NAG Library Manual, Mark 29
```!   E04US_T1W_F Example Program Text
!   Mark 29.0 Release. NAG Copyright 2023.
Module e04us_t1w_fe_mod

!     E04US_T1W_F Example Program Module:
!            Parameters and User-defined Routines

!     .. Use Statements ..
Use iso_c_binding, Only: c_ptr
Operator (*), Operator (+), Operator (-)
Use nag_library, Only: nag_wp
!     .. Implicit None Statement ..
Implicit None
!     .. Accessibility Statements ..
Private
Public                           :: confun, objfun
!     .. Parameters ..
Integer, Parameter, Public       :: nin = 5, nout = 6
Contains
ruser)
!       Routine to evaluate the subfunctions and their 1st derivatives.
!       .. Scalar Arguments ..
Type (c_ptr), Intent (Inout)   :: ad_handle
Integer, Intent (In)           :: ldfj, m, n, needfi, nstate
Integer, Intent (Inout)        :: mode
!       .. Array Arguments ..
Type (nagad_t1w_w_rtype), Intent (Out) :: f(m)
Type (nagad_t1w_w_rtype), Intent (Inout) :: fjac(ldfj,n), ruser(*)
Type (nagad_t1w_w_rtype), Intent (In) :: x(n)
Integer, Intent (Inout)        :: iuser(*)
!       .. Local Scalars ..
Type (nagad_t1w_w_rtype)       :: ai, temp, x1, x2
Integer                        :: i
Logical                        :: mode02, mode12
!       .. Executable Statements ..
x1 = x(1)
x2 = x(2)

If (mode==0 .And. needfi>0) Then
f(needfi) = x1 + (0.49_nag_wp-x1)*exp(-x2*(ruser(needfi)-8.0_nag_wp) &
)
Else

mode02 = (mode==0 .Or. mode==2)
mode12 = (mode==1 .Or. mode==2)

Do i = 1, m

ai = ruser(i) - 8.0_nag_wp
temp = exp(-x2*ai)

If (mode02) Then
f(i) = x1 + (0.49_nag_wp-x1)*temp
End If

If (mode12) Then
fjac(i,1) = 1.0_nag_wp - temp
fjac(i,2) = -(0.49_nag_wp-x1)*ai*temp
End If

End Do
End If

Return

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

!       .. Scalar Arguments ..
Type (c_ptr), Intent (Inout)   :: ad_handle
Integer, Intent (In)           :: ldcj, n, ncnln, nstate
Integer, Intent (Inout)        :: mode
!       .. Array Arguments ..
Type (nagad_t1w_w_rtype), Intent (Out) :: c(ncnln)
Type (nagad_t1w_w_rtype), Intent (Inout) :: cjac(ldcj,n), ruser(*)
Type (nagad_t1w_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) = 0.0_nag_wp
End If

If (needc(1)>0) Then

If (mode==0 .Or. mode==2) Then
c(1) = -0.09_nag_wp - x(1)*x(2) + 0.49_nag_wp*x(2)
End If

If (mode==1 .Or. mode==2) Then
cjac(1,1) = -x(2)

cjac(1,2) = -x(1) + 0.49_nag_wp
End If

End If

Return

End Subroutine confun
End Module e04us_t1w_fe_mod
Program e04us_t1w_fe

!     E04US_T1W_F Example Main Program

!     .. Use Statements ..
Use e04us_t1w_fe_mod, Only: confun, nin, nout, objfun
Use iso_c_binding, Only: c_ptr
Use nagad_library, Only: e04ur_t1w_f, e04us_t1w_f, e04wb_t1w_f,          &
x10aa_t1w_f, x10ab_t1w_f, Assignment (=)
Use nag_library, Only: nag_wp, x04caf
!     .. Implicit None Statement ..
Implicit None
!     .. Local Scalars ..
Integer                          :: i, ifail, inform, iter, lb, lda,     &
ldcj, ldfj, ldr, liwork, lwork, m,   &
n, nclin, ncnln, sda
!     .. Local Arrays ..
Type (nagad_t1w_w_rtype), Allocatable :: a(:,:), bl(:), bu(:), c(:),     &
cjac(:,:), clamda(:), f(:),          &
fjac(:,:), r(:,:), rwsav(:),         &
work(:), x(:), y(:)
Real (Kind=nag_wp), Allocatable  :: ar(:,:), blr(:), bur(:), dr(:),      &
rwsav_r(:), xr(:), yr(:)
Real (Kind=nag_wp)               :: rr(44)
Integer, Allocatable             :: istate(:), iwork(:), iwsav(:)
Integer                          :: iuser(1)
Logical, Allocatable             :: lwsav(:)
Character (80)                   :: cwsav(1)
!     .. Intrinsic Procedures ..
Intrinsic                        :: max
!     .. Executable Statements ..
Write (nout,*) 'E04US_T1W_F Example Program Results'

!     Skip heading in data file

!     Read the computational mode: 1 = algorithmic, 2 = symbolic
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)

ldfj = m
ldr = n

If (ncnln==0 .And. nclin>0) Then
lwork = 2*n**2 + 20*n + 11*nclin + m*(n+3)
Else If (ncnln>0 .And. nclin>=0) Then
lwork = 2*n**2 + n*nclin + 2*n*ncnln + 20*n + 11*nclin + 21*ncnln +    &
m*(n+3)
Else
lwork = 20*n + m*(n+3)
End If

lb = n + nclin + ncnln
Allocate (istate(lb),iwork(liwork),a(lda,sda),bl(lb),bu(lb),y(m),        &
c(ncnln),cjac(ncnln,n),f(m),fjac(m,n),clamda(lb),r(ldr,n),x(n),        &
work(lwork),lwsav(120),iwsav(610),rwsav(475),rwsav_r(475),dr(m),yr(m), &
blr(lb),bur(lb),xr(n),ar(lda,sda))

If (nclin>0) Then
End If
a(1:nclin,1:sda) = ar(1:nclin,1:sda)

y(1:m) = yr(1:m)
bl(1:lb) = blr(1:lb)
bu(1:lb) = bur(1:lb)

rr(1:44) = (/8.0E0_nag_wp,8.0E0_nag_wp,10.0E0_nag_wp,10.0E0_nag_wp,      &
10.0E0_nag_wp,10.0E0_nag_wp,12.0E0_nag_wp,12.0E0_nag_wp,12.0E0_nag_wp, &
12.0E0_nag_wp,14.0E0_nag_wp,14.0E0_nag_wp,14.0E0_nag_wp,16.0E0_nag_wp, &
16.0E0_nag_wp,16.0E0_nag_wp,18.0E0_nag_wp,18.0E0_nag_wp,20.0E0_nag_wp, &
20.0E0_nag_wp,20.0E0_nag_wp,22.0E0_nag_wp,22.0E0_nag_wp,22.0E0_nag_wp, &
24.0E0_nag_wp,24.0E0_nag_wp,24.0E0_nag_wp,26.0E0_nag_wp,26.0E0_nag_wp, &
26.0E0_nag_wp,28.0E0_nag_wp,28.0E0_nag_wp,30.0E0_nag_wp,30.0E0_nag_wp, &
30.0E0_nag_wp,32.0E0_nag_wp,32.0E0_nag_wp,34.0E0_nag_wp,36.0E0_nag_wp, &
36.0E0_nag_wp,38.0E0_nag_wp,38.0E0_nag_wp,40.0E0_nag_wp,               &
42.0E0_nag_wp/)

ruser(1:44) = rr(1:44)

!     Create AD configuration data object
ifail = 0

Do i = 1, 44

x(1:n) = xr(1:n)
!       Initialize sav arrays
ifail = 0
Call e04wb_t1w_f('E04USA',cwsav,1,lwsav,120,iwsav,610,rwsav,475,ifail)

If (i==44) Then
!         Set option via string
Call e04ur_t1w_f('Print Level = 1',lwsav,iwsav,rwsav,inform)
End If

!       Solve the problem
ifail = 0
y,confun,objfun,iter,istate,c,cjac,f,fjac,clamda,objf,r,x,iwork,     &
liwork,work,lwork,iuser,ruser,lwsav,iwsav,rwsav,ifail)

ruser(i)%tangent = 0.0_nag_wp
dr(i) = x(1)%tangent
End Do

Write (nout,99999) ' Optimal solution = ', objf%value
99999 Format (1X,A,F10.5)
Write (nout,*)

xr(1:n) = x(1:n)%value
Call x04caf('General',' ',1,n,xr,1,' Solution point, x',ifail)

!     Primal results are printed by default

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

Write (nout,*)
Write (nout,*) ' Derivatives:'

ifail = 0
Call x04caf('General',' ',1,44,dr,1,'     dx(1)/druser(1:44)',ifail)

!     Remove computational data object