SSYR2K  performs one of the symmetric rank 2k operations
    C := alpha*A*B**T + alpha*B*A**T + beta*C,
 or
    C := alpha*A**T*B + alpha*B**T*A + beta*C,
 where  alpha and beta  are scalars, C is an  n by n  symmetric matrix
 and  A and B  are  n by k  matrices  in the  first  case  and  k by n
 matrices in the second case.

UPLO

          UPLO is CHARACTER*1
           On  entry,   UPLO  specifies  whether  the  upper  or  lower
           triangular  part  of the  array  C  is to be  referenced  as
           follows:
              UPLO = 'U' or 'u'   Only the  upper triangular part of  C
                                  is to be referenced.
              UPLO = 'L' or 'l'   Only the  lower triangular part of  C
                                  is to be referenced.

TRANS

          TRANS is CHARACTER*1
           On entry,  TRANS  specifies the operation to be performed as
           follows:
              TRANS = 'N' or 'n'   C := alpha*A*B**T + alpha*B*A**T +
                                        beta*C.
              TRANS = 'T' or 't'   C := alpha*A**T*B + alpha*B**T*A +
                                        beta*C.
              TRANS = 'C' or 'c'   C := alpha*A**T*B + alpha*B**T*A +
                                        beta*C.

N

          N is INTEGER
           On entry,  N specifies the order of the matrix C.  N must be
           at least zero.

K

          K is INTEGER
           On entry with  TRANS = 'N' or 'n',  K  specifies  the number
           of  columns  of the  matrices  A and B,  and on  entry  with
           TRANS = 'T' or 't' or 'C' or 'c',  K  specifies  the  number
           of rows of the matrices  A and B.  K must be at least  zero.

ALPHA

          ALPHA is REAL
           On entry, ALPHA specifies the scalar alpha.

A

          A is REAL array, dimension ( LDA, ka ), where ka is
           k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
           Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
           part of the array  A  must contain the matrix  A,  otherwise
           the leading  k by n  part of the array  A  must contain  the
           matrix A.

LDA

          LDA is INTEGER
           On entry, LDA specifies the first dimension of A as declared
           in  the  calling  (sub)  program.   When  TRANS = 'N' or 'n'
           then  LDA must be at least  max( 1, n ), otherwise  LDA must
           be at least  max( 1, k ).

B

          B is REAL array, dimension ( LDB, kb ), where kb is
           k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
           Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
           part of the array  B  must contain the matrix  B,  otherwise
           the leading  k by n  part of the array  B  must contain  the
           matrix B.

LDB

          LDB is INTEGER
           On entry, LDB specifies the first dimension of B as declared
           in  the  calling  (sub)  program.   When  TRANS = 'N' or 'n'
           then  LDB must be at least  max( 1, n ), otherwise  LDB must
           be at least  max( 1, k ).

BETA

          BETA is REAL
           On entry, BETA specifies the scalar beta.

C

          C is REAL array, dimension ( LDC, N )
           Before entry  with  UPLO = 'U' or 'u',  the leading  n by n
           upper triangular part of the array C must contain the upper
           triangular part  of the  symmetric matrix  and the strictly
           lower triangular part of C is not referenced.  On exit, the
           upper triangular part of the array  C is overwritten by the
           upper triangular part of the updated matrix.
           Before entry  with  UPLO = 'L' or 'l',  the leading  n by n
           lower triangular part of the array C must contain the lower
           triangular part  of the  symmetric matrix  and the strictly
           upper triangular part of C is not referenced.  On exit, the
           lower triangular part of the array  C is overwritten by the
           lower triangular part of the updated matrix.

LDC

          LDC is INTEGER
           On entry, LDC specifies the first dimension of C as declared
           in  the  calling  (sub)  program.   LDC  must  be  at  least
           max( 1, n ).

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

  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.