NAG Library Manual, Mark 27.2
```    Program c05qdfe

!     C05QDF Example Program Text

!     Mark 27.2 Release. NAG Copyright 2021.

!     .. Use Statements ..
Use nag_library, Only: c05qdf, dnrm2, nag_wp, x02ajf
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Integer, Parameter               :: n = 9, nout = 6
!     .. Local Scalars ..
Real (Kind=nag_wp)               :: epsfcn, factor, fnorm, xtol
Integer                          :: i, icount, ifail, irevcm, ml, mode,  &
mu
!     .. Local Arrays ..
Real (Kind=nag_wp), Allocatable  :: diag(:), fjac(:,:), fvec(:), qtf(:), &
r(:), rwsav(:), x(:)
Integer, Allocatable             :: iwsav(:)
!     .. Intrinsic Procedures ..
Intrinsic                        :: sqrt
!     .. Executable Statements ..
Write (nout,*) 'C05QDF Example Program Results'

Allocate (diag(n),fjac(n,n),fvec(n),qtf(n),r(n*(n+                       &
1)/2),rwsav(4*n+10),iwsav(17),x(n))

!     The following starting values provide a rough solution.

x(1:n) = -1.0E0_nag_wp
xtol = sqrt(x02ajf())
diag(1:n) = 1.0E0_nag_wp
ml = 1
mu = 1
epsfcn = 0.0E0_nag_wp
mode = 2
factor = 100.0E0_nag_wp
icount = 0
irevcm = 0
ifail = -1

revcomm: Do

Call c05qdf(irevcm,n,x,fvec,xtol,ml,mu,epsfcn,mode,diag,factor,fjac,r, &
qtf,iwsav,rwsav,ifail)

Select Case (irevcm)
Case (1)
icount = icount + 1

!         Insert print statements here to monitor progress if desired.

Cycle revcomm
Case (2)

!         Evaluate functions at given point

fvec(1:n) = (3.0E0_nag_wp-2.0E0_nag_wp*x(1:n))*x(1:n) + 1.0E0_nag_wp
fvec(2:n) = fvec(2:n) - x(1:(n-1))
fvec(1:(n-1)) = fvec(1:(n-1)) - 2.0E0_nag_wp*x(2:n)
Cycle revcomm
Case Default
Exit revcomm
End Select

End Do revcomm

If (ifail==0 .Or. ifail==3 .Or. ifail==4 .Or. ifail==5) Then
If (ifail==0) Then
!         The NAG name equivalent of dnrm2 is f06ejf
fnorm = dnrm2(n,fvec,1)
Write (nout,*)
Write (nout,99999) 'Final 2-norm of the residuals after', icount,    &
' iterations is ', fnorm
Write (nout,*)
Write (nout,*) 'Final approximate solution'
Else
Write (nout,*)
Write (nout,*) 'Approximate solution'
End If
Write (nout,*)
Write (nout,99998)(x(i),i=1,n)
End If

99999 Format (1X,A,I4,A,E12.4)
99998 Format (5X,3F12.4)
End Program c05qdfe
```