Package org.drip.numerical.integration

Class NewtonCotesQuadratureGenerator

java.lang.Object
org.drip.numerical.integration.NewtonCotesQuadratureGenerator
public class NewtonCotesQuadratureGenerator
extends java.lang.Object
NewtonCotesQuadratureGenerator generates the Array of Newton-Cotes Based Quadrature Abscissa and their corresponding Weights. The References are:

  • Briol, F. X., C. J. Oates, M. Girolami, and M. A. Osborne (2015): Frank-Wolfe Bayesian Quadrature: Probabilistic Integration with Theoretical Guarantees arXiv
  • Forsythe, G. E., M. A. Malcolm, and C. B. Moler (1977): Computer Methods for Mathematical Computation Prentice Hall Englewood Cliffs NJ
  • Leader, J. J. (2004): Numerical Analysis and Scientific Computation Addison Wesley
  • Stoer, J., and R. Bulirsch (1980): Introduction to Numerical Analysis Springer-Verlag New York
  • Wikipedia (2019): Numerical Integration https://en.wikipedia.org/wiki/Numerical_integration


Author:
Lakshmi Krishnamurthy

  • Constructor Summary

    Constructors
    Constructor Description
    NewtonCotesQuadratureGenerator()  

  • Method Summary

    Modifier and Type Method Description
    static QuadratureEstimator GaussHermite​(int intermediatePointCount)
    Generate the Newton-Cotes Quadrature for the Gauss-Hermite Indefinite Integral over (-Infinity, +Infinity)
    static QuadratureEstimator GaussLaguerreLeftDefinite​(double left, int intermediatePointCount)
    Generate the Newton-Cotes Quadrature for the Gauss-Laguerre Left-Definite Integral over (a, +Infinity)
    static QuadratureEstimator GaussLaguerreRightDefinite​(double right, int intermediatePointCount)
    Generate the Newton-Cotes Quadrature for the Gauss-Laguerre Left-Definite Integral over (-Infinity, a)
    static QuadratureEstimator MinusOne_PlusOne​(double left, double right, int intermediatePointCount)
    Generate the Newton-Cotes of Equally Spaced Quadrature over (a, b) onto (-1, +1)
    static QuadratureEstimator MinusOne_PlusOne​(AbscissaTransform abscissaTransformer, int intermediatePointCount)
    Generate the Newton-Cotes of Equally Spaced Quadrature over (-1, +1)
    static QuadratureEstimator Zero_PlusOne​(double left, double right, int intermediatePointCount)
    Generate the Newton-Cotes of Equally Spaced Quadrature over (a, b) onto (0, +1)
    static QuadratureEstimator Zero_PlusOne​(AbscissaTransform abscissaTransformer, int intermediatePointCount)
    Generate the Newton-Cotes of Equally Spaced Quadrature over (0, +1)

    Methods inherited from class java.lang.Object

    equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Constructor Details

    • NewtonCotesQuadratureGenerator

      public NewtonCotesQuadratureGenerator()

  • Method Details

    • Zero_PlusOne

      public static final QuadratureEstimator Zero_PlusOne​(AbscissaTransform abscissaTransformer, int intermediatePointCount)
      Generate the Newton-Cotes of Equally Spaced Quadrature over (0, +1)
      Parameters:
      abscissaTransformer - The Abscissa Transformer
      intermediatePointCount - Number of Intermediate Points
      Returns:
      The Newton-Cotes of Equally Spaced Quadrature over (0, +1)

    • MinusOne_PlusOne

      public static final QuadratureEstimator MinusOne_PlusOne​(AbscissaTransform abscissaTransformer, int intermediatePointCount)
      Generate the Newton-Cotes of Equally Spaced Quadrature over (-1, +1)
      Parameters:
      abscissaTransformer - The Abscissa Transformer
      intermediatePointCount - Number of Intermediate Points
      Returns:
      The Newton-Cotes of Equally Spaced Quadrature over (1, +1)

    • Zero_PlusOne

      public static final QuadratureEstimator Zero_PlusOne​(double left, double right, int intermediatePointCount)
      Generate the Newton-Cotes of Equally Spaced Quadrature over (a, b) onto (0, +1)
      Parameters:
      left - Left Integrand Quadrature Limit
      right - Right Integrand Quadrature Limit
      intermediatePointCount - Number of Intermediate Points
      Returns:
      The Newton-Cotes of Equally Spaced Quadrature over (a, b) onto (0, +1)

    • MinusOne_PlusOne

      public static final QuadratureEstimator MinusOne_PlusOne​(double left, double right, int intermediatePointCount)
      Generate the Newton-Cotes of Equally Spaced Quadrature over (a, b) onto (-1, +1)
      Parameters:
      left - Left Integrand Quadrature Limit
      right - Right Integrand Quadrature Limit
      intermediatePointCount - Number of Intermediate Points
      Returns:
      The Newton-Cotes of Equally Spaced Quadrature over (a, b) onto (-1, +1)

    • GaussLaguerreLeftDefinite

      public static final QuadratureEstimator GaussLaguerreLeftDefinite​(double left, int intermediatePointCount)
      Generate the Newton-Cotes Quadrature for the Gauss-Laguerre Left-Definite Integral over (a, +Infinity)
      Parameters:
      left - Left Integrand Quadrature Limit
      intermediatePointCount - Number of Intermediate Points
      Returns:
      The Newton-Cotes Quadrature for the Gauss-Laguerre Left-Definite Integral over (a, +Infinity)

    • GaussLaguerreRightDefinite

      public static final QuadratureEstimator GaussLaguerreRightDefinite​(double right, int intermediatePointCount)
      Generate the Newton-Cotes Quadrature for the Gauss-Laguerre Left-Definite Integral over (-Infinity, a)
      Parameters:
      right - Right Integrand Quadrature Limit
      intermediatePointCount - Number of Intermediate Points
      Returns:
      The Newton-Cotes Quadrature for the Gauss-Laguerre Left-Definite Integral over (-Infinity, a)

    • GaussHermite

      public static final QuadratureEstimator GaussHermite​(int intermediatePointCount)
      Generate the Newton-Cotes Quadrature for the Gauss-Hermite Indefinite Integral over (-Infinity, +Infinity)
      Parameters:
      intermediatePointCount - Number of Intermediate Points
      Returns:
      The Newton-Cotes Quadrature for the Gauss-Hermite Indefinite Integral over (-Infinity, +Infinity)