(R) Generate a semi-orthogonal random matrix

Question

I need to generate a random NxK matrix (where N > K), where the columns K are orthogonal random vectors.

An option I tried is to generate a squared orthogonal matrix with size NxN and then select the first K columns, but I wonder if there is a more efficient way of doing so.

Current code (in R):

library(pracma)
Z <- rortho(N)[,1:K]

Answer 1

You can do that with the rstiefel package:

library(rstiefel)
rustiefel(N, K)