maddyscientist
commented
9 years ago Ok, on closer inspection I see that the clover term relation isn't quite I wrote above. Since the regular Wilson diagonal term contribution is included in the clover matrix, the actual form is like this:
/ 1+A B \
\ B* 1-A /so the relation we need to relate the upper and lower diagonal parts is slightly more involved and likely means that the only way to do the memory saving for inverse matrix is to invert the clover matrix on the fly.
AlexVaq
mathiaswagner
There is symmetry in the clover them that is not exploited that could reduce the memory footprint and reduce the memory traffic in the kernels that use the clover term.
Specifically, if we consider the 2x2 block form each of chiral block of the clover matrix, we have
We presently only store B* and don't double store with B, however, we do double store A and -A. If we only stored A, then the number of real numbers required to store the clover term is reduced from 72 to 54, which represents 25% reduction in both memory footprint and memory traffic.
I suspect this optimization is of most utility for the twisted clover formulation, since I believe it requires two clover matrices, hence is more memory footprint bound.
This symmetry does not hold directly for the clover inverse, so it would only apply to the kernels with the direct clover term. However, clearly we can use only 54 numbers for the clover inverse, since we could just load the direct matrix (using 54 numbers) and invert on the fly. This may be too computationally expensive, but more insight may be gained from considering the 2x2 block form of the inverse.
Anyway, as a first step, we should replace the clover direct matrix using this reduced storage form. After that is done, we can consider reduced storage options for the inverse.