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NAME

```       CHER2 - perform the hermitian rank 2 operation   A := alpha*x*conjg( y’
) + conjg( alpha )*y*conjg( x’ ) + A,

```

SYNOPSIS

```       SUBROUTINE CHER2 ( UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA )

COMPLEX      ALPHA

INTEGER      INCX, INCY, LDA, N

CHARACTER*1  UPLO

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

```

PURPOSE

```       CHER2  performs the hermitian rank 2 operation

where alpha is a scalar, x and y are n element vectors 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  - COMPLEX         .
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.

Y      - COMPLEX          array of dimension at least
(  1  +  ( n - 1 )*abs( INCY ) ).  Before entry, the incremented
array Y must contain the n element vector y.  Unchanged on exit.

INCY   - INTEGER.
On  entry,  INCY  specifies the increment for the elements of Y.
INCY 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.
```