code: 
  
  
  import importlib.util
  import weakref
  from functools import partialmethod
  
  from .dependency_versions_check import dep_version_check
  from .utils import is_accelerate_available, is_torch_available, logging
  
  
  if is_torch_available():
  	import torch
  
  lowerCAmelCase					 =	logging.get_logger(__name__)
  
  
  
  
  
  
  
  def  _lowerCamelCase(			)		->			Dict:
  
  		'''simple docstring'''
  
  
  
  
  
  
  
  		return importlib.util.find_spec('deepspeed'			) is not None
  
  
  if is_accelerate_available() and is_deepspeed_available():
  	from accelerate.utils.deepspeed import HfDeepSpeedConfig as DeepSpeedConfig
  else:
  	# Inherits from a dummy `object` if accelerate is not available, so that python succeeds to import this file.
  	# Deepspeed glue code will never inherit this dummy object as it checks if accelerate is available.
  	from builtins import object as DeepSpeedConfig
  
  
  
  
  
  class    A					(     A_				):
  
  
  							def __init__(self   ,       lowerCAmelCase      ):
  									# set global weakref object
  									set_hf_deepspeed_config(self      )
  									dep_version_check('accelerate'      )
  									dep_version_check('deepspeed'      )
  									super().__init__(lowerCAmelCase      )
  
  
  
  
  
  class    A					(     A_				):
  
  
  							def __init__(self   ,       lowerCAmelCase      ):
  									super().__init__(lowerCAmelCase      )
  									__lowercase=    None
  									__lowercase=    []
  
  
  							def     _A (self      ):
  									if self._dtype is None:
  											raise ValueError('trainer_config_process() wasn\'t called yet to tell dtype'      )
  									return self._dtype
  
  
  							def     _A (self   ,       lowerCAmelCase      ):
  									__lowercase=    self.get_value(lowerCAmelCase      )
  									if val is None:
  											return False
  									else:
  											return val == "auto"
  
  
  							def     _A (self   ,       lowerCAmelCase   ,       lowerCAmelCase   ,       lowerCAmelCase=None   ,       lowerCAmelCase=True      ):
  									__lowercase,							__lowercase=    self.find_config_node(lowerCAmelCase      )
  									if config is None:
  											return
  
  									if config.get(lowerCAmelCase      ) == "auto":
  											__lowercase=    hf_val
  											return
  
  									if not must_match:
  											return
  
  									__lowercase=    config.get(lowerCAmelCase      )
  									if ds_val is not None and ds_val != hf_val:
  											self.mismatches.append(f'- ds {ds_key_long}={ds_val} vs hf {hf_key}={hf_val}'      )
  
  							UpperCamelCase_     :							str =partialmethod(A_      ,       must_match=A_				)
  
  
  							def     _A (self   ,       lowerCAmelCase      ):
  									__lowercase=    args.world_size * args.per_device_train_batch_size * args.gradient_accumulation_steps
  									self.fill_match(
  									    'train_micro_batch_size_per_gpu'   ,       args.per_device_train_batch_size   ,       'per_device_train_batch_size'      )
  									self.fill_match('gradient_accumulation_steps'   ,       args.gradient_accumulation_steps   ,       'gradient_accumulation_steps'      )
  									self.fill_match('train_batch_size'   ,       lowerCAmelCase   ,       'train_batch_size (calculated)'      )
  									self.fill_match('gradient_clipping'   ,       args.max_grad_norm   ,       'max_grad_norm'      )
  
  									self.fill_match('optimizer.params.lr'   ,       args.learning_rate   ,       'learning_rate'      )
  									self.fill_match('optimizer.params.betas'   ,       [args.adam_betaa, args.adam_betaa]   ,       'adam_beta1+adam_beta2'      )
  									self.fill_match('optimizer.params.eps'   ,       args.adam_epsilon   ,       'adam_epsilon'      )
  									self.fill_match('optimizer.params.weight_decay'   ,       args.weight_decay   ,       'weight_decay'      )
  
  									self.fill_only('scheduler.params.warmup_min_lr'   ,       0      )  # not a trainer arg
  									self.fill_match('scheduler.params.warmup_max_lr'   ,       args.learning_rate   ,       'learning_rate'      )
  									# total_num_steps - will get set in trainer_config_finalize
  
  									# fp16
  									if args.fpaa or args.fpaa_full_eval:
  											__lowercase=    'apex' if args.fpaa_backend == 'apex' else 'amp'
  									else:
  											__lowercase=    None
  
  									if args.save_on_each_node:
  											# deepspeed uses shared storage by default. Let's override this setting if save_on_each_node == True
  											__lowercase=    self.config.get('checkpoint'   ,       {}      )
  											__lowercase=    args.save_on_each_node
  
  									# amp: similar to the pytorch native amp - it has a bunch of optional params but we won't set
  									# any here unless the user did the work
  									self.fill_match(
  									    'fp16.enabled'   ,       ((args.fpaa or args.fpaa_full_eval) and fpaa_backend == 'amp')   ,       'fp16|fp16_full_eval+fp16_backend(amp)'   ,       )
  
  									# apex: delegates amp work to apex (which needs to be available), but it cannot be used with any
  									# ZeRO features
  									self.fill_match('amp.enabled'   ,       fpaa_backend == 'apex'   ,       'fp16+fp16_backend(apex)'      )
  									self.fill_match('amp.opt_level'   ,       args.fpaa_opt_level   ,       'fp16_opt_level'      )
  
  									self.fill_match('bf16.enabled'   ,       (args.bfaa or args.bfaa_full_eval)   ,       'bf16|bf16_full_eval'      )
  
  									# deepspeed's default mode is fp16 unless there is a config that says differently
  									if self.is_true('bf16.enabled'      ):
  											__lowercase=    torch.bfloataa
  									elif self.is_false('fp16.enabled'      ):
  											__lowercase=    torch.floataa
  									else:
  											__lowercase=    torch.floataa
  
  
  
  
  
  
  
  							def     _A (self   ,       lowerCAmelCase   ,       lowerCAmelCase   ,       lowerCAmelCase      ):
  									__lowercase=    [
  									    'zero_optimization.reduce_bucket_size',
  									    'zero_optimization.stage3_prefetch_bucket_size',
  									    'zero_optimization.stage3_param_persistence_threshold',
  									]
  									__lowercase=    [x for x in hidden_size_based_keys if self.is_auto(lowerCAmelCase      )]
  
  									if len(lowerCAmelCase      ) > 0:
  											if hasattr(model.config   ,       'hidden_size'      ):
  													__lowercase=    model.config.hidden_size
  											elif hasattr(model.config   ,       'hidden_sizes'      ):
  													# if there are many hidden sizes pick the largest one
  													__lowercase=    max(model.config.hidden_sizes      )
  											else:
  													raise ValueError(
  													    'The model\'s config file has neither `hidden_size` nor `hidden_sizes` entry, '
  													    'therefore it\'s not possible to automatically fill out the following `auto` entries '
  													    f'in the DeepSpeed config file: {hidden_size_auto_keys}. You can fix that by replacing '
  													    '`auto` values for these keys with an integer value of your choice.'      )
  
  											self.fill_only('zero_optimization.reduce_bucket_size'   ,       hidden_size * hidden_size      )
  											if self.is_zeroa():
  													# automatically assign the optimal config values based on model config
  													self.fill_only('zero_optimization.stage3_prefetch_bucket_size'   ,       0.9 * hidden_size * hidden_size      )
  													self.fill_only('zero_optimization.stage3_param_persistence_threshold'   ,       1_0 * hidden_size      )
  
          # scheduler
  									self.fill_match('scheduler.params.total_num_steps'   ,       lowerCAmelCase   ,       'num_training_steps (calculated)'      )
  									self.fill_match('scheduler.params.warmup_num_steps'   ,       args.get_warmup_steps(lowerCAmelCase      )   ,       'warmup_steps'      )
  
  									if len(self.mismatches      ) > 0:
  											__lowercase=    '\n'.join(self.mismatches      )
  											raise ValueError(
  											    'Please correct the following DeepSpeed config values that mismatch TrainingArguments'
  											    f' values:\n{mismatches}\nThe easiest method is to set these DeepSpeed config values to \'auto\'.'      )
  
  
  lowerCAmelCase					 =	None
  
  
  
  
  
  
  
  def  _lowerCamelCase(			lowercase__			)		->			str:
  
  		'''simple docstring'''
  
  
  
  
  
  
  
  		global _hf_deepspeed_config_weak_ref
  		# will go away automatically when HfDeepSpeedConfig is destroyed (when TrainingArguments is destroyed)
  		__lowercase=    weakref.ref(lowercase__			)
  
  
  
  
  
  
  
  def  _lowerCamelCase(			)		->			Dict:
  
  		'''simple docstring'''
  
  
  
  
  
  
  
  		global _hf_deepspeed_config_weak_ref
  		__lowercase=    None
  
  
  
  
  
  
  
  def  _lowerCamelCase(			)		->			Optional[Any]:
  
  		'''simple docstring'''
  
  
  
  
  
  
  
  		if _hf_deepspeed_config_weak_ref is not None and _hf_deepspeed_config_weak_ref() is not None:
  				return _hf_deepspeed_config_weak_ref().is_zeroa()
  		else:
  				return False
  
  
  
  
  
  
  
  def  _lowerCamelCase(			)		->			int:
  
  		'''simple docstring'''
  
  
  
  
  
  
  
  		if _hf_deepspeed_config_weak_ref is not None and _hf_deepspeed_config_weak_ref() is not None:
  				return _hf_deepspeed_config_weak_ref().config
  		else:
  				return None
  
  
  
  
  
  
  
  def  _lowerCamelCase(			lowercase__     ,				lowercase__     ,				lowercase__     ,				lowercase__     ,				lowercase__			)		->			List[str]:
  
  		'''simple docstring'''
  
  
  
  
  
  
  
  		from accelerate.utils import DummyOptim, DummyScheduler
  
  		__lowercase=    hf_deepspeed_config.config
  
  		# Optimizer + Scheduler
  		# Currently supported combos:
  		# 1. DS scheduler + DS optimizer: Yes
  		# 2. HF scheduler + HF optimizer: Yes
  		# 3. DS scheduler + HF optimizer: Yes
  		# 4. HF scheduler + DS optimizer: No
  		#
  		# Unless Offload is enabled in which case it's:
  		# 1. DS scheduler + DS optimizer: Yes
  		# 2. HF scheduler + HF optimizer: Mostly*
  		# 3. DS scheduler + HF optimizer: Mostly*
  		# 4. HF scheduler + DS optimizer: No
  		#
  		# Mostly*: All non-native DeepSpeed optimizers that have both CPU and GPU implementation should work (except LAMB)
  
  		__lowercase=    None
  		if "optimizer" in config:
  				if args.adafactor:
  						raise ValueError(
  						    '--adafactor was passed, but also found `optimizer` configured in the DeepSpeed config. '
  						    'Only one optimizer can be configured.'			)
  				__lowercase=    DummyOptim(params=lowercase__			)
  		else:
  				if hf_deepspeed_config.is_offload():
  						logger.info(
  						    'Detected ZeRO Offload and non-DeepSpeed optimizers: This combination should work as long as the'
  						    ' custom optimizer has both CPU and GPU implementation (except LAMB)'			)
  
  				# ds supports Adam, OneBitAdam, and Lamb optimizers and can import other optimizers from torch.
  				# But trainer uses AdamW by default.
  				__lowercase=    trainer.create_optimizer()
  				# To use other optimizers requires voiding warranty with: `zero_allow_untested_optimizer`
  				__lowercase=    True
  
  		__lowercase=    None
  		if "scheduler" in config:
  				__lowercase=    DummyScheduler(lowercase__			)
  		else:
  				if isinstance(lowercase__     ,				lowercase__			):
  						raise ValueError(
  						    'Found `optimizer` configured in the DeepSpeed config, but no `scheduler`. '
  						    'Please configure a scheduler in the DeepSpeed config.'			)
  				__lowercase=    trainer.create_scheduler(num_training_steps=lowercase__     ,				optimizer=lowercase__			)
  
  		return optimizer, lr_scheduler
  
  
  
  
  
  
  
  def  _lowerCamelCase(			lowercase__     ,				lowercase__     ,				lowercase__=False			)		->			List[Any]:
  
  		'''simple docstring'''
  
  
  
  
  
  
  
  		from deepspeed.utils import logger as ds_logger
  
  		__lowercase=    trainer.model
  		__lowercase=    trainer.args
  
  		__lowercase=    trainer.accelerator.state.deepspeed_plugin.hf_ds_config
  
  		# resume config update - some bits like `model` and `num_training_steps` only become available during train
  		hf_deepspeed_config.trainer_config_finalize(lowercase__     ,				lowercase__     ,				lowercase__			)
  
  		# set the Deepspeed log level consistent with the Trainer
  		ds_logger.setLevel(args.get_process_log_level()			)
  
  		if inference:
  				# only Z3 makes sense for the inference
  				if not hf_deepspeed_config.is_zeroa():
  						raise ValueError('ZeRO inference only makes sense with ZeRO Stage 3 - please adjust your config'			)
  
  				# in case the training config is re-used for inference
  				hf_deepspeed_config.del_config_sub_tree('optimizer'			)
  				hf_deepspeed_config.del_config_sub_tree('lr_scheduler'			)
  				__lowercase,							__lowercase=    None, None
  				__lowercase=    None
  		else:
  				__lowercase=    None  # important for when deepspeed_init is used as re-init
  				__lowercase=    list(filter(lambda lowercase__			: p.requires_grad     ,				model.parameters()			)			)
  				__lowercase,							__lowercase=    deepspeed_optim_sched(
  				    lowercase__     ,				lowercase__     ,				lowercase__     ,				lowercase__     ,				lowercase__			)
  
  		# keep for quick debug:
  		# from pprint import pprint; pprint(config)
  
  		return optimizer, lr_scheduler
  
  
  
  
  
  
  
  def  _lowerCamelCase(			lowercase__     ,				lowercase__			)		->			str:
  
  		'''simple docstring'''
  
  
  
  
  
  
  
  		import glob
  
  		__lowercase=    sorted(glob.glob(F'{checkpoint_path}/global_step*'			)			)
  
  		if len(lowercase__			) > 0:
  				logger.info(F'Attempting to resume from {checkpoint_path}'			)
  				# this magically updates self.optimizer and self.lr_scheduler
  				__lowercase,							__lowercase=    deepspeed_engine.load_checkpoint(
  				    lowercase__     ,				load_optimizer_states=lowercase__     ,				load_lr_scheduler_states=lowercase__			)
  				if load_path is None:
  						raise ValueError(F'[deepspeed] failed to resume from checkpoint {checkpoint_path}'			)
  		else:
  				raise ValueError(F'Can\'t find a valid checkpoint at {checkpoint_path}'			)
  
  
  
  
  
  
  
style_context: 
  
  
  def  _lowerCamelCase(			lowercase__			)		->			str:
  
  		'''simple docstring'''
  
  
  
  
  
  
  
  		if len(lowercase__			) == 0 or not all(len(lowercase__			) == 2 for pair in coordinates			):
  				raise ValueError('The program cannot work out a fitting polynomial.'			)
  
  		if len({tuple(lowercase__			) for pair in coordinates}			) != len(lowercase__			):
  				raise ValueError('The program cannot work out a fitting polynomial.'			)
  
  		__lowercase=    {x for x, _ in coordinates}
  		if len(lowercase__			) == 1:
  				return F'x={coordinates[0][0]}'
  
  		if len(lowercase__			) != len(lowercase__			):
  				raise ValueError('The program cannot work out a fitting polynomial.'			)
  
  		__lowercase=    len(lowercase__			)
  
  		__lowercase=    0
  		__lowercase=    []
  		# put the x and x to the power values in a matrix
  		while count_of_line < x:
  				__lowercase=    0
  				__lowercase=    coordinates[count_of_line][0]
  				__lowercase=    []
  				while count_in_line < x:
  						count_line.append(a ** (x - (count_in_line + 1))			)
  						count_in_line += 1
  				matrix.append(lowercase__			)
  				count_of_line += 1
  
  		__lowercase=    0
  		# put the y values into a vector
  		__lowercase=    []
  		while count_of_line < x:
  				vector.append(coordinates[count_of_line][1]			)
  				count_of_line += 1
  
  		__lowercase=    0
  
  		while count < x:
  				__lowercase=    0
  				while zahlen < x:
  						if count == zahlen:
  								zahlen += 1
  						if zahlen == x:
  								break
  						__lowercase=    matrix[zahlen][count] / matrix[count][count]
  						for counting_columns, item in enumerate(matrix[count]			):
  								# manipulating all the values in the matrix
  								matrix[zahlen][counting_columns] -= item * bruch
  						# manipulating the values in the vector
  						vector[zahlen] -= vector[count] * bruch
  						zahlen += 1
  				count += 1
  
  		__lowercase=    0
  		# make solutions
  		__lowercase=    []
  		while count < x:
  				solution.append(str(vector[count] / matrix[count][count]			)			)
  				count += 1
  
  		__lowercase=    0
  		__lowercase=    'f(x)='
  
  		while count < x:
  				__lowercase=    solution[count].split('E'			)
  				if len(lowercase__			) > 1:
  						__lowercase=    F'{remove_e[0]}*10^{remove_e[1]}'
  				solved += F'x^{x - (count + 1)}*{solution[count]}'
  				if count + 1 != x:
  						solved += "+"
  				count += 1
  
  		return solved
  
  
  if __name__ == "__main__":
  	print(points_to_polynomial([]))
  	print(points_to_polynomial([[]]))
  	print(points_to_polynomial([[1, 0], [2, 0], [3, 0]]))
  	print(points_to_polynomial([[1, 1], [2, 1], [3, 1]]))
  	print(points_to_polynomial([[1, 3], [2, 3], [3, 3]]))
  	print(points_to_polynomial([[1, 1], [2, 2], [3, 3]]))
  	print(points_to_polynomial([[1, 1], [2, 4], [3, 9]]))
  	print(points_to_polynomial([[1, 3], [2, 6], [3, 1_1]]))
  	print(points_to_polynomial([[1, -3], [2, -6], [3, -1_1]]))
  	print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))
  
  
  
  
  
  
  