# Example: math_optimize_lm_example

Example implementation source code `LevMarqTest_impl.cpp` :

```/* +------------------------------------------------------------------------+
|                     Mobile Robot Programming Toolkit (MRPT)            |
|                          https://www.mrpt.org/                         |
|                                                                        |
| Copyright (c) 2005-2022, Individual contributors, see AUTHORS file     |
| See: https://www.mrpt.org/Authors - All rights reserved.               |
| Released under BSD License. See: https://www.mrpt.org/License          |
+------------------------------------------------------------------------+ */

#include <mrpt/math/CLevenbergMarquardt.h>
#include <mrpt/system/CTicTac.h>

#include <cmath>
#include <iostream>

using namespace mrpt;
using namespace mrpt::math;
using namespace mrpt::system;
using namespace std;

double levmarq_final_error = 1e10;

// The error function F(x):
void myFunction(
const CVectorDouble& x, const CVectorDouble& y, CVectorDouble& out_f)
{
out_f.resize(1);
// 1-cos(x+1) *cos(x*y+1)
out_f[0] = 1 - cos(x[0] + 1) * cos(x[0] * x[1] + 1);
}

void TestLevMarq()
{
CVectorDouble optimal_x;
CVectorDouble initial_x;
CVectorDouble y;

CLevenbergMarquardt::TResultInfo info;
CTicTac tictac;

initial_x.resize(2);
initial_x[0] = 1.4;  // x
initial_x[1] = 2.5;  // y

CVectorDouble increments_x(2);
increments_x.fill(0.0001);

size_t N = 1;

CLevenbergMarquardt lm;
tictac.Tic();
for (size_t k = 0; k < N; k++)
lm.execute(optimal_x, initial_x, myFunction, increments_x, y, info);

levmarq_final_error = std::sqrt(info.final_sqr_err);

#ifdef LEVMARQ_EXAMPLE_VERBOSE
const auto T = tictac.Tac() / N;
cout << "Iterations: " << info.iterations_executed << endl;
cout << "Final sqr error: " << info.final_sqr_err << endl;

cout << endl << "Final optimized position: " << optimal_x << endl;

cout << "Time: " << T * 1e6 << " us" << endl;

info.path.saveToTextFile("lm-path.txt");
cout << "Path saved to 'lm-path.txt'" << endl;
#endif
}```

C++ example source code:

```/* +------------------------------------------------------------------------+
|                     Mobile Robot Programming Toolkit (MRPT)            |
|                          https://www.mrpt.org/                         |
|                                                                        |
| Copyright (c) 2005-2022, Individual contributors, see AUTHORS file     |
| See: https://www.mrpt.org/Authors - All rights reserved.               |
| Released under BSD License. See: https://www.mrpt.org/License          |
+------------------------------------------------------------------------+ */

#define LEVMARQ_EXAMPLE_VERBOSE
#include "LevMarqTest_impl.cpp"

int main()
{
try
{
TestLevMarq();
return 0;
}
catch (const std::exception& e)
{
std::cerr << "MRPT error: " << mrpt::exception_to_str(e) << std::endl;
return -1;
}
}```