SUBROUTINE SSYMVF ( UPLO, N, ALPHA, A, LDA, X, INCX,

     $                   BETA, Y, INCY )

*     .. Scalar Arguments ..

      REAL               ALPHA, BETA

      INTEGER            INCX, INCY, LDA, N

      CHARACTER*1        UPLO

*     .. Array Arguments ..

      REAL               A( LDA, * ), X( * ), Y( * )

*     ..

*

*  Purpose

*  =======

*

*  SSYMV  performs the matrix-vector  operation

*

*     y := alpha*A*x + beta*y,

*

*  where alpha and beta are scalars, 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  - REAL            .

*           On entry, ALPHA specifies the scalar alpha.

*           Unchanged on exit.

*

*  A      - REAL             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.

*           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.

*           Unchanged on exit.

*

*  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.

*

*  X      - REAL             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.

*

*  BETA   - REAL            .

*           On entry, BETA specifies the scalar beta. When BETA is

*           supplied as zero then Y need not be set on input.

*           Unchanged on exit.

*

*  Y      - REAL             array of dimension at least

*           ( 1 + ( n - 1 )*abs( INCY ) ).

*           Before entry, the incremented array Y must contain the n

*           element vector y. On exit, Y is overwritten by the updated

*           vector y.

*

*  INCY   - INTEGER.

*           On entry, INCY specifies the increment for the elements of

*           Y. INCY must not be zero.

*           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 ..

      REAL               ONE         , ZERO

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

*     .. Local Scalars ..

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

         INFO = 5

      ELSE IF( INCX.EQ.0 )THEN

         INFO = 7

      ELSE IF( INCY.EQ.0 )THEN

         INFO = 10

      END IF

      IF( INFO.NE.0 )THEN

         CALL XERBLA( 'SSYMV ', INFO )

         RETURN

      END IF

*

*     Quick return if possible.

*

      IF( ( N.EQ.0 ).OR.( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) )

     $   RETURN

*

*     Set up the start points in  X  and  Y.

*

      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

*

*     Start the operations. In this version the elements of A are

*     accessed sequentially with one pass through the triangular part

*     of A.

*

*     First form  y := beta*y.

*

      IF( BETA.NE.ONE )THEN

         IF( INCY.EQ.1 )THEN

            IF( BETA.EQ.ZERO )THEN

               DO 10, I = 1, N

                  Y( I ) = ZERO

   10          CONTINUE

            ELSE

               DO 20, I = 1, N

                  Y( I ) = BETA*Y( I )

   20          CONTINUE

            END IF

         ELSE

            IY = KY

            IF( BETA.EQ.ZERO )THEN

               DO 30, I = 1, N

                  Y( IY ) = ZERO

                  IY      = IY   + INCY

   30          CONTINUE

            ELSE

               DO 40, I = 1, N

                  Y( IY ) = BETA*Y( IY )

                  IY      = IY           + INCY

   40          CONTINUE

            END IF

         END IF

      END IF

      IF( ALPHA.EQ.ZERO )

     $   RETURN

      IF( LSAME( UPLO, 'U' ) )THEN

*

*        Form  y  when A is stored in upper triangle.

*

         IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN

            DO 60, J = 1, N

               TEMP1 = ALPHA*X( J )

               TEMP2 = ZERO

               DO 50, I = 1, J - 1

                  Y( I ) = Y( I ) + TEMP1*A( I, J )

                  TEMP2  = TEMP2  + A( I, J )*X( I )

   50          CONTINUE

               Y( J ) = Y( J ) + TEMP1*A( J, J ) + ALPHA*TEMP2

   60       CONTINUE

         ELSE

            JX = KX

            JY = KY

            DO 80, J = 1, N

               TEMP1 = ALPHA*X( JX )

               TEMP2 = ZERO

               IX    = KX

               IY    = KY

               DO 70, I = 1, J - 1

                  Y( IY ) = Y( IY ) + TEMP1*A( I, J )

                  TEMP2   = TEMP2   + A( I, J )*X( IX )

                  IX      = IX      + INCX

                  IY      = IY      + INCY

   70          CONTINUE

               Y( JY ) = Y( JY ) + TEMP1*A( J, J ) + ALPHA*TEMP2

               JX      = JX      + INCX

               JY      = JY      + INCY

   80       CONTINUE

         END IF

      ELSE

*

*        Form  y  when A is stored in lower triangle.

*

         IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN

            DO 100, J = 1, N

               TEMP1  = ALPHA*X( J )

               TEMP2  = ZERO

               Y( J ) = Y( J )       + TEMP1*A( J, J )

               DO 90, I = J + 1, N

                  Y( I ) = Y( I ) + TEMP1*A( I, J )

                  TEMP2  = TEMP2  + A( I, J )*X( I )

   90          CONTINUE

               Y( J ) = Y( J ) + ALPHA*TEMP2

  100       CONTINUE

         ELSE

            JX = KX

            JY = KY

            DO 120, J = 1, N

               TEMP1   = ALPHA*X( JX )

               TEMP2   = ZERO

               Y( JY ) = Y( JY )       + TEMP1*A( J, J )

               IX      = JX

               IY      = JY

               DO 110, I = J + 1, N

                  IX      = IX      + INCX

                  IY      = IY      + INCY

                  Y( IY ) = Y( IY ) + TEMP1*A( I, J )

                  TEMP2   = TEMP2   + A( I, J )*X( IX )

  110          CONTINUE

               Y( JY ) = Y( JY ) + ALPHA*TEMP2

               JX      = JX      + INCX

               JY      = JY      + INCY

  120       CONTINUE

         END IF

      END IF

*

      RETURN

*

*     End of SSYMV .

*

      END