Norm of a One-Dimensional Tensor in Python Libraries

# Install the prerequisites for you to run the notebook
!pip install numpy
!pip install scipy
%pip install torch
!pip install tensorflow

# Define a single dimensional (1D) tensor 
import numpy as np

vector1 = np.array([3,7]) #np.random.randint(1,5,2)
vector2 = np.array([5,2]) #np.random.randint(1,5,2)
print("Vector 1:",vector1)
print("Vector 2:",vector2)
print(f"shape & size of Vector1 & Vector2:", vector1.shape, vector1.size)

Vector 1: [3 7]
Vector 2: [5 2]
shape & size of Vector1 & Vector2: (2,) 2

# Draw the vectors using MatplotLib
import matplotlib.pyplot as plt
%matplotlib inline

origin = np.array([0,0])
plt.quiver(*origin, vector1[0],vector1[1], angles='xy', color='r', scale_units='xy', scale=1)
plt.quiver(*origin, vector2[0],vector2[1], angles='xy', color='b', scale_units='xy', scale=1)
plt.plot([vector1[0],vector2[0]], [vector1[1],vector2[1]], 'go', linestyle="--")
plt.title('Vector Representation') 

plt.xlim([0,10])
plt.ylim([0,10])

plt.grid() 
plt.show()

# L2 (Euclidean) norm of a vector
# NumPy
norm1 = np.linalg.norm(vector1, ord=2)
print("The magnitude / distance from the origin",norm1)

norm2 = np.linalg.norm(vector2, ord=2)
print("The magnitude / distance from the origin",norm2)

The magnitude / distance from the origin 7.615773105863909
The magnitude / distance from the origin 5.385164807134504

# SciPy
import scipy 
norm_vector1 = scipy.linalg.norm(vector1, ord=2)
print("L2 norm in scipy for vector1:", norm_vector1)

norm_vector2 = scipy.linalg.norm(vector2, ord=2)
print("L2 norm in scipy for vector2:", norm_vector2)

L2 norm in scipy for vector1: 7.615773105863909
L2 norm in scipy for vector2: 5.385164807134504

# Sklearn
from sklearn.metrics.pairwise import euclidean_distances
vector1_reshape = vector1.reshape(1,-1)
## Scikit-learn expects the vector to be 2-Dimensional
euclidean_distances(vector1_reshape, [[0, 0]])[0,0]

7.615773105863909

# TensorFlow
import os
os.environ['TF_CPP_MIN_LOG_LEVEL'] = '1' 

import tensorflow as tf
print("TensorFlow version:", tf.__version__)

## Tensorflow expects Tensor of types float32, float64, complex64, complex128
vector1_tf = vector1.astype(np.float64)
tf_norm = tf.norm(vector1_tf, ord=2)
print("Euclidean(l2) norm in TensorFlow:",tf_norm.numpy())

TensorFlow version: 2.15.0
Euclidean(l2) norm in TensorFlow: 7.615773105863909

# PyTorch
import torch
print("PyTorch version:", torch.__version__)

norm_torch = torch.linalg.norm(torch.from_numpy(vector1_tf), ord=2)
norm_torch.item()

PyTorch version: 2.1.2

7.615773105863909

# Euclidean distance between the vectors
import math
vector_diff = vector1 - vector2

# Using norm
euclidean_distance = np.linalg.norm(vector_diff, ord=2)
print(euclidean_distance)

# Using dot product
norm_dot = math.sqrt(np.dot(vector_diff.T,vector_diff))
print(norm_dot)

5.385164807134504
5.385164807134504

# SciPy
from scipy.spatial import distance
distance.euclidean(vector1,vector2)