Add Support for GetAttribute and Indirect Access to Einsum Interpreter

[TheRealMichaelWang]

• Added support for GetAttribute Einsum AST Node
  • Currently supports shape, elems, and coords which query attributes from sparse tnesors
  • Has a dim field which is required for some queries
• Added support for indirect access
  • Includes support for indirect access with one index-operand (i.e. B[ACoords[k]])
  • Includes support for mixing indirect accessors and regular indices (i.e. B[AcoordsI[k], j])

[willow-ahrens]

Great work, thanks! My first request: Please rename to GetAttr (like it is in FinchAssembly, FinchNotation). Additionally, please just use e.g. coords3 rather than coords, 3, to keep a uniform interface to attributes in finch-lite. Once you've fixed this I'll take another look.

[TheRealMichaelWang]

Great work, thanks! My first request: Please rename to GetAttr (like it is in FinchAssembly, FinchNotation). Additionally, please just use e.g. coords3 rather than coords, 3, to keep a uniform interface to attributes in finch-lite. Once you've fixed this I'll take another look.

I renamed GetAttribute to GetAttr. But I am not sure if removing the dim: int field from the Einsum GetAttr is a good idea or not. The dim field is particularly important for the shape query. This is useful to get the size of a specific axis/dimension, which is required for calculating the size of the reduced fiber when lowering from regular einsums to indirect einsums.

Furthermore querying coords as a hardcoded value like coords3 will greatly limit the type of einsums one can write.

[TheRealMichaelWang]

I have greatly implemented the implementation for all cases of ein.Access.

• There are now only two cases to handle ein.Access
  • One case for handling one giant index tensor that covers all dimensions of the tensor being accessed
  • A greatly simplified ein.Access that handles multiple indices mixed with indirect and direct accesses.

The new implementation is slightly longer than 10 lines/statements (it clocks in at 13 statements), but avoids any meshgrid calls, and does so recursively (like A[B[i], j, C[i]] -> A2[i, j])

Essentially, while an ein.Access has any indirect access indices.

• We find the first indirect access index and collect all associated indices (which share the same top level iterator).
• We use those indices to metaphorically "shave" off fibers in the tensor.
• Given the smaller tensor, we replace the set of current indices with the top level iterator index
• Repeat until no indirect accesses remain; then proceed with permuting and expanding dimensions as the old ein.Access did