Docs: V0.2-tutorials/least square example

[Tuna2222]

Description

Docs:

• Add the "Tutorials" section. The "Tutorials" section is designed to show users how to use RLinearAlgebra.jl to solve typical linear algebra problems.
  • Add tutorials/introduction.md
  • Add a least squares example to the tutorials/getting_started.md.
• Add "checklist.md" subsection to the dev docs.
  • Add checklist for Compressors and Loggers in dev/checklists
• Add 3 subsections to dev docs contributing.md, design.md, and style_guide.md.
• Add custom_html.css to format the HTML block in the documents.

Fix: Some spellings and CI's inconsistencies.

Motivation and Context

Refer to the JuMP.jl Tutorials section.

How has this been tested

First, download the RLinearAlgebra.jl to your local Julia environment.
Then, open Julia in the folder of RLinearAlgebra.jl, and use the following codes to see the document:

] activate docs/
using LiveServer
servedocs()

Types of changes

• CI
• Docs
• Feature
• Fix
• Performance
• Refactor
• Style
• Test
• Other (use sparingly):

Checklists:

Code and Comments
If this PR includes modification to the code base, please select all that apply.

• My code follows the code style of this project.
• I have updated all package dependencies (if any).
• I have included all relevant files to realize the functionality of the PR.
• I have exported relevant functionality (if any).

API Documentation

• For every exported function (if any), I have included a detailed docstring.
• I have checked the spelling and grammar of all docstring updates through an external tool.
• I have checked that the docstring's function signature is correctly formatted and has all arguments.
• I have checked that the docstring's list of arguments, fields, or return values match the function.
• I have compiled the docs locally and read through all docstring updates to check for errors.

Manual Documentation

• I have checked the spelling and grammar of all manual updates through an external tool.
• Any code included in the docstring is tested using doc tests to ensure consistency.
• I have compiled the docs locally and read through all manual updates to check for errors.

Testing

• I have added unit tests to cover my changes. (For Macros, be sure to check
  @code_lowered and
  @code_typed)
• All new and existing tests passed.
• I have achieved sufficient code coverage.

[Copilot]

Pull Request Overview

This PR adds a "Tutorials" section to the documentation, specifically including a least squares example that demonstrates how to use the RLinearAlgebra.jl package's SparseSign compression method. The purpose is to provide hands-on examples for new users to quickly understand the package usage.

• Adds a complete tutorials framework with introduction and getting started guides
• Creates a comprehensive least squares solving example using SparseSign compression
• Adds development documentation including style guides, contributing guidelines, and checklists

Reviewed Changes

Copilot reviewed 22 out of 22 changed files in this pull request and generated 6 comments.

Show a summary per file

File	Description
src/Compressors/sparse_sign.jl	Fixes typo in documentation comment
readme.md	Comments out Aqua QA badge
docs/src/tutorials/	Adds new tutorial section with introduction and getting started guide
docs/src/manual/introduction.md	Adds comprehensive manual introduction to randomized linear algebra
docs/src/dev/	Adds development documentation including style guide, design docs, and contributing checklists
docs/make.jl	Updates documentation structure and deployment configuration
.github/workflows/	Adds new CI/CD workflows for automated version management and documentation

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[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.

📢 Thoughts on this report? Let us know!

[vp314]

I think removing Dev Docs from this PR and splitting up the tutorials into increasingly more customized pieces would be a better approach.

[vp314]

Suggested change

	new users quickly get hands on the usage of `RLinearAlgebra.jl`.
	new users quickly get hands experience using `RLinearAlgebra.jl`.

[vp314]

Suggested change

	- Least squre problem, solving $$\min_{x} \|Ax - b\|_2^2$$
	- Least squares problem, solving $$\min_{x} \|Ax - b\|_2^2$$

[vp314]

Should be "main"

[vp314]

Suggested change

	"Least square" => "tutorials/least_square.md"
	"Least squares" => "tutorials/least_square.md"

[vp314]

Change filename to "least_squares.md"

[vp314]

Since we are looking at a consistent linear system in this example, I think we should not present the least squares formulation.

[vp314]

I would remove this. The previous sentence explains things well.

[vp314]

I think you do not need Random

[vp314]

Be sure to respect the 92 character limit even in markdown files.

[vp314]

Maybe split up the tutorials into pieces