#! /usr/bin/env python3
#
from forward_euler import forward_euler
from stiff_ode import stiff_ode, stiff_solution, stiff_lambda
import matplotlib.pyplot as plt
import numpy as np

print ( "exercise1:" )

#
#  Set the value of lambda to 4.
#
LAMBDA = 0.25
stiff_lambda ( LAMBDA )
#
#  Solve the ODE.
#
f_ode = stiff_ode
xRange = np.array ( [ 0.0, 2.0 * np.pi ] )
yInit = 0.0
numSteps = 50
x1, y1 = forward_euler ( f_ode, xRange, yInit, numSteps )
#
#  Get the exact solution.
#
x2 = np.linspace ( 0.0, 2.0 * np.pi, 101 )
y2 = stiff_solution ( x2 )
#
#  Plot them together.
#
plt.plot ( x1, y1, 'b-' )
plt.plot ( x2, y2, 'r-' )
plt.legend ( [ 'forward_euler()', 'Exact' ] )
plt.grid ( True )
plt.title ( 'y = stiff_solution(x), LAMBDA = ' + str ( LAMBDA ) )
filename = 'exercise1.jpg'
plt.savefig ( filename )
print ( "  Graphics saved as ", filename )
plt.show ( )
plt.close ( )