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.math4.legacy.ode;
19
20
21 /** This class converts second order differential equations to first
22 * order ones.
23 *
24 * <p>This class is a wrapper around a {@link
25 * SecondOrderDifferentialEquations} which allow to use a {@link
26 * FirstOrderIntegrator} to integrate it.</p>
27 *
28 * <p>The transformation is done by changing the n dimension state
29 * vector to a 2n dimension vector, where the first n components are
30 * the initial state variables and the n last components are their
31 * first time derivative. The first time derivative of this state
32 * vector then really contains both the first and second time
33 * derivative of the initial state vector, which can be handled by the
34 * underlying second order equations set.</p>
35 *
36 * <p>One should be aware that the data is duplicated during the
37 * transformation process and that for each call to {@link
38 * #computeDerivatives computeDerivatives}, this wrapper does copy 4n
39 * scalars : 2n before the call to {@link
40 * SecondOrderDifferentialEquations#computeSecondDerivatives
41 * computeSecondDerivatives} in order to dispatch the y state vector
42 * into z and zDot, and 2n after the call to gather zDot and zDDot
43 * into yDot. Since the underlying problem by itself perhaps also
44 * needs to copy data and dispatch the arrays into domain objects,
45 * this has an impact on both memory and CPU usage. The only way to
46 * avoid this duplication is to perform the transformation at the
47 * problem level, i.e. to implement the problem as a first order one
48 * and then avoid using this class.</p>
49 *
50 * @see FirstOrderIntegrator
51 * @see FirstOrderDifferentialEquations
52 * @see SecondOrderDifferentialEquations
53 * @since 1.2
54 */
55
56 public class FirstOrderConverter implements FirstOrderDifferentialEquations {
57
58 /** Underlying second order equations set. */
59 private final SecondOrderDifferentialEquations equations;
60
61 /** second order problem dimension. */
62 private final int dimension;
63
64 /** state vector. */
65 private final double[] z;
66
67 /** first time derivative of the state vector. */
68 private final double[] zDot;
69
70 /** second time derivative of the state vector. */
71 private final double[] zDDot;
72
73 /** Simple constructor.
74 * Build a converter around a second order equations set.
75 * @param equations second order equations set to convert
76 */
77 public FirstOrderConverter (final SecondOrderDifferentialEquations equations) {
78 this.equations = equations;
79 dimension = equations.getDimension();
80 z = new double[dimension];
81 zDot = new double[dimension];
82 zDDot = new double[dimension];
83 }
84
85 /** Get the dimension of the problem.
86 * <p>The dimension of the first order problem is twice the
87 * dimension of the underlying second order problem.</p>
88 * @return dimension of the problem
89 */
90 @Override
91 public int getDimension() {
92 return 2 * dimension;
93 }
94
95 /** Get the current time derivative of the state vector.
96 * @param t current value of the independent <I>time</I> variable
97 * @param y array containing the current value of the state vector
98 * @param yDot placeholder array where to put the time derivative of the state vector
99 */
100 @Override
101 public void computeDerivatives(final double t, final double[] y, final double[] yDot) {
102
103 // split the state vector in two
104 System.arraycopy(y, 0, z, 0, dimension);
105 System.arraycopy(y, dimension, zDot, 0, dimension);
106
107 // apply the underlying equations set
108 equations.computeSecondDerivatives(t, z, zDot, zDDot);
109
110 // build the result state derivative
111 System.arraycopy(zDot, 0, yDot, 0, dimension);
112 System.arraycopy(zDDot, 0, yDot, dimension, dimension);
113 }
114 }