| /* |
| * 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) 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</i>, 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></p> |
| * |
| * @version $Revision: 990655 $ $Date: 2010-08-29 23:49:40 +0200 (dim. 29 août 2010) $ |
| * @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 < mainSetDimension; ++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 = 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); |
| |
| } |
| |
| } |
