NAG Library Manual, Mark 28.5
```    Program f07hbfe

!     F07HBF Example Program Text

!     Mark 28.5 Release. NAG Copyright 2022.

!     .. Use Statements ..
Use nag_library, Only: dpbsvx, nag_wp, x04caf
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Integer, Parameter               :: nin = 5, nout = 6
Character (1), Parameter         :: uplo = 'U'
!     .. Local Scalars ..
Real (Kind=nag_wp)               :: rcond
Integer                          :: i, ifail, info, j, kd, ldab, ldafb,  &
ldb, ldx, n, nrhs
Character (1)                    :: equed
!     .. Local Arrays ..
Real (Kind=nag_wp), Allocatable  :: ab(:,:), afb(:,:), b(:,:), berr(:),  &
ferr(:), s(:), work(:), x(:,:)
Integer, Allocatable             :: iwork(:)
!     .. Intrinsic Procedures ..
Intrinsic                        :: max, min
!     .. Executable Statements ..
Write (nout,*) 'F07HBF Example Program Results'
Write (nout,*)
Flush (nout)
!     Skip heading in data file
ldb = n
ldx = n
ldab = kd + 1
ldafb = kd + 1
Allocate (ab(ldab,n),afb(ldafb,n),b(ldb,nrhs),berr(nrhs),ferr(nrhs),     &
s(n),work(3*n),x(ldx,nrhs),iwork(n))

!     Read the upper or lower triangular part of the band matrix A
!     from data file

If (uplo=='U') Then
Else If (uplo=='L') Then
End If

!     Read B from data file

!     Solve the equations AX = B for X
!     The NAG name equivalent of dpbsvx is f07hbf
Call dpbsvx('Equilibration',uplo,n,kd,nrhs,ab,ldab,afb,ldafb,equed,s,b,  &
ldb,x,ldx,rcond,ferr,berr,work,iwork,info)

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

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

!       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,*)
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=='Y') Then
Write (nout,*)                                                       &
'A has been row and column scaled as diag(S)*A*diag(S)'
End If

If (info==n+1) Then
Write (nout,*)
Write (nout,*) 'The matrix A is singular to working precision'
End If
Else
Write (nout,99998) 'The leading minor of order ', info,                &
' is not positive definite'
End If

99999 Format ((3X,1P,7E11.1))
99998 Format (1X,A,I3,A)
End Program f07hbfe
```