[Python] How can I vectorize a function that returns eigenvalues and eigenvectors of a matrix...

I'm working with a function in Python that constructs a 4×4 matrix based on inputs (x1, y1, x2, y2), and computes its eigenvalues and eigenvectors using np.linalg.eigh.

Here is a simplified version of my code:

import numpy as np

def f(kx, ky):
return kx + 1j * ky

def fs(kx, ky):
return np.conj(f(kx, ky))

def eig(x1, y1, x2, y2):
a = 10
x = x1 + x2
y = y1 + y2
H = np.array([
[a, f(x, y), f(x, y), fs(x, y)],
[fs(x, y), a, 0, f(x, y)],
[fs(x, y), 0, -a, f(x, y)],
[f(x, y), fs(x, y), fs(x, y), -a]
])

Eval, Evec = np.linalg.eigh(H)
sorted_indices = np.argsort(Eval)
return Eval[sorted_indices], Evec[:, sorted_indices]



Now, I have 1-d arrays of input values:

x1_array, y1_array, x2_array, y2_array # all same shape


I want to efficiently vectorize this function across those arrays — i.e., compute all eigenvalues/eigenvectors in a batched way without writing an explicit Python loop if possible.

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