array_ops.py

# Copyright 2015 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.
# ==============================================================================

"""Support for manipulating tensors.

See the @{$python/array_ops} guide.

@@string_to_number
@@to_double
@@to_float
@@to_bfloat16
@@to_int32
@@to_int64
@@cast
@@bitcast
@@saturate_cast
@@broadcast_dynamic_shape
@@broadcast_static_shape
@@shape
@@shape_n
@@size
@@rank
@@reshape
@@squeeze
@@expand_dims
@@meshgrid
@@slice
@@strided_slice
@@split
@@tile
@@pad
@@concat
@@stack
@@parallel_stack
@@unstack
@@reverse_sequence
@@reverse
@@reverse_v2
@@transpose
@@extract_image_patches
@@space_to_batch_nd
@@space_to_batch
@@required_space_to_batch_paddings
@@batch_to_space_nd
@@batch_to_space
@@space_to_depth
@@depth_to_space
@@gather
@@gather_nd
@@unique_with_counts
@@scatter_nd
@@dynamic_partition
@@dynamic_stitch
@@boolean_mask
@@one_hot
@@sequence_mask
@@dequantize
@@quantize_v2
@@quantized_concat
@@setdiff1d
@@fake_quant_with_min_max_args
@@fake_quant_with_min_max_args_gradient
@@fake_quant_with_min_max_vars
@@fake_quant_with_min_max_vars_gradient
@@fake_quant_with_min_max_vars_per_channel
@@fake_quant_with_min_max_vars_per_channel_gradient
"""

from __future__ import absolute_import
from __future__ import division
from __future__ import print_function

import sys
import numpy as np

from tensorflow.python.framework import common_shapes
from tensorflow.python.framework import constant_op
from tensorflow.python.framework import dtypes
from tensorflow.python.framework import ops
from tensorflow.python.framework import sparse_tensor
from tensorflow.python.framework import tensor_shape
from tensorflow.python.framework import tensor_util
# 'Constant' gets imported in the module 'array_ops'.
from tensorflow.python.framework.constant_op import constant
from tensorflow.python.ops import gen_array_ops
from tensorflow.python.ops import gen_math_ops
# go/tf-wildcard-import
# pylint: disable=wildcard-import
from tensorflow.python.ops.gen_array_ops import *
from tensorflow.python.util import deprecation
from tensorflow.python.util.deprecation import deprecated
# pylint: enable=wildcard-import


# Used for slicing to specify a new 1 size dimension
newaxis = None

# We override the 'slice' for the "slice" op, so we keep python's
# existing 'slice' for later use in this module.
_baseslice = slice


# pylint: disable=redefined-builtin,protected-access
def expand_dims(input, axis=None, name=None, dim=None):
  """Inserts a dimension of 1 into a tensor's shape.

  Given a tensor `input`, this operation inserts a dimension of 1 at the
  dimension index `axis` of `input`'s shape. The dimension index `axis` starts
  at zero; if you specify a negative number for `axis` it is counted backward
  from the end.

  This operation is useful if you want to add a batch dimension to a single
  element. For example, if you have a single image of shape `[height, width,
  channels]`, you can make it a batch of 1 image with `expand_dims(image, 0)`,
  which will make the shape `[1, height, width, channels]`.

  Other examples:

  ```python
  # 't' is a tensor of shape [2]
  shape(expand_dims(t, 0)) ==> [1, 2]
  shape(expand_dims(t, 1)) ==> [2, 1]
  shape(expand_dims(t, -1)) ==> [2, 1]

  # 't2' is a tensor of shape [2, 3, 5]
  shape(expand_dims(t2, 0)) ==> [1, 2, 3, 5]
  shape(expand_dims(t2, 2)) ==> [2, 3, 1, 5]
  shape(expand_dims(t2, 3)) ==> [2, 3, 5, 1]
  ```

  This operation requires that:

  `-1-input.dims() <= dim <= input.dims()`

  This operation is related to `squeeze()`, which removes dimensions of
  size 1.

  Args:
    input: A `Tensor`.
    axis: 0-D (scalar). Specifies the dimension index at which to
      expand the shape of `input`.
    name: The name of the output `Tensor`.
    dim: 0-D (scalar). Equivalent to `axis`, to be deprecated.

  Returns:
    A `Tensor` with the same data as `input`, but its shape has an additional
    dimension of size 1 added.

  Raises:
    ValueError: if both `dim` and `axis` are specified.
  """
  # TODO(aselle): Remove argument dim
  if dim is not None:
    if axis is not None:
      raise ValueError("can't specify both 'dim' and 'axis'")
    axis = dim
  return gen_array_ops._expand_dims(input, axis, name)
# pylint: enable=redefined-builtin,protected-access


# Aliases for some automatically-generated names.
# pylint: disable=protected-access
@deprecated(
    "2016-11-30",
    "This op will be removed after the deprecation date. "
    "Please switch to tf.setdiff1d().")
def listdiff(x, y, out_idx=None, name=None):
  return gen_array_ops._list_diff(x, y, out_idx, name)
listdiff.__doc__ = gen_array_ops._list_diff.__doc__ + "\n" + listdiff.__doc__
# pylint: enable=protected-access


# pylint: disable=undefined-variable,protected-access
def setdiff1d(x, y, index_dtype=dtypes.int32, name=None):
  return gen_array_ops._list_diff(x, y, index_dtype, name)
setdiff1d.__doc__ = gen_array_ops._list_diff.__doc__
# pylint: enable=protected-access


def broadcast_dynamic_shape(shape_x, shape_y):
  # pylint: disable=protected-access
  """Returns the broadcasted dynamic shape between `shape_x` and `shape_y`.

  Args:
    shape_x: A rank 1 integer `Tensor`, representing the shape of x.
    shape_y: A rank 1 integer `Tensor`, representing the shape of y.
  Returns:
    A rank 1 integer `Tensor` representing the broadcasted shape.
  """
  return gen_array_ops._broadcast_args(shape_x, shape_y)
  # pylint: enable=protected-access


def broadcast_static_shape(shape_x, shape_y):
  """Returns the broadcasted static shape between `shape_x` and `shape_y`.

  Args:
    shape_x: A `TensorShape`
    shape_y: A `TensorShape`

  Returns:
    A `TensorShape` representing the broadcasted shape.

  Raises:
    ValueError: If the two shapes can not be broadcasted.
  """
  return common_shapes.broadcast_shape(shape_x, shape_y)


def shape(input, name=None, out_type=dtypes.int32):
  # pylint: disable=redefined-builtin
  """Returns the shape of a tensor.

  This operation returns a 1-D integer tensor representing the shape of `input`.

  For example:

  ```python
  # 't' is [[[1, 1, 1], [2, 2, 2]], [[3, 3, 3], [4, 4, 4]]]
  shape(t) ==> [2, 2, 3]
  ```

  Args:
    input: A `Tensor` or `SparseTensor`.
    name: A name for the operation (optional).
    out_type: (Optional) The specified output type of the operation
      (`int32` or `int64`). Defaults to `tf.int32`.

  Returns:
    A `Tensor` of type `out_type`.
  """
  return shape_internal(input, name, optimize=True, out_type=out_type)


def shape_internal(input, name=None, optimize=True, out_type=dtypes.int32):
  # pylint: disable=redefined-builtin
  """Returns the shape of a tensor.

  Args:
    input: A `Tensor` or `SparseTensor`.
    name: A name for the operation (optional).
    optimize: if true, encode the shape as a constant when possible.
    out_type: (Optional) The specified output type of the operation
      (`int32` or `int64`). Defaults to tf.int32.

  Returns:
    A `Tensor` of type `out_type`.

  """
  with ops.name_scope(name, "Shape", [input]) as name:
    if isinstance(
        input, (sparse_tensor.SparseTensor, sparse_tensor.SparseTensorValue)):
      return gen_math_ops.cast(input.dense_shape, out_type)
    else:
      input_tensor = ops.convert_to_tensor(input)
      input_shape = input_tensor.get_shape()
      if optimize and input_shape.is_fully_defined():
        return constant(input_shape.as_list(), out_type, name=name)
      return gen_array_ops.shape(input, name=name, out_type=out_type)


def size(input, name=None, out_type=dtypes.int32):
  # pylint: disable=redefined-builtin
  """Returns the size of a tensor.

  This operation returns an integer representing the number of elements in
  `input`.

  For example:

  ```python
  # 't' is [[[1, 1, 1], [2, 2, 2]], [[3, 3, 3], [4, 4, 4]]]]
  size(t) ==> 12
  ```

  Args:
    input: A `Tensor` or `SparseTensor`.
    name: A name for the operation (optional).
    out_type: (Optional) The specified output type of the operation
      (`int32` or `int64`). Defaults to tf.int32.

  Returns:
    A `Tensor` of type `out_type`. Defaults to tf.int32.
  """
  return size_internal(input, name, optimize=True, out_type=out_type)


def size_internal(input, name=None, optimize=True, out_type=dtypes.int32):
  # pylint: disable=redefined-builtin,protected-access
  """Returns the size of a tensor.

  Args:
    input: A `Tensor` or `SparseTensor`.
    name: A name for the operation (optional).
    optimize: if true, encode the size as a constant when possible.
    out_type: (Optional) The specified output type of the operation
      (`int32` or `int64`). Defaults to tf.int32.

  Returns:
    A `Tensor` of type `out_type`.
  """
  with ops.name_scope(name, "Size", [input]) as name:
    if isinstance(
        input, (sparse_tensor.SparseTensor, sparse_tensor.SparseTensorValue)):
      return gen_math_ops._prod(
          gen_math_ops.cast(input.dense_shape, out_type), 0, name=name)
    else:
      input_tensor = ops.convert_to_tensor(input)
      input_shape = input_tensor.get_shape()
      if optimize and input_shape.is_fully_defined():
        return constant(input_shape.num_elements(), out_type, name=name)
      return gen_array_ops.size(input, name=name, out_type=out_type)


def rank(input, name=None):
  # pylint: disable=redefined-builtin
  """Returns the rank of a tensor.

  This operation returns an integer representing the rank of `input`.

  For example:

  ```python
  # 't' is [[[1, 1, 1], [2, 2, 2]], [[3, 3, 3], [4, 4, 4]]]
  # shape of tensor 't' is [2, 2, 3]
  rank(t) ==> 3
  ```

  **Note**: The rank of a tensor is not the same as the rank of a matrix. The
  rank of a tensor is the number of indices required to uniquely select each
  element of the tensor. Rank is also known as "order", "degree", or "ndims."

  Args:
    input: A `Tensor` or `SparseTensor`.
    name: A name for the operation (optional).

  Returns:
    A `Tensor` of type `int32`.

  @compatibility(numpy)
  Equivalent to np.ndim
  @end_compatibility
  """
  return rank_internal(input, name, optimize=True)


def rank_internal(input, name=None, optimize=True):
  # pylint: disable=redefined-builtin
  """Returns the rank of a tensor.

  Args:
    input: A `Tensor` or `SparseTensor`.
    name: A name for the operation (optional).
    optimize: if true, encode the rank as a constant when possible.

  Returns:
    A `Tensor` of type `int32`.
  """
  with ops.name_scope(name, "Rank", [input]) as name:
    if isinstance(
        input, (sparse_tensor.SparseTensor, sparse_tensor.SparseTensorValue)):
      return gen_array_ops.size(input.dense_shape, name=name)
    else:
      input_tensor = ops.convert_to_tensor(input)
      input_shape = input_tensor.get_shape()
      if optimize and input_shape.ndims is not None:
        return constant(input_shape.ndims, dtypes.int32, name=name)
      return gen_array_ops.rank(input, name=name)


def _SliceHelper(tensor, slice_spec, var=None):
  """Overload for Tensor.__getitem__.

  This operation extracts the specified region from the tensor.
  The notation is similar to NumPy with the restriction that
  currently only support basic indexing. That means that
  using a tensor as input is not currently allowed

  Some useful examples:

  ```python
  # strip leading and trailing 2 elements
  foo = tf.constant([1,2,3,4,5,6])
  print(foo[2:-2].eval()) # => [3,4]

  # skip every row and reverse every column
  foo = tf.constant([[1,2,3], [4,5,6], [7,8,9]])
  print(foo[::2,::-1].eval()) # => [[3,2,1], [9,8,7]]

  # Insert another dimension
  foo = tf.constant([[1,2,3], [4,5,6], [7,8,9]])
  print(foo[tf.newaxis, :, :].eval()) # => [[[3,2,1], [9,8,7]]]
  print(foo[:, tf.newaxis, :].eval()) # => [[[3,2,1]], [[9,8,7]]]
  print(foo[:, :, tf.newaxis].eval()) # => [[[3],[2],[1]], [[9],[8],[7]]]

  # Ellipses (3 equivalent operations)
  print(foo[tf.newaxis, :, :].eval()) # => [[[3,2,1], [9,8,7]]]
  print(foo[tf.newaxis, ...].eval()) # => [[[3,2,1], [9,8,7]]]
  print(foo[tf.newaxis].eval()) # => [[[3,2,1], [9,8,7]]]
  ```

  Notes:
    - `tf.newaxis` is `None` as in NumPy.
    - An implicit ellipsis is placed at the end of the `slice_spec`
    - NumPy advanced indexing is currently not supported.

  Args:
    tensor: An ops.Tensor object.
    slice_spec: The arguments to Tensor.__getitem__.
    var: In the case of variable slice assignment, the Variable
      object to slice (i.e. tensor is the read-only view of this
      variable).

  Returns:
    The appropriate slice of "tensor", based on "slice_spec".

  Raises:
    ValueError: If a slice range is negative size.
    TypeError: If the slice indices aren't int, slice, or Ellipsis.
  """

  if not isinstance(slice_spec, (list, tuple)):
    slice_spec = [slice_spec]

  begin, end, strides = [], [], []
  index = 0

  new_axis_mask, shrink_axis_mask = 0, 0
  begin_mask, end_mask = 0, 0
  ellipsis_mask = 0
  for s in slice_spec:
    if isinstance(s, _baseslice):
      strides.append(s.step if s.step is not None else 1)
      # python doesn't always use None when constructing ranges
      # for example a[:] gives slice(None,sys.maxsize,None)
      # whereas a[::1] gives slice(None,None,None)
      if s.start is not None and s.start is not sys.maxsize:
        begin.append(s.start)
      else:
        begin.append(0)
        begin_mask |= (1 << index)
      if s.stop is not None and s.stop != sys.maxsize:
        end.append(s.stop)
      else:
        end.append(0)
        end_mask |= (1 << index)
    elif s is Ellipsis:
      begin.append(0)
      end.append(0)
      strides.append(1)
      ellipsis_mask |= (1 << index)
    elif s is newaxis:
      begin.append(0)
      end.append(0)
      strides.append(1)
      new_axis_mask |= (1 << index)
    else:
      begin.append(s)
      end.append(s + 1)
      if isinstance(s, ops.Tensor):
        strides.append(constant(1, s.dtype))
      else:
        strides.append(np.ones_like(s).dtype.type(1))
      shrink_axis_mask |= (1 << index)
    index += 1

  # stack possibly involves no tensors, so we must use op_scope correct graph.
  with ops.name_scope(None, "strided_slice",
                      [tensor] + begin + end + strides) as name:
    if begin:
      packed_begin, packed_end, packed_strides = (
          stack(begin), stack(end), stack(strides))
    else:
      var_empty = constant([], dtype=dtypes.int32)
      packed_begin = packed_end = packed_strides = var_empty
    return strided_slice(
        tensor,
        packed_begin,
        packed_end,
        packed_strides,
        begin_mask=begin_mask,
        end_mask=end_mask,
        shrink_axis_mask=shrink_axis_mask,
        new_axis_mask=new_axis_mask,
        ellipsis_mask=ellipsis_mask,
        var=var,
        name=name)


# pylint: disable=undefined-variable,protected-access
def slice(input_, begin, size, name=None):
  # pylint: disable=redefined-builtin
  """Extracts a slice from a tensor.

  This operation extracts a slice of size `size` from a tensor `input` starting
  at the location specified by `begin`. The slice `size` is represented as a
  tensor shape, where `size[i]` is the number of elements of the 'i'th dimension
  of `input` that you want to slice. The starting location (`begin`) for the
  slice is represented as an offset in each dimension of `input`. In other
  words, `begin[i]` is the offset into the 'i'th dimension of `input` that you
  want to slice from.

  `begin` is zero-based; `size` is one-based. If `size[i]` is -1,
  all remaining elements in dimension i are included in the
  slice. In other words, this is equivalent to setting:

  `size[i] = input.dim_size(i) - begin[i]`

  This operation requires that:

  `0 <= begin[i] <= begin[i] + size[i] <= Di  for i in [0, n]`

  For example:

  ```python
  # 'input' is [[[1, 1, 1], [2, 2, 2]],
  #             [[3, 3, 3], [4, 4, 4]],
  #             [[5, 5, 5], [6, 6, 6]]]
  tf.slice(input, [1, 0, 0], [1, 1, 3]) ==> [[[3, 3, 3]]]
  tf.slice(input, [1, 0, 0], [1, 2, 3]) ==> [[[3, 3, 3],
                                              [4, 4, 4]]]
  tf.slice(input, [1, 0, 0], [2, 1, 3]) ==> [[[3, 3, 3]],
                                             [[5, 5, 5]]]
  ```

  Args:
    input_: A `Tensor`.
    begin: An `int32` or `int64` `Tensor`.
    size: An `int32` or `int64` `Tensor`.
    name: A name for the operation (optional).

  Returns:
    A `Tensor` the same type as `input`.
  """
  return gen_array_ops._slice(input_, begin, size, name=name)


# pylint: disable=invalid-name
def strided_slice(input_,
                  begin,
                  end,
                  strides=None,
                  begin_mask=0,
                  end_mask=0,
                  ellipsis_mask=0,
                  new_axis_mask=0,
                  shrink_axis_mask=0,
                  var=None,
                  name=None):
  """Extracts a strided slice of a tensor (generalized python array indexing).

  **Most users will want to use @{tf.Tensor.__getitem__} and
  @{tf.Variable.__getitem__}.** That allows  NumPy style slicing syntax (i.e.
  `tensor[..., 3:4:-1, tf.newaxis, 3]`).
  This op is the low-level interface that are used to implement operators.
  Those interfaces are much more friendly, and highly recommended.

  To a first order, this operation extracts a slice of size `end - begin`
  from a tensor `input`
  starting at the location specified by `begin`. The slice continues by adding
  `stride` to the `begin` index until all dimensions are not less than `end`.
  Note that components of stride can be negative, which causes a reverse
  slice.

  This operation can be thought of an encoding of a numpy style sliced
  range. Given a python slice input[<spec0>, <spec1>, ..., <specn>]
  this function will be called as follows.

  `begin`, `end`, and `strides` will be all length n. n is in general
  not the same dimensionality as `input`.

  For the ith spec,
  `begin_mask`, `end_mask`, `ellipsis_mask`, `new_axis_mask`,
  and `shrink_axis_mask` will have the ith bit corresponding to
  the ith spec.

  If the ith bit of `begin_mask` is non-zero, `begin[i]` is ignored and
  the fullest possible range in that dimension is used instead.
  `end_mask` works analogously, except with the end range.

  `foo[5:,:,:3]` on a 7x8x9 tensor is equivalent to `foo[5:7,0:8,0:3]`.
  `foo[::-1]` reverses a tensor with shape 8.


  If the ith bit of `ellipsis_mask` is non-zero, as many unspecified dimensions
  as needed will be inserted between other dimensions. Only one
  non-zero bit is allowed in `ellipsis_mask`.

  For example `foo[3:5,...,4:5]` on a shape 10x3x3x10 tensor is
  equivalent to `foo[3:5,:,:,4:5]` and
  `foo[3:5,...]` is equivalent to `foo[3:5,:,:,:]`.

  If the ith bit of `new_axis_mask` is one, then `begin`,
  `end`, and `stride` are ignored and a new length 1 dimension is
  added at this point in the output tensor.

  For example `foo[3:5,4]` on a 10x8 tensor produces a shape 2 tensor
  whereas `foo[3:5,4:5]` produces a shape 2x1 tensor with shrink_mask
  being 1<<1 == 2.

  If the ith bit of `shrink_axis_mask` is one, then `begin`,
  `end[i]`, and `stride[i]` are used to do a slice in the appropriate
  dimension, but the output tensor will be reduced in dimensionality
  by one. This is only valid if the ith entry of slice[i]==1.

  NOTE: `begin` and `end` are zero-indexed`.
  `strides` entries must be non-zero.


  ```python
  # 'input' is [[[1, 1, 1], [2, 2, 2]],
  #             [[3, 3, 3], [4, 4, 4]],
  #             [[5, 5, 5], [6, 6, 6]]]
  tf.strided_slice(input, [1, 0, 0], [2, 1, 3], [1, 1, 1]) ==> [[[3, 3, 3]]]
  tf.strided_slice(input, [1, 0, 0], [2, 2, 3], [1, 1, 1]) ==> [[[3, 3, 3],
                                                                 [4, 4, 4]]]
  tf.strided_slice(input, [1, -1, 0], [2, -3, 3], [1, -1, 1]) ==>[[[4, 4, 4],
                                                                   [3, 3, 3]]]
  ```

  Args:
    input_: A `Tensor`.
    begin: An `int32` or `int64` `Tensor`.
    end: An `int32` or `int64` `Tensor`.
    strides: An `int32` or `int64` `Tensor`.
    begin_mask: An `int32` mask.
    end_mask: An `int32` mask.
    ellipsis_mask: An `int32` mask.
    new_axis_mask: An `int32` mask.
    shrink_axis_mask: An `int32` mask.
    var: The variable corresponding to `input_` or None
    name: A name for the operation (optional).

  Returns:
    A `Tensor` the same type as `input`.
  """

  if strides is None:
    strides = ones_like(begin)

  op = gen_array_ops.strided_slice(
      input=input_,
      begin=begin,
      end=end,
      strides=strides,
      name=name,
      begin_mask=begin_mask,
      end_mask=end_mask,
      ellipsis_mask=ellipsis_mask,
      new_axis_mask=new_axis_mask,
      shrink_axis_mask=shrink_axis_mask)

  parent_name = name

  def assign(val, name=None):
    """Closure that holds all the arguments to create an assignment."""

    if var is None:
      raise ValueError("Sliced assignment is only supported for variables")

    if name is None:
      name = parent_name + "_assign"

    return var._strided_slice_assign(
        begin=begin,
        end=end,
        strides=strides,
        value=val,
        name=name,
        begin_mask=begin_mask,
        end_mask=end_mask,
        ellipsis_mask=ellipsis_mask,
        new_axis_mask=new_axis_mask,
        shrink_axis_mask=shrink_axis_mask)

  op.assign = assign
  return op


def _SliceHelperVar(var, slice_spec):
  """Creates a slice helper object given a variable.

  This allows creating a sub-tensor from part of the current contents
  of a variable.  See ${tf.Tensor$`Tensor.__getitem__`}
  for detailed examples of slicing.

  This function in addition also allows assignment to a sliced range.
  This is similar to `__setitem__` functionality in Python. However,
  the syntax is different so that the user can capture the assignment
  operation for grouping or passing to `sess.run()`.
  For example,

  ```prettyprint
  import tensorflow as tf
  A = tf.Variable([[1,2,3], [4,5,6], [7,8,9]], dtype=tf.float32)
  with tf.Session() as sess:
    sess.run(tf.global_variables_initializer())
    print sess.run(A[:2, :2]) # => [[1,2], [4,5]]

    op = A[:2,:2].assign(22. * tf.ones((2, 2)))
    print sess.run(op) # => [[22, 22, 3], [22, 22, 6], [7,8,9]]
  ```

  Note that assignments currently do not support NumPy broadcasting
  semantics.

  Args:
    var: An `ops.Variable` object.
    slice_spec: The arguments to `Tensor.__getitem__`.

  Returns:
    The appropriate slice of "tensor", based on "slice_spec".
    As an operator. The operator also has a `assign()` method
    that can be used to generate an assignment operator.

  Raises:
    ValueError: If a slice range is negative size.
    TypeError: If the slice indices aren't int, slice, or Ellipsis.

  """

  return _SliceHelper(var._AsTensor(), slice_spec, var)

ops.Tensor._override_operator("__getitem__", _SliceHelper)


def parallel_stack(values, name="parallel_stack"):
  """Stacks a list of rank-`R` tensors into one rank-`(R+1)` tensor in parallel.

  Requires that the shape of inputs be known at graph construction time.

  Packs the list of tensors in `values` into a tensor with rank one higher than
  each tensor in `values`, by packing them along the first dimension.
  Given a list of length `N` of tensors of shape `(A, B, C)`; the `output`
  tensor will have the shape `(N, A, B, C)`.

  For example:

  ```prettyprint
  # 'x' is [1, 4]
  # 'y' is [2, 5]
  # 'z' is [3, 6]
  parallel_stack([x, y, z]) => [[1, 4], [2, 5], [3, 6]]
  ```

  The difference between stack and parallel_stack is that stack requires all
  of the inputs be computed before the operation will begin but doesn't require
  that the input shapes be known during graph construction.  Parallel stack
  will copy pieces of the input into the output as they become available, in
  some situations this can provide a performance benefit.

  This is the opposite of unstack.  The numpy equivalent is

      tf.parallel_stack([x, y, z]) = np.asarray([x, y, z])

  Args:
    values: A list of `Tensor` objects with the same shape and type.
    name: A name for this operation (optional).

  Returns:
    output: A stacked `Tensor` with the same type as `values`.
  """
  with ops.name_scope(name):
    value_t = ops.convert_to_tensor(values[0])
    value_shape = ops.convert_to_tensor(value_t).get_shape()

    output_shape = tensor_shape.TensorShape([len(values)])
    output_shape = output_shape.concatenate(value_shape)
    # expand_dims converts concat to stack.
    return gen_array_ops._parallel_concat(
        [expand_dims(value, 0) for value in values], shape=output_shape)

def stack(values, axis=0, name="stack"):
  """Stacks a list of rank-`R` tensors into one rank-`(R+1)` tensor.

  Packs the list of tensors in `values` into a tensor with rank one higher than
  each tensor in `values`, by packing them along the `axis` dimension.
  Given a list of length `N` of tensors of shape `(A, B, C)`;

  if `axis == 0` then the `output` tensor will have the shape `(N, A, B, C)`.
  if `axis == 1` then the `output` tensor will have the shape `(A, N, B, C)`.
  Etc.

  For example:

  ```prettyprint
  # 'x' is [1, 4]
  # 'y' is [2, 5]
  # 'z' is [3, 6]
  stack([x, y, z]) => [[1, 4], [2, 5], [3, 6]]  # Pack along first dim.
  stack([x, y, z], axis=1) => [[1, 2, 3], [4, 5, 6]]
  ```

  This is the opposite of unstack.  The numpy equivalent is

  ```python
  tf.stack([x, y, z]) = np.asarray([x, y, z])
  ```

  Args:
    values: A list of `Tensor` objects with the same shape and type.
    axis: An `int`. The axis to stack along. Defaults to the first dimension.
      Supports negative indexes.
    name: A name for this operation (optional).

  Returns:
    output: A stacked `Tensor` with the same type as `values`.

  Raises:
    ValueError: If `axis` is out of the range [-(R+1), R+1).
  """
  if axis == 0:
    try:
      # If the input is a constant list, it can be converted to a constant op
      return ops.convert_to_tensor(values, name=name)
    except (TypeError, ValueError):
      pass  # Input list contains non-constant tensors

  value_shape = ops.convert_to_tensor(values[0], name=name).get_shape()
  if value_shape.ndims is not None:
    expanded_num_dims = value_shape.ndims + 1
    if axis < -expanded_num_dims or axis >= expanded_num_dims:
      raise ValueError("axis = %d not in [%d, %d)" %
                       (axis, -expanded_num_dims, expanded_num_dims))

  return gen_array_ops._pack(values, axis=axis, name=name)


# pylint: disable=invalid-name
def _autopacking_helper(list_or_tuple, dtype, name):
  """Converts the given list or tuple to a tensor by packing.

  Args:
    list_or_tuple: A (possibly nested) list or tuple containing a tensor.
    dtype: The element type of the returned tensor.
    name: A name for the returned tensor.

  Returns:
    A `tf.Tensor` with value equivalent to `list_or_tuple`.
  """
  must_pack = False
  converted_elems = []
  with ops.name_scope(name) as scope:
    for i, elem in enumerate(list_or_tuple):
      if ops.is_dense_tensor_like(elem):
        if dtype is not None and elem.dtype.base_dtype != dtype:
          raise TypeError(
              "Cannot convert a list containing a tensor of dtype "
              "%s to %s (Tensor is: %r)" % (elem.dtype, dtype, elem))
        converted_elems.append(elem)
        must_pack = True
      elif isinstance(elem, (list, tuple)):
        converted_elem = _autopacking_helper(elem, dtype, str(i))
        if ops.is_dense_tensor_like(converted_elem):
          must_pack = True
        converted_elems.append(converted_elem)
      else:
        converted_elems.append(elem)
    if must_pack:
      elems_as_tensors = []
      for i, elem in enumerate(converted_elems):
        if ops.is_dense_tensor_like(elem):
          elems_as_tensors.append(elem)
        else:
          # NOTE(mrry): This is inefficient, but it enables us to
          # handle the case where the list arguments are other
          # convertible-to-tensor types, such as numpy arrays.
          elems_as_tensors.append(
              constant_op.constant(elem, dtype=dtype, name=str(i)))
      return gen_array_ops._pack(elems_as_tensors, name=scope)
    else:
      return converted_elems


def _get_dtype_from_nested_lists(list_or_tuple):
  """Returns the dtype of any tensor-like object in `list_or_tuple`, if found.

  Args:
    list_or_tuple: A list or tuple representing an object that can be
      converted to a `tf.Tensor`.

  Returns:
    The dtype of any tensor-like object in `list_or_tuple`, or `None` if no
    such object exists.
  """
  for elem in list_or_tuple:
    if ops.is_dense_tensor_like(elem):
      return elem.dtype.base_dtype
    elif isinstance(elem, (list, tuple)):
      maybe_dtype = _get_dtype_from_nested_lists(elem)
      if maybe_dtype is not None:
        return maybe_dtype
  return None


def _autopacking_conversion_function(v, dtype=None, name=None, as_ref=False):
  """Tensor conversion function that automatically packs arguments."""
  if as_ref:
    return NotImplemented
  inferred_dtype = _get_dtype_from_nested_lists(v)
  if inferred_dtype is None:
    # We did not find any tensor-like objects in the nested lists, so defer to
    # other conversion functions.
    return NotImplemented
  if dtype is not None and dtype != inferred_dtype:
    return NotImplemented
  return _autopacking_helper(v, inferred_dtype, name or "packed")
# pylint: enable=invalid-name


# NOTE: Register this conversion function to run *before* one that
# assumes every element is a value.
ops.register_tensor_conversion_function(
    (list, tuple), _autopacking_conversion_function, 99)


def unstack(value, num=None, axis=0, name="unstack"):
  """Unpacks the given dimension of a rank-`R` tensor into rank-`(R-1)` tensors.

  Unpacks `num` tensors from `value` by chipping it along the `axis` dimension.
  If `num` is not specified (the default), it is inferred from `value`'s shape.
  If `value.shape[axis]` is not known, `ValueError` is raised.

  For example, given a tensor of shape `(A, B, C, D)`;

  If `axis == 0` then the i'th tensor in `output` is the slice
    `value[i, :, :, :]` and each tensor in `output` will have shape `(B, C, D)`.
    (Note that the dimension unpacked along is gone, unlike `split`).

  If `axis == 1` then the i'th tensor in `output` is the slice
    `value[:, i, :, :]` and each tensor in `output` will have shape `(A, C, D)`.
  Etc.

  This is the opposite of pack.  The numpy equivalent is

      tf.unstack(x, n) = list(x)

  Args:
    value: A rank `R > 0` `Tensor` to be unstacked.
    num: An `int`. The length of the dimension `axis`. Automatically inferred
      if `None` (the default).
    axis: An `int`. The axis to unstack along. Defaults to the first
      dimension. Supports negative indexes.
    name: A name for the operation (optional).

  Returns:
    The list of `Tensor` objects unstacked from `value`.

  Raises:
    ValueError: If `num` is unspecified and cannot be inferred.
    ValueError: If `axis` is out of the range [-R, R).
  """
  if num is None:
    value = ops.convert_to_tensor(value)
    value_shape = value.get_shape()
    if value_shape.ndims is not None:
      if axis < -value_shape.ndims or axis >= value_shape.ndims:
        raise ValueError("axis = %d not in [%d, %d)" %
                         (axis, -value_shape.ndims, value_shape.ndims))
      num = value_shape[axis].value
  if num is None:
    raise ValueError("Cannot infer num from shape %s" % value_shape)
  return gen_array_ops._unpack(value, num=num, axis=axis, name=name)


def concat(values, axis, name="concat"):
  """Concatenates tensors along one dimension.

  Concatenates the list of tensors `values` along dimension `axis`.  If
  `values[i].shape = [D0, D1, ... Daxis(i), ...Dn]`, the concatenated
  result has shape

      [D0, D1, ... Raxis, ...Dn]

  where

      Raxis = sum(Daxis(i))

  That is, the data from the input tensors is joined along the `axis`
  dimension.

  The number of dimensions of the input tensors must match, and all dimensions
  except `axis` must be equal.

  For example:

  ```python
  t1 = [[1, 2, 3], [4, 5, 6]]
  t2 = [[7, 8, 9], [10, 11, 12]]
  tf.concat([t1, t2], 0) ==> [[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]]
  tf.concat([t1, t2], 1) ==> [[1, 2, 3, 7, 8, 9], [4, 5, 6, 10, 11, 12]]

  # tensor t3 with shape [2, 3]
  # tensor t4 with shape [2, 3]
  tf.shape(tf.concat([t3, t4], 0)) ==> [4, 3]
  tf.shape(tf.concat([t3, t4], 1)) ==> [2, 6]
  ```

  Note: If you are concatenating along a new axis consider using stack.
  E.g.

  ```python
  tf.concat([tf.expand_dims(t, axis) for t in tensors], axis)
  ```

  can be rewritten as

  ```python
  tf.stack(tensors, axis=axis)
  ```

  Args:
    values: A list of `Tensor` objects or a single `Tensor`.
    axis: 0-D `int32` `Tensor`.  Dimension along which to concatenate.
    name: A name for the operation (optional).

  Returns:
    A `Tensor` resulting from concatenation of the input tensors.
  """
  if not isinstance(values, (list, tuple)):
    values = [values]
  # TODO(mrry): Change to return values?
  if len(values) == 1:  # Degenerate case of one tensor.
    # Make a throwaway call to convert_to_tensor to make sure
    # that axis is of the correct type, and make sure that
    # the returned tensor is a scalar.
    # TODO(keveman): Implement a standalone type and shape checker.
    with ops.name_scope(name) as scope:
      ops.convert_to_tensor(axis,
                            name="concat_dim",
                            dtype=dtypes.int32).get_shape(
                            ).assert_is_compatible_with(tensor_shape.scalar())
      return identity(values[0], name=scope)
  return gen_array_ops._concat_v2(values=values,
                                  axis=axis,
                                  name=name)


def boolean_mask(tensor, mask, name="boolean_mask"):
  """Apply boolean mask to tensor.  Numpy equivalent is `tensor[mask]`.

  ```python
  # 1-D example
  tensor = [0, 1, 2, 3]
  mask = np.array([True, False, True, False])
  boolean_mask(tensor, mask) ==> [0, 2]
  ```

  In general, `0 < dim(mask) = K <= dim(tensor)`, and `mask`'s shape must match
  the first K dimensions of `tensor`'s shape.  We then have:
    `boolean_mask(tensor, mask)[i, j1,...,jd] = tensor[i1,...,iK,j1,...,jd]`
  where `(i1,...,iK)` is the ith `True` entry of `mask` (row-major order).

  Args:
    tensor:  N-D tensor.
    mask:  K-D boolean tensor, K <= N and K must be known statically.
    name:  A name for this operation (optional).

  Returns:
    (N-K+1)-dimensional tensor populated by entries in `tensor` corresponding
    to `True` values in `mask`.

  Raises:
    ValueError:  If shapes do not conform.

  Examples:

  ```python
  # 2-D example
  tensor = [[1, 2], [3, 4], [5, 6]]
  mask = np.array([True, False, True])
  boolean_mask(tensor, mask) ==> [[1, 2], [5, 6]]
  ```
  """
  def _apply_mask_1d(reshaped_tensor, mask):
    """Mask tensor along dimension 0 with a 1-D mask."""
    indices = squeeze(where(mask), squeeze_dims=[1])
    return gather(reshaped_tensor, indices)

  with ops.name_scope(name, values=[tensor, mask]):
    tensor = ops.convert_to_tensor(tensor, name="tensor")
    mask = ops.convert_to_tensor(mask, name="mask")

    shape_mask = mask.get_shape()
    ndims_mask = shape_mask.ndims
    shape_tensor = tensor.get_shape()
    if ndims_mask == 0:
      raise ValueError("mask cannot be scalar.")
    if ndims_mask is None:
      raise ValueError(
          "Number of mask dimensions must be specified, even if some dimensions"
          " are None.  E.g. shape=[None] is ok, but shape=None is not.")
    shape_tensor[:ndims_mask].assert_is_compatible_with(shape_mask)

    leading_size = gen_math_ops._prod(shape(tensor)[:ndims_mask], [0])
    tensor = reshape(
        tensor,
        concat([[leading_size], shape(tensor)[ndims_mask:]], 0))
    first_dim = shape_tensor[:ndims_mask].num_elements()
    tensor.set_shape(
        tensor_shape.as_shape([first_dim])
        .concatenate(shape_tensor[ndims_mask:]))

    mask = reshape(mask, [-1])
    return _apply_mask_1d(tensor, mask)


def sparse_mask(a, mask_indices, name=None):
  """Masks elements of `IndexedSlices`.

  Given an `IndexedSlices` instance `a`, returns another `IndexedSlices` that
  contains a subset of the slices of `a`. Only the slices at indices not
  specified in `mask_indices` are returned.

  This is useful when you need to extract a subset of slices in an
  `IndexedSlices` object.

  For example:

  ```python
  # `a` contains slices at indices [12, 26, 37, 45] from a large tensor
  # with shape [1000, 10]
  a.indices => [12, 26, 37, 45]
  tf.shape(a.values) => [4, 10]

  # `b` will be the subset of `a` slices at its second and third indices, so
  # we want to mask its first and last indices (which are at absolute
  # indices 12, 45)
  b = tf.sparse_mask(a, [12, 45])

  b.indices => [26, 37]
  tf.shape(b.values) => [2, 10]

  ```

  Args:
    a: An `IndexedSlices` instance.
    mask_indices: Indices of elements to mask.
    name: A name for the operation (optional).

  Returns:
    The masked `IndexedSlices` instance.
  """
  with ops.name_scope(name, "sparse_mask", [a, mask_indices]) as name:
    indices = a.indices
    out_indices, to_gather = setdiff1d(indices, mask_indices)
    out_values = gather(a.values, to_gather, name=name)
    return ops.IndexedSlices(out_values, out_indices, a.dense_shape)


def split(value, num_or_size_splits, axis=0, num=None, name="split"):
  """Splits a tensor into sub tensors.

  If `num_or_size_splits` is an integer type, `num_split`, then splits `value`
  along dimension `axis` into `num_split` smaller tensors.
  Requires that `num_split` evenly divides `value.shape[axis]`.

  If `num_or_size_splits` is not an integer type, it is presumed to be a Tensor
  `size_splits`, then splits `value` into `len(size_splits)` pieces. The shape
  of the `i`-th piece has the same size as the `value` except along dimension
  `axis` where the size is `size_splits[i]`.

  For example:

  ```python
  # 'value' is a tensor with shape [5, 30]
  # Split 'value' into 3 tensors with sizes [4, 15, 11] along dimension 1
  split0, split1, split2 = tf.split(value, [4, 15, 11], 1)
  tf.shape(split0) ==> [5, 4]
  tf.shape(split1) ==> [5, 15]
  tf.shape(split2) ==> [5, 11]
  # Split 'value' into 3 tensors along dimension 1
  split0, split1, split2 = tf.split(value, num_or_size_splits=3, axis=1)
  tf.shape(split0) ==> [5, 10]
  ```

  Args:
    value: The `Tensor` to split.
    num_or_size_splits: Either a 0-D integer `Tensor` indicating the number of
      splits along split_dim or a 1-D integer `Tensor` integer tensor containing
      the sizes of each output tensor along split_dim. If a scalar then it must
      evenly divide `value.shape[axis]`; otherwise the sum of sizes along the
      split dimension must match that of the `value`.
    axis: A 0-D `int32` `Tensor`. The dimension along which to split.
      Must be in the range `[0, rank(value))`. Defaults to 0.
    num: Optional, used to specify the number of outputs when it cannot be
      inferred from the shape of `size_splits`.
    name: A name for the operation (optional).

  Returns:
    if `num_or_size_splits` is a scalar returns `num_or_size_splits` `Tensor`
    objects; if `num_or_size_splits` is a 1-D Tensor returns
    `num_or_size_splits.get_shape[0]` `Tensor` objects resulting from splitting
    `value`.

  Raises:
    ValueError: If `num` is unspecified and cannot be inferred.
  """
  size_splits = ops.convert_to_tensor(num_or_size_splits)
  if size_splits.get_shape().ndims == 0 and size_splits.dtype.is_integer:
    return gen_array_ops._split(
        split_dim=axis, num_split=num_or_size_splits, value=value, name=name)
  else:
    if num is None:
      size_splits_shape = size_splits.get_shape()
      num = size_splits_shape.dims[0]
      if num._value is None:
        raise ValueError("Cannot infer num from shape %s" % num_or_size_splits)
    return gen_array_ops._split_v(
        value=value,
        size_splits=size_splits,
        split_dim=axis,
        num_split=num,
        name=name)


def transpose(a, perm=None, name="transpose"):
  """Transposes `a`. Permutes the dimensions according to `perm`.

  The returned tensor's dimension i will correspond to the input dimension
  `perm[i]`. If `perm` is not given, it is set to (n-1...0), where n is
  the rank of the input tensor. Hence by default, this operation performs a
  regular matrix transpose on 2-D input Tensors.

  For example:

  ```python
  # 'x' is [[1 2 3]
  #         [4 5 6]]
  tf.transpose(x) ==> [[1 4]
                       [2 5]
                       [3 6]]

  # Equivalently
  tf.transpose(x, perm=[1, 0]) ==> [[1 4]
                                    [2 5]
                                    [3 6]]

  # 'perm' is more useful for n-dimensional tensors, for n > 2
  # 'x' is   [[[1  2  3]
  #            [4  5  6]]
  #           [[7  8  9]
  #            [10 11 12]]]
  # Take the transpose of the matrices in dimension-0
  tf.transpose(x, perm=[0, 2, 1]) ==> [[[1  4]
                                        [2  5]
                                        [3  6]]

                                       [[7 10]
                                        [8 11]
                                        [9 12]]]
  ```

  Args:
    a: A `Tensor`.
    perm: A permutation of the dimensions of `a`.
    name: A name for the operation (optional).

  Returns:
    A transposed `Tensor`.
  """
  with ops.name_scope(name, "transpose", [a]) as name:
    if perm is None:
      rank = gen_array_ops.rank(a)
      perm = (rank - 1) - gen_math_ops._range(0, rank, 1)
      ret = gen_array_ops.transpose(a, perm, name=name)
      # NOTE(mrry): Setting the shape explicitly because
      #   reverse is not handled by the shape function.
      input_shape = ret.op.inputs[0].get_shape().dims
      if input_shape is not None:
        ret.set_shape(input_shape[::-1])
    else:
      ret = gen_array_ops.transpose(a, perm, name=name)
    return ret


# pylint: disable=invalid-name
def matrix_transpose(a, name="matrix_transpose"):
  """Transposes last two dimensions of tensor `a`.

  For example:

  ```python
  # Matrix with no batch dimension.
  # 'x' is [[1 2 3]
  #         [4 5 6]]
  tf.matrix_transpose(x) ==> [[1 4]
                                   [2 5]
                                   [3 6]]

  # Matrix with two batch dimensions.
  # x.shape is [1, 2, 3, 4]
  # tf.matrix_transpose(x) is shape [1, 2, 4, 3]
  ```

  Note that `tf.matmul` provides kwargs allowing for transpose of arguments.
  This is done with minimal cost, and is preferable to using this function. E.g.

  ```
  # Good!  Transpose is taken at minimal additional cost.
  tf.matmul(matrix, b, transpose_b=True)

  # Inefficient!
  tf.matmul(matrix, tf.matrix_transpose(b))
  ```

  Args:
    a: A `Tensor` with `rank >= 2`.
    name: A name for the operation (optional).

  Returns:
    A transposed batch matrix `Tensor`.

  Raises:
    ValueError:  If `a` is determined statically to have `rank < 2`.
  """
  with ops.name_scope(name, values=[a]):
    a = ops.convert_to_tensor(a, name="a")

    # If we know the number of dimensions (statically), we can do two things:
    # 1. Check that `a` is a (batch) matrix.
    # 2. Use a python list for perm.  This preserves static shape information
    #    and avoids extra computations.
    a_shape = a.get_shape()
    ndims = a_shape.ndims
    if ndims is not None:
      if ndims < 2:
        raise ValueError(
            "Argument 'a' should be a (batch) matrix, with rank >= 2.  Found: "
            "%s" % a_shape)
      perm = list(range(ndims - 2)) + [ndims - 1] + [ndims - 2]
    else:
      a_rank = rank(a)
      perm = concat(
          (gen_math_ops._range(0, a_rank - 2, 1), [a_rank - 1, a_rank - 2]), 0)

    return transpose(a, perm=perm)
# pylint: enable=invalid-name


def zeros(shape, dtype=dtypes.float32, name=None):
  """Creates a tensor with all elements set to zero.

  This operation returns a tensor of type `dtype` with shape `shape` and
  all elements set to zero.

  For example:

  ```python
  tf.zeros([3, 4], tf.int32) ==> [[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]
  ```

  Args:
    shape: Either a list of integers, or a 1-D `Tensor` of type `int32`.
    dtype: The type of an element in the resulting `Tensor`.
    name: A name for the operation (optional).

  Returns:
    A `Tensor` with all elements set to zero.
  """
  dtype = dtypes.as_dtype(dtype).base_dtype
  with ops.name_scope(name, "zeros", [shape]) as name:
    if dtype == dtypes.bool:
      zero = False
    elif dtype == dtypes.string:
      zero = ""
    else:
      zero = 0
    try:
      shape = tensor_shape.as_shape(shape)
      output = constant(zero, shape=shape, dtype=dtype, name=name)
    except (TypeError, ValueError):
      shape = ops.convert_to_tensor(shape, dtype=dtypes.int32, name="shape")
      output = fill(shape, constant(zero, dtype=dtype), name=name)
  assert output.dtype.base_dtype == dtype
  return output


def zeros_like(tensor, dtype=None, name=None, optimize=True):
  """Creates a tensor with all elements set to zero.

  Given a single tensor (`tensor`), this operation returns a tensor of the
  same type and shape as `tensor` with all elements set to zero. Optionally,
  you can use `dtype` to specify a new type for the returned tensor.

  For example:

  ```python
  # 'tensor' is [[1, 2, 3], [4, 5, 6]]
  tf.zeros_like(tensor) ==> [[0, 0, 0], [0, 0, 0]]
  ```

  Args:
    tensor: A `Tensor`.
    dtype: A type for the returned `Tensor`. Must be `float32`, `float64`,
    `int8`, `int16`, `int32`, `int64`, `uint8`, `complex64`, or `complex128`.
    name: A name for the operation (optional).
    optimize: if true, attempt to statically determine the shape of 'tensor'
    and encode it as a constant.

  Returns:
    A `Tensor` with all elements set to zero.
  """
  with ops.name_scope(name, "zeros_like", [tensor]) as name:
    tensor = ops.convert_to_tensor(tensor, name="tensor")

    if tensor.shape.is_fully_defined():
      # We can produce a zeros tensor independent of the value of 'tensor',
      # since the shape is known statically.
      return zeros(tensor.shape, dtype=dtype or tensor.dtype, name=name)

    if dtype is not None and dtype != tensor.dtype:
      return zeros(shape_internal(tensor, optimize=optimize), dtype=dtype,
                   name=name)
    else:
      return gen_array_ops._zeros_like(tensor, name=name)


def ones_like(tensor, dtype=None, name=None, optimize=True):
  """Creates a tensor with all elements set to 1.

  Given a single tensor (`tensor`), this operation returns a tensor of the same
  type and shape as `tensor` with all elements set to 1. Optionally, you can
  specify a new type (`dtype`) for the returned tensor.

  For example:

  ```python
  # 'tensor' is [[1, 2, 3], [4, 5, 6]]
  tf.ones_like(tensor) ==> [[1, 1, 1], [1, 1, 1]]
  ```

  Args:
    tensor: A `Tensor`.
    dtype: A type for the returned `Tensor`. Must be `float32`, `float64`,
      `int8`, `int16`, `int32`, `int64`, `uint8`, `complex64`, `complex128` or
      `bool`.
    name: A name for the operation (optional).
    optimize: if true, attempt to statically determine the shape of 'tensor'
    and encode it as a constant.

  Returns:
    A `Tensor` with all elements set to 1.
  """
  with ops.name_scope(name, "ones_like", [tensor]) as name:
    tensor = ops.convert_to_tensor(tensor, name="tensor")
    ones_shape = shape_internal(tensor, optimize=optimize)
    if dtype is None:
      dtype = tensor.dtype
    ret = ones(ones_shape, dtype=dtype, name=name)
    ret.set_shape(tensor.get_shape())
    return ret


def ones(shape, dtype=dtypes.float32, name=None):
  """Creates a tensor with all elements set to 1.

  This operation returns a tensor of type `dtype` with shape `shape` and all
  elements set to 1.

  For example:

  ```python
  tf.ones([2, 3], tf.int32) ==> [[1, 1, 1], [1, 1, 1]]
  ```

  Args:
    shape: Either a list of integers, or a 1-D `Tensor` of type `int32`.
    dtype: The type of an element in the resulting `Tensor`.
    name: A name for the operation (optional).

  Returns:
    A `Tensor` with all elements set to 1.
  """
  dtype = dtypes.as_dtype(dtype).base_dtype
  with ops.name_scope(name, "ones", [shape]) as name:
    one = True if dtype == dtypes.bool else 1
    try:
      shape = tensor_shape.as_shape(shape)
      output = constant(one, shape=shape, dtype=dtype, name=name)
    except (TypeError, ValueError):
      shape = ops.convert_to_tensor(shape, dtype=dtypes.int32, name="shape")
      output = fill(shape, constant(one, dtype=dtype), name=name)
  assert output.dtype.base_dtype == dtype
  return output


def placeholder(dtype, shape=None, name=None):
  """Inserts a placeholder for a tensor that will be always fed.

  **Important**: This tensor will produce an error if evaluated. Its value must
  be fed using the `feed_dict` optional argument to `Session.run()`,
  `Tensor.eval()`, or `Operation.run()`.

  For example:

  ```python
  x = tf.placeholder(tf.float32, shape=(1024, 1024))
  y = tf.matmul(x, x)

  with tf.Session() as sess:
    print(sess.run(y))  # ERROR: will fail because x was not fed.

    rand_array = np.random.rand(1024, 1024)
    print(sess.run(y, feed_dict={x: rand_array}))  # Will succeed.
  ```

  Args:
    dtype: The type of elements in the tensor to be fed.
    shape: The shape of the tensor to be fed (optional). If the shape is not
      specified, you can feed a tensor of any shape.
    name: A name for the operation (optional).

  Returns:
    A `Tensor` that may be used as a handle for feeding a value, but not
    evaluated directly.
  """
  return gen_array_ops._placeholder(dtype=dtype, shape=shape, name=name)


# pylint: disable=redefined-outer-name
def _normalize_sparse_shape(shape, name):
  """Takes numpy array or Tensor or None and returns either None or Tensor."""
  if shape is None: return None
  if not isinstance(shape, ops.Tensor):
    for el in shape:
      if el is None:
        return None
  return ops.convert_to_tensor(shape, name=name)


def sparse_placeholder(dtype, shape=None, name=None):
  """Inserts a placeholder for a sparse tensor that will be always fed.

  **Important**: This sparse tensor will produce an error if evaluated.
  Its value must be fed using the `feed_dict` optional argument to
  `Session.run()`, `Tensor.eval()`, or `Operation.run()`.

  For example:

  ```python
  x = tf.sparse_placeholder(tf.float32)
  y = tf.sparse_reduce_sum(x)

  with tf.Session() as sess:
    print(sess.run(y))  # ERROR: will fail because x was not fed.

    indices = np.array([[3, 2, 0], [4, 5, 1]], dtype=np.int64)
    values = np.array([1.0, 2.0], dtype=np.float32)
    shape = np.array([7, 9, 2], dtype=np.int64)
    print(sess.run(y, feed_dict={
      x: tf.SparseTensorValue(indices, values, shape)}))  # Will succeed.
    print(sess.run(y, feed_dict={
      x: (indices, values, shape)}))  # Will succeed.

    sp = tf.SparseTensor(indices=indices, values=values, dense_shape=shape)
    sp_value = sp.eval(session=sess)
    print(sess.run(y, feed_dict={x: sp_value}))  # Will succeed.
  ```

  Args:
    dtype: The type of `values` elements in the tensor to be fed.
    shape: The shape of the tensor to be fed (optional). If the shape is not
      specified, you can feed a sparse tensor of any shape.
    name: A name for prefixing the operations (optional).

  Returns:
    A `SparseTensor` that may be used as a handle for feeding a value, but not
    evaluated directly.
  """
  shape_name = (name + "/shape") if name is not None else None
  shape = _normalize_sparse_shape(shape, shape_name)
  if shape is None:
    shape = placeholder(dtypes.int64, shape=[None], name=shape_name)
  return sparse_tensor.SparseTensor(
      values=placeholder(
          dtype, shape=[None],
          name=(name + "/values") if name is not None else None),
      indices=placeholder(
          dtypes.int64, shape=[None, None],
          name=(name + "/indices") if name is not None else None),
      dense_shape=shape)
# pylint: enable=redefined-outer-name


def pad(tensor, paddings, mode="CONSTANT", name=None):  # pylint: disable=invalid-name
  """Pads a tensor.

  This operation pads a `tensor` according to the `paddings` you specify.
  `paddings` is an integer tensor with shape `[n, 2]`, where n is the rank of
  `tensor`. For each dimension D of `input`, `paddings[D, 0]` indicates how
  many values to add before the contents of `tensor` in that dimension, and
  `paddings[D, 1]` indicates how many values to add after the contents of
  `tensor` in that dimension. If `mode` is "REFLECT" then both `paddings[D, 0]`
  and `paddings[D, 1]` must be no greater than `tensor.dim_size(D) - 1`. If
  `mode` is "SYMMETRIC" then both `paddings[D, 0]` and `paddings[D, 1]` must be
  no greater than `tensor.dim_size(D)`.

  The padded size of each dimension D of the output is:

  `paddings[D, 0] + tensor.dim_size(D) + paddings[D, 1]`

  For example:

  ```python
  # 't' is [[1, 2, 3], [4, 5, 6]].
  # 'paddings' is [[1, 1,], [2, 2]].
  # rank of 't' is 2.
  pad(t, paddings, "CONSTANT") ==> [[0, 0, 0, 0, 0, 0, 0],
                                    [0, 0, 1, 2, 3, 0, 0],
                                    [0, 0, 4, 5, 6, 0, 0],
                                    [0, 0, 0, 0, 0, 0, 0]]

  pad(t, paddings, "REFLECT") ==> [[6, 5, 4, 5, 6, 5, 4],
                                   [3, 2, 1, 2, 3, 2, 1],
                                   [6, 5, 4, 5, 6, 5, 4],
                                   [3, 2, 1, 2, 3, 2, 1]]

  pad(t, paddings, "SYMMETRIC") ==> [[2, 1, 1, 2, 3, 3, 2],
                                     [2, 1, 1, 2, 3, 3, 2],
                                     [5, 4, 4, 5, 6, 6, 5],
                                     [5, 4, 4, 5, 6, 6, 5]]
  ```

  Args:
    tensor: A `Tensor`.
    paddings: A `Tensor` of type `int32`.
    mode: One of "CONSTANT", "REFLECT", or "SYMMETRIC" (case-insensitive)
    name: A name for the operation (optional).

  Returns:
    A `Tensor`. Has the same type as `tensor`.

  Raises:
    ValueError: When mode is not one of "CONSTANT", "REFLECT", or "SYMMETRIC".
  """

  # Convert lower/mixed case to upper for NumPy compatibility
  # NumPy uses all lower-case modes.
  mode = mode.upper()
  if mode == "CONSTANT":
    return gen_array_ops._pad(tensor, paddings, name=name)
  if mode == "REFLECT":
    return gen_array_ops._mirror_pad(tensor,
                                     paddings,
                                     mode="REFLECT",
                                     name=name)
  if mode == "SYMMETRIC":
    return gen_array_ops._mirror_pad(tensor,
                                     paddings,
                                     mode="SYMMETRIC",
                                     name=name)
  raise ValueError("Unknown padding mode: %s" % mode)


def meshgrid(*args, **kwargs):
  """Broadcasts parameters for evaluation on an N-D grid.

  Given N one-dimensional coordinate arrays `*args`, returns a list `outputs`
  of N-D coordinate arrays for evaluating expressions on an N-D grid.

  Notes:

  `meshgrid` supports cartesian ('xy') and matrix ('ij') indexing conventions.
  When the `indexing` argument is set to 'xy' (the default), the broadcasting
  instructions for the first two dimensions are swapped.

  Examples:

  Calling `X, Y = meshgrid(x, y)` with the tensors

  ```prettyprint
    x = [1, 2, 3]
    y = [4, 5, 6]
  ```

  results in

  ```prettyprint
    X = [[1, 2, 3],
         [1, 2, 3],
         [1, 2, 3]]
    Y = [[4, 4, 4],
         [5, 5, 5],
         [6, 6, 6]]
  ```

  Args:
    *args: `Tensor`s with rank 1.
    indexing: Either 'xy' or 'ij' (optional, default: 'xy').
    name: A name for the operation (optional).

  Returns:
    outputs: A list of N `Tensor`s with rank N.
  """

  indexing = kwargs.pop("indexing", "xy")
  name = kwargs.pop("name", "meshgrid")
  if kwargs:
    key = list(kwargs.keys())[0]
    raise TypeError("'{}' is an invalid keyword argument "
                    "for this function".format(key))

  if indexing not in ("xy", "ij"):
    raise ValueError("indexing parameter must be either 'xy' or 'ij'")

  with ops.name_scope(name, "meshgrid", args) as name:
    ndim = len(args)
    s0 = (1,) * ndim

    # Prepare reshape by inserting dimensions with size 1 where needed
    output = []
    for i, x in enumerate(args):
      output.append(reshape(stack(x), (s0[:i] + (-1,) + s0[i + 1::])) )
    # Create parameters for broadcasting each tensor to the full size
    shapes = [size(x) for x in args]

    output_dtype = ops.convert_to_tensor(args[0]).dtype.base_dtype

    if indexing == "xy" and ndim > 1:
      output[0] = reshape(output[0], (1, -1) + (1,)*(ndim - 2))
      output[1] = reshape(output[1], (-1, 1) + (1,)*(ndim - 2))
      shapes[0], shapes[1] = shapes[1], shapes[0]

    # TODO: improve performance with a broadcast
    mult_fact = ones(shapes, output_dtype)
    return [x * mult_fact for x in output]


NEW_AXIS = -1
SHRINK_AXIS = -2


# PEP-8 naming
# pylint: disable=invalid-name
def _compute_size_of_strided_dim(shrink, spec, size):
  """Computes the size of a single strided slice dimension."""

  unknown = None  # Document what None means here.
  use_full_range = None  # Document other use of None.
  # if this is a shrink axis (i.e. a non-range index)
  # it either will produce an error or return 1
  if shrink:
    return 1
  if size is unknown or size.value is unknown:
    return unknown
  size = size.value
  stride = spec.step
  if stride is not unknown:
    if stride == 0:
      return unknown
    stride = spec.step
    valid_range = [0, size] if stride > 0 else [-1, size - 1]

    # PEP-8 naming
    # pylint: disable=invalid-name
    def canonical(x, c):
      if x is use_full_range:
        return valid_range[c] if stride > 0 else valid_range[(c + 1) & 1]
      else:
        x_fwd = size + x if x < 0 else x  # make negative indices positive
        return max(valid_range[0], min(valid_range[1], x_fwd))

    begin = canonical(spec.start, 0)
    end = canonical(spec.stop, 1)
    interval_length = end - begin
    if interval_length == 0 or ((interval_length < 0) != (stride < 0)):
      return 0
    else:
      remainder = 1 if interval_length % stride != 0 else 0
      return interval_length // stride + remainder
  else:
    return unknown  # unknown because stride is unknown


def _TileGradShape(op):
  """Shape function for the TileGrad op."""
  multiples_shape = op.inputs[1].get_shape().with_rank(1)
  input_shape = op.inputs[0].get_shape().with_rank(multiples_shape[0])
  # NOTE(mrry): Represent `multiples` as a `TensorShape` because (i)
  # it is a vector of non-negative integers, and (ii) doing so allows
  # us to handle partially-known multiples.
  multiples = tensor_util.constant_value_as_shape(op.inputs[1]).with_rank(
      input_shape.ndims)
  if multiples.ndims is None:
    return [tensor_shape.unknown_shape()]
  else:
    output_dims = []
    for dim, multiple in zip(input_shape.dims, multiples.dims):
      output_dims.append(dim // multiple)
    return [tensor_shape.TensorShape(output_dims)]


def edit_distance(hypothesis, truth, normalize=True, name="edit_distance"):
  """Computes the Levenshtein distance between sequences.

  This operation takes variable-length sequences (`hypothesis` and `truth`),
  each provided as a `SparseTensor`, and computes the Levenshtein distance.
  You can normalize the edit distance by length of `truth` by setting
  `normalize` to true.

  For example, given the following input:

  ```python
  # 'hypothesis' is a tensor of shape `[2, 1]` with variable-length values:
  #   (0,0) = ["a"]
  #   (1,0) = ["b"]
  hypothesis = tf.SparseTensor(
      [[0, 0, 0],
       [1, 0, 0]],
      ["a", "b"]
      (2, 1, 1))

  # 'truth' is a tensor of shape `[2, 2]` with variable-length values:
  #   (0,0) = []
  #   (0,1) = ["a"]
  #   (1,0) = ["b", "c"]
  #   (1,1) = ["a"]
  truth = tf.SparseTensor(
      [[0, 1, 0],
       [1, 0, 0],
       [1, 0, 1],
       [1, 1, 0]]
      ["a", "b", "c", "a"],
      (2, 2, 2))

  normalize = True
  ```

  This operation would return the following:

  ```python
  # 'output' is a tensor of shape `[2, 2]` with edit distances normalized
  # by 'truth' lengths.
  output ==> [[inf, 1.0],  # (0,0): no truth, (0,1): no hypothesis
             [0.5, 1.0]]  # (1,0): addition, (1,1): no hypothesis
  ```

  Args:
    hypothesis: A `SparseTensor` containing hypothesis sequences.
    truth: A `SparseTensor` containing truth sequences.
    normalize: A `bool`. If `True`, normalizes the Levenshtein distance by
      length of `truth.`
    name: A name for the operation (optional).

  Returns:
    A dense `Tensor` with rank `R - 1`, where R is the rank of the
    `SparseTensor` inputs `hypothesis` and `truth`.

  Raises:
    TypeError: If either `hypothesis` or `truth` are not a `SparseTensor`.
  """
  if not isinstance(
      hypothesis, (sparse_tensor.SparseTensor,
                   sparse_tensor.SparseTensorValue)):
    raise TypeError("Hypothesis must be a SparseTensor.")
  if not isinstance(
      truth, (sparse_tensor.SparseTensor,
              sparse_tensor.SparseTensorValue)):
    raise TypeError("Truth must be a SparseTensor.")

  return gen_array_ops._edit_distance(hypothesis.indices,
                                      hypothesis.values,
                                      hypothesis.dense_shape,
                                      truth.indices,
                                      truth.values,
                                      truth.dense_shape,
                                      normalize=normalize,
                                      name=name)


@ops.RegisterGradient("FakeQuantWithMinMaxArgs")
def _FakeQuantWithMinMaxArgsGradient(op, grad):
  """Gradient for FakeQuantWithMinMaxArgs op."""
  return fake_quant_with_min_max_args_gradient(
      grad, op.inputs[0], min=op.get_attr("min"), max=op.get_attr("max"))


@ops.RegisterGradient("FakeQuantWithMinMaxVars")
def _FakeQuantWithMinMaxVarsGradient(op, grad):
  """Gradient for FakeQuantWithMinMaxVars op."""
  return fake_quant_with_min_max_vars_gradient(grad, op.inputs[0], op.inputs[1],
                                               op.inputs[2])


@ops.RegisterGradient("FakeQuantWithMinMaxVarsPerChannel")
def _FakeQuantWithMinMaxVarsPerChannelGradient(op, grad):
  """Gradient for FakeQuantWithMinMaxVarsPerChannel op."""
  return fake_quant_with_min_max_vars_per_channel_gradient(grad, op.inputs[0],
                                                           op.inputs[1],
                                                           op.inputs[2])


def required_space_to_batch_paddings(input_shape,
                                     block_shape,
                                     base_paddings=None,
                                     name=None):
  """Calculate padding required to make block_shape divide input_shape.

  This function can be used to calculate a suitable paddings argument for use
  with space_to_batch_nd and batch_to_space_nd.

  Args:
    input_shape: int32 Tensor of shape [N].
    block_shape: int32 Tensor of shape [N].
    base_paddings: Optional int32 Tensor of shape [N, 2].  Specifies the minimum
      amount of padding to use.  All elements must be >= 0.  If not specified,
      defaults to 0.
    name: string.  Optional name prefix.

  Returns:
    (paddings, crops), where:

    `paddings` and `crops` are int32 Tensors of rank 2 and shape [N, 2]
    satisfying:

        paddings[i, 0] = base_paddings[i, 0].
        0 <= paddings[i, 1] - base_paddings[i, 1] < block_shape[i]
        (input_shape[i] + paddings[i, 0] + paddings[i, 1]) % block_shape[i] == 0

        crops[i, 0] = 0
        crops[i, 1] = paddings[i, 1] - base_paddings[i, 1]

  Raises: ValueError if called with incompatible shapes.
  """
  with ops.name_scope(name, "required_space_to_batch_paddings",
                      [input_shape, block_shape]):
    input_shape = ops.convert_to_tensor(input_shape,
                                        dtype=dtypes.int32,
                                        name="input_shape")
    block_shape = ops.convert_to_tensor(block_shape,
                                        dtype=dtypes.int32,
                                        name="block_shape")

    block_shape.get_shape().assert_is_fully_defined()
    block_shape.get_shape().assert_has_rank(1)
    num_block_dims = block_shape.get_shape()[0].value
    if num_block_dims == 0:
      return zeros([0, 2], dtypes.int32), zeros([0, 2], dtypes.int32)

    input_shape.get_shape().assert_is_compatible_with([num_block_dims])

    if base_paddings is not None:
      base_paddings = ops.convert_to_tensor(base_paddings,
                                            dtype=dtypes.int32,
                                            name="base_paddings")
      base_paddings.get_shape().assert_is_compatible_with([num_block_dims, 2])
    else:
      base_paddings = zeros([num_block_dims, 2], dtypes.int32)

    const_block_shape = tensor_util.constant_value(block_shape)
    const_input_shape = tensor_util.constant_value(input_shape)
    const_base_paddings = tensor_util.constant_value(base_paddings)
    if (const_block_shape is not None and const_input_shape is not None and
        const_base_paddings is not None):
      block_shape = const_block_shape
      input_shape = const_input_shape
      base_paddings = const_base_paddings

    # Use same expression for both constant and non-constant case.
    pad_start = base_paddings[:, 0]
    orig_pad_end = base_paddings[:, 1]
    full_input_shape = input_shape + pad_start + orig_pad_end
    pad_end_extra = (block_shape - full_input_shape % block_shape) % block_shape
    pad_end = orig_pad_end + pad_end_extra

    result_paddings = stack(
        [[pad_start[i], pad_end[i]] for i in range(num_block_dims)],
        name="paddings")
    result_crops = stack(
        [[0, pad_end_extra[i]] for i in range(num_block_dims)], name="crops")
    return result_paddings, result_crops


def space_to_batch(input, paddings, block_size, name=None):  # pylint: disable=redefined-builtin
  result = space_to_batch_nd(input,
                             paddings=paddings,
                             block_shape=np.array([block_size, block_size],
                                                  dtype=np.int64),
                             name=name)
  result.set_shape(result.get_shape().with_rank(4))
  return result


space_to_batch.__doc__ = gen_array_ops._space_to_batch.__doc__


def batch_to_space(input, crops, block_size, name=None):  # pylint: disable=redefined-builtin
  result = batch_to_space_nd(input,
                             crops=crops,
                             block_shape=np.array([block_size, block_size],
                                                  dtype=np.int64),
                             name=name)
  result.set_shape(result.get_shape().with_rank(4))
  return result


batch_to_space.__doc__ = gen_array_ops._batch_to_space.__doc__


def one_hot(indices, depth, on_value=None, off_value=None,
            axis=None, dtype=None, name=None):
  """Returns a one-hot tensor.

  The locations represented by indices in `indices` take value `on_value`,
  while all other locations take value `off_value`.

  `on_value` and `off_value` must have matching data types. If `dtype` is also
  provided, they must be the same data type as specified by `dtype`.

  If `on_value` is not provided, it will default to the value `1` with type
  `dtype`

  If `off_value` is not provided, it will default to the value `0` with type
  `dtype`

  If the input `indices` is rank `N`, the output will have rank `N+1`. The
  new axis is created at dimension `axis` (default: the new axis is appended
  at the end).

  If `indices` is a scalar the output shape will be a vector of length `depth`

  If `indices` is a vector of length `features`, the output shape will be:

  ```
    features x depth if axis == -1
    depth x features if axis == 0
  ```

  If `indices` is a matrix (batch) with shape `[batch, features]`, the output
  shape will be:

  ```
    batch x features x depth if axis == -1
    batch x depth x features if axis == 1
    depth x batch x features if axis == 0
  ```

  If `dtype` is not provided, it will attempt to assume the data type of
  `on_value` or `off_value`, if one or both are passed in. If none of
  `on_value`, `off_value`, or `dtype` are provided, `dtype` will default to the
  value `tf.float32`.

  Note: If a non-numeric data type output is desired (`tf.string`, `tf.bool`,
  etc.), both `on_value` and `off_value` _must_ be provided to `one_hot`.

  Examples
  =========

  Suppose that

  ```python
    indices = [0, 2, -1, 1]
    depth = 3
    on_value = 5.0
    off_value = 0.0
    axis = -1
  ```

  Then output is `[4 x 3]`:

  ```python
    output =
    [5.0 0.0 0.0]  // one_hot(0)
    [0.0 0.0 5.0]  // one_hot(2)
    [0.0 0.0 0.0]  // one_hot(-1)
    [0.0 5.0 0.0]  // one_hot(1)
  ```

  Suppose that

  ```python
    indices = [[0, 2], [1, -1]]
    depth = 3
    on_value = 1.0
    off_value = 0.0
    axis = -1
  ```

  Then output is `[2 x 2 x 3]`:

  ```python
    output =
    [
      [1.0, 0.0, 0.0]  // one_hot(0)
      [0.0, 0.0, 1.0]  // one_hot(2)
    ][
      [0.0, 1.0, 0.0]  // one_hot(1)
      [0.0, 0.0, 0.0]  // one_hot(-1)
    ]
  ```

  Using default values for `on_value` and `off_value`:

  ```python
    indices = [0, 1, 2]
    depth = 3
  ```

  The output will be

  ```python
    output =
    [[1., 0., 0.],
     [0., 1., 0.],
     [0., 0., 1.]]
  ```

  Args:
    indices: A `Tensor` of indices.
    depth: A scalar defining the depth of the one hot dimension.
    on_value: A scalar defining the value to fill in output when `indices[j]
      = i`. (default: 1)
    off_value: A scalar defining the value to fill in output when `indices[j]
      != i`. (default: 0)
    axis: The axis to fill (default: -1, a new inner-most axis).
    dtype: The data type of the output tensor.

  Returns:
    output: The one-hot tensor.

  Raises:
    TypeError: If dtype of either `on_value` or `off_value` don't match `dtype`
    TypeError: If dtype of `on_value` and `off_value` don't match one another
  """
  with ops.name_scope(name, "one_hot", [indices, depth, on_value, off_value,
                                        axis, dtype]) as name:
    on_exists = on_value is not None
    off_exists = off_value is not None

    on_dtype = ops.convert_to_tensor(on_value).dtype.base_dtype if on_exists \
                  else None
    off_dtype = ops.convert_to_tensor(off_value).dtype.base_dtype if off_exists\
                  else None

    if on_exists or off_exists:
      if dtype is not None:
        # Ensure provided on_value and/or off_value match dtype
        if (on_exists and on_dtype != dtype):
          raise TypeError("dtype {0} of on_value does not match " \
                          "dtype parameter {1}".format(on_dtype, dtype))
        if (off_exists and off_dtype != dtype):
          raise TypeError("dtype {0} of off_value does not match " \
                          "dtype parameter {1}".format(off_dtype, dtype))
      else:
        # dtype not provided: automatically assign it
        dtype = on_dtype if on_exists else off_dtype
    elif dtype is None:
      # None of on_value, off_value, or dtype provided. Default dtype to float32
      dtype = dtypes.float32

    if not on_exists:
      # on_value not provided: assign to value 1 of type dtype
      on_value = ops.convert_to_tensor(1, dtype, name="on_value")
      on_dtype = dtype
    if not off_exists:
      # off_value not provided: assign to value 0 of type dtype
      off_value = ops.convert_to_tensor(0, dtype, name="off_value")
      off_dtype = dtype

    if on_dtype != off_dtype:
      raise TypeError("dtype {0} of on_value does not match " \
                      "dtype {1} of off_value".format(on_dtype, off_dtype))

    return gen_array_ops._one_hot(indices, depth, on_value, off_value, axis,
                                  name)


def sequence_mask(lengths, maxlen=None, dtype=dtypes.bool, name=None):
  """Return a mask tensor representing the first N positions of each row.

  Example:

  ```python
  tf.sequence_mask([1, 3, 2], 5) =
    [[True, False, False, False, False],
     [True, True, True, False, False],
     [True, True, False, False, False]]
  ```

  Args:
    lengths: 1D integer tensor, all its values < maxlen.
    maxlen: scalar integer tensor, maximum length of each row. Default: use
            maximum over lengths.
    dtype: output type of the resulting tensor.
    name: name of the op.
  Returns:
    A 2D mask tensor, as shown in the example above, cast to specified dtype.

  Raises:
    ValueError: if the arguments have invalid rank.
  """
  with ops.name_scope(name, "SequenceMask", [lengths, maxlen]):
    lengths = ops.convert_to_tensor(lengths)
    if lengths.get_shape().ndims != 1:
      raise ValueError("lengths must be 1D for sequence_mask")

    if maxlen is None:
      maxlen = gen_math_ops._max(lengths, [0])
    else:
      maxlen = ops.convert_to_tensor(maxlen)
    if maxlen.get_shape().ndims != 0:
      raise ValueError("maxlen must be scalar for sequence_mask")

    # The basic idea is to compare a range row vector of size maxlen:
    # [0, 1, 2, 3, 4]
    # to length as a matrix with 1 column: [[1], [3], [2]].
    # Because of broadcasting on both arguments this comparison results
    # in a matrix of size (len(lengths), maxlen)
    row_vector = gen_math_ops._range(constant(0, maxlen.dtype),
                                     maxlen,
                                     constant(1, maxlen.dtype))
    # Since maxlen >= max(lengths), it is safe to use maxlen as a cast
    # authoritative type. Whenever maxlen fits into tf.int32, so do the lengths.
    matrix = gen_math_ops.cast(expand_dims(lengths, 1), maxlen.dtype)
    result = row_vector < matrix

    if dtype is None or result.dtype.base_dtype == dtype.base_dtype:
      return result
    else:
      return gen_math_ops.cast(result, dtype)


def squeeze(input, axis=None, name=None, squeeze_dims=None):
  # pylint: disable=redefined-builtin
  """Removes dimensions of size 1 from the shape of a tensor.

  Given a tensor `input`, this operation returns a tensor of the same type with
  all dimensions of size 1 removed. If you don't want to remove all size 1
  dimensions, you can remove specific size 1 dimensions by specifying
  `axis`.

  For example:

  ```prettyprint
  # 't' is a tensor of shape [1, 2, 1, 3, 1, 1]
  shape(squeeze(t)) ==> [2, 3]
  ```

  Or, to remove specific size 1 dimensions:

  ```prettyprint
  # 't' is a tensor of shape [1, 2, 1, 3, 1, 1]
  shape(squeeze(t, [2, 4])) ==> [1, 2, 3, 1]
  ```

  Args:
    input: A `Tensor`. The `input` to squeeze.
    axis: An optional list of `ints`. Defaults to `[]`.
      If specified, only squeezes the dimensions listed. The dimension
      index starts at 0. It is an error to squeeze a dimension that is not 1.
    name: A name for the operation (optional).
    squeeze_dims: Deprecated keyword argument that is now axis.

  Returns:
    A `Tensor`. Has the same type as `input`.
    Contains the same data as `input`, but has one or more dimensions of
    size 1 removed.

  Raises:
    ValueError: When both `squeeze_dims` and `axis` are specified.
  """
  if squeeze_dims is not None:
    if axis is not None:
      raise ValueError("Cannot specify both 'squeeze_dims' and 'axis'")
    axis = squeeze_dims
  if np.isscalar(axis):
    axis = [axis]
  return gen_array_ops._squeeze(input, axis, name)


def where(condition, x=None, y=None, name=None):
  """Return the elements, either from `x` or `y`, depending on the `condition`.

  If both `x` and `y` are None, then this operation returns the coordinates of
  true elements of `condition`.  The coordinates are returned in a 2-D tensor
  where the first dimension (rows) represents the number of true elements, and
  the second dimension (columns) represents the coordinates of the true
  elements. Keep in mind, the shape of the output tensor can vary depending on
  how many true values there are in input. Indices are output in row-major
  order.

  If both non-None, `x` and `y` must have the same shape.
  The `condition` tensor must be a scalar if `x` and `y` are scalar.
  If `x` and `y` are vectors of higher rank, then `condition` must be either a
  vector with size matching the first dimension of `x`, or must have the same
  shape as `x`.

  The `condition` tensor acts as a mask that chooses, based on the value at each
  element, whether the corresponding element / row in the output should be taken
  from `x` (if true) or `y` (if false).

  If `condition` is a vector and `x` and `y` are higher rank matrices, then it
  chooses which row (outer dimension) to copy from `x` and `y`. If `condition`
  has the same shape as `x` and `y`, then it chooses which element to copy from
  `x` and `y`.

  Args:
    condition: A `Tensor` of type `bool`
    x: A Tensor which may have the same shape as `condition`. If `condition` is
      rank 1, `x` may have higher rank, but its first dimension must match the
      size of `condition`.
    y: A `tensor` with the same shape and type as `x`.
    name: A name of the operation (optional)

  Returns:
    A `Tensor` with the same type and shape as `x`, `y` if they are non-None.
    A `Tensor` with shape `(num_true, dim_size(condition))`.

  Raises:
    ValueError: When exactly one of `x` or `y` is non-None.
  """
  if x is None and y is None:
    return gen_array_ops.where(input=condition, name=name)
  elif x is not None and y is not None:
    return gen_math_ops._select(condition=condition, t=x, e=y, name=name)
  else:
    raise ValueError("x and y must both be non-None or both be None.")


def reverse(tensor, axis, name=None):
  return gen_array_ops.reverse_v2(tensor, axis, name)
reverse.__doc__ = gen_array_ops.reverse_v2.__doc__


# pylint: disable=redefined-builtin
def reverse_sequence(input,
                     seq_lengths,
                     seq_axis=None,
                     batch_axis=None,
                     name=None,
                     seq_dim=None,
                     batch_dim=None):
  seq_axis = deprecation.deprecated_argument_lookup("seq_axis", seq_axis,
                                                    "seq_dim", seq_dim)
  batch_axis = deprecation.deprecated_argument_lookup("batch_axis", batch_axis,
                                                      "batch_dim", batch_dim)
  return gen_array_ops.reverse_sequence(
      input=input,
      seq_lengths=seq_lengths,
      seq_dim=seq_axis,
      batch_dim=batch_axis,
      name=name)
# pylint: enable=redefined-builtin


reverse_sequence.__doc__ = deprecation.rewrite_argument_docstring(
    deprecation.rewrite_argument_docstring(
        gen_array_ops.reverse_sequence.__doc__, "batch_dim", "batch_axis"),
    "seq_dim", "seq_axis")