**?gerfs**
refines the solution of a system of linear equations with a general matrix and estimates its error.

```
call sgerfs (
```

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

call dgerfs (*trans, n, nrhs, a, lda, af, ldaf, ipiv, b, ldb, x, ldx, ferr, berr, work, iwork, info*)

call cgerfs (*trans, n, nrhs, a, lda, af, ldaf, ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info*)

call zgerfs (*trans, n, nrhs, a, lda, af, ldaf, ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info*)

**?gbrfs**
refines the solution of a system of linear
equations with a general band matrix
and estimates its error.

```
call sgbrfs (
```

*trans, n, kl, ku, nrhs, ab, ldab, afb, ldafb, ipiv, b, ldb, x, ldx, ferr, berr, work, iwork, info*)

call dgbrfs (*trans, n, kl, ku, nrhs, ab, ldab, afb, ldafb, ipiv, b, ldb, x, ldx, ferr, berr, work, iwork, info*)

call cgbrfs (*trans, n, kl, ku, nrhs, ab, ldab, afb, ldafb, ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info*)

call zgbrfs (*trans, n, kl, ku, nrhs, ab, ldab, afb, ldafb, ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info*)

**?gtrfs**
refines the solution of a system of linear equations with a tridiagonal matrix and estimates its error.

```
call sgtrfs (
```

*trans, n, nrhs, dl, d, du, dlf, df, duf, du2, ipiv, b, ldb, x, ldx, ferr, berr, work, iwork, info*)

call dgtrfs (*trans, n, nrhs, dl, d, du, dlf, df, duf, du2, ipiv, b, ldb, x, ldx, ferr, berr, work, iwork, info*)

call cgtrfs (*trans, n, nrhs, dl, d, du, dlf, df, duf, du2, ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info*)

call zgtrfs (*trans, n, nrhs, dl, d, du, dlf, df, duf, du2, ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info*)

**?porfs**
refines the solution of a system of linear
equations with a symmetric (Hermitian)
positive-definite matrix and estimates its
error.

```
call sporfs (
```

*uplo, n, nrhs, a, lda, af, ldaf, b, ldb, x, ldx, ferr, berr, work, iwork, info*)

call dporfs (*uplo, n, nrhs, a, lda, af, ldaf, b, ldb, x, ldx, ferr, berr, work, iwork, info*)

call cporfs (*uplo, n, nrhs, a, lda, af, ldaf, b, ldb, x, ldx, ferr, berr, work, rwork, info*)

call zporfs (*uplo, n, nrhs, a, lda, af, ldaf, b, ldb, x, ldx, ferr, berr, work, rwork, info*)

**?pprfs**
refines the solution of a system of linear
equations with a packed symmetric
(Hermitian) positive-definite matrix and
estimates its error.

```
call spprfs (
```

*uplo, n, nrhs, ap, afp, b, ldb, x, ldx, ferr, berr, work, iwork, info*)

call dpprfs (*uplo, n, nrhs, ap, afp, b, ldb, x, ldx, ferr, berr, work, iwork, info*)

call cpprfs (*uplo, n, nrhs, ap, afp, b, ldb, x, ldx, ferr, berr, work, rwork, info*)

call zpprfs (*uplo, n, nrhs, ap, afp, b, ldb, x, ldx, ferr, berr, work, rwork, info*)

**?pbrfs**
refines the solution of a system of linear
equations with a band symmetric
(Hermitian) positive-definite matrix and
estimates its error.

```
call spbrfs (
```

*uplo, n, kd, nrhs, ab, ldab, afb, ldafb, b, ldb, x, ldx, ferr, berr, work, iwork, info*)

call dpbrfs (*uplo, n, kd, nrhs, ab, ldab, afb, ldafb, b, ldb, x, ldx, ferr, berr, work, iwork, info*)

call cpbrfs (*uplo, n, kd, nrhs, ab, ldab, afb, ldafb, b, ldb, x, ldx, ferr, berr, work, rwork, info*)

call zpbrfs (*uplo, n, kd, nrhs, ab, ldab, afb, ldafb, b, ldb, x, ldx, ferr, berr, work, rwork, info*)

**?ptrfs**
refines the solution of a system of linear
equations with a symmetric (Hermitian) positive-definite tridiagonal matrix and estimates its error.

```
call sptrfs (
```

*n, nrhs, d, e, df, ef, b, ldb, x, ldx, ferr, berr, work, info*)

call dptrfs (*n, nrhs, d, e, df, ef, b, ldb, x, ldx, ferr, berr, work, info*)

call cptrfs (*uplo, n, nrhs, d, e, df, ef, b, ldb, x, ldx, ferr, berr, work, rwork, info*)

call zptrfs (*uplo, n, nrhs, d, e, df, ef, b, ldb, x, ldx, ferr, berr, work, rwork, info*)

**?syrfs**
refines the solution of a system of linear
equations with a symmetric matrix and
estimates its error.

```
call ssyrfs (
```

*uplo, n, nrhs, a, lda, af, ldaf, ipiv, b, ldb, x, ldx, ferr, berr, work, iwork, info*)

call dsyrfs (*uplo, n, nrhs, a, lda, af, ldaf, ipiv, b, ldb, x, ldx, ferr, berr, work, iwork, info*)

call csyrfs (*uplo, n, nrhs, a, lda, af, ldaf, ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info*)

call zsyrfs (*uplo, n, nrhs, a, lda, af, ldaf, ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info*)

**?herfs**
refines the solution of a system of linear equations with a complex Hermitian matrix and estimates its error.

```
call cherfs (
```

*uplo, n, nrhs, a, lda, af, ldaf, ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info*)

call zherfs (*uplo, n, nrhs, a, lda, af, ldaf, ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info*)

**?sprfs**
refines the solution of a system of linear
equations with a packed symmetric
matrix and estimates the solution error.

```
call ssprfs (
```

*uplo, n, nrhs, ap, afp, ipiv, b, ldb, x, ldx, ferr, berr, work, iwork, info*)

call dsprfs (*uplo, n, nrhs, ap, afp, ipiv, b, ldb, x, ldx, ferr, berr, work, iwork, info*)

call csprfs (*uplo, n, nrhs, ap, afp, ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info*)

call zsprfs (*uplo, n, nrhs, ap, afp, ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info*)

**?hprfs**
refines the solution of a system of linear
equations with a packed complex Hermitian
matrix and estimates the solution error.

```
call chprfs (
```

*uplo, n, nrhs, ap, afp, ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info*)

call zhprfs (*uplo, n, nrhs, ap, afp, ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info*)

**?trrfs**
estimates the error in the solution of
a system of linear equations with a
triangular matrix.

```
call strrfs (
```

*uplo, trans, diag, n, nrhs, a, lda, b, ldb, x, ldx, ferr, berr, work, iwork, info*)

call dtrrfs (*uplo, trans, diag, n, nrhs, a, lda, b, ldb, x, ldx, ferr, berr, work, iwork, info*)

call ctrrfs (*uplo, trans, diag, n, nrhs, a, lda, b, ldb, x, ldx, ferr, berr, work, rwork, info*)

call ztrrfs (*uplo, trans, diag, n, nrhs, a, lda, b, ldb, x, ldx, ferr, berr, work, rwork, info*)

**?tprfs**
estimates the error in the solution of
a system of linear equations with a
packed triangular matrix.

```
call stprfs (
```

*uplo, trans, diag, n, nrhs, ap, b, ldb, x, ldx, ferr, berr, work, iwork, info*)

call dtprfs (*uplo, trans, diag, n, nrhs, ap, b, ldb, x, ldx, ferr, berr, work, iwork, info*)

call ctprfs (*uplo, trans, diag, n, nrhs, ap, b, ldb, x, ldx, ferr, berr, work, rwork, info*)

call ztprfs (*uplo, trans, diag, n, nrhs, ap, b, ldb, x, ldx, ferr, berr, work, rwork, info*)

**?tbrfs**
estimates the error in the solution of
a system of linear equations with a
triangular band matrix.

```
call stbrfs (
```

*uplo, trans, diag, n, kd, nrhs, ab, ldab, b, ldb, x, ldx, ferr, berr, work, iwork, info*)

call dtbrfs (*uplo, trans, diag, n, kd, nrhs, ab, ldab, b, ldb, x, ldx, ferr, berr, work, iwork, info*)

call ctbrfs (*uplo, trans, diag, n, kd, nrhs, ab, ldab, b, ldb, x, ldx, ferr, berr, work, rwork, info*)

call ztbrfs (*uplo, trans, diag, n, kd, nrhs, ab, ldab, b, ldb, x, ldx, ferr, berr, work, rwork, info*)

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