com.opengamma.strata.math.impl.integration

Class GaussJacobiWeightAndAbscissaFunction

java.lang.Object

com.opengamma.strata.math.impl.integration.GaussJacobiWeightAndAbscissaFunction

All Implemented Interfaces:

QuadratureWeightAndAbscissaFunction

public class GaussJacobiWeightAndAbscissaFunction
extends Object
implements QuadratureWeightAndAbscissaFunction

Class that generates weights and abscissas for Gauss-Jacobi quadrature. The weights $w_i$ are given by: $$ \begin{align*} w_i = \frac{2^{\alpha + \beta}(2n + \alpha + \beta)\Gamma(\alpha + n)\Gamma(\beta + n)} {n!\Gamma(n + \alpha + \beta + 1)J_i'(x_i) J_{i - 1}} \end{align*} $$ where $x_i$ is the $i^{th}$ root of the orthogonal polynomial, $J_i$ is the $i^{th}$ polynomial and $J_i'$ is the first derivative of the $i^{th}$ polynomial. The orthogonal polynomial is generated by JacobiPolynomialFunction.

Constructor Summary

Constructors

Constructor and Description
GaussJacobiWeightAndAbscissaFunction() Creates an instance.
GaussJacobiWeightAndAbscissaFunction(double alpha, double beta) Creates an instance.

Method Summary

Modifier and Type	Method and Description
GaussianQuadratureData	generate(int n)

Methods inherited from class java.lang.Object

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

Constructor Detail

GaussJacobiWeightAndAbscissaFunction

public GaussJacobiWeightAndAbscissaFunction()

Creates an instance. Sets $\alpha = 0$ and $\beta = 0$

GaussJacobiWeightAndAbscissaFunction

public GaussJacobiWeightAndAbscissaFunction(double alpha,
                                            double beta)

Creates an instance.

Parameters:

alpha - The value of $\alpha$ to use when generating the polynomials

beta - The value of $\beta$ to use when generating the polynomials

Method Detail

generate

public GaussianQuadratureData generate(int n)

Specified by:

generate in interface QuadratureWeightAndAbscissaFunction

Parameters:

n - The number of weights and abscissas to generate, not negative or zero

Returns:

An object containing the weights and abscissas