ihs/ihs.html

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      IHS - Improved Distributed Hypercube Sampling
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      IHS <br> Improved Distributed Hypercube Sampling
    </h1>

    <hr>

    <p>
      <b>IHS</b>
      is a FORTRAN90 library which
      carries out the improved distributed hypercube sampling algorithm.
    </p>

    <p>
      N Points in an M dimensional Latin hypercube are to be selected.
      Each of the M coordinate dimensions is discretized to the values
      1 through N.  The points are to be chosen in such a way that
      no two points have any coordinate value in common.  This is
      a standard Latin hypercube requirement, and there are many
      solutions.
    </p>

    <p>
      This algorithm differs in that it tries to pick a solution
      which has the property that the points are "spread out"
      as evenly as possible.  It does this by determining an optimal
      even spacing, and using the duplication factor D to allow it
      to choose the best of the various options available to it
      (the more duplication, the better chance of optimization).
    </p>

    <p>
      One drawback to this algorithm is that it requires an internal
      real distance array of dimension D * N * N.  For a relatively moderate
      problem with N = 1000, this can exceed the easily accessible
      memory.  Moreover, the program is inherently quadratic
      in execution time as well as memory; the computation of the I-th
      point in the set of N requires a consideration of the value of
      the coordinates used up by the previous points, and the distances
      from each of those points to the candidates for the next point.
    </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>IHS</b> is available in
      <a href = "../../cpp_src/ihs/ihs.html">a C++ version</a> and
      <a href = "../../f_src/ihs/ihs.html">a FORTRAN90 version</a> and
      <a href = "../../m_src/ihs/ihs.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 = "../../f_src/faure/faure.html">
      FAURE</a>,
      a FORTRAN90 library which
      computes elements of a Faure quasirandom sequence.
    </p>

    <p>
      <a href = "../../f_src/grid/grid.html">
      GRID</a>,
      a FORTRAN90 library which
      computes elements of a grid sequence.
    </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/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 using 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 = "../../cpp_src/table_quality/table_quality.html">
      TABLE_QUALITY</a>,
      a C++ program which
      measures the dispersion quality of points in a dataset read from a file.
    </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 1D van der Corput sequence.
    </p>

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

    <p>
      <ol>
        <li>
          Brian Beachkofski, Ramana Grandhi,<br>
          Improved Distributed Hypercube Sampling,<br>
          American Institute of Aeronautics and Astronautics Paper 2002-1274.
        </li>
      </ol>
    </p>

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

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

    <h3 align = "center">
      Examples and Tests:
    </h3>

    <p>
      <ul>
        <li>
          <a href = "ihs_prb.f90">ihs_prb.f90</a>,
          a sample calling program.
        </li>
        <li>
          <a href = "ihs_prb.sh">ihs_prb.sh</a>,
          commands to compile and run the sample program.
        </li>
        <li>
          <a href = "ihs_prb_output.txt">ihs_prb_output.txt</a>,
          the output file.
        </li>
      </ul>
    </p>

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

    <p>
      <ul>
        <li>
          <b>COVARIANCE</b> does a covariance calculation for IHS solutions.
        </li>
        <li>
          <b>GET_SEED</b> returns a seed for the random number generator.
        </li>
        <li>
          <b>GET_UNIT</b> returns a free FORTRAN unit number.
        </li>
        <li>
          <b>I4_UNIFORM</b> returns a scaled pseudorandom I4.
        </li>
        <li>
          <b>I4VEC_UNIFORM</b> returns a scaled pseudorandom I4VEC.
        </li>
        <li>
          <b>IHS</b> implements the improved distributed hypercube sampling algorithm.
        </li>
        <li>
          <b>IHS_WRITE</b> writes an IHS dataset to a file.
        </li>
        <li>
          <b>R4_UNIFORM_01</b> returns a unit pseudorandom R4.
        </li>
        <li>
          <b>R8_UNIFORM_01</b> returns a unit pseudorandom R8.
        </li>
        <li>
          <b>R8VEC_STD</b> returns the standard deviation of a real vector.
        </li>
        <li>
          <b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
        </li>
        <li>
          <b>TIMESTRING</b> writes the current YMDHMS date into a string.
        </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 27 November 2006.
    </i>

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