Class EmbeddedRungeKuttaIntegrator
- All Implemented Interfaces:
ButcherArrayProvider
,ExplicitRungeKuttaIntegrator
,ODEIntegrator
- Direct Known Subclasses:
DormandPrince54Integrator
,DormandPrince853Integrator
,HighamHall54Integrator
These methods are embedded explicit Runge-Kutta methods with two sets of coefficients allowing to estimate the error, their Butcher arrays are as follows :
0 | c2 | a21 c3 | a31 a32 ... | ... cs | as1 as2 ... ass-1 |-------------------------- | b1 b2 ... bs-1 bs | b'1 b'2 ... b's-1 b's
In fact, we rather use the array defined by ej = bj - b'j to compute directly the error rather than computing two estimates and then comparing them.
Some methods are qualified as fsal (first same as last) methods. This means the last evaluation of the derivatives in one step is the same as the first in the next step. Then, this evaluation can be reused from one step to the next one and the cost of such a method is really s-1 evaluations despite the method still has s stages. This behaviour is true only for successful steps, if the step is rejected after the error estimation phase, no evaluation is saved. For an fsal method, we have cs = 1 and asi = bi for all i.
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Constructor Summary
ModifierConstructorDescriptionprotected
EmbeddedRungeKuttaIntegrator
(String name, int fsal, double minStep, double maxStep, double[] vecAbsoluteTolerance, double[] vecRelativeTolerance) Build a Runge-Kutta integrator with the given Butcher array.protected
EmbeddedRungeKuttaIntegrator
(String name, int fsal, double minStep, double maxStep, double scalAbsoluteTolerance, double scalRelativeTolerance) Build a Runge-Kutta integrator with the given Butcher array. -
Method Summary
Modifier and TypeMethodDescriptionprotected abstract org.hipparchus.ode.nonstiff.RungeKuttaStateInterpolator
createInterpolator
(boolean forward, double[][] yDotK, ODEStateAndDerivative globalPreviousState, ODEStateAndDerivative globalCurrentState, EquationsMapper mapper) Create an interpolator.protected abstract double
estimateError
(double[][] yDotK, double[] y0, double[] y1, double h) Compute the error ratio.double
Get the maximal growth factor for stepsize control.double
Get the minimal reduction factor for stepsize control.abstract int
getOrder()
Get the order of the method.double
Get the safety factor for stepsize control.integrate
(ExpandableODE equations, ODEState initialState, double finalTime) Integrate the differential equations up to the given time.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.Methods inherited from class org.hipparchus.ode.nonstiff.AdaptiveStepsizeIntegrator
getMaxStep, getMinStep, getStepSizeHelper, initializeStep, resetInternalState, sanityChecks, setInitialStepSize, setStepSizeControl, setStepSizeControl
Methods inherited from class org.hipparchus.ode.AbstractIntegrator
acceptStep, addEventDetector, addStepEndHandler, addStepHandler, clearEventDetectors, clearStepEndHandlers, clearStepHandlers, computeDerivatives, getCurrentSignedStepsize, getEquations, getEvaluations, getEvaluationsCounter, getEventDetectors, getMaxEvaluations, getName, getStepEndHandlers, getStepHandlers, getStepSize, getStepStart, incrementEvaluations, 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
Methods inherited from interface org.hipparchus.ode.nonstiff.ButcherArrayProvider
getA, getB, getC
Methods inherited from interface org.hipparchus.ode.nonstiff.ExplicitRungeKuttaIntegrator
getNumberOfStages, singleStep
Methods inherited from interface org.hipparchus.ode.ODEIntegrator
addEventDetector, addStepEndHandler, addStepHandler, clearEventDetectors, clearStepEndHandlers, clearStepHandlers, getCurrentSignedStepsize, getEvaluations, getEventDetectors, getMaxEvaluations, getName, getStepEndHandlers, getStepHandlers, getStepStart, integrate, setMaxEvaluations
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Constructor Details
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EmbeddedRungeKuttaIntegrator
protected EmbeddedRungeKuttaIntegrator(String name, int fsal, double minStep, double maxStep, double scalAbsoluteTolerance, double scalRelativeTolerance) Build a Runge-Kutta integrator with the given Butcher array.- Parameters:
name
- name of the methodfsal
- index of the pre-computed derivative for fsal methods or -1 if method is not fsalminStep
- minimal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than thismaxStep
- maximal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than thisscalAbsoluteTolerance
- allowed absolute errorscalRelativeTolerance
- allowed relative error
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EmbeddedRungeKuttaIntegrator
protected EmbeddedRungeKuttaIntegrator(String name, int fsal, double minStep, double maxStep, double[] vecAbsoluteTolerance, double[] vecRelativeTolerance) Build a Runge-Kutta integrator with the given Butcher array.- Parameters:
name
- name of the methodfsal
- index of the pre-computed derivative for fsal methods or -1 if method is not fsalminStep
- 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 error
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Method Details
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createInterpolator
protected abstract org.hipparchus.ode.nonstiff.RungeKuttaStateInterpolator createInterpolator(boolean forward, double[][] yDotK, ODEStateAndDerivative globalPreviousState, ODEStateAndDerivative globalCurrentState, EquationsMapper mapper) Create an interpolator.- Parameters:
forward
- integration direction indicatoryDotK
- slopes at the intermediate pointsglobalPreviousState
- start of the global stepglobalCurrentState
- end of the global stepmapper
- equations mapper for the all equations- Returns:
- external weights for the high order method from Butcher array
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getOrder
public abstract int getOrder()Get the order of the method.- Returns:
- order of the method
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getSafety
public double getSafety()Get the safety factor for stepsize control.- Returns:
- safety factor
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setSafety
public void setSafety(double safety) Set the safety factor for stepsize control.- Parameters:
safety
- safety factor
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integrate
public ODEStateAndDerivative integrate(ExpandableODE equations, ODEState initialState, double finalTime) throws MathIllegalArgumentException, MathIllegalStateException 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 (
ODEIntegrator.getCurrentSignedStepsize()
), it is not thread-safe.- Specified by:
integrate
in interfaceODEIntegrator
- Parameters:
equations
- differential equations to integrateinitialState
- initial state (time, primary and secondary state vectors)finalTime
- target time for the integration (can be set to a value smaller thant0
for backward integration)- Returns:
- final state, its time will be the same as
finalTime
if integration reached its target, but may be different if someODEEventHandler
stops it at some point. - Throws:
MathIllegalArgumentException
- if integration step is too smallMathIllegalStateException
- if the number of functions evaluations is exceeded
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getMinReduction
public double getMinReduction()Get the minimal reduction factor for stepsize control.- Returns:
- minimal reduction factor
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setMinReduction
public void setMinReduction(double minReduction) Set the minimal reduction factor for stepsize control.- Parameters:
minReduction
- minimal reduction factor
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getMaxGrowth
public double getMaxGrowth()Get the maximal growth factor for stepsize control.- Returns:
- maximal growth factor
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setMaxGrowth
public void setMaxGrowth(double maxGrowth) Set the maximal growth factor for stepsize control.- Parameters:
maxGrowth
- maximal growth factor
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estimateError
protected abstract double estimateError(double[][] yDotK, double[] y0, double[] y1, double h) Compute the error ratio.- Parameters:
yDotK
- derivatives computed during the first stagesy0
- estimate of the step at the start of the stepy1
- estimate of the step at the end of the steph
- current step- Returns:
- error ratio, greater than 1 if step should be rejected
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