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QuantLib::GaussLobattoIntegral – Integral of a one-dimensional function.

Synopsis

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

Inherits QuantLib::Integrator.

Public Member Functions

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

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 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 $ \psilon $, 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

Author

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