ZUNMRZ  -  overwrite  the  general complex M-by-N matrix C
       with  SIDE = 'L' SIDE = 'R' TRANS = 'N'


SYNOPSIS

       SUBROUTINE ZUNMRZ( SIDE, TRANS, M, N, K, L, A,  LDA,  TAU,
                          C, LDC, WORK, LWORK, INFO )

           CHARACTER      SIDE, TRANS

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

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


PURPOSE

       ZUNMRZ overwrites the general complex M-by-N matrix C with
       SIDE  =  'L'  SIDE  = 'R' TRANS = 'N': Q * C C * Q TRANS =
       'C':      Q**H * C       C * Q**H

       where Q is a complex unitary matrix defined as the product
       of k elementary reflectors

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

       as  returned  by ZTZRZF. Q is of order M if SIDE = 'L' and
       of order N if SIDE = 'R'.


ARGUMENTS

       SIDE    (input) CHARACTER*1
               = 'L': apply Q or Q**H from the Left;
               = 'R': apply Q or Q**H from the Right.

       TRANS   (input) CHARACTER*1
               = 'N':  No transpose, apply Q;
               = 'C':  Conjugate transpose, apply Q**H.

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

       N       (input) INTEGER
               The number of columns of the matrix C. N >= 0.

       K       (input) INTEGER
               The number of elementary reflectors whose  product
               defines the matrix Q.  If SIDE = 'L', M >= K >= 0;
               if SIDE = 'R', N >= K >= 0.

       L       (input) INTEGER
               The number of columns of the matrix  A  containing
               the meaningful part of the Householder reflectors.
               If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >=  L
               >= 0.

               (LDA,M)  if  SIDE = 'L', (LDA,N) if SIDE = 'R' The
               i-th row must contain the vector which defines the
               elementary  reflector  H(i), for i = 1,2,...,k, as
               returned by ZTZRZF in the last k rows of its array
               argument  A.   A  is  modified  by the routine but
               restored on exit.

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

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

       C       (input/output) COMPLEX*16 array, dimension (LDC,N)
               On  entry,  the  M-by-N  matrix  C.  On exit, C is
               overwritten by Q*C or Q**H*C or C*Q**H or C*Q.

       LDC     (input) INTEGER
               The leading dimension  of  the  array  C.  LDC  >=
               max(1,M).

       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.  If SIDE = 'L',
               LWORK  >=  max(1,N);  if  SIDE  =  'R',  LWORK  >=
               max(1,M).   For  optimum performance LWORK >= N*NB
               if SIDE = 'L', and LWORK >= M*NB if  SIDE  =  'R',
               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 had an ille­
               gal value


FURTHER DETAILS

       Based on contributions by
         A. Petitet, Computer  Science  Dept.,  Univ.  of  Tenn.,
       Knoxville, USA


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