          SUBROUTINE ZSYMV( UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY )
    *
    *  -- LAPACK auxiliary routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          UPLO
          INTEGER            INCX, INCY, LDA, N
          COMPLEX*16         ALPHA, BETA
    *     ..
    *     .. Array Arguments ..
          COMPLEX*16         A( LDA, * ), X( * ), Y( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  ZSYMV  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.
    *
    *  Arguments
    *  ==========
    *
    *  UPLO     (input) 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        (input) INTEGER
    *           On entry, N specifies the order of the matrix A.
    *           N must be at least zero.
    *           Unchanged on exit.
    *
    *  ALPHA    (input) COMPLEX*16
    *           On entry, ALPHA specifies the scalar alpha.
    *           Unchanged on exit.
    *
    *  A        (input) COMPLEX*16 array, 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      (input) 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        (input) COMPLEX*16 array, 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     (input) INTEGER
    *           On entry, INCX specifies the increment for the elements of
    *           X. INCX must not be zero.
    *           Unchanged on exit.
    *
    *  BETA     (input) COMPLEX*16
    *           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        (input/output) COMPLEX*16 array, 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     (input) INTEGER
    *           On entry, INCY specifies the increment for the elements of
    *           Y. INCY must not be zero.
    *           Unchanged on exit.
    *
    * =====================================================================
    *
    *     .. Parameters ..
          COMPLEX*16         ONE
          PARAMETER          ( ONE = ( 1.0D+0, 0.0D+0 ) )
          COMPLEX*16         ZERO
          PARAMETER          ( ZERO = ( 0.0D+0, 0.0D+0 ) )
    *     ..
    *     .. Local Scalars ..
          INTEGER            I, INFO, IX, IY, J, JX, JY, KX, KY
          COMPLEX*16         TEMP1, TEMP2
    *     ..
    *     .. 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( 'ZSYMV ', 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 ZSYMV
    *
          END