code: def test_finite_differences(self):
      # if the Hessian is estimated by finite differences or
      # a HessianUpdateStrategy (and no hessp is provided) then creation
      # of a hessp is possible.
      # GH13754
      methods = ["trust-ncg", "trust-krylov", "dogleg"]
      product = itertools.product(FD_METHODS + (BFGS,), methods)
      # a hessian needs to be specified for trustregion
      for method in methods:
          with pytest.raises(ValueError):
              minimize(
                  rosen, x0=self.x_opt, jac=rosen_der, method=method
              )
  
      # estimate hessian by finite differences. In _trustregion.py this
      # creates a hessp from the LinearOperator/HessianUpdateStrategy
      # that's returned from ScalarFunction.
      for fd, method in product:
          hess = fd
          if fd == BFGS:
              # don't want to use the same object over and over
              hess = deepcopy(fd())
  
          r = minimize(
              rosen,
              x0=self.x_opt,
              jac=rosen_der,
              hess=hess,
              tol=1e-8,
              method=method,
          )
          assert_allclose(self.x_opt, r["x"])
  
file_path: catboost/contrib/python/scipy/py3/scipy/optimize/tests/test_trustregion.py
imports: import itertools
  from copy import deepcopy
  import numpy
  from numpy.testing import assert_, assert_equal, assert_allclose
  from scipy.optimize import minimize, rosen, rosen_der, rosen_hess, rosen_hess_prod, BFGS
  from scipy.optimize._differentiable_functions import FD_METHODS
  import pytest
label_desc: Use image node_id 9 for calling the TestTrustRegionSolvers obj's underlying member method code with example usage: obj.test_finite_differences() without return types