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 018package org.apache.commons.math3.ode.nonstiff; 019 020import 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 * @since 1.2 034 */ 035 036public class HighamHall54Integrator extends EmbeddedRungeKuttaIntegrator { 037 038 /** Integrator method name. */ 039 private static final String METHOD_NAME = "Higham-Hall 5(4)"; 040 041 /** Time steps Butcher array. */ 042 private static final double[] STATIC_C = { 043 2.0/9.0, 1.0/3.0, 1.0/2.0, 3.0/5.0, 1.0, 1.0 044 }; 045 046 /** Internal weights Butcher array. */ 047 private static final double[][] STATIC_A = { 048 {2.0/9.0}, 049 {1.0/12.0, 1.0/4.0}, 050 {1.0/8.0, 0.0, 3.0/8.0}, 051 {91.0/500.0, -27.0/100.0, 78.0/125.0, 8.0/125.0}, 052 {-11.0/20.0, 27.0/20.0, 12.0/5.0, -36.0/5.0, 5.0}, 053 {1.0/12.0, 0.0, 27.0/32.0, -4.0/3.0, 125.0/96.0, 5.0/48.0} 054 }; 055 056 /** Propagation weights Butcher array. */ 057 private static final double[] STATIC_B = { 058 1.0/12.0, 0.0, 27.0/32.0, -4.0/3.0, 125.0/96.0, 5.0/48.0, 0.0 059 }; 060 061 /** Error weights Butcher array. */ 062 private static final double[] STATIC_E = { 063 -1.0/20.0, 0.0, 81.0/160.0, -6.0/5.0, 25.0/32.0, 1.0/16.0, -1.0/10.0 064 }; 065 066 /** Simple constructor. 067 * Build a fifth order Higham and Hall integrator with the given step bounds 068 * @param minStep minimal step (sign is irrelevant, regardless of 069 * integration direction, forward or backward), the last step can 070 * be smaller than this 071 * @param maxStep maximal step (sign is irrelevant, regardless of 072 * integration direction, forward or backward), the last step can 073 * be smaller than this 074 * @param scalAbsoluteTolerance allowed absolute error 075 * @param scalRelativeTolerance allowed relative error 076 */ 077 public HighamHall54Integrator(final double minStep, final double maxStep, 078 final double scalAbsoluteTolerance, 079 final double scalRelativeTolerance) { 080 super(METHOD_NAME, false, STATIC_C, STATIC_A, STATIC_B, new HighamHall54StepInterpolator(), 081 minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance); 082 } 083 084 /** Simple constructor. 085 * Build a fifth order Higham and Hall integrator with the given step bounds 086 * @param minStep minimal step (sign is irrelevant, regardless of 087 * integration direction, forward or backward), the last step can 088 * be smaller than this 089 * @param maxStep maximal step (sign is irrelevant, regardless of 090 * integration direction, forward or backward), the last step can 091 * be smaller than this 092 * @param vecAbsoluteTolerance allowed absolute error 093 * @param vecRelativeTolerance allowed relative error 094 */ 095 public HighamHall54Integrator(final double minStep, final double maxStep, 096 final double[] vecAbsoluteTolerance, 097 final double[] vecRelativeTolerance) { 098 super(METHOD_NAME, false, STATIC_C, STATIC_A, STATIC_B, new HighamHall54StepInterpolator(), 099 minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance); 100 } 101 102 /** {@inheritDoc} */ 103 @Override 104 public int getOrder() { 105 return 5; 106 } 107 108 /** {@inheritDoc} */ 109 @Override 110 protected double estimateError(final double[][] yDotK, 111 final double[] y0, final double[] y1, 112 final double h) { 113 114 double error = 0; 115 116 for (int j = 0; j < mainSetDimension; ++j) { 117 double errSum = STATIC_E[0] * yDotK[0][j]; 118 for (int l = 1; l < STATIC_E.length; ++l) { 119 errSum += STATIC_E[l] * yDotK[l][j]; 120 } 121 122 final double yScale = FastMath.max(FastMath.abs(y0[j]), FastMath.abs(y1[j])); 123 final double tol = (vecAbsoluteTolerance == null) ? 124 (scalAbsoluteTolerance + scalRelativeTolerance * yScale) : 125 (vecAbsoluteTolerance[j] + vecRelativeTolerance[j] * yScale); 126 final double ratio = h * errSum / tol; 127 error += ratio * ratio; 128 129 } 130 131 return FastMath.sqrt(error / mainSetDimension); 132 133 } 134 135}