Sobol sequences are quasi-random low-discrepancy sequences that are useful for creating sample distributions.
Install as usual with setuptools - source available from https://github.com/naught101/sobol_seq.
Or a decent package manager like conda:
conda install -c https://conda.binstar.org/naught101 sobol_seq
Use i4_sobol to generate a single Sobol vector:
import sobol_seq
vec, seed = sobol_seq.i4_sobol(4, 1)
vec
# array([ 0.5, 0.5, 0.5, 0.5])
seed
# 2
# generate the next vector in the sequence:
vec,seed=sobol_seq.i4_sobol(4, seed)
Use i4_sobol_generate to generate a Sobol sequence. For example, if you want to have the first 5 three-dimensional Sobol numbers, run:
sobol_seq.i4_sobol_generate(3, 5)
# array([[ 0.5 , 0.5 , 0.5 ],
# [ 0.75 , 0.25 , 0.75 ],
# [ 0.25 , 0.75 , 0.25 ],
# [ 0.375, 0.375, 0.625],
# [ 0.875, 0.875, 0.125]])
Use i4_sobol_generate_std_normal to generate (multivariate) standard normal quasi-random variables. For example, if you want to have the first 5 realisations of a three-dimensional standard normal quasi-random variable, run:
sobol_seq.i4_sobol_generate_std_normal(3, 5)
# array([[ 0. , 0. , 0. ],
# [ 0.67448975, -0.67448975, 0.67448975],
# [-0.67448975, 0.67448975, -0.67448975],
# [-0.31863936, -0.31863936, 0.31863936],
# [ 1.15034938, 1.15034938, -1.15034938]])
All functions have detailed documentation available via help(func).
This package is heavily based on Sobol, a Python library for generating Sobols by John Burkardt and Corrado Chisari who made their code available under the MIT license. Any additions and/or changes to their code are also made available under the MIT license.