/* nag::ad::e04gb Passive Example Program.
 */

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

// Function which calls NAG AD Library routines.
// Computes the minimum of the sum of squares of m nonlinear functions,
// the solution point and the corresponding residuals.
template <typename T>
void func(std::vector<T> &y,
          std::vector<T> &t,
          std::vector<T> &x,
          std::vector<T> &fvec,
          T &             fsumsq);

int main()
{
  std::cout << " nag::ad::e04gb Passive Example Program Results\n";

  // Problem dimensions
  const Integer       m = 15, n = 3;
  std::vector<double> yv = {0.14, 0.18, 0.22, 0.25, 0.29, 0.32, 0.35, 0.39,
                            0.37, 0.58, 0.73, 0.96, 1.34, 2.10, 4.39};
  std::vector<double> tv = {
      1.0,  2.0,  3.0,  4.0,  5.0,  6.0,  7.0,  8.0,  9.0,  10.0, 11.0, 12.0,
      13.0, 14.0, 15.0, 15.0, 14.0, 13.0, 12.0, 11.0, 10.0, 9.0,  8.0,  7.0,
      6.0,  5.0,  4.0,  3.0,  2.0,  1.0,  1.0,  2.0,  3.0,  4.0,  5.0,  6.0,
      7.0,  8.0,  7.0,  6.0,  5.0,  4.0,  3.0,  2.0,  1.0};

  std::vector<double> xv(n), fvecv(m);

  // Sum of squares of the residuals at the computed point xv
  double fsumsqv;

  // Call the NAG AD Lib functions
  func(yv, tv, xv, fvecv, fsumsqv);

  // Primal results
  std::cout.setf(std::ios::scientific, std::ios::floatfield);
  std::cout.precision(12);
  std::cout << "\n Sum of squares = ";
  std::cout.width(20);
  std::cout << fsumsqv;
  std::cout << "\n Solution point = ";
  for (int i = 0; i < n; i++)
  {
    std::cout.width(20);
    std::cout << xv[i];
  }
  std::cout << std::endl;

  std::cout << "\n Residuals :\n";
  for (int i = 0; i < m; i++)
  {
    std::cout.width(20);
    std::cout << fvecv[i] << std::endl;
  }
  std::cout << std::endl;

  return 0;
}

// Function which calls NAG AD Library routines.
template <typename T>
void func(std::vector<T> &y,
          std::vector<T> &t,
          std::vector<T> &x,
          std::vector<T> &fvec,
          T &             fsumsq)
{
  // Problem dimensions
  const Integer m = fvec.size(), n = x.size();
  const Integer ldfjac = m, nt = n, ldv = n;

  // Initial guess of the position of the minimum
  dco::passive_value(x[0]) = 0.5;
  for (int i = 1; i < n; i++)
  {
    dco::passive_value(x[i]) = dco::passive_value(x[i - 1]) + 0.5;
  }

  std::vector<T> s(n), v(ldv * n), fjac(m * n);
  Integer        niter, nf;

  Integer iprint = -1;
  Integer selct  = 2;
  Integer maxcal = 200 * n;
  T       eta    = 0.5;
  T       xtol   = 10.0 * sqrt(X02AJC);
  T       stepmx = 10.0;

  auto lsqfun = [&](nag::ad::handle_t&,
                    Integer &          iflag,
                    const Integer &    m,
                    const Integer &    n,
                    const T            xc[],
                    T                  fvec[],
                    T                  fjac[],
                    const Integer &    ldfjac)
                {
                  const T x1 = xc[0], x2 = xc[1], x3 = xc[2];
                  
                  for (int i = 0; i < m; i++)
                    {
                      T di = x2 * t[m + i] + x3 * t[2 * m + i];
                      T yi = x1 + t[i] / di;
                      // The values of the residuals
                      fvec[i] = yi - y[i];
                      // Evaluate the Jacobian
                      if (iflag > 0)
                        {
                          // dF/dx1
                          fjac[i] = 1.0;
                          // dF/dx2
                          fjac[i + m] = -(t[i] * t[m + i]) / (di * di);
                          // dF/dx3
                          fjac[i + 2 * m] = -(t[i] * t[2 * m + i]) / (di * di);
                        }
                    }
                };
  
  // Create AD configuration data object
  Integer           ifail = 0;
  nag::ad::handle_t ad_handle;

  // Routine for computing the minimum of the sum of squares of m nonlinear
  // functions.
  ifail = 0;
  nag::ad::e04gb(ad_handle, m, n, selct, lsqfun, nullptr, iprint, maxcal, eta,
                 xtol, stepmx, x.data(), fsumsq, fvec.data(), fjac.data(),
                 ldfjac, s.data(), v.data(), ldv, niter, nf, ifail);
}