NAG Library Manual, Mark 28.5
```    Program f07bpfe

!     F07BPF Example Program Text

!     Mark 28.5 Release. NAG Copyright 2022.

!     .. Use Statements ..
Use nag_library, Only: nag_wp, x04dbf, zgbsvx
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Integer, Parameter               :: nin = 5, nout = 6
!     .. Local Scalars ..
Real (Kind=nag_wp)               :: rcond
Integer                          :: i, ifail, info, j, k, kl, ku, ldab,  &
ldafb, ldb, ldx, n, nrhs
Character (1)                    :: equed
!     .. Local Arrays ..
Complex (Kind=nag_wp), Allocatable :: ab(:,:), afb(:,:), b(:,:),         &
work(:), x(:,:)
Real (Kind=nag_wp), Allocatable  :: berr(:), c(:), ferr(:), r(:),        &
rwork(:)
Integer, Allocatable             :: ipiv(:)
Character (1)                    :: clabs(1), rlabs(1)
!     .. Intrinsic Procedures ..
Intrinsic                        :: max, min
!     .. Executable Statements ..
Write (nout,*) 'F07BPF Example Program Results'
Write (nout,*)
Flush (nout)
!     Skip heading in data file
Read (nin,*) n, nrhs, kl, ku
ldb = n
ldx = n
ldab = kl + ku + 1
ldafb = ldab + kl
Allocate (ab(ldab,n),afb(ldafb,n),b(ldb,nrhs),work(2*n),x(ldx,nrhs),     &
berr(nrhs),c(n),ferr(nrhs),r(n),rwork(n),ipiv(n))

!     Read the band matrix A and B from data file

k = ku + 1

!     Solve the equations AX = B for X

!     The NAG name equivalent of zgbsvx is f07bpf
Call zgbsvx('Equilibration','No transpose',n,kl,ku,nrhs,ab,ldab,afb,     &
ldafb,ipiv,equed,r,c,b,ldb,x,ldx,rcond,ferr,berr,work,rwork,info)

If ((info==0) .Or. (info==n+1)) Then

!       Print solution, error bounds, condition number, the form
!       of equilibration and the pivot growth factor

!       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,*)
Write (nout,*) 'Estimated forward error bounds (machine-dependent)'
Write (nout,99999) ferr(1:nrhs)
Write (nout,*)
Write (nout,*) 'Estimate of reciprocal condition number'
Write (nout,99999) rcond
Write (nout,*)
If (equed=='N') Then
Write (nout,*) 'A has not been equilibrated'
Else If (equed=='R') Then
Write (nout,*) 'A has been row scaled as diag(R)*A'
Else If (equed=='C') Then
Write (nout,*) 'A has been column scaled as A*diag(C)'
Else If (equed=='B') Then
Write (nout,*)                                                       &
'A has been row and column scaled as diag(R)*A*diag(C)'
End If
Write (nout,*)
Write (nout,*) 'Estimate of reciprocal pivot growth factor'
Write (nout,99999) rwork(1)

If (info==n+1) Then
Write (nout,*)
Write (nout,*) 'The matrix A is singular to working precision'
End If
Else
Write (nout,99998) 'The (', info, ',', info, ')',                      &
' element of the factor U is zero'
End If

99999 Format ((3X,1P,7E11.1))
99998 Format (1X,A,I3,A,I3,A,A)
End Program f07bpfe
```