can not detect knee/elbow point in python 3.9

[kk120120]

Hi guys,
Not sure if as below showing, it not supports 3.9x?

If it is supposed to support 3.9x, the below most probably is an issue.
Thanks!

===================================
Python 3.9.7
Name: kneed
Version: 0.7.0

import scipy.stats as st
import plotly.express as px
import numpy as np
import kneed as kd

x2 = np.linspace(-3,3,500)
y2 = np.apply_along_axis(st.norm.cdf,0,x2)

fig = px.line(x=x2,y=y2)
fig.update_layout(height=600,
                  width=900,
                  title="-3到+3正态分数据的布累积概率图"
                 )
fig.show()

def find_elbows(c,d,fc=0):
    ew = kd.KneeLocator(x=x2,y=y2,S=fc,
                     curve=c,
                     direction=d,
                     online=False
                    )
    return ew

ews = [ find_elbows(x,y) for x in ['concave','convex'] for y in ['increasing','decreasing']]

for x in ews:
    x.plot_knee()

[AdrienWehrle]

This issue was most likely raised due to the use of a very smooth curve with default parameters, and not because of the Python version. Reducing x2 to e.g. np.linspace(-3,3,500)[::80] and plotting find_elbows('convex', 'increasing').plot_knee() gives the following:

Because downsampled, the data now shows a real elbow!

[arvkevi]

This seems like a good use case to set online=True. The documentation discusses how setting this will alter the identification of knee points by self-correcting and avoiding local maxima. I don't think the "issue" above is primarily a function of the smooth line. I also don't think it's a Python 3.9 issue, I just ran some tests in a Python 3.9 env locally.

I find it helpful to use plot_normalized_knee() to look at the difference curve when cases like these arise. The knee should, in theory, be the max value of the difference curve.

I hope this helps!