GRID
Uniform Grid Datasets

GRID is a collection of datasets of points generated on an M-dimensional uniform grid, but with "holes".

The datasets are distinguished by the values of the following parameters:

• M, the spatial dimension;
• N, the number of points to generate;
• SEED, a seed for the random number generator;
• CENTER, the initial number of points to skip over (default = 0);

Note that, unless N is an Mth power of an integer, the program must generate a regular grid with too many points, and then omit some. Choosing which points to omit is done with a random number generator, whose actions are controlled by SEED.

The actual placement of the grid within the unit hypercube leaves some options for the use. It is easiest to describe the options in the 1 dimensional case, and in terms of where the first and last grid point are. Assuming we have N evenly spaced points to place between 0 and 1, the centering options are

• CENTER = 1: first point is 0.0, last point is 1.0;
• CENTER = 2: first point is 1/(N+1), last point is N/(N+1);
• CENTER = 3: first point is 0, last point is (N-1)/N;
• CENTER = 4: first point is 1/N, last point is 1;
• CENTER = 5: first point is 1/(2*N), last point is (2*N-1)/(2*N);

Related Data and Programs:

GRID_DATASET is an interactive program used to generate these datasets. The program is available in a C++ version, and a FORTRAN90 version, and a MATLAB version,

PLOT_POINTS is a FORTRAN90 program which can create Encapsulated PostScript images (EPS) of some of the two dimensional datasets.

TABLE is a file format used to store the data.

TABLE_TOP is a FORTRAN90 program which can display pairwise coordinate plots of higher dimensional datasets.

Example dataset:

A typical (but small) dataset looks like this:

#  grid_02_00010_1.txt
#  created by GRID_DATASET.
#
#  File generated on May 16 2003  11:58:31.614 AM
#
#  Spatial dimension M =      2
#  Number of points N =     10
#  Initial seed =    123456789
#  Grid centering =      1
#
  0.000000  0.000000
  0.000000  1.000000
  0.333333  0.000000
  0.333333  0.333333
  0.333333  0.666667
  0.333333  1.000000
  0.666667  0.000000
  0.666667  0.666667
  1.000000  0.000000
  1.000000  1.000000
      

Datasets:

Datasets in M = 2 dimensions, with CENTER = 1, include:

• grid_02_00010_1.txt, M = 2, N = 10, SEED = 123456789, CENTER = 1;
• grid_02_00010_1.png, a PNG image of the dataset;
• grid_02_00100_1.txt, M = 2, N = 100, SEED = 123456789, CENTER = 1;
• grid_02_00100_1.png, a PNG image of the dataset;
• grid_02_01000_1.txt, M = 2, N = 1000, SEED = 123456789, CENTER = 1;
• grid_02_01000_1.png, a PNG image of the dataset;
• grid_02_10000_1.txt, M = 2, N = 10000, SEED = 123456789, CENTER = 1;

Datasets in M = 2 dimensions, with CENTER = 2, include:

• grid_02_00010_2.txt, M = 2, N = 10, SEED = 123456789, CENTER = 2;
• grid_02_00100_2.txt, M = 2, N = 100, SEED = 123456789, CENTER = 2;
• grid_02_01000_2.txt, M = 2, N = 1000, SEED = 123456789, CENTER = 2;
• grid_02_10000_2.txt, M = 2, N = 10000, SEED = 123456789, CENTER = 2;

Datasets in M = 2 dimensions, with CENTER = 3, include:

• grid_02_00010_3.txt, M = 2, N = 10, SEED = 123456789, CENTER = 3;
• grid_02_00100_3.txt, M = 2, N = 100, SEED = 123456789, CENTER = 3;
• grid_02_01000_3.txt, M = 2, N = 1000, SEED = 123456789, CENTER = 3;
• grid_02_10000_3.txt, M = 2, N = 10000, SEED = 123456789, CENTER = 3;

Datasets in M = 2 dimensions, with CENTER = 4, include:

• grid_02_00010_4.txt, M = 2, N = 10, SEED = 123456789, CENTER = 4;
• grid_02_00100_4.txt, M = 2, N = 100, SEED = 123456789, CENTER = 4;
• grid_02_01000_4.txt, M = 2, N = 1000, SEED = 123456789, CENTER = 4;
• grid_02_10000_4.txt, M = 2, N = 10000, SEED = 123456789, CENTER = 4;

Datasets in M = 2 dimensions, with CENTER = 5, include:

• grid_02_00010_5.txt, M = 2, N = 10, SEED = 123456789, CENTER = 5;
• grid_02_00100_5.txt, M = 2, N = 100, SEED = 123456789, CENTER = 5;
• grid_02_01000_5.txt, M = 2, N = 1000, SEED = 123456789, CENTER = 5;
• grid_02_10000_5.txt, M = 2, N = 10000, SEED = 123456789, CENTER = 5;

Datasets in M = 7 dimensions, with CENTER = 1, include:

• grid_07_00010_1.txt, M = 7, N = 10, SEED = 123456789, CENTER = 1;
• grid_07_00100_1.txt, M = 7, N = 100, SEED = 123456789, CENTER = 1;
• grid_07_01000_1.txt, M = 7, N = 1000, SEED = 123456789, CENTER = 1;
• grid_07_10000_1.txt, M = 7, N = 10000, SEED = 123456789, CENTER = 1;

Datasets in M = 7 dimensions, with CENTER = 2, include:

• grid_07_00010_2.txt, M = 7, N = 10, SEED = 123456789, CENTER = 2;
• grid_07_00100_2.txt, M = 7, N = 100, SEED = 123456789, CENTER = 2;
• grid_07_01000_2.txt, M = 7, N = 1000, SEED = 123456789, CENTER = 2;
• grid_07_10000_2.txt, M = 7, N = 10000, SEED = 123456789, CENTER = 2;

Datasets in M = 7 dimensions, with CENTER = 3, include:

• grid_07_00010_3.txt, M = 7, N = 10, SEED = 123456789, CENTER = 3;
• grid_07_00100_3.txt, M = 7, N = 100, SEED = 123456789, CENTER = 3;
• grid_07_01000_3.txt, M = 7, N = 1000, SEED = 123456789, CENTER = 3;
• grid_07_10000_3.txt, M = 7, N = 10000, SEED = 123456789, CENTER = 3;

Datasets in M = 7 dimensions, with CENTER = 4, include:

• grid_07_00010_4.txt, M = 7, N = 10, SEED = 123456789, CENTER = 4;
• grid_07_00100_4.txt, M = 7, N = 100, SEED = 123456789, CENTER = 4;
• grid_07_01000_4.txt, M = 7, N = 1000, SEED = 123456789, CENTER = 4;
• grid_07_10000_4.txt, M = 7, N = 10000, SEED = 123456789, CENTER = 4;

Datasets in M = 7 dimensions, with CENTER = 5, include:

• grid_07_00010_5.txt, M = 7, N = 10, SEED = 123456789, CENTER = 5;
• grid_07_00100_5.txt, M = 7, N = 100, SEED = 123456789, CENTER = 5;
• grid_07_01000_5.txt, M = 7, N = 1000, SEED = 123456789, CENTER = 5;
• grid_07_10000_5.txt, M = 7, N = 10000, SEED = 123456789, CENTER = 5;

Datasets in M = 16 dimensions, with CENTER = 1, include:

• grid_16_00010_1.txt, M = 16, N = 10, SEED = 123456789, CENTER = 1;
• grid_16_00100_1.txt, M = 16, N = 100, SEED = 123456789, CENTER = 1;
• grid_16_01000_1.txt, M = 16, N = 1000, SEED = 123456789, CENTER = 1;
• grid_16_10000_1.txt, M = 16, N = 10000, SEED = 123456789, CENTER = 1;

Datasets in M = 16 dimensions, with CENTER = 2, include:

• grid_16_00010_2.txt, M = 16, N = 10, SEED = 123456789, CENTER = 2;
• grid_16_00100_2.txt, M = 16, N = 100, SEED = 123456789, CENTER = 2;
• grid_16_01000_2.txt, M = 16, N = 1000, SEED = 123456789, CENTER = 2;
• grid_16_10000_2.txt, M = 16, N = 10000, SEED = 123456789, CENTER = 2;

Datasets in M = 16 dimensions, with CENTER = 3, include:

• grid_16_00010_3.txt, M = 16, N = 10, SEED = 123456789, CENTER = 3;
• grid_16_00100_3.txt, M = 16, N = 100, SEED = 123456789, CENTER = 3;
• grid_16_01000_3.txt, M = 16, N = 1000, SEED = 123456789, CENTER = 3;
• grid_16_10000_3.txt, M = 16, N = 10000, SEED = 123456789, CENTER = 3;

Datasets in M = 16 dimensions, with CENTER = 4, include:

• grid_16_00010_4.txt, M = 16, N = 10, SEED = 123456789, CENTER = 4;
• grid_16_00100_4.txt, M = 16, N = 100, SEED = 123456789, CENTER = 4;
• grid_16_01000_4.txt, M = 16, N = 1000, SEED = 123456789, CENTER = 4;
• grid_16_10000_4.txt, M = 16, N = 10000, SEED = 123456789, CENTER = 4;

Datasets in M = 16 dimensions, with CENTER = 5, include:

• grid_16_00010_5.txt, M = 16, N = 10, SEED = 123456789, CENTER = 5;
• grid_16_00100_5.txt, M = 16, N = 100, SEED = 123456789, CENTER = 5;
• grid_16_01000_5.txt, M = 16, N = 1000, SEED = 123456789, CENTER = 5;
• grid_16_10000_5.txt, M = 16, N = 10000, SEED = 123456789, CENTER = 5;

You can go up one level to the DATASETS directory.