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"""Routines for solving a linear system of equations."""
import numpy as np
from numpy.typing import NDArray
def gaussian_eliminate(aa: NDArray[np.float_], bb: NDArray[np.float_]) -> NDArray[np.float_] | None:
"""Solves a linear system of equations (Ax = b) by Gauss-elimination
Args:
aa: Matrix with the coefficients. Shape: (n, n).
bb: Right hand side of the equation. Shape: (n,)
Returns:
Vector xx with the solution of the linear equation or None
if the equations are linearly dependent.
"""
nn = aa.shape[0]
xx = np.zeros((nn,), dtype=np.float_)
return xx
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