ZSYR (3lapack)

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 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.

  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 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.