How can I get variable values from a plot?

Question

I would like to know if there is any way in python to automatically determine the values of point a and b marked in the graph below. Said a different way, finding the values when my plot shows a marked decrease or after a marked increase.

This is the source code of my plot if it is helpful:

#load data

min_duration = data['Time_Secondes'].min()
max_duration = data['Time_Secondes'].max()
xr_ = list(range(min_duration,  max_duration,  60))
y_ = []

for i in range(0,(len(xr_)-1)):
    Time_proba_ = np.logical_and(data['Time_Secondes'].values >= xr_[i], data['Time_Secondes'].values < xr_[i+1])
    Time_proba_1_ = np.logical_and(np.logical_and(data['Time_Secondes'].values >= xr_[i], data['Time_Secondes'].values < xr_[i+1]), data['outcome'].values==1)
    y_.append(sum(Time_proba_1_ )/sum(Time_proba_))


import matplotlib
matplotlib.pyplot.plot(xr_[1:len(xr_)], y_)

```

Answer 1

It seems what you are looking for is a function of your data, not of matplotlib. I would think of this as a second derivative problem -- you care about differences in slopes of successive lines.

1. Sort a dataframe [x,y] by x values, in increasing order.
2. Calculate the first discrete derivative delta1 = (y[i+1] - y[i]) / (x[i+1] - x[i]). This tells you the slope of each line.
3. Now you can do one of two things, depending on what you want to identify.
   1. Calculate the second discrete derivative delta2 = (delta1[i+1] - delta1[i]) / (x[i+1] - x[i]).
   2. Calculate the difference of successive slopes diff = delta1[i+1] - delta1[i]
4. Select all is for which absolute value of {diff or delta2} is greater than a certain threshold.

Selecting all x values for which np.abs(x[i]) > threshold will give you the x-locations of these large changes in slope.

Here's an example I just coded up,for identifying the jump in a jump function $x / |x|$.

import numpy as np
import pandas as pd

n_data = 100

x = np.random.uniform(-10,10,n_data)
y = x / np.abs(x)

delta = [0] * n_data
diff = [0] * n_data

data = pd.DataFrame({'x':x, 'y':y})
data = data.sort_values('x')

for i in range(n_data - 1):
    a, fa = data.iloc[i]
    b, fb = data.iloc[i+1]
    diff_quot = (fb - fa) / (b-a)
    delta[i] = diff_quot

data['delta'] = delta

for i in range(n_data - 1):
    a, fa, da = data.iloc[i]
    b, fb, db = data.iloc[i+1]
    dd = db - da
    diff[i] = np.abs(dd)

data['diff'] = diff

plt.plot(data['x'],data['y'])
plt.plot(data['x'],data['diff'])

threshold = 1
jumps = [dd > threshold for dd in diff]

Here is the jump function, whose jump we might want to locate

Here is a graph of the differences in slopes, where we see the jump is located near x = 0