NAG Library Manual, Mark 27.3
Program e01bg_t2w_fe

!     E01BG_T2W_F Example Program Text
!     Mark 27.3 Release. NAG Copyright 2021.

!     .. Use Statements ..
Use iso_c_binding, Only: c_ptr
x10aa_t2w_f, x10ab_t2w_f, Assignment (=),       &
Operator (*), Operator (+)
Use nag_library, Only: nag_wp
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Integer, Parameter               :: nin = 5, nout = 6
!     .. Local Scalars ..
Real (Kind=nag_wp)               :: fr, xr
Integer                          :: i, ifail, m, n, r
!     .. Local Arrays ..
Type (nagad_t2w_w_rtype), Allocatable :: d(:), f(:), pd(:), pf(:),       &
px(:), x(:)
Real (Kind=nag_wp), Allocatable  :: df(:), dx(:)
!     .. Executable Statements ..

Write (nout,*) 'E01BG_T2W_F Example Program Results'

!     Skip heading in data file

m = 1
Allocate (d(n),f(n),x(n),dx(n),df(n),px(m),pf(m),pd(m))

!     Initialize x and f arrays using data
Do r = 1, n
x(r) = xr
f(r) = fr
End Do

!     Create AD configuration data object
ifail = 0

px(1) = 0.5_nag_wp*(x(n/2)+x(n/2+1))

Do i = 1, 2*n
If (i<=n) Then
x(i)%value%tangent = 1.0_nag_wp
x(i)%tangent%value = 1.0_nag_wp
Else
f(i-n)%value%tangent = 1.0_nag_wp
f(i-n)%tangent%value = 1.0_nag_wp
End If
ifail = 0

!       Evaluate interpolant and derivatives at a mid-point

If (i<=n) Then
dx(i) = pf(1)%tangent%tangent
x(i)%value%tangent = 0.0_nag_wp
x(i)%tangent%value = 0.0_nag_wp
Else
df(i-n) = pf(1)%tangent%tangent
f(i-n)%value%tangent = 0.0_nag_wp
f(i-n)%tangent%value = 0.0_nag_wp
End If
End Do
Write (nout,*)
Write (nout,*) ' Derivatives calculated: Second order tangents'
Write (nout,*) ' Computational mode    : algorithmic'

!     Get derivative of interpolated value w.r.t data points and values

Write (nout,*)
Write (nout,99999) 'Interpolated value at x = ', px(1)%value%value,      &
' is: ', pf(1)%value%value
99999 Format (1X,A,F7.3,A,E12.5)
Write (nout,*)
Write (nout,*) ' Derivatives of interpolated value w.r.t. x and f:'
Write (nout,*)
Write (nout,*) '    i     d^2/d^2x     d^2/df^2'
Do i = 1, n
Write (nout,99998) i, dx(i), df(i)
End Do
99998 Format (1X,I5,1X,E12.5,1X,E12.5)

!     Remove computational data object
ifail = 0