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


SYNOPSIS

       SUBROUTINE CSYR( UPLO, N, ALPHA, X, INCX, A, LDA )

           CHARACTER    UPLO

           INTEGER      INCX, LDA, N

           COMPLEX      ALPHA

           COMPLEX      A( LDA, * ), X( * )


PURPOSE

       CSYR  performs  the  symmetric  rank  1  operation  A   :=
       alpha*x*(  x' ) + A, where alpha is a complex scalar, x is
       an n element vector and A is an n by n symmetric matrix.


ARGUMENTS

       UPLO   - CHARACTER*1
              On entry, UPLO specifies whether the upper or lower
              triangular  part of the array A is to be referenced
              as follows:

              UPLO = 'U' or 'u'   Only the upper triangular  part
              of A is to be referenced.

              UPLO  = 'L' or 'l'   Only the lower triangular part
              of A is to be referenced.

              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.

              Before entry, with  UPLO = 'U' or 'u', the  leading
              n  by  n  upper triangular part of the array A must
              contain the upper triangular part of the  symmetric
              matrix  and the strictly lower triangular part of A
              is not referenced. On exit,  the  upper  triangular
              part  of  the  array  A is overwritten by the upper
              triangular part  of  the  updated  matrix.   Before
              entry,  with  UPLO = 'L' or 'l', the leading n by n
              lower triangular part of the array A  must  contain
              the  lower  triangular part of the symmetric matrix
              and the strictly upper triangular part of A is  not
              referenced.  On  exit, the lower triangular part of
              the array A is overwritten by the lower  triangular
              part of the updated matrix.

       LDA    - INTEGER
              On entry, LDA specifies the first dimension of A as
              declared in the calling (sub) program. LDA must  be
              at least max( 1, N ).  Unchanged on exit.


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