def compare(self, dist_1, dist_2):
convolution = self.function_convolution(dist_1, dist_2)
a_1, b_1 = self.bounds[dist_1]
a_2, b_2 = self.bounds[dist_2]
same_bound = fabs(max(a_1, a_2) - min(b_1, b_2))
before = integral(convolution, NEGATIVE_INFINITY, -same_bound)
same = integral(convolution, -same_bound, same_bound)
after = integral(convolution, same_bound, POSITIVE_INFINITY)
return before, same, after
def compare(self, dist_1, dist_2):
convolution = self.function_convolution(dist_1, dist_2)
a_1, b_1 = self.bounds[dist_1]
a_2, b_2 = self.bounds[dist_2]
same_bound = fabs(max(a_1, a_2) - min(b_1, b_2))
before = integral(convolution, NEGATIVE_INFINITY, -same_bound)
same = integral(convolution, -same_bound, same_bound)
after = integral(convolution, same_bound, POSITIVE_INFINITY)
return before, same, after
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 same(self, dist_1, dist_2):
dist_1_a, dist_1_b = self.bounds_of(dist_1)
dist_2_a, dist_2_b = self.bounds_of(dist_2)
a, b = max(dist_1_a, dist_2_a), min(dist_1_b, dist_2_b)
interval = TimeInterval(a, b)
dictionary_input_output = {}
for time_step in interval:
dictionary_input_output[time_step] = dist_1.pdf(time_step) * dist_2.pdf(time_step)
function = FunctionPiecewiseLinear(dictionary_input_output, FUNCTION_ZERO)
return integral(function, a, b)
def before(self, dist_1, dist_2):
a, b = self.bounds_of(dist_1)
# Cancel pdf's error
a += EPSILON
b -= EPSILON
interval = TimeInterval(a, b)
dictionary_input_output = {}
for time_step in interval:
dictionary_input_output[time_step] = dist_1.pdf(time_step) * (1 - dist_2.cdf(time_step))
function = FunctionPiecewiseLinear(dictionary_input_output, FUNCTION_ZERO)
return integral(function, a, b)
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 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 = min(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)
after = portion_after / (portion_after + portion_before) * non_same_portion
return 1.0 - same - after, same, after
def same(self, dist_1, dist_2):
dist_1_a, dist_1_b = self.bounds_of(dist_1)
dist_2_a, dist_2_b = self.bounds_of(dist_2)
a, b = max(dist_1_a, dist_2_a), min(dist_1_b, dist_2_b)
interval = TimeInterval(a, b)
dictionary_input_output = {}
for time_step in interval:
dictionary_input_output[time_step] = dist_1.pdf(
time_step) * dist_2.pdf(time_step)
function = FunctionPiecewiseLinear(dictionary_input_output,
FUNCTION_ZERO)
return integral(function, a, b)
def before(self, dist_1, dist_2):
a, b = self.bounds_of(dist_1)
# Cancel pdf's error
a += EPSILON
b -= EPSILON
interval = TimeInterval(a, b)
dictionary_input_output = {}
for time_step in interval:
dictionary_input_output[time_step] = dist_1.pdf(time_step) * (
1 - dist_2.cdf(time_step))
function = FunctionPiecewiseLinear(dictionary_input_output,
FUNCTION_ZERO)
return integral(function, a, b)
def before(self, dist_1, dist_2):
if (dist_1, dist_2) in self.before_integrals:
return self.before_integrals[(dist_1, dist_2)]
if (dist_1, dist_2) in self.convolutions:
convolution = self.convolutions[(dist_1, dist_2)]
else:
convolution = self.function_convolution_generic(dist_1, dist_2)
self.convolutions[(dist_1, dist_2)] = convolution
result = integral(convolution, NEGATIVE_INFINITY, 0)
self.before_integrals[(dist_1, dist_2)] = result
return result
def before(self, dist_1, dist_2):
if (dist_1, dist_2) in self.before_integrals:
return self.before_integrals[(dist_1, dist_2)]
if (dist_1, dist_2) in self.convolutions:
convolution = self.convolutions[(dist_1, dist_2)]
else:
convolution = self.function_convolution_generic(dist_1, dist_2)
self.convolutions[(dist_1, dist_2)] = convolution
result = integral(convolution, NEGATIVE_INFINITY, 0)
self.before_integrals[(dist_1, dist_2)] = result
return result
def degree(self, time_step=None, a=None, b=None, interval=None):
"""
usage: provide 'time_step' or 'a' and 'b' or 'interval'
"""
if time_step is not None:
return self.membership_function(time_step)
if interval is None:
if (a, b) == (None, None):
interval = self
else:
interval = TimeInterval(a, b)
else:
check_is_time_interval(interval)
return integral(self.membership_function, interval.a, interval.b)
def degree(self, time_step=None, a=None, b=None, interval=None):
"""
usage: provide 'time_step' or 'a' and 'b' or 'interval'
"""
if time_step is not None:
return self.membership_function(time_step)
if interval is None:
if (a, b) == (None, None):
interval = self
else:
interval = TimeInterval(a, b)
else:
check_is_time_interval(interval)
return integral(self.membership_function, interval.a, interval.b)
def same(self, dist_1, dist_2):
if (dist_1, dist_2) in self.same_integrals:
return self.same_integrals[(dist_1, dist_2)]
if (dist_1, dist_2) in self.convolutions:
convolution = self.convolutions[(dist_1, dist_2)]
else:
convolution = self.function_convolution_generic(dist_1, dist_2)
self.convolutions[(dist_1, dist_2)] = convolution
a1, b1 = self.bounds[dist_1]
a2, b2 = self.bounds[dist_2]
integral_length = fabs(max(a1, a2) - min(b1, b2))
result = integral(convolution, -integral_length, integral_length)
self.same_integrals[(dist_1, dist_2)] = result
return result
def same(self, dist_1, dist_2):
if (dist_1, dist_2) in self.same_integrals:
return self.same_integrals[(dist_1, dist_2)]
if (dist_1, dist_2) in self.convolutions:
convolution = self.convolutions[(dist_1, dist_2)]
else:
convolution = self.function_convolution_generic(dist_1, dist_2)
self.convolutions[(dist_1, dist_2)] = convolution
a1, b1 = self.bounds[dist_1]
a2, b2 = self.bounds[dist_2]
integral_length = fabs(max(a1, a2) - min(b1, b2))
result = integral(convolution, -integral_length, integral_length)
self.same_integrals[(dist_1, dist_2)] = result
return result
def fn_after(dist_1, dist_2):
a1, b1 = calculate_bounds_of_probability_distribution(dist_1)
a2, b2 = calculate_bounds_of_probability_distribution(dist_2)
return integral(lambda z: dist_2.pdf(z) * fn_before_point(dist_1, z),
min(a1, a2), max(b1, b2))
9: 0.1,
10: 0
}),
TemporalEventPiecewiseLinear({
1: 0,
2: 0.1,
3: 0.3,
4: 0.7,
5: 1
}, {
3.5: 1,
4.5: 0.9,
8: 0.6,
9: 0.1,
10: 0
})
]
print type(events[0])
print events[0] * events[1]
for event in events:
plt = event.plot()
print integral(event.distribution_beginning.pdf, event.a,
event.beginning)
print event.distribution_beginning.rvs(10)
plt.ylim(ymax=1.1)
#plt.figure()
plt.show()
if __name__ == '__main__':
from utility.geometric import integral
from scipy.stats import norm
import matplotlib.pyplot as plt
#event = TemporalInstance(datetime(2010, 1, 1), datetime(2011, 2, 1))
#plt = event.plot()
#plt.show()
events = [
TemporalEvent(norm(loc=10, scale=2), norm(loc=30, scale=2), 100),
TemporalEvent(norm(loc=5, scale=2), norm(loc=15, scale=4), 100),
#TemporalEventPiecewiseLinear({1: 0, 2: 0.1, 3: 0.3, 4: 0.7, 5: 1}, {6: 1, 7: 0.9, 8: 0.6, 9: 0.1, 10: 0}),
#TemporalEventPiecewiseLinear({1: 0, 2: 0.1, 3: 0.3, 4: 0.7, 5: 1}, {3.5: 1, 4.5: 0.9, 8: 0.6, 9: 0.1, 10: 0})
]
print type(events[0])
print events[0] * events[1]
for event in events:
plt = event.plot()
print integral(event.distribution_beginning.pdf, event.a, event.beginning)
print event.distribution_beginning.rvs(10)
plt.ylim(ymax=1.1)
#plt.figure()
plt.show()
def same(self, dist_1, dist_2):
return integral(lambda x: self.same_point(dist_1.pdf(x), dist_2.pdf(x)),
*self.same_integral_bounds(dist_1, dist_2))
def fn_after(dist_1, dist_2):
a1, b1 = calculate_bounds_of_probability_distribution(dist_1)
a2, b2 = calculate_bounds_of_probability_distribution(dist_2)
return integral(lambda z: dist_2.pdf(z) * fn_before_point(dist_1, z), min(a1, a2), max(b1, b2))
def after(self, dist_1, dist_2):
return integral(lambda x: self.after_point(dist_1.pdf(x), dist_2.pdf(x)),
*self.after_integral_bounds(dist_1, dist_2))
def after(self, dist_1, dist_2):
return integral(
lambda x: self.after_point(dist_1.pdf(x), dist_2.pdf(x)),
*self.after_integral_bounds(dist_1, dist_2))
def same(self, dist_1, dist_2):
return integral(
lambda x: self.same_point(dist_1.pdf(x), dist_2.pdf(x)),
*self.same_integral_bounds(dist_1, dist_2))
