code: def sherman_morrison(A: np.ndarray, u: np.ndarray, v: np.ndarray):
      """Sherman-Morrison formula.
  
      This is an inplace function.
  
      Parameters
      ----------
      A
      u
      v
  
      References
      ----------
      [^1]: [Fast rank-one updates to matrix inverse? — Tim Vieira](https://timvieira.github.io/blog/post/2021/03/25/fast-rank-one-updates-to-matrix-inverse/)
  
      """
      Au = A @ u
      alpha = -1 / (1 + v.T @ Au)
      sp.linalg.blas.dger(alpha, Au, v.T @ A, a=A, overwrite_a=1)
  
imports: from __future__ import annotations
  import functools
  import itertools
  import math
  import operator
  import numpy
  import scipy
label_desc: Use image node_id 14 for calling a global function with example usage: sherman_morrison(A, u, v) without return types