org.hipparchus.analysis.integration.gauss

Class AbstractRuleFactory

java.lang.Object

org.hipparchus.analysis.integration.gauss.AbstractRuleFactory

All Implemented Interfaces:

RuleFactory

Direct Known Subclasses:

ConvertingRuleFactory, HermiteRuleFactory, LaguerreRuleFactory, LegendreRuleFactory

public abstract class AbstractRuleFactory
extends Object
implements RuleFactory

Base class for rules that determines the integration nodes and their weights. Subclasses must implement the computeRule method.

Since:

2.0

Constructor Summary

Constructors

Constructor and Description
AbstractRuleFactory()

Method Summary

Modifier and Type	Method and Description
protected abstract Pair<double[],double[]>	computeRule(int numberOfPoints) Computes the rule for the given order.
protected void	enforceSymmetry(double[] roots) Enforce symmetry of roots.
protected double[]	findRoots(int n, UnivariateFunction ratioEvaluator) Computes roots of the associated orthogonal polynomials.
Pair<double[],double[]>	getRule(int numberOfPoints) Gets a copy of the quadrature rule with the given number of integration points.

Methods inherited from class java.lang.Object

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

Constructor Detail

AbstractRuleFactory

public AbstractRuleFactory()

Method Detail

getRule

public Pair<double[],double[]> getRule(int numberOfPoints)
                                throws MathIllegalArgumentException

Gets a copy of the quadrature rule with the given number of integration points. The number of points is arbitrarily limited to 1000. It prevents resources exhaustion. In practice the number of points is often much lower.

Specified by:

getRule in interface RuleFactory

Parameters:

numberOfPoints - Number of integration points.

Returns:

a copy of the integration rule.

Throws:

MathIllegalArgumentException - if numberOfPoints < 1.

computeRule

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

Computes the rule for the given order.

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.

findRoots

protected double[] findRoots(int n,
                             UnivariateFunction ratioEvaluator)

Computes roots of the associated orthogonal polynomials.

The roots are found using the Aberth method. The guess points for initializing search for degree n are fixed for degrees 1 and 2 and are selected from n-1 roots of rule n-1 (the two extreme roots are used, plus the n-1 intermediate points between all roots).

Parameters:

n - number of roots to search for

ratioEvaluator - function evaluating the ratio Pₙ(x)/Pₙ'(x)

Returns:

sorted array of roots

enforceSymmetry

protected void enforceSymmetry(double[] roots)

Enforce symmetry of roots.

Parameters:

roots - roots to process in place