ZUNGQL   -  generate  an  M-by-N  complex  matrix  Q  with
       orthonormal columns,


SYNOPSIS

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

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

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


PURPOSE

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

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

       as returned by ZGEQLF.


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. M >= N >=
               0.

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

       A       (input/output) COMPLEX*16 array, dimension (LDA,N)
               On entry, the (n-k+i)-th column must  contain  the
               vector  which  defines  the  elementary  reflector
               H(i), for i = 1,2,...,k, as returned by ZGEQLF  in
               the  last  k  columns 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 ZGEQLF.

       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,N).   For optimum performance LWORK >= N*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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