How to improve speed of execution for huge matrix multiplication ?

Question

Edouard Sergent 2016-9-12

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https://ww2.mathworks.cn/matlabcentral/answers/302740-how-to-improve-speed-of-execution-for-huge-matrix-multiplication

回答： Farouk Moukaddem 2016-9-19

Hi everyone, I am currently working on a neural project in which I need to handle a lot of data. The goal is to minimize this function :

Variables : N = 10 000 000 C = 500 A = vecteur (100, 1) W = matrice (100,100) B = vecteur (100,1)

The problem is that I can't optimize directly this function. Indeed, even if I can make the multiplication in 1e-6s, I would need 500*10000000=5e3s for one step. Thus, I have to vectorize the problem, which is possible in this case. Instead of having a matrix A (100,1), I can transform it to A (100,10000000). The function to minimize become :

If A is a matrix of singles (100,10000000), it means there are 1e9 elements. Each element is coded on 4 bytes. To store this kind of matrix, I would need 4GB of RAM.

Of course, my computer (6GB, 4cores) is not going to handle this type of problem so I thought about cloud computing. I think I should benefit from multiple cores computer (~30) with a big amount of RAM (~200 GB) to parallelize the execution of the function. Do you think I am doing it the right way or should I use GPU calculation instead for example ? If you have any suggestions, please let me know. Thanks in advance.