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mik 记做矩阵M的第i行和第k列，nkj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）：
pij=(M*N)ij=∑miknkj=mi1*n1j+mi2*n2j+……+mik*nkj （公式1-1）
由公式（1-1）可以看出，最后决定pij是(i,j)，所以可以将其作为Reducer的输入key值。为了求出pij分别需要知道mik和nkj，对于mik，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mik；同样对于nkj，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nkj，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mik ，产生一系列的key-value对<(i,j),(M,k,mik)>，其中，k=1,2……直到矩阵N的总列数，对于矩阵N的每个元素nkj，产生一系列的key-value对，<(i,j),(N,k,nkj)>，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,mik)及(N,k,nkj)，根据相同的k值将mik和nkj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pij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