AdaptiveStepsizeIntegrator (Apache Commons Math 3.3 API)

java.lang.Object
- org.apache.commons.math3.ode.AbstractIntegrator
- - 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

Fields
Modifier and Type	Field and 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.math3.ode.AbstractIntegrator
isLastStep, resetOccurred, stepHandlers, stepSize, stepStart

Constructor Summary

Constructors
Constructor and Description
`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

Methods
Modifier and Type	Method and 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 t_i.
`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, getEvaluationsCounter, getEventHandlers, getExpandable, 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 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

Class AdaptiveStepsizeIntegrator

Field Summary

Fields inherited from class org.apache.commons.math3.ode.AbstractIntegrator

Constructor Summary

Method Summary

Methods inherited from class org.apache.commons.math3.ode.AbstractIntegrator

Methods inherited from class java.lang.Object

Field Detail

scalAbsoluteTolerance

scalRelativeTolerance

vecAbsoluteTolerance

vecRelativeTolerance

mainSetDimension

Constructor Detail

AdaptiveStepsizeIntegrator

AdaptiveStepsizeIntegrator

Method Detail

setStepSizeControl

setStepSizeControl

setInitialStepSize

sanityChecks

initializeStep

filterStep

integrate

getCurrentStepStart

resetInternalState

getMinStep

getMaxStep