class_docstr: Tests the integration of ``_reconstruct_equ`` and ``_reconstruct_gen`` via
  the full ``reconstruct`` function as well as the differentiability of the
  reconstructed function with respect to their single scalar argument.
docstr: Tests the reconstruction and differentiability with TensorFlow.
docstr_tok: ["Tests","the","reconstruction","and","differentiability","with","TensorFlow","."]
code: def test_differentiability_tensorflow(
      self,
      qnode,
      params,
      ids,
      nums_frequency,
      spectra,
      shifts,
      exp_calls,
  ):
      """Tests the reconstruction and differentiability with TensorFlow."""
      if qnode is qnode_4:
          pytest.skip(
              "Gradients are empty in TensorFlow for independent functions."
          )
      import tensorflow as tf
  
      qnode = qml.QNode(qnode, dev_1, interface="tf")
      params = tuple(
          tf.Variable(par, dtype=tf.float64) for par in params
      )
      if spectra is not None:
          spectra = {
              outer_key: {
                  inner_key: tf.constant(val, dtype=tf.float64)
                  for inner_key, val in outer_val.items()
              }
              for outer_key, outer_val in spectra.items()
          }
      if shifts is not None:
          shifts = {
              outer_key: {
                  inner_key: tf.constant(val, dtype=tf.float64)
                  for inner_key, val in outer_val.items()
              }
              for outer_key, outer_val in shifts.items()
          }
      with qml.Tracker(qnode.device) as tracker:
          recons = reconstruct(
              qnode, ids, nums_frequency, spectra, shifts
          )(*params)
      assert tracker.totals["executions"] == exp_calls
      arg_names = list(signature(qnode.func).parameters.keys())
      for outer_key in recons:
          outer_key_num = arg_names.index(outer_key)
          for inner_key, rec in recons[outer_key].items():
              if outer_key == "Z" and inner_key == (1, 3):
                  # This is a constant function dependence, which can
                  # not be properly resolved by this test.
                  continue
              x0 = params[outer_key_num]
              if not len(qml.math.shape(x0)) == 0:
                  x0 = x0[inner_key]
                  shift_vec = qml.math.zeros_like(params[outer_key_num])
                  shift_vec = qml.math.scatter_element_add(
                      shift_vec, inner_key, 1.0
                  )
                  mask = (
                      pnp.ones(qml.math.shape(params[outer_key_num]))
                      - shift_vec
                  )
              else:
                  shift_vec = 1.0
                  mask = 0.0
              univariate = lambda x: qnode(
                  *params[:outer_key_num],
                  params[outer_key_num] * mask + x * shift_vec,
                  *params[outer_key_num + 1 :],
              )
              with tf.GradientTape() as tape:
                  out = qnode(*params)
              exp_qnode_grad = tape.gradient(out, params[outer_key_num])
  
              def exp_grad(x):
                  x = tf.Variable(x, dtype=tf.float64)
                  with tf.GradientTape() as tape:
                      out = univariate(x)
                  return tape.gradient(out, x)
  
              def grad(x):
                  x = tf.Variable(x, dtype=tf.float64)
                  with tf.GradientTape() as tape:
                      out = rec(x)
                  return tape.gradient(out, x)
  
              if nums_frequency is None:
                  # Gradient evaluation at reconstruction point not supported for
                  # Dirichlet reconstruction
                  assert np.isclose(grad(x0), exp_qnode_grad[inner_key])
              assert np.isclose(grad(x0 + 0.1), exp_grad(x0 + 0.1))
              assert fun_close(grad, exp_grad, 10)
  
imports: from inspect import signature
  from itertools import chain
  from functools import reduce
  import pytest
  import numpy
  import pennylane
  from pennylane import numpy
  from pennylane.fourier.reconstruct import _reconstruct_equ, _reconstruct_gen, _prepare_jobs, reconstruct
  from pennylane.fourier.utils import join_spectra
label_desc: Use image node_id 4 for calling the TestReconstruct obj's underlying member method code with example usage: obj.test_differentiability_tensorflow(qnode, params, ids, nums_frequency, spectra, shifts, exp_calls) and returns: tape, tape