NAG Library Manual, Mark 28.6
Interfaces:  FL   CL   CPP   AD 

NAG AD Library Introduction
Example description
/* E04WB_A1W_F C++ Header Example Program.
 *
 * Copyright 2022 Numerical Algorithms Group.
 * Mark 28.6, 2022.
 */

#include <dco.hpp>
#include <iostream>
#include <math.h>
#include <nag.h>
#include <nagad.h>
#include <stdio.h>
#include <string>
using namespace std;

int main()
{
  // Scalars
  int exit_status = 0;

  cout << "E04WB_A1W_F C++ Header Example Program Results\n\n";

  // Create AD tape
  dco::ga1s<double>::global_tape = dco::ga1s<double>::tape_t::create();

  // Create AD configuration data object
  Integer           ifail = 0;
  nag::ad::handle_t ad_handle;

  // Skip first line of data file
  string mystr;
  getline(cin, mystr);

  // Read problem sizes
  Integer m, n, nclin, ncnln;
  cin >> m;
  cin >> n;
  cin >> nclin;
  cin >> ncnln;

  Integer liwork = 3 * n + nclin + 2 * ncnln;
  Integer lda = nclin, sda = n, ldcj = ncnln, ldfj = m, ldr = n;
  Integer lwork;

  lwork = 20 * n + m * (n + 3);
  if (nclin > 0)
  {
    lwork = lwork + 2 * n * n + 11 * nclin;
  }
  if (ncnln > 0)
  {
    lwork = lwork + n * nclin + (2 * n + 21) * ncnln;
  }
  Integer            lb = n + nclin + ncnln;
  nagad_a1w_w_rtype *a = 0, *bl = 0, *bu = 0, *y = 0, *c = 0, *cjac = 0, *f = 0;
  nagad_a1w_w_rtype *fjac = 0, *clamda = 0, *r = 0, *x = 0, *work = 0,
                    *rwsav = 0;
  Integer *istate = 0, *iwork = 0, *iwsav = 0;
  logical *lwsav = 0;
  double * dr = 0, *rwsav_r = 0;
  if (!(a = NAG_ALLOC(lda * sda, nagad_a1w_w_rtype)) ||
      !(bl = NAG_ALLOC(lb, nagad_a1w_w_rtype)) ||
      !(bu = NAG_ALLOC(lb, nagad_a1w_w_rtype)) ||
      !(y = NAG_ALLOC(m, nagad_a1w_w_rtype)) ||
      !(c = NAG_ALLOC(ncnln, nagad_a1w_w_rtype)) ||
      !(cjac = NAG_ALLOC(ncnln * n, nagad_a1w_w_rtype)) ||
      !(f = NAG_ALLOC(m, nagad_a1w_w_rtype)) ||
      !(fjac = NAG_ALLOC(m * n, nagad_a1w_w_rtype)) ||
      !(clamda = NAG_ALLOC(lb, nagad_a1w_w_rtype)) ||
      !(r = NAG_ALLOC(ldr * n, nagad_a1w_w_rtype)) ||
      !(x = NAG_ALLOC(n, nagad_a1w_w_rtype)) ||
      !(work = NAG_ALLOC(lwork, nagad_a1w_w_rtype)) ||
      !(rwsav = NAG_ALLOC(475, nagad_a1w_w_rtype)) ||
      !(lwsav = NAG_ALLOC(120, logical)) ||
      !(rwsav_r = NAG_ALLOC(475, double)) || !(dr = NAG_ALLOC(n * n, double)) ||
      !(istate = NAG_ALLOC(lb, Integer)) ||
      !(iwork = NAG_ALLOC(liwork, Integer)) ||
      !(iwsav = NAG_ALLOC(610, Integer)))
  {
    cout << "Allocation failure\n";
    exit_status = -1;
  }
  else
  {

    // Read problem parameters and register for differentiation
    double yr;
    for (int i = 0; i < nclin; i++)
    {
      for (int j = 0; j < sda; j++)
      {
        Integer k = i + j * nclin;
        cin >> yr;
        a[k] = yr;
      }
    }
    for (int i = 0; i < m; i++)
    {
      cin >> yr;
      y[i] = yr;
    }
    for (int i = 0; i < lb; i++)
    {
      cin >> yr;
      bl[i] = yr;
    }
    for (int i = 0; i < lb; i++)
    {
      cin >> yr;
      bu[i] = yr;
    }
    for (int i = 0; i < n; i++)
    {
      cin >> yr;
      x[i] = yr;
    }

    double rr[44] = {8.0,  8.0,  10.0, 10.0, 10.0, 10.0, 12.0, 12.0, 12.0,
                     12.0, 14.0, 14.0, 14.0, 16.0, 16.0, 16.0, 18.0, 18.0,
                     20.0, 20.0, 20.0, 22.0, 22.0, 22.0, 24.0, 24.0, 24.0,
                     26.0, 26.0, 26.0, 28.0, 28.0, 30.0, 30.0, 30.0, 32.0,
                     32.0, 34.0, 36.0, 36.0, 38.0, 38.0, 40.0, 42.0};
    nagad_a1w_w_rtype ruser[44];
    for (int i = 0; i < 44; i++)
    {
      ruser[i] = rr[i];
      dco::ga1s<double>::global_tape->register_variable(ruser[i]);
    }

    // Initialize sav arrays
    ifail = 0;
    char cwsav[1];
    nag::ad::e04wb("E04USA", cwsav, 1, lwsav, 120, iwsav, 610, rwsav, 475,
                   ifail);

    
  auto objfun = [&](nag::ad::handle_t &     ad_handle,
                  Integer &               mode,
                  const Integer &         m,
                  const Integer &         n,
                  const Integer &         ldfj,
                  const Integer &         needfi,
                  const nagad_a1w_w_rtype *x,
                  nagad_a1w_w_rtype *f,
                  nagad_a1w_w_rtype *fjac,
                  const Integer &         nstate)
                {
                  nagad_a1w_w_rtype x1, x2;
                  x1 = x[0];
                  x2 = x[1];

                  if (mode == 0 && needfi > 0)
                  {
                    f[needfi - 1] = x1 + (0.49 - x1) * exp(-x2 * (ruser[needfi - 1] - 8.0));
                  }
                  else
                  {
                    for (int i = 0; i < m; ++i)
                    {
                      nagad_a1w_w_rtype ai   = ruser[i] - 8.0;
                      nagad_a1w_w_rtype temp = exp(-x2 * ai);

                      if (mode == 0 || mode == 2)
                      {
                        f[i] = x1 + (0.49 - x1) * temp;
                      }
                      if (mode == 1 || mode == 2)
                      {
                        fjac[i]     = 1.0 - temp;
                        fjac[i + m] = -(0.49 - x1) * ai * temp;
                      }
                    }
                  }
                };
  auto confun = [&](nag::ad::handle_t &     ad_handle,
                  Integer &               mode,
                  const Integer &         ncnln,
                  const Integer &         n,
                  const Integer &         ldcj,
                  const Integer           needc[],
                  const nagad_a1w_w_rtype *x,
                  nagad_a1w_w_rtype *c,
                  nagad_a1w_w_rtype *cjac,
                  const Integer &         nstate)
                {
                  if (nstate == 1)
                  {
                    for (int i = 0; i < ncnln * n; ++i)
                    {
                      cjac[i] = 0.0;
                    }
                  }
                  if (needc[0] > 0)
                  {
                    if (mode == 0 || mode == 2)
                    {
                      c[0] = -0.09 - x[0] * x[1] + 0.49 * x[1];
                    }
                    if (mode == 1 || mode == 2)
                    {
                      cjac[0]     = -x[1];
                      cjac[ncnln] = -x[0] + 0.49;
                    }
                  }
                };
    // Solve the problem
    Integer           iter;
    nagad_a1w_w_rtype objf;
    ifail = -1;
    nag::ad::e04us(ad_handle, m, n, nclin, ncnln, lda, ldcj, ldfj, ldr, a, bl,
                   bu, y, confun, objfun, iter, istate, c, cjac, f, fjac,
                   clamda, objf, r, x, iwork, liwork, work, lwork, lwsav, iwsav, rwsav, ifail);

    // Primal results
    cout.setf(ios::scientific, ios::floatfield);
    if (ifail == 0 || ifail > 1)
    {
      cout.precision(4);
      cout << "\n Optimal objective function value = ";
      cout.width(12);
      cout << dco::value(objf);
      cout << "\n Solution point = ";
      for (int i = 0; i < n; i++)
      {
        cout.width(12);
        cout << dco::value(x[i]);
      }
      cout << endl;
    }
    else
    {
      cout << "nag::ad::e04us failed with ifail = " << ifail << endl;
      goto END;
    }

    cout << "\n Derivatives calculated: First order adjoints\n";
    cout << " Computational mode    : algorithmic\n\n";
    cout << " Derivatives:\n\n";

    // Setup evaluation of derivatives of fsumsq via adjoints.
    double inc = 1.0;
    dco::derivative(x[0]) += inc;
    ifail                                              = 0;
    dco::ga1s<double>::global_tape->sparse_interpret() = true;
    dco::ga1s<double>::global_tape->interpret_adjoint();

    // Get derivatives of x[0] w.r.t. ruser
    cout << "  derivatives of x[0] w.r.t ruser[0:43]:\n";
    for (int i = 0; i < 44; i++)
    {
      double d = dco::derivative(ruser[i]);
      cout.width(12);
      cout << d;
      if (i % 4 == 3)
      {
        cout << endl;
      }
    }
  }
END:

  dco::ga1s<double>::tape_t::remove(dco::ga1s<double>::global_tape);

  return exit_status;
}