?la_geamv

Computes a matrix-vector product using a general matrix to calculate error bounds.

Syntax

call sla_geamv(trans, m, n, alpha, a, lda, x, incx, beta, y, incy)

call dla_geamv(trans, m, n, alpha, a, lda, x, incx, beta, y, incy)

call cla_geamv(trans, m, n, alpha, a, lda, x, incx, beta, y, incy)

call zla_geamv(trans, m, n, alpha, a, lda, x, incx, beta, y, incy)

• mkl.fi

Description

The ?la_geamv routines perform a matrix-vector operation defined as

y := alpha*abs(A)*(x) + beta*abs(y),

or

y := alpha*abs(AT)*abs(x) + beta*abs(y),

where:

alpha and beta are scalars,

x and y are vectors,

A is an m-by-n matrix.

This function is primarily used in calculating error bounds. To protect against underflow during evaluation, the function perturbs components in the resulting vector away from zero by (n + 1) times the underflow threshold. To prevent unnecessarily large errors for block structure embedded in general matrices, the function does not perturb symbolically zero components. A zero entry is considered symbolic if all multiplications involved in computing that entry have at least one zero multiplicand.

Input Parameters

trans

CHARACTER*1. Specifies the operation:

if trans = BLAS_NO_TRANS , then y := alpha*abs(A)*abs(x) + beta*abs(y)

if trans = BLAS_TRANS, then y := alpha*abs(AT)*abs(x) + beta*abs(y)

if trans = 'BLAS_CONJ_TRANS, then y := alpha*abs(AT)*abs(x) + beta*abs(y).

m

INTEGER. Specifies the number of rows of the matrix A. The value of m must be at least zero.

n

INTEGER. Specifies the number of columns of the matrix A. The value of n must be at least zero.

alpha

REAL for sla_geamv and for cla_geamv

DOUBLE PRECISION for dla_geamv and zla_geamv

Specifies the scalar alpha.

a

REAL for sla_geamv

DOUBLE PRECISION for dla_geamv

COMPLEX for cla_geamv

DOUBLE COMPLEX for zla_geamv

Array, DIMENSION(lda, *). Before entry, the leading m-by-n part of the array a must contain the matrix of coefficients. The second dimension of a must be at least max(1,n).

lda

INTEGER. Specifies the leading dimension of a as declared in the calling (sub)program. The value of lda must be at least max(1, m).

x

REAL for sla_geamv

DOUBLE PRECISION for dla_geamv

COMPLEX for cla_geamv

DOUBLE COMPLEX for zla_geamv

Array, DIMENSION at least (1+(n-1)*abs(incx)) when trans = 'N' or 'n' and at least (1+(m - 1)*abs(incx)) otherwise. Before entry, the incremented array x must contain the vector X.

incx

INTEGER. Specifies the increment for the elements of x.

The value of incx must be non-zero.

beta

REAL for sla_geamv and for cla_geamv

DOUBLE PRECISION for dla_geamv and zla_geamv

Specifies the scalar beta. When beta is zero, you do not need to set y on input.

y

REAL for sla_geamv and for cla_geamv

DOUBLE PRECISION for dla_geamv and zla_geamv

Array, DIMENSION at least (1 +(m - 1)*abs(incy)) when trans = 'N' or 'n' and at least (1 +(n - 1)*abs(incy)) otherwise. Before entry with non-zero beta, the incremented array y must contain the vector Y.

incy

INTEGER. Specifies the increment for the elements of y.

The value of incy must be non-zero.

Output Parameters

y

Updated vector Y.

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