      SUBROUTINE DSYR2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA)
*     .. Scalar Arguments ..
      DOUBLE PRECISION ALPHA
      INTEGER INCX,INCY,LDA,N
      CHARACTER UPLO
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION A(LDA,*),X(*),Y(*)
*     ..
*
*  Purpose
*  =======
*
*  DSYR2  performs the symmetric rank 2 operation
*
*     A := alpha*x*y' + alpha*y*x' + A,
*
*  where alpha is a scalar, x and y are n element vectors and A is an n
*  by n symmetric matrix.
*
*  Arguments
*  ==========
*
*  UPLO   - CHARACTER*1.
*           On entry, UPLO specifies whether the upper or lower
*           triangular part of the array A is to be referenced as
*           follows:
*
*              UPLO = 'U' or 'u'   Only the upper triangular part of A
*                                  is to be referenced.
*
*              UPLO = 'L' or 'l'   Only the lower triangular part of A
*                                  is to be referenced.
*
*           Unchanged on exit.
*
*  N      - INTEGER.
*           On entry, N specifies the order of the matrix A.
*           N must be at least zero.
*           Unchanged on exit.
*
*  ALPHA  - DOUBLE PRECISION.
*           On entry, ALPHA specifies the scalar alpha.
*           Unchanged on exit.
*
*  X      - DOUBLE PRECISION array of dimension at least
*           ( 1 + ( n - 1 )*abs( INCX ) ).
*           Before entry, the incremented array X must contain the n
*           element vector x.
*           Unchanged on exit.
*
*  INCX   - INTEGER.
*           On entry, INCX specifies the increment for the elements of
*           X. INCX must not be zero.
*           Unchanged on exit.
*
*  Y      - DOUBLE PRECISION array of dimension at least
*           ( 1 + ( n - 1 )*abs( INCY ) ).
*           Before entry, the incremented array Y must contain the n
*           element vector y.
*           Unchanged on exit.
*
*  INCY   - INTEGER.
*           On entry, INCY specifies the increment for the elements of
*           Y. INCY must not be zero.
*           Unchanged on exit.
*
*  A      - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
*           Before entry with  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. On exit, the
*           upper triangular part of the array A 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 A must contain the lower
*           triangular part of the symmetric matrix and the strictly
*           upper triangular part of A is not referenced. On exit, the
*           lower triangular part of the array A is overwritten by the
*           lower triangular part of the updated matrix.
*
*  LDA    - INTEGER.
*           On entry, LDA specifies the first dimension of A as declared
*           in the calling (sub) program. LDA must be at least
*           max( 1, n ).
*           Unchanged on exit.
*
*
*  Level 2 Blas routine.
*
*  -- Written on 22-October-1986.
*     Jack Dongarra, Argonne National Lab.
*     Jeremy Du Croz, Nag Central Office.
*     Sven Hammarling, Nag Central Office.
*     Richard Hanson, Sandia National Labs.
*
*
*     .. Parameters ..
      DOUBLE PRECISION ZERO
      PARAMETER (ZERO=0.0D+0)
*     ..
*     .. Local Scalars ..
      DOUBLE PRECISION TEMP1,TEMP2
      INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY
*     ..
*     .. External Functions ..
      LOGICAL LSAME
      EXTERNAL LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC MAX
*     ..
*
*     Test the input parameters.
*
      INFO = 0
      IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
          INFO = 1
      ELSE IF (N.LT.0) THEN
          INFO = 2
      ELSE IF (INCX.EQ.0) THEN
          INFO = 5
      ELSE IF (INCY.EQ.0) THEN
          INFO = 7
      ELSE IF (LDA.LT.MAX(1,N)) THEN
          INFO = 9
      END IF
      IF (INFO.NE.0) THEN
          CALL XERBLA('DSYR2 ',INFO)
          RETURN
      END IF
*
*     Quick return if possible.
*
      IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN
*
*     Set up the start points in X and Y if the increments are not both
*     unity.
*
      IF ((INCX.NE.1) .OR. (INCY.NE.1)) THEN
          IF (INCX.GT.0) THEN
              KX = 1
          ELSE
              KX = 1 - (N-1)*INCX
          END IF
          IF (INCY.GT.0) THEN
              KY = 1
          ELSE
              KY = 1 - (N-1)*INCY
          END IF
          JX = KX
          JY = KY
      END IF
*
*     Start the operations. In this version the elements of A are
*     accessed sequentially with one pass through the triangular part
*     of A.
*
      IF (LSAME(UPLO,'U')) THEN
*
*        Form  A  when A is stored in the upper triangle.
*
          IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
              DO 20 J = 1,N
                  IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN
                      TEMP1 = ALPHA*Y(J)
                      TEMP2 = ALPHA*X(J)
                      DO 10 I = 1,J
                          A(I,J) = A(I,J) + X(I)*TEMP1 + Y(I)*TEMP2
   10                 CONTINUE
                  END IF
   20         CONTINUE
          ELSE
              DO 40 J = 1,N
                  IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN
                      TEMP1 = ALPHA*Y(JY)
                      TEMP2 = ALPHA*X(JX)
                      IX = KX
                      IY = KY
                      DO 30 I = 1,J
                          A(I,J) = A(I,J) + X(IX)*TEMP1 + Y(IY)*TEMP2
                          IX = IX + INCX
                          IY = IY + INCY
   30                 CONTINUE
                  END IF
                  JX = JX + INCX
                  JY = JY + INCY
   40         CONTINUE
          END IF
      ELSE
*
*        Form  A  when A is stored in the lower triangle.
*
          IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
              DO 60 J = 1,N
                  IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN
                      TEMP1 = ALPHA*Y(J)
                      TEMP2 = ALPHA*X(J)
                      DO 50 I = J,N
                          A(I,J) = A(I,J) + X(I)*TEMP1 + Y(I)*TEMP2
   50                 CONTINUE
                  END IF
   60         CONTINUE
          ELSE
              DO 80 J = 1,N
                  IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN
                      TEMP1 = ALPHA*Y(JY)
                      TEMP2 = ALPHA*X(JX)
                      IX = JX
                      IY = JY
                      DO 70 I = J,N
                          A(I,J) = A(I,J) + X(IX)*TEMP1 + Y(IY)*TEMP2
                          IX = IX + INCX
                          IY = IY + INCY
   70                 CONTINUE
                  END IF
                  JX = JX + INCX
                  JY = JY + INCY
   80         CONTINUE
          END IF
      END IF
*
      RETURN
*
*     End of DSYR2 .
*
      END
