Metadata-Version: 2.1
Name: python-intervals
Version: 1.3.1
Summary: Interval arithmetic for Python
Home-page: https://github.com/AlexandreDecan/python-intervals
Author: Alexandre Decan
License: LGPL3
Keywords: interval arithmetic range math
Platform: UNKNOWN
Classifier: Development Status :: 5 - Production/Stable
Classifier: Intended Audience :: Developers
Classifier: Intended Audience :: Education
Classifier: Intended Audience :: Information Technology
Classifier: Intended Audience :: Science/Research
Classifier: Topic :: Scientific/Engineering :: Mathematics
Classifier: License :: OSI Approved :: GNU Lesser General Public License v3 (LGPLv3)
Classifier: Programming Language :: Python :: 3 :: Only
Classifier: Programming Language :: Python :: 3.4
Classifier: Programming Language :: Python :: 3.5
Classifier: Programming Language :: Python :: 3.6
Requires-Python: >=3.4
Description-Content-Type: text/markdown

# Interval arithmetic for Python

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[![PyPI](https://badge.fury.io/py/python-intervals.svg)](https://pypi.org/project/python-intervals)


This library provides 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.


## Installation

You can use ``pip`` to install this library:

``pip install python-intervals``

This will install the latest available version from [PyPI](https://pypi.org/project/python-intervals).
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 helpers:

```python
>>> I.open(1, 2)
(1,2)
>>> I.closed(1, 2)
[1,2]
>>> I.openclosed(1, 2)
(1,2]
>>> I.closedopen(1, 2)
[1,2)
>>> I.singleton(1)
[1]
>>> I.empty()
()

```

Intervals created with this library are ``Interval`` instances.
An ``Interval`` object is a disjunction of atomic intervals that represent single intervals (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:
```python
>>> 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.empty() | I.closed(0, 1)
[0,1]
>>> I.closed(1, 2) | I.closed(2, 3) | I.closed(4, 5)
[1,3] | [4,5]

```

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.

```python
>>> 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)

```

The bounds of an interval can be any arbitrary values, as long as they are comparable:

```python
>>> I.closed(1.2, 2.4)
[1.2,2.4]
>>> I.closed('a', 'z')
['a','z']
>>> from datetime import date
>>> I.closed(date(2011, 3, 15), date(2013, 10, 10))
[datetime.date(2011, 3, 15),datetime.date(2013, 10, 10)]

```

Note that discrete intervals are **not** supported, e.g., combining ``[0,1]`` with ``[2,3]`` will **not** result
in ``[0,3]`` even if there is no integer between ``1`` and ``2``.


### Arithmetic operations

Both ``Interval`` and ``AtomicInterval`` support following interval arithmetic operations:

 - ``x.is_empty()`` tests if the interval is empty.
   ```python
   >>> 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.
   ```python
   >>> 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.
   ```python
   >>> 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.
   ```python
   >>> ~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``.
   ```python
   >>> 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.
   ```python
   >>> 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]).
   ```python
   >>> 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.
   ```python
   >>> (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.
   ```python
   >>> 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``).

```python
>> I.CLOSED, I.OPEN
True, False
>>> x = I.closedopen(0, 1).to_atomic()
>>> x.left, x.lower, x.upper, x.right
(True, 0, 1, False)

```


### Comparison operators

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

```python
>>> 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``.

```python
>>> 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``.

```python
>>> 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:

```python
>>> 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.

```python
>>> 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:

```python
>>> (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

This library adheres to a [semantic versioning](https://semver.org) scheme.


**1.3.1** (2018-04-12)

 - Define `__slots__` to lower memory usage, and to speed up attribute access.
 - Define `Interval.__rand__` (and other magic methods) to support `Interval` from `AtomicInterval` instead of
 having a dedicated piece of code in `AtomicInterval`.
 - Fix `__all__`.
 - More tests to cover all comparisons.


**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.


