非線形最小二乗問題

nag_opt_nlin_lsq (e04unc) Example Program Data

Values of m and n
  44  2

Values of nclin and ncnln
  1   1

Linear constraint matrix A
  1.0   1.0

Objective vector y
  0.49  0.49  0.48  0.47  0.48  0.47  0.46  0.46  0.45  0.43  0.45
  0.43  0.43  0.44  0.43  0.43  0.46  0.45  0.42  0.42  0.43  0.41
  0.41  0.40  0.42  0.40  0.40  0.41  0.40  0.41  0.41  0.40  0.40
  0.40  0.38  0.41  0.40  0.40  0.41  0.38  0.40  0.40  0.39  0.39

Lower bounds
  0.4      -4.0      1.0      0.0

Upper bounds
  1.0e+25   1.0e+25  1.0e+25  1.0e+25

Initial estimate of x
  0.4   0.0

nag_opt_nlin_lsq (e04unc) Example Program Results

Parameters to e04unc
--------------------

Number of variables...........   2
Linear constraints............   1    Nonlinear constraints.........   1

start...................  Nag_Cold
step_limit..............  2.00e+00    machine precision.......  1.11e-16
lin_feas_tol............  1.05e-08    nonlin_feas_tol.........  1.05e-08
optim_tol...............  3.26e-12    linesearch_tol..........  9.00e-01
crash_tol...............  1.00e-02    f_prec..................  4.37e-15
inf_bound...............  1.00e+20    inf_step................  1.00e+20
max_iter................        50    minor_max_iter..........        50
hessian................. Nag_FALSE    h_reset_freq............         2
h_unit_init............. Nag_FALSE
f_diff_int.............. Automatic    c_diff_int.............. Automatic
obj_deriv...............  Nag_TRUE    con_deriv...............  Nag_TRUE
verify_grad....... Nag_SimpleCheck    print_deriv............ Nag_D_Full
print_level......... Nag_Soln_Iter    minor_print_level..... Nag_NoPrint
outfile.................    stdout


Verification of the objective gradients.
----------------------------------------

All objective gradient elements have been set.

Simple Check:

The Jacobian seems to be ok.

The largest relative error was 1.04e-08 in subfunction 3  


Verification of the constraint gradients.
-----------------------------------------

All constraint gradient elements have been set.

Simple Check:

The Jacobian seems to be ok.

The largest relative error was 1.89e-08 in constraint 1  

   Maj  Mnr    Step   Merit function  Violtn  Norm Gz  Cond Hz
    0    2  0.0e+00    2.224070e-02  3.6e-02  8.5e-02  1.0e+00       
    1    1  1.0e+00    1.455402e-02  9.8e-03  1.5e-03  1.0e+00    
    2    1  1.0e+00    1.436491e-02  7.2e-04  4.9e-03  1.0e+00    
    3    1  1.0e+00    1.427013e-02  9.2e-06  2.9e-03  1.0e+00    
    4    1  1.0e+00    1.422989e-02  3.6e-05  1.6e-04  1.0e+00    
    5    1  1.0e+00    1.422983e-02  6.4e-08  5.4e-07  1.0e+00    
    6    1  1.0e+00    1.422983e-02  9.8e-13  3.4e-09  1.0e+00    
Exit from NP problem after 6 major iterations, 8 minor iterations.


Varbl State     Value      Lower Bound   Upper Bound    Lagr Mult    Residual
V   1   FR   4.19953e-01   4.00000e-01      None       0.0000e+00   1.9953e-02
V   2   FR   1.28485e+00  -4.00000e+00      None       0.0000e+00   5.2848e+00


L Con State     Value      Lower Bound   Upper Bound    Lagr Mult    Residual
L   1   FR   1.70480e+00   1.00000e+00      None       0.0000e+00   7.0480e-01


N Con State     Value      Lower Bound   Upper Bound    Lagr Mult    Residual
N   1   LL  -9.76885e-13   0.00000e+00      None       3.3358e-02  -9.7689e-13

Optimal solution found.

Final objective value =    1.4229835e-02

/* nag_opt_nlin_lsq (e04unc) Example Program.
 *
 * CLL6I261D/CLL6I261DL Version.
 *
 * Copyright 2017 Numerical Algorithms Group.
 *
 * Mark 26.1, 2017.
 *
 *
 */

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

#ifdef __cplusplus
extern "C"
{
#endif
  static void nAG_CALL objfun(Integer m, Integer n, const double x[],
                              double f[], double fjac[], Integer tdfjac,
                              Nag_Comm *comm);
  static void nAG_CALL confun(Integer n, Integer ncnlin,
                              const Integer needc[], const double x[],
                              double conf[], double cjac[], Nag_Comm *comm);
#ifdef __cplusplus
}
#endif

static void nAG_CALL objfun(Integer m, Integer n, const double x[],
                            double f[], double fjac[], Integer tdfjac,
                            Nag_Comm *comm)
{
#define FJAC(I, J) fjac[(I) *tdfjac + (J)]

  /* Initialized data */
  static double a[44] = { 8.0, 8.0, 10.0, 10.0, 10.0, 10.0, 12.0, 12.0, 12.0,
    12.0, 14.0, 14.0, 14.0, 16.0, 16.0, 16.0, 18.0, 18.0,
    20.0, 20.0, 20.0, 22.0, 22.0, 22.0, 24.0, 24.0, 24.0,
    26.0, 26.0, 26.0, 28.0, 28.0, 30.0, 30.0, 30.0, 32.0,
    32.0, 34.0, 36.0, 36.0, 38.0, 38.0, 40.0, 42.0
  };

  /* Local variables */
  double temp;
  Integer i;
  double x0, x1, ai;

  /* Function to evaluate the objective subfunctions
   * and their 1st derivatives.
   */
  x0 = x[0];
  x1 = x[1];
  for (i = 0; i < m; ++i) {
    ai = a[i];
    temp = exp(-x1 * (ai - 8.0));
    /* Evaluate objective subfunction f(i+1) only if required */
    if (comm->needf == i + 1 || comm->needf == 0)
      f[i] = x0 + (.49 - x0) * temp;
    if (comm->flag == 2) {
      FJAC(i, 0) = 1.0 - temp;
      FJAC(i, 1) = -(.49 - x0) * (ai - 8.0) * temp;
    }
  }
} /* objfun */

static void nAG_CALL confun(Integer n, Integer ncnlin, const Integer needc[],
                            const double x[], double conf[], double cjac[],
                            Nag_Comm *comm)
{
#define CJAC(I, J) cjac[(I) *n + (J)]

  /* Function to evaluate the nonlinear constraints and its 1st derivatives. */

  if (comm->first == Nag_TRUE) {
    /* First call to confun.  Set all Jacobian elements to zero.
     *  Note that this will only work when  options.obj_deriv = TRUE
     *  (the default).
     */
    CJAC(0, 0) = CJAC(0, 1) = 0.0;
  }

  if (needc[0] > 0) {
    conf[0] = -0.09 - x[0] * x[1] + 0.49 * x[1];

    if (comm->flag == 2) {
      CJAC(0, 0) = -x[1];
      CJAC(0, 1) = -x[0] + 0.49;
    }
  }
} /* confun */

#define A(I, J) a[(I) *tda + J]

int main(void)
{
  Integer exit_status = 0, i, j, m, n, nbnd, nclin, ncnlin, tda, tdfjac;
  Nag_E04_Opt options;
  Nag_Comm comm;
  double *a = 0, *bl = 0, *bu = 0, *f = 0, *fjac = 0, objf, *x = 0;
  double *y = 0;
  NagError fail;

  INIT_FAIL(fail);

  printf("nag_opt_nlin_lsq (e04unc) Example Program Results\n");
  fflush(stdout);

  scanf(" %*[^\n]"); /* Skip heading in data file */

  /* Read problem dimensions */
  scanf(" %*[^\n]");
  scanf("%ld%ld%*[^\n]", &m, &n);
  scanf(" %*[^\n]");
  scanf("%ld%ld%*[^\n]", &nclin, &ncnlin);

  if (m > 0 && n > 0 && nclin >= 0 && ncnlin >= 0) {
    nbnd = n + nclin + ncnlin;
    if (!(x = nAG_ALLOC(n, double)) ||
        !(a = nAG_ALLOC(nclin * n, double)) ||
        !(f = nAG_ALLOC(m, double)) ||
        !(y = nAG_ALLOC(m, double)) ||
        !(fjac = nAG_ALLOC(m * n, double)) ||
        !(bl = nAG_ALLOC(nbnd, double)) || !(bu = nAG_ALLOC(nbnd, double)))
    {
      printf("Allocation failure\n");
      exit_status = -1;
      goto END;
    }
    tda = n;
    tdfjac = n;
  }
  else {
    printf("Invalid m or n nclin or ncnlin.\n");
    exit_status = 1;
    return exit_status;
  }
  /* Read a, y, bl, bu and x from data file */

  if (nclin > 0) {
    scanf(" %*[^\n]");
    for (i = 0; i < nclin; ++i)
      for (j = 0; j < n; ++j)
        scanf("%lf", &A(i, j));
  }

  /* Read the y vector of the objective */
  scanf(" %*[^\n]");
  for (i = 0; i < m; ++i)
    scanf("%lf", &y[i]);

  /* Read lower bounds */
  scanf(" %*[^\n]");
  for (i = 0; i < n + nclin + ncnlin; ++i)
    scanf("%lf", &bl[i]);

  /* Read upper bounds */
  scanf(" %*[^\n]");
  for (i = 0; i < n + nclin + ncnlin; ++i)
    scanf("%lf", &bu[i]);

  /* Read the initial point x */
  scanf(" %*[^\n]");
  for (i = 0; i < n; ++i)
    scanf("%lf", &x[i]);

  /* Set an option */
  /* nag_opt_init (e04xxc).
   * Initialization function for option setting
   */
  nag_opt_init(&options);

  /* Solve the problem */
  /* nag_opt_nlin_lsq (e04unc), see above. */
  nag_opt_nlin_lsq(m, n, nclin, ncnlin, a, tda, bl, bu, y, objfun,
                   confun, x, &objf, f, fjac, tdfjac, &options, &comm, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_opt_nlin_lsq (e04unc).\n%s\n", fail.message);
    exit_status = 1;
  }
  /* nag_opt_free (e04xzc).
   * Memory freeing function for use with option setting
   */
  nag_opt_free(&options, "all", &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_opt_free (e04xzc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

END:
  nAG_FREE(x);
  nAG_FREE(a);
  nAG_FREE(f);
  nAG_FREE(y);
  nAG_FREE(fjac);
  nAG_FREE(bl);
  nAG_FREE(bu);

  return exit_status;
}