Vectors vs. Tuples and multiple dispatch

[stevengj]

@jbshannon

Is this the most idiomatic way to do something like this in Julia? Are there some nuances of the compiler I’m missing that would make all of this unnecessary?

Use StaticArrays.jl instead of tuples. Then you can use your original f definition and it will be fast (by avoiding heap allocations and unrolling loops):

julia> using BenchmarkTools, StaticArrays

julia> F(x, a) = 1.2*exp(-a*x)
F (generic function with 1 method)

julia> f(x,a) = vcat(1, F.(cumsum(x),a))
f (generic function with 1 method)

julia> x = @SVector[0.1, 0.2]
2-element SVector{2, Float64} with indices SOneTo(2):
 0.1
 0.2

julia> @btime f($x, 0.5)
  0.051 ns (0 allocations: 0 bytes)
3-element SVector{3, Float64} with indices SOneTo(3):
 1.0
 1.1414753094008567
 1.0328495717100694

In general, StaticArrays are a good idea when you have small (≲ 10 element) arrays whose size is more-or-less fixed (typically it should be inferred at compile-time from the function inputs).