Package org.drip.numerical.integration

Class GeneralizedMidPointQuadrature

java.lang.Object

org.drip.numerical.integration.GeneralizedMidPointQuadrature

public class GeneralizedMidPointQuadrature
extends java.lang.Object

GeneralizedMidPointQuadrature computes the R¹ Numerical Estimate of a Function Quadrature using the Generalized Mid-Point Scheme. 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

• Module = Computational Core Module
• Library = Numerical Analysis Library
• Project = Numerical Quadrature, Differentiation, Eigenization, Linear Algebra, and Utilities
• Package = R¹ R^d Numerical Integration Schemes

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor	Description
GeneralizedMidPointQuadrature(R1ToR1 r1ToR1, int nodeCount, int seriesTermCount)	GeneralizedMidPointQuadrature Constructor

Method Summary

Modifier and Type	Method	Description
double	integrate(double left, double right)	Integrate the Integrand from Left Through Right
int	nodeCount()	Retrieve the Quadrature Node Count
R1ToR1	r1ToR1()	Retrieve the R1 To R1 Integrand
int	seriesTermCount()	Retrieve the Series Term Count

Methods inherited from class java.lang.Object

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

Constructor Details

GeneralizedMidPointQuadrature

public GeneralizedMidPointQuadrature(R1ToR1 r1ToR1,
int nodeCount,
int seriesTermCount)
                              throws java.lang.Exception

GeneralizedMidPointQuadrature Constructor

Parameters:

r1ToR1 - R¹ To R¹ Integrand

nodeCount - Quadrature Node Count

seriesTermCount - Series Term Count

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

Method Details

r1ToR1

public R1ToR1 r1ToR1()

Retrieve the R¹ To R¹ Integrand

Returns:

The R¹ To R¹ Integrand

nodeCount

public int nodeCount()

Retrieve the Quadrature Node Count

Returns:

The Quadrature Node Count

seriesTermCount

public int seriesTermCount()

Retrieve the Series Term Count

Returns:

The Series Term Count

integrate

public double integrate(double left,
double right)
                 throws java.lang.Exception

Integrate the Integrand from Left Through Right

Parameters:

left - Left Limit

right - Right Limit

Returns:

The Integrand Quadrature

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid