T - the type of the field elementspublic abstract class EmbeddedRungeKuttaFieldIntegrator<T extends RealFieldElement<T>> extends AdaptiveStepsizeFieldIntegrator<T> implements FieldButcherArrayProvider<T>
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.
mainSetDimension, scalAbsoluteTolerance, scalRelativeTolerance, vecAbsoluteTolerance, vecRelativeTolerance| Modifier | Constructor and Description |
|---|---|
protected |
EmbeddedRungeKuttaFieldIntegrator(Field<T> field,
String name,
int fsal,
double minStep,
double maxStep,
double[] vecAbsoluteTolerance,
double[] vecRelativeTolerance)
Build a Runge-Kutta integrator with the given Butcher array.
|
protected |
EmbeddedRungeKuttaFieldIntegrator(Field<T> field,
String name,
int fsal,
double minStep,
double maxStep,
double scalAbsoluteTolerance,
double scalRelativeTolerance)
Build a Runge-Kutta integrator with the given Butcher array.
|
| Modifier and Type | Method and Description |
|---|---|
protected abstract org.apache.commons.math3.ode.nonstiff.RungeKuttaFieldStepInterpolator<T> |
createInterpolator(boolean forward,
T[][] yDotK,
FieldODEStateAndDerivative<T> globalPreviousState,
FieldODEStateAndDerivative<T> globalCurrentState,
FieldEquationsMapper<T> mapper)
Create an interpolator.
|
protected abstract T |
estimateError(T[][] yDotK,
T[] y0,
T[] y1,
T h)
Compute the error ratio.
|
protected T |
fraction(double p,
double q)
Create a fraction.
|
protected T |
fraction(int p,
int q)
Create a fraction.
|
T |
getMaxGrowth()
Get the maximal growth factor for stepsize control.
|
T |
getMinReduction()
Get the minimal reduction factor for stepsize control.
|
abstract int |
getOrder()
Get the order of the method.
|
T |
getSafety()
Get the safety factor for stepsize control.
|
FieldODEStateAndDerivative<T> |
integrate(FieldExpandableODE<T> equations,
FieldODEState<T> initialState,
T finalTime)
Integrate the differential equations up to the given time.
|
void |
setMaxGrowth(T maxGrowth)
Set the maximal growth factor for stepsize control.
|
void |
setMinReduction(T minReduction)
Set the minimal reduction factor for stepsize control.
|
void |
setSafety(T safety)
Set the safety factor for stepsize control.
|
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, waitgetA, getB, getCprotected EmbeddedRungeKuttaFieldIntegrator(Field<T> field, String name, int fsal, double minStep, double maxStep, double scalAbsoluteTolerance, double scalRelativeTolerance)
field - field to which the time and state vector elements belongname - 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 errorprotected EmbeddedRungeKuttaFieldIntegrator(Field<T> field, String name, int fsal, double minStep, double maxStep, double[] vecAbsoluteTolerance, double[] vecRelativeTolerance)
field - field to which the time and state vector elements belongname - 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 errorprotected T fraction(int p, int q)
p - numeratorq - denominatorprotected T fraction(double p, double q)
p - numeratorq - denominatorprotected abstract org.apache.commons.math3.ode.nonstiff.RungeKuttaFieldStepInterpolator<T> createInterpolator(boolean forward, T[][] yDotK, FieldODEStateAndDerivative<T> globalPreviousState, FieldODEStateAndDerivative<T> globalCurrentState, FieldEquationsMapper<T> mapper)
forward - integration direction indicatoryDotK - slopes at the intermediate pointsglobalPreviousState - start of the global stepglobalCurrentState - end of the global stepmapper - equations mapper for the all equationspublic abstract int getOrder()
public T getSafety()
public void setSafety(T safety)
safety - safety factorpublic FieldODEStateAndDerivative<T> integrate(FieldExpandableODE<T> equations, FieldODEState<T> initialState, T finalTime) throws NumberIsTooSmallException, DimensionMismatchException, MaxCountExceededException, NoBracketingException
This method solves an Initial Value Problem (IVP).
Since this method stores some internal state variables made
available in its public interface during integration (FirstOrderFieldIntegrator.getCurrentSignedStepsize()), it is not thread-safe.
integrate in interface FirstOrderFieldIntegrator<T extends RealFieldElement<T>>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 than t0 for backward integration)finalTime if
integration reached its target, but may be different if some FieldEventHandler stops it at some point.NumberIsTooSmallException - if integration step is too smallMaxCountExceededException - if the number of functions evaluations is exceededNoBracketingException - if the location of an event cannot be bracketedDimensionMismatchExceptionpublic T getMinReduction()
public void setMinReduction(T minReduction)
minReduction - minimal reduction factorpublic T getMaxGrowth()
public void setMaxGrowth(T maxGrowth)
maxGrowth - maximal growth factorprotected abstract T estimateError(T[][] yDotK, T[] y0, T[] y1, T h)
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 stepCopyright © 2003–2016 The Apache Software Foundation. All rights reserved.