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event = {'Burglary': True, 'Earthquake': True}
event = {'Burglary': False, 'Earthquake': True}
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')
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)
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)
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
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
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(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]
assert enumeration_ask(
'Burglary', dict(JohnCalls=T, MaryCalls=T),
burglary).show_approx() == 'False: 0.716, True: 0.284'
elimination_ask(
'Burglary', dict(JohnCalls=T, MaryCalls=T),
burglary).show_approx() == 'False: 0.716, True: 0.284'
def test_rejection_sampling():
random.seed(47)
rejection_sampling(
'Burglary', dict(JohnCalls=T, MaryCalls=T),
burglary, 10000).show_approx() == 'False: 0.7, True: 0.3'
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'
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_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]
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)
Darius Bacon
a validé
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 uncertainity 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
# 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
"""