






def    UpperCamelCase						(	_A			):






						"""simple docstring"""







						__magic_name__      :       List[str]       						= current_set.copy()
						for row_index, row in enumerate(_A			):
												__magic_name__      :       Dict       						= row[0]
												for column_index, column in enumerate(_A			):
																		if magnitude == 0:
																								__magic_name__      :       int       						= column
																								continue
																		__magic_name__      :       Any       						= column / magnitude
    # Subtract to cancel term
						__magic_name__      :       Tuple       						= current_set[0]
						__magic_name__      :       int       						= [first_row]
						__magic_name__      :       Optional[Any]       						= current_set[1::]
						for row in current_set:
												__magic_name__      :       Any       						= []
												# 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:
												__magic_name__      :       int       						= final_set[0]
												__magic_name__      :       Optional[int]       						= []
												__magic_name__      :       Dict       						= []
												for row in final_set[1::]:
																		current_first_column.append(row[0]			)
																		next_iteration.append(row[1::]			)
												__magic_name__      :       List[str]       						= simplify(_A			)
												for i in range(len(_A			)			):
																		resultant[i].insert(0,   current_first_column[i]			)
												resultant.insert(0,   _A			)
												__magic_name__      :       List[Any]       						= resultant
						return final_set

def    UpperCamelCase						(	_A			):






						"""simple docstring"""







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


if __name__ == "__main__":
		import doctest

		doctest.testmod()
		__magic_name__:					str							=     [
		    [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]]))








from __future__ import annotations

import math

import numpy as np
from numpy.linalg import norm

def    UpperCamelCase						(	_A,   _A			):






						"""simple docstring"""







						return math.sqrt(sum(pow(a - b,   2			) for a, b in zip(_A,   _A			)			)			)

def    UpperCamelCase						(	_A,   _A			):






						"""simple docstring"""







						if dataset.ndim != value_array.ndim:
												__magic_name__      :       str       						= (
												    """Wrong input data's dimensions... """
												    f'dataset : {dataset.ndim}, value_array : {value_array.ndim}'
												)
												raise ValueError(_A			)

						try:
												if dataset.shape[1] != value_array.shape[1]:
																		__magic_name__      :       Optional[Any]       						= (
																		    """Wrong input data's shape... """
																		    f'dataset : {dataset.shape[1]}, value_array : {value_array.shape[1]}'
																		)
																		raise ValueError(_A			)
						except IndexError:
												if dataset.ndim != value_array.ndim:
																		raise TypeError("""Wrong shape"""			)

						if dataset.dtype != value_array.dtype:
												__magic_name__      :       List[Any]       						= (
												    """Input data have different datatype... """
												    f'dataset : {dataset.dtype}, value_array : {value_array.dtype}'
												)
												raise TypeError(_A			)

						__magic_name__      :       Dict       						= []

						for value in value_array:
												__magic_name__      :       Tuple       						= euclidean(_A,   dataset[0]			)
												__magic_name__      :       Any       						= dataset[0].tolist()

												for dataset_value in dataset[1:]:
																		__magic_name__      :       Any       						= euclidean(_A,   _A			)

																		if dist > temp_dist:
																								__magic_name__      :       Dict       						= temp_dist
																								__magic_name__      :       Any       						= dataset_value.tolist()

												answer.append([vector, dist]			)

						return answer

def    UpperCamelCase						(	_A,   _A			):






						"""simple docstring"""







						return np.dot(_A,   _A			) / (norm(_A			) * norm(_A			))


if __name__ == "__main__":
		import doctest

		doctest.testmod()
