SYNOPSIS

SUBROUTINE SLA_SYAMV(

UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY )

    

IMPLICIT NONE

    

REAL ALPHA, BETA

    

INTEGER INCX, INCY, LDA, N, UPLO

    

REAL A( LDA, * ), X( * ), Y( * )

PURPOSE

SLA_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 protect 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 considered "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 referenced. 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 - REAL .

On entry, ALPHA specifies the scalar alpha. Unchanged on exit.

A - REAL array of DIMENSION ( LDA, n ).

Before entry, the leading m by n part of the array A must contain 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 - REAL 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 - REAL .

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 - REAL 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