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


def     lowerCamelCase_    (	lowerCamelCase_	,				lowerCamelCase_ )     ->			NDArray[floataa]:


					'''simple docstring'''
					__a    ,				__a:						Optional[int]		    =					np.shape(lowerCamelCase_ )

					__a:						NDArray[floataa]		    =					np.zeros((rows, 1)	,				dtype=lowerCamelCase_ )
					for row in reversed(range(lowerCamelCase_ ) ):
										__a:						Tuple		    =					0
										for col in range(row + 1	,				lowerCamelCase_ ):
															total += coefficients[row, col] * x[col]

										__a:						Any		    =					(vector[row] - total) / coefficients[row, row]

					return x


def     lowerCamelCase_    (	lowerCamelCase_	,				lowerCamelCase_ )     ->			NDArray[floataa]:


					'''simple docstring'''
					__a    ,				__a:						Union[str, Any]		    =					np.shape(lowerCamelCase_ )
					if rows != columns:
										return np.array(()	,				dtype=lowerCamelCase_ )

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

					# scale the matrix leaving it triangular
					for row in range(rows - 1 ):
										__a:						Union[str, Any]		    =					augmented_mat[row, row]
										for col in range(row + 1	,				lowerCamelCase_ ):
															__a:						Union[str, Any]		    =					augmented_mat[col, row] / pivot
															augmented_mat[col, :] -= factor * augmented_mat[row, :]

					__a:						Any		    =					retroactive_resolution(
					    augmented_mat[:, 0:columns]	,				augmented_mat[:, columns : columns + 1] )

					return x


if __name__ == "__main__":
			import doctest

			doctest.testmod()


"""simple docstring"""
def     lowerCamelCase_    (	lowerCamelCase_	,				lowerCamelCase_ )     ->			int:


					'''simple docstring'''
					for index, item in enumerate(lowerCamelCase_ ):
										if item == target:
															return index
					return -1


def     lowerCamelCase_    (	lowerCamelCase_	,				lowerCamelCase_	,				lowerCamelCase_	,				lowerCamelCase_ )     ->			int:


					'''simple docstring'''
					if not (0 <= high < len(lowerCamelCase_ ) and 0 <= low < len(lowerCamelCase_ )):
										raise Exception("""Invalid upper or lower bound!""" )
					if high < low:
										return -1
					if sequence[low] == target:
										return low
					if sequence[high] == target:
										return high
					return rec_linear_search(lowerCamelCase_	,				low + 1	,				high - 1	,				lowerCamelCase_ )


if __name__ == "__main__":
			lowercase		:						str =					input('Enter numbers separated by comma:\n').strip()
			lowercase		:						int =					[int(item.strip()) for item in user_input.split(',')]

			lowercase		:						Optional[Any] =					int(input('Enter a single number to be found in the list:\n').strip())
			lowercase		:						str =					linear_search(sequence, target)
			if result != -1:
						print(F"linear_search({sequence}, {target}) = {result}")
			else:
						print(F"{target} was not found in {sequence}")
