# How to create random values given a restriction?
**URL:** https://discourse.julialang.org/t/how-to-create-random-values-given-a-restriction/28977
**Category:** New to Julia
**Tags:** question
**Created:** [September 20, 2019, 4:10am UTC](https://discourse.julialang.org/t/how-to-create-random-values-given-a-restriction/28977 "2019-09-20T04:10:42Z")
**Posts on this page:** 4
**Page:** 1
### Author:  [@msechecs](https://discourse.julialang.org/u/msechecs)
#### Post date: [September 20, 2019, 4:10am UTC](https://discourse.julialang.org/t/how-to-create-random-values-given-a-restriction/28977/1 "2019-09-20T04:10:42Z")
Hello everyone,
I’m trying to generate three vectors `(ωa, ωb, ωc)` made up of random numbers.
The only restriction is that: `ωa[i] + ωb[i] + ωa[i] ==1`
However I am new in the Julia and I don’t know how to do it or if there is a package that does something similar.
This will help me later to create a Markowitz model where I decide the proportions where I will distribute the total of my investment in 3 assets
I hope someone can take a look at it and give me his thoughts!
```julia
ωa = ones(n,1)
ωb = ones(n,1)
ωc = ones(n,1)
for i=1:n
ωa[i] = rand()
ωb[i] = rand()
ωc[i] = rand()
return [ωa+ωb+ωc]
end
```
---
### Author:  [@jling](https://discourse.julialang.org/u/jling)
#### Post date: [September 20, 2019, 4:45am UTC](https://discourse.julialang.org/t/how-to-create-random-values-given-a-restriction/28977/2 "2019-09-20T04:45:24Z")
use triple ` to denote a code block; ` "his" => "their"`
in general it’s difficult, for example, imagine generating a random Sudoku obeying uniform distribution.
But in your case, I think you can generate a `rand(3)` and normalize it so that the sum is `1`, this should give a uniform distribution. (I think)
```julia
julia> a = Matrix{Float64}(undef, 10, 3);
julia> for i in 1:size(a)[1]
v = rand(3)
a[i,:] = v / sum(v)
end
julia> (sum(a, dims=2) .≈ 1) |> all
true
```
edit: I realized this the problem is highly dependent on what is the range of your `ω` s, and what is their distribution, in that regards, use [`Distributions.jl`](https://github.com/JuliaStats/Distributions.jl)
---
### Author:  [@Tamas\_Papp](https://discourse.julialang.org/u/Tamas_Papp)
#### Post date: [September 20, 2019, 5:12am UTC](https://discourse.julialang.org/t/how-to-create-random-values-given-a-restriction/28977/3 "2019-09-20T05:12:06Z")
Normalization, as suggested by @jling, is probably the simplest approach here, and the easiest to customize by using different univariate distributions.
You can also use a Dirichlet distribution to draw a random value in a simplex:
```julia
using Distributions
rand(Dirichlet(3, 2))
```
Finally, you can also use [stick-breaking](https://en.wikipedia.org/wiki/Dirichlet_process#The_stick-breaking_process) to transform 2 random values (but the result will not be symmetric unless you apply a correction):
```julia
using Random
function rand_simplex(rng, n)
z = 1.0
s = Vector{Float64}(undef, n)
for i in 1:(n-1)
r = rand(rng, Float64)
s[i] = z * r
z *= 1 - r
end
s[end] = z
s
end
rand_simplex(Random.GLOBAL_RNG, 3)
```
---
### Author:  [@msechecs](https://discourse.julialang.org/u/msechecs)
#### Post date: [September 20, 2019, 3:12pm UTC](https://discourse.julialang.org/t/how-to-create-random-values-given-a-restriction/28977/4 "2019-09-20T15:12:20Z")
Thanks you both @jling and @Tamas_Papp for your aproaches, in all cases they were very useful to me, in particular I think I will lean towards the Dirichlet method of the distribution package.