The LAPACK routine dgels was deeply modified (into rdgels) to use a
slightly modified modified dgeqp3 (rdgeqp3) for performing a
rank-revealing QR with column-pivoting (or optionally dgeqrf without
pivoting, but only for full rank problems). rdgeqp3 calls rdlaqp2,
a highly modified dlaqp2, to perform the actual QR+rank detection.
Overwhelmingly, the computation for rdgels is in the application
of the elementary reflector via the call to dlarf in rdlaqp2.
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