def compare(self, dist_1, dist_2):
dist_1_interval = TimeInterval(*self.bounds_of(dist_1))
dist_2_interval = TimeInterval(*self.bounds_of(dist_2))
dictionary_input_output = {}
for time_step in dist_1_interval + dist_2_interval:
dictionary_input_output[time_step] = sqrt(dist_1.pdf(time_step) * dist_2.pdf(time_step))
geometric_mean = FunctionPiecewiseLinear(dictionary_input_output, function_undefined=FUNCTION_ZERO)
same = integral(geometric_mean, NEGATIVE_INFINITY, POSITIVE_INFINITY)
dist_1_mean, dist_1_skewness, dist_1_kurtosis = dist_1.stats(moments='msk')
dist_1_standard_deviation = dist_1.std()
dist_2_mean, dist_2_skewness, dist_2_kurtosis = dist_2.stats(moments='msk')
dist_2_standard_deviation = dist_2.std()
distance = fabs(dist_1_standard_deviation - dist_2_standard_deviation) + fabs(dist_1_skewness - dist_2_skewness)
distance += fabs(dist_1_kurtosis - dist_2_kurtosis)
delta = dist_1_mean - dist_2_mean
non_same_portion = 1.0 - same
portion_after, portion_before = 1.0, 0.0
if almost_equals(distance, 0):
if delta < 0:
portion_after, portion_before = 0.0, 1.0
else:
dist_1_standardized_pdf = lambda x: dist_1.pdf(dist_1_standard_deviation * x + dist_1_mean)
dist_2_standardized_pdf = lambda x: dist_2.pdf(dist_2_standard_deviation * x + dist_2_mean)
geometric_mean = lambda t: sqrt(dist_1_standardized_pdf(t) * dist_2_standardized_pdf(t))
geometric_mean_scaled = lambda p: geometric_mean(p / distance)
geometric_mean_scaled_length = max(self.duration_of(dist_1), self.duration_of(dist_2))
dictionary_input_output = {}
for time_step in TimeInterval(-geometric_mean_scaled_length / 2.0, geometric_mean_scaled_length / 2.0):
dictionary_input_output[time_step] = geometric_mean_scaled(time_step)
geometric_mean_scaled = FunctionPiecewiseLinear(dictionary_input_output, function_undefined=FUNCTION_ZERO)
portion_after = integral(geometric_mean_scaled, NEGATIVE_INFINITY, delta)
portion_before = integral(geometric_mean_scaled, delta, POSITIVE_INFINITY)
if (portion_after + portion_before) == 0:
pass
after = portion_after / (portion_after + portion_before) * non_same_portion
return 1.0 - same - after, same, after
def unpack(self, relation_a_b_beginning, relation_a_b_ending):
before_a_b_beginning, same_a_b_beginning, after_a_b_beginning = relation_a_b_beginning
before_a_b_ending, same_a_b_ending, after_a_b_ending = relation_a_b_ending
if almost_equals(before_a_b_beginning + same_a_b_beginning + same_a_b_ending + after_a_b_ending, 2.0, epsilon):
return [], uniform_reference # Inconsistent
if almost_equals(before_a_b_beginning + before_a_b_ending, 2.0, epsilon):
return [], uniform_reference
if almost_equals(after_a_b_beginning + after_a_b_ending, 2.0, epsilon):
return [], uniform_reference
if almost_equals(before_a_b_ending, 1.0, epsilon):
return self.unpack_partial(relation_a_b_beginning), uniform_reference
if almost_equals(after_a_b_beginning, 1.0, epsilon):
return self.unpack_partial(relation_a_b_ending), uniform_reference
a_possibilities = self.unpack_partial(relation_a_b_beginning)
if len(a_possibilities) == 1:
a_possibility = a_possibilities[0]
return
else:
a_possibility_1, a_possibility_2 = a_possibilities
a_possibility = a_possibility_1
if a_possibility.args[1] < a_possibility_2.args[1]:
a_possibility = a_possibility_2
a_start_point, length_a = a_possibility.args
if before_a_b_ending * same_a_b_ending * after_a_b_ending > 0:
if almost_equals(before_a_b_beginning, 0, epsilon):
length_b_ending = length_a * same_a_b_ending ** 2
else:
length_b_ending = same_a_b_ending ** 2 / same_a_b_beginning ** 2
b_ending = uniform(a_start_point + before_a_b_ending * (length_a - length_b_ending) /
(before_a_b_ending + after_a_b_ending), length_b_ending)
return [a_possibility], b_ending
else:
denominator = length_a * same_a_b_ending ** 2
length_b_ending_lower_bound = (length_a * same_a_b_ending ** 2) ** 2 / denominator
length_b_ending_upper_bound = (a_start_point + length_a - 1) ** 2 / denominator
length_b_ending = (length_b_ending_lower_bound + length_b_ending_upper_bound) / 2.0
b_start_point = a_start_point + length_a - same_a_b_ending * sqrt(length_b_ending * length_a)
b_ending = uniform(b_start_point, length_b_ending)
return [a_possibility], b_ending
def compare(self, dist_1, dist_2):
dist_1_interval = TimeInterval(*self.bounds_of(dist_1))
dist_2_interval = TimeInterval(*self.bounds_of(dist_2))
dictionary_input_output = {}
for time_step in dist_1_interval + dist_2_interval:
dictionary_input_output[time_step] = sqrt(
dist_1.pdf(time_step) * dist_2.pdf(time_step))
geometric_mean = FunctionPiecewiseLinear(
dictionary_input_output, function_undefined=FUNCTION_ZERO)
same = integral(geometric_mean, NEGATIVE_INFINITY, POSITIVE_INFINITY)
dist_1_mean, dist_1_skewness, dist_1_kurtosis = dist_1.stats(
moments='msk')
dist_1_standard_deviation = dist_1.std()
dist_2_mean, dist_2_skewness, dist_2_kurtosis = dist_2.stats(
moments='msk')
dist_2_standard_deviation = dist_2.std()
distance = fabs(dist_1_standard_deviation -
dist_2_standard_deviation) + fabs(dist_1_skewness -
dist_2_skewness)
distance += fabs(dist_1_kurtosis - dist_2_kurtosis)
delta = dist_1_mean - dist_2_mean
non_same_portion = 1.0 - same
portion_after, portion_before = 1.0, 0.0
if almost_equals(distance, 0):
if delta < 0:
portion_after, portion_before = 0.0, 1.0
else:
dist_1_standardized_pdf = lambda x: dist_1.pdf(
dist_1_standard_deviation * x + dist_1_mean)
dist_2_standardized_pdf = lambda x: dist_2.pdf(
dist_2_standard_deviation * x + dist_2_mean)
geometric_mean = lambda t: sqrt(
dist_1_standardized_pdf(t) * dist_2_standardized_pdf(t))
geometric_mean_scaled = lambda p: geometric_mean(p / distance)
geometric_mean_scaled_length = max(self.duration_of(dist_1),
self.duration_of(dist_2))
dictionary_input_output = {}
for time_step in TimeInterval(-geometric_mean_scaled_length / 2.0,
geometric_mean_scaled_length / 2.0):
dictionary_input_output[time_step] = geometric_mean_scaled(
time_step)
geometric_mean_scaled = FunctionPiecewiseLinear(
dictionary_input_output, function_undefined=FUNCTION_ZERO)
portion_after = integral(geometric_mean_scaled, NEGATIVE_INFINITY,
delta)
portion_before = integral(geometric_mean_scaled, delta,
POSITIVE_INFINITY)
if (portion_after + portion_before) == 0:
pass
after = portion_after / (portion_after +
portion_before) * non_same_portion
return 1.0 - same - after, same, after
def combine(self, relation_a_b_beginning, relation_a_b_ending, relation_b_beginning_c, relation_b_ending_c):
before_a_b, same_a_b, after_a_b = relation_a_b_beginning
before_b_c, same_b_c, after_b_c = relation_b_beginning_c
unknown = 1.0 / 3
if almost_equals(before_a_b + before_b_c, 2.0, epsilon)\
or almost_equals(before_a_b + same_b_c, 2.0, epsilon)\
or almost_equals(same_a_b + before_b_c, 2.0, epsilon):
return [(1.0, 0.0, 0.0)]
if almost_equals(after_a_b + after_b_c, 2.0, epsilon)\
or almost_equals(after_a_b + same_b_c, 2.0, epsilon)\
or almost_equals(same_a_b + after_b_c, 2.0, epsilon):
return [(1.0, 0.0, 0.0)]
if almost_equals(same_a_b + same_b_c, 2.0, epsilon):
return [(0.0, 1.0, 0.0)]
if almost_equals(before_a_b + after_b_c, 2.0, epsilon) or almost_equals(after_a_b + before_b_c, 2.0, epsilon):
return [(unknown, unknown, unknown)]
relation_a_c_possibilities = []
a_possibilities, b_ending_1 = self.unpack(relation_a_b_beginning, relation_a_b_ending)
c_possibilities, b_ending_2 = self.unpack(tuple(reversed(relation_b_beginning_c)), tuple(reversed(relation_b_ending_c)))
if len(a_possibilities) == 0:
if before_a_b == 0:
if len(c_possibilities) == 1:
if before_b_c == 0:
relation_a_c_possibilities.append((0.0, 0.0, 1.0))
else:
relation_a_c_possibilities.append((unknown, unknown, unknown))
else:
relation_a_c_possibilities.append((unknown, unknown, unknown))
relation_a_c_possibilities.append((0.0, 0.0, 1.0))
else:
if len(c_possibilities) == 1:
if after_b_c == 0:
relation_a_c_possibilities.append((1.0, 0.0, 0.0))
else:
relation_a_c_possibilities.append((unknown, unknown, unknown))
else:
relation_a_c_possibilities.append((unknown, unknown, unknown))
relation_a_c_possibilities.append((1.0, 0.0, 0.0))
if len(c_possibilities) == 0:
if before_b_c == 0:
if len(a_possibilities) == 1:
if before_a_b == 0:
relation_a_c_possibilities.append((0.0, 0.0, 1.0))
else:
relation_a_c_possibilities.append((unknown, unknown, unknown))
else:
relation_a_c_possibilities.append((unknown, unknown, unknown))
relation_a_c_possibilities.append((0.0, 0.0, 1.0))
else:
if len(a_possibilities) == 1:
if after_a_b == 0:
relation_a_c_possibilities.append((1.0, 0.0, 0.0))
else:
relation_a_c_possibilities.append((unknown, unknown, unknown))
else:
relation_a_c_possibilities.append((unknown, unknown, unknown))
relation_a_c_possibilities.append((1.0, 0.0, 0.0))
for possible_a in a_possibilities:
for possible_c in c_possibilities:
relation_a_c_possibilities.append(self.relation_formula.compare(possible_a, possible_c))
return relation_a_c_possibilities
