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.

              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  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  symmetric 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
              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   con­
              tain  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

              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 Har­
              well.  Jeremy Du Croz, Numerical  Algorithms  Group
              Ltd.   Sven  Hammarling, Numerical Algorithms Group
              Ltd.


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