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


SYNOPSIS

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

           CHARACTER      SIDE, TRANS

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

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


PURPOSE

       ZUNMQR 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 ZGEQRF. 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.

       A       (input) COMPLEX*16 array, dimension (LDA,K)
               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.  A is modified by


       LDA     (input) INTEGER
               The leading dimension of the array A.  If  SIDE  =
               'L',  LDA  >=  max(1,M);  if  SIDE  =  'R', LDA >=
               max(1,N).

       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.

       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


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