How to Find the Intersection of a Curve with y==0 Using Linear Interpolation in Python?

Finding the Intersection of a Curve with y==0 Using Linear Interpolation

In Python, we can create a plot from data stored in arrays using the matplotlib library. However, obtaining the exact y-axis value of a curve's intersection with y==0 can be challenging.

To address this, we can employ linear interpolation to approximate the intersection point, as follows:

1. Define the problem: Given arrays containing data points gradient(temperature_data) and vertical_data, we need to determine the value on the y-axis where the curve intersects y==0.

2. Implement the solution: We can find the roots or zeros of the data array using linear interpolation:

   <code class="python">import numpy as np
   
   def find_roots(x, y):
       s = np.abs(np.diff(np.sign(y))).astype(bool)
       return x[:-1][s] + np.diff(x)[s]/(np.abs(y[1:][s]/y[:-1][s])+1)</code>

3. Apply the solution:

   <code class="python">z = find_roots(gradient(temperature_data), vertical_data)</code>

4. Plot the results: To visualize the intersection, we can plot the data points and mark the zero-crossing with a marker:

   <code class="python">import matplotlib.pyplot as plt
   
   plt.plot(gradient(temperature_data), vertical_data)
   plt.plot(z, np.zeros(len(z)), marker="o", ls="", ms=4)
   
   plt.show()</code>

This method provides an approximation of the exact intersection point between the curve and y==0.

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