TABLE Files
A file format for double indexed data

These are some examples of TABLE files, which are a simple homegrown storage format for doubly indexed data.

A TABLE file has a simple structure. There are three kinds of records:

• COMMENT LINES begin with the character '#' and are ignored;
• BLANK LINES are ignored, but could be used by a particular program to indicate some intending grouping or separation of records.
• COORDINATE LINES each contain one set of point coordinates;

Example TABLE Files:

Example: 3 points in 2D

        #  Corners of a triangle
        #
        0.0  0.0
        1.0  0.0
        0.0  1.0
      

Example: 4 points in 3D

        #  Corners of a tetrahedron
        #
        0.0  0.0  0.0
        1.0  0.0  0.0
        0.0  1.0  0.0
        0.0  0.0  1.0
      

Example: 3 points in 7D

        #  Three points in 7 dimensions.
        #
        0.7  0.2  0.2  0.3  0.5  0.6  0.3
        1.9  1.3  1.2  2.2  2.2  2.2  9.1
        0.9  0.7  1.1  0.4  0.8  2.7  0.0
      

Related Data and Programs:

Two special cases of this format are

• XY files, for 2D data;
• XYZ files, for 3D data;

TABLE File Characteristics:

• ASCII
• No compression
• 1 "image"

Programs to create a TABLE file:

• CCVT_BOX produces a TABLE file of N points in 2 dimensions, as a centroidal Voronoi tessellation, in a box, with given point density, and with some points projected onto the boundary.
• CVT_DATASET, available in a C++ version, a FORTRAN90 version, and a MATLAB version, produces a TABLE file of N points in M dimensions, as a centroidal Voronoi tessellation.
• CVT_MOD_DATASET produces a TABLE file of N points in M dimensions, as a centroidal Voronoi tessellation on a unit hypercube with modular arithmetic.
• FAURE_DATASET produces a TABLE file of N points in M dimensions, from a Faure sequence.
• GRID_DATASET produces a TABLE file of N points in M dimensions, as a regular grid.
• HALTON_DATASET, available in a C++ version and a FORTRAN90 version, and a MATLAB version, produces a TABLE file of N points in M dimensions, from a Halton sequence.
• HAMMERSLEY_DATASET, available in a C++ version and a FORTRAN90 version, and a MATLAB version, produces a TABLE file of N points in M dimensions, from a Hammersley sequence.
• HEX_GRID_DATASET, available in a C++ version, a FORTRAN90 version, and a MATLAB version, produces a TABLE file of N points in 2 dimensions, as a hexagonal grid of points in a rectangle.
• IHS_DATASET produces a TABLE file of N points in M dimensions, from an Improved Hypercube Sampling pointset.
• LATIN_CENTER_DATASET produces a TABLE file of N points in M dimensions, from a Latin hypercube pointset with centering.
• LATIN_EDGE_DATASET produces a TABLE file of N points in M dimensions, from a Latin hypercube pointset with edge "centering".
• LATIN_RANDOM_DATASET produces a TABLE file of N points in M dimensions, from a Latin hypercube pointset with random "centering".
• LCVT_DATASET produces a TABLE file of N points in M dimensions, containing a Latin hypercube dataset derived from a centroidal Voronoi tessellation.
• NIEDERREITER2_DATASET produces a TABLE file of N points in M dimensions, from a Niederreiter sequence base 2.
• RANDOM_DATA can produce a set of points that are randomly sampled from a given 2D or 3D geometric shape.
• RBOX will produce a random sample of points according to a given distribution, and over a given geometric shape. The resulting output file is ALMOST a TABLE file (you just need to delete the two initial records that list the spatial dimension and number of points.)
• RSITES will produce a set of N points in M dimensional space, with the user allowed to specify the SEED to be passed to the C++ RAND routine. Point coordinates are integers between 0 and 999999.
• SOBOL_DATASET produces a TABLE file of N points in M dimensions, from a Sobol sequence.
• UNIFORM_DATASET, available in a C++ version, a FORTRAN90 version, and a MATLAB version, produces a TABLE file of N points in M dimensions, containing a uniform pseudorandom sequence.

Programs to view a TABLE file:

• PLOT_POINTS will read a TABLE file, allow the user to choose any two coordinates to play the role of X and Y, and create an Encapsulated PostScript graphics file image of the (X,Y) projection of the points. It can also compute and display Voronoi diagrams and Delaunay triangulations in this two dimensional projection.
• TABLE_BARPLOT_PPMA will read a TABLE file and create a PPMA graphics file representation of the data as a bar plot.
• TABLE_HISTOGRAM will read a TABLE file and create a historgram of the data.
• TABLE_TOP reads a TABLE file and creates plots of all pairs of data coordinates, creating one PostScript graphics file of the results.
• TABLE_VORONOI will read a TABLE file of N points in 2D, compute and print information about the Voronoi diagram defined by the points.

Programs to process a TABLE file:

• DECOMMENT will read a TABLE file and write out a copy, from which all the comment lines have been deleted.
• TABLE_BORDER will read a TABLE file representing an N1 by N2 dataset and write out a copy, representing an (N1+2) by (N2+2) dataset, in which the additional entries are zeros, presumably representing boundary values along the geometric border of the N1 by N2 data.
• TABLE_COLUMNS will read a TABLE file and write out a copy, in which the user can specify which columns are to be selected, in what order they show up, and whether they are repeated.
• TABLE_DELAUNAY will read a TABLE file of N points in 2D, compute and print information about the Delaunay triangulation defined by the points.
• TABLE_DIAPHONY will read a TABLE file and compute the diaphony, a measure of the uniformity of the point dispersion in the unit hypercube.
• TABLE_DISCREPANCY will read a TABLE file and compute upper and lower bounds for the discrepancy, a measure of the uniformity of the point dispersion in the unit hypercube.
• TABLE_LATINIZE, available in a C++ version, a FORTRAN90 version, and a MATLAB version, is a program which reads a TABLE file and adjusts it so that it is a Latin hypercube.
• TABLE_ORTHONORMALIZE reads a set of 2D TABLE files (XY files) with numerically increasing names, and outputs an orthonormal set of vectors that span the same space.
• TABLE_QUALITY, available in a C++ version, a FORTRAN90 version, and a MATLAB version, reads a TABLE file of N points in M dimensions, contained in the unit hypercube, and produces measures of the uniform dispersion of the points.
• TABLE_SCALE is a FORTRAN90 program which reads a TABLE file and outputs a copy with every vector multiplied by a given scale vector.
• TABLE_SHIFT is a FORTRAN90 program which reads a TABLE file and outputs a copy with a fixed displacement vector added to every data point.
• TABLE_UNIFORM_NOISE is a FORTRAN90 program which reads a TABLE file and outputs a copy with every entry modified by the addition of scaled uniform noise.
• TABLE_VORONOI will read a TABLE file of N points in 2D, compute and print information about the Voronoi diagram defined by the points.

Routines to read a TABLE file:

• TABLE_IO, available in a C++ version, a FORTRAN90 version, and a MATLAB version, is a library of routines that can read a TABLE file.
• TABLE_READ is a simple MATLAB script which will read a TABLE file.

Routines to write a TABLE file:

• TABLE_IO, available in a C++ version, a FORTRAN90 version, and a MATLAB version, is a library of routines that can write a TABLE file.

Examples of TABLE files:

• The CVT dataset collection, tables of pointsets in M dimensions, generated by the centroidal Voronoi tessellation technique;
• The CVT MOD dataset collection, tables of pointsets in M dimensions, generated by the centroidal Voronoi tessellation technique with a special modularized geometry that eliminates boundary effects;
• diamond_02_00009.txt, 9 points in 2D, whose Voronoi diagram includes a diamond;
• The FAURE dataset collection, tables of pointsets in M dimensions, generated by the Faure quasirandom sequence;
• The GRID dataset collection, tables of pointsets in M dimensions, generated by choosing (some) points on a regular grid;
• The HALTON dataset collection, tables of pointsets in M dimensions, generated by the Halton quasirandom sequence;
• The HAMMERSLEY dataset collection, tables of pointsets in M dimensions, generated by the Hammersley quasirandom sequence;
• The HEX GRID dataset collection, tables of pointsets in M dimensions, generated by constructing a hexagonal grid in a rectangle;
• The Improved Hyper Square dataset collection, tables of pointsets in M dimensions which are Latin hypercubes, with a shuffling scheme applied to improve the distribution;
• The LATIN CENTER dataset collection, tables of pointsets in M dimensions which are Latin hypercubes, with each point chosen in the center of its subsquare;
• The LATIN EDGE dataset collection, tables of pointsets in M dimensions which are Latin hypercubes, with the point chosens as the corners of the subsquares;
• The LATIN RANDOM dataset collection, tables of pointsets in M dimensions which are Latin hypercubes, with each point chosen randomly from a subsquare;
• The LCVT dataset collection, tables of pointsets in M dimensions, generated by the "latinized" CVT technique;
• The LCVT MOD dataset collection, tables of pointsets in M dimensions, generated by the "latinized" CVT technique with a MOD operation employed to eliminate boundary effects;
• The LHS dataset collection, tables of pointsets in M dimensions, generated by the Latin Hyper Square system;
• The NIEDERREITER2 dataset collection, tables of pointsets in M dimensions, generated by the Niederreiter quasirandom sequence with base 2;
• The orthogonal array collection, tables of integer matrices, which are a generalization of Latin squares;
• The Romero dataset collection, tables of pointsets in M dimensions, generated by the "latinized" CVT technique;
• The SAMPLE2D dataset collection, tables of pointsets in M dimensions, generated by a variety of techniques;
• The SOBOL dataset collection, tables of pointsets in M dimensions, generated by the Sobol quasirandom sequence;
• the SPAETH dataset, a set of files of data for demonstrating clustering techniques.
• the SPAETH2 dataset, a set of files of data for demonstrating clustering techniques.
• tetrahedron_03_00004.txt, 4 points in 3D, which form a tetrahedron;
• The UNIFORM dataset collection, tables of pointsets in M dimensions, generated by a a simple uniform pseudorandom number generator;

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