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

# include "doughnut_ode.h"

int main ( );
void doughnut_euler ( int n );
double *r8vec_linspace_new ( int n, double a, double b );
void timestamp ( );

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

int main ( )

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

    doughnut_ode_test() tests doughnut_ode().

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    13 October 2025

  Author:

    John Burkardt
*/
{
  double m;
  double n;
  int nt;
  double t0;
  double tstop;
  double y0[3];

  timestamp ( );
  printf ( "\n" );
  printf ( "double_ode_test():\n" );
  printf ( "  C version\n" );
  printf ( "  Test double_ode(), which solves a stiff ODE using euler().\n" );
/*
  Get current parameter values.
*/
  doughnut_parameters ( NULL, NULL, NULL, NULL, NULL,
                        &m,   &n,   &t0,  y0,   &tstop );

  printf ( "\n" );
  printf ( "  Parameter values:\n" );
  printf ( "    m      = %g\n", m );
  printf ( "    n      = %g\n", n );
  printf ( "    t0     = %g\n", t0 );
  printf ( "    y0     = %g, %g, %g\n", y0[0], y0[1], y0[2] );
  printf ( "    tstop  = %g\n", tstop );

  nt = 10001;

  doughnut_euler ( nt );
/*
  Terminate.
*/
  printf ( "\n" );
  printf ( "doughnut_ode_test():\n" );
  printf ( "  Normal end of execution.\n" );
  timestamp ( );

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

void doughnut_euler ( int nt )

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

    doughnut_euler() uses euler() to solve the doughnut ode.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    13 October 2025

  Author:

    John Burkardt

  Input:

    int NT: the number of steps to take.
*/
{
  char command_filename[] = "doughnut_ode_commands.txt";
  FILE *command_unit;
  char data_filename[] = "doughnut_ode_data.txt";
  FILE *data_unit;
  double dt;
  double dydt[3];
  int i;
  int j;
  double t0;
  double *t;
  double tstop;
  double *y;
  double y0[3];

  printf ( "\n" );
  printf ( "doughnut_euler():\n" );
  printf ( "  Solve doughnut ODE using the Euler method.\n" );

  doughnut_parameters ( NULL, NULL, NULL, NULL, NULL, 
                        NULL, NULL, &t0,  y0,   &tstop );

  dt = ( tstop - t0 ) / ( nt - 1 );
  t = r8vec_linspace_new ( nt, t0, tstop );
  y = ( double * ) malloc ( nt * 3 * sizeof ( double ) );

  for ( i = 0; i < nt; i++ )
  {
    if ( i == 0 )
    {
      for ( j = 0; j < 3; j++ )
      {
        y[i*3+j] = y0[j];
      }
    }
    else
    {
      doughnut_deriv ( t[i-1], y+(i-1)*3, dydt );
      for ( j = 0; j < 3; j++ )
      {
        y[i*3+j] = y[(i-1)*3+j] + dt * dydt[j];
      }
    }
  }
/*
  Plot.
*/
  data_unit = fopen ( data_filename, "wt" );
  for ( i = 0; i < nt; i++ )
  {
    fprintf ( data_unit, "  %14.6g  %14.6g  %14.6g  %14.6g\n", 
      t[i], y[i*3+0], y[i*3+1], y[i*3+2] );
  }
  fclose ( data_unit );
  printf ( "  Created data file \"%s\".\n", data_filename );
/*
  Create the command file.
*/
  command_unit = fopen ( command_filename, "wt" );
  fprintf ( command_unit, "# %s\n", command_filename );
  fprintf ( command_unit, "#\n" );
  fprintf ( command_unit, "# Usage:\n" );
  fprintf ( command_unit, "#  gnuplot < %s\n", command_filename );
  fprintf ( command_unit, "#\n" );
  fprintf ( command_unit, "set term png\n" );
  fprintf ( command_unit, "set output 'doughnut_ode.png'\n" );
  fprintf ( command_unit, "set xlabel '<--- X(T) --->'\n" );
  fprintf ( command_unit, "set ylabel '<--- Y(T) --->'\n" );
  fprintf ( command_unit, "set zlabel '<--- Z(T) --->'\n" );
  fprintf ( command_unit, "set title '(X(T),Y(T),Z(T)) trajectory'\n" );
  fprintf ( command_unit, "set grid\n" );
  fprintf ( command_unit, "set style data lines\n" );
  fprintf ( command_unit, 
    "splot '%s' using 2:3:4 lw 2 linecolor rgb 'blue'\n", data_filename );
  fprintf ( command_unit, "quit\n" );
  fclose ( command_unit );
  printf ( "  Created command file '%s'\n", command_filename );
/*
  Free memory.
*/
  free ( t );
  free ( y );

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

double *r8vec_linspace_new ( int n, double a, double b )

/******************************************************************************/
/*
  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, B, the first and last entries.

  Output:

    double R8VEC_LINSPACE_NEW[N], a vector of linearly spaced data.
*/
{
  int i;
  double *x;

  x = ( double * ) malloc ( n * sizeof ( double ) );

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

void timestamp ( )

/******************************************************************************/
/*
  Purpose:
 
    timestamp() prints the current YMDHMS date as a time stamp.

  Example:

    17 June 2014 09:45:54 AM

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    01 May 2021

  Author:

    John Burkardt
*/
{
# define TIME_SIZE 40

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

  now = time ( NULL );
  tm = localtime ( &now );

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

  printf ( "%s\n", time_buffer );

  return;
# undef TIME_SIZE
}