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

print ( '' )
print ( 'exercise9:' )
print ( 'Use midpoint 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
x, y = midpoint ( f_ode, xRange, yInit, numSteps )

plt.plot ( x, y, 'r-' )
plt.grid ( True )
plt.xlabel ( '<--- X --->' )
plt.ylabel ( '<--- Y(X) --->' )
plt.title ( 'van der Pol ODE' )

filename = 'exercise9.jpg'
plt.savefig ( filename )
print ( 'Graphics saved as "%s"' % ( filename ) )
plt.show ( )
plt.close ( )