NAME
ZSYR2K - perform one of the symmetric rank 2k operations 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, * )
PURPOSE
ZSYR2K performs one of the symmetric rank 2k operations
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 specifies 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 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*16 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 - 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 symmetric 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
symmetric 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.
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.