org.apache.commons.math3.ode.nonstiff
Class AdaptiveStepsizeIntegrator

java.lang.Object
  extended by org.apache.commons.math3.ode.AbstractIntegrator
      extended by org.apache.commons.math3.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 primary 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:
$Id: AdaptiveStepsizeIntegrator.java 1416643 2012-12-03 19:37:14Z tn $

Field Summary
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.math3.ode.AbstractIntegrator
isLastStep, resetOccurred, stepHandlers, stepSize, stepStart
 
Constructor Summary
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.
 
Method Summary
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(boolean forward, int order, double[] scale, double t0, double[] y0, double[] yDot0, double[] y1, double[] yDot1)
          Initialize the integration step.
abstract  void integrate(ExpandableStatefulODE equations, double t)
          Integrate a set of differential equations up to the given time.
protected  void resetInternalState()
          Reset internal state to dummy values.
protected  void sanityChecks(ExpandableStatefulODE equations, double t)
          Check the integration span.
 void setInitialStepSize(double initialStepSize)
          Set the initial step size.
 void setStepSizeControl(double minimalStep, double maximalStep, double[] absoluteTolerance, double[] relativeTolerance)
          Set the adaptive step size control parameters.
 void setStepSizeControl(double minimalStep, double maximalStep, double absoluteTolerance, double relativeTolerance)
          Set the adaptive step size control parameters.
 
Methods inherited from class org.apache.commons.math3.ode.AbstractIntegrator
acceptStep, addEventHandler, addEventHandler, addStepHandler, clearEventHandlers, clearStepHandlers, computeDerivatives, getCurrentSignedStepsize, getEvaluations, getEventHandlers, getMaxEvaluations, getName, getStepHandlers, initIntegration, integrate, 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 double scalAbsoluteTolerance
Allowed absolute scalar error.


scalRelativeTolerance

protected double scalRelativeTolerance
Allowed relative scalar error.


vecAbsoluteTolerance

protected double[] vecAbsoluteTolerance
Allowed absolute vectorial error.


vecRelativeTolerance

protected double[] vecRelativeTolerance
Allowed relative vectorial error.


mainSetDimension

protected int mainSetDimension
Main set dimension.

Constructor Detail

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 method
minStep - minimal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than this
maxStep - maximal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than this
scalAbsoluteTolerance - allowed absolute error
scalRelativeTolerance - allowed relative error

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 method
minStep - minimal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than this
maxStep - maximal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than this
vecAbsoluteTolerance - allowed absolute error
vecRelativeTolerance - allowed relative error
Method Detail

setStepSizeControl

public void setStepSizeControl(double minimalStep,
                               double maximalStep,
                               double absoluteTolerance,
                               double relativeTolerance)
Set the adaptive step size control parameters.

A side effect of this method is to also reset the initial step so it will be automatically computed by the integrator if setInitialStepSize is not called by the user.

Parameters:
minimalStep - minimal step (must be positive even for backward integration), the last step can be smaller than this
maximalStep - maximal step (must be positive even for backward integration)
absoluteTolerance - allowed absolute error
relativeTolerance - allowed relative error

setStepSizeControl

public void setStepSizeControl(double minimalStep,
                               double maximalStep,
                               double[] absoluteTolerance,
                               double[] relativeTolerance)
Set the adaptive step size control parameters.

A side effect of this method is to also reset the initial step so it will be automatically computed by the integrator if setInitialStepSize is not called by the user.

Parameters:
minimalStep - minimal step (must be positive even for backward integration), the last step can be smaller than this
maximalStep - maximal step (must be positive even for backward integration)
absoluteTolerance - allowed absolute error
relativeTolerance - allowed relative error

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(ExpandableStatefulODE equations,
                            double t)
                     throws DimensionMismatchException,
                            NumberIsTooSmallException
Check the integration span.

Overrides:
sanityChecks in class AbstractIntegrator
Parameters:
equations - set of differential equations
t - target time for the integration
Throws:
DimensionMismatchException - if adaptive step size integrators tolerance arrays dimensions are not compatible with equations settings
NumberIsTooSmallException - if integration span is too small

initializeStep

public double initializeStep(boolean forward,
                             int order,
                             double[] scale,
                             double t0,
                             double[] y0,
                             double[] yDot0,
                             double[] y1,
                             double[] yDot1)
                      throws MaxCountExceededException,
                             DimensionMismatchException
Initialize the integration step.

Parameters:
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:
MaxCountExceededException - if the number of functions evaluations is exceeded
DimensionMismatchException - if arrays dimensions do not match equations settings

filterStep

protected double filterStep(double h,
                            boolean forward,
                            boolean acceptSmall)
                     throws NumberIsTooSmallException
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:
NumberIsTooSmallException - if the step is too small and acceptSmall is false

integrate

public abstract void integrate(ExpandableStatefulODE equations,
                               double t)
                        throws NumberIsTooSmallException,
                               DimensionMismatchException,
                               MaxCountExceededException,
                               NoBracketingException
Integrate a set of differential equations up to the given time.

This method solves an Initial Value Problem (IVP).

The set of differential equations is composed of a main set, which can be extended by some sets of secondary equations. The set of equations must be already set up with initial time and partial states. At integration completion, the final time and partial states will be available in the same object.

Since this method stores some internal state variables made available in its public interface during integration (AbstractIntegrator.getCurrentSignedStepsize()), it is not thread-safe.

Specified by:
integrate in class AbstractIntegrator
Parameters:
equations - complete set of differential equations to integrate
t - target time for the integration (can be set to a value smaller than t0 for backward integration)
Throws:
NumberIsTooSmallException - if integration step is too small
DimensionMismatchException - if the dimension of the complete state does not match the complete equations sets dimension
MaxCountExceededException - if the number of functions evaluations is exceeded
NoBracketingException - if the location of an event cannot be bracketed

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 interface ODEIntegrator
Overrides:
getCurrentStepStart in class AbstractIntegrator
Returns:
current value of the step start time ti

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


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