RoPE Frequency Wavelength

Problem

Compute the wavelength of a RoPE frequency band: 2 * pi * theta_base^(2 * pair_index / dim). Long wavelengths rotate slowly and carry long-range position information.

The signature is rope_wavelength(dim, pair_index, theta_base=10000.0). Return a float.

Hint

Pair index 0 has wavelength 2 * pi regardless of the base or dimension.

Test cases

case 1

in: [4,0]

expected: 6.2831853072

case 2

in: [4,1]

expected: 628.318530718

case 3

in: [8,2,100]

expected: 62.8318530718

case 4

in: [64,31]

expected: 47117.2427801674

Starter codePython

import math
def rope_wavelength(dim, pair_index, theta_base=10000.0):
    # Your code here
    pass

4 test cases · run your code against them in the editor