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

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, * )

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.

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.