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I have periodic data and the distribution for it is best visualised around a circle. Now the question is how can I do this visualisation using matplotlib? If not, can it be done easily in Python?

My code here will demonstrate a crude approximation of distribution around a circle:

from matplotlib import pyplot as plt
import numpy as np

#generatin random data
a=np.random.uniform(low=0,high=2*np.pi,size=50)

#real circle
b=np.linspace(0,2*np.pi,1000)
a=sorted(a)
plt.plot(np.sin(a)*0.5,np.cos(a)*0.5)
plt.plot(np.sin(b),np.cos(b))
plt.show()

There are a few examples in a question on SX for Mathematica:

Building off of this example from the gallery, you can do

import numpy as np
import matplotlib.pyplot as plt

N = 80
bottom = 8
max_height = 4

theta = np.linspace(0.0, 2 * np.pi, N, endpoint=False)
radii = max_height*np.random.rand(N)
width = (2*np.pi) / N

ax = plt.subplot(111, polar=True)
bars = ax.bar(theta, radii, width=width, bottom=bottom)

# Use custom colors and opacity
for r, bar in zip(radii, bars):
 bar.set_facecolor(plt.cm.jet(r / 10.))
 bar.set_alpha(0.8)

plt.show()

Of course, there are many variations and tweeks, but this should get you started.

In general, a browse through the matplotlib gallery is usually a good place to start.

Here, I used the bottom keyword to leave the center empty, because I think I saw an earlier question by you with a graph more like what I have, so I assume that's what you want. To get the full wedges that you show above, just use bottom=0 (or leave it out since 0 is the default).

I'm 5 years late to the game, but...

Circular histograms can very easily mislead readers. As such I'd always recommend caution when using them.

In particular, I'd advise staying away from circular / polar histograms that plot frequency radially. This is because the mind is affected by the area of the bins as well as their radial extent. Instead of visualising the number of points in a bin by radius, I advise visualising by area.

The problem

Consider the consequences of doubling the number of data points in a given bin. In a circular frequency histogram the radius of this bin will increase by a factor of 2, however, the area of this bin will increase by a factor of 4. This is because the area of the bin is proportional to the radius squared, and here we have the opportunity to be misled.

If this doesn't sound like too much of a problem yet, let's see it graphically:

Both of the above plots visualise the same dataset.

In the lefthand plot it's easy to see that there are twice as many datapoints in the (0, pi/4) bin than there are in the (-pi/4, 0) bin.

However, take a look at the right hand plot. At first glance your mind is greatly affected by the area of the bins. You'd be forgiven for thinking there are more than twice as many points in the (0, pi/4) bin than there are in the (-pi/4, 0) bin. However, you'd have been misled. It is only on closer inspection of the graphic that you realise there are exactly twice as many datapoints in the (0, pi/4) bin than in the (-pi/4, 0) bin. Not more than twice as many, as the graph may have originally suggested.

The graphics above can be recreated with the following code:

import numpy as np
import matplotlib.pyplot as plt

angles = np.hstack([np.random.uniform(0, np.pi/4, size=100),
 np.random.uniform(-np.pi/4, 0, size=50)])

bins = 2

fig = plt.figure()
ax = fig.add_subplot(1, 2, 1)
polar_ax = fig.add_subplot(1, 2, 2, projection="polar")

ax.hist(angles, bins=bins)
ax.set_xlim([-np.pi/4, np.pi/4])
ax.set_xticks()
ax.set_xticklabels([r'$-pi/4$', r'$0$', r'$pi/4$'])

count, bin = np.histogram(angles, bins=2)
polar_ax.bar(bin[:-1], count, align='edge', color='C0')

polar_ax.set_xticks([0, np.pi/4, 2*np.pi - np.pi/4])
polar_ax.set_xticklabels([r'$0$', r'$pi/4$', r'$-pi/4$'])
polar_ax.set_rlabel_position(90)
fig.tight_layout()

A solution

Since we are so greatly affected by the area of the bins in circular histograms, I find it more effective to ensure that the area of each bin is proportional to the number of observations in each bin, instead of the radius. This is similar to how we are used to interpreting pie charts, where area is important.

Let's use the dataset we used earlier to reproduce the graphics based on area, instead of radius:

I personally find this polar histogram more intuitive and hypothesise that readers have less chance of being mislead at first glance. Of course I'd ensure that an informative caption was placed alongside the figure to explain that here we visualise bins with area, not radius.

These plots were created as:

fig = plt.figure()
ax = fig.add_subplot(1, 2, 1)
polar_ax = fig.add_subplot(1, 2, 2, projection="polar")

ax.hist(angles, bins=bins, density=True)
ax.set_xlim([-np.pi/4, np.pi/4])
ax.set_xticks([-np.pi/4, 0, np.pi/4])
ax.set_xticklabels([r'$-pi/4$', r'$0$', r'$pi/4$'])

counts, bin = np.histogram(angles, bins=2)
area = counts / angles.size
radius = (area / np.pi)**.5

polar_ax.bar(bin[:-1], radius, align='edge', color='C0')

# Label angles according to convention
polar_ax.set_xticks([0, np.pi/4, 2*np.pi - np.pi/4])
polar_ax.set_xticklabels([r'$0$', r'$pi/4$', r'$-pi/4$'])
fig.tight_layout()

Putting it all together

If you create lots of circular histograms, you'd do best to create some plotting function which you can reuse easily. Below I include a function I wrote and use in my work:

def rose_plot(ax, angles, bins=16, density=None, xticks=True, **param_dict):
 """ Plots polar histogram of angles. ax must have been created with using
 kwarg subplot_kw=dict(projection='polar').
 """
 # To be safe, make a coppy of angles before wrapping
 data = angles.copy()
 # Wrap angles to range [0, 2pi)
 data %= 2*np.pi

 # Remove distracting grid
 ax.grid(False)

 # Bin data and record counts
 count, bin = np.histogram(data, bins=np.linspace(0, 2*np.pi, num=bins+1))

 # By default plot density (frequency potentially misleading)
 if density is None or density is True:
 # Area to assign each bin
 area = count / data.size
 # Calculate corresponding bin radius
 radius = (area / np.pi)**.5
 else:
 radius = count

 # Plot data on ax
 ax.bar(bin[:-1] + np.pi/bins, radius, width=2*np.pi/bins, zorder=1,
 edgecolor='C0', fill=False, linewidth=1, **param_dict)

 # Remove ylabels, they are obstructive and not informative
 ax.set_yticks([])

 if xticks:
 # Label angles according to convention
 angle_pos = [0, np.pi/2, np.pi, 3*np.pi/2]
 angle_label = ['$0$', r'$pi/2$', r'$-pi, pi$', r'-$pi/2$']
 ax.set_xticks(angle_pos)
 ax.set_xticklabels(angle_label)
 else:
 ax.set_xticks([])

It's super easy to use this function. Here I demonstrate it's use for some randomly generated directions:

angles0 = np.random.normal(loc=0, scale=1, size=10000)
angles1 = np.random.uniform(-np.pi, np.pi, size=100)

# Visualise with polar histogram
fig, ax = plt.subplots(1, 2, subplot_kw=dict(projection='polar'))
rose_plot(ax[0], angles0)
rose_plot(ax[1], angles1)
fig.tight_layout()

A final note on convention

Directions can be represented as rotations with respect to some zero–direction, or origin. The practitioner is free to chose the zero–direction as they feel appropriate. In a similar way, the practitioner may choose whether a clockwise or anti–clockwise rotation is taken as the positive direction.

Above, I took the zero angle as the direction from (0,0) and along the positive x–axis, and anti-clockwise rotations as the positive direction. I like my angles in radians and restricted to the range (-pi, pi), however, you might not.

Changing a couple of lines in the above function, however, you can plot to any convention you desire: