Generic vecdot requires dot be implemented for scalars

[IainNZ]

The definition of vecdot (and its documentation) requires that user types define dot for scalars, instead of * like I would have guessed:

julia/base/linalg/generic.jl

Lines 278 to 287 in 70477b7

	s = zero(dot(x[1], y[1]))
	if size(x) == size(y)
	for I in eachindex(x, y)
	@inbounds s += dot(x[I], y[I])
	end
	else
	for (Ix, Iy) in zip(eachindex(x), eachindex(y))
	@inbounds s += dot(x[Ix], y[Iy])
	end
	end

I'm not sure what case this is expected to handle, but it increases the burden on people defining custom types, as in addition to multiplication (e.g. *(MyType,Number) and *(Number,MyType)) users must also define an analogous dot just for this case (and in the case of JuMP, where we have multiple types, all the other interaction terms).

I'm wondering if its too general. If the current functionality is desirable, then perhaps a generic dot(x::Any,y::Any) = x*y could be defined as a fallback?

[andreasnoack]

Is YourType <: Number. It's difficult to think of general behavior for Any so would it work if we had dot(x::Number,y::Numner)=x'y? It would then be similar to this definition

julia/base/linalg/generic.jl

Line 214 in 70477b7

@inline vecnorm(x::Number, p::Real=2) = p == 0 ? real(x==0 ? zero(x) : one(x)) : abs(x)

for norm.

[tkelman]

JuMP types aren't subtypes of number AIUI, they're numberlike containers but inheriting from Number would result in too many behaviors that aren't all wanted. There have been other issues that mentioned having an AbstractScalar above Number in the hierarchy.

[IainNZ]

Yes not a number.
I mean, I'm a little confused about what vecdot is supposed to be doing. I thought it was Euclidean dot product, which would be a sum of multiplied scalars, but it seems that its coded for something much more general. Is there an example use-case for this more general "recursive" definition?

[andreasnoack]

See https://groups.google.com/forum/#!topic/julia-users/cPZnKPK4Hbw, #6057, and #11067 for the origins of this behavior. @stevengj has determined how these functions work so we should hear him about ideas here.

[stevengj]

dot(x::Any,y::Any) = x*y is incorrect as a fallback for non-real types. vecdot really needs an inner product, which is in general distinct from multiplication.

[IainNZ]

Tidying up old issues/PRs.