NAG Library Manual, Mark 28.4
```    Program c05qd_t1w_fe
!     C05QD_T1W_F Example Main Program

!     Mark 28.4 Release. NAG Copyright 2022.

!     .. Use Statements ..
Use iso_c_binding, Only: c_ptr
x10ab_t1w_f, Assignment (=), Operator (-),      &
Operator (*), Operator (+)
Use nag_library, Only: nag_wp, x02ajf, x04caf
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Integer, Parameter               :: mode = 2, n = 7, nout = 6
!     .. Local Scalars ..
Type (nagad_t1w_w_rtype)         :: epsfcn, factor, xtol
Integer                          :: i, ifail, irevcm, ml, mu
!     .. Local Arrays ..
Type (nagad_t1w_w_rtype), Allocatable :: diag(:), fjac(:,:), fvec(:),    &
qtf(:), r(:), rwsav(:), x(:)
Real (Kind=nag_wp), Allocatable  :: dr(:,:)
Integer, Allocatable             :: iwsav(:)
!     .. Intrinsic Procedures ..
Intrinsic                        :: sqrt
!     .. Executable Statements ..

Write (nout,*) 'C05QD_T1W_F Example Program Results'

Allocate (diag(n),fjac(n,n),fvec(n),qtf(n),r(n*(n+                       &
1)/2),x(n),rwsav(4*n+10),iwsav(17),dr(n,5))

!     Create AD configuration data object
ifail = 0

ruser(1) = -1.0_nag_wp
ruser(2) = 3.0_nag_wp
ruser(3) = -2.0_nag_wp
ruser(4) = -2.0_nag_wp
ruser(5) = -1.0_nag_wp

xtol = sqrt(x02ajf())
factor = 100._nag_wp
ml = 1
mu = 1
epsfcn = 0.0E0_nag_wp

Do i = 1, 5

!       The following starting values provide a rough solution.
x(1:n) = -1.0_nag_wp

diag(1:n) = 1.0_nag_wp

ruser(i)%tangent = 0.5_nag_wp

irevcm = 0

revcomm: Do

ifail = 0
diag,factor,fjac,r,qtf,iwsav,rwsav,ifail)

Select Case (irevcm)
Case (1)
!           Monitoring exit.
Cycle revcomm
Case (2)
fvec(:) = (ruser(2)+ruser(3)*x)*x - ruser(5)
fvec(2:n) = fvec(2:n) + ruser(1)*x(1:n-1)
fvec(1:n-1) = fvec(1:n-1) + ruser(4)*x(2:n)
Case Default
Exit revcomm
End Select

End Do revcomm

dr(:,i) = 2._nag_wp*x%tangent

ruser(i)%tangent = 0._nag_wp
End Do

Write (nout,*) 'Final approximate solution'
Write (nout,99999)(x(i)%value,i=1,n)
99999 Format (1X,3F12.4)

Write (nout,*)
Write (nout,*) ' Derivatives calculated: First order tangents'
Write (nout,*) ' Computational mode    : algorithmic'
Write (nout,*)
Write (nout,*) ' Derivatives are of solution w.r.t function params'
Write (nout,*)

Call x04caf('General',' ',n,5,dr,n,'       dx/druser',ifail)

!     Remove computational data object