*
************************************************************************
*
      SUBROUTINE DSYR2 ( UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA )
*     .. Scalar Arguments ..
      DOUBLE PRECISION   ALPHA
      INTEGER            INCX, INCY, LDA, N
      CHARACTER*1        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.
*
*  Parameters
*  ==========
*
*  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
*     ..
*     .. Executable Statements ..
*
*     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