text: # Copyright 2017 The TensorFlow Authors. All Rights Reserved.
  #
  # Licensed under the Apache License, Version 2.0 (the "License");
  # you may not use this file except in compliance with the License.
  # You may obtain a copy of the License at
  #
  #     http://www.apache.org/licenses/LICENSE-2.0
  #
  # Unless required by applicable law or agreed to in writing, software
  # distributed under the License is distributed on an "AS IS" BASIS,
  # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  # See the License for the specific language governing permissions and
  # limitations under the License.
  # ==============================================================================
  """Code for backpropagation using the tape utilities."""
  
  from __future__ import absolute_import
  from __future__ import division
  from __future__ import print_function
  
  import functools
  import operator
  import sys
  
  import six
  
  from tensorflow.python import pywrap_tensorflow
  from tensorflow.python.eager import context
  from tensorflow.python.eager import execute
  from tensorflow.python.eager import imperative_grad
  from tensorflow.python.eager import tape
  from tensorflow.python.framework import constant_op
  from tensorflow.python.framework import dtypes
  from tensorflow.python.framework import ops
  from tensorflow.python.framework import tensor_shape
  from tensorflow.python.ops import array_ops
  from tensorflow.python.ops import check_ops
  from tensorflow.python.ops import gen_array_ops
  from tensorflow.python.ops import gen_math_ops
  from tensorflow.python.ops import math_ops
  from tensorflow.python.ops import resource_variable_ops
  from tensorflow.python.ops.unconnected_gradients import UnconnectedGradients
  from tensorflow.python.platform import tf_logging as logging
  from tensorflow.python.util import nest
  from tensorflow.python.util import tf_contextlib
  from tensorflow.python.util import tf_inspect
  from tensorflow.python.util.lazy_loader import LazyLoader
  from tensorflow.python.util.tf_export import tf_export
  
  
  # Note that we need to lazy load the following two modules to avoid creating
  # circular dependencies.
  # TODO(b/119775953): fix the circular dependencies.
  pfor_ops = LazyLoader(
      "pfor_ops", globals(),
      "tensorflow.python.ops.parallel_for.control_flow_ops")
  
  function = LazyLoader("function", globals(),
                        "tensorflow.python.eager.function")
  
  _op_attr_type_cache = {}
  
  
  def op_attr_type(op_type, attr_name):
    try:
      return _op_attr_type_cache[(op_type, attr_name)]
    except KeyError:
      h = context.context()._handle  # pylint: disable=protected-access
      attr_type = pywrap_tensorflow.TFE_OpNameGetAttrType(h, op_type, attr_name)
    _op_attr_type_cache[(op_type, attr_name)] = attr_type
    return attr_type
  
  
  def make_attr(attr_type, value):
    if attr_type == pywrap_tensorflow.TF_ATTR_TYPE:
      return dtypes.as_dtype(value)
    elif attr_type == [pywrap_tensorflow.TF_ATTR_TYPE]:
      return [dtypes.as_dtype(v) for v in value]
    elif attr_type == pywrap_tensorflow.TF_ATTR_SHAPE:
      return tensor_shape.as_shape(value).as_proto()
    elif attr_type == [pywrap_tensorflow.TF_ATTR_SHAPE]:
      return [tensor_shape.as_shape(v).as_proto() for v in value]
    return value
  
  
  class _MockOp(object):
    """Pretends to be a tf.Operation for the gradient functions."""
  
    def __init__(self, attrs, inputs, outputs, typ):
      self.attrs = attrs
      self.inputs = inputs
      self.outputs = outputs
      self.type = typ
  
    def get_attr(self, attr):
      typ = op_attr_type(self.type, attr)
      for i in range(0, len(self.attrs), 2):
        if self.attrs[i] == attr:
          return make_attr(typ, self.attrs[i + 1])
      raise KeyError(attr)
  
    def _get_control_flow_context(self):
      raise NotImplementedError(
          "tf.GradientTape.gradients() does not support graph control flow "
          "operations like tf.cond or tf.while at this time. Use tf.gradients() "
          "instead. If you need this feature, please file a feature request at "
          "https://github.com/tensorflow/tensorflow/issues/new"
      )
  
  
  def _gradient_function(op_name, attr_tuple, num_inputs, inputs, outputs,
                         out_grads):
    """Calls the gradient function of the op.
  
    Args:
      op_name: the name of the op to be differentiated.
      attr_tuple: the attrs, as a tuple.
      num_inputs: the number of inputs to the op.
      inputs: inputs to the original operation.
      outputs: outputs to the original operation.
      out_grads: gradients of the operation wrt its outputs.
  
    Returns:
      The gradients with respect to the inputs of the function, as a list.
    """
    mock_op = _MockOp(attr_tuple, inputs, outputs, op_name)
    grad_fn = ops._gradient_registry.lookup(op_name)  # pylint: disable=protected-access
    if grad_fn is None:
      return [None] * num_inputs
  
    return grad_fn(mock_op, *out_grads)
  
  
  pywrap_tensorflow.TFE_Py_RegisterGradientFunction(_gradient_function)
  
  
  def _record_gradient(op_name, inputs, attrs, results, name):
    return pywrap_tensorflow.TFE_Py_RecordGradient(op_name, inputs, attrs,
                                                   results, name)
  
  
  execute.record_gradient = _record_gradient
  
  
  def implicit_val_and_grad(f):
    """Returns a function which differentiates f with respect to variables.
  
    The wrapped function returns the value and the gradient of f when called with
    the same arguments. The gradient is with respect to all trainable TFE
    variables accessed by `f`.
  
    This function is useful when the exact set of variables to differentiate with
    is not known ahead of time.
  
    Example:
  
    ```python
    dense_layer = tf.layers.Dense(1)
    def loss(x, y):
      return tf.reduce_sum(tf.square(dense_layer(x) - y))
  
    # Obtain the gradient function.
    val_grad_fn = tfe.implicit_value_and_gradients(loss)
  
    # Invoke the gradient function with concrete values of x and y.
    x = tf.constant([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]])
    y = tf.constant([[10.0], [20.0]])
    value, grads_and_vars = val_grad_fn(x, y)
    print('Value of loss: %s' % value)
  
    # Apply the gradients to Variables.
    optimizer = tf.train.GradientDescentOptimizer(0.1)
    optimizer.apply_gradients(grads_and_vars)
    ```
  
    Args:
      f: function to be differentiated. If `f` returns a scalar, this scalar will
        be differentiated. If `f` returns a tensor or list of tensors, by default
        a scalar will be computed by adding all their values to produce a single
        scalar.
  
    Returns:
      A function which, when called, returns a tuple pair.
      Its first element is the value to which the function evaluates.
      Its second element is list of (gradient, variable) pairs.
  
    Raises:
      ValueError: if `f` returns None.
    """
    # TODO(cais): Remove calls to tf.constant() once the gradients functions
    # accept lists and np.ndarrays.
  
    def grad_fn(*args, **kwds):
      """Computes the gradient of the wrapped function."""
      this_tape = tape.push_new_tape()
      try:
        end_node = f(*args, **kwds)
        if end_node is None:
          raise ValueError("Cannot differentiate a function that returns None; "
                           "did you forget to return a value from {}?".format(
                               f.__name__))
      finally:
        tape.pop_tape(this_tape)
      # Note: variables are returned in construction order. This ensures unique
      # order across executions.
      variables = this_tape.watched_variables()
      if not variables:
        raise ValueError("No trainable variables were accessed while the "
                         "function was being computed.")
  
      sources = [v.handle for v in variables]
      grad = imperative_grad.imperative_grad(this_tape, nest.flatten(end_node),
                                             sources)
      return end_node, list(zip(grad, variables))
  
    return grad_fn
  
  
  def implicit_grad(f):
    """Returns a function which differentiates f with respect to variables.
  
    The wrapped function returns the gradient of f when called with the same
    arguments. The gradient is with respect to all trainable TFE variables
    accessed by `f`.
  
    This function is useful when the exact set of variables to differentiate with
    is not known ahead of time.
  
    Example:
  
    ```python
    dense_layer = tf.layers.Dense(1)
    def loss(x, y):
      return tf.reduce_sum(tf.square(dense_layer(x) - y))
  
    # Obtain the gradient function.
    grad_fn = tfe.implicit_gradients(loss)
  
    # Invoke the gradient function with concrete values of x and y.
    x = tf.constant([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]])
    y = tf.constant([[10.0], [20.0]])
    grads_and_vars = grad_fn(x, y)
  
    # Apply the gradients to Variables.
    optimizer = tf.train.GradientDescentOptimizer(0.1)
    optimizer.apply_gradients(grads_and_vars)
    ```
  
    Args:
      f: function to be differentiated. If `f` returns a scalar, this scalar will
        be differentiated. If `f` returns a tensor or list of tensors, by default
        a scalar will be computed by adding all their values to produce a single
        scalar.
  
    Returns:
      A function which, when called, returns a list of (gradient, variable) pairs.
    """
    # TODO(cais): Remove calls to tf.constant() once the gradients functions
    # accept lists and np.ndarrays.
  
    def grad_fn(*args, **kwds):
      """Computes the gradient of the wrapped function."""
      return implicit_val_and_grad(f)(*args, **kwds)[1]
  
    return grad_fn
  
  
  def _get_arg_spec(f, params, param_args):
    """The positions of the parameters of f to be differentiated in param_args."""
    try:
      args = tf_inspect.getfullargspec(f).args
    except TypeError as e:
      # TypeError can happen when f is a callable object.
      if params is None:
        return range(len(param_args))
      elif all(isinstance(x, int) for x in params):
        return params
      raise ValueError("Either callable provided is not a function or could not "
                       "inspect its arguments by name: %s. Original error: %s"
                       % (f, e))
    if params is None:
      if not args:
        return range(len(param_args))
      return range(len(args))
    elif all(isinstance(x, six.string_types) for x in params):
      return [args.index(n) for n in params]
    elif all(isinstance(x, int) for x in params):
      return params
    else:
      raise ValueError(
          "params must be all strings or all integers; got %s." % params)
  
  
  def gradients_function(f, params=None):
    """Returns a function which differentiates f with respect to params.
  
    Example:
    ```python
    # f(x, y) = (x ^ 3) * y - x * (y ^ 2)
    # Therefore, the 1st order derivatives are:
    #   df / dx = 3 * (x ^ 2) * y - y ^ 2
    #   df / dy = x ^ 3 - 2 * x * y
    # The 2nd order derivatives with respect to x is:
    #   d^2 f / (dx)^2 = 6 * x * y
    def f(x, y):
      return x * x * x * y - x * y * y
  
    # Obtain a function that returns 1st order gradients.
    grad_fn = tfe.gradients_function(f)
  
    x = 2.0
    y = 3.0
  
    # Invoke the 1st order gradient function.
    x_grad, y_grad = grad_fn(x, y)
    assert x_grad.numpy() == 3 * (2 ** 2) * 3 - 3 ** 2
    assert y_grad.numpy() == (2 ** 3) - 2 * 2 * 3
  
    # Obtain a function that returns the 2nd order gradient with respect to x.
    gradgrad_fn = tfe.gradients_function(lambda x, y: grad_fn(x, y)[0])
  
    # Invoke the 2nd order gradient function.
    x_gradgrad = gradgrad_fn(x, y)[0]
    assert x_gradgrad.numpy() == 6 * 2 * 3
  
    # To obtain a callable that returns the gradient(s) of `f` with respect to a
    # subset of its inputs, use the `params` keyword argument with
    # `gradients_function()`.
    ygrad_fn = tfe.gradients_function(f, params=[1])
  
    (y_grad,) = ygrad_fn(x, y)
    assert y_grad.numpy() == (2 ** 3) - 2 * 2 * 3
    ```
  
    Note that only tensors with real or complex dtypes are differentiable.
  
    Args:
      f: function to be differentiated. If `f` returns a scalar, this scalar will
        be differentiated. If `f` returns a tensor or list of tensors, by default
        a scalar will be computed by adding all their values to produce a single
        scalar. If desired, the tensors can be elementwise multiplied by the
        tensors passed as the `dy` keyword argument to the returned gradient
        function.
      params: list of parameter names of f or list of integers indexing the
        parameters with respect to which we'll differentiate. Passing None
        differentiates with respect to all parameters.
  
    Returns:
      function which, when called, returns the value of f and the gradient
      of `f` with respect to all of `params`. The function takes an extra optional
      keyword argument `dy`. Setting it allows computation of vector jacobian
      products for vectors other than the vector of ones.
  
    Raises:
      ValueError: if the params are not all strings or all integers.
    """
  
    def decorated(*args, **kwds):
      """Computes the gradient of the decorated function."""
  
      _, grad = val_and_grad_function(f, params=params)(*args, **kwds)
      return grad
  
    return decorated
  
  
  def _ensure_unique_tensor_objects(parameter_positions, args):
    """Make each of the parameter_positions in args a unique ops.Tensor object.
  
    Ensure that each parameter is treated independently.
    For example:
  
    def f(x, y): return x * y
    g = gradients_function(f)
    one = tf.constant(1.)
  
    g(one, one) should return [1., 1.]
    (even though the two arguments are the same Tensor object).
  
    Args:
      parameter_positions: List of indices into args defining the arguments to
        differentiate against.
      args: A list of arguments to the function to be differentiated.
  
    Returns:
      args, possibly edited in-place.
    """
    s = set()
    for (i, t) in enumerate(args):
      if i in parameter_positions:
        tid = ops.tensor_id(t)
        if tid in s:
          args[i] = gen_array_ops.identity(args[i])
        else:
          s.add(tid)
    return args
  
  
  def val_and_grad_function(f, params=None):
    """Returns a function that computes f and its derivative w.r.t. params.
  
    Example:
    ```python
    # f(x, y) = (x ^ 3) * y - x * (y ^ 2)
    # Therefore, the 1st order derivatives are:
    #   df / dx = 3 * (x ^ 2) * y - y ^ 2
    #   df / dy = x ^ 3 - 2 * x * y
    def f(x, y):
      return x * x * x * y - x * y * y
  
    # Obtain a function that returns the function value and the 1st order
    # gradients.
    val_grads_fn = tfe.value_and_gradients_function(f)
  
    x = 2.0
    y = 3.0
  
    # Invoke the value-and-gradients function.
    f_val, (x_grad, y_grad) = val_grads_fn(x, y)
    assert f_val.numpy() == (2 ** 3) * 3 - 2 * (3 ** 2)
    assert x_grad.numpy() == 3 * (2 ** 2) * 3 - 3 ** 2
    assert y_grad.numpy() == (2 ** 3) - 2 * 2 * 3
  
    # To obtain a callable that returns the value of `f` and the gradient(s) of
    # `f` with respect to a subset of its inputs, use the `params` keyword
    # argument with `value_and_gradients_function()`.
    val_ygrad_fn = tfe.value_and_gradients_function(f, params=[1])
  
    f_val, (y_grad,) = val_ygrad_fn(x, y)
    assert f_val.numpy() == (2 ** 3) * 3 - 2 * (3 ** 2)
    assert y_grad.numpy() == (2 ** 3) - 2 * 2 * 3
    ```
  
    Args:
      f: function to be differentiated. If `f` returns a scalar, this scalar will
        be differentiated. If `f` returns a tensor or list of tensors, by default
        a scalar will be computed by adding all their values to produce a single
        scalar. If desired, the tensors can be elementwise multiplied by the
        tensors passed as the `dy` keyword argument to the returned gradient
        function.
      params: list of parameter names of f or list of integers indexing the
        parameters with respect to which we'll differentiate. Passing `None`
        differentiates with respect to all parameters.
  
    Returns:
      function which, when called, returns the value of f and the gradient
      of f with respect to all of `params`. The function takes an extra optional
      keyword argument "dy". Setting it allows computation of vector jacobian
      products for vectors other than the vector of ones.
  
    Raises:
      ValueError: if the params are not all strings or all integers.
    """
  
    def decorated(*args, **kwds):
      """Computes the value and gradient of the decorated function."""
      dy = kwds.pop("dy", None)
      if kwds:
        raise ValueError("Functions to be differentiated cannot "
                         "receive keyword arguments.")
      val, vjp = make_vjp(f, params)(*args, **kwds)
      return val, vjp(dy=dy)
  
    return decorated
  
  
  def make_vjp(f, params=None, persistent=True):
    """Returns a function that computes f and is vjp w.r.t. params.
  
    The term "vjp" here is an abbreviation for vector-jacobian product.
  
    Args:
      f: the function to be differentiated.
      params: the parameters (numbers or names) to differentiate with respect to.
         A value of None will differentiate with respect to all parameters.
      persistent: Boolean controlling whether the VJP function can be re-used.
        Must be True or False.
  
    Returns:
      A function, which when called, returns a tuple (value, vjp), where:
      - value is the result of calling f.
      - vjp is a function, which takes a vector as an argument and
        returns the product of that vector with the Jacobian of f.
        Providing no argument to vjp is equivalent to providing a
        vector of ones.
  
      For example,
      ```python
      def f(x):
        return x * x
  
      wrapped_fn = tfe.make_vjp(f)
      result, vjp = wrapped_fn(tf.constant(3.0))
      # result is 9.0
      vjp()  # the vjp function rturns 6.0
  
    Raises:
      ValueError: if `f` returns None.
    """
  
    def decorated(*args, **kwds):
      """Computes the value and gradient of the decorated function."""
      parameter_positions = _get_arg_spec(f, params, args)
      assert not kwds, "The gradient function can't take keyword arguments."
      this_tape = tape.push_new_tape(persistent=persistent)
      try:
        sources = []
        args = [
            ops.convert_to_tensor(args[i])
            if i in parameter_positions else args[i]
            for i in range(len(args))
        ]
        args = _ensure_unique_tensor_objects(parameter_positions, args)
        for i in parameter_positions:
          sources.append(args[i])
          tape.watch(this_tape, args[i])
        result = f(*args)
        if result is None:
          raise ValueError("Cannot differentiate a function that returns None; "
                           "did you forget to return a value from {}?".format(
                               f.__name__))
        flat_result = nest.flatten(result)
        flat_result = [gen_array_ops.identity(x) for x in flat_result]
        result = nest.pack_sequence_as(result, flat_result)
      finally:
        tape.pop_tape(this_tape)
      def vjp(dy=None):
        if dy is not None:
          dy = [ops.convert_to_tensor(x) for x in nest.flatten(dy)]
        return imperative_grad.imperative_grad(
            this_tape, nest.flatten(result), sources, output_gradients=dy)
  
      return result, vjp
  
    return decorated
  
  
  def _aggregate_grads(gradients):
    """Aggregate gradients from multiple sources.
  
    Args:
      gradients: A list of 'Tensor' or 'IndexedSlices' gradients.
  
    Returns:
      If 'gradients' only has 'Tensor', returns an aggregated 'Tensor'.
      Otherwise returns an aggregated 'IndexedSlices'.
    """
    assert gradients, "No gradients to aggregate"
  
    if len(gradients) == 1:
      return gradients[0]
    if all(isinstance(g, ops.Tensor) for g in gradients):
      return gen_math_ops.add_n(gradients)
    else:
      assert all(isinstance(g, (ops.Tensor, ops.IndexedSlices))
                 for g in gradients)
      indexed_slices_list = []
      for grad in gradients:
        # TODO(xpan): Support nested IndexedSlices and core IndexedSlices
        if isinstance(grad, ops.Tensor):
          indexed_slices = ops.IndexedSlices(
              grad,
              math_ops.range(grad.shape[0]),
              constant_op.constant(grad.shape.as_list()))
          indexed_slices_list.append(indexed_slices)
        else:
          indexed_slices_list.append(grad)
  
      # Dense shapes from all gradients should be the same.
      dense_shape = indexed_slices_list[0].dense_shape
      # For simplicity now, always cast to int64.
      indices = array_ops.concat([math_ops.cast(x.indices, dtypes.int64)
                                  for x in indexed_slices_list], 0)
      values = array_ops.concat([x.values for x in indexed_slices_list], 0)
      return ops.IndexedSlices(values, indices, dense_shape)
  
  
  def _num_elements(grad):
    """The number of elements in the `grad` tensor."""
    if isinstance(grad, ops.Tensor):
      shape_tuple = grad._shape_tuple()  # pylint: disable=protected-access
      if shape_tuple is None or None in shape_tuple:
        return 0
      return functools.reduce(operator.mul, shape_tuple, 1)
    if isinstance(grad, ops.IndexedSlices):
      return functools.reduce(operator.mul, grad.values._shape_tuple(), 1)  # pylint: disable=protected-access
    raise ValueError("`grad` not a Tensor or IndexedSlices.")
  
  
  def _fast_fill(value, shape, dtype):
    return array_ops.fill(
        constant_op.constant(shape, dtype=dtypes.int32),
        constant_op.constant(value, dtype=dtype))
  
  
  def _zeros(shape, dtype):
    """Helper to return (possibly cached) zero tensors in eager mode."""
    if dtype == dtypes.variant or dtype == dtypes.string:
      # TODO(apassos): need to save enough information about variant tensors to do
      # a zeros
      return None
  
    ctx = context.context()
    if not ctx.executing_eagerly():
      return array_ops.zeros(shape, dtype)
  
    device = ctx.device_name
    cache_key = shape, dtype, device
    cached = ctx.zeros_cache().get(cache_key)
    if cached is None:
      if dtypes.as_dtype(dtype).is_bool:
        value = False
      else:
        value = 0
      cached = _fast_fill(value, shape, dtype)
      ctx.zeros_cache().put(cache_key, cached)
    return cached
  
  
  def _ones(shape, dtype):
    if dtypes.as_dtype(dtype) == dtypes.string:
      return None
  
    if not context.context().executing_eagerly():
      return array_ops.ones(shape, dtype)
  
    if dtypes.as_dtype(dtype).is_bool:
      value = True
    else:
      value = 1
  
    if shape == ():  # pylint: disable=g-explicit-bool-comparison
      return constant_op.constant(value, dtype=dtype)
    return _fast_fill(value, shape, dtype)
  
  
  _default_vspace = imperative_grad.VSpace(
      num_elements_fn=_num_elements,
      aggregate_fn=_aggregate_grads,
      zeros_fn=_zeros,
      ones_fn=_ones,
      graph_shape_fn=gen_array_ops.shape)
  pywrap_tensorflow.TFE_Py_RegisterVSpace(_default_vspace)
  
  
  def _handle_or_self(x):
    """If x is ResourceVariable, return its handle, else x."""
    if resource_variable_ops.is_resource_variable(x):
      x = x.handle
    return x
  
  
  @tf_export("GradientTape")
  class GradientTape(object):
    """Record operations for automatic differentiation.
  
    Operations are recorded if they are executed within this context manager and
    at least one of their inputs is being "watched".
  
    Trainable variables (created by `tf.Variable` or `tf.get_variable`, where
    `trainable=True` is default in both cases) are automatically watched. Tensors
    can be manually watched by invoking the `watch` method on this context
    manager.
  
    For example, consider the function `y = x * x`. The gradient at `x = 3.0` can
    be computed as:
  
    ```python
    x = tf.constant(3.0)
    with tf.GradientTape() as g:
      g.watch(x)
      y = x * x
    dy_dx = g.gradient(y, x) # Will compute to 6.0
    ```
  
    GradientTapes can be nested to compute higher-order derivatives. For example,
  
    ```python
    x = tf.constant(3.0)
    with tf.GradientTape() as g:
      g.watch(x)
      with tf.GradientTape() as gg:
        gg.watch(x)
        y = x * x
      dy_dx = gg.gradient(y, x)     # Will compute to 6.0
    d2y_dx2 = g.gradient(dy_dx, x)  # Will compute to 2.0
    ```
  
    By default, the resources held by a GradientTape are released as soon as
    GradientTape.gradient() method is called. To compute multiple gradients over
    the same computation, create a persistent gradient tape. This allows multiple
    calls to the gradient() method as resources are released when the tape object
    is garbage collected. For example:
  
    ```python
    x = tf.constant(3.0)
    with tf.GradientTape(persistent=True) as g:
      g.watch(x)
      y = x * x
      z = y * y
    dz_dx = g.gradient(z, x)  # 108.0 (4*x^3 at x = 3)
    dy_dx = g.gradient(y, x)  # 6.0
    del g  # Drop the reference to the tape
    ```
  
    By default GradientTape will automatically watch any trainable variables that
    are accessed inside the context. If you want fine grained control over which
    variables are watched you can disable automatic tracking by passing
    `watch_accessed_variables=False` to the tape constructor:
  
    ```python
    with tf.GradientTape(watch_accessed_variables=False) as tape:
      tape.watch(variable_a)
      y = variable_a ** 2  # Gradients will be available for `variable_a`.
      z = variable_b ** 3  # No gradients will be avaialble since `variable_b` is
                           # not being watched.
    ```
  
    Note that when using models you should ensure that your variables exist when
    using `watch_accessed_variables=False`. Otherwise it's quite easy to make your
    first iteration not have any gradients:
  
    ```python
    a = tf.keras.layers.Dense(32)
    b = tf.keras.layers.Dense(32)
  
    with tf.GradientTape(watch_accessed_variables=False) as tape:
      tape.watch(a.variables)  # Since `a.build` has not been called at this point
                               # `a.variables` will return an empty list and the
                               # tape will not be watching anything.
      result = b(a(inputs))
      tape.gradient(result, a.variables)  # The result of this computation will be
                                          # a list of `None`s since a's variables
                                          # are not being watched.
    ```
  
    Note that only tensors with real or complex dtypes are differentiable.
    """
  
    def __init__(self, persistent=False, watch_accessed_variables=True):
      """Creates a new GradientTape.
  
      Args:
        persistent: Boolean controlling whether a persistent gradient tape
          is created. False by default, which means at most one call can
          be made to the gradient() method on this object.
        watch_accessed_variables: Boolean controlling whether the tape will
          automatically `watch` any (trainable) variables accessed while the tape
          is active. Defaults to True meaning gradients can be requested from any
          result computed in the tape derived from reading a trainable `Variable`.
          If False users must explicitly `watch` any `Variable`s they want to
          request gradients from.
      """
      self._tape = None
      self._persistent = persistent
      self._watch_accessed_variables = watch_accessed_variables
      self._recording = False
      self._created_eagerly = context.executing_eagerly()
      if self._created_eagerly:
        context.context().start_step()
  
    def __enter__(self):
      """Enters a context inside which operations are recorded on this tape."""
      self._push_tape()
      return self
  
    def __exit__(self, typ, value, traceback):
      """Exits the recording context, no further operations are traced."""
      if self._recording:
        self._pop_tape()
  
    def _push_tape(self):
      if self._recording:
        raise ValueError("Tape is already recording.")
      if self._tape is None:
        self._tape = tape.push_new_tape(
            persistent=self._persistent,
            watch_accessed_variables=self._watch_accessed_variables)
      else:
        tape.push_tape(self._tape)
      self._recording = True
  
    def _pop_tape(self):
      if not self._recording:
        raise ValueError("Tape is not recording.")
      tape.pop_tape(self._tape)
      self._recording = False
  
    def __del__(self):
      if self._created_eagerly:
        try:
          context.context().end_step()
        except AttributeError:
          pass
        except TypeError:
          pass
  
    def watch(self, tensor):
      """Ensures that `tensor` is being traced by this tape.
  
      Args:
        tensor: a Tensor or list of Tensors.
      """
      for t in nest.flatten(tensor):
        if hasattr(t, "handle"):
          # There are many variable-like objects, all of them currently have
          # `handle` attribute that points to a tensor. If this changes, internals
          # of watch_variable need to change as well.
          tape.watch_variable(self._tape, t)
        else:
          tape.watch(self._tape, t)
  
    @tf_contextlib.contextmanager
    def stop_recording(self):
      """Temporarily stops recording operations on this tape.
  
      Operations executed while this context manager is active will not be
      recorded on the tape. This is useful for reducing the memory used by tracing
      all computations.
  
      For example:
  
      ```
        with tf.GradientTape(persistent=True) as t:
          loss = compute_loss(model)
          with t.stop_recording():
            # The gradient computation below is not traced, saving memory.
            grads = t.gradient(loss, model.variables)
      ```
  
      Yields:
        None
      Raises:
        RuntimeError: if the tape is not currently recording.
      """
      if self._tape is None:
        raise RuntimeError(
            "Trying to stop recording a tape which is not recording.")
      self._pop_tape()
      try:
        yield
      finally:
        self._push_tape()
  
    def reset(self):
      """Clears all information stored in this tape.
  
      Equivalent to exiting and reentering the tape context manager with a new
      tape. For example, the two following code blocks are equivalent:
      ```
      with tf.GradientTape() as t:
        loss = loss_fn()
      with tf.GradientTape() as t:
        loss += other_loss_fn()
      t.gradient(loss, ...)  # Only differentiates other_loss_fn, not loss_fn
  
  
      # The following is equivalent to the above
      with tf.GradientTape() as t:
        loss = loss_fn()
        t.reset()
        loss += other_loss_fn()
      t.gradient(loss, ...)  # Only differentiates other_loss_fn, not loss_fn
      ```
  
      This is useful if you don't want to exit the context manager for the tape,
      or can't because the desired reset point is inside a control flow construct:
  
      ```
      with tf.GradientTape() as t:
        loss = ...
        if loss > k:
          t.reset()
      ```
      """
      self._pop_tape()
      self._tape = None
      self._push_tape()
  
    def watched_variables(self):
      """Returns variables watched by this tape in order of construction."""
      return self._tape.watched_variables()
  
    def gradient(self,
                 target,
                 sources,
                 output_gradients=None,
                 unconnected_gradients=UnconnectedGradients.NONE):
      """Computes the gradient using operations recorded in context of this tape.
  
      Args:
        target: Tensor (or list of tensors) to be differentiated.
        sources: a list or nested structure of Tensors or Variables. `target`
          will be differentiated against elements in `sources`.
        output_gradients: a list of gradients, one for each element of
          target. Defaults to None.
        unconnected_gradients: a value which can either hold 'none' or 'zero' and
          alters the value which will be returned if the target and sources are
          unconnected. The possible values and effects are detailed in
          'UnconnectedGradients' and it defaults to 'none'.
  
      Returns:
        a list or nested structure of Tensors (or IndexedSlices, or None),
        one for each element in `sources`. Returned structure is the same as
        the structure of `sources`.
  
      Raises:
        RuntimeError: if called inside the context of the tape, or if called more
         than once on a non-persistent tape.
        ValueError: if the target is a variable or if unconnected gradients is
         called with an unknown value.
      """
      if self._tape is None:
        raise RuntimeError("GradientTape.gradient can only be called once on "
                           "non-persistent tapes.")
      if self._recording:
        if not self._persistent:
          self._pop_tape()
        else:
          logging.log_first_n(logging.WARN,
                              "Calling GradientTape.gradient on a persistent "
                              "tape inside it's context is significantly less "
                              "efficient than calling it outside the context (it "
                              "causes the gradient ops to be recorded on the "
                              "tape, leading to increased CPU and memory usage). "
                              "Only call GradientTape.gradient inside the "
                              "context if you actually want to trace the "
                              "gradient in order to compute higher order "
                              "derrivatives.", 1)
  
      flat_targets = nest.flatten(target)
      for t in flat_targets:
        if resource_variable_ops.is_resource_variable(t):
          raise ValueError("GradientTape.gradient is not supported for variable "
                           "targets.")
  
      flat_sources = nest.flatten(sources)
      flat_sources = [_handle_or_self(x) for x in flat_sources]
  
      if output_gradients is not None:
        output_gradients = [None if x is None else ops.convert_to_tensor(x)
                            for x in nest.flatten(output_gradients)]
  
      flat_grad = imperative_grad.imperative_grad(
          self._tape,
          flat_targets,
          flat_sources,
          output_gradients=output_gradients,
          unconnected_gradients=unconnected_gradients)
  
      if not self._persistent:
        self._tape = None
  
      grad = nest.pack_sequence_as(sources, flat_grad)
      return grad
  
    def jacobian(self,
                 target,
                 sources,
                 unconnected_gradients=UnconnectedGradients.NONE,
                 parallel_iterations=None,
                 experimental_use_pfor=True):
      """Computes the jacobian using operations recorded in context of this tape.
  
      See http://en.wikipedia.org/wiki/jacobian_matrix_and_determinant for the
      definition of a Jacobian.
  
      Example usage:
  
      with tf.GradientTape() as g:
        x  = tf.constant([1.0, 2.0])
        g.watch(x)
        y = x * x
      jacobian = g.jacobian(y, x)
      # jacobian value is [[2., 0.], [0., 4.]]
  
      Args:
        target: Tensor to be differentiated.
        sources: a list or nested structure of Tensors or Variables. `target`
          will be differentiated against elements in `sources`.
        unconnected_gradients: a value which can either hold 'none' or 'zero' and
          alters the value which will be returned if the target and sources are
          unconnected. The possible values and effects are detailed in
          'UnconnectedGradients' and it defaults to 'none'.
        parallel_iterations: A knob to control how many iterations are dispatched
          in parallel. This knob can be used to control the total memory usage.
        experimental_use_pfor: If true, vectorizes the jacobian computation. Else
          falls back to a sequential while_loop. Vectorization can sometimes fail
          or lead to excessive memory usage. This option can be used to disable
          vectorization in such cases.
  
      Returns:
        a list or nested structure of Tensors (or IndexedSlices, or None),
        one for each element in `sources`. Returned structure is the same as
        the structure of `sources`.
  
      Raises:
        RuntimeError: If called on a non-persistent tape with eager execution
          enabled and without enabling experimental_use_pfor.
        ValueError: If vectorization of jacobian computation fails.
      """
      flat_sources = nest.flatten(sources)
      target_static_shape = target.shape
      target_shape = array_ops.shape(target)
      # Note that we push and pop the tape here and below. This is needed since we
      # need gradients through the enclosed operations.
      self._push_tape()
      target = array_ops.reshape(target, [-1])
      self._pop_tape()
  
      def loop_fn(i):
        self._push_tape()
        y = array_ops.gather(target, i)
        self._pop_tape()
        return self.gradient(y, flat_sources,
                             unconnected_gradients=unconnected_gradients)
  
      try:
        target_size = int(target.shape[0])
      except TypeError:
        target_size = array_ops.shape(target)[0]
  
      if experimental_use_pfor:
        try:
          output = pfor_ops.pfor(loop_fn, target_size,
                                 parallel_iterations=parallel_iterations)
        except ValueError as err:
          six.reraise(
              ValueError,
              ValueError(
                  str(err) + "\nEncountered an exception while vectorizing the "
                  "jacobian computation. Vectorization can be disabled by setting"
                  " experimental_use_pfor to False."),
              sys.exc_info()[2])
      else:
        if context.executing_eagerly() and not self._persistent:
          raise RuntimeError(
              "GradientTape must be created with persistent=True"
              " to compute the jacobian with eager execution enabled and with "
              " experimental_use_pfor set to False.")
        output = pfor_ops.for_loop(
            loop_fn, [target.dtype] * len(flat_sources), target_size,
            parallel_iterations=parallel_iterations)
  
      for i, out in enumerate(output):
        if out is not None:
          new_shape = array_ops.concat(
              [target_shape, array_ops.shape(out)[1:]], axis=0)
          out = array_ops.reshape(out, new_shape)
          if context.executing_eagerly():
            out.set_shape(target_static_shape.concatenate(flat_sources[i].shape))
        output[i] = out
  
      return nest.pack_sequence_as(sources, output)
  
    def batch_jacobian(self,
                       target,
                       source,
                       unconnected_gradients=UnconnectedGradients.NONE,
                       parallel_iterations=None,
                       experimental_use_pfor=True):
      """Computes and stacks per-example jacobians.
  
      See http://en.wikipedia.org/wiki/jacobian_matrix_and_determinant for the
      definition of a Jacobian.  This function is essentially an efficient
      implementation of the following:
      `tf.stack([self.jacobian(y[i], x[i]) for i in range(x.shape[0])])`.
  
      Note that compared to `GradientTape.jacobian` which computes gradient of
      each output value w.r.t each input value, this function is useful when
      `target[i,...] is independent of `source[j,...]` for `j != i`. This
      independence assumption allows more efficient computation as compared to
      `GradientTape.jacobian`. The output, as well as intermediate activations,
      are lower dimensional and avoid a bunch of redundant zeros which would
      result in the jacobian computation given the independence assumption.
  
      Example usage:
      with tf.GradientTape() as g:
        x = tf.constant([[1, 2], [3, 4]], dtype=tf.float32)
        g.watch(x)
        y = x * x
      batch_jacobian = g.batch_jacobian(y, x)
      # batch_jacobian is [[[2,  0], [0,  4]], [[6,  0], [0,  8]]]
  
      Args:
        target: A tensor with rank 2 or higher and with shape [b, y1, ..., y_n].
          `target[i,...]` should only depend on `source[i,...]`.
        source: A tensor with rank 2 or higher and with shape [b, x1, ..., x_m].
        unconnected_gradients: a value which can either hold 'none' or 'zero' and
          alters the value which will be returned if the target and sources are
          unconnected. The possible values and effects are detailed in
          'UnconnectedGradients' and it defaults to 'none'.
        parallel_iterations: A knob to control how many iterations are dispatched
          in parallel. This knob can be used to control the total memory usage.
        experimental_use_pfor: If true, uses pfor for computing the Jacobian. Else
          uses a tf.while_loop.
  
      Returns:
        A tensor `t` with shape [b, y_1, ..., y_n, x1, ..., x_m] where `t[i, ...]`
        is the jacobian of `target[i, ...]` w.r.t. `source[i, ...]`, i.e. stacked
        per-example jacobians.
  
      Raises:
        RuntimeError: If called on a non-persistent tape with eager execution
          enabled and without enabling experimental_use_pfor.
        ValueError: If vectorization of jacobian computation fails or if first
          dimension of `target` and `source` do not match.
      """
      target_shape = target.shape
      if target_shape.rank is None:
        dim = Dimension(None)
      else:
        dim = target_shape.dims[0]
      if not (target_shape.with_rank_at_least(2) and
              source.shape.with_rank_at_least(2) and
              dim.is_compatible_with(source.shape[0])):
        raise ValueError(
            "Need first dimension of target shape (%s) and "
            "source shape (%s) to match." % (target.shape, source.shape))
      if target_shape.is_fully_defined():
        batch_size = int(target_shape[0])
        target_row_size = target_shape.num_elements() // batch_size
      else:
        target_shape = array_ops.shape(target)
        batch_size = target_shape[0]
        target_row_size = array_ops.size(target) // batch_size
      source_shape = array_ops.shape(source)
      # Flatten target to 2-D.
      # Note that we push and pop the tape here and below. This is needed since we
      # need gradients through the enclosed operations.
      self._push_tape()
      with ops.control_dependencies(
          [check_ops.assert_equal(batch_size, source_shape[0])]):
        target = array_ops.reshape(target, [batch_size, target_row_size])
      self._pop_tape()
  
      def loop_fn(i):
        self._push_tape()
        y = array_ops.gather(target, i, axis=1)
        self._pop_tape()
        return self.gradient(y, source,
                             unconnected_gradients=unconnected_gradients)
  
      if experimental_use_pfor:
        try:
          output = pfor_ops.pfor(loop_fn, target_row_size,
                                 parallel_iterations=parallel_iterations)
        except ValueError as err:
          six.reraise(
              ValueError,
              ValueError(
                  str(err) + "\nEncountered an exception while vectorizing the "
                  "batch_jacobian computation. Vectorization can be disabled by "
                  "setting experimental_use_pfor to False."),
              sys.exc_info()[2])
      else:
        if context.executing_eagerly() and not self._persistent:
          raise RuntimeError(
              "GradientTape must be created with persistent=True"
              " to compute the batch_jacobian with eager execution enabled and "
              " with experimental_use_pfor set to False.")
        output = pfor_ops.for_loop(loop_fn, target.dtype, target_row_size,
                                   parallel_iterations=parallel_iterations)
      if output is None:
        return None
      output = array_ops.reshape(output,
                                 [target_row_size, batch_size, -1])
      output = array_ops.transpose(output, [1, 0, 2])
      new_shape = array_ops.concat([target_shape, source_shape[1:]], axis=0)
      return array_ops.reshape(output, new_shape)
  