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## org.apache.commons.math.ode.nonstiff
Class GraggBulirschStoerStepInterpolator

    java.lang.Object
      org.apache.commons.math.ode.sampling.AbstractStepInterpolator
          org.apache.commons.math.ode.nonstiff.GraggBulirschStoerStepInterpolator

All Implemented Interfaces:
  Externalizable, Serializable, StepInterpolator

     class GraggBulirschStoerStepInterpolator

extends AbstractStepInterpolator

This class implements an interpolator for the Gragg-Bulirsch-Stoer integrator.

This interpolator compute dense output inside the last step produced by a Gragg-Bulirsch-Stoer integrator.

This implementation is basically a reimplementation in Java of the odex fortran code by E. Hairer and G. Wanner. The redistribution policy for this code is available here, for convenience, it is reproduced below.

Copyright (c) 2004, Ernst Hairer
Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

Since:
  1.2
Version:
  $Revision: 1061507 $ $Date: 2011-01-20 21:55:00 +0100 (jeu. 20 janv. 2011) $
See Also:
  `GraggBulirschStoerIntegrator`

Field Summary
`private int` | `currentDegree` Degree of the interpolation polynoms.
`private double[]` | `errfac` Error coefficients for the interpolation.
`private double[][]` | `polynoms` Interpolation polynoms.
`private static long` | `serialVersionUID` Serializable version identifier.
`private double[]` | `y0Dot` Slope at the beginning of the step.
`private double[]` | `y1` State at the end of the step.
`private double[]` | `y1Dot` Slope at the end of the step.
`private double[][]` | `yMidDots` Derivatives at the middle of the step.

Fields inherited from class org.apache.commons.math.ode.sampling.AbstractStepInterpolator
`currentState, h, interpolatedDerivatives, interpolatedState, interpolatedTime`

Constructor Summary
`GraggBulirschStoerStepInterpolator()` Simple constructor.
`GraggBulirschStoerStepInterpolator(double[] y, double[] y0Dot, double[] y1, double[] y1Dot, double[][] yMidDots, boolean forward)` Simple constructor.
`GraggBulirschStoerStepInterpolator(GraggBulirschStoerStepInterpolator interpolator)` Copy constructor.

Method Summary
`void` | `computeCoefficients(int mu, double h)` Compute the interpolation coefficients for dense output.
`protected void` | `computeInterpolatedStateAndDerivatives(double theta, double oneMinusThetaH)` Compute the state and derivatives at the interpolated time.
`protected StepInterpolator` | `doCopy()` Really copy the finalized instance.
`double` | `estimateError(double[] scale)` Estimate interpolation error.
`void` | `readExternal(ObjectInput in)`
`private void` | `resetTables(int maxDegree)` Reallocate the internal tables.
`void` | `writeExternal(ObjectOutput out)`

Methods inherited from class org.apache.commons.math.ode.sampling.AbstractStepInterpolator
`copy, doFinalize, finalizeStep, getCurrentTime, getGlobalCurrentTime, getGlobalPreviousTime, getInterpolatedDerivatives, getInterpolatedState, getInterpolatedTime, getPreviousTime, isForward, readBaseExternal, reinitialize, setInterpolatedTime, setSoftCurrentTime, setSoftPreviousTime, shift, storeTime, writeBaseExternal`

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

Field Detail

### serialVersionUID

    private static final long serialVersionUID

  Serializable version identifier.

  See Also:
    Constant Field Values

### y0Dot

    private double[] y0Dot

  Slope at the beginning of the step.

### y1

    private double[] y1

  State at the end of the step.

### y1Dot

    private double[] y1Dot

  Slope at the end of the step.

### yMidDots

    private double[][] yMidDots

  Derivatives at the middle of the step. element 0 is state at midpoint, element 1 is first derivative ...

### polynoms

    private double[][] polynoms

  Interpolation polynoms.

### errfac

    private double[] errfac

  Error coefficients for the interpolation.

### currentDegree

    private int currentDegree

  Degree of the interpolation polynoms.

Constructor Detail

### GraggBulirschStoerStepInterpolator

    public GraggBulirschStoerStepInterpolator()

  Simple constructor. This constructor should not be used directly, it is only intended for the serialization process.

### GraggBulirschStoerStepInterpolator

    public GraggBulirschStoerStepInterpolator(double[] y,
                                              double[] y0Dot,
                                              double[] y1,
                                              double[] y1Dot,
                                              double[][] yMidDots,
                                              boolean forward)

  Simple constructor.

  Parameters:
    `y` - reference to the integrator array holding the current state
    `y0Dot` - reference to the integrator array holding the slope at the beginning of the step
    `y1` - reference to the integrator array holding the state at the end of the step
    `y1Dot` - reference to the integrator array holding the slope at the end of the step
    `yMidDots` - reference to the integrator array holding the derivatives at the middle point of the step
    `forward` - integration direction indicator

### GraggBulirschStoerStepInterpolator

    public GraggBulirschStoerStepInterpolator(GraggBulirschStoerStepInterpolator interpolator)

  Copy constructor.

  Parameters:
    `interpolator` - interpolator to copy from. The copy is a deep copy: its arrays are separated from the original arrays of the instance

Method Detail

### resetTables

    private void resetTables(int maxDegree)

  Reallocate the internal tables. Reallocate the internal tables in order to be able to handle interpolation polynoms up to the given degree

  Parameters:
    `maxDegree` - maximal degree to handle

### doCopy

    protected StepInterpolator doCopy()

  Really copy the finalized instance.

  This method is called by `AbstractStepInterpolator.copy()` after the step has been finalized. It must perform a deep copy to have an new instance completely independent for the original instance.

  Specified by:
    `doCopy` in class `AbstractStepInterpolator`
  Returns:
    a copy of the finalized instance

### computeCoefficients

    public void computeCoefficients(int mu,
                                    double h)

  Compute the interpolation coefficients for dense output.

  Parameters:
    `mu` - degree of the interpolation polynomial
    `h` - current step

### estimateError

    public double estimateError(double[] scale)

  Estimate interpolation error.

  Parameters:
    `scale` - scaling array
  Returns:
    estimate of the interpolation error

### computeInterpolatedStateAndDerivatives

    protected void computeInterpolatedStateAndDerivatives(double theta,
                                                          double oneMinusThetaH)

  Compute the state and derivatives at the interpolated time. This is the main processing method that should be implemented by the derived classes to perform the interpolation.

  Specified by:
    `computeInterpolatedStateAndDerivatives` in class `AbstractStepInterpolator`
  Parameters:
    `theta` - normalized interpolation abscissa within the step (theta is zero at the previous time step and one at the current time step)
    `oneMinusThetaH` - time gap between the interpolated time and the current time

### writeExternal

    public void writeExternal(ObjectOutput out)
                       throws IOException

  Specified by:
    `writeExternal` in interface `Externalizable`
  Specified by:
    `writeExternal` in class `AbstractStepInterpolator`
  Throws:
    `IOException`

### readExternal

    public void readExternal(ObjectInput in)
                      throws IOException

  Specified by:
    `readExternal` in interface `Externalizable`
  Specified by:
    `readExternal` in class `AbstractStepInterpolator`
  Throws:
    `IOException`

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