






'''simple docstring'''
import argparse

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
#
# 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 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__				:						Tuple,	UpperCamelCase__				:						Union[str, Any] = 1_6							):




      '''simple docstring'''






      SCREAMING_SNAKE_CASE__     :				Tuple									=AutoTokenizer.from_pretrained('''bert-base-cased'''							)
      SCREAMING_SNAKE_CASE__     :				Tuple									=load_dataset('''glue''',	'''mrpc'''							)

      def tokenize_function(UpperCamelCase__				:						Optional[Any]							):
            # max_length=None => use the model max length (it's actually the default)
            SCREAMING_SNAKE_CASE__     :				Optional[int]									=tokenizer(examples['''sentence1'''],	examples['''sentence2'''],	truncation=lowerCAmelCase_,	max_length=lowerCAmelCase_							)
            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():
            SCREAMING_SNAKE_CASE__     :				Tuple									=datasets.map(
                lowerCAmelCase_,	batched=lowerCAmelCase_,	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
      SCREAMING_SNAKE_CASE__     :				List[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.
            SCREAMING_SNAKE_CASE__     :				Tuple									=1_2_8 if accelerator.distributed_type == DistributedType.TPU else None
            # When using mixed precision we want round multiples of 8/16
            if accelerator.mixed_precision == "fp8":
                  SCREAMING_SNAKE_CASE__     :				Optional[int]									=1_6
            elif accelerator.mixed_precision != "no":
                  SCREAMING_SNAKE_CASE__     :				Optional[int]									=8
            else:
                  SCREAMING_SNAKE_CASE__     :				Optional[int]									=None

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

      # Instantiate dataloaders.
      SCREAMING_SNAKE_CASE__     :				str									=DataLoader(
          tokenized_datasets['''train'''],	shuffle=lowerCAmelCase_,	collate_fn=lowerCAmelCase_,	batch_size=lowerCAmelCase_,	drop_last=lowerCAmelCase_							)
      SCREAMING_SNAKE_CASE__     :				int									=DataLoader(
          tokenized_datasets['''validation'''],	shuffle=lowerCAmelCase_,	collate_fn=lowerCAmelCase_,	batch_size=lowerCAmelCase_,	drop_last=(accelerator.mixed_precision == '''fp8'''),	)

      return train_dataloader, eval_dataloader





def  _a(  UpperCamelCase__				:						Dict,	UpperCamelCase__				:						Optional[Any]							):




      '''simple docstring'''






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

      SCREAMING_SNAKE_CASE__     :				str									=evaluate.load('''glue''',	'''mrpc'''							)

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

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

      # 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).
      SCREAMING_SNAKE_CASE__     :				Union[str, Any]									=model.to(accelerator.device							)
      # Instantiate optimizer
      SCREAMING_SNAKE_CASE__     :				str									=AdamW(params=model.parameters(),	lr=lowerCAmelCase_							)

      # Instantiate scheduler
      SCREAMING_SNAKE_CASE__     :				Tuple									=get_linear_schedule_with_warmup(
          optimizer=lowerCAmelCase_,	num_warmup_steps=1_0_0,	num_training_steps=(len(lowerCAmelCase_							) * 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.

      SCREAMING_SNAKE_CASE__     :				int									=accelerator.prepare(
          lowerCAmelCase_,	lowerCAmelCase_,	lowerCAmelCase_,	lowerCAmelCase_,	lowerCAmelCase_							)

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

            model.eval()
            for step, batch in enumerate(lowerCAmelCase_							):
                  # We could avoid this line since we set the accelerator with `device_placement=True`.
                  batch.to(accelerator.device							)
                  with torch.no_grad():
                        SCREAMING_SNAKE_CASE__     :				str									=model(**lowerCAmelCase_							)
                  SCREAMING_SNAKE_CASE__     :				str									=outputs.logits.argmax(dim=-1							)
                  SCREAMING_SNAKE_CASE__     :				Any									=accelerator.gather_for_metrics((predictions, batch['''labels'''])							)
                  metric.add_batch(
                      predictions=lowerCAmelCase_,	references=lowerCAmelCase_,	)

            SCREAMING_SNAKE_CASE__     :				List[str]									=metric.compute()
            # Use accelerator.print to print only on the main process.
            accelerator.print(f"epoch {epoch}:",	lowerCAmelCase_							)





def  _a(  ):




      '''simple docstring'''






      SCREAMING_SNAKE_CASE__     :				int									=argparse.ArgumentParser(description='''Simple example of training script.'''							)
      parser.add_argument(
          '''--mixed_precision''',	type=lowerCAmelCase_,	default=lowerCAmelCase_,	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.'''							)
      SCREAMING_SNAKE_CASE__     :				str									=parser.parse_args()
      SCREAMING_SNAKE_CASE__     :				Tuple									={"lr": 2e-5, "num_epochs": 3, "seed": 4_2, "batch_size": 1_6}
      training_function(lowerCAmelCase_,	lowerCAmelCase_							)


if __name__ == "__main__":
      main()







'''simple docstring'''
from __future__ import annotations

from collections.abc import Callable

a_					= list[list[float | int]]





def  _a(  UpperCamelCase__				:						Matrix,	UpperCamelCase__				:						Matrix							):




      '''simple docstring'''






      SCREAMING_SNAKE_CASE__     :				int									=len(UpperCamelCase__							)
      SCREAMING_SNAKE_CASE__     :				Matrix									=[[0 for _ in range(size + 1							)] for _ in range(UpperCamelCase__							)]
      SCREAMING_SNAKE_CASE__     :				int
      SCREAMING_SNAKE_CASE__     :				int
      SCREAMING_SNAKE_CASE__     :				int
      SCREAMING_SNAKE_CASE__     :				int
      SCREAMING_SNAKE_CASE__     :				int
      SCREAMING_SNAKE_CASE__     :				float

      for row in range(UpperCamelCase__							):
            for col in range(UpperCamelCase__							):
                  SCREAMING_SNAKE_CASE__     :				Tuple									=matrix[row][col]

            SCREAMING_SNAKE_CASE__     :				Optional[int]									=vector[row][0]

      SCREAMING_SNAKE_CASE__     :				Any									=0
      SCREAMING_SNAKE_CASE__     :				Union[str, Any]									=0
      while row < size and col < size:
            # pivoting
            SCREAMING_SNAKE_CASE__     :				Any									=max((abs(augmented[rowa][col]							), rowa) for rowa in range(UpperCamelCase__,	UpperCamelCase__							)							)[
                1
            ]
            if augmented[pivot_row][col] == 0:
                  col += 1
                  continue
            else:
                  SCREAMING_SNAKE_CASE__		,	SCREAMING_SNAKE_CASE__     :				Optional[Any]									=augmented[pivot_row], augmented[row]

            for rowa in range(row + 1,	UpperCamelCase__							):
                  SCREAMING_SNAKE_CASE__     :				Union[str, Any]									=augmented[rowa][col] / augmented[row][col]
                  SCREAMING_SNAKE_CASE__     :				Tuple									=0
                  for cola in range(col + 1,	size + 1							):
                        augmented[rowa][cola] -= augmented[row][cola] * ratio

            row += 1
            col += 1

      # back substitution
      for col in range(1,	UpperCamelCase__							):
            for row in range(UpperCamelCase__							):
                  SCREAMING_SNAKE_CASE__     :				Optional[Any]									=augmented[row][col] / augmented[col][col]
                  for cola in range(UpperCamelCase__,	size + 1							):
                        augmented[row][cola] -= augmented[col][cola] * ratio

    # round to get rid of numbers like 2.000000000000004
      return [
          [round(augmented[row][size] / augmented[row][row],	1_0							)] for row in range(UpperCamelCase__							)
      ]





def  _a(  UpperCamelCase__				:						list[int]							):




      '''simple docstring'''






      SCREAMING_SNAKE_CASE__     :				int									=len(UpperCamelCase__							)
      SCREAMING_SNAKE_CASE__     :				Matrix									=[[0 for _ in range(UpperCamelCase__							)] for _ in range(UpperCamelCase__							)]
      SCREAMING_SNAKE_CASE__     :				Matrix									=[[0] for _ in range(UpperCamelCase__							)]
      SCREAMING_SNAKE_CASE__     :				Matrix
      SCREAMING_SNAKE_CASE__     :				int
      SCREAMING_SNAKE_CASE__     :				int
      SCREAMING_SNAKE_CASE__     :				int

      for x_val, y_val in enumerate(UpperCamelCase__							):
            for col in range(UpperCamelCase__							):
                  SCREAMING_SNAKE_CASE__     :				Optional[int]									=(x_val + 1) ** (size - col - 1)
            SCREAMING_SNAKE_CASE__     :				Dict									=y_val

      SCREAMING_SNAKE_CASE__     :				Optional[int]									=solve(UpperCamelCase__,	UpperCamelCase__							)

      def interpolated_func(UpperCamelCase__				:						int							) -> int:
            return sum(
                round(coeffs[x_val][0]							) * (var ** (size - x_val - 1))
                for x_val in range(UpperCamelCase__							)							)

      return interpolated_func





def  _a(  UpperCamelCase__				:						int							):




      '''simple docstring'''






      return (
          1
          - variable
          + variable**2
          - variable**3
          + variable**4
          - variable**5
          + variable**6
          - variable**7
          + variable**8
          - variable**9
          + variable**1_0
      )





def  _a(  UpperCamelCase__				:						Callable[[int], int] = question_function,	UpperCamelCase__				:						int = 1_0							):




      '''simple docstring'''






      SCREAMING_SNAKE_CASE__     :				list[int]									=[func(UpperCamelCase__							) for x_val in range(1,	order + 1							)]

      SCREAMING_SNAKE_CASE__     :				list[Callable[[int], int]]									=[
          interpolate(data_points[:max_coeff]							) for max_coeff in range(1,	order + 1							)
      ]

      SCREAMING_SNAKE_CASE__     :				int									=0
      SCREAMING_SNAKE_CASE__     :				Callable[[int], int]
      SCREAMING_SNAKE_CASE__     :				int

      for poly in polynomials:
            SCREAMING_SNAKE_CASE__     :				Any									=1
            while func(UpperCamelCase__							) == poly(UpperCamelCase__							):
                  x_val += 1

            ret += poly(UpperCamelCase__							)

      return ret


if __name__ == "__main__":
  print(F'''{solution() = }''')