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

# include "logistic_exact.h"

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

void logistic_exact ( int n, double t[], double *y )

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

    logistic_exact() evaluates the exact solution for the logistic ODE.

  Discussion:

    Evaluating the exact solution requires the Lambert W function.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    26 May 2024

  Author:

    John Burkardt

  Input:

    int n: the number of times.

    double t[n]: the times.

  Output:

    double y[n]: the exact solution values.
*/
{
  int i;
  double k;
  double r;
  double t0;
  double y0;
/*
  Retrieve current parameter values.
*/
  logistic_parameters ( NULL, NULL, NULL, NULL, NULL, 
                        &r,   &k,   &t0,  &y0,  NULL );
  for ( i = 0; i < n; i++ )
  {
    y[i] = ( k * y0 *   exp ( r * ( t[i] - t0 ) ) ) 
         / ( k + y0 * ( exp ( r * ( t[i] - t0 ) ) - 1.0 ) );
  }

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

void logistic_parameters ( double *r_in, double *k_in, double *t0_in, 
  double *y0_in, double *tstop_in, double *r_out, double *k_out,
  double *t0_out, double *y0_out, double *tstop_out )

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

    logistic_parameters() returns parameters for logistic_ode().

  Discussion:

    If input values are specified, this resets the default parameters.
    Otherwise, the output will be the current defaults.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    26 May 2024

  Author:

    John Burkardt

  Input:

    double *r_in: the reproduction rate.

    double *k_in: the carrying capacity.

    double *t0_in: the initial time.

    double *y0_in: the initial condition at time T0.

    double *tstop_in: the final time.

  Output:

    double *r_out: the reproduction rate.

    double *k_out: the carrying capacity.

    double *t0_out: the initial time.

    double *y0_out: the initial condition at time T0.

    double *tstop_out: the final time.
*/
{
  static double r_default = 1.0;
  static double k_default = 1.0;
  static double t0_default = 0.0;
  static double y0_default = 0.5;
  static double tstop_default = 8.0;
/*
  New values, if supplied on input, overwrite the current values.
*/
  if ( r_in )
  {
    r_default = *r_in;
  }

  if ( k_in )
  {
    k_default = *k_in;
  }

  if ( t0_in )
  {
    t0_default = *t0_in;
  }

  if ( y0_in )
  {
    y0_default = *y0_in;
  }

  if ( tstop_in )
  {
    tstop_default = *tstop_in;
  }
/*
  The current values are copied to the output.
*/
  if ( r_out )
  {
    *r_out = r_default;
  }

  if ( k_out )
  {
    *k_out = k_default;
  }

  if ( t0_out )
  {
    *t0_out = t0_default;
  }

  if ( y0_out )
  {
    *y0_out = y0_default;
  }

  if ( tstop_out )
  {
    *tstop_out = tstop_default;
  }

  return;
}