CombinatorialProbability 0.0.3

A POC for a combinatorial probability library using integer partitions as one example

Why?

This library was created to perform operations like iterating or random sampling of combinatorial structures like integer partition, permutations, set partitions etc.

What?

Right now only integer partitions are implemented, minimally. One can randomly sample using several different methods.

Example

from CombinatorialProbability import IntegerPartition
ip = IntegerPartition()
ip.fit(weight=10, make_array=True, make_table=True, make_tilt=True)
ip.sampling(size=10, method='rejection')

Right now sample returns a tuple, the first element is the sample, the second element is the number of iterations before a successful sample was found, by default it is a list of all 1s if a method is not a rejection method.

Other arguments for method are:

• pdcdsh -- Probabilistic divide-and-conquer deterministic second half
• table_only -- The (tabular) recursive method of Nijenhuis--Wilf
• array_only -- The (array) recursive method of Nijenhuis--Wilf
• pdc-recursive -- Probabilistic divide-and-conquer combined with the table method of Nijenhuis--Wilf

Additional parameters for a given method should be in the form of a dictionary method_params = {} also input to the sample() method.

ip.sampling(size=10, method='pdcdsh')
ip.sampling(size=10, method='table_only')
ip.sampling(size=10, method='array_only')
ip.sampling(size=10, method='pdc-recursive', method_params={'rows': 3})