The package `ivalutils` provides classes for basic interval arithmetics as
well as classes for building sequences of adjacent intervals and for building
mappings of intervals to arbitrary values.
An Interval defines a subset of a set of values by optionally giving a lower
and / or an upper limit.
The base set of values - and therefore the given limits - must have a
common base type which defines a total order on the values.
Creating intervals
==================
The simplest way is calling the class `Interval` without arguments, resulting
in both endpoints to be infinite:
>>> ival = Interval()
>>> ival
Interval()
>>> str(ival)
'(-inf .. +inf)'
For getting a more useful interval, it's neccessary to specify atleast one
endpoint:
>>> ival = Interval(LowerClosedLimit(0))
>>> ival
Interval(lower_limit=Limit(True, 0, True))
>>> str(ival)
'[0 .. +inf)'
>>> ival = Interval(upper_limit=UpperClosedLimit(100.))
>>> ival
Interval(upper_limit=Limit(False, 100.0, True))
>>> str(ival)
'(-inf .. 100.0]'
>>> ival = Interval(LowerClosedLimit(0), UpperOpenLimit(27))
>>> ival
Interval(lower_limit=Limit(True, 0, True), upper_limit=Limit(False, 27, False))
>>> str(ival)
'[0 .. 27)'
Any type which defines a total ordering can be used for the limits:
>>> ClosedInterval('a', 'zzz')
Interval(lower_limit=Limit(True, 'a', True), upper_limit=Limit(False, 'zzz', True))
Several factory functions can be used as shortcut. For example:
>>> LowerClosedInterval(30)
Interval(lower_limit=Limit(True, 30, True))
>>> UpperOpenInterval(0)
Interval(upper_limit=Limit(False, 0, False))
>>> ClosedInterval(1, 3)
Interval(lower_limit=Limit(True, 1, True), upper_limit=Limit(False, 3, True))
>>> ChainableInterval(0, 5)
Interval(lower_limit=Limit(True, 0, True), upper_limit=Limit(False, 5, False))
Operations on intervals
=======================
The limits of an interval can be retrieved via properties:
>>> ival = ClosedInterval(0, 100)
>>> ival.lower_limit
Limit(True, 0, True)
>>> ival.upper_limit
Limit(False, 100, True)
>>> ival.limits
(Limit(True, 0, True), Limit(False, 100, True))
Several methods can be used to test for specifics of an interval. For example:
>>> ival.is_bounded()
True
>>> ival.is_finite()
True
>>> ival.is_left_open()
False
Intervals can be tested for including a value:
>>> 74 in ival
True
>>> -4 in ival
False
Intervals can be compared:
>>> ival2 = LowerOpenInterval(100)
>>> ival3 = LowerClosedInterval(100)
>>> ival < ival2
True
>>> ival < ival3
True
>>> ival2 < ival3
False
>>> ival2 == ival3
False
>>> ival3 < ival2
True
>>> ival2.is_adjacent(ival3)
False
>>> ival3.is_adjacent(ival2)
False
>>> ival4 = UpperClosedInterval(100)
>>> ival4.is_adjacent(ival2)
True
>>> ival.is_overlapping(ival3)
True
>>> ival.is_subset(ival4)
True
Creating sequences of adjacent intervals
========================================
The class `IntervalChain` is used to create sequences of adjacent intervals:
>>> ic = IntervalChain(('a', 'd', 'g', 'z'))
>>> ic
IntervalChain(('a', 'd', 'g', 'z'))
The default is to create an interval sequence which is lower-bound and
upper-infinite and containing lower-closed intervals:
>>> str(ic)
"[['a' .. 'd'), ['d' .. 'g'), ['g' .. 'z'), ['z' .. +inf)]"
By specifying additional parameters, you can determine which endpoints will be
closed and whether a lower and / or upper infinite endpoint will be added:
>>> ic = IntervalChain(('a', 'd', 'g', 'z'), lower_closed = False, add_lower_inf=True, add_upper_inf=False)
>>> str(ic)
"[(-inf .. 'a'], ('a' .. 'd'], ('d' .. 'g'], ('g' .. 'z']]"
Operations on interval chains
=============================
Interval chains can be indexed and iterated like lists ...:
>>> ic[2]
Interval(lower_limit=Limit(True, 'd', False), upper_limit=Limit(False, 'g', True))
>>> [ival.upper_limit.value for ival in ic]
['a', 'd', 'g', 'z']
... and can be searched for the index of the interval holding a specified
value:
>>> ic.map2idx('b')
1
>>> ic.map2idx('a')
0
>>> ic.map2idx('aa')
1
Creating interval mappings
==========================
The class `IntervalMapping` is used to create a mapping from intervals to
arbitrary values.
Instances can be created by giving an IntervalChain and a sequence of
associated values ...:
>>> im1 = IntervalMapping(IntervalChain((0, 300, 500, 1000)), (0., .10, .15, .20))
... or a sequence of limiting values and a sequence of associated values ...:
>>> im2 = IntervalMapping((0, 300, 500, 1000), (0., .10, .15, .20))
... or a sequence of tuples, each holding a limiting value and an associated
value:
>>> im3 = IntervalMapping(((0, 0.), (300, .10), (500, .15), (1000, .20)))
>>> im1 == im2 == im3
True
Operations on IntervalMappings
==============================
Interval mappings behave like ordinary mappings:
>>> list(im3.keys())
[Interval(lower_limit=Limit(True, 0, True), upper_limit=Limit(False, 300, False)),
Interval(lower_limit=Limit(True, 300, True), upper_limit=Limit(False, 500, False)),
Interval(lower_limit=Limit(True, 500, True), upper_limit=Limit(False, 1000, False)),
Interval(lower_limit=Limit(True, 1000, True))]
>>> list(im3.values())
[0.0, 0.1, 0.15, 0.2]
>>> im3[Interval(lower_limit=Limit(True, 300, True), upper_limit=Limit(False, 500, False))]
0.1
In addition they can be looked-up for the value associated with the interval
which contains a given value:
>>> im3.map(583)
0.15
As a short-cut, the interval mapping can be used like a function:
>>> im3(412)
0.1
Use cases for interval mappings are for example:
* determine the discount to be applied depending on an order value,
* rating customers depending on their sales turnover,
* classifying cities based on the number of inhabitants,
* mapping booking dates to accounting periods,
* grouping of measured values in discrete ranges.
For more details see the documentation on GitHub or at http://ivalutils.readthedocs.io.