1 /* 2 * Licensed to the Apache Software Foundation (ASF) under one or more 3 * contributor license agreements. See the NOTICE file distributed with 4 * this work for additional information regarding copyright ownership. 5 * The ASF licenses this file to You under the Apache License, Version 2.0 6 * (the "License"); you may not use this file except in compliance with 7 * the License. You may obtain a copy of the License at 8 * 9 * http://www.apache.org/licenses/LICENSE-2.0 10 * 11 * Unless required by applicable law or agreed to in writing, software 12 * distributed under the License is distributed on an "AS IS" BASIS, 13 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 14 * See the License for the specific language governing permissions and 15 * limitations under the License. 16 */ 17 18 package org.apache.commons.math.ode.nonstiff; 19 20 import org.apache.commons.math.util.FastMath; 21 22 23 /** 24 * This class implements the 5(4) Higham and Hall integrator for 25 * Ordinary Differential Equations. 26 * 27 * <p>This integrator is an embedded Runge-Kutta integrator 28 * of order 5(4) used in local extrapolation mode (i.e. the solution 29 * is computed using the high order formula) with stepsize control 30 * (and automatic step initialization) and continuous output. This 31 * method uses 7 functions evaluations per step.</p> 32 * 33 * @version $Revision: 990655 $ $Date: 2010-08-29 23:49:40 +0200 (dim. 29 aot 2010) $ 34 * @since 1.2 35 */ 36 37 public class HighamHall54Integrator extends EmbeddedRungeKuttaIntegrator { 38 39 /** Integrator method name. */ 40 private static final String METHOD_NAME = "Higham-Hall 5(4)"; 41 42 /** Time steps Butcher array. */ 43 private static final double[] STATIC_C = { 44 2.0/9.0, 1.0/3.0, 1.0/2.0, 3.0/5.0, 1.0, 1.0 45 }; 46 47 /** Internal weights Butcher array. */ 48 private static final double[][] STATIC_A = { 49 {2.0/9.0}, 50 {1.0/12.0, 1.0/4.0}, 51 {1.0/8.0, 0.0, 3.0/8.0}, 52 {91.0/500.0, -27.0/100.0, 78.0/125.0, 8.0/125.0}, 53 {-11.0/20.0, 27.0/20.0, 12.0/5.0, -36.0/5.0, 5.0}, 54 {1.0/12.0, 0.0, 27.0/32.0, -4.0/3.0, 125.0/96.0, 5.0/48.0} 55 }; 56 57 /** Propagation weights Butcher array. */ 58 private static final double[] STATIC_B = { 59 1.0/12.0, 0.0, 27.0/32.0, -4.0/3.0, 125.0/96.0, 5.0/48.0, 0.0 60 }; 61 62 /** Error weights Butcher array. */ 63 private static final double[] STATIC_E = { 64 -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 65 }; 66 67 /** Simple constructor. 68 * Build a fifth order Higham and Hall integrator with the given step bounds 69 * @param minStep minimal step (must be positive even for backward 70 * integration), the last step can be smaller than this 71 * @param maxStep maximal step (must be positive even for backward 72 * integration) 73 * @param scalAbsoluteTolerance allowed absolute error 74 * @param scalRelativeTolerance allowed relative error 75 */ 76 public HighamHall54Integrator(final double minStep, final double maxStep, 77 final double scalAbsoluteTolerance, 78 final double scalRelativeTolerance) { 79 super(METHOD_NAME, false, STATIC_C, STATIC_A, STATIC_B, new HighamHall54StepInterpolator(), 80 minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance); 81 } 82 83 /** Simple constructor. 84 * Build a fifth order Higham and Hall integrator with the given step bounds 85 * @param minStep minimal step (must be positive even for backward 86 * integration), the last step can be smaller than this 87 * @param maxStep maximal step (must be positive even for backward 88 * integration) 89 * @param vecAbsoluteTolerance allowed absolute error 90 * @param vecRelativeTolerance allowed relative error 91 */ 92 public HighamHall54Integrator(final double minStep, final double maxStep, 93 final double[] vecAbsoluteTolerance, 94 final double[] vecRelativeTolerance) { 95 super(METHOD_NAME, false, STATIC_C, STATIC_A, STATIC_B, new HighamHall54StepInterpolator(), 96 minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance); 97 } 98 99 /** {@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 } 133