Package org.apache.commons.math.ode.nonstiff

Class AdaptiveStepsizeIntegrator

java.lang.Object

org.apache.commons.math.ode.AbstractIntegrator

org.apache.commons.math.ode.nonstiff.AdaptiveStepsizeIntegrator

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 a basic ODE, then only the main 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

Version:

$Revision: 1073158 $ $Date: 2011-02-21 22:46:52 +0100 (lun. 21 févr. 2011) $

Field Summary

Fields

Modifier and Type	Field	Description
protected int	mainSetDimension	Main set dimension.
protected double	scalAbsoluteTolerance	Allowed absolute scalar error.
protected double	scalRelativeTolerance	Allowed relative scalar error.
protected double[]	vecAbsoluteTolerance	Allowed absolute vectorial error.
protected double[]	vecRelativeTolerance	Allowed relative vectorial error.

Fields inherited from class org.apache.commons.math.ode.AbstractIntegrator

isLastStep, resetOccurred, stepHandlers, stepSize, stepStart

Constructor Summary

Constructors

Constructor	Description
AdaptiveStepsizeIntegrator(java.lang.String name, double minStep, double maxStep, double[] vecAbsoluteTolerance, double[] vecRelativeTolerance)	Build an integrator with the given stepsize bounds.
AdaptiveStepsizeIntegrator(java.lang.String name, double minStep, double maxStep, double scalAbsoluteTolerance, double scalRelativeTolerance)	Build an integrator with the given stepsize bounds.

Method Summary

Modifier and Type	Method	Description
protected double	filterStep(double h, boolean forward, boolean acceptSmall)	Filter the integration step.
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.
protected void	resetInternalState()	Reset internal state to dummy values.
protected void	sanityChecks(FirstOrderDifferentialEquations equations, double t0, double[] y0, double t, double[] y)	Perform some sanity checks on the integration parameters.
void	setInitialStepSize(double initialStepSize)	Set the initial step size.

Methods inherited from class org.apache.commons.math.ode.AbstractIntegrator

acceptStep, addEndTimeChecker, addEventHandler, addStepHandler, clearEventHandlers, clearStepHandlers, computeDerivatives, getCurrentSignedStepsize, getEvaluations, getEventHandlers, getMaxEvaluations, getName, getStepHandlers, requiresDenseOutput, resetEvaluations, setEquations, setMaxEvaluations, setStateInitialized

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

scalAbsoluteTolerance

protected final double scalAbsoluteTolerance

Allowed absolute scalar error.

scalRelativeTolerance

protected final double scalRelativeTolerance

Allowed relative scalar error.

vecAbsoluteTolerance

protected final double[] vecAbsoluteTolerance

Allowed absolute vectorial error.

vecRelativeTolerance

protected final double[] vecRelativeTolerance

Allowed relative vectorial error.

mainSetDimension

protected int mainSetDimension

Main set dimension.

Constructor Detail

AdaptiveStepsizeIntegrator

public AdaptiveStepsizeIntegrator(java.lang.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 method

minStep - minimal step (must be positive even for backward integration), the last step can be smaller than this

maxStep - maximal step (must be positive even for backward integration)

scalAbsoluteTolerance - allowed absolute error

scalRelativeTolerance - allowed relative error

AdaptiveStepsizeIntegrator

public AdaptiveStepsizeIntegrator(java.lang.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 method

minStep - minimal step (must be positive even for backward integration), the last step can be smaller than this

maxStep - maximal step (must be positive even for backward integration)

vecAbsoluteTolerance - allowed absolute error

vecRelativeTolerance - allowed relative error

Method Detail

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)

sanityChecks

protected void sanityChecks(FirstOrderDifferentialEquations equations,
                            double t0,
                            double[] y0,
                            double t,
                            double[] y)
                     throws IntegratorException

Perform some sanity checks on the integration parameters.

Overrides:

sanityChecks in class AbstractIntegrator

Parameters:

equations - differential equations set

t0 - start time

y0 - state vector at t0

t - target time for the integration

y - placeholder where to put the state vector

Throws:

IntegratorException - if some inconsistency is detected

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 set

forward - forward integration indicator

order - order of the method

scale - scaling vector for the state vector (can be shorter than state vector)

t0 - start time

y0 - state vector at t0

yDot0 - first time derivative of y0

y1 - work array for a state vector

yDot1 - 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

filterStep

protected double filterStep(double h,
                            boolean forward,
                            boolean acceptSmall)
                     throws IntegratorException

Filter the integration step.

Parameters:

h - signed step

forward - forward integration indicator

acceptSmall - if true, steps smaller than the minimal value are silently increased up to this value, if false such small steps generate an exception

Returns:

a bounded integration step (h if no bound is reach, or a bounded value)

Throws:

IntegratorException - if the step is too small and acceptSmall is false

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 integrate

t0 - initial time

y0 - initial value of the state vector at t0

t - target time for the integration (can be set to a value smaller than t0 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 one

IntegratorException - if the integrator cannot perform integration

getCurrentStepStart

public double getCurrentStepStart()

Get the current value of the step start time t_i.

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 interface ODEIntegrator

Overrides:

getCurrentStepStart in class AbstractIntegrator

Returns:

current value of the step start time t_i

resetInternalState

protected void resetInternalState()

Reset internal state to dummy values.

getMinStep

public double getMinStep()

Get the minimal step.

Returns:

minimal step

getMaxStep

public double getMaxStep()

Get the maximal step.

Returns:

maximal step