org.apache.commons.math.ode.jacobians
Class FirstOrderIntegratorWithJacobians

java.lang.Object
  extended by org.apache.commons.math.ode.jacobians.FirstOrderIntegratorWithJacobians

public class FirstOrderIntegratorWithJacobians
extends java.lang.Object

This class enhances a first order integrator for differential equations to compute also partial derivatives of the solution with respect to initial state and parameters.

In order to compute both the state and its derivatives, the ODE problem is extended with jacobians of the raw ODE and the variational equations are added to form a new compound problem of higher dimension. If the original ODE problem has dimension n and there are p parameters, the compound problem will have dimension n × (1 + n + p).

Since:
2.1
Version:
$Revision: 927342 $ $Date: 2010-03-25 06:55:55 -0400 (Thu, 25 Mar 2010) $
See Also:
ParameterizedODE, ODEWithJacobians

Nested Class Summary
private static class FirstOrderIntegratorWithJacobians.EventHandlerWrapper
          Wrapper for event handlers.
private  class FirstOrderIntegratorWithJacobians.FiniteDifferencesWrapper
          Wrapper class to compute jacobians by finite differences for ODE which do not compute them themselves.
private  class FirstOrderIntegratorWithJacobians.MappingWrapper
          Wrapper class used to map state and jacobians into compound state.
private static class FirstOrderIntegratorWithJacobians.StepHandlerWrapper
          Wrapper for step handlers.
private static class FirstOrderIntegratorWithJacobians.StepInterpolatorWrapper
          Wrapper for step interpolators.
 
Field Summary
private  int evaluations
          Number of evaluations already performed.
private  FirstOrderIntegrator integrator
          Underlying integrator for compound problem.
private  int maxEvaluations
          Maximal number of evaluations allowed.
private  ODEWithJacobians ode
          Raw equations to integrate.
 
Constructor Summary
FirstOrderIntegratorWithJacobians(FirstOrderIntegrator integrator, ODEWithJacobians ode)
          Build an enhanced integrator using ODE builtin jacobian computation features.
FirstOrderIntegratorWithJacobians(FirstOrderIntegrator integrator, ParameterizedODE ode, double[] p, double[] hY, double[] hP)
          Build an enhanced integrator using internal differentiation to compute jacobians.
 
Method Summary
 void addEventHandler(EventHandlerWithJacobians handler, double maxCheckInterval, double convergence, int maxIterationCount)
          Add an event handler to the integrator.
 void addStepHandler(StepHandlerWithJacobians handler)
          Add a step handler to this integrator.
private  void checkDimension(int expected, java.lang.Object array)
          Check array dimensions.
 void clearEventHandlers()
          Remove all the event handlers that have been added to the integrator.
 void clearStepHandlers()
          Remove all the step handlers that have been added to the integrator.
private static void dispatchCompoundState(double[] z, double[] y, double[][] dydy0, double[][] dydp)
          Dispatch a compound state array into state and jacobians arrays.
 double getCurrentSignedStepsize()
          Get the current signed value of the integration stepsize.
 double getCurrentStepStart()
          Get the current value of the step start time ti.
 int getEvaluations()
          Get the number of evaluations of the differential equations function.
 java.util.Collection<EventHandlerWithJacobians> getEventHandlers()
          Get all the event handlers that have been added to the integrator.
 int getMaxEvaluations()
          Get the maximal number of functions evaluations.
 java.util.Collection<StepHandlerWithJacobians> getStepHandlers()
          Get all the step handlers that have been added to the integrator.
 double integrate(double t0, double[] y0, double[][] dY0dP, double t, double[] y, double[][] dYdY0, double[][] dYdP)
          Integrate the differential equations and the variational equations up to the given time.
 void setMaxEvaluations(int maxEvaluations)
          Set the maximal number of differential equations function evaluations.
 
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Field Detail

integrator

private final FirstOrderIntegrator integrator
Underlying integrator for compound problem.


ode

private final ODEWithJacobians ode
Raw equations to integrate.


maxEvaluations

private int maxEvaluations
Maximal number of evaluations allowed.


evaluations

private int evaluations
Number of evaluations already performed.

Constructor Detail

FirstOrderIntegratorWithJacobians

public FirstOrderIntegratorWithJacobians(FirstOrderIntegrator integrator,
                                         ParameterizedODE ode,
                                         double[] p,
                                         double[] hY,
                                         double[] hP)
Build an enhanced integrator using internal differentiation to compute jacobians.

Parameters:
integrator - underlying integrator to solve the compound problem
ode - original problem (f in the equation y' = f(t, y))
p - parameters array (may be null if getParametersDimension() from original problem is zero)
hY - step sizes to use for computing the jacobian df/dy, must have the same dimension as the original problem
hP - step sizes to use for computing the jacobian df/dp, must have the same dimension as the original problem parameters dimension
See Also:
FirstOrderIntegratorWithJacobians(FirstOrderIntegrator, ODEWithJacobians)

FirstOrderIntegratorWithJacobians

public FirstOrderIntegratorWithJacobians(FirstOrderIntegrator integrator,
                                         ODEWithJacobians ode)
Build an enhanced integrator using ODE builtin jacobian computation features.

Parameters:
integrator - underlying integrator to solve the compound problem
ode - original problem, which can compute the jacobians by itself
See Also:
FirstOrderIntegratorWithJacobians(FirstOrderIntegrator, ParameterizedODE, double[], double[], double[])
Method Detail

addStepHandler

public void addStepHandler(StepHandlerWithJacobians handler)
Add a step handler to this integrator.

The handler will be called by the integrator for each accepted step.

Parameters:
handler - handler for the accepted steps
See Also:
getStepHandlers(), clearStepHandlers()

getStepHandlers

public java.util.Collection<StepHandlerWithJacobians> getStepHandlers()
Get all the step handlers that have been added to the integrator.

Returns:
an unmodifiable collection of the added events handlers
See Also:
addStepHandler(StepHandlerWithJacobians), clearStepHandlers()

clearStepHandlers

public void clearStepHandlers()
Remove all the step handlers that have been added to the integrator.

See Also:
addStepHandler(StepHandlerWithJacobians), getStepHandlers()

addEventHandler

public void addEventHandler(EventHandlerWithJacobians handler,
                            double maxCheckInterval,
                            double convergence,
                            int maxIterationCount)
Add an event handler to the integrator.

Parameters:
handler - event handler
maxCheckInterval - maximal time interval between switching function checks (this interval prevents missing sign changes in case the integration steps becomes very large)
convergence - convergence threshold in the event time search
maxIterationCount - upper limit of the iteration count in the event time search
See Also:
getEventHandlers(), clearEventHandlers()

getEventHandlers

public java.util.Collection<EventHandlerWithJacobians> getEventHandlers()
Get all the event handlers that have been added to the integrator.

Returns:
an unmodifiable collection of the added events handlers
See Also:
addEventHandler(EventHandlerWithJacobians, double, double, int), clearEventHandlers()

clearEventHandlers

public void clearEventHandlers()
Remove all the event handlers that have been added to the integrator.

See Also:
addEventHandler(EventHandlerWithJacobians, double, double, int), getEventHandlers()

integrate

public double integrate(double t0,
                        double[] y0,
                        double[][] dY0dP,
                        double t,
                        double[] y,
                        double[][] dYdY0,
                        double[][] dYdP)
                 throws DerivativeException,
                        IntegratorException
Integrate the differential equations and the variational equations up to the given time.

This method solves an Initial Value Problem (IVP) and also computes the derivatives of the solution with respect to initial state and parameters. This can be used as a basis to solve Boundary Value Problems (BVP).

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

Parameters:
t0 - initial time
y0 - initial value of the state vector at t0
dY0dP - initial value of the state vector derivative with respect to the parameters 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
dYdY0 - placeholder where to put the state vector derivative with respect to the initial state (dy[i]/dy0[j] is in element array dYdY0[i][j]) at each successful step (and hence at the end of integration)
dYdP - placeholder where to put the state vector derivative with respect to the parameters (dy[i]/dp[j] is in element array dYdP[i][j]) at each successful step (and hence at the end of integration)
Returns:
stop time, will be the same as target time if integration reached its target, but may be different if some event handler stops it at some point.
Throws:
IntegratorException - if the integrator cannot perform integration
DerivativeException - this exception is propagated to the caller if the underlying user function triggers one

dispatchCompoundState

private static void dispatchCompoundState(double[] z,
                                          double[] y,
                                          double[][] dydy0,
                                          double[][] dydp)
Dispatch a compound state array into state and jacobians arrays.

Parameters:
z - compound state
y - raw state array to fill
dydy0 - jacobian array to fill
dydp - jacobian array to fill

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.

Returns:
current value of the step start time ti

getCurrentSignedStepsize

public double getCurrentSignedStepsize()
Get the current signed value of the integration stepsize.

This method can be called during integration (typically by the object implementing the differential equations problem) if the signed value of the current stepsize that is tried is needed.

The result is undefined if the method is called outside of calls to integrate.

Returns:
current signed value of the stepsize

setMaxEvaluations

public void setMaxEvaluations(int maxEvaluations)
Set the maximal number of differential equations function evaluations.

The purpose of this method is to avoid infinite loops which can occur for example when stringent error constraints are set or when lots of discrete events are triggered, thus leading to many rejected steps.

Parameters:
maxEvaluations - maximal number of function evaluations (negative values are silently converted to maximal integer value, thus representing almost unlimited evaluations)

getMaxEvaluations

public int getMaxEvaluations()
Get the maximal number of functions evaluations.

Returns:
maximal number of functions evaluations

getEvaluations

public int getEvaluations()
Get the number of evaluations of the differential equations function.

The number of evaluations corresponds to the last call to the integrate method. It is 0 if the method has not been called yet.

Returns:
number of evaluations of the differential equations function

checkDimension

private void checkDimension(int expected,
                            java.lang.Object array)
                     throws java.lang.IllegalArgumentException
Check array dimensions.

Parameters:
expected - expected dimension
array - (may be null if expected is 0)
Throws:
java.lang.IllegalArgumentException - if the array dimension does not match the expected one


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