因子分析法 C++代码

以下是一个简单的 C++ 代码示例，用于执行因子分析：

#include <iostream>
#include <fstream>
#include <cmath>
#include <vector>
#include <algorithm>
using namespace std;

// 计算均值
double mean(vector<double> data) {
    double sum = 0.0;
    for (int i = 0; i < data.size(); i++) {
        sum += data[i];
    }
    return sum / data.size();
}

// 计算方差
double variance(vector<double> data) {
    double m = mean(data);
    double var = 0.0;
    for (int i = 0; i < data.size(); i++) {
        var += pow(data[i] - m, 2);
    }
    return var / (data.size() - 1);
}

// 计算协方差矩阵
vector<vector<double>> covarianceMatrix(vector<vector<double>> data) {
    int n = data.size();
    int m = data[0].size();
    vector<vector<double>> cov(n, vector<double>(n, 0.0));
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            double sum = 0.0;
            for (int k = 0; k < m; k++) {
                sum += (data[i][k] - mean(data[i])) * (data[j][k] - mean(data[j]));
            }
            cov[i][j] = sum / (m - 1);
        }
    }
    return cov;
}

// 计算特征值和特征向量
void eigen(vector<vector<double>> matrix, vector<double>& eigenvalues, vector<vector<double>>& eigenvectors) {
    int n = matrix.size();
    vector<vector<double>> A(n, vector<double>(n, 0.0));
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            A[i][j] = matrix[i][j];
        }
    }
    eigenvectors.resize(n, vector<double>(n, 0.0));
    eigenvalues.resize(n, 0.0);
    vector<double> d(n, 0.0), e(n, 0.0);
    int l, k, j, i;
    double scale, hh, h, g, f;

    for (i = n - 1; i > 0; i--) {
        l = i - 1;
        h = scale = 0.0;
        if (l > 0) {
            for (k = 0; k <= l; k++) {
                scale += abs(A[i][k]);
            }
            if (scale == 0.0) {
                e[i] = A[i][l];
            }
            else {
                for (k = 0; k <= l; k++) {
                    A[i][k] /= scale;
                    h += A[i][k] * A[i][k];
                }
                f = A[i][l];
                g = f > 0 ? -sqrt(h) : sqrt(h);
                e[i] = scale * g;
                h -= f * g;
                A[i][l] = f - g;
                f = 0.0;
                for (j = 0; j <= l; j++) {
                    A[j][i] = A[i][j] / h;
                    g = 0.0;
                    for (k = 0; k <= j; k++) {
                        g += A[j][k] * A[i][k];
                    }
                    for (k = j + 1; k <= l; k++) {
                        g += A[k][j] * A[i][k];
                    }
                    e[j] = g / h;
                    f += e[j] * A[i][j];
                }
                hh = f / (h + h);
                for (j = 0; j <= l; j++) {
                    f = A[i][j];
                    e[j] = g = e[j] - hh * f;
                    for (k = 0; k <= j; k++) {
                        A[j][k] -= (f * e[k] + g * A[i][k]);
                    }
                }
            }
        }
        else {
            e[i] = A[i][l];
        }
        d[i] = h;
    }

    d[0] = 0.0;
    e[0] = 0.0;
    for (i = 0; i < n; i++) {
        if (d[i] != 0.0) {
            for (j = 0; j < i; j++) {
                g = 0.0;
                for (k = 0; k < i; k++) {
                    g += A[i][k] * A[k][j];
                }
                for (k = 0; k < i; k++) {
                    A[k][j] -= g * A[k][i];
                }
            }
        }
        d[i] = A[i][i];
        A[i][i] = 1.0;
        for (j = 0; j < i; j++) {
            A[j][i] = A[i][j] = 0.0;
        }
    }

    for (i = 0; i < n - 1; i++) {
        k = i;
        double p = d[i];
        for (j = i + 1; j < n; j++) {
            if (d[j] > p) {
                k = j;
                p = d[j];
            }
        }
        if (k != i) {
            d[k] = d[i];
            d[i] = p;
            for (j = 0; j < n; j++) {
                p = A[j][i];
                A[j][i] = A[j][k];
                A[j][k] = p;
            }
        }
    }

    for (i = 0; i < n; i++) {
        eigenvalues[i] = d[i];
        for (j = 0; j < n; j++) {
            eigenvectors[i][j] = A[j][i];
        }
    }
}

// 执行因子分析
void factorAnalysis(vector<vector<double>> data, int k) {
    int n = data.size();
    int m = data[0].size();
    vector<vector<double>> cov = covarianceMatrix(data);
    vector<double> eigenvalues(n, 0.0);
    vector<vector<double>> eigenvectors(n, vector<double>(n, 0.0));
    eigen(cov, eigenvalues, eigenvectors);
    vector<pair<double, int>> ev(n);
    for (int i = 0; i < n; i++) {
        ev[i] = make_pair(eigenvalues[i], i);
    }
    sort(ev.rbegin(), ev.rend());
    vector<vector<double>> factors(n, vector<double>(k, 0.0));
    for (int i = 0; i < k; i++) {
        for (int j = 0; j < n; j++) {
            factors[j][i] = eigenvectors[j][ev[i].second];
        }
    }
    vector<vector<double>> loadings(m, vector<double>(k, 0.0));
    for (int i = 0; i < m; i++) {
        for (int j = 0; j < k; j++) {
            double sum = 0.0;
            for (int l = 0; l < n; l++) {
                sum += factors[l][j] * (data[l][i] - mean(data[l]));
            }
            loadings[i][j] = sum / sqrt(variance(data[i]));
        }
    }
    cout << "Factors:\n";
    for (int i = 0; i < n; i++) {
        cout << "Factor " << i + 1 << ": ";
        for (int j = 0; j < k; j++) {
            cout << factors[i][j] << " ";
        }
        cout << "\n";
    }
    cout << "Loadings:\n";
    for (int i = 0; i < m; i++) {
        cout << "Variable " << i + 1 << ": ";
        for (int j = 0; j < k; j++) {
            cout << loadings[i][j] << " ";
        }
        cout << "\n";
    }
}

int main() {
    ifstream infile("data.txt");
    vector<vector<double>> data;
    double value;
    while (infile >> value) {
        vector<double> row;
        row.push_back(value);
        for (int i = 0; i < 4; i++) {
            infile >> value;
            row.push_back(value);
        }
        data.push_back(row);
    }
    factorAnalysis(data, 2);
    return 0;
}

需要注意的是，此代码只是一个简单的示例，可能需要根据实际情况进行调整和优化。