def diameter(self):
"""Returns the distance between supremum and infimum of the interval
Some examples:
>>> rounding_mode_backup = rounding.get_mode()
>>> IReal(-10, 1).diameter()
11.0
>>> IReal().diameter() # doctest: +ELLIPSIS
Traceback (most recent call last):
...
EmptyIntervalError:...
>>> IReal("undefined").diameter() # doctest: +ELLIPSIS
Traceback (most recent call last):
...
UndefinedIntervalError:...
>>> rounding_mode_backup == rounding.get_mode()
True
"""
if self.empty:
raise EmptyIntervalError()
if self.undefined:
raise UndefinedIntervalError()
rounding_mode_backup = rounding.get_mode()
rounding.set_mode(1)
ret = self.sup - self.inf
rounding.set_mode(rounding_mode_backup)
return ret
def middle(self):
"""Returns the middle point of the interval
Some examples:
>>> rounding_mode_backup = rounding.get_mode()
>>> IReal(-10, 5).middle()
-2.5
>>> IReal().middle() # doctest: +ELLIPSIS
Traceback (most recent call last):
...
EmptyIntervalError:...
>>> IReal("undefined").middle() # doctest: +ELLIPSIS
Traceback (most recent call last):
...
UndefinedIntervalError:...
>>> rounding_mode_backup == rounding.get_mode()
True
"""
if self.empty:
raise EmptyIntervalError()
if self.undefined:
raise UndefinedIntervalError()
rounding_mode_backup = rounding.get_mode()
rounding.set_mode(1)
ret = (self.inf + self.sup) / 2.0
rounding.set_mode(rounding_mode_backup)
return ret
def diameter(self):
"""Returns the distance between supremum and infimum of the interval
Some examples:
>>> rounding_mode_backup = rounding.get_mode()
>>> IReal(-10, 1).diameter()
11.0
>>> IReal().diameter() # doctest: +ELLIPSIS
Traceback (most recent call last):
...
EmptyIntervalError:...
>>> IReal("undefined").diameter() # doctest: +ELLIPSIS
Traceback (most recent call last):
...
UndefinedIntervalError:...
>>> rounding_mode_backup == rounding.get_mode()
True
"""
if self.empty:
raise EmptyIntervalError()
if self.undefined:
raise UndefinedIntervalError()
rounding_mode_backup = rounding.get_mode()
rounding.set_mode(1)
ret = self.sup - self.inf
rounding.set_mode(rounding_mode_backup)
return ret
def middle(self):
"""Returns the middle point of the interval
Some examples:
>>> rounding_mode_backup = rounding.get_mode()
>>> IReal(-10, 5).middle()
-2.5
>>> IReal().middle() # doctest: +ELLIPSIS
Traceback (most recent call last):
...
EmptyIntervalError:...
>>> IReal("undefined").middle() # doctest: +ELLIPSIS
Traceback (most recent call last):
...
UndefinedIntervalError:...
>>> rounding_mode_backup == rounding.get_mode()
True
"""
if self.empty:
raise EmptyIntervalError()
if self.undefined:
raise UndefinedIntervalError()
rounding_mode_backup = rounding.get_mode()
rounding.set_mode(1)
ret = (self.inf + self.sup) / 2.0
rounding.set_mode(rounding_mode_backup)
return ret
def _parse_limits(inf, sup):
"""Adjusts the entered limits applying directed rounding if possible
Some examples of how it works are below:
>>> rounding_mode_backup = rounding.get_mode()
>>> x = _parse_limits(0.1, 0.1); x[0] == x[1]
True
>>> x = _parse_limits("0.1", "0.1"); x[0] < x[1] and str(x[0]) == str(x[1])
True
>>> x = _parse_limits("0.25", 0.25); x[0] == x[1]
True
>>> x = _parse_limits("0.1", "0.3")
>>> x[0] < 0.1 and x[1] > 0.3 and str(x[0]) == "0.1" and str(x[1]) == "0.3"
True
>>> _parse_limits(1, "1e1000") # doctest: +ELLIPSIS
Traceback (most recent call last):
...
OverflowError: 'inf' or 'sup' fraction parts are too large...
>>> _parse_limits("1e1000", 1) # doctest: +ELLIPSIS
Traceback (most recent call last):
...
OverflowError: 'inf' or 'sup' fraction parts are too large...
>>> rounding_mode_backup == rounding.get_mode()
True
"""
new_inf, new_sup = inf, sup
try:
rounding_mode_backup = rounding.get_mode()
if type(inf) == type(str()):
number_fraction = rational2fraction(inf)
rounding.set_mode(0)
fp_numerator = float(number_fraction[0])
fp_denominator = float(number_fraction[1])
rounding.set_mode(-1)
new_inf = fp_numerator / fp_denominator
if type(sup) == type(str()):
if inf != sup:
number_fraction = rational2fraction(sup)
rounding.set_mode(0)
fp_numerator = float(number_fraction[0])
fp_denominator = float(number_fraction[1])
rounding.set_mode(1)
new_sup = fp_numerator / fp_denominator
except OverflowError:
raise OverflowError("'inf' or 'sup' fraction parts are too large to"
" convert them to float")
finally:
rounding.set_mode(rounding_mode_backup)
return (float(new_inf), float(new_sup))
def _parse_limits(inf, sup):
"""Adjusts the entered limits applying directed rounding if possible
Some examples of how it works are below:
>>> rounding_mode_backup = rounding.get_mode()
>>> x = _parse_limits(0.1, 0.1); x[0] == x[1]
True
>>> x = _parse_limits("0.1", "0.1"); x[0] < x[1] and str(x[0]) == str(x[1])
True
>>> x = _parse_limits("0.25", 0.25); x[0] == x[1]
True
>>> x = _parse_limits("0.1", "0.3")
>>> x[0] < 0.1 and x[1] > 0.3 and str(x[0]) == "0.1" and str(x[1]) == "0.3"
True
>>> _parse_limits(1, "1e1000") # doctest: +ELLIPSIS
Traceback (most recent call last):
...
OverflowError: 'inf' or 'sup' fraction parts are too large...
>>> _parse_limits("1e1000", 1) # doctest: +ELLIPSIS
Traceback (most recent call last):
...
OverflowError: 'inf' or 'sup' fraction parts are too large...
>>> rounding_mode_backup == rounding.get_mode()
True
"""
new_inf, new_sup = inf, sup
try:
rounding_mode_backup = rounding.get_mode()
if type(inf) == type(str()):
number_fraction = rational2fraction(inf)
rounding.set_mode(0)
fp_numerator = float(number_fraction[0])
fp_denominator = float(number_fraction[1])
rounding.set_mode(-1)
new_inf = fp_numerator / fp_denominator
if type(sup) == type(str()):
if inf != sup:
number_fraction = rational2fraction(sup)
rounding.set_mode(0)
fp_numerator = float(number_fraction[0])
fp_denominator = float(number_fraction[1])
rounding.set_mode(1)
new_sup = fp_numerator / fp_denominator
except OverflowError:
raise OverflowError("'inf' or 'sup' fraction parts are too large to"
" convert them to float")
finally:
rounding.set_mode(rounding_mode_backup)
return (float(new_inf), float(new_sup))
def distance(self, other):
"""Returns the Hausdorff distance of the interval
Some examples:
>>> rounding_mode_backup = rounding.get_mode()
>>> IReal(-10, 5).distance(IReal(10))
20.0
>>> IReal(-10, 5).distance(IReal(10, 50))
45.0
>>> x = IReal(-10, 5); x.distance(x)
0.0
>>> IReal(-1).distance(IReal()) # doctest: +ELLIPSIS
Traceback (most recent call last):
...
EmptyIntervalError:...
>>> IReal().distance(IReal(-1)) # doctest: +ELLIPSIS
Traceback (most recent call last):
...
EmptyIntervalError:...
>>> IReal("undefined").distance(IReal(12)) # doctest: +ELLIPSIS
Traceback (most recent call last):
...
UndefinedIntervalError:...
>>> IReal(10).distance(IReal("undefined")) # doctest: +ELLIPSIS
Traceback (most recent call last):
...
UndefinedIntervalError:...
>>> rounding_mode_backup == rounding.get_mode()
True
"""
if self.empty or other.empty:
raise EmptyIntervalError()
if self.undefined or other.undefined:
raise UndefinedIntervalError()
rounding_mode_backup = rounding.get_mode()
rounding.set_mode(1)
ret = max(abs(self.inf-other.inf), abs(self.sup-other.sup))
rounding.set_mode(rounding_mode_backup)
return ret
def __mul__(self, other):
"""Multiplication operator
Some examples:
>>> rounding_mode_backup = rounding.get_mode()
>>> IReal(0.25, 0.5) * IReal(2, 3)
[0.5, 1.5]
>>> IReal(-0.75, 0.75) * 2
[-1.5, 1.5]
>>> x = IReal("0.1") * "0.1"
>>> x.inf < x.sup and str(x.inf) == str(x.sup)
True
>>> IReal("undefined") * 2
undefined interval
>>> IReal(2) * IReal() # doctest: +ELLIPSIS
Traceback (most recent call last):
...
EmptyIntervalError:...
>>> rounding_mode_backup == rounding.get_mode()
True
"""
if type(other) != type(self):
other = IReal(other)
if self.empty or other.empty:
raise EmptyIntervalError()
x1, y1, x2, y2 = self.inf, self.sup, other.inf, other.sup
rounding_mode_backup = rounding.get_mode()
rounding.set_mode(-1)
inf = min(x1*x2, x1*y2, y1*x2, y1*y2)
rounding.set_mode(1)
sup = max(x1*x2, x1*y2, y1*x2, y1*y2)
rounding.set_mode(rounding_mode_backup)
return IReal(inf, sup)
def __sub__(self, other):
"""Binary minus operator
Some examples:
>>> rounding_mode_backup = rounding.get_mode()
>>> IReal(0.25, 0.5) - IReal(2)
[-1.75, -1.5]
>>> IReal(-0.75, 0.75) - 2
[-2.75, -1.25]
>>> x = IReal("0.1") - "0.1"
>>> x.inf < x.sup and str(-x.inf) == str(x.sup)
True
>>> IReal("undefined") + 2
undefined interval
>>> IReal(2) + IReal() # doctest: +ELLIPSIS
Traceback (most recent call last):
...
EmptyIntervalError:...
>>> rounding_mode_backup == rounding.get_mode()
True
"""
if type(other) != type(self):
other = IReal(other)
if self.empty or other.empty:
raise EmptyIntervalError()
rounding_mode_backup = rounding.get_mode()
rounding.set_mode(-1)
inf = self.inf - other.sup
rounding.set_mode(1)
sup = self.sup - other.inf
rounding.set_mode(rounding_mode_backup)
return IReal(inf, sup)
def __invert__(self):
"""Inversion operator
Some examples:
>>> rounding_mode_backup = rounding.get_mode()
>>> ~IReal(0.25, 0.5)
[2.0, 4.0]
>>> x = ~IReal(0.1); x.inf < x.sup and str(x.inf) == str(x.sup)
True
>>> ~IReal("undefined")
undefined interval
>>> ~IReal(-2, 2)
undefined interval
>>> ~IReal() # doctest: +ELLIPSIS
Traceback (most recent call last):
...
EmptyIntervalError:...
>>> rounding_mode_backup == rounding.get_mode()
True
"""
if self.empty:
raise EmptyIntervalError()
if 0.0 in self:
return IReal("undefined")
rounding_mode_backup = rounding.get_mode()
rounding.set_mode(-1)
inf = 1.0 / self.sup
rounding.set_mode(1)
sup = 1.0 / self.inf
rounding.set_mode(rounding_mode_backup)
return IReal(inf, sup)
def distance(self, other):
"""Returns the Hausdorff distance of the interval
Some examples:
>>> rounding_mode_backup = rounding.get_mode()
>>> IReal(-10, 5).distance(IReal(10))
20.0
>>> IReal(-10, 5).distance(IReal(10, 50))
45.0
>>> x = IReal(-10, 5); x.distance(x)
0.0
>>> IReal(-1).distance(IReal()) # doctest: +ELLIPSIS
Traceback (most recent call last):
...
EmptyIntervalError:...
>>> IReal().distance(IReal(-1)) # doctest: +ELLIPSIS
Traceback (most recent call last):
...
EmptyIntervalError:...
>>> IReal("undefined").distance(IReal(12)) # doctest: +ELLIPSIS
Traceback (most recent call last):
...
UndefinedIntervalError:...
>>> IReal(10).distance(IReal("undefined")) # doctest: +ELLIPSIS
Traceback (most recent call last):
...
UndefinedIntervalError:...
>>> rounding_mode_backup == rounding.get_mode()
True
"""
if self.empty or other.empty:
raise EmptyIntervalError()
if self.undefined or other.undefined:
raise UndefinedIntervalError()
rounding_mode_backup = rounding.get_mode()
rounding.set_mode(1)
ret = max(abs(self.inf-other.inf), abs(self.sup-other.sup))
rounding.set_mode(rounding_mode_backup)
return ret
def __mul__(self, other):
"""Multiplication operator
Some examples:
>>> rounding_mode_backup = rounding.get_mode()
>>> IReal(0.25, 0.5) * IReal(2, 3)
[0.5, 1.5]
>>> IReal(-0.75, 0.75) * 2
[-1.5, 1.5]
>>> x = IReal("0.1") * "0.1"
>>> x.inf < x.sup and str(x.inf) == str(x.sup)
True
>>> IReal("undefined") * 2
undefined interval
>>> IReal(2) * IReal() # doctest: +ELLIPSIS
Traceback (most recent call last):
...
EmptyIntervalError:...
>>> rounding_mode_backup == rounding.get_mode()
True
"""
if type(other) != type(self):
other = IReal(other)
if self.empty or other.empty:
raise EmptyIntervalError()
x1, y1, x2, y2 = self.inf, self.sup, other.inf, other.sup
rounding_mode_backup = rounding.get_mode()
rounding.set_mode(-1)
inf = min(x1*x2, x1*y2, y1*x2, y1*y2)
rounding.set_mode(1)
sup = max(x1*x2, x1*y2, y1*x2, y1*y2)
rounding.set_mode(rounding_mode_backup)
return IReal(inf, sup)
def __sub__(self, other):
"""Binary minus operator
Some examples:
>>> rounding_mode_backup = rounding.get_mode()
>>> IReal(0.25, 0.5) - IReal(2)
[-1.75, -1.5]
>>> IReal(-0.75, 0.75) - 2
[-2.75, -1.25]
>>> x = IReal("0.1") - "0.1"
>>> x.inf < x.sup and str(-x.inf) == str(x.sup)
True
>>> IReal("undefined") + 2
undefined interval
>>> IReal(2) + IReal() # doctest: +ELLIPSIS
Traceback (most recent call last):
...
EmptyIntervalError:...
>>> rounding_mode_backup == rounding.get_mode()
True
"""
if type(other) != type(self):
other = IReal(other)
if self.empty or other.empty:
raise EmptyIntervalError()
rounding_mode_backup = rounding.get_mode()
rounding.set_mode(-1)
inf = self.inf - other.sup
rounding.set_mode(1)
sup = self.sup - other.inf
rounding.set_mode(rounding_mode_backup)
return IReal(inf, sup)
def __invert__(self):
"""Inversion operator
Some examples:
>>> rounding_mode_backup = rounding.get_mode()
>>> ~IReal(0.25, 0.5)
[2.0, 4.0]
>>> x = ~IReal(0.1); x.inf < x.sup and str(x.inf) == str(x.sup)
True
>>> ~IReal("undefined")
undefined interval
>>> ~IReal(-2, 2)
undefined interval
>>> ~IReal() # doctest: +ELLIPSIS
Traceback (most recent call last):
...
EmptyIntervalError:...
>>> rounding_mode_backup == rounding.get_mode()
True
"""
if self.empty:
raise EmptyIntervalError()
if 0.0 in self:
return IReal("undefined")
rounding_mode_backup = rounding.get_mode()
rounding.set_mode(-1)
inf = 1.0 / self.sup
rounding.set_mode(1)
sup = 1.0 / self.inf
rounding.set_mode(rounding_mode_backup)
return IReal(inf, sup)
def __div__(self, other):
"""Division operator
Some examples:
>>> rounding_mode_backup = rounding.get_mode()
>>> IReal(0.25, 0.5) / IReal(2, 4)
[0.0625, 0.25]
>>> IReal(-0.75, 0.75) / 2
[-0.375, 0.375]
>>> x = IReal("0.1") / "0.1"
>>> x.inf < x.sup and str(x.inf) == str(x.sup)
True
>>> IReal(1) / IReal(-2, 2)
undefined interval
>>> IReal("undefined") / 2
undefined interval
>>> IReal(2) / IReal() # doctest: +ELLIPSIS
Traceback (most recent call last):
...
EmptyIntervalError:...
>>> rounding_mode_backup == rounding.get_mode()
True
"""
if type(other) != type(self):
other = IReal(other)
if self.empty or other.empty:
raise EmptyIntervalError()
if 0.0 in other:
return IReal("undefined")
x1, y1, x2, y2 = self.inf, self.sup, other.inf, other.sup
rounding_mode_backup = rounding.get_mode()
rounding.set_mode(-1)
inf = min(x1/x2, x1/y2, y1/x2, y1/y2)
rounding.set_mode(1)
sup = max(x1/x2, x1/y2, y1/x2, y1/y2)
rounding.set_mode(rounding_mode_backup)
return IReal(inf, sup)
def __div__(self, other):
"""Division operator
Some examples:
>>> rounding_mode_backup = rounding.get_mode()
>>> IReal(0.25, 0.5) / IReal(2, 4)
[0.0625, 0.25]
>>> IReal(-0.75, 0.75) / 2
[-0.375, 0.375]
>>> x = IReal("0.1") / "0.1"
>>> x.inf < x.sup and str(x.inf) == str(x.sup)
True
>>> IReal(1) / IReal(-2, 2)
undefined interval
>>> IReal("undefined") / 2
undefined interval
>>> IReal(2) / IReal() # doctest: +ELLIPSIS
Traceback (most recent call last):
...
EmptyIntervalError:...
>>> rounding_mode_backup == rounding.get_mode()
True
"""
if type(other) != type(self):
other = IReal(other)
if self.empty or other.empty:
raise EmptyIntervalError()
if 0.0 in other:
return IReal("undefined")
x1, y1, x2, y2 = self.inf, self.sup, other.inf, other.sup
rounding_mode_backup = rounding.get_mode()
rounding.set_mode(-1)
inf = min(x1/x2, x1/y2, y1/x2, y1/y2)
rounding.set_mode(1)
sup = max(x1/x2, x1/y2, y1/x2, y1/y2)
rounding.set_mode(rounding_mode_backup)
return IReal(inf, sup)
