




"""simple docstring"""






from __future__ import annotations

from collections.abc import Callable

UpperCamelCase__						=			list[list[float | int]]





def 							UpperCAmelCase		(		snake_case			:					Matrix      ,       snake_case			:					Matrix    ):
					_lowerCAmelCase:int									=  len(snake_case    )
					_lowerCAmelCase:Matrix									=  [[0 for _ in range(size + 1    )] for _ in range(snake_case    )]
					_lowerCAmelCase:int
					_lowerCAmelCase:int
					_lowerCAmelCase:int
					_lowerCAmelCase:int
					_lowerCAmelCase:int
					_lowerCAmelCase:float

					for row in range(snake_case    ):
										for col in range(snake_case    ):
															_lowerCAmelCase:Optional[Any]									=  matrix[row][col]

										_lowerCAmelCase:Tuple									=  vector[row][0]

					_lowerCAmelCase:str									=  0
					_lowerCAmelCase:str									=  0
					while row < size and col < size:
										# pivoting
										_lowerCAmelCase:Optional[int]									=  max((abs(augmented[rowa][col]    ), rowa) for rowa in range(snake_case      ,       snake_case    )    )[
										    1
										]
										if augmented[pivot_row][col] == 0:
															col += 1
															continue
										else:
															_lowerCAmelCase:Optional[int]									=  augmented[pivot_row], augmented[row]

										for rowa in range(row + 1      ,       snake_case    ):
															_lowerCAmelCase:str									=  augmented[rowa][col] / augmented[row][col]
															_lowerCAmelCase:List[str]									=  0
															for cola in range(col + 1      ,       size + 1    ):
																				augmented[rowa][cola] -= augmented[row][cola] * ratio

										row += 1
										col += 1

					# back substitution
					for col in range(1      ,       snake_case    ):
										for row in range(snake_case    ):
															_lowerCAmelCase:Dict									=  augmented[row][col] / augmented[col][col]
															for cola in range(snake_case      ,       size + 1    ):
																				augmented[row][cola] -= augmented[col][cola] * ratio

    # round to get rid of numbers like 2.000000000000004
					return [
					    [round(augmented[row][size] / augmented[row][row]      ,       10    )] for row in range(snake_case    )
					]





def 							UpperCAmelCase		(		snake_case			:					list[int]    ):
					_lowerCAmelCase:int									=  len(snake_case    )
					_lowerCAmelCase:Matrix									=  [[0 for _ in range(snake_case    )] for _ in range(snake_case    )]
					_lowerCAmelCase:Matrix									=  [[0] for _ in range(snake_case    )]
					_lowerCAmelCase:Matrix
					_lowerCAmelCase:int
					_lowerCAmelCase:int
					_lowerCAmelCase:int

					for x_val, y_val in enumerate(snake_case    ):
										for col in range(snake_case    ):
															_lowerCAmelCase:Optional[int]									=  (x_val + 1) ** (size - col - 1)
										_lowerCAmelCase:Optional[Any]									=  y_val

					_lowerCAmelCase:Optional[int]									=  solve(snake_case      ,       snake_case    )

					def interpolated_func(snake_case			:					int    ) -> int:
										return sum(
										    round(coeffs[x_val][0]    ) * (var ** (size - x_val - 1))
										    for x_val in range(snake_case    )    )

					return interpolated_func





def 							UpperCAmelCase		(		snake_case			:					int    ):
					return (
					    1
					    - variable
					    + variable**2
					    - variable**3
					    + variable**4
					    - variable**5
					    + variable**6
					    - variable**7
					    + variable**8
					    - variable**9
					    + variable**10
					)





def 							UpperCAmelCase		(		snake_case			:					Callable[[int], int] = question_function      ,       snake_case			:					int = 10    ):
					_lowerCAmelCase:list[int]									=  [func(snake_case    ) for x_val in range(1      ,       order + 1    )]

					_lowerCAmelCase:list[Callable[[int], int]]									=  [
					    interpolate(data_points[:max_coeff]    ) for max_coeff in range(1      ,       order + 1    )
					]

					_lowerCAmelCase:int									=  0
					_lowerCAmelCase:Callable[[int], int]
					_lowerCAmelCase:int

					for poly in polynomials:
										_lowerCAmelCase:Optional[int]									=  1
										while func(snake_case    ) == poly(snake_case    ):
															x_val += 1

										ret += poly(snake_case    )

					return ret


if __name__ == "__main__":
				print(F"{solution() = }")







"""simple docstring"""






import unittest

import numpy as np

from transformers import DistilBertConfig, is_flax_available
from transformers.testing_utils import require_flax, slow

from ...test_modeling_flax_common import FlaxModelTesterMixin, ids_tensor, random_attention_mask


if is_flax_available():
				import jax.numpy as jnp

				from transformers.models.distilbert.modeling_flax_distilbert import (
				    FlaxDistilBertForMaskedLM,
				    FlaxDistilBertForMultipleChoice,
				    FlaxDistilBertForQuestionAnswering,
				    FlaxDistilBertForSequenceClassification,
				    FlaxDistilBertForTokenClassification,
				    FlaxDistilBertModel,
				)




class   a__			(       unittest.TestCase  ):





						def __init__(							self      :	Dict     ,a__      :	List[Any]     ,a__      :	Optional[int]=13     ,a__      :	Dict=7     ,a__      :	Any=True     ,a__      :	Tuple=True     ,a__      :	Union[str, Any]=True     ,a__      :	Dict=True     ,a__      :	Dict=99     ,a__      :	Optional[Any]=32     ,a__      :	Dict=5     ,a__      :	List[Any]=4     ,a__      :	Union[str, Any]=37     ,a__      :	str="gelu"     ,a__      :	Any=0.1     ,a__      :	Optional[int]=0.1     ,a__      :	Tuple=512     ,a__      :	Any=16     ,a__      :	Any=2     ,a__      :	Dict=0.02     ,a__      :	int=4     ,)						->       Union[str, Any]:




											"""simple docstring"""







											_lowerCAmelCase:Optional[int]									=  parent
											_lowerCAmelCase:List[str]									=  batch_size
											_lowerCAmelCase:Tuple									=  seq_length
											_lowerCAmelCase:List[Any]									=  is_training
											_lowerCAmelCase:Dict									=  use_attention_mask
											_lowerCAmelCase:Dict									=  use_token_type_ids
											_lowerCAmelCase:Any									=  use_labels
											_lowerCAmelCase:str									=  vocab_size
											_lowerCAmelCase:int									=  hidden_size
											_lowerCAmelCase:Union[str, Any]									=  num_hidden_layers
											_lowerCAmelCase:List[str]									=  num_attention_heads
											_lowerCAmelCase:Optional[int]									=  intermediate_size
											_lowerCAmelCase:str									=  hidden_act
											_lowerCAmelCase:Optional[int]									=  hidden_dropout_prob
											_lowerCAmelCase:Optional[int]									=  attention_probs_dropout_prob
											_lowerCAmelCase:Any									=  max_position_embeddings
											_lowerCAmelCase:Optional[int]									=  type_vocab_size
											_lowerCAmelCase:Optional[int]									=  type_sequence_label_size
											_lowerCAmelCase:Tuple									=  initializer_range
											_lowerCAmelCase:Dict									=  num_choices





						def       __UpperCamelCase     (							self      :	List[str])						->       int:




											"""simple docstring"""







											_lowerCAmelCase:int									=  ids_tensor([self.batch_size, self.seq_length]     ,self.vocab_size)

											_lowerCAmelCase:List[Any]									=  None
											if self.use_attention_mask:
																_lowerCAmelCase:str									=  random_attention_mask([self.batch_size, self.seq_length])

											_lowerCAmelCase:Dict									=  DistilBertConfig(
											    vocab_size=self.vocab_size     ,dim=self.hidden_size     ,n_layers=self.num_hidden_layers     ,n_heads=self.num_attention_heads     ,hidden_dim=self.intermediate_size     ,hidden_act=self.hidden_act     ,dropout=self.hidden_dropout_prob     ,attention_dropout=self.attention_probs_dropout_prob     ,max_position_embeddings=self.max_position_embeddings     ,initializer_range=self.initializer_range     ,tie_weights_=a__     ,)

											return config, input_ids, attention_mask







						def       __UpperCamelCase     (							self      :	Any)						->       Any:




											"""simple docstring"""







											_lowerCAmelCase:Optional[Any]									=  self.prepare_config_and_inputs()
											_lowerCAmelCase							,   _lowerCAmelCase							,   _lowerCAmelCase:Optional[Any]									=  config_and_inputs
											_lowerCAmelCase:Any									=  {'''input_ids''': input_ids, '''attention_mask''': attention_mask}
											return config, inputs_dict




@require_flax
class   a__			(       UpperCamelCase_					,	unittest.TestCase  ):
						snake_case__             = (
						    (
						        FlaxDistilBertModel,
						        FlaxDistilBertForMaskedLM,
						        FlaxDistilBertForMultipleChoice,
						        FlaxDistilBertForQuestionAnswering,
						        FlaxDistilBertForSequenceClassification,
						        FlaxDistilBertForTokenClassification,
						        FlaxDistilBertForQuestionAnswering,
						    )
						    if is_flax_available()
						    else ()
						)





						def       __UpperCamelCase     (							self      :	str)						->       Dict:




											"""simple docstring"""







											_lowerCAmelCase:str									=  FlaxDistilBertModelTester(self)







						@slow
						def       __UpperCamelCase     (							self      :	List[str])						->       int:




											"""simple docstring"""







											for model_class_name in self.all_model_classes:
																_lowerCAmelCase:List[str]									=  model_class_name.from_pretrained('''distilbert-base-uncased''')
																_lowerCAmelCase:Tuple									=  model(np.ones((1, 1)))
																self.assertIsNotNone(a__)




@require_flax
class   a__			(       unittest.TestCase  ):





						@slow
						def       __UpperCamelCase     (							self      :	Union[str, Any])						->       Optional[Any]:




											"""simple docstring"""







											_lowerCAmelCase:Any									=  FlaxDistilBertModel.from_pretrained('''distilbert-base-uncased''')
											_lowerCAmelCase:Optional[int]									=  np.array([[0, 345, 232, 328, 740, 140, 1695, 69, 6078, 1588, 2]])
											_lowerCAmelCase:Tuple									=  np.array([[0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]])
											_lowerCAmelCase:List[str]									=  model(a__     ,attention_mask=a__)[0]
											_lowerCAmelCase:List[str]									=  (1, 11, 768)
											self.assertEqual(output.shape     ,a__)
											_lowerCAmelCase:int									=  np.array([[[-0.1639, 0.3299, 0.1648], [-0.1746, 0.3289, 0.1710], [-0.1884, 0.3357, 0.1810]]])

											self.assertTrue(jnp.allclose(output[:, 1:4, 1:4]     ,a__     ,atol=1E-4))






