T - the type of the field elementspublic abstract class MultistepFieldIntegrator<T extends RealFieldElement<T>> extends AdaptiveStepsizeFieldIntegrator<T>
We define scaled derivatives si(n) at step n as:
s1(n) = h y'n for first derivative s2(n) = h2/2 y''n for second derivative s3(n) = h3/6 y'''n for third derivative ... sk(n) = hk/k! y(k)n for kth derivative
Rather than storing several previous steps separately, this implementation uses the Nordsieck vector with higher degrees scaled derivatives all taken at the same step (yn, s1(n) and rn) where rn is defined as:
rn = [ s2(n), s3(n) ... sk(n) ]T(we omit the k index in the notation for clarity)
Multistep integrators with Nordsieck representation are highly sensitive to large step changes because when the step is multiplied by factor a, the kth component of the Nordsieck vector is multiplied by ak and the last components are the least accurate ones. The default max growth factor is therefore set to a quite low value: 21/order.
AdamsBashforthFieldIntegrator,
AdamsMoultonFieldIntegrator| Modifier and Type | Field and Description |
|---|---|
protected Array2DRowFieldMatrix<T> |
nordsieck
Nordsieck matrix of the higher scaled derivatives.
|
protected T[] |
scaled
First scaled derivative (h y').
|
mainSetDimension, scalAbsoluteTolerance, scalRelativeTolerance, vecAbsoluteTolerance, vecRelativeTolerance| Modifier | Constructor and Description |
|---|---|
protected |
MultistepFieldIntegrator(Field<T> field,
String name,
int nSteps,
int order,
double minStep,
double maxStep,
double[] vecAbsoluteTolerance,
double[] vecRelativeTolerance)
Build a multistep integrator with the given stepsize bounds.
|
protected |
MultistepFieldIntegrator(Field<T> field,
String name,
int nSteps,
int order,
double minStep,
double maxStep,
double scalAbsoluteTolerance,
double scalRelativeTolerance)
Build a multistep integrator with the given stepsize bounds.
|
| Modifier and Type | Method and Description |
|---|---|
protected T |
computeStepGrowShrinkFactor(T error)
Compute step grow/shrink factor according to normalized error.
|
double |
getMaxGrowth()
Get the maximal growth factor for stepsize control.
|
double |
getMinReduction()
Get the minimal reduction factor for stepsize control.
|
int |
getNSteps()
Get the number of steps of the multistep method (excluding the one being computed).
|
double |
getSafety()
Get the safety factor for stepsize control.
|
FirstOrderFieldIntegrator<T> |
getStarterIntegrator()
Get the starter integrator.
|
protected abstract Array2DRowFieldMatrix<T> |
initializeHighOrderDerivatives(T h,
T[] t,
T[][] y,
T[][] yDot)
Initialize the high order scaled derivatives at step start.
|
protected void |
rescale(T newStepSize)
Rescale the instance.
|
void |
setMaxGrowth(double maxGrowth)
Set the maximal growth factor for stepsize control.
|
void |
setMinReduction(double minReduction)
Set the minimal reduction factor for stepsize control.
|
void |
setSafety(double safety)
Set the safety factor for stepsize control.
|
void |
setStarterIntegrator(FirstOrderFieldIntegrator<T> starterIntegrator)
Set the starter integrator.
|
protected void |
start(FieldExpandableODE<T> equations,
FieldODEState<T> initialState,
T t)
Start the integration.
|
filterStep, getMaxStep, getMinStep, initializeStep, resetInternalState, sanityChecks, setInitialStepSize, setStepSizeControl, setStepSizeControlacceptStep, 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, setStepStartclone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, waitintegrateprotected T extends RealFieldElement<T>[] scaled
protected Array2DRowFieldMatrix<T extends RealFieldElement<T>> nordsieck
(h2/2 y'', h3/6 y''' ..., hk/k! y(k))
protected MultistepFieldIntegrator(Field<T> field, String name, int nSteps, int order, double minStep, double maxStep, double scalAbsoluteTolerance, double scalRelativeTolerance) throws NumberIsTooSmallException
The default starter integrator is set to the Dormand-Prince 8(5,3) integrator with
some defaults settings.
The default max growth factor is set to a quite low value: 21/order.
field - field to which the time and state vector elements belongname - name of the methodnSteps - number of steps of the multistep method
(excluding the one being computed)order - order of the methodminStep - minimal step (must be positive even for backward
integration), the last step can be smaller than thismaxStep - maximal step (must be positive even for backward
integration)scalAbsoluteTolerance - allowed absolute errorscalRelativeTolerance - allowed relative errorNumberIsTooSmallException - if number of steps is smaller than 2protected MultistepFieldIntegrator(Field<T> field, String name, int nSteps, int order, double minStep, double maxStep, double[] vecAbsoluteTolerance, double[] vecRelativeTolerance)
The default starter integrator is set to the Dormand-Prince 8(5,3) integrator with
some defaults settings.
The default max growth factor is set to a quite low value: 21/order.
field - field to which the time and state vector elements belongname - name of the methodnSteps - number of steps of the multistep method
(excluding the one being computed)order - order of the methodminStep - minimal step (must be positive even for backward
integration), the last step can be smaller than thismaxStep - maximal step (must be positive even for backward
integration)vecAbsoluteTolerance - allowed absolute errorvecRelativeTolerance - allowed relative errorpublic FirstOrderFieldIntegrator<T> getStarterIntegrator()
public void setStarterIntegrator(FirstOrderFieldIntegrator<T> starterIntegrator)
The various step and event handlers for this starter integrator will be managed automatically by the multi-step integrator. Any user configuration for these elements will be cleared before use.
starterIntegrator - starter integratorprotected void start(FieldExpandableODE<T> equations, FieldODEState<T> initialState, T t) throws DimensionMismatchException, NumberIsTooSmallException, MaxCountExceededException, NoBracketingException
This method computes one step using the underlying starter integrator, and initializes the Nordsieck vector at step start. The starter integrator purpose is only to establish initial conditions, it does not really change time by itself. The top level multistep integrator remains in charge of handling time propagation and events handling as it will starts its own computation right from the beginning. In a sense, the starter integrator can be seen as a dummy one and so it will never trigger any user event nor call any user step handler.
equations - complete set of differential equations to integrateinitialState - initial state (time, primary and secondary state vectors)t - target time for the integration
(can be set to a value smaller than t0 for backward integration)DimensionMismatchException - if arrays dimension do not match equations settingsNumberIsTooSmallException - if integration step is too smallMaxCountExceededException - if the number of functions evaluations is exceededNoBracketingException - if the location of an event cannot be bracketedprotected abstract Array2DRowFieldMatrix<T> initializeHighOrderDerivatives(T h, T[] t, T[][] y, T[][] yDot)
h - step size to use for scalingt - first steps timesy - first steps statesyDot - first steps derivativespublic double getMinReduction()
public void setMinReduction(double minReduction)
minReduction - minimal reduction factorpublic double getMaxGrowth()
public void setMaxGrowth(double maxGrowth)
maxGrowth - maximal growth factorpublic double getSafety()
public void setSafety(double safety)
safety - safety factorpublic int getNSteps()
protected void rescale(T newStepSize)
Since the scaled and Nordsieck arrays are shared with the caller, this method has the side effect of rescaling this arrays in the caller too.
newStepSize - new step size to use in the scaled and Nordsieck arraysCopyright © 2003–2016 The Apache Software Foundation. All rights reserved.