python-intervals 1.3.0

Python Intervals Arithmetic

Interval arithmetic for Python

Provide interval arithmetic for Python 3.4+.

Features

• Support intervals of any (comparable) objects.
• Closed or open, finite or infinite intervals.
• Atomic intervals and interval sets are supported.
• Automatic simplification of intervals.
• Support iteration, comparison, intersection, union, complement, difference and containment.

Inspired by pyinter.

Installation

You can use pip to install this library:

pip install python-intervals

This will install the latest available version from pypi branch. Prereleases are available from the master branch.

For convenience, the library is contained within a single Python file, and can thus be easily integrated in other projects without the need for an explicit dependency (hint: don't do that!).

Documentation & usage

Interval creation

Assuming this library is imported using import intervals as I, intervals can be easily created using one of the following functions:

• I.open(1, 2) corresponds to (1,2);
• I.closed(1, 2) corresponds to [1,2];
• I.openclosed(1, 2) corresponds to (1,2];
• I.closedopen(1, 2) corresponds to [1,2);
• I.singleton(1) corresponds to [1,1];
• I.empty() corresponds to the empty interval ().

>>> I.closed(0, 3)
[0,3]
>>> I.openclosed('a', 'z')
('a','z']
>>> I.singleton(2.5)
[2.5]
>>> I.empty()
()

Intervals created with this library are Interval instances. An Interval object is a disjunction of atomic intervals that represent a single interval (e.g. [1,2]) corresponding to AtomicInterval instances. Except when atomic intervals are explicitly created or retrieved, only Interval instances are exposed.

For convenience, intervals are automatically simplified:

>>> I.closed(0, 2) | I.closed(2, 4)
[0,4]
>>> I.closed(1, 2) | I.closed(3, 4) | I.closed(2, 3)
[1,4]
>>> I.closed(1, 2) | I.openclosed(2, 3) | I.closedopen(5, 5)
[1,3]

Infinite and semi-infinite intervals are supported using I.inf and -I.inf as upper or lower bounds. These two objects support comparison with any other object. When infinites are used as a lower or upper bound, the corresponding boundary is automatically converted to an open one.

>>> I.inf > 'a', I.inf > 0, I.inf > True
(True, True, True)
>>> I.openclosed(-I.inf, 0)
(-inf,0]
>>> I.closed(-I.inf, I.inf)  # Automatically converted to an open interval
(-inf,+inf)

Arithmetic operations

Both Interval and AtomicInterval support following interval arithmetic operations:

• x.is_empty() tests if the interval is empty.

  >>> I.closed(0, 1).is_empty()
  False
  >>> I.closed(0, 0).is_empty()
  False
  >>> I.openclosed(0, 0).is_empty()
  True
  >>> I.empty().is_empty()
  True
  

• x.intersection(other) or x & other return the intersection of two intervals.

  >>> I.closed(0, 2) & I.closed(1, 3)
  [1,2]
  >>> I.closed(0, 4) & I.open(2, 3)
  (2,3)
  >>> I.closed(0, 2) & I.closed(2, 3)
  [2]
  >>> I.closed(0, 2) & I.closed(3, 4)
  ()
  

• x.union(other) or x | other return the union of two intervals.

  >>> I.closed(0, 1) | I.closed(1, 2)
  [0,2]
  >>> I.closed(0, 1) | I.closed(2, 3)
  [0,1] | [2,3]
  

• x.complement(other) or ~x return the complement of the interval.

  >>> ~I.closed(0, 1)
  (-inf,0) | (1,+inf)
  >>> ~(I.open(-I.inf, 0) | I.open(1, I.inf))
  [0,1]
  >>> ~I.open(-I.inf, I.inf)
  ()
  

• x.difference(other) or x - other return the difference between x and other.

  >>> I.closed(0,2) - I.closed(1,2)
  [0,1)
  >>> I.closed(0, 4) - I.closed(1, 2)
  [0,1) | (2,4]
  

• x.contains(other) or other in x return True if given item is contained in the interval. Support Interval, AtomicInterval and arbitrary comparable values.

  >>> 2 in I.closed(0, 2)
  True
  >>> 2 in I.open(0, 2)
  False
  >> I.open(0, 1) in I.closed(0, 2)
  True
  

• x.overlaps(other) tests if there is an overlap between two intervals. This method accepts a permissive parameter which defaults to False. If True, it considers that [1, 2) and [2, 3] have an overlap on 2 (but not [1, 2) and (2, 3]).

  >>> I.closed(1, 2).overlaps(I.closed(2, 3))
  True
  >>> I.closed(1, 2).overlaps(I.open(2, 3))
  False
  >>> I.closed(1, 2).overlaps(I.open(2, 3), permissive=True)
  True
  

Other methods and attributes

The following methods are only available for Interval instances:

• x.enclosure() returns the smallest interval that includes the current one.

  >>> (I.closed(0, 1) | I.closed(2, 3)).enclosure()
  [0,3]
  

• x.to_atomic() is equivalent to x.enclosure() but returns an AtomicInterval instead of an Interval object.
• x.is_atomic() evaluates to True if interval is composed of a single (possibly empty) atomic interval.

  >>> I.closed(0, 2).is_atomic()
  True
  >>> (I.closed(0, 1) | I.closed(1, 2)).is_atomic()
  True
  >>> (I.closed(0, 1) | I.closed(2, 3)).is_atomic()
  False
  

The left and right boundaries, and the lower and upper bound of an AtomicInterval can be respectively accessed with its left, right, lower and upper attributes. The left and right bounds are either I.CLOSED (True) or I.OPEN (False).

>> I.CLOSED, I.OPEN
True, False
>>> [getattr(I.closedopen(0, 1).to_atomic(), attr) for attr in ['left', 'lower', 'upper', 'right']]
[True, 0, 1, False]

Comparison operators

Equality between intervals can be checked using the classical == operator:

>>> I.closed(0, 2) == I.closed(0, 1) | I.closed(1, 2)
True
>>> I.closed(0, 2) == I.closed(0, 2).to_atomic()
True

Moreover, both Interval and AtomicInterval are comparable using e.g. >, >=, < or <=. The comparison is based on the interval itself, not on its lower or upper bound only. For instance, a < b holds if a is entirely on the left of b and a > b holds if a is entirely on the right of b.

>>> I.closed(0, 1) < I.closed(2, 3)
True
>>> I.closed(0, 1) < I.closed(1, 2)
False

Similarly, a <= b holds if a is entirely on the left of the upper bound of b, and a >= b holds if a is entirely on the right of the lower bound of b.

>>> I.closed(0, 1) <= I.closed(2, 3)
True
>>> I.closed(0, 2) <= I.closed(1, 3)
True
>>> I.closed(0, 3) <= I.closed(1, 2)
False

Note that this semantics differ from classical comparison operators. As a consequence, some intervals are never comparable in the classical sense, as illustrated hereafter:

>>> I.closed(0, 4) <= I.closed(1, 2) or I.closed(0, 4) >= I.closed(1, 2)
False
>>> I.closed(0, 4) < I.closed(1, 2) or I.closed(0, 4) > I.closed(1, 2)
False

Iteration & indexing

Intervals can be iterated to access the underlying AtomicInterval objects, sorted by their lower and upper bounds.

>>> list(I.open(2, 3) | I.closed(0, 1) | I.closed(21, 24))
[[0,1], (2,3), [21,24]]

The AtomicInterval objects of an Interval can also be accessed using their indexes:

>>> (I.open(2, 3) | I.closed(0, 1) | I.closed(21, 24))[0]
[0,1]
>>> (I.open(2, 3) | I.closed(0, 1) | I.closed(21, 24))[-2]
(2,3)

Contributions

Contributions are very welcome! Feel free to report bugs or suggest new features using GitHub issues and/or pull requests.

Licence

Distributed under LGPLv3 - GNU Lesser General Public License, version 3.

Changelog

1.3.0 (2018-04-04)

• Meaningful <= and >= comparisons for intervals.

1.2.0 (2018-04-04)

• Interval supports indexing to retrieve the underlying AtomicInterval objects.

1.1.0 (2018-04-04)

• Both AtomicInterval and Interval are fully comparable.
• Add singleton(x) to create a singleton interval [x].
• Add empty() to create an empty interval.
• Add Interval.enclosure() that returns the smallest interval that includes the current one.
• Interval simplification is in O(n) instead of O(n*m).
• AtomicInterval objects in an Interval are sorted by lower and upper bounds.

1.0.4 (2018-04-03)

• All operations of AtomicInterval (except overlaps) accept Interval.
• Raise TypeError instead of ValueError if type is not supported (coherent with NotImplemented).

1.0.3 (2018-04-03)

• Initial working release on PyPi.

1.0.0 (2018-04-03)

• Initial release.