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

using namespace std;

# include "stiff_exact.hpp"

int main ( );
void stiff_value ( );
void stiff_euler_test ( int n );
void stiff_euler ( int n, double t[], double y[] );
void plot2 ( int n1, double t1[], double y1[], int n2, double t2[], 
  double y2[], string header, string title );
void plot4 ( 
  int n1, double t1[], double y1[], 
  int n2, double t2[], double y2[],
  int n3, double t3[], double y3[], 
  int n4, double t4[], double y4[],
  string header, string title );
double *r8vec_linspace_new ( int n, double a, double b );
void timestamp ( );

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

int main ( )

//****************************************************************************80
//
//  Purpose:
//
//    stiff_exact_test() tests stiff_exact().
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    23 June 2025
//
//  Author:
//
//    John Burkardt
//
{
  int n;

  timestamp ( );
  cout << "\n";
  cout << "stiff_exact_test():\n";
  cout << "  C++ version\n";
  cout << "  Test stiff_exact(), which evaluates exact solutions\n";
  cout << "  of a stiff ODE.\n";

  stiff_value ( );

  n = 27;
  stiff_euler_test ( n );
//
//  Terminate.
//
 cout << "\n";
 cout << "stiff_exact_test():\n";
 cout << "  Normal end of execution.\n";
 timestamp ( );

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

void stiff_value ( )

//****************************************************************************80
//
//  Purpose:
//
//    stiff_value() evaluates the exact solution for various initial conditions.
//
//  Discussion:
//
//    y' = lambda * ( cos(t-t0) - y )
//    y(t0) = y0
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    23 June 2025
//
//  Author:
//
//    John Burkardt
//
{
  double lambda;
  int nt;
  double t0;
  double *t1;
  double *t2;
  double *t3;
  double *t4;
  double tstop;
  double y0;
  double *y1;
  double *y2;
  double *y3;
  double *y4;

  nt = 101;
//
//  Set initial parameter values.
//
  lambda = 50.0;
  t0 = 0.0;
  y0 = 0.0;
  tstop = 1.0;

  stiff_parameters ( &lambda, &t0, &y0, &tstop, NULL, NULL, NULL, NULL );
//
//  Report initial parameter values.
//
 cout << "\n";
 cout << "  Initial parameters:\n";
 cout << "    lambda = " << lambda << "\n";
 cout << "    t0     = " << t0 << "\n";
 cout << "    y0     = " << y0 << "\n";
 cout << "    tstop  = " << tstop << "\n";
//
//  Default with t0 = 0, y0 = 0.
//
  t0 = 0.0;
  y0 = 0.0;
  stiff_parameters ( &lambda, &t0, &y0, &tstop, NULL, NULL, NULL, NULL );
  t1 = r8vec_linspace_new ( nt, t0, tstop );
  y1 = stiff_exact ( nt, t1 );
//
//  Try t0=0, y0=0.9.
//
  t0 = 0.0;
  y0 = 0.9;
  stiff_parameters ( &lambda, &t0, &y0, &tstop, NULL, NULL, NULL, NULL );
  t2 = r8vec_linspace_new ( nt, t0, tstop );
  y2 = stiff_exact ( nt, t2 );
//
//  Try t0=0, y0=1.5.
//
  t0 = 0.0;
  y0 = 1.5;
  stiff_parameters ( &lambda, &t0, &y0, &tstop, NULL, NULL, NULL, NULL );
  t3 = r8vec_linspace_new ( nt, t0, tstop );
  y3 = stiff_exact ( nt, t3 );
//
//  t0 = 0.25, y0 = 0.5
//
  t0 = 0.25;
  y0 = 0.5;
  stiff_parameters ( &lambda, &t0, &y0, &tstop, NULL, NULL, NULL, NULL );
  t4 = r8vec_linspace_new ( nt, t0, tstop );
  y4 = stiff_exact ( nt, t4 );
//
//  Plot them.
//
  plot4 ( nt, t1, y1, nt, t2, y2, nt, t3, y3, nt, t4, y4,
    "stiff_value", "Stiff ODE exact solutions" );
//
//  Free memory.
//
  delete [] t1;
  delete [] t2;
  delete [] t3;
  delete [] t4;
  delete [] y1;
  delete [] y2;
  delete [] y3;
  delete [] y4;

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

void stiff_euler_test ( int n )

//****************************************************************************80
//
//  Purpose:
//
//    stiff_euler_test() tests stiff_euler().
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    23 June 2025
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    int N: the number of steps to take.
//
{
  double lambda;
  const int n2 = 101;
  double t0;
  double *t1;
  double *t2;
  double tstop;
  double y0;
  double *y1;
  double *y2;

 cout << "\n";
 cout << "stiff_euler_test():\n";
 cout << "  Solve stiff ODE using the Euler method.\n";
//
//  Set initial parameter values.
//
  lambda = 50;
  t0 = 0.0;
  y0 = 0.0;
  tstop = 1.0;

  stiff_parameters ( &lambda, &t0, &y0, &tstop, NULL, NULL, NULL, NULL );

 cout << "\n";
 cout << "  Parameters:\n";
 cout << "    lambda = " << lambda << "\n";
 cout << "    t0     = " << t0 << "\n";
 cout << "    y0     = " << y0 << "\n";
 cout << "    tstop  = " << tstop << "\n";

  stiff_parameters ( NULL, NULL, NULL, NULL, NULL, &t0, NULL, &tstop );

  t1 = new double[n+1];
  y1 = new double[n+1];
  stiff_euler ( n, t1, y1 );

  t2 = r8vec_linspace_new ( n2, t0, tstop );
  y2 = stiff_exact ( n2, t2 );

  plot2 ( n+1, t1, y1, n2, t2, y2, "stiff_euler", 
    "Stiff ODE solved using euler method" );

  delete [] t1;
  delete [] t2;
  delete [] y1;
  delete [] y2;

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

void stiff_euler ( int n, double t[], double y[] )

//****************************************************************************80
//
//  Purpose:
//
//    stiff_euler() uses the Euler method on the stiff equation.
//
//  Discussion:
//
//    y' = lambda * ( cos(t-t0) - y )
//    y(t0) = y0
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    20 June 2025
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    int N: the number of steps to take.
//
//  Output:
//
//    double T[N+1], Y[N+1]: the times and estimated solutions.
//
{
  double dt;
  int i;
  double lambda;
  double t0;
  double tstop;
  double y0;

  stiff_parameters ( NULL, NULL, NULL, NULL, &lambda, &t0, &y0, &tstop );

  dt = ( tstop - t0 ) / ( double ) ( n );

  t[0] = t0;
  y[0] = y0;

  for ( i = 0; i < n; i++ )
  {
    t[i+1] = t[i] + dt;
    y[i+1] = y[i] + dt * lambda * ( cos ( t[i] - t0 ) - y[i] );
  }

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

void plot2 ( int n1, double t1[], double y1[], int n2, double t2[], 
  double y2[], string header, string title )

//****************************************************************************80
//
//  Purpose:
//
//    plot2() plots two curves together.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    29 April 2020
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    int N1: the size of the first data set.
//
//    double T1(N1), Y1(N1), the first dataset.
//
//    int N2: the size of the second data set.
//
//    double T2(N2), Y2(N2), the secod dataset.
//
//    string HEADER: an identifier for the data.
//
//    string TITLE: a title to appear in the plot.
//
{
  string command_filename;
  ofstream command;
  string data1_filename;
  string data2_filename;
  ofstream data;
  int i;
//
//  Create the data files.
//
  data1_filename = header + "_data1.txt";
  data.open ( data1_filename.c_str ( ) );
  for ( i = 0; i < n1; i++ )
  {
    data << "  " << t1[i] << "  " << y1[i] << "\n";
  }
  data.close ( );

  data2_filename = header + "_data2.txt";
  data.open ( data2_filename.c_str ( ) );
  for ( i = 0; i < n2; i++ )
  {
    data << "  " << t2[i] << "  " << y2[i] << "\n";
  }
  data.close ( );

  cout << "\n";
  cout << "  plot2: data stored in '" << data1_filename
       << "' and '" << data2_filename << "'\n";
//
//  Create the command file.
//
  command_filename = header + "_commands.txt";
  command.open ( command_filename.c_str ( ) );

  command << "# " << command_filename << "\n";
  command << "#\n";
  command << "# Usage:\n";
  command << "#  gnuplot < " << command_filename << "\n";
  command << "#\n";
  command << "set term png\n";
  command << "set output '" << header << ".png'\n";
  command << "set xlabel '<-- T -->'\n";
  command << "set ylabel '<-- Y(T) -->'\n";
  command << "set title '" << title << "'\n";
  command << "set grid\n";
  command << "set style data lines\n";
  command << "plot '" << data1_filename << "' using 1:2 with lines lw 3 lt rgb 'red',\\\n";
  command << "     '" << data2_filename << "' using 1:2 with lines lw 3 lt rgb 'blue'\n";
  command << "quit\n";

  command.close ( );

  cout << "  plot2: plot commands stored in '" << command_filename << "'.\n";

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

void plot4 ( 
  int n1, double t1[], double y1[], 
  int n2, double t2[], double y2[],
  int n3, double t3[], double y3[], 
  int n4, double t4[], double y4[],
  string header, string title )

//****************************************************************************80
//
//  Purpose:
//
//    plot4() plots four curves together.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    23 June 2025
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    int N1: the size of the first data set.
//
//    double T1(N1), Y1(N1), the first dataset.
//
//    int N2: the size of the second data set.
//
//    double T2(N2), Y2(N2), the second dataset.
//
//    int N3: the size of the data set 3.
//
//    double T3(N3), Y3(N3), dataset 3.
//
//    int N3: the size of the data set 4.
//
//    double T4(N4), Y4(N4), dataset 4.
//
//    string HEADER: an identifier for the data.
//
//    string TITLE: a title to appear in the plot.
//
{
  string command_filename;
  ofstream command;
  string data1_filename;
  string data2_filename;
  string data3_filename;
  string data4_filename;
  ofstream data;
  int i;
//
//  Create the data files.
//
  data1_filename = header + "_data1.txt";
  data.open ( data1_filename.c_str ( ) );
  for ( i = 0; i < n1; i++ )
  {
    data << "  " << t1[i] << "  " << y1[i] << "\n";
  }
  data.close ( );

  data2_filename = header + "_data2.txt";
  data.open ( data2_filename.c_str ( ) );
  for ( i = 0; i < n2; i++ )
  {
    data << "  " << t2[i] << "  " << y2[i] << "\n";
  }
  data.close ( );

  data3_filename = header + "_data3.txt";
  data.open ( data3_filename.c_str ( ) );
  for ( i = 0; i < n3; i++ )
  {
    data << "  " << t3[i] << "  " << y3[i] << "\n";
  }
  data.close ( );

  data4_filename = header + "_data4.txt";
  data.open ( data4_filename.c_str ( ) );
  for ( i = 0; i < n4; i++ )
  {
    data << "  " << t4[i] << "  " << y4[i] << "\n";
  }
  data.close ( );

  cout << "\n";
  cout << "  plot4: data stored in '" 
       << data1_filename << "', '" 
       << data2_filename << "', '" 
       << data3_filename << "', '" 
       << data4_filename<< "'\n";
//
//  Create the command file.
//
  command_filename = header + "_commands.txt";
  command.open ( command_filename.c_str ( ) );

  command << "# " << command_filename << "\n";
  command << "#\n";
  command << "# Usage:\n";
  command << "#  gnuplot < " << command_filename << "\n";
  command << "#\n";
  command << "set term png\n";
  command << "set output '" << header << ".png'\n";
  command << "set xlabel '<-- T -->'\n";
  command << "set ylabel '<-- Y(T) -->'\n";
  command << "set title '" << title << "'\n";
  command << "set grid\n";
  command << "set style data lines\n";
  command << "plot '" << data1_filename << "' using 1:2 with lines lw 3 lt rgb 'red',\\\n";
  command << "     '" << data2_filename << "' using 1:2 with lines lw 3 lt rgb 'blue',\\\n";
  command << "     '" << data3_filename << "' using 1:2 with lines lw 3 lt rgb 'green',\\\n";
  command << "     '" << data4_filename << "' using 1:2 with lines lw 3 lt rgb 'magenta'\n";

  command << "quit\n";

  command.close ( );

  cout << "  plot4: plot commands stored in '" << 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
}