# gerfs - Man Page

gerfs: iterative refinement

## Synopsis

### Functions

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

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

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

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

## Detailed Description

## Function Documentation

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

**CGERFS**

**Purpose:**

CGERFS 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)

*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 COMPLEX 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 COMPLEX array, dimension (LDAF,N) The factors L and U from the factorization A = P*L*U as computed by CGETRF.

*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 CGETRF; for 1<=i<=N, row i of the matrix was interchanged with row IPIV(i).

*B*B is COMPLEX 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 COMPLEX array, dimension (LDX,NRHS) On entry, the solution matrix X, as computed by CGETRS. 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 COMPLEX array, dimension (2*N)

*RWORK*RWORK is REAL 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 **184** of file **cgerfs.f**.

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

**DGERFS**

**Purpose:**

DGERFS 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDAF,N) The factors L and U from the factorization A = P*L*U as computed by DGETRF.

*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 DGETRF; for 1<=i<=N, row i of the matrix was interchanged with row IPIV(i).

*B*B is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDX,NRHS) On entry, the solution matrix X, as computed by DGETRS. 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 **dgerfs.f**.

### 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**.

### subroutine zgerfs (character trans, integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( ldx, * ) x, integer ldx, double precision, dimension( * ) ferr, double precision, dimension( * ) berr, complex*16, dimension( * ) work, double precision, dimension( * ) rwork, integer info)

**ZGERFS**

**Purpose:**

ZGERFS 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)

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

*NRHS**A*A is COMPLEX*16 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 COMPLEX*16 array, dimension (LDAF,N) The factors L and U from the factorization A = P*L*U as computed by ZGETRF.

*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 ZGETRF; for 1<=i<=N, row i of the matrix was interchanged with row IPIV(i).

*B*B is COMPLEX*16 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 COMPLEX*16 array, dimension (LDX,NRHS) On entry, the solution matrix X, as computed by ZGETRS. 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 COMPLEX*16 array, dimension (2*N)

*RWORK*RWORK is DOUBLE PRECISION 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 **184** of file **zgerfs.f**.

## Author

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