sobol_dataset/sobol_dataset.html

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      SOBOL_DATASET - Generate Sobol Datasets
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      SOBOL_DATASET <br> Generate Sobol Datasets
    </h1>

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    <p>
      <b>SOBOL_DATASET</b>
      is a FORTRAN90 program which
      creates a Sobol dataset.
    </p>

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

    <p>
      <blockquote>
        <b>sobol_dataset</b> <i>m</i> <i>n</i> <i>skip</i>
      </blockquote>
      where
      <ul>
        <li>
          <i>m</i> is the spatial dimension.
        </li>
        <li>
          <i>n</i> is the number of points to generate;
        </li>
        <li>
          <i>skip</i> is the initial number of points to skip over.
          The value of <i>skip</i> is used to allow the sequence to
          "warm up".  One common strategy is to set <i>skip</i> to
          the smallest power of 2 which is equal to or greater than <i>n</i>.
        </li>
      </ul>
      The data is written to the file <b>sobol_<i>m</i>_<i>n</i>.txt</b>.
    </p>

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      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>

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      Languages:
    </h3>

    <p>
      <b>SOBOL_DATASET</b> is available in
      <a href = "../../cpp_src/sobol_dataset/sobol_dataset.html">a C++ version</a> and
      <a href = "../../f_src/sobol_dataset/sobol_dataset.html">a FORTRAN90 version</a> and
      <a href = "../../m_src/sobol_dataset/sobol_dataset.html">a MATLAB version</a>.
    </p>

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

    <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 = "../../datasets/sobol/sobol.html">
      SOBOL</a>,
      a dataset directory which
      contains sample Sobol datasets
      created by <b>SOBOL_DATASET</b>.
    </p>

    <p>
      <a href = "../../f_src/sobol/sobol.html">
      SOBOL</a>,
      a FORTRAN90 library which
      computes elements of a Sobol quasirandom sequence.
    </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>
          IA Antonov, VM Saleev,<br>
          An Economic Method of Computing LP Tau-Sequences,<br>
          USSR Computational Mathematics and Mathematical Physics,<br>
          Volume 19, 1980, pages 252 - 256.
        </li>
        <li>
          Paul Bratley, Bennett Fox,<br>
          Algorithm 659:
          Implementing Sobol's Quasirandom Sequence Generator,<br>
          ACM Transactions on Mathematical Software,<br>
          Volume 14, Number 1, pages 88-100, 1988.
        </li>
        <li>
          Paul Bratley, Bennett Fox, Linus Schrage,<br>
          A Guide to Simulation,<br>
          Springer Verlag, pages 201-202, 1983.
        </li>
        <li>
          Paul Bratley, Bennett Fox, Harald Niederreiter,<br>
          Implementation and Tests of Low Discrepancy Sequences,<br>
          ACM Transactions on Modeling and Computer Simulation,<br>
          Volume 2, Number 3, pages 195-213, 1992.
        </li>
        <li>
          Bennett Fox,<br>
          Algorithm 647:
          Implementation and Relative Efficiency of Quasirandom
          Sequence Generators,<br>
          ACM Transactions on Mathematical Software,<br>
          Volume 12, Number 4, pages 362-376, 1986.
        </li>
        <li>
          Harald Niederreiter,<br>
          Random Number Generation and quasi-Monte Carlo Methods,<br>
          SIAM, 1992.
        </li>
        <li>
          William Press, Brian Flannery, Saul Teukolsky, William Vetterling,<br>
          Numerical Recipes: The Art of Scientific Computing,<br>
          Cambridge University Press.
        </li>
        <li>
          Ilya Sobol,<br>
          USSR Computational Mathematics and Mathematical Physics,<br>
          Volume 16, pages 236-242, 1977.
        </li>
        <li>
          Ilya Sobol, Levitan, <br>
          The Production of Points Uniformly Distributed in a Multidimensional
          Cube (in Russian),<br>
          Preprint IPM Akad. Nauk SSSR, <br>
          Number 40, Moscow 1976.
        </li>
      </ol>
    </p>

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      Source Code:
    </h3>

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

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      Examples and Tests:
    </h3>

    <p>
      <ul>
        <li>
          <a href = "sobol_02_00100.txt">sobol_02_00100.txt</a>,
          the Sobol dataset of dimension 2, computing 100 points, after skipping 128 points.
        </li>
      </ul>
    </p>

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      List of Routines:
    </h3>

    <p>
      <ul>
        <li>
          <b>MAIN</b> is the main program for SOBOL_DATASET.
        </li>
        <li>
          <b>GET_UNIT</b> returns a free FORTRAN unit number.
        </li>
        <li>
          <b>I8_BIT_HI1</b> returns the position of the high 1 bit base 2 in an integer.
        </li>
        <li>
          <b>I8_BIT_LO0</b> returns the position of the low 0 bit base 2 in an integer.
        </li>
        <li>
          <b>I8_SOBOL</b> generates a new quasirandom Sobol vector with each call.
        </li>
        <li>
          <b>I8_SOBOL_GENERATE</b> generates a Sobol dataset.
        </li>
        <li>
          <b>R8MAT_WRITE</b> writes an R8MAT file.
        </li>
        <li>
          <b>S_TO_I4</b> reads an integer value from a string.
        </li>
        <li>
          <b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
        </li>
      </ul>
    </p>

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

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    <i>
      Last revised on 30 August 2005.
    </i>

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