Lazy infinite cached sequences

Infinite sequences for Python

The infseq module implements cached lazy infinite sequences for Python 3.

Here, the word “lazy” means that values of the sequence will never be calculated unless they are really used, and the word “cached” means that every value will be calculated no more than once.

Sequences can contain items of any type — such as numbers, strings or even other sequences.

Using this module is pretty straightforward — everything just works. Here are some usage examples:

Creating sequences

>>> from infseq import InfSequence
>>> InfSequence(5)
<InfSequence: 5 5 5 5 5 5 ...>
>>> InfSequence(5, 6, ...)
<InfSequence: 5 6 7 8 9 10 ...>
>>> InfSequence(lambda index: index * 2 + 1)
<InfSequence: 1 3 5 7 9 11 ...>
>>> InfSequence.geometric_progression(3)
<InfSequence: 1 3 9 27 81 243 ...>
>>> InfSequence.cycle('a', 'b', 'c')
<InfSequence: 'a' 'b' 'c' 'a' 'b' 'c' ...>
>>> InfSequence.fibonacci()
<InfSequence: 0 1 1 2 3 5 ...>

Note: for the ease of debugging the first six values are calculated when repr() is called on the sequence. If you just create the sequence without printing it, the values are not calculated. The number of items can be adjusted by modifying the infseq.REPR_VALUES number (it is set to 6 by default).

Retrieving the values

>>> a = InfSequence.geometric_progression(2)
>>> a
<InfSequence: 1 2 4 8 16 32 ...>
>>> a[10]
1024
>>> a.partial_sum(10)  # a[0] + ... + a[9]
1023
>>> a.partial_sum(4, 10)  # sum(a[i] for i in range(4, 10))
1008
>>> a.partial_product(5)  # a[0] * ... * a[4]
1024

Slicing and prepending elements

>>> a[5:]
<InfSequence: 32 64 128 256 512 1024 ...>
>>> a[::2]
<InfSequence: 1 4 16 64 256 1024 ...>
>>> list(a[5:10])  # a[5:10] returns a map object, because of laziness
[32, 64, 128, 256, 512]
>>> list(a[4::-1])  # reverse slices also work
[16, 8, 4, 2, 1]
>>> (5, 7) + a
<InfSequence: 5 7 1 2 4 8 ...>

Arithmetic operations

>>> b = InfSequence(1, 2, ...)
>>> b
<InfSequence: 1 2 3 4 5 6 ...>
>>> b * 2
<InfSequence: 2 4 6 8 10 12 ...>
>>> b ** 2
<InfSequence: 1 4 9 16 25 36 ...>
>>> a + b
<InfSequence: 2 4 7 12 21 38 ...>

Applying any functions

>>> c = InfSequence.geometric_progression(9)
>>> c
<InfSequence: 1 9 81 729 6561 59049 ...>
>>> import math
>>> c.apply_function(math.sqrt)
<InfSequence: 1.0 3.0 9.0 27.0 81.0 243.0 ...>

Using the accumulate method

The accumulate method returns a sequence of partial sums of the original sequence (similar to itertools.accumulate):

result[0] = a[0]
result[1] = a[0] + a[1]
result[2] = a[0] + a[1] + a[2]
...

If a custom function is passed as an argument, it is used to do the reducing instead of the sum function.

In the examples below we can get the sequence of n(n+1)/2 and the sequence of n! using this method:

>>> from operator import mul
>>> b
<InfSequence: 1 2 3 4 5 6 ...>
>>> b.accumulate()
<InfSequence: 1 3 6 10 15 21 ...>
>>> b.accumulate(mul)
<InfSequence: 1 2 6 24 120 720 ...>

Using the matrix multiplication operator

If you are using Python 3.5+, you can use the new “matrix multiplication” operator that was introduced in that version.

The expression a @ b will produce the following result:

result[0] = a[0] * b[0]
result[1] = a[0] * b[1] + a[1] * b[0]
result[2] = a[0] * b[2] + a[1] * b[1] + a[2] * b[0]
...

Example:

>>> InfSequence(0, 2, ...) @ InfSequence(1)
<InfSequence: 1 4 9 16 25 36 ...>

Installing the module and running the tests

The module is available on PyPI. To install the module, simply use:

pip3 install infseq

The source code is hosted on GitHub.

To run the doctests in this module, use:

python3 -m doctest ./README.rst

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