


'''simple docstring'''



def       _UpperCamelCase (						UpperCamelCase__	, UpperCamelCase__	, UpperCamelCase__   ):
			UpperCAmelCase__					:   Any       				=       len(UpperCamelCase__   )
			UpperCAmelCase__					:   List[Any]       				=       [[0] * n for i in range(UpperCamelCase__   )]
			for i in range(UpperCamelCase__   ):
						UpperCAmelCase__					:   Dict       				=       y_points[i]

			for i in range(2	, UpperCamelCase__   ):
						for j in range(UpperCamelCase__	, UpperCamelCase__   ):
									UpperCAmelCase__					:   int       				=       (
									    (xa - x_points[j - i + 1]) * q[j][i - 1]
									    - (xa - x_points[j]) * q[j - 1][i - 1]
									) / (x_points[j] - x_points[j - i + 1])

			return [q[n - 1][n - 1], q]


if __name__ == "__main__":
		import doctest

		doctest.testmod()



'''simple docstring'''



import unittest

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


class 						_snake_case   (       unittest.TestCase		):




					def 			snake_case__  ( self):
								UpperCAmelCase__					:   str       				=       Vector([1, 2, 3])
								self.assertEqual(x.component(0)							,							1)
								self.assertEqual(x.component(2)							,							3)
								UpperCAmelCase__					:   List[str]       				=       Vector()




					def 			snake_case__  ( self):
								UpperCAmelCase__					:   Any       				=       Vector([0, 0, 0, 0, 0, 1])
								self.assertEqual(str(_lowerCamelCase)							,							"""(0,0,0,0,0,1)""")




					def 			snake_case__  ( self):
								UpperCAmelCase__					:   Optional[int]       				=       Vector([1, 2, 3, 4])
								self.assertEqual(len(_lowerCamelCase)							,							4)




					def 			snake_case__  ( self):
								UpperCAmelCase__					:   List[str]       				=       Vector([1, 2])
								UpperCAmelCase__					:   Optional[int]       				=       Vector([1, 2, 3, 4, 5])
								UpperCAmelCase__					:   Optional[Any]       				=       Vector([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])
								UpperCAmelCase__					:   Union[str, 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 			snake_case__  ( self):
								UpperCAmelCase__					:   int       				=       Vector([1, 2, 3])
								UpperCAmelCase__					:   Optional[Any]       				=       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 			snake_case__  ( self):
								UpperCAmelCase__					:   Optional[int]       				=       Vector([1, 2, 3])
								UpperCAmelCase__					:   Dict       				=       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 			snake_case__  ( self):
								UpperCAmelCase__					:   Tuple       				=       Vector([1, 2, 3])
								UpperCAmelCase__					:   Optional[int]       				=       Vector([2, -1, 4])  # for test of dot product
								UpperCAmelCase__					:   Any       				=       Vector([1, -2, -1])
								self.assertEqual(str(x * 3.0)							,							"""(3.0,6.0,9.0)""")
								self.assertEqual((a * b)							,							0)




					def 			snake_case__  ( self):
								self.assertEqual(str(zero_vector(10)).count("""0""")							,							10)




					def 			snake_case__  ( self):
								self.assertEqual(str(unit_basis_vector(3							,							1))							,							"""(0,1,0)""")




					def 			snake_case__  ( self):
								UpperCAmelCase__					:   Any       				=       Vector([1, 2, 3])
								UpperCAmelCase__					:   List[str]       				=       Vector([1, 0, 1])
								self.assertEqual(str(axpy(2							,							_lowerCamelCase							,							_lowerCamelCase))							,							"""(3,4,7)""")




					def 			snake_case__  ( self):
								UpperCAmelCase__					:   Optional[int]       				=       Vector([1, 0, 0, 0, 0, 0])
								UpperCAmelCase__					:   Optional[int]       				=       x.copy()
								self.assertEqual(str(_lowerCamelCase)							,							str(_lowerCamelCase))




					def 			snake_case__  ( self):
								UpperCAmelCase__					:   str       				=       Vector([1, 0, 0])
								x.change_component(0							,							0)
								x.change_component(1							,							1)
								self.assertEqual(str(_lowerCamelCase)							,							"""(0,1,0)""")




					def 			snake_case__  ( self):
								UpperCAmelCase__					:   str       				=       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 			snake_case__  ( self):
								UpperCAmelCase__					:   List[str]       				=       Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]							,							3							,							3)
								UpperCAmelCase__					:   Dict       				=       [[-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(_lowerCamelCase							,							_lowerCamelCase))




					def 			snake_case__  ( self):
								UpperCAmelCase__					:   Any       				=       Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]							,							3							,							3)
								UpperCAmelCase__					:   Tuple       				=       [[-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(_lowerCamelCase							,							_lowerCamelCase))




					def 			snake_case__  ( self):
								UpperCAmelCase__					:   Any       				=       Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]							,							3							,							3)
								self.assertEqual(-5							,							a.determinant())




					def 			snake_case__  ( self):
								UpperCAmelCase__					:   str       				=       Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]							,							3							,							3)
								UpperCAmelCase__					:   List[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 			snake_case__  ( self):
								UpperCAmelCase__					:   Union[str, 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 			snake_case__  ( self):
								UpperCAmelCase__					:   Any       				=       Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]							,							3							,							3)
								self.assertEqual(7							,							a.component(2							,							1)							,							0.01)




					def 			snake_case__  ( self):
								UpperCAmelCase__					:   str       				=       Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]							,							3							,							3)
								UpperCAmelCase__					:   List[Any]       				=       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 			snake_case__  ( self):
								UpperCAmelCase__					:   List[Any]       				=       Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]							,							3							,							3)
								UpperCAmelCase__					:   Dict       				=       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 			snake_case__  ( self):
								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()