NAG Library Manual, Mark 29.3
```    Program f07bhfe

!     F07BHF Example Program Text

!     Mark 29.3 Release. NAG Copyright 2023.

!     .. Use Statements ..
Use nag_library, Only: dgbrfs, dgbtrf, dgbtrs, nag_wp, x04caf
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Real (Kind=nag_wp), Parameter    :: zero = 0.0E0_nag_wp
Integer, Parameter               :: nin = 5, nout = 6
Character (1), Parameter         :: trans = 'N'
!     .. Local Scalars ..
Integer                          :: i, ifail, info, j, k, kl, ku, ldab,  &
ldafb, ldb, ldx, n, nrhs
!     .. Local Arrays ..
Real (Kind=nag_wp), Allocatable  :: ab(:,:), afb(:,:), b(:,:), berr(:),  &
ferr(:), work(:), x(:,:)
Integer, Allocatable             :: ipiv(:), iwork(:)
!     .. Intrinsic Procedures ..
Intrinsic                        :: max, min
!     .. Executable Statements ..
Write (nout,*) 'F07BHF Example Program Results'
!     Skip heading in data file
Read (nin,*) n, nrhs, kl, ku
ldab = kl + ku + 1
ldafb = 2*kl + ku + 1
ldb = n
ldx = n
Allocate (ab(ldab,n),afb(ldafb,n),b(ldb,nrhs),berr(nrhs),ferr(nrhs),     &
work(3*n),x(ldx,n),ipiv(n),iwork(n))

!     Set A to zero to avoid referencing uninitialized elements

ab(1:kl+ku+1,1:n) = zero

!     Read A and B from data file, and copy A to AFB and B to X

k = ku + 1

afb(kl+1:2*kl+ku+1,1:n) = ab(1:kl+ku+1,1:n)
x(1:n,1:nrhs) = b(1:n,1:nrhs)

!     Factorize A in the array AFB
!     The NAG name equivalent of dgbtrf is f07bdf
Call dgbtrf(n,n,kl,ku,afb,ldafb,ipiv,info)

Write (nout,*)
Flush (nout)
If (info==0) Then

!       Compute solution in the array X
!       The NAG name equivalent of dgbtrs is f07bef
Call dgbtrs(trans,n,kl,ku,nrhs,afb,ldafb,ipiv,x,ldx,info)

!       Improve solution, and compute backward errors and
!       estimated bounds on the forward errors

!       The NAG name equivalent of dgbrfs is f07bhf
Call dgbrfs(trans,n,kl,ku,nrhs,ab,ldab,afb,ldafb,ipiv,b,ldb,x,ldx,     &
ferr,berr,work,iwork,info)

!       Print solution

!       ifail: behaviour on error exit
!              =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
ifail = 0
Call x04caf('General',' ',n,nrhs,x,ldx,'Solution(s)',ifail)

Write (nout,*)
Write (nout,*) 'Backward errors (machine-dependent)'
Write (nout,99999) berr(1:nrhs)
Write (nout,*) 'Estimated forward error bounds (machine-dependent)'
Write (nout,99999) ferr(1:nrhs)
Else
Write (nout,*) 'The factor U is singular'
End If

99999 Format ((3X,1P,7E11.1))
End Program f07bhfe
```