/**
   \file num_diff.hpp
   \brief performing n-dim differential operation on func objects
   \author Junhua Gu
 */


#ifndef NUMDIFF_HPP
#define NUMDIFF_HPP
#define OPT_HEADER
#include <core/optimizer.hpp>
#include <core/opt_traits.hpp>
#include <algorithm>
#include <limits>
#include <cmath>

namespace opt_utilities
{
  /**
     calculate the numerical differential of a func_obj
  */
  template<typename rT,typename pT>
  class diff_func_obj
    :public func_obj<rT,pT>
  {
  private:
    virtual pT do_gradient(const pT& p)=0;
  public:
    pT gradient(const pT& p)
    {
      return do_gradient(p);
    }
  };
  


  template <typename rT,typename pT>
  rT gradient(func_obj<rT,pT>& f,pT& p,size_t n)
  {
    rT ep=std::sqrt(std::numeric_limits<rT>::epsilon());
    
    rT result;
    
    typename element_type_trait<pT>::element_type old_value=get_element(p,n);
    
    typename element_type_trait<pT>::element_type h=
      std::max(get_element(p,n),rT(1))*ep;
    set_element(p,n,old_value+h);
    rT v2=f(p);
    set_element(p,n,old_value-h);
    rT v1=f(p);
    set_element(p,n,old_value);
    result=(v2-v1)/h/2;
    return result;
  }

  template <typename rT,typename pT>
  pT gradient(func_obj<rT,pT>& f,pT& p)
  {
    diff_func_obj<rT,pT>* pdfo=0;
    if(pdfo=dynamic_cast<diff_func_obj<rT,pT>*>(&f))
      {
	return pdfo->gradient(p);
      }
    pT result;
    resize(result,get_size(p));
    for(int i=0;i<get_size(p);++i)
      {
	set_element(result,i,gradient(f,p,i));
      }
    return result;
  }

  
  template <typename rT,typename pT>
  rT hessian(func_obj<rT,pT>& f,const pT& p,size_t m,size_t n)
  {
    rT ep=std::sqrt(std::numeric_limits<rT>::epsilon());
    typename element_type_trait<pT>::element_type hn=
      std::max(get_element(p,n),rT(1))*ep;
    typename element_type_trait<pT>::element_type hm=
      std::max(get_element(p,m),rT(1))*ep;
    pT p11;
    resize(p11,get_size(p));
    pT p00;
    resize(p00,get_size(p));
    pT p10;
    resize(p10,get_size(p));
    pT p01;
    resize(p01,get_size(p));
    
    for(size_t i=0;i<get_size(p);++i)
      {
	set_element(p11,i,get_element(p,i));
	set_element(p00,i,get_element(p,i));
	set_element(p01,i,get_element(p,i));
	set_element(p10,i,get_element(p,i));
      }
    
    set_element(p11,m,get_element(p11,m)+hm);
    set_element(p11,n,get_element(p11,n)+hn);
    set_element(p00,m,get_element(p00,m)-hm);
    set_element(p00,n,get_element(p00,n)-hn);
    set_element(p10,m,get_element(p10,m)+hm);
    set_element(p10,n,get_element(p10,n)-hn);
    set_element(p01,m,get_element(p01,m)-hm);
    set_element(p01,n,get_element(p01,n)+hn);

    rT result=(f(p11)+f(p00)-f(p01)-f(p10))/(4*hm*hn);
    return result;
  }


  template<typename rT,typename pT>
  rT div(func_obj<rT,pT>& f,const pT& p)
  {
    rT result=0;
    for(int i=0;i<get_size(p);++i)
      {
	result+=hessian(f,p,i,i);
      }
    return result;
  }

}

#endif