# 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

TensorFlow supports a `SparseTensor` representation for data that is sparse
in multiple dimensions. Contrast this representation with `IndexedSlices`,
which is efficient for representing tensors that are sparse in their first
dimension, and dense along all other dimensions.

@@SparseTensor
@@SparseTensorValue

## Conversion

@@sparse_to_dense
@@sparse_tensor_to_dense
@@sparse_to_indicator
@@sparse_merge

## Manipulation

@@sparse_concat
@@sparse_reorder
@@sparse_reshape
@@sparse_split
@@sparse_retain
@@sparse_reset_shape
@@sparse_fill_empty_rows
@@sparse_transpose

## Reduction
@@sparse_reduce_sum
@@sparse_reduce_sum_sparse

## Math Operations
@@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 numpy as np

from tensorflow.python.framework import common_shapes
from tensorflow.python.framework import dtypes
from tensorflow.python.framework import ops
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


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, ops.SparseTensorValue):
    return ops.SparseTensor.from_value(sp_input)
  if not isinstance(sp_input, ops.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(concat_dim, sp_inputs, name=None, expand_nonconcat_dim=False):
  """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
  allowd 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 `concat_dim = 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 'concat_dim = 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:
    concat_dim: 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.

  Returns:
    A `SparseTensor` with the concatenated output.

  Raises:
    TypeError: If `sp_inputs` is not a list of `SparseTensor`.
  """
  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.shape for sp_input in sp_inputs]

  if expand_nonconcat_dim:
    max_shape = math_ops.reduce_max(array_ops.concat(0, [array_ops.reshape(
        shape, [1, -1]) for shape in shapes]), 0)
    shapes = [array_ops.concat(0, [
        max_shape[:concat_dim],
        shape[-1:] if concat_dim == -1 else shape[concat_dim:concat_dim + 1],
        [] if concat_dim == -1 else max_shape[concat_dim + 1:]
    ]) for shape in shapes]

  output_ind, output_val, output_shape = (
      gen_sparse_ops._sparse_concat(inds,
                                    vals,
                                    shapes,
                                    concat_dim,
                                    name=name))

  return ops.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 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 = (ops.SparseTensor, ops.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)
    thresh = ops.convert_to_tensor(thresh, dtype=a.values.dtype.real_dtype,
                                   name="thresh")
    output_ind, output_val, output_shape = (
        gen_sparse_ops._sparse_add(a.indices,
                                   a.values,
                                   a.shape,
                                   b.indices,
                                   b.values,
                                   b.shape,
                                   thresh))
    return ops.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.shape, b)


ops.RegisterShape("SparseAdd")(common_shapes.call_cpp_shape_fn)


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.shape, dense_t)
  return ops.SparseTensor(sp_t.indices, result, sp_t.shape)


ops.RegisterShape("SparseTensorDenseAdd")(common_shapes.call_cpp_shape_fn)
ops.RegisterShape("SparseAddGrad")(common_shapes.call_cpp_shape_fn)
ops.RegisterShape("SparseConcat")(common_shapes.call_cpp_shape_fn)


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.shape,
                                     name=name))

  return ops.SparseTensor(reordered_ind, reordered_val,
                          array_ops.identity(sp_input.shape))


ops.RegisterShape("SparseReorder")(common_shapes.call_cpp_shape_fn)


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`.
  """
  sp_input = _convert_to_sparse_tensor(sp_input)

  with ops.name_scope(name, "SparseReshape", [sp_input]) as name:
    reshaped_ind, reshaped_shape = gen_sparse_ops._sparse_reshape(
        sp_input.indices, sp_input.shape, shape, name=name)

    return ops.SparseTensor(reshaped_ind, array_ops.identity(sp_input.values),
                            reshaped_shape)


ops.RegisterShape("SparseReshape")(common_shapes.call_cpp_shape_fn)


def sparse_split(split_dim, num_split, sp_input, name=None):
  """Split a `SparseTensor` into `num_split` tensors along `split_dim`.

  If the `sp_input.shape[split_dim]` is not an integer multiple of `num_split`
  each slice starting from 0:`shape[split_dim] % num_split` gets extra one
  dimension. For example, if `split_dim = 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:
    split_dim: A 0-D `int32` `Tensor`. The dimension along which to split.
    num_split: A Python integer. The number of ways to split.
    sp_input: The `SparseTensor` to split.
    name: A name for the operation (optional).

  Returns:
    `num_split` `SparseTensor` objects resulting from splitting `value`.

  Raises:
    TypeError: If `sp_input` is not a `SparseTensor`.
  """
  sp_input = _convert_to_sparse_tensor(sp_input)

  output_inds, output_vals, output_shapes = (
      gen_sparse_ops._sparse_split(split_dim,
                                   sp_input.indices,
                                   sp_input.values,
                                   sp_input.shape,
                                   num_split,
                                   name=name))
  sparse_tensors = []
  for i in range(0, num_split):
    sparse_tensors.append(ops.SparseTensor(output_inds[i], output_vals[i],
                                           output_shapes[i]))
  return sparse_tensors


ops.RegisterShape("SparseSplit")(common_shapes.call_cpp_shape_fn)


@ops.RegisterShape("SparseToDense")
def _SparseToDenseShape(op):
  return common_shapes.call_cpp_shape_fn(op, input_tensors_needed=[1])


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_sum(sp_input, reduction_axes=None, keep_dims=False):
  """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.
    reduction_axes: The dimensions to reduce; list or scalar. If `None` (the
      default), reduces all dimensions.
    keep_dims: If true, retain reduced dimensions with length 1.

  Returns:
    The reduced Tensor.
  """
  return gen_sparse_ops.sparse_reduce_sum(sp_input.indices,
                                          sp_input.values,
                                          sp_input.shape,
                                          math_ops._ReductionDims(
                                              sp_input, reduction_axes),
                                          keep_dims)


ops.RegisterShape("SparseReduceSum")(common_shapes.call_cpp_shape_fn)


def sparse_reduce_sum_sparse(sp_input, reduction_axes=None, keep_dims=False):
  """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.
    reduction_axes: The dimensions to reduce; list or scalar. If `None` (the
      default), reduces all dimensions.
    keep_dims: If true, retain reduced dimensions with length 1.

  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.shape,
          math_ops._ReductionDims(sp_input, reduction_axes), keep_dims))

  return ops.SparseTensor(output_ind, output_val, output_shape)


ops.RegisterShape("SparseReduceSumSparse")(common_shapes.call_cpp_shape_fn)


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.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.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.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.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 = ops.SparseTensor(sp_input.indices, new_values, sp_input.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.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],
                 shape=[3, 6])
  ```

  Args:
    sp_ids: A `SparseTensor` with `values` property of type `int32`
      or `int64`.
    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)`.
    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_ids` or `sp_values` are not a `SparseTensor`.
  """
  sp_ids = _convert_to_sparse_tensor(sp_ids)
  sp_values = _convert_to_sparse_tensor(sp_values)

  with ops.name_scope(name, "SparseMerge", [sp_ids, sp_values]):
    indices_shape = array_ops.shape(sp_ids.indices)
    rank = indices_shape[1]

    ids = sp_ids.values
    if ids.dtype != dtypes.int64:
      ids = math_ops.cast(ids, dtypes.int64)

    # Slice off the last dimension of indices, then tack on the ids
    indices_columns_to_preserve = array_ops.slice(
        sp_ids.indices, [0, 0], array_ops.pack([-1, rank - 1]))
    new_indices = array_ops.concat(1, [indices_columns_to_preserve,
                                       array_ops.reshape(ids, [-1, 1])])

    new_values = sp_values.values
    new_shape = array_ops.concat(
        0,
        [array_ops.slice(sp_ids.shape, [0], array_ops.expand_dims(rank - 1, 0)),
         math_ops.cast(array_ops.pack([vocab_size]), dtypes.int64)])

    result = ops.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 ops.SparseTensor(new_indices, new_values,
                          array_ops.identity(sp_input.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`.

  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).
    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.shape)

  if new_shape is None:
    dim_low_bound = math_ops.reduce_max(in_indices, 0)
    output_shape_tensor = 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 ops.SparseTensor catches it.
    output_shape_tensor.get_shape()[0].merge_with(in_shape.get_shape()[0])

    # 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 ops.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)

    num_rows = math_ops.cast(sp_input.shape[0], dtypes.int32)
    all_row_indices = math_ops.cast(math_ops.range(num_rows), dtypes.int64)
    empty_row_indices, _ = array_ops.list_diff(all_row_indices,
                                               sp_input.indices[:, 0])
    empty_row_indicator = sparse_to_dense(
        empty_row_indices, array_ops.expand_dims(sp_input.shape[0], -1), True,
        False)

    empty_row_indices_as_column = array_ops.reshape(empty_row_indices, [-1, 1])
    additional_indices = array_ops.concat(
        1, [empty_row_indices_as_column,
            array_ops.zeros_like(empty_row_indices_as_column)])
    additional_values = array_ops.fill(
        array_ops.shape(empty_row_indices), default_value)

    all_indices_unordered = array_ops.concat(0, [sp_input.indices,
                                                 additional_indices])
    all_values_unordered = array_ops.concat(0, [sp_input.values,
                                                additional_values])
    sp_unordered_output = ops.SparseTensor(all_indices_unordered,
                                           all_values_unordered, sp_input.shape)
    sp_ordered_output = sparse_reorder(sp_unordered_output)

    return sp_ordered_output, 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.shape,
      name=name)


ops.RegisterShape("SerializeSparse")(common_shapes.call_cpp_shape_fn)


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.shape,
      name=name)


ops.RegisterShape("SerializeManySparse")(common_shapes.call_cpp_shape_fn)


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 ops.SparseTensor(output_indices, output_values, output_shape)


ops.RegisterShape("DeserializeManySparse")(common_shapes.call_cpp_shape_fn)


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).

  Deciding when to use sparse_tensor_dense_matmul vs. matmul(sp_a=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 sp_a=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.shape
  takes on large values.

  Below is a rough speed comparison between sparse_tensor_dense_matmul,
  labelled 'sparse', and matmul(sp_a=True), labelled '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      0.000141583     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.shape,
        b=b,
        adjoint_a=adjoint_a,
        adjoint_b=adjoint_b)


ops.RegisterShape("SparseTensorDenseMatMul")(common_shapes.call_cpp_shape_fn)


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.shape)
    return ops.SparseTensor(sp_input.indices, out_vals, sp_input.shape)


ops.RegisterShape("SparseSoftmax")(common_shapes.call_cpp_shape_fn)


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 = ops.SparseTensor([[0]], [0], [7])
  sp_one = ops.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.shape,
                                                                   sp_b.indices,
                                                                   sp_b.values,
                                                                   sp_b.shape,
                                                                   name=name)
  return ops.SparseTensor(out_indices, out_values, sp_a.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 = ops.SparseTensor([[0]], [0], [7])
  sp_one = ops.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.shape,
                                                                   sp_b.indices,
                                                                   sp_b.values,
                                                                   sp_b.shape,
                                                                   name=name)
  return ops.SparseTensor(out_indices, out_values, sp_a.shape)


ops.RegisterShape("SparseSparseMaximum")(common_shapes.call_cpp_shape_fn)
ops.RegisterShape("SparseSparseMinimum")(common_shapes.call_cpp_shape_fn)


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.op_scope([sp_input], name, "SparseTranspose") 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.shape
    transposed_dense_shape = array_ops.gather(dense_shape, perm)
    transposed_st = ops.SparseTensor(transposed_indices, sp_input.values, transposed_dense_shape)
    transposed_st = sparse_reorder(transposed_st)
    return transposed_st
