Class AdaptiveStepsizeFieldIntegrator<T extends CalculusFieldElement<T>>

  • Type Parameters:
    T - the type of the field elements
    All Implemented Interfaces:
    FieldODEIntegrator<T>
    Direct Known Subclasses:
    EmbeddedRungeKuttaFieldIntegrator, MultistepFieldIntegrator

    public abstract class AdaptiveStepsizeFieldIntegrator<T extends CalculusFieldElement<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.

    • 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
      • getStepSizeHelper

        protected StepsizeHelper getStepSizeHelper()
        Get the stepsize helper.
        Returns:
        stepsize helper
        Since:
        2.0
      • 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)
      • 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