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/**
\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
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