/* * Licensed to the Apache Software Foundation (ASF) under one or more * contributor license agreements. See the NOTICE file distributed with * this work for additional information regarding copyright ownership. * The ASF licenses this file to You under the Apache License, Version 2.0 * (the "License"); you may not use this file except in compliance with * the License. You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ package org.apache.commons.math.ode.nonstiff; import org.apache.commons.math.util.FastMath; /** * This class implements the 5(4) Higham and Hall integrator for * Ordinary Differential Equations. * * <p>This integrator is an embedded Runge-Kutta integrator * of order 5(4) used in local extrapolation mode (i.e. the solution * is computed using the high order formula) with stepsize control * (and automatic step initialization) and continuous output. This * method uses 7 functions evaluations per step.</p> * * @version $Id: HighamHall54Integrator.java 1131229 2011-06-03 20:49:25Z luc $ * @since 1.2 */ public class HighamHall54Integrator extends EmbeddedRungeKuttaIntegrator { /** Integrator method name. */ private static final String METHOD_NAME = "Higham-Hall 5(4)"; /** Time steps Butcher array. */ private static final double[] STATIC_C = { 2.0/9.0, 1.0/3.0, 1.0/2.0, 3.0/5.0, 1.0, 1.0 }; /** Internal weights Butcher array. */ private static final double[][] STATIC_A = { {2.0/9.0}, {1.0/12.0, 1.0/4.0}, {1.0/8.0, 0.0, 3.0/8.0}, {91.0/500.0, -27.0/100.0, 78.0/125.0, 8.0/125.0}, {-11.0/20.0, 27.0/20.0, 12.0/5.0, -36.0/5.0, 5.0}, {1.0/12.0, 0.0, 27.0/32.0, -4.0/3.0, 125.0/96.0, 5.0/48.0} }; /** Propagation weights Butcher array. */ private static final double[] STATIC_B = { 1.0/12.0, 0.0, 27.0/32.0, -4.0/3.0, 125.0/96.0, 5.0/48.0, 0.0 }; /** Error weights Butcher array. */ private static final double[] STATIC_E = { -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 }; /** Simple constructor. * Build a fifth order Higham and Hall integrator with the given step bounds * @param minStep minimal step (sign is irrelevant, regardless of * integration direction, forward or backward), the last step can * be smaller than this * @param maxStep maximal step (sign is irrelevant, regardless of * integration direction, forward or backward), the last step can * be smaller than this * @param scalAbsoluteTolerance allowed absolute error * @param scalRelativeTolerance allowed relative error */ public HighamHall54Integrator(final double minStep, final double maxStep, final double scalAbsoluteTolerance, final double scalRelativeTolerance) { super(METHOD_NAME, false, STATIC_C, STATIC_A, STATIC_B, new HighamHall54StepInterpolator(), minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance); } /** Simple constructor. * Build a fifth order Higham and Hall integrator with the given step bounds * @param minStep minimal step (sign is irrelevant, regardless of * integration direction, forward or backward), the last step can * be smaller than this * @param maxStep maximal step (sign is irrelevant, regardless of * integration direction, forward or backward), the last step can * be smaller than this * @param vecAbsoluteTolerance allowed absolute error * @param vecRelativeTolerance allowed relative error */ public HighamHall54Integrator(final double minStep, final double maxStep, final double[] vecAbsoluteTolerance, final double[] vecRelativeTolerance) { super(METHOD_NAME, false, STATIC_C, STATIC_A, STATIC_B, new HighamHall54StepInterpolator(), minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance); } /** {@inheritDoc} */ @Override public int getOrder() { return 5; } /** {@inheritDoc} */ @Override protected double estimateError(final double[][] yDotK, final double[] y0, final double[] y1, final double h) { double error = 0; for (int j = 0; j < mainSetDimension; ++j) { double errSum = STATIC_E[0] * yDotK[0][j]; for (int l = 1; l < STATIC_E.length; ++l) { errSum += STATIC_E[l] * yDotK[l][j]; } final double yScale = FastMath.max(FastMath.abs(y0[j]), FastMath.abs(y1[j])); final double tol = (vecAbsoluteTolerance == null) ? (scalAbsoluteTolerance + scalRelativeTolerance * yScale) : (vecAbsoluteTolerance[j] + vecRelativeTolerance[j] * yScale); final double ratio = h * errSum / tol; error += ratio * ratio; } return FastMath.sqrt(error / mainSetDimension); } }