**π‘ Problem Formulation:** In the context of PyTorch, a popular machine learning library in Python, there’s often a need to create an identity matrix for various operations, such as initializing weights or loss calculations. An identity matrix is a square matrix with ones on the main diagonal and zeros elsewhere. For example, if the input is the integer `3`

, the output should be a 3×3 matrix with 1’s down the diagonal and 0’s filling the rest.

## Method 1: Using `torch.eye()`

The `torch.eye()`

function is the most straightforward way to create an identity matrix in PyTorch. It simply requires the size of the matrix (since an identity matrix is square, a single integer is enough). This function returns a 2-D tensor with ones on the diagonal and zeros elsewhere.

Here’s an example:

import torch identity_matrix = torch.eye(3) print(identity_matrix)

Output:

tensor([[1., 0., 0.], [0., 1., 0.], [0., 0., 1.]])

In this code snippet, we’ve imported PyTorch and created a 3×3 identity matrix using `torch.eye()`

. This is the easiest and most commonly used method for this task.

## Method 2: Using `torch.diag()`

with `torch.ones()`

Another method involves creating a diagonal matrix from a one-dimensional tensor of ones, using the `torch.diag()`

function. This function will place the elements of the input tensor on the diagonal of the new matrix, with zeros filling the rest.

Here’s an example:

import torch ones_vector = torch.ones(3) identity_matrix = torch.diag(ones_vector) print(identity_matrix)

Output:

tensor([[1., 0., 0.], [0., 1., 0.], [0., 0., 1.]])

This snippet showcases the creation of a tensor filled with ones, which is then converted into a diagonal matrix to form an identity matrix. This method is useful when you want precise control over the diagonal values.

## Method 3: Using `torch.diag()`

Directly

PyTorch’s `torch.diag()`

function is quite flexible. When it is provided with a single argument of an integer, it will return an identity matrix of the specified size. This abstracts away the creation of the ones tensor seen in the second method.

Here’s an example:

import torch identity_matrix = torch.diag(torch.ones(3)) print(identity_matrix)

Output:

tensor([[1., 0., 0.], [0., 1., 0.], [0., 0., 1.]])

This code snippet is a shorthand version of Method 2. Instead of creating the ones tensor and then passing it to `torch.diag()`

, it does both steps in one line. This is more concise and easier to read.

## Method 4: Using `torch.eye()`

with Non-Default Data Types

Sometimes, you might need an identity matrix with a specific data type different from the default. PyTorch’s `torch.eye()`

function allows specifying the data type using the `dtype`

argument.

Here’s an example:

import torch identity_matrix = torch.eye(3, dtype=torch.int32) print(identity_matrix)

Output:

tensor([[1, 0, 0], [0, 1, 0], [0, 0, 1]], dtype=torch.int32)

This example demonstrates creating an identity matrix with integer data type using `torch.eye()`

. Choosing the right data type can be crucial depending on your computational needs.

## Bonus One-Liner Method 5: Using Advanced Indexing

Advanced indexing with PyTorch can also be used to create an identity matrix. By creating a tensor of zeros and then setting the diagonal elements to one using slicing, an identity matrix is formed.

Here’s an example:

import torch size = 3 identity_matrix = torch.zeros(size, size) identity_matrix[range(size), range(size)] = 1 print(identity_matrix)

Output:

tensor([[1., 0., 0.], [0., 1., 0.], [0., 0., 1.]])

This snippet creates a square matrix of zeros and then uses advanced indexing to fill the diagonal with ones to produce the identity matrix. This method is not as straightforward but illustrates the flexibility of tensor operations in PyTorch.

## Summary/Discussion

**Method 1:**torch.eye(). Easy and straightforward. No control over non-diagonal elements if needed.**Method 2:**torch.diag() with torch.ones(). More steps, but offers control over the diagonal values.**Method 3:**torch.diag() Direct. Short and convenient for quickly creating an identity matrix.**Method 4:**torch.eye() with Non-Default Data Types. Useful when specific tensor data types are required.**Method 5:**Advanced Indexing. Less intuitive, but shows off PyTorch’s advanced capabilities.