| /* |
| * 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.math4.legacy.ode.nonstiff; |
| |
| import org.apache.commons.math4.core.jdkmath.JdkMath; |
| |
| |
| /** |
| * 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> |
| * |
| * @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 = JdkMath.max(JdkMath.abs(y0[j]), JdkMath.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 JdkMath.sqrt(error / mainSetDimension); |
| |
| } |
| |
| } |