CUNMR3  -  overwrite  the  general complex m by n matrix C
       with  Q * C if SIDE = 'L' and TRANS = 'N', or   Q'*  C  if
       SIDE  =  'L'  and TRANS = 'C', or  C * Q if SIDE = 'R' and
       TRANS = 'N', or  C * Q' if SIDE = 'R' and TRANS = 'C',


SYNOPSIS

       SUBROUTINE CUNMR3( SIDE, TRANS, M, N, K, L, A,  LDA,  TAU,
                          C, LDC, WORK, INFO )

           CHARACTER      SIDE, TRANS

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

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


PURPOSE

       CUNMR3 overwrites the general complex m by n matrix C with
       Q  *  C  if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE =
       'L' and TRANS = 'C', or C * Q if SIDE = 'R'  and  TRANS  =
       'N', or C * Q' if SIDE = 'R' and TRANS = 'C', where Q is a
       complex unitary matrix defined as the product of k elemen­
       tary reflectors

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

       as  returned  by CTZRZF. 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' from the Left
               = 'R': apply Q or Q' from the Right

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

       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.

               >= 0.

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

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

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

       WORK    (workspace) COMPLEX array, dimension
               (N) if SIDE = 'L', (M) if SIDE = 'R'

       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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