Number of arrowheads on matplotlib streamplot - python

Is there anyway to increase the number of arrowheads on a matplotlib streamplot? Right now it appears as if three is only one arrowhead per streamline, which is a problem if I want to change to x/y axes limits to zoom in on the data.

Building on #Richard_wth's answer, I wrote a function to provide control on the location of the arrows on a streamplot. One can choose n arrows per streamline, or choose to have the arrows equally spaced on a streamline.
First, you do a normal streamplot, until you are happy with the location and number of streamlines. You keep the returned argument sp. For instance:
sp = ax.streamplot(x,y,u,v,arrowstyle='-',density=10)
What's important here is to have arrowstyle='-' so that arrows are not displayed.
Then, you can call the function streamQuiver (provided below) to control the arrows on the each streamline. If you want 3 arrows per streamline:
streamQuiver(ax, sp, n=3, ...)
If you want a streamline every 1.5 curvilinear length:
streamQuiver(ax, sp, spacing=1.5, ...)
where ... are options that would be passed to quiver.
The function streamQuiver is probably not fully bulletproof and may need some additional handling for particular cases. It relies on 4 subfunctions:
curve_coord to get the curvilinear length along a path
curve extract to extract equidistant point along a path
seg_to_lines to convert the segments from streamplot into continuous lines. There might be a better way to do that!
lines_to_arrows: this is the main function that extract arrows on each lines
Here's an example where the arrows are at equidistant points on each streamlines.
import numpy as np
import matplotlib.pyplot as plt
def streamQuiver(ax,sp,*args,spacing=None,n=5,**kwargs):
""" Plot arrows from streamplot data
The number of arrows per streamline is controlled either by `spacing` or by `n`.
See `lines_to_arrows`.
"""
def curve_coord(line=None):
""" return curvilinear coordinate """
x=line[:,0]
y=line[:,1]
s = np.zeros(x.shape)
s[1:] = np.sqrt((x[1:]-x[0:-1])**2+ (y[1:]-y[0:-1])**2)
s = np.cumsum(s)
return s
def curve_extract(line,spacing,offset=None):
""" Extract points at equidistant space along a curve"""
x=line[:,0]
y=line[:,1]
if offset is None:
offset=spacing/2
# Computing curvilinear length
s = curve_coord(line)
offset=np.mod(offset,s[-1]) # making sure we always get one point
# New (equidistant) curvilinear coordinate
sExtract=np.arange(offset,s[-1],spacing)
# Interpolating based on new curvilinear coordinate
xx=np.interp(sExtract,s,x);
yy=np.interp(sExtract,s,y);
return np.array([xx,yy]).T
def seg_to_lines(seg):
""" Convert a list of segments to a list of lines """
def extract_continuous(i):
x=[]
y=[]
# Special case, we have only 1 segment remaining:
if i==len(seg)-1:
x.append(seg[i][0,0])
y.append(seg[i][0,1])
x.append(seg[i][1,0])
y.append(seg[i][1,1])
return i,x,y
# Looping on continuous segment
while i<len(seg)-1:
# Adding our start point
x.append(seg[i][0,0])
y.append(seg[i][0,1])
# Checking whether next segment continues our line
Continuous= all(seg[i][1,:]==seg[i+1][0,:])
if not Continuous:
# We add our end point then
x.append(seg[i][1,0])
y.append(seg[i][1,1])
break
elif i==len(seg)-2:
# we add the last segment
x.append(seg[i+1][0,0])
y.append(seg[i+1][0,1])
x.append(seg[i+1][1,0])
y.append(seg[i+1][1,1])
i=i+1
return i,x,y
lines=[]
i=0
while i<len(seg):
iEnd,x,y=extract_continuous(i)
lines.append(np.array( [x,y] ).T)
i=iEnd+1
return lines
def lines_to_arrows(lines,n=5,spacing=None,normalize=True):
""" Extract "streamlines" arrows from a set of lines
Either: `n` arrows per line
or an arrow every `spacing` distance
If `normalize` is true, the arrows have a unit length
"""
if spacing is None:
# if n is provided we estimate the spacing based on each curve lenght)
spacing = [ curve_coord(l)[-1]/n for l in lines]
try:
len(spacing)
except:
spacing=[spacing]*len(lines)
lines_s=[curve_extract(l,spacing=sp,offset=sp/2) for l,sp in zip(lines,spacing)]
lines_e=[curve_extract(l,spacing=sp,offset=sp/2+0.01*sp) for l,sp in zip(lines,spacing)]
arrow_x = [l[i,0] for l in lines_s for i in range(len(l))]
arrow_y = [l[i,1] for l in lines_s for i in range(len(l))]
arrow_dx = [le[i,0]-ls[i,0] for ls,le in zip(lines_s,lines_e) for i in range(len(ls))]
arrow_dy = [le[i,1]-ls[i,1] for ls,le in zip(lines_s,lines_e) for i in range(len(ls))]
if normalize:
dn = [ np.sqrt(ddx**2 + ddy**2) for ddx,ddy in zip(arrow_dx,arrow_dy)]
arrow_dx = [ddx/ddn for ddx,ddn in zip(arrow_dx,dn)]
arrow_dy = [ddy/ddn for ddy,ddn in zip(arrow_dy,dn)]
return arrow_x,arrow_y,arrow_dx,arrow_dy
# --- Main body of streamQuiver
# Extracting lines
seg = sp.lines.get_segments() # list of (2, 2) numpy arrays
lines = seg_to_lines(seg) # list of (N,2) numpy arrays
# Convert lines to arrows
ar_x, ar_y, ar_dx, ar_dy = lines_to_arrows(lines,spacing=spacing,n=n,normalize=True)
# Plot arrows
qv=ax.quiver(ar_x, ar_y, ar_dx, ar_dy, *args, angles='xy', **kwargs)
return qv
# --- Example
x = np.linspace(-1,1,100)
y = np.linspace(-1,1,100)
X,Y=np.meshgrid(x,y)
u = -np.sin(np.arctan2(Y,X))
v = np.cos(np.arctan2(Y,X))
xseed=np.linspace(0.1,1,4)
fig=plt.figure()
ax=fig.add_subplot(111)
sp = ax.streamplot(x,y,u,v,color='k',arrowstyle='-',start_points=np.array([xseed,xseed*0]).T,density=30)
qv = streamQuiver(ax,sp,spacing=0.5, scale=60)
plt.show()

I'm not sure about just increasing the number of arrowheads - but you can increase the density of streamlines with the density parameter in the streamplot function, here's the documentation:
*density* : float or 2-tuple
Controls the closeness of streamlines. When `density = 1`, the domain
is divided into a 30x30 grid---*density* linearly scales this grid.
Each cell in the grid can have, at most, one traversing streamline.
For different densities in each direction, use [density_x, density_y].
Here is an example:
import matplotlib.pyplot as plt
import numpy as np
x = np.arange(0,20,1)
y = np.arange(0,20,1)
u=np.random.random((x.shape[0], y.shape[0]))
v=np.random.random((x.shape[0], y.shape[0]))
fig, ax = plt.subplots(2,2)
ax[0,0].streamplot(x,y,u,v,density=1)
ax[0,0].set_title('Original')
ax[0,1].streamplot(x,y,u,v,density=4)
ax[0,1].set_xlim(5,10)
ax[0,1].set_ylim(5,10)
ax[0,1].set_title('Zoomed, higher density')
ax[1,1].streamplot(x,y,u,v,density=1)
ax[1,1].set_xlim(5,10)
ax[1,1].set_ylim(5,10)
ax[1,1].set_title('Zoomed, same density')
ax[1,0].streamplot(x,y,u,v,density=4)
ax[1,0].set_title('Original, higher density')
fig.show()

I have found a way to customize the number of arrowheads on streamline plot.
The idea is to plot streamline and arrows separately:
plt.streamplot returns a stream_container with two attributes: lines and arrows. The lines contain line segments that can be used to reconstruct streamline without arrows.
plt.quiver can be used to plot gradient fields. With the proper scaling, the length of the arrows is neglectable, leaving only arrowheads.
Thus, we only need to define the positions of arrows using the line segments and pass them to plt.quiver.
Here is a toy example:
import matplotlib.pyplot as plt
from matplotlib import collections as mc
import numpy as np
# get line segments
fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
sp = ax.streamplot(x, y, u, v, start_points=start_points, density=10)
seg = sps.lines.get_segments() # seg is a list of (2, 2) numpy arrays
lc = mc.LineCollection(seg, ...)
# define arrows
# here I define one arrow every 50 segments
# you could also select segs based on some criterion, e.g. intersect with certain lines
period = 50
arrow_x = np.array([seg[i][0, 0] for i in range(0, len(seg), period)])
arrow_y = np.array([seg[i][0, 1] for i in range(0, len(seg), period)])
arrow_dx = np.array([seg[i][1, 0] - seg[i][0, 0] for i in range(0, len(seg), period)])
arrow_dy = np.array([seg[i][1, 1] - seg[i][0, 1] for i in range(0, len(seg), period)])
# plot the final streamline
fig = plt.figure(figsize=(12.8, 10.8))
ax = fig.add_subplot(1, 1, 1)
ax.add_collection(lc)
ax.autoscale()
ax.quiver(
arrow_x, arrow_y, arrow_dx, arrow_dy, angles='xy', # arrow position
scale=0.2, scale_units='inches', units='y', minshaft=0, # arrow scaling
headwidth=6, headlength=10, headaxislength=9) # arrow style
fig.show()
There is more than one way to scale the arrows so that they appear to have zero length.

Related

How to split a 3D array of positions into subvolumes

Not sure if this question has been asked before–I looked through similar examples and they weren't exactly what I need to do.
I have an array of positions (shape = (8855470, 3)) in a cube with physical coordinates in between 0 and 787.5. These positions represent point masses in some space. Here's a look at the first three entries of this array:
array([[224.90635586, 720.494766 , 19.40263367],
[491.25279546, 41.26026654, 7.35436416],
[407.70436788, 340.32618713, 328.88192913]])
I want to split this giant cube into a number of smaller cubes. For example, if I wanted to split it on each side into 10 cubes, making 1,000 subcubes total, then each subcube would contain only the points that have positions within that subcube. I have been experimenting with np.meshgrid to create the 3D grid necessary to conditionally apportion the appropriate entries of the positions array to subcubes:
split = np.arange(0.,(787.5+787.5/10.),step=787.5/10.)
xg,yg,zg = np.meshgrid(split,split,split,indexing='ij')
But I'm not sure if this is the way to go about this.
Let me know if this question is too vague or if you need any additional information.
For sake of problem I will work with toy data. I think you're near with the meshgrid. Here's a propossal
Create grid but with points until 757.5 not included, with values as you did in arange.
Reshape then to have a 1d_array. for in arrays zip to get masks with the cube shape.
create a list to save all subcube points.
import numpy as np
data = np.random.randint(0,787,( 10000,3))
start = 0
end = 787.5
step = (end-start)/10
split = np.arange(start,end,step)
xg,yg,zg = np.meshgrid(split,split,split,indexing='ij')
xg = xg.reshape(-1)
yg = yg.reshape(-1)
zg = zg.reshape(-1)
subcube_data = []
for x,y,z in zip(xg,yg,zg):
mask_x = (x<= data[:,0] ) * ( data[:,0] < x+step) #data_x between start and end for this subcube
mask_y = (y<= data[:,1] ) * ( data[:,1] < y+step) #data_y between start and end for this subcube
mask_z = (z<= data[:,2] ) * ( data[:,2] < z+step) #data_z between start and end for this subcube
mask = mask_x * mask_y * mask_z
subcube_data.append(data[mask])
Now you will have a list with 1000 elements where each element is a sub_cube containing an Nx3 point list. If you want to recover the 3d index corresponding to every sub_cube[i] you just could do [xg[i],yg[i],zg[i]].
Last you can plot to see some of the sub_cubes and the rest of data
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
#plot data as 3d scatter border black
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
#plot subcubes 0 1 2 3 4 in colors
for i in range(5):
ax.scatter(subcube_data[i][:,0],
subcube_data[i][:,1],
subcube_data[i][:,2], marker='o', s=2)
for i in range(5,len(subcube_data)):
ax.scatter(subcube_data[i][:,0],
subcube_data[i][:,1],
subcube_data[i][:,2],marker='o', s=1, color='black')

Color gradient on one contour line

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.

Add subplots row header that scales properly in matplotlib

How can I use annotate() (or any other command for that matter) to add a second "ylabel" to the right of a figure which makes the text "scale" the same way as the other texts (axis x,y-label and title)? With scaling I mean that I don't want to hack text offsets manually or have a solution which fails as soon as I rescale the figure/add more plots/add a colorbar or similar. I don't want to use twinx, because I'm not plotting any additional data, and I don't need another axis.
Here's an image of what I want to achieve:
Here is my code to produce this image, I want to change the ax.annotate part:
import numpy as np
import matplotlib.pyplot as plt
numPlotsY = 3
numPlotsX = 3
f, ax_grid = plt.subplots(numPlotsY,numPlotsX,sharex=True,sharey=True)
A = np.arange(numPlotsY)+1.0 # Amplitude
phi = np.arange(numPlotsX) # Phase shift
x = np.linspace(0,2.0,100) # x
for y_i in range(0,numPlotsY):
for x_i in range(0,numPlotsX):
ax = ax_grid[y_i,x_i]
y = A[y_i]*np.sin(x*np.pi + phi[x_i])
ax.plot(x,y,lw=2.0)
# Add xlabel to the left column
if x_i == 0:
ax.set_ylabel(r'$y$')
ax.set_yticks([-4,-2,0,2,4])
# Add ylabel below bottom row
if y_i == numPlotsY-1:
ax.set_xlabel(r'$x/\pi$')
ax.set_xticks([0.5,1.0,1.5])
# Add Phi label above top row
if y_i == 0:
ax.set_title(r'$\phi=%s$' % phi[x_i])
# Add amplitude label to the right... how??
if x_i == numPlotsX-1:
ax.annotate(r'$A=%d$' % A[x_i], xy=(1.1,0.5), rotation=90,
ha='center',va='center',xycoords='axes fraction')
f.subplots_adjust(wspace=0,hspace=0)
plt.suptitle(r'$A\cdot\sin\left(2\pi x + \phi\right)$',fontsize=18)
plt.show()
I've seen this topic discussed several times without an elegant solution. There's always so much hacking involved. I really think this boils down to the way matplotlib treats the axes. Why can't there be one label for each of the four sides of the figure, that behave the same way?

Transformations in matplotlib

I'm trying to draw objects (lines/patches) with a fixed size (in device coordinates) at a certain position (in data coordinates). This behavior is akin to markers and the tips of annotation arrows, both of which are (size-) invariant under zoom and pan.
Why does the following example not work as expected?
The expected output is two crossed lines forming the diagonals of a 50x50 point square (device coordinates). The left lower corner of said square should be at point (1,0) in data coordinates.
While the computed points appear to be correct, the second diagonal is simply not visible.
import matplotlib.pyplot as plt
import matplotlib.patches as mpatches
import matplotlib.path as mpath
import matplotlib.transforms as mtrans
import matplotlib as mpl
import numpy as np
class FixedPointOffsetTransform(mtrans.Transform):
"""
Always returns the same transformed point plus
the given point in device coordinates as an offset.
"""
def __init__(self, trans, fixed_point):
mtrans.Transform.__init__(self)
self.input_dims = self.output_dims = 2
self.has_inverse = False
self.trans = trans
self.fixed_point = np.array(fixed_point).reshape(1, 2)
def transform(self, values):
fp = self.trans.transform(self.fixed_point)
values = np.array(values)
if values.ndim == 1:
return fp.flatten() + values
else:
return fp + values
fig , ax = plt.subplots(1,1)
ax.set_xlim([-1,10])
ax.set_ylim([-1,10])
# this transformation shifts the input by the given offset
# the offset is transformed with the given transformation
# and then added to the input
fixed_pt_trans = FixedPointOffsetTransform(ax.transData, (1, 0))
# these values are in device coordinates i.e. points
height = 50
width = 50
# two points in device coordinates, that are modified with the above transformation
A = fixed_pt_trans.transform((0,0))
B = fixed_pt_trans.transform((width,height))
l1 = mpl.lines.Line2D([A[0],B[0]], [A[1],B[1]])
ax.add_line(l1)
# already in device coordinates with the offset applied,
# no further transformation nessesary
l1.set_transform(None)
print(A)
print(B)
print(l1.get_transform().transform(A))
print(l1.get_transform().transform(B))
# two points in device coordinates (unmodified)
A = (width,0)
B = (0,height)
l2 = mpl.lines.Line2D([A[0],B[0]], [A[1],B[1]])
ax.add_line(l2)
# apply transformation to add offset
l2.set_transform(fixed_pt_trans)
print(l2.get_transform().transform(A))
print(l2.get_transform().transform(B))
fig.show()
According to matplotlib API Changes documentation, starting with matplotlib 1.2.x:
Transform subclassing behaviour is now subtly changed. If your transform implements a non-affine transformation, then it should override the transform_non_affine method, rather than the generic transform method.
Therefore, simply reimplementing the transform_non_affine instead of the transform method, as said above, in the FixedPointOffsetTransform class seems to solve the issue:
class FixedPointOffsetTransform(mtrans.Transform):
"""
Always returns the same transformed point plus
the given point in device coordinates as an offset.
"""
def __init__(self, trans, fixed_point):
mtrans.Transform.__init__(self)
self.input_dims = self.output_dims = 2
self.has_inverse = False
self.trans = trans
self.fixed_point = np.array(fixed_point).reshape(1, 2)
def transform_non_affine(self, values):
fp = self.trans.transform(self.fixed_point)
values = np.array(values)
if values.ndim == 1:
return fp.flatten() + values
else:
return fp + values

get bins coordinates with hexbin in matplotlib

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))

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