def function_convolution(self, dist_1, dist_2, bins=50):
a_1, b_1, a_2, b_2 = 0, 0, 0, 0
if dist_1 in self.bounds:
a_1, b_1 = self.bounds[dist_1]
else:
a_1, b_1 = calculate_bounds_of_probability_distribution(dist_1)
self.bounds[dist_1] = a_1, b_1
if dist_2 in self.bounds:
a_2, b_2 = self.bounds[dist_2]
else:
a_2, b_2 = calculate_bounds_of_probability_distribution(dist_2)
self.bounds[dist_2] = a_2, b_2
if (type(dist_1.dist), type(dist_2.dist)) == (uniform_gen, uniform_gen):
return self.function_convolution_uniform((a_1, b_1), (a_2, b_2))
convolution_bounds_a, convolution_bounds_b = min(a_1, a_2), max(b_1, b_2)
delta = fabs(convolution_bounds_a - convolution_bounds_b) / bins
convolution_interval = TimeInterval(convolution_bounds_a, convolution_bounds_b, bins)
x = [dist_1.pdf(t) for t in convolution_interval]
y = [dist_2.pdf(t) for t in reversed(convolution_interval)]
c = convolve(x, y)
dictionary_convolution = {}
for t in xrange(len(c)):
dictionary_convolution[delta * t] = c[t]
bias = calculateCenterMass(dictionary_convolution)[0] + dist_2.mean() - dist_1.mean()
dictionary_convolution_biased = {}
for t in dictionary_convolution:
dictionary_convolution_biased[t - bias] = dictionary_convolution[t]
convolution_function = FunctionPiecewiseLinear(dictionary_convolution_biased, FunctionHorizontalLinear(0))
return convolution_function.normalised()
def function_convolution_uniform(self,
bounds_1,
bounds_2,
probability=None):
a1, b1 = bounds_1
a2, b2 = bounds_2
length_1 = fabs(a1 - b1)
length_2 = fabs(a2 - b2)
convolution_bounds_a, convolution_bounds_b = a1 - b2, b1 - a2
trapezium_0, trapezium_1 = convolution_bounds_a, convolution_bounds_a + min(
length_2, length_1)
trapezium_2, trapezium_3 = trapezium_1 + fabs(
length_1 - length_2), convolution_bounds_b
#assert trapezium_2 + min(length_2, length_1) == trapezium_3
if probability is None:
probability = min(1 / length_1, 1 / length_2)
result = FunctionPiecewiseLinear(
{
trapezium_0: 0,
trapezium_1: probability,
trapezium_2: probability,
trapezium_3: 0
}, FUNCTION_ZERO)
result.is_normalised = True
return result
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)
after = portion_after / (portion_after +
portion_before) * non_same_portion
return 1.0 - same - after, same, after
def __init__(self, dictionary_input_output):
cdf_input_list, cdf_output_list = convert_dict_to_sorted_lists(dictionary_input_output)
list.__init__(self, cdf_input_list)
TimeInterval.__init__(self, self[0], self[-1], 2)
self.cdf = FunctionPiecewiseLinear(dictionary_input_output, function_undefined=FUNCTION_ZERO)
self.cdf.dictionary_bounds_function[(self.b, POSITIVE_INFINITY)] = FUNCTION_ONE
pdf_output_list = []
dictionary_bounds_function = {}
for bounds in sorted(self.cdf.dictionary_bounds_function):
a, b = bounds
if a in [NEGATIVE_INFINITY, POSITIVE_INFINITY] or b in [NEGATIVE_INFINITY, POSITIVE_INFINITY]:
continue
pdf_y_intercept = fabs(self.cdf.derivative((a + b) / 2.0))
pdf_output_list.append(pdf_y_intercept)
dictionary_bounds_function[bounds] = FunctionHorizontalLinear(pdf_y_intercept)
self.pdf = FunctionComposite(dictionary_bounds_function, function_undefined=FUNCTION_ZERO, domain=self,
is_normalised=True)
self.roulette_wheel = []
self._mean = 0
for bounds in sorted(self.pdf.dictionary_bounds_function):
(a, b) = bounds
if a in [NEGATIVE_INFINITY, POSITIVE_INFINITY] and b in [NEGATIVE_INFINITY, POSITIVE_INFINITY]:
continue
cdf = self.cdf.dictionary_bounds_function[bounds]
pdf = self.pdf.dictionary_bounds_function[bounds]
share = cdf(b)
self.roulette_wheel.append((a, b, share))
self._mean += (a + b) / 2.0 * pdf(a) * (b - a)
def function_convolution_uniform(self, bounds_1, bounds_2, probability=None):
a1, b1 = bounds_1
a2, b2 = bounds_2
length_1 = fabs(a1 - b1)
length_2 = fabs(a2 - b2)
convolution_bounds_a, convolution_bounds_b = a1 - b2, b1 - a2
trapezium_0, trapezium_1 = convolution_bounds_a, convolution_bounds_a + min(length_2, length_1)
trapezium_2, trapezium_3 = trapezium_1 + fabs(length_1 - length_2), convolution_bounds_b
#assert trapezium_2 + min(length_2, length_1) == trapezium_3
if probability is None:
probability = min(1 / length_1, 1 / length_2)
result = FunctionPiecewiseLinear(
{trapezium_0: 0, trapezium_1: probability, trapezium_2: probability, trapezium_3: 0},
FUNCTION_ZERO)
result.is_normalised = True
return result
def __init__(self, dictionary_input_output):
cdf_input_list, cdf_output_list = convert_dict_to_sorted_lists(
dictionary_input_output)
list.__init__(self, cdf_input_list)
TimeInterval.__init__(self, self[0], self[-1], 2)
self.cdf = FunctionPiecewiseLinear(dictionary_input_output,
function_undefined=FUNCTION_ZERO)
self.cdf.dictionary_bounds_function[(self.b,
POSITIVE_INFINITY)] = FUNCTION_ONE
pdf_output_list = []
dictionary_bounds_function = {}
for bounds in sorted(self.cdf.dictionary_bounds_function):
a, b = bounds
if a in [NEGATIVE_INFINITY, POSITIVE_INFINITY
] or b in [NEGATIVE_INFINITY, POSITIVE_INFINITY]:
continue
pdf_y_intercept = fabs(self.cdf.derivative((a + b) / 2.0))
pdf_output_list.append(pdf_y_intercept)
dictionary_bounds_function[bounds] = FunctionHorizontalLinear(
pdf_y_intercept)
self.pdf = FunctionComposite(dictionary_bounds_function,
function_undefined=FUNCTION_ZERO,
domain=self,
is_normalised=True)
self.roulette_wheel = []
self._mean = 0
for bounds in sorted(self.pdf.dictionary_bounds_function):
(a, b) = bounds
if a in [NEGATIVE_INFINITY, POSITIVE_INFINITY
] and b in [NEGATIVE_INFINITY, POSITIVE_INFINITY]:
continue
cdf = self.cdf.dictionary_bounds_function[bounds]
pdf = self.pdf.dictionary_bounds_function[bounds]
share = cdf(b)
self.roulette_wheel.append((a, b, share))
self._mean += (a + b) / 2.0 * pdf(a) * (b - a)
def function_convolution(self, dist_1, dist_2, bins=50):
a_1, b_1, a_2, b_2 = 0, 0, 0, 0
if dist_1 in self.bounds:
a_1, b_1 = self.bounds[dist_1]
else:
a_1, b_1 = calculate_bounds_of_probability_distribution(dist_1)
self.bounds[dist_1] = a_1, b_1
if dist_2 in self.bounds:
a_2, b_2 = self.bounds[dist_2]
else:
a_2, b_2 = calculate_bounds_of_probability_distribution(dist_2)
self.bounds[dist_2] = a_2, b_2
if (type(dist_1.dist), type(dist_2.dist)) == (uniform_gen,
uniform_gen):
return self.function_convolution_uniform((a_1, b_1), (a_2, b_2))
convolution_bounds_a, convolution_bounds_b = min(a_1,
a_2), max(b_1, b_2)
delta = fabs(convolution_bounds_a - convolution_bounds_b) / bins
convolution_interval = TimeInterval(convolution_bounds_a,
convolution_bounds_b, bins)
x = [dist_1.pdf(t) for t in convolution_interval]
y = [dist_2.pdf(t) for t in reversed(convolution_interval)]
c = convolve(x, y)
dictionary_convolution = {}
for t in xrange(len(c)):
dictionary_convolution[delta * t] = c[t]
bias = calculateCenterMass(
dictionary_convolution)[0] + dist_2.mean() - dist_1.mean()
dictionary_convolution_biased = {}
for t in dictionary_convolution:
dictionary_convolution_biased[t - bias] = dictionary_convolution[t]
convolution_function = FunctionPiecewiseLinear(
dictionary_convolution_biased, FunctionHorizontalLinear(0))
return convolution_function.normalised()
def __init__(self, dictionary_beginning, dictionary_ending, bins=50):
input_list_beginning, output_list_beginning = convert_dict_to_sorted_lists(dictionary_beginning)
for i in xrange(1, len(input_list_beginning)):
if not dictionary_beginning[input_list_beginning[i]] > dictionary_beginning[input_list_beginning[i - 1]]:
raise TypeError("values of 'dictionary_beginning' should be increasing in time")
input_list_ending, output_list_ending = convert_dict_to_sorted_lists(dictionary_ending)
for i in xrange(1, len(input_list_ending)):
if not dictionary_ending[input_list_ending[i]] < dictionary_ending[input_list_ending[i - 1]]:
raise TypeError("values of 'dictionary_ending' should be decreasing in time")
dictionary_ending = {}
for i, time_step in enumerate(input_list_ending):
dictionary_ending[time_step] = output_list_ending[len(input_list_ending) - i - 1]
input_list_ending, output_list_ending = convert_dict_to_sorted_lists(dictionary_ending)
distribution_beginning = ProbabilityDistributionPiecewiseLinear(dictionary_beginning)
distribution_ending = ProbabilityDistributionPiecewiseLinear(dictionary_ending)
TemporalEvent.__init__(self, distribution_beginning, distribution_ending, bins=bins)
self._list = sorted(set(input_list_beginning + input_list_ending))
self.membership_function = FunctionPiecewiseLinear(self.to_dict(), FUNCTION_ZERO)
class ProbabilityDistributionPiecewiseLinear(list, TimeInterval, rv_frozen):
dist = 'ProbabilityDistributionPiecewiseLinear'
_mean = None
asd = None
def __init__(self, dictionary_input_output):
cdf_input_list, cdf_output_list = convert_dict_to_sorted_lists(dictionary_input_output)
list.__init__(self, cdf_input_list)
TimeInterval.__init__(self, self[0], self[-1], 2)
self.cdf = FunctionPiecewiseLinear(dictionary_input_output, function_undefined=FUNCTION_ZERO)
self.cdf.dictionary_bounds_function[(self.b, POSITIVE_INFINITY)] = FUNCTION_ONE
pdf_output_list = []
dictionary_bounds_function = {}
for bounds in sorted(self.cdf.dictionary_bounds_function):
a, b = bounds
if a in [NEGATIVE_INFINITY, POSITIVE_INFINITY] or b in [NEGATIVE_INFINITY, POSITIVE_INFINITY]:
continue
pdf_y_intercept = fabs(self.cdf.derivative((a + b) / 2.0))
pdf_output_list.append(pdf_y_intercept)
dictionary_bounds_function[bounds] = FunctionHorizontalLinear(pdf_y_intercept)
self.pdf = FunctionComposite(dictionary_bounds_function, function_undefined=FUNCTION_ZERO, domain=self,
is_normalised=True)
self.roulette_wheel = []
self._mean = 0
for bounds in sorted(self.pdf.dictionary_bounds_function):
(a, b) = bounds
if a in [NEGATIVE_INFINITY, POSITIVE_INFINITY] and b in [NEGATIVE_INFINITY, POSITIVE_INFINITY]:
continue
cdf = self.cdf.dictionary_bounds_function[bounds]
pdf = self.pdf.dictionary_bounds_function[bounds]
share = cdf(b)
self.roulette_wheel.append((a, b, share))
self._mean += (a + b) / 2.0 * pdf(a) * (b - a)
def std(self):
# Not properly implemented
return 0
def stats(self, moments='mv'):
# Not properly implemented
# m, s, k
return self.mean(), 0, 0
def mean(self):
return self._mean
def interval(self, alpha):
if alpha == 1:
return self.a, self.b
raise NotImplementedError("'interval' is not implemented for 'alpha' other than 1")
def rvs(self, size=None):
if size is None:
size = 1
else:
assert isinstance(size, int)
result = []
start, end = 0, 0
for i in xrange(size):
rand = random()
for a, b, share in self.roulette_wheel:
if rand < share:
start, end = a, b
break
result.append(random_time(start, end))
if size == 1:
return result[0]
return result
# def plot(self):
# import matplotlib.pyplot as plt
# x_axis, y_axis = [], []
# for time_step in self:
# x_axis.append(UnixTime(time_step - EPSILON).to_datetime())
# x_axis.append(UnixTime(time_step + EPSILON).to_datetime())
# y_axis.append(self.pdf(time_step - EPSILON))
# y_axis.append(self.pdf(time_step + EPSILON))
# plt.plot(x_axis, y_axis)
# return plt
def plot(self):
import matplotlib.pyplot as plt
x_axis, y_axis = [], []
for time_step in self:
x_axis.append(time_step - EPSILON)
x_axis.append(time_step + EPSILON)
y_axis.append(self.pdf(time_step - EPSILON))
y_axis.append(self.pdf(time_step + EPSILON))
plt.plot(x_axis, y_axis)
return plt
def __hash__(self):
return object.__hash__(self)
def __repr__(self):
return TimeInterval.__repr__(self)
def __str__(self):
return repr(self)
class ProbabilityDistributionPiecewiseLinear(list, TimeInterval, rv_frozen):
dist = 'ProbabilityDistributionPiecewiseLinear'
_mean = None
asd = None
def __init__(self, dictionary_input_output):
cdf_input_list, cdf_output_list = convert_dict_to_sorted_lists(
dictionary_input_output)
list.__init__(self, cdf_input_list)
TimeInterval.__init__(self, self[0], self[-1], 2)
self.cdf = FunctionPiecewiseLinear(dictionary_input_output,
function_undefined=FUNCTION_ZERO)
self.cdf.dictionary_bounds_function[(self.b,
POSITIVE_INFINITY)] = FUNCTION_ONE
pdf_output_list = []
dictionary_bounds_function = {}
for bounds in sorted(self.cdf.dictionary_bounds_function):
a, b = bounds
if a in [NEGATIVE_INFINITY, POSITIVE_INFINITY
] or b in [NEGATIVE_INFINITY, POSITIVE_INFINITY]:
continue
pdf_y_intercept = fabs(self.cdf.derivative((a + b) / 2.0))
pdf_output_list.append(pdf_y_intercept)
dictionary_bounds_function[bounds] = FunctionHorizontalLinear(
pdf_y_intercept)
self.pdf = FunctionComposite(dictionary_bounds_function,
function_undefined=FUNCTION_ZERO,
domain=self,
is_normalised=True)
self.roulette_wheel = []
self._mean = 0
for bounds in sorted(self.pdf.dictionary_bounds_function):
(a, b) = bounds
if a in [NEGATIVE_INFINITY, POSITIVE_INFINITY
] and b in [NEGATIVE_INFINITY, POSITIVE_INFINITY]:
continue
cdf = self.cdf.dictionary_bounds_function[bounds]
pdf = self.pdf.dictionary_bounds_function[bounds]
share = cdf(b)
self.roulette_wheel.append((a, b, share))
self._mean += (a + b) / 2.0 * pdf(a) * (b - a)
def std(self):
# Not properly implemented
return 0
def stats(self, moments='mv'):
# Not properly implemented
# m, s, k
return self.mean(), 0, 0
def mean(self):
return self._mean
def interval(self, alpha):
if alpha == 1:
return self.a, self.b
raise NotImplementedError(
"'interval' is not implemented for 'alpha' other than 1")
def rvs(self, size=None):
if size is None:
size = 1
else:
assert isinstance(size, int)
result = []
start, end = 0, 0
for i in xrange(size):
rand = random()
for a, b, share in self.roulette_wheel:
if rand < share:
start, end = a, b
break
result.append(random_time(start, end))
if size == 1:
return result[0]
return result
# def plot(self):
# import matplotlib.pyplot as plt
# x_axis, y_axis = [], []
# for time_step in self:
# x_axis.append(UnixTime(time_step - EPSILON).to_datetime())
# x_axis.append(UnixTime(time_step + EPSILON).to_datetime())
# y_axis.append(self.pdf(time_step - EPSILON))
# y_axis.append(self.pdf(time_step + EPSILON))
# plt.plot(x_axis, y_axis)
# return plt
def plot(self):
import matplotlib.pyplot as plt
x_axis, y_axis = [], []
for time_step in self:
x_axis.append(time_step - EPSILON)
x_axis.append(time_step + EPSILON)
y_axis.append(self.pdf(time_step - EPSILON))
y_axis.append(self.pdf(time_step + EPSILON))
plt.plot(x_axis, y_axis)
return plt
def __hash__(self):
return object.__hash__(self)
def __repr__(self):
return TimeInterval.__repr__(self)
def __str__(self):
return repr(self)
