使⽤ceres进⾏曲线拟合本⽂⾸先通过下⾯的公式⽣成⼀系列的数据。
然后构造如下所⽰的最⼩⼆乘问题：
下⾯来看⼀下如何使⽤ceres对该问题进⾏优化吧！
#include <iostream>
#include <ceres/ceres.h>
#include <glog/logging.h>
#include<chrono>
#include <math.h>
#include <algorithm>
#include <fstream>
using namespace std;
using ceres::AutoDiffCostFunction;
using ceres::CostFunction;
using ceres::Problem;
using ceres::Solve;
using ceres::Solver;
//使⽤define来定义⼀个宏
//⽣成a,b中的随机数
#define random(a,b) (rand()%(b-a+1)+a)
//x表⽰待优化参数块，residual表⽰残差块
/
/通过⾮线性优化到函数梯度下降的⾃变量的取值。
//定义残差块
struct CostFunctor {
CostFunctor(double x,double y):x_(x),y_(y){
}
template <typename T>
bool operator()(const T* const  m,const T* const  c,T* residual) const {
//residual[0] = exp(m[0]*T(x_)+c[0])-T(y_);
residual[0] = (ceres::exp(m[0]*T(x_)+c[0]))-T(y_);
return true;
}
private:
const double x_,y_;
};
int main(int argc, char** argv) {
const double data[] = {
0.000000e+00, 1.133898e+00,
7.500000e-02, 1.334902e+00,
1.500000e-01, 1.213546e+00,
2.250000e-01, 1.252016e+00,
3.000000e-01, 1.392265e+00,
3.750000e-01, 1.314458e+00,
4.500000e-01, 1.472541e+00,
5.250000e-01, 1.536218e+00,
6.000000e-01, 1.355679e+00,
6.750000e-01, 1.463566e+00,
7.500000e-01, 1.490201e+00,
8.250000e-01, 1.658699e+00,
9.000000e-01, 1.067574e+00,
9.750000e-01, 1.464629e+00,
1.050000e+00, 1.402653e+00,
1.125000e+00, 1.713141e+00,
1.125000e+00, 1.713141e+00,
1.200000e+00, 1.527021e+00,
1.275000e+00, 1.702632e+00,
1.350000e+00, 1.423899e+00,
1.425000e+00, 1.543078e+00,
1.500000e+00, 1.664015e+00,
1.575000e+00, 1.732484e+00,
1.650000e+00, 1.543296e+00,
1.725000e+00, 1.959523e+00,
1.800000e+00, 1.685132e+00,
1.875000e+00, 1.951791e+00,
1.950000e+00,
2.095346e+00,
2.025000e+00, 2.361460e+00,
2.100000e+00, 2.169119e+00,
2.175000e+00, 2.061745e+00,
2.250000e+00, 2.178641e+00,
2.325000e+00, 2.104346e+00,
2.400000e+00, 2.584470e+00,
2.475000e+00, 1.914158e+00,
2.550000e+00, 2.368375e+00,
2.625000e+00, 2.686125e+00,
2.700000e+00, 2.712395e+00,
2.775000e+00, 2.499511e+00,
2.850000e+00, 2.558897e+00,
2.925000e+00, 2.309154e+00,
3.000000e+00, 2.869503e+00,
3.075000e+00, 3.116645e+00,
cmake如何使用3.150000e+00, 3.094907e+00,
3.225000e+00, 2.471759e+00,
3.300000e+00, 3.017131e+00,
3.375000e+00, 3.232381e+00,
3.450000e+00, 2.944596e+00,
3.525000e+00, 3.385343e+00,
3.600000e+00, 3.199826e+00,
3.675000e+00, 3.423039e+00,
3.750000e+00, 3.621552e+00,
3.825000e+00, 3.559255e+00,
3.900000e+00, 3.530713e+00,
3.975000e+00, 3.561766e+00,
4.050000e+00, 3.544574e+00,
4.125000e+00, 3.867945e+00,
4.200000e+00, 4.049776e+00,
4.275000e+00, 3.885601e+00,
4.350000e+00, 4.110505e+00,
4.425000e+00, 4.345320e+00,
4.500000e+00, 4.161241e+00,
4.575000e+00, 4.363407e+00,
4.650000e+00, 4.161576e+00,
4.725000e+00, 4.619728e+00,
4.800000e+00, 4.737410e+00,
4.875000e+00, 4.727863e+00,
4.950000e+00, 4.669206e+00,
};
const int kNumObservations = 67;
google::InitGoogleLogging(argv[0]);
/
/设置待优化变量初值
double m=0,c=0;
const double initial_m = 0;
const double initial_c=0;
//构建优化问题
Problem problem;
// Set up the only cost function (also known as residual). This uses  // auto-differentiation to obtain the derivative (jacobian).
for(int i=0;i<kNumObservations;i++)
for(int i=0;i<kNumObservations;i++)
{
openfile<<data[2*i]<<"          "<<data[2*i+1]<<endl;
//定义残差块，误差类型，输⼊维度，输出维度
CostFunction* cost_function =new AutoDiffCostFunction<CostFunctor, 1,1,1>(new CostFunctor(data[2*i],data[2*i+1]));      //problem.AddResidualBlock(cost_function, nullptr,&m,&c );
//添加残差块
problem.AddResidualBlock(cost_function,    new ceres:: CauchyLoss(0.5),&m,&c );
}
//优化问题添加残差块，不使⽤核函数
//配置求解器
ceres::Solver::Options options;
options.linear_solver_type=ceres::DENSE_QR;//增量⽅程求解
options.minimizer_progress_to_stdout=true;//输出到cout
ceres::Solver::Summary summary;
//开始求解
ceres::Solve(options,&problem,&summary);
//输出求解过程
cout<<summary.BriefReport()<<endl;
//输出优化后的参数
std::cout << "m: " << initial_m<< " -> " << m << "\n";
std::cout << "c: " << initial_c<< " -> " << c << "\n";
openfile.close();
return 0;
}
cmake_minimum_required(VERSION 2.6)
project(ceres_learn)
set(CMAKE_THREAD_LIBS_INIT "-lpthread")
set(CMAKE_HAVE_THREADS_LIBRARY 1)
set(CMAKE_USE_WIN32_THREADS_INIT 0)
set(CMAKE_USE_PTHREADS_INIT 1)
set(THREADS_PREFER_PTHREAD_FLAG ON)
find_package( Ceres REQUIRED)
include_directories( ${CERES_INCLUDE_DIRS})
add_executable(ceres_learn curve_fitting.cpp)
target_link_libraries(ceres_learn ${CERES_LIBRARIES})