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)

Protected Member Functions
Real	integrate (const ext::function< Real(Real)> &f, Real a, Real b) const
Real	adaptivGaussLobattoStep (const ext::function< Real(Real)> &f, Real a, Real b, Real fa, Real fb, Real is) const
Real	calculateAbsTolerance (const ext::function< Real(Real)> &f, Real a, Real b) 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 \( \epsilon \), 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