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 implements a step interpolator for the 3/8 fourth
22 * order Runge-Kutta integrator.
23 *
24 * <p>This interpolator allows to compute dense output inside the last
25 * step computed. The interpolation equation is consistent with the
26 * integration scheme :
27 *
28 * <pre>
29 * y(t_n + theta h) = y (t_n + h)
30 * - (1 - theta) (h/8) [ (1 - 7 theta + 8 theta^2) y'_1
31 * + 3 (1 + theta - 4 theta^2) y'_2
32 * + 3 (1 + theta) y'_3
33 * + (1 + theta + 4 theta^2) y'_4
34 * ]
35 * </pre>
36 *
37 * where theta belongs to [0 ; 1] and where y'_1 to y'_4 are the four
38 * evaluations of the derivatives already computed during the
39 * step.</p>
40 *
41 * @see ThreeEighthesIntegrator
42 * @version $Revision: 620312 $ $Date: 2008-02-10 12:28:59 -0700 (Sun, 10 Feb 2008) $
43 * @since 1.2
44 */
45
46 class ThreeEighthesStepInterpolator
47 extends RungeKuttaStepInterpolator {
48
49 /** Simple constructor.
50 * This constructor builds an instance that is not usable yet, the
51 * {@link AbstractStepInterpolator#reinitialize} method should be called
52 * before using the instance in order to initialize the internal arrays. This
53 * constructor is used only in order to delay the initialization in
54 * some cases. The {@link RungeKuttaIntegrator} class uses the
55 * prototyping design pattern to create the step interpolators by
56 * cloning an uninitialized model and latter initializing the copy.
57 */
58 public ThreeEighthesStepInterpolator() {
59 }
60
61 /** Copy constructor.
62 * @param interpolator interpolator to copy from. The copy is a deep
63 * copy: its arrays are separated from the original arrays of the
64 * instance
65 */
66 public ThreeEighthesStepInterpolator(ThreeEighthesStepInterpolator interpolator) {
67 super(interpolator);
68 }
69
70 /** Really copy the finalized instance.
71 * @return a copy of the finalized instance
72 */
73 protected StepInterpolator doCopy() {
74 return new ThreeEighthesStepInterpolator(this);
75 }
76
77
78 /** Compute the state at the interpolated time.
79 * This is the main processing method that should be implemented by
80 * the derived classes to perform the interpolation.
81 * @param theta normalized interpolation abscissa within the step
82 * (theta is zero at the previous time step and one at the current time step)
83 * @param oneMinusThetaH time gap between the interpolated time and
84 * the current time
85 * @throws DerivativeException this exception is propagated to the caller if the
86 * underlying user function triggers one
87 */
88 protected void computeInterpolatedState(double theta,
89 double oneMinusThetaH)
90 throws DerivativeException {
91
92 double fourTheta2 = 4 * theta * theta;
93 double s = oneMinusThetaH / 8.0;
94 double coeff1 = s * (1 - 7 * theta + 2 * fourTheta2);
95 double coeff2 = 3 * s * (1 + theta - fourTheta2);
96 double coeff3 = 3 * s * (1 + theta);
97 double coeff4 = s * (1 + theta + fourTheta2);
98
99 for (int i = 0; i < interpolatedState.length; ++i) {
100 interpolatedState[i] = currentState[i] -
101 coeff1 * yDotK[0][i] - coeff2 * yDotK[1][i] -
102 coeff3 * yDotK[2][i] - coeff4 * yDotK[3][i];
103 }
104
105 }
106
107 /** Serializable version identifier */
108 private static final long serialVersionUID = -3345024435978721931L;
109
110 }