dsyr (l) - Linux Manuals

dsyr: performs the symmetric rank 1 operation A := alpha*x*xaq + A,

NAME

DSYR - performs the symmetric rank 1 operation A := alpha*x*xaq + A,

SYNOPSIS

SUBROUTINE DSYR(UPLO,N,ALPHA,X,INCX,A,LDA)

    
DOUBLE PRECISION ALPHA

    
INTEGER INCX,LDA,N

    
CHARACTER UPLO

    
DOUBLE PRECISION A(LDA,*),X(*)

PURPOSE

DSYR performs the symmetric rank 1 operation

where alpha is a real scalar, x is an n element vector and A is an n by n symmetric matrix.

ARGUMENTS

UPLO - CHARACTER*1.
On entry, UPLO specifies whether the upper or lower triangular part of the array A is to be referenced as follows:

UPLO = aqUaq or aquaq Only the upper triangular part of A is to be referenced.

UPLO = aqLaq or aqlaq Only the lower triangular part of A is to be referenced.

Unchanged on exit.

N - INTEGER.
On entry, N specifies the order of the matrix A. N must be at least zero. Unchanged on exit.
ALPHA - DOUBLE PRECISION.
On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
X - DOUBLE PRECISION array of dimension at least
( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x. Unchanged on exit.
INCX - INTEGER.
On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit.
A - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
Before entry with UPLO = aqUaq or aquaq, the leading n by n upper triangular part of the array A must contain the upper triangular part of the symmetric matrix and the strictly lower triangular part of A is not referenced. On exit, the upper triangular part of the array A 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 A must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of A is not referenced. On exit, the lower triangular part of the array A is overwritten by the lower triangular part of the updated matrix.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, n ). Unchanged on exit.

FURTHER DETAILS

Level 2 Blas routine.

-- Written on 22-October-1986.

Jack Dongarra, Argonne National Lab.

Jeremy Du Croz, Nag Central Office.

Sven Hammarling, Nag Central Office.

Richard Hanson, Sandia National Labs.

Pages related to dsyr

  • dsyr (3)
  • 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
  • dsyrk (l) - performs one of the symmetric rank k operations C := alpha*A*Aaq + beta*C,
  • 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
  • dsyevd (l) - computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A