Package org.drip.numerical.integration

Class AbscissaTransform

java.lang.Object

org.drip.numerical.integration.AbscissaTransform

public class AbscissaTransform
extends java.lang.Object

AbscissaTransform transforms the Abscissa over into Corresponding Integrand Variable. 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
AbscissaTransform(R1ToR1 r1ToR1VariateChange, R1ToR1 r1PointValueScale, double quadratureScale)	AbscissaTransform Constructor

Method Summary

Modifier and Type	Method	Description
static AbscissaTransform	DisplaceAndScaleMinusOne_PlusOne(double left, double right)	Generate the Scaled and Displaced Abscissa Transform from (left, right) To (-1, +1)
static AbscissaTransform	DisplaceAndScaleZero_PlusOne(double left, double right)	Generate the Scaled and Displaced Abscissa Transform from (left, right) To (0, +1)
static AbscissaTransform	GaussHermite()	Generate the Gauss-Hermite Abscissa Transform
static AbscissaTransform	GaussLaguerreLeftDefinite(double left)	Generate the Gauss-Laguerre Abscissa Transform for Integrals in [a, +Infinity]
static AbscissaTransform	GaussLaguerreRightDefinite(double right)	Generate the Gauss-Laguerre Abscissa Transform for Integrals in [-Infinity, a]
R1ToR1	pointValueScale()	Retrieve the R1 Point Value Scale Function
double	quadratureScale()	Retrieve the Quadrature Scale
R1ToR1	variateChange()	Retrieve the R1 to R1 Variate Change Function

Methods inherited from class java.lang.Object

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

Constructor Details

AbscissaTransform

public AbscissaTransform(R1ToR1 r1ToR1VariateChange,
R1ToR1 r1PointValueScale,
double quadratureScale)
                  throws java.lang.Exception

AbscissaTransform Constructor

Parameters:

r1ToR1VariateChange - R¹ to R¹ Variate Change Function

r1PointValueScale - R¹ Point Value Scale Function

quadratureScale - Quadrature Scale

Throws:

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

Method Details

DisplaceAndScaleZero_PlusOne

public static final AbscissaTransform DisplaceAndScaleZero_PlusOne(double left,
double right)

Generate the Scaled and Displaced Abscissa Transform from (left, right) To (0, +1)

Parameters:

left - Span Left

right - Span Right

Returns:

The Scaled and Displaced Abscissa Transform from (left, right) To (0, +1)

DisplaceAndScaleMinusOne_PlusOne

public static final AbscissaTransform DisplaceAndScaleMinusOne_PlusOne(double left,
double right)

Generate the Scaled and Displaced Abscissa Transform from (left, right) To (-1, +1)

Parameters:

left - Span Left

right - Span Right

Returns:

The Scaled and Displaced Abscissa Transform from (left, right) To (-1, +1)

GaussHermite

public static final AbscissaTransform GaussHermite()

Generate the Gauss-Hermite Abscissa Transform

Returns:

The Gauss-Hermite Abscissa Transform

GaussLaguerreLeftDefinite

public static final AbscissaTransform GaussLaguerreLeftDefinite(double left)

Generate the Gauss-Laguerre Abscissa Transform for Integrals in [a, +Infinity]

Parameters:

left - Span Left

Returns:

The Gauss-Laguerre Abscissa Transform for Integrals in [a, +Infinity]

GaussLaguerreRightDefinite

public static final AbscissaTransform GaussLaguerreRightDefinite(double right)

Generate the Gauss-Laguerre Abscissa Transform for Integrals in [-Infinity, a]

Parameters:

right - Span Right

Returns:

The Gauss-Laguerre Abscissa Transform for Integrals in [-Infinity, a]

variateChange

public R1ToR1 variateChange()

Retrieve the R¹ to R¹ Variate Change Function

Returns:

The R¹ to R¹ Variate Change Function

pointValueScale

public R1ToR1 pointValueScale()

Retrieve the R¹ Point Value Scale Function

Returns:

The R¹ Point Value Scale Function

quadratureScale

public double quadratureScale()

Retrieve the Quadrature Scale

Returns:

The Quadrature Scale