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 __le__(self, other):
"""Less Than Or Equal relation order operator
Some examples:
>>> IReal(2, 3) <= IReal(2.5)
False
>>> IReal(2, 3) <= IReal(3.1)
True
>>> IReal(3) <= IReal(3)
True
>>> IReal("undefined") <= IReal(3.1)
False
>>> IReal(3) <= IReal() # doctest: +ELLIPSIS
Traceback (most recent call last):
...
EmptyIntervalError: this order relation can't be applied...
>>> IReal() <= IReal()
True
"""
if self.empty and other.empty:
return True
if self.empty or other.empty:
raise EmptyIntervalError("this order relation can't be applied "
"to an empty and a non-empty interval")
if self.undefined or other.undefined:
return False
return self.inf <= other.inf and self.sup <= other.sup
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 __neg__(self):
"""Unary minus operator
Some examples:
>>> -IReal("-25/100", 0.5)
[-0.5, 0.25]
>>> -IReal("undefined")
undefined interval
>>> -IReal() # doctest: +ELLIPSIS
Traceback (most recent call last):
...
EmptyIntervalError:...
"""
if self.empty:
raise EmptyIntervalError()
return IReal(-self.sup, -self.inf)
def __pos__(self):
"""Unary plus operator
Some examples:
>>> +IReal("25/100", 0.5)
[0.25, 0.5]
>>> +IReal("undefined")
undefined interval
>>> +IReal() # doctest: +ELLIPSIS
Traceback (most recent call last):
...
EmptyIntervalError:...
"""
if self.empty:
raise EmptyIntervalError()
return self
def __lt__(self, other):
"""Less Than relation order operator
Some examples:
>>> IReal(2, 3) < IReal(2.5)
False
>>> IReal(2, 3) < IReal(3.1)
True
>>> IReal("undefined") < IReal(3.1)
False
>>> IReal(3) < IReal() # doctest: +ELLIPSIS
Traceback (most recent call last):
...
EmptyIntervalError:...
"""
if self.empty or other.empty:
raise EmptyIntervalError()
if self.undefined or other.undefined:
return False
return self.sup < other.inf
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 __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 __abs__(self):
"""Calculates the absolute value of the interval
Some examples:
>>> abs(IReal(-1, 1))
1.0
>>> abs(IReal(0.25, 1))
1.0
>>> abs(IReal()) # doctest: +ELLIPSIS
Traceback (most recent call last):
...
EmptyIntervalError:...
>>> abs(IReal("undefined")) # doctest: +ELLIPSIS
Traceback (most recent call last):
...
UndefinedIntervalError:...
"""
if self.empty:
raise EmptyIntervalError()
if self.undefined:
raise UndefinedIntervalError()
return max(abs(self.inf), abs(self.sup))