Return the Norm of the vector over given axis in Linear Algebra using NumPy in Python
In this article, we will how to return the Norm of the vector over a given axis in Linear Algebra in Python.
numpy.linalg.norm() method
The numpy.linalg.norm() method is used to return the Norm of the vector over a given axis in Linear algebra in Python. Depending on the value of the ord parameter, this function can return one of the possible matrix norms or one of an unlimited number of vector norms. The Euclidean distance of a vector from the origin, A norm known as the Euclidean norm, or 2-norm, which can also be defined as the square root of the inner product of a vector with itself. axis =0 is used to find the norm along the rows and axis =1 is used to find the norm along with the columns. Below is the syntax of linalg.norm, In this the first parameter should be a 1-D or 2-D array whereas ord is the order of the norm and the axis computes the vector norms along with the axis:
Syntax: numpy.linalg.norm(x, ord, axis):
Parameters:
- x: array of inputs Unless ord is None, x must be 1-D or 2-D if axis is None. The 2-norm of x.ravel will be returned if both axis and ord are None.
- ord: non-zero int, inf, -inf, ‘fro’, ‘nuc’. (optional )
- axis: {None, int, 2-tuple of ints}.If axis is an integer, it indicates the x-axis along which the vector norms should be computed. (optional )
Returns: float or ndarray. Norm of the matrix or vector is returned.
Example 1:
Here, the packages are imported and np.arrange() method is used to create an array. The .shape attribute finds the shape of the array, the .ndim attribute finds the dimension of the array, and the data type of the array is the .dtype attribute. np.linalg.norm() method is used to return the Norm of the vector according to the axis given. axis=0 represents that we’re finding the norm of the vector along rows.
Python3
import numpy.linalg as l
import numpy as np
array = np.arange( 12 )
print (array)
print ( "Shape of the array is : " , array.shape)
print ( "The dimension of the array is : " , array.ndim)
print ( "Datatype of our Array is : " , array.dtype)
print (l.norm(array, axis = 0 ))
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Output:
[ 0 1 2 3 4 5 6 7 8 9 10 11]
Shape of the array is : (12,)
The dimension of the array is : 1
Datatype of our Array is : int64
22.494443758403985
Example 2:
In this example, the input is a matrix and the norm of the matrix is found, by specifying axis =1. It represents along with columns.
Python3
import numpy.linalg as l
import numpy as np
array = np.arange( 12 ).reshape(( 3 , 4 ))
print (array)
print ( "Shape of the array is : " , array.shape)
print ( "The dimension of the array is : " , array.ndim)
print ( "Datatype of our Array is : " , array.dtype)
print (l.norm(array, axis = 1 ))
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Output:
[[ 0 1 2 3]
[ 4 5 6 7]
[ 8 9 10 11]]
Shape of the array is : (3, 4)
The dimension of the array is : 2
Datatype of our Array is : int64
[ 3.74165739 11.22497216 19.13112647]
Last Updated :
05 Jun, 2022
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