Member Sherman-Morrison?

You should, because of this. Actually, that was the Woodbury formula. As a special case, we have the Sherman-Morrison update, which we here implement in Python:

def sherman_morrison(M_inv, x):
    """
    Input:
        - x: (np.array) column vector
        - M_inv: (np.array) inverse of M matrix
    Output:
        (M + x*x')^-1 computed using Sherman-Morrison formula
    """
    x = x.reshape((-1, 1))
    M_inv -= M_inv.dot(x.dot(x.T.dot(M_inv))) / (1 + x.T.dot(M_inv.dot(x)))
    return M_inv

Written on May 23, 2018