#include <iostream>
#include <g2o/core/base_vertex.h>
#include <g2o/core/base_unary_edge.h>
#include <g2o/core/block_solver.h>
#include <g2o/core/optimization_algorithm_levenberg.h>
#include <g2o/core/optimization_algorithm_gauss_newton.h>
#include <g2o/core/optimization_algorithm_dogleg.h>
#include <g2o/solvers/dense/linear_solver_dense.h>
#include <Eigen/Core>
#include <opencv2/core/core.hpp>
#include <cmath>
#include <chrono>
using namespace std; 
// 曲线模型的顶点，模板参数：优化变量维度和数据类型(此处为自定义定点，具体可以参考下方的点定义)
class CurveFittingVertex: public g2o::BaseVertex<3, Eigen::Vector3d>
{
public:
    EIGEN_MAKE_ALIGNED_OPERATOR_NEW// 字节对齐
    virtual void setToOriginImpl() // 重置，设定被优化变量的原始值 
    {
        _estimate << 0,0,0;
    }
   
    virtual void oplusImpl( const double* update ) // 更新
    {
        _estimate += Eigen::Vector3d(update);//update强制类型转换为Vector3d
    }
    // 存盘和读盘：留空
    virtual bool read( istream& in ) {}
    virtual bool write( ostream& out ) const {}
};
// 误差模型 模板参数：观测值维度，类型，连接顶点类型
class CurveFittingEdge: public g2o::BaseUnaryEdge<1,double,CurveFittingVertex>
{
public:
    EIGEN_MAKE_ALIGNED_OPERATOR_NEW
    CurveFittingEdge( double x ): BaseUnaryEdge(), _x(x) {}
    // 计算曲线模型误差
    void computeError()
    {
        const CurveFittingVertex* v = static_cast<const CurveFittingVertex*> (_vertices[0]);
        const Eigen::Vector3d abc = v->estimate();
        _error(0,0) = _measurement - std::exp( abc(0,0)*_x*_x + abc(1,0)*_x + abc(2,0) ) ;
    }
    virtual bool read( istream& in ) {}
    virtual bool write( ostream& out ) const {}
public:
    double _x;  // x 值， y 值为 _measurement
};
int main( int argc, char** argv )
{
    double a=1.0, b=2.0, c=1.0;         // 真实参数值
    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
    double abc[3] = {0,0,0};            // abc参数的估计值
    vector<double> x_data, y_data;      // 数据
   
    cout<<"generating data: "<<endl;
    for ( int i=0; i<N; i++ )
    {
        double x = i/100.0;
        x_data.push_back ( x );
        y_data.push_back (
            exp ( a*x*x + b*x + c ) + rng.gaussian ( w_sigma )
        );
        cout<<x_data[i]<<" "<<y_data[i]<<endl;
    }
   
    // 构建图优化，先设定g2o
    typedef g2o::BlockSolver< g2o::BlockSolverTraits<3,1> > Block;  // 每个误差项优化变量维度为3，误差值维度为1
    Block::LinearSolverType* linearSolver = new g2o::LinearSolverDense<Block::PoseMatrixType>(); // 线性方程求解器。第一步：创建一个线性求解器LinearSolver。
    Block* solver_ptr = new Block( linearSolver );      // 矩阵块求解器。第二步：创建BlockSolver，并用上面定义的线性求解器初始化。
    // 梯度下降方法，从GN, LM, DogLeg 中选
    g2o::OptimizationAlgorithmLevenberg* solver = new g2o::OptimizationAlgorithmLevenberg( solver_ptr );//第三步：创建BlockSolver，并用上面定义的线性求解器初始化。
    // g2o::OptimizationAlgorithmGaussNewton* solver = new g2o::OptimizationAlgorithmGaussNewton( solver_ptr );
    // g2o::OptimizationAlgorithmDogleg* solver = new g2o::OptimizationAlgorithmDogleg( solver_ptr );
    g2o::SparseOptimizer optimizer;     // 图模型。第四步：创建图优化的核心：稀疏优化器（SparseOptimizer）。
    optimizer.setAlgorithm( solver );   // 设置求解器
    optimizer.setVerbose( true );       // 打开调试输出
   
    // 往图中增加顶点。第五步：定义图的顶点和边HyperGraph，并添加到SparseOptimizer中。
    CurveFittingVertex* v = new CurveFittingVertex();
    v->setEstimate( Eigen::Vector3d(0,0,0) );
    v->setId(0);
    optimizer.addVertex( v );
   
    // 往图中增加边
    for ( int i=0; i<N; i++ )
    {
        CurveFittingEdge* edge = new CurveFittingEdge( x_data[i] );
        edge->setId(i);
        edge->setVertex( 0, v );                // 设置连接的顶点
        edge->setMeasurement( y_data[i] );      // 观测数值
        edge->setInformation( Eigen::Matrix<double,1,1>::Identity()*1/(w_sigma*w_sigma) ); // 信息矩阵：协方差矩阵之逆
        optimizer.addEdge( edge );
    }
   
    // 执行优化。第六步：设置优化参数，开始执行优化。
    cout<<"start optimization"<<endl;
    chrono::steady_clock::time_point t1 = chrono::steady_clock::now();
    optimizer.initializeOptimization();
    optimizer.optimize(100);
    chrono::steady_clock::time_point t2 = chrono::steady_clock::now();
    chrono::duration<double> time_used = chrono::duration_cast<chrono::duration<double>>( t2-t1 );
    cout<<"solve time cost = "<<time_used.count()<<" seconds. "<<endl;
   
    // 输出优化值
    Eigen::Vector3d abc_estimate = v->estimate();
    cout<<"estimated model: "<<abc_estimate.transpose()<<endl;
   
    return 0;
}