





'''simple docstring'''






from dataclasses import dataclass
from typing import Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput, randn_tensor
from .scheduling_utils import SchedulerMixin
@dataclass
class 					__snake_case  (					__SCREAMING_SNAKE_CASE							):






   '''simple docstring'''





   lowerCamelCase__    							=      42
   lowerCamelCase__    							=      42
   lowerCamelCase__    							=      None



class 					__snake_case  (					__SCREAMING_SNAKE_CASE		,				__SCREAMING_SNAKE_CASE							):






   '''simple docstring'''





   lowerCamelCase__    							=      2

   @register_to_config
   def __init__(							self	,		__SCREAMING_SNAKE_CASE = 0.02	,		__SCREAMING_SNAKE_CASE = 1_0_0	,		__SCREAMING_SNAKE_CASE = 1.007	,		__SCREAMING_SNAKE_CASE = 8_0	,		__SCREAMING_SNAKE_CASE = 0.05	,		__SCREAMING_SNAKE_CASE = 5_0	,		):
    # standard deviation of the initial noise distribution
    snake_case__     :					int    =  sigma_max

    # setable values
    snake_case__     :					int    =  None
    snake_case__     :					np.IntTensor    =  None
    snake_case__     :					torch.FloatTensor    =  None  # sigma(t_i)

   def 		__UpperCamelCase						(							self	,		__SCREAMING_SNAKE_CASE	,		__SCREAMING_SNAKE_CASE = None       ):
    return sample

   def 		__UpperCamelCase						(							self	,		__SCREAMING_SNAKE_CASE	,		__SCREAMING_SNAKE_CASE = None       ):
    snake_case__     :					Tuple    =  num_inference_steps
    snake_case__     :					List[Any]    =  np.arange(0	,		self.num_inference_steps       )[::-1].copy()
    snake_case__     :					Any    =  torch.from_numpy(__SCREAMING_SNAKE_CASE       ).to(__SCREAMING_SNAKE_CASE       )
    snake_case__     :					Optional[Any]    =  [
        (
            self.config.sigma_max**2
            * (self.config.sigma_min**2 / self.config.sigma_max**2) ** (i / (num_inference_steps - 1))
        )
        for i in self.timesteps
    ]
    snake_case__     :					List[Any]    =  torch.tensor(__SCREAMING_SNAKE_CASE	,		dtype=torch.floataa	,		device=__SCREAMING_SNAKE_CASE       )

   def 		__UpperCamelCase						(							self	,		__SCREAMING_SNAKE_CASE	,		__SCREAMING_SNAKE_CASE	,		__SCREAMING_SNAKE_CASE = None       ):
    if self.config.s_min <= sigma <= self.config.s_max:
     snake_case__     :					Any    =  min(self.config.s_churn / self.num_inference_steps	,		2**0.5 - 1       )
    else:
     snake_case__     :					Union[str, Any]    =  0

    # sample eps ~ N(0, S_noise^2 * I)
    snake_case__     :					Optional[int]    =  self.config.s_noise * randn_tensor(sample.shape	,		generator=__SCREAMING_SNAKE_CASE       ).to(sample.device       )
    snake_case__     :					List[Any]    =  sigma + gamma * sigma
    snake_case__     :					Optional[int]    =  sample + ((sigma_hat**2 - sigma**2) ** 0.5 * eps)

    return sample_hat, sigma_hat

   def 		__UpperCamelCase						(							self	,		__SCREAMING_SNAKE_CASE	,		__SCREAMING_SNAKE_CASE	,		__SCREAMING_SNAKE_CASE	,		__SCREAMING_SNAKE_CASE	,		__SCREAMING_SNAKE_CASE = True	,		):
    snake_case__     :					Union[str, Any]    =  sample_hat + sigma_hat * model_output
    snake_case__     :					List[Any]    =  (sample_hat - pred_original_sample) / sigma_hat
    snake_case__     :					Optional[int]    =  sample_hat + (sigma_prev - sigma_hat) * derivative

    if not return_dict:
     return (sample_prev, derivative)

    return KarrasVeOutput(
        prev_sample=__SCREAMING_SNAKE_CASE	,		derivative=__SCREAMING_SNAKE_CASE	,		pred_original_sample=__SCREAMING_SNAKE_CASE       )

   def 		__UpperCamelCase						(							self	,		__SCREAMING_SNAKE_CASE	,		__SCREAMING_SNAKE_CASE	,		__SCREAMING_SNAKE_CASE	,		__SCREAMING_SNAKE_CASE	,		__SCREAMING_SNAKE_CASE	,		__SCREAMING_SNAKE_CASE	,		__SCREAMING_SNAKE_CASE = True	,		):
    snake_case__     :					List[str]    =  sample_prev + sigma_prev * model_output
    snake_case__     :					Tuple    =  (sample_prev - pred_original_sample) / sigma_prev
    snake_case__     :					List[str]    =  sample_hat + (sigma_prev - sigma_hat) * (0.5 * derivative + 0.5 * derivative_corr)

    if not return_dict:
     return (sample_prev, derivative)

    return KarrasVeOutput(
        prev_sample=__SCREAMING_SNAKE_CASE	,		derivative=__SCREAMING_SNAKE_CASE	,		pred_original_sample=__SCREAMING_SNAKE_CASE       )


   def 		__UpperCamelCase						(							self	,		__SCREAMING_SNAKE_CASE	,		__SCREAMING_SNAKE_CASE	,		__SCREAMING_SNAKE_CASE       ):
    raise NotImplementedError()












"""simple docstring"""







from __future__ import annotations

from scipy.special import comb  # type: ignore


class      UpperCamelCase		:






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






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






						def      __snake_case      (		self  :List[str]			, __magic_name__  :float				)      ->tuple[float, float]:
										assert 0 <= t <= 1, "Time t must be between 0 and 1."

										lowercase    :      str       = self.basis_function(__magic_name__				)
										lowercase    :      Optional[int]       = 0.0
										lowercase    :      List[str]       = 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  :Tuple			, __magic_name__  :float = 0.01				)      ->List[str]:
										from matplotlib import pyplot as plt  # type: ignore

										lowercase    :      list[float]       = []  # x coordinates of points to plot
										lowercase    :      list[float]       = []  # y coordinates of points to plot

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

										lowercase    :      Union[str, Any]       = [i[0] for i in self.list_of_points]
										lowercase    :      Optional[int]       = [i[1] for i in self.list_of_points]

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