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.math3.ode.nonstiff;
019
020 import org.apache.commons.math3.util.FastMath;
021
022
023 /**
024 * This class implements the 5(4) Higham and Hall integrator for
025 * Ordinary Differential Equations.
026 *
027 * <p>This integrator is an embedded Runge-Kutta integrator
028 * of order 5(4) used in local extrapolation mode (i.e. the solution
029 * is computed using the high order formula) with stepsize control
030 * (and automatic step initialization) and continuous output. This
031 * method uses 7 functions evaluations per step.</p>
032 *
033 * @version $Id: HighamHall54Integrator.java 1416643 2012-12-03 19:37:14Z tn $
034 * @since 1.2
035 */
036
037 public class HighamHall54Integrator extends EmbeddedRungeKuttaIntegrator {
038
039 /** Integrator method name. */
040 private static final String METHOD_NAME = "Higham-Hall 5(4)";
041
042 /** Time steps Butcher array. */
043 private static final double[] STATIC_C = {
044 2.0/9.0, 1.0/3.0, 1.0/2.0, 3.0/5.0, 1.0, 1.0
045 };
046
047 /** Internal weights Butcher array. */
048 private static final double[][] STATIC_A = {
049 {2.0/9.0},
050 {1.0/12.0, 1.0/4.0},
051 {1.0/8.0, 0.0, 3.0/8.0},
052 {91.0/500.0, -27.0/100.0, 78.0/125.0, 8.0/125.0},
053 {-11.0/20.0, 27.0/20.0, 12.0/5.0, -36.0/5.0, 5.0},
054 {1.0/12.0, 0.0, 27.0/32.0, -4.0/3.0, 125.0/96.0, 5.0/48.0}
055 };
056
057 /** Propagation weights Butcher array. */
058 private static final double[] STATIC_B = {
059 1.0/12.0, 0.0, 27.0/32.0, -4.0/3.0, 125.0/96.0, 5.0/48.0, 0.0
060 };
061
062 /** Error weights Butcher array. */
063 private static final double[] STATIC_E = {
064 -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
065 };
066
067 /** Simple constructor.
068 * Build a fifth order Higham and Hall integrator with the given step bounds
069 * @param minStep minimal step (sign is irrelevant, regardless of
070 * integration direction, forward or backward), the last step can
071 * be smaller than this
072 * @param maxStep maximal step (sign is irrelevant, regardless of
073 * integration direction, forward or backward), the last step can
074 * be smaller than this
075 * @param scalAbsoluteTolerance allowed absolute error
076 * @param scalRelativeTolerance allowed relative error
077 */
078 public HighamHall54Integrator(final double minStep, final double maxStep,
079 final double scalAbsoluteTolerance,
080 final double scalRelativeTolerance) {
081 super(METHOD_NAME, false, STATIC_C, STATIC_A, STATIC_B, new HighamHall54StepInterpolator(),
082 minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance);
083 }
084
085 /** Simple constructor.
086 * Build a fifth order Higham and Hall integrator with the given step bounds
087 * @param minStep minimal step (sign is irrelevant, regardless of
088 * integration direction, forward or backward), the last step can
089 * be smaller than this
090 * @param maxStep maximal step (sign is irrelevant, regardless of
091 * integration direction, forward or backward), the last step can
092 * be smaller than this
093 * @param vecAbsoluteTolerance allowed absolute error
094 * @param vecRelativeTolerance allowed relative error
095 */
096 public HighamHall54Integrator(final double minStep, final double maxStep,
097 final double[] vecAbsoluteTolerance,
098 final double[] vecRelativeTolerance) {
099 super(METHOD_NAME, false, STATIC_C, STATIC_A, STATIC_B, new HighamHall54StepInterpolator(),
100 minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance);
101 }
102
103 /** {@inheritDoc} */
104 @Override
105 public int getOrder() {
106 return 5;
107 }
108
109 /** {@inheritDoc} */
110 @Override
111 protected double estimateError(final double[][] yDotK,
112 final double[] y0, final double[] y1,
113 final double h) {
114
115 double error = 0;
116
117 for (int j = 0; j < mainSetDimension; ++j) {
118 double errSum = STATIC_E[0] * yDotK[0][j];
119 for (int l = 1; l < STATIC_E.length; ++l) {
120 errSum += STATIC_E[l] * yDotK[l][j];
121 }
122
123 final double yScale = FastMath.max(FastMath.abs(y0[j]), FastMath.abs(y1[j]));
124 final double tol = (vecAbsoluteTolerance == null) ?
125 (scalAbsoluteTolerance + scalRelativeTolerance * yScale) :
126 (vecAbsoluteTolerance[j] + vecRelativeTolerance[j] * yScale);
127 final double ratio = h * errSum / tol;
128 error += ratio * ratio;
129
130 }
131
132 return FastMath.sqrt(error / mainSetDimension);
133
134 }
135
136 }