# include <cmath>
# include <iomanip>
# include <iostream>

using namespace std;

# include "stiff_ode.hpp"

//****************************************************************************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 stiff_deriv ( double t, double y[], double dydt[] )

//****************************************************************************80
//
//  stiff_deriv evaluates the right hand side of the stiff ODE.
//
//  Discussion:
//
//    y' = lambda * ( cos(t) - y )
//    y(t0) = y0
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    20 June 2025
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    double T, Y[1]: the time and solution value.
//
//  Output:
//
//    double DYDT[1]: the derivative value.
//
{
  double lambda;

  stiff_parameters ( NULL, NULL, NULL, NULL, &lambda, NULL, NULL, NULL );

  dydt[0] = lambda * ( cos ( t ) - y[0] );

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

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

//****************************************************************************80
//
//  Purpose:
//
//    stiff_euler() uses the Euler method on the stiff ODE.
//
//  Discussion:
//
//    y' = lambda * ( cos(t) - 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] ) - y[i] );
  }

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

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

//****************************************************************************80
//
//  Purpose:
//
//    stiff_euler_backward() uses the backward Euler method on the stiff ODE.
//
//  Discussion:
//
//    y' = lambda * ( cos(t) - 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+1] ) ) 
      / ( 1.0 + lambda * dt );
  }

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

double *stiff_exact ( int n, double t[] )

//****************************************************************************80
//
//  Purpose:
//
//    stiff_exact() evaluates the exact solution of the stiff ODE.
//
//  Discussion:
//
//    y' = lambda * ( cos(t) - 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 values.
//
//    double T[N]: the evaluation times.
//
//  Output:
//
//    double STIFF_EXACT[N]: the exact solution values.
//
{
  int i;
  double lambda;
  double *y;

  stiff_parameters ( NULL, NULL, NULL, NULL, &lambda, NULL, NULL, NULL );

  y = new double[n];

  for ( i = 0; i < n; i++ )
  {
    y[i] = lambda * ( sin ( t[i] ) + lambda * cos ( t[i] )
      - lambda * exp ( - lambda * t[i] ) ) / ( lambda * lambda + 1.0 );
  }

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

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

//****************************************************************************80
//
//  Purpose:
//
//    stiff_midpoint() uses the midpoint method on the stiff ODE.
//
//  Discussion:
//
//    y' = lambda * ( cos(t) - 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] + lambda * 0.5 * dt * ( 
                                     cos ( t[i] ) - y[i] + cos ( t[i+1] ) 
                                   ) 
      ) 
      / ( 1.0 + lambda * 0.5 * dt );
  }

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

void stiff_parameters ( 
  double *lambda_in,  double *t0_in,  double *y0_in,  double *tstop_in, 
  double *lambda_out, double *t0_out, double *y0_out, double *tstop_out )

//****************************************************************************80
//
//  Purpose:
//
//    stiff_parameters() returns parameters of the stiff ODE.
//
//  Discussion:
//
//    y' = lambda * ( cos(t) - y )
//    y(t0) = y0
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    20 June 2025
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    double *lambda_in, a parameter.
//
//    double *t0_in, double *y0_in: the initial time and value.
//
//    double *tstop_in: the final time.
//
//  Output:
//
//    double *lambda_out, a parameter.
//
//    double *t0_out, double *y0_out: the initial time and value.
//
//    double *tstop_out: the final time.
//
{
  static double lambda_default = 50.0;
  static double t0_default = 0.0;
  static double y0_default = 0.0;
  static double tstop_default = 1.0;
//
//  New values, if supplied on input, overwrite the current values.
//
  if ( lambda_in )
  {
    lambda_default = *lambda_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 ( lambda_out )
  {
    *lambda_out = lambda_default;
  }
  if ( t0_out )
  {
    *t0_out = t0_default;
  }
  if ( y0_out )
  {
    *y0_out = y0_default;
  }
  if ( tstop_out )
  {
    *tstop_out = tstop_default;
  }

  return;
}