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* Licensed to the Apache Software Foundation (ASF) under one
* or more contributor license agreements. See the NOTICE file
* distributed with this work for additional information
* regarding copyright ownership. The ASF licenses this file
* to you under the Apache License, Version 2.0 (the
* "License"); you may not use this file except in compliance
* with the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.hadoop.examples;
import java.io.IOException;
import java.math.BigDecimal;
import java.math.RoundingMode;
import java.util.Random;
import org.apache.hadoop.conf.Configuration;
import org.apache.hadoop.conf.Configured;
import org.apache.hadoop.fs.FileSystem;
import org.apache.hadoop.fs.Path;
import org.apache.hadoop.io.BooleanWritable;
import org.apache.hadoop.io.LongWritable;
import org.apache.hadoop.io.SequenceFile;
import org.apache.hadoop.io.Writable;
import org.apache.hadoop.io.WritableComparable;
import org.apache.hadoop.io.SequenceFile.CompressionType;
import org.apache.hadoop.mapreduce.*;
import org.apache.hadoop.mapreduce.lib.input.FileInputFormat;
import org.apache.hadoop.mapreduce.lib.input.SequenceFileInputFormat;
import org.apache.hadoop.mapreduce.lib.output.FileOutputFormat;
import org.apache.hadoop.mapreduce.lib.output.SequenceFileOutputFormat;
import org.apache.hadoop.util.Tool;
import org.apache.hadoop.util.ToolRunner;
/**
* 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).
*/
public class QuasiMonteCarlo extends Configured implements Tool {
static final String DESCRIPTION
= "A map/reduce program that estimates Pi using a quasi-Monte Carlo method.";
/** tmp directory for input/output */
static private final String TMP_DIR_PREFIX = QuasiMonteCarlo.class.getSimpleName();
/** 2-dimensional Halton sequence {H(i)},
* where H(i) is a 2-dimensional point and i >= 1 is the index.
* Halton sequence is used to generate sample points for Pi estimation.
*/
private static class HaltonSequence {
/** Bases */
static final int[] P = {2, 3};
/** Maximum number of digits allowed */
static final int[] K = {63, 40};
private long index;
private double[] x;
private double[][] q;
private int[][] d;
/** Initialize to H(startindex),
* so the sequence begins with H(startindex+1).
*/
HaltonSequence(long startindex) {
index = startindex;
x = new double[K.length];
q = new double[K.length][];
d = new int[K.length][];
for(int i = 0; i < K.length; i++) {
q[i] = new double[K[i]];
d[i] = new int[K[i]];
}
for(int i = 0; i < K.length; i++) {
long k = index;
x[i] = 0;
for(int j = 0; j < K[i]; j++) {
q[i][j] = (j == 0? 1.0: q[i][j-1])/P[i];
d[i][j] = (int)(k % P[i]);
k = (k - d[i][j])/P[i];
x[i] += d[i][j] * q[i][j];
}
}
}
/** Compute next point.
* Assume the current point is H(index).
* Compute H(index+1).
*
* @return a 2-dimensional point with coordinates in [0,1)^2
*/
double[] nextPoint() {
index++;
for(int i = 0; i < K.length; i++) {
for(int j = 0; j < K[i]; j++) {
d[i][j]++;
x[i] += q[i][j];
if (d[i][j] < P[i]) {
break;
}
d[i][j] = 0;
x[i] -= (j == 0? 1.0: q[i][j-1]);
}
}
return x;
}
}
/**
* Mapper class for Pi estimation.
* Generate points in a unit square
* and then count points inside/outside of the inscribed circle of the square.
*/
public static class QmcMapper extends
Mapper<LongWritable, LongWritable, BooleanWritable, LongWritable> {
/** Map method.
* @param offset samples starting from the (offset+1)th sample.
* @param size the number of samples for this map
* @param context output {ture->numInside, false->numOutside}
*/
public void map(LongWritable offset,
LongWritable size,
Context context)
throws IOException, InterruptedException {
final HaltonSequence haltonsequence = new HaltonSequence(offset.get());
long numInside = 0L;
long numOutside = 0L;
for(long i = 0; i < size.get(); ) {
//generate points in a unit square
final double[] point = haltonsequence.nextPoint();
//count points inside/outside of the inscribed circle of the square
final double x = point[0] - 0.5;
final double y = point[1] - 0.5;
if (x*x + y*y > 0.25) {
numOutside++;
} else {
numInside++;
}
//report status
i++;
if (i % 1000 == 0) {
context.setStatus("Generated " + i + " samples.");
}
}
//output map results
context.write(new BooleanWritable(true), new LongWritable(numInside));
context.write(new BooleanWritable(false), new LongWritable(numOutside));
}
}
/**
* Reducer class for Pi estimation.
* Accumulate points inside/outside results from the mappers.
*/
public static class QmcReducer extends
Reducer<BooleanWritable, LongWritable, WritableComparable<?>, Writable> {
private long numInside = 0;
private long numOutside = 0;
/**
* Accumulate number of points inside/outside results from the mappers.
* @param isInside Is the points inside?
* @param values An iterator to a list of point counts
* @param context dummy, not used here.
*/
public void reduce(BooleanWritable isInside,
Iterable<LongWritable> values, Context context)
throws IOException, InterruptedException {
if (isInside.get()) {
for (LongWritable val : values) {
numInside += val.get();
}
} else {
for (LongWritable val : values) {
numOutside += val.get();
}
}
}
/**
* Reduce task done, write output to a file.
*/
@Override
public void cleanup(Context context) throws IOException {
//write output to a file
Configuration conf = context.getConfiguration();
Path outDir = new Path(conf.get(FileOutputFormat.OUTDIR));
Path outFile = new Path(outDir, "reduce-out");
FileSystem fileSys = FileSystem.get(conf);
SequenceFile.Writer writer = SequenceFile.createWriter(fileSys, conf,
outFile, LongWritable.class, LongWritable.class,
CompressionType.NONE);
writer.append(new LongWritable(numInside), new LongWritable(numOutside));
writer.close();
}
}
/**
* Run a map/reduce job for estimating Pi.
*
* @return the estimated value of Pi
*/
public static BigDecimal estimatePi(int numMaps, long numPoints,
Path tmpDir, Configuration conf
) throws IOException, ClassNotFoundException, InterruptedException {
Job job = new Job(conf);
//setup job conf
job.setJobName(QuasiMonteCarlo.class.getSimpleName());
job.setJarByClass(QuasiMonteCarlo.class);
job.setInputFormatClass(SequenceFileInputFormat.class);
job.setOutputKeyClass(BooleanWritable.class);
job.setOutputValueClass(LongWritable.class);
job.setOutputFormatClass(SequenceFileOutputFormat.class);
job.setMapperClass(QmcMapper.class);
job.setReducerClass(QmcReducer.class);
job.setNumReduceTasks(1);
// turn off speculative execution, because DFS doesn't handle
// multiple writers to the same file.
job.setSpeculativeExecution(false);
//setup input/output directories
final Path inDir = new Path(tmpDir, "in");
final Path outDir = new Path(tmpDir, "out");
FileInputFormat.setInputPaths(job, inDir);
FileOutputFormat.setOutputPath(job, outDir);
final FileSystem fs = FileSystem.get(conf);
if (fs.exists(tmpDir)) {
throw new IOException("Tmp directory " + fs.makeQualified(tmpDir)
+ " already exists. Please remove it first.");
}
if (!fs.mkdirs(inDir)) {
throw new IOException("Cannot create input directory " + inDir);
}
try {
//generate an input file for each map task
for(int i=0; i < numMaps; ++i) {
final Path file = new Path(inDir, "part"+i);
final LongWritable offset = new LongWritable(i * numPoints);
final LongWritable size = new LongWritable(numPoints);
final SequenceFile.Writer writer = SequenceFile.createWriter(
fs, conf, file,
LongWritable.class, LongWritable.class, CompressionType.NONE);
try {
writer.append(offset, size);
} finally {
writer.close();
}
System.out.println("Wrote input for Map #"+i);
}
//start a map/reduce job
System.out.println("Starting Job");
final long startTime = System.currentTimeMillis();
job.waitForCompletion(true);
final double duration = (System.currentTimeMillis() - startTime)/1000.0;
System.out.println("Job Finished in " + duration + " seconds");
//read outputs
Path inFile = new Path(outDir, "reduce-out");
LongWritable numInside = new LongWritable();
LongWritable numOutside = new LongWritable();
SequenceFile.Reader reader = new SequenceFile.Reader(fs, inFile, conf);
try {
reader.next(numInside, numOutside);
} finally {
reader.close();
}
//compute estimated value
final BigDecimal numTotal
= BigDecimal.valueOf(numMaps).multiply(BigDecimal.valueOf(numPoints));
return BigDecimal.valueOf(4).setScale(20)
.multiply(BigDecimal.valueOf(numInside.get()))
.divide(numTotal, RoundingMode.HALF_UP);
} finally {
fs.delete(tmpDir, true);
}
}
/**
* Parse arguments and then runs a map/reduce job.
* Print output in standard out.
*
* @return a non-zero if there is an error. Otherwise, return 0.
*/
public int run(String[] args) throws Exception {
if (args.length != 2) {
System.err.println("Usage: "+getClass().getName()+" <nMaps> <nSamples>");
ToolRunner.printGenericCommandUsage(System.err);
return 2;
}
final int nMaps = Integer.parseInt(args[0]);
final long nSamples = Long.parseLong(args[1]);
long now = System.currentTimeMillis();
int rand = new Random().nextInt(Integer.MAX_VALUE);
final Path tmpDir = new Path(TMP_DIR_PREFIX + "_" + now + "_" + rand);
System.out.println("Number of Maps = " + nMaps);
System.out.println("Samples per Map = " + nSamples);
System.out.println("Estimated value of Pi is "
+ estimatePi(nMaps, nSamples, tmpDir, getConf()));
return 0;
}
/**
* main method for running it as a stand alone command.
*/
public static void main(String[] argv) throws Exception {
System.exit(ToolRunner.run(null, new QuasiMonteCarlo(), argv));
}
}