Torus 2D Stochastic Gradient Descent

This example demonstrates how to use the Stochastic Gradient Descent (SGD) layout algorithm with torus 2D drawings.

Basic Torus SGD Example

import networkx as nx
import egraph as eg
import matplotlib.pyplot as plt
import numpy as np

# Create a graph from NetworkX
nx_graph = nx.les_miserables_graph()
graph = eg.Graph()
indices = {}
for u in nx_graph.nodes:
    indices[u] = graph.add_node(u)
for u, v in nx_graph.edges:
    graph.add_edge(indices[u], indices[v], (u, v))

# Create a torus drawing using the factory method
drawing = eg.DrawingTorus2d.initial_placement(graph)

# Create a random number generator with a seed for reproducibility
rng = eg.Rng.seed_from(0)

# Create a SparseSgd instance using the builder pattern
sgd = eg.SparseSgd().h(50).build(graph, lambda _: 0.2, rng)

# Create a scheduler for the SGD algorithm
scheduler = sgd.scheduler(
    100,  # number of iterations
    0.1,  # eps: eta_min = eps * min d[i, j] ^ 2
)

# Define a step function for the scheduler
def step(eta):
    sgd.shuffle(rng)
    sgd.apply(drawing, eta)

# Run the scheduler
scheduler.run(step)

# Extract node positions
pos = {u: (drawing.x(i), drawing.y(i)) for u, i in indices.items()}

# Visualize with NetworkX and Matplotlib
fig, ax = plt.subplots(figsize=(10, 10))

# Draw the torus boundary
ax.add_patch(plt.Rectangle((0, 0), 1, 1, fill=False, color='gray', linestyle='--'))

# Draw the graph
nx.draw(nx_graph, pos, ax=ax, node_size=50)

# Draw edges that cross the boundary
for u, v in nx_graph.edges():
    x1, y1 = pos[u]
    x2, y2 = pos[v]

    # Check if the edge crosses the boundary
    dx = abs(x2 - x1)
    dy = abs(y2 - y1)

    if dx > 0.5 or dy > 0.5:
        # This edge crosses the boundary, draw it as a pair of segments
        segments = drawing.edge_segments(indices[u], indices[v])
        for ((sx1, sy1), (sx2, sy2)) in segments:
            ax.plot([sx1, sx2], [sy1, sy2], 'k-', alpha=0.5)

# Set limits and aspect ratio
ax.set_xlim(-0.1, 1.1)
ax.set_ylim(-0.1, 1.1)
ax.set_aspect('equal')

Visualizing the Torus in 3D

The torus topology can be visualized in 3D by mapping the 2D coordinates to a 3D torus surface. The torus has two radii: the major radius (distance from the center of the tube to the center of the torus) and the minor radius (radius of the tube itself).