fit gauss with opencv Nelder–Mead method downhill solver

gistfile1.txt

#include "opencv2/core.hpp"
#include "opencv2/imgproc.hpp"
#include "opencv2/highgui.hpp"
#include "opencv2/videoio.hpp"
#include <opencv2/calib3d.hpp>
#include <opencv2/core/cvstd.hpp>
#include <iostream>
using namespace cv;
using namespace std;
double my_exp(double a,double s, double x0,double x){
    return a*exp(-pow(x-x0,2)/(2*s*s));
}
int main(){
    vector<double> ys={0,0,0,0,0,1,2,3,6,8,7,5,2,1,0,0,0,1,0,0,0,0};
    class Loss:public MinProblemSolver::Function{
    public:
        vector<double> ys;
        Loss(vector<double> ys_):ys(ys_){}
        int getDims() const { return 3; }
        double calc(const double* params)const{
            double a = params[0];
            double s = params[1];
            double x0 = params[2];
            double sum=0;
            for(int i=0;i<ys.size();i++){
                sum+=pow(my_exp(a,s,x0,i)-ys[i],2);
            }          
            return sum;
        }
    };
    cv::Ptr<cv::MinProblemSolver::Function> ptr_F = cv::makePtr<Loss>(ys);
    cv::Ptr<cv::DownhillSolver> solver=cv::DownhillSolver::create();
    Mat step=(cv::Mat_<double>(3,1)<<0.05,0.05,.05);
    Mat params=(cv::Mat_<double>(3,1)<<5,4,5);
    step*=.0001;
    solver->setInitStep(step);
    solver->setFunction(ptr_F);
    solver->minimize(params);
    Mat img = Mat::zeros(300,300,CV_8UC3);
    for(int x =0;x<img.cols;x++){
        double xx=x;
        double*prms=(double*)params.data;
        double a = prms[0];
        double s = prms[1];
        double x0 = prms[2];
        int y=my_exp(a,s,x0,x);
        img.at<Vec3b>(y,x)=Vec3b(255,255,255);
        if (x<ys.size()){
            int y1 = ys[x];
            img.at<Vec3b>(y1, x) = Vec3b(255, 0, 255);
        }
    }
    imshow("img",img);
    waitKey(0);
    cout << "params"<<params;
    return 0;
}