Consolidate init

[ChrisRackauckas]

Fixes #353

[ai-maintainer]

AI-Maintainer Review for PR - Consolidate init

Title and Description ⚠️

Title is clear but description is missing

The title of the pull request is clear and indicates the purpose of the changes. However, the description is missing. It would be beneficial to include a detailed description explaining the motivation behind consolidating the `init` code and how the changes were tested.

Scope of Changes 👍

Changes are narrowly focused

The changes in this pull request are narrowly focused on consolidating the `init` code. There are no other changes or modifications in the diff, indicating that the author is specifically addressing the `init` code consolidation and not trying to resolve multiple issues simultaneously.

Testing ⚠️

Testing methodology is not described

The description does not provide any information about how the changes were tested. It would be beneficial for the author to include information about the testing methodology employed to ensure the correctness and functionality of the consolidated `init` code.

Code Changes 👍

No new functions, classes, or methods added

Based on the provided diff, there are no newly added functions, classes, or methods. Therefore, there are no docstrings that need to be added.

Suggested Changes

Please provide a detailed description of the changes, including the motivation behind the consolidation of the init code and the testing methodology employed. This will help reviewers understand the context and the impact of the changes.

Reviewed with AI Maintainer

[codecov]

Codecov Report

Merging #360 (f077588) into main (38e824e) will decrease coverage by 0.70%.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##             main     #360      +/-   ##
==========================================
- Coverage   73.76%   73.07%   -0.70%     
==========================================
  Files          19       19              
  Lines        1353     1348       -5     
==========================================
- Hits          998      985      -13     
- Misses        355      363       +8     

Files Changed	Coverage Δ
src/LinearSolve.jl	89.18% <ø> (-1.72%)	⬇️
src/init.jl	77.77% <100.00%> (+37.77%)	⬆️

... and 5 files with indirect coverage changes

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