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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.nonstiff;
19  
20  import org.apache.commons.math.ode.DerivativeException;
21  import org.apache.commons.math.ode.sampling.AbstractStepInterpolator;
22  import org.apache.commons.math.ode.sampling.StepInterpolator;
23  
24  /**
25   * This class implements a step interpolator for the Gill fourth
26   * order Runge-Kutta integrator.
27   *
28   * <p>This interpolator allows to compute dense output inside the last
29   * step computed. The interpolation equation is consistent with the
30   * integration scheme :
31   *
32   * <pre>
33   *   y(t_n + theta h) = y (t_n + h)
34   *                    - (1 - theta) (h/6) [ (1 - theta) (1 - 4 theta) y'_1
35   *                                        + (1 - theta) (1 + 2 theta) ((2-q) y'_2 + (2+q) y'_3)
36   *                                        + (1 + theta + 4 theta^2) y'_4
37   *                                        ]
38   * </pre>
39   * where theta belongs to [0 ; 1], q = sqrt(2) and where y'_1 to y'_4
40   * are the four evaluations of the derivatives already computed during
41   * the step.</p>
42   *
43   * @see GillIntegrator
44   * @version $Revision: 782432 $ $Date: 2009-06-07 15:08:26 -0400 (Sun, 07 Jun 2009) $
45   * @since 1.2
46   */
47  
48  class GillStepInterpolator
49    extends RungeKuttaStepInterpolator {
50      
51    /** Simple constructor.
52     * This constructor builds an instance that is not usable yet, the
53     * {@link AbstractStepInterpolator#reinitialize} method should be called
54     * before using the instance in order to initialize the internal arrays. This
55     * constructor is used only in order to delay the initialization in
56     * some cases. The {@link RungeKuttaIntegrator} class uses the
57     * prototyping design pattern to create the step interpolators by
58     * cloning an uninitialized model and latter initializing the copy.
59     */
60    public GillStepInterpolator() {
61    }
62  
63    /** Copy constructor.
64     * @param interpolator interpolator to copy from. The copy is a deep
65     * copy: its arrays are separated from the original arrays of the
66     * instance
67     */
68    public GillStepInterpolator(final GillStepInterpolator interpolator) {
69      super(interpolator);
70    }
71  
72    /** {@inheritDoc} */
73    @Override
74    protected StepInterpolator doCopy() {
75      return new GillStepInterpolator(this);
76    }
77  
78  
79    /** {@inheritDoc} */
80    @Override
81    protected void computeInterpolatedStateAndDerivatives(final double theta,
82                                            final double oneMinusThetaH)
83      throws DerivativeException {
84  
85      final double twoTheta  = 2 * theta;
86      final double fourTheta = 4 * theta;
87      final double s         = oneMinusThetaH / 6.0;
88      final double oMt       = 1 - theta;
89      final double soMt      = s * oMt;
90      final double c23       = soMt * (1 + twoTheta);
91      final double coeff1    = soMt * (1 - fourTheta);
92      final double coeff2    = c23  * tMq;
93      final double coeff3    = c23  * tPq;
94      final double coeff4    = s * (1 + theta * (1 + fourTheta));
95      final double coeffDot1 = theta * (twoTheta - 3) + 1;
96      final double cDot23    = theta * oMt;
97      final double coeffDot2 = cDot23  * tMq;
98      final double coeffDot3 = cDot23  * tPq;
99      final double coeffDot4 = theta * (twoTheta - 1);
100 
101     for (int i = 0; i < interpolatedState.length; ++i) {
102         final double yDot1 = yDotK[0][i];
103         final double yDot2 = yDotK[1][i];
104         final double yDot3 = yDotK[2][i];
105         final double yDot4 = yDotK[3][i];
106         interpolatedState[i] =
107             currentState[i] - coeff1 * yDot1 - coeff2 * yDot2 - coeff3 * yDot3 - coeff4 * yDot4;
108         interpolatedDerivatives[i] =
109             coeffDot1 * yDot1 + coeffDot2 * yDot2 + coeffDot3 * yDot3 + coeffDot4 * yDot4;
110      }
111 
112   }
113 
114   /** First Gill coefficient. */
115   private static final double tMq = 2 - Math.sqrt(2.0);
116 
117   /** Second Gill coefficient. */
118   private static final double tPq = 2 + Math.sqrt(2.0);
119 
120   /** Serializable version identifier */
121   private static final long serialVersionUID = -107804074496313322L;
122 
123 }