NAG Library Manual, Mark 28.7
```    Program f04bgfe

!     F04BGF Example Program Text

!     Mark 28.7 Release. NAG Copyright 2022.

!     .. Use Statements ..
Use nag_library, Only: f04bgf, nag_wp, x04caf
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Integer, Parameter               :: nin = 5, nout = 6
!     .. Local Scalars ..
Real (Kind=nag_wp)               :: errbnd, rcond
Integer                          :: i, ierr, ifail, ldb, n, nrhs
!     .. Local Arrays ..
Real (Kind=nag_wp), Allocatable  :: b(:,:), d(:), e(:)
!     .. Executable Statements ..
Write (nout,*) 'F04BGF Example Program Results'
Write (nout,*)
Flush (nout)
!     Skip heading in data file
ldb = n
Allocate (b(ldb,nrhs),d(n),e(n-1))
!     Read A from data file

!     Read B from data file

!     Solve the equations AX = B for X

!     ifail: behaviour on error exit
!            =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
ifail = 1
Call f04bgf(n,nrhs,d,e,b,ldb,rcond,errbnd,ifail)

If (ifail==0) Then
!       Print solution, estimate of condition number and approximate
!       error bound

ierr = 0
Call x04caf('General',' ',n,nrhs,b,ldb,'Solution',ierr)

Write (nout,*)
Write (nout,*) 'Estimate of condition number'
Write (nout,99999) 1.0E0_nag_wp/rcond
Write (nout,*)
Write (nout,*) 'Estimate of error bound for computed solutions'
Write (nout,99999) errbnd
Else If (ifail==n+1) Then
!       Matrix A is numerically singular.  Print estimate of
!       reciprocal of condition number and solution
Write (nout,*)
Write (nout,*) 'Estimate of reciprocal of condition number'
Write (nout,99999) rcond
Write (nout,*)
Flush (nout)

ierr = 0
Call x04caf('General',' ',n,nrhs,b,ldb,'Solution',ierr)

Else If (ifail>0 .And. ifail<=n) Then
Write (nout,99998) 'The leading minor of order ', ifail,               &
' is not positive definite'
Else
Write (nout,99997) ifail
End If

99999 Format (6X,1P,E9.1)
99998 Format (1X,A,I3,A)
99997 Format (1X,' ** F04BGF returned with IFAIL = ',I5)
End Program f04bgfe
```