Starting in LAPACK v3.12.0, there is a routine geqp3rk (double precision subroutine here), that performs a truncated QR factorization based on of three stopping conditions:

• kmax: if an integer kmax is provided, it provides a QR factorization truncated at kmax columns, i.e. its the same as pqrfact(A; sketch=:none, rank = kmax)
• abstol: if provided stops when pivot element has value less than the tolerance, similar to pqrfact(A; sketch=:none, atol = abstol)
• reltol: similar to above but uses reltol instead, similar to pqrfact(A; sketch=:none, rtol = reltol)

That is, there is now a lapack routine to do exactly what perfect does.

I think we should be using this going forward, since it seems to be a little bit faster than the Julia native implementation that is the function geqp3_adap_main!.

There is one major caveat: I am still not sure why but the R factor differs a little when the stopping criteria are abstol or reltol. Submitting a PR related to this.