



"""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 :int					)				->			List[str]:
												UpperCAmelCase             = Vector([1, 2, 3]					)
												self.assertEqual(x.component(0					)   ,  1					)
												self.assertEqual(x.component(2					)   ,  3					)
												UpperCAmelCase             = Vector()






						def 	UpperCAmelCase__     (					self :Tuple					)				->			Optional[int]:
												UpperCAmelCase             = Vector([0, 0, 0, 0, 0, 1]					)
												self.assertEqual(str(a_					)   ,  '(0,0,0,0,0,1)'					)






						def 	UpperCAmelCase__     (					self :List[str]					)				->			Dict:
												UpperCAmelCase             = Vector([1, 2, 3, 4]					)
												self.assertEqual(len(a_					)   ,  4					)






						def 	UpperCAmelCase__     (					self :List[Any]					)				->			Union[str, Any]:
												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 :Optional[int]					)				->			Optional[Any]:
												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 :List[str]					)				->			Any:
												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 :Any					)				->			str:
												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 :List[Any]					)				->			Dict:
												self.assertEqual(str(zero_vector(10					)					).count('0'					)   ,  10					)






						def 	UpperCAmelCase__     (					self :List[str]					)				->			Tuple:
												self.assertEqual(str(unit_basis_vector(3   ,  1					)					)   ,  '(0,1,0)'					)






						def 	UpperCAmelCase__     (					self :Optional[int]					)				->			str:
												UpperCAmelCase             = Vector([1, 2, 3]					)
												UpperCAmelCase             = Vector([1, 0, 1]					)
												self.assertEqual(str(axpy(2   ,  a_   ,  a_					)					)   ,  '(3,4,7)'					)






						def 	UpperCAmelCase__     (					self :Union[str, Any]					)				->			Optional[Any]:
												UpperCAmelCase             = Vector([1, 0, 0, 0, 0, 0]					)
												UpperCAmelCase             = x.copy()
												self.assertEqual(str(a_					)   ,  str(a_					)					)






						def 	UpperCAmelCase__     (					self :Any					)				->			List[Any]:
												UpperCAmelCase             = Vector([1, 0, 0]					)
												x.change_component(0   ,  0					)
												x.change_component(1   ,  1					)
												self.assertEqual(str(a_					)   ,  '(0,1,0)'					)






						def 	UpperCAmelCase__     (					self :Dict					)				->			List[Any]:
												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(a_					)					)






						def 	UpperCAmelCase__     (					self :List[str]					)				->			Union[str, Any]:
												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(a_   ,  a_					)					)






						def 	UpperCAmelCase__     (					self :Any					)				->			List[str]:
												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(a_   ,  a_					)					)






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






						def 	UpperCAmelCase__     (					self :str					)				->			Optional[int]:
												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 :Any					)				->			Optional[Any]:
												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(a_					)					)






						def 	UpperCAmelCase__     (					self :Tuple					)				->			List[str]:
												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 :Dict					)				->			Union[str, Any]:
												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 :Dict					)				->			Optional[Any]:
												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 :Any					)				->			Dict:
												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

from scipy.special import comb  # type: ignore



class 			_UpperCAmelCase :






		'''simple docstring'''

		def __init__(self				,       a_					):





			'''simple docstring'''

			__snake_case	:						List[str]						=				list_of_points
			# Degree determines the flexibility of the curve.
			# Degree = 1 will produce a straight line.
			__snake_case	:						Optional[Any]						=				len(a_					) - 1



		def 				SCREAMING_SNAKE_CASE  (self				,       a_					):





			'''simple docstring'''

			assert 0 <= t <= 1, "Time t must be between 0 and 1."
			__snake_case	:						list[float]						=				[]
			for i in range(len(self.list_of_points					)					):
				# basis function for each i
				output_values.append(
				    comb(self.degree				,       a_					) * ((1 - t) ** (self.degree - i)) * (t**i)					)
			# the basis must sum up to 1 for it to produce a valid Bezier curve.
			assert round(sum(a_					)				,       5					) == 1
			return output_values



		def 				SCREAMING_SNAKE_CASE  (self				,       a_					):





			'''simple docstring'''

			assert 0 <= t <= 1, "Time t must be between 0 and 1."

			__snake_case	:						List[str]						=				self.basis_function(a_					)
			__snake_case	:						str						=				0.0
			__snake_case	:						Union[str, Any]						=				0.0
			for i in range(len(self.list_of_points					)					):
				# For all points, sum up the product of i-th basis function and i-th point.
				x += basis_function[i] * self.list_of_points[i][0]
				y += basis_function[i] * self.list_of_points[i][1]
			return (x, y)



		def 				SCREAMING_SNAKE_CASE  (self				,       a_ = 0.01					):





			'''simple docstring'''

			from matplotlib import pyplot as plt  # type: ignore

			__snake_case	:						list[float]						=				[]  # x coordinates of points to plot
			__snake_case	:						list[float]						=				[]  # y coordinates of points to plot

			__snake_case	:						int						=				0.0
			while t <= 1:
				__snake_case	:						Union[str, Any]						=				self.bezier_curve_function(a_					)
				to_plot_x.append(value[0]					)
				to_plot_y.append(value[1]					)
				t += step_size

			__snake_case	:						List[Any]						=				[i[0] for i in self.list_of_points]
			__snake_case	:						Any						=				[i[1] for i in self.list_of_points]

			plt.plot(
			    a_				,       a_				,       color='''blue'''				,       label='''Curve of Degree ''' + str(self.degree					)				,       )
			plt.scatter(a_				,       a_				,       color='''red'''				,       label='''Control Points'''					)
			plt.legend()
			plt.show()


if __name__ == "__main__":
			import doctest

			doctest.testmod()

			BezierCurve([(1, 2), (3, 5)]).plot_curve()  # degree 1
			BezierCurve([(0, 0), (5, 5), (5, 0)]).plot_curve()  # degree 2
			BezierCurve([(0, 0), (5, 5), (5, 0), (2.5, -2.5)]).plot_curve()  # degree 3





