[Python] NumPy array assignment gives different result from direct computation despite...

Problem Description


I'm performing linear interpolation between two arrays x1 and x2 using weights i/N. The calculation is mathematically simple:

x = (1 - i/N) * x1 + (i/N) * x2


However, when I compare the assigned x with the same formula computed directly in print(), the results differ significantly (e.g., 0.0196 vs 0.02). This contradicts both mathematical equivalence and floating-point error expectations.

Minimal Reproducible Example


import numpy as np

x1 = np.arange(0, 0.5, 0.01) # 0 to 0.49
x2 = np.arange(0.5, 1, 0.01) # 0.5 to 0.99
x = np.zeros_like(x1)
y = x # Shared memory (intentional? bug?)

N = x1.size
for i in range(N):
x = (1 - i/N) * x1 + (i/N) * x2
print(
f"i={i:2d} | weight={i/N:.4f} | "
f"theory: {(1-i/N)*x1 + (i/N)*x2:.6f} | "
f"assigned x: {x:.6f}"
)

Actual Output


0 0 0 0 0 0
1 0.02 0.0098 0.0102 0.0196 0.02
2 0.04 0.0192 0.0208 0.0384 0.04
3 0.06 0.0282 0.0318 0.0564 0.06
4 0.08 0.0368 0.0432 0.0736 0.08
5 0.1 0.045 0.055 0.09 0.1
6 0.12 0.0528 0.0672 0.106 0.12
7 0.14 0.0602 0.0798 0.12 0.14
...
46 0.92 0.0368 0.883 0.0736 0.92
47 0.94 0.0282 0.912 0.0564 0.94
48 0.96 0.0192 0.941 0.0384 0.96
49 0.98 0.0098 0.97 0.0196 0.98


Discrepancy grows with i!

What I've Checked

1. Floating-point precision: Used %.6f to rule out display rounding.
2. Array independence: Initially suspected y = x causing interference, but even removing y assignment doesn't fix it.

Question


Why does the assigned value x differ from the direct computation of the same formula?

• Is this a NumPy-specific behavior?
• Could it be due to memory allocation or implicit type conversion?

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