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copied!<p>Very interesting question! I have recently stumbled upon exactly such situation while answering <a href="https://stackoverflow.com/questions/12867524/matlab-calculation-on-subset-of-vector-then-shift-and-repeat/12872704#12872704">this</a> question. Consider the following code that computes indices of a sliding window of size 3 through a vector <code>a</code>:</p> <pre><code>a = rand(1e7,1); tic; idx = bsxfun(@plus, [0:2]', 1:numel(a)-2); toc % equivalent code from im2col function in MATLAB tic; idx0 = repmat([0:2]', 1, numel(a)-2); idx1 = repmat(1:numel(a)-2, 3, 1); idx2 = idx0+idx1; toc; isequal(idx, idx2) Elapsed time is 0.297987 seconds. Elapsed time is 0.501047 seconds. ans = 1 </code></pre> <p>In this case <code>bsxfun</code> is almost twice faster! It is useful and fast because it <strong>avoids explicit allocation of memory</strong> for matrices <code>idx0</code> and <code>idx1</code>, saving them to the memory, and then reading them again just to add them. Since memory bandwidth is a valuable asset and often the bottleneck on todays architectures, you want to use it wisely and decrease the memory requirements of your code to improve the performance.</p> <p><code>bsxfun</code> allows you to do just that: create a matrix based on applying an arbitrary operator to all pairs of elements of two vectors, instead of operating explicitly on two matrices obtained by replicating the vectors. That is <em>singleton expansion</em>. You can also think about it as the <strong>outer product</strong> from BLAS:</p> <pre><code>v1=[0:2]'; v2 = 1:numel(a)-2; tic; vout = v1*v2; toc Elapsed time is 0.309763 seconds. </code></pre> <p>You multiply two vectors to obtain a matrix. Just that the outer product only performs multiplication, and <code>bsxfun</code> can apply arbitrary operators. As a side note, it is very interesting to see that <code>bsxfun</code> is as fast as the BLAS outer product. And BLAS is usually considered to deliver <strong>the</strong> performance..</p> <p><strong>Edit</strong> Thanks to Dan's comment, here is a great <a href="http://blogs.mathworks.com/loren/2008/08/04/comparing-repmat-and-bsxfun-performance/" rel="nofollow noreferrer">article by Loren</a> discussing exactly that.</p>

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