SUBROUTINE DSYR2KF( UPLO, TRANS, N, K, ALPHA, A, LDA, B, LDB,

     $                   BETA, C, LDC )

*     .. Scalar Arguments ..

      CHARACTER*1        UPLO, TRANS

      INTEGER            N, K, LDA, LDB, LDC

      DOUBLE PRECISION   ALPHA, BETA

*     .. Array Arguments ..

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

*     ..

*

*  Purpose

*  =======

*

*  DSYR2K  performs one of the symmetric rank 2k operations

*

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

*

*  or

*

*     C := alpha*A'*B + alpha*B'*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.

*

*  Parameters

*  ==========

*

*  UPLO   - 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.

*

*           Unchanged on exit.

*

*  TRANS  - CHARACTER*1.

*           On entry,  TRANS  specifies the operation to be performed as

*           follows:

*

*              TRANS = 'N' or 'n'   C := alpha*A*B' + alpha*B*A' +

*                                        beta*C.

*

*              TRANS = 'T' or 't'   C := alpha*A'*B + alpha*B'*A +

*                                        beta*C.

*

*              TRANS = 'C' or 'c'   C := alpha*A'*B + alpha*B'*A +

*                                        beta*C.

*

*           Unchanged on exit.

*

*  N      - INTEGER.

*           On entry,  N specifies the order of the matrix C.  N must be

*           at least zero.

*           Unchanged on exit.

*

*  K      - 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.

*           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

*           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.

*           Unchanged on exit.

*

*  LDA    - 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 ).

*           Unchanged on exit.

*

*  B      - DOUBLE PRECISION array of 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.

*           Unchanged on exit.

*

*  LDB    - 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 ).

*           Unchanged on exit.

*

*  BETA   - DOUBLE PRECISION.

*           On entry, BETA specifies the scalar beta.

*           Unchanged on exit.

*

*  C      - DOUBLE PRECISION array of 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    - 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 ).

*           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.

*

*

*     .. External Functions ..

      LOGICAL            LSAME

      EXTERNAL           LSAME

*     .. External Subroutines ..

      EXTERNAL           XERBLA

*     .. Intrinsic Functions ..

      INTRINSIC          MAX

*     .. Local Scalars ..

      LOGICAL            UPPER

      INTEGER            I, INFO, J, L, NROWA

      DOUBLE PRECISION   TEMP1, TEMP2

*     .. Parameters ..

      DOUBLE PRECISION   ONE         , ZERO

      PARAMETER        ( ONE = 1.0D+0, ZERO = 0.0D+0 )

*     ..

*     .. Executable Statements ..

*

*     Test the input parameters.

*

      IF( LSAME( TRANS, 'N' ) )THEN

         NROWA = N

      ELSE

         NROWA = K

      END IF

      UPPER = LSAME( UPLO, 'U' )

*

      INFO = 0

      IF(      ( .NOT.UPPER               ).AND.

     $         ( .NOT.LSAME( UPLO , 'L' ) )      )THEN

         INFO = 1

      ELSE IF( ( .NOT.LSAME( TRANS, 'N' ) ).AND.

     $         ( .NOT.LSAME( TRANS, 'T' ) ).AND.

     $         ( .NOT.LSAME( TRANS, 'C' ) )      )THEN

         INFO = 2

      ELSE IF( N  .LT.0               )THEN

         INFO = 3

      ELSE IF( K  .LT.0               )THEN

         INFO = 4

      ELSE IF( LDA.LT.MAX( 1, NROWA ) )THEN

         INFO = 7

      ELSE IF( LDB.LT.MAX( 1, NROWA ) )THEN

         INFO = 9

      ELSE IF( LDC.LT.MAX( 1, N     ) )THEN

         INFO = 12

      END IF

      IF( INFO.NE.0 )THEN

         CALL XERBLA( 'DSYR2K', INFO )

         RETURN

      END IF

*

*     Quick return if possible.

*

      IF( ( N.EQ.0 ).OR.

     $    ( ( ( ALPHA.EQ.ZERO ).OR.( K.EQ.0 ) ).AND.( BETA.EQ.ONE ) ) )

     $   RETURN

*

*     And when  alpha.eq.zero.

*

      IF( ALPHA.EQ.ZERO )THEN

         IF( UPPER )THEN

            IF( BETA.EQ.ZERO )THEN

               DO 20, J = 1, N

                  DO 10, I = 1, J

                     C( I, J ) = ZERO

   10             CONTINUE

   20          CONTINUE

            ELSE

               DO 40, J = 1, N

                  DO 30, I = 1, J

                     C( I, J ) = BETA*C( I, J )

   30             CONTINUE

   40          CONTINUE

            END IF

         ELSE

            IF( BETA.EQ.ZERO )THEN

               DO 60, J = 1, N

                  DO 50, I = J, N

                     C( I, J ) = ZERO

   50             CONTINUE

   60          CONTINUE

            ELSE

               DO 80, J = 1, N

                  DO 70, I = J, N

                     C( I, J ) = BETA*C( I, J )

   70             CONTINUE

   80          CONTINUE

            END IF

         END IF

         RETURN

      END IF

*

*     Start the operations.

*

      IF( LSAME( TRANS, 'N' ) )THEN

*

*        Form  C := alpha*A*B' + alpha*B*A' + C.

*

         IF( UPPER )THEN

            DO 130, J = 1, N

               IF( BETA.EQ.ZERO )THEN

                  DO 90, I = 1, J

                     C( I, J ) = ZERO

   90             CONTINUE

               ELSE IF( BETA.NE.ONE )THEN

                  DO 100, I = 1, J

                     C( I, J ) = BETA*C( I, J )

  100             CONTINUE

               END IF

               DO 120, L = 1, K

                  IF( ( A( J, L ).NE.ZERO ).OR.

     $                ( B( J, L ).NE.ZERO )     )THEN

                     TEMP1 = ALPHA*B( J, L )

                     TEMP2 = ALPHA*A( J, L )

                     DO 110, I = 1, J

                        C( I, J ) = C( I, J ) +

     $                              A( I, L )*TEMP1 + B( I, L )*TEMP2

  110                CONTINUE

                  END IF

  120          CONTINUE

  130       CONTINUE

         ELSE

            DO 180, J = 1, N

               IF( BETA.EQ.ZERO )THEN

                  DO 140, I = J, N

                     C( I, J ) = ZERO

  140             CONTINUE

               ELSE IF( BETA.NE.ONE )THEN

                  DO 150, I = J, N

                     C( I, J ) = BETA*C( I, J )

  150             CONTINUE

               END IF

               DO 170, L = 1, K

                  IF( ( A( J, L ).NE.ZERO ).OR.

     $                ( B( J, L ).NE.ZERO )     )THEN

                     TEMP1 = ALPHA*B( J, L )

                     TEMP2 = ALPHA*A( J, L )

                     DO 160, I = J, N

                        C( I, J ) = C( I, J ) +

     $                              A( I, L )*TEMP1 + B( I, L )*TEMP2

  160                CONTINUE

                  END IF

  170          CONTINUE

  180       CONTINUE

         END IF

      ELSE

*

*        Form  C := alpha*A'*B + alpha*B'*A + C.

*

         IF( UPPER )THEN

            DO 210, J = 1, N

               DO 200, I = 1, J

                  TEMP1 = ZERO

                  TEMP2 = ZERO

                  DO 190, L = 1, K

                     TEMP1 = TEMP1 + A( L, I )*B( L, J )

                     TEMP2 = TEMP2 + B( L, I )*A( L, J )

  190             CONTINUE

                  IF( BETA.EQ.ZERO )THEN

                     C( I, J ) = ALPHA*TEMP1 + ALPHA*TEMP2

                  ELSE

                     C( I, J ) = BETA *C( I, J ) +

     $                           ALPHA*TEMP1 + ALPHA*TEMP2

                  END IF

  200          CONTINUE

  210       CONTINUE

         ELSE

            DO 240, J = 1, N

               DO 230, I = J, N

                  TEMP1 = ZERO

                  TEMP2 = ZERO

                  DO 220, L = 1, K

                     TEMP1 = TEMP1 + A( L, I )*B( L, J )

                     TEMP2 = TEMP2 + B( L, I )*A( L, J )

  220             CONTINUE

                  IF( BETA.EQ.ZERO )THEN

                     C( I, J ) = ALPHA*TEMP1 + ALPHA*TEMP2

                  ELSE

                     C( I, J ) = BETA *C( I, J ) +

     $                           ALPHA*TEMP1 + ALPHA*TEMP2

                  END IF

  230          CONTINUE

  240       CONTINUE

         END IF

      END IF

*

      RETURN

*

*     End of DSYR2K.

*

      END