A friend of came up with the problem. There are a set of points [(x, y), (x1, y1), (x2, …]. He wanted to find the points at which this line would pass the value Z less than the peak. If the maximum value is 100 and Z = 20. He wanted to find the points where it would cross y = 80.

Now there are multiple ways to solve this problem. I attempted a simple linear interpolation solution.

I don’t the solution itself to be a big thing. What I am really impressed is, how neatly I was able to present the solution using Jupyter Notebook to him.

I was able to document the solution in a step by step fashion, with visual representation of how I solved it.

Take a look

from IPython.display import display import matplotlib.pyplot as plt f = [100, 102, 103.5, 105.5, 106.5, 107.5, 108.5, 110] mag = [0, 30, 40, 145.3, 166.5, 164.5, 75.79, 65.3] fig, ax = plt.subplots() ax.plot(f, mag) for x,y in zip(f, mag): label = ax.text(x, y, y) fig.tight_layout()

gap = 30 # 1. Find the maximum value max_mag = max(mag) # 2. Set the threshold value y = max_mag - gap ax.hlines(y, f[0], f[-1], linewidth=0.5, color="cyan") display(fig)

max_idx = mag.index(max_mag) # 4. Find the left and right values which are lower than the "y" you are looking for left_start_idx = None left_end_idx = max_idx right_start_idx = max_idx right_end_idx = None for i in range(max_idx): left_idx = max_idx - i right_idx = max_idx + i # if left index is more than Zero (array left most is 0) and left is not yet set if left_idx >= 0 and not left_start_idx: value = mag[left_idx] # if the value is lower than our threshold then pickup the point # and the one next to it # that will form our segment to interoploate if value < y: left_start_idx = left_idx left_end_idx = left_idx + 1 # if the right index is less than our array size (0..N) and right is not yet set if right_idx < len(mag) and not right_end_idx: value = mag[right_idx] if value < y: right_end_idx = right_idx right_start_idx = right_idx - 1 if not right_end_idx: print("Cannot find point on the right lower than %d" % (y)) if not left_start_idx: print("Cannot find point on the left lower than %d" % (y)) # Plotting the lines we will be interpolating if left_mag and right_mag: ax.plot( [f[left_start_idx], f[left_end_idx]], [mag[left_start_idx], mag[left_end_idx]], color='red' ) ax.plot( [f[right_start_idx], f[right_end_idx]], [mag[right_start_idx], mag[right_end_idx]], color='red' ) display(fig)

#### Now Let us use the line equation

Solving for x we get

# Left point interpolation y1 = mag[left_start_idx] y2 = mag[left_end_idx] x1 = f[left_start_idx] x2 = f[left_end_idx] x = x1 + (x2 - x1) * (y - y1) / (y2 - y1) ax.scatter([x], [y], color="green") display(fig)

# Right point interpolation y1 = mag[right_start_idx] y2 = mag[right_end_idx] x1 = f[right_start_idx] x2 = f[right_end_idx] x = x1 + (x2 - x1) * (y - y1) / (y2 - y1) ax.scatter([x], [y], color="green") display(fig)

I was able to export the whole thing as a PDF and send it to him.