"""
Source https://github.com/internetarchive/analyze_ocr/blob/master/interval.py
Liscence Not Specified
Provides the Interval and IntervalSet classes
The interval module provides the Interval and IntervalSet data types.
Intervals describe continuous ranges that can be open, closed, half-open,
or infinite. IntervalSets contain zero to many disjoint sets of
Intervals.
Intervals don't have to pertain to numbers. They can contain any data
that is comparable via the Python operators <, <=, ==, >=, and >. Here's
an example of how strings can be used with Intervals:
>>> volume1 = Interval.between("A", "Foe")
>>> volume2 = Interval.between("Fog", "McAfee")
>>> volume3 = Interval.between("McDonalds", "Space")
>>> volume4 = Interval.between("Spade", "Zygote")
>>> encyclopedia = IntervalSet([volume1, volume2, volume3, volume4])
>>> mySet = IntervalSet([volume1, volume3, volume4])
>>> "Meteor" in encyclopedia
True
>>> "Goose" in encyclopedia
True
>>> "Goose" in mySet
False
>>> volume2 in (encyclopedia ^ mySet)
True
Here's an example of how times can be used with Intervals:
>>> officeHours = IntervalSet.between("08:00", "17:00")
>>> myLunch = IntervalSet.between("11:30", "12:30")
>>> myHours = IntervalSet.between("08:30", "19:30") - myLunch
>>> myHours.issubset(officeHours)
False
>>> "12:00" in myHours
False
>>> "15:30" in myHours
True
>>> inOffice = officeHours & myHours
>>> print inOffice
['08:30'..'11:30'),('12:30'..'17:00']
>>> overtime = myHours - officeHours
>>> print overtime
('17:00'..'19:30']
"""
import copy
import datetime
start_time_format = "%Y%m%d_%H%M%S"
[docs]class Smallest:
"""Represents the smallest value
This type doesn't do much; it implements a pseudo-value that's smaller
than everything but itself.
>>> negInf = Smallest()
>>> smallest = Smallest()
>>> -264 < negInf
False
>>> -264 == negInf
False
>>> -264 > negInf
True
>>> negInf < negInf
False
>>> negInf == smallest
True
"""
def __neg__(self):
"""Returns the largest value
The opposite of negative infinity is infinity, the largest value.
>>> print -Smallest()
~
"""
return Largest()
def __cmp__(self, other):
"""Compares this with another object
Always indicates that self is less than other, unless both are of
type Smallest, in which case they are equal.
>>> 0 < Smallest()
False
>>> -9999999 < Smallest()
False
>>> Smallest() < -9999999
True
>>> Smallest() < Smallest()
False
>>> Smallest() == Smallest()
True
"""
if other.__class__ == self.__class__:
retval = 0
else:
retval = -1
return retval
def __str__(self):
"""Returns a printable representation of this value
The string for the smallest number is -~, which means negative infinity.
>>> print Smallest()
-~
"""
return "-~"
def __repr__(self):
"""Returns an evaluable representation of the object
The representation of the smallest number is -Inf, which means
negative infinity.
>>> Smallest()
-Inf
"""
return "-Inf"
def __hash__(self):
"Returns a value that can be used for generating hashes"
return 0x55555555
[docs]class Largest:
"""Class representing the universal largest value
This type doesn't do much; it implements a pseudo-value that's larger
than everything but itself.
>>> infinity = Largest()
>>> greatest = Largest()
>>> 6234 < infinity
True
>>> 6234 == infinity
False
>>> 6234 > infinity
False
>>> infinity > infinity
False
>>> infinity == greatest
True
"""
def __neg__(self):
"""Returns the smallest universal value
The opposite of infinity is negative infinity, the smallest value.
>>> print -Largest()
-~
"""
return Smallest()
def __cmp__(self, other):
"""Compares object with another object
Always indicates that self is greater than other, unless both are of
type Largest, in which case they are equal.
>>> 0 > Largest()
False
>>> Largest() < 9999999
False
>>> Largest() > 9999999
True
>>> Largest() < Largest()
False
>>> Largest() == Largest()
True
"""
if other.__class__ == self.__class__:
retval = 0
else:
retval = 1
return retval
def __str__(self):
"""Returns a string representation of the object
The largest number is displayed as ~ (it sort of looks like infinity...)
>>> print Largest()
~
"""
return "~"
def __repr__(self):
"""Returns an evaluable expression representing this object
>>> Largest()
Inf
"""
return "Inf"
def __hash__(self):
"Returns a value that can be used for generating hashes"
return -0x55555555
Inf = Largest()
# Use -Inf for the smallest value
[docs]class Interval(object):
"""Represents a continuous range of values
An Interval is composed of the lower bound, a closed lower bound
flag, an upper bound, and a closed upper bound flag. The attributes
are called lower_bound, lower_closed, upper_bound, and upper_closed,
respectively. For an infinite interval, the bound is set to inf or
-inf. IntervalSets are composed of zero to many Intervals.
"""
def __init__(self, lower_bound=-Inf, upper_bound=Inf, **kwargs):
"""Initializes an interval
Parameters
==========
- lower_bound: The lower bound of an interval (default -Inf)
- upper_bound: The upper bound of an interval (default Inf)
- closed: Boolean telling whether both ends of the interval are closed
(default True). Setting this sets both lower_closed and upper_closed
- lower_closed: Boolean telling whether the lower end of the interval
is closed (default True)
- upper_closed: Boolean telling whether the upper end of the interval
is closed (default True)
An Interval can represent an infinite set.
>>> r = Interval(-Inf, Inf) # All values
An Interval can represent sets unbounded on an end.
>>> r = Interval(upper_bound=62, closed=False)
>>> r = Interval(upper_bound=37)
>>> r = Interval(lower_bound=246)
>>> r = Interval(lower_bound=2468, closed=False)
An Interval can represent a set of values up to, but not including a
value.
>>> r = Interval(25, 28, closed=False)
An Interval can represent a set of values that have an inclusive
boundary.
>>> r = Interval(29, 216)
An Interval can represent a single value
>>> r = Interval(82, 82)
Intervals that are not normalized, i.e. that have a lower bound
exceeding an upper bound, are silently normalized.
>>> print Interval(5, 2, lower_closed=False)
[2..5)
Intervals can represent an empty set.
>>> r = Interval(5, 5, closed=False)
Intervals can only contain hashable (immutable) objects.
>>> r = Interval([], 12)
Traceback (most recent call last):
...
TypeError: lower_bound is not hashable.
>>> r = Interval(12, [])
Traceback (most recent call last):
...
TypeError: upper_bound is not hashable.
"""
try:
hash(lower_bound)
except TypeError:
raise TypeError("lower_bound is not hashable.")
try:
hash(upper_bound)
except TypeError:
raise TypeError("upper_bound is not hashable.")
lower_closed = not (
isinstance(lower_bound, Smallest) or isinstance(lower_bound, Largest)
) and kwargs.get("lower_closed", kwargs.get("closed", True))
upper_closed = not (
isinstance(upper_bound, Smallest) or isinstance(upper_bound, Largest)
) and kwargs.get("upper_closed", kwargs.get("closed", True))
if upper_bound < lower_bound:
lower_bound, lower_closed, upper_bound, upper_closed = (
upper_bound,
upper_closed,
lower_bound,
lower_closed,
)
if ((lower_bound == -Inf) and lower_closed) or (
(upper_bound == Inf) and upper_closed
):
raise ValueError("Unbound ends cannot be included in an interval.")
self.lower_bound = lower_bound
self.lower_closed = lower_closed
self.upper_bound = upper_bound
self.upper_closed = upper_closed
def __hash__(self):
"""Returns a hashed value of the object
Intervals are to be considered immutable. Thus, a 32-bit hash can
be generated for them.
>>> h = hash(Interval.less_than(5))
"""
return hash(
(self.lower_bound, self.lower_closed, self.upper_bound, self.upper_closed)
)
def __repr__(self):
"""Returns an evaluable expression that can reproduce the object
>>> Interval(3, 6)
Interval(3, 6, lower_closed=True, upper_closed=True)
>>> Interval(3, 6, closed=False)
Interval(3, 6, lower_closed=False, upper_closed=False)
>>> Interval(3, 6, lower_closed=False)
Interval(3, 6, lower_closed=False, upper_closed=True)
>>> Interval()
Interval(-Inf, Inf, lower_closed=False, upper_closed=False)
"""
return "Interval(%s, %s, lower_closed=%s, upper_closed=%s)" % (
repr(self.lower_bound),
repr(self.upper_bound),
self.lower_closed,
self.upper_closed,
)
def __str__(self):
"""Returns a string representation of the object
This function yields a graphical representation of an Interval.
It is included in the __str__ of an IntervalSet. Non-inclusive
boundaries are bordered by a ( or ). Inclusive boundaries are
bordered by [ or ]. Unbound values are shown as .... Intervals
consisting of only a single value are shown as that value. Empty
intervals are shown as the string <Empty>
>>> print Interval.all()
(...)
>>> print Interval.less_than(100)
(...100)
>>> print Interval.less_than_or_equal_to(2593)
(...2593]
>>> print Interval.greater_than(2378)
(2378...)
>>> print Interval.between(26, 8234, False)
(26..8234)
>>> print Interval(237, 2348, lower_closed=False)
(237..2348]
>>> print Interval.greater_than_or_equal_to(347)
[347...)
>>> print Interval(237, 278, upper_closed=False)
[237..278)
>>> print Interval.between(723, 2378)
[723..2378]
>>> print Interval.equal_to(5)
5
>>> print Interval.none()
<Empty>
"""
if self.lower_bound == self.upper_bound:
if self.lower_closed or self.upper_closed:
retval = repr(self.lower_bound)
else:
retval = "<Empty>"
else:
between = ".."
if self.lower_closed:
lbchar = "["
else:
lbchar = "("
if self.lower_bound == -Inf:
lstr = ""
between = "..."
else:
lstr = repr(self.lower_bound)
if self.upper_closed:
ubchar = "]"
else:
ubchar = ")"
if self.upper_bound == Inf:
ustr = ""
between = "..."
else:
ustr = repr(self.upper_bound)
retval = "".join([lbchar, lstr, between, ustr, ubchar])
return retval
def __nonzero__(self):
"""Tells whether the interval is empty
>>> if Interval(12, 12, closed=False):
... print "Non-empty"
>>> if Interval(12, 12, upper_closed=False):
... print "Non-empty"
>>> if Interval(12, 12):
... print "Non-empty"
Non-empty
@change 20170509: for some reason this was choking on numpy.bool_ being
returned so I'm forcing cast as straight bool
"""
result = bool(
(self.lower_bound != self.upper_bound)
or (self.upper_closed and self.lower_closed)
)
return result
def __cmp__(self, other):
"""Compares two intervals for ordering purposes
>>> Interval.equal_to(-1) < Interval.equal_to(2)
True
>>> Interval.equal_to(-1) == Interval.equal_to(2)
False
>>> Interval.equal_to(-1) > Interval.equal_to(2)
False
>>> Interval.between(2, 5) > Interval.between(2, 4)
True
>>> Interval.between(2, 5) == Interval.between(2, 4)
False
>>> Interval.between(2, 5) == Interval.between(2, 5)
True
>>> Interval.between(2, 5) >= Interval.between(2, 5)
True
"""
if self == other:
result = 0
elif self.comes_before(other):
result = -1
else:
result = 1
return result
def __and__(self, other):
"""Returns the intersection of two intervals
>>> print Interval.greater_than(3) & Interval.greater_than(5)
(5...)
>>> print Interval.greater_than(3) & Interval.equal_to(3)
<Empty>
>>> print Interval.greater_than_or_equal_to(3) & Interval.equal_to(3)
3
>>> print Interval.all() & Interval.all()
(...)
>>> print Interval.greater_than(3) & Interval.less_than(10)
(3..10)
"""
if self == other:
result = Interval()
result.lower_bound = self.lower_bound
result.upper_bound = self.upper_bound
result.lower_closed = self.lower_closed
result.upper_closed = self.upper_closed
elif self.comes_before(other):
if self.overlaps(other):
if self.lower_bound == other.lower_bound:
lower = self.lower_bound
lower_closed = min(self.lower_closed, other.lower_closed)
elif self.lower_bound > other.lower_bound:
lower = self.lower_bound
lower_closed = self.lower_closed
else:
lower = other.lower_bound
lower_closed = other.lower_closed
if self.upper_bound == other.upper_bound:
upper = self.upper_bound
upper_closed = min(self.upper_closed, other.upper_closed)
elif self.upper_bound < other.upper_bound:
upper = self.upper_bound
upper_closed = self.upper_closed
else:
upper = other.upper_bound
upper_closed = other.upper_closed
result = Interval(
lower, upper, lower_closed=lower_closed, upper_closed=upper_closed
)
else:
result = Interval.none()
else:
result = other & self
return result
def _get_start_time(self, **kwargs):
"""
Custom add for QF project. Normally return YMD_HMS but in this case
must also return ms
"""
ms = kwargs.get("ms", False)
if isinstance(self.lower_bound, datetime.datetime):
if ms:
time_format = start_time_format + "_%f"
else:
time_format = start_time_format
starttime = self.lower_bound.strftime(time_format)
if ms:
starttime = starttime[:-3]
else:
print(
"This interval does not appear to relate to time\
so start time is not well defined"
)
starttime = None
starttime_string = starttime
return starttime_string
[docs] @classmethod
def none(cls):
"""Returns an empty interval
>>> print Interval.none()
<Empty>
"""
return cls(0, 0, closed=False)
[docs] @classmethod
def all(cls):
"""Returns an interval encompassing all values
>>> print Interval.all()
(...)
"""
return cls()
[docs] @classmethod
def between(cls, a, b, closed=True):
"""Returns an interval between two values
Returns an interval between values a and b. If closed is True,
then the endpoints are included. Otherwise, the endpoints are
excluded.
>>> print Interval.between(2, 4)
[2..4]
>>> print Interval.between(2, 4, False)
(2..4)
"""
return cls(a, b, closed=closed)
[docs] @classmethod
def equal_to(cls, a):
"""Returns an point interval
Returns an interval containing only a.
>>> print Interval.equal_to(32)
32
"""
return cls(a, a)
[docs] @classmethod
def less_than(cls, a):
"""Returns interval of all values less than the given value
Returns an interval containing all values less than a. If closed
is True, then all values less than or equal to a are returned.
>>> print Interval.less_than(32)
(...32)
"""
return cls(upper_bound=a, upper_closed=False)
[docs] @classmethod
def less_than_or_equal_to(cls, a):
"""Returns an interval containing the given values and everything less
>>> print Interval.less_than_or_equal_to(32)
(...32]
"""
return cls(upper_bound=a, upper_closed=True)
[docs] @classmethod
def greater_than(cls, a):
"""Returns interval of all values greater than the given value
>>> print Interval.greater_than(32)
(32...)
"""
return cls(lower_bound=a, lower_closed=False)
[docs] @classmethod
def greater_than_or_equal_to(cls, a):
"""Returns interval of all values greater than or equal to the given value
>>> print Interval.greater_than_or_equal_to(32)
[32...)
"""
return cls(lower_bound=a, lower_closed=True)
[docs] def comes_before(self, other):
"""Tells whether an interval lies before the object
self comes before other when sorted if its lower bound is less
than other's smallest value. If the smallest value is the same,
then the Interval with the smallest upper bound comes first.
Otherwise, they are equal.
>>> Interval.equal_to(1).comes_before(Interval.equal_to(4))
True
>>> Interval.less_than_or_equal_to(1).comes_before(Interval.equal_to(4))
True
>>> Interval.less_than_or_equal_to(5).comes_before(
... Interval.less_than(5))
False
>>> Interval.less_than(5).comes_before(
... Interval.less_than_or_equal_to(5))
True
>>> Interval.all().comes_before(Interval.all())
False
"""
if self == other:
result = False
elif self.lower_bound < other.lower_bound:
result = True
elif self.lower_bound > other.lower_bound:
result = False
elif self.lower_closed == other.lower_closed:
if self.upper_bound < other.upper_bound:
result = True
elif (
self.upper_bound > other.upper_bound
or self.upper_closed == other.upper_closed
or self.upper_closed
):
result = False
else:
result = True
elif self.lower_closed:
result = True
else:
result = False
return result
[docs] def join(self, other):
"""Combines two continous Intervals
Combines two continuous Intervals into one Interval. If the two
Intervals are disjoint, then an exception is raised.
>>> r1 = Interval.less_than(-100)
>>> r2 = Interval.less_than_or_equal_to(-100)
>>> r3 = Interval.less_than(100)
>>> r4 = Interval.less_than_or_equal_to(100)
>>> r5 = Interval.all()
>>> r6 = Interval.between(-100, 100, False)
>>> r7 = Interval(-100, 100, lower_closed=False)
>>> r8 = Interval.greater_than(-100)
>>> r9 = Interval.equal_to(-100)
>>> r10 = Interval(-100, 100, upper_closed=False)
>>> r11 = Interval.between(-100, 100)
>>> r12 = Interval.greater_than_or_equal_to(-100)
>>> r13 = Interval.greater_than(100)
>>> r14 = Interval.equal_to(100)
>>> r15 = Interval.greater_than_or_equal_to(100)
>>> print r13.join(r15)
[100...)
>>> print r7.join(r6)
(-100..100]
>>> print r11.join(r2)
(...100]
>>> print r4.join(r15)
(...)
>>> print r8.join(r8)
(-100...)
>>> print r3.join(r7)
(...100]
>>> print r5.join(r10)
(...)
>>> print r9.join(r1)
(...-100]
>>> print r12.join(r5)
(...)
>>> print r13.join(r1)
Traceback (most recent call last):
...
ArithmeticError: The Intervals are disjoint.
>>> print r14.join(r2)
Traceback (most recent call last):
...
ArithmeticError: The Intervals are disjoint.
"""
if self.overlaps(other) or self.adjacent_to(other):
if self.lower_bound < other.lower_bound:
lbound = self.lower_bound
linc = self.lower_closed
elif self.lower_bound == other.lower_bound:
lbound = self.lower_bound
linc = max(self.lower_closed, other.lower_closed)
else:
lbound = other.lower_bound
linc = other.lower_closed
if self.upper_bound > other.upper_bound:
ubound = self.upper_bound
uinc = self.upper_closed
elif self.upper_bound == other.upper_bound:
ubound = self.upper_bound
uinc = max(self.upper_closed, other.upper_closed)
else:
ubound = other.upper_bound
uinc = other.upper_closed
return Interval(lbound, ubound, upper_closed=uinc, lower_closed=linc)
else:
raise ArithmeticError("The Intervals are disjoint.")
def __contains__(self, obj):
"""Returns True if obj lies wholly within the Interval.
>>> all = Interval.all()
>>> lt = Interval.less_than(10)
>>> le = Interval.less_than_or_equal_to(10)
>>> some = Interval(10, 20, lower_closed=False)
>>> single = Interval.equal_to(10)
>>> ge = Interval.greater_than_or_equal_to(10)
>>> gt = Interval.greater_than(10)
>>> ne = Interval.equal_to(17)
>>> 10 in all
True
>>> 10 in lt
False
>>> 10 in le
True
>>> 10 in some
False
>>> 10 in single
True
>>> 10 in ge
True
>>> 10 in gt
False
>>> 10 in ne
False
>>> all in some
False
>>> lt in all
True
>>> lt in some
False
>>> single in ge
True
>>> ne in some
True
"""
if isinstance(obj, Interval):
if obj.lower_bound < self.lower_bound:
insideLower = False
elif obj.lower_bound == self.lower_bound:
insideLower = obj.lower_closed <= self.lower_closed
else:
insideLower = True
if obj.upper_bound > self.upper_bound:
insideUpper = False
elif obj.upper_bound == self.upper_bound:
insideUpper = obj.upper_closed <= self.upper_closed
else:
insideUpper = True
result = insideLower and insideUpper
else:
result = Interval.equal_to(obj) in self
return result
[docs] def overlaps(self, other):
"""Tells whether the given interval overlaps the object
Returns True if the one Interval overlaps another. If they are
immediately adjacent, then this returns False. Use the adjacent_to
function for testing for adjacent Intervals.
>>> r1 = Interval.less_than(-100)
>>> r2 = Interval.less_than_or_equal_to(-100)
>>> r3 = Interval.less_than(100)
>>> r4 = Interval.less_than_or_equal_to(100)
>>> r5 = Interval.all()
>>> r6 = Interval.between(-100, 100, False)
>>> r7 = Interval(-100, 100, lower_closed=False)
>>> r8 = Interval.greater_than(-100)
>>> r9 = Interval.equal_to(-100)
>>> r10 = Interval(-100, 100, upper_closed=False)
>>> r11 = Interval.between(-100, 100)
>>> r12 = Interval.greater_than_or_equal_to(-100)
>>> r13 = Interval.greater_than(100)
>>> r14 = Interval.equal_to(100)
>>> r15 = Interval.greater_than_or_equal_to(100)
>>> r8.overlaps(r9)
False
>>> r12.overlaps(r6)
True
>>> r7.overlaps(r8)
True
>>> r8.overlaps(r4)
True
>>> r14.overlaps(r11)
True
>>> r10.overlaps(r13)
False
>>> r5.overlaps(r1)
True
>>> r5.overlaps(r2)
True
>>> r15.overlaps(r6)
False
>>> r3.overlaps(r1)
True
"""
if self == other:
result = True
elif other.comes_before(self):
result = other.overlaps(self)
elif other.lower_bound < self.upper_bound:
result = True
elif other.lower_bound == self.upper_bound:
result = other.lower_closed and self.upper_closed
else:
result = False
return result
[docs] def adjacent_to(self, other):
"""Tells whether an Interval is adjacent to the object without overlap
Returns True if self is adjacent to other, meaning that if they
were joined, there would be no discontinuity. They cannot
overlap.
>>> r1 = Interval.less_than(-100)
>>> r2 = Interval.less_than_or_equal_to(-100)
>>> r3 = Interval.less_than(100)
>>> r4 = Interval.less_than_or_equal_to(100)
>>> r5 = Interval.all()
>>> r6 = Interval.between(-100, 100, False)
>>> r7 = Interval(-100, 100, lower_closed=False)
>>> r8 = Interval.greater_than(-100)
>>> r9 = Interval.equal_to(-100)
>>> r10 = Interval(-100, 100, upper_closed=False)
>>> r11 = Interval.between(-100, 100)
>>> r12 = Interval.greater_than_or_equal_to(-100)
>>> r13 = Interval.greater_than(100)
>>> r14 = Interval.equal_to(100)
>>> r15 = Interval.greater_than_or_equal_to(100)
>>> r1.adjacent_to(r6)
False
>>> r6.adjacent_to(r11)
False
>>> r7.adjacent_to(r9)
True
>>> r3.adjacent_to(r10)
False
>>> r5.adjacent_to(r14)
False
>>> r6.adjacent_to(r15)
True
>>> r1.adjacent_to(r8)
False
>>> r12.adjacent_to(r14)
False
>>> r6.adjacent_to(r13)
False
>>> r2.adjacent_to(r15)
False
>>> r1.adjacent_to(r4)
False
"""
if self.comes_before(other):
if self.upper_bound == other.lower_bound:
result = self.upper_closed != other.lower_closed
else:
result = False
elif self == other:
result = False
else:
result = other.adjacent_to(self)
return result
def __eq__(self, other):
"""Test if an interval is equivalent to the object
>>> Interval.all() == Interval.none()
False
>>> Interval.equal_to(4) == Interval(4, 4)
True
>>> Interval(2, 2, closed=False) == Interval(0, 0, closed=False)
True
"""
return (
self.lower_bound == self.upper_bound
and (not self.lower_closed or not self.upper_closed)
and other.lower_bound == other.upper_bound
and (not other.lower_closed or not other.upper_closed)
) or (
self.lower_bound == other.lower_bound
and self.upper_bound == other.upper_bound
and self.lower_closed == other.lower_closed
and self.upper_closed == other.upper_closed
)
[docs] def duration(self):
"""
@note: added 20140618 kkappler
returns the duration of interval
"""
duration = self.upper_bound - self.lower_bound
if isinstance(self.upper_bound, datetime.datetime):
duration = duration.total_seconds()
return duration
[docs] def pad(self, pad_width):
"""
@note: added 20140618 kkappler
returns a padded interval;
Intent was to add a little so that open-intervals, or adjacent
intervals would easily make an interval set
"""
if isinstance(self.upper_bound, datetime.datetime):
pad = datetime.timedelta(seconds=pad_width)
else:
pass
IV = Interval(self.lower_bound - pad, self.upper_bound + pad)
return IV
[docs]class BaseIntervalSet(object):
"Base class for IntervalSet and FrozenIntervalSet."
def __init__(self, items=[]):
"""Initializes a BaseIntervalSet
This function initializes an IntervalSet. It takes an iterable
object, such as a set, list, or generator. The elements returned
by the iterator are interpreted as intervals for Interval objects
and discrete values for all other values.
If no parameters are provided, then an empty IntervalSet is
constructed.
>>> print IntervalSet() # An empty set
<Empty>
Interval objects arguments are added directly to the IntervalSet.
>>> print IntervalSet([Interval(4, 6, lower_closed=False)])
(4..6]
>>> print IntervalSet([Interval.less_than_or_equal_to(2)])
(...2]
Each non-Interval value of an iterator is added as a discrete
value.
>>> print IntervalSet(set([3, 7, 2, 1]))
1,2,3,7
>>> print IntervalSet(["Bob", "Fred", "Mary"])
'Bob','Fred','Mary'
>>> print IntervalSet(range(10))
0,1,2,3,4,5,6,7,8,9
>>> print IntervalSet(
... Interval.between(l, u) for l, u in [(10, 20), (30, 40)])
[10..20],[30..40]
"""
self.intervals = []
for i in items:
self._add(i)
self.intervals.sort()
def __len__(self):
"""Returns the number of intervals contained in the object
>>> len(IntervalSet.empty())
0
>>> len(IntervalSet.all())
1
>>> len(IntervalSet([2, 6, 34]))
3
>>> len(IntervalSet.greater_than(0))
1
>>> nonempty = IntervalSet([3])
>>> if IntervalSet.empty():
... print "Non-empty"
>>> if nonempty:
... print "Non-empty"
Non-empty
"""
return len(self.intervals)
def __str__(self):
"""Returns a string representation of the object
This function shows a string representation of an IntervalSet.
The string is shown sorted, with all intervals normalized.
>>> print IntervalSet()
<Empty>
>>> print IntervalSet([62])
62
>>> print IntervalSet([62, 56])
56,62
>>> print IntervalSet([23, Interval(26, 32, upper_closed=False)])
23,[26..32)
>>> print IntervalSet.less_than(3) + IntervalSet.greater_than(3)
(...3),(3...)
>>> print IntervalSet([Interval.less_than_or_equal_to(6)])
(...6]
"""
if len(self.intervals) == 0:
rangeStr = "<Empty>"
else:
def sortFn(x, y):
if x.comes_before(y):
retval = -1
elif y.comes_before(x):
retval = 1
else:
retval = 0
return retval
rangeStr = ",".join([str(r) for r in self.intervals])
return rangeStr
def __getitem__(self, index):
"""Gets the interval at the given index
Unlike sets, which do not have ordering, BaseIntervalSets do. Therefore,
indexing was implemented. Intervals are stored in order, starting with
that with the left-most lower bound to that with the right-most.
>>> IntervalSet()[0]
Traceback (most recent call last):
...
IndexError: Index is out of range
>>> interval = IntervalSet.greater_than(5)
>>> print interval[0]
(5...)
>>> print interval[1]
Traceback (most recent call last):
...
IndexError: Index is out of range
>>> print interval[-1]
(5...)
>>> interval = IntervalSet([3, 6])
>>> print interval[1]
6
>>> print interval[0]
3
>>> print interval[2]
Traceback (most recent call last):
...
IndexError: Index is out of range
"""
try:
return self.intervals[index]
except IndexError:
raise IndexError("Index is out of range")
[docs] def lower_bound(self):
"""Returns the lower boundary of the BaseIntervalSet
>>> IntervalSet([Interval.between(4, 6), 2, 12]).lower_bound()
2
>>> IntervalSet().lower_bound()
Traceback (most recent call last):
...
IndexError: The BaseIntervalSet is empty
>>> IntervalSet.all().lower_bound()
-Inf
"""
if len(self.intervals) > 0:
return self.intervals[0].lower_bound
else:
raise IndexError("The BaseIntervalSet is empty")
[docs] def upper_bound(self):
"""Returns the upper boundary of the BaseIntervalSet
>>> IntervalSet([Interval.between(4, 6), 2, 12]).upper_bound()
12
>>> IntervalSet().upper_bound()
Traceback (most recent call last):
...
IndexError: The BaseIntervalSet is empty
>>> IntervalSet.all().upper_bound()
Inf
"""
if len(self.intervals) > 0:
return self.intervals[-1].upper_bound
else:
raise IndexError("The BaseIntervalSet is empty")
[docs] def lower_closed(self):
"""Returns a boolean telling whether the lower bound is closed or not
>>> IntervalSet([Interval.between(4, 6), 2, 12]).lower_closed()
True
>>> IntervalSet().lower_closed()
Traceback (most recent call last):
...
IndexError: The BaseIntervalSet is empty
>>> IntervalSet.all().lower_closed()
False
"""
if len(self.intervals) > 0:
return self.intervals[0].lower_closed
else:
raise IndexError("The BaseIntervalSet is empty")
[docs] def upper_closed(self):
"""Returns a boolean telling whether the upper bound is closed or not
>>> IntervalSet([Interval.between(4, 6), 2, 12]).upper_closed()
True
>>> IntervalSet().upper_closed()
Traceback (most recent call last):
...
IndexError: The BaseIntervalSet is empty
>>> IntervalSet.all().upper_closed()
False
"""
if len(self.intervals) > 0:
return self.intervals[0].upper_closed
else:
raise IndexError("The BaseIntervalSet is empty")
[docs] def bounds(self):
"""Returns an interval that encompasses the entire BaseIntervalSet
>>> print IntervalSet([Interval.between(4, 6), 2, 12]).bounds()
[2..12]
>>> print IntervalSet().bounds()
<Empty>
>>> print IntervalSet.all().bounds()
(...)
"""
if len(self.intervals) == 0:
result = Interval.none()
else:
result = Interval(
self.lower_bound(),
self.upper_bound(),
lower_closed=self.lower_closed(),
upper_closed=self.upper_closed(),
)
return result
[docs] def issubset(self, other):
"""Tells if the given object is a subset of the object
Returns true if self is a subset of other. other can be any
iterable object.
>>> zero = IntervalSet([0])
>>> positives = IntervalSet.greater_than(0)
>>> naturals = IntervalSet.greater_than_or_equal_to(0)
>>> negatives = IntervalSet.less_than(0)
>>> r = IntervalSet.between(3, 6)
>>> r2 = IntervalSet.between(-8, -2)
>>> zero.issubset(positives)
False
>>> zero.issubset(naturals)
True
>>> positives.issubset(zero)
False
>>> r.issubset(zero)
False
>>> r.issubset(positives)
True
>>> positives.issubset(r)
False
>>> negatives.issubset(IntervalSet.all())
True
>>> r2.issubset(negatives)
True
>>> negatives.issubset(positives)
False
>>> zero.issubset([0, 1, 2, 3])
True
"""
if isinstance(other, BaseIntervalSet):
operand = other
else:
operand = self.__class__(other)
return self <= operand
[docs] def issuperset(self, other):
"""Tells whether the given object is a superset of the object
Returns true if self is a superset of other. other can be any
iterable object.
>>> zero = IntervalSet([0])
>>> positives = IntervalSet.greater_than(0)
>>> naturals = IntervalSet.greater_than_or_equal_to(0)
>>> negatives = IntervalSet.less_than(0)
>>> r = IntervalSet.between(3, 6)
>>> r2 = IntervalSet.between(-8, -2)
>>> zero.issuperset(positives)
False
>>> zero.issuperset(naturals)
False
>>> positives.issuperset(zero)
False
>>> r.issuperset(zero)
False
>>> r.issuperset(positives)
False
>>> positives.issuperset(r)
True
>>> negatives.issuperset(IntervalSet.all())
False
>>> r2.issuperset(negatives)
False
>>> negatives.issuperset(positives)
False
>>> negatives.issuperset([-2, -632])
True
"""
if isinstance(other, BaseIntervalSet):
operand = other
else:
operand = self.__class__(other)
return self >= operand
def __contains__(self, obj):
"""Tells whether the BaseIntervalSet contains the given value
Returns True if obj is contained in self. obj can be either a
discrete value, a sequence, or an Interval.
>>> some = IntervalSet([
... 2, 8, Interval(12, 17, upper_closed=False),
... Interval.greater_than(17)])
>>> all = IntervalSet.all()
>>> empty = IntervalSet.empty()
>>> 17 in empty
False
>>> 17 in all
True
>>> 17 in some
False
>>> r = Interval(100, 400, upper_closed=False)
>>> r in empty
False
>>> r in all
True
>>> r in some
True
"""
result = False
for r in self.intervals:
if obj in r:
result = True
break
return result
# def __iter__(self):
# """Returns an iterator to iterate through the intervals
#
# Unlike sets, which do not have ordering, BaseIntervalSets do. Therefore,
# iterating was implemented. Intervals are stored in order, starting with
# that with the left-most lower bound to that with the right-most.
#
# >>> for i in IntervalSet():
# ... print i
# ...
# >>> for i in IntervalSet.between(3, 5):
# ... print i
# ...
# [3..5]
# >>> for i in IntervalSet([2, 5, 3]):
# ... print i
# ...
# 2
# 3
# 5
# """
# return self.intervals.__iter__()
def __iter__(self):
"""Returns an iterator over the intervals in the set
>>> s = IntervalSet(
... [2, 7, 2, 87, 4, 3, Interval.greater_than(12),
... Interval.less_than(-2)])
>>> l = set()
>>> for i in s:
... l.add(str(i))
...
>>> print len(l)
6
>>> "2" in l
True
>>> "7" in l
True
>>> "87" in l
False
>>> "4" in l
True
>>> "3" in l
True
>>> "(12...)" in l
True
>>> "(...-2)" in l
True
Though an IntervalSet contains only Interval objects, we pretend
that they contain discrete objects as well.
>>> s = IntervalSet([2])
>>> for i in s:
... i == 2
...
True
"""
for i in self.intervals:
# Return point Intervals as the values they abstract
if i.lower_bound == i.upper_bound:
yield i.lower_bound
else:
yield i
def __add__(self, other):
"""Returns the union of two IntervalSets
>>> empty = IntervalSet()
>>> negatives = IntervalSet.less_than(0)
>>> positives = IntervalSet.greater_than(0)
>>> naturals = IntervalSet.greater_than_or_equal_to(0)
>>> evens = IntervalSet([-8, -6, -4, -2, 0, 2, 4, 6, 8])
>>> zero = IntervalSet([0])
>>> nonzero = IntervalSet.not_equal_to(0)
>>> empty = IntervalSet.empty()
>>> print evens + positives
-8,-6,-4,-2,[0...)
>>> print negatives + zero
(...0]
>>> print empty + negatives
(...0)
>>> print empty + naturals
[0...)
>>> print nonzero + evens
(...)
"""
return self.__or__(other)
def __sub__(self, other):
"""Subtracts intervals in the given object from the object and returns
the result
>>> negatives = IntervalSet.less_than(0)
>>> positives = IntervalSet.greater_than(0)
>>> naturals = IntervalSet.greater_than_or_equal_to(0)
>>> evens = IntervalSet([-8, -6, -4, -2, 0, 2, 4, 6, 8])
>>> zero = IntervalSet([0])
>>> nonzero = IntervalSet.not_equal_to(0)
>>> empty = IntervalSet.empty()
>>> all = IntervalSet.all()
>>> print evens - nonzero
0
>>> print empty - naturals
<Empty>
>>> print zero - naturals
<Empty>
>>> print positives - zero
(0...)
>>> print naturals - negatives
[0...)
>>> print all - zero
(...0),(0...)
>>> all - zero == nonzero
True
>>> naturals - [0]
Traceback (most recent call last):
...
TypeError: unsupported operand type(s) for -: expected BaseIntervalSet
"""
if isinstance(other, BaseIntervalSet):
result = IntervalSet(self)
for j in other.intervals:
temp = IntervalSet()
for i in result.intervals:
if i.overlaps(j):
if i in j:
pass
elif j in i:
if j.lower_bound is not None:
temp.add(
Interval(
i.lower_bound,
j.lower_bound,
lower_closed=i.lower_closed,
upper_closed=not j.lower_closed,
)
)
if j.upper_bound is not None:
temp.add(
Interval(
j.upper_bound,
i.upper_bound,
lower_closed=not j.upper_closed,
upper_closed=i.upper_closed,
)
)
elif j.comes_before(i):
temp.add(
Interval(
j.upper_bound,
i.upper_bound,
lower_closed=not j.upper_closed,
upper_closed=i.upper_closed,
)
)
else:
temp.add(
Interval(
i.lower_bound,
j.lower_bound,
lower_closed=i.lower_closed,
upper_closed=not j.lower_closed,
)
)
else:
temp.add(copy.deepcopy(i))
result = temp
else:
raise TypeError(
"unsupported operand type(s) for -: expected BaseIntervalSet"
)
return self.__class__(result)
[docs] def difference(self, other):
"""Returns the difference between the object and the given object
Returns all values of self minus all matching values in other. It
is identical to the - operator, only it accepts any iterable as
the operand.
>>> negatives = IntervalSet.less_than(0)
>>> positives = IntervalSet.greater_than(0)
>>> naturals = IntervalSet.greater_than_or_equal_to(0)
>>> evens = IntervalSet([-8, -6, -4, -2, 0, 2, 4, 6, 8])
>>> zero = IntervalSet([0])
>>> nonzero = IntervalSet.not_equal_to(0)
>>> empty = IntervalSet.empty()
>>> all = IntervalSet.all()
>>> print evens.difference(nonzero)
0
>>> print empty.difference(naturals)
<Empty>
>>> print zero.difference(naturals)
<Empty>
>>> print positives.difference(zero)
(0...)
>>> print naturals.difference(negatives)
[0...)
>>> print all.difference(zero)
(...0),(0...)
>>> all.difference(zero) == nonzero
True
>>> naturals.difference([0]) == positives
True
"""
if isinstance(other, BaseIntervalSet):
operand = other
else:
operand = self.__class__(other)
return self - operand
def __and__(self, other):
"""Returns the intersection of self and other.
>>> negatives = IntervalSet.less_than(0)
>>> positives = IntervalSet.greater_than(0)
>>> naturals = IntervalSet.greater_than_or_equal_to(0)
>>> evens = IntervalSet([-8, -6, -4, -2, 0, 2, 4, 6, 8])
>>> zero = IntervalSet([0])
>>> nonzero = IntervalSet.not_equal_to(0)
>>> empty = IntervalSet.empty()
>>> print naturals and naturals
[0...)
>>> print evens & zero
0
>>> print negatives & zero
<Empty>
>>> print nonzero & positives
(0...)
>>> print empty & zero
<Empty>
>>> positives & [0]
Traceback (most recent call last):
...
TypeError: unsupported operand type(s) for &: expected BaseIntervalSet
"""
if isinstance(other, BaseIntervalSet):
result = IntervalSet()
for j in other.intervals:
for i in self.intervals:
if i.overlaps(j):
if i in j:
result.add(copy.deepcopy(i))
elif j in i:
result.add(copy.deepcopy(j))
elif j.comes_before(i):
result.add(
Interval(
i.lower_bound,
j.upper_bound,
lower_closed=i.lower_closed,
upper_closed=j.upper_closed,
)
)
else:
result.add(
Interval(
j.lower_bound,
i.upper_bound,
lower_closed=j.lower_closed,
upper_closed=i.upper_closed,
)
)
# Convert IntervalSet to correct type
result = self.__class__(result)
else:
raise TypeError(
"unsupported operand type(s) for &: expected BaseIntervalSet"
)
return result
[docs] def intersection(self, other):
"""Returns the intersection between the object and the given value
This function returns the intersection of self and other. It is
identical to the & operator, except this function accepts any
iterable as an operand, and & accepts only another
BaseIntervalSet.
>>> negatives = IntervalSet.less_than(0)
>>> positives = IntervalSet.greater_than(0)
>>> naturals = IntervalSet.greater_than_or_equal_to(0)
>>> evens = IntervalSet([-8, -6, -4, -2, 0, 2, 4, 6, 8])
>>> zero = IntervalSet([0])
>>> nonzero = IntervalSet.not_equal_to(0)
>>> empty = IntervalSet.empty()
>>> print naturals.intersection(naturals)
[0...)
>>> print evens.intersection(zero)
0
>>> print negatives.intersection(zero)
<Empty>
>>> print nonzero.intersection(positives)
(0...)
>>> print empty.intersection(zero)
<Empty>
"""
if isinstance(other, BaseIntervalSet):
operand = other
else:
operand = self.__class__(other)
return self & operand
def __or__(self, other):
"""Returns the union of two IntervalSets.
>>> negatives = IntervalSet.less_than(0)
>>> positives = IntervalSet.greater_than(0)
>>> naturals = IntervalSet.greater_than_or_equal_to(0)
>>> evens = IntervalSet([-8, -6, -4, -2, 0, 2, 4, 6, 8])
>>> zero = IntervalSet([0])
>>> nonzero = IntervalSet.not_equal_to(0)
>>> empty = IntervalSet.empty()
>>> all = IntervalSet.all()
>>> print evens | positives
-8,-6,-4,-2,[0...)
>>> print negatives | zero
(...0]
>>> print empty | negatives
(...0)
>>> print empty | naturals
[0...)
>>> print nonzero | evens
(...)
>>> print negatives | range(5)
Traceback (most recent call last):
...
TypeError: unsupported operand type(s) for |: expected BaseIntervalSet
"""
if isinstance(other, BaseIntervalSet):
union = IntervalSet(self)
for r in other.intervals:
union.add(r)
else:
raise TypeError(
"unsupported operand type(s) for |: expected BaseIntervalSet"
)
return self.__class__(union)
[docs] def union(self, other):
"""Returns the union of the given value with the object
This function returns the union of a BaseIntervalSet and an
iterable object. It is identical to the | operator, except that
| only accepts a BaseIntervalSet operand and union accepts any
iterable.
>>> negatives = IntervalSet.less_than(0)
>>> positives = IntervalSet.greater_than(0)
>>> naturals = IntervalSet.greater_than_or_equal_to(0)
>>> evens = IntervalSet([-8, -6, -4, -2, 0, 2, 4, 6, 8])
>>> zero = IntervalSet([0])
>>> nonzero = IntervalSet.not_equal_to(0)
>>> empty = IntervalSet.empty()
>>> all = IntervalSet.all()
>>> print evens.union(positives)
-8,-6,-4,-2,[0...)
>>> print negatives.union(zero)
(...0]
>>> print empty.union(negatives)
(...0)
>>> print empty.union(naturals)
[0...)
>>> print nonzero.union(evens)
(...)
>>> print negatives.union(range(5))
(...0],1,2,3,4
"""
if isinstance(other, BaseIntervalSet):
operand = other
else:
operand = self.__class__(other)
return self | operand
def __xor__(self, other):
"""Returns the exclusive or of two IntervalSets.
>>> negatives = IntervalSet.less_than(0)
>>> positives = IntervalSet.greater_than(0)
>>> naturals = IntervalSet.greater_than_or_equal_to(0)
>>> evens = IntervalSet([-8, -6, -4, -2, 0, 2, 4, 6, 8])
>>> zero = IntervalSet([0])
>>> nonzero = IntervalSet.not_equal_to(0)
>>> empty = IntervalSet.empty()
>>> print nonzero ^ naturals
(...0]
>>> print zero ^ negatives
(...0]
>>> print positives ^ empty
(0...)
>>> print evens ^ zero
-8,-6,-4,-2,2,4,6,8
>>> negatives ^ [0]
Traceback (most recent call last):
...
TypeError: unsupported operand type(s) for ^: expected BaseIntervalSet
"""
if isinstance(other, BaseIntervalSet):
return (self | other) - (self & other)
else:
raise TypeError(
"unsupported operand type(s) for ^: expected BaseIntervalSet"
)
[docs] def symmetric_difference(self, other):
"""Returns the exclusive or of the given value with the object
This function returns the exclusive or of two IntervalSets.
It is identical to the ^ operator, except it accepts any iterable
object for the operand.
>>> negatives = IntervalSet.less_than(0)
>>> positives = IntervalSet.greater_than(0)
>>> naturals = IntervalSet.greater_than_or_equal_to(0)
>>> evens = IntervalSet([-8, -6, -4, -2, 0, 2, 4, 6, 8])
>>> zero = IntervalSet([0])
>>> nonzero = IntervalSet.not_equal_to(0)
>>> empty = IntervalSet.empty()
>>> print nonzero.symmetric_difference(naturals)
(...0]
>>> print zero.symmetric_difference(negatives)
(...0]
>>> print positives.symmetric_difference(empty)
(0...)
>>> print evens.symmetric_difference(zero)
-8,-6,-4,-2,2,4,6,8
>>> print evens.symmetric_difference(range(0, 9, 2))
-8,-6,-4,-2
"""
if isinstance(other, BaseIntervalSet):
operand = other
else:
operand = self.__class__(other)
return self ^ operand
def __invert__(self):
"""Returns the disjoint set of self
>>> negatives = IntervalSet.less_than(0)
>>> positives = IntervalSet.greater_than(0)
>>> naturals = IntervalSet.greater_than_or_equal_to(0)
>>> evens = IntervalSet([-8, -6, -4, -2, 0, 2, 4, 6, 8])
>>> zero = IntervalSet([0])
>>> nonzero = IntervalSet.not_equal_to(0)
>>> print ~(IntervalSet.empty())
(...)
>>> ~negatives == naturals
True
>>> print ~positives
(...0]
>>> ~naturals == negatives
True
>>> print ~evens
(...-8),(-8..-6),(-6..-4),(-4..-2),(-2..0),(0..2),(2..4),(4..6),(6..8),(8...)
>>> ~zero == nonzero
True
>>> ~nonzero == zero
True
"""
return self.__class__.all() - self
def __cmp__(self, other):
"""Compares two BaseIntervalSets
Like set, raises a TypeError when invoked.
>>> IntervalSet().__cmp__(IntervalSet())
Traceback (most recent call last):
...
TypeError: cannot compare BaseIntervalSets using cmp()
"""
raise TypeError("cannot compare BaseIntervalSets using cmp()")
def __eq__(self, other):
"""Tests if two BaseIntervalSets are equivalent
Two IntervalSets are identical if they contain the exact same
sets.
>>> IntervalSet([4]) == IntervalSet([1])
False
>>> IntervalSet([5]) == IntervalSet([5])
True
>>> s1 = IntervalSet.between(4, 7)
>>> s2 = IntervalSet([Interval(4, 7, upper_closed=False)])
>>> s1 == s2
False
>>> s2.add(7)
>>> s1 == s2
True
>>> s1.clear()
>>> s1 == IntervalSet.empty()
True
An IntervalSet, when compared to a non-BaseIntervalSet, yields
False
>>> s1 == [0, 2, 7, 4]
False
>>> IntervalSet([3, 4, 5]) == set([3, 4, 5])
False
>>> IntervalSet([3, 4, 5]) == [3, 4, 5, 3]
False
>>> IntervalSet([3]) == 3
False
"""
if isinstance(other, BaseIntervalSet):
# If len(other) != len(operand), then that means extra objects were
# discarded from other. Thus it can't be equal to any sort of set.
result = self.issubset(other) and other.issubset(self)
else:
result = False
return result
def __ne__(self, other):
"""Tests if two BaseIntervalSets are not equivalent
Two IntervalSets are not identical if they contain different
values or Intervals.
>>> IntervalSet([4]) != IntervalSet([1])
True
>>> IntervalSet([5]) != IntervalSet([5])
False
>>> s1 = IntervalSet.between(4, 7)
>>> s2 = IntervalSet([Interval(4, 7, upper_closed=False)])
>>> s1 != s2
True
>>> s2.add(7)
>>> s1 != s2
False
>>> s1.clear()
>>> s1 != IntervalSet.empty()
False
An IntervalSet can also be compared to any other value. The result
is always True.
>>> s1 != [0, 2, 7, 4]
True
>>> IntervalSet([3, 4, 5]) != set([3, 4, 5])
True
>>> IntervalSet([3, 4, 5]) != [3, 4, 5, 3]
True
"""
return not (self == other)
def __lt__(self, other):
"""Tests if the given operand is a subset of the object
To test if a set is a subset that's not equal to another, you can
use the < operator. I don't like this, personally, but in my
attempt to implement a set-like object, I've duplicated this
functionality.
>>> zero = IntervalSet([0])
>>> positives = IntervalSet.greater_than(0)
>>> naturals = IntervalSet.greater_than_or_equal_to(0)
>>> negatives = IntervalSet.less_than(0)
>>> r = IntervalSet.between(3, 6)
>>> r2 = IntervalSet.between(-8, -2)
>>> zero < positives
False
>>> zero < naturals
True
>>> positives < zero
False
>>> r < zero
False
>>> r < positives
True
>>> positives < r
False
>>> negatives < IntervalSet.all()
True
>>> r2 < negatives
True
>>> negatives < positives
False
>>> zero < [0, 2, 6, 7]
Traceback (most recent call last):
...
TypeError: unsupported operand type(s) for <: expected BaseIntervalSet
>>> positives < positives
False
"""
if isinstance(other, BaseIntervalSet):
return self <= other and not self == other
else:
raise TypeError(
"unsupported operand type(s) for <: expected BaseIntervalSet"
)
def __le__(self, other):
"""Tests if the given operand is a subset or is equal to the object
To test if a set is a subset of another, you can use the <=
operator. I don't like this, personally, but in my attempt
to implement a set-like object, I've duplicated this
functionality.
>>> zero = IntervalSet([0])
>>> positives = IntervalSet.greater_than(0)
>>> naturals = IntervalSet.greater_than_or_equal_to(0)
>>> negatives = IntervalSet.less_than(0)
>>> r = IntervalSet.between(3, 6)
>>> r2 = IntervalSet.between(-8, -2)
>>> zero <= positives
False
>>> zero <= naturals
True
>>> positives <= zero
False
>>> r <= zero
False
>>> r <= positives
True
>>> positives <= r
False
>>> negatives <= IntervalSet.all()
True
>>> r2 <= negatives
True
>>> negatives <= positives
False
>>> zero <= [0, 2, 6, 7]
Traceback (most recent call last):
...
TypeError: unsupported operand type(s) for <=: expected BaseIntervalSet
>>> positives <= positives
True
"""
if isinstance(other, BaseIntervalSet):
result = True
for i in self.intervals:
if i not in other:
result = False
break
else:
raise TypeError(
"unsupported operand type(s) for <=: expected BaseIntervalSet"
)
return result
def __ge__(self, other):
"""Tests if the given operand is a superset or is equal to the object
To test if a set is a superset of another, you can use the >=
operator. I don't like this, personally, but in my attempt
to implement a set-like object, I've duplicated this
functionality.
>>> zero = IntervalSet([0])
>>> positives = IntervalSet.greater_than(0)
>>> naturals = IntervalSet.greater_than_or_equal_to(0)
>>> negatives = IntervalSet.less_than(0)
>>> r = IntervalSet.between(3, 6)
>>> r2 = IntervalSet.between(-8, -2)
>>> zero >= positives
False
>>> zero >= naturals
False
>>> positives >= zero
False
>>> r >= zero
False
>>> r >= positives
False
>>> positives >= r
True
>>> negatives >= IntervalSet.all()
False
>>> r2 >= negatives
False
>>> negatives >= positives
False
>>> negatives >= [-2, -63]
Traceback (most recent call last):
...
TypeError: unsupported operand type(s) for >=: expected BaseIntervalSet
"""
if isinstance(other, BaseIntervalSet):
result = True
for i in other.intervals:
if i not in self:
result = False
break
else:
raise TypeError(
"unsupported operand type(s) for >=: expected BaseIntervalSet"
)
return result
def __gt__(self, other):
"""Tests if the given operand is a superset of the object
To test if a set is a superset of another, but not equal to it,
you can use the > operator. I don't like this, personally, but in
my attempt to implement a set-like object, I've duplicated this
functionality.
>>> zero = IntervalSet([0])
>>> positives = IntervalSet.greater_than(0)
>>> naturals = IntervalSet.greater_than_or_equal_to(0)
>>> negatives = IntervalSet.less_than(0)
>>> r = IntervalSet.between(3, 6)
>>> r2 = IntervalSet.between(-8, -2)
>>> zero > positives
False
>>> zero > naturals
False
>>> positives > zero
False
>>> r > zero
False
>>> r > positives
False
>>> positives > r
True
>>> negatives > IntervalSet.all()
False
>>> r2 > negatives
False
>>> negatives > positives
False
>>> positives > positives
False
>>> negatives > [-2, -63]
Traceback (most recent call last):
...
TypeError: unsupported operand type(s) for >: expected BaseIntervalSet
"""
if isinstance(other, BaseIntervalSet):
return self >= other and not self == other
else:
raise TypeError(
"unsupported operand type(s) for >: expected BaseIntervalSet"
)
def _add(self, obj):
"Appends an Interval or BaseIntervalSet to the object"
if isinstance(obj, Interval):
r = obj
else:
r = Interval.equal_to(obj)
if r: # Don't bother appending an empty Interval
# If r continuously joins with any of the other
newIntervals = []
for i in self.intervals:
if i.overlaps(r) or i.adjacent_to(r):
r = r.join(i)
else:
newIntervals.append(i)
newIntervals.append(r)
self.intervals = newIntervals
self.intervals.sort()
[docs] def copy(self):
"""Returns a copy of the object
>>> s = IntervalSet(
... [7, 2, 3, 2, 6, 2, Interval.greater_than(3)])
>>> s2 = s.copy()
>>> s == s2
True
>>> s = FrozenIntervalSet(
... [7, 2, 3, 2, 6, 2, Interval.greater_than(3)])
>>> s2 = s.copy()
>>> s == s2
True
"""
return copy.copy(self)
[docs] @classmethod
def less_than(cls, n):
"""Returns an IntervalSet containing values less than the given value
>>> print IntervalSet.less_than(0)
(...0)
>>> print IntervalSet.less_than(-23)
(...-23)
"""
return cls([Interval.less_than(n)])
[docs] @classmethod
def less_than_or_equal_to(cls, n, closed=False):
"""Returns an IntervalSet containing values less than or equal to the
given value
>>> print IntervalSet.less_than_or_equal_to(0)
(...0]
>>> print IntervalSet.less_than_or_equal_to(-23)
(...-23]
"""
return cls([Interval.less_than_or_equal_to(n)])
[docs] @classmethod
def greater_than(cls, n):
"""Returns an IntervalSet containing values greater than the given value
>>> print IntervalSet.greater_than(0)
(0...)
>>> print IntervalSet.greater_than(-23)
(-23...)
"""
return cls([Interval.greater_than(n)])
[docs] @classmethod
def greater_than_or_equal_to(cls, n):
"""Returns an IntervalSet containing values greater than or equal to
the given value
>>> print IntervalSet.greater_than_or_equal_to(0)
[0...)
>>> print IntervalSet.greater_than_or_equal_to(-23)
[-23...)
"""
return cls([Interval.greater_than_or_equal_to(n)])
[docs] @classmethod
def not_equal_to(cls, n):
"""Returns an IntervalSet of all values not equal to n
>>> print IntervalSet.not_equal_to(0)
(...0),(0...)
>>> print IntervalSet.not_equal_to(-23)
(...-23),(-23...)
"""
return cls([Interval.less_than(n), Interval.greater_than(n)])
[docs] @classmethod
def between(cls, a, b, closed=True):
"""Returns an IntervalSet of all values between a and b.
If closed is True, then the endpoints are included; otherwise, they
aren't.
>>> print IntervalSet.between(0, 100)
[0..100]
>>> print IntervalSet.between(-1, 1)
[-1..1]
"""
return cls([Interval.between(a, b, closed)])
[docs] @classmethod
def all(cls):
"""Returns an interval set containing all values
>>> print IntervalSet.all()
(...)
"""
return cls([Interval.all()])
[docs] @classmethod
def empty(cls):
"""Returns an interval set containing no values.
>>> print IntervalSet.empty()
<Empty>
"""
return cls()
[docs]class IntervalSet(BaseIntervalSet):
"""The mutable version of BaseIntervalSet
IntervalSet is a class representing sets of continuous values, as
opposed to a discrete set, which is already implemented by the set
type in Python.
IntervalSets can be bounded, unbounded, and non-continuous. They were
designed to accomodate any sort of mathematical set dealing with
continuous values. This will usually mean numbers, but any Python
type that has valid comparison operations can be used in an
IntervalSet.
Because IntervalSets are mutable, it cannot be used as a dictionary
key.
>>> {IntervalSet([3, 66]) : 52}
Traceback (most recent call last):
...
TypeError: unhashable instance
"""
def __init__(self, items=[]):
"Initializes the IntervalSet"
BaseIntervalSet.__init__(self, items)
def __repr__(self):
"""Returns an evaluable representation of the object
>>> IntervalSet([Interval()])
IntervalSet([Interval(-Inf, Inf, lower_closed=False, upper_closed=False)])
>>> IntervalSet()
IntervalSet([])
>>> IntervalSet([2, 4])
IntervalSet([Interval(2, 2, lower_closed=True, upper_closed=True),
Interval(4, 4, lower_closed=True, upper_closed=True)])
"""
return "IntervalSet([%s])" % (", ".join(repr(i) for i in self.intervals),)
def __delitem__(self, index):
"""Removes the interval at the given index from the IntervalSet
>>> interval = IntervalSet()
>>> del interval[0]
Traceback (most recent call last):
...
IndexError: Index is out of range
>>> interval = IntervalSet.between(-12, 2)
>>> del interval[1]
Traceback (most recent call last):
...
IndexError: Index is out of range
>>> len(interval)
1
>>> del interval[0]
>>> len(interval)
0
>>> interval = IntervalSet([2, 7, -2])
>>> len(interval)
3
>>> del interval[1]
>>> len(interval)
2
>>> print interval
-2,7
"""
try:
del self.intervals[index]
except IndexError:
raise IndexError("Index is out of range")
[docs] def add(self, obj):
"""Adds an Interval or discrete value to the object
>>> r = IntervalSet()
>>> r.add(4)
>>> print r
4
>>> r.add(Interval(23, 39, lower_closed=False))
>>> print r
4,(23..39]
>>> r.add(Interval.less_than(25))
>>> print r
(...39]
"""
BaseIntervalSet._add(self, obj)
[docs] def remove(self, obj):
"""Removes a value from the object
This function removes an Interval, discrete value, or set
from an IntervalSet. If the object is not in the set, a KeyError
is raised.
>>> r = IntervalSet.all()
>>> r.remove(4)
>>> print r
(...4),(4...)
>>> r.remove(Interval(23, 39, lower_closed=False))
>>> print r
(...4),(4..23],(39...)
>>> r.remove(Interval.less_than(25))
Traceback (most recent call last):
...
KeyError: '(...25)'
"""
if obj in self:
self.discard(obj)
else:
raise KeyError(str(obj))
[docs] def discard(self, obj):
"""Removes a value from the object
This function removes an Interval or discrete value from an
IntervalSet.
>>> r = IntervalSet.all()
>>> r.discard(4)
>>> print r
(...4),(4...)
>>> r.discard(Interval(23, 39, lower_closed=False))
>>> print r
(...4),(4..23],(39...)
>>> r.discard(Interval.less_than(25))
>>> print r
(39...)
"""
diff = self - IntervalSet([obj])
self.intervals = diff.intervals
[docs] def difference_update(self, other):
"""Removes any elements in the given value from the object
This function removes the elements in other from self. other can
be any iterable object.
>>> r = IntervalSet.all()
>>> r.difference_update([4])
>>> print r
(...4),(4...)
>>> r.difference_update(
... IntervalSet([Interval(23, 39, lower_closed=False)]))
>>> print r
(...4),(4..23],(39...)
>>> r.difference_update(IntervalSet.less_than(25))
>>> print r
(39...)
>>> r2 = IntervalSet.all()
>>> r.difference_update(r2)
>>> print r
<Empty>
"""
diff = self.difference(other)
self.intervals = diff.intervals
[docs] def clear(self):
"""Removes all Intervals from the object
>>> s = IntervalSet([2, 7, Interval.greater_than(8), 2, 6, 34])
>>> print s
2,6,7,(8...)
>>> s.clear()
>>> print s
<Empty>
"""
self.intervals = []
[docs] def update(self, other):
"""Adds elements from the given value to the object
Adds elements from other to self. other can be any iterable
object.
>>> r = IntervalSet()
>>> r.update([4])
>>> print r
4
>>> r.update(IntervalSet([Interval(23, 39, lower_closed=False)]))
>>> print r
4,(23..39]
>>> r.update(IntervalSet.less_than(25))
>>> print r
(...39]
>>> r2 = IntervalSet.all()
>>> r.update(r2)
>>> print r
(...)
"""
union = self.union(other)
self.intervals = union.intervals
[docs] def intersection_update(self, other):
"""Removes values not found in the parameter
Removes elements not found in other. other can be any iterable
object
>>> r = IntervalSet.all()
>>> r.intersection_update([4])
>>> print r
4
>>> r = IntervalSet.all()
>>> r.intersection_update(
... IntervalSet([Interval(23, 39, lower_closed=False)]))
>>> print r
(23..39]
>>> r.intersection_update(IntervalSet.less_than(25))
>>> print r
(23..25)
>>> r2 = IntervalSet.all()
>>> r.intersection_update(r2)
>>> print r
(23..25)
"""
intersection = self.intersection(other)
self.intervals = intersection.intervals
[docs] def symmetric_difference_update(self, other):
"""Updates the object as though doing an xor with the parameter
Removes elements found in other and adds elements in other that
are not in self. other can be any iterable object.
>>> r = IntervalSet.empty()
>>> r.symmetric_difference_update([4])
>>> print r
4
>>> r.symmetric_difference_update(
... IntervalSet([Interval(23, 39, lower_closed=False)]))
>>> print r
4,(23..39]
>>> r.symmetric_difference_update(IntervalSet.less_than(25))
>>> print r
(...4),(4..23],[25..39]
>>> r2 = IntervalSet.all()
>>> r.symmetric_difference_update(r2)
>>> print r
4,(23..25),(39...)
"""
xor = self.symmetric_difference(other)
self.intervals = xor.intervals
[docs] def pop(self):
"""Returns and discards an Interval or value from the IntervalSet
>>> s = IntervalSet([7, Interval.less_than(2), 2, 0])
>>> l = []
>>> l.append(str(s.pop()))
>>> l.append(str(s.pop()))
>>> "(...2)" in l
False
>>> "(...2]" in l
True
>>> "7" in l
True
>>> print s
<Empty>
>>> i = s.pop()
Traceback (most recent call last):
...
KeyError: 'pop from an empty IntervalSet'
"""
if len(self.intervals) > 0:
i = self.intervals.pop()
if i.lower_bound == i.upper_bound:
i = i.lower_bound
else:
raise KeyError("pop from an empty IntervalSet")
return i
def __hash__(self):
"Raises an error since IntervalSets are mutable"
raise TypeError("unhashable instance")
[docs]class FrozenIntervalSet(BaseIntervalSet):
"""An immutable version of BaseIntervalSet
FrozenIntervalSet is like IntervalSet, only add and remove are not
implemented, and hashes can be generated.
>>> fs = FrozenIntervalSet([3, 6, 2, 4])
>>> fs.add(12)
Traceback (most recent call last):
...
AttributeError: 'FrozenIntervalSet' object has no attribute 'add'
>>> fs.remove(4)
Traceback (most recent call last):
...
AttributeError: 'FrozenIntervalSet' object has no attribute 'remove'
>>> fs.clear()
Traceback (most recent call last):
...
AttributeError: 'FrozenIntervalSet' object has no attribute 'clear'
Because FrozenIntervalSets are immutable, they can be used as a
dictionary key.
>>> d = {
... FrozenIntervalSet([3, 66]) : 52,
... FrozenIntervalSet.less_than(3) : 3}
"""
def __new__(cls, items=[]):
"""Constructs a new FrozenInteralSet
Object creation is just like with a regular IntervalSet, except for
the special case where another FrozenIntervalSet is passed as the
initializer iterable. If it is, then the result points to the
same object.
>>> fs1 = FrozenIntervalSet.greater_than(12)
>>> fs2 = FrozenIntervalSet(fs1)
>>> id(fs1) == id(fs2)
True
"""
if (cls == FrozenIntervalSet) and isinstance(items, FrozenIntervalSet):
result = items
else:
s = IntervalSet(items)
result = super(FrozenIntervalSet, cls).__new__(cls, items)
result.intervals = s.intervals
return result
def __init__(self, items=[]):
"Initializes the FrozenIntervalSet"
pass
def __repr__(self):
"""Returns an evaluable representation of the object
>>> FrozenIntervalSet([Interval()])
FrozenIntervalSet([Interval(-Inf, Inf, lower_closed=False, upper_closed=False)])
>>> FrozenIntervalSet()
FrozenIntervalSet([])
>>> FrozenIntervalSet([2, 4])
FrozenIntervalSet([Interval(2, 2, lower_closed=True, upper_closed=True),
Interval(4, 4, lower_closed=True, upper_closed=True)])
"""
return "FrozenIntervalSet([%s])" % (", ".join(repr(i) for i in self.intervals),)
def __hash__(self):
"""Generates a 32-bit hash key
>>> fs = FrozenIntervalSet([4, 7, 3])
>>> key = hash(fs)
"""
h = 0
for i in self.intervals:
h = h ^ hash(i)
return h
[docs] def copy(self):
"""Duplicates the object
For FrozenIntervalSet objects, since they're immutable, a
reference, not a copy, of self is returned.
>>> s = FrozenIntervalSet(
... [7, 2, 3, 2, 6, 2, Interval.greater_than(3)])
>>> s2 = s.copy()
>>> s == s2
True
>>> id(s) == id(s2)
True
"""
if self.__class__ == FrozenIntervalSet:
return self
else:
copy.copy(self)
[docs]class TimePeriod(Interval):
""" """
def __init__(self, **kwargs):
""" """
Interval.__init__(self, **kwargs)
[docs] def duration(self):
""" """
duration = self.upper_bound - self.lower_bound
return duration.total_seconds()
[docs]def generate_interval_list(startTime, endTime, delta):
"""
generic function used for specifying timeintervals to load
probably place in gmi.core.interval
Ideally would support endtime, number of segments or other
"""
interval_list = []
while startTime < endTime:
interval_list.append(
Interval(
lower_bound=startTime,
upper_bound=startTime + delta,
lower_closed=False,
upper_closed=False,
)
)
startTime = startTime + delta
return interval_list
if __name__ == "__main__":
import doctest
doctest.testmod()
[docs]def merge_interval_list(interval_list):
"""
Can think of a stack of unassembled parts. Put the first part in your
left hand, then draw the next part in your right. Check if the pieces
mate, if so, attach and keep in your left hand, draw the next piece,
and so on. Once a piece does not fit, place the assembled piece in
the left hand down and transfer the new 'no-fit' piece from your
right to your left hand and contine ...
KEY: This assumes the interval list is sorted. If the intervals are not sorted
then you need to use set union. This is way faster though.
"""
new_interval_list = []
if len(interval_list) > 0:
left_hand_event = interval_list.pop(0)
else:
return new_interval_list
for i_ivl in range(len(interval_list)):
right_hand_event = interval_list.pop(0)
if left_hand_event.overlaps(right_hand_event):
left_hand_event = left_hand_event.join(right_hand_event)
else:
new_interval_list.append(left_hand_event)
left_hand_event = right_hand_event
new_interval_list.append(left_hand_event)
return new_interval_list