


def 				_lowercase     (		SCREAMING_SNAKE_CASE_ :		Tuple						):





			"""simple docstring"""




			UpperCamelCase								=       current_set.copy()
			for row_index, row in enumerate(a__						):
						UpperCamelCase								=       row[0]
						for column_index, column in enumerate(a__						):
									if magnitude == 0:
												UpperCamelCase								=       column
												continue
									UpperCamelCase								=       column / magnitude
    # Subtract to cancel term
			UpperCamelCase								=       current_set[0]
			UpperCamelCase								=       [first_row]
			UpperCamelCase								=       current_set[1::]
			for row in current_set:
						UpperCamelCase								=       []
						# 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:
						UpperCamelCase								=       final_set[0]
						UpperCamelCase								=       []
						UpperCamelCase								=       []
						for row in final_set[1::]:
									current_first_column.append(row[0]						)
									next_iteration.append(row[1::]						)
						UpperCamelCase								=       simplify(a__						)
						for i in range(len(a__						)						):
									resultant[i].insert(0							,	current_first_column[i]						)
						resultant.insert(0							,	a__						)
						UpperCamelCase								=       resultant
			return final_set






def 				_lowercase     (		SCREAMING_SNAKE_CASE_ :		List[str]						):





			"""simple docstring"""




			if len(a__						) == 0:
						raise IndexError("""solve_simultaneous() requires n lists of length n+1"""						)
			UpperCamelCase								=       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]]
			UpperCamelCase								=       equations.copy()
			if any(0 in row for row in data_set						):
						UpperCamelCase								=       data_set.copy()
						UpperCamelCase								=       []
						for row_index, row in enumerate(a__						):
									if 0 not in row:
												UpperCamelCase								=       data_set.pop(a__						)
												break
						if not full_row:
									raise ValueError("""solve_simultaneous() requires at least 1 full equation"""						)
						data_set.insert(0							,	a__						)
			UpperCamelCase								=       data_set.copy()
			UpperCamelCase								=       simplify(a__						)
			UpperCamelCase								=       simplified[::-1]
			UpperCamelCase								=       []
			for row in simplified:
						UpperCamelCase								=       row[-1]
						if not solutions:
									if row[-2] == 0:
												solutions.append(0						)
												continue
									solutions.append(current_solution / row[-2]						)
									continue
						UpperCamelCase								=       row.copy()[: len(a__						) - 1 :]
						while temp_row[0] == 0:
									temp_row.pop(0						)
						if len(a__						) == 0:
									solutions.append(0						)
									continue
						UpperCamelCase								=       temp_row[1::]
						UpperCamelCase								=       temp_row[::-1]
						for column_index, column in enumerate(a__						):
									current_solution -= column * solutions[column_index]
						solutions.append(a__						)
			UpperCamelCase								=       []
			for item in solutions:
						final.append(float(round(a__							,	5						)						)						)
			return final[::-1]


if __name__ == "__main__":
			import doctest

			doctest.testmod()
			__snake_case      = [
			    [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]]))







'''simple docstring'''



from ...configuration_utils import PretrainedConfig
from ...utils import logging


UpperCAmelCase					:			Union[str, Any]       =	logging.get_logger(__name__)

UpperCAmelCase					:			Any       =	{
    'uw-madison/mra-base-512-4': 'https://huggingface.co/uw-madison/mra-base-512-4/resolve/main/config.json',
}







class 		lowerCAmelCase__  ( a   ):



 """simple docstring"""



 lowerCAmelCase__       = "mra"
 def __init__(						self   :			Tuple   ,				__SCREAMING_SNAKE_CASE   :			Dict=50_265   ,				__SCREAMING_SNAKE_CASE   :			Union[str, Any]=768   ,				__SCREAMING_SNAKE_CASE   :			int=12   ,				__SCREAMING_SNAKE_CASE   :			List[Any]=12   ,				__SCREAMING_SNAKE_CASE   :			Union[str, Any]=3_072   ,				__SCREAMING_SNAKE_CASE   :			Optional[Any]="gelu"   ,				__SCREAMING_SNAKE_CASE   :			List[str]=0.1   ,				__SCREAMING_SNAKE_CASE   :			List[Any]=0.1   ,				__SCREAMING_SNAKE_CASE   :			List[Any]=512   ,				__SCREAMING_SNAKE_CASE   :			Union[str, Any]=1   ,				__SCREAMING_SNAKE_CASE   :			Any=0.02   ,				__SCREAMING_SNAKE_CASE   :			Optional[Any]=1E-5   ,				__SCREAMING_SNAKE_CASE   :			str="absolute"   ,				__SCREAMING_SNAKE_CASE   :			List[Any]=4   ,				__SCREAMING_SNAKE_CASE   :			Optional[Any]="full"   ,				__SCREAMING_SNAKE_CASE   :			str=0   ,				__SCREAMING_SNAKE_CASE   :			Dict=0   ,				__SCREAMING_SNAKE_CASE   :			Optional[Any]=1   ,				__SCREAMING_SNAKE_CASE   :			Dict=0   ,				__SCREAMING_SNAKE_CASE   :			Dict=2   ,				**__SCREAMING_SNAKE_CASE   :			Optional[int]   ,				)    ->					Tuple:


      """simple docstring"""




      super().__init__(pad_token_id=__SCREAMING_SNAKE_CASE   ,				bos_token_id=__SCREAMING_SNAKE_CASE   ,				eos_token_id=__SCREAMING_SNAKE_CASE   ,				**__SCREAMING_SNAKE_CASE     )

      __SCREAMING_SNAKE_CASE      = vocab_size
      __SCREAMING_SNAKE_CASE      = max_position_embeddings
      __SCREAMING_SNAKE_CASE      = hidden_size
      __SCREAMING_SNAKE_CASE      = num_hidden_layers
      __SCREAMING_SNAKE_CASE      = num_attention_heads
      __SCREAMING_SNAKE_CASE      = intermediate_size
      __SCREAMING_SNAKE_CASE      = hidden_act
      __SCREAMING_SNAKE_CASE      = hidden_dropout_prob
      __SCREAMING_SNAKE_CASE      = attention_probs_dropout_prob
      __SCREAMING_SNAKE_CASE      = initializer_range
      __SCREAMING_SNAKE_CASE      = type_vocab_size
      __SCREAMING_SNAKE_CASE      = layer_norm_eps
      __SCREAMING_SNAKE_CASE      = position_embedding_type
      __SCREAMING_SNAKE_CASE      = block_per_row
      __SCREAMING_SNAKE_CASE      = approx_mode
      __SCREAMING_SNAKE_CASE      = initial_prior_first_n_blocks
      __SCREAMING_SNAKE_CASE      = initial_prior_diagonal_n_blocks






