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<html>
<head>
<title>
LAMBERT - The Lambert Quasirandom Sequence.
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
LAMBERT <br> The Lambert Quasirandom Sequence.
</h1>
<hr>
<p>
<b>LAMBERT</b>
is a FORTRAN90 library which
implements the Lambert sequence in 1, 2, 3 or 4 dimensions.
</p>
<p>
The Lambert sequence is a sequence of points in M dimensions,
contained in the unit hypercube, and expressible as dyadic fractions,
that is, fractions whose denominator is a power of 2.
</p>
<p>
Drawbacks of the current implementation are that I don't
really understand the underlying principle, so I can't extend
it to higher dimensions, and I don't see how to "jump ahead"
in the sequence and compute, say, the 137th point without
computing the previous 136 values. It would also be nice to
extend the sequence to using other fractional bases besides 2.
</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">
Related 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 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/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/subpak/subpak.html">
SUBPAK</a>,
a FORTRAN90 library which
includes a routine <b>random_initialize</b>
that can be used to try to initialize the seed for the FORTRAN90
random number generator.
</p>
<p>
<a href = "../../f_src/uniform/uniform.html">
UNIFORM</a>,
a FORTRAN90 library which
computes elements of a uniform quasirandom sequence.
</p>
<p>
<a href = "../../f_src/uniform_dataset/uniform_dataset.html">
UNIFORM_DATASET</a>,
a FORTRAN90 program which
generates
a dataset of uniform pseudorandom values and write them to a file.
</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>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
J P Lambert,<br>
Quasi-Random Sequences for Optimization and Numerical Integration,<br>
in Numerical Integration,<br>
edited by P Keast and G Fairweather,<br>
D Reidel, 1987, pages 193-203.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "lambert.f90">lambert.f90</a>, the source code.
</li>
<li>
<a href = "lambert.sh">lambert.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "lambert_prb.f90">lambert_prb.f90</a>,
a sample calling program.
</li>
<li>
<a href = "lambert_prb.sh">lambert_prb.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "lambert_prb_output.txt">lambert_prb_output.txt</a>,
the output file.
</li>
<li>
<a href = "lambert_01_00050.txt">lambert_01_00050.txt</a>,
50 points of the 1D Lambert sequence.
</li>
<li>
<a href = "lambert_02_00050.txt">lambert_02_00050.txt</a>,
50 points of the 2D Lambert sequence.
</li>
<li>
<a href = "lambert_03_00050.txt">lambert_03_00050.txt</a>,
50 points of the 3D Lambert sequence.
</li>
<li>
<a href = "lambert_04_00050.txt">lambert_04_00050.txt</a>,
50 points of the 4D Lambert sequence.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>GET_UNIT</b> returns a free FORTRAN unit number.
</li>
<li>
<b>LAMBERT1</b> computes the Lambert sequence in 1D.
</li>
<li>
<b>LAMBERT2</b> computes the Lambert sequence in 2D.
</li>
<li>
<b>LAMBERT3</b> computes the Lambert sequence in 3D.
</li>
<li>
<b>LAMBERT4</b> computes the Lambert sequence in 4D.
</li>
<li>
<b>LAMBERT_WRITE</b> writes a Lambert dataset to a 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>
<hr>
<i>
Last revised on 08 December 2007.
</i>
<!-- John Burkardt -->
</body>
</html>