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example2.5

README.md

Example 2.5

How to use?

  • Requirement

    • Linux - ubuntu 16.04
    • gnuplot
    sudo apt install gnuplot build-essential

  • Compile and run the default testcase:

    • range: 1~5
    • testcase: 100
    make

Run the program

  • Let's see the content in Makefile:
    • First, compile and generate sim.out for simulation program, and math.out for mathematic model program.
    # compile the simulation
g++ simulation.cc -o sim.out -I../utils -std=c++11
# compile the mathematic proof
g++ mathematic.cc -o math.out -std=c++11
    • Second, run the program of sim.out and math.out to generate the simulation result and mathematic result.
      • In this step, specify the range upperbound (e.g. -m) and X (e.g. P{X>N}) in sim.out, with default testcase = 100
      • If you want to generate the result with large testcase, you can specify the number with argument -n [large_testcase], for example : "./sim.out -m 5 -x 10 -n 1000000"
      • And run the math.out, only using argument without specify parameter flag, and parse out the first line of the result simulation.output which generated from sim.out, to get the MAXIMUM value to set the upperbound, and then math.out will generate the output file mathematic.output
    # Feed the testdata
# Run the simulation first: 
./sim.out -m 5 -x 10 
# generate with large testcase
#./sim.out -m 5 -x 10 -n 10^6
# And then get the maximum, to generate the mathematic result
./math.out 10 $$(head -1 simulation.output | awk '{print $$4}')
    • Last step, after generating all the results (e.g. simulation.output, mathematic.output), we can use gnuplot to generate the line chart from these 2 files.
    # Using gnuplot the plot
gnuplot simulation.gp
    • After gnuplot plotting process, we now can open the line chart image simulation.png
    > eog simulation.png

Result

  • As you can see the figure down below, the simulation(red line) and the mathematic(green line) have the similar curve.

  • And then we increase the testcase to 10^6 (run with ./sim.out -m 5 -x 10 -n 1000000):

    • You can see it's more fit with the curve from mathematic model!

Difference (TODO)

  • Measure the difference between simulation and mathematic result!
Difference = 100%×(Simulation - Math) / Math

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