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.

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