# Function with multiple arguments with all subsets of variables
**URL:** https://discourse.julialang.org/t/function-with-multiple-arguments-with-all-subsets-of-variables/42022
**Category:** General Usage
**Tags:** function
**Created:** [June 25, 2020, 3:23am UTC](https://discourse.julialang.org/t/function-with-multiple-arguments-with-all-subsets-of-variables/42022 "2020-06-25T03:23:09Z")
**Posts on this page:** 8
**Page:** 1
### Author:  [@sergevic](https://discourse.julialang.org/u/sergevic)
#### Post date: [June 25, 2020, 3:23am UTC](https://discourse.julialang.org/t/function-with-multiple-arguments-with-all-subsets-of-variables/42022/1 "2020-06-25T03:23:09Z")
I have to construct a set of functions that I want to optimize. The set consists of functions with all subsets I can build with p variables. If p is small, that’s easy. For example, with p=2, I can build 2^2-1=3 functions, one for each subset of variables (I excluded the empty subset):
```julia
f(x)=2*x^2+1
f(y)=2*y^2+1
f(x)=2*x[1]^2+2*x[2]^2+1
```
But if I have p=6 variables, how can I construct all the 2^6-1=63 possible functions to optimize without having to create 63 functions? I thought about creating an Array like `x=[x[1],x[2],x[3],x[4],x[5],x[6]]` and then building all the functions, setting to 0 all the variables that are not present in the function corresponding to the selected subset.
---
### Author:  [@xiaodai](https://discourse.julialang.org/u/xiaodai)
#### Post date: [June 25, 2020, 3:44am UTC](https://discourse.julialang.org/t/function-with-multiple-arguments-with-all-subsets-of-variables/42022/2 "2020-06-25T03:44:06Z")
> [@sergevic](#):
>
> of functions with all subsets I can build with pp variables
Functions of what form exactly? Looking at your code it’s functions of the form `2x^2 + 2y^2+2z^2`?
---
### Author:  [@xiaodai](https://discourse.julialang.org/u/xiaodai)
#### Post date: [June 25, 2020, 3:57am UTC](https://discourse.julialang.org/t/function-with-multiple-arguments-with-all-subsets-of-variables/42022/3 "2020-06-25T03:57:40Z")
I think something like this
```julia
function one_func(x)
# x nees to be iterable of bool
return function(x1::AbstractVector)
res = 1
for (i, doit) in enumerate(x)
if doit
res += 2x1[i]^2
end
end
res
end
end
function func_factory(len)
seed = ((false, true) for i in 1:len)
collect(one_func(x) for x in Iterators.drop(Iterators.product(seed...),1))
end
funs = func_factory(2)
funs[1]([1, 2])
funs[2]([1, 2])
funs[3]([1, 2])
funs6 = func_factory(6)
[fun([1,2, 3, 4, 5, 6]) for fun in funs6]
```
You can also use macros for even better results. For this is sufficient for me.
---
### Author:  [@sergevic](https://discourse.julialang.org/u/sergevic)
#### Post date: [June 25, 2020, 4:39pm UTC](https://discourse.julialang.org/t/function-with-multiple-arguments-with-all-subsets-of-variables/42022/4 "2020-06-25T16:39:56Z")
Sorry for the delay. I went to bed a few minutes after my post… Yes exactly that’s the form of the function!
---
### Author:  [@sergevic](https://discourse.julialang.org/u/sergevic)
#### Post date: [June 25, 2020, 4:41pm UTC](https://discourse.julialang.org/t/function-with-multiple-arguments-with-all-subsets-of-variables/42022/5 "2020-06-25T16:41:09Z")
Ah I think this solution will do the trick, because I have another similar problem to treat with a more complex function! I will post this more challenging problem 😉
---
### Author:  [@sergevic](https://discourse.julialang.org/u/sergevic)
#### Post date: [June 25, 2020, 5:09pm UTC](https://discourse.julialang.org/t/function-with-multiple-arguments-with-all-subsets-of-variables/42022/6 "2020-06-25T17:09:37Z")
Here is a more challenging problem with p=5 variables, to see if the proposed solution can be adapted. I have 2 coefficient matrices, say
`X=rand(10,5)` and `Y=rand(10,1)`,
where each column of X represents each variable. I must construct the following function:
```julia
h(betak)=-sum([Y[i]*transpose(X[i,:])*[betak[1],betak[2],betak[3],betak[4],betak[5],betak[6]] for i in 1:size(X,1)])+
sum([log(1+exp(transpose(X[i,:])*[betak[1],betak[2],betak[3],betak[4],betak[5],betak[6]])) for i in 1:size(X,1)])+
length(betak)/2*log(2*pi)
```
Basically, the function has to multiply each row of X by the subset of variables selected. In this example, I have the whole subset of variables `[betak[1],betak[2],betak[3],betak[4],betak[5],betak[6]]` but I’d like to build the same function for each subset. For example, if the subset is `[betak[1],betak[4],betak[5]]` I wonder how I can write the same function for that subset and for all other subsets. I thought about using the same code but with `[betak[1],0,0,betak[4],betak[5],0]`. However, I’m not sure how to do it… I don’t want to write all the 2^5-1=31 possible functions…
---
### Author:  [@xiaodai](https://discourse.julialang.org/u/xiaodai)
#### Post date: [June 26, 2020, 2:05am UTC](https://discourse.julialang.org/t/function-with-multiple-arguments-with-all-subsets-of-variables/42022/7 "2020-06-26T02:05:55Z")
> [@xiaodai](#):
>
> `seed = ((false, true) for i in 1:len)`
Feels like u can change this line to output `false` where u don’t want. E.g.
```julia
keep = [1, 4, 5]
seed = (i in keep ? (false, true) : (false,) for in in 1:len)
```
Now u gotta figure out how to generate all possible `keep`. Look into the `Combinatorics.combination` function and see what u can figure out. To get you started:
```julia
using Combinatorics
collect(combinations(1:6, 3))
```
---
### Author:  [@sergevic](https://discourse.julialang.org/u/sergevic)
#### Post date: [June 26, 2020, 2:08am UTC](https://discourse.julialang.org/t/function-with-multiple-arguments-with-all-subsets-of-variables/42022/8 "2020-06-26T02:08:31Z")
Thanks! Yes I already have all the combinations with `Combinatorics` 🙂