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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 FORTRAN77 program which
      simulates a Poisson process in which events occur uniformly at random,
      with an average waiting time of Lambda.
    </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 = "../../f77_src/brownian_motion_simulation/brownian_motion_simulation.html">
      BROWNIAN_MOTION_SIMULATION</a>,
      a FORTRAN77 library which
      simulates Brownian motion in an M-dimensional region.
    </p>

    <p>
      <a href = "../../f77_src/duel_simulation/duel_simulation.html">
      DUEL_SIMULATION</a>,
      a FORTRAN77 program which
      simulates N repetitions of a duel between two players, each of
      whom has a known firing accuracy.
    </p>

    <p>
      <a href = "../../f77_src/fair_dice_simulation/fair_dice_simulation.html">
      FAIR_DICE_SIMULATION</a>,
      a FORTRAN77 program which
      simulates N tosses of 2 dice, making a histogram of the results.
    </p>

    <p>
      <a href = "../../examples/gnuplot/gnuplot.html">
      GNUPLOT</a>,
      examples which
      illustrate the use of the gnuplot graphics program.
    </p>

    <p>
      <a href = "../../f77_src/ising_2d_simulation/ising_2d_simulation.html">
      ISING_2D_SIMULATION</a>,
      a FORTRAN77 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 = "../../f77_src/reactor_simulation/reactor_simulation.html">
      REACTOR_SIMULATION</a>,
      a FORTRAN77 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 = "../../f77_src/three_body_simulation/three_body_simulation.html">
      THREE_BODY_SIMULATION</a>,
      a FORTRAN77 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.f">poisson_simulation.f</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.f">poisson_simulation_prb.f</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>GET_UNIT</b> returns a free FORTRAN unit number.
        </li>
        <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_MAX</b> returns the maximum value in an R8VEC.
        </li>
        <li>
          <b>R8VEC_MEAN</b> returns the mean of an R8VEC.
        </li>
        <li>
          <b>R8VEC_MIDSPACE</b> creates a vector of linearly spaced values.
        </li>
        <li>
          <b>R8VEC_MIN</b> returns the minimum value in an R8VEC.
        </li>
        <li>
          <b>R8VEC_SUM</b> sums the entries of an R8VEC.
        </li>
        <li>
          <b>R8VEC_UNIFORM_01</b> returns a unit pseudorandom R8VEC.
        </li>
        <li>
          <b>R8VEC_VARIANCE</b> returns the variance of an R8VEC.
        </li>
        <li>
          <b>TIMESTAMP</b> prints out the current YMDHMS date as a timestamp.
        </li>
      </ul>
    </p>

    <p>
      You can go up one level to <a href = "../f77_src.html">
      the FORTRAN77 source codes</a>.
    </p>

    <hr>

    <i>
      Last revised on 28 September 2012.
    </i>

    <!-- John Burkardt -->

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