org.apache.commons.math3.ode.nonstiff
Class AdamsIntegrator

java.lang.Object
  org.apache.commons.math3.ode.AbstractIntegrator
      org.apache.commons.math3.ode.nonstiff.AdaptiveStepsizeIntegrator
          org.apache.commons.math3.ode.MultistepIntegrator
              org.apache.commons.math3.ode.nonstiff.AdamsIntegrator

All Implemented Interfaces:

FirstOrderIntegrator, ODEIntegrator

Direct Known Subclasses:

AdamsBashforthIntegrator, AdamsMoultonIntegrator

public abstract class AdamsIntegrator
extends MultistepIntegrator

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

Since:

2.0

Version:

$Id: AdamsIntegrator.java 7721 2013-02-14 14:07:13Z CardosoP $

Nested Class Summary

Nested classes/interfaces inherited from class org.apache.commons.math3.ode.MultistepIntegrator

MultistepIntegrator.NordsieckTransformer

Field Summary

Fields inherited from class org.apache.commons.math3.ode.MultistepIntegrator

nordsieck, scaled

Fields inherited from class org.apache.commons.math3.ode.nonstiff.AdaptiveStepsizeIntegrator

mainSetDimension, scalAbsoluteTolerance, scalRelativeTolerance, vecAbsoluteTolerance, vecRelativeTolerance

Fields inherited from class org.apache.commons.math3.ode.AbstractIntegrator

isLastStep, resetOccurred, stepHandlers, stepSize, stepStart

Constructor Summary

AdamsIntegrator(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.

AdamsIntegrator(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

protected Array2DRowRealMatrix	initializeHighOrderDerivatives(double h, double[] t, double[][] y, double[][] yDot) Initialize the high order scaled derivatives at step start.
abstract void	integrate(ExpandableStatefulODE equations, double t) Integrate a set of differential equations up to the given time.
Array2DRowRealMatrix	updateHighOrderDerivativesPhase1(Array2DRowRealMatrix highOrder) Update the high order scaled derivatives for Adams integrators (phase 1).
void	updateHighOrderDerivativesPhase2(double[] start, double[] end, Array2DRowRealMatrix highOrder) Update the high order scaled derivatives Adams integrators (phase 2).

Methods inherited from class org.apache.commons.math3.ode.MultistepIntegrator

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

Methods inherited from class org.apache.commons.math3.ode.nonstiff.AdaptiveStepsizeIntegrator

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

Methods inherited from class org.apache.commons.math3.ode.AbstractIntegrator

acceptStep, addEventHandler, addEventHandler, addStepHandler, clearEventHandlers, clearStepHandlers, computeDerivatives, getCurrentSignedStepsize, getEvaluations, getEventHandlers, getMaxEvaluations, getName, getStepHandlers, initIntegration, integrate, setEquations, setMaxEvaluations, setStateInitialized

Methods inherited from class java.lang.Object

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

Constructor Detail

AdamsIntegrator

public AdamsIntegrator(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:

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

AdamsIntegrator

public AdamsIntegrator(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:

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 void integrate(ExpandableStatefulODE equations,
                               double t)
                        throws NumberIsTooSmallException,
                               DimensionMismatchException,
                               MaxCountExceededException,
                               NoBracketingException

Integrate a set of differential equations up to the given time.

This method solves an Initial Value Problem (IVP).

The set of differential equations is composed of a main set, which can be extended by some sets of secondary equations. The set of equations must be already set up with initial time and partial states. At integration completion, the final time and partial states will be available in the same object.

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

Specified by:

integrate in class AdaptiveStepsizeIntegrator

Parameters:

equations - complete set of differential equations to integrate

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

Throws:

NumberIsTooSmallException - if integration step is too small

DimensionMismatchException - if the dimension of the complete state does not match the complete equations sets dimension

MaxCountExceededException - if the number of functions evaluations is exceeded

NoBracketingException - if the location of an event cannot be bracketed

initializeHighOrderDerivatives

protected Array2DRowRealMatrix initializeHighOrderDerivatives(double h,
                                                              double[] t,
                                                              double[][] y,
                                                              double[][] yDot)

Initialize the high order scaled derivatives at step start.

Specified by:

initializeHighOrderDerivatives in class MultistepIntegrator

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 Array2DRowRealMatrix updateHighOrderDerivativesPhase1(Array2DRowRealMatrix 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(double[], double[], Array2DRowRealMatrix)

updateHighOrderDerivativesPhase2

public void updateHighOrderDerivativesPhase2(double[] start,
                                             double[] end,
                                             Array2DRowRealMatrix 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(Array2DRowRealMatrix)