POISSON_SIMULATION
Simulation of a Poisson Process

POISSON_SIMULATION is a FORTRAN77 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.

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.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

POISSON_SIMULATION is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

BROWNIAN_MOTION_SIMULATION, a FORTRAN77 library which simulates Brownian motion in an M-dimensional region.

DUEL_SIMULATION, a FORTRAN77 program which simulates N repetitions of a duel between two players, each of whom has a known firing accuracy.

FAIR_DICE_SIMULATION, a FORTRAN77 program which simulates N tosses of 2 dice, making a histogram of the results.

GNUPLOT, FORTRAN77 programs which illustrate the use of the gnuplot graphics program.

HIGH_CARD_SIMULATION, a FORTRAN77 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.

ISING_2D_SIMULATION, 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.

REACTOR_SIMULATION, 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."

THREE_BODY_SIMULATION, 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.

Source Code:

• poisson_simulation.f, the source code.
• poisson_simulation.sh, BASH commands to compile the source code.

Examples and Tests:

• poisson_simulation_prb.f, a sample calling program.
• poisson_simulation_prb.sh, BASH commands to compile and run the sample program.
• poisson_simulation_prb_output.txt, the output file.

The calling program creates data and command files which can be used by GNUPLOT to create images.

• poisson_events_data.txt, data for Poisson events plot.
• poisson_events_commands.txt, commands for Poisson events plot.
• poisson_events.png, the Poisson events plot.
• poisson_timeline_data.txt, data for Poisson timeline plot.
• poisson_timeline_commands.txt, commands for Poisson timeline plot.
• poisson_timeline.png, the Poisson timeline plot.
• poisson_times_data.txt, data for Poisson events plot.
• poisson_times_commands.txt, commands for Poisson events plot.
• poisson_times.png, the Poisson events plot.

List of Routines:

• GET_UNIT returns a free FORTRAN unit number.
• I4VEC_MEAN returns the mean of an I4VEC.
• I4VEC_PRINT prints an I4VEC.
• I4VEC_VARIANCE returns the variance of an I4VEC.
• POISSON_FIXED_EVENTS waits for a given number of Poisson events.
• POISSON_FIXED_TIME counts the Poisson events in a fied time.
• R8_UNIFORM_01 returns a unit pseudorandom R8.
• R8VEC_CUM computes the cumulutive sums of an R8VEC.
• R8VEC_MAX returns the maximum value in an R8VEC.
• R8VEC_MEAN returns the mean of an R8VEC.
• R8VEC_MIDSPACE creates a vector of linearly spaced values.
• R8VEC_MIN returns the minimum value in an R8VEC.
• R8VEC_SUM sums the entries of an R8VEC.
• R8VEC_UNIFORM_01 returns a unit pseudorandom R8VEC.
• R8VEC_VARIANCE returns the variance of an R8VEC.
• TIMESTAMP prints out the current YMDHMS date as a timestamp.

You can go up one level to the FORTRAN77 source codes.