cvt_mod_dataset/cvt_mod_dataset.html

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      CVT_MOD_DATASET - Centroidal Voronoi Tessellation on Logical Torus
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      CVT_MOD_DATASET <br> Centroidal Voronoi Tessellation on Logical Torus
    </h1>

    <hr>

    <p>
      <b>CVT_MOD_DATASET</b>
      is a FORTRAN90 program which
      creates Centroidal Voronoi Tessellation (CVT) datasets in which the
      geometry is a logical torus.
    </p>

    <p>
      A 2D unit logical torus is the unit square, but with "wraparound".
      This is the connectivity frequently seen in video games, in which
      a spaceship flies off the top of the screen and immediately reappears
      at the bottom of the screen.  In the general M-dimensional case,
      the extreme minimum and maximum values of each coordinate are
      identified, and modular arithmetic may be used to determine
      distances.
    </p>

    <p>
      For details on the underlying CVT calculation, refer to
      <a href =
      "../../f_src/cvt_dataset/cvt_dataset.html">
      CVT_DATASET</a>.  This program is a modification of that one, in
      which distances are computed using modular arithmetic.  For the
      current code, the region is a unit hypercube, although there's
      no real difficulty in allowing the widths in each dimension to
      vary.
    </p>

    <p>
      A reasonable set of input commands might be:
      <pre>
        #  cvt_mod_02_00010.inp
        #
        m = 2
        n = 10
        seed = 123456789
        #
        initialize random
        sample_function_cvt = random
        sample_num_cvt = 500000
        iterate 100
        write cvt_mod_02_00010.txt
        #
        quit
      </pre>
    </p>

    <p>
      Here, the user first specifies the spatial dimension <b>M</b>, the
      number of generators <b>N</b>, and the random number seed
      (for later reproducibility).
    </p>

    <p>
      Then, the user specifies that the initial positions of the generators
      are to chosen at random; that during the iterations, the volume
      estimation will also be done using random sampling, and that the
      number of sampling points in an iteration will be 500,000.
      The <b>iterate 100</b> command causes 100 iterations to be carried
      out, and then the resulting generators are written to a file.
    </p>

    <h3 align = "center">
      Licensing:
    </h3>

    <p>
      The computer code and data files described and made available on this web page
      are distributed under
      <a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
    </p>

    <h3 align = "center">
      Related Data and Programs:
    </h3>

    <p>
      <a href = "../../f_src/cvt_mod/cvt_mod.html">
      CVT_MOD</a>,
      a FORTRAN90 library which
      contains routines which compute the datasets.
      A compiled copy of this library is necessary to build
      <b>CVT_MOD_DATASET</b>.
    </p>

    <p>
      <a href = "../../datasets/cvt_mod/cvt_mod.html">
      CVT_MOD</a>,
      a dataset directory which
      contains sample files created
      by <b>CVT_MOD_DATASET</b>.
    </p>

    <p>
      <a href = "../../f_src/faure_dataset/faure_dataset.html">
      FAURE_DATASET</a>,
      a FORTRAN90 program which
      creates a Faure quasirandom dataset;
    </p>

    <p>
      <a href = "../../f_src/grid_dataset/grid_dataset.html">
      GRID_DATASET</a>,
      a FORTRAN90 program which
      creates a grid sequence and writes it to a file.
    </p>

    <p>
      <a href = "../../f_src/latin_center_dataset/latin_center_dataset.html">
      LATIN_CENTER_DATASET</a>,
      a FORTRAN90 program which
      creates a Latin Center Hypercube dataset;
    </p>

    <p>
      <a href = "../../f_src/latin_edge_dataset/latin_edge_dataset.html">
      LATIN_EDGE_DATASET</a>,
      a FORTRAN90 program which
      creates a Latin Edge Hypercube dataset;
    </p>

    <p>
      <a href = "../../f_src/latin_random_dataset/latin_random_dataset.html">
      LATIN_RANDOM_DATASET</a>,
      a FORTRAN90 program which
      creates a Latin Random Hypercube dataset;
    </p>

    <p>
      <a href = "../../f_src/niederreiter2_dataset/niederreiter2_dataset.html">
      NIEDERREITER2_DATASET</a>,
      a FORTRAN90 program which
      creates a Niederreiter quasirandom dataset with base 2;
    </p>

    <p>
      <a href = "../../f_src/normal_dataset/normal_dataset.html">
      NORMAL_DATASET</a>,
      a FORTRAN90 program which
      generates a dataset of multivariate normal pseudorandom values and writes them to a file.
    </p>

    <p>
      <a href = "../../f_src/sobol_dataset/sobol_dataset.html">
      SOBOL_DATASET</a>,
      a FORTRAN90 program which
      computes a Sobol quasirandom sequence and writes it to a file.
    </p>

    <p>
      <a href = "../../f_src/uniform_dataset/uniform_dataset.html">
      UNIFORM_DATASET</a>,
      a FORTRAN90 program which
      generates a dataset of multivariate uniform pseudorandom values and writes them to a file.
    </p>

    <p>
      <a href = "../../f_src/van_der_corput_dataset/van_der_corput_dataset.html">
      VAN_DER_CORPUT_DATASET</a>,
      a FORTRAN90 program which
      creates a van der Corput quasirandom sequence and writes it to a file.
    </p>

    <h3 align = "center">
      Reference:
    </h3>

    <p>
      <ol>
        <li>
          Franz Aurenhammer,<br>
          Voronoi diagrams -
          a study of a fundamental geometric data structure,<br>
          ACM Computing Surveys,<br>
          Volume 23, Number 3, pages 345-405, September 1991.
        </li>
        <li>
          John Burkardt, Max Gunzburger, Janet Peterson, Rebecca Brannon,<br>
          User Manual and Supporting Information for Library of Codes
          for Centroidal Voronoi Placement and Associated Zeroth,
          First, and Second Moment Determination,<br>
          Sandia National Laboratories Technical Report SAND2002-0099,<br>
          February 2002,<br>
          <a href = "../../publications/bgpb_2002.pdf">
                    ../../publications/bgpb_2002.pdf </a>
        </li>
        <li>
          Qiang Du, Vance Faber, Max Gunzburger,<br>
          Centroidal Voronoi Tessellations: Applications and Algorithms,<br>
          SIAM Review, Volume 41, 1999, pages 637-676.
        </li>
        <li>
          Lili Ju, Qiang Du, Max Gunzburger,<br>
          Probabilistic methods for centroidal Voronoi tessellations
          and their parallel implementations,<br>
          Parallel Computing,<br>
          Volume 28, 2002, pages 1477-1500.
        </li>
      </ol>
    </p>

    <h3 align = "center">
      Source Code:
    </h3>

    <p>
      <ul>
        <li>
          <a href = "cvt_mod_dataset.f90">cvt_mod_dataset.f90</a>,
          the source code;
        </li>
        <li>
          <a href = "cvt_mod_dataset.sh">cvt_mod_dataset.sh</a>,
          commands to compile and load the source code;
        </li>
      </ul>
    </p>

    <h3 align = "center">
      List of Routines:
    </h3>

    <p>
      <ul>
        <li>
          <b>MAIN</b> is the main program for CVT_MOD_DATASET.
        </li>
      </ul>
    </p>

    <p>
      You can go up one level to <a href = "../f_src.html">
      the FORTRAN90 source codes</a>.
    </p>

    <hr>

    <i>
      Last revised on 26 November 2006.
    </i>

    <!-- John Burkardt -->

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