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/**
\file num_diff.hpp
*/
#ifndef NUMDIFF_HPP
#define NUMDIFF_HPP
#include <core/optimizer.hpp>
#include <core/opt_traits.hpp>
#include <algorithm>
#include <limits>
#include <cmath>
namespace opt_utilities
{
/**
differentiable function
\tparam rT the return type
\tparam the parameter type
*/
template <typename rT,typename pT>
class dfunc_obj
:public func_obj<rT,pT>
{
private:
virtual pT do_diff(const pT& p)=0;
public:
/**
calculate the differentiation
\param p the self-var
\return the gradient at p
*/
pT diff(const pT& p)
{
return do_diff(p);
}
};
/**
When trying to diff an object function, when it is not differentiable,
this exception will be thrown.
*/
class underivable
:public opt_exception
{
public:
underivable()
:opt_exception("underivable")
{}
};
/**
calculate the numerical differential of a func_obj
*/
template <typename rT,typename pT>
pT numdiff(func_obj<rT,pT>& f,const pT& p)
{
rT ep=std::sqrt(std::numeric_limits<rT>::epsilon());
pT result;
resize(result,get_size(p));
pT p2;
resize(p2,get_size(p));
pT p1;
resize(p1,get_size(p));
for(size_t i=0;i<get_size(p);++i)
{
set_element(p2,i,get_element(p,i));
set_element(p1,i,get_element(p,i));
}
for(size_t i=0;i<get_size(p);++i)
{
typename element_type_trait<pT>::element_type h=
std::max(get_element(p,i),rT(1))*ep;
set_element(p2,i,get_element(p,i)+h);
set_element(p1,i,get_element(p,i)-h);
rT v2=f(p2);
rT v1=f(p1);
set_element(result,i,
(v2-v1)/h/2
);
set_element(p2,i,get_element(p,i));
set_element(p1,i,get_element(p,i));
}
return result;
}
/**
Help function to calculate the gradient of an objection function
func_obj, whether it is differentiable or not. If it is differentiable,
the gradient will be calculated by calling the diff member in the func_obj,
or a numerical calculation will be performed.
*/
template <typename rT,typename pT>
pT diff(func_obj<rT,pT>& f,const pT& p)
{
dfunc_obj<rT,pT>* pdf=dynamic_cast<dfunc_obj<rT,pT>*>(&f);
if(pdf)
{
return pdf->diff(p);
}
return numdiff(f,p);
}
}
#endif
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