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

@Deprecated
public class LegendreGaussIntegrator
extends BaseAbstractUnivariateIntegrator

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

Version:

$Id: LegendreGaussIntegrator.java 7721 2013-02-14 14:07:13Z CardosoP $

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

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

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, integrate, setup

Methods inherited from class java.lang.Object

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

Constructor Detail

LegendreGaussIntegrator

public LegendreGaussIntegrator(int n,
                               double relativeAccuracy,
                               double absoluteAccuracy,
                               int minimalIterationCount,
                               int maximalIterationCount)
                        throws 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:

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)

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

LegendreGaussIntegrator

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

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:

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 Detail

doIntegrate

protected double doIntegrate()
                      throws 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