org.hipparchus.analysis.integration.gauss

Class FieldAbstractRuleFactory<T extends CalculusFieldElement<T>>

java.lang.Object

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

Type Parameters:

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

All Implemented Interfaces:

FieldRuleFactory<T>

Direct Known Subclasses:

FieldHermiteRuleFactory, FieldLaguerreRuleFactory, FieldLegendreRuleFactory

public abstract class FieldAbstractRuleFactory<T extends CalculusFieldElement<T>>
extends Object
implements FieldRuleFactory<T>

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
FieldAbstractRuleFactory(Field<T> field) Simple constructor

Method Summary

Modifier and Type	Method and Description
protected abstract Pair<T[],T[]>	computeRule(int numberOfPoints) Computes the rule for the given order.
protected void	enforceSymmetry(T[] roots) Enforce symmetry of roots.
protected T[]	findRoots(int n, CalculusFieldUnivariateFunction<T> ratioEvaluator) Computes roots of the associated orthogonal polynomials.
Field<T>	getField() Get the field to which rule coefficients belong.
Pair<T[],T[]>	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

FieldAbstractRuleFactory

public FieldAbstractRuleFactory(Field<T> field)

Simple constructor

Parameters:

field - field to which rule coefficients belong

Method Detail

getField

public Field<T> getField()

Get the field to which rule coefficients belong.

Returns:

field to which rule coefficients belong

getRule

public Pair<T[],T[]> 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 FieldRuleFactory<T extends CalculusFieldElement<T>>

Parameters:

numberOfPoints - Number of integration points.

Returns:

a copy of the integration rule.

Throws:

MathIllegalArgumentException - if numberOfPoints < 1.

computeRule

protected abstract Pair<T[],T[]> 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 T[] findRoots(int n,
                        CalculusFieldUnivariateFunction<T> 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(T[] roots)

Enforce symmetry of roots.

Parameters:

roots - roots to process in place