6.使用样例
提供三个官方使用样例，封装为三个类：
(1)AboutPowellEquation：四个残差模型、每个残差模型仅一个残差项、LM算法。
(2)AboutCurveFitting：一个残差模型、此残差模型对应多个残差项、LM算法。
(3)AboutRosenbrock：两个残差模型、每个残差模型仅一个残差项、梯度下降法、可配置为其它优化算法测试收敛性。
以下是详细代码，依赖于C++14、Ceres和Spdlog。
1 #include <ceres/ceres.h> 2 #include <spdlog/spdlog.h> 3 using namespace std; 4 5 class AboutPowellEquation //CeresBasicDemo: multiple residual models + no input vector 6 { 7 public: 8 static void TestMe(int argc = 0, char** argv = 0) 9 { 10 double param[4] = { 3.0, -1.0, 0.0, 1.0 }; 11 ceres::Problem problem; 12 problem.AddResidualBlock(new ceres::AutoDiffCostFunction<AboutPowellEquation, 4, 4>(new AboutPowellEquation), NULL, param); 13 14 ceres::Solver::Options options; 15 options.minimizer_progress_to_stdout = true; 16 ceres::Solver::Summary summary; 17 ceres::Solve(options, &problem, &summary); 18 19 cout << summary.FullReport() << endl; 20 spdlog::info("x1={:.9f}, x2={:.9f} x3={:.9f} x4={:.9f}", param[0], param[1], param[2], param[3]); 21 } 22 23 public: 24 template <typename tp> bool operator()(const tp* const param, tp* residual) const 25 { 26 tp x1 = param[0]; 27 tp x2 = param[1]; 28 tp x3 = param[2]; 29 tp x4 = param[3]; 30 residual[0] = x1 + 10. * x2; 31 residual[1] = sqrt(5.) * (x3 - x4); 32 residual[2] = (x2 - 2. * x3) * (x2 - 2. * x3); 33 residual[3] = sqrt(10.) * (x1 - x4) * (x1 - x4); 34 return true; 35 } 36 }; 37 38 class AboutCurveFitting //CeresBasicDemo: single residual model + multiple input vectors 39 { 40 public: 41 static void TestMe(int argc = 0, char** argv = 0) 42 { 43 vector<double> xys = 44 { 45 0.000000e+00, 1.133898e+00, 46 7.500000e-02, 1.334902e+00, 47 1.500000e-01, 1.213546e+00, 48 2.250000e-01, 1.252016e+00, 49 3.000000e-01, 1.392265e+00, 50 3.750000e-01, 1.314458e+00, 51 4.500000e-01, 1.472541e+00, 52 5.250000e-01, 1.536218e+00, 53 6.000000e-01, 1.355679e+00, 54 6.750000e-01, 1.463566e+00, 55 7.500000e-01, 1.490201e+00, 56 8.250000e-01, 1.658699e+00, 57 9.000000e-01, 1.067574e+00, 58 9.750000e-01, 1.464629e+00, 59 1.050000e+00, 1.402653e+00, 60 1.125000e+00, 1.713141e+00, 61 1.200000e+00, 1.527021e+00, 62 1.275000e+00, 1.702632e+00, 63 1.350000e+00, 1.423899e+00, 64 1.425000e+00, 1.543078e+00, 65 1.500000e+00, 1.664015e+00, 66 1.575000e+00, 1.732484e+00, 67 1.650000e+00, 1.543296e+00, 68 1.725000e+00, 1.959523e+00, 69 1.800000e+00, 1.685132e+00, 70 1.875000e+00, 1.951791e+00, 71 1.950000e+00, 2.095346e+00, 72 2.025000e+00, 2.361460e+00, 73 2.100000e+00, 2.169119e+00, 74 2.175000e+00, 2.061745e+00, 75 2.250000e+00, 2.178641e+00, 76 2.325000e+00, 2.104346e+00, 77 2.400000e+00, 2.584470e+00, 78 2.475000e+00, 1.914158e+00, 79 2.550000e+00, 2.368375e+00, 80 2.625000e+00, 2.686125e+00, 81 2.700000e+00, 2.712395e+00, 82 2.775000e+00, 2.499511e+00, 83 2.850000e+00, 2.558897e+00, 84 2.925000e+00, 2.309154e+00, 85 3.000000e+00, 2.869503e+00, 86 3.075000e+00, 3.116645e+00, 87 3.150000e+00, 3.094907e+00, 88 3.225000e+00, 2.471759e+00, 89 3.300000e+00, 3.017131e+00, 90 3.375000e+00, 3.232381e+00, 91 3.450000e+00, 2.944596e+00, 92 3.525000e+00, 3.385343e+00, 93 3.600000e+00, 3.199826e+00, 94 3.675000e+00, 3.423039e+00, 95 3.750000e+00, 3.621552e+00, 96 3.825000e+00, 3.559255e+00, 97 3.900000e+00, 3.530713e+00, 98 3.975000e+00, 3.561766e+00, 99 4.050000e+00, 3.544574e+00, 100 4.125000e+00, 3.867945e+00, 101 4.200000e+00, 4.049776e+00, 102 4.275000e+00, 3.885601e+00, 103 4.350000e+00, 4.110505e+00, 104 4.425000e+00, 4.345320e+00, 105 4.500000e+00, 4.161241e+00, 106 4.575000e+00, 4.363407e+00, 107 4.650000e+00, 4.161576e+00, 108 4.725000e+00, 4.619728e+00, 109 4.800000e+00, 4.737410e+00, 110 4.875000e+00, 4.727863e+00, 111 4.950000e+00, 4.669206e+00 112 }; 113 114 vector<double> xs, ys; 115 for (int i = 0; i < (int)xys.size(); i += 2) 116 { 117 xs.push_back(xys[i]); 118 ys.push_back(xys[i + 1]); 119 } 120 121 double param[2] = { 0.0, 0.0 }; 122 ceres::Problem problem; 123 problem.AddResidualBlock(new ceres::AutoDiffCostFunction<AboutCurveFitting, ceres::DYNAMIC, 2>(new AboutCurveFitting((int)xs.size(), xs.data(), ys.data()), (int)xs.size()), NULL, param); 124 125 ceres::Solver::Options options; 126 options.minimizer_progress_to_stdout = true; 127 ceres::Solver::Summary summary; 128 ceres::Solve(options, &problem, &summary); 129 130 cout << summary.FullReport() << endl; 131 spdlog::info("x1={:.9f} x2={:.9f}", param[0], param[1]); 132 } 133 134 public: 135 int count; 136 double* xs; 137 double* ys; 138 AboutCurveFitting(int count0, double* xs0, double* ys0) : count(count0), xs(xs0), ys(ys0) {} 139 140 public: 141 template <typename tp> bool operator()(const tp* const param, tp* residual) const 142 { 143 tp m = param[0]; 144 tp c = param[1]; 145 for (int k = 0; k < count; ++k) residual[k] = ys[k] - exp(m * xs[k] + c); 146 return true; 147 } 148 }; 149 150 class AboutRosenbrock //CeresApplication: GradientDescent, ConjugateGradient, BFGS, LBFGS, LM, DL 151 { 152 public: 153 static void TestMe(int argc = 0, char** argv = 0) 154 { 155 double param[2] = { 3.0, -1.0 }; 156 ceres::Problem problem; 157 problem.AddResidualBlock(new ceres::AutoDiffCostFunction<AboutRosenbrock, 2, 2>(new AboutRosenbrock), NULL, param); 158 159 ceres::Solver::Options options; 160 options.minimizer_type = ceres::LINE_SEARCH; 161 options.line_search_direction_type = ceres::STEEPEST_DESCENT; 162 options.minimizer_progress_to_stdout = true; 163 ceres::Solver::Summary summary; 164 ceres::Solve(options, &problem, &summary); 165 166 cout << summary.FullReport() << endl; 167 spdlog::info("x1={:.9f}, x2={:.9f}", param[0], param[1]); 168 } 169 170 public: 171 template <typename tp> bool operator()(const tp* const param, tp* residual) const 172 { 173 tp x = param[0]; 174 tp y = param[1]; 175 residual[0] = 1. - x; 176 residual[1] = 10. * y - 10. * x * x; 177 return true; 178 } 179 }; 180 181 int main(int argc, char** argv) 182 { 183 spdlog::set_pattern("%v"); 184 AboutPowellEquation::TestMe(argc, argv); 185 spdlog::info(" "); 186 AboutCurveFitting::TestMe(argc, argv); 187 spdlog::info(" "); 188 AboutRosenbrock::TestMe(argc, argv); 189 std::getchar(); 190 return 0; 191 }