





# DISCLAIMER: This code is strongly influenced by https://github.com/pesser/pytorch_diffusion
# and https://github.com/hojonathanho/diffusion
import math
from dataclasses import dataclass
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from diffusers.configuration_utils import ConfigMixin, register_to_config
from diffusers.schedulers.scheduling_utils import SchedulerMixin
from diffusers.utils import BaseOutput, deprecate







@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->DDIM
class     __snake_case       (							__lowerCamelCase			):





       '''simple docstring'''







       lowerCAmelCase__      		=     42
       lowerCAmelCase__      		=     None







def 			A__							(    SCREAMING_SNAKE_CASE__					,					SCREAMING_SNAKE_CASE__=0.999					,					SCREAMING_SNAKE_CASE__="cosine"					,					)   ->    Tuple:
  if alpha_transform_type == "cosine":

    def alpha_bar_fn(SCREAMING_SNAKE_CASE__):
      return math.cos((t + 0.008) / 1.008 * math.pi / 2) ** 2

  elif alpha_transform_type == "exp":

    def alpha_bar_fn(SCREAMING_SNAKE_CASE__):
      return math.exp(t * -12.0)

  else:
    raise ValueError(F'''Unsupported alpha_tranform_type: {alpha_transform_type}''')

  __snake_case:						str   =						[]
  for i in range(__lowercase):
    __snake_case:						Any   =						i / num_diffusion_timesteps
    __snake_case:						Tuple   =						(i + 1) / num_diffusion_timesteps
    betas.append(min(1 - alpha_bar_fn(__lowercase) / alpha_bar_fn(__lowercase)					,					__lowercase))
  return torch.tensor(__lowercase					,					dtype=torch.floataa)







class     __snake_case       (							__lowerCamelCase   ,			__lowerCamelCase			):





       '''simple docstring'''







       lowerCAmelCase__      		=     1




       @register_to_config
       def __init__(  self :    str							,				A :    int = 1_000							,				A :    float = 0.0001							,				A :    float = 0.02							,				A :    str = "linear"							,				A :    Optional[Union[np.ndarray, List[float]]] = None							,				A :    bool = True							,				A :    bool = True							,				A :    int = 0							,				A :    str = "epsilon"							,				A :    float = 1.0							,				**A :    Union[str, Any]							,				):


         if kwargs.get("""set_alpha_to_one"""							,				A		) is not None:
           __snake_case:						List[str]   =						(
               """The `set_alpha_to_one` argument is deprecated. Please use `set_alpha_to_zero` instead."""
           )
           deprecate("""set_alpha_to_one"""							,				"""1.0.0"""							,				A							,				standard_warn=A		)
           __snake_case:						Optional[Any]   =						kwargs["""set_alpha_to_one"""]
         if trained_betas is not None:
           __snake_case:						Optional[int]   =						torch.tensor(A							,				dtype=torch.floataa		)
         elif beta_schedule == "linear":
           __snake_case:						str   =						torch.linspace(A							,				A							,				A							,				dtype=torch.floataa		)
         elif beta_schedule == "scaled_linear":
           # this schedule is very specific to the latent diffusion model.
           __snake_case:						List[str]   =						(
               torch.linspace(beta_start**0.5							,				beta_end**0.5							,				A							,				dtype=torch.floataa		) ** 2
           )
         elif beta_schedule == "squaredcos_cap_v2":
           # Glide cosine schedule
           __snake_case:						Optional[Any]   =						betas_for_alpha_bar(A		)
         else:
           raise NotImplementedError(f'''{beta_schedule} does is not implemented for {self.__class__}'''		)

         __snake_case:						int   =						1.0 - self.betas
         __snake_case:						Any   =						torch.cumprod(self.alphas							,				dim=0		)

         # At every step in inverted ddim, we are looking into the next alphas_cumprod
         # For the final step, there is no next alphas_cumprod, and the index is out of bounds
         # `set_alpha_to_zero` decides whether we set this parameter simply to zero
         # in this case, self.step() just output the predicted noise
         # or whether we use the final alpha of the "non-previous" one.
         __snake_case:						Tuple   =						torch.tensor(0.0		) if set_alpha_to_zero else self.alphas_cumprod[-1]

         # standard deviation of the initial noise distribution
         __snake_case:						Tuple   =						1.0

         # setable values
         __snake_case:						int   =						None
         __snake_case:						Dict   =						torch.from_numpy(np.arange(0							,				A		).copy().astype(np.intaa		)		)




       def 							UpperCAmelCase__ (  self :    List[str]							,				A :    torch.FloatTensor							,				A :    Optional[int] = None		):
         return sample




       def 							UpperCAmelCase__ (  self :    List[Any]							,				A :    int							,				A :    Union[str, torch.device] = None		):


         if num_inference_steps > self.config.num_train_timesteps:
           raise ValueError(
               f'''`num_inference_steps`: {num_inference_steps} cannot be larger than `self.config.train_timesteps`:'''
               f''' {self.config.num_train_timesteps} as the unet model trained with this scheduler can only handle'''
               f''' maximal {self.config.num_train_timesteps} timesteps.'''		)

         __snake_case:						int   =						num_inference_steps
         __snake_case:						Any   =						self.config.num_train_timesteps // self.num_inference_steps
         # creates integer timesteps by multiplying by ratio
         # casting to int to avoid issues when num_inference_step is power of 3
         __snake_case:						Any   =						(np.arange(0							,				A		) * step_ratio).round().copy().astype(np.intaa		)
         __snake_case:						List[Any]   =						torch.from_numpy(A		).to(A		)
         self.timesteps += self.config.steps_offset




       def 							UpperCAmelCase__ (  self :    str							,				A :    torch.FloatTensor							,				A :    int							,				A :    torch.FloatTensor							,				A :    float = 0.0							,				A :    bool = False							,				A :    Optional[torch.FloatTensor] = None							,				A :    bool = True							,				):
         __snake_case:						Tuple   =						timestep + self.config.num_train_timesteps // self.num_inference_steps

         # 2. compute alphas, betas
         # change original implementation to exactly match noise levels for analogous forward process
         __snake_case:						Union[str, Any]   =						self.alphas_cumprod[timestep]
         __snake_case:						str   =						(
             self.alphas_cumprod[prev_timestep]
             if prev_timestep < self.config.num_train_timesteps
             else self.final_alpha_cumprod
         )

         __snake_case:						Optional[Any]   =						1 - alpha_prod_t

         # 3. compute predicted original sample from predicted noise also called
         # "predicted x_0" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
         if self.config.prediction_type == "epsilon":
           __snake_case:						Any   =						(sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
           __snake_case:						str   =						model_output
         elif self.config.prediction_type == "sample":
           __snake_case:						Union[str, Any]   =						model_output
           __snake_case:						str   =						(sample - alpha_prod_t ** 0.5 * pred_original_sample) / beta_prod_t ** 0.5
         elif self.config.prediction_type == "v_prediction":
           __snake_case:						List[Any]   =						(alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
           __snake_case:						List[Any]   =						(alpha_prod_t**0.5) * model_output + (beta_prod_t**0.5) * sample
         else:
           raise ValueError(
               f'''prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or'''
               """ `v_prediction`"""		)

         # 4. Clip or threshold "predicted x_0"
         if self.config.clip_sample:
           __snake_case:						Tuple   =						pred_original_sample.clamp(
               -self.config.clip_sample_range							,				self.config.clip_sample_range		)

         # 5. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
         __snake_case:						Optional[int]   =						(1 - alpha_prod_t_prev) ** 0.5 * pred_epsilon

         # 6. compute x_t without "random noise" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
         __snake_case:						int   =						alpha_prod_t_prev ** 0.5 * pred_original_sample + pred_sample_direction

         if not return_dict:
           return (prev_sample, pred_original_sample)
         return DDIMSchedulerOutput(prev_sample=A							,				pred_original_sample=A		)






       def __len__(  self :    Union[str, Any]		):
         return self.config.num_train_timesteps








from collections.abc import Sequence






def        a_		(       __lowercase   :	Sequence[float]       ,					__lowercase   :	float ) ->  float:
			return sum(c * (x**i) for i, c in enumerate(__lowercase ) )






def        a_		(       __lowercase   :	Sequence[float]       ,					__lowercase   :	float ) ->  float:
			_snake_case		=			0.0
			for coeff in reversed(__lowercase ):
						_snake_case		=			result * x + coeff
			return result


if __name__ == "__main__":
			_lowerCamelCase       :				Optional[Any]       =			(0.0, 0.0, 5.0, 9.3, 7.0)
			_lowerCamelCase       :				Optional[int]       =			1_0.0
			print(evaluate_poly(poly, x))
			print(horner(poly, x))