稀疏矩阵乘法加法等的java实现

原创声明：本文系作者原创，转载请写明出处。

一、前言

前几天由于科研需要，一直在搞矩阵的稀疏表示的乘法，不过最近虽然把程序写出来了，还是无法处理大规模的矩阵（虽然已经是稀疏了）。原因可能是结果不够稀疏。或者相乘的矩阵本来也不稀疏。

还是把实现的程序放在这里。以供以后研究使用。

二、程序实现功能

首先封装稀疏矩阵为三元组形式。

程序的主要功能有：

稀疏矩阵的转置

稀疏矩阵的乘法

稀疏矩阵的加法

以及相应的导入文本文件（矩阵）等。

三、代码展示

以下程序由eclipse下编写的java

package others;

import java.io.BufferedReader;
import java.io.File;
import java.io.FileOutputStream;
import java.io.FileReader;
import java.io.IOException;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.Iterator;
import java.util.Map;
import java.util.Map.Entry;

import weka.clusterers.SimpleKMeans;
import weka.core.DistanceFunction;
import weka.core.Instances;
import weka.core.converters.ArffLoader;
import Jama.Matrix;
/*
 * 本类可实现稀疏矩阵三元组表示下的矩阵乘法和矩阵加法，以及矩阵转置等。结果也是三元组存储。
 * 但是当数据量非常庞大时，乘积的结果无法存储，会出现内存溢出的现象。
 */
public class SMatrix {

	public Map<ArrayList<Integer>,Integer> Triples;//矩阵的三元组表示
	public int rowNum;//矩阵行数
	public int colNum;//矩阵列数
	
	
	public int getRowNum() {
		return rowNum;
	}

	public void setRowNum(int rowNum) {
		this.rowNum = rowNum;
	}

	public int getColNum() {
		return colNum;
	}

	public void setColNum(int colNum) {
		this.colNum = colNum;
	}

	/*
	 * 构造函数1
	 */
	public SMatrix(){
		
	}
	
	
	/*
	 * 构造函数2
	 */
	public SMatrix(Map<ArrayList<Integer>, Integer> triples, int rowNum, int colNum) {

		Triples = triples;
		this.rowNum = rowNum;
		this.colNum = colNum;
	}
	
	/*
	 * 构造函数3
	 */
	public SMatrix(Map<ArrayList<Integer>, Integer> triples) {

		Triples = triples;
	}
	
	/*
	 * 稀疏矩阵相乘函数
	 */
	public SMatrix Multiply(SMatrix M,SMatrix N){
		if(M.colNum != N.rowNum){
			System.out.println("矩阵相乘不满足条件");
			return null;
		}		
		
		Map<ArrayList<Integer>,Integer> triples = new HashMap<ArrayList<Integer>,Integer>();
		Iterator<Map.Entry<ArrayList<Integer>, Integer>> it1 = M.Triples.entrySet().iterator();
		
		
		int iter = 0;
		while(it1.hasNext()){
			iter++;
//			System.out.println("迭代次数："+iter);
			Entry<ArrayList<Integer>, Integer> entry = it1.next();
			ArrayList<Integer> position = entry.getKey();
//			System.out.println("检查程序：" + position);
			int value = entry.getValue();	
			int flag = 0;
			Iterator<Map.Entry<ArrayList<Integer>, Integer>> it2 = N.Triples.entrySet().iterator();
			while(it2.hasNext()){
				Entry<ArrayList<Integer>,Integer> entry2 = it2.next();
				ArrayList<Integer> position2 = entry2.getKey();
				int value2 = entry2.getValue();
				
				
				if(position.get(1) == position2.get(0)){
					flag = 1;
					ArrayList<Integer> temp = new ArrayList<Integer>();
					temp.add(position.get(0));
					temp.add(position2.get(1));
					int v = value * value2;
					if(triples.containsKey(temp)){
						triples.put(temp, triples.get(temp) + v);
						System.out.println(temp+ "\t"+(triples.get(temp) + v));
						
					}
					else{
						triples.put(temp, v);
						System.out.println(temp + "\t" + v);
					}				
				}
				
			}	
		}	
		SMatrix s = new SMatrix(triples,M.rowNum,N.colNum);
		return s;
	}
	
	
	
	/*
	 * 稀疏矩阵相加函数
	 */
	public static SMatrix Add(SMatrix M,SMatrix N){
		if(M.colNum != N.colNum || M.rowNum != N.rowNum){
			System.out.println("矩阵相加不满足条件");
			return null;
		}
		SMatrix s = new SMatrix();
		Map<ArrayList<Integer>,Integer> triples = new HashMap<ArrayList<Integer>,Integer>();
		Iterator<Map.Entry<ArrayList<Integer>, Integer>> it1 = M.Triples.entrySet().iterator();
		Iterator<Map.Entry<ArrayList<Integer>, Integer>> it2 = N.Triples.entrySet().iterator();
		
		while(it1.hasNext()){
			Entry<ArrayList<Integer>, Integer> entry = it1.next();
			ArrayList<Integer> position = entry.getKey();
			int value = entry.getValue();
			if(triples.containsKey(position)){
				triples.put(position, triples.get(position) + value);
			}else{
				triples.put(position, value);
			}
			
			
		}
		
		while(it2.hasNext()){
			Entry<ArrayList<Integer>,Integer> entry = it2.next();
			ArrayList<Integer> position = entry.getKey();
			int value = entry.getValue();
			if(triples.containsKey(position)){
				triples.put(position, triples.get(position) + value);
			}else{
				triples.put(position, value);
			}
			
		}
		return s;
	}
	
	
	/*
	 * 稀疏矩阵求转置矩阵函数
	 */
	public SMatrix Transposition(){
		
		Map<ArrayList<Integer>,Integer> triples = new HashMap<ArrayList<Integer>,Integer>();
		Iterator<Map.Entry<ArrayList<Integer>, Integer>> it = this.Triples.entrySet().iterator();
		while(it.hasNext()){
			Entry<ArrayList<Integer>, Integer> entry = it.next();
			ArrayList<Integer> position = entry.getKey();
			int value = entry.getValue();
			ArrayList<Integer> transP = new ArrayList<Integer>();
			transP.add(position.get(1));
			transP.add(position.get(0));
			
			triples.put(transP, value);
			
		}
		SMatrix s = new SMatrix(triples,this.colNum,this.rowNum);
		return s;
	}

	
	/*
	 * 加载文本数据为稀疏矩阵三元组形式的函数
	 */
	public SMatrix Load(String file, String delimeter){
		
		
		Map<ArrayList<Integer>,Integer> triples = new HashMap<ArrayList<Integer>,Integer>();
		
		try{
			File f = new File(file);
			FileReader fr = new FileReader(f);
			BufferedReader br = new BufferedReader(fr);
			
			String line;
			
			while((line = br.readLine()) != null){
				String[] str = line.trim().split(delimeter);
				
				ArrayList<Integer> s = new ArrayList<Integer>();
				for(int i = 0;i < str.length - 1; i++){
					s.add(Integer.parseInt(str[i]));
				}
				
				triples.put(s, Integer.parseInt(str[str.length - 1]));
				
			}
			
			
			br.close();
			fr.close();
			
		}catch(IOException e){
			e.printStackTrace();
		}
		SMatrix sm = new SMatrix(triples);
		return sm;
	}
	/*
	 * 打印稀疏矩阵（三元组形式）
	 */
	public void Print(){
		Map<ArrayList<Integer>, Integer> triples = this.Triples;
		Iterator<Map.Entry<ArrayList<Integer>, Integer>> it = triples.entrySet().iterator();
		int num = 0;
		while(it.hasNext()){
			Entry<ArrayList<Integer>, Integer> entry = it.next();
			ArrayList<Integer> position = entry.getKey();
			num++;
			System.out.print(num+":");
			for(Integer in:position){
				System.out.print(in + "\t");
			}
			
			System.out.println(entry.getValue());
		}
		
	}
	
	
	
public static void main(String[] args){
		
	/*
	 * 测试程序
	 
	String testS = "data/me";
	int k = 3;
	SMatrix te = new SMatrix();
	te = te.Load(testS,"\t");
	te.rowNum = 4;
	te.colNum = 6;
	System.out.println("打印原矩阵");
	te.Print();
	System.out.println("打印原矩阵的转置矩阵");
	te.Transposition().Print();
	
	System.out.println("打印乘积矩阵");
	SMatrix A2 = new SMatrix();

	A2 = te.Multiply(te, te.Transposition());
	A2.Print();
	*/

	
	
	
	
	
	long start = System.currentTimeMillis();
	
		String file1 = "data/AT.txt";//author to term 的稀疏矩阵
		String file2 = "data/CA.txt";//conference to author 的稀疏矩阵
		String delimeter = "	";
		int k = 11;
		SMatrix M = new SMatrix();
		SMatrix MT = new SMatrix();
	
		SMatrix N = new SMatrix();
		SMatrix NT = new SMatrix();
		SMatrix P = new SMatrix();
		SMatrix Q = new SMatrix();
		
		M = M.Load(file1, delimeter);
		M.colNum = 9225;
		M.rowNum = 6456;
		System.out.println("打印矩阵M");
		M.Print();
		MT = M.Transposition();
		System.out.println("打印矩阵MT");
		MT.Print();
		
		System.out.println("计算M和MT的乘积");
		System.out.println(M.rowNum);
		P = M.Multiply(M, MT);
		System.out.println("打印矩阵M与矩阵M转置的乘积");
		P.Print();
		
		
		
		
		N = N.Load(file2, delimeter);
		N.colNum = 6456;
		N.rowNum = 20;
		System.out.println("打印矩阵N");
		N.Print();
		NT = N.Transposition();
		
		System.out.println("打印矩阵NT：");
		NT.Print();
		
		System.out.println("计算NT 和  N的乘积");
		System.out.println(NT.colNum);
		System.out.println(N.rowNum);
		Q = M.Multiply(NT, N);		
		Q.Print();
		
		
		
		
		
		
		SMatrix A = new SMatrix();
		A = A.Load("data/AA.txt","	");
		
		SMatrix A1 = new SMatrix();
		SMatrix A2 = new SMatrix();
		System.out.println("计算矩阵A1=P+Q:");
		A1 = SMatrix.Add(Q, P);
		
		System.out.println("打印矩阵A1：");
		A1.Print();
		A2 = SMatrix.Add(A1, A);//得到了比较全面的author to author 矩阵三元组
		
		A2.Print();
		
		
		double[][] matrix = new double[A2.rowNum][A2.colNum];
		
		for(int i = 0;i < A2.rowNum;i++){
			for (int j = 0; j < A2.colNum; j++) {
				
				ArrayList<Integer> list = new ArrayList<Integer>();
				list.add(i);
				list.add(j);

				if (A2.Triples.containsKey(list)) {
					matrix[i][j] = A2.Triples.get(list);
				}
				else{
					matrix[i][j] = 0;	
				}
				
			}
		}

		for(int i = 0;i<A2.rowNum;i++){
			for(int j = 0;j < A2.colNum;j++){
				System.out.print(matrix[i][j]+"\t");
			}
			System.out.println();
		}
		Matrix Author = new Matrix(matrix);

		//第二步：求矩阵的特征值eigValue及其相应的特征向量矩阵，取前K个（最大的）
		Matrix diagA = Author.eig().getD();

		diagA.print(4, 2);
		int m = diagA.getRowDimension();
		int n = diagA.getColumnDimension();
		
		Matrix eigVector = Author.eig().getV();
		
		eigVector.print(eigVector.getRowDimension(),4);

		//将特征向量输出到文本中。
		String outFile = "data/eigenVector.txt";
		try{
			File f = new File(outFile);
			FileOutputStream fout = new FileOutputStream(f);
			
			fout.write("@RELATION\teigenVector\n".getBytes());
			for(int i = n-k;i<n;i++){
				fout.write(("@ATTRIBUTE\t"+i + "\tREAL\n").getBytes());
			}
			fout.write("@DATA\n".getBytes());
			if(k <= n){
				for(int i = 0;i < m;i++){
					for(int j = n-k;j<n;j++){
						Double temp = new Double(eigVector.getArray()[i][j]);
						String tem = temp.toString();
						fout.write((tem + "\t").getBytes());
						
					}
					fout.write(("\n").getBytes());
				}
			}
		}
		catch(IOException e){
			e.printStackTrace();
		}
		//第三步：对特征向量矩阵进行kmeans聚类
		Instances ins = null;
		
		SimpleKMeans KM = null;
		
		// 目前没有使用到，但是在3.7.10的版本之中可以指定距离算法
		// 默认是欧几里得距离
		DistanceFunction disFun = null;
		
		try {
			// 读入样本数据
			File file = new File("data/eigenVector.txt");
			ArffLoader loader = new ArffLoader();
			loader.setFile(file);
			ins = loader.getDataSet();
			
			// 初始化聚类器 （加载算法）
			KM = new SimpleKMeans();
			KM.setNumClusters(2); 		//设置聚类要得到的类别数量
			
			KM.setMaxIterations(100);
			KM.buildClusterer(ins);		//开始进行聚类
			System.out.println(KM.preserveInstancesOrderTipText());
			// 打印聚类结果
			System.out.println(KM.toString());
			
		
//			for(String option : KM.getOptions()) {
//				System.out.println(option);
//			}
//			System.out.println("CentroIds:" + tempIns);
		} catch(Exception e) {
			e.printStackTrace();
		}
		
		
		System.out.println("程序正常结束");
		
		
		long end = System.currentTimeMillis();
		System.out.println(end - start);
		
		
	}
	
}