def test_steady_state(set_up_2x2):
weather, correct_answer = set_up_2x2
# Test case using problem 1 to generate a steady state matrix.
markov_matrix = mc.random_chain(4)
steady_state_x = mc.steady_state(markov_matrix)
assert(np.allclose(markov_matrix @ steady_state_x, steady_state_x))
# Test weather 2×2 example from book
assert np.allclose(mc.steady_state(weather), correct_answer)
def test_forecast():
"""Tests the forecast() function with respect to the steady_state() function."""
#Set tolerance for error
tol = 1e-2
transition = np.array([[0.7, 0.6], [0.3, 0.4]])
x = MC.steady_state(transition)
fcast = MC.forecast(int(1e5))
assert fcast.count(0) / len(
fcast) - x[0] < tol, "failed on ratio of hot days"
assert fcast.count(1) / len(
fcast) - x[1] < tol, "failed on ratio of cold days"
def test_four_state_forecast():
"""Tests the four_state_forecast() function with respect to the steady_state()
function."""
#Set tolerance for error
tol = 1e-2
transition = np.array([[0.5, 0.3, 0.1, 0], [0.3, 0.3, 0.3, 0.3],
[0.2, 0.3, 0.4, 0.5], [0, 0.1, 0.2, 0.2]])
x = MC.steady_state(transition)
fcast = MC.four_state_forecast(int(1e5))
assert fcast.count(0) / len(
fcast) - x[0] < tol, "failed on ratio of hot days"
assert fcast.count(1) / len(
fcast) - x[1] < tol, "failed on ratio of mild days"
assert fcast.count(2) / len(
fcast) - x[2] < tol, "failed on ratio of cold days"
assert fcast.count(3) / len(
fcast) - x[3] < tol, "failed on ratio of freezing days"
def test_steady_state():
"""A function for testing the steady_state function. Also validates the results of
forecast() and four_state_forecast()."""
#Set tolerance for error
tol = 1e-6
for n in range(1, 6):
#Make a random transition matrix and it's steady state distribution
A = MC.random_chain(n)
x = MC.steady_state(A)
#Compare x and Ax
x_new = A @ x
for i in range(n):
assert x_new[i] - x[i] < tol, "failed on Ax = x"
#Verify that the columns of A^k approach x as k approaches infinity
Ak = np.linalg.matrix_power(A, 20)
for i in range(n):
for j in range(n):
assert Ak[i, j] - x[
i] < tol, "failed on A^k approaches x column-wise"
def test_forcast(set_up_2x2):
transition, correct_answer = set_up_2x2
# Test if all the values are zeroes and ones... how else could you test this???
n = 10
weather = mc.forecast(n)
print(weather)
assert all([weather[i] in [0, 1] for i in range(n)])
steady_state_x = mc.steady_state(transition)
# Make sure steady_state calculated from problem 4 is correct
assert(np.allclose(transition @ steady_state_x, steady_state_x))
trials = int(1e4)
results = mc.forecast(trials)
average_hot_days = np.array(results).sum() / trials
assert np.allclose(average_hot_days, correct_answer[1], atol=.01)
def test_four_state_forcast(set_up_4x4):
# get 4x4 matrix
weather_matrix = set_up_4x4
# number of samples
n = int(1e5)
weather = mc.four_state_forecast(n)
# Test: is each entry valid?
assert all( [weather[i] in [0, 1, 2, 3] for i in range(n)] )
# Test: does the steady state match
steady_state = mc.steady_state(weather_matrix)
# count number of 0's, 1's, 2's, and 3's and divide by length of weather
answer = np.array([ # list comprehension
sum( [weather[j] == i for j in range(len(weather))] ) / len(weather)
for i in [0, 1, 2, 3]
])
print(answer)
assert np.allclose(steady_state, answer, atol=.005)