.TH SSYR2K 1 "November 2006" "BLAS routine" "BLAS routine"
.SH NAME
SSYR2K - one of the symmetric rank 2k operations C := alpha*A*B\(aq + alpha*B*A\(aq + beta*C,
.SH SYNOPSIS
.TP 63
SUBROUTINE SSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
.TP 63
.ti +4
REAL
ALPHA,BETA
.TP 63
.ti +4
INTEGER
K,LDA,LDB,LDC,N
.TP 63
.ti +4
CHARACTER
TRANS,UPLO
.TP 63
.ti +4
REAL
A(LDA,*),B(LDB,*),C(LDC,*)
.SH PURPOSE
SSYR2K performs one of the symmetric rank 2k operations
or
.br
C := alpha*A\(aq*B + alpha*B\(aq*A + beta*C,
.br
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.
.br
.SH ARGUMENTS
.TP 7
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 = \(aqU\(aq or \(aqu\(aq Only the upper triangular part of C
is to be referenced.
UPLO = \(aqL\(aq or \(aql\(aq Only the lower triangular part of C
is to be referenced.
Unchanged on exit.
.TP 7
TRANS - CHARACTER*1.
On entry, TRANS specifies the operation to be performed as
follows:
TRANS = \(aqN\(aq or \(aqn\(aq C := alpha*A*B\(aq + alpha*B*A\(aq +
beta*C.
TRANS = \(aqT\(aq or \(aqt\(aq C := alpha*A\(aq*B + alpha*B\(aq*A +
beta*C.
TRANS = \(aqC\(aq or \(aqc\(aq C := alpha*A\(aq*B + alpha*B\(aq*A +
beta*C.
Unchanged on exit.
.TP 7
N - INTEGER.
On entry, N specifies the order of the matrix C. N must be
at least zero.
Unchanged on exit.
.TP 7
K - INTEGER.
On entry with TRANS = \(aqN\(aq or \(aqn\(aq, K specifies the number
of columns of the matrices A and B, and on entry with
TRANS = \(aqT\(aq or \(aqt\(aq or \(aqC\(aq or \(aqc\(aq, K specifies the number
of rows of the matrices A and B. K must be at least zero.
Unchanged on exit.
.TP 7
ALPHA - REAL .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
.TP 7
A - REAL array of DIMENSION ( LDA, ka ), where ka is
k when TRANS = \(aqN\(aq or \(aqn\(aq, and is n otherwise.
Before entry with TRANS = \(aqN\(aq or \(aqn\(aq, 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.
.TP 7
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. When TRANS = \(aqN\(aq or \(aqn\(aq
then LDA must be at least max( 1, n ), otherwise LDA must
be at least max( 1, k ).
Unchanged on exit.
.TP 7
B - REAL array of DIMENSION ( LDB, kb ), where kb is
k when TRANS = \(aqN\(aq or \(aqn\(aq, and is n otherwise.
Before entry with TRANS = \(aqN\(aq or \(aqn\(aq, 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.
.TP 7
LDB - INTEGER.
On entry, LDB specifies the first dimension of B as declared
in the calling (sub) program. When TRANS = \(aqN\(aq or \(aqn\(aq
then LDB must be at least max( 1, n ), otherwise LDB must
be at least max( 1, k ).
Unchanged on exit.
.TP 7
BETA - REAL .
On entry, BETA specifies the scalar beta.
Unchanged on exit.
.TP 7
C - REAL array of DIMENSION ( LDC, n ).
Before entry with UPLO = \(aqU\(aq or \(aqu\(aq, 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 = \(aqL\(aq or \(aql\(aq, 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.
.TP 7
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.
.. External Functions ..
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.. External Subroutines ..
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