# include <math.h>
# include <stdio.h>
# include <stdlib.h>

# include "golden_section.h"

/******************************************************************************/

void golden_section ( double f ( double x ), int n, double x_tol, double *a, 
  double *b, int * it )

/******************************************************************************/
/*
  Purpose:

    golden_section() seeks a minimizer of a unimodal function in [a,b].

  Discussion:

    A unimodal function f(x) in [a,b] has a minimizer a <= c <= b such that
    f(x) strictly decreases between a and c, and strictly increases between
    c and b.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    23 February 2026

  Author:

    Original MATLAB code by J Nathan Kutz.
    This version by John Burkardt.

  Reference:

    J Nathan Kutz,
    Data Driven Modeling and Scientific Computation,
    Oxford University Press, 2013,
    ISBN: 978-0-19-966034-6.

  Input:

    double f ( double x ): the function to be minimized.

    int n: the maximum number of iterations allowed.
    n must be at least 1.

    double x_tol: a tolerance for the width of the x interval.

    double *a, *b: the left and right endpoints.

  Output:

    double *a, *b: the current interval containing the minimizer.

    int *it: the number of steps taken.
*/
{
  double f1;
  double f2;
  double g;
  double x1;
  double x2;

  for ( *it = 0; *it <= n; (*it)++ )
  {
    if ( *it == 0 )
    {
      g = ( - 1.0 + sqrt ( 5.0 ) ) / 2.0;
      x1 =         g   * *a + ( 1.0 - g ) * *b;
      x2 = ( 1.0 - g ) * *a +         g   * *b;
      f1 = f ( x1 );
      f2 = f ( x2 );
    }
    else
    {
      if ( f1 < f2 )
      {
        *b = x2;
        x2 = x1;
        f2 = f1;
        x1 = g * *a + ( 1.0 - g ) * *b;
        f1 = f ( x1 );
      }
      else
      {
        *a = x1;
        x1 = x2;
        f1 = f2;
        x2 = ( 1.0 - g ) * *a + g * *b;
        f2 = f ( x2 );
      }
    }

    if ( fabs ( *b - *a ) <= x_tol )
    {
      break;
    }
  }

  return;
}