Making a point-sampling matrix

k <- 5
mat <- diag(1,nrow=k,ncol=k)
set.seed(10)
samp <- mat[sample(1:k,3,rep=FALSE),]
samp

#check
apply(samp,1,sum)

apply(samp,2,sum)

Dear all,
I would like to create a k,n matrix which that will include



- k random elements with value 1
-all rest zeros

-one single "1" in each row

- each column will have maximum one "1"


so far I have a so stupid function that with nested while tries to fit k numbers randomly in a row by row fashion, checking also if the c column rule is violated. In that case there is also another loop that will try to find a new solution.

That way it takes ages, as it is natural to complete a matrix of 300,512 as the new ones conflict all the time.

I am trying to find an easy way to make this algorithm way simpler that will help me reduce the time needed.
I was thinking then if R can help me by shuffling number from 1? to 300 randomly, so to avoid the first loop that does that goes row by row.. and then find an easy way to check if the column rule is violated.

Do you think that you can spend some time help me?

Have a nice weekend

Regards
Alex

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