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Commons Math example source code file (GillStepInterpolator.java)

This example Commons Math source code file (GillStepInterpolator.java) is included in the DevDaily.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Java - Commons Math tags/keywords

derivativeexception, gillstepinterpolator, gillstepinterpolator, override, override, rungekuttastepinterpolator, stepinterpolator, two_minus_sqrt_2, two_minus_sqrt_2, two_plus_sqrt_2, two_plus_sqrt_2

The Commons Math GillStepInterpolator.java source code

/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

package org.apache.commons.math.ode.nonstiff;

import org.apache.commons.math.ode.DerivativeException;
import org.apache.commons.math.ode.sampling.StepInterpolator;

/**
 * This class implements a step interpolator for the Gill fourth
 * order Runge-Kutta integrator.
 *
 * <p>This interpolator allows to compute dense output inside the last
 * step computed. The interpolation equation is consistent with the
 * integration scheme :
 *
 * <pre>
 *   y(t_n + theta h) = y (t_n + h)
 *                    - (1 - theta) (h/6) [ (1 - theta) (1 - 4 theta) y'_1
 *                                        + (1 - theta) (1 + 2 theta) ((2-q) y'_2 + (2+q) y'_3)
 *                                        + (1 + theta + 4 theta^2) y'_4
 *                                        ]
 * </pre>
 * where theta belongs to [0 ; 1], q = sqrt(2) and where y'_1 to y'_4
 * are the four evaluations of the derivatives already computed during
 * the step.</p>
 *
 * @see GillIntegrator
 * @version $Revision: 811827 $ $Date: 2009-09-06 11:32:50 -0400 (Sun, 06 Sep 2009) $
 * @since 1.2
 */

class GillStepInterpolator
  extends RungeKuttaStepInterpolator {

    /** First Gill coefficient. */
    private static final double TWO_MINUS_SQRT_2 = 2 - Math.sqrt(2.0);

    /** Second Gill coefficient. */
    private static final double TWO_PLUS_SQRT_2 = 2 + Math.sqrt(2.0);

    /** Serializable version identifier */
    private static final long serialVersionUID = -107804074496313322L;

  /** Simple constructor.
   * This constructor builds an instance that is not usable yet, the
   * {@link
   * org.apache.commons.math.ode.sampling.AbstractStepInterpolator#reinitialize}
   * method should be called before using the instance in order to
   * initialize the internal arrays. This constructor is used only
   * in order to delay the initialization in some cases. The {@link
   * RungeKuttaIntegrator} class uses the prototyping design pattern
   * to create the step interpolators by cloning an uninitialized model
   * and later initializing the copy.
   */
  public GillStepInterpolator() {
  }

  /** Copy constructor.
   * @param interpolator interpolator to copy from. The copy is a deep
   * copy: its arrays are separated from the original arrays of the
   * instance
   */
  public GillStepInterpolator(final GillStepInterpolator interpolator) {
    super(interpolator);
  }

  /** {@inheritDoc} */
  @Override
  protected StepInterpolator doCopy() {
    return new GillStepInterpolator(this);
  }


  /** {@inheritDoc} */
  @Override
  protected void computeInterpolatedStateAndDerivatives(final double theta,
                                          final double oneMinusThetaH)
    throws DerivativeException {

    final double twoTheta  = 2 * theta;
    final double fourTheta = 4 * theta;
    final double s         = oneMinusThetaH / 6.0;
    final double oMt       = 1 - theta;
    final double soMt      = s * oMt;
    final double c23       = soMt * (1 + twoTheta);
    final double coeff1    = soMt * (1 - fourTheta);
    final double coeff2    = c23  * TWO_MINUS_SQRT_2;
    final double coeff3    = c23  * TWO_PLUS_SQRT_2;
    final double coeff4    = s * (1 + theta * (1 + fourTheta));
    final double coeffDot1 = theta * (twoTheta - 3) + 1;
    final double cDot23    = theta * oMt;
    final double coeffDot2 = cDot23  * TWO_MINUS_SQRT_2;
    final double coeffDot3 = cDot23  * TWO_PLUS_SQRT_2;
    final double coeffDot4 = theta * (twoTheta - 1);

    for (int i = 0; i < interpolatedState.length; ++i) {
        final double yDot1 = yDotK[0][i];
        final double yDot2 = yDotK[1][i];
        final double yDot3 = yDotK[2][i];
        final double yDot4 = yDotK[3][i];
        interpolatedState[i] =
            currentState[i] - coeff1 * yDot1 - coeff2 * yDot2 - coeff3 * yDot3 - coeff4 * yDot4;
        interpolatedDerivatives[i] =
            coeffDot1 * yDot1 + coeffDot2 * yDot2 + coeffDot3 * yDot3 + coeffDot4 * yDot4;
     }

  }

}

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