  A QR factorization of a tall and skinny matrix with n columns can be
represented as a reduction. The operation used along the reduction tree has in
input two n-by-n upper triangular matrices and in output an n-by-n upper
triangular matrix which is defined as the R factor of the two input matrices
stacked the one on top of the other. This operation is binary, associative, and
commutative. We can therefore leverage the MPI library capabilities by using
user-defined MPI operations and MPI_Reduce to perform this reduction. The
resulting code is compact and portable. In this context, the user relies on the
MPI library to select a reduction tree appropriate for the underlying
architecture.
