LU_Doolittle.m

clc;
clear;
fprintf('\n');
n=input('Enter the dimension of the square matrix : ');
a=input('Enter the entries the matrix rowwise: ');
L=diag(ones(n,1));
U=zeros(n);
fprintf("Given matrix is: \n");
disp(a);
z=0;
% Step-1
if a(1,1)==0
    fprintf("Factorization is not possible. \n");
else
    U(1,1)=a(1,1);
    for j=2:n
        % Step-2
        U(1,j)=a(1,j)/L(1,1);
        L(j,1)=a(j,1)/U(1,1);
    end
    % Step-3
    for i=2:n-1
        % Step-4
        s=0;
        for k=1:i-1
            s=s+L(i,k)*U(k,i);
        end
        U(i,i)=(a(i,i)-s)/L(i,i);
        if U(i,i)==0
            z=1;
            fprintf("Factorization is not possible. \n");
        else
            % Step-5
            for j=i+1:n
                r=0;
                for k=1:i-1
                    r=r+L(i,k)*U(k,j);
                end
                U(i,j)=(a(i,j)-r)/L(i,i);
                t=0;
                for k=1:i-1
                    t=t+L(j,k)*U(k,i);
                end
                L(j,i)=(a(j,i)-t)/U(i,i);
            end
        end
        if z==0
            % Step-6
            w=0;
            for k=1:n-1
                w=w+L(n,k)*U(k,n);
            end
            U(n,n)=(a(n,n)-w)/L(n,n);
        end
    end
    if z==0
        fprintf("Dolittle's LU decomposition of the givem matrix is: \n\n");
        disp([L U]);
        % disp(L);
        % disp(U);
    end
end