performance optimization when using np.linalg.inv on large matrices in NumPy 1.24.0
I'm working with important performance optimization when trying to compute the inverse of large matrices using `np.linalg.inv` in NumPy 1.24.0. My matrices are typically 1000x1000 and occasionally larger, and the computation takes an unexpectedly long time. I've tried using `np.linalg.pinv` as an alternative, but it also seems to be slow, potentially due to the size. Here's the code snippet I'm using: ```python import numpy as np # Generate a random 1000x1000 matrix matrix = np.random.rand(1000, 1000) # Attempt to compute the inverse try: inv_matrix = np.linalg.inv(matrix) except np.linalg.LinAlgError as e: print(f'behavior: {e}') ``` On my machine, the inversion process takes around 15-20 seconds, which feels excessive. I've also checked that the matrix is non-singular before performing the inversion to avoid any `LinAlgError`. Is there a more efficient way to handle large matrix inversions in NumPy? Would using a different approach like LU decomposition be advisable in this case? Any tips on optimizing this operation would be greatly appreciated.