How to find corresponding X values when the curve equation is unknown in python

I have data belonging to cumulative distribution. But the range of the x-axis depends on the input data. The y-axis is equally divided into 5 segments. I need to find the corresponding X-axis segments to that.

I tried it with the torch quantile as follows

x_segments = torch.quantile(Cumulative_curve, torch.tensor(y_segemts))

Then the obtained x_segments multiply with the x-axis range. but the result is not as expected as shown in the following figure

How can I do this using python?

I don't have your sample data to test but I used my sample data and tried the following if this could help you

import torch

# Cumulative distribution data
cumulative_curve = torch.tensor([0.1, 0.3, 0.5, 0.7, 0.9])

# Define the number of segments on the y-axis
num_segments = 5

# Calculate the y-axis segment values
y_segments = torch.linspace(0, 1, num_segments + 1)

# Find the corresponding x-axis segments
x_segments = torch.quantile(cumulative_curve, y_segments)

# Multiply the x-axis segments with the desired x-axis range
x_range_min = 0  # Minimum value of the x-axis range
x_range_max = 100  # Maximum value of the x-axis range
x_segments *= (x_range_max - x_range_min)
x_segments += x_range_min

# Print the x-axis segments
for i in range(len(y_segments)):
    print(f"Segment {i+1}: [{x_segments[i]:.2f}, {x_segments[i+1]:.2f}]")

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

# Define your cumulative distribution curve as a list or a tensor
cumulative_curve = [0.1, 0.3, 0.55, 0.8, 1.0]  # Example values
x= [0,1, 2,3, 4]
# Define the corresponding y-axis segments
y_segments = [0.2, 0.4, 0.6, 0.8, 1.0]  # Example values

# Define the maximum value of the x-axis
N = 4 # Example value

# Convert the cumulative curve to a PyTorch tensor
cumulative_curve_tensor = torch.tensor(cumulative_curve)

# Find the corresponding x-axis segments for each scaled y-axis segment

x_seg = np.interp(y_segments, np.array(cumulative_curve ), np.array(x) )




plt.figure()
plt.plot(cumulative_curve_tensor.numpy().T,label = 'tanh-allJ')
for xc in y_segments:
    print('xc = ',xc)
    plt.axhline(y=xc, color='gray', linestyle='--')  

for yc in list(x_seg):
    print('yc= ', yc)
    
    plt.axvline(x=yc, color='gray', linestyle='--')
print("Corresponding x-axis segments:", x_seg)

This code solved my problem. If anybody needs you also can use this one.