!   C05RB_A1W_F Example Program Text
!   Mark 28.7 Release. NAG Copyright 2022.
    Module c05rb_a1w_fe_mod

!     C05RB_A1W_F Example Program Module:
!            Parameters and User-defined Routines

!     .. Use Statements ..
      Use iso_c_binding, Only: c_ptr
      Use nagad_library, Only: nagad_a1w_w_rtype, Operator (-), Operator (+),  &
                               Assignment (=), Operator (*)
      Use nag_library, Only: nag_wp
!     .. Implicit None Statement ..
      Implicit None
!     .. Accessibility Statements ..
      Private
      Public                           :: fcn
!     .. Parameters ..
      Integer, Parameter, Public       :: n = 7, nout = 6
    Contains
      Subroutine fcn(ad_handle,n,x,fvec,fjac,iuser,ruser,iflag)

!       .. Scalar Arguments ..
        Type (c_ptr), Intent (Inout)   :: ad_handle
        Integer, Intent (Inout)        :: iflag
        Integer, Intent (In)           :: n
!       .. Array Arguments ..
        Type (nagad_a1w_w_rtype), Intent (Inout) :: fjac(n,n), fvec(n),        &
                                          ruser(*)
        Type (nagad_a1w_w_rtype), Intent (In) :: x(n)
        Integer, Intent (Inout)        :: iuser(*)
!       .. Local Scalars ..
        Integer                        :: i, k
!       .. Executable Statements ..

        If (iflag/=2) Then
          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
        Else
          fjac(1:n,1:n) = 0.0_nag_wp
          fjac(1,1) = ruser(2) + 2.0_nag_wp*ruser(3)*x(1)
          fjac(1,2) = ruser(4)
          Do k = 2, n - 1
            fjac(k,k-1) = ruser(1)
            fjac(k,k) = ruser(2) + 2.0_nag_wp*ruser(3)*x(k)
            fjac(k,k+1) = ruser(4)
          End Do
          fjac(n,n-1) = ruser(1)
          fjac(n,n) = ruser(2) + 2.0_nag_wp*ruser(3)*x(n)
        End If
!       Set iflag negative to terminate execution for any reason.
        iflag = 0

        Return

      End Subroutine fcn

    End Module c05rb_a1w_fe_mod

    Program c05rb_a1w_fe
!     C05RB_A1W_F Example Main Program

!     .. Use Statements ..
      Use c05rb_a1w_fe_mod, Only: fcn, n, nout
      Use iso_c_binding, Only: c_ptr
      Use nagad_library, Only: c05rb_a1w_f, nagad_a1w_get_derivative,          &
                               nagad_a1w_ir_create => x10za_a1w_f,             &
                               nagad_a1w_ir_interpret_adjoint_sparse,          &
                               nagad_a1w_ir_register_variable,                 &
                               nagad_a1w_ir_remove, nagad_a1w_ir_zero_adjoints &
                               , nagad_a1w_set_derivative, nagad_a1w_w_rtype,  &
                               x10aa_a1w_f, x10ab_a1w_f, Assignment (=)
      Use nag_library, Only: nag_wp, x02ajf, x04caf
!     .. Implicit None Statement ..
      Implicit None
!     .. Local Scalars ..
      Type (c_ptr)                     :: ad_handle
      Type (nagad_a1w_w_rtype)         :: xtol
      Integer                          :: i, ifail
!     .. Local Arrays ..
      Type (nagad_a1w_w_rtype), Allocatable :: fjac(:,:), fvec(:), x(:)
      Type (nagad_a1w_w_rtype)         :: ruser(5)
      Real (Kind=nag_wp), Allocatable  :: dr(:,:)
      Integer                          :: iuser(1)
!     .. Intrinsic Procedures ..
      Intrinsic                        :: sqrt
!     .. Executable Statements ..

      Write (nout,*) 'C05RB_A1W_F Example Program Results'

      Allocate (fjac(n,n),fvec(n),x(n),dr(n,5))

!     The following starting values provide a rough solution.
      x(1:n) = -1.0_nag_wp
      x(1:n)%tapeindex = 0.0_nag_wp

!     Create AD tape
      Call nagad_a1w_ir_create

!     Create AD configuration data object
      ifail = 0
      Call x10aa_a1w_f(ad_handle,ifail)

      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
      ruser(1:5)%tapeindex = 0

!     Register variables to differentiate w.r.t.
      Call nagad_a1w_ir_register_variable(ruser)

      xtol = sqrt(x02ajf())

      ifail = 0
      Call c05rb_a1w_f(ad_handle,fcn,n,x,fvec,fjac,xtol,iuser,ruser,ifail)

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

!     Setup evaluation of derivatives via adjoints

      Write (nout,*)
      Write (nout,*) ' Derivatives calculated: First order adjoints'
      Write (nout,*) ' Computational mode    : algorithmic'
      Write (nout,*)
      Write (nout,*) ' Derivatives are of solution w.r.t function params'
      Write (nout,*)

      Do i = 1, n
        Call nagad_a1w_ir_zero_adjoints
        Call nagad_a1w_set_derivative(x(i),1.0_nag_wp)
        ifail = 0
        Call nagad_a1w_ir_interpret_adjoint_sparse(ifail)

!       Get derivatives
        dr(i,1) = nagad_a1w_get_derivative(ruser(1))
        dr(i,2) = nagad_a1w_get_derivative(ruser(2))
        dr(i,3) = nagad_a1w_get_derivative(ruser(3))
        dr(i,4) = nagad_a1w_get_derivative(ruser(4))
        dr(i,5) = nagad_a1w_get_derivative(ruser(5))
      End Do

      Call x04caf('General',' ',n,5,dr,n,'       dx/druser',ifail)

!     Remove computational data object and tape
      Call x10ab_a1w_f(ad_handle,ifail)
      Call nagad_a1w_ir_remove

    End Program c05rb_a1w_fe