Manual: Linear Systems

[nathanielpritchard]

Description

This provides documentation of linear systems solvers. It provides a brief overview of the types of problems that can be solved with the rsolve function, a brief description of all the possible sub-structures used in a Solver structure, and an example of how to use the kaczmarz solver with these sub-structures.

Motivation and Context

There was no documentation detailing how to actually use Solvers in RLinearAlgebra, this provides the description.

How has this been tested

I have compiled, read through 3 times, tested the examples, and read it backwards to check for spelling mistakes.

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

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  @code_lowered and
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• All new and existing tests passed.
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[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.

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