def mode(self, name="mode"):
    """Mode of the distribution.

    Note that the mode for the Beta distribution is only defined
    when `a > 1`, `b > 1`. This returns the mode when `a > 1` and `b > 1`,
    and NaN otherwise. If `self.allow_nan_stats` is `False`, an exception
    will be raised rather than returning `NaN`.

    Args:
      name: The name for this op.

    Returns:
      Mode of the Beta distribution.
    """
    with ops.name_scope(self.name):
      with ops.op_scope([self._a, self._b, self._a_b_sum], name):
        a = self._a
        b = self._b
        a_b_sum = self._a_b_sum
        one = constant_op.constant(1, self.dtype)
        mode = (a - 1)/ (a_b_sum - 2)

        if self.allow_nan_stats:
          return math_ops.select(
              math_ops.logical_and(
                  math_ops.greater(a, 1), math_ops.greater(b, 1)),
              mode,
              (constant_op.constant(float("NaN"), dtype=self.dtype) *
               array_ops.ones_like(a_b_sum, dtype=self.dtype)))
        else:
          return control_flow_ops.with_dependencies([
              check_ops.assert_less(one, a),
              check_ops.assert_less(one, b)], mode)

  def _variance(self):
    # We need to put the tf.where inside the outer tf.where to ensure we never
    # hit a NaN in the gradient.
    denom = array_ops.where(math_ops.greater(self.df, 2.),
                            self.df - 2.,
                            array_ops.ones_like(self.df))
    # Abs(scale) superfluous.
    var = (array_ops.ones(self.batch_shape_tensor(), dtype=self.dtype) *
           math_ops.square(self.scale) * self.df / denom)
    # When 1 < df <= 2, variance is infinite.
    inf = np.array(np.inf, dtype=self.dtype.as_numpy_dtype())
    result_where_defined = array_ops.where(
        self.df > array_ops.fill(self.batch_shape_tensor(), 2.),
        var,
        array_ops.fill(self.batch_shape_tensor(), inf, name="inf"))

    if self.allow_nan_stats:
      nan = np.array(np.nan, dtype=self.dtype.as_numpy_dtype())
      return array_ops.where(
          math_ops.greater(
              self.df,
              array_ops.ones(self.batch_shape_tensor(), dtype=self.dtype)),
          result_where_defined,
          array_ops.fill(self.batch_shape_tensor(), nan, name="nan"))
    else:
      return control_flow_ops.with_dependencies(
          [
              check_ops.assert_less(
                  array_ops.ones([], dtype=self.dtype),
                  self.df,
                  message="variance not defined for components of df <= 1"),
          ],
          result_where_defined)

 def _mode(self):
     mode = (self.a - 1.0) / (self.a_b_sum - 2.0)
     if self.allow_nan_stats:
         nan = np.array(np.nan, dtype=self.dtype.as_numpy_dtype())
         return math_ops.select(
             math_ops.logical_and(math_ops.greater(self.a, 1.0), math_ops.greater(self.b, 1.0)),
             mode,
             array_ops.fill(self.batch_shape(), nan, name="nan"),
         )
     else:
         return control_flow_ops.with_dependencies(
             [
                 check_ops.assert_less(
                     array_ops.ones((), dtype=self.dtype),
                     self.a,
                     message="Mode not defined for components of a <= 1.",
                 ),
                 check_ops.assert_less(
                     array_ops.ones((), dtype=self.dtype),
                     self.b,
                     message="Mode not defined for components of b <= 1.",
                 ),
             ],
             mode,
         )

    def _variance(self):
        var = self._ones() * math_ops.square(self.sigma) * self.df / (self.df - 2)
        # When 1 < df <= 2, variance is infinite.
        inf = np.array(np.inf, dtype=self.dtype.as_numpy_dtype())
        result_where_defined = math_ops.select(
            math_ops.greater(self.df, array_ops.fill(self.batch_shape(), 2.0)),
            var,
            array_ops.fill(self.batch_shape(), inf, name="inf"),
        )

        if self.allow_nan_stats:
            nan = np.array(np.nan, dtype=self.dtype.as_numpy_dtype())
            return math_ops.select(
                math_ops.greater(self.df, self._ones()),
                result_where_defined,
                array_ops.fill(self.batch_shape(), nan, name="nan"),
            )
        else:
            return control_flow_ops.with_dependencies(
                [
                    check_ops.assert_less(
                        array_ops.ones((), dtype=self.dtype),
                        self.df,
                        message="variance not defined for components of df <= 1",
                    )
                ],
                result_where_defined,
            )

 def compute_lr(self, grad, var):
   scaled_lr = self._learning_rate
   if self._skip_list is None or not any(v in var.name
                                         for v in self._skip_list):
     w_norm = linalg_ops.norm(var, ord=2)
     g_norm = linalg_ops.norm(grad, ord=2)
     trust_ratio = array_ops.where(
         math_ops.greater(w_norm, 0),
         array_ops.where(
             math_ops.greater(g_norm, 0),
             (self._eeta * w_norm /
              (g_norm + self._weight_decay * w_norm + self._epsilon)), 1.0),
         1.0)
     scaled_lr = self._learning_rate * trust_ratio
   return scaled_lr

def _safe_div(numerator, denominator, name="value"):
  """Computes a safe divide which returns 0 if the denominator is zero.

  Note that the function contains an additional conditional check that is
  necessary for avoiding situations where the loss is zero causing NaNs to
  creep into the gradient computation.

  Args:
    numerator: An arbitrary `Tensor`.
    denominator: `Tensor` whose shape matches `numerator` and whose values are
      assumed to be non-negative.
    name: An optional name for the returned op.

  Returns:
    The element-wise value of the numerator divided by the denominator.
  """
  if isinstance(denominator, float):
    if math_ops.equal(denominator, 0.0):
      return ops.convert_to_tensor(0.0, dtype=numerator.dtype)
    return math_ops.div(numerator, denominator)
  if context.in_eager_mode() and denominator._rank() == 0:  # pylint: disable=protected-access
    if math_ops.equal(denominator, 0.0):
      return ops.convert_to_tensor(0.0, dtype=numerator.dtype)
    return math_ops.div(numerator, denominator)
  return array_ops.where(
      math_ops.greater(denominator, 0),
      math_ops.div(numerator, array_ops.where(
          math_ops.equal(denominator, 0),
          array_ops.ones_like(denominator), denominator)),
      array_ops.zeros_like(numerator),
      name=name)

  def filter_functions():
    take_all = lambda x: constant_op.constant(True)
    is_zero = lambda x: math_ops.equal(x, 0)
    greater = lambda x: math_ops.greater(x + 5, 0)

    tests = []
    filters = [take_all, is_zero, greater]
    identity = lambda x: x
    for x, predicate_1 in enumerate(filters):
      for y, predicate_2 in enumerate(filters):
        tests.append(("Mixed{}{}".format(x, y), identity,
                      [predicate_1, predicate_2]))
        for z, predicate_3 in enumerate(filters):
          tests.append(("Mixed{}{}{}".format(x, y, z), identity,
                        [predicate_1, predicate_2, predicate_3]))

    take_all_multiple = lambda x, y: constant_op.constant(True)
    # Multi output
    tests.append(("Multi1", lambda x: (x, x),
                  [take_all_multiple, take_all_multiple]))
    tests.append(("Multi2", lambda x: (x, 2), [
        take_all_multiple,
        lambda x, y: math_ops.equal(x * math_ops.cast(y, dtypes.int64), 0)
    ]))
    return tuple(tests)

  def map_and_filter_functions():
    identity = lambda x: x
    increment = lambda x: x + 1
    minus_five = lambda x: x - 5

    def increment_and_square(x):
      y = x + 1
      return y * y

    take_all = lambda x: constant_op.constant(True)
    is_zero = lambda x: math_ops.equal(x, 0)
    is_odd = lambda x: math_ops.equal(x % 2, 0)
    greater = lambda x: math_ops.greater(x + 5, 0)

    functions = [identity, increment, minus_five, increment_and_square]
    filters = [take_all, is_zero, is_odd, greater]
    tests = []

    for x, fun in enumerate(functions):
      for y, predicate in enumerate(filters):
        tests.append(("Mixed{}{}".format(x, y), fun, predicate))

    # Multi output
    tests.append(("Multi1", lambda x: (x, x),
                  lambda x, y: constant_op.constant(True)))
    tests.append(
        ("Multi2", lambda x: (x, 2),
         lambda x, y: math_ops.equal(x * math_ops.cast(y, dtypes.int64), 0)))
    return tuple(tests)

def _prune_invalid_weights(sparse_ids, sparse_weights):
  """Prune invalid weights (< 0) from the input ids and weights."""
  if sparse_weights is not None:
    is_weights_valid = math_ops.greater(sparse_weights.values, 0)
    sparse_ids = sparse_ops.sparse_retain(sparse_ids, is_weights_valid)
    sparse_weights = sparse_ops.sparse_retain(sparse_weights, is_weights_valid)
  return sparse_ids, sparse_weights

def gcd(a, b, name=None):
  """Returns the greatest common divisor via Euclid's algorithm.

  Args:
    a: The dividend. A scalar integer `Tensor`.
    b: The divisor. A scalar integer `Tensor`.
    name: An optional name for the operation.

  Returns:
    A scalar `Tensor` representing the greatest common divisor between `a` and
    `b`.

  Raises:
    ValueError: If `a` or `b` are not scalar integers.
  """
  with ops.name_scope(name, 'gcd', [a, b]):
    a = ops.convert_to_tensor(a)
    b = ops.convert_to_tensor(b)

    a.shape.assert_has_rank(0)
    b.shape.assert_has_rank(0)

    if not a.dtype.is_integer:
      raise ValueError('a must be an integer type. Got: %s' % a.dtype)
    if not b.dtype.is_integer:
      raise ValueError('b must be an integer type. Got: %s' % b.dtype)

    cond = lambda _, b: math_ops.greater(b, array_ops.zeros_like(b))
    body = lambda a, b: [b, math_ops.mod(a, b)]
    a, b = control_flow_ops.while_loop(cond, body, [a, b], back_prop=False)
    return a

  def average_impurity(self):
    """Constructs a TF graph for evaluating the average leaf impurity of a tree.

    If in regression mode, this is the leaf variance. If in classification mode,
    this is the gini impurity.

    Returns:
      The last op in the graph.
    """
    children = array_ops.squeeze(array_ops.slice(
        self.variables.tree, [0, 0], [-1, 1]), squeeze_dims=[1])
    is_leaf = math_ops.equal(constants.LEAF_NODE, children)
    leaves = math_ops.to_int32(array_ops.squeeze(array_ops.where(is_leaf),
                                                 squeeze_dims=[1]))
    counts = array_ops.gather(self.variables.node_sums, leaves)
    gini = self._weighted_gini(counts)
    # Guard against step 1, when there often are no leaves yet.
    def impurity():
      return gini
    # Since average impurity can be used for loss, when there's no data just
    # return a big number so that loss always decreases.
    def big():
      return array_ops.ones_like(gini, dtype=dtypes.float32) * 10000000.
    return control_flow_ops.cond(math_ops.greater(
        array_ops.shape(leaves)[0], 0), impurity, big)

  def mode(self, name="mode"):
    """Mode of the distribution.

    Note that the mode for the Beta distribution is only defined
    when `alpha > 1`. This returns the mode when `alpha > 1`,
    and NaN otherwise. If `self.allow_nan_stats` is `False`, an exception
    will be raised rather than returning `NaN`.

    Args:
      name: The name for this op.

    Returns:
      Mode of the Dirichlet distribution.
    """
    with ops.name_scope(self.name):
      with ops.op_scope([self._alpha, self._alpha_0], name):
        one = constant_op.constant(1, self.dtype)
        mode = (self._alpha - 1)/ (
            array_ops.expand_dims(self._alpha_0, -1) - math_ops.cast(
                self.event_shape()[0], self.dtype))

        if self.allow_nan_stats:
          return math_ops.select(
              math_ops.greater(self._alpha, 1),
              mode,
              (constant_op.constant(float("NaN"), dtype=self.dtype) *
               array_ops.ones_like(self._alpha, dtype=self.dtype)))
        else:
          return control_flow_ops.with_dependencies([
              check_ops.assert_less(
                  one, self._alpha,
                  message="mode not defined for components of alpha <= 1")
          ], mode)

def _safe_div(numerator, denominator, name="value"):
  """Computes a safe divide which returns 0 if the denominator is zero.

  Note that the function contains an additional conditional check that is
  necessary for avoiding situations where the loss is zero causing NaNs to
  creep into the gradient computation.

  Args:
    numerator: An arbitrary `Tensor`.
    denominator: A `Tensor` whose shape matches `numerator` and whose values are
      assumed to be non-negative.
    name: An optional name for the returned op.

  Returns:
    The element-wise value of the numerator divided by the denominator.
  """
  if compat.forward_compatible(2018, 11, 1):
    return math_ops.div_no_nan(numerator, denominator, name=name)
  return array_ops.where(
      math_ops.greater(denominator, 0),
      math_ops.div(numerator,
                   array_ops.where(
                       math_ops.equal(denominator, 0),
                       array_ops.ones_like(denominator), denominator)),
      array_ops.zeros_like(numerator),
      name=name)

def _get_stratified_batch_from_tensors(val, label, reject_probs, batch_size,
                                       queue_threads=3):
  """Reject examples one-at-a-time based on class."""
  # Make rejection probabilities into a tensor so they can be dynamically
  # accessed by tensors.
  reject_probs = constant_op.constant(
      reject_probs, dtype=dtypes.float32, name='rejection_probabilities')

  # Make queue that will have proper class proportions. Contains exactly one
  # batch at a time.
  val_shape = val.get_shape()
  label_shape = label.get_shape()
  final_q = data_flow_ops.FIFOQueue(capacity=batch_size,
                                    shapes=[val_shape, label_shape],
                                    dtypes=[val.dtype, label.dtype],
                                    name='batched_queue')

  # Conditionally enqueue.
  eq_tf = array_ops.reshape(math_ops.greater(
      random_ops.random_uniform([1]),
      array_ops.slice(reject_probs, [label], [1])),
                            [])
  conditional_enqueue = control_flow_ops.cond(
      eq_tf,
      lambda: final_q.enqueue([val, label]),
      control_flow_ops.no_op)
  queue_runner.add_queue_runner(queue_runner.QueueRunner(
      final_q, [conditional_enqueue] * queue_threads))

  return final_q.dequeue_many(batch_size)

  def testLargeCase(self):
    shape = [32, 512, 256, 1]
    predictions = random_ops.random_uniform(
        shape, 0.0, 1.0, dtype=dtypes_lib.float32)
    labels = math_ops.greater(random_ops.random_uniform(shape, 0.0, 1.0), 0.5)

    result, update_op = metric_ops.precision_recall_at_equal_thresholds(
        labels=labels, predictions=predictions, num_thresholds=201)
    # Run many updates, enough to cause highly inaccurate values if the
    # code used float32 for accumulation.
    num_updates = 71

    with self.test_session() as sess:
      sess.run(variables.local_variables_initializer())
      for _ in xrange(num_updates):
        sess.run(update_op)

      prdata = sess.run(result)

      # Since we use random values, we won't know the tp/fp/tn/fn values, but
      # tp and fp at threshold 0 should be the total number of positive and
      # negative labels, hence their sum should be total number of pixels.
      expected_value = 1.0 * np.product(shape) * num_updates
      got_value = prdata.tp[0] + prdata.fp[0]
      # They should be at least within 1.
      self.assertNear(got_value, expected_value, 1.0)

def string_input_producer(string_tensor,
                          num_epochs=None,
                          shuffle=True,
                          seed=None,
                          capacity=32,
                          shared_name=None,
                          name=None,
                          cancel_op=None):
  """Output strings (e.g. filenames) to a queue for an input pipeline.

  Note: if `num_epochs` is not `None`, this function creates local counter
  `epochs`. Use `local_variable_initializer()` to initialize local variables.

  Args:
    string_tensor: A 1-D string tensor with the strings to produce.
    num_epochs: An integer (optional). If specified, `string_input_producer`
      produces each string from `string_tensor` `num_epochs` times before
      generating an `OutOfRange` error. If not specified,
      `string_input_producer` can cycle through the strings in `string_tensor`
      an unlimited number of times.
    shuffle: Boolean. If true, the strings are randomly shuffled within each
      epoch.
    seed: An integer (optional). Seed used if shuffle == True.
    capacity: An integer. Sets the queue capacity.
    shared_name: (optional). If set, this queue will be shared under the given
      name across multiple sessions.
    name: A name for the operations (optional).
    cancel_op: Cancel op for the queue (optional).

  Returns:
    A queue with the output strings.  A `QueueRunner` for the Queue
    is added to the current `Graph`'s `QUEUE_RUNNER` collection.

  Raises:
    ValueError: If the string_tensor is a null Python list.  At runtime,
    will fail with an assertion if string_tensor becomes a null tensor.
  """
  not_null_err = "string_input_producer requires a non-null input tensor"
  if not isinstance(string_tensor, ops.Tensor) and not string_tensor:
    raise ValueError(not_null_err)

  with ops.name_scope(name, "input_producer", [string_tensor]) as name:
    string_tensor = ops.convert_to_tensor(string_tensor, dtype=dtypes.string)
    with ops.control_dependencies([
        control_flow_ops.Assert(
            math_ops.greater(array_ops.size(string_tensor), 0),
            [not_null_err])]):
      string_tensor = array_ops.identity(string_tensor)
    return input_producer(
        input_tensor=string_tensor,
        element_shape=[],
        num_epochs=num_epochs,
        shuffle=shuffle,
        seed=seed,
        capacity=capacity,
        shared_name=shared_name,
        name=name,
        summary_name="fraction_of_%d_full" % capacity,
        cancel_op=cancel_op)

def _prune_invalid_ids(sparse_ids, sparse_weights):
    """Prune invalid IDs (< 0) from the input ids and weights."""
    is_id_valid = math_ops.greater_equal(sparse_ids.values, 0)
    if sparse_weights is not None:
        is_id_valid = math_ops.logical_and(is_id_valid, math_ops.greater(sparse_weights.values, 0))
    sparse_ids = sparse_ops.sparse_retain(sparse_ids, is_id_valid)
    if sparse_weights is not None:
        sparse_weights = sparse_ops.sparse_retain(sparse_weights, is_id_valid)
    return sparse_ids, sparse_weights

 def _logits_to_prediction(self, logits=None):
   predictions = {PredictionKey.LOGITS: logits}
   if self.logits_dimension == 1:
     predictions[PredictionKey.LOGISTIC] = math_ops.sigmoid(logits)
     logits = array_ops.concat(1, [array_ops.zeros_like(logits), logits])
   predictions[PredictionKey.PROBABILITIES] = math_ops.sigmoid(logits)
   predictions[PredictionKey.CLASSES] = math_ops.to_int64(
       math_ops.greater(logits, 0))
   return predictions

def _SegmentMinGrad(op, grad):
  """Gradient for SegmentMin."""
  zeros = array_ops.zeros(array_ops.shape(op.inputs[0]),
                          dtype=op.inputs[0].dtype)
  gathered_grads = array_ops.gather(grad, op.inputs[1])
  gathered_outputs = array_ops.gather(op.outputs[0], op.inputs[1])
  return math_ops.select(math_ops.greater(op.inputs[0], gathered_outputs),
                         zeros,
                         gathered_grads), None

  def AddForwardAccumulateLoop(self, value):
    """Add an accumulation loop for each value needed in backprop.

    This is added to the forward loop at the first time when a value
    in the forward loop is used by backprop gradient computation loop.

    The pseudocode is:
    ```
      acc;
      while (_pivot) {
        if (index == 0) [value] else Concat(acc, [value]);
      }
    ```

    Args:
      value: The tensor that is accumulated.

    Returns:
      The accumulated history of value.

    Raises:
      ValueError: If the shape of "value" is not known statically.
    """
    if not value.get_shape().is_fully_defined():
      raise ValueError("Must have known shape: %s" % value)
    self._grad_context.Exit()
    # TODO(irving): Now that acc starts out empty, most of the
    # conditional logic can go away.
    acc = constant_op.constant([],
                               value.dtype,
                               shape=[0] + value.get_shape().as_list(),
                               name="f_acc")
    self.Enter()
    self.AddName(acc.name)
    enter_acc = _Enter(acc, self._name, is_constant=False,
                       parallel_iterations=self._parallel_iterations,
                       name="f_acc")
    merge_acc = merge([enter_acc, enter_acc])[0]
    switch_acc = switch(merge_acc, self._pivot)

    # If index = 0 then [value] else Concat(acc, [value]).
    cond = math_ops.greater(self._index, 0)
    switch_add_acc = switch(switch_acc[1], cond)
    expand_value = array_ops.expand_dims(value, 0)
    true_branch = array_ops.concat(0, [switch_add_acc[1], expand_value])
    false_branch = array_ops.identity(switch_add_acc[0])
    false_branch = with_dependencies([false_branch], expand_value)
    add_acc = merge([false_branch, true_branch])[0]

    next_acc = next_iteration(add_acc)
    merge_acc.op._update_input(1, next_acc)

    exit_acc = exit(switch_acc[0], name="f_acc")
    self.Exit()
    self._grad_context.Enter()
    return exit_acc