Julia: RFE: syntactic sugar f(x) .= 3+4x for vectorized function definition

[alhirzel]

New to Julia, so please have patience if I am missing something in this suggestion.

Since the .= operator is used for in-place assignment, it does not currently make sense to define a function using this operator. That is to say, the statement f(x) .= 3+4x would not have any meaning. The statement and variations such as f .= x -> 3+4x indeed trigger strange errors.

I think it would be elegant to hijack the .= operator when the LHS is a function definition or RHS is a lambda; my hijack proposal is to make f(x) .= 3+4x and/or f .= x -> 3+4x into f(x) = @. 3+4x or something similar. This is less in-line with the behavior of .= as an "in-place assignment" operator, and more in-line with the dot as a broadcast operator.

[antoine-levitt]

The standard way to do this kind of things in julia is to define functions for scalars, then vectorize: f(x) =2x+3;f.(X) if X is an array. Does this not do what you want?

[xanfus]

Thinking: _"Limit argument types to Array{Any,N} by dot-before-equal-sign. Which syntactic sugar could be assigned to execute f(x::Scalar)? Sole "@" macro!"_
Measures taken wouldn't improve readability for me.
Anyway, code can be reprocessed with some macro just to translate your new definitions to current standard, @alhirzel .

[stevengj]

Defining "vectorized" functions (rather than using explicit "dot calls" f.(array)) is actively frowned on these days. The advantage of dot calls is that they fuse with other dot calls into a single loop.

That is, if you define a vectorized (elementwise) function f(array), then if you do 2 .* f(array) .+ 1 your f(array) call will allocate a temporary array and perform a separate loop. Whereas if you define only f(scalar) then 2 .* f.(array) .+ 1 or @. 2f(array) + 1 would allocate only a single array and fill it in with a single loop.

See also #17302 — we used to have a special macro for defining vectorized methods, which was removed for precisely this reason.

[alhirzel]

Thank you for the info. I did not previously have this clear of a picture. If the Julian style is to define scalar functions and promote, then I agree the .= operation for creating broadcasted functions is unmotivated. I wondered how one would keep track of which functions are "internally dotted" and which ones aren't, but if I summarize: this is resolved by assuming you broadcast at the vector call and all functions operate on scalars until you see a dot. If you want to avoid "along-the-way allocations", this is done by convention, and you assume there is sensible or no internal broadcasting for functions when you call them.

The only gap is behavior of the .= operator for function definition or lambdas. I don't know if it would be in best style to error out, but it is not intuitive what this operator would do from the "in-place assignment" perspective when applied to function arguments (as in the f(x) .= 3x+4 example). Any thoughts on what this should do? Here is a specific REPL session that is unintuitive IMO:

julia> f(x) .= 3x+4
ERROR: UndefVarError: f not defined
Stacktrace:
 [1] top-level scope at none:0

julia> f(x) = 3x+4
f (generic function with 1 method)

julia> f(x) .= 5x+6
ERROR: UndefVarError: x not defined
Stacktrace:
 [1] top-level scope at none:0

julia> f .= x -> 5+6
ERROR: MethodError: no method matching size(::typeof(f))
Closest candidates are:
  size(::BitArray{1}) at bitarray.jl:70
  size(::BitArray{1}, ::Any) at bitarray.jl:74
  size(::Core.Compiler.StmtRange) at show.jl:1561
  ...
Stacktrace:
 [1] axes at ./abstractarray.jl:75 [inlined]
 [2] materialize!(::Function, ::Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{0},Nothing,typeof(identity),Tuple{Base.RefValue{getfield(Main, Symbol("##3#4"))}}}) at ./broadcast.jl:759
 [3] top-level scope at none:0

[stevengj]

f(x) .= 3x+4 currently means broadcast!(identity, f(x), 3x+4). That is,it calls broadcast! and writes the output to the result of calling f(x).

This is actually potentially useful behavior if f(x) is some special array-allocation function. For example:

foo(x) = sort!(myallocate(length(x)) .= x .+ 1)  # several in-place operations on result of myallocate(n)

(Changing this into a new kind of function definition would be breaking, and hence cannot happen in Julia 1.x.)

[mbauman]

With your other example, f .= x->…, that's doing broadcasted assignment of the anonymous function _into_ f, which must already exist as a mutable collection. That's why it's erroring in your example — you're trying to assign into a function that you've already defined! .= is different from straight = assignment as the left-hand-side must _already exist_ and so it doesn't introduce a new binding. It just modifies something… so you're able to put _any_ expression there and it'll modify it.

Given that we all agree that a "vectorized function definition" isn't really needed and that we have a defined meaning here, I think we can close this.

[alhirzel]

Yep agree on closing; thank you for answering my questions!