def Qparameter(parts, distfunc=None):
"""
Calculates the minimum spanning tree Q parameter (Cartwright & Whitworth 2004)
for a projection of the particle set.
:argument distfunc: distfunc is the distance function which can be used to select
the projection plane.
"""
if distfunc is None:
def distfunc(p,q):
return (((p.x-q.x)**2+(p.y-q.y)**2)**0.5).value_in(p.x.unit)
N=len(parts)
graph=Graph()
for p in parts:
d=distfunc(p,parts)
for i,q in enumerate(parts):
if p!=q:
graph.add_edge(p,q, d[i] )
all_edges=graph.all_edges()
ml=reduce(lambda x,y: x+y[0],all_edges,zero )/len(all_edges)
mst=MinimumSpanningTreeFromEdges(all_edges)
mlmst=reduce(lambda x,y: x+y[0],mst, zero )/len(mst)
# normalize
mlmst=mlmst/(N*numpy.pi)**0.5*(N-1)
return mlmst/ml
def Qparameter(parts, distfunc=None):
"""
Calculates the minimum spanning tree Q parameter (Cartwright & Whitworth 2004)
for a projection of the particle set.
:argument distfunc: distfunc is the distance function which can be used to select
the projection plane.
"""
if distfunc is None:
def distfunc(p, q):
return (((p.x - q.x)**2 + (p.y - q.y)**2)**0.5).value_in(p.x.unit)
N = len(parts)
graph = Graph()
for p in parts:
d = distfunc(p, parts)
for i, q in enumerate(parts):
if p != q:
graph.add_edge(p, q, d[i])
all_edges = graph.all_edges()
ml = reduce(lambda x, y: x + y[0], all_edges, zero) / len(all_edges)
mst = MinimumSpanningTreeFromEdges(all_edges)
mlmst = reduce(lambda x, y: x + y[0], mst, zero) / len(mst)
# normalize
mlmst = mlmst / (N * numpy.pi)**0.5 * (N - 1)
return mlmst / ml
def minimum_spanning_tree_length(particles):
"""
Calculates the length of the minimum spanning tree (MST) of a set of particles
using David Eppstein's Python implemention of Kruskal's algorithm.
"""
graph = Graph()
for particle in particles:
others = particles - particle
distances = (particle.position - others.position).lengths()
for other, distance in zip(others, distances):
graph.add_edge(particle, other, distance)
return sum([edge[0] for edge in MinimumSpanningTree(graph)], zero)
def minimum_spanning_tree_length(particles):
"""
Calculates the length of the minimum spanning tree (MST) of a set of particles
using David Eppstein's Python implemention of Kruskal's algorithm.
"""
graph = Graph()
for particle in particles:
others = particles - particle
distances = (particle.position - others.position).lengths()
for other, distance in zip(others, distances):
graph.add_edge(particle, other, distance)
return sum([edge[0] for edge in MinimumSpanningTree(graph)], zero)
def connected_components(parts, treshold=None, distfunc=None):
if distfunc is None:
def distfunc(p, q):
return ((p.x - q.x)**2 + (p.y - q.y)**2 + (p.z - q.z)**2)**0.5
print "making graph"
graph = Graph()
for p in parts:
graph.add_node(p)
d = distfunc(p, parts)
edges = [(d[i], p, q) for i, q in enumerate(parts) if p != q]
edges = filter(lambda x: x[0] < treshold, edges)
for e in edges:
graph.add_edge(e[1], e[2], e[0])
print "done"
cc = ConnectedComponents(graph)
print "number of edges:", len(graph.all_edges())
print "number of CC:", len(cc)
return graph, cc