SFMT Randomstate

Random generator

class randomstate.prng.sfmt.RandomState(seed=None)

Container for the SIMD-based Mersenne Twister pseudo-random number generator.

sfmt.RandomState exposes a number of methods for generating random numbers drawn from a variety of probability distributions [1] . In addition to the distribution-specific arguments, each method takes a keyword argument size that defaults to None. If size is None, then a single value is generated and returned. If size is an integer, then a 1-D array filled with generated values is returned. If size is a tuple, then an array with that shape is filled and returned.

No Compatibility Guarantee

sfmt.RandomState does not make a guarantee that a fixed seed and a fixed series of calls to sfmt.RandomState methods using the same parameters will always produce the same results. This is different from numpy.random.RandomState guarantee. This is done to simplify improving random number generators. To ensure identical results, you must use the same release version.

Parameters:seed ({None, int, array_like}, optional) – Random seed initializing the pseudo-random number generator. Can be an integer in [0, 2**32-1], array of integers in [0, 2**32-1] or None (the default). If seed is None, then sfmt.RandomState will try to read entropy from /dev/urandom (or the Windows analog) if available to produce a 64-bit seed. If unavailable, the a 64-bit hash of the time and process ID is used.

Notes

The Python stdlib module “random” also contains a Mersenne Twister pseudo-random number generator with a number of methods that are similar to the ones available in RandomState. The RandomState object, besides being NumPy-aware, also has the advantage that it provides a much larger number of probability distributions to choose from.

>>> from randomstate.entropy import random_entropy
>>> import randomstate.prng.sfmt as rnd
>>> seed = random_entropy()
>>> rs = [rnd.RandomState(seed) for _ in range(10)]

Parallel Features

sfmt.RandomState can be used in parallel applications by calling the method jump which advances the state as-if \(2^{128}\) random numbers have been generated [2]. This allows the original sequence to be split so that distinct segments can be used in each worker process. All generators should be initialized with the same seed to ensure that the segments come from the same sequence.

>>> from randomstate.entropy import random_entropy
>>> import randomstate.prng.sfmt as rnd
>>> seed = random_entropy()
>>> rs = [rnd.RandomState(seed) for _ in range(10)]
# Advance rs[i] by i jumps
>>> for i in range(10):
        rs[i].jump(i)

State and Seeding

The sfmt.RandomState state vector consists of a 624 element array of 32-bit unsigned integers plus a single integer value between 0 and 624 indicating the current position within the main array. The implementation used here augments this with a array of 64-bit unsigned integers which are used to efficiently access the random numbers produced by the SFMT generator.

sfmt.RandomState is seeded using either a single 32-bit unsigned integer or a vector of 32-bit unsigned integers. In either case, the input seed is used as an input (or inputs) for a hashing function, and the output of the hashing function is used as the initial state. Using a single 32-bit value for the seed can only initialize a small range of the possible initial state values.

References

[1]	Mutsuo Saito and Makoto Matsumoto, “SIMD-oriented Fast Mersenne Twister: a 128-bit Pseudorandom Number Generator.” Monte Carlo and Quasi-Monte Carlo Methods 2006, Springer, pp. 607 – 622, 2008.

[2]	Hiroshi Haramoto, Makoto Matsumoto, and Pierre L’Ecuyer, “A Fast Jump Ahead Algorithm for Linear Recurrences in a Polynomial Space”, Sequences and Their Applications - SETA, 290–298, 2008.

seed([seed])	Seed the generator.
get_state()	Return a dict containing the internal state of the generator.
set_state(state)	Set the internal state of the generator from a tuple.

Parallel generation

jump(iter = 1)

Jumps the state of the random number generator as-if 2**128 random numbers have been generated.

Simple random data

rand(d0, d1, …, dn[, dtype])	Random values in a given shape.
randn(d0, d1, …, dn[, method, dtype])	Return a sample (or samples) from the “standard normal” distribution.
randint(low[, high, size, dtype])	Return random integers from low (inclusive) to high (exclusive).
random_integers(low[, high, size])	Random integers of type np.int between low and high, inclusive.
random_sample([size, dtype, out])	Return random floats in the half-open interval [0.0, 1.0).
random	random_sample(size=None, dtype=’d’, out=None)
ranf	random_sample(size=None, dtype=’d’, out=None)
sample	random_sample(size=None, dtype=’d’, out=None)
choice(a[, size, replace, p])	Generates a random sample from a given 1-D array
bytes(length)	Return random bytes.
random_uintegers([size, bits])	Return random unsigned integers
random_raw(self[, size])	Return randoms as generated by the underlying PRNG

Permutations

shuffle(x)	Modify a sequence in-place by shuffling its contents.
permutation(x)	Randomly permute a sequence, or return a permuted range.

Distributions

beta(a, b[, size])	Draw samples from a Beta distribution.
binomial(n, p[, size])	Draw samples from a binomial distribution.
chisquare(df[, size])	Draw samples from a chi-square distribution.
complex_normal([loc, gamma, relation, size, …])	Draw random samples from a complex normal (Gaussian) distribution.
dirichlet(alpha[, size])	Draw samples from the Dirichlet distribution.
exponential([scale, size])	Draw samples from an exponential distribution.
f(dfnum, dfden[, size])	Draw samples from an F distribution.
gamma(shape[, scale, size])	Draw samples from a Gamma distribution.
geometric(p[, size])	Draw samples from the geometric distribution.
gumbel([loc, scale, size])	Draw samples from a Gumbel distribution.
hypergeometric(ngood, nbad, nsample[, size])	Draw samples from a Hypergeometric distribution.
laplace([loc, scale, size])	Draw samples from the Laplace or double exponential distribution with specified location (or mean) and scale (decay).
logistic([loc, scale, size])	Draw samples from a logistic distribution.
lognormal([mean, sigma, size])	Draw samples from a log-normal distribution.
logseries(p[, size])	Draw samples from a logarithmic series distribution.
multinomial(n, pvals[, size])	Draw samples from a multinomial distribution.
multivariate_normal(mean, cov[, size, …)	Draw random samples from a multivariate normal distribution.
negative_binomial(n, p[, size])	Draw samples from a negative binomial distribution.
noncentral_chisquare(df, nonc[, size])	Draw samples from a noncentral chi-square distribution.
noncentral_f(dfnum, dfden, nonc[, size])	Draw samples from the noncentral F distribution.
normal([loc, scale, size, method])	Draw random samples from a normal (Gaussian) distribution.
pareto(a[, size])	Draw samples from a Pareto II or Lomax distribution with specified shape.
poisson([lam, size])	Draw samples from a Poisson distribution.
power(a[, size])	Draws samples in [0, 1] from a power distribution with positive exponent a - 1.
rayleigh([scale, size])	Draw samples from a Rayleigh distribution.
standard_cauchy([size])	Draw samples from a standard Cauchy distribution with mode = 0.
standard_exponential([size, dtype, method, out])	Draw samples from the standard exponential distribution.
standard_gamma(shape[, size, dtype, method, out])	Draw samples from a standard Gamma distribution.
standard_normal([size, dtype, method, out])	Draw samples from a standard Normal distribution (mean=0, stdev=1).
standard_t(df[, size])	Draw samples from a standard Student’s t distribution with df degrees of freedom.
triangular(left, mode, right[, size])	Draw samples from the triangular distribution over the interval [left, right].
uniform([low, high, size])	Draw samples from a uniform distribution.
vonmises(mu, kappa[, size])	Draw samples from a von Mises distribution.
wald(mean, scale[, size])	Draw samples from a Wald, or inverse Gaussian, distribution.
weibull(a[, size])	Draw samples from a Weibull distribution.
zipf(a[, size])	Draw samples from a Zipf distribution.