

from __future__ import annotations

from typing import Any


def 			_UpperCAmelCase							(		*a__):

			'''simple docstring'''



			if all(_check_not_integer(lowercase__) for m in matrix_s):
						for i in matrix_s[1:]:
									_verify_matrix_sizes(matrix_s[0]       ,					lowercase__)
						return [[sum(lowercase__) for t in zip(*lowercase__)] for m in zip(*lowercase__)]
			raise TypeError("""Expected a matrix, got int/list instead""")


def 			_UpperCAmelCase							(		a__       ,					a__):

			'''simple docstring'''



			if (
			    _check_not_integer(lowercase__)
			    and _check_not_integer(lowercase__)
			    and _verify_matrix_sizes(lowercase__       ,					lowercase__)
			):
						return [[i - j for i, j in zip(*lowercase__)] for m in zip(lowercase__       ,					lowercase__)]
			raise TypeError("""Expected a matrix, got int/list instead""")


def 			_UpperCAmelCase							(		a__       ,					a__):

			'''simple docstring'''



			return [[x * n for x in row] for row in matrix]


def 			_UpperCAmelCase							(		a__       ,					a__):

			'''simple docstring'''



			if _check_not_integer(lowercase__) and _check_not_integer(lowercase__):
						a_    ,			a_		:		List[str]				    =				_verify_matrix_sizes(lowercase__       ,					lowercase__)

			if cols[0] != rows[1]:
						a_		:		List[str]				    =				(
						    """Cannot multiply matrix of dimensions """
						    f'''({rows[0]},{cols[0]}) and ({rows[1]},{cols[1]})'''
						)
						raise ValueError(lowercase__)
			return [
			    [sum(m * n for m, n in zip(lowercase__       ,					lowercase__)) for j in zip(*lowercase__)] for i in matrix_a
			]


def 			_UpperCAmelCase							(		a__):

			'''simple docstring'''



			a_		:		List[str]				    =				int(lowercase__)
			return [[int(row == column) for column in range(lowercase__)] for row in range(lowercase__)]


def 			_UpperCAmelCase							(		a__       ,					a__ = True):

			'''simple docstring'''



			if _check_not_integer(lowercase__):
						if return_map:
									return map(lowercase__       ,					zip(*lowercase__))
						else:
									return list(map(lowercase__       ,					zip(*lowercase__)))
			raise TypeError("""Expected a matrix, got int/list instead""")


def 			_UpperCAmelCase							(		a__       ,					a__       ,					a__):

			'''simple docstring'''



			a_		:		Any				    =				matrix[:row] + matrix[row + 1 :]
			return [row[:column] + row[column + 1 :] for row in minor]


def 			_UpperCAmelCase							(		a__):

			'''simple docstring'''



			if len(lowercase__) == 1:
						return matrix[0][0]

			return sum(
			    x * determinant(minor(lowercase__       ,					0       ,					lowercase__)) * (-1) ** i
			    for i, x in enumerate(matrix[0]))


def 			_UpperCAmelCase							(		a__):

			'''simple docstring'''



			a_		:		Optional[Any]				    =				determinant(lowercase__)
			if det == 0:
						return None

			a_		:		Optional[Any]				    =				[
			    [determinant(minor(lowercase__       ,					lowercase__       ,					lowercase__)) for j in range(len(lowercase__))]
			    for i in range(len(lowercase__))
			]

			a_		:		Optional[int]				    =				[
			    [x * (-1) ** (row + col) for col, x in enumerate(matrix_minor[row])]
			    for row in range(len(lowercase__))
			]
			a_		:		List[str]				    =				list(transpose(lowercase__))
			return scalar_multiply(lowercase__       ,					1 / det)


def 			_UpperCAmelCase							(		a__):

			'''simple docstring'''



			return not isinstance(lowercase__       ,					lowercase__) and not isinstance(matrix[0]       ,					lowercase__)


def 			_UpperCAmelCase							(		a__):

			'''simple docstring'''



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


def 			_UpperCAmelCase							(		a__       ,					a__):

			'''simple docstring'''



			a_		:		Any				    =				_shape(lowercase__) + _shape(lowercase__)
			if shape[0] != shape[3] or shape[1] != shape[2]:
						a_		:		Optional[int]				    =				(
						    """operands could not be broadcast together with shape """
						    f'''({shape[0], shape[1]}), ({shape[2], shape[3]})'''
						)
						raise ValueError(lowercase__)
			return (shape[0], shape[2]), (shape[1], shape[3])


def 			_UpperCAmelCase							(		):

			'''simple docstring'''



			a_		:		int				    =				[[1_2, 1_0], [3, 9]]
			a_		:		List[Any]				    =				[[3, 4], [7, 4]]
			a_		:		int				    =				[[1_1, 1_2, 1_3, 1_4], [2_1, 2_2, 2_3, 2_4], [3_1, 3_2, 3_3, 3_4], [4_1, 4_2, 4_3, 4_4]]
			a_		:		Any				    =				[[3, 0, 2], [2, 0, -2], [0, 1, 1]]
			print(f'''Add Operation, {add(lowercase__       ,					lowercase__) = } \n''')
			print(
			    f'''Multiply Operation, {multiply(lowercase__       ,					lowercase__) = } \n'''       ,					)
			print(f'''Identity: {identity(5)}\n''')
			print(f'''Minor of {matrix_c} = {minor(lowercase__       ,					1       ,					2)} \n''')
			print(f'''Determinant of {matrix_b} = {determinant(lowercase__)} \n''')
			print(f'''Inverse of {matrix_d} = {inverse(lowercase__)}\n''')


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	main()





import unittest
from functools import partial

import torch

from accelerate import Accelerator, debug_launcher
from accelerate.state import AcceleratorState, GradientState
from accelerate.test_utils import require_cpu, require_huggingface_suite
from accelerate.utils import GradientAccumulationPlugin


def 			_UpperCAmelCase							(		a__=2       ,					a__=True       ,					a__=False):

			'''simple docstring'''



			a_		:		Optional[Any]				    =				Accelerator(step_scheduler_with_optimizer=a__       ,					split_batches=a__)
			a_		:		Dict				    =				torch.nn.Linear(2       ,					4)
			a_		:		int				    =				torch.optim.AdamW(model.parameters()       ,					lr=1.0)
			a_		:		Optional[int]				    =				torch.optim.lr_scheduler.OneCycleLR(a__       ,					max_lr=0.01       ,					steps_per_epoch=2       ,					epochs=1)
			a_    ,			a_    ,			a_		:		List[Any]				    =				accelerator.prepare(a__       ,					a__       ,					a__)

			# Optimizer has stepped
			scheduler.step()
			if step_scheduler_with_optimizer or (num_processes == 1):
						assert (
						    scheduler.scheduler.last_epoch == num_processes
						), f'''Last Epoch ({scheduler.scheduler.last_epoch}) != Num Processes ({num_processes})'''
			else:
						assert (
						    scheduler.scheduler.last_epoch != num_processes
						), f'''Last Epoch ({scheduler.scheduler.last_epoch}) == Num Processes ({num_processes})'''


def 			_UpperCAmelCase							(		a__=2       ,					a__=True       ,					a__=False):

			'''simple docstring'''



			a_		:		int				    =				Accelerator(step_scheduler_with_optimizer=a__       ,					split_batches=a__)
			a_		:		Tuple				    =				torch.nn.Linear(2       ,					4)
			a_		:		str				    =				torch.optim.AdamW(model.parameters()       ,					lr=1.0)
			a_		:		Optional[int]				    =				torch.optim.lr_scheduler.LambdaLR(a__       ,					lr_lambda=lambda a__: 1 - n / 1_0)
			a_    ,			a_    ,			a_		:		List[str]				    =				accelerator.prepare(a__       ,					a__       ,					a__)

			# Optimizer has stepped
			a_		:		Optional[Any]				    =				False
			scheduler.step()
			a_		:		Union[str, Any]				    =				1 - (num_processes if (step_scheduler_with_optimizer and not split_batches) else 1) / 1_0
			assert (
			    scheduler.get_last_lr()[0] == expected_lr
			), f'''Wrong lr found at first step, expected {expected_lr}, got {scheduler.get_last_lr()[0]}'''

			# Optimizer has not stepped
			a_		:		Any				    =				True
			scheduler.step()
			if not step_scheduler_with_optimizer:
						a_		:		Any				    =				1 - 2 / 1_0
			assert (
			    scheduler.get_last_lr()[0] == expected_lr
			), f'''Wrong lr found at second step, expected {expected_lr}, got {scheduler.get_last_lr()[0]}'''


def 			_UpperCAmelCase							(		a__ = 2):

			'''simple docstring'''



			from transformers import get_linear_schedule_with_warmup

			a_		:		int				    =				[1, 2, 4]
			for num_steps in steps:
						a_		:		List[str]				    =				GradientAccumulationPlugin(num_steps=a__       ,					adjust_scheduler=num_steps > 1)
						a_		:		List[str]				    =				Accelerator(gradient_accumulation_plugin=a__)
						a_		:		int				    =				torch.nn.Linear(2       ,					4)
						a_		:		Any				    =				torch.optim.AdamW(model.parameters()       ,					lr=10.0)
						a_		:		List[Any]				    =				get_linear_schedule_with_warmup(optimizer=a__       ,					num_warmup_steps=0       ,					num_training_steps=2_0)

						a_    ,			a_    ,			a_		:		int				    =				accelerator.prepare(a__       ,					a__       ,					a__)

						for i in range(1_0 * num_steps):
									with accelerator.accumulate(a__):
												optimizer.step()
												scheduler.step()

									if i == (1_0 * num_steps - 2):
												assert (
												    scheduler.get_last_lr()[0] != 0
												), f'''Wrong lr found at second-to-last step, expected non-zero, got {scheduler.get_last_lr()[0]}. num_steps: {num_steps}'''
						assert (
						    scheduler.get_last_lr()[0] == 0
						), f'''Wrong lr found at last step, expected 0, got {scheduler.get_last_lr()[0]}'''
						GradientState._reset_state()



@require_cpu
class    A__(unittest.TestCase    ):
						"""simple docstring"""






						def 	UpperCamelCase__			(  self  )      ->				str:
									debug_launcher(partial(_lowercase       ,     num_processes=1  )       ,     num_processes=1  )
									debug_launcher(partial(_lowercase       ,     num_processes=1       ,     split_batches=_lowercase  )       ,     num_processes=1  )





						def 	UpperCamelCase__			(  self  )      ->				Dict:
									debug_launcher(partial(_lowercase       ,     num_processes=1  )       ,     num_processes=1  )
									debug_launcher(partial(_lowercase       ,     num_processes=1       ,     split_batches=_lowercase  )       ,     num_processes=1  )





						def 	UpperCamelCase__			(  self  )      ->				Any:
									debug_launcher(partial(_lowercase       ,     num_processes=1       ,     step_scheduler_with_optimizer=_lowercase  )       ,     num_processes=1  )





						def 	UpperCamelCase__			(  self  )      ->				Tuple:
									debug_launcher(partial(_lowercase       ,     num_processes=1       ,     step_scheduler_with_optimizer=_lowercase  )       ,     num_processes=1  )





						def 	UpperCamelCase__			(  self  )      ->				List[Any]:
									AcceleratorState._reset_state(_lowercase  )
									debug_launcher(_lowercase  )
									debug_launcher(partial(_lowercase       ,     num_processes=1       ,     split_batches=_lowercase  )       ,     num_processes=1  )





						def 	UpperCamelCase__			(  self  )      ->				Any:
									AcceleratorState._reset_state(_lowercase  )
									debug_launcher(_lowercase  )
									debug_launcher(partial(_lowercase       ,     num_processes=1       ,     split_batches=_lowercase  )       ,     num_processes=1  )





						def 	UpperCamelCase__			(  self  )      ->				Any:
									AcceleratorState._reset_state(_lowercase  )
									debug_launcher(partial(_lowercase       ,     step_scheduler_with_optimizer=_lowercase  )  )





						def 	UpperCamelCase__			(  self  )      ->				str:
									AcceleratorState._reset_state(_lowercase  )
									debug_launcher(partial(_lowercase       ,     step_scheduler_with_optimizer=_lowercase  )  )





						@require_huggingface_suite
						def 	UpperCamelCase__			(  self  )      ->				Optional[int]:
									AcceleratorState._reset_state(_lowercase  )
									debug_launcher(partial(_lowercase       ,     num_processes=1  )  )
									debug_launcher(_lowercase  )


