ZUNGTR  -  generate  a  complex  unitary matrix Q which is
       defined as the product of  n-1  elementary  reflectors  of
       order N, as returned by ZHETRD


SYNOPSIS

       SUBROUTINE ZUNGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO
                          )

           CHARACTER      UPLO

           INTEGER        INFO, LDA, LWORK, N

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


PURPOSE

       ZUNGTR generates a  complex  unitary  matrix  Q  which  is
       defined  as  the  product  of n-1 elementary reflectors of
       order N, as returned by ZHETRD: if UPLO = 'U', Q =  H(n-1)
       . . . H(2) H(1),

       if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).


ARGUMENTS

       UPLO    (input) CHARACTER*1
               =  'U':  Upper  triangle  of A contains elementary
               reflectors from ZHETRD; = 'L': Lower triangle of A
               contains elementary reflectors from ZHETRD.

       N       (input) INTEGER
               The order of the matrix Q. N >= 0.

       A       (input/output) COMPLEX*16 array, dimension (LDA,N)
               On entry, the vectors which define the  elementary
               reflectors,  as  returned by ZHETRD.  On exit, the
               N-by-N unitary matrix Q.

       LDA     (input) INTEGER
               The leading dimension of the array A. LDA >= N.

       TAU     (input) COMPLEX*16 array, dimension (N-1)
               TAU(i) must contain the scalar factor of the  ele­
               mentary reflector H(i), as returned by ZHETRD.

       WORK    (workspace/output) COMPLEX*16 array, dimension
               (LWORK)
               On exit, if INFO = 0, WORK(1) returns the  optimal
               LWORK.

       LWORK   (input) INTEGER
               The  dimension  of  the  array WORK. LWORK >= N-1.
               For optimum performance LWORK >=  (N-1)*NB,  where
               NB is the optimal blocksize.

               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 had an ille­
               gal value


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