/* sat1.c   Simple experiments with simulated annealing   find the minumum of a function, there are two examples here   one uses a simple cost function, the other imposes range constraints   by making illegal values very costly*/static char rcsid[] = "@(#)sat1.c	1.1 09:47:16 10/30/92   EFC";#include <stdio.h>#include <math.h>#include <float.h>#include "sa.h"#ifndef HUGE#define HUGE     HUGE_VAL#endif/* use ONE or the other *//* #include <rands.h> */#include <r250.h>#ifdef _R250_H_#define uniform(a,b)    ( a + (b - a) * dr250() )#endif/* Define ONE of the following *//* #define EXAMPLE_1 */#define EXAMPLE_2/* #define MELT_ONLY  *//* #define EQUIL_ONLY	*/#define MAXIT 400float lambda = 0.1;		/* derivative weight factor */float func(float*), f(float), fprime(float), newton(float);void main(int argc, char **argv){	int i;	float y, t0, t, xbest, ybest;	float x[1], x_init;		if ( SAInit(func,1) == 0 )        {        	fprintf(stderr,"trouble initializing in SAInit\n");                exit(1);        }	xbest = x[0] = uniform(-1.0, 1.0);	ybest = y = func( x );	fprintf(stderr,"Boltzman constant: %f\tlearning rate:%f\n",        		SABoltzmann( NO_VALUE ), SAlearning_rate( NO_VALUE ) );	SAinitial(x);		/* set initial condition */	SAmelt( NO_VALUE );		/* melt the system  */#ifndef MELT_ONLY	/* make it a bit warmer than melting temperature */	t0 = 1.2 * SAtemperature( NO_VALUE );	SAtemperature( t0 );		x_init = x[0];#ifndef EQUIL_ONLY		t = SAanneal( MAXIT );	SAoptimum( x );#endif#endif	fprintf(stderr,"Initial temperature: %f\tfinal temperature: %f\n", t0, t);	fprintf(stderr,"Estimated minumum at: %f\n", x[0]);        fprintf(stderr,"\tf(%f) = %f\tf'(%f) = %g\n", x[0], f(x[0]), x[0],		fprime(x[0]) );	y = newton( x[0] );  fprintf(stderr,"newton (%f) = %g\nf(%f) = %g, fprime(%f) = %g\nnewton(%f) = %g\n",			x[0], y, y, f(y), y, fprime( y ), x[0], newton( x[0] ) );						}#ifdef EXAMPLE_1float func(float* x)		/* the cost function */{	return f(x[0]) + lambda * fabs( fprime(x[0]) );}float f(float x)		/* the function to minimize */{	float fret;	fret = (x + 0.2 ) * x + cos( 14.5 * x - 0.3 );	return fret;}float fprime(float x){	float f;	f = 0.2 + 2 * x - 14.5 * sin( 14.5 * x - 0.3 );	return f;}float newton(float x)		/* estimate minimum near x */{	int iter;	float fpp;	for (iter = 0; iter < 50; iter++)	{		fpp = 2.0 - 210.25 * cos( 14.5 * x - 0.3 );		if (fpp == 0.0)			break;		x -= fprime(x) / fpp;	}	return x;}#endif#ifdef EXAMPLE_2float func(float* x)		/* the cost function with constraints */{	if ( x[0] < -2.0 || x[0] > 2.0)        	return HUGE;                	return f(x[0]) + lambda * fabs( fprime(x[0]) );}float f(float x)		/* the function to minimize */{	float fret;	fret = ( (3.0 * x + 5.0 ) * x - 2.0) * x + 3.0;	return fret;}float fprime(float x){	float f;	f = (9 * x + 10 ) * x - 2;	return f;}float newton(float x)		/* estimate minimum near x */{	int iter;	float fpp;	for (iter = 0; iter < 50; iter++)	{		fpp = 18 * x + 10;		if (fpp == 0.0)			break;		x -= fprime(x) / fpp;	}	return x;}#endif