Lanczos Eigenvector

[jeffreyyancey]

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.

• [X] Add an algorithm?
• [ ] Fix a bug or typo in an existing algorithm?
• [X] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request.
• [ ] Documentation change?

Checklist:

• [X] I have read CONTRIBUTING.md.
• [X] This pull request is all my own work -- I have not plagiarized.
• [X] I know that pull requests will not be merged if they fail the automated tests.
• [X] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
• [X] All new Python files are placed inside an existing directory.
• [X] All filenames are in all lowercase characters with no spaces or dashes.
• [X] All functions and variable names follow Python naming conventions.
• [X] All function parameters and return values are annotated with Python type hints.
• [X] All functions have doctests that pass the automated testing.
• [X] All new algorithms include at least one URL that points to Wikipedia or another similar explanation.
• [X] 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".