




def 						lowerCamelCase__   (		_A					,     _A							):







	'''simple docstring'''





	snake_case_		   =					[]
	snake_case_		   =					len(_A							)
	for i in range(_A							):
		snake_case_		   =					[]
		for j in range(_A							):
			snake_case_		   =					0
			for k in range(_A							):
				snake_case_		   =					val + matrix_a[i][k] * matrix_b[k][j]
			list_a.append(_A							)
		matrix_c.append(_A							)
	return matrix_c


def 						lowerCamelCase__   (		_A							):







	'''simple docstring'''





	return [[int(row == column							) for column in range(_A							)] for row in range(_A							)]


def 						lowerCamelCase__   (		_A							):







	'''simple docstring'''





	if n <= 1:
		return n
	snake_case_		   =					identity(2							)
	snake_case_		   =					[[1, 1], [1, 0]]
	snake_case_		   =					n - 1
	while n > 0:
		if n % 2 == 1:
			snake_case_		   =					multiply(_A					,     _A							)
		snake_case_		   =					multiply(_A					,     _A							)
		snake_case_		   =					int(n / 2							)
	return res_matrix[0][0]


def 						lowerCamelCase__   (		_A							):







	'''simple docstring'''





	if n <= 1:
		return n
	snake_case_		   =					0
	snake_case_		   =					1
	for _ in range(2					,     n + 1							):
		snake_case_   ,				snake_case_		   =					fiba, fiba + fiba
	return fiba


def 						lowerCamelCase__   (		):







	'''simple docstring'''





	for ordinal in "0th 1st 2nd 3rd 10th 100th 1000th".split():
		snake_case_		   =					int("".join(c for c in ordinal if c in "0123456789"							)							)  # 1000th --> 1000
		print(
		    f"{ordinal} fibonacci number using matrix exponentiation is "
		    f"{nth_fibonacci_matrix(_A							)} and using bruteforce is "
		    f"{nth_fibonacci_bruteforce(_A							)}\n"							)
	# from timeit import timeit
	# print(timeit("nth_fibonacci_matrix(1000000)",
	#              "from main import nth_fibonacci_matrix", number=5))
	# print(timeit("nth_fibonacci_bruteforce(1000000)",
	#              "from main import nth_fibonacci_bruteforce", number=5))
	# 2.3342058970001744
	# 57.256506615000035


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 						lowerCamelCase__   (		_A=2					,     _A=True					,     _A=False							):







	'''simple docstring'''





	snake_case_		   =					Accelerator(step_scheduler_with_optimizer=_A					,     split_batches=_A							)
	snake_case_		   =					torch.nn.Linear(2					,     4							)
	snake_case_		   =					torch.optim.AdamW(model.parameters()					,     lr=1.0							)
	snake_case_		   =					torch.optim.lr_scheduler.OneCycleLR(_A					,     max_lr=0.01					,     steps_per_epoch=2					,     epochs=1							)
	snake_case_   ,				snake_case_   ,				snake_case_		   =					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 						lowerCamelCase__   (		_A=2					,     _A=True					,     _A=False							):







	'''simple docstring'''





	snake_case_		   =					Accelerator(step_scheduler_with_optimizer=_A					,     split_batches=_A							)
	snake_case_		   =					torch.nn.Linear(2					,     4							)
	snake_case_		   =					torch.optim.AdamW(model.parameters()					,     lr=1.0							)
	snake_case_		   =					torch.optim.lr_scheduler.LambdaLR(_A					,     lr_lambda=lambda _A							: 1 - n / 10							)
	snake_case_   ,				snake_case_   ,				snake_case_		   =					accelerator.prepare(_A					,     _A					,     _A							)

	# Optimizer has stepped
	snake_case_		   =					False
	scheduler.step()
	snake_case_		   =					1 - (num_processes if (step_scheduler_with_optimizer and not split_batches) else 1) / 10
	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
	snake_case_		   =					True
	scheduler.step()
	if not step_scheduler_with_optimizer:
		snake_case_		   =					1 - 2 / 10
	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 						lowerCamelCase__   (		_A = 2							):







	'''simple docstring'''





	from transformers import get_linear_schedule_with_warmup

	snake_case_		   =					[1, 2, 4]
	for num_steps in steps:
		snake_case_		   =					GradientAccumulationPlugin(num_steps=_A					,     adjust_scheduler=num_steps > 1							)
		snake_case_		   =					Accelerator(gradient_accumulation_plugin=_A							)
		snake_case_		   =					torch.nn.Linear(2					,     4							)
		snake_case_		   =					torch.optim.AdamW(model.parameters()					,     lr=10.0							)
		snake_case_		   =					get_linear_schedule_with_warmup(optimizer=_A					,     num_warmup_steps=0					,     num_training_steps=20							)

		snake_case_   ,				snake_case_   ,				snake_case_		   =					accelerator.prepare(_A					,     _A					,     _A							)

		for i in range(10 * num_steps							):
			with accelerator.accumulate(_A							):
				optimizer.step()
				scheduler.step()

			if i == (10 * 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 		UpperCAmelCase       (    unittest.TestCase      ):







						'''simple docstring'''





						def 	snake_case__						(						self							:					Tuple						):






							"""simple docstring"""






							debug_launcher(partial(__lowercase	,     num_processes=1						)	,     num_processes=1						)
							debug_launcher(partial(__lowercase	,     num_processes=1	,     split_batches=__lowercase						)	,     num_processes=1						)






						def 	snake_case__						(						self							:					int						):






							"""simple docstring"""






							debug_launcher(partial(__lowercase	,     num_processes=1						)	,     num_processes=1						)
							debug_launcher(partial(__lowercase	,     num_processes=1	,     split_batches=__lowercase						)	,     num_processes=1						)






						def 	snake_case__						(						self							:					Dict						):






							"""simple docstring"""






							debug_launcher(partial(__lowercase	,     num_processes=1	,     step_scheduler_with_optimizer=__lowercase						)	,     num_processes=1						)






						def 	snake_case__						(						self							:					Union[str, Any]						):






							"""simple docstring"""






							debug_launcher(partial(__lowercase	,     num_processes=1	,     step_scheduler_with_optimizer=__lowercase						)	,     num_processes=1						)






						def 	snake_case__						(						self							:					List[Any]						):






							"""simple docstring"""






							AcceleratorState._reset_state(__lowercase						)
							debug_launcher(__lowercase						)
							debug_launcher(partial(__lowercase	,     num_processes=1	,     split_batches=__lowercase						)	,     num_processes=1						)






						def 	snake_case__						(						self							:					Dict						):






							"""simple docstring"""






							AcceleratorState._reset_state(__lowercase						)
							debug_launcher(__lowercase						)
							debug_launcher(partial(__lowercase	,     num_processes=1	,     split_batches=__lowercase						)	,     num_processes=1						)






						def 	snake_case__						(						self							:					List[str]						):






							"""simple docstring"""






							AcceleratorState._reset_state(__lowercase						)
							debug_launcher(partial(__lowercase	,     step_scheduler_with_optimizer=__lowercase						)						)






						def 	snake_case__						(						self							:					Optional[Any]						):






							"""simple docstring"""






							AcceleratorState._reset_state(__lowercase						)
							debug_launcher(partial(__lowercase	,     step_scheduler_with_optimizer=__lowercase						)						)






						@require_huggingface_suite
						def 	snake_case__						(						self							:					Optional[Any]						):






							"""simple docstring"""






							AcceleratorState._reset_state(__lowercase						)
							debug_launcher(partial(__lowercase	,     num_processes=1						)						)
							debug_launcher(__lowercase						)
