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"""
Utilities for generating random numbers, random sequences, and
random selections.
"""
# Copyright (C) 2004-2011 by
# Aric Hagberg <hagberg@lanl.gov>
# Dan Schult <dschult@colgate.edu>
# Pieter Swart <swart@lanl.gov>
# All rights reserved.
# BSD license.
import random
import sys
import networkx as nx
__author__ = '\n'.join(['Aric Hagberg (hagberg@lanl.gov)',
'Dan Schult(dschult@colgate.edu)',
'Ben Edwards(bedwards@cs.unm.edu)'])
def create_degree_sequence(n, sfunction=None, max_tries=50, **kwds):
""" Attempt to create a valid degree sequence of length n using
specified function sfunction(n,**kwds).
Parameters
----------
n : int
Length of degree sequence = number of nodes
sfunction: function
Function which returns a list of n real or integer values.
Called as "sfunction(n,**kwds)".
max_tries: int
Max number of attempts at creating valid degree sequence.
Notes
-----
Repeatedly create a degree sequence by calling sfunction(n,**kwds)
until achieving a valid degree sequence. If unsuccessful after
max_tries attempts, raise an exception.
For examples of sfunctions that return sequences of random numbers,
see networkx.Utils.
Examples
--------
>>> from networkx.utils import uniform_sequence, create_degree_sequence
>>> seq=create_degree_sequence(10,uniform_sequence)
"""
tries=0
max_deg=n
while tries < max_tries:
trialseq=sfunction(n,**kwds)
# round to integer values in the range [0,max_deg]
seq=[min(max_deg, max( int(round(s)),0 )) for s in trialseq]
# if graphical return, else throw away and try again
if nx.is_valid_degree_sequence(seq):
return seq
tries+=1
raise nx.NetworkXError(\
"Exceeded max (%d) attempts at a valid sequence."%max_tries)
# The same helpers for choosing random sequences from distributions
# uses Python's random module
# http://www.python.org/doc/current/lib/module-random.html
def pareto_sequence(n,exponent=1.0):
"""
Return sample sequence of length n from a Pareto distribution.
"""
return [random.paretovariate(exponent) for i in range(n)]
def powerlaw_sequence(n,exponent=2.0):
"""
Return sample sequence of length n from a power law distribution.
"""
return [random.paretovariate(exponent-1) for i in range(n)]
def zipf_rv(alpha, xmin=1, seed=None):
r"""Return 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 : int
Seed value for random number generator
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 [1] for details on its operation.
Examples
--------
>>> nx.zipf_rv(alpha=2, xmin=3, seed=42) # doctest: +SKIP
References
----------
..[1] 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")
if not seed is None:
random.seed(seed)
a1 = alpha - 1.0
b = 2**a1
while True:
u = 1.0 - random.random() # u in (0,1]
v = random.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
def zipf_sequence(n, alpha=2.0, xmin=1):
"""Return a sample sequence of length n from a Zipf distribution with
exponent parameter alpha and minimum value xmin.
See Also
--------
zipf_rv
"""
return [ zipf_rv(alpha,xmin) for _ in range(n)]
def uniform_sequence(n):
"""
Return sample sequence of length n from a uniform distribution.
"""
return [ random.uniform(0,n) for i in range(n)]
def cumulative_distribution(distribution):
"""Return normalized cumulative distribution from discrete distribution."""
cdf=[]
cdf.append(0.0)
psum=float(sum(distribution))
for i in range(0,len(distribution)):
cdf.append(cdf[i]+distribution[i]/psum)
return cdf
def discrete_sequence(n, distribution=None, cdistribution=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=[random.random() for i in range(n)]
# choose from CDF
seq=[bisect.bisect_left(cdf,s)-1 for s in inputseq]
return seq
def random_weighted_sample(mapping, k):
"""Return 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))
return list(sample)
def weighted_choice(mapping):
"""Return a single element from a weighted sample.
The input is a dictionary of items with weights as values.
"""
# use roulette method
rnd = random.random() * sum(mapping.values())
for k, w in mapping.items():
rnd -= w
if rnd < 0:
return k
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