'''simple docstring'''

import unittest

from transformers import XLMConfig, is_torch_available
from transformers.testing_utils import require_torch, slow, torch_device

from ...generation.test_utils import GenerationTesterMixin
from ...test_configuration_common import ConfigTester
from ...test_modeling_common import ModelTesterMixin, ids_tensor, random_attention_mask
from ...test_pipeline_mixin import PipelineTesterMixin


if is_torch_available():
  import torch

  from transformers import (
      XLMForMultipleChoice,
      XLMForQuestionAnswering,
      XLMForQuestionAnsweringSimple,
      XLMForSequenceClassification,
      XLMForTokenClassification,
      XLMModel,
      XLMWithLMHeadModel,
  )
  from transformers.models.xlm.modeling_xlm import XLM_PRETRAINED_MODEL_ARCHIVE_LIST


class 				_lowercase	:
      '''simple docstring'''


      def __init__(				self					,lowerCamelCase_					,lowerCamelCase_=13					,lowerCamelCase_=7					,lowerCamelCase_=True					,lowerCamelCase_=True					,lowerCamelCase_=True					,lowerCamelCase_=True					,lowerCamelCase_=True					,lowerCamelCase_=False					,lowerCamelCase_=False					,lowerCamelCase_=False					,lowerCamelCase_=2					,lowerCamelCase_=99					,lowerCamelCase_=0					,lowerCamelCase_=32					,lowerCamelCase_=5					,lowerCamelCase_=4					,lowerCamelCase_=0.1					,lowerCamelCase_=0.1					,lowerCamelCase_=512					,lowerCamelCase_=2					,lowerCamelCase_=0.02					,lowerCamelCase_=2					,lowerCamelCase_=4					,lowerCamelCase_="last"					,lowerCamelCase_=True					,lowerCamelCase_=None					,lowerCamelCase_=0					,)			->			Optional[Any]:



         '''simple docstring'''



         UpperCAmelCase__							:				List[str]   				=  parent
         UpperCAmelCase__							:				Tuple   				=  batch_size
         UpperCAmelCase__							:				Tuple   				=  seq_length
         UpperCAmelCase__							:				Optional[Any]   				=  is_training
         UpperCAmelCase__							:				Any   				=  use_input_lengths
         UpperCAmelCase__							:				Dict   				=  use_token_type_ids
         UpperCAmelCase__							:				Union[str, Any]   				=  use_labels
         UpperCAmelCase__							:				int   				=  gelu_activation
         UpperCAmelCase__							:				Optional[int]   				=  sinusoidal_embeddings
         UpperCAmelCase__							:				Tuple   				=  causal
         UpperCAmelCase__							:				Dict   				=  asm
         UpperCAmelCase__							:				Dict   				=  n_langs
         UpperCAmelCase__							:				List[str]   				=  vocab_size
         UpperCAmelCase__							:				Optional[int]   				=  n_special
         UpperCAmelCase__							:				Optional[Any]   				=  hidden_size
         UpperCAmelCase__							:				Tuple   				=  num_hidden_layers
         UpperCAmelCase__							:				str   				=  num_attention_heads
         UpperCAmelCase__							:				Dict   				=  hidden_dropout_prob
         UpperCAmelCase__							:				Dict   				=  attention_probs_dropout_prob
         UpperCAmelCase__							:				Optional[int]   				=  max_position_embeddings
         UpperCAmelCase__							:				Optional[Any]   				=  type_sequence_label_size
         UpperCAmelCase__							:				int   				=  initializer_range
         UpperCAmelCase__							:				int   				=  num_labels
         UpperCAmelCase__							:				str   				=  num_choices
         UpperCAmelCase__							:				Dict   				=  summary_type
         UpperCAmelCase__							:				Union[str, Any]   				=  use_proj
         UpperCAmelCase__							:				Any   				=  scope
         UpperCAmelCase__							:				Dict   				=  bos_token_id




      def 		lowerCAmelCase__					(				self							)			->			List[Any]:



         '''simple docstring'''



         UpperCAmelCase__							:				Union[str, Any]   				=  ids_tensor([self.batch_size, self.seq_length]					,self.vocab_size							)
         UpperCAmelCase__							:				List[Any]   				=  random_attention_mask([self.batch_size, self.seq_length]							)

         UpperCAmelCase__							:				List[str]   				=  None
         if self.use_input_lengths:
            UpperCAmelCase__							:				Optional[int]   				=  (
                ids_tensor([self.batch_size]					,vocab_size=2							) + self.seq_length - 2
            )  # small variation of seq_length

         UpperCAmelCase__							:				Dict   				=  None
         if self.use_token_type_ids:
            UpperCAmelCase__							:				Any   				=  ids_tensor([self.batch_size, self.seq_length]					,self.n_langs							)

         UpperCAmelCase__							:				str   				=  None
         UpperCAmelCase__							:				Tuple   				=  None
         UpperCAmelCase__							:				List[Any]   				=  None
         if self.use_labels:
            UpperCAmelCase__							:				Optional[int]   				=  ids_tensor([self.batch_size]					,self.type_sequence_label_size							)
            UpperCAmelCase__							:				int   				=  ids_tensor([self.batch_size, self.seq_length]					,self.num_labels							)
            UpperCAmelCase__							:				str   				=  ids_tensor([self.batch_size]					,2							).float()
            UpperCAmelCase__							:				str   				=  ids_tensor([self.batch_size]					,self.num_choices							)

         UpperCAmelCase__							:				List[str]   				=  self.get_config()

         return (
             config,
             input_ids,
             token_type_ids,
             input_lengths,
             sequence_labels,
             token_labels,
             is_impossible_labels,
             choice_labels,
             input_mask,
         )




      def 		lowerCAmelCase__					(				self							)			->			int:



         '''simple docstring'''



         return XLMConfig(
             vocab_size=self.vocab_size					,n_special=self.n_special					,emb_dim=self.hidden_size					,n_layers=self.num_hidden_layers					,n_heads=self.num_attention_heads					,dropout=self.hidden_dropout_prob					,attention_dropout=self.attention_probs_dropout_prob					,gelu_activation=self.gelu_activation					,sinusoidal_embeddings=self.sinusoidal_embeddings					,asm=self.asm					,causal=self.causal					,n_langs=self.n_langs					,max_position_embeddings=self.max_position_embeddings					,initializer_range=self.initializer_range					,summary_type=self.summary_type					,use_proj=self.use_proj					,num_labels=self.num_labels					,bos_token_id=self.bos_token_id					,)




      def 		lowerCAmelCase__					(				self					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,)			->			Dict:



         '''simple docstring'''



         UpperCAmelCase__							:				int   				=  XLMModel(config=lowerCamelCase_							)
         model.to(lowerCamelCase_							)
         model.eval()
         UpperCAmelCase__							:				int   				=  model(lowerCamelCase_					,lengths=lowerCamelCase_					,langs=lowerCamelCase_							)
         UpperCAmelCase__							:				List[Any]   				=  model(lowerCamelCase_					,langs=lowerCamelCase_							)
         UpperCAmelCase__							:				str   				=  model(lowerCamelCase_							)
         self.parent.assertEqual(result.last_hidden_state.shape					,(self.batch_size, self.seq_length, self.hidden_size)							)




      def 		lowerCAmelCase__					(				self					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,)			->			Union[str, Any]:



         '''simple docstring'''



         UpperCAmelCase__							:				Dict   				=  XLMWithLMHeadModel(lowerCamelCase_							)
         model.to(lowerCamelCase_							)
         model.eval()

         UpperCAmelCase__							:				Dict   				=  model(lowerCamelCase_					,token_type_ids=lowerCamelCase_					,labels=lowerCamelCase_							)
         self.parent.assertEqual(result.loss.shape					,()							)
         self.parent.assertEqual(result.logits.shape					,(self.batch_size, self.seq_length, self.vocab_size)							)




      def 		lowerCAmelCase__					(				self					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,)			->			Optional[Any]:



         '''simple docstring'''



         UpperCAmelCase__							:				Optional[Any]   				=  XLMForQuestionAnsweringSimple(lowerCamelCase_							)
         model.to(lowerCamelCase_							)
         model.eval()

         UpperCAmelCase__							:				Dict   				=  model(lowerCamelCase_							)

         UpperCAmelCase__							:				List[str]   				=  model(lowerCamelCase_					,start_positions=lowerCamelCase_					,end_positions=lowerCamelCase_							)
         UpperCAmelCase__							:				Union[str, Any]   				=  outputs
         self.parent.assertEqual(result.start_logits.shape					,(self.batch_size, self.seq_length)							)
         self.parent.assertEqual(result.end_logits.shape					,(self.batch_size, self.seq_length)							)




      def 		lowerCAmelCase__					(				self					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,)			->			List[Any]:



         '''simple docstring'''



         UpperCAmelCase__							:				str   				=  XLMForQuestionAnswering(lowerCamelCase_							)
         model.to(lowerCamelCase_							)
         model.eval()

         UpperCAmelCase__							:				Dict   				=  model(lowerCamelCase_							)

         UpperCAmelCase__							:				Any   				=  model(
             lowerCamelCase_					,start_positions=lowerCamelCase_					,end_positions=lowerCamelCase_					,cls_index=lowerCamelCase_					,is_impossible=lowerCamelCase_					,p_mask=lowerCamelCase_					,)

         UpperCAmelCase__							:				Optional[Any]   				=  model(
             lowerCamelCase_					,start_positions=lowerCamelCase_					,end_positions=lowerCamelCase_					,cls_index=lowerCamelCase_					,is_impossible=lowerCamelCase_					,)

         (UpperCAmelCase__    )							:				int   				=  result_with_labels.to_tuple()

         UpperCAmelCase__							:				Dict   				=  model(lowerCamelCase_					,start_positions=lowerCamelCase_					,end_positions=lowerCamelCase_							)

         (UpperCAmelCase__    )							:				Any   				=  result_with_labels.to_tuple()

         self.parent.assertEqual(result_with_labels.loss.shape					,()							)
         self.parent.assertEqual(result.start_top_log_probs.shape					,(self.batch_size, model.config.start_n_top)							)
         self.parent.assertEqual(result.start_top_index.shape					,(self.batch_size, model.config.start_n_top)							)
         self.parent.assertEqual(
             result.end_top_log_probs.shape					,(self.batch_size, model.config.start_n_top * model.config.end_n_top)							)
         self.parent.assertEqual(
             result.end_top_index.shape					,(self.batch_size, model.config.start_n_top * model.config.end_n_top)							)
         self.parent.assertEqual(result.cls_logits.shape					,(self.batch_size,)							)




      def 		lowerCAmelCase__					(				self					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,)			->			Tuple:



         '''simple docstring'''



         UpperCAmelCase__							:				Union[str, Any]   				=  XLMForSequenceClassification(lowerCamelCase_							)
         model.to(lowerCamelCase_							)
         model.eval()

         UpperCAmelCase__							:				Optional[Any]   				=  model(lowerCamelCase_							)
         UpperCAmelCase__							:				int   				=  model(lowerCamelCase_					,labels=lowerCamelCase_							)
         self.parent.assertEqual(result.loss.shape					,()							)
         self.parent.assertEqual(result.logits.shape					,(self.batch_size, self.type_sequence_label_size)							)




      def 		lowerCAmelCase__					(				self					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,)			->			List[str]:



         '''simple docstring'''



         UpperCAmelCase__							:				int   				=  self.num_labels
         UpperCAmelCase__							:				List[str]   				=  XLMForTokenClassification(lowerCamelCase_							)
         model.to(lowerCamelCase_							)
         model.eval()

         UpperCAmelCase__							:				List[str]   				=  model(lowerCamelCase_					,attention_mask=lowerCamelCase_					,labels=lowerCamelCase_							)
         self.parent.assertEqual(result.logits.shape					,(self.batch_size, self.seq_length, self.num_labels)							)




      def 		lowerCAmelCase__					(				self					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,)			->			str:



         '''simple docstring'''



         UpperCAmelCase__							:				str   				=  self.num_choices
         UpperCAmelCase__							:				Optional[Any]   				=  XLMForMultipleChoice(config=lowerCamelCase_							)
         model.to(lowerCamelCase_							)
         model.eval()
         UpperCAmelCase__							:				List[Any]   				=  input_ids.unsqueeze(1							).expand(-1					,self.num_choices					,-1							).contiguous()
         UpperCAmelCase__							:				Union[str, Any]   				=  token_type_ids.unsqueeze(1							).expand(-1					,self.num_choices					,-1							).contiguous()
         UpperCAmelCase__							:				Optional[int]   				=  input_mask.unsqueeze(1							).expand(-1					,self.num_choices					,-1							).contiguous()
         UpperCAmelCase__							:				str   				=  model(
             lowerCamelCase_					,attention_mask=lowerCamelCase_					,token_type_ids=lowerCamelCase_					,labels=lowerCamelCase_					,)
         self.parent.assertEqual(result.logits.shape					,(self.batch_size, self.num_choices)							)




      def 		lowerCAmelCase__					(				self							)			->			List[str]:



         '''simple docstring'''



         UpperCAmelCase__							:				Any   				=  self.prepare_config_and_inputs()
         (
             UpperCAmelCase__    
         )							:				Any   				=  config_and_inputs
         UpperCAmelCase__							:				str   				=  {'input_ids': input_ids, 'token_type_ids': token_type_ids, 'lengths': input_lengths}
         return config, inputs_dict





@require_torch
class 				_lowercase	(      __A		,__A		,__A		,unittest.TestCase   ):
      '''simple docstring'''


      UpperCAmelCase_      :      Any      							=   (
          (
              XLMModel,
              XLMWithLMHeadModel,
              XLMForQuestionAnswering,
              XLMForSequenceClassification,
              XLMForQuestionAnsweringSimple,
              XLMForTokenClassification,
              XLMForMultipleChoice,
          )
          if is_torch_available()
          else ()
      )
      UpperCAmelCase_      :      List[Any]      							=   (
          (XLMWithLMHeadModel,) if is_torch_available() else ()
      )  # TODO (PVP): Check other models whether language generation is also applicable
      UpperCAmelCase_      :      Optional[int]      							=   (
          {
              '''feature-extraction''': XLMModel,
              '''fill-mask''': XLMWithLMHeadModel,
              '''question-answering''': XLMForQuestionAnsweringSimple,
              '''text-classification''': XLMForSequenceClassification,
              '''text-generation''': XLMWithLMHeadModel,
              '''token-classification''': XLMForTokenClassification,
              '''zero-shot''': XLMForSequenceClassification,
          }
          if is_torch_available()
          else {}
      )




      def 		lowerCAmelCase__					(				self					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_							)			->			int:



         '''simple docstring'''



         if (
             pipeline_test_casse_name == "QAPipelineTests"
             and tokenizer_name is not None
             and not tokenizer_name.endswith('''Fast'''							)
         ):
            # `QAPipelineTests` fails for a few models when the slower tokenizer are used.
            # (The slower tokenizers were never used for pipeline tests before the pipeline testing rework)
            # TODO: check (and possibly fix) the `QAPipelineTests` with slower tokenizer
            return True

         return False




      def 		lowerCAmelCase__					(				self					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_=False							)			->			Optional[Any]:



         '''simple docstring'''



         UpperCAmelCase__							:				Union[str, Any]   				=  super()._prepare_for_class(lowerCamelCase_					,lowerCamelCase_					,return_labels=lowerCamelCase_							)

         if return_labels:
            if model_class.__name__ == "XLMForQuestionAnswering":
               UpperCAmelCase__							:				Any   				=  torch.zeros(
                   self.model_tester.batch_size					,dtype=torch.long					,device=lowerCamelCase_							)
               UpperCAmelCase__							:				Optional[int]   				=  torch.zeros(
                   self.model_tester.batch_size					,dtype=torch.long					,device=lowerCamelCase_							)

         return inputs_dict




      def 		lowerCAmelCase__					(				self							)			->			Tuple:



         '''simple docstring'''



         UpperCAmelCase__							:				Dict   				=  XLMModelTester(self							)
         UpperCAmelCase__							:				Tuple   				=  ConfigTester(self					,config_class=lowerCamelCase_					,emb_dim=37							)




      def 		lowerCAmelCase__					(				self							)			->			Dict:



         '''simple docstring'''



         self.config_tester.run_common_tests()




      def 		lowerCAmelCase__					(				self							)			->			Tuple:



         '''simple docstring'''



         UpperCAmelCase__							:				Dict   				=  self.model_tester.prepare_config_and_inputs()
         self.model_tester.create_and_check_xlm_model(*lowerCamelCase_							)




      def 		lowerCAmelCase__					(				self							)			->			Tuple:



         '''simple docstring'''



         UpperCAmelCase__							:				Optional[int]   				=  self.model_tester.prepare_config_and_inputs()
         self.model_tester.create_and_check_xlm_lm_head(*lowerCamelCase_							)




      def 		lowerCAmelCase__					(				self							)			->			Optional[int]:



         '''simple docstring'''



         UpperCAmelCase__							:				str   				=  self.model_tester.prepare_config_and_inputs()
         self.model_tester.create_and_check_xlm_simple_qa(*lowerCamelCase_							)




      def 		lowerCAmelCase__					(				self							)			->			Optional[Any]:



         '''simple docstring'''



         UpperCAmelCase__							:				Dict   				=  self.model_tester.prepare_config_and_inputs()
         self.model_tester.create_and_check_xlm_qa(*lowerCamelCase_							)




      def 		lowerCAmelCase__					(				self							)			->			Union[str, Any]:



         '''simple docstring'''



         UpperCAmelCase__							:				Tuple   				=  self.model_tester.prepare_config_and_inputs()
         self.model_tester.create_and_check_xlm_sequence_classif(*lowerCamelCase_							)




      def 		lowerCAmelCase__					(				self							)			->			Tuple:



         '''simple docstring'''



         UpperCAmelCase__							:				Union[str, Any]   				=  self.model_tester.prepare_config_and_inputs()
         self.model_tester.create_and_check_xlm_token_classif(*lowerCamelCase_							)




      def 		lowerCAmelCase__					(				self							)			->			Tuple:



         '''simple docstring'''



         UpperCAmelCase__							:				List[str]   				=  self.model_tester.prepare_config_and_inputs()
         self.model_tester.create_and_check_xlm_for_multiple_choice(*lowerCamelCase_							)




      def 		lowerCAmelCase__					(				self					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_=False					,lowerCamelCase_=1							)			->			int:



         '''simple docstring'''



         self.assertIsInstance(lowerCamelCase_					,lowerCamelCase_							)
         self.assertListEqual(
             [isinstance(lowerCamelCase_					,lowerCamelCase_							) for iter_attentions in attentions]					,[True] * len(lowerCamelCase_							)							)
         self.assertEqual(len(lowerCamelCase_							)					,(max_length - min_length) * num_beam_groups							)

         for idx, iter_attentions in enumerate(lowerCamelCase_							):
            # adds PAD dummy token
            UpperCAmelCase__							:				List[str]   				=  min_length + idx + 1
            UpperCAmelCase__							:				Optional[Any]   				=  min_length + idx + 1

            UpperCAmelCase__							:				Optional[int]   				=  (
                batch_size * num_beam_groups,
                config.num_attention_heads,
                tgt_len,
                src_len,
            )
            # check attn size
            self.assertListEqual(
                [layer_attention.shape for layer_attention in iter_attentions]					,[expected_shape] * len(lowerCamelCase_							)							)




      def 		lowerCAmelCase__					(				self					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_=False					,lowerCamelCase_=1							)			->			Optional[Any]:



         '''simple docstring'''



         self.assertIsInstance(lowerCamelCase_					,lowerCamelCase_							)
         self.assertListEqual(
             [isinstance(lowerCamelCase_					,lowerCamelCase_							) for iter_hidden_states in hidden_states]					,[True] * len(lowerCamelCase_							)					,)
         self.assertEqual(len(lowerCamelCase_							)					,(max_length - min_length) * num_beam_groups							)

         for idx, iter_hidden_states in enumerate(lowerCamelCase_							):
            # adds PAD dummy token
            UpperCAmelCase__							:				Any   				=  min_length + idx + 1
            UpperCAmelCase__							:				Dict   				=  (batch_size * num_beam_groups, seq_len, config.hidden_size)
            # check hidden size
            self.assertListEqual(
                [layer_hidden_states.shape for layer_hidden_states in iter_hidden_states]					,[expected_shape] * len(lowerCamelCase_							)					,)
         pass




      @slow
      def 		lowerCAmelCase__					(				self							)			->			Optional[Any]:



         '''simple docstring'''



         for model_name in XLM_PRETRAINED_MODEL_ARCHIVE_LIST[:1]:
            UpperCAmelCase__							:				Optional[int]   				=  XLMModel.from_pretrained(lowerCamelCase_							)
            self.assertIsNotNone(lowerCamelCase_							)





@require_torch
class 				_lowercase	(      unittest.TestCase   ):
      '''simple docstring'''


      @slow
      def 		lowerCAmelCase__					(				self							)			->			Dict:



         '''simple docstring'''



         UpperCAmelCase__							:				Union[str, Any]   				=  XLMWithLMHeadModel.from_pretrained('''xlm-mlm-en-2048'''							)
         model.to(lowerCamelCase_							)
         UpperCAmelCase__							:				List[str]   				=  torch.tensor([[14, 447]]					,dtype=torch.long					,device=lowerCamelCase_							)  # the president
         UpperCAmelCase__							:				Optional[int]   				=  [
             14,
             447,
             14,
             447,
             14,
             447,
             14,
             447,
             14,
             447,
             14,
             447,
             14,
             447,
             14,
             447,
             14,
             447,
             14,
             447,
         ]  # the president the president the president the president the president the president the president the president the president the president
         # TODO(PVP): this and other input_ids I tried for generation give pretty bad results. Not sure why. Model might just not be made for auto-regressive inference
         UpperCAmelCase__							:				Union[str, Any]   				=  model.generate(lowerCamelCase_					,do_sample=lowerCamelCase_							)
         self.assertListEqual(output_ids[0].cpu().numpy().tolist()					,lowerCamelCase_							)





'''simple docstring'''

import unittest

import numpy as np







def __UpperCamelCase(   _A					:				np.ndarray  ,			_A					:				np.ndarray  ,			_A					:				np.ndarray  ,			_A					:				np.ndarray | None = None  ,			):
   '''simple docstring'''
   UpperCAmelCase__							:				Any   				=  np.shape(_A    )
   UpperCAmelCase__							:				List[Any]   				=  np.shape(_A    )
   UpperCAmelCase__							:				Tuple   				=  np.shape(_A    )

   if shape_a[0] != shape_b[0]:
      UpperCAmelCase__							:				Any   				=  (
          '''Expected the same number of rows for A and B. '''
          F'''Instead found A of size {shape_a} and B of size {shape_b}'''
      )
      raise ValueError(_A    )

   if shape_b[1] != shape_c[1]:
      UpperCAmelCase__							:				List[str]   				=  (
          '''Expected the same number of columns for B and C. '''
          F'''Instead found B of size {shape_b} and C of size {shape_c}'''
      )
      raise ValueError(_A    )

   UpperCAmelCase__							:				Optional[Any]   				=  pseudo_inv
   if a_inv is None:
      try:
         UpperCAmelCase__							:				str   				=  np.linalg.inv(_A    )
      except np.linalg.LinAlgError:
         raise ValueError(
             '''Input matrix A is not invertible. Cannot compute Schur complement.'''    )

   return mat_c - mat_b.T @ a_inv @ mat_b


class 				_lowercase	(      unittest.TestCase   ):
      '''simple docstring'''


      def 		lowerCAmelCase__					(				self							)			->			None:



         '''simple docstring'''



         UpperCAmelCase__							:				int   				=  np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]							)
         UpperCAmelCase__							:				List[Any]   				=  np.array([[0, 3], [3, 0], [2, 3]]							)
         UpperCAmelCase__							:				Optional[Any]   				=  np.array([[2, 1], [6, 3]]							)

         UpperCAmelCase__							:				Tuple   				=  schur_complement(lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_							)

         UpperCAmelCase__							:				Tuple   				=  np.block([[a, b], [b.T, c]]							)

         UpperCAmelCase__							:				int   				=  np.linalg.det(lowerCamelCase_							)
         UpperCAmelCase__							:				Optional[Any]   				=  np.linalg.det(lowerCamelCase_							)
         UpperCAmelCase__							:				Union[str, Any]   				=  np.linalg.det(lowerCamelCase_							)

         self.assertAlmostEqual(lowerCamelCase_					,det_a * det_s							)




      def 		lowerCAmelCase__					(				self							)			->			None:



         '''simple docstring'''



         UpperCAmelCase__							:				Optional[Any]   				=  np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]							)
         UpperCAmelCase__							:				Tuple   				=  np.array([[0, 3], [3, 0], [2, 3]]							)
         UpperCAmelCase__							:				Tuple   				=  np.array([[2, 1], [6, 3]]							)

         with self.assertRaises(lowerCamelCase_							):
            schur_complement(lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_							)




      def 		lowerCAmelCase__					(				self							)			->			None:



         '''simple docstring'''



         UpperCAmelCase__							:				Dict   				=  np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]							)
         UpperCAmelCase__							:				str   				=  np.array([[0, 3], [3, 0], [2, 3]]							)
         UpperCAmelCase__							:				Any   				=  np.array([[2, 1, 3], [6, 3, 5]]							)

         with self.assertRaises(lowerCamelCase_							):
            schur_complement(lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_							)


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  unittest.main()




