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) Dormand-Prince integrator for Ordinary 25dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * 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. However, since this 32dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * is an <i>fsal</i>, the last evaluation of one step is the same as 33dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * the first evaluation of the next step and hence can be avoided. So 34dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * the cost is really 6 functions evaluations per step.</p> 35dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * 36dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * <p>This method has been published (whithout the continuous output 37dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * that was added by Shampine in 1986) in the following article : 38dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * <pre> 39dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * A family of embedded Runge-Kutta formulae 40dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * J. R. Dormand and P. J. Prince 41dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * Journal of Computational and Applied Mathematics 42dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * volume 6, no 1, 1980, pp. 19-26 43dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * </pre></p> 44dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * 45dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @version $Revision: 990655 $ $Date: 2010-08-29 23:49:40 +0200 (dim. 29 août 2010) $ 46dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @since 1.2 47dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond */ 48dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 49dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondpublic class DormandPrince54Integrator extends EmbeddedRungeKuttaIntegrator { 50dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 51dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** Integrator method name. */ 52dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond private static final String METHOD_NAME = "Dormand-Prince 5(4)"; 53dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 54dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** Time steps Butcher array. */ 55dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond private static final double[] STATIC_C = { 56dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 1.0/5.0, 3.0/10.0, 4.0/5.0, 8.0/9.0, 1.0, 1.0 57dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond }; 58dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 59dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** Internal weights Butcher array. */ 60dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond private static final double[][] STATIC_A = { 61dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond {1.0/5.0}, 62dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond {3.0/40.0, 9.0/40.0}, 63dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond {44.0/45.0, -56.0/15.0, 32.0/9.0}, 64dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond {19372.0/6561.0, -25360.0/2187.0, 64448.0/6561.0, -212.0/729.0}, 65dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond {9017.0/3168.0, -355.0/33.0, 46732.0/5247.0, 49.0/176.0, -5103.0/18656.0}, 66dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond {35.0/384.0, 0.0, 500.0/1113.0, 125.0/192.0, -2187.0/6784.0, 11.0/84.0} 67dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond }; 68dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 69dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** Propagation weights Butcher array. */ 70dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond private static final double[] STATIC_B = { 71dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 35.0/384.0, 0.0, 500.0/1113.0, 125.0/192.0, -2187.0/6784.0, 11.0/84.0, 0.0 72dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond }; 73dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 74dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** Error array, element 1. */ 75dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond private static final double E1 = 71.0 / 57600.0; 76dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 77dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond // element 2 is zero, so it is neither stored nor used 78dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 79dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** Error array, element 3. */ 80dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond private static final double E3 = -71.0 / 16695.0; 81dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 82dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** Error array, element 4. */ 83dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond private static final double E4 = 71.0 / 1920.0; 84dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 85dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** Error array, element 5. */ 86dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond private static final double E5 = -17253.0 / 339200.0; 87dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 88dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** Error array, element 6. */ 89dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond private static final double E6 = 22.0 / 525.0; 90dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 91dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** Error array, element 7. */ 92dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond private static final double E7 = -1.0 / 40.0; 93dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 94dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** Simple constructor. 95dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * Build a fifth order Dormand-Prince integrator with the given step bounds 96dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @param minStep minimal step (must be positive even for backward 97dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * integration), the last step can be smaller than this 98dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @param maxStep maximal step (must be positive even for backward 99dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * integration) 100dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @param scalAbsoluteTolerance allowed absolute error 101dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @param scalRelativeTolerance allowed relative error 102dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond */ 103dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond public DormandPrince54Integrator(final double minStep, final double maxStep, 104dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final double scalAbsoluteTolerance, 105dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final double scalRelativeTolerance) { 106dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond super(METHOD_NAME, true, STATIC_C, STATIC_A, STATIC_B, new DormandPrince54StepInterpolator(), 107dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance); 108dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 109dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 110dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** Simple constructor. 111dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * Build a fifth order Dormand-Prince integrator with the given step bounds 112dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @param minStep minimal step (must be positive even for backward 113dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * integration), the last step can be smaller than this 114dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @param maxStep maximal step (must be positive even for backward 115dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * integration) 116dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @param vecAbsoluteTolerance allowed absolute error 117dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @param vecRelativeTolerance allowed relative error 118dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond */ 119dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond public DormandPrince54Integrator(final double minStep, final double maxStep, 120dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final double[] vecAbsoluteTolerance, 121dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final double[] vecRelativeTolerance) { 122dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond super(METHOD_NAME, true, STATIC_C, STATIC_A, STATIC_B, new DormandPrince54StepInterpolator(), 123dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance); 124dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 125dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 126dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** {@inheritDoc} */ 127dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond @Override 128dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond public int getOrder() { 129dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond return 5; 130dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 131dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 132dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** {@inheritDoc} */ 133dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond @Override 134dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond protected double estimateError(final double[][] yDotK, 135dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final double[] y0, final double[] y1, 136dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final double h) { 137dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 138dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond double error = 0; 139dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 140dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int j = 0; j < mainSetDimension; ++j) { 141dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final double errSum = E1 * yDotK[0][j] + E3 * yDotK[2][j] + 142dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond E4 * yDotK[3][j] + E5 * yDotK[4][j] + 143dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond E6 * yDotK[5][j] + E7 * yDotK[6][j]; 144dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 145dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final double yScale = FastMath.max(FastMath.abs(y0[j]), FastMath.abs(y1[j])); 146dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final double tol = (vecAbsoluteTolerance == null) ? 147dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond (scalAbsoluteTolerance + scalRelativeTolerance * yScale) : 148dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond (vecAbsoluteTolerance[j] + vecRelativeTolerance[j] * yScale); 149dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final double ratio = h * errSum / tol; 150dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond error += ratio * ratio; 151dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 152dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 153dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 154dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond return FastMath.sqrt(error / mainSetDimension); 155dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 156dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 157dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 158dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond} 159