ZHERK - perform one of the hermitian rank k operations C
:= alpha*A*conjg( A' ) + beta*C,
SYNOPSIS
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, * )
PURPOSE
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.
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( A' ) +
beta*C.
TRANS = 'C' or 'c' C := alpha*conjg( A' )*A +
beta*C.
Unchanged on exit.
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 lead
ing 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 hermi
tian matrix and the strictly lower triangular part
of C is not referenced. On exit, the upper trian
gular 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 hermi
tian matrix and the strictly upper triangular part
of C is not referenced. On exit, the lower trian
gular 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.
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 Har
well. Jeremy Du Croz, Numerical Algorithms Group
Ltd. Sven Hammarling, Numerical Algorithms Group
Ltd.
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