improve a[...] .= handling of arrays of arrays and dicts of arrays

[stevengj]

My ideal in #17510 was to have x .= f.(y) be a synonym for broadcast!(f, x, y). However, because slices return copies and not views, in #17546 I had to modify this so that x[...] .= f.(y) turns into broadcast!(f, view(x, ...), y). This PR extends that solution so that in-place semantics are achieved for arrays of arrays and dictionaries of arrays, to fix a problem pointed out by @iamed2.

In particular, x[...] .= f.(y) now turns into broadcast!(f, Base.dotview(x, ...), y). The dotview function defaults to calling view, but we can override it for dictionaries and arrays-of-arrays to achieve the desired semantics without affecting explicit calls to view.

[iamed2]

Hey, thanks! :)

[stevengj]

Once the Arraypocolypse (#13157) lands and slices become views, I think all of this dotview machinery can disappear and we can just use broadcast!(f, x, y) in all cases.

So, hopefully this is all just a temporary hack for Julia 0.5.

[stevengj]

@StefanKarpinski, merge?

[StefanKarpinski]

Seems good to me. I think @JeffBezanson should probably also review it.

[JeffBezanson]

Would it work to have dotview default to getindex, and only have it call view for AbstractArray arguments? That way we might need fewer ad-hoc definitions, e.g. for Associative.

[stevengj]

Sure.

[stevengj]

Changed to default to getindex, using view only for AbstractArray as suggested by @JeffBezanson.

[StefanKarpinski]

seems considerably simpler 👍

[andreasnoack]

@stevengj Why did you decide to default to getindex and not view in this case? @alanedelman showed me this example today

s = zeros(2,2) 
A = fill(s, 4, 4)
A[1:3,1:3] .= [ones(2,2)]

which doesn't set A because of this.

[stevengj]

You're right, it should be view also. I was thinking that view wasn't necessary, since A[i,j] returns a mutable object.