NAG Library Manual, Mark 28.5
```    Program f07ae_t1w_fe

!     F07AE_T1W_F Example Program Text
!     Mark 28.5 Release. NAG Copyright 2022.

!     .. 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, lwork, n, nrhs
!     .. Local Arrays ..
Type (nagad_t1w_w_rtype), Allocatable :: a(:,:), a_in(:,:), b(:,:),      &
b_in(:,:)
Real (Kind=nag_wp), Allocatable  :: ar(:,:), br(:,:), dxdb(:,:)
Integer, Allocatable             :: ipiv(:)
!     .. Executable Statements ..
Write (nout,*) 'F07AE_T1W_F Example Program Results'
!     Skip heading in data file

lwork = 64*n
Allocate (a(n,n),a_in(n,n),ipiv(n))
Allocate (b(n,nrhs),b_in(n,nrhs))
Allocate (ar(n,n),br(n,nrhs),dxdb(n,n))

!     Read A from data file
a_in = ar

!     Read B from data file
b_in = br

!     Create AD configuration data object
ifail = 0

a = a_in

!     Factorize A
ifail = 0

Write (nout,*)
Flush (nout)

Do i = 1, n

b = b_in

!       Solve system

dxdb(1:n,i) = b(1:n,1)%tangent
b_in(i,1)%tangent = 0.0_nag_wp
End Do

!     Print solution
br(1:n,1:nrhs) = b(1:n,1:nrhs)%value

!     ifail: behaviour on error exit
!            =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
ifail = 0
Call x04caf('General',' ',n,nrhs,br,n,'Solution',ifail)

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

Write (nout,*)
Write (nout,*) ' Derivatives of solution X w.r.t. RHS B (A inverse)'
Write (nout,*)
Call x04caf('General',' ',n,n,dxdb,n,'       dx(i,1)/db(j,1)',ifail)

!     Remove computational data object