Using Matlab, Write a function MYLU to perform LU factorization for an arbitrary

Question

Using Matlab, Write a function MYLU to perform LU factorization for an arbitrary n×n matrix (under the assumption that elimination can be performed without row exchanges). Run the function on the input (Please base the code off of the templet shown below)

Thanks

% MYLU-The function in this m-file computes an LU factorization % of an n x n matrix under the assumption that elimination can be % performed without row exchanges. % Input: n x n matrix A. % Output: lower triangular matrix L and upper triangular matrix U. function [L,U] = MYLU (A) n = L = U % Get the row or column dimension of A. % Initialize L. % Initialize U. % Perform elimination. % The nested for loops fix a column first, and then go to each row. for j= % Span certain columns of A. for i= % span certain rows of A. L( ) = U ) = % Do not forget the semicolons here % to suppress intermediate output! end end end

Explanation / Answer

function [L, U, P] = myLU4(A)

%A must be square

%get size of input matrix
sizeofA=size(A);
n=sizeofA(1);

%instantiate L, P, U
L=eye(n);
P=eye(n);
U=A;

% process
for i=1:n
  
    %Row Reduction
    if U(i,i) == 0
        maxofU = max(abs(U(i:end,1)));
        for j=1:n
            if maxofU == abs(U(j,i))
                temp = U(1,:);
                U(1,:) = U(j,:);
                U(j,:) = temp;
              
                temp = P(:,1);
                P(1,i) = P(j,:);
                P(j,:) = temp;
            end
        end
    end
  
    if U(i,i) ~=1
        temp = eye(n);
        temp(i,i)=U(i,i);
        L=L*temp;
        U(i,:) = U(i,:)/U(i,i); %Ensure pivots are 1
    end
  
    if i~=n
      
        for k=i+1:length(U)
            temp = eye(n);
            temp(k,i) = U(k,i);
            L=L*temp;
            U(k,:)=U(k,:)-U(k,i)*U(i,:);
        end
    end
end

P = P';
end

Related Questions

Navigate

• Browse (All)
• Browse U
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.