




"""simple docstring"""




from __future__ import annotations

import math



def     a__ (				snake_case__       , snake_case__				)						->					list:
			if len(snake_case__				) != 2 or len(a[0]				) != 2 or len(snake_case__				) != 2 or len(b[0]				) != 2:
						raise Exception("""Matrices are not 2x2"""				)
			lowerCamelCase			      =					[
			    [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     a__ (				snake_case__       , snake_case__				)						->					Union[str, Any]:
			return [
			    [matrix_a[row][col] + matrix_b[row][col] for col in range(len(matrix_a[row]				)				)]
			    for row in range(len(snake_case__				)				)
			]



def     a__ (				snake_case__       , snake_case__				)						->					List[str]:
			return [
			    [matrix_a[row][col] - matrix_b[row][col] for col in range(len(matrix_a[row]				)				)]
			    for row in range(len(snake_case__				)				)
			]



def     a__ (				snake_case__				)						->					tuple[list, list, list, list]:
			if len(snake_case__				) % 2 != 0 or len(a[0]				) % 2 != 0:
						raise Exception("""Odd matrices are not supported!"""				)

			lowerCamelCase			      =					len(snake_case__				)
			lowerCamelCase			      =					matrix_length // 2

			lowerCamelCase			      =					[[a[i][j] for j in range(snake_case__       , snake_case__				)] for i in range(snake_case__				)]
			lowerCamelCase			      =					[
			    [a[i][j] for j in range(snake_case__       , snake_case__				)] for i in range(snake_case__       , snake_case__				)
			]

			lowerCamelCase			      =					[[a[i][j] for j in range(snake_case__				)] for i in range(snake_case__				)]
			lowerCamelCase			      =					[[a[i][j] for j in range(snake_case__				)] for i in range(snake_case__       , snake_case__				)]

			return top_left, top_right, bot_left, bot_right



def     a__ (				snake_case__				)						->					tuple[int, int]:
			return len(snake_case__				), len(matrix[0]				)



def     a__ (				snake_case__				)						->					None:
			print("""\n""".join(str(snake_case__				) for line in matrix				)				)



def     a__ (				snake_case__       , snake_case__				)						->					list:
			if matrix_dimensions(snake_case__				) == (2, 2):
						return default_matrix_multiplication(snake_case__       , snake_case__				)

			lowerCamelCase      ,   lowerCamelCase      ,   lowerCamelCase      ,   lowerCamelCase			      =					split_matrix(snake_case__				)
			lowerCamelCase      ,   lowerCamelCase      ,   lowerCamelCase      ,   lowerCamelCase			      =					split_matrix(snake_case__				)

			lowerCamelCase			      =					actual_strassen(snake_case__       , matrix_subtraction(snake_case__       , snake_case__				)				)
			lowerCamelCase			      =					actual_strassen(matrix_addition(snake_case__       , snake_case__				)       , snake_case__				)
			lowerCamelCase			      =					actual_strassen(matrix_addition(snake_case__       , snake_case__				)       , snake_case__				)
			lowerCamelCase			      =					actual_strassen(snake_case__       , matrix_subtraction(snake_case__       , snake_case__				)				)
			lowerCamelCase			      =					actual_strassen(matrix_addition(snake_case__       , snake_case__				)       , matrix_addition(snake_case__       , snake_case__				)				)
			lowerCamelCase			      =					actual_strassen(matrix_subtraction(snake_case__       , snake_case__				)       , matrix_addition(snake_case__       , snake_case__				)				)
			lowerCamelCase			      =					actual_strassen(matrix_subtraction(snake_case__       , snake_case__				)       , matrix_addition(snake_case__       , snake_case__				)				)

			lowerCamelCase			      =					matrix_addition(matrix_subtraction(matrix_addition(snake_case__       , snake_case__				)       , snake_case__				)       , snake_case__				)
			lowerCamelCase			      =					matrix_addition(snake_case__       , snake_case__				)
			lowerCamelCase			      =					matrix_addition(snake_case__       , snake_case__				)
			lowerCamelCase			      =					matrix_subtraction(matrix_subtraction(matrix_addition(snake_case__       , snake_case__				)       , snake_case__				)       , snake_case__				)

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



def     a__ (				snake_case__       , snake_case__				)						->					list:
			if matrix_dimensions(snake_case__				)[1] != matrix_dimensions(snake_case__				)[0]:
						lowerCamelCase			      =					(
						    """Unable to multiply these matrices, please check the dimensions.\n"""
						    F'Matrix A: {matrixa}\n'
						    F'Matrix B: {matrixa}'
						)
						raise Exception(snake_case__				)
			lowerCamelCase			      =					matrix_dimensions(snake_case__				)
			lowerCamelCase			      =					matrix_dimensions(snake_case__				)

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

			lowerCamelCase			      =					max(*snake_case__       , *snake_case__				)
			lowerCamelCase			      =					int(math.pow(2       , math.ceil(math.loga(snake_case__				)				)				)				)
			lowerCamelCase			      =					matrixa
			lowerCamelCase			      =					matrixa

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

			lowerCamelCase			      =					actual_strassen(snake_case__       , snake_case__				)

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


if __name__ == "__main__":
					lowerCAmelCase							:			Optional[int]     							=							[
					    [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],
					]
					lowerCAmelCase							:			Optional[Any]     							=							[[0, 2, 1, 1], [16, 2, 3, 3], [2, 2, 7, 7], [13, 11, 22, 4]]
					print(strassen(matrixa, matrixa))









"""simple docstring"""




import importlib
import sys
from argparse import REMAINDER, ArgumentParser
from pathlib import Path

import torch_xla.distributed.xla_multiprocessing as xmp



def     a__ (				)						->					Union[str, Any]:
			lowerCamelCase			      =					ArgumentParser(
			    description=(
			        """PyTorch TPU distributed training launch """
			        """helper utility that will spawn up """
			        """multiple distributed processes"""
			    )				)

			# Optional arguments for the launch helper
			parser.add_argument("""--num_cores"""       , type=snake_case__       , default=1       , help="""Number of TPU cores to use (1 or 8)."""				)

			# positional
			parser.add_argument(
			    """training_script"""       , type=snake_case__       , help=(
			        """The full path to the single TPU training """
			        """program/script to be launched in parallel, """
			        """followed by all the arguments for the """
			        """training script"""
			    )       , )

			# rest from the training program
			parser.add_argument("""training_script_args"""       , nargs=snake_case__				)

			return parser.parse_args()



def     a__ (				)						->					List[str]:
			lowerCamelCase			      =					parse_args()

			# Import training_script as a module.
			lowerCamelCase			      =					Path(args.training_script				)
			sys.path.append(str(script_fpath.parent.resolve()				)				)
			lowerCamelCase			      =					script_fpath.stem
			lowerCamelCase			      =					importlib.import_module(snake_case__				)

			# Patch sys.argv
			lowerCamelCase			      =					[args.training_script] + args.training_script_args + ["""--tpu_num_cores""", str(args.num_cores				)]
			xmp.spawn(mod._mp_fn       , args=()       , nprocs=args.num_cores				)


if __name__ == "__main__":
					main()



