# NumPy Magnitude in Python

Muhammad Maisam Abbas Jan 30, 2023

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.

Maisam is a highly skilled and motivated Data Scientist. He has over 4 years of experience with Python programming language. He loves solving complex problems and sharing his results on the internet.

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