Using MATLAB, develop an M-file to determine LU factorization of a square matrix

Question

Using MATLAB, develop an M-file to determine LU factorization of a square matrix with partial pivoting. That is, develop a function called mylu that is passed the square matrix [A] and returns the triangular matrices [L] and [U] and the permutation P. You are not to use MATLAB built-in function lu in your codes. Test your function by using it to solve a system of equations listed below in part 3. Confirm that your function is working properly by verifying that [L][U]=P[A] and by using the MATLAB built-in function lu.

Explanation / Answer

function [L,U,P]=mylu(A)
% LU factorization with partial (row) pivoting

n=size(A,1);
L=eye(n); P=L; U=A;
for k=1:n
[pivot,m]=max(abs(U(k:n,k)));
m=m+k-1;
if m~=k
% interchange rows m and k in U
temp=U(k,:);
U(k,:)=U(m,:);
U(m,:)=temp;
% interchange rows m and k in P
temp=P(k,:);
P(k,:)=P(m,:);
P(m,:)=temp;
if k >= 2
temp=L(k,1:k-1);
L(k,1:k-1)=L(m,1:k-1);
L(m,1:k-1)=temp;
end
end
for j=k+1:n
L(j,k)=U(j,k)/U(k,k);
U(j,:)=U(j,:)-L(j,k)*U(k,:);
end
end

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