1dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond/* 2dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * Licensed to the Apache Software Foundation (ASF) under one or more 3dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * contributor license agreements. See the NOTICE file distributed with 4dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * this work for additional information regarding copyright ownership. 5dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * The ASF licenses this file to You under the Apache License, Version 2.0 6dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * (the "License"); you may not use this file except in compliance with 7dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * the License. You may obtain a copy of the License at 8dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * 9dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * http://www.apache.org/licenses/LICENSE-2.0 10dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * 11dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * Unless required by applicable law or agreed to in writing, software 12dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * distributed under the License is distributed on an "AS IS" BASIS, 13dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 14dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * See the License for the specific language governing permissions and 15dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * limitations under the License. 16dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond */ 17dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 18dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondpackage org.apache.commons.math.ode.nonstiff; 19dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 20dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondimport org.apache.commons.math.util.FastMath; 21dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 22dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 23dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond/** 24dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * This class implements the 5(4) Higham and Hall integrator for 25dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * Ordinary Differential Equations. 26dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * 27dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * <p>This integrator is an embedded Runge-Kutta integrator 28dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * of order 5(4) used in local extrapolation mode (i.e. the solution 29dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * is computed using the high order formula) with stepsize control 30dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * (and automatic step initialization) and continuous output. This 31dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * method uses 7 functions evaluations per step.</p> 32dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * 33dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @version $Revision: 990655 $ $Date: 2010-08-29 23:49:40 +0200 (dim. 29 août 2010) $ 34dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @since 1.2 35dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond */ 36dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 37dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondpublic class HighamHall54Integrator extends EmbeddedRungeKuttaIntegrator { 38dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 39dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** Integrator method name. */ 40dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond private static final String METHOD_NAME = "Higham-Hall 5(4)"; 41dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 42dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** Time steps Butcher array. */ 43dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond private static final double[] STATIC_C = { 44dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 2.0/9.0, 1.0/3.0, 1.0/2.0, 3.0/5.0, 1.0, 1.0 45dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond }; 46dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 47dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** Internal weights Butcher array. */ 48dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond private static final double[][] STATIC_A = { 49dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond {2.0/9.0}, 50dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond {1.0/12.0, 1.0/4.0}, 51dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond {1.0/8.0, 0.0, 3.0/8.0}, 52dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond {91.0/500.0, -27.0/100.0, 78.0/125.0, 8.0/125.0}, 53dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond {-11.0/20.0, 27.0/20.0, 12.0/5.0, -36.0/5.0, 5.0}, 54dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond {1.0/12.0, 0.0, 27.0/32.0, -4.0/3.0, 125.0/96.0, 5.0/48.0} 55dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond }; 56dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 57dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** Propagation weights Butcher array. */ 58dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond private static final double[] STATIC_B = { 59dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 1.0/12.0, 0.0, 27.0/32.0, -4.0/3.0, 125.0/96.0, 5.0/48.0, 0.0 60dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond }; 61dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 62dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** Error weights Butcher array. */ 63dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond private static final double[] STATIC_E = { 64dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond -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 65dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond }; 66dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 67dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** Simple constructor. 68dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * Build a fifth order Higham and Hall integrator with the given step bounds 69dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @param minStep minimal step (must be positive even for backward 70dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * integration), the last step can be smaller than this 71dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @param maxStep maximal step (must be positive even for backward 72dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * integration) 73dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @param scalAbsoluteTolerance allowed absolute error 74dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @param scalRelativeTolerance allowed relative error 75dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond */ 76dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond public HighamHall54Integrator(final double minStep, final double maxStep, 77dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final double scalAbsoluteTolerance, 78dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final double scalRelativeTolerance) { 79dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond super(METHOD_NAME, false, STATIC_C, STATIC_A, STATIC_B, new HighamHall54StepInterpolator(), 80dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance); 81dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 82dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 83dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** Simple constructor. 84dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * Build a fifth order Higham and Hall integrator with the given step bounds 85dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @param minStep minimal step (must be positive even for backward 86dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * integration), the last step can be smaller than this 87dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @param maxStep maximal step (must be positive even for backward 88dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * integration) 89dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @param vecAbsoluteTolerance allowed absolute error 90dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @param vecRelativeTolerance allowed relative error 91dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond */ 92dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond public HighamHall54Integrator(final double minStep, final double maxStep, 93dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final double[] vecAbsoluteTolerance, 94dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final double[] vecRelativeTolerance) { 95dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond super(METHOD_NAME, false, STATIC_C, STATIC_A, STATIC_B, new HighamHall54StepInterpolator(), 96dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance); 97dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 98dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 99dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** {@inheritDoc} */ 100dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond @Override 101dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond public int getOrder() { 102dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond return 5; 103dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 104dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 105dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** {@inheritDoc} */ 106dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond @Override 107dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond protected double estimateError(final double[][] yDotK, 108dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final double[] y0, final double[] y1, 109dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final double h) { 110dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 111dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond double error = 0; 112dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 113dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int j = 0; j < mainSetDimension; ++j) { 114dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond double errSum = STATIC_E[0] * yDotK[0][j]; 115dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int l = 1; l < STATIC_E.length; ++l) { 116dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond errSum += STATIC_E[l] * yDotK[l][j]; 117dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 118dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 119dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final double yScale = FastMath.max(FastMath.abs(y0[j]), FastMath.abs(y1[j])); 120dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final double tol = (vecAbsoluteTolerance == null) ? 121dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond (scalAbsoluteTolerance + scalRelativeTolerance * yScale) : 122dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond (vecAbsoluteTolerance[j] + vecRelativeTolerance[j] * yScale); 123dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final double ratio = h * errSum / tol; 124dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond error += ratio * ratio; 125dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 126dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 127dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 128dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond return FastMath.sqrt(error / mainSetDimension); 129dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 130dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 131dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 132dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond} 133