NAG Library Manual, Mark 29.3
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NAG AD Library Introduction
Example description
/* E05UC_T1W_F C++ Header Example Program.
 *
 * Copyright 2023 Numerical Algorithms Group.
 * Mark 29.3, 2023.
 */

#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 << "E05UC_T1W_F C++ Header Example Program Results\n\n";

  // 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);

  // problem sizes
  const Integer n = 2, nclin = 1, ncnln = 2;
  Integer       nb, npts;
  cin >> nb >> npts;
  logical repeat = true;

  const Integer liopts = 740, lopts = 485;
  Integer       lda = nclin, sda = n, ldc = ncnln, ldcj = ncnln, ldr = n;

  Integer            lb = n + nclin + ncnln, listat = n + nclin + ncnln;
  nagad_t1w_w_rtype *a = 0, *bl = 0, *bu = 0, *c = 0, *cjac = 0, *objf = 0;
  nagad_t1w_w_rtype *objgrd = 0, *clamda = 0, *r = 0, *x = 0, *work = 0,
                    *opts = 0;
  Integer *iopts = 0, *info = 0, *iter = 0, *istate = 0;
  a      = new nagad_t1w_w_rtype[lda * sda];
  bl     = new nagad_t1w_w_rtype[lb];
  bu     = new nagad_t1w_w_rtype[lb];
  c      = new nagad_t1w_w_rtype[ldc * nb];
  cjac   = new nagad_t1w_w_rtype[ldcj * n * nb];
  clamda = new nagad_t1w_w_rtype[lb * nb];
  r      = new nagad_t1w_w_rtype[ldr * n * nb];
  x      = new nagad_t1w_w_rtype[n * nb];
  objgrd = new nagad_t1w_w_rtype[n * nb];
  work   = new nagad_t1w_w_rtype[nclin];
  opts   = new nagad_t1w_w_rtype[lopts];
  objf   = new nagad_t1w_w_rtype[nb];
  istate = new Integer[listat * nb];
  iopts  = new Integer[liopts];
  info   = new Integer[nb];
  iter   = new Integer[nb];

  bl[0] = -500.0;
  bl[1] = -500.0;
  bl[2] = -10000.0;
  bl[3] = -1.0;
  bl[4] = -0.9;
  bu[0] = 500.0;
  bu[1] = 500.0;
  bu[2] = 10.0;
  bu[3] = 500000.0;
  bu[4] = 0.9;

  a[0] = 3.0;
  a[1] = -2.0;

  nagad_t1w_w_rtype ruser[6];
  ruser[0] = 1.0;
  ruser[1] = 1.0;
  ruser[2] = 1.0;
  ruser[3] = 3.0;
  ruser[4] = 0.005;
  ruser[5] = 0.01;

  double inc = 1.0, zero = 0.0, dfdr[6];
  for (int i = 0; i < 6; i++)
  {
    dco::derivative(ruser[i]) = inc;
    // Initialize the solver.

    ifail = 0;
    nag::ad::e05zk(ad_handle, "Initialize = E05UCF", iopts, liopts, opts, lopts,
                   ifail);

    // Solve the problem
    Integer iuser[1];
    
  auto objfun = [&](nag::ad::handle_t &     ad_handle,
                  Integer &               mode,
                  const Integer &         n,
                  const nagad_t1w_w_rtype *x,
                  nagad_t1w_w_rtype &     objf,
                  nagad_t1w_w_rtype *objgrd,
                  const Integer &         nstate)
                {
                  if (mode == 0 || mode == 2)
                  {
                    objf = 0.0;
                    for (int i = 0; i < n; i++)
                    {
                      if (x[i] >= 0.0)
                      {
                        objf += x[i] * sin(ruser[0] * sqrt(x[i]));
                      }
                      else
                      {
                        objf += x[i] * sin(ruser[0] * sqrt(-x[i]));
                      }
                    }
                  }
                  if (mode == 1 || mode == 2)
                  {
                    for (int i = 0; i < n; i++)
                    {
                      if (x[i] >= 0.0)
                      {
                        objgrd[i] = sin(ruser[0] * sqrt(x[i])) +
                                    0.5 * ruser[0] * sqrt(x[i]) * cos(ruser[0] * sqrt(x[i]));
                      }
                      else
                      {
                        objgrd[i] = sin(ruser[0] * sqrt(-x[i])) +
                                    0.5 * ruser[0] * sqrt(-x[i]) * cos(ruser[0] * sqrt(-x[i]));
                      }
                    }
                  }
                };
  auto confun = [&](nag::ad::handle_t &     ad_handle,
                  Integer &               mode,
                  const Integer &         ncnln,
                  const Integer &         n,
                  const Integer &         ldcj,
                  const Integer           needc[],
                  const nagad_t1w_w_rtype *x,
                  nagad_t1w_w_rtype *c,
                  nagad_t1w_w_rtype *cjac,
                  const Integer &         nstate)
                {
                  for (int k = 0; k < ncnln; ++k)
                  {
                    if (mode == 0 || mode == 2)
                    {
                      if (k == 0)
                      {
                        c[k] = ruser[1] * x[0] * x[0] - ruser[2] * x[1] * x[1] +
                              ruser[3] * x[0] * x[1];
                      }
                      else
                      {
                        c[k] = cos(x[0] * x[0] * ruser[4] * ruser[4] + x[1] * ruser[5]);
                      }
                    }
                    if (mode == 1 || mode == 2)
                    {
                      if (k == 0)
                      {
                        cjac[0]     = 2.0 * ruser[1] * x[0] + ruser[3] * x[1];
                        cjac[ncnln] = -2.0 * ruser[2] * x[1] + ruser[3] * x[0];
                      }
                      else
                      {
                        nagad_t1w_w_rtype theta;
                        theta           = x[0] * x[0] * ruser[4] * ruser[4] + x[1] * ruser[5];
                        cjac[1]         = -sin(theta) * 2.0 * x[0] * ruser[4] * ruser[4];
                        cjac[ncnln + 1] = -sin(theta) * ruser[5];
                      }
                    }
                  }
                };
  auto mystart = [&](nag::ad::handle_t &     ad_handle,
                             const Integer &         npts,
                             nagad_t1w_w_rtype *quas,
                             const Integer &         n,
                             const logical &         repeat,
                             const nagad_t1w_w_rtype *bl,
                             const nagad_t1w_w_rtype *bu,
                             Integer &               mode)
                {
                  if (repeat)
                  {
                    // Generate a uniform spread of points between bl and bu.
                    for (int i = 0; i < npts; i++)
                    {
                      double rq = ((double)(i - 1)) / ((double)(npts - 1));
                      for (int j = 0; j < n; j++)
                      {
                        quas[j + i * n] = bl[j] + rq * (bu[j] - bl[j]);
                      }
                    }
                  }
                  else
                  {
                    // Generate a non-repeatable spread of points between bl and bu.
                    const Integer genid = 2, subid = 53;
                    Integer       lstate = -1, sdum[1];
                    Integer       ifail  = 0;
                    g05kgf_(genid, subid, sdum, lstate, ifail);
                    Integer *state = 0;
                    double * rquas = 0;
                    state          = new Integer[lstate];
                    rquas          = new double[n];
                    ifail          = 0;
                    g05kgf_(genid, subid, state, lstate, ifail);
                    for (int i = 0; i < npts; i++)
                    {
                      ifail = 0;
                      g05saf_(n, state, rquas, ifail);
                      for (int j = 0; j < n; j++)
                      {
                        quas[j + n * i] = bl[j] + (bu[j] - bl[j]) * rquas[j];
                      }
                    }
                    delete[] state;
                    delete[] rquas;
                  }
                  // Set mode negative to terminate execution for any reason.
                  mode = 0;
                };
    ifail = -1;
    nag::ad::e05uc(ad_handle, n, nclin, ncnln, a, lda, bl, bu, confun, objfun,
                   npts, x, n, mystart, repeat, nb, objf, objgrd, n, iter, c,
                   ldc, cjac, ldcj, n, r, ldr, n, clamda, lb, istate, listat,
                   iopts, opts, info, ifail);

    dco::derivative(ruser[i]) = zero;
    dfdr[i]                   = dco::derivative(objf[0]);
  }

  // Primal results
  cout.setf(ios::scientific, ios::floatfield);
  cout.precision(4);
  Integer l;
  if (ifail == 0)
  {
    l = nb;
  }
  else if (ifail == 8)
  {
    l = info[nb - 1];
    cout.width(16);
    cout << iter[nb - 1] << " starting points converged" << endl;
  }
  else
  {
    goto END;
  }
  for (int i = 0; i < l; i++)
  {
    cout << "\n Solution number " << i + 1 << endl;
    cout << "\n Local minimization exited with code " << info[i] << endl;
    cout << "\n Varbl  Istate   Value         Lagr Mult" << endl;
    cout << endl;
    for (int j = 0; j < n; j++)
    {
      cout << " V ";
      cout.width(4);
      cout << j + 1;
      cout.width(4);
      cout << istate[j + i * lb];
      cout.width(12);
      cout << dco::value(x[j + i * n]);
      cout.width(12);
      cout << dco::value(clamda[j + i * lb]) << endl;
    }
    if (nclin > 0)
    {
      cout << "\n L con  Istate   Value         Lagr Mult" << endl;
      const nagad_t1w_w_rtype alpha = 1.0;
      const nagad_t1w_w_rtype beta  = 0.0;
      ifail                         = 0;
      nag::ad::f06pa(ad_handle, "N", nclin, n, alpha, a, lda, &x[n * i], 1,
                     beta, work, 1, ifail);

      cout << endl;
      for (int k = n; k < n + nclin; k++)
      {
        int j = k - n;
        cout << " L ";
        cout.width(4);
        cout << j + 1;
        cout.width(4);
        cout << istate[k + i * lb];
        cout.width(12);
        cout << dco::value(work[j]);
        cout.width(12);
        cout << dco::value(clamda[k + i * lb]) << endl;
      }
    }
    if (ncnln > 0)
    {
      cout << "\n N con  Istate   Value         Lagr Mult" << endl;
      cout << endl;
      for (int k = n + nclin; k < n + nclin + ncnln; k++)
      {
        int j = k - n - nclin;
        cout << " N ";
        cout.width(4);
        cout << j + 1;
        cout.width(4);
        cout << istate[k + i * lb];
        cout.width(12);
        cout << dco::value(c[j + i * ncnln]);
        cout.width(12);
        cout << dco::value(clamda[k + i * lb]) << endl;
      }
    }
    cout << "\n Final objective value = ";
    cout.width(12);
    cout << dco::value(objf[i]);
    cout << "\n QP multipliers" << endl;
    for (int k = 0; k < n + nclin + ncnln; k++)
    {
      cout.width(12);
      cout << dco::value(clamda[k + i * lb]) << endl;
    }
    cout << endl;
    if (l > 1)
    {
      cout << "\n ---------------------------------------------------------\n";
    }
  }

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

  // Get derivatives of objf w.r.t. ruser
  cout << "  derivatives of objf[0] w.r.t ruser[0:5]:\n";
  for (int i = 0; i < 6; i++)
  {
    cout.width(4);
    cout << i << " ";
    cout.width(12);
    cout << dfdr[i] << endl;
  }
END:

  delete[] a;
  delete[] bl;
  delete[] bu;
  delete[] c;
  delete[] cjac;
  delete[] clamda;
  delete[] r;
  delete[] x;
  delete[] objgrd;
  delete[] work;
  delete[] opts;
  delete[] objf;
  delete[] istate;
  delete[] iopts;
  delete[] info;
  delete[] iter;
  return exit_status;
}

static void NAG_CALL objfun(nag::ad::handle_t &     ad_handle,
                            Integer &               mode,
                            const Integer &         n,
                            const nagad_t1w_w_rtype x[],
                            nagad_t1w_w_rtype &     objf,
                            nagad_t1w_w_rtype       objgrd[],
                            const Integer &         nstate,
                            Integer                 iuser[],
                            nagad_t1w_w_rtype       ruser[])
{
  if (mode == 0 || mode == 2)
  {
    objf = 0.0;
    for (int i = 0; i < n; i++)
    {
      if (x[i] >= 0.0)
      {
        objf += x[i] * sin(ruser[0] * sqrt(x[i]));
      }
      else
      {
        objf += x[i] * sin(ruser[0] * sqrt(-x[i]));
      }
    }
  }
  if (mode == 1 || mode == 2)
  {
    for (int i = 0; i < n; i++)
    {
      if (x[i] >= 0.0)
      {
        objgrd[i] = sin(ruser[0] * sqrt(x[i])) +
                    0.5 * ruser[0] * sqrt(x[i]) * cos(ruser[0] * sqrt(x[i]));
      }
      else
      {
        objgrd[i] = sin(ruser[0] * sqrt(-x[i])) +
                    0.5 * ruser[0] * sqrt(-x[i]) * cos(ruser[0] * sqrt(-x[i]));
      }
    }
  }
  return;
}
static void NAG_CALL confun(nag::ad::handle_t &     ad_handle,
                            Integer &               mode,
                            const Integer &         ncnln,
                            const Integer &         n,
                            const Integer &         ldcj,
                            const Integer           needc[],
                            const nagad_t1w_w_rtype x[],
                            nagad_t1w_w_rtype       c[],
                            nagad_t1w_w_rtype       cjac[],
                            const Integer &         nstate,
                            Integer                 iuser[],
                            nagad_t1w_w_rtype       ruser[])
{
  for (int k = 0; k < ncnln; ++k)
  {
    if (mode == 0 || mode == 2)
    {
      if (k == 0)
      {
        c[k] = ruser[1] * x[0] * x[0] - ruser[2] * x[1] * x[1] +
               ruser[3] * x[0] * x[1];
      }
      else
      {
        c[k] = cos(x[0] * x[0] * ruser[4] * ruser[4] + x[1] * ruser[5]);
      }
    }
    if (mode == 1 || mode == 2)
    {
      if (k == 0)
      {
        cjac[0]     = 2.0 * ruser[1] * x[0] + ruser[3] * x[1];
        cjac[ncnln] = -2.0 * ruser[2] * x[1] + ruser[3] * x[0];
      }
      else
      {
        nagad_t1w_w_rtype theta;
        theta           = x[0] * x[0] * ruser[4] * ruser[4] + x[1] * ruser[5];
        cjac[1]         = -sin(theta) * 2.0 * x[0] * ruser[4] * ruser[4];
        cjac[ncnln + 1] = -sin(theta) * ruser[5];
      }
    }
  }
  return;
}
static void NAG_CALL mystart(nag::ad::handle_t &     ad_handle,
                             const Integer &         npts,
                             nagad_t1w_w_rtype       quas[],
                             const Integer &         n,
                             const logical &         repeat,
                             const nagad_t1w_w_rtype bl[],
                             const nagad_t1w_w_rtype bu[],
                             Integer                 iuser[],
                             nagad_t1w_w_rtype       ruser[],
                             Integer &               mode)
{
  if (repeat)
  {
    // Generate a uniform spread of points between bl and bu.
    for (int i = 0; i < npts; i++)
    {
      double rq = ((double)(i - 1)) / ((double)(npts - 1));
      for (int j = 0; j < n; j++)
      {
        quas[j + i * n] = bl[j] + rq * (bu[j] - bl[j]);
      }
    }
  }
  else
  {
    // Generate a non-repeatable spread of points between bl and bu.
    const Integer genid = 2, subid = 53;
    Integer       lstate = -1, sdum[1];
    Integer       ifail  = 0;
    g05kgf_(genid, subid, sdum, lstate, ifail);
    Integer *state = 0;
    double * rquas = 0;
    state          = new Integer[lstate];
    rquas          = new double[n];
    ifail          = 0;
    g05kgf_(genid, subid, state, lstate, ifail);
    for (int i = 0; i < npts; i++)
    {
      ifail = 0;
      g05saf_(n, state, rquas, ifail);
      for (int j = 0; j < n; j++)
      {
        quas[j + n * i] = bl[j] + (bu[j] - bl[j]) * rquas[j];
      }
    }
    delete[] state;
    delete[] rquas;
  }
  // Set mode negative to terminate execution for any reason.
  mode = 0;
  return;
}