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

java.lang.Object
  extended by org.apache.commons.math3.ode.AbstractIntegrator
      extended by org.apache.commons.math3.ode.nonstiff.AdaptiveStepsizeIntegrator
          extended by org.apache.commons.math3.ode.nonstiff.EmbeddedRungeKuttaIntegrator
All Implemented Interfaces:
FirstOrderIntegrator, ODEIntegrator
Direct Known Subclasses:
DormandPrince54Integrator, DormandPrince853Integrator, HighamHall54Integrator

public abstract class EmbeddedRungeKuttaIntegrator
extends AdaptiveStepsizeIntegrator

This class implements the common part of all embedded Runge-Kutta integrators for Ordinary Differential Equations.

These methods are embedded explicit Runge-Kutta methods with two sets of coefficients allowing to estimate the error, their Butcher arrays are as follows :

    0  |
   c2  | a21
   c3  | a31  a32
   ... |        ...
   cs  | as1  as2  ...  ass-1
       |--------------------------
       |  b1   b2  ...   bs-1  bs
       |  b'1  b'2 ...   b's-1 b's
 

In fact, we rather use the array defined by ej = bj - b'j to compute directly the error rather than computing two estimates and then comparing them.

Some methods are qualified as fsal (first same as last) methods. This means the last evaluation of the derivatives in one step is the same as the first in the next step. Then, this evaluation can be reused from one step to the next one and the cost of such a method is really s-1 evaluations despite the method still has s stages. This behaviour is true only for successful steps, if the step is rejected after the error estimation phase, no evaluation is saved. For an fsal method, we have cs = 1 and asi = bi for all i.

Since:
1.2
Version:
$Id: EmbeddedRungeKuttaIntegrator.java 1416643 2012-12-03 19:37:14Z tn $

Field Summary
 
Fields inherited from class org.apache.commons.math3.ode.nonstiff.AdaptiveStepsizeIntegrator
mainSetDimension, scalAbsoluteTolerance, scalRelativeTolerance, vecAbsoluteTolerance, vecRelativeTolerance
 
Fields inherited from class org.apache.commons.math3.ode.AbstractIntegrator
isLastStep, resetOccurred, stepHandlers, stepSize, stepStart
 
Constructor Summary
protected EmbeddedRungeKuttaIntegrator(String name, boolean fsal, double[] c, double[][] a, double[] b, org.apache.commons.math3.ode.nonstiff.RungeKuttaStepInterpolator prototype, double minStep, double maxStep, double[] vecAbsoluteTolerance, double[] vecRelativeTolerance)
          Build a Runge-Kutta integrator with the given Butcher array.
protected EmbeddedRungeKuttaIntegrator(String name, boolean fsal, double[] c, double[][] a, double[] b, org.apache.commons.math3.ode.nonstiff.RungeKuttaStepInterpolator prototype, double minStep, double maxStep, double scalAbsoluteTolerance, double scalRelativeTolerance)
          Build a Runge-Kutta integrator with the given Butcher array.
 
Method Summary
protected abstract  double estimateError(double[][] yDotK, double[] y0, double[] y1, double h)
          Compute the error ratio.
 double getMaxGrowth()
          Get the maximal growth factor for stepsize control.
 double getMinReduction()
          Get the minimal reduction factor for stepsize control.
abstract  int getOrder()
          Get the order of the method.
 double getSafety()
          Get the safety factor for stepsize control.
 void integrate(ExpandableStatefulODE equations, double t)
          Integrate a set of differential equations up to the given time.
 void setMaxGrowth(double maxGrowth)
          Set the maximal growth factor for stepsize control.
 void setMinReduction(double minReduction)
          Set the minimal reduction factor for stepsize control.
 void setSafety(double safety)
          Set the safety factor for stepsize control.
 
Methods inherited from class org.apache.commons.math3.ode.nonstiff.AdaptiveStepsizeIntegrator
filterStep, getCurrentStepStart, getMaxStep, getMinStep, initializeStep, resetInternalState, sanityChecks, setInitialStepSize, setStepSizeControl, setStepSizeControl
 
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
 

Constructor Detail

EmbeddedRungeKuttaIntegrator

protected EmbeddedRungeKuttaIntegrator(String name,
                                       boolean fsal,
                                       double[] c,
                                       double[][] a,
                                       double[] b,
                                       org.apache.commons.math3.ode.nonstiff.RungeKuttaStepInterpolator prototype,
                                       double minStep,
                                       double maxStep,
                                       double scalAbsoluteTolerance,
                                       double scalRelativeTolerance)
Build a Runge-Kutta integrator with the given Butcher array.

Parameters:
name - name of the method
fsal - indicate that the method is an fsal
c - time steps from Butcher array (without the first zero)
a - internal weights from Butcher array (without the first empty row)
b - propagation weights for the high order method from Butcher array
prototype - prototype of the step interpolator to use
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

EmbeddedRungeKuttaIntegrator

protected EmbeddedRungeKuttaIntegrator(String name,
                                       boolean fsal,
                                       double[] c,
                                       double[][] a,
                                       double[] b,
                                       org.apache.commons.math3.ode.nonstiff.RungeKuttaStepInterpolator prototype,
                                       double minStep,
                                       double maxStep,
                                       double[] vecAbsoluteTolerance,
                                       double[] vecRelativeTolerance)
Build a Runge-Kutta integrator with the given Butcher array.

Parameters:
name - name of the method
fsal - indicate that the method is an fsal
c - time steps from Butcher array (without the first zero)
a - internal weights from Butcher array (without the first empty row)
b - propagation weights for the high order method from Butcher array
prototype - prototype of the step interpolator to use
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

getOrder

public abstract int getOrder()
Get the order of the method.

Returns:
order of the method

getSafety

public double getSafety()
Get the safety factor for stepsize control.

Returns:
safety factor

setSafety

public void setSafety(double safety)
Set the safety factor for stepsize control.

Parameters:
safety - safety factor

integrate

public 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 AdaptiveStepsizeIntegrator
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

getMinReduction

public double getMinReduction()
Get the minimal reduction factor for stepsize control.

Returns:
minimal reduction factor

setMinReduction

public void setMinReduction(double minReduction)
Set the minimal reduction factor for stepsize control.

Parameters:
minReduction - minimal reduction factor

getMaxGrowth

public double getMaxGrowth()
Get the maximal growth factor for stepsize control.

Returns:
maximal growth factor

setMaxGrowth

public void setMaxGrowth(double maxGrowth)
Set the maximal growth factor for stepsize control.

Parameters:
maxGrowth - maximal growth factor

estimateError

protected abstract double estimateError(double[][] yDotK,
                                        double[] y0,
                                        double[] y1,
                                        double h)
Compute the error ratio.

Parameters:
yDotK - derivatives computed during the first stages
y0 - estimate of the step at the start of the step
y1 - estimate of the step at the end of the step
h - current step
Returns:
error ratio, greater than 1 if step should be rejected


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