algebraicjulia / diagrammaticequations.jl Goto Github PK

That way we don't mangle nice decapodes by converting them to SSA.

DiagrammaticEquations is double-exporting infer_states in multiple modules apparently

  1 dependency had output during precompilation:
┌ DiagrammaticEquations
│  WARNING: using Deca.infer_states in module DiagrammaticEquations conflicts with an existing identifier.
└  

In the code that @GeorgeR227 presented today, it looked like there was var"1.4" = 1.4 in the generated output. We should probably just propagate the constant into the generated AST everywhere.

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We note that we can take this idea of contracting chains further by eliminating branches.

In other words, a binary tree of depth 2, (with update steps at the leaves) requires (assuming all functions on edges are unique) 6 matrices, 2 intermediary vectors, and performs 6 matrix-vector multiplications. This could be re-written as an equivalent 1-deep 4-ary tree which requires just 4 matrices, 0 intermediary vectors, and performs 4 matrix-vector multiplications. This result cannot be improved upon, unless edge pruning of duplicate operations is performed.

This speed-up and memory improvement of an entire decapode in this fashion is unlikely to occur, since Op2s are likely to break this downwards tree-like property.

Originally posted by @lukem12345 in AlgebraicJulia/Decapodes.jl#93 (comment)

Currently, Decapodes are flexible. That is, an object of the type SummationDecapode could represent equations in the 2D Exterior Calculus, or 1D Exterior Calculus, and so on.

Programming with Decapodes would become more well-typed if the Decapode objects had something like a type parameter with the degree of the DEC being used. Compilation steps like type inference could then automatically pick the correct set of inference rules.

The typing system could most likely be improved in other ways, but some brainstorming needs to happen first.