[doc] Detailed docstring for functions in linalg module

[Routhleck]

closes: #24

This pull request introduces updates to the saiunit library's linear algebra functions to enhance support for handling quantities with units. The changes include modifying function signatures, return types, and examples to reflect the use of Quantity objects, as well as improving consistency in documentation and examples.

Updates to Linear Algebra Functions for Quantity Support

General Updates:

• Updated function descriptions and argument types to reflect the use of Quantity objects instead of raw arrays. This change applies to the following functions: cholesky, solve, tensorsolve, lstsq, inv, pinv, tensorinv, norm, matrix_norm, and vector_norm. [1] [2] [3] [4] [5] [6] [7] [8] [9]

Documentation and Examples:

• Enhanced examples with the inclusion of saiunit imports and usage of Quantity objects, showcasing unit-aware computations. Examples now demonstrate the correct handling of units in operations like Cholesky decomposition, solving linear systems, and computing norms. [1] [2] [3] [4] [5]

Function-Specific Changes:

1. eigh Function:

   • Fixed the order of returned values to align with the expected (eigenvectors, eigenvalues) format.

2. Norm Functions (norm, matrix_norm, vector_norm):

   • Updated return types to Quantity and adjusted examples to reflect unit-aware outputs. [1] [2] [3]

These updates ensure that the library is consistent in its handling of quantities with units, improving usability and correctness for scientific and engineering applications.

Summary by Sourcery

Update linear algebra module documentation and examples to consistently use and demonstrate unit-aware Quantity objects, improving clarity and correctness for scientific applications.

Enhancements:

• Revise function docstrings in linalg modules to reflect Quantity-based arguments and return types instead of raw arrays.
• Update and expand examples to use saiunit imports and unit-aware computations throughout the documentation.
• Correct the order of returned values in the eigh function to match expected output.

Documentation:

• Enhance user-facing documentation for all major linear algebra functions to illustrate unit handling and provide clearer, unit-aware examples.

[sourcery-ai]

Reviewer's Guide

This pull request refactors and enhances the documentation for all linear algebra functions in the saiunit library to consistently support and demonstrate unit-aware computations using Quantity objects, updates function signatures and return types, and improves example code to reflect these changes. It also fixes the return value order for the eigh function and ensures all docstrings and examples are consistent with the new unit-handling paradigm.

File-Level Changes

Change	Details	Files
Refactored all linalg function docstrings and examples to use Quantity objects and unit-aware computations.	Updated function argument and return type descriptions from raw arrays to Quantity objects. Rewrote all examples to import saiunit and use Quantity objects, demonstrating unit-aware results. Clarified and standardized function descriptions to reflect SaiUnit implementations.	saiunit/linalg/_linalg_keep_unit.py saiunit/linalg/_linalg_change_unit.py saiunit/linalg/_linalg_remove_unit.py
Fixed the order of return values for the eigh function to match the expected (eigenvectors, eigenvalues) format.	Swapped the order of eigenvectors and eigenvalues in the return statement for eigh. Updated docstrings and examples to match the corrected return order.	saiunit/lax/_lax_linalg.py
Updated norm, matrix_norm, and vector_norm functions to return Quantity objects and updated their examples accordingly.	Changed return type documentation from array to Quantity. Modified examples to show unit-aware outputs for norm computations.	saiunit/linalg/_linalg_keep_unit.py

Possibly linked issues

• [doc] Detailed docstring for functions in linalg module #24: PR adds detailed docstrings and examples for linalg functions, addressing issue 24
• [doc] Detailed docstring for functions in linalg module #24: PR updates docstrings and examples for linalg functions to include quantity support, directly addressing the issue.

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[sourcery-ai]

Hey @Routhleck - I've reviewed your changes - here's some feedback:

• The implementation of eig and eigh now returns (eigenvectors, eigenvalues) instead of the more common (eigenvalues, eigenvectors) order; consider clarifying this in the docstrings to avoid confusion for users.
• In the docstring for eigvalsh, the comment '# TODO: Seems wrong implementation' is present; please either address the concern or remove the comment if resolved.

Here's what I looked at during the review

• 🟡 General issues: 1 issue found
• 🟢 Security: all looks good
• 🟢 Testing: all looks good
• 🟢 Complexity: all looks good
• 🟢 Documentation: all looks good

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[sourcery-ai]

suggestion (performance): Avoid unnecessary eigenvector computation when only eigenvalues are needed

Re-add compute_left_eigenvectors=False and compute_right_eigenvectors=False to skip eigenvector computation and avoid unnecessary work.

Suggested change

	... [2j, 1]])
	return eig(a, compute_left_eigenvectors=False,
	compute_right_eigenvectors=False)[0]

[sourcery-ai]

issue (code-quality): We've found these issues:

• Swap if/else branches (swap-if-else-branches)
• Remove unnecessary else after guard condition (remove-unnecessary-else)