


def        SCREAMING_SNAKE_CASE_						(			__A :			list[list]				)	->		list[list]:

       """simple docstring"""

       a_					:		List[str]							=  current_set.copy()
       for row_index, row in enumerate(__A				):
              a_					:		List[str]							=  row[0]
              for column_index, column in enumerate(__A				):
                     if magnitude == 0:
                            a_					:		Any							=  column
                            continue
                     a_					:		List[str]							=  column / magnitude
    # Subtract to cancel term
       a_					:		Any							=  current_set[0]
       a_					:		Optional[int]							=  [first_row]
       a_					:		Dict							=  current_set[1::]
       for row in current_set:
              a_					:		str							=  []
              # If first term is 0, it is already in form we want, so we preserve it
              if row[0] == 0:
                     final_set.append(__A				)
                     continue
              for column_index in range(len(__A				)				):
                     temp_row.append(first_row[column_index] - row[column_index]				)
              final_set.append(__A				)
       # Create next recursion iteration set
       if len(final_set[0]				) != 3:
              a_					:		Dict							=  final_set[0]
              a_					:		Union[str, Any]							=  []
              a_					:		Optional[int]							=  []
              for row in final_set[1::]:
                     current_first_column.append(row[0]				)
                     next_iteration.append(row[1::]				)
              a_					:		List[Any]							=  simplify(__A				)
              for i in range(len(__A				)				):
                     resultant[i].insert(0  ,    current_first_column[i]				)
              resultant.insert(0  ,    __A				)
              a_					:		Any							=  resultant
       return final_set







def        SCREAMING_SNAKE_CASE_						(			__A :			list[list]				)	->		list:

       """simple docstring"""

       if len(__A				) == 0:
              raise IndexError('solve_simultaneous() requires n lists of length n+1'				)
       a_					:		List[Any]							=  len(__A				) + 1
       if any(len(__A				) != _length for item in equations				):
              raise IndexError('solve_simultaneous() requires n lists of length n+1'				)
       for row in equations:
              if any(not isinstance(__A  ,    (int, float)				) for column in row				):
                     raise ValueError('solve_simultaneous() requires lists of integers'				)
       if len(__A				) == 1:
              return [equations[0][-1] / equations[0][0]]
       a_					:		Union[str, Any]							=  equations.copy()
       if any(0 in row for row in data_set				):
              a_					:		Any							=  data_set.copy()
              a_					:		Tuple							=  []
              for row_index, row in enumerate(__A				):
                     if 0 not in row:
                            a_					:		Any							=  data_set.pop(__A				)
                            break
              if not full_row:
                     raise ValueError('solve_simultaneous() requires at least 1 full equation'				)
              data_set.insert(0  ,    __A				)
       a_					:		List[Any]							=  data_set.copy()
       a_					:		Optional[Any]							=  simplify(__A				)
       a_					:		Union[str, Any]							=  simplified[::-1]
       a_					:		list							=  []
       for row in simplified:
              a_					:		Tuple							=  row[-1]
              if not solutions:
                     if row[-2] == 0:
                            solutions.append(0				)
                            continue
                     solutions.append(current_solution / row[-2]				)
                     continue
              a_					:		int							=  row.copy()[: len(__A				) - 1 :]
              while temp_row[0] == 0:
                     temp_row.pop(0				)
              if len(__A				) == 0:
                     solutions.append(0				)
                     continue
              a_					:		List[Any]							=  temp_row[1::]
              a_					:		Optional[int]							=  temp_row[::-1]
              for column_index, column in enumerate(__A				):
                     current_solution -= column * solutions[column_index]
              solutions.append(__A				)
       a_					:		Tuple							=  []
       for item in solutions:
              final.append(float(round(__A  ,    5				)				)				)
       return final[::-1]


if __name__ == "__main__":
   import doctest

   doctest.testmod()
   UpperCAmelCase_      : Any  					=       [
       [2, 1, 1, 1, 1, 4],
       [1, 2, 1, 1, 1, 5],
       [1, 1, 2, 1, 1, 6],
       [1, 1, 1, 2, 1, 7],
       [1, 1, 1, 1, 2, 8],
   ]
   print(solve_simultaneous(eq))
   print(solve_simultaneous([[4, 2]]))






import unittest

from transformers import LiltConfig, 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
from ...test_pipeline_mixin import PipelineTesterMixin


if is_torch_available():
   import torch

   from transformers import (
       LiltForQuestionAnswering,
       LiltForSequenceClassification,
       LiltForTokenClassification,
       LiltModel,
   )
   from transformers.models.lilt.modeling_lilt import LILT_PRETRAINED_MODEL_ARCHIVE_LIST
class  SCREAMING_SNAKE_CASE__  :
      def __init__(       self				:       Tuple     ,							SCREAMING_SNAKE_CASE__				:       List[Any]     ,							SCREAMING_SNAKE_CASE__				:       str=1_3     ,							SCREAMING_SNAKE_CASE__				:       Optional[int]=7     ,							SCREAMING_SNAKE_CASE__				:       str=True     ,							SCREAMING_SNAKE_CASE__				:       int=True     ,							SCREAMING_SNAKE_CASE__				:       Dict=True     ,							SCREAMING_SNAKE_CASE__				:       str=True     ,							SCREAMING_SNAKE_CASE__				:       str=9_9     ,							SCREAMING_SNAKE_CASE__				:       str=2_4     ,							SCREAMING_SNAKE_CASE__				:       Union[str, Any]=2     ,							SCREAMING_SNAKE_CASE__				:       Optional[Any]=6     ,							SCREAMING_SNAKE_CASE__				:       Optional[int]=3_7     ,							SCREAMING_SNAKE_CASE__				:       List[Any]="gelu"     ,							SCREAMING_SNAKE_CASE__				:       str=0.1     ,							SCREAMING_SNAKE_CASE__				:       List[Any]=0.1     ,							SCREAMING_SNAKE_CASE__				:       List[str]=5_1_2     ,							SCREAMING_SNAKE_CASE__				:       List[str]=1_6     ,							SCREAMING_SNAKE_CASE__				:       Union[str, Any]=2     ,							SCREAMING_SNAKE_CASE__				:       int=0.02     ,							SCREAMING_SNAKE_CASE__				:       Optional[Any]=3     ,							SCREAMING_SNAKE_CASE__				:       Optional[int]=None     ,							SCREAMING_SNAKE_CASE__				:       Tuple=1_0_0_0     ,							)		->			str:
             a_					:		Optional[Any]							=  parent
             a_					:		List[str]							=  batch_size
             a_					:		List[str]							=  seq_length
             a_					:		str							=  is_training
             a_					:		str							=  use_input_mask
             a_					:		int							=  use_token_type_ids
             a_					:		List[str]							=  use_labels
             a_					:		Optional[int]							=  vocab_size
             a_					:		Any							=  hidden_size
             a_					:		int							=  num_hidden_layers
             a_					:		List[str]							=  num_attention_heads
             a_					:		str							=  intermediate_size
             a_					:		Union[str, Any]							=  hidden_act
             a_					:		List[str]							=  hidden_dropout_prob
             a_					:		int							=  attention_probs_dropout_prob
             a_					:		int							=  max_position_embeddings
             a_					:		Tuple							=  type_vocab_size
             a_					:		Optional[Any]							=  type_sequence_label_size
             a_					:		Tuple							=  initializer_range
             a_					:		Dict							=  num_labels
             a_					:		str							=  scope
             a_					:		Optional[int]							=  range_bbox
      def        SCREAMING_SNAKE_CASE							(       self				:       List[str]     )		->			int:
             a_					:		Dict							=  ids_tensor([self.batch_size, self.seq_length]     ,							self.vocab_size     )

             a_					:		Any							=  ids_tensor([self.batch_size, self.seq_length, 4]     ,							self.range_bbox     )
             # Ensure that bbox is legal
             for i in range(bbox.shape[0]     ):
                    for j in range(bbox.shape[1]     ):
                           if bbox[i, j, 3] < bbox[i, j, 1]:
                                  a_					:		int							=  bbox[i, j, 3]
                                  a_					:		str							=  bbox[i, j, 1]
                                  a_					:		List[str]							=  t
                           if bbox[i, j, 2] < bbox[i, j, 0]:
                                  a_					:		Tuple							=  bbox[i, j, 2]
                                  a_					:		List[str]							=  bbox[i, j, 0]
                                  a_					:		Union[str, Any]							=  t

             a_					:		List[Any]							=  None
             if self.use_input_mask:
                    a_					:		Dict							=  ids_tensor([self.batch_size, self.seq_length]     ,							vocab_size=2     )

             a_					:		List[Any]							=  None
             if self.use_token_type_ids:
                    a_					:		Optional[Any]							=  ids_tensor([self.batch_size, self.seq_length]     ,							self.type_vocab_size     )

             a_					:		int							=  None
             a_					:		Tuple							=  None
             if self.use_labels:
                    a_					:		List[Any]							=  ids_tensor([self.batch_size]     ,							self.type_sequence_label_size     )
                    a_					:		int							=  ids_tensor([self.batch_size, self.seq_length]     ,							self.num_labels     )

             a_					:		Optional[int]							=  self.get_config()

             return config, input_ids, bbox, token_type_ids, input_mask, sequence_labels, token_labels
      def        SCREAMING_SNAKE_CASE							(       self				:       Dict     )		->			int:
             return LiltConfig(
                 vocab_size=self.vocab_size     ,							hidden_size=self.hidden_size     ,							num_hidden_layers=self.num_hidden_layers     ,							num_attention_heads=self.num_attention_heads     ,							intermediate_size=self.intermediate_size     ,							hidden_act=self.hidden_act     ,							hidden_dropout_prob=self.hidden_dropout_prob     ,							attention_probs_dropout_prob=self.attention_probs_dropout_prob     ,							max_position_embeddings=self.max_position_embeddings     ,							type_vocab_size=self.type_vocab_size     ,							initializer_range=self.initializer_range     ,							)
      def        SCREAMING_SNAKE_CASE							(       self				:       Optional[int]     ,							SCREAMING_SNAKE_CASE__				:       Dict     ,							SCREAMING_SNAKE_CASE__				:       Any     ,							SCREAMING_SNAKE_CASE__				:       Any     ,							SCREAMING_SNAKE_CASE__				:       Optional[int]     ,							SCREAMING_SNAKE_CASE__				:       int     ,							SCREAMING_SNAKE_CASE__				:       Union[str, Any]     ,							SCREAMING_SNAKE_CASE__				:       Optional[Any]     ,							)		->			str:
             a_					:		Any							=  LiltModel(config=SCREAMING_SNAKE_CASE__     )
             model.to(SCREAMING_SNAKE_CASE__     )
             model.eval()
             a_					:		Any							=  model(SCREAMING_SNAKE_CASE__     ,							bbox=SCREAMING_SNAKE_CASE__     ,							attention_mask=SCREAMING_SNAKE_CASE__     ,							token_type_ids=SCREAMING_SNAKE_CASE__     )
             a_					:		Optional[int]							=  model(SCREAMING_SNAKE_CASE__     ,							bbox=SCREAMING_SNAKE_CASE__     ,							token_type_ids=SCREAMING_SNAKE_CASE__     )
             a_					:		List[Any]							=  model(SCREAMING_SNAKE_CASE__     ,							bbox=SCREAMING_SNAKE_CASE__     )

             self.parent.assertEqual(result.last_hidden_state.shape     ,							(self.batch_size, self.seq_length, self.hidden_size)     )
             self.parent.assertEqual(result.pooler_output.shape     ,							(self.batch_size, self.hidden_size)     )
      def        SCREAMING_SNAKE_CASE							(       self				:       Tuple     ,							SCREAMING_SNAKE_CASE__				:       str     ,							SCREAMING_SNAKE_CASE__				:       int     ,							SCREAMING_SNAKE_CASE__				:       int     ,							SCREAMING_SNAKE_CASE__				:       Union[str, Any]     ,							SCREAMING_SNAKE_CASE__				:       Optional[int]     ,							SCREAMING_SNAKE_CASE__				:       Any     ,							SCREAMING_SNAKE_CASE__				:       Optional[Any]     ,							)		->			int:
             a_					:		Any							=  self.num_labels
             a_					:		str							=  LiltForTokenClassification(config=SCREAMING_SNAKE_CASE__     )
             model.to(SCREAMING_SNAKE_CASE__     )
             model.eval()
             a_					:		str							=  model(
                 SCREAMING_SNAKE_CASE__     ,							bbox=SCREAMING_SNAKE_CASE__     ,							attention_mask=SCREAMING_SNAKE_CASE__     ,							token_type_ids=SCREAMING_SNAKE_CASE__     ,							labels=SCREAMING_SNAKE_CASE__     )
             self.parent.assertEqual(result.logits.shape     ,							(self.batch_size, self.seq_length, self.num_labels)     )
      def        SCREAMING_SNAKE_CASE							(       self				:       Any     ,							SCREAMING_SNAKE_CASE__				:       Tuple     ,							SCREAMING_SNAKE_CASE__				:       List[str]     ,							SCREAMING_SNAKE_CASE__				:       List[str]     ,							SCREAMING_SNAKE_CASE__				:       int     ,							SCREAMING_SNAKE_CASE__				:       Any     ,							SCREAMING_SNAKE_CASE__				:       Dict     ,							SCREAMING_SNAKE_CASE__				:       Union[str, Any]     ,							)		->			str:
             a_					:		Union[str, Any]							=  LiltForQuestionAnswering(config=SCREAMING_SNAKE_CASE__     )
             model.to(SCREAMING_SNAKE_CASE__     )
             model.eval()
             a_					:		List[str]							=  model(
                 SCREAMING_SNAKE_CASE__     ,							bbox=SCREAMING_SNAKE_CASE__     ,							attention_mask=SCREAMING_SNAKE_CASE__     ,							token_type_ids=SCREAMING_SNAKE_CASE__     ,							start_positions=SCREAMING_SNAKE_CASE__     ,							end_positions=SCREAMING_SNAKE_CASE__     ,							)
             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        SCREAMING_SNAKE_CASE							(       self				:       int     )		->			List[str]:
             a_					:		int							=  self.prepare_config_and_inputs()
             (
                 (
                 a_
             )							,		(
                 a_
             )							,		(
                 a_
             )							,		(
                 a_
             )							,		(
                 a_
             )							,		(
                 a_
             )							,		(
                 a_
             )							,		
             )					:		List[Any]							=  config_and_inputs
             a_					:		Optional[int]							=  {
                 'input_ids': input_ids,
                 'bbox': bbox,
                 'token_type_ids': token_type_ids,
                 'attention_mask': input_mask,
             }
             return config, inputs_dict
@require_torch
class  SCREAMING_SNAKE_CASE__  (				lowercase__						,    lowercase__						,    lowercase__						,    unittest.TestCase			):
      snake_case__				:     Union[str, Any]        =						(
          (
              LiltModel,
              LiltForSequenceClassification,
              LiltForTokenClassification,
              LiltForQuestionAnswering,
          )
          if is_torch_available()
          else ()
      )
      snake_case__				:     str        =						(
          {
              '''feature-extraction''': LiltModel,
              '''question-answering''': LiltForQuestionAnswering,
              '''text-classification''': LiltForSequenceClassification,
              '''token-classification''': LiltForTokenClassification,
              '''zero-shot''': LiltForSequenceClassification,
          }
          if is_torch_available()
          else {}
      )
      snake_case__				:     List[str]        =						False
      snake_case__				:     str        =						False
      def        SCREAMING_SNAKE_CASE							(       self				:       Dict     ,							SCREAMING_SNAKE_CASE__				:       str     ,							SCREAMING_SNAKE_CASE__				:       Tuple     ,							SCREAMING_SNAKE_CASE__				:       List[str]     ,							SCREAMING_SNAKE_CASE__				:       Optional[int]     ,							SCREAMING_SNAKE_CASE__				:       int     )		->			int:
             return True
      def        SCREAMING_SNAKE_CASE							(       self				:       Optional[Any]     )		->			Tuple:
             a_					:		str							=  LiltModelTester(self     )
             a_					:		List[Any]							=  ConfigTester(self     ,							config_class=SCREAMING_SNAKE_CASE__     ,							hidden_size=3_7     )
      def        SCREAMING_SNAKE_CASE							(       self				:       Dict     )		->			List[Any]:
             self.config_tester.run_common_tests()
      def        SCREAMING_SNAKE_CASE							(       self				:       Optional[int]     )		->			str:
             a_					:		Dict							=  self.model_tester.prepare_config_and_inputs()
             self.model_tester.create_and_check_model(*SCREAMING_SNAKE_CASE__     )
      def        SCREAMING_SNAKE_CASE							(       self				:       Dict     )		->			Optional[int]:
             a_					:		Tuple							=  self.model_tester.prepare_config_and_inputs()
             for type in ["absolute", "relative_key", "relative_key_query"]:
                    a_					:		List[str]							=  type
                    self.model_tester.create_and_check_model(*SCREAMING_SNAKE_CASE__     )
      def        SCREAMING_SNAKE_CASE							(       self				:       int     )		->			Optional[Any]:
             a_					:		List[Any]							=  self.model_tester.prepare_config_and_inputs()
             self.model_tester.create_and_check_for_token_classification(*SCREAMING_SNAKE_CASE__     )
      def        SCREAMING_SNAKE_CASE							(       self				:       List[str]     )		->			List[str]:
             a_					:		Optional[Any]							=  self.model_tester.prepare_config_and_inputs()
             self.model_tester.create_and_check_for_question_answering(*SCREAMING_SNAKE_CASE__     )

      @slow
      def        SCREAMING_SNAKE_CASE							(       self				:       str     )		->			Union[str, Any]:
             for model_name in LILT_PRETRAINED_MODEL_ARCHIVE_LIST[:1]:
                    a_					:		List[Any]							=  LiltModel.from_pretrained(SCREAMING_SNAKE_CASE__     )
                    self.assertIsNotNone(SCREAMING_SNAKE_CASE__     )
@require_torch
@slow
class  SCREAMING_SNAKE_CASE__  (				unittest.TestCase			):
      def        SCREAMING_SNAKE_CASE							(       self				:       Union[str, Any]     )		->			Union[str, Any]:
             a_					:		List[str]							=  LiltModel.from_pretrained('SCUT-DLVCLab/lilt-roberta-en-base'     ).to(SCREAMING_SNAKE_CASE__     )

             a_					:		str							=  torch.tensor([[1, 2]]     ,							device=SCREAMING_SNAKE_CASE__     )
             a_					:		List[Any]							=  torch.tensor([[[1, 2, 3, 4], [5, 6, 7, 8]]]     ,							device=SCREAMING_SNAKE_CASE__     )

             # forward pass
             with torch.no_grad():
                    a_					:		str							=  model(input_ids=SCREAMING_SNAKE_CASE__     ,							bbox=SCREAMING_SNAKE_CASE__     )

             a_					:		Optional[int]							=  torch.Size([1, 2, 7_6_8]     )
             a_					:		int							=  torch.tensor(
                 [[-0.0653, 0.0950, -0.0061], [-0.0545, 0.0926, -0.0324]]     ,							device=SCREAMING_SNAKE_CASE__     ,							)

             self.assertTrue(outputs.last_hidden_state.shape     ,							SCREAMING_SNAKE_CASE__     )
             self.assertTrue(torch.allclose(outputs.last_hidden_state[0, :, :3]     ,							SCREAMING_SNAKE_CASE__     ,							atol=1E-3     )     )


