DLA_SYAMV(1LAPACK routine (version 3.2)DLA_SYAMV(1)NAME
DLA_SYAMV - performs the matrix-vector operation y :=
alpha*abs(A)*abs(x) + beta*abs(y),
SYNOPSIS
SUBROUTINE DLA_SYAMV( UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY )
IMPLICIT NONE
DOUBLE PRECISION ALPHA, BETA
INTEGER INCX, INCY, LDA, N, UPLO
DOUBLE PRECISION A( LDA, * ), X( * ), Y( * )
PURPOSE
DLA_SYAMV performs the matrix-vector operation where alpha and beta
are scalars, x and y are vectors and A is an n by n symmetric matrix.
This function is primarily used in calculating error bounds. To pro‐
tect against underflow during evaluation, components in the resulting
vector are perturbed away from zero by (N+1) times the underflow
threshold. To prevent unnecessarily large errors for block-structure
embedded in general matrices,
"symbolically" zero components are not perturbed. A zero entry is con‐
sidered "symbolic" if all multiplications involved in computing that
entry have at least one zero multiplicand.
ARGUMENTS
UPLO - INTEGER
On entry, UPLO specifies whether the upper or lower triangular
part of the array A is to be referenced as follows: UPLO =
BLAS_UPPER Only the upper triangular part of A is to be refer‐
enced. UPLO = BLAS_LOWER Only the lower triangular part of A
is to be referenced. Unchanged on exit.
N - INTEGER.
On entry, N specifies the number of columns 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.
A - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
Before entry, the leading m by n part of the array A must con‐
tain the matrix of coefficients. Unchanged on exit.
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.
X - DOUBLE PRECISION array of DIMENSION at least
( 1 + ( n - 1 )*abs( INCX ) ) Before entry, the incremented
array X must contain the 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.
BETA - DOUBLE PRECISION .
On entry, BETA specifies the scalar beta. When BETA is supplied
as zero then Y need not be set on input. Unchanged on exit.
Y - DOUBLE PRECISION array of DIMENSION at least
( 1 + ( n - 1 )*abs( INCY ) ) Before entry with BETA non-zero,
the incremented array Y must contain the vector y. On exit, Y is
overwritten by the updated vector y.
INCY - INTEGER.
On entry, INCY specifies the increment for the elements of Y.
INCY must not be zero. 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.
-- Modified for the absolute-value product, April 2006
Jason Riedy, UC Berkeley
LAPACK routine (version 3.2) November 2008 DLA_SYAMV(1)
