.. _method-fsu_quasi_mc-halton:

""""""
halton
""""""


Generate samples from a Halton sequence



**Topics**


package_fsudace


.. toctree::
   :hidden:
   :maxdepth: 1



**Specification**

- *Alias:* None

- *Arguments:* None


**Description**


The quasi-Monte Carlo sequences of Halton are deterministic
sequences determined by a set of prime bases.
These sequences generate random numbers with the goal of
filling a unit hypercube uniformly.

Generally, we recommend that the user leave the default
setting for the bases, which are the lowest primes.
Thus, if one wants to generate a sample set for 3 random variables,
the default bases used are 2, 3, and 5 in the Halton sequence.
To give an example of how these sequences look, the Halton sequence
in base 2 starts with points 0.5, 0.25, 0.75, 0.125, 0.625, etc.
The first few points in a Halton base 3 sequence are
0.33333, 0.66667, 0.11111, 0.44444, 0.77777, etc. Notice that the Halton
sequence tends to alternate back and forth, generating a point closer to zero
then a point closer to one. An individual sequence is based on a radix
inverse function defined on a prime base. The prime base determines
how quickly the [0,1] interval is filled in.



**Theory**


For more information about
these sequences, see :cite:p:`Halton1960`,
:cite:p:`Halton1964`, and
:cite:p:`Kocis1997`.