SUBROUTINE DSYRF  ( UPLO, N, ALPHA, X, INCX, A, LDA )

*     .. Scalar Arguments ..

      DOUBLE PRECISION   ALPHA

      INTEGER            INCX, LDA, N

      CHARACTER*1        UPLO

*     .. Array Arguments ..

      DOUBLE PRECISION   A( LDA, * ), X( * )

*     ..

*

*  Purpose

*  =======

*

*  DSYR   performs the symmetric rank 1 operation

*

*     A := alpha*x*x' + A,

*

*  where alpha is a real scalar, x is an n element vector 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.

*

*  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   TEMP

      INTEGER            I, INFO, IX, J, JX, KX

*     .. 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( LDA.LT.MAX( 1, N ) )THEN

         INFO = 7

      END IF

      IF( INFO.NE.0 )THEN

         CALL XERBLA( 'DSYR  ', INFO )

         RETURN

      END IF

*

*     Quick return if possible.

*

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

     $   RETURN

*

*     Set the start point in X if the increment is not unity.

*

      IF( INCX.LE.0 )THEN

         KX = 1 - ( N - 1 )*INCX

      ELSE IF( INCX.NE.1 )THEN

         KX = 1

      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 upper triangle.

*

         IF( INCX.EQ.1 )THEN

            DO 20, J = 1, N

               IF( X( J ).NE.ZERO )THEN

                  TEMP = ALPHA*X( J )

                  DO 10, I = 1, J

                     A( I, J ) = A( I, J ) + X( I )*TEMP

   10             CONTINUE

               END IF

   20       CONTINUE

         ELSE

            JX = KX

            DO 40, J = 1, N

               IF( X( JX ).NE.ZERO )THEN

                  TEMP = ALPHA*X( JX )

                  IX   = KX

                  DO 30, I = 1, J

                     A( I, J ) = A( I, J ) + X( IX )*TEMP

                     IX        = IX        + INCX

   30             CONTINUE

               END IF

               JX = JX + INCX

   40       CONTINUE

         END IF

      ELSE

*

*        Form  A  when A is stored in lower triangle.

*

         IF( INCX.EQ.1 )THEN

            DO 60, J = 1, N

               IF( X( J ).NE.ZERO )THEN

                  TEMP = ALPHA*X( J )

                  DO 50, I = J, N

                     A( I, J ) = A( I, J ) + X( I )*TEMP

   50             CONTINUE

               END IF

   60       CONTINUE

         ELSE

            JX = KX

            DO 80, J = 1, N

               IF( X( JX ).NE.ZERO )THEN

                  TEMP = ALPHA*X( JX )

                  IX   = JX

                  DO 70, I = J, N

                     A( I, J ) = A( I, J ) + X( IX )*TEMP

                     IX        = IX        + INCX

   70             CONTINUE

               END IF

               JX = JX + INCX

   80       CONTINUE

         END IF

      END IF

*

      RETURN

*

*     End of DSYR  .

*

      END