Matlab matrix multiplication speed

Question

I was wondering how can matlab multiply two matrices so fast. When multiplying two NxN matrices, N^3 multiplications are performed. Even with the Strassen Algorithm it take

Answer 1

To check whether you do or not use multi-threading in MATLAB use this command

maxNumCompThreads(n)

This sets the number of cores to use to n. Now I have a Core i7-2620M, which has a maximum frequency of 2.7GHz, but it also has a turbo mode with 3.4GHz. The CPU has two cores. Let's see:

A = rand(5000);
B = rand(5000);
maxNumCompThreads(1);
tic; C=A*B; toc
Elapsed time is 10.167093 seconds.

maxNumCompThreads(2);
tic; C=A*B; toc
Elapsed time is 5.864663 seconds.

So there is multi-threading.

Let's look at the single CPU results. A*B executes approximately 5000^3 multiplications and additions. So the performance of single-threaded code is

5000^3*2/10.8 = 23 GFLOP/s

Now the CPU. 3.4 GHz, and Sandy Bridge can do maximum 8 FLOPs per cycle with AVX:

3.4 [Ginstructions/second] * 8 [FLOPs/instruction] = 27.2 GFLOP/s peak performance

So single core performance is around 85% peak, which is to be expected for this problem.

You really need to look deeply into the capabilities of your CPU to get accurate performannce estimates.