```    Program f07ahfe

!     F07AHF Example Program Text

!     Mark 26.1 Release. NAG Copyright 2017.

!     .. Use Statements ..
Use nag_library, Only: dgerfs, dgetrf, dgetrs, nag_wp, x04caf
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Integer, Parameter               :: nin = 5, nout = 6
Character (1), Parameter         :: trans = 'N'
!     .. Local Scalars ..
Integer                          :: i, ifail, info, lda, ldaf, ldb, ldx, &
n, nrhs
!     .. Local Arrays ..
Real (Kind=nag_wp), Allocatable  :: a(:,:), af(:,:), b(:,:), berr(:),    &
ferr(:), work(:), x(:,:)
Integer, Allocatable             :: ipiv(:), iwork(:)
!     .. Executable Statements ..
Write (nout,*) 'F07AHF Example Program Results'
!     Skip heading in data file
lda = n
ldaf = n
ldb = n
ldx = n
Allocate (a(lda,n),af(ldaf,n),b(ldb,nrhs),berr(nrhs),ferr(nrhs),         &
work(3*n),x(ldx,n),ipiv(n),iwork(n))

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

af(1:n,1:n) = a(1:n,1:n)
x(1:n,1:nrhs) = b(1:n,1:nrhs)

!     Factorize A in the array AF

!     The NAG name equivalent of dgetrf is f07adf
Call dgetrf(n,n,af,ldaf,ipiv,info)

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

!       Compute solution in the array X

!       The NAG name equivalent of dgetrs is f07aef
Call dgetrs(trans,n,nrhs,af,ldaf,ipiv,x,ldx,info)

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

!       The NAG name equivalent of dgerfs is f07ahf
Call dgerfs(trans,n,nrhs,a,lda,af,ldaf,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 f07ahfe
```