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## NAME

```       CHERK  -  perform  one  of  the  hermitian  rank  k  operations    C :=
alpha*A*conjg( A’ ) + beta*C,

```

## SYNOPSIS

```       SUBROUTINE CHERK ( UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC )

CHARACTER*1  UPLO, TRANS

INTEGER      N, K, LDA, LDC

REAL         ALPHA, BETA

COMPLEX      A( LDA, * ), C( LDC, * )

```

## PURPOSE

```       CHERK  performs one of the hermitian rank k operations

or

C := alpha*conjg( A’ )*A + beta*C,

where  alpha and beta  are  real scalars,  C is an  n by  n   hermitian
matrix  and   A  is an  n by k  matrix in the  first case and a  k by n
matrix in the second case.

```

## PARAMETERS

```       UPLO   - CHARACTER*1.
On  entry,   UPLO  specifies  whether   the   upper   or   lower
triangular   part   of  the   array  C  is to be  referenced  as
follows:

UPLO = ’U’ or ’u’   Only the  upper triangular part of  C is  to
be referenced.

UPLO  = ’L’ or ’l’   Only the  lower triangular part of  C is to
be referenced.

Unchanged on exit.

TRANS  - CHARACTER*1.
On entry,  TRANS  specifies the operation  to  be  performed  as
follows:

TRANS = ’N’ or ’n’   C := alpha*A*conjg( A’ ) + beta*C.

TRANS = ’C’ or ’c’   C := alpha*conjg( A’ )*A + beta*C.

Unchanged on exit.

N      - INTEGER.
On  entry,  N specifies the order of the matrix C.  N must be at
least zero.  Unchanged on exit.

K      - INTEGER.
On entry with  TRANS = ’N’ or ’n’,  K  specifies  the number  of
columns   of  the   matrix   A,   and  on   entry   with TRANS =
’C’ or ’c’,  K  specifies  the number of rows of the  matrix  A.
K must be at least zero.  Unchanged on exit.

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

A      - COMPLEX          array of DIMENSION ( LDA, ka ), where ka is
k  when  TRANS = ’N’ or ’n’,   and  is   n   otherwise.   Before
entry  with   TRANS  = ’N’ or ’n’,  the  leading  n by k part of
the array  A  must contain the matrix  A,  otherwise the leading
k  by  n   part  of  the  array   A  must contain  the matrix A.
Unchanged on exit.

LDA    - INTEGER.
On entry, LDA specifies the first dimension of A as declared  in
the   calling   (sub)   program.   When  TRANS = ’N’ or ’n’ then
LDA must be at least  max( 1, n ), otherwise   LDA  must  be  at
least  max( 1, k ).  Unchanged on exit.

BETA   - REAL            .
On entry, BETA specifies the scalar beta.  Unchanged on exit.

C      - COMPLEX          array of DIMENSION ( LDC, n ).
Before  entry   with   UPLO  =  ’U’ or ’u’,  the leading  n by n
upper triangular part of the array  C  must  contain  the  upper
triangular  part   of  the   hermitian  matrix  and the strictly
lower triangular part of C is  not  referenced.   On  exit,  the
upper  triangular  part  of  the  array  C 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 C must contain  the  lower  triangular  part   of  the
hermitian matrix  and the strictly upper triangular part of C is
not referenced.  On exit, the lower triangular part of the array
C  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.

LDC    - INTEGER.
On entry, LDC specifies the first dimension of C as declared  in
the  calling  (sub)  program.   LDC  must  be  at  least max( 1,
n ).  Unchanged on exit.

Level 3 Blas routine.

-- Written on 8-February-1989.  Jack Dongarra, Argonne  National
Laboratory.  Iain Duff, AERE Harwell.  Jeremy Du Croz, Numerical
Algorithms Group Ltd.   Sven  Hammarling,  Numerical  Algorithms
Group Ltd.
```