




"""simple docstring"""







from __future__ import annotations

import math
import random
from collections.abc import Collection
from typing import overload






class       SCREAMING_SNAKE_CASE__					:


						def __init__(							self				:			Dict						,						lowerCAmelCase				:			Collection[float] | None = None					):
										if components is None:
														lowerCAmelCase  =				[]
										lowerCAmelCase  =				list(lowerCAmelCase					)


						def __len__(							self				:			List[Any]					):
										return len(self.__components					)


						def __str__(							self				:			str					):
										return "(" + ",".join(map(lowerCAmelCase						,						self.__components					)					) + ")"


						def __add__(							self				:			Any						,						lowerCAmelCase				:			Vector					):
										lowerCAmelCase  =				len(self					)
										if size == len(lowerCAmelCase					):
														lowerCAmelCase  =				[self.__components[i] + other.component(lowerCAmelCase					) for i in range(lowerCAmelCase					)]
														return Vector(lowerCAmelCase					)
										else:
														raise Exception("""must have the same size"""					)


						def __sub__(							self				:			List[Any]						,						lowerCAmelCase				:			Vector					):
										lowerCAmelCase  =				len(self					)
										if size == len(lowerCAmelCase					):
														lowerCAmelCase  =				[self.__components[i] - other.component(lowerCAmelCase					) for i in range(lowerCAmelCase					)]
														return Vector(lowerCAmelCase					)
										else:  # error case
														raise Exception("""must have the same size"""					)


						@overload
						def __mul__(							self				:			Optional[int]						,						lowerCAmelCase				:			float					):
										...


						@overload
						def __mul__(							self				:			List[Any]						,						lowerCAmelCase				:			Vector					):
										...


						def __mul__(							self				:			Dict						,						lowerCAmelCase				:			float | Vector					):
										if isinstance(lowerCAmelCase						,						(float, int)					):
														lowerCAmelCase  =				[c * other for c in self.__components]
														return Vector(lowerCAmelCase					)
										elif isinstance(lowerCAmelCase						,						lowerCAmelCase					) and len(self					) == len(lowerCAmelCase					):
														lowerCAmelCase  =				len(self					)
														lowerCAmelCase  =				[self.__components[i] * other.component(lowerCAmelCase					) for i in range(lowerCAmelCase					)]
														return sum(lowerCAmelCase					)
										else:  # error case
														raise Exception("""invalid operand!"""					)


						def   __lowercase (							self				:			Tuple					):
										return Vector(self.__components					)


						def   __lowercase (							self				:			Dict						,						lowerCAmelCase				:			int					):
										if isinstance(lowerCAmelCase						,						lowerCAmelCase					) and -len(self.__components					) <= i < len(self.__components					):
														return self.__components[i]
										else:
														raise Exception("""index out of range"""					)


						def   __lowercase (							self				:			Any						,						lowerCAmelCase				:			int						,						lowerCAmelCase				:			float					):
										assert -len(self.__components					) <= pos < len(self.__components					)
										lowerCAmelCase  =				value


						def   __lowercase (							self				:			Optional[int]					):
										if len(self.__components					) == 0:
														raise Exception("""Vector is empty"""					)
										lowerCAmelCase  =				[c**2 for c in self.__components]
										return math.sqrt(sum(lowerCAmelCase					)					)




						def   __lowercase (							self				:			str						,						lowerCAmelCase				:			Vector						,						lowerCAmelCase				:			bool = False					):
										lowerCAmelCase  =				self * other
										lowerCAmelCase  =				self.euclidean_length() * other.euclidean_length()
										if deg:
														return math.degrees(math.acos(num / den					)					)
										else:
														return math.acos(num / den					)





def 							lowercase					(snake_case__   : int )     ->  Vector:


				'''simple docstring'''






				assert isinstance(snake_case__      ,       snake_case__ )
				return Vector([0] * dimension )





def 							lowercase					(snake_case__   : int      ,       snake_case__   : int )     ->  Vector:


				'''simple docstring'''






				assert isinstance(snake_case__      ,       snake_case__ ) and (isinstance(snake_case__      ,       snake_case__ ))
				lowerCAmelCase  =				[0] * dimension
				lowerCAmelCase  =				1
				return Vector(snake_case__ )





def 							lowercase					(snake_case__   : float      ,       snake_case__   : Vector      ,       snake_case__   : Vector )     ->  Vector:


				'''simple docstring'''






				assert (
				    isinstance(snake_case__      ,       snake_case__ )
				    and isinstance(snake_case__      ,       snake_case__ )
				    and (isinstance(snake_case__      ,       (int, float) ))
				)
				return x * scalar + y





def 							lowercase					(snake_case__   : int      ,       snake_case__   : int      ,       snake_case__   : int )     ->  Vector:


				'''simple docstring'''






				random.seed(snake_case__ )
				lowerCAmelCase  =				[random.randint(snake_case__      ,       snake_case__ ) for _ in range(snake_case__ )]
				return Vector(snake_case__ )






class       SCREAMING_SNAKE_CASE__					:


						def __init__(							self				:			Any						,						lowerCAmelCase				:			list[list[float]]						,						lowerCAmelCase				:			int						,						lowerCAmelCase				:			int					):
										lowerCAmelCase  =				matrix
										lowerCAmelCase  =				w
										lowerCAmelCase  =				h


						def __str__(							self				:			List[str]					):
										lowerCAmelCase  =				""""""
										for i in range(self.__height					):
														ans += "|"
														for j in range(self.__width					):
																		if j < self.__width - 1:
																						ans += str(self.__matrix[i][j]					) + ","
																		else:
																						ans += str(self.__matrix[i][j]					) + "|\n"
										return ans


						def __add__(							self				:			Optional[Any]						,						lowerCAmelCase				:			Matrix					):
										if self.__width == other.width() and self.__height == other.height():
														lowerCAmelCase  =				[]
														for i in range(self.__height					):
																		lowerCAmelCase  =				[
																		    self.__matrix[i][j] + other.component(lowerCAmelCase						,						lowerCAmelCase					)
																		    for j in range(self.__width					)
																		]
																		matrix.append(lowerCAmelCase					)
														return Matrix(lowerCAmelCase						,						self.__width						,						self.__height					)
										else:
														raise Exception("""matrix must have the same dimension!"""					)


						def __sub__(							self				:			Union[str, Any]						,						lowerCAmelCase				:			Matrix					):
										if self.__width == other.width() and self.__height == other.height():
														lowerCAmelCase  =				[]
														for i in range(self.__height					):
																		lowerCAmelCase  =				[
																		    self.__matrix[i][j] - other.component(lowerCAmelCase						,						lowerCAmelCase					)
																		    for j in range(self.__width					)
																		]
																		matrix.append(lowerCAmelCase					)
														return Matrix(lowerCAmelCase						,						self.__width						,						self.__height					)
										else:
														raise Exception("""matrices must have the same dimension!"""					)


						@overload
						def __mul__(							self				:			Any						,						lowerCAmelCase				:			float					):
										...


						@overload
						def __mul__(							self				:			Optional[int]						,						lowerCAmelCase				:			Vector					):
										...


						def __mul__(							self				:			Dict						,						lowerCAmelCase				:			float | Vector					):
										if isinstance(lowerCAmelCase						,						lowerCAmelCase					):  # matrix-vector
														if len(lowerCAmelCase					) == self.__width:
																		lowerCAmelCase  =				zero_vector(self.__height					)
																		for i in range(self.__height					):
																						lowerCAmelCase  =				[
																						    self.__matrix[i][j] * other.component(lowerCAmelCase					)
																						    for j in range(self.__width					)
																						]
																						ans.change_component(lowerCAmelCase						,						sum(lowerCAmelCase					)					)
																		return ans
														else:
																		raise Exception(
																		    """vector must have the same size as the """
																		    """number of columns of the matrix!"""					)
										elif isinstance(lowerCAmelCase						,						(int, float)					):  # matrix-scalar
														lowerCAmelCase  =				[
														    [self.__matrix[i][j] * other for j in range(self.__width					)]
														    for i in range(self.__height					)
														]
														return Matrix(lowerCAmelCase						,						self.__width						,						self.__height					)
										return None


						def   __lowercase (							self				:			Any					):
										return self.__height


						def   __lowercase (							self				:			int					):
										return self.__width


						def   __lowercase (							self				:			Optional[Any]						,						lowerCAmelCase				:			int						,						lowerCAmelCase				:			int					):
										if 0 <= x < self.__height and 0 <= y < self.__width:
														return self.__matrix[x][y]
										else:
														raise Exception("""change_component: indices out of bounds"""					)


						def   __lowercase (							self				:			int						,						lowerCAmelCase				:			int						,						lowerCAmelCase				:			int						,						lowerCAmelCase				:			float					):
										if 0 <= x < self.__height and 0 <= y < self.__width:
														lowerCAmelCase  =				value
										else:
														raise Exception("""change_component: indices out of bounds"""					)


						def   __lowercase (							self				:			int						,						lowerCAmelCase				:			int						,						lowerCAmelCase				:			int					):
										if self.__height != self.__width:
														raise Exception("""Matrix is not square"""					)
										lowerCAmelCase  =				self.__matrix[:x] + self.__matrix[x + 1 :]
										for i in range(len(lowerCAmelCase					)					):
														lowerCAmelCase  =				minor[i][:y] + minor[i][y + 1 :]
										return Matrix(lowerCAmelCase						,						self.__width - 1						,						self.__height - 1					).determinant()


						def   __lowercase (							self				:			Optional[Any]						,						lowerCAmelCase				:			int						,						lowerCAmelCase				:			int					):
										if self.__height != self.__width:
														raise Exception("""Matrix is not square"""					)
										if 0 <= x < self.__height and 0 <= y < self.__width:
														return (-1) ** (x + y) * self.minor(lowerCAmelCase						,						lowerCAmelCase					)
										else:
														raise Exception("""Indices out of bounds"""					)




						def   __lowercase (							self				:			List[Any]					):
										if self.__height != self.__width:
														raise Exception("""Matrix is not square"""					)
										if self.__height < 1:
														raise Exception("""Matrix has no element"""					)
										elif self.__height == 1:
														return self.__matrix[0][0]
										elif self.__height == 2:
														return (
														    self.__matrix[0][0] * self.__matrix[1][1]
														    - self.__matrix[0][1] * self.__matrix[1][0]
														)
										else:
														lowerCAmelCase  =				[
														    self.__matrix[0][y] * self.cofactor(0						,						lowerCAmelCase					) for y in range(self.__width					)
														]
														return sum(lowerCAmelCase					)





def 							lowercase					(snake_case__   : int )     ->  Matrix:


				'''simple docstring'''






				lowerCAmelCase  =				[[0] * n for _ in range(snake_case__ )]
				return Matrix(snake_case__      ,       snake_case__      ,       snake_case__ )






def 							lowercase					(snake_case__   : int      ,       snake_case__   : int      ,       snake_case__   : int      ,       snake_case__   : int )     ->  Matrix:


				'''simple docstring'''






				random.seed(snake_case__ )
				lowerCAmelCase  =				[
				    [random.randint(snake_case__      ,       snake_case__ ) for _ in range(snake_case__ )] for _ in range(snake_case__ )
				]
				return Matrix(snake_case__      ,       snake_case__      ,       snake_case__ )











"""simple docstring"""







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 the experiment tracking capability,
# 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 							lowercase					(snake_case__   : Accelerator      ,       snake_case__   : int = 16 )     ->  Dict:


				'''simple docstring'''






				lowerCAmelCase  =				AutoTokenizer.from_pretrained("""bert-base-cased""" )
				lowerCAmelCase  =				load_dataset("""glue"""      ,       """mrpc""" )

				def tokenize_function(snake_case__   : List[Any] ):
								# max_length=None => use the model max length (it's actually the default)
								lowerCAmelCase  =				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
				# starting with the main process first:
				with accelerator.main_process_first():
								lowerCAmelCase  =				datasets.map(
								    snake_case__      ,       batched=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
				lowerCAmelCase  =				tokenized_datasets.rename_column("""label"""      ,       """labels""" )

				def collate_fn(snake_case__   : Union[str, Any] ):
								# On TPU it's best to pad everything to the same length or training will be very slow.
								lowerCAmelCase  =				128 if accelerator.distributed_type == DistributedType.TPU else None
								# When using mixed precision we want round multiples of 8/16
								if accelerator.mixed_precision == "fp8":
												lowerCAmelCase  =				16
								elif accelerator.mixed_precision != "no":
												lowerCAmelCase  =				8
								else:
												lowerCAmelCase  =				None

								return tokenizer.pad(
								    snake_case__      ,       padding="""longest"""      ,       max_length=snake_case__      ,       pad_to_multiple_of=snake_case__      ,       return_tensors="""pt"""      ,       )

				# Instantiate dataloaders.
				lowerCAmelCase  =				DataLoader(
				    tokenized_datasets["""train"""]      ,       shuffle=snake_case__      ,       collate_fn=snake_case__      ,       batch_size=snake_case__ )
				lowerCAmelCase  =				DataLoader(
				    tokenized_datasets["""validation"""]      ,       shuffle=snake_case__      ,       collate_fn=snake_case__      ,       batch_size=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      =							mocked_dataloaders  # noqa: F811





def 							lowercase					(snake_case__   : int      ,       snake_case__   : Tuple )     ->  int:


				'''simple docstring'''






				if os.environ.get("""TESTING_MOCKED_DATALOADERS"""      ,       snake_case__ ) == "1":
								lowerCAmelCase  =				2
				# Initialize Accelerator

				# New Code #
				# We pass in "all" to `log_with` to grab all available trackers in the environment
				# Note: If using a custom `Tracker` class, should be passed in here such as:
				# >>> log_with = ["all", MyCustomTrackerClassInstance()]
				if args.with_tracking:
								lowerCAmelCase  =				Accelerator(
								    cpu=args.cpu      ,       mixed_precision=args.mixed_precision      ,       log_with="""all"""      ,       project_dir=args.project_dir )
				else:
								lowerCAmelCase  =				Accelerator(cpu=args.cpu      ,       mixed_precision=args.mixed_precision )
				# Sample hyper-parameters for learning rate, batch size, seed and a few other HPs
				lowerCAmelCase  =				config["""lr"""]
				lowerCAmelCase  =				int(config["""num_epochs"""] )
				lowerCAmelCase  =				int(config["""seed"""] )
				lowerCAmelCase  =				int(config["""batch_size"""] )
				set_seed(snake_case__ )

				lowerCAmelCase ,						lowerCAmelCase  =				get_dataloaders(snake_case__      ,       snake_case__ )
				lowerCAmelCase  =				evaluate.load("""glue"""      ,       """mrpc""" )

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

				# Instantiate the model (we build the model here so that the seed also control new weights initialization)
				lowerCAmelCase  =				AutoModelForSequenceClassification.from_pretrained("""bert-base-cased"""      ,       return_dict=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).
				lowerCAmelCase  =				model.to(accelerator.device )

				# Instantiate optimizer
				lowerCAmelCase  =				AdamW(params=model.parameters()      ,       lr=snake_case__ )

				# Instantiate scheduler
				lowerCAmelCase  =				get_linear_schedule_with_warmup(
				    optimizer=snake_case__      ,       num_warmup_steps=100      ,       num_training_steps=(len(snake_case__ ) * 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.
				lowerCAmelCase ,						lowerCAmelCase ,						lowerCAmelCase ,						lowerCAmelCase ,						lowerCAmelCase  =				accelerator.prepare(
				    snake_case__      ,       snake_case__      ,       snake_case__      ,       snake_case__      ,       snake_case__ )

				# New Code #
				# We need to initialize the trackers we use. Overall configurations can also be stored
				if args.with_tracking:
								lowerCAmelCase  =				os.path.split(snake_case__ )[-1].split(""".""" )[0]
								accelerator.init_trackers(snake_case__      ,       snake_case__ )

				# Now we train the model
				for epoch in range(snake_case__ ):
								model.train()
								# New Code #
								# For our tracking example, we will log the total loss of each epoch
								if args.with_tracking:
												lowerCAmelCase  =				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 )
												lowerCAmelCase  =				model(**snake_case__ )
												lowerCAmelCase  =				outputs.loss
												# New Code #
												if args.with_tracking:
																total_loss += loss.detach().float()
												lowerCAmelCase  =				loss / gradient_accumulation_steps
												accelerator.backward(snake_case__ )
												if step % gradient_accumulation_steps == 0:
																optimizer.step()
																lr_scheduler.step()
																optimizer.zero_grad()

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

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

								# New Code #
								# To actually log, we call `Accelerator.log`
								# The values passed can be of `str`, `int`, `float` or `dict` of `str` to `float`/`int`
								if args.with_tracking:
												accelerator.log(
												    {
												        """accuracy""": eval_metric["""accuracy"""],
												        """f1""": eval_metric["""f1"""],
												        """train_loss""": total_loss.item() / len(snake_case__ ),
												        """epoch""": epoch,
												    }      ,       step=snake_case__      ,       )

    # New Code #
    # When a run is finished, you should call `accelerator.end_training()`
    # to close all of the open trackers
				if args.with_tracking:
								accelerator.end_training()





def 							lowercase					()     ->  str:


				'''simple docstring'''






				lowerCAmelCase  =				argparse.ArgumentParser(description="""Simple example of training script.""" )
				parser.add_argument(
				    """--mixed_precision"""      ,       type=snake_case__      ,       default=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.""" )
				parser.add_argument(
				    """--with_tracking"""      ,       action="""store_true"""      ,       help="""Whether to load in all available experiment trackers from the environment and use them for logging."""      ,       )
				parser.add_argument(
				    """--project_dir"""      ,       type=snake_case__      ,       default="""logs"""      ,       help="""Location on where to store experiment tracking logs` and relevent project information"""      ,       )
				lowerCAmelCase  =				parser.parse_args()
				lowerCAmelCase  =				{"""lr""": 2e-5, """num_epochs""": 3, """seed""": 42, """batch_size""": 16}
				training_function(snake_case__      ,       snake_case__ )


if __name__ == "__main__":
		main()





