# 5 Best Ways to Create a Circular Polar Histogram in Python

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π‘ Problem Formulation: A circular polar histogram is a graphical representation of data with a circular layout, often used to show the distribution of directional data. In Python, we seek to convert an input array of angles, perhaps wind directions or orientations, into a circular histogram to visualize the frequency of each direction. The desired output is a plot that shows the angular data points distributed around a circle, with the histogram bars’ length corresponding to the frequency of the data points in each angular bin.

## Method 1: Using Matplotlib

Matplotlib’s `pyplot` module offers a flexible way to create circular polar histograms. You can use the `hist` method providing the parameter `bins` for resolution control and `polar=True` to create the circular histogram.

Here’s an example:

```import matplotlib.pyplot as plt
import numpy as np

angles = np.random.uniform(0, 2*np.pi, 100)  # Sample data
ax = plt.subplot(111, polar=True)
ax.hist(angles, bins=30, alpha=0.75)
ax.set_title('Circular Polar Histogram')
plt.show()```

Output: A circular polar histogram displayed in a popup window.

This snippet generates random angles and creates a polar histogram with 30 bins. The `subplot(111, polar=True)` configures the plot to be circular, and the `hist` function creates the histogram on the polar axis. `plt.show()` displays the plot.

## Method 2: Using Seaborn

Although Seaborn doesn’t natively support polar histograms, you can combine it with Matplotlib to take advantage of its elegant styling. Seaborn’s `set_style` method can be used for aesthetic enhancements.

Here’s an example:

```import matplotlib.pyplot as plt
import seaborn as sns
import numpy as np

sns.set_style("whitegrid")
angles = np.random.uniform(0, 2*np.pi, 100)
ax = plt.subplot(111, polar=True)
ax.hist(angles, bins=16, alpha=0.75, color='skyblue')
ax.set_title('Circular Polar Histogram with Seaborn Styling')
plt.show()```

Output: A circular polar histogram displayed with Seaborn’s style in a popup window.

In this code, we first set the plot style using Seaborn, then follow a similar approach to Matplotlib for the histogram. Seaborn’s style control features enhance the resulting plot’s appearance without adding complexity to the histogram creation itself.

## Method 3: Using Plotly

Plotly is a versatile graphing library that allows for interactive plots, including circular polar histograms, which are created using its `Barpolar` trace.

Here’s an example:

```import plotly.graph_objects as go
import numpy as np

angles = np.random.uniform(0, 360, 100)  # Sample data in degrees
fig = go.Figure(go.Barpolar(
r=np.histogram(angles, bins=18)[0],
theta=np.linspace(0, 360, 18, endpoint=False)
))
fig.update_layout(title='Interactive Circular Polar Histogram with Plotly')
fig.show()```

Output: An interactive circular polar histogram displayed in a web browser.

This uses Plotly’s `Barpolar` trace to create an interactive polar bar chart. We convert our sample angle data into a histogram using NumPy’s `histogram` function, then plot the frequency counts versus the bin angles.

## Method 4: Using Bokeh

Bokeh is another library for interactive visualization, providing an interface for creating circular polar histograms through its plotting methods and glyph functions.

Here’s an example:

```from bokeh.plotting import figure, show, output_file
from math import pi
import numpy as np

output_file('bokeh_polar_histogram.html')
angles = np.random.uniform(0, 2*np.pi, 100)
hist, edges = np.histogram(angles, bins=16)

p = figure(title="Circular Polar Histogram with Bokeh", sizing_mode="stretch_width", height=350, x_axis_type=None, y_axis_type=None, tools="reset,save", toolbar_location=None, match_aspect=True)

show(p)```

Output: An interactive circular polar histogram displayed in a web browser.

This script creates a circular polar histogram using Bokeh’s high-level `annular_wedge` glyph, which is perfect for drawing the individual sections of our histogram. We create a histogram from our angle data and then plot each of the wedges accordingly.

## Bonus One-Liner Method 5: Using Hack

For those looking to generate a circular polar histogram quickly, here’s a one-line hack that leverages NumPy and Matplotlib:

Here’s an example:

`(plt.subplot(111, polar=True).hist(np.random.vonmises(0, 4, 100), bins=30, alpha=0.75), plt.show())`

Output: A circular polar histogram displayed in a popup window.

This one-liner creates a circular polar histogram using a von Mises distribution for some variety in the input data. This code is compact but not as readable or flexible for customization.

## Summary/Discussion

• Method 1: Matplotlib. Versatile. Straightforward for simple cases. Limited interactive features.
• Method 2: Seaborn. Stylish. Requires Matplotlib backbone. No native polar histogram functionality.
• Method 3: Plotly. Interactive. More complex syntax. Excellent for web-app integration.
• Method 4: Bokeh. Interactive. Flexible layout. Ideal for standalone web visualizations.
• Method 5: One-liner Hack. Quick. Not customizable. Best for fast prototyping or data exploration.