NAG Library Manual, Mark 28.5
```    Program f07bvfe

!     F07BVF Example Program Text

!     Mark 28.5 Release. NAG Copyright 2022.

!     .. Use Statements ..
Use nag_library, Only: nag_wp, x04dbf, zgbrfs, zgbtrf, zgbtrs
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Complex (Kind=nag_wp), Parameter :: zero = (0.0_nag_wp,0.0_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 ..
Complex (Kind=nag_wp), Allocatable :: ab(:,:), afb(:,:), b(:,:),         &
work(:), x(:,:)
Real (Kind=nag_wp), Allocatable  :: berr(:), ferr(:), rwork(:)
Integer, Allocatable             :: ipiv(:)
Character (1)                    :: clabs(1), rlabs(1)
!     .. Intrinsic Procedures ..
Intrinsic                        :: max, min
!     .. Executable Statements ..
Write (nout,*) 'F07BVF Example Program Results'
!     Skip heading in data file
Read (nin,*) n, nrhs, kl, ku
ldb = n
ldx = n
ldab = kl + ku + 1
ldafb = 2*kl + ku + 1
Allocate (ab(ldab,n),afb(ldafb,n),b(ldb,nrhs),work(2*n),x(ldx,n),        &
berr(nrhs),ferr(nrhs),rwork(n),ipiv(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 zgbtrf is f07brf
Call zgbtrf(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 zgbtrs is f07bsf
Call zgbtrs(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 zgbrfs is f07bvf
Call zgbrfs(trans,n,kl,ku,nrhs,ab,ldab,afb,ldafb,ipiv,b,ldb,x,ldx,     &
ferr,berr,work,rwork,info)

!       Print solution

!       ifail: behaviour on error exit
!              =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
ifail = 0
Call x04dbf('General',' ',n,nrhs,x,ldx,'Bracketed','F7.4',             &
'Solution(s)','Integer',rlabs,'Integer',clabs,80,0,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 ((5X,1P,4(E11.1,7X)))
End Program f07bvfe
```