Matplotlib patch not getting applied properly

Question

I expected something like above to be applied to my scatter plot.but instead i received this

code is as below

# Data
import matplotlib.patches as patches
df1=pd.DataFrame({'x_pos': x, 'y_pos': y })
print(df1)

 
# Plot
fig1 = plt.figure(figsize=(20,10))
ax1 = fig1.add_subplot(111)
ax1.plot( 'x_pos', 'y_pos', data=df1, linestyle='none', marker='o')

 
# Annotation
ax1.add_patch(
patches.Circle(
(35, 40),          
3,                
alpha=0.3, facecolor="green", edgecolor="black", linewidth=1, linestyle='solid'
)
)

# Show the graph
plt.show()

Dataframe

   x_pos  y_pos
0       38  62506
3       33  64991
4       32  50825
5       44  57568
7       38  59365
..     ...    ...
301     44  55140
302     38  58062
303     48  59728
307     39  48513
310     43  45046

what am I doing wrong here ?

You are creating a circle with center (35, 40), while the data points are far away, having x-values around 40 and y-values around 60,000. Also note that when there is a large difference in aspect ratio between the x and y direction, the circle will be squeezed to a thin ellipse. — JohanC
– JohanC, Commented Dec 1, 2021 at 16:59
Maybe use another center? Maybe draw an ellipse with a larger y radius? What do you want to show? — JohanC
– JohanC, Commented Dec 1, 2021 at 18:54
i want to highlight the middle section of the graph with a patch — Sithija Piyuman Thewa Hettige
– Sithija Piyuman Thewa Hettige, Commented Dec 1, 2021 at 18:57

JohanC · Accepted Answer · 2021-12-01 23:11:42Z

You could use the mean of the x and the y positions as the center for an ellipse. And the standard deviation in x and in y for its radius in both directions. Note that for an ellipse, the parameters are the width and height, so the double of the radius.

from matplotlib import pyplot as plt
from matplotlib import patches
import pandas as pd
import numpy as np

df1 = pd.DataFrame({'x_pos': np.random.randint(32, 49, 100),
                    'y_pos': np.random.randint(45000, 63000, 100)})
fig1 = plt.figure(figsize=(20, 10))
ax1 = fig1.add_subplot(111)
ax1.plot('x_pos', 'y_pos', data=df1, linestyle='none', marker='o')

ax1.add_patch(
    patches.Ellipse(
        (df1['x_pos'].mean(), df1['y_pos'].mean()),
        df1['x_pos'].std() * 2, df1['y_pos'].std() * 2,
        alpha=0.3, facecolor="green", edgecolor="black", linewidth=1, linestyle='solid'))

plt.show()

See also this tutorial example or this post about drawing a confidence ellipse.

Here is how the code could look like to draw confidence ellipses for 1,2 and 3 standard deviations (using rotated data to test the ellipse rotation):

from matplotlib import pyplot as plt
from matplotlib import patches
import pandas as pd
import numpy as np

x = np.random.randint(32, 49, 100)
y = np.random.randint(45000, 50000, 100) + x * 500
df1 = pd.DataFrame({'x_pos': x, 'y_pos': y})

lamda, v = np.linalg.eig(np.cov(df1['x_pos'], df1['y_pos']))
lamda = np.sqrt(lamda)

fig1 = plt.figure(figsize=(20, 10))
ax1 = fig1.add_subplot(111)
ax1.plot('x_pos', 'y_pos', data=df1, linestyle='none', marker='o')

for num_std in range(1, 4):
    ax1.add_patch(
        patches.Ellipse(
            xy=(df1['x_pos'].mean(), df1['y_pos'].mean()),
            angle=np.rad2deg(np.arctan2(*v[:, 0][::-1])),
            width=lamda[0] * num_std * 2, height=lamda[1] * num_std * 2,
            alpha=0.1, facecolor="green", edgecolor="black", linewidth=1, linestyle='solid'))
plt.show()

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