
DSYR2K(l) BLAS routine DSYR2K(l)
NAME
DSYR2K  perform one of the symmetric rank 2k operations C := alpha*A*B' + alpha*B*A' +
beta*C,
SYNOPSIS
SUBROUTINE DSYR2K( UPLO, TRANS, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC )
CHARACTER*1 UPLO, TRANS
INTEGER N, K, LDA, LDB, LDC
DOUBLE PRECISION ALPHA, BETA
DOUBLE PRECISION A( LDA, * ), B( LDB, * ), C( LDC, * )
PURPOSE
DSYR2K 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.
TRANS = 'C' or 'c' 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' or 'C' or 'c', K spec
ifies the number of rows of the matrices A and B. K must be at least zero.
Unchanged on exit.
ALPHA  DOUBLE PRECISION.
On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
A  DOUBLE PRECISION 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  DOUBLE PRECISION 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  DOUBLE PRECISION.
On entry, BETA specifies the scalar beta. Unchanged on exit.
C  DOUBLE PRECISION 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 sym
metric 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 trian
gular 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 8February1989. Jack Dongarra, Argonne National Laboratory. Iain
Duff, AERE Harwell. Jeremy Du Croz, Numerical Algorithms Group Ltd. Sven Hammar
ling, Numerical Algorithms Group Ltd.
BLAS routine 16 October 1992 DSYR2K(l) 
