org.apache.commons.math3.ode.sampling
Class AbstractStepInterpolator

java.lang.Object
  extended by org.apache.commons.math3.ode.sampling.AbstractStepInterpolator
All Implemented Interfaces:
Externalizable, Serializable, StepInterpolator
Direct Known Subclasses:
NordsieckStepInterpolator

public abstract class AbstractStepInterpolator
extends Object
implements StepInterpolator

This abstract class represents an interpolator over the last step during an ODE integration.

The various ODE integrators provide objects extending this class to the step handlers. The handlers can use these objects to retrieve the state vector at intermediate times between the previous and the current grid points (dense output).

Since:
1.2
Version:
$Id: AbstractStepInterpolator.java 1416643 2012-12-03 19:37:14Z tn $
See Also:
FirstOrderIntegrator, SecondOrderIntegrator, StepHandler, Serialized Form

Field Summary
protected  double[] currentState
          current state
protected  double h
          current time step
protected  double[] interpolatedDerivatives
          interpolated derivatives
protected  double[] interpolatedPrimaryDerivatives
          interpolated primary derivatives
protected  double[] interpolatedPrimaryState
          interpolated primary state
protected  double[][] interpolatedSecondaryDerivatives
          interpolated secondary derivatives
protected  double[][] interpolatedSecondaryState
          interpolated secondary state
protected  double[] interpolatedState
          interpolated state
protected  double interpolatedTime
          interpolated time
 
Constructor Summary
protected AbstractStepInterpolator()
          Simple constructor.
protected AbstractStepInterpolator(AbstractStepInterpolator interpolator)
          Copy constructor.
protected AbstractStepInterpolator(double[] y, boolean forward, EquationsMapper primaryMapper, EquationsMapper[] secondaryMappers)
          Simple constructor.
 
Method Summary
protected abstract  void computeInterpolatedStateAndDerivatives(double theta, double oneMinusThetaH)
          Compute the state and derivatives at the interpolated time.
 StepInterpolator copy()
          Copy the instance.
protected abstract  StepInterpolator doCopy()
          Really copy the finalized instance.
protected  void doFinalize()
          Really finalize the step.
 void finalizeStep()
          Finalize the step.
 double getCurrentTime()
          Get the current soft grid point time.
 double getGlobalCurrentTime()
          Get the current global grid point time.
 double getGlobalPreviousTime()
          Get the previous global grid point time.
 double[] getInterpolatedDerivatives()
          Get the derivatives of the state vector of the interpolated point.
 double[] getInterpolatedSecondaryDerivatives(int index)
          Get the interpolated secondary derivatives corresponding to the secondary equations.
 double[] getInterpolatedSecondaryState(int index)
          Get the interpolated secondary state corresponding to the secondary equations.
 double[] getInterpolatedState()
          Get the state vector of the interpolated point.
 double getInterpolatedTime()
          Get the time of the interpolated point.
 double getPreviousTime()
          Get the previous soft grid point time.
 boolean isForward()
          Check if the natural integration direction is forward.
protected  double readBaseExternal(ObjectInput in)
          Read the base state of the instance.
abstract  void readExternal(ObjectInput in)
          
protected  void reinitialize(double[] y, boolean isForward, EquationsMapper primary, EquationsMapper[] secondary)
          Reinitialize the instance
 void setInterpolatedTime(double time)
          Set the time of the interpolated point.
 void setSoftCurrentTime(double softCurrentTime)
          Restrict step range to a limited part of the global step.
 void setSoftPreviousTime(double softPreviousTime)
          Restrict step range to a limited part of the global step.
 void shift()
          Shift one step forward.
 void storeTime(double t)
          Store the current step time.
protected  void writeBaseExternal(ObjectOutput out)
          Save the base state of the instance.
abstract  void writeExternal(ObjectOutput out)
          
 
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Field Detail

h

protected double h
current time step


currentState

protected double[] currentState
current state


interpolatedTime

protected double interpolatedTime
interpolated time


interpolatedState

protected double[] interpolatedState
interpolated state


interpolatedDerivatives

protected double[] interpolatedDerivatives
interpolated derivatives


interpolatedPrimaryState

protected double[] interpolatedPrimaryState
interpolated primary state


interpolatedPrimaryDerivatives

protected double[] interpolatedPrimaryDerivatives
interpolated primary derivatives


interpolatedSecondaryState

protected double[][] interpolatedSecondaryState
interpolated secondary state


interpolatedSecondaryDerivatives

protected double[][] interpolatedSecondaryDerivatives
interpolated secondary derivatives

Constructor Detail

AbstractStepInterpolator

protected AbstractStepInterpolator()
Simple constructor. This constructor builds an instance that is not usable yet, the reinitialize(double[], boolean, org.apache.commons.math3.ode.EquationsMapper, org.apache.commons.math3.ode.EquationsMapper[]) method should be called before using the instance in order to initialize the internal arrays. This constructor is used only in order to delay the initialization in some cases. As an example, the EmbeddedRungeKuttaIntegrator class uses the prototyping design pattern to create the step interpolators by cloning an uninitialized model and latter initializing the copy.


AbstractStepInterpolator

protected AbstractStepInterpolator(double[] y,
                                   boolean forward,
                                   EquationsMapper primaryMapper,
                                   EquationsMapper[] secondaryMappers)
Simple constructor.

Parameters:
y - reference to the integrator array holding the state at the end of the step
forward - integration direction indicator
primaryMapper - equations mapper for the primary equations set
secondaryMappers - equations mappers for the secondary equations sets

AbstractStepInterpolator

protected AbstractStepInterpolator(AbstractStepInterpolator interpolator)
Copy constructor.

The copied interpolator should have been finalized before the copy, otherwise the copy will not be able to perform correctly any derivative computation and will throw a NullPointerException later. Since we don't want this constructor to throw the exceptions finalization may involve and since we don't want this method to modify the state of the copied interpolator, finalization is not done automatically, it remains under user control.

The copy is a deep copy: its arrays are separated from the original arrays of the instance.

Parameters:
interpolator - interpolator to copy from.
Method Detail

reinitialize

protected void reinitialize(double[] y,
                            boolean isForward,
                            EquationsMapper primary,
                            EquationsMapper[] secondary)
Reinitialize the instance

Parameters:
y - reference to the integrator array holding the state at the end of the step
isForward - integration direction indicator
primary - equations mapper for the primary equations set
secondary - equations mappers for the secondary equations sets

copy

public StepInterpolator copy()
                      throws MaxCountExceededException
Copy the instance.

The copied instance is guaranteed to be independent from the original one. Both can be used with different settings for interpolated time without any side effect.

Specified by:
copy in interface StepInterpolator
Returns:
a deep copy of the instance, which can be used independently.
Throws:
MaxCountExceededException - if the number of functions evaluations is exceeded during step finalization
See Also:
StepInterpolator.setInterpolatedTime(double)

doCopy

protected abstract StepInterpolator doCopy()
Really copy the finalized instance.

This method is called by copy() after the step has been finalized. It must perform a deep copy to have an new instance completely independent for the original instance.

Returns:
a copy of the finalized instance

shift

public void shift()
Shift one step forward. Copy the current time into the previous time, hence preparing the interpolator for future calls to storeTime


storeTime

public void storeTime(double t)
Store the current step time.

Parameters:
t - current time

setSoftPreviousTime

public void setSoftPreviousTime(double softPreviousTime)
Restrict step range to a limited part of the global step.

This method can be used to restrict a step and make it appear as if the original step was smaller. Calling this method only changes the value returned by getPreviousTime(), it does not change any other property

Parameters:
softPreviousTime - start of the restricted step
Since:
2.2

setSoftCurrentTime

public void setSoftCurrentTime(double softCurrentTime)
Restrict step range to a limited part of the global step.

This method can be used to restrict a step and make it appear as if the original step was smaller. Calling this method only changes the value returned by getCurrentTime(), it does not change any other property

Parameters:
softCurrentTime - end of the restricted step
Since:
2.2

getGlobalPreviousTime

public double getGlobalPreviousTime()
Get the previous global grid point time.

Returns:
previous global grid point time

getGlobalCurrentTime

public double getGlobalCurrentTime()
Get the current global grid point time.

Returns:
current global grid point time

getPreviousTime

public double getPreviousTime()
Get the previous soft grid point time.

Specified by:
getPreviousTime in interface StepInterpolator
Returns:
previous soft grid point time
See Also:
setSoftPreviousTime(double)

getCurrentTime

public double getCurrentTime()
Get the current soft grid point time.

Specified by:
getCurrentTime in interface StepInterpolator
Returns:
current soft grid point time
See Also:
setSoftCurrentTime(double)

getInterpolatedTime

public double getInterpolatedTime()
Get the time of the interpolated point. If StepInterpolator.setInterpolatedTime(double) has not been called, it returns the current grid point time.

Specified by:
getInterpolatedTime in interface StepInterpolator
Returns:
interpolation point time

setInterpolatedTime

public void setInterpolatedTime(double time)
Set the time of the interpolated point.

Setting the time outside of the current step is now allowed, but should be used with care since the accuracy of the interpolator will probably be very poor far from this step. This allowance has been added to simplify implementation of search algorithms near the step endpoints.

Setting the time changes the instance internal state. If a specific state must be preserved, a copy of the instance must be created using StepInterpolator.copy().

Specified by:
setInterpolatedTime in interface StepInterpolator
Parameters:
time - time of the interpolated point

isForward

public boolean isForward()
Check if the natural integration direction is forward.

This method provides the integration direction as specified by the integrator itself, it avoid some nasty problems in degenerated cases like null steps due to cancellation at step initialization, step control or discrete events triggering.

Specified by:
isForward in interface StepInterpolator
Returns:
true if the integration variable (time) increases during integration

computeInterpolatedStateAndDerivatives

protected abstract void computeInterpolatedStateAndDerivatives(double theta,
                                                               double oneMinusThetaH)
                                                        throws MaxCountExceededException
Compute the state and derivatives at the interpolated time. This is the main processing method that should be implemented by the derived classes to perform the interpolation.

Parameters:
theta - normalized interpolation abscissa within the step (theta is zero at the previous time step and one at the current time step)
oneMinusThetaH - time gap between the interpolated time and the current time
Throws:
MaxCountExceededException - if the number of functions evaluations is exceeded

getInterpolatedState

public double[] getInterpolatedState()
                              throws MaxCountExceededException
Get the state vector of the interpolated point.

The returned vector is a reference to a reused array, so it should not be modified and it should be copied if it needs to be preserved across several calls.

Specified by:
getInterpolatedState in interface StepInterpolator
Returns:
state vector at time StepInterpolator.getInterpolatedTime()
Throws:
MaxCountExceededException - if the number of functions evaluations is exceeded
See Also:
StepInterpolator.getInterpolatedDerivatives()

getInterpolatedDerivatives

public double[] getInterpolatedDerivatives()
                                    throws MaxCountExceededException
Get the derivatives of the state vector of the interpolated point.

The returned vector is a reference to a reused array, so it should not be modified and it should be copied if it needs to be preserved across several calls.

Specified by:
getInterpolatedDerivatives in interface StepInterpolator
Returns:
derivatives of the state vector at time StepInterpolator.getInterpolatedTime()
Throws:
MaxCountExceededException - if the number of functions evaluations is exceeded
See Also:
StepInterpolator.getInterpolatedState()

getInterpolatedSecondaryState

public double[] getInterpolatedSecondaryState(int index)
                                       throws MaxCountExceededException
Get the interpolated secondary state corresponding to the secondary equations.

The returned vector is a reference to a reused array, so it should not be modified and it should be copied if it needs to be preserved across several calls.

Specified by:
getInterpolatedSecondaryState in interface StepInterpolator
Parameters:
index - index of the secondary set, as returned by ExpandableStatefulODE.addSecondaryEquations(SecondaryEquations)
Returns:
interpolated secondary state at the current interpolation date
Throws:
MaxCountExceededException - if the number of functions evaluations is exceeded
See Also:
StepInterpolator.getInterpolatedState(), StepInterpolator.getInterpolatedDerivatives(), StepInterpolator.getInterpolatedSecondaryDerivatives(int), StepInterpolator.setInterpolatedTime(double)

getInterpolatedSecondaryDerivatives

public double[] getInterpolatedSecondaryDerivatives(int index)
                                             throws MaxCountExceededException
Get the interpolated secondary derivatives corresponding to the secondary equations.

The returned vector is a reference to a reused array, so it should not be modified and it should be copied if it needs to be preserved across several calls.

Specified by:
getInterpolatedSecondaryDerivatives in interface StepInterpolator
Parameters:
index - index of the secondary set, as returned by ExpandableStatefulODE.addSecondaryEquations(SecondaryEquations)
Returns:
interpolated secondary derivatives at the current interpolation date
Throws:
MaxCountExceededException - if the number of functions evaluations is exceeded
See Also:
StepInterpolator.getInterpolatedState(), StepInterpolator.getInterpolatedDerivatives(), StepInterpolator.getInterpolatedSecondaryState(int), StepInterpolator.setInterpolatedTime(double)

finalizeStep

public final void finalizeStep()
                        throws MaxCountExceededException
Finalize the step.

Some embedded Runge-Kutta integrators need fewer functions evaluations than their counterpart step interpolators. These interpolators should perform the last evaluations they need by themselves only if they need them. This method triggers these extra evaluations. It can be called directly by the user step handler and it is called automatically if setInterpolatedTime(double) is called.

Once this method has been called, no other evaluation will be performed on this step. If there is a need to have some side effects between the step handler and the differential equations (for example update some data in the equations once the step has been done), it is advised to call this method explicitly from the step handler before these side effects are set up. If the step handler induces no side effect, then this method can safely be ignored, it will be called transparently as needed.

Warning: since the step interpolator provided to the step handler as a parameter of the handleStep is valid only for the duration of the handleStep call, one cannot simply store a reference and reuse it later. One should first finalize the instance, then copy this finalized instance into a new object that can be kept.

This method calls the protected doFinalize method if it has never been called during this step and set a flag indicating that it has been called once. It is the doFinalize method which should perform the evaluations. This wrapping prevents from calling doFinalize several times and hence evaluating the differential equations too often. Therefore, subclasses are not allowed not reimplement it, they should rather reimplement doFinalize.

Throws:
MaxCountExceededException - if the number of functions evaluations is exceeded

doFinalize

protected void doFinalize()
                   throws MaxCountExceededException
Really finalize the step. The default implementation of this method does nothing.

Throws:
MaxCountExceededException - if the number of functions evaluations is exceeded

writeExternal

public abstract void writeExternal(ObjectOutput out)
                            throws IOException

Specified by:
writeExternal in interface Externalizable
Throws:
IOException

readExternal

public abstract void readExternal(ObjectInput in)
                           throws IOException,
                                  ClassNotFoundException

Specified by:
readExternal in interface Externalizable
Throws:
IOException
ClassNotFoundException

writeBaseExternal

protected void writeBaseExternal(ObjectOutput out)
                          throws IOException
Save the base state of the instance. This method performs step finalization if it has not been done before.

Parameters:
out - stream where to save the state
Throws:
IOException - in case of write error

readBaseExternal

protected double readBaseExternal(ObjectInput in)
                           throws IOException,
                                  ClassNotFoundException
Read the base state of the instance. This method does neither set the interpolated time nor state. It is up to the derived class to reset it properly calling the setInterpolatedTime(double) method later, once all rest of the object state has been set up properly.

Parameters:
in - stream where to read the state from
Returns:
interpolated time to be set later by the caller
Throws:
IOException - in case of read error
ClassNotFoundException - if an equation mapper class cannot be found


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