Sparse SGWT

A high-performance Python library for sparse Graph Signal Processing (GSP) and Spectral Graph Wavelet Transforms (SGWT). This package leverages the CHOLMOD library for efficient sparse direct solvers, providing significant speedups over traditional dense or iterative methods for large-scale graph convolution.

Key Features

• High-Performance Sparse Solvers: Direct integration with the CHOLMOD library for optimized sparse Cholesky factorizations and linear system solves.
• Generalized Graph Convolution: Support for arbitrary spectral kernels via rational approximation (Kernel Fitting), polynomial approximation (Chebyshev), and standard analytical filters (low-pass, band-pass, high-pass).
• Dynamic Topology Support: Specialized routines for graphs with evolving structures, utilizing efficient rank-1 updates for real-time topology changes.
• Resource-Aware Execution: Context-managed memory allocation and workspace reuse to minimize overhead in high-throughput applications.
• Integrated Graph Repository: Built-in access to standardized graph Laplacians and signals from power systems and infrastructure networks.

Installation

You can install sgwt from the Python Package Index (PyPI):

pip install sgwt

Documentation

For detailed usage, API reference, and theoretical background, please visit the documentation website.

Usage Example

Here is a quick example of applying a band-pass filter to an impulse signal on the built-in synthetic Texas grid Laplacian.

import sgwt

# 1. Load a built-in graph Laplacian, which defines the graph's topology.
L = sgwt.DELAY_TEXAS

# 2. Create a vertex-domain signal. Here, a Dirac impulse on the 600th vertex.
#    The `impulse` helper function ensures the required column-major memory order.
signal = sgwt.impulse(L, n=600)

# 3. Use the static convolution context manager. This performs a one-time
#    symbolic factorization of the Laplacian for efficient repeated solves.
with sgwt.Convolve(L) as conv:
    # 4. Apply an analytical band-pass filter. The scale parameter controls
    #    the filter's center frequency.
    filtered_signals = conv.bandpass(signal, scales=[10.0])

# 5. The result is a list of filtered signals, one for each input scale.
result = filtered_signals[0]

print(f"Graph has {L.shape[0]} vertices.")
print(f"Signal on vertex 600, shape: {signal.shape}")
print(f"Filtered signal shape: {result.shape}")

More Examples

The examples/ directory contains a comprehensive suite of demonstrations, also rendered in the Examples section of the documentation. Key applications include:

• Static Filtering: Basic low-pass, band-pass, and high-pass filtering on various graph sizes.
• Dynamic Graphs: Real-time topology updates, performance comparisons, and online stream processing.

Testing

The package includes a comprehensive test suite to verify its correctness. To run the tests on an installed version of sgwt, first install the test dependencies and then run pytest:

pip install sgwt[test]
pytest --pyargs sgwt.tests

For more detailed instructions, including how to run tests from a source checkout, see the Validation Tests section in the documentation.

Citation

If you use this library in your research, please cite it. The GitHub repository includes a CITATION.cff file that provides citation metadata. On GitHub, you can use the "Cite this repository" button on the sidebar to get the citation in your preferred format (including BibTeX).

For convenience, the BibTeX entry for the associated paper is:

@inproceedings{lowery-sgwt-2026,
  title={Using Spectral Graph Wavelets to Analyze Large Power System Oscillation Modes},
  author={Lowery, Luke and Baek, Jongoh and Birchfield, Adam},
  year={2026}
}

Author

Luke Lowery developed this module during his PhD studies at Texas A&M University. You can learn more on his research page or view his publications on Google Scholar.

An alternative implementation in Julia is also available and leverages native SuiteSparse support.

Acknowledgements

• The core performance of this library relies on the CHOLMOD library from SuiteSparse, developed by Dr. Tim Davis at Texas A&M University.
• The graph laplacians used in the examples are derived from the synthetic grid repository, made available by Dr. Adam Birchfield at Texas A&M University.