code: def test_x_storage_overlap(self):
      # Scalar_Function should not store references to arrays, it should
      # store copies - this checks that updating an array in-place causes
      # Scalar_Function.x to be updated.
  
      def f(x):
          return np.sum(np.asarray(x) ** 2)
  
      x = np.array([1.0, 2.0, 3.0])
      sf = ScalarFunction(
          f, x, (), "3-point", lambda x: x, None, (-np.inf, np.inf)
      )
  
      assert x is not sf.x
      assert_equal(sf.fun(x), 14.0)
      assert x is not sf.x
  
      x[0] = 0.0
      f1 = sf.fun(x)
      assert_equal(f1, 13.0)
  
      x[0] = 1
      f2 = sf.fun(x)
      assert_equal(f2, 14.0)
      assert x is not sf.x
  
      # now test with a HessianUpdate strategy specified
      hess = BFGS()
      x = np.array([1.0, 2.0, 3.0])
      sf = ScalarFunction(
          f, x, (), "3-point", hess, None, (-np.inf, np.inf)
      )
  
      assert x is not sf.x
      assert_equal(sf.fun(x), 14.0)
      assert x is not sf.x
  
      x[0] = 0.0
      f1 = sf.fun(x)
      assert_equal(f1, 13.0)
  
      x[0] = 1
      f2 = sf.fun(x)
      assert_equal(f2, 14.0)
      assert x is not sf.x
  
      # gh13740 x is changed in user function
      def ff(x):
          x *= x  # overwrite x
          return np.sum(x)
  
      x = np.array([1.0, 2.0, 3.0])
      sf = ScalarFunction(
          ff, x, (), "3-point", lambda x: x, None, (-np.inf, np.inf)
      )
      assert x is not sf.x
      assert_equal(sf.fun(x), 14.0)
      assert_equal(sf.x, np.array([1.0, 2.0, 3.0]))
      assert x is not sf.x
  
imports: import pytest
  import numpy
  from numpy.testing import TestCase, assert_array_almost_equal, assert_array_equal, assert_, assert_allclose, assert_equal
  from scipy.sparse import csr_matrix
  from scipy.sparse.linalg import LinearOperator
  from scipy.optimize._differentiable_functions import ScalarFunction, VectorFunction, LinearVectorFunction, IdentityVectorFunction
  from scipy.optimize import rosen, rosen_der, rosen_hess
  from scipy.optimize._hessian_update_strategy import BFGS
label_desc: Use image node_id 4 for calling the TestScalarFunction obj's underlying member method code with example usage: obj.test_x_storage_overlap() and returns: np, np