QuantLib: GaussLobattoIntegral Class Reference

A free/open-source library for quantitative finance Reference manual - version 1.20

Public Member Functions | Protected Member Functions | Protected Attributes | Static Protected Attributes | List of all members
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