# 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

## 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

```          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*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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## Info

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK