/*-------------------------------------------------------------
Copyright (C) 2000 Peter Clote. 
All Rights Reserved.

Permission to use, copy, modify, and distribute this
software and its documentation for NON-COMMERCIAL purposes
and without fee is hereby granted provided that this
copyright notice appears in all copies.


THE AUTHOR AND PUBLISHER MAKE NO REPRESENTATIONS OR
WARRANTIES ABOUT THE SUITABILITY OF THE SOFTWARE, EITHER
EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE
IMPLIED WARRANTIES OF MERCHANTABILITY, FITNESS FOR A
PARTICULAR PURPOSE, OR NON-INFRINGEMENT. THE AUTHORS
AND PUBLISHER SHALL NOT BE LIABLE FOR ANY DAMAGES SUFFERED
BY LICENSEE AS A RESULT OF USING, MODIFYING OR DISTRIBUTING
THIS SOFTWARE OR ITS DERIVATIVES.

-------------------------------------------------------------*/


/******************************************

	Program: gradientDescent.c
	P. Clote, 12 Feb 1997

	Assume 2N coin flips where outcome is
	10101010 ... 10
	L(p) = p^N (1-p)^N
	E = -log L(p)
	  = - N log p - N log(1-p)

	Want 
	\delta p = - k dE/dp
	         = - k ( - N/p + N/(1-p) )
                 = k (N/p - N/(1-p))

	USAGE: gradientDecent <k>
        k is the constant for delta p, e.g. k=0.00001 yields convergence

******************************************/

#include <stdio.h>
#include <stdlib.h>
#define N 20 	  	/*  2N coin flips */



main(int argc, char *argv[])
{
	float p = 0.001;	/* initial probability */
	float deltaP;		/* delta p */
	float k;   		/* constant in gradient descent, eg 0.01 */
	int i,n=0;		/* count number of iterations */
	float grad;             /* gradient */
	
	/********** check of input errors ***********/
	if (argc != 2)
		{
	     	fprintf(stderr,"%s float.\n",argv[0]);
		exit(1);
		}
	k = atof(argv[1]);

	/********** repeatedly update value of p ********/

	do
	{
		for (i=0;i<50;i++)
			{
			  grad = ((float)N)/p - ((float) N)/(1-p);
			  deltaP = k * grad;
			  //printf("n:%d p:%f grad:%f\n",n,p,grad);
			  p = p + deltaP;
			  n++;
			}
		printf("n = %d\t p = %2.4f\n",n,p);
	}
	while ( getchar() != 'q' );
}