import pytest

from probability import *

from utils import rounder

def tests():

cpt = burglary.variable_node('Alarm')

event = {'Burglary': True, 'Earthquake': True}

assert cpt.p(True, event) == 0.95

event = {'Burglary': False, 'Earthquake': True}

assert cpt.p(False, event) == 0.71

# enumeration_ask('Earthquake', {}, burglary)

s = {'A': True, 'B': False, 'C': True, 'D': False}

assert consistent_with(s, {})

assert consistent_with(s, s)

assert not consistent_with(s, {'A': False})

assert not consistent_with(s, {'D': True})

random.seed(21)

p = rejection_sampling('Earthquake', {}, burglary, 1000)

assert p[True], p[False] == (0.001, 0.999)

random.seed(71)

p = likelihood_weighting('Earthquake', {}, burglary, 1000)

assert p[True], p[False] == (0.002, 0.998)

def test_probdist_basic():

P = ProbDist('Flip')

P['H'], P['T'] = 0.25, 0.75

assert P['H'] == 0.25

assert P['T'] == 0.75

assert P['X'] == 0.00

P = ProbDist('BiasedDie')

P['1'], P['2'], P['3'], P['4'], P['5'], P['6'] = 10, 15, 25, 30, 40, 80

P.normalize()

assert P['2'] == 0.075

assert P['4'] == 0.15

assert P['6'] == 0.4

def test_probdist_frequency():

P = ProbDist('X', {'lo': 125, 'med': 375, 'hi': 500})

assert (P['lo'], P['med'], P['hi']) == (0.125, 0.375, 0.5)

P = ProbDist('Pascal-5', {'x1': 1, 'x2': 5, 'x3': 10, 'x4': 10, 'x5': 5, 'x6': 1})

assert (P['x1'], P['x2'], P['x3'], P['x4'], P['x5'], P['x6']) == (

0.03125, 0.15625, 0.3125, 0.3125, 0.15625, 0.03125)

def test_probdist_normalize():

P = ProbDist('Flip')

P['H'], P['T'] = 35, 65

P = P.normalize()

assert (P.prob['H'], P.prob['T']) == (0.350, 0.650)

P = ProbDist('BiasedDie')

P['1'], P['2'], P['3'], P['4'], P['5'], P['6'] = 10, 15, 25, 30, 40, 80

P = P.normalize()

assert (P.prob['1'], P.prob['2'], P.prob['3'], P.prob['4'], P.prob['5'], P.prob['6']) == (

0.05, 0.075, 0.125, 0.15, 0.2, 0.4)

def test_jointprob():

P = JointProbDist(['X', 'Y'])

P[1, 1] = 0.25

assert P[1, 1] == 0.25

P[dict(X=0, Y=1)] = 0.5

assert P[dict(X=0, Y=1)] == 0.5

def test_event_values():

assert event_values({'A': 10, 'B': 9, 'C': 8}, ['C', 'A']) == (8, 10)

assert event_values((1, 2), ['C', 'A']) == (1, 2)

def test_enumerate_joint():

P = JointProbDist(['X', 'Y'])

P[0, 0] = 0.25

P[0, 1] = 0.5

P[1, 1] = P[2, 1] = 0.125

assert enumerate_joint(['Y'], dict(X=0), P) == 0.75

assert enumerate_joint(['X'], dict(Y=2), P) == 0

assert enumerate_joint(['X'], dict(Y=1), P) == 0.75

Q = JointProbDist(['W', 'X', 'Y', 'Z'])

Q[0, 1, 1, 0] = 0.12

Q[1, 0, 1, 1] = 0.4

Q[0, 0, 1, 1] = 0.5

Q[0, 0, 1, 0] = 0.05

Q[0, 0, 0, 0] = 0.675

Q[1, 1, 1, 0] = 0.3

assert enumerate_joint(['W'], dict(X=0, Y=0, Z=1), Q) == 0

assert enumerate_joint(['W'], dict(X=0, Y=0, Z=0), Q) == 0.675

assert enumerate_joint(['W'], dict(X=0, Y=1, Z=1), Q) == 0.9

assert enumerate_joint(['Y'], dict(W=1, X=0, Z=1), Q) == 0.4

assert enumerate_joint(['Z'], dict(W=0, X=0, Y=0), Q) == 0.675

assert enumerate_joint(['Z'], dict(W=1, X=1, Y=1), Q) == 0.3

def test_enumerate_joint_ask():

P = JointProbDist(['X', 'Y'])

P[0, 0] = 0.25

P[0, 1] = 0.5

P[1, 1] = P[2, 1] = 0.125

assert enumerate_joint_ask(

'X', dict(Y=1), P).show_approx() == '0: 0.667, 1: 0.167, 2: 0.167'

def test_bayesnode_p():

bn = BayesNode('X', 'Burglary', {T: 0.2, F: 0.625})

assert bn.p(True, {'Burglary': True, 'Earthquake': False}) == 0.2

assert bn.p(False, {'Burglary': False, 'Earthquake': True}) == 0.375

assert BayesNode('W', '', 0.75).p(False, {'Random': True}) == 0.25

def test_bayesnode_sample():

X = BayesNode('X', 'Burglary', {T: 0.2, F: 0.625})

assert X.sample({'Burglary': False, 'Earthquake': True}) in [True, False]

Z = BayesNode('Z', 'P Q', {(True, True): 0.2, (True, False): 0.3,

(False, True): 0.5, (False, False): 0.7})

assert Z.sample({'P': True, 'Q': False}) in [True, False]

def test_enumeration_ask():

assert enumeration_ask(

'Burglary', dict(JohnCalls=T, MaryCalls=T),

burglary).show_approx() == 'False: 0.716, True: 0.284'

assert enumeration_ask(

'Burglary', dict(JohnCalls=T, MaryCalls=F),

burglary).show_approx() == 'False: 0.995, True: 0.00513'

assert enumeration_ask(

'Burglary', dict(JohnCalls=F, MaryCalls=T),

burglary).show_approx() == 'False: 0.993, True: 0.00688'

assert enumeration_ask(

'Burglary', dict(JohnCalls=T),

burglary).show_approx() == 'False: 0.984, True: 0.0163'

assert enumeration_ask(

'Burglary', dict(MaryCalls=T),

burglary).show_approx() == 'False: 0.944, True: 0.0561'

def test_elemination_ask():

assert elimination_ask(

'Burglary', dict(JohnCalls=T, MaryCalls=T),

burglary).show_approx() == 'False: 0.716, True: 0.284'

assert elimination_ask(

'Burglary', dict(JohnCalls=T, MaryCalls=F),

burglary).show_approx() == 'False: 0.995, True: 0.00513'

assert elimination_ask(

'Burglary', dict(JohnCalls=F, MaryCalls=T),

burglary).show_approx() == 'False: 0.993, True: 0.00688'

assert elimination_ask(

'Burglary', dict(JohnCalls=T),

burglary).show_approx() == 'False: 0.984, True: 0.0163'

assert elimination_ask(

'Burglary', dict(MaryCalls=T),

burglary).show_approx() == 'False: 0.944, True: 0.0561'

def test_prior_sample():

random.seed(42)

all_obs = [prior_sample(burglary) for x in range(1000)]

john_calls_true = [observation for observation in all_obs if observation['JohnCalls']]

mary_calls_true = [observation for observation in all_obs if observation['MaryCalls']]

burglary_and_john = [observation for observation in john_calls_true if observation['Burglary']]

burglary_and_mary = [observation for observation in mary_calls_true if observation['Burglary']]

assert len(john_calls_true) / 1000 == 46 / 1000

assert len(mary_calls_true) / 1000 == 13 / 1000

assert len(burglary_and_john) / len(john_calls_true) == 1 / 46

assert len(burglary_and_mary) / len(mary_calls_true) == 1 / 13

def test_prior_sample2():

random.seed(128)

all_obs = [prior_sample(sprinkler) for x in range(1000)]

rain_true = [observation for observation in all_obs if observation['Rain']]

sprinkler_true = [observation for observation in all_obs if observation['Sprinkler']]

rain_and_cloudy = [observation for observation in rain_true if observation['Cloudy']]

sprinkler_and_cloudy = [observation for observation in sprinkler_true if observation['Cloudy']]

assert len(rain_true) / 1000 == 0.476

assert len(sprinkler_true) / 1000 == 0.291

assert len(rain_and_cloudy) / len(rain_true) == 376 / 476

assert len(sprinkler_and_cloudy) / len(sprinkler_true) == 39 / 291

def test_rejection_sampling():

random.seed(47)

assert rejection_sampling(

'Burglary', dict(JohnCalls=T, MaryCalls=T),

burglary, 10000).show_approx() == 'False: 0.7, True: 0.3'

assert rejection_sampling(

'Burglary', dict(JohnCalls=T, MaryCalls=F),

burglary, 10000).show_approx() == 'False: 1, True: 0'

assert rejection_sampling(

'Burglary', dict(JohnCalls=F, MaryCalls=T),

burglary, 10000).show_approx() == 'False: 0.987, True: 0.0128'

assert rejection_sampling(

'Burglary', dict(JohnCalls=T),

burglary, 10000).show_approx() == 'False: 0.982, True: 0.0183'

assert rejection_sampling(

'Burglary', dict(MaryCalls=T),

burglary, 10000).show_approx() == 'False: 0.965, True: 0.0348'

def test_rejection_sampling2():

random.seed(42)

assert rejection_sampling(

'Cloudy', dict(Rain=T, Sprinkler=T),

sprinkler, 10000).show_approx() == 'False: 0.56, True: 0.44'

assert rejection_sampling(

'Cloudy', dict(Rain=T, Sprinkler=F),

sprinkler, 10000).show_approx() == 'False: 0.119, True: 0.881'

assert rejection_sampling(

'Cloudy', dict(Rain=F, Sprinkler=T),

sprinkler, 10000).show_approx() == 'False: 0.951, True: 0.049'

assert rejection_sampling(

'Cloudy', dict(Rain=T),

sprinkler, 10000).show_approx() == 'False: 0.205, True: 0.795'

assert rejection_sampling(

'Cloudy', dict(Sprinkler=T),

sprinkler, 10000).show_approx() == 'False: 0.835, True: 0.165'

def test_likelihood_weighting():

random.seed(1017)

assert likelihood_weighting(

'Burglary', dict(JohnCalls=T, MaryCalls=T),

burglary, 10000).show_approx() == 'False: 0.702, True: 0.298'

assert likelihood_weighting(

'Burglary', dict(JohnCalls=T, MaryCalls=F),

burglary, 10000).show_approx() == 'False: 0.993, True: 0.00656'

assert likelihood_weighting(

'Burglary', dict(JohnCalls=F, MaryCalls=T),

burglary, 10000).show_approx() == 'False: 0.996, True: 0.00363'

assert likelihood_weighting(

'Burglary', dict(JohnCalls=F, MaryCalls=F),

burglary, 10000).show_approx() == 'False: 1, True: 0.000126'

assert likelihood_weighting(

'Burglary', dict(JohnCalls=T),

burglary, 10000).show_approx() == 'False: 0.979, True: 0.0205'

assert likelihood_weighting(

'Burglary', dict(MaryCalls=T),

burglary, 10000).show_approx() == 'False: 0.94, True: 0.0601'

def test_likelihood_weighting2():

random.seed(42)

assert likelihood_weighting(

'Cloudy', dict(Rain=T, Sprinkler=T),

sprinkler, 10000).show_approx() == 'False: 0.559, True: 0.441'

assert likelihood_weighting(

'Cloudy', dict(Rain=T, Sprinkler=F),

sprinkler, 10000).show_approx() == 'False: 0.12, True: 0.88'

assert likelihood_weighting(

'Cloudy', dict(Rain=F, Sprinkler=T),

sprinkler, 10000).show_approx() == 'False: 0.951, True: 0.0486'

assert likelihood_weighting(

'Cloudy', dict(Rain=T),

sprinkler, 10000).show_approx() == 'False: 0.198, True: 0.802'

assert likelihood_weighting(

'Cloudy', dict(Sprinkler=T),

sprinkler, 10000).show_approx() == 'False: 0.833, True: 0.167'

def test_forward_backward():

umbrella_prior = [0.5, 0.5]

umbrella_transition = [[0.7, 0.3], [0.3, 0.7]]

umbrella_sensor = [[0.9, 0.2], [0.1, 0.8]]

umbrellaHMM = HiddenMarkovModel(umbrella_transition, umbrella_sensor)

umbrella_evidence = [T, T, F, T, T]

assert rounder(forward_backward(umbrellaHMM, umbrella_evidence, umbrella_prior)) == [

[0.6469, 0.3531], [0.8673, 0.1327], [0.8204, 0.1796], [0.3075, 0.6925], [0.8204, 0.1796], [0.8673, 0.1327]]

umbrella_evidence = [T, F, T, F, T]

assert rounder(forward_backward(umbrellaHMM, umbrella_evidence, umbrella_prior)) == [

[0.5871, 0.4129], [0.7177, 0.2823], [0.2324, 0.7676], [0.6072, 0.3928], [0.2324, 0.7676], [0.7177, 0.2823]]

def test_viterbi():

umbrella_prior = [0.5, 0.5]

umbrella_transition = [[0.7, 0.3], [0.3, 0.7]]

umbrella_sensor = [[0.9, 0.2], [0.1, 0.8]]

umbrellaHMM = HiddenMarkovModel(umbrella_transition, umbrella_sensor)

umbrella_evidence = [T, T, F, T, T]

assert rounder(viterbi(umbrellaHMM, umbrella_evidence, umbrella_prior)) == [0.8182, 0.5155, 0.1237, 0.0334, 0.0210]

umbrella_evidence = [T, F, T, F, T]

assert rounder(viterbi(umbrellaHMM, umbrella_evidence, umbrella_prior)) == [0.8182, 0.1964, 0.053, 0.0154, 0.0042]

def test_fixed_lag_smoothing():

umbrella_evidence = [T, F, T, F, T]

e_t = F

t = 4

umbrella_transition = [[0.7, 0.3], [0.3, 0.7]]

umbrella_sensor = [[0.9, 0.2], [0.1, 0.8]]

umbrellaHMM = HiddenMarkovModel(umbrella_transition, umbrella_sensor)

d = 2

assert rounder(fixed_lag_smoothing(e_t, umbrellaHMM, d, umbrella_evidence, t)) == [0.1111, 0.8889]

d = 5

assert fixed_lag_smoothing(e_t, umbrellaHMM, d, umbrella_evidence, t) is None

umbrella_evidence = [T, T, F, T, T]

# t = 4

e_t = T

d = 1

assert rounder(fixed_lag_smoothing(e_t, umbrellaHMM, d, umbrella_evidence, t)) == [0.9939, 0.0061]

def test_particle_filtering():

N = 10

umbrella_evidence = T

umbrella_transition = [[0.7, 0.3], [0.3, 0.7]]

umbrella_sensor = [[0.9, 0.2], [0.1, 0.8]]

umbrellaHMM = HiddenMarkovModel(umbrella_transition, umbrella_sensor)

s = particle_filtering(umbrella_evidence, N, umbrellaHMM)

assert len(s) == N

assert all(state in 'AB' for state in s)

# XXX 'A' and 'B' are really arbitrary names, but I'm letting it stand for now

def test_monte_carlo_localization():

# TODO: Add tests for random motion/inaccurate sensors

random.seed('aima-python')

m = MCLmap([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0],

[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0],

[1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0],

[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0],

[0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0],

[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0],

[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0],

[0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0],

[0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0],

[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0],

[0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0]])

def P_motion_sample(kin_state, v, w):

"""Sample from possible kinematic states.

Returns from a single element distribution (no uncertainty in motion)"""

pos = kin_state[:2]

orient = kin_state[2]

# for simplicity the robot first rotates and then moves

orient = (orient + w) % 4

for _ in range(orient):

v = (v[1], -v[0])

pos = vector_add(pos, v)

return pos + (orient,)

def P_sensor(x, y):

"""Conditional probability for sensor reading"""

# Need not be exact probability. Can use a scaled value.

if x == y:

return 0.8

elif abs(x - y) <= 2:

return 0.05

else:

return 0

from utils import print_table

a = {'v': (0, 0), 'w': 0}

z = (2, 4, 1, 6)

S = monte_carlo_localization(a, z, 1000, P_motion_sample, P_sensor, m)

grid = [[0] * 17 for _ in range(11)]

for x, y, _ in S:

if 0 <= x < 11 and 0 <= y < 17:

grid[x][y] += 1

print("GRID:")

print_table(grid)

a = {'v': (0, 1), 'w': 0}

z = (2, 3, 5, 7)

S = monte_carlo_localization(a, z, 1000, P_motion_sample, P_sensor, m, S)

grid = [[0] * 17 for _ in range(11)]

for x, y, _ in S:

if 0 <= x < 11 and 0 <= y < 17:

grid[x][y] += 1

print("GRID:")

print_table(grid)

assert grid[6][7] > 700

def test_gibbs_ask():

possible_solutions = ['False: 0.16, True: 0.84', 'False: 0.17, True: 0.83', 'False: 0.15, True: 0.85']

g_solution = gibbs_ask('Cloudy', dict(Rain=True), sprinkler, 200).show_approx()

assert g_solution in possible_solutions

# The following should probably go in .ipynb:

"""

# We can build up a probability distribution like this (p. 469):

>>> P = ProbDist()

>>> P['sunny'] = 0.7

>>> P['rain'] = 0.2

>>> P['cloudy'] = 0.08

>>> P['snow'] = 0.02

# and query it like this: (Never mind this ELLIPSIS option

# added to make the doctest portable.)

>>> P['rain'] #doctest:+ELLIPSIS

0.2...

# A Joint Probability Distribution is dealt with like this [Figure 13.3]:

>>> P = JointProbDist(['Toothache', 'Cavity', 'Catch'])

>>> T, F = True, False

>>> P[T, T, T] = 0.108; P[T, T, F] = 0.012; P[F, T, T] = 0.072; P[F, T, F] = 0.008

>>> P[T, F, T] = 0.016; P[T, F, F] = 0.064; P[F, F, T] = 0.144; P[F, F, F] = 0.576

>>> P[T, T, T]

0.108

# Ask for P(Cavity|Toothache=T)

>>> PC = enumerate_joint_ask('Cavity', {'Toothache': T}, P)

>>> PC.show_approx()

'False: 0.4, True: 0.6'

>>> 0.6-epsilon < PC[T] < 0.6+epsilon

True

>>> 0.4-epsilon < PC[F] < 0.4+epsilon

True

"""

if __name__ == '__main__':

pytest.main()