Sparse matrix-vector product: much more slow than Matlab

General Usage Performance
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  1. Please quote your code so that it’s easy to read: PSA: how to quote code with backticks
  2. semicolons at the end of each line are not necessary
  3. When benchmarking code, you will not get accurate results when timing in global scope. That’s why @StefanKarpinski asked you earlier. Instead, put the code you’re timing in a function. Running your code in a function, I see 3.699408 seconds (41.60 k allocations: 3.787 GiB, 5.39% gc time) which is already quite close to what you reported MATLAB as giving.

You are seeing a lot of allocations because your code really does allocate a lot of memory. In particular, you are constructing new matrices to hold a lot of intermediate quantities. Modifying your code to pre-allocate those matrices may help a lot. One easy improvement is to broadcast the first line in your loop to avoid allocating a matrix for (sparseR + reshape(q' * sparseS, 199, 199)) and then another one for 0.5 * 0.05 * (sparseR + reshape(q' * sparseS, 199, 199)):

tmp = 0.5 .* 0.05 .* (sparseR .+ reshape(q' * sparseS, 199, 199))
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