/* nag::ad::d02pf Tangent over Tangent Example Program.
 */

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

// Function which calls NAG AD routines.
template <typename T> void func(std::vector<T> &r, std::vector<T> &y);

// Driver with the tangent calls.
// Solves the equation y''=-y, y0(=y(0))=0, y0'(=y'(0))=1 by solving the ODE
// system:
//    y1'=r1*y2,  y2'=-r2*y1
// over the range [0,2*pi] with initial conditions y1=0, y2=1.
// Also computes the sum of all Hessian elements dy2/dr2.
void driver(const std::vector<double> &rv,
            std::vector<double> &      yv,
            double &                   d2y_dr2);

int main()
{
  std::cout
      << "nag::ad::d02pf Tangent over Tangent Example Program Results\n\n";

  // Set problem parameters
  std::vector<double> rv{1.0, 1.0};
  // Solution y
  std::vector<double> yv{0.0, 1.0};
  // Sum of Hessian elements
  double d2y_dr2;

  // Call driver
  driver(rv, yv, d2y_dr2);

  // Print outputs
  std::cout << "\n Derivatives calculated: Second order tangents\n";
  std::cout << " Computational mode    : algorithmic\n";

  std::cout.setf(std::ios::scientific, std::ios::floatfield);
  std::cout.precision(6);
  std::cout << "\n Solution computed with required tolerance " << 1e-4
            << std::endl;
  for (std::size_t i = 0; i < yv.size(); i++)
  {
    std::cout << " y" << i + 1 << " = " << yv[i] << std::endl;
  }

  // Print derivatives
  std::cout
      << "\n Sum of all Hessian elements of solution vector y w.r.t. problem parameters :\n";
  std::cout << " sum_ijk [d2y/dr2]_ijk = " << d2y_dr2 << std::endl;

  return 0;
}

// Driver with the tangent calls.
// Solves the equation y''=-y, y0(=y(0))=0, y0'(=y'(0))=1 by solving the ODE
// system:
//    y1'=r1*y2,  y2'=-r2*y1
// over the range [0,2*pi] with initial conditions y1=0, y2=1.
// Also computes the sum of all Hessian elements dy2/dr2.
void driver(const std::vector<double> &rv,
            std::vector<double> &      yv,
            double &                   d2y_dr2)
{
  using mode = dco::gt1s<dco::gt1s<double>::type>;
  using T    = mode::type;

  // Size of system of ODEs
  Integer n = rv.size();
  // Variables to differentiate w.r.t.
  std::vector<T> r(begin(rv), end(rv));
  dco::derivative(dco::value(r)) = std::vector<double>(n, 1.0);
  dco::value(dco::derivative(r)) = std::vector<double>(n, 1.0);

  // Solution y, variable to differentiate
  std::vector<T> y(begin(yv), end(yv));

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

  // Extract the computed solutions
  yv = dco::passive_value(y);

  // Sum the tangents of r
  d2y_dr2 = 0;
  for (T const &yi : y)
  {
    d2y_dr2 += dco::derivative(dco::derivative(yi));
  }
}

// function which calls NAG AD Library routines
template <typename T> void func(std::vector<T> &r, std::vector<T> &y)
{
  // Active variables
  const Integer n      = y.size();
  const Integer liwsav = 130, lrwsav = 350 + 32 * n;

  std::vector<T>       thresh(n, 1e-8), ypnow(n), rwsav(lrwsav);
  std::vector<Integer> iwsav(liwsav);

  // Set parameters for the integrator.
  Integer method = 2;
  T       tol = 1e-4, hstart = 0.0, tend = 2.0 * nag_math_pi, tstart = 0.0;
  // Create AD configuration data object
  Integer           ifail = 0;
  nag::ad::handle_t ad_handle;

  // Initialize Runge-Kutta method for integrating ODE
  ifail = 0;
  nag::ad::d02pq(ad_handle, n, tstart, tend, y.data(), tol, thresh.data(),
                 method, hstart, iwsav.data(), rwsav.data(), ifail);

  T tnow = tstart;
  
  auto f = [&](nag::ad::handle_t &ad_handle,
              const T &          t,
              const Integer &    n,
              const T            y[],
              T                  yp[])
            {
              yp[0] = r[0] * y[1];
              yp[1] = -r[1] * y[0];
            };
  do
  {
    ifail = 0;
    // Solve an initial value problem for a 1st order system of ODEs
    nag::ad::d02pf(ad_handle, f, n, tnow, y.data(), ypnow.data(), iwsav.data(), rwsav.data(), ifail);
  } while (tnow < tend);
}