SOBOL is a MATLAB library which computes elements of the Sobol quasirandom sequence, by Bennett Fox.
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 adapation 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 the 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. The FORTRAN90 and C++ versions of the code has been updated in this way, but updating the MATLAB code has not been simple, since MATLAB doesn't support 64 bit integers.
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 computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
SOBOL is available in a C++ version and a FORTRAN90 version and a MATLAB version and a Python version
CVT, a MATLAB library which computes points in a Centroidal Voronoi Tessellation.
FAURE, a MATLAB library which computes Faure sequences.
GRID, a MATLAB library which computes points on a grid.
HALTON, a MATLAB library which computes Halton sequences.
HAMMERSLEY, a MATLAB library which computes elements of a Hammersley Quasi Monte Carlo (QMC) sequence, using a simple interface.
HEX_GRID, a MATLAB library which computes sets of points in a 2D hexagonal grid.
IHS, a MATLAB library which computes improved Latin Hypercube datasets.
LATIN_CENTER, a MATLAB library which computes Latin square data choosing the center value.
LATIN_EDGE, a MATLAB library which computes Latin square data choosing the edge value.
LATIN_RANDOM, a MATLAB library which computes Latin square data choosing a random value in the square.
LATTICE_RULE, a MATLAB library which approximates multidimensional integrals using lattice rules.
NIEDERREITER2, a MATLAB library which computes Niederreiter sequences with base 2.
SOBOL_DATASET, a MATLAB program which computes a Sobol quasirandom sequence and writes it to a file.
TOMS647, a FORTRAN90 library which is a version of ACM TOMS algorithm 647, for evaluating Faure, Halton and Sobol sequences.
TOMS659, a FORTRAN77 library which evaluates Sobol sequences.
UNIFORM, a MATLAB library which computes uniform random values.
VAN_DER_CORPUT, a MATLAB library which computes van der Corput sequences.
Original FORTRAN77 version by Bennett Fox; Matlab version by John Burkardt.
SOBOL is the current version of the program, which is restricted to a maximum spatial dimension of 40.
You can go up one level to the MATLAB source codes.