code: 
  
  
  
  
  import argparse
  import logging
  import os
  from datetime import datetime
  
  import numpy as np
  import torch
  from torch import nn
  from torch.utils.data import DataLoader, SequentialSampler, Subset
  from torch.utils.data.distributed import DistributedSampler
  from tqdm import tqdm
  
  import transformers
  from transformers import (
      AutoConfig,
      AutoModelForSequenceClassification,
      AutoTokenizer,
      GlueDataset,
      default_data_collator,
      glue_compute_metrics,
      glue_output_modes,
      glue_processors,
      set_seed,
  )
  from transformers.trainer_utils import is_main_process
  
  
  _A							    =	logging.getLogger(__name__)
  def 						lowerCAmelCase_       (	__a )       ->			Union[str, Any]:
  
  
  
  
  
         """simple docstring"""
  
  
  
  
  
         SCREAMING_SNAKE_CASE			: List[Any]	     =p * torch.log(__lowerCamelCase )
         SCREAMING_SNAKE_CASE			: Union[str, Any]	     =0
         return -plogp.sum(dim=-1 )
  def 						lowerCAmelCase_       (	__a )       ->			Optional[Any]:
  
  
  
  
  
         """simple docstring"""
  
  
  
  
  
         logger.info('''lv, h >\t''' + '''\t'''.join(f'{x + 1}' for x in range(len(__lowerCamelCase ) ) ) )
         for row in range(len(__lowerCamelCase ) ):
                if tensor.dtype != torch.long:
                       logger.info(f'layer {row + 1}:\t' + '''\t'''.join(f'{x:.5f}' for x in tensor[row].cpu().data ) )
                else:
                       logger.info(f'layer {row + 1}:\t' + '''\t'''.join(f'{x:d}' for x in tensor[row].cpu().data ) )
  def 						lowerCAmelCase_       (	__a	,	__a	,	__a	,	__a=True	,	__a=True	,	__a=None	,	__a=False )       ->			List[str]:
  
  
  
  
  
         """simple docstring"""
  
  
  
  
  
         SCREAMING_SNAKE_CASE     ,							SCREAMING_SNAKE_CASE			: int	     =model.config.num_hidden_layers, model.config.num_attention_heads
         SCREAMING_SNAKE_CASE			: Tuple	     =torch.zeros(__lowerCamelCase	,	__lowerCamelCase ).to(args.device )
         SCREAMING_SNAKE_CASE			: Union[str, Any]	     =torch.zeros(__lowerCamelCase	,	__lowerCamelCase ).to(args.device )
  
         if head_mask is None:
                SCREAMING_SNAKE_CASE			: Optional[int]	     =torch.ones(__lowerCamelCase	,	__lowerCamelCase ).to(args.device )
  
         head_mask.requires_grad_(requires_grad=__lowerCamelCase )
         # If actually pruned attention multi-head, set head mask to None to avoid shape mismatch
         if actually_pruned:
                SCREAMING_SNAKE_CASE			: Tuple	     =None
  
         SCREAMING_SNAKE_CASE			: Union[str, Any]	     =None
         SCREAMING_SNAKE_CASE			: Optional[Any]	     =None
         SCREAMING_SNAKE_CASE			: int	     =0.0
  
         for step, inputs in enumerate(tqdm(__lowerCamelCase	,	desc='''Iteration'''	,	disable=args.local_rank not in [-1, 0] ) ):
                for k, v in inputs.items():
                       SCREAMING_SNAKE_CASE			: Union[str, Any]	     =v.to(args.device )
  
                # Do a forward pass (not with torch.no_grad() since we need gradients for importance score - see below)
                SCREAMING_SNAKE_CASE			: Any	     =model(**__lowerCamelCase	,	head_mask=__lowerCamelCase )
                SCREAMING_SNAKE_CASE     ,							SCREAMING_SNAKE_CASE     ,							SCREAMING_SNAKE_CASE			: Dict	     =(
                    outputs[0],
                    outputs[1],
                    outputs[-1],
                )  # Loss and logits are the first, attention the last
                loss.backward()  # Backpropagate to populate the gradients in the head mask
  
                if compute_entropy:
                       for layer, attn in enumerate(__lowerCamelCase ):
                              SCREAMING_SNAKE_CASE			: Any	     =entropy(attn.detach() ) * inputs['''attention_mask'''].float().unsqueeze(1 )
                              attn_entropy[layer] += masked_entropy.sum(-1 ).sum(0 ).detach()
  
                if compute_importance:
                       head_importance += head_mask.grad.abs().detach()
  
                # Also store our logits/labels if we want to compute metrics afterwards
                if preds is None:
                       SCREAMING_SNAKE_CASE			: Optional[int]	     =logits.detach().cpu().numpy()
                       SCREAMING_SNAKE_CASE			: Dict	     =inputs['''labels'''].detach().cpu().numpy()
                else:
                       SCREAMING_SNAKE_CASE			: Optional[Any]	     =np.append(__lowerCamelCase	,	logits.detach().cpu().numpy()	,	axis=0 )
                       SCREAMING_SNAKE_CASE			: List[str]	     =np.append(__lowerCamelCase	,	inputs['''labels'''].detach().cpu().numpy()	,	axis=0 )
  
                tot_tokens += inputs["attention_mask"].float().detach().sum().data
  
         # Normalize
         attn_entropy /= tot_tokens
         head_importance /= tot_tokens
         # Layerwise importance normalization
         if not args.dont_normalize_importance_by_layer:
                SCREAMING_SNAKE_CASE			: Union[str, Any]	     =2
                SCREAMING_SNAKE_CASE			: Optional[Any]	     =torch.pow(torch.pow(__lowerCamelCase	,	__lowerCamelCase ).sum(-1 )	,	1 / exponent )
                head_importance /= norm_by_layer.unsqueeze(-1 ) + 1E-20
  
         if not args.dont_normalize_global_importance:
                SCREAMING_SNAKE_CASE			: Tuple	     =(head_importance - head_importance.min()) / (head_importance.max() - head_importance.min())
  
         # Print/save matrices
         np.save(os.path.join(args.output_dir	,	'''attn_entropy.npy''' )	,	attn_entropy.detach().cpu().numpy() )
         np.save(os.path.join(args.output_dir	,	'''head_importance.npy''' )	,	head_importance.detach().cpu().numpy() )
  
         logger.info('''Attention entropies''' )
         print_ad_tensor(__lowerCamelCase )
         logger.info('''Head importance scores''' )
         print_ad_tensor(__lowerCamelCase )
         logger.info('''Head ranked by importance scores''' )
         SCREAMING_SNAKE_CASE			: Optional[Any]	     =torch.zeros(head_importance.numel()	,	dtype=torch.long	,	device=args.device )
         SCREAMING_SNAKE_CASE			: List[Any]	     =torch.arange(
             head_importance.numel()	,	device=args.device )
         SCREAMING_SNAKE_CASE			: Union[str, Any]	     =head_ranks.view_as(__lowerCamelCase )
         print_ad_tensor(__lowerCamelCase )
  
         return attn_entropy, head_importance, preds, labels
  def 						lowerCAmelCase_       (	__a	,	__a	,	__a )       ->			List[Any]:
  
  
  
  
  
         """simple docstring"""
  
  
  
  
  
         SCREAMING_SNAKE_CASE     ,							SCREAMING_SNAKE_CASE     ,							SCREAMING_SNAKE_CASE     ,							SCREAMING_SNAKE_CASE			: Optional[int]	     =compute_heads_importance(__lowerCamelCase	,	__lowerCamelCase	,	__lowerCamelCase	,	compute_entropy=__lowerCamelCase )
         SCREAMING_SNAKE_CASE			: Optional[int]	     =np.argmax(__lowerCamelCase	,	axis=1 ) if args.output_mode == '''classification''' else np.squeeze(__lowerCamelCase )
         SCREAMING_SNAKE_CASE			: Optional[Any]	     =glue_compute_metrics(args.task_name	,	__lowerCamelCase	,	__lowerCamelCase )[args.metric_name]
         logger.info('''Pruning: original score: %f, threshold: %f'''	,	__lowerCamelCase	,	original_score * args.masking_threshold )
  
         SCREAMING_SNAKE_CASE			: List[str]	     =torch.ones_like(__lowerCamelCase )
         SCREAMING_SNAKE_CASE			: Tuple	     =max(1	,	int(new_head_mask.numel() * args.masking_amount ) )
  
         SCREAMING_SNAKE_CASE			: List[str]	     =original_score
         while current_score >= original_score * args.masking_threshold:
                SCREAMING_SNAKE_CASE			: Any	     =new_head_mask.clone()  # save current head mask
                # heads from least important to most - keep only not-masked heads
                SCREAMING_SNAKE_CASE			: List[str]	     =float('''Inf''' )
                SCREAMING_SNAKE_CASE			: Optional[Any]	     =head_importance.view(-1 ).sort()[1]
  
                if len(__lowerCamelCase ) <= num_to_mask:
                       break
  
                # mask heads
                SCREAMING_SNAKE_CASE			: Union[str, Any]	     =current_heads_to_mask[:num_to_mask]
                logger.info('''Heads to mask: %s'''	,	str(current_heads_to_mask.tolist() ) )
                SCREAMING_SNAKE_CASE			: Union[str, Any]	     =new_head_mask.view(-1 )
                SCREAMING_SNAKE_CASE			: List[Any]	     =0.0
                SCREAMING_SNAKE_CASE			: Dict	     =new_head_mask.view_as(__lowerCamelCase )
                SCREAMING_SNAKE_CASE			: Dict	     =new_head_mask.clone().detach()
                print_ad_tensor(__lowerCamelCase )
  
                # Compute metric and head importance again
                SCREAMING_SNAKE_CASE     ,							SCREAMING_SNAKE_CASE     ,							SCREAMING_SNAKE_CASE     ,							SCREAMING_SNAKE_CASE			: int	     =compute_heads_importance(
                    __lowerCamelCase	,	__lowerCamelCase	,	__lowerCamelCase	,	compute_entropy=__lowerCamelCase	,	head_mask=__lowerCamelCase )
                SCREAMING_SNAKE_CASE			: List[str]	     =np.argmax(__lowerCamelCase	,	axis=1 ) if args.output_mode == '''classification''' else np.squeeze(__lowerCamelCase )
                SCREAMING_SNAKE_CASE			: Any	     =glue_compute_metrics(args.task_name	,	__lowerCamelCase	,	__lowerCamelCase )[args.metric_name]
                logger.info(
                    '''Masking: current score: %f, remaining heads %d (%.1f percents)'''	,	__lowerCamelCase	,	new_head_mask.sum()	,	new_head_mask.sum() / new_head_mask.numel() * 100	,	)
  
         logger.info('''Final head mask''' )
         print_ad_tensor(__lowerCamelCase )
         np.save(os.path.join(args.output_dir	,	'''head_mask.npy''' )	,	head_mask.detach().cpu().numpy() )
  
         return head_mask
  def 						lowerCAmelCase_       (	__a	,	__a	,	__a	,	__a )       ->			str:
  
  
  
  
  
         """simple docstring"""
  
  
  
  
  
         SCREAMING_SNAKE_CASE			: List[Any]	     =datetime.now()
         SCREAMING_SNAKE_CASE     ,							SCREAMING_SNAKE_CASE     ,							SCREAMING_SNAKE_CASE     ,							SCREAMING_SNAKE_CASE			: List[Any]	     =compute_heads_importance(
             __lowerCamelCase	,	__lowerCamelCase	,	__lowerCamelCase	,	compute_entropy=__lowerCamelCase	,	compute_importance=__lowerCamelCase	,	head_mask=__lowerCamelCase )
         SCREAMING_SNAKE_CASE			: int	     =np.argmax(__lowerCamelCase	,	axis=1 ) if args.output_mode == '''classification''' else np.squeeze(__lowerCamelCase )
         SCREAMING_SNAKE_CASE			: Tuple	     =glue_compute_metrics(args.task_name	,	__lowerCamelCase	,	__lowerCamelCase )[args.metric_name]
         SCREAMING_SNAKE_CASE			: str	     =datetime.now() - before_time
  
         SCREAMING_SNAKE_CASE			: Tuple	     =sum(p.numel() for p in model.parameters() )
         SCREAMING_SNAKE_CASE			: str	     ={
             layer: (1 - head_mask[layer].long()).nonzero().squeeze().tolist() for layer in range(len(__lowerCamelCase ) )
         }
  
         assert sum(len(__lowerCamelCase ) for h in heads_to_prune.values() ) == (1 - head_mask.long()).sum().item()
         model.prune_heads(__lowerCamelCase )
         SCREAMING_SNAKE_CASE			: str	     =sum(p.numel() for p in model.parameters() )
  
         SCREAMING_SNAKE_CASE			: Union[str, Any]	     =datetime.now()
         SCREAMING_SNAKE_CASE     ,							SCREAMING_SNAKE_CASE     ,							SCREAMING_SNAKE_CASE     ,							SCREAMING_SNAKE_CASE			: Union[str, Any]	     =compute_heads_importance(
             __lowerCamelCase	,	__lowerCamelCase	,	__lowerCamelCase	,	compute_entropy=__lowerCamelCase	,	compute_importance=__lowerCamelCase	,	head_mask=__lowerCamelCase	,	actually_pruned=__lowerCamelCase	,	)
         SCREAMING_SNAKE_CASE			: Tuple	     =np.argmax(__lowerCamelCase	,	axis=1 ) if args.output_mode == '''classification''' else np.squeeze(__lowerCamelCase )
         SCREAMING_SNAKE_CASE			: List[Any]	     =glue_compute_metrics(args.task_name	,	__lowerCamelCase	,	__lowerCamelCase )[args.metric_name]
         SCREAMING_SNAKE_CASE			: Dict	     =datetime.now() - before_time
  
         logger.info(
             '''Pruning: original num of params: %.2e, after pruning %.2e (%.1f percents)'''	,	__lowerCamelCase	,	__lowerCamelCase	,	pruned_num_params / original_num_params * 100	,	)
         logger.info('''Pruning: score with masking: %f score with pruning: %f'''	,	__lowerCamelCase	,	__lowerCamelCase )
         logger.info('''Pruning: speed ratio (new timing / original timing): %f percents'''	,	original_time / new_time * 100 )
  def 						lowerCAmelCase_       (	)       ->			Any:
  
  
  
  
  
         """simple docstring"""
  
  
  
  
  
         SCREAMING_SNAKE_CASE			: Optional[int]	     =argparse.ArgumentParser()
         # Required parameters
         parser.add_argument(
             '''--data_dir'''	,	default=__lowerCamelCase	,	type=__lowerCamelCase	,	required=__lowerCamelCase	,	help='''The input data dir. Should contain the .tsv files (or other data files) for the task.'''	,	)
         parser.add_argument(
             '''--model_name_or_path'''	,	default=__lowerCamelCase	,	type=__lowerCamelCase	,	required=__lowerCamelCase	,	help='''Path to pretrained model or model identifier from huggingface.co/models'''	,	)
         parser.add_argument(
             '''--task_name'''	,	default=__lowerCamelCase	,	type=__lowerCamelCase	,	required=__lowerCamelCase	,	help='''The name of the task to train selected in the list: ''' + ''', '''.join(glue_processors.keys() )	,	)
         parser.add_argument(
             '''--output_dir'''	,	default=__lowerCamelCase	,	type=__lowerCamelCase	,	required=__lowerCamelCase	,	help='''The output directory where the model predictions and checkpoints will be written.'''	,	)
  
         # Other parameters
         parser.add_argument(
             '''--config_name'''	,	default=''''''	,	type=__lowerCamelCase	,	help='''Pretrained config name or path if not the same as model_name_or_path'''	,	)
         parser.add_argument(
             '''--tokenizer_name'''	,	default=''''''	,	type=__lowerCamelCase	,	help='''Pretrained tokenizer name or path if not the same as model_name_or_path'''	,	)
         parser.add_argument(
             '''--cache_dir'''	,	default=__lowerCamelCase	,	type=__lowerCamelCase	,	help='''Where do you want to store the pre-trained models downloaded from huggingface.co'''	,	)
         parser.add_argument(
             '''--data_subset'''	,	type=__lowerCamelCase	,	default=-1	,	help='''If > 0: limit the data to a subset of data_subset instances.''' )
         parser.add_argument(
             '''--overwrite_output_dir'''	,	action='''store_true'''	,	help='''Whether to overwrite data in output directory''' )
         parser.add_argument(
             '''--overwrite_cache'''	,	action='''store_true'''	,	help='''Overwrite the cached training and evaluation sets''' )
  
         parser.add_argument(
             '''--dont_normalize_importance_by_layer'''	,	action='''store_true'''	,	help='''Don\'t normalize importance score by layers''' )
         parser.add_argument(
             '''--dont_normalize_global_importance'''	,	action='''store_true'''	,	help='''Don\'t normalize all importance scores between 0 and 1'''	,	)
  
         parser.add_argument(
             '''--try_masking'''	,	action='''store_true'''	,	help='''Whether to try to mask head until a threshold of accuracy.''' )
         parser.add_argument(
             '''--masking_threshold'''	,	default=0.9	,	type=__lowerCamelCase	,	help='''masking threshold in term of metrics (stop masking when metric < threshold * original metric value).'''	,	)
         parser.add_argument(
             '''--masking_amount'''	,	default=0.1	,	type=__lowerCamelCase	,	help='''Amount to heads to masking at each masking step.''' )
         parser.add_argument('''--metric_name'''	,	default='''acc'''	,	type=__lowerCamelCase	,	help='''Metric to use for head masking.''' )
  
         parser.add_argument(
             '''--max_seq_length'''	,	default=128	,	type=__lowerCamelCase	,	help=(
                 '''The maximum total input sequence length after WordPiece tokenization. \n'''
                 '''Sequences longer than this will be truncated, sequences shorter padded.'''
             )	,	)
         parser.add_argument('''--batch_size'''	,	default=1	,	type=__lowerCamelCase	,	help='''Batch size.''' )
  
         parser.add_argument('''--seed'''	,	type=__lowerCamelCase	,	default=42 )
         parser.add_argument('''--local_rank'''	,	type=__lowerCamelCase	,	default=-1	,	help='''local_rank for distributed training on gpus''' )
         parser.add_argument('''--no_cuda'''	,	action='''store_true'''	,	help='''Whether not to use CUDA when available''' )
         parser.add_argument('''--server_ip'''	,	type=__lowerCamelCase	,	default=''''''	,	help='''Can be used for distant debugging.''' )
         parser.add_argument('''--server_port'''	,	type=__lowerCamelCase	,	default=''''''	,	help='''Can be used for distant debugging.''' )
         SCREAMING_SNAKE_CASE			: List[Any]	     =parser.parse_args()
  
         if args.server_ip and args.server_port:
                # Distant debugging - see https://code.visualstudio.com/docs/python/debugging#_attach-to-a-local-script
                import ptvsd
  
                print('''Waiting for debugger attach''' )
                ptvsd.enable_attach(address=(args.server_ip, args.server_port)	,	redirect_output=__lowerCamelCase )
                ptvsd.wait_for_attach()
  
         # Setup devices and distributed training
         if args.local_rank == -1 or args.no_cuda:
                SCREAMING_SNAKE_CASE			: Any	     =torch.device('''cuda''' if torch.cuda.is_available() and not args.no_cuda else '''cpu''' )
                SCREAMING_SNAKE_CASE			: List[str]	     =0 if args.no_cuda else torch.cuda.device_count()
         else:
                torch.cuda.set_device(args.local_rank )
                SCREAMING_SNAKE_CASE			: str	     =torch.device('''cuda'''	,	args.local_rank )
                SCREAMING_SNAKE_CASE			: List[Any]	     =1
                torch.distributed.init_process_group(backend='''nccl''' )  # Initializes the distributed backend
  
         # Setup logging
         logging.basicConfig(level=logging.INFO if args.local_rank in [-1, 0] else logging.WARN )
         logger.info('''device: {} n_gpu: {}, distributed: {}'''.format(args.device	,	args.n_gpu	,	bool(args.local_rank != -1 ) ) )
         # Set the verbosity to info of the Transformers logger (on main process only):
         if is_main_process(args.local_rank ):
                transformers.utils.logging.set_verbosity_info()
                transformers.utils.logging.enable_default_handler()
                transformers.utils.logging.enable_explicit_format()
  
         # Set seeds
         set_seed(args.seed )
  
         # Prepare GLUE task
         SCREAMING_SNAKE_CASE			: int	     =args.task_name.lower()
         if args.task_name not in glue_processors:
                raise ValueError('''Task not found: %s''' % (args.task_name) )
         SCREAMING_SNAKE_CASE			: List[Any]	     =glue_processors[args.task_name]()
         SCREAMING_SNAKE_CASE			: Optional[int]	     =glue_output_modes[args.task_name]
         SCREAMING_SNAKE_CASE			: Optional[int]	     =processor.get_labels()
         SCREAMING_SNAKE_CASE			: Dict	     =len(__lowerCamelCase )
  
         # Load pretrained model and tokenizer
         #
         # Distributed training:
         # The .from_pretrained methods guarantee that only one local process can concurrently
         # download model & vocab.
  
         SCREAMING_SNAKE_CASE			: Optional[int]	     =AutoConfig.from_pretrained(
             args.config_name if args.config_name else args.model_name_or_path	,	num_labels=__lowerCamelCase	,	finetuning_task=args.task_name	,	output_attentions=__lowerCamelCase	,	cache_dir=args.cache_dir	,	)
         SCREAMING_SNAKE_CASE			: Any	     =AutoTokenizer.from_pretrained(
             args.tokenizer_name if args.tokenizer_name else args.model_name_or_path	,	cache_dir=args.cache_dir	,	)
         SCREAMING_SNAKE_CASE			: Dict	     =AutoModelForSequenceClassification.from_pretrained(
             args.model_name_or_path	,	from_tf=bool('''.ckpt''' in args.model_name_or_path )	,	config=__lowerCamelCase	,	cache_dir=args.cache_dir	,	)
  
         # Distributed and parallel training
         model.to(args.device )
         if args.local_rank != -1:
                SCREAMING_SNAKE_CASE			: Dict	     =nn.parallel.DistributedDataParallel(
                    __lowerCamelCase	,	device_ids=[args.local_rank]	,	output_device=args.local_rank	,	find_unused_parameters=__lowerCamelCase )
         elif args.n_gpu > 1:
                SCREAMING_SNAKE_CASE			: Optional[Any]	     =nn.DataParallel(__lowerCamelCase )
  
         # Print/save training arguments
         os.makedirs(args.output_dir	,	exist_ok=__lowerCamelCase )
         torch.save(__lowerCamelCase	,	os.path.join(args.output_dir	,	'''run_args.bin''' ) )
         logger.info('''Training/evaluation parameters %s'''	,	__lowerCamelCase )
  
         # Prepare dataset for the GLUE task
         SCREAMING_SNAKE_CASE			: Tuple	     =GlueDataset(__lowerCamelCase	,	tokenizer=__lowerCamelCase	,	mode='''dev''' )
         if args.data_subset > 0:
                SCREAMING_SNAKE_CASE			: Any	     =Subset(__lowerCamelCase	,	list(range(min(args.data_subset	,	len(__lowerCamelCase ) ) ) ) )
         SCREAMING_SNAKE_CASE			: Any	     =SequentialSampler(__lowerCamelCase ) if args.local_rank == -1 else DistributedSampler(__lowerCamelCase )
         SCREAMING_SNAKE_CASE			: Optional[Any]	     =DataLoader(
             __lowerCamelCase	,	sampler=__lowerCamelCase	,	batch_size=args.batch_size	,	collate_fn=__lowerCamelCase )
  
         # Compute head entropy and importance score
         compute_heads_importance(__lowerCamelCase	,	__lowerCamelCase	,	__lowerCamelCase )
  
         # Try head masking (set heads to zero until the score goes under a threshole)
         # and head pruning (remove masked heads and see the effect on the network)
         if args.try_masking and args.masking_threshold > 0.0 and args.masking_threshold < 1.0:
                SCREAMING_SNAKE_CASE			: int	     =mask_heads(__lowerCamelCase	,	__lowerCamelCase	,	__lowerCamelCase )
                prune_heads(__lowerCamelCase	,	__lowerCamelCase	,	__lowerCamelCase	,	__lowerCamelCase )
  
  
  if __name__ == "__main__":
         main()
  
  
  
  
  
  
  
style_context: 
  
  
  
  
  from typing import Any
  
  import numpy as np
  
  
  class 							_lowerCAmelCase		:
  
  
  
  
  				def __init__( self		,		snake_case_		,		snake_case_							)    ->      None:
  											# Check if RHS is negative
  											if np.any(tableau[:, -1]		,		where=tableau[:, -1] < 0							):
  																		raise ValueError('''RHS must be > 0'''							)
  
  											SCREAMING_SNAKE_CASE			: Tuple	     =tableau
  											SCREAMING_SNAKE_CASE     ,							SCREAMING_SNAKE_CASE			: Tuple	     =tableau.shape
  
  											# Number of decision variables x1, x2, x3...
  											SCREAMING_SNAKE_CASE			: Optional[int]	     =n_vars
  
  											# Number of artificial variables to be minimised
  											SCREAMING_SNAKE_CASE			: Union[str, Any]	     =len(np.where(tableau[self.n_vars : -1] == -1							)[0]							)
  
  											# 2 if there are >= or == constraints (nonstandard), 1 otherwise (std)
  											SCREAMING_SNAKE_CASE			: Optional[int]	     =(self.n_art_vars > 0) + 1
  
  											# Number of slack variables added to make inequalities into equalities
  											SCREAMING_SNAKE_CASE			: Optional[int]	     =self.n_rows - self.n_stages
  
  											# Objectives for each stage
  											SCREAMING_SNAKE_CASE			: str	     =['''max''']
  
  											# In two stage simplex, first minimise then maximise
  											if self.n_art_vars:
  																		self.objectives.append('''min'''							)
  
  											SCREAMING_SNAKE_CASE			: Dict	     =['''''']
  
  											# Index of current pivot row and column
  											SCREAMING_SNAKE_CASE			: str	     =None
  											SCREAMING_SNAKE_CASE			: Optional[Any]	     =None
  
  											# Does objective row only contain (non)-negative values?
  											SCREAMING_SNAKE_CASE			: Dict	     =False
  
  
  
  
  				@staticmethod
  				def     __a		( *snake_case_							)    ->      list[str]:
  											if len(snake_case_							) != 3:
  																		raise ValueError('''Must provide n_vars, n_slack, and n_art_vars'''							)
  
  											if not all(x >= 0 and isinstance(snake_case_		,		snake_case_							) for x in args							):
  																		raise ValueError('''All arguments must be non-negative integers'''							)
  
  											# decision | slack | artificial
  											SCREAMING_SNAKE_CASE			: Any	     =['''x''', '''s''', '''a''']
  											SCREAMING_SNAKE_CASE			: int	     =[]
  											for i in range(3							):
  																		for j in range(args[i]							):
  																									titles.append(string_starts[i] + str(j + 1							)							)
  											titles.append('''RHS'''							)
  											return titles
  
  
  
  
  				def     __a		( self		,		snake_case_							)    ->      tuple[Any, Any]:
  											SCREAMING_SNAKE_CASE			: Optional[int]	     =self.objectives[-1]
  
  											# Find entries of highest magnitude in objective rows
  											SCREAMING_SNAKE_CASE			: str	     =(objective == '''min''') - (objective == '''max''')
  											SCREAMING_SNAKE_CASE			: Union[str, Any]	     =np.argmax(sign * tableau[0, : self.n_vars]							)
  
  											# Choice is only valid if below 0 for maximise, and above for minimise
  											if sign * self.tableau[0, col_idx] <= 0:
  																		SCREAMING_SNAKE_CASE			: List[Any]	     =True
  																		return 0, 0
  
  											# Pivot row is chosen as having the lowest quotient when elements of
  											# the pivot column divide the right-hand side
  
  											# Slice excluding the objective rows
  											SCREAMING_SNAKE_CASE			: Tuple	     =slice(self.n_stages		,		self.n_rows							)
  
  											# RHS
  											SCREAMING_SNAKE_CASE			: Dict	     =tableau[s, -1]
  
  											# Elements of pivot column within slice
  											SCREAMING_SNAKE_CASE			: Tuple	     =tableau[s, col_idx]
  
  											# Array filled with nans
  											SCREAMING_SNAKE_CASE			: Union[str, Any]	     =np.full(self.n_rows - self.n_stages		,		np.nan							)
  
  											# If element in pivot column is greater than zeron_stages, return
  											# quotient or nan otherwise
  											SCREAMING_SNAKE_CASE			: Optional[Any]	     =np.divide(snake_case_		,		snake_case_		,		out=snake_case_		,		where=divisor > 0							)
  
  											# Arg of minimum quotient excluding the nan values. n_stages is added
  											# to compensate for earlier exclusion of objective columns
  											SCREAMING_SNAKE_CASE			: List[Any]	     =np.nanargmin(snake_case_							) + self.n_stages
  											return row_idx, col_idx
  
  
  
  
  				def     __a		( self		,		snake_case_		,		snake_case_		,		snake_case_							)    ->      np.ndarray:
  											SCREAMING_SNAKE_CASE			: Tuple	     =tableau[row_idx].copy()
  
  											SCREAMING_SNAKE_CASE			: Optional[Any]	     =piv_row[col_idx]
  
  											# Entry becomes 1
  											piv_row *= 1 / piv_val
  
  											# Variable in pivot column becomes basic, ie the only non-zero entry
  											for idx, coeff in enumerate(tableau[:, col_idx]							):
  																		tableau[idx] += -coeff * piv_row
  											SCREAMING_SNAKE_CASE			: Dict	     =piv_row
  											return tableau
  
  
  
  
  				def     __a		( self		,		snake_case_							)    ->      np.ndarray:
  											self.objectives.pop()
  
  											if not self.objectives:
  																		return tableau
  
  											# Slice containing ids for artificial columns
  											SCREAMING_SNAKE_CASE			: Optional[int]	     =slice(-self.n_art_vars - 1		,		-1							)
  
  											# Delete the artificial variable columns
  											SCREAMING_SNAKE_CASE			: Optional[int]	     =np.delete(snake_case_		,		snake_case_		,		axis=1							)
  
  											# Delete the objective row of the first stage
  											SCREAMING_SNAKE_CASE			: str	     =np.delete(snake_case_		,		0		,		axis=0							)
  
  											SCREAMING_SNAKE_CASE			: Any	     =1
  											self.n_rows -= 1
  											SCREAMING_SNAKE_CASE			: Optional[Any]	     =0
  											SCREAMING_SNAKE_CASE			: List[str]	     =False
  											return tableau
  
  
  
  
  				def     __a		( self							)    ->      dict[Any, Any]:
  											# Stop simplex algorithm from cycling.
  											for _ in range(100							):
  																		# Completion of each stage removes an objective. If both stages
  																		# are complete, then no objectives are left
  																		if not self.objectives:
  																									SCREAMING_SNAKE_CASE			: int	     =self.generate_col_titles(
  																									    self.n_vars		,		self.n_slack		,		self.n_art_vars							)
  
  																									# Find the values of each variable at optimal solution
  																									return self.interpret_tableau(self.tableau		,		self.col_titles							)
  
  																		SCREAMING_SNAKE_CASE     ,							SCREAMING_SNAKE_CASE			: Any	     =self.find_pivot(self.tableau							)
  
  																		# If there are no more negative values in objective row
  																		if self.stop_iter:
  																									# Delete artificial variable columns and rows. Update attributes
  																									SCREAMING_SNAKE_CASE			: Optional[int]	     =self.change_stage(self.tableau							)
  																		else:
  																									SCREAMING_SNAKE_CASE			: Dict	     =self.pivot(self.tableau		,		snake_case_		,		snake_case_							)
  											return {}
  
  
  
  
  
  
  
  				def     __a		( self		,		snake_case_		,		snake_case_							)    ->      dict[str, float]:
  											SCREAMING_SNAKE_CASE			: Any	     ={'''P''': abs(tableau[0, -1]							)}
  
  											for i in range(self.n_vars							):
  																		# Gives ids of nonzero entries in the ith column
  																		SCREAMING_SNAKE_CASE			: Any	     =np.nonzero(tableau[:, i]							)
  																		SCREAMING_SNAKE_CASE			: Union[str, Any]	     =len(nonzero[0]							)
  
  																		# First entry in the nonzero ids
  																		SCREAMING_SNAKE_CASE			: List[str]	     =nonzero[0][0]
  																		SCREAMING_SNAKE_CASE			: Any	     =tableau[nonzero_rowidx, i]
  
  																		# If there is only one nonzero value in column, which is one
  																		if n_nonzero == nonzero_val == 1:
  																									SCREAMING_SNAKE_CASE			: Union[str, Any]	     =tableau[nonzero_rowidx, -1]
  																									SCREAMING_SNAKE_CASE			: Any	     =rhs_val
  
          # Check for basic variables
  											for title in col_titles:
  																		# Don't add RHS or slack variables to output dict
  																		if title[0] not in "R-s-a":
  																									output_dict.setdefault(snake_case_		,		0							)
  											return output_dict
  
  
  if __name__ == "__main__":
  							import doctest
  
  							doctest.testmod()
  
  
  
  
  
  
  