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NAME
     zspr -  perform  the  symmetric  rank  1  operation    A  :=
     alpha*x*conjg( x' ) + A,

SYNOPSIS
     SUBROUTINE ZSPR( UPLO, N, ALPHA, X, INCX, AP )

     CHARACTER UPLO

     INTEGER INCX, N

     COMPLEX*16 ALPHA

     COMPLEX*16 AP( * ), X( * )



     #include <sunperf.h>

     void zspr(char *uplo, int *n, doublecomplex  *zalpha,  doub-
               lecomplex *zx, int *incx, doublecomplex *ap) ;

PURPOSE
     ZSPR    performs the symmetric rank 1 operation

     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      - 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     - COMPLEX*16
               On  entry,  ALPHA  specifies  the  scalar   alpha.
               Unchanged on exit.

     X         - 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      - INTEGER
               On entry, INCX specifies  the  increment  for  the
               elements  of  X. INCX must not be zero.  Unchanged
               on exit.

     AP        - 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 ele-
               ments need not be set,  they  are  assumed  to  be
               zero, and on exit they are set to zero.

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