```      SUBROUTINE ZSYR( UPLO, N, ALPHA, X, INCX, A, LDA )
*
*  -- LAPACK auxiliary routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. Scalar Arguments ..
CHARACTER          UPLO
INTEGER            INCX, LDA, N
COMPLEX*16         ALPHA
*     ..
*     .. Array Arguments ..
COMPLEX*16         A( LDA, * ), X( * )
*     ..
*
*  Purpose
*  =======
*
*  ZSYR   performs the symmetric rank 1 operation
*
*     A := alpha*x*( x' ) + A,
*
*  where alpha is a complex scalar, x is an n element vector 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.
*
*  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.
*
*  A        (input/output) 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. 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      (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.
*
* =====================================================================
*
*     .. Parameters ..
COMPLEX*16         ZERO
PARAMETER          ( ZERO = ( 0.0D+0, 0.0D+0 ) )
*     ..
*     .. Local Scalars ..
INTEGER            I, INFO, IX, J, JX, KX
COMPLEX*16         TEMP
*     ..
*     .. 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( 'ZSYR  ', 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 ZSYR
*
END

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