steep1.c~

c code for steepest decent method

#include<stdio.h>
#include<math.h>
#include<stdlib.h>

#define N 1000 /* ITERATIONS */    
	double  grad1,grad2,grad3;
double gradient (double x1,double x2,double x3,int i);
double main_function(double a,double x1,double grad1,double x2,double grad2,double x3,double grad3);
double alfa(double x1,double grad1,double x2,double grad2,double x3,double grad3);


double alfa(double x1,double grad1,double x2,double grad2,double x3,double grad3)
{
        double a[100], b[100], fxa, fxb, minimum;
        int i=0;
        a[0]=-10;
	b[0]=10;
        
        do{       
                   i++;
        
		   a[i] = a[i-1]+0.3819*(b[i-1]-a[i-1]);
                   b[i] = b[i-1]-0.3819*(b[i-1]-a[i-1]);

		 fxa = main_function(a[i],x1,grad1,x2,grad2,x3,grad3);
                 fxb = main_function(b[i],x1,grad1,x2,grad2,x3,grad3);

        	if(fxa < fxb){

	                    a[i]=a[i-1];    b[i]=b[i];
                            if(fabs(b[i]-a[i]) < 0.0000001){
                            	minimum=a[i];
			   	break;
			    	}
                }
	        else{    
		            a[i] = a[i]; b[i]=b[i-1];
              
                            if(fabs(b[i]-a[i]) < 0.0000001){
                            	minimum=b[i];
			    	break;
			    	}

                }
    }
       while(fabs(b[i]-a[i]) > 0.0000001);
       printf("Alfa =%lf\n", minimum);
       return minimum;
}

double main_function(double a,double x1,double grad1,double x2,double grad2,double x3,double grad3)
{
        double s = x1 -a*grad1 - 4;
        double t = x2 -a*grad2 - 3;
        double u = x3 -a*grad3 + 5;
        return (pow(s,4) + pow(t,2) + 4*pow(u,4));
}

double gradient(double x1,double x2,double x3, int i)
{
	if (i == 0)  {
	  return (4*pow((x1- 4),3));
	}else if (i == 1) { 
	  return (2*(pow((x2-3),1)));
	}else if (i ==  2) {
	  return (16*pow((x3+5),3));
	}
	return i;
}

int main (int argc,char*argv[])
{
	double a;    /* ALFA*/
	int i,j, k;
	double x[N][3];
	double eps = 0.0001;
	double grad[3];
	if (argc != 3+1) {
		printf("Please enter the initial 3 guesses.\n");
		exit(0);
	}	
	for (i=0;i<1;i++) {
		for (j=0;j<=(2);j++) {
		       sscanf(argv[j+1],"%lf",&x[i][j]);
			printf("\nThe intial guess x[%d][%d] is %lf",i,j,x[i][j]);
		}
	}

	printf("\n");
	j = 0;
	for (i=0; i<=N;i++) {
	       for(k=0;k<=2;k++){

	                         grad[k]= gradient ((x[i][j]),(x[i][j+1]),(x[i][j+2]),k);
	        }
	          
             
			a = alfa(x[i][j],grad[0],x[i][j+1],grad[1],x[i][j+2],grad[2]);

			printf("%lf\t%lf\t%lf\t\n",grad[0],grad[1],grad[2]);
		
			x[i+1][j]   = x[i][j]   - a * grad[0];
			x[i+1][j+1] = x[i][j+1] - a * grad[1];
			x[i+1][j+2] = x[i][j+2] - a * grad[2];

			printf("\nx[%d][%d]:%lf\t,x[%d][%d]:%lf\t,x[%d][%d]:%lf\n",i+1,j+1,(x[i+1][j]),i+1,j+2,(x[i+1][j+1]),i+1,j+3,(x[i+1][j+2]));
			
			if (fabs(x[i+1][j] - x[i][j]) < eps && fabs(x[i+1][j+1] - x[i][j+1]) < eps && fabs(x[i+1][j+2] - x[i][j+2]) < eps) {
				printf("\nx1: %lf\t,x2: %lf\t,x3: %lf\n",(x[i][j]),(x[i][j+1]),(x[i][j+2]));
				exit(0);						
			}
		}
	
	return 0;
}