Source code for networkx.utils.random_sequence

"""
Utilities for generating random numbers, random sequences, and
random selections.
"""

import networkx as nx
from networkx.utils import py_random_state

__all__ = [
"powerlaw_sequence",
"zipf_rv",
"cumulative_distribution",
"discrete_sequence",
"random_weighted_sample",
"weighted_choice",
]

# The same helpers for choosing random sequences from distributions
# uses Python's random module
# https://docs.python.org/3/library/random.html

[docs]@py_random_state(2) def powerlaw_sequence(n, exponent=2.0, seed=None): """ Return sample sequence of length n from a power law distribution. """ return [seed.paretovariate(exponent - 1) for i in range(n)]
[docs]@py_random_state(2) def zipf_rv(alpha, xmin=1, seed=None): r"""Returns a random value chosen from the Zipf distribution. The return value is an integer drawn from the probability distribution .. math:: p(x)=\frac{x^{-\alpha}}{\zeta(\alpha, x_{\min})}, where $\zeta(\alpha, x_{\min})$ is the Hurwitz zeta function. Parameters ---------- alpha : float Exponent value of the distribution xmin : int Minimum value seed : integer, random_state, or None (default) Indicator of random number generation state. See :ref:Randomness<randomness>. Returns ------- x : int Random value from Zipf distribution Raises ------ ValueError: If xmin < 1 or If alpha <= 1 Notes ----- The rejection algorithm generates random values for a the power-law distribution in uniformly bounded expected time dependent on parameters. See _ for details on its operation. Examples -------- >>> nx.utils.zipf_rv(alpha=2, xmin=3, seed=42) 8 References ---------- ..  Luc Devroye, Non-Uniform Random Variate Generation, Springer-Verlag, New York, 1986. """ if xmin < 1: raise ValueError("xmin < 1") if alpha <= 1: raise ValueError("a <= 1.0") a1 = alpha - 1.0 b = 2 ** a1 while True: u = 1.0 - seed.random() # u in (0,1] v = seed.random() # v in [0,1) x = int(xmin * u ** -(1.0 / a1)) t = (1.0 + (1.0 / x)) ** a1 if v * x * (t - 1.0) / (b - 1.0) <= t / b: break return x
[docs]def cumulative_distribution(distribution): """Returns normalized cumulative distribution from discrete distribution.""" cdf = [0.0] psum = float(sum(distribution)) for i in range(0, len(distribution)): cdf.append(cdf[i] + distribution[i] / psum) return cdf
[docs]@py_random_state(3) def discrete_sequence(n, distribution=None, cdistribution=None, seed=None): """ Return sample sequence of length n from a given discrete distribution or discrete cumulative distribution. One of the following must be specified. distribution = histogram of values, will be normalized cdistribution = normalized discrete cumulative distribution """ import bisect if cdistribution is not None: cdf = cdistribution elif distribution is not None: cdf = cumulative_distribution(distribution) else: raise nx.NetworkXError( "discrete_sequence: distribution or cdistribution missing" ) # get a uniform random number inputseq = [seed.random() for i in range(n)] # choose from CDF seq = [bisect.bisect_left(cdf, s) - 1 for s in inputseq] return seq
[docs]@py_random_state(2) def random_weighted_sample(mapping, k, seed=None): """Returns k items without replacement from a weighted sample. The input is a dictionary of items with weights as values. """ if k > len(mapping): raise ValueError("sample larger than population") sample = set() while len(sample) < k: sample.add(weighted_choice(mapping, seed)) return list(sample)
[docs]@py_random_state(1) def weighted_choice(mapping, seed=None): """Returns a single element from a weighted sample. The input is a dictionary of items with weights as values. """ # use roulette method rnd = seed.random() * sum(mapping.values()) for k, w in mapping.items(): rnd -= w if rnd < 0: return k