#! /usr/bin/env python3
#
from back_euler import back_euler
from forward_euler import forward_euler
from vanderpol_ode import vanderpol_nu, vanderpol_ode
import matplotlib.pyplot as plt
import numpy as np

print ( '' )
print ( 'exercise8:' )
print ( 'Compare forward_euler and back_euler on the van der Pol equation.' )

NU = 12.0
vanderpol_nu ( NU )

f_ode = vanderpol_ode
xRange = np.array ( [ 0.0, 2.0 ] )
yInit = np.array ( [ 0.0, 0.0 ] )
numSteps = 40
x1, y1 = forward_euler ( f_ode, xRange, yInit, numSteps )
x2, y2 = back_euler ( f_ode, xRange, yInit, numSteps )

plt.plot ( x1, y1, 'r-' )
plt.plot ( x2, y2, 'b-', linewidth = 2 )
plt.grid ( True )
plt.xlabel ( '<--- X --->' )
plt.ylabel ( '<--- Y(X) --->' )
plt.legend ( [ "forward_euler y", "forward_euler y'", "back_euler y", "back_euler y'" ] )
plt.title ( 'van der Pol ODE' )

filename = 'exercise8.jpg'
plt.savefig ( filename )
print ( 'Graphics saved as "%s"' % ( filename ) )
plt.show ( )
plt.close ( )