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zsyr

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

 SYNOPSIS
      SUBROUTINE ZSYR( UPLO, N, ALPHA, X, INCX, A, LDA )

          CHARACTER    UPLO

          INTEGER      INCX, LDA, N

          COMPLEX*16   ALPHA

          COMPLEX*16   A( LDA, * ), X( * )

 PURPOSE
      ZSYR   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.

 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*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 vec-
             tor 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.

      A      - COMPLEX*16 array, dimension( LDA, N )
             Before entry with  UPLO = 'U' or 'u', the leading n
             by n upper triangular part of the array A must con-
             tain 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 tri-
             angular 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.