Adding Permutation Matrix Into LU Factorization

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Kyle Fertig 2017-12-3

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https://ww2.mathworks.cn/matlabcentral/answers/370777-adding-permutation-matrix-into-lu-factorization

Hello, I am working to create a function to do LU Factorization with partial pivoting. Through watching some videos, I created the code below, but I forgot to make the code return the permutation matrix and am having trouble adding it into the code. Any help with this would be greatly appreciated!

Thanks,

-Kyle

 function f = mylu(A,b)
    %%LU Decomposition
    %Get Augmented Matrix
    Ab=[A,b]
    n = length(A);
    L = eye(n);
    P=eye(n)
    %With A(1,1) as pivot Element
    %Row exchange to make sure A(1,1) is the last in Column
    col1=Ab(:,1);
    [temp,idx] = max(col1);
    temp = Ab(1,:);
    Ab(1,:) = Ab(idx,:);
    Ab(idx,:) = temp;
    %Computation in the pivot column
    for i=2:3;
        alpha = Ab(i,1) / Ab(1,1);
        L(i,1) = alpha;
        Ab(i,:) = Ab(i,:) - alpha*Ab(1,:);
    end
    %With A(2,2) as pivot Element
    %Row exchange to ensure A(2,2) is the largest in column 2
    col2 = Ab(2:end,2);
    [temp,idx] = max(col2);
    temp = Ab(2,:);
    Ab(2,:) = Ab(idx,:);
    Ab(idx,:) = temp;
    for i=3;
        alpha = Ab(i,2) / Ab(2,2);
        L(i,2) = alpha
        Ab(i,:) = Ab(i,:) - alpha*Ab(2,:);
    end
    U=Ab(1:n,1:n)
end