CODEWITHSUNDEEP
setjulia
Denis Tolkachyov
Denis Tolkachyov

Reputation: 19

How can I randomly choose a point from a set with Julia lang?

I have set of points defined by inequalities

f.e 0<x<3, 0<y<3 and x^2+y^2>1,

How can I randomly choose a point from this set?

Upvotes: 0

Views: 173

Answers (1)

Bogumił Kamiński
Bogumił Kamiński

Reputation: 69869

You can use rejection sampling, e.g.:

function myrand(R)
    while true
        x, y = 3rand(), 3rand() # now x∈[0,3[ and y∈[0,3[
        x^2+y^2>R^2 && return (x,y)
    end
end

Of course you should make sure that R^2<18 as otherwise you will get an infinite loop. The function is more expensive (takes more time to finish) the closer R is to this boundary.

If you wanted to improve the speed of it and R>3 (e.g. when you are very close to the boundary) then you can sample x and y from the interval [sqrt(R^2-9),3] by rescaling rand() result appropriately. The reason is that you know that if x or y is less or equal than sqrt(R^2-9) you will reject such a sample for sure (effectively you sample from a smaller square).

Upvotes: 2

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