NAG Library Manual, Mark 27.2
```    Program f07aj_t1w_fe

!     F07AJ_T1W_F Example Program Text
!     Mark 27.2 Release. NAG Copyright 2021.

!     .. Use Statements ..
Use iso_c_binding, Only: c_ptr
x10aa_t1w_f, x10ab_t1w_f, Assignment (=)
Use nag_library, Only: nag_wp, x04caf
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Integer, Parameter               :: nin = 5, nout = 6
!     .. Local Scalars ..
Integer                          :: i, ifail, j, lwork, n
!     .. Local Arrays ..
Type (nagad_t1w_w_rtype), Allocatable :: a(:,:), a_in(:,:), work(:)
Real (Kind=nag_wp), Allocatable  :: ar(:,:), da(:,:)
Integer, Allocatable             :: ipiv(:)
!     .. Executable Statements ..
Write (nout,*) 'F07AJ_T1W_F Example Program Results'
!     Skip heading in data file

lwork = 64*n
Allocate (a(n,n),a_in(n,n),ipiv(n))
Allocate (ar(n,n),da(n,n),work(lwork))

!     Read A from data file
a_in = ar

!     Create AD configuration data object
ifail = 0

Do i = 1, n
a = a_in

!       Factorize A
ifail = 0

!       Compute inverse

If (i==1) Then
!         Print solution
ar(1:n,1:n) = a(1:n,1:n)%value

Write (nout,*)
Flush (nout)

!         ifail: behaviour on error exit
!             =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
ifail = 0
Call x04caf('General',' ',n,n,ar,n,'Inverse',ifail)
End If
Do j = 1, n
da(j,i) = a(j,j)%tangent
End Do
a_in(i,i)%tangent = 0.0_nag_wp
End Do

Write (nout,*)
Write (nout,*) ' Derivatives calculated: First order tangents'
Write (nout,*) ' Computational mode    : algorithmic'

Write (nout,*)
Write (nout,*) ' Derivatives of inverse diagonal w.r.t. diagonal of A'
Write (nout,*)

Call x04caf('General',' ',n,n,da,n,'       d(inv(i,i))/da(j,j)',ifail)

!     Remove computational data object