add generic fallback for Blas.LinAlg.axpy!

[stevengj]

In cases where one wants to use axpy! to reduce memory allocation (see e.g. JuliaLinearAlgebra/IterativeSolvers.jl#16), it is annoying that it is only defined for Arrays of BlasFloat types. This patch provides a fallback for arbitrary array-like and range-like types.

Also, I noticed that axpy!(alpha, x, y) for BLAS types returned y, but axpy!(alpha, x, rx, y, ry) returned a pointer to data in y. The latter exposure of the internal implementation seems undesirable and not very useful, so I modified it to return y.

[andreasnoack]

You have really turned your back to specifying types. Could there be a potential problem with difficult error messages when providing illegal inputs?

Besides that I think it looks good except that I think it belongs in generic.jl.

[stevengj]

It's hard to break the habit of specifying types, but I'm beginning to feel that in Julia you should have a concrete reason to declare a type rather than vice versa. But if people feel strongly I about this case I could sprinkle a few AbstractArray declarations in there.

If we put it in generic.jl then we should probably export axpy! from LinAlg, not just from LinAlg.BLAS. This seems reasonable to me, but the counter-argument is that axpy! is very BLASy (BLASé?) flavored.

[jiahao]

I'm fine the way it is. It's just a fallback.

I don't have a strong opinion on blas.jl vs generic.jl. it depends on whether blas.jl should only contain blas wrappers.

[simonster]

It may be worth specifying types for rx and ry. Otherwise if someone forgets n for axpy!(n::Integer,alpha::Complex{Float64},dx::Union(Ptr{Complex{Float64}},Array{Complex{Float64},N}),incx::Integer,dy::Union(Ptr{Complex{Float64}},Array{Complex{Float64},N}),incy::Integer) this method will get called instead and silently give different behavior.

Is it worth considering @inbounds?

[stevengj]

Moved to generic.jl in LinAlg, added a few AbstractArray type declarations (this routine seems unlikely to be used with non-AbstractArray types in practice), and used inbounds.

[jiahao]

With this and Givens, it's getting to the point where we'll have to make IterativeSolvers post-0.2.0-compatible only.

[StefanKarpinski]

You can always just do

if VERSION < v"0.3"
  # define things that weren't in 0.2 yet
end

It's a bit of an eyesore, but it's easy to isolate and easy to delete later when it's no longer needed.

[jiahao]

That's almost above my pay grade to care about.

[stevengj]

Who uses 0.2 anymore? Any Julia version more than two days old is obviously a fossil.

[StefanKarpinski]

0.2 is so last month.