





'''simple docstring'''


import unittest

import numpy as np
import timeout_decorator  # noqa

from transformers import MarianConfig, is_flax_available
from transformers.testing_utils import require_flax, require_sentencepiece, require_tokenizers, slow
from transformers.utils import cached_property

from ...generation.test_flax_utils import FlaxGenerationTesterMixin
from ...test_modeling_flax_common import FlaxModelTesterMixin, ids_tensor


if is_flax_available():
    import os

    # The slow tests are often failing with OOM error on GPU
    # This makes JAX allocate exactly what is needed on demand, and deallocate memory that is no longer needed
    # but will be slower as stated here https://jax.readthedocs.io/en/latest/gpu_memory_allocation.html
    A_				     =							"platform"

    import jax
    import jax.numpy as jnp

    from transformers import MarianTokenizer
    from transformers.models.marian.modeling_flax_marian import FlaxMarianModel, FlaxMarianMTModel, shift_tokens_right




def       A							(      _UpperCAmelCase   :				Any						,_UpperCAmelCase   :				Optional[Any]						,_UpperCAmelCase   :				Optional[Any]=None						,_UpperCAmelCase   :				int=None						,_UpperCAmelCase   :				Union[str, Any]=None						,_UpperCAmelCase   :				Optional[int]=None						,_UpperCAmelCase   :				List[str]=None						,_UpperCAmelCase   :				List[str]=None						,)  ->				Dict:


  '''simple docstring'''




  if attention_mask is None:
    __lowerCAmelCase		:    Optional[int]			     =  np.where(input_ids != config.pad_token_id						,1						,0					)
  if decoder_attention_mask is None:
    __lowerCAmelCase		:    Optional[Any]			     =  np.where(decoder_input_ids != config.pad_token_id						,1						,0					)
  if head_mask is None:
    __lowerCAmelCase		:    Optional[int]			     =  np.ones((config.encoder_layers, config.encoder_attention_heads)					)
  if decoder_head_mask is None:
    __lowerCAmelCase		:    List[str]			     =  np.ones((config.decoder_layers, config.decoder_attention_heads)					)
  if cross_attn_head_mask is None:
    __lowerCAmelCase		:    Tuple			     =  np.ones((config.decoder_layers, config.decoder_attention_heads)					)
  return {
      "input_ids": input_ids,
      "decoder_input_ids": decoder_input_ids,
      "attention_mask": attention_mask,
      "decoder_attention_mask": attention_mask,
  }


class 		UpperCamelCase__     :
      '''simple docstring'''






      def __init__(     self     , SCREAMING_SNAKE_CASE     , SCREAMING_SNAKE_CASE=13     , SCREAMING_SNAKE_CASE=7     , SCREAMING_SNAKE_CASE=True     , SCREAMING_SNAKE_CASE=False     , SCREAMING_SNAKE_CASE=99     , SCREAMING_SNAKE_CASE=16     , SCREAMING_SNAKE_CASE=2     , SCREAMING_SNAKE_CASE=4     , SCREAMING_SNAKE_CASE=4     , SCREAMING_SNAKE_CASE="gelu"     , SCREAMING_SNAKE_CASE=0.1     , SCREAMING_SNAKE_CASE=0.1     , SCREAMING_SNAKE_CASE=32     , SCREAMING_SNAKE_CASE=2     , SCREAMING_SNAKE_CASE=1     , SCREAMING_SNAKE_CASE=0     , SCREAMING_SNAKE_CASE=0.0_2     , )				->  Optional[Any]:
        __lowerCAmelCase		:    Optional[int]			     =  parent
        __lowerCAmelCase		:    Tuple			     =  batch_size
        __lowerCAmelCase		:    Union[str, Any]			     =  seq_length
        __lowerCAmelCase		:    List[str]			     =  is_training
        __lowerCAmelCase		:    Any			     =  use_labels
        __lowerCAmelCase		:    List[Any]			     =  vocab_size
        __lowerCAmelCase		:    Any			     =  hidden_size
        __lowerCAmelCase		:    List[Any]			     =  num_hidden_layers
        __lowerCAmelCase		:    int			     =  num_attention_heads
        __lowerCAmelCase		:    List[str]			     =  intermediate_size
        __lowerCAmelCase		:    List[Any]			     =  hidden_act
        __lowerCAmelCase		:    List[Any]			     =  hidden_dropout_prob
        __lowerCAmelCase		:    List[str]			     =  attention_probs_dropout_prob
        __lowerCAmelCase		:    List[Any]			     =  max_position_embeddings
        __lowerCAmelCase		:    Union[str, Any]			     =  eos_token_id
        __lowerCAmelCase		:    Optional[Any]			     =  pad_token_id
        __lowerCAmelCase		:    Dict			     =  bos_token_id
        __lowerCAmelCase		:    Union[str, Any]			     =  initializer_range




      def 	snake_case  (     self )				->  str:
        __lowerCAmelCase		:    List[str]			     =  np.clip(ids_tensor([self.batch_size, self.seq_length - 1]     , self.vocab_size )     , 3     , self.vocab_size )
        __lowerCAmelCase		:    List[Any]			     =  np.concatenate((input_ids, 2 * np.ones((self.batch_size, 1)     , dtype=np.intaa ))     , -1 )

        __lowerCAmelCase		:    Union[str, Any]			     =  shift_tokens_right(SCREAMING_SNAKE_CASE     , 1     , 2 )

        __lowerCAmelCase		:    Tuple			     =  MarianConfig(
            vocab_size=self.vocab_size     , d_model=self.hidden_size     , encoder_layers=self.num_hidden_layers     , decoder_layers=self.num_hidden_layers     , encoder_attention_heads=self.num_attention_heads     , decoder_attention_heads=self.num_attention_heads     , encoder_ffn_dim=self.intermediate_size     , decoder_ffn_dim=self.intermediate_size     , dropout=self.hidden_dropout_prob     , attention_dropout=self.attention_probs_dropout_prob     , max_position_embeddings=self.max_position_embeddings     , eos_token_id=self.eos_token_id     , bos_token_id=self.bos_token_id     , pad_token_id=self.pad_token_id     , initializer_range=self.initializer_range     , use_cache=SCREAMING_SNAKE_CASE     , )
        __lowerCAmelCase		:    Optional[Any]			     =  prepare_marian_inputs_dict(SCREAMING_SNAKE_CASE     , SCREAMING_SNAKE_CASE     , SCREAMING_SNAKE_CASE )
        return config, inputs_dict




      def 	snake_case  (     self )				->  Optional[int]:
        __lowerCAmelCase     ,					__lowerCAmelCase		:    List[str]			     =  self.prepare_config_and_inputs()
        return config, inputs_dict




      def 	snake_case  (     self     , SCREAMING_SNAKE_CASE     , SCREAMING_SNAKE_CASE     , SCREAMING_SNAKE_CASE )				->  Any:
        __lowerCAmelCase		:    Optional[int]			     =  20
        __lowerCAmelCase		:    int			     =  model_class_name(SCREAMING_SNAKE_CASE )

        __lowerCAmelCase		:    str			     =  model.encode(inputs_dict['input_ids'] )

        __lowerCAmelCase     ,					__lowerCAmelCase		:    Optional[int]			     =  (
            inputs_dict['decoder_input_ids'],
            inputs_dict['decoder_attention_mask'],
        )

        __lowerCAmelCase		:    str			     =  model.init_cache(decoder_input_ids.shape[0]     , SCREAMING_SNAKE_CASE     , SCREAMING_SNAKE_CASE )
        __lowerCAmelCase		:    List[Any]			     =  jnp.ones((decoder_input_ids.shape[0], max_decoder_length)     , dtype='i4' )

        __lowerCAmelCase		:    str			     =  jnp.broadcast_to(
            jnp.arange(decoder_input_ids.shape[-1] - 1 )[None, :]     , (decoder_input_ids.shape[0], decoder_input_ids.shape[-1] - 1)     , )
        __lowerCAmelCase		:    Dict			     =  model.decode(
            decoder_input_ids[:, :-1]     , SCREAMING_SNAKE_CASE     , decoder_attention_mask=SCREAMING_SNAKE_CASE     , past_key_values=SCREAMING_SNAKE_CASE     , decoder_position_ids=SCREAMING_SNAKE_CASE     , )

        __lowerCAmelCase		:    Optional[Any]			     =  jnp.array(decoder_input_ids.shape[0] * [[decoder_input_ids.shape[-1] - 1]]     , dtype='i4' )
        __lowerCAmelCase		:    Tuple			     =  model.decode(
            decoder_input_ids[:, -1:]     , SCREAMING_SNAKE_CASE     , decoder_attention_mask=SCREAMING_SNAKE_CASE     , past_key_values=outputs_cache.past_key_values     , decoder_position_ids=SCREAMING_SNAKE_CASE     , )

        __lowerCAmelCase		:    Tuple			     =  model.decode(SCREAMING_SNAKE_CASE     , SCREAMING_SNAKE_CASE )

        __lowerCAmelCase		:    Optional[Any]			     =  np.max(np.abs((outputs_cache_next[0][:, -1, :5] - outputs[0][:, -1, :5]) ) )
        self.parent.assertTrue(diff < 1e-3     , msg=F"""Max diff is {diff}""" )







      def 	snake_case  (     self     , SCREAMING_SNAKE_CASE     , SCREAMING_SNAKE_CASE     , SCREAMING_SNAKE_CASE )				->  Optional[int]:
        __lowerCAmelCase		:    List[str]			     =  20
        __lowerCAmelCase		:    List[str]			     =  model_class_name(SCREAMING_SNAKE_CASE )

        __lowerCAmelCase		:    int			     =  model.encode(inputs_dict['input_ids'] )

        __lowerCAmelCase     ,					__lowerCAmelCase		:    Tuple			     =  (
            inputs_dict['decoder_input_ids'],
            inputs_dict['decoder_attention_mask'],
        )

        __lowerCAmelCase		:    Union[str, Any]			     =  jnp.concatenate(
            [
                decoder_attention_mask,
                jnp.zeros((decoder_attention_mask.shape[0], max_decoder_length - decoder_attention_mask.shape[1]) ),
            ]     , axis=-1     , )

        __lowerCAmelCase		:    Optional[Any]			     =  model.init_cache(decoder_input_ids.shape[0]     , SCREAMING_SNAKE_CASE     , SCREAMING_SNAKE_CASE )
        __lowerCAmelCase		:    List[Any]			     =  jnp.broadcast_to(
            jnp.arange(decoder_input_ids.shape[-1] - 1 )[None, :]     , (decoder_input_ids.shape[0], decoder_input_ids.shape[-1] - 1)     , )

        __lowerCAmelCase		:    Optional[int]			     =  model.decode(
            decoder_input_ids[:, :-1]     , SCREAMING_SNAKE_CASE     , decoder_attention_mask=SCREAMING_SNAKE_CASE     , past_key_values=SCREAMING_SNAKE_CASE     , decoder_position_ids=SCREAMING_SNAKE_CASE     , )
        __lowerCAmelCase		:    Dict			     =  jnp.array(decoder_input_ids.shape[0] * [[decoder_input_ids.shape[-1] - 1]]     , dtype='i4' )
        __lowerCAmelCase		:    Optional[Any]			     =  model.decode(
            decoder_input_ids[:, -1:]     , SCREAMING_SNAKE_CASE     , past_key_values=outputs_cache.past_key_values     , decoder_attention_mask=SCREAMING_SNAKE_CASE     , decoder_position_ids=SCREAMING_SNAKE_CASE     , )

        __lowerCAmelCase		:    int			     =  model.decode(SCREAMING_SNAKE_CASE     , SCREAMING_SNAKE_CASE     , decoder_attention_mask=SCREAMING_SNAKE_CASE )

        __lowerCAmelCase		:    Optional[int]			     =  np.max(np.abs((outputs_cache_next[0][:, -1, :5] - outputs[0][:, -1, :5]) ) )
        self.parent.assertTrue(diff < 1e-3     , msg=F"""Max diff is {diff}""" )



@require_flax
class 		UpperCamelCase__     (       a	,	unittest.TestCase	,	a							):
      '''simple docstring'''






      _snake_case           =				True
      _snake_case           =				(FlaxMarianModel, FlaxMarianMTModel) if is_flax_available() else ()
      _snake_case           =				(FlaxMarianMTModel,) if is_flax_available() else ()




      def 	snake_case  (     self )				->  Union[str, Any]:
        __lowerCAmelCase		:    Union[str, Any]			     =  FlaxMarianModelTester(self )




      def 	snake_case  (     self )				->  Tuple:
        __lowerCAmelCase     ,					__lowerCAmelCase		:    Union[str, Any]			     =  self.model_tester.prepare_config_and_inputs()
        for model_class in self.all_model_classes:
          self.model_tester.check_use_cache_forward(SCREAMING_SNAKE_CASE     , SCREAMING_SNAKE_CASE     , SCREAMING_SNAKE_CASE )




      def 	snake_case  (     self )				->  Dict:
        __lowerCAmelCase     ,					__lowerCAmelCase		:    Any			     =  self.model_tester.prepare_config_and_inputs()
        for model_class in self.all_model_classes:
          self.model_tester.check_use_cache_forward_with_attn_mask(SCREAMING_SNAKE_CASE     , SCREAMING_SNAKE_CASE     , SCREAMING_SNAKE_CASE )




      def 	snake_case  (     self )				->  Optional[int]:
        __lowerCAmelCase     ,					__lowerCAmelCase		:    int			     =  self.model_tester.prepare_config_and_inputs_for_common()

        for model_class in self.all_model_classes:
          with self.subTest(model_class.__name__ ):
            __lowerCAmelCase		:    Optional[Any]			     =  self._prepare_for_class(SCREAMING_SNAKE_CASE     , SCREAMING_SNAKE_CASE )
            __lowerCAmelCase		:    Dict			     =  model_class(SCREAMING_SNAKE_CASE )

            @jax.jit
            def encode_jitted(SCREAMING_SNAKE_CASE     , SCREAMING_SNAKE_CASE=None     , **SCREAMING_SNAKE_CASE ):
              return model.encode(input_ids=SCREAMING_SNAKE_CASE     , attention_mask=SCREAMING_SNAKE_CASE )

            with self.subTest('JIT Enabled' ):
              __lowerCAmelCase		:    Optional[int]			     =  encode_jitted(**SCREAMING_SNAKE_CASE ).to_tuple()

            with self.subTest('JIT Disabled' ):
              with jax.disable_jit():
                __lowerCAmelCase		:    str			     =  encode_jitted(**SCREAMING_SNAKE_CASE ).to_tuple()

            self.assertEqual(len(SCREAMING_SNAKE_CASE )     , len(SCREAMING_SNAKE_CASE ) )
            for jitted_output, output in zip(SCREAMING_SNAKE_CASE     , SCREAMING_SNAKE_CASE ):
              self.assertEqual(jitted_output.shape     , output.shape )




      def 	snake_case  (     self )				->  str:
        __lowerCAmelCase     ,					__lowerCAmelCase		:    Optional[int]			     =  self.model_tester.prepare_config_and_inputs_for_common()

        for model_class in self.all_model_classes:
          with self.subTest(model_class.__name__ ):
            __lowerCAmelCase		:    Any			     =  model_class(SCREAMING_SNAKE_CASE )
            __lowerCAmelCase		:    List[Any]			     =  model.encode(inputs_dict['input_ids']     , inputs_dict['attention_mask'] )

            __lowerCAmelCase		:    List[Any]			     =  {
                'decoder_input_ids': inputs_dict['decoder_input_ids'],
                'decoder_attention_mask': inputs_dict['decoder_attention_mask'],
                'encoder_outputs': encoder_outputs,
            }

            @jax.jit
            def decode_jitted(SCREAMING_SNAKE_CASE     , SCREAMING_SNAKE_CASE     , SCREAMING_SNAKE_CASE ):
              return model.decode(
                  decoder_input_ids=SCREAMING_SNAKE_CASE     , decoder_attention_mask=SCREAMING_SNAKE_CASE     , encoder_outputs=SCREAMING_SNAKE_CASE     , )

            with self.subTest('JIT Enabled' ):
              __lowerCAmelCase		:    Optional[Any]			     =  decode_jitted(**SCREAMING_SNAKE_CASE ).to_tuple()

            with self.subTest('JIT Disabled' ):
              with jax.disable_jit():
                __lowerCAmelCase		:    str			     =  decode_jitted(**SCREAMING_SNAKE_CASE ).to_tuple()

            self.assertEqual(len(SCREAMING_SNAKE_CASE )     , len(SCREAMING_SNAKE_CASE ) )
            for jitted_output, output in zip(SCREAMING_SNAKE_CASE     , SCREAMING_SNAKE_CASE ):
              self.assertEqual(jitted_output.shape     , output.shape )







      @slow
      def 	snake_case  (     self )				->  Dict:
        for model_class_name in self.all_model_classes:
          __lowerCAmelCase		:    Optional[int]			     =  model_class_name.from_pretrained('Helsinki-NLP/opus-mt-en-de' )
          # FlaxMarianForSequenceClassification expects eos token in input_ids
          __lowerCAmelCase		:    str			     =  np.ones((1, 1) ) * model.config.eos_token_id
          __lowerCAmelCase		:    int			     =  model(SCREAMING_SNAKE_CASE )
          self.assertIsNotNone(SCREAMING_SNAKE_CASE )



@require_flax
@require_sentencepiece
@require_tokenizers
class 		UpperCamelCase__     (       unittest.TestCase							):
      '''simple docstring'''






      _snake_case           =				None
      _snake_case           =				None




      @classmethod
      def 	snake_case  (     cls )				->  None:
        __lowerCAmelCase		:    int			     =  F"""Helsinki-NLP/opus-mt-{cls.src}-{cls.tgt}"""
        return cls




      @cached_property
      def 	snake_case  (     self )				->  List[str]:
        return MarianTokenizer.from_pretrained(self.model_name )




      @property
      def 	snake_case  (     self )				->  int:
        return self.tokenizer.eos_token_id




      @cached_property
      def 	snake_case  (     self )				->  Tuple:
        __lowerCAmelCase		:    FlaxMarianMTModel			     =  FlaxMarianMTModel.from_pretrained(self.model_name )
        self.assertEqual(model.config.decoder_start_token_id     , model.config.pad_token_id )
        return model




      def 	snake_case  (     self     , **SCREAMING_SNAKE_CASE )				->  Tuple:
        __lowerCAmelCase		:    Any			     =  self.translate_src_text(**SCREAMING_SNAKE_CASE )
        self.assertListEqual(self.expected_text     , SCREAMING_SNAKE_CASE )







      def 	snake_case  (     self     , **SCREAMING_SNAKE_CASE )				->  Union[str, Any]:
        __lowerCAmelCase		:    Union[str, Any]			     =  self.tokenizer(self.src_text     , padding=SCREAMING_SNAKE_CASE     , return_tensors='np'     , **SCREAMING_SNAKE_CASE )
        __lowerCAmelCase		:    List[str]			     =  self.model.generate(
            model_inputs.input_ids     , attention_mask=model_inputs.attention_mask     , num_beams=2     , max_length=1_28     , ).sequences
        __lowerCAmelCase		:    int			     =  self.tokenizer.batch_decode(SCREAMING_SNAKE_CASE     , skip_special_tokens=SCREAMING_SNAKE_CASE )
        return generated_words



@require_flax
@require_sentencepiece
@require_tokenizers
class 		UpperCamelCase__     (       a							):
      '''simple docstring'''






      _snake_case           =				'''en'''
      _snake_case           =				'''fr'''
      _snake_case           =				[
          '''I am a small frog.''',
          '''Now I can forget the 100 words of german that I know.''',
      ]
      _snake_case           =				[
          '''Je suis une petite grenouille.''',
          '''Maintenant, je peux oublier les 100 mots d\'allemand que je connais.''',
      ]




      @slow
      def 	snake_case  (     self )				->  Optional[int]:
        self._assert_generated_batch_equal_expected()



@require_flax
@require_sentencepiece
@require_tokenizers
class 		UpperCamelCase__     (       a							):
      '''simple docstring'''






      _snake_case           =				'''fr'''
      _snake_case           =				'''en'''
      _snake_case           =				[
          '''Donnez moi le micro.''',
          '''Tom et Mary étaient assis à une table.''',  # Accents
      ]
      _snake_case           =				[
          '''Give me the microphone.''',
          '''Tom and Mary were sitting at a table.''',
      ]




      @slow
      def 	snake_case  (     self )				->  Union[str, Any]:
        self._assert_generated_batch_equal_expected()



@require_flax
@require_sentencepiece
@require_tokenizers
class 		UpperCamelCase__     (       a							):
      '''simple docstring'''






      _snake_case           =				'''mt'''
      _snake_case           =				'''en'''
      _snake_case           =				['''Billi messu b\'mod ġentili, Ġesù fejjaq raġel li kien milqut bil - marda kerha tal - ġdiem.''']
      _snake_case           =				['''Touching gently, Jesus healed a man who was affected by the sad disease of leprosy.''']




      @slow
      def 	snake_case  (     self )				->  Dict:
        self._assert_generated_batch_equal_expected()



@require_flax
@require_sentencepiece
@require_tokenizers
class 		UpperCamelCase__     (       a							):
      '''simple docstring'''






      _snake_case           =				'''en'''
      _snake_case           =				'''de'''
      _snake_case           =				[
          '''I am a small frog.''',
          '''Now I can forget the 100 words of german that I know.''',
          '''Tom asked his teacher for advice.''',
          '''That\'s how I would do it.''',
          '''Tom really admired Mary\'s courage.''',
          '''Turn around and close your eyes.''',
      ]
      _snake_case           =				[
          '''Ich bin ein kleiner Frosch.''',
          '''Jetzt kann ich die 100 Wörter des Deutschen vergessen, die ich kenne.''',
          '''Tom bat seinen Lehrer um Rat.''',
          '''So würde ich das machen.''',
          '''Tom bewunderte Marias Mut wirklich.''',
          '''Drehen Sie sich um und schließen Sie die Augen.''',
      ]




      @slow
      def 	snake_case  (     self )				->  Tuple:
        self._assert_generated_batch_equal_expected()



@require_flax
@require_sentencepiece
@require_tokenizers
class 		UpperCamelCase__     (       a							):
      '''simple docstring'''






      _snake_case           =				'''en'''
      _snake_case           =				'''zh'''
      _snake_case           =				['''My name is Wolfgang and I live in Berlin''']
      _snake_case           =				['''我叫沃尔夫冈 我住在柏林''']




      @slow
      def 	snake_case  (     self )				->  int:
        self._assert_generated_batch_equal_expected()



@require_flax
@require_sentencepiece
@require_tokenizers
class 		UpperCamelCase__     (       a							):
      '''simple docstring'''






      _snake_case           =				'''ru'''
      _snake_case           =				'''fr'''
      _snake_case           =				['''Он показал мне рукопись своей новой пьесы.''']
      _snake_case           =				['''Il m\'a montré le manuscrit de sa nouvelle pièce.''']




      @slow
      def 	snake_case  (     self )				->  List[Any]:
        self._assert_generated_batch_equal_expected()



@require_flax
@require_sentencepiece
@require_tokenizers
class 		UpperCamelCase__     (       a							):
      '''simple docstring'''






      _snake_case           =				'''en'''
      _snake_case           =				'''ROMANCE'''
      _snake_case           =				[
          '''>>fr<< Don\'t spend so much time watching TV.''',
          '''>>pt<< Your message has been sent.''',
          '''>>es<< He\'s two years older than me.''',
      ]
      _snake_case           =				[
          '''Ne passez pas autant de temps à regarder la télé.''',
          '''A sua mensagem foi enviada.''',
          '''Es dos años más viejo que yo.''',
      ]




      @slow
      def 	snake_case  (     self )				->  Optional[int]:
        self._assert_generated_batch_equal_expected()












'''simple docstring'''


from typing import Any

import numpy as np


class 		UpperCamelCase__     :
      '''simple docstring'''






      def __init__(     self     , SCREAMING_SNAKE_CASE     , SCREAMING_SNAKE_CASE )				->  None:
        # Check if RHS is negative
        if np.any(tableau[:, -1]     , where=tableau[:, -1] < 0 ):
          raise ValueError('RHS must be > 0' )

        __lowerCAmelCase		:    Any			     =  tableau
        __lowerCAmelCase     ,					__lowerCAmelCase		:    Optional[int]			     =  tableau.shape

        # Number of decision variables x1, x2, x3...
        __lowerCAmelCase		:    Any			     =  n_vars

        # Number of artificial variables to be minimised
        __lowerCAmelCase		:    str			     =  len(np.where(tableau[self.n_vars : -1] == -1 )[0] )

        # 2 if there are >= or == constraints (nonstandard), 1 otherwise (std)
        __lowerCAmelCase		:    Union[str, Any]			     =  (self.n_art_vars > 0) + 1

        # Number of slack variables added to make inequalities into equalities
        __lowerCAmelCase		:    Any			     =  self.n_rows - self.n_stages

        # Objectives for each stage
        __lowerCAmelCase		:    List[Any]			     =  ['max']

        # In two stage simplex, first minimise then maximise
        if self.n_art_vars:
          self.objectives.append('min' )

        __lowerCAmelCase		:    Optional[Any]			     =  ['']

        # Index of current pivot row and column
        __lowerCAmelCase		:    List[Any]			     =  None
        __lowerCAmelCase		:    Dict			     =  None

        # Does objective row only contain (non)-negative values?
        __lowerCAmelCase		:    Any			     =  False




      @staticmethod
      def 	snake_case  (     *SCREAMING_SNAKE_CASE )				->  list[str]:
        if len(SCREAMING_SNAKE_CASE ) != 3:
          raise ValueError('Must provide n_vars, n_slack, and n_art_vars' )

        if not all(x >= 0 and isinstance(SCREAMING_SNAKE_CASE     , SCREAMING_SNAKE_CASE ) for x in args ):
          raise ValueError('All arguments must be non-negative integers' )

        # decision | slack | artificial
        __lowerCAmelCase		:    int			     =  ['x', 's', 'a']
        __lowerCAmelCase		:    Tuple			     =  []
        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 	snake_case  (     self     , SCREAMING_SNAKE_CASE )				->  tuple[Any, Any]:
        __lowerCAmelCase		:    List[Any]			     =  self.objectives[-1]

        # Find entries of highest magnitude in objective rows
        __lowerCAmelCase		:    List[Any]			     =  (objective == 'min') - (objective == 'max')
        __lowerCAmelCase		:    Dict			     =  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:
          __lowerCAmelCase		:    Dict			     =  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
        __lowerCAmelCase		:    str			     =  slice(self.n_stages     , self.n_rows )

        # RHS
        __lowerCAmelCase		:    Union[str, Any]			     =  tableau[s, -1]

        # Elements of pivot column within slice
        __lowerCAmelCase		:    Optional[Any]			     =  tableau[s, col_idx]

        # Array filled with nans
        __lowerCAmelCase		:    Optional[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
        __lowerCAmelCase		:    Tuple			     =  np.divide(SCREAMING_SNAKE_CASE     , SCREAMING_SNAKE_CASE     , out=SCREAMING_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
        __lowerCAmelCase		:    Any			     =  np.nanargmin(SCREAMING_SNAKE_CASE ) + self.n_stages
        return row_idx, col_idx




      def 	snake_case  (     self     , SCREAMING_SNAKE_CASE     , SCREAMING_SNAKE_CASE     , SCREAMING_SNAKE_CASE )				->  np.ndarray:
        __lowerCAmelCase		:    Tuple			     =  tableau[row_idx].copy()

        __lowerCAmelCase		:    Optional[int]			     =  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
        __lowerCAmelCase		:    str			     =  piv_row
        return tableau




      def 	snake_case  (     self     , SCREAMING_SNAKE_CASE )				->  np.ndarray:
        self.objectives.pop()

        if not self.objectives:
          return tableau

        # Slice containing ids for artificial columns
        __lowerCAmelCase		:    Optional[Any]			     =  slice(-self.n_art_vars - 1     , -1 )

        # Delete the artificial variable columns
        __lowerCAmelCase		:    str			     =  np.delete(SCREAMING_SNAKE_CASE     , SCREAMING_SNAKE_CASE     , axis=1 )

        # Delete the objective row of the first stage
        __lowerCAmelCase		:    Optional[int]			     =  np.delete(SCREAMING_SNAKE_CASE     , 0     , axis=0 )

        __lowerCAmelCase		:    Tuple			     =  1
        self.n_rows -= 1
        __lowerCAmelCase		:    str			     =  0
        __lowerCAmelCase		:    Any			     =  False
        return tableau




      def 	snake_case  (     self )				->  dict[Any, Any]:
        # Stop simplex algorithm from cycling.
        for _ in range(1_00 ):
          # Completion of each stage removes an objective. If both stages
          # are complete, then no objectives are left
          if not self.objectives:
            __lowerCAmelCase		:    Any			     =  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 )

          __lowerCAmelCase     ,					__lowerCAmelCase		:    Tuple			     =  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
            __lowerCAmelCase		:    Dict			     =  self.change_stage(self.tableau )
          else:
            __lowerCAmelCase		:    Optional[Any]			     =  self.pivot(self.tableau     , SCREAMING_SNAKE_CASE     , SCREAMING_SNAKE_CASE )
        return {}







      def 	snake_case  (     self     , SCREAMING_SNAKE_CASE     , SCREAMING_SNAKE_CASE )				->  dict[str, float]:
        __lowerCAmelCase		:    List[Any]			     =  {'P': abs(tableau[0, -1] )}

        for i in range(self.n_vars ):
          # Gives ids of nonzero entries in the ith column
          __lowerCAmelCase		:    str			     =  np.nonzero(tableau[:, i] )
          __lowerCAmelCase		:    Union[str, Any]			     =  len(nonzero[0] )

          # First entry in the nonzero ids
          __lowerCAmelCase		:    Optional[Any]			     =  nonzero[0][0]
          __lowerCAmelCase		:    str			     =  tableau[nonzero_rowidx, i]

          # If there is only one nonzero value in column, which is one
          if n_nonzero == nonzero_val == 1:
            __lowerCAmelCase		:    Dict			     =  tableau[nonzero_rowidx, -1]
            __lowerCAmelCase		:    List[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(SCREAMING_SNAKE_CASE     , 0 )
        return output_dict


if __name__ == "__main__":
    import doctest

    doctest.testmod()





