In this tutorial, we will introduce how to use numpy.linalg.norm() in python. It can allow us to calculate matrix or vector norm easily.
numpy.linalg.norm()
It is defined as:
linalg.norm(x, ord=None, axis=None, keepdims=False)[source]
It will calculate matrix or vector norm of x array.
As to ord parameter, it can be:
| ord | norm for matrices | norm for vectors |
|---|---|---|
| None | Frobenius norm | 2-norm |
| ‘fro’ | Frobenius norm | – |
| ‘nuc’ | nuclear norm | – |
| inf | max(sum(abs(x), axis=1)) | max(abs(x)) |
| -inf | min(sum(abs(x), axis=1)) | min(abs(x)) |
| 0 | – | sum(x != 0) |
| 1 | max(sum(abs(x), axis=0)) | as below |
| -1 | min(sum(abs(x), axis=0)) | as below |
| 2 | 2-norm (largest sing. value) | as below |
| -2 | smallest singular value | as below |
| other | – | sum(abs(x)**ord)**(1./ord) |
In order to understand Frobenius Norm, you can read:
Understand Frobenius Norm: A Beginner Guide – Deep Learning Tutorial
How to use numpy.linalg.norm()?
Here we will use some examples to show you how to use this function.
Example 1:
import numpy as np x = np.random.random((2,3)) print(x) y = np.linalg.norm(x, ord = np.inf) print(y)
Here x is a matrix and ord = np.inf, which mean we will get max(sum(abs(x), axis=1))
Run this code, we will get:
[[0.01452971 0.3832144 0.17549253] [0.64189317 0.93303077 0.98318939]] 2.5581133288856686
Example 2:
x2 = np.random.random((3,)) print(x2) y = np.linalg.norm(x2, ord = np.inf) print(y)
Here x2 is the vector and ord = np.inf, which means we will calculate max(abs(x))
Run this code, we will get:
[0.28094103 0.703004 0.13909213] 0.7030039972017319
Example 3: calculate L2 norm
in order to calculate frobenius norm or l2-norm, we can set ord = None.
For example:
import numpy as np x = np.random.random((2,3)) print(x) y = np.linalg.norm(x) print(y) y = np.linalg.norm(x, axis= 1) print(y)
Run this code, we will see:
[[0.71908539 0.46834462 0.86676793] [0.77600852 0.12518566 0.4155249 ]] 1.5093835600025909 [1.2197201 0.88911282]