ratf.h File Reference

#include <cmath>
#include "config.h"
#include "util/numeric.h"
#include "util/poly.h"

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Namespaces
namespace	alfi::ratf
	Namespace providing support for rational functions.
namespace	alfi

Typedefs
template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>
using	alfi::ratf::RationalFunction = std::pair<Container<Number>, Container<Number>>
	Represents a rational function \(\displaystyle f(x) = \frac{A(x)}{B(x)}\), where \(A(x)\) and \(B(x)\) are polynomials.

Functions
template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>
std::enable_if_t<!traits::has_size< Number >::value, Number >	alfi::ratf::val_mul (const RationalFunction< Number, Container > &rf, const Number &x)
	Evaluates the rational function at a scalar point using Horner's method.
template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>
std::enable_if_t< traits::has_size< Container< Number > >::value, Container< Number > >	alfi::ratf::val_mul (const RationalFunction< Number, Container > &rf, const Container< Number > &xx)
	Evaluates the rational function at each point in the container using val_mul for scalar values.
template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>
std::enable_if_t<!traits::has_size< Number >::value, Number >	alfi::ratf::val_div (const RationalFunction< Number, Container > &rf, const Number &x)
	Evaluates the rational function at a scalar point by factoring out powers of x.
template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>
std::enable_if_t< traits::has_size< Container< Number > >::value, Container< Number > >	alfi::ratf::val_div (const RationalFunction< Number, Container > &rf, const Container< Number > &xx)
	Evaluates the rational function at each point in the container using val_div for scalar values.
template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>
std::enable_if_t<!traits::has_size< Number >::value, Number >	alfi::ratf::val (const RationalFunction< Number, Container > &rf, const Number &x)
	Evaluates the rational function at a scalar point.
template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>
std::enable_if_t< traits::has_size< Container< Number > >::value, Container< Number > >	alfi::ratf::val (const RationalFunction< Number, Container > &rf, const Container< Number > &xx)
	Evaluates the rational function at each point in the container using val for scalar values.
template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>
RationalFunction< Number, Container >	alfi::ratf::pade (Container< Number > P, SizeT n, SizeT m, const Number &epsilon=std::numeric_limits< Number >::epsilon())
	Computes the [n / m] Pade approximant of the polynomial P about the point \(x = 0\).