





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
class 							snake_case_		(      lowercase_):
		lowerCamelCase     :torch.FloatTensor
		lowerCamelCase     :torch.FloatTensor


def        A__						(							SCREAMING_SNAKE_CASE_				,							SCREAMING_SNAKE_CASE_=0.9_9_9				,							SCREAMING_SNAKE_CASE_="cosine"				,							) ->  Optional[int]:
		if alpha_transform_type == "cosine":

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

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

		lowerCamelCase :			int    		=[]
		for i in range(_UpperCamelCase		):
				lowerCamelCase :			Union[str, Any]    		=i / num_diffusion_timesteps
				lowerCamelCase :			Optional[Any]    		=(i + 1) / num_diffusion_timesteps
				betas.append(min(1 - alpha_bar_fn(_UpperCamelCase		) / alpha_bar_fn(_UpperCamelCase		)				,							_UpperCamelCase		)		)
		return torch.tensor(_UpperCamelCase				,							dtype=torch.floataa		)



class 							snake_case_		(      lowercase_    ,       lowercase_):
		lowerCamelCase     :Optional[int]							=  1







		@register_to_config
		def __init__(		self      ,  __lowercase = 1_0_0_0      ,  __lowercase = 0.0_0_0_1      ,  __lowercase = 0.0_2      ,  __lowercase = "linear"      ,  __lowercase = 0.0      ,  __lowercase = None      ,  __lowercase = True      ,  )					-> Union[str, Any]:







				if trained_betas is not None:
						lowerCamelCase :			Tuple    		=torch.from_numpy(UpperCAmelCase_ )
				elif beta_schedule == "linear":
						lowerCamelCase :			Tuple    		=torch.linspace(UpperCAmelCase_      ,  UpperCAmelCase_      ,  UpperCAmelCase_      ,  dtype=torch.floataa )
				elif beta_schedule == "scaled_linear":
						# this schedule is very specific to the latent diffusion model.
						lowerCamelCase :			Any    		=(
						    torch.linspace(beta_start**0.5      ,  beta_end**0.5      ,  UpperCAmelCase_      ,  dtype=torch.floataa ) ** 2
						)
				elif beta_schedule == "squaredcos_cap_v2":
						# Glide cosine schedule
						lowerCamelCase :			int    		=betas_for_alpha_bar(UpperCAmelCase_ )
				elif beta_schedule == "sigmoid":
						# GeoDiff sigmoid schedule
						lowerCamelCase :			Optional[Any]    		=torch.linspace(-6      ,  6      ,  UpperCAmelCase_ )
						lowerCamelCase :			Tuple    		=torch.sigmoid(UpperCAmelCase_ ) * (beta_end - beta_start) + beta_start
				else:
						raise NotImplementedError(F"{beta_schedule} does is not implemented for {self.__class__}" )

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

				lowerCamelCase :			Optional[int]    		=torch.tensor(1.0 )

				# standard deviation of the initial noise distribution
				lowerCamelCase :			int    		=1.0

				# setable values
				lowerCamelCase :			Optional[int]    		=None
				lowerCamelCase :			Tuple    		=torch.from_numpy(np.arange(0      ,  UpperCAmelCase_ )[::-1].copy() )

				lowerCamelCase :			int    		=eta







		def       __lowercase (		self      ,  __lowercase      ,  __lowercase = None )					-> torch.FloatTensor:
				return sample







		def       __lowercase (		self      ,  __lowercase      ,  __lowercase = 1_0      ,  __lowercase = 1_0      ,  __lowercase = None      ,  )					-> Optional[Any]:
				lowerCamelCase :			Optional[int]    		=min(self.config.num_train_timesteps      ,  UpperCAmelCase_ )
				lowerCamelCase :			List[Any]    		=num_inference_steps

				lowerCamelCase :			int    		=[]

				lowerCamelCase :			Union[str, Any]    		={}
				for j in range(0      ,  num_inference_steps - jump_length      ,  UpperCAmelCase_ ):
						lowerCamelCase :			Any    		=jump_n_sample - 1

				lowerCamelCase :			Optional[Any]    		=num_inference_steps
				while t >= 1:
						lowerCamelCase :			Dict    		=t - 1
						timesteps.append(UpperCAmelCase_ )

						if jumps.get(UpperCAmelCase_      ,  0 ) > 0:
								lowerCamelCase :			Union[str, Any]    		=jumps[t] - 1
								for _ in range(UpperCAmelCase_ ):
										lowerCamelCase :			str    		=t + 1
										timesteps.append(UpperCAmelCase_ )

				lowerCamelCase :			Dict    		=np.array(UpperCAmelCase_ ) * (self.config.num_train_timesteps // self.num_inference_steps)
				lowerCamelCase :			Any    		=torch.from_numpy(UpperCAmelCase_ ).to(UpperCAmelCase_ )







		def       __lowercase (		self      ,  __lowercase )					-> Optional[int]:
				lowerCamelCase :			Any    		=t - self.config.num_train_timesteps // self.num_inference_steps

				lowerCamelCase :			Tuple    		=self.alphas_cumprod[t]
				lowerCamelCase :			int    		=self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod
				lowerCamelCase :			Any    		=1 - alpha_prod_t
				lowerCamelCase :			List[str]    		=1 - 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
				# Is equivalent to formula (16) in https://arxiv.org/pdf/2010.02502.pdf
				# without eta.
				# variance = (1 - alpha_prod_t_prev) / (1 - alpha_prod_t) * self.betas[t]
				lowerCamelCase :			Union[str, Any]    		=(beta_prod_t_prev / beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev)

				return variance







		def       __lowercase (		self      ,  __lowercase      ,  __lowercase      ,  __lowercase      ,  __lowercase      ,  __lowercase      ,  __lowercase = None      ,  __lowercase = True      ,  )					-> Union[RePaintSchedulerOutput, Tuple]:
				lowerCamelCase :			int    		=timestep
				lowerCamelCase :			int    		=timestep - self.config.num_train_timesteps // self.num_inference_steps

				# 1. compute alphas, betas
				lowerCamelCase :			Tuple    		=self.alphas_cumprod[t]
				lowerCamelCase :			Optional[Any]    		=self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod
				lowerCamelCase :			Dict    		=1 - alpha_prod_t

				# 2. compute predicted original sample from predicted noise also called
				# "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf
				lowerCamelCase :			Optional[int]    		=(sample - beta_prod_t**0.5 * model_output) / alpha_prod_t**0.5

				# 3. Clip "predicted x_0"
				if self.config.clip_sample:
						lowerCamelCase :			Tuple    		=torch.clamp(UpperCAmelCase_      ,  -1      ,  1 )

				# We choose to follow RePaint Algorithm 1 to get x_{t-1}, however we
				# substitute formula (7) in the algorithm coming from DDPM paper
				# (formula (4) Algorithm 2 - Sampling) with formula (12) from DDIM paper.
				# DDIM schedule gives the same results as DDPM with eta = 1.0
				# Noise is being reused in 7. and 8., but no impact on quality has
				# been observed.

				# 5. Add noise
				lowerCamelCase :			Optional[int]    		=model_output.device
				lowerCamelCase :			Tuple    		=randn_tensor(model_output.shape      ,  generator=UpperCAmelCase_      ,  device=UpperCAmelCase_      ,  dtype=model_output.dtype )
				lowerCamelCase :			Optional[int]    		=self.eta * self._get_variance(UpperCAmelCase_ ) ** 0.5

				lowerCamelCase :			List[Any]    		=0
				if t > 0 and self.eta > 0:
						lowerCamelCase :			List[str]    		=std_dev_t * noise

				# 6. compute "direction pointing to x_t" of formula (12)
				# from https://arxiv.org/pdf/2010.02502.pdf
				lowerCamelCase :			Union[str, Any]    		=(1 - alpha_prod_t_prev - std_dev_t**2) ** 0.5 * model_output

				# 7. compute x_{t-1} of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
				lowerCamelCase :			List[str]    		=alpha_prod_t_prev**0.5 * pred_original_sample + pred_sample_direction + variance

				# 8. Algorithm 1 Line 5 https://arxiv.org/pdf/2201.09865.pdf
				lowerCamelCase :			Optional[int]    		=(alpha_prod_t_prev**0.5) * original_image + ((1 - alpha_prod_t_prev) ** 0.5) * noise

				# 9. Algorithm 1 Line 8 https://arxiv.org/pdf/2201.09865.pdf
				lowerCamelCase :			Dict    		=mask * prev_known_part + (1.0 - mask) * prev_unknown_part

				if not return_dict:
						return (
						    pred_prev_sample,
						    pred_original_sample,
						)

				return RePaintSchedulerOutput(prev_sample=UpperCAmelCase_      ,  pred_original_sample=UpperCAmelCase_ )







		def       __lowercase (		self      ,  __lowercase      ,  __lowercase      ,  __lowercase=None )					-> Optional[Any]:
				lowerCamelCase :			Dict    		=self.config.num_train_timesteps // self.num_inference_steps

				for i in range(UpperCAmelCase_ ):
						lowerCamelCase :			Optional[int]    		=self.betas[timestep + i]
						if sample.device.type == "mps":
								# randn does not work reproducibly on mps
								lowerCamelCase :			Dict    		=randn_tensor(sample.shape      ,  dtype=sample.dtype      ,  generator=UpperCAmelCase_ )
								lowerCamelCase :			int    		=noise.to(sample.device )
						else:
								lowerCamelCase :			int    		=randn_tensor(sample.shape      ,  generator=UpperCAmelCase_      ,  device=sample.device      ,  dtype=sample.dtype )

						# 10. Algorithm 1 Line 10 https://arxiv.org/pdf/2201.09865.pdf
						lowerCamelCase :			List[Any]    		=(1 - beta) ** 0.5 * sample + beta**0.5 * noise

				return sample







		def       __lowercase (		self      ,  __lowercase      ,  __lowercase      ,  __lowercase      ,  )					-> torch.FloatTensor:
				raise NotImplementedError('''Use `DDPMScheduler.add_noise()` to train for sampling with RePaint.''' )







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






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

import flax
import jax.numpy as jnp
from scipy import integrate

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils_flax import (
    CommonSchedulerState,
    FlaxKarrasDiffusionSchedulers,
    FlaxSchedulerMixin,
    FlaxSchedulerOutput,
    broadcast_to_shape_from_left,
)





@flax.struct.dataclass
class 							lowerCAmelCase_		:
		SCREAMING_SNAKE_CASE_       :			CommonSchedulerState

		# setable values
		SCREAMING_SNAKE_CASE_       :			jnp.ndarray
		SCREAMING_SNAKE_CASE_       :			jnp.ndarray
		SCREAMING_SNAKE_CASE_       :			jnp.ndarray
		SCREAMING_SNAKE_CASE_       :			Optional[int]					       =	None

		# running values
		SCREAMING_SNAKE_CASE_       :			Optional[jnp.ndarray]					       =	None







		@classmethod
		def 					a_  (    cls  :   List[Any]       ,		UpperCAmelCase_  :   CommonSchedulerState       ,		UpperCAmelCase_  :   jnp.ndarray       ,		UpperCAmelCase_  :   jnp.ndarray       ,		UpperCAmelCase_  :   jnp.ndarray					)       ->		Optional[Any]:


						'''simple docstring'''







						return cls(common=UpperCAmelCase_       ,		init_noise_sigma=UpperCAmelCase_       ,		timesteps=UpperCAmelCase_       ,		sigmas=UpperCAmelCase_					)





@dataclass
class 							lowerCAmelCase_		(		lowercase_     ):
		SCREAMING_SNAKE_CASE_       :			LMSDiscreteSchedulerState





class 							lowerCAmelCase_		(		lowercase_							,		lowercase_     ):
		SCREAMING_SNAKE_CASE_       :			Union[str, Any]					       =	[e.name for e in FlaxKarrasDiffusionSchedulers]

		SCREAMING_SNAKE_CASE_       :			jnp.dtype







		@property
		def 					a_  (    self  :   Union[str, Any]					)       ->		List[Any]:


						'''simple docstring'''







						return True







		@register_to_config
		def __init__(    self  :   Optional[Any]       ,		UpperCAmelCase_  :   int = 1000       ,		UpperCAmelCase_  :   float = 0.0_001       ,		UpperCAmelCase_  :   float = 0.02       ,		UpperCAmelCase_  :   str = "linear"       ,		UpperCAmelCase_  :   Optional[jnp.ndarray] = None       ,		UpperCAmelCase_  :   str = "epsilon"       ,		UpperCAmelCase_  :   jnp.dtype = jnp.floataa       ,		)       ->		List[str]:


						'''simple docstring'''







						_UpperCAmelCase						:  str     					=	dtype







		def 					a_  (    self  :   Tuple       ,		UpperCAmelCase_  :   Optional[CommonSchedulerState] = None					)       ->		LMSDiscreteSchedulerState:


						'''simple docstring'''







						if common is None:
										_UpperCAmelCase						:  int     					=	CommonSchedulerState.create(self					)

						_UpperCAmelCase						:  Any     					=	jnp.arange(0       ,		self.config.num_train_timesteps					).round()[::-1]
						_UpperCAmelCase						:  Any     					=	((1 - common.alphas_cumprod) / common.alphas_cumprod) ** 0.5

						# standard deviation of the initial noise distribution
						_UpperCAmelCase						:  Dict     					=	sigmas.max()

						return LMSDiscreteSchedulerState.create(
						    common=UpperCAmelCase_       ,		init_noise_sigma=UpperCAmelCase_       ,		timesteps=UpperCAmelCase_       ,		sigmas=UpperCAmelCase_       ,		)







		def 					a_  (    self  :   Optional[Any]       ,		UpperCAmelCase_  :   LMSDiscreteSchedulerState       ,		UpperCAmelCase_  :   jnp.ndarray       ,		UpperCAmelCase_  :   int					)       ->		jnp.ndarray:


						'''simple docstring'''







						((_UpperCAmelCase)					, )						:  Optional[Any]     					=	jnp.where(state.timesteps == timestep       ,		size=1					)
						_UpperCAmelCase						:  List[str]     					=	step_index[0]

						_UpperCAmelCase						:  List[Any]     					=	state.sigmas[step_index]
						_UpperCAmelCase						:  Union[str, Any]     					=	sample / ((sigma**2 + 1) ** 0.5)
						return sample







		def 					a_  (    self  :   List[Any]       ,		UpperCAmelCase_  :   LMSDiscreteSchedulerState       ,		UpperCAmelCase_  :   int       ,		UpperCAmelCase_  :   str       ,		UpperCAmelCase_  :   Union[str, Any]					)       ->		Union[str, Any]:


						'''simple docstring'''







						def lms_derivative(UpperCAmelCase_  :   Optional[int]					):
										_UpperCAmelCase						:  Optional[Any]     					=	1.0
										for k in range(UpperCAmelCase_					):
														if current_order == k:
																		continue
														prod *= (tau - state.sigmas[t - k]) / (state.sigmas[t - current_order] - state.sigmas[t - k])
										return prod

						_UpperCAmelCase						:  Optional[Any]     					=	integrate.quad(UpperCAmelCase_       ,		state.sigmas[t]       ,		state.sigmas[t + 1]       ,		epsrel=1E-4					)[0]

						return integrated_coeff







		def 					a_  (    self  :   Dict       ,		UpperCAmelCase_  :   LMSDiscreteSchedulerState       ,		UpperCAmelCase_  :   int       ,		UpperCAmelCase_  :   Tuple = ()					)       ->		LMSDiscreteSchedulerState:


						'''simple docstring'''







						_UpperCAmelCase						:  List[str]     					=	jnp.linspace(self.config.num_train_timesteps - 1       ,		0       ,		UpperCAmelCase_       ,		dtype=self.dtype					)

						_UpperCAmelCase						:  Any     					=	jnp.floor(UpperCAmelCase_					).astype(jnp.intaa					)
						_UpperCAmelCase						:  Optional[Any]     					=	jnp.ceil(UpperCAmelCase_					).astype(jnp.intaa					)

						_UpperCAmelCase						:  str     					=	jnp.mod(UpperCAmelCase_       ,		1.0					)

						_UpperCAmelCase						:  Optional[Any]     					=	((1 - state.common.alphas_cumprod) / state.common.alphas_cumprod) ** 0.5
						_UpperCAmelCase						:  Any     					=	(1 - frac) * sigmas[low_idx] + frac * sigmas[high_idx]
						_UpperCAmelCase						:  Tuple     					=	jnp.concatenate([sigmas, jnp.array([0.0]       ,		dtype=self.dtype					)]					)

						_UpperCAmelCase						:  int     					=	timesteps.astype(jnp.intaa					)

						# initial running values
						_UpperCAmelCase						:  List[str]     					=	jnp.zeros((0,) + shape       ,		dtype=self.dtype					)

						return state.replace(
						    timesteps=UpperCAmelCase_       ,		sigmas=UpperCAmelCase_       ,		num_inference_steps=UpperCAmelCase_       ,		derivatives=UpperCAmelCase_       ,		)







		def 					a_  (    self  :   Tuple       ,		UpperCAmelCase_  :   LMSDiscreteSchedulerState       ,		UpperCAmelCase_  :   jnp.ndarray       ,		UpperCAmelCase_  :   int       ,		UpperCAmelCase_  :   jnp.ndarray       ,		UpperCAmelCase_  :   int = 4       ,		UpperCAmelCase_  :   bool = True       ,		)       ->		Union[FlaxLMSSchedulerOutput, Tuple]:


						'''simple docstring'''







						if state.num_inference_steps is None:
										raise ValueError(
										    '''Number of inference steps is \'None\', you need to run \'set_timesteps\' after creating the scheduler'''					)

						_UpperCAmelCase						:  List[Any]     					=	state.sigmas[timestep]

						# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
						if self.config.prediction_type == "epsilon":
										_UpperCAmelCase						:  Optional[int]     					=	sample - sigma * model_output
						elif self.config.prediction_type == "v_prediction":
										# * c_out + input * c_skip
										_UpperCAmelCase						:  Tuple     					=	model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
						else:
										raise ValueError(
										    F'''prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`'''					)

						# 2. Convert to an ODE derivative
						_UpperCAmelCase						:  Tuple     					=	(sample - pred_original_sample) / sigma
						_UpperCAmelCase						:  Tuple     					=	state.replace(derivatives=jnp.append(state.derivatives       ,		UpperCAmelCase_					)					)
						if len(state.derivatives					) > order:
										_UpperCAmelCase						:  Union[str, Any]     					=	state.replace(derivatives=jnp.delete(state.derivatives       ,		0					)					)

						# 3. Compute linear multistep coefficients
						_UpperCAmelCase						:  int     					=	min(timestep + 1       ,		UpperCAmelCase_					)
						_UpperCAmelCase						:  Optional[int]     					=	[self.get_lms_coefficient(UpperCAmelCase_       ,		UpperCAmelCase_       ,		UpperCAmelCase_       ,		UpperCAmelCase_					) for curr_order in range(UpperCAmelCase_					)]

						# 4. Compute previous sample based on the derivatives path
						_UpperCAmelCase						:  int     					=	sample + sum(
						    coeff * derivative for coeff, derivative in zip(UpperCAmelCase_       ,		reversed(state.derivatives					)					)					)

						if not return_dict:
										return (prev_sample, state)

						return FlaxLMSSchedulerOutput(prev_sample=UpperCAmelCase_       ,		state=UpperCAmelCase_					)







		def 					a_  (    self  :   Union[str, Any]       ,		UpperCAmelCase_  :   LMSDiscreteSchedulerState       ,		UpperCAmelCase_  :   jnp.ndarray       ,		UpperCAmelCase_  :   jnp.ndarray       ,		UpperCAmelCase_  :   jnp.ndarray       ,		)       ->		jnp.ndarray:


						'''simple docstring'''







						_UpperCAmelCase						:  Union[str, Any]     					=	state.sigmas[timesteps].flatten()
						_UpperCAmelCase						:  Union[str, Any]     					=	broadcast_to_shape_from_left(UpperCAmelCase_       ,		noise.shape					)

						_UpperCAmelCase						:  Any     					=	original_samples + noise * sigma

						return noisy_samples







		def __len__(    self  :   Dict					)       ->		Tuple:


						'''simple docstring'''







						return self.config.num_train_timesteps
