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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.StepInterpolator;
22  
23  /**
24   * This class implements a step interpolator for the classical fourth
25   * order Runge-Kutta integrator.
26   *
27   * <p>This interpolator allows to compute dense output inside the last
28   * step computed. The interpolation equation is consistent with the
29   * integration scheme :
30  
31   * <pre>
32   *   y(t_n + theta h) = y (t_n + h)
33   *                    + (1 - theta) (h/6) [ (-4 theta^2 + 5 theta - 1) y'_1
34   *                                          +(4 theta^2 - 2 theta - 2) (y'_2 + y'_3)
35   *                                          -(4 theta^2 +   theta + 1) y'_4
36   *                                        ]
37   * </pre>
38   *
39   * where theta belongs to [0 ; 1] and where y'_1 to y'_4 are the four
40   * evaluations of the derivatives already computed during the
41   * step.</p>
42   *
43   * @see ClassicalRungeKuttaIntegrator
44   * @version $Revision: 782432 $ $Date: 2009-06-07 15:08:26 -0400 (Sun, 07 Jun 2009) $
45   * @since 1.2
46   */
47  
48  class ClassicalRungeKuttaStepInterpolator
49      extends RungeKuttaStepInterpolator {
50  
51      /** Serializable version identifier */
52      private static final long serialVersionUID = -6576285612589783992L;
53  
54      /** Simple constructor.
55       * This constructor builds an instance that is not usable yet, the
56       * {@link RungeKuttaStepInterpolator#reinitialize} method should be
57       * called before using the instance in order to initialize the
58       * internal arrays. This constructor is used only in order to delay
59       * the initialization in some cases. The {@link RungeKuttaIntegrator}
60       * class uses the prototyping design pattern to create the step
61       * interpolators by cloning an uninitialized model and latter initializing
62       * the copy.
63       */
64      public ClassicalRungeKuttaStepInterpolator() {
65      }
66  
67      /** Copy constructor.
68       * @param interpolator interpolator to copy from. The copy is a deep
69       * copy: its arrays are separated from the original arrays of the
70       * instance
71       */
72      public ClassicalRungeKuttaStepInterpolator(final ClassicalRungeKuttaStepInterpolator interpolator) {
73          super(interpolator);
74      }
75  
76      /** {@inheritDoc} */
77      @Override
78      protected StepInterpolator doCopy() {
79          return new ClassicalRungeKuttaStepInterpolator(this);
80      }
81  
82      /** {@inheritDoc} */
83      @Override
84      protected void computeInterpolatedStateAndDerivatives(final double theta,
85                                              final double oneMinusThetaH)
86          throws DerivativeException {
87  
88          final double fourTheta      = 4 * theta;
89          final double oneMinusTheta  = 1 - theta;
90          final double oneMinus2Theta = 1 - 2 * theta;
91          final double s             = oneMinusThetaH / 6.0;
92          final double coeff1        = s * ((-fourTheta + 5) * theta - 1);
93          final double coeff23       = s * (( fourTheta - 2) * theta - 2);
94          final double coeff4        = s * ((-fourTheta - 1) * theta - 1);
95          final double coeffDot1     = oneMinusTheta * oneMinus2Theta;
96          final double coeffDot23    = 2 * theta * oneMinusTheta;
97          final double coeffDot4     = -theta * oneMinus2Theta;
98          for (int i = 0; i < interpolatedState.length; ++i) {
99              final double yDot1  = yDotK[0][i];
100             final double yDot23 = yDotK[1][i] + yDotK[2][i];
101             final double yDot4  = yDotK[3][i];
102             interpolatedState[i] =
103                 currentState[i] + coeff1  * yDot1 + coeff23 * yDot23 + coeff4  * yDot4;
104             interpolatedDerivatives[i] =
105                 coeffDot1 * yDot1 + coeffDot23 * yDot23 + coeffDot4 * yDot4;
106         }
107 
108     }
109 
110 }