#include <iostream>
#include <opencv2/opencv.hpp>
#include <Eigen/Core>
#include <Eigen/Dense>
#include <ctime>
using namespace std;
using namespace Eigen;
int main(int argc, char **argv) {
    double ar = 1.0, br = 2.0, cr = 1.0;         // 真实参数值
    double ae = 2.0, be = -1.0, ce = 5.0;        // 估计参数值
    int N = 100;                                 // 数据点
    double w_sigma = 1.0;                        // 噪声Sigma值
    cv::RNG rng;                                 // OpenCV随机数产生器
    vector<double> x_data, y_data;      // 数据
    for (int i = 0; i < N; i++) {
        double x = i / 100.0;
        x_data.push_back(x);
        y_data.push_back(exp(ar * x * x + br * x + cr) + rng.gaussian(w_sigma));
    }
    // 开始Gauss-Newton迭代
    int iterations = 100;    // 迭代次数
    double cost = 0, lastCost = 0;  // 本次迭代的cost和上一次迭代的cost
    for (int iter = 0; iter < iterations; iter++) {
        Matrix3d H = Matrix3d::Zero();             // Hessian = J^T J in Gauss-Newton
        Vector3d b = Vector3d::Zero();             // bias
        cost = 0;
//-----------------用GN构建增量方程，HX=g---------------------------------//
        for (int i = 0; i < N; i++) {
            double xi = x_data[i], yi = y_data[i];  // 第i个数据点
            // start your code here
            // double error = 0; // 填写计算error的表达式
            double error = yi-exp(ae * xi * xi + be * xi + ce);   // 第i个数据点的计算误差
           
            Vector3d J; // 雅可比矩阵,3x1
            J[0] = -xi*xi*exp(ae * xi * xi + be * xi + ce);  // de/da,函数求倒数，-df/da
            J[1] = -xi*exp(ae * xi * xi + be * xi + ce);;  // de/db
            J[2] = -exp(ae * xi * xi + be * xi + ce);;  // de/dc
            H += J * J.transpose(); // GN近似的H
            b += -error * J;
            // end your code here
            cost += error * error;
        }
        // 求解线性方程 Hx=b，建议用ldlt
  // start your code here
        Vector3d dx;
        //LDL^T Cholesky求解
        // clock_t time_stt2 = clock();
        dx = H.ldlt().solve(b);//Hx=b,,,H.ldlt().solve(b)
        // cout<<"LDL^T分解，耗时:\n"<<(clock()-time_stt2)/(double)
        //     CLOCKS_PER_SEC<<"ms"<<endl;
        cout<<"\n dx:"<<dx.transpose()<<endl;
        // return 0;//一写就死
    // end your code here
        if (isnan(dx[0])) {
            cout << "result is nan!" << endl;
            break;
        }
        if (iter > 0 && cost > lastCost) {
            // 误差增长了，说明近似的不够好
            cout << "cost: " << cost << ", last cost: " << lastCost << endl;
            break;
        }
        // 更新abc估计值
        ae += dx[0];
        be += dx[1];
        ce += dx[2];
        lastCost = cost;
        cout << "total cost: " << cost << endl;
    }
    cout << "estimated abc = " << ae << ", " << be << ", " << ce << endl;
    return 0;
}

include_directories(BEFORE /home/xxx/eigen3_3/complex_eigen/install/include/eigen3/)