MT19937 Randomstate

Random generator

class randomstate.prng.mt19937.RandomState(seed=None)

Container for the Mersenne Twister pseudo-random number generator.

mt19937.RandomState exposes a number of methods for generating random numbers drawn from a variety of probability distributions. 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.

Compatibility Guarantee

mt19937.RandomState is identical to numpy.random.RandomState and makes the same compatibility guarantee. A fixed seed and a fixed series of calls to mt19937.RandomState methods using the same parameters will always produce the same results up to roundoff error except when the values were incorrect. Incorrect values will be fixed and the version in which the fix was made will be noted in the relevant docstring. Extension of existing parameter ranges and the addition of new parameters is allowed as long the previous behavior remains unchanged.

Parameters:seed ({None, int, array_like}, optional) – Random seed used to initialize the pseudo-random number generator. Can be any integer between 0 and 2**32 - 1 inclusive, an array (or other sequence) of such integers, or None (the default). If seed is None, then RandomState will try to read data from /dev/urandom (or the Windows analog) if available or seed from the clock otherwise.

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. RandomState, besides being NumPy-aware, has the advantage that it provides a much larger number of probability distributions to choose from.

Parallel Features

mt19937.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 ([1], [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.mt19937 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)

References

[1]	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.

[2]	Hiroshi Haramoto, Makoto Matsumoto, Takuji Nishimura, François Panneton, Pierre L’Ecuyer, “Efficient Jump Ahead for F2-Linear Random Number Generators”, INFORMS JOURNAL ON COMPUTING, Vol. 20, No. 3, Summer 2008, pp. 385-390.

seed([seed])	Seed the generator.
get_state()	Return a tuple or dict representing 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.