---
name: "sgerfs"
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/sgerfs.f"
---

# sgerfs(3)

Part of [sgerfs.f(3)](/sgerfs.f/3.md).

## NAME

SRC/sgerfs.f

## SYNOPSIS

### Functions/Subroutines

subroutine **sgerfs** (trans, n, nrhs, a, lda, af, ldaf, ipiv, b, ldb, x, ldx, ferr, berr, work, iwork, info)\
 **SGERFS**

## Function/Subroutine Documentation

### subroutine sgerfs (character trans, integer n, integer nrhs, real, dimension( lda, \* ) a, integer lda, real, dimension( ldaf, \* ) af, integer ldaf, integer, dimension( \* ) ipiv, real, dimension( ldb, \* ) b, integer ldb, real, dimension( ldx, \* ) x, integer ldx, real, dimension( \* ) ferr, real, dimension( \* ) berr, real, dimension( \* ) work, integer, dimension( \* ) iwork, integer info)

**SGERFS**

**Purpose:**

```
!>
!> SGERFS improves the computed solution to a system of linear
!> equations and provides error bounds and backward error estimates for
!> the solution.
!>
```

**Parameters**

*TRANS*

```
!>          TRANS is CHARACTER*1
!>          Specifies the form of the system of equations:
!>          = 'N':  A * X = B     (No transpose)
!>          = 'T':  A**T * X = B  (Transpose)
!>          = 'C':  A**H * X = B  (Conjugate transpose = Transpose)
!>
```

*N*

```
!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!>
```

*NRHS*

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

*A*

```
!>          A is REAL array, dimension (LDA,N)
!>          The original N-by-N matrix A.
!>
```

*LDA*

```
!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,N).
!>
```

*AF*

```
!>          AF is REAL array, dimension (LDAF,N)
!>          The factors L and U from the factorization A = P*L*U
!>          as computed by SGETRF.
!>
```

*LDAF*

```
!>          LDAF is INTEGER
!>          The leading dimension of the array AF.  LDAF >= max(1,N).
!>
```

*IPIV*

```
!>          IPIV is INTEGER array, dimension (N)
!>          The pivot indices from SGETRF; for 1<=i<=N, row i of the
!>          matrix was interchanged with row IPIV(i).
!>
```

*B*

```
!>          B is REAL array, dimension (LDB,NRHS)
!>          The right hand side matrix B.
!>
```

*LDB*

```
!>          LDB is INTEGER
!>          The leading dimension of the array B.  LDB >= max(1,N).
!>
```

*X*

```
!>          X is REAL array, dimension (LDX,NRHS)
!>          On entry, the solution matrix X, as computed by SGETRS.
!>          On exit, the improved solution matrix X.
!>
```

*LDX*

```
!>          LDX is INTEGER
!>          The leading dimension of the array X.  LDX >= max(1,N).
!>
```

*FERR*

```
!>          FERR is REAL array, dimension (NRHS)
!>          The estimated forward error bound for each solution vector
!>          X(j) (the j-th column of the solution matrix X).
!>          If XTRUE is the true solution corresponding to X(j), FERR(j)
!>          is an estimated upper bound for the magnitude of the largest
!>          element in (X(j) - XTRUE) divided by the magnitude of the
!>          largest element in X(j).  The estimate is as reliable as
!>          the estimate for RCOND, and is almost always a slight
!>          overestimate of the true error.
!>
```

*BERR*

```
!>          BERR is REAL array, dimension (NRHS)
!>          The componentwise relative backward error of each solution
!>          vector X(j) (i.e., the smallest relative change in
!>          any element of A or B that makes X(j) an exact solution).
!>
```

*WORK*

```
!>          WORK is REAL array, dimension (3*N)
!>
```

*IWORK*

```
!>          IWORK is INTEGER array, dimension (N)
!>
```

*INFO*

```
!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>
```

**Internal Parameters:**

```
!>  ITMAX is the maximum number of steps of iterative refinement.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **183** of file **sgerfs.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.