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

java.lang.Object
  extended by org.apache.commons.math3.analysis.integration.BaseAbstractUnivariateIntegrator
      extended by 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 xi are the roots of the degree n Legendre polynomial. The weights ai of the quadrature formula integrals from -1 to +1 ∫ Li2 where Li (x) = ∏ (x-xk)/(xi-xk) for k != i.

Since:
1.2
Version:
$Id: LegendreGaussIntegrator.java 1364452 2012-07-22 22:30:01Z erans $

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


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