# zher2k.f - Man Page

BLAS/SRC/zher2k.f

## Synopsis

### Functions/Subroutines

subroutine zher2k (uplo, trans, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
ZHER2K

## Function/Subroutine Documentation

### subroutine zher2k (character uplo, character trans, integer n, integer k, complex*16 alpha, complex*16, dimension(lda,*) a, integer lda, complex*16, dimension(ldb,*) b, integer ldb, double precision beta, complex*16, dimension(ldc,*) c, integer ldc)

ZHER2K

Purpose:

``` ZHER2K  performs one of the hermitian rank 2k operations

C := alpha*A*B**H + conjg( alpha )*B*A**H + beta*C,

or

C := alpha*A**H*B + conjg( alpha )*B**H*A + beta*C,

where  alpha and beta  are scalars with  beta  real,  C is an  n by n
hermitian matrix and  A and B  are  n by k matrices in the first case
and  k by n  matrices in the second case.```
Parameters

UPLO

```          UPLO is 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.```

TRANS

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

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

TRANS = 'C' or 'c'    C := alpha*A**H*B          +
conjg( alpha )*B**H*A +
beta*C.```

N

```          N is INTEGER
On entry,  N specifies the order of the matrix C.  N must be
at least zero.```

K

```          K is INTEGER
On entry with  TRANS = 'N' or 'n',  K  specifies  the number
of  columns  of the  matrices  A and B,  and on  entry  with
TRANS = 'C' or 'c',  K  specifies  the number of rows of the
matrices  A and B.  K must be at least zero.```

ALPHA

```          ALPHA is COMPLEX*16 .
On entry, ALPHA specifies the scalar alpha.```

A

```          A is COMPLEX*16 array, 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.```

LDA

```          LDA is 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 ).```

B

```          B is COMPLEX*16 array, dimension ( LDB, kb ), where kb 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  B  must contain the matrix  B,  otherwise
the leading  k by n  part of the array  B  must contain  the
matrix B.```

LDB

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

BETA

```          BETA is DOUBLE PRECISION .
On entry, BETA specifies the scalar beta.```

C

```          C is COMPLEX*16 array, 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

```          LDC is 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 ).```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Further Details:

```  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.

-- Modified 8-Nov-93 to set C(J,J) to DBLE( C(J,J) ) when BETA = 1.
Ed Anderson, Cray Research Inc.```

Definition at line 197 of file zher2k.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zher2k(3) is an alias of zher2k.f(3).

Tue Nov 28 2023 12:08:41 Version 3.12.0 LAPACK