Class AdaptiveStepsizeIntegrator
- java.lang.Object
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- org.apache.commons.math.ode.AbstractIntegrator
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- org.apache.commons.math.ode.nonstiff.AdaptiveStepsizeIntegrator
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- All Implemented Interfaces:
FirstOrderIntegrator
,ODEIntegrator
- Direct Known Subclasses:
EmbeddedRungeKuttaIntegrator
,GraggBulirschStoerIntegrator
,MultistepIntegrator
public abstract class AdaptiveStepsizeIntegrator extends AbstractIntegrator
This abstract class holds the common part of all adaptive stepsize integrators for Ordinary Differential Equations.These algorithms perform integration with stepsize control, which means the user does not specify the integration step but rather a tolerance on error. The error threshold is computed as
threshold_i = absTol_i + relTol_i * max (abs (ym), abs (ym+1))
where absTol_i is the absolute tolerance for component i of the state vector and relTol_i is the relative tolerance for the same component. The user can also use only two scalar values absTol and relTol which will be used for all components.If the Ordinary Differential Equations is an
extended ODE
rather than abasic ODE
, then only themain set
part of the state vector is used for stepsize control, not the complete state vector.If the estimated error for ym+1 is such that
sqrt((sum (errEst_i / threshold_i)^2 ) / n) < 1
(where n is the main set dimension) then the step is accepted, otherwise the step is rejected and a new attempt is made with a new stepsize.- Since:
- 1.2
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Constructor Summary
Constructors Constructor Description AdaptiveStepsizeIntegrator(String name, double minStep, double maxStep, double[] vecAbsoluteTolerance, double[] vecRelativeTolerance)
Build an integrator with the given stepsize bounds.AdaptiveStepsizeIntegrator(String name, double minStep, double maxStep, double scalAbsoluteTolerance, double scalRelativeTolerance)
Build an integrator with the given stepsize bounds.
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Method Summary
All Methods Instance Methods Abstract Methods Concrete Methods Modifier and Type Method Description double
getCurrentStepStart()
Get the current value of the step start time ti.double
getMaxStep()
Get the maximal step.double
getMinStep()
Get the minimal step.double
initializeStep(FirstOrderDifferentialEquations equations, boolean forward, int order, double[] scale, double t0, double[] y0, double[] yDot0, double[] y1, double[] yDot1)
Initialize the integration step.abstract double
integrate(FirstOrderDifferentialEquations equations, double t0, double[] y0, double t, double[] y)
Integrate the differential equations up to the given time.void
setInitialStepSize(double initialStepSize)
Set the initial step size.-
Methods inherited from class org.apache.commons.math.ode.AbstractIntegrator
addEventHandler, addStepHandler, clearEventHandlers, clearStepHandlers, computeDerivatives, getCurrentSignedStepsize, getEvaluations, getEventHandlers, getMaxEvaluations, getName, getStepHandlers, setMaxEvaluations
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Constructor Detail
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AdaptiveStepsizeIntegrator
public AdaptiveStepsizeIntegrator(String name, double minStep, double maxStep, double scalAbsoluteTolerance, double scalRelativeTolerance)
Build an integrator with the given stepsize bounds. The default step handler does nothing.- Parameters:
name
- name 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 error
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AdaptiveStepsizeIntegrator
public AdaptiveStepsizeIntegrator(String name, double minStep, double maxStep, double[] vecAbsoluteTolerance, double[] vecRelativeTolerance)
Build an integrator with the given stepsize bounds. The default step handler does nothing.- Parameters:
name
- name 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 error
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Method Detail
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setInitialStepSize
public void setInitialStepSize(double initialStepSize)
Set the initial step size.This method allows the user to specify an initial positive step size instead of letting the integrator guess it by itself. If this method is not called before integration is started, the initial step size will be estimated by the integrator.
- Parameters:
initialStepSize
- initial step size to use (must be positive even for backward integration ; providing a negative value or a value outside of the min/max step interval will lead the integrator to ignore the value and compute the initial step size by itself)
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initializeStep
public double initializeStep(FirstOrderDifferentialEquations equations, boolean forward, int order, double[] scale, double t0, double[] y0, double[] yDot0, double[] y1, double[] yDot1) throws DerivativeException
Initialize the integration step.- Parameters:
equations
- differential equations setforward
- forward integration indicatororder
- order of the methodscale
- scaling vector for the state vector (can be shorter than state vector)t0
- start timey0
- state vector at t0yDot0
- first time derivative of y0y1
- work array for a state vectoryDot1
- work array for the first time derivative of y1- Returns:
- first integration step
- Throws:
DerivativeException
- this exception is propagated to the caller if the underlying user function triggers one
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integrate
public abstract double integrate(FirstOrderDifferentialEquations equations, double t0, double[] y0, double t, double[] y) throws DerivativeException, IntegratorException
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.- Parameters:
equations
- differential equations to integratet0
- initial timey0
- initial value of the state vector at t0t
- target time for the integration (can be set to a value smaller thant0
for backward integration)y
- placeholder where to put the state vector at each successful step (and hence at the end of integration), can be the same object as y0- Returns:
- stop time, will be the same as target time if integration reached its
target, but may be different if some
EventHandler
stops it at some point. - Throws:
DerivativeException
- this exception is propagated to the caller if the underlying user function triggers oneIntegratorException
- if the integrator cannot perform integration
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getCurrentStepStart
public double getCurrentStepStart()
Get the current value of the step start time ti.This method can be called during integration (typically by the object implementing the
differential equations
problem) if the value of the current step that is attempted is needed.The result is undefined if the method is called outside of calls to
integrate
.- Specified by:
getCurrentStepStart
in interfaceODEIntegrator
- Overrides:
getCurrentStepStart
in classAbstractIntegrator
- Returns:
- current value of the step start time ti
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getMinStep
public double getMinStep()
Get the minimal step.- Returns:
- minimal step
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getMaxStep
public double getMaxStep()
Get the maximal step.- Returns:
- maximal step
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