View source on GitHub |

Computes the norm of vectors, matrices, and tensors.

tf.norm( tensor, ord='euclidean', axis=None, keepdims=None, name=None )

This function can compute several different vector norms (the 1-norm, the Euclidean or 2-norm, the inf-norm, and in general the p-norm for p > 0) and matrix norms (Frobenius, 1-norm, 2-norm and inf-norm).

Args | |
---|---|

`tensor` | `Tensor` of types `float32` , `float64` , `complex64` , `complex128` |

`ord` | Order of the norm. Supported values are `'fro'` , `'euclidean'` , `1` , `2` , `np.inf` and any positive real number yielding the corresponding p-norm. Default is `'euclidean'` which is equivalent to Frobenius norm if `tensor` is a matrix and equivalent to 2-norm for vectors. Some restrictions apply: a) The Frobenius norm `'fro'` is not defined for vectors, b) If axis is a 2-tuple (matrix norm), only `'euclidean'` , '`fro'` , `1` , `2` , `np.inf` are supported. See the description of `axis` on how to compute norms for a batch of vectors or matrices stored in a tensor. |

`axis` | If `axis` is `None` (the default), the input is considered a vector and a single vector norm is computed over the entire set of values in the tensor, i.e. `norm(tensor, ord=ord)` is equivalent to `norm(reshape(tensor, [-1]), ord=ord)` . If `axis` is a Python integer, the input is considered a batch of vectors, and `axis` determines the axis in `tensor` over which to compute vector norms. If `axis` is a 2-tuple of Python integers it is considered a batch of matrices and `axis` determines the axes in `tensor` over which to compute a matrix norm. Negative indices are supported. Example: If you are passing a tensor that can be either a matrix or a batch of matrices at runtime, pass `axis=[-2,-1]` instead of `axis=None` to make sure that matrix norms are computed. |

`keepdims` | If True, the axis indicated in `axis` are kept with size 1. Otherwise, the dimensions in `axis` are removed from the output shape. |

`name` | The name of the op. |

Returns | |
---|---|

`output` | A `Tensor` of the same type as tensor, containing the vector or matrix norms. If `keepdims` is True then the rank of output is equal to the rank of `tensor` . Otherwise, if `axis` is none the output is a scalar, if `axis` is an integer, the rank of `output` is one less than the rank of `tensor` , if `axis` is a 2-tuple the rank of `output` is two less than the rank of `tensor` . |

Raises | |
---|---|

`ValueError` | If `ord` or `axis` is invalid. |

Mostly equivalent to numpy.linalg.norm. Not supported: ord <= 0, 2-norm for matrices, nuclear norm. Other differences: a) If axis is `None`

, treats the flattened `tensor`

as a vector regardless of rank. b) Explicitly supports 'euclidean' norm as the default, including for higher order tensors.

© 2020 The TensorFlow Authors. All rights reserved.

Licensed under the Creative Commons Attribution License 3.0.

Code samples licensed under the Apache 2.0 License.

https://www.tensorflow.org/versions/r2.4/api_docs/python/tf/norm