

'''simple docstring'''




from __future__ import annotations

from scipy.special import comb  # type: ignore






class   _SCREAMING_SNAKE_CASE   :



 def __init__(   self		:   Tuple			,				a__		:   Union[str, Any]      ):
      __magic_name__						       =    list_of_points
      # Degree determines the flexibility of the curve.
      # Degree = 1 will produce a straight line.
      __magic_name__						       =    len(a__      ) - 1



 def 			snake_case__  (   self		:   Any			,				a__		:   int      ):
      assert 0 <= t <= 1, "Time t must be between 0 and 1."
      __magic_name__						       =    []
      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 			snake_case__  (   self		:   Optional[int]			,				a__		:   Tuple      ):
      assert 0 <= t <= 1, "Time t must be between 0 and 1."

      __magic_name__						       =    self.basis_function(a__      )
      __magic_name__						       =    0.0
      __magic_name__						       =    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		:   int			,				a__		:   Any = 0.01      ):
      from matplotlib import pyplot as plt  # type: ignore

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

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

      __magic_name__						       =    [i[0] for i in self.list_of_points]
      __magic_name__						       =    [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









'''simple docstring'''




import math
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils import SchedulerMixin, SchedulerOutput






class   _SCREAMING_SNAKE_CASE   (   __a		,__a     ):
 __SCREAMING_SNAKE_CASE					:Optional[Any]      	=					1



 @register_to_config
 def __init__(   self		:   Optional[int]			,				a__		:   int = 1000			,				a__		:   Optional[Union[np.ndarray, List[float]]] = None      ):
      # set `betas`, `alphas`, `timesteps`
      self.set_timesteps(a__      )

      # standard deviation of the initial noise distribution
      __magic_name__						       =    1.0

      # For now we only support F-PNDM, i.e. the runge-kutta method
      # For more information on the algorithm please take a look at the paper: https://arxiv.org/pdf/2202.09778.pdf
      # mainly at formula (9), (12), (13) and the Algorithm 2.
      __magic_name__						       =    4

      # running values
      __magic_name__						       =    []



 def 			snake_case__  (   self		:   Dict			,				a__		:   int			,				a__		:   Union[str, torch.device] = None      ):
      __magic_name__						       =    num_inference_steps
      __magic_name__						       =    torch.linspace(1			,				0			,				num_inference_steps + 1      )[:-1]
      __magic_name__						       =    torch.cat([steps, torch.tensor([0.0]      )]      )

      if self.config.trained_betas is not None:
           __magic_name__						       =    torch.tensor(self.config.trained_betas			,				dtype=torch.floataa      )
      else:
           __magic_name__						       =    torch.sin(steps * math.pi / 2      ) ** 2

      __magic_name__						       =    (1.0 - self.betas**2) ** 0.5

      __magic_name__						       =    (torch.atana(self.betas			,				self.alphas      ) / math.pi * 2)[:-1]
      __magic_name__						       =    timesteps.to(a__      )

      __magic_name__						       =    []



 def 			snake_case__  (   self		:   Union[str, Any]			,				a__		:   torch.FloatTensor			,				a__		:   int			,				a__		:   torch.FloatTensor			,				a__		:   bool = True			,				):
      if self.num_inference_steps is None:
           raise ValueError(
               '''Number of inference steps is \'None\', you need to run \'set_timesteps\' after creating the scheduler'''      )

      __magic_name__						       =    (self.timesteps == timestep).nonzero().item()
      __magic_name__						       =    timestep_index + 1

      __magic_name__						       =    sample * self.betas[timestep_index] + model_output * self.alphas[timestep_index]
      self.ets.append(a__      )

      if len(self.ets      ) == 1:
           __magic_name__						       =    self.ets[-1]
      elif len(self.ets      ) == 2:
           __magic_name__						       =    (3 * self.ets[-1] - self.ets[-2]) / 2
      elif len(self.ets      ) == 3:
           __magic_name__						       =    (23 * self.ets[-1] - 16 * self.ets[-2] + 5 * self.ets[-3]) / 12
      else:
           __magic_name__						       =    (1 / 24) * (55 * self.ets[-1] - 59 * self.ets[-2] + 37 * self.ets[-3] - 9 * self.ets[-4])

      __magic_name__						       =    self._get_prev_sample(a__			,				a__			,				a__			,				a__      )

      if not return_dict:
           return (prev_sample,)

      return SchedulerOutput(prev_sample=a__      )



 def 			snake_case__  (   self		:   Any			,				a__		:   torch.FloatTensor			,				*a__		:   Optional[int]			,				**a__		:   Union[str, Any]      ):
      return sample



 def 			snake_case__  (   self		:   str			,				a__		:   Optional[int]			,				a__		:   int			,				a__		:   List[Any]			,				a__		:   List[str]      ):
      __magic_name__						       =    self.alphas[timestep_index]
      __magic_name__						       =    self.betas[timestep_index]

      __magic_name__						       =    self.alphas[prev_timestep_index]
      __magic_name__						       =    self.betas[prev_timestep_index]

      __magic_name__						       =    (sample - sigma * ets) / max(a__			,				1E-8      )
      __magic_name__						       =    next_alpha * pred + ets * next_sigma

      return prev_sample



 def __len__(   self		:   int      ):
      return self.config.num_train_timesteps






