NAG Library Manual, Mark 29
Interfaces:  FL   CL   CPP   AD
```/* nag::ad::c05ay Tangent over Adjoint Example Program.
*/

#include <dco.hpp>
#include <iostream>

// Function which calls NAG AD Library routines.
template <typename T> void func(T r, T &x);

// Driver with the adjoint calls.
// Finds the zero point f(xv) = 0 for the function
// f(x) =  exp(-x) - r*x.
// Also, computes the Hessian d2x_dr2 = d2xv/dr2 using a symbolic adjoint of the
// root finder.
void driver(const double &rv, double &xv, double &d2x_dr2);

int main()
{
std::cout << " nag::ad::c05ay Tangent over Adjoint Example Program Results\n";

// Set problem parameters
double rv = 2.0;
// Solution x
double xv;
// Derivative of x
double d2x_dr2;

// Call driver
driver(rv, xv, d2x_dr2);

// sPrint outputs
std::cout << "\n Derivatives calculated: Second order adjoints\n";
std::cout << " Computational mode    : symbolic (expert mode)\n";

// Print derivatives
std::cout.setf(std::ios::scientific, std::ios::floatfield);
std::cout.precision(12);
std::cout << "\n Solution:\n";
std::cout << " x = " << xv << std::endl;
std::cout << "\n Second derivative of solution x w.r.t. parameter r:\n";
std::cout << " d2x/dr2(x) = " << d2x_dr2 << std::endl;

return 0;
}

// Driver with the adjoint calls.
// Finds the zero point f(xv) = 0 for the function
// f(x) =  exp(-x) - r*x.
// Also, computes the Hessian d2x_dr2 = d2xv/dr2 using a symbolic adjoint of the
// root finder.
void driver(const double &rv, double &xv, double &d2x_dr2)
{
using mode = dco::ga1s<dco::gt1s<double>::type>;
using T    = mode::type;

// Create the AD tape
mode::global_tape = mode::tape_t::create();

// Function parameter r
T r = rv;

// Register variable to differentiate w.r.t.
dco::derivative(dco::value(r)) = 1.0;
mode::global_tape->register_variable(r);

// Variable to differentiate
T x;

// Call the NAG AD Lib functions
func(r, x);

// Extract the computed solution
xv = dco::passive_value(x);

mode::global_tape->register_output_variable(x);
dco::derivative(x) = 1.0;
// Extract the derivatives
d2x_dr2 = dco::derivative(dco::derivative(r));

// Remove tape
mode::tape_t::remove(mode::global_tape);
}

// Function which calls NAG AD Library routines
template <typename T> void func(T r, T &x)
{
// Active variables
T a = 0.0, b = 1.0;
T eps = 1.0e-5, eta = 0.0;
// Create AD configuration data object
Integer           ifail = 0;

auto f = [&](nag::ad::handle_t const& handle, T const &x, T & z) {
switch (handle.active_inputs())
{
z = exp(-dco::value(x)) - dco::value(x) * dco::value(r);
break;
z = exp(-x) - x * dco::value(r);
break;
z = exp(-dco::value(x)) - dco::value(x) * r;
break;