





def 						__SCREAMING_SNAKE_CASE  (				UpperCamelCase__			,			UpperCamelCase__			,			UpperCamelCase__ )  ->				int:







			'''simple docstring'''

			UpperCAmelCase   		=				len(_UpperCAmelCase )
			UpperCAmelCase   		=				[[0] * n for i in range(_UpperCAmelCase )]
			for i in range(_UpperCAmelCase ):
						UpperCAmelCase   		=				y_points[i]

			for i in range(2			,			_UpperCAmelCase ):
						for j in range(_UpperCAmelCase			,			_UpperCAmelCase ):
									UpperCAmelCase   		=				(
									    (xa - x_points[j - i + 1]) * q[j][i - 1]
									    - (xa - x_points[j]) * q[j - 1][i - 1]
									) / (x_points[j] - x_points[j - i + 1])

			return [q[n - 1][n - 1], q]


if __name__ == "__main__":
				import doctest

				doctest.testmod()








import argparse
import os

import evaluate
import torch
from datasets import load_dataset
from torch.optim import AdamW
from torch.utils.data import DataLoader
from transformers import AutoModelForSequenceClassification, AutoTokenizer, get_linear_schedule_with_warmup, set_seed

from accelerate import Accelerator, DistributedType


########################################################################
# This is a fully working simple example to use Accelerate,
# specifically showcasing how to properly calculate the metrics on the
# validation dataset when in a distributed system, and builds off the
# `nlp_example.py` script.
#
# This example trains a Bert base model on GLUE MRPC
# in any of the following settings (with the same script):
#   - single CPU or single GPU
#   - multi GPUS (using PyTorch distributed mode)
#   - (multi) TPUs
#   - fp16 (mixed-precision) or fp32 (normal precision)
#
# To help focus on the differences in the code, building `DataLoaders`
# was refactored into its own function.
# New additions from the base script can be found quickly by
# looking for the # New Code # tags
#
# To run it in each of these various modes, follow the instructions
# in the readme for examples:
# https://github.com/huggingface/accelerate/tree/main/examples
#
########################################################################


__A   			=1_6
__A   			=3_2

def        a						(      _UpperCAmelCase							:					Accelerator ,   _UpperCAmelCase							:					int = 16						):







		'''simple docstring'''





		__UpperCAmelCase    :     Union[str, Any]													=	AutoTokenizer.from_pretrained('''bert-base-cased'''						)
		__UpperCAmelCase    :     Any													=	load_dataset('''glue''' ,   '''mrpc'''						)

		def tokenize_function(_UpperCAmelCase							:					List[Any]						):
				# max_length=None => use the model max length (it's actually the default)
				__UpperCAmelCase    :     str													=	tokenizer(examples['''sentence1'''] ,   examples['''sentence2'''] ,   truncation=_UpperCAmelCase ,   max_length=_UpperCAmelCase						)
				return outputs

		# Apply the method we just defined to all the examples in all the splits of the dataset
		# starting with the main process first:
		with accelerator.main_process_first():
				__UpperCAmelCase    :     Optional[int]													=	datasets.map(
				    _UpperCAmelCase ,   batched=_UpperCAmelCase ,   remove_columns=['''idx''', '''sentence1''', '''sentence2'''] ,   )

		# We also rename the 'label' column to 'labels' which is the expected name for labels by the models of the
		# transformers library
		__UpperCAmelCase    :     Optional[Any]													=	tokenized_datasets.rename_column('''label''' ,   '''labels'''						)

		def collate_fn(_UpperCAmelCase							:					str						):
				# On TPU it's best to pad everything to the same length or training will be very slow.
				__UpperCAmelCase    :     List[Any]													=	1_28 if accelerator.distributed_type == DistributedType.TPU else None
				# When using mixed precision we want round multiples of 8/16
				if accelerator.mixed_precision == "fp8":
						__UpperCAmelCase    :     Any													=	16
				elif accelerator.mixed_precision != "no":
						__UpperCAmelCase    :     Tuple													=	8
				else:
						__UpperCAmelCase    :     Optional[int]													=	None

				return tokenizer.pad(
				    _UpperCAmelCase ,   padding='''longest''' ,   max_length=_UpperCAmelCase ,   pad_to_multiple_of=_UpperCAmelCase ,   return_tensors='''pt''' ,   )

		# Instantiate dataloaders.
		__UpperCAmelCase    :     Optional[Any]													=	DataLoader(
		    tokenized_datasets['''train'''] ,   shuffle=_UpperCAmelCase ,   collate_fn=_UpperCAmelCase ,   batch_size=_UpperCAmelCase						)
		__UpperCAmelCase    :     str													=	DataLoader(
		    tokenized_datasets['''validation'''] ,   shuffle=_UpperCAmelCase ,   collate_fn=_UpperCAmelCase ,   batch_size=_UpperCAmelCase						)

		return train_dataloader, eval_dataloader


# For testing only
if os.environ.get("TESTING_MOCKED_DATALOADERS", None) == "1":
				from accelerate.test_utils.training import mocked_dataloaders

				__A   			=mocked_dataloaders  # noqa: F811

def        a						(      _UpperCAmelCase							:					List[str] ,   _UpperCAmelCase							:					Any						):







		'''simple docstring'''





		if os.environ.get('''TESTING_MOCKED_DATALOADERS''' ,   _UpperCAmelCase						) == "1":
				__UpperCAmelCase    :     Dict													=	2
		# Initialize accelerator
		__UpperCAmelCase    :     Dict													=	Accelerator(cpu=args.cpu ,   mixed_precision=args.mixed_precision						)
		# Sample hyper-parameters for learning rate, batch size, seed and a few other HPs
		__UpperCAmelCase    :     List[Any]													=	config['''lr''']
		__UpperCAmelCase    :     Optional[Any]													=	int(config['''num_epochs''']						)
		__UpperCAmelCase    :     Optional[int]													=	int(config['''seed''']						)
		__UpperCAmelCase    :     Any													=	int(config['''batch_size''']						)

		__UpperCAmelCase    :     Optional[Any]													=	evaluate.load('''glue''' ,   '''mrpc'''						)

		# If the batch size is too big we use gradient accumulation
		__UpperCAmelCase    :     List[str]													=	1
		if batch_size > MAX_GPU_BATCH_SIZE and accelerator.distributed_type != DistributedType.TPU:
				__UpperCAmelCase    :     Tuple													=	batch_size // MAX_GPU_BATCH_SIZE
				__UpperCAmelCase    :     List[str]													=	MAX_GPU_BATCH_SIZE

		set_seed(_UpperCAmelCase						)
		__UpperCAmelCase							,					__UpperCAmelCase    :     Union[str, Any]													=	get_dataloaders(_UpperCAmelCase ,   _UpperCAmelCase						)
		# Instantiate the model (we build the model here so that the seed also control new weights initialization)
		__UpperCAmelCase    :     List[str]													=	AutoModelForSequenceClassification.from_pretrained('''bert-base-cased''' ,   return_dict=_UpperCAmelCase						)

		# We could avoid this line since the accelerator is set with `device_placement=True` (default value).
		# Note that if you are placing tensors on devices manually, this line absolutely needs to be before the optimizer
		# creation otherwise training will not work on TPU (`accelerate` will kindly throw an error to make us aware of that).
		__UpperCAmelCase    :     Tuple													=	model.to(accelerator.device						)

		# Instantiate optimizer
		__UpperCAmelCase    :     Any													=	AdamW(params=model.parameters() ,   lr=_UpperCAmelCase						)

		# Instantiate scheduler
		__UpperCAmelCase    :     str													=	get_linear_schedule_with_warmup(
		    optimizer=_UpperCAmelCase ,   num_warmup_steps=1_00 ,   num_training_steps=(len(_UpperCAmelCase						) * num_epochs) // gradient_accumulation_steps ,   )

		# Prepare everything
		# There is no specific order to remember, we just need to unpack the objects in the same order we gave them to the
		# prepare method.
		__UpperCAmelCase							,					__UpperCAmelCase							,					__UpperCAmelCase							,					__UpperCAmelCase							,					__UpperCAmelCase    :     List[str]													=	accelerator.prepare(
		    _UpperCAmelCase ,   _UpperCAmelCase ,   _UpperCAmelCase ,   _UpperCAmelCase ,   _UpperCAmelCase						)

		# Now we train the model
		for epoch in range(_UpperCAmelCase						):
				model.train()
				for step, batch in enumerate(_UpperCAmelCase						):
						# We could avoid this line since we set the accelerator with `device_placement=True`.
						batch.to(accelerator.device						)
						__UpperCAmelCase    :     int													=	model(**_UpperCAmelCase						)
						__UpperCAmelCase    :     str													=	outputs.loss
						__UpperCAmelCase    :     str													=	loss / gradient_accumulation_steps
						accelerator.backward(_UpperCAmelCase						)
						if step % gradient_accumulation_steps == 0:
								optimizer.step()
								lr_scheduler.step()
								optimizer.zero_grad()

				model.eval()
				__UpperCAmelCase    :     Tuple													=	0
				for step, batch in enumerate(_UpperCAmelCase						):
						# We could avoid this line since we set the accelerator with `device_placement=True`.
						batch.to(accelerator.device						)
						with torch.no_grad():
								__UpperCAmelCase    :     Dict													=	model(**_UpperCAmelCase						)
						__UpperCAmelCase    :     str													=	outputs.logits.argmax(dim=-1						)
						__UpperCAmelCase							,					__UpperCAmelCase    :     List[Any]													=	accelerator.gather((predictions, batch['''labels'''])						)
						# New Code #
						# First we check if it's a distributed system
						if accelerator.use_distributed:
								# Then see if we're on the last batch of our eval dataloader
								if step == len(_UpperCAmelCase						) - 1:
										# Last batch needs to be truncated on distributed systems as it contains additional samples
										__UpperCAmelCase    :     Dict													=	predictions[: len(eval_dataloader.dataset						) - samples_seen]
										__UpperCAmelCase    :     List[str]													=	references[: len(eval_dataloader.dataset						) - samples_seen]
								else:
										# Otherwise we add the number of samples seen
										samples_seen += references.shape[0]
            # All of this can be avoided if you use `Accelerator.gather_for_metrics` instead of `Accelerator.gather`:
            # accelerator.gather_for_metrics((predictions, batch["labels"]))
						metric.add_batch(
						    predictions=_UpperCAmelCase ,   references=_UpperCAmelCase ,   )

				__UpperCAmelCase    :     Tuple													=	metric.compute()
				# Use accelerator.print to print only on the main process.
				accelerator.print(f'epoch {epoch}:' ,   _UpperCAmelCase						)

def        a						(      ):







		'''simple docstring'''





		__UpperCAmelCase    :     int													=	argparse.ArgumentParser(description='''Simple example of training script.'''						)
		parser.add_argument(
		    '''--mixed_precision''' ,   type=_UpperCAmelCase ,   default=_UpperCAmelCase ,   choices=['''no''', '''fp16''', '''bf16''', '''fp8'''] ,   help='''Whether to use mixed precision. Choose'''
		    '''between fp16 and bf16 (bfloat16). Bf16 requires PyTorch >= 1.10.'''
		    '''and an Nvidia Ampere GPU.''' ,   )
		parser.add_argument('''--cpu''' ,   action='''store_true''' ,   help='''If passed, will train on the CPU.'''						)
		__UpperCAmelCase    :     int													=	parser.parse_args()
		__UpperCAmelCase    :     Union[str, Any]													=	{'''lr''': 2e-5, '''num_epochs''': 3, '''seed''': 42, '''batch_size''': 16}
		training_function(_UpperCAmelCase ,   _UpperCAmelCase						)


if __name__ == "__main__":
				main()





