# ?la_lin_berr

Computes component-wise relative backward error.

## Syntax

call sla_lin_berr(n, nz, nrhs, res, ayb, berr )

call dla_lin_berr(n, nz, nrhs, res, ayb, berr )

call cla_lin_berr(n, nz, nrhs, res, ayb, berr )

call zla_lin_berr(n, nz, nrhs, res, ayb, berr )

• mkl.fi

## Description

The ?la_lin_berr computes a component-wise relative backward error from the formula:

max(i) ( abs(R(i))/( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )

where abs(Z) is the component-wise value of the matrix or vector Z.

## Input Parameters

n

INTEGER. The number of linear equations, the order of the matrix A; n 0.

nz

INTEGER. The parameter for guarding against spuriously zero residuals.

(nz+1)*slamch( 'Safe minimum' ) is added to R(i) in the numerator of the relative backward error formula. The default value is n.

nrhs

INTEGER. Number of right-hand sides, the number of columns in the matrices AYB, RES, and BERR; nrhs 0.

res, ayb

REAL for sla_lin_berr, cla_lin_berr

DOUBLE PRECISION for dla_lin_berr, zla_lin_berr

Arrays, DIMENSION (n,nrhs).

res is the residual matrix, that is, the matrix R in the relative backward error formula.

ayb is the denominator of that formula, that is, the matrix abs(op(A_s))*abs(Y) + abs(B_s). The matrices A, Y, and B are from iterative refinement. See description of ?la_gerfsx_extended.

## Output Parameters

berr

REAL for sla_lin_berr

DOUBLE PRECISION for dla_lin_berr

COMPLEX for cla_lin_berr

DOUBLE COMPLEX for zla_lin_berr

The component-wise relative backward error.