## The Array and Iterator Interface¶

Julia has a few "informal" interfaces. The idea is that, if you subclass a given abstract type and implement a few methods, then by multiple dispatch the type will now "act like" whatever you want it to act like, in any instance you would like.

One example is the array interface. The methods to implement are:

• size(A)
• getindex(A, i::Int)
• getindex(A, I::Vararg{Int, N})
• setindex!(A, v, i::Int)
• setindex!(A, v, I::Vararg{Int, N})

size(A) returns what the size of the array is as a tuple. For example, a 3-dimensional "array" (remember, it can be anything, we are just saying it acts like an array!) would have size(A) return a tuple (dim1,dim2,dim3) for the sizes along each dimension. getindex is the function that is used by A[i], and setindex! is the function for mutating A via A[i]=.

The Vararg{Int, N} just means variable numbers of arguments, so for example getindex(A,i1,i2) is what is called by A[i1,i2]. More generally, using slurping you can define getindex(A,I...) and the function for A[i1,i2,...,in], and I will be a tuple of (i1,i2,...,in).

## Usage Example¶

One usage example is in DifferentialEquations.jl. When you solve a differential equation, the solution returns a specialized solution type.

In :
using DifferentialEquations
prob = ODEProblem((u,p,t)->1.01u,0.5,(0.0,1.0))
sol = solve(prob)

Out:
retcode: Success
Interpolation: 3rd order Hermite
t: 5-element Array{Float64,1}:
0.0
0.09964258706516003
0.3457030604980719
0.6776923233260352
1.0
u: 5-element Array{Float64,1}:
0.5
0.552938681151017
0.7089380797962724
0.9913595829297396
1.3728004409038075

While there are many fields that the type could hold, such as the errors of a given analytical solution:

In :
println(sol)

retcode: Success
Interpolation: 3rd order Hermite
t: [0.0, 0.0996426, 0.345703, 0.677692, 1.0]
u: [0.5, 0.552939, 0.708938, 0.99136, 1.3728]


An array interface is provided so that the solution "acts" like a traditional solution: i.e. as an array of the numerically computed values:

In :
println(sol.t) # The third timestep
sol # The value at the third timestep

0.3457030604980719

Out:
0.7089380797962724

An entire Julia organization, JuliaArrays, is devoted to making fast, interesting, and easy to use arrays. It's an odd concept: arrays are just arrays, right? However, Julia's genericism makes it so that way this now works in any place which accepts an AbstractVector output, so the solution is directly usable in numerical optimization algorithms, regressions, etc.