/* nag_opt_bounds_2nd_deriv(e04lbc) Example Program.
 *
 * Copyright 1998 Numerical Algorithms Group.
 *
 * Mark 5, 1998.
 *
 * Mark 6 revised, 2000.
 * Mark 7 revised, 2001.
 *
 */

#include <nag.h>
#include <stdio.h>
#include <nag_stdlib.h>
#include <math.h>
#include <nage04.h>

#define NMAX 4

#ifdef __cplusplus
extern "C" {
#endif
static void funct(Integer n,  double xc[], double *fc, double gc[],
                  Nag_Comm *comm);
static void hess(Integer n,  double xc[], double fhesl[],
                 double fhesd[], Nag_Comm *comm);
#ifdef __cplusplus
}
#endif
static void ex1(void);
static void ex2(void);

static void funct(Integer n, double xc[], double *fc, double gc[],
           Nag_Comm *comm)
{
  /* Function to evaluate objective function and its 1st derivatives. */
  double term1, term1_sq;
  double term2, term2_sq;
  double term3, term3_sq, term3_cu;
  double term4, term4_sq, term4_cu;

  term1 = xc[0] + 10.0*xc[1];
  term1_sq = term1*term1;

  term2 = xc[2] - xc[3];
  term2_sq = term2*term2;

  term3 = xc[1] - 2.0*xc[2];
  term3_sq = term3*term3;
  term3_cu = term3*term3_sq;

  term4 = xc[0] - xc[3];
  term4_sq = term4*term4;
  term4_cu = term4_sq*term4;

  *fc = term1_sq + 5.0*term2_sq
    + term3_sq*term3_sq + 10.0*term4_sq*term4_sq;

  gc[0] =   2.0*term1 + 40.0*term4_cu;
  gc[1] =  20.0*term1 +  4.0*term3_cu;
  gc[2] =  10.0*term2 -  8.0*term3_cu;
  gc[3] = -10.0*term2 - 40.0*term4_cu;
}
/* funct */

static void hess(Integer n, double xc[], double fhesl[],
          double fhesd[], Nag_Comm *comm)
{
  /* Routine to evaluate 2nd derivatives */
  double term3_sq;
  double term4_sq;

  term3_sq = (xc[1] - 2.0*xc[2])*(xc[1] - 2.0*xc[2]);
  term4_sq = (xc[0] - xc[3])*(xc[0] - xc[3]);

  fhesd[0] = 2.0 + 120.0*term4_sq;
  fhesd[1] = 200.0 + 12.0*term3_sq;
  fhesd[2] = 10.0 + 48.0*term3_sq;
  fhesd[3] = 10.0 + 120.0*term4_sq;

  fhesl[0] = 20.0;
  fhesl[1] = 0.0;
  fhesl[2] = -24.0*term3_sq;
  fhesl[3] = -120.0*term4_sq;
  fhesl[4] = 0.0;
  fhesl[5] = -10.0;
}
/* hess */

int main(void)
{
  /* Two examples are called, ex1() which uses the
   * default settings to solve the problem and
   * ex2() which solves the same problem with
   * some optional parameters set by the user.
   */

  Vprintf("e04lbc Example Program Results.\n");
  ex1();
  ex2();
  return EXIT_SUCCESS;
}

static void ex1(void)
{
  double x[NMAX];
  double bl[NMAX], bu[NMAX], g[NMAX];
  double f;

  Integer n = NMAX;

  static NagError fail;

  /* Function Body */

  fail.print = TRUE;
  Vprintf("\ne04lbc example 1: no option setting.\n");

  x[0] = 1.46;
  x[1] = -0.82;
  x[2] = 0.57;
  x[3] = 1.21;

  bl[0] = 1.0;
  bu[0] = 3.0;
  bl[1] = -2.0;
  bu[1] = 0.0;

  /* x[2] is not bounded, so we set bl[2] to a large negative
   *  number and bu[2] to a large positive number
   */
  bl[2] = -1e6;
  bu[2] = 1e6;
  bl[3] = 1.0;
  bu[3] = 3.0;

  /* Set up starting point */
  x[0] = 3.0;
  x[1] = -1.0;
  x[2] = 0.0;
  x[3] = 1.0;

  e04lbc(n, funct, hess, Nag_Bounds, bl, bu, x, &f, g,
         E04_DEFAULT, NAGCOMM_NULL, &fail);
}
/* ex1 */

static void ex2(void)
{
  double x[NMAX];
  double bl[NMAX], bu[NMAX], g[NMAX];
  double f;

  Integer n = NMAX;

  Nag_Comm comm;
  Nag_E04_Opt options;
  static NagError fail, fail2;
  Boolean print;

  /* Function Body */

  fail.print = TRUE;
  Vprintf("\n\ne04lbc example 2: using option setting.\n");

  x[0] = 1.46;
  x[1] = -0.82;
  x[2] = 0.57;
  x[3] = 1.21;

  bl[0] = 1.0;
  bu[0] = 3.0;
  bl[1] = -2.0;
  bu[1] = 0.0;

  /* x[2] is not bounded, so we set bl[2] to a large negative
   *  number and bu[2] to a large positive number
   */
  bl[2] = -1e6;
  bu[2] = 1e6;
  bl[3] = 1.0;
  bu[3] = 3.0;

  /* Set up starting point */
  x[0] = 3.0;
  x[1] = -1.0;
  x[2] = 0.0;
  x[3] = 1.0;

  print = TRUE;
  e04xxc(&options);
  e04xyc("e04lbc", "stdin", &options, print, "stdout", &fail);
  e04lbc(n, funct, hess, Nag_Bounds, bl, bu, x, &f, g,
         &options, &comm, &fail);

  /* Free memory allocated by e04kbc to pointers hesd, hesl and state */
  fail2.print = TRUE;
  e04xzc(&options, "all", &fail2);
  if ((fail.code != NE_NOERROR && fail.code != NW_COND_MIN) ||
      fail2.code != NE_NOERROR) exit(EXIT_FAILURE);
} /* ex2 */