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

using namespace std;

# include "runge.hpp"

int main ( );
void runge_antideriv_test ( );
void runge_deriv_test ( );
void runge_deriv2_test ( );
void runge_fun_test ( );
void runge_power_series_test ( );
void gnuplot_fx ( int n, double *x, double *y, string header );
void gnuplot_fxdd ( int n, double *x, double *y1, double *y2, string header );
double *r8vec_linspace_new ( int n, double a, double b );
void timestamp ( );

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

int main ( )

//****************************************************************************80
//
//  Purpose:
//
//    runge_test() tests runge().
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    25 May 2024
//
//  Author:
//
//    John Burkardt
//
{
  timestamp ( );
  cout << "\n";
  cout << "runge_test():\n";
  cout << "  C++ version\n";
  cout << "  Test runge.\n";

  runge_antideriv_test ( );
  runge_deriv_test ( );
  runge_deriv2_test ( );
  runge_fun_test ( );
  runge_power_series_test ( );
//
//  Terminate.
//
  cout << "\n";
  cout << "runge_test():\n";
  cout << "  Normal end of execution.\n";
  cout << "\n";
  timestamp ( );

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

void runge_antideriv_test ( )

//****************************************************************************80
//
//  Purpose:
//
//    runge_antideriv_test() tests runge_antideriv().
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    24 May 2024
//
//  Author:
//
//    John Burkardt
//
{
  double a;
  double b;
  string header;
  int i;
  int n = 51;
  double *x;
  double *y;

  cout << "\n";
  cout << "runge_antideriv_test():\n";
  cout << "  runge_antideriv() evaluates the antiderivative\n";
  cout << "  of the runge function.\n";

  a = -1.0;
  b = +1.0;
  x = r8vec_linspace_new ( n, a, b );
  y = new double[n];

  for ( i = 0; i < n; i++ )
  {
    y[i] = runge_antideriv ( x[i] );
  }
  header = "runge_antideriv";
  gnuplot_fx ( n, x, y, header );

  delete [] x;
  delete [] y;

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

void runge_deriv_test ( )

//****************************************************************************80
//
//  Purpose:
//
//    runge_deriv_test() tests runge_deriv().
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    24 May 2024
//
//  Author:
//
//    John Burkardt
//
{
  double a;
  double b;
  string header;
  int i;
  int n = 51;
  double *x;
  double *y;

  cout << "\n";
  cout << "runge_deriv_test():\n";
  cout << "  runge_deriv() evaluates the derivative\n";
  cout << "  of the runge function.\n";

  a = -1.0;
  b = +1.0;
  x = r8vec_linspace_new ( n, a, b );
  y = new double[n];

  for ( i = 0; i < n; i++ )
  {
    y[i] = runge_deriv ( x[i] );
  }
  header = "runge_deriv";
  gnuplot_fx ( n, x, y, header );

  delete [] x;
  delete [] y;

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

void runge_deriv2_test ( )

//****************************************************************************80
//
//  Purpose:
//
//    runge_deriv2_test() tests runge_deriv2().
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    24 May 2024
//
//  Author:
//
//    John Burkardt
//
{
  double a;
  double b;
  string header;
  int i;
  int n = 51;
  double *x;
  double *y;

  cout << "\n";
  cout << "runge_deriv2_test():\n";
  cout << "  runge_deriv2() evaluates the second derivative\n";
  cout << "  of the runge function.\n";

  a = -1.0;
  b = +1.0;
  x = r8vec_linspace_new ( n, a, b );
  y = new double[n];

  for ( i = 0; i < n; i++ )
  {
    y[i] = runge_deriv2 ( x[i] );
  }
  header = "runge_deriv2";
  gnuplot_fx ( n, x, y, header );

  delete [] x;
  delete [] y;

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

void runge_fun_test ( )

//****************************************************************************80
//
//  Purpose:
//
//    runge_fun_test() tests runge_fun().
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    24 May 2024
//
//  Author:
//
//    John Burkardt
//
{
  double a;
  double b;
  string header;
  int i;
  int n = 51;
  double *x;
  double *y;

  cout << "\n";
  cout << "runge_fun_test():\n";
  cout << "  runge_fun() evaluates the runge function.\n";

  a = -1.0;
  b = +1.0;
  x = r8vec_linspace_new ( n, a, b );
  y = new double[n];

  for ( i = 0; i < n; i++ )
  {
    y[i] = runge_fun ( x[i] );
  }
  header = "runge_fun";
  gnuplot_fx ( n, x, y, header );

  delete [] x;
  delete [] y;

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

void runge_power_series_test ( )

//****************************************************************************80
//
//  Purpose:
//
//    runge_power_series_test() tests runge_power_series().
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    25 May 2024
//
//  Author:
//
//    John Burkardt
//
{
  double a;
  double b;
  string header;
  int i;
  int n = 51;
  int n2 = 8;
  double *x;
  double *y1;
  double *y2;

  cout << "\n";
  cout << "runge_power_series_test():\n";
  cout << "  runge_power_series() compares a power series to\n";
  cout << "  the runge function.\n";

  a = -0.2;
  b = +0.2;
  x = r8vec_linspace_new ( n, a, b );
  y1 = new double[n];
  y2 = new double[n];

  for ( i = 0; i < n; i++ )
  {
    y1[i] = runge_fun ( x[i] );
    y2[i] = runge_power_series ( x[i], n2 );
  }
  header = "runge_power_series";
  gnuplot_fxdd ( n, x, y1, y2, header );

  delete [] x;
  delete [] y1;
  delete [] y2;

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

void gnuplot_fx ( int n, double *x, double *y, string header )

//****************************************************************************80
//
//  Purpose:
//
//    gnuplot_fx() plots functional data x, f(x).
//
//  Discussion:
//
//    Actually, we simply create two files for processing by gnuplot().
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    24 May 2024
//
//  Author:
//
//    John Burkardt
//
{
  string command_filename;
  ofstream command_unit;
  string data_filename;
  ofstream data_unit;
  int i;
  string png_filename;
//
//  Create a graphics data file.
//
  data_filename = header + "_data.txt";
  data_unit.open ( data_filename.c_str ( ) );
  for ( i = 0; i < n; i++ )
  {
    data_unit << x[i] << "  "
              << y[i] << "\n";
  }
  data_unit.close ( );
  cout << "  Created graphics data file '" << data_filename << "'\n";

  png_filename = header + ".png";
//
//  Create graphics command file.
//
  command_filename = header + "_commands.txt";
  command_unit.open ( command_filename.c_str ( ) );
  command_unit << "# " << command_filename << "\n";
  command_unit << "#\n";
  command_unit << "# Usage:\n";
  command_unit << "#  gnuplot < " << command_filename << "\n";
  command_unit << "#\n";
  command_unit << "set term png\n";
  command_unit << "set output '" << png_filename << "'\n";
  command_unit << "set xlabel '<--- X --->'\n";
  command_unit << "set ylabel '<-- Y(X) -->'\n";
  command_unit << "set title '" << header << "'\n";
  command_unit << "set grid\n";
  command_unit << "set style data lines\n";
  command_unit << 
    "plot '" << data_filename << "' using 1:2 lw 3 linecolor rgb 'blue'\n";
  command_unit.close ( );
  cout << "  Created command file '" << command_filename << "'\n";

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

void gnuplot_fxdd ( int n, double *x, double *y1, double *y2, string header )

//****************************************************************************80
//
//  Purpose:
//
//    gnuplot_fxdd() plots n values of y1=f(x) (curve) and y2 = x2 (data)
//
//  Discussion:
//
//    Actually, we simply create two files for processing by gnuplot().
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    24 May 2024
//
//  Author:
//
//    John Burkardt
//
{
  string command_filename;
  ofstream command_unit;
  string data_filename;
  ofstream data_unit;
  int i;
  string png_filename;
//
//  Create a graphics data file.
//
  data_filename = header + "_data.txt";
  data_unit.open ( data_filename.c_str ( ) );
  for ( i = 0; i < n; i++ )
  {
    data_unit << x[i] << "  "
              << y1[i] << "  "
              << y2[i] << "\n";
  }
  data_unit.close ( );
  cout << "  Created graphics data file '" << data_filename << "'\n";

  png_filename = header + ".png";
//
//  Create graphics command file.
//
  command_filename = header + "_commands.txt";
  command_unit.open ( command_filename.c_str ( ) );
  command_unit << "# " << command_filename << "\n";
  command_unit << "#\n";
  command_unit << "# Usage:\n";
  command_unit << "#  gnuplot < " << command_filename << "\n";
  command_unit << "#\n";
  command_unit << "set term png\n";
  command_unit << "set output '" << png_filename << "'\n";
  command_unit << "set xlabel '<--- X --->'\n";
  command_unit << "set ylabel '<-- Y(X) -->'\n";
  command_unit << "set title '" << header << "'\n";
  command_unit << "set grid\n";
  command_unit << "set style data lines\n";
  command_unit << 
    "plot '" << data_filename 
    << "' using 1:2 lw 3 linecolor rgb 'blue',\\\n";
  command_unit << 
    "     '" << data_filename 
    << "' using 1:3 with points pointtype 7 linecolor 'red'\n";
  command_unit.close ( );
  cout << "  Created command file '" << command_filename << "'\n";

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

double *r8vec_linspace_new ( int n, double a_first, double a_last )

//****************************************************************************80
//
//  Purpose:
//
//    r8vec_linspace_new() creates a vector of linearly spaced values.
//
//  Discussion:
//
//    An R8VEC is a vector of R8's.
//
//    4 points evenly spaced between 0 and 12 will yield 0, 4, 8, 12.
//
//    In other words, the interval is divided into N-1 even subintervals,
//    and the endpoints of intervals are used as the points.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    29 March 2011
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    int N, the number of entries in the vector.
//
//    double A_FIRST, A_LAST, the first and last entries.
//
//  Output:
//
//    double R8VEC_LINSPACE_NEW[N], a vector of linearly spaced data.
//
{
  double *a;
  int i;

  a = new double[n];

  if ( n == 1 )
  {
    a[0] = ( a_first + a_last ) / 2.0;
  }
  else
  {
    for ( i = 0; i < n; i++ )
    {
      a[i] = ( ( double ) ( n - 1 - i ) * a_first 
             + ( double ) (         i ) * a_last ) 
             / ( double ) ( n - 1     );
    }
  }
  return a;
}
//****************************************************************************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
}