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: 786881 $ $Date: 2009-06-20 14:53:08 -0400 (Sat, 20 Jun 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[] staticC = { 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[][] staticA = { 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[] staticB = { 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[] staticE = { 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, staticC, staticA, staticB, 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, staticC, staticA, staticB, 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 = staticE[0] * yDotK[0][j]; 113 for (int l = 1; l < staticE.length; ++l) { 114 errSum += staticE[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 }