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

using namespace std;

# include "sigmoid_derivative.hpp"

int main ( );
void sigmoid_derivative_coef_test ( );
void sigmoid_derivative_value_test ( );
void sigmoid_derivative_plot ( int nvec, double *xvec, double *yvec, 
  string header );
void sigmoid_poly_print ( int n, double *a, string title );
double *r8vec_linspace_new ( int n, double a, double b );
void timestamp ( );

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

int main ( )

//****************************************************************************80
//
//  Purpose:
//
//    sigmoid_derivative_test() tests sigmoid_derivative().
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    23 May 2024
//
//  Author:
//
//    John Burkardt
//
{
  timestamp ( );
  cout << "\n";
  cout << "sigmoid_derivative_test():\n";
  cout << "  C++ version\n";
  cout << "  Test sigmoid_derivative.\n";

  sigmoid_derivative_coef_test ( );
  sigmoid_derivative_value_test ( );
//
//  Terminate.
//
  cout << "\n";
  cout << "sigmoid_derivative_test():\n";
  cout << "  Normal end of execution.\n";
  cout << "\n";
  timestamp ( );

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

void sigmoid_derivative_coef_test ( )

//****************************************************************************80
//
//  Purpose:
//
//    sigmoid_derivative_coef_test() tests sigmoid_derivative_coef().
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    23 May 2024
//
//  Author:
//
//    John Burkardt
//
{
  double *coef;
  string label;
  int n;

  cout << "\n";
  cout << "sigmoid_derivative_coef_test():\n";
  cout << "  sigmoid_derivative_coef() returns the coefficients of\n";
  cout << "  the expansion of the nth derivative of the sigmoid\n";
  cout << "  function in terms of powers of the sigmoid function.\n";

  for ( n = 0; n <= 4; n++ )
  {
    coef = sigmoid_derivative_coef ( n );
    label = "  s^(" + to_string ( n ) + ")(x)";
    sigmoid_poly_print ( n + 2, coef, label );
    delete [] coef;
  }

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

void sigmoid_derivative_value_test ( )

//****************************************************************************80
//
//  Purpose:
//
//    sigmoid_derivative_value_test() tests sigmoid_derivative_value().
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    23 May 2024
//
//  Author:
//
//    John Burkardt
//
{
  string header;
  int i;
  int n;
  int nvec = 51;
  double *xvec;
  double *yvec;

  cout << "\n";
  cout << "sigmoid_derivative_value_test():\n";
  cout << "  sigmoid_derivative_value() evaluates the nth derivative\n";
  cout << "  of the sigmoid function at the location x.\n";

  xvec = r8vec_linspace_new ( nvec, -5.0, +5.0 );
  yvec = new double[nvec];

  for ( n = 0; n <= 3; n++ )
  {
    for ( i = 0; i < nvec; i++ )
    {
      yvec[i] = sigmoid_derivative_value ( n, xvec[i] );
    }
    header = "sigmoid_derivative_" + to_string ( n );
    sigmoid_derivative_plot ( nvec, xvec, yvec, header );
  }

  delete [] xvec;
  delete [] yvec;

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

void sigmoid_derivative_plot ( int nvec, double *xvec, double *yvec, 
  string header )

//****************************************************************************80
//
//  Purpose:
//
//    sigmoid_derivative_plot() plots a sigmoid derivative.
//
//  Discussion:
//
//    Actually, we simply create two files for processing by gnuplot().
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    23 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 < nvec; i++ )
  {
    data_unit << xvec[i] << "  "
              << yvec[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 sigmoid_poly_print ( int n, double *a, string title )

//****************************************************************************80
//
//  Purpose:
//
//    sigmoid_poly_print() prints a polynomial in s(x).
//
//  Discussion:
//
//    The power sum form is:
//
//      p(x) = a(0) + a(1) * x + ... + a(n-1) * x^(n-1) + a(n) * x^(n)
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    22 May 2024
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    int N, the dimension of A.
//
//    double A[0:N-1], the polynomial coefficients.
//    A(0) is the constant term and
//    A(N-1) is the coefficient of X^N.
//
//    string TITLE, a title.
//
{
  int i;
  double mag;
  char plus_minus;

  cout << "\n";
  cout << title << " = \n";

  for ( i = 0; i < n; i++ )
  {

    if ( a[i] < 0.0 )
    {
      plus_minus = '-';
    }
    else
    {
      plus_minus = '+';
    }

    mag = fabs ( a[i] );

    if ( mag != 0.0 )
    {
      if ( 2 <= i )
      {
        cout << "         " << plus_minus << " " << mag << " * s(x) ^ " << i << "\n";
      }
      else if ( i == 1 )
      {
        cout << "         " << plus_minus << " " << mag << " * s(x)\n";
      }
      else if ( i == 0 )
      {
        cout << "         " << plus_minus << " " << mag << "\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
}