Function basics

So far, we did not show how to define functions. In Julia, a function is an object that maps a tuple of argument values to a return value. There are multiple ways to create a function. Each of them is useful in different situations. The following example shows the basic way how to define a function using function ... end syntax

function quadratic(x::Real; a::Real = 1, b::Real = 1, c::Real = 1)
    value = a*x^2 + b*x + c 
    deriv = 2* a*x + b

    return value, deriv
end

The function definition consists of multiple parts:

keywords function and end
function name quadratic
positional argument x with type annotation
separator ; of positional and keyword arguments
keyword arguments a, b and c with type annotations and default values
actual code that computed the output values
return keyword that specifies the function output followed by comma separated list of output values

Note that not all parts of the function definition above are mandatory. The following parts are optional:

type annotations
separator of positional and keyword arguments
return keyword

However, we highly recommend to use these optional features when writing your own functions, since it will improve code readability and prevent unwanted errors.

Exercise:

Test how the function behaves with different input values. Test what happens when the input is not a real number, i.e. x = "a".

Solution:

Positional arguments do not need to be named:

julia> quadratic(2)
(7, 5)

but the keyword arguments have to be specified. Their order of being called does not matter.

julia> quadratic(2; b=3, a=1)
(11, 7)

When a function has specific type annotation, the function throws a MethodError, because the function specifically needs x to be of type Real.

julia> quadratic("a")
ERROR: MethodError: no method matching quadratic(::String)

Closest candidates are:
  quadratic(!Matched::Real; a, b, c)
   @ Main none:1

Stacktrace:
 [1] top-level scope
   @ none:1

This is different to a a case when we would define the function without the type annotation:

function quadratic2(x; a = 1, b = 1, c = 1)
    value = a*x^2 + b*x + c 
    deriv = 2* a*x + b

    return value, deriv
end

which returns a different error when calling for x = "a":

julia> quadratic2("a")
ERROR: MethodError: no method matching *(::Int64, ::String)

Closest candidates are:
  *(::Any, ::Any, !Matched::Any, !Matched::Any...)
   @ Base operators.jl:587
  *(::Real, !Matched::Complex{Bool})
   @ Base complex.jl:327
  *(!Matched::Missing, ::Union{AbstractChar, AbstractString})
   @ Base missing.jl:184
  ...

Stacktrace:
 [1] quadratic2(x::String; a::Int64, b::Int64, c::Int64)
   @ Main ./none:2
 [2] quadratic2(x::String)
   @ Main ./none:1
 [3] top-level scope
   @ none:1

We will discuss the function declaration in more detail later.