Understanding the Dot Product

The dot product is a way to combine two lists of numbers (vectors) to get a single number. Think of it like a weighted sum:

1. You take each corresponding pair of numbers from the two lists.
2. Multiply them together.
3. Add up all those multiplied values.

For example, if you have two lists:

• a = (2, 3, 4)
• b = (1, 5, 2)

You multiply:

2 * 1, 3 * 5, 4 * 2

Then add the results:

2 + 15 + 8 = 25

So, the dot product of these two lists is 25.

This operation is useful in physics (finding work done by a force), computer graphics, and machine learning (measuring similarity between things). 🚀

🚀 Dot Product using NumPy

NumPy provides multiple ways to compute the dot product.

import numpy as np

# Define two 1D vectors
a = np.array([1, 2, 3])
b = np.array([4, 5, 6])

# Method 1: Using np.dot()
dot_product_1 = np.dot(a, b)

# Method 2: Using @ operator (Python 3.5+)
dot_product_2 = a @ b

# Method 3: Using np.sum()
dot_product_3 = np.sum(a * b)

print("NumPy Dot Product Results:")
print(dot_product_1)  # 1*4 + 2*5 + 3*6 = 32
print(dot_product_2)  # 32
print(dot_product_3)  # 32

🔥 Dot Product using PyTorch

In PyTorch, tensors are used instead of NumPy arrays. Similar methods exist for computing the dot product.

import torch

# Define two 1D tensors
a = torch.tensor([1, 2, 3], dtype=torch.float32)
b = torch.tensor([4, 5, 6], dtype=torch.float32)

# Method 1: Using torch.dot()
dot_product_1 = torch.dot(a, b)

# Method 2: Using @ operator
dot_product_2 = a @ b

# Method 3: Using element-wise multiplication and sum()
dot_product_3 = torch.sum(a * b)

print("PyTorch Dot Product Results:")
print(dot_product_1.item())  # Convert to Python scalar, output: 32.0
print(dot_product_2.item())  # 32.0
print(dot_product_3.item())  # 32.0

🔎 Key Differences Between NumPy and PyTorch

🎯 When to Use Which?

• Use NumPy when working with traditional numerical computations, statistics, or scientific computing.
• Use PyTorch when working with deep learning and GPU acceleration.