SOBOL, a C++ code 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 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. The FORTRAN90 and C++ versions of this program have been updated in this way. In particular, the extra data in the C++ version of the program was kindly formatted and supplied by Steffan Berridge.
The routines with a prefix of I8_ use 64 bit integers, and use the long int to get this. On some systems, a long int is simply 32 bits. In that case, try using the long long int datatype instead.
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 FORTRAN90, and other internal changes have been made to suit me.
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
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CVT, a C++ library which computes points in a Centroidal Voronoi Tessellation.
FAURE, a C++ library which computes Faure sequences.
HALTON, a C++ library which computes elements of a Halton Quasi Monte Carlo (QMC) sequence, using a simple interface.
HAMMERSLEY, a C++ library which computes elements of a Hammersley Quasi Monte Carlo (QMC) sequence, using a simple interface.
IHS, a C++ library which computes improved Latin Hypercube datasets.
LATIN_CENTER, a C++ library which computes Latin square data choosing the center value.
LATIN_EDGE, a C++ library which computes Latin square data choosing the edge value.
LATIN_RANDOM, a C++ library which computes Latin square data choosing a random value in the square.
NIEDERREITER2, a C++ library which computes Niederreiter sequences with base 2.
NORMAL, a C++ library which computes elements of a sequence of pseudorandom normally distributed values.
UNIFORM, a C++ library which computes uniform random values.
VAN_DER_CORPUT, a C++ library which computes a van der Corput sequences.
Original FORTRAN77 version by Bennett Fox; C++ version by John Burkardt.