Apache Commons Math 3.6.1 · org.apache.commons.math3.ode.nonstiff.AdaptiveStepsizeFieldIntegrator

This abstract class holds the common part of all adaptive stepsize integrators for Ordinary Differential Equations.

These algorithms perform integration with stepsize control, which means the user does not specify the integration step but rather a tolerance on error. The error threshold is computed as

threshold_i = absTol_i + relTol_i * max (abs (ym), abs (ym+1))

where absTol_i is the absolute tolerance for component i of the state vector and relTol_i is the relative tolerance for the same component. The user can also use only two scalar values absTol and relTol which will be used for all components.

Note that only the main part of the state vector is used for stepsize control. The secondary parts of the state vector are explicitly ignored for stepsize control.

If the estimated error for ym+1 is such that

sqrt((sum (errEst_i / threshold_i)^2 ) / n) < 1

(where n is the main set dimension) then the step is accepted, otherwise the step is rejected and a new attempt is made with a new stepsize.

Field Summary

Modifier and Type	Field and Description
private T	initialStep User supplied initial step.
protected int	mainSetDimension Main set dimension.
private T	maxStep Maximal step.
private T	minStep Minimal step.
protected double	scalAbsoluteTolerance Allowed absolute scalar error.
protected double	scalRelativeTolerance Allowed relative scalar error.
protected double[]	vecAbsoluteTolerance Allowed absolute vectorial error.
protected double[]	vecRelativeTolerance Allowed relative vectorial error.

Constructor Summary

Access	Constructor and Description
public	AdaptiveStepsizeFieldIntegrator(final Field<T> field to which the time and state vector elements belong field, final String name of the method name, final double minimal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than this minStep, final double maximal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than this maxStep, final double allowed absolute error scalAbsoluteTolerance, final double allowed relative error scalRelativeTolerance) Build an integrator with the given stepsize bounds.
public	AdaptiveStepsizeFieldIntegrator(final Field<T> field to which the time and state vector elements belong field, final String name of the method name, final double minimal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than this minStep, final double maximal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than this maxStep, final double[] allowed absolute error vecAbsoluteTolerance, final double[] allowed relative error vecRelativeTolerance) Build an integrator with the given stepsize bounds.

Access

Constructor and Description

public

AdaptiveStepsizeFieldIntegrator(final Field<T>

field to which the time and state vector elements belong

field, final String

name of the method

name, final double

minimal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than this

minStep, final double

maximal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than this

maxStep, final double

allowed absolute error

scalAbsoluteTolerance, final double

allowed relative error

scalRelativeTolerance)

Build an integrator with the given stepsize bounds.

public

AdaptiveStepsizeFieldIntegrator(final Field<T>

field to which the time and state vector elements belong

field, final String

name of the method

name, final double

minimal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than this

minStep, final double

maximal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than this

maxStep, final double[]

allowed absolute error

vecAbsoluteTolerance, final double[]

allowed relative error

vecRelativeTolerance)

Build an integrator with the given stepsize bounds.

Method Summary

Modifier and Type	Method and Description
protected T	Returns: a bounded integration step (h if no bound is reach, or a bounded value) filterStep(final T signed step h, final boolean forward integration indicator forward, final boolean if true, steps smaller than the minimal value are silently increased up to this value, if false such small steps generate an exception acceptSmall) Filter the integration step.
public T	Returns: maximal step getMaxStep() Get the maximal step.
public T	Returns: minimal step getMinStep() Get the minimal step.
public T	Returns: first integration step initializeStep(final boolean forward integration indicator forward, final int order of the method order, final T[] scaling vector for the state vector (can be shorter than state vector) scale, final FieldODEStateAndDerivative<T> state at integration start time state0, final FieldEquationsMapper<T> mapper for all the equations mapper) Initialize the integration step.
protected void	resetInternalState() Reset internal state to dummy values.
protected void	sanityChecks(final FieldODEState<T> set of differential equations eqn, final T target time for the integration t) Overrides org.apache.commons.math3.ode.AbstractFieldIntegrator.sanityChecks. Check the integration span.
public void	setInitialStepSize(final T initial step size to use (must be positive even for backward integration ; providing a negative value or a value outside of the min/max step interval will lead the integrator to ignore the value and compute the initial step size by itself) initialStepSize) Set the initial step size.
public void	setStepSizeControl(final double minimal step (must be positive even for backward integration), the last step can be smaller than this minimalStep, final double maximal step (must be positive even for backward integration) maximalStep, final double allowed absolute error absoluteTolerance, final double allowed relative error relativeTolerance) Set the adaptive step size control parameters.
public void	setStepSizeControl(final double minimal step (must be positive even for backward integration), the last step can be smaller than this minimalStep, final double maximal step (must be positive even for backward integration) maximalStep, final double[] allowed absolute error absoluteTolerance, final double[] allowed relative error relativeTolerance) Set the adaptive step size control parameters.

Field Detail

initialStep	back to summary
private T initialStep User supplied initial step.

mainSetDimension	back to summary
protected int mainSetDimension Main set dimension.

maxStep	back to summary
private T maxStep Maximal step.

minStep	back to summary
private T minStep Minimal step.

scalAbsoluteTolerance	back to summary
protected double scalAbsoluteTolerance Allowed absolute scalar error.

scalRelativeTolerance	back to summary
protected double scalRelativeTolerance Allowed relative scalar error.

vecAbsoluteTolerance	back to summary
protected double[] vecAbsoluteTolerance Allowed absolute vectorial error.

vecRelativeTolerance	back to summary
protected double[] vecRelativeTolerance Allowed relative vectorial error.

Constructor Detail

AdaptiveStepsizeFieldIntegrator	back to summary
public AdaptiveStepsizeFieldIntegrator(final Field<T> field, final String name, final double minStep, final double maxStep, final double scalAbsoluteTolerance, final double scalRelativeTolerance) Build an integrator with the given stepsize bounds. The default step handler does nothing. Parameters field:Field<T> field to which the time and state vector elements belong name:String name of the method minStep:double minimal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than this maxStep:double maximal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than this scalAbsoluteTolerance:double allowed absolute error scalRelativeTolerance:double allowed relative error

AdaptiveStepsizeFieldIntegrator

back to summary

public AdaptiveStepsizeFieldIntegrator(final Field<T> field, final String name, final double minStep, final double maxStep, final double scalAbsoluteTolerance, final double scalRelativeTolerance)

Build an integrator with the given stepsize bounds. The default step handler does nothing.

Parameters

field:Field<T>: field to which the time and state vector elements belong
name:String: name of the method
minStep:double: minimal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than this
maxStep:double: maximal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than this
scalAbsoluteTolerance:double: allowed absolute error
scalRelativeTolerance:double: allowed relative error

AdaptiveStepsizeFieldIntegrator	back to summary
public AdaptiveStepsizeFieldIntegrator(final Field<T> field, final String name, final double minStep, final double maxStep, final double[] vecAbsoluteTolerance, final double[] vecRelativeTolerance) Build an integrator with the given stepsize bounds. The default step handler does nothing. Parameters field:Field<T> field to which the time and state vector elements belong name:String name of the method minStep:double minimal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than this maxStep:double maximal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than this vecAbsoluteTolerance:double[] allowed absolute error vecRelativeTolerance:double[] allowed relative error

AdaptiveStepsizeFieldIntegrator

back to summary

public AdaptiveStepsizeFieldIntegrator(final Field<T> field, final String name, final double minStep, final double maxStep, final double[] vecAbsoluteTolerance, final double[] vecRelativeTolerance)

Build an integrator with the given stepsize bounds. The default step handler does nothing.

Parameters

field:Field<T>: field to which the time and state vector elements belong
name:String: name of the method
minStep:double: minimal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than this
maxStep:double: maximal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than this
vecAbsoluteTolerance:double[]: allowed absolute error
vecRelativeTolerance:double[]: allowed relative error

Method Detail

filterStep	back to summary
protected T filterStep(final T h, final boolean forward, final boolean acceptSmall) throws NumberIsTooSmallException Filter the integration step. Parameters h:T signed step forward:boolean forward integration indicator acceptSmall:boolean if true, steps smaller than the minimal value are silently increased up to this value, if false such small steps generate an exception Returns:T a bounded integration step (h if no bound is reach, or a bounded value) Exceptions NumberIsTooSmallException: if the step is too small and acceptSmall is false

filterStep

back to summary

protected T filterStep(final T h, final boolean forward, final boolean acceptSmall) throws NumberIsTooSmallException

Filter the integration step.

Parameters

h:T: signed step
forward:boolean: forward integration indicator
acceptSmall:boolean: if true, steps smaller than the minimal value are silently increased up to this value, if false such small steps generate an exception

Returns:T

a bounded integration step (h if no bound is reach, or a bounded value)

Exceptions

NumberIsTooSmallException:: if the step is too small and acceptSmall is false

getMaxStep	back to summary
public T getMaxStep() Get the maximal step. Returns:T maximal step

getMaxStep

back to summary

public T getMaxStep()

Get the maximal step.

Returns:T: maximal step

getMinStep	back to summary
public T getMinStep() Get the minimal step. Returns:T minimal step

getMinStep

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public T getMinStep()

Get the minimal step.

Returns:T: minimal step

initializeStep	back to summary
public T initializeStep(final boolean forward, final int order, final T[] scale, final FieldODEStateAndDerivative<T> state0, final FieldEquationsMapper<T> mapper) throws MaxCountExceededException, DimensionMismatchException Initialize the integration step. Parameters forward:boolean forward integration indicator order:int order of the method scale:T[] scaling vector for the state vector (can be shorter than state vector) state0:FieldODEStateAndDerivative<T> state at integration start time mapper:FieldEquationsMapper<T> mapper for all the equations Returns:T first integration step Exceptions MaxCountExceededException: if the number of functions evaluations is exceeded DimensionMismatchException: if arrays dimensions do not match equations settings

initializeStep

back to summary

public T initializeStep(final boolean forward, final int order, final T[] scale, final FieldODEStateAndDerivative<T> state0, final FieldEquationsMapper<T> mapper) throws MaxCountExceededException, DimensionMismatchException

Initialize the integration step.

Parameters

forward:boolean: forward integration indicator
order:int: order of the method
scale:T[]: scaling vector for the state vector (can be shorter than state vector)
state0:FieldODEStateAndDerivative<T>: state at integration start time
mapper:FieldEquationsMapper<T>: mapper for all the equations

Returns:T

first integration step

Exceptions

MaxCountExceededException:: if the number of functions evaluations is exceeded
DimensionMismatchException:: if arrays dimensions do not match equations settings

resetInternalState	back to summary
protected void resetInternalState() Reset internal state to dummy values.

sanityChecks	back to summary
protected void sanityChecks(final FieldODEState<T> eqn, final T t) throws DimensionMismatchException, NumberIsTooSmallException Overrides org.apache.commons.math3.ode.AbstractFieldIntegrator.sanityChecks. Doc from org.apache.commons.math3.ode.AbstractFieldIntegrator.sanityChecks. Check the integration span. Parameters eqn:FieldODEState<T> set of differential equations t:T target time for the integration Annotations @Override Exceptions DimensionMismatchException: if adaptive step size integrators tolerance arrays dimensions are not compatible with equations settings NumberIsTooSmallException: if integration span is too small

sanityChecks

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protected void sanityChecks(final FieldODEState<T> eqn, final T t) throws DimensionMismatchException, NumberIsTooSmallException

Overrides org.apache.commons.math3.ode.AbstractFieldIntegrator.sanityChecks.

Doc from org.apache.commons.math3.ode.AbstractFieldIntegrator.sanityChecks.

Check the integration span.

Parameters

eqn:FieldODEState<T>: set of differential equations
t:T: target time for the integration

Annotations

@Override

Exceptions

DimensionMismatchException:: if adaptive step size integrators tolerance arrays dimensions are not compatible with equations settings
NumberIsTooSmallException:: if integration span is too small

setInitialStepSize	back to summary
public void setInitialStepSize(final T initialStepSize) Set the initial step size. This method allows the user to specify an initial positive step size instead of letting the integrator guess it by itself. If this method is not called before integration is started, the initial step size will be estimated by the integrator. Parameters initialStepSize:T initial step size to use (must be positive even for backward integration ; providing a negative value or a value outside of the min/max step interval will lead the integrator to ignore the value and compute the initial step size by itself)

setInitialStepSize

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public void setInitialStepSize(final T initialStepSize)

Set the initial step size.

This method allows the user to specify an initial positive step size instead of letting the integrator guess it by itself. If this method is not called before integration is started, the initial step size will be estimated by the integrator.

Parameters

initialStepSize:T: initial step size to use (must be positive even for backward integration ; providing a negative value or a value outside of the min/max step interval will lead the integrator to ignore the value and compute the initial step size by itself)

setStepSizeControl back to summary

setStepSizeControl	back to summary
public void setStepSizeControl(final double minimalStep, final double maximalStep, final double absoluteTolerance, final double relativeTolerance) Set the adaptive step size control parameters. A side effect of this method is to also reset the initial step so it will be automatically computed by the integrator if `setInitialStepSize` is not called by the user. Parameters minimalStep:double minimal step (must be positive even for backward integration), the last step can be smaller than this maximalStep:double maximal step (must be positive even for backward integration) absoluteTolerance:double allowed absolute error relativeTolerance:double allowed relative error

public void setStepSizeControl(final double minimalStep, final double maximalStep, final double absoluteTolerance, final double relativeTolerance)

Set the adaptive step size control parameters.

A side effect of this method is to also reset the initial step so it will be automatically computed by the integrator if setInitialStepSize is not called by the user.

Parameters

minimalStep:double: minimal step (must be positive even for backward integration), the last step can be smaller than this
maximalStep:double: maximal step (must be positive even for backward integration)
absoluteTolerance:double: allowed absolute error
relativeTolerance:double: allowed relative error

setStepSizeControl back to summary

setStepSizeControl	back to summary
public void setStepSizeControl(final double minimalStep, final double maximalStep, final double[] absoluteTolerance, final double[] relativeTolerance) Set the adaptive step size control parameters. A side effect of this method is to also reset the initial step so it will be automatically computed by the integrator if `setInitialStepSize` is not called by the user. Parameters minimalStep:double minimal step (must be positive even for backward integration), the last step can be smaller than this maximalStep:double maximal step (must be positive even for backward integration) absoluteTolerance:double[] allowed absolute error relativeTolerance:double[] allowed relative error

public void setStepSizeControl(final double minimalStep, final double maximalStep, final double[] absoluteTolerance, final double[] relativeTolerance)

Set the adaptive step size control parameters.

A side effect of this method is to also reset the initial step so it will be automatically computed by the integrator if setInitialStepSize is not called by the user.

Parameters

minimalStep:double: minimal step (must be positive even for backward integration), the last step can be smaller than this
maximalStep:double: maximal step (must be positive even for backward integration)
absoluteTolerance:double[]: allowed absolute error
relativeTolerance:double[]: allowed relative error

public abstract Class AdaptiveStepsizeFieldIntegrator<T extends RealFieldElement<T>>

Field Summary

Constructor Summary

Method Summary

Field Detail

Constructor Detail

Method Detail