CHER(1)

NAME
LAPACK-3 - performs the hermitian rank 1 operation A := alpha*x*x**H + A,

SYNOPSIS

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

REAL
    ALPHA

INTEGER
    INCX,LDA,N

CHARACTER
    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.

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  - 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.

FURTHER DETAILS
 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.