src/java/org/apache/commons/math/ode/HighamHall54Integrator.java

/*
 * 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;

/**
 * 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>
 *
 * @version $Revision$ $Date$
 * @since 1.2
 */

public class HighamHall54Integrator
  extends EmbeddedRungeKuttaIntegrator {

  /** Integrator method name. */
  private static final String methodName = "Higham-Hall 5(4)";

  /** Time steps Butcher array. */
  private static final double[] staticC = {
    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[][] staticA = {
    {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[] staticB = {
    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[] staticE = {
    -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 (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 HighamHall54Integrator(double minStep, double maxStep,
                                double scalAbsoluteTolerance,
                                double scalRelativeTolerance) {
    super(false, staticC, staticA, staticB, 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 (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 HighamHall54Integrator(double minStep, double maxStep,
                                double[] vecAbsoluteTolerance,
                                double[] vecRelativeTolerance) {
    super(false, staticC, staticA, staticB, new HighamHall54StepInterpolator(),
          minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance);
  }

  /** Get the name of the method.
   * @return name of the method
   */
  public String getName() {
    return methodName;
  }

  /** Get the order of the method.
   * @return order of the method
   */
  public int getOrder() {
    return 5;
  }

  /** Compute the error ratio.
   * @param yDotK derivatives computed during the first stages
   * @param y0 estimate of the step at the start of the step
   * @param y1 estimate of the step at the end of the step
   * @param h  current step
   * @return error ratio, greater than 1 if step should be rejected
   */
  protected double estimateError(double[][] yDotK,
                                 double[] y0, double[] y1,
                                 double h) {

    double error = 0;

    for (int j = 0; j < y0.length; ++j) {
      double errSum = staticE[0] * yDotK[0][j];
      for (int l = 1; l < staticE.length; ++l) {
        errSum += staticE[l] * yDotK[l][j];
      }

      double yScale = Math.max(Math.abs(y0[j]), Math.abs(y1[j]));
      double tol = (vecAbsoluteTolerance == null) ?
                   (scalAbsoluteTolerance + scalRelativeTolerance * yScale) :
                   (vecAbsoluteTolerance[j] + vecRelativeTolerance[j] * yScale);
      double ratio  = h * errSum / tol;
      error += ratio * ratio;

    }

    return Math.sqrt(error / y0.length);

  }

}