/* nag_glopt_bnd_mcs_solve (e05jbc) Example Program.
*
* Copyright 2023 Numerical Algorithms Group.
*
* Mark 29.3, 2023.
*/
#include <math.h>
#include <nag.h>
#include <stdio.h>
#ifdef __cplusplus
extern "C" {
#endif
static void NAG_CALL objfun(Integer n, const double x[], double *f,
Integer nstate, Nag_Comm *comm, Integer *inform);
static void NAG_CALL monit(Integer n, Integer ncall, const double xbest[],
const Integer icount[], Integer sdlist,
const double list[], const Integer numpts[],
const Integer initpt[], Integer nbaskt,
const double xbaskt[], const double boxl[],
const double boxu[], Integer nstate, Nag_Comm *comm,
Integer *inform);
static void NAG_CALL output_current_box(const double boxl[],
const double boxu[]);
#ifdef __cplusplus
}
#endif
int main(void) {
/* Scalars */
double obj;
Integer exit_status = 0, i, n = 2, plot, sdlist;
Nag_BoundType boundenum;
Nag_MCSInitMethod initmethodenum;
/* Arrays */
static double ruser[2] = {-1.0, -1.0};
char bound[16], initmethod[18];
double *bl = 0, *bu = 0, *list = 0, *x = 0;
Integer *initpt = 0, *numpts = 0;
Integer iuser[1];
/* Nag Types */
Nag_E05State state;
NagError fail;
Nag_Comm comm;
INIT_FAIL(fail);
printf("nag_glopt_bnd_mcs_solve (e05jbc) Example Program Results\n");
/* For communication with user-supplied functions: */
comm.iuser = iuser;
comm.user = ruser;
/* Skip heading in data file */
scanf("%*[^\n] ");
/* Read sdlist from data file */
scanf("%" NAG_IFMT "%*[^\n] ", &sdlist);
if (n <= 0 || sdlist <= 0)
goto END;
if (!(bl = NAG_ALLOC(n, double)) || !(bu = NAG_ALLOC(n, double)) ||
!(list = NAG_ALLOC(n * sdlist, double)) || !(x = NAG_ALLOC(n, double)) ||
!(initpt = NAG_ALLOC(n, Integer)) || !(numpts = NAG_ALLOC(n, Integer))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
/* Read in bound (and bl and bu if necessary) */
scanf("%15s%*[^\n] ", bound);
/* nag_enum_name_to_value (x04nac).
* Converts NAG enum member name to value
*/
boundenum = (Nag_BoundType)nag_enum_name_to_value(bound);
if (boundenum == Nag_Bounds)
/* Read in the whole of each bound */
{
for (i = 0; i < n; ++i)
scanf("%lf", &bl[i]);
scanf("%*[^\n] ");
for (i = 0; i < n; ++i)
scanf("%lf", &bu[i]);
scanf("%*[^\n] ");
} else if (boundenum == Nag_BoundsEqual)
/* Bounds are uniform: read in only the first entry of each */
{
scanf("%lf%*[^\n] ", &bl[0]);
scanf("%lf%*[^\n] ", &bu[0]);
}
/* Read in initmethod */
scanf("%17s%*[^\n] ", initmethod);
/* nag_enum_name_to_value (x04nac).
* Converts NAG enum member name to value
*/
initmethodenum = (Nag_MCSInitMethod)nag_enum_name_to_value(initmethod);
/* Read in plot. Its value determines whether monit displays
* information on the current search box
*/
scanf("%" NAG_IFMT "%*[^\n] ", &plot);
/* Communicate plot through to monit */
iuser[0] = plot;
/* Call nag_glopt_bnd_mcs_init (e05jac) to initialize
* nag_glopt_bnd_mcs_solve (e05jbc). */
/* Its first argument is a legacy argument and has no significance. */
nag_glopt_bnd_mcs_init(0, &state, &fail);
if (fail.code != NE_NOERROR) {
printf("Initialization of nag_glopt_bnd_mcs_solve (e05jbc) failed.\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
/* Solve the problem. */
/* nag_glopt_bnd_mcs_solve (e05jbc).
* Global optimization by multilevel coordinate search, simple bounds.
*/
nag_glopt_bnd_mcs_solve(n, objfun, boundenum, initmethodenum, bl, bu, sdlist,
list, numpts, initpt, monit, x, &obj, &state, &comm,
&fail);
if (fail.code != NE_NOERROR) {
printf("Error message from nag_glopt_bnd_mcs_solve (e05jbc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
printf("Final objective value = %11.5f\n", obj);
printf("Global optimum x = ");
for (i = 0; i < n; ++i)
printf("%9.5f", x[i]);
printf("\n");
END:
NAG_FREE(bl);
NAG_FREE(bu);
NAG_FREE(list);
NAG_FREE(x);
NAG_FREE(initpt);
NAG_FREE(numpts);
return exit_status;
}
static void NAG_CALL objfun(Integer n, const double x[], double *f,
Integer nstate, Nag_Comm *comm, Integer *inform) {
/* Routine to evaluate objective function */
if (comm->user[0] == -1.0) {
printf("(User-supplied callback objfun, first invocation.)\n");
comm->user[0] = 0.0;
}
/* This is a two-dimensional objective function.
* As an example of using the inform mechanism,
* terminate if any other problem size is supplied.
*/
if (n != 2) {
*inform = -1;
return;
}
*inform = 0;
if (*inform >= 0)
/* Here we're prepared to evaluate objfun at the current x */
{
if (nstate == 1)
/* This is the first call to objfun */
{
printf("\n(objfun was just called for the first time)\n");
}
*f = (3.0 * pow((1.0 - x[0]), 2) * exp(-pow(x[0], 2) - pow((x[1] + 1), 2)) -
(10.0 * (x[0] / 5.0 - pow(x[0], 3) - pow(x[1], 5)) *
exp(-pow(x[0], 2) - pow(x[1], 2))) -
1.0 / 3.0 * exp(-pow((x[0] + 1.0), 2) - pow(x[1], 2)));
}
}
static void NAG_CALL monit(Integer n, Integer ncall, const double xbest[],
const Integer icount[], Integer sdlist,
const double list[], const Integer numpts[],
const Integer initpt[], Integer nbaskt,
const double xbaskt[], const double boxl[],
const double boxu[], Integer nstate, Nag_Comm *comm,
Integer *inform) {
/* Scalars */
Integer i, j;
Integer plot;
#define LIST(I, J) list[(I - 1) * sdlist + (J - 1)]
#define XBASKT(I, J) xbaskt[(I - 1) * nbaskt + (J - 1)]
if (comm->user[1] == -1.0) {
printf("(User-supplied callback monit, first invocation.)\n");
comm->user[1] = 0.0;
}
*inform = 0;
if (*inform >= 0)
/* We are going to allow the iterations to continue */
{
/* Extract plot from the communication structure */
plot = comm->iuser[0];
if (nstate == 0 || nstate == 1)
/* When nstate == 1, monit is called for the first time.
* When nstate == 0, monit is called for the first AND last time.
* Display a welcome message */
{
printf("\n*** Begin monitoring information ***\n\n");
printf("Values controlling initial splitting of a box:\n");
for (i = 1; i <= n; ++i) {
printf("**\n");
printf("In dimension %5" NAG_IFMT "\n", i);
printf("Extent of initialization list in this dimension ="
"%5" NAG_IFMT "\n",
numpts[i - 1]);
printf("Initialization points in this dimension:\n");
printf("LIST(i, 1:numpts[i - 1]) =");
for (j = 1; j <= numpts[i - 1]; ++j)
printf("%9.5f", LIST(i, j));
printf("\n");
printf("Initial point in this dimension: LIST(i,%5" NAG_IFMT ")\n",
initpt[i - 1]);
}
if (plot != 0 && n == 2)
printf("<Begin displaying search boxes>\n\n");
}
if (plot != 0 && n == 2) {
/* Display the coordinates of the edges of the current search box */
output_current_box(boxl, boxu);
}
if (nstate <= 0)
/* monit is called for the last time */
{
if (plot != 0 && n == 2)
printf("<End displaying search boxes>\n\n");
printf("Total sub-boxes = %5" NAG_IFMT "\n", icount[0]);
printf("Total function evaluations (rounded to nearest 20) = "
"%5" NAG_IFMT "\n",
20 * ((ncall + 10) / 20));
printf("Total function evaluations used in local search (rounded\n"
" to nearest 15) = %5" NAG_IFMT "\n",
15 * ((icount[1] + 7) / 15));
printf("Total points used in local search = %5" NAG_IFMT "\n", icount[2]);
printf("Total sweeps through levels = %5" NAG_IFMT "\n", icount[3]);
printf("Total splits by init. list = %5" NAG_IFMT "\n", icount[4]);
printf("Lowest level with nonsplit boxes = %5" NAG_IFMT "\n", icount[5]);
printf("Number of candidate minima in the 'shopping basket'"
" = %5" NAG_IFMT "\n",
nbaskt);
printf("Shopping basket:\n");
for (i = 1; i <= n; ++i) {
printf("xbaskt(%3" NAG_IFMT ",:) =", i);
for (j = 1; j <= nbaskt; ++j)
printf("%9.5f", XBASKT(i, j));
printf("\n");
}
printf("Best point:\n");
printf("xbest =");
for (i = 0; i < n; ++i)
printf("%9.5f", xbest[i]);
printf("\n");
printf("\n*** End monitoring information ***\n\n");
}
}
}
static void NAG_CALL output_current_box(const double boxl[],
const double boxu[]) {
printf("%20.15f %20.15f\n", boxl[0], boxl[1]);
printf("%20.15f %20.15f\n\n", boxl[0], boxu[1]);
printf("%20.15f %20.15f\n", boxl[0], boxl[1]);
printf("%20.15f %20.15f\n\n", boxu[0], boxl[1]);
printf("%20.15f %20.15f\n", boxl[0], boxu[1]);
printf("%20.15f %20.15f\n\n", boxu[0], boxu[1]);
printf("%20.15f %20.15f\n", boxu[0], boxl[1]);
printf("%20.15f %20.15f\n\n", boxu[0], boxu[1]);
}