org.apache.commons.math.analysis.integration
Class UnivariateRealIntegratorImpl

java.lang.Object
  org.apache.commons.math.analysis.integration.UnivariateRealIntegratorImpl

All Implemented Interfaces:

UnivariateRealIntegrator

Direct Known Subclasses:

LegendreGaussIntegrator, RombergIntegrator, SimpsonIntegrator, TrapezoidIntegrator

public abstract class UnivariateRealIntegratorImpl
extends java.lang.Object
implements UnivariateRealIntegrator

Provide a default implementation for several generic functions.

Since:

1.2

Version:

$Id: UnivariateRealIntegratorImpl.java 1179926 2011-10-07 03:18:05Z psteitz $

Field Summary

protected double	absoluteAccuracy Maximum absolute error.
static double	DEFAULT_ABSOLUTE_ACCURACY Default absolute accuracy.
static int	DEFAULT_MAX_ITERATIONS_COUNT Default maximal iteration count.
static int	DEFAULT_MIN_ITERATIONS_COUNT Default minimal iteration count.
static double	DEFAULT_RELATIVE_ACCURACY Default relative accuracy.
protected Incrementor	evaluations The functions evaluation count.
protected UnivariateRealFunction	function Function to integrate.
protected Incrementor	iterations The iteration count.
protected double	max Upper bound for the interval.
protected double	min Lower bound for the interval.
protected int	minimalIterationCount minimum number of iterations
protected double	relativeAccuracy Maximum relative error.

Constructor Summary

protected	UnivariateRealIntegratorImpl(double relativeAccuracy, double absoluteAccuracy) Construct an integrator with given accuracies.
protected	UnivariateRealIntegratorImpl(double relativeAccuracy, double absoluteAccuracy, int minimalIterationCount, int maximalIterationCount) Construct an integrator with given accuracies and iteration counts.
protected	UnivariateRealIntegratorImpl(int minimalIterationCount, int maximalIterationCount) Construct an integrator with given iteration counts.

Method Summary

protected double	computeObjectiveValue(double point) Compute the objective function value.
protected abstract double	doIntegrate() Method for implementing actual integration algorithms in derived classes.
double	getAbsoluteAccuracy() Get the actual absolute accuracy.
int	getEvaluations() Get the number of function evaluations of the last run of the integrator.
int	getIterations() Get the number of iterations of the last run of the integrator.
int	getMaximalIterationCount() Get the upper limit for the number of iterations.
int	getMinimalIterationCount() Get the min limit for the number of iterations.
double	getRelativeAccuracy() Get the actual relative accuracy.
double	integrate(int maxEval, UnivariateRealFunction f, double lower, double upper) Integrate the function in the given interval.
protected void	setup(int maxEval, UnivariateRealFunction f, double lower, double upper) Prepare for computation.

Methods inherited from class java.lang.Object

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

Field Detail

DEFAULT_ABSOLUTE_ACCURACY

public static final double DEFAULT_ABSOLUTE_ACCURACY

Default absolute accuracy.

See Also:

Constant Field Values

DEFAULT_RELATIVE_ACCURACY

public static final double DEFAULT_RELATIVE_ACCURACY

Default relative accuracy.

See Also:

Constant Field Values

DEFAULT_MIN_ITERATIONS_COUNT

public static final int DEFAULT_MIN_ITERATIONS_COUNT

Default minimal iteration count.

See Also:

Constant Field Values

DEFAULT_MAX_ITERATIONS_COUNT

public static final int DEFAULT_MAX_ITERATIONS_COUNT

Default maximal iteration count.

See Also:

Constant Field Values

absoluteAccuracy

protected double absoluteAccuracy

Maximum absolute error.

relativeAccuracy

protected double relativeAccuracy

Maximum relative error.

minimalIterationCount

protected int minimalIterationCount

minimum number of iterations

iterations

protected Incrementor iterations

The iteration count.

evaluations

protected Incrementor evaluations

The functions evaluation count.

function

protected UnivariateRealFunction function

Function to integrate.

min

protected double min

Lower bound for the interval.

max

protected double max

Upper bound for the interval.

Constructor Detail

UnivariateRealIntegratorImpl

protected UnivariateRealIntegratorImpl(double relativeAccuracy,
                                       double absoluteAccuracy,
                                       int minimalIterationCount,
                                       int maximalIterationCount)
                                throws NotStrictlyPositiveException,
                                       NumberIsTooSmallException

Construct an integrator with given accuracies and iteration counts.

The meanings of the various parameters are:

• relative accuracy: this is used to stop iterations if the absolute accuracy can't be achieved due to large values or short mantissa length. If this should be the primary criterion for convergence rather then a safety measure, set the absolute accuracy to a ridiculously small value, like MathUtils.SAFE_MIN.
• absolute accuracy: The default is usually chosen so that results in the interval -10..-0.1 and +0.1..+10 can be found with a reasonable accuracy. If the expected absolute value of your results is of much smaller magnitude, set this to a smaller value.
• minimum number of iterations: minimal iteration is needed to avoid false early convergence, e.g. the sample points happen to be zeroes of the function. Users can use the default value or choose one that they see as appropriate.
• maximum number of iterations: usually a high iteration count indicates convergence problems. However, the "reasonable value" varies widely for different algorithms. Users are advised to use the default value supplied by the algorithm.

Parameters:

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

UnivariateRealIntegratorImpl

protected UnivariateRealIntegratorImpl(double relativeAccuracy,
                                       double absoluteAccuracy)

Construct an integrator with given accuracies.

Parameters:

relativeAccuracy - relative accuracy of the result

absoluteAccuracy - absolute accuracy of the result

UnivariateRealIntegratorImpl

protected UnivariateRealIntegratorImpl(int minimalIterationCount,
                                       int maximalIterationCount)
                                throws NotStrictlyPositiveException,
                                       NumberIsTooSmallException

Construct an integrator with given iteration counts.

Parameters:

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

getRelativeAccuracy

public double getRelativeAccuracy()

Get the actual relative accuracy.

Specified by:

getRelativeAccuracy in interface UnivariateRealIntegrator

Returns:

the accuracy

getAbsoluteAccuracy

public double getAbsoluteAccuracy()

Get the actual absolute accuracy.

Specified by:

getAbsoluteAccuracy in interface UnivariateRealIntegrator

Returns:

the accuracy

getMinimalIterationCount

public int getMinimalIterationCount()

Get the min limit for the number of iterations.

Specified by:

getMinimalIterationCount in interface UnivariateRealIntegrator

Returns:

the actual min limit

getMaximalIterationCount

public int getMaximalIterationCount()

Get the upper limit for the number of iterations.

Specified by:

getMaximalIterationCount in interface UnivariateRealIntegrator

Returns:

the actual upper limit

getEvaluations

public int getEvaluations()

Get the number of function evaluations of the last run of the integrator.

Specified by:

getEvaluations in interface UnivariateRealIntegrator

Returns:

number of function evaluations

getIterations

public int getIterations()

Get the number of iterations of the last run of the integrator.

Specified by:

getIterations in interface UnivariateRealIntegrator

Returns:

number of iterations

computeObjectiveValue

protected double computeObjectiveValue(double point)
                                throws TooManyEvaluationsException

Compute the objective function value.

Parameters:

point - Point at which the objective function must be evaluated.

Returns:

the objective function value at specified point.

Throws:

TooManyEvaluationsException - if the maximal number of function evaluations is exceeded.

setup

protected void setup(int maxEval,
                     UnivariateRealFunction f,
                     double lower,
                     double upper)
              throws NullArgumentException,
                     MathIllegalArgumentException

Prepare for computation. Subclasses must call this method if they override any of the solve methods.

Parameters:

maxEval - Maximum number of evaluations.

f - the integrand function

lower - the min bound for the interval

upper - the upper bound for the interval

Throws:

NullArgumentException - if f is null.

MathIllegalArgumentException - if min >= max.

integrate

public double integrate(int maxEval,
                        UnivariateRealFunction f,
                        double lower,
                        double upper)
                 throws TooManyEvaluationsException,
                        MaxCountExceededException,
                        MathIllegalArgumentException,
                        NullArgumentException

Integrate the function in the given interval.

Specified by:

integrate in interface UnivariateRealIntegrator

Parameters:

maxEval - Maximum number of evaluations.

f - the integrand function

lower - the min bound for the interval

upper - the upper bound for the interval

Returns:

the value of integral

Throws:

TooManyEvaluationsException - if the maximum number of function evaluations is exceeded.

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

MathIllegalArgumentException - if min > max or the endpoints do not satisfy the requirements specified by the integrator

NullArgumentException - if f is null.

doIntegrate

protected abstract double doIntegrate()
                               throws TooManyEvaluationsException,
                                      MaxCountExceededException

Method for implementing actual integration algorithms in derived classes.

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