NumPy Magnitude in Python

1. Calculate NumPy Magnitude With the numpy.linalg.norm() Function in Python
2. Calculate NumPy Magnitude With the numpy.dot() Function in Python
3. Calculate NumPy Magnitude With the numpy.einsum() Function in Python

This tutorial will introduce the methods to calculate the magnitude of a vector in NumPy.

Calculate NumPy Magnitude With the numpy.linalg.norm() Function in Python

Suppose we have a vector in the form of a 1-dimensional NumPy array, and we want to calculate its magnitude. We can use the numpy.linalg.norm() function for this purpose. The numpy.linalg sub-module in the NumPy library contains functions related to linear algebra. The norm() function inside the numpy.linalg sub-module takes the vector as an input parameter and returns its magnitude.

import numpy as np

v = np.array([1, 1, 3, 4])

magnitude = np.linalg.norm(v)
print(magnitude)

Output:

5.196152422706632

In the above code, we calculated the magnitude of the vector v with the np.linalg.norm(v) function. We first created our vector v in the form of a 1D NumPy array with the n.array() function. We then calculated its magnitude with the np.linalg.norm(v) function and stored the output inside the magnitude variable.

Calculate NumPy Magnitude With the numpy.dot() Function in Python

We can also use the numpy.dot() function along with the numpy.sqrt() function to calculate the magnitude of a vector in NumPy. The numpy.dot() function calculates the dot-product between two different vectors, and the numpy.sqrt() function is used to calculate the square root of a particular number. We can calculate the dot-product of the vector with itself and then take the square root of the result to determine the magnitude of the vector.

import numpy as np

v = np.array([1, 1, 3, 4])

magnitude = np.sqrt(v.dot(v))
print(magnitude)

Output:

5.196152422706632

We first created our vector v in the form of a 1D NumPy array with the n.array() function. We then calculated the dot-product of the vector v with itself by v.dot(v) function and took square root of the resultant value with the np.sqrt(v.dot(v)) function. The result of the square root is the magnitude of the vector v.

Calculate NumPy Magnitude With the numpy.einsum() Function in Python

The numpy.einsum() function performs the Einstein summation convention on its operands. This method is similar to taking the dot-product of a vector with itself. We can use the numpy.einsum() function along with the numpy.sqrt() function to achieve the same goal as the previous examples. We can determine the magnitude of a vector by performing Einstein summation convention and then taking the square root of the resultant value.

import numpy as np

v = np.array([1, 1, 3, 4])

magnitude = np.sqrt(np.einsum("i,i", v, v))
print(magnitude)

Output:

5.196152422706632

We first created our vector v in the form of a 1D NumPy array with the n.array() function. We then performed the Einstein summation convention with the np.einsum('i,i',v,v) function. We then calculated the square root of the resultant value and stored the result in the magnitude variable.