rot_equal.py

import numpy

from collections import defaultdict
from numpy import newaxis

def rotate_packed(packed):
    """
    Return a rotated version of a 55-length
    array packed into 55 bits. Eg.

        rotate(0b1101) == 0b01101
        rotate(2**54)  == 0b1
    """

    mask = 2**55 - 1
    upper = (packed << 1) & mask
    lower = packed >> 54

    return upper | lower

# Test data
bits = numpy.random.randint(0, 2, (55, 26235))
bits[:, 10] = bits[:, 20] = bits[:, 30] = bits[:, 40] = bits[:, 50]

# Pack each into a 64-bit number by multiplying each bit
# by its value (2**pos) and summing along the arrays
bit_values = 2 ** numpy.arange(55)
packed = (bits * bit_values[:, newaxis]).sum(axis=0)

# Generate the rotation of each packed list with the
# minimum packed value. So 0b0001101 → 0b1101.
minimum_rotation = packed

for i in range(54):
    packed = rotate_packed(packed)
    minimum_rotation = numpy.minimum(minimum_rotation, packed)

# Generate a dictionary
# {packed value → all indexes with those value}
groups = defaultdict(set)

for i, value in enumerate(minimum_rotation):
    groups[value].add(i)

# Find the group with the most members
max(groups.values(), key=len)
#>>> {40, 10, 50, 20, 30}

Could you give as a step by step (in the comments) on what happens to your array as it goes through?