LU decomposition with partial pivoting Matlab

Question

I am trying to implement my own LU decomposition with partial pivoting. My code is below and apparently is working fine, but for some matrices it gives different results when comparing with the built-in `[L, U, P] = lu(A)` function in matlab Can anyone spot where is it wrong? ``` function [L, U, P] = lu_decomposition_pivot(A) n = size(A,1); Ak = A; L = zeros(n); U = zeros(n); P = eye(n); for k = 1:n-1 for i = k+1:n [~,r] = max(abs(Ak(:,k))); Ak([k r],:) = Ak([r k],:); P([k r],:) = P([r k],:); L(i,k) = Ak(i,k) / Ak(k,k); for j = k+1:n U(k,j-1) = Ak(k,j-1); Ak(i,j) = Ak(i,j) - L(i,k)*Ak(k,j); end end end L(1:n+1:end) = 1; U(:,end) = Ak(:,end); return ``` Here are the two matrices I've tested with. The first one is correct, whereas the second has some elements inverted. ``` A = [1 2 0; 2 4 8; 3 -1 2]; A = [0.8443 0.1707 0.3111; 0.1948 0.2277 0.9234; 0.2259 0.4357 0.4302]; ``` UPDATE I have checked my code and corrected some bugs, but still there's something missing with the partial pivot…

Accepted Answer

I forgot that If there was a swap in matrix P I had to swap also the matrix L. So just add the next line after after swapping P and everything will work excellent.

```
L([k r],:) = L([r k],:);
```

LU decomposition with partial pivoting Matlab

Solution

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