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


SYNOPSIS

       SUBROUTINE CUNMHR( SIDE, TRANS, M, N, ILO,  IHI,  A,  LDA,
                          TAU, C, LDC, WORK, LWORK, INFO )

           CHARACTER      SIDE, TRANS

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

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


PURPOSE

       CUNMHR 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 IHI-ILO elementary reflectors, as  returned
       by CGEHRD:

       Q = H(ilo) H(ilo+1) . . . H(ihi-1).


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': apply Q  (No transpose)
               = 'C': apply Q**H (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.

       ILO     (input) INTEGER
               IHI      (input) INTEGER ILO and IHI must have the
               same values as in the previous call of  CGEHRD.  Q
               is  equal  to the unit matrix except in the subma­
               trix Q(ilo+1:ihi,ilo+1:ihi).  If SIDE = 'L',  then
               1  <=  ILO  <= IHI <= M, if M > 0, and ILO = 1 and
               IHI = 0, if M = 0; if SIDE = 'R', then 1 <= ILO <=
               IHI  <= N, if N > 0, and ILO = 1 and IHI = 0, if N
               = 0.

               (LDA,M) if SIDE = 'L' (LDA,N) if SIDE  =  'R'  The
               vectors which define the elementary reflectors, as
               returned by CGEHRD.

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

       TAU     (input) COMPLEX 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 CGEHRD.

       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**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 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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