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<html>
<head>
<title>
BOX_BEHNKEN - Box-Behnken Sampling
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
BOX_BEHNKEN <br> Box-Behnken Sampling
</h1>
<hr>
<p>
<b>BOX_BEHNKEN</b>
is a C++ library which
returns a set of sample argument values to be
used to analyze the behavior of a function.
</p>
<p>
Given <b>DIM_NUM</b> parameters, each of which is prescribed to
lie between a minimum and maximum range, and a function taking
these parameters as arguments, this program returns a table of
sets of argument values that may be used to sample the function's
behavior.
</p>
<p>
One sample point is the average. All other sample points are generated
by setting a single spatial coordinate to its average value, and
all other spatial coordinates to either the minimum or maximum. In
this way, 1 + <b>DIM_NUM</b>*2**(<b>DIM_NUM</b>-1) points are generated.
</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>BOX_BEHNKEN</b> is available in
<a href = "../../c_src/box_behnken/box_behnken.html">a C version</a> and
<a href = "../../cpp_src/box_behnken/box_behnken.html">a C++ version</a> and
<a href = "../../f77_src/box_behnken/box_behnken.html">a FORTRAN77 version</a> and
<a href = "../../f_src/box_behnken/box_behnken.html">a FORTRAN90 version</a> and
<a href = "../../m_src/box_behnken/box_behnken.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/cvt/cvt.html">
CVT</a>,
a C++ library which
computes elements of a Centroidal Voronoi Tessellation.
</p>
<p>
<a href = "../../cpp_src/faure/faure.html">
FAURE</a>,
a C++ library which
computes elements of a Faure sequence.
</p>
<p>
<a href = "../../cpp_src/grid/grid.html">
GRID</a>,
a C++ library which
computes elements of a grid sequence.
</p>
<p>
<a href = "../../cpp_src/halton/halton.html">
HALTON</a>,
a C++ library which
computes elements of a Halton sequence.
</p>
<p>
<a href = "../../cpp_src/hammersley/hammersley.html">
HAMMERSLEY</a>,
a C++ library which
computes elements of a Hammersley sequence.
</p>
<p>
<a href = "../../cpp_src/hex_grid/hex_grid.html">
HEX_GRID</a>,
a C++ library which
computes elements of a hexagonal grid dataset.
</p>
<p>
<a href = "../../cpp_src/ihs/ihs.html">
IHS</a>,
a C++ library which
computes elements of an improved distributed Latin hypercube dataset.
</p>
<p>
<a href = "../../cpp_src/latin_center/latin_center.html">
LATIN_CENTER</a>,
a C++ library which
computes elements of a Latin Hypercube dataset, choosing center points.
</p>
<p>
<a href = "../../cpp_src/latin_edge/latin_edge.html">
LATIN_EDGE</a>,
a C++ library which
computes elements of a Latin Hypercube dataset, choosing edge points.
</p>
<p>
<a href = "../../cpp_src/latin_random/latin_random.html">
LATIN_RANDOM</a>,
a C++ library which
computes elements of a Latin Hypercube dataset, choosing
points at random.
</p>
<p>
<a href = "../../cpp_src/latinize/latinize.html">
LATINIZE</a>,
a C++ library which
can "latinize" a dataset.
</p>
<p>
<a href = "../../cpp_src/lcvt/lcvt.html">
LCVT</a>,
a C++ library which
computes a latinized Centroidal Voronoi Tessellation.
</p>
<p>
<a href = "../../cpp_src/niederreiter2/niederreiter2.html">
NIEDERREITER2</a>,
a C++ library which
computes elements of a Niederreiter sequence using base 2.
</p>
<p>
<a href = "../../cpp_src/sobol/sobol.html">
SOBOL</a>,
a C++ library which
computes elements of a Sobol sequence.
</p>
<p>
<a href = "../../cpp_src/table_latinize/table_latinize.html">
TABLE_LATINIZE</a>,
a C++ program which
reads a table file containing a set of data, and writes out a corresponding
"latinized" version.
</p>
<p>
<a href = "../../cpp_src/uniform/uniform.html">
UNIFORM</a>,
a C++ library which
computes elements of a uniform pseudorandom sequence.
</p>
<p>
<a href = "../../cpp_src/van_der_corput/van_der_corput.html">
VAN_DER_CORPUT</a>,
a C++ library which
computes elements of a (1 dimensional) van der Corput sequence.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
George Box, Donald Behnken,<br>
Some new three level designs for the study of quantitative variables,<br>
Technometrics,<br>
Volume 2, pages 455-475, 1960.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "box_behnken.cpp">box_behnken.cpp</a>, the source code.
</li>
<li>
<a href = "box_behnken.hpp">box_behnken.hpp</a>, the include file.
</li>
<li>
<a href = "box_behnken.sh">box_behnken.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "box_behnken_prb.cpp">box_behnken_prb.cpp</a>,
a sample calling program.
</li>
<li>
<a href = "box_behnken_prb.sh">box_behnken_prb.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "box_behnken_prb_output.txt">box_behnken_prb_output.txt</a>,
the output file.
</li>
<li>
<a href = "box_behnken_04_33.txt">box_behnken_04_33.txt</a>,
contains a Box-Behnken dataset of 33 values for 4 parameters.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>BOX_BEHNKEN</b> returns a Box-Behnken design for the given number of factors.
</li>
<li>
<b>BOX_BEHNKEN_SIZE</b> returns the size of a Box-Behnken design.
</li>
<li>
<b>I4_MAX</b> returns the maximum of two I4's.
</li>
<li>
<b>I4_MIN</b> returns the minimum of two I4's.
</li>
<li>
<b>I4_POWER</b> returns the value of I^J.
</li>
<li>
<b>R8MAT_TRANSPOSE_PRINT</b> prints an R8MAT, transposed.
</li>
<li>
<b>R8MAT_TRANSPOSE_PRINT_SOME</b> prints some of an R8MAT, transposed.
</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 = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last revised on 27 October 2008.
</i>
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