The script to verify the dataset generated by the attached latin(.exe) utility: that all squares are pandiagonal, how many are semi-cyclic (and in what directions), how many are (fully) cyclic

Please be warned that the script is sensitive to the newline symbols (and their quantity) at the end of the file (after the last square)

import numpy as np
from collections import Counter

def pandiagonal(matrix: np.ndarray, order: int) -> bool:
    matrix_ = matrix.copy()
    for i in range(1,order):
        matrix_[i,:] = matrix_[i,np.mod(np.arange(order) + i, order)]
    for i in range(order):
        if np.unique(matrix_[:,i]).size < order:
            #print(np.unique(matrix_[:,i]).size)
            return False
    matrix_ = matrix.copy()
    for i in range(1,order):
        matrix_[i,:] = matrix_[i,np.mod(np.arange(order) - i, order)]
    for i in range(order):
        if np.unique(matrix_[:,i]).size < order:
            #print(np.unique(matrix_[:,i]).size)
            return False
    return True


def cyclicity_list(matrices: list, order: int) -> list:
    non_pandiagonal = 0
    result = list()
    for square in matrices:
        if pandiagonal(square, order):
            result.append(cyclicity(square, order))
        else:
            non_pandiagonal += 1
    print('There are %d non-pandiagonal squares in the dataset' % non_pandiagonal)
    return result


def cyclicity(matrix: np.ndarray, order: int) -> tuple:
    not_horizontal = True
    for row in range(1, order):
        shift_answer = False
        for shift in range(1, order):
            if (np.roll(matrix[row], shift) == matrix[0]).all():
                shift_answer = True
        if not shift_answer:
            not_horizontal = False
            break
            

    not_vertical = True
    for column in range(1, order):
        shift_answer = False
        for shift in range(1, order):
            if (np.roll(matrix[:, column], shift) == matrix[:, 0]).all():
                shift_answer = True
        if not shift_answer:
            not_vertical = False
            break


    not_main_diagonal = True
    main_diag = matrix.copy()
    for column in range(1,order):
        main_diag[:,column] = np.roll(main_diag[:,column], column)
    for row in range(1, order):
        shift_answer = False
        for shift in range(1, order):
            if (np.roll(main_diag[row], shift) == main_diag[0]).all():
                shift_answer = True
        if not shift_answer:
            not_main_diagonal = False
            break
                
    not_antidiagonal = True
    anti_diag = matrix.copy()
    for column in range(1,order):
        anti_diag[:,column] = np.roll(anti_diag[:,column], -column)
    for row in range(1, order):
        shift_answer = False
        for shift in range(1, order):
            if (np.roll(anti_diag[row], shift) == anti_diag[0]).all():
                shift_answer = True
        if not shift_answer:
            not_antidiagonal = False
            break
                
    return (not_horizontal, not_vertical, not_main_diagonal, not_antidiagonal)

outcomes = [' horizontal', ' vertical', ' main-diagonal', ' antidiagonal']

squares = list()
count = 0
squares.append(list())

order = None

with open('semi_cyclic_pandiagonal_latin_squares_order_17.txt', 'r') as f:
    for line in f.readlines():
        if line.split():
            if order is None:
                order = len(line.split())
            squares[count].append(list(map(int, line.split())))
        else:
            count += 1
            squares.append(list())

            
if squares[-1] == []:
    del squares[-1]            
            

for i in range(len(squares)):
    squares[i] = np.array(squares[i])


result = cyclicity_list(squares, order)
print('%d squares were read' % count)



for outcome in Counter(result).most_common():
    the_length = sum(outcome[0])
    if the_length == 4:
        print(str(outcome[1]) + ' squares are cyclic in all four directions')
    else:
        output = ''
        for i, direction in enumerate(outcome[0]):
            if direction:
                if i + 1 < the_length:
                    output += outcomes[i] + ','
                elif the_length > 1:
                    output += ' and' + outcomes[i] + ' directions'
                elif the_length == 1:
                    output += ' a' + outcomes[i] + ' direction'
        print(str(outcome[1]) + ' squares are cyclic in' + output)
    
        

There are 0 non-pandiagonal squares in the dataset
16538 squares were read
8262 squares are cyclic in a horizontal direction
8262 squares are cyclic in a vertical direction
14 squares are cyclic in all four directions