docstr: Test step_and_cost() function with the single-input qnode. Both blocking settings
  (on/off) are tested.
docstr_tok: ["Test","step_and_cost","(",")","function","with","the","single-input","qnode",".","Both","blocking","settings","(","on\/off",")","are","tested","."]
code: def test_step_and_cost_from_single_input(
      self, finite_diff_step, seed
  ):
      """Test step_and_cost() function with the single-input qnode. Both blocking settings
      (on/off) are tested.
      """
      regularization = 1e-3
      stepsize = 1e-2
      opt_blocking = qml.QNSPSAOptimizer(
          stepsize=stepsize,
          regularization=regularization,
          finite_diff_step=finite_diff_step,
          resamplings=1,
          blocking=True,
          history_length=5,
          seed=seed,
      )
      opt_no_blocking = deepcopy(opt_blocking)
      opt_no_blocking.blocking = False
      # target opt is used to reproduce the result with step()
      target_opt = deepcopy(opt_blocking)
  
      qnode, params_shape = get_single_input_qnode()
      params = np.random.rand(*params_shape)
  
      (
          new_params_blocking_res,
          qnode_blocking_res,
      ) = opt_blocking.step_and_cost(qnode, params)
      with pytest.warns(UserWarning):
          new_params_expected = target_opt.step(qnode, params)
      # analytical expression of the qnode
      qnode_expected = np.cos(params[0][0] / 2) ** 2 - np.sin(
          params[0][0] / 2
      ) ** 2 * np.cos(params[0][1])
      assert np.allclose(new_params_blocking_res, new_params_expected)
      assert np.allclose(qnode_blocking_res, qnode_expected)
  
      (
          new_params_no_blocking_res,
          qnode_no_blocking_res,
      ) = opt_no_blocking.step_and_cost(qnode, params)
      assert np.allclose(
          new_params_no_blocking_res, new_params_expected
      )
      assert np.allclose(qnode_no_blocking_res, qnode_expected)
  
file_path: pennylane/tests/optimize/test_qnspsa.py
imports: from copy import deepcopy
  import pytest
  from scipy.linalg import sqrtm
  import pennylane
  from pennylane import numpy
label_desc: Use image node_id 5 for calling the TestQNSPSAOptimizer obj's underlying member method code with example usage: obj.test_step_and_cost_from_single_input(finite_diff_step, seed) without return types