/* nag_glopt_bnd_pso (e05sac) Example Program.
 *
 * Copyright 2017 Numerical Algorithms Group.
 *
 * Mark 26.2, 2017.
 */
#include <math.h>
#include <nag.h>
#include <nag_stdlib.h>
#include <nage05.h>
#include <nagx02.h>
#include <nagx04.h>

#ifdef __cplusplus
extern "C"
{
#endif
  static void NAG_CALL objfun_schwefel(Integer *mode, Integer ndim,
                                       const double x[], double *objf,
                                       double vecout[], Integer nstate,
                                       Nag_Comm *comm);
  static void NAG_CALL monmod(Integer ndim, Integer npar, double x[],
                              const double xb[], double fb,
                              const double xbest[], const double fbest[],
                              const Integer itt[], Nag_Comm *comm,
                              Integer *inform);
#ifdef __cplusplus
}
#endif

static void display_result(Integer ndim, const double xb[], const double
                           x_target[], double fb, double f_target,
                           const Integer itt[], Integer inform);
static void display_option(const char *optstr, Nag_VariableType optype,
                           Integer ivalue, double rvalue, const char *cvalue);
static void get_known_solution(Integer ndim, double x_target[],
                               double *f_target);

/* Global constants - set the behaviour of the monitoring function.*/
static const Integer detail_level = 0;
static const Integer report_freq = 100;

int main(void)
{
  /* This example program demonstrates how to use
   * nag_glopt_bnd_pso (e05sac) in standard execution, and with a
   * selection of coupled local minimizers.
   * The non-default option 'Repeatability = On' is used here, giving
   * repeatable results.
   */
  /* Scalars */
  Integer ndim = 2, npar = 5;
  Integer exit_status = 0, lcvalue = 17;
  Integer liopts = 100, lopts = 100;
  double fb, f_target, rvalue;
  Integer i, inform, ivalue;
  /* Arrays */
  static double ruser[2] = { -1.0, -1.0 };
  char cvalue[17], optstr[81];
  double *bl = 0, *bu = 0, opts[100], *xb = 0, *x_target = 0;
  Integer iopts[100], itt[6];
  /* Nag Types */
  Nag_VariableType optype;
  NagError fail;
  Nag_Comm comm;

  /* Print advisory information. */
  printf("nag_glopt_bnd_pso (e05sac) Example Program Results\n\n");

  /* For communication with user-supplied functions: */
  comm.user = ruser;

  printf("Minimization of the Schwefel function.\n\n");

  /* Allocate memory. */
  if (!(bl = NAG_ALLOC(ndim, double)) || !(bu = NAG_ALLOC(ndim, double)) ||
      !(xb = NAG_ALLOC(ndim, double))
      || !(x_target = NAG_ALLOC(ndim, double)))
  {
    printf("Allocation failure\n");
    exit_status = -1;
    goto END;
  }

  /* Store the known solution of the problem for a comparison. */
  get_known_solution(ndim, x_target, &f_target);

  /* Set box bounds for problem. */
  for (i = 0; i < ndim; i++) {
    bl[i] = -500.0;
    bu[i] = 500.0;
  }

  /* Initialize fail structures. */
  INIT_FAIL(fail);

  /* Initialize the option arrays for nag_glopt_bnd_pso (e05sac)
   * using nag_glopt_opt_set (e05zkc).
   */
  nag_glopt_opt_set("Initialize = e05sac", iopts, liopts, opts, lopts, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_glopt_opt_set (e05zkc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* Query some default option values. */
  printf("  Default Option Queries:\n\n");
  /* nag_glopt_opt_get (e05zlc).
   * Option getting routine for nag_glopt_bnd_pso (e05sac).
   */
  nag_glopt_opt_get("Boundary", &ivalue, &rvalue, cvalue, lcvalue, &optype,
                    iopts, opts, &fail);
  if (fail.code == NE_NOERROR) {
    display_option("Boundary", optype, ivalue, rvalue, cvalue);
    nag_glopt_opt_get("Maximum Iterations Completed", &ivalue, &rvalue,
                      cvalue, lcvalue, &optype, iopts, opts, &fail);
  }
  if (fail.code == NE_NOERROR) {
    display_option("Maximum Iterations Completed", optype, ivalue, rvalue,
                   cvalue);
    nag_glopt_opt_get("Distance Tolerance", &ivalue, &rvalue, cvalue, lcvalue,
                      &optype, iopts, opts, &fail);
  }
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_glopt_opt_set (e05zkc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }
  display_option("Distance Tolerance", optype, ivalue, rvalue, cvalue);

  /* ------------------------------------------------------------------ */

  printf("\n1. Solution without using coupled local minimizer.\n\n");

  /* Set various options to non-default values if required. */
  nag_glopt_opt_set("Repeatability = On", iopts, liopts, opts, lopts, &fail);
  if (fail.code == NE_NOERROR)
    nag_glopt_opt_set("Verify Gradients = Off", iopts, liopts, opts, lopts,
                      &fail);
  if (fail.code == NE_NOERROR)
    nag_glopt_opt_set("Boundary = Hyperspherical", iopts, liopts, opts, lopts,
                      &fail);
  if (fail.code == NE_NOERROR)
    nag_glopt_opt_set("Maximum iterations static = 150", iopts, liopts, opts,
                      lopts, &fail);
  if (fail.code == NE_NOERROR)
    nag_glopt_opt_set("Repulsion Initialize = 30", iopts, liopts, opts, lopts,
                      &fail);
  if (fail.code == NE_NOERROR)
    nag_glopt_opt_set("Repulsion Finalize = 30", iopts, liopts, opts, lopts,
                      &fail);

  if (fail.code != NE_NOERROR) {
    printf("Error from nag_glopt_opt_set (e05zkc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* nag_glopt_bnd_pso (e05sac).
   * Global optimization using particle swarm algorithm (PSO),
   * bound constraints only.
   */
  nag_glopt_bnd_pso(ndim, npar, xb, &fb, bl, bu, objfun_schwefel, monmod,
                    iopts, opts, &comm, itt, &inform, &fail);
  /* It is essential to test fail.code on exit. */
  switch (fail.code) {
  case NE_NOERROR:
  case NW_FAST_SOLUTION:
  case NW_SOLUTION_NOT_GUARANTEED:
    /* No errors, best found solution at xb returned in fb. */
    display_result(ndim, xb, x_target, fb, f_target, itt, inform);
    break;
  case NE_USER_STOP:
    /* Exit flag set in objfun or monmod and returned in inform. */
    display_result(ndim, xb, x_target, fb, f_target, itt, inform);
    break;
  default: /* An error was detected. */
    exit_status = 1;
    printf("Error from nag_glopt_bnd_pso (e05sac)\n%s\n", fail.message);
    goto END;
  }

  /* ------------------------------------------------------------------ */

  printf("2. Solution using coupled local minimizer "
         "nag_opt_simplex_easy (e04cbc).\n\n");

  /* Initialize fail structures. */
  INIT_FAIL(fail);

  /* Set an objective target. */
  sprintf(optstr, "Target Objective Value = %32.16e", f_target);
  nag_glopt_opt_set(optstr, iopts, liopts, opts, lopts, &fail);
  if (fail.code == NE_NOERROR)
    nag_glopt_opt_set("Target Objective Tolerance = 1.0e-5", iopts, liopts,
                      opts, lopts, &fail);
  if (fail.code == NE_NOERROR)
    nag_glopt_opt_set("Target Objective Safeguard = 1.0e-8", iopts, liopts,
                      opts, lopts, &fail);

  /* Set the local minimizer to be nag_opt_simplex_easy (e04cbc)
   * and set corresponding options.
   */
  if (fail.code == NE_NOERROR)
    nag_glopt_opt_set("Local Minimizer = e04cbc", iopts, liopts, opts, lopts,
                      &fail);
  if (fail.code == NE_NOERROR)
    nag_glopt_opt_set("Local Interior Iterations = 10", iopts, liopts, opts,
                      lopts, &fail);
  if (fail.code == NE_NOERROR)
    nag_glopt_opt_set("Local Exterior Iterations = 20", iopts, liopts, opts,
                      lopts, &fail);
  if (fail.code == NE_NOERROR)
    nag_glopt_opt_set("Local Interior Tolerance = 1.0e-4", iopts, liopts,
                      opts, lopts, &fail);
  if (fail.code == NE_NOERROR)
    nag_glopt_opt_set("Local Exterior Tolerance = 1.0e-4", iopts, liopts,
                      opts, lopts, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_glopt_opt_set (e05zkc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* Search for the global optimum. */
  nag_glopt_bnd_pso(ndim, npar, xb, &fb, bl, bu, objfun_schwefel, monmod,
                    iopts, opts, &comm, itt, &inform, &fail);
  /* It is essential to test fail.code on exit. */
  switch (fail.code) {
  case NE_NOERROR:
  case NW_FAST_SOLUTION:
  case NW_SOLUTION_NOT_GUARANTEED:
    /* No errors, best found solution at xb returned in fb. */
    display_result(ndim, xb, x_target, fb, f_target, itt, inform);
    break;
  case NE_USER_STOP:
    /* Exit flag set in objfun or monmod and returned in inform. */
    display_result(ndim, xb, x_target, fb, f_target, itt, inform);
    break;
  default: /* An error was detected. */
    exit_status = 1;
    printf("Error from nag_glopt_bnd_pso (e05sac)\n%s\n", fail.message);
    goto END;
  }

  /* ----------------------------------------------------------------- */

  printf("3. Solution using coupled local minimizer "
         "nag_opt_conj_grad (e04dgc).\n\n");

  /* Initialize fail structures. */
  INIT_FAIL(fail);

  /* set the local minimizer to be nag_opt_conj_grad (e04dgc)
   * and set corresponding options.
   */
  nag_glopt_opt_set("Local Minimizer = e04dgc", iopts, liopts, opts, lopts,
                    &fail);
  if (fail.code == NE_NOERROR)
    nag_glopt_opt_set("Local Interior Iterations = 5", iopts, liopts, opts,
                      lopts, &fail);
  if (fail.code == NE_NOERROR)
    nag_glopt_opt_set("Local Exterior Iterations = 20", iopts, liopts, opts,
                      lopts, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_glopt_opt_set (e05zkc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* Search for the global optimum. */
  nag_glopt_bnd_pso(ndim, npar, xb, &fb, bl, bu, objfun_schwefel, monmod,
                    iopts, opts, &comm, itt, &inform, &fail);
  /* It is essential to test fail.code on exit. */
  switch (fail.code) {
  case NE_NOERROR:
  case NW_FAST_SOLUTION:
  case NW_SOLUTION_NOT_GUARANTEED:
    /* No errors, best found solution at xb returned in fb. */
    display_result(ndim, xb, x_target, fb, f_target, itt, inform);
    break;
  case NE_USER_STOP:
    /* Exit flag set in objfun or monmod and returned in inform. */
    display_result(ndim, xb, x_target, fb, f_target, itt, inform);
    break;
  default: /* An error was detected. */
    exit_status = 1;
    printf("Error from nag_glopt_bnd_pso (e05sac)\n%s\n", fail.message);
    goto END;
  }

END:
  /* Clean up memory. */
  NAG_FREE(bl);
  NAG_FREE(bu);
  NAG_FREE(xb);
  NAG_FREE(x_target);

  return exit_status;
}

static void NAG_CALL objfun_schwefel(Integer *mode, Integer ndim,
                                     const double x[], double *objf,
                                     double vecout[], Integer nstate,
                                     Nag_Comm *comm)
{
  /* Objective function routine returning the schwefel function and
   * its gradient.
   */
  Nag_Boolean evalobjf, evalobjg;
  Integer i;
  if (comm->user[0] == -1.0) {
    printf("(User-supplied callback objfun_schwefel, first invocation.)\n");
    comm->user[0] = 0.0;
  }
  /* Test nstate to indicate what stage of computation has been reached. */
  switch (nstate) {
  case 2:
    /* objfun is called for the very first time. */
    break;
  case 1:
    /* objfun is called on entry to a NAG local minimizer. */
    break;
  default: /* This will be the normal value of nstate. */
    ;
  }
  /* Test mode to determine whether to calculate objf and/or objgrd. */
  evalobjf = Nag_FALSE;
  evalobjg = Nag_FALSE;
  switch (*mode) {
  case 0:
  case 5:
    /* Only the value of the objective function is needed. */
    evalobjf = Nag_TRUE;
    break;
  case 1:
  case 6:
    /* Only the values of the ndim gradients are required. */
    evalobjg = Nag_TRUE;
    break;
  case 2:
  case 7:
    /* Both the objective function and the ndim gradients are required. */
    evalobjf = Nag_TRUE;
    evalobjg = Nag_TRUE;
  }
  if (evalobjf) {
    /* Evaluate the objective function. */
    *objf = 0.0;
    for (i = 0; i < ndim; i++)
      *objf += x[i] * sin(sqrt(fabs(x[i])));
  }
  if (evalobjg) {
    /* Calculate the gradient of the objective function,
     * and return the result in vecout.
     */
    for (i = 0; i < ndim; i++) {
      vecout[i] = sqrt(fabs(x[i]));
      vecout[i] = sin(vecout[i]) + 0.5 * vecout[i] * cos(vecout[i]);
    }
  }
}

static void NAG_CALL monmod(Integer ndim, Integer npar, double x[],
                            const double xb[], double fb,
                            const double xbest[], const double fbest[],
                            const Integer itt[], Nag_Comm *comm,
                            Integer *inform)
{
  Integer i, j;
#define X(J, I) x[(J-1)*ndim + (I-1)]
#define XBEST(J, I) xbest[(J-1)*ndim + (I-1)]
  if (comm->user[1] == -1.0) {
    printf("(User-supplied callback monmod, first invocation.)\n");
    comm->user[1] = 0.0;
  }
  if (detail_level) {
    /* Report on the first iteration, and every report_freq iterations. */
    if (itt[0] == 1 || itt[0] % report_freq == 0) {
      printf("* Locations of particles\n");
      for (j = 1; j <= npar; j++) {
        printf("  * Particle %2" NAG_IFMT "\n", j);
        for (i = 1; i <= ndim; i++)
          printf("    %2" NAG_IFMT "  %13.5f\n", i, X(j, i));
      }
      printf("* Cognitive memory\n");
      for (j = 1; j <= npar; j++) {
        printf("  * Particle %2" NAG_IFMT "\n", j);
        printf("    * Best position\n");
        for (i = 1; i <= ndim; i++)
          printf("      %2" NAG_IFMT "  %13.5f\n", i, XBEST(j, i));
        printf("    * Function value at best position\n");
        printf("      %13.5f\n", fbest[j - 1]);
      }
      printf("* Current global optimum candidate\n");
      for (i = 1; i <= ndim; i++)
        printf("  %2" NAG_IFMT "  %13.5f\n", i, xb[i - 1]);
      printf("* Current global optimum value\n");
      printf("     %13.5f\n\n", fb);
    }
  }
  /* If required set *inform<0 to force exit. */
  *inform = 0;
#undef XBEST
#undef X
}

static void display_option(const char *optstr, Nag_VariableType optype,
                           Integer ivalue, double rvalue, const char *cvalue)
{
  /* Subroutine to query optype and print the appropriate option values. */
  switch (optype) {
  case Nag_Integer:
    printf("%-38s: %13" NAG_IFMT "\n", optstr, ivalue);
    break;
  case Nag_Real:
    printf("%-38s: %13.4f\n", optstr, rvalue);
    break;
  case Nag_Character:
    printf("%-38s: %13s\n", optstr, cvalue);
    break;
  case Nag_Integer_Additional:
    printf("%-38s: %13" NAG_IFMT " %16s\n", optstr, ivalue, cvalue);
    break;
  case Nag_Real_Additional:
    printf("%-38s: %13.4f %16s\n", optstr, rvalue, cvalue);
    break;
  default:;
  }
}

static void display_result(Integer ndim, const double xb[], const double
                           x_target[], double fb, double f_target,
                           const Integer itt[], Integer inform)
{
  /* Display final results in comparison to known global optimum. */
  Integer i;

  /* Display final counters. */
  printf(" Algorithm Statistics\n");
  printf(" --------------------\n");
  printf("%-38s: %13" NAG_IFMT "\n", "Total complete iterations", itt[0]);
  printf("%-38s: %13" NAG_IFMT "\n", "Complete iterations since improvement",
         itt[1]);
  printf("%-38s: %13" NAG_IFMT "\n", "Total particles converged to xb",
         itt[2]);
  printf("%-38s: %13" NAG_IFMT "\n", "Total improvements to global optimum",
         itt[3]);
  printf("%-38s: %13" NAG_IFMT "\n", "Total function evaluations", itt[4]);
  printf("%-38s: %13" NAG_IFMT "\n\n", "Total particles re-initialized",
         itt[5]);
  /* Display why finalization occurred. */
  switch (inform) {
  case 1:
    printf("Solution Status : Target value achieved\n");
    break;
  case 2:
    printf("Solution Status : Minimum swarm standard deviation obtained\n");
    break;
  case 3:
    printf("Solution Status : Sufficient number of particles converged\n");
    break;
  case 4:
    printf("Solution Status : Maximum static iterations attained\n");
    break;
  case 5:
    printf("Solution Status : Maximum complete iterations attained\n");
    break;
  case 6:
    printf("Solution Status : Maximum function evaluations exceeded\n");
    break;
  default:
    if (inform < 0)
      printf("Solution Status : User termination, inform = %16" NAG_IFMT "\n",
             inform);
    else
      printf("Solution Status : Termination, an error has been detected\n");
    break;
  }
  /* Display final objective value and location. */
  printf("  Known objective optimum             : %13.5f\n", f_target);
  printf("  Achieved objective value            : %13.5f\n\n", fb);

  printf("  Comparison between the known optimum and the achieved solution.\n");
  printf("          x_target            xb\n");
  for (i = 0; i < ndim; i++)
    printf("  %2" NAG_IFMT "  %12.2f  %12.2f\n", i + 1, x_target[i], xb[i]);

  printf("\n");
}

static void get_known_solution(Integer ndim, double x_target[],
                               double *f_target)
{
  /* Fill in the known solution of multidimensional Schwefel's function. */
  Integer i;

  if (f_target && x_target && ndim > 0) {
    *f_target = -418.9828872724337 * ndim;
    for (i = 0; i < ndim; i++)
      x_target[i] = -420.9687463599820;
  }
}