public abstract class MultistepIntegrator extends AdaptiveStepsizeIntegrator
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.
AdamsBashforthIntegrator,
AdamsMoultonIntegrator| Modifier and Type | Class and Description |
|---|---|
static interface |
MultistepIntegrator.NordsieckTransformer
Deprecated.
as of 3.6 this unused interface is deprecated
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| Modifier and Type | Field and Description |
|---|---|
protected Array2DRowRealMatrix |
nordsieck
Nordsieck matrix of the higher scaled derivatives.
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protected double[] |
scaled
First scaled derivative (h y').
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mainSetDimension, scalAbsoluteTolerance, scalRelativeTolerance, vecAbsoluteTolerance, vecRelativeToleranceisLastStep, resetOccurred, stepHandlers, stepSize, stepStart| Modifier | Constructor and Description |
|---|---|
protected |
MultistepIntegrator(String name,
int nSteps,
int order,
double minStep,
double maxStep,
double[] vecAbsoluteTolerance,
double[] vecRelativeTolerance)
Build a multistep integrator with the given stepsize bounds.
|
protected |
MultistepIntegrator(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 double |
computeStepGrowShrinkFactor(double error)
Compute step grow/shrink factor according to normalized error.
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double |
getMaxGrowth()
Get the maximal growth factor for stepsize control.
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double |
getMinReduction()
Get the minimal reduction factor for stepsize control.
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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.
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ODEIntegrator |
getStarterIntegrator()
Get the starter integrator.
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protected abstract Array2DRowRealMatrix |
initializeHighOrderDerivatives(double h,
double[] t,
double[][] y,
double[][] yDot)
Initialize the high order scaled derivatives at step start.
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void |
setMaxGrowth(double maxGrowth)
Set the maximal growth factor for stepsize control.
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void |
setMinReduction(double minReduction)
Set the minimal reduction factor for stepsize control.
|
void |
setSafety(double safety)
Set the safety factor for stepsize control.
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void |
setStarterIntegrator(FirstOrderIntegrator starterIntegrator)
Set the starter integrator.
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protected void |
start(double t0,
double[] y0,
double t)
Start the integration.
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filterStep, getCurrentStepStart, getMaxStep, getMinStep, initializeStep, integrate, resetInternalState, sanityChecks, setInitialStepSize, setStepSizeControl, setStepSizeControlacceptStep, addEventHandler, addEventHandler, addStepHandler, clearEventHandlers, clearStepHandlers, computeDerivatives, getCounter, getCurrentSignedStepsize, getEvaluations, getEvaluationsCounter, getEventHandlers, getExpandable, getMaxEvaluations, getName, getStepHandlers, initIntegration, integrate, setEquations, setMaxEvaluations, setStateInitializedprotected double[] scaled
protected Array2DRowRealMatrix nordsieck
(h2/2 y'', h3/6 y''' ..., hk/k! y(k))
protected MultistepIntegrator(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.
name - 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 MultistepIntegrator(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.
name - 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 ODEIntegrator getStarterIntegrator()
public void setStarterIntegrator(FirstOrderIntegrator 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(double t0,
double[] y0,
double 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.
t0 - initial timey0 - initial value of the state vector at t0t - 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 Array2DRowRealMatrix initializeHighOrderDerivatives(double h, double[] t, double[][] y, double[][] 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 double computeStepGrowShrinkFactor(double error)
error - normalized error of the current stepCopyright © 2003–2016 The Apache Software Foundation. All rights reserved.