# sgbrfs.f man page

sgbrfs.f

## Synopsis

### Functions/Subroutines

subroutine sgbrfs (TRANS, N, KL, KU, NRHS, AB, LDAB, AFB, LDAFB, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO)
SGBRFS

## Function/Subroutine Documentation

### subroutine sgbrfs (character TRANS, integer N, integer KL, integer KU, integer NRHS, real, dimension( ldab, * ) AB, integer LDAB, real, dimension( ldafb, * ) AFB, integer LDAFB, 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)

SGBRFS

Purpose:

``` SGBRFS improves the computed solution to a system of linear
equations when the coefficient matrix is banded, 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.```

KL

```          KL is INTEGER
The number of subdiagonals within the band of A.  KL >= 0.```

KU

```          KU is INTEGER
The number of superdiagonals within the band of A.  KU >= 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.```

AB

```          AB is REAL array, dimension (LDAB,N)
The original band matrix A, stored in rows 1 to KL+KU+1.
The j-th column of A is stored in the j-th column of the
array AB as follows:
AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).```

LDAB

```          LDAB is INTEGER
The leading dimension of the array AB.  LDAB >= KL+KU+1.```

AFB

```          AFB is REAL array, dimension (LDAFB,N)
Details of the LU factorization of the band matrix A, as
computed by SGBTRF.  U is stored as an upper triangular band
matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
the multipliers used during the factorization are stored in
rows KL+KU+2 to 2*KL+KU+1.```

LDAFB

```          LDAFB is INTEGER
The leading dimension of the array AFB.  LDAFB >= 2*KL*KU+1.```

IPIV

```          IPIV is INTEGER array, dimension (N)
The pivot indices from SGBTRF; 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 SGBTRS.
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

NAG Ltd.

Date:

December 2016

Definition at line 207 of file sgbrfs.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page sgbrfs(3) is an alias of sgbrfs.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK