Dear Julia users, I am trying to set up the normal equations ( https://en.wikipedia.org/wiki/Linear_least_squares ) which means constructing X'X and X'y in (X'X+\lambda M) w = X'y where M is SPD, and in my case, each row of X is a Kronecker product of two matrices, i.e.: X_{i,:}=A_{i,:} \otimes…

[image] Germinator: Note that batchSize = 10000; means that in the current example, you would first form the whole X matrix and then compute X’X and X’y in two separate steps. In practice, I have been considering batchSize = 10000; when N≈10^7. So your requirements are N around 10^7, but R an…

Well, the assertions are not correct, because it is just referring to the same array: normal!(C,Cx,x,A,B_r); CxNormal = Cx # CxNormal is just the same array as Cx normalTurbo!(C,Cx,x,A,B); @assert Cx ≈ CxNormal # this will always be true it should be CxNormal = copy(Cx). Also, since the fun…

Sorry for the mistake. I tried to correct my post above. As far as I understand we have three different results: normal!, normalTurbo! and normalTturbo! computing the same 3.404 s (20004 allocations: 5.81 MiB) 1.184 s (20004 allocations: 5.81 MiB) 1.179 s (20004 allocations: 5.81 MiB) n…

Sorry, I didn’t notice that before I replied. FWIW, I think that annotations far from their effect make such misinterpretations likely.

[image] goerch: Cx .= Cx .+ temp.*x[n] The temp here is transposed in some codes and not in others. That probably explains most of the differences in the results.

[image] lmiq: The temp here is transposed in some codes and not in others. That probably explains most of the differences in the results. Just added more validations: the problem seems to be more systematic, it also occurs with C

Thank you all for the inputs, apologies again for the sloppy code. @goerch @lmiq I fixed the source of different results. The results so far were identical under permutation due to calling kron(A,B) instead of kron(B,A). Also, the Matlab copy was missing broadcasting, which is actually needed. Below…

Hi @germinator , thanks for the updated MWE. We still have to discuss the difference in our results. These are my latest numbers for your consolidated MWE: 5.525 s (20001 allocations: 943.88 KiB) 1.204 s (20001 allocations: 943.88 KiB) 898.374 ms (30001 allocations: 1.07 MiB) 483.086 ms (4 …

Hi @goerch , thanks for your updates. I have the same versions of Tullio and LoopVectorization. (@v1.6) pkg> status Tullio Status `C:\Users\LocalAdmin\.julia\environments\v1.6\Project.toml` [bc48ee85] Tullio v0.3.2 (@v1.6) pkg> status LoopVectorization Status `C:\Users\LocalAdmin\.ju…

[image] Germinator: Now when it comes to the results: could it be simply due to the fact that you are running Julia on 6 threads? Hence you perform better when using @tturbo and thus also @tullio. This would explain the similar scaling when using kron! and in the Matlab functions, and the faster…

Outperformed by Matlab

General Usage Performance

goerch November 17, 2021, 10:29pm 32

I started a thread about the inards of kron here.

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