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
18package org.apache.commons.math.ode.nonstiff;
19
20import org.apache.commons.math.ode.DerivativeException;
21import 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: 1073158 $ $Date: 2011-02-21 22:46:52 +0100 (lun. 21 févr. 2011) $
45 * @since 1.2
46 */
47
48class 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}
111