add parabola

src/interface.cpp

@@ -1,5 +1,6 @@
 #include <autoopt/btls.hpp>
 #include <autoopt/ellipse.hpp>
+#include <autoopt/parabola.hpp>
 #include <autoopt/interface.hpp>
 #include <autoopt/optimization_problem.hpp>
 #include <iomanip>
@@ -46,3 +47,43 @@ Eigen::VectorX<double> autoopt::fit_ellipse(
   return fitted_params;
 }
 
+Eigen::VectorX<double> autoopt::fit_parabola(
+    const std::vector<std::pair<double, double>>& data,
+    const Eigen::VectorX<double>& initial_params,
+    const Eigen::VectorX<double>& delta) {
+  auto opt_func = [&]<typename T>(const Eigen::VectorX<T>& params) {
+    parabola<T> parab(params(0), params(1));
+    quadric<T> quad = parab.to_quadric().rotated_by(params(2));
+    T error = T(0);
+    for (const auto& [x, y] : data) {
+      T y_fit = quad.slope_at(T(x));
+      error = error + (y_fit - T(y)) * (y_fit - T(y));
+    }
+    return error / T(data.size());
+  };
+
+  auto_diff_optimization_problem problem(opt_func, initial_params);
+
+  log_barrier_optimization_problem lb_problem(problem, delta, 1e-4);
+
+  while (lb_problem._barrier_strength > 1e-20) {
+    btls(lb_problem);
+    lb_problem._barrier_strength *= 1e-2;
+  }
+
+  Eigen::VectorX<double> fitted_params = problem.x();
+
+  std::cout << "Fitted parameters: " << std::setprecision(10)
+            << fitted_params.transpose() << std::endl;
+
+  double obj_value = problem.objective(fitted_params);
+  std::cout << "Objective value: " << obj_value << std::endl;
+
+  // rms in radians
+  std::cout << "RMS error: " << std::sqrt(obj_value) << " radians" << std::endl;
+  // rms in arcsec
+  double rms_arcsec = std::sqrt(obj_value) * (3600.0 * 180.0 / M_PI);
+  std::cout << "RMS error: " << rms_arcsec << " arcsec" << std::endl;
+
+  return fitted_params;
+}