



"""simple docstring"""


import unittest

from .lib import (
    Matrix,
    Vector,
    axpy,
    square_zero_matrix,
    unit_basis_vector,
    zero_vector,
)







class       A_			(     unittest.TestCase				):



						"""simple docstring"""






						def 	UpperCAmelCase__     (					self :Optional[int]					)				->			None:
												UpperCAmelCase             = Vector([1, 2, 3]					)
												self.assertEqual(x.component(0					)   ,  1					)
												self.assertEqual(x.component(2					)   ,  3					)
												UpperCAmelCase             = Vector()






						def 	UpperCAmelCase__     (					self :Optional[int]					)				->			None:
												UpperCAmelCase             = Vector([0, 0, 0, 0, 0, 1]					)
												self.assertEqual(str(lowercase_					)   ,  '(0,0,0,0,0,1)'					)






						def 	UpperCAmelCase__     (					self :Union[str, Any]					)				->			None:
												UpperCAmelCase             = Vector([1, 2, 3, 4]					)
												self.assertEqual(len(lowercase_					)   ,  4					)






						def 	UpperCAmelCase__     (					self :Optional[int]					)				->			None:
												UpperCAmelCase             = Vector([1, 2]					)
												UpperCAmelCase             = Vector([1, 2, 3, 4, 5]					)
												UpperCAmelCase             = Vector([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]					)
												UpperCAmelCase             = 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 	UpperCAmelCase__     (					self :Dict					)				->			None:
												UpperCAmelCase             = Vector([1, 2, 3]					)
												UpperCAmelCase             = 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 	UpperCAmelCase__     (					self :Tuple					)				->			None:
												UpperCAmelCase             = Vector([1, 2, 3]					)
												UpperCAmelCase             = 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 	UpperCAmelCase__     (					self :Optional[int]					)				->			None:
												UpperCAmelCase             = Vector([1, 2, 3]					)
												UpperCAmelCase             = Vector([2, -1, 4]					)  # for test of dot product
												UpperCAmelCase             = Vector([1, -2, -1]					)
												self.assertEqual(str(x * 3.0					)   ,  '(3.0,6.0,9.0)'					)
												self.assertEqual((a * b)   ,  0					)






						def 	UpperCAmelCase__     (					self :Optional[int]					)				->			None:
												self.assertEqual(str(zero_vector(10					)					).count('0'					)   ,  10					)






						def 	UpperCAmelCase__     (					self :List[Any]					)				->			None:
												self.assertEqual(str(unit_basis_vector(3   ,  1					)					)   ,  '(0,1,0)'					)






						def 	UpperCAmelCase__     (					self :Dict					)				->			None:
												UpperCAmelCase             = Vector([1, 2, 3]					)
												UpperCAmelCase             = Vector([1, 0, 1]					)
												self.assertEqual(str(axpy(2   ,  lowercase_   ,  lowercase_					)					)   ,  '(3,4,7)'					)






						def 	UpperCAmelCase__     (					self :Tuple					)				->			None:
												UpperCAmelCase             = Vector([1, 0, 0, 0, 0, 0]					)
												UpperCAmelCase             = x.copy()
												self.assertEqual(str(lowercase_					)   ,  str(lowercase_					)					)






						def 	UpperCAmelCase__     (					self :List[str]					)				->			None:
												UpperCAmelCase             = Vector([1, 0, 0]					)
												x.change_component(0   ,  0					)
												x.change_component(1   ,  1					)
												self.assertEqual(str(lowercase_					)   ,  '(0,1,0)'					)






						def 	UpperCAmelCase__     (					self :str					)				->			None:
												UpperCAmelCase             = 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(lowercase_					)					)






						def 	UpperCAmelCase__     (					self :Union[str, Any]					)				->			None:
												UpperCAmelCase             = Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]   ,  3   ,  3					)
												UpperCAmelCase             = [[-3, -14, -10], [-5, -10, -5], [-2, -1, 0]]
												for x in range(a.height()					):
																		for y in range(a.width()					):
																								self.assertEqual(minors[x][y]   ,  a.minor(lowercase_   ,  lowercase_					)					)






						def 	UpperCAmelCase__     (					self :Optional[Any]					)				->			None:
												UpperCAmelCase             = Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]   ,  3   ,  3					)
												UpperCAmelCase             = [[-3, 14, -10], [5, -10, 5], [-2, 1, 0]]
												for x in range(a.height()					):
																		for y in range(a.width()					):
																								self.assertEqual(cofactors[x][y]   ,  a.cofactor(lowercase_   ,  lowercase_					)					)






						def 	UpperCAmelCase__     (					self :Optional[Any]					)				->			None:
												UpperCAmelCase             = Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]   ,  3   ,  3					)
												self.assertEqual(-5   ,  a.determinant()					)






						def 	UpperCAmelCase__     (					self :Union[str, Any]					)				->			None:
												UpperCAmelCase             = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]   ,  3   ,  3					)
												UpperCAmelCase             = 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 	UpperCAmelCase__     (					self :List[Any]					)				->			None:
												UpperCAmelCase             = 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(lowercase_					)					)






						def 	UpperCAmelCase__     (					self :int					)				->			None:
												UpperCAmelCase             = Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]   ,  3   ,  3					)
												self.assertEqual(7   ,  a.component(2   ,  1					)   ,  0.01					)






						def 	UpperCAmelCase__     (					self :Optional[Any]					)				->			None:
												UpperCAmelCase             = Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]   ,  3   ,  3					)
												UpperCAmelCase             = Matrix([[1, 2, 7], [2, 4, 5], [6, 7, 10]]   ,  3   ,  3					)
												self.assertEqual('|2,4,10|\n|4,8,10|\n|12,14,18|\n'   ,  str(a + b					)					)






						def 	UpperCAmelCase__     (					self :str					)				->			None:
												UpperCAmelCase             = Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]   ,  3   ,  3					)
												UpperCAmelCase             = Matrix([[1, 2, 7], [2, 4, 5], [6, 7, 10]]   ,  3   ,  3					)
												self.assertEqual('|0,0,-4|\n|0,0,0|\n|0,0,-2|\n'   ,  str(a - b					)					)






						def 	UpperCAmelCase__     (					self :Optional[Any]					)				->			None:
												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()









"""simple docstring"""







from __future__ import annotations




def    UpperCAmelCase__       (lowerCAmelCase_  ,						lowerCAmelCase_ = None  ,						lowerCAmelCase_ = None   ):




					'''simple docstring'''


					if start is None:
										__SCREAMING_SNAKE_CASE						   =				0

					if end is None:
										__SCREAMING_SNAKE_CASE						   =				len(lowerCAmelCase_   ) - 1

					if start >= end:
										return

					__SCREAMING_SNAKE_CASE						   =				(start + end) // 2

					slowsort(lowerCAmelCase_  ,						lowerCAmelCase_  ,						lowerCAmelCase_   )
					slowsort(lowerCAmelCase_  ,						mid + 1  ,						lowerCAmelCase_   )

					if sequence[end] < sequence[mid]:
										__SCREAMING_SNAKE_CASE   ,  __SCREAMING_SNAKE_CASE						   =				sequence[mid], sequence[end]

					slowsort(lowerCAmelCase_  ,						lowerCAmelCase_  ,						end - 1   )


if __name__ == "__main__":
		from doctest import testmod

		testmod()
