# Direct Sampling Method, Metropolis Algorithm-Computational Physics-Assignment, Exercises for Computational Physics. Acharya Nagarjuna University

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This lecture is delivered by Proff. Vikram Sharma at Acharya Nagarjuna University for discussing following points of Computational Physics: MATLAB, Program, Pdf, Efficiency, Distribution, Functions, Comparison, Metropoli...
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M.Phil Physics Course: Computational Physics (Stochastic Methods)

Home Work # 3 This assignment is based on Random Sampling of pdfs Due date: One Week after this distribution in class. Question 1

(a) Suppose that a given pdf for y is shown below: 10)2exp(4)( 2 <<−= yyyyf Then first normalize this pdf and then using Direct sampling method find out a proper formula to sample this distribution.

(b) Use MATLAB program and sample the pdf for N = 10000. Draw both the

exact and sampled distribution functions as histograms. (c) What happens when N is increased to 100000? Show results as graphs

and give some sort of comparison.

Question 2

(a) For above pdf use rejection method and sample randomly for N = 10000. Draw both the exact and sampled distribution function.

(a) Find out the efficiency of this technique. What happens when N is

increased to 100000? Show results as graphs and give some sort of comparison.

Question 3

(b) For above pdf use Metropolis Algorithm and sample randomly for N = 10000. Draw both the exact and sampled distribution function.

(c) Find out the efficiency of this technique. What happens when N is

increased to 100000? Show results as graphs and give some sort of comparison.

Home Work # 3

1

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