Python NumPy numpy.linalg.norm() Function

Syntax of
numpy.linalg.norm()

Example Codes:
numpy.linalg.norm()

Example Codes:
numpy.linalg.norm()
to Find the Norm of a TwoDimensional Array 
Example Codes:
numpy.linalg.norm()
to Find the Vector Norm and Matrix Norm Usingaxis
Parameter 
Example Codes:
numpy.linalg.norm()
to Useord
Parameter
Python NumPy numpy.linalg.norm()
function finds the value of the matrix norm or the vector norm. The parameter ord
decides whether the function will find the matrix norm or the vector norm. It has several defined values.
Syntax of numpy.linalg.norm()
numpy.linalg.norm(x,
ord= None,
axis= None,
keepdims= False)
Parameters
x 
It is an array like structure. It is the input array used for finding the value of the norm. The default value for the axis parameter is None so, the array should be onedimensional or twodimensional provided ord is None . 
ord 
The returned value of the function depends on this parameter. It defines the order of the norm. It has several values, check here. 
axis 
It is an integer , None or 2tuple of integers. If it is an integer then it represents the axis along which the function will find the vector norm. Its default value is None which means that the function will find either matrix norm or vector norm. If it is a 2tuple integer value then the function will return the value of matrix norm. 
keepdims 
It is a Boolean parameter. Its default value is False . If its value is True then it shows the dimensions of the normed axis with the size equal to one. 
Return
It returns the norm of the matrix or a vector in the form of a float
value or an Ndimensional array
.
Example Codes: numpy.linalg.norm()
We will use this function to find the norm of a onedimensional array
.
from numpy import linalg as la
import numpy as np
x = np.array([89, 34, 56, 87, 90, 23, 45, 12, 65, 78, 9, 34, 12, 11, 2, 65, 78, 82, 28, 78])
norm = la.norm(x)
print('The value of norm is:')
print(norm)
Output:
The value of norm is:
257.4800963181426
It has returned a float
value which is the value of norm.
Example Codes: numpy.linalg.norm()
to Find the Norm of a TwoDimensional Array
We will pass a twodimensional array
now.
from numpy import linalg as la
import numpy as np
x = np.array([[11, 12, 5], [15, 6,10], [10, 8, 12], [12,15,8], [34, 78, 90]])
norm = la.norm(x)
print('The value of norm is:')
print(norm)
Output:
The value of norm is:
129.35223229616102
If we set the ord
parameter to any other value than None
and pass an array
that is neither onedimensional nor twodimensional, the function will generate a ValueError
as the axis
parameter is None
.
from numpy import linalg as la
import numpy as np
x = np.array([[[4, 2], [6, 4]], [[5, 8], [7, 3]]])
norm = la.norm(x,'nuc')
print('The value of norm is:')
print(norm)
Output:
Traceback (most recent call last):
File "C:\Test\test.py", line 6, in <module>
norm = la.norm(x,'nuc')
File "<__array_function__ internals>", line 5, in norm
File "D:\WinPython\WPy643820\python3.8.2.amd64\lib\sitepackages\numpy\linalg\linalg.py", line 2557, in norm
raise ValueError("Improper number of dimensions to norm.")
ValueError: Improper number of dimensions to norm.
Example Codes: numpy.linalg.norm()
to Find the Vector Norm and Matrix Norm Using axis
Parameter
We will find the vector norm first.
from numpy import linalg as la
import numpy as np
x = np.array([[11, 12, 5], [15, 6,10], [10, 8, 12], [12,15,8], [34, 78, 90]])
norm = la.norm(x,axis= 0)
print('The vector norm is:')
print(norm)
Output:
The vector norm is:
[41.78516483 80.95060222 91.83136719]
Note that the function has returned an Ndimensional array
as the computed vector norm.
Now, we will compute the matrix norm. We will pass the axis
parameter as the 2tuple
of integer value.
from numpy import linalg as la
import numpy as np
x = np.array([[11, 12, 5], [15, 6,10], [10, 8, 12], [12,15,8], [34, 78, 90]])
norm = la.norm(x,axis= (0,1))
print('The value of matrix norm is:')
print(norm)
Output:
The value of matrix norm is:
129.35223229616102
Example Codes: numpy.linalg.norm()
to Use ord
Parameter
The parameter ord
has several values.
from numpy import linalg as la
import numpy as np
x = np.array([[11, 12, 5], [15, 6,10], [10, 8, 12], [12,15,8], [34, 78, 90]])
norm = la.norm(x,'fro')
print('The value of matrix norm is:')
print(norm)
Output:
The value of matrix norm is:
129.35223229616102
The function has generated the value of Frobenius
matrix norm.
from numpy import linalg as la
import numpy as np
x = np.array([[11, 12, 5], [15, 6,10], [10, 8, 12], [12,15,8], [34, 78, 90]])
norm = la.norm(x,'nuuc')
print('The value of matrix norm is:')
print(norm)
Output:
The value of matrix norm is:
152.28781231351272
The function has generated nuclear matrix norm. It is the sum of the singular values.