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
18package org.apache.commons.math.ode.nonstiff;
19
20import org.apache.commons.math.util.FastMath;
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 * @version $Revision: 990655 $ $Date: 2010-08-29 23:49:40 +0200 (dim. 29 août 2010) $
34 * @since 1.2
35 */
36
37public class HighamHall54Integrator extends EmbeddedRungeKuttaIntegrator {
38
39  /** Integrator method name. */
40  private static final String METHOD_NAME = "Higham-Hall 5(4)";
41
42  /** Time steps Butcher array. */
43  private static final double[] STATIC_C = {
44    2.0/9.0, 1.0/3.0, 1.0/2.0, 3.0/5.0, 1.0, 1.0
45  };
46
47  /** Internal weights Butcher array. */
48  private static final double[][] STATIC_A = {
49    {2.0/9.0},
50    {1.0/12.0, 1.0/4.0},
51    {1.0/8.0, 0.0, 3.0/8.0},
52    {91.0/500.0, -27.0/100.0, 78.0/125.0, 8.0/125.0},
53    {-11.0/20.0, 27.0/20.0, 12.0/5.0, -36.0/5.0, 5.0},
54    {1.0/12.0, 0.0, 27.0/32.0, -4.0/3.0, 125.0/96.0, 5.0/48.0}
55  };
56
57  /** Propagation weights Butcher array. */
58  private static final double[] STATIC_B = {
59    1.0/12.0, 0.0, 27.0/32.0, -4.0/3.0, 125.0/96.0, 5.0/48.0, 0.0
60  };
61
62  /** Error weights Butcher array. */
63  private static final double[] STATIC_E = {
64    -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
65  };
66
67  /** Simple constructor.
68   * Build a fifth order Higham and Hall integrator with the given step bounds
69   * @param minStep minimal step (must be positive even for backward
70   * integration), the last step can be smaller than this
71   * @param maxStep maximal step (must be positive even for backward
72   * integration)
73   * @param scalAbsoluteTolerance allowed absolute error
74   * @param scalRelativeTolerance allowed relative error
75   */
76  public HighamHall54Integrator(final double minStep, final double maxStep,
77                                final double scalAbsoluteTolerance,
78                                final double scalRelativeTolerance) {
79    super(METHOD_NAME, false, STATIC_C, STATIC_A, STATIC_B, new HighamHall54StepInterpolator(),
80          minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance);
81  }
82
83  /** Simple constructor.
84   * Build a fifth order Higham and Hall integrator with the given step bounds
85   * @param minStep minimal step (must be positive even for backward
86   * integration), the last step can be smaller than this
87   * @param maxStep maximal step (must be positive even for backward
88   * integration)
89   * @param vecAbsoluteTolerance allowed absolute error
90   * @param vecRelativeTolerance allowed relative error
91   */
92  public HighamHall54Integrator(final double minStep, final double maxStep,
93                                final double[] vecAbsoluteTolerance,
94                                final double[] vecRelativeTolerance) {
95    super(METHOD_NAME, false, STATIC_C, STATIC_A, STATIC_B, new HighamHall54StepInterpolator(),
96          minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance);
97  }
98
99  /** {@inheritDoc} */
100  @Override
101  public int getOrder() {
102    return 5;
103  }
104
105  /** {@inheritDoc} */
106  @Override
107  protected double estimateError(final double[][] yDotK,
108                                 final double[] y0, final double[] y1,
109                                 final double h) {
110
111    double error = 0;
112
113    for (int j = 0; j < mainSetDimension; ++j) {
114      double errSum = STATIC_E[0] * yDotK[0][j];
115      for (int l = 1; l < STATIC_E.length; ++l) {
116        errSum += STATIC_E[l] * yDotK[l][j];
117      }
118
119      final double yScale = FastMath.max(FastMath.abs(y0[j]), FastMath.abs(y1[j]));
120      final double tol = (vecAbsoluteTolerance == null) ?
121                         (scalAbsoluteTolerance + scalRelativeTolerance * yScale) :
122                         (vecAbsoluteTolerance[j] + vecRelativeTolerance[j] * yScale);
123      final double ratio  = h * errSum / tol;
124      error += ratio * ratio;
125
126    }
127
128    return FastMath.sqrt(error / mainSetDimension);
129
130  }
131
132}
133