SOBOL, a Python library which computes elements of the Sobol quasirandom sequence.
A quasirandom or low discrepancy sequence, such as the Faure, Halton, Hammersley, Niederreiter or Sobol sequences, is "less random" than a pseudorandom number sequence, but more useful for such tasks as approximation of integrals in higher dimensions, and in global optimization. This is because low discrepancy sequences tend to sample space "more uniformly" than random numbers. Algorithms that use such sequences may have superior convergence.
SOBOL is an adaptation of the INSOBL and GOSOBL routines in ACM TOMS Algorithm 647 and ACM TOMS Algorithm 659. The original code can only compute the "next" element of the sequence. The revised code allows the user to specify the index of any desired element.
A remark by Joe and Kuo shows how to extend the algorithm from the original maximum spatial dimension of 40 up to a maximum spatial dimension of 1111. These changes have been implemented in the FORTRAN90 and C++ versions of the program.
The original, true, correct versions of ACM TOMS Algorithm 647 and ACM TOMS Algorithm 659 are available in the TOMS subdirectory of the NETLIB web site. The version displayed here has been converted to Python, and other internal changes have been made.
The computer code and data files described and made available on this web page are distributed under the MIT license.
SOBOL is available in a C++ version and a FORTRAN90 version and a MATLAB version and a Python version
HALTON, a Python library which computes elements of a Halton Quasi Monte Carlo (QMC) sequence, using a simple interface.
HAMMERSLEY, a Python library which computes elements of a Hammersley Quasi Monte Carlo (QMC) sequence, using a simple interface.
NORMAL, a Python library which contains random number generators (RNG's) for normally distributed values.
VAN_DER_CORPUT, a Python library which computes elements of a 1D van der Corput Quasi Monte Carlo (QMC) sequence using a simple interface.
This Python implementation was written by Corrado Chisari.