code: 
  
  import argparse
  import os
  
  # New Code #
  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
  from accelerate.utils import find_executable_batch_size
  
  
  ########################################################################
  # This is a fully working simple example to use Accelerate,
  # specifically showcasing how to combine both the gradient accumulation
  # and automatic batch size finder utilities of Accelerate to perfrom
  # automatic gradient accumulation
  #
  # 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)
  #
  # 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_		:			List[Any]										=   32
  
  
  def       __a       (   SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE = 1_6      )      ->     Union[str, Any]:
  
  
  
  
  
  
      '''simple docstring'''
      __UpperCAmelCase									=			AutoTokenizer.from_pretrained('''bert-base-cased'''      )
      __UpperCAmelCase									=			load_dataset('''glue'''       ,   '''mrpc'''      )
  
      def tokenize_function(SCREAMING_SNAKE_CASE      ):
          # max_length=None => use the model max length (it's actually the default)
          __UpperCAmelCase									=			tokenizer(examples['''sentence1''']       ,   examples['''sentence2''']       ,   truncation=SCREAMING_SNAKE_CASE       ,   max_length=SCREAMING_SNAKE_CASE      )
          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									=			datasets.map(
              SCREAMING_SNAKE_CASE       ,   batched=SCREAMING_SNAKE_CASE       ,   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									=			tokenized_datasets.rename_column('''label'''       ,   '''labels'''      )
  
      def collate_fn(SCREAMING_SNAKE_CASE      ):
          # When using mixed precision we want round multiples of 8/16
          if accelerator.mixed_precision == "fp8":
              __UpperCAmelCase									=			1_6
          elif accelerator.mixed_precision != "no":
              __UpperCAmelCase									=			8
          else:
              __UpperCAmelCase									=			None
  
          return tokenizer.pad(
              SCREAMING_SNAKE_CASE       ,   padding='''longest'''       ,   pad_to_multiple_of=SCREAMING_SNAKE_CASE       ,   return_tensors='''pt'''       ,   )
  
      # Instantiate dataloaders.
      __UpperCAmelCase									=			DataLoader(
          tokenized_datasets['''train''']       ,   shuffle=SCREAMING_SNAKE_CASE       ,   collate_fn=SCREAMING_SNAKE_CASE       ,   batch_size=SCREAMING_SNAKE_CASE      )
      __UpperCAmelCase									=			DataLoader(
          tokenized_datasets['''validation''']       ,   shuffle=SCREAMING_SNAKE_CASE       ,   collate_fn=SCREAMING_SNAKE_CASE       ,   batch_size=SCREAMING_SNAKE_CASE      )
  
      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_		:			List[str]										=   mocked_dataloaders  # noqa: F811
  
  
  def       __a       (   SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE      )      ->     str:
  
  
  
  
  
  
      '''simple docstring'''
      # For testing only
      if os.environ.get('''TESTING_MOCKED_DATALOADERS'''       ,   SCREAMING_SNAKE_CASE      ) == "1":
          __UpperCAmelCase									=			2
      # Initialize accelerator
      __UpperCAmelCase									=			Accelerator(cpu=args.cpu       ,   mixed_precision=args.mixed_precision      )
      # Sample hyper-parameters for learning rate, batch size, seed and a few other HPs
      __UpperCAmelCase									=			config['''lr''']
      __UpperCAmelCase									=			int(config['''num_epochs''']      )
      __UpperCAmelCase									=			int(config['''seed''']      )
      __UpperCAmelCase									=			int(config['''batch_size''']      )
  
      __UpperCAmelCase									=			evaluate.load('''glue'''       ,   '''mrpc'''      )
  
      # New Code #
      # We use the `find_executable_batch_size` decorator, passing in the desired observed batch size
      # to train on. If a CUDA OOM error occurs, it will retry this loop cutting the batch size in
      # half each time. From this, we can calculate the number of gradient accumulation steps needed
      # and modify the Accelerator object as a result
      @find_executable_batch_size(starting_batch_size=int(SCREAMING_SNAKE_CASE      )      )
      def inner_training_loop(SCREAMING_SNAKE_CASE      ):
          # Since we need to modify the outside accelerator object, we need to bring it
          # to the local scope
          nonlocal accelerator
  
          # We can calculate the number of gradient accumulation steps based on the current
          # batch size vs the starting batch size
          __UpperCAmelCase									=			observed_batch_size // batch_size
  
          # And then set it in the Accelerator directly:
          __UpperCAmelCase									=			num_gradient_accumulation_steps
  
          # Next we need to free all of the stored model references in the Accelerator each time
          accelerator.free_memory()
  
          # And set the seed so our results are reproducable each reset
          set_seed(SCREAMING_SNAKE_CASE      )
  
          # Instantiate the model (we build the model here so that the seed also control new weights initialization)
          __UpperCAmelCase									=			AutoModelForSequenceClassification.from_pretrained('''bert-base-cased'''       ,   return_dict=SCREAMING_SNAKE_CASE      )
  
          # 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									=			model.to(accelerator.device      )
  
          # Instantiate optimizer
          __UpperCAmelCase									=			AdamW(params=model.parameters()       ,   lr=SCREAMING_SNAKE_CASE      )
          __UpperCAmelCase					,     __UpperCAmelCase									=			get_dataloaders(SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE      )
  
          # Instantiate scheduler
          __UpperCAmelCase									=			get_linear_schedule_with_warmup(
              optimizer=SCREAMING_SNAKE_CASE       ,   num_warmup_steps=1_0_0       ,   num_training_steps=(len(SCREAMING_SNAKE_CASE      ) * num_epochs)       ,   )
  
          # 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									=			accelerator.prepare(
              SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE      )
  
          # Now we train the model
          for epoch in range(SCREAMING_SNAKE_CASE      ):
              model.train()
              for step, batch in enumerate(SCREAMING_SNAKE_CASE      ):
                  # And perform gradient accumulation
                  with accelerator.accumulate(SCREAMING_SNAKE_CASE      ):
                      # We could avoid this line since we set the accelerator with `device_placement=True`.
                      batch.to(accelerator.device      )
                      __UpperCAmelCase									=			model(**SCREAMING_SNAKE_CASE      )
                      __UpperCAmelCase									=			outputs.loss
                      accelerator.backward(SCREAMING_SNAKE_CASE      )
                      optimizer.step()
                      lr_scheduler.step()
                      optimizer.zero_grad()
  
              model.eval()
              for step, batch in enumerate(SCREAMING_SNAKE_CASE      ):
                  # We could avoid this line since we set the accelerator with `device_placement=True`.
                  batch.to(accelerator.device      )
                  with torch.no_grad():
                      __UpperCAmelCase									=			model(**SCREAMING_SNAKE_CASE      )
                  __UpperCAmelCase									=			outputs.logits.argmax(dim=-1      )
                  __UpperCAmelCase					,     __UpperCAmelCase									=			accelerator.gather_for_metrics((predictions, batch['''labels'''])      )
                  metric.add_batch(
                      predictions=SCREAMING_SNAKE_CASE       ,   references=SCREAMING_SNAKE_CASE       ,   )
  
              __UpperCAmelCase									=			metric.compute()
              # Use accelerator.print to print only on the main process.
              accelerator.print(f'''epoch {epoch}:'''       ,   SCREAMING_SNAKE_CASE      )
  
      # New Code #
      # And call it at the end with no arguments
      # Note: You could also refactor this outside of your training loop function
      inner_training_loop()
  
  
  def       __a       (   )      ->     str:
  
  
  
  
  
  
      '''simple docstring'''
      __UpperCAmelCase									=			argparse.ArgumentParser(description='''Simple example of training script.'''      )
      parser.add_argument(
          '''--mixed_precision'''       ,   type=SCREAMING_SNAKE_CASE       ,   default=SCREAMING_SNAKE_CASE       ,   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									=			parser.parse_args()
      # New Code #
      # We modify the starting batch size to be an observed batch size of 256, to guarentee an initial CUDA OOM
      __UpperCAmelCase									=			{'''lr''': 2e-5, '''num_epochs''': 3, '''seed''': 4_2, '''batch_size''': 2_5_6}
      training_function(SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE      )
  
  
  if __name__ == "__main__":
         main()
  
  
  
  
  
style_context: 
  
  import numpy as np
  
  
  def       __a       (   SCREAMING_SNAKE_CASE      )      ->     Tuple:
  
  
  
  
  
  
      '''simple docstring'''
      __UpperCAmelCase					,     __UpperCAmelCase									=			a.shape
      __UpperCAmelCase									=			min(SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE      )
      __UpperCAmelCase									=			np.eye(SCREAMING_SNAKE_CASE      )
      __UpperCAmelCase									=			a.copy()
  
      for k in range(t - 1      ):
          # select a column of modified matrix A':
          __UpperCAmelCase									=			r[k:, [k]]
          # construct first basis vector
          __UpperCAmelCase									=			np.zeros_like(SCREAMING_SNAKE_CASE      )
          __UpperCAmelCase									=			1.0
          # determine scaling factor
          __UpperCAmelCase									=			np.linalg.norm(SCREAMING_SNAKE_CASE      )
          # construct vector v for Householder reflection
          __UpperCAmelCase									=			x + np.sign(x[0]      ) * alpha * ea
          v /= np.linalg.norm(SCREAMING_SNAKE_CASE      )
  
          # construct the Householder matrix
          __UpperCAmelCase									=			np.eye(m - k      ) - 2.0 * v @ v.T
          # pad with ones and zeros as necessary
          __UpperCAmelCase									=			np.block([[np.eye(SCREAMING_SNAKE_CASE      ), np.zeros((k, m - k)      )], [np.zeros((m - k, k)      ), q_k]]      )
  
          __UpperCAmelCase									=			q @ q_k.T
          __UpperCAmelCase									=			q_k @ r
  
      return q, r
  
  
  if __name__ == "__main__":
         import doctest
  
         doctest.testmod()
  
  
  
  
  