double sum = 0.0;
    //***** FINDING Z; LZ=b*********//
    for(i=0;i<n;i++)
    {                                        //forward subtitution method
        sum=0.0;
        for(p=0;p<i;p++)
            sum+=l[i][p]*z[p];
        z[i]=(b[i]-sum)/l[i][i];
    }

    //********** FINDING X; UX=Z***********//
    for(i=n-1;i>0;i--)
    {
        sum=0.0;
        for(p=n-1;p>i;p--) {
            sum+=u[i][p]*x[p];
        }
        x[i]=(z[i]-sum)/u[i][i];
    }

    for (int i = 0; i < n; i++) {
        if (x[i] < 1) {
            x[i] = 0.0;
        }
    }