NAG Library Manual, Mark 27.2
```    Program c05mdfe

!     C05MDF Example Program Text

!     Mark 27.2 Release. NAG Copyright 2021.

!     .. Use Statements ..
Use nag_library, Only: c05mdf, dnrm2, nag_wp, x02ajf
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Integer, Parameter               :: imax = 50, n = 4, nout = 6
!     .. Local Scalars ..
Real (Kind=nag_wp)               :: atol, cndtol, fnorm, rtol
Integer                          :: astart, i, icount, ifail, irevcm, m
!     .. Local Arrays ..
Real (Kind=nag_wp), Allocatable  :: fvec(:), rwsav(:), x(:)
Integer, Allocatable             :: iwsav(:)
!     .. Intrinsic Procedures ..
Intrinsic                        :: cos, max, min, sin, sqrt
!     .. Executable Statements ..

Write (nout,*) 'C05MDF Example Program Results'

m = 2
Allocate (fvec(n),iwsav(14+m),x(n),rwsav(2*m*n+m*m+m+2*n+1+min(m,        &
1)*max(n,3*m)))

!     The following starting values provide a rough solution.

x(1) = 2.0E0_nag_wp
x(2) = 0.5E0_nag_wp
x(3) = 2.0E0_nag_wp
x(4) = 0.5E0_nag_wp

atol = sqrt(x02ajf())
rtol = sqrt(x02ajf())
cndtol = 0.0_nag_wp
astart = 0
icount = 0
irevcm = 0
ifail = -1

revcomm: Do

Call c05mdf(irevcm,n,x,fvec,atol,rtol,m,cndtol,astart,iwsav,rwsav,     &
ifail)

Select Case (irevcm)
Case (1)

If (icount==imax) Then
Write (nout,*) 'Exiting after the maximum number of iterations'
Exit revcomm
End If

icount = icount + 1

!         Insert print statements here to monitor progress if desired.

Cycle revcomm
Case (2)

!          Evaluate functions at given point

fvec(1) = cos(x(3)) - x(1)
fvec(2) = sqrt(1.0_nag_wp-x(4)**2) - x(2)
fvec(3) = sin(x(1)) - x(3)
fvec(4) = x(2)**2 - x(4)

Cycle revcomm
Case Default
Exit revcomm
End Select

End Do revcomm

If (ifail==0 .Or. icount==imax) 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'
Write (nout,*)
Write (nout,99998)(x(i),i=1,n)
End If

99999 Format (1X,A,I4,A,E12.4)
99998 Format (1X,4F12.4)
End Program c05mdfe
```