dormandprince54integrator.java

Apache的common math数学软件包

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 * 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) 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: 620312 $ $Date: 2008-02-10 12:28:59 -0700 (Sun, 10 Feb 2008) $
 * @since 1.2
 */

public class DormandPrince54Integrator
  extends EmbeddedRungeKuttaIntegrator {

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

  /** Time steps Butcher array. */
  private static final double[] staticC = {
    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[][] staticA = {
    {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[] staticB = {
    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(double minStep, double maxStep,
                                   double scalAbsoluteTolerance,
                                   double scalRelativeTolerance) {
    super(true, staticC, staticA, staticB, 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(double minStep, double maxStep,
                                   double[] vecAbsoluteTolerance,
                                   double[] vecRelativeTolerance) {
    super(true, staticC, staticA, staticB, new DormandPrince54StepInterpolator(),
          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 = e1 * yDotK[0][j] +  e3 * yDotK[2][j] +
                      e4 * yDotK[3][j] +  e5 * yDotK[4][j] +
                      e6 * yDotK[5][j] +  e7 * yDotK[6][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);

  }

}