Package org.apache.commons.math3.analysis.integration

Class LegendreGaussIntegrator

java.lang.Object

org.apache.commons.math3.analysis.integration.BaseAbstractUnivariateIntegrator

org.apache.commons.math3.analysis.integration.LegendreGaussIntegrator

All Implemented Interfaces:

UnivariateIntegrator

@Deprecated
public class LegendreGaussIntegrator
extends BaseAbstractUnivariateIntegrator

Deprecated.

As of 3.1 (to be removed in 4.0). Please use IterativeLegendreGaussIntegrator instead.

Implements the Legendre-Gauss quadrature formula.

Legendre-Gauss integrators are efficient integrators that can accurately integrate functions with few function evaluations. A Legendre-Gauss integrator using an n-points quadrature formula can integrate 2n-1 degree polynomials exactly.

These integrators evaluate the function on n carefully chosen abscissas in each step interval (mapped to the canonical [-1,1] interval). The evaluation abscissas are not evenly spaced and none of them are at the interval endpoints. This implies the function integrated can be undefined at integration interval endpoints.

The evaluation abscissas x_i are the roots of the degree n Legendre polynomial. The weights a_i of the quadrature formula integrals from -1 to +1 ∫ Li² where Li (x) = ∏ (x-x_k)/(x_i-x_k) for k != i.

Since:

1.2

Field Summary

Fields inherited from class org.apache.commons.math3.analysis.integration.BaseAbstractUnivariateIntegrator

DEFAULT_ABSOLUTE_ACCURACY, DEFAULT_MAX_ITERATIONS_COUNT, DEFAULT_MIN_ITERATIONS_COUNT, DEFAULT_RELATIVE_ACCURACY, iterations

Constructor Summary

Constructors

Constructor	Description
LegendreGaussIntegrator(int n, double relativeAccuracy, double absoluteAccuracy)	Deprecated. Build a Legendre-Gauss integrator with given accuracies.
LegendreGaussIntegrator(int n, double relativeAccuracy, double absoluteAccuracy, int minimalIterationCount, int maximalIterationCount)	Deprecated. Build a Legendre-Gauss integrator with given accuracies and iterations counts.
LegendreGaussIntegrator(int n, int minimalIterationCount, int maximalIterationCount)	Deprecated. Build a Legendre-Gauss integrator with given iteration counts.

Method Summary

Modifier and Type	Method	Description
protected double	doIntegrate()	Deprecated. Method for implementing actual integration algorithms in derived classes.

Methods inherited from class org.apache.commons.math3.analysis.integration.BaseAbstractUnivariateIntegrator

computeObjectiveValue, getAbsoluteAccuracy, getEvaluations, getIterations, getMax, getMaximalIterationCount, getMin, getMinimalIterationCount, getRelativeAccuracy, incrementCount, integrate, setup

Methods inherited from class java.lang.Object

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

Constructor Details

LegendreGaussIntegrator

public LegendreGaussIntegrator(int n,
 double relativeAccuracy,
 double absoluteAccuracy,
 int minimalIterationCount,
 int maximalIterationCount)
                        throws MathIllegalArgumentException,
NotStrictlyPositiveException,
NumberIsTooSmallException

Deprecated.

Build a Legendre-Gauss integrator with given accuracies and iterations counts.

Parameters:

n - number of points desired (must be between 2 and 5 inclusive)

relativeAccuracy - relative accuracy of the result

absoluteAccuracy - absolute accuracy of the result

minimalIterationCount - minimum number of iterations

maximalIterationCount - maximum number of iterations

Throws:

MathIllegalArgumentException - if number of points is out of [2; 5]

NotStrictlyPositiveException - if minimal number of iterations is not strictly positive

NumberIsTooSmallException - if maximal number of iterations is lesser than or equal to the minimal number of iterations

LegendreGaussIntegrator

public LegendreGaussIntegrator(int n,
 double relativeAccuracy,
 double absoluteAccuracy)
                        throws MathIllegalArgumentException

Deprecated.

Build a Legendre-Gauss integrator with given accuracies.

Parameters:

n - number of points desired (must be between 2 and 5 inclusive)

relativeAccuracy - relative accuracy of the result

absoluteAccuracy - absolute accuracy of the result

Throws:

MathIllegalArgumentException - if number of points is out of [2; 5]

LegendreGaussIntegrator

public LegendreGaussIntegrator(int n,
 int minimalIterationCount,
 int maximalIterationCount)
                        throws MathIllegalArgumentException

Deprecated.

Build a Legendre-Gauss integrator with given iteration counts.

Parameters:

n - number of points desired (must be between 2 and 5 inclusive)

minimalIterationCount - minimum number of iterations

maximalIterationCount - maximum number of iterations

Throws:

MathIllegalArgumentException - if number of points is out of [2; 5]

NotStrictlyPositiveException - if minimal number of iterations is not strictly positive

NumberIsTooSmallException - if maximal number of iterations is lesser than or equal to the minimal number of iterations

Method Details

doIntegrate

protected double doIntegrate()
                      throws MathIllegalArgumentException,
TooManyEvaluationsException,
MaxCountExceededException

Deprecated.

Method for implementing actual integration algorithms in derived classes.

Specified by:

doIntegrate in class BaseAbstractUnivariateIntegrator

Returns:

the root.

Throws:

TooManyEvaluationsException - if the maximal number of evaluations is exceeded.

MaxCountExceededException - if the maximum iteration count is exceeded or the integrator detects convergence problems otherwise

MathIllegalArgumentException