# include <cfloat>
# include <cmath>
# include <cstdlib>
# include <ctime>
# include <iomanip>
# include <iostream>
# include <string>

using namespace std;

# include "zero_itp.hpp"

int main ( );
void zero_itp_example ( double f ( double x ), double a, double b, double epsi,
  double k1, double k2, int n0, bool verbose, string title );
double f_01 ( double x );
double f_02 ( double x );
double f_03 ( double x );
double f_04 ( double x );
double f_05 ( double x );
double f_06 ( double x );
void timestamp ( );

//****************************************************************************80

int main ( )

//****************************************************************************80
//
//  Purpose:
//
//    zero_itp_test() tests zero_itp().
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    03 March 2024
//
//  Author:
//
//    John Burkardt
//
{
  double a;
  double b;
  double epsi;
  double k1;
  double k2;
  int n0;
  string title;
  bool verbose;

  timestamp ( );
  cout << "\n";
  cout << "zero_itp_test():\n";
  cout << "  C++ version\n";
  cout << "  Test zero_itp(), which seeks a root of a function F(X)\n";
  cout << "  in an interval [A,B].\n";

  a = 1.0;
  b = 2.0;
  epsi = sqrt ( DBL_EPSILON );
  k1 = 1.0 / ( b - a ) / 5.0;
  k2 = 2.0;
  n0 = 1;
  title = "f_01(x) = sin ( x ) - x / 2";
  verbose = false;
  zero_itp_example ( f_01, a, b, epsi, k1, k2, n0, verbose, title );

  a = 0.0;
  b = 1.0;
  epsi = sqrt ( DBL_EPSILON );
  k1 = 1.0 / ( b - a ) / 5.0;
  k2 = 2.0;
  n0 = 1;
  title = "f_02(x) = 2 * x - exp ( - x )";
  verbose = false;
  zero_itp_example ( f_02, a, b, epsi, k1, k2, n0, verbose, title );

  a = -1.0;
  b =  0.5;
  epsi = sqrt ( DBL_EPSILON );
  k1 = 1.0 / ( b - a ) / 5.0;
  k2 = 2.0;
  n0 = 1;
  title = "f_03(x) = x * exp ( - x )";
  verbose = false;
  zero_itp_example ( f_03, a, b, epsi, k1, k2, n0, verbose, title );

  a =  0.0001;
  b =  20.0;
  epsi = sqrt ( DBL_EPSILON );
  k1 = 1.0 / ( b - a ) / 5.0;
  k2 = 2.0;
  n0 = 1;
  title = "f_04(x) = exp ( x ) - 1 / ( 100 * x * x )";
  verbose = false;
  zero_itp_example ( f_04, a, b, epsi, k1, k2, n0, verbose, title );

  a = -5.0;
  b =  2.0;
  epsi = sqrt ( DBL_EPSILON );
  k1 = 1.0 / ( b - a ) / 5.0;
  k2 = 2.0;
  n0 = 1;
  title = "f_05(x) = (x+3) * (x-1) * (x-1)";
  verbose = false;
  zero_itp_example ( f_05, a, b, epsi, k1, k2, n0, verbose, title );

  a =  1.0;
  b =  2.0;
  epsi = 0.0005;
  k1 = 1.0 / ( b - a ) / 5.0;
  k2 = 2.0;
  n0 = 1;
  title = "f_06(x) = x^3 - x - 2";
  verbose = true;
  zero_itp_example ( f_06, a, b, epsi, k1, k2, n0, verbose, title );
//
//  Terminate.
//
  cout << "\n";
  cout << "zero_itp_test():\n";
  cout << "  Normal end of execution.\n";
  cout << "\n";
  timestamp ( );

  return 0;
}
//****************************************************************************80

void zero_itp_example ( double f ( double x ), double a, double b, 
  double epsi, double k1, double k2, int n0, bool verbose, string title )

//****************************************************************************80
//
//  Purpose:
//
//    zero_itp_example() tests zero_itp() on one test function.
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    03 March 2024
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    double F ( double x ), the name of a user-supplied
//    function which evaluates the function whose zero is being sought.
//
//    double A, B, the endpoints of the change of sign interval.
//
//    string TITLE, a title for the problem.
//
//    bool verbose: true if extra output is desired from zero_itp();
//
{
  int calls;
  double fa;
  double fb;
  double fz;
  double z;
  
  zero_itp ( f, a, b, epsi, k1, k2, n0, verbose, z, fz, calls );
  fa = f ( a );
  fb = f ( b );

  cout << "\n";
  cout << "  " << title << "\n";
  cout << "\n";
  cout << "      A                 Z             B\n";
  cout << "    F(A)              F(Z)          F(B)\n";
  cout << "\n";
  cout << "  " << setw(14) << a
       << "  " << setw(14) << z
       << "  " << setw(14) << b << "\n";
  cout << "  " << setw(14) << fa
       << "  " << setw(14) << fz
       << "  " << setw(14) << fb << "\n";
  cout << "  Number of calls to F = " << calls << "\n";
  cout << "  Tolerance epsi = " << epsi << "\n";
  cout << "  Parameters k1 = " << k1 
       << ", k2 = " << k2 
       << ", n0 = " << n0 << "\n";

  return;
}
//****************************************************************************80

double f_01 ( double x )

//****************************************************************************80
//
//  Purpose:
//
//    f_01() evaluates sin ( x ) - x / 2.
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    13 April 2008
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    double X, the evaluation point.
//
//  Output: 
//
//    double F_01, the value of the function at X.
//
{
  double value;

  value = sin ( x ) - 0.5 * x;

  return value;
}
//****************************************************************************80

double f_02 ( double x )

//****************************************************************************80
//
//  Purpose:
//
//    f_02() evaluates 2*x-exp(-x).
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    13 April 2008
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    double X, the evaluation point.
//
//  Output: 
//
//    double F_02, the value of the function at X.
//
{
  double value;

  value = 2.0 * x - exp ( - x );

  return value;
}
//****************************************************************************80

double f_03 ( double x )

//****************************************************************************80
//
//  Purpose:
//
//    f_03() evaluates x*exp(-x).
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    13 April 2008
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    double X, the evaluation point.
//
//  Output: 
//
//    double F_03, the value of the function at X.
//
{
  double value;

  value = x * exp ( - x );

  return value;
}
//****************************************************************************80

double f_04 ( double x )

//****************************************************************************80
//
//  Purpose:
//
//    f_04() evaluates exp(x) - 1 / (100*x*x).
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    13 April 2008
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    double X, the evaluation point.
//
//  Output: 
//
//    double F_04, the value of the function at X.
//
{
  double value;

  value = exp ( x ) - 1.0 / 100.0 / x / x;

  return value;
}
//****************************************************************************80

double f_05 ( double x )

//****************************************************************************80
//
//  Purpose:
//
//    f_05() evaluates (x+3)*(x-1)*(x-1).
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    13 April 2008
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    double X, the evaluation point.
//
//  Output: 
//
//    double F_05, the value of the function at X.
//
{
  double value;

  value = ( x + 3.0 ) * ( x - 1.0 ) * ( x - 1.0 );

  return value;
}
//****************************************************************************80

double f_06 ( double x )

//****************************************************************************80
//
//  Purpose:
//
//    f_06() evaluates x^3 - x - 2.
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    02 March 2024
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    double X, the evaluation point.
//
//  Output: 
//
//    double F_06, the value of the function at X.
//
{
  double value;

  value = x * x * x - x - 2;

  return value;
}
//****************************************************************************80

void timestamp ( )

//****************************************************************************80
//
//  Purpose:
//
//    timestamp() prints the current YMDHMS date as a time stamp.
//
//  Example:
//
//    31 May 2001 09:45:54 AM
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    19 March 2018
//
//  Author:
//
//    John Burkardt
//
{
# define TIME_SIZE 40

  static char time_buffer[TIME_SIZE];
  const struct std::tm *tm_ptr;
  std::time_t now;

  now = std::time ( NULL );
  tm_ptr = std::localtime ( &now );

  std::strftime ( time_buffer, TIME_SIZE, "%d %B %Y %I:%M:%S %p", tm_ptr );

  std::cout << time_buffer << "\n";

  return;
# undef TIME_SIZE
}