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


SYNOPSIS

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

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

           COMPLEX*16     A( LDA, * ), TAU( * ), WORK( * )


PURPOSE

       ZUNGRQ 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 ZGERQF.


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*16 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 ZGERQF 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*16 array, dimension (K)
               TAU(i) must contain the scalar factor of the  ele­
               mentary reflector H(i), as returned by ZGERQF.

       WORK    (workspace/output) COMPLEX*16 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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