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# LAPACK-3

## man page of LAPACK-3

### LAPACK-3: ZLA_LIN_BERR compute componentwise relative backward error from the formula max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y)

```NAME
LAPACK-3  -  ZLA_LIN_BERR compute componentwise 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 componentwise absolute value of
the matrix  or vector Z

SYNOPSIS
SUBROUTINE ZLA_LIN_BERR ( N, NZ, NRHS, RES, AYB, BERR )

IMPLICIT            NONE

INTEGER             N, NZ, NRHS

DOUBLE              PRECISION AYB( N, NRHS ), BERR( NRHS )

COMPLEX*16          RES( N, NRHS )

PURPOSE
ZLA_LIN_BERR computes componentwise 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 componentwise absolute value of the matrix
or vector Z.
N       (input) INTEGER
The number of linear equations, i.e., the order of the
matrix A.  N >= 0.
NZ      (input) INTEGER
We add (NZ+1)*SLAMCH( 'Safe minimum' ) to R(i) in the numerator to
guard against spuriously zero residuals. Default value is N.
NRHS    (input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices AYB, RES, and BERR.  NRHS >= 0.
RES    (input) DOUBLE PRECISION array, dimension (N,NRHS)
The residual matrix, i.e., the matrix R in the relative backward
error formula above.
AYB    (input) DOUBLE PRECISION array, dimension (N, NRHS)
The denominator in the relative backward error formula above, i.e.,
the matrix abs(op(A_s))*abs(Y) + abs(B_s). The matrices A, Y, and B
are from iterative refinement (see zla_gerfsx_extended.f).

BERR   (output) COMPLEX*16 array, dimension (NRHS)
The componentwise relative backward error from the formula above.

LAPACK routine (version 3.2.2)March 2011                       LAPACK-3(3)
```