package org.spaceroots.mantissa.ode;

/**
 * This class implements the 5(4) Dormand-Prince integrator for Ordinary
 * Differential Equations.

 * 
This integrator is an embedded Runge-Kutta-Fehlberg 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 fsal, 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.

 * 
This method has been published (whithout the continuous output
 * that was added by Shampine in 1986) in the following article :
 * 
 *  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
 * 


 * @version $Id: DormandPrince54Integrator.java 1709 2006-12-03 21:16:50Z luc $
 * @author L. Maisonobe

 */

public class DormandPrince54Integrator
  extends RungeKuttaFehlbergIntegrator {

  private static final String methodName = "Dormand-Prince 5(4)";

  private static final double[] c = {
    1.0/5.0, 3.0/10.0, 4.0/5.0, 8.0/9.0, 1.0, 1.0
  };

  private static final double[][] a = {
    {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}
  };

  private static final double[] b = {
    35.0/384.0, 0.0, 500.0/1113.0, 125.0/192.0, -2187.0/6784.0, 11.0/84.0, 0.0
  };

  private static final double e1 =     71.0 / 57600.0;
  private static final double e3 =    -71.0 / 16695.0;
  private static final double e4 =     71.0 / 1920.0;
  private static final double e5 = -17253.0 / 339200.0;
  private static final double e6 =     22.0 / 525.0;
  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, c, a, b, 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, c, a, b, 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);

  }

}