CHER2K(3)

SYNOPSIS
SUBROUTINE CHER2K (UPLO, TRANS, N, K, ALPHA, A, LDA, B, LDB, BETA, $ C, LDC)

NAME
cher2k - Perform Hermitian rank 2k update of a complex.

LIBRARY
SLATEC (BLAS)

CATEGORY
D1B6

TYPE
COMPLEX (SHER2-S, DHER2-D, CHER2-C, CHER2K-C)

KEYWORDS
LEVEL 3 BLAS, LINEAR ALGEBRA

AUTHOR
Dongarra, J., (ANL) Duff, I., (AERE) Du Croz, J., (NAG) Hammarling, S. (NAG)

DESCRIPTION
CHER2K 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 . On entry, ALPHA specifies the scalar alpha. Unchanged on exit. A - COMPLEX 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 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 - REAL . On entry, BETA specifies the scalar beta. Unchanged on exit. C - COMPLEX 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.

REFERENCES
Dongarra, J., Du Croz, J., Duff, I., and Hammarling, S. A set of level 3 basic linear algebra subprograms. ACM TOMS, Vol. 16, No. 1, pp. 1-17, March 1990.

ROUTINES CALLED
LSAME, XERBLA

REVISION HISTORY (YYMMDD)
890208 DATE WRITTEN
910605 Modified to meet SLATEC prologue standards. Only comment lines were modified. (BKS)