I have following script:
import pandas as pd
from igraph import *
df_p_c = pd.read_csv('data/edges.csv')
...
edges = list_edges
vertices = list(dict_case_to_number.keys())
g = Graph(edges=edges, directed=True)
plot(g, bbox=(6000, 6000))
I have 2300 edges with rare connection. This is my plot of it:
And here are zooms of a few parts of it:
This plot is not readable because the distance between edges is too small. How can I have a bigger distance between edges? Only edges from the same 'family' have small distance.
Is there any other way to improve plots with a lot of edges?
I'm looking for any way to visualize parent-child correlation, it could be another python packet.
You seem to have a lot of small, disconnected components. If you want an informative graph, I think you should sort and group the connected components by size. Furthermore, the underlying assumption of many network layout algorithms is that there is a single giant component. Hence if you want sensible coordinates, you will often need to compute the layout for each component separately and then arrange the components with respect to each other. I would re-plot your graph in this way:
I have written the code for this graph using networkx as that is my module of choice. However, it would be very easy to substitute the networkx functions with igraph functions. The two functions that you need to replace are networkx.connected_component_subgraphs and whatever you want to use for the component_layout_func.
#!/usr/bin/env python
import numpy as np
import matplotlib.pyplot as plt
import networkx
def layout_many_components(graph,
component_layout_func=networkx.layout.spring_layout,
pad_x=1., pad_y=1.):
"""
Arguments:
----------
graph: networkx.Graph object
The graph to plot.
component_layout_func: function (default networkx.layout.spring_layout)
Function used to layout individual components.
You can parameterize the layout function by partially evaluating the
function first. For example:
from functools import partial
my_layout_func = partial(networkx.layout.spring_layout, k=10.)
pos = layout_many_components(graph, my_layout_func)
pad_x, pad_y: float
Padding between subgraphs in the x and y dimension.
Returns:
--------
pos : dict node : (float x, float y)
The layout of the graph.
"""
components = _get_components_sorted_by_size(graph)
component_sizes = [len(component) for component in components]
bboxes = _get_component_bboxes(component_sizes, pad_x, pad_y)
pos = dict()
for component, bbox in zip(components, bboxes):
component_pos = _layout_component(component, bbox, component_layout_func)
pos.update(component_pos)
return pos
def _get_components_sorted_by_size(g):
subgraphs = list(networkx.connected_component_subgraphs(g))
return sorted(subgraphs, key=len)
def _get_component_bboxes(component_sizes, pad_x=1., pad_y=1.):
bboxes = []
x, y = (0, 0)
current_n = 1
for n in component_sizes:
width, height = _get_bbox_dimensions(n, power=0.8)
if not n == current_n: # create a "new line"
x = 0 # reset x
y += height + pad_y # shift y up
current_n = n
bbox = x, y, width, height
bboxes.append(bbox)
x += width + pad_x # shift x down the line
return bboxes
def _get_bbox_dimensions(n, power=0.5):
# return (np.sqrt(n), np.sqrt(n))
return (n**power, n**power)
def _layout_component(component, bbox, component_layout_func):
pos = component_layout_func(component)
rescaled_pos = _rescale_layout(pos, bbox)
return rescaled_pos
def _rescale_layout(pos, bbox):
min_x, min_y = np.min([v for v in pos.values()], axis=0)
max_x, max_y = np.max([v for v in pos.values()], axis=0)
if not min_x == max_x:
delta_x = max_x - min_x
else: # graph probably only has a single node
delta_x = 1.
if not min_y == max_y:
delta_y = max_y - min_y
else: # graph probably only has a single node
delta_y = 1.
new_min_x, new_min_y, new_delta_x, new_delta_y = bbox
new_pos = dict()
for node, (x, y) in pos.items():
new_x = (x - min_x) / delta_x * new_delta_x + new_min_x
new_y = (y - min_y) / delta_y * new_delta_y + new_min_y
new_pos[node] = (new_x, new_y)
return new_pos
def test():
from itertools import combinations
g = networkx.Graph()
# add 100 unconnected nodes
g.add_nodes_from(range(100))
# add 50 2-node components
g.add_edges_from([(ii, ii+1) for ii in range(100, 200, 2)])
# add 33 3-node components
for ii in range(200, 300, 3):
g.add_edges_from([(ii, ii+1), (ii, ii+2), (ii+1, ii+2)])
# add a couple of larger components
n = 300
for ii in np.random.randint(4, 30, size=10):
g.add_edges_from(combinations(range(n, n+ii), 2))
n += ii
pos = layout_many_components(g, component_layout_func=networkx.layout.circular_layout)
networkx.draw(g, pos, node_size=100)
plt.show()
if __name__ == '__main__':
test()
EDIT
If you want the subgraphs tightly arranged, you need to install rectangle-packer (pip install rectangle-packer), and substitute _get_component_bboxes with this version:
import rpack
def _get_component_bboxes(component_sizes, pad_x=1., pad_y=1.):
dimensions = [_get_bbox_dimensions(n, power=0.8) for n in component_sizes]
# rpack only works on integers; sizes should be in descending order
dimensions = [(int(width + pad_x), int(height + pad_y)) for (width, height) in dimensions[::-1]]
origins = rpack.pack(dimensions)
bboxes = [(x, y, width-pad_x, height-pad_y) for (x,y), (width, height) in zip(origins, dimensions)]
return bboxes[::-1]
Edit #2
I have written a library for visualising networks, which is called netgraph. It automatically handles networks with multiple components in the way outlined above. It is fully compatible with networkx and igraph Graph objects, so it should be easy and fast to make great looking graphs of graphs (at least that is the idea).
import itertools
import matplotlib.pyplot as plt
import networkx as nx
# installation easiest via pip:
# pip install netgraph
from netgraph import Graph
# construct the graph as before:
g = nx.Graph()
# add 30 unconnected nodes
g.add_nodes_from(range(30))
# add 15 2-node components
g.add_edges_from([(ii, ii+1) for ii in range(30, 60, 2)])
# add 10 3-node components
for ii in range(60, 90, 3):
g.add_edges_from([(ii, ii+1), (ii, ii+2), (ii+1, ii+2)])
# add a couple of larger components
n = 90
for ii in [10, 20, 40]:
g.add_edges_from(itertools.combinations(range(n, n+ii), 2))
n += ii
# if there are any disconnected components, netgraph automatically handles them separately
Graph(g, node_layout='circular', node_size=1, node_edge_width=0.1, edge_width=0.1, edge_color='black', edge_alpha=1.)
plt.show()
You could checkout networkx, which is a pretty nice graph library. Networkx has direct plotting support for matplotlib.
It supports various layout types, for example spring layout, random layout, and a few more
You should especially look at spring layout, which has a few interesting parameters for your use-case:
k (float (default=None)) – Optimal distance between nodes. If None the
distance is set to 1/sqrt(n) where n is the number of nodes. Increase
this value to move nodes farther apart.
Or both of these in combination with a custom layout:
pos (dict or None optional (default=None)) – Initial positions for
nodes as a dictionary with node as keys and values as a coordinate
list or tuple. If None, then use random initial positions.
fixed (list or None optional (default=None)) – Nodes to keep fixed at initial
position.
The edge weight might also be something you can tune in order to get results you like:
weight (string or None optional (default=’weight’)) – The edge
attribute that holds the numerical value used for the edge weight. If
None, then all edge weights are 1.
I would recommend combining networkx with bokeh, which is a new plotting library that creates web-based html/js plots. It has direct support for networkx, and has some nice features like easy integration of node hover tools. If your graph isn't too big, the performance is pretty good. (I've plotted graphs with about 20000 nodes and a few thousand edges).
With both libraries combined, all you need is the following bit of code for a simple example (from the documentation) that tries to build an optimized layout:
import networkx as nx
from bokeh.io import show, output_file
from bokeh.plotting import figure
from bokeh.models.graphs import from_networkx
G=nx.karate_club_graph() # Replace with your own graph
plot = figure(title="Networkx Integration Demonstration", x_range=(-1.1,1.1), y_range=(-1.1,1.1),
tools="", toolbar_location=None)
graph = from_networkx(G, nx.spring_layout, scale=2, center=(0,0))
plot.renderers.append(graph)
output_file("networkx_graph.html")
show(plot)
Do you know what meaning you are looking for? Or are you exploring? Or is this a specific question about zooming issues?
So far, you have done a good job of seeing the overall structure. Some ideas you might consider making new vocabulary with a few routines to support it. For example, if you make a small cluster be the set of points and edges that are together, then you can plot histograms, visualizations of clusters overlayed on each other, compare clusters with and without long nodes, and so one.
Related
I'm very very new to Python, i usually do my animations with AfterEffects, but it requires a lot of computation time for quite simple things.
• So I would like to create this kind of animation (or at least image) :
AfterEffects graph (forget the shadows, i don't really need it at this point)
Those are circles merging together as they collide, one of them being highlighted (the orange one).
• For now i only managed to do the "merging thing" computing a "distance map" and ploting a contour line :
Python + Matplotlib graph with the following code :
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.animation import FuncAnimation
part_size = 0.0002
nb_part = 200
mesh_res = 500 # resolution of grid
x = np.linspace(0, 1.9, mesh_res)
y = np.linspace(0, 1, mesh_res)
Xgrid, Ygrid = np.meshgrid(x, y)
centers = np.random.uniform(0,1,(nb_part,2)) # array filled with disks centers positions
sizes = part_size*np.ones(nb_part) # array filled whith disks sizes
#sizes = np.random.uniform(0,part_size,nb_part)
dist_map = np.zeros((mesh_res,mesh_res),float) # array to plot the contour of
for i in range(nb_part):
dist_map += sizes[i] / ((Xgrid - centers[i][0]) ** 2 + (Ygrid - centers[i][1]) ** 2) # function with (almost) value of 1 when on a cricle, so we want the contour of this array
fig, ax = plt.subplots()
contour_opts = {'levels': np.linspace(0.9, 1., 1), 'color':'red', 'linewidths': 4} # to plot only the one-ish values of contour
ax.contour(x, y, dist_map, **contour_opts)
def update(frame_number):
ax.collections = [] # reset the graph
centers[:] += 0.01*np.sin(2*np.pi*frame_number/100+np.stack((np.arange(nb_part),np.arange(nb_part)),axis=-1)) # just to move circles "randomly"
dist_map = np.zeros((mesh_res, mesh_res), float) # updating array of distances
for i in range(nb_part):
dist_map += sizes[i] / ((Xgrid - centers[i][0]) ** 2 + (Ygrid - centers[i][1]) ** 2)
ax.contour(x, y, dist_map, **contour_opts) # calculate the new contour
ani = FuncAnimation(fig, update, interval=20)
plt.show()
The result is not that bad but :
i can't figure how to highlight just one circle keeping the merging effect (ideally, the colors should merge as well, and i would like to keep the image transparency when exported)
it still requires some time to compute each frame (it is way faster than AfterEffects though), so i guess i'm still very far from using optimally python, numpy, and matplotlib. Maybe there are even libraries able to do that kind of things ? So if there is a better strategy to implement it, i'll take it.
For a bond percolation model I want to build a square lattice with NetworkX using grid_2d_graph(l,l). This gives me a square lattice of size lxl with every edge open.
The idea is that I want to pick an edge of the graph randomly, then check if the edge has already been assigned (1 to leave the edge as it is, 0 to add it to the list of edges to remove from the graph) and if it hasn't been assigned yet (edge has 'state' = -1), I want to randomly choose with a specific probability p, if the edge is open (leave it as it is), or if it is closed (put it on the list of the edges to remove).
Therefor, I saved all edges with data attribute 'state' = -1 as a list and then tried to randomly access an entry of this list to then change the attribute 'state' to some value. But it seems that this operation is not allowed. When I try to edit the states, I receive the following error:
File "bond-percolation.py", line 39, in <module>
ed[10][2] = 1
TypeError: 'tuple' object does not support item assignment
So my question is, how can I randomly pick an edge and change the value of 'state' efficiently?
Here is my code:
import numpy as np
import networkx as nx
import matplotlib.pyplot as plt
import random
#Width of the quadratic lattice
l = 30
#Create grid
G = nx.grid_2d_graph(l,l)
#Total number of edges in the lattice
n = 2 * l * (l-1)
m = 0
#Set probability if an edge is open
p = 0.17
#Create empty list to add closed edges later
ed = []
ld = []
for e in G.edges(data = 'state', default = -1):
ed.append(e)
#Creating the lattice
while (m != n):
i = np.random.randint(n-1)
a = random.random()
if (ed[i][2] == -1):
if (a > p):
ld.append(ed[i])
else:
ed[i][2] = 1
m = m + 1
#We need this so that the lattice is drawn vertically to the horizon
pos = dict( (l,l) for l in G.nodes() )
#Draw the lattice
nx.draw_networkx(G, pos = pos, with_labels = False, node_size = 0)
#Plot it on the screen
plt.axis('off')
plt.show()
I believe you can simply search for it using the edge selector.
There's no built-in selector (afaik) but you can create a helper function that loops through the edges and returns your list.
def filter_edges(value):
edge_list = []
for u,v,s in G.edges(data='state'):
if s == value:
edge_list.append((u,v))
return edge_list
Re-reading your error, I don't think your error is related to randomly picking edges. Instead, you are incorrectly trying to assign the state values.
ed[10][2] returns the whole edge (presumably a dict). It'd be helpful to include the output when you just run ed[10][2].
You can't assign an int to that. You likely want to do ed[10][2]['state'] = 1
I'm using NetworkX in python. Given any undirected and unweighted graph, I want to loop through all the nodes. With each node, I want to add a random edge and/or delete an existing random edge for that node with probability p. Is there a simple way to do this? Thanks a lot!
Create a new random edge in networkx
Let's set up a test graph:
import networkx as nx
import random
import matplotlib.pyplot as plt
graph = nx.Graph()
graph.add_edges_from([(1,3), (3,5), (2,4)])
nx.draw(graph, with_labels=True)
plt.show()
Now we can pick a random edge from a list of non-edge from the graph. It is not totally clear yet what is the probability you mentioned. Since you add a comment stating that you want to use random.choice I'll stick to that.
def random_edge(graph, del_orig=True):
'''
Create a new random edge and delete one of its current edge if del_orig is True.
:param graph: networkx graph
:param del_orig: bool
:return: networkx graph
'''
edges = list(graph.edges)
nonedges = list(nx.non_edges(graph))
# random edge choice
chosen_edge = random.choice(edges)
chosen_nonedge = random.choice([x for x in nonedges if chosen_edge[0] == x[0]])
if del_orig:
# delete chosen edge
graph.remove_edge(chosen_edge[0], chosen_edge[1])
# add new edge
graph.add_edge(chosen_nonedge[0], chosen_nonedge[1])
return graph
Usage exemple:
new_graph = random_edge(graph, del_orig=True)
nx.draw(new_graph, with_labels=True)
plt.show()
We can still add a probability distribution over the edges in random.choiceif you need to (using numpy.random.choice() for instance).
Given a node i, To add edges without duplication you need to know (1) what edges from i already exist and then compute (2) the set of candidate edges that don't exist from i. For removals, you already defined a method in the comment - which is based simply on (1).
Here is a function that will provide one round of randomised addition and removal, based on list comprehensions
def add_and_remove_edges(G, p_new_connection, p_remove_connection):
'''
for each node,
add a new connection to random other node, with prob p_new_connection,
remove a connection, with prob p_remove_connection
operates on G in-place
'''
new_edges = []
rem_edges = []
for node in G.nodes():
# find the other nodes this one is connected to
connected = [to for (fr, to) in G.edges(node)]
# and find the remainder of nodes, which are candidates for new edges
unconnected = [n for n in G.nodes() if not n in connected]
# probabilistically add a random edge
if len(unconnected): # only try if new edge is possible
if random.random() < p_new_connection:
new = random.choice(unconnected)
G.add_edge(node, new)
print "\tnew edge:\t {} -- {}".format(node, new)
new_edges.append( (node, new) )
# book-keeping, in case both add and remove done in same cycle
unconnected.remove(new)
connected.append(new)
# probabilistically remove a random edge
if len(connected): # only try if an edge exists to remove
if random.random() < p_remove_connection:
remove = random.choice(connected)
G.remove_edge(node, remove)
print "\tedge removed:\t {} -- {}".format(node, remove)
rem_edges.append( (node, remove) )
# book-keeping, in case lists are important later?
connected.remove(remove)
unconnected.append(remove)
return rem_edges, new_edges
To see this function in action:
import networkx as nx
import random
import matplotlib.pyplot as plt
p_new_connection = 0.1
p_remove_connection = 0.1
G = nx.karate_club_graph() # sample graph (undirected, unweighted)
# show original
plt.figure(1); plt.clf()
fig, ax = plt.subplots(2,1, num=1, sharex=True, sharey=True)
pos = nx.spring_layout(G)
nx.draw_networkx(G, pos=pos, ax=ax[0])
# now apply one round of changes
rem_edges, new_edges = add_and_remove_edges(G, p_new_connection, p_remove_connection)
# and draw new version and highlight changes
nx.draw_networkx(G, pos=pos, ax=ax[1])
nx.draw_networkx_edges(G, pos=pos, ax=ax[1], edgelist=new_edges,
edge_color='b', width=4)
# note: to highlight edges that were removed, add them back in;
# This is obviously just for display!
G.add_edges_from(rem_edges)
nx.draw_networkx_edges(G, pos=pos, ax=ax[1], edgelist=rem_edges,
edge_color='r', style='dashed', width=4)
G.remove_edges_from(rem_edges)
plt.show()
And you should see something like this.
Note that you could also do something similar with the adjacency matrix,
A = nx.adjacency_matrix(G).todense() (it's a numpy matrix so operations like A[i,:].nonzero() would be relevant). This might be more efficient if you have extremely large networks.
I've been studying the other networkx plotting posts, but I've been having a hard time adapting them to my problem.
1) How do I create subplots with network graphs, without a PREDEFINED number of objects to plot? The function grabs this dynamically.
2) Is there an easy way to filter the network graph by limiting only those edges with over a weight of 2, for instance? or do I have to edit the network object itself to do so?
UPDATE #2: I figured out a way to filter by degree (see below). I'm wondering more generally if there are better ways to make my network data more understandable?
nol comes in the format [ [Year, networkobject], [Year, networkobject]]
def standardgraph_multiyear(nol, minimumdegree):
"""
Plots multiple graphs based on year
nol = takes in a LIST of [year, network object]
minimum = takes in a digit to filter nodes by degree
"""
#Each iteration prints a new subplot
numrows = len(nol)
fig = plt.figure(figsize=(10,60))
for i, val in enumerate(nol):
gloc = numrows,1,i+1
plt.subplot(numrows, 1, i+1)
if minimumdegree > 0:
outdeg = val[1].degree()
to_keep = [n for n in outdeg if outdeg[n] > minimumdegree]
mingraph = val[1].subgraph(to_keep)
pos = nx.spring_layout(mingraph, iterations=200)
nx.draw(mingraph, pos, font_size=8, with_labels=True)
nx.draw_networkx_edges(mingraph, pos, alpha=.2)
nx.draw_networkx_nodes(mingraph, pos, node_size=60, font_size =8, labels=True)
nx.draw_networkx_labels(mingraph, pos, font_color='k', font_size=8)
plt.title("Year {0}".format(val[0]), loc = 'center', fontsize=20)
if minimumdegree == 0:
outdeg = val[1].degree()
to_keep = [n for n in outdeg if outdeg[n] > minimumdegree]
mingraph = val[1].subgraph(to_keep)
pos = nx.spring_layout(mingraph, iterations=200)
nx.draw(mingraph, pos, font_size=8, with_labels=True)
nx.draw_networkx_edges(mingraph, pos, alpha=.2)
nx.draw_networkx_nodes(mingraph, pos, node_size=60, font_size =8, labels=True)
nx.draw_networkx_labels(mingraph, pos, font_color='k', font_size=8)
plt.title("Year {0}".format(val[0]), loc = 'center', fontsize=20)
return
fig.savefig('out.png', dpi=100)
Your out of range error likely comes from the call to plt.subplot(221+i), since you don't seem to limit i to be <4; thus matplotlib will not know what subplot you intend to refer to?
(You also seem to have some conflicting code assembling the plots: a call to plt.subplots(1,1) and a later which requests a 2x2 grid).
In a different question I used the more basic plt.subplot(xxx) syntax to generate multiple subplots (following the four grids example from networkx). But you can also do it as shown below, setting the ax= keyword argument to an already existing set of axes. Note the call to sca() before rendering to each axis, which I needed to get this to work.
I've also shown one way to filter the edges that are shown below, and it does not require modifying the underlying graph: instead, you construct the edge lineweights you want based on the data from your graph, and use that as argument to draw_networkx_edges.
Edit (re updated question): the example code now includes a more explicit illustration of how to handle an unknown number of networks.
import matplotlib.pyplot as plt
import networkx as nx
import numpy as np
n = 15; m = 40 # graph size
L = np.random.choice(xrange(n), 2*m) # select some edge destinations
weights = 0.5 + 5 * np.random.rand(m) # give each edge a weight
G = nx.Graph() # create a graph object
G.add_nodes_from(xrange(n)) # add n nodes to it
for i, (fr, to) in enumerate(zip(L[1::2], L[::2])):
G.add_edge(fr, to, weight=weights[i]) # add each edge
# use one of the edge properties to control line thickness
edgewidth = [ d['weight'] for (u,v,d) in G.edges(data=True)]
# and create a filtered version (still need an entry for each edge)
w_threshold = 2
edgewidth_filtered = [ d['weight'] if d['weight'] > w_threshold else 0
for (u,v,d) in G.edges(data=True)]
# alt. filtering - all edges that meet some criterion are displayed uniformly
binary_filtered_edges = [ 1 if d['weight'] > w_threshold else 0
for (u,v,d) in G.edges(data=True)]
titles = [ 'edges drawn with lineweight=1', 'edge width from edge weight',
'edge width from edge weight, only strong edges',
'strong edges shown as lineweight=1', ]
edge_display_params = [ np.ones(len(edgewidth),), edgewidth,
edgewidth_filtered, binary_filtered_edges,]
# to illustrate drawing an unknown number of graphs, add some repeats repeats
n_extra = np.random.randint(0, 5)
indices = range(len(edge_display_params)) * 3
indices = indices[len(edge_display_params) + n_extra:]
# layout
pos = nx.spring_layout(G, iterations=50)
pos = nx.circular_layout(G)
#pos = nx.random_layout(G)
# rendering
fig = plt.figure(1); plt.clf()
# compute a grid size that will fit all graphs on it (couple blanks likely)
nr = int(np.ceil(np.sqrt(len(indices))))
fig, ax = plt.subplots(nr, nr, num=1)
for i, j in enumerate(indices):
# dereference index into valid data (needed here since some repeated rather
# than creating more, to illustrate handling unknown amount of data)
k = indices[j]
widths = edge_display_params[k]
# compute index for the subplot, and set this subplot as current
ix = np.unravel_index(i, ax.shape)
plt.sca(ax[ix])
# draw all nodes homogeneously, and edge weights as filtered
nx.draw_networkx_nodes(G, pos, ax=ax[ix])
nx.draw_networkx_edges(G, pos, width=widths, ax=ax[ix],)
ax[ix].set_title(titles[k], fontsize=10)
ax[ix].set_axis_off()
plt.show()
This example uses the same input graph four times over but obviously you could apply a single filter to different graphs (by filtering within the plotting loop) instead of applying different filters.
Below shows one run that created an extra 4 graphs, and so we have one unused pane:
I use matplotlib's method hexbin to compute 2d histograms on my data.
But I would like to get the coordinates of the centers of the hexagons in order to further process the results.
I got the values using get_array() method on the result, but I cannot figure out how to get the bins coordinates.
I tried to compute them given number of bins and the extent of my data but i don't know the exact number of bins in each direction. gridsize=(10,2) should do the trick but it does not seem to work.
Any idea?
I think this works.
from __future__ import division
import numpy as np
import math
import matplotlib.pyplot as plt
def generate_data(n):
"""Make random, correlated x & y arrays"""
points = np.random.multivariate_normal(mean=(0,0),
cov=[[0.4,9],[9,10]],size=int(n))
return points
if __name__ =='__main__':
color_map = plt.cm.Spectral_r
n = 1e4
points = generate_data(n)
xbnds = np.array([-20.0,20.0])
ybnds = np.array([-20.0,20.0])
extent = [xbnds[0],xbnds[1],ybnds[0],ybnds[1]]
fig=plt.figure(figsize=(10,9))
ax = fig.add_subplot(111)
x, y = points.T
# Set gridsize just to make them visually large
image = plt.hexbin(x,y,cmap=color_map,gridsize=20,extent=extent,mincnt=1,bins='log')
# Note that mincnt=1 adds 1 to each count
counts = image.get_array()
ncnts = np.count_nonzero(np.power(10,counts))
verts = image.get_offsets()
for offc in xrange(verts.shape[0]):
binx,biny = verts[offc][0],verts[offc][1]
if counts[offc]:
plt.plot(binx,biny,'k.',zorder=100)
ax.set_xlim(xbnds)
ax.set_ylim(ybnds)
plt.grid(True)
cb = plt.colorbar(image,spacing='uniform',extend='max')
plt.show()
I would love to confirm that the code by Hooked using get_offsets() works, but I tried several iterations of the code mentioned above to retrieve center positions and, as Dave mentioned, get_offsets() remains empty. The workaround that I found is to use the non-empty 'image.get_paths()' option. My code takes the mean to find centers but which means it is just a smidge longer, but it does work.
The get_paths() option returns a set of x,y coordinates embedded that can be looped over and then averaged to return the center position for each hexagram.
The code that I have is as follows:
counts=image.get_array() #counts in each hexagon, works great
verts=image.get_offsets() #empty, don't use this
b=image.get_paths() #this does work, gives Path([[]][]) which can be plotted
for x in xrange(len(b)):
xav=np.mean(b[x].vertices[0:6,0]) #center in x (RA)
yav=np.mean(b[x].vertices[0:6,1]) #center in y (DEC)
plt.plot(xav,yav,'k.',zorder=100)
I had this same problem. I think what needs to be developed is a framework to have a HexagonalGrid object which can then be applied to many different data sets (and it would be awesome to do it for N dimensions). This is possible and it surprises me that neither Scipy or Numpy has anything for it (furthermore there seems to be nothing else like it except perhaps binify)
That said, I assume you want to use hexbinning to compare multiple binned data sets. This requires some common base. I got this to work using matplotlib's hexbin the following way:
import numpy as np
import matplotlib.pyplot as plt
def get_data (mean,cov,n=1e3):
"""
Quick fake data builder
"""
np.random.seed(101)
points = np.random.multivariate_normal(mean=mean,cov=cov,size=int(n))
x, y = points.T
return x,y
def get_centers (hexbin_output):
"""
about 40% faster than previous post only cause you're not calculating the
min/max every time
"""
paths = hexbin_output.get_paths()
v = paths[0].vertices[:-1] # adds a value [0,0] to the end
vx,vy = v.T
idx = [3,0,5,2] # index for [xmin,xmax,ymin,ymax]
xmin,xmax,ymin,ymax = vx[idx[0]],vx[idx[1]],vy[idx[2]],vy[idx[3]]
half_width_x = abs(xmax-xmin)/2.0
half_width_y = abs(ymax-ymin)/2.0
centers = []
for i in xrange(len(paths)):
cx = paths[i].vertices[idx[0],0]+half_width_x
cy = paths[i].vertices[idx[2],1]+half_width_y
centers.append((cx,cy))
return np.asarray(centers)
# important parts ==>
class Hexagonal2DGrid (object):
"""
Used to fix the gridsize, extent, and bins
"""
def __init__ (self,gridsize,extent,bins=None):
self.gridsize = gridsize
self.extent = extent
self.bins = bins
def hexbin (x,y,hexgrid):
"""
To hexagonally bin the data in 2 dimensions
"""
fig = plt.figure()
ax = fig.add_subplot(111)
# Note mincnt=0 so that it will return a value for every point in the
# hexgrid, not just those with count>mincnt
# Basically you fix the gridsize, extent, and bins to keep them the same
# then the resulting count array is the same
hexbin = plt.hexbin(x,y, mincnt=0,
gridsize=hexgrid.gridsize,
extent=hexgrid.extent,
bins=hexgrid.bins)
# you could close the figure if you don't want it
# plt.close(fig.number)
counts = hexbin.get_array().copy()
return counts, hexbin
# Example ===>
if __name__ == "__main__":
hexgrid = Hexagonal2DGrid((21,5),[-70,70,-20,20])
x_data,y_data = get_data((0,0),[[-40,95],[90,10]])
x_model,y_model = get_data((0,10),[[100,30],[3,30]])
counts_data, hexbin_data = hexbin(x_data,y_data,hexgrid)
counts_model, hexbin_model = hexbin(x_model,y_model,hexgrid)
# if you want the centers, they will be the same for both
centers = get_centers(hexbin_data)
# if you want to ignore the cells with zeros then use the following mask.
# But if want zeros for some bins and not others I'm not sure an elegant way
# to do this without using the centers
nonzero = counts_data != 0
# now you can compare the two data sets
variance_data = counts_data[nonzero]
square_diffs = (counts_data[nonzero]-counts_model[nonzero])**2
chi2 = np.sum(square_diffs/variance_data)
print(" chi2={}".format(chi2))