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Commons Math example source code file (DormandPrince54Integrator.java)

This example Commons Math source code file (DormandPrince54Integrator.java) is included in the DevDaily.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Java - Commons Math tags/keywords

dormandprince54integrator, dormandprince54integrator, dormandprince54stepinterpolator, e1, e3, e5, e7, override, static_a, static_a, static_b, static_b, static_c, static_c

The Commons Math DormandPrince54Integrator.java source code

/*
 * 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;


/**
 * This class implements the 5(4) Dormand-Prince 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. However, since this
 * is an <i>fsal, the last evaluation of one step is the same as
 * the first evaluation of the next step and hence can be avoided. So
 * the cost is really 6 functions evaluations per step.</p>
 *
 * <p>This method has been published (whithout the continuous output
 * that was added by Shampine in 1986) in the following article :
 * <pre>
 *  A family of embedded Runge-Kutta formulae
 *  J. R. Dormand and P. J. Prince
 *  Journal of Computational and Applied Mathematics
 *  volume 6, no 1, 1980, pp. 19-26
 * </pre>

* * @version $Revision: 810196 $ $Date: 2009-09-01 15:47:46 -0400 (Tue, 01 Sep 2009) $ * @since 1.2 */ public class DormandPrince54Integrator extends EmbeddedRungeKuttaIntegrator { /** Integrator method name. */ private static final String METHOD_NAME = "Dormand-Prince 5(4)"; /** Time steps Butcher array. */ private static final double[] STATIC_C = { 1.0/5.0, 3.0/10.0, 4.0/5.0, 8.0/9.0, 1.0, 1.0 }; /** Internal weights Butcher array. */ private static final double[][] STATIC_A = { {1.0/5.0}, {3.0/40.0, 9.0/40.0}, {44.0/45.0, -56.0/15.0, 32.0/9.0}, {19372.0/6561.0, -25360.0/2187.0, 64448.0/6561.0, -212.0/729.0}, {9017.0/3168.0, -355.0/33.0, 46732.0/5247.0, 49.0/176.0, -5103.0/18656.0}, {35.0/384.0, 0.0, 500.0/1113.0, 125.0/192.0, -2187.0/6784.0, 11.0/84.0} }; /** Propagation weights Butcher array. */ private static final double[] STATIC_B = { 35.0/384.0, 0.0, 500.0/1113.0, 125.0/192.0, -2187.0/6784.0, 11.0/84.0, 0.0 }; /** Error array, element 1. */ private static final double E1 = 71.0 / 57600.0; // element 2 is zero, so it is neither stored nor used /** Error array, element 3. */ private static final double E3 = -71.0 / 16695.0; /** Error array, element 4. */ private static final double E4 = 71.0 / 1920.0; /** Error array, element 5. */ private static final double E5 = -17253.0 / 339200.0; /** Error array, element 6. */ private static final double E6 = 22.0 / 525.0; /** Error array, element 7. */ private static final double E7 = -1.0 / 40.0; /** Simple constructor. * Build a fifth order Dormand-Prince integrator with the given step bounds * @param minStep minimal step (must be positive even for backward * integration), the last step can be smaller than this * @param maxStep maximal step (must be positive even for backward * integration) * @param scalAbsoluteTolerance allowed absolute error * @param scalRelativeTolerance allowed relative error */ public DormandPrince54Integrator(final double minStep, final double maxStep, final double scalAbsoluteTolerance, final double scalRelativeTolerance) { super(METHOD_NAME, true, STATIC_C, STATIC_A, STATIC_B, new DormandPrince54StepInterpolator(), minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance); } /** Simple constructor. * Build a fifth order Dormand-Prince integrator with the given step bounds * @param minStep minimal step (must be positive even for backward * integration), the last step can be smaller than this * @param maxStep maximal step (must be positive even for backward * integration) * @param vecAbsoluteTolerance allowed absolute error * @param vecRelativeTolerance allowed relative error */ public DormandPrince54Integrator(final double minStep, final double maxStep, final double[] vecAbsoluteTolerance, final double[] vecRelativeTolerance) { super(METHOD_NAME, true, STATIC_C, STATIC_A, STATIC_B, new DormandPrince54StepInterpolator(), 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 < y0.length; ++j) { final double errSum = E1 * yDotK[0][j] + E3 * yDotK[2][j] + E4 * yDotK[3][j] + E5 * yDotK[4][j] + E6 * yDotK[5][j] + E7 * yDotK[6][j]; final double yScale = Math.max(Math.abs(y0[j]), Math.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 Math.sqrt(error / y0.length); } }

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