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 the 5(4) Higham and Hall integrator for
22 * Ordinary Differential Equations.
23 *
24 * <p>This integrator is an embedded Runge-Kutta integrator
25 * of order 5(4) used in local extrapolation mode (i.e. the solution
26 * is computed using the high order formula) with stepsize control
27 * (and automatic step initialization) and continuous output. This
28 * method uses 7 functions evaluations per step.</p>
29 *
30 * @version $Revision: 620312 $ $Date: 2008-02-10 12:28:59 -0700 (Sun, 10 Feb 2008) $
31 * @since 1.2
32 */
33
34 public class HighamHall54Integrator
35 extends EmbeddedRungeKuttaIntegrator {
36
37 /** Integrator method name. */
38 private static final String methodName = "Higham-Hall 5(4)";
39
40 /** Time steps Butcher array. */
41 private static final double[] staticC = {
42 2.0/9.0, 1.0/3.0, 1.0/2.0, 3.0/5.0, 1.0, 1.0
43 };
44
45 /** Internal weights Butcher array. */
46 private static final double[][] staticA = {
47 {2.0/9.0},
48 {1.0/12.0, 1.0/4.0},
49 {1.0/8.0, 0.0, 3.0/8.0},
50 {91.0/500.0, -27.0/100.0, 78.0/125.0, 8.0/125.0},
51 {-11.0/20.0, 27.0/20.0, 12.0/5.0, -36.0/5.0, 5.0},
52 {1.0/12.0, 0.0, 27.0/32.0, -4.0/3.0, 125.0/96.0, 5.0/48.0}
53 };
54
55 /** Propagation weights Butcher array. */
56 private static final double[] staticB = {
57 1.0/12.0, 0.0, 27.0/32.0, -4.0/3.0, 125.0/96.0, 5.0/48.0, 0.0
58 };
59
60 /** Error weights Butcher array. */
61 private static final double[] staticE = {
62 -1.0/20.0, 0.0, 81.0/160.0, -6.0/5.0, 25.0/32.0, 1.0/16.0, -1.0/10.0
63 };
64
65 /** Simple constructor.
66 * Build a fifth order Higham and Hall integrator with the given step bounds
67 * @param minStep minimal step (must be positive even for backward
68 * integration), the last step can be smaller than this
69 * @param maxStep maximal step (must be positive even for backward
70 * integration)
71 * @param scalAbsoluteTolerance allowed absolute error
72 * @param scalRelativeTolerance allowed relative error
73 */
74 public HighamHall54Integrator(double minStep, double maxStep,
75 double scalAbsoluteTolerance,
76 double scalRelativeTolerance) {
77 super(false, staticC, staticA, staticB, new HighamHall54StepInterpolator(),
78 minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance);
79 }
80
81 /** Simple constructor.
82 * Build a fifth order Higham and Hall integrator with the given step bounds
83 * @param minStep minimal step (must be positive even for backward
84 * integration), the last step can be smaller than this
85 * @param maxStep maximal step (must be positive even for backward
86 * integration)
87 * @param vecAbsoluteTolerance allowed absolute error
88 * @param vecRelativeTolerance allowed relative error
89 */
90 public HighamHall54Integrator(double minStep, double maxStep,
91 double[] vecAbsoluteTolerance,
92 double[] vecRelativeTolerance) {
93 super(false, staticC, staticA, staticB, new HighamHall54StepInterpolator(),
94 minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance);
95 }
96
97 /** Get the name of the method.
98 * @return name of the method
99 */
100 public String getName() {
101 return methodName;
102 }
103
104 /** Get the order of the method.
105 * @return order of the method
106 */
107 public int getOrder() {
108 return 5;
109 }
110
111 /** Compute the error ratio.
112 * @param yDotK derivatives computed during the first stages
113 * @param y0 estimate of the step at the start of the step
114 * @param y1 estimate of the step at the end of the step
115 * @param h current step
116 * @return error ratio, greater than 1 if step should be rejected
117 */
118 protected double estimateError(double[][] yDotK,
119 double[] y0, double[] y1,
120 double h) {
121
122 double error = 0;
123
124 for (int j = 0; j < y0.length; ++j) {
125 double errSum = staticE[0] * yDotK[0][j];
126 for (int l = 1; l < staticE.length; ++l) {
127 errSum += staticE[l] * yDotK[l][j];
128 }
129
130 double yScale = Math.max(Math.abs(y0[j]), Math.abs(y1[j]));
131 double tol = (vecAbsoluteTolerance == null) ?
132 (scalAbsoluteTolerance + scalRelativeTolerance * yScale) :
133 (vecAbsoluteTolerance[j] + vecRelativeTolerance[j] * yScale);
134 double ratio = h * errSum / tol;
135 error += ratio * ratio;
136
137 }
138
139 return Math.sqrt(error / y0.length);
140
141 }
142
143 }