U :v f@sdZddlZddlmZdddddd gZed dd dZed dddZddZeddddZ ed dddZ ed ddd Z dS)zS Utilities for generating random numbers, random sequences, and random selections. N)py_random_statepowerlaw_sequencezipf_rvcumulative_distributiondiscrete_sequencerandom_weighted_sampleweighted_choice@csfddt|DS)zK Return sample sequence of length n from a power law distribution. csg|]}dqS) paretovariate.0iexponentseedB/tmp/pip-unpacked-wheel-_lngutwb/networkx/utils/random_sequence.py sz%powerlaw_sequence..)range)nrrrrrrsr c Cs|dkrtd|dkr td|d}d|}d|}|}t||d| }dd||}|||d|d||kr0qq0|S)awReturns 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`. 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.utils.zipf_rv(alpha=2, xmin=3, seed=42) 8 References ---------- .. [1] Luc Devroye, Non-Uniform Random Variate Generation, Springer-Verlag, New York, 1986. r zxmin < 1za <= 1.0g?r ) ValueErrorrandomint) alphaZxminrZa1buvxtrrrr s1  cCs@dg}t|}tdt|D]}||||||q|S)zFReturns normalized cumulative distribution from discrete distribution.gr)sumrlenappend) distributioncdfZpsumrrrrras cs`ddl|dk r|n|dk r(t|n tdfddt|D}fdd|D}|S)a# 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 rNz8discrete_sequence: distribution or cdistribution missingcsg|] }qSr)rr)rrrrsz%discrete_sequence..csg|]}|dqSr ) bisect_left)rs)bisectr&rrrs)r*rnxZ NetworkXErrorr)rr%Z cdistributionrZinputseqseqr)r*r&rrrks  cCs@|t|krtdt}t||kr8|t||qt|S)zReturns k items without replacement from a weighted sample. The input is a dictionary of items with weights as values. zsample larger than population)r#rsetaddrlist)mappingkrsamplerrrrs   cCsB|t|}|D] \}}||8}|dkr|SqdS)zuReturns a single element from a weighted sample. The input is a dictionary of items with weights as values. rN)rr"valuesitems)r0rZrndr1wrrrrs )r N)r N)NNN)N)N) __doc__Znetworkxr+Znetworkx.utilsr__all__rrrrrrrrrrs(   @