





# 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 SCREAMING_SNAKE_CASE_ (					lowercase_   ):





					"""simple docstring"""


					A__				 =    42
					A__				 =    None





def    __UpperCamelCase      (    a,     a=0.9_9_9,     a="cosine",     ) ->str:
					if alpha_transform_type == "cosine":

										def alpha_bar_fn(a):
															return math.cos((t + 0.0_0_8) / 1.0_0_8 * math.pi / 2) ** 2

					elif alpha_transform_type == "exp":

										def alpha_bar_fn(a):
															return math.exp(t * -1_2.0)

					else:
										raise ValueError(f"Unsupported alpha_tranform_type: {alpha_transform_type}")

					lowerCamelCase__       =       []
					for i in range(a):
										lowerCamelCase__       =       i / num_diffusion_timesteps
										lowerCamelCase__       =       (i + 1) / num_diffusion_timesteps
										betas.append(min(1 - alpha_bar_fn(a) / alpha_bar_fn(a),     a))
					return torch.tensor(a,     dtype=torch.floataa)







class SCREAMING_SNAKE_CASE_ (					lowercase_							,       lowercase_   ):





					"""simple docstring"""


					A__				 =    1





					@register_to_config
					def __init__( self	,  _lowerCAmelCase = 1000	,  _lowerCAmelCase = 0.0_001	,  _lowerCAmelCase = 0.02	,  _lowerCAmelCase = "linear"	,  _lowerCAmelCase = None	,  _lowerCAmelCase = True	,  _lowerCAmelCase = True	,  _lowerCAmelCase = 0	,  _lowerCAmelCase = "epsilon"	,  _lowerCAmelCase = 1.0	,  **_lowerCAmelCase	,  ):
										if kwargs.get("set_alpha_to_one"	,  _lowerCAmelCase	) is not None:
															lowerCamelCase__       =       (
															    "The `set_alpha_to_one` argument is deprecated. Please use `set_alpha_to_zero` instead."
															)
															deprecate("set_alpha_to_one"	,  "1.0.0"	,  _lowerCAmelCase	,  standard_warn=_lowerCAmelCase	)
															lowerCamelCase__       =       kwargs["set_alpha_to_one"]
										if trained_betas is not None:
															lowerCamelCase__       =       torch.tensor(_lowerCAmelCase	,  dtype=torch.floataa	)
										elif beta_schedule == "linear":
															lowerCamelCase__       =       torch.linspace(_lowerCAmelCase	,  _lowerCAmelCase	,  _lowerCAmelCase	,  dtype=torch.floataa	)
										elif beta_schedule == "scaled_linear":
															# this schedule is very specific to the latent diffusion model.
															lowerCamelCase__       =       (
															    torch.linspace(beta_start**0.5	,  beta_end**0.5	,  _lowerCAmelCase	,  dtype=torch.floataa	) ** 2
															)
										elif beta_schedule == "squaredcos_cap_v2":
															# Glide cosine schedule
															lowerCamelCase__       =       betas_for_alpha_bar(_lowerCAmelCase	)
										else:
															raise NotImplementedError(F"{beta_schedule} does is not implemented for {self.__class__}"	)

										lowerCamelCase__       =       1.0 - self.betas
										lowerCamelCase__       =       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.
										lowerCamelCase__       =       torch.tensor(0.0	) if set_alpha_to_zero else self.alphas_cumprod[-1]

										# standard deviation of the initial noise distribution
										lowerCamelCase__       =       1.0

										# setable values
										lowerCamelCase__       =       None
										lowerCamelCase__       =       torch.from_numpy(np.arange(0	,  _lowerCAmelCase	).copy().astype(np.intaa	)	)





					def 					__magic_name__ ( self	,  _lowerCAmelCase	,  _lowerCAmelCase = None	):
										return sample





					def 					__magic_name__ ( self	,  _lowerCAmelCase	,  _lowerCAmelCase = 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."	)

										lowerCamelCase__       =       num_inference_steps
										lowerCamelCase__       =       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
										lowerCamelCase__       =       (np.arange(0	,  _lowerCAmelCase	) * step_ratio).round().copy().astype(np.intaa	)
										lowerCamelCase__       =       torch.from_numpy(_lowerCAmelCase	).to(_lowerCAmelCase	)
										self.timesteps += self.config.steps_offset





					def 					__magic_name__ ( self	,  _lowerCAmelCase	,  _lowerCAmelCase	,  _lowerCAmelCase	,  _lowerCAmelCase = 0.0	,  _lowerCAmelCase = False	,  _lowerCAmelCase = None	,  _lowerCAmelCase = True	,  ):
										# 1. get previous step value (=t+1)
										lowerCamelCase__       =       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
										lowerCamelCase__       =       self.alphas_cumprod[timestep]
										lowerCamelCase__       =       (
										    self.alphas_cumprod[prev_timestep]
										    if prev_timestep < self.config.num_train_timesteps
										    else self.final_alpha_cumprod
										)

										lowerCamelCase__       =       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":
															lowerCamelCase__       =       (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
															lowerCamelCase__       =       model_output
										elif self.config.prediction_type == "sample":
															lowerCamelCase__       =       model_output
															lowerCamelCase__       =       (sample - alpha_prod_t ** 0.5 * pred_original_sample) / beta_prod_t ** 0.5
										elif self.config.prediction_type == "v_prediction":
															lowerCamelCase__       =       (alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
															lowerCamelCase__       =       (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:
															lowerCamelCase__       =       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
										lowerCamelCase__       =       (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
										lowerCamelCase__       =       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=_lowerCAmelCase	,  pred_original_sample=_lowerCAmelCase	)






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








def    __UpperCamelCase      (    a = 100) ->int:
					lowerCamelCase__       =       (n * (n + 1) // 2) ** 2
					lowerCamelCase__       =       n * (n + 1) * (2 * n + 1) // 6
					return sum_cubes - sum_squares


if __name__ == "__main__":
						print(f"""{solution() = }""")

