QuatIca: Advanced Quaternion Linear Algebra for Scientific Computing

QuatIca provides robust implementations of quaternion matrix operations (QR, LU, QSVD, Hessenberg form, etc), solvers, and applications.

Choose your installation method based on your needs:

Option 1: GitHub (Full Framework)

For examples, benchmarks, and Jupyter notebooks:

git clone https://github.com/vleplat/QuatIca

cd QuatIca

python -m venv quat # Create virtual environment "quat"

# Activate environment:

source quat/bin/activate # Linux/macOS

.\quat\Scripts\activate # Windows

pip install -r requirements.txt # Install dependencies

Includes:

Option 2: PyPI (Lightweight Library)

pip install quatica

Verify installation:

import quatica

print(quatica.__version__) # Should return 0.1.3+

GitHub Users

# Interactive tutorial

python run_analysis.py tutorial

# Image deblurring benchmark

python run_analysis.py deblur_benchmark

PyPI Users

from quatica import create_test_matrix, NewtonSchulzPseudoinverse

# Create random quaternion matrix

A = create_test_matrix(100, 50)

# Compute pseudoinverse

solver = NewtonSchulzPseudoinverse(gamma=1,verbose=True)

A_pinv, residuals, covariances = solver.compute(A)

Colab Demos

Test core functionality → Open

Image Completion → Open

Lorenz attractor filtering → Open

Image Deblurring → Open - Open

Pseudoinverse benchmark → Open

Q-GMRES benchmark → Open

Matrix Operations: QR, LU, SVD, eigenvalue decompositions, and more
High-Performance Solvers:
- Newton-Schulz pseudoinverse (16s for 800×1000 matrices)
- Q-GMRES with LU preconditioning
Applications:
- Image deblurring (QSLST/NS methods)
- 3D Lorenz attractor signal processing
Tensor Tools preview : Order-3 quaternion tensor operations, more coming soon !

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