NAG Library Manual, Mark 28.4
```    Program c05qd_p0w_fe
!     C05QD_P0W_F Example Main Program

!     Mark 28.4 Release. NAG Copyright 2022.

!     .. Use Statements ..
Use iso_c_binding, Only: c_ptr
Use nag_library, Only: nag_wp, x02ajf
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Integer, Parameter               :: mode = 2, n = 7, nout = 6
!     .. Local Scalars ..
Real (Kind=nag_wp)               :: epsfcn, factor, xtol
Integer                          :: i, ifail, irevcm, ml, mu
!     .. Local Arrays ..
Real (Kind=nag_wp), Allocatable  :: diag(:), fjac(:,:), fvec(:), qtf(:), &
r(:), rwsav(:), x(:)
Real (Kind=nag_wp)               :: ruser(5)
Integer, Allocatable             :: iwsav(:)
!     .. Intrinsic Procedures ..
Intrinsic                        :: sqrt
!     .. Executable Statements ..

Write (nout,*) 'C05QD_P0W_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))

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

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())
diag(1:n) = 1.0_nag_wp
ml = 1
mu = 1
epsfcn = 0.0E0_nag_wp
factor = 100._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)
Do i = 1, n
fvec(i) = (ruser(2)+ruser(3)*x(i))*x(i) - ruser(5)
End Do
Do i = 2, n
fvec(i) = fvec(i) + ruser(1)*x(i-1)
End Do
Do i = 1, n - 1
fvec(i) = fvec(i) + ruser(4)*x(i+1)
End Do
Case Default
Exit revcomm
End Select

End Do revcomm

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

End Program c05qd_p0w_fe
```