src/java/org/apache/commons/math/ode/ClassicalRungeKuttaStepInterpolator.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;

/**
 * This class implements a step interpolator for the classical 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) [ (-4 theta^2 + 5 theta - 1) y'_1
 *                                          +(4 theta^2 - 2 theta - 2) (y'_2 + y'_3)
 *                                          -(4 theta^2 +   theta + 1) y'_4
 *                                        ]
 * </pre>
 *
 * where theta belongs to [0 ; 1] and where y'_1 to y'_4 are the four
 * evaluations of the derivatives already computed during the
 * step.</p>
 *
 * @see ClassicalRungeKuttaIntegrator
 * @version $Revision$ $Date$
 * @since 1.2
 */

class ClassicalRungeKuttaStepInterpolator
  extends RungeKuttaStepInterpolator {
    
  /** Simple constructor.
   * This constructor builds an instance that is not usable yet, the
   * {@link RungeKuttaStepInterpolator#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 latter initializing
   * the copy.
   */
  public ClassicalRungeKuttaStepInterpolator() {
  }

  /** 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 ClassicalRungeKuttaStepInterpolator(ClassicalRungeKuttaStepInterpolator interpolator) {
    super(interpolator);
  }

  /** Really copy the finalized instance.
   * @return a copy of the finalized instance
   */
  protected StepInterpolator doCopy() {
    return new ClassicalRungeKuttaStepInterpolator(this);
  }

  /** Compute the state at the interpolated time.
   * This is the main processing method that should be implemented by
   * the derived classes to perform the interpolation.
   * @param theta normalized interpolation abscissa within the step
   * (theta is zero at the previous time step and one at the current time step)
   * @param oneMinusThetaH time gap between the interpolated time and
   * the current time
   * @throws DerivativeException this exception is propagated to the caller if the
   * underlying user function triggers one
   */
  protected void computeInterpolatedState(double theta,
                                          double oneMinusThetaH)
    throws DerivativeException {

    double fourTheta = 4 * theta;
    double s         = oneMinusThetaH / 6.0;
    double coeff1    = s * ((-fourTheta + 5) * theta - 1);
    double coeff23   = s * (( fourTheta - 2) * theta - 2);
    double coeff4    = s * ((-fourTheta - 1) * theta - 1);

    for (int i = 0; i < interpolatedState.length; ++i) {
      interpolatedState[i] = currentState[i] +
                             coeff1  * yDotK[0][i] +
                             coeff23 * (yDotK[1][i] + yDotK[2][i]) +
                             coeff4  * yDotK[3][i];
     }

  }

  /** Serializable version identifier */
  private static final long serialVersionUID = -6576285612589783992L;

}