Selection Technique: QR with Column Pivoting

[nathanielpritchard]

Description

This PR implements a selection technique useful for interpolatory and CUR decompositions, which selects column indices based on the results to QR with column pivoting,

Motivation and Context

• This is one technique that is commonly applied for selecting column indices from a matrix. Implementing this technique is important when one wants to examine different approaches to the CUR and interpolators decompositions.

How has this been tested

This has been tested by calling the select_indices function in the following example:

A = [0 1 0;
        0 0 2;
        3 0 0]
idx = zeros(Int64, 3)
start_idx = 1
n_idx = 3

select_indices!(idx, QRCPRecipe(), A, n_idx, start_idx) 

Types of changes

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

Checklists:

Code and Comments
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• 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.
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Manual Documentation

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• Any code included in the docstring is tested using doc tests to ensure consistency.
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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.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.

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