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


SYNOPSIS

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

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

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


PURPOSE

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

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

       as returned by ZGEQRF.


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 i-th column must contain the  vector
               which defines the elementary reflector H(i), for i
               = 1,2,...,k, as returned by ZGEQRF in the first  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 ZGEQRF.

       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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