I want to ask pymesh issue, not sure if it is a bug. when I call
pymesh, info = pm.collapse_short_edges(pymesh, 1e-6)
print("face: ", pymesh.num_faces)
print("vertices: ", pymesh.num_vertices)
pymesh, info1 = pm.collapse_short_edges(pymesh, 0.05, preserve_feature=True)
print("face: ", pymesh.num_faces)
print("vertices: ", pymesh.num_vertices)
It prints out as below:
INFO:pymesh.meshutils.collapse_short_edges:0 edges collapsed
face: 12
vertices: 8
INFO:pymesh.meshutils.collapse_short_edges:Minimum edge threshold: 0.05
INFO:pymesh.meshutils.collapse_short_edges:6 edges collapsed
face: 0
vertices: 0
so after "collapse_short_edges" func, the mesh no longer has any faces nor vertices. It happened to some of my meshes. How do we fix this?
Based on their documentation, "It is possible for a mesh to consist of 0 vertices or 0 faces or 0 voxels."
What you can do are:
1. Save it to see if the mesh still looks normal
pymesh.save_mesh()
Save a tmp mesh and decide if you want it or not.
tmp, info = pm.collapse_short_edges(original_mesh, threshold)
Related
I have a graph with an adjacency matrix shape (adj_mat.shape = (4000, 4000)). My current problem involves finding the list of path lengths (the sequence of nodes is not so important) that traverses from the source (row = 0 ) to the target (col = trans_mat.shape[0] -1).
I am not interested in finding the path sequences; I am only interested in propagating the path length. As a result, this is different from finding all simple paths - which would be too slow (ie. find all paths from source to target; then score each path). Is there a performant way to do this quickly?
DFS is suggested as one possible strategy (noted here). My current implementation (below) is simply not optimal:
# create graph
G = nx.from_numpy_matrix(adj_mat, create_using=nx.DiGraph())
# initialize nodes
for node in G.nodes:
G.nodes[node]['cprob'] = []
# set starting node value
G.nodes[0]['cprob'] = [0]
def propagate_prob(G, node):
# find incoming edges to node
predecessors = list(G.predecessors(node))
curr_node_arr = []
for prev_node in predecessors:
# get incoming edge weight
edge_weight = G.get_edge_data(prev_node, node)['weight']
# get predecessor node value
if len(G.nodes[prev_node]['cprob']) == 0:
G.nodes[prev_node]['cprob'] = propagate_prob(G, prev_node)
prev_node_arr = G.nodes[prev_node]['cprob']
# add incoming edge weight to prev_node arr
curr_node_arr = np.concatenate([curr_node_arr, np.array(edge_weight) + np.array(prev_node_arr)])
# update current node array
G.nodes[node]['cprob'] = curr_node_arr
return G.nodes[node]['cprob']
# calculate all path lengths from source to sink
part_func = propagate_prob(G, 4000)
I don't have a large example by hand (e.g. >300 nodes), but I found a non recursive solution:
import networkx as nx
g = nx.DiGraph()
nx.add_path(g, range(7))
g.add_edge(0, 3)
g.add_edge(0, 5)
g.add_edge(1, 4)
g.add_edge(3, 6)
# first step retrieve topological sorting
sorted_nodes = nx.algorithms.topological_sort(g)
start = 0
target = 6
path_lengths = {start: [0]}
for node in sorted_nodes:
if node == target:
print(path_lengths[node])
break
if node not in path_lengths or g.out_degree(node) == 0:
continue
new_path_length = path_lengths[node]
new_path_length = [i + 1 for i in new_path_length]
for successor in g.successors(node):
if successor in path_lengths:
path_lengths[successor].extend(new_path_length)
else:
path_lengths[successor] = new_path_length.copy()
if node != target:
del path_lengths[node]
Output: [2, 4, 2, 4, 4, 6]
If you are only interested in the number of paths with different length, e.g. {2:2, 4:3, 6:1} for above example, you could even reduce the lists to dicts.
Background
Some explanation what I'm doing (and I hope works for larger examples as well). First step is to retrieve the topological sorting. Why? Then I know in which "direction" the edges flow and I can simply process the nodes in that order without "missing any edge" or any "backtracking" like in a recursive variant. Afterwards, I initialise the start node with a list containing the current path length ([0]). This list is copied to all successors, while updating the path length (all elements +1). The goal is that in each iteration the path length from the starting node to all processed nodes is calculated and stored in the dict path_lengths. The loop stops after reaching the target-node.
With igraph I can calculate up to 300 nodes in ~ 1 second. I also found that accessing the adjacency matrix itself (rather than calling functions of igraph to retrieve edges/vertices) also saves time. The two key bottlenecks are 1) appending a long list in an efficient manner (while also keeping memory) 2) finding a way to parallelize. This time grows exponentially past ~300 nodes, I would love to see if someone has a faster solution (while also fitting into memory).
import igraph
# create graph from adjacency matrix
G = igraph.Graph.Adjacency((trans_mat_pad > 0).tolist())
# add edge weights
G.es['weight'] = trans_mat_pad[trans_mat_pad.nonzero()]
# initialize nodes
for node in range(trans_mat_pad.shape[0]):
G.vs[node]['cprob'] = []
# set starting node value
G.vs[0]['cprob'] = [0]
def propagate_prob(G, node, trans_mat_pad):
# find incoming edges to node
predecessors = trans_mat_pad[:, node].nonzero()[0] # G.get_adjlist(mode='IN')[node]
curr_node_arr = []
for prev_node in predecessors:
# get incoming edge weight
edge_weight = trans_mat_pad[prev_node, node] # G.es[prev_node]['weight']
# get predecessor node value
if len(G.vs[prev_node]['cprob']) == 0:
curr_node_arr = np.concatenate([curr_node_arr, np.array(edge_weight) + propagate_prob(G, prev_node, trans_mat_pad)])
else:
curr_node_arr = np.concatenate([curr_node_arr, np.array(edge_weight) + np.array(G.vs[prev_node]['cprob'])])
## NB: If memory constraint, uncomment below
# set max size
# if len(curr_node_arr) > 100:
# curr_node_arr = np.sort(curr_node_arr)[:100]
# update current node array
G.vs[node]['cprob'] = curr_node_arr
return G.vs[node]['cprob']
# calculate path lengths
path_len = propagate_prob(G, trans_mat_pad.shape[0]-1, trans_mat_pad)
I have these Circles:
I want to get the list of all possible solution of maximum non-intersecting circles. This is the illustration of the solution I wanted from node A.
Therefore the possible solutions from node A:
1 = [A,B,C], 2 = [A,B,E], 3 = [A,C,B], 4 = [A,E,B] ..etc
I want to store all of the possibilities into a list, which the will be used for weighting and selecting the best result. However, I'm still trying to create the list of all possibilities.
I've tried to code the structure here, however I still confused about backtracking and recursive. Anyone could help here?
# List of circle
# List of circle
list_of_circle = ['A','B','C','D','E']
# List of all possible solutions
result = []
# List of possible nodes
ways = []
for k in list_of_circle:
if len(list_of_circle)==0:
result.append(ways)
else:
ways.append[k]
list_of_circle.remove(k)
for j in list_of_circle:
if k.intersects(j):
list_of_circle.remove(j)
return result
Here is a possible solution (pseudocode).
def get_max_non_intersect(selected_circles, current_circle_idx, all_circles):
if current_circle_idx == len(all_circles): # final case
return selected_circles
# we recursively get the biggest selection of circles if the current circle is not selected
list_without_current_circle = get_max_non_intersect(selected_circles, current_circle_idx + 1, all_circles)
# now we check if we can add the current circle to the ones selected
current_intersects_selected = false
current_circle = all_circles[current_circle_idx]
for selected_circle in selected_circles:
if intersects(current_circle, selected_circle):
current_intersects_selected = true
break
if current_intersects_selected is true: # we cannot add the current circle
return list_without_current_circle
else: # we can add the current circle
list_with_current_circle = get_max_non_intersect(selected_circles + [current_circle], current_circle_idx + 1, all_circles)
return list_with_current_circle + list_without_current_circle
I have a NetworkX problem. I create a digraph with a pandas DataFrame and there is data that I set along the edge. I now need to count the # of unique sources for nodes descendants and access the edge attribute.
This is my code and it works for one node but I need to pass a lot of nodes to this and get unique counts.
graph = nx.from_pandas_edgelist(df, source="source", target="target",
edge_attr=["domain", "category"], create_using=nx.DiGraph)
downstream_nodes = list(nx.descendants(graph, node))
downstream_nodes.append(node)
subgraph = graph.subgraph(downstream_nodes).copy()
domain_sources = {}
for s, t, v in subgraph.edges(data=True):
if v["domain"] in domain_sources:
domain_sources[v["domain"]].append(s)
else:
domain_sources[v["domain"]] = [s]
down_count = {}
for k, v in domain_sources.items():
down_count[k] = len(list(set(v)))
It works but, again, for one node the time is not a big deal but I'm feeding this routine at least 40 to 50 nodes. Is this the best way? Is there something else I can do that can group by an edge attribute and uniquely count the nodes?
Two possible enhancements:
Remove copy from line creating the sub graph. You are not changing anything and the copy is redundant.
Create a defaultdict with keys of set. Read more here.
from collections import defaultdict
import networkx as nx
# missing part of df creation
graph = nx.from_pandas_edgelist(df, source="source", target="target",
edge_attr=["domain", "category"], create_using=nx.DiGraph)
downstream_nodes = list(nx.descendants(graph, node))
downstream_nodes.append(node)
subgraph = graph.subgraph(downstream_nodes)
domain_sources = defaultdict(set)
for s, t, v in subgraph.edges(data=True):
domain_sources[v["domain"]].add(s)
down_count = {}
for k, v in domain_sources.items():
down_count[k] = len(set(v))
im trying to implement the prim algorithm in julia.
My function gets the adjacency matrix with the weights but isnt working correctly. I dont know what i have to change. There is some problem with the append!() function i guess.
Is there maybe another/better way to implement the algorithm by just passing the adjacency matrix?
Thank you.
function prims(AD)
n = size(AD)
n1 = n[1]
# choose initial vertex from graph
vertex = 1
# initialize empty edges array and empty MST
MST = []
edges = []
visited = []
minEdge = [nothing, nothing, float(Inf)]
# run prims algorithm until we create an MST
# that contains every vertex from the graph
while length(MST) != n1 - 1
# mark this vertex as visited
append!(visited, vertex)
# add each edge to list of potential edges
for r in 1:n1
if AD[vertex][r] != 0
append!(edges, [vertex, r, AD[vertex][r]])
end
end
# find edge with the smallest weight to a vertex
# that has not yet been visited
for e in 1:length(edges)
if edges[e][3] < minEdge[3] && edges[e][2] not in visited
minEdge = edges[e]
end
end
# remove min weight edge from list of edges
deleteat!(edges, minEdge)
# push min edge to MST
append!(MST, minEdge)
# start at new vertex and reset min edge
vertex = minEdge[2]
minEdge = [nothing, nothing, float(Inf)]
end
return MST
end
For example. When im trying the algorithm with this adjacency Matrix
C = [0 2 3 0 0 0; 2 0 5 3 4 0; 3 5 0 0 4 0; 0 3 0 0 2 3; 0 4 4 2 0 5; 0 0 0 3 5 0]
i get
ERROR: BoundsError
Stacktrace:
[1] getindex(::Int64, ::Int64) at .\number.jl:78
[2] prims(::Array{Int64,2}) at .\untitled-8b8d609f2ac8a0848a18622e46d9d721:70
[3] top-level scope at none:0
I guess i have to "reshape" my Matrix C in a form like this
D = [ [0,2,3,0,0,0], [2,0,5,3,4,0], [3,5,0,0,4,0], [0,3,0,0,2,3], [0,4,4,2,0,5], [0,0,0,3,5,0
]]
But also with this i get the same Error.
First note that LightGraphs.jl has this algorithm implemented. You can find the code here.
I have also made some notes on your algorithm to make it working and indicate the potential improvements without changing its general structure:
using DataStructures # library defining PriorityQueue type
function prims(AD::Matrix{T}) where {T<:Real} # make sure we get what we expect
# make sure the matrix is symmetric
#assert transpose(AD) == AD
n1 = size(AD, 1)
vertex = 1
# it is better to keep edge information as Tuple rather than a vector
# also note that I add type annotation for the collection to improve speed
# and make sure that the stored edge weight has a correct type
MST = Tuple{Int, Int, T}[]
# using PriorityQueue makes the lookup of the shortest edge fast
edges = PriorityQueue{Tuple{Int, Int, T}, T}()
# we will eventually visit almost all vertices so we can use indicator vector
visited = falses(n1)
while length(MST) != n1 - 1
visited[vertex] = true
for r in 1:n1
# you access a matrix by passing indices separated by a comma
dist = AD[vertex, r]
# no need to add edges to vertices that were already visited
if dist != 0 && !visited[r]
edges[(vertex, r, dist)] = dist
end
end
# we will iterate till we find an unvisited destination vertex
while true
# handle the case if the graph was not connected
isempty(edges) && return nothing
minEdge = dequeue!(edges)
if !visited[minEdge[2]]
# use push! instead of append!
push!(MST, minEdge)
vertex = minEdge[2]
break
end
end
end
return MST
end
I've got to do up a state space graph for my AI course, and I was hoping to use GraphViz to make it (so much faster than Dia). The one thing I can't seem to figure out how to do is how to do an "And" connection, which is basically an arc between two lines connecting to the same node. Is this possible?
Yes. While there's no explicit dot syntax for this, here's the way it's nearly always done:
# just graph set-up
digraph new_graph {
ratio = "auto"
mincross = 2.0
# draw some nodes
"001" [shape=box, regular=1, style=filled, fillcolor="#FCD975"] ;
"017" [shape=circle , regular=1,style=filled,fillcolor="#9ACEEB" ] ;
"007" [shape=diamond , regular=1,style=filled,fillcolor="#FCD975" ] ;
# the key line--creating tiny node w/ no label, no color
# i use this style because it mimics the 'midpoint' style used in Omnigraffle et al.
"LN01" [shape=diamond,style=filled,label="",height=.1,width=.1] ;
# draw the edges
"001" -> "LN01" [dir=none,weight=1] ;
"007" -> "LN01" [dir=none,weight=1] ;
"LN01" -> "017" [dir=none, weight=2] ;
}
alt text http://img121.imageshack.us/img121/2547/dotgvziv.png