NAG Library Manual, Mark 28.5
```    Program f07fe_t1w_fe

!     F07FE_T1W_F Example Program Text
!     Mark 28.5 Release. NAG Copyright 2022.

!     .. Use Statements ..
Use iso_c_binding, Only: c_ptr
Use nagad_library, Only: f07fd_t1w_f, f07fe_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, lda, ldb, n, nrhs
Character (1)                    :: uplo
!     .. Local Arrays ..
Type (nagad_t1w_w_rtype), Allocatable :: a(:,:), ax(:,:), b(:,:), x(:,:)
Real (Kind=nag_wp), Allocatable  :: ar(:,:), dxdb(:,:), xr(:,:)
!     .. Executable Statements ..
Write (nout,*) 'F07FE_T1W_F Example Program Results'
!     Skip heading in data file
lda = n
ldb = n
Allocate (a(lda,n),b(ldb,nrhs),ax(lda,n),x(ldb,nrhs))
Allocate (ar(lda,n),xr(ldb,nrhs),dxdb(n,n))

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

!     Create AD configuration data object
ifail = 0

Do i = 1, n
ax = a
x = b

!       Factorize A
ifail = 0

!       Compute solution
b(i,1)%tangent = 0.0_nag_wp
dxdb(1:n,i) = x(1:n,1)%tangent
End Do

!     Print solution
xr(1:n,1:nrhs) = x(1:n,1:nrhs)%value

ifail = 0
Call x04caf('General',' ',n,nrhs,xr,ldb,'Solution(s)',ifail)

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

Write (nout,*)
Write (nout,*) ' Derivatives of solution x(:,1) w.r.t. b(:,1)'
Write (nout,*) ' (i.e. The inverse of A) :'

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

!     Remove computational data object