```      SUBROUTINE ZHER(UPLO,N,ALPHA,X,INCX,A,LDA)
*     .. Scalar Arguments ..
DOUBLE PRECISION ALPHA
INTEGER INCX,LDA,N
CHARACTER UPLO
*     ..
*     .. Array Arguments ..
DOUBLE COMPLEX A(LDA,*),X(*)
*     ..
*
*  Purpose
*  =======
*
*  ZHER   performs the hermitian rank 1 operation
*
*     A := alpha*x*conjg( x' ) + A,
*
*  where alpha is a real scalar, x is an n element vector and A is an
*  n by n hermitian matrix.
*
*  Arguments
*  ==========
*
*  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      - COMPLEX*16       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      - COMPLEX*16       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 hermitian 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 hermitian 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.
*           Note that the imaginary parts of the diagonal elements need
*           not be set, they are assumed to be zero, and on exit they
*           are set to zero.
*
*  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 COMPLEX ZERO
PARAMETER (ZERO= (0.0D+0,0.0D+0))
*     ..
*     .. Local Scalars ..
DOUBLE COMPLEX TEMP
INTEGER I,INFO,IX,J,JX,KX
*     ..
*     .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
*     ..
*     .. External Subroutines ..
EXTERNAL XERBLA
*     ..
*     .. Intrinsic Functions ..
INTRINSIC DBLE,DCONJG,MAX
*     ..
*
*     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('ZHER  ',INFO)
RETURN
END IF
*
*     Quick return if possible.
*
IF ((N.EQ.0) .OR. (ALPHA.EQ.DBLE(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*DCONJG(X(J))
DO 10 I = 1,J - 1
A(I,J) = A(I,J) + X(I)*TEMP
10                 CONTINUE
A(J,J) = DBLE(A(J,J)) + DBLE(X(J)*TEMP)
ELSE
A(J,J) = DBLE(A(J,J))
END IF
20         CONTINUE
ELSE
JX = KX
DO 40 J = 1,N
IF (X(JX).NE.ZERO) THEN
TEMP = ALPHA*DCONJG(X(JX))
IX = KX
DO 30 I = 1,J - 1
A(I,J) = A(I,J) + X(IX)*TEMP
IX = IX + INCX
30                 CONTINUE
A(J,J) = DBLE(A(J,J)) + DBLE(X(JX)*TEMP)
ELSE
A(J,J) = DBLE(A(J,J))
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*DCONJG(X(J))
A(J,J) = DBLE(A(J,J)) + DBLE(TEMP*X(J))
DO 50 I = J + 1,N
A(I,J) = A(I,J) + X(I)*TEMP
50                 CONTINUE
ELSE
A(J,J) = DBLE(A(J,J))
END IF
60         CONTINUE
ELSE
JX = KX
DO 80 J = 1,N
IF (X(JX).NE.ZERO) THEN
TEMP = ALPHA*DCONJG(X(JX))
A(J,J) = DBLE(A(J,J)) + DBLE(TEMP*X(JX))
IX = JX
DO 70 I = J + 1,N
IX = IX + INCX
A(I,J) = A(I,J) + X(IX)*TEMP
70                 CONTINUE
ELSE
A(J,J) = DBLE(A(J,J))
END IF
JX = JX + INCX
80         CONTINUE
END IF
END IF
*
RETURN
*
*     End of ZHER  .
*
END

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