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<html>
<head>
<title>
IHS - Improved Distributed Hypercube Sampling
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
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>
<hr>
<i>
Last revised on 27 November 2006.
</i>
<!-- John Burkardt -->
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</html>