NAG Library Manual, Mark 29
```    Program f07ar_t1w_fe

!     F07AR_T1W_F Example Program Text
!     Mark 29.0 Release. NAG Copyright 2023.

!     .. Use Statements ..
Use iso_c_binding, Only: c_ptr
Use nagad_library, Only: f07ar_t1w_f, f07aw_t1w_f,                       &
x10aa_t1w_f, x10ab_t1w_f, Assignment (=)
Use nag_library, Only: nag_wp, x04daf
!     .. 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_ctype), Allocatable :: a(:,:), a_in(:,:), work(:)
Complex (Kind=nag_wp), Allocatable :: ar(:,:), da(:,:), db(:,:)
Integer, Allocatable             :: ipiv(:)
!     .. Intrinsic Procedures ..
Intrinsic                        :: cmplx
!     .. Executable Statements ..
Write (nout,*) 'F07AR_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),db(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

Do j = 1, n
da(i,j) = a(j,j)%vreal%tangent
db(i,j) = a(j,j)%vimag%tangent
End Do

a_in(i,i)%vreal%tangent = 0.0_nag_wp

a = a_in

!       Factorize A
ifail = 0

!       Compute inverse

Do j = 1, n
da(i,j) = da(i,j) + cmplx(0.0_nag_wp,a(j,j)%vreal%tangent,kind=      &
nag_wp)
db(i,j) = db(i,j) + cmplx(0.0_nag_wp,a(j,j)%vimag%tangent,kind=      &
nag_wp)
End Do
a_in(i,i)%vimag%tangent = 0.0_nag_wp
End Do

!     Print solution
ar(1:n,1:n) = a(1:n,1:n)

!     ifail: behaviour on error exit
!            =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
Write (nout,*)
ifail = 0
Call x04daf('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 inverse diagonal w.r.t. diagonal of A'
Write (nout,*)
Call x04daf('General',' ',n,n,da,n,' d(real(inva(i,i)))/da(j,j)',ifail)
Write (nout,*)
Call x04daf('General',' ',n,n,db,n,' d(imag(inva(i,i)))/da(j,j)',ifail)

!     Remove computational data object