Package com.irurueta.numerical.integration

Class SimpsonMatrixIntegrator<T extends MatrixQuadrature>

java.lang.Object

com.irurueta.numerical.integration.MatrixIntegrator

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

Type Parameters:

T - a quadrature.

Direct Known Subclasses:

SimpsonDoubleExponentialRuleQuadratureMatrixIntegrator, SimpsonInfinityMidPointQuadratureMatrixIntegrator, SimpsonLowerSquareRootMidPointQuadratureMatrixIntegrator, SimpsonMidPointQuadratureMatrixIntegrator, SimpsonTrapezoidalQuadratureMatrixIntegrator, SimpsonUpperSquareRootMidPointQuadratureMatrixIntegrator

public abstract class SimpsonMatrixIntegrator<T extends MatrixQuadrature>
extends MatrixIntegrator

Base integrator for implementations based on Simpson's method. Simpson's method is an optimization of Trapezoidal quadrature integrator. Implementations of this class will in general be more efficient than Trapezoidal quadrature matrix integrators (i.e., require fewer function evaluations) when the matrix function to be integrated has a finite fourth derivative (i.e., a continuous third derivative).

Field Summary

Fields

Modifier and Type	Field	Description
private final double	eps	Required accuracy.
static final double	EPS	Default accuracy.
private static final int	JMAX	Maximum number of allowed steps.
private static final int	JMIN	Minimum required number of steps.
private final T	q	Quadrature used for integration.

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

DEFAULT_INTEGRATOR_TYPE, DEFAULT_QUADRATURE_TYPE

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method	Description
private static SimpsonMatrixIntegrator<MatrixQuadrature>	cast(SimpsonMatrixIntegrator<?> integrator)	Casts integrator to a quadrature integrator without wildcard parameter.
static SimpsonMatrixIntegrator<MatrixQuadrature>	create(double a, double b, MatrixSingleDimensionFunctionEvaluatorListener listener)	Creates an integrator using Simpson's method and having default accuracy and quadrature type.
static SimpsonMatrixIntegrator<MatrixQuadrature>	create(double a, double b, MatrixSingleDimensionFunctionEvaluatorListener listener, double eps)	Creates an integrator using Simpson's method and default quadrature type.
static SimpsonMatrixIntegrator<MatrixQuadrature>	create(double a, double b, MatrixSingleDimensionFunctionEvaluatorListener listener, double eps, QuadratureType quadratureType)	Creates an integrator using Simpson's method.
static SimpsonMatrixIntegrator<MatrixQuadrature>	create(double a, double b, MatrixSingleDimensionFunctionEvaluatorListener listener, QuadratureType quadratureType)	Creates an integrator using Simpson'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.
private static double	normMin(com.irurueta.algebra.Matrix a)	Estimates smallest norm of provided matrix.

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

JMIN

private static final int JMIN

Minimum required number of steps.

See Also:

• Constant Field Values

JMAX

private static final int JMAX

Maximum number of allowed steps.

See Also:

• Constant Field Values

q

private final T extends MatrixQuadrature q

Quadrature used for integration.

eps

private final double eps

Required accuracy.

Constructor Details

SimpsonMatrixIntegrator

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

Creates an integrator using Simpson's method.

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

Creates an integrator using Simpson's method and having default accuracy.

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

Creates an integrator using Simpson's method and default 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 SimpsonMatrixIntegrator<MatrixQuadrature> create(double a,
 double b,
 MatrixSingleDimensionFunctionEvaluatorListener listener)
                                                        throws com.irurueta.algebra.WrongSizeException

Creates an integrator using Simpson's method and having default accuracy and 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.

normMin

private static double normMin(com.irurueta.algebra.Matrix a)

Estimates smallest norm of provided matrix. Smallest norm is used to ensure convergence of all elements in matrix.

Parameters:

a - matrix to compute min norm for.

Returns:

estimated min norm.

cast

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

Casts integrator to a quadrature integrator without wildcard parameter.

Parameters:

integrator - integrator to be cast.

Returns:

cast integrator.