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 taking a Python list as an input, to be converted to a std::vector and invoking the actual constructor.
2. Provide Python bindings for the addition (__add__), the read (__getitem__) and write (__setitem__) access, and the output stream (__str__) operators.
3. Package the Python module with the compiled C++ library using setuptools.
4. Write a Python script to replicate the functionalities implemented in 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 2 from session 05.

1. Modify the NewtonSolver::solve() method in order to throw a std::runtime_error exception instead of returning NaN when failed to converge to a root.
2. Bind the NewtonClass class and its member functions, providing explicit instantiations for double and std::complex<double> numbers. The Python interface should provide consistent default arguments. Python bindings should be implemented in a separate newton_py.cpp file. Translate the std::runtime_error C++ exception to a RuntimeError Python exception.
3. Use CMake to setup the build process.
4. Write a Python script to replicate the functionalities implemented in the main.cpp file.
5. 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 code implemented.
3. Use CMake and setuptools to setup 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 a function.
5. Compare the execution time of these operations to equivalent operations in NumPy (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.