/*
  Copyright � 1999 CERN - European Organization for Nuclear Research.
  Permission to use, copy, modify, distribute and sell this software and its documentation for any purpose 
  is hereby granted without fee, provided that the above copyright notice appear in all copies and 
  that both that copyright notice and this permission notice appear in supporting documentation. 
  CERN makes no representations about the suitability of this software for any purpose. 
  It is provided "as is" without expressed or implied warranty.
*/
package sim.util.distribution;
import ec.util.MersenneTwisterFast;

/**
 * Von Mises distribution.
 * <p>
 * Valid parameter ranges: <tt>k &gt; 0</tt>.
 * <p>
 * Instance methods operate on a user supplied uniform random number generator; they are unsynchronized.
 * <dt>
 * Static methods operate on a default uniform random number generator; they are synchronized.
 * <p>
 * <b>Implementation:</b> 
 * <dt>
 * Method: Acceptance Rejection.
 * <dt>
 * This is a port of <tt>mwc.c</tt> from the <A HREF="http://www.cis.tu-graz.ac.at/stat/stadl/random.html">C-RAND / WIN-RAND</A> library.
 * C-RAND's implementation, in turn, is based upon
 * <p>
 * D.J. Best, N.I. Fisher (1979): Efficient simulation of the von Mises distribution, Appl. Statist. 28, 152-157.
 *
 * @author wolfgang.hoschek@cern.ch
 * @version 1.0, 09/24/99
 */
public class VonMises extends AbstractContinousDistribution {
    protected double my_k;

    // cached vars for method nextDouble(a) (for performance only)
    private double k_set = -1.0;
    private double tau,rho,r;

/**
 * Constructs a Von Mises distribution.
 * Example: k=1.0.
 * @throws IllegalArgumentException if <tt>k &lt;= 0.0</tt>.
 */
    public VonMises(double freedom, MersenneTwisterFast randomGenerator) {
        setRandomGenerator(randomGenerator);
        setState(freedom);
        }
/**
 * Returns a random number from the distribution.
 */
    public double nextDouble() {
        return nextDouble(this.my_k);
        }
/**
 * Returns a random number from the distribution; bypasses the internal state.
 * @throws IllegalArgumentException if <tt>k &lt;= 0.0</tt>.
 */
    public double nextDouble(double k) {
/******************************************************************
 *                                                                *
 *         Von Mises Distribution - Acceptance Rejection          *
 *                                                                *
 ******************************************************************
 *                                                                *
 * FUNCTION :  - mwc samples a random number from the von Mises   *
 *               distribution ( -Pi <= x <= Pi) with parameter    *
 *               k > 0  via  rejection from the wrapped Cauchy    *
 *               distibution.                                     *
 * REFERENCE:  - D.J. Best, N.I. Fisher (1979): Efficient         *
 *               simulation of the von Mises distribution,        *
 *               Appl. Statist. 28, 152-157.                      *
 * SUBPROGRAM: - drand(seed) ... (0,1)-Uniform generator with     *
 *               unsigned long integer *seed.                     *
 *                                                                *
 * Implemented by F. Niederl, August 1992                         *
 ******************************************************************/
        double u,v,w,c,z;

        if (k<=0.0) throw new IllegalArgumentException();
        
        if (k_set!=k) {                                               // SET-UP
            tau = 1.0 + Math.sqrt(1.0 + 4.0*k*k);
            rho = (tau-Math.sqrt(2.0*tau)) / (2.0*k);
            r = (1.0+rho*rho) / (2.0*rho);
            k_set = k;
            }

        // GENERATOR 
        do {  
            u = randomGenerator.nextDouble();                                // U(0/1) 
            v = randomGenerator.nextDouble();                                // U(0/1) 
            z = Math.cos(Math.PI * u);
            w = (1.0+r*z) / (r+z);
            c = k*(r-w);
            } while ((c*(2.0-c) < v) && (Math.log(c/v)+1.0 < c));         // Acceptance/Rejection 
                
        return (randomGenerator.nextDouble() > 0.5)? Math.acos(w): -Math.acos(w);        // Random sign //
        // 0 <= x <= Pi : -Pi <= x <= 0 //
        }
/**
 * Sets the distribution parameter.
 * @throws IllegalArgumentException if <tt>k &lt;= 0.0</tt>.
 */
    public void setState(double k) {
        if (k<=0.0) throw new IllegalArgumentException();
        this.my_k = k;
        }
/**
 * Returns a String representation of the receiver.
 */
    public String toString() {
        return this.getClass().getName()+"("+my_k+")";
        }
    }
