code: def simplified_woodbury_update(
      a_inv: types.Float, u: types.Float
  ) -> types.Float:
      """Returns `w` such that `inverse(a + u.T.dot(u)) = a_inv + w`.
  
      Makes use of the Woodbury matrix identity. See
      https://en.wikipedia.org/wiki/Woodbury_matrix_identity.
  
      **NOTE**: This implementation assumes that a_inv is symmetric. Since it's too
      expensive to check symmetricity, the function silently outputs a wrong answer
      in case `a` is not symmetric.
  
      Args:
        a_inv: an invertible SYMMETRIC `Tensor` of shape `[m, m]`.
        u: a `Tensor` of shape `[n, m]`.
  
      Returns:
        A `Tensor` `w` of shape `[m, m]` such that
        `inverse(a + u.T.dot(u)) = a_inv + w`.
      Raises:
        ValueError: if `a_inv` is not square or `a_inv` and `u` have incompatible
        shapes.
      """
      _check_shapes(a_inv, u)
      u_x_a_inv = tf.matmul(u, a_inv)
      capacitance = tf.eye(tf.shape(u)[0], dtype=u.dtype) + tf.matmul(
          u_x_a_inv, u, transpose_b=True
      )
      return -1.0 * tf.matmul(
          u_x_a_inv,
          tf.linalg.solve(capacitance, u_x_a_inv),
          transpose_a=True,
      )
  
file_path: agents/tf_agents/bandits/policies/linalg.py
imports: from __future__ import absolute_import
  from __future__ import division
  from __future__ import print_function
  import tensorflow
  from tf_agents.typing import types
  from tf_agents.utils import common
label_desc: Use image node_id 4 for calling a global function with example usage: simplified_woodbury_update(a_inv, u) and returns: unknown