Understanding PyTorch: Tensors, Vectors, and Matrices

Understanding PyTorch: Tensors, Vectors, and Matrices

By: Bindeshwar Singh Kushwaha
Institute: PostNetwork Academy

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What is PyTorch?

• PyTorch is an open-source deep learning framework.
• It supports dynamic computation graphs.
• Designed to be Pythonic and flexible.
• Commonly used for research and production in AI/ML.

Types of Tensors

• A scalar is a 0-dimensional tensor.
• A vector is a 1-dimensional tensor.
• A matrix is a 2-dimensional tensor.
• Tensors can be of higher dimensions (3D, 4D, …).

import torch
s = torch.tensor(5)                       # Scalar
v = torch.tensor([1.0, 2.0, 3.0])         # Vector
m = torch.tensor([[1, 2], [3, 4]])        # Matrix
print("Scalar:", s)
print("Vector:", v)
print("Matrix:", m)

Creating Tensors

Use torch.tensor(), torch.zeros(), torch.ones(), etc.

You can specify shape, data type, and device.

import torch
a = torch.tensor([1, 2, 3])
b = torch.zeros((2, 3))
c = torch.ones((3, 3), dtype=torch.float32)
print(a)
print(b)
print(c)

Tensor Properties

• .shape: shape of the tensor
• .dtype: data type
• .device: location (CPU or GPU)

import torch
x = torch.tensor([[1, 2, 3], [4, 5, 6]])
print(x.shape)   # torch.Size([2, 3])
print(x.dtype)   # torch.int64
print(x.device)  # cpu

Arithmetic Operations

• Element-wise operations: +, -, *, /
• Matrix multiplication: torch.mm() or @

import torch
a = torch.tensor([[1, 2], [3, 4]])
b = torch.tensor([[5, 6], [7, 8]])
print(a + b)          # Addition
print(a * b)          # Element-wise multiplication
print(torch.mm(a, b)) # Matrix multiplication

Using GPU

• Use .to('cuda') or .cuda() to move tensor to GPU.
• Check for GPU with torch.cuda.is_available().
• CUDA = Compute Unified Device Architecture (by NVIDIA)
• Allows general-purpose GPU computing (not just graphics)

import torch
if torch.cuda.is_available():
  x = torch.tensor([1.0, 2.0])
  x = x.to('cuda')
  print(x.device)  # Should print "cuda:0"

Automatic Differentiation (Autograd)

• PyTorch tracks operations with requires_grad=True
• Use .backward() to compute gradients

import torch
x = torch.tensor(2.0, requires_grad=True)
y = x**3 + 2*x**2 + 3*x + 1
y.backward()
print(x.grad)  # dy/dx = 3x² + 4x + 3 = 23 when x = 2

As a formula: $$ \\frac{dy}{dx} = 3x^2 + 4x + 3 $$

PDF

intropytorch

Video

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