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Commons Math example source code file (HighamHall54Integrator.java)

This example Commons Math source code file (HighamHall54Integrator.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

higham-hall, highamhall54integrator, highamhall54integrator, highamhall54stepinterpolator, method_name, override, static_a, static_b, static_b, static_c, static_c, static_e, static_e, string

The Commons Math HighamHall54Integrator.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) 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: 810196 $ $Date: 2009-09-01 15:47:46 -0400 (Tue, 01 Sep 2009) $
 * @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 (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(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 (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(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 < y0.length; ++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 = 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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