o calculate a QR factorization of the first block column and
  apply the orthogonal transformations (from the left) also to the
  second block column of a structured matrix, as follows
                       _
         [ R   0 ]   [ R   C ]
    Q' * [       ] = [       ]
         [ A   B ]   [ 0   D ]
              _
  where R and R are upper triangular. The matrix A can be full or
  upper trapezoidal/triangular. The problem structure is exploited.
  This computation is useful, for instance, in combined mea