```!   E04GZF Example Program Text
!   Mark 26.1 Release. NAG Copyright 2017.
Module e04gzfe_mod

!     E04GZF 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                           :: lsfun2
!     .. Parameters ..
Integer, Parameter, Public       :: m = 15, n = 3, nin = 5, nout = 6,    &
nt = 3
Integer, Parameter, Public       :: lw = 8*n + 2*n*n + 2*m*n + 3*m
!     .. Local Arrays ..
Real (Kind=nag_wp), Public, Save :: t(m,nt), y(m)
Contains
Subroutine lsfun2(m,n,xc,fvec,fjac,ldfjac,iuser,ruser)
!       Routine to evaluate the residuals and their 1st derivatives.

!       .. Scalar Arguments ..
Integer, Intent (In)           :: ldfjac, m, n
!       .. Array Arguments ..
Real (Kind=nag_wp), Intent (Inout) :: fjac(ldfjac,n), ruser(*)
Real (Kind=nag_wp), Intent (Out) :: fvec(m)
Real (Kind=nag_wp), Intent (In) :: xc(n)
Integer, Intent (Inout)        :: iuser(*)
!       .. Local Scalars ..
Real (Kind=nag_wp)             :: denom, dummy
Integer                        :: i
!       .. Executable Statements ..
Do i = 1, m
denom = xc(2)*t(i,2) + xc(3)*t(i,3)
fvec(i) = xc(1) + t(i,1)/denom - y(i)
fjac(i,1) = 1.0E0_nag_wp
dummy = -1.0E0_nag_wp/(denom*denom)
fjac(i,2) = t(i,1)*t(i,2)*dummy
fjac(i,3) = t(i,1)*t(i,3)*dummy
End Do

Return

End Subroutine lsfun2
End Module e04gzfe_mod
Program e04gzfe

!     E04GZF Example Main Program

!     .. Use Statements ..
Use e04gzfe_mod, Only: lsfun2, lw, m, n, nin, nout, nt, t, y
Use nag_library, Only: e04gzf, nag_wp
!     .. Implicit None Statement ..
Implicit None
!     .. Local Scalars ..
Real (Kind=nag_wp)               :: fsumsq
Integer                          :: i, ifail
!     .. Local Arrays ..
Real (Kind=nag_wp)               :: ruser(1), w(lw), x(n)
Integer                          :: iuser(1)
!     .. Executable Statements ..
Write (nout,*) 'E04GZF Example Program Results'

!     Skip heading in data file

!     Observations of TJ (J = 1, 2, ..., nt) are held in T(I, J)
!     (I = 1, 2, ..., m)

Do i = 1, m
End Do

x(1:nt) = (/0.5E0_nag_wp,1.0E0_nag_wp,1.5E0_nag_wp/)

ifail = -1
Call e04gzf(m,n,lsfun2,x,fsumsq,w,lw,iuser,ruser,ifail)

Select Case (ifail)
Case (0,2:8,10:)
Write (nout,*)
Write (nout,99999) 'On exit, the sum of squares is', fsumsq
Write (nout,99999) 'at the point', x(1:n)
End Select

99999 Format (1X,A,3F12.4)
End Program e04gzfe
```