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


SYNOPSIS

       SUBROUTINE CSPR( UPLO, N, ALPHA, X, INCX, AP )

           CHARACTER    UPLO

           INTEGER      INCX, N

           COMPLEX      ALPHA

           COMPLEX      AP( * ), X( * )


PURPOSE

       CSPR  performs  the  symmetric  rank  1  operation  A   :=
       alpha*x*conjg(  x' ) + 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   - 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
              On  entry,  ALPHA  specifies  the   scalar   alpha.
              Unchanged on exit.

       X      - COMPLEX 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 ele­
              ments of X. INCX must not be  zero.   Unchanged  on
              exit.

              (  ( 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 tri­
              angular 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 tri­
              angular  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.


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