GaussLobattoIntegral Class Reference

Integral of a one-dimensional function. More...

#include <gausslobattointegral.hpp>

Inheritance diagram for GaussLobattoIntegral:

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Public Member Functions
	GaussLobattoIntegral (Size maxIterations, Real absAccuracy, Real relAccuracy=Null< Real >(), bool useConvergenceEstimate=true)
Public Member Functions inherited from Integrator
	Integrator (Real absoluteAccuracy, Size maxEvaluations)
virtual	~Integrator ()=default
Real	operator() (const std::function< Real(Real)> &f, Real a, Real b) const
void	setAbsoluteAccuracy (Real)
void	setMaxEvaluations (Size)
Real	absoluteAccuracy () const
Size	maxEvaluations () const
Real	absoluteError () const
Size	numberOfEvaluations () const
virtual bool	integrationSuccess () const

Protected Member Functions
Real	integrate (const std::function< Real(Real)> &f, Real a, Real b) const override
Real	adaptivGaussLobattoStep (const std::function< Real(Real)> &f, Real a, Real b, Real fa, Real fb, Real is) const
Real	calculateAbsTolerance (const std::function< Real(Real)> &f, Real a, Real b) const
Protected Member Functions inherited from Integrator
void	setAbsoluteError (Real error) const
void	setNumberOfEvaluations (Size evaluations) const
void	increaseNumberOfEvaluations (Size increase) const

Protected Attributes
Real	relAccuracy_
const bool	useConvergenceEstimate_

Static Protected Attributes
static const Real	alpha_ = std::sqrt(2.0/3.0)
static const Real	beta_ = 1.0/std::sqrt(5.0)
static const Real	x1_ = 0.94288241569547971906
static const Real	x2_ = 0.64185334234578130578
static const Real	x3_ = 0.23638319966214988028

Detailed Description

Integral of a one-dimensional function.

Given a target accuracy \( \epsilon \), the integral of a function \( f \) between \( a \) and \( b \) is calculated by means of the Gauss-Lobatto formula

References: This algorithm is a C++ implementation of the algorithm outlined in

W. Gander and W. Gautschi, Adaptive Quadrature - Revisited. BIT, 40(1):84-101, March 2000. CS technical report: ftp.inf.ethz.ch/pub/publications/tech-reports/3xx/306.ps.gz

The original MATLAB version can be downloaded here http://www.inf.ethz.ch/personal/gander/adaptlob.m

Definition at line 51 of file gausslobattointegral.hpp.

Constructor & Destructor Documentation

GaussLobattoIntegral()

GaussLobattoIntegral	(	Size	maxIterations,
		Real	absAccuracy,
		Real	relAccuracy = Null<Real>(),
		bool	useConvergenceEstimate = true
	)

Definition at line 36 of file gausslobattointegral.cpp.

Member Function Documentation

integrate()

Real integrate ( const std::function< Real(Real)> &  f, Real  a, Real  b  ) const

overrideprotectedvirtual

Implements Integrator.

Definition at line 45 of file gausslobattointegral.cpp.

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adaptivGaussLobattoStep()

Real adaptivGaussLobattoStep ( const std::function< Real(Real)> &  f, Real  a, Real  b, Real  fa, Real  fb, Real  is  ) const

protected

Definition at line 114 of file gausslobattointegral.cpp.

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calculateAbsTolerance()

Real calculateAbsTolerance ( const std::function< Real(Real)> &  f, Real  a, Real  b  ) const

protected

Definition at line 56 of file gausslobattointegral.cpp.

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Member Data Documentation

relAccuracy_

Real relAccuracy_

protected

Definition at line 67 of file gausslobattointegral.hpp.

useConvergenceEstimate_

const bool useConvergenceEstimate_

protected

Definition at line 68 of file gausslobattointegral.hpp.

alpha_

const Real alpha_ = std::sqrt(2.0/3.0)

staticprotected

Definition at line 69 of file gausslobattointegral.hpp.

beta_

const Real beta_ = 1.0/std::sqrt(5.0)

staticprotected

Definition at line 69 of file gausslobattointegral.hpp.

x1_

const Real x1_ = 0.94288241569547971906

staticprotected

Definition at line 69 of file gausslobattointegral.hpp.

x2_

const Real x2_ = 0.64185334234578130578

staticprotected

Definition at line 69 of file gausslobattointegral.hpp.

x3_

const Real x3_ = 0.23638319966214988028

staticprotected

Definition at line 69 of file gausslobattointegral.hpp.