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.nonstiff;
19
20 import org.apache.commons.math4.core.jdkmath.JdkMath;
21
22
23 /**
24 * This class implements the 5(4) Dormand-Prince integrator for Ordinary
25 * Differential Equations.
26
27 * <p>This integrator is an embedded Runge-Kutta integrator
28 * of order 5(4) used in local extrapolation mode (i.e. the solution
29 * is computed using the high order formula) with stepsize control
30 * (and automatic step initialization) and continuous output. This
31 * method uses 7 functions evaluations per step. However, since this
32 * is an <i>fsal</i>, the last evaluation of one step is the same as
33 * the first evaluation of the next step and hence can be avoided. So
34 * the cost is really 6 functions evaluations per step.</p>
35 *
36 * <p>This method has been published (whithout the continuous output
37 * that was added by Shampine in 1986) in the following article :
38 * <pre>
39 * A family of embedded Runge-Kutta formulae
40 * J. R. Dormand and P. J. Prince
41 * Journal of Computational and Applied Mathematics
42 * volume 6, no 1, 1980, pp. 19-26
43 * </pre>
44 *
45 * @since 1.2
46 */
47
48 public class DormandPrince54Integrator extends EmbeddedRungeKuttaIntegrator {
49
50 /** Integrator method name. */
51 private static final String METHOD_NAME = "Dormand-Prince 5(4)";
52
53 /** Time steps Butcher array. */
54 private static final double[] STATIC_C = {
55 1.0/5.0, 3.0/10.0, 4.0/5.0, 8.0/9.0, 1.0, 1.0
56 };
57
58 /** Internal weights Butcher array. */
59 private static final double[][] STATIC_A = {
60 {1.0/5.0},
61 {3.0/40.0, 9.0/40.0},
62 {44.0/45.0, -56.0/15.0, 32.0/9.0},
63 {19372.0/6561.0, -25360.0/2187.0, 64448.0/6561.0, -212.0/729.0},
64 {9017.0/3168.0, -355.0/33.0, 46732.0/5247.0, 49.0/176.0, -5103.0/18656.0},
65 {35.0/384.0, 0.0, 500.0/1113.0, 125.0/192.0, -2187.0/6784.0, 11.0/84.0}
66 };
67
68 /** Propagation weights Butcher array. */
69 private static final double[] STATIC_B = {
70 35.0/384.0, 0.0, 500.0/1113.0, 125.0/192.0, -2187.0/6784.0, 11.0/84.0, 0.0
71 };
72
73 /** Error array, element 1. */
74 private static final double E1 = 71.0 / 57600.0;
75
76 // element 2 is zero, so it is neither stored nor used
77
78 /** Error array, element 3. */
79 private static final double E3 = -71.0 / 16695.0;
80
81 /** Error array, element 4. */
82 private static final double E4 = 71.0 / 1920.0;
83
84 /** Error array, element 5. */
85 private static final double E5 = -17253.0 / 339200.0;
86
87 /** Error array, element 6. */
88 private static final double E6 = 22.0 / 525.0;
89
90 /** Error array, element 7. */
91 private static final double E7 = -1.0 / 40.0;
92
93 /** Simple constructor.
94 * Build a fifth order Dormand-Prince integrator with the given step bounds
95 * @param minStep minimal step (sign is irrelevant, regardless of
96 * integration direction, forward or backward), the last step can
97 * be smaller than this
98 * @param maxStep maximal step (sign is irrelevant, regardless of
99 * integration direction, forward or backward), the last step can
100 * be smaller than this
101 * @param scalAbsoluteTolerance allowed absolute error
102 * @param scalRelativeTolerance allowed relative error
103 */
104 public DormandPrince54Integrator(final double minStep, final double maxStep,
105 final double scalAbsoluteTolerance,
106 final double scalRelativeTolerance) {
107 super(METHOD_NAME, true, STATIC_C, STATIC_A, STATIC_B, new DormandPrince54StepInterpolator(),
108 minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance);
109 }
110
111 /** Simple constructor.
112 * Build a fifth order Dormand-Prince integrator with the given step bounds
113 * @param minStep minimal step (sign is irrelevant, regardless of
114 * integration direction, forward or backward), the last step can
115 * be smaller than this
116 * @param maxStep maximal step (sign is irrelevant, regardless of
117 * integration direction, forward or backward), the last step can
118 * be smaller than this
119 * @param vecAbsoluteTolerance allowed absolute error
120 * @param vecRelativeTolerance allowed relative error
121 */
122 public DormandPrince54Integrator(final double minStep, final double maxStep,
123 final double[] vecAbsoluteTolerance,
124 final double[] vecRelativeTolerance) {
125 super(METHOD_NAME, true, STATIC_C, STATIC_A, STATIC_B, new DormandPrince54StepInterpolator(),
126 minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance);
127 }
128
129 /** {@inheritDoc} */
130 @Override
131 public int getOrder() {
132 return 5;
133 }
134
135 /** {@inheritDoc} */
136 @Override
137 protected double estimateError(final double[][] yDotK,
138 final double[] y0, final double[] y1,
139 final double h) {
140
141 double error = 0;
142
143 for (int j = 0; j < mainSetDimension; ++j) {
144 final double errSum = E1 * yDotK[0][j] + E3 * yDotK[2][j] +
145 E4 * yDotK[3][j] + E5 * yDotK[4][j] +
146 E6 * yDotK[5][j] + E7 * yDotK[6][j];
147
148 final double yScale = JdkMath.max(JdkMath.abs(y0[j]), JdkMath.abs(y1[j]));
149 final double tol = (vecAbsoluteTolerance == null) ?
150 (scalAbsoluteTolerance + scalRelativeTolerance * yScale) :
151 (vecAbsoluteTolerance[j] + vecRelativeTolerance[j] * yScale);
152 final double ratio = h * errSum / tol;
153 error += ratio * ratio;
154 }
155
156 return JdkMath.sqrt(error / mainSetDimension);
157 }
158 }