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// }
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// void add_interpolation_point(IC xval, Coeff yval){
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void add_interpolation_point(std::pair<IC,Coeff> point){
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valid = false;
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// CGAL_precondition(0 == std::count(xval, xvals.begin(), yvals.end()));
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xvals.push_back(point.first);
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yvals.push_back(point.second);
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Coeff num, den;
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int k = static_cast<int>(xvals.size()) - 1;
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if(k == 0){
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b.push_back(yvals[0]);
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}else{
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num = yvals[k] - eval_newton(k-1,xvals[k]);
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den = Coeff(1);
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for (int j = 0; j < k; j++) {
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// (k-j) if xvals's are sequential
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den *= (xvals[k] - xvals[j]);
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}
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b.push_back(num / den);
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}
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}
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Polynomial_d get_interpolant(){
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if (xvals.size() == 0) return Polynomial_d(0);
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// TODO: compute new interpolant from old interpolant ?
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if(!valid)
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interpolant = eval_newton_poly(static_cast<int>(xvals.size())-1);
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return interpolant;
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}
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};
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} // namespace internal
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} //namespace CGAL
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#endif // CGAL_POLYNOMIAL_INTERPOLATE_H
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