Package org.drip.numerical.quadrature

Class OrthogonalPolynomial

java.lang.Object

org.drip.function.definition.R1ToR1

org.drip.numerical.estimation.RxToR1Series

org.drip.numerical.estimation.R1ToR1Series

org.drip.numerical.quadrature.OrthogonalPolynomial

public class OrthogonalPolynomial
extends R1ToR1Series

OrthogonalPolynomial implements a Single Basis Orthogonal Polynomial used in the Construction of the Quadrature. The References are:

• Abramowitz, M., and I. A. Stegun (2007): Handbook of Mathematics Functions Dover Book on Mathematics
• Gil, A., J. Segura, and N. M. Temme (2007): Numerical Methods for Special Functions Society for Industrial and Applied Mathematics Philadelphia
• Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery (2007): Numerical Recipes: The Art of Scientific Computing 3rd Edition Cambridge University Press New York
• Stoer, J., and R. Bulirsch (2002): Introduction to Numerical Analysis 3rd Edition Springer
• Wikipedia (2019): Gaussian Quadrature https://en.wikipedia.org/wiki/Gaussian_quadrature

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

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor	Description
OrthogonalPolynomial(java.util.TreeMap<java.lang.Integer,java.lang.Double> termWeightMap)	OrthogonalPolynomial Constructor

Method Summary

Modifier and Type	Method	Description
int	degree()	Retrieve the Degree of the Orthogonal Polynomial
double	degreeCoefficient()	Retrieve the Coefficient of the Degree of the Orthogonal Polynomial
double	legendreNodeWeight(double xNode)	Compute the Legendre (i.e., Unit Orthogonal Weight) Node Weight
double	lobattoNodeWeight(double xNode)	Compute the Lobatto (i.e., Unit Orthogonal Weight) Node Weight

Methods inherited from class org.drip.numerical.estimation.R1ToR1Series

cumulative, derivative, evaluate, generate, r1ToR1SeriesTerm

Methods inherited from class org.drip.numerical.estimation.RxToR1Series

proportional, termWeightMap

Methods inherited from class org.drip.function.definition.R1ToR1

antiDerivative, differential, differential, integrate, maxima, maxima, minima, minima, poleResidue

Methods inherited from class java.lang.Object

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

Constructor Details

OrthogonalPolynomial

public OrthogonalPolynomial(java.util.TreeMap<java.lang.Integer,java.lang.Double> termWeightMap)
                     throws java.lang.Exception

OrthogonalPolynomial Constructor

Parameters:

termWeightMap - Error Term Weight Map

Throws:

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

Method Details

degree

public int degree()

Retrieve the Degree of the Orthogonal Polynomial

Returns:

Degree of the Orthogonal Polynomial

degreeCoefficient

public double degreeCoefficient()

Retrieve the Coefficient of the Degree of the Orthogonal Polynomial

Returns:

Coefficient of the Degree of the Orthogonal Polynomial

legendreNodeWeight

public double legendreNodeWeight(double xNode)
                          throws java.lang.Exception

Compute the Legendre (i.e., Unit Orthogonal Weight) Node Weight

Parameters:

xNode - The Node X

Returns:

The Legendre (i.e., Unit Orthogonal Weight) Node Weight

Throws:

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

lobattoNodeWeight

public double lobattoNodeWeight(double xNode)
                         throws java.lang.Exception

Compute the Lobatto (i.e., Unit Orthogonal Weight) Node Weight

Parameters:

xNode - The Node X

Returns:

The Lobatto (i.e., Unit Orthogonal Weight) Node Weight

Throws:

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