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

java.lang.Object
  extended by org.apache.commons.math3.ode.AbstractIntegrator
      extended by org.apache.commons.math3.ode.nonstiff.AdaptiveStepsizeIntegrator
          extended by org.apache.commons.math3.ode.MultistepIntegrator
              extended by 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 1416643 2012-12-03 19:37:14Z tn $

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, getEvaluationsCounter, getEventHandlers, getExpandable, 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 ... hk/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 rn part.

Parameters:
highOrder - high order scaled derivatives (h2/2 y'', ... hk/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'', ... hk/k! y(k))
See Also:
updateHighOrderDerivativesPhase1(Array2DRowRealMatrix)


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