tinyLM

A tiny C++17 implementation of a Levenberg-Marquardt non-linear least-squares solver.

Based on the Eigen matrix/numerical library for c++.

Install

To install this single-file header library, just download the tinyLM.hpp file, and include it somewhere appropriate in your project.

Everything is wrapped nicely into a tinyLM namespace, so you can safely include it anywhere. I would suggest making yourself a single-file wrapper any incorporate as an invisible dependency in your project, for example, like so:

// file: LM_wrapper.hpp
#include "tinyLM.hpp"

namespace MyAwesomeProject {
  using tinyLM;
}
// end-of-file

You should have Eigen available before including the tinyLM header.

It is really as easy as that!

Usage

// file: problem.hpp
#include "tinyLM.hpp"

#include <tuple>
#include <iostream>

// Include some project-specific headers to define load_data()!!

function eval_sphere_fit(const Eigen::Vector4d& x) {
  auto radius = x[0];
  auto center = x.tail<3>();
  
  Eigen::ArrayXXd data_centered = data.colwise() - center;
  Eigen::ArrayXd data_radius = data_centered.colwise().norm();
  Eigen::ArrayXd residuals = data_radius - radius;

  Eigen::Matrix<double, Eigen::Dynamic, 4> Jacobian(data.cols(), 4);
  Jacobian.col(0).array() = -1;
  Jacobian.col(1) = data_centered.row(0).array() / data_radius.array();
  Jacobian.col(2) = data_centered.row(1).array() / data_radius.array();
  Jacobian.col(3) = data_centered.row(2).array() / data_radius.array();
  
  return std::make_tuple(residuals, Jacobian);
}

int main() {
  
  Eigen::ArrayXXd data = load_data();
  auto [x, LM_state] = tinyLM::LM(eval_sphere_fit, Eigen::Vector4d::Zero())

  double radius = x[0];
  Eigen::Vector3d center = x.tail<3>();

  std::cout << "Radius: " << radius << std::endl;
  std::cout << "Center: " << center.transpose() << std::endl;

  std::cout << LM_state << std::endl;
}

// end-of-file

What licence?

For now, I will retain all rights until I find the right licence. I expect the licence to be rather permissive, but cannot yet say how much.