Gauss-Seidel.c

#include <stdio.h>
#include <math.h>
#define ep 1e-9

double f1(double x2, double x3, double a11, double a12, double a13, double b1){
    return (b1-(a12*x2)-(a13*x3))/a11;
}

double f2(double x1, double x3, double a21, double a22, double a23, double b2){
    return (b2-(a21*x1)-(a23*x3))/a22;
}

double f3(double x1, double x2, double a31, double a32, double a33, double b3){
    return (b3-(a31*x1)-(a32*x2))/a33;
}


int main(void){
    double a11, a12, a13, b1, a21, a22, a23, b2, a31, a32, a33, b3;
    double x1_old, x2_old, x3_old, x1_new, x2_new, x3_new, e1, e2, e3, max_error;
    x1_old = x2_old = x3_old = 0.0;
    int itr=0;
   
    //input a11, a12, a13, b1
    scanf("%lf%lf%lf%lf",&a11,&a12,&a13,&b1);
    //input a21, a22, a23, b2
    scanf("%lf%lf%lf%lf",&a21,&a22,&a23,&b2);
    //input a31, a32, a33, b3
    scanf("%lf%lf%lf%lf",&a31,&a32,&a33,&b3);

    //check
    if((!(fabs(a11)>fabs(a12)+fabs(a13)) &&
        !(fabs(a22)>fabs(a21)+fabs(a23)) &&
        !(fabs(a33)>fabs(a31)+fabs(a33))))
    {
        printf("This is not valid for Jacobis iteration method!");
        return 0;
    }

    while(1){
        itr++;

        //Gauss-Seidel
        x1_new = f1(x2_old,x3_old, a11, a12, a13, b1);
        x2_new = f2(x1_new,x3_old, a21, a22, a23, b2);
        x3_new = f3(x1_new,x2_new, a31, a32, a33, b3);

        e1 = fabs(x1_old-x1_new);
        e2 = fabs(x2_old-x2_new);
        e3 = fabs(x3_old-x3_new);

        if(e1>e2 && e2>e1){
            max_error = e1;
        }
        else if(e2>e1 && e1>e3){
            max_error = e2;
        }
        else{
            max_error = e3;
        }

        x1_old = x1_new;
        x2_old = x2_new;
        x3_old = x3_new;

        if(max_error<ep)
            break;
    }

    printf("Total iteration: %d\n", itr);
    printf("Answer: x=%0.3lf, y=%0.3lf and z = %0.3lf\n",x1_new,x2_new,x3_new);

    return 0;
}