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


SYNOPSIS

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

           CHARACTER      SIDE, TRANS, UPLO

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

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


PURPOSE

       ZUNMTR 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 of order nq, with nq =
       m  if SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as
       the product of nq-1 elementary reflectors, as returned  by
       ZHETRD:

       if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);

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


ARGUMENTS

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

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

       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.

       A       (input) COMPLEX*16 array, dimension
               (LDA,M)  if  SIDE  = 'L' (LDA,N) if SIDE = 'R' The
               vectors which define the elementary reflectors, as
               returned by ZHETRD.

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

       TAU     (input) COMPLEX*16 array, dimension
               (M-1)  if  SIDE  =  'L' (N-1) if SIDE = 'R' TAU(i)
               must contain the scalar factor of  the  elementary
               reflector H(i), as returned by ZHETRD.

       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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