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/TensorFlow Guide

# 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.