

"""simple docstring"""




# Lint as: python3
import sys
from collections.abc import Mapping
from typing import TYPE_CHECKING

import numpy as np
import pyarrow as pa

from .. import config
from ..utils.py_utils import map_nested
from .formatting import TensorFormatter


if TYPE_CHECKING:
						import torch





class       lowerCamelCase  (TensorFormatter[Mapping, 'torch.Tensor', Mapping]	):

			def __init__(    self :  Tuple			, __UpperCAmelCase :  Union[str, Any]=None			, **__UpperCAmelCase :  Any				)      ->			Optional[Any]:
						super().__init__(features=__lowerCamelCase				)
						SCREAMING_SNAKE_CASE__									=					torch_tensor_kwargs
						import torch  # noqa import torch at initialization

			def     SCREAMING_SNAKE_CASE (    self :  List[str]			, __UpperCAmelCase :  Dict				)      ->			Dict:
						import torch

						if isinstance(__lowerCamelCase			, __lowerCamelCase				) and column:
									if all(
									    isinstance(__lowerCamelCase			, torch.Tensor				) and x.shape == column[0].shape and x.dtype == column[0].dtype
									    for x in column				):
												return torch.stack(__lowerCamelCase				)
						return column

			def     SCREAMING_SNAKE_CASE (    self :  Optional[Any]			, __UpperCAmelCase :  List[Any]				)      ->			str:
						import torch

						if isinstance(__lowerCamelCase			, (str, bytes, type(__lowerCamelCase				))				):
									return value
						elif isinstance(__lowerCamelCase			, (np.character, np.ndarray)				) and np.issubdtype(value.dtype			, np.character				):
									return value.tolist()

						SCREAMING_SNAKE_CASE__									=					{}

						if isinstance(__lowerCamelCase			, (np.number, np.ndarray)				) and np.issubdtype(value.dtype			, np.integer				):
									SCREAMING_SNAKE_CASE__									=					{"""dtype""": torch.intaa}
						elif isinstance(__lowerCamelCase			, (np.number, np.ndarray)				) and np.issubdtype(value.dtype			, np.floating				):
									SCREAMING_SNAKE_CASE__									=					{"""dtype""": torch.floataa}
						elif config.PIL_AVAILABLE and "PIL" in sys.modules:
									import PIL.Image

									if isinstance(__lowerCamelCase			, PIL.Image.Image				):
												SCREAMING_SNAKE_CASE__									=					np.asarray(__lowerCamelCase				)
						return torch.tensor(__lowerCamelCase			, **{**default_dtype, **self.torch_tensor_kwargs}				)

			def     SCREAMING_SNAKE_CASE (    self :  List[str]			, __UpperCAmelCase :  Tuple				)      ->			List[str]:
						import torch

						# support for torch, tf, jax etc.
						if hasattr(__lowerCamelCase			, """__array__"""				) and not isinstance(__lowerCamelCase			, torch.Tensor				):
									SCREAMING_SNAKE_CASE__									=					data_struct.__array__()
						# support for nested types like struct of list of struct
						if isinstance(__lowerCamelCase			, np.ndarray				):
									if data_struct.dtype == object:  # torch tensors cannot be instantied from an array of objects
												return self._consolidate([self.recursive_tensorize(__lowerCamelCase				) for substruct in data_struct]				)
						elif isinstance(__lowerCamelCase			, (list, tuple)				):
									return self._consolidate([self.recursive_tensorize(__lowerCamelCase				) for substruct in data_struct]				)
						return self._tensorize(__lowerCamelCase				)

			def     SCREAMING_SNAKE_CASE (    self :  int			, __UpperCAmelCase :  dict				)      ->			str:
						return map_nested(self._recursive_tensorize			, __lowerCamelCase			, map_list=__lowerCamelCase				)

			def     SCREAMING_SNAKE_CASE (    self :  Optional[Any]			, __UpperCAmelCase :  pa.Table				)      ->			Mapping:
						SCREAMING_SNAKE_CASE__									=					self.numpy_arrow_extractor().extract_row(__lowerCamelCase				)
						SCREAMING_SNAKE_CASE__									=					self.python_features_decoder.decode_row(__lowerCamelCase				)
						return self.recursive_tensorize(__lowerCamelCase				)

			def     SCREAMING_SNAKE_CASE (    self :  int			, __UpperCAmelCase :  pa.Table				)      ->			"torch.Tensor":
						SCREAMING_SNAKE_CASE__									=					self.numpy_arrow_extractor().extract_column(__lowerCamelCase				)
						SCREAMING_SNAKE_CASE__									=					self.python_features_decoder.decode_column(__lowerCamelCase			, pa_table.column_names[0]				)
						SCREAMING_SNAKE_CASE__									=					self.recursive_tensorize(__lowerCamelCase				)
						SCREAMING_SNAKE_CASE__									=					self._consolidate(__lowerCamelCase				)
						return column





			def     SCREAMING_SNAKE_CASE (    self :  Optional[Any]			, __UpperCAmelCase :  pa.Table				)      ->			Mapping:
						SCREAMING_SNAKE_CASE__									=					self.numpy_arrow_extractor().extract_batch(__lowerCamelCase				)
						SCREAMING_SNAKE_CASE__									=					self.python_features_decoder.decode_batch(__lowerCamelCase				)
						SCREAMING_SNAKE_CASE__									=					self.recursive_tensorize(__lowerCamelCase				)
						for column_name in batch:
									SCREAMING_SNAKE_CASE__									=					self._consolidate(batch[column_name]				)
						return batch








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






