dsyrk (l) - Linux Manuals
dsyrk: performs one of the symmetric rank k operations C := alpha*A*Aaq + beta*C,
Command to display dsyrk
manual in Linux: $ man l dsyrk
NAME
DSYRK - performs one of the symmetric rank k operations C := alpha*A*Aaq + beta*C,
SYNOPSIS
- SUBROUTINE DSYRK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC)
-
-
DOUBLE
PRECISION ALPHA,BETA
-
INTEGER
K,LDA,LDC,N
-
CHARACTER
TRANS,UPLO
-
DOUBLE
PRECISION A(LDA,*),C(LDC,*)
PURPOSE
DSYRK performs one of the symmetric rank k operations
or
C := alpha*Aaq*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.
ARGUMENTS
- 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 = aqUaq or aquaq Only the upper triangular part of C
is to be referenced.
UPLO = aqLaq or aqlaq 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 = aqNaq or aqnaq C := alpha*A*Aaq + beta*C.
TRANS = aqTaq or aqtaq C := alpha*Aaq*A + beta*C.
TRANS = aqCaq or aqcaq C := alpha*Aaq*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 = aqNaq or aqnaq, K specifies the number
of columns of the matrix A, and on entry with
TRANS = aqTaq or aqtaq or aqCaq or aqcaq, K specifies the number
of rows of the matrix A. 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 = aqNaq or aqnaq, and is n otherwise.
Before entry with TRANS = aqNaq or aqnaq, 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 = aqNaq or aqnaq
then LDA must be at least max( 1, n ), otherwise LDA 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 = aqUaq or aquaq, 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 = aqLaq or aqlaq, 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.
FURTHER DETAILS
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.
Pages related to dsyrk
- dsyrk (3)
- dsyr (l) - performs the symmetric rank 1 operation A := alpha*x*xaq + A,
- dsyr2 (l) - performs the symmetric rank 2 operation A := alpha*x*yaq + alpha*y*xaq + A,
- dsyr2k (l) - performs one of the symmetric rank 2k operations C := alpha*A*Baq + alpha*B*Aaq + beta*C,
- dsyrfs (l) - improves the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite, and provides error bounds and backward error estimates for the solution
- dsyrfsx (l) - DSYRFSX improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite, and provides error bounds and backward error estimates for the solution
- dsycon (l) - estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by DSYTRF
- dsyequb (l) - computes row and column scalings intended to equilibrate a symmetric matrix A and reduce its condition number (with respect to the two-norm)
- dsyev (l) - computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A