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

# include "midpoint_adaptive.h"

int main ( );
void lotka_dydt ( double t, double y[], double dy[] );
void lotka_test ( );
void timestamp ( );

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

int main ( )

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

    midpoint_adaptive_test() tests midpoint_adaptive().

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    15 July 2024

  Author:

    John Burkardt
*/
{
  timestamp ( );
  printf ( "\n" );
  printf ( "midpoint_adaptive_test():\n" );
  printf ( "  C version\n" );
  printf ( "  midpoint_adaptive() solves ODE's using an adaptive\n" );
  printf ( "  version of the midpoint method.\n" );

  lotka_test ( );
/*
  Terminate.
*/
  printf ( "\n" );
  printf ( "midpoint_adaptive_test():\n" );
  printf ( "  Normal end of execution.\n" );
  printf ( "\n" );
  timestamp ( );

  return ( 0 );
}
/******************************************************************************/

void lotka_test ( )

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

    lotka_test() solves lotka_ode() using midpoint_adaptive().

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    11 July 2024

  Author:

    John Burkardt

  Reference:

    George Lindfield, John Penny,
    Numerical Methods Using MATLAB,
    Second Edition,
    Prentice Hall, 1999,
    ISBN: 0-13-012641-1,
    LC: QA297.P45.
*/
{
  double abstol;
  char label[] = "lotka";
  int m;
  int n_fsolve;
  int n_rejected;
  int nstep;
  int nmax;
  double reltol;
  double *t;
  double t0;
  double tau0;
  double tmax;
  double *y;
  double y0[2];

  printf ( "\n" );
  printf ( "lotka_test():\n" );
  printf ( "  A pair of ordinary differential equations for a population\n" );
  printf ( "  of predators and prey are solved using midpoint().\n" );
  printf ( "\n" );
  printf ( "  Steady state at r = 5000, f = 2000.\n" );

  t0 = 0.0;
  tmax = 20.0;
  m = 2;
  y0[0] = 5000.0;
  y0[1] = 100.0;
  tau0 = 2.5E-2;
  reltol = 1.0E-3;
  abstol = 1.0E-3;
  nmax = 400;
  nstep = 0;
  t = ( double * ) malloc ( ( nmax + 1 ) * sizeof ( double ) );
  y = ( double * ) malloc ( ( nmax + 1 ) * m * sizeof ( double ) );

  mad_compute ( lotka_dydt, t0, tmax, m, y0, tau0, reltol, abstol, nmax, 
    &nstep, &n_rejected, &n_fsolve, t, y );

  mad_phase_plot ( nstep, m, t, y, label );

  mad_solution_plot ( nstep, m, t, y, label );

  mad_timestep_plot ( nstep, t, label );

  mad_stats ( nstep, n_rejected, n_fsolve, t );
/*
  Free memory.
*/
  free ( y );
  free ( t );

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

void lotka_dydt ( double t, double y[], double dydt[] )

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

    lotka_dydt() evaluates the right hand side of lotka_ode().

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    27 April 2020

  Author:

    John Burkardt

  Reference:

    George Lindfield, John Penny,
    Numerical Methods Using MATLAB,
    Second Edition,
    Prentice Hall, 1999,
    ISBN: 0-13-012641-1,
    LC: QA297.P45.

  Input:

    double t: the current time.

    double y[2]: the current solution variables, rabbits and foxes.

  Output:

    double dydt[2]: the right hand side of the 2 ODE's.
*/
{
  dydt[0] =    2.0 * y[0] - 0.001 * y[0] * y[1];
  dydt[1] = - 10.0 * y[1] + 0.002 * y[0] * y[1];

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

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:

    17 June 2014

  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
}