[julia-users] How does the colon actually get parsed in array indexing?

[Spencer Lyon]

I am trying to construct a type with this definition:

# are two ranges disjoint?
isdisjoint(r1::UnitRange, r2::UnitRange) = isempty(intersect(r1, r2))

# are a collection of ranges all disjoint?
function all_disjoint(rs::UnitRange...)
    n = length(rs)
    for i=1:n, j=i+1:n
        if !(isdisjoint(rs[i], rs[j]))
            return false
        end
    end
    return true
end

type TimeVaryingParam{T<:Real, S<:Integer}
    mats::Vector{Matrix{T}}
    ranges::Vector{UnitRange{S}}

    function TimeVaryingParam(mats, ranges)
        if !(all_disjoint(ranges...))
            throw(ArugumentError("Ranges are overlapping"))
        end
        new(mats, ranges)
    end
end

function TimeVaryingParam{T<:Real, S<:Integer}(mats::Vector{Matrix{T}},
                                               ranges::Vector{UnitRange{S}})
    TimeVaryingParam{T, S}(mats, ranges)
end

# constructor of the form (mat, period_range), (mat2, period_range2)
function TimeVaryingParam{T<:Real, S<:Integer}(input::(Matrix{T}, 
UnitRange{S})...)
    mats = Matrix{T}[]
    ranges = UnitRange{S}[]
    for t in input
        push!(mats, t[1])
        push!(ranges, t[2])
    end
    TimeVaryingParam(mats, ranges)
end

function getindex(tvp::TimeVaryingParam, t::Int)
    # b/c all ranges are disjoint, ind has exactly zero or one elements
    ind = find(x->t in x, tvp.ranges)
    isempty(ind) && error("Invalid index. t=$t not in any supplied ranges")
    return tvp.mats[ind[1]]
end

The application is to be able to represent time-varying coefficient 
matrices of a linear state space system without having to make explicit 
copies of the matrices when they are the same for multiple periods.

What I am trying to figure out is a convenient way for users to specify 
that a given matrix is the same for all periods. In other words, if the 
user was going to use the outer constructor I provided, I would like the 
following behavior to be true:

a = [1 2; 3 4]
tva = TimeVaryingParam((a, Colon()))
t = rand(1:10000)   # really just any integer
tva[t] == a  # returns true

Now for the question/title of the post. I don’t know how : gets parsed in 
an indexing expression, so I don’t know how to enable this functionality. 
Can anyone help with this?

Also, if someone has a better idea for how to enable this kind of 
functionality (i.e. an approach that doesn’t rely on Colon()) I am very 
happy to hear about it.

Thanks!
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