NAG Library Manual, Mark 28.4
```!   C05RCF Example Program Text
!   Mark 28.4 Release. NAG Copyright 2022.

Module c05rcfe_mod

!     C05RCF 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                           :: fcn
!     .. Parameters ..
Real (Kind=nag_wp), Parameter, Public :: factor = 100.0_nag_wp
Integer, Parameter, Public       :: maxfev = 1000, mode = 2, n = 9,      &
nout = 6, nprint = 0
Contains
Subroutine fcn(n,x,fvec,fjac,iuser,ruser,iflag)

!       .. Parameters ..
Real (Kind=nag_wp), Parameter  :: coeff(5) = (/-1.0_nag_wp,3.0_nag_wp, &
-2.0_nag_wp,-2.0_nag_wp,             &
-1.0_nag_wp/)
!       .. Scalar Arguments ..
Integer, Intent (Inout)        :: iflag
Integer, Intent (In)           :: n
!       .. Array Arguments ..
Real (Kind=nag_wp), Intent (Inout) :: fjac(n,n), fvec(n), ruser(*)
Real (Kind=nag_wp), Intent (In) :: x(n)
Integer, Intent (Inout)        :: iuser(*)
!       .. Local Scalars ..
Integer                        :: k
!       .. Executable Statements ..
If (iflag==0) Then
If (nprint>0) Then
!           Insert print statements here if desired.
End If
Else If (iflag/=2) Then
fvec(1:n) = (coeff(2)+coeff(3)*x(1:n))*x(1:n) - coeff(5)
fvec(2:n) = fvec(2:n) + coeff(1)*x(1:(n-1))
fvec(1:(n-1)) = fvec(1:(n-1)) + coeff(4)*x(2:n)
Else
fjac(1:n,1:n) = 0.0_nag_wp
fjac(1,1) = coeff(2) + 2.0_nag_wp*coeff(3)*x(1)
fjac(1,2) = coeff(4)
Do k = 2, n - 1
fjac(k,k-1) = coeff(1)
fjac(k,k) = coeff(2) + 2.0_nag_wp*coeff(3)*x(k)
fjac(k,k+1) = coeff(4)
End Do
fjac(n,n-1) = coeff(1)
fjac(n,n) = coeff(2) + 2.0_nag_wp*coeff(3)*x(n)
End If
!       Set iflag negative to terminate execution for any reason.
iflag = 0
Return
End Subroutine fcn
End Module c05rcfe_mod
Program c05rcfe

!     C05RCF Example Main Program

!     .. Use Statements ..
Use c05rcfe_mod, Only: factor, fcn, maxfev, mode, n, nout, nprint
Use nag_library, Only: c05rcf, dnrm2, nag_wp, x02ajf
!     .. Implicit None Statement ..
Implicit None
!     .. Local Scalars ..
Real (Kind=nag_wp)               :: fnorm, xtol
Integer                          :: i, ifail, nfev, njev
!     .. Local Arrays ..
Real (Kind=nag_wp), Allocatable  :: diag(:), fjac(:,:), fvec(:), qtf(:), &
r(:), x(:)
Real (Kind=nag_wp)               :: ruser(1)
Integer                          :: iuser(1)
!     .. Intrinsic Procedures ..
Intrinsic                        :: sqrt
!     .. Executable Statements ..
Write (nout,*) 'C05RCF Example Program Results'

Allocate (diag(n),fjac(n,n),fvec(n),qtf(n),r(n*(n+1)/2),x(n))

!     The following starting values provide a rough solution.

x(1:n) = -1.0_nag_wp

xtol = sqrt(x02ajf())
diag(1:n) = 1.0_nag_wp

ifail = -1
Call c05rcf(fcn,n,x,fvec,fjac,xtol,maxfev,mode,diag,factor,nprint,nfev,  &
njev,r,qtf,iuser,ruser,ifail)

If (ifail==0 .Or. ifail==2 .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 =', 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,E12.4)
99998 Format (1X,3F12.4)
End Program c05rcfe
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