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version 1.8, 2011/07/22 07:38:20 version 1.9, 2011/11/21 20:43:20
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   *> \brief \b ZSPR
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download ZSPR + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zspr.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zspr.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zspr.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE ZSPR( UPLO, N, ALPHA, X, INCX, AP )
   * 
   *       .. Scalar Arguments ..
   *       CHARACTER          UPLO
   *       INTEGER            INCX, N
   *       COMPLEX*16         ALPHA
   *       ..
   *       .. Array Arguments ..
   *       COMPLEX*16         AP( * ), X( * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> ZSPR    performs the symmetric rank 1 operation
   *>
   *>    A := alpha*x*x**H + A,
   *>
   *> where alpha is a complex scalar, x is an n element vector and A is an
   *> n by n symmetric 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.
   *>
   *>           Unchanged on exit.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>           On entry, N specifies the order of the matrix A.
   *>           N must be at least zero.
   *>           Unchanged on exit.
   *> \endverbatim
   *>
   *> \param[in] ALPHA
   *> \verbatim
   *>          ALPHA is COMPLEX*16
   *>           On entry, ALPHA specifies the scalar alpha.
   *>           Unchanged on exit.
   *> \endverbatim
   *>
   *> \param[in] X
   *> \verbatim
   *>          X is 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.
   *> \endverbatim
   *>
   *> \param[in] INCX
   *> \verbatim
   *>          INCX is INTEGER
   *>           On entry, INCX specifies the increment for the elements of
   *>           X. INCX must not be zero.
   *>           Unchanged on exit.
   *> \endverbatim
   *>
   *> \param[in,out] AP
   *> \verbatim
   *>          AP is COMPLEX*16 array, 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 symmetric 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 symmetric 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 complex16OTHERauxiliary
   *
   *  =====================================================================
       SUBROUTINE ZSPR( UPLO, N, ALPHA, X, INCX, AP )        SUBROUTINE ZSPR( UPLO, N, ALPHA, X, INCX, AP )
 *  *
 *  -- LAPACK auxiliary routine (version 3.2) --  *  -- LAPACK auxiliary routine (version 3.4.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --  *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--  *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     November 2006  *     November 2011
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          UPLO        CHARACTER          UPLO
Line 14 Line 146
       COMPLEX*16         AP( * ), X( * )        COMPLEX*16         AP( * ), X( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  ZSPR    performs the symmetric rank 1 operation  
 *  
 *     A := alpha*x*x**H + A,  
 *  
 *  where alpha is a complex scalar, x is an n element vector and A is an  
 *  n by n symmetric matrix, supplied in packed form.  
 *  
 *  Arguments  
 *  ==========  
 *  
 *  UPLO     (input) 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        (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.  
 *  
 *  AP       (input/output) COMPLEX*16 array, 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 symmetric 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 symmetric 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.  
 *  
 * =====================================================================  * =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
Removed from v.1.8  
changed lines
  Added in v.1.9

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