Polar histogram in Python for given r, theta and z values

Question

I have a dataframe consisting of measurements from a particular magnetometer station over time, with columns corresponding to:

its latitude (which I think of as a radius)
its azimuthal angle
a measured quantity at this specific time

I was wondering of a way to plot this dataframe as a polar histogram for the measured variable: ie something like this:

I have looked at the special histogram in physt but this allows me to only put in x,y values and I'm quite confused by it all.

Could anybody help?

Seconding on the cool chart. The closest I've ever encountered is https://matplotlib.org/basemap/users/paeqd.html but I'm not sure it can be stretched for this kind of output — roganjosh, Mar 08 '19 at 13:39
Are you sure you want a histogram? That seems to contradict the third requirement "a measured quantity at this specific time". Can you clarify what exactly you need? — ImportanceOfBeingErnest, Mar 08 '19 at 13:53
Essential what I want to show is a certain characteristic of the measured quantity at a specific radius-azimuth bin. So with histogram what I mean is an occurrence number in the specific radius-azimuth bin. Does that help? — R Thompson, Mar 08 '19 at 14:20
No, it doesn't. It's easy: Do you have 2 columns, `radius` and `azimut`? Then you can plot occurance as histogram. Do you have 3 columns, `radius` and `azimut`, `measured quantity`, then you cannot plot a histogram, but rather the `measured quantity` as a function of the other two. Which one is it? — ImportanceOfBeingErnest, Mar 08 '19 at 17:16
Right now the first one, and I’ve managed to plot it now. In the future I’ll need to do the second, but I believe in my mind I know how to do that now too — R Thompson, Mar 08 '19 at 17:23

score 7 · Accepted Answer · answered Mar 08 '19 at 17:46

Calculating a histogram is easily done with numpy.histogram2d. Plotting the resulting 2D array can be done with matplotlib's pcolormesh.

import numpy as np; np.random.seed(42)
import matplotlib.pyplot as plt

# two input arrays
azimut = np.random.rand(3000)*2*np.pi
radius = np.random.rayleigh(29, size=3000)

# define binning
rbins = np.linspace(0,radius.max(), 30)
abins = np.linspace(0,2*np.pi, 60)

#calculate histogram
hist, _, _ = np.histogram2d(azimut, radius, bins=(abins, rbins))
A, R = np.meshgrid(abins, rbins)

# plot
fig, ax = plt.subplots(subplot_kw=dict(projection="polar"))

pc = ax.pcolormesh(A, R, hist.T, cmap="magma_r")
fig.colorbar(pc)

plt.show()

Thanks this was exactly what I wanted! – R Thompson Mar 08 '19 at 18:48 — R Thompson, Mar 08 '19 at 18:48

rgk · Answer 2 · 2019-03-08T14:57:00.280

4

This appears to be what you're looking for: https://physt.readthedocs.io/en/latest/special_histograms.html#Polar-histogram

from physt import histogram, binnings, special
import numpy as np
import matplotlib.pyplot as plt

# Generate some points in the Cartesian coordinates
np.random.seed(42)

x = np.random.rand(1000)
y = np.random.rand(1000)
z = np.random.rand(1000)

# Create a polar histogram with default parameters
hist = special.polar_histogram(x, y)
ax = hist.plot.polar_map()

The docs linked include more examples with colors, bin sizing etc.

Edit: I think this is going to take a bit of munging to get your data into the right shape, but I think this example illustrates the library's capabilities and can be adjusted to your use case:

import random
import numpy as np
import matplotlib.pyplot as plt
from physt import special

# Generate some points in the Cartesian coordinates
np.random.seed(42)

gen = lambda l, h, s = 3000: np.asarray([random.random() * (h - l) + l for _ in range(s)])

X = gen(-100, 100)
Y = gen(-1000, 1000)
Z = gen(0, 1400)

hist = special.polar_histogram(X, Y, weights=Z, radial_bins=40)
# ax = hist.plot.polar_map()

hist.plot.polar_map(density=True, show_zero=False, cmap="inferno", lw=0.5, figsize=(5, 5))
plt.show()

edited Mar 08 '19 at 14:57

answered Mar 08 '19 at 13:39

rgk

985
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This is what I originally tried, but it doesn't allow for any z information as far as I could figure out – R Thompson Mar 08 '19 at 13:40
z information as in magnitude? Isn't that just the values in the data? Forgive me if I'm not fully understanding your question – rgk Mar 08 '19 at 13:44
I guess for now the values in the data of the measured quantity might not be the most relevant. So forget that apart for now. So I have effectively a time series for r and theta, how would I put that into the function above to get the histogram over the whole azimuthal space? – R Thompson Mar 08 '19 at 13:54
Edited my example above - the package receives X & Y as cartesian coordinates, and your polar coodinate data can be transformed to fit the function and produce the chart you want (see more: https://www.math.uh.edu/~mmsosa/Math1330/Calendar/1330Day28.pdf). I used extreme values for Y to illustrate the point, but symmetrically scaled X & Y inputs would produce a radially symmetric chart. – rgk Mar 08 '19 at 15:05

Polar histogram in Python for given r, theta and z values

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