c++ vector求m*n阶矩阵平均值、方差、协方差、特征向量、特征值

以下是使用 C++ 的 vector 实现求解 m*n 阶矩阵的平均值、方差、协方差、特征向量和特征值的代码：

#include <iostream>
#include <vector>
#include <cmath>
#include <algorithm>

using namespace std;

int main() {
    int m, n;
    cout << "请输入矩阵的行数和列数（空格隔开）：" << endl;
    cin >> m >> n;

    vector<vector<double>> matrix(m, vector<double>(n));

    // 输入矩阵
    cout << "请输入矩阵的元素（按行输入）：" << endl;
    for (int i=0; i<m; i++) {
        for (int j=0; j<n; j++) {
            cin >> matrix[i][j];
        }
    }

    // 计算平均值
    double average = 0.0;
    for (int i=0; i<m; i++) {
        for (int j=0; j<n; j++) {
            average += matrix[i][j];
        }
    }
    average /= m * n;
    cout << "平均值为：" << average << endl;

    // 计算方差
    double variance = 0.0;
    for (int i=0; i<m; i++) {
        for (int j=0; j<n; j++) {
            variance += pow(matrix[i][j] - average, 2);
        }
    }
    variance /= m * n;
    cout << "方差为：" << variance << endl;

    // 计算协方差矩阵
    vector<vector<double>> covariance(n, vector<double>(n));
    for (int i=0; i<n; i++) {
        for (int j=0; j<n; j++) {
            covariance[i][j] = 0.0;
            for (int k=0; k<m; k++) {
                covariance[i][j] += (matrix[k][i] - average) * (matrix[k][j] - average);
            }
            covariance[i][j] /= m - 1;
        }
    }
    cout << "协方差矩阵为：" << endl;
    for (int i=0; i<n; i++) {
        for (int j=0; j<n; j++) {
            cout << covariance[i][j] << " ";
        }
        cout << endl;
    }

    // 计算特征值和特征向量
    vector<double> eigenvalues(n);
    vector<vector<double>> eigenvectors(n, vector<double>(n));
    for (int i=0; i<n; i++) {
        eigenvectors[i][i] = 1.0;
    }
    for (int i=0; i<n; i++) {
        eigenvalues[i] = covariance[i][i];
    }
    int max_iter = 100;
    double eps = 1e-6;
    for (int iter=0; iter<max_iter; iter++) {
        double max_eigenv = 0.0;
        int max_index = 0;
        for (int i=0; i<n; i++) {
            if (eigenvalues[i] > max_eigenv) {
                max_eigenv = eigenvalues[i];
                max_index = i;
            }
        }
        if (max_eigenv < eps) {
            break;
        }
        for (int i=0; i<n; i++) {
            eigenvectors[i][max_index] = covariance[i][max_index];
        }
        for (int i=0; i<n; i++) {
            eigenvalues[i] = 0.0;
            for (int j=0; j<n; j++) {
                eigenvalues[i] += eigenvectors[j][i] * covariance[j][i];
            }
        }
    }
    cout << "特征向量为：" << endl;
    for (int i=0; i<n; i++) {
        for (int j=0; j<n; j++) {
            cout << eigenvectors[i][j] << " ";
        }
        cout << endl;
    }
    cout << "特征值为：" << endl;
    for (int i=0; i<n; i++) {
        cout << eigenvalues[i] << " ";
    }
    cout << endl;

    return 0;
}

要注意的是，vector 的下标是从 0 开始，所以在计算特征向量时需要将对角线上的元素初始化为 1.0。另外，特征值和特征向量的计算方法与使用数组的方法相同。