ZSYRK - perform one of the symmetric rank k operations C
:= alpha*A*A' + beta*C,
SYNOPSIS
SUBROUTINE ZSYRK ( UPLO, TRANS, N, K, ALPHA, A, LDA, BETA,
C, LDC )
CHARACTER*1 UPLO, TRANS
INTEGER N, K, LDA, LDC
COMPLEX*16 ALPHA, BETA
COMPLEX*16 A( LDA, * ), C( LDC, * )
PURPOSE
ZSYRK performs one of the symmetric rank k operations
or
C := alpha*A'*A + beta*C,
where alpha and beta are scalars, C is an n by n sym
metric 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*A' + beta*C.
TRANS = 'T' or 't' C := alpha*A'*A + beta*C.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix C.
K - INTEGER.
On entry with TRANS = 'N' or 'n', K specifies
the number of columns of the matrix A,
and on entry with TRANS = 'T' or 't', K
specifies the number of rows of the matrix A. K
must be at least zero. Unchanged on exit.
ALPHA - COMPLEX*16 .
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 - COMPLEX*16 .
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 symmet
ric 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 symmet
ric 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.
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.
-- 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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