How to create a function of n variables (Julia) - julia

For a fixed n, I would like to create a function with n variables
f(x_1, ..., x_n)
For example if n=3, I would like to create an algorithm such that
f(x_1, x_2, x_3) = x_1 + x_2 + x_3
It would be very nice to have an algorithm for every n:
f(x_1, ..., x_n) = x_1 + ... + x_n
I don't know how to declare the function and how can create the n variables.
Thank you for your help,

In Julia you can just do
function f(x...)
sum(x)
end
And now:
julia> f(1,2,3)
6
Note that within the function f, x is just seen as a Tuple so you can do whatever you want (including asking for type of elements etc).
More generally you can define function f(x...;y...). Let us give it a spin
function f(x...;y...)
#show x
#show Dict(y)
end
And now run it:
julia> f(1,2,"hello";a=22, b=777)
x = (1, 2, "hello")
Dict(y) = Dict(:a => 22, :b => 777)
Dict{Symbol, Int64} with 2 entries:
:a => 22
:b => 777
Finally, another one (perhaps less elegant) way could be:
g(v::NTuple{3,Int}) = sum(v)
This forces v to be a 3-element Tuple and g be called as g((1,2,3))

If your n is small, you can do this manually thanks to multiple dispatch.
julia> f(x) = x + 1 # Method definition for one variable.
f (generic function with 1 method)
julia> f(x, y) = x + y + 1 # Method definition for two variables.
f (generic function with 2 methods)
julia> f(2)
3
julia> f(2, 4)
7
You could use macro programming to generate a set of these methods automatically, but that quickly becomes complicated. You are likely better off structuring your function so that it operates on either a Vector or a Tuple of arbitrary length. The definition of the function will depend on what you want to do. Some examples which expect x to be a Tuple, Vector, or other similar datatype are below.
julia> g(x) = sum(x) # Add all the elements
g (generic function with 1 method)
julia> h(x) = x[end - 1] # Return the second to last element
h (generic function with 1 method)
julia> g([10, 11, 12])
33
julia> h([10, 11, 12])
11
If you would rather the function accept an arbitrary number of inputs rather than a single Tuple or Vector as you wrote in the original question, then you should define a method for the functions with the slurping operator ... as below. Note that the bodies of the function definitions and the outputs from the functions are exactly the same as before. Thus, the slurping operator ... is just for syntactical convenience. The functions below still operate on the Tuple x. The function arguments are just slurped into the tuple before doing anything else. Also note that you can define both the above and below methods simultaneously so that the user can choose either input method.
julia> g(x...) = sum(x) # Add all the variables
g (generic function with 2 methods)
julia> h(x...) = x[end - 1] # Return the second to last variable
h (generic function with 2 methods)
julia> g(10, 11, 12)
33
julia> h(10, 11, 12)
11
Finally, another trick that is sometimes useful is to call a function recursively. In other words, to have a function call itself (potentially using a different method).
julia> q(x) = 2 * x # Double the input
q (generic function with 1 method)
julia> q(x...) = q(sum(x)) # Add all the inputs and call the function again on the result
q (generic function with 2 methods)
julia> q(3)
6
julia> q(3, 4, 5)
24

Related

Outputting variable name and value in a loop

I want to loop over a list of variables nad output the variable name and value. E.g., say I have x=1 and y=2, then I want an output
x is 1
y is 2
I suspect I need to use Symbols for this. Here is my approach, but it isn't working:
function t(x,y)
for i in [x,y]
println("$(Symbol(i)) is $(eval(i))") # outputs "1 is 1" and "2 is 2"
end
end
t(1, 2)
Is there a way to achieve this? I guess a Dictionary would work, but would be interested to see if Symbols can also be used here.
One option is to use a NamedTuple:
julia> x = 1; y = 2
2
julia> vals = (; x, y)
(x = 1, y = 2)
julia> for (n, v) ∈ pairs(vals)
println("$n is $v")
end
x is 1
y is 2
Note the semicolon in (; x, y), which turns the x and y into kwargs so that the whole expression becomes shorthand for (x = x, y = y).
I will also add that your question looks like like you are trying to dynamically work with variable names in global scope, which is generally discouraged and an indication that you probably should be considering a datastructure that holds values alongside labels, such as the dictionary proposed in the other answer or a NamedTuple. You can google around if you want to read more on this, here's a related SO question:
Is it a good idea to dynamically create variables?
You can do this by passing the variable names:
x = 1
y = 2
function t(a, b)
for i in [a, b]
println("$(i) is $(eval(i))")
end
end
t(:x, :y)
x is 1
y is 2
At the start of the function, there's no record of the "x"-ness of x, or the "y"-ness of y. The function only sees 1 and 2. It's a bit confusing that you also called your two local variables x and y, I renamed them to show what's happening more clearly.
A solution with dictionaries would be nicer:
dict = Dict()
dict[:x] = 1
dict[:y] = 2
function t(d)
for k in keys(d)
println("$(k) is $(d[k])")
end
end
t(dict)
y is 2
x is 1
If you rather want to see programmatically what variables are present you could use varinfo or names:
julia> x=5; y=7;
julia> varinfo()
name size summary
–––––––––––––––– ––––––––––– –––––––
Base Module
Core Module
InteractiveUtils 316.128 KiB Module
Main Module
ans 8 bytes Int64
x 8 bytes Int64
y 8 bytes Int64
julia> names(Main)
7-element Vector{Symbol}:
:Base
:Core
:InteractiveUtils
:Main
:ans
:x
With any given name it's value can be obtained via getfield:
julia> getfield(Main, :x)
5
If you are rather inside a function than use #locals macro:
julia> function f(a)
b=5
c=8
#show Base.#locals
end;
julia> f(1)
#= REPL[13]:4 =# Base.#locals() = Dict{Symbol, Any}(:a => 1, :b => 5, :c => 8)
Dict{Symbol, Any} with 3 entries:
:a => 1
:b => 5
:c => 8

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

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!
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.
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

Evaluate vectors or tuples in a function (julia)

I want to evaluate a set of vectors (or tuples) in a function $f$ but Julia says me that is imposible.
For example: If I have an array of tuples p=[(1,1), (1,-1), (-1,1), (-1,-1)] and a function f(x,y)=x+y. I would like to calculate f(p[1]) = f(1,1)= 2. But Julia says me that the types are incompatible.
Can you help me please?
You have to splat a tuple like this:
julia> p=[(1,1), (1,-1), (-1,1), (-1,-1)]
4-element Array{Tuple{Int64,Int64},1}:
(1, 1)
(1, -1)
(-1, 1)
(-1, -1)
julia> f(x,y)=x+y
f (generic function with 1 method)
julia> f(p[1]...)
2
you could also define a higher order function splat that would conveniently wrap any function and perform splatting. It is useful as then you can e.g. broadcast such function:
julia> splat(f) = x -> f(x...)
splat (generic function with 1 method)
julia> splat(f)(p[1])
2
julia> splat(f).(p)
4-element Array{Int64,1}:
2
0
0
-2
Alternatively you can define your function f like this:
julia> f((x,y),)=x+y
f (generic function with 1 method)
julia> f(p[1])
2
and now you do not have to do splatting.
Just use the ... operator to unpack the tuple as parameters:
julia> f(p[1]...)
2
In addition to other answers, if your task allows you, you can just define
julia> f(x) = f(x...)
and use it as
julia> f.(p)
4-element Vector{Int64}:
2
0
0
-2

Repeat a function N times in Julia (composition)

I'm trying to make a function that compose a function f(x) by itself N times, something like that:
function CompositionN(f,N)
for i in 1:N
f(x) = f(f(x))
end
return f(x)
I need that the function CompositionN returns another function, not a value.
The solution with ntuple and splatting works very well up to a certain number of compositions, say 10, and then falls off a performance cliff.
An alternative solution, using reduce, is fast for large numbers of compositions, n, but comparatively slow for small numbers:
compose_(f, n) = reduce(∘, ntuple(_ -> f, n))
I think that the following solution is optimal for both large and small n:
function compose(f, n)
function (x) # <- this is syntax for an anonymous function
val = f(x)
for _ in 2:n
val = f(val)
end
return val
end
end
BTW: it is the construction of the composed function which is faster in the approach suggested here. The runtimes of the resulting functions seem to be identical.
You can take advantage of the ∘ function, which allows you to compose multiple functions:
julia> composition(f, n) = ∘(ntuple(_ -> f, n)...)
composition (generic function with 1 method)
julia> composition(sin, 3)(3.14)
0.001592651569876818
julia> sin(sin(sin(3.14)))
0.001592651569876818
Here's a recursive approach:
julia> compose(f, n) = n <= 1 ? f : f ∘ compose(f, n-1)
compose (generic function with 1 method)
julia> compose(x -> 2x, 3)(1)
8
If we're willing to do a little type piracy, we can use the power operator ^ on functions to represent n-th order self-composition:
julia> Base.:^(f::Union{Type,Function}, n::Integer) = n <= 1 ? f : f ∘ f^(n-1)
julia> f(x) = 2x
f (generic function with 1 method)
julia> (f^3)(1)
8

Outer constructor that has the same number of arguments as the field values

How can I define an outer constructor that has same number of arguments as the field values? What I want to do is something like this:
struct data
x
y
end
function data(x, y)
return data(x-y, x*y)
end
But it obviously causes stackoverflow.
Based on the various helpful comments, thanks to all, I changed my answer. Here is an example in Julia 1.0.0 of what you may be after. I am learning Julia myself, so maybe further comments can improve this example code.
# File test_code2.jl
struct Data
x
y
Data(x, y) = new(x - y, x * y)
end
test_data = Data(105, 5)
println("Constructor example: test_data = Data(105, 5)")
println("test_data now is...: ", test_data)
#= Output
julia> include("test_code2.jl")
Constructor example: test_data = Data(105, 5)
test_data now is...: Data(100, 525)
=#
This works for me
julia> struct datatype
x
y
end
julia> function datatype_create(a,b)
datatype(a - b, a * b)
end
datatype_create (generic function with 1 method)
julia> methods(datatype_create)
# 1 method for generic function "datatype_create":
[1] datatype_create(a, b) in Main at none:2
julia> methods(datatype)
# 1 method for generic function "(::Type)":
[1] datatype(x, y) in Main at none:2
julia> a = datatype_create(105,5)
datatype(100, 525)
julia> b = datatype_create(1+2im,3-4im)
datatype(-2 + 6im, 11 + 2im)
julia> c = datatype_create([1 2;3 4],[4 5;6 7])
datatype([-3 -3; -3 -3], [16 19; 36 43])
julia> d = datatype_create(1.5,0.2)
datatype(1.3, 0.30000000000000004)
If you are absolutely Ideologically Hell Bent on using an outer constructor, then you can do something like this
julia> datatype(a,b,dummy) = datatype(a - b,a * b)
datatype
julia> e = datatype(105,5,"dummy")
datatype(100, 525)
Antman's solution using the power of MACRO
julia> macro datatype(a,b)
return :( datatype($a - $b , $a * $b) )
end
#datatype (macro with 1 method)
julia> f = #datatype( 105 , 5 )
datatype(100, 525)

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