RungeKuttaFieldIntegrator (Apache Commons Math 3.6.1 API)

org.apache.commons.math3.ode.nonstiff

## Class RungeKuttaFieldIntegrator<T extends RealFieldElement<T>>

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

- Type Parameters:
    `T` - the type of the field elements
  All Implemented Interfaces:
    FirstOrderFieldIntegrator<T>, FieldButcherArrayProvider<T>
  Direct Known Subclasses:
    ClassicalRungeKuttaFieldIntegrator, EulerFieldIntegrator, GillFieldIntegrator, LutherFieldIntegrator, MidpointFieldIntegrator, ThreeEighthesFieldIntegrator

      public abstract class RungeKuttaFieldIntegrator<T extends RealFieldElement<T>>
      extends AbstractFieldIntegrator<T>
      implements FieldButcherArrayProvider<T>

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

  These methods are explicit Runge-Kutta methods, their Butcher arrays are as follows :

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

  Since:
    3.6
  See Also:
    `EulerFieldIntegrator`, `ClassicalRungeKuttaFieldIntegrator`, `GillFieldIntegrator`, `MidpointFieldIntegrator`

- - ### Constructor Summary

    Constructors
    Modifier | Constructor and Description
    --- | ---
    `protected` | `RungeKuttaFieldIntegrator(Field<T> field, String name, T step)` Simple constructor.

  - ### Method Summary

    Methods
    Modifier and Type | Method and Description
    --- | ---
    `protected abstract org.apache.commons.math3.ode.nonstiff.RungeKuttaFieldStepInterpolator<T>` | `createInterpolator(boolean forward, T[][] yDotK, FieldODEStateAndDerivative<T> globalPreviousState, FieldODEStateAndDerivative<T> globalCurrentState, FieldEquationsMapper<T> mapper)` Create an interpolator.
    `protected T` | `fraction(int p, int q)` Create a fraction.
    `FieldODEStateAndDerivative<T>` | `integrate(FieldExpandableODE<T> equations, FieldODEState<T> initialState, T finalTime)` Integrate the differential equations up to the given time.
    `T[]` | `singleStep(FirstOrderFieldDifferentialEquations<T> equations, T t0, T[] y0, T t)` Fast computation of a single step of ODE integration.

    - ### 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, sanityChecks, 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.nonstiff.FieldButcherArrayProvider

      `getA, getB, getC`

- - ### Constructor Detail

    - #### RungeKuttaFieldIntegrator

          protected RungeKuttaFieldIntegrator(Field<T> field,
                                   String name,
                                   T step)

      Simple constructor. Build a Runge-Kutta integrator with the given step. The default step handler does nothing.
      Parameters:
        `field` - field to which the time and state vector elements belong
        `name` - name of the method
        `step` - integration step

  - ### Method Detail

    - #### fraction

          protected T fraction(int p,
                   int q)

      Create a fraction.
      Parameters:
        `p` - numerator
        `q` - denominator
      Returns:
        p/q computed in the instance field

    - #### createInterpolator

          protected abstract org.apache.commons.math3.ode.nonstiff.RungeKuttaFieldStepInterpolator<T> createInterpolator(boolean forward,
                                                                                                    T[][] yDotK,
                                                                                                    FieldODEStateAndDerivative<T> globalPreviousState,
                                                                                                    FieldODEStateAndDerivative<T> globalCurrentState,
                                                                                                    FieldEquationsMapper<T> mapper)

      Create an interpolator.
      Parameters:
        `forward` - integration direction indicator
        `yDotK` - slopes at the intermediate points
        `globalPreviousState` - start of the global step
        `globalCurrentState` - end of the global step
        `mapper` - equations mapper for the all equations
      Returns:
        external weights for the high order method from Butcher array

    - #### integrate

          public FieldODEStateAndDerivative<T> integrate(FieldExpandableODE<T> equations,
                                                FieldODEState<T> initialState,
                                                T finalTime)
                                                                              throws NumberIsTooSmallException,
                                                                                     DimensionMismatchException,
                                                                                     MaxCountExceededException,
                                                                                     NoBracketingException

      Integrate the differential equations up to the given time.

      This method solves an Initial Value Problem (IVP).

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

      Specified by:
        `integrate` in interface `FirstOrderFieldIntegrator<T extends RealFieldElement<T>>`
      Parameters:
        `equations` - differential equations to integrate
        `initialState` - initial state (time, primary and secondary state vectors)
        `finalTime` - target time for the integration (can be set to a value smaller than `t0` for backward integration)
      Returns:
        final state, its time will be the same as `finalTime` if integration reached its target, but may be different if some `FieldEventHandler` stops it at some point.
      Throws:
        `NumberIsTooSmallException` - if integration step is too small
        `MaxCountExceededException` - if the number of functions evaluations is exceeded
        `NoBracketingException` - if the location of an event cannot be bracketed
        `DimensionMismatchException`

    - #### singleStep

          public T[] singleStep(FirstOrderFieldDifferentialEquations<T> equations,
                       T t0,
                       T[] y0,
                       T t)

      Fast computation of a single step of ODE integration.

      This method is intended for the limited use case of very fast computation of only one step without using any of the rich features of general integrators that may take some time to set up (i.e. no step handlers, no events handlers, no additional states, no interpolators, no error control, no evaluations count, no sanity checks ...). It handles the strict minimum of computation, so it can be embedded in outer loops.

      This method is not used at all by the `integrate(FieldExpandableODE, FieldODEState, RealFieldElement)` method. It also completely ignores the step set at construction time, and uses only a single step to go from `t0` to `t`.

      As this method does not use any of the state-dependent features of the integrator, it should be reasonably thread-safe if and only if the provided differential equations are themselves thread-safe.

      Parameters:
        `equations` - differential equations to integrate
        `t0` - initial time
        `y0` - initial value of the state vector at t0
        `t` - target time for the integration (can be set to a value smaller than `t0` for backward integration)
      Returns:
        state vector at `t`

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