

from __future__ import annotations

from scipy.special import comb  # type: ignore
class     A_      :


    '''simple docstring'''






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


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

        __UpperCAmelCase     =	self.basis_function(_a     )
        __UpperCAmelCase     =	0.0
        __UpperCAmelCase     =	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    lowerCAmelCase_  (self   ,					lowercase__ = 0.01     )   ->					str:
        from matplotlib import pyplot as plt  # type: ignore

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

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

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










# DISCLAIMER: This file is strongly influenced by https://github.com/yang-song/score_sde_pytorch

import math
from typing import Union

import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import randn_tensor
from .scheduling_utils import SchedulerMixin







class 						lowercase							(   UpperCamelCase__,UpperCamelCase__		):
     _a							 =						1

     @register_to_config
     def __init__(  self		,     _a=2000		,     _a=0.1		,     _a=20		,     _a=1e-3				)						->							List[Any]:
           _A							:     Dict			=						None
           _A							:     List[Any]			=						None
           _A							:     Dict			=						None

     def 					a__	(  self		,     _a		,     _a = None				)						->							Union[str, Any]:
           _A							:     Union[str, Any]			=						torch.linspace(1		,     self.config.sampling_eps		,     _a		,     device=_a				)

     def 					a__	(  self		,     _a		,     _a		,     _a		,     _a=None				)						->							Dict:
           if self.timesteps is None:
                 raise ValueError(
                     """`self.timesteps` is not set, you need to run 'set_timesteps' after creating the scheduler"""				)

           # TODO(Patrick) better comments + non-PyTorch
           # postprocess model score
           _A							:     Any			=						(
               -0.25 * t**2 * (self.config.beta_max - self.config.beta_min) - 0.5 * t * self.config.beta_min
           )
           _A							:     List[Any]			=						torch.sqrt(1.0 - torch.exp(2.0 * log_mean_coeff				)				)
           _A							:     List[str]			=						std.flatten()
           while len(std.shape				) < len(score.shape				):
                 _A							:     List[Any]			=						std.unsqueeze(-1				)
           _A							:     int			=						-score / std

           # compute
           _A							:     Tuple			=						-1.0 / len(self.timesteps				)

           _A							:     str			=						self.config.beta_min + t * (self.config.beta_max - self.config.beta_min)
           _A							:     List[str]			=						beta_t.flatten()
           while len(beta_t.shape				) < len(x.shape				):
                 _A							:     Union[str, Any]			=						beta_t.unsqueeze(-1				)
           _A							:     Tuple			=						-0.5 * beta_t * x

           _A							:     Tuple			=						torch.sqrt(_a				)
           _A							:     Dict			=						drift - diffusion**2 * score
           _A							:     Dict			=						x + drift * dt

           # add noise
           _A							:     Any			=						randn_tensor(x.shape		,     layout=x.layout		,     generator=_a		,     device=x.device		,     dtype=x.dtype				)
           _A							:     str			=						x_mean + diffusion * math.sqrt(-dt				) * noise

           return x, x_mean



     def __len__(  self				)						->							Optional[Any]:
           return self.config.num_train_timesteps

