org.apache.commons.math3.analysis.integration

Class TrapezoidIntegrator

java.lang.Object

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

org.apache.commons.math3.analysis.integration.TrapezoidIntegrator

All Implemented Interfaces:

UnivariateIntegrator

public class TrapezoidIntegrator
extends BaseAbstractUnivariateIntegrator

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

The function should be integrable.

Since:

1.2

Field Summary

Fields

Modifier and Type	Field and Description
private double	s Intermediate result.
static int	TRAPEZOID_MAX_ITERATIONS_COUNT Maximum number of iterations for trapezoid.

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 and Description
TrapezoidIntegrator() Construct a trapezoid integrator with default settings.
TrapezoidIntegrator(double relativeAccuracy, double absoluteAccuracy, int minimalIterationCount, int maximalIterationCount) Build a trapezoid integrator with given accuracies and iterations counts.
TrapezoidIntegrator(int minimalIterationCount, int maximalIterationCount) Build a trapezoid integrator with given iteration counts.

Method Summary

Methods

Modifier and Type	Method and Description
protected double	doIntegrate() Method for implementing actual integration algorithms in derived classes.
(package private) double	stage(BaseAbstractUnivariateIntegrator baseIntegrator, int n) Compute the n-th stage integral of trapezoid rule.

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

TRAPEZOID_MAX_ITERATIONS_COUNT

public static final int TRAPEZOID_MAX_ITERATIONS_COUNT

Maximum number of iterations for trapezoid.

See Also:

Constant Field Values

s

private double s

Intermediate result.

Constructor Detail

TrapezoidIntegrator

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

Build a trapezoid 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 TRAPEZOID_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 TRAPEZOID_MAX_ITERATIONS_COUNT

TrapezoidIntegrator

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

Build a trapezoid integrator with given iteration counts.

Parameters:

minimalIterationCount - minimum number of iterations

maximalIterationCount - maximum number of iterations (must be less than or equal to TRAPEZOID_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 TRAPEZOID_MAX_ITERATIONS_COUNT

TrapezoidIntegrator

public TrapezoidIntegrator()

Construct a trapezoid integrator with default settings. (max iteration count set to TRAPEZOID_MAX_ITERATIONS_COUNT)

Method Detail

stage

double stage(BaseAbstractUnivariateIntegrator baseIntegrator,
           int n)
       throws TooManyEvaluationsException

Compute the n-th stage integral of trapezoid rule. This function should only be called by API integrate() in the package. To save time it does not verify arguments - caller does.

The interval is divided equally into 2^n sections rather than an arbitrary m sections because this configuration can best utilize the already computed values.

Parameters:

baseIntegrator - integrator holding integration parameters

n - the stage of 1/2 refinement, n = 0 is no refinement

Returns:

the value of n-th stage integral

Throws:

TooManyEvaluationsException - if the maximal number of evaluations is exceeded.

doIntegrate

protected double doIntegrate()
                      throws MathIllegalArgumentException,
                             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

MathIllegalArgumentException