## SYNOPSIS

- SUBROUTINE ZLA_SYAMV(
- UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY )

- IMPLICIT NONE

- DOUBLE PRECISION ALPHA, BETA

- INTEGER INCX, INCY, LDA, N

- INTEGER UPLO

- COMPLEX*16 A( LDA, * ), X( * )

- DOUBLE PRECISION Y( * )

## PURPOSE

ZLA_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 - DOUBLE PRECISION .
- On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
- A - COMPLEX*16 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 - COMPLEX*16 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