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      SUBROUTINE ZSYMVF(UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY )
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*
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*  -- LAPACK auxiliary routine (version 3.1) --
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*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
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*     November 2006
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*
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*     .. Scalar Arguments ..
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      CHARACTER          UPLO
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      INTEGER            INCX, INCY, LDA, N
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      COMPLEX*16         ALPHA, BETA
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*     ..
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*     .. Array Arguments ..
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      COMPLEX*16         A( LDA, * ), X( * ), Y( * )
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*     ..
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*
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*  Purpose
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*  =======
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*
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*  ZSYMV  performs the matrix-vector  operation
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*
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*     y := alpha*A*x + beta*y,
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*
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*  where alpha and beta are scalars, x and y are n element vectors and
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*  A is an n by n symmetric matrix.
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*
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*  Arguments
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*  ==========
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*
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*  UPLO     (input) CHARACTER*1
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*           On entry, UPLO specifies whether the upper or lower
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*           triangular part of the array A is to be referenced as
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*           follows:
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*
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*              UPLO = 'U' or 'u'   Only the upper triangular part of A
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*                                  is to be referenced.
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*
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*              UPLO = 'L' or 'l'   Only the lower triangular part of A
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*                                  is to be referenced.
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*
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*           Unchanged on exit.
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*
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*  N        (input) INTEGER
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*           On entry, N specifies the order of the matrix A.
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*           N must be at least zero.
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*           Unchanged on exit.
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*
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*  ALPHA    (input) COMPLEX*16
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*           On entry, ALPHA specifies the scalar alpha.
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*           Unchanged on exit.
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*
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*  A        (input) COMPLEX*16 array, dimension ( LDA, N )
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*           Before entry, with  UPLO = 'U' or 'u', the leading n by n
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*           upper triangular part of the array A must contain the upper
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*           triangular part of the symmetric matrix and the strictly
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*           lower triangular part of A is not referenced.
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*           Before entry, with UPLO = 'L' or 'l', the leading n by n
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*           lower triangular part of the array A must contain the lower
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*           triangular part of the symmetric matrix and the strictly
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*           upper triangular part of A is not referenced.
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*           Unchanged on exit.
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*
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*  LDA      (input) INTEGER
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*           On entry, LDA specifies the first dimension of A as declared
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*           in the calling (sub) program. LDA must be at least
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*           max( 1, N ).
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*           Unchanged on exit.
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*
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*  X        (input) COMPLEX*16 array, dimension at least
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*           ( 1 + ( N - 1 )*abs( INCX ) ).
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*           Before entry, the incremented array X must contain the N-
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*           element vector x.
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*           Unchanged on exit.
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*
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*  INCX     (input) INTEGER
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*           On entry, INCX specifies the increment for the elements of
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*           X. INCX must not be zero.
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*           Unchanged on exit.
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*
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*  BETA     (input) COMPLEX*16
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*           On entry, BETA specifies the scalar beta. When BETA is
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*           supplied as zero then Y need not be set on input.
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*           Unchanged on exit.
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*
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*  Y        (input/output) COMPLEX*16 array, dimension at least
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*           ( 1 + ( N - 1 )*abs( INCY ) ).
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*           Before entry, the incremented array Y must contain the n
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*           element vector y. On exit, Y is overwritten by the updated
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*           vector y.
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*
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*  INCY     (input) INTEGER
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*           On entry, INCY specifies the increment for the elements of
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*           Y. INCY must not be zero.
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*           Unchanged on exit.
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*
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* =====================================================================
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*
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*     .. Parameters ..
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      COMPLEX*16         ONE
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      PARAMETER          ( ONE = ( 1.0D+0, 0.0D+0 ) )
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      COMPLEX*16         ZERO
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      PARAMETER          ( ZERO = ( 0.0D+0, 0.0D+0 ) )
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*     ..
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*     .. Local Scalars ..
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      INTEGER            I, INFO, IX, IY, J, JX, JY, KX, KY
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      COMPLEX*16         TEMP1, TEMP2
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*     ..
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*     .. External Functions ..
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      LOGICAL            LSAME
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      EXTERNAL           LSAME
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*     ..
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*     .. External Subroutines ..
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      EXTERNAL           XERBLA
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*     ..
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*     .. Intrinsic Functions ..
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      INTRINSIC          MAX
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*     ..
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*     .. Executable Statements ..
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*
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*     Test the input parameters.
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*
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      INFO = 0
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      IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
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         INFO = 1
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      ELSE IF( N.LT.0 ) THEN
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         INFO = 2
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      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
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         INFO = 5
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      ELSE IF( INCX.EQ.0 ) THEN
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         INFO = 7
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      ELSE IF( INCY.EQ.0 ) THEN
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         INFO = 10
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      END IF
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      IF( INFO.NE.0 ) THEN
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         CALL XERBLA( 'ZSYMV ', INFO )
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         RETURN
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      END IF
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*
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*     Quick return if possible.
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*
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      IF( ( N.EQ.0 ) .OR. ( ( ALPHA.EQ.ZERO ) .AND. ( BETA.EQ.ONE ) ) )
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     $   RETURN
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*
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*     Set up the start points in  X  and  Y.
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*
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      IF( INCX.GT.0 ) THEN
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         KX = 1
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      ELSE
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         KX = 1 - ( N-1 )*INCX
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      END IF
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      IF( INCY.GT.0 ) THEN
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         KY = 1
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      ELSE
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         KY = 1 - ( N-1 )*INCY
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      END IF
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*
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*     Start the operations. In this version the elements of A are
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*     accessed sequentially with one pass through the triangular part
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*     of A.
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*
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*     First form  y := beta*y.
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*
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      IF( BETA.NE.ONE ) THEN
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         IF( INCY.EQ.1 ) THEN
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            IF( BETA.EQ.ZERO ) THEN
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               DO 10 I = 1, N
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                  Y( I ) = ZERO
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   10          CONTINUE
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            ELSE
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               DO 20 I = 1, N
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                  Y( I ) = BETA*Y( I )
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   20          CONTINUE
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            END IF
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         ELSE
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            IY = KY
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            IF( BETA.EQ.ZERO ) THEN
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               DO 30 I = 1, N
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                  Y( IY ) = ZERO
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                  IY = IY + INCY
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   30          CONTINUE
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            ELSE
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               DO 40 I = 1, N
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                  Y( IY ) = BETA*Y( IY )
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                  IY = IY + INCY
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   40          CONTINUE
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            END IF
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         END IF
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      END IF
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      IF( ALPHA.EQ.ZERO )
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     $   RETURN
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      IF( LSAME( UPLO, 'U' ) ) THEN
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*
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*        Form  y  when A is stored in upper triangle.
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*
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         IF( ( INCX.EQ.1 ) .AND. ( INCY.EQ.1 ) ) THEN
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            DO 60 J = 1, N
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               TEMP1 = ALPHA*X( J )
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               TEMP2 = ZERO
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               DO 50 I = 1, J - 1
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                  Y( I ) = Y( I ) + TEMP1*A( I, J )
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                  TEMP2 = TEMP2 + A( I, J )*X( I )
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   50          CONTINUE
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               Y( J ) = Y( J ) + TEMP1*A( J, J ) + ALPHA*TEMP2
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   60       CONTINUE
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         ELSE
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            JX = KX
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            JY = KY
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            DO 80 J = 1, N
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               TEMP1 = ALPHA*X( JX )
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               TEMP2 = ZERO
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               IX = KX
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               IY = KY
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               DO 70 I = 1, J - 1
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                  Y( IY ) = Y( IY ) + TEMP1*A( I, J )
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                  TEMP2 = TEMP2 + A( I, J )*X( IX )
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                  IX = IX + INCX
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                  IY = IY + INCY
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   70          CONTINUE
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               Y( JY ) = Y( JY ) + TEMP1*A( J, J ) + ALPHA*TEMP2
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               JX = JX + INCX
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               JY = JY + INCY
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   80       CONTINUE
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         END IF
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      ELSE
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*
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*        Form  y  when A is stored in lower triangle.
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*
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         IF( ( INCX.EQ.1 ) .AND. ( INCY.EQ.1 ) ) THEN
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            DO 100 J = 1, N
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               TEMP1 = ALPHA*X( J )
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               TEMP2 = ZERO
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               Y( J ) = Y( J ) + TEMP1*A( J, J )
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               DO 90 I = J + 1, N
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                  Y( I ) = Y( I ) + TEMP1*A( I, J )
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                  TEMP2 = TEMP2 + A( I, J )*X( I )
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   90          CONTINUE
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               Y( J ) = Y( J ) + ALPHA*TEMP2
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  100       CONTINUE
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         ELSE
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            JX = KX
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            JY = KY
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            DO 120 J = 1, N
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               TEMP1 = ALPHA*X( JX )
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               TEMP2 = ZERO
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               Y( JY ) = Y( JY ) + TEMP1*A( J, J )
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               IX = JX
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               IY = JY
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               DO 110 I = J + 1, N
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                  IX = IX + INCX
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                  IY = IY + INCY
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                  Y( IY ) = Y( IY ) + TEMP1*A( I, J )
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                  TEMP2 = TEMP2 + A( I, J )*X( IX )
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  110          CONTINUE
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               Y( JY ) = Y( JY ) + ALPHA*TEMP2
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               JX = JX + INCX
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               JY = JY + INCY
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  120       CONTINUE
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         END IF
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      END IF
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*
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      RETURN
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*
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*     End of ZSYMV
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*
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      END