ZHEMM - perform one of the matrix-matrix operations   C :=
       alpha*A*B + beta*C,


SYNOPSIS

       SUBROUTINE ZHEMM ( SIDE, UPLO, M, N,  ALPHA,  A,  LDA,  B,
                        LDB, BETA, C, LDC )

           CHARACTER*1  SIDE, UPLO

           INTEGER      M, N, LDA, LDB, LDC

           COMPLEX*16   ALPHA, BETA

           COMPLEX*16   A( LDA, * ), B( LDB, * ), C( LDC, * )


PURPOSE

       ZHEMM  performs one of the matrix-matrix operations

       or

          C := alpha*B*A + beta*C,

       where alpha and beta are scalars, A is an hermitian matrix
       and  B and C are m by n matrices.


PARAMETERS

       SIDE   - CHARACTER*1.
              On entry,  SIDE  specifies whether  the   hermitian
              matrix   A  appears  on  the  left or right  in the
              operation as follows:

              SIDE = 'L' or 'l'   C := alpha*A*B + beta*C,

              SIDE = 'R' or 'r'   C := alpha*B*A + beta*C,

              Unchanged on exit.

       UPLO   - CHARACTER*1.
              On  entry,   UPLO  specifies  whether   the   upper
              or   lower  triangular   part   of   the  hermitian
              matrix   A  is  to  be referenced as follows:

              UPLO = 'U' or 'u'   Only the upper triangular  part
              of the hermitian matrix is to be referenced.

              UPLO  = 'L' or 'l'   Only the lower triangular part
              of the hermitian matrix is to be referenced.

              Unchanged on exit.

       M      - INTEGER.
              On entry,  M  specifies the number of rows  of  the

              exit.

       N      - INTEGER.
              On entry, N specifies the number of columns of  the
              matrix  C.  N  must be at least zero.  Unchanged on
              exit.

       ALPHA  - COMPLEX*16      .
              On  entry,  ALPHA  specifies  the   scalar   alpha.
              Unchanged on exit.

       A       -  COMPLEX*16       array of DIMENSION ( LDA, ka
              ), where ka is
              m   when   SIDE  = 'L' or 'l'  and is n  otherwise.
              Before entry  with  SIDE = 'L' or 'l',  the  m by m
              part  of  the array  A  must contain the  hermitian
              matrix,  such that when  UPLO =  'U'  or  'u',  the
              leading  m  by m upper triangular part of the array
              A  must contain the upper triangular  part  of  the
              hermitian  matrix and the  strictly  lower triangu­
              lar part of  A  is not referenced,  and when   UPLO
              = 'L' or 'l', the leading  m by m  lower triangular
              part  of the  array  A must   contain   the   lower
              triangular  part   of the  hermitian matrix and the
              strictly upper triangular part of  A  is not refer­
              enced.  Before entry  with  SIDE = 'R' or 'r',  the
              n by n  part of the  array   A   must  contain  the
              hermitian  matrix,   such  that when  UPLO = 'U' or
              'u', the leading n by n upper  triangular  part  of
              the  array   A   must  contain the upper triangular
              part of the  hermitian  matrix  and  the   strictly
              lower  triangular  part  of   A  is not referenced,
              and when  UPLO = 'L' or 'l', the leading   n  by  n
              lower  triangular part  of the  array  A must  con­
              tain  the  lower triangular part  of the  hermitian
              matrix  and  the  strictly upper triangular part of
              A  is not  referenced.   Note  that  the  imaginary
              parts   of  the  diagonal elements need not be set,
              they are assumed to be zero.  Unchanged on exit.

       LDA    - INTEGER.
              On entry, LDA specifies the first dimension of A as
              declared  in the  calling (sub) program. When  SIDE
              = 'L' or 'l'  then LDA must be at least  max( 1,  m
              ),  otherwise   LDA  must  be at least max( 1, n ).
              Unchanged on exit.

       B      - COMPLEX*16       array of DIMENSION ( LDB, n ).
              Before entry, the leading  m by n part of the array
              B  must contain the matrix B.  Unchanged on exit.

       LDB    - INTEGER.
              On entry, LDB specifies the first dimension of B as

              must   be   at   least  max(  1, m ).  Unchanged on
              exit.

       BETA   - COMPLEX*16      .
              On entry,  BETA  specifies the scalar  beta.   When
              BETA  is supplied as zero then C need not be set on
              input.  Unchanged on exit.

       C      - COMPLEX*16       array of DIMENSION ( LDC, n ).
              Before entry, the leading  m  by  n   part  of  the
              array   C  must contain the matrix  C,  except when
              beta  is zero, in which case C need not be  set  on
              entry.   On  exit,  the array  C  is overwritten by
              the  m by n updated matrix.

       LDC    - INTEGER.
              On entry, LDC specifies the first dimension of C as
              declared  in   the   calling  (sub)  program.   LDC
              must  be  at  least max(  1,  m  ).   Unchanged  on
              exit.

              Level 3 Blas routine.

              --  Written  on  8-February-1989.   Jack  Dongarra,
              Argonne National Laboratory.  Iain Duff, AERE  Har­
              well.   Jeremy  Du Croz, Numerical Algorithms Group
              Ltd.  Sven Hammarling, Numerical  Algorithms  Group
              Ltd.


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