*> \brief \b DSYR2K
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE DSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
*
*       .. Scalar Arguments ..
*       DOUBLE PRECISION ALPHA,BETA
*       INTEGER K,LDA,LDB,LDC,N
*       CHARACTER TRANS,UPLO
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*)
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DSYR2K  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.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] UPLO
*> \verbatim
*>          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.
*> \endverbatim
*>
*> \param[in] TRANS
*> \verbatim
*>          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.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>           On entry,  N specifies the order of the matrix C.  N must be
*>           at least zero.
*> \endverbatim
*>
*> \param[in] K
*> \verbatim
*>          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.
*> \endverbatim
*>
*> \param[in] ALPHA
*> \verbatim
*>          ALPHA is DOUBLE PRECISION.
*>           On entry, ALPHA specifies the scalar alpha.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*>          A is DOUBLE PRECISION 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.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          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 ).
*> \endverbatim
*>
*> \param[in] B
*> \verbatim
*>          B is DOUBLE PRECISION 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.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*>          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 ).
*> \endverbatim
*>
*> \param[in] BETA
*> \verbatim
*>          BETA is DOUBLE PRECISION.
*>           On entry, BETA specifies the scalar beta.
*> \endverbatim
*>
*> \param[in,out] C
*> \verbatim
*>          C is DOUBLE PRECISION 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.
*> \endverbatim
*>
*> \param[in] LDC
*> \verbatim
*>          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 ).
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup double_blas_level3
*
*> \par Further Details:
*  =====================
*>
*> \verbatim
*>
*>  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.
*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE DSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
*
*  -- Reference BLAS level3 routine --
*  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      DOUBLE PRECISION ALPHA,BETA
      INTEGER K,LDA,LDB,LDC,N
      CHARACTER TRANS,UPLO
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*)
*     ..
*
*  =====================================================================
*
*     .. External Functions ..
      LOGICAL LSAME
      EXTERNAL LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC MAX
*     ..
*     .. Local Scalars ..
      DOUBLE PRECISION TEMP1,TEMP2
      INTEGER I,INFO,J,L,NROWA
      LOGICAL UPPER
*     ..
*     .. Parameters ..
      DOUBLE PRECISION ONE,ZERO
      PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
*     ..
*
*     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**T + alpha*B*A**T + 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**T*B + alpha*B**T*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
