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Technical Reference: Base Operating System and Extensions , Volume 2
Performs symmetric rank 2k
operations.
BLAS Library
(libblas.a)
SUBROUTINE SSYR2K(UPLO, TRANS, N, K, ALPHA,
A, LDA, B, LDB, BETA, C, LDC)
CHARACTER*1 UPLO, TRANS
INTEGER N, K, LDA, LDB, LDC
REAL ALPHA, BETA
REAL A(LDA,*), B(LDB,*), C(LDC,*)
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,*)
SUBROUTINE CSYR2K(UPLO, TRANS, N, K, ALPHA,
A, LDA, B, LDB, BETA, C, LDC)
CHARACTER*1 UPLO,TRANS
INTEGER N,K,LDA,LDB,LDC
COMPLEX ALPHA,BETA
COMPLEX A(LDA,*), B(LDB,*), C(LDC,*)
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,*)
The SSYR2K,
DSYR2K, CSYR2K, or ZSYR2K subroutine 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.
UPLO
 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
 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
 On entry, N specifies the order of the matrix
C; N must be at least 0; unchanged on
exit.

K
 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 0;
unchanged on exit.

ALPHA
 On entry, ALPHA specifies the scalar alpha; unchanged on
exit.

A
 An array of dimension ( LDA, KA ), where
KA is K when TRANS = 'N' or
'n', and is N otherwise; on 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
 On entry, LDA specifies the first dimension of A as
declared in the calling (sub) program. When TRANS =
'N' or 'n', LDA must be at least max( 1,
N ); otherwise LDA must be at least max( 1,
K ); unchanged on exit.

B
 An array of dimension ( LDB, KB ), where
KB is K when TRANS = 'N' or
'n', and is N otherwise; on 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
 On entry, LDB specifies the first dimension of B as
declared in the calling (sub) program. When TRANS =
'N' or 'n', LDB must be at least max( 1,
N ); otherwise LDB must be at least max( 1,
K ); unchanged on exit.

BETA
 On entry, BETA specifies the scalar beta; unchanged on
exit.

C
 An array of dimension ( LDC, N ); on 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. On 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
 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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