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

java.lang.Object
  org.apache.commons.math3.analysis.integration.BaseAbstractUnivariateIntegrator
      org.apache.commons.math3.analysis.integration.RombergIntegrator

All Implemented Interfaces:

UnivariateIntegrator

public class RombergIntegrator
extends BaseAbstractUnivariateIntegrator

Implements the Romberg Algorithm for integration of real univariate functions. For reference, see Introduction to Numerical Analysis, ISBN 038795452X, chapter 3.

Romberg integration employs k successive refinements of the trapezoid rule to remove error terms less than order O(N^(-2k)). Simpson's rule is a special case of k = 2.

Since:

1.2

Version:

$Id: RombergIntegrator.java 3720 2012-03-16 16:34:17Z CardosoP $

Field Summary

static int

ROMBERG_MAX_ITERATIONS_COUNT Maximal number of iterations for Romberg.

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

RombergIntegrator()
Construct a Romberg integrator with default settings (max iteration count set to ROMBERG_MAX_ITERATIONS_COUNT)

RombergIntegrator(double relativeAccuracy, double absoluteAccuracy, int minimalIterationCount, int maximalIterationCount)
Build a Romberg integrator with given accuracies and iterations counts.

RombergIntegrator(int minimalIterationCount, int maximalIterationCount)
Build a Romberg integrator with given iteration counts.

Method Summary

protected double

doIntegrate() 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

Field Detail

ROMBERG_MAX_ITERATIONS_COUNT

public static final int ROMBERG_MAX_ITERATIONS_COUNT

Maximal number of iterations for Romberg.

See Also:

Constant Field Values

Constructor Detail

RombergIntegrator

public RombergIntegrator(double relativeAccuracy,
                         double absoluteAccuracy,
                         int minimalIterationCount,
                         int maximalIterationCount)
                  throws NotStrictlyPositiveException,
                         NumberIsTooSmallException,
                         NumberIsTooLargeException

Build a Romberg integrator with given accuracies and iterations counts.

Parameters:

relativeAccuracy - relative accuracy of the result

absoluteAccuracy - absolute accuracy of the result

minimalIterationCount - minimum number of iterations

maximalIterationCount - maximum number of iterations (must be less than or equal to ROMBERG_MAX_ITERATIONS_COUNT)

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

NumberIsTooLargeException - if maximal number of iterations is greater than ROMBERG_MAX_ITERATIONS_COUNT

RombergIntegrator

public RombergIntegrator(int minimalIterationCount,
                         int maximalIterationCount)
                  throws NotStrictlyPositiveException,
                         NumberIsTooSmallException,
                         NumberIsTooLargeException

Build a Romberg integrator with given iteration counts.

Parameters:

minimalIterationCount - minimum number of iterations

maximalIterationCount - maximum number of iterations (must be less than or equal to ROMBERG_MAX_ITERATIONS_COUNT)

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

NumberIsTooLargeException - if maximal number of iterations is greater than ROMBERG_MAX_ITERATIONS_COUNT

RombergIntegrator

public RombergIntegrator()

Construct a Romberg integrator with default settings (max iteration count set to ROMBERG_MAX_ITERATIONS_COUNT)

Method Detail

doIntegrate

protected double doIntegrate()
                      throws TooManyEvaluationsException,
                             MaxCountExceededException

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