001 /*
002 * Licensed to the Apache Software Foundation (ASF) under one or more
003 * contributor license agreements. See the NOTICE file distributed with
004 * this work for additional information regarding copyright ownership.
005 * The ASF licenses this file to You under the Apache License, Version 2.0
006 * (the "License"); you may not use this file except in compliance with
007 * the License. You may obtain a copy of the License at
008 *
009 * http://www.apache.org/licenses/LICENSE-2.0
010 *
011 * Unless required by applicable law or agreed to in writing, software
012 * distributed under the License is distributed on an "AS IS" BASIS,
013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014 * See the License for the specific language governing permissions and
015 * limitations under the License.
016 */
017
018 package org.apache.commons.math.ode.nonstiff;
019
020
021 /**
022 * This class implements the 5(4) Higham and Hall integrator for
023 * Ordinary Differential Equations.
024 *
025 * <p>This integrator is an embedded Runge-Kutta integrator
026 * of order 5(4) used in local extrapolation mode (i.e. the solution
027 * is computed using the high order formula) with stepsize control
028 * (and automatic step initialization) and continuous output. This
029 * method uses 7 functions evaluations per step.</p>
030 *
031 * @version $Revision: 810196 $ $Date: 2009-09-01 15:47:46 -0400 (Tue, 01 Sep 2009) $
032 * @since 1.2
033 */
034
035 public class HighamHall54Integrator extends EmbeddedRungeKuttaIntegrator {
036
037 /** Integrator method name. */
038 private static final String METHOD_NAME = "Higham-Hall 5(4)";
039
040 /** Time steps Butcher array. */
041 private static final double[] STATIC_C = {
042 2.0/9.0, 1.0/3.0, 1.0/2.0, 3.0/5.0, 1.0, 1.0
043 };
044
045 /** Internal weights Butcher array. */
046 private static final double[][] STATIC_A = {
047 {2.0/9.0},
048 {1.0/12.0, 1.0/4.0},
049 {1.0/8.0, 0.0, 3.0/8.0},
050 {91.0/500.0, -27.0/100.0, 78.0/125.0, 8.0/125.0},
051 {-11.0/20.0, 27.0/20.0, 12.0/5.0, -36.0/5.0, 5.0},
052 {1.0/12.0, 0.0, 27.0/32.0, -4.0/3.0, 125.0/96.0, 5.0/48.0}
053 };
054
055 /** Propagation weights Butcher array. */
056 private static final double[] STATIC_B = {
057 1.0/12.0, 0.0, 27.0/32.0, -4.0/3.0, 125.0/96.0, 5.0/48.0, 0.0
058 };
059
060 /** Error weights Butcher array. */
061 private static final double[] STATIC_E = {
062 -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
063 };
064
065 /** Simple constructor.
066 * Build a fifth order Higham and Hall integrator with the given step bounds
067 * @param minStep minimal step (must be positive even for backward
068 * integration), the last step can be smaller than this
069 * @param maxStep maximal step (must be positive even for backward
070 * integration)
071 * @param scalAbsoluteTolerance allowed absolute error
072 * @param scalRelativeTolerance allowed relative error
073 */
074 public HighamHall54Integrator(final double minStep, final double maxStep,
075 final double scalAbsoluteTolerance,
076 final double scalRelativeTolerance) {
077 super(METHOD_NAME, false, STATIC_C, STATIC_A, STATIC_B, new HighamHall54StepInterpolator(),
078 minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance);
079 }
080
081 /** Simple constructor.
082 * Build a fifth order Higham and Hall integrator with the given step bounds
083 * @param minStep minimal step (must be positive even for backward
084 * integration), the last step can be smaller than this
085 * @param maxStep maximal step (must be positive even for backward
086 * integration)
087 * @param vecAbsoluteTolerance allowed absolute error
088 * @param vecRelativeTolerance allowed relative error
089 */
090 public HighamHall54Integrator(final double minStep, final double maxStep,
091 final double[] vecAbsoluteTolerance,
092 final double[] vecRelativeTolerance) {
093 super(METHOD_NAME, false, STATIC_C, STATIC_A, STATIC_B, new HighamHall54StepInterpolator(),
094 minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance);
095 }
096
097 /** {@inheritDoc} */
098 @Override
099 public int getOrder() {
100 return 5;
101 }
102
103 /** {@inheritDoc} */
104 @Override
105 protected double estimateError(final double[][] yDotK,
106 final double[] y0, final double[] y1,
107 final double h) {
108
109 double error = 0;
110
111 for (int j = 0; j < y0.length; ++j) {
112 double errSum = STATIC_E[0] * yDotK[0][j];
113 for (int l = 1; l < STATIC_E.length; ++l) {
114 errSum += STATIC_E[l] * yDotK[l][j];
115 }
116
117 final double yScale = Math.max(Math.abs(y0[j]), Math.abs(y1[j]));
118 final double tol = (vecAbsoluteTolerance == null) ?
119 (scalAbsoluteTolerance + scalRelativeTolerance * yScale) :
120 (vecAbsoluteTolerance[j] + vecRelativeTolerance[j] * yScale);
121 final double ratio = h * errSum / tol;
122 error += ratio * ratio;
123
124 }
125
126 return Math.sqrt(error / y0.length);
127
128 }
129
130 }