org.apache.hadoop.examples

Class QuasiMonteCarlo

java.lang.Object

org.apache.hadoop.conf.Configured

org.apache.hadoop.examples.QuasiMonteCarlo

All Implemented Interfaces:

Configurable, Tool

public class QuasiMonteCarlo
extends Configured
implements Tool

A map/reduce program that estimates the value of Pi using a quasi-Monte Carlo (qMC) method. Arbitrary integrals can be approximated numerically by qMC methods. In this example, we use a qMC method to approximate the integral $I = \int_S f(x) dx$, where $S=[0,1)^2$ is a unit square, $x=(x_1,x_2)$ is a 2-dimensional point, and $f$ is a function describing the inscribed circle of the square $S$, $f(x)=1$ if $(2x_1-1)^2+(2x_2-1)^2 <= 1$ and $f(x)=0$, otherwise. It is easy to see that Pi is equal to $4I$. So an approximation of Pi is obtained once $I$ is evaluated numerically. There are better methods for computing Pi. We emphasize numerical approximation of arbitrary integrals in this example. For computing many digits of Pi, consider using bbp. The implementation is discussed below. Mapper: Generate points in a unit square and then count points inside/outside of the inscribed circle of the square. Reducer: Accumulate points inside/outside results from the mappers. Let numTotal = numInside + numOutside. The fraction numInside/numTotal is a rational approximation of the value (Area of the circle)/(Area of the square) = $I$, where the area of the inscribed circle is Pi/4 and the area of unit square is 1. Finally, the estimated value of Pi is 4(numInside/numTotal).

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	QuasiMonteCarlo.QmcMapper Mapper class for Pi estimation.
static class	QuasiMonteCarlo.QmcReducer Reducer class for Pi estimation.

Constructor Summary

Constructors

Constructor and Description
QuasiMonteCarlo()

Method Summary

Modifier and Type	Method and Description
static BigDecimal	estimatePi(int numMaps, long numPoints, Path tmpDir, Configuration conf) Run a map/reduce job for estimating Pi.
static void	main(String[] argv) main method for running it as a stand alone command.
int	run(String[] args) Parse arguments and then runs a map/reduce job.

Methods inherited from class org.apache.hadoop.conf.Configured

getConf, setConf

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface org.apache.hadoop.conf.Configurable

getConf, setConf

Constructor Detail

QuasiMonteCarlo

public QuasiMonteCarlo()

Method Detail

estimatePi

public static BigDecimal estimatePi(int numMaps,
                                    long numPoints,
                                    Path tmpDir,
                                    Configuration conf)
                             throws IOException,
                                    ClassNotFoundException,
                                    InterruptedException

Run a map/reduce job for estimating Pi.

Returns:

the estimated value of Pi

Throws:

IOException

ClassNotFoundException

InterruptedException

run

public int run(String[] args)
        throws Exception

Parse arguments and then runs a map/reduce job. Print output in standard out.

Specified by:

run in interface Tool

Returns:

a non-zero if there is an error. Otherwise, return 0.

Throws:

Exception

main

public static void main(String[] argv)
                 throws Exception

main method for running it as a stand alone command.

Throws:

Exception