def test_can_initiate_distribution_with_intersecting_ranges(self): prob_dist = [ ((4, 7), 0.3), ((5, 8), 0.3), ((5, 6), 0.4), ] p = ProbabilityDistribution(prob_dist) self.assertAlmostEqual(p.p((5, 6)), 0.6) self.assertAlmostEqual(p.interval(0.6)[0], 5 + 1/6) self.assertAlmostEqual(p.interval(0.6)[1], 6.5)
class TestProbabilityUtils(unittest.TestCase):
def setUp(self):
self.p1_dict = {
0: 0.1,
1: 0.2,
2: 0.3,
3: 0.3,
4: 0.1
# mean: 2.1
}
self.p1 = ProbabilityDistribution(self.p1_dict)
self.p2_dict = {
(1, 2): 0.5,
4: 0.2,
(4, 5): 0.3
# mean: 2.9
}
self.p2 = ProbabilityDistribution(self.p2_dict)
def test_can_get_probability(self):
prob = self.p1.p(0)
self.assertAlmostEqual(prob, 0.1)
def test_can_get_probability_outside_definition(self):
prob = self.p1.p(10)
self.assertEqual(prob, 0)
def test_can_get_probability_for_range(self):
prob = self.p1.p([0, 2.5])
self.assertAlmostEqual(prob, 0.6)
def test_raises_valueerror_for_badly_defined_ranges(self):
# contains only one value
self.assertRaisesRegex(ValueError, 'Expected length of interval to be 2, but length is', self.p1.p, [0])
# contains three values value
self.assertRaisesRegex(ValueError, 'Expected length of interval to be 2, but length is', self.p1.p, [0, 1, 3])
def test_can_get_mean(self):
self.assertAlmostEqual(self.p1.mean, 2.1)
def test_can_get_interval(self):
interval = self.p1.interval(0.95)
self.assertEqual(interval, (0, 4))
interval = self.p1.interval(0.5)
self.assertEqual(interval, (1, 3))
# bordering
interval = self.p1.interval(0.8)
self.assertEqual(interval, (1, 3))
# complete
interval = self.p1.interval(1)
self.assertEqual(interval, (0, 4))
def test_raises_when_interval_value_wrong(self):
self.assertRaisesRegex(ValueError, 'Confidence value for interval should be', self.p1.interval, 0)
self.assertRaisesRegex(ValueError, 'Confidence value for interval should be', self.p1.interval, 1.2)
def test_supports_ranges_for_probabilities(self):
# only in a range
self.assertEqual(self.p2.p(1), 0)
# specified both in range and as point
self.assertEqual(self.p2.p(4), 0.2)
self.assertEqual(self.p2.p((4.5, 5)), 0.15)
def test_supports_ranges_for_mean(self):
self.assertEqual(self.p2.mean, 2.9)
def test_supports_ranges_for_interval(self):
self.assertEqual(self.p2.interval(0.95), (1.05, 4.916666666666667))
def test_can_add_distributions(self):
p3 = self.p1 + self.p2
self.assertEqual(type(p3), ProbabilityDistribution)
p3.normalize()
self.assertEqual(p3.mean, 2.5)
self.assertAlmostEqual(p3.p(4), 0.15)
def test_can_add_distributions_with_intersection_ranges(self):
p4 = ProbabilityDistribution({
(1, 3): 0.5,
(4, 5): 0.5
# mean: 3.25
})
p5 = ProbabilityDistribution({
(2, 4): 0.5,
(5, 6): 0.5
# mean: 4.25
})
p6 = p4 + p5
p6.normalize()
self.assertEqual(p6.mean, 3.75)
self.assertEqual(p6.p((2, 3)), 0.25)
def test_can_add_distributions_with_multiple_intersection_ranges(self):
p4 = ProbabilityDistribution({
(1, 4): 0.3,
(4, 6): 0.6,
(7, 8): 0.1
})
p5 = ProbabilityDistribution({
(0, 2): 0.2,
(2, 3): 0.3,
(3, 9): 0.5 # intersects all ranges
})
p6 = p4 + p5
p6.normalize()
p6_prob_ranges_expected = {
(0, 1): 0.05,
(1, 2): 0.1,
(2, 3): 0.2,
(3, 4): (0.3/3 + 0.5/6)/2,
(4, 6): (0.6 + 0.5/6*2)/2,
(6, 7): (0.5/6)/2,
(7, 8): (0.1 + 0.5/6)/2,
(8, 9): (0.5/6)/2
}
# custom asserting since the dicts contain floats
self.assertEqual(set(p6.prob_ranges.keys()), set(p6_prob_ranges_expected.keys()))
for key in p6.prob_ranges.keys():
# need AlmostEqual for floats
self.assertAlmostEqual(p6.prob_ranges[key], p6_prob_ranges_expected[key])
def test_can_sum_distributions(self):
p3 = ProbabilityDistribution({
1: 0.5,
2: 0.5
# mean: 1.5
})
p4 = sum([self.p1, self.p2, p3])
p4.normalize()
# mean: (2.1 + 2.9 + 1.5) / 3 = 2 1/6
self.assertAlmostEqual(p4.mean, 2 + 1/6)
def test_raises_when_adding_not_distribution(self):
try:
self.p1 + 1
except TypeError:
pass
except Exception as e:
self.fail(f'Should have raised TypeError, but raised {type(e)}')
else:
self.fail('Should have raised')
def test_can_initiate_distribution_with_list_of_values(self):
prob_dist = [
(4, 0.5),
(5, 0.2),
((5, 6), 0.3)
]
try:
p = ProbabilityDistribution(prob_dist)
except AttributeError as e:
self.fail(f'Should not have raised error "{e}"')
self.assertAlmostEqual(p.p(4), 0.5)
self.assertAlmostEqual(p.p((5, 6)), 0.5)
self.assertAlmostEqual(p.p((5.5, 6)), 0.15)
def test_can_initiate_distribution_with_duplicate_entries(self):
prob_dist = [
(4, 0.5),
(4, 0.2),
(5, 0.3)
]
p = ProbabilityDistribution(prob_dist)
self.assertAlmostEqual(p.p(4), 0.7)
def test_can_initiate_distribution_with_intersecting_ranges(self):
prob_dist = [
((4, 7), 0.3),
((5, 8), 0.3),
((5, 6), 0.4),
]
p = ProbabilityDistribution(prob_dist)
self.assertAlmostEqual(p.p((5, 6)), 0.6)
self.assertAlmostEqual(p.interval(0.6)[0], 5 + 1/6)
self.assertAlmostEqual(p.interval(0.6)[1], 6.5)
def test_can_multiply_distribution_by_number(self):
p7 = self.p1 * 0.5
self.assertEqual(type(p7), ProbabilityDistribution)
# this is not a true ProbabilityDistribution, probabilities sum to 0.5
self.assertAlmostEqual(p7.p(4), 0.05)
def test_can_multiply_distributions_with_ranges(self):
p3 = ProbabilityDistribution({(0.5, 0.625): 1.0})
p4 = p3 * 3
self.assertAlmostEqual(p4.p((0.5, 0.625)), 3)
def test_can_multiply_distribution_left_hand(self):
p7 = 0.5 * self.p1
self.assertEqual(type(p7), ProbabilityDistribution)
# this is not a true ProbabilityDistribution, probabilities sum to 0.5
self.assertAlmostEqual(p7.p(4), 0.05)
def test_can_normalize_distribution(self):
p3 = ProbabilityDistribution({1: 1, (2, 3): 1}, normalize=False)
self.assertFalse(p3.is_normalized)
p3.normalize()
self.assertTrue(p3.is_normalized)
self.assertAlmostEqual(p3.p(1), 0.5)
self.assertAlmostEqual(p3.mean, 1.75)
def test_automatically_normalized_distribution_on_creation(self):
p3 = ProbabilityDistribution({1: 1, (2, 3): 1})
# No need to call .normalize() manually.
self.assertAlmostEqual(p3.p(1), 0.5)
self.assertAlmostEqual(p3.mean, 1.75)
def test_raises_ValueError_when_calculating_intervals_on_not_normalized_distribution(self):
p = ProbabilityDistribution({1: 0.5}, normalize=False)
self.assertRaisesRegex(ValueError, 'Cannot compute interval\(\) for the ProbabilityDistribution since it is not normalized', p.interval, 0.5)
def test_mean_is_None_for_not_normalized_distribution(self):
p = ProbabilityDistribution({1: 0.5}, normalize=False)
self.assertEqual(p.mean, None)
def test_add_range_to_ranges_raises_on_wrong_input(self):
# Get the function from an instance.
add_range_to_ranges = self.p1.add_range_to_ranges
# ranges is a list
self.assertRaises(ValueError, add_range_to_ranges, [], {(0, 1): 1})
# new_range_value is a list
self.assertRaises(ValueError, add_range_to_ranges, {}, [])
# empty new range
self.assertRaises(ValueError, add_range_to_ranges, {}, {})
def test_add_range_to_ranges_simple(self):
add_range_to_ranges = self.p1.add_range_to_ranges
ranges = {
(0, 1): 0.5,
(1, 2): 0.5
}
new_range_value = {
(2, 3): 1
}
expected = {
(0, 1): 0.5,
(1, 2): 0.5,
(2, 3): 1
}
add_range_to_ranges(ranges, new_range_value)
self.assertEqual(ranges, expected)
def test_add_range_to_ranges_one_intersection(self):
add_range_to_ranges = self.p1.add_range_to_ranges
ranges = {
(0, 1): 0.5,
(1, 2): 0.5
}
new_range_value = {
(1, 3): 1
}
expected = {
(0, 1): 0.5,
(1, 2): 1,
(2, 3): 0.5
}
add_range_to_ranges(ranges, new_range_value)
self.assertEqual(ranges, expected)
def test_add_range_to_ranges(self):
# Extra test since this went wrong, although the other tests worked.
add_range_to_ranges = self.p1.add_range_to_ranges
prob_ranges = {(1, 3): 0.5, (4, 5): 0.5}
prob_range = {(2, 4): 0.5}
add_range_to_ranges(prob_ranges, prob_range)
expected_ranges = {
(1, 2): 0.25,
(2, 3): 0.5,
(3, 4): 0.25,
(4, 5): 0.5
}
self.assertEqual(prob_ranges, expected_ranges)
def test_split_range(self):
split_range = self.p1.split_range
test_range = (1, 4)
points = [3, 2]
self.assertEqual(split_range(test_range, points), [(1, 2), (2, 3), (3, 4)])
test_range = (1, 4)
points = [4, 2]
self.assertEqual(split_range(test_range, points), [(1, 2), (2, 4)])
def test_split_prob_range(self):
# Extra test of values that didn't work out at first.
split_prob_range = self.p1.split_prob_range
prob_range = {
(1, 4): 0.5
}
points = [3, 2]
self.assertEqual(split_prob_range(prob_range, points), {
(1, 2): 1/6,
(2, 3): 1/6,
(3, 4): 1/6
})
points = [4, 2]
self.assertEqual(split_prob_range(prob_range, points), {
(1, 2): 1/6,
(2, 4): 2/6
})
def test_split_prob_range_extra(self):
split_prob_range = self.p1.split_prob_range
prob_range = {(1, 3): 0.5}
points = [1, 2, 3, 4]
expected_split_prob_range = {
(1, 2): 0.25,
(2, 3): 0.25
}
self.assertEqual(split_prob_range(prob_range, points), expected_split_prob_range)
def test_split_range_extra(self):
split_range = self.p1.split_range
split = split_range((1,3), [1, 2, 3, 4])
expected_split = [(1, 2), (2, 3)]
self.assertEqual(split, expected_split)
def test_merge_prob_ranges(self):
merge_prob_ranges = self.p1.merge_prob_ranges
prob_ranges_1 = {
(1, 3): 0.5,
(4, 5): 0.5
}
prob_ranges_2 = {
(2, 4): 0.5,
(5, 6): 0.5
}
merged_prob_ranges = merge_prob_ranges(prob_ranges_1, prob_ranges_2)
merged_prob_ranges_expected = {
(1, 2): 0.25,
(2, 3): 0.5,
(3, 4): 0.25,
(4, 5): 0.5,
(5, 6): 0.5
}
self.assertEqual(merged_prob_ranges, merged_prob_ranges_expected)
def test_can_add_values(self):
# This is different from adding the distributions,
# but if
# X ~ pd_x, Y ~ pd_y
# and Z ~ pd_z,
# then pd_x & pd_y ~ pd_z.
# TODO: consider whether switching '+' and '&'
# makes more sense?
# flipping a coin
coin = ProbabilityDistribution({
0: 0.5,
1: 0.5
})
# flipping two
p4 = coin & coin
self.assertEqual(type(p4), ProbabilityDistribution)
self.assertEqual(p4.mean, 1)
self.assertEqual(p4.p(0), 0.25)
self.assertEqual(p4.p(0), 0.25)
def test_can_add_values_with_at_most_one_range(self):
# This is different from adding the distributions,
# but if
# X ~ pd_x, Y ~ pd_y
# and Z ~ pd_z,
# then pd_x & pd_y ~ pd_z.
# TODO: consider whether switching '+' and '&'
# makes more sense?
# flipping a coin
coin = ProbabilityDistribution({
0: 0.5,
1: 0.5
})
p3 = ProbabilityDistribution({
(0, 1): 0.5,
(2, 3): 0.5
})
p4 = coin & p3
self.assertEqual(type(p4), ProbabilityDistribution)
self.assertEqual(p4.mean, coin.mean + p3.mean)
self.assertEqual(p4.p(0), 0)
self.assertEqual(p4.p((0, 1)), 0.25)
def test_raises_NotImplementedError_when_adding_distributions_with_both_ranges(self):
p3 = ProbabilityDistribution({
(0, 1): 0.5,
(2, 3): 0.5
})
try:
p4 = p3 & p3
except NotImplementedError:
pass
def test_can_add_number(self):
p3 = ProbabilityDistribution({
5: 0.2,
(0, 1): 0.3,
(2, 3): 0.5
})
p4 = 2 & p3
self.assertEqual(type(p4), ProbabilityDistribution)
self.assertEqual(p4.mean, p3.mean + 2)
self.assertEqual(p4.p(7), 0.2)
self.assertEqual(p4.p((4, 5)), 0.5)
p5 = p3 & 2
self.assertEqual(type(p5), ProbabilityDistribution)
self.assertEqual(p5.mean, p3.mean + 2)
self.assertEqual(p5.p(7), 0.2)
self.assertEqual(p5.p((4, 5)), 0.5)
def test_can_pad_with_zero(self):
# probability sums up to 0.7
p3 = ProbabilityDistribution({
1: 0.5,
2: 0.2
}, normalize=False)
# sanity check
self.assertAlmostEqual(p3.p(0), 0)
self.assertEqual(p3.mean, None)
p3.pad()
self.assertAlmostEqual(p3.p(0), 0.3)
self.assertEqual(p3.mean, 0.9)
def test_can_copy(self):
p3 = ProbabilityDistribution({
1: 0.5,
2: 0.2
}, normalize=False)
p4 = p3.copy()
self.assertEqual(type(p4), ProbabilityDistribution)
self.assertNotEqual(id(p3), id(p4))
# Same as p3
self.assertEqual(p4.mean, None)
p4.normalize()
self.assertAlmostEqual(p4.mean, 0.9/0.7)
# Original object is unchanged.
self.assertEqual(p3.mean, None)
def test_filters_out_p_0_values(self):
p3 = ProbabilityDistribution({
1: 1,
2: 0
})
self.assertEqual(list(p3.prob_points.keys()), [1])
def test_string_representation_sorts_keys(self):
p3 = ProbabilityDistribution({
2: 0.5,
1: 0.3,
(0, 1): 0.2
})
# Note that it should be sorted
expected_str = "ProbabilityDistribution({(0, 1): 0.2, 1: 0.3, 2: 0.5})"
self.assertEqual(str(p3), expected_str)