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1   /*
2    * Licensed to the Apache Software Foundation (ASF) under one or more
3    * contributor license agreements.  See the NOTICE file distributed with
4    * this work for additional information regarding copyright ownership.
5    * The ASF licenses this file to You under the Apache License, Version 2.0
6    * (the "License"); you may not use this file except in compliance with
7    * the License.  You may obtain a copy of the License at
8    *
9    *      http://www.apache.org/licenses/LICENSE-2.0
10   *
11   * Unless required by applicable law or agreed to in writing, software
12   * distributed under the License is distributed on an "AS IS" BASIS,
13   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14   * See the License for the specific language governing permissions and
15   * limitations under the License.
16   */
17  
18  package org.apache.commons.math.ode;
19  
20  /**
21   * This class represents an interpolator over the last step during an
22   * ODE integration for the 5(4) Higham and Hall integrator.
23   *
24   * @see HighamHall54Integrator
25   *
26   * @version $Revision: 620312 $ $Date: 2008-02-10 12:28:59 -0700 (Sun, 10 Feb 2008) $
27   * @since 1.2
28   */
29  
30  class HighamHall54StepInterpolator
31    extends RungeKuttaStepInterpolator {
32  
33    /** Simple constructor.
34     * This constructor builds an instance that is not usable yet, the
35     * {@link AbstractStepInterpolator#reinitialize} method should be called
36     * before using the instance in order to initialize the internal arrays. This
37     * constructor is used only in order to delay the initialization in
38     * some cases. The {@link EmbeddedRungeKuttaIntegrator} uses the
39     * prototyping design pattern to create the step interpolators by
40     * cloning an uninitialized model and latter initializing the copy.
41     */
42    public HighamHall54StepInterpolator() {
43      super();
44    }
45  
46    /** Copy constructor.
47     * @param interpolator interpolator to copy from. The copy is a deep
48     * copy: its arrays are separated from the original arrays of the
49     * instance
50     */
51    public HighamHall54StepInterpolator(HighamHall54StepInterpolator interpolator) {
52      super(interpolator);
53    }
54  
55    /** Really copy the finalized instance.
56     * @return a copy of the finalized instance
57     */
58    protected StepInterpolator doCopy() {
59      return new HighamHall54StepInterpolator(this);
60    }
61  
62  
63    /** Compute the state at the interpolated time.
64     * @param theta normalized interpolation abscissa within the step
65     * (theta is zero at the previous time step and one at the current time step)
66     * @param oneMinusThetaH time gap between the interpolated time and
67     * the current time
68     * @throws DerivativeException this exception is propagated to the caller if the
69     * underlying user function triggers one
70     */
71    protected void computeInterpolatedState(double theta,
72                                            double oneMinusThetaH)
73      throws DerivativeException {
74  
75      double theta2 = theta * theta;
76  
77      double b0 = h * (-1.0/12.0 + theta * (1.0 + theta * (-15.0/4.0 + theta * (16.0/3.0 + theta * -5.0/2.0))));
78      double b2 = h * (-27.0/32.0 + theta2 * (459.0/32.0 + theta * (-243.0/8.0 + theta * 135.0/8.0)));
79      double b3 = h * (4.0/3.0 + theta2 * (-22.0 + theta * (152.0/3.0  + theta * -30.0)));
80      double b4 = h * (-125.0/96.0 + theta2 * (375.0/32.0 + theta * (-625.0/24.0 + theta * 125.0/8.0)));
81      double b5 = h * (-5.0/48.0 + theta2 * (-5.0/16.0 + theta * 5.0/12.0));
82  
83      for (int i = 0; i < interpolatedState.length; ++i) {
84        interpolatedState[i] = currentState[i] +
85                               b0 * yDotK[0][i] + b2 * yDotK[2][i] + b3 * yDotK[3][i] +
86                               b4 * yDotK[4][i] + b5 * yDotK[5][i];
87      }
88  
89    }
90  
91    /** Serializable version identifier */
92    private static final long serialVersionUID = -3583240427587318654L;
93  
94  }