ZHEMM(3)        BLAS routine of NEC Numeric Library Collection        ZHEMM(3)



NAME
       ZHEMM  -  perform one of the matrix-matrix operations  C := alpha*A*B +
       beta*C,  C := alpha*B*A + 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
          C := alpha*A*B + beta*C
       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 hermi-
              tian matrix is to be referenced.

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

              Unchanged on exit.

       M      - INTEGER.
              On  entry,  M  specifies the number of rows of the matrix  C.  M
              must be at least zero.  Unchanged on 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 triangular part of  A  is not refer-
              enced,  and when  UPLO = 'L' or 'l', the leading  m by m   lower
              triangular part  of the  array  A must  contain  the  lower tri-
              angular part  of the  hermitian matrix and the   strictly  upper
              triangular  part  of   A  is not referenced.  Before entry  with
              SIDE = 'R' or 'r',  the  n by n  part of the array  A  must con-
              tain  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 triangu-
              lar part  of the  array  A must  contain  the  lower  triangular
              part   of the  hermitian matrix and the  strictly upper triangu-
              lar 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 declared  in
              the  calling  (sub)  program.   LDB  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 Harwell.  Jeremy Du Croz, Numerical
              Algorithms  Group  Ltd.   Sven  Hammarling, Numerical Algorithms
              Group Ltd.



BLAS routine                    16 October 1992                       ZHEMM(3)