Radial-Functions-Interpolation/RBF_functions.hpp

#ifndef RBF_functions_hpp
#define RBF_functions_hpp
// Les RBF
// classe de base
template<typename real> class RBF{
  // Radial Basis Functions: base.
  protected:
  real epsilon;
  RBF(real eps):epsilon(eps){};
  void set_epsilon(real eps) {epsilon = eps;}
};


template<typename real> class MQI: public RBF<real> {
  // Multiquadratique inverse.
 
public:
  using RBF<real>::set_epsilon; //utiliser le set-epsilon de la classe
  // de base (C++ 11 !).

  // constructeur: on appelle de constructeur de la base.
  MQI(real eps): RBF<real>(eps){}
  // la veur en x (distance au noeud)
  inline real operator()(real x){return 1./sqrt(1.+
						RBF<real>::epsilon*x*x);}
  };
///
template<typename real> class TPS: public RBF<real> {
  // plaque mince.
public:
  TPS(real eps): RBF<real>(eps){}
  inline real operator()(real x){return exp(-RBF<real>::epsilon*x)*
      (1.+RBF<real>::epsilon*x);}
  };
template<typename real> class Gauss: public RBF<real> {
  // Gaussienne
public:
  Gauss(real eps): RBF<real>(eps){}
  inline real operator()(real x){
    if(x<1.e-10)
      return 1.;
    else
      return exp(-RBF<real>::epsilon*x*x);}
  };
template<typename real> class TPSD: public RBF<real> {
  // plaque mince à la Duchon..
public:
  TPSD(real eps): RBF<real>(eps){}
  inline real operator()(real x){
    if(x<1.e-9)
      return 1.;
    else
      return 1/(1.+
	      pow(RBF<real>::epsilon*x,2)*log(RBF<real>::epsilon*x));}
  
  };
#endif