Hi everybody,
For my research I will have to deal with extremely nonsquare matrices. That
is potentially 32*10 000, 4*80 000, or even 128*1 000 000.
This often occurs in statistics, where one has a few numbers of variables
in the first dimensions, and a significant number of samples in the other
dimension. This results in extremely non-square matrices, who do not hold
the samebehavior, both implementation-wise and algorithm wise
Consider I want to compute the covariance (let's forget the symmetry of the
resulting matrix for now) of 32 variables over 100 000 samples. An
implementation for square matrices would probably launch it on one single
result block/2-4 work groups (the result matrix is only 32*32). Indeed,
what we want here is not one work-group per block in the result matrix.
What we would want here would be more something like multiple matrix-vector
product. for each column of the result matrix. That way, if each
matrix-vector product launches on 32 work groups (one work group per row),
we get a much better occupancy.
For even more extreme case (4*100 000, think of 4 images of 100 000 pixel
each, for example), we might just want to go for the computation of 16
inner products.
The problem doesn't really arise when the resulting matrix is big enough
(256*100 000) since this results in enough result blocks.
This would be, to me, more than a nice-to-have feature, since without
dispatching, GPUs don't make any sense for these operations. Now, the
question is : how to handle it? Do you guys think we should do it
transparently in the backend, or let the user choose the dispatching he
wants?
C = viennacl::linalg::prod(A, B, compute_bound()) //default
C = viennacl::linalg::prod(A, B, bandwidth_compute_bound())) //GEMV based
C = viennacl::linalg::prod(A, B, bandwidth_bound()) //DOT based
Best regards,
Philippe
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