GillStepInterpolator.java

/*
 * 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.exception.MathUserException;
import org.apache.commons.math.ode.sampling.StepInterpolator;
import org.apache.commons.math.util.FastMath;

/**
 * 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 $Id: GillStepInterpolator.java 1131229 2011-06-03 20:49:25Z luc $
 * @since 1.2
 */

class GillStepInterpolator
  extends RungeKuttaStepInterpolator {

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

    /** Second Gill coefficient. */
    private static final double TWO_PLUS_SQRT_2 = 2 + FastMath.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 MathUserException {

    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;
     }

  }

}