Homepage > Man Pages > Category > Subroutines
Homepage > Man Pages > Name > Z

# zherk

## man page of zherk

### zherk: perform one of the hermitian rank k operations C := alpha*A*conjg( A' ) + beta*C,

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

SYNOPSIS
SUBROUTINE ZHERK ( UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC )

CHARACTER*1  UPLO, TRANS

INTEGER      N, K, LDA, LDC

DOUBLE       PRECISION ALPHA, BETA

COMPLEX*16   A( LDA, * ), C( LDC, * )

PURPOSE
ZHERK  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  - DOUBLE PRECISION.
On entry, ALPHA specifies the scalar alpha.  Unchanged on exit.

A      - COMPLEX*16       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   - DOUBLE PRECISION.
On entry, BETA specifies the scalar beta.  Unchanged on exit.

C      - COMPLEX*16       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.

ZHERK(3)
```