NAG Library Manual, Mark 27.2
```!   E04UC_A1W_F Example Program Text
!   Mark 27.2 Release. NAG Copyright 2021.

Module e04uc_a1w_fe_mod

!     E04UC_A1W_F Example Program Module:
!            Parameters and User-defined Routines

!     .. Use Statements ..
Use nag_library, Only: nag_wp
!     .. Implicit None Statement ..
Implicit None
!     .. Accessibility Statements ..
Private
Public                           :: confun, objfun
!     .. Parameters ..
Real (Kind=nag_wp), Parameter, Public :: one = 1.0_nag_wp
Real (Kind=nag_wp), Parameter, Public :: zero = 0.0_nag_wp
Integer, Parameter, Public       :: inc1 = 1, lcwsav = 1, liwsav = 610,  &
llwsav = 120, lrwsav = 475, nin = 5, &
nout = 6
Contains
!       Routine to evaluate objective function and its 1st derivatives.

!       .. Use Statements ..
Use iso_c_binding, Only: c_ptr
Assignment (=), Operator (+)
!       .. Scalar Arguments ..
Type (c_ptr), Intent (Inout)   :: ad_handle
Type (nagad_a1w_w_rtype), Intent (Out) :: objf
Integer, Intent (Inout)        :: mode
Integer, Intent (In)           :: n, nstate
!       .. Array Arguments ..
Type (nagad_a1w_w_rtype), Intent (Inout) :: objgrd(n), ruser(*)
Type (nagad_a1w_w_rtype), Intent (In) :: x(n)
Integer, Intent (Inout)        :: iuser(*)
!       .. Executable Statements ..
If (mode==0 .Or. mode==2) Then
objf = x(1)*x(4)*(ruser(1)*x(1)+ruser(2)*x(2)+ruser(3)*x(3)) + x(3)
End If

If (mode==1 .Or. mode==2) Then
objgrd(1) = x(4)*(ruser(1)*x(1)+ruser(1)*x(1)+ruser(2)*x(2)+ruser(3) &
*x(3))
objgrd(2) = x(1)*x(4)*ruser(2)
objgrd(3) = x(1)*x(4)*ruser(3) + one
objgrd(4) = x(1)*(x(1)*ruser(1)+x(2)*ruser(2)+x(3)*ruser(3))
End If

Return

End Subroutine objfun
iuser,ruser)
!       Routine to evaluate the nonlinear constraints and their 1st
!       derivatives.

!       .. Use Statements ..
Use iso_c_binding, Only: c_ptr
Operator (**), Operator (+), Operator (*)
!       .. Scalar Arguments ..
Type (c_ptr), Intent (Inout)   :: ad_handle
Integer, Intent (In)           :: ldcj, n, ncnln, nstate
Integer, Intent (Inout)        :: mode
!       .. Array Arguments ..
Type (nagad_a1w_w_rtype), Intent (Out) :: c(ncnln)
Type (nagad_a1w_w_rtype), Intent (Inout) :: cjac(ldcj,n), ruser(*)
Type (nagad_a1w_w_rtype), Intent (In) :: x(n)
Integer, Intent (Inout)        :: iuser(*)
Integer, Intent (In)           :: needc(ncnln)
!       .. Executable Statements ..
If (nstate==1) Then

!         First call to CONFUN.  Set all Jacobian elements to zero.
!         Note that this will only work when 'Derivative Level = 3'
!         (the default; see Section 11.2).

cjac(1:ncnln,1:n) = zero
End If

If (needc(1)>0) Then

If (mode==0 .Or. mode==2) Then
c(1) = x(1)**2 + x(2)**2 + x(3)**2 + x(4)**2
End If

If (mode==1 .Or. mode==2) Then
cjac(1,1) = x(1) + x(1)
cjac(1,2) = x(2) + x(2)
cjac(1,3) = x(3) + x(3)
cjac(1,4) = x(4) + x(4)
End If

End If

If (needc(2)>0) Then

If (mode==0 .Or. mode==2) Then
c(2) = x(1)*x(2)*x(3)*x(4)
End If

If (mode==1 .Or. mode==2) Then
cjac(2,1) = x(2)*x(3)*x(4)
cjac(2,2) = x(1)*x(3)*x(4)
cjac(2,3) = x(1)*x(2)*x(4)
cjac(2,4) = x(1)*x(2)*x(3)
End If

End If

Return

End Subroutine confun
End Module e04uc_a1w_fe_mod
Program e04uc_a1w_fe
!     E04UC_A1W_F Example Main Program

!     .. Use Statements ..
Use e04uc_a1w_fe_mod, Only: confun, lcwsav, liwsav, llwsav, lrwsav, nin, &
nout, objfun
Use iso_c_binding, Only: c_ptr
Use nagad_library, Only: e04uc_a1w_f, e04ue_a1w_f, e04wb_a1w_f,          &
x10aa_a1w_f, x10ab_a1w_f, x10za_a1w_f,          &
Assignment (=)
Use nag_library, Only: nag_wp, x04caf
!     .. Implicit None Statement ..
Implicit None
!     .. Local Scalars ..
Integer                          :: i, ifail, iter, lda, ldcj, ldr,      &
liwork, lwork, n, nclin, ncnln, sda, &
sdcjac
!     .. Local Arrays ..
Type (nagad_a1w_w_rtype), Allocatable :: a(:,:), bl(:), bu(:), c(:),     &
cjac(:,:), clamda(:), objgrd(:),     &
r(:,:), work(:), x(:)
Real (Kind=nag_wp), Allocatable  :: a_r(:,:), bl_r(:), bu_r(:), x_r(:)
Integer, Allocatable             :: istate(:), iwork(:)
Integer                          :: iuser(1), iwsav(liwsav)
Logical                          :: lwsav(llwsav)
Character (80)                   :: cwsav(lcwsav)
!     .. Intrinsic Procedures ..
Intrinsic                        :: max, size
!     .. Executable Statements ..
Write (nout,*) 'E04UC_A1W_F Example Program Results'

ruser(1) = 1.0_nag_wp
ruser(2) = 1.0_nag_wp
ruser(3) = 1.0_nag_wp
!     Skip heading in data file

liwork = 3*n + nclin + 2*ncnln
lda = max(1,nclin)

If (nclin>0) Then
sda = n
Else
sda = 1
End If

ldcj = max(1,ncnln)

If (ncnln>0) Then
sdcjac = n
Else
sdcjac = 1
End If

ldr = n

If (ncnln==0 .And. nclin>0) Then
lwork = 2*n**2 + 20*n + 11*nclin
Else If (ncnln>0 .And. nclin>=0) Then
lwork = 2*n**2 + n*nclin + 2*n*ncnln + 20*n + 11*nclin + 21*ncnln
Else
lwork = 20*n
End If

Allocate (istate(n+nclin+ncnln),iwork(liwork),a_r(lda,sda),              &
bl_r(n+nclin+ncnln),bu_r(n+nclin+ncnln),c(max(1,                       &
ncnln)),cjac(ldcj,sdcjac),clamda(n+nclin+ncnln),objgrd(n),r(ldr,n),    &
x_r(n),work(lwork))

If (nclin>0) Then
End If

Call x10za_a1w_f

!     Create AD configuration data object
ifail = 0

!     Initialise E04UC
ifail = 0
Call e04wb_a1w_f('E04UCA',cwsav,lcwsav,lwsav,llwsav,iwsav,liwsav,rwsav,  &
lrwsav,ifail)

!     Set option via string
Call e04ue_a1w_f('Print Level = 1',lwsav,iwsav,rwsav)

Allocate (a(size(a_r,1),size(a_r,2)),bl(size(bl_r)),bu(size(bu_r)),x(    &
size(x_r)))
a(:,:) = a_r(:,:)
bl(:) = bl_r(:)
bu(:) = bu_r(:)
x(:) = x_r(:)

!     Register variables to differentiate w.r.t.

!     Solve the problem
ifail = -1
objfun,iter,istate,c,cjac,clamda,objf,objgrd,r,x,iwork,liwork,work,    &
lwork,iuser,ruser,lwsav,iwsav,rwsav,ifail)

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