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 import org.apache.commons.math.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 $Revision: 990655 $ $Date: 2010-08-29 23:49:40 +0200 (dim. 29 ao??t 2010) $ 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 (must be positive even for backward 070 * integration), the last step can be smaller than this 071 * @param maxStep maximal step (must be positive even for backward 072 * integration) 073 * @param scalAbsoluteTolerance allowed absolute error 074 * @param scalRelativeTolerance allowed relative error 075 */ 076 public HighamHall54Integrator(final double minStep, final double maxStep, 077 final double scalAbsoluteTolerance, 078 final double scalRelativeTolerance) { 079 super(METHOD_NAME, false, STATIC_C, STATIC_A, STATIC_B, new HighamHall54StepInterpolator(), 080 minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance); 081 } 082 083 /** Simple constructor. 084 * Build a fifth order Higham and Hall integrator with the given step bounds 085 * @param minStep minimal step (must be positive even for backward 086 * integration), the last step can be smaller than this 087 * @param maxStep maximal step (must be positive even for backward 088 * integration) 089 * @param vecAbsoluteTolerance allowed absolute error 090 * @param vecRelativeTolerance allowed relative error 091 */ 092 public HighamHall54Integrator(final double minStep, final double maxStep, 093 final double[] vecAbsoluteTolerance, 094 final double[] vecRelativeTolerance) { 095 super(METHOD_NAME, false, STATIC_C, STATIC_A, STATIC_B, new HighamHall54StepInterpolator(), 096 minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance); 097 } 098 099 /** {@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 }