






'''simple docstring'''
import numpy as np
from numpy import floataa
from numpy.typing import NDArray


def   lowercase_	(   lowerCAmelCase__	:  NDArray[floataa]			,							lowerCAmelCase__	:  NDArray[floataa] ):

			"""simple docstring"""





			__UpperCAmelCase   :      int										=     np.shape(lowerCAmelCase__ )

			__UpperCAmelCase   :      NDArray[floataa]										=     np.zeros((rows, 1)			,							dtype=lowerCAmelCase__ )
			for row in reversed(range(lowerCAmelCase__ ) ):
						__UpperCAmelCase   :      Optional[Any]										=     0
						for col in range(row + 1			,							lowerCAmelCase__ ):
									total += coefficients[row, col] * x[col]

						__UpperCAmelCase   :      str										=     (vector[row] - total) / coefficients[row, row]

			return x


def   lowercase_	(   lowerCAmelCase__	:  NDArray[floataa]			,							lowerCAmelCase__	:  NDArray[floataa] ):

			"""simple docstring"""





			__UpperCAmelCase   :      Optional[Any]										=     np.shape(lowerCAmelCase__ )
			if rows != columns:
						return np.array(()			,							dtype=lowerCAmelCase__ )

			# augmented matrix
			__UpperCAmelCase   :      NDArray[floataa]										=     np.concatenate((coefficients, vector)			,							axis=1 )
			__UpperCAmelCase   :      Tuple										=     augmented_mat.astype("""float64""" )

			# scale the matrix leaving it triangular
			for row in range(rows - 1 ):
						__UpperCAmelCase   :      Tuple										=     augmented_mat[row, row]
						for col in range(row + 1			,							lowerCAmelCase__ ):
									__UpperCAmelCase   :      Optional[int]										=     augmented_mat[col, row] / pivot
									augmented_mat[col, :] -= factor * augmented_mat[row, :]

			__UpperCAmelCase   :      Union[str, Any]										=     retroactive_resolution(
			    augmented_mat[:, 0:columns]			,							augmented_mat[:, columns : columns + 1] )

			return x


if __name__ == "__main__":
					import doctest

					doctest.testmod()









'''simple docstring'''
import torch

from transformers import AutoTokenizer



class _A  (    __SCREAMING_SNAKE_CASE    ):





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

					'''simple docstring'''
					__UpperCAmelCase   :      Any										=     AutoTokenizer.from_pretrained(__UpperCAmelCase				)





		def 							__A       (     self ,       __UpperCAmelCase				)       ->     Any:

					'''simple docstring'''

					if isinstance(__UpperCAmelCase ,       __UpperCAmelCase				) and all(isinstance(_x ,       __UpperCAmelCase				) for _x in x				):
								__UpperCAmelCase   :      Dict										=     None
								for l in x:
											__UpperCAmelCase   :      Dict										=     self.tokenizer(
											    __UpperCAmelCase ,       padding="""max_length""" ,       max_length=384 ,       truncation=__UpperCAmelCase ,       return_tensors="""pt""" ,       )
											__UpperCAmelCase   :      Union[str, Any]										=     torch.tensor([len(__UpperCAmelCase				)]				)
											if d is not None:
														for k in d.keys():
																	__UpperCAmelCase   :      Dict										=     torch.cat((d[k], t[k]) ,       0				)
											else:
														__UpperCAmelCase   :      List[str]										=     t

								__UpperCAmelCase   :      Union[str, Any]										=     torch.tensor(self.tokenizer.convert_tokens_to_ids("""[E]"""				)				)
								__UpperCAmelCase   :      Any										=     torch.tensor(self.tokenizer.convert_tokens_to_ids("""[/E]"""				)				)

					elif isinstance(__UpperCAmelCase ,       __UpperCAmelCase				) and all(isinstance(_x ,       __UpperCAmelCase				) for _x in x				):
								__UpperCAmelCase   :      int										=     self.tokenizer(
								    __UpperCAmelCase ,       padding="""max_length""" ,       max_length=384 ,       truncation=__UpperCAmelCase ,       return_tensors="""pt""" ,       )

					else:
								raise Exception(
								    """Type of parameter x was not recognized! Only `list of strings` for query or `list of lists of"""
								    """ strings` for supports are supported."""				)

					return d





		def 							__A       (     self ,       __UpperCAmelCase ,       __UpperCAmelCase ,       __UpperCAmelCase ,       __UpperCAmelCase ,       __UpperCAmelCase=0.70				)       ->     Dict:

					'''simple docstring'''
					__UpperCAmelCase   :      Tuple										=     []
					for idx in range(len(W_query["""input_ids"""]				)				):
								__UpperCAmelCase   :      Optional[int]										=     range(p_start.shape[1]				)

								__UpperCAmelCase   :      Union[str, Any]										=     []
								for start_id in start_indexes:
											for end_id in end_indexes:
														if start_id < end_id:
																	output.append(
																	    (
																	        start_id,
																	        end_id,
																	        p_start[idx][start_id].item(),
																	        p_end[idx][end_id].item(),
																	    )				)

								output.sort(key=lambda __UpperCAmelCase				: (tup[2] * tup[3]) ,       reverse=__UpperCAmelCase				)
								__UpperCAmelCase   :      Optional[Any]										=     []
								for k in range(len(__UpperCAmelCase				)				):
											if output[k][2] * output[k][3] >= thresh:
														__UpperCAmelCase				,  __UpperCAmelCase   :      Tuple										=     output[k][0], output[k][1]
														__UpperCAmelCase   :      int										=     self.tokenizer.decode(W_query["""input_ids"""][idx][c_start_pos:c_end_pos]				)
														temp.append((decoded, output[k][2] * output[k][3])				)

								final_outputs.append(__UpperCAmelCase				)

					return final_outputs




