I am working on a custom LU decomposition function in MATLAB, aiming to optimize it for handling large matrices and frequent function calls. My current implementation uses a loop to perform the decomposition, but I’m looking for ways to optimize this process, possibly by eliminating or vectorizing the outer loop to enhance performance.
Here is the current implementation of the function:
function [L, U] = lu_factor(A)
n = size(A, 1);
L = eye(n);
U = A;
for k = 1:n-1
L(k+1:n, k) = U(k+1:n, k) / U(k, k);
U(k+1:n, k:n) = U(k+1:n, k:n) - L(k+1:n, k) * U(k, k:n);
end
end
Key Points:
- I am aware of MATLAB’s built-in
lu
function. However, understanding and optimizing this form of the algorithm has broader implications for other similar tasks I am working on, so I am focusing on manual implementations. - My function works correctly, but performance degrades significantly with larger matrices and frequent calls.
- Post-MATLAB 2016, I understand
bsxfun
is no longer necessary due to automatic broadcasting. I attempted to utilize vectorization to optimize the loop but have struggled to remove or optimize the outer loop effectively. - Ideally, I would like to keep this as a MATLAB-native solution without resorting to MEX or other external optimizations.
Questions:
- Are there MATLAB-specific techniques or best practices that could be employed to optimize such a loop for larger-scale problems?
- How can one effectively vectorize or possibly eliminate the outer loop in the LU decomposition algorithm to improve performance?
Any guidance or suggestions on how to approach this would be greatly appreciated!
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