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<html>
<head>
<title>
POISSON_SIMULATION - Simulation of a Poisson Process
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
POISSON_SIMULATION <br> Simulation of a Poisson Process
</h1>
<hr>
<p>
<b>POISSON_SIMULATION</b>
is a C++ program which
simulates a Poisson process in which events occur uniformly at random,
with an average waiting time of Lambda,
creating output for graphics by gnuplot.
</p>
<p>
Note that the Poisson distribution therefore also describes the
distribution of distances from one point to the next, assuming the
points are distributed uniformly at random along a line, with
average density Lambda per unit length.
</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>POISSON_SIMULATION</b> is available in
<a href = "../../c_src/poisson_simulation/poisson_simulation.html">a C version</a> and
<a href = "../../cpp_src/poisson_simulation/poisson_simulation.html">a C++ version</a> and
<a href = "../../f77_src/poisson_simulation/poisson_simulation.html">a FORTRAN77 version</a> and
<a href = "../../f_src/poisson_simulation/poisson_simulation.html">a FORTRAN90 version</a> and
<a href = "../../m_src/poisson_simulation/poisson_simulation.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/brownian_motion_simulation/brownian_motion_simulation.html">
BROWNIAN_MOTION_SIMULATION</a>,
a C++ library which
simulates Brownian motion in an M-dimensional region.
</p>
<p>
<a href = "../../cpp_src/duel_simulation/duel_simulation.html">
DUEL_SIMULATION</a>,
a C++ program which
simulates N repetitions of a duel between two players, each of
whom has a known firing accuracy.
</p>
<p>
<a href = "../../cpp_src/fair_dice_simulation/fair_dice_simulation.html">
FAIR_DICE_SIMULATION</a>,
a C++ program which
simulates N tosses of 2 dice, making a histogram of the results.
</p>
<p>
<a href = "../../cpp_src/gnuplot/gnuplot.html">
GNUPLOT</a>,
C++ programs which
illustrate the use of the gnuplot graphics program.
</p>
<p>
<a href = "../../cpp_src/high_card_simulation/high_card_simulation.html">
HIGH_CARD_SIMULATION</a>,
a C++ program which
simulates a situation in which you see the cards in a deck one by one,
and must select the one you think is the highest and stop;
the program uses GNUPLOT for graphics.
</p>
<p>
<a href = "../../cpp_src/ising_2d_simulation/ising_2d_simulation.html">
ISING_2D_SIMULATION</a>,
a C++ program which
carries out a Monte Carlo simulation of an Ising model,
a 2D array of positive and negative charges,
each of which is likely to "flip" to be in agreement with neighbors.
</p>
<p>
<a href = "../../cpp_src/life_opengl/life_opengl.html">
LIFE_OPENGL</a>,
a C++ program which
uses OpenGL to display the evolution of John Conway's "Game of Life".
</p>
<p>
<a href = "../../cpp_src/reactor_simulation/reactor_simulation.html">
REACTOR_SIMULATION</a>,
a C++ program which
a simple Monte Carlo simulation of the shielding effect of a slab
of a certain thickness in front of a neutron source. This program was
provided as an example with the book "Numerical Methods and Software."
</p>
<p>
<a href = "../../cpp_src/three_body_simulation/three_body_simulation.html">
THREE_BODY_SIMULATION</a>,
a C++ program which
simulates the behavior of three planets, constrained to lie in a plane,
and moving under the influence of gravity,
by Walter Gander and Jiri Hrebicek.
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "poisson_simulation.cpp">poisson_simulation.cpp</a>, the source code.
</li>
<li>
<a href = "poisson_simulation.hpp">poisson_simulation.hpp</a>, the source code.
</li>
<li>
<a href = "poisson_simulation.sh">poisson_simulation.sh</a>,
BASH commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "poisson_simulation_prb.cpp">poisson_simulation_prb.cpp</a>,
a sample calling program.
</li>
<li>
<a href = "poisson_simulation_prb.sh">poisson_simulation_prb.sh</a>,
BASH commands to compile and run the sample program.
</li>
<li>
<a href = "poisson_simulation_prb_output.txt">poisson_simulation_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<p>
The calling program creates data and command files which can be used by
GNUPLOT to create images.
<ul>
<li>
<a href = "poisson_events_data.txt">poisson_events_data.txt</a>,
data for Poisson events plot.
</li>
<li>
<a href = "poisson_events_commands.txt">poisson_events_commands.txt</a>,
commands for Poisson events plot.
</li>
<li>
<a href = "poisson_events.png">poisson_events.png</a>,
the Poisson events plot.
</li>
<li>
<a href = "poisson_timeline_data.txt">poisson_timeline_data.txt</a>,
data for Poisson timeline plot.
</li>
<li>
<a href = "poisson_timeline_commands.txt">poisson_timeline_commands.txt</a>,
commands for Poisson timeline plot.
</li>
<li>
<a href = "poisson_timeline.png">poisson_timeline.png</a>,
the Poisson timeline plot.
</li>
<li>
<a href = "poisson_times_data.txt">poisson_times_data.txt</a>,
data for Poisson events plot.
</li>
<li>
<a href = "poisson_times_commands.txt">poisson_times_commands.txt</a>,
commands for Poisson events plot.
</li>
<li>
<a href = "poisson_times.png">poisson_times.png</a>,
the Poisson events plot.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>I4VEC_MEAN</b> returns the mean of an I4VEC.
</li>
<li>
<b>I4VEC_PRINT</b> prints an I4VEC.
</li>
<li>
<b>I4VEC_VARIANCE</b> returns the variance of an I4VEC.
</li>
<li>
<b>POISSON_FIXED_EVENTS</b> waits for a given number of Poisson events.
</li>
<li>
<b>POISSON_FIXED_TIME</b> counts the Poisson events in a fied time.
</li>
<li>
<b>R8_UNIFORM_01</b> returns a unit pseudorandom R8.
</li>
<li>
<b>R8VEC_CUM</b> computes the cumulutive sums of an R8VEC.
</li>
<li>
<b>R8VEC_MEAN</b> returns the mean of an R8VEC.
</li>
<li>
<b>R8VEC_MIDSPACE_NEW</b> creates a vector of linearly spaced values.
</li>
<li>
<b>R8VEC_UNIFORM_01_NEW</b> returns a new unit pseudorandom R8VEC.
</li>
<li>
<b>R8VEC_VARIANCE</b> returns the variance of an R8VEC.
</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 September 2012.
</i>
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