NAME
CHER2K - perform one of the hermitian rank 2k operations C :=
alpha*A*conjg( B’ ) + conjg( alpha )*B*conjg( A’ ) + beta*C,
SYNOPSIS
SUBROUTINE CHER2K( UPLO, TRANS, N, K, ALPHA, A, LDA, B, LDB, BETA, C,
LDC )
CHARACTER*1 UPLO, TRANS
INTEGER N, K, LDA, LDB, LDC
REAL BETA
COMPLEX ALPHA
COMPLEX A( LDA, * ), B( LDB, * ), C( LDC, * )
PURPOSE
CHER2K performs one of the hermitian rank 2k operations
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.
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.