
'''simple docstring'''
def    _UpperCamelCase						(       SCREAMING_SNAKE_CASE__			)  ->							list[list]:


		'''simple docstring'''


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




def    _UpperCamelCase						(       SCREAMING_SNAKE_CASE__			)  ->							list:


		'''simple docstring'''


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


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						lowercase__						       =      [
						    [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'''
import numpy as np




def    _UpperCamelCase						(       SCREAMING_SNAKE_CASE__			)  ->							np.ndarray:


		'''simple docstring'''


		return 1 / (1 + np.exp(-vector			))




def    _UpperCamelCase						(       SCREAMING_SNAKE_CASE__			)  ->							np.ndarray:


		'''simple docstring'''


		return vector * sigmoid(SCREAMING_SNAKE_CASE__			)


if __name__ == "__main__":
						import doctest

						doctest.testmod()


