linalg-fromscratch 0.1.1

Cosine similarity and PCA (cov + SVD) from scratch in NumPy with tests

Run in Google Colab

Notebooks

Interactive demos are in the notebooks/ folder.

• Cosine_PCA_FromScratch.ipynb
  Demonstrates cosine similarity, PCA (covariance + SVD), explained variance plots, and reconstruction.

Run in Binder

Cosine_PCA

linalg_fromscratch (NumPy) — Cosine + PCA with Tests

A tiny, dependency-light set of linear algebra utilities implemented from scratch in NumPy, with a pytest suite you can drop into any repo.

Structure

linalg_fromscratch/
├── src/
│   └── linalg_fromscratch/
│       ├── __init__.py
│       ├── cosine.py
│       └── pca.py
├── tests/
│   ├── test_cosine.py
│   └── test_pca.py
├── pytest.ini
├── requirements.txt
└── README.md

Run tests

pip install -r requirements.txt
pytest

Notes

• Cosine similarity guards against zero vectors.
• PCA_FromScratch: covariance eigendecomposition.
• PCA_SVD: SVD-based PCA. Tests confirm equivalence up to sign flips.
• Tests include:
  • Cosine edge cases
  • Orthonormality of components
  • Variance-along-PCs equals eigenvalues
  • Reconstruction error decreases with more components
  • Covariance-PCA vs SVD-PCA numerical equivalence