CUNGRQ   -  generate  an  M-by-N  complex  matrix  Q  with
       orthonormal rows,


SYNOPSIS

       SUBROUTINE CUNGRQ( M, N, K, A, LDA, TAU, WORK, LWORK, INFO
                          )

           INTEGER        INFO, K, LDA, LWORK, M, N

           COMPLEX        A( LDA, * ), TAU( * ), WORK( * )


PURPOSE

       CUNGRQ generates an M-by-N complex matrix Q with orthonor­
       mal rows, which is defined as the last M rows of a product
       of K elementary reflectors of order N

             Q  =  H(1)' H(2)' . . . H(k)'

       as returned by CGERQF.


ARGUMENTS

       M       (input) INTEGER
               The number of rows of the matrix Q. M >= 0.

       N       (input) INTEGER
               The number of columns of the matrix Q. N >= M.

       K       (input) INTEGER
               The  number of elementary reflectors whose product
               defines the matrix Q. M >= K >= 0.

       A       (input/output) COMPLEX array, dimension (LDA,N)
               On entry, the (m-k+i)-th row must contain the vec­
               tor  which  defines the elementary reflector H(i),
               for i = 1,2,...,k, as returned by  CGERQF  in  the
               last k rows of its array argument A.  On exit, the
               M-by-N matrix Q.

       LDA     (input) INTEGER
               The  first  dimension  of  the  array  A.  LDA  >=
               max(1,M).

       TAU     (input) COMPLEX array, dimension (K)
               TAU(i)  must contain the scalar factor of the ele­
               mentary reflector H(i), as returned by CGERQF.

       WORK    (workspace/output) COMPLEX array, dimension
               (LWORK)
               On  exit, if INFO = 0, WORK(1) returns the optimal
               LWORK.

               The  dimension  of  the  array  WORK.   LWORK   >=
               max(1,M).   For optimum performance LWORK >= M*NB,
               where NB is the optimal blocksize.

               If LWORK = -1, then a workspace query is  assumed;
               the  routine  only  calculates the optimal size of
               the WORK array, returns this value  as  the  first
               entry  of  the  WORK  array,  and no error message
               related to LWORK is issued by XERBLA.

       INFO    (output) INTEGER
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument has an ille­
               gal value


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