AdaptiveStepsizeFieldIntegrator (Apache Commons Math 3.6.1 API)

java.lang.Object
- org.apache.commons.math3.ode.AbstractFieldIntegrator<T>
- - org.apache.commons.math3.ode.nonstiff.AdaptiveStepsizeFieldIntegrator<T>

Type Parameters:
T - the type of the field elements

All Implemented Interfaces:

FirstOrderFieldIntegrator<T>

Direct Known Subclasses:

EmbeddedRungeKuttaFieldIntegrator, MultistepFieldIntegrator
```
public abstract class AdaptiveStepsizeFieldIntegrator<T extends RealFieldElement<T>>
extends AbstractFieldIntegrator<T>
```
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.

Note that only the main part of the state vector is used for stepsize control. The secondary parts of the state vector are explicitly ignored for stepsize control.

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:

3.6

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.

Constructor Summary

Constructors
Constructor and Description
`AdaptiveStepsizeFieldIntegrator(Field<T> field, String name, double minStep, double maxStep, double[] vecAbsoluteTolerance, double[] vecRelativeTolerance)` Build an integrator with the given stepsize bounds.
`AdaptiveStepsizeFieldIntegrator(Field<T> field, 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 T`	`filterStep(T h, boolean forward, boolean acceptSmall)` Filter the integration step.
`T`	`getMaxStep()` Get the maximal step.
`T`	`getMinStep()` Get the minimal step.
`T`	`initializeStep(boolean forward, int order, T[] scale, FieldODEStateAndDerivative<T> state0, FieldEquationsMapper<T> mapper)` Initialize the integration step.
`protected void`	`resetInternalState()` Reset internal state to dummy values.
`protected void`	`sanityChecks(FieldODEState<T> eqn, T t)` Check the integration span.
`void`	`setInitialStepSize(T 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.AbstractFieldIntegrator
acceptStep, addEventHandler, addEventHandler, addStepHandler, clearEventHandlers, clearStepHandlers, computeDerivatives, getCurrentSignedStepsize, getCurrentStepStart, getEquations, getEvaluations, getEvaluationsCounter, getEventHandlers, getField, getMaxEvaluations, getName, getStepHandlers, getStepSize, getStepStart, initIntegration, isLastStep, resetOccurred, setIsLastStep, setMaxEvaluations, setStateInitialized, setStepSize, setStepStart

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface org.apache.commons.math3.ode.FirstOrderFieldIntegrator
integrate

- 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
  - AdaptiveStepsizeFieldIntegrator
```
public AdaptiveStepsizeFieldIntegrator(Field<T> field,
                               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:
    field - field to which the time and state vector elements belong
    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
  - AdaptiveStepsizeFieldIntegrator
```
public AdaptiveStepsizeFieldIntegrator(Field<T> field,
                               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:
    field - field to which the time and state vector elements belong
    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(T 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(FieldODEState<T> eqn,
                T t)
                     throws DimensionMismatchException,
                            NumberIsTooSmallException
```
    Check the integration span.
    
    Overrides:
    
    sanityChecks in class AbstractFieldIntegrator<T extends RealFieldElement<T>>
    
    Parameters:
    eqn - 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 T initializeStep(boolean forward,
               int order,
               T[] scale,
               FieldODEStateAndDerivative<T> state0,
               FieldEquationsMapper<T> mapper)
                                             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)
    state0 - state at integration start time
    mapper - mapper for all the equations
    
    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 T filterStep(T 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
  - resetInternalState
```
protected void resetInternalState()
```
    Reset internal state to dummy values.
  - getMinStep
```
public T getMinStep()
```
    Get the minimal step.
    
    Returns:
    minimal step
  - getMaxStep
```
public T getMaxStep()
```
    Get the maximal step.
    
    Returns:
    maximal step

Class AdaptiveStepsizeFieldIntegrator<T extends RealFieldElement<T>>

Field Summary

Constructor Summary

Method Summary

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

Methods inherited from class java.lang.Object

Methods inherited from interface org.apache.commons.math3.ode.FirstOrderFieldIntegrator

Field Detail

scalAbsoluteTolerance

scalRelativeTolerance

vecAbsoluteTolerance

vecRelativeTolerance

mainSetDimension

Constructor Detail

AdaptiveStepsizeFieldIntegrator

AdaptiveStepsizeFieldIntegrator

Method Detail

setStepSizeControl

setStepSizeControl

setInitialStepSize

sanityChecks

initializeStep

filterStep

resetInternalState

getMinStep

getMaxStep