Global Coordinate Awareness in `Tile`

[wavefunction91]

Describe the problem you are solving

For applications which manually specify the tiling of a matrix, it would be desirable for Tile to carry (or to be able to resolve) information pertaining to its locale relative to a global matrix. This is useful in matrix generation when the starting indices of a tile cannot be simply computed (i.e. non-uniform tiling)

Describe your proposed solution

One potential solution would be to have Tile store it's global row/column starting indices relative to its owning matrix (and defaulting to 0)

[mgates3]

Do you mean the block row & block col? For instance:

  T = A( i, j )
  T.block_row() == i
  T.block_col() == j

That would be fairly trivial to do, but I'm not sure how beneficial it is. Obviously the function that just got the tile A( i, j ) knows what i, j are.

Or do you mean the actual row & col? For instance, for a matrix with fixed tile size mb x nb:

    T = A( i, j );
    T.first_row() == i * A.mb();
    T.first_col() == j * A.nb();

That would be easy for a fixed tile size, and rather hard & expensive for a variable tile size. We would basically have to iterate over the tileMb() and tileNb() functions to compute what the row & col are.

Thinking more on this — we could do use an alternate representation using the first row / col of each tile, then tileMb = row[ i+1 ] - row[ i ], and tileNb = col[ i+1 ] - col[ i ]. That would have some other benefits like making A.m() and A.n() easier to compute. Whereas currently, we would have to compute row = sum_{0..i} mb[ i ].

[wavefunction91]

Thinking more on this

This is essentially what TiledArray does (by introducing the concept of TiledRange), however, the individual tiles also carry information pertaining to their global location (i.e. a tile can be passed around external to its owner and one can still resolve its global location).

Expanding on this, you could also remove the need for user tileMb/tileNb functors if you internally populate row/col bounds to look up dimensions. tileRank/Dev should probably still exist since to store them requires $O(N^2)$ storage