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) Higham and Hall integrator for
25 * Ordinary 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.</p>
32 *
33 * @since 1.2
34 */
35
36 public class HighamHall54Integrator extends EmbeddedRungeKuttaIntegrator {
37
38 /** Integrator method name. */
39 private static final String METHOD_NAME = "Higham-Hall 5(4)";
40
41 /** Time steps Butcher array. */
42 private static final double[] STATIC_C = {
43 2.0/9.0, 1.0/3.0, 1.0/2.0, 3.0/5.0, 1.0, 1.0
44 };
45
46 /** Internal weights Butcher array. */
47 private static final double[][] STATIC_A = {
48 {2.0/9.0},
49 {1.0/12.0, 1.0/4.0},
50 {1.0/8.0, 0.0, 3.0/8.0},
51 {91.0/500.0, -27.0/100.0, 78.0/125.0, 8.0/125.0},
52 {-11.0/20.0, 27.0/20.0, 12.0/5.0, -36.0/5.0, 5.0},
53 {1.0/12.0, 0.0, 27.0/32.0, -4.0/3.0, 125.0/96.0, 5.0/48.0}
54 };
55
56 /** Propagation weights Butcher array. */
57 private static final double[] STATIC_B = {
58 1.0/12.0, 0.0, 27.0/32.0, -4.0/3.0, 125.0/96.0, 5.0/48.0, 0.0
59 };
60
61 /** Error weights Butcher array. */
62 private static final double[] STATIC_E = {
63 -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
64 };
65
66 /** Simple constructor.
67 * Build a fifth order Higham and Hall integrator with the given step bounds
68 * @param minStep minimal step (sign is irrelevant, regardless of
69 * integration direction, forward or backward), the last step can
70 * be smaller than this
71 * @param maxStep maximal step (sign is irrelevant, regardless of
72 * integration direction, forward or backward), the last step can
73 * be smaller than this
74 * @param scalAbsoluteTolerance allowed absolute error
75 * @param scalRelativeTolerance allowed relative error
76 */
77 public HighamHall54Integrator(final double minStep, final double maxStep,
78 final double scalAbsoluteTolerance,
79 final double scalRelativeTolerance) {
80 super(METHOD_NAME, false, STATIC_C, STATIC_A, STATIC_B, new HighamHall54StepInterpolator(),
81 minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance);
82 }
83
84 /** Simple constructor.
85 * Build a fifth order Higham and Hall integrator with the given step bounds
86 * @param minStep minimal step (sign is irrelevant, regardless of
87 * integration direction, forward or backward), the last step can
88 * be smaller than this
89 * @param maxStep maximal step (sign is irrelevant, regardless of
90 * integration direction, forward or backward), the last step can
91 * be smaller than this
92 * @param vecAbsoluteTolerance allowed absolute error
93 * @param vecRelativeTolerance allowed relative error
94 */
95 public HighamHall54Integrator(final double minStep, final double maxStep,
96 final double[] vecAbsoluteTolerance,
97 final double[] vecRelativeTolerance) {
98 super(METHOD_NAME, false, STATIC_C, STATIC_A, STATIC_B, new HighamHall54StepInterpolator(),
99 minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance);
100 }
101
102 /** {@inheritDoc} */
103 @Override
104 public int getOrder() {
105 return 5;
106 }
107
108 /** {@inheritDoc} */
109 @Override
110 protected double estimateError(final double[][] yDotK,
111 final double[] y0, final double[] y1,
112 final double h) {
113
114 double error = 0;
115
116 for (int j = 0; j < mainSetDimension; ++j) {
117 double errSum = STATIC_E[0] * yDotK[0][j];
118 for (int l = 1; l < STATIC_E.length; ++l) {
119 errSum += STATIC_E[l] * yDotK[l][j];
120 }
121
122 final double yScale = JdkMath.max(JdkMath.abs(y0[j]), JdkMath.abs(y1[j]));
123 final double tol = (vecAbsoluteTolerance == null) ?
124 (scalAbsoluteTolerance + scalRelativeTolerance * yScale) :
125 (vecAbsoluteTolerance[j] + vecRelativeTolerance[j] * yScale);
126 final double ratio = h * errSum / tol;
127 error += ratio * ratio;
128 }
129
130 return JdkMath.sqrt(error / mainSetDimension);
131 }
132 }