## Function Zher2k

### Part of:

package f77
( zher2k < uplo > < trans > < n > < k > < alpha > < a > < lda > < b > < ldb > < beta > < c > < ldc > )

Purpose
=======

ZHER2K performs one of the hermitian rank 2k operations

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

or

C := alpha*conjg( A' )*B + conjg( alpha )*conjg( B' )*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 - 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( B' ) +
conjg( alpha )*B*conjg( A' ) +
beta*C.

TRANS = 'C' or 'c' C := alpha*conjg( A' )*B +
conjg( alpha )*conjg( B' )*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 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.
Unchanged on exit.

ALPHA - COMPLEX*16 .
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.

B - COMPLEX*16 array of 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.
Unchanged on exit.

LDB - 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 - 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.

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