Non-square Matrix Transpose

[Ioan_Hadade]

Hi guys,

Are there any highly optimized MKL routines or maybe performance primitives that can do rectangle matrix transposition but without scaling?

I've been using mkl_omatcopy but it seems to perform worse than a normal baseline implementation and I suspect this is due to the additional scaling that is performed. I've attached a plot running a naive baseline implementation with comparison on omatcopy and imatcopy. The latter I know runs very poorly on non-square matrices. 

I just want to know whether I should start spending some time optimizing my own transpose routine with AVX/AVX2 and blocking or whether there's a very efficient one out there already. 

Also, swapping indices is not viable for what I am trying to achieve. 

Thank you in advance!

Ioan

[Gennady_F_Intel]

Ioan,  Could you give us M x N sizes instead of the # of elements? 

[Ioan_Hadade]

Hi Gennady,

Thanks for your reply. The transpositions I am performing are related to the dimension lifted transposition as seen in Henretty et al (http://repository.cmu.edu/cgi/viewcontent.cgi?article=1263&context=ece). Basically, it performs the required data layout organisation as to allow for aligned vector loads and stores of stencils in the x-direction path.

Anyway, I am basically transposing these large vectors into MxN arrays where N is always the SIMD register size which for this case is 4 as I am doing double precision. Therefore, on the graph, all matrix sizes will be MxN where M=no of element/veclen and N=veclen.

I guess this could be a cause for the poor performance due to gather and scatters? By the way, I am running this on a Xeon E5-2650 (Sandy Bridge).

The code looks something like this:

       // out of place MKL transposition

  
        mkl_domatcopy('r','t',VECLEN,NV,1,&q,NV,&qt,VECLEN);
 

        mkl_domatcopy('r','t',VECLEN,NV,1,&aux,NV,&auxt, VECLEN);

       roe_fluxes_xplane(); 

       // retranspose data back into original format for y-sweep of flucrd

        mkl_domatcopy('r','t',NV,VECLEN,1,&qt,VECLEN,&q,NV);

        mkl_domatcopy('r','t',NV,VECLEN,1,&auxt,VECLEN,&aux,NV);
 

So basically I need to transpose the data into the DLT format and then back again. Originally, the matrices will have a rectangle shape format, as they represent distinct blocks from a multiblock grid.

Thank you in advance for your kind consideration.