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Technical Reference: Base Operating System and Extensions , Volume 2
Perform symmetric rank k
operations.
BLAS Library
(libblas.a)
SUBROUTINE SSYRK(UPLO, TRANS, N, K, ALPHA,
A, LDA, BETA, C, LDC)
CHARACTER*1 UPLO, TRANS
INTEGER N, K, LDA, LDC
REAL ALPHA, BETA
REAL A(LDA,*), C(LDC,*)
SUBROUTINE DSYRK(UPLO, TRANS, N, K, ALPHA,
A, LDA, BETA, C, LDC)
CHARACTER*1 UPLO,TRANS
INTEGER N,K,LDA,LDC
DOUBLE PRECISION ALPHA,BETA
DOUBLE PRECISION A(LDA,*), C(LDC,*)
SUBROUTINE CSYRK(UPLO, TRANS, N, K, ALPHA,
A, LDA, BETA, C, LDC)
CHARACTER*1 UPLO,TRANS
INTEGER N,K,LDA,LDC
COMPLEX ALPHA,BETA
COMPLEX A(LDA,*), C(LDC,*)
SUBROUTINE ZSYRK(UPLO, TRANS, N, K, ALPHA,
A, LDA, BETA, C, LDC)
CHARACTER*1 UPLO,TRANS
INTEGER N,K,LDA,LDC
COMPLEX*16 ALPHA,BETA
COMPLEX*16 A(LDA,*), C(LDC,*)
The SSYRK,
DSYRK, CSYRK or ZSYRK subroutine performs one
of the symmetric rank k operations:
C := alpha
* A * A' + beta *
C
OR
C := alpha
* A' * A + beta *
C
where alpha and beta are scalars,
C is an N by N symmetric matrix, and
A is an N by K matrix in the first case and a
K by N matrix 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 * A' + beta * C
 TRANS = 'T'
or 't'
 C := alpha * A' * A + beta * C
 TRANS = 'C'
or 'c'
 C := alpha * A' * 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 matrix A, and
on entry with TRANS = 'T' or 't' or
'C' or 'c', K specifies the number of rows of
the matrix A; 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.

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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