HAMMERSLEY
The Hammersley Quasi Monte Carlo (QMC) Sequence

HAMMERSLEY is a FORTRAN90 library which computes elements of a Hammersley Quasi Monte Carlo (QMC) sequence using a simple interface.

A more sophisticated library is available in HAMMERSLEY_ADVANCED, but I find this simple version to be preferable for everyday use!

The standard M-dimensional Hammersley sequence based on N is simply composed of a first component of successive fractions 0/N, 1/N, ..., N/N, paired with M-1 1-dimensional van der Corput sequences, using as bases the first M-1 primes.

The HAMMERSLEY function will return the M-dimensional element of this sequence with index I.

The HAMMERSLEY_SEQUENCE function will return the M-dimensional elements of this sequence with indices I1 through I2.

The HAMMERSLEY_INVERSE function accepts an M-dimensional value, presumably computed by HAMMERSLEY, and returns its original index I.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

HAMMERSLEY is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

CVT, a FORTRAN90 library which computes elements of a Centroidal Voronoi Tessellation.

FAURE, a FORTRAN90 library which computes elements of a Faure sequence.

HALTON, a FORTRAN90 library which computes elements of a Halton Quasi Monte Carlo (QMC) sequence.

HAMMERSLEY_ADVANCED, a FORTRAN90 library which computes elements of a Hammersley Quasi Monte Carlo (QMC) sequence, using an advanced interface with many input options.

HAMMERSLEY_DATASET, a FORTRAN90 library which creates a Hammersley sequence and writes it to a file.

HEX_GRID, a FORTRAN90 library which computes elements of a hexagonal grid dataset.

IHS, a FORTRAN90 library which computes elements of an improved distributed Latin hypercube dataset.

LATIN_CENTER, a FORTRAN90 library which computes elements of a Latin Hypercube dataset, choosing center points.

LATIN_EDGE, a FORTRAN90 library which computes elements of a Latin Hypercube dataset, choosing edge points.

LATIN_RANDOM, a FORTRAN90 library which computes elements of a Latin Hypercube dataset, choosing points at random.

LATTICE_RULE, a FORTRAN90 library which approximates multidimensional integrals using lattice rules.

LCVT, a FORTRAN90 library which computes a latinized Centroidal Voronoi Tessellation.

NIEDERREITER2, a FORTRAN90 library which computes elements of a Niederreiter sequence using base 2.

SOBOL, a FORTRAN90 library which computes elements of a Sobol sequence.

TOMS647, a FORTRAN90 library which is a version of ACM TOMS algorithm 647, for evaluating Faure, Hammersley and Sobol sequences.

UNIFORM, a FORTRAN90 library which computes elements of a uniform pseudorandom sequence.

VAN_DER_CORPUT, a FORTRAN90 library which computes elements of a 1D van der Corput Quasi Monte Carlo (QMC) sequence using a simple interface.

Reference:

1. John Hammersley, Monte Carlo methods for solving multivariable problems, Proceedings of the New York Academy of Science, Volume 86, 1960, pages 844-874.
2. Ladislav Kocis, William Whiten,
   Computational Investigations of Low-Discrepancy Sequences,
   ACM Transactions on Mathematical Software,
   Volume 23, Number 2, 1997, pages 266-294.

Source Code:

• hammersley.f90, the source code.

Examples and Tests:

• hammersley_test.f90, a sample calling program.
• hammersley_test.txt, the output file.

List of Routines:

• HAMMERSLEY computes an element of a Hammersley sequence.
• HAMMERSLEY_INVERSE inverts an element of the Hammersley sequence.
• HAMMERSLEY_SEQUENCE computes elements I1 through I2 of a Hammersley sequence.
• PRIME returns any of the first PRIME_MAX prime numbers.
• R8MAT_PRINT prints an R8MAT.
• R8MAT_PRINT_SOME prints some of an R8MAT.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the FORTRAN90 source codes.