---
name: "cla_lin_berr.f"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/cla_lin_berr.f"
---

# cla\_lin\_berr.f(3)

## NAME

SRC/cla\_lin\_berr.f

## SYNOPSIS

### Functions/Subroutines

subroutine **cla\_lin\_berr** (n, nz, nrhs, res, ayb, berr)\
 **CLA\_LIN\_BERR** computes a component-wise relative backward error.

## Function/Subroutine Documentation

### subroutine cla\_lin\_berr (integer n, integer nz, integer nrhs, complex, dimension( n, nrhs ) res, real, dimension( n, nrhs ) ayb, real, dimension( nrhs ) berr)

**CLA\_LIN\_BERR** computes a component-wise relative backward error.

**Purpose:**

```
!>
!>    CLA_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.
!>
```

**Parameters**

*N*

```
!>          N is INTEGER
!>     The number of linear equations, i.e., the order of the
!>     matrix A.  N >= 0.
!>
```

*NZ*

```
!>          NZ is 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*

```
!>          NRHS is INTEGER
!>     The number of right hand sides, i.e., the number of columns
!>     of the matrices AYB, RES, and BERR.  NRHS >= 0.
!>
```

*RES*

```
!>          RES is COMPLEX array, dimension (N,NRHS)
!>     The residual matrix, i.e., the matrix R in the relative backward
!>     error formula above.
!>
```

*AYB*

```
!>          AYB is REAL 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 cla_gerfsx_extended.f).
!>
```

*BERR*

```
!>          BERR is REAL array, dimension (NRHS)
!>     The componentwise relative backward error from the formula above.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **100** of file **cla\_lin\_berr.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.