NAG Library Manual, Mark 27.2
Interfaces:  FL   CL   CPP   AD 

NAG AD Library Introduction
Example description
/* E05UC_P0W_F C++ Header Example Program.
 *
 * Copyright 2021 Numerical Algorithms Group.
 * Mark 27.2, 2021.
 */

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

extern "C"
{
  static void NAG_CALL objfun(void *&        ad_handle,
                              Integer &      mode,
                              const Integer &n,
                              const double   x[],
                              double &       objf,
                              double         objgrd[],
                              const Integer &nstate,
                              Integer        iuser[],
                              double         ruser[]);
  static void NAG_CALL confun(void *&        ad_handle,
                              Integer &      mode,
                              const Integer &ncnln,
                              const Integer &n,
                              const Integer &ldcj,
                              const Integer  needc[],
                              const double   x[],
                              double         c[],
                              double         cjac[],
                              const Integer &nstate,
                              Integer        iuser[],
                              double         ruser[]);
  static void NAG_CALL mystart(void *&        ad_handle,
                               const Integer &npts,
                               double         quas[],
                               const Integer &n,
                               const logical &repeat,
                               const double   bl[],
                               const double   bu[],
                               Integer        iuser[],
                               double         ruser[],
                               Integer &      mode);
}

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

  cout << "E05UC_P0W_F C++ Header Example Program Results\n\n";

  Integer ifail     = 0;
  void *  ad_handle = 0;

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

  double 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;

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

  // Solve the problem
  Integer iuser[1];
  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, -1, iuser, -1, ruser, info, ifail);

  // 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 << x[j + i * n];
          cout.width(12);
          cout << clamda[j + i * lb] << endl;
        }
      if (nclin > 0)
        {
          cout << "\n L con  Istate   Value         Lagr Mult" << endl;
          const double alpha = 1.0;
          const double 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 << work[j];
              cout.width(12);
              cout << 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 << c[j + i * ncnln];
              cout.width(12);
              cout << clamda[k + i * lb] << endl;
            }
        }
      cout << "\n Final objective value = ";
      cout.width(12);
      cout << objf[i];
      cout << "\n QP multipliers" << endl;
      for (int k = 0; k < n + nclin + ncnln; k++)
        {
          cout.width(12);
          cout << clamda[k + i * lb] << endl;
        }
      cout << endl;
      if (l > 1)
        {
          cout
              << "\n ---------------------------------------------------------\n";
        }
    }

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(void *&        ad_handle,
                            Integer &      mode,
                            const Integer &n,
                            const double   x[],
                            double &       objf,
                            double         objgrd[],
                            const Integer &nstate,
                            Integer        iuser[],
                            double         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(void *&        ad_handle,
                            Integer &      mode,
                            const Integer &ncnln,
                            const Integer &n,
                            const Integer &ldcj,
                            const Integer  needc[],
                            const double   x[],
                            double         c[],
                            double         cjac[],
                            const Integer &nstate,
                            Integer        iuser[],
                            double         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
            {
              double 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(void *&        ad_handle,
                             const Integer &npts,
                             double         quas[],
                             const Integer &n,
                             const logical &repeat,
                             const double   bl[],
                             const double   bu[],
                             Integer        iuser[],
                             double         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;
}