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BLAS is short for "Basic Linear Algebra Subprograms". It is a famous collection of routines for doing linear algebra. I just know from Oleksandr R. that mma can directly call BLAS under the context "LinearAlgebra`BLAS". I don't know why mma makes it undocumented.

Oleksandr R. provide an example of using GER

$$ \mathrm{GER}: \alpha, \vec{x}, \vec{y}, \mathbf{A} : \mathbf{A} \leftarrow \alpha \vec{x} {\vec{y}}^\mathrm{T} + \mathbf{A} $$

like this 

A = RandomReal[1., {40000000, 2}];
alpha = 1.;
x = ConstantArray[1., Length[A]];
y = {1., 2.};
LinearAlgebra`BLAS`GER[alpha, x, y, A]; // AbsoluteTiming

to achieve the same result of

Transpose[{1., 2.} + Transpose@A]; // AbsoluteTiming

Oleksandr R.'s timing shows that BLAS approach is faster. While strangely, on my computer, I tried many times BLAS is much slower than double transpose with mma 10.3, windows system.

enter image description here

I also tried it on an HPC with linux version mma 10.3 installed

enter image description here

At this moment, it seems that maybe it is the problem of windows version 10.3. But after I tried on my friend's computer, I know it is not. Here is timing on his computer, also windows system

enter image description here

So what is wrong, how to explain this? My cpu is Intel Core i3-4500U, and 64 bit win8 system. My memory is 8GB, and there is 1.2GB for ramdisk

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matheorem
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  • Try adding parentheses, e.g. (LinearAlgebra\BLAS`GER[alpha, x, y, A]; // AbsoluteTiming)to be sure you are not timing something else. Also keep in mind, as @OleksandrR mentioned, that it is not a fair comparison if you are overwritingA`. – ilian Nov 21 '15 at 17:00
  • Does your computer have an AMD processor? How about the HPC cluster? It seems unlikely, but perhaps this could explain it. – Oleksandr R. Nov 21 '15 at 21:10
  • @OleksandrR. Yeah, unlikely, both are intel – matheorem Nov 22 '15 at 00:50
  • @ilian Actually, I didn't see any significant different whether to add overwriting A or not. So I just omitted. And after all, this is apparently not the point. Since on my friend's computer, the code is exactly the same – matheorem Nov 22 '15 at 00:53
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    @matheorem In your Linux screenshot, the timing measured for In[1] definitely includes generating A which is not correct. As for the Windows difference, I haven't been able to reproduce it. Could you perhaps include the exact CPU models and the amount of RAM for both machines? I'd also suggest setting $HistoryLength=0 first. – ilian Nov 22 '15 at 01:12
  • @ilian You are right. I made a mistake in timing linux version. The new timing shows there is no problem on my HPC. So now, the only problem is my computer, I replaced my original timing according to your request, and add my cpu info at the end of my post. – matheorem Nov 22 '15 at 07:46
  • So far it looks like an unreproducible result (unreproducible by a site user other than the OP)... – Michael E2 Nov 24 '15 at 19:41
  • @MichaelE2 yeah, this is the strangest point, because I can reproduce it every time: ) even I reinstalled mathematica ... – matheorem Nov 25 '15 at 01:12

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