limes::methods Namespace Reference

Classes
struct	adaptive
	Adaptive integration with recursive interval subdivision until convergence. More...
struct	adaptive_composed
	Wraps any base method with adaptive interval subdivision until convergence. More...
struct	gauss_legendre
	N-point Gauss-Legendre quadrature, achieving degree 2N-1 polynomial exactness. More...
struct	is_integration_method
	Type trait to tag types as integration methods (specialized per method struct) More...
struct	is_integration_method< adaptive< T > >
struct	is_integration_method< adaptive_composed< M, T > >
struct	is_integration_method< gauss_legendre< N, T > >
struct	is_integration_method< monte_carlo< T > >
struct	is_integration_method< simpson< N, T > >
struct	is_integration_method< trapezoidal< N, T > >
struct	monte_carlo
	Monte Carlo integration using random sampling. Error decreases as O(1/sqrt(n)). More...
struct	simpson
	Simpson's 1/3 rule with N subdivisions (N must be even). Achieves O(h^4) convergence. More...
struct	trapezoidal
	Trapezoidal rule with N subdivisions. Achieves O(h^2) convergence. More...

Concepts
concept	IntegrationMethod
	A 1D integration method: callable with (function, lower, upper) returning integration_result.

Typedefs
template<typename T = double>
using	default_method = adaptive< T >
	The default integration method (adaptive Gauss-Legendre)

Functions
template<std::size_t N, typename T = double>
constexpr auto	gauss ()
	Factory for Gauss-Legendre quadrature.
template<typename T = double>
constexpr auto	adaptive_method (T tol=T(1e-10))
	Factory for adaptive integration.
template<typename T = double>
constexpr auto	monte_carlo_method (std::size_t n)
	Factory for Monte Carlo integration.
template<std::size_t N, typename T = double>
constexpr auto	simpson_method ()
	Factory for Simpson's rule.
template<std::size_t N, typename T = double>
constexpr auto	trapezoidal_method ()
	Factory for trapezoidal rule.
template<typename M , typename T = double>
constexpr auto	make_adaptive (M base_method, T tol=T(1e-10))
	Factory for adaptive composition of any base method.

Variables
template<typename M >
constexpr bool	is_integration_method_v = is_integration_method<M>::value

Typedef Documentation

default_method

template<typename T = double>

using limes::methods::default_method = typedef adaptive<T>

The default integration method (adaptive Gauss-Legendre)

Definition at line 314 of file methods.hpp.

Function Documentation

adaptive_method()

template<typename T = double>

constexpr auto limes::methods::adaptive_method ( T  tol = T(1e-10) )

constexpr

Factory for adaptive integration.

Definition at line 97 of file methods.hpp.

gauss()

template<std::size_t N, typename T = double>

constexpr auto limes::methods::gauss ( )

constexpr

Factory for Gauss-Legendre quadrature.

Definition at line 58 of file methods.hpp.

make_adaptive()

template<typename M , typename T = double>

constexpr auto limes::methods::make_adaptive ( M  base_method, T  tol = T(1e-10)  )

constexpr

Factory for adaptive composition of any base method.

Definition at line 304 of file methods.hpp.

monte_carlo_method()

template<typename T = double>

constexpr auto limes::methods::monte_carlo_method ( std::size_t  n )

constexpr

Factory for Monte Carlo integration.

Definition at line 162 of file methods.hpp.

simpson_method()

template<std::size_t N, typename T = double>

constexpr auto limes::methods::simpson_method ( )

constexpr

Factory for Simpson's rule.

Definition at line 204 of file methods.hpp.

trapezoidal_method()

template<std::size_t N, typename T = double>

constexpr auto limes::methods::trapezoidal_method ( )

constexpr

Factory for trapezoidal rule.

Definition at line 241 of file methods.hpp.

Variable Documentation

is_integration_method_v

template<typename M >

constexpr bool limes::methods::is_integration_method_v = is_integration_method<M>::value

inlineconstexpr

Definition at line 20 of file concepts.hpp.