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copied!<p>If I understand amit's question, what you can do in Matlab is the following:</p> <p>Data:</p> <pre><code>M = 4e3; % M different cases N = 5e2; % N sources K = 5e1; % K targets 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 (?) </code></pre> <p>First solution</p> <pre><code>% One-liner solution: tic C = squeeze(1 - prod(1 - repmat(A, [1 1 K]) .* permute(repmat(B, [1 1 M]), [3 1 2]), 2)); toc % Elapsed time is 6.695364 seconds. </code></pre> <p>Second solution</p> <pre><code>% Partial vectorization 1 tic D = zeros(M, K); for hh = 1:M tmp = repmat(A(hh, :)', 1, K); D(hh, :) = 1 - prod((1 - tmp .* B), 1); end toc % Elapsed time is 0.686487 seconds. </code></pre> <p>Third solution</p> <pre><code>% Partial vectorization 2 tic E = zeros(M, K); for hh = 1:M for ii = 1:K E(hh, ii) = 1 - prod(1 - A(hh, :)' .* B(:, ii)); end end toc % Elapsed time is 2.003891 seconds. </code></pre> <p>Fourth solution</p> <pre><code>% No vectorization at all tic F = ones(M, K); for hh = 1:M for ii = 1:K for jj = 1:N F(hh, ii) = F(hh, ii) * prod(1 - A(hh, jj) .* B(jj, ii)); end F(hh, ii) = 1 - F(hh, ii); end end toc % Elapsed time is 19.201042 seconds. </code></pre> <p>The solutions are equivalent …</p> <pre><code>chck1 = C - D; chck2 = C - E; chck3 = C - F; figure plot(sort(chck1(:))) figure plot(sort(chck2(:))) figure plot(sort(chck3(:))) </code></pre> <p>… but apparently the approaches with partial vectorization, without repmat and permute, are more efficient in terms of memory and execution time.</p>

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