Matrix-Vector, Vector-Matrix, Vector-Vector product

[oxinabox]

I think this can probably use the same rules as out Matrix-Matrix products,
but it wants some tests to confirm.
Might even be just swapping AbstractMatrix for AbstractVecOrMat

A lot of these products are nonsense.
but that is ok, they will error on the primal pass

[gxyd]

Though a vector-matrix product is valid and can be computed.

julia> A
2-element Array{Float64,1}:
 -3.0
  0.0
julia> B
1×4 Array{Float64,2}:
 -9.0  7.0  -5.0  -7.0
julia> A * B
2×4 Array{Float64,2}:
 27.0  -21.0  15.0  21.0
  0.0    0.0   0.0   0.0

But in the rule definition mul! is used, documentation of which says:

mul!(Y, A, B) -> Y

Calculates the matrix-matrix or matrix-vector product $AB$
and stores the result in Y, overwriting the existing value of Y.
Note that Y must not be aliased with either A or B.

So it would be ok from the primal computation side, but would error while computing its derivative.

[gxyd]

@oxinabox anything on the above?

[oxinabox]

I don't understand the problem.

mul! works fine for any mixture of matrixes, vectors, and numbers, that doesn't result in a dimension mismatch.
Except for Union{Transpose{<:Vector}, Adjoint{<:Vector}}, * Vector since that one yeilds a scalar.

But in anycase for things that don't work by relaxing signatures we just write a seperate rule, and it is not a problem?