integration::Integrator< T > Class Template Reference

Class Integrator contains all kinds of weights for integration and differentiation of a function at equally spaced abscissae, up to a certain order k of accuray. More...

#include <integration.hpp>

Public Member Functions
T	bd_weights (int l)
	Returns the the backwards differencing coefficients. More...
int	get_k (void)
	Returns the order \(k\) of the integrator class. More...
T	gregory_omega (int j)
	Returns the Gregory weights at the integral boundaries (see gregory_weights). More...
T	gregory_weights (int n, int j)
	Returns the Gregory weights for integration. More...
template<class M >
M	integrate (const std::vector< M > &f, int n)
	Integrates a function using Gregory quadrature. More...
	Integrator (int k=0)
	Initializes the Integrator class for a given order k. More...
	Integrator (const Integrator &I)
int	k (void)
	Returns the order \(k\) of the integrator class. More...
Integrator &	operator= (const Integrator &I)
T	poly_differentiation (int i, int l)
	Returns the the weight needed for polynomial differentiation. More...
T	poly_integration (int i, int j, int l)
	Returns the the weight needed for polynomial integration. More...
T	poly_interpolation (int alpha, int l)
	Returns the the weight needed for polynomial interpolation. More...
T	rcorr (int m, int j, int l)
	Returns the special quadrature weights for computing integrals on the Matsubara axis. More...
	~Integrator ()

Detailed Description

template<typename T = double>
class integration::Integrator< T >

Class Integrator contains all kinds of weights for integration and differentiation of a function at equally spaced abscissae, up to a certain order k of accuray.

Purpose

Class Integrator contains all kinds of weights for integration and differentiation of a function at equally spaced abscissae, up to a certain order k of accuray. In particular, the class contains coefficients for

• Gregory quadrature
• polynomial quadrature
• polynomial interpolation
• polynomial differentiation
• coefficients for the backwards differencing formula (BDF)

Definition at line 128 of file integration.hpp.

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The documentation for this class was generated from the following file:

• integration.hpp