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## NAME

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

```

## SYNOPSIS

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

CHARACTER*1  SIDE, UPLO

INTEGER      M, N, LDA, LDB, LDC

DOUBLE       PRECISION ALPHA, BETA

DOUBLE       PRECISION A( LDA, * ), B( LDB, * ), C( LDC, * )

```

## PURPOSE

```       DSYMM  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  - DOUBLE PRECISION.
On  entry, ALPHA specifies the scalar alpha.  Unchanged on exit.

A      - DOUBLE PRECISION 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      - DOUBLE PRECISION 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   - DOUBLE PRECISION.
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      - DOUBLE PRECISION 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.
```