





from math import factorial


class 					_snake_case						:






	def __init__(		self					,UpperCamelCase					,UpperCamelCase       )						->    Optional[int]:
					snake_case__      :str         =   real
					if isinstance(UpperCamelCase__					,UpperCamelCase__       ):
									snake_case__      :Dict         =   [1] * rank
					else:
									snake_case__      :Optional[int]         =   rank






	def __repr__(		self       )						->    List[Any]:
					return (
					    f'{self.real}+'
					    f'{"+".join(str(UpperCamelCase__       )+"E"+str(n+1       )for n,dual in enumerate(self.duals       )       )}'
					)






	def    lowerCAmelCase_							(		self       )						->    int:
					snake_case__      :List[str]         =   self.duals.copy()
					while cur[-1] == 0:
									cur.pop(-1       )
					return Dual(self.real					,UpperCamelCase__       )






	def __add__(		self					,UpperCamelCase       )						->    Dict:





					if not isinstance(UpperCamelCase__					,UpperCamelCase__       ):
									return Dual(self.real + other					,self.duals       )
					snake_case__      :List[Any]         =   self.duals.copy()
					snake_case__      :List[str]         =   other.duals.copy()
					if len(UpperCamelCase__       ) > len(UpperCamelCase__       ):
									o_dual.extend([1] * (len(UpperCamelCase__       ) - len(UpperCamelCase__       ))       )
					elif len(UpperCamelCase__       ) < len(UpperCamelCase__       ):
									s_dual.extend([1] * (len(UpperCamelCase__       ) - len(UpperCamelCase__       ))       )
					snake_case__      :Dict         =   []
					for i in range(len(UpperCamelCase__       )       ):
									new_duals.append(s_dual[i] + o_dual[i]       )
					return Dual(self.real + other.real					,UpperCamelCase__       )

	_A          =   __add__






	def __sub__(		self					,UpperCamelCase       )						->    Any:
					return self + other * -1






	def __mul__(		self					,UpperCamelCase       )						->    List[Any]:





					if not isinstance(UpperCamelCase__					,UpperCamelCase__       ):
									snake_case__      :Union[str, Any]         =   []
									for i in self.duals:
													new_duals.append(i * other       )
									return Dual(self.real * other					,UpperCamelCase__       )
					snake_case__      :Optional[int]         =   [0] * (len(self.duals       ) + len(other.duals       ) + 1)
					for i, item in enumerate(self.duals       ):
									for j, jtem in enumerate(other.duals       ):
													new_duals[i + j + 1] += item * jtem
					for k in range(len(self.duals       )       ):
									new_duals[k] += self.duals[k] * other.real
					for index in range(len(other.duals       )       ):
									new_duals[index] += other.duals[index] * self.real
					return Dual(self.real * other.real					,UpperCamelCase__       )

	_A          =   __mul__






	def __truediv__(		self					,UpperCamelCase       )						->    int:





					if not isinstance(UpperCamelCase__					,UpperCamelCase__       ):
									snake_case__      :Any         =   []
									for i in self.duals:
													new_duals.append(i / other       )
									return Dual(self.real / other					,UpperCamelCase__       )
					raise ValueError






	def __floordiv__(		self					,UpperCamelCase       )						->    Union[str, Any]:





					if not isinstance(UpperCamelCase__					,UpperCamelCase__       ):
									snake_case__      :Optional[Any]         =   []
									for i in self.duals:
													new_duals.append(i // other       )
									return Dual(self.real // other					,UpperCamelCase__       )
					raise ValueError






	def __pow__(		self					,UpperCamelCase       )						->    List[str]:





					if n < 0 or isinstance(UpperCamelCase__					,UpperCamelCase__       ):
									raise ValueError("power must be a positive integer"       )
					if n == 0:
									return 1
					if n == 1:
									return self
					snake_case__      :str         =   self
					for _ in range(n - 1       ):
									x *= self
					return x





def 					lowercase_ (    __snake_case     :							int	,	__snake_case     :							Dict	,	__snake_case     :							Any      )     -> Optional[Any]:





				'''simple docstring'''


				if not callable(_lowercase      ):
								raise ValueError("differentiate() requires a function as input for func"      )
				if not isinstance(_lowercase	,	(float, int)      ):
								raise ValueError("differentiate() requires a float as input for position"      )
				if not isinstance(_lowercase	,	_lowercase      ):
								raise ValueError("differentiate() requires an int as input for order"      )
				snake_case__      :List[Any]         =   Dual(_lowercase	,	1      )
				snake_case__      :Dict         =   func(_lowercase      )
				if order == 0:
								return result.real
				return result.duals[order - 1] * factorial(_lowercase      )


if __name__ == "__main__":
	import doctest

	doctest.testmod()





	def 					lowercase_ (    __snake_case     :							Dict      )     -> Any:





					'''simple docstring'''


					return y**2 * y**4
	print(differentiate(f, 9, 2))







import argparse
import json
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
from accelerate.utils.deepspeed import DummyOptim, DummyScheduler


__UpperCAmelCase							:   Optional[Any]							=  1_6
__UpperCAmelCase							:   Optional[int]							=  3_2





def 					lowercase_ (    __snake_case     :							Accelerator	,	__snake_case     :							int = 16	,	__snake_case     :							str = "bert-base-cased"      )     -> Optional[Any]:





				'''simple docstring'''


				snake_case__      :int         =   AutoTokenizer.from_pretrained(__snake_case      )
				snake_case__      :Optional[int]         =   load_dataset("glue"	,	"mrpc"      )

				def tokenize_function(__snake_case     :							Tuple      ):
								# max_length=None => use the model max length (it's actually the default)
								snake_case__      :Any         =   tokenizer(examples["sentence1"]	,	examples["sentence2"]	,	truncation=__snake_case	,	max_length=__snake_case      )
								return outputs

				# Apply the method we just defined to all the examples in all the splits of the dataset
				snake_case__      :List[Any]         =   datasets.map(
				    __snake_case	,	batched=__snake_case	,	remove_columns=["idx", "sentence1", "sentence2"]	,	load_from_cache_file=__snake_case      )

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

				def collate_fn(__snake_case     :							Dict      ):
								# On TPU it's best to pad everything to the same length or training will be very slow.
								if accelerator.distributed_type == DistributedType.TPU:
												return tokenizer.pad(__snake_case	,	padding="max_length"	,	max_length=1_28	,	return_tensors="pt"      )
								return tokenizer.pad(__snake_case	,	padding="longest"	,	return_tensors="pt"      )

				# Instantiate dataloaders.
				snake_case__      :Any         =   DataLoader(
				    tokenized_datasets["train"]	,	shuffle=__snake_case	,	collate_fn=__snake_case	,	batch_size=__snake_case      )
				snake_case__      :Tuple         =   DataLoader(
				    tokenized_datasets["validation"]	,	shuffle=__snake_case	,	collate_fn=__snake_case	,	batch_size=__snake_case      )

				return train_dataloader, eval_dataloader





def 					lowercase_ (    __snake_case     :							List[Any]	,	__snake_case     :							Union[str, Any]	,	__snake_case     :							int	,	__snake_case     :							Optional[int]      )     -> Tuple:





				'''simple docstring'''


				model.eval()
				snake_case__      :Union[str, Any]         =   0
				for step, batch in enumerate(__snake_case      ):
								# We could avoid this line since we set the accelerator with `device_placement=True`.
								batch.to(accelerator.device      )
								with torch.no_grad():
												snake_case__      :List[Any]         =   model(**__snake_case      )
								snake_case__      :Any         =   outputs.logits.argmax(dim=-1      )
								# It is slightly faster to call this once, than multiple times
								snake_case__    ,						snake_case__      :Tuple         =   accelerator.gather(
								    (predictions, batch["labels"])      )  # If we are in a multiprocess environment, the last batch has duplicates
								if accelerator.use_distributed:
												if step == len(__snake_case      ) - 1:
																snake_case__      :List[str]         =   predictions[: len(eval_dataloader.dataset      ) - samples_seen]
																snake_case__      :Optional[int]         =   references[: len(eval_dataloader.dataset      ) - samples_seen]
												else:
																samples_seen += references.shape[0]
								metric.add_batch(
								    predictions=__snake_case	,	references=__snake_case	,	)

				snake_case__      :int         =   metric.compute()
				return eval_metric["accuracy"]





def 					lowercase_ (    __snake_case     :							Union[str, Any]	,	__snake_case     :							Optional[Any]      )     -> Any:





				'''simple docstring'''


				snake_case__      :Any         =   Accelerator()

				# Sample hyper-parameters for learning rate, batch size, seed and a few other HPs
				snake_case__      :Union[str, Any]         =   config["lr"]
				snake_case__      :List[str]         =   int(config["num_epochs"]      )
				snake_case__      :Optional[Any]         =   int(config["seed"]      )
				snake_case__      :List[Any]         =   int(config["batch_size"]      )
				snake_case__      :List[Any]         =   args.model_name_or_path

				set_seed(__snake_case      )
				snake_case__    ,						snake_case__      :List[Any]         =   get_dataloaders(__snake_case	,	__snake_case	,	__snake_case      )

				# Instantiate the model (we build the model here so that the seed also control new weights initialization)
				snake_case__      :List[Any]         =   AutoModelForSequenceClassification.from_pretrained(__snake_case	,	return_dict=__snake_case      )

				# Instantiate optimizer
				snake_case__      :int         =   (
				    AdamW
				    if accelerator.state.deepspeed_plugin is None
				    or "optimizer" not in accelerator.state.deepspeed_plugin.deepspeed_config
				    else DummyOptim
				)
				snake_case__      :Tuple         =   optimizer_cls(params=model.parameters()	,	lr=__snake_case      )

				if accelerator.state.deepspeed_plugin is not None:
								snake_case__      :List[str]         =   accelerator.state.deepspeed_plugin.deepspeed_config[
								    "gradient_accumulation_steps"
								]
				else:
								snake_case__      :Any         =   1
				snake_case__      :List[Any]         =   (len(__snake_case      ) * num_epochs) // gradient_accumulation_steps

				# Instantiate scheduler
				if (
				    accelerator.state.deepspeed_plugin is None
				    or "scheduler" not in accelerator.state.deepspeed_plugin.deepspeed_config
				):
								snake_case__      :Optional[Any]         =   get_linear_schedule_with_warmup(
								    optimizer=__snake_case	,	num_warmup_steps=0	,	num_training_steps=__snake_case	,	)
				else:
								snake_case__      :Any         =   DummyScheduler(__snake_case	,	total_num_steps=__snake_case	,	warmup_num_steps=0      )

				# 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.
				snake_case__    ,						snake_case__    ,						snake_case__    ,						snake_case__    ,						snake_case__      :int         =   accelerator.prepare(
				    __snake_case	,	__snake_case	,	__snake_case	,	__snake_case	,	__snake_case      )

				# We need to keep track of how many total steps we have iterated over
				snake_case__      :Dict         =   0
				# We also need to keep track of the stating epoch so files are named properly
				snake_case__      :Union[str, Any]         =   0
				snake_case__      :List[str]         =   evaluate.load("glue"	,	"mrpc"      )
				snake_case__      :Optional[Any]         =   num_epochs

				if args.partial_train_epoch is not None:
								snake_case__      :List[Any]         =   args.partial_train_epoch

				if args.resume_from_checkpoint:
								accelerator.load_state(args.resume_from_checkpoint      )
								snake_case__      :Union[str, Any]         =   args.resume_from_checkpoint.split("epoch_"      )[1]
								snake_case__      :Dict         =   ""
								for char in epoch_string:
												if char.isdigit():
																state_epoch_num += char
												else:
																break
								snake_case__      :str         =   int(__snake_case      ) + 1
								snake_case__      :List[Any]         =   evaluation_loop(__snake_case	,	__snake_case	,	__snake_case	,	__snake_case      )
								accelerator.print("resumed checkpoint performance:"	,	__snake_case      )
								accelerator.print("resumed checkpoint's scheduler's lr:"	,	lr_scheduler.get_lr()[0]      )
								accelerator.print("resumed optimizers's lr:"	,	optimizer.param_groups[0]["lr"]      )
								with open(os.path.join(args.output_dir	,	F'state_{starting_epoch-1}.json'      )	,	"r"      ) as f:
												snake_case__      :Tuple         =   json.load(__snake_case      )
												assert resumed_state["accuracy"] == accuracy, "Accuracy mismatch, loading from checkpoint failed"
												assert (
												    resumed_state["lr"] == lr_scheduler.get_lr()[0]
												), "Scheduler learning rate mismatch, loading from checkpoint failed"
												assert (
												    resumed_state["optimizer_lr"] == optimizer.param_groups[0]["lr"]
												), "Optimizer learning rate mismatch, loading from checkpoint failed"
												assert resumed_state["epoch"] == starting_epoch - 1, "Epoch mismatch, loading from checkpoint failed"
												return

    # Now we train the model
				snake_case__      :Optional[int]         =   {}
				for epoch in range(__snake_case	,	__snake_case      ):
								model.train()
								for step, batch in enumerate(__snake_case      ):
												snake_case__      :str         =   model(**__snake_case      )
												snake_case__      :List[str]         =   outputs.loss
												snake_case__      :List[Any]         =   loss / gradient_accumulation_steps
												accelerator.backward(__snake_case      )
												if step % gradient_accumulation_steps == 0:
																optimizer.step()
																lr_scheduler.step()
																optimizer.zero_grad()

												overall_step += 1
								snake_case__      :int         =   F'epoch_{epoch}'
								snake_case__      :str         =   os.path.join(args.output_dir	,	__snake_case      )
								accelerator.save_state(__snake_case      )
								snake_case__      :Union[str, Any]         =   evaluation_loop(__snake_case	,	__snake_case	,	__snake_case	,	__snake_case      )
								snake_case__      :List[str]         =   accuracy
								snake_case__      :List[str]         =   lr_scheduler.get_lr()[0]
								snake_case__      :List[Any]         =   optimizer.param_groups[0]["lr"]
								snake_case__      :Dict         =   epoch
								snake_case__      :List[Any]         =   overall_step
								accelerator.print(F'epoch {epoch}:'	,	__snake_case      )

								accelerator.wait_for_everyone()
								if accelerator.is_main_process:
												with open(os.path.join(args.output_dir	,	F'state_{epoch}.json'      )	,	"w"      ) as f:
																json.dump(__snake_case	,	__snake_case      )





def 					lowercase_ (    )     -> Any:





				'''simple docstring'''


				snake_case__      :List[Any]         =   argparse.ArgumentParser(description="Simple example of training script tracking peak GPU memory usage."      )
				parser.add_argument(
				    "--model_name_or_path"	,	type=__snake_case	,	default="bert-base-cased"	,	help="Path to pretrained model or model identifier from huggingface.co/models."	,	required=__snake_case	,	)
				parser.add_argument(
				    "--output_dir"	,	type=__snake_case	,	default="."	,	help="Optional save directory where all checkpoint folders will be stored. Default is the current working directory."	,	)
				parser.add_argument(
				    "--resume_from_checkpoint"	,	type=__snake_case	,	default=__snake_case	,	help="If the training should continue from a checkpoint folder."	,	)
				parser.add_argument(
				    "--partial_train_epoch"	,	type=__snake_case	,	default=__snake_case	,	help="If passed, the training will stop after this number of epochs."	,	)
				parser.add_argument(
				    "--num_epochs"	,	type=__snake_case	,	default=2	,	help="Number of train epochs."	,	)
				snake_case__      :Any         =   parser.parse_args()
				snake_case__      :int         =   {"lr": 2e-5, "num_epochs": args.num_epochs, "seed": 42, "batch_size": 16}

				training_function(__snake_case	,	__snake_case      )


if __name__ == "__main__":
	main()