analisis en matlab

7/25/2019 Analisis en matlab

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In the first chapter, we already had a look at the Monte Carlo method.

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Now its a good time to dig into the details.

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First the deterministic problem to find a numerical value for pi is solved.

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We generate random values for points within a square of 2 by 2 with centerpoint

(0,0).The x-coordinates and the y-coordinates are independent results of a uniform

distributed random experiment.

They range from -1 to 1.

In the square lets look at a circle with center point (0,0) and radius 1.

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The area of the circle and the area of the square have approximately the same ratio

as the number of points in the circle to the number of points in the square.

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Thus we obtain a simple equation for pi.

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This is an easy code in Matlab calculating pi

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and visualizing the method. It is straightforward, but somewhat specialized in Matlab.

Especially Lines 2-5 make use of vectoring. Some people with a classical C-programming background are not so familiar with vectoring. Therefore I will also

present a more classical variant.

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It is not possible to declare an empty array in Matlab.

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But the typical combination, declaration and definition of an array can be done by the

zeros command.

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For really big amounts of points, the plot is not very useful. Therefore only the pi-

calculating part is done.

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Comparing C-style to vectoring style, the vectoring style is a little bit faster.

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But when stepping to even more points, the vectoring approach can cause out of

memory errors, as very big arrays have to be generated. N=1E9 worked for the C-stylecode only on my machine.

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Now to Gary Foshees famous boy born on a Tuesday problemI have two children. One is a boy born on a Tuesday. What is the probability I have

two boys?

Do you think the Tuesday is important information?

Well see by employing the Monte Carlo method.

And we try to do it like this:

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two boys?




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two boys?




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Here is the code for the boy born on a Tuesday problem

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The first and the last line of this code are used to measure the cpu-time for the

program.

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In line two the number of families is hard coded , this means the user of the

program is not asked a number, but the number is written into the code.

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Randi in lines 3-6 is the random number generator for discrete uniform distributions.

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Note the bitwise logical operators | and & in line 7 and 8. You might have tried .|| or

.&& which might give the same result if they were defined within Matlab.The bitwise &, | and == operators have arrays as operands and arrays as results. If the

conditions are met, the corresponding array element is 1, otherwise it is 0.

Nnz (read number of non zeros) then just counts the ones.

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Note that the solution 0.48 clearly shows that the Tuesday information is important

(the strange point is, Wednesday would work as well, the day just has to be fixed).Without the Tuesday, the probability of two boys would be only one third.

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We have reached the end of our little problem solvers toolbox journey.

I hope you enjoyed it and will find it useful.

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In fact we did cover a wide range of problems. Maybe after dealing with the tools and

some Matlab details this is a good time to step back to the modelling. Any modelreduces the worlds complexity, keeping phenomena that are important for the

problem at hand and forgetting about the rest. Like good managers do first things first

and second not all.

Think about which phenomena we kept, what were the phenomena we neglected or

didnt care about. (Like we did not care about the modulus of the gear wheels, or the

width of the gear wheels, or the material the gear box was made of. But we used the

non slipping assumption.) So this is goodbye from me, but maybe we will meet on the

discussion board or in our next Mooc, modelling and simulation using Simulink.

analisis en matlab

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