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<html>
<head>
<title>
GRID - Random Points on a Uniform Grid
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
GRID <br> Random Points on a Uniform Grid
</h1>
<hr>
<p>
<b>GRID</b>
is a FORTRAN90 library which
randomly selects N points on a uniform
grid in the unit hypercube in M-dimensional space.
</p>
<p>
Note that, unless N is an Mth power of an integer, the program
must generate a regular grid with too many points, and then omit some.
Choosing which points to omit is done with a random number generator,
whose actions are controlled by SEED.
</p>
<p>
The actual placement of the grid within the unit hypercube
leaves some options for the use. It is easiest to describe the
options in the 1 dimensional case, and in terms of where the
first and last grid point are. Assuming we have N evenly spaced
points to place between 0 and 1, the centering options are
<ul>
<li>
CENTER = 1: first point is 0.0, last point is 1.0;
</li>
<li>
CENTER = 2: first point is 1/(N+1), last point is N/(N+1);
</li>
<li>
CENTER = 3: first point is 0, last point is (N-1)/N;
</li>
<li>
CENTER = 4: first point is 1/N, last point is 1;
</li>
<li>
CENTER = 5: first point is 1/(2*N), last point is (2*N-1)/(2*N);
</li>
</ul>
</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>GRID</b> is available in
<a href = "../../cpp_src/grid/grid.html">a C++ version</a> and
<a href = "../../f_src/grid/grid.html">a FORTRAN90 version</a> and
<a href = "../../m_src/grid/grid.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/clenshaw_curtis_rule/clenshaw_curtis_rule.html">
CLENSHAW_CURTIS_RULE</a>,
a FORTRAN90 library which
can set up a
Clenshaw Curtis quadrature grid in multiple dimensions.
</p>
<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_dataset/grid_dataset.html">
GRID_DATASET</a>,
a FORTRAN90 program which
allows the user to specify 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/triangle_grid/triangle_grid.html">
TRIANGLE_GRID</a>,
a FORTRAN90 library which
computes a triangular grid of points.
</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>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "grid.f90">grid.f90</a>, the source code.
</li>
<li>
<a href = "grid.sh">grid.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "grid_prb.f90">grid_prb.f90</a>, a sample problem.
</li>
<li>
<a href = "grid_prb.sh">grid_prb.sh</a>,
commands to compile, link and run the sample problem.
</li>
<li>
<a href = "grid_prb_output.txt">grid_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<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>GRID_GENERATE</b> generates a grid dataset.
</li>
<li>
<b>GRID_SIDE</b> finds the smallest grid containing at least N points.
</li>
<li>
<b>I4_HUGE</b> returns a "huge" I4.
</li>
<li>
<b>KSUB_RANDOM2</b> selects a random subset of size K from a set of size N.
</li>
<li>
<b>R8_UNIFORM_01</b> returns a unit pseudorandom R8.
</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>
<li>
<b>TUPLE_NEXT_FAST</b> computes the next element of a tuple space, "fast".
</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 13 December 2009.
</i>
<!-- John Burkardt -->
</body>
</html>