NumPy functions for dot product and cosine similarity

 To calculate dot products and cosine similarity in NumPy, you primarily use np.dot() and np.linalg.norm(). While NumPy has a direct function for the dot product, cosine similarity is typically calculated by combining several operations. 

1. Dot Product

The dot product of two vectors is the sum of the products of their corresponding elements. 

• np.dot(a, b): The standard function for computing the dot product.
• a @ b: A more modern and readable operator for matrix multiplication and dot products introduced in Python 3.5.
• np.inner(a, b): Computes the inner product, which for 1D arrays is identical to the dot product. 

2. Cosine Similarity

NumPy does not have a single "cosine_similarity" function, so you must implement the formula:
similarity  = A(dot)B/Magnitude(A).Magnitude(B)

You can implement this using:

• np.dot(): For the numerator (A.B)
• np.linalg.norm(): For the denominator magnitudes Magnitude(A).Magnitude(B)

Example Implementation:

python

import numpy as np
from numpy.linalg import norm

def cosine_similarity(a, b):
    return np.dot(a, b) / (norm(a) * norm(b))

Quick Comparison

Metric	NumPy Function(s)	Result Range
Dot Product	np.dot(a, b) or a @ b	-infinity to +infinity
Cosine Similarity	np.dot(a, b) / (norm(a) * norm(b))	-1 to 1

Note: For a direct, single-function implementation, many developers use the Scikit-learn cosine_similarity function or SciPy's spatial.distance.cosine (which returns cosine distance, or 1 - similarity)