RFC: Make sparse multiplication work for AbstractArrays

[andreasnoack]

This gives warnings of the type:

Warning: New definition 
    *(SparseMatrixCSC{T1,Ti<:Integer},AbstractArray{T2,1}) at linalg/sparse.jl:13
is ambiguous with 
    *(AbstractArray{T,N},BitArray{N}) at linalg/bitarray.jl:67.
Make sure 
    *(SparseMatrixCSC{T,Ti<:Integer},BitArray{1})
is defined first.

but works fine. What is the better solution to get rid of the warnings?

[timholy]

What's happening is that Julia is indicating that it's not clear "who" should be handling the product of a sparse matrix and a BitVector: is it the sparse-array code, or the BitVector code? It's not surprising that you're getting the correct answer, because both sparse matrices and BitVectors support elementwise access, and so you should get the right answer no matter which multiplication code is used to compute the answer. However, from an efficiency perspective, Julia cannot guess by itself which one should be "in charge" (presumably it should be the sparse-multiplication code); it may well be computing that product by using the BitVector code, and accessing every element of the matrix (even the zeros).

As the warning suggests, I think your best option is to define a special case for the product SparseMatrixCSC*BitVector. You don't necessarily have to write a separate routine; you can define a sparsemat_vec_mul function and then write several versions of (*) that call it for a variety of types.

[simonster]

I think you could also define a method for the ambiguous types that calls the desired * method using invoke.

[StefanKarpinski]

I'm not sure if invoke still has significant overhead – it might. cc: @JeffBezanson

[ViralBShah]

This PR is a good idea - but we need to get rid of the warnings.

[andreasnoack]

The warnings are gone now by using the invoke trick.

[ViralBShah]

@JeffBezanson ?

[JeffBezanson]

invoke can be type-inferred just fine, but is still not the fastest thing around. I have no problem with it though, since eventually making it as fast as anything else is pretty straightforward.

[ViralBShah]

@andreasnoackjensen I guess you could merge this when you are ready.