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      SUBROUTINE ZHPRF ( UPLO, N, ALPHA, X, INCX, AP )
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*     .. Scalar Arguments ..
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      DOUBLE PRECISION   ALPHA
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      INTEGER            INCX, N
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      CHARACTER*1        UPLO
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*     .. Array Arguments ..
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      COMPLEX*16         AP( * ), X( * )
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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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*  ZHPR    performs the hermitian rank 1 operation
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*
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*     A := alpha*x*conjg( x' ) + A,
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*
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*  where alpha is a real scalar, x is an n element vector and A is an
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*  n by n hermitian matrix, supplied in packed form.
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*
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*  Parameters
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*  ==========
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*
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*  UPLO   - CHARACTER*1.
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*           On entry, UPLO specifies whether the upper or lower
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*           triangular part of the matrix A is supplied in the packed
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*           array AP as follows:
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*
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*              UPLO = 'U' or 'u'   The upper triangular part of A is
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*                                  supplied in AP.
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*
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*              UPLO = 'L' or 'l'   The lower triangular part of A is
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*                                  supplied in AP.
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*
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*           Unchanged on exit.
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*
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*  N      - 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  - DOUBLE PRECISION.
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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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*  X      - COMPLEX*16       array of 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   - 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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*  AP     - COMPLEX*16       array of DIMENSION at least
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*           ( ( n*( n + 1 ) )/2 ).
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*           Before entry with  UPLO = 'U' or 'u', the array AP must
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*           contain the upper triangular part of the hermitian matrix
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*           packed sequentially, column by column, so that AP( 1 )
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*           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
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*           and a( 2, 2 ) respectively, and so on. On exit, the array
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*           AP is overwritten by the upper triangular part of the
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*           updated matrix.
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*           Before entry with UPLO = 'L' or 'l', the array AP must
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*           contain the lower triangular part of the hermitian matrix
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*           packed sequentially, column by column, so that AP( 1 )
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*           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
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*           and a( 3, 1 ) respectively, and so on. On exit, the array
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*           AP is overwritten by the lower triangular part of the
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*           updated matrix.
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*           Note that the imaginary parts of the diagonal elements need
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*           not be set, they are assumed to be zero, and on exit they
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*           are set to zero.
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*
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*
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*  Level 2 Blas routine.
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*
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*  -- Written on 22-October-1986.
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*     Jack Dongarra, Argonne National Lab.
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*     Jeremy Du Croz, Nag Central Office.
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*     Sven Hammarling, Nag Central Office.
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*     Richard Hanson, Sandia National Labs.
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*
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*
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*     .. Parameters ..
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      COMPLEX*16         ZERO
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      PARAMETER        ( ZERO = ( 0.0D+0, 0.0D+0 ) )
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*     .. Local Scalars ..
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      COMPLEX*16         TEMP
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      INTEGER            I, INFO, IX, J, JX, K, KK, KX
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*     .. External Functions ..
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      LOGICAL            LSAME
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      EXTERNAL           LSAME
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*     .. External Subroutines ..
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      EXTERNAL           XERBLA
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*     .. Intrinsic Functions ..
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      INTRINSIC          DCONJG, DBLE
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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.
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     $         .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( INCX.EQ.0 )THEN
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         INFO = 5
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      END IF
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      IF( INFO.NE.0 )THEN
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         CALL XERBLA( 'ZHPR  ', 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.DBLE( ZERO ) ) )
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     $   RETURN
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*
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*     Set the start point in X if the increment is not unity.
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*
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      IF( INCX.LE.0 )THEN
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         KX = 1 - ( N - 1 )*INCX
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      ELSE IF( INCX.NE.1 )THEN
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         KX = 1
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      END IF
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*
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*     Start the operations. In this version the elements of the array AP
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*     are accessed sequentially with one pass through AP.
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*
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      KK = 1
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      IF( LSAME( UPLO, 'U' ) )THEN
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*
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*        Form  A  when upper triangle is stored in AP.
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*
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         IF( INCX.EQ.1 )THEN
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            DO 20, J = 1, N
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               IF( X( J ).NE.ZERO )THEN
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                  TEMP = ALPHA*DCONJG( X( J ) )
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                  K    = KK
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                  DO 10, I = 1, J - 1
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                     AP( K ) = AP( K ) + X( I )*TEMP
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                     K       = K       + 1
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   10             CONTINUE
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                  AP( KK + J - 1 ) = DBLE( AP( KK + J - 1 ) )
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     $                               + DBLE( X( J )*TEMP )
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               ELSE
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                  AP( KK + J - 1 ) = DBLE( AP( KK + J - 1 ) )
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               END IF
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               KK = KK + J
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   20       CONTINUE
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         ELSE
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            JX = KX
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            DO 40, J = 1, N
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               IF( X( JX ).NE.ZERO )THEN
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                  TEMP = ALPHA*DCONJG( X( JX ) )
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                  IX   = KX
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                  DO 30, K = KK, KK + J - 2
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                     AP( K ) = AP( K ) + X( IX )*TEMP
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                     IX      = IX      + INCX
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   30             CONTINUE
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                  AP( KK + J - 1 ) = DBLE( AP( KK + J - 1 ) )
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     $                               + DBLE( X( JX )*TEMP )
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               ELSE
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                  AP( KK + J - 1 ) = DBLE( AP( KK + J - 1 ) )
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               END IF
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               JX = JX + INCX
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               KK = KK + J
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   40       CONTINUE
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         END IF
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      ELSE
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*
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*        Form  A  when lower triangle is stored in AP.
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*
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         IF( INCX.EQ.1 )THEN
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            DO 60, J = 1, N
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               IF( X( J ).NE.ZERO )THEN
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                  TEMP     = ALPHA*DCONJG( X( J ) )
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                  AP( KK ) = DBLE( AP( KK ) ) + DBLE( TEMP*X( J ) )
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                  K        = KK               + 1
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                  DO 50, I = J + 1, N
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                     AP( K ) = AP( K ) + X( I )*TEMP
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                     K       = K       + 1
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   50             CONTINUE
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               ELSE
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                  AP( KK ) = DBLE( AP( KK ) )
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               END IF
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               KK = KK + N - J + 1
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   60       CONTINUE
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         ELSE
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            JX = KX
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            DO 80, J = 1, N
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               IF( X( JX ).NE.ZERO )THEN
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                  TEMP    = ALPHA*DCONJG( X( JX ) )
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                  AP( KK ) = DBLE( AP( KK ) ) + DBLE( TEMP*X( JX ) )
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                  IX      = JX
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                  DO 70, K = KK + 1, KK + N - J
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                     IX      = IX      + INCX
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                     AP( K ) = AP( K ) + X( IX )*TEMP
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   70             CONTINUE
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               ELSE
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                  AP( KK ) = DBLE( AP( KK ) )
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               END IF
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               JX = JX + INCX
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               KK = KK + N - J + 1
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   80       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 ZHPR  .
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*
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      END