text: # 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.
  # ==============================================================================
  
  # pylint: disable=g-short-docstring-punctuation
  """Sparse Tensor Representation. See the @{$python/sparse_ops} guide.
  
  @@SparseTensor
  @@SparseTensorValue
  @@sparse_to_dense
  @@sparse_tensor_to_dense
  @@sparse_to_indicator
  @@sparse_merge
  @@sparse_concat
  @@sparse_reorder
  @@sparse_reshape
  @@sparse_slice
  @@sparse_split
  @@sparse_retain
  @@sparse_reset_shape
  @@sparse_fill_empty_rows
  @@sparse_transpose
  @@sparse_reduce_max
  @@sparse_reduce_max_sparse
  @@sparse_reduce_sum
  @@sparse_reduce_sum_sparse
  @@sparse_add
  @@sparse_softmax
  @@sparse_tensor_dense_matmul
  @@sparse_maximum
  @@sparse_minimum
  """
  
  from __future__ import absolute_import
  from __future__ import division
  from __future__ import print_function
  
  import collections
  import numbers
  
  import numpy as np
  
  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_util
  from tensorflow.python.ops import array_ops
  from tensorflow.python.ops import check_ops
  from tensorflow.python.ops import control_flow_ops
  from tensorflow.python.ops import gen_sparse_ops
  from tensorflow.python.ops import math_ops
  # go/tf-wildcard-import
  # pylint: disable=wildcard-import
  from tensorflow.python.ops.gen_sparse_ops import *
  # pylint: enable=wildcard-import
  from tensorflow.python.util import deprecation
  
  
  def _convert_to_sparse_tensor(sp_input):
    """Convert `sp_input` to `SparseTensor` and return it.
  
    Args:
      sp_input: `SparseTensor` or `SparseTensorValue`.
  
    Returns:
      `sp_input` converted to `SparseTensor`.
  
    Raises:
      ValueError: if `sp_input` is neither `SparseTensor` nor `SparseTensorValue`.
    """
    if isinstance(sp_input, sparse_tensor.SparseTensorValue):
      return sparse_tensor.SparseTensor.from_value(sp_input)
    if not isinstance(sp_input, sparse_tensor.SparseTensor):
      raise TypeError("Input must be a SparseTensor.")
    return sp_input
  
  
  def _convert_to_sparse_tensors(sp_inputs):
    """Convert `sp_inputs` to `SparseTensor` objects and return them.
  
    Args:
      sp_inputs: `list` or `tuple` of `SparseTensor` or `SparseTensorValue`
        objects.
  
    Returns:
      `sp_inputs` converted to `SparseTensor` objects.
  
    Raises:
      ValueError: if any item in `sp_inputs` is neither `SparseTensor` nor
        `SparseTensorValue`.
    """
    if isinstance(sp_inputs, list):
      return [_convert_to_sparse_tensor(sp_input) for sp_input in sp_inputs]
    if isinstance(sp_inputs, tuple):
      return (_convert_to_sparse_tensor(sp_input) for sp_input in sp_inputs)
    raise TypeError("Inputs must be a list or tuple.")
  
  
  # pylint: disable=protected-access
  def sparse_concat(axis,
                    sp_inputs,
                    name=None,
                    expand_nonconcat_dim=False,
                    concat_dim=None):
    """Concatenates a list of `SparseTensor` along the specified dimension.
  
    Concatenation is with respect to the dense versions of each sparse input.
    It is assumed that each inputs is a `SparseTensor` whose elements are ordered
    along increasing dimension number.
  
    If expand_nonconcat_dim is False, all inputs' shapes must match, except for
    the concat dimension. If expand_nonconcat_dim is True, then inputs' shapes are
    allowed to vary among all inputs.
  
    The `indices`, `values`, and `shapes` lists must have the same length.
  
    If expand_nonconcat_dim is False, then the output shape is identical to the
    inputs', except along the concat dimension, where it is the sum of the inputs'
    sizes along that dimension.
  
    If expand_nonconcat_dim is True, then the output shape along the non-concat
    dimensions will be expand to be the largest among all inputs, and it is the
    sum of the inputs sizes along the concat dimension.
  
    The output elements will be resorted to preserve the sort order along
    increasing dimension number.
  
    This op runs in `O(M log M)` time, where `M` is the total number of non-empty
    values across all inputs. This is due to the need for an internal sort in
    order to concatenate efficiently across an arbitrary dimension.
  
    For example, if `axis = 1` and the inputs are
  
        sp_inputs[0]: shape = [2, 3]
        [0, 2]: "a"
        [1, 0]: "b"
        [1, 1]: "c"
  
        sp_inputs[1]: shape = [2, 4]
        [0, 1]: "d"
        [0, 2]: "e"
  
    then the output will be
  
        shape = [2, 7]
        [0, 2]: "a"
        [0, 4]: "d"
        [0, 5]: "e"
        [1, 0]: "b"
        [1, 1]: "c"
  
    Graphically this is equivalent to doing
  
        [    a] concat [  d e  ] = [    a   d e  ]
        [b c  ]        [       ]   [b c          ]
  
    Another example, if 'axis = 1' and the inputs are
  
        sp_inputs[0]: shape = [3, 3]
        [0, 2]: "a"
        [1, 0]: "b"
        [2, 1]: "c"
  
        sp_inputs[1]: shape = [2, 4]
        [0, 1]: "d"
        [0, 2]: "e"
  
    if expand_nonconcat_dim = False, this will result in an error. But if
    expand_nonconcat_dim = True, this will result in:
  
        shape = [3, 7]
        [0, 2]: "a"
        [0, 4]: "d"
        [0, 5]: "e"
        [1, 0]: "b"
        [2, 1]: "c"
  
    Graphically this is equivalent to doing
  
        [    a] concat [  d e  ] = [    a   d e  ]
        [b    ]        [       ]   [b            ]
        [  c  ]                    [  c          ]
  
  
    Args:
      axis: Dimension to concatenate along. Must be in range [-rank, rank),
        where rank is the number of dimensions in each input `SparseTensor`.
      sp_inputs: List of `SparseTensor` to concatenate.
      name: A name prefix for the returned tensors (optional).
      expand_nonconcat_dim: Whether to allow the expansion in the non-concat
        dimensions. Defaulted to False.
      concat_dim: The old (deprecated) name for axis.
  
    Returns:
      A `SparseTensor` with the concatenated output.
  
    Raises:
      TypeError: If `sp_inputs` is not a list of `SparseTensor`.
    """
    axis = deprecation.deprecated_argument_lookup("axis", axis, "concat_dim",
                                                  concat_dim)
    sp_inputs = _convert_to_sparse_tensors(sp_inputs)
  
    if len(sp_inputs) == 1:  # Degenerate case of one tensor.
      return sp_inputs[0]
  
    inds = [sp_input.indices for sp_input in sp_inputs]
    vals = [sp_input.values for sp_input in sp_inputs]
    shapes = [sp_input.dense_shape for sp_input in sp_inputs]
  
    if expand_nonconcat_dim:
      max_shape = math_ops.reduce_max(
          array_ops.concat(
              [array_ops.reshape(shape, [1, -1]) for shape in shapes], 0), 0)
      shapes = [
          array_ops.concat([
              max_shape[:axis], shape[-1:] if axis == -1 else
              shape[axis:axis + 1], [] if axis == -1 else max_shape[axis + 1:]
          ], 0) for shape in shapes
      ]
  
    output_ind, output_val, output_shape = (gen_sparse_ops._sparse_concat(
        inds, vals, shapes, axis, name=name))
  
    return sparse_tensor.SparseTensor(output_ind, output_val, output_shape)
  
  
  def sparse_add(a, b, thresh=0):
    """Adds two tensors, at least one of each is a `SparseTensor`.
  
    If one `SparseTensor` and one `Tensor` are passed in, returns a `Tensor`.  If
    both arguments are `SparseTensor`s, this returns a `SparseTensor`.  The order
    of arguments does not matter.  Use vanilla `tf.add()` for adding two dense
    `Tensor`s.
  
    The shapes of the two operands must match: broadcasting is not supported.
  
    The indices of any input `SparseTensor` are assumed ordered in standard
    lexicographic order.  If this is not the case, before this step run
    `SparseReorder` to restore index ordering.
  
    If both arguments are sparse, we perform "clipping" as follows.  By default,
    if two values sum to zero at some index, the output `SparseTensor` would still
    include that particular location in its index, storing a zero in the
    corresponding value slot.  To override this, callers can specify `thresh`,
    indicating that if the sum has a magnitude strictly smaller than `thresh`, its
    corresponding value and index would then not be included.  In particular,
    `thresh == 0.0` (default) means everything is kept and actual thresholding
    happens only for a positive value.
  
    For example, suppose the logical sum of two sparse operands is (densified):
  
        [       2]
        [.1     0]
        [ 6   -.2]
  
    Then,
  
        * `thresh == 0` (the default): all 5 index/value pairs will be returned.
        * `thresh == 0.11`: only .1 and 0 will vanish, and the remaining three
            index/value pairs will be returned.
        * `thresh == 0.21`: .1, 0, and -.2 will vanish.
  
    Args:
      a: The first operand; `SparseTensor` or `Tensor`.
      b: The second operand; `SparseTensor` or `Tensor`.  At least one operand
        must be sparse.
      thresh: A 0-D `Tensor`.  The magnitude threshold that determines if an
      output value/index pair takes space.  Its dtype should match that of the
      values if they are real; if the latter are complex64/complex128, then the
      dtype should be float32/float64, correspondingly.
  
    Returns:
      A `SparseTensor` or a `Tensor`, representing the sum.
  
    Raises:
      TypeError: If both `a` and `b` are `Tensor`s.  Use `tf.add()` instead.
    """
    sparse_classes = (sparse_tensor.SparseTensor, sparse_tensor.SparseTensorValue)
    if not any(isinstance(inp, sparse_classes) for inp in [a, b]):
      raise TypeError("At least one input should be SparseTensor; do you mean to"
                      " use tf.add()?")
  
    if all(isinstance(inp, sparse_classes) for inp in [a, b]):
      a = _convert_to_sparse_tensor(a)
      b = _convert_to_sparse_tensor(b)
      thresh = ops.convert_to_tensor(
          thresh, dtype=a.values.dtype.real_dtype.base_dtype, name="thresh")
      output_ind, output_val, output_shape = (gen_sparse_ops._sparse_add(
          a.indices, a.values, a.dense_shape,
          b.indices, b.values, b.dense_shape,
          thresh))
  
      # Attempt to get output_shape statically.
      a.get_shape().assert_is_compatible_with(b.get_shape())
      static_shape = array_ops.broadcast_static_shape(
          a.get_shape(), b.get_shape())
      if static_shape.is_fully_defined():
        output_shape = static_shape.as_list()
  
      return sparse_tensor.SparseTensor(output_ind, output_val, output_shape)
    else:
      # swap to make `a` the SparseTensor.
      if isinstance(b, sparse_classes):
        a, b = b, a
      return gen_sparse_ops._sparse_tensor_dense_add(
          a.indices, a.values, a.dense_shape, b)
  
  
  def _sparse_cross(inputs, name=None):
    """Generates sparse cross from a list of sparse and dense tensors.
  
    For example, if the inputs are
    * inputs[0]: SparseTensor with shape = [2, 2]
      [0, 0]: "a"
      [1, 0]: "b"
      [1, 1]: "c"
    * inputs[1]: SparseTensor with shape = [2, 1]
      [0, 0]: "d"
      [1, 0]: "e"
    * inputs[2]: Tensor [["f"], ["g"]]
  
    then the output will be:
      shape = [2, 2]
      [0, 0]: "a_X_d_X_f"
      [1, 0]: "b_X_e_X_g"
      [1, 1]: "c_X_e_X_g"
  
    Args:
      inputs: An iterable of `Tensor` or `SparseTensor`.
      name: Optional name for the op.
  
    Returns:
      A `SparseTensor` of type `string`.
    """
    return _sparse_cross_internal(inputs=inputs, hashed_output=False, name=name)
  
  
  def _sparse_cross_hashed(inputs, num_buckets=0, hash_key=None, name=None):
    """Generates hashed sparse cross from a list of sparse and dense tensors.
  
    For example, if the inputs are
    * inputs[0]: SparseTensor with shape = [2, 2]
      [0, 0]: "a"
      [1, 0]: "b"
      [1, 1]: "c"
    * inputs[1]: SparseTensor with shape = [2, 1]
      [0, 0]: "d"
      [1, 0]: "e"
    * inputs[2]: Tensor [["f"], ["g"]]
  
    then the output will be:
      shape = [2, 2]
      [0, 0]: FingerprintCat64(
                  Fingerprint64("f"), FingerprintCat64(
                      Fingerprint64("d"), Fingerprint64("a")))
      [1, 0]: FingerprintCat64(
                  Fingerprint64("g"), FingerprintCat64(
                      Fingerprint64("e"), Fingerprint64("b")))
      [1, 1]: FingerprintCat64(
                  Fingerprint64("g"), FingerprintCat64(
                      Fingerprint64("e"), Fingerprint64("c")))
  
    Args:
      inputs: An iterable of `Tensor` or `SparseTensor`.
      num_buckets: An `int` that is `>= 0`.
        output = hashed_value%num_buckets if num_buckets > 0 else hashed_value.
      hash_key: Integer hash_key that will be used by the `FingerprintCat64`
        function. If not given, will use a default key.
      name: Optional name for the op.
  
    Returns:
      A `SparseTensor` of type `int64`.
    """
    return _sparse_cross_internal(
        inputs=inputs,
        hashed_output=True,
        num_buckets=num_buckets,
        hash_key=hash_key,
        name=name)
  
  
  _DEFAULT_HASH_KEY = 0xDECAFCAFFE
  
  
  def _sparse_cross_internal(
      inputs, hashed_output=False, num_buckets=0, hash_key=None, name=None):
    """See gen_sparse_ops._sparse_cross."""
    if not isinstance(inputs, list):
      raise TypeError("Inputs must be a list")
    if not all(isinstance(i, sparse_tensor.SparseTensor) or
               isinstance(i, ops.Tensor) for i in inputs):
      raise TypeError("All inputs must be SparseTensors")
  
    sparse_inputs = [i for i in inputs
                     if isinstance(i, sparse_tensor.SparseTensor)]
    dense_inputs = [i for i in inputs
                    if not isinstance(i, sparse_tensor.SparseTensor)]
  
    indices = [sp_input.indices for sp_input in sparse_inputs]
    values = [sp_input.values for sp_input in sparse_inputs]
    shapes = [sp_input.dense_shape for sp_input in sparse_inputs]
    out_type = dtypes.int64 if hashed_output else dtypes.string
  
    internal_type = dtypes.string
    for i in range(len(values)):
      if values[i].dtype != dtypes.string:
        values[i] = math_ops.to_int64(values[i])
        internal_type = dtypes.int64
    for i in range(len(dense_inputs)):
      if dense_inputs[i].dtype != dtypes.string:
        dense_inputs[i] = math_ops.to_int64(dense_inputs[i])
        internal_type = dtypes.int64
  
    indices_out, values_out, shape_out = gen_sparse_ops._sparse_cross(
        indices=indices,
        values=values,
        shapes=shapes,
        dense_inputs=dense_inputs,
        hashed_output=hashed_output,
        num_buckets=num_buckets,
        hash_key=hash_key or _DEFAULT_HASH_KEY,
        out_type=out_type,
        internal_type=internal_type,
        name=name)
  
    return sparse_tensor.SparseTensor(indices_out, values_out, shape_out)
  
  
  def sparse_dense_cwise_add(sp_t, dense_t):
    """Adds up a SparseTensor and a dense Tensor, using these special rules:
  
    (1) Broadcasts the dense side to have the same shape as the sparse side, if
        eligible;
    (2) Then, only the dense values pointed to by the indices of the SparseTensor
        participate in the cwise addition.
  
    By the rules, the result is a logical SparseTensor with exactly the same
    indices and shape, but possibly with different non-zero values.  The output of
    this Op is the resultant non-zero values.
  
    Args:
      sp_t: the SparseTensor operand.
      dense_t: the dense Tensor operand; must have the same dtype and a
        broadcast-compatible shape as `sp_t`.
  
    Returns:
      output: the SparseTensor output.
    """
    result = gen_sparse_ops.sparse_dense_cwise_add(sp_t.indices, sp_t.values,
                                                   sp_t.dense_shape, dense_t)
    return sparse_tensor.SparseTensor(sp_t.indices, result, sp_t.dense_shape)
  
  
  def sparse_reorder(sp_input, name=None):
    """Reorders a `SparseTensor` into the canonical, row-major ordering.
  
    Note that by convention, all sparse ops preserve the canonical ordering
    along increasing dimension number. The only time ordering can be violated
    is during manual manipulation of the indices and values to add entries.
  
    Reordering does not affect the shape of the `SparseTensor`.
  
    For example, if `sp_input` has shape `[4, 5]` and `indices` / `values`:
  
        [0, 3]: b
        [0, 1]: a
        [3, 1]: d
        [2, 0]: c
  
    then the output will be a `SparseTensor` of shape `[4, 5]` and
    `indices` / `values`:
  
        [0, 1]: a
        [0, 3]: b
        [2, 0]: c
        [3, 1]: d
  
    Args:
      sp_input: The input `SparseTensor`.
      name: A name prefix for the returned tensors (optional)
  
    Returns:
      A `SparseTensor` with the same shape and non-empty values, but in
      canonical ordering.
  
    Raises:
      TypeError: If `sp_input` is not a `SparseTensor`.
    """
    sp_input = _convert_to_sparse_tensor(sp_input)
  
    reordered_ind, reordered_val = (gen_sparse_ops._sparse_reorder(
        sp_input.indices, sp_input.values, sp_input.dense_shape, name=name))
  
    if sp_input.get_shape().is_fully_defined():
      dense_shape = sp_input.get_shape().as_list()
    else:
      dense_shape = array_ops.identity(sp_input.dense_shape)
  
    return sparse_tensor.SparseTensor(reordered_ind, reordered_val, dense_shape)
  
  
  def sparse_reshape(sp_input, shape, name=None):
    """Reshapes a `SparseTensor` to represent values in a new dense shape.
  
    This operation has the same semantics as `reshape` on the represented dense
    tensor.  The indices of non-empty values in `sp_input` are recomputed based
    on the new dense shape, and a new `SparseTensor` is returned containing the
    new indices and new shape.  The order of non-empty values in `sp_input` is
    unchanged.
  
    If one component of `shape` is the special value -1, the size of that
    dimension is computed so that the total dense size remains constant.  At
    most one component of `shape` can be -1.  The number of dense elements
    implied by `shape` must be the same as the number of dense elements
    originally represented by `sp_input`.
  
    For example, if `sp_input` has shape `[2, 3, 6]` and `indices` / `values`:
  
        [0, 0, 0]: a
        [0, 0, 1]: b
        [0, 1, 0]: c
        [1, 0, 0]: d
        [1, 2, 3]: e
  
    and `shape` is `[9, -1]`, then the output will be a `SparseTensor` of
    shape `[9, 4]` and `indices` / `values`:
  
        [0, 0]: a
        [0, 1]: b
        [1, 2]: c
        [4, 2]: d
        [8, 1]: e
  
    Args:
      sp_input: The input `SparseTensor`.
      shape: A 1-D (vector) int64 `Tensor` specifying the new dense shape of the
        represented `SparseTensor`.
      name: A name prefix for the returned tensors (optional)
  
    Returns:
      A `SparseTensor` with the same non-empty values but with indices calculated
      by the new dense shape.
  
    Raises:
      TypeError: If `sp_input` is not a `SparseTensor`.
      ValueError:  If argument `shape` requests a `SparseTensor` with a different
        number of elements than `sp_input`.
    """
    sp_input = _convert_to_sparse_tensor(sp_input)
    shape = math_ops.cast(shape, dtype=dtypes.int64)
  
    with ops.name_scope(name, "SparseReshape", [sp_input]) as name:
      reshaped_ind, reshaped_shape = gen_sparse_ops._sparse_reshape(
          sp_input.indices, sp_input.dense_shape, shape, name=name)
  
      reshaped_shape_const = tensor_util.constant_value(shape)
      if (reshaped_shape_const is not None
          and sp_input.get_shape().is_fully_defined()):
        # Don't deal with inferred dimensions. That would add significant code.
        if all(n >= 0 for n in reshaped_shape_const):
          reshaped_size = np.prod(reshaped_shape_const)
          in_shape_size = np.prod(sp_input.get_shape().as_list())
          if reshaped_size != in_shape_size:
            raise ValueError(
                "Cannot reshape a tensor with %d elements to shape %s "
                "(%d elements)."
                % (in_shape_size, reshaped_shape_const, reshaped_size))
          reshaped_shape = reshaped_shape_const
  
      return sparse_tensor.SparseTensor(
          reshaped_ind, array_ops.identity(sp_input.values),
          reshaped_shape)
  
  
  # TODO(aselle): Remove keyword required once for 1.0 final
  class KeywordRequired(object):
  
    def __repr__(self):
      # This is needed to make documentation without fully qualified module paths
      return "KeywordRequired()"
  
  
  def sparse_split(keyword_required=KeywordRequired(),
                   sp_input=None, num_split=None, axis=None,
                   name=None, split_dim=None):
    """Split a `SparseTensor` into `num_split` tensors along `axis`.
  
    If the `sp_input.dense_shape[axis]` is not an integer multiple of `num_split`
    each slice starting from 0:`shape[axis] % num_split` gets extra one
    dimension. For example, if `axis = 1` and `num_split = 2` and the
    input is:
  
        input_tensor = shape = [2, 7]
        [    a   d e  ]
        [b c          ]
  
    Graphically the output tensors are:
  
        output_tensor[0] =
        [    a ]
        [b c   ]
  
        output_tensor[1] =
        [ d e  ]
        [      ]
  
    Args:
      keyword_required: Python 2 standin for * (temporary for argument reorder)
      sp_input: The `SparseTensor` to split.
      num_split: A Python integer. The number of ways to split.
      axis: A 0-D `int32` `Tensor`. The dimension along which to split.
      name: A name for the operation (optional).
      split_dim: Deprecated old name for axis.
  
    Returns:
      `num_split` `SparseTensor` objects resulting from splitting `value`.
  
    Raises:
      TypeError: If `sp_input` is not a `SparseTensor`.
      ValueError: If the deprecated `split_dim` and `axis` are both non None.
    """
    if not isinstance(keyword_required, KeywordRequired):
      raise ValueError("Keyword arguments are required for this function.")
    if sp_input is None:
      raise ValueError("sp_input is required")
    if num_split is None:
      raise ValueError("num_split is required")
    if axis is None:
      raise ValueError("axis is required")
    axis = deprecation.deprecated_argument_lookup("axis", axis, "split_dim",
                                                  split_dim)
    sp_input = _convert_to_sparse_tensor(sp_input)
  
    output_inds, output_vals, output_shapes = (gen_sparse_ops._sparse_split(
        axis,
        sp_input.indices,
        sp_input.values,
        sp_input.dense_shape,
        num_split,
        name=name))
    sparse_tensors = []
    for i in range(0, num_split):
      sparse_tensors.append(
          sparse_tensor.SparseTensor(
              output_inds[i], output_vals[i], output_shapes[i]))
    return sparse_tensors
  
  
  def sparse_slice(sp_input, start, size, name=None):
    """Slice a `SparseTensor` based on the `start` and `size.
  
    For example, if the input is
  
        input_tensor = shape = [2, 7]
        [    a   d e  ]
        [b c          ]
  
    Graphically the output tensors are:
  
        sparse_slice([0, 0], [2, 4]) = shape = [2, 4]
        [    a  ]
        [b c    ]
  
        sparse_slice([0, 4], [2, 3]) = shape = [2, 3]
        [ d e  ]
        [      ]
  
    Args:
      sp_input: The `SparseTensor` to split.
      start: 1-D. tensor represents the start of the slice.
      size: 1-D. tensor represents the size of the slice.
      name: A name for the operation (optional).
  
    Returns:
      A `SparseTensor` objects resulting from splicing.
  
    Raises:
      TypeError: If `sp_input` is not a `SparseTensor`.
    """
    sp_input = _convert_to_sparse_tensor(sp_input)
    start = ops.convert_to_tensor(start, dtypes.int64)
    size = ops.convert_to_tensor(size, dtypes.int64)
  
    with ops.name_scope(name, "SparseSlice", [sp_input]) as name:
      output_indices, output_values, output_shape = gen_sparse_ops.sparse_slice(
          sp_input.indices, sp_input.values, sp_input.dense_shape, start, size, name=name)
  
      return sparse_tensor.SparseTensor(
          output_indices,
          output_values,
          output_shape)
  
  def sparse_to_dense(sparse_indices,
                      output_shape,
                      sparse_values,
                      default_value=0,
                      validate_indices=True,
                      name=None):
    """Converts a sparse representation into a dense tensor.
  
    Builds an array `dense` with shape `output_shape` such that
  
    ```python
    # If sparse_indices is scalar
    dense[i] = (i == sparse_indices ? sparse_values : default_value)
  
    # If sparse_indices is a vector, then for each i
    dense[sparse_indices[i]] = sparse_values[i]
  
    # If sparse_indices is an n by d matrix, then for each i in [0, n)
    dense[sparse_indices[i][0], ..., sparse_indices[i][d-1]] = sparse_values[i]
    ```
  
    All other values in `dense` are set to `default_value`.  If `sparse_values`
    is a scalar, all sparse indices are set to this single value.
  
    Indices should be sorted in lexicographic order, and indices must not
    contain any repeats. If `validate_indices` is True, these properties
    are checked during execution.
  
    Args:
      sparse_indices: A 0-D, 1-D, or 2-D `Tensor` of type `int32` or `int64`.
        `sparse_indices[i]` contains the complete index where `sparse_values[i]`
        will be placed.
      output_shape: A 1-D `Tensor` of the same type as `sparse_indices`.  Shape
        of the dense output tensor.
      sparse_values: A 0-D or 1-D `Tensor`.  Values corresponding to each row of
        `sparse_indices`, or a scalar value to be used for all sparse indices.
      default_value: A 0-D `Tensor` of the same type as `sparse_values`.  Value
        to set for indices not specified in `sparse_indices`.  Defaults to zero.
      validate_indices: A boolean value.  If True, indices are checked to make
        sure they are sorted in lexicographic order and that there are no repeats.
      name: A name for the operation (optional).
  
    Returns:
      Dense `Tensor` of shape `output_shape`.  Has the same type as
      `sparse_values`.
    """
    return gen_sparse_ops._sparse_to_dense(
        sparse_indices,
        output_shape,
        sparse_values,
        default_value=default_value,
        validate_indices=validate_indices,
        name=name)
  
  
  def sparse_reduce_max(sp_input, axis=None, keep_dims=False,
                        reduction_axes=None):
    """Computes the max of elements across dimensions of a SparseTensor.
  
    This Op takes a SparseTensor and is the sparse counterpart to
    `tf.reduce_max()`.  In particular, this Op also returns a dense `Tensor`
    instead of a sparse one.
  
    Reduces `sp_input` along the dimensions given in `reduction_axes`.  Unless
    `keep_dims` is true, the rank of the tensor is reduced by 1 for each entry in
    `reduction_axes`. If `keep_dims` is true, the reduced dimensions are retained
    with length 1.
  
    If `reduction_axes` has no entries, all dimensions are reduced, and a tensor
    with a single element is returned.  Additionally, the axes can be negative,
    similar to the indexing rules in Python.
  
    For example:
  
    ```python
    # 'x' represents [[1, ?, 2]
    #                 [?, 3, ?]]
    # where ? is implicitly-zero.
    tf.sparse_reduce_max(x) ==> 3
    tf.sparse_reduce_max(x, 0) ==> [1, 3, 2]
    tf.sparse_reduce_max(x, 1) ==> [2, 3]  # Can also use -1 as the axis.
    tf.sparse_reduce_max(x, 1, keep_dims=True) ==> [[2], [3]]
    tf.sparse_reduce_max(x, [0, 1]) ==> 3
    ```
  
    Args:
      sp_input: The SparseTensor to reduce. Should have numeric type.
      axis: The dimensions to reduce; list or scalar. If `None` (the
        default), reduces all dimensions.
      keep_dims: If true, retain reduced dimensions with length 1.
      reduction_axes: Deprecated name of axis.
  
    Returns:
      The reduced Tensor.
    """
    return gen_sparse_ops.sparse_reduce_max(
        sp_input.indices, sp_input.values,
        sp_input.dense_shape,
        math_ops._ReductionDims(sp_input, axis, reduction_axes),
        keep_dims)
  
  
  def sparse_reduce_max_sparse(sp_input, axis=None, keep_dims=False,
                               reduction_axes=None):
    """Computes the max of elements across dimensions of a SparseTensor.
  
    This Op takes a SparseTensor and is the sparse counterpart to
    `tf.reduce_max()`.  In contrast to SparseReduceSum, this Op returns a
    SparseTensor.
  
    Reduces `sp_input` along the dimensions given in `reduction_axes`.  Unless
    `keep_dims` is true, the rank of the tensor is reduced by 1 for each entry in
    `reduction_axes`. If `keep_dims` is true, the reduced dimensions are retained
    with length 1.
  
    If `reduction_axes` has no entries, all dimensions are reduced, and a tensor
    with a single element is returned.  Additionally, the axes can be negative,
    which are interpreted according to the indexing rules in Python.
  
    Args:
      sp_input: The SparseTensor to reduce. Should have numeric type.
      axis: The dimensions to reduce; list or scalar. If `None` (the
        default), reduces all dimensions.
      keep_dims: If true, retain reduced dimensions with length 1.
      reduction_axes: Deprecated name of axis
  
    Returns:
      The reduced SparseTensor.
    """
    output_ind, output_val, output_shape = (
        gen_sparse_ops.sparse_reduce_max_sparse(
            sp_input.indices, sp_input.values,
            sp_input.dense_shape, math_ops._ReductionDims(sp_input, axis,
                                                          reduction_axes),
            keep_dims))
  
    return sparse_tensor.SparseTensor(output_ind, output_val, output_shape)
  
  
  def sparse_reduce_sum(sp_input, axis=None, keep_dims=False,
                        reduction_axes=None):
    """Computes the sum of elements across dimensions of a SparseTensor.
  
    This Op takes a SparseTensor and is the sparse counterpart to
    `tf.reduce_sum()`.  In particular, this Op also returns a dense `Tensor`
    instead of a sparse one.
  
    Reduces `sp_input` along the dimensions given in `reduction_axes`.  Unless
    `keep_dims` is true, the rank of the tensor is reduced by 1 for each entry in
    `reduction_axes`. If `keep_dims` is true, the reduced dimensions are retained
    with length 1.
  
    If `reduction_axes` has no entries, all dimensions are reduced, and a tensor
    with a single element is returned.  Additionally, the axes can be negative,
    similar to the indexing rules in Python.
  
    For example:
  
    ```python
    # 'x' represents [[1, ?, 1]
    #                 [?, 1, ?]]
    # where ? is implicitly-zero.
    tf.sparse_reduce_sum(x) ==> 3
    tf.sparse_reduce_sum(x, 0) ==> [1, 1, 1]
    tf.sparse_reduce_sum(x, 1) ==> [2, 1]  # Can also use -1 as the axis.
    tf.sparse_reduce_sum(x, 1, keep_dims=True) ==> [[2], [1]]
    tf.sparse_reduce_sum(x, [0, 1]) ==> 3
    ```
  
    Args:
      sp_input: The SparseTensor to reduce. Should have numeric type.
      axis: The dimensions to reduce; list or scalar. If `None` (the
        default), reduces all dimensions.
      keep_dims: If true, retain reduced dimensions with length 1.
      reduction_axes: Deprecated name of axis.
  
    Returns:
      The reduced Tensor.
    """
    return gen_sparse_ops.sparse_reduce_sum(
        sp_input.indices, sp_input.values,
        sp_input.dense_shape,
        math_ops._ReductionDims(sp_input, axis, reduction_axes),
        keep_dims)
  
  
  def sparse_reduce_sum_sparse(sp_input, axis=None, keep_dims=False,
                               reduction_axes=None):
    """Computes the sum of elements across dimensions of a SparseTensor.
  
    This Op takes a SparseTensor and is the sparse counterpart to
    `tf.reduce_sum()`.  In contrast to SparseReduceSum, this Op returns a
    SparseTensor.
  
    Reduces `sp_input` along the dimensions given in `reduction_axes`.  Unless
    `keep_dims` is true, the rank of the tensor is reduced by 1 for each entry in
    `reduction_axes`. If `keep_dims` is true, the reduced dimensions are retained
    with length 1.
  
    If `reduction_axes` has no entries, all dimensions are reduced, and a tensor
    with a single element is returned.  Additionally, the axes can be negative,
    which are interpreted according to the indexing rules in Python.
  
    Args:
      sp_input: The SparseTensor to reduce. Should have numeric type.
      axis: The dimensions to reduce; list or scalar. If `None` (the
        default), reduces all dimensions.
      keep_dims: If true, retain reduced dimensions with length 1.
      reduction_axes: Deprecated name of axis
  
    Returns:
      The reduced SparseTensor.
    """
    output_ind, output_val, output_shape = (
        gen_sparse_ops.sparse_reduce_sum_sparse(
            sp_input.indices, sp_input.values,
            sp_input.dense_shape, math_ops._ReductionDims(sp_input, axis,
                                                          reduction_axes),
            keep_dims))
  
    return sparse_tensor.SparseTensor(output_ind, output_val, output_shape)
  
  
  def sparse_tensor_to_dense(sp_input,
                             default_value=0,
                             validate_indices=True,
                             name=None):
    """Converts a `SparseTensor` into a dense tensor.
  
    This op is a convenience wrapper around `sparse_to_dense` for `SparseTensor`s.
  
    For example, if `sp_input` has shape `[3, 5]` and non-empty string values:
  
        [0, 1]: a
        [0, 3]: b
        [2, 0]: c
  
    and `default_value` is `x`, then the output will be a dense `[3, 5]`
    string tensor with values:
  
        [[x a x b x]
         [x x x x x]
         [c x x x x]]
  
    Indices must be without repeats.  This is only
    tested if validate_indices is True.
  
    Args:
      sp_input: The input `SparseTensor`.
      default_value: Scalar value to set for indices not specified in
        `sp_input`.  Defaults to zero.
      validate_indices: A boolean value.  If `True`, indices are checked to make
        sure they are sorted in lexicographic order and that there are no repeats.
      name: A name prefix for the returned tensors (optional).
  
    Returns:
      A dense tensor with shape `sp_input.dense_shape` and values specified by
      the non-empty values in `sp_input`. Indices not in `sp_input` are assigned
      `default_value`.
  
    Raises:
      TypeError: If `sp_input` is not a `SparseTensor`.
    """
    sp_input = _convert_to_sparse_tensor(sp_input)
  
    return sparse_to_dense(
        sp_input.indices,
        sp_input.dense_shape,
        sp_input.values,
        default_value=default_value,
        validate_indices=validate_indices,
        name=name)
  
  
  def sparse_to_indicator(sp_input, vocab_size, name=None):
    """Converts a `SparseTensor` of ids into a dense bool indicator tensor.
  
    The last dimension of `sp_input.indices` is discarded and replaced with
    the values of `sp_input`.  If `sp_input.dense_shape = [D0, D1, ..., Dn, K]`,
    then `output.shape = [D0, D1, ..., Dn, vocab_size]`, where
  
        output[d_0, d_1, ..., d_n, sp_input[d_0, d_1, ..., d_n, k]] = True
  
    and False elsewhere in `output`.
  
    For example, if `sp_input.dense_shape = [2, 3, 4]` with non-empty values:
  
        [0, 0, 0]: 0
        [0, 1, 0]: 10
        [1, 0, 3]: 103
        [1, 1, 2]: 150
        [1, 1, 3]: 149
        [1, 1, 4]: 150
        [1, 2, 1]: 121
  
    and `vocab_size = 200`, then the output will be a `[2, 3, 200]` dense bool
    tensor with False everywhere except at positions
  
        (0, 0, 0), (0, 1, 10), (1, 0, 103), (1, 1, 149), (1, 1, 150),
        (1, 2, 121).
  
    Note that repeats are allowed in the input SparseTensor.
    This op is useful for converting `SparseTensor`s into dense formats for
    compatibility with ops that expect dense tensors.
  
    The input `SparseTensor` must be in row-major order.
  
    Args:
      sp_input: A `SparseTensor` with `values` property of type `int32` or
        `int64`.
      vocab_size: A scalar int64 Tensor (or Python int) containing the new size
        of the last dimension, `all(0 <= sp_input.values < vocab_size)`.
      name: A name prefix for the returned tensors (optional)
  
    Returns:
      A dense bool indicator tensor representing the indices with specified value.
  
    Raises:
      TypeError: If `sp_input` is not a `SparseTensor`.
    """
    sp_input = _convert_to_sparse_tensor(sp_input)
  
    with ops.name_scope(name, "SparseToIndicator", [sp_input]) as name:
      num_entries = array_ops.shape(sp_input.indices)[0]
      new_values = array_ops.fill(array_ops.expand_dims(num_entries, 0), True)
      sp_values = sparse_tensor.SparseTensor(
          sp_input.indices, new_values, sp_input.dense_shape)
  
      sp_new = sparse_merge(sp_input, sp_values, vocab_size, name)
  
      # validate_indices may be False because we allow duplicates in new_indices:
      # repeated indices are allowed when creating an indicator matrix.
      return sparse_tensor_to_dense(
          sp_new, default_value=False, validate_indices=False, name=name)
  
  
  def sparse_merge(sp_ids, sp_values, vocab_size, name=None,
                   already_sorted=False):
    """Combines a batch of feature ids and values into a single `SparseTensor`.
  
    The most common use case for this function occurs when feature ids and
    their corresponding values are stored in `Example` protos on disk.
    `parse_example` will return a batch of ids and a batch of values, and this
    function joins them into a single logical `SparseTensor` for use in
    functions such as `sparse_tensor_dense_matmul`, `sparse_to_dense`, etc.
  
    The `SparseTensor` returned by this function has the following properties:
  
      - `indices` is equivalent to `sp_ids.indices` with the last
        dimension discarded and replaced with `sp_ids.values`.
      - `values` is simply `sp_values.values`.
      - If `sp_ids.dense_shape = [D0, D1, ..., Dn, K]`, then
        `output.shape = [D0, D1, ..., Dn, vocab_size]`.
  
    For example, consider the following feature vectors:
  
    ```python
      vector1 = [-3, 0, 0, 0, 0, 0]
      vector2 = [ 0, 1, 0, 4, 1, 0]
      vector3 = [ 5, 0, 0, 9, 0, 0]
    ```
  
    These might be stored sparsely in the following Example protos by storing
    only the feature ids (column number if the vectors are treated as a matrix)
    of the non-zero elements and the corresponding values:
  
    ```python
      examples = [Example(features={
                      "ids": Feature(int64_list=Int64List(value=[0])),
                      "values": Feature(float_list=FloatList(value=[-3]))}),
                  Example(features={
                      "ids": Feature(int64_list=Int64List(value=[1, 4, 3])),
                      "values": Feature(float_list=FloatList(value=[1, 1, 4]))}),
                  Example(features={
                      "ids": Feature(int64_list=Int64List(value=[0, 3])),
                      "values": Feature(float_list=FloatList(value=[5, 9]))})]
    ```
  
    The result of calling parse_example on these examples will produce a
    dictionary with entries for "ids" and "values". Passing those two objects
    to this function along with vocab_size=6, will produce a `SparseTensor` that
    sparsely represents all three instances. Namely, the `indices` property will
    contain the coordinates of the non-zero entries in the feature matrix (the
    first dimension is the row number in the matrix, i.e., the index within the
    batch, and the second dimension is the column number, i.e., the feature id);
    `values` will contain the actual values. `shape` will be the shape of the
    original matrix, i.e., (3, 6). For our example above, the output will be
    equal to:
  
    ```python
      SparseTensor(indices=[[0, 0], [1, 1], [1, 3], [1, 4], [2, 0], [2, 3]],
                   values=[-3, 1, 4, 1, 5, 9],
                   dense_shape=[3, 6])
    ```
  
    This method generalizes to higher-dimensions by simply providing a list for
    both the sp_ids as well as the vocab_size.
    In this case the resulting `SparseTensor` has the following properties:
      - `indices` is equivalent to `sp_ids[0].indices` with the last
        dimension discarded and concatenated with
        `sp_ids[0].values, sp_ids[1].values, ...`.
      - `values` is simply `sp_values.values`.
      - If `sp_ids.dense_shape = [D0, D1, ..., Dn, K]`, then
        `output.shape = [D0, D1, ..., Dn] + vocab_size`.
  
    Args:
      sp_ids: A single `SparseTensor` with `values` property of type `int32`
        or `int64` or a Python list of such `SparseTensor`s or a list thereof.
      sp_values: A `SparseTensor` of any type.
      vocab_size: A scalar `int64` Tensor (or Python int) containing the new size
        of the last dimension, `all(0 <= sp_ids.values < vocab_size)`.
        Or a list thereof with `all(0 <= sp_ids[i].values < vocab_size[i])` for
        all `i`.
      name: A name prefix for the returned tensors (optional)
      already_sorted: A boolean to specify whether the per-batch values in
       `sp_values` are already sorted. If so skip sorting, False by default
       (optional).
  
    Returns:
      A `SparseTensor` compactly representing a batch of feature ids and values,
      useful for passing to functions that expect such a `SparseTensor`.
  
    Raises:
      TypeError: If `sp_values` is not a `SparseTensor`. Or if `sp_ids` is neither
        a `SparseTensor` nor a list thereof. Or if `vocab_size` is not a
        `Tensor` or a Python int and `sp_ids` is a `SparseTensor`. Or if
        `vocab_size` is not a or list thereof and `sp_ids` is a list.
      ValueError: If `sp_ids` and `vocab_size` are lists of different lengths.
    """
    if isinstance(sp_ids, sparse_tensor.SparseTensorValue) or isinstance(
        sp_ids, sparse_tensor.SparseTensor):
      sp_ids = [sp_ids]
      if not (isinstance(vocab_size, ops.Tensor) or
              isinstance(vocab_size, numbers.Integral)):
        raise TypeError("vocab_size has to be a Tensor or Python int. Found %s" %
                        type(vocab_size))
      vocab_size = [vocab_size]
    else:
      if not isinstance(sp_ids, collections.Iterable):
        raise TypeError("sp_ids has to be a SparseTensor or list thereof. "
                        "Found %s" % type(sp_ids))
      if not isinstance(vocab_size, collections.Iterable):
        raise TypeError("vocab_size has to be a list of Tensors or Python ints. "
                        "Found %s" % type(vocab_size))
      for dim in vocab_size:
        if not (isinstance(dim, ops.Tensor) or
                isinstance(dim, numbers.Integral)):
          raise TypeError(
              "vocab_size has to be a list of Tensors or Python ints. Found %s" %
              type(dim))
    if len(sp_ids) != len(vocab_size):
      raise ValueError("sp_ids and vocab_size have to have equal lengths.")
  
    with ops.name_scope(name, "SparseMerge", [sp_ids, sp_values]):
      sp_ids = [_convert_to_sparse_tensor(sp_ids_dim) for sp_ids_dim in sp_ids]
      sp_values = _convert_to_sparse_tensor(sp_values)
      ids = []
      for sp_ids_dim in sp_ids:
        ids_dim = sp_ids_dim.values
        if sp_ids_dim.dtype != dtypes.int64:
          ids_dim = math_ops.cast(ids_dim, dtypes.int64)
        ids += [array_ops.expand_dims(ids_dim, axis=1)]
  
      vocab_size = [math_ops.cast(x, dtypes.int64) for x in vocab_size]
  
      # Slice off the last dimension of indices, then tack on the ids
      indices_columns_to_preserve = sp_ids[0].indices[:, :-1]
      new_indices = array_ops.concat([indices_columns_to_preserve] + ids, 1)
  
      new_values = sp_values.values
      new_shape = array_ops.concat([sp_ids[0].dense_shape[:-1], vocab_size], 0)
  
      result = sparse_tensor.SparseTensor(new_indices, new_values, new_shape)
      return result if already_sorted else sparse_reorder(result)
  
  
  def sparse_retain(sp_input, to_retain):
    """Retains specified non-empty values within a `SparseTensor`.
  
    For example, if `sp_input` has shape `[4, 5]` and 4 non-empty string values:
  
        [0, 1]: a
        [0, 3]: b
        [2, 0]: c
        [3, 1]: d
  
    and `to_retain = [True, False, False, True]`, then the output will
    be a `SparseTensor` of shape `[4, 5]` with 2 non-empty values:
  
        [0, 1]: a
        [3, 1]: d
  
    Args:
      sp_input: The input `SparseTensor` with `N` non-empty elements.
      to_retain: A bool vector of length `N` with `M` true values.
  
    Returns:
      A `SparseTensor` with the same shape as the input and `M` non-empty
      elements corresponding to the true positions in `to_retain`.
  
    Raises:
      TypeError: If `sp_input` is not a `SparseTensor`.
    """
    sp_input = _convert_to_sparse_tensor(sp_input)
  
    to_retain = ops.convert_to_tensor(to_retain)
  
    # Shape checking, if shape is known at graph construction time
    retain_shape = to_retain.get_shape()
    retain_shape.assert_has_rank(1)
    sp_input.values.get_shape()[0].merge_with(retain_shape[0])
  
    where_true = array_ops.reshape(array_ops.where(to_retain), [-1])
    new_indices = array_ops.gather(sp_input.indices, where_true)
    new_values = array_ops.gather(sp_input.values, where_true)
    return sparse_tensor.SparseTensor(new_indices, new_values,
                                      array_ops.identity(sp_input.dense_shape))
  
  
  def sparse_reset_shape(sp_input, new_shape=None):
    """Resets the shape of a `SparseTensor` with indices and values unchanged.
  
    If `new_shape` is None, returns a copy of `sp_input` with its shape reset
    to the tight bounding box of `sp_input`. This will be a shape consisting of
    all zeros if sp_input has no values.
  
    If `new_shape` is provided, then it must be larger or equal in all dimensions
    compared to the shape of `sp_input`. When this condition is met, the returned
    SparseTensor will have its shape reset to `new_shape` and its indices and
    values unchanged from that of `sp_input.`
  
    For example:
  
      Consider a `sp_input` with shape [2, 3, 5]:
  
        [0, 0, 1]: a
        [0, 1, 0]: b
        [0, 2, 2]: c
        [1, 0, 3]: d
  
      - It is an error to set `new_shape` as [3, 7] since this represents a
        rank-2 tensor while `sp_input` is rank-3. This is either a ValueError
        during graph construction (if both shapes are known) or an OpError during
        run time.
  
      - Setting `new_shape` as [2, 3, 6] will be fine as this shape is larger or
        equal in every dimension compared to the original shape [2, 3, 5].
  
      - On the other hand, setting new_shape as [2, 3, 4] is also an error: The
        third dimension is smaller than the original shape [2, 3, 5] (and an
        `InvalidArgumentError` will be raised).
  
      - If `new_shape` is None, the returned SparseTensor will have a shape
        [2, 3, 4], which is the tight bounding box of `sp_input`.
  
    Args:
      sp_input: The input `SparseTensor`.
      new_shape: None or a vector representing the new shape for the returned
        `SparseTensor`.
  
    Returns:
      A `SparseTensor` indices and values unchanged from `input_sp`. Its shape is
        `new_shape` if that is set. Otherwise it is the tight bounding box of
         `input_sp`
  
    Raises:
      TypeError: If `sp_input` is not a `SparseTensor`.
      ValueError: If `new_shape` represents a tensor with a different rank from
        that of `sp_input` (if shapes are known when graph is constructed).
      ValueError:  If `new_shape` is determined during graph build to have
        dimension sizes that are too small.
      OpError:
        - If `new_shape` has dimension sizes that are too small.
        - If shapes are not known during graph construction time, and during run
          time it is found out that the ranks do not match.
    """
    sp_input = _convert_to_sparse_tensor(sp_input)
  
    in_indices = array_ops.identity(sp_input.indices)
    in_values = array_ops.identity(sp_input.values)
    in_shape = array_ops.identity(sp_input.dense_shape)
  
    if new_shape is None:
      dim_low_bound = math_ops.reduce_max(in_indices, axis=0)
      output_shape_tensor = math_ops.maximum(
          array_ops.constant(0, dtype=dtypes.int64),
          math_ops.add(dim_low_bound, array_ops.ones_like(in_shape)))
    else:
      output_shape_tensor = ops.convert_to_tensor(new_shape)
      output_shape_tensor.get_shape().assert_has_rank(1)
      output_shape_tensor = math_ops.cast(output_shape_tensor, dtypes.int64)
      # For cases when shape is known during graph construction, this catches the
      # error before the sparse_tensor.SparseTensor catches it.
      output_shape_tensor.get_shape()[0].merge_with(in_shape.get_shape()[0])
  
      output_shape_tensor_const = tensor_util.constant_value(
          output_shape_tensor)
      # For cases where all shapes are known during graph construction
      if (output_shape_tensor_const is not None
          and sp_input.get_shape().is_fully_defined()):
        in_shape_const = np.array(sp_input.get_shape().as_list())
        if not np.all(in_shape_const <= output_shape_tensor_const):
          raise ValueError(
              "Requested new_shape should have dimension sizes >= sp_input.shape."
              "  Found new_shape (%s), sp_input.shape (%s)."
              % (in_shape_const, output_shape_tensor_const))
        output_shape_tensor = output_shape_tensor_const
      else:
        # For cases where shape is not known during graph construction.
        output_shape_tensor = control_flow_ops.with_dependencies(
            [check_ops.assert_equal(
                array_ops.shape(in_shape), array_ops.shape(output_shape_tensor))],
            output_shape_tensor)
        output_shape_tensor = control_flow_ops.with_dependencies(
            [check_ops.assert_less_equal(in_shape, output_shape_tensor)],
            output_shape_tensor)
  
    return sparse_tensor.SparseTensor(in_indices, in_values, output_shape_tensor)
  
  
  def sparse_fill_empty_rows(sp_input, default_value, name=None):
    """Fills empty rows in the input 2-D `SparseTensor` with a default value.
  
    This op adds entries with the specified `default_value` at index
    `[row, 0]` for any row in the input that does not already have a value.
  
    For example, suppose `sp_input` has shape `[5, 6]` and non-empty values:
  
        [0, 1]: a
        [0, 3]: b
        [2, 0]: c
        [3, 1]: d
  
    Rows 1 and 4 are empty, so the output will be of shape `[5, 6]` with values:
  
        [0, 1]: a
        [0, 3]: b
        [1, 0]: default_value
        [2, 0]: c
        [3, 1]: d
        [4, 0]: default_value
  
    Note that the input may have empty columns at the end, with no effect on
    this op.
  
    The output `SparseTensor` will be in row-major order and will have the
    same shape as the input.
  
    This op also returns an indicator vector such that
  
        empty_row_indicator[i] = True iff row i was an empty row.
  
    Args:
      sp_input: A `SparseTensor` with shape `[N, M]`.
      default_value: The value to fill for empty rows, with the same type as
        `sp_input.`
      name: A name prefix for the returned tensors (optional)
  
    Returns:
      sp_ordered_output: A `SparseTensor` with shape `[N, M]`, and with all empty
        rows filled in with `default_value`.
      empty_row_indicator: A bool vector of length `N` indicating whether each
        input row was empty.
  
    Raises:
      TypeError: If `sp_input` is not a `SparseTensor`.
    """
    sp_input = _convert_to_sparse_tensor(sp_input)
    with ops.name_scope(name, "SparseFillEmptyRows", [sp_input]):
      default_value = ops.convert_to_tensor(
          default_value, dtype=sp_input.values.dtype)
      (output_indices, output_values, empty_row_indicator,
       unused_reverse_index_map) = gen_sparse_ops._sparse_fill_empty_rows(
           indices=sp_input.indices,
           values=sp_input.values,
           dense_shape=sp_input.dense_shape,
           default_value=default_value)
      return (sparse_tensor.SparseTensor(indices=output_indices,
                                         values=output_values,
                                         dense_shape=sp_input.dense_shape),
              empty_row_indicator)
  
  
  def serialize_sparse(sp_input, name=None):
    """Serialize a `SparseTensor` into a string 3-vector (1-D `Tensor`) object.
  
    Args:
      sp_input: The input `SparseTensor`.
      name: A name prefix for the returned tensors (optional).
  
    Returns:
      A string 3-vector (1D `Tensor`), with each column representing the
      serialized `SparseTensor`'s indices, values, and shape (respectively).
  
    Raises:
      TypeError: If `sp_input` is not a `SparseTensor`.
    """
    sp_input = _convert_to_sparse_tensor(sp_input)
  
    return gen_sparse_ops._serialize_sparse(
        sp_input.indices, sp_input.values, sp_input.dense_shape, name=name)
  
  
  def serialize_many_sparse(sp_input, name=None):
    """Serialize an `N`-minibatch `SparseTensor` into an `[N, 3]` string `Tensor`.
  
    The `SparseTensor` must have rank `R` greater than 1, and the first dimension
    is treated as the minibatch dimension.  Elements of the `SparseTensor`
    must be sorted in increasing order of this first dimension.  The serialized
    `SparseTensor` objects going into each row of the output `Tensor` will have
    rank `R-1`.
  
    The minibatch size `N` is extracted from `sparse_shape[0]`.
  
    Args:
      sp_input: The input rank `R` `SparseTensor`.
      name: A name prefix for the returned tensors (optional).
  
    Returns:
      A string matrix (2-D `Tensor`) with `N` rows and `3` columns.
      Each column represents serialized `SparseTensor`'s indices, values, and
      shape (respectively).
  
    Raises:
      TypeError: If `sp_input` is not a `SparseTensor`.
    """
    sp_input = _convert_to_sparse_tensor(sp_input)
  
    return gen_sparse_ops._serialize_many_sparse(
        sp_input.indices, sp_input.values, sp_input.dense_shape, name=name)
  
  
  def deserialize_many_sparse(serialized_sparse, dtype, rank=None, name=None):
    """Deserialize and concatenate `SparseTensors` from a serialized minibatch.
  
    The input `serialized_sparse` must be a string matrix of shape `[N x 3]` where
    `N` is the minibatch size and the rows correspond to packed outputs of
    `serialize_sparse`.  The ranks of the original `SparseTensor` objects
    must all match.  When the final `SparseTensor` is created, it has rank one
    higher than the ranks of the incoming `SparseTensor` objects (they have been
    concatenated along a new row dimension).
  
    The output `SparseTensor` object's shape values for all dimensions but the
    first are the max across the input `SparseTensor` objects' shape values
    for the corresponding dimensions.  Its first shape value is `N`, the minibatch
    size.
  
    The input `SparseTensor` objects' indices are assumed ordered in
    standard lexicographic order.  If this is not the case, after this
    step run `sparse_reorder` to restore index ordering.
  
    For example, if the serialized input is a `[2, 3]` matrix representing two
    original `SparseTensor` objects:
  
        index = [ 0]
                [10]
                [20]
        values = [1, 2, 3]
        shape = [50]
  
    and
  
        index = [ 2]
                [10]
        values = [4, 5]
        shape = [30]
  
    then the final deserialized `SparseTensor` will be:
  
        index = [0  0]
                [0 10]
                [0 20]
                [1  2]
                [1 10]
        values = [1, 2, 3, 4, 5]
        shape = [2 50]
  
    Args:
      serialized_sparse: 2-D `Tensor` of type `string` of shape `[N, 3]`.
        The serialized and packed `SparseTensor` objects.
      dtype: The `dtype` of the serialized `SparseTensor` objects.
      rank: (optional) Python int, the rank of the `SparseTensor` objects.
      name: A name prefix for the returned tensors (optional)
  
    Returns:
      A `SparseTensor` representing the deserialized `SparseTensor`s,
      concatenated along the `SparseTensor`s' first dimension.
  
      All of the serialized `SparseTensor`s must have had the same rank and type.
    """
    output_indices, output_values, output_shape = (
        gen_sparse_ops._deserialize_many_sparse(
            serialized_sparse, dtype, name=name))
  
    # Feed rank data back in, if available
    output_indices.set_shape([None, rank])
    output_shape.set_shape([rank])
  
    return sparse_tensor.SparseTensor(output_indices, output_values, output_shape)
  
  
  def sparse_tensor_dense_matmul(sp_a,
                                 b,
                                 adjoint_a=False,
                                 adjoint_b=False,
                                 name=None):
    # pylint: disable=line-too-long
    """Multiply SparseTensor (of rank 2) "A" by dense matrix "B".
  
    No validity checking is performed on the indices of `A`.  However, the
    following input format is recommended for optimal behavior:
  
    * If `adjoint_a == false`: `A` should be sorted in lexicographically
      increasing order.  Use `sparse_reorder` if you're not sure.
    * If `adjoint_a == true`: `A` should be sorted in order of increasing
      dimension 1 (i.e., "column major" order instead of "row major" order).
  
    Using `tf.nn.embedding_lookup_sparse` for sparse multiplication:
  
    It's not obvious but you can consider `embedding_lookup_sparse` as another
    sparse and dense multiplication. In some situations, you may prefer to use
    `embedding_lookup_sparse` even though you're not dealing with embeddings.
  
    There are two questions to ask in the decision process: Do you need gradients
    computed as sparse too? Is your sparse data represented as two
    `SparseTensor`s: ids and values? There is more explanation about data format
    below. If you answer any of these questions as yes, consider using
    `tf.nn.embedding_lookup_sparse`.
  
    Following explains differences between the expected SparseTensors:
    For example if dense form of your sparse data has shape `[3, 5]` and values:
  
        [[  a      ]
         [b       c]
         [    d    ]]
  
  
    `SparseTensor` format expected by `sparse_tensor_dense_matmul`:
     `sp_a` (indices, values):
  
        [0, 1]: a
        [1, 0]: b
        [1, 4]: c
        [2, 2]: d
  
    `SparseTensor` format expected by `embedding_lookup_sparse`:
     `sp_ids`                 `sp_weights`
  
        [0, 0]: 1                [0, 0]: a
        [1, 0]: 0                [1, 0]: b
        [1, 1]: 4                [1, 1]: c
        [2, 0]: 2                [2, 0]: d
  
  
    Deciding when to use `sparse_tensor_dense_matmul` vs.
    `matmul`(a_is_sparse=True):
  
    There are a number of questions to ask in the decision process, including:
  
    * Will the SparseTensor `A` fit in memory if densified?
    * Is the column count of the product large (>> 1)?
    * Is the density of `A` larger than approximately 15%?
  
    If the answer to several of these questions is yes, consider
    converting the `SparseTensor` to a dense one and using `tf.matmul` with
    `a_is_sparse=True`.
  
    This operation tends to perform well when `A` is more sparse, if the column
    size of the product is small (e.g. matrix-vector multiplication), if
    `sp_a.dense_shape` takes on large values.
  
    Below is a rough speed comparison between `sparse_tensor_dense_matmul`,
    labeled 'sparse', and `matmul`(a_is_sparse=True), labeled 'dense'.  For
    purposes of the comparison, the time spent converting from a `SparseTensor` to
    a dense `Tensor` is not included, so it is overly conservative with respect to
    the time ratio.
  
    Benchmark system:
    CPU: Intel Ivybridge with HyperThreading (6 cores) dL1:32KB dL2:256KB dL3:12MB
    GPU: NVidia Tesla k40c
  
    Compiled with:
    `-c opt --config=cuda --copt=-mavx`
  
    ```
    tensorflow/python/sparse_tensor_dense_matmul_op_test --benchmarks
    A sparse [m, k] with % nonzero values between 1% and 80%
    B dense [k, n]
  
    % nnz  n   gpu   m     k     dt(dense)     dt(sparse)   dt(sparse)/dt(dense)
    0.01   1   True  100   100   0.000221166   0.00010154   0.459112
    0.01   1   True  100   1000  0.00033858    0.000109275  0.322745
    0.01   1   True  1000  100   0.000310557   9.85661e-05  0.317385
    0.01   1   True  1000  1000  0.0008721     0.000100875  0.115669
    0.01   1   False 100   100   0.000208085   0.000107603  0.51711
    0.01   1   False 100   1000  0.000327112   9.51118e-05  0.290762
    0.01   1   False 1000  100   0.000308222   0.00010345   0.335635
    0.01   1   False 1000  1000  0.000865721   0.000101397  0.117124
    0.01   10  True  100   100   0.000218522   0.000105537  0.482958
    0.01   10  True  100   1000  0.000340882   0.000111641  0.327506
    0.01   10  True  1000  100   0.000315472   0.000117376  0.372064
    0.01   10  True  1000  1000  0.000905493   0.000123263  0.136128
    0.01   10  False 100   100   0.000221529   9.82571e-05  0.44354
    0.01   10  False 100   1000  0.000330552   0.000112615  0.340687
    0.01   10  False 1000  100   0.000341277   0.000114097  0.334324
    0.01   10  False 1000  1000  0.000819944   0.000120982  0.147549
    0.01   25  True  100   100   0.000207806   0.000105977  0.509981
    0.01   25  True  100   1000  0.000322879   0.00012921   0.400181
    0.01   25  True  1000  100   0.00038262    0.00014158   0.370035
    0.01   25  True  1000  1000  0.000865438   0.000202083  0.233504
    0.01   25  False 100   100   0.000209401   0.000104696  0.499979
    0.01   25  False 100   1000  0.000321161   0.000130737  0.407076
    0.01   25  False 1000  100   0.000377012   0.000136801  0.362856
    0.01   25  False 1000  1000  0.000861125   0.00020272   0.235413
    0.2    1   True  100   100   0.000206952   9.69219e-05  0.46833
    0.2    1   True  100   1000  0.000348674   0.000147475  0.422959
    0.2    1   True  1000  100   0.000336908   0.00010122   0.300439
    0.2    1   True  1000  1000  0.001022      0.000203274  0.198898
    0.2    1   False 100   100   0.000207532   9.5412e-05   0.459746
    0.2    1   False 100   1000  0.000356127   0.000146824  0.41228
    0.2    1   False 1000  100   0.000322664   0.000100918  0.312764
    0.2    1   False 1000  1000  0.000998987   0.000203442  0.203648
    0.2    10  True  100   100   0.000211692   0.000109903  0.519165
    0.2    10  True  100   1000  0.000372819   0.000164321  0.440753
    0.2    10  True  1000  100   0.000338651   0.000144806  0.427596
    0.2    10  True  1000  1000  0.00108312    0.000758876  0.70064
    0.2    10  False 100   100   0.000215727   0.000110502  0.512231
    0.2    10  False 100   1000  0.000375419   0.0001613    0.429653
    0.2    10  False 1000  100   0.000336999   0.000145628  0.432132
    0.2    10  False 1000  1000  0.00110502    0.000762043  0.689618
    0.2    25  True  100   100   0.000218705   0.000129913  0.594009
    0.2    25  True  100   1000  0.000394794   0.00029428   0.745402
    0.2    25  True  1000  100   0.000404483   0.0002693    0.665788
    0.2    25  True  1000  1000  0.0012002     0.00194494   1.62052
    0.2    25  False 100   100   0.000221494   0.0001306    0.589632
    0.2    25  False 100   1000  0.000396436   0.000297204  0.74969
    0.2    25  False 1000  100   0.000409346   0.000270068  0.659754
    0.2    25  False 1000  1000  0.00121051    0.00193737   1.60046
    0.5    1   True  100   100   0.000214981   9.82111e-05  0.456836
    0.5    1   True  100   1000  0.000415328   0.000223073  0.537101
    0.5    1   True  1000  100   0.000358324   0.00011269   0.314492
    0.5    1   True  1000  1000  0.00137612    0.000437401  0.317851
    0.5    1   False 100   100   0.000224196   0.000101423  0.452386
    0.5    1   False 100   1000  0.000400987   0.000223286  0.556841
    0.5    1   False 1000  100   0.000368825   0.00011224   0.304318
    0.5    1   False 1000  1000  0.00136036    0.000429369  0.31563
    0.5    10  True  100   100   0.000222125   0.000112308  0.505608
    0.5    10  True  100   1000  0.000461088   0.00032357   0.701753
    0.5    10  True  1000  100   0.000394624   0.000225497  0.571422
    0.5    10  True  1000  1000  0.00158027    0.00190898   1.20801
    0.5    10  False 100   100   0.000232083   0.000114978  0.495418
    0.5    10  False 100   1000  0.000454574   0.000324632  0.714146
    0.5    10  False 1000  100   0.000379097   0.000227768  0.600817
    0.5    10  False 1000  1000  0.00160292    0.00190168   1.18638
    0.5    25  True  100   100   0.00023429    0.000151703  0.647501
    0.5    25  True  100   1000  0.000497462   0.000598873  1.20386
    0.5    25  True  1000  100   0.000460778   0.000557038  1.20891
    0.5    25  True  1000  1000  0.00170036    0.00467336   2.74845
    0.5    25  False 100   100   0.000228981   0.000155334  0.678371
    0.5    25  False 100   1000  0.000496139   0.000620789  1.25124
    0.5    25  False 1000  100   0.00045473    0.000551528  1.21287
    0.5    25  False 1000  1000  0.00171793    0.00467152   2.71927
    0.8    1   True  100   100   0.000222037   0.000105301  0.47425
    0.8    1   True  100   1000  0.000410804   0.000329327  0.801664
    0.8    1   True  1000  100   0.000349735   0.000131225  0.375212
    0.8    1   True  1000  1000  0.00139219    0.000677065  0.48633
    0.8    1   False 100   100   0.000214079   0.000107486  0.502085
    0.8    1   False 100   1000  0.000413746   0.000323244  0.781261
    0.8    1   False 1000  100   0.000348983   0.000131983  0.378193
    0.8    1   False 1000  1000  0.00136296    0.000685325  0.50282
    0.8    10  True  100   100   0.000229159   0.00011825   0.516017
    0.8    10  True  100   1000  0.000498845   0.000532618  1.0677
    0.8    10  True  1000  100   0.000383126   0.00029935   0.781336
    0.8    10  True  1000  1000  0.00162866    0.00307312   1.88689
    0.8    10  False 100   100   0.000230783   0.000124958  0.541452
    0.8    10  False 100   1000  0.000493393   0.000550654  1.11606
    0.8    10  False 1000  100   0.000377167   0.000298581  0.791642
    0.8    10  False 1000  1000  0.00165795    0.00305103   1.84024
    0.8    25  True  100   100   0.000233496   0.000175241  0.75051
    0.8    25  True  100   1000  0.00055654    0.00102658   1.84458
    0.8    25  True  1000  100   0.000463814   0.000783267  1.68875
    0.8    25  True  1000  1000  0.00186905    0.00755344   4.04132
    0.8    25  False 100   100   0.000240243   0.000175047  0.728625
    0.8    25  False 100   1000  0.000578102   0.00104499   1.80763
    0.8    25  False 1000  100   0.000485113   0.000776849  1.60138
    0.8    25  False 1000  1000  0.00211448    0.00752736   3.55992
    ```
  
    Args:
      sp_a: SparseTensor A, of rank 2.
      b: A dense Matrix with the same dtype as sp_a.
      adjoint_a: Use the adjoint of A in the matrix multiply.  If A is complex,
        this is transpose(conj(A)).  Otherwise it's transpose(A).
      adjoint_b: Use the adjoint of B in the matrix multiply.  If B is complex,
        this is transpose(conj(B)).  Otherwise it's transpose(B).
      name: A name prefix for the returned tensors (optional)
  
    Returns:
      A dense matrix (pseudo-code in dense np.matrix notation):
        `A = A.H if adjoint_a else A`
        `B = B.H if adjoint_b else B`
        `return A*B`
    """
    # pylint: enable=line-too-long
    sp_a = _convert_to_sparse_tensor(sp_a)
    with ops.name_scope(name, "SparseTensorDenseMatMul",
                        [sp_a.indices, sp_a.values, b]) as name:
      b = ops.convert_to_tensor(b, name="b")
      return gen_sparse_ops._sparse_tensor_dense_mat_mul(
          a_indices=sp_a.indices,
          a_values=sp_a.values,
          a_shape=sp_a.dense_shape,
          b=b,
          adjoint_a=adjoint_a,
          adjoint_b=adjoint_b)
  
  
  def sparse_softmax(sp_input, name=None):
    """Applies softmax to a batched N-D `SparseTensor`.
  
    The inputs represent an N-D SparseTensor with logical shape `[..., B, C]`
    (where `N >= 2`), and with indices sorted in the canonical lexicographic
    order.
  
    This op is equivalent to applying the normal `tf.nn.softmax()` to each
    innermost logical submatrix with shape `[B, C]`, but with the catch that *the
    implicitly zero elements do not participate*.  Specifically, the algorithm is
    equivalent to:
  
      (1) Applies `tf.nn.softmax()` to a densified view of each innermost
          submatrix with shape `[B, C]`, along the size-C dimension;
      (2) Masks out the original implicitly-zero locations;
      (3) Renormalizes the remaining elements.
  
    Hence, the `SparseTensor` result has exactly the same non-zero indices and
    shape.
  
    Example:
  
    ```python
    # First batch:
    # [?   e.]
    # [1.  ? ]
    # Second batch:
    # [e   ? ]
    # [e   e ]
    shape = [2, 2, 2]  # 3-D SparseTensor
    values = np.asarray([[[0., np.e], [1., 0.]], [[np.e, 0.], [np.e, np.e]]])
    indices = np.vstack(np.where(values)).astype(np.int64).T
  
    result = tf.sparse_softmax(tf.SparseTensor(indices, values, shape))
    # ...returning a 3-D SparseTensor, equivalent to:
    # [?   1.]     [1    ?]
    # [1.  ? ] and [.5  .5]
    # where ? means implicitly zero.
    ```
  
    Args:
      sp_input: N-D `SparseTensor`, where `N >= 2`.
      name: optional name of the operation.
    Returns:
      output: N-D `SparseTensor` representing the results.
    """
    with ops.name_scope(name, "SparseSoftmax",
                        [sp_input.indices, sp_input.values]) as name:
      out_vals = gen_sparse_ops.sparse_softmax(sp_input.indices, sp_input.values,
                                               sp_input.dense_shape)
      return sparse_tensor.SparseTensor(
          sp_input.indices, out_vals, sp_input.dense_shape)
  
  
  def sparse_maximum(sp_a, sp_b, name=None):
    """Returns the element-wise max of two SparseTensors.
  
    Assumes the two SparseTensors have the same shape, i.e., no broadcasting.
    Example:
  
    ```python
    sp_zero = sparse_tensor.SparseTensor([[0]], [0], [7])
    sp_one = sparse_tensor.SparseTensor([[1]], [1], [7])
    res = tf.sparse_maximum(sp_zero, sp_one).eval()
    # "res" should be equal to SparseTensor([[0], [1]], [0, 1], [7]).
    ```
  
    Args:
      sp_a: a `SparseTensor` operand whose dtype is real, and indices
        lexicographically ordered.
      sp_b: the other `SparseTensor` operand with the same requirements (and the
        same shape).
      name: optional name of the operation.
    Returns:
      output: the output SparseTensor.
    """
    with ops.name_scope(name, "SparseSparseMaximum", [sp_a.indices, sp_a.values,
                                                      sp_b.indices,
                                                      sp_b.values]) as name:
      out_indices, out_values = gen_sparse_ops.sparse_sparse_maximum(
          sp_a.indices,
          sp_a.values,
          sp_a.dense_shape,
          sp_b.indices,
          sp_b.values,
          sp_b.dense_shape,
          name=name)
    return sparse_tensor.SparseTensor(out_indices, out_values, sp_a.dense_shape)
  
  
  def sparse_minimum(sp_a, sp_b, name=None):
    """Returns the element-wise min of two SparseTensors.
  
    Assumes the two SparseTensors have the same shape, i.e., no broadcasting.
    Example:
  
    ```python
    sp_zero = sparse_tensor.SparseTensor([[0]], [0], [7])
    sp_one = sparse_tensor.SparseTensor([[1]], [1], [7])
    res = tf.sparse_minimum(sp_zero, sp_one).eval()
    # "res" should be equal to SparseTensor([[0], [1]], [0, 0], [7]).
    ```
  
    Args:
      sp_a: a `SparseTensor` operand whose dtype is real, and indices
        lexicographically ordered.
      sp_b: the other `SparseTensor` operand with the same requirements (and the
        same shape).
      name: optional name of the operation.
    Returns:
      output: the output SparseTensor.
    """
    with ops.name_scope(name, "SparseSparseMinimum", [sp_a.indices, sp_a.values,
                                                      sp_b.indices,
                                                      sp_b.values]) as name:
      out_indices, out_values = gen_sparse_ops.sparse_sparse_minimum(
          sp_a.indices,
          sp_a.values,
          sp_a.dense_shape,
          sp_b.indices,
          sp_b.values,
          sp_b.dense_shape,
          name=name)
    return sparse_tensor.SparseTensor(out_indices, out_values, sp_a.dense_shape)
  
  
  def sparse_transpose(sp_input, perm=None, name=None):
    """Transposes a `SparseTensor`
  
    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, if `sp_input` has shape `[4, 5]` and `indices` / `values`:
  
        [0, 3]: b
        [0, 1]: a
        [3, 1]: d
        [2, 0]: c
  
    then the output will be a `SparseTensor` of shape `[5, 4]` and
    `indices` / `values`:
  
        [0, 2]: c
        [1, 0]: a
        [1, 3]: d
        [3, 0]: b
  
    Args:
      sp_input: The input `SparseTensor`.
      perm: A permutation of the dimensions of `sp_input`.
      name: A name prefix for the returned tensors (optional)
    Returns:
      A transposed `SparseTensor`.
  
    Raises:
      TypeError: If `sp_input` is not a `SparseTensor`.
    """
    with ops.name_scope(name, "SparseTranspose", [sp_input]) as name:
      if perm is None:
        rank = array_ops.rank(sp_input)
        perm = (rank - 1) - math_ops.range(0, rank, 1)
      indices = sp_input.indices
      transposed_indices = array_ops.transpose(
          array_ops.gather(array_ops.transpose(indices), perm))
      dense_shape = sp_input.dense_shape
      transposed_dense_shape = array_ops.gather(dense_shape, perm)
      transposed_st = sparse_tensor.SparseTensor(
          transposed_indices, sp_input.values,
          transposed_dense_shape)
      transposed_st = sparse_reorder(transposed_st)
      return transposed_st
  
  
  def _add_sparse_to_tensors_map(sp_input, container=None,
                                 shared_name=None, name=None):
    """Add a `SparseTensor` to a `SparseTensorsMap` and return its handle.
  
    Args:
      sp_input: The input `SparseTensor`.
      container: The container for the underlying `SparseTensorsMap` (optional).
      shared_name: The shared name for the underlying `SparseTensorsMap`
        (optional, defaults to the name of the newly created op).
      name: A name prefix for the returned tensors (optional).
  
    Returns:
      A string 1-vector (1D `Tensor`), with the single element representing the
      a unique handle to a `SparseTensor` stored by the `SparseTensorMap`
      underlying this op.
  
    Raises:
      TypeError: If `sp_input` is not a `SparseTensor`.
    """
    sp_input = _convert_to_sparse_tensor(sp_input)
  
    return gen_sparse_ops._add_sparse_to_tensors_map(
        sp_input.indices, sp_input.values, sp_input.dense_shape,
        container=container, shared_name=shared_name, name=name)
  
  
  def _add_many_sparse_to_tensors_map(sp_input, container=None,
                                      shared_name=None, name=None):
    """Add a minibatch `SparseTensor` to a `SparseTensorsMap`, return `N` handles.
  
    The `SparseTensor` must have rank `R` greater than 1, and the first dimension
    is treated as the minibatch dimension.  Elements of the `SparseTensor`
    must be sorted in increasing order of this first dimension.  The serialized
    `SparseTensor` objects going into each row of the output `Tensor` will have
    rank `R-1`.
  
    The minibatch size `N` is extracted from `sparse_shape[0]`.
  
    Args:
      sp_input: The input rank `R` `SparseTensor`.
      container: The container for the underlying `SparseTensorsMap` (optional).
      shared_name: The shared name for the underlying `SparseTensorsMap`
        (optional, defaults to the name of the newly created op).
      name: A name prefix for the returned tensors (optional).
  
    Returns:
      A string matrix (2-D `Tensor`) with `N` rows and `1` column.
      Each row represents a unique handle to a `SparseTensor` stored by
      the `SparseTensorMap` underlying this op.
  
    Raises:
      TypeError: If `sp_input` is not a `SparseTensor`.
    """
    sp_input = _convert_to_sparse_tensor(sp_input)
  
    return gen_sparse_ops._add_many_sparse_to_tensors_map(
        sp_input.indices, sp_input.values, sp_input.dense_shape,
        container=container, shared_name=shared_name, name=name)
  
  
  def _take_many_sparse_from_tensors_map(
      sparse_map_op, sparse_handles, rank=None, name=None):
    """Read `SparseTensors` from a `SparseTensorsMap` and concatenate them.
  
    The input `sparse_handles` must be a string matrix of shape `[N, 1]` where
    `N` is the minibatch size and the rows correspond to packed outputs of
    `add_sparse_to_tensors_map`.  The ranks of the original `SparseTensor` objects
    must all match.  When the final `SparseTensor` is created, it has rank one
    higher than the ranks of the incoming `SparseTensor` objects (they have been
    concatenated along a new row dimension).
  
    The output `SparseTensor` object's shape values for all dimensions but the
    first are the max across the input `SparseTensor` objects' shape values
    for the corresponding dimensions.  Its first shape value is `N`, the minibatch
    size.
  
    The input `SparseTensor` objects' indices are assumed ordered in
    standard lexicographic order.  If this is not the case, after this
    step run `sparse_reorder` to restore index ordering.
  
    For example, if the serialized input is a `[2, 3]` matrix representing two
    original `SparseTensor` objects:
  
        index = [ 0]
                [10]
                [20]
        values = [1, 2, 3]
        shape = [50]
  
    and
  
        index = [ 2]
                [10]
        values = [4, 5]
        shape = [30]
  
    then the final deserialized `SparseTensor` will be:
  
        index = [0  0]
                [0 10]
                [0 20]
                [1  2]
                [1 10]
        values = [1, 2, 3, 4, 5]
        shape = [2 50]
  
    Args:
      sparse_map_op: The `Operation` that created the original handles.
        Usually this is, e.g., `add_sparse_to_tensors_map(...).op`.
      sparse_handles: 2-D `Tensor` of type `string` of shape `[N, 1]`.
        The serialized and packed `SparseTensor` objects.
      rank: (optional) Python int, the rank of the `SparseTensor` objects.
      name: A name prefix for the returned tensors (optional)
  
    Returns:
      A `SparseTensor` representing the deserialized `SparseTensor`s,
      concatenated along the `SparseTensor`s' first dimension.
  
      All of the serialized `SparseTensor`s must have had the same rank and type.
    """
    if not isinstance(sparse_map_op, ops.Operation):
      raise TypeError("sparse_map_op be an Operation")
    if sparse_map_op.type not in ("AddSparseToTensorsMap",
                                  "AddManySparseToTensorsMap"):
      raise TypeError("sparse_map_op must be one of AddSparseToTensorsMap or "
                      "AddSparseToTensorsMap. Instead, found `%s`." %
                      sparse_map_op.type)
    with ops.colocate_with(sparse_map_op):
      shared_name = sparse_map_op.get_attr("shared_name") or sparse_map_op.name
      output_indices, output_values, output_shape = (
          gen_sparse_ops._take_many_sparse_from_tensors_map(
              sparse_handles, dtype=sparse_map_op.get_attr("T"),
              container=sparse_map_op.get_attr("container"),
              shared_name=shared_name, name=name))
  
    # Feed rank data back in, if available
    output_indices.set_shape([None, rank])
    output_shape.set_shape([rank])
  
    return sparse_tensor.SparseTensor(output_indices, output_values, output_shape)
  