infseq 0.1

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.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 ...>

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]
>>> (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 ...>
>>> b.accumulate()  # a[0],  a[0] + a[1],  a[0] + a[1] + a[2], ...
<InfSequence: 1 3 6 10 15 21 ...>

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 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