



from __future__ import annotations

from scipy.special import comb  # type: ignore
class 			_lowerCAmelCase   :






			"""simple docstring"""





			def __init__(				self	:       Tuple			,     lowercase	:       list[tuple[float, float]]   )						->					List[str]:
									"""simple docstring"""







									__lowercase					=				list_of_points
									# Degree determines the flexibility of the curve.
									# Degree = 1 will produce a straight line.
									__lowercase					=				len(lowercase   ) - 1





			def 		snake_case__			(				self	:       Optional[Any]			,     lowercase	:       float   )						->					list[float]:
									"""simple docstring"""







									assert 0 <= t <= 1, "Time t must be between 0 and 1."
									__lowercase					=				[]
									for i in range(len(self.list_of_points   )   ):
															# basis function for each i
															output_values.append(
															    comb(self.degree			,     lowercase   ) * ((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(lowercase   )			,     5   ) == 1
									return output_values





			def 		snake_case__			(				self	:       List[str]			,     lowercase	:       float   )						->					tuple[float, float]:
									"""simple docstring"""







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

									__lowercase					=				self.basis_function(lowercase   )
									__lowercase					=				0.0
									__lowercase					=				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 		snake_case__			(				self	:       Optional[Any]			,     lowercase	:       float = 0.01   )						->					Any:
									"""simple docstring"""







									from matplotlib import pyplot as plt  # type: ignore

									__lowercase					=				[]  # x coordinates of points to plot
									__lowercase					=				[]  # y coordinates of points to plot

									__lowercase					=				0.0
									while t <= 1:
															__lowercase					=				self.bezier_curve_function(lowercase   )
															to_plot_x.append(value[0]   )
															to_plot_y.append(value[1]   )
															t += step_size

									__lowercase					=				[i[0] for i in self.list_of_points]
									__lowercase					=				[i[1] for i in self.list_of_points]

									plt.plot(
									    lowercase			,     lowercase			,     color="""blue"""			,     label="""Curve of Degree """ + str(self.degree   )			,     )
									plt.scatter(lowercase			,     lowercase			,     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










import os
import unittest

from transformers import LxmertTokenizer, LxmertTokenizerFast
from transformers.models.bert.tokenization_bert import VOCAB_FILES_NAMES
from transformers.testing_utils import require_tokenizers

from ...test_tokenization_common import TokenizerTesterMixin
@require_tokenizers
class 			_lowerCAmelCase   ( _UpperCAmelCase    ,					unittest.TestCase			):






			"""simple docstring"""





			lowercase__      :  Tuple      =			LxmertTokenizer
			lowercase__      :  List[str]      =			LxmertTokenizerFast
			lowercase__      :  Optional[Any]      =			True
			lowercase__      :  List[Any]      =			True





			def 		snake_case__			(				self	:       Tuple   )						->					Tuple:
									"""simple docstring"""







									super().setUp()

									__lowercase					=				[
									    """[UNK]""",
									    """[CLS]""",
									    """[SEP]""",
									    """want""",
									    """##want""",
									    """##ed""",
									    """wa""",
									    """un""",
									    """runn""",
									    """##ing""",
									    """,""",
									    """low""",
									    """lowest""",
									]
									__lowercase					=				os.path.join(self.tmpdirname			,     VOCAB_FILES_NAMES["""vocab_file"""]   )
									with open(self.vocab_file			,     """w"""			,     encoding="""utf-8"""   ) as vocab_writer:
															vocab_writer.write("""""".join([x + """\n""" for x in vocab_tokens]   )   )





			def 		snake_case__			(				self	:       Optional[int]			,     lowercase	:       int   )						->					List[Any]:
									"""simple docstring"""







									__lowercase					=				"""UNwant\u00E9d,running"""
									__lowercase					=				"""unwanted, running"""
									return input_text, output_text





			def 		snake_case__			(				self	:       str   )						->					Any:
									"""simple docstring"""







									__lowercase					=				self.tokenizer_class(self.vocab_file   )

									__lowercase					=				tokenizer.tokenize("""UNwant\u00E9d,running"""   )
									self.assertListEqual(lowercase			,     ["""un""", """##want""", """##ed""", """,""", """runn""", """##ing"""]   )
									self.assertListEqual(tokenizer.convert_tokens_to_ids(lowercase   )			,     [7, 4, 5, 10, 8, 9]   )







			def 		snake_case__			(				self	:       Union[str, Any]   )						->					int:
									"""simple docstring"""







									if not self.test_rust_tokenizer:
															return

									__lowercase					=				self.get_tokenizer()
									__lowercase					=				self.get_rust_tokenizer()

									__lowercase					=				"""I was born in 92000, and this is falsé."""

									__lowercase					=				tokenizer.tokenize(lowercase   )
									__lowercase					=				rust_tokenizer.tokenize(lowercase   )
									self.assertListEqual(lowercase			,     lowercase   )

									__lowercase					=				tokenizer.encode(lowercase			,     add_special_tokens=lowercase   )
									__lowercase					=				rust_tokenizer.encode(lowercase			,     add_special_tokens=lowercase   )
									self.assertListEqual(lowercase			,     lowercase   )

									__lowercase					=				self.get_rust_tokenizer()
									__lowercase					=				tokenizer.encode(lowercase   )
									__lowercase					=				rust_tokenizer.encode(lowercase   )
									self.assertListEqual(lowercase			,     lowercase   )





