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# -*- coding: utf-8 -*-
# Copyright (c) Vispy Development Team. All Rights Reserved.
# Distributed under the (new) BSD License. See LICENSE.txt for more info.
"""
Force-Directed Graph Layout
===========================
This module contains implementations for a force-directed layout, where the
graph is modelled like a collection of springs or as a collection of
particles attracting and repelling each other. The whole graph tries to
reach a state which requires the minimum energy.
"""
import numpy as np
try:
from scipy.sparse import issparse
except ImportError:
def issparse(*args, **kwargs):
return False
from ..util import _straight_line_vertices, _rescale_layout
class fruchterman_reingold(object):
r"""Fruchterman-Reingold implementation adapted from NetworkX.
In the Fruchterman-Reingold algorithm, the whole graph is modelled as a
collection of particles, it runs a simplified particle simulation to
find a nice layout for the graph.
Parameters
----------
optimal : number
Optimal distance between nodes. Defaults to :math:`1/\\sqrt{N}` where
N is the number of nodes.
iterations : int
Number of iterations to perform for layout calculation.
pos : array
Initial positions of the nodes
Notes
-----
The algorithm is explained in more detail in the original paper [1]_.
.. [1] Fruchterman, Thomas MJ, and Edward M. Reingold. "Graph drawing by
force-directed placement." Softw., Pract. Exper. 21.11 (1991),
1129-1164.
"""
def __init__(self, optimal=None, iterations=50, pos=None):
self.dim = 2
self.optimal = optimal
self.iterations = iterations
self.num_nodes = None
self.pos = pos
def __call__(self, adjacency_mat, directed=False):
"""
Starts the calculation of the graph layout.
This is a generator, and after each iteration it yields the new
positions for the nodes, together with the vertices for the edges
and the arrows.
There are two solvers here: one specially adapted for SciPy sparse
matrices, and the other for larger networks.
Parameters
----------
adjacency_mat : array
The graph adjacency matrix.
directed : bool
Wether the graph is directed or not. If this is True,
it will draw arrows for directed edges.
Yields
------
layout : tuple
For each iteration of the layout calculation it yields a tuple
containing (node_vertices, line_vertices, arrow_vertices). These
vertices can be passed to the `MarkersVisual` and `ArrowVisual`.
"""
if adjacency_mat.shape[0] != adjacency_mat.shape[1]:
raise ValueError("Adjacency matrix should be square.")
self.num_nodes = adjacency_mat.shape[0]
if issparse(adjacency_mat):
# Use the sparse solver
solver = self._sparse_fruchterman_reingold
else:
solver = self._fruchterman_reingold
for result in solver(adjacency_mat, directed):
yield result
def _fruchterman_reingold(self, adjacency_mat, directed=False):
if self.optimal is None:
self.optimal = 1 / np.sqrt(self.num_nodes)
if self.pos is None:
# Random initial positions
pos = np.asarray(
np.random.random((self.num_nodes, self.dim)),
dtype=np.float32
)
else:
pos = self.pos.astype(np.float32)
# Yield initial positions
line_vertices, arrows = _straight_line_vertices(adjacency_mat, pos,
directed)
yield pos, line_vertices, arrows
# The initial "temperature" is about .1 of domain area (=1x1)
# this is the largest step allowed in the dynamics.
t = 0.1
# Simple cooling scheme.
# Linearly step down by dt on each iteration so last iteration is
# size dt.
dt = t / float(self.iterations+1)
# The inscrutable (but fast) version
# This is still O(V^2)
# Could use multilevel methods to speed this up significantly
for iteration in range(self.iterations):
delta_pos = _calculate_delta_pos(adjacency_mat, pos, t,
self.optimal)
pos += delta_pos
_rescale_layout(pos)
# cool temperature
t -= dt
# Calculate edge vertices and arrows
line_vertices, arrows = _straight_line_vertices(adjacency_mat,
pos, directed)
yield pos, line_vertices, arrows
def _sparse_fruchterman_reingold(self, adjacency_mat, directed=False):
# Optimal distance between nodes
if self.optimal is None:
self.optimal = 1 / np.sqrt(self.num_nodes)
# Change to list of list format
# Also construct the matrix in COO format for easy edge construction
adjacency_arr = adjacency_mat.toarray()
adjacency_coo = adjacency_mat.tocoo()
if self.pos is None:
# Random initial positions
pos = np.asarray(
np.random.random((self.num_nodes, self.dim)),
dtype=np.float32
)
else:
pos = self.pos.astype(np.float32)
# Yield initial positions
line_vertices, arrows = _straight_line_vertices(adjacency_coo, pos,
directed)
yield pos, line_vertices, arrows
# The initial "temperature" is about .1 of domain area (=1x1)
# This is the largest step allowed in the dynamics.
t = 0.1
# Simple cooling scheme.
# Linearly step down by dt on each iteration so last iteration is
# size dt.
dt = t / float(self.iterations+1)
for iteration in range(self.iterations):
delta_pos = _calculate_delta_pos(adjacency_arr, pos, t,
self.optimal)
pos += delta_pos
_rescale_layout(pos)
# Cool temperature
t -= dt
# Calculate line vertices
line_vertices, arrows = _straight_line_vertices(adjacency_coo,
pos, directed)
yield pos, line_vertices, arrows
def _calculate_delta_pos(adjacency_arr, pos, t, optimal):
"""Helper to calculate the delta position"""
# XXX eventually this should be refactored for the sparse case to only
# do the necessary pairwise distances
delta = pos[:, np.newaxis, :] - pos
# Distance between points
distance2 = (delta*delta).sum(axis=-1)
# Enforce minimum distance of 0.01
distance2 = np.where(distance2 < 0.0001, 0.0001, distance2)
distance = np.sqrt(distance2)
# Displacement "force"
displacement = np.zeros((len(delta), 2))
for ii in range(2):
displacement[:, ii] = (
delta[:, :, ii] *
((optimal * optimal) / (distance*distance) -
(adjacency_arr * distance) / optimal)).sum(axis=1)
length = np.sqrt((displacement**2).sum(axis=1))
length = np.where(length < 0.01, 0.1, length)
delta_pos = displacement * t / length[:, np.newaxis]
return delta_pos
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