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Purpose

=======

ZHERK performs one of the hermitian rank k operations

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

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.

-- Modified 8-Nov-93 to set C(J,J) to DBLE( C(J,J) ) when BETA = 1.

Ed Anderson, Cray Research Inc.