Vectorization: friend or foe? bsxfun/arrayfun to avoid loops, repmat, permute, squeeze, etc

Question

This question is related to this question and probably to this other as well. Suppose you have two matrices A and B. A is M-by-N and B is N-by-K. I want to obtain an M-by-K matrix C such that `C(i, j) = 1 - prod(1 - A(i, :)' .* B(:, j))`. I have tried some solutions in Matlab - I am here comparing their computation performance. ``` % Size of matrices: M = 4e3; N = 5e2; K = 5e1; GG = 50; % GG instances rntm1 = zeros(GG, 1); % running time of first algorithm rntm2 = zeros(GG, 1); % running time of second algorithm rntm3 = zeros(GG, 1); % running time of third algorithm rntm4 = zeros(GG, 1); % running time of fourth algorithm rntm5 = zeros(GG, 1); % running time of fifth algorithm for gg = 1:GG A = rand(M, N); % M-by-N matrix of random numbers A = A ./ repmat(sum(A, 2), 1, N); % M-by-N matrix of probabilities (?) B = rand(N, K); % N-by-K matrix of random numbers B = B ./ repmat(sum(B), N, 1); % N-by-K matrix of probabilities (?) %% First solution % One-liner solution: tic C = squeeze(1 -…

Accepted Answer

You can get a minor performance gain with `bsxfun`:

```
E = zeros(M, K);
for hh = 1:M
  E(hh, :) = 1 - prod((1 - bsxfun(@times, A(hh,:)', B)), 1);
end
```

And you could squeeze (pun intended) a tiny bit more performance with this:

```
E = squeeze(1 - prod((1-bsxfun(@times, permute(B, [3 1 2]), A)),2));
```

Or you could try pre-compute the transpose for my first suggestion:

```
E = zeros(M, K);
At = A';
for hh = 1:M
  E(hh, :) = 1 - prod((1 - bsxfun(@times, At(:,hh), B)), 1);
end
```

Vectorization: friend or foe? bsxfun/arrayfun to avoid loops, repmat, permute, squeeze, etc

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