/***************************
* Akka Integral Calculator *
*                          *
*             Yann Nicolas *
*        yannart@gmail.com *
****************************/


INTRODUCTION

This application calculates an approximation of the integral of a polynomial in a defined interval using Akka actors.
For that, the area under the curve is calculated using the Simpson rule (http://en.wikipedia.org/wiki/Simpson's_rule)
As the area under the curve for an interval is equal to the sum of the areas of subintervals, that computation can be done parallely.

To make it more interesting, there are two instances of the program running:
	
	- Server
		The server performs the computation with the parameters sent by the client.
		For this example it runs locally (localhost) but can be running in another machine.
		
	- Client
		The client configures the values of the computation: Polynomial coefficients, precision.
		It also calculates the exact integral to verify the result of the approximation. 
		
	Note that in this example, the client connects only to a single server,
	but it is easy to add more of them dividing the integral interval.


INSTRUCTIONS

- REQUIREMENTS

	- Java 1.6

	- Install Akka: http://akka.io/downloads/

	- Install SBT: http://code.google.com/p/simple-build-tool/

	- Download the project with Git or unzip it if you download the archive (https://github.com/yannart/ParallelPolynomialIntegral)

- BUILD
	- Go to the project folder on your terminal
	- run the following commands to download the dependencies and compile the project:
		> sbt update
		> sbt compile
		- optionally, to generate an Eclipse project with the configuration for Scala IDE, run:
		> sbt eclipse

- RUN
	- Open two terminals
	- Terminal 1, Server:
		> sbt console
		> scala> import com.yannart.akka.integralcalculator._
		> scala> Runner.runServer
		
	- Terminal 2, Client:
		> sbt console
		> scala> import com.yannart.akka.integralcalculator._
		> scala> Runner.runClient
		
	Note that you can execute again the client without restarting the server.
		
- EXAMPLE OF RUN

	Depending of your Akka configuration, you will have a lot of log messages,
	but at the end, in the Client terminal, you will have a message like:

		Polynomial equation is  - 1.0 - 4.0X + 3.0X^2 - 2.0X^3 + X^4 + 4.0X^5
		Integral to be calculated in [ -10.0 , 10.0 ]
		Approximate integral calculated using steps of 0.0010
		Integral equation is  - X - 2.0X^2 + X^3 - 0.5X^4 + 0.2X^5 + 0.6666666666666666X^6
		Real integral value = 41980.0 (calculated in 3 ms)
		Approximate integral value = 41979.999999922395 (calculated in 6381 ms)
		Error = 1.8486270584297384E-10%