def adjust_ret_list(retlist):
retlist[0].cdf_low="0.0"
retlist[-1].cdf_up="1.0"
with gmpy2.local_context(gmpy2.context(), round=gmpy2.RoundUp, precision=mpfr_proxy_precision) as ctx:
min_value=gmpy2.exp10(-digits_for_input_cdf)
current=min_value
for pbox in retlist:
with gmpy2.local_context(gmpy2.context(), round=gmpy2.RoundDown, precision=mpfr_proxy_precision) as ctx:
if gmpy2.is_zero(gmpy2.mpfr(pbox.cdf_low)) or gmpy2.mpfr(pbox.cdf_low)<current:
pbox.cdf_low=round_number_down_to_digits(current, digits_for_input_cdf)
with gmpy2.local_context(gmpy2.context(), round=gmpy2.RoundUp, precision=mpfr_proxy_precision) as ctx:
current=current+min_value
if gmpy2.is_zero(gmpy2.mpfr(pbox.cdf_up)) or gmpy2.mpfr(pbox.cdf_up)<current:
pbox.cdf_up=round_number_down_to_digits(current, digits_for_input_cdf)
with gmpy2.local_context(gmpy2.context(), round=gmpy2.RoundDown, precision=mpfr_proxy_precision) as ctx:
current=gmpy2.sub(gmpy2.mpfr("1.0"), min_value)
for pbox in retlist[::-1]:
with gmpy2.local_context(gmpy2.context(), round=gmpy2.RoundDown, precision=mpfr_proxy_precision) as ctx:
if gmpy2.mpfr(pbox.cdf_up)==gmpy2.mpfr("1.0") or gmpy2.mpfr(pbox.cdf_up)>current:
pbox.cdf_up=round_number_up_to_digits(current, digits_for_input_cdf)
current=gmpy2.sub(current, min_value)
if gmpy2.mpfr(pbox.cdf_low)==gmpy2.mpfr("1.0") or gmpy2.mpfr(pbox.cdf_low)>current:
pbox.cdf_low=round_number_up_to_digits(current, digits_for_input_cdf)
retlist[0].cdf_low = "0.0"
retlist[-1].cdf_up = "1.0"
return retlist
def subtraction(self, interval):
reset_default_precision()
res_inc_left = False
res_inc_right = False
if self.include_lower and interval.include_lower:
res_inc_left = True
if self.include_upper and interval.include_upper:
res_inc_right = True
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundDown,
precision=mpfr_proxy_precision) as ctx:
res_left = gmpy2.sub(mpfr(self.lower), mpfr(interval.upper))
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundUp,
precision=mpfr_proxy_precision) as ctx:
res_right = gmpy2.sub(mpfr(self.upper), mpfr(interval.lower))
if res_left <= res_right:
res_right = round_number_up_to_digits(res_right, self.digits)
res_left = round_number_down_to_digits(res_left, self.digits)
return Interval(res_left, res_right, res_inc_left, res_inc_right,
self.digits)
else:
res_right = round_number_down_to_digits(res_right, self.digits)
res_left = round_number_up_to_digits(res_left, self.digits)
return Interval(res_right, res_left, res_inc_right, res_inc_left,
self.digits)
def find_min_abs_interval(interval):
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundToZero,
precision=mpfr_proxy_precision) as ctx:
left = abs(mpfr(interval.lower))
right = abs(mpfr(interval.upper))
if left < right:
#Now the number is positive so we can round down
return round_number_down_to_digits(left, digits_for_range)
else:
#Now the number is positive so we can round down
return round_number_down_to_digits(right, digits_for_range)
def createDSIfromDistribution(distribution, n=50):
#np.logspace(-9, 5, base=2, num=50) spacing should be done by powers of 2
if distribution.range_()[0]==0.0 and distribution.range_()[-1]==1.0 and use_powers_of_two_spacing:
lin_space = powers_of_two_spacing()
elif "FTE" in distribution.name and use_powers_of_two_spacing:
lin_space = powers_of_two_error(distribution.d.precision)
else:
lin_space = np.linspace(distribution.range_()[0], distribution.range_()[-1], num=n + 1, endpoint=True)
if custom_spacing:
try:
lin_space = distribution.get_my_spacing()
except:
lin_space = np.linspace(distribution.range_()[0], distribution.range_()[-1], num=n + 1, endpoint=True)
cdf_distr=distribution.get_piecewise_cdf()
ret_list=[]
for i in range(0, len(lin_space)-1):
with gmpy2.local_context(gmpy2.context(), round=gmpy2.RoundDown, precision=mpfr_proxy_precision) as ctx:
lower=round_number_down_to_digits(gmpy2.mpfr(lin_space[i]), digits_for_input_discretization)
with gmpy2.local_context(gmpy2.context(), round=gmpy2.RoundUp, precision=mpfr_proxy_precision) as ctx:
upper=round_number_up_to_digits(gmpy2.mpfr(lin_space[i+1]), digits_for_input_discretization)
cdf_low_bound=min(1.0, max(0.0, cdf_distr(float(lin_space[i]))))
cdf_up_bound=min(1.0, max(0.0, cdf_distr(float(lin_space[i+1]))))
cdf_low_string=dec2Str(round_near(cdf_low_bound, digits_for_input_cdf))
cdf_up_string=dec2Str(round_near(cdf_up_bound, digits_for_input_cdf))
pbox = PBox(Interval(lower, upper, True, False, digits_for_range),
cdf_low_string, cdf_up_string)
ret_list.append(pbox)
ret_list=adjust_ret_list(ret_list)
with gmpy2.local_context(gmpy2.context(), round=gmpy2.RoundDown, precision=mpfr_proxy_precision) as ctx:
ret_list[0].interval.lower = \
round_number_down_to_digits(gmpy2.mpfr(distribution.a_real), digits_for_input_discretization)
with gmpy2.local_context(gmpy2.context(), round=gmpy2.RoundUp, precision=mpfr_proxy_precision) as ctx:
ret_list[-1].interval.upper = \
round_number_up_to_digits(gmpy2.mpfr(distribution.b_real), digits_for_input_discretization)
ret_list[-1].interval.include_upper = True
mixarith=MixedArithmetic(ret_list[0].interval.lower,ret_list[-1].interval.upper,ret_list)
return mixarith
def compute_interval(self):
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundDown,
precision=mpfr_proxy_precision) as ctx:
res_left = gmpy2.sub(mpfr(self.center.lower),
mpfr(self.add_all_coefficients_lower_abs()))
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundUp,
precision=mpfr_proxy_precision) as ctx:
res_right = gmpy2.add(mpfr(self.center.upper),
mpfr(self.add_all_coefficients_upper_abs()))
if res_left <= res_right:
return Interval(
round_number_down_to_digits(res_left, digits_for_range),
round_number_up_to_digits(res_right, digits_for_range), True,
True, digits_for_range)
else:
return Interval(
round_number_down_to_digits(res_right, digits_for_range),
round_number_up_to_digits(res_left, digits_for_range), True,
True, digits_for_range)
def round_value_to_interval(str_value):
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundDown,
precision=mpfr_proxy_precision) as ctx:
res_left = mpfr(str_value)
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundUp,
precision=mpfr_proxy_precision) as ctx:
res_right = mpfr(str_value)
return Interval(
round_number_down_to_digits(res_left, digits_for_range),
round_number_up_to_digits(res_right, digits_for_range), True, True,
digits_for_range)
def compute_middle_point_given_interval(low, upper):
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundDown,
precision=mpfr_proxy_precision) as ctx:
res_left = gmpy2.add(gmpy2.div(mpfr(upper), mpfr("2.0")),
gmpy2.div(mpfr(low), mpfr("2.0")))
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundUp,
precision=mpfr_proxy_precision) as ctx:
res_right = gmpy2.add(gmpy2.div(mpfr(upper), mpfr("2.0")),
gmpy2.div(mpfr(low), mpfr("2.0")))
return Interval(
round_number_down_to_digits(res_left, digits_for_range),
round_number_up_to_digits(res_right, digits_for_range), True, True,
digits_for_range)
def compute_uncertainty_given_interval(low, upper):
coefficients = {}
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundDown,
precision=mpfr_proxy_precision) as ctx:
res_left = gmpy2.sub(gmpy2.div(mpfr(upper), mpfr("2.0")),
gmpy2.div(mpfr(low), mpfr("2.0")))
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundUp,
precision=mpfr_proxy_precision) as ctx:
res_right = gmpy2.sub(gmpy2.div(mpfr(upper), mpfr("2.0")),
gmpy2.div(mpfr(low), mpfr("2.0")))
coefficients[AffineManager.get_new_error_index()]=\
Interval(round_number_down_to_digits(res_left, digits_for_range),
round_number_up_to_digits(res_right, digits_for_range), True, True, digits_for_range)
return coefficients
def division(self, interval):
reset_default_precision()
tmp_res_left = []
tmp_res_right = []
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundDown,
precision=mpfr_proxy_precision) as ctx:
new_right_lower = gmpy2.div(1.0, mpfr(interval.upper))
new_right_upper = gmpy2.div(1.0, mpfr(interval.lower))
tmp_res_left.append(
gmpy2.mul(mpfr(self.lower), mpfr(new_right_lower)))
tmp_res_left.append(
gmpy2.mul(mpfr(self.lower), mpfr(new_right_upper)))
tmp_res_left.append(
gmpy2.mul(mpfr(self.upper), mpfr(new_right_lower)))
tmp_res_left.append(
gmpy2.mul(mpfr(self.upper), mpfr(new_right_upper)))
min_index = [
i for i, value in enumerate(tmp_res_left)
if value == min(tmp_res_left)
]
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundUp,
precision=mpfr_proxy_precision) as ctx:
new_right_lower = gmpy2.div(1.0, mpfr(interval.upper))
new_right_upper = gmpy2.div(1.0, mpfr(interval.lower))
tmp_res_right.append(
gmpy2.mul(mpfr(self.lower), mpfr(new_right_lower)))
tmp_res_right.append(
gmpy2.mul(mpfr(self.lower), mpfr(new_right_upper)))
tmp_res_right.append(
gmpy2.mul(mpfr(self.upper), mpfr(new_right_lower)))
tmp_res_right.append(
gmpy2.mul(mpfr(self.upper), mpfr(new_right_upper)))
max_index = [
i for i, value in enumerate(tmp_res_right)
if value == max(tmp_res_right)
]
# We have to swap the boundaries here 1/[1,2]=[.5, 1]
new_right_lower_inc = interval.include_upper
new_right_upper_inc = interval.include_lower
tmp_bounds = [
self.include_lower * new_right_lower_inc,
self.include_lower * new_right_upper_inc,
self.include_upper * new_right_lower_inc,
self.include_upper * new_right_upper_inc
]
res_inc_left = any([tmp_bounds[index] for index in min_index])
res_inc_right = any([tmp_bounds[index] for index in max_index])
res_left = round_number_down_to_digits(tmp_res_left[min_index[0]],
self.digits)
res_right = round_number_up_to_digits(tmp_res_right[max_index[0]],
self.digits)
return Interval(res_left, res_right, res_inc_left, res_inc_right,
self.digits)
def multiplication(self, interval):
reset_default_precision()
tmp_res_left = []
tmp_res_right = []
zero_is_included = self.check_zero_is_in_interval(
) or interval.check_zero_is_in_interval()
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundDown,
precision=mpfr_proxy_precision) as ctx:
tmp_res_left.append(
gmpy2.mul(mpfr(self.lower), mpfr(interval.lower)))
tmp_res_left.append(
gmpy2.mul(mpfr(self.lower), mpfr(interval.upper)))
tmp_res_left.append(
gmpy2.mul(mpfr(self.upper), mpfr(interval.lower)))
tmp_res_left.append(
gmpy2.mul(mpfr(self.upper), mpfr(interval.upper)))
min_index = [
i for i, value in enumerate(tmp_res_left)
if value == min(tmp_res_left)
]
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundUp,
precision=mpfr_proxy_precision) as ctx:
tmp_res_right.append(
gmpy2.mul(mpfr(self.lower), mpfr(interval.lower)))
tmp_res_right.append(
gmpy2.mul(mpfr(self.lower), mpfr(interval.upper)))
tmp_res_right.append(
gmpy2.mul(mpfr(self.upper), mpfr(interval.lower)))
tmp_res_right.append(
gmpy2.mul(mpfr(self.upper), mpfr(interval.upper)))
max_index = [
i for i, value in enumerate(tmp_res_right)
if value == max(tmp_res_right)
]
tmp_bounds = [
self.include_lower * interval.include_lower,
self.include_lower * interval.include_upper,
self.include_upper * interval.include_lower,
self.include_upper * interval.include_upper
]
res_inc_left = any([tmp_bounds[index] for index in min_index])
res_inc_right = any([tmp_bounds[index] for index in max_index])
min_value = tmp_res_left[min_index[0]]
max_value = tmp_res_right[max_index[0]]
if gmpy2.is_zero(min_value) and zero_is_included:
res_inc_left = True
if gmpy2.is_zero(max_value) and zero_is_included:
res_inc_right = True
res_left = round_number_down_to_digits(min_value, self.digits)
res_right = round_number_up_to_digits(max_value, self.digits)
return Interval(res_left, res_right, res_inc_left, res_inc_right,
self.digits)
