# zsymm

```ZSYMM(l)                         BLAS routine                         ZSYMM(l)

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

SYNOPSIS
SUBROUTINE ZSYMM ( 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
ZSYMM  performs one of the matrix-matrix operations

or

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

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

PARAMETERS
SIDE   - CHARACTER*1.
On entry,  SIDE  specifies whether  the  symmetric 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  symmetric  matrix   A  is  to  be
referenced as follows:

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

UPLO = 'L' or 'l'   Only the lower triangular part of the
symmetric 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  symmetric 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  symmetric 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  symmetric 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  symmetric 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
symmetric 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  symmetric matrix and the
strictly upper triangular part of  A  is not referenced.
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                       ZSYMM(l)```