faure/faure.html

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      FAURE - The Faure Quasirandom Sequence
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      FAURE <br> The Faure Quasirandom Sequence
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    <p>
      <b>FAURE</b>
      is a FORTRAN90 library which
      computes elements of the Faure quasirandom sequence.
    </p>

    <p>
      A quasirandom or low discrepancy sequence, such as the Faure,
      Halton, Hammersley, Niederreiter or Sobol sequences, is
      "less random" than a pseudorandom number sequence, but
      more useful for such tasks as approximation of integrals in
      higher dimensions, and in global optimization.
      This is because low discrepancy sequences tend to sample
      space "more uniformly" than random numbers.  Algorithms
      that use such sequences may have superior convergence.
      Faure sequences, in particular, seem to have become popular
      in mathematical finance simulations.
    </p>

    <p>
      <b>FAURE</b> is adapted from code in ACM TOMS Algorithm 647.
      The original, true, correct version of ACM TOMS Algorithm 647
      is available in the TOMS subdirectory of
      <a href = "http://www.netlib.org/">the NETLIB web site</a>.
    </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">
      Languages:
    </h3>

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

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

    <p>
      <a href = "../../f_src/cvt/cvt.html">
      CVT</a>,
      a FORTRAN90 library which
      computes elements of a Centroidal Voronoi Tessellation.
    </p>

    <p>
      <a href = "../../datasets/faure/faure.html">
      FAURE</a>,
      a dataset directory which
      contains files of sample Faure datasets.
    </p>

    <p>
      <a href = "../../f_src/faure_dataset/faure_dataset.html">
      FAURE_DATASET</a>,
      a FORTRAN90 program which
      can create a Faure dataset.
    </p>

    <p>
      <a href = "../../f_src/grid/grid.html">
      GRID</a>,
      a FORTRAN90 library which
      computes elements of a grid dataset.
    </p>

    <p>
      <a href = "../../f_src/halton/halton.html">
      HALTON</a>,
      a FORTRAN90 library which
      computes elements of a Halton quasirandom sequence.
    </p>

    <p>
      <a href = "../../f_src/hammersley/hammersley.html">
      HAMMERSLEY</a>,
      a FORTRAN90 library which
      computes elements of a Hammersley quasirandom sequence.
    </p>

    <p>
      <a href = "../../f_src/hex_grid/hex_grid.html">
      HEX_GRID</a>,
      a FORTRAN90 library which
      computes elements of a hexagonal grid dataset.
    </p>

    <p>
      <a href = "../../f_src/hex_grid_angle/hex_grid_angle.html">
      HEX_GRID_ANGLE</a>,
      a FORTRAN90 library which
      computes elements of an angled hexagonal grid dataset.
    </p>

    <p>
      <a href = "../../f_src/ihs/ihs.html">
      IHS</a>,
      a FORTRAN90 library which
      computes elements of an improved distributed Latin hypercube dataset.
    </p>

    <p>
      <a href = "../../f_src/latin_center/latin_center.html">
      LATIN_CENTER</a>,
      a FORTRAN90 library which
      computes elements of a Latin Hypercube dataset, choosing center points.
    </p>

    <p>
      <a href = "../../f_src/latin_edge/latin_edge.html">
      LATIN_EDGE</a>,
      a FORTRAN90 library which
      computes elements of a Latin Hypercube dataset, choosing edge points.
    </p>

    <p>
      <a href = "../../f_src/latin_random/latin_random.html">
      LATIN_RANDOM</a>,
      a FORTRAN90 library which
      computes elements of a Latin Hypercube dataset, choosing
      points at random.
    </p>

    <p>
      <a href = "../../f_src/lattice_rule/lattice_rule.html">
      LATTICE_RULE</a>,
      a FORTRAN90 library which
      approximates multidimensional integrals using lattice rules.
    </p>

    <p>
      <a href = "../../f_src/lcvt/lcvt.html">
      LCVT</a>,
      a FORTRAN90 library which
      computes a latinized Centroidal Voronoi Tessellation.
    </p>

    <p>
      <a href = "../../f_src/niederreiter2/niederreiter2.html">
      NIEDERREITER2</a>,
      a FORTRAN90 library which
      computes elements of a Niederreiter quasirandom sequence with base 2.
    </p>

    <p>
      <a href = "../../f_src/normal/normal.html">
      NORMAL</a>,
      a FORTRAN90 library which
      computes elements of a sequence of pseudorandom normally distributed values.
    </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/toms647/toms647.html">
      TOMS647</a>,
      a FORTRAN90 library which
      is a version of ACM TOMS algorithm 647,
      for evaluating Faure, Halton and Sobol sequences.
    </p>

    <p>
      <a href = "../../f_src/uniform/uniform.html">
      UNIFORM</a>,
      a FORTRAN90 library which
      computes elements of a uniform pseudorandom sequence.
    </p>

    <p>
      <a href = "../../f_src/van_der_corput/van_der_corput.html">
      VAN_DER_CORPUT</a>,
      a FORTRAN90 library which
      computes elements of a van der Corput quasirandom sequence.
    </p>

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      Reference:
    </h3>

    <p>
      <ol>
        <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, July 1992, pages 195-213.
        </li>
        <li>
          Henri Faure,<br>
          Discrepance de suites associees a un systeme de numeration
          (en dimension s),<br>
          Acta Arithmetica,<br>
          Volume 41, 1982, pages 337-351.
        </li>
        <li>
          Henri Faure,<br>
          Good permutations for extreme discrepancy,<br>
          Journal of Number Theory,<br>
          Volume 42, 1992, pages 47-56.
        </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, December 1986, pages 362-376.
        </li>
      </ol>
    </p>

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      Source Code:
    </h3>

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

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      Examples and Tests:
    </h3>

    <p>
      <ul>
        <li>
          <a href = "faure_prb.f90">faure_prb.f90</a>,
          the sample test code;
        </li>
        <li>
          <a href = "faure_prb.sh">faure_prb.sh</a>,
          commands to compile the test code;
        </li>
        <li>
          <a href = "faure_prb_output.txt">faure_prb_output.txt</a>,
          the output file.
        </li>
      </ul>
    </p>

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

    <p>
      <ul>
        <li>
          <b>BINOMIAL_TABLE</b> computes a table of bionomial coefficients MOD QS.
        </li>
        <li>
          <b>FAURE</b> generates a new quasirandom Faure vector with each call.
        </li>
        <li>
          <b>FAURE_GENERATE</b> generates a Faure dataset.
        </li>
        <li>
          <b>GET_UNIT</b> returns a free FORTRAN unit number.
        </li>
        <li>
          <b>I4_LOG_I4</b> returns the logarithm of an I4 to an I4 base.
        </li>
        <li>
          <b>PRIME_GE</b> returns the smallest prime greater than or equal to N.
        </li>
        <li>
          <b>PRIME</b> returns any of the first PRIME_MAX prime numbers.
        </li>
        <li>
          <b>R8MAT_WRITE</b> writes an R8MAT file.
        </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 11 December 2009.
    </i>

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