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.

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) | `....` |

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 `TensorShape`

class.

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_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. |