intervals

Python tools for handling intervals (ranges of comparable objects).

Interval initialization

# All integers between 1 and 4
interval = Interval([1, 4])

interval.lower      # 1
interval.upper      # 4

interval.lower_inc  # True
interval.upper_inc  # True

Open, half-open and closed intervals

Intervals can be either open, half-open or closed. Properties lower_inc and upper_inc denote whether or not given endpoint is included (open) or not.

• An open interval is an interval where both endpoints are open.

interval = Interval((1, 4))

interval.open           # True
interval.lower_inc      # False
interval.upper_inc      # False

• Half-open interval has one of the endpoints as open

interval = Interval('[1, 4)')

interval.open           # False
interval.lower_inc      # True
interval.upper_inc      # False

• Closed interval includes both endpoints

interval = Interval([1, 4])

interval.closed         # True
interval.lower_inc      # True
interval.upper_inc      # True

Interval types

Each interval encapsulates a type. Interval is not actually a class. Its a convenient factory that generates AbstractInterval subclasses. Whenever you call Interval() the IntervalFactory tries to guess to best matching interval for given bounds.

from datetime import date


interval = Interval([1, 4])
interval                        # IntInterval('[1, 4]')
interval.type                   # int

interval = Interval([1.5, 4])
interval                        # FloatInterval('[1.5, 4]')
interval.type                   # float

interval = Interval([date(2000, 1, 1), inf])
interval                        # DateInterval('[2000-1-1,)')
interval.type                   # date

You can also create interval subtypes directly (this is also faster than using Interval).

IntInterval([1, 4])

FloatInterval((1.4, 2.7))

Currently provided subtypes are:

• IntInterval
• FloatInterval
• DecimalInterval
• DateInterval
• DateTimeInterval

Properties

• radius gives the half-length of an interval

Interval([1, 4]).radius             # 2.5

• length gives the length of an interval.

Interval([1, 4]).length             # 3

• centre gives the centre (midpoint) of an interval

Interval([-1, 1]).centre            # 0

• Interval [a, b] is degenerate if a == b

Interval([1, 1]).degenerate         # True
Interval([1, 2]).degenerate         # False

Operators

Interval([1, 5]) > Interval([0, 3])     # True

Interval([1, 5]) == Interval([1, 5])    # True

Interval([2, 3]) in Interval([2, 6])    # True

Interval([2, 3]) in Interval([2, 3])    # True

Interval([2, 3]) in Interval((2, 3))    # False

Discrete intervals

Interval([2, 4]) == Interval((1, 5))    # True

Arithmetics

Interval([1, 5]) + Interval([1, 8])     # Interval([2, 13])


# intersection

Interval([2, 6]) & Interval([3, 8])     # Interval([3, 6])