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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

Hierarchy

Implements

Index

Constructors

constructor

  • Parameters

    • maxIterations: Size
    • absAccuracy: Real
    • Default value relAccuracy: Real = QL_NULL_REAL
    • Default value useConvergenceEstimate: boolean = true

    Returns GaussLobattoIntegral

Properties

Protected _relAccuracy

_relAccuracy: Real

Protected _useConvergenceEstimate

_useConvergenceEstimate: boolean

Methods

absoluteAccuracy

  • absoluteAccuracy(): Real

absoluteError

  • absoluteError(): Real

Protected adaptivGaussLobattoStep

Protected calculateAbsTolerance

f

increaseNumberOfEvaluations

  • increaseNumberOfEvaluations(increase: Size): void

Protected integrate

integrationSuccess

  • integrationSuccess(): boolean

maxEvaluations

  • maxEvaluations(): Size

numberOfEvaluations

  • numberOfEvaluations(): Size

setAbsoluteAccuracy

  • setAbsoluteAccuracy(accuracy: Real): void

setAbsoluteError

  • setAbsoluteError(error: Real): void

setMaxEvaluations

  • setMaxEvaluations(maxEvaluations: Size): void

setNumberOfEvaluations

  • setNumberOfEvaluations(evaluations: Size): void