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Lanczos Eigenvector #11906

Merged
merged 1 commit into from
Dec 30, 2024
Merged

Lanczos Eigenvector #11906

merged 1 commit into from
Dec 30, 2024

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jeffreyyancey
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@jeffreyyancey jeffreyyancey commented Oct 8, 2024 •
edited by cclauss
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Fixes: #12386

Title: Add Lanczos Eigenvector Algorithm for Graph-based Eigenvalue Computation

Description:

This pull request introduces a new algorithm for approximating the largest eigenvalues and eigenvectors of a symmetric matrix in the context of graphs, using the Lanczos method. The implementation leverages adjacency list representation to handle sparse graphs effectively and includes the following:

Commit:

Initial Commit: Add Lanczos Eigenvector Algorithm for Graph-based Eigenvalue Computation

  • Implemented find_lanczos_eigenvectors for efficient computation of k-largest eigenvalues and eigenvectors in sparse graphs.
  • Developed lanczos_iteration for constructing tridiagonal matrices.
  • Added multiply_matrix_vector for efficient adjacency-list matrix-vector multiplication.
  • Ensured code meets PEP 8 standards and passed ruff linting.
  • Included a comprehensive module-level docstring, explaining the algorithm, complexity, and example usage for context.
  • Add an algorithm?
  • Fix a bug or typo in an existing algorithm?
  • Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request.
  • Documentation change?

Checklist:

  • I have read CONTRIBUTING.md.
  • This pull request is all my own work -- I have not plagiarized.
  • I know that pull requests will not be merged if they fail the automated tests.
  • This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
  • All new Python files are placed inside an existing directory.
  • All filenames are in all lowercase characters with no spaces or dashes.
  • All functions and variable names follow Python naming conventions.
  • All function parameters and return values are annotated with Python type hints.
  • All functions have doctests that pass the automated testing.
  • All new algorithms include at least one URL that points to Wikipedia or another similar explanation.
  • If this pull request resolves one or more open issues then the description above includes the issue number(s) with a closing keyword: "Fixes #ISSUE-NUMBER".

@jeffreyyancey
- Implemented find_lanczos_eigenvectors to approximate the largest …
e4e2095 
…eigenvalues and corresponding eigenvectors of a graph based on its adjacency list.

- Utilized `lanczos_iteration` to construct tridiagonal matrices, optimized for large, sparse matrices.
- Added `multiply_matrix_vector` for efficient matrix-vector multiplication using adjacency lists.
- Included `validate_adjacency_list` for input validation.

- Supports varied graph analysis applications, particularly for analyzing graph centrality.
- Included type hints, comprehensive docstrings, and doctests.
- PEP-8 compliant, with optimized handling of inputs and outputs.

This module provides essential tools for eigenvalue-based graph analysis, ideal for centrality insights and structural assessments.
imSanko
imSanko approved these changes Oct 9, 2024
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Looks Fine wait for [at] clauss

@cclauss cclauss merged commit 7e55fb6 into TheAlgorithms:master Dec 30, 2024
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@isidroas isidroas mentioned this pull request Jan 25, 2025
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@cclauss cclauss cclauss approved these changes

@imSanko imSanko imSanko approved these changes

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@jeffreyyancey @cclauss @imSanko