层次分析法两种实现方法

前几天看了看层次分析法，这是一个比较经典的算法，一般在评价和数据融合方面应用比较多，网上也有很多针对这个算法改进也是比较多的，大多数只是给这个方法加了点模糊运算。其实在现在的系统中单用它做评价或是评估的话，显得有点单调。但是单单应用它给出指标的权重，然后再融合和评价用用其它算法，如基于神经网络、基于证据理论、基于云模型、基于空间坐标等等算法，这样感觉上就比较完整。
下面就给出层次分析法的两个实现，其实这个算法主要是实现矩阵的最大特征值和对应的特征向量。高等代数与线性代数中都给出矩阵的特征值和特征向量的定义，但是用定义求对于阶数较高的时候，运算量较大。为此一般采用近视运算。常用的就是和法和幂法。幂法网上已经给出实现了，我就针对幂法的实现改编一下，给出和法的实现。
1.和法

import java.math.BigDecimal;
import java.util.Arrays;

public class AHPCompute2 {
	/**
	 * @param args
	 */
	public static void main(String[] args) {
		/** a为N*N矩阵 */
		double[][] a = new double[][] { { 1, 1.8, 2.2, 1 }, { 0.6, 1, 3, 1.7 },
				{ 0.4, 0.3, 1, 0.5 }, { 1, 0.5, 2, 1 } };
		int N = a[0].length;
		double[] weight = new double[N];
		AHPCompute2 instance = AHPCompute2.getInstance();
		instance.weight(a, weight, N);
		System.out.println(Arrays.toString(weight));
	}

	// 单例
	private static final AHPCompute2 acw = new AHPCompute2();

	// 平均随机一致性指针
	private double[] RI = { 0.00, 0.00, 0.58, 0.90, 1.12, 1.21, 1.32, 1.41,
			1.45, 1.49 };

	// 随机一致性比率
	private double CR = 0.0;

	// 最大特征值
	private double lamta = 0.0;

	/**
	 * 私有构造
	 */
	private AHPCompute2() {

	}

	/**
	 * 返回单例
	 * 
	 * @return
	 */
	public static AHPCompute2 getInstance() {
		return acw;
	}

	/**
	 * 计算权重
	 * 
	 * @param a
	 * @param weight
	 * @param N
	 */
	public void weight(double[][] a, double[] weight, int N) {

		double[] w1 = new double[N];		
		double[] w2 = new double[N];
		double sum = 0.0;	

		//按行求和
		for (int j = 0; j < N; j++) {
			double t = 0.0;
			for (int l = 0; l < N; l++)
				t += a[l][j];
			w1[j] = t;
		}

		//按行归一化，然后按列求和，最后得到特征向量w2
		for (int k = 0; k < N; k++) {
			sum = 0;
			for (int i = 0; i < N; i++) {
				sum = sum + a[k][i] / w1[i];
			}
			w2[k] = sum / N;
		}

		lamta = 0.0;

		//求矩阵和特征向量的积,然后求出特征值
		for (int k = 0; k < N; k++) {
			sum = 0;
			for (int i = 0; i < N; i++) {
				sum = sum + a[k][i] * w2[i];
			}
			w1[k] = sum;
			lamta = lamta + w1[k] / w2[k];
		}

		// 计算矩阵最大特征值lamta，CI，RI
		lamta = lamta / N;

		double CI = (lamta - N) / (N - 1);

		if (RI[N - 1] != 0) {
			CR = CI / RI[N - 1];
		}

		// 四舍五入处理
		lamta = round(lamta, 3);
		CI = round(CI, 3);
		CR = round(CR, 3);

		for (int i = 0; i < N; i++) {
			w1[i] = round(w1[i], 4);
			w2[i] = round(w2[i], 4);
		}
		// 控制台打印输出

		System.out.println("lamta=" + lamta);
		System.out.println("CI=" + CI);
		System.out.println("CR=" + CR);

		// 控制台打印权重
		System.out.println("");

		System.out.println("w1[]=");
		for (int i = 0; i < N; i++) {
			System.out.print(w1[i] + " ");
		}
		System.out.println("");

		System.out.println("w2[]=");
		for (int i = 0; i < N; i++) {
			weight[i] = w2[i];
			System.out.print(weight[i] + " ");
		}
		System.out.println("");
	}

	/**
	 * 四舍五入
	 * 
	 * @param v
	 * @param scale
	 * @return
	 */
	public double round(double v, int scale) {
		if (scale < 0) {
			throw new IllegalArgumentException(
					"The scale must be a positive integer or zero");
		}
		BigDecimal b = new BigDecimal(Double.toString(v));
		BigDecimal one = new BigDecimal("1");
		return b.divide(one, scale, BigDecimal.ROUND_HALF_UP).doubleValue();
	}

	/**
	 * 返回随机一致性比率
	 * 
	 * @return
	 */
	public double getCR() {
		return CR;
	}
}

2.幂法

public class AHPComputeWeight { 
    /** 
     * @param args 
     */  
    public static void main(String[] args) { 
        /** a为N*N矩阵 */  
        double[][] a = new double[][] { { 1 ,1.8, 2.2, 1 },  
                { 0.6, 1, 3, 1.7 },  
                { 0.4 ,0.3, 1 ,0.5 }, {  1 ,0.5, 2, 1 }
                 };  
        int N = a[0].length;  
        double[] weight = new double[N];  
        AHPComputeWeight instance = AHPComputeWeight.getInstance();  
        instance.weight(a, weight, N);  
        System.out.println(Arrays.toString(weight));  
    }  

    // 单例  
    private static final AHPComputeWeight acw = new AHPComputeWeight();  

    // 平均随机一致性指针  
    private double[] RI = { 0.00, 0.00, 0.58, 0.90, 1.12, 1.21, 1.32, 1.41,  
            1.45, 1.49 };  

    // 随机一致性比率  
    private double CR = 0.0;  

    // 最大特征值  
    private double lamta = 0.0;  

    /** 
     * 私有构造 
     */  
    private AHPComputeWeight() {  

    }  

    /** 
     * 返回单例 
     *  
     * @return 
     */  
    public static AHPComputeWeight getInstance() {  
        return acw;  
    }  

    /** 
     * 计算权重 
     *  
     * @param a 
     * @param weight 
     * @param N 
     */  
    public void weight(double[][] a, double[] weight, int N) {  
        // 初始向量Wk  
        double[] w0 = new double[N];  
        for (int i = 0; i < N; i++) {  
            w0[i] = 1.0 / N;  
        }  

        // 一般向量W（k+1）  
        double[] w1 = new double[N];  

        // W（k+1）的归一化向量  
        double[] w2 = new double[N];  

        double sum = 1.0;  

        double d = 1.0;  

        // 误差  
        double delt = 0.00001;  

       while (d > delt) {  
            d = 0.0;  
            sum = 0;  

            // 获取向量  
            //int index = 0;  
            for (int j = 0; j < N; j++) {  
                double t = 0.0;  
                for (int l = 0; l < N; l++)  
                    t += a[j][l] * w0[l];  
                // w1[j] = a[j][0] * w0[0] + a[j][1] * w0[1] + a[j][2] * w0[2];  
                w1[j] = t;  
                sum += w1[j];  
            }  

            // 向量归一化  
            for (int k = 0; k < N; k++) {  
                w2[k] = w1[k] / sum;  

                // 最大差值  
                d = Math.max(Math.abs(w2[k] - w0[k]), d);  

                // 用于下次迭代使用  
                w0[k] = w2[k];  
            }  
       }  

        // 计算矩阵最大特征值lamta，CI，RI  
        lamta = 0.0;  

        for (int k = 0; k < N; k++) {  
            lamta += w1[k] / (N * w0[k]);  
        }  

        double CI = (lamta - N) / (N - 1);  

        if (RI[N - 1] != 0) {  
            CR = CI / RI[N - 1];  
        }  

        // 四舍五入处理  
        lamta = round(lamta, 3);  
        CI = round(CI, 3);  
        CR = round(CR, 3);  

        for (int i = 0; i < N; i++) {  
            w0[i] = round(w0[i], 4);  
            w1[i] = round(w1[i], 4);  
            w2[i] = round(w2[i], 4);  
        }  
        // 控制台打印输出  

        System.out.println("lamta=" + lamta);  
        System.out.println("CI=" + CI);  
        System.out.println("CR=" + CR);  

        // 控制台打印权重  
        System.out.println("w0[]=");  
        for (int i = 0; i < N; i++) {  
            System.out.print(w0[i] + " ");  
        }  
        System.out.println("");  

        System.out.println("w1[]=");  
        for (int i = 0; i < N; i++) {  
            System.out.print(w1[i] + " ");  
        }  
        System.out.println("");  

        System.out.println("w2[]=");  
        for (int i = 0; i < N; i++) {  
            weight[i] = w2[i];  
            System.out.print(w2[i] + " ");  
        }  
        System.out.println("");  
    }  

    /** 
     * 四舍五入 
     *  
     * @param v 
     * @param scale 
     * @return 
     */  
    public double round(double v, int scale) {  
        if (scale < 0) {  
            throw new IllegalArgumentException(  
                    "The scale must be a positive integer or zero");  
        }  
        BigDecimal b = new BigDecimal(Double.toString(v));  
        BigDecimal one = new BigDecimal("1");  
        return b.divide(one, scale, BigDecimal.ROUND_HALF_UP).doubleValue();  
    }  

    /** 
     * 返回随机一致性比率 
     *  
     * @return 
     */  
    public double getCR() {  
        return CR;  
    }  
}