ZHERK(1)

NAME
LAPACK-3 - performs one of the hermitian rank k operations C := alpha*A*A**H + beta*C,

SYNOPSIS

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

DOUBLE
    PRECISION ALPHA,BETA

INTEGER
    K,LDA,LDC,N

CHARACTER
    TRANS,UPLO

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

PURPOSE
ZHERK performs one of the hermitian rank k operations
 or
    C := alpha*A**H*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.

ARGUMENTS

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*A**H + beta*C.
     TRANS = 'C' or 'c' C := alpha*A**H*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.

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.