Tiling tensor with overalp

[IuriiKobein]

Currently I am working on validating idea to use CuTe/CUTLASS for finite difference method.
It requires to divide input by tile with overlaps to take into consideration halo region.
The input is 2D tensor that already has allocated halo regions on boundaries.

For example following 2D input divide into 3 overlapped tiles:

In:             tile0:   tile1:   tile2:
0 0 0 0           0 0      0 0     0 0
0 1 3 0  =>       0 1 ,    1 3,    3 0
0 2 4 0           0 2      2 4     4 0
0 0 0 0           0 0      0 0     0 0

Is there utils to do it using CuTe?

[thakkarV]

No, but @ccecka and I have discussed an idea for implementing a stencil div for example 59 in the past. This is a lower priority for us at the moment, but our internal discussions suggest that this is most certainly doable and a generalization of the im2col transformed used for convolutions.

[YuraCobain]

I mean having 4 tiles 16x16 that have coordinates mentioned above view on them as single 32x32 tile.

[thakkarV]

you mentioned a 8x8 tiler above, so I am confused now. can you please rephrase your question?

[YuraCobain]

Sorry, let's start from scratch.
Assume division of tensor 32x48 by tiler 16x16 into following enumerated tiles
0 2 4
1 3 5

Is possible in CuTe for example to view tiles 2, 3, 4, 5 as a single tile 32x32?

[thakkarV]

I see what you are trying to do. Here is what I would recommend you do instead:

Think of your input tensor's layout as a surjective function from a domain of size 64x64 = 4096 onto a codomain of size 32x32 = 1024
Then tile this tensor with whatever 32x32 tiler you want.
Done.

This is exactly what example 59 does.

[IuriiKobein]

@thakkarV thanks for the recommendation. I will try this approach and be back in case of additional question.