'''simple docstring'''






from __future__ import annotations

from scipy.special import comb  # type: ignore







class lowercase_       :







   """simple docstring"""

   def __init__(      self      :			Tuple, UpperCamelCase__      :			list[tuple[float, float]]     )  ->			Any:
        _A    		=  list_of_points
        # Degree determines the flexibility of the curve.
        # Degree = 1 will produce a straight line.
        _A    		=  len(UpperCamelCase__     ) - 1
   def 	__UpperCAmelCase   (      self      :			Optional[Any], UpperCamelCase__      :			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, UpperCamelCase__     ) * ((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(UpperCamelCase__     ), 5     ) == 1
        return output_values
   def 	__UpperCAmelCase   (      self      :			Dict, UpperCamelCase__      :			float     )  ->			tuple[float, float]:
        assert 0 <= t <= 1, "Time t must be between 0 and 1."

        _A    		=  self.basis_function(UpperCamelCase__     )
        _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      :			Dict, UpperCamelCase__      :			float = 0.01     )  ->			List[Any]:
        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(UpperCamelCase__     )
             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(
            UpperCamelCase__, UpperCamelCase__, color='blue', label='Curve of Degree ' + str(self.degree     ), )
        plt.scatter(UpperCamelCase__, UpperCamelCase__, 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




'''simple docstring'''






import os
from pathlib import Path
from unittest.mock import patch

import pytest
import zstandard as zstd

from datasets.download.download_config import DownloadConfig
from datasets.utils.file_utils import (
    OfflineModeIsEnabled,
    cached_path,
    fsspec_get,
    fsspec_head,
    ftp_get,
    ftp_head,
    get_from_cache,
    http_get,
    http_head,
)


_UpperCAmelCase    :     Optional[int]         =       '''\
    Text data.
    Second line of data.'''

_UpperCAmelCase    :     Optional[Any]         =       '''file'''





@pytest.fixture(scope='session'				)
def  _SCREAMING_SNAKE_CASE		(      __snake_case							:			Any				):
     _A    		=  tmp_path_factory.mktemp('data'				) / (FILE_PATH + '.zstd')
     _A    		=  bytes(__snake_case   ,		'utf-8'				)
     with zstd.open(__snake_case   ,		'wb'				) as f:
          f.write(__snake_case				)
     return path





@pytest.fixture
def  _SCREAMING_SNAKE_CASE		(      __snake_case							:			Union[str, Any]				):
     with open(os.path.join(tmpfs.local_root_dir   ,		__snake_case				)   ,		'w'				) as f:
          f.write(__snake_case				)
     return FILE_PATH





@pytest.mark.parametrize('compression_format'   ,		['gzip', 'xz', 'zstd']				)
def  _SCREAMING_SNAKE_CASE		(      __snake_case							:			Dict   ,		__snake_case							:			str   ,		__snake_case							:			Any   ,		__snake_case							:			Any   ,		__snake_case							:			List[str]   ,		__snake_case							:			List[str]				):
     _A    		=  {'gzip': gz_file, 'xz': xz_file, 'zstd': zstd_path}
     _A    		=  input_paths[compression_format]
     _A    		=  tmp_path / 'cache'
     _A    		=  DownloadConfig(cache_dir=__snake_case   ,		extract_compressed_file=__snake_case				)
     _A    		=  cached_path(__snake_case   ,		download_config=__snake_case				)
     with open(__snake_case				) as f:
          _A    		=  f.read()
     with open(__snake_case				) as f:
          _A    		=  f.read()
     assert extracted_file_content == expected_file_content





@pytest.mark.parametrize('default_extracted'   ,		[True, False]				)
@pytest.mark.parametrize('default_cache_dir'   ,		[True, False]				)
def  _SCREAMING_SNAKE_CASE		(      __snake_case							:			Union[str, Any]   ,		__snake_case							:			List[str]   ,		__snake_case							:			Union[str, Any]   ,		__snake_case							:			int   ,		__snake_case							:			List[str]				):
     _A    		=  'custom_cache'
     _A    		=  'custom_extracted_dir'
     _A    		=  tmp_path / 'custom_extracted_path'
     if default_extracted:
          _A    		=  ('downloads' if default_cache_dir else custom_cache_dir, 'extracted')
     else:
          monkeypatch.setattr('datasets.config.EXTRACTED_DATASETS_DIR'   ,		__snake_case				)
          monkeypatch.setattr('datasets.config.EXTRACTED_DATASETS_PATH'   ,		str(__snake_case				)				)
          _A    		=  custom_extracted_path.parts[-2:] if default_cache_dir else (custom_cache_dir, custom_extracted_dir)

     _A    		=  xz_file
     _A    		=  (
         DownloadConfig(extract_compressed_file=__snake_case				)
         if default_cache_dir
         else DownloadConfig(cache_dir=tmp_path / custom_cache_dir   ,		extract_compressed_file=__snake_case				)
     )
     _A    		=  cached_path(__snake_case   ,		download_config=__snake_case				)
     assert Path(__snake_case				).parent.parts[-2:] == expected





def  _SCREAMING_SNAKE_CASE		(      __snake_case							:			str				):
     # absolute path
     _A    		=  str(Path(__snake_case				).resolve()				)
     assert cached_path(__snake_case				) == text_file
     # relative path
     _A    		=  str(Path(__snake_case				).resolve().relative_to(Path(os.getcwd()				)				)				)
     assert cached_path(__snake_case				) == text_file





def  _SCREAMING_SNAKE_CASE		(      __snake_case							:			List[str]				):
     # absolute path
     _A    		=  str(tmp_path.resolve() / '__missing_file__.txt'				)
     with pytest.raises(__snake_case				):
          cached_path(__snake_case				)
     # relative path
     _A    		=  './__missing_file__.txt'
     with pytest.raises(__snake_case				):
          cached_path(__snake_case				)





def  _SCREAMING_SNAKE_CASE		(      __snake_case							:			int				):
     _A    		=  get_from_cache(F'tmp://{tmpfs_file}'				)
     with open(__snake_case				) as f:
          _A    		=  f.read()
     assert output_file_content == FILE_CONTENT





@patch('datasets.config.HF_DATASETS_OFFLINE'   ,		__snake_case				)
def  _SCREAMING_SNAKE_CASE		(      ):
     with pytest.raises(__snake_case				):
          cached_path('https://huggingface.co'				)





@patch('datasets.config.HF_DATASETS_OFFLINE'   ,		__snake_case				)
def  _SCREAMING_SNAKE_CASE		(      __snake_case							:			Tuple				):
     _A    		=  tmp_path_factory.mktemp('data'				) / 'file.html'
     with pytest.raises(__snake_case				):
          http_get('https://huggingface.co'   ,		temp_file=__snake_case				)
     with pytest.raises(__snake_case				):
          http_head('https://huggingface.co'				)





@patch('datasets.config.HF_DATASETS_OFFLINE'   ,		__snake_case				)
def  _SCREAMING_SNAKE_CASE		(      __snake_case							:			Optional[int]				):
     _A    		=  tmp_path_factory.mktemp('data'				) / 'file.html'
     with pytest.raises(__snake_case				):
          ftp_get('ftp://huggingface.co'   ,		temp_file=__snake_case				)
     with pytest.raises(__snake_case				):
          ftp_head('ftp://huggingface.co'				)





@patch('datasets.config.HF_DATASETS_OFFLINE'   ,		__snake_case				)
def  _SCREAMING_SNAKE_CASE		(      __snake_case							:			List[str]				):
     _A    		=  tmp_path_factory.mktemp('data'				) / 'file.html'
     with pytest.raises(__snake_case				):
          fsspec_get('s3://huggingface.co'   ,		temp_file=__snake_case				)
     with pytest.raises(__snake_case				):
          fsspec_head('s3://huggingface.co'				)



