class_docstr: Vector function and its derivatives.
  
  This class defines a vector function F: R^n->R^m and methods for
  computing or approximating its first and second derivatives.
  
  Notes
  -----
  This class implements a memoization logic. There are methods `fun`,
  `jac`, hess` and corresponding attributes `f`, `J` and `H`. The following
  things should be considered:
  
      1. Use only public methods `fun`, `jac` and `hess`.
      2. After one of the methods is called, the corresponding attribute
         will be set. However, a subsequent call with a different argument
         of *any* of the methods may overwrite the attribute.
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code: def hess(self, x, v):
      # v should be updated before x.
      self._update_v(v)
      self._update_x(x)
      self._update_hess()
      return self.H
  
imports: import numpy
  import scipy.sparse
  from ._numdiff import approx_derivative, group_columns
  from ._hessian_update_strategy import HessianUpdateStrategy
  from scipy.sparse.linalg import LinearOperator
  from scipy._lib._array_api import atleast_nd, array_namespace
label_desc: Use image node_id 9 for calling the VectorFunction obj's underlying member method code with example usage: obj.hess(x, v) and returns: self