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Non-square Matrix Transpose


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!




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2 Replies

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


Hi Gennady,


Thanks for your reply. The transpositions I am performing are related to the dimension lifted transposition as seen in Henretty et al ( 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,&aux,NV,&auxt, VECLEN);



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





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.