Esercitazione 11

Exercise 1

Write a program that generates the value according to the distribution function 
                     f(θ) = (sin^2 θ + a cos^2 θ)^{-1} 
In the range 0 ≤ θ ≤ 2π.

*Compare the rejection technique and the inversion technique:
*Generate 10000 values for each method using a = 0,5 and also for a = 0,001
*Plot the results for each and overlay the distribution curve f(θ) properly normalized 
*Compare the CPU time request for the 4 runs

Alternative

Alternatively,  write a class that inherits with public inheritance from the ROOT TRandom3 class.
In the class, the inversion and rejection method for the function
                                    f(θ) = (sin2 θ + a cos2 θ)-1 
in the range 0 ≤ θ ≤ 2π have to be implemented
*Compare the rejection technique and the inversion technique:
*Generate 1000000 values for each method using a = 0,5 and also for a = 0,001
*Plot the results for each and overlay the distribution curve f() properly normalized
*Compare the CPU time request for the 4 runs (hint: in ROOT it is possible the use the TStopwatch class)