Exercise 1: binding classes and magic methods

Provide Python bindings using pybind11 for the code provided as the solution to exercise 1 from session 03.

1. Bind the DataProcessor class and its member functions. Using a lambda function, expose a constructor that takes a Python list as input, converts it to a std::vector, and invokes the actual C++ constructor.

2. Provide Python bindings for:

   • Addition operator (__add__)
   • Read/write access operator (__getitem__, __setitem__)
   • Output stream operator (__str__)

3. Package the Python module with the compiled C++ library using setuptools.

4. Write a Python script to replicate the functionalities from the main.cpp file.

Exercise 2: binding class templates and exceptions

Provide Python bindings using pybind11 for the code provided as the solution to exercise 3 from session 05.

1. Modify the NewtonSolver::solve() method to throw a std::runtime_error exception instead of returning NaN when it fails to converge to a root.

2. Bind the NewtonSolver class and its member functions, providing explicit instantiations for double and std::complex<double> types. The Python interface should provide consistent default arguments. Translate the std::runtime_error C++ exception to a RuntimeError Python exception. Implement Python bindings in a separate newton_py.cpp file.

3. Use CMake to set up the build process.

4. Write a Python script to replicate the functionalities implemented in the main.cpp file, and verify that exception handling works properly.

Exercise 3: binding with external libraries

1. Implement C++ functions using the Eigen library to perform matrix-matrix multiplication and matrix inversion.

2. Provide Python bindings using pybind11 for the implemented code.

3. Use CMake and setuptools with pyproject.toml to set up the build process.

4. Write a Python script to test the performance of the Eigen-based operations. Implement a log_execution_time decorator to print the execution time of each function.

5. Compare the execution time of these operations to equivalent NumPy operations (e.g., numpy.matmul for multiplication and numpy.linalg.inv for inversion). Use a large matrix (e.g., ) of random integers between 0 and 1000 for the test.