Package com.irurueta.numerical.integration

Class RombergMatrixIntegrator<T extends MatrixQuadrature>

java.lang.Object

com.irurueta.numerical.integration.MatrixIntegrator

com.irurueta.numerical.integration.RombergMatrixIntegrator<T>

Type Parameters:

T - instance of a quadrature to be used for Romberg's method integration.

Direct Known Subclasses:

RombergDoubleExponentialRuleQuadratureMatrixIntegrator, RombergExponentialMidPointQuadratureMatrixIntegrator, RombergInfinityMidPointQuadratureMatrixIntegrator, RombergLowerSquareRootMidPointQuadratureMatrixIntegrator, RombergMidPointQuadratureMatrixIntegrator, RombergTrapezoidalQuadratureMatrixIntegrator, RombergUpperSquareRootMidPointQuadratureMatrixIntegrator

public abstract class RombergMatrixIntegrator<T extends MatrixQuadrature>
extends MatrixIntegrator

Base integrator for implementations based on Romberg's method. Romberg's method is a generalization of Simpson's method for higher order integration schemes. This can be used to computed integration with less function evaluations for the same level of accuracy when more assumptions of function "smoothness" can be made. Implementations of Romberg's method are quite powerful for sufficiently smooth (e.g., analytic) integrands, integrated over intervals that contain no singularities, and where the endpoints are also non-singular. In such circumstances, Romberg's method, takes many, many fewer function evaluations than other method's such as Simpson's.

Field Summary

Fields

Modifier and Type	Field	Description
protected final double	eps	Required accuracy.
static final double	EPS	Default accuracy.
private final double[]	h	Successive trapezoidal step sizes.
private static final int	JMAX	Maximum number of allowed steps.
private static final int	JMAXP	Maximum number of allowed steps + 1.
private static final int	K	Minimum required number of steps.
protected final T	q	Quadrature used for integration.
private final com.irurueta.algebra.Matrix[]	s	Successive trapezoidal approximations.

Fields inherited from class com.irurueta.numerical.integration.MatrixIntegrator

DEFAULT_INTEGRATOR_TYPE, DEFAULT_QUADRATURE_TYPE

Constructor Summary

Constructors

Modifier	Constructor	Description
protected	RombergMatrixIntegrator(T q, double eps)	Constructor.

Method Summary

Modifier and Type	Method	Description
private static RombergMatrixIntegrator<MatrixQuadrature>	cast(RombergMatrixIntegrator<?> integrator)	Casts integrator to a quadrature integrator without wildcard parameter.
static RombergMatrixIntegrator<MatrixQuadrature>	create(double a, double b, MatrixSingleDimensionFunctionEvaluatorListener listener)	Creates an integrator using Romberg's method and having default accuracy and quadrature type.
static RombergMatrixIntegrator<MatrixQuadrature>	create(double a, double b, MatrixSingleDimensionFunctionEvaluatorListener listener, double eps)	Creates an integrator using Romberg's method and default quadrature type.
static RombergMatrixIntegrator<MatrixQuadrature>	create(double a, double b, MatrixSingleDimensionFunctionEvaluatorListener listener, double eps, QuadratureType quadratureType)	Creates an integrator using Romberg's method.
static RombergMatrixIntegrator<MatrixQuadrature>	create(double a, double b, MatrixSingleDimensionFunctionEvaluatorListener listener, QuadratureType quadratureType)	Creates an integrator using Romberg's method and having default accuracy.
IntegratorType	getIntegratorType()	Gets type of integrator.
void	integrate(com.irurueta.algebra.Matrix result)	Integrates function between provided lower and upper limits.

Methods inherited from class com.irurueta.numerical.integration.MatrixIntegrator

create, create, create, create, getQuadratureType

Methods inherited from class java.lang.Object

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

Field Details

EPS

public static final double EPS

Default accuracy.

See Also:

• Constant Field Values

JMAX

private static final int JMAX

Maximum number of allowed steps.

See Also:

• Constant Field Values

JMAXP

private static final int JMAXP

Maximum number of allowed steps + 1.

See Also:

• Constant Field Values

K

private static final int K

Minimum required number of steps.

See Also:

• Constant Field Values

q

protected final T extends MatrixQuadrature q

Quadrature used for integration.

eps

protected final double eps

Required accuracy.

s

private final com.irurueta.algebra.Matrix[] s

Successive trapezoidal approximations.

h

private final double[] h

Successive trapezoidal step sizes.

Constructor Details

RombergMatrixIntegrator

protected RombergMatrixIntegrator(T q,
 double eps)

Constructor.

Parameters:

q - Quadrature used for integration.

eps - Required accuracy.

Method Details

integrate

public void integrate(com.irurueta.algebra.Matrix result)
               throws IntegrationException

Integrates function between provided lower and upper limits.

Specified by:

integrate in class MatrixIntegrator

Parameters:

result - instance where result of integration will be stored.

Throws:

IntegrationException - if integration fails for numerical reasons.

getIntegratorType

public IntegratorType getIntegratorType()

Gets type of integrator.

Specified by:

getIntegratorType in class MatrixIntegrator

Returns:

type of integrator.

create

public static RombergMatrixIntegrator<MatrixQuadrature> create(double a,
 double b,
 MatrixSingleDimensionFunctionEvaluatorListener listener,
 double eps,
 QuadratureType quadratureType)
                                                        throws com.irurueta.algebra.WrongSizeException

Creates an integrator using Romberg's method. It must be noticed that upper limit of integration is ignored when using exponential mid-point quadrature type.

Parameters:

a - Lower limit of integration.

b - Upper limit of integration.

listener - listener to evaluate a single dimension function at required points.

eps - required accuracy.

quadratureType - quadrature type.

Returns:

created integrator.

Throws:

IllegalArgumentException - if provided quadrature type is not supported.

com.irurueta.algebra.WrongSizeException - if size notified by provided listener is invalid.

create

public static RombergMatrixIntegrator<MatrixQuadrature> create(double a,
 double b,
 MatrixSingleDimensionFunctionEvaluatorListener listener,
 QuadratureType quadratureType)
                                                        throws com.irurueta.algebra.WrongSizeException

Creates an integrator using Romberg's method and having default accuracy. It must be noticed that upper limit of integration is ignored when using exponential mid-point quadrature type.

Parameters:

a - Lower limit of integration.

b - Upper limit of integration.

listener - listener to evaluate a single dimension function at required points.

quadratureType - quadrature type.

Returns:

created integrator.

Throws:

IllegalArgumentException - if provided quadrature type is not supported.

com.irurueta.algebra.WrongSizeException - if size notified by provided listener is invalid.

create

public static RombergMatrixIntegrator<MatrixQuadrature> create(double a,
 double b,
 MatrixSingleDimensionFunctionEvaluatorListener listener,
 double eps)
                                                        throws com.irurueta.algebra.WrongSizeException

Creates an integrator using Romberg's method and default quadrature type. It must be noticed that upper limit of integration is ignored when using exponential mid-point quadrature type.

Parameters:

a - Lower limit of integration.

b - Upper limit of integration.

listener - listener to evaluate a single dimension function at required points.

eps - required accuracy.

Returns:

created integrator.

Throws:

com.irurueta.algebra.WrongSizeException - if size notified by provided listener is invalid.

create

public static RombergMatrixIntegrator<MatrixQuadrature> create(double a,
 double b,
 MatrixSingleDimensionFunctionEvaluatorListener listener)
                                                        throws com.irurueta.algebra.WrongSizeException

Creates an integrator using Romberg's method and having default accuracy and quadrature type. It must be noticed that upper limit of integration is ignored when using exponential mid-point quadrature type.

Parameters:

a - Lower limit of integration.

b - Upper limit of integration.

listener - listener to evaluate a single dimension function at required points.

Returns:

created integrator.

Throws:

com.irurueta.algebra.WrongSizeException - if size notified by provided listener is invalid.

cast

private static RombergMatrixIntegrator<MatrixQuadrature> cast(RombergMatrixIntegrator<?> integrator)

Casts integrator to a quadrature integrator without wildcard parameter.

Parameters:

integrator - integrator to be cast.

Returns:

cast integrator.