NAG Library Manual, Mark 27.2
```    Program f07fj_t1w_fe

!     F07FJ_T1W_F Example Program Text
!     Mark 27.2 Release. NAG Copyright 2021.

!     .. Use Statements ..
Use iso_c_binding, Only: c_ptr
Use nagad_library, Only: f07fd_t1w_f, f07fj_t1w_f,                       &
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, lda, n
Character (1)                    :: uplo
!     .. Local Arrays ..
Type (nagad_t1w_w_rtype), Allocatable :: a(:,:), ax(:,:)
Real (Kind=nag_wp), Allocatable  :: ar(:,:), d(:,:)
!     .. Executable Statements ..
Write (nout,*) 'F07FJ_T1W_F Example Program Results'
!     Skip heading in data file
lda = n
Allocate (a(lda,n),ax(lda,n),ar(lda,n),d(n,n))

!     Read A from data file
ar = 0.0_nag_wp
If (uplo=='U') Then
Else If (uplo=='L') Then
End If
a = ar

!     Create AD configuration data object
ifail = 0

Do i = 1, n
ax = a

!       Factorize A
ifail = 0

!       Compute inverse of A
ifail = 0

a(i,i)%tangent = 0.0_nag_wp
Do j = 1, n
d(j,i) = ax(j,j)%tangent
End Do
End Do

!     Print inverse
ar(1:n,1:n) = ax(1:n,1:n)%value
ifail = 0
Call x04caf('General',' ',n,n,ar,n,'Inverse',ifail)

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

Write (nout,*)
Write (nout,*) ' Derivatives of Ainv_ii w.r.t. A_jj'
!     Setup evaluation of derivatives via adjoints

Call x04caf('General',' ',n,n,d,n,'',ifail)

!     Remove computational data object