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# zhemm

```
NAME
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
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.

ka is
A      -
COMPLEX*16       array of DIMENSION ( LDA, ka ), where
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 lead-
ing m by m upper triangular part of the array  A
must contain the upper triangular part of the  hermi-
tian matrix and the  strictly  lower triangular 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 referenced.
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 lead-
ing n by n upper triangular part of the array  A
must contain the upper triangular part of the  hermi-
tian 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  contain  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
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.
```