矩阵乘法的MapReduce实现

对于任意矩阵M和N，若矩阵M的列数等于矩阵N的行数，则记M和N的乘积为P=M*N，其中m_ik 记做矩阵M的第i行和第k列，n_kj记做矩阵N的第k行和第j列，则矩阵P中，第i行第j列的元素可表示为公式（1-1）：

p_ij=(M*N)_ij=∑m_ikn_kj=m_i1*n_1j+m_i2*n_2j+……+m_ik*n_kj（公式1-1）

由公式（1-1）可以看出，最后决定p_ij是(i,j)，所以可以将其作为Reducer的输入key值。为了求出p_ij分别需要知道m_ik和n_kj，对于m_ik，其所需要的属性有矩阵M，所在行数i、所在列数k，和其本身的数值大小m_ik；同样对于n_kj，其所需要的属性有矩阵N，所在行数k、所在列数j，和其本身数值大小n_kj，这些属性值可由Mapper处理得到

Map函数：对于矩阵M中的每个元素m_ik ，产生一系列的key-value对<(i,j),(M,k,m_ik)>，其中，k=1,2……直到矩阵N的总列数，对于矩阵N的每个元素n_kj，产生一系列的key-value对，<(i,j),(N,k,n_kj)>，其中i=1,2……直到矩阵M的总行数

Reduce函数：对于每个键(i,j)相关联的值(M,k,m_ik)及(N,k,n_kj)，根据相同的k值将m_ik和n_kj分别放入不同的数组中，然后将两者的第k个元素抽取出来分别相乘，再累加，即可得到p_ij的值

有M和N两个文件分别存放两个矩阵，文件内容的每一行的形式是“行号，列号\t元素值”，本例中，使用shell脚本生成数据

代码1-2

root@lejian:/data# cat matrix
#!/bin/bash
for i in `seq 1 $1`
do
        for j in `seq 1 $2`
        do
                s=$(($RANDOM % 100))
                echo -e "$i,$j\t$s" >> M_$1_$2
        done
done

for i in `seq 1 $2`
do
        for j in `seq 1 $3`
        do
                s=$(($RANDOM%100))
                echo -e "$i,$j\t$s" >> N_$2_$3
        done
done

代码1-3，执行matrix脚本，生成一个2行3列和3行3列的矩阵，并在HDFS下新建一个data文件夹，将生成的两个矩阵放入data文件夹下

代码1-3

root@lejian:/data# ./matrix 2 3 3
root@lejian:/data# cat M_2_3
1,1     6
1,2     84
1,3     40
2,1     51
2,2     37
2,3     97
root@lejian:/data# cat N_3_3
1,1     97
1,2     34
1,3     95
2,1     93
2,2     10
2,3     70
3,1     71
3,2     24
3,3     47
root@lejian:/data# hadoop fs -mkdir /data
root@lejian:/data# hadoop fs -put /data/M_2_3 /data/
root@lejian:/data# hadoop fs -put /data/N_3_3 /data/
root@lejian:/data# hadoop fs -ls -R /data
-rw-r--r--   1 root supergroup         41 2017-01-07 11:57 /data/M_2_3
-rw-r--r--   1 root supergroup         63 2017-01-07 11:57 /data/N_3_3

矩阵乘法Mapper类程序如代码1-4

代码1-4

package com.hadoop.mapreduce;

import java.io.IOException;

import org.apache.hadoop.conf.Configuration;
import org.apache.hadoop.io.LongWritable;
import org.apache.hadoop.io.Text;
import org.apache.hadoop.mapreduce.Mapper;
import org.apache.hadoop.mapreduce.lib.input.FileSplit;

public class MatrixMapper extends Mapper<LongWritable, Text, Text, Text> {

	private int columnN = 0;
	private int rowM = 0;
	private Text mapKey = new Text();
	private Text mapValue = new Text();

	protected void setup(Context context) throws IOException, InterruptedException {
		Configuration conf = context.getConfiguration();
		columnN = Integer.parseInt(conf.get("columnN"));
		rowM = Integer.parseInt(conf.get("rowM"));
	};

	protected void map(LongWritable key, Text value, Context context) throws IOException, InterruptedException {
		FileSplit file = (FileSplit) context.getInputSplit();
		String fileName = file.getPath().getName();
		String line = value.toString();
		String[] tuple = line.split(",");
		if (tuple.length != 2) {
			throw new RuntimeException("MatrixMapper tuple error");
		}
		int row = Integer.parseInt(tuple[0]);
		String[] tuples = tuple[1].split("\t");
		if (tuples.length != 2) {
			throw new RuntimeException("MatrixMapper tuples error");
		}
		if (fileName.contains("M")) {
			matrixM(row, Integer.parseInt(tuples[0]), Integer.parseInt(tuples[1]), context);
		} else {
			matrixN(row, Integer.parseInt(tuples[0]), Integer.parseInt(tuples[1]), context);
		}

	};

	private void matrixM(int row, int column, int value, Context context) throws IOException, InterruptedException {
		for (int i = 1; i < columnN + 1; i++) {
			mapKey.set(row + "," + i);
			mapValue.set("M," + column + "," + value);
			context.write(mapKey, mapValue);
		}
	}

	private void matrixN(int row, int column, int value, Context context) throws IOException, InterruptedException {
		for (int i = 1; i < rowM + 1; i++) {
			mapKey.set(i + "," + column);
			mapValue.set("N," + row + "," + value);
			context.write(mapKey, mapValue);
		}
	}

}

矩阵乘法Reducer类程序如代码1-5

代码1-5

package com.hadoop.mapreduce;

import java.io.IOException;

import org.apache.hadoop.conf.Configuration;
import org.apache.hadoop.io.Text;
import org.apache.hadoop.mapreduce.Reducer;

public class MatrixReducer extends Reducer<Text, Text, Text, Text> {

	private int columnM = 0;

	protected void setup(Context context) throws IOException, InterruptedException {
		Configuration conf = context.getConfiguration();
		columnM = Integer.parseInt(conf.get("columnM"));
	};

	protected void reduce(Text key, Iterable<Text> values, Context context) throws IOException, InterruptedException {
		int sum = 0;
		int[] m = new int[columnM + 1];
		int[] n = new int[columnM + 1];
		for (Text val : values) {
			String[] tuple = val.toString().split(",");
			if (tuple.length != 3) {
				throw new RuntimeException("MatrixReducer tuple error");
			}
			if ("M".equals(tuple[0])) {
				m[Integer.parseInt(tuple[1])] = Integer.parseInt(tuple[2]);
			} else {
				n[Integer.parseInt(tuple[1])] = Integer.parseInt(tuple[2]);
			}
		}
		for (int i = 1; i < columnM + 1; i++) {
			sum += m[i] * n[i];
		}
		context.write(key, new Text(sum + ""));
	};

}

矩阵乘法主函数如代码1-5

package com.hadoop.mapreduce;

import java.io.IOException;

import org.apache.hadoop.conf.Configuration;
import org.apache.hadoop.fs.Path;
import org.apache.hadoop.io.Text;
import org.apache.hadoop.mapreduce.Job;
import org.apache.hadoop.mapreduce.lib.input.FileInputFormat;
import org.apache.hadoop.mapreduce.lib.output.FileOutputFormat;

public class Matrix {

	public static void main(String[] args) throws IOException, ClassNotFoundException, InterruptedException {
		if (args == null || args.length != 5) {
			throw new RuntimeException("请输入输入路径、输出路径、矩阵M的行数、矩阵M的列数、矩阵N的列数");
		}
		Configuration conf = new Configuration();
		conf.set("rowM", args[2]);
		conf.set("columnM", args[3]);
		conf.set("columnN", args[4]);
		Job job = Job.getInstance(conf);
		job.setJobName("Matrix");
		job.setJarByClass(Matrix.class);
		job.setMapperClass(MatrixMapper.class);
		job.setReducerClass(MatrixReducer.class);
		job.setOutputKeyClass(Text.class);
		job.setOutputValueClass(Text.class);
		FileInputFormat.addInputPaths(job, args[0]);
		FileOutputFormat.setOutputPath(job, new Path(args[1]));
		System.exit(job.waitForCompletion(true) ? 0 : 1);
	}

}

运行代码1-5，运行结果如代码1-6所示（注：代码1-6省略部分MapReduce执行内容）

代码1-6

root@lejian:/data# hadoop jar matrix.jar com.hadoop.mapreduce.Matrix /data/ /output/ 2 3 3
…………
root@lejian:/data# hadoop fs -ls -R /output
-rw-r--r--   1 root supergroup          0 2017-01-07 12:04 /output/_SUCCESS
-rw-r--r--   1 root supergroup         57 2017-01-07 12:04 /output/part-r-00000
root@lejian:/data# hadoop fs -cat /output/part-r-00000
1,1     11234
1,2     2004
1,3     8330
2,1     15275
2,2     4432
2,3     11994