






import numpy as np

def      __lowercase					( snake_case,  snake_case ):







				"""simple docstring"""






				return np.where(vector > 0,  snake_case,  (alpha * (np.exp(snake_case ) - 1)) )


if __name__ == "__main__":
					import doctest

					doctest.testmod()














import unittest

from .lib import (
    Matrix,
    Vector,
    axpy,
    square_zero_matrix,
    unit_basis_vector,
    zero_vector,
)
class 						lowerCamelCase_				(      unittest.TestCase ):







				def 			A	(						self     ):
								"""simple docstring"""
								__magic_name__		:Union[str, Any]        =      Vector([1, 2, 3]     )
								self.assertEqual(x.component(0     )       ,					1     )
								self.assertEqual(x.component(2     )       ,					3     )
								__magic_name__		:Tuple        =      Vector()







				def 			A	(						self     ):
								"""simple docstring"""
								__magic_name__		:Any        =      Vector([0, 0, 0, 0, 0, 1]     )
								self.assertEqual(str(__lowerCAmelCase     )       ,					'''(0,0,0,0,0,1)'''     )







				def 			A	(						self     ):
								"""simple docstring"""
								__magic_name__		:Optional[int]        =      Vector([1, 2, 3, 4]     )
								self.assertEqual(len(__lowerCAmelCase     )       ,					4     )







				def 			A	(						self     ):
								"""simple docstring"""
								__magic_name__		:Optional[Any]        =      Vector([1, 2]     )
								__magic_name__		:int        =      Vector([1, 2, 3, 4, 5]     )
								__magic_name__		:Any        =      Vector([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]     )
								__magic_name__		:Optional[Any]        =      Vector([1, -1, 1, -1, 2, -3, 4, -5]     )
								self.assertAlmostEqual(x.euclidean_length()       ,					2.236       ,					3     )
								self.assertAlmostEqual(y.euclidean_length()       ,					7.416       ,					3     )
								self.assertEqual(z.euclidean_length()       ,					0     )
								self.assertAlmostEqual(w.euclidean_length()       ,					7.616       ,					3     )







				def 			A	(						self     ):
								"""simple docstring"""
								__magic_name__		:Union[str, Any]        =      Vector([1, 2, 3]     )
								__magic_name__		:List[str]        =      Vector([1, 1, 1]     )
								self.assertEqual((x + y).component(0     )       ,					2     )
								self.assertEqual((x + y).component(1     )       ,					3     )
								self.assertEqual((x + y).component(2     )       ,					4     )







				def 			A	(						self     ):
								"""simple docstring"""
								__magic_name__		:List[str]        =      Vector([1, 2, 3]     )
								__magic_name__		:Union[str, Any]        =      Vector([1, 1, 1]     )
								self.assertEqual((x - y).component(0     )       ,					0     )
								self.assertEqual((x - y).component(1     )       ,					1     )
								self.assertEqual((x - y).component(2     )       ,					2     )







				def 			A	(						self     ):
								"""simple docstring"""
								__magic_name__		:int        =      Vector([1, 2, 3]     )
								__magic_name__		:Optional[int]        =      Vector([2, -1, 4]     )  # for test of dot product
								__magic_name__		:List[Any]        =      Vector([1, -2, -1]     )
								self.assertEqual(str(x * 3.0     )       ,					'''(3.0,6.0,9.0)'''     )
								self.assertEqual((a * b)       ,					0     )







				def 			A	(						self     ):
								"""simple docstring"""
								self.assertEqual(str(zero_vector(1_0     )     ).count('''0'''     )       ,					1_0     )







				def 			A	(						self     ):
								"""simple docstring"""
								self.assertEqual(str(unit_basis_vector(3       ,					1     )     )       ,					'''(0,1,0)'''     )







				def 			A	(						self     ):
								"""simple docstring"""
								__magic_name__		:Dict        =      Vector([1, 2, 3]     )
								__magic_name__		:List[Any]        =      Vector([1, 0, 1]     )
								self.assertEqual(str(axpy(2       ,					__lowerCAmelCase       ,					__lowerCAmelCase     )     )       ,					'''(3,4,7)'''     )







				def 			A	(						self     ):
								"""simple docstring"""
								__magic_name__		:List[str]        =      Vector([1, 0, 0, 0, 0, 0]     )
								__magic_name__		:Optional[int]        =      x.copy()
								self.assertEqual(str(__lowerCAmelCase     )       ,					str(__lowerCAmelCase     )     )







				def 			A	(						self     ):
								"""simple docstring"""
								__magic_name__		:List[str]        =      Vector([1, 0, 0]     )
								x.change_component(0       ,					0     )
								x.change_component(1       ,					1     )
								self.assertEqual(str(__lowerCAmelCase     )       ,					'''(0,1,0)'''     )







				def 			A	(						self     ):
								"""simple docstring"""
								__magic_name__		:Any        =      Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]       ,					3       ,					3     )
								self.assertEqual('''|1,2,3|\n|2,4,5|\n|6,7,8|\n'''       ,					str(__lowerCAmelCase     )     )







				def 			A	(						self     ):
								"""simple docstring"""
								__magic_name__		:Union[str, Any]        =      Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]       ,					3       ,					3     )
								__magic_name__		:List[str]        =      [[-3, -1_4, -1_0], [-5, -1_0, -5], [-2, -1, 0]]
								for x in range(a.height()     ):
												for y in range(a.width()     ):
																self.assertEqual(minors[x][y]       ,					a.minor(__lowerCAmelCase       ,					__lowerCAmelCase     )     )







				def 			A	(						self     ):
								"""simple docstring"""
								__magic_name__		:int        =      Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]       ,					3       ,					3     )
								__magic_name__		:Any        =      [[-3, 1_4, -1_0], [5, -1_0, 5], [-2, 1, 0]]
								for x in range(a.height()     ):
												for y in range(a.width()     ):
																self.assertEqual(cofactors[x][y]       ,					a.cofactor(__lowerCAmelCase       ,					__lowerCAmelCase     )     )







				def 			A	(						self     ):
								"""simple docstring"""
								__magic_name__		:Tuple        =      Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]       ,					3       ,					3     )
								self.assertEqual(-5       ,					a.determinant()     )







				def 			A	(						self     ):
								"""simple docstring"""
								__magic_name__		:str        =      Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]       ,					3       ,					3     )
								__magic_name__		:Any        =      Vector([1, 2, 3]     )
								self.assertEqual('''(14,32,50)'''       ,					str(a * x     )     )
								self.assertEqual('''|2,4,6|\n|8,10,12|\n|14,16,18|\n'''       ,					str(a * 2     )     )







				def 			A	(						self     ):
								"""simple docstring"""
								__magic_name__		:List[Any]        =      Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]       ,					3       ,					3     )
								a.change_component(0       ,					2       ,					5     )
								self.assertEqual('''|1,2,5|\n|2,4,5|\n|6,7,8|\n'''       ,					str(__lowerCAmelCase     )     )







				def 			A	(						self     ):
								"""simple docstring"""
								__magic_name__		:List[Any]        =      Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]       ,					3       ,					3     )
								self.assertEqual(7       ,					a.component(2       ,					1     )       ,					0.01     )







				def 			A	(						self     ):
								"""simple docstring"""
								__magic_name__		:List[str]        =      Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]       ,					3       ,					3     )
								__magic_name__		:Optional[Any]        =      Matrix([[1, 2, 7], [2, 4, 5], [6, 7, 1_0]]       ,					3       ,					3     )
								self.assertEqual('''|2,4,10|\n|4,8,10|\n|12,14,18|\n'''       ,					str(a + b     )     )







				def 			A	(						self     ):
								"""simple docstring"""
								__magic_name__		:Dict        =      Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]       ,					3       ,					3     )
								__magic_name__		:Union[str, Any]        =      Matrix([[1, 2, 7], [2, 4, 5], [6, 7, 1_0]]       ,					3       ,					3     )
								self.assertEqual('''|0,0,-4|\n|0,0,0|\n|0,0,-2|\n'''       ,					str(a - b     )     )







				def 			A	(						self     ):
								"""simple docstring"""
								self.assertEqual(
								    '''|0,0,0,0,0|\n|0,0,0,0,0|\n|0,0,0,0,0|\n|0,0,0,0,0|\n|0,0,0,0,0|\n'''       ,					str(square_zero_matrix(5     )     )       ,					)


if __name__ == "__main__":
					unittest.main()






