org.apache.commons.math3.analysis.integration.gauss

Class HermiteRuleFactory

java.lang.Object

org.apache.commons.math3.analysis.integration.gauss.BaseRuleFactory<java.lang.Double>

org.apache.commons.math3.analysis.integration.gauss.HermiteRuleFactory

public class HermiteRuleFactory
extends BaseRuleFactory<java.lang.Double>

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-x2
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. The initial interval for the application of the bisection method is based on the roots of the previous Hermite polynomial (interlacing). Upper and lower bounds of these roots are provided by

I. Krasikov,
Nonnegative quadratic forms and bounds on orthogonal polynomials,
Journal of Approximation theory 111, 31-49

Since:

3.3

Field Summary

Fields

Modifier and Type	Field and Description
private static double	H0 π-1/4
private static double	H1 π-1/4 √2
private static double	SQRT_PI π1/2

Constructor Summary

Constructors

Constructor and Description
HermiteRuleFactory()

Method Summary

Methods

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

Methods inherited from class org.apache.commons.math3.analysis.integration.gauss.BaseRuleFactory

addRule, getRule, getRuleInternal

Methods inherited from class java.lang.Object

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

Field Detail

SQRT_PI

private static final double SQRT_PI

π^1/2

See Also:

Constant Field Values

H0

private static final double H0

π^-1/4

See Also:

Constant Field Values

H1

private static final double H1

π^-1/4 √2

See Also:

Constant Field Values

Constructor Detail

HermiteRuleFactory

public HermiteRuleFactory()

Method Detail

computeRule

protected Pair<java.lang.Double[],java.lang.Double[]> computeRule(int numberOfPoints)
                                                           throws DimensionMismatchException

Computes the rule for the given order.

Specified by:

computeRule in class BaseRuleFactory<java.lang.Double>

Parameters:

numberOfPoints - Order of the rule to be computed.

Returns:

the computed rule.

Throws:

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