Python module supporting math intervals. Functions as an abstraction and superset of the range function.
Many methods and examples herein are taken from Interval Arithmetic—Wikipedia .
In [1]: # INITIALIZATION
In [2]: interval_1 = Interval.from_string("[0, 5)") # [0.0, 5.0)
In [3]: interval_2 = Interval(3, 6) # [3, 6)
In [4]: # METHODS & PROPERTIES
In [5]: print(interval_1)
Out[5]: [0.0, 5.0)
In [6]: list(interval_1.step(2, start=0))
Out[6]: [0, 2, 4]
In [7]: list(interval_1.step(2, start=-1))
Out[7]: [1, 3]
In [8]: list(interval_1.step(-1, start=5)) # does not include 5 because upper_bound is open
Out[8]: [4, 3, 2, 1, 0]
In [9]: interval_1.interval_type
Out[9]: <IntervalType.HALF_OPEN: 'half-open'>
In [10]: interval_1.width
Out[10]: 5.0
In [11]: 0 in interval_1
Out[11]: True
In [12]: 5 in interval_1
Out[12]: False
In [13]: print(interval_1 + 2)
[2.0, 7.0)
In [14]: print(-interval_1) # note that the closed and opened bounds swap order too
(-5.0, 0.0]
In [15]: print(5 / interval_1)
[1.0, inf)
In [16]: print(interval_1 & interval_2)
[3, 5.0)
>>> print(interval_1 | interval_2)
[0.0, 6)
>>> print((interval_1 + interval_2) / 2)
[1.5, 5.5)
In [1]: interval_3 = Interval.from_string("2 +- 1.2") # 2 plus or minus 1.2
In [2]: print(interval_3)
[0.8, 3.2)
In [3]: print(interval_3.width)
2.4000000000000004
The following (all spaces are removed, so others are also possible) are also equivalent:
Interval.from_string("2 pm 1.2")
Interval.from_string("2 +- 1.2")
Interval.from_string("2 +/- 1.2")
Interval.from_string("2 ± 1.2")
Interval.from_string("2 pm 1.2")
Interval.from_string("2 p/m 1.2")
Interval(0.8, 3.2)Instead of the following examples:
# 1.
for x in range(10):
...
# 2.
[x**2 for x in range(10, 15, 2)]you can now write
# 1.
for x in Interval(10):
...
# 2.
[x**2 for x in Interval(10, 15).step(2)]and you can do a lot more, like floating point values:
In [1]: from math import tau
In [2]: theta = tau / 12
In [3]: print(*(
...: Interval(0, tau)
...: .closed()
...: .step(theta)
...: ), sep=",\n")
0,
0.5235987755982988,
1.0471975511965976,
1.5707963267948966,
2.0943951023931953,
2.617993877991494,
3.141592653589793,
3.665191429188092,
4.1887902047863905,
4.71238898038469,
5.235987755982988,
5.759586531581287,
6.283185307179586
In [1]: weight = Interval.from_string("80 +- 0.5") # accurate to the nearest kg
In [2]: height = Interval.from_string("1.79 +- 0.005") # accurate to the nearest cm
In [3]: bmi = weight / height ** 2
In [4]: print(round(bmi, 3))
[24.673, 25.266)
You can create infinite (unbounded) intervals. I recommend combining this with the itertools modules islice and takewhile, since the outputs tend to be infinite generators.
Any side that is unbounded like this must be closed; doing integers = Interval(-inf, +inf, lower_closure="open") does the same thing as integers = Interval(-inf, +inf, lower_closure="closed").
In [1]: from itertools import islice, takewhile
In [2]: from random import random
In [3]: interval_4 = POSITIVE_REALS + 1
In [4]: n_1mod4 = interval_4.step(4)
In [5]: list(islice(n_1mod4, 10))
Out[5]: [1, 5, 9, 13, 17, 21, 25, 29, 33, 37]
In [6]: list(takewhile(lambda _: random() > 1/4, n_1mod4))
Out[6]: [1, 5, 9, 13]
In [7]: list(takewhile(lambda _: random() > 1/4, n_1mod4))
Out[7]: []
In [8]: list(takewhile(lambda _: random() > 1/4, n_1mod4))
Out[8]: [21, 25]
In [1]: interval_5 = Interval(0, 5)
In [2]: interval_6 = Interval(3, 12)
(Uses random.random—not cryptographically secure.) Generates values random floats within the interval's bounds.
In [3]: rand_uniform(interval_5)
Out[3]: [4.64997216360891]
In [4]: rand_uniform(interval_5, values=5)
Out[4]:
[2.545513603508707,
0.5394888009944876,
3.872705211980179,
0.8273514007287991,
4.209282455847249]
In [5]: lerp(interval_5, 0.3)
Out[5]: 1.5
In [6]: invlerp(interval_5, 1.5)
Out[6]: 0.3
In [7]: remap(interval_5, interval_6, 2.5)
Out[7]: 7.5