1.46 Tensor Ranks, Shapes, and Types
TensorFlow programs use a tensor data structure to represent all data. You can think of a TensorFlow tensor as an n-dimensional array or list. A tensor has a static type and dynamic dimensions. Only tensors may be passed between nodes in the computation graph.
Rank
In the TensorFlow system, tensors are described by a unit of dimensionality known as rank. Tensor rank is not the same as matrix rank. Tensor rank (sometimes referred to as order or degree or n-dimension) is the number of dimensions of the tensor. For example, the following tensor (defined as a Python list) has a rank of 2:
t = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
A rank two tensor is what we typically think of as a matrix, a rank one tensor is a vector. For a rank two tensor you can access any element with the syntax t[i, j]. For a rank three tensor you would need to address an element with t[i, j, k].
| Rank | Math entity | Python example |
|---|---|---|
| 0 | Scalar (magnitude only) | s = 483 |
| 1 | Vector (magnitude and direction) | v = [1.1, 2.2, 3.3] |
| 2 | Matrix (table of numbers) | m = [[1, 2, 3], [4, 5, 6], [7, 8, 9]] |
| 3 | 3-Tensor (cube of numbers) | t = [[[2], [4], [6]], [[8], [10], [12]], [[14], [16], [18]]] |
| n | n-Tensor (you get the idea) | .... |
Shape
The TensorFlow documentation uses three notational conventions to describe tensor dimensionality: rank, shape, and dimension number. The following table shows how these relate to one another:
| Rank | Shape | Dimension number | Example |
|---|---|---|---|
| 0 | [] | 0-D | A 0-D tensor. A scalar. |
| 1 | [D0] | 1-D | A 1-D tensor with shape [5]. |
| 2 | [D0, D1] | 2-D | A 2-D tensor with shape [3, 4]. |
| 3 | [D0, D1, D2] | 3-D | A 3-D tensor with shape [1, 4, 3]. |
| n | [D0, D1, ... Dn-1] | n-D | A tensor with shape [D0, D1, ... Dn-1]. |
Shapes can be represented via Python lists / tuples of ints, or with the @{tf.TensorShape}.
Data types
In addition to dimensionality, Tensors have a data type. You can assign any one of the following data types to a tensor:
| Data type | Python type | Description |
|---|---|---|
DT_FLOAT | tf.float32 | 32 bits floating point. |
DT_DOUBLE | tf.float64 | 64 bits floating point. |
DT_INT8 | tf.int8 | 8 bits signed integer. |
DT_INT16 | tf.int16 | 16 bits signed integer. |
DT_INT32 | tf.int32 | 32 bits signed integer. |
DT_INT64 | tf.int64 | 64 bits signed integer. |
DT_UINT8 | tf.uint8 | 8 bits unsigned integer. |
DT_UINT16 | tf.uint16 | 16 bits unsigned integer. |
DT_STRING | tf.string | Variable length byte arrays. Each element of a Tensor is a byte array. |
DT_BOOL | tf.bool | Boolean. |
DT_COMPLEX64 | tf.complex64 | Complex number made of two 32 bits floating points: real and imaginary parts. |
DT_COMPLEX128 | tf.complex128 | Complex number made of two 64 bits floating points: real and imaginary parts. |
DT_QINT8 | tf.qint8 | 8 bits signed integer used in quantized Ops. |
DT_QINT32 | tf.qint32 | 32 bits signed integer used in quantized Ops. |
DT_QUINT8 | tf.quint8 | 8 bits unsigned integer used in quantized Ops. |