Python tensorflow.python.ops.math_ops.reduce_prod() Examples

def prod(x, axis=None, keepdims=False):
  """Multiplies the values in a tensor, alongside the specified axis.

  Arguments:
      x: A tensor or variable.
      axis: An integer, the axis to compute the product.
      keepdims: A boolean, whether to keep the dimensions or not.
          If `keepdims` is `False`, the rank of the tensor is reduced
          by 1. If `keepdims` is `True`,
          the reduced dimension is retained with length 1.

  Returns:
      A tensor with the product of elements of `x`.
  """
  axis = _normalize_axis(axis, ndim(x))
  return math_ops.reduce_prod(x, reduction_indices=axis, keep_dims=keepdims) 

def _MeanGrad(op, grad):
  """Gradient for Mean."""
  sum_grad = _SumGrad(op, grad)[0]
  input_shape = array_ops.shape(op.inputs[0])
  output_shape = array_ops.shape(op.outputs[0])
  # TODO(apassos) remove this device hackery as eager copy to device becomes
  # more seamless.
  with ops.colocate_with(input_shape):
    factor = _safe_shape_div(
        math_ops.reduce_prod(input_shape), math_ops.reduce_prod(output_shape))
  if context.in_eager_mode():
    # Note that we go through numpy here just so we use the eager per-device
    # scalar cache. We know the factor is a host memory tensor because it's a
    # shape, and we also know that converting a scalar into a tensor triggers a
    # per-device cache.
    factor = factor.numpy()
    factor = constant_op.constant(factor, dtype=sum_grad.dtype)
  return sum_grad / math_ops.cast(factor, sum_grad.dtype), None 

def _entropy(self):
    if not self.bijector.is_constant_jacobian:
      raise NotImplementedError("entropy is not implemented")
    if not self.bijector._is_injective:  # pylint: disable=protected-access
      raise NotImplementedError("entropy is not implemented when "
                                "bijector is not injective.")
    # Suppose Y = g(X) where g is a diffeomorphism and X is a continuous rv. It
    # can be shown that:
    #   H[Y] = H[X] + E_X[(log o abs o det o J o g)(X)].
    # If is_constant_jacobian then:
    #   E_X[(log o abs o det o J o g)(X)] = (log o abs o det o J o g)(c)
    # where c can by anything.
    entropy = self.distribution.entropy()
    if self._is_maybe_event_override:
      # H[X] = sum_i H[X_i] if X_i are mutually independent.
      # This means that a reduce_sum is a simple rescaling.
      entropy *= math_ops.cast(math_ops.reduce_prod(self._override_event_shape),
                               dtype=entropy.dtype.base_dtype)
    if self._is_maybe_batch_override:
      new_shape = array_ops.concat([
          _ones_like(self._override_batch_shape),
          self.distribution.batch_shape_tensor()
      ], 0)
      entropy = array_ops.reshape(entropy, new_shape)
      multiples = array_ops.concat([
          self._override_batch_shape,
          _ones_like(self.distribution.batch_shape_tensor())
      ], 0)
      entropy = array_ops.tile(entropy, multiples)
    dummy = array_ops.zeros([], self.dtype)
    entropy -= self.bijector.inverse_log_det_jacobian(dummy)
    entropy.set_shape(self.batch_shape)
    return entropy 

def _FFTSizeForGrad(grad, rank):
  return math_ops.reduce_prod(
      array_ops.slice(
          array_ops.reverse_v2(array_ops.shape(grad), [0]), (0,), (rank,))) 

def _ProdGrad(op, grad):
  """Gradient for Prod."""
  # The gradient can be expressed by dividing the product by each entry of the
  # input tensor, but this approach can't deal with zeros in the input.
  # Here, we avoid this problem by composing the output as a product of two
  # cumprod operations.

  input_shape = array_ops.shape(op.inputs[0])
  # Reshape reduction indices for the case where the parameter is a scalar
  reduction_indices = array_ops.reshape(op.inputs[1], [-1])

  # Expand grad to full input shape
  output_shape_kept_dims = math_ops.reduced_shape(input_shape, op.inputs[1])
  tile_scaling = _safe_shape_div(input_shape, output_shape_kept_dims)
  grad = array_ops.reshape(grad, output_shape_kept_dims)
  grad = array_ops.tile(grad, tile_scaling)

  # Pack all reduced dimensions into a single one, so we can perform the
  # cumprod ops. If the reduction dims list is empty, it defaults to float32,
  # so we need to cast here.  We put all the shape-related ops on CPU to avoid
  # copying back and forth, and since listdiff is CPU only.
  with ops.device("/cpu:0"):
    reduced = math_ops.cast(reduction_indices, dtypes.int32)
    idx = math_ops.range(0, array_ops.rank(op.inputs[0]))
    other, _ = array_ops.setdiff1d(idx, reduced)
    perm = array_ops.concat([reduced, other], 0)
    reduced_num = math_ops.reduce_prod(array_ops.gather(input_shape, reduced))
    other_num = math_ops.reduce_prod(array_ops.gather(input_shape, other))
  permuted = array_ops.transpose(op.inputs[0], perm)
  permuted_shape = array_ops.shape(permuted)
  reshaped = array_ops.reshape(permuted, (reduced_num, other_num))

  # Calculate product, leaving out the current entry
  left = math_ops.cumprod(reshaped, axis=0, exclusive=True)
  right = math_ops.cumprod(reshaped, axis=0, exclusive=True, reverse=True)
  y = array_ops.reshape(left * right, permuted_shape)

  # Invert the transpose and reshape operations.
  # Make sure to set the statically known shape information through a reshape.
  out = grad * array_ops.transpose(y, array_ops.invert_permutation(perm))
  return array_ops.reshape(out, input_shape), None 

def _MeanGrad(op, grad):
  """Gradient for Mean."""
  sum_grad = _SumGrad(op, grad)[0]
  input_shape = array_ops.shape(op.inputs[0])
  output_shape = array_ops.shape(op.outputs[0])
  factor = _safe_shape_div(
      math_ops.reduce_prod(input_shape), math_ops.reduce_prod(output_shape))
  return sum_grad / math_ops.cast(factor, sum_grad.dtype), None 

def _flip_vector_to_matrix_dynamic(vec, batch_shape):
  """flip_vector_to_matrix with dynamic shapes."""
  # Shapes associated with batch_shape
  batch_rank = array_ops.size(batch_shape)

  # Shapes associated with vec.
  vec = ops.convert_to_tensor(vec, name="vec")
  vec_shape = array_ops.shape(vec)
  vec_rank = array_ops.rank(vec)
  vec_batch_rank = vec_rank - 1

  m = vec_batch_rank - batch_rank
  # vec_shape_left = [M1,...,Mm] or [].
  vec_shape_left = array_ops.strided_slice(vec_shape, [0], [m])
  # If vec_shape_left = [], then condensed_shape = [1] since reduce_prod([]) = 1
  # If vec_shape_left = [M1,...,Mm], condensed_shape = [M1*...*Mm]
  condensed_shape = [math_ops.reduce_prod(vec_shape_left)]
  k = array_ops.gather(vec_shape, vec_rank - 1)
  new_shape = array_ops.concat((batch_shape, [k], condensed_shape), 0)

  def _flip_front_dims_to_back():
    # Permutation corresponding to [N1,...,Nn] + [k, M1,...,Mm]
    perm = array_ops.concat((math_ops.range(m, vec_rank), math_ops.range(0, m)),
                            0)
    return array_ops.transpose(vec, perm=perm)

  x_flipped = control_flow_ops.cond(
      math_ops.less(0, m),
      _flip_front_dims_to_back,
      lambda: array_ops.expand_dims(vec, -1))

  return array_ops.reshape(x_flipped, new_shape) 

def _flip_vector_to_matrix_static(vec, batch_shape):
  """flip_vector_to_matrix with static shapes."""
  # Shapes associated with batch_shape
  batch_rank = batch_shape.ndims

  # Shapes associated with vec.
  vec = ops.convert_to_tensor(vec, name="vec")
  vec_shape = vec.get_shape()
  vec_rank = len(vec_shape)
  vec_batch_rank = vec_rank - 1

  m = vec_batch_rank - batch_rank
  # vec_shape_left = [M1,...,Mm] or [].
  vec_shape_left = vec_shape[:m]
  # If vec_shape_left = [], then condensed_shape = [1] since reduce_prod([]) = 1
  # If vec_shape_left = [M1,...,Mm], condensed_shape = [M1*...*Mm]
  condensed_shape = [np.prod(vec_shape_left)]
  k = vec_shape[-1]
  new_shape = batch_shape.concatenate(k).concatenate(condensed_shape)

  def _flip_front_dims_to_back():
    # Permutation corresponding to [N1,...,Nn] + [k, M1,...,Mm]
    perm = array_ops.concat((math_ops.range(m, vec_rank), math_ops.range(0, m)),
                            0)
    return array_ops.transpose(vec, perm=perm)

  if 0 < m:
    x_flipped = _flip_front_dims_to_back()
  else:
    x_flipped = array_ops.expand_dims(vec, -1)

  return array_ops.reshape(x_flipped, new_shape) 

def _entropy(self):
    if (not self.distribution.is_continuous or
        not self.bijector.is_constant_jacobian):
      raise NotImplementedError("entropy is not implemented")
    # Suppose Y = g(X) where g is a diffeomorphism and X is a continuous rv. It
    # can be shown that:
    #   H[Y] = H[X] + E_X[(log o abs o det o J o g)(X)].
    # If is_constant_jacobian then:
    #   E_X[(log o abs o det o J o g)(X)] = (log o abs o det o J o g)(c)
    # where c can by anything.
    entropy = self.distribution.entropy()
    if self._is_maybe_event_override:
      # H[X] = sum_i H[X_i] if X_i are mutually independent.
      # This means that a reduce_sum is a simple rescaling.
      entropy *= math_ops.cast(math_ops.reduce_prod(self._override_event_shape),
                               dtype=entropy.dtype.base_dtype)
    if self._is_maybe_batch_override:
      new_shape = array_ops.concat([
          _ones_like(self._override_batch_shape),
          self.distribution.batch_shape()
      ], 0)
      entropy = array_ops.reshape(entropy, new_shape)
      multiples = array_ops.concat([
          self._override_batch_shape,
          _ones_like(self.distribution.batch_shape())
      ], 0)
      entropy = array_ops.tile(entropy, multiples)
    dummy = 0.
    return entropy - self.bijector.inverse_log_det_jacobian(dummy) 

def _expand_sample_shape_to_vector(self, x, name):
    """Helper to `sample` which ensures input is 1D."""
    x_static_val = tensor_util.constant_value(x)
    if x_static_val is None:
      prod = math_ops.reduce_prod(x)
    else:
      prod = np.prod(x_static_val, dtype=x.dtype.as_numpy_dtype())

    ndims = x.get_shape().ndims  # != sample_ndims
    if ndims is None:
      # Maybe expand_dims.
      ndims = array_ops.rank(x)
      expanded_shape = distribution_util.pick_vector(
          math_ops.equal(ndims, 0),
          np.array([1], dtype=np.int32),
          array_ops.shape(x))
      x = array_ops.reshape(x, expanded_shape)
    elif ndims == 0:
      # Definitely expand_dims.
      if x_static_val is not None:
        x = ops.convert_to_tensor(
            np.array([x_static_val], dtype=x.dtype.as_numpy_dtype()),
            name=name)
      else:
        x = array_ops.reshape(x, [1])
    elif ndims != 1:
      raise ValueError("Input is neither scalar nor vector.")

    return x, prod 

def test_name(self):
    result_lt = ops.reduce_prod(self.original_lt, {'channel'})
    self.assertIn('lt_reduce_prod', result_lt.name) 

def test(self):
    result_lt = ops.reduce_prod(self.original_lt, {'channel'})
    golden_lt = core.LabeledTensor(
        math_ops.reduce_prod(self.original_lt.tensor, 1),
        [self.a0, self.a2, self.a3])
    self.assertLabeledTensorsEqual(result_lt, golden_lt) 

def _determinant(self):
    return math_ops.reduce_prod(self._diag, reduction_indices=[-1]) 

def per_image_standardization(image):
  """Linearly scales `image` to have zero mean and unit norm.

  This op computes `(x - mean) / adjusted_stddev`, where `mean` is the average
  of all values in image, and
  `adjusted_stddev = max(stddev, 1.0/sqrt(image.NumElements()))`.

  `stddev` is the standard deviation of all values in `image`. It is capped
  away from zero to protect against division by 0 when handling uniform images.

  Args:
    image: 3-D tensor of shape `[height, width, channels]`.

  Returns:
    The standardized image with same shape as `image`.

  Raises:
    ValueError: if the shape of 'image' is incompatible with this function.
  """
  image = ops.convert_to_tensor(image, name='image')
  image = control_flow_ops.with_dependencies(
      _Check3DImage(image, require_static=False), image)
  num_pixels = math_ops.reduce_prod(array_ops.shape(image))

  image = math_ops.cast(image, dtype=dtypes.float32)
  image_mean = math_ops.reduce_mean(image)

  variance = (math_ops.reduce_mean(math_ops.square(image)) -
              math_ops.square(image_mean))
  variance = gen_nn_ops.relu(variance)
  stddev = math_ops.sqrt(variance)

  # Apply a minimum normalization that protects us against uniform images.
  min_stddev = math_ops.rsqrt(math_ops.cast(num_pixels, dtypes.float32))
  pixel_value_scale = math_ops.maximum(stddev, min_stddev)
  pixel_value_offset = image_mean

  image = math_ops.subtract(image, pixel_value_offset)
  image = math_ops.div(image, pixel_value_scale)
  return image 

def _sparse_inner_flatten(inputs, new_rank):
  """Helper function for `inner_flatten`."""
  outer_dimensions = inputs.dense_shape[:new_rank - 1]
  inner_dimensions = inputs.dense_shape[new_rank - 1:]
  new_shape = array_ops.concat((outer_dimensions,
                                [math_ops.reduce_prod(inner_dimensions)]), 0)
  flattened = sparse_ops.sparse_reshape(inputs, new_shape)
  return flattened 

def _expand_sample_shape_to_vector(self, x, name):
    """Helper to `sample` which ensures input is 1D."""
    x_static_val = tensor_util.constant_value(x)
    if x_static_val is None:
      prod = math_ops.reduce_prod(x)
    else:
      prod = np.prod(x_static_val, dtype=x.dtype.as_numpy_dtype())

    ndims = x.get_shape().ndims  # != sample_ndims
    if ndims is None:
      # Maybe expand_dims.
      ndims = array_ops.rank(x)
      expanded_shape = util.pick_vector(
          math_ops.equal(ndims, 0),
          np.array([1], dtype=np.int32), array_ops.shape(x))
      x = array_ops.reshape(x, expanded_shape)
    elif ndims == 0:
      # Definitely expand_dims.
      if x_static_val is not None:
        x = ops.convert_to_tensor(
            np.array([x_static_val], dtype=x.dtype.as_numpy_dtype()),
            name=name)
      else:
        x = array_ops.reshape(x, [1])
    elif ndims != 1:
      raise ValueError("Input is neither scalar nor vector.")

    return x, prod 

def per_image_standardization(image):
  """Linearly scales `image` to have zero mean and unit norm.

  This op computes `(x - mean) / adjusted_stddev`, where `mean` is the average
  of all values in image, and
  `adjusted_stddev = max(stddev, 1.0/sqrt(image.NumElements()))`.

  `stddev` is the standard deviation of all values in `image`. It is capped
  away from zero to protect against division by 0 when handling uniform images.

  Args:
    image: 3-D tensor of shape `[height, width, channels]`.

  Returns:
    The standardized image with same shape as `image`.

  Raises:
    ValueError: if the shape of 'image' is incompatible with this function.
  """
  image = ops.convert_to_tensor(image, name='image')
  _Check3DImage(image, require_static=False)
  num_pixels = math_ops.reduce_prod(array_ops.shape(image))

  image = math_ops.cast(image, dtype=dtypes.float32)
  image_mean = math_ops.reduce_mean(image)

  variance = (math_ops.reduce_mean(math_ops.square(image)) -
              math_ops.square(image_mean))
  variance = gen_nn_ops.relu(variance)
  stddev = math_ops.sqrt(variance)

  # Apply a minimum normalization that protects us against uniform images.
  min_stddev = math_ops.rsqrt(math_ops.cast(num_pixels, dtypes.float32))
  pixel_value_scale = math_ops.maximum(stddev, min_stddev)
  pixel_value_offset = image_mean

  image = math_ops.subtract(image, pixel_value_offset)
  image = math_ops.div(image, pixel_value_scale)
  return image 

def _finish_prob_for_one_fiber(self, y, x, ildj):
    """Finish computation of prob on one element of the inverse image."""
    x = self._maybe_rotate_dims(x, rotate_right=True)
    prob = self.distribution.prob(x)
    if self._is_maybe_event_override:
      prob = math_ops.reduce_prod(prob, self._reduce_event_indices)
    prob *= math_ops.exp(ildj)
    if self._is_maybe_event_override:
      prob.set_shape(array_ops.broadcast_static_shape(
          y.get_shape().with_rank_at_least(1)[:-1], self.batch_shape))
    return prob 

def _FFTSizeForGrad(grad, rank):
  return math_ops.reduce_prod(array_ops.shape(grad)[-rank:]) 

def per_image_standardization(image):
  """Linearly scales `image` to have zero mean and unit norm.

  This op computes `(x - mean) / adjusted_stddev`, where `mean` is the average
  of all values in image, and
  `adjusted_stddev = max(stddev, 1.0/sqrt(image.NumElements()))`.

  `stddev` is the standard deviation of all values in `image`. It is capped
  away from zero to protect against division by 0 when handling uniform images.

  Args:
    image: 3-D tensor of shape `[height, width, channels]`.

  Returns:
    The standardized image with same shape as `image`.

  Raises:
    ValueError: if the shape of 'image' is incompatible with this function.
  """
  image = ops.convert_to_tensor(image, name='image')
  image = control_flow_ops.with_dependencies(
      _Check3DImage(image, require_static=False), image)
  num_pixels = math_ops.reduce_prod(array_ops.shape(image))

  image = math_ops.cast(image, dtype=dtypes.float32)
  image_mean = math_ops.reduce_mean(image)

  variance = (math_ops.reduce_mean(math_ops.square(image)) -
              math_ops.square(image_mean))
  variance = gen_nn_ops.relu(variance)
  stddev = math_ops.sqrt(variance)

  # Apply a minimum normalization that protects us against uniform images.
  min_stddev = math_ops.rsqrt(math_ops.cast(num_pixels, dtypes.float32))
  pixel_value_scale = math_ops.maximum(stddev, min_stddev)
  pixel_value_offset = image_mean

  image = math_ops.subtract(image, pixel_value_offset)
  image = math_ops.div(image, pixel_value_scale)
  return image 

def prod(x, axis=None, keepdims=False):
  """Multiplies the values in a tensor, alongside the specified axis.

  Arguments:
      x: A tensor or variable.
      axis: An integer, the axis to compute the product.
      keepdims: A boolean, whether to keep the dimensions or not.
          If `keepdims` is `False`, the rank of the tensor is reduced
          by 1. If `keepdims` is `True`,
          the reduced dimension is retained with length 1.

  Returns:
      A tensor with the product of elements of `x`.
  """
  return math_ops.reduce_prod(x, axis=axis, keep_dims=keepdims) 

def _test_reduce_prod(data, keep_dims=None):
    """ One iteration of reduce_prod """
    return _test_reduce(math_ops.reduce_prod, data, keep_dims)

#######################################################################
# Reduce_sum
# ----------- 

def _flip_vector_to_matrix_static(vec, batch_shape):
  """flip_vector_to_matrix with static shapes."""
  # Shapes associated with batch_shape
  batch_rank = batch_shape.ndims

  # Shapes associated with vec.
  vec = ops.convert_to_tensor(vec, name="vec")
  vec_shape = vec.get_shape()
  vec_rank = len(vec_shape)
  vec_batch_rank = vec_rank - 1

  m = vec_batch_rank - batch_rank
  # vec_shape_left = [M1,...,Mm] or [].
  vec_shape_left = vec_shape[:m]
  # If vec_shape_left = [], then condensed_shape = [1] since reduce_prod([]) = 1
  # If vec_shape_left = [M1,...,Mm], condensed_shape = [M1*...*Mm]
  condensed_shape = [np.prod(vec_shape_left)]
  k = vec_shape[-1]
  new_shape = batch_shape.concatenate(k).concatenate(condensed_shape)

  def _flip_front_dims_to_back():
    # Permutation corresponding to [N1,...,Nn] + [k, M1,...,Mm]
    perm = array_ops.concat(
        0, (math_ops.range(m, vec_rank), math_ops.range(0, m)))
    return array_ops.transpose(vec, perm=perm)

  if 0 < m:
    x_flipped = _flip_front_dims_to_back()
  else:
    x_flipped = array_ops.expand_dims(vec, -1)

  return array_ops.reshape(x_flipped, new_shape) 

def _flip_vector_to_matrix_dynamic(vec, batch_shape):
  """flip_vector_to_matrix with dynamic shapes."""
  # Shapes associated with batch_shape
  batch_rank = array_ops.size(batch_shape)

  # Shapes associated with vec.
  vec = ops.convert_to_tensor(vec, name="vec")
  vec_shape = array_ops.shape(vec)
  vec_rank = array_ops.rank(vec)
  vec_batch_rank = vec_rank - 1

  m = vec_batch_rank - batch_rank
  # vec_shape_left = [M1,...,Mm] or [].
  vec_shape_left = array_ops.slice(vec_shape, [0], [m])
  # If vec_shape_left = [], then condensed_shape = [1] since reduce_prod([]) = 1
  # If vec_shape_left = [M1,...,Mm], condensed_shape = [M1*...*Mm]
  condensed_shape = [math_ops.reduce_prod(vec_shape_left)]
  k = array_ops.gather(vec_shape, vec_rank - 1)
  new_shape = array_ops.concat(0, (batch_shape, [k], condensed_shape))

  def _flip_front_dims_to_back():
    # Permutation corresponding to [N1,...,Nn] + [k, M1,...,Mm]
    perm = array_ops.concat(
        0, (math_ops.range(m, vec_rank), math_ops.range(0, m)))
    return array_ops.transpose(vec, perm=perm)

  x_flipped = control_flow_ops.cond(
      math_ops.less(0, m),
      _flip_front_dims_to_back,
      lambda: array_ops.expand_dims(vec, -1))

  return array_ops.reshape(x_flipped, new_shape) 

def _sparse_inner_flatten(inputs, new_rank):
  """Helper function for `inner_flatten`."""
  outer_dimensions = inputs.shape[:new_rank - 1]
  inner_dimensions = inputs.shape[new_rank - 1:]
  new_shape = array_ops.concat(0, (outer_dimensions,
                                   [math_ops.reduce_prod(inner_dimensions)]))
  flattened = sparse_ops.sparse_reshape(inputs, new_shape)
  return flattened 

def embedding_lookup_unique(params, ids, name=None):
  """Version of embedding_lookup that avoids duplicate lookups.

  This can save communication in the case of repeated ids.
  Same interface as embedding_lookup. Except it supports multi-dimensional `ids`
  which allows to not reshape input/output to fit gather.

  Args:
    params: A list of tensors with the same shape and type, or a
      `PartitionedVariable`. Shape `[index, d1, d2, ...]`.
    ids: A one-dimensional `Tensor` with type `int32` or `int64` containing
      the ids to be looked up in `params`. Shape `[ids1, ids2, ...]`.
    name: A name for this operation (optional).

  Returns:
    A `Tensor` with the same type as the tensors in `params` and dimension of
    `[ids1, ids2, d1, d2, ...]`.

  Raises:
    ValueError: If `params` is empty.
  """
  with ops.name_scope(name, "EmbeddingLookupUnique", [params, ids]):
    ids = ops.convert_to_tensor(ids)
    shape = array_ops.shape(ids)
    ids_flat = array_ops.reshape(
        ids, math_ops.reduce_prod(shape, keep_dims=True))
    unique_ids, idx = array_ops.unique(ids_flat)
    unique_embeddings = embedding_ops.embedding_lookup(params, unique_ids)
    embeds_flat = array_ops.gather(unique_embeddings, idx)
    embed_shape = array_ops.concat(
        0, [shape, array_ops.shape(unique_embeddings)[1:]])
    embeds = array_ops.reshape(embeds_flat, embed_shape)
    embeds.set_shape(ids.get_shape().concatenate(
        unique_embeddings.get_shape()[1:]))
    return embeds 

def embedding_lookup(params, ids, name="embedding_lookup"):
  """Provides a N dimensional version of tf.embedding_lookup.

  Ids are flattened to a 1d tensor before being passed to embedding_lookup
  then, they are unflattend to match the original ids shape plus an extra
  leading dimension of the size of the embeddings.

  Args:
    params: List of tensors of size D0 x D1 x ... x Dn-2 x Dn-1.
    ids: N-dimensional tensor of B0 x B1 x .. x Bn-2 x Bn-1.
      Must contain indexes into params.
    name: Optional name for the op.

  Returns:
    A tensor of size B0 x B1 x .. x Bn-2 x Bn-1 x D1 x ... x Dn-2 x Dn-1
    containing the values from the params tensor(s) for indecies in ids.

  Raises:
    ValueError: if some parameters are invalid.
  """
  with ops.name_scope(name, "embedding_lookup", [params, ids]):
    params = ops.convert_to_tensor(params)
    ids = ops.convert_to_tensor(ids)
    shape = array_ops_.shape(ids)
    ids_flat = array_ops_.reshape(
        ids, math_ops.reduce_prod(shape, keep_dims=True))
    embeds_flat = nn.embedding_lookup(params, ids_flat, name)
    embed_shape = array_ops_.concat(0, [shape, [-1]])
    embeds = array_ops_.reshape(embeds_flat, embed_shape)
    embeds.set_shape(ids.get_shape().concatenate(params.get_shape()[1:]))
    return embeds 

def _FFTSizeForGrad(grad, rank):
  return math_ops.reduce_prod(
      array_ops.slice(
          array_ops.reverse(array_ops.shape(grad), (True,)), (0,), (rank,))) 

def _ProdGrad(op, grad):
  """Gradient for Prod."""
  # The gradient can be expressed by dividing the product by each entry of the
  # input tensor, but this approach can't deal with zeros in the input.
  # Here, we avoid this problem by composing the output as a product of two
  # cumprod operations.

  input_shape = array_ops.shape(op.inputs[0])
  # Reshape reduction indices for the case where the parameter is a scalar
  reduction_indices = array_ops.reshape(op.inputs[1], [-1])

  # Expand grad to full input shape
  output_shape_kept_dims = math_ops.reduced_shape(input_shape, op.inputs[1])
  tile_scaling = _safe_shape_div(input_shape, output_shape_kept_dims)
  grad = array_ops.reshape(grad, output_shape_kept_dims)
  grad = array_ops.tile(grad, tile_scaling)

  # Pack all reduced dimensions into a single one, so we can perform the
  # cumprod ops. If the reduction dims list is empty, it defaults to float32,
  # so we need to cast here.  We put all the shape-related ops on CPU to avoid
  # copying back and forth, and since listdiff is CPU only.
  with ops.device("/cpu:0"):
    reduced = math_ops.cast(reduction_indices, dtypes.int32)
    idx = math_ops.range(0, array_ops.rank(op.inputs[0]))
    other, _ = array_ops.setdiff1d(idx, reduced)
    perm = array_ops.concat(0, [reduced, other])
    reduced_num = math_ops.reduce_prod(array_ops.gather(input_shape, reduced))
    other_num = math_ops.reduce_prod(array_ops.gather(input_shape, other))
  permuted = array_ops.transpose(op.inputs[0], perm)
  permuted_shape = array_ops.shape(permuted)
  reshaped = array_ops.reshape(permuted, (reduced_num, other_num))

  # Calculate product, leaving out the current entry
  left = math_ops.cumprod(reshaped, axis=0, exclusive=True)
  right = math_ops.cumprod(reshaped, axis=0, exclusive=True, reverse=True)
  y = array_ops.reshape(left * right, permuted_shape)

  # Invert the transpose and reshape operations.
  # Make sure to set the statically known shape information through a reshape.
  out = grad * array_ops.transpose(y, array_ops.invert_permutation(perm))
  return array_ops.reshape(out, input_shape), None 

def _MeanGrad(op, grad):
  """Gradient for Mean."""
  sum_grad = _SumGrad(op, grad)[0]
  input_shape = array_ops.shape(op.inputs[0])
  output_shape = array_ops.shape(op.outputs[0])
  factor = _safe_shape_div(math_ops.reduce_prod(input_shape),
                           math_ops.reduce_prod(output_shape))
  return sum_grad / math_ops.cast(factor, sum_grad.dtype), None