有A,B,C,D,E五個網頁，其中
1)A網頁有鏈接指向B,C,D,E
2)B網頁有鏈接指向A,D
3)C網頁有鏈接指向A,D
4)D網頁有鏈接指向C
5)E網頁有鏈接指向A,C

思想：
1、計算矩陣S
2、計算矩陣G
3、根據q=Gq',迭代

public class PageRank {
    private static final double ALPHA = 0.85;
    private static final double DISTANCE = 0.0000001;

    private static final double[][] matrixS = {
            {0, 1 / 2.0, 1 / 2.0, 0, 1 / 2.0},
            {1 / 4.0, 0, 0, 0, 0},
            {1 / 4.0, 0, 0, 1, 1 / 2.0},
            {1 / 4.0, 1 / 2.0, 1 / 2.0, 0, 0},
            {1 / 4.0, 0, 0, 0, 0}
    };

    private static final double[][] matrixU = {
            {1.0, 1.0, 1.0, 1.0, 1.0},
            {1.0, 1.0, 1.0, 1.0, 1.0},
            {1.0, 1.0, 1.0, 1.0, 1.0},
            {1.0, 1.0, 1.0, 1.0, 1.0},
            {1.0, 1.0, 1.0, 1.0, 1.0}
    };

    public static void main(String[] args) {

        System.out.println("S矩陣:");
        printMatrix(matrixS);

        double[][] matrixG = calMatrixG();

        System.out.println("G矩陣:");
        printMatrix(matrixG);

        double[] vector = {1.0, 1.0, 1.0, 1.0, 1.0};

        double[] vectorQ = calVectorQ(matrixG, vector);

        System.out.println("向量:");
        printVector(vectorQ);
    }

    private static void printMatrix(double[][] matrix) {
        for (int i = 0; i < matrix.length; i++) {
            for (int j = 0; j < matrix[i].length; j++) {

//                String result = String.format("%1$10s", matrix[i][j]);
                String result = String.format("%.5f", matrix[i][j]);

                System.out.print(result + " ");
            }
            System.out.println();
        }
    }

    private static void printVector(double[] vector) {
        for (int i = 0; i < vector.length; i++) {

            String result = String.format("%.5f", vector[i]);

            System.out.print(result + " ");
        }
    }

    private static double[][] calMatrixG() {
        return calMatrixPlus(calMatrixMultiDouble(matrixS, ALPHA),
                calMatrixMultiDouble(matrixU, (1 - ALPHA) * (1.0 / matrixS.length)));
    }

    private static double[][] calMatrixMultiDouble(double[][] matrix, double value) {
        for (int i = 0; i < matrix.length; i++) {
            for (int j = 0; j < matrix[i].length; j++) {
                matrix[i][j] *= value;
            }

        }
        return matrix;
    }

    private static double[][] calMatrixPlus(double[][] matrix1, double[][] matrix2) {
        for (int i = 0; i < matrix1.length; i++) {
            for (int j = 0; j < matrix1[i].length; j++) {
                matrix1[i][j] += matrix2[i][j];
            }

        }
        return matrix1;
    }

    private static double[] calMatrixMultiVetor(double[][] matrix, double[] vetor) {
        double[] tmp = new double[matrix.length];

        for (int i = 0; i < matrix.length; i++) {
            for (int j = 0; j < matrix[i].length; j++) {
                tmp[i] += matrix[i][j] * vetor[j];
            }
        }

        return tmp;
    }

    private static double calVectorDistance(double[] vector1, double[] vector2) {
        double sum = 0;

        for (int i = 0; i < vector1.length; i++) {
            sum += Math.pow(vector1[i] - vector2[i], 2);
        }
        return Math.sqrt(sum);
    }

    private static double[] calVectorQ(double[][] matrixG, double[] vector) {

        double[] vector2 = calMatrixMultiVetor(matrixG, vector);

        double distance = calVectorDistance(vector, vector2);

        int n = 1;

//        System.out.print(distance);

        vector = vector2;
        while (distance > DISTANCE) {
            n++;

            vector2 = calMatrixMultiVetor(matrixG, vector);

            distance = calVectorDistance(vector, vector2);

            vector = vector2;

//            System.out.println(distance);
        }

        System.out.println("計算次數" + n);

        return vector2;
    }
}

輸出
S矩陣:
0.00000 0.50000 0.50000 0.00000 0.50000
0.25000 0.00000 0.00000 0.00000 0.00000
0.25000 0.00000 0.00000 1.00000 0.50000
0.25000 0.50000 0.50000 0.00000 0.00000
0.25000 0.00000 0.00000 0.00000 0.00000
G矩陣:
0.03000 0.45500 0.45500 0.03000 0.45500
0.24250 0.03000 0.03000 0.03000 0.03000
0.24250 0.03000 0.03000 0.88000 0.45500
0.24250 0.45500 0.45500 0.03000 0.03000
0.24250 0.03000 0.03000 0.03000 0.03000
計算次數29
向量:
1.21040 0.40721 1.68064 1.29454 0.40721