ZSYR(3)        LAPACK routine of NEC Numeric Library Collection        ZSYR(3)



NAME
       ZSYR

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



PURPOSE
            ZSYR   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.




ARGUMENTS
           UPLO      (input)
                     UPLO is 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         (input)
                     N is INTEGER
                      On entry, N specifies the order of the matrix A.
                      N must be at least zero.
                      Unchanged on exit.

           ALPHA     (input)
                     ALPHA is COMPLEX*16
                      On entry, ALPHA specifies the scalar alpha.
                      Unchanged on exit.

           X         (input)
                     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.

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

           A         (input/output)
                     A is 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 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       (input)
                     LDA is 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.



LAPACK routine                  31 October 2017                        ZSYR(3)