Allow users to Use Sparse Solver

[s3alfisc]

Sometimes, we might want to fit a model with fixed effects, but without projecting them out. I.e. a model as

pf.feols("Y ~ C(f1) + C(f2)", data = data)

In this case, it would be nice if users could use the sparse solver in scipy.sparse.linalg.lsqr.

We would have to add this option to the "solver" function argument of pf.feols()

pyfixest/pyfixest/estimation/estimation.py

Line 34 in 77e7080

solver: SolverOptions = "np.linalg.solve",

and propagate this to

pyfixest/pyfixest/estimation/feols_.py

Line 427 in 77e7080

def solve_ols(self, tZX: np.ndarray, tZY: np.ndarray, solver: str):

Note that this will only speed up the model fit, but not necessarily the computation of standard errors (which are not so easily adapted to a sparse solver).

[s3alfisc]

Actually, I realize that the sparse solver is already supported, but does not compute on sparse matrices.

To support this, we'd have to update the following lines

pyfixest/pyfixest/estimation/feols_.py

Line 475 in 77e7080

self._tZX = _Z.T @ _X

to

if _solver == "scipy.sparse.lsqr": 
           
            self._tZX = csr_matrix(_Z.T) @ csr_matrix(_X)
            self._tZy = csr_matrix(_Z.T) @ csr_matrix(_Y)
else: 
    ... as before