





from __future__ import annotations

import math





def 						lowerCamelCase__     (     UpperCamelCase__			:       list       ,    UpperCamelCase__			:       list						)			-> list:



					'''simple docstring'''




					if len(UpperCamelCase__						) != 2 or len(a[0]						) != 2 or len(UpperCamelCase__						) != 2 or len(b[0]						) != 2:
										raise Exception('Matrices are not 2x2'						)
					_snake_case									=				[
					    [a[0][0] * b[0][0] + a[0][1] * b[1][0], a[0][0] * b[0][1] + a[0][1] * b[1][1]],
					    [a[1][0] * b[0][0] + a[1][1] * b[1][0], a[1][0] * b[0][1] + a[1][1] * b[1][1]],
					]
					return new_matrix





def 						lowerCamelCase__     (     UpperCamelCase__			:       list       ,    UpperCamelCase__			:       list						)			-> Union[str, Any]:



					'''simple docstring'''




					return [
					    [matrix_a[row][col] + matrix_b[row][col] for col in range(len(matrix_a[row]						)						)]
					    for row in range(len(UpperCamelCase__						)						)
					]





def 						lowerCamelCase__     (     UpperCamelCase__			:       list       ,    UpperCamelCase__			:       list						)			-> Tuple:



					'''simple docstring'''




					return [
					    [matrix_a[row][col] - matrix_b[row][col] for col in range(len(matrix_a[row]						)						)]
					    for row in range(len(UpperCamelCase__						)						)
					]





def 						lowerCamelCase__     (     UpperCamelCase__			:       list						)			-> tuple[list, list, list, list]:



					'''simple docstring'''




					if len(UpperCamelCase__						) % 2 != 0 or len(a[0]						) % 2 != 0:
										raise Exception('Odd matrices are not supported!'						)

					_snake_case									=				len(UpperCamelCase__						)
					_snake_case									=				matrix_length // 2

					_snake_case									=				[[a[i][j] for j in range(UpperCamelCase__       ,    UpperCamelCase__						)] for i in range(UpperCamelCase__						)]
					_snake_case									=				[
					    [a[i][j] for j in range(UpperCamelCase__       ,    UpperCamelCase__						)] for i in range(UpperCamelCase__       ,    UpperCamelCase__						)
					]

					_snake_case									=				[[a[i][j] for j in range(UpperCamelCase__						)] for i in range(UpperCamelCase__						)]
					_snake_case									=				[[a[i][j] for j in range(UpperCamelCase__						)] for i in range(UpperCamelCase__       ,    UpperCamelCase__						)]

					return top_left, top_right, bot_left, bot_right





def 						lowerCamelCase__     (     UpperCamelCase__			:       list						)			-> tuple[int, int]:



					'''simple docstring'''




					return len(UpperCamelCase__						), len(matrix[0]						)





def 						lowerCamelCase__     (     UpperCamelCase__			:       list						)			-> None:



					'''simple docstring'''




					print('\n'.join(str(UpperCamelCase__						) for line in matrix						)						)





def 						lowerCamelCase__     (     UpperCamelCase__			:       list       ,    UpperCamelCase__			:       list						)			-> list:



					'''simple docstring'''




					if matrix_dimensions(UpperCamelCase__						) == (2, 2):
										return default_matrix_multiplication(UpperCamelCase__       ,    UpperCamelCase__						)

					_snake_case							,     _snake_case							,     _snake_case							,     _snake_case									=				split_matrix(UpperCamelCase__						)
					_snake_case							,     _snake_case							,     _snake_case							,     _snake_case									=				split_matrix(UpperCamelCase__						)

					_snake_case									=				actual_strassen(UpperCamelCase__       ,    matrix_subtraction(UpperCamelCase__       ,    UpperCamelCase__						)						)
					_snake_case									=				actual_strassen(matrix_addition(UpperCamelCase__       ,    UpperCamelCase__						)       ,    UpperCamelCase__						)
					_snake_case									=				actual_strassen(matrix_addition(UpperCamelCase__       ,    UpperCamelCase__						)       ,    UpperCamelCase__						)
					_snake_case									=				actual_strassen(UpperCamelCase__       ,    matrix_subtraction(UpperCamelCase__       ,    UpperCamelCase__						)						)
					_snake_case									=				actual_strassen(matrix_addition(UpperCamelCase__       ,    UpperCamelCase__						)       ,    matrix_addition(UpperCamelCase__       ,    UpperCamelCase__						)						)
					_snake_case									=				actual_strassen(matrix_subtraction(UpperCamelCase__       ,    UpperCamelCase__						)       ,    matrix_addition(UpperCamelCase__       ,    UpperCamelCase__						)						)
					_snake_case									=				actual_strassen(matrix_subtraction(UpperCamelCase__       ,    UpperCamelCase__						)       ,    matrix_addition(UpperCamelCase__       ,    UpperCamelCase__						)						)

					_snake_case									=				matrix_addition(matrix_subtraction(matrix_addition(UpperCamelCase__       ,    UpperCamelCase__						)       ,    UpperCamelCase__						)       ,    UpperCamelCase__						)
					_snake_case									=				matrix_addition(UpperCamelCase__       ,    UpperCamelCase__						)
					_snake_case									=				matrix_addition(UpperCamelCase__       ,    UpperCamelCase__						)
					_snake_case									=				matrix_subtraction(matrix_subtraction(matrix_addition(UpperCamelCase__       ,    UpperCamelCase__						)       ,    UpperCamelCase__						)       ,    UpperCamelCase__						)

					# construct the new matrix from our 4 quadrants
					_snake_case									=				[]
					for i in range(len(UpperCamelCase__						)						):
										new_matrix.append(top_left[i] + top_right[i]						)
					for i in range(len(UpperCamelCase__						)						):
										new_matrix.append(bot_left[i] + bot_right[i]						)
					return new_matrix





def 						lowerCamelCase__     (     UpperCamelCase__			:       list       ,    UpperCamelCase__			:       list						)			-> list:



					'''simple docstring'''




					if matrix_dimensions(UpperCamelCase__						)[1] != matrix_dimensions(UpperCamelCase__						)[0]:
										_snake_case									=				(
										    'Unable to multiply these matrices, please check the dimensions.\n'
										    F'''Matrix A: {matrixa}\n'''
										    F'''Matrix B: {matrixa}'''
										)
										raise Exception(UpperCamelCase__						)
					_snake_case									=				matrix_dimensions(UpperCamelCase__						)
					_snake_case									=				matrix_dimensions(UpperCamelCase__						)

					if dimensiona[0] == dimensiona[1] and dimensiona[0] == dimensiona[1]:
										return [matrixa, matrixa]

					_snake_case									=				max(*UpperCamelCase__       ,    *UpperCamelCase__						)
					_snake_case									=				int(math.pow(2       ,    math.ceil(math.loga(UpperCamelCase__						)						)						)						)
					_snake_case									=				matrixa
					_snake_case									=				matrixa

					# Adding zeros to the matrices so that the arrays dimensions are the same and also
					# power of 2
					for i in range(0       ,    UpperCamelCase__						):
										if i < dimensiona[0]:
															for _ in range(dimensiona[1]       ,    UpperCamelCase__						):
																				new_matrixa[i].append(0						)
										else:
															new_matrixa.append([0] * maxim						)
										if i < dimensiona[0]:
															for _ in range(dimensiona[1]       ,    UpperCamelCase__						):
																				new_matrixa[i].append(0						)
										else:
															new_matrixa.append([0] * maxim						)

					_snake_case									=				actual_strassen(UpperCamelCase__       ,    UpperCamelCase__						)

					# Removing the additional zeros
					for i in range(0       ,    UpperCamelCase__						):
										if i < dimensiona[0]:
															for _ in range(dimensiona[1]       ,    UpperCamelCase__						):
																				final_matrix[i].pop()
										else:
															final_matrix.pop()
					return final_matrix


if __name__ == "__main__":
						UpperCAmelCase_      							=     [
						    [2, 3, 4, 5],
						    [6, 4, 3, 1],
						    [2, 3, 6, 7],
						    [3, 1, 2, 4],
						    [2, 3, 4, 5],
						    [6, 4, 3, 1],
						    [2, 3, 6, 7],
						    [3, 1, 2, 4],
						    [2, 3, 4, 5],
						    [6, 2, 3, 1],
						]
						UpperCAmelCase_      							=     [[0, 2, 1, 1], [16, 2, 3, 3], [2, 2, 7, 7], [13, 11, 22, 4]]
						print(strassen(matrixa, matrixa))










import unittest

from accelerate import debug_launcher
from accelerate.test_utils import require_cpu, test_ops, test_script
@require_cpu
class 			UpperCamelCase_		(  unittest.TestCase					):




					def 	lowerCAmelCase			(		self  )		->							List[Any]:
										debug_launcher(test_script.main  )






					def 	lowerCAmelCase			(		self  )		->							Optional[Any]:
										debug_launcher(test_ops.main  )



