4. (Partial Pivoting: MATLAB program) write a programa to find the LU partial pi

Question

4. (Partial Pivoting: MATLAB program) write a programa to find the LU partial pivoting. The program should return the updated matrix A and the pivot vector p. In MATLAB, name your file mylu.m, the first few lines of whi should be as follows: decomposition of a given n x n matrix A using function [a,p]-mylu(a) [n n]=size (a); p= (1 :n)'; (your code here !) The code above sets n equal to the dimension of the matrix and initializes the pivot vector p. Make sure to store the multipliers my in the proper matrix en- tries. For more help on function m-files see pages 9-13 of the MATLAB Primer by Kermit Sigmon available from the course webpage. You should experiment with a few small matrices to make sure your code is correct. Check if matrices resulting in LU decomposition satisfy PA LU. As a test of your code, in MATLAB execute the statements >diary mylu.txt >>format short e >type mylu.m >>a-t2 2-3:3 1-2:6 8 1); >>[a,pl-mylu(a) >>diary off Print and hand-in the text file containing your program.

Explanation / Answer

Matlab code

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function [a,P]=mylu(A)
% LU factorization with partial (row) pivoting
[n,n]=size(A);
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
    a=U;
    for i=2:n
        for j=1:i-1
            a(i,j)=L(i,j);
        end
    end
end

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