


"""simple docstring"""




# Copyright 2023 The HuggingFace Team. All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


lowercase_			     =  {
    "configuration_xmod": [
        "XMOD_PRETRAINED_CONFIG_ARCHIVE_MAP",
        "XmodConfig",
        "XmodOnnxConfig",
    ],
}

try:
				if not is_torch_available():
								raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
				pass
else:
				lowercase_			     =  [
				    "XMOD_PRETRAINED_MODEL_ARCHIVE_LIST",
				    "XmodForCausalLM",
				    "XmodForMaskedLM",
				    "XmodForMultipleChoice",
				    "XmodForQuestionAnswering",
				    "XmodForSequenceClassification",
				    "XmodForTokenClassification",
				    "XmodModel",
				    "XmodPreTrainedModel",
				]

if TYPE_CHECKING:
				from .configuration_xmod import XMOD_PRETRAINED_CONFIG_ARCHIVE_MAP, XmodConfig, XmodOnnxConfig

				try:
								if not is_torch_available():
												raise OptionalDependencyNotAvailable()
				except OptionalDependencyNotAvailable:
								pass
				else:
								from .modeling_xmod import (
								    XMOD_PRETRAINED_MODEL_ARCHIVE_LIST,
								    XmodForCausalLM,
								    XmodForMaskedLM,
								    XmodForMultipleChoice,
								    XmodForQuestionAnswering,
								    XmodForSequenceClassification,
								    XmodForTokenClassification,
								    XmodModel,
								    XmodPreTrainedModel,
								)

else:
				import sys

				lowercase_			     =  _LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)












from __future__ import annotations

from scipy.special import comb  # type: ignore




class     snake_case__							:
				"""simple docstring"""



				def __init__(      self				:     Any					,      __lowerCamelCase				:     list[tuple[float, float]]							)					->     Tuple:
							a    =			list_of_points
							# Degree determines the flexibility of the curve.
							# Degree = 1 will produce a straight line.
							a    =			len(__lowerCamelCase							) - 1





				def 							__UpperCAmelCase							(      self				:     Union[str, Any]					,      __lowerCamelCase				:     float							)					->     list[float]:
							assert 0 <= t <= 1, "Time t must be between 0 and 1."
							a    =			[]
							for i in range(len(self.list_of_points							)							):
										# basis function for each i
										output_values.append(
										    comb(self.degree					,      __lowerCamelCase							) * ((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(__lowerCamelCase							)					,      5							) == 1
							return output_values





				def 							__UpperCAmelCase							(      self				:     Optional[Any]					,      __lowerCamelCase				:     float							)					->     tuple[float, float]:
							assert 0 <= t <= 1, "Time t must be between 0 and 1."

							a    =			self.basis_function(__lowerCamelCase							)
							a    =			0.0
							a    =			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 							__UpperCAmelCase							(      self				:     Optional[Any]					,      __lowerCamelCase				:     float = 0.01							)					->     List[str]:
							from matplotlib import pyplot as plt  # type: ignore

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

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

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

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






