disp ('                This is the code of LU  method.Is writen by Ali Ashouri')
disp (' ')
disp (' ')
disp ('    ********Before enter anything read all of introduction that will write. read all of them*******')
disp (' ')
format long
disp (' ')
n=input('   enter (n) the number of array of matrix (n*n)  :');
disp('     enter the data of matrix: from left to right then up to down ');
A=cell(n,n);
x=cell(n,1);
y=cell(n,1);
B=cell(n,1);
L=cell(n,n);
U=cell(n,n);
for i=1:n
    x(i,1)={0};
    y(i,1)={0};
end;
disp(' The Matrix B is :')
for i=1:n
        b=input('the number for B: ');
        B(i,1)={b};
end;
disp(' ')
disp('  The Matrix of B is : ')
disp(B);
for i=1:n
    for j=1:n
        b=input('the number A : ');
        A(i,j)={b};
    end;
end;
tic
W=A;
disp(' ')
disp('  The Matrix of A is : ')
disp(A);
for i=1:n-1
    for j=i+1:n
        g=-cell2mat(W(j,i))./cell2mat(W(i,i));
        if g==0
        else
            for t=i:n
                W(j,t)={cell2mat(W(i,t))*g+cell2mat(W(j,t))};
            end;
        end;
    end;
end;
for i=1:n
    for j=1:n
        if abs(cell2mat(W(i,j)))<0.000009
            W(i,j)={0};
        end;
    end;
end;
for i=1:n
    for j=1:n
        if abs(cell2mat(W(i,j)))<0.00009
            W(i,j)={0};
        end;
    end;
end;
disp(' ')
disp('  The Matrix of U is : ')
disp(cell2mat(W))
U=W;
for i=1:n-1
    for j=i+1:n
        L(i,j)={0};
    end;
end;
for i=2:n
    j=i;
    L(i,j)={1};
end;
j=1;
for i=1:n
    L(i,j)={(cell2mat(A(i,j)))./(cell2mat(U(1,1)))};
end
if n<3
else
    for i=3:n
        for j=2:i-1
            a=0;
            for k=1:j-1
                b=(cell2mat(L(i,k))).*(cell2mat(U(k,j)))+a;
                a=b;
            end;
            L(i,j)={(cell2mat(A(i,j))-a)./(cell2mat(U(j,j)))};
        end;
    end;
end;
disp('  The Matrix of L is : ')
disp(cell2mat(L));
for j=1:n
    g=cell2mat(L(j,j));
    m=0;
    for t=1:j-1
        m=m+cell2mat(L(j,t))*cell2mat(y(t,1));
    end;
    if g==0
    else
        y(j,1)={(cell2mat(B(j,1))-m)/g};
    end;
end;
disp(' ')
disp(' ')
disp(' The values of y are : ')
for i=1:+1:n;
    q=cell2mat(y(i,1));
    disp(['   ',num2str(q)]);
end;
for j=n:-1:1
    g=cell2mat(U(j,j));
    m=0;
    for t=j+1:+1:n
        m=m+cell2mat(U(j,t))*cell2mat(x(t,1));
    end;
    if g==0
    else
        x(j,1)={(cell2mat(y(j,1))-m)/g};
    end;
end;
disp(' ')
disp(' ')
disp(' The values of x are : ')
for i=1:+1:n;
    q=cell2mat(x(i,1));
    disp(['  ',num2str(q)]);
end;
disp(' ')
disp(' ')
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