How to Determine the Exact y-Axis Intersection of Data Points in Python?

Finding the Exact Intersection of Data Points with the y-Axis

When plotting data in Python, it can be useful to obtain the exact value where a curve intersects the y-axis. This value can be determined using numerical methods, specifically through linear interpolation.

Solution Using Linear Interpolation

The following code demonstrates how to find the zero crossings of a data array using linear interpolation:

<code class="python">import numpy as np

# Generate sample data
N = 750
x = .4 + np.sort(np.random.rand(N)) * 3.5
y = (x - 4) * np.cos(x * 9.) * np.cos(x * 6 + 0.05) + 0.1

# Define function to find roots (zero crossings)
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)

# Find zero crossings
z = find_roots(x, y)

# Plot data and zero crossings
import matplotlib.pyplot as plt
plt.plot(x, y)
plt.plot(z, np.zeros(len(z)), marker="o", ls="", ms=4)
plt.show()</code>

Inverse Plot for Intercepts at Non-Zero y-Values

The above method can be modified to find intercepts at non-zero y-values (y0) by finding the zeros of y - y0:

<code class="python">y0 = 1.4
z = find_roots(x, y - y0)
plt.plot(z, np.zeros(len(z)) + y0)</code>

Intersections Between Two Curves

Similar to the first method, finding the intersection point between two curves involves finding the zeros of the difference between the two data arrays:

<code class="python"># Generate sample data
x = .4 + np.sort(np.random.rand(N)) * 3.5
y1 = (x - 4) * np.cos(x * 9.) * np.cos(x * 6 + 0.05) + 0.1
y2 = (x - 2) * np.cos(x * 8.) * np.cos(x * 5 + 0.03) + 0.3

# Find intersection points
z = find_roots(x, y2 - y1)

# Plot data and intersection points
plt.plot(x, y1)
plt.plot(x, y2, color="C2")
plt.plot(z, np.interp(z, x, y1), marker="o", ls="", ms=4, color="C1")</code>

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