subroutine zher2k (UPLO, TRANS, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZHER2K
ZHER2K
Purpose:
ZHER2K performs one of the hermitian rank 2k operations
C := alpha*A*B**H + conjg( alpha )*B*A**H + beta*C,
or
C := alpha*A**H*B + conjg( alpha )*B**H*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 is 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.
TRANS
TRANS is CHARACTER*1
On entry, TRANS specifies the operation to be performed as
follows:
TRANS = 'N' or 'n' C := alpha*A*B**H +
conjg( alpha )*B*A**H +
beta*C.
TRANS = 'C' or 'c' C := alpha*A**H*B +
conjg( alpha )*B**H*A +
beta*C.
N
N is INTEGER
On entry, N specifies the order of the matrix C. N must be
at least zero.
K
K is 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.
ALPHA
ALPHA is COMPLEX*16 .
On entry, ALPHA specifies the scalar alpha.
A
A is COMPLEX*16 array, 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.
LDA
LDA is 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 ).
B
B is COMPLEX*16 array, 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.
LDB
LDB is 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
BETA is DOUBLE PRECISION .
On entry, BETA specifies the scalar beta.
C
C is COMPLEX*16 array, 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
LDC is 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 ).
Author:
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
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.
Definition at line 200 of file zher2k.f.
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