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_01.txt, the points.
• set_01_dot.png, a PNG image of a dot plot.
• set_01_balloon.png, a PNG image of a balloon plot.

SET_02 is a set of CVT points from MDG:

• set_02.txt, the points.
• set_02_dot.png, a PNG image of a dot plot.
• set_02_balloon.png, a PNG image of a balloon plot.

SET_03 is a set of CVT points from MDG:

• set_03.txt, the points.
• set_03_dot.png, a PNG image of a dot plot.
• set_03_balloon.png, a PNG image of a balloon plot.

SET_04 is a set of CVT points from MDG:

• set_04.txt, the points.
• set_04_dot.png, a PNG image of a dot plot.
• set_04_balloon.png, a PNG image of a balloon plot.

SET_05 is a set of CVT points from MDG:

• set_05.txt, the points.
• set_05_dot.png, a PNG image of a dot plot.
• set_05_balloon.png, a PNG image of a balloon plot.

SET_06 is a set of CVT points from MDG:

• set_06.txt, the points.
• set_06_dot.png, a PNG image of a dot plot.
• set_06_balloon.png, a PNG image of a balloon plot.

SET_07 is a set of CVT points from MDG:

• set_07.txt, the points.
• set_07_dot.png, a PNG image of a dot plot.
• set_07_balloon.png, a PNG image of a balloon plot.

SET_08 is a set of CVT points from MDG:

• set_08.txt, the points.
• set_08_dot.png, a PNG image of a dot plot.
• set_08_balloon.png, a PNG image of a balloon plot.

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

• set_09.txt, the points.
• set_09_dot.png, a PNG image of a dot plot.
• set_09_balloon.png, a PNG image of a balloon plot.

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

• set_10.txt, the points.
• set_10_dot.png, a PNG image of a dot plot.
• set_10_balloon.png, a PNG image of a balloon plot.

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

• set_11.txt, the points.
• set_11_dot.png, a PNG image of a dot plot.
• set_11_balloon.png, a PNG image of a balloon plot.

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

• set_12.txt, the points.
• set_12_dot.png, a PNG image of a dot plot.
• set_12_balloon.png, a PNG image of a balloon plot.

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

• set_13.txt, the points.
• set_13_dot.png, a PNG image of a dot plot.
• set_13_balloon.png, a PNG image of a balloon plot.

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

• set_14.txt, the points.
• set_14_dot.png, a PNG image of a dot plot.
• set_14_balloon.png, a PNG image of a balloon plot.

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

• set_15.txt, the points.
• set_15_dot.png, a PNG image of a dot plot.
• set_15_balloon.png, a PNG image of a balloon plot.

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

• set_16.txt, the points.
• set_16_dot.png, a PNG image of a dot plot.
• set_16_balloon.png, a PNG image of a balloon plot.

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

• set_17.txt, the points.
• set_17_dot.png, a PNG image of a dot plot.
• set_17_balloon.png, a PNG image of a balloon plot.

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

• set_18.txt, the points.
• set_18_dot.png, a PNG image of a dot plot.
• set_18_balloon.png, a PNG image of a balloon plot.

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

• set_19.txt, the points.
• set_19_dot.png, a PNG image of a dot plot.
• set_19_balloon.png, a PNG image of a balloon plot.

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

• set_20.txt, the points.
• set_20_dot.png, a PNG image of a dot plot.
• set_20_balloon.png, a PNG image of a balloon plot.

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

• set_21.txt, the points.
• set_21_dot.png, a PNG image of a dot plot.
• set_21_balloon.png, a PNG image of a balloon plot.

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

• set_22.txt, the points.
• set_22_dot.png, a PNG image of a dot plot.
• set_22_balloon.png, a PNG image of a balloon plot.

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

• set_23.txt, the points.
• set_23_dot.png, a PNG image of a dot plot.
• set_23_balloon.png, a PNG image of a balloon plot.

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

• set_24.txt, the points.
• set_24_dot.png, a PNG image of a dot plot.
• set_24_balloon.png, a PNG image of a balloon plot.

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

• set_25.txt, the points.
• set_25_dot.png, a PNG image of a dot plot.
• set_25_balloon.png, a PNG image of a balloon plot.

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

• set_26.txt, the points.
• set_26_dot.png, a PNG image of a dot plot.
• set_26_balloon.png, a PNG image of a balloon plot.

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

• set_27.txt, the points.
• set_27_dot.png, a PNG image of a dot plot.
• set_27_balloon.png, a PNG image of a balloon plot.

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

• set_28.txt, the points.
• set_28_dot.png, a PNG image of a dot plot.
• set_28_balloon.png, a PNG image of a balloon plot.

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

• set_29.txt, the points.
• set_29_dot.png, a PNG image of a dot plot.
• set_29_balloon.png, a PNG image of a balloon plot.

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

• set_30.txt, the points.
• set_30_dot.png, a PNG image of a dot plot.
• set_30_balloon.png, a PNG image of a balloon plot.

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

• set_31.txt, the points.
• set_31_dot.png, a PNG image of a dot plot.
• set_31_balloon.png, a PNG image of a balloon plot.

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

• set_32.txt, the points.
• set_32_dot.png, a PNG image of a dot plot.
• set_32_balloon.png, a PNG image of a balloon plot.

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_33.txt, the points.
• set_33_dot.png, a PNG image of a dot plot.
• set_33_balloon.png, a PNG image of a balloon plot.

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

• set_34.txt, the points.
• set_34_dot.png, a PNG image of a dot plot.

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

• set_35.txt, the points.
• set_35_dot.png, a PNG image of a dot plot.

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

• set_36.txt, the points.
• set_36_dot.png, a PNG image of a dot plot.

You can go up one level to the DATASETS directory.