Scientific computing

(for the rest of us)

The ternary operator

In this module, we will look at the “ternary operator”, a very efficient shortcut to perform a logical test in a single line. This is a construct we will use quite a lot to express both possible outcomes of a conditional expression using a single line!

Based on what we have seen in the previous modules, the way to store different values in a variable according to some condition we set would be to write something like:

x::Float64 = 0.0
if rand() < 0.5
    x = 0.25
else
    x = 0.75
end

0.25

In the words of Stephen King, “it goes somewhere, but it ain’t, you know, boss”. Thankfully there is a way to simplify this expression greatly, and it does of course involve learning some more operators.

But before we start doing this, as a little bit of recall from the previous module, note that we can do the same thing with short-circuit operators:

x = 0.75
rand() < 0.5 && (x = 0.25)

false

But there is a reason why we don’t do everything we technically can, and in this instance, the reason is that this notation is absolutely vile. So we will address our problem in a more elegant way, using the ternary operator:

x = rand() < 0.5 ? 0.25 : 0.75

0.75

This little =/?/: sequence is called a ternary operator. The basic syntax is condition ? if true : if false. It fits in a single line, and we can handle both cases. Note that the cases are returned as a function of whether the condition is satisfied, which is a way to rapidly give a value to a variable.

Another source of efficiency is that both sides of the : are not evaluated, unlike other languages:

true ? print(2) : print(3)

2

We can check this using the @lower macro from Meta: it is translating Julia code into something of a lower-level, and is an interesting opportunity to check what is going on “under the hood”:

Meta.@lower true ? cos(4) : sin(3)

:($(Expr(:thunk, CodeInfo(
    @ none within `top-level scope`
1 ─      goto #3 if not true
2 ─ %2 = cos(4)
└──      return %2
3 ─ %4 = sin(3)
└──      return %4
))))

We see in the output above that the operations (like cos(4)) have not been expanded yet – the ternary operator is “pointing” Julia towards the right branch.

We can use the ternary operator as the most basic ingredient in a very naive function that reproduces the Kronecker $\delta$ function: it returns 1 if the two inputs are equal, and 0 if they are not. This function is generally applied to non-negative integers.

Of course, if we wanted to do this properly, we could remember that false is 0 and true is 1, and our function is not necessary. Nevertheless, this is an interesting example to write from scratch:
function δ(i::T, j::T) where {T <: Integer}
    return i == j ? one(T) : zero(T)
end

δ (generic function with 1 method)
We have not yet covered how to declare functions, and how to handle the types of arguments. This will happen later in the material. For now, just trust us when we say that all of the bits that aren’t the ternary operator are required for a function to run.

We can see what our function would do when applied to actual numbers:

for i in 1:3, j in 1:3
    @info "δ($(i), $(j)) = $(δ(i, j))"
end

[ Info: δ(1, 1) = 1
[ Info: δ(1, 2) = 0
[ Info: δ(1, 3) = 0
[ Info: δ(2, 1) = 0
[ Info: δ(2, 2) = 1
[ Info: δ(2, 3) = 0
[ Info: δ(3, 1) = 0
[ Info: δ(3, 2) = 0
[ Info: δ(3, 3) = 1