Laplacians

The library includes Laplacians for various synthetic power grid networks. These are provided as scipy.sparse.csc_matrix objects. The naming convention is METRIC_REGION.

See also

Graph Laplacian

For the mathematical derivation and physical interpretation of the DELAY, LENGTH, and IMPEDANCE weighting schemes.

Usage

import sgwt

# Load the Laplacian for the synthetic Texas grid
# where edge weights are based on phase delay.
L_texas = sgwt.DELAY_TEXAS

print(type(L_texas))
# <class 'scipy.sparse.csc.csc_matrix'>
print(L_texas.shape)
# (2000, 2000)

Signals

Vertex-domain signals are provided for some graphs, most commonly geographic coordinates.

• COORDS: An (n_vertices,2) NumPy array containing the longitude and latitude of each node.

Usage

import sgwt

# Load the geographic coordinates for the Texas grid
coords_texas = sgwt.COORD_TEXAS

print(type(coords_texas))
# <class 'numpy.ndarray'>
print(coords_texas.shape)
# (2000, 2)

Kernels

Pre-computed rational approximations for common spectral graph wavelets are available as dictionaries. These can be loaded into VFKernel objects for use with convolve().

• MEXICAN_HAT: Mexican Hat wavelet.

• MODIFIED_MORLET: Modified Morlet wavelet.

• SHANNON: Shannon (ideal band-pass) wavelet.

• GAUSSIAN_WAV: Gaussian wavelet.

Usage

from sgwt import VFKernel, MODIFIED_MORLET

# The built-in kernel is a dictionary
print(type(MODIFIED_MORLET))
# <class 'dict'>

# Load it into a VFKernel object for use in convolution
kernel = VFKernel.from_dict(MODIFIED_MORLET)

print(kernel.R.shape)
# (14, 1)

See also

See Kernel JSON Structure for details on the JSON file format for custom kernels.

Available Data Summary

The following table summarizes all available built-in datasets, including both power grid networks and 3D mesh models. The original mesh datasets can be found at the Laplacian Library.

Dataset	Vertices	Edges	Vertex Signals	Edge Weights
BUNNY	35947	103731	x, y, z
HORSE	48485	145449	x, y, z
LBRAIN	144490	433464	x, y, z
RBRAIN	145071	435207	x, y, z
HAWAII	46	67	long, lat	length, impedance, delay
TEXAS	2000	2667	long, lat	length, impedance, delay
EASTWEST	80000	95544	long, lat	length, impedance, delay
USA	82000	98205	long, lat	length, impedance, delay
WECC	243	351		length, impedance, delay
NEISO	39	46		length, delay

Adding New Data

The library uses auto-discovery to find data files. To add new datasets, simply place files in the appropriate folder with the correct naming convention:

Laplacians (stored as .mat files containing a sparse matrix):

sgwt/library/DELAY/{REGION}.mat      →  sgwt.DELAY_{REGION}
sgwt/library/IMPEDANCE/{REGION}.mat  →  sgwt.IMPEDANCE_{REGION}
sgwt/library/LENGTH/{REGION}.mat     →  sgwt.LENGTH_{REGION}

Signals (stored as .mat files containing an array):

sgwt/library/SIGNALS/{REGION}.mat    →  sgwt.COORD_{REGION}

Meshes (stored as .ply files):

sgwt/library/MESH/{NAME}.ply         →  sgwt.MESH_{NAME}  (Laplacian)
                                     →  sgwt.{NAME}_XYZ   (coordinates)

Kernels (stored as .json files):

sgwt/library/KERNELS/{NAME}.json     →  sgwt.{NAME}

No code changes are required—new files are automatically discovered at runtime