org.hipparchus.analysis.integration.gauss

Class FieldHermiteRuleFactory<T extends CalculusFieldElement<T>>

java.lang.Object

org.hipparchus.analysis.integration.gauss.FieldAbstractRuleFactory<T>

org.hipparchus.analysis.integration.gauss.FieldHermiteRuleFactory<T>

Type Parameters:

T - Type of the number used to represent the points and weights of the quadrature rules.

All Implemented Interfaces:

FieldRuleFactory<T>

public class FieldHermiteRuleFactory<T extends CalculusFieldElement<T>>
extends FieldAbstractRuleFactory<T>

Factory that creates a Gauss-type quadrature rule using Hermite polynomials of the first kind. Such a quadrature rule allows the calculation of improper integrals of a function

\(f(x) e^{-x^2}\)

Recurrence relation and weights computation follow Abramowitz and Stegun, 1964.

The coefficients of the standard Hermite polynomials grow very rapidly. In order to avoid overflows, each Hermite polynomial is normalized with respect to the underlying scalar product.

Since:

2.0

Constructor Summary

Constructors

Constructor and Description
FieldHermiteRuleFactory(Field<T> field) Simple constructor

Method Summary

Modifier and Type	Method and Description
protected Pair<T[],T[]>	computeRule(int numberOfPoints) Computes the rule for the given order.

Methods inherited from class org.hipparchus.analysis.integration.gauss.FieldAbstractRuleFactory

enforceSymmetry, findRoots, getField, getRule

Methods inherited from class java.lang.Object

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

Constructor Detail

FieldHermiteRuleFactory

public FieldHermiteRuleFactory(Field<T> field)

Simple constructor

Parameters:

field - field to which rule coefficients belong

Method Detail

computeRule

protected Pair<T[],T[]> computeRule(int numberOfPoints)
                             throws MathIllegalArgumentException

Computes the rule for the given order.

Specified by:

computeRule in class FieldAbstractRuleFactory<T extends CalculusFieldElement<T>>

Parameters:

numberOfPoints - Order of the rule to be computed.

Returns:

the computed rule.

Throws:

MathIllegalArgumentException - if the elements of the pair do not have the same length.