NAME

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

SYNOPSIS

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

           REAL        ALPHA

           INTEGER     INCX, LDA, N

           CHARACTER*1 UPLO

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

PURPOSE

       CHER   performs the hermitian rank 1 operation

       where alpha is a real scalar, x is an n element vector and A is an n by n hermitian matrix.

PARAMETERS

       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  - REAL            .
              On entry, ALPHA specifies the scalar alpha.  Unchanged on exit.

       X      - COMPLEX          array of 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          array of 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 hermitian 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  hermitian
              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.
              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.

       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.

              Level 2 Blas routine.

              --  Written on 22-October-1986.  Jack Dongarra, Argonne National Lab.  Jeremy Du Croz, Nag Central
              Office.  Sven Hammarling, Nag Central Office.  Richard Hanson, Sandia National Labs.

BLAS routine                                     16 October 1992                                         CHER(3)