Extracting restricted results from polyroots()

[John Shannon]

I'm trying to find the real-valued x in (0,1) that solves this polynomial:
\[ Nx^{N-1} - (N-1)x^N = y \] where y is in (0,1) and N is a given integer. I can get solutions using Mata's polyroots function for a given value of y:

mata
   c = -y, rangen(0, 0, N)', N, N-1
   polyroots(c)
end

But this gives me a bunch of complex solutions that fall outside my desired range. Is there a way to extract a certain restricted value from the solutions vector? I can of course look at the solutions and copy them directly, but I want to run this as part of an ado-file and so need a way to automate the process.

[Christophe Kolodziejczyk]

You can for example use select() in order to get the solutions which are real

s = polyroots(c)
sReal = select(s,Im(s):==0)

[John Shannon]

Thanks, I hadn't thought of that. Using your code produces a vector of complex numbers, so I needed to make it real and then apply the other restrictions one by one. This is what I ended up with:

s = polyroots(c)
sReal = select(s, Im(s):==0)
sReal = Re(sReal)
sGeq0 = select(sReal, sReal[.,.]:>0)
sLeq1 = select(sGeq0, sGeq0[.,.]:<1)
solution = sLeq1

I can then put this entry into a view matrix to export the results to a Stata variable. Problem solved!

[Christophe Kolodziejczyk]

John Shannon I think you can save one line of code with

solution = select(sReal, sReal :> 0 :& sReal:<1)