Package org.apache.commons.math4.legacy.ode.nonstiff

Class AdamsFieldIntegrator<T extends RealFieldElement<T>>

java.lang.Object

org.apache.commons.math4.legacy.ode.AbstractFieldIntegrator<T>

org.apache.commons.math4.legacy.ode.nonstiff.AdaptiveStepsizeFieldIntegrator<T>

org.apache.commons.math4.legacy.ode.MultistepFieldIntegrator<T>

org.apache.commons.math4.legacy.ode.nonstiff.AdamsFieldIntegrator<T>

Type Parameters:

T - the type of the field elements

All Implemented Interfaces:

FirstOrderFieldIntegrator<T>

Direct Known Subclasses:

AdamsBashforthFieldIntegrator, AdamsMoultonFieldIntegrator

public abstract class AdamsFieldIntegrator<T extends RealFieldElement<T>>
extends MultistepFieldIntegrator<T>

Base class for Adams-Bashforth and Adams-Moulton integrators.

Since:

3.6

Field Summary

Fields inherited from class org.apache.commons.math4.legacy.ode.MultistepFieldIntegrator

nordsieck, scaled

Fields inherited from class org.apache.commons.math4.legacy.ode.nonstiff.AdaptiveStepsizeFieldIntegrator

mainSetDimension, scalAbsoluteTolerance, scalRelativeTolerance, vecAbsoluteTolerance, vecRelativeTolerance

Constructor Summary

Constructors

Constructor	Description
AdamsFieldIntegrator(Field<T> field, String name, int nSteps, int order, double minStep, double maxStep, double[] vecAbsoluteTolerance, double[] vecRelativeTolerance)	Build an Adams integrator with the given order and step control parameters.
AdamsFieldIntegrator(Field<T> field, String name, int nSteps, int order, double minStep, double maxStep, double scalAbsoluteTolerance, double scalRelativeTolerance)	Build an Adams integrator with the given order and step control parameters.

Method Summary

Modifier and Type	Method	Description
protected Array2DRowFieldMatrix<T>	initializeHighOrderDerivatives(T h, T[] t, T[][] y, T[][] yDot)	Initialize the high order scaled derivatives at step start.
abstract FieldODEStateAndDerivative<T>	integrate(FieldExpandableODE<T> equations, FieldODEState<T> initialState, T finalTime)	Integrate the differential equations up to the given time.
Array2DRowFieldMatrix<T>	updateHighOrderDerivativesPhase1(Array2DRowFieldMatrix<T> highOrder)	Update the high order scaled derivatives for Adams integrators (phase 1).
void	updateHighOrderDerivativesPhase2(T[] start, T[] end, Array2DRowFieldMatrix<T> highOrder)	Update the high order scaled derivatives Adams integrators (phase 2).

Methods inherited from class org.apache.commons.math4.legacy.ode.MultistepFieldIntegrator

computeStepGrowShrinkFactor, getMaxGrowth, getMinReduction, getNSteps, getSafety, getStarterIntegrator, rescale, setMaxGrowth, setMinReduction, setSafety, setStarterIntegrator, start

Methods inherited from class org.apache.commons.math4.legacy.ode.nonstiff.AdaptiveStepsizeFieldIntegrator

filterStep, getMaxStep, getMinStep, initializeStep, resetInternalState, sanityChecks, setInitialStepSize, setStepSizeControl, setStepSizeControl

Methods inherited from class org.apache.commons.math4.legacy.ode.AbstractFieldIntegrator

acceptStep, addEventHandler, addEventHandler, addStepHandler, clearEventHandlers, clearStepHandlers, computeDerivatives, getCurrentSignedStepsize, getCurrentStepStart, getEquations, getEvaluations, getEvaluationsCounter, getEventHandlers, getField, getMaxEvaluations, getName, getStepHandlers, getStepSize, getStepStart, initIntegration, isLastStep, resetOccurred, setIsLastStep, setMaxEvaluations, setStateInitialized, setStepSize, setStepStart

Methods inherited from class java.lang.Object

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

Constructor Detail

AdamsFieldIntegrator

public AdamsFieldIntegrator(Field<T> field,
                            String name,
                            int nSteps,
                            int order,
                            double minStep,
                            double maxStep,
                            double scalAbsoluteTolerance,
                            double scalRelativeTolerance)
                     throws NumberIsTooSmallException

Build an Adams integrator with the given order and step control parameters.

Parameters:

field - field to which the time and state vector elements belong

name - name of the method

nSteps - number of steps of the method excluding the one being computed

order - order of the method

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

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

scalAbsoluteTolerance - allowed absolute error

scalRelativeTolerance - allowed relative error

Throws:

NumberIsTooSmallException - if order is 1 or less

AdamsFieldIntegrator

public AdamsFieldIntegrator(Field<T> field,
                            String name,
                            int nSteps,
                            int order,
                            double minStep,
                            double maxStep,
                            double[] vecAbsoluteTolerance,
                            double[] vecRelativeTolerance)
                     throws IllegalArgumentException

Build an Adams integrator with the given order and step control parameters.

Parameters:

field - field to which the time and state vector elements belong

name - name of the method

nSteps - number of steps of the method excluding the one being computed

order - order of the method

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

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

vecAbsoluteTolerance - allowed absolute error

vecRelativeTolerance - allowed relative error

Throws:

IllegalArgumentException - if order is 1 or less

Method Detail

integrate

public abstract FieldODEStateAndDerivative<T> integrate(FieldExpandableODE<T> equations,
                                                        FieldODEState<T> initialState,
                                                        T finalTime)
                                                 throws NumberIsTooSmallException,
                                                        DimensionMismatchException,
                                                        MaxCountExceededException,
                                                        NoBracketingException

Integrate the differential equations up to the given time.

This method solves an Initial Value Problem (IVP).

Since this method stores some internal state variables made available in its public interface during integration (FirstOrderFieldIntegrator.getCurrentSignedStepsize()), it is not thread-safe.

Parameters:

equations - differential equations to integrate

initialState - initial state (time, primary and secondary state vectors)

finalTime - target time for the integration (can be set to a value smaller than t0 for backward integration)

Returns:

final state, its time will be the same as finalTime if integration reached its target, but may be different if some FieldEventHandler stops it at some point.

Throws:

NumberIsTooSmallException - if integration step is too small

MaxCountExceededException - if the number of functions evaluations is exceeded

NoBracketingException - if the location of an event cannot be bracketed

DimensionMismatchException

initializeHighOrderDerivatives

protected Array2DRowFieldMatrix<T> initializeHighOrderDerivatives(T h,
                                                                  T[] t,
                                                                  T[][] y,
                                                                  T[][] yDot)

Initialize the high order scaled derivatives at step start.

Specified by:

initializeHighOrderDerivatives in class MultistepFieldIntegrator<T extends RealFieldElement<T>>

Parameters:

h - step size to use for scaling

t - first steps times

y - first steps states

yDot - first steps derivatives

Returns:

Nordieck vector at first step (h²/2 y''_n, h³/6 y'''_n ... h^k/k! y^(k)_n)

updateHighOrderDerivativesPhase1

public Array2DRowFieldMatrix<T> updateHighOrderDerivativesPhase1(Array2DRowFieldMatrix<T> highOrder)

Update the high order scaled derivatives for Adams integrators (phase 1).

The complete update of high order derivatives has a form similar to:

rn+1 = (s1(n) - s1(n+1)) P-1 u + P-1 A P rn

this method computes the P^-1 A P r_n part.

Parameters:

highOrder - high order scaled derivatives (h²/2 y'', ... h^k/k! y(k))

Returns:

updated high order derivatives

See Also:

updateHighOrderDerivativesPhase2(RealFieldElement[], RealFieldElement[], Array2DRowFieldMatrix)

updateHighOrderDerivativesPhase2

public void updateHighOrderDerivativesPhase2(T[] start,
                                             T[] end,
                                             Array2DRowFieldMatrix<T> highOrder)

Update the high order scaled derivatives Adams integrators (phase 2).

The complete update of high order derivatives has a form similar to:

rn+1 = (s1(n) - s1(n+1)) P-1 u + P-1 A P rn

this method computes the (s₁(n) - s₁(n+1)) P^-1 u part.

Phase 1 of the update must already have been performed.

Parameters:

start - first order scaled derivatives at step start

end - first order scaled derivatives at step end

highOrder - high order scaled derivatives, will be modified (h²/2 y'', ... h^k/k! y(k))

See Also:

updateHighOrderDerivativesPhase1(Array2DRowFieldMatrix)