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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.