001/*
002 * Licensed to the Apache Software Foundation (ASF) under one or more
003 * contributor license agreements.  See the NOTICE file distributed with
004 * this work for additional information regarding copyright ownership.
005 * The ASF licenses this file to You under the Apache License, Version 2.0
006 * (the "License"); you may not use this file except in compliance with
007 * the License.  You may obtain a copy of the License at
008 *
009 *      http://www.apache.org/licenses/LICENSE-2.0
010 *
011 * Unless required by applicable law or agreed to in writing, software
012 * distributed under the License is distributed on an "AS IS" BASIS,
013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014 * See the License for the specific language governing permissions and
015 * limitations under the License.
016 */
017
018package org.apache.commons.math3.ode.nonstiff;
019
020import org.apache.commons.math3.util.FastMath;
021
022
023/**
024 * This class implements the 5(4) Higham and Hall integrator for
025 * Ordinary Differential Equations.
026 *
027 * <p>This integrator is an embedded Runge-Kutta integrator
028 * of order 5(4) used in local extrapolation mode (i.e. the solution
029 * is computed using the high order formula) with stepsize control
030 * (and automatic step initialization) and continuous output. This
031 * method uses 7 functions evaluations per step.</p>
032 *
033 * @version $Id: HighamHall54Integrator.java 1416643 2012-12-03 19:37:14Z tn $
034 * @since 1.2
035 */
036
037public class HighamHall54Integrator extends EmbeddedRungeKuttaIntegrator {
038
039  /** Integrator method name. */
040  private static final String METHOD_NAME = "Higham-Hall 5(4)";
041
042  /** Time steps Butcher array. */
043  private static final double[] STATIC_C = {
044    2.0/9.0, 1.0/3.0, 1.0/2.0, 3.0/5.0, 1.0, 1.0
045  };
046
047  /** Internal weights Butcher array. */
048  private static final double[][] STATIC_A = {
049    {2.0/9.0},
050    {1.0/12.0, 1.0/4.0},
051    {1.0/8.0, 0.0, 3.0/8.0},
052    {91.0/500.0, -27.0/100.0, 78.0/125.0, 8.0/125.0},
053    {-11.0/20.0, 27.0/20.0, 12.0/5.0, -36.0/5.0, 5.0},
054    {1.0/12.0, 0.0, 27.0/32.0, -4.0/3.0, 125.0/96.0, 5.0/48.0}
055  };
056
057  /** Propagation weights Butcher array. */
058  private static final double[] STATIC_B = {
059    1.0/12.0, 0.0, 27.0/32.0, -4.0/3.0, 125.0/96.0, 5.0/48.0, 0.0
060  };
061
062  /** Error weights Butcher array. */
063  private static final double[] STATIC_E = {
064    -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
065  };
066
067  /** Simple constructor.
068   * Build a fifth order Higham and Hall integrator with the given step bounds
069   * @param minStep minimal step (sign is irrelevant, regardless of
070   * integration direction, forward or backward), the last step can
071   * be smaller than this
072   * @param maxStep maximal step (sign is irrelevant, regardless of
073   * integration direction, forward or backward), the last step can
074   * be smaller than this
075   * @param scalAbsoluteTolerance allowed absolute error
076   * @param scalRelativeTolerance allowed relative error
077   */
078  public HighamHall54Integrator(final double minStep, final double maxStep,
079                                final double scalAbsoluteTolerance,
080                                final double scalRelativeTolerance) {
081    super(METHOD_NAME, false, STATIC_C, STATIC_A, STATIC_B, new HighamHall54StepInterpolator(),
082          minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance);
083  }
084
085  /** Simple constructor.
086   * Build a fifth order Higham and Hall integrator with the given step bounds
087   * @param minStep minimal step (sign is irrelevant, regardless of
088   * integration direction, forward or backward), the last step can
089   * be smaller than this
090   * @param maxStep maximal step (sign is irrelevant, regardless of
091   * integration direction, forward or backward), the last step can
092   * be smaller than this
093   * @param vecAbsoluteTolerance allowed absolute error
094   * @param vecRelativeTolerance allowed relative error
095   */
096  public HighamHall54Integrator(final double minStep, final double maxStep,
097                                final double[] vecAbsoluteTolerance,
098                                final double[] vecRelativeTolerance) {
099    super(METHOD_NAME, false, STATIC_C, STATIC_A, STATIC_B, new HighamHall54StepInterpolator(),
100          minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance);
101  }
102
103  /** {@inheritDoc} */
104  @Override
105  public int getOrder() {
106    return 5;
107  }
108
109  /** {@inheritDoc} */
110  @Override
111  protected double estimateError(final double[][] yDotK,
112                                 final double[] y0, final double[] y1,
113                                 final double h) {
114
115    double error = 0;
116
117    for (int j = 0; j < mainSetDimension; ++j) {
118      double errSum = STATIC_E[0] * yDotK[0][j];
119      for (int l = 1; l < STATIC_E.length; ++l) {
120        errSum += STATIC_E[l] * yDotK[l][j];
121      }
122
123      final double yScale = FastMath.max(FastMath.abs(y0[j]), FastMath.abs(y1[j]));
124      final double tol = (vecAbsoluteTolerance == null) ?
125                         (scalAbsoluteTolerance + scalRelativeTolerance * yScale) :
126                         (vecAbsoluteTolerance[j] + vecRelativeTolerance[j] * yScale);
127      final double ratio  = h * errSum / tol;
128      error += ratio * ratio;
129
130    }
131
132    return FastMath.sqrt(error / mainSetDimension);
133
134  }
135
136}