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NAME
zsyr2k - perform one of the symmetric rank 2k operations C
:= alpha*A*B' + alpha*B*A' + beta*C or C := alpha*A'*B +
alpha*B'*A + beta*C
SYNOPSIS
SUBROUTINE ZSYR2K(UPLO, TRANS, N, K, ALPHA, A, LDA, B, LDB,
BETA, C, LDC )
CHARACTER*1 UPLO, TRANS
INTEGER N, K, LDA, LDB, LDC
COMPLEX*16 ALPHA, BETA
COMPLEX*16 A( LDA, * ), B( LDB, * ), C( LDC, * )
#include <sunperf.h>
void zsyr2k(char uplo, char trans, int n, int k, doublecom-
plex *zalpha, doublecomplex *za, int lda, doub-
lecomplex * b, int ldb, doublecomplex *zbeta,
doublecomplex *zc, int ldc) ;
PURPOSE
ZSYR2K performs one of the symmetric rank 2k operations C
:= alpha*A*B' + alpha*B*A' + beta*C or C := alpha*A'*B +
alpha*B'*A + beta*C where alpha and beta are scalars, C
is an n by n symmetric 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*B' + alpha*B*A'
+ beta*C.
TRANS = 'T' or 't' C := alpha*A'*B + alpha*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 = 'T' or 't', K speci-
fies the number of rows of the matrices A and B.
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 other-
wise.
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.
B - COMPLEX*16 array of DIMENSION ( LDB, kb ), where
kb is
k when TRANS = 'N' or 'n', and is n other-
wise.
Before entry with TRANS = 'N' or 'n', the lead-
ing 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 - 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 lead-
ing n by n upper triangular part of the array C
must contain the upper triangular part of the
symmetric matrix and the strictly lower triangu-
lar part of C is not referenced. On exit, the
upper triangular part of the array C is overwrit-
ten by the upper triangular part of the updated
matrix.
Before entry with UPLO = 'L' or 'l', the lead-
ing n by n lower triangular part of the array C
must contain the lower triangular part of the
symmetric matrix and the strictly upper triangu-
lar part of C is not referenced. On exit, the
lower triangular part of the array C is overwrit-
ten 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.
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