Union of Integer, AbstractVector{Integer}, and String - julia

Question

I have a function in which the user passes an argument to select which columns of a matrix should be processed as in the minimalistic example below:
function foo{P<:Real, T<:Integer}(;x::AbstractMatrix{P}=zeros(3, 10), colN::Union(T, AbstractVector{T})=1)
x[:,colN] = x[:,colN]+1
return x
end
I want to have a way for the user to specify that all columns should be processed, in the end I changed the function so that this would be the default behavior:
function foo{P<:Real, T<:Integer}(;x::AbstractMatrix{P}=zeros(3, 10), colN::Union(T, AbstractVector{T})=[1:size(x)[2]])
x[:,colN] = x[:,colN]+1
return x
end
originally, however, I wanted to allow the colN argument to take a String, so that the user could pass it the value "all" to mean that all columns should be processed, but the following doesn't work as I expected:
function foo{P<:Real, T<:Integer}(;x::AbstractMatrix{P}=zeros(3, 10), colN::Union(T, AbstractVector{T}, String)="all")
if colN == "all"
colN = [1:size(x)[2]]
end
x[:,colN] = x[:,colN]+1
return x
end
calling this last version of the function gives:
foo(colN="all")
ERROR: `__foo#8__` has no method matching __foo#8__(::Array{Float64,2}, ::ASCIIString)
why such an union between an Integer, a vector of integers, and a string doesn't seem to work?

Answer 1

The problem is that Julia can't deduce the type T when you pass a string, and is thus not able to resolve which method to call.
Consider the following two functions, f and g:
function f{T<:Integer}(x::Union(T,String))
x
end
function g{T<:Integer}(y::T, x::Union(T,String))
x
end
In this case, you will observe the following behavior:
f(1) is 1 because the value of T can be deduced
f("hello") gives an error because the value of T is unknown
g(1, "hello") is "hello" because the value of T can be deduced
That being said, I think that it would be more idiomatic Julia to use multiple dispatch instead of Union types to achieve what you want to do.
Update. Seeing as your colN is either a string or a list of indexes, I believe you would be fine with T = Int (or Int64 if you want to address a lot of memory). Compare the following function h to f and g above:
function h(x::Union(Int,String))
x
end
In this case, both h(1) and h("hello") work as expected (and e.g. h(1.0) raises an error).

Answer 2

There is no need to pass a string in this function to indicate handling all columns.
Also, it looks like the matrix should be passed in as a positional argument,
instead of a keyword argument.
so that Julia can specialize on it.
There are many ways to handle this more efficiently in Julia.
function foo{P<:Real, T<:Integer}(x::AbstractMatrix{P}, colN::Union(T, AbstractVector{T}))
x[:,colN] += 1
return x
end
function foo{P<:Real}(x::AbstractMatrix{P})
x[:,[1:size(x)[2]]] += 1
return x
end
so foo(zeros(10,3)) will give you:
3x10 Array{Float64,2}:
1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
and foo(zeros(3,10),5) will give you:
3x10 Array{Float64,2}:
0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0