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version 1.3, 2010/08/06 15:32:21 version 1.11, 2014/01/27 09:28:14
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   *> \brief \b ZHPR
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE ZHPR(UPLO,N,ALPHA,X,INCX,AP)
   * 
   *       .. Scalar Arguments ..
   *       DOUBLE PRECISION ALPHA
   *       INTEGER INCX,N
   *       CHARACTER UPLO
   *       ..
   *       .. Array Arguments ..
   *       COMPLEX*16 AP(*),X(*)
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> ZHPR    performs the hermitian rank 1 operation
   *>
   *>    A := alpha*x*x**H + A,
   *>
   *> where alpha is a real scalar, x is an n element vector and A is an
   *> n by n hermitian matrix, supplied in packed form.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] UPLO
   *> \verbatim
   *>          UPLO is CHARACTER*1
   *>           On entry, UPLO specifies whether the upper or lower
   *>           triangular part of the matrix A is supplied in the packed
   *>           array AP as follows:
   *>
   *>              UPLO = 'U' or 'u'   The upper triangular part of A is
   *>                                  supplied in AP.
   *>
   *>              UPLO = 'L' or 'l'   The lower triangular part of A is
   *>                                  supplied in AP.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>           On entry, N specifies the order of the matrix A.
   *>           N must be at least zero.
   *> \endverbatim
   *>
   *> \param[in] ALPHA
   *> \verbatim
   *>          ALPHA is DOUBLE PRECISION.
   *>           On entry, ALPHA specifies the scalar alpha.
   *> \endverbatim
   *>
   *> \param[in] X
   *> \verbatim
   *>          X is 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.
   *> \endverbatim
   *>
   *> \param[in] INCX
   *> \verbatim
   *>          INCX is INTEGER
   *>           On entry, INCX specifies the increment for the elements of
   *>           X. INCX must not be zero.
   *> \endverbatim
   *>
   *> \param[in,out] AP
   *> \verbatim
   *>          AP is COMPLEX*16 array of DIMENSION at least
   *>           ( ( n*( n + 1 ) )/2 ).
   *>           Before entry with  UPLO = 'U' or 'u', the array AP must
   *>           contain the upper triangular part of the hermitian matrix
   *>           packed sequentially, column by column, so that AP( 1 )
   *>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
   *>           and a( 2, 2 ) respectively, and so on. On exit, the array
   *>           AP is overwritten by the upper triangular part of the
   *>           updated matrix.
   *>           Before entry with UPLO = 'L' or 'l', the array AP must
   *>           contain the lower triangular part of the hermitian matrix
   *>           packed sequentially, column by column, so that AP( 1 )
   *>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
   *>           and a( 3, 1 ) respectively, and so on. On exit, the array
   *>           AP 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.
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup complex16_blas_level2
   *
   *> \par Further Details:
   *  =====================
   *>
   *> \verbatim
   *>
   *>  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.
   *> \endverbatim
   *>
   *  =====================================================================
       SUBROUTINE ZHPR(UPLO,N,ALPHA,X,INCX,AP)        SUBROUTINE ZHPR(UPLO,N,ALPHA,X,INCX,AP)
   *
   *  -- Reference BLAS level2 routine (version 3.4.0) --
   *  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
   *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
   *     November 2011
   *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       DOUBLE PRECISION ALPHA        DOUBLE PRECISION ALPHA
       INTEGER INCX,N        INTEGER INCX,N
       CHARACTER UPLO        CHARACTER UPLO
 *     ..  *     ..
 *     .. Array Arguments ..  *     .. Array Arguments ..
       DOUBLE COMPLEX AP(*),X(*)        COMPLEX*16 AP(*),X(*)
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  ZHPR    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, supplied in packed form.  
 *  
 *  Arguments  
 *  ==========  
 *  
 *  UPLO   - CHARACTER*1.  
 *           On entry, UPLO specifies whether the upper or lower  
 *           triangular part of the matrix A is supplied in the packed  
 *           array AP as follows:  
 *  
 *              UPLO = 'U' or 'u'   The upper triangular part of A is  
 *                                  supplied in AP.  
 *  
 *              UPLO = 'L' or 'l'   The lower triangular part of A is  
 *                                  supplied in AP.  
 *  
 *           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.  
 *  
 *  AP     - COMPLEX*16       array of DIMENSION at least  
 *           ( ( n*( n + 1 ) )/2 ).  
 *           Before entry with  UPLO = 'U' or 'u', the array AP must  
 *           contain the upper triangular part of the hermitian matrix  
 *           packed sequentially, column by column, so that AP( 1 )  
 *           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )  
 *           and a( 2, 2 ) respectively, and so on. On exit, the array  
 *           AP is overwritten by the upper triangular part of the  
 *           updated matrix.  
 *           Before entry with UPLO = 'L' or 'l', the array AP must  
 *           contain the lower triangular part of the hermitian matrix  
 *           packed sequentially, column by column, so that AP( 1 )  
 *           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )  
 *           and a( 3, 1 ) respectively, and so on. On exit, the array  
 *           AP 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.  
 *  
 *  Further Details  
 *  ===============  
 *  
 *  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 ..  *     .. Parameters ..
       DOUBLE COMPLEX ZERO        COMPLEX*16 ZERO
       PARAMETER (ZERO= (0.0D+0,0.0D+0))        PARAMETER (ZERO= (0.0D+0,0.0D+0))
 *     ..  *     ..
 *     .. Local Scalars ..  *     .. Local Scalars ..
       DOUBLE COMPLEX TEMP        COMPLEX*16 TEMP
       INTEGER I,INFO,IX,J,JX,K,KK,KX        INTEGER I,INFO,IX,J,JX,K,KK,KX
 *     ..  *     ..
 *     .. External Functions ..  *     .. External Functions ..
Removed from v.1.3  
changed lines
  Added in v.1.11

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