Typing of array operations

[timholy]

Illustrated with SIUnits, although this issue is not specific to that case:

julia> using SIUnits

julia> a = [1Meter, 2Meter]
2-element Array{SIQuantity{Int64,1,0,0,0,0,0,0},1}:
 1 m 
 2 m 

julia> l = 0.5Meter
0.5 m 

julia> r = l./a
2-element Array{SIQuantity{Float64,m,kg,s,A,K,mol,cd},1}:
  0.5 
 0.25 

julia> r[1]
0.5 

julia> typeof(r[1])
SIQuantity{Float64,0,0,0,0,0,0,0} (constructor with 1 method)

julia> typeof(l./a[1])
Float64

Fixing this seems a little delicate. For the functions here, I tested a solution that allocates the output in the following manner:

F = Array(typeof(($f)((isempty(A) ? one(S) : A[1])::S, (isempty(B) ? one(B) : B[1])::T)),
                      promote_shape(size(A),size(B)))

To try to avoid problems from when one(T) isn't defined, it uses the first element of the array and only falls back to one(T) if the array is empty. That still leaves the possibility for error (and is therefore far from ideal), but it narrows the frequency with which it should happen.

While this fixes this particular example, unfortunately it causes trouble for some of the bitarray tests:

    JULIA test/bitarray
     * bitarray
exception on 1: ERROR: no method convert(Type{Array{Bool,1}}, Int64)
 in & at array.jl:763
 in check_bitop at bitarray.jl:8
 in runtests at /home/tim/src/julia/test/testdefs.jl:5
 in anonymous at multi.jl:629
 in run_work_thunk at multi.jl:590
 in remotecall_fetch at multi.jl:663
 in remotecall_fetch at multi.jl:678
 in anonymous at task.jl:1309
while loading bitarray.jl, in expression starting on line 552
ERROR: no method convert(Type{Array{Bool,1}}, Int64)
 in & at array.jl:763
 in check_bitop at bitarray.jl:8
 in runtests at /home/tim/src/julia/test/testdefs.jl:5
 in anonymous at multi.jl:629
 in run_work_thunk at multi.jl:590
 in remotecall_fetch at multi.jl:663
 in remotecall_fetch at multi.jl:678
 in anonymous at task.jl:1309
while loading bitarray.jl, in expression starting on line 552
while loading /home/tim/src/julia/test/runtests.jl, in expression starting on line 34

make[1]: *** [bitarray] Error 1
make: *** [test-bitarray] Error 2

Not sure what folks think would be the right way forward here. I don't really see an ideal solution.

[andreasnoack]

I ended up doing something very similar for the LU and QR but hadn't seen the deep problem of non-existence of one for arrays types before the discussion in JuliaLang/LinearAlgebra.jl#94

[toivoh]

The trouble with using the first element is that it can give unexpected
results for loosely typed arrays.

[timholy]

Hmm, an excellent point. Here's a fun one:

julia> a = Any[1Meter, 2Meter]
2-element Array{Any,1}:
 1 m 
 2 m 

julia> l = 0.5Meter
0.5 m 

julia> l./a
ERROR: type: SIQuantity: in T, expected T<:Number, got Type{Any}
 in ./ at array.jl:793

[andreasnoack]

but the result of one(Real) or any other abstract type is also difficult to predict.

[timholy]

I should have clarified that this result is with current master, because of:

julia> Base.promote_array_type(typeof(l), eltype(a))
ERROR: type: SIQuantity: in T, expected T<:Number, got Type{Any}
 in promote_array_type at array.jl:730

This is ultimately a consequence of

T = typeof(l)
S = Any
julia> Base.promote_rule(S,T)
ERROR: type: SIQuantity: in T, expected T<:Number, got Type{Any}
 in promote_rule at /home/tim/.julia/v0.3/SIUnits/src/SIUnits.jl:95

Presumably this could be fixed to return Any.

However, note another hazard with the one(T) solution:

julia> one(Any)
1

[JeffBezanson]

I think this is now fixed by our broadcast machinery?