text: /* min/test.c
   * 
   * Copyright (C) 1996, 1997, 1998, 1999, 2000 Brian Gough
   * 
   * This program is free software; you can redistribute it and/or modify
   * it under the terms of the GNU General Public License as published by
   * the Free Software Foundation; either version 2 of the License, or (at
   * your option) any later version.
   * 
   * This program is distributed in the hope that it will be useful, but
   * WITHOUT ANY WARRANTY; without even the implied warranty of
   * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
   * General Public License for more details.
   * 
   * You should have received a copy of the GNU General Public License
   * along with this program; if not, write to the Free Software
   * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
   */
  #include <config.h>
  #include <stdlib.h>
  #include <gsl/gsl_math.h>
  #include <gsl/gsl_min.h>
  #include <gsl/gsl_errno.h>
  #include <gsl/gsl_test.h>
  #include <gsl/gsl_ieee_utils.h>
  
  #include "test.h"
  #include "min.h"
  
  /* stopping parameters */
  
  const double EPSABS = 0.001 ;
  const double EPSREL = 0.001 ;
  
  const unsigned int MAX_ITERATIONS = 100;
  
  void my_error_handler (const char *reason, const char *file,
                         int line, int err);
  
  #define WITHIN_TOL(a, b, epsrel, epsabs) \
   (fabs((a) - (b)) < (epsrel) * GSL_MIN(fabs(a), fabs(b)) + (epsabs))
  
  int
  main (void)
  {
    gsl_function F_cos, F_func1, F_func2, F_func3, F_func4;
    
    const gsl_min_fminimizer_type * fminimizer[4] ;
    const gsl_min_fminimizer_type ** T;
  
    gsl_ieee_env_setup ();
  
    fminimizer[0] = gsl_min_fminimizer_goldensection;
    fminimizer[1] = gsl_min_fminimizer_brent;
    fminimizer[2] = 0;
  
    F_cos = create_function (f_cos) ;
    F_func1 = create_function (func1) ;
    F_func2 = create_function (func2) ;
    F_func3 = create_function (func3) ;
    F_func4 = create_function (func4) ;
  
    gsl_set_error_handler (&my_error_handler);
  
    for (T = fminimizer ; *T != 0 ; T++)
      {
        test_f (*T, "cos(x) [0 (3) 6]", &F_cos, 0.0, 3.0, 6.0, M_PI);
        test_f (*T, "x^4 - 1 [-3 (-1) 17]", &F_func1, -3.0, -1.0, 17.0, 0.0);
        test_f (*T, "sqrt(|x|) [-2 (-1) 1.5]", &F_func2, -2.0, -1.0, 1.5, 0.0);
        test_f (*T, "func3(x) [-2 (3) 4]", &F_func3, -2.0, 3.0, 4.0, 1.0);
        test_f (*T, "func4(x) [0 (0.782) 1]", &F_func4, 0, 0.782, 1.0, 0.8);
  
        test_f_e (*T, "invalid range check [4, 0]", &F_cos, 4.0, 3.0, 0.0, M_PI);
        test_f_e (*T, "invalid range check [1, 1]", &F_cos, 1.0, 1.0, 1.0, M_PI);
        test_f_e (*T, "invalid range check [-1, 1]", &F_cos, -1.0, 0.0, 1.0, M_PI);
      }
    test_bracket("cos(x) [1,2]",&F_cos,1.0,2.0,15);
    test_bracket("sqrt(|x|) [-1,0]",&F_func2,-1.0,0.0,15);
    test_bracket("sqrt(|x|) [-1,-0.6]",&F_func2,-1.0,-0.6,15);
    test_bracket("sqrt(|x|) [-1,1]",&F_func2,-1.0,1.0,15);
  
    exit (gsl_test_summary ());
  }
  
  void
  test_f (const gsl_min_fminimizer_type * T, 
          const char * description, gsl_function *f,
          double lower_bound, double middle, double upper_bound, 
          double correct_minimum)
  {
    int status;
    size_t iterations = 0;
    double m, a, b;
    double x_lower, x_upper;
    gsl_min_fminimizer * s;
  
    x_lower = lower_bound;
    x_upper = upper_bound;
  
    s = gsl_min_fminimizer_alloc (T) ;
    gsl_min_fminimizer_set (s, f, middle, x_lower, x_upper) ;
    
    do 
      {
        iterations++ ;
  
        status = gsl_min_fminimizer_iterate (s);
  
        m = gsl_min_fminimizer_x_minimum(s);
        a = gsl_min_fminimizer_x_lower(s);
        b = gsl_min_fminimizer_x_upper(s);
  
  #ifdef DEBUG
        printf("%.12f %.18f %.12f %.18f %.12f %.18f\n", 
               a, GSL_FN_EVAL(f, a), m, GSL_FN_EVAL(f, m), b, GSL_FN_EVAL(f, b));
  #endif
  
        if (a > b)
          gsl_test (GSL_FAILURE, "interval is invalid (%g,%g)", a, b);
  
        if (m < a || m > b)
          gsl_test (GSL_FAILURE, "m lies outside interval %g (%g,%g)", m, a, b);
  
        if (status) break ;
  
        status = gsl_min_test_interval (a, b, EPSABS, EPSREL);
      }
    while (status == GSL_CONTINUE && iterations < MAX_ITERATIONS);
  
    gsl_test (status, "%s, %s (%g obs vs %g expected) ", 
              gsl_min_fminimizer_name(s), description, 
              gsl_min_fminimizer_x_minimum(s), correct_minimum);
  
    /* check the validity of the returned result */
  
    if (!WITHIN_TOL (m, correct_minimum, EPSREL, EPSABS))
      {
        gsl_test (GSL_FAILURE, "incorrect precision (%g obs vs %g expected)", 
                  m, correct_minimum);
      }
  
    gsl_min_fminimizer_free (s);
  
  }
  
  void
  test_f_e (const gsl_min_fminimizer_type * T, 
            const char * description, gsl_function *f,
            double lower_bound, double middle, double upper_bound, 
            double correct_minimum)
  {
    int status;
    size_t iterations = 0;
    double x_lower, x_upper;
    double a, b;
    gsl_min_fminimizer * s;
  
    x_lower = lower_bound;
    x_upper = upper_bound;
  
    s = gsl_min_fminimizer_alloc (T) ;
    status = gsl_min_fminimizer_set (s, f, middle, x_lower, x_upper) ; 
  
    if (status != GSL_SUCCESS) 
      {
        gsl_min_fminimizer_free (s) ;
        gsl_test (status == GSL_SUCCESS, "%s, %s", T->name, description);
        return ;
      }
  
    do 
      {
        iterations++ ;
        gsl_min_fminimizer_iterate (s);
        a = gsl_min_fminimizer_x_lower(s);
        b = gsl_min_fminimizer_x_upper(s);
  
        status = gsl_min_test_interval (a, b, EPSABS, EPSREL);
      }
    while (status == GSL_CONTINUE && iterations < MAX_ITERATIONS);
  
    gsl_test (!status, "%s, %s", gsl_min_fminimizer_name(s), description, 
              gsl_min_fminimizer_x_minimum(s) - correct_minimum);
  
    gsl_min_fminimizer_free (s);
  }
  
  void
  my_error_handler (const char *reason, const char *file, int line, int err)
  {
    if (0)
      printf ("(caught [%s:%d: %s (%d)])\n", file, line, reason, err);
  }
  
  int
  test_bracket (const char * description,gsl_function *f,double lower_bound, 
                double upper_bound, unsigned int max)
  {
    int status;
    double x_lower, x_upper;
    double f_upper,f_lower,f_minimum;
    double x_minimum;
  
    x_lower=lower_bound;
    x_upper=upper_bound;
    SAFE_FUNC_CALL (f,x_lower,&f_lower);
    SAFE_FUNC_CALL (f,x_upper,&f_upper);
    status=gsl_min_find_bracket(f,&x_minimum,&f_minimum,&x_lower,&f_lower,&x_upper,&f_upper,max);
    gsl_test (status,"%s, interval: [%g,%g], values: (%g,%g), minimum at: %g, value: %g",
              description,x_lower,x_upper,f_lower,f_upper,x_minimum,f_minimum);
    return status;
  }
  
  
  
  