```!   E04UDF Example Program Text
!   Mark 26.1 Release. NAG Copyright 2016.

Module e04udfe_mod

!     E04UDF 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 ..
Integer, Parameter, Public       :: iset = 1, nin = 5, ninopt = 7,       &
nout = 6
Contains
Subroutine objfun(mode,n,x,objf,objgrd,nstate,iuser,ruser)
!       Routine to evaluate objective function and its 1st derivatives.

!       .. Scalar Arguments ..
Real (Kind=nag_wp), Intent (Out) :: objf
Integer, Intent (Inout)        :: mode
Integer, Intent (In)           :: n, nstate
!       .. Array Arguments ..
Real (Kind=nag_wp), Intent (Inout) :: objgrd(n), ruser(*)
Real (Kind=nag_wp), Intent (In) :: x(n)
Integer, Intent (Inout)        :: iuser(*)
!       .. Executable Statements ..
If (mode==0 .Or. mode==2) Then
objf = x(1)*x(4)*(x(1)+x(2)+x(3)) + x(3)
End If

If (mode==1 .Or. mode==2) Then
objgrd(1) = x(4)*(2.0E0_nag_wp*x(1)+x(2)+x(3))
objgrd(2) = x(1)*x(4)
objgrd(3) = x(1)*x(4) + 1.0E0_nag_wp
objgrd(4) = x(1)*(x(1)+x(2)+x(3))
End If

Return

End Subroutine objfun
Subroutine confun(mode,ncnln,n,ldcj,needc,x,c,cjac,nstate,iuser,ruser)
!       Routine to evaluate the nonlinear constraints and their 1st
!       derivatives.

!       .. Scalar Arguments ..
Integer, Intent (In)           :: ldcj, n, ncnln, nstate
Integer, Intent (Inout)        :: mode
!       .. Array Arguments ..
Real (Kind=nag_wp), Intent (Out) :: c(ncnln)
Real (Kind=nag_wp), Intent (Inout) :: cjac(ldcj,n), ruser(*)
Real (Kind=nag_wp), 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) = 0.0E0_nag_wp
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) = 2.0E0_nag_wp*x(1)
cjac(1,2) = 2.0E0_nag_wp*x(2)
cjac(1,3) = 2.0E0_nag_wp*x(3)
cjac(1,4) = 2.0E0_nag_wp*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 e04udfe_mod
Program e04udfe

!     E04UDF Example Main Program

!     .. Use Statements ..
Use e04udfe_mod, Only: confun, iset, nin, ninopt, nout, objfun
Use nag_library, Only: e04ucf, e04udf, e04uef, nag_wp, x04abf, x04acf,   &
x04baf
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Character (*), Parameter         :: fname = 'e04udfe.opt'
!     .. Local Scalars ..
Real (Kind=nag_wp)               :: objf
Integer                          :: i, ifail, inform, iter, lda, ldcj,   &
ldr, liwork, lwork, mode, n, nclin,  &
ncnln, outchn, sda, sdcjac
Character (80)                   :: rec
!     .. Local Arrays ..
Real (Kind=nag_wp), Allocatable  :: a(:,:), bl(:), bu(:), c(:),          &
cjac(:,:), clamda(:), objgrd(:),     &
r(:,:), work(:), x(:)
Real (Kind=nag_wp)               :: ruser(1)
Integer, Allocatable             :: istate(:), iwork(:)
Integer                          :: iuser(1)
!     .. Intrinsic Procedures ..
Intrinsic                        :: max
!     .. Executable Statements ..
Write (rec,99998) 'E04UDF Example Program Results'
Call x04baf(nout,rec)

!     Skip heading in data file

Read (nin,*) n, nclin, ncnln
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(lda,sda),                &
bl(n+nclin+ncnln),bu(n+nclin+ncnln),c(max(1,                           &
ncnln)),cjac(ldcj,sdcjac),clamda(n+nclin+ncnln),objgrd(n),r(ldr,n),    &
x(n),work(lwork))

If (nclin>0) Then
End If

!     Set the unit number for advisory messages to OUTCHN

outchn = nout
Call x04abf(iset,outchn)

!     Set three options using E04UEF

Call e04uef(' Infinite Bound Size = 1.0D+25 ')

Call e04uef(' Print Level = 1 ')

Call e04uef(' Verify Level = -1 ')

!     Open the options file for reading

mode = 0

ifail = 0
Call x04acf(ninopt,fname,mode,ifail)

!     Read the options file for the remaining options

Call e04udf(ninopt,inform)

If (inform/=0) Then
Write (rec,99999) 'E04UDF terminated with ' // 'INFORM = ', inform
Call x04baf(nout,rec)
End If

!     Solve the problem

ifail = 0
Call e04ucf(n,nclin,ncnln,lda,ldcj,ldr,a,bl,bu,confun,objfun,iter,       &
istate,c,cjac,clamda,objf,objgrd,r,x,iwork,liwork,work,lwork,iuser,    &
ruser,ifail)

99999 Format (1X,A,I5)
99998 Format (1X,A)
End Program e04udfe
```