import math
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
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->UnCLIP
class UpperCAmelCase						( _a  ):


				'''simple docstring'''






				lowerCamelCase_    = 4_2
				lowerCamelCase_    = None




def     UpperCamelCase						(	__lowercase						:			List[str]						,__lowercase						:			Optional[int]=0.9_99						,__lowercase						:			str="cosine"						,) ->    Any:
		'''simple docstring'''




		if alpha_transform_type == "cosine":

				def alpha_bar_fn(__lowercase						:			str     ):
						return math.cos((t + 0.0_08) / 1.0_08 * math.pi / 2     ) ** 2

		elif alpha_transform_type == "exp":

				def alpha_bar_fn(__lowercase						:			Union[str, Any]     ):
						return math.exp(t * -12.0     )

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

		A_		:    List[Any]         =				[]
		for i in range(__lowercase     ):
				A_		:    Any         =				i / num_diffusion_timesteps
				A_		:    Union[str, Any]         =				(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 UpperCAmelCase						( _a ,	_a  ):


				'''simple docstring'''






				@register_to_config
				def __init__(						self		,     lowercase = 1_0_0_0		,     lowercase = "fixed_small_log"		,     lowercase = True		,     lowercase = 1.0		,     lowercase = "epsilon"		,     lowercase = "squaredcos_cap_v2"		,     ):



						"""simple docstring"""





						if beta_schedule != "squaredcos_cap_v2":
								raise ValueError('UnCLIPScheduler only supports `beta_schedule`: \'squaredcos_cap_v2\'' )

						A_		:    List[Any]         =				betas_for_alpha_bar(_a )

						A_		:    List[Any]         =				1.0 - self.betas
						A_		:    List[Any]         =				torch.cumprod(self.alphas		,     dim=0 )
						A_		:    str         =				torch.tensor(1.0 )

						# standard deviation of the initial noise distribution
						A_		:    Any         =				1.0

						# setable values
						A_		:    List[Any]         =				None
						A_		:    Dict         =				torch.from_numpy(np.arange(0		,     _a )[::-1].copy() )

						A_		:    int         =				variance_type
				def   lowerCAmelCase_       (						self		,     lowercase		,     lowercase = None ):



						"""simple docstring"""





						return sample
				def   lowerCAmelCase_       (						self		,     lowercase		,     lowercase = None ):



						"""simple docstring"""





						A_		:    Union[str, Any]         =				num_inference_steps
						A_		:    Any         =				(self.config.num_train_timesteps - 1) / (self.num_inference_steps - 1)
						A_		:    Optional[int]         =				(np.arange(0		,     _a ) * step_ratio).round()[::-1].copy().astype(np.intaa )
						A_		:    Dict         =				torch.from_numpy(_a ).to(_a )
				def   lowerCAmelCase_       (						self		,     lowercase		,     lowercase=None		,     lowercase=None		,     lowercase=None ):



						"""simple docstring"""





						if prev_timestep is None:
								A_		:    Dict         =				t - 1

						A_		:    Dict         =				self.alphas_cumprod[t]
						A_		:    List[str]         =				self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.one
						A_		:    Optional[Any]         =				1 - alpha_prod_t
						A_		:    Union[str, Any]         =				1 - alpha_prod_t_prev

						if prev_timestep == t - 1:
								A_		:    List[str]         =				self.betas[t]
						else:
								A_		:    List[Any]         =				1 - alpha_prod_t / alpha_prod_t_prev

						# For t > 0, compute predicted variance βt (see formula (6) and (7) from https://arxiv.org/pdf/2006.11239.pdf)
						# and sample from it to get previous sample
						# x_{t-1} ~ N(pred_prev_sample, variance) == add variance to pred_sample
						A_		:    Dict         =				beta_prod_t_prev / beta_prod_t * beta

						if variance_type is None:
								A_		:    str         =				self.config.variance_type

						# hacks - were probably added for training stability
						if variance_type == "fixed_small_log":
								A_		:    Optional[Any]         =				torch.log(torch.clamp(_a		,     min=1E-20 ) )
								A_		:    Optional[int]         =				torch.exp(0.5 * variance )
						elif variance_type == "learned_range":
								# NOTE difference with DDPM scheduler
								A_		:    int         =				variance.log()
								A_		:    List[str]         =				beta.log()

								A_		:    Optional[int]         =				(predicted_variance + 1) / 2
								A_		:    Optional[int]         =				frac * max_log + (1 - frac) * min_log

						return variance
				def   lowerCAmelCase_       (						self		,     lowercase		,     lowercase		,     lowercase		,     lowercase = None		,     lowercase=None		,     lowercase = True		,     ):



						"""simple docstring"""





						A_		:    Tuple         =				timestep

						if model_output.shape[1] == sample.shape[1] * 2 and self.variance_type == "learned_range":
								A_		:    List[Any]         =				torch.split(_a		,     sample.shape[1]		,     dim=1 )
						else:
								A_		:    Optional[Any]         =				None

						# 1. compute alphas, betas
						if prev_timestep is None:
								A_		:    Any         =				t - 1

						A_		:    str         =				self.alphas_cumprod[t]
						A_		:    Union[str, Any]         =				self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.one
						A_		:    Optional[int]         =				1 - alpha_prod_t
						A_		:    Optional[Any]         =				1 - alpha_prod_t_prev

						if prev_timestep == t - 1:
								A_		:    List[Any]         =				self.betas[t]
								A_		:    int         =				self.alphas[t]
						else:
								A_		:    List[str]         =				1 - alpha_prod_t / alpha_prod_t_prev
								A_		:    Union[str, Any]         =				1 - beta

						# 2. compute predicted original sample from predicted noise also called
						# "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf
						if self.config.prediction_type == "epsilon":
								A_		:    str         =				(sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
						elif self.config.prediction_type == "sample":
								A_		:    Optional[int]         =				model_output
						else:
								raise ValueError(
								    F'''prediction_type given as {self.config.prediction_type} must be one of `epsilon` or `sample`'''
								    ' for the UnCLIPScheduler.' )

						# 3. Clip "predicted x_0"
						if self.config.clip_sample:
								A_		:    Optional[int]         =				torch.clamp(
								    _a		,     -self.config.clip_sample_range		,     self.config.clip_sample_range )

						# 4. Compute coefficients for pred_original_sample x_0 and current sample x_t
						# See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
						A_		:    Optional[int]         =				(alpha_prod_t_prev ** 0.5 * beta) / beta_prod_t
						A_		:    Tuple         =				alpha ** 0.5 * beta_prod_t_prev / beta_prod_t

						# 5. Compute predicted previous sample µ_t
						# See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
						A_		:    int         =				pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

						# 6. Add noise
						A_		:    Any         =				0
						if t > 0:
								A_		:    str         =				randn_tensor(
								    model_output.shape		,     dtype=model_output.dtype		,     generator=_a		,     device=model_output.device )

								A_		:    List[Any]         =				self._get_variance(
								    _a		,     predicted_variance=_a		,     prev_timestep=_a		,     )

								if self.variance_type == "fixed_small_log":
										A_		:    int         =				variance
								elif self.variance_type == "learned_range":
										A_		:    List[str]         =				(0.5 * variance).exp()
								else:
										raise ValueError(
										    F'''variance_type given as {self.variance_type} must be one of `fixed_small_log` or `learned_range`'''
										    ' for the UnCLIPScheduler.' )

								A_		:    Union[str, Any]         =				variance * variance_noise

						A_		:    str         =				pred_prev_sample + variance

						if not return_dict:
								return (pred_prev_sample,)

						return UnCLIPSchedulerOutput(prev_sample=_a		,     pred_original_sample=_a )







				def   lowerCAmelCase_       (						self		,     lowercase		,     lowercase		,     lowercase		,     ):



						"""simple docstring"""





						A_		:    Optional[Any]         =				self.alphas_cumprod.to(device=original_samples.device		,     dtype=original_samples.dtype )
						A_		:    Optional[Any]         =				timesteps.to(original_samples.device )

						A_		:    Optional[Any]         =				alphas_cumprod[timesteps] ** 0.5
						A_		:    Dict         =				sqrt_alpha_prod.flatten()
						while len(sqrt_alpha_prod.shape ) < len(original_samples.shape ):
								A_		:    Any         =				sqrt_alpha_prod.unsqueeze(-1 )

						A_		:    List[str]         =				(1 - alphas_cumprod[timesteps]) ** 0.5
						A_		:    Union[str, Any]         =				sqrt_one_minus_alpha_prod.flatten()
						while len(sqrt_one_minus_alpha_prod.shape ) < len(original_samples.shape ):
								A_		:    int         =				sqrt_one_minus_alpha_prod.unsqueeze(-1 )

						A_		:    Optional[int]         =				sqrt_alpha_prod * original_samples + sqrt_one_minus_alpha_prod * noise
						return noisy_samples







import math




def     UpperCamelCase						(	__lowercase						:			int = 1_00     ):
		'''simple docstring'''




		A_		:    List[Any]         =				sum(i * i for i in range(1						,n + 1     )     )
		A_		:    int         =				int(math.pow(sum(range(1						,n + 1     )     )						,2     )     )
		return square_of_sum - sum_of_squares


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






