SAMPLE_2D
Samples in the Unit Square.


SAMPLE_2D is a dataset directory which collects sets of points that sample the unit square.

There are a number of datasets, each containing about 100 points in 2D, in the unit square [0,1]x[0,1]. Some of the datasets are "pseudo-random", or "Monte Carlo" samplings, which attempt to minic the behavior of a uniformly random distribution. Other datasets, particularly Faure, Halton, Hammersley and Sobol, represent low discrepancy "quasi-random" sequences. Other samplings are generated by iterations or trial and error backtracking procedures.

Licensing:

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

Related Data and Programs:

CIRCLE_TEST, a FORTRAN90 program which performs a circle-spacing test on sets of points;

INTEGRAL_TEST, a FORTRAN90 program which tests the suitability of a set of N points for use in an equal-weight quadrature rule over the M-dimensional unit hypercube.

Reference:

  1. Paul Bratley, Bennett Fox, Harald Niederreiter,
    Implementation and Tests of Low-Discrepancy Sequences,
    ACM Transactions on Modeling and Computer Simulation,
    Volume 2, Number 3, pages 195-213, 1992.
  2. Paul Bratley, Bennett Fox, Harald Niederreiter,
    Algorithm 738: Programs to Generate Niederreiter's Low-Discrepancy Sequences,
    ACM Transactions on Mathematical Software,
    Volume 20, Number 4, pages 494-495, 1994.
  3. Bennett Fox,
    Algorithm 647: Implementation and Relative Efficiency of Quasirandom Sequence Generators,
    ACM Transactions on Mathematical Software,
    Volume 12, Number 4, pages 362-376, 1986.

Datasets:

SET_01 is a set of CVT points from MDG:

SET_02 is a set of CVT points from MDG:

SET_03 is a set of CVT points from MDG:

SET_04 is a set of CVT points from MDG:

SET_05 is a set of CVT points from MDG:

SET_06 is a set of CVT points from MDG:

SET_07 is a set of CVT points from MDG:

SET_08 is a set of CVT points from MDG:

SET_09 is a set of 100 Hammersley points, JVB code:

SET_10 is a set of 100 Faure points, ACM TOMS 647 code:

SET_11 is a set of 100 Halton points, ACM TOMS 647 code:

SET_12 is a set of 100 Sobol points, ACM TOMS 647 code:

SET_13 is a set of 100 Monte Carlo points, ACM TOMS 647 code:

SET_14 is a set of 100 Niederreiter points, ACM TOMS 738 code:

SET_15 is a set of 100 Monte Carlo points, set 1, MDG code.

SET_16 is a set of 100 Monte Carlo points, set 2, MDG code:

SET_17 is a set of 100 Monte Carlo points, set 3, MDG code:

SET_18 is a set of 100 Halton points, MDG code:

SET_19 is a set of 100 Hammersley points, MDG code:

SET_20 is a set of 100 Latin hypercube points, set 1, MDG code:

SET_21 is a set of 100 Latin hypercube points, set 2, MDG code.

SET_22 is a set of 100 Latin hypercube points, set 3, MDG code:

SET_23 is a set of 100 Hanson points, set 1, MDG code.

SET_24 is a set of 100 Hanson points, set 2, MDG code:

SET_25 is a set of 100 Halton points, JVB code.

SET_26 is a set of 100 Sobol points, Numerical Recipes code.

SET_27 is a set of 100 Improved Hypercube Sampling points, "COV=0.127910", set #1, Beachkofski MATLAB code.

SET_28 is a set of 100 Improved Hypercube Sampling points, "COV=0.159586", set #2, Beachkofski MATLAB code.

SET_29 is a set of 100 Improved Hypercube Sampling points, "COV=0.206873", set #3, Beachkofski MATLAB code.

SET_30 is a set of 100 points on a 10 by 10 evenly-spaced product grid.

SET_31 is a set of 100 points on a 10 by 10 offset evenly-spaced product grid.

SET_32 is a set of 99 points on a 9 by 11 hexagonal grid, with points on the boundary.

SET_33 is a set of 99 points on a 9 by 11 hexagonal grid, with all the points in the interior of the region.

SET_34 is a set of 100 Monte Carlo points, under a nonuniform distribution, set 1, MDG code.

SET_35 is a set of 100 Monte Carlo points, under a nonuniform distribution, set 2, MDG code.

SET_36 is a set of 100 Monte Carlo points, under a nonuniform distribution, set 3, MDG code.

You can go up one level to the DATASETS directory.


Last revised on 11 March 2006.