Question

Finish the following M-file. Run your function on the same matrix A as given in the lab.

% LU4 - The function in this M-file computes an LU factorization

% of a 4 x 4 matrix under the assumption that elimination can be

% performed without row exchanges. % Input: 4 x 4 matrix A;

% Output: lower triangular matrix L and upper triangular matrix U.

function [L,U] = LU4(A)

L = eye(4);

U = A;

for j= ...

for i= ...

L(...) = ...; % Do not forget the semicolons here

U(...) = ...; % to suppress intermediate output!

end

end

end

Answer 1

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