sobol, a FORTRAN90 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.
The code 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.
At the request of a user, the library now contains two versions of the algorithm, one using the default integer and real precision, and one using the higher precision obtainable by requesting "(KIND=8)". The two sets of code are distinguished by names that begin with I4_ and I8_. I am aware that using the KIND attribute with an explicit value is not the correct way of asking for higher precision, but it's natural, and the correct way looks a little too awkward and obscure to me today. I am aware that many variables in the higher precision code need not themselves be calculated in higher precision. I'd just like to see if and how the higher precision code runs at all.
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 C++ and FORTRAN90 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 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
CVT, a FORTRAN90 code which computes elements of a Centroidal Voronoi Tessellation.
FAURE, a FORTRAN90 code which computes elements of a Faure quasirandom sequence.
HALTON, a FORTRAN90 code which computes elements of a Halton Quasi Monte Carlo (QMC) sequence, using a simple interface.
HAMMERSLEY, a FORTRAN90 code which computes elements of a Hammersley Quasi Monte Carlo (QMC) sequence, using a simple interface.
IEEE_UNIFORM_SAMPLE, a FORTRAN90 code which tries to uniformly sample the discrete set of values that represent the legal IEEE real numbers;
LATTICE_RULE, a FORTRAN90 code which approximates multidimensional integrals using lattice rules.
LCVT, a FORTRAN90 code which computes a latinized Centroidal Voronoi Tessellation.
NIEDERREITER2, a FORTRAN90 code which computes elements of a Niederreiter quasirandom sequence with base 2.
NORMAL, a FORTRAN90 code which computes elements of a sequence of pseudorandom normally distributed values.
TOMS647, a FORTRAN90 code 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 FORTRAN90 code which computes elements of a uniform pseudorandom sequence.
VAN_DER_CORPUT, a FORTRAN90 code which computes elements of a van der Corput quasirandom sequence.
Original FORTRAN77 version by Bennett Fox; FORTRAN90 version by John Burkardt.