chaospy.create_halton_samples

chaospy.create_halton_samples(order, dim=1, burnin=- 1, primes=())

Create samples from the Halton sequence.

In statistics, Halton sequences are sequences used to generate points in space for numerical methods such as Monte Carlo simulations. Although these sequences are deterministic, they are of low discrepancy, that is, appear to be random for many purposes. They were first introduced in 1960 and are an example of a quasi-random number sequence. They generalise the one-dimensional van der Corput sequences. For dim == 1 the sequence falls back to Van Der Corput sequence.

Args:

order (int):

The order of the Halton sequence. Defines the number of samples.

dim (int):

The number of dimensions in the Halton sequence.

burnin (int):

Skip the first burnin samples. If negative, the maximum of primes is used.

primes (tuple):

The (non-)prime base to calculate values along each axis. If empty, growing prime values starting from 2 will be used.

Returns:

(numpy.ndarray):

Halton sequence with shape == (dim, order).

Examples:

>>> distribution = chaospy.J(chaospy.Uniform(0, 1), chaospy.Uniform(0, 1))
>>> samples = distribution.sample(3, rule="halton")
>>> samples.round(4)
array([[0.125 , 0.625 , 0.375 ],
       [0.4444, 0.7778, 0.2222]])
>>> samples = distribution.sample(4, rule="halton")
>>> samples.round(4)
array([[0.125 , 0.625 , 0.375 , 0.875 ],
       [0.4444, 0.7778, 0.2222, 0.5556]])