### Refining the Solution and Estimating Its Error

?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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