def Fig1():
# Figure #1 in the Lab: The solution of y'=y-2x+4, y(0)=0, is
# y(x) = -2 + 2x + (ya + 2)e^x. This code plots the solution for 0<x<2,
# and then plots the approximation given by Euler's method
# Text Example
a, b, ya = 0.0, 2.0, 0.0
def f(x,ya): return -2. + 2.*x + (ya + 2.)*np.exp(x)
def ode_f(x,y): return np.array([1.*y -2.*x + 4.])
plt.plot(np.linspace(a,b,11), Euler(ode_f,a,b,10,ya) , 'b-',label="h = 0.2")
plt.plot(np.linspace(a,b,21), Euler(ode_f,a,b,20,ya) , 'g-',label="h = 0.1")
plt.plot(np.linspace(a,b,41), Euler(ode_f,a,b,40,ya) , 'r-',label="h = 0.05")
x = np.linspace(0,2,200); k =int(200/40)
plt.plot(x[::k], solution.function(x,f,0.0)[::k], 'k*-',label="Solution") # The solution
plt.plot(x[k-1::k], solution.function(x,f,0.0)[k-1::k], 'k-') # The solution
plt.legend(loc='best')
plt.xlabel('x')
plt.ylabel('y')
plt.savefig('Fig1.pdf')
# plt.show()
plt.clf()
return
def test_non_integer_argument(self):
with self.assertRaises(TypeError) as context:
arg = "arg"
result = function(arg)
self.assertEqual('Argument must be interger',
context.exception.message,
'Only integers are allowed as input')
def test_negative_integer_argument(self):
with self.assertRaises(ValueError) as context:
arg = -10
result = function(arg)
self.assertEqual('Argument must be positive interger',
context.exception.message,
'Only positive integers are allowed as input')
def Exercise4old():
# Integral curves for f(x).
a , b, n = 0.0, 1.6, 200
k, x = int(n/20), np.linspace(a,b,n+1)
def f(x,ya): return 4. - 2.*x + (ya - 4.)*np.exp(-x)
plt.plot(x, solution.function(x,f,0.0), 'k-')
plt.plot(x, solution.function(x,f,2.0), 'k-')
plt.plot(x[::k], solution.function(x,f,4.0)[::k], 'k*-', label='Particular solution for 'r"$y' +y = - 2x + 2 $.")
plt.plot(x, solution.function(x,f,6.0), 'k-')
plt.plot(x, solution.function(x,f,8.0), 'k-')
plt.legend(loc='best')
plt.xlabel('x')
plt.ylabel('y')
# plt.show()
plt.savefig('Exercise4.pdf')
plt.clf()
return
def Exercise1():
a, b, ya = 0.0, 2.0, 0.0
def f(x,ya): return 4. - 2.*x + (ya - 4.)*np.exp(-x)
def ode_f(x,y): return np.array([-1.*y -2.*x + 2.])
plt.plot(np.linspace(a,b,11), Euler(ode_f,a,b,10,ya) , 'b-',label="h = 0.2")
plt.plot(np.linspace(a,b,21), Euler(ode_f,a,b,20,ya) , 'g-',label="h = 0.1")
plt.plot(np.linspace(a,b,41), Euler(ode_f,a,b,40,ya) , 'r-',label="h = 0.05")
x = np.linspace(0,2,200); k =int(200/40)
plt.plot(x[::k], solution.function(x,f,0.0)[::k], 'k*-',label="Solution") # The solution
plt.plot(x[k-1::k], solution.function(x,f,0.0)[k-1::k], 'k-') # The solution
plt.legend(loc='best')
plt.xlabel('x')
plt.ylabel('y')
plt.savefig('Exercise1.pdf')
# plt.show()
plt.clf()
return
def test_0_returns_empty_list(self):
arg = 0
result = function(arg)
self.assertEqual(result, [],
msg='Expected {}, got {}'.format([], result))
def test_ouput1(self):
arg = 10
result = function(arg)
self.assertEqual(result, [2, 3, 5, 7],
msg='Expected {}, got {}'.format([2, 3, 5, 7],
result))
def test_function(self):
self.assertEqual(42, solution.function(7, 3))