#! /usr/bin/env python3
#
def vanderpol_ode ( x, y ):

#*****************************************************************************80
#
## vanderpol_ode() evaluates the right hand side of the vanderpol ODE.
#
  import numpy as np

  nu = vanderpol_nu ( )

  fValue = np.zeros ( 2 )

  fValue[0] = y[1]
  fValue[1] = - nu * ( y[0]**2 - 1.0 ) * y[1] - y[0] + np.exp ( - x )

  return fValue

def vanderpol_nu ( nu_input = None ):

#*****************************************************************************80
#
## vanderpol_nu() allows the user to work with a global variable nu.
#
#  Modified:
#
#    02 October 2021
#
#  Author:
#
#    John Burkardt
#
  if ( not hasattr ( vanderpol_nu, "nu_default" ) ):
    vanderpol_nu.nu_default = 11.0

  if ( nu_input is not None ):
    vanderpol_nu.nu_default = nu_input

  nu_output = vanderpol_nu.nu_default

  return nu_output

if ( __name__ == '__main__' ):
  from forward_euler import forward_euler
  import matplotlib.pyplot as plt
  import numpy as np

  NU = 11.0
  vanderpol_nu ( NU )
  f_ode = vanderpol_ode
  xRange = np.array ( [ 0.0, 2.0 ] )
  yInit = np.array ( [ 0.0, 0.0 ] )
  numSteps = 40
  x, y = forward_euler ( f_ode, xRange, yInit, numSteps )

  plt.plot ( x, y, 'b-' )
  plt.grid ( True )
  plt.title ( 'Vanderpol ODE, NU = ' + str ( NU ) )
  filename = 'vanderpol_ode.jpg'
  plt.savefig ( filename )
  print ( "  Graphics saved as ", filename )
  plt.show ( )
  plt.close ( )