GaussLobattoIntegral Class Reference

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

#include <ql/math/integrals/gausslobattointegral.hpp>

Inherits Integrator.

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)
Real	operator() (const boost::function< Real(Real)> &f, Real a, Real b) const
Real	absoluteError () const
Size	numberOfEvaluations () const
virtual bool	integrationSuccess () const
void	setAbsoluteAccuracy (Real)
void	setMaxEvaluations (Size)
Real	absoluteAccuracy () const
Size	maxEvaluations () const

Protected Member Functions
Real	integrate (const boost::function< Real(Real)> &f, Real a, Real b) const
Real	adaptivGaussLobattoStep (const boost::function< Real(Real)> &f, Real a, Real b, Real fa, Real fb, Real is) const
Real	calculateAbsTolerance (const boost::function< Real(Real)> &f, Real a, Real b) const
Protected Member Functions inherited from Integrator
virtual Real	integrate (const boost::function< Real(Real)> &f, Real a, Real b) const =0
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_
static const Real	beta_
static const Real	x1_
static const Real	x2_
static const Real	x3_

Detailed Description

Integral of a one-dimensional function.

Given a target accuracy , the integral of a function between and 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