Is there a way in Julia to modify a function f(x) such that it will return f(x)*g(x)

user_16530167 0
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I came across Julia in some graduate research and have done a few projects already in C++. I'm trying to "translate" some of my C++ work into Julia to compare performance, among other things.

Basically what I'm trying to do is implement something like the functional library from C++ such that I can do something like

g(x, b) = x*b # Modifier function

A = [1,2,...] # Some array of values

f(x) = 1 # Initialize the function

### This is the part that I am seeking
for i = 1:length(A) 
  f(x) = f(x)*g(x, A[i]) # This thing right here
end
###

and then be able to call f(x) and get the value of all the g(x, _) terms included (similar to using bind in C++) I'm not sure if there is native syntax to support this, or if I'll need to look into some symbolic representation stuff. Any help is appreciated!

julia functional-programming
2 Answers

You are probably looking for this:

julia> g(x, b) = x * b
g (generic function with 1 method)

julia> bind(g, b) = x -> g(x, b) # a general way to bind the second argument in a two argument function
bind (generic function with 1 method)

julia> A = [1, 2, 3]
3-element Vector{Int64}:
 1
 2
 3

julia> const f = bind(g, 10) # bind a second argument of our specific function g to 10; I use use const for performance reasons only
#1 (generic function with 1 method)

julia> f.(A) # broadcasting f, as you want to apply it to a collection of arguments
3-element Vector{Int64}:
 10
 20
 30

julia> f(A) # in this particular case this also works as A*10 is a valid operation, but in general broadcasting would be required
3-element Vector{Int64}:
 10
 20
 30

In particular for fixing the first and the second argument of the two argument function there are standard functions in Julia Base that are called Base.Fix1 and Base.Fix2 respectively.

user_12695670

You may be looking for the function composition operator ∘

help?> ∘
"∘" can be typed by \circ<tab>

search: ∘

  f ∘ g

  Compose functions: i.e. (f ∘ g)(args...) means f(g(args...)). The ∘ symbol can be
  entered in the Julia REPL (and most editors, appropriately configured) by typing
  \circ<tab>.

  Function composition also works in prefix form: ∘(f, g) is the same as f ∘ g. The
  prefix form supports composition of multiple functions: ∘(f, g, h) = f ∘ g ∘ h and
  splatting ∘(fs...) for composing an iterable collection of functions.

  Examples
  ≡≡≡≡≡≡≡≡≡≡

  julia> map(uppercase∘first, ["apple", "banana", "carrot"])
  3-element Vector{Char}:
   'A': ASCII/Unicode U+0041 (category Lu: Letter, uppercase)
   'B': ASCII/Unicode U+0042 (category Lu: Letter, uppercase)
   'C': ASCII/Unicode U+0043 (category Lu: Letter, uppercase)

  julia> fs = [
             x -> 2x
             x -> x/2
             x -> x-1
             x -> x+1
         ];

  julia> ∘(fs...)(3)
  3.0

so, for example

julia> g(b) = function(x); x*b; end # modifier function
g (generic function with 1 method)

julia> g(3)(2)
6

julia> f() = 3.14
f (generic function with 1 method)

julia> h = g(2) ∘ f
var"#1#2"{Int64}(2) ∘ f

julia> h()
6.28
user_136397340
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