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Finding PI using Monte Carlo Method Distributed Using MPI
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090185B Hettiarachchi H.A.C.
CS4552 Scientific Computing Project
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Take a uniformly distributed random point within the square with width and height of 1.   
Consider the circle encapsulated within the square with radius 0.5

                                  Area of Circle        Pi * R * R
P(random point within circle) = ------------------  = --------------  = Pi/4
                                Area of the Square       4 * R * R

Pi = 4 * (No. of tries within circle) / (Total no. of Tries)


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			First attempt: mpi_findpi
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Load Balance			: Equally Distributed
Termination condition	: Square of error between two iterations is less than 0.001 
Communication Pattern	: MPI_REDUCE
Random Number Generator : Uniform RANF (See comments in code)
Notes					: 

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			Second attempt: pi_parallel_lb
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Load Balance			: Equal timeouts for each process
Termination condition	: One cycle of processing 
Communication Pattern	: MPI_SEND and MPI_RECEIVE
Random Number Generator : Uniform RANF (See comments in code)
Notes					:
	Each process is given two seconds to process. When that interval  is finished, total and 
	success counts are returned to the main process in order. PI is calculated there.
	Might overflow integers, as the limit is just bounded by time, not from the count. But 
	but here, time is hard coded for favourable number. 

	This assumed each process will handle LOCAL_TOTAL number of operations in similat time period
	So load is equally distributed.



Build the PI Calculation program 
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Dependencies: 1. gfortran
              2. Install mpich. Follow the readme. http://www.mpich.org/static/downloads/3.0.4/mpich-3.0.4.tar.gz


Make the given target i.e: for pi_parallel_lb execute
		
				make pi_parallel_lb

Running
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In a single machine, with 4 processes:

mpiexec -n 4 bin/pi_parallel_lb


In multiple machines (which has visible IP addresses for each of the machines):

Create a file named hostfile containing hosts ips and expected processes at ones for each host.

e.g.(which tells to run on two hosts given, with two processes at ones per each host): 

192.168.1.1:2
192.168.1.2:2


mpiexec -launcher ssh -f hostfile -n 4 bin/pi_parallel_lb

Both hosts should have the executable and you migh need to change the paths to full paths.

 (You will be asked for ssh authentication after executing this)