含有Rayleigh商加速的幂法求矩阵的特征值及特征向量代码c＋＋

以下是C++代码，实现含有Rayleigh商加速的幂法求矩阵的特征值及特征向量：

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

using namespace std;

const int maxn = 100;
const double eps = 1e-8;

int n;
double A[maxn][maxn];
double x[maxn], y[maxn];

double dot(double x[], double y[]) {
    double res = 0;
    for (int i = 0; i < n; ++i) {
        res += x[i] * y[i];
    }
    return res;
}

void mul(double A[][maxn], double x[], double y[]) {
    for (int i = 0; i < n; ++i) {
        y[i] = 0;
        for (int j = 0; j < n; ++j) {
            y[i] += A[i][j] * x[j];
        }
    }
}

void rayleigh(double A[][maxn], double x[], double &lambda) {
    double a = dot(x, mul(A, x, y));
    double b = dot(x, y);
    lambda = a / b;
    for (int i = 0; i < n; ++i) {
        x[i] = y[i] / b;
    }
}

void powerIteration(double A[][maxn], double &lambda, vector<double> &v) {
    double norm = 0;
    for (int i = 0; i < n; ++i) {
        v[i] = 1;
    }
    while (true) {
        mul(A, v.data(), x);
        double maxv = fabs(x[0]);
        for (int i = 1; i < n; ++i) {
            if (fabs(x[i]) > maxv) {
                maxv = fabs(x[i]);
            }
        }
        for (int i = 0; i < n; ++i) {
            v[i] = x[i] / maxv;
        }
        double lambda0 = lambda;
        rayleigh(A, v.data(), lambda);
        if (fabs(lambda - lambda0) < eps) {
            break;
        }
    }
    norm = 0;
    for (int i = 0; i < n; ++i) {
        norm += v[i] * v[i];
    }
    norm = sqrt(norm);
    for (int i = 0; i < n; ++i) {
        v[i] /= norm;
    }
}

int main() {
    cin >> n;
    for (int i = 0; i < n; ++i) {
        for (int j = 0; j < n; ++j) {
            cin >> A[i][j];
        }
    }
    double lambda;
    vector<double> v(n);
    powerIteration(A, lambda, v);
    cout << "Eigenvalue: " << lambda << endl;
    cout << "Eigenvector: ";
    for (int i = 0; i < n; ++i) {
        cout << v[i] << " ";
    }
    cout << endl;
    return 0;
}

其中，函数`mul`和`dot`分别实现了矩阵向量乘法和向量点积。函数`rayleigh`实现了Rayleigh商加速。函数`powerIteration`实现了幂法求矩阵的特征值及特征向量。在主函数中，首先读入矩阵的大小和元素，然后调用`powerIteration`函数求解特征值和特征向量，最后输出结果。