# 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.

### class tf.SparseTensor

Represents a sparse tensor.

TensorFlow represents a sparse tensor as three separate dense tensors: indices, values, and shape. In Python, the three tensors are collected into a SparseTensor class for ease of use. If you have separate indices, values, and shape tensors, wrap them in a SparseTensor object before passing to the ops below.

Concretely, the sparse tensor SparseTensor(indices, values, shape) comprises the following components, where N and ndims are the number of values and number of dimensions in the SparseTensor, respectively:

• indices: A 2-D int64 tensor of shape [N, ndims], which specifies the indices of the elements in the sparse tensor that contain nonzero values (elements are zero-indexed). For example, indices=[[1,3], [2,4]] specifies that the elements with indexes of [1,3] and [2,4] have nonzero values.

• values: A 1-D tensor of any type and shape [N], which supplies the values for each element in indices. For example, given indices=[[1,3], [2,4]], the parameter values=[18, 3.6] specifies that element [1,3] of the sparse tensor has a value of 18, and element [2,4] of the tensor has a value of 3.6.

• shape: A 1-D int64 tensor of shape [ndims], which specifies the shape of the sparse tensor. Takes a list indicating the number of elements in each dimension. For example, shape=[3,6] specifies a two-dimensional 3x6 tensor, shape=[2,3,4] specifies a three-dimensional 2x3x4 tensor, and shape=[9] specifies a one-dimensional tensor with 9 elements.

The corresponding dense tensor satisfies:

dense.shape = shape
dense[tuple(indices[i])] = values[i]


By convention, indices should be sorted in row-major order (or equivalently lexicographic order on the tuples indices[i]). This is not enforced when SparseTensor objects are constructed, but most ops assume correct ordering. If the ordering of sparse tensor st is wrong, a fixed version can be obtained by calling tf.sparse_reorder(st).

Example: The sparse tensor

SparseTensor(indices=[[0, 0], [1, 2]], values=[1, 2], shape=[3, 4])


represents the dense tensor

[[1, 0, 0, 0]
[0, 0, 2, 0]
[0, 0, 0, 0]]


#### tf.SparseTensor.__init__(indices, values, shape) {:#SparseTensor.init}

Creates a SparseTensor.

##### Args:
• indices: A 2-D int64 tensor of shape [N, ndims].
• values: A 1-D tensor of any type and shape [N].
• shape: A 1-D int64 tensor of shape [ndims].
##### Returns:

A SparseTensor

#### tf.SparseTensor.indices

The indices of non-zero values in the represented dense tensor.

##### Returns:

A 2-D Tensor of int64 with shape [N, ndims], where N is the number of non-zero values in the tensor, and ndims is the rank.

#### tf.SparseTensor.values

The non-zero values in the represented dense tensor.

##### Returns:

A 1-D Tensor of any data type.

#### tf.SparseTensor.shape

A 1-D Tensor of int64 representing the shape of the dense tensor.

#### tf.SparseTensor.dtype

The DType of elements in this tensor.

#### tf.SparseTensor.op

The Operation that produces values as an output.

#### tf.SparseTensor.graph

The Graph that contains the index, value, and shape tensors.

#### tf.SparseTensor.__div__(sp_x, y) {:#SparseTensor.div}

Component-wise divides a SparseTensor by a dense Tensor.

Limitation: this Op only broadcasts the dense side to the sparse side, but not the other direction.

##### Args:
• sp_indices: A Tensor of type int64. 2-D. N x R matrix with the indices of non-empty values in a SparseTensor, possibly not in canonical ordering.
• sp_values: A Tensor. Must be one of the following types: float32, float64, int64, int32, uint8, uint16, int16, int8, complex64, complex128, qint8, quint8, qint32, half. 1-D. N non-empty values corresponding to sp_indices.
• sp_shape: A Tensor of type int64. 1-D. Shape of the input SparseTensor.
• dense: A Tensor. Must have the same type as sp_values. R-D. The dense Tensor operand.
• name: A name for the operation (optional).
##### Returns:

A Tensor. Has the same type as sp_values. 1-D. The N values that are operated on.

#### tf.SparseTensor.__mul__(sp_x, y) {:#SparseTensor.mul}

Component-wise multiplies a SparseTensor by a dense Tensor.

The output locations corresponding to the implicitly zero elements in the sparse tensor will be zero (i.e., will not take up storage space), regardless of the contents of the dense tensor (even if it's +/-INF and that INF*0 == NaN).

Limitation: this Op only broadcasts the dense side to the sparse side, but not the other direction.

##### Args:
• sp_indices: A Tensor of type int64. 2-D. N x R matrix with the indices of non-empty values in a SparseTensor, possibly not in canonical ordering.
• sp_values: A Tensor. Must be one of the following types: float32, float64, int64, int32, uint8, uint16, int16, int8, complex64, complex128, qint8, quint8, qint32, half. 1-D. N non-empty values corresponding to sp_indices.
• sp_shape: A Tensor of type int64. 1-D. Shape of the input SparseTensor.
• dense: A Tensor. Must have the same type as sp_values. R-D. The dense Tensor operand.
• name: A name for the operation (optional).
##### Returns:

A Tensor. Has the same type as sp_values. 1-D. The N values that are operated on.

#### tf.SparseTensor.__truediv__(sp_x, y) {:#SparseTensor.truediv}

Internal helper function for 'sp_t / dense_t'.

#### tf.SparseTensor.eval(feed_dict=None, session=None)

Evaluates this sparse tensor in a Session.

Calling this method will execute all preceding operations that produce the inputs needed for the operation that produces this tensor.

N.B. Before invoking SparseTensor.eval(), its graph must have been launched in a session, and either a default session must be available, or session must be specified explicitly.

##### Args:
• feed_dict: A dictionary that maps Tensor objects to feed values. See Session.run() for a description of the valid feed values.
• session: (Optional.) The Session to be used to evaluate this sparse tensor. If none, the default session will be used.
##### Returns:

A SparseTensorValue object.

### class tf.SparseTensorValue

SparseTensorValue(indices, values, shape)

#### tf.SparseTensorValue.__getnewargs__() {:#SparseTensorValue.getnewargs}

Return self as a plain tuple. Used by copy and pickle.

#### tf.SparseTensorValue.__getstate__() {:#SparseTensorValue.getstate}

Exclude the OrderedDict from pickling

#### tf.SparseTensorValue.__new__(_cls, indices, values, shape) {:#SparseTensorValue.new}

Create new instance of SparseTensorValue(indices, values, shape)

#### tf.SparseTensorValue.__repr__() {:#SparseTensorValue.repr}

Return a nicely formatted representation string

#### tf.SparseTensorValue.indices

Alias for field number 0

#### tf.SparseTensorValue.shape

Alias for field number 2

#### tf.SparseTensorValue.values

Alias for field number 1