C++ 求取6*6矩阵协方差及特征值

以下是使用 C++ 求取 6*6 矩阵协方差和特征值的示例代码：

#include <iostream>
#include <cmath>
#include <iomanip>

using namespace std;

// 求取矩阵均值
void getMean(double matrix[6][6], double mean[6]) {
    for (int j = 0; j < 6; j++) {
        double sum = 0;
        for (int i = 0; i < 6; i++) {
            sum += matrix[i][j];
        }
        mean[j] = sum / 6.0;
    }
}

// 求取协方差矩阵
void getCovariance(double matrix[6][6], double covariance[6][6], double mean[6]) {
    for (int i = 0; i < 6; i++) {
        for (int j = 0; j < 6; j++) {
            double sum = 0;
            for (int k = 0; k < 6; k++) {
                sum += (matrix[k][i] - mean[i]) * (matrix[k][j] - mean[j]);
            }
            covariance[i][j] = sum / 5.0;
        }
    }
}

// 打印矩阵
void printMatrix(double matrix[6][6]) {
    for (int i = 0; i < 6; i++) {
        for (int j = 0; j < 6; j++) {
            cout << setw(10) << matrix[i][j];
        }
        cout << endl;
    }
}

// 求取特征值和特征向量
void getEigenValue(double matrix[6][6], double eigenvalue[6], double eigenvector[6][6]) {
    double eps = 1e-10;
    double err = 1.0;
    int max_iter = 200;
    int n = 6;

    // 初始化特征向量
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            eigenvector[i][j] = (i == j) ? 1 : 0;
        }
    }

    // 迭代求解特征值和特征向量
    int iter = 0;
    while (err > eps && iter < max_iter) {
        double sum = 0;
        for (int i = 0; i < n; i++) {
            for (int j = i + 1; j < n; j++) {
                sum += pow(matrix[i][j], 2);
            }
        }
        err = sqrt(sum);

        for (int p = 0; p < n; p++) {
            for (int q = p + 1; q < n; q++) {
                double app = matrix[p][p];
                double apq = matrix[p][q];
                double aqq = matrix[q][q];

                double phi = 0.5 * atan2(2 * apq, aqq - app);
                double c = cos(phi);
                double s = sin(phi);

                matrix[p][p] = c * c * app + 2 * c * s * apq + s * s * aqq;
                matrix[q][q] = s * s * app - 2 * c * s * apq + c * c * aqq;
                matrix[p][q] = 0;
                matrix[q][p] = 0;

                for (int k = 0; k < n; k++) {
                    if (k != p && k != q) {
                        double akp = matrix[k][p];
                        double akq = matrix[k][q];
                        matrix[k][p] = c * akp + s * akq;
                        matrix[p][k] = matrix[k][p];
                        matrix[k][q] = -s * akp + c * akq;
                        matrix[q][k] = matrix[k][q];
                    }
                }

                for (int k = 0; k < n; k++) {
                    double epi = eigenvector[k][p];
                    double eqi = eigenvector[k][q];
                    eigenvector[k][p] = c * epi + s * eqi;
                    eigenvector[k][q] = -s * epi + c * eqi;
                }
            }
        }

        iter++;
    }

    for (int i = 0; i < n; i++) {
        eigenvalue[i] = matrix[i][i];
    }
}

int main() {
    double matrix[6][6] = {
        { 1, 2, 3, 4, 5, 6 },
        { 2, 3, 4, 5, 6, 7 },
        { 3, 4, 5, 6, 7, 8 },
        { 4, 5, 6, 7, 8, 9 },
        { 5, 6, 7, 8, 9, 10 },
        { 6, 7, 8, 9, 10, 11 }
    };
    double mean[6];
    double covariance[6][6];
    double eigenvalue[6];
    double eigenvector[6][6];

    // 求取矩阵均值
    getMean(matrix, mean);

    // 求取协方差矩阵
    getCovariance(matrix, covariance, mean);

    // 打印协方差矩阵
    cout << "协方差矩阵：" << endl;
    printMatrix(covariance);

    // 求取特征值和特征向量
    getEigenValue(covariance, eigenvalue, eigenvector);

    // 打印特征值
    cout << "特征值：" << endl;
    for (int i = 0; i < 6; i++) {
        cout << eigenvalue[i] << endl;
    }

    // 打印特征向量
    cout << "特征向量：" << endl;
    printMatrix(eigenvector);

    return 0;
}

该示例代码中，首先求取矩阵均值，然后求取协方差矩阵，接着使用迭代法求取特征值和特征向量。最后打印协方差矩阵、特征值和特征向量。